LMFDB - Embedded newform 720.2.t.c.541.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(181,720)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("720.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.t (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			541.7
Root			$-0.530822 - 1.31081i$ of defining polynomial
Character	$\chi$	$=$	720.541
Dual form			720.2.t.c.181.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17275 + 0.790349i) q^{2} +(0.750696 + 1.85377i) q^{4} +(0.707107 - 0.707107i) q^{5} +2.73482i q^{7} +(-0.584744 + 2.76732i) q^{8} +O(q^{10})$	\(q+(1.17275 + 0.790349i) q^{2} +(0.750696 + 1.85377i) q^{4} +(0.707107 - 0.707107i) q^{5} +2.73482i q^{7} +(-0.584744 + 2.76732i) q^{8} +(1.38812 - 0.270400i) q^{10} +(-4.12175 + 4.12175i) q^{11} +(-1.37919 - 1.37919i) q^{13} +(-2.16146 + 3.20726i) q^{14} +(-2.87291 + 2.78323i) q^{16} +4.94921 q^{17} +(-0.292715 - 0.292715i) q^{19} +(1.84163 + 0.779990i) q^{20} +(-8.09141 + 1.57617i) q^{22} -1.64818i q^{23} -1.00000i q^{25} +(-0.527407 - 2.70749i) q^{26} +(-5.06972 + 2.05302i) q^{28} +(5.67267 + 5.67267i) q^{29} +3.95550 q^{31} +(-5.56894 + 0.993438i) q^{32} +(5.80420 + 3.91161i) q^{34} +(1.93381 + 1.93381i) q^{35} +(2.48772 - 2.48772i) q^{37} +(-0.111935 - 0.574630i) q^{38} +(1.54332 + 2.37027i) q^{40} -8.40843i q^{41} +(-3.22713 + 3.22713i) q^{43} +(-10.7349 - 4.54659i) q^{44} +(1.30264 - 1.93291i) q^{46} +5.19809 q^{47} -0.479225 q^{49} +(0.790349 - 1.17275i) q^{50} +(1.52135 - 3.59205i) q^{52} +(-7.20537 + 7.20537i) q^{53} +5.82903i q^{55} +(-7.56812 - 1.59917i) q^{56} +(2.16925 + 11.1360i) q^{58} +(6.41142 - 6.41142i) q^{59} +(-3.82618 - 3.82618i) q^{61} +(4.63883 + 3.12623i) q^{62} +(-7.31615 - 3.23635i) q^{64} -1.95047 q^{65} +(5.76044 + 5.76044i) q^{67} +(3.71535 + 9.17470i) q^{68} +(0.739494 + 3.79626i) q^{70} -7.92245i q^{71} -4.36276i q^{73} +(4.88365 - 0.951312i) q^{74} +(0.322886 - 0.762367i) q^{76} +(-11.2722 - 11.2722i) q^{77} -5.56087 q^{79} +(-0.0634130 + 3.99950i) q^{80} +(6.64559 - 9.86100i) q^{82} +(0.516191 + 0.516191i) q^{83} +(3.49962 - 3.49962i) q^{85} +(-6.33518 + 1.23406i) q^{86} +(-8.99604 - 13.8164i) q^{88} -6.42236i q^{89} +(3.77184 - 3.77184i) q^{91} +(3.05535 - 1.23729i) q^{92} +(6.09607 + 4.10830i) q^{94} -0.413962 q^{95} -9.44534 q^{97} +(-0.562012 - 0.378755i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4}+O(q^{10}) $ 16 * q - 4 * q^4	$ 16 q - 4 q^{4} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 8 q^{20} - 20 q^{22} + 16 q^{26} - 4 q^{28} + 16 q^{29} + 16 q^{34} - 16 q^{37} - 20 q^{38} + 8 q^{43} - 40 q^{44} - 4 q^{46} + 40 q^{47} - 16 q^{49} + 4 q^{50} + 56 q^{52} - 16 q^{53} - 16 q^{56} - 12 q^{58} + 8 q^{59} + 16 q^{61} + 8 q^{62} - 16 q^{64} + 40 q^{67} + 48 q^{68} - 8 q^{70} + 72 q^{74} - 16 q^{77} + 16 q^{79} - 16 q^{80} - 76 q^{82} - 40 q^{83} - 16 q^{85} - 28 q^{86} + 32 q^{91} + 52 q^{92} - 36 q^{94} - 32 q^{95} - 60 q^{98}+O(q^{100}) $ 16 * q - 4 * q^4 + 4 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 8 * q^20 - 20 * q^22 + 16 * q^26 - 4 * q^28 + 16 * q^29 + 16 * q^34 - 16 * q^37 - 20 * q^38 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 40 * q^47 - 16 * q^49 + 4 * q^50 + 56 * q^52 - 16 * q^53 - 16 * q^56 - 12 * q^58 + 8 * q^59 + 16 * q^61 + 8 * q^62 - 16 * q^64 + 40 * q^67 + 48 * q^68 - 8 * q^70 + 72 * q^74 - 16 * q^77 + 16 * q^79 - 16 * q^80 - 76 * q^82 - 40 * q^83 - 16 * q^85 - 28 * q^86 + 32 * q^91 + 52 * q^92 - 36 * q^94 - 32 * q^95 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

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 $

$2$	1.17275	+	0.790349i	0.829261	+	0.558861i
$2$	1.17275	+	0.790349i	0.829261	+	0.558861i
$3$		0			0
$3$		0			0
$4$	0.750696	+	1.85377i	0.375348	+	0.926884i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$			2.73482i			1.03366i	0.856087	+	0.516832i	$0.172889\pi$
$7$			2.73482i			1.03366i	−0.856087	+	0.516832i	$0.827111\pi$
$8$	−0.584744	+	2.76732i	−0.206738	+	0.978396i
$9$		0			0
$10$	1.38812	−	0.270400i	0.438963	−	0.0855079i
$11$	−4.12175	+	4.12175i	−1.24275	+	1.24275i	−0.283900	+	0.958854i	$0.591629\pi$
$11$	−4.12175	+	4.12175i	−1.24275	+	1.24275i	−0.958854	+	0.283900i	$0.908371\pi$
$12$		0			0
$13$	−1.37919	−	1.37919i	−0.382519	−	0.382519i	0.489490	−	0.872009i	$-0.337183\pi$
$13$	−1.37919	−	1.37919i	−0.382519	−	0.382519i	−0.872009	+	0.489490i	$0.837183\pi$
$14$	−2.16146	+	3.20726i	−0.577675	+	0.857177i
$15$		0			0
$16$	−2.87291	+	2.78323i	−0.718228	+	0.695808i
$17$	4.94921			1.20036			0.600180	−	0.799865i	$-0.295095\pi$
$17$	4.94921			1.20036			0.600180	+	0.799865i	$0.295095\pi$
$18$		0			0
$19$	−0.292715	−	0.292715i	−0.0671535	−	0.0671535i	0.672732	−	0.739886i	$-0.265121\pi$
$19$	−0.292715	−	0.292715i	−0.0671535	−	0.0671535i	−0.739886	+	0.672732i	$0.765121\pi$
$20$	1.84163	+	0.779990i	0.411802	+	0.174411i
$21$		0			0
$22$	−8.09141	+	1.57617i	−1.72510	+	0.336040i
$23$		−	1.64818i		−	0.343670i	−0.985126	−	0.171835i	$-0.945030\pi$
$23$		−	1.64818i		−	0.343670i	0.985126	−	0.171835i	$-0.0549696\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	−0.527407	−	2.70749i	−0.103433	−	0.530983i
$27$		0			0
$28$	−5.06972	+	2.05302i	−0.958086	+	0.387984i
$29$	5.67267	+	5.67267i	1.05339	+	1.05339i	0.998492	+	0.0548963i	$0.0174828\pi$
$29$	5.67267	+	5.67267i	1.05339	+	1.05339i	0.0548963	+	0.998492i	$0.482517\pi$
$30$		0			0
$31$	3.95550			0.710430			0.355215	−	0.934785i	$-0.384408\pi$
$31$	3.95550			0.710430			0.355215	+	0.934785i	$0.384408\pi$
$32$	−5.56894	+	0.993438i	−0.984459	+	0.175617i
$33$		0			0
$34$	5.80420	+	3.91161i	0.995413	+	0.670835i
$35$	1.93381	+	1.93381i	0.326873	+	0.326873i
$36$		0			0
$37$	2.48772	−	2.48772i	0.408979	−	0.408979i	−0.472403	−	0.881382i	$-0.656613\pi$
$37$	2.48772	−	2.48772i	0.408979	−	0.408979i	0.881382	+	0.472403i	$0.156613\pi$
$38$	−0.111935	−	0.574630i	−0.0181583	−	0.0932173i
$39$		0			0
$40$	1.54332	+	2.37027i	0.244020	+	0.374772i
$41$		−	8.40843i		−	1.31318i	−0.754250	−	0.656588i	$-0.771999\pi$
$41$		−	8.40843i		−	1.31318i	0.754250	−	0.656588i	$-0.228001\pi$
$42$		0			0
$43$	−3.22713	+	3.22713i	−0.492133	+	0.492133i	−0.908978	−	0.416845i	$-0.863136\pi$
$43$	−3.22713	+	3.22713i	−0.492133	+	0.492133i	0.416845	+	0.908978i	$0.363136\pi$
$44$	−10.7349	−	4.54659i	−1.61835	−	0.685424i
$45$		0			0
$46$	1.30264	−	1.93291i	0.192064	−	0.284992i
$47$	5.19809			0.758219			0.379109	−	0.925352i	$-0.376230\pi$
$47$	5.19809			0.758219			0.379109	+	0.925352i	$0.376230\pi$
$48$		0			0
$49$	−0.479225			−0.0684607
$50$	0.790349	−	1.17275i	0.111772	−	0.165852i
$51$		0			0
$52$	1.52135	−	3.59205i	0.210973	−	0.498128i
$53$	−7.20537	+	7.20537i	−0.989733	+	0.989733i	−0.999948	−	0.0102143i	$-0.996749\pi$
$53$	−7.20537	+	7.20537i	−0.989733	+	0.989733i	0.0102143	+	0.999948i	$0.496749\pi$
$54$		0			0
$55$			5.82903i			0.785987i
$56$	−7.56812	−	1.59917i	−1.01133	−	0.213698i
$57$		0			0
$58$	2.16925	+	11.1360i	0.284836	+	1.46223i
$59$	6.41142	−	6.41142i	0.834695	−	0.834695i	−0.153459	−	0.988155i	$-0.549041\pi$
$59$	6.41142	−	6.41142i	0.834695	−	0.834695i	0.988155	+	0.153459i	$0.0490414\pi$
$60$		0			0
$61$	−3.82618	−	3.82618i	−0.489892	−	0.489892i	0.418380	−	0.908272i	$-0.362598\pi$
$61$	−3.82618	−	3.82618i	−0.489892	−	0.489892i	−0.908272	+	0.418380i	$0.862598\pi$
$62$	4.63883	+	3.12623i	0.589132	+	0.397032i
$63$		0			0
$64$	−7.31615	−	3.23635i	−0.914519	−	0.404544i
$65$	−1.95047			−0.241926
$66$		0			0
$67$	5.76044	+	5.76044i	0.703750	+	0.703750i	0.965213	−	0.261463i	$-0.0842050\pi$
$67$	5.76044	+	5.76044i	0.703750	+	0.703750i	−0.261463	+	0.965213i	$0.584205\pi$
$68$	3.71535	+	9.17470i	0.450553	+	1.11260i
$69$		0			0
$70$	0.739494	+	3.79626i	0.0883864	+	0.453740i
$71$		−	7.92245i		−	0.940222i	−0.882607	−	0.470111i	$-0.844214\pi$
$71$		−	7.92245i		−	0.940222i	0.882607	−	0.470111i	$-0.155786\pi$
$72$		0			0
$73$		−	4.36276i		−	0.510622i	−0.966859	−	0.255311i	$-0.917822\pi$
$73$		−	4.36276i		−	0.510622i	0.966859	−	0.255311i	$-0.0821779\pi$
$74$	4.88365	−	0.951312i	0.567713	−	0.110588i
$75$		0			0
$76$	0.322886	−	0.762367i	0.0370376	−	0.0874495i
$77$	−11.2722	−	11.2722i	−1.28459	−	1.28459i
$78$		0			0
$79$	−5.56087			−0.625647			−0.312824	−	0.949811i	$-0.601275\pi$
$79$	−5.56087			−0.625647			−0.312824	+	0.949811i	$0.601275\pi$
$80$	−0.0634130	+	3.99950i	−0.00708979	+	0.447157i
$81$		0			0
$82$	6.64559	−	9.86100i	0.733883	−	1.08897i
$83$	0.516191	+	0.516191i	0.0566594	+	0.0566594i	0.734869	−	0.678209i	$-0.237244\pi$
$83$	0.516191	+	0.516191i	0.0566594	+	0.0566594i	−0.678209	+	0.734869i	$0.737244\pi$
$84$		0			0
$85$	3.49962	−	3.49962i	0.379587	−	0.379587i
$86$	−6.33518	+	1.23406i	−0.683140	+	0.133073i
$87$		0			0
$88$	−8.99604	−	13.8164i	−0.958981	−	1.47283i
$89$		−	6.42236i		−	0.680768i	−0.940286	−	0.340384i	$-0.889443\pi$
$89$		−	6.42236i		−	0.680768i	0.940286	−	0.340384i	$-0.110557\pi$
$90$		0			0
$91$	3.77184	−	3.77184i	0.395396	−	0.395396i
$92$	3.05535	−	1.23729i	0.318542	−	0.128996i
$93$		0			0
$94$	6.09607	+	4.10830i	0.628761	+	0.423739i
$95$	−0.413962			−0.0424716
$96$		0			0
$97$	−9.44534			−0.959029			−0.479515	−	0.877534i	$-0.659187\pi$
$97$	−9.44534			−0.959029			−0.479515	+	0.877534i	$0.659187\pi$
$98$	−0.562012	−	0.378755i	−0.0567718	−	0.0382600i
$99$		0			0
$100$	1.85377	−	0.750696i	0.185377	−	0.0750696i
$101$	11.0542	−	11.0542i	1.09993	−	1.09993i	0.105515	−	0.994418i	$-0.466351\pi$
$101$	11.0542	−	11.0542i	1.09993	−	1.09993i	0.994418	−	0.105515i	$-0.0336491\pi$
$102$		0			0
$103$			5.46824i			0.538801i	0.963028	+	0.269401i	$0.0868256\pi$
$103$			5.46824i			0.538801i	−0.963028	+	0.269401i	$0.913174\pi$
$104$	4.62314	−	3.01019i	0.453336	−	0.295174i
$105$		0			0
$106$	−14.1449	+	2.75535i	−1.37387	+	0.267624i
$107$	−0.293704	+	0.293704i	−0.0283934	+	0.0283934i	−0.721161	−	0.692768i	$-0.756391\pi$
$107$	−0.293704	+	0.293704i	−0.0283934	+	0.0283934i	0.692768	+	0.721161i	$0.256391\pi$
$108$		0			0
$109$	10.4135	+	10.4135i	0.997429	+	0.997429i	0.999997	−	0.00256817i	$-0.000817475\pi$
$109$	10.4135	+	10.4135i	0.997429	+	0.997429i	−0.00256817	+	0.999997i	$0.500817\pi$
$110$	−4.60697	+	6.83601i	−0.439258	+	0.651788i
$111$		0			0
$112$	−7.61163	−	7.85689i	−0.719231	−	0.742406i
$113$	17.4145			1.63822			0.819108	−	0.573639i	$-0.194469\pi$
$113$	17.4145			1.63822			0.819108	+	0.573639i	$0.194469\pi$
$114$		0			0
$115$	−1.16544	−	1.16544i	−0.108678	−	0.108678i
$116$	−6.25736	+	14.7743i	−0.580982	+	1.37176i
$117$		0			0
$118$	12.5863	−	2.45175i	1.15866	−	0.225701i
$119$			13.5352i			1.24077i
$120$		0			0
$121$		−	22.9776i		−	2.08888i
$122$	−1.46314	−	7.51117i	−0.132467	−	0.680030i
$123$		0			0
$124$	2.96938	+	7.33259i	0.266658	+	0.658486i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	10.9793			0.974254			0.487127	−	0.873331i	$-0.338045\pi$
$127$	10.9793			0.974254			0.487127	+	0.873331i	$0.338045\pi$
$128$	−6.02218	−	9.57775i	−0.532291	−	0.846562i
$129$		0			0
$130$	−2.28742	−	1.54155i	−0.200620	−	0.135203i
$131$	−5.77044	−	5.77044i	−0.504166	−	0.504166i	0.408564	−	0.912730i	$-0.366030\pi$
$131$	−5.77044	−	5.77044i	−0.504166	−	0.504166i	−0.912730	+	0.408564i	$0.866030\pi$
$132$		0			0
$133$	0.800523	−	0.800523i	0.0694142	−	0.0694142i
$134$	2.20281	+	11.3083i	0.190294	+	0.976892i
$135$		0			0
$136$	−2.89402	+	13.6961i	−0.248160	+	1.17443i
$137$		−	7.18832i		−	0.614139i	−0.951687	−	0.307070i	$-0.900652\pi$
$137$		−	7.18832i		−	0.614139i	0.951687	−	0.307070i	$-0.0993484\pi$
$138$		0			0
$139$	4.91327	−	4.91327i	0.416738	−	0.416738i	−0.467340	−	0.884078i	$-0.654788\pi$
$139$	4.91327	−	4.91327i	0.416738	−	0.416738i	0.884078	+	0.467340i	$0.154788\pi$
$140$	−2.13313	+	5.03653i	−0.180282	+	0.425665i
$141$		0			0
$142$	6.26150	−	9.29107i	0.525454	−	0.779689i
$143$	11.3694			0.950754
$144$		0			0
$145$	8.02237			0.666221
$146$	3.44810	−	5.11644i	0.285367	−	0.423439i
$147$		0			0
$148$	6.47918	+	2.74414i	0.532585	+	0.225567i
$149$	−9.76620	+	9.76620i	−0.800078	+	0.800078i	−0.983107	−	0.183029i	$-0.941410\pi$
$149$	−9.76620	+	9.76620i	−0.800078	+	0.800078i	0.183029	+	0.983107i	$0.441410\pi$
$150$		0			0
$151$		−	1.90755i		−	0.155234i	−0.996983	−	0.0776169i	$-0.975269\pi$
$151$		−	1.90755i		−	0.155234i	0.996983	−	0.0776169i	$-0.0247311\pi$
$152$	0.981202	−	0.638874i	0.0795860	−	0.0518196i
$153$		0			0
$154$	−4.31053	−	22.1285i	−0.347353	−	1.78317i
$155$	2.79696	−	2.79696i	0.224658	−	0.224658i
$156$		0			0
$157$	−4.41296	−	4.41296i	−0.352192	−	0.352192i	0.508732	−	0.860925i	$-0.330114\pi$
$157$	−4.41296	−	4.41296i	−0.352192	−	0.352192i	−0.860925	+	0.508732i	$0.830114\pi$
$158$	−6.52153	−	4.39503i	−0.518825	−	0.349650i
$159$		0			0
$160$	−3.23537	+	4.64030i	−0.255778	+	0.366848i
$161$	4.50748			0.355240
$162$		0			0
$163$	−3.58912	−	3.58912i	−0.281122	−	0.281122i	0.552435	−	0.833556i	$-0.313699\pi$
$163$	−3.58912	−	3.58912i	−0.281122	−	0.281122i	−0.833556	+	0.552435i	$0.813699\pi$
$164$	15.5873	−	6.31217i	1.21716	−	0.492898i
$165$		0			0
$166$	0.197393	+	1.01334i	0.0153207	+	0.0786501i
$167$			17.5993i			1.36188i	0.732341	+	0.680938i	$0.238428\pi$
$167$			17.5993i			1.36188i	−0.732341	+	0.680938i	$0.761572\pi$
$168$		0			0
$169$		−	9.19566i		−	0.707359i
$170$	6.87012	−	1.33827i	0.526914	−	0.102640i
$171$		0			0
$172$	−8.40494	−	3.55976i	−0.640871	−	0.271429i
$173$	7.32377	+	7.32377i	0.556816	+	0.556816i	0.928400	−	0.371584i	$-0.121185\pi$
$173$	7.32377	+	7.32377i	0.556816	+	0.556816i	−0.371584	+	0.928400i	$0.621185\pi$
$174$		0			0
$175$	2.73482			0.206733
$176$	0.369636	−	23.3132i	0.0278624	−	1.75730i
$177$		0			0
$178$	5.07590	−	7.53183i	0.380455	−	0.564535i
$179$	−6.42849	−	6.42849i	−0.480488	−	0.480488i	0.424800	−	0.905287i	$-0.360345\pi$
$179$	−6.42849	−	6.42849i	−0.480488	−	0.480488i	−0.905287	+	0.424800i	$0.860345\pi$
$180$		0			0
$181$	−3.67884	+	3.67884i	−0.273446	+	0.273446i	−0.830486	−	0.557040i	$-0.811937\pi$
$181$	−3.67884	+	3.67884i	−0.273446	+	0.273446i	0.557040	+	0.830486i	$0.311937\pi$
$182$	7.40450	−	1.44236i	0.548858	−	0.106915i
$183$		0			0
$184$	4.56106	+	0.963766i	0.336246	+	0.0710498i
$185$		−	3.51817i		−	0.258661i
$186$		0			0
$187$	−20.3994	+	20.3994i	−1.49175	+	1.49175i
$188$	3.90218	+	9.63605i	0.284596	+	0.702781i
$189$		0			0
$190$	−0.485475	−	0.327175i	−0.0352201	−	0.0237357i
$191$	5.39093			0.390074			0.195037	−	0.980796i	$-0.437517\pi$
$191$	5.39093			0.390074			0.195037	+	0.980796i	$0.437517\pi$
$192$		0			0
$193$	−3.53818			−0.254684			−0.127342	−	0.991859i	$-0.540645\pi$
$193$	−3.53818			−0.254684			−0.127342	+	0.991859i	$0.540645\pi$
$194$	−11.0770	−	7.46512i	−0.795286	−	0.535964i
$195$		0			0
$196$	−0.359752	−	0.888371i	−0.0256966	−	0.0634551i
$197$	−10.6900	+	10.6900i	−0.761627	+	0.761627i	−0.976616	−	0.214989i	$-0.931028\pi$
$197$	−10.6900	+	10.6900i	−0.761627	+	0.761627i	0.214989	+	0.976616i	$0.431028\pi$
$198$		0			0
$199$			15.6543i			1.10971i	0.831948	+	0.554853i	$0.187226\pi$
$199$			15.6543i			1.10971i	−0.831948	+	0.554853i	$0.812774\pi$
$200$	2.76732	+	0.584744i	0.195679	+	0.0413476i
$201$		0			0
$202$	21.7005	−	4.22715i	1.52684	−	0.297421i
$203$	−15.5137	+	15.5137i	−1.08885	+	1.08885i
$204$		0			0
$205$	−5.94566	−	5.94566i	−0.415263	−	0.415263i
$206$	−4.32182	+	6.41289i	−0.301115	+	0.446807i
$207$		0			0
$208$	7.80090	+	0.123685i	0.540895	+	0.00857603i
$209$	2.41300			0.166911
$210$		0			0
$211$	−19.9359	−	19.9359i	−1.37244	−	1.37244i	−0.856809	−	0.515634i	$-0.827556\pi$
$211$	−19.9359	−	19.9359i	−1.37244	−	1.37244i	−0.515634	−	0.856809i	$-0.672444\pi$
$212$	−18.7661	−	7.94804i	−1.28886	−	0.545874i
$213$		0			0
$214$	−0.576570	+	0.112313i	−0.0394135	+	0.00767757i
$215$			4.56385i			0.311252i
$216$		0			0
$217$			10.8176i			0.734345i
$218$	3.98214	+	20.4427i	0.269704	+	1.38455i
$219$		0			0
$220$	−10.8057	+	4.37583i	−0.728519	+	0.295019i
$221$	−6.82591	−	6.82591i	−0.459161	−	0.459161i
$222$		0			0
$223$	21.2173			1.42081			0.710406	−	0.703792i	$-0.248511\pi$
$223$	21.2173			1.42081			0.710406	+	0.703792i	$0.248511\pi$
$224$	−2.71687	−	15.2300i	−0.181529	−	1.01760i
$225$		0			0
$226$	20.4229	+	13.7635i	1.35851	+	0.915536i
$227$	−12.0356	−	12.0356i	−0.798832	−	0.798832i	0.184079	−	0.982911i	$-0.441070\pi$
$227$	−12.0356	−	12.0356i	−0.798832	−	0.798832i	−0.982911	+	0.184079i	$0.941070\pi$
$228$		0			0
$229$	6.70809	−	6.70809i	0.443283	−	0.443283i	−0.449831	−	0.893114i	$-0.648516\pi$
$229$	6.70809	−	6.70809i	0.443283	−	0.443283i	0.893114	+	0.449831i	$0.148516\pi$
$230$	−0.445669	−	2.28788i	−0.0293865	−	0.150858i
$231$		0			0
$232$	−19.0152	+	12.3810i	−1.24841	+	0.812856i
$233$		−	5.40431i		−	0.354048i	−0.984207	−	0.177024i	$-0.943353\pi$
$233$		−	5.40431i		−	0.354048i	0.984207	−	0.177024i	$-0.0566470\pi$
$234$		0			0
$235$	3.67560	−	3.67560i	0.239770	−	0.239770i
$236$	16.6983	+	7.07226i	1.08697	+	0.460365i
$237$		0			0
$238$	−10.6975	+	15.8734i	−0.693418	+	1.02892i
$239$	1.86569			0.120681			0.0603406	−	0.998178i	$-0.480781\pi$
$239$	1.86569			0.120681			0.0603406	+	0.998178i	$0.480781\pi$
$240$		0			0
$241$	16.3740			1.05474			0.527369	−	0.849636i	$-0.323178\pi$
$241$	16.3740			1.05474			0.527369	+	0.849636i	$0.323178\pi$
$242$	18.1604	−	26.9471i	1.16739	−	1.73222i
$243$		0			0
$244$	4.22055	−	9.96514i	0.270193	−	0.637953i
$245$	−0.338863	+	0.338863i	−0.0216492	+	0.0216492i
$246$		0			0
$247$			0.807421i			0.0513750i
$248$	−2.31296	+	10.9462i	−0.146873	+	0.695082i
$249$		0			0
$250$	−0.270400	−	1.38812i	−0.0171016	−	0.0877926i
$251$	−3.01154	+	3.01154i	−0.190087	+	0.190087i	−0.795734	−	0.605647i	$-0.792914\pi$
$251$	−3.01154	+	3.01154i	−0.190087	+	0.190087i	0.605647	+	0.795734i	$0.292914\pi$
$252$		0			0
$253$	6.79340	+	6.79340i	0.427098	+	0.427098i
$254$	12.8760	+	8.67747i	0.807911	+	0.544473i
$255$		0			0
$256$	0.507240	−	15.9920i	0.0317025	−	0.999497i
$257$	−22.7407			−1.41853			−0.709263	−	0.704944i	$-0.750972\pi$
$257$	−22.7407			−1.41853			−0.709263	+	0.704944i	$0.750972\pi$
$258$		0			0
$259$	6.80346	+	6.80346i	0.422747	+	0.422747i
$260$	−1.46421	−	3.61572i	−0.0908065	−	0.224237i
$261$		0			0
$262$	−2.20663	−	11.3280i	−0.136326	−	0.699844i
$263$			12.0300i			0.741805i	0.928672	+	0.370902i	$0.120952\pi$
$263$			12.0300i			0.741805i	−0.928672	+	0.370902i	$0.879048\pi$
$264$		0			0
$265$			10.1899i			0.625962i
$266$	1.57151	−	0.306122i	0.0963554	−	0.0187696i
$267$		0			0
$268$	−6.35419	+	15.0029i	−0.388144	+	0.916446i
$269$	−4.90068	−	4.90068i	−0.298800	−	0.298800i	0.541744	−	0.840544i	$-0.317764\pi$
$269$	−4.90068	−	4.90068i	−0.298800	−	0.298800i	−0.840544	+	0.541744i	$0.817764\pi$
$270$		0			0
$271$	−4.14616			−0.251862			−0.125931	−	0.992039i	$-0.540192\pi$
$271$	−4.14616			−0.251862			−0.125931	+	0.992039i	$0.540192\pi$
$272$	−14.2187	+	13.7748i	−0.862133	+	0.835221i
$273$		0			0
$274$	5.68128	−	8.43011i	0.343219	−	0.509282i
$275$	4.12175	+	4.12175i	0.248551	+	0.248551i
$276$		0			0
$277$	−10.4815	+	10.4815i	−0.629775	+	0.629775i	−0.948011	−	0.318236i	$-0.896909\pi$
$277$	−10.4815	+	10.4815i	−0.629775	+	0.629775i	0.318236	+	0.948011i	$0.396909\pi$
$278$	9.64525	−	1.87885i	0.578483	−	0.112686i
$279$		0			0
$280$	−6.48225	+	4.22069i	−0.387389	+	0.252234i
$281$		−	3.51927i		−	0.209942i	−0.994475	−	0.104971i	$-0.966525\pi$
$281$		−	3.51927i		−	0.209942i	0.994475	−	0.104971i	$-0.0334750\pi$
$282$		0			0
$283$	−2.88462	+	2.88462i	−0.171473	+	0.171473i	−0.787626	−	0.616153i	$-0.788690\pi$
$283$	−2.88462	+	2.88462i	−0.171473	+	0.171473i	0.616153	+	0.787626i	$0.288690\pi$
$284$	14.6864	−	5.94735i	0.871477	−	0.352910i
$285$		0			0
$286$	13.3334	+	8.98577i	0.788423	+	0.531340i
$287$	22.9955			1.35738
$288$		0			0
$289$	7.49472			0.440866
$290$	9.40825	+	6.34047i	0.552471	+	0.372325i
$291$		0			0
$292$	8.08754	−	3.27511i	0.473288	−	0.191661i
$293$	−3.92351	+	3.92351i	−0.229214	+	0.229214i	−0.812364	−	0.583150i	$-0.801820\pi$
$293$	−3.92351	+	3.92351i	−0.229214	+	0.229214i	0.583150	+	0.812364i	$0.301820\pi$
$294$		0			0
$295$		−	9.06711i		−	0.527908i
$296$	5.42965	+	8.33901i	0.315592	+	0.484695i
$297$		0			0
$298$	−19.1720	+	3.73462i	−1.11061	+	0.216341i
$299$	−2.27316	+	2.27316i	−0.131460	+	0.131460i
$300$		0			0
$301$	−8.82561	−	8.82561i	−0.508700	−	0.508700i
$302$	1.50763	−	2.23708i	0.0867542	−	0.128729i
$303$		0			0
$304$	1.65564	+	0.0262506i	0.0949575	+	0.00150557i
$305$	−5.41103			−0.309835
$306$		0			0
$307$	−0.196482	−	0.196482i	−0.0112138	−	0.0112138i	0.701478	−	0.712691i	$-0.252524\pi$
$307$	−0.196482	−	0.196482i	−0.0112138	−	0.0112138i	−0.712691	+	0.701478i	$0.752524\pi$
$308$	12.4341	−	29.3581i	0.708498	−	1.67283i
$309$		0			0
$310$	5.49072	−	1.06957i	0.311852	−	0.0607473i
$311$			2.52927i			0.143422i	0.997425	+	0.0717110i	$0.0228459\pi$
$311$			2.52927i			0.143422i	−0.997425	+	0.0717110i	$0.977154\pi$
$312$		0			0
$313$			3.84874i			0.217543i	0.994067	+	0.108772i	$0.0346917\pi$
$313$			3.84874i			0.217543i	−0.994067	+	0.108772i	$0.965308\pi$
$314$	−1.68753	−	8.66308i	−0.0952327	−	0.488886i
$315$		0			0
$316$	−4.17453	−	10.3086i	−0.234835	−	0.579902i
$317$	6.78901	+	6.78901i	0.381309	+	0.381309i	0.871574	−	0.490265i	$-0.163100\pi$
$317$	6.78901	+	6.78901i	0.381309	+	0.381309i	−0.490265	+	0.871574i	$0.663100\pi$
$318$		0			0
$319$	−46.7627			−2.61821
$320$	−7.46174	+	2.88485i	−0.417124	+	0.161268i
$321$		0			0
$322$	5.28616	+	3.56249i	0.294586	+	0.198530i
$323$	−1.44871	−	1.44871i	−0.0806085	−	0.0806085i
$324$		0			0
$325$	−1.37919	+	1.37919i	−0.0765038	+	0.0765038i
$326$	−1.37249	−	7.04581i	−0.0760152	−	0.390231i
$327$		0			0
$328$	23.2688	+	4.91678i	1.28481	+	0.271484i
$329$			14.2158i			0.783743i
$330$		0			0
$331$	1.79195	−	1.79195i	0.0984944	−	0.0984944i	−0.656143	−	0.754637i	$-0.727813\pi$
$331$	1.79195	−	1.79195i	0.0984944	−	0.0984944i	0.754637	+	0.656143i	$0.227813\pi$
$332$	−0.569396	+	1.34440i	−0.0312497	+	0.0737836i
$333$		0			0
$334$	−13.9096	+	20.6396i	−0.761100	+	1.12935i
$335$	8.14650			0.445091
$336$		0			0
$337$	16.1071			0.877411			0.438706	−	0.898631i	$-0.355437\pi$
$337$	16.1071			0.877411			0.438706	+	0.898631i	$0.355437\pi$
$338$	7.26779	−	10.7842i	0.395315	−	0.586585i
$339$		0			0
$340$	9.11464	+	3.86034i	0.494311	+	0.209356i
$341$	−16.3036	+	16.3036i	−0.882889	+	0.882889i
$342$		0			0
$343$			17.8331i			0.962898i
$344$	−7.04347	−	10.8176i	−0.379758	−	0.583243i
$345$		0			0
$346$	2.80063	+	14.3773i	0.150563	+	0.772929i
$347$	−12.6577	+	12.6577i	−0.679502	+	0.679502i	−0.959888	−	0.280385i	$-0.909538\pi$
$347$	−12.6577	+	12.6577i	−0.679502	+	0.679502i	0.280385	+	0.959888i	$0.409538\pi$
$348$		0			0
$349$	−16.3020	−	16.3020i	−0.872627	−	0.872627i	0.120131	−	0.992758i	$-0.461669\pi$
$349$	−16.3020	−	16.3020i	−0.872627	−	0.872627i	−0.992758	+	0.120131i	$0.961669\pi$
$350$	3.20726	+	2.16146i	0.171435	+	0.115535i
$351$		0			0
$352$	18.8591	−	27.0485i	1.00519	−	1.44169i
$353$	13.2637			0.705954			0.352977	−	0.935632i	$-0.385169\pi$
$353$	13.2637			0.705954			0.352977	+	0.935632i	$0.385169\pi$
$354$		0			0
$355$	−5.60202	−	5.60202i	−0.297324	−	0.297324i
$356$	11.9056	−	4.82124i	0.630993	−	0.255525i
$357$		0			0
$358$	−2.45827	−	12.6198i	−0.129924	−	0.666976i
$359$		−	13.3561i		−	0.704906i	−0.935830	−	0.352453i	$-0.885348\pi$
$359$		−	13.3561i		−	0.704906i	0.935830	−	0.352453i	$-0.114652\pi$
$360$		0			0
$361$		−	18.8286i		−	0.990981i
$362$	−7.22194	+	1.40680i	−0.379577	+	0.0739398i
$363$		0			0
$364$	9.82361	+	4.16061i	0.514897	+	0.218075i
$365$	−3.08494	−	3.08494i	−0.161473	−	0.161473i
$366$		0			0
$367$	11.8938			0.620852			0.310426	−	0.950598i	$-0.399528\pi$
$367$	11.8938			0.620852			0.310426	+	0.950598i	$0.399528\pi$
$368$	4.58728	+	4.73509i	0.239129	+	0.246834i
$369$		0			0
$370$	2.78058	−	4.12594i	0.144556	−	0.214498i
$371$	−19.7054	−	19.7054i	−1.02305	−	1.02305i
$372$		0			0
$373$	−19.0494	+	19.0494i	−0.986342	+	0.986342i	−0.999908	−	0.0135655i	$-0.995682\pi$
$373$	−19.0494	+	19.0494i	−0.986342	+	0.986342i	0.0135655	+	0.999908i	$0.495682\pi$
$374$	−40.0461	+	7.80080i	−2.07074	+	0.403370i
$375$		0			0
$376$	−3.03955	+	14.3848i	−0.156753	+	0.741839i
$377$		−	15.6474i		−	0.805882i
$378$		0			0
$379$	−4.64554	+	4.64554i	−0.238625	+	0.238625i	−0.816281	−	0.577655i	$-0.803968\pi$
$379$	−4.64554	+	4.64554i	−0.238625	+	0.238625i	0.577655	+	0.816281i	$0.303968\pi$
$380$	−0.310760	−	0.767390i	−0.0159416	−	0.0393663i
$381$		0			0
$382$	6.32222	+	4.26072i	0.323473	+	0.217997i
$383$	−38.5131			−1.96793			−0.983964	−	0.178366i	$-0.942919\pi$
$383$	−38.5131			−1.96793			−0.983964	+	0.178366i	$0.942919\pi$
$384$		0			0
$385$	−15.9413			−0.812446
$386$	−4.14941	−	2.79640i	−0.211200	−	0.142333i
$387$		0			0
$388$	−7.09058	−	17.5095i	−0.359970	−	0.888909i
$389$	0.903192	−	0.903192i	0.0457937	−	0.0457937i	−0.683839	−	0.729633i	$-0.739691\pi$
$389$	0.903192	−	0.903192i	0.0457937	−	0.0457937i	0.729633	+	0.683839i	$0.239691\pi$
$390$		0			0
$391$		−	8.15722i		−	0.412528i
$392$	0.280224	−	1.32617i	0.0141534	−	0.0669817i
$393$		0			0
$394$	−20.9855	+	4.08787i	−1.05723	+	0.205944i
$395$	−3.93213	+	3.93213i	−0.197847	+	0.197847i
$396$		0			0
$397$	4.44748	+	4.44748i	0.223212	+	0.223212i	0.809850	−	0.586637i	$-0.199549\pi$
$397$	4.44748	+	4.44748i	0.223212	+	0.223212i	−0.586637	+	0.809850i	$0.699549\pi$
$398$	−12.3724	+	18.3587i	−0.620172	+	0.920237i
$399$		0			0
$400$	2.78323	+	2.87291i	0.139162	+	0.143646i
$401$	−27.3379			−1.36519			−0.682596	−	0.730796i	$-0.739149\pi$
$401$	−27.3379			−1.36519			−0.682596	+	0.730796i	$0.739149\pi$
$402$		0			0
$403$	−5.45540	−	5.45540i	−0.271753	−	0.271753i
$404$	28.7902	+	12.1936i	1.43237	+	0.606652i
$405$		0			0
$406$	−30.4550	+	5.93249i	−1.51146	+	0.294425i
$407$			20.5075i			1.01652i
$408$		0			0
$409$			38.6889i			1.91304i	0.291661	+	0.956522i	$0.405792\pi$
$409$			38.6889i			1.91304i	−0.291661	+	0.956522i	$0.594208\pi$
$410$	−2.27364	−	11.6719i	−0.112287	−	0.576435i
$411$		0			0
$412$	−10.1368	+	4.10498i	−0.499406	+	0.202238i
$413$	17.5341	+	17.5341i	0.862794	+	0.862794i
$414$		0			0
$415$	0.730005			0.0358345
$416$	9.05077	+	6.31049i	0.443751	+	0.309397i
$417$		0			0
$418$	2.82985	+	1.90711i	0.138413	+	0.0932799i
$419$	−7.41439	−	7.41439i	−0.362217	−	0.362217i	0.502412	−	0.864628i	$-0.332446\pi$
$419$	−7.41439	−	7.41439i	−0.362217	−	0.362217i	−0.864628	+	0.502412i	$0.832446\pi$
$420$		0			0
$421$	−10.3279	+	10.3279i	−0.503351	+	0.503351i	−0.912478	−	0.409127i	$-0.865833\pi$
$421$	−10.3279	+	10.3279i	−0.503351	+	0.503351i	0.409127	+	0.912478i	$0.365833\pi$
$422$	−7.62354	−	39.1362i	−0.371108	−	1.90512i
$423$		0			0
$424$	−15.7263	−	24.1529i	−0.763736	−	1.17297i
$425$		−	4.94921i		−	0.240072i
$426$		0			0
$427$	10.4639	−	10.4639i	0.506383	−	0.506383i
$428$	−0.764940	−	0.323976i	−0.0369748	−	0.0156600i
$429$		0			0
$430$	−3.60704	+	5.35227i	−0.173947	+	0.258109i
$431$	14.8644			0.715991			0.357995	−	0.933723i	$-0.383460\pi$
$431$	14.8644			0.715991			0.357995	+	0.933723i	$0.383460\pi$
$432$		0			0
$433$	−4.96284			−0.238499			−0.119249	−	0.992864i	$-0.538049\pi$
$433$	−4.96284			−0.238499			−0.119249	+	0.992864i	$0.538049\pi$
$434$	−8.54967	+	12.6863i	−0.410397	+	0.608964i
$435$		0			0
$436$	−11.4868	+	27.1215i	−0.550118	+	1.29888i
$437$	−0.482449	+	0.482449i	−0.0230787	+	0.0230787i
$438$		0			0
$439$		−	13.7348i		−	0.655527i	−0.944760	−	0.327763i	$-0.893705\pi$
$439$		−	13.7348i		−	0.655527i	0.944760	−	0.327763i	$-0.106295\pi$
$440$	−16.1308	−	3.40849i	−0.769007	−	0.162494i
$441$		0			0
$442$	−2.61025	−	13.4000i	−0.124157	−	0.637371i
$443$	7.62584	−	7.62584i	0.362315	−	0.362315i	−0.502350	−	0.864664i	$-0.667531\pi$
$443$	7.62584	−	7.62584i	0.362315	−	0.362315i	0.864664	+	0.502350i	$0.167531\pi$
$444$		0			0
$445$	−4.54129	−	4.54129i	−0.215278	−	0.215278i
$446$	24.8826	+	16.7690i	1.17822	+	0.794037i
$447$		0			0
$448$	8.85083	−	20.0083i	0.418162	−	0.945305i
$449$	15.8544			0.748215			0.374108	−	0.927385i	$-0.377949\pi$
$449$	15.8544			0.748215			0.374108	+	0.927385i	$0.377949\pi$
$450$		0			0
$451$	34.6574	+	34.6574i	1.63195	+	1.63195i
$452$	13.0730	+	32.2824i	0.614901	+	1.51844i
$453$		0			0
$454$	−4.60246	−	23.6271i	−0.216004	−	1.10888i
$455$		−	5.33418i		−	0.250070i
$456$		0			0
$457$		−	14.1978i		−	0.664144i	−0.943254	−	0.332072i	$-0.892252\pi$
$457$		−	14.1978i		−	0.664144i	0.943254	−	0.332072i	$-0.107748\pi$
$458$	13.1687	−	2.56519i	0.615331	−	0.119864i
$459$		0			0
$460$	1.28557	−	3.03535i	0.0599399	−	0.141524i
$461$	22.8952	+	22.8952i	1.06634	+	1.06634i	0.997638	+	0.0686980i	$0.0218845\pi$
$461$	22.8952	+	22.8952i	1.06634	+	1.06634i	0.0686980	+	0.997638i	$0.478116\pi$
$462$		0			0
$463$	25.0175			1.16266			0.581330	−	0.813668i	$-0.302533\pi$
$463$	25.0175			1.16266			0.581330	+	0.813668i	$0.302533\pi$
$464$	−32.0854	−	0.508722i	−1.48953	−	0.0236168i
$465$		0			0
$466$	4.27129	−	6.33792i	0.197864	−	0.293598i
$467$	23.5446	+	23.5446i	1.08951	+	1.08951i	0.995578	+	0.0939334i	$0.0299441\pi$
$467$	23.5446	+	23.5446i	1.08951	+	1.08951i	0.0939334	+	0.995578i	$0.470056\pi$
$468$		0			0
$469$	−15.7538	+	15.7538i	−0.727441	+	0.727441i
$470$	7.21558	−	1.40556i	0.332830	−	0.0648337i
$471$		0			0
$472$	13.9934	+	21.4915i	0.644100	+	0.989226i
$473$		−	26.6028i		−	1.22320i
$474$		0			0
$475$	−0.292715	+	0.292715i	−0.0134307	+	0.0134307i
$476$	−25.0911	+	10.1608i	−1.15005	+	0.465720i
$477$		0			0
$478$	2.18799	+	1.47454i	0.100076	+	0.0674441i
$479$	−39.3416			−1.79756			−0.898781	−	0.438398i	$-0.855546\pi$
$479$	−39.3416			−1.79756			−0.898781	+	0.438398i	$0.855546\pi$
$480$		0			0
$481$	−6.86209			−0.312884
$482$	19.2026	+	12.9411i	0.874654	+	0.589453i
$483$		0			0
$484$	42.5952	−	17.2492i	1.93615	−	0.784055i
$485$	−6.67886	+	6.67886i	−0.303272	+	0.303272i
$486$		0			0
$487$			25.6970i			1.16444i	0.813030	+	0.582222i	$0.197816\pi$
$487$			25.6970i			1.16444i	−0.813030	+	0.582222i	$0.802184\pi$
$488$	12.8256	−	8.35093i	0.580588	−	0.378029i
$489$		0			0
$490$	−0.665222	+	0.129582i	−0.0300517	+	0.00585393i
$491$	29.0344	−	29.0344i	1.31030	−	1.31030i	0.389113	−	0.921190i	$-0.372781\pi$
$491$	29.0344	−	29.0344i	1.31030	−	1.31030i	0.921190	−	0.389113i	$-0.127219\pi$
$492$		0			0
$493$	28.0753	+	28.0753i	1.26445	+	1.26445i
$494$	−0.638145	+	0.946905i	−0.0287115	+	0.0426033i
$495$		0			0
$496$	−11.3638	+	11.0091i	−0.510250	+	0.494323i
$497$	21.6665			0.971873
$498$		0			0
$499$	−7.89904	−	7.89904i	−0.353610	−	0.353610i	0.507841	−	0.861451i	$-0.330444\pi$
$499$	−7.89904	−	7.89904i	−0.353610	−	0.353610i	−0.861451	+	0.507841i	$0.830444\pi$
$500$	0.779990	−	1.84163i	0.0348822	−	0.0823604i
$501$		0			0
$502$	−5.91197	+	1.15162i	−0.263864	+	0.0513995i
$503$		−	9.53668i		−	0.425220i	−0.977137	−	0.212610i	$-0.931804\pi$
$503$		−	9.53668i		−	0.425220i	0.977137	−	0.212610i	$-0.0681963\pi$
$504$		0			0
$505$		−	15.6330i		−	0.695658i
$506$	2.59782	+	13.3361i	0.115487	+	0.592864i
$507$		0			0
$508$	8.24211	+	20.3531i	0.365684	+	0.903021i
$509$	4.24956	+	4.24956i	0.188358	+	0.188358i	0.794986	−	0.606628i	$-0.207478\pi$
$509$	4.24956	+	4.24956i	0.188358	+	0.188358i	−0.606628	+	0.794986i	$0.707478\pi$
$510$		0			0
$511$	11.9313			0.527812
$512$	13.2341	−	18.3537i	0.584870	−	0.811127i
$513$		0			0
$514$	−26.6692	−	17.9731i	−1.17633	−	0.792759i
$515$	3.86663	+	3.86663i	0.170384	+	0.170384i
$516$		0			0
$517$	−21.4252	+	21.4252i	−0.942280	+	0.942280i
$518$	2.60166	+	13.3559i	0.114311	+	0.586824i
$519$		0			0
$520$	1.14053	−	5.39758i	0.0500154	−	0.236700i
$521$			9.71766i			0.425739i	0.977081	+	0.212869i	$0.0682809\pi$
$521$			9.71766i			0.425739i	−0.977081	+	0.212869i	$0.931719\pi$
$522$		0			0
$523$	−4.62580	+	4.62580i	−0.202272	+	0.202272i	−0.800973	−	0.598701i	$-0.795684\pi$
$523$	−4.62580	+	4.62580i	−0.202272	+	0.202272i	0.598701	+	0.800973i	$0.295684\pi$
$524$	6.36521	−	15.0289i	0.278066	−	0.656541i
$525$		0			0
$526$	−9.50794	+	14.1083i	−0.414566	+	0.615150i
$527$	19.5766			0.852772
$528$		0			0
$529$	20.2835			0.881891
$530$	−8.05360	+	11.9503i	−0.349826	+	0.519086i
$531$		0			0
$532$	2.08493	+	0.883035i	0.0903933	+	0.0382844i
$533$	−11.5968	+	11.5968i	−0.502314	+	0.502314i
$534$		0			0
$535$			0.415360i			0.0179576i
$536$	−19.3094	+	12.5726i	−0.834039	+	0.543055i
$537$		0			0
$538$	−1.87403	−	9.62053i	−0.0807953	−	0.414771i
$539$	1.97524	−	1.97524i	0.0850798	−	0.0850798i
$540$		0			0
$541$	24.0206	+	24.0206i	1.03272	+	1.03272i	0.999446	+	0.0332788i	$0.0105949\pi$
$541$	24.0206	+	24.0206i	1.03272	+	1.03272i	0.0332788	+	0.999446i	$0.489405\pi$
$542$	−4.86242	−	3.27692i	−0.208859	−	0.140756i
$543$		0			0
$544$	−27.5619	+	4.91674i	−1.18171	+	0.210803i
$545$	14.7269			0.630829
$546$		0			0
$547$	4.63900	+	4.63900i	0.198349	+	0.198349i	0.799292	−	0.600943i	$-0.205208\pi$
$547$	4.63900	+	4.63900i	0.198349	+	0.198349i	−0.600943	+	0.799292i	$0.705208\pi$
$548$	13.3255	−	5.39624i	0.569236	−	0.230516i
$549$		0			0
$550$	1.57617	+	8.09141i	0.0672081	+	0.345019i
$551$		−	3.32096i		−	0.141477i
$552$		0			0
$553$		−	15.2080i		−	0.646709i
$554$	−20.5763	+	4.00818i	−0.874205	+	0.170291i
$555$		0			0
$556$	12.7964	+	5.41969i	0.542690	+	0.229846i
$557$	−13.6258	−	13.6258i	−0.577345	−	0.577345i	0.356826	−	0.934171i	$-0.383859\pi$
$557$	−13.6258	−	13.6258i	−0.577345	−	0.577345i	−0.934171	+	0.356826i	$0.883859\pi$
$558$		0			0
$559$	8.90166			0.376500
$560$	−10.9379	−	0.173423i	−0.462210	−	0.00732846i
$561$		0			0
$562$	2.78145	−	4.12723i	0.117328	−	0.174097i
$563$	−28.0885	−	28.0885i	−1.18379	−	1.18379i	−0.978755	−	0.205035i	$-0.934269\pi$
$563$	−28.0885	−	28.0885i	−1.18379	−	1.18379i	−0.205035	−	0.978755i	$-0.565731\pi$
$564$		0			0
$565$	12.3139	−	12.3139i	0.518050	−	0.518050i
$566$	−5.66280	+	1.10309i	−0.238025	+	0.0463662i
$567$		0			0
$568$	21.9240	+	4.63261i	0.919910	+	0.194380i
$569$			42.3770i			1.77654i	0.459326	+	0.888268i	$0.348091\pi$
$569$			42.3770i			1.77654i	−0.459326	+	0.888268i	$0.651909\pi$
$570$		0			0
$571$	7.99217	−	7.99217i	0.334462	−	0.334462i	−0.519816	−	0.854278i	$-0.674000\pi$
$571$	7.99217	−	7.99217i	0.334462	−	0.334462i	0.854278	+	0.519816i	$0.174000\pi$
$572$	8.53493	+	21.0762i	0.356863	+	0.881239i
$573$		0			0
$574$	26.9680	+	18.1745i	1.12562	+	0.758588i
$575$	−1.64818			−0.0687341
$576$		0			0
$577$	−20.4651			−0.851972			−0.425986	−	0.904730i	$-0.640073\pi$
$577$	−20.4651			−0.851972			−0.425986	+	0.904730i	$0.640073\pi$
$578$	8.78945	+	5.92345i	0.365593	+	0.246383i
$579$		0			0
$580$	6.02236	+	14.8716i	0.250065	+	0.617510i
$581$	−1.41169	+	1.41169i	−0.0585667	+	0.0585667i
$582$		0			0
$583$		−	59.3974i		−	2.45999i
$584$	12.0732	+	2.55110i	0.499591	+	0.105565i
$585$		0			0
$586$	−7.70224	+	1.50036i	−0.318177	+	0.0619793i
$587$	−0.429976	+	0.429976i	−0.0177470	+	0.0177470i	−0.715925	−	0.698178i	$-0.753995\pi$
$587$	−0.429976	+	0.429976i	−0.0177470	+	0.0177470i	0.698178	+	0.715925i	$0.253995\pi$
$588$		0			0
$589$	−1.15784	−	1.15784i	−0.0477079	−	0.0477079i
$590$	7.16619	−	10.6335i	0.295027	−	0.437773i
$591$		0			0
$592$	−0.223098	+	14.0709i	−0.00916926	+	0.578311i
$593$	−37.9620			−1.55891			−0.779455	−	0.626458i	$-0.784504\pi$
$593$	−37.9620			−1.55891			−0.779455	+	0.626458i	$0.784504\pi$
$594$		0			0
$595$	9.57083	+	9.57083i	0.392366	+	0.392366i
$596$	−25.4357	−	10.7728i	−1.04189	−	0.441272i
$597$		0			0
$598$	−4.46245	+	0.869264i	−0.182483	+	0.0355468i
$599$		−	13.7108i		−	0.560207i	−0.959970	−	0.280104i	$-0.909631\pi$
$599$		−	13.7108i		−	0.560207i	0.959970	−	0.280104i	$-0.0903688\pi$
$600$		0			0
$601$			2.84070i			0.115875i	0.998320	+	0.0579373i	$0.0184523\pi$
$601$			2.84070i			0.115875i	−0.998320	+	0.0579373i	$0.981548\pi$
$602$	−3.37494	−	17.3256i	−0.137552	−	0.706138i
$603$		0			0
$604$	3.53615	−	1.43199i	0.143884	−	0.0582667i
$605$	−16.2476	−	16.2476i	−0.660561	−	0.660561i
$606$		0			0
$607$	−42.8562			−1.73948			−0.869740	−	0.493510i	$-0.835713\pi$
$607$	−42.8562			−1.73948			−0.869740	+	0.493510i	$0.835713\pi$
$608$	1.92091	+	1.33932i	0.0779032	+	0.0543166i
$609$		0			0
$610$	−6.34580	−	4.27661i	−0.256934	−	0.173155i
$611$	−7.16916	−	7.16916i	−0.290033	−	0.290033i
$612$		0			0
$613$	5.48393	−	5.48393i	0.221494	−	0.221494i	−0.587633	−	0.809127i	$-0.699940\pi$
$613$	5.48393	−	5.48393i	0.221494	−	0.221494i	0.809127	+	0.587633i	$0.199940\pi$
$614$	−0.0751353	−	0.385714i	−0.00303221	−	0.0155661i
$615$		0			0
$616$	37.7853	−	24.6025i	1.52241	−	0.991264i
$617$			22.2539i			0.895908i	0.894057	+	0.447954i	$0.147847\pi$
$617$			22.2539i			0.895908i	−0.894057	+	0.447954i	$0.852153\pi$
$618$		0			0
$619$	10.0974	−	10.0974i	0.405849	−	0.405849i	−0.474439	−	0.880288i	$-0.657349\pi$
$619$	10.0974	−	10.0974i	0.405849	−	0.405849i	0.880288	+	0.474439i	$0.157349\pi$
$620$	7.28459	+	3.08525i	0.292556	+	0.123907i
$621$		0			0
$622$	−1.99901	+	2.96621i	−0.0801530	+	0.118934i
$623$	17.5640			0.703685
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	−3.04185	+	4.51361i	−0.121577	+	0.180400i
$627$		0			0
$628$	4.86781	−	11.4934i	0.194247	−	0.458636i
$629$	12.3123	−	12.3123i	0.490922	−	0.490922i
$630$		0			0
$631$		−	49.5996i		−	1.97453i	−0.159086	−	0.987265i	$-0.550855\pi$
$631$		−	49.5996i		−	1.97453i	0.159086	−	0.987265i	$-0.449145\pi$
$632$	3.25169	−	15.3887i	0.129345	−	0.612131i
$633$		0			0
$634$	2.59614	+	13.3275i	0.103106	+	0.529303i
$635$	7.76353	−	7.76353i	0.308086	−	0.308086i
$636$		0			0
$637$	0.660942	+	0.660942i	0.0261875	+	0.0261875i
$638$	−54.8410	−	36.9588i	−2.17118	−	1.46321i
$639$		0			0
$640$	−11.0308	−	2.51417i	−0.436031	−	0.0993811i
$641$	42.5379			1.68015			0.840074	−	0.542472i	$-0.182512\pi$
$641$	42.5379			1.68015			0.840074	+	0.542472i	$0.182512\pi$
$642$		0			0
$643$	−29.3128	−	29.3128i	−1.15598	−	1.15598i	−0.985331	−	0.170653i	$-0.945412\pi$
$643$	−29.3128	−	29.3128i	−1.15598	−	1.15598i	−0.170653	−	0.985331i	$-0.554588\pi$
$644$	3.38375	+	8.35583i	0.133338	+	0.329266i
$645$		0			0
$646$	−0.553992	−	2.84397i	−0.0217965	−	0.111894i
$647$			4.35345i			0.171152i	0.996332	+	0.0855759i	$0.0272730\pi$
$647$			4.35345i			0.171152i	−0.996332	+	0.0855759i	$0.972727\pi$
$648$		0			0
$649$			52.8525i			2.07464i
$650$	−2.70749	+	0.527407i	−0.106197	+	0.0206866i
$651$		0			0
$652$	3.95906	−	9.34774i	0.155049	−	0.366086i
$653$	12.3460	+	12.3460i	0.483137	+	0.483137i	0.906132	−	0.422995i	$-0.139021\pi$
$653$	12.3460	+	12.3460i	0.483137	+	0.483137i	−0.422995	+	0.906132i	$0.639021\pi$
$654$		0			0
$655$	−8.16063			−0.318862
$656$	23.4026	+	24.1567i	0.913718	+	0.943159i
$657$		0			0
$658$	−11.2355	+	16.6716i	−0.438004	+	0.649928i
$659$	−19.5367	−	19.5367i	−0.761040	−	0.761040i	0.215470	−	0.976510i	$-0.430872\pi$
$659$	−19.5367	−	19.5367i	−0.761040	−	0.761040i	−0.976510	+	0.215470i	$0.930872\pi$
$660$		0			0
$661$	26.4901	−	26.4901i	1.03035	−	1.03035i	0.0308210	−	0.999525i	$-0.490188\pi$
$661$	26.4901	−	26.4901i	1.03035	−	1.03035i	0.999525	−	0.0308210i	$-0.00981219\pi$
$662$	3.51778	−	0.685247i	0.136722	−	0.0266329i
$663$		0			0
$664$	−1.73031	+	1.12663i	−0.0671490	+	0.0437217i
$665$		−	1.13211i		−	0.0439014i
$666$		0			0
$667$	9.34961	−	9.34961i	0.362018	−	0.362018i
$668$	−32.6250	+	13.2117i	−1.26230	+	0.511177i
$669$		0			0
$670$	9.55382	+	6.43858i	0.369096	+	0.248744i
$671$	31.5411			1.21763
$672$		0			0
$673$	−11.5260			−0.444295			−0.222148	−	0.975013i	$-0.571307\pi$
$673$	−11.5260			−0.444295			−0.222148	+	0.975013i	$0.571307\pi$
$674$	18.8897	+	12.7303i	0.727603	+	0.490351i
$675$		0			0
$676$	17.0466	−	6.90315i	0.655639	−	0.265506i
$677$	15.8009	−	15.8009i	0.607278	−	0.607278i	−0.334956	−	0.942234i	$-0.608721\pi$
$677$	15.8009	−	15.8009i	0.607278	−	0.607278i	0.942234	+	0.334956i	$0.108721\pi$
$678$		0			0
$679$		−	25.8313i		−	0.991314i
$680$	7.63820	+	11.7310i	0.292912	+	0.449862i
$681$		0			0
$682$	−32.0056	+	6.23454i	−1.22556	+	0.238733i
$683$	25.1439	−	25.1439i	0.962105	−	0.962105i	−0.0372032	−	0.999308i	$-0.511845\pi$
$683$	25.1439	−	25.1439i	0.962105	−	0.962105i	0.999308	+	0.0372032i	$0.0118449\pi$
$684$		0			0
$685$	−5.08291	−	5.08291i	−0.194208	−	0.194208i
$686$	−14.0944	+	20.9138i	−0.538127	+	0.798494i
$687$		0			0
$688$	0.289407	−	18.2531i	0.0110336	−	0.695893i
$689$	19.8752			0.757183
$690$		0			0
$691$	−27.2647	−	27.2647i	−1.03720	−	1.03720i	−0.999281	−	0.0379162i	$-0.987928\pi$
$691$	−27.2647	−	27.2647i	−1.03720	−	1.03720i	−0.0379162	−	0.999281i	$-0.512072\pi$
$692$	−8.07865	+	19.0745i	−0.307104	+	0.725103i
$693$		0			0
$694$	−24.8484	+	4.84035i	−0.943232	+	0.183737i
$695$		−	6.94841i		−	0.263568i
$696$		0			0
$697$		−	41.6151i		−	1.57628i
$698$	−6.23394	−	32.0025i	−0.235958	−	1.21131i
$699$		0			0
$700$	2.05302	+	5.06972i	0.0775967	+	0.191617i
$701$	−12.5566	−	12.5566i	−0.474257	−	0.474257i	0.429032	−	0.903289i	$-0.358855\pi$
$701$	−12.5566	−	12.5566i	−0.474257	−	0.474257i	−0.903289	+	0.429032i	$0.858855\pi$
$702$		0			0
$703$	−1.45639			−0.0549288
$704$	43.4948	−	16.8159i	1.63927	−	0.633773i
$705$		0			0
$706$	15.5550	+	10.4829i	0.585420	+	0.394531i
$707$	30.2312	+	30.2312i	1.13696	+	1.13696i
$708$		0			0
$709$	18.0518	−	18.0518i	0.677950	−	0.677950i	−0.281586	−	0.959536i	$-0.590860\pi$
$709$	18.0518	−	18.0518i	0.677950	−	0.677950i	0.959536	+	0.281586i	$0.0908604\pi$
$710$	−2.14223	−	10.9973i	−0.0803964	−	0.412723i
$711$		0			0
$712$	17.7727	+	3.75543i	0.666061	+	0.140741i
$713$		−	6.51940i		−	0.244154i
$714$		0			0
$715$	8.03935	−	8.03935i	0.300655	−	0.300655i
$716$	7.09109	−	16.7428i	0.265006	−	0.625707i
$717$		0			0
$718$	10.5560	−	15.6633i	0.393945	−	0.584551i
$719$	1.68053			0.0626731			0.0313366	−	0.999509i	$-0.490024\pi$
$719$	1.68053			0.0626731			0.0313366	+	0.999509i	$0.490024\pi$
$720$		0			0
$721$	−14.9546			−0.556939
$722$	14.8812	−	22.0813i	0.553821	−	0.821782i
$723$		0			0
$724$	−9.58141	−	4.05803i	−0.356090	−	0.150815i
$725$	5.67267	−	5.67267i	0.210678	−	0.210678i
$726$		0			0
$727$			15.5235i			0.575735i	0.957670	+	0.287867i	$0.0929462\pi$
$727$			15.5235i			0.575735i	−0.957670	+	0.287867i	$0.907054\pi$
$728$	8.23233	+	12.6434i	0.305110	+	0.468597i
$729$		0			0
$730$	−1.17969	−	6.05604i	−0.0436622	−	0.224144i
$731$	−15.9718	+	15.9718i	−0.590737	+	0.590737i
$732$		0			0
$733$	−8.79758	−	8.79758i	−0.324946	−	0.324946i	0.525715	−	0.850661i	$-0.323798\pi$
$733$	−8.79758	−	8.79758i	−0.324946	−	0.324946i	−0.850661	+	0.525715i	$0.823798\pi$
$734$	13.9485	+	9.40027i	0.514849	+	0.346970i
$735$		0			0
$736$	1.63737	+	9.17864i	0.0603542	+	0.338329i
$737$	−47.4862			−1.74918
$738$		0			0
$739$	−6.44190	−	6.44190i	−0.236969	−	0.236969i	0.578625	−	0.815594i	$-0.303590\pi$
$739$	−6.44190	−	6.44190i	−0.236969	−	0.236969i	−0.815594	+	0.578625i	$0.803590\pi$
$740$	6.52187	−	2.64108i	0.239749	−	0.0970879i
$741$		0			0
$742$	−7.53539	−	38.6836i	−0.276633	−	1.42012i
$743$		−	34.8920i		−	1.28006i	−0.768348	−	0.640032i	$-0.778921\pi$
$743$		−	34.8920i		−	1.28006i	0.768348	−	0.640032i	$-0.221079\pi$
$744$		0			0
$745$			13.8115i			0.506014i
$746$	−37.3960	+	7.28456i	−1.36916	+	0.266707i
$747$		0			0
$748$	−53.1296	−	22.5020i	−1.94261	−	0.822756i
$749$	−0.803225	−	0.803225i	−0.0293492	−	0.0293492i
$750$		0			0
$751$	17.4058			0.635148			0.317574	−	0.948234i	$-0.397132\pi$
$751$	17.4058			0.635148			0.317574	+	0.948234i	$0.397132\pi$
$752$	−14.9336	+	14.4675i	−0.544574	+	0.527575i
$753$		0			0
$754$	12.3669	−	18.3505i	0.450376	−	0.668286i
$755$	−1.34884	−	1.34884i	−0.0490893	−	0.0490893i
$756$		0			0
$757$	20.6521	−	20.6521i	0.750614	−	0.750614i	−0.223980	−	0.974594i	$-0.571905\pi$
$757$	20.6521	−	20.6521i	0.750614	−	0.750614i	0.974594	+	0.223980i	$0.0719050\pi$
$758$	−9.11967	+	1.77647i	−0.331241	+	0.0645242i
$759$		0			0
$760$	0.242062	−	1.14557i	0.00878051	−	0.0415541i
$761$		−	8.36636i		−	0.303280i	−0.988436	−	0.151640i	$-0.951545\pi$
$761$		−	8.36636i		−	0.303280i	0.988436	−	0.151640i	$-0.0484555\pi$
$762$		0			0
$763$	−28.4789	+	28.4789i	−1.03101	+	1.03101i
$764$	4.04695	+	9.99353i	0.146413	+	0.361553i
$765$		0			0
$766$	−45.1663	−	30.4388i	−1.63193	−	1.09980i
$767$	−17.6851			−0.638574
$768$		0			0
$769$	45.1264			1.62730			0.813650	−	0.581356i	$-0.197477\pi$
$769$	45.1264			1.62730			0.813650	+	0.581356i	$0.197477\pi$
$770$	−18.6952	−	12.5992i	−0.673730	−	0.454045i
$771$		0			0
$772$	−2.65610	−	6.55897i	−0.0955951	−	0.236062i
$773$	11.1233	−	11.1233i	0.400076	−	0.400076i	−0.478184	−	0.878260i	$-0.658705\pi$
$773$	11.1233	−	11.1233i	0.400076	−	0.400076i	0.878260	+	0.478184i	$0.158705\pi$
$774$		0			0
$775$		−	3.95550i		−	0.142086i
$776$	5.52311	−	26.1383i	0.198268	−	0.938311i
$777$		0			0
$778$	1.77306	−	0.345383i	0.0635672	−	0.0123826i
$779$	−2.46128	+	2.46128i	−0.0881844	+	0.0881844i
$780$		0			0
$781$	32.6544	+	32.6544i	1.16846	+	1.16846i
$782$	6.44705	−	9.56640i	0.230546	−	0.342094i
$783$		0			0
$784$	1.37677	−	1.33379i	0.0491704	−	0.0476355i
$785$	−6.24086			−0.222746
$786$		0			0
$787$	7.41779	+	7.41779i	0.264416	+	0.264416i	0.826845	−	0.562430i	$-0.190133\pi$
$787$	7.41779	+	7.41779i	0.264416	+	0.264416i	−0.562430	+	0.826845i	$0.690133\pi$
$788$	−27.8416	−	11.7918i	−0.991816	−	0.420065i
$789$		0			0
$790$	−7.71917	+	1.50366i	−0.274636	+	0.0534978i
$791$			47.6254i			1.69337i
$792$		0			0
$793$			10.5541i			0.374786i
$794$	1.70073	+	8.73085i	0.0603566	+	0.309846i
$795$		0			0
$796$	−29.0195	+	11.7516i	−1.02857	+	0.416526i
$797$	8.05803	+	8.05803i	0.285430	+	0.285430i	0.835270	−	0.549840i	$-0.185311\pi$
$797$	8.05803	+	8.05803i	0.285430	+	0.285430i	−0.549840	+	0.835270i	$0.685311\pi$
$798$		0			0
$799$	25.7264			0.910136
$800$	0.993438	+	5.56894i	0.0351233	+	0.196892i
$801$		0			0
$802$	−32.0606	−	21.6065i	−1.13210	−	0.762953i
$803$	17.9822	+	17.9822i	0.634578	+	0.634578i
$804$		0			0
$805$	3.18727	−	3.18727i	0.112337	−	0.112337i
$806$	−2.08616	−	10.7095i	−0.0734819	−	0.377226i
$807$		0			0
$808$	24.1266	+	37.0544i	0.848772	+	1.30357i
$809$			20.1500i			0.708436i	0.935163	+	0.354218i	$0.115253\pi$
$809$			20.1500i			0.708436i	−0.935163	+	0.354218i	$0.884747\pi$
$810$		0			0
$811$	−10.5575	+	10.5575i	−0.370723	+	0.370723i	−0.867741	−	0.497018i	$-0.834428\pi$
$811$	−10.5575	+	10.5575i	−0.370723	+	0.370723i	0.497018	+	0.867741i	$0.334428\pi$
$812$	−40.4049	−	17.1127i	−1.41793	−	0.600540i
$813$		0			0
$814$	−16.2081	+	24.0503i	−0.568094	+	0.842961i
$815$	−5.07578			−0.177797
$816$		0			0
$817$	1.88926			0.0660969
$818$	−30.5778	+	45.3725i	−1.06913	+	1.58641i
$819$		0			0
$820$	6.55849	−	15.4852i	0.229032	−	0.540768i
$821$	24.3826	−	24.3826i	0.850957	−	0.850957i	−0.139294	−	0.990251i	$-0.544483\pi$
$821$	24.3826	−	24.3826i	0.850957	−	0.850957i	0.990251	+	0.139294i	$0.0444833\pi$
$822$		0			0
$823$			32.5617i			1.13503i	0.823363	+	0.567515i	$0.192095\pi$
$823$			32.5617i			1.13503i	−0.823363	+	0.567515i	$0.807905\pi$
$824$	−15.1324	−	3.19752i	−0.527161	−	0.111391i
$825$		0			0
$826$	6.70507	+	34.4211i	0.233299	+	1.19766i
$827$	1.31121	−	1.31121i	0.0455952	−	0.0455952i	−0.683942	−	0.729537i	$-0.739736\pi$
$827$	1.31121	−	1.31121i	0.0455952	−	0.0455952i	0.729537	+	0.683942i	$0.239736\pi$
$828$		0			0
$829$	−20.8346	−	20.8346i	−0.723617	−	0.723617i	0.245723	−	0.969340i	$-0.420975\pi$
$829$	−20.8346	−	20.8346i	−0.723617	−	0.723617i	−0.969340	+	0.245723i	$0.920975\pi$
$830$	0.856115	+	0.576959i	0.0297162	+	0.0200265i
$831$		0			0
$832$	5.62682	+	14.5539i	0.195075	+	0.504566i
$833$	−2.37179			−0.0821775
$834$		0			0
$835$	12.4446	+	12.4446i	0.430663	+	0.430663i
$836$	1.81143	+	4.47314i	0.0626496	+	0.154707i
$837$		0			0
$838$	−2.83528	−	14.5552i	−0.0979432	−	0.502801i
$839$		−	54.2029i		−	1.87129i	−0.352939	−	0.935646i	$-0.614818\pi$
$839$		−	54.2029i		−	1.87129i	0.352939	−	0.935646i	$-0.385182\pi$
$840$		0			0
$841$			35.3584i			1.21925i
$842$	−20.2747	+	3.94942i	−0.698712	+	0.136106i
$843$		0			0
$844$	21.9907	−	51.9223i	0.756952	−	1.78724i
$845$	−6.50232	−	6.50232i	−0.223686	−	0.223686i
$846$		0			0
$847$	62.8396			2.15920
$848$	0.646174	−	40.7546i	0.0221897	−	1.39952i
$849$		0			0
$850$	3.91161	−	5.80420i	0.134167	−	0.199083i
$851$	−4.10023	−	4.10023i	−0.140554	−	0.140554i
$852$		0			0
$853$	28.4548	−	28.4548i	0.974274	−	0.974274i	−0.0254034	−	0.999677i	$-0.508087\pi$
$853$	28.4548	−	28.4548i	0.974274	−	0.974274i	0.999677	+	0.0254034i	$0.00808702\pi$
$854$	20.5417	−	4.00142i	0.702922	−	0.136926i
$855$		0			0
$856$	−0.641031	−	0.984514i	−0.0219100	−	0.0336500i
$857$		−	28.9592i		−	0.989228i	−0.869113	−	0.494614i	$-0.835309\pi$
$857$		−	28.9592i		−	0.989228i	0.869113	−	0.494614i	$-0.164691\pi$
$858$		0			0
$859$	35.6101	−	35.6101i	1.21500	−	1.21500i	0.245640	−	0.969361i	$-0.421002\pi$
$859$	35.6101	−	35.6101i	1.21500	−	1.21500i	0.969361	−	0.245640i	$-0.0789982\pi$
$860$	−8.46032	+	3.42606i	−0.288495	+	0.116828i
$861$		0			0
$862$	17.4322	+	11.7480i	0.593743	+	0.400140i
$863$	31.8081			1.08276			0.541380	−	0.840778i	$-0.317902\pi$
$863$	31.8081			1.08276			0.541380	+	0.840778i	$0.317902\pi$
$864$		0			0
$865$	10.3574			0.352161
$866$	−5.82018	−	3.92237i	−0.197778	−	0.133288i
$867$		0			0
$868$	−20.0533	+	8.12071i	−0.680653	+	0.275635i
$869$	22.9205	−	22.9205i	0.777526	−	0.777526i
$870$		0			0
$871$		−	15.8895i		−	0.538396i
$872$	−34.9066	+	22.7282i	−1.18209	+	0.769674i
$873$		0			0
$874$	−0.947097	+	0.184490i	−0.0320360	+	0.00624047i
$875$	1.93381	−	1.93381i	0.0653746	−	0.0653746i
$876$		0			0
$877$	−29.2864	−	29.2864i	−0.988932	−	0.988932i	0.0110076	−	0.999939i	$-0.496496\pi$
$877$	−29.2864	−	29.2864i	−0.988932	−	0.988932i	−0.999939	+	0.0110076i	$0.996496\pi$
$878$	10.8553	−	16.1075i	0.366349	−	0.543603i
$879$		0			0
$880$	−16.2236	−	16.7463i	−0.546896	−	0.564518i
$881$	6.72061			0.226423			0.113212	−	0.993571i	$-0.463886\pi$
$881$	6.72061			0.226423			0.113212	+	0.993571i	$0.463886\pi$
$882$		0			0
$883$	−26.2186	−	26.2186i	−0.882327	−	0.882327i	0.111444	−	0.993771i	$-0.464453\pi$
$883$	−26.2186	−	26.2186i	−0.882327	−	0.882327i	−0.993771	+	0.111444i	$0.964453\pi$
$884$	7.52947	−	17.7778i	0.253244	−	0.597934i
$885$		0			0
$886$	14.9703	−	2.91614i	0.502937	−	0.0979697i
$887$		−	10.4628i		−	0.351307i	−0.984452	−	0.175654i	$-0.943796\pi$
$887$		−	10.4628i		−	0.351307i	0.984452	−	0.175654i	$-0.0562039\pi$
$888$		0			0
$889$			30.0263i			1.00705i
$890$	−1.73660	−	8.91502i	−0.0582111	−	0.298832i
$891$		0			0
$892$	15.9277	+	39.3319i	0.533299	+	1.31693i
$893$	−1.52156	−	1.52156i	−0.0509171	−	0.0509171i
$894$		0			0
$895$	−9.09126			−0.303887
$896$	26.1934	−	16.4696i	0.875060	−	0.550210i
$897$		0			0
$898$	18.5933	+	12.5305i	0.620466	+	0.418148i
$899$	22.4383	+	22.4383i	0.748358	+	0.748358i
$900$		0			0
$901$	−35.6609	+	35.6609i	−1.18804	+	1.18804i
$902$	13.2531	+	68.0361i	0.441280	+	2.26535i
$903$		0			0
$904$	−10.1830	+	48.1915i	−0.338682	+	1.60283i
$905$			5.20267i			0.172943i
$906$		0			0
$907$	12.4762	−	12.4762i	0.414267	−	0.414267i	−0.468955	−	0.883222i	$-0.655369\pi$
$907$	12.4762	−	12.4762i	0.414267	−	0.414267i	0.883222	+	0.468955i	$0.155369\pi$
$908$	13.2762	−	31.3463i	0.440585	−	1.04026i
$909$		0			0
$910$	4.21587	−	6.25567i	0.139755	−	0.207374i
$911$	−49.3786			−1.63599			−0.817994	−	0.575227i	$-0.804914\pi$
$911$	−49.3786			−1.63599			−0.817994	+	0.575227i	$0.804914\pi$
$912$		0			0
$913$	−4.25522			−0.140827
$914$	11.2212	−	16.6505i	0.371164	−	0.550749i
$915$		0			0
$916$	17.4710	+	7.39951i	0.577257	+	0.244487i
$917$	15.7811	−	15.7811i	0.521138	−	0.521138i
$918$		0			0
$919$			26.6465i			0.878988i	0.898246	+	0.439494i	$0.144842\pi$
$919$			26.6465i			0.878988i	−0.898246	+	0.439494i	$0.855158\pi$
$920$	3.90664	−	2.54367i	0.128798	−	0.0838623i
$921$		0			0
$922$	8.75519	+	44.9456i	0.288337	+	1.48020i
$923$	−10.9266	+	10.9266i	−0.359653	+	0.359653i
$924$		0			0
$925$	−2.48772	−	2.48772i	−0.0817958	−	0.0817958i
$926$	29.3393	+	19.7725i	0.964149	+	0.649766i
$927$		0			0
$928$	−37.2262	−	25.9553i	−1.22201	−	0.852025i
$929$	29.5531			0.969606			0.484803	−	0.874623i	$-0.338891\pi$
$929$	29.5531			0.969606			0.484803	+	0.874623i	$0.338891\pi$
$930$		0			0
$931$	0.140276	+	0.140276i	0.00459737	+	0.00459737i
$932$	10.0183	−	4.05699i	0.328162	−	0.132891i
$933$		0			0
$934$	9.00351	+	46.2203i	0.294604	+	1.51238i
$935$			28.8491i			0.943468i
$936$		0			0
$937$			30.5505i			0.998042i	0.866590	+	0.499021i	$0.166307\pi$
$937$			30.5505i			0.998042i	−0.866590	+	0.499021i	$0.833693\pi$
$938$	−30.9262	+	6.02429i	−1.00978	+	0.196700i
$939$		0			0
$940$	9.57297	+	4.05445i	0.312236	+	0.132242i
$941$	−0.808622	−	0.808622i	−0.0263603	−	0.0263603i	0.693804	−	0.720164i	$-0.255933\pi$
$941$	−0.808622	−	0.808622i	−0.0263603	−	0.0263603i	−0.720164	+	0.693804i	$0.755933\pi$
$942$		0			0
$943$	−13.8586			−0.451299
$944$	−0.574973	+	36.2639i	−0.0187138	+	1.18029i
$945$		0			0
$946$	21.0255	−	31.1985i	0.683599	−	1.01435i
$947$	16.7181	+	16.7181i	0.543265	+	0.543265i	0.924484	−	0.381220i	$-0.124496\pi$
$947$	16.7181	+	16.7181i	0.543265	+	0.543265i	−0.381220	+	0.924484i	$0.624496\pi$
$948$		0			0
$949$	−6.01708	+	6.01708i	−0.195323	+	0.195323i
$950$	−0.574630	+	0.111935i	−0.0186435	+	0.00363166i
$951$		0			0
$952$	−37.4563	−	7.91462i	−1.21396	−	0.256514i
$953$		−	5.39705i		−	0.174828i	−0.996172	−	0.0874138i	$-0.972140\pi$
$953$		−	5.39705i		−	0.174828i	0.996172	−	0.0874138i	$-0.0278603\pi$
$954$		0			0
$955$	3.81196	−	3.81196i	0.123352	−	0.123352i
$956$	1.40056	+	3.45855i	0.0452974	+	0.111857i
$957$		0			0
$958$	−46.1379	−	31.0936i	−1.49065	−	1.00459i
$959$	19.6587			0.634813
$960$		0			0
$961$	−15.3540			−0.495290
$962$	−8.04753	−	5.42345i	−0.259463	−	0.174859i
$963$		0			0
$964$	12.2919	+	30.3535i	0.395894	+	0.977621i
$965$	−2.50187	+	2.50187i	−0.0805381	+	0.0805381i
$966$		0			0
$967$		−	14.0430i		−	0.451593i	−0.974175	−	0.225796i	$-0.927502\pi$
$967$		−	14.0430i		−	0.451593i	0.974175	−	0.225796i	$-0.0724984\pi$
$968$	63.5865	+	13.4360i	2.04375	+	0.431851i
$969$		0			0
$970$	−13.1113	+	2.55402i	−0.420978	+	0.0820046i
$971$	−13.5960	+	13.5960i	−0.436316	+	0.436316i	−0.890770	−	0.454454i	$-0.849834\pi$
$971$	−13.5960	+	13.5960i	−0.436316	+	0.436316i	0.454454	+	0.890770i	$0.349834\pi$
$972$		0			0
$973$	13.4369	+	13.4369i	0.430767	+	0.430767i
$974$	−20.3096	+	30.1363i	−0.650763	+	0.965628i
$975$		0			0
$976$	21.6414	+	0.343130i	0.692725	+	0.0109833i
$977$	−44.9303			−1.43745			−0.718724	−	0.695295i	$-0.755274\pi$
$977$	−44.9303			−1.43745			−0.718724	+	0.695295i	$0.755274\pi$
$978$		0			0
$979$	26.4713	+	26.4713i	0.846028	+	0.846028i
$980$	−0.882556	−	0.373790i	−0.0281922	−	0.0119403i
$981$		0			0
$982$	56.9974	−	11.1028i	1.81886	−	0.354306i
$983$		−	55.7813i		−	1.77915i	−0.456791	−	0.889574i	$-0.651001\pi$
$983$		−	55.7813i		−	1.77915i	0.456791	−	0.889574i	$-0.348999\pi$
$984$		0			0
$985$			15.1179i			0.481696i
$986$	10.7361	+	55.1146i	0.341906	+	1.75521i
$987$		0			0
$988$	−1.49677	+	0.606128i	−0.0476186	+	0.0192835i
$989$	5.31891	+	5.31891i	0.169131	+	0.169131i
$990$		0			0
$991$	−46.1815			−1.46700			−0.733502	−	0.679688i	$-0.762115\pi$
$991$	−46.1815			−1.46700			−0.733502	+	0.679688i	$0.762115\pi$
$992$	−22.0280	+	3.92955i	−0.699389	+	0.124763i
$993$		0			0
$994$	25.4094	+	17.1241i	0.805937	+	0.543142i
$995$	11.0693	+	11.0693i	0.350920	+	0.350920i
$996$		0			0
$997$	−33.4837	+	33.4837i	−1.06044	+	1.06044i	−0.0623860	+	0.998052i	$0.519871\pi$
$997$	−33.4837	+	33.4837i	−1.06044	+	1.06044i	−0.998052	+	0.0623860i	$0.980129\pi$
$998$	−3.02062	−	15.5066i	−0.0956160	−	0.490854i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.t.c.541.7		16
3.2	odd	2		80.2.l.a.61.2	yes	16
4.3	odd	2		2880.2.t.c.721.5		16
12.11	even	2		320.2.l.a.81.3		16
15.2	even	4		400.2.q.h.349.5		16
15.8	even	4		400.2.q.g.349.4		16
15.14	odd	2		400.2.l.h.301.7		16
16.5	even	4	inner	720.2.t.c.181.7		16
16.11	odd	4		2880.2.t.c.2161.8		16
24.5	odd	2		640.2.l.b.161.3		16
24.11	even	2		640.2.l.a.161.6		16
48.5	odd	4		80.2.l.a.21.2	✓	16
48.11	even	4		320.2.l.a.241.3		16
48.29	odd	4		640.2.l.b.481.3		16
48.35	even	4		640.2.l.a.481.6		16
60.23	odd	4		1600.2.q.h.849.6		16
60.47	odd	4		1600.2.q.g.849.3		16
60.59	even	2		1600.2.l.i.401.6		16
96.5	odd	8		5120.2.a.s.1.3		8
96.11	even	8		5120.2.a.t.1.3		8
96.53	odd	8		5120.2.a.v.1.6		8
96.59	even	8		5120.2.a.u.1.6		8
240.53	even	4		400.2.q.h.149.5		16
240.59	even	4		1600.2.l.i.1201.6		16
240.107	odd	4		1600.2.q.h.49.6		16
240.149	odd	4		400.2.l.h.101.7		16
240.197	even	4		400.2.q.g.149.4		16
240.203	odd	4		1600.2.q.g.49.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.2	✓	16	48.5	odd	4
80.2.l.a.61.2	yes	16	3.2	odd	2
320.2.l.a.81.3		16	12.11	even	2
320.2.l.a.241.3		16	48.11	even	4
400.2.l.h.101.7		16	240.149	odd	4
400.2.l.h.301.7		16	15.14	odd	2
400.2.q.g.149.4		16	240.197	even	4
400.2.q.g.349.4		16	15.8	even	4
400.2.q.h.149.5		16	240.53	even	4
400.2.q.h.349.5		16	15.2	even	4
640.2.l.a.161.6		16	24.11	even	2
640.2.l.a.481.6		16	48.35	even	4
640.2.l.b.161.3		16	24.5	odd	2
640.2.l.b.481.3		16	48.29	odd	4
720.2.t.c.181.7		16	16.5	even	4	inner
720.2.t.c.541.7		16	1.1	even	1	trivial
1600.2.l.i.401.6		16	60.59	even	2
1600.2.l.i.1201.6		16	240.59	even	4
1600.2.q.g.49.3		16	240.203	odd	4
1600.2.q.g.849.3		16	60.47	odd	4
1600.2.q.h.49.6		16	240.107	odd	4
1600.2.q.h.849.6		16	60.23	odd	4
2880.2.t.c.721.5		16	4.3	odd	2
2880.2.t.c.2161.8		16	16.11	odd	4
5120.2.a.s.1.3		8	96.5	odd	8
5120.2.a.t.1.3		8	96.11	even	8
5120.2.a.u.1.6		8	96.59	even	8
5120.2.a.v.1.6		8	96.53	odd	8

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17275 + 0.790349i) q^{2} +(0.750696 + 1.85377i) q^{4} +(0.707107 - 0.707107i) q^{5} +2.73482i q^{7} +(-0.584744 + 2.76732i) q^{8} +O(q^{10})\)	\(q+(1.17275 + 0.790349i) q^{2} +(0.750696 + 1.85377i) q^{4} +(0.707107 - 0.707107i) q^{5} +2.73482i q^{7} +(-0.584744 + 2.76732i) q^{8} +(1.38812 - 0.270400i) q^{10} +(-4.12175 + 4.12175i) q^{11} +(-1.37919 - 1.37919i) q^{13} +(-2.16146 + 3.20726i) q^{14} +(-2.87291 + 2.78323i) q^{16} +4.94921 q^{17} +(-0.292715 - 0.292715i) q^{19} +(1.84163 + 0.779990i) q^{20} +(-8.09141 + 1.57617i) q^{22} -1.64818i q^{23} -1.00000i q^{25} +(-0.527407 - 2.70749i) q^{26} +(-5.06972 + 2.05302i) q^{28} +(5.67267 + 5.67267i) q^{29} +3.95550 q^{31} +(-5.56894 + 0.993438i) q^{32} +(5.80420 + 3.91161i) q^{34} +(1.93381 + 1.93381i) q^{35} +(2.48772 - 2.48772i) q^{37} +(-0.111935 - 0.574630i) q^{38} +(1.54332 + 2.37027i) q^{40} -8.40843i q^{41} +(-3.22713 + 3.22713i) q^{43} +(-10.7349 - 4.54659i) q^{44} +(1.30264 - 1.93291i) q^{46} +5.19809 q^{47} -0.479225 q^{49} +(0.790349 - 1.17275i) q^{50} +(1.52135 - 3.59205i) q^{52} +(-7.20537 + 7.20537i) q^{53} +5.82903i q^{55} +(-7.56812 - 1.59917i) q^{56} +(2.16925 + 11.1360i) q^{58} +(6.41142 - 6.41142i) q^{59} +(-3.82618 - 3.82618i) q^{61} +(4.63883 + 3.12623i) q^{62} +(-7.31615 - 3.23635i) q^{64} -1.95047 q^{65} +(5.76044 + 5.76044i) q^{67} +(3.71535 + 9.17470i) q^{68} +(0.739494 + 3.79626i) q^{70} -7.92245i q^{71} -4.36276i q^{73} +(4.88365 - 0.951312i) q^{74} +(0.322886 - 0.762367i) q^{76} +(-11.2722 - 11.2722i) q^{77} -5.56087 q^{79} +(-0.0634130 + 3.99950i) q^{80} +(6.64559 - 9.86100i) q^{82} +(0.516191 + 0.516191i) q^{83} +(3.49962 - 3.49962i) q^{85} +(-6.33518 + 1.23406i) q^{86} +(-8.99604 - 13.8164i) q^{88} -6.42236i q^{89} +(3.77184 - 3.77184i) q^{91} +(3.05535 - 1.23729i) q^{92} +(6.09607 + 4.10830i) q^{94} -0.413962 q^{95} -9.44534 q^{97} +(-0.562012 - 0.378755i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4}+O(q^{10}) \) 16 * q - 4 * q^4	\( 16 q - 4 q^{4} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 8 q^{20} - 20 q^{22} + 16 q^{26} - 4 q^{28} + 16 q^{29} + 16 q^{34} - 16 q^{37} - 20 q^{38} + 8 q^{43} - 40 q^{44} - 4 q^{46} + 40 q^{47} - 16 q^{49} + 4 q^{50} + 56 q^{52} - 16 q^{53} - 16 q^{56} - 12 q^{58} + 8 q^{59} + 16 q^{61} + 8 q^{62} - 16 q^{64} + 40 q^{67} + 48 q^{68} - 8 q^{70} + 72 q^{74} - 16 q^{77} + 16 q^{79} - 16 q^{80} - 76 q^{82} - 40 q^{83} - 16 q^{85} - 28 q^{86} + 32 q^{91} + 52 q^{92} - 36 q^{94} - 32 q^{95} - 60 q^{98}+O(q^{100}) \) 16 * q - 4 * q^4 + 4 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 8 * q^20 - 20 * q^22 + 16 * q^26 - 4 * q^28 + 16 * q^29 + 16 * q^34 - 16 * q^37 - 20 * q^38 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 40 * q^47 - 16 * q^49 + 4 * q^50 + 56 * q^52 - 16 * q^53 - 16 * q^56 - 12 * q^58 + 8 * q^59 + 16 * q^61 + 8 * q^62 - 16 * q^64 + 40 * q^67 + 48 * q^68 - 8 * q^70 + 72 * q^74 - 16 * q^77 + 16 * q^79 - 16 * q^80 - 76 * q^82 - 40 * q^83 - 16 * q^85 - 28 * q^86 + 32 * q^91 + 52 * q^92 - 36 * q^94 - 32 * q^95 - 60 * q^98

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