LMFDB - Embedded newform 456.2.bm.b.89.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(41,456)] 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("456.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 9, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bm (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.7
Character	$\chi$	$=$	456.89
Dual form			456.2.bm.b.41.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.505407 - 1.65667i) q^{3} +(2.78114 - 0.490390i) q^{5} +(-1.12097 + 1.94159i) q^{7} +(-2.48913 - 1.67459i) q^{9} +(5.69741 - 3.28940i) q^{11} +(1.84678 + 5.07399i) q^{13} +(0.593192 - 4.85529i) q^{15} +(-0.460192 - 0.548435i) q^{17} +(-0.336683 - 4.34588i) q^{19} +(2.65002 + 2.83838i) q^{21} +(-4.12489 - 0.727330i) q^{23} +(2.79580 - 1.01759i) q^{25} +(-4.03226 + 3.27732i) q^{27} +(1.34454 + 1.12820i) q^{29} +(-7.07240 - 4.08325i) q^{31} +(-2.56995 - 11.1012i) q^{33} +(-2.16546 + 5.94954i) q^{35} +3.68487i q^{37} +(9.33932 - 0.495083i) q^{39} +(4.12620 + 1.50181i) q^{41} +(-0.824974 - 4.67866i) q^{43} +(-7.74382 - 3.43662i) q^{45} +(-3.25644 + 3.88087i) q^{47} +(0.986831 + 1.70924i) q^{49} +(-1.14116 + 0.485204i) q^{51} +(1.20330 - 6.82425i) q^{53} +(14.2322 - 11.9423i) q^{55} +(-7.36986 - 1.63866i) q^{57} +(8.27991 - 6.94767i) q^{59} +(-1.03142 + 5.84947i) q^{61} +(6.04160 - 2.95568i) q^{63} +(7.62440 + 13.2058i) q^{65} +(-6.75064 + 8.04510i) q^{67} +(-3.28969 + 6.46600i) q^{69} +(2.19569 + 12.4524i) q^{71} +(-7.23344 - 2.63276i) q^{73} +(-0.272794 - 5.14603i) q^{75} +14.7494i q^{77} +(-2.10301 + 5.77799i) q^{79} +(3.39152 + 8.33652i) q^{81} +(6.08101 + 3.51087i) q^{83} +(-1.54881 - 1.29960i) q^{85} +(2.54860 - 1.65726i) q^{87} +(-13.9565 + 5.07976i) q^{89} +(-11.9218 - 2.10213i) q^{91} +(-10.3391 + 9.65295i) q^{93} +(-3.06754 - 11.9214i) q^{95} +(6.33856 + 7.55401i) q^{97} +(-19.6900 - 1.35307i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{9} + 3 q^{13} - 3 q^{15} - 6 q^{17} + 3 q^{19} + 6 q^{25} + 3 q^{27} + 6 q^{29} + 24 q^{35} + 18 q^{39} + 3 q^{41} - 21 q^{43} + 63 q^{45} - 18 q^{47} - 30 q^{49} + 33 q^{51} - 36 q^{53} + 18 q^{55}+ \cdots - 39 q^{99}+O(q^{100}) $ 60 * q - 6 * q^9 + 3 * q^13 - 3 * q^15 - 6 * q^17 + 3 * q^19 + 6 * q^25 + 3 * q^27 + 6 * q^29 + 24 * q^35 + 18 * q^39 + 3 * q^41 - 21 * q^43 + 63 * q^45 - 18 * q^47 - 30 * q^49 + 33 * q^51 - 36 * q^53 + 18 * q^55 - 24 * q^57 - 21 * q^59 - 6 * q^61 - 24 * q^63 + 24 * q^65 - 48 * q^67 - 21 * q^69 + 36 * q^71 - 57 * q^73 - 36 * q^79 + 6 * q^81 - 36 * q^83 + 6 * q^85 + 72 * q^87 - 24 * q^89 - 18 * q^91 + 108 * q^93 + 30 * q^95 + 15 * q^97 - 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.505407	−	1.65667i	0.291797	−	0.956480i
$3$	0.505407	−	1.65667i	0.291797	−	0.956480i
$4$		0			0
$5$	2.78114	−	0.490390i	1.24376	−	0.219309i	0.487236	−	0.873270i	$-0.338005\pi$
$5$	2.78114	−	0.490390i	1.24376	−	0.219309i	0.756528	+	0.653961i	$0.226894\pi$
$6$		0			0
$7$	−1.12097	+	1.94159i	−0.423689	+	0.733850i	−0.996297	−	0.0859788i	$-0.972598\pi$
$7$	−1.12097	+	1.94159i	−0.423689	+	0.733850i	0.572608	+	0.819829i	$0.305932\pi$
$8$		0			0
$9$	−2.48913	−	1.67459i	−0.829709	−	0.558196i
$10$		0			0
$11$	5.69741	−	3.28940i	1.71783	−	0.991792i	0.794987	−	0.606626i	$-0.207477\pi$
$11$	5.69741	−	3.28940i	1.71783	−	0.991792i	0.922847	−	0.385166i	$-0.125856\pi$
$12$		0			0
$13$	1.84678	+	5.07399i	0.512205	+	1.40727i	0.878934	+	0.476944i	$0.158256\pi$
$13$	1.84678	+	5.07399i	0.512205	+	1.40727i	−0.366729	+	0.930328i	$0.619522\pi$
$14$		0			0
$15$	0.593192	−	4.85529i	0.153161	−	1.25363i
$16$		0			0
$17$	−0.460192	−	0.548435i	−0.111613	−	0.133015i	0.707345	−	0.706868i	$-0.249893\pi$
$17$	−0.460192	−	0.548435i	−0.111613	−	0.133015i	−0.818958	+	0.573853i	$0.805448\pi$
$18$		0			0
$19$	−0.336683	−	4.34588i	−0.0772404	−	0.997012i
$19$	−0.336683	−	4.34588i	−0.0772404	−	0.997012i
$20$		0			0
$21$	2.65002	+	2.83838i	0.578282	+	0.619385i
$22$		0			0
$23$	−4.12489	−	0.727330i	−0.860099	−	0.151659i	−0.273833	−	0.961777i	$-0.588292\pi$
$23$	−4.12489	−	0.727330i	−0.860099	−	0.151659i	−0.586266	+	0.810119i	$0.699403\pi$
$24$		0			0
$25$	2.79580	−	1.01759i	0.559161	−	0.203518i
$26$		0			0
$27$	−4.03226	+	3.27732i	−0.776010	+	0.630721i
$28$		0			0
$29$	1.34454	+	1.12820i	0.249674	+	0.209502i	0.759032	−	0.651053i	$-0.225673\pi$
$29$	1.34454	+	1.12820i	0.249674	+	0.209502i	−0.509358	+	0.860555i	$0.670117\pi$
$30$		0			0
$31$	−7.07240	−	4.08325i	−1.27024	−	0.733374i	−0.295208	−	0.955433i	$-0.595389\pi$
$31$	−7.07240	−	4.08325i	−1.27024	−	0.733374i	−0.975033	+	0.222059i	$0.928722\pi$
$32$		0			0
$33$	−2.56995	−	11.1012i	−0.447371	−	1.93248i
$34$		0			0
$35$	−2.16546	+	5.94954i	−0.366029	+	1.00566i
$36$		0			0
$37$			3.68487i			0.605789i	0.953024	+	0.302894i	$0.0979529\pi$
$37$			3.68487i			0.605789i	−0.953024	+	0.302894i	$0.902047\pi$
$38$		0			0
$39$	9.33932	−	0.495083i	1.49549	−	0.0792768i
$40$		0			0
$41$	4.12620	+	1.50181i	0.644404	+	0.234544i	0.643488	−	0.765456i	$-0.277486\pi$
$41$	4.12620	+	1.50181i	0.644404	+	0.234544i	0.000915237		1.00000i	$0.499709\pi$
$42$		0			0
$43$	−0.824974	−	4.67866i	−0.125807	−	0.713489i	−0.980825	−	0.194890i	$-0.937565\pi$
$43$	−0.824974	−	4.67866i	−0.125807	−	0.713489i	0.855018	−	0.518599i	$-0.173546\pi$
$44$		0			0
$45$	−7.74382	−	3.43662i	−1.15438	−	0.512301i
$46$		0			0
$47$	−3.25644	+	3.88087i	−0.475000	+	0.566084i	−0.949337	−	0.314260i	$-0.898244\pi$
$47$	−3.25644	+	3.88087i	−0.475000	+	0.566084i	0.474336	+	0.880344i	$0.342688\pi$
$48$		0			0
$49$	0.986831	+	1.70924i	0.140976	+	0.244177i
$50$		0			0
$51$	−1.14116	+	0.485204i	−0.159795	+	0.0679422i
$52$		0			0
$53$	1.20330	−	6.82425i	0.165286	−	0.937383i	−0.783483	−	0.621413i	$-0.786559\pi$
$53$	1.20330	−	6.82425i	0.165286	−	0.937383i	0.948769	−	0.315970i	$-0.102330\pi$
$54$		0			0
$55$	14.2322	−	11.9423i	1.91907	−	1.61029i
$56$		0			0
$57$	−7.36986	−	1.63866i	−0.976161	−	0.217046i
$58$		0			0
$59$	8.27991	−	6.94767i	1.07795	−	0.904510i	0.0822033	−	0.996616i	$-0.473804\pi$
$59$	8.27991	−	6.94767i	1.07795	−	0.904510i	0.995749	+	0.0921060i	$0.0293599\pi$
$60$		0			0
$61$	−1.03142	+	5.84947i	−0.132060	+	0.748948i	0.844802	+	0.535078i	$0.179718\pi$
$61$	−1.03142	+	5.84947i	−0.132060	+	0.748948i	−0.976862	+	0.213870i	$0.931393\pi$
$62$		0			0
$63$	6.04160	−	2.95568i	0.761171	−	0.372381i
$64$		0			0
$65$	7.62440	+	13.2058i	0.945690	+	1.63798i
$66$		0			0
$67$	−6.75064	+	8.04510i	−0.824722	+	0.982865i	−0.999999	−	0.00165397i	$-0.999474\pi$
$67$	−6.75064	+	8.04510i	−0.824722	+	0.982865i	0.175277	+	0.984519i	$0.443918\pi$
$68$		0			0
$69$	−3.28969	+	6.46600i	−0.396033	+	0.778414i
$70$		0			0
$71$	2.19569	+	12.4524i	0.260581	+	1.47783i	0.781330	+	0.624118i	$0.214541\pi$
$71$	2.19569	+	12.4524i	0.260581	+	1.47783i	−0.520749	+	0.853710i	$0.674347\pi$
$72$		0			0
$73$	−7.23344	−	2.63276i	−0.846610	−	0.308141i	−0.117953	−	0.993019i	$-0.537633\pi$
$73$	−7.23344	−	2.63276i	−0.846610	−	0.308141i	−0.728657	+	0.684878i	$0.759855\pi$
$74$		0			0
$75$	−0.272794	−	5.14603i	−0.0314996	−	0.594212i
$76$		0			0
$77$			14.7494i			1.68084i
$78$		0			0
$79$	−2.10301	+	5.77799i	−0.236608	+	0.650074i	0.763384	+	0.645945i	$0.223537\pi$
$79$	−2.10301	+	5.77799i	−0.236608	+	0.650074i	−0.999991	+	0.00412906i	$0.998686\pi$
$80$		0			0
$81$	3.39152	+	8.33652i	0.376835	+	0.926280i
$82$		0			0
$83$	6.08101	+	3.51087i	0.667478	+	0.385369i	0.795120	−	0.606452i	$-0.207408\pi$
$83$	6.08101	+	3.51087i	0.667478	+	0.385369i	−0.127642	+	0.991820i	$0.540741\pi$
$84$		0			0
$85$	−1.54881	−	1.29960i	−0.167992	−	0.140962i
$86$		0			0
$87$	2.54860	−	1.65726i	0.273238	−	0.177677i
$88$		0			0
$89$	−13.9565	+	5.07976i	−1.47939	+	0.538453i	−0.950632	−	0.310320i	$-0.899564\pi$
$89$	−13.9565	+	5.07976i	−1.47939	+	0.538453i	−0.528757	+	0.848774i	$0.677342\pi$
$90$		0			0
$91$	−11.9218	−	2.10213i	−1.24974	−	0.220363i
$92$		0			0
$93$	−10.3391	+	9.65295i	−1.07211	+	1.00096i
$94$		0			0
$95$	−3.06754	−	11.9214i	−0.314723	−	1.22311i
$96$		0			0
$97$	6.33856	+	7.55401i	0.643584	+	0.766993i	0.984932	−	0.172944i	$-0.0553279\pi$
$97$	6.33856	+	7.55401i	0.643584	+	0.766993i	−0.341348	+	0.939937i	$0.610883\pi$
$98$		0			0
$99$	−19.6900	−	1.35307i	−1.97892	−	0.135988i
$100$		0			0
$101$	−3.32961	−	9.14804i	−0.331309	−	0.910264i	−0.987772	−	0.155906i	$-0.950170\pi$
$101$	−3.32961	−	9.14804i	−0.331309	−	0.910264i	0.656463	−	0.754358i	$-0.272052\pi$
$102$		0			0
$103$	4.50028	−	2.59824i	0.443426	−	0.256012i	−0.261624	−	0.965170i	$-0.584258\pi$
$103$	4.50028	−	2.59824i	0.443426	−	0.256012i	0.705050	+	0.709158i	$0.250925\pi$
$104$		0			0
$105$	8.76200	+	6.59439i	0.855084	+	0.643546i
$106$		0			0
$107$	−8.76381	+	15.1794i	−0.847229	+	1.46744i	0.0364419	+	0.999336i	$0.488398\pi$
$107$	−8.76381	+	15.1794i	−0.847229	+	1.46744i	−0.883671	+	0.468108i	$0.844936\pi$
$108$		0			0
$109$	4.63286	−	0.816899i	0.443748	−	0.0782447i	0.0526901	−	0.998611i	$-0.483220\pi$
$109$	4.63286	−	0.816899i	0.443748	−	0.0782447i	0.391058	+	0.920366i	$0.372109\pi$
$110$		0			0
$111$	6.10462	+	1.86236i	0.579425	+	0.176767i
$112$		0			0
$113$	−0.795701			−0.0748532			−0.0374266	−	0.999299i	$-0.511916\pi$
$113$	−0.795701			−0.0748532			−0.0374266	+	0.999299i	$0.511916\pi$
$114$		0			0
$115$	−11.8286			−1.10302
$116$		0			0
$117$	3.89996	−	15.7224i	0.360552	−	1.45354i
$118$		0			0
$119$	1.58070	−	0.278720i	0.144902	−	0.0255502i
$120$		0			0
$121$	16.1403	−	27.9559i	1.46730	−	2.54144i
$122$		0			0
$123$	4.57342	−	6.07673i	0.412371	−	0.547920i
$124$		0			0
$125$	−4.95196	+	2.85902i	−0.442917	+	0.255718i
$126$		0			0
$127$	2.07272	+	5.69475i	0.183924	+	0.505328i	0.997050	−	0.0767610i	$-0.0244578\pi$
$127$	2.07272	+	5.69475i	0.183924	+	0.505328i	−0.813125	+	0.582089i	$0.802236\pi$
$128$		0			0
$129$	−8.16795	−	0.997914i	−0.719148	−	0.0878614i
$130$		0			0
$131$	0.245621	+	0.292720i	0.0214600	+	0.0255751i	0.776668	−	0.629911i	$-0.216908\pi$
$131$	0.245621	+	0.292720i	0.0214600	+	0.0255751i	−0.755208	+	0.655486i	$0.772464\pi$
$132$		0			0
$133$	8.81530	+	4.21792i	0.764384	+	0.365740i
$134$		0			0
$135$	−9.60713	+	11.0921i	−0.826850	+	0.954654i
$136$		0			0
$137$	−13.8890	−	2.44900i	−1.18661	−	0.209232i	−0.454710	−	0.890640i	$-0.650257\pi$
$137$	−13.8890	−	2.44900i	−1.18661	−	0.209232i	−0.731904	+	0.681408i	$0.761368\pi$
$138$		0			0
$139$	−0.257841	+	0.0938465i	−0.0218698	+	0.00795995i	−0.352932	−	0.935649i	$-0.614815\pi$
$139$	−0.257841	+	0.0938465i	−0.0218698	+	0.00795995i	0.331062	+	0.943609i	$0.392593\pi$
$140$		0			0
$141$	4.78351	+	7.35627i	0.402844	+	0.619510i
$142$		0			0
$143$	27.2123	+	22.8338i	2.27561	+	1.90946i
$144$		0			0
$145$	4.29261	+	2.47834i	0.356482	+	0.205815i
$146$		0			0
$147$	3.33040	−	0.770993i	0.274687	−	0.0635905i
$148$		0			0
$149$	4.30153	−	11.8184i	0.352395	−	0.968198i	−0.629203	−	0.777241i	$-0.716619\pi$
$149$	4.30153	−	11.8184i	0.352395	−	0.968198i	0.981598	−	0.190957i	$-0.0611592\pi$
$150$		0			0
$151$			17.9408i			1.46001i	0.683444	+	0.730003i	$0.260481\pi$
$151$			17.9408i			1.46001i	−0.683444	+	0.730003i	$0.739519\pi$
$152$		0			0
$153$	0.227074	+	2.13576i	0.0183578	+	0.172666i
$154$		0			0
$155$	−21.6717	−	7.88787i	−1.74072	−	0.633569i
$156$		0			0
$157$	−1.20226	−	6.81837i	−0.0959510	−	0.544165i	−0.994452	−	0.105193i	$-0.966454\pi$
$157$	−1.20226	−	6.81837i	−0.0959510	−	0.544165i	0.898501	−	0.438972i	$-0.144657\pi$
$158$		0			0
$159$	−10.6974	−	5.44249i	−0.848358	−	0.431618i
$160$		0			0
$161$	6.03607	−	7.19351i	0.475709	−	0.566928i
$162$		0			0
$163$	−0.335462	−	0.581037i	−0.0262754	−	0.0455103i	0.852589	−	0.522583i	$-0.175031\pi$
$163$	−0.335462	−	0.581037i	−0.0262754	−	0.0455103i	−0.878864	+	0.477072i	$0.841698\pi$
$164$		0			0
$165$	−12.5913	−	29.6138i	−0.980235	−	2.30543i
$166$		0			0
$167$	0.567367	−	3.21770i	0.0439042	−	0.248993i	−0.954955	−	0.296751i	$-0.904097\pi$
$167$	0.567367	−	3.21770i	0.0439042	−	0.248993i	0.998859	+	0.0477586i	$0.0152078\pi$
$168$		0			0
$169$	−12.3762	+	10.3849i	−0.952016	+	0.798836i
$170$		0			0
$171$	−6.43950	+	11.3812i	−0.492441	+	0.870346i
$172$		0			0
$173$	3.27667	−	2.74946i	0.249121	−	0.209037i	−0.509673	−	0.860368i	$-0.670234\pi$
$173$	3.27667	−	2.74946i	0.249121	−	0.209037i	0.758794	+	0.651331i	$0.225789\pi$
$174$		0			0
$175$	−1.15829	+	6.56898i	−0.0875584	+	0.496569i
$176$		0			0
$177$	−7.32529	−	17.2285i	−0.550603	−	1.29497i
$178$		0			0
$179$	−3.12472	−	5.41218i	−0.233553	−	0.404525i	0.725298	−	0.688435i	$-0.241702\pi$
$179$	−3.12472	−	5.41218i	−0.233553	−	0.404525i	−0.958851	+	0.283910i	$0.908368\pi$
$180$		0			0
$181$	−3.63150	+	4.32785i	−0.269927	+	0.321687i	−0.883932	−	0.467616i	$-0.845113\pi$
$181$	−3.63150	+	4.32785i	−0.269927	+	0.321687i	0.614005	+	0.789302i	$0.289558\pi$
$182$		0			0
$183$	9.16937	+	4.66509i	0.677819	+	0.344853i
$184$		0			0
$185$	1.80702	+	10.2481i	0.132855	+	0.753458i
$186$		0			0
$187$	−4.42593	−	1.61091i	−0.323656	−	0.117801i
$188$		0			0
$189$	−1.84314	−	11.5028i	−0.134068	−	0.836704i
$190$		0			0
$191$		−	15.8727i		−	1.14851i	−0.818678	−	0.574253i	$-0.805293\pi$
$191$		−	15.8727i		−	1.14851i	0.818678	−	0.574253i	$-0.194707\pi$
$192$		0			0
$193$	−2.22289	+	6.10735i	−0.160007	+	0.439616i	−0.993626	−	0.112723i	$-0.964043\pi$
$193$	−2.22289	+	6.10735i	−0.160007	+	0.439616i	0.833619	+	0.552340i	$0.186265\pi$
$194$		0			0
$195$	25.7312	−	5.95681i	1.84265	−	0.426576i
$196$		0			0
$197$	12.2587	+	7.07756i	0.873396	+	0.504256i	0.868475	−	0.495732i	$-0.165100\pi$
$197$	12.2587	+	7.07756i	0.873396	+	0.504256i	0.00492088	+	0.999988i	$0.498434\pi$
$198$		0			0
$199$	2.94354	+	2.46993i	0.208662	+	0.175088i	0.741129	−	0.671362i	$-0.234291\pi$
$199$	2.94354	+	2.46993i	0.208662	+	0.175088i	−0.532467	+	0.846451i	$0.678735\pi$
$200$		0			0
$201$	9.91628	+	15.2496i	0.699440	+	1.07563i
$202$		0			0
$203$	−3.69769	+	1.34585i	−0.259527	+	0.0944601i
$204$		0			0
$205$	12.2120	+	2.15331i	0.852924	+	0.150394i
$206$		0			0
$207$	9.04941	+	8.71790i	0.628977	+	0.605936i
$208$		0			0
$209$	−16.2136	−	23.6528i	−1.12152	−	1.63610i
$210$		0			0
$211$	−6.36827	−	7.58941i	−0.438410	−	0.522477i	0.500919	−	0.865494i	$-0.332995\pi$
$211$	−6.36827	−	7.58941i	−0.438410	−	0.522477i	−0.939329	+	0.343017i	$0.888551\pi$
$212$		0			0
$213$	21.7393	+	2.65598i	1.48955	+	0.181985i
$214$		0			0
$215$	−4.58874	−	12.6075i	−0.312949	−	0.859821i
$216$		0			0
$217$	15.8560	−	9.15445i	1.07637	−	0.621445i
$218$		0			0
$219$	−8.01745	+	10.6528i	−0.541769	+	0.719852i
$220$		0			0
$221$	1.93288	−	3.34785i	0.130020	−	0.225201i
$222$		0			0
$223$	−6.35203	+	1.12003i	−0.425363	+	0.0750030i	−0.382232	−	0.924066i	$-0.624844\pi$
$223$	−6.35203	+	1.12003i	−0.425363	+	0.0750030i	−0.0431313	+	0.999069i	$0.513733\pi$
$224$		0			0
$225$	−8.66316	−	2.14891i	−0.577544	−	0.143260i
$226$		0			0
$227$	1.93669			0.128543			0.0642715	−	0.997932i	$-0.479528\pi$
$227$	1.93669			0.128543			0.0642715	+	0.997932i	$0.479528\pi$
$228$		0			0
$229$	−0.732337			−0.0483942			−0.0241971	−	0.999707i	$-0.507703\pi$
$229$	−0.732337			−0.0483942			−0.0241971	+	0.999707i	$0.507703\pi$
$230$		0			0
$231$	24.4348	+	7.45442i	1.60769	+	0.490465i
$232$		0			0
$233$	16.3556	−	2.88393i	1.07149	−	0.188933i	0.390041	−	0.920798i	$-0.372461\pi$
$233$	16.3556	−	2.88393i	1.07149	−	0.188933i	0.681450	+	0.731865i	$0.261350\pi$
$234$		0			0
$235$	−7.15348	+	12.3902i	−0.466641	+	0.808247i
$236$		0			0
$237$	8.50935	+	6.40424i	0.552742	+	0.416000i
$238$		0			0
$239$	3.12565	−	1.80459i	0.202181	−	0.116729i	−0.395491	−	0.918470i	$-0.629426\pi$
$239$	3.12565	−	1.80459i	0.202181	−	0.116729i	0.597673	+	0.801740i	$0.296092\pi$
$240$		0			0
$241$	−4.61225	−	12.6721i	−0.297101	−	0.816279i	−0.994981	−	0.100064i	$-0.968095\pi$
$241$	−4.61225	−	12.6721i	−0.297101	−	0.816279i	0.697880	−	0.716215i	$-0.254127\pi$
$242$		0			0
$243$	15.5250	−	1.40530i	0.995928	−	0.0901500i
$244$		0			0
$245$	3.58271	+	4.26971i	0.228891	+	0.272782i
$246$		0			0
$247$	21.4292	−	9.73421i	1.36350	−	0.619373i
$248$		0			0
$249$	8.88976	−	8.29983i	0.563365	−	0.525980i
$250$		0			0
$251$	−8.20040	−	1.44595i	−0.517604	−	0.0912676i	−0.0912575	−	0.995827i	$-0.529089\pi$
$251$	−8.20040	−	1.44595i	−0.517604	−	0.0912676i	−0.426347	+	0.904560i	$0.640200\pi$
$252$		0			0
$253$	−25.8937	+	9.42453i	−1.62792	+	0.592515i
$254$		0			0
$255$	−2.93579	+	1.90904i	−0.183846	+	0.119549i
$256$		0			0
$257$	14.7338	+	12.3631i	0.919070	+	0.771191i	0.973823	−	0.227309i	$-0.0729927\pi$
$257$	14.7338	+	12.3631i	0.919070	+	0.771191i	−0.0547529	+	0.998500i	$0.517437\pi$
$258$		0			0
$259$	−7.15449	−	4.13065i	−0.444558	−	0.256666i
$260$		0			0
$261$	−1.45746	−	5.05978i	−0.0902142	−	0.313193i
$262$		0			0
$263$	9.82773	−	27.0015i	0.606004	−	1.66498i	−0.132866	−	0.991134i	$-0.542418\pi$
$263$	9.82773	−	27.0015i	0.606004	−	1.66498i	0.738870	−	0.673848i	$-0.235360\pi$
$264$		0			0
$265$		−	19.5693i		−	1.20213i
$266$		0			0
$267$	1.36178	+	25.6887i	0.0833394	+	1.57213i
$268$		0			0
$269$	−4.18387	−	1.52281i	−0.255095	−	0.0928471i	0.211307	−	0.977420i	$-0.432228\pi$
$269$	−4.18387	−	1.52281i	−0.255095	−	0.0928471i	−0.466403	+	0.884573i	$0.654450\pi$
$270$		0			0
$271$	−0.0517699	−	0.293602i	−0.00314480	−	0.0178350i	0.983195	−	0.182559i	$-0.0584379\pi$
$271$	−0.0517699	−	0.293602i	−0.00314480	−	0.0178350i	−0.986340	+	0.164724i	$0.947327\pi$
$272$		0			0
$273$	−9.50789	+	18.6881i	−0.575444	+	1.13105i
$274$		0			0
$275$	12.5816	−	14.9942i	0.758698	−	0.904181i
$276$		0			0
$277$	−12.4130	−	21.4999i	−0.745824	−	1.29180i	−0.949809	−	0.312830i	$-0.898723\pi$
$277$	−12.4130	−	21.4999i	−0.745824	−	1.29180i	0.203985	−	0.978974i	$-0.434610\pi$
$278$		0			0
$279$	10.7664	+	22.0071i	0.644565	+	1.31753i
$280$		0			0
$281$	3.85999	−	21.8911i	0.230268	−	1.30591i	−0.622087	−	0.782949i	$-0.713715\pi$
$281$	3.85999	−	21.8911i	0.230268	−	1.30591i	0.852354	−	0.522965i	$-0.175174\pi$
$282$		0			0
$283$	4.64172	−	3.89487i	0.275922	−	0.231526i	−0.494317	−	0.869282i	$-0.664582\pi$
$283$	4.64172	−	3.89487i	0.275922	−	0.231526i	0.770238	+	0.637756i	$0.220137\pi$
$284$		0			0
$285$	−21.3002	−	0.943244i	−1.26171	−	0.0558730i
$286$		0			0
$287$	−7.54126	+	6.32787i	−0.445147	+	0.373522i
$288$		0			0
$289$	2.86301	−	16.2370i	0.168413	−	0.955115i
$290$		0			0
$291$	15.7181	−	6.68308i	0.921409	−	0.391769i
$292$		0			0
$293$	−7.15307	−	12.3895i	−0.417887	−	0.723801i	0.577840	−	0.816150i	$-0.303896\pi$
$293$	−7.15307	−	12.3895i	−0.417887	−	0.723801i	−0.995727	+	0.0923488i	$0.970563\pi$
$294$		0			0
$295$	19.6205	−	23.3828i	1.14235	−	1.36140i
$296$		0			0
$297$	−12.1930	+	31.9360i	−0.707512	+	1.85311i
$298$		0			0
$299$	−3.92731	−	22.2729i	−0.227122	−	1.28807i
$300$		0			0
$301$	10.0088	+	3.64290i	0.576897	+	0.209973i
$302$		0			0
$303$	−16.8381	+	0.892600i	−0.967324	+	0.0512785i
$304$		0			0
$305$			16.7740i			0.960477i
$306$		0			0
$307$	−2.50006	+	6.86886i	−0.142686	+	0.392026i	−0.990365	−	0.138483i	$-0.955777\pi$
$307$	−2.50006	+	6.86886i	−0.142686	+	0.392026i	0.847679	+	0.530510i	$0.177999\pi$
$308$		0			0
$309$	−2.02996	−	8.76866i	−0.115480	−	0.498831i
$310$		0			0
$311$	−29.4386	−	16.9964i	−1.66931	−	0.963778i	−0.968009	−	0.250915i	$-0.919268\pi$
$311$	−29.4386	−	16.9964i	−1.66931	−	0.963778i	−0.701304	−	0.712863i	$-0.747398\pi$
$312$		0			0
$313$	14.8670	+	12.4749i	0.840335	+	0.705125i	0.957639	−	0.287971i	$-0.0929808\pi$
$313$	14.8670	+	12.4749i	0.840335	+	0.705125i	−0.117304	+	0.993096i	$0.537425\pi$
$314$		0			0
$315$	15.3531	−	11.1829i	0.865050	−	0.630086i
$316$		0			0
$317$	22.4188	−	8.15976i	1.25916	−	0.458298i	0.375675	−	0.926752i	$-0.377411\pi$
$317$	22.4188	−	8.15976i	1.25916	−	0.458298i	0.883488	+	0.468454i	$0.155189\pi$
$318$		0			0
$319$	11.3715	+	2.00510i	0.636681	+	0.112264i
$320$		0			0
$321$	20.7179	+	22.1905i	1.15636	+	1.23855i
$322$		0			0
$323$	−2.22849	+	2.18459i	−0.123997	+	0.121554i
$324$		0			0
$325$	10.3265	+	12.3066i	0.572810	+	0.682648i
$326$		0			0
$327$	0.988146	−	8.08800i	0.0546446	−	0.447268i
$328$		0			0
$329$	−3.88466	−	10.6730i	−0.214168	−	0.588422i
$330$		0			0
$331$	−13.5946	+	7.84886i	−0.747229	+	0.431413i	−0.824692	−	0.565583i	$-0.808651\pi$
$331$	−13.5946	+	7.84886i	−0.747229	+	0.431413i	0.0774631	+	0.996995i	$0.475318\pi$
$332$		0			0
$333$	6.17063	−	9.17211i	0.338149	−	0.502629i
$334$		0			0
$335$	−14.8292	+	25.6850i	−0.810208	+	1.40332i
$336$		0			0
$337$	−23.2235	+	4.09493i	−1.26506	+	0.223065i	−0.765627	−	0.643285i	$-0.777571\pi$
$337$	−23.2235	+	4.09493i	−1.26506	+	0.223065i	−0.499438	+	0.866350i	$0.666460\pi$
$338$		0			0
$339$	−0.402152	+	1.31822i	−0.0218419	+	0.0715956i
$340$		0			0
$341$	−53.7259			−2.90942
$342$		0			0
$343$	−20.1185			−1.08630
$344$		0			0
$345$	−5.97824	+	19.5961i	−0.321858	+	1.05502i
$346$		0			0
$347$	5.21261	−	0.919124i	0.279828	−	0.0493412i	−0.0319729	−	0.999489i	$-0.510179\pi$
$347$	5.21261	−	0.919124i	0.279828	−	0.0493412i	0.311801	+	0.950148i	$0.399068\pi$
$348$		0			0
$349$	−7.15845	+	12.3988i	−0.383183	+	0.663692i	−0.991515	−	0.129990i	$-0.958505\pi$
$349$	−7.15845	+	12.3988i	−0.383183	+	0.663692i	0.608332	+	0.793682i	$0.291839\pi$
$350$		0			0
$351$	−24.0758	−	14.4072i	−1.28507	−	0.768998i
$352$		0			0
$353$	−3.97636	+	2.29575i	−0.211640	+	0.122191i	−0.602073	−	0.798441i	$-0.705659\pi$
$353$	−3.97636	+	2.29575i	−0.211640	+	0.122191i	0.390433	+	0.920631i	$0.372325\pi$
$354$		0			0
$355$	12.2131	+	33.5551i	0.648202	+	1.78092i
$356$		0			0
$357$	0.337148	−	2.75956i	0.0178438	−	0.146052i
$358$		0			0
$359$	6.35129	+	7.56917i	0.335208	+	0.399485i	0.907149	−	0.420809i	$-0.138254\pi$
$359$	6.35129	+	7.56917i	0.335208	+	0.399485i	−0.571941	+	0.820295i	$0.693809\pi$
$360$		0			0
$361$	−18.7733	+	2.92637i	−0.988068	+	0.154019i
$362$		0			0
$363$	−38.1563	−	40.8684i	−2.00269	−	2.14503i
$364$		0			0
$365$	−21.4083	−	3.77486i	−1.12056	−	0.197585i
$366$		0			0
$367$	−0.473661	+	0.172399i	−0.0247249	+	0.00899913i	−0.354353	−	0.935112i	$-0.615299\pi$
$367$	−0.473661	+	0.172399i	−0.0247249	+	0.00899913i	0.329628	+	0.944111i	$0.393077\pi$
$368$		0			0
$369$	−7.75572	−	10.6479i	−0.403746	−	0.554306i
$370$		0			0
$371$	11.9010	+	9.98612i	0.617869	+	0.518454i
$372$		0			0
$373$	0.239135	+	0.138065i	0.0123819	+	0.00714871i	0.506178	−	0.862429i	$-0.331058\pi$
$373$	0.239135	+	0.138065i	0.0123819	+	0.00714871i	−0.493796	+	0.869578i	$0.664391\pi$
$374$		0			0
$375$	2.23370	+	9.64875i	0.115348	+	0.498259i
$376$		0			0
$377$	−3.24141	+	8.90571i	−0.166941	+	0.458667i
$378$		0			0
$379$			12.3487i			0.634308i	0.948374	+	0.317154i	$0.102727\pi$
$379$			12.3487i			0.634308i	−0.948374	+	0.317154i	$0.897273\pi$
$380$		0			0
$381$	10.4819	−	0.555653i	0.537005	−	0.0284670i
$382$		0			0
$383$	−18.5993	−	6.76960i	−0.950381	−	0.345910i	−0.180124	−	0.983644i	$-0.557650\pi$
$383$	−18.5993	−	6.76960i	−0.950381	−	0.345910i	−0.770257	+	0.637734i	$0.779872\pi$
$384$		0			0
$385$	7.23294	+	41.0200i	0.368625	+	2.09057i
$386$		0			0
$387$	−5.78136	+	13.0273i	−0.293883	+	0.662213i
$388$		0			0
$389$	12.4909	−	14.8860i	0.633312	−	0.754751i	−0.349986	−	0.936755i	$-0.613814\pi$
$389$	12.4909	−	14.8860i	0.633312	−	0.754751i	0.983298	+	0.182003i	$0.0582582\pi$
$390$		0			0
$391$	1.49935	+	2.59695i	0.0758253	+	0.131333i
$392$		0			0
$393$	0.609080	−	0.258971i	0.0307240	−	0.0130634i
$394$		0			0
$395$	−3.01531	+	17.1007i	−0.151717	+	0.860429i
$396$		0			0
$397$	−11.7235	+	9.83720i	−0.588386	+	0.493715i	−0.887689	−	0.460443i	$-0.847690\pi$
$397$	−11.7235	+	9.83720i	−0.588386	+	0.493715i	0.299303	+	0.954158i	$0.403246\pi$
$398$		0			0
$399$	11.4430	−	12.4723i	0.572868	−	0.624396i
$400$		0			0
$401$	3.93117	−	3.29864i	0.196313	−	0.164726i	−0.539332	−	0.842093i	$-0.681323\pi$
$401$	3.93117	−	3.29864i	0.196313	−	0.164726i	0.735646	+	0.677367i	$0.236879\pi$
$402$		0			0
$403$	7.65721	−	43.4262i	0.381433	−	2.16321i
$404$		0			0
$405$	13.5204	+	21.5219i	0.671836	+	1.06943i
$406$		0			0
$407$	12.1210	+	20.9942i	0.600817	+	1.04064i
$408$		0			0
$409$	14.3999	−	17.1612i	0.712031	−	0.848566i	−0.281800	−	0.959473i	$-0.590931\pi$
$409$	14.3999	−	17.1612i	0.712031	−	0.848566i	0.993831	+	0.110908i	$0.0353758\pi$
$410$		0			0
$411$	−11.0768	+	21.7717i	−0.546376	+	1.07392i
$412$		0			0
$413$	4.20792	+	23.8643i	0.207058	+	1.17429i
$414$		0			0
$415$	18.6339	+	6.78217i	0.914700	+	0.332924i
$416$		0			0
$417$	0.0251583	+	0.474589i	0.00123201	+	0.0232407i
$418$		0			0
$419$			33.9260i			1.65739i	0.559698	+	0.828697i	$0.310917\pi$
$419$			33.9260i			1.65739i	−0.559698	+	0.828697i	$0.689083\pi$
$420$		0			0
$421$	7.50801	−	20.6281i	0.365918	−	1.00535i	−0.610980	−	0.791646i	$-0.709224\pi$
$421$	7.50801	−	20.6281i	0.365918	−	1.00535i	0.976898	−	0.213706i	$-0.0685533\pi$
$422$		0			0
$423$	14.6046	−	4.20680i	0.710098	−	0.204542i
$424$		0			0
$425$	−1.84469	−	1.06503i	−0.0894805	−	0.0516616i
$426$		0			0
$427$	−10.2011	−	8.55970i	−0.493664	−	0.414233i
$428$		0			0
$429$	51.5814	−	33.5415i	2.49037	−	1.61940i
$430$		0			0
$431$	4.74408	−	1.72670i	0.228514	−	0.0831724i	−0.225225	−	0.974307i	$-0.572312\pi$
$431$	4.74408	−	1.72670i	0.228514	−	0.0831724i	0.453740	+	0.891134i	$0.350090\pi$
$432$		0			0
$433$	29.6453	+	5.22727i	1.42466	+	0.251207i	0.832238	−	0.554419i	$-0.187059\pi$
$433$	29.6453	+	5.22727i	1.42466	+	0.251207i	0.592426	+	0.805625i	$0.298170\pi$
$434$		0			0
$435$	6.27531	−	5.85888i	0.300878	−	0.280912i
$436$		0			0
$437$	−1.77210	+	18.1711i	−0.0847712	+	0.869244i
$438$		0			0
$439$	−1.56606	−	1.86636i	−0.0747439	−	0.0890763i	0.727377	−	0.686238i	$-0.240739\pi$
$439$	−1.56606	−	1.86636i	−0.0747439	−	0.0890763i	−0.802121	+	0.597162i	$0.796295\pi$
$440$		0			0
$441$	0.405924	−	5.90705i	0.0193297	−	0.281288i
$442$		0			0
$443$	3.77403	+	10.3691i	0.179310	+	0.492649i	0.996488	−	0.0837359i	$-0.0266852\pi$
$443$	3.77403	+	10.3691i	0.179310	+	0.492649i	−0.817178	+	0.576385i	$0.804463\pi$
$444$		0			0
$445$	−36.3240	+	20.9717i	−1.72192	+	0.994153i
$446$		0			0
$447$	−17.4051	−	13.0993i	−0.823235	−	0.619576i
$448$		0			0
$449$	4.92205	−	8.52525i	0.232286	−	0.402331i	−0.726194	−	0.687489i	$-0.758713\pi$
$449$	4.92205	−	8.52525i	0.232286	−	0.402331i	0.958480	+	0.285158i	$0.0920461\pi$
$450$		0			0
$451$	28.4487	−	5.01628i	1.33960	−	0.236207i
$452$		0			0
$453$	29.7221	+	9.06742i	1.39647	+	0.426025i
$454$		0			0
$455$	−34.1870			−1.60271
$456$		0			0
$457$	34.7856			1.62720			0.813601	−	0.581424i	$-0.197504\pi$
$457$	34.7856			1.62720			0.813601	+	0.581424i	$0.197504\pi$
$458$		0			0
$459$	3.65301	+	0.703239i	0.170508	+	0.0328244i
$460$		0			0
$461$	−10.0178	+	1.76641i	−0.466575	+	0.0822697i	−0.401993	−	0.915643i	$-0.631682\pi$
$461$	−10.0178	+	1.76641i	−0.466575	+	0.0822697i	−0.0645817	+	0.997912i	$0.520571\pi$
$462$		0			0
$463$	−4.91533	+	8.51360i	−0.228435	+	0.395661i	−0.957344	−	0.288949i	$-0.906694\pi$
$463$	−4.91533	+	8.51360i	−0.228435	+	0.395661i	0.728910	+	0.684610i	$0.240027\pi$
$464$		0			0
$465$	−24.0207	+	31.9164i	−1.11393	+	1.48009i
$466$		0			0
$467$	−0.244993	+	0.141447i	−0.0113369	+	0.00654538i	−0.505658	−	0.862734i	$-0.668750\pi$
$467$	−0.244993	+	0.141447i	−0.0113369	+	0.00654538i	0.494321	+	0.869280i	$0.335417\pi$
$468$		0			0
$469$	−8.05295	−	22.1253i	−0.371851	−	1.02165i
$470$		0			0
$471$	−11.9034	−	1.45429i	−0.548482	−	0.0670104i
$472$		0			0
$473$	−20.0902	−	23.9426i	−0.923749	−	1.10088i
$474$		0			0
$475$	−5.36362	−	11.8076i	−0.246100	−	0.541770i
$476$		0			0
$477$	−14.4230	+	14.9714i	−0.660382	+	0.685493i
$478$		0			0
$479$	18.9911	+	3.34864i	0.867724	+	0.153003i	0.589750	−	0.807586i	$-0.299226\pi$
$479$	18.9911	+	3.34864i	0.867724	+	0.153003i	0.277973	+	0.960589i	$0.410337\pi$
$480$		0			0
$481$	−18.6970	+	6.80515i	−0.852509	+	0.310288i
$482$		0			0
$483$	−8.86662	−	13.6354i	−0.403445	−	0.620434i
$484$		0			0
$485$	21.3329	+	17.9004i	0.968675	+	0.812815i
$486$		0			0
$487$	−24.9285	−	14.3925i	−1.12962	−	0.652185i	−0.185779	−	0.982592i	$-0.559481\pi$
$487$	−24.9285	−	14.3925i	−1.12962	−	0.652185i	−0.943839	+	0.330407i	$0.892814\pi$
$488$		0			0
$489$	−1.13213	+	0.262091i	−0.0511968	+	0.0118521i
$490$		0			0
$491$	11.8893	−	32.6655i	0.536556	−	1.47417i	−0.314581	−	0.949231i	$-0.601864\pi$
$491$	11.8893	−	32.6655i	0.536556	−	1.47417i	0.851137	−	0.524944i	$-0.175914\pi$
$492$		0			0
$493$		−	1.25658i		−	0.0565935i
$494$		0			0
$495$	−55.4242	+	5.89270i	−2.49113	+	0.264857i
$496$		0			0
$497$	−26.6387	−	9.69570i	−1.19491	−	0.434911i
$498$		0			0
$499$	−1.79554	−	10.1830i	−0.0803793	−	0.455854i	−0.998258	−	0.0589934i	$-0.981211\pi$
$499$	−1.79554	−	10.1830i	−0.0803793	−	0.455854i	0.917879	−	0.396860i	$-0.129900\pi$
$500$		0			0
$501$	−5.04392	−	2.56619i	−0.225346	−	0.114649i
$502$		0			0
$503$	5.38397	−	6.41636i	0.240059	−	0.286092i	−0.632541	−	0.774527i	$-0.717988\pi$
$503$	5.38397	−	6.41636i	0.240059	−	0.286092i	0.872600	+	0.488436i	$0.162432\pi$
$504$		0			0
$505$	−13.7462	−	23.8092i	−0.611700	−	1.05949i
$506$		0			0
$507$	10.9493	+	25.7519i	0.486276	+	1.14368i
$508$		0			0
$509$	−3.41126	+	19.3462i	−0.151202	+	0.857506i	0.810975	+	0.585080i	$0.198937\pi$
$509$	−3.41126	+	19.3462i	−0.151202	+	0.857506i	−0.962177	+	0.272426i	$0.912174\pi$
$510$		0			0
$511$	13.2202	−	11.0931i	0.584828	−	0.490729i
$512$		0			0
$513$	15.6004	+	16.4203i	0.688776	+	0.724974i
$514$		0			0
$515$	11.2418	−	9.43296i	0.495371	−	0.415666i
$516$		0			0
$517$	−5.78752	+	32.8227i	−0.254535	+	1.44354i
$518$		0			0
$519$	−2.89889	−	6.81797i	−0.127247	−	0.299276i
$520$		0			0
$521$	17.7743	+	30.7860i	0.778705	+	1.34876i	0.932688	+	0.360684i	$0.117457\pi$
$521$	17.7743	+	30.7860i	0.778705	+	1.34876i	−0.153983	+	0.988074i	$0.549210\pi$
$522$		0			0
$523$	7.32928	−	8.73469i	0.320487	−	0.381942i	−0.581615	−	0.813464i	$-0.697579\pi$
$523$	7.32928	−	8.73469i	0.320487	−	0.381942i	0.902102	+	0.431523i	$0.142023\pi$
$524$		0			0
$525$	10.2972	+	5.23891i	0.449409	+	0.228645i
$526$		0			0
$527$	1.01526	+	5.75784i	0.0442255	+	0.250815i
$528$		0			0
$529$	−5.12721	−	1.86615i	−0.222922	−	0.0811371i
$530$		0			0
$531$	−32.2442	+	3.42821i	−1.39928	+	0.148772i
$532$		0			0
$533$			23.7098i			1.02699i
$534$		0			0
$535$	−16.9296	+	46.5136i	−0.731930	+	2.01096i
$536$		0			0
$537$	−10.5455	+	2.44129i	−0.455070	+	0.105349i
$538$		0			0
$539$	11.2448	+	6.49217i	0.484346	+	0.279637i
$540$		0			0
$541$	17.9188	+	15.0357i	0.770390	+	0.646434i	0.940809	−	0.338938i	$-0.110068\pi$
$541$	17.9188	+	15.0357i	0.770390	+	0.646434i	−0.170419	+	0.985372i	$0.554512\pi$
$542$		0			0
$543$	5.33445	+	8.20353i	0.228923	+	0.352047i
$544$		0			0
$545$	12.4840	−	4.54382i	0.534758	−	0.194636i
$546$		0			0
$547$	−15.8120	−	2.78808i	−0.676071	−	0.119210i	−0.174937	−	0.984580i	$-0.555972\pi$
$547$	−15.8120	−	2.78808i	−0.676071	−	0.119210i	−0.501133	+	0.865370i	$0.667083\pi$
$548$		0			0
$549$	12.3628	−	12.8329i	0.527631	−	0.547694i
$550$		0			0
$551$	4.45034	−	6.22304i	0.189591	−	0.265110i
$552$		0			0
$553$	−8.86103	−	10.5602i	−0.376809	−	0.449064i
$554$		0			0
$555$	17.8911	+	2.18583i	0.759435	+	0.0927834i
$556$		0			0
$557$	12.8621	+	35.3383i	0.544984	+	1.49733i	0.840402	+	0.541964i	$0.182319\pi$
$557$	12.8621	+	35.3383i	0.544984	+	1.49733i	−0.295417	+	0.955368i	$0.595459\pi$
$558$		0			0
$559$	22.2159	−	12.8264i	0.939634	−	0.542498i
$560$		0			0
$561$	−4.90564	+	6.51815i	−0.207116	+	0.275197i
$562$		0			0
$563$	8.24918	−	14.2880i	0.347662	−	0.602168i	−0.638172	−	0.769894i	$-0.720309\pi$
$563$	8.24918	−	14.2880i	0.347662	−	0.602168i	0.985834	+	0.167726i	$0.0536425\pi$
$564$		0			0
$565$	−2.21296	+	0.390204i	−0.0930998	+	0.0164160i
$566$		0			0
$567$	−19.9879	−	2.76011i	−0.839412	−	0.115914i
$568$		0			0
$569$	6.34727			0.266091			0.133046	−	0.991110i	$-0.457524\pi$
$569$	6.34727			0.266091			0.133046	+	0.991110i	$0.457524\pi$
$570$		0			0
$571$	32.7448			1.37033			0.685163	−	0.728390i	$-0.259731\pi$
$571$	32.7448			1.37033			0.685163	+	0.728390i	$0.259731\pi$
$572$		0			0
$573$	−26.2958	−	8.02215i	−1.09852	−	0.335130i
$574$		0			0
$575$	−12.2725	+	2.16397i	−0.511799	+	0.0902440i
$576$		0			0
$577$	0.927339	−	1.60620i	0.0386056	−	0.0668669i	−0.846077	−	0.533061i	$-0.821042\pi$
$577$	0.927339	−	1.60620i	0.0386056	−	0.0668669i	0.884683	+	0.466194i	$0.154375\pi$
$578$		0			0
$579$	8.99441	+	6.76930i	0.373795	+	0.281322i
$580$		0			0
$581$	−13.6333	+	7.87121i	−0.565606	+	0.326553i
$582$		0			0
$583$	−15.5920	−	42.8387i	−0.645755	−	1.77420i
$584$		0			0
$585$	3.13623	−	45.6388i	0.129667	−	1.88693i
$586$		0			0
$587$	−14.8603	−	17.7099i	−0.613352	−	0.730964i	0.366560	−	0.930394i	$-0.380535\pi$
$587$	−14.8603	−	17.7099i	−0.613352	−	0.730964i	−0.979912	+	0.199430i	$0.936091\pi$
$588$		0			0
$589$	−15.3642	+	32.1106i	−0.633069	+	1.32309i
$590$		0			0
$591$	17.9208	−	16.7316i	0.737165	−	0.688246i
$592$		0			0
$593$	−29.7078	−	5.23829i	−1.21995	−	0.215111i	−0.473648	−	0.880714i	$-0.657063\pi$
$593$	−29.7078	−	5.23829i	−1.21995	−	0.215111i	−0.746305	+	0.665604i	$0.768174\pi$
$594$		0			0
$595$	4.25946	−	1.55032i	0.174621	−	0.0635568i
$596$		0			0
$597$	5.57955	−	3.62817i	0.228356	−	0.148491i
$598$		0			0
$599$	13.2364	+	11.1067i	0.540826	+	0.453807i	0.871820	−	0.489826i	$-0.162940\pi$
$599$	13.2364	+	11.1067i	0.540826	+	0.453807i	−0.330994	+	0.943633i	$0.607384\pi$
$600$		0			0
$601$	−29.8194	−	17.2163i	−1.21636	−	0.702266i	−0.252223	−	0.967669i	$-0.581162\pi$
$601$	−29.8194	−	17.2163i	−1.21636	−	0.702266i	−0.964138	+	0.265403i	$0.914495\pi$
$602$		0			0
$603$	30.2754	−	8.72075i	1.23291	−	0.355136i
$604$		0			0
$605$	31.1793	−	85.6644i	1.26762	−	3.48275i
$606$		0			0
$607$		−	35.2061i		−	1.42897i	−0.699651	−	0.714485i	$-0.746661\pi$
$607$		−	35.2061i		−	1.42897i	0.699651	−	0.714485i	$-0.253339\pi$
$608$		0			0
$609$	0.360794	+	6.80606i	0.0146201	+	0.275796i
$610$		0			0
$611$	−25.7054	−	9.35602i	−1.03993	−	0.378504i
$612$		0			0
$613$	4.56485	+	25.8886i	0.184373	+	1.04563i	0.926759	+	0.375657i	$0.122583\pi$
$613$	4.56485	+	25.8886i	0.184373	+	1.04563i	−0.742386	+	0.669972i	$0.766306\pi$
$614$		0			0
$615$	9.73936	−	19.1430i	0.392729	−	0.771921i
$616$		0			0
$617$	24.8664	−	29.6347i	1.00108	−	1.19305i	0.0199340	−	0.999801i	$-0.493654\pi$
$617$	24.8664	−	29.6347i	1.00108	−	1.19305i	0.981151	−	0.193245i	$-0.0619012\pi$
$618$		0			0
$619$	12.5787	+	21.7869i	0.505579	+	0.875688i	0.999979	+	0.00645396i	$0.00205437\pi$
$619$	12.5787	+	21.7869i	0.505579	+	0.875688i	−0.494400	+	0.869234i	$0.664612\pi$
$620$		0			0
$621$	19.0163	−	10.5858i	0.763100	−	0.424794i
$622$		0			0
$623$	5.78213	−	32.7921i	0.231656	−	1.31379i
$624$		0			0
$625$	−23.7659	+	19.9419i	−0.950635	+	0.797678i
$626$		0			0
$627$	−47.3793	+	14.9063i	−1.89215	+	0.595300i
$628$		0			0
$629$	2.02091	−	1.69575i	0.0805790	−	0.0676138i
$630$		0			0
$631$	−7.34421	+	41.6511i	−0.292368	+	1.65810i	0.385341	+	0.922774i	$0.374084\pi$
$631$	−7.34421	+	41.6511i	−0.292368	+	1.65810i	−0.677710	+	0.735330i	$0.737027\pi$
$632$		0			0
$633$	−15.7917	+	6.71440i	−0.627665	+	0.266874i
$634$		0			0
$635$	8.55718	+	14.8215i	0.339581	+	0.588172i
$636$		0			0
$637$	−6.85021	+	8.16376i	−0.271415	+	0.323460i
$638$		0			0
$639$	15.3873	−	34.6725i	0.608710	−	1.37162i
$640$		0			0
$641$	0.626666	+	3.55400i	0.0247518	+	0.140374i	0.994679	−	0.103019i	$-0.0328504\pi$
$641$	0.626666	+	3.55400i	0.0247518	+	0.140374i	−0.969928	+	0.243394i	$0.921739\pi$
$642$		0			0
$643$	16.2051	+	5.89817i	0.639066	+	0.232601i	0.641173	−	0.767397i	$-0.278448\pi$
$643$	16.2051	+	5.89817i	0.639066	+	0.232601i	−0.00210635	+	0.999998i	$0.500670\pi$
$644$		0			0
$645$	−23.2056	+	1.23014i	−0.913720	+	0.0484369i
$646$		0			0
$647$			43.1987i			1.69832i	0.528138	+	0.849158i	$0.322890\pi$
$647$			43.1987i			1.69832i	−0.528138	+	0.849158i	$0.677110\pi$
$648$		0			0
$649$	24.3204	−	66.8197i	0.954659	−	2.62290i
$650$		0			0
$651$	−7.15221	−	30.8949i	−0.280317	−	1.21087i
$652$		0			0
$653$	−32.6444	−	18.8473i	−1.27747	−	0.737550i	−0.301091	−	0.953595i	$-0.597351\pi$
$653$	−32.6444	−	18.8473i	−1.27747	−	0.737550i	−0.976383	+	0.216045i	$0.930684\pi$
$654$		0			0
$655$	0.826654	+	0.693645i	0.0323001	+	0.0271030i
$656$		0			0
$657$	13.5962	+	18.6663i	0.530438	+	0.728242i
$658$		0			0
$659$	−8.64651	+	3.14707i	−0.336820	+	0.122593i	−0.504893	−	0.863182i	$-0.668468\pi$
$659$	−8.64651	+	3.14707i	−0.336820	+	0.122593i	0.168073	+	0.985775i	$0.446246\pi$
$660$		0			0
$661$	−0.272839	−	0.0481089i	−0.0106122	−	0.00187122i	0.168340	−	0.985729i	$-0.446159\pi$
$661$	−0.272839	−	0.0481089i	−0.0106122	−	0.00187122i	−0.178952	+	0.983858i	$0.557271\pi$
$662$		0			0
$663$	−4.56940	−	4.89418i	−0.177461	−	0.190074i
$664$		0			0
$665$	26.5850	+	7.40769i	1.03092	+	0.287258i
$666$		0			0
$667$	−4.72550	−	5.63163i	−0.182972	−	0.218057i
$668$		0			0
$669$	−1.35483	+	11.0893i	−0.0523807	+	0.428737i
$670$		0			0
$671$	13.3648	+	36.7196i	0.515944	+	1.41754i
$672$		0			0
$673$	13.7853	−	7.95895i	0.531385	−	0.306795i	−0.210196	−	0.977659i	$-0.567410\pi$
$673$	13.7853	−	7.95895i	0.531385	−	0.306795i	0.741580	+	0.670864i	$0.234077\pi$
$674$		0			0
$675$	−7.93845	+	13.2659i	−0.305551	+	0.510606i
$676$		0			0
$677$	−13.0452	+	22.5950i	−0.501369	+	0.868397i	0.498630	+	0.866815i	$0.333837\pi$
$677$	−13.0452	+	22.5950i	−0.501369	+	0.868397i	−0.999999	+	0.00158170i	$0.999497\pi$
$678$		0			0
$679$	−21.7721	+	3.83901i	−0.835537	+	0.147328i
$680$		0			0
$681$	0.978819	−	3.20847i	0.0375084	−	0.122949i
$682$		0			0
$683$	21.9973			0.841702			0.420851	−	0.907130i	$-0.361732\pi$
$683$	21.9973			0.841702			0.420851	+	0.907130i	$0.361732\pi$
$684$		0			0
$685$	−39.8281			−1.52175
$686$		0			0
$687$	−0.370128	+	1.21324i	−0.0141213	+	0.0462881i
$688$		0			0
$689$	36.8484	−	6.49737i	1.40381	−	0.247530i
$690$		0			0
$691$	18.1605	−	31.4548i	0.690857	−	1.19660i	−0.280701	−	0.959795i	$-0.590567\pi$
$691$	18.1605	−	31.4548i	0.690857	−	1.19660i	0.971558	−	0.236804i	$-0.0760998\pi$
$692$		0			0
$693$	24.6991	−	36.7130i	0.938240	−	1.39461i
$694$		0			0
$695$	−0.671071	+	0.387443i	−0.0254552	+	0.0146966i
$696$		0			0
$697$	−1.07520	−	2.95407i	−0.0407259	−	0.111894i
$698$		0			0
$699$	3.48850	−	28.5534i	0.131947	−	1.07999i
$700$		0			0
$701$	−6.19222	−	7.37960i	−0.233877	−	0.278724i	0.636323	−	0.771423i	$-0.280455\pi$
$701$	−6.19222	−	7.37960i	−0.233877	−	0.278724i	−0.870200	+	0.492699i	$0.836010\pi$
$702$		0			0
$703$	16.0140	−	1.24063i	0.603979	−	0.0467914i
$704$		0			0
$705$	16.9111	+	18.1131i	0.636908	+	0.682177i
$706$		0			0
$707$	21.4941	+	3.78999i	0.808369	+	0.142537i
$708$		0			0
$709$	30.2012	−	10.9924i	1.13423	−	0.412827i	0.294405	−	0.955681i	$-0.404879\pi$
$709$	30.2012	−	10.9924i	1.13423	−	0.412827i	0.839827	+	0.542854i	$0.182656\pi$
$710$		0			0
$711$	14.9104	−	10.8605i	0.559184	−	0.407299i
$712$		0			0
$713$	26.2030	+	21.9869i	0.981311	+	0.823418i
$714$		0			0
$715$	86.8787	+	50.1594i	3.24908	+	1.87586i
$716$		0			0
$717$	−1.40990	−	6.09023i	−0.0526536	−	0.227444i
$718$		0			0
$719$	16.1565	−	44.3896i	0.602535	−	1.65545i	−0.143584	−	0.989638i	$-0.545863\pi$
$719$	16.1565	−	44.3896i	0.602535	−	1.65545i	0.746119	−	0.665813i	$-0.231915\pi$
$720$		0			0
$721$			11.6502i			0.433877i
$722$		0			0
$723$	−23.3245	+	1.23645i	−0.867448	+	0.0459840i
$724$		0			0
$725$	4.90711	+	1.78604i	0.182245	+	0.0663319i
$726$		0			0
$727$	−3.16767	−	17.9648i	−0.117482	−	0.666276i	−0.985491	−	0.169727i	$-0.945711\pi$
$727$	−3.16767	−	17.9648i	−0.117482	−	0.666276i	0.868009	−	0.496549i	$-0.165400\pi$
$728$		0			0
$729$	5.51831	−	26.4301i	0.204382	−	0.978891i
$730$		0			0
$731$	−2.18630	+	2.60553i	−0.0808631	+	0.0963688i
$732$		0			0
$733$	−11.2370	−	19.4630i	−0.415047	−	0.718883i	0.580386	−	0.814341i	$-0.302902\pi$
$733$	−11.2370	−	19.4630i	−0.415047	−	0.718883i	−0.995433	+	0.0954585i	$0.969568\pi$
$734$		0			0
$735$	8.88424	−	3.77744i	0.327700	−	0.139333i
$736$		0			0
$737$	−11.9976	+	68.0418i	−0.441938	+	2.50635i
$738$		0			0
$739$	−6.08433	+	5.10536i	−0.223816	+	0.187804i	−0.747800	−	0.663925i	$-0.768890\pi$
$739$	−6.08433	+	5.10536i	−0.223816	+	0.187804i	0.523984	+	0.851728i	$0.324445\pi$
$740$		0			0
$741$	−5.29596	−	40.4208i	−0.194552	−	1.48490i
$742$		0			0
$743$	14.9235	−	12.5223i	0.547489	−	0.459398i	−0.326601	−	0.945162i	$-0.605903\pi$
$743$	14.9235	−	12.5223i	0.547489	−	0.459398i	0.874090	+	0.485765i	$0.161459\pi$
$744$		0			0
$745$	6.16756	−	34.9780i	0.225962	−	1.28149i
$746$		0			0
$747$	−9.25716	−	18.9222i	−0.338702	−	0.692327i
$748$		0			0
$749$	−19.6480	−	34.0314i	−0.717923	−	1.24348i
$750$		0			0
$751$	−32.7761	+	39.0610i	−1.19602	+	1.42536i	−0.317091	+	0.948395i	$0.602706\pi$
$751$	−32.7761	+	39.0610i	−1.19602	+	1.42536i	−0.878925	+	0.476961i	$0.841738\pi$
$752$		0			0
$753$	−6.54000	+	12.8546i	−0.238331	+	0.468447i
$754$		0			0
$755$	8.79802	+	49.8960i	0.320193	+	1.81590i
$756$		0			0
$757$	−20.7277	−	7.54428i	−0.753363	−	0.274202i	−0.0633426	−	0.997992i	$-0.520176\pi$
$757$	−20.7277	−	7.54428i	−0.753363	−	0.274202i	−0.690020	+	0.723790i	$0.742398\pi$
$758$		0			0
$759$	2.52652	+	47.6606i	0.0917068	+	1.72997i
$760$		0			0
$761$		−	21.1505i		−	0.766705i	−0.923602	−	0.383352i	$-0.874769\pi$
$761$		−	21.1505i		−	0.766705i	0.923602	−	0.383352i	$-0.125231\pi$
$762$		0			0
$763$	−3.60724	+	9.91082i	−0.130591	+	0.358796i
$764$		0			0
$765$	1.67888	+	5.82849i	0.0607000	+	0.210729i
$766$		0			0
$767$	50.5436	+	29.1814i	1.82502	+	1.05368i
$768$		0			0
$769$	−31.5049	−	26.4358i	−1.13610	−	0.953298i	−0.136792	−	0.990600i	$-0.543679\pi$
$769$	−31.5049	−	26.4358i	−1.13610	−	0.953298i	−0.999304	+	0.0373021i	$0.988124\pi$
$770$		0			0
$771$	27.9282	−	18.1607i	1.00581	−	0.654041i
$772$		0			0
$773$	12.4014	−	4.51375i	0.446049	−	0.162348i	−0.109223	−	0.994017i	$-0.534836\pi$
$773$	12.4014	−	4.51375i	0.446049	−	0.162348i	0.555272	+	0.831669i	$0.312614\pi$
$774$		0			0
$775$	−23.9281	−	4.21918i	−0.859524	−	0.151557i
$776$		0			0
$777$	−10.4591	+	9.76499i	−0.375216	+	0.350317i
$778$		0			0
$779$	5.13747	−	18.4376i	0.184069	−	0.660595i
$780$		0			0
$781$	53.4707	+	63.7239i	1.91333	+	2.28022i
$782$		0			0
$783$	−9.11901	−	0.142721i	−0.325887	−	0.00510043i
$784$		0			0
$785$	−6.68733	−	18.3733i	−0.238681	−	0.655770i
$786$		0			0
$787$	10.3999	−	6.00436i	0.370715	−	0.214032i	−0.303056	−	0.952973i	$-0.598007\pi$
$787$	10.3999	−	6.00436i	0.370715	−	0.214032i	0.673771	+	0.738941i	$0.264674\pi$
$788$		0			0
$789$	−39.7656	−	29.9281i	−1.41569	−	1.06547i
$790$		0			0
$791$	0.891961	−	1.54492i	0.0317145	−	0.0549311i
$792$		0			0
$793$	−31.5850	+	5.56928i	−1.12162	+	0.197771i
$794$		0			0
$795$	−32.4199	−	9.89045i	−1.14982	−	0.350778i
$796$		0			0
$797$	35.7099			1.26491			0.632454	−	0.774598i	$-0.282048\pi$
$797$	35.7099			1.26491			0.632454	+	0.774598i	$0.282048\pi$
$798$		0			0
$799$	3.62699			0.128314
$800$		0			0
$801$	43.2461	+	10.7272i	1.52802	+	0.379028i
$802$		0			0
$803$	−49.8721	+	8.79380i	−1.75995	+	0.310326i
$804$		0			0
$805$	13.2595	−	22.9662i	0.467337	−	0.809452i
$806$		0			0
$807$	−4.63735	+	6.16167i	−0.163242	+	0.216901i
$808$		0			0
$809$	30.9982	−	17.8968i	1.08984	−	0.629218i	0.156305	−	0.987709i	$-0.450042\pi$
$809$	30.9982	−	17.8968i	1.08984	−	0.629218i	0.933533	+	0.358491i	$0.116709\pi$
$810$		0			0
$811$	6.17957	+	16.9782i	0.216994	+	0.596186i	0.999655	−	0.0262620i	$-0.00836040\pi$
$811$	6.17957	+	16.9782i	0.216994	+	0.596186i	−0.782661	+	0.622448i	$0.786138\pi$
$812$		0			0
$813$	−0.512566	−	0.0626225i	−0.0179765	−	0.00219627i
$814$		0			0
$815$	−1.21790	−	1.45144i	−0.0426613	−	0.0508417i
$816$		0			0
$817$	−20.0551	+	5.16046i	−0.701640	+	0.180542i
$818$		0			0
$819$	26.1546	+	25.1965i	0.913917	+	0.880438i
$820$		0			0
$821$	49.7488	+	8.77205i	1.73624	+	0.306147i	0.950111	−	0.311911i	$-0.100969\pi$
$821$	49.7488	+	8.77205i	1.73624	+	0.306147i	0.786133	+	0.618057i	$0.212080\pi$
$822$		0			0
$823$	−25.9399	+	9.44137i	−0.904209	+	0.329105i	−0.751938	−	0.659233i	$-0.770881\pi$
$823$	−25.9399	+	9.44137i	−0.904209	+	0.329105i	−0.152271	+	0.988339i	$0.548659\pi$
$824$		0			0
$825$	−18.4816	−	28.4217i	−0.643446	−	0.989517i
$826$		0			0
$827$	−8.24033	−	6.91446i	−0.286544	−	0.240439i	0.488173	−	0.872747i	$-0.337663\pi$
$827$	−8.24033	−	6.91446i	−0.286544	−	0.240439i	−0.774717	+	0.632308i	$0.782108\pi$
$828$		0			0
$829$	11.4217	+	6.59431i	0.396691	+	0.229030i	0.685055	−	0.728491i	$-0.259778\pi$
$829$	11.4217	+	6.59431i	0.396691	+	0.229030i	−0.288364	+	0.957521i	$0.593111\pi$
$830$		0			0
$831$	−41.8919	+	9.69804i	−1.45321	+	0.336421i
$832$		0			0
$833$	0.483277	−	1.32779i	0.0167445	−	0.0460052i
$834$		0			0
$835$		−	9.22711i		−	0.319317i
$836$		0			0
$837$	41.8999	−	6.71379i	1.44827	−	0.232063i
$838$		0			0
$839$	−28.9419	−	10.5340i	−0.999184	−	0.363673i	−0.209914	−	0.977720i	$-0.567318\pi$
$839$	−28.9419	−	10.5340i	−0.999184	−	0.363673i	−0.789270	+	0.614047i	$0.789541\pi$
$840$		0			0
$841$	−4.50085	−	25.5256i	−0.155202	−	0.880193i
$842$		0			0
$843$	−34.3155	−	17.4586i	−1.18189	−	0.601308i
$844$		0			0
$845$	−29.3273	+	34.9510i	−1.00889	+	1.20235i
$846$		0			0
$847$	36.1858	+	62.6757i	1.24336	+	2.15356i
$848$		0			0
$849$	−4.10656	−	9.65831i	−0.140937	−	0.331472i
$850$		0			0
$851$	2.68011	−	15.1997i	0.0918731	−	0.521038i
$852$		0			0
$853$	−20.5969	+	17.2829i	−0.705224	+	0.591754i	−0.923255	−	0.384188i	$-0.874481\pi$
$853$	−20.5969	+	17.2829i	−0.705224	+	0.591754i	0.218030	+	0.975942i	$0.430037\pi$
$854$		0			0
$855$	−12.3279	+	34.8107i	−0.421606	+	1.19050i
$856$		0			0
$857$	−33.1805	+	27.8418i	−1.13343	+	0.951057i	−0.999204	−	0.0398942i	$-0.987298\pi$
$857$	−33.1805	+	27.8418i	−1.13343	+	0.951057i	−0.134222	+	0.990951i	$0.542853\pi$
$858$		0			0
$859$	−5.68652	+	32.2498i	−0.194021	+	1.10035i	0.719784	+	0.694198i	$0.244241\pi$
$859$	−5.68652	+	32.2498i	−0.194021	+	1.10035i	−0.913805	+	0.406152i	$0.866870\pi$
$860$		0			0
$861$	6.67180	+	15.6915i	0.227374	+	0.534767i
$862$		0			0
$863$	8.86606	+	15.3565i	0.301804	+	0.522740i	0.976545	−	0.215315i	$-0.0690778\pi$
$863$	8.86606	+	15.3565i	0.301804	+	0.522740i	−0.674741	+	0.738055i	$0.735744\pi$
$864$		0			0
$865$	7.76459	−	9.25347i	0.264004	−	0.314628i
$866$		0			0
$867$	−25.4523	−	12.9493i	−0.864407	−	0.439783i
$868$		0			0
$869$	7.02438	+	39.8372i	0.238286	+	1.35139i
$870$		0			0
$871$	−53.2877	−	19.3951i	−1.80559	−	0.657179i
$872$		0			0
$873$	−3.12766	−	29.4174i	−0.105855	−	0.995627i
$874$		0			0
$875$		−	12.8195i		−	0.433380i
$876$		0			0
$877$	7.68252	−	21.1076i	0.259420	−	0.712752i	−0.739783	−	0.672845i	$-0.765072\pi$
$877$	7.68252	−	21.1076i	0.259420	−	0.712752i	0.999203	−	0.0399061i	$-0.0127059\pi$
$878$		0			0
$879$	−24.1405	+	5.58857i	−0.814240	+	0.188498i
$880$		0			0
$881$	−20.2208	−	11.6745i	−0.681255	−	0.393323i	0.119073	−	0.992886i	$-0.462008\pi$
$881$	−20.2208	−	11.6745i	−0.681255	−	0.393323i	−0.800328	+	0.599563i	$0.795341\pi$
$882$		0			0
$883$	26.9464	+	22.6107i	0.906818	+	0.760911i	0.971511	−	0.236995i	$-0.0761624\pi$
$883$	26.9464	+	22.6107i	0.906818	+	0.760911i	−0.0646931	+	0.997905i	$0.520607\pi$
$884$		0			0
$885$	−28.8214	−	44.3226i	−0.968820	−	1.48989i
$886$		0			0
$887$	−12.6213	+	4.59379i	−0.423782	+	0.154244i	−0.545103	−	0.838369i	$-0.683509\pi$
$887$	−12.6213	+	4.59379i	−0.423782	+	0.154244i	0.121320	+	0.992613i	$0.461287\pi$
$888$		0			0
$889$	−13.3803	−	2.35931i	−0.448762	−	0.0791288i
$890$		0			0
$891$	46.7451	+	36.3405i	1.56602	+	1.21745i
$892$		0			0
$893$	17.9622	+	12.8455i	0.601082	+	0.429857i
$894$		0			0
$895$	−11.3444	−	13.5197i	−0.379201	−	0.451914i
$896$		0			0
$897$	−38.8838	−	4.75060i	−1.29829	−	0.158618i
$898$		0			0
$899$	−4.90238	−	13.4692i	−0.163504	−	0.449222i
$900$		0			0
$901$	−4.29641	+	2.48053i	−0.143134	+	0.0826385i
$902$		0			0
$903$	11.0936	−	14.7401i	0.369172	−	0.490521i
$904$		0			0
$905$	−7.97737	+	13.8172i	−0.265177	+	0.459300i
$906$		0			0
$907$	49.3405	−	8.70005i	1.63832	−	0.288881i	0.722773	−	0.691085i	$-0.242867\pi$
$907$	49.3405	−	8.70005i	1.63832	−	0.288881i	0.915550	+	0.402205i	$0.131756\pi$
$908$		0			0
$909$	−7.03135	+	28.3464i	−0.233215	+	0.940190i
$910$		0			0
$911$	−26.2541			−0.869837			−0.434918	−	0.900470i	$-0.643223\pi$
$911$	−26.2541			−0.869837			−0.434918	+	0.900470i	$0.643223\pi$
$912$		0			0
$913$	46.1947			1.52882
$914$		0			0
$915$	27.7890	+	8.47770i	0.918677	+	0.280264i
$916$		0			0
$917$	−0.843676	+	0.148763i	−0.0278606	+	0.00491258i
$918$		0			0
$919$	−15.8522	+	27.4568i	−0.522915	+	0.905716i	0.476729	+	0.879050i	$0.341822\pi$
$919$	−15.8522	+	27.4568i	−0.522915	+	0.905716i	−0.999644	+	0.0266656i	$0.991511\pi$
$920$		0			0
$921$	10.1159	+	7.61335i	0.333330	+	0.250868i
$922$		0			0
$923$	−59.1284	+	34.1378i	−1.94623	+	1.12366i
$924$		0			0
$925$	3.74968	+	10.3022i	0.123289	+	0.338733i
$926$		0			0
$927$	−15.5527	−	1.06876i	−0.510819	−	0.0351028i
$928$		0			0
$929$	4.17179	+	4.97174i	0.136872	+	0.163118i	0.830126	−	0.557575i	$-0.188268\pi$
$929$	4.17179	+	4.97174i	0.136872	+	0.163118i	−0.693254	+	0.720693i	$0.743824\pi$
$930$		0			0
$931$	7.09590	−	4.86412i	0.232559	−	0.159415i
$932$		0			0
$933$	−43.0360	+	40.1801i	−1.40893	+	1.31544i
$934$		0			0
$935$	−13.0991	−	2.30973i	−0.428387	−	0.0755361i
$936$		0			0
$937$	43.0174	−	15.6570i	1.40532	−	0.511493i	0.475565	−	0.879681i	$-0.342244\pi$
$937$	43.0174	−	15.6570i	1.40532	−	0.511493i	0.929752	+	0.368188i	$0.120022\pi$
$938$		0			0
$939$	28.1808	−	18.3249i	0.919645	−	0.598011i
$940$		0			0
$941$	−16.6900	−	14.0045i	−0.544078	−	0.456535i	0.328852	−	0.944381i	$-0.393338\pi$
$941$	−16.6900	−	14.0045i	−0.544078	−	0.456535i	−0.872930	+	0.487846i	$0.837783\pi$
$942$		0			0
$943$	−15.9278	−	9.19592i	−0.518680	−	0.299460i
$944$		0			0
$945$	−10.7669	−	31.0870i	−0.350246	−	1.01126i
$946$		0			0
$947$	−0.722218	+	1.98428i	−0.0234689	+	0.0644804i	−0.950874	−	0.309579i	$-0.899812\pi$
$947$	−0.722218	+	1.98428i	−0.0234689	+	0.0644804i	0.927405	+	0.374059i	$0.122034\pi$
$948$		0			0
$949$		−	41.5645i		−	1.34924i
$950$		0			0
$951$	−2.18746	−	41.2645i	−0.0709333	−	1.33809i
$952$		0			0
$953$	−18.2260	−	6.63373i	−0.590398	−	0.214887i	0.0295062	−	0.999565i	$-0.490607\pi$
$953$	−18.2260	−	6.63373i	−0.590398	−	0.214887i	−0.619905	+	0.784677i	$0.712829\pi$
$954$		0			0
$955$	−7.78380	−	44.1441i	−0.251878	−	1.42847i
$956$		0			0
$957$	9.06902	−	17.8254i	0.293160	−	0.576215i
$958$		0			0
$959$	20.3241	−	24.2213i	0.656300	−	0.782148i
$960$		0			0
$961$	17.8459	+	30.9101i	0.575675	+	0.997099i
$962$		0			0
$963$	47.2334	−	23.1076i	1.52207	−	0.744632i
$964$		0			0
$965$	−3.18720	+	18.0755i	−0.102599	+	0.581870i
$966$		0			0
$967$	42.8069	−	35.9193i	1.37658	−	1.15509i	0.406118	−	0.913821i	$-0.366882\pi$
$967$	42.8069	−	35.9193i	1.37658	−	1.15509i	0.970459	−	0.241265i	$-0.0775622\pi$
$968$		0			0
$969$	2.49285	+	4.79599i	0.0800818	+	0.154069i
$970$		0			0
$971$	−40.7240	+	34.1715i	−1.30690	+	1.09662i	−0.317986	+	0.948096i	$0.603006\pi$
$971$	−40.7240	+	34.1715i	−1.30690	+	1.09662i	−0.988909	+	0.148520i	$0.952549\pi$
$972$		0			0
$973$	0.106822	−	0.605820i	0.00342457	−	0.0194217i
$974$		0			0
$975$	25.6071	−	10.8877i	0.820084	−	0.348687i
$976$		0			0
$977$	6.21256	+	10.7605i	0.198757	+	0.344258i	0.948126	−	0.317895i	$-0.102976\pi$
$977$	6.21256	+	10.7605i	0.198757	+	0.344258i	−0.749368	+	0.662153i	$0.769643\pi$
$978$		0			0
$979$	−62.8067	+	74.8501i	−2.00731	+	2.39222i
$980$		0			0
$981$	−12.8998	−	5.72477i	−0.411857	−	0.182778i
$982$		0			0
$983$	−8.84945	−	50.1877i	−0.282254	−	1.60074i	−0.714933	−	0.699193i	$-0.753543\pi$
$983$	−8.84945	−	50.1877i	−0.282254	−	1.60074i	0.432680	−	0.901548i	$-0.357568\pi$
$984$		0			0
$985$	37.5640	+	13.6722i	1.19689	+	0.435631i
$986$		0			0
$987$	−19.6450	+	1.04140i	−0.625308	+	0.0331480i
$988$		0			0
$989$			19.8990i			0.632751i
$990$		0			0
$991$	3.50077	−	9.61828i	0.111206	−	0.305535i	−0.871589	−	0.490238i	$-0.836910\pi$
$991$	3.50077	−	9.61828i	0.111206	−	0.305535i	0.982794	+	0.184703i	$0.0591322\pi$
$992$		0			0
$993$	6.13218	+	26.4887i	0.194599	+	0.840594i
$994$		0			0
$995$	9.39764	+	5.42573i	0.297925	+	0.172007i
$996$		0			0
$997$	−26.1449	−	21.9382i	−0.828018	−	0.694789i	0.126817	−	0.991926i	$-0.459524\pi$
$997$	−26.1449	−	21.9382i	−0.828018	−	0.694789i	−0.954835	+	0.297137i	$0.903968\pi$
$998$		0			0
$999$	−12.0765	−	14.8584i	−0.382084	−	0.470098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bm.b.89.7	yes	60
3.2	odd	2		456.2.bm.a.89.7	yes	60
4.3	odd	2		912.2.cc.g.545.4		60
12.11	even	2		912.2.cc.h.545.4		60
19.3	odd	18		456.2.bm.a.41.7	✓	60
57.41	even	18	inner	456.2.bm.b.41.7	yes	60
76.3	even	18		912.2.cc.h.497.4		60
228.155	odd	18		912.2.cc.g.497.4		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bm.a.41.7	✓	60	19.3	odd	18
456.2.bm.a.89.7	yes	60	3.2	odd	2
456.2.bm.b.41.7	yes	60	57.41	even	18	inner
456.2.bm.b.89.7	yes	60	1.1	even	1	trivial
912.2.cc.g.497.4		60	228.155	odd	18
912.2.cc.g.545.4		60	4.3	odd	2
912.2.cc.h.497.4		60	76.3	even	18
912.2.cc.h.545.4		60	12.11	even	2

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bm (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.505407 - 1.65667i) q^{3} +(2.78114 - 0.490390i) q^{5} +(-1.12097 + 1.94159i) q^{7} +(-2.48913 - 1.67459i) q^{9} +(5.69741 - 3.28940i) q^{11} +(1.84678 + 5.07399i) q^{13} +(0.593192 - 4.85529i) q^{15} +(-0.460192 - 0.548435i) q^{17} +(-0.336683 - 4.34588i) q^{19} +(2.65002 + 2.83838i) q^{21} +(-4.12489 - 0.727330i) q^{23} +(2.79580 - 1.01759i) q^{25} +(-4.03226 + 3.27732i) q^{27} +(1.34454 + 1.12820i) q^{29} +(-7.07240 - 4.08325i) q^{31} +(-2.56995 - 11.1012i) q^{33} +(-2.16546 + 5.94954i) q^{35} +3.68487i q^{37} +(9.33932 - 0.495083i) q^{39} +(4.12620 + 1.50181i) q^{41} +(-0.824974 - 4.67866i) q^{43} +(-7.74382 - 3.43662i) q^{45} +(-3.25644 + 3.88087i) q^{47} +(0.986831 + 1.70924i) q^{49} +(-1.14116 + 0.485204i) q^{51} +(1.20330 - 6.82425i) q^{53} +(14.2322 - 11.9423i) q^{55} +(-7.36986 - 1.63866i) q^{57} +(8.27991 - 6.94767i) q^{59} +(-1.03142 + 5.84947i) q^{61} +(6.04160 - 2.95568i) q^{63} +(7.62440 + 13.2058i) q^{65} +(-6.75064 + 8.04510i) q^{67} +(-3.28969 + 6.46600i) q^{69} +(2.19569 + 12.4524i) q^{71} +(-7.23344 - 2.63276i) q^{73} +(-0.272794 - 5.14603i) q^{75} +14.7494i q^{77} +(-2.10301 + 5.77799i) q^{79} +(3.39152 + 8.33652i) q^{81} +(6.08101 + 3.51087i) q^{83} +(-1.54881 - 1.29960i) q^{85} +(2.54860 - 1.65726i) q^{87} +(-13.9565 + 5.07976i) q^{89} +(-11.9218 - 2.10213i) q^{91} +(-10.3391 + 9.65295i) q^{93} +(-3.06754 - 11.9214i) q^{95} +(6.33856 + 7.55401i) q^{97} +(-19.6900 - 1.35307i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{9} + 3 q^{13} - 3 q^{15} - 6 q^{17} + 3 q^{19} + 6 q^{25} + 3 q^{27} + 6 q^{29} + 24 q^{35} + 18 q^{39} + 3 q^{41} - 21 q^{43} + 63 q^{45} - 18 q^{47} - 30 q^{49} + 33 q^{51} - 36 q^{53} + 18 q^{55}+ \cdots - 39 q^{99}+O(q^{100}) \) 60 * q - 6 * q^9 + 3 * q^13 - 3 * q^15 - 6 * q^17 + 3 * q^19 + 6 * q^25 + 3 * q^27 + 6 * q^29 + 24 * q^35 + 18 * q^39 + 3 * q^41 - 21 * q^43 + 63 * q^45 - 18 * q^47 - 30 * q^49 + 33 * q^51 - 36 * q^53 + 18 * q^55 - 24 * q^57 - 21 * q^59 - 6 * q^61 - 24 * q^63 + 24 * q^65 - 48 * q^67 - 21 * q^69 + 36 * q^71 - 57 * q^73 - 36 * q^79 + 6 * q^81 - 36 * q^83 + 6 * q^85 + 72 * q^87 - 24 * q^89 - 18 * q^91 + 108 * q^93 + 30 * q^95 + 15 * q^97 - 39 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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