LMFDB - Embedded newform 684.2.r.b.487.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [684,2,Mod(487,684)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(684, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("684.487"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 3 x^{18} - 2 x^{17} + x^{16} + 3 x^{14} - 12 x^{13} + 28 x^{12} - 24 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 3x^18 - 2x^17 + x^16 + 3x^14 - 12x^13 + 28x^12 - 24x^11 + 40x^10 - 48x^9 + 112x^8 - 96x^7 + 48x^6 + 64x^4 - 256x^3 + 768x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			487.3
Root			$-0.237943 - 1.39405i$ of defining polynomial
Character	$\chi$	$=$	684.487
Dual form			684.2.r.b.559.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08831 + 0.903091i) q^{2} +(0.368852 - 1.96569i) q^{4} +(-1.43271 - 2.48152i) q^{5} +2.64551i q^{7} +(1.37377 + 2.47240i) q^{8} +(3.80027 + 1.40681i) q^{10} +2.73265i q^{11} +(-1.86752 - 1.07822i) q^{13} +(-2.38914 - 2.87915i) q^{14} +(-3.72790 - 1.45010i) q^{16} +(1.26747 + 2.19532i) q^{17} +(1.53443 - 4.07989i) q^{19} +(-5.40636 + 1.90095i) q^{20} +(-2.46783 - 2.97398i) q^{22} +(3.37287 + 1.94733i) q^{23} +(-1.60529 + 2.78044i) q^{25} +(3.00618 - 0.513109i) q^{26} +(5.20027 + 0.975802i) q^{28} +(2.79010 + 1.61086i) q^{29} +8.83425 q^{31} +(5.36669 - 1.78847i) q^{32} +(-3.36199 - 1.24456i) q^{34} +(6.56489 - 3.79024i) q^{35} +12.0463i q^{37} +(2.01457 + 5.82593i) q^{38} +(4.16708 - 6.95126i) q^{40} +(4.75850 - 2.74732i) q^{41} +(1.31272 - 0.757900i) q^{43} +(5.37154 + 1.00794i) q^{44} +(-5.42935 + 0.926708i) q^{46} +(9.19542 + 5.30898i) q^{47} +0.00125668 q^{49} +(-0.763936 - 4.47571i) q^{50} +(-2.80828 + 3.27328i) q^{52} +(-4.25386 - 2.45597i) q^{53} +(6.78111 - 3.91508i) q^{55} +(-6.54076 + 3.63434i) q^{56} +(-4.49126 + 0.766589i) q^{58} +(-3.80546 - 6.59126i) q^{59} +(0.788072 - 1.36498i) q^{61} +(-9.61444 + 7.97814i) q^{62} +(-4.22549 + 6.79303i) q^{64} +6.17906i q^{65} +(-5.23140 + 9.06106i) q^{67} +(4.78284 - 1.68171i) q^{68} +(-3.72172 + 10.0537i) q^{70} +(2.82329 + 4.89008i) q^{71} +(-6.42096 - 11.1214i) q^{73} +(-10.8789 - 13.1102i) q^{74} +(-7.45383 - 4.52110i) q^{76} -7.22925 q^{77} +(8.67850 + 15.0316i) q^{79} +(1.74253 + 11.3284i) q^{80} +(-2.69766 + 7.28730i) q^{82} -5.64965i q^{83} +(3.63183 - 6.29051i) q^{85} +(-0.744199 + 2.01034i) q^{86} +(-6.75619 + 3.75404i) q^{88} +(-1.33617 - 0.771439i) q^{89} +(2.85244 - 4.94056i) q^{91} +(5.07194 - 5.91175i) q^{92} +(-14.8020 + 2.52647i) q^{94} +(-12.3227 + 2.03755i) q^{95} +(-2.09143 + 1.20749i) q^{97} +(-0.00136766 + 0.00113490i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} + q^{4} - 4 q^{8} + 6 q^{10} + 6 q^{13} - 9 q^{14} - 11 q^{16} + 12 q^{19} + 14 q^{20} + 8 q^{22} - 10 q^{25} + 7 q^{28} + 12 q^{31} + 29 q^{32} - 6 q^{34} - 25 q^{38} - 46 q^{40} - 12 q^{41}+ \cdots - 12 q^{97}+O(q^{100}) $ 20 * q - q^2 + q^4 - 4 * q^8 + 6 * q^10 + 6 * q^13 - 9 * q^14 - 11 * q^16 + 12 * q^19 + 14 * q^20 + 8 * q^22 - 10 * q^25 + 7 * q^28 + 12 * q^31 + 29 * q^32 - 6 * q^34 - 25 * q^38 - 46 * q^40 - 12 * q^41 - 18 * q^43 + 12 * q^44 - 32 * q^46 + 36 * q^47 - 24 * q^49 + 34 * q^50 + 3 * q^52 + 12 * q^53 - 38 * q^56 + 16 * q^58 + 10 * q^61 + 55 * q^62 - 14 * q^64 + 14 * q^67 - 40 * q^68 + 26 * q^70 - 8 * q^71 - 6 * q^73 - 45 * q^74 - 69 * q^76 + 32 * q^77 - 6 * q^79 - 22 * q^80 + 24 * q^82 + 8 * q^85 - 7 * q^86 + 44 * q^88 + 24 * q^89 + 26 * q^91 + 18 * q^92 - 52 * q^94 - 4 * q^95 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	−1.08831	+	0.903091i	−0.769554	+	0.638582i
$2$	−1.08831	+	0.903091i	−0.769554	+	0.638582i
$3$		0			0
$3$		0			0
$4$	0.368852	−	1.96569i	0.184426	−	0.982846i
$5$	−1.43271	−	2.48152i	−0.640725	−	1.10977i	−0.985271	−	0.170999i	$-0.945300\pi$
$5$	−1.43271	−	2.48152i	−0.640725	−	1.10977i	0.344546	−	0.938769i	$-0.388033\pi$
$6$		0			0
$7$			2.64551i			0.999910i	0.866051	+	0.499955i	$0.166650\pi$
$7$			2.64551i			0.999910i	−0.866051	+	0.499955i	$0.833350\pi$
$8$	1.37377	+	2.47240i	0.485703	+	0.874124i
$9$		0			0
$10$	3.80027	+	1.40681i	1.20175	+	0.444871i
$11$			2.73265i			0.823924i	0.911201	+	0.411962i	$0.135156\pi$
$11$			2.73265i			0.823924i	−0.911201	+	0.411962i	$0.864844\pi$
$12$		0			0
$13$	−1.86752	−	1.07822i	−0.517958	−	0.299043i	0.218141	−	0.975917i	$-0.430001\pi$
$13$	−1.86752	−	1.07822i	−0.517958	−	0.299043i	−0.736099	+	0.676874i	$0.763334\pi$
$14$	−2.38914	−	2.87915i	−0.638525	−	0.769485i
$15$		0			0
$16$	−3.72790	−	1.45010i	−0.931974	−	0.362525i
$17$	1.26747	+	2.19532i	0.307407	+	0.532445i	0.977794	−	0.209567i	$-0.0672054\pi$
$17$	1.26747	+	2.19532i	0.307407	+	0.532445i	−0.670387	+	0.742011i	$0.733872\pi$
$18$		0			0
$19$	1.53443	−	4.07989i	0.352024	−	0.935991i
$19$	1.53443	−	4.07989i	0.352024	−	0.935991i
$20$	−5.40636	+	1.90095i	−1.20890	+	0.425064i
$21$		0			0
$22$	−2.46783	−	2.97398i	−0.526143	−	0.634054i
$23$	3.37287	+	1.94733i	0.703292	+	0.406046i	0.808572	−	0.588397i	$-0.200241\pi$
$23$	3.37287	+	1.94733i	0.703292	+	0.406046i	−0.105280	+	0.994443i	$0.533574\pi$
$24$		0			0
$25$	−1.60529	+	2.78044i	−0.321058	+	0.556088i
$26$	3.00618	−	0.513109i	0.589560	−	0.100629i
$27$		0			0
$28$	5.20027	+	0.975802i	0.982758	+	0.184409i
$29$	2.79010	+	1.61086i	0.518108	+	0.299130i	0.736160	−	0.676807i	$-0.236637\pi$
$29$	2.79010	+	1.61086i	0.518108	+	0.299130i	−0.218052	+	0.975937i	$0.569970\pi$
$30$		0			0
$31$	8.83425			1.58668			0.793339	−	0.608780i	$-0.208341\pi$
$31$	8.83425			1.58668			0.793339	+	0.608780i	$0.208341\pi$
$32$	5.36669	−	1.78847i	0.948706	−	0.316160i
$33$		0			0
$34$	−3.36199	−	1.24456i	−0.576576	−	0.213440i
$35$	6.56489	−	3.79024i	1.10967	−	0.640668i
$36$		0			0
$37$			12.0463i			1.98040i	0.139656	+	0.990200i	$0.455400\pi$
$37$			12.0463i			1.98040i	−0.139656	+	0.990200i	$0.544600\pi$
$38$	2.01457	+	5.82593i	0.326806	+	0.945091i
$39$		0			0
$40$	4.16708	−	6.95126i	0.658874	−	1.09909i
$41$	4.75850	−	2.74732i	0.743153	−	0.429059i	−0.0800618	−	0.996790i	$-0.525512\pi$
$41$	4.75850	−	2.74732i	0.743153	−	0.429059i	0.823214	+	0.567731i	$0.192178\pi$
$42$		0			0
$43$	1.31272	−	0.757900i	0.200188	−	0.115579i	−0.396555	−	0.918011i	$-0.629794\pi$
$43$	1.31272	−	0.757900i	0.200188	−	0.115579i	0.596743	+	0.802432i	$0.296461\pi$
$44$	5.37154	+	1.00794i	0.809791	+	0.151953i
$45$		0			0
$46$	−5.42935	+	0.926708i	−0.800515	+	0.136636i
$47$	9.19542	+	5.30898i	1.34129	+	0.774394i	0.986997	−	0.160740i	$-0.0513880\pi$
$47$	9.19542	+	5.30898i	1.34129	+	0.774394i	0.354294	+	0.935134i	$0.384721\pi$
$48$		0			0
$49$	0.00125668			0.000179525
$50$	−0.763936	−	4.47571i	−0.108037	−	0.632961i
$51$		0			0
$52$	−2.80828	+	3.27328i	−0.389439	+	0.453922i
$53$	−4.25386	−	2.45597i	−0.584312	−	0.337353i	0.178533	−	0.983934i	$-0.442865\pi$
$53$	−4.25386	−	2.45597i	−0.584312	−	0.337353i	−0.762845	+	0.646581i	$0.776198\pi$
$54$		0			0
$55$	6.78111	−	3.91508i	0.914365	−	0.527909i
$56$	−6.54076	+	3.63434i	−0.874046	+	0.485659i
$57$		0			0
$58$	−4.49126	+	0.766589i	−0.589731	+	0.100658i
$59$	−3.80546	−	6.59126i	−0.495429	−	0.858109i	0.504557	−	0.863378i	$-0.331656\pi$
$59$	−3.80546	−	6.59126i	−0.495429	−	0.858109i	−0.999986	+	0.00526981i	$0.998323\pi$
$60$		0			0
$61$	0.788072	−	1.36498i	0.100902	−	0.174768i	−0.811154	−	0.584832i	$-0.801160\pi$
$61$	0.788072	−	1.36498i	0.100902	−	0.174768i	0.912057	+	0.410064i	$0.134494\pi$
$62$	−9.61444	+	7.97814i	−1.22103	+	1.01322i
$63$		0			0
$64$	−4.22549	+	6.79303i	−0.528186	+	0.849129i
$65$			6.17906i			0.766418i
$66$		0			0
$67$	−5.23140	+	9.06106i	−0.639118	+	1.10698i	0.346509	+	0.938047i	$0.387367\pi$
$67$	−5.23140	+	9.06106i	−0.639118	+	1.10698i	−0.985627	+	0.168938i	$0.945966\pi$
$68$	4.78284	−	1.68171i	0.580005	−	0.203937i
$69$		0			0
$70$	−3.72172	+	10.0537i	−0.444831	+	1.20164i
$71$	2.82329	+	4.89008i	0.335063	+	0.580346i	0.983497	−	0.180925i	$-0.0579090\pi$
$71$	2.82329	+	4.89008i	0.335063	+	0.580346i	−0.648434	+	0.761271i	$0.724576\pi$
$72$		0			0
$73$	−6.42096	−	11.1214i	−0.751517	−	1.30167i	−0.947087	−	0.320976i	$-0.895989\pi$
$73$	−6.42096	−	11.1214i	−0.751517	−	1.30167i	0.195571	−	0.980690i	$-0.437344\pi$
$74$	−10.8789	−	13.1102i	−1.26465	−	1.52402i
$75$		0			0
$76$	−7.45383	−	4.52110i	−0.855013	−	0.518606i
$77$	−7.22925			−0.823850
$78$		0			0
$79$	8.67850	+	15.0316i	0.976408	+	1.69119i	0.675209	+	0.737626i	$0.264053\pi$
$79$	8.67850	+	15.0316i	0.976408	+	1.69119i	0.301198	+	0.953561i	$0.402613\pi$
$80$	1.74253	+	11.3284i	0.194821	+	1.26655i
$81$		0			0
$82$	−2.69766	+	7.28730i	−0.297906	+	0.804748i
$83$		−	5.64965i		−	0.620130i	−0.950715	−	0.310065i	$-0.899649\pi$
$83$		−	5.64965i		−	0.620130i	0.950715	−	0.310065i	$-0.100351\pi$
$84$		0			0
$85$	3.63183	−	6.29051i	0.393927	−	0.682301i
$86$	−0.744199	+	2.01034i	−0.0802490	+	0.216780i
$87$		0			0
$88$	−6.75619	+	3.75404i	−0.720212	+	0.400182i
$89$	−1.33617	−	0.771439i	−0.141634	−	0.0817724i	0.427509	−	0.904011i	$-0.359391\pi$
$89$	−1.33617	−	0.771439i	−0.141634	−	0.0817724i	−0.569142	+	0.822239i	$0.692725\pi$
$90$		0			0
$91$	2.85244	−	4.94056i	0.299016	−	0.517912i
$92$	5.07194	−	5.91175i	0.528786	−	0.616343i
$93$		0			0
$94$	−14.8020	+	2.52647i	−1.52671	+	0.260586i
$95$	−12.3227	+	2.03755i	−1.26428	+	0.209048i
$96$		0			0
$97$	−2.09143	+	1.20749i	−0.212353	+	0.122602i	−0.602404	−	0.798191i	$-0.705791\pi$
$97$	−2.09143	+	1.20749i	−0.212353	+	0.122602i	0.390052	+	0.920793i	$0.372457\pi$
$98$	−0.00136766	+	0.00113490i	−0.000138154	+	0.000114642i
$99$		0			0
$100$	4.87338	+	4.18107i	0.487338	+	0.418107i
$101$	−3.32390	+	5.75717i	−0.330741	+	0.572860i	−0.982657	−	0.185431i	$-0.940632\pi$
$101$	−3.32390	+	5.75717i	−0.330741	+	0.572860i	0.651916	+	0.758291i	$0.273965\pi$
$102$		0			0
$103$	9.22228			0.908698			0.454349	−	0.890824i	$-0.349872\pi$
$103$	9.22228			0.908698			0.454349	+	0.890824i	$0.349872\pi$
$104$	0.100220	−	6.09849i	0.00982737	−	0.598006i
$105$		0			0
$106$	6.84749	−	1.16876i	0.665087	−	0.113520i
$107$	11.0441			1.06767			0.533836	−	0.845588i	$-0.320750\pi$
$107$	11.0441			1.06767			0.533836	+	0.845588i	$0.320750\pi$
$108$		0			0
$109$	8.11096	−	4.68287i	0.776889	−	0.448537i	−0.0584373	−	0.998291i	$-0.518612\pi$
$109$	8.11096	−	4.68287i	0.776889	−	0.448537i	0.835327	+	0.549754i	$0.185278\pi$
$110$	−3.84430	+	10.3848i	−0.366540	+	0.990151i
$111$		0			0
$112$	3.83625	−	9.86220i	0.362492	−	0.931891i
$113$			19.9991i			1.88136i	0.339298	+	0.940679i	$0.389811\pi$
$113$			19.9991i			1.88136i	−0.339298	+	0.940679i	$0.610189\pi$
$114$		0			0
$115$		−	11.1598i		−	1.04066i
$116$	4.19560	−	4.89031i	0.389551	−	0.454054i
$117$		0			0
$118$	10.0940	+	3.73667i	0.929232	+	0.343988i
$119$	−5.80776	+	3.35311i	−0.532397	+	0.307379i
$120$		0			0
$121$	3.53264			0.321149
$122$	0.375033	+	2.19723i	0.0339539	+	0.198928i
$123$		0			0
$124$	3.25853	−	17.3654i	0.292625	−	1.55946i
$125$	−5.12743			−0.458612
$126$		0			0
$127$	0.531496	−	0.920577i	0.0471626	−	0.0816880i	−0.841480	−	0.540288i	$-0.818315\pi$
$127$	0.531496	−	0.920577i	0.0471626	−	0.0816880i	0.888643	+	0.458600i	$0.151649\pi$
$128$	−1.53607	−	11.2089i	−0.135771	−	0.990740i
$129$		0			0
$130$	−5.58026	−	6.72476i	−0.489421	−	0.589800i
$131$	−7.64858	+	4.41591i	−0.668259	+	0.385820i	−0.795417	−	0.606063i	$-0.792748\pi$
$131$	−7.64858	+	4.41591i	−0.668259	+	0.385820i	0.127158	+	0.991883i	$0.459415\pi$
$132$		0			0
$133$	10.7934	+	4.05937i	0.935907	+	0.351992i
$134$	−2.48956	−	14.5857i	−0.215065	−	1.26001i
$135$		0			0
$136$	−3.68649	+	6.14957i	−0.316114	+	0.527322i
$137$	10.2489	−	17.7515i	0.875619	−	1.51662i	0.0195162	−	0.999810i	$-0.493787\pi$
$137$	10.2489	−	17.7515i	0.875619	−	1.51662i	0.856102	−	0.516806i	$-0.172879\pi$
$138$		0			0
$139$	−3.61248	−	2.08566i	−0.306406	−	0.176904i	0.338911	−	0.940818i	$-0.389941\pi$
$139$	−3.61248	−	2.08566i	−0.306406	−	0.176904i	−0.645317	+	0.763915i	$0.723275\pi$
$140$	−5.02898	−	14.3026i	−0.425026	−	1.20879i
$141$		0			0
$142$	−7.48882	−	2.77225i	−0.628448	−	0.232642i
$143$	2.94638	−	5.10329i	0.246389	−	0.426758i
$144$		0			0
$145$		−	9.23157i		−	0.766640i
$146$	17.0317	+	6.30489i	1.40955	+	0.521796i
$147$		0			0
$148$	23.6793	+	4.44330i	1.94643	+	0.365237i
$149$	−8.11424	−	14.0543i	−0.664744	−	1.15137i	−0.979355	−	0.202150i	$-0.935207\pi$
$149$	−8.11424	−	14.0543i	−0.664744	−	1.15137i	0.314610	−	0.949221i	$-0.398126\pi$
$150$		0			0
$151$	−22.7285			−1.84962			−0.924809	−	0.380431i	$-0.875776\pi$
$151$	−22.7285			−1.84962			−0.924809	+	0.380431i	$0.875776\pi$
$152$	12.1951	−	1.81112i	0.989151	−	0.146901i
$153$		0			0
$154$	7.86769	−	6.52868i	0.633997	−	0.526096i
$155$	−12.6569	−	21.9224i	−1.01663	−	1.76085i
$156$		0			0
$157$	4.24706	+	7.35612i	0.338952	+	0.587082i	0.984236	−	0.176861i	$-0.0565943\pi$
$157$	4.24706	+	7.35612i	0.338952	+	0.587082i	−0.645284	+	0.763943i	$0.723261\pi$
$158$	−23.0198	−	8.52162i	−1.83136	−	0.677943i
$159$		0			0
$160$	−12.1270	−	10.7552i	−0.958724	−	0.850272i
$161$	−5.15168	+	8.92297i	−0.406009	+	0.703229i
$162$		0			0
$163$		−	0.960892i		−	0.0752629i	−0.999292	−	0.0376314i	$-0.988019\pi$
$163$		−	0.960892i		−	0.0752629i	0.999292	−	0.0376314i	$-0.0119813\pi$
$164$	−3.64521	−	10.3671i	−0.284643	−	0.809535i
$165$		0			0
$166$	5.10215	+	6.14859i	0.396004	+	0.477223i
$167$	−8.88741	+	15.3934i	−0.687728	+	1.19118i	0.284843	+	0.958574i	$0.408059\pi$
$167$	−8.88741	+	15.3934i	−0.687728	+	1.19118i	−0.972571	+	0.232606i	$0.925275\pi$
$168$		0			0
$169$	−4.17490	−	7.23114i	−0.321146	−	0.556242i
$170$	1.72834	+	10.1259i	0.132558	+	0.776622i
$171$		0			0
$172$	−1.00560	−	2.85996i	−0.0766762	−	0.218070i
$173$	−1.94298	+	1.12178i	−0.147722	+	0.0852875i	−0.572039	−	0.820226i	$-0.693848\pi$
$173$	−1.94298	+	1.12178i	−0.147722	+	0.0852875i	0.424317	+	0.905514i	$0.360514\pi$
$174$		0			0
$175$	−7.35569	−	4.24681i	−0.556038	−	0.321029i
$176$	3.96261	−	10.1870i	0.298693	−	0.767876i
$177$		0			0
$178$	2.15085	−	0.367118i	0.161213	−	0.0275167i
$179$	−2.69305			−0.201288			−0.100644	−	0.994922i	$-0.532090\pi$
$179$	−2.69305			−0.201288			−0.100644	+	0.994922i	$0.532090\pi$
$180$		0			0
$181$	7.51874	+	4.34095i	0.558864	+	0.322660i	0.752689	−	0.658376i	$-0.228756\pi$
$181$	7.51874	+	4.34095i	0.558864	+	0.322660i	−0.193825	+	0.981036i	$0.562090\pi$
$182$	1.35744	+	7.95289i	0.100620	+	0.589507i
$183$		0			0
$184$	−0.181003	+	11.0143i	−0.0133438	+	0.811982i
$185$	29.8931	−	17.2588i	2.19779	−	1.26889i
$186$		0			0
$187$	−5.99905	+	3.46355i	−0.438694	+	0.253280i
$188$	13.8276	−	16.1172i	1.00848	−	1.17546i
$189$		0			0
$190$	11.5709	−	13.3460i	0.839440	−	0.968223i
$191$		−	15.4264i		−	1.11622i	−0.829768	−	0.558109i	$-0.811527\pi$
$191$		−	15.4264i		−	1.11622i	0.829768	−	0.558109i	$-0.188473\pi$
$192$		0			0
$193$	−13.1165	+	7.57281i	−0.944146	+	0.545103i	−0.891258	−	0.453497i	$-0.850176\pi$
$193$	−13.1165	+	7.57281i	−0.944146	+	0.545103i	−0.0528886	+	0.998600i	$0.516843\pi$
$194$	1.18566	−	3.20288i	0.0851255	−	0.229953i
$195$		0			0
$196$	0.000463528	−	0.00247024i	3.31091e−5	−	0.000176446i
$197$	−1.69549			−0.120799			−0.0603994	−	0.998174i	$-0.519237\pi$
$197$	−1.69549			−0.120799			−0.0603994	+	0.998174i	$0.519237\pi$
$198$		0			0
$199$	−13.3077	−	7.68321i	−0.943358	−	0.544648i	−0.0523468	−	0.998629i	$-0.516670\pi$
$199$	−13.3077	−	7.68321i	−0.943358	−	0.544648i	−0.891011	+	0.453981i	$0.850003\pi$
$200$	−9.07965	−	0.149211i	−0.642028	−	0.0105508i
$201$		0			0
$202$	−1.58180	−	9.26740i	−0.111295	−	0.652052i
$203$	−4.26156	+	7.38124i	−0.299103	+	0.518062i
$204$		0			0
$205$	−13.6351	−	7.87220i	−0.952313	−	0.549818i
$206$	−10.0367	+	8.32856i	−0.699292	+	0.580279i
$207$		0			0
$208$	5.39842	+	6.72757i	0.374313	+	0.466473i
$209$	11.1489	+	4.19307i	0.771185	+	0.290041i
$210$		0			0
$211$	2.98218	+	5.16529i	0.205302	+	0.355593i	0.950229	−	0.311553i	$-0.100849\pi$
$211$	2.98218	+	5.16529i	0.205302	+	0.355593i	−0.744927	+	0.667146i	$0.767516\pi$
$212$	−6.39672	+	7.45589i	−0.439328	+	0.512073i
$213$		0			0
$214$	−12.0194	+	9.97382i	−0.821631	+	0.681797i
$215$	−3.76148	−	2.17169i	−0.256531	−	0.148108i
$216$		0			0
$217$			23.3711i			1.58654i
$218$	−4.59821	+	12.4214i	−0.311430	+	0.841281i
$219$		0			0
$220$	−5.19461	−	14.7737i	−0.350221	−	0.996040i
$221$		−	5.46643i		−	0.367712i
$222$		0			0
$223$	5.15998	+	8.93736i	0.345538	+	0.598490i	0.985451	−	0.169958i	$-0.0543631\pi$
$223$	5.15998	+	8.93736i	0.345538	+	0.598490i	−0.639913	+	0.768447i	$0.721030\pi$
$224$	4.73142	+	14.1977i	0.316132	+	0.948621i
$225$		0			0
$226$	−18.0610	−	21.7653i	−1.20140	−	1.44781i
$227$	7.97639			0.529411			0.264706	−	0.964329i	$-0.414725\pi$
$227$	7.97639			0.529411			0.264706	+	0.964329i	$0.414725\pi$
$228$		0			0
$229$	−5.24797			−0.346796			−0.173398	−	0.984852i	$-0.555475\pi$
$229$	−5.24797			−0.346796			−0.173398	+	0.984852i	$0.555475\pi$
$230$	10.0783	+	12.1453i	0.664544	+	0.800840i
$231$		0			0
$232$	−0.149729	+	9.11119i	−0.00983021	+	0.598179i
$233$	6.29168	+	10.8975i	0.412181	+	0.713919i	0.995128	−	0.0985913i	$-0.0314336\pi$
$233$	6.29168	+	10.8975i	0.412181	+	0.713919i	−0.582947	+	0.812510i	$0.698100\pi$
$234$		0			0
$235$		−	30.4248i		−	1.98470i
$236$	−14.3600	+	5.04918i	−0.934759	+	0.328673i
$237$		0			0
$238$	3.29250	−	8.89418i	0.213421	−	0.576524i
$239$			10.3998i			0.672707i	0.941736	+	0.336354i	$0.109194\pi$
$239$			10.3998i			0.672707i	−0.941736	+	0.336354i	$0.890806\pi$
$240$		0			0
$241$	−13.6723	−	7.89370i	−0.880710	−	0.508478i	−0.00981747	−	0.999952i	$-0.503125\pi$
$241$	−13.6723	−	7.89370i	−0.880710	−	0.508478i	−0.870892	+	0.491474i	$0.836458\pi$
$242$	−3.84462	+	3.19030i	−0.247142	+	0.205080i
$243$		0			0
$244$	−2.39245	−	2.05258i	−0.153161	−	0.131403i
$245$	−0.00180045	−	0.00311847i	−0.000115026	−	0.000199232i
$246$		0			0
$247$	−7.26460	+	5.96485i	−0.462235	+	0.379534i
$248$	12.1363	+	21.8418i	0.770654	+	1.38695i
$249$		0			0
$250$	5.58026	−	4.63054i	0.352926	−	0.292861i
$251$	−3.72142	−	2.14856i	−0.234894	−	0.135616i	0.377934	−	0.925833i	$-0.376635\pi$
$251$	−3.72142	−	2.14856i	−0.234894	−	0.135616i	−0.612828	+	0.790216i	$0.709968\pi$
$252$		0			0
$253$	−5.32136	+	9.21686i	−0.334551	+	0.579459i
$254$	0.252932	+	1.48187i	0.0158704	+	0.0929805i
$255$		0			0
$256$	11.7944	+	10.8116i	0.737152	+	0.675727i
$257$	−24.0830	−	13.9043i	−1.50226	−	0.867328i	−0.999997	−	0.00261095i	$-0.999169\pi$
$257$	−24.0830	−	13.9043i	−1.50226	−	0.867328i	−0.502259	−	0.864717i	$-0.667498\pi$
$258$		0			0
$259$	−31.8687			−1.98022
$260$	12.1461	+	2.27916i	0.753272	+	0.141347i
$261$		0			0
$262$	4.33608	−	11.7133i	0.267884	−	0.723647i
$263$	19.9939	−	11.5435i	1.23288	−	0.711803i	0.265250	−	0.964180i	$-0.414545\pi$
$263$	19.9939	−	11.5435i	1.23288	−	0.711803i	0.967629	+	0.252376i	$0.0812121\pi$
$264$		0			0
$265$			14.0747i			0.864602i
$266$	−15.4126	+	5.32957i	−0.945007	+	0.326777i
$267$		0			0
$268$	15.8816	+	13.6255i	0.970126	+	0.832311i
$269$	23.3260	−	13.4673i	1.42221	−	0.821113i	0.425722	−	0.904854i	$-0.360020\pi$
$269$	23.3260	−	13.4673i	1.42221	−	0.821113i	0.996488	+	0.0837405i	$0.0266867\pi$
$270$		0			0
$271$	15.9754	−	9.22339i	0.970435	−	0.560281i	0.0710661	−	0.997472i	$-0.477360\pi$
$271$	15.9754	−	9.22339i	0.970435	−	0.560281i	0.899369	+	0.437191i	$0.144027\pi$
$272$	−1.54157	−	10.0219i	−0.0934712	−	0.607667i
$273$		0			0
$274$	4.87730	+	28.5749i	0.294648	+	1.72627i
$275$	−7.59796	−	4.38668i	−0.458174	−	0.264527i
$276$		0			0
$277$	4.74769			0.285261			0.142631	−	0.989776i	$-0.454444\pi$
$277$	4.74769			0.285261			0.142631	+	0.989776i	$0.454444\pi$
$278$	5.81505	−	0.992541i	0.348764	−	0.0595286i
$279$		0			0
$280$	18.3897	+	11.0241i	1.09899	+	0.658815i
$281$	−0.594707	−	0.343354i	−0.0354773	−	0.0204828i	0.482156	−	0.876085i	$-0.339854\pi$
$281$	−0.594707	−	0.343354i	−0.0354773	−	0.0204828i	−0.517634	+	0.855602i	$0.673187\pi$
$282$		0			0
$283$	12.0092	−	6.93350i	0.713871	−	0.412154i	−0.0986215	−	0.995125i	$-0.531443\pi$
$283$	12.0092	−	6.93350i	0.713871	−	0.412154i	0.812493	+	0.582971i	$0.198110\pi$
$284$	10.6538	−	3.74601i	0.632186	−	0.222285i
$285$		0			0
$286$	1.40215	+	8.21483i	0.0829106	+	0.485753i
$287$	7.26807	+	12.5887i	0.429021	+	0.743086i
$288$		0			0
$289$	5.28703	−	9.15741i	0.311002	−	0.538671i
$290$	8.33695	+	10.0468i	0.489563	+	0.589971i
$291$		0			0
$292$	−24.2297	+	8.51948i	−1.41794	+	0.498565i
$293$		−	12.9508i		−	0.756594i	−0.925684	−	0.378297i	$-0.876510\pi$
$293$		−	12.9508i		−	0.756594i	0.925684	−	0.378297i	$-0.123490\pi$
$294$		0			0
$295$	−10.9042	+	18.8867i	−0.634868	+	1.09962i
$296$	−29.7832	+	16.5489i	−1.73112	+	0.961885i
$297$		0			0
$298$	21.5231	+	7.96755i	1.24680	+	0.461548i
$299$	−4.19928	−	7.27337i	−0.242851	−	0.420630i
$300$		0			0
$301$	2.00503	+	3.47282i	0.115568	+	0.200170i
$302$	24.7357	−	20.5259i	1.42338	−	1.18113i
$303$		0			0
$304$	−11.6365	+	12.9843i	−0.667397	+	0.744702i
$305$	−4.51630			−0.258603
$306$		0			0
$307$	15.3302	+	26.5527i	0.874940	+	1.51544i	0.856826	+	0.515605i	$0.172433\pi$
$307$	15.3302	+	26.5527i	0.874940	+	1.51544i	0.0181139	+	0.999836i	$0.494234\pi$
$308$	−2.66652	+	14.2105i	−0.151939	+	0.809718i
$309$		0			0
$310$	33.5725	+	12.4281i	1.90679	+	0.705867i
$311$			16.5211i			0.936826i	0.883510	+	0.468413i	$0.155174\pi$
$311$			16.5211i			0.936826i	−0.883510	+	0.468413i	$0.844826\pi$
$312$		0			0
$313$	11.5598	−	20.0221i	0.653397	−	1.13172i	−0.328897	−	0.944366i	$-0.606677\pi$
$313$	11.5598	−	20.0221i	0.653397	−	1.13172i	0.982293	−	0.187350i	$-0.0599899\pi$
$314$	−11.2654	−	4.17028i	−0.635742	−	0.235342i
$315$		0			0
$316$	32.7486	−	11.5148i	1.84225	−	0.647760i
$317$	−9.01160	−	5.20285i	−0.506142	−	0.292221i	0.225104	−	0.974335i	$-0.427728\pi$
$317$	−9.01160	−	5.20285i	−0.506142	−	0.292221i	−0.731246	+	0.682114i	$0.761061\pi$
$318$		0			0
$319$	−4.40192	+	7.62435i	−0.246460	+	0.426882i
$320$	22.9109	+	0.753219i	1.28076	+	0.0421062i
$321$		0			0
$322$	−2.45162	−	14.3634i	−0.136623	−	0.800443i
$323$	10.9015	−	1.80256i	0.606578	−	0.100297i
$324$		0			0
$325$	5.99583	−	3.46169i	0.332589	−	0.192020i
$326$	0.867773	+	1.04575i	0.0480615	+	0.0579188i
$327$		0			0
$328$	13.3296	+	7.99070i	0.736002	+	0.441212i
$329$	−14.0450	+	24.3266i	−0.774325	+	1.34117i
$330$		0			0
$331$	−2.96358			−0.162893			−0.0814465	−	0.996678i	$-0.525954\pi$
$331$	−2.96358			−0.162893			−0.0814465	+	0.996678i	$0.525954\pi$
$332$	−11.1055	−	2.08388i	−0.609492	−	0.114368i
$333$		0			0
$334$	−4.22940	−	24.7790i	−0.231423	−	1.35585i
$335$	29.9802			1.63800
$336$		0			0
$337$	17.9284	−	10.3510i	0.976625	−	0.563854i	0.0753752	−	0.997155i	$-0.475985\pi$
$337$	17.9284	−	10.3510i	0.976625	−	0.563854i	0.901249	+	0.433301i	$0.142651\pi$
$338$	11.0740	+	4.09943i	0.602345	+	0.222980i
$339$		0			0
$340$	−11.0256	−	9.45932i	−0.597947	−	0.513004i
$341$			24.1409i			1.30730i
$342$		0			0
$343$			18.5219i			1.00009i
$344$	3.67721	+	2.20438i	0.198262	+	0.118852i
$345$		0			0
$346$	1.10150	−	2.97554i	0.0592172	−	0.159966i
$347$	−23.9465	+	13.8255i	−1.28552	+	0.742192i	−0.977851	−	0.209303i	$-0.932881\pi$
$347$	−23.9465	+	13.8255i	−1.28552	+	0.742192i	−0.307664	+	0.951495i	$0.599547\pi$
$348$		0			0
$349$	−20.6404			−1.10486			−0.552428	−	0.833560i	$-0.686299\pi$
$349$	−20.6404			−1.10486			−0.552428	+	0.833560i	$0.686299\pi$
$350$	11.8406	−	2.02100i	0.632904	−	0.108027i
$351$		0			0
$352$	4.88726	+	14.6653i	0.260492	+	0.781661i
$353$	−7.25841			−0.386326			−0.193163	−	0.981167i	$-0.561875\pi$
$353$	−7.25841			−0.386326			−0.193163	+	0.981167i	$0.561875\pi$
$354$		0			0
$355$	8.08989	−	14.0121i	0.429367	−	0.743685i
$356$	−2.00926	+	2.34196i	−0.106491	+	0.124123i
$357$		0			0
$358$	2.93089	−	2.43207i	0.154902	−	0.128539i
$359$	−31.4803	+	18.1752i	−1.66147	+	0.959249i	−0.689453	+	0.724330i	$0.742149\pi$
$359$	−31.4803	+	18.1752i	−1.66147	+	0.959249i	−0.972015	+	0.234919i	$0.924517\pi$
$360$		0			0
$361$	−14.2910	−	12.5207i	−0.752159	−	0.658982i
$362$	−12.1030	+	2.06580i	−0.636121	+	0.108576i
$363$		0			0
$364$	−8.65950	−	7.42935i	−0.453881	−	0.389404i
$365$	−18.3987	+	31.8675i	−0.963031	+	1.66802i
$366$		0			0
$367$	−24.0822	−	13.9038i	−1.25708	−	0.725774i	−0.284573	−	0.958654i	$-0.591852\pi$
$367$	−24.0822	−	13.9038i	−1.25708	−	0.725774i	−0.972505	+	0.232880i	$0.925185\pi$
$368$	−9.74990	−	12.1504i	−0.508248	−	0.633385i
$369$		0			0
$370$	−16.9468	+	45.7792i	−0.881022	+	2.37995i
$371$	6.49729	−	11.2536i	0.337323	−	0.584260i
$372$		0			0
$373$		−	14.1662i		−	0.733496i	−0.930320	−	0.366748i	$-0.880471\pi$
$373$		−	14.1662i		−	0.733496i	0.930320	−	0.366748i	$-0.119529\pi$
$374$	3.40094	−	9.18712i	0.175858	−	0.475054i
$375$		0			0
$376$	−0.493468	+	30.0281i	−0.0254487	+	1.54858i
$377$	−3.47372	−	6.01666i	−0.178906	−	0.309874i
$378$		0			0
$379$	8.17116			0.419724			0.209862	−	0.977731i	$-0.432699\pi$
$379$	8.17116			0.419724			0.209862	+	0.977731i	$0.432699\pi$
$380$	−0.540052	+	24.9742i	−0.0277041	+	1.28115i
$381$		0			0
$382$	13.9315	+	16.7888i	0.712797	+	0.858990i
$383$	5.41972	+	9.38723i	0.276935	+	0.479665i	0.970621	−	0.240612i	$-0.0773481\pi$
$383$	5.41972	+	9.38723i	0.276935	+	0.479665i	−0.693687	+	0.720277i	$0.744015\pi$
$384$		0			0
$385$	10.3574	+	17.9395i	0.527861	+	0.914283i
$386$	7.43592	−	20.0870i	0.378478	−	1.02240i
$387$		0			0
$388$	1.60212	+	4.55650i	0.0813355	+	0.231321i
$389$	−1.89844	+	3.28819i	−0.0962545	+	0.166718i	−0.910132	−	0.414319i	$-0.864020\pi$
$389$	−1.89844	+	3.28819i	−0.0962545	+	0.166718i	0.813877	+	0.581037i	$0.197353\pi$
$390$		0			0
$391$			9.87273i			0.499285i
$392$	0.00172639	+	0.00310701i	8.71960e−5	+	0.000156928i
$393$		0			0
$394$	1.84523	−	1.53118i	0.0929612	−	0.0771400i
$395$	24.8675	−	43.0717i	1.25122	−	2.16717i
$396$		0			0
$397$	14.4380	+	25.0074i	0.724625	+	1.25509i	0.959128	+	0.282971i	$0.0913202\pi$
$397$	14.4380	+	25.0074i	0.724625	+	1.25509i	−0.234504	+	0.972115i	$0.575347\pi$
$398$	21.4216	−	3.65634i	1.07377	−	0.183276i
$399$		0			0
$400$	10.0163	−	8.03737i	0.500813	−	0.401868i
$401$	−5.26528	+	3.03991i	−0.262936	+	0.151806i	−0.625673	−	0.780085i	$-0.715176\pi$
$401$	−5.26528	+	3.03991i	−0.262936	+	0.151806i	0.362737	+	0.931891i	$0.381842\pi$
$402$		0			0
$403$	−16.4982	−	9.52523i	−0.821833	−	0.474486i
$404$	10.0908	+	8.65732i	0.502036	+	0.430718i
$405$		0			0
$406$	−2.02802	−	11.8817i	−0.100649	−	0.589678i
$407$	−32.9183			−1.63170
$408$		0			0
$409$	−10.5135	−	6.06998i	−0.519860	−	0.300141i	0.217017	−	0.976168i	$-0.430367\pi$
$409$	−10.5135	−	6.06998i	−0.519860	−	0.300141i	−0.736877	+	0.676026i	$0.763701\pi$
$410$	21.9485	−	3.74628i	1.08396	−	0.185015i
$411$		0			0
$412$	3.40165	−	18.1282i	0.167587	−	0.893111i
$413$	17.4373	−	10.0674i	0.858032	−	0.495385i
$414$		0			0
$415$	−14.0197	+	8.09428i	−0.688200	+	0.397333i
$416$	−11.9508	−	2.44644i	−0.585936	−	0.119947i
$417$		0			0
$418$	−15.9202	+	5.50510i	−0.778683	+	0.269263i
$419$			29.9456i			1.46294i	0.681875	+	0.731468i	$0.261165\pi$
$419$			29.9456i			1.46294i	−0.681875	+	0.731468i	$0.738835\pi$
$420$		0			0
$421$	25.1779	−	14.5365i	1.22710	−	0.708465i	0.260676	−	0.965426i	$-0.416055\pi$
$421$	25.1779	−	14.5365i	1.22710	−	0.708465i	0.966422	+	0.256962i	$0.0827214\pi$
$422$	−7.91028	−	2.92827i	−0.385066	−	0.142546i
$423$		0			0
$424$	0.228281	−	13.8912i	0.0110863	−	0.674615i
$425$	−8.13863			−0.394781
$426$		0			0
$427$	3.61108	+	2.08486i	0.174752	+	0.100893i
$428$	4.07363	−	21.7093i	0.196906	−	1.04936i
$429$		0			0
$430$	6.05491	−	1.03348i	0.291994	−	0.0498389i
$431$	−13.2187	+	22.8955i	−0.636724	+	1.10284i	0.349423	+	0.936965i	$0.386378\pi$
$431$	−13.2187	+	22.8955i	−0.636724	+	1.10284i	−0.986147	+	0.165873i	$0.946956\pi$
$432$		0			0
$433$	7.80644	+	4.50705i	0.375154	+	0.216595i	0.675708	−	0.737170i	$-0.263838\pi$
$433$	7.80644	+	4.50705i	0.375154	+	0.216595i	−0.300554	+	0.953765i	$0.597172\pi$
$434$	−21.1063	−	25.4351i	−1.01313	−	1.22092i
$435$		0			0
$436$	−6.21334	−	17.6709i	−0.297565	−	0.846285i
$437$	13.1203	−	10.7729i	0.627631	−	0.515337i
$438$		0			0
$439$	−1.79046	−	3.10116i	−0.0854539	−	0.148011i	0.820131	−	0.572176i	$-0.193901\pi$
$439$	−1.79046	−	3.10116i	−0.0854539	−	0.148011i	−0.905585	+	0.424166i	$0.860567\pi$
$440$	18.9953	+	11.3872i	0.905567	+	0.542862i
$441$		0			0
$442$	4.93669	+	5.94919i	0.234814	+	0.282974i
$443$	24.9361	+	14.3969i	1.18475	+	0.684015i	0.957108	−	0.289730i	$-0.0935655\pi$
$443$	24.9361	+	14.3969i	1.18475	+	0.684015i	0.227641	+	0.973745i	$0.426899\pi$
$444$		0			0
$445$			4.42098i			0.209575i
$446$	−13.6869	−	5.06671i	−0.648095	−	0.239915i
$447$		0			0
$448$	−17.9711	−	11.1786i	−0.849052	−	0.528139i
$449$		−	6.55031i		−	0.309128i	−0.987983	−	0.154564i	$-0.950603\pi$
$449$		−	6.55031i		−	0.309128i	0.987983	−	0.154564i	$-0.0493973\pi$
$450$		0			0
$451$	7.50746	+	13.0033i	0.353512	+	0.612301i
$452$	39.3121	+	7.37671i	1.84909	+	0.346971i
$453$		0			0
$454$	−8.68081	+	7.20341i	−0.407410	+	0.338073i
$455$	−16.3468			−0.766350
$456$		0			0
$457$	−22.7229			−1.06293			−0.531467	−	0.847079i	$-0.678359\pi$
$457$	−22.7229			−1.06293			−0.531467	+	0.847079i	$0.678359\pi$
$458$	5.71144	−	4.73940i	0.266878	−	0.221458i
$459$		0			0
$460$	−21.9367	−	4.11631i	−1.02280	−	0.191924i
$461$	2.15879	+	3.73913i	0.100545	+	0.174149i	0.911909	−	0.410392i	$-0.134608\pi$
$461$	2.15879	+	3.73913i	0.100545	+	0.174149i	−0.811364	+	0.584541i	$0.801275\pi$
$462$		0			0
$463$		−	4.45527i		−	0.207054i	−0.994627	−	0.103527i	$-0.966987\pi$
$463$		−	4.45527i		−	0.207054i	0.994627	−	0.103527i	$-0.0330128\pi$
$464$	−8.06529	−	10.0511i	−0.374422	−	0.466608i
$465$		0			0
$466$	−16.6888	−	6.17794i	−0.773092	−	0.286187i
$467$		−	29.6919i		−	1.37398i	−0.726669	−	0.686988i	$-0.758933\pi$
$467$		−	29.6919i		−	1.37398i	0.726669	−	0.686988i	$-0.241067\pi$
$468$		0			0
$469$	−23.9711	−	13.8397i	−1.10688	−	0.639060i
$470$	27.4764	+	33.1117i	1.26739	+	1.52733i
$471$		0			0
$472$	11.0684	−	18.4635i	0.509462	−	0.849852i
$473$	2.07107	+	3.58720i	0.0952280	+	0.164940i
$474$		0			0
$475$	8.88068	+	10.8158i	0.407474	+	0.496263i
$476$	4.44899	+	12.6531i	0.203919	+	0.579953i
$477$		0			0
$478$	−9.39197	−	11.3182i	−0.429579	−	0.517684i
$479$	0.612140	+	0.353419i	0.0279694	+	0.0161481i	0.513920	−	0.857838i	$-0.328193\pi$
$479$	0.612140	+	0.353419i	0.0279694	+	0.0161481i	−0.485950	+	0.873987i	$0.661526\pi$
$480$		0			0
$481$	12.9885	−	22.4968i	0.592225	−	1.02576i
$482$	22.0085	−	3.75651i	1.00246	−	0.171104i
$483$		0			0
$484$	1.30302	−	6.94409i	0.0592283	−	0.315641i
$485$	5.99281	+	3.45995i	0.272120	+	0.157108i
$486$		0			0
$487$	2.51995			0.114190			0.0570950	−	0.998369i	$-0.481816\pi$
$487$	2.51995			0.114190			0.0570950	+	0.998369i	$0.481816\pi$
$488$	4.45741	+	0.0732511i	0.201777	+	0.00331592i
$489$		0			0
$490$	0.00477572	+	0.00176790i	0.000215745	+	7.98657e-5i
$491$	1.58171	−	0.913203i	0.0713817	−	0.0412123i	−0.463884	−	0.885896i	$-0.653545\pi$
$491$	1.58171	−	0.913203i	0.0713817	−	0.0412123i	0.535266	+	0.844684i	$0.320211\pi$
$492$		0			0
$493$			8.16690i			0.367819i
$494$	2.51936	−	13.0522i	0.113351	−	0.587247i
$495$		0			0
$496$	−32.9332	−	12.8105i	−1.47874	−	0.575210i
$497$	−12.9368	+	7.46906i	−0.580294	+	0.335033i
$498$		0			0
$499$	−1.45988	+	0.842864i	−0.0653534	+	0.0377318i	−0.532321	−	0.846543i	$-0.678680\pi$
$499$	−1.45988	+	0.842864i	−0.0653534	+	0.0377318i	0.466967	+	0.884275i	$0.345347\pi$
$500$	−1.89126	+	10.0790i	−0.0845798	+	0.450745i
$501$		0			0
$502$	5.99042	−	1.02247i	0.267366	−	0.0456352i
$503$	0.506143	+	0.292222i	0.0225678	+	0.0130295i	0.511241	−	0.859437i	$-0.329186\pi$
$503$	0.506143	+	0.292222i	0.0225678	+	0.0130295i	−0.488674	+	0.872467i	$0.662519\pi$
$504$		0			0
$505$	19.0487			0.847656
$506$	−2.53236	−	14.8365i	−0.112577	−	0.659563i
$507$		0			0
$508$	−1.61353	−	1.38431i	−0.0715888	−	0.0614190i
$509$	27.4296	+	15.8365i	1.21579	+	0.701939i	0.964015	−	0.265846i	$-0.0856513\pi$
$509$	27.4296	+	15.8365i	1.21579	+	0.701939i	0.251778	+	0.967785i	$0.418985\pi$
$510$		0			0
$511$	29.4219	−	16.9867i	1.30155	−	0.751449i
$512$	−22.5999	−	1.11499i	−0.998785	−	0.0492763i
$513$		0			0
$514$	38.7667	−	6.61689i	1.70993	−	0.291858i
$515$	−13.2128	−	22.8853i	−0.582226	−	1.00845i
$516$		0			0
$517$	−14.5076	+	25.1278i	−0.638042	+	1.10512i
$518$	34.6831	−	28.7803i	1.52389	−	1.26453i
$519$		0			0
$520$	−15.2771	+	8.48864i	−0.669945	+	0.372251i
$521$			9.96539i			0.436592i	0.975883	+	0.218296i	$0.0700498\pi$
$521$			9.96539i			0.436592i	−0.975883	+	0.218296i	$0.929950\pi$
$522$		0			0
$523$	6.71352	−	11.6282i	0.293562	−	0.508464i	−0.681088	−	0.732202i	$-0.738493\pi$
$523$	6.71352	−	11.6282i	0.293562	−	0.508464i	0.974649	+	0.223738i	$0.0718261\pi$
$524$	5.85913	+	16.6636i	0.255957	+	0.727951i
$525$		0			0
$526$	−11.3348	+	30.6193i	−0.494222	+	1.33507i
$527$	11.1972	+	19.3941i	0.487756	+	0.844818i
$528$		0			0
$529$	−3.91583	−	6.78242i	−0.170254	−	0.294888i
$530$	−12.7107	−	15.3177i	−0.552119	−	0.665358i
$531$		0			0
$532$	11.9606	−	19.7192i	0.518559	−	0.854937i
$533$	−11.8488			−0.513229
$534$		0			0
$535$	−15.8229	−	27.4061i	−0.684085	−	1.18487i
$536$	−29.5893	−	0.486257i	−1.27806	−	0.0210031i
$537$		0			0
$538$	−13.2238	+	35.7221i	−0.570119	+	1.54009i
$539$			0.00343406i			0.000147915i
$540$		0			0
$541$	−8.23202	+	14.2583i	−0.353922	+	0.613011i	−0.986933	−	0.161132i	$-0.948486\pi$
$541$	−8.23202	+	14.2583i	−0.353922	+	0.613011i	0.633011	+	0.774143i	$0.281819\pi$
$542$	−9.05665	+	24.4652i	−0.389016	+	1.05087i
$543$		0			0
$544$	10.7284	+	9.51480i	0.459976	+	0.407943i
$545$	−23.2412	−	13.4183i	−0.995545	−	0.574778i
$546$		0			0
$547$	−3.77873	+	6.54495i	−0.161567	+	0.279842i	−0.935431	−	0.353510i	$-0.884988\pi$
$547$	−3.77873	+	6.54495i	−0.161567	+	0.279842i	0.773864	+	0.633352i	$0.218321\pi$
$548$	−31.1138	−	26.6938i	−1.32911	−	1.14030i
$549$		0			0
$550$	12.2305	−	2.08757i	0.521512	−	0.0890141i
$551$	10.8534	−	8.91153i	0.462369	−	0.379644i
$552$		0			0
$553$	−39.7663	+	22.9591i	−1.69104	+	0.976320i
$554$	−5.16698	+	4.28760i	−0.219524	+	0.182163i
$555$		0			0
$556$	−5.43224	+	6.33172i	−0.230378	+	0.268525i
$557$	16.7655	−	29.0386i	0.710376	−	1.23041i	−0.254340	−	0.967115i	$-0.581858\pi$
$557$	16.7655	−	29.0386i	0.710376	−	1.23041i	0.964716	−	0.263292i	$-0.0848083\pi$
$558$		0			0
$559$	−3.26872			−0.138252
$560$	−29.9695	+	4.60989i	−1.26644	+	0.194804i
$561$		0			0
$562$	0.957308	−	0.163398i	0.0403816	−	0.00689252i
$563$	8.75511			0.368984			0.184492	−	0.982834i	$-0.440936\pi$
$563$	8.75511			0.368984			0.184492	+	0.982834i	$0.440936\pi$
$564$		0			0
$565$	49.6282	−	28.6528i	2.08787	−	1.20543i
$566$	−6.80816	+	18.3912i	−0.286168	+	0.773040i
$567$		0			0
$568$	−8.21166	+	13.6982i	−0.344554	+	0.574762i
$569$		−	6.32953i		−	0.265348i	−0.991160	−	0.132674i	$-0.957644\pi$
$569$		−	6.32953i		−	0.265348i	0.991160	−	0.132674i	$-0.0423563\pi$
$570$		0			0
$571$		−	20.2768i		−	0.848559i	−0.905531	−	0.424279i	$-0.860527\pi$
$571$		−	20.2768i		−	0.848559i	0.905531	−	0.424279i	$-0.139473\pi$
$572$	−8.94471	−	7.67404i	−0.373997	−	0.320868i
$573$		0			0
$574$	−19.2787	−	7.13669i	−0.804676	−	0.297879i
$575$	−10.8289	+	6.25204i	−0.451594	+	0.260728i
$576$		0			0
$577$	11.2386			0.467870			0.233935	−	0.972252i	$-0.424840\pi$
$577$	11.2386			0.467870			0.233935	+	0.972252i	$0.424840\pi$
$578$	2.51603	+	14.7408i	0.104653	+	0.613137i
$579$		0			0
$580$	−18.1464	−	3.40508i	−0.753490	−	0.141388i
$581$	14.9462			0.620074
$582$		0			0
$583$	6.71129	−	11.6243i	0.277953	−	0.481429i
$584$	18.6756	−	31.1535i	0.772803	−	1.28914i
$585$		0			0
$586$	11.6958	+	14.0945i	0.483147	+	0.582240i
$587$	18.7495	−	10.8250i	0.773874	−	0.446797i	−0.0603806	−	0.998175i	$-0.519231\pi$
$587$	18.7495	−	10.8250i	0.773874	−	0.446797i	0.834255	+	0.551379i	$0.185898\pi$
$588$		0			0
$589$	13.5556	−	36.0428i	0.558548	−	1.48512i
$590$	−5.18917	−	30.4021i	−0.213635	−	1.25163i
$591$		0			0
$592$	17.4683	−	44.9074i	0.717944	−	1.84568i
$593$	−10.8984	+	18.8765i	−0.447542	+	0.775166i	−0.998225	−	0.0595485i	$-0.981034\pi$
$593$	−10.8984	+	18.8765i	−0.447542	+	0.775166i	0.550683	+	0.834714i	$0.314367\pi$
$594$		0			0
$595$	16.6416	+	9.60804i	0.682240	+	0.393891i
$596$	−30.6193	+	10.7662i	−1.25422	+	0.440999i
$597$		0			0
$598$	11.1386	+	4.12337i	0.455493	+	0.168617i
$599$	12.9904	−	22.5000i	0.530773	−	0.919326i	−0.468582	−	0.883420i	$-0.655235\pi$
$599$	12.9904	−	22.5000i	0.530773	−	0.919326i	0.999355	−	0.0359059i	$-0.0114317\pi$
$600$		0			0
$601$			5.80590i			0.236828i	0.992964	+	0.118414i	$0.0377809\pi$
$601$			5.80590i			0.236828i	−0.992964	+	0.118414i	$0.962219\pi$
$602$	−5.31838	−	1.96879i	−0.216761	−	0.0802418i
$603$		0			0
$604$	−8.38344	+	44.6772i	−0.341117	+	1.81789i
$605$	−5.06124	−	8.76632i	−0.205769	−	0.356402i
$606$		0			0
$607$	−16.2119			−0.658022			−0.329011	−	0.944326i	$-0.606715\pi$
$607$	−16.2119			−0.658022			−0.329011	+	0.944326i	$0.606715\pi$
$608$	0.938073	−	24.6398i	0.0380439	−	0.999276i
$609$		0			0
$610$	4.91515	−	4.07863i	0.199009	−	0.165139i
$611$	−11.4485	−	19.8293i	−0.463155	−	0.802208i
$612$		0			0
$613$	−11.3947	−	19.7362i	−0.460227	−	0.797136i	0.538745	−	0.842469i	$-0.318899\pi$
$613$	−11.3947	−	19.7362i	−0.460227	−	0.797136i	−0.998972	+	0.0453327i	$0.985565\pi$
$614$	−40.6635	−	15.0531i	−1.64105	−	0.607492i
$615$		0			0
$616$	−9.93136	−	17.8736i	−0.400146	−	0.720147i
$617$	16.2450	−	28.1372i	0.653999	−	1.13276i	−0.328144	−	0.944628i	$-0.606423\pi$
$617$	16.2450	−	28.1372i	0.653999	−	1.13276i	0.982144	−	0.188132i	$-0.0602434\pi$
$618$		0			0
$619$		−	6.61987i		−	0.266075i	−0.991111	−	0.133037i	$-0.957527\pi$
$619$		−	6.61987i		−	0.266075i	0.991111	−	0.133037i	$-0.0424731\pi$
$620$	−47.7611	+	16.7934i	−1.91813	+	0.674441i
$621$		0			0
$622$	−14.9201	−	17.9801i	−0.598241	−	0.720938i
$623$	2.04085	−	3.53486i	0.0817651	−	0.141621i
$624$		0			0
$625$	15.3725	+	26.6260i	0.614902	+	1.06504i
$626$	5.50114	+	32.2298i	0.219870	+	1.28816i
$627$		0			0
$628$	16.0264	−	5.63509i	0.639523	−	0.224865i
$629$	−26.4456	+	15.2683i	−1.05445	+	0.608789i
$630$		0			0
$631$	6.62256	+	3.82354i	0.263640	+	0.152213i	0.625994	−	0.779828i	$-0.284693\pi$
$631$	6.62256	+	3.82354i	0.263640	+	0.152213i	−0.362354	+	0.932041i	$0.618027\pi$
$632$	−25.2418	+	42.1067i	−1.00406	+	1.67492i
$633$		0			0
$634$	14.5061	−	2.47597i	0.576111	−	0.0983333i
$635$	−3.04591			−0.120873
$636$		0			0
$637$	−0.00234688	−	0.00135497i	−9.29867e−5	−	5.36859e-5i
$638$	−2.09482	−	12.2730i	−0.0829346	−	0.485894i
$639$		0			0
$640$	−25.6145	+	19.8709i	−1.01250	+	0.785466i
$641$	34.0636	−	19.6666i	1.34543	−	0.776785i	0.357833	−	0.933786i	$-0.383516\pi$
$641$	34.0636	−	19.6666i	1.34543	−	0.776785i	0.987598	+	0.157001i	$0.0501825\pi$
$642$		0			0
$643$	26.2592	−	15.1608i	1.03556	−	0.597882i	0.116989	−	0.993133i	$-0.462676\pi$
$643$	26.2592	−	15.1608i	1.03556	−	0.597882i	0.918573	+	0.395251i	$0.129342\pi$
$644$	15.6396	+	13.4179i	0.616287	+	0.528738i
$645$		0			0
$646$	−10.2364	+	11.8068i	−0.402746	+	0.464534i
$647$		−	16.9422i		−	0.666068i	−0.942915	−	0.333034i	$-0.891928\pi$
$647$		−	16.9422i		−	0.666068i	0.942915	−	0.333034i	$-0.108072\pi$
$648$		0			0
$649$	18.0116	−	10.3990i	0.707016	−	0.408196i
$650$	−3.39912	+	9.18219i	−0.133324	+	0.360155i
$651$		0			0
$652$	−1.88882	−	0.354427i	−0.0739718	−	0.0138804i
$653$	20.3739			0.797293			0.398647	−	0.917105i	$-0.369480\pi$
$653$	20.3739			0.797293			0.398647	+	0.917105i	$0.369480\pi$
$654$		0			0
$655$	21.9163	+	12.6534i	0.856341	+	0.494409i
$656$	−21.7231	+	3.34144i	−0.848144	+	0.130461i
$657$		0			0
$658$	−6.68382	−	39.1589i	−0.260563	−	1.52657i
$659$	9.33757	−	16.1732i	0.363740	−	0.630017i	−0.624833	−	0.780758i	$-0.714833\pi$
$659$	9.33757	−	16.1732i	0.363740	−	0.630017i	0.988573	+	0.150742i	$0.0481662\pi$
$660$		0			0
$661$	−4.59355	−	2.65209i	−0.178668	−	0.103154i	0.407999	−	0.912983i	$-0.366227\pi$
$661$	−4.59355	−	2.65209i	−0.178668	−	0.103154i	−0.586667	+	0.809828i	$0.699560\pi$
$662$	3.22530	−	2.67638i	0.125355	−	0.104020i
$663$		0			0
$664$	13.9682	−	7.76134i	0.542070	−	0.301198i
$665$	−5.39037	−	32.5999i	−0.209030	−	1.26417i
$666$		0			0
$667$	6.27376	+	10.8665i	0.242921	+	0.420751i
$668$	26.9806	+	23.1478i	1.04391	+	0.895616i
$669$		0			0
$670$	−32.6279	+	27.0749i	−1.26053	+	1.04599i
$671$	3.73001	+	2.15352i	0.143995	+	0.0831358i
$672$		0			0
$673$			46.2022i			1.78096i	0.455018	+	0.890482i	$0.349633\pi$
$673$			46.2022i			1.78096i	−0.455018	+	0.890482i	$0.650367\pi$
$674$	−10.1639	+	27.4561i	−0.391498	+	1.05757i
$675$		0			0
$676$	−15.7541	+	5.53935i	−0.605928	+	0.213052i
$677$			6.63900i			0.255157i	0.991828	+	0.127579i	$0.0407205\pi$
$677$			6.63900i			0.255157i	−0.991828	+	0.127579i	$0.959279\pi$
$678$		0			0
$679$	−3.19443	−	5.53291i	−0.122591	−	0.212334i
$680$	20.5419	+	0.337577i	0.787747	+	0.0129455i
$681$		0			0
$682$	−21.8014	−	26.2729i	−0.834820	−	1.00604i
$683$	−17.9771			−0.687875			−0.343938	−	0.938992i	$-0.611761\pi$
$683$	−17.9771			−0.687875			−0.343938	+	0.938992i	$0.611761\pi$
$684$		0			0
$685$	−58.7343			−2.24412
$686$	−16.7270	−	20.1577i	−0.638639	−	0.769623i
$687$		0			0
$688$	−5.99272	+	0.921798i	−0.228470	+	0.0351432i
$689$	5.29612	+	9.17316i	0.201766	+	0.349469i
$690$		0			0
$691$			5.97635i			0.227351i	0.993518	+	0.113675i	$0.0362624\pi$
$691$			5.97635i			0.227351i	−0.993518	+	0.113675i	$0.963738\pi$
$692$	1.48841	+	4.23308i	0.0565807	+	0.160918i
$693$		0			0
$694$	13.5756	−	36.6724i	0.515322	−	1.39206i
$695$			11.9526i			0.453387i
$696$		0			0
$697$	12.0625	+	6.96430i	0.456901	+	0.263792i
$698$	22.4633	−	18.6402i	0.850247	−	0.705542i
$699$		0			0
$700$	−11.0611	+	12.8926i	−0.418070	+	0.487294i
$701$	−10.7697	−	18.6537i	−0.406766	−	0.704540i	0.587759	−	0.809036i	$-0.300010\pi$
$701$	−10.7697	−	18.6537i	−0.406766	−	0.704540i	−0.994525	+	0.104496i	$0.966677\pi$
$702$		0			0
$703$	49.1476	+	18.4843i	1.85364	+	0.697147i
$704$	−18.5629	−	11.5468i	−0.699617	−	0.435185i
$705$		0			0
$706$	7.89942	−	6.55501i	0.297299	−	0.246701i
$707$	−15.2307	−	8.79344i	−0.572809	−	0.330711i
$708$		0			0
$709$	−13.0879	+	22.6689i	−0.491526	+	0.851348i	−0.999952	−	0.00975743i	$-0.996894\pi$
$709$	−13.0879	+	22.6689i	−0.491526	+	0.851348i	0.508426	+	0.861105i	$0.330227\pi$
$710$	3.84987	+	22.5555i	0.144483	+	0.846491i
$711$		0			0
$712$	0.0717050	−	4.36333i	0.00268726	−	0.163523i
$713$	29.7968	+	17.2032i	1.11590	+	0.644264i
$714$		0			0
$715$	−16.8852			−0.631470
$716$	−0.993338	+	5.29372i	−0.0371228	+	0.197836i
$717$		0			0
$718$	17.8466	−	48.2099i	0.666030	−	1.79918i
$719$	−8.14319	+	4.70147i	−0.303690	+	0.175335i	−0.644099	−	0.764942i	$-0.722768\pi$
$719$	−8.14319	+	4.70147i	−0.303690	+	0.175335i	0.340409	+	0.940277i	$0.389434\pi$
$720$		0			0
$721$			24.3977i			0.908617i
$722$	26.8604	+	0.720297i	0.999641	+	0.0268067i
$723$		0			0
$724$	11.3063	−	13.1784i	0.420194	−	0.489770i
$725$	−8.95782	+	5.17180i	−0.332685	+	0.192076i
$726$		0			0
$727$	−9.47912	+	5.47277i	−0.351561	+	0.202974i	−0.665373	−	0.746511i	$-0.731727\pi$
$727$	−9.47912	+	5.47277i	−0.351561	+	0.202974i	0.313811	+	0.949485i	$0.398394\pi$
$728$	16.1336	+	0.265133i	0.597952	+	0.00982648i
$729$		0			0
$730$	−8.75570	−	51.2975i	−0.324063	−	1.89861i
$731$	3.32767	+	1.92123i	0.123078	+	0.0710593i
$732$		0			0
$733$	7.49814			0.276950			0.138475	−	0.990366i	$-0.455780\pi$
$733$	7.49814			0.276950			0.138475	+	0.990366i	$0.455780\pi$
$734$	38.7654	−	6.61665i	1.43086	−	0.244225i
$735$		0			0
$736$	21.5839	+	4.41843i	0.795593	+	0.162865i
$737$	−24.7607	−	14.2956i	−0.912071	−	0.526584i
$738$		0			0
$739$	−25.4925	+	14.7181i	−0.937758	+	0.541415i	−0.889257	−	0.457409i	$-0.848778\pi$
$739$	−25.4925	+	14.7181i	−0.937758	+	0.541415i	−0.0485009	+	0.998823i	$0.515444\pi$
$740$	−22.8994	−	65.1266i	−0.841798	−	2.39410i
$741$		0			0
$742$	3.09198	+	18.1151i	0.113510	+	0.665027i
$743$	10.1494	+	17.5793i	0.372345	+	0.644921i	0.989926	−	0.141587i	$-0.0452204\pi$
$743$	10.1494	+	17.5793i	0.372345	+	0.644921i	−0.617581	+	0.786508i	$0.711887\pi$
$744$		0			0
$745$	−23.2506	+	40.2713i	−0.851837	+	1.47542i
$746$	12.7933	+	15.4172i	0.468398	+	0.564465i
$747$		0			0
$748$	4.59552	+	13.0698i	0.168029	+	0.477880i
$749$			29.2173i			1.06758i
$750$		0			0
$751$	4.68855	−	8.12080i	0.171087	−	0.296332i	−0.767713	−	0.640794i	$-0.778605\pi$
$751$	4.68855	−	8.12080i	0.171087	−	0.296332i	0.938800	+	0.344462i	$0.111939\pi$
$752$	−26.5810	−	33.1256i	−0.969311	−	1.20797i
$753$		0			0
$754$	9.21409	+	3.41092i	0.335557	+	0.124218i
$755$	32.5632	+	56.4012i	1.18510	+	2.05265i
$756$		0			0
$757$	−11.3062	−	19.5829i	−0.410930	−	0.711752i	0.584062	−	0.811709i	$-0.301463\pi$
$757$	−11.3062	−	19.5829i	−0.410930	−	0.711752i	−0.994992	+	0.0999576i	$0.968129\pi$
$758$	−8.89278	+	7.37930i	−0.323000	+	0.268028i
$759$		0			0
$760$	−21.9663	−	27.6675i	−0.796800	−	1.00361i
$761$	−22.6617			−0.821484			−0.410742	−	0.911752i	$-0.634730\pi$
$761$	−22.6617			−0.821484			−0.410742	+	0.911752i	$0.634730\pi$
$762$		0			0
$763$	12.3886	+	21.4577i	0.448497	+	0.776820i
$764$	−30.3236	−	5.69007i	−1.09707	−	0.205859i
$765$		0			0
$766$	−14.3759	−	5.32174i	−0.519422	−	0.192282i
$767$			16.4125i			0.592619i
$768$		0			0
$769$	23.0145	−	39.8622i	0.829923	−	1.43747i	−0.0681747	−	0.997673i	$-0.521718\pi$
$769$	23.0145	−	39.8622i	0.829923	−	1.43747i	0.898098	−	0.439796i	$-0.144949\pi$
$770$	−27.4731	−	10.1702i	−0.990062	−	0.366507i
$771$		0			0
$772$	10.0478	+	28.5763i	0.361628	+	1.02848i
$773$	−0.612546	−	0.353654i	−0.0220318	−	0.0127200i	0.488944	−	0.872315i	$-0.337382\pi$
$773$	−0.612546	−	0.353654i	−0.0220318	−	0.0127200i	−0.510975	+	0.859595i	$0.670716\pi$
$774$		0			0
$775$	−14.1815	+	24.5631i	−0.509415	+	0.882333i
$776$	−5.85855	−	3.51203i	−0.210310	−	0.126075i
$777$		0			0
$778$	−0.903441	−	5.29304i	−0.0323899	−	0.189765i
$779$	−3.90716	−	23.6297i	−0.139989	−	0.846623i
$780$		0			0
$781$	−13.3629	+	7.71506i	−0.478161	+	0.276066i
$782$	−8.91598	−	10.7446i	−0.318835	−	0.384227i
$783$		0			0
$784$	−0.00468477	−	0.00182231i	−0.000167313	−	6.50824e-5i
$785$	12.1696	−	21.0783i	0.434350	−	0.752316i
$786$		0			0
$787$	−18.5369			−0.660769			−0.330385	−	0.943846i	$-0.607178\pi$
$787$	−18.5369			−0.660769			−0.330385	+	0.943846i	$0.607178\pi$
$788$	−0.625385	+	3.33282i	−0.0222784	+	0.118727i
$789$		0			0
$790$	11.8341	+	69.3331i	0.421039	+	2.46676i
$791$	−52.9079			−1.88119
$792$		0			0
$793$	−2.94349	+	1.69942i	−0.104526	+	0.0603483i
$794$	−38.2971	−	14.1770i	−1.35911	−	0.503124i
$795$		0			0
$796$	−20.0114	+	23.3249i	−0.709285	+	0.826729i
$797$			9.45153i			0.334790i	0.985890	+	0.167395i	$0.0535356\pi$
$797$			9.45153i			0.334790i	−0.985890	+	0.167395i	$0.946464\pi$
$798$		0			0
$799$			26.9159i			0.952217i
$800$	−3.64235	+	17.7928i	−0.128776	+	0.629070i
$801$		0			0
$802$	2.98496	−	8.06341i	0.105402	−	0.284729i
$803$	30.3909	−	17.5462i	1.07247	−	0.619193i
$804$		0			0
$805$	29.5234			1.04056
$806$	26.5574	−	4.53293i	0.935443	−	0.159666i
$807$		0			0
$808$	−18.8003	−	0.308956i	−0.661393	−	0.0108690i
$809$	43.4906			1.52905			0.764524	−	0.644596i	$-0.222974\pi$
$809$	43.4906			1.52905			0.764524	+	0.644596i	$0.222974\pi$
$810$		0			0
$811$	26.7843	−	46.3918i	0.940525	−	1.62904i	0.176053	−	0.984381i	$-0.443667\pi$
$811$	26.7843	−	46.3918i	0.940525	−	1.62904i	0.764472	−	0.644657i	$-0.223000\pi$
$812$	12.9374	+	11.0995i	0.454013	+	0.389516i
$813$		0			0
$814$	35.8254	−	29.7282i	1.25568	−	1.04197i
$815$	−2.38447	+	1.37667i	−0.0835244	+	0.0482228i
$816$		0			0
$817$	−1.07786	−	6.51870i	−0.0377097	−	0.228061i
$818$	16.9238	−	2.88863i	0.591725	−	0.100998i
$819$		0			0
$820$	−20.5036	+	23.8986i	−0.716018	+	0.834577i
$821$	−8.34812	+	14.4594i	−0.291351	+	0.504635i	−0.974130	−	0.225990i	$-0.927438\pi$
$821$	−8.34812	+	14.4594i	−0.291351	+	0.504635i	0.682778	+	0.730626i	$0.260772\pi$
$822$		0			0
$823$	−0.302319	−	0.174544i	−0.0105382	−	0.00608423i	0.494722	−	0.869051i	$-0.335270\pi$
$823$	−0.302319	−	0.174544i	−0.0105382	−	0.00608423i	−0.505260	+	0.862967i	$0.668603\pi$
$824$	12.6693	+	22.8011i	0.441357	+	0.794315i
$825$		0			0
$826$	−9.88541	+	26.7039i	−0.343958	+	0.929149i
$827$	−0.101413	+	0.175653i	−0.00352648	+	0.00610804i	−0.867783	−	0.496943i	$-0.834456\pi$
$827$	−0.101413	+	0.175653i	−0.00352648	+	0.00610804i	0.864257	+	0.503051i	$0.167789\pi$
$828$		0			0
$829$			44.0142i			1.52868i	0.644815	+	0.764339i	$0.276934\pi$
$829$			44.0142i			1.52868i	−0.644815	+	0.764339i	$0.723066\pi$
$830$	7.94796	−	21.4702i	0.275878	−	0.745241i
$831$		0			0
$832$	15.2156	−	8.13016i	0.527505	−	0.281863i
$833$	0.00159280	+	0.00275882i	5.51874e−5	+	9.55873e-5i
$834$		0			0
$835$	50.9321			1.76258
$836$	12.3546	−	20.3687i	0.427292	−	0.704466i
$837$		0			0
$838$	−27.0436	−	32.5902i	−0.934205	−	1.12581i
$839$	3.76071	+	6.51373i	0.129834	+	0.224879i	0.923612	−	0.383328i	$-0.125222\pi$
$839$	3.76071	+	6.51373i	0.129834	+	0.224879i	−0.793778	+	0.608207i	$0.791889\pi$
$840$		0			0
$841$	−9.31023	−	16.1258i	−0.321043	−	0.556062i
$842$	−14.2737	+	38.5582i	−0.491904	+	1.32880i
$843$		0			0
$844$	11.2534	−	3.95683i	0.387357	−	0.136200i
$845$	−11.9628	+	20.7202i	−0.411533	+	0.712796i
$846$		0			0
$847$			9.34566i			0.321121i
$848$	12.2966	+	15.3241i	0.422265	+	0.526232i
$849$		0			0
$850$	8.85738	−	7.34992i	0.303805	−	0.252100i
$851$	−23.4581	+	40.6306i	−0.804133	+	1.39280i
$852$		0			0
$853$	−14.0714	−	24.3724i	−0.481797	−	0.834497i	0.517985	−	0.855390i	$-0.326682\pi$
$853$	−14.0714	−	24.3724i	−0.481797	−	0.834497i	−0.999782	+	0.0208932i	$0.993349\pi$
$854$	−5.81280	+	0.992156i	−0.198910	+	0.0339509i
$855$		0			0
$856$	15.1721	+	27.3054i	0.518571	+	0.933278i
$857$	−36.3583	+	20.9915i	−1.24197	+	0.717054i	−0.969496	−	0.245108i	$-0.921177\pi$
$857$	−36.3583	+	20.9915i	−1.24197	+	0.717054i	−0.272479	+	0.962162i	$0.587843\pi$
$858$		0			0
$859$	34.5524	+	19.9488i	1.17891	+	0.680645i	0.955763	−	0.294139i	$-0.0950329\pi$
$859$	34.5524	+	19.9488i	1.17891	+	0.680645i	0.223149	+	0.974784i	$0.428366\pi$
$860$	−5.65631	+	6.59289i	−0.192879	+	0.224816i
$861$		0			0
$862$	−6.29062	−	36.8552i	−0.214259	−	1.25529i
$863$	29.5216			1.00493			0.502463	−	0.864598i	$-0.332427\pi$
$863$	29.5216			1.00493			0.502463	+	0.864598i	$0.332427\pi$
$864$		0			0
$865$	5.56745	+	3.21437i	0.189299	+	0.109292i
$866$	−12.5661	+	2.14485i	−0.427015	+	0.0728849i
$867$		0			0
$868$	45.9405	+	8.62048i	1.55932	+	0.292598i
$869$	−41.0761	+	23.7153i	−1.39341	+	0.804486i
$870$		0			0
$871$	19.5396	−	11.2812i	0.662072	−	0.382248i
$872$	22.7205	+	13.6203i	0.769414	+	0.461242i
$873$		0			0
$874$	−4.55012	+	23.5731i	−0.153910	+	0.797374i
$875$		−	13.5647i		−	0.458571i
$876$		0			0
$877$	−23.1449	+	13.3627i	−0.781549	+	0.451227i	−0.836979	−	0.547235i	$-0.815680\pi$
$877$	−23.1449	+	13.3627i	−0.781549	+	0.451227i	0.0554303	+	0.998463i	$0.482347\pi$
$878$	4.74921	+	1.75809i	0.160278	+	0.0593327i
$879$		0			0
$880$	−30.9565	+	4.76172i	−1.04354	+	0.160518i
$881$	16.4961			0.555767			0.277883	−	0.960615i	$-0.410367\pi$
$881$	16.4961			0.555767			0.277883	+	0.960615i	$0.410367\pi$
$882$		0			0
$883$	−20.0563	−	11.5795i	−0.674950	−	0.389682i	0.123000	−	0.992407i	$-0.460749\pi$
$883$	−20.0563	−	11.5795i	−0.674950	−	0.389682i	−0.797949	+	0.602724i	$0.794082\pi$
$884$	−10.7453	−	2.01630i	−0.361404	−	0.0678156i
$885$		0			0
$886$	−40.1399	+	6.85128i	−1.34853	+	0.230173i
$887$	−6.35899	+	11.0141i	−0.213514	+	0.369817i	−0.952812	−	0.303561i	$-0.901824\pi$
$887$	−6.35899	+	11.0141i	−0.213514	+	0.369817i	0.739298	+	0.673379i	$0.235158\pi$
$888$		0			0
$889$	2.43540	+	1.40608i	0.0816807	+	0.0471584i
$890$	−3.99255	−	4.81141i	−0.133831	−	0.161279i
$891$		0			0
$892$	19.4714	−	6.84639i	0.651950	−	0.229234i
$893$	35.7698	−	29.3700i	1.19699	−	0.982831i
$894$		0			0
$895$	3.85835	+	6.68286i	0.128970	+	0.223383i
$896$	29.6534	−	4.06370i	0.990651	−	0.135759i
$897$		0			0
$898$	5.91553	+	7.12879i	0.197404	+	0.237891i
$899$	24.6484	+	14.2308i	0.822071	+	0.474623i
$900$		0			0
$901$		−	12.4515i		−	0.414818i
$902$	−19.9136	−	7.37174i	−0.663051	−	0.245452i
$903$		0			0
$904$	−49.4457	+	27.4743i	−1.64454	+	0.913780i
$905$		−	24.8772i		−	0.826946i
$906$		0			0
$907$	−22.0367	−	38.1687i	−0.731717	−	1.26737i	−0.956149	−	0.292881i	$-0.905386\pi$
$907$	−22.0367	−	38.1687i	−0.731717	−	1.26737i	0.224432	−	0.974490i	$-0.427947\pi$
$908$	2.94210	−	15.6791i	0.0976371	−	0.520330i
$909$		0			0
$910$	17.7904	−	14.7627i	0.589747	−	0.489377i
$911$	25.3618			0.840273			0.420136	−	0.907461i	$-0.361982\pi$
$911$	25.3618			0.840273			0.420136	+	0.907461i	$0.361982\pi$
$912$		0			0
$913$	15.4385			0.510940
$914$	24.7297	−	20.5209i	0.817985	−	0.678771i
$915$		0			0
$916$	−1.93572	+	10.3159i	−0.0639581	+	0.340847i
$917$	−11.6823	−	20.2344i	−0.385785	−	0.668199i
$918$		0			0
$919$		−	0.0795611i		−	0.00262448i	−0.999999	−	0.00131224i	$-0.999582\pi$
$919$		−	0.0795611i		−	0.00262448i	0.999999	−	0.00131224i	$-0.000417699\pi$
$920$	27.5914	−	15.3310i	0.909662	−	0.505449i
$921$		0			0
$922$	−5.72621	−	2.11976i	−0.188583	−	0.0698106i
$923$		−	12.1765i		−	0.400793i
$924$		0			0
$925$	−33.4940	−	19.3378i	−1.10128	−	0.635823i
$926$	4.02352	+	4.84873i	0.132221	+	0.159339i
$927$		0			0
$928$	17.8546	+	3.65500i	0.586105	+	0.119981i
$929$	−3.96340	−	6.86481i	−0.130035	−	0.225227i	0.793655	−	0.608368i	$-0.208176\pi$
$929$	−3.96340	−	6.86481i	−0.130035	−	0.225227i	−0.923690	+	0.383141i	$0.874842\pi$
$930$		0			0
$931$	0.00192829	−	0.00512711i	6.31972e−5	−	0.000168034i
$932$	23.7418	−	8.34794i	0.777690	−	0.273446i
$933$		0			0
$934$	26.8145	+	32.3140i	0.877396	+	1.05735i
$935$	17.1897	+	9.92450i	0.562164	+	0.324566i
$936$		0			0
$937$	20.9870	−	36.3506i	0.685616	−	1.18752i	−0.287627	−	0.957742i	$-0.592866\pi$
$937$	20.9870	−	36.3506i	0.685616	−	1.18752i	0.973243	−	0.229779i	$-0.0738002\pi$
$938$	38.5867	−	6.58616i	1.25990	−	0.215046i
$939$		0			0
$940$	−59.8058	−	11.2222i	−1.95065	−	0.366029i
$941$	−17.0598	−	9.84946i	−0.556132	−	0.321083i	0.195459	−	0.980712i	$-0.437380\pi$
$941$	−17.0598	−	9.84946i	−0.556132	−	0.321083i	−0.751592	+	0.659629i	$0.770714\pi$
$942$		0			0
$943$	21.3997			0.696871
$944$	4.62841	+	30.0898i	0.150642	+	0.979340i
$945$		0			0
$946$	−5.49355	−	2.03363i	−0.178611	−	0.0661191i
$947$	−4.89713	+	2.82736i	−0.159135	+	0.0918768i	−0.577453	−	0.816424i	$-0.695953\pi$
$947$	−4.89713	+	2.82736i	−0.159135	+	0.0918768i	0.418318	+	0.908301i	$0.362620\pi$
$948$		0			0
$949$			27.6927i			0.898944i
$950$	−19.4326	−	3.75091i	−0.630478	−	0.121696i
$951$		0			0
$952$	−16.2688	−	9.75267i	−0.527274	−	0.316086i
$953$	−7.89881	+	4.56038i	−0.255868	+	0.147725i	−0.622448	−	0.782661i	$-0.713862\pi$
$953$	−7.89881	+	4.56038i	−0.255868	+	0.147725i	0.366580	+	0.930386i	$0.380528\pi$
$954$		0			0
$955$	−38.2810	+	22.1015i	−1.23874	+	0.715189i
$956$	20.4428	+	3.83598i	0.661168	+	0.124065i
$957$		0			0
$958$	−0.985370	+	0.168188i	−0.0318359	+	0.00543389i
$959$	46.9619	+	27.1135i	1.51648	+	0.875540i
$960$		0			0
$961$	47.0440			1.51755
$962$	6.18107	+	36.2134i	0.199286	+	1.16757i
$963$		0			0
$964$	−20.5596	+	23.9639i	−0.662182	+	0.771826i
$965$	37.5841	+	21.6992i	1.20988	+	0.698523i
$966$		0			0
$967$	−20.6723	+	11.9351i	−0.664775	+	0.383808i	−0.794094	−	0.607795i	$-0.792054\pi$
$967$	−20.6723	+	11.9351i	−0.664775	+	0.383808i	0.129319	+	0.991603i	$0.458721\pi$
$968$	4.85306	+	8.73410i	0.155983	+	0.280724i
$969$		0			0
$970$	−9.64671	+	1.64655i	−0.309737	+	0.0528674i
$971$	−28.0027	−	48.5022i	−0.898651	−	1.55651i	−0.829220	−	0.558922i	$-0.811215\pi$
$971$	−28.0027	−	48.5022i	−0.898651	−	1.55651i	−0.0694307	−	0.997587i	$-0.522118\pi$
$972$		0			0
$973$	5.51766	−	9.55686i	0.176888	−	0.306379i
$974$	−2.74250	+	2.27575i	−0.0878753	+	0.0729197i
$975$		0			0
$976$	−4.91721	+	3.94573i	−0.157396	+	0.126300i
$977$		−	7.94428i		−	0.254160i	−0.991892	−	0.127080i	$-0.959439\pi$
$977$		−	7.94428i		−	0.254160i	0.991892	−	0.127080i	$-0.0405605\pi$
$978$		0			0
$979$	2.10807	−	3.65129i	0.0673742	−	0.116696i
$980$	−0.00679405	+	0.00238888i	−0.000217028	+	7.63099e-5i
$981$		0			0
$982$	−0.896694	+	2.42228i	−0.0286147	+	0.0772981i
$983$	−19.4039	−	33.6085i	−0.618887	−	1.07194i	−0.989689	−	0.143232i	$-0.954251\pi$
$983$	−19.4039	−	33.6085i	−0.618887	−	1.07194i	0.370802	−	0.928712i	$-0.379083\pi$
$984$		0			0
$985$	2.42914	+	4.20740i	0.0773989	+	0.134059i
$986$	−7.37545	−	8.88814i	−0.234882	−	0.283056i
$987$		0			0
$988$	9.04550	+	16.4801i	0.287776	+	0.524302i
$989$	5.90351			0.187721
$990$		0			0
$991$	−10.7169	−	18.5622i	−0.340433	−	0.589648i	0.644080	−	0.764958i	$-0.277240\pi$
$991$	−10.7169	−	18.5622i	−0.340433	−	0.589648i	−0.984513	+	0.175310i	$0.943907\pi$
$992$	47.4107	−	15.7998i	1.50529	−	0.501644i
$993$		0			0
$994$	7.33403	−	19.8118i	0.232621	−	0.628391i
$995$			44.0311i			1.39588i
$996$		0			0
$997$	17.7924	−	30.8174i	0.563492	−	0.975997i	−0.433696	−	0.901059i	$-0.642791\pi$
$997$	17.7924	−	30.8174i	0.563492	−	0.975997i	0.997188	−	0.0749376i	$-0.0238758\pi$
$998$	0.827627	−	2.23571i	0.0261981	−	0.0707701i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.r.b.487.3		20
3.2	odd	2		228.2.k.b.31.8	yes	20
4.3	odd	2		684.2.r.c.487.1		20
12.11	even	2		228.2.k.a.31.10	✓	20
19.8	odd	6		684.2.r.c.559.1		20
57.8	even	6		228.2.k.a.103.10	yes	20
76.27	even	6	inner	684.2.r.b.559.3		20
228.179	odd	6		228.2.k.b.103.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.k.a.31.10	✓	20	12.11	even	2
228.2.k.a.103.10	yes	20	57.8	even	6
228.2.k.b.31.8	yes	20	3.2	odd	2
228.2.k.b.103.8	yes	20	228.179	odd	6
684.2.r.b.487.3		20	1.1	even	1	trivial
684.2.r.b.559.3		20	76.27	even	6	inner
684.2.r.c.487.1		20	4.3	odd	2
684.2.r.c.559.1		20	19.8	odd	6

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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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08831 + 0.903091i) q^{2} +(0.368852 - 1.96569i) q^{4} +(-1.43271 - 2.48152i) q^{5} +2.64551i q^{7} +(1.37377 + 2.47240i) q^{8} +(3.80027 + 1.40681i) q^{10} +2.73265i q^{11} +(-1.86752 - 1.07822i) q^{13} +(-2.38914 - 2.87915i) q^{14} +(-3.72790 - 1.45010i) q^{16} +(1.26747 + 2.19532i) q^{17} +(1.53443 - 4.07989i) q^{19} +(-5.40636 + 1.90095i) q^{20} +(-2.46783 - 2.97398i) q^{22} +(3.37287 + 1.94733i) q^{23} +(-1.60529 + 2.78044i) q^{25} +(3.00618 - 0.513109i) q^{26} +(5.20027 + 0.975802i) q^{28} +(2.79010 + 1.61086i) q^{29} +8.83425 q^{31} +(5.36669 - 1.78847i) q^{32} +(-3.36199 - 1.24456i) q^{34} +(6.56489 - 3.79024i) q^{35} +12.0463i q^{37} +(2.01457 + 5.82593i) q^{38} +(4.16708 - 6.95126i) q^{40} +(4.75850 - 2.74732i) q^{41} +(1.31272 - 0.757900i) q^{43} +(5.37154 + 1.00794i) q^{44} +(-5.42935 + 0.926708i) q^{46} +(9.19542 + 5.30898i) q^{47} +0.00125668 q^{49} +(-0.763936 - 4.47571i) q^{50} +(-2.80828 + 3.27328i) q^{52} +(-4.25386 - 2.45597i) q^{53} +(6.78111 - 3.91508i) q^{55} +(-6.54076 + 3.63434i) q^{56} +(-4.49126 + 0.766589i) q^{58} +(-3.80546 - 6.59126i) q^{59} +(0.788072 - 1.36498i) q^{61} +(-9.61444 + 7.97814i) q^{62} +(-4.22549 + 6.79303i) q^{64} +6.17906i q^{65} +(-5.23140 + 9.06106i) q^{67} +(4.78284 - 1.68171i) q^{68} +(-3.72172 + 10.0537i) q^{70} +(2.82329 + 4.89008i) q^{71} +(-6.42096 - 11.1214i) q^{73} +(-10.8789 - 13.1102i) q^{74} +(-7.45383 - 4.52110i) q^{76} -7.22925 q^{77} +(8.67850 + 15.0316i) q^{79} +(1.74253 + 11.3284i) q^{80} +(-2.69766 + 7.28730i) q^{82} -5.64965i q^{83} +(3.63183 - 6.29051i) q^{85} +(-0.744199 + 2.01034i) q^{86} +(-6.75619 + 3.75404i) q^{88} +(-1.33617 - 0.771439i) q^{89} +(2.85244 - 4.94056i) q^{91} +(5.07194 - 5.91175i) q^{92} +(-14.8020 + 2.52647i) q^{94} +(-12.3227 + 2.03755i) q^{95} +(-2.09143 + 1.20749i) q^{97} +(-0.00136766 + 0.00113490i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + q^{4} - 4 q^{8} + 6 q^{10} + 6 q^{13} - 9 q^{14} - 11 q^{16} + 12 q^{19} + 14 q^{20} + 8 q^{22} - 10 q^{25} + 7 q^{28} + 12 q^{31} + 29 q^{32} - 6 q^{34} - 25 q^{38} - 46 q^{40} - 12 q^{41}+ \cdots - 12 q^{97}+O(q^{100}) \) 20 * q - q^2 + q^4 - 4 * q^8 + 6 * q^10 + 6 * q^13 - 9 * q^14 - 11 * q^16 + 12 * q^19 + 14 * q^20 + 8 * q^22 - 10 * q^25 + 7 * q^28 + 12 * q^31 + 29 * q^32 - 6 * q^34 - 25 * q^38 - 46 * q^40 - 12 * q^41 - 18 * q^43 + 12 * q^44 - 32 * q^46 + 36 * q^47 - 24 * q^49 + 34 * q^50 + 3 * q^52 + 12 * q^53 - 38 * q^56 + 16 * q^58 + 10 * q^61 + 55 * q^62 - 14 * q^64 + 14 * q^67 - 40 * q^68 + 26 * q^70 - 8 * q^71 - 6 * q^73 - 45 * q^74 - 69 * q^76 + 32 * q^77 - 6 * q^79 - 22 * q^80 + 24 * q^82 + 8 * q^85 - 7 * q^86 + 44 * q^88 + 24 * q^89 + 26 * q^91 + 18 * q^92 - 52 * q^94 - 4 * q^95 - 12 * q^97

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