LMFDB - Embedded newform 351.2.bf.a.314.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(206,351)] 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("351.206"); 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, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.bf (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			314.8
Character	$\chi$	$=$	351.314
Dual form			351.2.bf.a.332.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03000 - 0.275986i) q^{2} +(-0.747329 + 0.431471i) q^{4} +(-2.22216 + 0.595426i) q^{5} +(-3.66177 - 3.66177i) q^{7} +(-2.15868 + 2.15868i) q^{8} +(-2.12448 + 1.22657i) q^{10} +(0.708887 + 2.64560i) q^{11} +(-2.69526 - 2.39491i) q^{13} +(-4.78220 - 2.76100i) q^{14} +(-0.764725 + 1.32454i) q^{16} +(0.0716242 - 0.124057i) q^{17} +(0.552200 + 2.06084i) q^{19} +(1.40377 - 1.40377i) q^{20} +(1.46030 + 2.52931i) q^{22} -0.843617 q^{23} +(0.253329 - 0.146260i) q^{25} +(-3.43707 - 1.72289i) q^{26} +(4.31649 + 1.15660i) q^{28} +(-0.523977 - 0.302518i) q^{29} +(-0.905716 - 3.38018i) q^{31} +(1.15816 - 4.32230i) q^{32} +(0.0395346 - 0.147545i) q^{34} +(10.3173 + 5.95671i) q^{35} +(0.973046 - 3.63146i) q^{37} +(1.13753 + 1.97025i) q^{38} +(3.51160 - 6.08227i) q^{40} +(5.53029 + 5.53029i) q^{41} +0.216584i q^{43} +(-1.67127 - 1.67127i) q^{44} +(-0.868921 + 0.232827i) q^{46} +(-10.1867 - 2.72952i) q^{47} +19.8171i q^{49} +(0.220562 - 0.220562i) q^{50} +(3.04758 + 0.626857i) q^{52} +8.00631i q^{53} +(-3.15052 - 5.45686i) q^{55} +15.8092 q^{56} +(-0.623185 - 0.166982i) q^{58} +(-7.19256 - 1.92724i) q^{59} -1.35088 q^{61} +(-1.86577 - 3.23160i) q^{62} -7.83049i q^{64} +(7.41528 + 3.71703i) q^{65} +(5.41892 - 5.41892i) q^{67} +0.123615i q^{68} +(12.2708 + 3.28794i) q^{70} +(-7.04646 + 1.88809i) q^{71} +(-3.76736 - 3.76736i) q^{73} -4.00893i q^{74} +(-1.30187 - 1.30187i) q^{76} +(7.09179 - 12.2833i) q^{77} +(1.62641 + 2.81703i) q^{79} +(0.910674 - 3.39868i) q^{80} +(7.22246 + 4.16989i) q^{82} +(3.94150 - 14.7099i) q^{83} +(-0.0852937 + 0.318321i) q^{85} +(0.0597743 + 0.223081i) q^{86} +(-7.24128 - 4.18075i) q^{88} +(-14.2431 - 3.81643i) q^{89} +(1.09983 + 18.6390i) q^{91} +(0.630459 - 0.363996i) q^{92} -11.2456 q^{94} +(-2.45415 - 4.25071i) q^{95} +(-0.384858 + 0.384858i) q^{97} +(5.46924 + 20.4115i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{2} - 6 q^{4} + 6 q^{5} + 2 q^{7} + 30 q^{8} - 12 q^{10} - 6 q^{11} - 2 q^{13} + 12 q^{14} + 14 q^{16} - 4 q^{19} + 6 q^{20} + 2 q^{22} + 12 q^{23} - 48 q^{26} + 6 q^{29} + 6 q^{31} - 30 q^{32}+ \cdots + 36 q^{98}+O(q^{100}) $ 48 * q + 6 * q^2 - 6 * q^4 + 6 * q^5 + 2 * q^7 + 30 * q^8 - 12 * q^10 - 6 * q^11 - 2 * q^13 + 12 * q^14 + 14 * q^16 - 4 * q^19 + 6 * q^20 + 2 * q^22 + 12 * q^23 - 48 * q^26 + 6 * q^29 + 6 * q^31 - 30 * q^32 - 6 * q^34 + 6 * q^35 - 6 * q^37 + 36 * q^38 - 12 * q^40 - 18 * q^41 + 12 * q^44 - 12 * q^46 - 30 * q^47 + 12 * q^50 - 16 * q^52 - 4 * q^55 + 12 * q^56 - 28 * q^58 - 30 * q^59 - 4 * q^61 + 18 * q^62 - 30 * q^65 - 16 * q^67 - 46 * q^70 - 48 * q^71 - 22 * q^73 - 18 * q^76 + 72 * q^77 + 8 * q^79 - 54 * q^80 - 12 * q^82 - 72 * q^83 + 78 * q^85 - 102 * q^86 - 6 * q^88 - 16 * q^91 - 120 * q^92 - 52 * q^94 + 6 * q^95 + 48 * q^97 + 36 * q^98

Character values

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

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.03000	−	0.275986i	0.728317	−	0.195152i	0.124437	−	0.992227i	$-0.460287\pi$
$2$	1.03000	−	0.275986i	0.728317	−	0.195152i	0.603880	+	0.797076i	$0.293621\pi$
$3$		0			0
$3$		0			0
$4$	−0.747329	+	0.431471i	−0.373664	+	0.215735i
$5$	−2.22216	+	0.595426i	−0.993779	+	0.266282i	−0.718837	−	0.695178i	$-0.755325\pi$
$5$	−2.22216	+	0.595426i	−0.993779	+	0.266282i	−0.274942	+	0.961461i	$0.588659\pi$
$6$		0			0
$7$	−3.66177	−	3.66177i	−1.38402	−	1.38402i	−0.837350	−	0.546668i	$-0.815896\pi$
$7$	−3.66177	−	3.66177i	−1.38402	−	1.38402i	−0.546668	−	0.837350i	$-0.684104\pi$
$8$	−2.15868	+	2.15868i	−0.763210	+	0.763210i
$9$		0			0
$10$	−2.12448	+	1.22657i	−0.671821	+	0.387876i
$11$	0.708887	+	2.64560i	0.213737	+	0.797679i	0.986607	+	0.163114i	$0.0521539\pi$
$11$	0.708887	+	2.64560i	0.213737	+	0.797679i	−0.772870	+	0.634565i	$0.781179\pi$
$12$		0			0
$13$	−2.69526	−	2.39491i	−0.747531	−	0.664227i
$13$	−2.69526	−	2.39491i	−0.747531	−	0.664227i
$14$	−4.78220	−	2.76100i	−1.27810	−	0.737909i
$15$		0			0
$16$	−0.764725	+	1.32454i	−0.191181	+	0.331136i
$17$	0.0716242	−	0.124057i	0.0173714	−	0.0300882i	−0.857209	−	0.514969i	$-0.827804\pi$
$17$	0.0716242	−	0.124057i	0.0173714	−	0.0300882i	0.874580	+	0.484880i	$0.161137\pi$
$18$		0			0
$19$	0.552200	+	2.06084i	0.126683	+	0.472789i	0.999894	−	0.0145541i	$-0.00463288\pi$
$19$	0.552200	+	2.06084i	0.126683	+	0.472789i	−0.873211	+	0.487343i	$0.837966\pi$
$20$	1.40377	−	1.40377i	0.313894	−	0.313894i
$21$		0			0
$22$	1.46030	+	2.52931i	0.311337	+	0.539252i
$23$	−0.843617			−0.175906			−0.0879531	−	0.996125i	$-0.528033\pi$
$23$	−0.843617			−0.175906			−0.0879531	+	0.996125i	$0.528033\pi$
$24$		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
$29$	−0.523977	−	0.302518i	−0.0973001	−	0.0561762i	0.450560	−	0.892746i	$-0.351224\pi$
$29$	−0.523977	−	0.302518i	−0.0973001	−	0.0561762i	−0.547860	+	0.836570i	$0.684558\pi$
$30$		0			0
$31$	−0.905716	−	3.38018i	−0.162671	−	0.607098i	−0.998326	−	0.0578423i	$-0.981578\pi$
$31$	−0.905716	−	3.38018i	−0.162671	−	0.607098i	0.835654	−	0.549256i	$-0.185089\pi$
$32$	1.15816	−	4.32230i	0.204735	−	0.764083i
$33$		0			0
$34$	0.0395346	−	0.147545i	0.00678013	−	0.0253038i
$35$	10.3173	+	5.95671i	1.74395	+	1.00687i
$36$		0			0
$37$	0.973046	−	3.63146i	0.159968	−	0.597008i	−0.838661	−	0.544654i	$-0.816661\pi$
$37$	0.973046	−	3.63146i	0.159968	−	0.597008i	0.998629	−	0.0523539i	$-0.0166724\pi$
$38$	1.13753	+	1.97025i	0.184531	+	0.319617i
$39$		0			0
$40$	3.51160	−	6.08227i	0.555233	−	0.961691i
$41$	5.53029	+	5.53029i	0.863686	+	0.863686i	0.991764	−	0.128078i	$-0.0408807\pi$
$41$	5.53029	+	5.53029i	0.863686	+	0.863686i	−0.128078	+	0.991764i	$0.540881\pi$
$42$		0			0
$43$			0.216584i			0.0330288i	0.999864	+	0.0165144i	$0.00525693\pi$
$43$			0.216584i			0.0330288i	−0.999864	+	0.0165144i	$0.994743\pi$
$44$	−1.67127	−	1.67127i	−0.251953	−	0.251953i
$45$		0			0
$46$	−0.868921	+	0.232827i	−0.128115	+	0.0343284i
$47$	−10.1867	−	2.72952i	−1.48588	−	0.398141i	−0.577539	−	0.816363i	$-0.695987\pi$
$47$	−10.1867	−	2.72952i	−1.48588	−	0.398141i	−0.908345	+	0.418222i	$0.862653\pi$
$48$		0			0
$49$			19.8171i			2.83101i
$50$	0.220562	−	0.220562i	0.0311922	−	0.0311922i
$51$		0			0
$52$	3.04758	+	0.626857i	0.422623	+	0.0869294i
$53$			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
$56$	15.8092			2.11259
$57$		0			0
$58$	−0.623185	−	0.166982i	−0.0818282	−	0.0219258i
$59$	−7.19256	−	1.92724i	−0.936392	−	0.250906i	−0.241814	−	0.970323i	$-0.577742\pi$
$59$	−7.19256	−	1.92724i	−0.936392	−	0.250906i	−0.694578	+	0.719417i	$0.744409\pi$
$60$		0			0
$61$	−1.35088			−0.172963			−0.0864815	−	0.996253i	$-0.527562\pi$
$61$	−1.35088			−0.172963			−0.0864815	+	0.996253i	$0.527562\pi$
$62$	−1.86577	−	3.23160i	−0.236953	−	0.410414i
$63$		0			0
$64$		−	7.83049i		−	0.978811i
$65$	7.41528	+	3.71703i	0.919753	+	0.461041i
$66$		0			0
$67$	5.41892	−	5.41892i	0.662026	−	0.662026i	−0.293831	−	0.955857i	$-0.594930\pi$
$67$	5.41892	−	5.41892i	0.662026	−	0.662026i	0.955857	+	0.293831i	$0.0949303\pi$
$68$			0.123615i			0.0149905i
$69$		0			0
$70$	12.2708	+	3.28794i	1.46664	+	0.392985i
$71$	−7.04646	+	1.88809i	−0.836261	+	0.224075i	−0.651443	−	0.758697i	$-0.725836\pi$
$71$	−7.04646	+	1.88809i	−0.836261	+	0.224075i	−0.184818	+	0.982773i	$0.559169\pi$
$72$		0			0
$73$	−3.76736	−	3.76736i	−0.440936	−	0.440936i	0.451391	−	0.892326i	$-0.350928\pi$
$73$	−3.76736	−	3.76736i	−0.440936	−	0.440936i	−0.892326	+	0.451391i	$0.850928\pi$
$74$		−	4.00893i		−	0.466029i
$75$		0			0
$76$	−1.30187	−	1.30187i	−0.149334	−	0.149334i
$77$	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
$83$	3.94150	−	14.7099i	0.432636	−	1.61462i	−0.314025	−	0.949415i	$-0.601677\pi$
$83$	3.94150	−	14.7099i	0.432636	−	1.61462i	0.746661	−	0.665205i	$-0.231656\pi$
$84$		0			0
$85$	−0.0852937	+	0.318321i	−0.00925141	+	0.0345267i
$86$	0.0597743	+	0.223081i	0.00644563	+	0.0240554i
$87$		0			0
$88$	−7.24128	−	4.18075i	−0.771923	−	0.445670i
$89$	−14.2431	−	3.81643i	−1.50977	−	0.404541i	−0.593409	−	0.804901i	$-0.702218\pi$
$89$	−14.2431	−	3.81643i	−1.50977	−	0.404541i	−0.916358	+	0.400361i	$0.868885\pi$
$90$		0			0
$91$	1.09983	+	18.6390i	0.115293	+	1.95390i
$92$	0.630459	−	0.363996i	0.0657299	−	0.0379492i
$93$		0			0
$94$	−11.2456			−1.15989
$95$	−2.45415	−	4.25071i	−0.251791	−	0.436114i
$96$		0			0
$97$	−0.384858	+	0.384858i	−0.0390764	+	0.0390764i	−0.726375	−	0.687299i	$-0.758796\pi$
$97$	−0.384858	+	0.384858i	−0.0390764	+	0.0390764i	0.687299	+	0.726375i	$0.258796\pi$
$98$	5.46924	+	20.4115i	0.552476	+	2.06187i
$99$		0			0
$100$	−0.126213	+	0.218608i	−0.0126213	+	0.0218608i
$101$	−1.75545	+	3.04053i	−0.174674	+	0.302544i	−0.940048	−	0.341041i	$-0.889220\pi$
$101$	−1.75545	+	3.04053i	−0.174674	+	0.302544i	0.765375	+	0.643585i	$0.222554\pi$
$102$		0			0
$103$	−0.661851	−	0.382120i	−0.0652141	−	0.0376514i	0.467038	−	0.884237i	$-0.345321\pi$
$103$	−0.661851	−	0.382120i	−0.0652141	−	0.0376514i	−0.532253	+	0.846586i	$0.678654\pi$
$104$	10.9881	−	0.648369i	1.07747	−	0.0635778i
$105$		0			0
$106$	2.20963	+	8.24647i	0.214619	+	0.800968i
$107$	5.29840	−	3.05903i	0.512216	−	0.295728i	−0.221528	−	0.975154i	$-0.571104\pi$
$107$	5.29840	−	3.05903i	0.512216	−	0.295728i	0.733744	+	0.679426i	$0.237771\pi$
$108$		0			0
$109$	−3.64352	+	3.64352i	−0.348986	+	0.348986i	−0.859732	−	0.510746i	$-0.829369\pi$
$109$	−3.64352	+	3.64352i	−0.348986	+	0.348986i	0.510746	+	0.859732i	$0.329369\pi$
$110$	−4.75104	−	4.75104i	−0.452994	−	0.452994i
$111$		0			0
$112$	7.65041	−	2.04992i	0.722896	−	0.193699i
$113$	−8.06300	+	4.65517i	−0.758503	+	0.437922i	−0.828758	−	0.559607i	$-0.810952\pi$
$113$	−8.06300	+	4.65517i	−0.758503	+	0.437922i	0.0702550	+	0.997529i	$0.477619\pi$
$114$		0			0
$115$	1.87465	−	0.502311i	0.174812	−	0.0468407i
$116$	0.522111			0.0484768
$117$		0			0
$118$	−7.94020			−0.730955
$119$	−0.716538	+	0.191996i	−0.0656849	+	0.0176002i
$120$		0			0
$121$	3.02959	−	1.74914i	0.275418	−	0.159012i
$122$	−1.39140	+	0.372826i	−0.125972	+	0.0337541i
$123$		0			0
$124$	2.13532	+	2.13532i	0.191757	+	0.191757i
$125$	7.65781	−	7.65781i	0.684936	−	0.684936i
$126$		0			0
$127$	0.310458	−	0.179243i	0.0275487	−	0.0159052i	−0.486162	−	0.873868i	$-0.661604\pi$
$127$	0.310458	−	0.179243i	0.0275487	−	0.0159052i	0.513711	+	0.857963i	$0.328270\pi$
$128$	0.155207	+	0.579240i	0.0137185	+	0.0511981i
$129$		0			0
$130$	8.66356	+	1.78201i	0.759844	+	0.156293i
$131$	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
$133$	5.52428	−	9.56833i	0.479016	−	0.829680i
$134$	4.08591	−	7.07701i	0.352969	−	0.611361i
$135$		0			0
$136$	0.113185	+	0.422413i	0.00970556	+	0.0362216i
$137$	−11.1179	+	11.1179i	−0.949866	+	0.949866i	−0.998802	−	0.0489364i	$-0.984417\pi$
$137$	−11.1179	+	11.1179i	−0.949866	+	0.949866i	0.0489364	+	0.998802i	$0.484417\pi$
$138$		0			0
$139$	−6.88251	−	11.9208i	−0.583767	−	1.01111i	−0.995028	−	0.0995958i	$-0.968245\pi$
$139$	−6.88251	−	11.9208i	−0.583767	−	1.01111i	0.411261	−	0.911517i	$-0.365088\pi$
$140$	−10.2806			−0.868868
$141$		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
$146$	−4.92010	−	2.84062i	−0.407191	−	0.235092i
$147$		0			0
$148$	0.839681	+	3.13373i	0.0690214	+	0.257591i
$149$	−3.42366	+	12.7773i	−0.280477	+	1.04676i	0.671604	+	0.740910i	$0.265606\pi$
$149$	−3.42366	+	12.7773i	−0.280477	+	1.04676i	−0.952081	+	0.305845i	$0.901061\pi$
$150$		0			0
$151$	2.97615	−	11.1072i	0.242196	−	0.903888i	−0.732576	−	0.680685i	$-0.761682\pi$
$151$	2.97615	−	11.1072i	0.242196	−	0.903888i	0.974772	−	0.223203i	$-0.0716511\pi$
$152$	−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	$0.288777\pi$
$158$	2.45266	+	2.45266i	0.195123	+	0.195123i
$159$		0			0
$160$			10.2944i			0.813847i
$161$	3.08913	+	3.08913i	0.243457	+	0.243457i
$162$		0			0
$163$	−14.3617	+	3.84819i	−1.12489	+	0.301414i	−0.772861	−	0.634575i	$-0.781175\pi$
$163$	−14.3617	+	3.84819i	−1.12489	+	0.301414i	−0.352030	+	0.935989i	$0.614508\pi$
$164$	−6.51910	−	1.74679i	−0.509056	−	0.136401i
$165$		0			0
$166$		−	16.2389i		−	1.26038i
$167$	−1.52630	+	1.52630i	−0.118109	+	0.118109i	−0.763691	−	0.645582i	$-0.776615\pi$
$167$	−1.52630	+	1.52630i	−0.118109	+	0.118109i	0.645582	+	0.763691i	$0.276615\pi$
$168$		0			0
$169$	1.52885	+	12.9098i	0.117604	+	0.993061i
$170$			0.351409i			0.0269518i
$171$		0			0
$172$	−0.0934497	−	0.161860i	−0.00712547	−	0.0123417i
$173$	−12.0841			−0.918738			−0.459369	−	0.888246i	$-0.651924\pi$
$173$	−12.0841			−0.918738			−0.459369	+	0.888246i	$0.651924\pi$
$174$		0			0
$175$	−1.46320	−	0.392063i	−0.110608	−	0.0296372i
$176$	−4.04632	−	1.08421i	−0.305003	−	0.0817252i
$177$		0			0
$178$	−15.7236			−1.17853
$179$	−1.54606	−	2.67786i	−0.115558	−	0.200152i	0.802445	−	0.596727i	$-0.203532\pi$
$179$	−1.54606	−	2.67786i	−0.115558	−	0.200152i	−0.918003	+	0.396574i	$0.870199\pi$
$180$		0			0
$181$		−	20.3888i		−	1.51549i	−0.652550	−	0.757745i	$-0.726301\pi$
$181$		−	20.3888i		−	1.51549i	0.652550	−	0.757745i	$-0.273699\pi$
$182$	6.27692	+	18.8945i	0.465277	+	1.40056i
$183$		0			0
$184$	1.82110	−	1.82110i	0.134253	−	0.134253i
$185$			8.64905i			0.635891i
$186$		0			0
$187$	0.378978	+	0.101547i	0.0277136	+	0.00742584i
$188$	8.79053	−	2.35541i	0.641115	−	0.171786i
$189$		0			0
$190$	−3.70090	−	3.70090i	−0.268492	−	0.268492i
$191$			9.45616i			0.684224i	0.939659	+	0.342112i	$0.111142\pi$
$191$			9.45616i			0.684224i	−0.939659	+	0.342112i	$0.888858\pi$
$192$		0			0
$193$	−0.280723	−	0.280723i	−0.0202069	−	0.0202069i	0.696931	−	0.717138i	$-0.254548\pi$
$193$	−0.280723	−	0.280723i	−0.0202069	−	0.0202069i	−0.717138	+	0.696931i	$0.754548\pi$
$194$	−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	$-0.885352\pi$
$197$	0.713601	−	2.66320i	0.0508420	−	0.189745i	0.986676	+	0.162695i	$0.0520187\pi$
$198$		0			0
$199$	13.4785	+	7.78181i	0.955465	+	0.551638i	0.894774	−	0.446519i	$-0.147336\pi$
$199$	13.4785	+	7.78181i	0.955465	+	0.551638i	0.0606908	+	0.998157i	$0.480670\pi$
$200$	−0.231129	+	0.862586i	−0.0163433	+	0.0609940i
$201$		0			0
$202$	−0.968960	+	3.61621i	−0.0681758	+	0.254435i
$203$	0.810930	+	3.02643i	0.0569161	+	0.212414i
$204$		0			0
$205$	−15.5821	−	8.99630i	−1.08830	−	0.628329i
$206$	−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
$211$	9.22383			0.634994			0.317497	−	0.948259i	$-0.397158\pi$
$211$	9.22383			0.634994			0.317497	+	0.948259i	$0.397158\pi$
$212$	−3.45449	−	5.98335i	−0.237255	−	0.410938i
$213$		0			0
$214$	4.61308	−	4.61308i	0.315343	−	0.315343i
$215$	−0.128960	−	0.481284i	−0.00879498	−	0.0328233i
$216$		0			0
$217$	−9.06090	+	15.6939i	−0.615094	+	1.06537i
$218$	−2.74725	+	4.75837i	−0.186067	+	0.322277i
$219$		0			0
$220$	4.70894	+	2.71871i	0.317477	+	0.183295i
$221$	−0.490150	+	0.162832i	−0.0329711	+	0.0109533i
$222$		0			0
$223$	0.500502	+	1.86790i	0.0335161	+	0.125084i	0.980657	−	0.195734i	$-0.0627090\pi$
$223$	0.500502	+	1.86790i	0.0335161	+	0.125084i	−0.947141	+	0.320818i	$0.896042\pi$
$224$	−20.0682	+	11.5864i	−1.34086	+	0.774146i
$225$		0			0
$226$	−7.02009	+	7.02009i	−0.466969	+	0.466969i
$227$	13.5565	+	13.5565i	0.899775	+	0.899775i	0.995416	−	0.0956412i	$-0.0304902\pi$
$227$	13.5565	+	13.5565i	0.899775	+	0.899775i	−0.0956412	+	0.995416i	$0.530490\pi$
$228$		0			0
$229$	−18.2579	+	4.89219i	−1.20652	+	0.323285i	−0.805394	−	0.592739i	$-0.798046\pi$
$229$	−18.2579	+	4.89219i	−1.20652	+	0.323285i	−0.401122	+	0.916025i	$0.631380\pi$
$230$	1.79225	−	1.03476i	0.118177	−	0.0682298i
$231$		0			0
$232$	1.78414	−	0.478059i	0.117135	−	0.0313861i
$233$	−15.0092			−0.983286			−0.491643	−	0.870797i	$-0.663603\pi$
$233$	−15.0092			−0.983286			−0.491643	+	0.870797i	$0.663603\pi$
$234$		0			0
$235$	24.2617			1.58266
$236$	6.20676	−	1.66310i	0.404026	−	0.108258i
$237$		0			0
$238$	−0.685042	+	0.395509i	−0.0444047	+	0.0256371i
$239$	−6.64956	+	1.78174i	−0.430124	+	0.115251i	−0.467384	−	0.884054i	$-0.654804\pi$
$239$	−6.64956	+	1.78174i	−0.430124	+	0.115251i	0.0372603	+	0.999306i	$0.488137\pi$
$240$		0			0
$241$	0.721284	+	0.721284i	0.0464620	+	0.0464620i	0.729956	−	0.683494i	$-0.239540\pi$
$241$	0.721284	+	0.721284i	0.0464620	+	0.0464620i	−0.683494	+	0.729956i	$0.739540\pi$
$242$	2.63773	−	2.63773i	0.169560	−	0.169560i
$243$		0			0
$244$	1.00956	−	0.582867i	0.0646301	−	0.0373142i
$245$	−11.7996	−	44.0366i	−0.753848	−	2.81340i
$246$		0			0
$247$	3.44719	−	6.87696i	0.219340	−	0.437571i
$248$	9.25189	+	5.34158i	0.587496	+	0.339191i
$249$		0			0
$250$	5.77406	−	10.0010i	0.365184	−	0.632517i
$251$	14.6482	−	25.3714i	0.924586	−	1.60143i	0.132359	−	0.991202i	$-0.457745\pi$
$251$	14.6482	−	25.3714i	0.924586	−	1.60143i	0.792226	−	0.610228i	$-0.208922\pi$
$252$		0			0
$253$	−0.598029	−	2.23187i	−0.0375977	−	0.140317i
$254$	0.270302	−	0.270302i	0.0169602	−	0.0169602i
$255$		0			0
$256$	8.15022	+	14.1166i	0.509389	+	0.882287i
$257$	18.1845			1.13432			0.567159	−	0.823609i	$-0.308043\pi$
$257$	18.1845			1.13432			0.567159	+	0.823609i	$0.308043\pi$
$258$		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
$263$	−16.9338	−	9.77671i	−1.04418	−	0.602858i	−0.123166	−	0.992386i	$-0.539305\pi$
$263$	−16.9338	−	9.77671i	−1.04418	−	0.602858i	−0.921015	+	0.389528i	$0.872638\pi$
$264$		0			0
$265$	−4.76716	−	17.7913i	−0.292845	−	1.09291i
$266$	3.04925	−	11.3800i	0.186962	−	0.697750i
$267$		0			0
$268$	−1.71161	+	6.38782i	−0.104553	+	0.390198i
$269$	23.9955	+	13.8538i	1.46303	+	0.844683i	0.999150	−	0.0412138i	$-0.0131225\pi$
$269$	23.9955	+	13.8538i	1.46303	+	0.844683i	0.463883	+	0.885896i	$0.346456\pi$
$270$		0			0
$271$	2.16310	−	8.07278i	0.131399	−	0.490387i	−0.868588	−	0.495535i	$-0.834972\pi$
$271$	2.16310	−	8.07278i	0.131399	−	0.490387i	0.999987	+	0.00514827i	$0.00163875\pi$
$272$	0.109546	+	0.189739i	0.00664218	+	0.0115046i
$273$		0			0
$274$	−8.38299	+	14.5198i	−0.506435	+	0.877171i
$275$	0.566526	+	0.566526i	0.0341628	+	0.0341628i
$276$		0			0
$277$			15.7692i			0.947479i	0.880665	+	0.473740i	$0.157096\pi$
$277$			15.7692i			0.947479i	−0.880665	+	0.473740i	$0.842904\pi$
$278$	−10.3789	−	10.3789i	−0.622488	−	0.622488i
$279$		0			0
$280$	−35.1305	+	9.41319i	−2.09945	+	0.562546i
$281$	−13.2097	−	3.53952i	−0.788022	−	0.211150i	−0.157704	−	0.987486i	$-0.550409\pi$
$281$	−13.2097	−	3.53952i	−0.788022	−	0.211150i	−0.630319	+	0.776337i	$0.717076\pi$
$282$		0			0
$283$			13.4590i			0.800056i	0.916503	+	0.400028i	$0.131000\pi$
$283$			13.4590i			0.800056i	−0.916503	+	0.400028i	$0.869000\pi$
$284$	4.45137	−	4.45137i	0.264140	−	0.264140i
$285$		0			0
$286$	2.12158	−	10.3144i	0.125452	−	0.609906i
$287$		−	40.5013i		−	2.39071i
$288$		0			0
$289$	8.48974	+	14.7047i	0.499396	+	0.864980i
$290$	1.48424			0.0871576
$291$		0			0
$292$	4.44096	+	1.18995i	0.259888	+	0.0696367i
$293$	−6.88486	−	1.84479i	−0.402218	−	0.107774i	0.0520382	−	0.998645i	$-0.483428\pi$
$293$	−6.88486	−	1.84479i	−0.402218	−	0.107774i	−0.454256	+	0.890871i	$0.650095\pi$
$294$		0			0
$295$	17.1305			0.997379
$296$	5.73867	+	9.93966i	0.333553	+	0.577731i
$297$		0			0
$298$			14.1054i			0.817105i
$299$	2.27377	+	2.02038i	0.131495	+	0.116842i
$300$		0			0
$301$	0.793080	−	0.793080i	0.0457124	−	0.0457124i
$302$		−	12.2617i		−	0.705581i
$303$		0			0
$304$	−3.15195	−	0.844562i	−0.180777	−	0.0484390i
$305$	3.00188	−	0.804351i	0.171887	−	0.0460570i
$306$		0			0
$307$	−8.37481	−	8.37481i	−0.477976	−	0.477976i	0.426508	−	0.904484i	$-0.359744\pi$
$307$	−8.37481	−	8.37481i	−0.477976	−	0.477976i	−0.904484	+	0.426508i	$0.859744\pi$
$308$			12.2396i			0.697416i
$309$		0			0
$310$	6.07021	+	6.07021i	0.344765	+	0.344765i
$311$	1.34766	−	2.33421i	0.0764186	−	0.132361i	−0.825284	−	0.564718i	$-0.808985\pi$
$311$	1.34766	−	2.33421i	0.0764186	−	0.132361i	0.901702	+	0.432357i	$0.142318\pi$
$312$		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
$317$	0.825569	−	3.08107i	0.0463686	−	0.173050i	−0.938858	−	0.344304i	$-0.888115\pi$
$317$	0.825569	−	3.08107i	0.0463686	−	0.173050i	0.985227	+	0.171254i	$0.0547818\pi$
$318$		0			0
$319$	0.428902	−	1.60069i	0.0240139	−	0.0896212i
$320$	4.66247	+	17.4006i	0.260640	+	0.972723i
$321$		0			0
$322$	4.03434	+	2.32923i	0.224825	+	0.129803i
$323$	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
$328$	−23.8763			−1.31835
$329$	27.3065	+	47.2962i	1.50545	+	2.60752i
$330$		0			0
$331$	21.8083	−	21.8083i	1.19869	−	1.19869i	0.224137	−	0.974558i	$-0.428044\pi$
$331$	21.8083	−	21.8083i	1.19869	−	1.19869i	0.974558	−	0.224137i	$-0.0719564\pi$
$332$	3.40128	+	12.6938i	0.186670	+	0.696661i
$333$		0			0
$334$	−1.15084	+	1.99332i	−0.0629714	+	0.109070i
$335$	−8.81513	+	15.2683i	−0.481622	+	0.834194i
$336$		0			0
$337$	4.37979	+	2.52867i	0.238582	+	0.137745i	0.614525	−	0.788897i	$-0.289348\pi$
$337$	4.37979	+	2.52867i	0.238582	+	0.137745i	−0.375943	+	0.926643i	$0.622681\pi$
$338$	5.13764	+	12.8751i	0.279451	+	0.700312i
$339$		0			0
$340$	−0.0736035	−	0.274692i	−0.00399171	−	0.0148973i
$341$	8.30056	−	4.79233i	0.449500	−	0.259519i
$342$		0			0
$343$	46.9330	−	46.9330i	2.53415	−	2.53415i
$344$	−0.467536	−	0.467536i	−0.0252079	−	0.0252079i
$345$		0			0
$346$	−12.4466	+	3.33505i	−0.669132	+	0.179293i
$347$	8.60125	−	4.96593i	0.461739	−	0.266585i	−0.251036	−	0.967978i	$-0.580771\pi$
$347$	8.60125	−	4.96593i	0.461739	−	0.266585i	0.712775	+	0.701393i	$0.247438\pi$
$348$		0			0
$349$	22.9183	−	6.14095i	1.22679	−	0.328717i	0.413461	−	0.910522i	$-0.364320\pi$
$349$	22.9183	−	6.14095i	1.22679	−	0.328717i	0.813329	+	0.581804i	$0.197653\pi$
$350$	−1.61529			−0.0863411
$351$		0			0
$352$	12.2561			0.653252
$353$	20.2838	−	5.43504i	1.07960	−	0.289278i	0.325168	−	0.945656i	$-0.394579\pi$
$353$	20.2838	−	5.43504i	1.07960	−	0.289278i	0.754432	+	0.656378i	$0.227913\pi$
$354$		0			0
$355$	14.5341	−	8.39128i	0.771392	−	0.445363i
$356$	12.2910	−	3.29335i	0.651420	−	0.174547i
$357$		0			0
$358$	−2.33149	−	2.33149i	−0.123223	−	0.123223i
$359$	−8.32119	+	8.32119i	−0.439175	+	0.439175i	−0.891734	−	0.452559i	$-0.850511\pi$
$359$	−8.32119	+	8.32119i	−0.439175	+	0.439175i	0.452559	+	0.891734i	$0.350511\pi$
$360$		0			0
$361$	12.5124	−	7.22401i	0.658545	−	0.380211i
$362$	−5.62704	−	21.0004i	−0.295751	−	1.10376i
$363$		0			0
$364$	−8.86411	−	13.4549i	−0.464606	−	0.705229i
$365$	10.6148	+	6.12849i	0.555607	+	0.320780i
$366$		0			0
$367$	2.83530	−	4.91088i	0.148001	−	0.256346i	−0.782487	−	0.622667i	$-0.786049\pi$
$367$	2.83530	−	4.91088i	0.148001	−	0.256346i	0.930489	+	0.366321i	$0.119383\pi$
$368$	0.645135	−	1.11741i	0.0336300	−	0.0582489i
$369$		0			0
$370$	2.38702	+	8.90848i	0.124095	+	0.463130i
$371$	29.3172	−	29.3172i	1.52208	−	1.52208i
$372$		0			0
$373$	13.4553	+	23.3053i	0.696690	+	1.20670i	0.969608	+	0.244665i	$0.0786779\pi$
$373$	13.4553	+	23.3053i	0.696690	+	1.20670i	−0.272918	+	0.962037i	$0.587989\pi$
$374$	0.418371			0.0216335
$375$		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	−0.492966	−	0.870049i	$-0.664087\pi$
$379$	−26.3773	−	7.06778i	−1.35491	−	0.363047i	−0.861945	+	0.507001i	$0.830754\pi$
$380$	3.66812	+	2.11779i	0.188170	+	0.108640i
$381$		0			0
$382$	2.60977	+	9.73981i	0.133528	+	0.498332i
$383$	4.34016	−	16.1977i	0.221772	−	0.827663i	−0.761901	−	0.647694i	$-0.775734\pi$
$383$	4.34016	−	16.1977i	0.221772	−	0.827663i	0.983672	−	0.179969i	$-0.0575997\pi$
$384$		0			0
$385$	−8.44527	+	31.5182i	−0.430411	+	1.60632i
$386$	−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	0.880032	−	0.474914i	$-0.157521\pi$
$389$	0.566623	+	0.981420i	0.0287289	+	0.0497600i	−0.851303	+	0.524674i	$0.824187\pi$
$390$		0			0
$391$	−0.0604234	+	0.104656i	−0.00305574	+	0.00529270i
$392$	−42.7787	−	42.7787i	−2.16065	−	2.16065i
$393$		0			0
$394$		−	2.94002i		−	0.148116i
$395$	−5.29148	−	5.29148i	−0.266243	−	0.266243i
$396$		0			0
$397$	17.9346	−	4.80557i	0.900114	−	0.241185i	0.221049	−	0.975263i	$-0.429052\pi$
$397$	17.9346	−	4.80557i	0.900114	−	0.241185i	0.679065	+	0.734078i	$0.262385\pi$
$398$	16.0305	+	4.29535i	0.803534	+	0.215306i
$399$		0			0
$400$			0.447394i			0.0223697i
$401$	−12.3178	+	12.3178i	−0.615124	+	0.615124i	−0.944277	−	0.329153i	$-0.893237\pi$
$401$	−12.3178	+	12.3178i	−0.615124	+	0.615124i	0.329153	+	0.944277i	$0.393237\pi$
$402$		0			0
$403$	−5.65407	+	11.2796i	−0.281649	+	0.561875i
$404$		−	3.02970i		−	0.150733i
$405$		0			0
$406$	1.67051	+	2.89340i	0.0829059	+	0.143597i
$407$	10.2972			0.510412
$408$		0			0
$409$	−29.9191	−	8.01681i	−1.47941	−	0.396406i	−0.573261	−	0.819373i	$-0.694322\pi$
$409$	−29.9191	−	8.01681i	−1.47941	−	0.396406i	−0.906145	+	0.422967i	$0.860989\pi$
$410$	−18.5323	−	4.96572i	−0.915245	−	0.245239i
$411$		0			0
$412$	0.659494			0.0324909
$413$	19.2804	+	33.3946i	0.948725	+	1.64324i
$414$		0			0
$415$			35.0346i			1.71978i
$416$	−13.4731	+	8.87606i	−0.660571	+	0.435184i
$417$		0			0
$418$	−4.40613	+	4.40613i	−0.215511	+	0.215511i
$419$		−	21.4719i		−	1.04897i	−0.851419	−	0.524486i	$-0.824258\pi$
$419$		−	21.4719i		−	1.04897i	0.851419	−	0.524486i	$-0.175742\pi$
$420$		0			0
$421$	−22.9186	−	6.14101i	−1.11698	−	0.299295i	−0.347321	−	0.937746i	$-0.612908\pi$
$421$	−22.9186	−	6.14101i	−1.11698	−	0.299295i	−0.769662	+	0.638452i	$0.779575\pi$
$422$	9.50050	−	2.54565i	0.462477	−	0.123920i
$423$		0			0
$424$	−17.2831	−	17.2831i	−0.839341	−	0.839341i
$425$		−	0.0419029i		−	0.00203259i
$426$		0			0
$427$	4.94662	+	4.94662i	0.239384	+	0.239384i
$428$	−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	0.652000	+	0.758219i	$0.273930\pi$
$431$	−6.05706	+	22.6052i	−0.291758	+	1.08886i	−0.943758	+	0.330637i	$0.892736\pi$
$432$		0			0
$433$	−23.0080	−	13.2837i	−1.10569	−	0.638372i	−0.167982	−	0.985790i	$-0.553725\pi$
$433$	−23.0080	−	13.2837i	−1.10569	−	0.638372i	−0.937710	+	0.347418i	$0.887058\pi$
$434$	−5.00137	+	18.6654i	−0.240074	+	0.895967i
$435$		0			0
$436$	1.15084	−	4.29498i	0.0551150	−	0.205692i
$437$	−0.465845	−	1.73856i	−0.0222844	−	0.0831665i
$438$		0			0
$439$	0.369772	+	0.213488i	0.0176482	+	0.0101892i	0.508798	−	0.860886i	$-0.330090\pi$
$439$	0.369772	+	0.213488i	0.0176482	+	0.0101892i	−0.491150	+	0.871075i	$0.663423\pi$
$440$	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
$445$	33.9228			1.60810
$446$	1.03103	+	1.78579i	0.0488206	+	0.0845598i
$447$		0			0
$448$	−28.6734	+	28.6734i	−1.35469	+	1.35469i
$449$	1.66954	+	6.23079i	0.0787903	+	0.294049i	0.994066	−	0.108779i	$-0.0346940\pi$
$449$	1.66954	+	6.23079i	0.0787903	+	0.294049i	−0.915276	+	0.402828i	$0.868027\pi$
$450$		0			0
$451$	−10.7106	+	18.5513i	−0.504342	+	0.873546i
$452$	4.01714	−	6.95789i	0.188950	−	0.327272i
$453$		0			0
$454$	17.7045	+	10.2217i	0.830914	+	0.479728i
$455$	−13.5421	−	40.7639i	−0.634864	−	1.91104i
$456$		0			0
$457$	2.81333	+	10.4995i	0.131602	+	0.491145i	0.999989	−	0.00474244i	$-0.00150957\pi$
$457$	2.81333	+	10.4995i	0.131602	+	0.491145i	−0.868387	+	0.495887i	$0.834843\pi$
$458$	−17.4554	+	10.0779i	−0.815636	+	0.470908i
$459$		0			0
$460$	−1.18425	+	1.18425i	−0.0552158	+	0.0552158i
$461$	−12.0225	−	12.0225i	−0.559943	−	0.559943i	0.369348	−	0.929291i	$-0.379581\pi$
$461$	−12.0225	−	12.0225i	−0.559943	−	0.559943i	−0.929291	+	0.369348i	$0.879581\pi$
$462$		0			0
$463$	37.4724	−	10.0407i	1.74149	−	0.466630i	0.758712	−	0.651427i	$-0.225829\pi$
$463$	37.4724	−	10.0407i	1.74149	−	0.466630i	0.982777	+	0.184796i	$0.0591625\pi$
$464$	0.801397	−	0.462687i	0.0372039	−	0.0214797i
$465$		0			0
$466$	−15.4594	+	4.14234i	−0.716144	+	0.191890i
$467$	−37.7239			−1.74566			−0.872828	−	0.488028i	$-0.837716\pi$
$467$	−37.7239			−1.74566			−0.872828	+	0.488028i	$0.837716\pi$
$468$		0			0
$469$	−39.6856			−1.83251
$470$	24.9894	−	6.69590i	1.15268	−	0.308859i
$471$		0			0
$472$	19.6868	−	11.3662i	0.906157	−	0.523170i
$473$	−0.572995	+	0.153534i	−0.0263463	+	0.00705948i
$474$		0			0
$475$	0.441306	+	0.441306i	0.0202485	+	0.0202485i
$476$	0.452649	−	0.452649i	0.0207471	−	0.0207471i
$477$		0			0
$478$	−6.35728	+	3.67037i	−0.290775	+	0.167879i
$479$	5.40418	+	20.1687i	0.246923	+	0.921531i	0.972407	+	0.233291i	$0.0749495\pi$
$479$	5.40418	+	20.1687i	0.246923	+	0.921531i	−0.725484	+	0.688240i	$0.758384\pi$
$480$		0			0
$481$	−11.3196	+	7.45737i	−0.516130	+	0.340027i
$482$	0.941984	+	0.543855i	0.0429062	+	0.0247719i
$483$		0			0
$484$	−1.50940	+	2.61436i	−0.0686092	+	0.118835i
$485$	0.626060	−	1.08437i	0.0284279	−	0.0492386i
$486$		0			0
$487$	4.59917	+	17.1643i	0.208408	+	0.777791i	0.988384	+	0.151980i	$0.0485650\pi$
$487$	4.59917	+	17.1643i	0.208408	+	0.777791i	−0.779975	+	0.625811i	$0.784768\pi$
$488$	2.91613	−	2.91613i	0.132007	−	0.132007i
$489$		0			0
$490$	−24.3070	−	42.1010i	−1.09808	−	1.90193i
$491$	−14.5919			−0.658523			−0.329261	−	0.944239i	$-0.606800\pi$
$491$	−14.5919			−0.658523			−0.329261	+	0.944239i	$0.606800\pi$
$492$		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
$497$	32.7162	+	18.8887i	1.46752	+	0.847275i
$498$		0			0
$499$	−3.09645	−	11.5561i	−0.138616	−	0.517323i	−0.999957	−	0.00929473i	$-0.997041\pi$
$499$	−3.09645	−	11.5561i	−0.138616	−	0.517323i	0.861341	−	0.508028i	$-0.169625\pi$
$500$	−2.41878	+	9.02703i	−0.108171	+	0.403701i
$501$		0			0
$502$	8.08540	−	30.1751i	0.360869	−	1.34678i
$503$	−24.4849	−	14.1364i	−1.09173	−	0.630310i	−0.157693	−	0.987488i	$-0.550406\pi$
$503$	−24.4849	−	14.1364i	−1.09173	−	0.630310i	−0.934036	+	0.357178i	$0.883739\pi$
$504$		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
$509$	−6.43830	−	6.43830i	−0.285373	−	0.285373i	0.549874	−	0.835247i	$-0.314676\pi$
$509$	−6.43830	−	6.43830i	−0.285373	−	0.285373i	−0.835247	+	0.549874i	$0.814676\pi$
$510$		0			0
$511$			27.5904i			1.22053i
$512$	11.4426	+	11.4426i	0.505696	+	0.505696i
$513$		0			0
$514$	18.7299	−	5.01867i	0.826142	−	0.221364i
$515$	1.69826	+	0.455048i	0.0748344	+	0.0200518i
$516$		0			0
$517$		−	28.8849i		−	1.27036i
$518$	−14.6798	+	14.6798i	−0.644992	+	0.644992i
$519$		0			0
$520$	−24.0311	+	7.98335i	−1.05384	+	0.350093i
$521$		−	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	−0.954228	−	0.299080i	$-0.903320\pi$
$523$	−16.8346	−	29.1584i	−0.736125	−	1.27501i	0.218103	−	0.975926i	$-0.430013\pi$
$524$	−10.0809			−0.440386
$525$		0			0
$526$	−20.1399	−	5.39648i	−0.878143	−	0.235298i
$527$	−0.484205	−	0.129742i	−0.0210923	−	0.00565167i
$528$		0			0
$529$	−22.2883			−0.969057
$530$	−9.82031	−	17.0093i	−0.426567	−	0.738836i
$531$		0			0
$532$			9.53425i			0.413362i
$533$	−1.66104	−	28.1501i	−0.0719478	−	1.21932i
$534$		0			0
$535$	−9.95246	+	9.95246i	−0.430282	+	0.430282i
$536$			23.3955i			1.01053i
$537$		0			0
$538$	28.5388	+	7.64694i	1.23039	+	0.329683i
$539$	−52.4280	+	14.0480i	−2.25823	+	0.605092i
$540$		0			0
$541$	19.2044	+	19.2044i	0.825663	+	0.825663i	0.986914	−	0.161250i	$-0.0515526\pi$
$541$	19.2044	+	19.2044i	0.825663	+	0.825663i	−0.161250	+	0.986914i	$0.551553\pi$
$542$		−	8.91191i		−	0.382799i
$543$		0			0
$544$	−0.453259	−	0.453259i	−0.0194333	−	0.0194333i
$545$	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
$551$	0.334101	−	1.24688i	0.0142332	−	0.0531190i
$552$		0			0
$553$	4.35976	−	16.2709i	0.185396	−	0.691907i
$554$	4.35208	+	16.2422i	0.184902	+	0.690065i
$555$		0			0
$556$	10.2870	+	5.93920i	0.436266	+	0.251878i
$557$	25.0352	+	6.70816i	1.06078	+	0.284234i	0.746698	−	0.665163i	$-0.231638\pi$
$557$	25.0352	+	6.70816i	1.06078	+	0.284234i	0.314078	+	0.949397i	$0.398305\pi$
$558$		0			0
$559$	0.518699	−	0.583750i	0.0219386	−	0.0246900i
$560$	−15.7798	+	9.11050i	−0.666820	+	0.384989i
$561$		0			0
$562$	−14.5827			−0.615136
$563$	−8.22579	−	14.2475i	−0.346676	−	0.600460i	0.638981	−	0.769223i	$-0.279356\pi$
$563$	−8.22579	−	14.2475i	−0.346676	−	0.600460i	−0.985657	+	0.168762i	$0.946023\pi$
$564$		0			0
$565$	15.1454	−	15.1454i	0.637174	−	0.637174i
$566$	3.71451	+	13.8627i	0.156132	+	0.582694i
$567$		0			0
$568$	11.1353	−	19.2869i	0.467226	−	0.809259i
$569$	−7.11456	+	12.3228i	−0.298258	+	0.516598i	−0.975737	−	0.218944i	$-0.929739\pi$
$569$	−7.11456	+	12.3228i	−0.298258	+	0.516598i	0.677480	+	0.735541i	$0.263072\pi$
$570$		0			0
$571$	−18.0451	−	10.4184i	−0.755164	−	0.435994i	0.0723925	−	0.997376i	$-0.476937\pi$
$571$	−18.0451	−	10.4184i	−0.755164	−	0.435994i	−0.827557	+	0.561382i	$0.810270\pi$
$572$	0.501973	+	8.50704i	0.0209885	+	0.355697i
$573$		0			0
$574$	−11.1778	−	41.7161i	−0.466552	−	1.74120i
$575$	−0.213713	+	0.123387i	−0.00891244	+	0.00514560i
$576$		0			0
$577$	−32.0720	+	32.0720i	−1.33517	+	1.33517i	−0.434505	+	0.900670i	$0.643076\pi$
$577$	−32.0720	+	32.0720i	−1.33517	+	1.33517i	−0.900670	+	0.434505i	$0.856924\pi$
$578$	12.8027	+	12.8027i	0.532521	+	0.532521i
$579$		0			0
$580$	−1.16021	+	0.310878i	−0.0481752	+	0.0129085i
$581$	−68.2970	+	39.4313i	−2.83344	+	1.63589i
$582$		0			0
$583$	−21.1815	+	5.67557i	−0.877249	+	0.235058i
$584$	16.2651			0.673053
$585$		0			0
$586$	−7.60051			−0.313974
$587$	−15.2613	+	4.08926i	−0.629903	+	0.168782i	−0.559626	−	0.828746i	$-0.689055\pi$
$587$	−15.2613	+	4.08926i	−0.629903	+	0.168782i	−0.0702771	+	0.997528i	$0.522388\pi$
$588$		0			0
$589$	6.46587	−	3.73307i	0.266421	−	0.153818i
$590$	17.6444	−	4.72780i	0.726408	−	0.194640i
$591$		0			0
$592$	4.06591	+	4.06591i	0.167108	+	0.167108i
$593$	25.1695	−	25.1695i	1.03359	−	1.03359i	0.0341707	−	0.999416i	$-0.489121\pi$
$593$	25.1695	−	25.1695i	1.03359	−	1.03359i	0.999416	−	0.0341707i	$-0.0108790\pi$
$594$		0			0
$595$	1.47794	−	0.853290i	0.0605897	−	0.0349815i
$596$	−2.95442	−	11.0260i	−0.121018	−	0.451644i
$597$		0			0
$598$	2.89957	+	1.45346i	0.118572	+	0.0594362i
$599$	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
$601$	−14.6937	+	25.4502i	−0.599369	+	1.03814i	0.393546	+	0.919305i	$0.371248\pi$
$601$	−14.6937	+	25.4502i	−0.599369	+	1.03814i	−0.992914	+	0.118832i	$0.962085\pi$
$602$	0.597990	−	1.03575i	0.0243722	−	0.0422140i
$603$		0			0
$604$	2.56825	+	9.58482i	0.104500	+	0.390001i
$605$	−5.69076	+	5.69076i	−0.231362	+	0.231362i
$606$		0			0
$607$	10.4263	+	18.0589i	0.423191	+	0.732988i	0.996250	−	0.0865261i	$-0.0275766\pi$
$607$	10.4263	+	18.0589i	0.423191	+	0.732988i	−0.573059	+	0.819514i	$0.694243\pi$
$608$	9.54711			0.387186
$609$		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	−0.201809	−	0.979425i	$-0.564682\pi$
$613$	−21.4484	−	5.74708i	−0.866292	−	0.232122i	−0.664484	+	0.747303i	$0.731349\pi$
$614$	−10.9374	−	6.31468i	−0.441396	−	0.254840i
$615$		0			0
$616$	11.2069	+	41.8248i	0.451540	+	1.68517i
$617$	3.14191	−	11.7258i	0.126488	−	0.472061i	−0.873400	−	0.487004i	$-0.838090\pi$
$617$	3.14191	−	11.7258i	0.126488	−	0.472061i	0.999888	+	0.0149425i	$0.00475652\pi$
$618$		0			0
$619$	1.49281	−	5.57125i	0.0600012	−	0.223928i	−0.929414	−	0.369038i	$-0.879687\pi$
$619$	1.49281	−	5.57125i	0.0600012	−	0.223928i	0.989415	+	0.145111i	$0.0463538\pi$
$620$	−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
$626$	2.52377	+	2.52377i	0.100870	+	0.100870i
$627$		0			0
$628$		−	8.09390i		−	0.322982i
$629$	−0.380813	−	0.380813i	−0.0151840	−	0.0151840i
$630$		0			0
$631$	−0.701230	+	0.187894i	−0.0279155	+	0.00747994i	−0.272750	−	0.962085i	$-0.587933\pi$
$631$	−0.701230	+	0.187894i	−0.0279155	+	0.00747994i	0.244834	+	0.969565i	$0.421266\pi$
$632$	−9.59200	−	2.57017i	−0.381549	−	0.102236i
$633$		0			0
$634$		−	3.40133i		−	0.135084i
$635$	−0.583161	+	0.583161i	−0.0231420	+	0.0231420i
$636$		0			0
$637$	47.4600	−	53.4121i	1.88043	−	2.11626i
$638$		−	1.76707i		−	0.0699589i
$639$		0			0
$640$	−0.689789	−	1.19475i	−0.0272663	−	0.0472266i
$641$	1.93672			0.0764960			0.0382480	−	0.999268i	$-0.487822\pi$
$641$	1.93672			0.0764960			0.0382480	+	0.999268i	$0.487822\pi$
$642$		0			0
$643$	−5.23973	−	1.40398i	−0.206635	−	0.0553676i	0.154017	−	0.988068i	$-0.450779\pi$
$643$	−5.23973	−	1.40398i	−0.206635	−	0.0553676i	−0.360652	+	0.932701i	$0.617446\pi$
$644$	−3.64146	−	0.975727i	−0.143494	−	0.0384490i
$645$		0			0
$646$	0.325898			0.0128223
$647$	−5.52455	−	9.56880i	−0.217192	−	0.376188i	0.736756	−	0.676159i	$-0.236357\pi$
$647$	−5.52455	−	9.56880i	−0.217192	−	0.376188i	−0.953949	+	0.299970i	$0.903023\pi$
$648$		0			0
$649$		−	20.3949i		−	0.800568i
$650$	−1.12270	+	0.0662467i	−0.0440358	+	0.00259841i
$651$		0			0
$652$	9.07249	−	9.07249i	0.355306	−	0.355306i
$653$		−	26.4693i		−	1.03582i	−0.855434	−	0.517912i	$-0.826710\pi$
$653$		−	26.4693i		−	1.03582i	0.855434	−	0.517912i	$-0.173290\pi$
$654$		0			0
$655$	−25.9593	−	6.95577i	−1.01431	−	0.271784i
$656$	−11.5543	+	3.09595i	−0.451118	+	0.120877i
$657$		0			0
$658$	41.1786	+	41.1786i	1.60531	+	1.60531i
$659$		−	44.2149i		−	1.72237i	−0.508294	−	0.861184i	$-0.669724\pi$
$659$		−	44.2149i		−	1.72237i	0.508294	−	0.861184i	$-0.330276\pi$
$660$		0			0
$661$	−22.3707	−	22.3707i	−0.870118	−	0.870118i	0.122367	−	0.992485i	$-0.460952\pi$
$661$	−22.3707	−	22.3707i	−0.870118	−	0.870118i	−0.992485	+	0.122367i	$0.960952\pi$
$662$	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
$668$	0.482095	−	1.79920i	0.0186528	−	0.0696132i
$669$		0			0
$670$	−4.86571	+	18.1591i	−0.187979	+	0.701547i
$671$	−0.957624	−	3.57390i	−0.0369687	−	0.137969i
$672$		0			0
$673$	15.8801	+	9.16836i	0.612132	+	0.353414i	0.773799	−	0.633431i	$-0.218354\pi$
$673$	15.8801	+	9.16836i	0.612132	+	0.353414i	−0.161668	+	0.986845i	$0.551687\pi$
$674$	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
$679$	2.81852			0.108165
$680$	−0.503031	−	0.871276i	−0.0192904	−	0.0334119i
$681$		0			0
$682$	7.22692	−	7.22692i	0.276733	−	0.276733i
$683$	6.10105	+	22.7694i	0.233450	+	0.871249i	0.978841	+	0.204621i	$0.0655962\pi$
$683$	6.10105	+	22.7694i	0.233450	+	0.871249i	−0.745391	+	0.666628i	$0.767737\pi$
$684$		0			0
$685$	18.0858	−	31.3256i	0.691024	−	1.19689i
$686$	35.3879	−	61.2937i	1.35112	−	2.34020i
$687$		0			0
$688$	−0.286875	−	0.165627i	−0.0109370	−	0.00631448i
$689$	19.1744	−	21.5791i	0.730485	−	0.822098i
$690$		0			0
$691$	11.1642	+	41.6653i	0.424705	+	1.58502i	0.764566	+	0.644545i	$0.222953\pi$
$691$	11.1642	+	41.6653i	0.424705	+	1.58502i	−0.339861	+	0.940476i	$0.610380\pi$
$692$	9.03080	−	5.21394i	0.343300	−	0.198204i
$693$		0			0
$694$	7.48871	−	7.48871i	0.284268	−	0.284268i
$695$	22.3920	+	22.3920i	0.849377	+	0.849377i
$696$		0			0
$697$	1.08217	−	0.289967i	0.0409902	−	0.0109833i
$698$	21.9110	−	12.6503i	0.829342	−	0.478821i
$699$		0			0
$700$	1.26266	−	0.338328i	0.0477239	−	0.0127876i
$701$	−16.2764			−0.614753			−0.307376	−	0.951588i	$-0.599451\pi$
$701$	−16.2764			−0.614753			−0.307376	+	0.951588i	$0.599451\pi$
$702$		0			0
$703$	8.02116			0.302524
$704$	20.7164	−	5.55093i	0.780777	−	0.209209i
$705$		0			0
$706$	19.3923	−	11.1961i	0.729837	−	0.421372i
$707$	17.5617	−	4.70565i	0.660477	−	0.176974i
$708$		0			0
$709$	−3.46292	−	3.46292i	−0.130053	−	0.130053i	0.639084	−	0.769137i	$-0.279314\pi$
$709$	−3.46292	−	3.46292i	−0.130053	−	0.130053i	−0.769137	+	0.639084i	$0.779314\pi$
$710$	12.6542	−	12.6542i	0.474904	−	0.474904i
$711$		0			0
$712$	38.9848	−	22.5079i	1.46102	−	0.843519i
$713$	0.764077	+	2.85158i	0.0286149	+	0.106792i
$714$		0			0
$715$	−4.57719	+	22.2528i	−0.171177	+	0.832209i
$716$	2.31083	+	1.33416i	0.0863599	+	0.0498599i
$717$		0			0
$718$	−6.27425	+	10.8673i	−0.234153	+	0.405565i
$719$	−17.2570	+	29.8900i	−0.643577	+	1.11471i	0.341052	+	0.940045i	$0.389217\pi$
$719$	−17.2570	+	29.8900i	−0.643577	+	1.11471i	−0.984628	+	0.174663i	$0.944116\pi$
$720$		0			0
$721$	1.02431	+	3.82278i	0.0381473	+	0.142368i
$722$	10.8939	−	10.8939i	0.405430	−	0.405430i
$723$		0			0
$724$	8.79719	+	15.2372i	0.326945	+	0.566285i
$725$	−0.176985			−0.00657305
$726$		0			0
$727$	−6.05240	+	3.49435i	−0.224471	+	0.129598i	−0.608019	−	0.793923i	$-0.708035\pi$
$727$	−6.05240	+	3.49435i	−0.224471	+	0.129598i	0.383548	+	0.923521i	$0.374702\pi$
$728$	−42.6099	−	37.8615i	−1.57923	−	1.40324i
$729$		0			0
$730$	12.6246	+	3.38276i	0.467258	+	0.125201i
$731$	0.0268687	+	0.0155127i	0.000993776	+	0.000573757i
$732$		0			0
$733$	5.89883	+	22.0147i	0.217878	+	0.813133i	0.985133	+	0.171791i	$0.0549554\pi$
$733$	5.89883	+	22.0147i	0.217878	+	0.813133i	−0.767255	+	0.641342i	$0.778378\pi$
$734$	1.56501	−	5.84069i	0.0577655	−	0.215584i
$735$		0			0
$736$	−0.977042	+	3.64637i	−0.0360142	+	0.134407i
$737$	18.1777	+	10.4949i	0.669584	+	0.386585i
$738$		0			0
$739$	−3.70607	+	13.8313i	−0.136330	+	0.508791i	0.863659	+	0.504077i	$0.168167\pi$
$739$	−3.70607	+	13.8313i	−0.136330	+	0.508791i	−0.999989	+	0.00471409i	$0.998499\pi$
$740$	−3.73181	−	6.46368i	−0.137184	−	0.237610i
$741$		0			0
$742$	22.1055	−	38.2878i	0.811517	−	1.40559i
$743$	4.39820	+	4.39820i	0.161354	+	0.161354i	0.783166	−	0.621812i	$-0.213603\pi$
$743$	4.39820	+	4.39820i	0.161354	+	0.161354i	−0.621812	+	0.783166i	$0.713603\pi$
$744$		0			0
$745$		−	30.4317i		−	1.11493i
$746$	20.2909	+	20.2909i	0.742901	+	0.742901i
$747$		0			0
$748$	−0.327036	+	0.0876290i	−0.0119576	+	0.00320403i
$749$	−30.6030	−	8.20004i	−1.11821	−	0.299623i
$750$		0			0
$751$			43.6578i			1.59309i	0.604576	+	0.796547i	$0.293343\pi$
$751$			43.6578i			1.59309i	−0.604576	+	0.796547i	$0.706657\pi$
$752$	11.4054	−	11.4054i	0.415912	−	0.415912i
$753$		0			0
$754$	1.27974	+	1.94253i	0.0466053	+	0.0707427i
$755$			26.4539i			0.962757i
$756$		0			0
$757$	9.84349	+	17.0494i	0.357768	+	0.619672i	0.987588	−	0.157069i	$-0.0502046\pi$
$757$	9.84349	+	17.0494i	0.357768	+	0.619672i	−0.629820	+	0.776741i	$0.716871\pi$
$758$	−29.1191			−1.05765
$759$		0			0
$760$	14.4737	+	3.87821i	0.525016	+	0.140678i
$761$	−8.35027	−	2.23745i	−0.302697	−	0.0811074i	0.104274	−	0.994549i	$-0.466748\pi$
$761$	−8.35027	−	2.23745i	−0.302697	−	0.0811074i	−0.406971	+	0.913441i	$0.633415\pi$
$762$		0			0
$763$	26.6834			0.966005
$764$	−4.08006	−	7.06686i	−0.147611	−	0.255670i
$765$		0			0
$766$		−	17.8814i		−	0.646080i
$767$	14.7703	+	22.4199i	0.533323	+	0.809537i
$768$		0			0
$769$	−6.20131	+	6.20131i	−0.223625	+	0.223625i	−0.810023	−	0.586398i	$-0.800545\pi$
$769$	−6.20131	+	6.20131i	−0.223625	+	0.223625i	0.586398	+	0.810023i	$0.300545\pi$
$770$			34.7944i			1.25390i
$771$		0			0
$772$	0.330916	+	0.0886686i	0.0119099	+	0.00319125i
$773$	3.74962	−	1.00471i	0.134865	−	0.0361368i	−0.190755	−	0.981638i	$-0.561094\pi$
$773$	3.74962	−	1.00471i	0.134865	−	0.0361368i	0.325620	+	0.945501i	$0.394427\pi$
$774$		0			0
$775$	−0.723828	−	0.723828i	−0.0260007	−	0.0260007i
$776$		−	1.66157i		−	0.0596469i
$777$		0			0
$778$	0.854478	+	0.854478i	0.0306345	+	0.0306345i
$779$	−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
$785$	5.58475	−	20.8426i	0.199328	−	0.743904i
$786$		0			0
$787$	1.10975	−	4.14166i	0.0395585	−	0.147634i	−0.943322	−	0.331879i	$-0.892317\pi$
$787$	1.10975	−	4.14166i	0.0395585	−	0.147634i	0.982880	+	0.184245i	$0.0589840\pi$
$788$	0.615796	+	2.29818i	0.0219368	+	0.0818693i
$789$		0			0
$790$	−6.91058	−	3.98983i	−0.245867	−	0.141952i
$791$	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
$796$	−13.4305			−0.476031
$797$	−5.45712	−	9.45202i	−0.193301	−	0.334808i	0.753041	−	0.657974i	$-0.228586\pi$
$797$	−5.45712	−	9.45202i	−0.193301	−	0.334808i	−0.946342	+	0.323166i	$0.895253\pi$
$798$		0			0
$799$	−1.06823	+	1.06823i	−0.0377913	+	0.0377913i
$800$	−0.338784	−	1.26436i	−0.0119778	−	0.0447018i
$801$		0			0
$802$	−9.28776	+	16.0869i	−0.327962	+	0.568047i
$803$	7.29630	−	12.6376i	0.257481	−	0.445970i
$804$		0			0
$805$	−8.70387	−	5.02518i	−0.306771	−	0.177114i
$806$	−2.71066	+	13.1783i	−0.0954789	+	0.464188i
$807$		0			0
$808$	−2.77408	−	10.3530i	−0.0975916	−	0.364217i
$809$	24.7010	−	14.2611i	0.868439	−	0.501394i	0.00160994	−	0.999999i	$-0.499488\pi$
$809$	24.7010	−	14.2611i	0.868439	−	0.501394i	0.866829	+	0.498605i	$0.166154\pi$
$810$		0			0
$811$	−14.4345	+	14.4345i	−0.506862	+	0.506862i	−0.913562	−	0.406700i	$-0.866680\pi$
$811$	−14.4345	+	14.4345i	−0.506862	+	0.506862i	0.406700	+	0.913562i	$0.366680\pi$
$812$	−1.91185	−	1.91185i	−0.0670927	−	0.0670927i
$813$		0			0
$814$	10.6060	−	2.84188i	0.371741	−	0.0996078i
$815$	29.6225	−	17.1026i	1.03763	−	0.599077i
$816$		0			0
$817$	−0.446345	+	0.119598i	−0.0156156	+	0.00418419i
$818$	−33.0291			−1.15484
$819$		0			0
$820$	15.5266			0.542211
$821$	−21.4587	+	5.74984i	−0.748914	+	0.200671i	−0.613036	−	0.790055i	$-0.710052\pi$
$821$	−21.4587	+	5.74984i	−0.748914	+	0.200671i	−0.135878	+	0.990726i	$0.543385\pi$
$822$		0			0
$823$	−48.6206	+	28.0711i	−1.69481	+	0.978498i	−0.744277	+	0.667871i	$0.767206\pi$
$823$	−48.6206	+	28.0711i	−1.69481	+	0.978498i	−0.950532	+	0.310627i	$0.899461\pi$
$824$	2.25360	−	0.603851i	0.0785080	−	0.0210361i
$825$		0			0
$826$	29.0752	+	29.0752i	1.01165	+	1.01165i
$827$	−7.73555	+	7.73555i	−0.268991	+	0.268991i	−0.828694	−	0.559702i	$-0.810915\pi$
$827$	−7.73555	+	7.73555i	−0.268991	+	0.268991i	0.559702	+	0.828694i	$0.310915\pi$
$828$		0			0
$829$	−22.3717	+	12.9163i	−0.777001	+	0.448602i	−0.835366	−	0.549693i	$-0.814745\pi$
$829$	−22.3717	+	12.9163i	−0.777001	+	0.448602i	0.0583652	+	0.998295i	$0.481411\pi$
$830$	9.66907	+	36.0854i	0.335618	+	1.25254i
$831$		0			0
$832$	−18.7533	+	21.1052i	−0.650153	+	0.731691i
$833$	2.45844	+	1.41938i	0.0851799	+	0.0491786i
$834$		0			0
$835$	2.48288	−	4.30048i	0.0859237	−	0.148824i
$836$	2.52134	−	4.36709i	0.0872024	−	0.151039i
$837$		0			0
$838$	−5.92596	−	22.1160i	−0.204709	−	0.763984i
$839$	25.1564	−	25.1564i	0.868497	−	0.868497i	−0.123809	−	0.992306i	$-0.539511\pi$
$839$	25.1564	−	25.1564i	0.868497	−	0.868497i	0.992306	+	0.123809i	$0.0395111\pi$
$840$		0			0
$841$	−14.3170	−	24.7977i	−0.493688	−	0.855094i
$842$	−25.3009			−0.871925
$843$		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
$848$	−10.6047	−	6.12263i	−0.364167	−	0.210252i
$849$		0			0
$850$	−0.0115646	−	0.0431598i	−0.000396664	−	0.00148037i
$851$	−0.820878	+	3.06356i	−0.0281393	+	0.105017i
$852$		0			0
$853$	3.20271	−	11.9527i	0.109659	−	0.409252i	−0.889173	−	0.457571i	$-0.848720\pi$
$853$	3.20271	−	11.9527i	0.109659	−	0.409252i	0.998832	+	0.0483186i	$0.0153863\pi$
$854$	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	0.840002	−	0.542584i	$-0.182554\pi$
$857$	−1.46053	−	2.52971i	−0.0498907	−	0.0864132i	−0.889892	+	0.456171i	$0.849221\pi$
$858$		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	$0.00654052\pi$
$860$	0.304035	+	0.304035i	0.0103675	+	0.0103675i
$861$		0			0
$862$			24.9550i			0.849969i
$863$	−32.6894	−	32.6894i	−1.11276	−	1.11276i	−0.992776	−	0.119986i	$-0.961715\pi$
$863$	−32.6894	−	32.6894i	−1.11276	−	1.11276i	−0.119986	−	0.992776i	$-0.538285\pi$
$864$		0			0
$865$	26.8528	−	7.19519i	0.913023	−	0.244644i
$866$	−27.3642	−	7.33222i	−0.929874	−	0.249159i
$867$		0			0
$868$		−	15.6381i		−	0.530790i
$869$	−6.29980	+	6.29980i	−0.213706	+	0.213706i
$870$		0			0
$871$	−27.5832	+	1.62759i	−0.934621	+	0.0551489i
$872$		−	15.7304i		−	0.532699i
$873$		0			0
$874$	−0.959637	−	1.66214i	−0.0324602	−	0.0562227i
$875$	−56.0822			−1.89593
$876$		0			0
$877$	54.6344	+	14.6393i	1.84487	+	0.494332i	0.999223	−	0.0394048i	$-0.0125462\pi$
$877$	54.6344	+	14.6393i	1.84487	+	0.494332i	0.845650	+	0.533737i	$0.179213\pi$
$878$	0.439783	+	0.117839i	0.0148420	+	0.00397689i
$879$		0			0
$880$	9.63712			0.324867
$881$	−14.1084	−	24.4364i	−0.475323	−	0.823284i	0.524278	−	0.851547i	$-0.324335\pi$
$881$	−14.1084	−	24.4364i	−0.475323	−	0.823284i	−0.999600	+	0.0282639i	$0.991002\pi$
$882$		0			0
$883$		−	7.20265i		−	0.242388i	−0.992629	−	0.121194i	$-0.961328\pi$
$883$		−	7.20265i		−	0.242388i	0.992629	−	0.121194i	$-0.0386724\pi$
$884$	0.296046	−	0.333174i	0.00995711	−	0.0112059i
$885$		0			0
$886$	−8.64222	+	8.64222i	−0.290341	+	0.290341i
$887$			31.5868i			1.06058i	0.847816	+	0.530291i	$0.177917\pi$
$887$			31.5868i			1.06058i	−0.847816	+	0.530291i	$0.822083\pi$
$888$		0			0
$889$	−1.79317	−	0.480478i	−0.0601410	−	0.0161147i
$890$	34.9404	−	9.36224i	1.17120	−	0.313823i
$891$		0			0
$892$	−1.17998	−	1.17998i	−0.0395087	−	0.0395087i
$893$		−	22.5004i		−	0.752947i
$894$		0			0
$895$	5.03006	+	5.03006i	0.168136	+	0.168136i
$896$	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
$902$	−5.91196	+	22.0637i	−0.196847	+	0.734642i
$903$		0			0
$904$	7.35641	−	27.4545i	0.244671	−	0.913123i
$905$	12.1400	+	45.3072i	0.403549	+	1.50606i
$906$		0			0
$907$	−19.5861	−	11.3080i	−0.650346	−	0.375477i	0.138243	−	0.990398i	$-0.455854\pi$
$907$	−19.5861	−	11.3080i	−0.650346	−	0.375477i	−0.788589	+	0.614921i	$0.789188\pi$
$908$	−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
$913$	41.7106			1.38042
$914$	5.79543	+	10.0380i	0.191696	+	0.332027i
$915$		0			0
$916$	11.5338	−	11.5338i	0.381088	−	0.381088i
$917$	−15.6574	−	58.4342i	−0.517053	−	1.92967i
$918$		0			0
$919$	13.0969	−	22.6845i	0.432027	−	0.748293i	−0.565020	−	0.825077i	$-0.691132\pi$
$919$	13.0969	−	22.6845i	0.432027	−	0.748293i	0.997048	+	0.0767835i	$0.0244650\pi$
$920$	−2.96245	+	5.13111i	−0.0976689	+	0.169168i
$921$		0			0
$922$	−15.7012	−	9.06506i	−0.517090	−	0.298542i
$923$	23.5138	+	11.7867i	0.773968	+	0.387964i
$924$		0			0
$925$	−0.284635	−	1.06227i	−0.00935873	−	0.0349273i
$926$	35.8253	−	20.6837i	1.17729	−	0.679710i
$927$		0			0
$928$	−1.91442	+	1.91442i	−0.0628440	+	0.0628440i
$929$	6.89279	+	6.89279i	0.226145	+	0.226145i	0.811080	−	0.584935i	$-0.198880\pi$
$929$	6.89279	+	6.89279i	0.226145	+	0.226145i	−0.584935	+	0.811080i	$0.698880\pi$
$930$		0			0
$931$	−40.8397	+	10.9430i	−1.33847	+	0.358642i
$932$	11.2168	−	6.47603i	0.367419	−	0.212129i
$933$		0			0
$934$	−38.8555	+	10.4113i	−1.27139	+	0.340668i
$935$	−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	$0.281987\pi$
$938$	−40.8760	+	10.9527i	−1.33465	+	0.357618i
$939$		0			0
$940$	−18.1315	+	10.4682i	−0.591383	+	0.341435i
$941$	−50.7507	+	13.5986i	−1.65442	+	0.443302i	−0.960847	−	0.277080i	$-0.910633\pi$
$941$	−50.7507	+	13.5986i	−1.65442	+	0.443302i	−0.693578	+	0.720382i	$0.743967\pi$
$942$		0			0
$943$	−4.66545	−	4.66545i	−0.151928	−	0.151928i
$944$	8.05305	−	8.05305i	0.262104	−	0.262104i
$945$		0			0
$946$	−0.547809	+	0.316278i	−0.0178108	+	0.0102831i
$947$	12.1957	+	45.5150i	0.396307	+	1.47904i	0.819542	+	0.573019i	$0.194228\pi$
$947$	12.1957	+	45.5150i	0.396307	+	1.47904i	−0.423234	+	0.906020i	$0.639105\pi$
$948$		0			0
$949$	1.13154	+	19.1765i	0.0367314	+	0.622495i
$950$	0.576337	+	0.332749i	0.0186989	+	0.0107958i
$951$		0			0
$952$	1.13232	−	1.96124i	0.0366987	−	0.0635640i
$953$	−24.8010	+	42.9566i	−0.803383	+	1.39150i	0.113994	+	0.993481i	$0.463636\pi$
$953$	−24.8010	+	42.9566i	−0.803383	+	1.39150i	−0.917377	+	0.398019i	$0.869698\pi$
$954$		0			0
$955$	−5.63044	−	21.0131i	−0.182197	−	0.679968i
$956$	4.20064	−	4.20064i	0.135858	−	0.135858i
$957$		0			0
$958$	11.1326	+	19.2822i	0.359677	+	0.622979i
$959$	81.4222			2.62926
$960$		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
$965$	0.790960	+	0.456661i	0.0254619	+	0.0147004i
$966$		0			0
$967$	−15.3349	−	57.2307i	−0.493138	−	1.84042i	−0.540218	−	0.841525i	$-0.681658\pi$
$967$	−15.3349	−	57.2307i	−0.493138	−	1.84042i	0.0470805	−	0.998891i	$-0.485008\pi$
$968$	−2.76410	+	10.3158i	−0.0888416	+	0.331561i
$969$		0			0
$970$	0.345568	−	1.28968i	0.0110955	−	0.0414091i
$971$	19.4119	+	11.2075i	0.622957	+	0.359665i	0.778019	−	0.628240i	$-0.216224\pi$
$971$	19.4119	+	11.2075i	0.622957	+	0.359665i	−0.155062	+	0.987905i	$0.549558\pi$
$972$		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
$977$	10.9746	+	10.9746i	0.351109	+	0.351109i	0.860522	−	0.509413i	$-0.170137\pi$
$977$	10.9746	+	10.9746i	0.351109	+	0.351109i	−0.509413	+	0.860522i	$0.670137\pi$
$978$		0			0
$979$		−	40.3870i		−	1.29077i
$980$	27.8187	+	27.8187i	0.888635	+	0.888635i
$981$		0			0
$982$	−15.0296	+	4.02716i	−0.479613	+	0.128512i
$983$	−2.42828	−	0.650655i	−0.0774500	−	0.0207527i	0.219886	−	0.975526i	$-0.429431\pi$
$983$	−2.42828	−	0.650655i	−0.0774500	−	0.0207527i	−0.297336	+	0.954773i	$0.596098\pi$
$984$		0			0
$985$			6.34294i			0.202103i
$986$	−0.0653503	+	0.0653503i	−0.00208118	+	0.00208118i
$987$		0			0
$988$	0.391021	+	6.62671i	0.0124400	+	0.210824i
$989$		−	0.182714i		−	0.00580997i
$990$		0			0
$991$	15.2437	+	26.4028i	0.484231	+	0.838713i	0.999836	−	0.0181139i	$-0.00576614\pi$
$991$	15.2437	+	26.4028i	0.484231	+	0.838713i	−0.515605	+	0.856826i	$0.672433\pi$
$992$	−15.6591			−0.497178
$993$		0			0
$994$	38.9106	+	10.4261i	1.23417	+	0.330695i
$995$	−34.5848	−	9.26698i	−1.09641	−	0.293783i
$996$		0			0
$997$	−7.98608			−0.252922			−0.126461	−	0.991972i	$-0.540362\pi$
$997$	−7.98608			−0.252922			−0.126461	+	0.991972i	$0.540362\pi$
$998$	−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.bf.a.314.8		48
3.2	odd	2		117.2.bc.a.41.5	yes	48
9.2	odd	6		351.2.ba.a.197.8		48
9.7	even	3		117.2.x.a.2.5	✓	48
13.7	odd	12		351.2.ba.a.98.8		48
39.20	even	12		117.2.x.a.59.5	yes	48
117.7	odd	12		117.2.bc.a.20.5	yes	48
117.20	even	12	inner	351.2.bf.a.332.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.2.5	✓	48	9.7	even	3
117.2.x.a.59.5	yes	48	39.20	even	12
117.2.bc.a.20.5	yes	48	117.7	odd	12
117.2.bc.a.41.5	yes	48	3.2	odd	2
351.2.ba.a.98.8		48	13.7	odd	12
351.2.ba.a.197.8		48	9.2	odd	6
351.2.bf.a.314.8		48	1.1	even	1	trivial
351.2.bf.a.332.8		48	117.20	even	12	inner

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.bf (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.03000 - 0.275986i) q^{2} +(-0.747329 + 0.431471i) q^{4} +(-2.22216 + 0.595426i) q^{5} +(-3.66177 - 3.66177i) q^{7} +(-2.15868 + 2.15868i) q^{8} +(-2.12448 + 1.22657i) q^{10} +(0.708887 + 2.64560i) q^{11} +(-2.69526 - 2.39491i) q^{13} +(-4.78220 - 2.76100i) q^{14} +(-0.764725 + 1.32454i) q^{16} +(0.0716242 - 0.124057i) q^{17} +(0.552200 + 2.06084i) q^{19} +(1.40377 - 1.40377i) q^{20} +(1.46030 + 2.52931i) q^{22} -0.843617 q^{23} +(0.253329 - 0.146260i) q^{25} +(-3.43707 - 1.72289i) q^{26} +(4.31649 + 1.15660i) q^{28} +(-0.523977 - 0.302518i) q^{29} +(-0.905716 - 3.38018i) q^{31} +(1.15816 - 4.32230i) q^{32} +(0.0395346 - 0.147545i) q^{34} +(10.3173 + 5.95671i) q^{35} +(0.973046 - 3.63146i) q^{37} +(1.13753 + 1.97025i) q^{38} +(3.51160 - 6.08227i) q^{40} +(5.53029 + 5.53029i) q^{41} +0.216584i q^{43} +(-1.67127 - 1.67127i) q^{44} +(-0.868921 + 0.232827i) q^{46} +(-10.1867 - 2.72952i) q^{47} +19.8171i q^{49} +(0.220562 - 0.220562i) q^{50} +(3.04758 + 0.626857i) q^{52} +8.00631i q^{53} +(-3.15052 - 5.45686i) q^{55} +15.8092 q^{56} +(-0.623185 - 0.166982i) q^{58} +(-7.19256 - 1.92724i) q^{59} -1.35088 q^{61} +(-1.86577 - 3.23160i) q^{62} -7.83049i q^{64} +(7.41528 + 3.71703i) q^{65} +(5.41892 - 5.41892i) q^{67} +0.123615i q^{68} +(12.2708 + 3.28794i) q^{70} +(-7.04646 + 1.88809i) q^{71} +(-3.76736 - 3.76736i) q^{73} -4.00893i q^{74} +(-1.30187 - 1.30187i) q^{76} +(7.09179 - 12.2833i) q^{77} +(1.62641 + 2.81703i) q^{79} +(0.910674 - 3.39868i) q^{80} +(7.22246 + 4.16989i) q^{82} +(3.94150 - 14.7099i) q^{83} +(-0.0852937 + 0.318321i) q^{85} +(0.0597743 + 0.223081i) q^{86} +(-7.24128 - 4.18075i) q^{88} +(-14.2431 - 3.81643i) q^{89} +(1.09983 + 18.6390i) q^{91} +(0.630459 - 0.363996i) q^{92} -11.2456 q^{94} +(-2.45415 - 4.25071i) q^{95} +(-0.384858 + 0.384858i) q^{97} +(5.46924 + 20.4115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{2} - 6 q^{4} + 6 q^{5} + 2 q^{7} + 30 q^{8} - 12 q^{10} - 6 q^{11} - 2 q^{13} + 12 q^{14} + 14 q^{16} - 4 q^{19} + 6 q^{20} + 2 q^{22} + 12 q^{23} - 48 q^{26} + 6 q^{29} + 6 q^{31} - 30 q^{32}+ \cdots + 36 q^{98}+O(q^{100}) \) 48 * q + 6 * q^2 - 6 * q^4 + 6 * q^5 + 2 * q^7 + 30 * q^8 - 12 * q^10 - 6 * q^11 - 2 * q^13 + 12 * q^14 + 14 * q^16 - 4 * q^19 + 6 * q^20 + 2 * q^22 + 12 * q^23 - 48 * q^26 + 6 * q^29 + 6 * q^31 - 30 * q^32 - 6 * q^34 + 6 * q^35 - 6 * q^37 + 36 * q^38 - 12 * q^40 - 18 * q^41 + 12 * q^44 - 12 * q^46 - 30 * q^47 + 12 * q^50 - 16 * q^52 - 4 * q^55 + 12 * q^56 - 28 * q^58 - 30 * q^59 - 4 * q^61 + 18 * q^62 - 30 * q^65 - 16 * q^67 - 46 * q^70 - 48 * q^71 - 22 * q^73 - 18 * q^76 + 72 * q^77 + 8 * q^79 - 54 * q^80 - 12 * q^82 - 72 * q^83 + 78 * q^85 - 102 * q^86 - 6 * q^88 - 16 * q^91 - 120 * q^92 - 52 * q^94 + 6 * q^95 + 48 * q^97 + 36 * q^98

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