LMFDB - Embedded newform 648.2.l.f.107.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(107,648)] 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("648.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,4,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.534694406811304329216.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.4
Root			$-0.238945 + 1.39388i$ of defining polynomial
Character	$\chi$	$=$	648.107
Dual form			648.2.l.f.539.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.238945 - 1.39388i) q^{2} +(-1.88581 + 0.666123i) q^{4} +(0.796225 + 1.37910i) q^{5} +(-1.24653 - 0.719687i) q^{7} +(1.37910 + 2.46943i) q^{8} +(1.73205 - 1.43937i) q^{10} +(-4.27718 - 2.46943i) q^{11} +(4.65213 - 2.68591i) q^{13} +(-0.705304 + 1.90949i) q^{14} +(3.11256 - 2.51236i) q^{16} -1.32336i q^{17} +0.267949 q^{19} +(-2.42018 - 2.07034i) q^{20} +(-2.42008 + 6.55193i) q^{22} +(-2.97155 - 5.14688i) q^{23} +(1.23205 - 2.13397i) q^{25} +(-4.85544 - 5.84273i) q^{26} +(2.83013 + 0.526847i) q^{28} +(4.35066 - 7.53556i) q^{29} +(6.81119 - 3.93244i) q^{31} +(-4.24567 - 3.73822i) q^{32} +(-1.84461 + 0.316212i) q^{34} -2.29213i q^{35} -2.49307i q^{37} +(-0.0640252 - 0.373489i) q^{38} +(-2.30752 + 3.86814i) q^{40} +(-8.55435 + 4.93886i) q^{41} +(-1.00000 + 1.73205i) q^{43} +(9.71088 + 1.80775i) q^{44} +(-6.46410 + 5.37182i) q^{46} +(-4.56400 + 7.90509i) q^{47} +(-2.46410 - 4.26795i) q^{49} +(-3.26890 - 1.20743i) q^{50} +(-6.98389 + 8.16400i) q^{52} +5.51641 q^{53} -7.86488i q^{55} +(0.0581166 - 4.07075i) q^{56} +(-11.5432 - 4.26371i) q^{58} +(4.27718 - 2.46943i) q^{59} +(4.65213 + 2.68591i) q^{61} +(-7.10886 - 8.55435i) q^{62} +(-4.19615 + 6.81119i) q^{64} +(7.40828 + 4.27718i) q^{65} +(-0.598076 - 1.03590i) q^{67} +(0.881523 + 2.49561i) q^{68} +(-3.19496 + 0.547694i) q^{70} -5.51641 q^{71} -7.92820 q^{73} +(-3.47504 + 0.595707i) q^{74} +(-0.505301 + 0.178487i) q^{76} +(3.55443 + 6.15645i) q^{77} +(10.5508 + 6.09150i) q^{79} +(5.94311 + 2.29213i) q^{80} +(8.92820 + 10.7436i) q^{82} +(-6.26222 - 3.61549i) q^{83} +(1.82505 - 1.05369i) q^{85} +(2.65322 + 0.980016i) q^{86} +(0.199413 - 13.9678i) q^{88} +15.7853i q^{89} -7.73205 q^{91} +(9.03224 + 7.72662i) q^{92} +(12.1093 + 4.47279i) q^{94} +(0.213348 + 0.369529i) q^{95} +(-4.69615 + 8.13397i) q^{97} +(-5.36023 + 4.45447i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 16 q^{16} + 32 q^{19} + 8 q^{22} - 8 q^{25} - 24 q^{28} + 32 q^{34} - 24 q^{40} - 16 q^{43} - 48 q^{46} + 16 q^{49} - 36 q^{52} - 48 q^{58} + 16 q^{64} + 32 q^{67} - 72 q^{70} - 16 q^{73}+ \cdots + 8 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 + 16 * q^16 + 32 * q^19 + 8 * q^22 - 8 * q^25 - 24 * q^28 + 32 * q^34 - 24 * q^40 - 16 * q^43 - 48 * q^46 + 16 * q^49 - 36 * q^52 - 48 * q^58 + 16 * q^64 + 32 * q^67 - 72 * q^70 - 16 * q^73 + 20 * q^76 + 32 * q^82 + 56 * q^88 - 96 * q^91 + 24 * q^94 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.238945	−	1.39388i	−0.168960	−	0.985623i
$2$	−0.238945	−	1.39388i	−0.168960	−	0.985623i
$3$		0			0
$3$		0			0
$4$	−1.88581	+	0.666123i	−0.942905	+	0.333062i
$5$	0.796225	+	1.37910i	0.356083	+	0.616753i	0.987303	−	0.158851i	$-0.0507788\pi$
$5$	0.796225	+	1.37910i	0.356083	+	0.616753i	−0.631220	+	0.775604i	$0.717445\pi$
$6$		0			0
$7$	−1.24653	−	0.719687i	−0.471146	−	0.272016i	0.245574	−	0.969378i	$-0.421024\pi$
$7$	−1.24653	−	0.719687i	−0.471146	−	0.272016i	−0.716719	+	0.697362i	$0.754357\pi$
$8$	1.37910	+	2.46943i	0.487586	+	0.873075i
$9$		0			0
$10$	1.73205	−	1.43937i	0.547723	−	0.455170i
$11$	−4.27718	−	2.46943i	−1.28962	−	0.744561i	−0.311031	−	0.950400i	$-0.600674\pi$
$11$	−4.27718	−	2.46943i	−1.28962	−	0.744561i	−0.978586	+	0.205839i	$0.934008\pi$
$12$		0			0
$13$	4.65213	−	2.68591i	1.29027	−	0.744937i	0.311567	−	0.950224i	$-0.399146\pi$
$13$	4.65213	−	2.68591i	1.29027	−	0.744937i	0.978702	+	0.205287i	$0.0658129\pi$
$14$	−0.705304	+	1.90949i	−0.188501	+	0.510332i
$15$		0			0
$16$	3.11256	−	2.51236i	0.778140	−	0.628091i
$17$		−	1.32336i		−	0.320963i	−0.987039	−	0.160481i	$-0.948695\pi$
$17$		−	1.32336i		−	0.320963i	0.987039	−	0.160481i	$-0.0513046\pi$
$18$		0			0
$19$	0.267949			0.0614718			0.0307359	−	0.999528i	$-0.490215\pi$
$19$	0.267949			0.0614718			0.0307359	+	0.999528i	$0.490215\pi$
$20$	−2.42018	−	2.07034i	−0.541169	−	0.462942i
$21$		0			0
$22$	−2.42008	+	6.55193i	−0.515962	+	1.39688i
$23$	−2.97155	−	5.14688i	−0.619612	−	1.07320i	−0.989557	−	0.144145i	$-0.953957\pi$
$23$	−2.97155	−	5.14688i	−0.619612	−	1.07320i	0.369945	−	0.929054i	$-0.379377\pi$
$24$		0			0
$25$	1.23205	−	2.13397i	0.246410	−	0.426795i
$26$	−4.85544	−	5.84273i	−0.952231	−	1.14585i
$27$		0			0
$28$	2.83013	+	0.526847i	0.534844	+	0.0995648i
$29$	4.35066	−	7.53556i	0.807896	−	1.39932i	−0.106422	−	0.994321i	$-0.533939\pi$
$29$	4.35066	−	7.53556i	0.807896	−	1.39932i	0.914318	−	0.404997i	$-0.132727\pi$
$30$		0			0
$31$	6.81119	−	3.93244i	1.22333	−	0.706287i	0.257700	−	0.966225i	$-0.417035\pi$
$31$	6.81119	−	3.93244i	1.22333	−	0.706287i	0.965625	+	0.259937i	$0.0837019\pi$
$32$	−4.24567	−	3.73822i	−0.750535	−	0.660830i
$33$		0			0
$34$	−1.84461	+	0.316212i	−0.316348	+	0.0542298i
$35$		−	2.29213i		−	0.387441i
$36$		0			0
$37$		−	2.49307i		−	0.409858i	−0.978777	−	0.204929i	$-0.934304\pi$
$37$		−	2.49307i		−	0.409858i	0.978777	−	0.204929i	$-0.0656963\pi$
$38$	−0.0640252	−	0.373489i	−0.0103863	−	0.0605880i
$39$		0			0
$40$	−2.30752	+	3.86814i	−0.364851	+	0.611607i
$41$	−8.55435	+	4.93886i	−1.33597	+	0.771320i	−0.986206	−	0.165520i	$-0.947070\pi$
$41$	−8.55435	+	4.93886i	−1.33597	+	0.771320i	−0.349759	+	0.936840i	$0.613736\pi$
$42$		0			0
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	−0.932145	−	0.362084i	$-0.882065\pi$
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	0.779647	+	0.626219i	$0.215399\pi$
$44$	9.71088	+	1.80775i	1.46397	+	0.272528i
$45$		0			0
$46$	−6.46410	+	5.37182i	−0.953080	+	0.792031i
$47$	−4.56400	+	7.90509i	−0.665728	+	1.15308i	0.313359	+	0.949635i	$0.398546\pi$
$47$	−4.56400	+	7.90509i	−0.665728	+	1.15308i	−0.979087	+	0.203441i	$0.934788\pi$
$48$		0			0
$49$	−2.46410	−	4.26795i	−0.352015	−	0.609707i
$50$	−3.26890	−	1.20743i	−0.462292	−	0.170756i
$51$		0			0
$52$	−6.98389	+	8.16400i	−0.968491	+	1.13214i
$53$	5.51641			0.757737			0.378869	−	0.925450i	$-0.376313\pi$
$53$	5.51641			0.757737			0.378869	+	0.925450i	$0.376313\pi$
$54$		0			0
$55$		−	7.86488i		−	1.06050i
$56$	0.0581166	−	4.07075i	0.00776616	−	0.543977i
$57$		0			0
$58$	−11.5432	−	4.26371i	−1.51570	−	0.559853i
$59$	4.27718	−	2.46943i	0.556841	−	0.321492i	−0.195036	−	0.980796i	$-0.562482\pi$
$59$	4.27718	−	2.46943i	0.556841	−	0.321492i	0.751877	+	0.659304i	$0.229149\pi$
$60$		0			0
$61$	4.65213	+	2.68591i	0.595644	+	0.343895i	0.767326	−	0.641257i	$-0.221587\pi$
$61$	4.65213	+	2.68591i	0.595644	+	0.343895i	−0.171682	+	0.985152i	$0.554920\pi$
$62$	−7.10886	−	8.55435i	−0.902826	−	1.08640i
$63$		0			0
$64$	−4.19615	+	6.81119i	−0.524519	+	0.851399i
$65$	7.40828	+	4.27718i	0.918885	+	0.530518i
$66$		0			0
$67$	−0.598076	−	1.03590i	−0.0730666	−	0.126555i	0.827177	−	0.561941i	$-0.189945\pi$
$67$	−0.598076	−	1.03590i	−0.0730666	−	0.126555i	−0.900244	+	0.435386i	$0.856612\pi$
$68$	0.881523	+	2.49561i	0.106900	+	0.302637i
$69$		0			0
$70$	−3.19496	+	0.547694i	−0.381871	+	0.0654620i
$71$	−5.51641			−0.654677			−0.327339	−	0.944907i	$-0.606152\pi$
$71$	−5.51641			−0.654677			−0.327339	+	0.944907i	$0.606152\pi$
$72$		0			0
$73$	−7.92820			−0.927926			−0.463963	−	0.885855i	$-0.653573\pi$
$73$	−7.92820			−0.927926			−0.463963	+	0.885855i	$0.653573\pi$
$74$	−3.47504	+	0.595707i	−0.403965	+	0.0692496i
$75$		0			0
$76$	−0.505301	+	0.178487i	−0.0579620	+	0.0204739i
$77$	3.55443	+	6.15645i	0.405065	+	0.701593i
$78$		0			0
$79$	10.5508	+	6.09150i	1.18706	+	0.685348i	0.957636	−	0.287980i	$-0.0929836\pi$
$79$	10.5508	+	6.09150i	1.18706	+	0.685348i	0.229420	+	0.973327i	$0.426317\pi$
$80$	5.94311	+	2.29213i	0.664459	+	0.256268i
$81$		0			0
$82$	8.92820	+	10.7436i	0.985955	+	1.18644i
$83$	−6.26222	−	3.61549i	−0.687368	−	0.396852i	0.115257	−	0.993336i	$-0.463231\pi$
$83$	−6.26222	−	3.61549i	−0.687368	−	0.396852i	−0.802625	+	0.596484i	$0.796564\pi$
$84$		0			0
$85$	1.82505	−	1.05369i	0.197955	−	0.114289i
$86$	2.65322	+	0.980016i	0.286104	+	0.105678i
$87$		0			0
$88$	0.199413	−	13.9678i	0.0212575	−	1.48897i
$89$			15.7853i			1.67324i	0.547782	+	0.836621i	$0.315472\pi$
$89$			15.7853i			1.67324i	−0.547782	+	0.836621i	$0.684528\pi$
$90$		0			0
$91$	−7.73205			−0.810539
$92$	9.03224	+	7.72662i	0.941676	+	0.805556i
$93$		0			0
$94$	12.1093	+	4.47279i	1.24898	+	0.461334i
$95$	0.213348	+	0.369529i	0.0218890	+	0.0379129i
$96$		0			0
$97$	−4.69615	+	8.13397i	−0.476822	+	0.825880i	−0.999647	−	0.0265599i	$-0.991545\pi$
$97$	−4.69615	+	8.13397i	−0.476822	+	0.825880i	0.522825	+	0.852440i	$0.324878\pi$
$98$	−5.36023	+	4.45447i	−0.541465	+	0.449970i
$99$		0			0
$100$	−0.901924	+	4.84497i	−0.0901924	+	0.484497i
$101$	1.59245	−	2.75821i	0.158455	−	0.274452i	−0.775857	−	0.630909i	$-0.782682\pi$
$101$	1.59245	−	2.75821i	0.158455	−	0.274452i	0.934312	+	0.356457i	$0.116015\pi$
$102$		0			0
$103$	−1.24653	+	0.719687i	−0.122825	+	0.0709129i	−0.560154	−	0.828389i	$-0.689258\pi$
$103$	−1.24653	+	0.719687i	−0.122825	+	0.0709129i	0.437329	+	0.899302i	$0.355925\pi$
$104$	13.0484	+	7.78396i	1.27950	+	0.763280i
$105$		0			0
$106$	−1.31812	−	7.68922i	−0.128027	−	0.746843i
$107$		−	12.1698i		−	1.17650i	−0.808678	−	0.588252i	$-0.799816\pi$
$107$		−	12.1698i		−	1.17650i	0.808678	−	0.588252i	$-0.200184\pi$
$108$		0			0
$109$		−	13.6224i		−	1.30479i	−0.757880	−	0.652394i	$-0.773765\pi$
$109$		−	13.6224i		−	1.30479i	0.757880	−	0.652394i	$-0.226235\pi$
$110$	−10.9627	+	1.87928i	−1.04525	+	0.179182i
$111$		0			0
$112$	−5.68803	+	0.891679i	−0.537468	+	0.0842558i
$113$	9.70042	−	5.60054i	0.912538	−	0.526854i	0.0312914	−	0.999510i	$-0.490038\pi$
$113$	9.70042	−	5.60054i	0.912538	−	0.526854i	0.881247	+	0.472656i	$0.156705\pi$
$114$		0			0
$115$	4.73205	−	8.19615i	0.441266	−	0.764295i
$116$	−3.18490	+	17.1087i	−0.295711	+	1.58850i
$117$		0			0
$118$	−4.46410	−	5.37182i	−0.410954	−	0.494516i
$119$	−0.952407	+	1.64962i	−0.0873070	+	0.151220i
$120$		0			0
$121$	6.69615	+	11.5981i	0.608741	+	1.05437i
$122$	2.63223	−	7.12630i	0.238311	−	0.645185i
$123$		0			0
$124$	−10.2251	+	11.9529i	−0.918243	+	1.07340i
$125$	11.8862			1.06314
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	10.4966	+	4.22144i	0.927781	+	0.373126i
$129$		0			0
$130$	4.19170	−	11.3483i	0.367636	−	0.995310i
$131$	6.26222	−	3.61549i	0.547133	−	0.315887i	−0.200832	−	0.979626i	$-0.564365\pi$
$131$	6.26222	−	3.61549i	0.547133	−	0.315887i	0.747965	+	0.663739i	$0.231031\pi$
$132$		0			0
$133$	−0.334008	−	0.192840i	−0.0289622	−	0.0167213i
$134$	−1.30101	+	1.08117i	−0.112390	+	0.0933989i
$135$		0			0
$136$	3.26795	−	1.82505i	0.280224	−	0.156497i
$137$	5.11615	+	2.95381i	0.437103	+	0.252361i	0.702368	−	0.711814i	$-0.252126\pi$
$137$	5.11615	+	2.95381i	0.437103	+	0.252361i	−0.265265	+	0.964175i	$0.585460\pi$
$138$		0			0
$139$	−3.59808	−	6.23205i	−0.305185	−	0.528596i	0.672118	−	0.740444i	$-0.265385\pi$
$139$	−3.59808	−	6.23205i	−0.305185	−	0.528596i	−0.977302	+	0.211849i	$0.932052\pi$
$140$	1.52684	+	4.32252i	0.129042	+	0.365320i
$141$		0			0
$142$	1.31812	+	7.68922i	0.110614	+	0.645265i
$143$	−26.5306			−2.21860
$144$		0			0
$145$	13.8564			1.15071
$146$	1.89441	+	11.0510i	0.156782	+	0.914585i
$147$		0			0
$148$	1.66069	+	4.70145i	0.136508	+	0.386457i
$149$	−1.59245	−	2.75821i	−0.130459	−	0.225961i	0.793395	−	0.608707i	$-0.208312\pi$
$149$	−1.59245	−	2.75821i	−0.130459	−	0.225961i	−0.923853	+	0.382746i	$0.874978\pi$
$150$		0			0
$151$	−5.56466	−	3.21276i	−0.452845	−	0.261450i	0.256186	−	0.966628i	$-0.417534\pi$
$151$	−5.56466	−	3.21276i	−0.452845	−	0.261450i	−0.709031	+	0.705177i	$0.750867\pi$
$152$	0.369529	+	0.661681i	0.0299728	+	0.0536694i
$153$		0			0
$154$	7.73205	−	6.42551i	0.623066	−	0.517782i
$155$	10.8465	+	6.26222i	0.871210	+	0.502994i
$156$		0			0
$157$	−1.82505	+	1.05369i	−0.145655	+	0.0840940i	−0.571056	−	0.820911i	$-0.693466\pi$
$157$	−1.82505	+	1.05369i	−0.145655	+	0.0840940i	0.425401	+	0.905005i	$0.360133\pi$
$158$	5.96977	−	16.1621i	0.474929	−	1.28579i
$159$		0			0
$160$	1.77488	−	8.83168i	0.140317	−	0.698205i
$161$			8.55435i			0.674177i
$162$		0			0
$163$	19.1962			1.50356			0.751779	−	0.659415i	$-0.229196\pi$
$163$	19.1962			1.50356			0.751779	+	0.659415i	$0.229196\pi$
$164$	12.8420	−	15.0120i	1.00279	−	1.17224i
$165$		0			0
$166$	−3.54324	+	9.59270i	−0.275009	+	0.744538i
$167$	2.54486	+	4.40782i	0.196927	+	0.341087i	0.947531	−	0.319665i	$-0.103570\pi$
$167$	2.54486	+	4.40782i	0.196927	+	0.341087i	−0.750604	+	0.660753i	$0.770237\pi$
$168$		0			0
$169$	7.92820	−	13.7321i	0.609862	−	1.05631i
$170$	−1.90481	−	2.29213i	−0.146093	−	0.175798i
$171$		0			0
$172$	0.732051	−	3.93244i	0.0558184	−	0.299846i
$173$	−5.94311	+	10.2938i	−0.451846	+	0.782620i	−0.998501	−	0.0547379i	$-0.982568\pi$
$173$	−5.94311	+	10.2938i	−0.451846	+	0.782620i	0.546655	+	0.837358i	$0.315901\pi$
$174$		0			0
$175$	−3.07159	+	1.77338i	−0.232190	+	0.134055i
$176$	−19.5171	+	3.05958i	−1.47115	+	0.230624i
$177$		0			0
$178$	22.0029	−	3.77184i	1.64919	−	0.282711i
$179$		−	9.87771i		−	0.738295i	−0.929371	−	0.369147i	$-0.879650\pi$
$179$		−	9.87771i		−	0.738295i	0.929371	−	0.369147i	$-0.120350\pi$
$180$		0			0
$181$			16.1154i			1.19785i	0.800804	+	0.598926i	$0.204406\pi$
$181$			16.1154i			1.19785i	−0.800804	+	0.598926i	$0.795594\pi$
$182$	1.84754	+	10.7776i	0.136949	+	0.798886i
$183$		0			0
$184$	8.61178	−	14.4361i	0.634869	−	1.06424i
$185$	3.43820	−	1.98504i	0.252781	−	0.145943i
$186$		0			0
$187$	−3.26795	+	5.66025i	−0.238976	+	0.413919i
$188$	3.34108	−	17.9477i	0.243673	−	1.30897i
$189$		0			0
$190$	0.464102	−	0.385679i	0.0336695	−	0.0279801i
$191$	−4.56400	+	7.90509i	−0.330240	+	0.571992i	−0.982559	−	0.185953i	$-0.940463\pi$
$191$	−4.56400	+	7.90509i	−0.330240	+	0.571992i	0.652319	+	0.757945i	$0.273796\pi$
$192$		0			0
$193$	−7.69615	−	13.3301i	−0.553981	−	0.959524i	−0.997982	−	0.0634972i	$-0.979775\pi$
$193$	−7.69615	−	13.3301i	−0.553981	−	0.959524i	0.444001	−	0.896026i	$-0.353559\pi$
$194$	12.4599	+	4.60230i	0.894570	+	0.330426i
$195$		0			0
$196$	7.48981	+	6.40715i	0.534986	+	0.457653i
$197$	19.8485			1.41414			0.707072	−	0.707141i	$-0.250016\pi$
$197$	19.8485			1.41414			0.707072	+	0.707141i	$0.250016\pi$
$198$		0			0
$199$			14.2904i			1.01302i	0.862234	+	0.506510i	$0.169065\pi$
$199$			14.2904i			1.01302i	−0.862234	+	0.506510i	$0.830935\pi$
$200$	6.96882	+	0.0994914i	0.492770	+	0.00703510i
$201$		0			0
$202$	−4.22512	−	1.56063i	−0.297278	−	0.109805i
$203$	−10.8465	+	6.26222i	−0.761274	+	0.439522i
$204$		0			0
$205$	−13.6224	−	7.86488i	−0.951428	−	0.549307i
$206$	1.30101	+	1.56555i	0.0906458	+	0.109077i
$207$		0			0
$208$	7.73205	−	20.0479i	0.536121	−	1.39007i
$209$	−1.14607	−	0.661681i	−0.0792750	−	0.0457695i
$210$		0			0
$211$	8.52628	+	14.7679i	0.586973	+	1.01667i	0.994626	+	0.103531i	$0.0330140\pi$
$211$	8.52628	+	14.7679i	0.586973	+	1.01667i	−0.407653	+	0.913137i	$0.633653\pi$
$212$	−10.4029	+	3.67461i	−0.714474	+	0.252373i
$213$		0			0
$214$	−16.9633	+	2.90793i	−1.15959	+	0.198782i
$215$	−3.18490			−0.217208
$216$		0			0
$217$	−11.3205			−0.768486
$218$	−18.9880	+	3.25501i	−1.28603	+	0.220457i
$219$		0			0
$220$	5.23898	+	14.8317i	0.353212	+	0.999952i
$221$	−3.55443	−	6.15645i	−0.239097	−	0.414128i
$222$		0			0
$223$	−16.7835	−	9.68994i	−1.12390	−	0.648886i	−0.181509	−	0.983389i	$-0.558098\pi$
$223$	−16.7835	−	9.68994i	−1.12390	−	0.648886i	−0.942395	+	0.334503i	$0.891432\pi$
$224$	2.60202	+	7.71537i	0.173855	+	0.515505i
$225$		0			0
$226$	−10.1244	−	12.1830i	−0.673462	−	0.810401i
$227$	8.55435	+	4.93886i	0.567772	+	0.327803i	0.756259	−	0.654272i	$-0.227025\pi$
$227$	8.55435	+	4.93886i	0.567772	+	0.327803i	−0.188487	+	0.982076i	$0.560358\pi$
$228$		0			0
$229$	−13.6224	+	7.86488i	−0.900192	+	0.519726i	−0.877263	−	0.480011i	$-0.840633\pi$
$229$	−13.6224	+	7.86488i	−0.900192	+	0.519726i	−0.0229296	+	0.999737i	$0.507299\pi$
$230$	−12.5552	−	4.63748i	−0.827863	−	0.305787i
$231$		0			0
$232$	24.6085	+	0.351327i	1.61563	+	0.0230657i
$233$			2.64673i			0.173393i	0.996235	+	0.0866964i	$0.0276310\pi$
$233$			2.64673i			0.173393i	−0.996235	+	0.0866964i	$0.972369\pi$
$234$		0			0
$235$	−14.5359			−0.948217
$236$	−6.42100	+	7.50600i	−0.417971	+	0.488599i
$237$		0			0
$238$	2.52694	+	0.933373i	0.163797	+	0.0605016i
$239$	3.18490	+	5.51641i	0.206014	+	0.356827i	0.950455	−	0.310861i	$-0.100617\pi$
$239$	3.18490	+	5.51641i	0.206014	+	0.356827i	−0.744441	+	0.667688i	$0.767284\pi$
$240$		0			0
$241$	−7.69615	+	13.3301i	−0.495753	+	0.858669i	−0.999988	−	0.00489737i	$-0.998441\pi$
$241$	−7.69615	+	13.3301i	−0.495753	+	0.858669i	0.504235	+	0.863566i	$0.331774\pi$
$242$	14.5663	−	12.1049i	0.936359	−	0.778136i
$243$		0			0
$244$	−10.5622	−	1.96622i	−0.676174	−	0.125874i
$245$	3.92396	−	6.79650i	0.250693	−	0.434212i
$246$		0			0
$247$	1.24653	−	0.719687i	0.0793151	−	0.0457926i
$248$	19.1042	+	11.3965i	1.21312	+	0.723679i
$249$		0			0
$250$	−2.84016	−	16.5680i	−0.179627	−	1.04785i
$251$			2.64673i			0.167060i	0.996505	+	0.0835299i	$0.0266194\pi$
$251$			2.64673i			0.167060i	−0.996505	+	0.0835299i	$0.973381\pi$
$252$		0			0
$253$			29.3521i			1.84535i
$254$		0			0
$255$		0			0
$256$	3.37605	−	15.6398i	0.211003	−	0.977485i
$257$	−8.55435	+	4.93886i	−0.533606	+	0.308077i	−0.742484	−	0.669864i	$-0.766352\pi$
$257$	−8.55435	+	4.93886i	−0.533606	+	0.308077i	0.208878	+	0.977942i	$0.433019\pi$
$258$		0			0
$259$	−1.79423	+	3.10770i	−0.111488	+	0.193103i
$260$	−16.8197	−	3.13111i	−1.04312	−	0.194183i
$261$		0			0
$262$	−6.53590	−	7.86488i	−0.403789	−	0.485894i
$263$	11.8862	−	20.5875i	0.732935	−	1.26948i	−0.222688	−	0.974890i	$-0.571483\pi$
$263$	11.8862	−	20.5875i	0.732935	−	1.26948i	0.955623	−	0.294591i	$-0.0951835\pi$
$264$		0			0
$265$	4.39230	+	7.60770i	0.269817	+	0.467337i
$266$	−0.188986	+	0.511645i	−0.0115875	+	0.0313710i
$267$		0			0
$268$	1.81789	+	1.55512i	0.111046	+	0.0949938i
$269$	0.739059			0.0450612			0.0225306	−	0.999746i	$-0.492828\pi$
$269$	0.739059			0.0450612			0.0225306	+	0.999746i	$0.492828\pi$
$270$		0			0
$271$			4.31812i			0.262307i	0.991362	+	0.131154i	$0.0418681\pi$
$271$			4.31812i			0.262307i	−0.991362	+	0.131154i	$0.958132\pi$
$272$	−3.32477	−	4.11905i	−0.201594	−	0.249754i
$273$		0			0
$274$	2.89478	−	7.83711i	0.174880	−	0.473457i
$275$	−10.5394	+	6.08492i	−0.635549	+	0.366935i
$276$		0			0
$277$	−1.82505	−	1.05369i	−0.109657	−	0.0633104i	0.444169	−	0.895943i	$-0.353499\pi$
$277$	−1.82505	−	1.05369i	−0.109657	−	0.0633104i	−0.553825	+	0.832633i	$0.686832\pi$
$278$	−7.82700	+	6.50441i	−0.469432	+	0.390109i
$279$		0			0
$280$	5.66025	−	3.16108i	0.338265	−	0.188911i
$281$	−6.26222	−	3.61549i	−0.373573	−	0.215682i	0.301445	−	0.953483i	$-0.402531\pi$
$281$	−6.26222	−	3.61549i	−0.373573	−	0.215682i	−0.675018	+	0.737801i	$0.735864\pi$
$282$		0			0
$283$	−0.0717968	−	0.124356i	−0.00426787	−	0.00739218i	0.863884	−	0.503692i	$-0.168025\pi$
$283$	−0.0717968	−	0.124356i	−0.00426787	−	0.00739218i	−0.868151	+	0.496299i	$0.834692\pi$
$284$	10.4029	−	3.67461i	0.617299	−	0.218048i
$285$		0			0
$286$	6.33937	+	36.9805i	0.374855	+	2.18671i
$287$	14.2177			0.839246
$288$		0			0
$289$	15.2487			0.896983
$290$	−3.31093	−	19.3142i	−0.194424	−	1.13417i
$291$		0			0
$292$	14.9511	−	5.28116i	0.874946	−	0.309057i
$293$	3.55443	+	6.15645i	0.207652	+	0.359664i	0.950974	−	0.309269i	$-0.100084\pi$
$293$	3.55443	+	6.15645i	0.207652	+	0.359664i	−0.743322	+	0.668933i	$0.766751\pi$
$294$		0			0
$295$	6.81119	+	3.93244i	0.396563	+	0.228956i
$296$	6.15645	−	3.43820i	0.357837	−	0.199841i
$297$		0			0
$298$	−3.46410	+	2.87875i	−0.200670	+	0.166761i
$299$	−27.6481	−	15.9626i	−1.59893	−	0.923143i
$300$		0			0
$301$	2.49307	−	1.43937i	0.143698	−	0.0829641i
$302$	−3.14855	+	8.52414i	−0.181179	+	0.490509i
$303$		0			0
$304$	0.834008	−	0.673186i	0.0478336	−	0.0386099i
$305$			8.55435i			0.489821i
$306$		0			0
$307$	7.07180			0.403609			0.201804	−	0.979426i	$-0.435319\pi$
$307$	7.07180			0.403609			0.201804	+	0.979426i	$0.435319\pi$
$308$	−10.8039	−	9.24221i	−0.615611	−	0.526624i
$309$		0			0
$310$	6.13707	−	16.6150i	0.348562	−	0.943671i
$311$	−8.48796	−	14.7016i	−0.481308	−	0.833650i	0.518462	−	0.855101i	$-0.326505\pi$
$311$	−8.48796	−	14.7016i	−0.481308	−	0.833650i	−0.999770	+	0.0214506i	$0.993172\pi$
$312$		0			0
$313$	5.69615	−	9.86603i	0.321966	−	0.557661i	−0.658928	−	0.752206i	$-0.728990\pi$
$313$	5.69615	−	9.86603i	0.321966	−	0.557661i	0.980894	+	0.194545i	$0.0623231\pi$
$314$	1.90481	+	2.29213i	0.107495	+	0.129352i
$315$		0			0
$316$	−23.9545	−	4.45929i	−1.34754	−	0.250855i
$317$	−1.16575	+	2.01915i	−0.0654753	+	0.113407i	−0.896905	−	0.442224i	$-0.854190\pi$
$317$	−1.16575	+	2.01915i	−0.0654753	+	0.113407i	0.831429	+	0.555630i	$0.187523\pi$
$318$		0			0
$319$	−37.2170	+	21.4873i	−2.08375	+	1.20306i
$320$	−12.7344	−	0.363683i	−0.711875	−	0.0203305i
$321$		0			0
$322$	11.9237	−	2.04402i	0.664485	−	0.113909i
$323$		−	0.354594i		−	0.0197301i
$324$		0			0
$325$		−	13.2367i		−	0.734240i
$326$	−4.58683	−	26.7572i	−0.254041	−	1.48194i
$327$		0			0
$328$	−23.9935	−	14.3132i	−1.32482	−	0.790312i
$329$	11.3784	−	6.56931i	0.627310	−	0.362178i
$330$		0			0
$331$	−13.0622	+	22.6244i	−0.717962	+	1.24355i	0.243844	+	0.969815i	$0.421592\pi$
$331$	−13.0622	+	22.6244i	−0.717962	+	1.24355i	−0.961806	+	0.273732i	$0.911742\pi$
$332$	14.2177	+	2.64673i	0.780299	+	0.145258i
$333$		0			0
$334$	5.53590	−	4.60046i	0.302911	−	0.251726i
$335$	0.952407	−	1.64962i	0.0520355	−	0.0901282i
$336$		0			0
$337$	−4.69615	−	8.13397i	−0.255816	−	0.443086i	0.709301	−	0.704906i	$-0.249011\pi$
$337$	−4.69615	−	8.13397i	−0.255816	−	0.443086i	−0.965117	+	0.261820i	$0.915677\pi$
$338$	−21.0353	−	7.76976i	−1.14417	−	0.422619i
$339$		0			0
$340$	−2.73981	+	3.20278i	−0.148587	+	0.173695i
$341$	−38.8435			−2.10350
$342$		0			0
$343$			17.1691i			0.927047i
$344$	−5.65628	−	0.0807527i	−0.304966	−	0.00435389i
$345$		0			0
$346$	15.7684	+	5.82434i	0.847712	+	0.313118i
$347$	17.1087	−	9.87771i	0.918443	−	0.530263i	0.0353051	−	0.999377i	$-0.488760\pi$
$347$	17.1087	−	9.87771i	0.918443	−	0.530263i	0.883138	+	0.469113i	$0.155426\pi$
$348$		0			0
$349$	20.7676	+	11.9902i	1.11166	+	0.641819i	0.939260	−	0.343208i	$-0.111513\pi$
$349$	20.7676	+	11.9902i	1.11166	+	0.641819i	0.172403	+	0.985026i	$0.444847\pi$
$350$	3.20583	+	3.85769i	0.171359	+	0.206202i
$351$		0			0
$352$	8.92820	+	26.4734i	0.475875	+	1.41104i
$353$	−17.1087	−	9.87771i	−0.910604	−	0.525738i	−0.0299788	−	0.999551i	$-0.509544\pi$
$353$	−17.1087	−	9.87771i	−0.910604	−	0.525738i	−0.880626	+	0.473813i	$0.842877\pi$
$354$		0			0
$355$	−4.39230	−	7.60770i	−0.233119	−	0.403775i
$356$	−10.5150	−	29.7682i	−0.557293	−	1.57771i
$357$		0			0
$358$	−13.7684	+	2.36023i	−0.727680	+	0.124742i
$359$	6.79650			0.358705			0.179353	−	0.983785i	$-0.442600\pi$
$359$	6.79650			0.358705			0.179353	+	0.983785i	$0.442600\pi$
$360$		0			0
$361$	−18.9282			−0.996221
$362$	22.4630	−	3.85071i	1.18063	−	0.202389i
$363$		0			0
$364$	14.5812	−	5.15050i	0.764261	−	0.269959i
$365$	−6.31264	−	10.9338i	−0.330418	−	0.572302i
$366$		0			0
$367$	−14.2009	−	8.19889i	−0.741281	−	0.427979i	0.0812540	−	0.996693i	$-0.474108\pi$
$367$	−14.2009	−	8.19889i	−0.741281	−	0.427979i	−0.822535	+	0.568715i	$0.807441\pi$
$368$	−22.1800	−	8.55435i	−1.15621	−	0.445926i
$369$		0			0
$370$	−3.58846	−	4.31812i	−0.186555	−	0.224488i
$371$	−6.87639	−	3.97009i	−0.357005	−	0.206117i
$372$		0			0
$373$	−15.7814	+	9.11142i	−0.817132	+	0.471771i	−0.849426	−	0.527707i	$-0.823052\pi$
$373$	−15.7814	+	9.11142i	−0.817132	+	0.471771i	0.0322945	+	0.999478i	$0.489719\pi$
$374$	8.67058	+	3.20264i	0.448345	+	0.165605i
$375$		0			0
$376$	−25.8153	−	0.368555i	−1.33132	−	0.0190068i
$377$		−	46.7418i		−	2.40733i
$378$		0			0
$379$	−29.7321			−1.52723			−0.763616	−	0.645670i	$-0.776578\pi$
$379$	−29.7321			−1.52723			−0.763616	+	0.645670i	$0.776578\pi$
$380$	−0.648486	−	0.554746i	−0.0332666	−	0.0284579i
$381$		0			0
$382$	12.1093	+	4.47279i	0.619566	+	0.228848i
$383$	5.94311	+	10.2938i	0.303679	+	0.525987i	0.976966	−	0.213394i	$-0.0684518\pi$
$383$	5.94311	+	10.2938i	0.303679	+	0.525987i	−0.673288	+	0.739381i	$0.735118\pi$
$384$		0			0
$385$	−5.66025	+	9.80385i	−0.288473	+	0.499650i
$386$	−16.7417	+	13.9127i	−0.852128	+	0.708138i
$387$		0			0
$388$	3.43782	−	18.4673i	0.174529	−	0.937538i
$389$	3.98113	−	6.89551i	0.201851	−	0.349616i	−0.747274	−	0.664516i	$-0.768638\pi$
$389$	3.98113	−	6.89551i	0.201851	−	0.349616i	0.949125	+	0.314900i	$0.101971\pi$
$390$		0			0
$391$	−6.81119	+	3.93244i	−0.344457	+	0.198872i
$392$	7.14115	−	11.9709i	0.360682	−	0.604620i
$393$		0			0
$394$	−4.74270	−	27.6664i	−0.238934	−	1.39381i
$395$			19.4008i			0.976162i
$396$		0			0
$397$		−	13.6224i		−	0.683688i	−0.939757	−	0.341844i	$-0.888949\pi$
$397$		−	13.6224i		−	0.683688i	0.939757	−	0.341844i	$-0.111051\pi$
$398$	19.9191	−	3.41463i	0.998455	−	0.171160i
$399$		0			0
$400$	−1.52649	−	9.73748i	−0.0763245	−	0.486874i
$401$	−34.2174	+	19.7554i	−1.70874	+	0.986539i	−0.772604	+	0.634888i	$0.781046\pi$
$401$	−34.2174	+	19.7554i	−1.70874	+	0.986539i	−0.936131	+	0.351651i	$0.885620\pi$
$402$		0			0
$403$	21.1244	−	36.5885i	1.05228	−	1.82260i
$404$	−1.16575	+	6.26222i	−0.0579985	+	0.311557i
$405$		0			0
$406$	11.3205	+	13.6224i	0.561827	+	0.676067i
$407$	−6.15645	+	10.6633i	−0.305164	+	0.528560i
$408$		0			0
$409$	14.6962	+	25.4545i	0.726678	+	1.25864i	0.958280	+	0.285832i	$0.0922701\pi$
$409$	14.6962	+	25.4545i	0.726678	+	1.25864i	−0.231602	+	0.972811i	$0.574397\pi$
$410$	−7.70771	+	20.8673i	−0.380657	+	1.03056i
$411$		0			0
$412$	1.87133	−	2.18754i	0.0921936	−	0.107772i
$413$	−7.10886			−0.349804
$414$		0			0
$415$		−	11.5150i		−	0.565249i
$416$	−29.7919	−	5.98721i	−1.46067	−	0.293547i
$417$		0			0
$418$	−0.648458	+	1.75559i	−0.0317171	+	0.0858685i
$419$	0.307087	−	0.177297i	0.0150022	−	0.00866152i	−0.492480	−	0.870324i	$-0.663910\pi$
$419$	0.307087	−	0.177297i	0.0150022	−	0.00866152i	0.507482	+	0.861662i	$0.330576\pi$
$420$		0			0
$421$	−11.4633	−	6.61835i	−0.558688	−	0.322559i	0.193931	−	0.981015i	$-0.437876\pi$
$421$	−11.4633	−	6.61835i	−0.558688	−	0.322559i	−0.752619	+	0.658457i	$0.771210\pi$
$422$	18.5475	−	15.4134i	0.902876	−	0.750310i
$423$		0			0
$424$	7.60770	+	13.6224i	0.369462	+	0.661561i
$425$	−2.82402	−	1.63045i	−0.136985	−	0.0790884i
$426$		0			0
$427$	−3.86603	−	6.69615i	−0.187090	−	0.324050i
$428$	8.10662	+	22.9500i	0.391848	+	1.10933i
$429$		0			0
$430$	0.761018	+	4.43937i	0.0366995	+	0.214086i
$431$	38.4168			1.85047			0.925237	−	0.379390i	$-0.123866\pi$
$431$	38.4168			1.85047			0.925237	+	0.379390i	$0.123866\pi$
$432$		0			0
$433$	11.4641			0.550930			0.275465	−	0.961311i	$-0.411168\pi$
$433$	11.4641			0.550930			0.275465	+	0.961311i	$0.411168\pi$
$434$	2.70498	+	15.7794i	0.129843	+	0.757438i
$435$		0			0
$436$	9.07418	+	25.6892i	0.434575	+	1.23029i
$437$	−0.796225	−	1.37910i	−0.0380886	−	0.0659714i
$438$		0			0
$439$	30.4058	+	17.5548i	1.45119	+	0.837846i	0.998549	−	0.0538462i	$-0.0171481\pi$
$439$	30.4058	+	17.5548i	1.45119	+	0.837846i	0.452642	+	0.891692i	$0.350481\pi$
$440$	19.4218	−	10.8465i	0.925896	−	0.517086i
$441$		0			0
$442$	−7.73205	+	6.42551i	−0.367776	+	0.305630i
$443$	27.3410	+	15.7853i	1.29901	+	0.749984i	0.980233	−	0.197846i	$-0.0633945\pi$
$443$	27.3410	+	15.7853i	1.29901	+	0.749984i	0.318777	+	0.947830i	$0.396728\pi$
$444$		0			0
$445$	−21.7696	+	12.5687i	−1.03198	+	0.595813i
$446$	−9.49629	+	25.7095i	−0.449662	+	1.21738i
$447$		0			0
$448$	10.1326	−	5.47047i	0.478719	−	0.258455i
$449$		−	23.0163i		−	1.08621i	−0.839666	−	0.543104i	$-0.817249\pi$
$449$		−	23.0163i		−	1.08621i	0.839666	−	0.543104i	$-0.182751\pi$
$450$		0			0
$451$	48.7846			2.29718
$452$	−14.5625	+	17.0232i	−0.684962	+	0.800705i
$453$		0			0
$454$	4.84016	−	13.1039i	0.227160	−	0.614995i
$455$	−6.15645	−	10.6633i	−0.288619	−	0.499903i
$456$		0			0
$457$	7.19615	−	12.4641i	0.336622	−	0.583046i	−0.647173	−	0.762343i	$-0.724049\pi$
$457$	7.19615	−	12.4641i	0.336622	−	0.583046i	0.983795	+	0.179297i	$0.0573823\pi$
$458$	14.2177	+	17.1087i	0.664350	+	0.799437i
$459$		0			0
$460$	−3.46410	+	18.6085i	−0.161515	+	0.867627i
$461$	9.49754	−	16.4502i	0.442344	−	0.766163i	−0.555519	−	0.831504i	$-0.687480\pi$
$461$	9.49754	−	16.4502i	0.442344	−	0.766163i	0.997863	+	0.0653412i	$0.0208136\pi$
$462$		0			0
$463$	26.6662	−	15.3958i	1.23929	−	0.715502i	0.270337	−	0.962766i	$-0.412865\pi$
$463$	26.6662	−	15.3958i	1.23929	−	0.715502i	0.968948	+	0.247264i	$0.0795315\pi$
$464$	−5.39039	−	34.3853i	−0.250242	−	1.59630i
$465$		0			0
$466$	3.68922	−	0.632423i	0.170900	−	0.0292964i
$467$			17.4633i			0.808105i	0.914736	+	0.404052i	$0.132399\pi$
$467$			17.4633i			0.808105i	−0.914736	+	0.404052i	$0.867601\pi$
$468$		0			0
$469$			1.72171i			0.0795012i
$470$	3.47329	+	20.2613i	0.160211	+	0.934585i
$471$		0			0
$472$	11.9967	+	7.15658i	0.552195	+	0.329408i
$473$	8.55435	−	4.93886i	0.393329	−	0.227089i
$474$		0			0
$475$	0.330127	−	0.571797i	0.0151473	−	0.0262358i
$476$	0.697210	−	3.74528i	0.0319566	−	0.171665i
$477$		0			0
$478$	6.92820	−	5.75749i	0.316889	−	0.263342i
$479$	1.59245	−	2.75821i	0.0727609	−	0.126026i	−0.827349	−	0.561688i	$-0.810152\pi$
$479$	1.59245	−	2.75821i	0.0727609	−	0.126026i	0.900110	+	0.435662i	$0.143486\pi$
$480$		0			0
$481$	−6.69615	−	11.5981i	−0.305318	−	0.528827i
$482$	20.4196	+	7.54235i	0.930086	+	0.343545i
$483$		0			0
$484$	−20.3534	−	17.4113i	−0.925155	−	0.791423i
$485$	−14.9568			−0.679152
$486$		0			0
$487$		−	37.8850i		−	1.71674i	−0.513035	−	0.858368i	$-0.671479\pi$
$487$		−	37.8850i		−	1.71674i	0.513035	−	0.858368i	$-0.328521\pi$
$488$	−0.216894	+	15.1922i	−0.00981834	+	0.687720i
$489$		0			0
$490$	−10.4111	−	3.84554i	−0.470327	−	0.173724i
$491$	−14.5095	+	8.37705i	−0.654804	+	0.378051i	−0.790294	−	0.612728i	$-0.790072\pi$
$491$	−14.5095	+	8.37705i	−0.654804	+	0.378051i	0.135490	+	0.990779i	$0.456739\pi$
$492$		0			0
$493$	−9.97227	−	5.75749i	−0.449129	−	0.259305i
$494$	−1.30101	−	1.56555i	−0.0585353	−	0.0704376i
$495$		0			0
$496$	11.3205	−	29.3521i	0.508306	−	1.31795i
$497$	6.87639	+	3.97009i	0.308448	+	0.178083i
$498$		0			0
$499$	13.1962	+	22.8564i	0.590741	+	1.02319i	0.994133	+	0.108166i	$0.0344978\pi$
$499$	13.1962	+	22.8564i	0.590741	+	1.02319i	−0.403392	+	0.915027i	$0.632169\pi$
$500$	−22.4151	+	7.91768i	−1.00244	+	0.354090i
$501$		0			0
$502$	3.68922	−	0.632423i	0.164658	−	0.0282264i
$503$	34.3785			1.53286			0.766432	−	0.642326i	$-0.222030\pi$
$503$	34.3785			1.53286			0.766432	+	0.642326i	$0.222030\pi$
$504$		0			0
$505$	5.07180			0.225692
$506$	40.9134	−	7.01356i	1.81882	−	0.311791i
$507$		0			0
$508$		0			0
$509$	11.0900	+	19.2084i	0.491555	+	0.851398i	0.999953	−	0.00972413i	$-0.00309534\pi$
$509$	11.0900	+	19.2084i	0.491555	+	0.851398i	−0.508398	+	0.861122i	$0.669762\pi$
$510$		0			0
$511$	9.88278	+	5.70582i	0.437188	+	0.252411i
$512$	−22.6067	−	0.968769i	−0.999083	−	0.0428139i
$513$		0			0
$514$	8.92820	+	10.7436i	0.393806	+	0.473881i
$515$	−1.98504	−	1.14607i	−0.0874715	−	0.0505017i
$516$		0			0
$517$	39.0421	−	22.5410i	1.71707	−	0.991350i
$518$	4.76048	+	1.75837i	0.209164	+	0.0772584i
$519$		0			0
$520$	−0.345393	+	24.1929i	−0.0151465	+	1.06093i
$521$		−	1.32336i		−	0.0579776i	−0.999580	−	0.0289888i	$-0.990771\pi$
$521$		−	1.32336i		−	0.0579776i	0.999580	−	0.0289888i	$-0.00922871\pi$
$522$		0			0
$523$	−6.41154			−0.280357			−0.140179	−	0.990126i	$-0.544768\pi$
$523$	−6.41154			−0.280357			−0.140179	+	0.990126i	$0.544768\pi$
$524$	−9.40099	+	10.9895i	−0.410684	+	0.480081i
$525$		0			0
$526$	−31.5367	−	11.6487i	−1.37507	−	0.507906i
$527$	−5.20405	−	9.01367i	−0.226692	−	0.392642i
$528$		0			0
$529$	−6.16025	+	10.6699i	−0.267837	+	0.463908i
$530$	9.55470	−	7.94018i	0.415030	−	0.344899i
$531$		0			0
$532$	0.758330	+	0.141168i	0.0328778	+	0.00612042i
$533$	−26.5306	+	45.9524i	−1.14917	+	1.99042i
$534$		0			0
$535$	16.7835	−	9.68994i	0.725612	−	0.418933i
$536$	1.73327	−	2.90552i	0.0748658	−	0.125499i
$537$		0			0
$538$	−0.176595	−	1.03016i	−0.00761354	−	0.0444134i
$539$			24.3397i			1.04838i
$540$		0			0
$541$		−	12.4653i		−	0.535927i	−0.963429	−	0.267963i	$-0.913649\pi$
$541$		−	12.4653i		−	0.535927i	0.963429	−	0.267963i	$-0.0863506\pi$
$542$	6.01895	−	1.03180i	0.258536	−	0.0443194i
$543$		0			0
$544$	−4.94702	+	5.61856i	−0.212102	+	0.240894i
$545$	18.7867	−	10.8465i	0.804732	−	0.464612i
$546$		0			0
$547$	0.205771	−	0.356406i	0.00879815	−	0.0152388i	−0.861593	−	0.507600i	$-0.830533\pi$
$547$	0.205771	−	0.356406i	0.00879815	−	0.0152388i	0.870391	+	0.492361i	$0.163866\pi$
$548$	−11.6157	−	2.16234i	−0.496198	−	0.0923706i
$549$		0			0
$550$	11.0000	+	13.2367i	0.469042	+	0.564415i
$551$	1.16575	−	2.01915i	0.0496628	−	0.0860185i
$552$		0			0
$553$	−8.76795	−	15.1865i	−0.372851	−	0.645797i
$554$	−1.03264	+	2.79568i	−0.0438726	+	0.118777i
$555$		0			0
$556$	10.9366	+	9.35570i	0.463815	+	0.396770i
$557$	−36.3977			−1.54222			−0.771110	−	0.636702i	$-0.780298\pi$
$557$	−36.3977			−1.54222			−0.771110	+	0.636702i	$0.780298\pi$
$558$		0			0
$559$			10.7436i			0.454407i
$560$	−5.75867	−	7.13440i	−0.243348	−	0.301483i
$561$		0			0
$562$	−3.54324	+	9.59270i	−0.149463	+	0.404643i
$563$	10.2323	−	5.90763i	0.431240	−	0.248977i	−0.268635	−	0.963242i	$-0.586572\pi$
$563$	10.2323	−	5.90763i	0.431240	−	0.248977i	0.699875	+	0.714265i	$0.253239\pi$
$564$		0			0
$565$	15.4474	+	8.91858i	0.649878	+	0.375207i
$566$	−0.156182	+	0.129790i	−0.00656480	+	0.00545550i
$567$		0			0
$568$	−7.60770	−	13.6224i	−0.319212	−	0.571582i
$569$	30.7792	+	17.7704i	1.29033	+	0.744973i	0.978713	−	0.205234i	$-0.0657956\pi$
$569$	30.7792	+	17.7704i	1.29033	+	0.744973i	0.311619	+	0.950207i	$0.399129\pi$
$570$		0			0
$571$	−3.59808	−	6.23205i	−0.150575	−	0.260803i	0.780864	−	0.624701i	$-0.214779\pi$
$571$	−3.59808	−	6.23205i	−0.150575	−	0.260803i	−0.931439	+	0.363898i	$0.881446\pi$
$572$	50.0317	−	17.6727i	2.09193	−	0.738931i
$573$		0			0
$574$	−3.39726	−	19.8178i	−0.141799	−	0.827180i
$575$	−14.6444			−0.610714
$576$		0			0
$577$	−1.92820			−0.0802722			−0.0401361	−	0.999194i	$-0.512779\pi$
$577$	−1.92820			−0.0802722			−0.0401361	+	0.999194i	$0.512779\pi$
$578$	−3.64361	−	21.2549i	−0.151554	−	0.884087i
$579$		0			0
$580$	−26.1306	+	9.23007i	−1.08501	+	0.383258i
$581$	5.20405	+	9.01367i	0.215900	+	0.373950i
$582$		0			0
$583$	−23.5947	−	13.6224i	−0.977191	−	0.564181i
$584$	−10.9338	−	19.5781i	−0.452444	−	0.810149i
$585$		0			0
$586$	7.73205	−	6.42551i	0.319408	−	0.265435i
$587$	14.5095	+	8.37705i	0.598870	+	0.345758i	0.768597	−	0.639733i	$-0.220955\pi$
$587$	14.5095	+	8.37705i	0.598870	+	0.345758i	−0.169727	+	0.985491i	$0.554288\pi$
$588$		0			0
$589$	1.82505	−	1.05369i	0.0752000	−	0.0434167i
$590$	3.85385	−	10.4336i	0.158661	−	0.429546i
$591$		0			0
$592$	−6.26350	−	7.75982i	−0.257428	−	0.318927i
$593$		−	1.93754i		−	0.0795651i	−0.999208	−	0.0397826i	$-0.987333\pi$
$593$		−	1.93754i		−	0.0795651i	0.999208	−	0.0397826i	$-0.0126665\pi$
$594$		0			0
$595$	−3.03332			−0.124354
$596$	4.84036	+	4.14068i	0.198269	+	0.169609i
$597$		0			0
$598$	−15.6436	+	42.3524i	−0.639716	+	1.73192i
$599$	21.7533	+	37.6778i	0.888815	+	1.53947i	0.841278	+	0.540603i	$0.181804\pi$
$599$	21.7533	+	37.6778i	0.888815	+	1.53947i	0.0475370	+	0.998869i	$0.484863\pi$
$600$		0			0
$601$	−4.80385	+	8.32051i	−0.195953	+	0.339401i	−0.947213	−	0.320606i	$-0.896113\pi$
$601$	−4.80385	+	8.32051i	−0.195953	+	0.339401i	0.751259	+	0.660007i	$0.229447\pi$
$602$	−2.60202	−	3.13111i	−0.106051	−	0.127615i
$603$		0			0
$604$	12.6340	+	2.35190i	0.514069	+	0.0956975i
$605$	−10.6633	+	18.4694i	−0.433524	+	0.750886i
$606$		0			0
$607$	23.5052	−	13.5707i	0.954045	−	0.550818i	0.0597098	−	0.998216i	$-0.480982\pi$
$607$	23.5052	−	13.5707i	0.954045	−	0.550818i	0.894335	+	0.447398i	$0.147649\pi$
$608$	−1.13762	−	1.00165i	−0.0461367	−	0.0406224i
$609$		0			0
$610$	11.9237	−	2.04402i	0.482778	−	0.0827601i
$611$			49.0340i			1.98370i
$612$		0			0
$613$			2.49307i			0.100694i	0.998732	+	0.0503470i	$0.0160327\pi$
$613$			2.49307i			0.100694i	−0.998732	+	0.0503470i	$0.983967\pi$
$614$	−1.68977	−	9.85725i	−0.0681937	−	0.397806i
$615$		0			0
$616$	−10.3010	+	17.2678i	−0.415039	+	0.695739i
$617$	20.5469	−	11.8628i	0.827187	−	0.477577i	−0.0257016	−	0.999670i	$-0.508182\pi$
$617$	20.5469	−	11.8628i	0.827187	−	0.477577i	0.852889	+	0.522093i	$0.174849\pi$
$618$		0			0
$619$	−13.4019	+	23.2128i	−0.538669	+	0.933002i	0.460307	+	0.887760i	$0.347739\pi$
$619$	−13.4019	+	23.2128i	−0.538669	+	0.933002i	−0.998976	+	0.0452421i	$0.985594\pi$
$620$	−24.6258	−	4.58426i	−0.988997	−	0.184108i
$621$		0			0
$622$	−18.4641	+	15.3441i	−0.740343	+	0.615242i
$623$	11.3605	−	19.6770i	0.455149	−	0.788341i
$624$		0			0
$625$	3.30385	+	5.72243i	0.132154	+	0.228897i
$626$	−15.1131	−	5.58232i	−0.604042	−	0.223114i
$627$		0			0
$628$	2.73981	−	3.20278i	0.109330	−	0.127805i
$629$	−3.29923			−0.131549
$630$		0			0
$631$			17.9405i			0.714200i	0.934066	+	0.357100i	$0.116234\pi$
$631$			17.9405i			0.714200i	−0.934066	+	0.357100i	$0.883766\pi$
$632$	−0.491905	+	34.4552i	−0.0195669	+	1.37056i
$633$		0			0
$634$	3.09300	+	1.14246i	0.122839	+	0.0453728i
$635$		0			0
$636$		0			0
$637$	−22.9266	−	13.2367i	−0.908386	−	0.524457i
$638$	38.8435	+	46.7418i	1.53783	+	1.85053i
$639$		0			0
$640$	2.53590	+	17.8372i	0.100240	+	0.705076i
$641$	−10.2323	−	5.90763i	−0.404152	−	0.233337i	0.284122	−	0.958788i	$-0.408298\pi$
$641$	−10.2323	−	5.90763i	−0.404152	−	0.233337i	−0.688274	+	0.725451i	$0.741631\pi$
$642$		0			0
$643$	−11.3923	−	19.7321i	−0.449269	−	0.778156i	0.549070	−	0.835776i	$-0.314982\pi$
$643$	−11.3923	−	19.7321i	−0.449269	−	0.778156i	−0.998339	+	0.0576203i	$0.981649\pi$
$644$	−5.69825	−	16.1319i	−0.224543	−	0.635685i
$645$		0			0
$646$	−0.494262	+	0.0847286i	−0.0194465	+	0.00333360i
$647$	1.47812			0.0581108			0.0290554	−	0.999578i	$-0.490750\pi$
$647$	1.47812			0.0581108			0.0290554	+	0.999578i	$0.490750\pi$
$648$		0			0
$649$	−24.3923			−0.957482
$650$	−18.4504	+	3.16285i	−0.723684	+	0.124057i
$651$		0			0
$652$	−36.2003	+	12.7870i	−1.41771	+	0.500778i
$653$	−13.9054	−	24.0848i	−0.544159	−	0.942511i	−0.998659	−	0.0517641i	$-0.983516\pi$
$653$	−13.9054	−	24.0848i	−0.544159	−	0.942511i	0.454501	−	0.890746i	$-0.349818\pi$
$654$		0			0
$655$	9.97227	+	5.75749i	0.389649	+	0.224964i
$656$	−14.2177	+	36.8641i	−0.555109	+	1.43930i
$657$		0			0
$658$	−11.8756	−	14.2904i	−0.462961	−	0.557098i
$659$	19.4008	+	11.2011i	0.755749	+	0.436332i	0.827767	−	0.561071i	$-0.189611\pi$
$659$	19.4008	+	11.2011i	0.755749	+	0.436332i	−0.0720183	+	0.997403i	$0.522944\pi$
$660$		0			0
$661$	35.7260	−	20.6264i	1.38958	−	0.802274i	0.396312	−	0.918116i	$-0.370290\pi$
$661$	35.7260	−	20.6264i	1.38958	−	0.802274i	0.993268	+	0.115842i	$0.0369565\pi$
$662$	34.6568	+	12.8011i	1.34698	+	0.497530i
$663$		0			0
$664$	0.291961	−	20.4502i	0.0113303	−	0.793623i
$665$		−	0.614175i		−	0.0238167i
$666$		0			0
$667$	−51.7128			−2.00233
$668$	−7.73527	−	6.61713i	−0.299287	−	0.256024i
$669$		0			0
$670$	−2.52694	−	0.933373i	−0.0976243	−	0.0360594i
$671$	−13.2653	−	22.9762i	−0.512102	−	0.886986i
$672$		0			0
$673$	6.62436	−	11.4737i	0.255350	−	0.442279i	−0.709640	−	0.704564i	$-0.751143\pi$
$673$	6.62436	−	11.4737i	0.255350	−	0.442279i	0.964991	+	0.262285i	$0.0844759\pi$
$674$	−10.2157	+	8.48946i	−0.393493	+	0.327002i
$675$		0			0
$676$	−5.80385	+	31.1772i	−0.223225	+	1.19912i
$677$	6.00027	−	10.3928i	0.230609	−	0.399427i	−0.727378	−	0.686237i	$-0.759261\pi$
$677$	6.00027	−	10.3928i	0.230609	−	0.399427i	0.957988	+	0.286810i	$0.0925948\pi$
$678$		0			0
$679$	11.7078	−	6.75952i	0.449305	−	0.259407i
$680$	5.11896	+	3.05368i	0.196303	+	0.117103i
$681$		0			0
$682$	9.28149	+	54.1433i	0.355407	+	2.07325i
$683$		−	34.9266i		−	1.33643i	−0.743969	−	0.668214i	$-0.767059\pi$
$683$		−	34.9266i		−	1.33643i	0.743969	−	0.668214i	$-0.232941\pi$
$684$		0			0
$685$			9.40760i			0.359446i
$686$	23.9317	−	4.10249i	0.913718	−	0.156634i
$687$		0			0
$688$	1.23898	+	7.90348i	0.0472358	+	0.301317i
$689$	25.6631	−	14.8166i	0.977684	−	0.564466i
$690$		0			0
$691$	11.9282	−	20.6603i	0.453770	−	0.785953i	−0.544846	−	0.838536i	$-0.683412\pi$
$691$	11.9282	−	20.6603i	0.453770	−	0.785953i	0.998617	+	0.0525828i	$0.0167454\pi$
$692$	4.35066	−	23.3709i	0.165387	−	0.888429i
$693$		0			0
$694$	−17.8564	−	21.4873i	−0.677820	−	0.815645i
$695$	5.72976	−	9.92423i	0.217342	−	0.376448i
$696$		0			0
$697$	6.53590	+	11.3205i	0.247565	+	0.428795i
$698$	11.7505	−	31.8125i	0.444765	−	1.20412i
$699$		0			0
$700$	4.61114	−	5.39032i	0.174285	−	0.203735i
$701$	−17.2883			−0.652970			−0.326485	−	0.945202i	$-0.605864\pi$
$701$	−17.2883			−0.652970			−0.326485	+	0.945202i	$0.605864\pi$
$702$		0			0
$703$		−	0.668016i		−	0.0251947i
$704$	34.7674	−	18.7706i	1.31035	−	0.707442i
$705$		0			0
$706$	−9.68031	+	26.2077i	−0.364323	+	0.986341i
$707$	−3.97009	+	2.29213i	−0.149311	+	0.0862045i
$708$		0			0
$709$	23.9287	+	13.8152i	0.898660	+	0.518841i	0.876765	−	0.480919i	$-0.159697\pi$
$709$	23.9287	+	13.8152i	0.898660	+	0.518841i	0.0218946	+	0.999760i	$0.493030\pi$
$710$	−9.55470	+	7.94018i	−0.358582	+	0.297989i
$711$		0			0
$712$	−38.9808	+	21.7696i	−1.46087	+	0.815850i
$713$	−40.4796	−	23.3709i	−1.51597	−	0.875248i
$714$		0			0
$715$	−21.1244	−	36.5885i	−0.790006	−	1.36833i
$716$	6.57977	+	18.6275i	0.245898	+	0.696142i
$717$		0			0
$718$	−1.62399	−	9.47351i	−0.0606069	−	0.353548i
$719$	15.0711			0.562058			0.281029	−	0.959699i	$-0.409324\pi$
$719$	15.0711			0.562058			0.281029	+	0.959699i	$0.409324\pi$
$720$		0			0
$721$	2.07180			0.0771577
$722$	4.52281	+	26.3837i	0.168322	+	0.981898i
$723$		0			0
$724$	−10.7349	−	30.3907i	−0.398958	−	1.12946i
$725$	−10.7205	−	18.5684i	−0.398148	−	0.689612i
$726$		0			0
$727$	−16.7835	−	9.68994i	−0.622464	−	0.359380i	0.155364	−	0.987857i	$-0.450345\pi$
$727$	−16.7835	−	9.68994i	−0.622464	−	0.359380i	−0.777828	+	0.628477i	$0.783678\pi$
$728$	−10.6633	−	19.0937i	−0.395208	−	0.707661i
$729$		0			0
$730$	−13.7321	+	11.4116i	−0.508246	+	0.422364i
$731$	2.29213	+	1.32336i	0.0847775	+	0.0489463i
$732$		0			0
$733$	39.0421	−	22.5410i	1.44205	−	0.832569i	0.444066	−	0.895994i	$-0.353536\pi$
$733$	39.0421	−	22.5410i	1.44205	−	0.832569i	0.997987	+	0.0634249i	$0.0202023\pi$
$734$	−8.03504	+	21.7535i	−0.296579	+	0.802935i
$735$		0			0
$736$	−6.62395	+	32.9603i	−0.244162	+	1.21493i
$737$			5.90763i			0.217610i
$738$		0			0
$739$	48.6410			1.78929			0.894644	−	0.446779i	$-0.147429\pi$
$739$	48.6410			1.78929			0.894644	+	0.446779i	$0.147429\pi$
$740$	−5.16150	+	6.03368i	−0.189741	+	0.221802i
$741$		0			0
$742$	−3.89075	+	10.5335i	−0.142834	+	0.386697i
$743$	21.6543	+	37.5063i	0.794418	+	1.37597i	0.923208	+	0.384300i	$0.125557\pi$
$743$	21.6543	+	37.5063i	0.794418	+	1.37597i	−0.128790	+	0.991672i	$0.541109\pi$
$744$		0			0
$745$	2.53590	−	4.39230i	0.0929081	−	0.160922i
$746$	16.4711	+	19.8203i	0.603051	+	0.725674i
$747$		0			0
$748$	2.39230	−	12.8510i	0.0874713	−	0.469880i
$749$	−8.75848	+	15.1701i	−0.320028	+	0.554304i
$750$		0			0
$751$	6.23267	−	3.59843i	0.227433	−	0.131309i	−0.381954	−	0.924181i	$-0.624749\pi$
$751$	6.23267	−	3.59843i	0.227433	−	0.131309i	0.609387	+	0.792873i	$0.291415\pi$
$752$	5.65472	+	36.0715i	0.206206	+	1.31539i
$753$		0			0
$754$	−65.1526	+	11.1688i	−2.37272	+	0.406742i
$755$		−	10.2323i		−	0.372392i
$756$		0			0
$757$		−	36.0600i		−	1.31062i	−0.755359	−	0.655311i	$-0.772537\pi$
$757$		−	36.0600i		−	1.31062i	0.755359	−	0.655311i	$-0.227463\pi$
$758$	7.10434	+	41.4429i	0.258041	+	1.50528i
$759$		0			0
$760$	−0.618298	+	1.03647i	−0.0224280	+	0.0375966i
$761$	−22.8390	+	13.1861i	−0.827914	+	0.477996i	−0.853138	−	0.521685i	$-0.825304\pi$
$761$	−22.8390	+	13.1861i	−0.827914	+	0.477996i	0.0252238	+	0.999682i	$0.491970\pi$
$762$		0			0
$763$	−9.80385	+	16.9808i	−0.354923	+	0.614745i
$764$	3.34108	−	17.9477i	0.120876	−	0.649324i
$765$		0			0
$766$	12.9282	−	10.7436i	0.467115	−	0.388183i
$767$	13.2653	−	22.9762i	0.478983	−	0.829622i
$768$		0			0
$769$	−8.96410	−	15.5263i	−0.323254	−	0.559892i	0.657904	−	0.753102i	$-0.271443\pi$
$769$	−8.96410	−	15.5263i	−0.323254	−	0.559892i	−0.981157	+	0.193210i	$0.938110\pi$
$770$	15.0179	+	5.54714i	0.541207	+	0.199905i
$771$		0			0
$772$	23.3930	+	20.0115i	0.841932	+	0.720230i
$773$	34.1805			1.22939			0.614694	−	0.788766i	$-0.289280\pi$
$773$	34.1805			1.22939			0.614694	+	0.788766i	$0.289280\pi$
$774$		0			0
$775$		−	19.3799i		−	0.696146i
$776$	−26.5627	−	0.379227i	−0.953547	−	0.0136134i
$777$		0			0
$778$	−10.5628	−	3.90157i	−0.378695	−	0.139878i
$779$	−2.29213	+	1.32336i	−0.0821241	+	0.0474144i
$780$		0			0
$781$	23.5947	+	13.6224i	0.844283	+	0.487447i
$782$	7.10886	+	8.55435i	0.254212	+	0.305903i
$783$		0			0
$784$	−18.3923	−	7.09353i	−0.656868	−	0.253340i
$785$	−2.90631	−	1.67796i	−0.103731	−	0.0598888i
$786$		0			0
$787$	25.7224	+	44.5526i	0.916906	+	1.58813i	0.804087	+	0.594512i	$0.202655\pi$
$787$	25.7224	+	44.5526i	0.916906	+	1.58813i	0.112819	+	0.993616i	$0.464012\pi$
$788$	−37.4304	+	13.2215i	−1.33340	+	0.470997i
$789$		0			0
$790$	27.0425	−	4.63574i	0.962127	−	0.164932i
$791$	−16.1225			−0.573251
$792$		0			0
$793$	28.8564			1.02472
$794$	−18.9880	+	3.25501i	−0.673858	+	0.115516i
$795$		0			0
$796$	−9.51916	−	26.9490i	−0.337398	−	0.955181i
$797$	3.92396	+	6.79650i	0.138994	+	0.240744i	0.927116	−	0.374774i	$-0.122280\pi$
$797$	3.92396	+	6.79650i	0.138994	+	0.240744i	−0.788122	+	0.615519i	$0.788947\pi$
$798$		0			0
$799$	10.4613	+	6.03983i	0.370094	+	0.213674i
$800$	−13.2081	+	4.45447i	−0.466979	+	0.157489i
$801$		0			0
$802$	35.7128	+	42.9745i	1.26106	+	1.51748i
$803$	33.9103	+	19.5781i	1.19667	+	0.690897i
$804$		0			0
$805$	−11.7973	+	6.81119i	−0.415801	+	0.240063i
$806$	−56.0475	−	20.7022i	−1.97419	−	0.729204i
$807$		0			0
$808$	9.00734	+	0.128595i	0.316877	+	0.00452394i
$809$			2.64673i			0.0930539i	0.998917	+	0.0465270i	$0.0148153\pi$
$809$			2.64673i			0.0930539i	−0.998917	+	0.0465270i	$0.985185\pi$
$810$		0			0
$811$	−40.9282			−1.43718			−0.718592	−	0.695432i	$-0.755213\pi$
$811$	−40.9282			−1.43718			−0.718592	+	0.695432i	$0.755213\pi$
$812$	16.2830	−	19.0345i	0.571421	−	0.667978i
$813$		0			0
$814$	16.3344	+	6.03342i	0.572521	+	0.211471i
$815$	15.2845	+	26.4735i	0.535391	+	0.927325i
$816$		0			0
$817$	−0.267949	+	0.464102i	−0.00937436	+	0.0162369i
$818$	31.9689	−	26.5669i	1.11777	−	0.928891i
$819$		0			0
$820$	30.9282	+	5.75749i	1.08006	+	0.201060i
$821$	−8.33178	+	14.4311i	−0.290781	+	0.503648i	−0.973995	−	0.226571i	$-0.927249\pi$
$821$	−8.33178	+	14.4311i	−0.290781	+	0.503648i	0.683213	+	0.730219i	$0.260582\pi$
$822$		0			0
$823$	−24.8412	+	14.3421i	−0.865909	+	0.499933i	−0.865987	−	0.500067i	$-0.833309\pi$
$823$	−24.8412	+	14.3421i	−0.865909	+	0.499933i	7.73618e−5		1.00000i	$0.499975\pi$
$824$	−3.49631	−	2.08570i	−0.121800	−	0.0726590i
$825$		0			0
$826$	1.69863	+	9.90891i	0.0591029	+	0.344775i
$827$		−	3.00132i		−	0.104366i	−0.998638	−	0.0521830i	$-0.983382\pi$
$827$		−	3.00132i		−	0.104366i	0.998638	−	0.0521830i	$-0.0166179\pi$
$828$		0			0
$829$			12.4653i			0.432939i	0.976289	+	0.216470i	$0.0694542\pi$
$829$			12.4653i			0.432939i	−0.976289	+	0.216470i	$0.930546\pi$
$830$	−16.0505	+	2.75145i	−0.557122	+	0.0955044i
$831$		0			0
$832$	−1.22681	+	42.9570i	−0.0425321	+	1.48927i
$833$	−5.64804	+	3.26090i	−0.195693	+	0.112983i
$834$		0			0
$835$	−4.05256	+	7.01924i	−0.140245	+	0.242911i
$836$	2.60202	+	0.484384i	0.0899929	+	0.0167528i
$837$		0			0
$838$	−0.320508	−	0.385679i	−0.0110718	−	0.0133231i
$839$	−28.5498	+	49.4497i	−0.985648	+	1.70719i	−0.346625	+	0.938004i	$0.612673\pi$
$839$	−28.5498	+	49.4497i	−0.985648	+	1.70719i	−0.639022	+	0.769188i	$0.720661\pi$
$840$		0			0
$841$	−23.3564	−	40.4545i	−0.805393	−	1.39498i
$842$	−6.48609	+	17.5599i	−0.223525	+	0.605155i
$843$		0			0
$844$	−25.9162	−	22.1700i	−0.892073	−	0.763123i
$845$	25.2505			0.868645
$846$		0			0
$847$		−	19.2765i		−	0.662349i
$848$	17.1702	−	13.8592i	0.589626	−	0.475928i
$849$		0			0
$850$	−1.59787	+	4.32594i	−0.0548064	+	0.148379i
$851$	−12.8315	+	7.40828i	−0.439859	+	0.253953i
$852$		0			0
$853$	0.334008	+	0.192840i	0.0114362	+	0.00660270i	0.505707	−	0.862705i	$-0.331232\pi$
$853$	0.334008	+	0.192840i	0.0114362	+	0.00660270i	−0.494271	+	0.869308i	$0.664565\pi$
$854$	−8.40987	+	6.98880i	−0.287780	+	0.239152i
$855$		0			0
$856$	30.0526	−	16.7835i	1.02718	−	0.573647i
$857$	−31.9253	−	18.4321i	−1.09055	−	0.629627i	−0.156825	−	0.987626i	$-0.550126\pi$
$857$	−31.9253	−	18.4321i	−1.09055	−	0.629627i	−0.933722	+	0.357999i	$0.883459\pi$
$858$		0			0
$859$	9.79423	+	16.9641i	0.334175	+	0.578808i	0.983326	−	0.181852i	$-0.0582091\pi$
$859$	9.79423	+	16.9641i	0.334175	+	0.578808i	−0.649151	+	0.760659i	$0.724876\pi$
$860$	6.00612	−	2.12154i	0.204807	−	0.0723438i
$861$		0			0
$862$	−9.17953	−	53.5485i	−0.312656	−	1.82387i
$863$	−8.27462			−0.281671			−0.140836	−	0.990033i	$-0.544979\pi$
$863$	−8.27462			−0.281671			−0.140836	+	0.990033i	$0.544979\pi$
$864$		0			0
$865$	−18.9282			−0.643578
$866$	−2.73930	−	15.9796i	−0.0930850	−	0.543009i
$867$		0			0
$868$	21.3483	−	7.54085i	0.724609	−	0.255953i
$869$	−30.0851	−	52.1089i	−1.02057	−	1.76767i
$870$		0			0
$871$	−5.56466	−	3.21276i	−0.188551	−	0.108860i
$872$	33.6395	−	18.7867i	1.13918	−	0.636197i
$873$		0			0
$874$	−1.73205	+	1.43937i	−0.0585875	+	0.0486875i
$875$	−14.8166	−	8.55435i	−0.500891	−	0.289190i
$876$		0			0
$877$	−18.9425	+	10.9365i	−0.639644	+	0.369298i	−0.784477	−	0.620158i	$-0.787069\pi$
$877$	−18.9425	+	10.9365i	−0.639644	+	0.369298i	0.144834	+	0.989456i	$0.453735\pi$
$878$	17.2040	−	46.5768i	0.580607	−	1.57189i
$879$		0			0
$880$	−19.7595	−	24.4799i	−0.666091	−	0.825218i
$881$		−	35.5408i		−	1.19740i	−0.800974	−	0.598699i	$-0.795684\pi$
$881$		−	35.5408i		−	1.19740i	0.800974	−	0.598699i	$-0.204316\pi$
$882$		0			0
$883$	19.8756			0.668869			0.334434	−	0.942419i	$-0.391455\pi$
$883$	19.8756			0.668869			0.334434	+	0.942419i	$0.391455\pi$
$884$	10.8039	+	9.24221i	0.363376	+	0.310849i
$885$		0			0
$886$	15.4699	−	41.8820i	0.519721	−	1.40705i
$887$	−9.86707	−	17.0903i	−0.331304	−	0.573835i	0.651464	−	0.758679i	$-0.274155\pi$
$887$	−9.86707	−	17.0903i	−0.331304	−	0.573835i	−0.982768	+	0.184845i	$0.940822\pi$
$888$		0			0
$889$		0			0
$890$	22.7210	+	27.3410i	0.761610	+	0.916473i
$891$		0			0
$892$	38.1051	+	7.09353i	1.27585	+	0.237509i
$893$	−1.22292	+	2.11816i	−0.0409235	+	0.0708816i
$894$		0			0
$895$	13.6224	−	7.86488i	0.455346	−	0.262894i
$896$	−10.0463	−	12.8165i	−0.335624	−	0.428168i
$897$		0			0
$898$	−32.0820	+	5.49965i	−1.07059	+	0.183526i
$899$		−	68.4348i		−	2.28243i
$900$		0			0
$901$		−	7.30021i		−	0.243205i
$902$	−11.6569	−	68.0000i	−0.388131	−	2.26415i
$903$		0			0
$904$	27.2080	+	16.2308i	0.904924	+	0.539827i
$905$	−22.2249	+	12.8315i	−0.738779	+	0.426534i
$906$		0			0
$907$	−13.1865	+	22.8397i	−0.437852	+	0.758381i	−0.997524	−	0.0703330i	$-0.977594\pi$
$907$	−13.1865	+	22.8397i	−0.437852	+	0.758381i	0.559672	+	0.828714i	$0.310927\pi$
$908$	−19.4218	−	3.61549i	−0.644534	−	0.119984i
$909$		0			0
$910$	−13.3923	+	11.1293i	−0.443951	+	0.368933i
$911$	22.1800	−	38.4168i	0.734855	−	1.27281i	−0.219931	−	0.975515i	$-0.570583\pi$
$911$	22.1800	−	38.4168i	0.734855	−	1.27281i	0.954787	−	0.297291i	$-0.0960833\pi$
$912$		0			0
$913$	17.8564	+	30.9282i	0.590961	+	1.02357i
$914$	−19.0930	−	7.05234i	−0.631539	−	0.233271i
$915$		0			0
$916$	20.4502	−	23.9059i	0.675695	−	0.789872i
$917$	−10.4081			−0.343706
$918$		0			0
$919$		−	30.8949i		−	1.01913i	−0.860433	−	0.509564i	$-0.829807\pi$
$919$		−	30.8949i		−	1.01913i	0.860433	−	0.509564i	$-0.170193\pi$
$920$	26.7658	+	0.382126i	0.882442	+	0.0125983i
$921$		0			0
$922$	−25.1990	−	9.30773i	−0.829886	−	0.306534i
$923$	−25.6631	+	14.8166i	−0.844710	+	0.487693i
$924$		0			0
$925$	−5.32014	−	3.07159i	−0.174925	−	0.100993i
$926$	−27.8316	−	33.4908i	−0.914604	−	1.10058i
$927$		0			0
$928$	−46.6410	+	15.7298i	−1.53107	+	0.516355i
$929$	12.5244	+	7.23099i	0.410913	+	0.237241i	0.691182	−	0.722681i	$-0.257090\pi$
$929$	12.5244	+	7.23099i	0.410913	+	0.237241i	−0.280269	+	0.959922i	$0.590424\pi$
$930$		0			0
$931$	−0.660254	−	1.14359i	−0.0216390	−	0.0374798i
$932$	−1.76305	−	4.99122i	−0.0577505	−	0.163493i
$933$		0			0
$934$	24.3418	−	4.17278i	0.796487	−	0.136537i
$935$	−10.4081			−0.340381
$936$		0			0
$937$	−2.60770			−0.0851897			−0.0425948	−	0.999092i	$-0.513562\pi$
$937$	−2.60770			−0.0851897			−0.0425948	+	0.999092i	$0.513562\pi$
$938$	2.39986	−	0.411395i	0.0783582	−	0.0134325i
$939$		0			0
$940$	27.4119	−	9.68270i	0.894079	−	0.315815i
$941$	15.8673	+	27.4830i	0.517260	+	0.895921i	0.999799	+	0.0200467i	$0.00638148\pi$
$941$	15.8673	+	27.4830i	0.517260	+	0.895921i	−0.482539	+	0.875875i	$0.660285\pi$
$942$		0			0
$943$	50.8394	+	29.3521i	1.65556	+	0.955837i
$944$	7.10886	−	18.4321i	0.231374	−	0.599913i
$945$		0			0
$946$	−8.92820	−	10.7436i	−0.290281	−	0.349306i
$947$	−23.0638	−	13.3159i	−0.749474	−	0.432709i	0.0760299	−	0.997106i	$-0.475776\pi$
$947$	−23.0638	−	13.3159i	−0.749474	−	0.432709i	−0.825504	+	0.564397i	$0.809109\pi$
$948$		0			0
$949$	−36.8830	+	21.2944i	−1.19727	+	0.691246i
$950$	−0.875899	−	0.323530i	−0.0284179	−	0.0104967i
$951$		0			0
$952$	−5.38708	−	0.0769094i	−0.174596	−	0.00249265i
$953$			57.9429i			1.87696i	0.345340	+	0.938478i	$0.387764\pi$
$953$			57.9429i			1.87696i	−0.345340	+	0.938478i	$0.612236\pi$
$954$		0			0
$955$	−14.5359			−0.470371
$956$	−9.68073	−	8.28137i	−0.313097	−	0.267839i
$957$		0			0
$958$	−4.22512	−	1.56063i	−0.136507	−	0.0504215i
$959$	−4.25164	−	7.36406i	−0.137293	−	0.237798i
$960$		0			0
$961$	15.4282	−	26.7224i	0.497684	−	0.862014i
$962$	−14.5663	+	12.1049i	−0.469637	+	0.390279i
$963$		0			0
$964$	5.63397	−	30.2647i	0.181458	−	0.974760i
$965$	12.2557	−	21.2276i	0.394526	−	0.683340i
$966$		0			0
$967$	−5.56466	+	3.21276i	−0.178947	+	0.103315i	−0.586798	−	0.809733i	$-0.699612\pi$
$967$	−5.56466	+	3.21276i	−0.178947	+	0.103315i	0.407851	+	0.913049i	$0.366278\pi$
$968$	−19.4059	+	32.5306i	−0.623730	+	1.04557i
$969$		0			0
$970$	3.57385	+	20.8480i	0.114750	+	0.669388i
$971$			42.5122i			1.36428i	0.731221	+	0.682140i	$0.238951\pi$
$971$			42.5122i			1.36428i	−0.731221	+	0.682140i	$0.761049\pi$
$972$		0			0
$973$			10.3580i			0.332061i
$974$	−52.8073	+	9.05246i	−1.69205	+	0.290060i
$975$		0			0
$976$	21.2280	−	3.32779i	0.679492	−	0.106520i
$977$	35.8954	−	20.7242i	1.14839	−	0.663026i	0.199899	−	0.979817i	$-0.435939\pi$
$977$	35.8954	−	20.7242i	1.14839	−	0.663026i	0.948495	+	0.316791i	$0.102605\pi$
$978$		0			0
$979$	38.9808	−	67.5167i	1.24583	−	2.15784i
$980$	−2.87254	+	15.4307i	−0.0917599	+	0.492917i
$981$		0			0
$982$	15.1436	+	18.2228i	0.483251	+	0.581514i
$983$	27.0563	−	46.8630i	0.862963	−	1.49470i	−0.00609223	−	0.999981i	$-0.501939\pi$
$983$	27.0563	−	46.8630i	0.862963	−	1.49470i	0.869055	−	0.494715i	$-0.164727\pi$
$984$		0			0
$985$	15.8038	+	27.3731i	0.503552	+	0.872178i
$986$	−5.64243	+	15.2759i	−0.179692	+	0.486484i
$987$		0			0
$988$	−1.87133	+	2.18754i	−0.0595348	+	0.0695949i
$989$	11.8862			0.377960
$990$		0			0
$991$			0.668016i			0.0212202i	0.999944	+	0.0106101i	$0.00337737\pi$
$991$			0.668016i			0.0212202i	−0.999944	+	0.0106101i	$0.996623\pi$
$992$	−43.6184	−	8.76588i	−1.38489	−	0.278317i
$993$		0			0
$994$	3.89075	−	10.5335i	0.123407	−	0.334103i
$995$	−19.7079	+	11.3784i	−0.624783	+	0.360719i
$996$		0			0
$997$	−25.4197	−	14.6761i	−0.805050	−	0.464796i	0.0401838	−	0.999192i	$-0.487206\pi$
$997$	−25.4197	−	14.6761i	−0.805050	−	0.464796i	−0.845234	+	0.534396i	$0.820539\pi$
$998$	28.7060	−	23.8553i	0.908671	−	0.755126i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.l.f.107.4		16
3.2	odd	2	inner	648.2.l.f.107.5		16
4.3	odd	2		2592.2.p.f.431.6		16
8.3	odd	2	inner	648.2.l.f.107.2		16
8.5	even	2		2592.2.p.f.431.3		16
9.2	odd	6		216.2.f.a.107.7	yes	8
9.4	even	3	inner	648.2.l.f.539.7		16
9.5	odd	6	inner	648.2.l.f.539.2		16
9.7	even	3		216.2.f.a.107.2	yes	8
12.11	even	2		2592.2.p.f.431.4		16
24.5	odd	2		2592.2.p.f.431.5		16
24.11	even	2	inner	648.2.l.f.107.7		16
36.7	odd	6		864.2.f.a.431.3		8
36.11	even	6		864.2.f.a.431.5		8
36.23	even	6		2592.2.p.f.2159.3		16
36.31	odd	6		2592.2.p.f.2159.5		16
72.5	odd	6		2592.2.p.f.2159.6		16
72.11	even	6		216.2.f.a.107.1	✓	8
72.13	even	6		2592.2.p.f.2159.4		16
72.29	odd	6		864.2.f.a.431.4		8
72.43	odd	6		216.2.f.a.107.8	yes	8
72.59	even	6	inner	648.2.l.f.539.4		16
72.61	even	6		864.2.f.a.431.6		8
72.67	odd	6	inner	648.2.l.f.539.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.f.a.107.1	✓	8	72.11	even	6
216.2.f.a.107.2	yes	8	9.7	even	3
216.2.f.a.107.7	yes	8	9.2	odd	6
216.2.f.a.107.8	yes	8	72.43	odd	6
648.2.l.f.107.2		16	8.3	odd	2	inner
648.2.l.f.107.4		16	1.1	even	1	trivial
648.2.l.f.107.5		16	3.2	odd	2	inner
648.2.l.f.107.7		16	24.11	even	2	inner
648.2.l.f.539.2		16	9.5	odd	6	inner
648.2.l.f.539.4		16	72.59	even	6	inner
648.2.l.f.539.5		16	72.67	odd	6	inner
648.2.l.f.539.7		16	9.4	even	3	inner
864.2.f.a.431.3		8	36.7	odd	6
864.2.f.a.431.4		8	72.29	odd	6
864.2.f.a.431.5		8	36.11	even	6
864.2.f.a.431.6		8	72.61	even	6
2592.2.p.f.431.3		16	8.5	even	2
2592.2.p.f.431.4		16	12.11	even	2
2592.2.p.f.431.5		16	24.5	odd	2
2592.2.p.f.431.6		16	4.3	odd	2
2592.2.p.f.2159.3		16	36.23	even	6
2592.2.p.f.2159.4		16	72.13	even	6
2592.2.p.f.2159.5		16	36.31	odd	6
2592.2.p.f.2159.6		16	72.5	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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.238945 - 1.39388i) q^{2} +(-1.88581 + 0.666123i) q^{4} +(0.796225 + 1.37910i) q^{5} +(-1.24653 - 0.719687i) q^{7} +(1.37910 + 2.46943i) q^{8} +(1.73205 - 1.43937i) q^{10} +(-4.27718 - 2.46943i) q^{11} +(4.65213 - 2.68591i) q^{13} +(-0.705304 + 1.90949i) q^{14} +(3.11256 - 2.51236i) q^{16} -1.32336i q^{17} +0.267949 q^{19} +(-2.42018 - 2.07034i) q^{20} +(-2.42008 + 6.55193i) q^{22} +(-2.97155 - 5.14688i) q^{23} +(1.23205 - 2.13397i) q^{25} +(-4.85544 - 5.84273i) q^{26} +(2.83013 + 0.526847i) q^{28} +(4.35066 - 7.53556i) q^{29} +(6.81119 - 3.93244i) q^{31} +(-4.24567 - 3.73822i) q^{32} +(-1.84461 + 0.316212i) q^{34} -2.29213i q^{35} -2.49307i q^{37} +(-0.0640252 - 0.373489i) q^{38} +(-2.30752 + 3.86814i) q^{40} +(-8.55435 + 4.93886i) q^{41} +(-1.00000 + 1.73205i) q^{43} +(9.71088 + 1.80775i) q^{44} +(-6.46410 + 5.37182i) q^{46} +(-4.56400 + 7.90509i) q^{47} +(-2.46410 - 4.26795i) q^{49} +(-3.26890 - 1.20743i) q^{50} +(-6.98389 + 8.16400i) q^{52} +5.51641 q^{53} -7.86488i q^{55} +(0.0581166 - 4.07075i) q^{56} +(-11.5432 - 4.26371i) q^{58} +(4.27718 - 2.46943i) q^{59} +(4.65213 + 2.68591i) q^{61} +(-7.10886 - 8.55435i) q^{62} +(-4.19615 + 6.81119i) q^{64} +(7.40828 + 4.27718i) q^{65} +(-0.598076 - 1.03590i) q^{67} +(0.881523 + 2.49561i) q^{68} +(-3.19496 + 0.547694i) q^{70} -5.51641 q^{71} -7.92820 q^{73} +(-3.47504 + 0.595707i) q^{74} +(-0.505301 + 0.178487i) q^{76} +(3.55443 + 6.15645i) q^{77} +(10.5508 + 6.09150i) q^{79} +(5.94311 + 2.29213i) q^{80} +(8.92820 + 10.7436i) q^{82} +(-6.26222 - 3.61549i) q^{83} +(1.82505 - 1.05369i) q^{85} +(2.65322 + 0.980016i) q^{86} +(0.199413 - 13.9678i) q^{88} +15.7853i q^{89} -7.73205 q^{91} +(9.03224 + 7.72662i) q^{92} +(12.1093 + 4.47279i) q^{94} +(0.213348 + 0.369529i) q^{95} +(-4.69615 + 8.13397i) q^{97} +(-5.36023 + 4.45447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 16 q^{16} + 32 q^{19} + 8 q^{22} - 8 q^{25} - 24 q^{28} + 32 q^{34} - 24 q^{40} - 16 q^{43} - 48 q^{46} + 16 q^{49} - 36 q^{52} - 48 q^{58} + 16 q^{64} + 32 q^{67} - 72 q^{70} - 16 q^{73}+ \cdots + 8 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 + 16 * q^16 + 32 * q^19 + 8 * q^22 - 8 * q^25 - 24 * q^28 + 32 * q^34 - 24 * q^40 - 16 * q^43 - 48 * q^46 + 16 * q^49 - 36 * q^52 - 48 * q^58 + 16 * q^64 + 32 * q^67 - 72 * q^70 - 16 * q^73 + 20 * q^76 + 32 * q^82 + 56 * q^88 - 96 * q^91 + 24 * q^94 + 8 * q^97

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