LMFDB - Embedded newform 660.2.y.a.301.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [660,2,Mod(181,660)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("660.181"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(660, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	660.y (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-2,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.27012653340$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.1
Root			$-0.386111 - 0.280526i$ of defining polynomial
Character	$\chi$	$=$	660.301
Dual form			660.2.y.a.421.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(0.408851 + 1.25832i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-0.105203 - 3.31496i) q^{11} +(-4.83807 - 3.51506i) q^{13} +(0.309017 + 0.951057i) q^{15} +(6.44876 - 4.68530i) q^{17} +(1.37486 - 4.23139i) q^{19} +1.32307 q^{21} +4.02566 q^{23} +(0.309017 - 0.951057i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(2.56916 + 7.90707i) q^{29} +(-1.68107 - 1.22137i) q^{31} +(-3.18522 - 0.924324i) q^{33} +(-1.07039 - 0.777682i) q^{35} +(-2.83392 - 8.72192i) q^{37} +(-4.83807 + 3.51506i) q^{39} +(2.41714 - 7.43920i) q^{41} -3.08621 q^{43} +1.00000 q^{45} +(-0.886111 + 2.72717i) q^{47} +(4.24692 - 3.08557i) q^{49} +(-2.46321 - 7.58097i) q^{51} +(-3.31118 - 2.40572i) q^{53} +(2.03359 + 2.62002i) q^{55} +(-3.59944 - 2.61515i) q^{57} +(1.63220 + 5.02341i) q^{59} +(-2.49009 + 1.80916i) q^{61} +(0.408851 - 1.25832i) q^{63} +5.98018 q^{65} -14.1976 q^{67} +(1.24400 - 3.82863i) q^{69} +(-7.33551 + 5.32956i) q^{71} +(2.83100 + 8.71293i) q^{73} +(-0.809017 - 0.587785i) q^{75} +(4.12825 - 1.48770i) q^{77} +(8.99857 + 6.53784i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-6.63047 + 4.81732i) q^{83} +(-2.46321 + 7.58097i) q^{85} +8.31399 q^{87} +9.73424 q^{89} +(2.44501 - 7.52496i) q^{91} +(-1.68107 + 1.22137i) q^{93} +(1.37486 + 4.23139i) q^{95} +(9.54725 + 6.93648i) q^{97} +(-1.86337 + 2.74369i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 2 q^{5} + 3 q^{7} - 2 q^{9} - 3 q^{11} - 6 q^{13} - 2 q^{15} + 8 q^{17} - 14 q^{19} + 8 q^{21} + 10 q^{23} - 2 q^{25} - 2 q^{27} + 6 q^{29} - q^{31} + 2 q^{33} - 7 q^{35} - 5 q^{37} - 6 q^{39}+ \cdots - 3 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 2 * q^5 + 3 * q^7 - 2 * q^9 - 3 * q^11 - 6 * q^13 - 2 * q^15 + 8 * q^17 - 14 * q^19 + 8 * q^21 + 10 * q^23 - 2 * q^25 - 2 * q^27 + 6 * q^29 - q^31 + 2 * q^33 - 7 * q^35 - 5 * q^37 - 6 * q^39 - 11 * q^41 + 28 * q^43 + 8 * q^45 - q^47 + q^49 - 12 * q^51 - 3 * q^53 + 7 * q^55 + q^57 - 5 * q^59 - 3 * q^61 + 3 * q^63 + 14 * q^65 - 50 * q^67 + 5 * q^69 - 11 * q^71 + 33 * q^73 - 2 * q^75 + 7 * q^77 + 2 * q^79 - 2 * q^81 + q^83 - 12 * q^85 + 26 * q^87 - 44 * q^89 + 25 * q^91 - q^93 - 14 * q^95 + 35 * q^97 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/660\mathbb{Z}\right)^\times$.

$n$	$221$	$331$	$397$	$541$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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			0
$2$		0			0
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$		0			0
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$		0			0
$7$	0.408851	+	1.25832i	0.154531	+	0.475599i	0.998113	−	0.0614022i	$-0.0195572\pi$
$7$	0.408851	+	1.25832i	0.154531	+	0.475599i	−0.843582	+	0.537001i	$0.819557\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	−0.105203	−	3.31496i	−0.0317198	−	0.999497i
$11$	−0.105203	−	3.31496i	−0.0317198	−	0.999497i
$12$		0			0
$13$	−4.83807	−	3.51506i	−1.34184	−	0.974903i	−0.999374	−	0.0353725i	$-0.988738\pi$
$13$	−4.83807	−	3.51506i	−1.34184	−	0.974903i	−0.342465	−	0.939531i	$-0.611262\pi$
$14$		0			0
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$		0			0
$17$	6.44876	−	4.68530i	1.56405	−	1.13635i	0.631468	−	0.775402i	$-0.282453\pi$
$17$	6.44876	−	4.68530i	1.56405	−	1.13635i	0.932586	−	0.360949i	$-0.117547\pi$
$18$		0			0
$19$	1.37486	−	4.23139i	0.315415	−	0.970749i	−0.660168	−	0.751118i	$-0.729515\pi$
$19$	1.37486	−	4.23139i	0.315415	−	0.970749i	0.975583	−	0.219630i	$-0.0704851\pi$
$20$		0			0
$21$	1.32307			0.288718
$22$		0			0
$23$	4.02566			0.839409			0.419704	−	0.907661i	$-0.362134\pi$
$23$	4.02566			0.839409			0.419704	+	0.907661i	$0.362134\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$		0			0
$29$	2.56916	+	7.90707i	0.477082	+	1.46831i	0.843129	+	0.537711i	$0.180711\pi$
$29$	2.56916	+	7.90707i	0.477082	+	1.46831i	−0.366048	+	0.930596i	$0.619289\pi$
$30$		0			0
$31$	−1.68107	−	1.22137i	−0.301930	−	0.219365i	0.426496	−	0.904489i	$-0.359748\pi$
$31$	−1.68107	−	1.22137i	−0.301930	−	0.219365i	−0.728426	+	0.685125i	$0.759748\pi$
$32$		0			0
$33$	−3.18522	−	0.924324i	−0.554476	−	0.160904i
$34$		0			0
$35$	−1.07039	−	0.777682i	−0.180928	−	0.131452i
$36$		0			0
$37$	−2.83392	−	8.72192i	−0.465894	−	1.43388i	−0.857854	−	0.513893i	$-0.828203\pi$
$37$	−2.83392	−	8.72192i	−0.465894	−	1.43388i	0.391960	−	0.919982i	$-0.371797\pi$
$38$		0			0
$39$	−4.83807	+	3.51506i	−0.774711	+	0.562861i
$40$		0			0
$41$	2.41714	−	7.43920i	0.377494	−	1.16181i	−0.564286	−	0.825579i	$-0.690849\pi$
$41$	2.41714	−	7.43920i	0.377494	−	1.16181i	0.941780	−	0.336228i	$-0.109151\pi$
$42$		0			0
$43$	−3.08621			−0.470643			−0.235322	−	0.971918i	$-0.575614\pi$
$43$	−3.08621			−0.470643			−0.235322	+	0.971918i	$0.575614\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−0.886111	+	2.72717i	−0.129253	+	0.397799i	−0.994652	−	0.103284i	$-0.967065\pi$
$47$	−0.886111	+	2.72717i	−0.129253	+	0.397799i	0.865399	+	0.501083i	$0.167065\pi$
$48$		0			0
$49$	4.24692	−	3.08557i	0.606703	−	0.440796i
$50$		0			0
$51$	−2.46321	−	7.58097i	−0.344918	−	1.06155i
$52$		0			0
$53$	−3.31118	−	2.40572i	−0.454826	−	0.330451i	0.336672	−	0.941622i	$-0.390699\pi$
$53$	−3.31118	−	2.40572i	−0.454826	−	0.330451i	−0.791498	+	0.611171i	$0.790699\pi$
$54$		0			0
$55$	2.03359	+	2.62002i	0.274210	+	0.353283i
$56$		0			0
$57$	−3.59944	−	2.61515i	−0.476757	−	0.346385i
$58$		0			0
$59$	1.63220	+	5.02341i	0.212495	+	0.653992i	0.999322	+	0.0368186i	$0.0117224\pi$
$59$	1.63220	+	5.02341i	0.212495	+	0.653992i	−0.786827	+	0.617174i	$0.788278\pi$
$60$		0			0
$61$	−2.49009	+	1.80916i	−0.318824	+	0.231639i	−0.735673	−	0.677337i	$-0.763134\pi$
$61$	−2.49009	+	1.80916i	−0.318824	+	0.231639i	0.416850	+	0.908975i	$0.363134\pi$
$62$		0			0
$63$	0.408851	−	1.25832i	0.0515104	−	0.158533i
$64$		0			0
$65$	5.98018			0.741750
$66$		0			0
$67$	−14.1976			−1.73451			−0.867256	−	0.497862i	$-0.834119\pi$
$67$	−14.1976			−1.73451			−0.867256	+	0.497862i	$0.834119\pi$
$68$		0			0
$69$	1.24400	−	3.82863i	0.149760	−	0.460913i
$70$		0			0
$71$	−7.33551	+	5.32956i	−0.870565	+	0.632502i	−0.930738	−	0.365686i	$-0.880834\pi$
$71$	−7.33551	+	5.32956i	−0.870565	+	0.632502i	0.0601738	+	0.998188i	$0.480834\pi$
$72$		0			0
$73$	2.83100	+	8.71293i	0.331344	+	1.01977i	0.968495	+	0.249032i	$0.0801125\pi$
$73$	2.83100	+	8.71293i	0.331344	+	1.01977i	−0.637152	+	0.770739i	$0.719887\pi$
$74$		0			0
$75$	−0.809017	−	0.587785i	−0.0934172	−	0.0678716i
$76$		0			0
$77$	4.12825	−	1.48770i	0.470457	−	0.169539i
$78$		0			0
$79$	8.99857	+	6.53784i	1.01242	+	0.735565i	0.964715	−	0.263297i	$-0.0848098\pi$
$79$	8.99857	+	6.53784i	1.01242	+	0.735565i	0.0477034	+	0.998862i	$0.484810\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	−6.63047	+	4.81732i	−0.727789	+	0.528769i	−0.888863	−	0.458173i	$-0.848504\pi$
$83$	−6.63047	+	4.81732i	−0.727789	+	0.528769i	0.161074	+	0.986942i	$0.448504\pi$
$84$		0			0
$85$	−2.46321	+	7.58097i	−0.267172	+	0.822271i
$86$		0			0
$87$	8.31399			0.891353
$88$		0			0
$89$	9.73424			1.03183			0.515914	−	0.856640i	$-0.327452\pi$
$89$	9.73424			1.03183			0.515914	+	0.856640i	$0.327452\pi$
$90$		0			0
$91$	2.44501	−	7.52496i	0.256306	−	0.788830i
$92$		0			0
$93$	−1.68107	+	1.22137i	−0.174319	+	0.126650i
$94$		0			0
$95$	1.37486	+	4.23139i	0.141058	+	0.434132i
$96$		0			0
$97$	9.54725	+	6.93648i	0.969377	+	0.704293i	0.955309	−	0.295608i	$-0.0955221\pi$
$97$	9.54725	+	6.93648i	0.969377	+	0.704293i	0.0140672	+	0.999901i	$0.495522\pi$
$98$		0			0
$99$	−1.86337	+	2.74369i	−0.187276	+	0.275751i
$100$		0			0
$101$	11.5092	+	8.36195i	1.14521	+	0.832045i	0.987837	−	0.155494i	$-0.0496969\pi$
$101$	11.5092	+	8.36195i	1.14521	+	0.832045i	0.157375	+	0.987539i	$0.449697\pi$
$102$		0			0
$103$	−6.12806	−	18.8602i	−0.603816	−	1.85835i	−0.504736	−	0.863274i	$-0.668410\pi$
$103$	−6.12806	−	18.8602i	−0.603816	−	1.85835i	−0.0990798	−	0.995079i	$-0.531590\pi$
$104$		0			0
$105$	−1.07039	+	0.777682i	−0.104459	+	0.0758940i
$106$		0			0
$107$	−0.939127	+	2.89033i	−0.0907888	+	0.279419i	−0.986133	−	0.165955i	$-0.946929\pi$
$107$	−0.939127	+	2.89033i	−0.0907888	+	0.279419i	0.895345	+	0.445374i	$0.146929\pi$
$108$		0			0
$109$	−1.25740			−0.120437			−0.0602184	−	0.998185i	$-0.519180\pi$
$109$	−1.25740			−0.120437			−0.0602184	+	0.998185i	$0.519180\pi$
$110$		0			0
$111$	−9.17077			−0.870451
$112$		0			0
$113$	6.09127	−	18.7470i	0.573018	−	1.76357i	−0.0698130	−	0.997560i	$-0.522240\pi$
$113$	6.09127	−	18.7470i	0.573018	−	1.76357i	0.642831	−	0.766008i	$-0.277760\pi$
$114$		0			0
$115$	−3.25683	+	2.36623i	−0.303701	+	0.220652i
$116$		0			0
$117$	1.84798	+	5.68749i	0.170846	+	0.525809i
$118$		0			0
$119$	8.53216	+	6.19898i	0.782142	+	0.568260i
$120$		0			0
$121$	−10.9779	+	0.697484i	−0.997988	+	0.0634077i
$122$		0			0
$123$	−6.32816	−	4.59768i	−0.570591	−	0.414559i
$124$		0			0
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$		0			0
$127$	−9.65888	+	7.01759i	−0.857087	+	0.622710i	−0.927091	−	0.374836i	$-0.877699\pi$
$127$	−9.65888	+	7.01759i	−0.857087	+	0.622710i	0.0700037	+	0.997547i	$0.477699\pi$
$128$		0			0
$129$	−0.953692	+	2.93516i	−0.0839679	+	0.258427i
$130$		0			0
$131$	19.4042			1.69535			0.847675	−	0.530516i	$-0.178002\pi$
$131$	19.4042			1.69535			0.847675	+	0.530516i	$0.178002\pi$
$132$		0			0
$133$	5.88654			0.510428
$134$		0			0
$135$	0.309017	−	0.951057i	0.0265959	−	0.0818539i
$136$		0			0
$137$	−3.67955	+	2.67335i	−0.314365	+	0.228399i	−0.733767	−	0.679401i	$-0.762240\pi$
$137$	−3.67955	+	2.67335i	−0.314365	+	0.228399i	0.419402	+	0.907800i	$0.362240\pi$
$138$		0			0
$139$	5.81853	+	17.9076i	0.493521	+	1.51890i	0.819249	+	0.573439i	$0.194391\pi$
$139$	5.81853	+	17.9076i	0.493521	+	1.51890i	−0.325727	+	0.945464i	$0.605609\pi$
$140$		0			0
$141$	2.31987	+	1.68548i	0.195368	+	0.141943i
$142$		0			0
$143$	−11.1433	+	16.4078i	−0.931850	+	1.37209i
$144$		0			0
$145$	−6.72616	−	4.88684i	−0.558577	−	0.405830i
$146$		0			0
$147$	−1.62218	−	4.99255i	−0.133795	−	0.411779i
$148$		0			0
$149$	−3.11669	+	2.26441i	−0.255330	+	0.185508i	−0.708086	−	0.706127i	$-0.750441\pi$
$149$	−3.11669	+	2.26441i	−0.255330	+	0.185508i	0.452756	+	0.891634i	$0.350441\pi$
$150$		0			0
$151$	0.873524	−	2.68843i	0.0710864	−	0.218781i	−0.909201	−	0.416357i	$-0.863307\pi$
$151$	0.873524	−	2.68843i	0.0710864	−	0.218781i	0.980288	+	0.197575i	$0.0633067\pi$
$152$		0			0
$153$	−7.97110			−0.644425
$154$		0			0
$155$	2.07792			0.166903
$156$		0			0
$157$	−2.50631	+	7.71364i	−0.200026	+	0.615615i	0.799856	+	0.600193i	$0.204909\pi$
$157$	−2.50631	+	7.71364i	−0.200026	+	0.615615i	−0.999881	+	0.0154227i	$0.995091\pi$
$158$		0			0
$159$	−3.31118	+	2.40572i	−0.262594	+	0.190786i
$160$		0			0
$161$	1.64590	+	5.06555i	0.129715	+	0.399222i
$162$		0			0
$163$	−1.94480	−	1.41298i	−0.152328	−	0.110673i	0.509010	−	0.860760i	$-0.330011\pi$
$163$	−1.94480	−	1.41298i	−0.152328	−	0.110673i	−0.661339	+	0.750087i	$0.730011\pi$
$164$		0			0
$165$	3.12020	−	1.12443i	0.242907	−	0.0875369i
$166$		0			0
$167$	4.29496	+	3.12047i	0.332354	+	0.241469i	0.741429	−	0.671031i	$-0.234148\pi$
$167$	4.29496	+	3.12047i	0.332354	+	0.241469i	−0.409075	+	0.912501i	$0.634148\pi$
$168$		0			0
$169$	7.03403	+	21.6485i	0.541079	+	1.66527i
$170$		0			0
$171$	−3.59944	+	2.61515i	−0.275256	+	0.199985i
$172$		0			0
$173$	3.99744	−	12.3028i	0.303920	−	0.935368i	−0.676159	−	0.736756i	$-0.736357\pi$
$173$	3.99744	−	12.3028i	0.303920	−	0.935368i	0.980078	−	0.198612i	$-0.0636434\pi$
$174$		0			0
$175$	1.32307			0.100015
$176$		0			0
$177$	5.28193			0.397014
$178$		0			0
$179$	−5.35505	+	16.4811i	−0.400255	+	1.23186i	0.524538	+	0.851387i	$0.324238\pi$
$179$	−5.35505	+	16.4811i	−0.400255	+	1.23186i	−0.924793	+	0.380471i	$0.875762\pi$
$180$		0			0
$181$	5.81853	−	4.22741i	0.432488	−	0.314221i	−0.350155	−	0.936692i	$-0.613871\pi$
$181$	5.81853	−	4.22741i	0.432488	−	0.314221i	0.782643	+	0.622471i	$0.213871\pi$
$182$		0			0
$183$	0.951130	+	2.92728i	0.0703096	+	0.216391i
$184$		0			0
$185$	7.41931	+	5.39044i	0.545478	+	0.396313i
$186$		0			0
$187$	−16.2100	−	20.8844i	−1.18539	−	1.52722i
$188$		0			0
$189$	−1.07039	−	0.777682i	−0.0778592	−	0.0565680i
$190$		0			0
$191$	−2.27103	−	6.98953i	−0.164326	−	0.505744i	0.834660	−	0.550766i	$-0.185664\pi$
$191$	−2.27103	−	6.98953i	−0.164326	−	0.505744i	−0.998986	+	0.0450216i	$0.985664\pi$
$192$		0			0
$193$	14.7801	−	10.7384i	1.06390	−	0.772966i	0.0890910	−	0.996023i	$-0.471604\pi$
$193$	14.7801	−	10.7384i	1.06390	−	0.772966i	0.974805	+	0.223058i	$0.0716038\pi$
$194$		0			0
$195$	1.84798	−	5.68749i	0.132336	−	0.407290i
$196$		0			0
$197$	16.0090			1.14059			0.570297	−	0.821438i	$-0.306828\pi$
$197$	16.0090			1.14059			0.570297	+	0.821438i	$0.306828\pi$
$198$		0			0
$199$	−15.4438			−1.09478			−0.547391	−	0.836877i	$-0.684379\pi$
$199$	−15.4438			−1.09478			−0.547391	+	0.836877i	$0.684379\pi$
$200$		0			0
$201$	−4.38730	+	13.5027i	−0.309456	+	0.952408i
$202$		0			0
$203$	−8.89919	+	6.46564i	−0.624600	+	0.453799i
$204$		0			0
$205$	2.41714	+	7.43920i	0.168821	+	0.519576i
$206$		0			0
$207$	−3.25683	−	2.36623i	−0.226365	−	0.164464i
$208$		0			0
$209$	−14.1715	−	4.11246i	−0.980265	−	0.284465i
$210$		0			0
$211$	−1.29610	−	0.941669i	−0.0892269	−	0.0648271i	0.542277	−	0.840200i	$-0.317562\pi$
$211$	−1.29610	−	0.941669i	−0.0892269	−	0.0648271i	−0.631504	+	0.775372i	$0.717562\pi$
$212$		0			0
$213$	2.80191	+	8.62341i	0.191984	+	0.590866i
$214$		0			0
$215$	2.49680	−	1.81403i	0.170280	−	0.123716i
$216$		0			0
$217$	0.849561	−	2.61468i	0.0576720	−	0.177496i
$218$		0			0
$219$	9.16131			0.619064
$220$		0			0
$221$	−47.6686			−3.20654
$222$		0			0
$223$	0.973942	−	2.99749i	0.0652200	−	0.200727i	−0.913136	−	0.407655i	$-0.866347\pi$
$223$	0.973942	−	2.99749i	0.0652200	−	0.200727i	0.978356	+	0.206928i	$0.0663467\pi$
$224$		0			0
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$		0			0
$227$	0.145142	+	0.446702i	0.00963343	+	0.0296487i	0.955758	−	0.294155i	$-0.0950382\pi$
$227$	0.145142	+	0.446702i	0.00963343	+	0.0296487i	−0.946124	+	0.323804i	$0.895038\pi$
$228$		0			0
$229$	20.5047	+	14.8975i	1.35499	+	0.984457i	0.998746	+	0.0500631i	$0.0159422\pi$
$229$	20.5047	+	14.8975i	1.35499	+	0.984457i	0.356242	+	0.934394i	$0.384058\pi$
$230$		0			0
$231$	−0.139191	−	4.38592i	−0.00915807	−	0.288572i
$232$		0			0
$233$	1.78597	+	1.29758i	0.117003	+	0.0850076i	0.644748	−	0.764395i	$-0.276962\pi$
$233$	1.78597	+	1.29758i	0.117003	+	0.0850076i	−0.527745	+	0.849403i	$0.676962\pi$
$234$		0			0
$235$	−0.886111	−	2.72717i	−0.0578035	−	0.177901i
$236$		0			0
$237$	8.99857	−	6.53784i	0.584520	−	0.424679i
$238$		0			0
$239$	0.522006	−	1.60657i	0.0337657	−	0.103920i	−0.932753	−	0.360516i	$-0.882601\pi$
$239$	0.522006	−	1.60657i	0.0337657	−	0.103920i	0.966519	+	0.256595i	$0.0826008\pi$
$240$		0			0
$241$	−13.6730			−0.880754			−0.440377	−	0.897813i	$-0.645155\pi$
$241$	−13.6730			−0.880754			−0.440377	+	0.897813i	$0.645155\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−1.62218	+	4.99255i	−0.103637	+	0.318963i
$246$		0			0
$247$	−21.5253	+	15.6390i	−1.36962	+	0.995089i
$248$		0			0
$249$	2.53261	+	7.79459i	0.160498	+	0.493962i
$250$		0			0
$251$	−10.9407	−	7.94889i	−0.690571	−	0.501730i	0.186276	−	0.982497i	$-0.440358\pi$
$251$	−10.9407	−	7.94889i	−0.690571	−	0.501730i	−0.876848	+	0.480768i	$0.840358\pi$
$252$		0			0
$253$	−0.423510	−	13.3449i	−0.0266259	−	0.838986i
$254$		0			0
$255$	6.44876	+	4.68530i	0.403837	+	0.293405i
$256$		0			0
$257$	2.42596	+	7.46632i	0.151327	+	0.465737i	0.997770	−	0.0667424i	$-0.0212606\pi$
$257$	2.42596	+	7.46632i	0.151327	+	0.465737i	−0.846443	+	0.532479i	$0.821261\pi$
$258$		0			0
$259$	9.81627	−	7.13194i	0.609954	−	0.443157i
$260$		0			0
$261$	2.56916	−	7.90707i	0.159027	−	0.489436i
$262$		0			0
$263$	12.4132			0.765433			0.382717	−	0.923866i	$-0.374989\pi$
$263$	12.4132			0.765433			0.382717	+	0.923866i	$0.374989\pi$
$264$		0			0
$265$	4.09285			0.251422
$266$		0			0
$267$	3.00805	−	9.25782i	0.184089	−	0.566569i
$268$		0			0
$269$	13.2873	−	9.65377i	0.810140	−	0.588601i	−0.103732	−	0.994605i	$-0.533078\pi$
$269$	13.2873	−	9.65377i	0.810140	−	0.588601i	0.913871	+	0.406004i	$0.133078\pi$
$270$		0			0
$271$	5.32895	+	16.4008i	0.323711	+	0.996279i	0.972019	+	0.234901i	$0.0754767\pi$
$271$	5.32895	+	16.4008i	0.323711	+	0.996279i	−0.648309	+	0.761378i	$0.724523\pi$
$272$		0			0
$273$	−6.40111	−	4.65068i	−0.387413	−	0.281472i
$274$		0			0
$275$	−3.18522	−	0.924324i	−0.192076	−	0.0557388i
$276$		0			0
$277$	3.67199	+	2.66786i	0.220629	+	0.160296i	0.692610	−	0.721313i	$-0.256461\pi$
$277$	3.67199	+	2.66786i	0.220629	+	0.160296i	−0.471981	+	0.881609i	$0.656461\pi$
$278$		0			0
$279$	0.642113	+	1.97622i	0.0384423	+	0.118313i
$280$		0			0
$281$	9.96448	−	7.23962i	0.594431	−	0.431880i	−0.249467	−	0.968383i	$-0.580255\pi$
$281$	9.96448	−	7.23962i	0.594431	−	0.431880i	0.843898	+	0.536504i	$0.180255\pi$
$282$		0			0
$283$	5.74487	−	17.6809i	0.341497	−	1.05102i	−0.621935	−	0.783069i	$-0.713653\pi$
$283$	5.74487	−	17.6809i	0.341497	−	1.05102i	0.963432	−	0.267951i	$-0.0863467\pi$
$284$		0			0
$285$	4.44915			0.263545
$286$		0			0
$287$	10.3491			0.610889
$288$		0			0
$289$	14.3812	−	44.2607i	0.845952	−	2.60357i
$290$		0			0
$291$	9.54725	−	6.93648i	0.559670	−	0.406624i
$292$		0			0
$293$	−5.23345	−	16.1069i	−0.305741	−	0.940975i	−0.979400	−	0.201932i	$-0.935278\pi$
$293$	−5.23345	−	16.1069i	−0.305741	−	0.940975i	0.673658	−	0.739043i	$-0.264722\pi$
$294$		0			0
$295$	−4.27317	−	3.10464i	−0.248793	−	0.180759i
$296$		0			0
$297$	2.03359	+	2.62002i	0.118001	+	0.152029i
$298$		0			0
$299$	−19.4764	−	14.1505i	−1.12635	−	0.818342i
$300$		0			0
$301$	−1.26180	−	3.88343i	−0.0727291	−	0.223837i
$302$		0			0
$303$	11.5092	−	8.36195i	0.661188	−	0.480381i
$304$		0			0
$305$	0.951130	−	2.92728i	0.0544616	−	0.167615i
$306$		0			0
$307$	−11.1953			−0.638949			−0.319475	−	0.947595i	$-0.603506\pi$
$307$	−11.1953			−0.638949			−0.319475	+	0.947595i	$0.603506\pi$
$308$		0			0
$309$	−19.8308			−1.12814
$310$		0			0
$311$	−1.32004	+	4.06267i	−0.0748527	+	0.230373i	−0.981482	−	0.191556i	$-0.938647\pi$
$311$	−1.32004	+	4.06267i	−0.0748527	+	0.230373i	0.906629	+	0.421929i	$0.138647\pi$
$312$		0			0
$313$	−22.4356	+	16.3004i	−1.26813	+	0.921353i	−0.999127	−	0.0417845i	$-0.986696\pi$
$313$	−22.4356	+	16.3004i	−1.26813	+	0.921353i	−0.269008	+	0.963138i	$0.586696\pi$
$314$		0			0
$315$	0.408851	+	1.25832i	0.0230362	+	0.0708980i
$316$		0			0
$317$	−7.15608	−	5.19919i	−0.401925	−	0.292016i	0.368399	−	0.929668i	$-0.379906\pi$
$317$	−7.15608	−	5.19919i	−0.401925	−	0.292016i	−0.770325	+	0.637652i	$0.779906\pi$
$318$		0			0
$319$	25.9413	−	9.34851i	1.45244	−	0.523416i
$320$		0			0
$321$	2.45867	+	1.78632i	0.137229	+	0.0997029i
$322$		0			0
$323$	−10.9592	−	33.7289i	−0.609785	−	1.87673i
$324$		0			0
$325$	−4.83807	+	3.51506i	−0.268368	+	0.194981i
$326$		0			0
$327$	−0.388557	+	1.19586i	−0.0214872	+	0.0661310i
$328$		0			0
$329$	−3.79393			−0.209166
$330$		0			0
$331$	29.2241			1.60630			0.803150	−	0.595777i	$-0.203156\pi$
$331$	29.2241			1.60630			0.803150	+	0.595777i	$0.203156\pi$
$332$		0			0
$333$	−2.83392	+	8.72192i	−0.155298	+	0.477958i
$334$		0			0
$335$	11.4861	−	8.34514i	0.627553	−	0.455944i
$336$		0			0
$337$	−1.77586	−	5.46553i	−0.0967371	−	0.297726i	0.890965	−	0.454071i	$-0.150029\pi$
$337$	−1.77586	−	5.46553i	−0.0967371	−	0.297726i	−0.987702	+	0.156345i	$0.950029\pi$
$338$		0			0
$339$	−15.9471	−	11.5863i	−0.866130	−	0.629280i
$340$		0			0
$341$	−3.87194	+	5.70118i	−0.209677	+	0.308736i
$342$		0			0
$343$	13.1117	+	9.52620i	0.707965	+	0.514366i
$344$		0			0
$345$	1.24400	+	3.82863i	0.0669746	+	0.206127i
$346$		0			0
$347$	6.45382	−	4.68897i	0.346459	−	0.251717i	−0.400923	−	0.916112i	$-0.631310\pi$
$347$	6.45382	−	4.68897i	0.346459	−	0.251717i	0.747382	+	0.664394i	$0.231310\pi$
$348$		0			0
$349$	−2.80783	+	8.64161i	−0.150300	+	0.462575i	−0.997654	−	0.0684526i	$-0.978194\pi$
$349$	−2.80783	+	8.64161i	−0.150300	+	0.462575i	0.847355	+	0.531027i	$0.178194\pi$
$350$		0			0
$351$	5.98018			0.319199
$352$		0			0
$353$	−17.0715			−0.908625			−0.454313	−	0.890842i	$-0.650115\pi$
$353$	−17.0715			−0.908625			−0.454313	+	0.890842i	$0.650115\pi$
$354$		0			0
$355$	2.80191	−	8.62341i	0.148710	−	0.457683i
$356$		0			0
$357$	8.53216	−	6.19898i	0.451570	−	0.328085i
$358$		0			0
$359$	11.3507	+	34.9338i	0.599066	+	1.84374i	0.533346	+	0.845897i	$0.320934\pi$
$359$	11.3507	+	34.9338i	0.599066	+	1.84374i	0.0657196	+	0.997838i	$0.479066\pi$
$360$		0			0
$361$	−0.643130	−	0.467261i	−0.0338489	−	0.0245927i
$362$		0			0
$363$	−2.72900	+	10.6561i	−0.143235	+	0.559300i
$364$		0			0
$365$	−7.41166	−	5.38488i	−0.387944	−	0.281858i
$366$		0			0
$367$	9.82154	+	30.2276i	0.512680	+	1.57787i	0.787464	+	0.616361i	$0.211394\pi$
$367$	9.82154	+	30.2276i	0.512680	+	1.57787i	−0.274784	+	0.961506i	$0.588606\pi$
$368$		0			0
$369$	−6.32816	+	4.59768i	−0.329431	+	0.239346i
$370$		0			0
$371$	1.67337	−	5.15009i	0.0868769	−	0.267380i
$372$		0			0
$373$	9.17548			0.475088			0.237544	−	0.971377i	$-0.423658\pi$
$373$	9.17548			0.475088			0.237544	+	0.971377i	$0.423658\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	15.3641	−	47.2858i	0.791290	−	2.43534i
$378$		0			0
$379$	0.640018	−	0.465001i	0.0328755	−	0.0238855i	−0.571226	−	0.820793i	$-0.693532\pi$
$379$	0.640018	−	0.465001i	0.0328755	−	0.0238855i	0.604102	+	0.796907i	$0.293532\pi$
$380$		0			0
$381$	3.68937	+	11.3547i	0.189012	+	0.581719i
$382$		0			0
$383$	5.67065	+	4.11997i	0.289757	+	0.210521i	0.723162	−	0.690679i	$-0.242688\pi$
$383$	5.67065	+	4.11997i	0.289757	+	0.210521i	−0.433405	+	0.901199i	$0.642688\pi$
$384$		0			0
$385$	−2.46537	+	3.63010i	−0.125647	+	0.185007i
$386$		0			0
$387$	2.49680	+	1.81403i	0.126919	+	0.0922124i
$388$		0			0
$389$	−3.99979	−	12.3101i	−0.202798	−	0.624147i	−0.999797	−	0.0201662i	$-0.993580\pi$
$389$	−3.99979	−	12.3101i	−0.202798	−	0.624147i	0.796999	−	0.603981i	$-0.206420\pi$
$390$		0			0
$391$	25.9605	−	18.8614i	1.31288	−	0.953863i
$392$		0			0
$393$	5.99622	−	18.4545i	0.302469	−	0.930904i
$394$		0			0
$395$	−11.1228			−0.559651
$396$		0			0
$397$	−34.5780			−1.73542			−0.867710	−	0.497071i	$-0.834409\pi$
$397$	−34.5780			−1.73542			−0.867710	+	0.497071i	$0.834409\pi$
$398$		0			0
$399$	1.81904	−	5.59844i	0.0910660	−	0.280272i
$400$		0			0
$401$	1.21570	−	0.883259i	0.0607092	−	0.0441078i	−0.557017	−	0.830501i	$-0.688054\pi$
$401$	1.21570	−	0.883259i	0.0607092	−	0.0441078i	0.617726	+	0.786393i	$0.288054\pi$
$402$		0			0
$403$	3.83995	+	11.8182i	0.191282	+	0.588705i
$404$		0			0
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$		0			0
$407$	−28.6146	+	10.3119i	−1.41838	+	0.511142i
$408$		0			0
$409$	1.94299	+	1.41167i	0.0960748	+	0.0698025i	0.634786	−	0.772688i	$-0.281088\pi$
$409$	1.94299	+	1.41167i	0.0960748	+	0.0698025i	−0.538711	+	0.842491i	$0.681088\pi$
$410$		0			0
$411$	1.40546	+	4.32557i	0.0693263	+	0.213364i
$412$		0			0
$413$	−5.65370	+	4.10766i	−0.278201	+	0.202125i
$414$		0			0
$415$	2.53261	−	7.79459i	0.124321	−	0.382621i
$416$		0			0
$417$	18.8292			0.922068
$418$		0			0
$419$	−34.5961			−1.69013			−0.845065	−	0.534664i	$-0.820438\pi$
$419$	−34.5961			−1.69013			−0.845065	+	0.534664i	$0.820438\pi$
$420$		0			0
$421$	9.70713	−	29.8755i	0.473097	−	1.45604i	−0.375411	−	0.926859i	$-0.622498\pi$
$421$	9.70713	−	29.8755i	0.473097	−	1.45604i	0.848508	−	0.529183i	$-0.177502\pi$
$422$		0			0
$423$	2.31987	−	1.68548i	0.112796	−	0.0819510i
$424$		0			0
$425$	−2.46321	−	7.58097i	−0.119483	−	0.367731i
$426$		0			0
$427$	−3.29457	−	2.39364i	−0.159435	−	0.115837i
$428$		0			0
$429$	12.1613	+	15.6682i	0.587151	+	0.756467i
$430$		0			0
$431$	−7.11519	−	5.16949i	−0.342727	−	0.249006i	0.403085	−	0.915163i	$-0.367938\pi$
$431$	−7.11519	−	5.16949i	−0.342727	−	0.249006i	−0.745811	+	0.666157i	$0.767938\pi$
$432$		0			0
$433$	−1.42435	−	4.38370i	−0.0684500	−	0.210667i	0.910980	−	0.412450i	$-0.135327\pi$
$433$	−1.42435	−	4.38370i	−0.0684500	−	0.210667i	−0.979430	+	0.201782i	$0.935327\pi$
$434$		0			0
$435$	−6.72616	+	4.88684i	−0.322495	+	0.234306i
$436$		0			0
$437$	5.53474	−	17.0342i	0.264762	−	0.814855i
$438$		0			0
$439$	37.8748			1.80767			0.903834	−	0.427884i	$-0.140741\pi$
$439$	37.8748			1.80767			0.903834	+	0.427884i	$0.140741\pi$
$440$		0			0
$441$	−5.24948			−0.249975
$442$		0			0
$443$	−4.92666	+	15.1627i	−0.234072	+	0.720401i	0.763171	+	0.646197i	$0.223642\pi$
$443$	−4.92666	+	15.1627i	−0.234072	+	0.720401i	−0.997243	+	0.0742040i	$0.976358\pi$
$444$		0			0
$445$	−7.87517	+	5.72164i	−0.373319	+	0.271232i
$446$		0			0
$447$	1.19047	+	3.66389i	0.0563074	+	0.173296i
$448$		0			0
$449$	−15.4511	−	11.2259i	−0.729181	−	0.529781i	0.160123	−	0.987097i	$-0.448811\pi$
$449$	−15.4511	−	11.2259i	−0.729181	−	0.529781i	−0.889304	+	0.457316i	$0.848811\pi$
$450$		0			0
$451$	−24.9149	−	7.23010i	−1.17320	−	0.340452i
$452$		0			0
$453$	−2.28692	−	1.66154i	−0.107449	−	0.0780660i
$454$		0			0
$455$	2.44501	+	7.52496i	0.114624	+	0.352775i
$456$		0			0
$457$	−10.2623	+	7.45599i	−0.480050	+	0.348777i	−0.801345	−	0.598202i	$-0.795882\pi$
$457$	−10.2623	+	7.45599i	−0.480050	+	0.348777i	0.321295	+	0.946979i	$0.395882\pi$
$458$		0			0
$459$	−2.46321	+	7.58097i	−0.114973	+	0.353849i
$460$		0			0
$461$	−2.87253			−0.133787			−0.0668935	−	0.997760i	$-0.521309\pi$
$461$	−2.87253			−0.133787			−0.0668935	+	0.997760i	$0.521309\pi$
$462$		0			0
$463$	−6.29101			−0.292368			−0.146184	−	0.989257i	$-0.546699\pi$
$463$	−6.29101			−0.292368			−0.146184	+	0.989257i	$0.546699\pi$
$464$		0			0
$465$	0.642113	−	1.97622i	0.0297773	−	0.0916451i
$466$		0			0
$467$	2.74814	−	1.99664i	0.127169	−	0.0923936i	−0.522383	−	0.852711i	$-0.674957\pi$
$467$	2.74814	−	1.99664i	0.127169	−	0.0923936i	0.649551	+	0.760318i	$0.274957\pi$
$468$		0			0
$469$	−5.80471	−	17.8651i	−0.268037	−	0.824932i
$470$		0			0
$471$	6.56161	+	4.76729i	0.302343	+	0.219665i
$472$		0			0
$473$	0.324678	+	10.2307i	0.0149287	+	0.470406i
$474$		0			0
$475$	−3.59944	−	2.61515i	−0.165154	−	0.119991i
$476$		0			0
$477$	1.26476	+	3.89253i	0.0579094	+	0.178227i
$478$		0			0
$479$	−12.3946	+	9.00524i	−0.566326	+	0.411460i	−0.833769	−	0.552114i	$-0.813821\pi$
$479$	−12.3946	+	9.00524i	−0.566326	+	0.411460i	0.267443	+	0.963574i	$0.413821\pi$
$480$		0			0
$481$	−16.9474	+	52.1587i	−0.772734	+	2.37823i
$482$		0			0
$483$	5.32624			0.242352
$484$		0			0
$485$	−11.8011			−0.535858
$486$		0			0
$487$	5.84044	−	17.9750i	0.264656	−	0.814527i	−0.727117	−	0.686514i	$-0.759140\pi$
$487$	5.84044	−	17.9750i	0.264656	−	0.814527i	0.991773	−	0.128013i	$-0.0408599\pi$
$488$		0			0
$489$	−1.94480	+	1.41298i	−0.0879469	+	0.0638972i
$490$		0			0
$491$	−2.64555	−	8.14216i	−0.119392	−	0.367450i	0.873446	−	0.486921i	$-0.161880\pi$
$491$	−2.64555	−	8.14216i	−0.119392	−	0.367450i	−0.992838	+	0.119471i	$0.961880\pi$
$492$		0			0
$493$	53.6149	+	38.9535i	2.41469	+	1.75438i
$494$		0			0
$495$	−0.105203	−	3.31496i	−0.00472851	−	0.148996i
$496$		0			0
$497$	−9.70540	−	7.05138i	−0.435347	−	0.316298i
$498$		0			0
$499$	−11.0689	−	34.0664i	−0.495510	−	1.52502i	−0.816161	−	0.577825i	$-0.803902\pi$
$499$	−11.0689	−	34.0664i	−0.495510	−	1.52502i	0.320651	−	0.947197i	$-0.396098\pi$
$500$		0			0
$501$	4.29496	−	3.12047i	0.191885	−	0.139412i
$502$		0			0
$503$	2.11424	−	6.50696i	0.0942693	−	0.290131i	−0.892793	−	0.450467i	$-0.851258\pi$
$503$	2.11424	−	6.50696i	0.0942693	−	0.290131i	0.987063	+	0.160336i	$0.0512577\pi$
$504$		0			0
$505$	−14.2262			−0.633057
$506$		0			0
$507$	22.7626			1.01092
$508$		0			0
$509$	0.567708	−	1.74723i	0.0251632	−	0.0774445i	−0.937686	−	0.347483i	$-0.887036\pi$
$509$	0.567708	−	1.74723i	0.0251632	−	0.0774445i	0.962850	+	0.270039i	$0.0870364\pi$
$510$		0			0
$511$	−9.80615	+	7.12458i	−0.433799	+	0.315173i
$512$		0			0
$513$	1.37486	+	4.23139i	0.0607017	+	0.186821i
$514$		0			0
$515$	16.0435	+	11.6563i	0.706960	+	0.513636i
$516$		0			0
$517$	9.13367	+	2.65051i	0.401698	+	0.116570i
$518$		0			0
$519$	−10.4654	−	7.60358i	−0.459381	−	0.333760i
$520$		0			0
$521$	5.56920	+	17.1402i	0.243991	+	0.750928i	0.995801	+	0.0915473i	$0.0291813\pi$
$521$	5.56920	+	17.1402i	0.243991	+	0.750928i	−0.751810	+	0.659380i	$0.770819\pi$
$522$		0			0
$523$	11.0172	−	8.00444i	0.481747	−	0.350010i	−0.320255	−	0.947331i	$-0.603768\pi$
$523$	11.0172	−	8.00444i	0.481747	−	0.350010i	0.802002	+	0.597322i	$0.203768\pi$
$524$		0			0
$525$	0.408851	−	1.25832i	0.0178437	−	0.0549174i
$526$		0			0
$527$	−16.5633			−0.721510
$528$		0			0
$529$	−6.79404			−0.295393
$530$		0			0
$531$	1.63220	−	5.02341i	0.0708316	−	0.217997i
$532$		0			0
$533$	−37.8436	+	27.4950i	−1.63919	+	1.19094i
$534$		0			0
$535$	−0.939127	−	2.89033i	−0.0406020	−	0.124960i
$536$		0			0
$537$	14.0197	+	10.1859i	0.604994	+	0.439554i
$538$		0			0
$539$	−10.6753	−	13.7537i	−0.459818	−	0.592416i
$540$		0			0
$541$	−1.18837	−	0.863398i	−0.0510918	−	0.0371204i	0.561946	−	0.827174i	$-0.310053\pi$
$541$	−1.18837	−	0.863398i	−0.0510918	−	0.0371204i	−0.613038	+	0.790053i	$0.710053\pi$
$542$		0			0
$543$	−2.22248	−	6.84009i	−0.0953758	−	0.293536i
$544$		0			0
$545$	1.01726	−	0.739079i	0.0435744	−	0.0316587i
$546$		0			0
$547$	−7.74300	+	23.8305i	−0.331067	+	1.01892i	0.637561	+	0.770400i	$0.279944\pi$
$547$	−7.74300	+	23.8305i	−0.331067	+	1.01892i	−0.968627	+	0.248518i	$0.920056\pi$
$548$		0			0
$549$	3.07792			0.131363
$550$		0			0
$551$	36.9902			1.57584
$552$		0			0
$553$	−4.54759	+	13.9960i	−0.193383	+	0.595172i
$554$		0			0
$555$	7.41931	−	5.39044i	0.314932	−	0.228812i
$556$		0			0
$557$	1.23801	+	3.81021i	0.0524563	+	0.161444i	0.973853	−	0.227180i	$-0.0729506\pi$
$557$	1.23801	+	3.81021i	0.0524563	+	0.161444i	−0.921397	+	0.388624i	$0.872951\pi$
$558$		0			0
$559$	14.9313	+	10.8482i	0.631527	+	0.458831i
$560$		0			0
$561$	−24.8714	+	8.96296i	−1.05007	+	0.378416i
$562$		0			0
$563$	32.7914	+	23.8244i	1.38199	+	1.00408i	0.996691	+	0.0812875i	$0.0259032\pi$
$563$	32.7914	+	23.8244i	1.38199	+	1.00408i	0.385303	+	0.922790i	$0.374097\pi$
$564$		0			0
$565$	6.09127	+	18.7470i	0.256261	+	0.788692i
$566$		0			0
$567$	−1.07039	+	0.777682i	−0.0449520	+	0.0326596i
$568$		0			0
$569$	0.322604	−	0.992873i	0.0135243	−	0.0416234i	−0.944067	−	0.329755i	$-0.893034\pi$
$569$	0.322604	−	0.992873i	0.0135243	−	0.0416234i	0.957591	+	0.288131i	$0.0930340\pi$
$570$		0			0
$571$	13.3111			0.557054			0.278527	−	0.960428i	$-0.410154\pi$
$571$	13.3111			0.557054			0.278527	+	0.960428i	$0.410154\pi$
$572$		0			0
$573$	−7.34922			−0.307018
$574$		0			0
$575$	1.24400	−	3.82863i	0.0518783	−	0.159665i
$576$		0			0
$577$	−6.11389	+	4.44200i	−0.254525	+	0.184923i	−0.707730	−	0.706483i	$-0.750281\pi$
$577$	−6.11389	+	4.44200i	−0.254525	+	0.184923i	0.453205	+	0.891406i	$0.350281\pi$
$578$		0			0
$579$	−5.64550	−	17.3751i	−0.234619	−	0.722083i
$580$		0			0
$581$	−8.77258	−	6.37366i	−0.363948	−	0.264424i
$582$		0			0
$583$	−7.62650	+	11.2295i	−0.315857	+	0.465079i
$584$		0			0
$585$	−4.83807	−	3.51506i	−0.200030	−	0.145330i
$586$		0			0
$587$	11.6185	+	35.7580i	0.479545	+	1.47589i	0.839728	+	0.543007i	$0.182714\pi$
$587$	11.6185	+	35.7580i	0.479545	+	1.47589i	−0.360183	+	0.932882i	$0.617286\pi$
$588$		0			0
$589$	−7.47935	+	5.43407i	−0.308181	+	0.223907i
$590$		0			0
$591$	4.94706	−	15.2255i	0.203495	−	0.626292i
$592$		0			0
$593$	1.36380			0.0560047			0.0280024	−	0.999608i	$-0.491085\pi$
$593$	1.36380			0.0560047			0.0280024	+	0.999608i	$0.491085\pi$
$594$		0			0
$595$	−10.5463			−0.432358
$596$		0			0
$597$	−4.77240	+	14.6879i	−0.195321	+	0.601137i
$598$		0			0
$599$	8.12176	−	5.90080i	0.331846	−	0.241100i	−0.409367	−	0.912370i	$-0.634251\pi$
$599$	8.12176	−	5.90080i	0.331846	−	0.241100i	0.741214	+	0.671269i	$0.234251\pi$
$600$		0			0
$601$	6.79845	+	20.9235i	0.277314	+	0.853486i	0.988598	+	0.150581i	$0.0481143\pi$
$601$	6.79845	+	20.9235i	0.277314	+	0.853486i	−0.711283	+	0.702906i	$0.751886\pi$
$602$		0			0
$603$	11.4861	+	8.34514i	0.467750	+	0.339840i
$604$		0			0
$605$	8.47131	−	7.01690i	0.344408	−	0.285278i
$606$		0			0
$607$	17.1112	+	12.4320i	0.694521	+	0.504599i	0.878143	−	0.478398i	$-0.158782\pi$
$607$	17.1112	+	12.4320i	0.694521	+	0.504599i	−0.183622	+	0.982997i	$0.558782\pi$
$608$		0			0
$609$	3.39919	+	10.4616i	0.137742	+	0.423926i
$610$		0			0
$611$	13.8732	−	10.0795i	0.561251	−	0.407773i
$612$		0			0
$613$	0.833203	−	2.56433i	0.0336527	−	0.103572i	−0.932819	−	0.360345i	$-0.882659\pi$
$613$	0.833203	−	2.56433i	0.0336527	−	0.103572i	0.966472	+	0.256772i	$0.0826590\pi$
$614$		0			0
$615$	7.82204			0.315415
$616$		0			0
$617$	−9.26666			−0.373062			−0.186531	−	0.982449i	$-0.559724\pi$
$617$	−9.26666			−0.373062			−0.186531	+	0.982449i	$0.559724\pi$
$618$		0			0
$619$	4.75896	−	14.6466i	0.191279	−	0.588695i	−0.808721	−	0.588192i	$-0.799840\pi$
$619$	4.75896	−	14.6466i	0.191279	−	0.588695i	1.00000		0.000503118i	$-0.000160147\pi$
$620$		0			0
$621$	−3.25683	+	2.36623i	−0.130692	+	0.0949533i
$622$		0			0
$623$	3.97986	+	12.2487i	0.159450	+	0.490736i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	−8.29042	+	12.2071i	−0.331088	+	0.487505i
$628$		0			0
$629$	−59.1401	−	42.9678i	−2.35807	−	1.71324i
$630$		0			0
$631$	−6.94137	−	21.3633i	−0.276332	−	0.850461i	−0.988864	−	0.148822i	$-0.952452\pi$
$631$	−6.94137	−	21.3633i	−0.276332	−	0.850461i	0.712532	−	0.701639i	$-0.247548\pi$
$632$		0			0
$633$	−1.29610	+	0.941669i	−0.0515152	+	0.0374280i
$634$		0			0
$635$	3.68937	−	11.3547i	0.146408	−	0.450597i
$636$		0			0
$637$	−31.3929			−1.24383
$638$		0			0
$639$	9.06719			0.358692
$640$		0			0
$641$	−6.32794	+	19.4754i	−0.249939	+	0.769232i	0.744846	+	0.667236i	$0.232523\pi$
$641$	−6.32794	+	19.4754i	−0.249939	+	0.769232i	−0.994785	+	0.101996i	$0.967477\pi$
$642$		0			0
$643$	4.72609	−	3.43370i	0.186379	−	0.135412i	−0.490683	−	0.871338i	$-0.663253\pi$
$643$	4.72609	−	3.43370i	0.186379	−	0.135412i	0.677062	+	0.735926i	$0.263253\pi$
$644$		0			0
$645$	−0.953692	−	2.93516i	−0.0375516	−	0.115572i
$646$		0			0
$647$	4.00539	+	2.91009i	0.157468	+	0.114407i	0.663729	−	0.747973i	$-0.268973\pi$
$647$	4.00539	+	2.91009i	0.157468	+	0.114407i	−0.506261	+	0.862380i	$0.668973\pi$
$648$		0			0
$649$	16.4807	−	5.93916i	0.646923	−	0.233133i
$650$		0			0
$651$	−2.22418	−	1.61596i	−0.0871725	−	0.0633345i
$652$		0			0
$653$	9.37985	+	28.8682i	0.367062	+	1.12970i	0.948680	+	0.316238i	$0.102420\pi$
$653$	9.37985	+	28.8682i	0.367062	+	1.12970i	−0.581618	+	0.813462i	$0.697580\pi$
$654$		0			0
$655$	−15.6983	+	11.4055i	−0.613383	+	0.445649i
$656$		0			0
$657$	2.83100	−	8.71293i	0.110448	−	0.339924i
$658$		0			0
$659$	12.9400			0.504071			0.252036	−	0.967718i	$-0.418900\pi$
$659$	12.9400			0.504071			0.252036	+	0.967718i	$0.418900\pi$
$660$		0			0
$661$	−5.41592			−0.210655			−0.105327	−	0.994438i	$-0.533589\pi$
$661$	−5.41592			−0.210655			−0.105327	+	0.994438i	$0.533589\pi$
$662$		0			0
$663$	−14.7304	+	45.3356i	−0.572082	+	1.76069i
$664$		0			0
$665$	−4.76231	+	3.46002i	−0.184675	+	0.134174i
$666$		0			0
$667$	10.3426	+	31.8312i	0.400467	+	1.23251i
$668$		0			0
$669$	−2.54981	−	1.85255i	−0.0985815	−	0.0716237i
$670$		0			0
$671$	6.25924	+	8.06421i	0.241635	+	0.311316i
$672$		0			0
$673$	33.6903	+	24.4774i	1.29867	+	0.943536i	0.999942	−	0.0108032i	$-0.00343884\pi$
$673$	33.6903	+	24.4774i	1.29867	+	0.943536i	0.298724	+	0.954339i	$0.403439\pi$
$674$		0			0
$675$	0.309017	+	0.951057i	0.0118941	+	0.0366062i
$676$		0			0
$677$	37.1606	−	26.9988i	1.42820	−	1.03765i	0.437850	−	0.899048i	$-0.355740\pi$
$677$	37.1606	−	26.9988i	1.42820	−	1.03765i	0.990349	−	0.138599i	$-0.0442599\pi$
$678$		0			0
$679$	−4.82488	+	14.8494i	−0.185162	+	0.569869i
$680$		0			0
$681$	0.469690			0.0179986
$682$		0			0
$683$	−0.462944			−0.0177141			−0.00885703	−	0.999961i	$-0.502819\pi$
$683$	−0.462944			−0.0177141			−0.00885703	+	0.999961i	$0.502819\pi$
$684$		0			0
$685$	1.40546	−	4.32557i	0.0536999	−	0.165271i
$686$		0			0
$687$	20.5047	−	14.8975i	0.782303	−	0.568376i
$688$		0			0
$689$	7.56349	+	23.2780i	0.288146	+	0.886823i
$690$		0			0
$691$	26.6269	+	19.3455i	1.01293	+	0.735939i	0.964822	−	0.262903i	$-0.0846799\pi$
$691$	26.6269	+	19.3455i	1.01293	+	0.735939i	0.0481110	+	0.998842i	$0.484680\pi$
$692$		0			0
$693$	−4.21427	−	1.22295i	−0.160087	−	0.0464559i
$694$		0			0
$695$	−15.2331	−	11.0675i	−0.577825	−	0.419814i
$696$		0			0
$697$	−19.2673	−	59.2986i	−0.729801	−	2.24610i
$698$		0			0
$699$	1.78597	−	1.29758i	0.0675517	−	0.0490792i
$700$		0			0
$701$	−9.87750	+	30.3998i	−0.373068	+	1.14819i	0.571705	+	0.820459i	$0.306282\pi$
$701$	−9.87750	+	30.3998i	−0.373068	+	1.14819i	−0.944773	+	0.327726i	$0.893718\pi$
$702$		0			0
$703$	−40.8022			−1.53888
$704$		0			0
$705$	−2.86752			−0.107997
$706$		0			0
$707$	−5.81640	+	17.9010i	−0.218748	+	0.673238i
$708$		0			0
$709$	24.1808	−	17.5684i	0.908129	−	0.659794i	−0.0324120	−	0.999475i	$-0.510319\pi$
$709$	24.1808	−	17.5684i	0.908129	−	0.659794i	0.940541	+	0.339680i	$0.110319\pi$
$710$		0			0
$711$	−3.43715	−	10.5785i	−0.128903	−	0.396723i
$712$		0			0
$713$	−6.76744	−	4.91683i	−0.253443	−	0.184137i
$714$		0			0
$715$	−0.629131	−	19.8240i	−0.0235282	−	0.741377i
$716$		0			0
$717$	−1.36663	−	0.992914i	−0.0510377	−	0.0370810i
$718$		0			0
$719$	6.37070	+	19.6070i	0.237587	+	0.731217i	0.996768	+	0.0803375i	$0.0255998\pi$
$719$	6.37070	+	19.6070i	0.237587	+	0.731217i	−0.759181	+	0.650880i	$0.774400\pi$
$720$		0			0
$721$	21.2266	−	15.4221i	0.790522	−	0.574348i
$722$		0			0
$723$	−4.22518	+	13.0038i	−0.157136	+	0.483615i
$724$		0			0
$725$	8.31399			0.308774
$726$		0			0
$727$	26.4641			0.981499			0.490749	−	0.871301i	$-0.336723\pi$
$727$	26.4641			0.981499			0.490749	+	0.871301i	$0.336723\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−19.9022	+	14.4598i	−0.736111	+	0.534816i
$732$		0			0
$733$	−5.62538	−	17.3131i	−0.207778	−	0.639475i	−0.999588	−	0.0287076i	$-0.990861\pi$
$733$	−5.62538	−	17.3131i	−0.207778	−	0.639475i	0.791810	−	0.610768i	$-0.209139\pi$
$734$		0			0
$735$	4.24692	+	3.08557i	0.156650	+	0.113813i
$736$		0			0
$737$	1.49363	+	47.0644i	0.0550184	+	1.73364i
$738$		0			0
$739$	−32.8386	−	23.8586i	−1.20799	−	0.877653i	−0.212940	−	0.977065i	$-0.568304\pi$
$739$	−32.8386	−	23.8586i	−1.20799	−	0.877653i	−0.995046	+	0.0994120i	$0.968304\pi$
$740$		0			0
$741$	8.22194	+	25.3045i	0.302040	+	0.929585i
$742$		0			0
$743$	−26.3393	+	19.1366i	−0.966296	+	0.702055i	−0.954604	−	0.297877i	$-0.903722\pi$
$743$	−26.3393	+	19.1366i	−0.966296	+	0.702055i	−0.0116914	+	0.999932i	$0.503722\pi$
$744$		0			0
$745$	1.19047	−	3.66389i	0.0436155	−	0.134235i
$746$		0			0
$747$	8.19571			0.299865
$748$		0			0
$749$	−4.02092			−0.146921
$750$		0			0
$751$	1.53589	−	4.72698i	0.0560453	−	0.172490i	−0.919115	−	0.393989i	$-0.871095\pi$
$751$	1.53589	−	4.72698i	0.0560453	−	0.172490i	0.975161	+	0.221499i	$0.0710949\pi$
$752$		0			0
$753$	−10.9407	+	7.94889i	−0.398702	+	0.289674i
$754$		0			0
$755$	0.873524	+	2.68843i	0.0317908	+	0.0978420i
$756$		0			0
$757$	−20.3767	−	14.8045i	−0.740602	−	0.538079i	0.152297	−	0.988335i	$-0.451333\pi$
$757$	−20.3767	−	14.8045i	−0.740602	−	0.538079i	−0.892900	+	0.450256i	$0.851333\pi$
$758$		0			0
$759$	−12.8226	−	3.72102i	−0.465432	−	0.135064i
$760$		0			0
$761$	9.05151	+	6.57631i	0.328117	+	0.238391i	0.739631	−	0.673012i	$-0.235000\pi$
$761$	9.05151	+	6.57631i	0.328117	+	0.238391i	−0.411514	+	0.911403i	$0.635000\pi$
$762$		0			0
$763$	−0.514088	−	1.58220i	−0.0186113	−	0.0572795i
$764$		0			0
$765$	6.44876	−	4.68530i	0.233155	−	0.169397i
$766$		0			0
$767$	9.76088	−	30.0409i	0.352445	−	1.08471i
$768$		0			0
$769$	−53.3116			−1.92246			−0.961232	−	0.275741i	$-0.911077\pi$
$769$	−53.3116			−1.92246			−0.961232	+	0.275741i	$0.911077\pi$
$770$		0			0
$771$	7.85056			0.282731
$772$		0			0
$773$	−5.30689	+	16.3329i	−0.190876	+	0.587455i	−1.00000		0.000182505i	$-0.999942\pi$
$773$	−5.30689	+	16.3329i	−0.190876	+	0.587455i	0.809124	+	0.587638i	$0.199942\pi$
$774$		0			0
$775$	−1.68107	+	1.22137i	−0.0603860	+	0.0438730i
$776$		0			0
$777$	−3.74948	−	11.5397i	−0.134512	−	0.413985i
$778$		0			0
$779$	−28.1549	−	20.4558i	−1.00876	−	0.732904i
$780$		0			0
$781$	18.4390	+	23.7562i	0.659798	+	0.850064i
$782$		0			0
$783$	−6.72616	−	4.88684i	−0.240373	−	0.174641i
$784$		0			0
$785$	−2.50631	−	7.71364i	−0.0894541	−	0.275311i
$786$		0			0
$787$	−3.48717	+	2.53358i	−0.124304	+	0.0903122i	−0.648200	−	0.761470i	$-0.724478\pi$
$787$	−3.48717	+	2.53358i	−0.124304	+	0.0903122i	0.523896	+	0.851782i	$0.324478\pi$
$788$		0			0
$789$	3.83590	−	11.8057i	0.136562	−	0.420294i
$790$		0			0
$791$	26.0800			0.927300
$792$		0			0
$793$	18.4065			0.653635
$794$		0			0
$795$	1.26476	−	3.89253i	0.0448564	−	0.138054i
$796$		0			0
$797$	13.1444	−	9.54996i	0.465598	−	0.338277i	−0.330125	−	0.943937i	$-0.607091\pi$
$797$	13.1444	−	9.54996i	0.465598	−	0.338277i	0.795723	+	0.605660i	$0.207091\pi$
$798$		0			0
$799$	7.06328	+	21.7386i	0.249881	+	0.769055i
$800$		0			0
$801$	−7.87517	−	5.72164i	−0.278255	−	0.202164i
$802$		0			0
$803$	28.5851	−	10.3013i	1.00875	−	0.363524i
$804$		0			0
$805$	−4.30902	−	3.13068i	−0.151873	−	0.110342i
$806$		0			0
$807$	−5.07529	−	15.6201i	−0.178659	−	0.549855i
$808$		0			0
$809$	12.7235	−	9.24413i	0.447333	−	0.325006i	−0.341209	−	0.939987i	$-0.610836\pi$
$809$	12.7235	−	9.24413i	0.447333	−	0.325006i	0.788542	+	0.614981i	$0.210836\pi$
$810$		0			0
$811$	5.02578	−	15.4678i	0.176479	−	0.543146i	−0.823219	−	0.567724i	$-0.807824\pi$
$811$	5.02578	−	15.4678i	0.176479	−	0.543146i	0.999698	+	0.0245776i	$0.00782407\pi$
$812$		0			0
$813$	17.2448			0.604803
$814$		0			0
$815$	2.40390			0.0842051
$816$		0			0
$817$	−4.24312	+	13.0590i	−0.148448	+	0.456876i
$818$		0			0
$819$	−6.40111	+	4.65068i	−0.223673	+	0.162508i
$820$		0			0
$821$	−3.81964	−	11.7556i	−0.133306	−	0.410274i	0.862016	−	0.506880i	$-0.169201\pi$
$821$	−3.81964	−	11.7556i	−0.133306	−	0.410274i	−0.995323	+	0.0966058i	$0.969201\pi$
$822$		0			0
$823$	7.90757	+	5.74518i	0.275640	+	0.200265i	0.717014	−	0.697059i	$-0.245508\pi$
$823$	7.90757	+	5.74518i	0.275640	+	0.200265i	−0.441373	+	0.897324i	$0.645508\pi$
$824$		0			0
$825$	−1.86337	+	2.74369i	−0.0648743	+	0.0955231i
$826$		0			0
$827$	20.7322	+	15.0629i	0.720931	+	0.523787i	0.886681	−	0.462381i	$-0.153005\pi$
$827$	20.7322	+	15.0629i	0.720931	+	0.523787i	−0.165751	+	0.986168i	$0.553005\pi$
$828$		0			0
$829$	10.0035	+	30.7877i	0.347437	+	1.06930i	0.960266	+	0.279086i	$0.0900316\pi$
$829$	10.0035	+	30.7877i	0.347437	+	1.06930i	−0.612829	+	0.790216i	$0.709968\pi$
$830$		0			0
$831$	3.67199	−	2.66786i	0.127380	−	0.0925470i
$832$		0			0
$833$	12.9306	−	39.7962i	0.448017	−	1.37886i
$834$		0			0
$835$	−5.30887			−0.183721
$836$		0			0
$837$	2.07792			0.0718235
$838$		0			0
$839$	3.09372	−	9.52149i	0.106807	−	0.328718i	−0.883343	−	0.468727i	$-0.844713\pi$
$839$	3.09372	−	9.52149i	0.106807	−	0.328718i	0.990150	+	0.140008i	$0.0447129\pi$
$840$		0			0
$841$	−32.4597	+	23.5834i	−1.11930	+	0.813220i
$842$		0			0
$843$	−3.80609	−	11.7140i	−0.131089	−	0.403450i
$844$		0			0
$845$	−18.4153	−	13.3795i	−0.633506	−	0.460269i
$846$		0			0
$847$	−5.36597	−	13.5284i	−0.184377	−	0.464843i
$848$		0			0
$849$	−15.0403	−	10.9274i	−0.516181	−	0.375027i
$850$		0			0
$851$	−11.4084	−	35.1115i	−0.391076	−	1.20361i
$852$		0			0
$853$	8.16802	−	5.93441i	0.279668	−	0.203190i	−0.439105	−	0.898436i	$-0.644704\pi$
$853$	8.16802	−	5.93441i	0.279668	−	0.203190i	0.718772	+	0.695245i	$0.244704\pi$
$854$		0			0
$855$	1.37486	−	4.23139i	0.0470193	−	0.144711i
$856$		0			0
$857$	26.9504			0.920609			0.460305	−	0.887761i	$-0.347740\pi$
$857$	26.9504			0.920609			0.460305	+	0.887761i	$0.347740\pi$
$858$		0			0
$859$	−23.4354			−0.799606			−0.399803	−	0.916601i	$-0.630921\pi$
$859$	−23.4354			−0.799606			−0.399803	+	0.916601i	$0.630921\pi$
$860$		0			0
$861$	3.19805	−	9.84259i	0.108989	−	0.335435i
$862$		0			0
$863$	−10.8203	+	7.86141i	−0.368327	+	0.267606i	−0.756517	−	0.653974i	$-0.773101\pi$
$863$	−10.8203	+	7.86141i	−0.368327	+	0.267606i	0.388190	+	0.921580i	$0.373101\pi$
$864$		0			0
$865$	3.99744	+	12.3028i	0.135917	+	0.418309i
$866$		0			0
$867$	−37.6504	−	27.3546i	−1.27867	−	0.929012i
$868$		0			0
$869$	20.7260	−	30.5177i	0.703081	−	1.03524i
$870$		0			0
$871$	68.6890	+	49.9055i	2.32744	+	1.69098i
$872$		0			0
$873$	−3.64673	−	11.2235i	−0.123423	−	0.379857i
$874$		0			0
$875$	−1.07039	+	0.777682i	−0.0361857	+	0.0262904i
$876$		0			0
$877$	−3.92517	+	12.0804i	−0.132543	+	0.407927i	−0.995200	−	0.0978637i	$-0.968799\pi$
$877$	−3.92517	+	12.0804i	−0.132543	+	0.407927i	0.862656	+	0.505790i	$0.168799\pi$
$878$		0			0
$879$	−16.9358			−0.571230
$880$		0			0
$881$	22.5811			0.760778			0.380389	−	0.924827i	$-0.375790\pi$
$881$	22.5811			0.760778			0.380389	+	0.924827i	$0.375790\pi$
$882$		0			0
$883$	8.87708	−	27.3208i	0.298737	−	0.919419i	−0.683203	−	0.730228i	$-0.739414\pi$
$883$	8.87708	−	27.3208i	0.298737	−	0.919419i	0.981940	−	0.189191i	$-0.0605864\pi$
$884$		0			0
$885$	−4.27317	+	3.10464i	−0.143641	+	0.104361i
$886$		0			0
$887$	−2.35720	−	7.25473i	−0.0791471	−	0.243590i	0.903652	−	0.428267i	$-0.140876\pi$
$887$	−2.35720	−	7.25473i	−0.0791471	−	0.243590i	−0.982799	+	0.184678i	$0.940876\pi$
$888$		0			0
$889$	−12.7794	−	9.28477i	−0.428607	−	0.311401i
$890$		0			0
$891$	3.12020	−	1.12443i	0.104531	−	0.0376699i
$892$		0			0
$893$	10.3215	+	7.49897i	0.345394	+	0.250944i
$894$		0			0
$895$	−5.35505	−	16.4811i	−0.178999	−	0.550904i
$896$		0			0
$897$	−19.4764	+	14.1505i	−0.650299	+	0.472470i
$898$		0			0
$899$	5.33852	−	16.4303i	0.178050	−	0.547981i
$900$		0			0
$901$	−32.6245			−1.08688
$902$		0			0
$903$	−4.08328			−0.135883
$904$		0			0
$905$	−2.22248	+	6.84009i	−0.0738778	+	0.227372i
$906$		0			0
$907$	−15.0288	+	10.9191i	−0.499023	+	0.362562i	−0.808644	−	0.588298i	$-0.799798\pi$
$907$	−15.0288	+	10.9191i	−0.499023	+	0.362562i	0.309620	+	0.950860i	$0.399798\pi$
$908$		0			0
$909$	−4.39614	−	13.5299i	−0.145811	−	0.448759i
$910$		0			0
$911$	−26.1152	−	18.9738i	−0.865234	−	0.628630i	0.0640696	−	0.997945i	$-0.479592\pi$
$911$	−26.1152	−	18.9738i	−0.865234	−	0.628630i	−0.929304	+	0.369316i	$0.879592\pi$
$912$		0			0
$913$	16.6667	+	21.4729i	0.551589	+	0.710650i
$914$		0			0
$915$	−2.49009	−	1.80916i	−0.0823199	−	0.0598089i
$916$		0			0
$917$	7.93342	+	24.4166i	0.261985	+	0.806306i
$918$		0			0
$919$	−23.9513	+	17.4017i	−0.790082	+	0.574028i	−0.907988	−	0.418997i	$-0.862382\pi$
$919$	−23.9513	+	17.4017i	−0.790082	+	0.574028i	0.117906	+	0.993025i	$0.462382\pi$
$920$		0			0
$921$	−3.45954	+	10.6474i	−0.113996	+	0.350843i
$922$		0			0
$923$	54.2234			1.78479
$924$		0			0
$925$	−9.17077			−0.301533
$926$		0			0
$927$	−6.12806	+	18.8602i	−0.201272	+	0.619451i
$928$		0			0
$929$	29.6500	−	21.5420i	0.972784	−	0.706769i	0.0166993	−	0.999861i	$-0.494684\pi$
$929$	29.6500	−	21.5420i	0.972784	−	0.706769i	0.956084	+	0.293092i	$0.0946842\pi$
$930$		0			0
$931$	−7.21732	−	22.2126i	−0.236538	−	0.727990i
$932$		0			0
$933$	3.45591	+	2.51087i	0.113142	+	0.0822022i
$934$		0			0
$935$	25.3897	+	7.36788i	0.830332	+	0.240955i
$936$		0			0
$937$	−11.2165	−	8.14929i	−0.366428	−	0.266226i	0.389300	−	0.921111i	$-0.372717\pi$
$937$	−11.2165	−	8.14929i	−0.366428	−	0.266226i	−0.755728	+	0.654885i	$0.772717\pi$
$938$		0			0
$939$	8.56963	+	26.3746i	0.279659	+	0.860703i
$940$		0			0
$941$	−23.8062	+	17.2962i	−0.776059	+	0.563840i	−0.903794	−	0.427969i	$-0.859229\pi$
$941$	−23.8062	+	17.2962i	−0.776059	+	0.563840i	0.127735	+	0.991808i	$0.459229\pi$
$942$		0			0
$943$	9.73060	−	29.9477i	0.316872	−	0.975232i
$944$		0			0
$945$	1.32307			0.0430395
$946$		0			0
$947$	−21.3123			−0.692557			−0.346278	−	0.938132i	$-0.612555\pi$
$947$	−21.3123			−0.692557			−0.346278	+	0.938132i	$0.612555\pi$
$948$		0			0
$949$	16.9299	−	52.1049i	0.549568	−	1.69140i
$950$		0			0
$951$	−7.15608	+	5.19919i	−0.232052	+	0.168595i
$952$		0			0
$953$	−2.17738	−	6.70130i	−0.0705323	−	0.217076i	0.909577	−	0.415536i	$-0.136406\pi$
$953$	−2.17738	−	6.70130i	−0.0705323	−	0.217076i	−0.980109	+	0.198460i	$0.936406\pi$
$954$		0			0
$955$	5.94565	+	4.31976i	0.192397	+	0.139784i
$956$		0			0
$957$	−0.874654	−	27.5605i	−0.0282735	−	0.890905i
$958$		0			0
$959$	−4.86830	−	3.53703i	−0.157206	−	0.114217i
$960$		0			0
$961$	−8.24527	−	25.3763i	−0.265976	−	0.818591i
$962$		0			0
$963$	2.45867	−	1.78632i	0.0792294	−	0.0575635i
$964$		0			0
$965$	−5.64550	+	17.3751i	−0.181735	+	0.559323i
$966$		0			0
$967$	−16.4122			−0.527781			−0.263891	−	0.964553i	$-0.585006\pi$
$967$	−16.4122			−0.527781			−0.263891	+	0.964553i	$0.585006\pi$
$968$		0			0
$969$	−35.4646			−1.13929
$970$		0			0
$971$	3.72502	−	11.4644i	0.119542	−	0.367911i	−0.873326	−	0.487137i	$-0.838041\pi$
$971$	3.72502	−	11.4644i	0.119542	−	0.367911i	0.992867	+	0.119226i	$0.0380413\pi$
$972$		0			0
$973$	−20.1545	+	14.6431i	−0.646123	+	0.469436i
$974$		0			0
$975$	1.84798	+	5.68749i	0.0591827	+	0.182146i
$976$		0			0
$977$	38.2903	+	27.8195i	1.22501	+	0.890025i	0.996506	−	0.0835173i	$-0.0266154\pi$
$977$	38.2903	+	27.8195i	1.22501	+	0.890025i	0.228508	+	0.973542i	$0.426615\pi$
$978$		0			0
$979$	−1.02407	−	32.2686i	−0.0327294	−	1.03131i
$980$		0			0
$981$	1.01726	+	0.739079i	0.0324785	+	0.0235970i
$982$		0			0
$983$	−0.439405	−	1.35235i	−0.0140148	−	0.0431333i	0.943805	−	0.330504i	$-0.107219\pi$
$983$	−0.439405	−	1.35235i	−0.0140148	−	0.0431333i	−0.957819	+	0.287371i	$0.907219\pi$
$984$		0			0
$985$	−12.9516	+	9.40986i	−0.412671	+	0.299823i
$986$		0			0
$987$	−1.17239	+	3.60824i	−0.0373175	+	0.114852i
$988$		0			0
$989$	−12.4241			−0.395062
$990$		0			0
$991$	−41.5050			−1.31845			−0.659225	−	0.751946i	$-0.729116\pi$
$991$	−41.5050			−1.31845			−0.659225	+	0.751946i	$0.729116\pi$
$992$		0			0
$993$	9.03073	−	27.7937i	0.286582	−	0.882007i
$994$		0			0
$995$	12.4943	−	9.07763i	0.396096	−	0.287780i
$996$		0			0
$997$	1.08772	+	3.34767i	0.0344486	+	0.106022i	0.966802	−	0.255526i	$-0.0822485\pi$
$997$	1.08772	+	3.34767i	0.0344486	+	0.106022i	−0.932354	+	0.361548i	$0.882249\pi$
$998$		0			0
$999$	7.41931	+	5.39044i	0.234737	+	0.170546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	660.2.y.a.301.1	✓	8
3.2	odd	2		1980.2.z.e.1621.1		8
11.3	even	5	inner	660.2.y.a.421.1	yes	8
11.5	even	5		7260.2.a.bj.1.2		4
11.6	odd	10		7260.2.a.bh.1.3		4
33.14	odd	10		1980.2.z.e.1081.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
660.2.y.a.301.1	✓	8	1.1	even	1	trivial
660.2.y.a.421.1	yes	8	11.3	even	5	inner
1980.2.z.e.1081.1		8	33.14	odd	10
1980.2.z.e.1621.1		8	3.2	odd	2
7260.2.a.bh.1.3		4	11.6	odd	10
7260.2.a.bj.1.2		4	11.5	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	660.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(0.408851 + 1.25832i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-0.105203 - 3.31496i) q^{11} +(-4.83807 - 3.51506i) q^{13} +(0.309017 + 0.951057i) q^{15} +(6.44876 - 4.68530i) q^{17} +(1.37486 - 4.23139i) q^{19} +1.32307 q^{21} +4.02566 q^{23} +(0.309017 - 0.951057i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(2.56916 + 7.90707i) q^{29} +(-1.68107 - 1.22137i) q^{31} +(-3.18522 - 0.924324i) q^{33} +(-1.07039 - 0.777682i) q^{35} +(-2.83392 - 8.72192i) q^{37} +(-4.83807 + 3.51506i) q^{39} +(2.41714 - 7.43920i) q^{41} -3.08621 q^{43} +1.00000 q^{45} +(-0.886111 + 2.72717i) q^{47} +(4.24692 - 3.08557i) q^{49} +(-2.46321 - 7.58097i) q^{51} +(-3.31118 - 2.40572i) q^{53} +(2.03359 + 2.62002i) q^{55} +(-3.59944 - 2.61515i) q^{57} +(1.63220 + 5.02341i) q^{59} +(-2.49009 + 1.80916i) q^{61} +(0.408851 - 1.25832i) q^{63} +5.98018 q^{65} -14.1976 q^{67} +(1.24400 - 3.82863i) q^{69} +(-7.33551 + 5.32956i) q^{71} +(2.83100 + 8.71293i) q^{73} +(-0.809017 - 0.587785i) q^{75} +(4.12825 - 1.48770i) q^{77} +(8.99857 + 6.53784i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-6.63047 + 4.81732i) q^{83} +(-2.46321 + 7.58097i) q^{85} +8.31399 q^{87} +9.73424 q^{89} +(2.44501 - 7.52496i) q^{91} +(-1.68107 + 1.22137i) q^{93} +(1.37486 + 4.23139i) q^{95} +(9.54725 + 6.93648i) q^{97} +(-1.86337 + 2.74369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 2 q^{5} + 3 q^{7} - 2 q^{9} - 3 q^{11} - 6 q^{13} - 2 q^{15} + 8 q^{17} - 14 q^{19} + 8 q^{21} + 10 q^{23} - 2 q^{25} - 2 q^{27} + 6 q^{29} - q^{31} + 2 q^{33} - 7 q^{35} - 5 q^{37} - 6 q^{39}+ \cdots - 3 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 2 * q^5 + 3 * q^7 - 2 * q^9 - 3 * q^11 - 6 * q^13 - 2 * q^15 + 8 * q^17 - 14 * q^19 + 8 * q^21 + 10 * q^23 - 2 * q^25 - 2 * q^27 + 6 * q^29 - q^31 + 2 * q^33 - 7 * q^35 - 5 * q^37 - 6 * q^39 - 11 * q^41 + 28 * q^43 + 8 * q^45 - q^47 + q^49 - 12 * q^51 - 3 * q^53 + 7 * q^55 + q^57 - 5 * q^59 - 3 * q^61 + 3 * q^63 + 14 * q^65 - 50 * q^67 + 5 * q^69 - 11 * q^71 + 33 * q^73 - 2 * q^75 + 7 * q^77 + 2 * q^79 - 2 * q^81 + q^83 - 12 * q^85 + 26 * q^87 - 44 * q^89 + 25 * q^91 - q^93 - 14 * q^95 + 35 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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