LMFDB - Embedded newform 666.2.be.d.125.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(125,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 11]))

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

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

chi := DirichletCharacter("666.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.be (of order $12$, degree $4$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.6040479020157644046336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 $ x^16 - 7x^12 - 32x^8 - 567*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			125.4
Root			$1.73122 + 0.0537601i$ of defining polynomial
Character	$\chi$	$=$	666.125
Dual form			666.2.be.d.341.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.205059 - 0.765290i) q^{5} +(-0.103857 - 0.179885i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.205059 - 0.765290i) q^{5} +(-0.103857 - 0.179885i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.792287 q^{10} +2.15574 q^{11} +(3.34445 + 0.896143i) q^{13} +(0.146875 - 0.146875i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.47240 + 0.394528i) q^{17} +(5.53059 + 1.48192i) q^{19} +(0.205059 + 0.765290i) q^{20} +(0.557946 + 2.08228i) q^{22} +(-0.186230 - 0.186230i) q^{23} +(3.78651 + 2.18614i) q^{25} +3.46243i q^{26} +(0.179885 + 0.103857i) q^{28} +(-0.667752 + 0.667752i) q^{29} +(2.39265 + 2.39265i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-0.762169 - 1.32012i) q^{34} +(-0.158961 + 0.0425934i) q^{35} +(5.85071 + 1.66409i) q^{37} +5.72569i q^{38} +(-0.686141 + 0.396143i) q^{40} +(-2.63222 - 4.55913i) q^{41} +(-1.86832 + 1.86832i) q^{43} +(-1.86692 + 1.07787i) q^{44} +(0.131685 - 0.228085i) q^{46} +3.73385i q^{47} +(3.47843 - 6.02481i) q^{49} +(-1.13163 + 4.22330i) q^{50} +(-3.34445 + 0.896143i) q^{52} +(-0.970349 - 0.560232i) q^{53} +(0.442054 - 1.64977i) q^{55} +(-0.0537601 + 0.200635i) q^{56} +(-0.817825 - 0.472172i) q^{58} +(-6.83901 + 1.83251i) q^{59} +(-0.320115 + 1.19469i) q^{61} +(-1.69186 + 2.93039i) q^{62} +1.00000i q^{64} +(1.37162 - 2.37572i) q^{65} +(-6.44325 + 3.72001i) q^{67} +(1.07787 - 1.07787i) q^{68} +(-0.0822842 - 0.142520i) q^{70} +(3.47385 - 2.00563i) q^{71} -9.83638i q^{73} +(-0.0931152 + 6.08205i) q^{74} +(-5.53059 + 1.48192i) q^{76} +(-0.223888 - 0.387785i) q^{77} +(-3.34445 - 0.896143i) q^{79} +(-0.560232 - 0.560232i) q^{80} +(3.72251 - 3.72251i) q^{82} +(7.29563 + 4.21213i) q^{83} +1.20771i q^{85} +(-2.28821 - 1.32110i) q^{86} +(-1.52434 - 1.52434i) q^{88} +(-0.507657 - 1.89460i) q^{89} +(-0.186141 - 0.694686i) q^{91} +(0.254395 + 0.0681651i) q^{92} +(-3.60662 + 0.966391i) q^{94} +(2.26820 - 3.92863i) q^{95} +(-4.15831 + 4.15831i) q^{97} +(6.71981 + 1.80057i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 4 q^{13} + 8 q^{16} + 16 q^{19} + 20 q^{22} + 12 q^{28} - 12 q^{31} + 8 q^{34} + 12 q^{37} + 12 q^{40} - 20 q^{43} + 12 q^{46} + 20 q^{49} - 4 q^{52} - 4 q^{55} + 4 q^{61} - 132 q^{67} + 28 q^{70} - 16 q^{76} - 4 q^{79} + 12 q^{82} + 16 q^{88} + 20 q^{91} + 12 q^{94} - 40 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 4 * q^13 + 8 * q^16 + 16 * q^19 + 20 * q^22 + 12 * q^28 - 12 * q^31 + 8 * q^34 + 12 * q^37 + 12 * q^40 - 20 * q^43 + 12 * q^46 + 20 * q^49 - 4 * q^52 - 4 * q^55 + 4 * q^61 - 132 * q^67 + 28 * q^70 - 16 * q^76 - 4 * q^79 + 12 * q^82 + 16 * q^88 + 20 * q^91 + 12 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.205059	−	0.765290i	0.0917052	−	0.342248i	−0.904794	−	0.425849i	$-0.859975\pi$
$5$	0.205059	−	0.765290i	0.0917052	−	0.342248i	0.996499	+	0.0836009i	$0.0266421\pi$
$6$		0			0
$7$	−0.103857	−	0.179885i	−0.0392541	−	0.0679900i	0.845731	−	0.533610i	$-0.179165\pi$
$7$	−0.103857	−	0.179885i	−0.0392541	−	0.0679900i	−0.884985	+	0.465620i	$0.845832\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	0.792287			0.250543
$11$	2.15574			0.649980			0.324990	−	0.945717i	$-0.394639\pi$
$11$	2.15574			0.649980			0.324990	+	0.945717i	$0.394639\pi$
$12$		0			0
$13$	3.34445	+	0.896143i	0.927584	+	0.248545i	0.690824	−	0.723023i	$-0.257248\pi$
$13$	3.34445	+	0.896143i	0.927584	+	0.248545i	0.236760	+	0.971568i	$0.423914\pi$
$14$	0.146875	−	0.146875i	0.0392541	−	0.0392541i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.47240	+	0.394528i	−0.357109	+	0.0956870i	−0.432913	−	0.901436i	$-0.642514\pi$
$17$	−1.47240	+	0.394528i	−0.357109	+	0.0956870i	0.0758042	+	0.997123i	$0.475848\pi$
$18$		0			0
$19$	5.53059	+	1.48192i	1.26881	+	0.339975i	0.829573	−	0.558398i	$-0.188584\pi$
$19$	5.53059	+	1.48192i	1.26881	+	0.339975i	0.439232	+	0.898374i	$0.355251\pi$
$20$	0.205059	+	0.765290i	0.0458526	+	0.171124i
$21$		0			0
$22$	0.557946	+	2.08228i	0.118955	+	0.443944i
$23$	−0.186230	−	0.186230i	−0.0388317	−	0.0388317i	0.687424	−	0.726256i	$-0.258741\pi$
$23$	−0.186230	−	0.186230i	−0.0388317	−	0.0388317i	−0.726256	+	0.687424i	$0.758741\pi$
$24$		0			0
$25$	3.78651	+	2.18614i	0.757301	+	0.437228i
$26$			3.46243i			0.679039i
$27$		0			0
$28$	0.179885	+	0.103857i	0.0339950	+	0.0196270i
$29$	−0.667752	+	0.667752i	−0.123998	+	0.123998i	−0.766383	−	0.642384i	$-0.777945\pi$
$29$	−0.667752	+	0.667752i	−0.123998	+	0.123998i	0.642384	+	0.766383i	$0.277945\pi$
$30$		0			0
$31$	2.39265	+	2.39265i	0.429733	+	0.429733i	0.888537	−	0.458804i	$-0.151722\pi$
$31$	2.39265	+	2.39265i	0.429733	+	0.429733i	−0.458804	+	0.888537i	$0.651722\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$		0			0
$34$	−0.762169	−	1.32012i	−0.130711	−	0.226398i
$35$	−0.158961	+	0.0425934i	−0.0268693	+	0.00719960i
$36$		0			0
$37$	5.85071	+	1.66409i	0.961851	+	0.273575i
$37$	5.85071	+	1.66409i	0.961851	+	0.273575i
$38$			5.72569i			0.928830i
$39$		0			0
$40$	−0.686141	+	0.396143i	−0.108488	+	0.0626358i
$41$	−2.63222	−	4.55913i	−0.411083	−	0.712017i	0.583925	−	0.811807i	$-0.301516\pi$
$41$	−2.63222	−	4.55913i	−0.411083	−	0.712017i	−0.995008	+	0.0997907i	$0.968183\pi$
$42$		0			0
$43$	−1.86832	+	1.86832i	−0.284915	+	0.284915i	−0.835066	−	0.550150i	$-0.814570\pi$
$43$	−1.86832	+	1.86832i	−0.284915	+	0.284915i	0.550150	+	0.835066i	$0.314570\pi$
$44$	−1.86692	+	1.07787i	−0.281450	+	0.162495i
$45$		0			0
$46$	0.131685	−	0.228085i	0.0194159	−	0.0336293i
$47$			3.73385i			0.544638i	0.962207	+	0.272319i	$0.0877906\pi$
$47$			3.73385i			0.544638i	−0.962207	+	0.272319i	$0.912209\pi$
$48$		0			0
$49$	3.47843	−	6.02481i	0.496918	−	0.860688i
$50$	−1.13163	+	4.22330i	−0.160037	+	0.597265i
$51$		0			0
$52$	−3.34445	+	0.896143i	−0.463792	+	0.124273i
$53$	−0.970349	−	0.560232i	−0.133288	−	0.0769537i	0.431873	−	0.901934i	$-0.357853\pi$
$53$	−0.970349	−	0.560232i	−0.133288	−	0.0769537i	−0.565161	+	0.824980i	$0.691186\pi$
$54$		0			0
$55$	0.442054	−	1.64977i	0.0596065	−	0.222454i
$56$	−0.0537601	+	0.200635i	−0.00718399	+	0.0268110i
$57$		0			0
$58$	−0.817825	−	0.472172i	−0.107386	−	0.0619992i
$59$	−6.83901	+	1.83251i	−0.890363	+	0.238572i	−0.674873	−	0.737934i	$-0.735802\pi$
$59$	−6.83901	+	1.83251i	−0.890363	+	0.238572i	−0.215490	+	0.976506i	$0.569135\pi$
$60$		0			0
$61$	−0.320115	+	1.19469i	−0.0409866	+	0.152964i	−0.983386	−	0.181524i	$-0.941897\pi$
$61$	−0.320115	+	1.19469i	−0.0409866	+	0.152964i	0.942400	+	0.334488i	$0.108564\pi$
$62$	−1.69186	+	2.93039i	−0.214867	+	0.372160i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	1.37162	−	2.37572i	0.170129	−	0.294671i
$66$		0			0
$67$	−6.44325	+	3.72001i	−0.787169	+	0.454472i	−0.838965	−	0.544186i	$-0.816839\pi$
$67$	−6.44325	+	3.72001i	−0.787169	+	0.454472i	0.0517961	+	0.998658i	$0.483505\pi$
$68$	1.07787	−	1.07787i	0.130711	−	0.130711i
$69$		0			0
$70$	−0.0822842	−	0.142520i	−0.00983484	−	0.0170344i
$71$	3.47385	−	2.00563i	0.412270	−	0.238024i	−0.279495	−	0.960147i	$-0.590167\pi$
$71$	3.47385	−	2.00563i	0.412270	−	0.238024i	0.691764	+	0.722123i	$0.256834\pi$
$72$		0			0
$73$		−	9.83638i		−	1.15126i	−0.817710	−	0.575631i	$-0.804757\pi$
$73$		−	9.83638i		−	1.15126i	0.817710	−	0.575631i	$-0.195243\pi$
$74$	−0.0931152	+	6.08205i	−0.0108244	+	0.707024i
$75$		0			0
$76$	−5.53059	+	1.48192i	−0.634403	+	0.169988i
$77$	−0.223888	−	0.387785i	−0.0255144	−	0.0441922i
$78$		0			0
$79$	−3.34445	−	0.896143i	−0.376280	−	0.100824i	0.0657218	−	0.997838i	$-0.479065\pi$
$79$	−3.34445	−	0.896143i	−0.376280	−	0.100824i	−0.442002	+	0.897014i	$0.645732\pi$
$80$	−0.560232	−	0.560232i	−0.0626358	−	0.0626358i
$81$		0			0
$82$	3.72251	−	3.72251i	0.411083	−	0.411083i
$83$	7.29563	+	4.21213i	0.800799	+	0.462342i	0.843751	−	0.536736i	$-0.180343\pi$
$83$	7.29563	+	4.21213i	0.800799	+	0.462342i	−0.0429513	+	0.999077i	$0.513676\pi$
$84$		0			0
$85$			1.20771i			0.130995i
$86$	−2.28821	−	1.32110i	−0.246744	−	0.142458i
$87$		0			0
$88$	−1.52434	−	1.52434i	−0.162495	−	0.162495i
$89$	−0.507657	−	1.89460i	−0.0538115	−	0.200827i	0.933787	−	0.357830i	$-0.116483\pi$
$89$	−0.507657	−	1.89460i	−0.0538115	−	0.200827i	−0.987598	+	0.157003i	$0.949817\pi$
$90$		0			0
$91$	−0.186141	−	0.694686i	−0.0195128	−	0.0728229i
$92$	0.254395	+	0.0681651i	0.0265226	+	0.00710670i
$93$		0			0
$94$	−3.60662	+	0.966391i	−0.371995	+	0.0996757i
$95$	2.26820	−	3.92863i	0.232712	−	0.403069i
$96$		0			0
$97$	−4.15831	+	4.15831i	−0.422213	+	0.422213i	−0.885965	−	0.463752i	$-0.846503\pi$
$97$	−4.15831	+	4.15831i	−0.422213	+	0.422213i	0.463752	+	0.885965i	$0.346503\pi$
$98$	6.71981	+	1.80057i	0.678803	+	0.181885i
$99$		0			0
$100$	−4.37228			−0.437228
$101$	2.14225			0.213162			0.106581	−	0.994304i	$-0.466010\pi$
$101$	2.14225			0.213162			0.106581	+	0.994304i	$0.466010\pi$
$102$		0			0
$103$	−2.16915	−	2.16915i	−0.213732	−	0.213732i	0.592118	−	0.805851i	$-0.298292\pi$
$103$	−2.16915	−	2.16915i	−0.213732	−	0.213732i	−0.805851	+	0.592118i	$0.798292\pi$
$104$	−1.73122	−	2.99855i	−0.169760	−	0.294032i
$105$		0			0
$106$	0.289997	−	1.08228i	0.0281670	−	0.105121i
$107$	−6.57967	+	3.79878i	−0.636081	+	0.367242i	−0.783103	−	0.621892i	$-0.786364\pi$
$107$	−6.57967	+	3.79878i	−0.636081	+	0.367242i	0.147022	+	0.989133i	$0.453031\pi$
$108$		0			0
$109$	−1.44602	−	5.39662i	−0.138504	−	0.516902i	−0.999959	−	0.00906897i	$-0.997113\pi$
$109$	−1.44602	−	5.39662i	−0.138504	−	0.516902i	0.861455	−	0.507833i	$-0.169553\pi$
$110$	1.70796			0.162848
$111$		0			0
$112$	−0.207713			−0.0196270
$113$	−5.04416	−	18.8250i	−0.474514	−	1.77091i	−0.623237	−	0.782033i	$-0.714183\pi$
$113$	−5.04416	−	18.8250i	−0.474514	−	1.77091i	0.148723	−	0.988879i	$-0.452484\pi$
$114$		0			0
$115$	−0.180709	+	0.104332i	−0.0168512	+	0.00972902i
$116$	0.244414	−	0.912166i	0.0226933	−	0.0846925i
$117$		0			0
$118$	−3.54013	−	6.13168i	−0.325895	−	0.564467i
$119$	0.223888	+	0.223888i	0.0205237	+	0.0205237i
$120$		0			0
$121$	−6.35279			−0.577526
$122$	−1.23683			−0.111977
$123$		0			0
$124$	−3.26842	−	0.875772i	−0.293513	−	0.0786466i
$125$	5.25065	−	5.25065i	0.469632	−	0.469632i
$126$		0			0
$127$	−1.96264	+	3.39938i	−0.174156	+	0.301647i	−0.939869	−	0.341536i	$-0.889053\pi$
$127$	−1.96264	+	3.39938i	−0.174156	+	0.301647i	0.765713	+	0.643182i	$0.222386\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$		0			0
$130$	2.64977	+	0.710003i	0.232400	+	0.0622714i
$131$	−3.20156	−	11.9484i	−0.279722	−	1.04394i	−0.952611	−	0.304192i	$-0.901614\pi$
$131$	−3.20156	−	11.9484i	−0.279722	−	1.04394i	0.672889	−	0.739743i	$-0.265053\pi$
$132$		0			0
$133$	−0.307814	−	1.14878i	−0.0266908	−	0.0996115i
$134$	−5.26090	−	5.26090i	−0.454472	−	0.454472i
$135$		0			0
$136$	1.32012	+	0.762169i	0.113199	+	0.0653554i
$137$			5.16937i			0.441649i	0.975314	+	0.220825i	$0.0708748\pi$
$137$			5.16937i			0.441649i	−0.975314	+	0.220825i	$0.929125\pi$
$138$		0			0
$139$	−1.16795	−	0.674315i	−0.0990640	−	0.0571946i	0.449650	−	0.893205i	$-0.351549\pi$
$139$	−1.16795	−	0.674315i	−0.0990640	−	0.0571946i	−0.548714	+	0.836010i	$0.684882\pi$
$140$	0.116367	−	0.116367i	0.00983484	−	0.00983484i
$141$		0			0
$142$	2.83638	+	2.83638i	0.238024	+	0.238024i
$143$	7.20977	+	1.93185i	0.602911	+	0.161550i
$144$		0			0
$145$	0.374096	+	0.647952i	0.0310669	+	0.0538095i
$146$	9.50122	−	2.54584i	0.786326	−	0.210695i
$147$		0			0
$148$	−5.89891	+	1.48421i	−0.484887	+	0.122001i
$149$		−	6.39137i		−	0.523601i	−0.965122	−	0.261801i	$-0.915684\pi$
$149$		−	6.39137i		−	0.523601i	0.965122	−	0.261801i	$-0.0843163\pi$
$150$		0			0
$151$	−2.80360	+	1.61866i	−0.228154	+	0.131725i	−0.609720	−	0.792617i	$-0.708718\pi$
$151$	−2.80360	+	1.61866i	−0.228154	+	0.131725i	0.381566	+	0.924341i	$0.375385\pi$
$152$	−2.86285	−	4.95859i	−0.232207	−	0.402195i
$153$		0			0
$154$	0.316625	−	0.316625i	0.0255144	−	0.0255144i
$155$	2.32171	−	1.34044i	0.186484	−	0.107667i
$156$		0			0
$157$	4.34592	−	7.52735i	0.346842	−	0.600748i	−0.638845	−	0.769336i	$-0.720587\pi$
$157$	4.34592	−	7.52735i	0.346842	−	0.600748i	0.985687	+	0.168588i	$0.0539206\pi$
$158$		−	3.46243i		−	0.275456i
$159$		0			0
$160$	0.396143	−	0.686141i	0.0313179	−	0.0542442i
$161$	−0.0141588	+	0.0528412i	−0.00111587	+	0.00416447i
$162$		0			0
$163$	−5.23304	+	1.40219i	−0.409883	+	0.109828i	−0.457868	−	0.889020i	$-0.651387\pi$
$163$	−5.23304	+	1.40219i	−0.409883	+	0.109828i	0.0479847	+	0.998848i	$0.484720\pi$
$164$	4.55913	+	2.63222i	0.356008	+	0.205541i
$165$		0			0
$166$	−2.18036	+	8.13722i	−0.169229	+	0.631570i
$167$	−3.55293	+	13.2597i	−0.274934	+	1.02607i	0.680952	+	0.732329i	$0.261566\pi$
$167$	−3.55293	+	13.2597i	−0.274934	+	1.02607i	−0.955886	+	0.293739i	$0.905100\pi$
$168$		0			0
$169$	−0.876037	−	0.505780i	−0.0673875	−	0.0389062i
$170$	−1.16656	+	0.312579i	−0.0894712	+	0.0239737i
$171$		0			0
$172$	0.683851	−	2.55217i	0.0521431	−	0.194601i
$173$	3.93073	−	6.80823i	0.298848	−	0.517620i	−0.677025	−	0.735960i	$-0.736731\pi$
$173$	3.93073	−	6.80823i	0.298848	−	0.517620i	0.975873	+	0.218340i	$0.0700642\pi$
$174$		0			0
$175$		−	0.908180i		−	0.0686519i
$176$	1.07787	−	1.86692i	0.0812475	−	0.140725i
$177$		0			0
$178$	1.69865	−	0.980717i	0.127319	−	0.0735079i
$179$	13.0230	−	13.0230i	0.973386	−	0.973386i	−0.0262689	−	0.999655i	$-0.508363\pi$
$179$	13.0230	−	13.0230i	0.973386	−	0.973386i	0.999655	+	0.0262689i	$0.00836260\pi$
$180$		0			0
$181$	8.14279	+	14.1037i	0.605248	+	1.04832i	0.992012	+	0.126142i	$0.0402596\pi$
$181$	8.14279	+	14.1037i	0.605248	+	1.04832i	−0.386764	+	0.922179i	$0.626407\pi$
$182$	0.622839	−	0.359596i	0.0461679	−	0.0266550i
$183$		0			0
$184$			0.263370i			0.0194159i
$185$	2.47325	−	4.13625i	0.181837	−	0.304103i
$186$		0			0
$187$	−3.17410	+	0.850499i	−0.232114	+	0.0621946i
$188$	−1.86692	−	3.23361i	−0.136159	−	0.235835i
$189$		0			0
$190$	4.38182	+	1.17410i	0.317890	+	0.0851785i
$191$	14.5448	+	14.5448i	1.05242	+	1.05242i	0.998548	+	0.0538735i	$0.0171568\pi$
$191$	14.5448	+	14.5448i	1.05242	+	1.05242i	0.0538735	+	0.998548i	$0.482843\pi$
$192$		0			0
$193$	1.48192	−	1.48192i	0.106671	−	0.106671i	−0.651757	−	0.758428i	$-0.725968\pi$
$193$	1.48192	−	1.48192i	0.106671	−	0.106671i	0.758428	+	0.651757i	$0.225968\pi$
$194$	−5.09287	−	2.94037i	−0.365647	−	0.211106i
$195$		0			0
$196$			6.95686i			0.496918i
$197$	−22.8424	−	13.1880i	−1.62745	−	0.939610i	−0.984850	−	0.173409i	$-0.944522\pi$
$197$	−22.8424	−	13.1880i	−1.62745	−	0.939610i	−0.642602	−	0.766200i	$-0.722145\pi$
$198$		0			0
$199$	−8.26062	−	8.26062i	−0.585580	−	0.585580i	0.350851	−	0.936431i	$-0.385892\pi$
$199$	−8.26062	−	8.26062i	−0.585580	−	0.585580i	−0.936431	+	0.350851i	$0.885892\pi$
$200$	−1.13163	−	4.22330i	−0.0800183	−	0.298632i
$201$		0			0
$202$	0.554456	+	2.06926i	0.0390114	+	0.145592i
$203$	0.189469	+	0.0507680i	0.0132981	+	0.00356321i
$204$		0			0
$205$	−4.02882	+	1.07952i	−0.281385	+	0.0753969i
$206$	1.53382	−	2.65665i	0.106866	−	0.185098i
$207$		0			0
$208$	2.44831	−	2.44831i	0.169760	−	0.169760i
$209$	11.9225	+	3.19463i	0.824698	+	0.220977i
$210$		0			0
$211$	−8.02407			−0.552400			−0.276200	−	0.961100i	$-0.589075\pi$
$211$	−8.02407			−0.552400			−0.276200	+	0.961100i	$0.589075\pi$
$212$	1.12046			0.0769537
$213$		0			0
$214$	−5.37228	−	5.37228i	−0.367242	−	0.367242i
$215$	1.04669	+	1.81292i	0.0713836	+	0.123640i
$216$		0			0
$217$	0.181909	−	0.678894i	0.0123488	−	0.0460864i
$218$	4.83848	−	2.79350i	0.327703	−	0.189199i
$219$		0			0
$220$	0.442054	+	1.64977i	0.0298033	+	0.111227i
$221$	−5.27792			−0.355031
$222$		0			0
$223$	−28.3426			−1.89796			−0.948980	−	0.315335i	$-0.897883\pi$
$223$	−28.3426			−1.89796			−0.948980	+	0.315335i	$0.897883\pi$
$224$	−0.0537601	−	0.200635i	−0.00359200	−	0.0134055i
$225$		0			0
$226$	16.8781	−	9.74456i	1.12271	−	0.648199i
$227$	−5.98789	+	22.3471i	−0.397430	+	1.48323i	0.420172	+	0.907445i	$0.361970\pi$
$227$	−5.98789	+	22.3471i	−0.397430	+	1.48323i	−0.817602	+	0.575784i	$0.804697\pi$
$228$		0			0
$229$	−8.49965	−	14.7218i	−0.561673	−	0.972846i	−0.997351	−	0.0727432i	$-0.976825\pi$
$229$	−8.49965	−	14.7218i	−0.561673	−	0.972846i	0.435678	−	0.900103i	$-0.356509\pi$
$230$	−0.147548	−	0.147548i	−0.00972902	−	0.00972902i
$231$		0			0
$232$	0.944343			0.0619992
$233$	−6.79080			−0.444880			−0.222440	−	0.974946i	$-0.571402\pi$
$233$	−6.79080			−0.444880			−0.222440	+	0.974946i	$0.571402\pi$
$234$		0			0
$235$	2.85748	+	0.765659i	0.186401	+	0.0499461i
$236$	5.00650	−	5.00650i	0.325895	−	0.325895i
$237$		0			0
$238$	−0.158312	+	0.274205i	−0.0102619	+	0.0177741i
$239$	7.24419	−	1.94107i	0.468588	−	0.125558i	−0.0167961	−	0.999859i	$-0.505347\pi$
$239$	7.24419	−	1.94107i	0.468588	−	0.125558i	0.485384	+	0.874301i	$0.338680\pi$
$240$		0			0
$241$	16.7654	+	4.49228i	1.07995	+	0.289373i	0.754577	−	0.656211i	$-0.227842\pi$
$241$	16.7654	+	4.49228i	1.07995	+	0.289373i	0.325378	+	0.945584i	$0.394509\pi$
$242$	−1.64422	−	6.13632i	−0.105695	−	0.394458i
$243$		0			0
$244$	−0.320115	−	1.19469i	−0.0204933	−	0.0764820i
$245$	−3.89745	−	3.89745i	−0.248999	−	0.248999i
$246$		0			0
$247$	17.1688	+	9.91241i	1.09242	+	0.630712i
$248$		−	3.38372i		−	0.214867i
$249$		0			0
$250$	6.43070	+	3.71277i	0.406713	+	0.234816i
$251$	−11.6628	+	11.6628i	−0.736150	+	0.736150i	−0.971831	−	0.235681i	$-0.924268\pi$
$251$	−11.6628	+	11.6628i	−0.736150	+	0.736150i	0.235681	+	0.971831i	$0.424268\pi$
$252$		0			0
$253$	−0.401464	−	0.401464i	−0.0252398	−	0.0252398i
$254$	−3.79152	−	1.01593i	−0.237901	−	0.0637454i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.96871	+	1.59931i	−0.372318	+	0.0997622i	−0.440126	−	0.897936i	$-0.645066\pi$
$257$	−5.96871	+	1.59931i	−0.372318	+	0.0997622i	0.0678081	+	0.997698i	$0.478399\pi$
$258$		0			0
$259$	−0.308289	−	1.22528i	−0.0191562	−	0.0761352i
$260$			2.74324i			0.170129i
$261$		0			0
$262$	10.7126	−	6.18494i	0.661829	−	0.382107i
$263$	11.7333	+	20.3228i	0.723509	+	1.25315i	0.959585	+	0.281420i	$0.0908054\pi$
$263$	11.7333	+	20.3228i	0.723509	+	1.25315i	−0.236076	+	0.971735i	$0.575861\pi$
$264$		0			0
$265$	−0.627719	+	0.627719i	−0.0385605	+	0.0385605i
$266$	1.02996	−	0.594650i	0.0631512	−	0.0364604i
$267$		0			0
$268$	3.72001	−	6.44325i	0.227236	−	0.393584i
$269$			1.73861i			0.106005i	0.998594	+	0.0530025i	$0.0168791\pi$
$269$			1.73861i			0.106005i	−0.998594	+	0.0530025i	$0.983121\pi$
$270$		0			0
$271$	−8.83686	+	15.3059i	−0.536801	+	0.929766i	0.462273	+	0.886738i	$0.347034\pi$
$271$	−8.83686	+	15.3059i	−0.536801	+	0.929766i	−0.999074	+	0.0430288i	$0.986299\pi$
$272$	−0.394528	+	1.47240i	−0.0239218	+	0.0892772i
$273$		0			0
$274$	−4.99323	+	1.33793i	−0.301652	+	0.0808274i
$275$	8.16272	+	4.71275i	0.492231	+	0.284189i
$276$		0			0
$277$	3.43143	−	12.8063i	0.206175	−	0.769454i	−0.782914	−	0.622130i	$-0.786267\pi$
$277$	3.43143	−	12.8063i	0.206175	−	0.769454i	0.989088	−	0.147324i	$-0.0470659\pi$
$278$	0.349051	−	1.30268i	0.0209347	−	0.0781293i
$279$		0			0
$280$	0.142520	+	0.0822842i	0.00851722	+	0.00491742i
$281$	−10.2688	+	2.75152i	−0.612587	+	0.164142i	−0.551755	−	0.834006i	$-0.686042\pi$
$281$	−10.2688	+	2.75152i	−0.612587	+	0.164142i	−0.0608313	+	0.998148i	$0.519375\pi$
$282$		0			0
$283$	5.74832	−	21.4530i	0.341702	−	1.27525i	−0.554716	−	0.832040i	$-0.687173\pi$
$283$	5.74832	−	21.4530i	0.341702	−	1.27525i	0.896418	−	0.443210i	$-0.146160\pi$
$284$	−2.00563	+	3.47385i	−0.119012	+	0.206135i
$285$		0			0
$286$			7.46410i			0.441362i
$287$	−0.546745	+	0.946991i	−0.0322734	+	0.0558991i
$288$		0			0
$289$	−12.7101	+	7.33820i	−0.747655	+	0.431659i
$290$	−0.529051	+	0.529051i	−0.0310669	+	0.0310669i
$291$		0			0
$292$	4.91819	+	8.51856i	0.287815	+	0.498511i
$293$	−10.8956	+	6.29059i	−0.636529	+	0.367500i	−0.783276	−	0.621674i	$-0.786453\pi$
$293$	−10.8956	+	6.29059i	−0.636529	+	0.367500i	0.146747	+	0.989174i	$0.453120\pi$
$294$		0			0
$295$			5.60960i			0.326603i
$296$	−2.96038	−	5.31377i	−0.172069	−	0.308856i
$297$		0			0
$298$	6.17359	−	1.65421i	0.357626	−	0.0958257i
$299$	−0.455950	−	0.789728i	−0.0263682	−	0.0456711i
$300$		0			0
$301$	0.530118	+	0.142045i	0.0305555	+	0.00818732i
$302$	−2.28913	−	2.28913i	−0.131725	−	0.131725i
$303$		0			0
$304$	4.04868	−	4.04868i	0.232207	−	0.232207i
$305$	0.848640	+	0.489962i	0.0485930	+	0.0280552i
$306$		0			0
$307$			10.6981i			0.610571i	0.952261	+	0.305285i	$0.0987519\pi$
$307$			10.6981i			0.610571i	−0.952261	+	0.305285i	$0.901248\pi$
$308$	0.387785	+	0.223888i	0.0220961	+	0.0127572i
$309$		0			0
$310$	1.89567	+	1.89567i	0.107667	+	0.107667i
$311$	5.12012	+	19.1086i	0.290335	+	1.08355i	0.944852	+	0.327499i	$0.106206\pi$
$311$	5.12012	+	19.1086i	0.290335	+	1.08355i	−0.654516	+	0.756048i	$0.727128\pi$
$312$		0			0
$313$	0.530256	+	1.97894i	0.0299718	+	0.111856i	0.979291	−	0.202457i	$-0.0648925\pi$
$313$	0.530256	+	1.97894i	0.0299718	+	0.111856i	−0.949319	+	0.314313i	$0.898226\pi$
$314$	8.39567	+	2.24961i	0.473795	+	0.126953i
$315$		0			0
$316$	3.34445	−	0.896143i	0.188140	−	0.0504120i
$317$	−2.20300	+	3.81571i	−0.123733	+	0.214312i	−0.921237	−	0.389002i	$-0.872820\pi$
$317$	−2.20300	+	3.81571i	−0.123733	+	0.214312i	0.797504	+	0.603314i	$0.206153\pi$
$318$		0			0
$319$	−1.43950	+	1.43950i	−0.0805964	+	0.0805964i
$320$	0.765290	+	0.205059i	0.0427810	+	0.0114631i
$321$		0			0
$322$	−0.0547053			−0.00304861
$323$	−8.72789			−0.485633
$324$		0			0
$325$	10.7047	+	10.7047i	0.593790	+	0.593790i
$326$	−2.70882	−	4.69182i	−0.150028	−	0.259856i
$327$		0			0
$328$	−1.36253	+	5.08505i	−0.0752334	+	0.280775i
$329$	0.671663	−	0.387785i	0.0370300	−	0.0213793i
$330$		0			0
$331$	−0.762434	−	2.84544i	−0.0419072	−	0.156400i	0.941802	−	0.336169i	$-0.109131\pi$
$331$	−0.762434	−	2.84544i	−0.0419072	−	0.156400i	−0.983709	+	0.179770i	$0.942465\pi$
$332$	−8.42427			−0.462342
$333$		0			0
$334$	−13.7275			−0.751134
$335$	1.52564	+	5.69378i	0.0833549	+	0.311085i
$336$		0			0
$337$	19.9921	−	11.5424i	1.08904	−	0.628756i	0.155717	−	0.987802i	$-0.450231\pi$
$337$	19.9921	−	11.5424i	1.08904	−	0.628756i	0.933320	+	0.359046i	$0.116898\pi$
$338$	0.261811	−	0.977092i	0.0142406	−	0.0531468i
$339$		0			0
$340$	−0.603857	−	1.04591i	−0.0327487	−	0.0567224i
$341$	5.15794	+	5.15794i	0.279318	+	0.279318i
$342$		0			0
$343$	−2.89902			−0.156532
$344$	2.64220			0.142458
$345$		0			0
$346$	7.59360	+	2.03470i	0.408234	+	0.109386i
$347$	−18.6640	+	18.6640i	−1.00194	+	1.00194i	−0.00193872	+	0.999998i	$0.500617\pi$
$347$	−18.6640	+	18.6640i	−1.00194	+	1.00194i	−0.999998	+	0.00193872i	$0.999383\pi$
$348$		0			0
$349$	−2.57025	+	4.45180i	−0.137582	+	0.238299i	−0.926581	−	0.376095i	$-0.877266\pi$
$349$	−2.57025	+	4.45180i	−0.137582	+	0.238299i	0.788999	+	0.614395i	$0.210600\pi$
$350$	0.877234	−	0.235054i	0.0468901	−	0.0125642i
$351$		0			0
$352$	2.08228	+	0.557946i	0.110986	+	0.0297386i
$353$	5.16859	+	19.2894i	0.275096	+	1.02667i	0.955777	+	0.294093i	$0.0950175\pi$
$353$	5.16859	+	19.2894i	0.275096	+	1.02667i	−0.680681	+	0.732580i	$0.738316\pi$
$354$		0			0
$355$	−0.822543	−	3.06977i	−0.0436561	−	0.162927i
$356$	1.38694	+	1.38694i	0.0735079	+	0.0735079i
$357$		0			0
$358$	15.9499	+	9.20866i	0.842977	+	0.486693i
$359$			2.10460i			0.111076i	0.998457	+	0.0555382i	$0.0176874\pi$
$359$			2.10460i			0.111076i	−0.998457	+	0.0555382i	$0.982313\pi$
$360$		0			0
$361$	11.9369	+	6.89177i	0.628258	+	0.362725i
$362$	−11.5156	+	11.5156i	−0.605248	+	0.605248i
$363$		0			0
$364$	0.508546	+	0.508546i	0.0266550	+	0.0266550i
$365$	−7.52769	−	2.01704i	−0.394017	−	0.105577i
$366$		0			0
$367$	8.26217	+	14.3105i	0.431282	+	0.747002i	0.996984	−	0.0776077i	$-0.0247282\pi$
$367$	8.26217	+	14.3105i	0.431282	+	0.747002i	−0.565702	+	0.824610i	$0.691395\pi$
$368$	−0.254395	+	0.0681651i	−0.0132613	+	0.00355335i
$369$		0			0
$370$	4.63544	+	1.31844i	0.240985	+	0.0685424i
$371$			0.232735i			0.0120830i
$372$		0			0
$373$	22.8102	−	13.1695i	1.18107	−	0.681890i	0.224807	−	0.974403i	$-0.427825\pi$
$373$	22.8102	−	13.1695i	1.18107	−	0.681890i	0.956261	+	0.292513i	$0.0944916\pi$
$374$	−1.64304	−	2.84582i	−0.0849594	−	0.147154i
$375$		0			0
$376$	2.64023	−	2.64023i	0.136159	−	0.136159i
$377$	−2.83167	+	1.63486i	−0.145838	+	0.0841997i
$378$		0			0
$379$	9.03456	−	15.6483i	0.464074	−	0.803800i	−0.535085	−	0.844798i	$-0.679720\pi$
$379$	9.03456	−	15.6483i	0.464074	−	0.803800i	0.999159	+	0.0409982i	$0.0130538\pi$
$380$			4.53639i			0.232712i
$381$		0			0
$382$	−10.2847	+	17.8136i	−0.526211	+	0.911424i
$383$	−3.51271	+	13.1096i	−0.179491	+	0.669870i	0.816252	+	0.577696i	$0.196048\pi$
$383$	−3.51271	+	13.1096i	−0.179491	+	0.669870i	−0.995743	+	0.0921735i	$0.970619\pi$
$384$		0			0
$385$	−0.342678	+	0.0918203i	−0.0174645	+	0.00467960i
$386$	1.81497	+	1.04787i	0.0923796	+	0.0533354i
$387$		0			0
$388$	1.52205	−	5.68036i	0.0772703	−	0.288377i
$389$	−6.76990	+	25.2656i	−0.343248	+	1.28102i	0.551398	+	0.834242i	$0.314094\pi$
$389$	−6.76990	+	25.2656i	−0.343248	+	1.28102i	−0.894646	+	0.446776i	$0.852572\pi$
$390$		0			0
$391$	0.347678	+	0.200732i	0.0175828	+	0.0101515i
$392$	−6.71981	+	1.80057i	−0.339401	+	0.0909423i
$393$		0			0
$394$	6.82664	−	25.4774i	0.343921	−	1.28353i
$395$	−1.37162	+	2.37572i	−0.0690137	+	0.119535i
$396$		0			0
$397$			18.0722i			0.907020i	0.891251	+	0.453510i	$0.149828\pi$
$397$			18.0722i			0.907020i	−0.891251	+	0.453510i	$0.850172\pi$
$398$	5.84114	−	10.1172i	0.292790	−	0.507127i
$399$		0			0
$400$	3.78651	−	2.18614i	0.189325	−	0.109307i
$401$	10.1834	−	10.1834i	0.508533	−	0.508533i	−0.405543	−	0.914076i	$-0.632917\pi$
$401$	10.1834	−	10.1834i	0.508533	−	0.508533i	0.914076	+	0.405543i	$0.132917\pi$
$402$		0			0
$403$	5.85796	+	10.1463i	0.291806	+	0.505422i
$404$	−1.85525	+	1.07113i	−0.0923019	+	0.0532905i
$405$		0			0
$406$			0.196152i			0.00973488i
$407$	12.6126	+	3.58735i	0.625184	+	0.177818i
$408$		0			0
$409$	−13.5661	+	3.63504i	−0.670803	+	0.179741i	−0.578116	−	0.815954i	$-0.696212\pi$
$409$	−13.5661	+	3.63504i	−0.670803	+	0.179741i	−0.0926863	+	0.995695i	$0.529545\pi$
$410$	−2.08547	−	3.61214i	−0.102994	−	0.178391i
$411$		0			0
$412$	2.96311	+	0.793963i	0.145982	+	0.0391158i
$413$	1.03992	+	1.03992i	0.0511709	+	0.0511709i
$414$		0			0
$415$	4.71954	−	4.71954i	0.231673	−	0.231673i
$416$	2.99855	+	1.73122i	0.147016	+	0.0848799i
$417$		0			0
$418$			12.3431i			0.603721i
$419$	−25.9316	−	14.9716i	−1.26684	−	0.731410i	−0.292451	−	0.956281i	$-0.594471\pi$
$419$	−25.9316	−	14.9716i	−1.26684	−	0.731410i	−0.974389	+	0.224870i	$0.927804\pi$
$420$		0			0
$421$	−25.0315	−	25.0315i	−1.21996	−	1.21996i	−0.967646	−	0.252313i	$-0.918809\pi$
$421$	−25.0315	−	25.0315i	−1.21996	−	1.21996i	−0.252313	−	0.967646i	$-0.581191\pi$
$422$	−2.07678	−	7.75066i	−0.101096	−	0.377296i
$423$		0			0
$424$	0.289997	+	1.08228i	0.0140835	+	0.0525604i
$425$	−6.43773	−	1.72499i	−0.312276	−	0.0836741i
$426$		0			0
$427$	0.248152	−	0.0664921i	0.0120089	−	0.00321778i
$428$	3.79878	−	6.57967i	0.183621	−	0.318041i
$429$		0			0
$430$	−1.48024	+	1.48024i	−0.0713836	+	0.0713836i
$431$	22.3148	+	5.97922i	1.07486	+	0.288009i	0.752490	−	0.658604i	$-0.228853\pi$
$431$	22.3148	+	5.97922i	1.07486	+	0.288009i	0.322374	+	0.946612i	$0.395519\pi$
$432$		0			0
$433$	−18.0727			−0.868521			−0.434260	−	0.900787i	$-0.642990\pi$
$433$	−18.0727			−0.868521			−0.434260	+	0.900787i	$0.642990\pi$
$434$	0.702843			0.0337376
$435$		0			0
$436$	3.95060	+	3.95060i	0.189199	+	0.189199i
$437$	−0.753986	−	1.30594i	−0.0360681	−	0.0624717i
$438$		0			0
$439$	−6.15844	+	22.9836i	−0.293926	+	1.09695i	0.648140	+	0.761521i	$0.275547\pi$
$439$	−6.15844	+	22.9836i	−0.293926	+	1.09695i	−0.942066	+	0.335427i	$0.891120\pi$
$440$	−1.47914	+	0.853982i	−0.0705152	+	0.0407120i
$441$		0			0
$442$	−1.36603	−	5.09808i	−0.0649752	−	0.242491i
$443$	−7.45001			−0.353960			−0.176980	−	0.984214i	$-0.556633\pi$
$443$	−7.45001			−0.353960			−0.176980	+	0.984214i	$0.556633\pi$
$444$		0			0
$445$	−1.55402			−0.0736676
$446$	−7.33560	−	27.3768i	−0.347351	−	1.29633i
$447$		0			0
$448$	0.179885	−	0.103857i	0.00849876	−	0.00490676i
$449$	−1.14860	+	4.28663i	−0.0542058	+	0.202299i	−0.987718	−	0.156247i	$-0.950061\pi$
$449$	−1.14860	+	4.28663i	−0.0542058	+	0.202299i	0.933512	+	0.358545i	$0.116727\pi$
$450$		0			0
$451$	−5.67437	−	9.82830i	−0.267196	−	0.462796i
$452$	13.7809	+	13.7809i	0.648199	+	0.648199i
$453$		0			0
$454$	−23.1354			−1.08580
$455$	−0.569807			−0.0267129
$456$		0			0
$457$	22.1278	+	5.92914i	1.03510	+	0.277353i	0.736080	−	0.676894i	$-0.236675\pi$
$457$	22.1278	+	5.92914i	1.03510	+	0.277353i	0.299017	+	0.954248i	$0.403341\pi$
$458$	12.0203	−	12.0203i	0.561673	−	0.561673i
$459$		0			0
$460$	0.104332	−	0.180709i	0.00486451	−	0.00842558i
$461$	39.9679	−	10.7094i	1.86149	−	0.498785i	0.861530	−	0.507706i	$-0.169506\pi$
$461$	39.9679	−	10.7094i	1.86149	−	0.498785i	0.999960	+	0.00892116i	$0.00283973\pi$
$462$		0			0
$463$	6.44653	+	1.72734i	0.299596	+	0.0802765i	0.405486	−	0.914101i	$-0.367102\pi$
$463$	6.44653	+	1.72734i	0.299596	+	0.0802765i	−0.105890	+	0.994378i	$0.533769\pi$
$464$	0.244414	+	0.912166i	0.0113466	+	0.0423462i
$465$		0			0
$466$	−1.75759	−	6.55941i	−0.0814187	−	0.303859i
$467$	−21.4473	−	21.4473i	−0.992462	−	0.992462i	0.00750988	−	0.999972i	$-0.497610\pi$
$467$	−21.4473	−	21.4473i	−0.992462	−	0.992462i	−0.999972	+	0.00750988i	$0.997610\pi$
$468$		0			0
$469$	1.33835	+	0.772695i	0.0617992	+	0.0356798i
$470$			2.95828i			0.136455i
$471$		0			0
$472$	6.13168	+	3.54013i	0.282234	+	0.162948i
$473$	−4.02760	+	4.02760i	−0.185189	+	0.185189i
$474$		0			0
$475$	17.7019	+	17.7019i	0.812221	+	0.812221i
$476$	−0.305836	−	0.0819485i	−0.0140180	−	0.00375610i
$477$		0			0
$478$	3.74987	+	6.49496i	0.171515	+	0.297073i
$479$	37.5596	−	10.0641i	1.71614	−	0.459839i	0.739225	−	0.673458i	$-0.235192\pi$
$479$	37.5596	−	10.0641i	1.71614	−	0.459839i	0.976917	+	0.213620i	$0.0685253\pi$
$480$		0			0
$481$	18.0762	+	10.8086i	0.824202	+	0.492828i
$482$			17.3568i			0.790582i
$483$		0			0
$484$	5.50168	−	3.17639i	0.250076	−	0.144382i
$485$	2.32962	+	4.03502i	0.105782	+	0.183221i
$486$		0			0
$487$	−8.39395	+	8.39395i	−0.380366	+	0.380366i	−0.871234	−	0.490868i	$-0.836680\pi$
$487$	−8.39395	+	8.39395i	−0.380366	+	0.380366i	0.490868	+	0.871234i	$0.336680\pi$
$488$	1.07113	−	0.618415i	0.0484876	−	0.0279943i
$489$		0			0
$490$	2.75591	−	4.77338i	0.124499	−	0.215639i
$491$		−	34.0396i		−	1.53619i	−0.640338	−	0.768093i	$-0.721206\pi$
$491$		−	34.0396i		−	1.53619i	0.640338	−	0.768093i	$-0.278794\pi$
$492$		0			0
$493$	0.719749	−	1.24664i	0.0324159	−	0.0561459i
$494$	−5.13104	+	19.1493i	−0.230856	+	0.861568i
$495$		0			0
$496$	3.26842	−	0.875772i	0.146757	−	0.0393233i
$497$	−0.721563	−	0.416595i	−0.0323665	−	0.0186868i
$498$		0			0
$499$	10.2161	−	38.1272i	0.457338	−	1.70681i	−0.223786	−	0.974638i	$-0.571842\pi$
$499$	10.2161	−	38.1272i	0.457338	−	1.70681i	0.681123	−	0.732169i	$-0.261492\pi$
$500$	−1.92187	+	7.17252i	−0.0859487	+	0.320765i
$501$		0			0
$502$	−14.2840	−	8.24685i	−0.637525	−	0.368075i
$503$	−6.97380	+	1.86862i	−0.310946	+	0.0833178i	−0.410917	−	0.911673i	$-0.634792\pi$
$503$	−6.97380	+	1.86862i	−0.310946	+	0.0833178i	0.0999713	+	0.994990i	$0.468125\pi$
$504$		0			0
$505$	0.439288	−	1.63945i	0.0195481	−	0.0729544i
$506$	0.283878	−	0.491691i	0.0126199	−	0.0218583i
$507$		0			0
$508$		−	3.92527i		−	0.174156i
$509$	16.3312	−	28.2864i	0.723866	−	1.25377i	−0.235573	−	0.971857i	$-0.575697\pi$
$509$	16.3312	−	28.2864i	0.723866	−	1.25377i	0.959439	−	0.281916i	$-0.0909699\pi$
$510$		0			0
$511$	−1.76942	+	1.02157i	−0.0782743	+	0.0451917i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−3.08963	−	5.35139i	−0.136278	−	0.236040i
$515$	−2.10483	+	1.21523i	−0.0927500	+	0.0535492i
$516$		0			0
$517$			8.04921i			0.354004i
$518$	1.10374	−	0.614910i	0.0484955	−	0.0270176i
$519$		0			0
$520$	−2.64977	+	0.710003i	−0.116200	+	0.0311357i
$521$	−12.5526	−	21.7418i	−0.549940	−	0.952524i	−0.998278	−	0.0586598i	$-0.981317\pi$
$521$	−12.5526	−	21.7418i	−0.549940	−	0.952524i	0.448338	−	0.893864i	$-0.352016\pi$
$522$		0			0
$523$	−20.9135	−	5.60375i	−0.914482	−	0.245035i	−0.229257	−	0.973366i	$-0.573630\pi$
$523$	−20.9135	−	5.60375i	−0.914482	−	0.245035i	−0.685225	+	0.728331i	$0.740296\pi$
$524$	8.74683	+	8.74683i	0.382107	+	0.382107i
$525$		0			0
$526$	−16.5935	+	16.5935i	−0.723509	+	0.723509i
$527$	−4.46690	−	2.57897i	−0.194581	−	0.112342i
$528$		0			0
$529$		−	22.9306i		−	0.996984i
$530$	−0.768795	−	0.443864i	−0.0333943	−	0.0192802i
$531$		0			0
$532$	0.840963	+	0.840963i	0.0364604	+	0.0364604i
$533$	−4.71769	−	17.6066i	−0.204346	−	0.762628i
$534$		0			0
$535$	1.55795	+	5.81433i	0.0673559	+	0.251376i
$536$	7.18652	+	1.92562i	0.310410	+	0.0831742i
$537$		0			0
$538$	−1.67937	+	0.449986i	−0.0724028	+	0.0194003i
$539$	7.49858	−	12.9879i	0.322987	−	0.559430i
$540$		0			0
$541$	−2.16194	+	2.16194i	−0.0929491	+	0.0929491i	−0.752052	−	0.659103i	$-0.770936\pi$
$541$	−2.16194	+	2.16194i	−0.0929491	+	0.0929491i	0.659103	+	0.752052i	$0.270936\pi$
$542$	−17.0715	−	4.57429i	−0.733284	−	0.196483i
$543$		0			0
$544$	−1.52434			−0.0653554
$545$	−4.42650			−0.189610
$546$		0			0
$547$	1.73723	+	1.73723i	0.0742787	+	0.0742787i	0.743270	−	0.668991i	$-0.233274\pi$
$547$	1.73723	+	1.73723i	0.0742787	+	0.0742787i	−0.668991	+	0.743270i	$0.733274\pi$
$548$	−2.58469	−	4.47681i	−0.110412	−	0.191240i
$549$		0			0
$550$	−2.43950	+	9.10433i	−0.104021	+	0.388210i
$551$	−4.68262	+	2.70351i	−0.199486	+	0.115173i
$552$		0			0
$553$	0.186141	+	0.694686i	0.00791551	+	0.0295411i
$554$	13.2580			0.563279
$555$		0			0
$556$	1.34863			0.0571946
$557$	−4.09072	−	15.2668i	−0.173329	−	0.646874i	−0.996830	−	0.0795589i	$-0.974649\pi$
$557$	−4.09072	−	15.2668i	−0.173329	−	0.646874i	0.823501	−	0.567315i	$-0.192018\pi$
$558$		0			0
$559$	−7.92277	+	4.57421i	−0.335098	+	0.193469i
$560$	−0.0425934	+	0.158961i	−0.00179990	+	0.00671732i
$561$		0			0
$562$	−5.31554	−	9.20678i	−0.224222	−	0.388364i
$563$	2.09338	+	2.09338i	0.0882254	+	0.0882254i	0.749842	−	0.661617i	$-0.230129\pi$
$563$	2.09338	+	2.09338i	0.0882254	+	0.0882254i	−0.661617	+	0.749842i	$0.730129\pi$
$564$		0			0
$565$	−15.4410			−0.649607
$566$	22.2098			0.933547
$567$		0			0
$568$	−3.87457	−	1.03819i	−0.162573	−	0.0435614i
$569$	24.1344	−	24.1344i	1.01177	−	1.01177i	0.0118386	−	0.999930i	$-0.496232\pi$
$569$	24.1344	−	24.1344i	1.01177	−	1.01177i	0.999930	−	0.0118386i	$-0.00376844\pi$
$570$		0			0
$571$	8.52409	−	14.7642i	0.356722	−	0.617861i	−0.630689	−	0.776036i	$-0.717228\pi$
$571$	8.52409	−	14.7642i	0.356722	−	0.617861i	0.987411	+	0.158175i	$0.0505610\pi$
$572$	−7.20977	+	1.93185i	−0.301456	+	0.0807748i
$573$		0			0
$574$	−1.05623	−	0.283016i	−0.0440862	−	0.0118129i
$575$	−0.298037	−	1.11229i	−0.0124290	−	0.0463856i
$576$		0			0
$577$	−2.77757	−	10.3660i	−0.115632	−	0.431543i	0.883702	−	0.468051i	$-0.155043\pi$
$577$	−2.77757	−	10.3660i	−0.115632	−	0.431543i	−0.999333	+	0.0365072i	$0.988377\pi$
$578$	−10.3778	−	10.3778i	−0.431659	−	0.431659i
$579$		0			0
$580$	−0.647952	−	0.374096i	−0.0269048	−	0.0155335i
$581$		−	1.74983i		−	0.0725952i
$582$		0			0
$583$	−2.09182	−	1.20771i	−0.0866343	−	0.0500184i
$584$	−6.95537	+	6.95537i	−0.287815	+	0.287815i
$585$		0			0
$586$	−8.89624	−	8.89624i	−0.367500	−	0.367500i
$587$	−5.81973	−	1.55939i	−0.240206	−	0.0643629i	0.136708	−	0.990611i	$-0.456348\pi$
$587$	−5.81973	−	1.55939i	−0.240206	−	0.0643629i	−0.376913	+	0.926248i	$0.623015\pi$
$588$		0			0
$589$	9.68708	+	16.7785i	0.399149	+	0.691346i
$590$	−5.41846	+	1.45187i	−0.223074	+	0.0597726i
$591$		0			0
$592$	4.36650	−	4.23482i	0.179462	−	0.174050i
$593$		−	9.42836i		−	0.387176i	−0.981083	−	0.193588i	$-0.937987\pi$
$593$		−	9.42836i		−	0.387176i	0.981083	−	0.193588i	$-0.0620126\pi$
$594$		0			0
$595$	0.217249	−	0.125429i	0.00890635	−	0.00514208i
$596$	3.19569	+	5.53509i	0.130900	+	0.226726i
$597$		0			0
$598$	0.644810	−	0.644810i	0.0263682	−	0.0263682i
$599$	30.7145	−	17.7330i	1.25496	−	0.724552i	0.282870	−	0.959158i	$-0.408714\pi$
$599$	30.7145	−	17.7330i	1.25496	−	0.724552i	0.972090	+	0.234607i	$0.0753802\pi$
$600$		0			0
$601$	7.96833	−	13.8016i	0.325035	−	0.562977i	−0.656484	−	0.754340i	$-0.727957\pi$
$601$	7.96833	−	13.8016i	0.325035	−	0.562977i	0.981519	+	0.191362i	$0.0612906\pi$
$602$			0.548819i			0.0223682i
$603$		0			0
$604$	1.61866	−	2.80360i	0.0658623	−	0.114077i
$605$	−1.30270	+	4.86173i	−0.0529621	+	0.197657i
$606$		0			0
$607$	−26.3699	+	7.06580i	−1.07032	+	0.286792i	−0.750625	−	0.660728i	$-0.770248\pi$
$607$	−26.3699	+	7.06580i	−1.07032	+	0.286792i	−0.319696	+	0.947520i	$0.603581\pi$
$608$	4.95859	+	2.86285i	0.201098	+	0.116104i
$609$		0			0
$610$	−0.253623	+	0.946534i	−0.0102689	+	0.0383241i
$611$	−3.34607	+	12.4877i	−0.135367	+	0.505198i
$612$		0			0
$613$	−24.2170	−	13.9817i	−0.978114	−	0.564714i	−0.0764137	−	0.997076i	$-0.524347\pi$
$613$	−24.2170	−	13.9817i	−0.978114	−	0.564714i	−0.901700	+	0.432362i	$0.857680\pi$
$614$	−10.3335	+	2.76886i	−0.417028	+	0.111742i
$615$		0			0
$616$	−0.115893	+	0.432518i	−0.00466945	+	0.0174266i
$617$	−16.3688	+	28.3516i	−0.658983	+	1.14139i	0.321897	+	0.946775i	$0.395680\pi$
$617$	−16.3688	+	28.3516i	−0.658983	+	1.14139i	−0.980879	+	0.194616i	$0.937654\pi$
$618$		0			0
$619$			29.7284i			1.19489i	0.801911	+	0.597443i	$0.203817\pi$
$619$			29.7284i			1.19489i	−0.801911	+	0.597443i	$0.796183\pi$
$620$	−1.34044	+	2.32171i	−0.0538334	+	0.0932421i
$621$		0			0
$622$	−17.1323	+	9.89131i	−0.686941	+	0.396606i
$623$	−0.288086	+	0.288086i	−0.0115419	+	0.0115419i
$624$		0			0
$625$	7.98913	+	13.8376i	0.319565	+	0.553503i
$626$	−1.77427	+	1.02438i	−0.0709141	+	0.0409423i
$627$		0			0
$628$			8.69184i			0.346842i
$629$	−9.27110	−	0.141939i	−0.369663	−	0.00565948i
$630$		0			0
$631$	−38.3750	+	10.2825i	−1.52768	+	0.409341i	−0.922263	−	0.386564i	$-0.873662\pi$
$631$	−38.3750	+	10.2825i	−1.52768	+	0.409341i	−0.605421	+	0.795906i	$0.706995\pi$
$632$	1.73122	+	2.99855i	0.0688641	+	0.119276i
$633$		0			0
$634$	−4.25587	−	1.14036i	−0.169022	−	0.0452894i
$635$	2.19906	+	2.19906i	0.0872671	+	0.0872671i
$636$		0			0
$637$	17.0325	−	17.0325i	0.674854	−	0.674854i
$638$	−1.76302	−	1.01788i	−0.0697986	−	0.0402982i
$639$		0			0
$640$			0.792287i			0.0313179i
$641$	−27.0600	−	15.6231i	−1.06880	−	0.617075i	−0.140950	−	0.990017i	$-0.545016\pi$
$641$	−27.0600	−	15.6231i	−1.06880	−	0.617075i	−0.927855	+	0.372942i	$0.878349\pi$
$642$		0			0
$643$	−28.6529	−	28.6529i	−1.12996	−	1.12996i	−0.990183	−	0.139778i	$-0.955361\pi$
$643$	−28.6529	−	28.6529i	−1.12996	−	1.12996i	−0.139778	−	0.990183i	$-0.544639\pi$
$644$	−0.0141588	−	0.0528412i	−0.000557934	−	0.00208224i
$645$		0			0
$646$	−2.25894	−	8.43049i	−0.0888770	−	0.331693i
$647$	31.6668	+	8.48509i	1.24495	+	0.333583i	0.820383	−	0.571814i	$-0.193760\pi$
$647$	31.6668	+	8.48509i	1.24495	+	0.333583i	0.424566	+	0.905397i	$0.360427\pi$
$648$		0			0
$649$	−14.7431	+	3.95041i	−0.578718	+	0.155067i
$650$	−7.56936	+	13.1105i	−0.296895	+	0.514237i
$651$		0			0
$652$	3.83085	−	3.83085i	0.150028	−	0.150028i
$653$	33.7192	+	9.03504i	1.31954	+	0.353568i	0.848804	−	0.528708i	$-0.177323\pi$
$653$	33.7192	+	9.03504i	1.31954	+	0.353568i	0.470732	+	0.882277i	$0.343990\pi$
$654$		0			0
$655$	−9.80050			−0.382937
$656$	−5.26443			−0.205541
$657$		0			0
$658$	0.548410	+	0.548410i	0.0213793	+	0.0213793i
$659$	−17.6212	−	30.5209i	−0.686426	−	1.18892i	−0.972986	−	0.230862i	$-0.925845\pi$
$659$	−17.6212	−	30.5209i	−0.686426	−	1.18892i	0.286560	−	0.958062i	$-0.407488\pi$
$660$		0			0
$661$	−1.13382	+	4.23148i	−0.0441005	+	0.164585i	−0.984464	−	0.175585i	$-0.943818\pi$
$661$	−1.13382	+	4.23148i	−0.0441005	+	0.164585i	0.940364	+	0.340171i	$0.110485\pi$
$662$	2.55115	−	1.47291i	0.0991534	−	0.0572463i
$663$		0			0
$664$	−2.18036	−	8.13722i	−0.0846144	−	0.315785i
$665$	−0.942267			−0.0365396
$666$		0			0
$667$	0.248711			0.00963014
$668$	−3.55293	−	13.2597i	−0.137467	−	0.513034i
$669$		0			0
$670$	−5.10491	+	2.94732i	−0.197220	+	0.113865i
$671$	−0.690085	+	2.57543i	−0.0266404	+	0.0994235i
$672$		0			0
$673$	−20.9949	−	36.3643i	−0.809295	−	1.40174i	−0.913353	−	0.407168i	$-0.866516\pi$
$673$	−20.9949	−	36.3643i	−0.809295	−	1.40174i	0.104058	−	0.994571i	$-0.466817\pi$
$674$	16.3234	+	16.3234i	0.628756	+	0.628756i
$675$		0			0
$676$	1.01156			0.0389062
$677$	−22.5025			−0.864842			−0.432421	−	0.901672i	$-0.642341\pi$
$677$	−22.5025			−0.864842			−0.432421	+	0.901672i	$0.642341\pi$
$678$		0			0
$679$	1.17988	+	0.316149i	0.0452798	+	0.0121327i
$680$	0.853982	−	0.853982i	0.0327487	−	0.0327487i
$681$		0			0
$682$	−3.64721	+	6.31716i	−0.139659	+	0.241896i
$683$	3.67240	−	0.984016i	0.140520	−	0.0376523i	−0.187873	−	0.982193i	$-0.560159\pi$
$683$	3.67240	−	0.984016i	0.140520	−	0.0376523i	0.328394	+	0.944541i	$0.393493\pi$
$684$		0			0
$685$	3.95607	+	1.06003i	0.151154	+	0.0405015i
$686$	−0.750322	−	2.80024i	−0.0286474	−	0.106914i
$687$		0			0
$688$	0.683851	+	2.55217i	0.0260716	+	0.0973004i
$689$	−2.74324	−	2.74324i	−0.104509	−	0.104509i
$690$		0			0
$691$	32.2170	+	18.6005i	1.22559	+	0.707596i	0.966105	−	0.258150i	$-0.0831130\pi$
$691$	32.2170	+	18.6005i	1.22559	+	0.707596i	0.259488	+	0.965746i	$0.416446\pi$
$692$			7.86147i			0.298848i
$693$		0			0
$694$	−22.8587	−	13.1975i	−0.867703	−	0.500968i
$695$	−0.755545	+	0.755545i	−0.0286594	+	0.0286594i
$696$		0			0
$697$	5.67437	+	5.67437i	0.214932	+	0.214932i
$698$	−4.96534	−	1.33046i	−0.187941	−	0.0503586i
$699$		0			0
$700$	0.454090	+	0.786507i	0.0171630	+	0.0297272i
$701$	5.13355	−	1.37553i	0.193892	−	0.0519531i	−0.160566	−	0.987025i	$-0.551332\pi$
$701$	5.13355	−	1.37553i	0.193892	−	0.0519531i	0.354458	+	0.935072i	$0.384665\pi$
$702$		0			0
$703$	29.8918	+	17.8737i	1.12739	+	0.674119i
$704$			2.15574i			0.0812475i
$705$		0			0
$706$	−17.2944	+	9.98495i	−0.650885	+	0.375789i
$707$	−0.222487	−	0.385359i	−0.00836748	−	0.0144929i
$708$		0			0
$709$	16.1493	−	16.1493i	0.606500	−	0.606500i	−0.335530	−	0.942030i	$-0.608915\pi$
$709$	16.1493	−	16.1493i	0.606500	−	0.606500i	0.942030	+	0.335530i	$0.108915\pi$
$710$	2.75228	−	1.58903i	0.103291	−	0.0596353i
$711$		0			0
$712$	−0.980717	+	1.69865i	−0.0367539	+	0.0636597i
$713$		−	0.891169i		−	0.0333746i
$714$		0			0
$715$	2.95686	−	5.12142i	0.110580	−	0.191530i
$716$	−4.76676	+	17.7898i	−0.178142	+	0.664835i
$717$		0			0
$718$	−2.03288	+	0.544710i	−0.0758665	+	0.0203284i
$719$	−14.3762	−	8.30008i	−0.536140	−	0.309541i	0.207373	−	0.978262i	$-0.433509\pi$
$719$	−14.3762	−	8.30008i	−0.536140	−	0.309541i	−0.743513	+	0.668721i	$0.766842\pi$
$720$		0			0
$721$	−0.164916	+	0.615477i	−0.00614181	+	0.0229216i
$722$	−3.56744	+	13.3139i	−0.132767	+	0.495491i
$723$		0			0
$724$	−14.1037	−	8.14279i	−0.524161	−	0.302624i
$725$	−3.98825	+	1.06865i	−0.148120	+	0.0396886i
$726$		0			0
$727$	3.74206	−	13.9656i	0.138785	−	0.517954i	−0.861168	−	0.508320i	$-0.830267\pi$
$727$	3.74206	−	13.9656i	0.138785	−	0.517954i	0.999954	−	0.00963408i	$-0.00306667\pi$
$728$	−0.359596	+	0.622839i	−0.0133275	+	0.0230839i
$729$		0			0
$730$		−	7.79324i		−	0.288441i
$731$	2.01380	−	3.48800i	0.0744831	−	0.129008i
$732$		0			0
$733$	−32.0631	+	18.5116i	−1.18428	+	0.683743i	−0.957000	−	0.290087i	$-0.906316\pi$
$733$	−32.0631	+	18.5116i	−1.18428	+	0.683743i	−0.227278	+	0.973830i	$0.572983\pi$
$734$	−11.6845	+	11.6845i	−0.431282	+	0.431282i
$735$		0			0
$736$	−0.131685	−	0.228085i	−0.00485397	−	0.00840731i
$737$	−13.8900	+	8.01938i	−0.511644	+	0.295398i
$738$		0			0
$739$		−	24.7696i		−	0.911164i	−0.890194	−	0.455582i	$-0.849431\pi$
$739$		−	24.7696i		−	0.911164i	0.890194	−	0.455582i	$-0.150569\pi$
$740$	−0.0737740	+	4.81873i	−0.00271198	+	0.177140i
$741$		0			0
$742$	−0.224804	+	0.0602362i	−0.00825283	+	0.00221134i
$743$	−11.3728	−	19.6983i	−0.417229	−	0.722661i	0.578431	−	0.815731i	$-0.303665\pi$
$743$	−11.3728	−	19.6983i	−0.417229	−	0.722661i	−0.995660	+	0.0930701i	$0.970332\pi$
$744$		0			0
$745$	−4.89125	−	1.31061i	−0.179202	−	0.0480170i
$746$	18.6245	+	18.6245i	0.681890	+	0.681890i
$747$		0			0
$748$	2.32361	−	2.32361i	0.0849594	−	0.0849594i
$749$	1.36668	+	0.789055i	0.0499375	+	0.0288315i
$750$		0			0
$751$		−	36.2542i		−	1.32293i	−0.749975	−	0.661467i	$-0.769934\pi$
$751$		−	36.2542i		−	1.32293i	0.749975	−	0.661467i	$-0.230066\pi$
$752$	3.23361	+	1.86692i	0.117918	+	0.0680797i
$753$		0			0
$754$	−2.31205	−	2.31205i	−0.0841997	−	0.0841997i
$755$	0.663841	+	2.47749i	0.0241596	+	0.0901650i
$756$		0			0
$757$	12.3584	+	46.1223i	0.449175	+	1.67634i	0.704672	+	0.709533i	$0.251094\pi$
$757$	12.3584	+	46.1223i	0.449175	+	1.67634i	−0.255497	+	0.966810i	$0.582239\pi$
$758$	17.4534	+	4.67663i	0.633937	+	0.169863i
$759$		0			0
$760$	−4.38182	+	1.17410i	−0.158945	+	0.0425892i
$761$	18.0732	−	31.3038i	0.655155	−	1.13476i	−0.326700	−	0.945128i	$-0.605937\pi$
$761$	18.0732	−	31.3038i	0.655155	−	1.13476i	0.981855	−	0.189633i	$-0.0607299\pi$
$762$		0			0
$763$	−0.820591	+	0.820591i	−0.0297074	+	0.0297074i
$764$	−19.8685	−	5.32375i	−0.718817	−	0.192606i
$765$		0			0
$766$	−13.5721			−0.490379
$767$	−24.5149			−0.885183
$768$		0			0
$769$	−5.57431	−	5.57431i	−0.201015	−	0.201015i	0.599420	−	0.800435i	$-0.295398\pi$
$769$	−5.57431	−	5.57431i	−0.201015	−	0.201015i	−0.800435	+	0.599420i	$0.795398\pi$
$770$	−0.177383	−	0.307237i	−0.00639245	−	0.0110720i
$771$		0			0
$772$	−0.542420	+	2.02434i	−0.0195221	+	0.0728575i
$773$	2.92122	−	1.68657i	0.105069	−	0.0606617i	−0.446545	−	0.894761i	$-0.647346\pi$
$773$	2.92122	−	1.68657i	0.105069	−	0.0606617i	0.551614	+	0.834100i	$0.314012\pi$
$774$		0			0
$775$	3.82912	+	14.2905i	0.137546	+	0.513329i
$776$	5.88074			0.211106
$777$		0			0
$778$	−26.1569			−0.937770
$779$	−7.80146	−	29.1154i	−0.279516	−	1.04317i
$780$		0			0
$781$	7.48870	−	4.32361i	0.267967	−	0.154711i
$782$	−0.103907	+	0.387785i	−0.00371569	+	0.0138671i
$783$		0			0
$784$	−3.47843	−	6.02481i	−0.124230	−	0.215172i
$785$	−4.86944	−	4.86944i	−0.173798	−	0.173798i
$786$		0			0
$787$	22.3992			0.798446			0.399223	−	0.916854i	$-0.369280\pi$
$787$	22.3992			0.798446			0.399223	+	0.916854i	$0.369280\pi$
$788$	26.3761			0.939610
$789$		0			0
$790$	−2.64977	−	0.710003i	−0.0942745	−	0.0252608i
$791$	−2.86247	+	2.86247i	−0.101778	+	0.101778i
$792$		0			0
$793$	−2.14122	+	3.70870i	−0.0760370	+	0.131700i
$794$	−17.4565	+	4.67744i	−0.619506	+	0.165996i
$795$		0			0
$796$	11.2842	+	3.02360i	0.399958	+	0.107169i
$797$	10.8632	+	40.5421i	0.384795	+	1.43607i	0.838490	+	0.544916i	$0.183439\pi$
$797$	10.8632	+	40.5421i	0.384795	+	1.43607i	−0.453696	+	0.891157i	$0.649895\pi$
$798$		0			0
$799$	−1.47311	−	5.49771i	−0.0521148	−	0.194495i
$800$	3.09167	+	3.09167i	0.109307	+	0.109307i
$801$		0			0
$802$	12.4720	+	7.20073i	0.440403	+	0.254267i
$803$		−	21.2047i		−	0.748297i
$804$		0			0
$805$	0.0375355	+	0.0216711i	0.00132295	+	0.000763807i
$806$	−8.28440	+	8.28440i	−0.291806	+	0.291806i
$807$		0			0
$808$	−1.51480	−	1.51480i	−0.0532905	−	0.0532905i
$809$	42.0116	+	11.2570i	1.47705	+	0.395774i	0.905342	−	0.424683i	$-0.139614\pi$
$809$	42.0116	+	11.2570i	1.47705	+	0.395774i	0.571708	+	0.820457i	$0.306281\pi$
$810$		0			0
$811$	−6.54478	−	11.3359i	−0.229818	−	0.398057i	0.727936	−	0.685645i	$-0.240480\pi$
$811$	−6.54478	−	11.3359i	−0.229818	−	0.398057i	−0.957754	+	0.287588i	$0.907147\pi$
$812$	−0.189469	+	0.0507680i	−0.00664905	+	0.00178161i
$813$		0			0
$814$	−0.200732	+	13.1113i	−0.00703566	+	0.459551i
$815$			4.29233i			0.150354i
$816$		0			0
$817$	−13.1016	+	7.56420i	−0.458366	+	0.264638i
$818$	−7.02235	−	12.1631i	−0.245531	−	0.425272i
$819$		0			0
$820$	2.94930	−	2.94930i	0.102994	−	0.102994i
$821$	−2.66787	+	1.54030i	−0.0931093	+	0.0537567i	−0.545832	−	0.837895i	$-0.683786\pi$
$821$	−2.66787	+	1.54030i	−0.0931093	+	0.0537567i	0.452722	+	0.891652i	$0.350453\pi$
$822$		0			0
$823$	21.3957	−	37.0584i	0.745807	−	1.29178i	−0.204010	−	0.978969i	$-0.565398\pi$
$823$	21.3957	−	37.0584i	0.745807	−	1.29178i	0.949817	−	0.312806i	$-0.101269\pi$
$824$			3.06764i			0.106866i
$825$		0			0
$826$	−0.735331	+	1.27363i	−0.0255854	+	0.0443153i
$827$	2.60570	−	9.72462i	0.0906092	−	0.338158i	−0.905708	−	0.423902i	$-0.860660\pi$
$827$	2.60570	−	9.72462i	0.0906092	−	0.338158i	0.996317	+	0.0857439i	$0.0273267\pi$
$828$		0			0
$829$	−21.5814	+	5.78272i	−0.749554	+	0.200842i	−0.613320	−	0.789834i	$-0.710166\pi$
$829$	−21.5814	+	5.78272i	−0.749554	+	0.200842i	−0.136234	+	0.990677i	$0.543500\pi$
$830$	5.78023	+	3.33722i	0.200635	+	0.115837i
$831$		0			0
$832$	−0.896143	+	3.34445i	−0.0310682	+	0.115948i
$833$	−2.74467	+	10.2433i	−0.0950972	+	0.354908i
$834$		0			0
$835$	9.41898	+	5.43805i	0.325957	+	0.188191i
$836$	−11.9225	+	3.19463i	−0.412349	+	0.110489i
$837$		0			0
$838$	7.74987	−	28.9229i	0.267715	−	0.999125i
$839$	2.27961	−	3.94840i	0.0787008	−	0.136314i	−0.823989	−	0.566606i	$-0.808256\pi$
$839$	2.27961	−	3.94840i	0.0787008	−	0.136314i	0.902690	+	0.430292i	$0.141589\pi$
$840$		0			0
$841$			28.1082i			0.969249i
$842$	17.6999	−	30.6572i	0.609979	−	1.05652i
$843$		0			0
$844$	6.94905	−	4.01204i	0.239196	−	0.138100i
$845$	−0.566708	+	0.566708i	−0.0194954	+	0.0194954i
$846$		0			0
$847$	0.659778	+	1.14277i	0.0226703	+	0.0392660i
$848$	−0.970349	+	0.560232i	−0.0333219	+	0.0192384i
$849$		0			0
$850$		−	6.66483i		−	0.228602i
$851$	−0.779675	−	1.39948i	−0.0267269	−	0.0479737i
$852$		0			0
$853$	−11.4771	+	3.07529i	−0.392969	+	0.105296i	−0.449892	−	0.893083i	$-0.648538\pi$
$853$	−11.4771	+	3.07529i	−0.392969	+	0.105296i	0.0569231	+	0.998379i	$0.481871\pi$
$854$	0.128453	+	0.222487i	0.00439557	+	0.00761335i
$855$		0			0
$856$	7.33867	+	1.96639i	0.250831	+	0.0672099i
$857$	36.2055	+	36.2055i	1.23676	+	1.23676i	0.961319	+	0.275439i	$0.0888232\pi$
$857$	36.2055	+	36.2055i	1.23676	+	1.23676i	0.275439	+	0.961319i	$0.411177\pi$
$858$		0			0
$859$	24.9045	−	24.9045i	0.849730	−	0.849730i	−0.140369	−	0.990099i	$-0.544829\pi$
$859$	24.9045	−	24.9045i	0.849730	−	0.849730i	0.990099	+	0.140369i	$0.0448290\pi$
$860$	−1.81292	−	1.04669i	−0.0618200	−	0.0356918i
$861$		0			0
$862$			23.1019i			0.786855i
$863$	−26.0794	−	15.0569i	−0.887753	−	0.512544i	−0.0145458	−	0.999894i	$-0.504630\pi$
$863$	−26.0794	−	15.0569i	−0.887753	−	0.512544i	−0.873207	+	0.487350i	$0.837964\pi$
$864$		0			0
$865$	−4.40424	−	4.40424i	−0.149749	−	0.149749i
$866$	−4.67757	−	17.4569i	−0.158950	−	0.593211i
$867$		0			0
$868$	0.181909	+	0.678894i	0.00617440	+	0.0230432i
$869$	−7.20977	−	1.93185i	−0.244575	−	0.0655336i
$870$		0			0
$871$	−24.8828	+	6.66733i	−0.843122	+	0.225914i
$872$	−2.79350	+	4.83848i	−0.0945997	+	0.163851i
$873$		0			0
$874$	1.06630	−	1.06630i	0.0360681	−	0.0360681i
$875$	−1.48983	−	0.399197i	−0.0503653	−	0.0134953i
$876$		0			0
$877$	20.5824			0.695019			0.347510	−	0.937676i	$-0.387027\pi$
$877$	20.5824			0.695019			0.347510	+	0.937676i	$0.387027\pi$
$878$	−23.7944			−0.803022
$879$		0			0
$880$	−1.20771	−	1.20771i	−0.0407120	−	0.0407120i
$881$	17.5919	+	30.4700i	0.592685	+	1.02656i	0.993869	+	0.110563i	$0.0352654\pi$
$881$	17.5919	+	30.4700i	0.592685	+	1.02656i	−0.401184	+	0.915997i	$0.631401\pi$
$882$		0			0
$883$	−4.24113	+	15.8281i	−0.142725	+	0.532658i	0.857121	+	0.515115i	$0.172251\pi$
$883$	−4.24113	+	15.8281i	−0.142725	+	0.532658i	−0.999846	+	0.0175426i	$0.994416\pi$
$884$	4.57081	−	2.63896i	0.153733	−	0.0887578i
$885$		0			0
$886$	−1.92820	−	7.19615i	−0.0647793	−	0.241759i
$887$	−20.4291			−0.685942			−0.342971	−	0.939346i	$-0.611433\pi$
$887$	−20.4291			−0.685942			−0.342971	+	0.939346i	$0.611433\pi$
$888$		0			0
$889$	0.815330			0.0273453
$890$	−0.402210	−	1.50107i	−0.0134821	−	0.0503159i
$891$		0			0
$892$	24.5454	−	14.1713i	0.821841	−	0.474490i
$893$	−5.53326	+	20.6504i	−0.185163	+	0.691039i
$894$		0			0
$895$	−7.29590	−	12.6369i	−0.243875	−	0.422404i
$896$	0.146875	+	0.146875i	0.00490676	+	0.00490676i
$897$		0			0
$898$	−4.43785			−0.148093
$899$	−3.19540			−0.106572
$900$		0			0
$901$	1.64977	+	0.442054i	0.0549617	+	0.0147269i
$902$	8.02477	−	8.02477i	0.267196	−	0.267196i
$903$		0			0
$904$	−9.74456	+	16.8781i	−0.324099	+	0.561357i
$905$	12.4632	−	3.33950i	0.414291	−	0.111009i
$906$		0			0
$907$	49.7014	+	13.3174i	1.65031	+	0.442199i	0.959699	−	0.281030i	$-0.0906760\pi$
$907$	49.7014	+	13.3174i	1.65031	+	0.442199i	0.690609	+	0.723229i	$0.257343\pi$
$908$	−5.98789	−	22.3471i	−0.198715	−	0.741614i
$909$		0			0
$910$	−0.147477	−	0.550391i	−0.00488881	−	0.0182453i
$911$	−2.41778	−	2.41778i	−0.0801045	−	0.0801045i	0.665919	−	0.746024i	$-0.268040\pi$
$911$	−2.41778	−	2.41778i	−0.0801045	−	0.0801045i	−0.746024	+	0.665919i	$0.768040\pi$
$912$		0			0
$913$	15.7275	+	9.08026i	0.520503	+	0.300513i
$914$			22.9084i			0.757744i
$915$		0			0
$916$	14.7218	+	8.49965i	0.486423	+	0.280836i
$917$	−1.81683	+	1.81683i	−0.0599970	+	0.0599970i
$918$		0			0
$919$	27.1102	+	27.1102i	0.894283	+	0.894283i	0.994923	−	0.100640i	$-0.0320889\pi$
$919$	27.1102	+	27.1102i	0.894283	+	0.894283i	−0.100640	+	0.994923i	$0.532089\pi$
$920$	0.201554	+	0.0540063i	0.00664505	+	0.00178053i
$921$		0			0
$922$	20.6889	+	35.8342i	0.681353	+	1.18014i
$923$	13.4154	−	3.59466i	0.441575	−	0.118320i
$924$		0			0
$925$	18.5158	+	19.0916i	0.608796	+	0.627727i
$926$			6.67394i			0.219319i
$927$		0			0
$928$	−0.817825	+	0.472172i	−0.0268464	+	0.0154998i
$929$	−3.79203	−	6.56799i	−0.124413	−	0.215489i	0.797091	−	0.603860i	$-0.206371\pi$
$929$	−3.79203	−	6.56799i	−0.124413	−	0.215489i	−0.921503	+	0.388371i	$0.873038\pi$
$930$		0			0
$931$	28.1661	−	28.1661i	0.923105	−	0.923105i
$932$	5.88101	−	3.39540i	0.192639	−	0.111220i
$933$		0			0
$934$	15.1655	−	26.2675i	0.496231	−	0.859497i
$935$			2.60351i			0.0851440i
$936$		0			0
$937$	−20.2758	+	35.1187i	−0.662381	+	1.14728i	0.317608	+	0.948222i	$0.397120\pi$
$937$	−20.2758	+	35.1187i	−0.662381	+	1.14728i	−0.979988	+	0.199055i	$0.936213\pi$
$938$	−0.399977	+	1.49273i	−0.0130597	+	0.0487395i
$939$		0			0
$940$	−2.85748	+	0.765659i	−0.0932007	+	0.0249731i
$941$	9.47853	+	5.47243i	0.308991	+	0.178396i	0.646475	−	0.762935i	$-0.276242\pi$
$941$	9.47853	+	5.47243i	0.308991	+	0.178396i	−0.337484	+	0.941331i	$0.609576\pi$
$942$		0			0
$943$	−0.358850	+	1.33925i	−0.0116858	+	0.0436119i
$944$	−1.83251	+	6.83901i	−0.0596430	+	0.222591i
$945$		0			0
$946$	−4.93278	−	2.84794i	−0.160379	−	0.0925946i
$947$	−22.8026	+	6.10994i	−0.740985	+	0.198546i	−0.609516	−	0.792774i	$-0.708636\pi$
$947$	−22.8026	+	6.10994i	−0.740985	+	0.198546i	−0.131469	+	0.991320i	$0.541969\pi$
$948$		0			0
$949$	8.81481	−	32.8973i	0.286141	−	1.06789i
$950$	−12.5172	+	21.6804i	−0.406111	+	0.703404i
$951$		0			0
$952$		−	0.316625i		−	0.0102619i
$953$	−18.1597	+	31.4535i	−0.588249	+	1.01888i	0.406212	+	0.913779i	$0.366849\pi$
$953$	−18.1597	+	31.4535i	−0.588249	+	1.01888i	−0.994462	+	0.105099i	$0.966484\pi$
$954$		0			0
$955$	14.1135	−	8.14843i	0.456702	−	0.263677i
$956$	−5.30311	+	5.30311i	−0.171515	+	0.171515i
$957$		0			0
$958$	19.4423	+	33.6750i	0.628152	+	1.08799i
$959$	0.929891	−	0.536873i	0.0300277	−	0.0173365i
$960$		0			0
$961$		−	19.5504i		−	0.630659i
$962$	−5.76181	+	20.2577i	−0.185768	+	0.653134i
$963$		0			0
$964$	−16.7654	+	4.49228i	−0.539977	+	0.144687i
$965$	−0.830217	−	1.43798i	−0.0267256	−	0.0462902i
$966$		0			0
$967$	32.1076	+	8.60321i	1.03251	+	0.276661i	0.735007	−	0.678060i	$-0.237179\pi$
$967$	32.1076	+	8.60321i	1.03251	+	0.276661i	0.297505	+	0.954720i	$0.403846\pi$
$968$	4.49210	+	4.49210i	0.144382	+	0.144382i
$969$		0			0
$970$	−3.29458	+	3.29458i	−0.105782	+	0.105782i
$971$	16.3954	+	9.46588i	0.526153	+	0.303775i	0.739448	−	0.673213i	$-0.235086\pi$
$971$	16.3954	+	9.46588i	0.526153	+	0.303775i	−0.213296	+	0.976988i	$0.568420\pi$
$972$		0			0
$973$			0.280128i			0.00898049i
$974$	−10.2805	−	5.93542i	−0.329407	−	0.190183i
$975$		0			0
$976$	0.874571	+	0.874571i	0.0279943	+	0.0279943i
$977$	−1.01807	−	3.79950i	−0.0325711	−	0.121557i	0.947726	−	0.319085i	$-0.103375\pi$
$977$	−1.01807	−	3.79950i	−0.0325711	−	0.121557i	−0.980297	+	0.197528i	$0.936709\pi$
$978$		0			0
$979$	−1.09438	−	4.08426i	−0.0349764	−	0.130534i
$980$	5.32402	+	1.42657i	0.170069	+	0.0455700i
$981$		0			0
$982$	32.8798	−	8.81010i	1.04924	−	0.281142i
$983$	13.7078	−	23.7426i	0.437211	−	0.757271i	−0.560263	−	0.828315i	$-0.689300\pi$
$983$	13.7078	−	23.7426i	0.437211	−	0.757271i	0.997473	+	0.0710440i	$0.0226331\pi$
$984$		0			0
$985$	−14.7767	+	14.7767i	−0.470825	+	0.470825i
$986$	1.39045	+	0.372570i	0.0442809	+	0.0118650i
$987$		0			0
$988$	−19.8248			−0.630712
$989$	0.695874			0.0221275
$990$		0			0
$991$	37.9734	+	37.9734i	1.20627	+	1.20627i	0.972227	+	0.234039i	$0.0751944\pi$
$991$	37.9734	+	37.9734i	1.20627	+	1.20627i	0.234039	+	0.972227i	$0.424806\pi$
$992$	1.69186	+	2.93039i	0.0537166	+	0.0930400i
$993$		0			0
$994$	0.215645	−	0.804799i	0.00683985	−	0.0255267i
$995$	−8.01569	+	4.62786i	−0.254114	+	0.146713i
$996$		0			0
$997$	−2.55584	−	9.53853i	−0.0809443	−	0.302088i	0.913571	−	0.406679i	$-0.133313\pi$
$997$	−2.55584	−	9.53853i	−0.0809443	−	0.302088i	−0.994515	+	0.104591i	$0.966647\pi$
$998$	39.4722			1.24947
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.be.d.125.4	yes	16
3.2	odd	2	inner	666.2.be.d.125.1	✓	16
37.8	odd	12	inner	666.2.be.d.341.1	yes	16
111.8	even	12	inner	666.2.be.d.341.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.be.d.125.1	✓	16	3.2	odd	2	inner
666.2.be.d.125.4	yes	16	1.1	even	1	trivial
666.2.be.d.341.1	yes	16	37.8	odd	12	inner
666.2.be.d.341.4	yes	16	111.8	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.205059 - 0.765290i) q^{5} +(-0.103857 - 0.179885i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.205059 - 0.765290i) q^{5} +(-0.103857 - 0.179885i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.792287 q^{10} +2.15574 q^{11} +(3.34445 + 0.896143i) q^{13} +(0.146875 - 0.146875i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.47240 + 0.394528i) q^{17} +(5.53059 + 1.48192i) q^{19} +(0.205059 + 0.765290i) q^{20} +(0.557946 + 2.08228i) q^{22} +(-0.186230 - 0.186230i) q^{23} +(3.78651 + 2.18614i) q^{25} +3.46243i q^{26} +(0.179885 + 0.103857i) q^{28} +(-0.667752 + 0.667752i) q^{29} +(2.39265 + 2.39265i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-0.762169 - 1.32012i) q^{34} +(-0.158961 + 0.0425934i) q^{35} +(5.85071 + 1.66409i) q^{37} +5.72569i q^{38} +(-0.686141 + 0.396143i) q^{40} +(-2.63222 - 4.55913i) q^{41} +(-1.86832 + 1.86832i) q^{43} +(-1.86692 + 1.07787i) q^{44} +(0.131685 - 0.228085i) q^{46} +3.73385i q^{47} +(3.47843 - 6.02481i) q^{49} +(-1.13163 + 4.22330i) q^{50} +(-3.34445 + 0.896143i) q^{52} +(-0.970349 - 0.560232i) q^{53} +(0.442054 - 1.64977i) q^{55} +(-0.0537601 + 0.200635i) q^{56} +(-0.817825 - 0.472172i) q^{58} +(-6.83901 + 1.83251i) q^{59} +(-0.320115 + 1.19469i) q^{61} +(-1.69186 + 2.93039i) q^{62} +1.00000i q^{64} +(1.37162 - 2.37572i) q^{65} +(-6.44325 + 3.72001i) q^{67} +(1.07787 - 1.07787i) q^{68} +(-0.0822842 - 0.142520i) q^{70} +(3.47385 - 2.00563i) q^{71} -9.83638i q^{73} +(-0.0931152 + 6.08205i) q^{74} +(-5.53059 + 1.48192i) q^{76} +(-0.223888 - 0.387785i) q^{77} +(-3.34445 - 0.896143i) q^{79} +(-0.560232 - 0.560232i) q^{80} +(3.72251 - 3.72251i) q^{82} +(7.29563 + 4.21213i) q^{83} +1.20771i q^{85} +(-2.28821 - 1.32110i) q^{86} +(-1.52434 - 1.52434i) q^{88} +(-0.507657 - 1.89460i) q^{89} +(-0.186141 - 0.694686i) q^{91} +(0.254395 + 0.0681651i) q^{92} +(-3.60662 + 0.966391i) q^{94} +(2.26820 - 3.92863i) q^{95} +(-4.15831 + 4.15831i) q^{97} +(6.71981 + 1.80057i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 4 q^{13} + 8 q^{16} + 16 q^{19} + 20 q^{22} + 12 q^{28} - 12 q^{31} + 8 q^{34} + 12 q^{37} + 12 q^{40} - 20 q^{43} + 12 q^{46} + 20 q^{49} - 4 q^{52} - 4 q^{55} + 4 q^{61} - 132 q^{67} + 28 q^{70} - 16 q^{76} - 4 q^{79} + 12 q^{82} + 16 q^{88} + 20 q^{91} + 12 q^{94} - 40 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 4 * q^13 + 8 * q^16 + 16 * q^19 + 20 * q^22 + 12 * q^28 - 12 * q^31 + 8 * q^34 + 12 * q^37 + 12 * q^40 - 20 * q^43 + 12 * q^46 + 20 * q^49 - 4 * q^52 - 4 * q^55 + 4 * q^61 - 132 * q^67 + 28 * q^70 - 16 * q^76 - 4 * q^79 + 12 * q^82 + 16 * q^88 + 20 * q^91 + 12 * q^94 - 40 * q^97

Introduction

L-functions

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