LMFDB - Embedded newform 2646.2.f.s.1765.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2646,2,Mod(883,2646)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2646, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2646.883"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,0,-4,0,0,0,-8,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.3317760000.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1765.4
Root			$1.72286 - 0.178197i$ of defining polynomial
Character	$\chi$	$=$	2646.1765
Dual form			2646.2.f.s.883.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.72286 - 2.98408i) q^{5} -1.00000 q^{8} +3.44572 q^{10} +(2.00000 + 3.46410i) q^{11} +(-2.12132 + 3.67423i) q^{13} +(-0.500000 - 0.866025i) q^{16} +1.41421 q^{17} +6.27415 q^{19} +(1.72286 + 2.98408i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(-4.37298 + 7.57423i) q^{23} +(-3.43649 - 5.95218i) q^{25} -4.24264 q^{26} +(0.563508 + 0.976025i) q^{29} +(2.73861 - 4.74342i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.707107 + 1.22474i) q^{34} +5.74597 q^{37} +(3.13707 + 5.43357i) q^{38} +(-1.72286 + 2.98408i) q^{40} +(-2.82843 + 4.89898i) q^{41} +(-0.563508 - 0.976025i) q^{43} -4.00000 q^{44} -8.74597 q^{46} +(2.03151 + 3.51867i) q^{47} +(3.43649 - 5.95218i) q^{50} +(-2.12132 - 3.67423i) q^{52} -12.6190 q^{53} +13.7829 q^{55} +(-0.563508 + 0.976025i) q^{58} +(4.15283 - 7.19291i) q^{59} +(3.13707 + 5.43357i) q^{61} +5.47723 q^{62} +1.00000 q^{64} +(7.30948 + 12.6604i) q^{65} +(3.43649 - 5.95218i) q^{67} +(-0.707107 + 1.22474i) q^{68} +9.87298 q^{71} -4.42227 q^{73} +(2.87298 + 4.97615i) q^{74} +(-3.13707 + 5.43357i) q^{76} +(0.936492 + 1.62205i) q^{79} -3.44572 q^{80} -5.65685 q^{82} +(1.32440 + 2.29393i) q^{83} +(2.43649 - 4.22013i) q^{85} +(0.563508 - 0.976025i) q^{86} +(-2.00000 - 3.46410i) q^{88} +7.07107 q^{89} +(-4.37298 - 7.57423i) q^{92} +(-2.03151 + 3.51867i) q^{94} +(10.8095 - 18.7226i) q^{95} +(7.50873 + 13.0055i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} + 16 q^{11} - 4 q^{16} - 16 q^{22} - 4 q^{23} - 12 q^{25} + 20 q^{29} + 4 q^{32} - 16 q^{37} - 20 q^{43} - 32 q^{44} - 8 q^{46} + 12 q^{50} - 8 q^{53} - 20 q^{58} + 8 q^{64}+ \cdots + 40 q^{95}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 + 16 * q^11 - 4 * q^16 - 16 * q^22 - 4 * q^23 - 12 * q^25 + 20 * q^29 + 4 * q^32 - 16 * q^37 - 20 * q^43 - 32 * q^44 - 8 * q^46 + 12 * q^50 - 8 * q^53 - 20 * q^58 + 8 * q^64 + 12 * q^65 + 12 * q^67 + 48 * q^71 - 8 * q^74 - 8 * q^79 + 4 * q^85 + 20 * q^86 - 16 * q^88 - 4 * q^92 + 40 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.72286	−	2.98408i	0.770486	−	1.33452i	−0.166810	−	0.985989i	$-0.553347\pi$
$5$	1.72286	−	2.98408i	0.770486	−	1.33452i	0.937297	−	0.348532i	$-0.113320\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	3.44572			1.08963
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	0.992361	+	0.123371i	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$		0			0
$13$	−2.12132	+	3.67423i	−0.588348	+	1.01905i	0.406100	+	0.913828i	$0.366888\pi$
$13$	−2.12132	+	3.67423i	−0.588348	+	1.01905i	−0.994449	+	0.105221i	$0.966445\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.41421			0.342997			0.171499	−	0.985184i	$-0.445139\pi$
$17$	1.41421			0.342997			0.171499	+	0.985184i	$0.445139\pi$
$18$		0			0
$19$	6.27415			1.43939			0.719694	−	0.694291i	$-0.244282\pi$
$19$	6.27415			1.43939			0.719694	+	0.694291i	$0.244282\pi$
$20$	1.72286	+	2.98408i	0.385243	+	0.667261i
$21$		0			0
$22$	−2.00000	+	3.46410i	−0.426401	+	0.738549i
$23$	−4.37298	+	7.57423i	−0.911830	+	1.57934i	−0.100353	+	0.994952i	$0.531997\pi$
$23$	−4.37298	+	7.57423i	−0.911830	+	1.57934i	−0.811477	+	0.584384i	$0.801336\pi$
$24$		0			0
$25$	−3.43649	−	5.95218i	−0.687298	−	1.19044i
$26$	−4.24264			−0.832050
$27$		0			0
$28$		0			0
$29$	0.563508	+	0.976025i	0.104641	+	0.181243i	0.913591	−	0.406633i	$-0.133297\pi$
$29$	0.563508	+	0.976025i	0.104641	+	0.181243i	−0.808951	+	0.587877i	$0.799964\pi$
$30$		0			0
$31$	2.73861	−	4.74342i	0.491869	−	0.851943i	−0.508087	−	0.861306i	$-0.669647\pi$
$31$	2.73861	−	4.74342i	0.491869	−	0.851943i	0.999956	+	0.00936313i	$0.00298042\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	0.707107	+	1.22474i	0.121268	+	0.210042i
$35$		0			0
$36$		0			0
$37$	5.74597			0.944631			0.472316	−	0.881430i	$-0.343418\pi$
$37$	5.74597			0.944631			0.472316	+	0.881430i	$0.343418\pi$
$38$	3.13707	+	5.43357i	0.508900	+	0.881442i
$39$		0			0
$40$	−1.72286	+	2.98408i	−0.272408	+	0.471825i
$41$	−2.82843	+	4.89898i	−0.441726	+	0.765092i	−0.997818	−	0.0660290i	$-0.978967\pi$
$41$	−2.82843	+	4.89898i	−0.441726	+	0.765092i	0.556092	+	0.831121i	$0.312300\pi$
$42$		0			0
$43$	−0.563508	−	0.976025i	−0.0859342	−	0.148842i	0.819855	−	0.572572i	$-0.194054\pi$
$43$	−0.563508	−	0.976025i	−0.0859342	−	0.148842i	−0.905789	+	0.423729i	$0.860721\pi$
$44$	−4.00000			−0.603023
$45$		0			0
$46$	−8.74597			−1.28952
$47$	2.03151	+	3.51867i	0.296326	+	0.513251i	0.975292	−	0.220918i	$-0.0709053\pi$
$47$	2.03151	+	3.51867i	0.296326	+	0.513251i	−0.678967	+	0.734169i	$0.737572\pi$
$48$		0			0
$49$		0			0
$50$	3.43649	−	5.95218i	0.485993	−	0.841765i
$51$		0			0
$52$	−2.12132	−	3.67423i	−0.294174	−	0.509525i
$53$	−12.6190			−1.73335			−0.866673	−	0.498877i	$-0.833746\pi$
$53$	−12.6190			−1.73335			−0.866673	+	0.498877i	$0.833746\pi$
$54$		0			0
$55$	13.7829			1.85848
$56$		0			0
$57$		0			0
$58$	−0.563508	+	0.976025i	−0.0739923	+	0.128158i
$59$	4.15283	−	7.19291i	0.540652	−	0.936437i	−0.458215	−	0.888842i	$-0.651511\pi$
$59$	4.15283	−	7.19291i	0.540652	−	0.936437i	0.998867	−	0.0475951i	$-0.0151557\pi$
$60$		0			0
$61$	3.13707	+	5.43357i	0.401661	+	0.695697i	0.993927	−	0.110045i	$-0.0350997\pi$
$61$	3.13707	+	5.43357i	0.401661	+	0.695697i	−0.592265	+	0.805743i	$0.701766\pi$
$62$	5.47723			0.695608
$63$		0			0
$64$	1.00000			0.125000
$65$	7.30948	+	12.6604i	0.906629	+	1.57033i
$66$		0			0
$67$	3.43649	−	5.95218i	0.419834	−	0.727174i	−0.576088	−	0.817388i	$-0.695422\pi$
$67$	3.43649	−	5.95218i	0.419834	−	0.727174i	0.995922	+	0.0902132i	$0.0287549\pi$
$68$	−0.707107	+	1.22474i	−0.0857493	+	0.148522i
$69$		0			0
$70$		0			0
$71$	9.87298			1.17171			0.585854	−	0.810417i	$-0.300759\pi$
$71$	9.87298			1.17171			0.585854	+	0.810417i	$0.300759\pi$
$72$		0			0
$73$	−4.42227			−0.517587			−0.258794	−	0.965933i	$-0.583325\pi$
$73$	−4.42227			−0.517587			−0.258794	+	0.965933i	$0.583325\pi$
$74$	2.87298	+	4.97615i	0.333978	+	0.578466i
$75$		0			0
$76$	−3.13707	+	5.43357i	−0.359847	+	0.623273i
$77$		0			0
$78$		0			0
$79$	0.936492	+	1.62205i	0.105364	+	0.182495i	0.913887	−	0.405969i	$-0.133066\pi$
$79$	0.936492	+	1.62205i	0.105364	+	0.182495i	−0.808523	+	0.588464i	$0.799733\pi$
$80$	−3.44572			−0.385243
$81$		0			0
$82$	−5.65685			−0.624695
$83$	1.32440	+	2.29393i	0.145372	+	0.251791i	0.929512	−	0.368793i	$-0.120229\pi$
$83$	1.32440	+	2.29393i	0.145372	+	0.251791i	−0.784140	+	0.620584i	$0.786896\pi$
$84$		0			0
$85$	2.43649	−	4.22013i	0.264275	−	0.457737i
$86$	0.563508	−	0.976025i	0.0607647	−	0.105247i
$87$		0			0
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	7.07107			0.749532			0.374766	−	0.927119i	$-0.377723\pi$
$89$	7.07107			0.749532			0.374766	+	0.927119i	$0.377723\pi$
$90$		0			0
$91$		0			0
$92$	−4.37298	−	7.57423i	−0.455915	−	0.789668i
$93$		0			0
$94$	−2.03151	+	3.51867i	−0.209534	+	0.362923i
$95$	10.8095	−	18.7226i	1.10903	−	1.92089i
$96$		0			0
$97$	7.50873	+	13.0055i	0.762396	+	1.32051i	0.941612	+	0.336699i	$0.109311\pi$
$97$	7.50873	+	13.0055i	0.762396	+	1.32051i	−0.179216	+	0.983810i	$0.557356\pi$
$98$		0			0
$99$		0			0
$100$	6.87298			0.687298
$101$	6.67261	+	11.5573i	0.663949	+	1.14999i	0.979569	+	0.201108i	$0.0644542\pi$
$101$	6.67261	+	11.5573i	0.663949	+	1.14999i	−0.315620	+	0.948886i	$0.602212\pi$
$102$		0			0
$103$	1.94169	−	3.36311i	0.191321	−	0.331377i	−0.754368	−	0.656452i	$-0.772056\pi$
$103$	1.94169	−	3.36311i	0.191321	−	0.331377i	0.945688	+	0.325075i	$0.105390\pi$
$104$	2.12132	−	3.67423i	0.208013	−	0.360288i
$105$		0			0
$106$	−6.30948	−	10.9283i	−0.612830	−	1.06145i
$107$	−0.254033			−0.0245583			−0.0122792	−	0.999925i	$-0.503909\pi$
$107$	−0.254033			−0.0245583			−0.0122792	+	0.999925i	$0.503909\pi$
$108$		0			0
$109$	16.8730			1.61614			0.808069	−	0.589087i	$-0.200513\pi$
$109$	16.8730			1.61614			0.808069	+	0.589087i	$0.200513\pi$
$110$	6.89144	+	11.9363i	0.657073	+	1.13808i
$111$		0			0
$112$		0			0
$113$	1.93649	−	3.35410i	0.182170	−	0.315527i	−0.760449	−	0.649397i	$-0.775021\pi$
$113$	1.93649	−	3.35410i	0.182170	−	0.315527i	0.942619	+	0.333870i	$0.108355\pi$
$114$		0			0
$115$	15.0681	+	26.0987i	1.40511	+	2.43371i
$116$	−1.12702			−0.104641
$117$		0			0
$118$	8.30565			0.764597
$119$		0			0
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	−3.13707	+	5.43357i	−0.284017	+	0.491932i
$123$		0			0
$124$	2.73861	+	4.74342i	0.245935	+	0.425971i
$125$	−6.45378			−0.577243
$126$		0			0
$127$	−0.745967			−0.0661938			−0.0330969	−	0.999452i	$-0.510537\pi$
$127$	−0.745967			−0.0661938			−0.0330969	+	0.999452i	$0.510537\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−7.30948	+	12.6604i	−0.641083	+	1.11039i
$131$	−6.67261	+	11.5573i	−0.582988	+	1.00977i	0.412135	+	0.911123i	$0.364783\pi$
$131$	−6.67261	+	11.5573i	−0.582988	+	1.00977i	−0.995123	+	0.0986425i	$0.968550\pi$
$132$		0			0
$133$		0			0
$134$	6.87298			0.593735
$135$		0			0
$136$	−1.41421			−0.121268
$137$	−7.74597	−	13.4164i	−0.661783	−	1.14624i	−0.980147	−	0.198273i	$-0.936467\pi$
$137$	−7.74597	−	13.4164i	−0.661783	−	1.14624i	0.318364	−	0.947968i	$-0.396866\pi$
$138$		0			0
$139$	9.93870	−	17.2143i	0.842989	−	1.46010i	−0.0443665	−	0.999015i	$-0.514127\pi$
$139$	9.93870	−	17.2143i	0.842989	−	1.46010i	0.887356	−	0.461085i	$-0.152540\pi$
$140$		0			0
$141$		0			0
$142$	4.93649	+	8.55025i	0.414261	+	0.717521i
$143$	−16.9706			−1.41915
$144$		0			0
$145$	3.88338			0.322497
$146$	−2.21113	−	3.82980i	−0.182995	−	0.316956i
$147$		0			0
$148$	−2.87298	+	4.97615i	−0.236158	+	0.409037i
$149$	−7.87298	+	13.6364i	−0.644980	+	1.11714i	0.339326	+	0.940669i	$0.389801\pi$
$149$	−7.87298	+	13.6364i	−0.644980	+	1.11714i	−0.984306	+	0.176469i	$0.943532\pi$
$150$		0			0
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	0.550645	−	0.834740i	$-0.314382\pi$
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	−0.998228	+	0.0595022i	$0.981049\pi$
$152$	−6.27415			−0.508900
$153$		0			0
$154$		0			0
$155$	−9.43649	−	16.3445i	−0.757957	−	1.31282i
$156$		0			0
$157$	5.96550	−	10.3325i	0.476099	−	0.824627i	−0.523526	−	0.852010i	$-0.675384\pi$
$157$	5.96550	−	10.3325i	0.476099	−	0.824627i	0.999625	+	0.0273823i	$0.00871714\pi$
$158$	−0.936492	+	1.62205i	−0.0745033	+	0.129043i
$159$		0			0
$160$	−1.72286	−	2.98408i	−0.136204	−	0.235912i
$161$		0			0
$162$		0			0
$163$	10.0000			0.783260			0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000			0.783260			0.391630	+	0.920123i	$0.371911\pi$
$164$	−2.82843	−	4.89898i	−0.220863	−	0.382546i
$165$		0			0
$166$	−1.32440	+	2.29393i	−0.102793	+	0.178043i
$167$	−4.77012	+	8.26209i	−0.369123	+	0.639340i	−0.989429	−	0.145021i	$-0.953675\pi$
$167$	−4.77012	+	8.26209i	−0.369123	+	0.639340i	0.620306	+	0.784360i	$0.287009\pi$
$168$		0			0
$169$	−2.50000	−	4.33013i	−0.192308	−	0.333087i
$170$	4.87298			0.373741
$171$		0			0
$172$	1.12702			0.0859342
$173$	−6.36396	−	11.0227i	−0.483843	−	0.838041i	0.515985	−	0.856598i	$-0.327426\pi$
$173$	−6.36396	−	11.0227i	−0.483843	−	0.838041i	−0.999828	+	0.0185571i	$0.994093\pi$
$174$		0			0
$175$		0			0
$176$	2.00000	−	3.46410i	0.150756	−	0.261116i
$177$		0			0
$178$	3.53553	+	6.12372i	0.264999	+	0.458993i
$179$	6.87298			0.513711			0.256855	−	0.966450i	$-0.417314\pi$
$179$	6.87298			0.513711			0.256855	+	0.966450i	$0.417314\pi$
$180$		0			0
$181$	13.3452			0.991942			0.495971	−	0.868339i	$-0.334812\pi$
$181$	13.3452			0.991942			0.495971	+	0.868339i	$0.334812\pi$
$182$		0			0
$183$		0			0
$184$	4.37298	−	7.57423i	0.322381	−	0.558380i
$185$	9.89949	−	17.1464i	0.727825	−	1.26063i
$186$		0			0
$187$	2.82843	+	4.89898i	0.206835	+	0.358249i
$188$	−4.06301			−0.296326
$189$		0			0
$190$	21.6190			1.56840
$191$	−3.06351	−	5.30615i	−0.221668	−	0.383940i	0.733647	−	0.679531i	$-0.237817\pi$
$191$	−3.06351	−	5.30615i	−0.221668	−	0.383940i	−0.955314	+	0.295591i	$0.904483\pi$
$192$		0			0
$193$	−11.9365	+	20.6746i	−0.859207	+	1.48819i	0.0134785	+	0.999909i	$0.495710\pi$
$193$	−11.9365	+	20.6746i	−0.859207	+	1.48819i	−0.872686	+	0.488282i	$0.837624\pi$
$194$	−7.50873	+	13.0055i	−0.539096	+	0.933741i
$195$		0			0
$196$		0			0
$197$	−16.6190			−1.18405			−0.592026	−	0.805919i	$-0.701672\pi$
$197$	−16.6190			−1.18405			−0.592026	+	0.805919i	$0.701672\pi$
$198$		0			0
$199$	−12.1890			−0.864058			−0.432029	−	0.901860i	$-0.642202\pi$
$199$	−12.1890			−0.864058			−0.432029	+	0.901860i	$0.642202\pi$
$200$	3.43649	+	5.95218i	0.242997	+	0.420883i
$201$		0			0
$202$	−6.67261	+	11.5573i	−0.469483	+	0.813168i
$203$		0			0
$204$		0			0
$205$	9.74597	+	16.8805i	0.680688	+	1.17899i
$206$	3.88338			0.270568
$207$		0			0
$208$	4.24264			0.294174
$209$	12.5483	+	21.7343i	0.867984	+	1.50339i
$210$		0			0
$211$	−10.3095	+	17.8565i	−0.709734	+	1.22929i	0.255222	+	0.966882i	$0.417851\pi$
$211$	−10.3095	+	17.8565i	−0.709734	+	1.22929i	−0.964956	+	0.262412i	$0.915482\pi$
$212$	6.30948	−	10.9283i	0.433337	−	0.750561i
$213$		0			0
$214$	−0.127017	−	0.219999i	−0.00868268	−	0.0150388i
$215$	−3.88338			−0.264845
$216$		0			0
$217$		0			0
$218$	8.43649	+	14.6124i	0.571391	+	0.989679i
$219$		0			0
$220$	−6.89144	+	11.9363i	−0.464621	+	0.804747i
$221$	−3.00000	+	5.19615i	−0.201802	+	0.349531i
$222$		0			0
$223$	−11.2239	−	19.4404i	−0.751608	−	1.30182i	−0.947043	−	0.321106i	$-0.895945\pi$
$223$	−11.2239	−	19.4404i	−0.751608	−	1.30182i	0.195436	−	0.980717i	$-0.437388\pi$
$224$		0			0
$225$		0			0
$226$	3.87298			0.257627
$227$	−5.16858	−	8.95224i	−0.343051	−	0.594181i	0.641947	−	0.766749i	$-0.278127\pi$
$227$	−5.16858	−	8.95224i	−0.343051	−	0.594181i	−0.984998	+	0.172568i	$0.944794\pi$
$228$		0			0
$229$	6.67261	−	11.5573i	0.440938	−	0.763728i	−0.556821	−	0.830632i	$-0.687979\pi$
$229$	6.67261	−	11.5573i	0.440938	−	0.763728i	0.997759	+	0.0669049i	$0.0213124\pi$
$230$	−15.0681	+	26.0987i	−0.993559	+	1.72090i
$231$		0			0
$232$	−0.563508	−	0.976025i	−0.0369961	−	0.0640792i
$233$	−7.25403			−0.475228			−0.237614	−	0.971360i	$-0.576365\pi$
$233$	−7.25403			−0.475228			−0.237614	+	0.971360i	$0.576365\pi$
$234$		0			0
$235$	14.0000			0.913259
$236$	4.15283	+	7.19291i	0.270326	+	0.468218i
$237$		0			0
$238$		0			0
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	−0.999854	−	0.0170808i	$-0.994563\pi$
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	0.514719	+	0.857359i	$0.327896\pi$
$240$		0			0
$241$	−11.8412	−	20.5095i	−0.762758	−	1.32114i	−0.941424	−	0.337226i	$-0.890511\pi$
$241$	−11.8412	−	20.5095i	−0.762758	−	1.32114i	0.178666	−	0.983910i	$-0.442822\pi$
$242$	−5.00000			−0.321412
$243$		0			0
$244$	−6.27415			−0.401661
$245$		0			0
$246$		0			0
$247$	−13.3095	+	23.0527i	−0.846862	+	1.46681i
$248$	−2.73861	+	4.74342i	−0.173902	+	0.301207i
$249$		0			0
$250$	−3.22689	−	5.58913i	−0.204086	−	0.353488i
$251$	9.46183			0.597225			0.298613	−	0.954374i	$-0.403476\pi$
$251$	9.46183			0.597225			0.298613	+	0.954374i	$0.403476\pi$
$252$		0			0
$253$	−34.9839			−2.19942
$254$	−0.372983	−	0.646026i	−0.0234031	−	0.0405353i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.50403	+	2.60505i	−0.0938187	+	0.162499i	−0.909115	−	0.416545i	$-0.863241\pi$
$257$	−1.50403	+	2.60505i	−0.0938187	+	0.162499i	0.815296	+	0.579044i	$0.196574\pi$
$258$		0			0
$259$		0			0
$260$	−14.6190			−0.906629
$261$		0			0
$262$	−13.3452			−0.824470
$263$	−8.80948	−	15.2585i	−0.543216	−	0.940877i	−0.998717	−	0.0506418i	$-0.983873\pi$
$263$	−8.80948	−	15.2585i	−0.543216	−	0.940877i	0.455501	−	0.890235i	$-0.349460\pi$
$264$		0			0
$265$	−21.7407	+	37.6560i	−1.33552	+	2.31319i
$266$		0			0
$267$		0			0
$268$	3.43649	+	5.95218i	0.209917	+	0.363587i
$269$	−2.03151			−0.123863			−0.0619316	−	0.998080i	$-0.519726\pi$
$269$	−2.03151			−0.123863			−0.0619316	+	0.998080i	$0.519726\pi$
$270$		0			0
$271$	−7.07107			−0.429537			−0.214768	−	0.976665i	$-0.568900\pi$
$271$	−7.07107			−0.429537			−0.214768	+	0.976665i	$0.568900\pi$
$272$	−0.707107	−	1.22474i	−0.0428746	−	0.0742611i
$273$		0			0
$274$	7.74597	−	13.4164i	0.467951	−	0.810515i
$275$	13.7460	−	23.8087i	0.828913	−	1.43572i
$276$		0			0
$277$	−7.18246	−	12.4404i	−0.431552	−	0.747470i	0.565455	−	0.824779i	$-0.308701\pi$
$277$	−7.18246	−	12.4404i	−0.431552	−	0.747470i	−0.997007	+	0.0773089i	$0.975367\pi$
$278$	19.8774			1.19217
$279$		0			0
$280$		0			0
$281$	4.37298	+	7.57423i	0.260870	+	0.451841i	0.966473	−	0.256767i	$-0.0826572\pi$
$281$	4.37298	+	7.57423i	0.260870	+	0.451841i	−0.705603	+	0.708607i	$0.749324\pi$
$282$		0			0
$283$	2.51978	−	4.36439i	0.149785	−	0.259436i	−0.781363	−	0.624077i	$-0.785475\pi$
$283$	2.51978	−	4.36439i	0.149785	−	0.259436i	0.931148	+	0.364641i	$0.118808\pi$
$284$	−4.93649	+	8.55025i	−0.292927	+	0.507364i
$285$		0			0
$286$	−8.48528	−	14.6969i	−0.501745	−	0.869048i
$287$		0			0
$288$		0			0
$289$	−15.0000			−0.882353
$290$	1.94169	+	3.36311i	0.114020	+	0.197489i
$291$		0			0
$292$	2.21113	−	3.82980i	0.129397	−	0.224122i
$293$	0.398461	−	0.690154i	0.0232783	−	0.0403192i	−0.854152	−	0.520024i	$-0.825923\pi$
$293$	0.398461	−	0.690154i	0.0232783	−	0.0403192i	0.877430	+	0.479705i	$0.159256\pi$
$294$		0			0
$295$	−14.3095	−	24.7847i	−0.833130	−	1.44302i
$296$	−5.74597			−0.333978
$297$		0			0
$298$	−15.7460			−0.912139
$299$	−18.5530	−	32.1347i	−1.07295	−	1.85840i
$300$		0			0
$301$		0			0
$302$	5.50000	−	9.52628i	0.316489	−	0.548176i
$303$		0			0
$304$	−3.13707	−	5.43357i	−0.179923	−	0.311637i
$305$	21.6190			1.23790
$306$		0			0
$307$	−14.2205			−0.811609			−0.405805	−	0.913960i	$-0.633009\pi$
$307$	−14.2205			−0.811609			−0.405805	+	0.913960i	$0.633009\pi$
$308$		0			0
$309$		0			0
$310$	9.43649	−	16.3445i	0.535957	−	0.928304i
$311$	0.707107	−	1.22474i	0.0400963	−	0.0694489i	−0.845281	−	0.534322i	$-0.820567\pi$
$311$	0.707107	−	1.22474i	0.0400963	−	0.0694489i	0.885377	+	0.464873i	$0.153900\pi$
$312$		0			0
$313$	7.86799	+	13.6278i	0.444725	+	0.770286i	0.998033	−	0.0626904i	$-0.0199681\pi$
$313$	7.86799	+	13.6278i	0.444725	+	0.770286i	−0.553308	+	0.832977i	$0.686635\pi$
$314$	11.9310			0.673305
$315$		0			0
$316$	−1.87298			−0.105364
$317$	12.3095	+	21.3206i	0.691369	+	1.19749i	0.971389	+	0.237492i	$0.0763254\pi$
$317$	12.3095	+	21.3206i	0.691369	+	1.19749i	−0.280020	+	0.959994i	$0.590341\pi$
$318$		0			0
$319$	−2.25403	+	3.90410i	−0.126202	+	0.218588i
$320$	1.72286	−	2.98408i	0.0963108	−	0.166815i
$321$		0			0
$322$		0			0
$323$	8.87298			0.493706
$324$		0			0
$325$	29.1596			1.61748
$326$	5.00000	+	8.66025i	0.276924	+	0.479647i
$327$		0			0
$328$	2.82843	−	4.89898i	0.156174	−	0.270501i
$329$		0			0
$330$		0			0
$331$	−10.1825	−	17.6365i	−0.559679	−	0.969392i	−0.997523	−	0.0703409i	$-0.977591\pi$
$331$	−10.1825	−	17.6365i	−0.559679	−	0.969392i	0.437844	−	0.899051i	$-0.355742\pi$
$332$	−2.64880			−0.145372
$333$		0			0
$334$	−9.54024			−0.522019
$335$	−11.8412	−	20.5095i	−0.646953	−	1.12056i
$336$		0			0
$337$	−7.87298	+	13.6364i	−0.428869	+	0.742822i	−0.996773	−	0.0802722i	$-0.974421\pi$
$337$	−7.87298	+	13.6364i	−0.428869	+	0.742822i	0.567904	+	0.823095i	$0.307754\pi$
$338$	2.50000	−	4.33013i	0.135982	−	0.235528i
$339$		0			0
$340$	2.43649	+	4.22013i	0.132137	+	0.228869i
$341$	21.9089			1.18643
$342$		0			0
$343$		0			0
$344$	0.563508	+	0.976025i	0.0303823	+	0.0526237i
$345$		0			0
$346$	6.36396	−	11.0227i	0.342129	−	0.592584i
$347$	3.87298	−	6.70820i	0.207913	−	0.360115i	−0.743144	−	0.669131i	$-0.766666\pi$
$347$	3.87298	−	6.70820i	0.207913	−	0.360115i	0.951057	+	0.309016i	$0.0999997\pi$
$348$		0			0
$349$	−8.21584	−	14.2302i	−0.439784	−	0.761728i	0.557889	−	0.829916i	$-0.311612\pi$
$349$	−8.21584	−	14.2302i	−0.439784	−	0.761728i	−0.997672	+	0.0681880i	$0.978278\pi$
$350$		0			0
$351$		0			0
$352$	4.00000			0.213201
$353$	−1.94169	−	3.36311i	−0.103346	−	0.179000i	0.809715	−	0.586823i	$-0.199622\pi$
$353$	−1.94169	−	3.36311i	−0.103346	−	0.179000i	−0.913061	+	0.407823i	$0.866288\pi$
$354$		0			0
$355$	17.0098	−	29.4618i	0.902785	−	1.56367i
$356$	−3.53553	+	6.12372i	−0.187383	+	0.324557i
$357$		0			0
$358$	3.43649	+	5.95218i	0.181624	+	0.314582i
$359$	−18.2379			−0.962560			−0.481280	−	0.876567i	$-0.659828\pi$
$359$	−18.2379			−0.962560			−0.481280	+	0.876567i	$0.659828\pi$
$360$		0			0
$361$	20.3649			1.07184
$362$	6.67261	+	11.5573i	0.350704	+	0.607438i
$363$		0			0
$364$		0			0
$365$	−7.61895	+	13.1964i	−0.398794	+	0.690732i
$366$		0			0
$367$	3.44572	+	5.96816i	0.179865	+	0.311535i	0.941834	−	0.336078i	$-0.109101\pi$
$367$	3.44572	+	5.96816i	0.179865	+	0.311535i	−0.761969	+	0.647613i	$0.775767\pi$
$368$	8.74597			0.455915
$369$		0			0
$370$	19.7990			1.02930
$371$		0			0
$372$		0			0
$373$	0.563508	−	0.976025i	0.0291774	−	0.0505367i	−0.851068	−	0.525055i	$-0.824045\pi$
$373$	0.563508	−	0.976025i	0.0291774	−	0.0505367i	0.880245	+	0.474519i	$0.157378\pi$
$374$	−2.82843	+	4.89898i	−0.146254	+	0.253320i
$375$		0			0
$376$	−2.03151	−	3.51867i	−0.104767	−	0.181462i
$377$	−4.78153			−0.246261
$378$		0			0
$379$	26.3649			1.35427			0.677137	−	0.735857i	$-0.263220\pi$
$379$	26.3649			1.35427			0.677137	+	0.735857i	$0.263220\pi$
$380$	10.8095	+	18.7226i	0.554514	+	0.960447i
$381$		0			0
$382$	3.06351	−	5.30615i	0.156743	−	0.271486i
$383$	6.45378	−	11.1783i	0.329773	−	0.571183i	−0.652694	−	0.757622i	$-0.726361\pi$
$383$	6.45378	−	11.1783i	0.329773	−	0.571183i	0.982467	+	0.186439i	$0.0596946\pi$
$384$		0			0
$385$		0			0
$386$	−23.8730			−1.21510
$387$		0			0
$388$	−15.0175			−0.762396
$389$	6.56351	+	11.3683i	0.332783	+	0.576397i	0.983056	−	0.183303i	$-0.0586790\pi$
$389$	6.56351	+	11.3683i	0.332783	+	0.576397i	−0.650273	+	0.759700i	$0.725346\pi$
$390$		0			0
$391$	−6.18433	+	10.7116i	−0.312755	+	0.541708i
$392$		0			0
$393$		0			0
$394$	−8.30948	−	14.3924i	−0.418625	−	0.725080i
$395$	6.45378			0.324725
$396$		0			0
$397$	−7.07107			−0.354887			−0.177443	−	0.984131i	$-0.556783\pi$
$397$	−7.07107			−0.354887			−0.177443	+	0.984131i	$0.556783\pi$
$398$	−6.09452	−	10.5560i	−0.305491	−	0.529125i
$399$		0			0
$400$	−3.43649	+	5.95218i	−0.171825	+	0.297609i
$401$	−1.93649	+	3.35410i	−0.0967038	+	0.167496i	−0.910318	−	0.413909i	$-0.864163\pi$
$401$	−1.93649	+	3.35410i	−0.0967038	+	0.167496i	0.813615	+	0.581405i	$0.197497\pi$
$402$		0			0
$403$	11.6190	+	20.1246i	0.578781	+	1.00248i
$404$	−13.3452			−0.663949
$405$		0			0
$406$		0			0
$407$	11.4919	+	19.9046i	0.569634	+	0.986635i
$408$		0			0
$409$	11.5717	−	20.0428i	0.572186	−	0.991055i	−0.424155	−	0.905589i	$-0.639429\pi$
$409$	11.5717	−	20.0428i	0.572186	−	0.991055i	0.996341	−	0.0854655i	$-0.0272378\pi$
$410$	−9.74597	+	16.8805i	−0.481319	+	0.833669i
$411$		0			0
$412$	1.94169	+	3.36311i	0.0956603	+	0.165688i
$413$		0			0
$414$		0			0
$415$	9.12702			0.448028
$416$	2.12132	+	3.67423i	0.104006	+	0.180144i
$417$		0			0
$418$	−12.5483	+	21.7343i	−0.613757	+	1.06306i
$419$	15.6854	−	27.1679i	0.766280	−	1.32724i	−0.173287	−	0.984871i	$-0.555439\pi$
$419$	15.6854	−	27.1679i	0.766280	−	1.32724i	0.939567	−	0.342365i	$-0.111228\pi$
$420$		0			0
$421$	6.43649	+	11.1483i	0.313695	+	0.543336i	0.979159	−	0.203094i	$-0.0650996\pi$
$421$	6.43649	+	11.1483i	0.313695	+	0.543336i	−0.665464	+	0.746430i	$0.731766\pi$
$422$	−20.6190			−1.00371
$423$		0			0
$424$	12.6190			0.612830
$425$	−4.85993	−	8.41765i	−0.235741	−	0.408316i
$426$		0			0
$427$		0			0
$428$	0.127017	−	0.219999i	0.00613958	−	0.0106341i
$429$		0			0
$430$	−1.94169	−	3.36311i	−0.0936367	−	0.162183i
$431$	21.4919			1.03523			0.517615	−	0.855614i	$-0.326820\pi$
$431$	21.4919			1.03523			0.517615	+	0.855614i	$0.326820\pi$
$432$		0			0
$433$	29.6985			1.42722			0.713609	−	0.700544i	$-0.247059\pi$
$433$	29.6985			1.42722			0.713609	+	0.700544i	$0.247059\pi$
$434$		0			0
$435$		0			0
$436$	−8.43649	+	14.6124i	−0.404035	+	0.699809i
$437$	−27.4367	+	47.5218i	−1.31248	+	2.27328i
$438$		0			0
$439$	−5.47723	−	9.48683i	−0.261414	−	0.452782i	0.705204	−	0.709004i	$-0.250855\pi$
$439$	−5.47723	−	9.48683i	−0.261414	−	0.452782i	−0.966618	+	0.256223i	$0.917522\pi$
$440$	−13.7829			−0.657073
$441$		0			0
$442$	−6.00000			−0.285391
$443$	−7.18246	−	12.4404i	−0.341249	−	0.591060i	0.643416	−	0.765517i	$-0.277517\pi$
$443$	−7.18246	−	12.4404i	−0.341249	−	0.591060i	−0.984665	+	0.174456i	$0.944183\pi$
$444$		0			0
$445$	12.1825	−	21.1006i	0.577504	−	1.00027i
$446$	11.2239	−	19.4404i	0.531467	−	0.920527i
$447$		0			0
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	−22.6274			−1.06548
$452$	1.93649	+	3.35410i	0.0910849	+	0.157764i
$453$		0			0
$454$	5.16858	−	8.95224i	0.242573	−	0.420150i
$455$		0			0
$456$		0			0
$457$	−13.0635	−	22.6267i	−0.611085	−	1.05843i	−0.991058	−	0.133433i	$-0.957400\pi$
$457$	−13.0635	−	22.6267i	−0.611085	−	1.05843i	0.379973	−	0.924998i	$-0.375933\pi$
$458$	13.3452			0.623581
$459$		0			0
$460$	−30.1361			−1.40511
$461$	−14.1813	−	24.5628i	−0.660491	−	1.14400i	−0.980487	−	0.196585i	$-0.937015\pi$
$461$	−14.1813	−	24.5628i	−0.660491	−	1.14400i	0.319996	−	0.947419i	$-0.396318\pi$
$462$		0			0
$463$	0.809475	−	1.40205i	0.0376195	−	0.0651589i	−0.846603	−	0.532226i	$-0.821356\pi$
$463$	0.809475	−	1.40205i	0.0376195	−	0.0651589i	0.884222	+	0.467067i	$0.154689\pi$
$464$	0.563508	−	0.976025i	0.0261602	−	0.0453108i
$465$		0			0
$466$	−3.62702	−	6.28218i	−0.168018	−	0.291016i
$467$	6.19574			0.286705			0.143352	−	0.989672i	$-0.454212\pi$
$467$	6.19574			0.286705			0.143352	+	0.989672i	$0.454212\pi$
$468$		0			0
$469$		0			0
$470$	7.00000	+	12.1244i	0.322886	+	0.559255i
$471$		0			0
$472$	−4.15283	+	7.19291i	−0.191149	+	0.331080i
$473$	2.25403	−	3.90410i	0.103641	−	0.179511i
$474$		0			0
$475$	−21.5611	−	37.3448i	−0.989289	−	1.71350i
$476$		0			0
$477$		0			0
$478$	−15.0000			−0.686084
$479$	−1.94169	−	3.36311i	−0.0887182	−	0.153664i	0.818251	−	0.574861i	$-0.194944\pi$
$479$	−1.94169	−	3.36311i	−0.0887182	−	0.153664i	−0.906970	+	0.421196i	$0.861610\pi$
$480$		0			0
$481$	−12.1890	+	21.1120i	−0.555772	+	0.962626i
$482$	11.8412	−	20.5095i	0.539351	−	0.934184i
$483$		0			0
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	51.7460			2.34966
$486$		0			0
$487$	−0.491933			−0.0222916			−0.0111458	−	0.999938i	$-0.503548\pi$
$487$	−0.491933			−0.0222916			−0.0111458	+	0.999938i	$0.503548\pi$
$488$	−3.13707	−	5.43357i	−0.142009	−	0.245966i
$489$		0			0
$490$		0			0
$491$	0.872983	−	1.51205i	0.0393972	−	0.0682379i	−0.845654	−	0.533731i	$-0.820790\pi$
$491$	0.872983	−	1.51205i	0.0393972	−	0.0682379i	0.885052	+	0.465493i	$0.154123\pi$
$492$		0			0
$493$	0.796921	+	1.38031i	0.0358915	+	0.0621659i
$494$	−26.6190			−1.19764
$495$		0			0
$496$	−5.47723			−0.245935
$497$		0			0
$498$		0			0
$499$	14.8730	−	25.7608i	0.665806	−	1.15321i	−0.313260	−	0.949667i	$-0.601421\pi$
$499$	14.8730	−	25.7608i	0.665806	−	1.15321i	0.979066	−	0.203543i	$-0.0652456\pi$
$500$	3.22689	−	5.58913i	0.144311	−	0.249954i
$501$		0			0
$502$	4.73092	+	8.19419i	0.211151	+	0.365724i
$503$	−3.88338			−0.173152			−0.0865758	−	0.996245i	$-0.527592\pi$
$503$	−3.88338			−0.173152			−0.0865758	+	0.996245i	$0.527592\pi$
$504$		0			0
$505$	45.9839			2.04626
$506$	−17.4919	−	30.2969i	−0.777611	−	1.34686i
$507$		0			0
$508$	0.372983	−	0.646026i	0.0165485	−	0.0286628i
$509$	−11.4035	+	19.7515i	−0.505452	+	0.875469i	0.494528	+	0.869162i	$0.335341\pi$
$509$	−11.4035	+	19.7515i	−0.505452	+	0.875469i	−0.999980	+	0.00630722i	$0.997992\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−3.00806			−0.132680
$515$	−6.69052	−	11.5883i	−0.294820	−	0.510643i
$516$		0			0
$517$	−8.12602	+	14.0747i	−0.357382	+	0.619004i
$518$		0			0
$519$		0			0
$520$	−7.30948	−	12.6604i	−0.320542	−	0.555194i
$521$	1.41421			0.0619578			0.0309789	−	0.999520i	$-0.490138\pi$
$521$	1.41421			0.0619578			0.0309789	+	0.999520i	$0.490138\pi$
$522$		0			0
$523$	−18.2836			−0.799484			−0.399742	−	0.916628i	$-0.630900\pi$
$523$	−18.2836			−0.799484			−0.399742	+	0.916628i	$0.630900\pi$
$524$	−6.67261	−	11.5573i	−0.291494	−	0.504883i
$525$		0			0
$526$	8.80948	−	15.2585i	0.384111	−	0.665300i
$527$	3.87298	−	6.70820i	0.168710	−	0.292214i
$528$		0			0
$529$	−26.7460	−	46.3254i	−1.16287	−	2.01415i
$530$	−43.4814			−1.88871
$531$		0			0
$532$		0			0
$533$	−12.0000	−	20.7846i	−0.519778	−	0.900281i
$534$		0			0
$535$	−0.437664	+	0.758056i	−0.0189219	+	0.0327736i
$536$	−3.43649	+	5.95218i	−0.148434	+	0.257095i
$537$		0			0
$538$	−1.01575	−	1.75934i	−0.0437922	−	0.0758504i
$539$		0			0
$540$		0			0
$541$	−38.1109			−1.63851			−0.819257	−	0.573426i	$-0.805614\pi$
$541$	−38.1109			−1.63851			−0.819257	+	0.573426i	$0.805614\pi$
$542$	−3.53553	−	6.12372i	−0.151864	−	0.263036i
$543$		0			0
$544$	0.707107	−	1.22474i	0.0303170	−	0.0525105i
$545$	29.0698	−	50.3503i	1.24521	−	2.15677i
$546$		0			0
$547$	16.4919	+	28.5649i	0.705144	+	1.22135i	0.966639	+	0.256141i	$0.0824511\pi$
$547$	16.4919	+	28.5649i	0.705144	+	1.22135i	−0.261495	+	0.965205i	$0.584216\pi$
$548$	15.4919			0.661783
$549$		0			0
$550$	27.4919			1.17226
$551$	3.53553	+	6.12372i	0.150619	+	0.260879i
$552$		0			0
$553$		0			0
$554$	7.18246	−	12.4404i	0.305153	−	0.528541i
$555$		0			0
$556$	9.93870	+	17.2143i	0.421495	+	0.730050i
$557$	−26.6190			−1.12788			−0.563941	−	0.825815i	$-0.690715\pi$
$557$	−26.6190			−1.12788			−0.563941	+	0.825815i	$0.690715\pi$
$558$		0			0
$559$	4.78153			0.202237
$560$		0			0
$561$		0			0
$562$	−4.37298	+	7.57423i	−0.184463	+	0.319500i
$563$	10.8254	−	18.7502i	0.456238	−	0.790227i	−0.542521	−	0.840042i	$-0.682530\pi$
$563$	10.8254	−	18.7502i	0.456238	−	0.790227i	0.998758	+	0.0498156i	$0.0158634\pi$
$564$		0			0
$565$	−6.67261	−	11.5573i	−0.280719	−	0.486219i
$566$	5.03956			0.211829
$567$		0			0
$568$	−9.87298			−0.414261
$569$	−11.7460	−	20.3446i	−0.492417	−	0.852890i	0.507545	−	0.861625i	$-0.330553\pi$
$569$	−11.7460	−	20.3446i	−0.492417	−	0.852890i	−0.999962	+	0.00873460i	$0.997220\pi$
$570$		0			0
$571$	−15.7460	+	27.2728i	−0.658948	+	1.14133i	0.321940	+	0.946760i	$0.395665\pi$
$571$	−15.7460	+	27.2728i	−0.658948	+	1.14133i	−0.980888	+	0.194572i	$0.937668\pi$
$572$	8.48528	−	14.6969i	0.354787	−	0.614510i
$573$		0			0
$574$		0			0
$575$	60.1109			2.50680
$576$		0			0
$577$	−24.2213			−1.00834			−0.504172	−	0.863603i	$-0.668202\pi$
$577$	−24.2213			−1.00834			−0.504172	+	0.863603i	$0.668202\pi$
$578$	−7.50000	−	12.9904i	−0.311959	−	0.540329i
$579$		0			0
$580$	−1.94169	+	3.36311i	−0.0806244	+	0.139645i
$581$		0			0
$582$		0			0
$583$	−25.2379	−	43.7133i	−1.04525	−	1.81042i
$584$	4.42227			0.182995
$585$		0			0
$586$	0.796921			0.0329205
$587$	−4.28184	−	7.41637i	−0.176731	−	0.306106i	0.764028	−	0.645183i	$-0.223219\pi$
$587$	−4.28184	−	7.41637i	−0.176731	−	0.306106i	−0.940759	+	0.339076i	$0.889885\pi$
$588$		0			0
$589$	17.1825	−	29.7609i	0.707991	−	1.22628i
$590$	14.3095	−	24.7847i	0.589112	−	1.02037i
$591$		0			0
$592$	−2.87298	−	4.97615i	−0.118079	−	0.204519i
$593$	33.7615			1.38642			0.693209	−	0.720736i	$-0.256196\pi$
$593$	33.7615			1.38642			0.693209	+	0.720736i	$0.256196\pi$
$594$		0			0
$595$		0			0
$596$	−7.87298	−	13.6364i	−0.322490	−	0.558569i
$597$		0			0
$598$	18.5530	−	32.1347i	0.758688	−	1.31409i
$599$	−22.6190	+	39.1772i	−0.924185	+	1.60074i	−0.131319	+	0.991340i	$0.541921\pi$
$599$	−22.6190	+	39.1772i	−0.924185	+	1.60074i	−0.792866	+	0.609396i	$0.791412\pi$
$600$		0			0
$601$	−2.39076	−	4.14092i	−0.0975213	−	0.168912i	0.813137	−	0.582073i	$-0.197758\pi$
$601$	−2.39076	−	4.14092i	−0.0975213	−	0.168912i	−0.910658	+	0.413161i	$0.864425\pi$
$602$		0			0
$603$		0			0
$604$	11.0000			0.447584
$605$	8.61430	+	14.9204i	0.350221	+	0.606601i
$606$		0			0
$607$	13.3452	−	23.1146i	0.541666	−	0.938192i	−0.457143	−	0.889393i	$-0.651127\pi$
$607$	13.3452	−	23.1146i	0.541666	−	0.938192i	0.998809	−	0.0487991i	$-0.0155394\pi$
$608$	3.13707	−	5.43357i	0.127225	−	0.220360i
$609$		0			0
$610$	10.8095	+	18.7226i	0.437663	+	0.758054i
$611$	−17.2379			−0.697371
$612$		0			0
$613$	26.6190			1.07513			0.537565	−	0.843223i	$-0.319344\pi$
$613$	26.6190			1.07513			0.537565	+	0.843223i	$0.319344\pi$
$614$	−7.11027	−	12.3154i	−0.286947	−	0.497007i
$615$		0			0
$616$		0			0
$617$	−6.12702	+	10.6123i	−0.246664	+	0.427235i	−0.962598	−	0.270933i	$-0.912668\pi$
$617$	−6.12702	+	10.6123i	−0.246664	+	0.427235i	0.715934	+	0.698168i	$0.246001\pi$
$618$		0			0
$619$	−18.9515	−	32.8249i	−0.761723	−	1.31934i	−0.941962	−	0.335721i	$-0.891020\pi$
$619$	−18.9515	−	32.8249i	−0.761723	−	1.31934i	0.180238	−	0.983623i	$-0.442313\pi$
$620$	18.8730			0.757957
$621$		0			0
$622$	1.41421			0.0567048
$623$		0			0
$624$		0			0
$625$	6.06351	−	10.5023i	0.242540	−	0.420092i
$626$	−7.86799	+	13.6278i	−0.314468	+	0.544675i
$627$		0			0
$628$	5.96550	+	10.3325i	0.238049	+	0.412314i
$629$	8.12602			0.324006
$630$		0			0
$631$	−4.38105			−0.174407			−0.0872034	−	0.996191i	$-0.527793\pi$
$631$	−4.38105			−0.174407			−0.0872034	+	0.996191i	$0.527793\pi$
$632$	−0.936492	−	1.62205i	−0.0372516	−	0.0645217i
$633$		0			0
$634$	−12.3095	+	21.3206i	−0.488872	+	0.846751i
$635$	−1.28520	+	2.22602i	−0.0510014	+	0.0883371i
$636$		0			0
$637$		0			0
$638$	−4.50807			−0.178476
$639$		0			0
$640$	3.44572			0.136204
$641$	8.55544	+	14.8185i	0.337920	+	0.585294i	0.984041	−	0.177941i	$-0.0569435\pi$
$641$	8.55544	+	14.8185i	0.337920	+	0.585294i	−0.646122	+	0.763234i	$0.723610\pi$
$642$		0			0
$643$	1.76206	−	3.05198i	0.0694890	−	0.120358i	−0.829187	−	0.558971i	$-0.811196\pi$
$643$	1.76206	−	3.05198i	0.0694890	−	0.120358i	0.898676	+	0.438612i	$0.144530\pi$
$644$		0			0
$645$		0			0
$646$	4.43649	+	7.68423i	0.174551	+	0.302332i
$647$	−5.47723			−0.215332			−0.107666	−	0.994187i	$-0.534338\pi$
$647$	−5.47723			−0.215332			−0.107666	+	0.994187i	$0.534338\pi$
$648$		0			0
$649$	33.2226			1.30410
$650$	14.5798	+	25.2530i	0.571867	+	0.990502i
$651$		0			0
$652$	−5.00000	+	8.66025i	−0.195815	+	0.339162i
$653$	−7.25403	+	12.5644i	−0.283872	+	0.491681i	−0.972335	−	0.233590i	$-0.924952\pi$
$653$	−7.25403	+	12.5644i	−0.283872	+	0.491681i	0.688463	+	0.725272i	$0.258286\pi$
$654$		0			0
$655$	22.9919	+	39.8232i	0.898369	+	1.55602i
$656$	5.65685			0.220863
$657$		0			0
$658$		0			0
$659$	14.5635	+	25.2247i	0.567314	+	0.982616i	0.996830	+	0.0795572i	$0.0253506\pi$
$659$	14.5635	+	25.2247i	0.567314	+	0.982616i	−0.429517	+	0.903059i	$0.641316\pi$
$660$		0			0
$661$	−23.1043	+	40.0178i	−0.898652	+	1.55651i	−0.0694345	+	0.997587i	$0.522119\pi$
$661$	−23.1043	+	40.0178i	−0.898652	+	1.55651i	−0.829218	+	0.558925i	$0.811214\pi$
$662$	10.1825	−	17.6365i	0.395752	−	0.685463i
$663$		0			0
$664$	−1.32440	−	2.29393i	−0.0513967	−	0.0890216i
$665$		0			0
$666$		0			0
$667$	−9.85685			−0.381659
$668$	−4.77012	−	8.26209i	−0.184561	−	0.319670i
$669$		0			0
$670$	11.8412	−	20.5095i	0.457465	−	0.792353i
$671$	−12.5483	+	21.7343i	−0.484421	+	0.839043i
$672$		0			0
$673$	−7.11895	−	12.3304i	−0.274415	−	0.475301i	0.695572	−	0.718456i	$-0.255151\pi$
$673$	−7.11895	−	12.3304i	−0.274415	−	0.475301i	−0.969987	+	0.243155i	$0.921818\pi$
$674$	−15.7460			−0.606512
$675$		0			0
$676$	5.00000			0.192308
$677$	−6.36396	−	11.0227i	−0.244587	−	0.423637i	0.717428	−	0.696632i	$-0.245319\pi$
$677$	−6.36396	−	11.0227i	−0.244587	−	0.423637i	−0.962015	+	0.272995i	$0.911986\pi$
$678$		0			0
$679$		0			0
$680$	−2.43649	+	4.22013i	−0.0934352	+	0.161834i
$681$		0			0
$682$	10.9545	+	18.9737i	0.419468	+	0.726539i
$683$	−7.74597			−0.296391			−0.148196	−	0.988958i	$-0.547347\pi$
$683$	−7.74597			−0.296391			−0.148196	+	0.988958i	$0.547347\pi$
$684$		0			0
$685$	−53.3809			−2.03958
$686$		0			0
$687$		0			0
$688$	−0.563508	+	0.976025i	−0.0214836	+	0.0372106i
$689$	26.7688	−	46.3650i	1.01981	−	1.76637i
$690$		0			0
$691$	8.52448	+	14.7648i	0.324287	+	0.561681i	0.981368	−	0.192139i	$-0.0615424\pi$
$691$	8.52448	+	14.7648i	0.324287	+	0.561681i	−0.657081	+	0.753820i	$0.728209\pi$
$692$	12.7279			0.483843
$693$		0			0
$694$	7.74597			0.294033
$695$	−34.2460	−	59.3158i	−1.29902	−	2.24997i
$696$		0			0
$697$	−4.00000	+	6.92820i	−0.151511	+	0.262424i
$698$	8.21584	−	14.2302i	0.310974	−	0.538623i
$699$		0			0
$700$		0			0
$701$	16.2540			0.613906			0.306953	−	0.951725i	$-0.400690\pi$
$701$	16.2540			0.613906			0.306953	+	0.951725i	$0.400690\pi$
$702$		0			0
$703$	36.0510			1.35969
$704$	2.00000	+	3.46410i	0.0753778	+	0.130558i
$705$		0			0
$706$	1.94169	−	3.36311i	0.0730765	−	0.126572i
$707$		0			0
$708$		0			0
$709$	26.3649	+	45.6654i	0.990155	+	1.71500i	0.616298	+	0.787513i	$0.288632\pi$
$709$	26.3649	+	45.6654i	0.990155	+	1.71500i	0.373857	+	0.927486i	$0.378035\pi$
$710$	34.0195			1.27673
$711$		0			0
$712$	−7.07107			−0.264999
$713$	23.9518	+	41.4858i	0.897003	+	1.55365i
$714$		0			0
$715$	−29.2379	+	50.6415i	−1.09344	+	1.89389i
$716$	−3.43649	+	5.95218i	−0.128428	+	0.222443i
$717$		0			0
$718$	−9.11895	−	15.7945i	−0.340316	−	0.589445i
$719$	−23.5027			−0.876504			−0.438252	−	0.898852i	$-0.644402\pi$
$719$	−23.5027			−0.876504			−0.438252	+	0.898852i	$0.644402\pi$
$720$		0			0
$721$		0			0
$722$	10.1825	+	17.6365i	0.378952	+	0.656364i
$723$		0			0
$724$	−6.67261	+	11.5573i	−0.247985	+	0.429523i
$725$	3.87298	−	6.70820i	0.143839	−	0.249136i
$726$		0			0
$727$	1.68366	+	2.91618i	0.0624434	+	0.108155i	0.895557	−	0.444947i	$-0.146777\pi$
$727$	1.68366	+	2.91618i	0.0624434	+	0.108155i	−0.833114	+	0.553102i	$0.813444\pi$
$728$		0			0
$729$		0			0
$730$	−15.2379			−0.563980
$731$	−0.796921	−	1.38031i	−0.0294752	−	0.0510525i
$732$		0			0
$733$	−18.5138	+	32.0668i	−0.683823	+	1.18442i	0.289983	+	0.957032i	$0.406350\pi$
$733$	−18.5138	+	32.0668i	−0.683823	+	1.18442i	−0.973805	+	0.227384i	$0.926983\pi$
$734$	−3.44572	+	5.96816i	−0.127184	+	0.220289i
$735$		0			0
$736$	4.37298	+	7.57423i	0.161190	+	0.279190i
$737$	27.4919			1.01268
$738$		0			0
$739$	−30.0000			−1.10357			−0.551784	−	0.833987i	$-0.686053\pi$
$739$	−30.0000			−1.10357			−0.551784	+	0.833987i	$0.686053\pi$
$740$	9.89949	+	17.1464i	0.363913	+	0.630315i
$741$		0			0
$742$		0			0
$743$	−6.12702	+	10.6123i	−0.224778	+	0.389328i	−0.956253	−	0.292541i	$-0.905499\pi$
$743$	−6.12702	+	10.6123i	−0.224778	+	0.389328i	0.731475	+	0.681869i	$0.238833\pi$
$744$		0			0
$745$	27.1281	+	46.9872i	0.993896	+	1.72148i
$746$	1.12702			0.0412630
$747$		0			0
$748$	−5.65685			−0.206835
$749$		0			0
$750$		0			0
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	−0.722718	−	0.691143i	$-0.757107\pi$
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	0.959906	+	0.280321i	$0.0904408\pi$
$752$	2.03151	−	3.51867i	0.0740814	−	0.128313i
$753$		0			0
$754$	−2.39076	−	4.14092i	−0.0870665	−	0.150804i
$755$	−37.9029			−1.37943
$756$		0			0
$757$	31.2379			1.13536			0.567680	−	0.823249i	$-0.307841\pi$
$757$	31.2379			1.13536			0.567680	+	0.823249i	$0.307841\pi$
$758$	13.1825	+	22.8327i	0.478808	+	0.829321i
$759$		0			0
$760$	−10.8095	+	18.7226i	−0.392101	+	0.679139i
$761$	15.2869	−	26.4777i	0.554150	−	0.959816i	−0.443819	−	0.896116i	$-0.646377\pi$
$761$	15.2869	−	26.4777i	0.554150	−	0.959816i	0.997969	−	0.0636995i	$-0.0202899\pi$
$762$		0			0
$763$		0			0
$764$	6.12702			0.221668
$765$		0			0
$766$	12.9076			0.466369
$767$	17.6190	+	30.5169i	0.636183	+	1.10190i
$768$		0			0
$769$	−0.617292	+	1.06918i	−0.0222601	+	0.0385557i	−0.876941	−	0.480598i	$-0.840420\pi$
$769$	−0.617292	+	1.06918i	−0.0222601	+	0.0385557i	0.854681	+	0.519154i	$0.173753\pi$
$770$		0			0
$771$		0			0
$772$	−11.9365	−	20.6746i	−0.429604	−	0.744095i
$773$	−2.03151			−0.0730682			−0.0365341	−	0.999332i	$-0.511632\pi$
$773$	−2.03151			−0.0730682			−0.0365341	+	0.999332i	$0.511632\pi$
$774$		0			0
$775$	−37.6449			−1.35224
$776$	−7.50873	−	13.0055i	−0.269548	−	0.466870i
$777$		0			0
$778$	−6.56351	+	11.3683i	−0.235313	+	0.407574i
$779$	−17.7460	+	30.7369i	−0.635815	+	1.10126i
$780$		0			0
$781$	19.7460	+	34.2010i	0.706566	+	1.22381i
$782$	−12.3687			−0.442303
$783$		0			0
$784$		0			0
$785$	−20.5554	−	35.6031i	−0.733655	−	1.27073i
$786$		0			0
$787$	6.18433	−	10.7116i	0.220448	−	0.381827i	−0.734496	−	0.678613i	$-0.762582\pi$
$787$	6.18433	−	10.7116i	0.220448	−	0.381827i	0.954944	+	0.296786i	$0.0959149\pi$
$788$	8.30948	−	14.3924i	0.296013	−	0.512709i
$789$		0			0
$790$	3.22689	+	5.58913i	0.114808	+	0.198852i
$791$		0			0
$792$		0			0
$793$	−26.6190			−0.945267
$794$	−3.53553	−	6.12372i	−0.125471	−	0.217323i
$795$		0			0
$796$	6.09452	−	10.5560i	0.216014	−	0.374148i
$797$	10.2980	−	17.8366i	0.364772	−	0.631804i	−0.623967	−	0.781450i	$-0.714480\pi$
$797$	10.2980	−	17.8366i	0.364772	−	0.631804i	0.988740	+	0.149646i	$0.0478135\pi$
$798$		0			0
$799$	2.87298	+	4.97615i	0.101639	+	0.176044i
$800$	−6.87298			−0.242997
$801$		0			0
$802$	−3.87298			−0.136760
$803$	−8.84454	−	15.3192i	−0.312117	−	0.540602i
$804$		0			0
$805$		0			0
$806$	−11.6190	+	20.1246i	−0.409260	+	0.708859i
$807$		0			0
$808$	−6.67261	−	11.5573i	−0.234742	−	0.406584i
$809$	−46.7298			−1.64293			−0.821467	−	0.570256i	$-0.806844\pi$
$809$	−46.7298			−1.64293			−0.821467	+	0.570256i	$0.806844\pi$
$810$		0			0
$811$	3.00806			0.105627			0.0528136	−	0.998604i	$-0.483181\pi$
$811$	3.00806			0.105627			0.0528136	+	0.998604i	$0.483181\pi$
$812$		0			0
$813$		0			0
$814$	−11.4919	+	19.9046i	−0.402792	+	0.697656i
$815$	17.2286	−	29.8408i	0.603491	−	1.04528i
$816$		0			0
$817$	−3.53553	−	6.12372i	−0.123693	−	0.214242i
$818$	23.1435			0.809193
$819$		0			0
$820$	−19.4919			−0.680688
$821$	−4.74597	−	8.22026i	−0.165635	−	0.286889i	0.771245	−	0.636538i	$-0.219634\pi$
$821$	−4.74597	−	8.22026i	−0.165635	−	0.286889i	−0.936881	+	0.349649i	$0.886301\pi$
$822$		0			0
$823$	3.12702	−	5.41615i	0.109001	−	0.188795i	−0.806365	−	0.591418i	$-0.798568\pi$
$823$	3.12702	−	5.41615i	0.109001	−	0.188795i	0.915366	+	0.402623i	$0.131902\pi$
$824$	−1.94169	+	3.36311i	−0.0676420	+	0.117159i
$825$		0			0
$826$		0			0
$827$	−48.8730			−1.69948			−0.849740	−	0.527202i	$-0.823241\pi$
$827$	−48.8730			−1.69948			−0.849740	+	0.527202i	$0.823241\pi$
$828$		0			0
$829$	10.6180			0.368779			0.184389	−	0.982853i	$-0.440969\pi$
$829$	10.6180			0.368779			0.184389	+	0.982853i	$0.440969\pi$
$830$	4.56351	+	7.90423i	0.158402	+	0.274360i
$831$		0			0
$832$	−2.12132	+	3.67423i	−0.0735436	+	0.127381i
$833$		0			0
$834$		0			0
$835$	16.4365	+	28.4688i	0.568808	+	0.985205i
$836$	−25.0966			−0.867984
$837$		0			0
$838$	31.3707			1.08368
$839$	−12.8961	−	22.3368i	−0.445224	−	0.771151i	0.552844	−	0.833285i	$-0.313543\pi$
$839$	−12.8961	−	22.3368i	−0.445224	−	0.771151i	−0.998068	+	0.0621340i	$0.980209\pi$
$840$		0			0
$841$	13.8649	−	24.0147i	0.478101	−	0.828094i
$842$	−6.43649	+	11.1483i	−0.221816	+	0.384197i
$843$		0			0
$844$	−10.3095	−	17.8565i	−0.354867	−	0.614647i
$845$	−17.2286			−0.592682
$846$		0			0
$847$		0			0
$848$	6.30948	+	10.9283i	0.216668	+	0.375280i
$849$		0			0
$850$	4.85993	−	8.41765i	0.166694	−	0.288723i
$851$	−25.1270	+	43.5213i	−0.861343	+	1.49189i
$852$		0			0
$853$	−9.06337	−	15.6982i	−0.310324	−	0.537497i	0.668109	−	0.744064i	$-0.267104\pi$
$853$	−9.06337	−	15.6982i	−0.310324	−	0.537497i	−0.978432	+	0.206567i	$0.933771\pi$
$854$		0			0
$855$		0			0
$856$	0.254033			0.00868268
$857$	−12.9076	−	22.3565i	−0.440914	−	0.763685i	0.556844	−	0.830617i	$-0.312012\pi$
$857$	−12.9076	−	22.3565i	−0.440914	−	0.763685i	−0.997758	+	0.0669325i	$0.978679\pi$
$858$		0			0
$859$	15.2869	−	26.4777i	0.521583	−	0.903407i	−0.478102	−	0.878304i	$-0.658675\pi$
$859$	15.2869	−	26.4777i	0.521583	−	0.903407i	0.999685	−	0.0251033i	$-0.00799146\pi$
$860$	1.94169	−	3.36311i	0.0662111	−	0.114681i
$861$		0			0
$862$	10.7460	+	18.6126i	0.366009	+	0.633946i
$863$	43.8730			1.49345			0.746727	−	0.665131i	$-0.231624\pi$
$863$	43.8730			1.49345			0.746727	+	0.665131i	$0.231624\pi$
$864$		0			0
$865$	−43.8569			−1.49118
$866$	14.8492	+	25.7196i	0.504598	+	0.873989i
$867$		0			0
$868$		0			0
$869$	−3.74597	+	6.48820i	−0.127073	+	0.220097i
$870$		0			0
$871$	14.5798	+	25.2530i	0.494018	+	0.855664i
$872$	−16.8730			−0.571391
$873$		0			0
$874$	−54.8735			−1.85612
$875$		0			0
$876$		0			0
$877$	−15.5635	+	26.9568i	−0.525542	+	0.910266i	0.474015	+	0.880517i	$0.342804\pi$
$877$	−15.5635	+	26.9568i	−0.525542	+	0.910266i	−0.999557	+	0.0297493i	$0.990529\pi$
$878$	5.47723	−	9.48683i	0.184847	−	0.320165i
$879$		0			0
$880$	−6.89144	−	11.9363i	−0.232310	−	0.402373i
$881$	26.6904			0.899223			0.449612	−	0.893224i	$-0.351562\pi$
$881$	26.6904			0.899223			0.449612	+	0.893224i	$0.351562\pi$
$882$		0			0
$883$	35.4919			1.19440			0.597199	−	0.802093i	$-0.296280\pi$
$883$	35.4919			1.19440			0.597199	+	0.802093i	$0.296280\pi$
$884$	−3.00000	−	5.19615i	−0.100901	−	0.174766i
$885$		0			0
$886$	7.18246	−	12.4404i	0.241299	−	0.417943i
$887$	−3.88338	+	6.72622i	−0.130391	+	0.225844i	−0.923827	−	0.382809i	$-0.874957\pi$
$887$	−3.88338	+	6.72622i	−0.130391	+	0.225844i	0.793436	+	0.608653i	$0.208290\pi$
$888$		0			0
$889$		0			0
$890$	24.3649			0.816714
$891$		0			0
$892$	22.4478			0.751608
$893$	12.7460	+	22.0767i	0.426528	+	0.738767i
$894$		0			0
$895$	11.8412	−	20.5095i	0.395807	−	0.685558i
$896$		0			0
$897$		0			0
$898$	−4.50000	−	7.79423i	−0.150167	−	0.260097i
$899$	6.17292			0.205879
$900$		0			0
$901$	−17.8459			−0.594533
$902$	−11.3137	−	19.5959i	−0.376705	−	0.652473i
$903$		0			0
$904$	−1.93649	+	3.35410i	−0.0644068	+	0.111556i
$905$	22.9919	−	39.8232i	0.764278	−	1.32377i
$906$		0			0
$907$	−9.30948	−	16.1245i	−0.309116	−	0.535405i	0.669053	−	0.743215i	$-0.266700\pi$
$907$	−9.30948	−	16.1245i	−0.309116	−	0.535405i	−0.978169	+	0.207810i	$0.933366\pi$
$908$	10.3372			0.343051
$909$		0			0
$910$		0			0
$911$	−19.3730	−	33.5550i	−0.641856	−	1.11173i	−0.985018	−	0.172450i	$-0.944832\pi$
$911$	−19.3730	−	33.5550i	−0.641856	−	1.11173i	0.343163	−	0.939276i	$-0.388502\pi$
$912$		0			0
$913$	−5.29760	+	9.17571i	−0.175325	+	0.303672i
$914$	13.0635	−	22.6267i	0.432102	−	0.748423i
$915$		0			0
$916$	6.67261	+	11.5573i	0.220469	+	0.381864i
$917$		0			0
$918$		0			0
$919$	−0.635083			−0.0209495			−0.0104747	−	0.999945i	$-0.503334\pi$
$919$	−0.635083			−0.0209495			−0.0104747	+	0.999945i	$0.503334\pi$
$920$	−15.0681	−	26.0987i	−0.496780	−	0.860448i
$921$		0			0
$922$	14.1813	−	24.5628i	0.467038	−	0.808933i
$923$	−20.9438	+	36.2757i	−0.689372	+	1.19403i
$924$		0			0
$925$	−19.7460	−	34.2010i	−0.649243	−	1.12452i
$926$	1.61895			0.0532020
$927$		0			0
$928$	1.12702			0.0369961
$929$	27.2179	+	47.1428i	0.892991	+	1.54671i	0.836272	+	0.548315i	$0.184730\pi$
$929$	27.2179	+	47.1428i	0.892991	+	1.54671i	0.0567186	+	0.998390i	$0.481936\pi$
$930$		0			0
$931$		0			0
$932$	3.62702	−	6.28218i	0.118807	−	0.205780i
$933$		0			0
$934$	3.09787	+	5.36567i	0.101365	+	0.175570i
$935$	19.4919			0.637454
$936$		0			0
$937$	45.2320			1.47767			0.738833	−	0.673889i	$-0.235377\pi$
$937$	45.2320			1.47767			0.738833	+	0.673889i	$0.235377\pi$
$938$		0			0
$939$		0			0
$940$	−7.00000	+	12.1244i	−0.228315	+	0.395453i
$941$	−12.8569	+	22.2689i	−0.419124	+	0.725945i	−0.995852	−	0.0909922i	$-0.970996\pi$
$941$	−12.8569	+	22.2689i	−0.419124	+	0.725945i	0.576727	+	0.816937i	$0.304330\pi$
$942$		0			0
$943$	−24.7373	−	42.8463i	−0.805558	−	1.39527i
$944$	−8.30565			−0.270326
$945$		0			0
$946$	4.50807			0.146570
$947$	−28.8014	−	49.8855i	−0.935920	−	1.62106i	−0.772985	−	0.634424i	$-0.781237\pi$
$947$	−28.8014	−	49.8855i	−0.935920	−	1.62106i	−0.162935	−	0.986637i	$-0.552096\pi$
$948$		0			0
$949$	9.38105	−	16.2485i	0.304522	−	0.527447i
$950$	21.5611	−	37.3448i	0.699533	−	1.21163i
$951$		0			0
$952$		0			0
$953$	59.4919			1.92713			0.963566	−	0.267469i	$-0.0861874\pi$
$953$	59.4919			1.92713			0.963566	+	0.267469i	$0.0861874\pi$
$954$		0			0
$955$	−21.1120			−0.683168
$956$	−7.50000	−	12.9904i	−0.242567	−	0.420139i
$957$		0			0
$958$	1.94169	−	3.36311i	0.0627332	−	0.108657i
$959$		0			0
$960$		0			0
$961$	0.500000	+	0.866025i	0.0161290	+	0.0279363i
$962$	−24.3781			−0.785981
$963$		0			0
$964$	23.6824			0.762758
$965$	41.1298	+	71.2389i	1.32402	+	2.29326i
$966$		0			0
$967$	−30.2460	+	52.3876i	−0.972645	+	1.68467i	−0.285147	+	0.958484i	$0.592042\pi$
$967$	−30.2460	+	52.3876i	−0.972645	+	1.68467i	−0.687498	+	0.726186i	$0.741291\pi$
$968$	2.50000	−	4.33013i	0.0803530	−	0.139176i
$969$		0			0
$970$	25.8730	+	44.8133i	0.830731	+	1.43887i
$971$	1.49262			0.0479005			0.0239502	−	0.999713i	$-0.492376\pi$
$971$	1.49262			0.0479005			0.0239502	+	0.999713i	$0.492376\pi$
$972$		0			0
$973$		0			0
$974$	−0.245967	−	0.426027i	−0.00788128	−	0.0136508i
$975$		0			0
$976$	3.13707	−	5.43357i	0.100415	−	0.173924i
$977$	22.7460	−	39.3972i	0.727708	−	1.26043i	−0.230142	−	0.973157i	$-0.573919\pi$
$977$	22.7460	−	39.3972i	0.727708	−	1.26043i	0.957850	−	0.287270i	$-0.0927477\pi$
$978$		0			0
$979$	14.1421	+	24.4949i	0.451985	+	0.782860i
$980$		0			0
$981$		0			0
$982$	1.74597			0.0557160
$983$	4.94975	+	8.57321i	0.157872	+	0.273443i	0.934101	−	0.357008i	$-0.116203\pi$
$983$	4.94975	+	8.57321i	0.157872	+	0.273443i	−0.776229	+	0.630451i	$0.782870\pi$
$984$		0			0
$985$	−28.6321	+	49.5923i	−0.912295	+	1.58014i
$986$	−0.796921	+	1.38031i	−0.0253791	+	0.0439580i
$987$		0			0
$988$	−13.3095	−	23.0527i	−0.423431	−	0.733404i
$989$	9.85685			0.313430
$990$		0			0
$991$	−11.7460			−0.373123			−0.186561	−	0.982443i	$-0.559734\pi$
$991$	−11.7460			−0.373123			−0.186561	+	0.982443i	$0.559734\pi$
$992$	−2.73861	−	4.74342i	−0.0869510	−	0.150604i
$993$		0			0
$994$		0			0
$995$	−21.0000	+	36.3731i	−0.665745	+	1.15310i
$996$		0			0
$997$	−13.5640	−	23.4936i	−0.429578	−	0.744050i	0.567258	−	0.823540i	$-0.308004\pi$
$997$	−13.5640	−	23.4936i	−0.429578	−	0.744050i	−0.996836	+	0.0794898i	$0.974671\pi$
$998$	29.7460			0.941592
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.f.s.1765.4		8
3.2	odd	2		882.2.f.p.589.1	yes	8
7.2	even	3		2646.2.h.s.361.1		8
7.3	odd	6		2646.2.e.r.1549.1		8
7.4	even	3		2646.2.e.r.1549.4		8
7.5	odd	6		2646.2.h.s.361.4		8
7.6	odd	2	inner	2646.2.f.s.1765.1		8
9.2	odd	6		882.2.f.p.295.2	✓	8
9.4	even	3		7938.2.a.cd.1.1		4
9.5	odd	6		7938.2.a.cu.1.4		4
9.7	even	3	inner	2646.2.f.s.883.4		8
21.2	odd	6		882.2.h.r.67.4		8
21.5	even	6		882.2.h.r.67.1		8
21.11	odd	6		882.2.e.t.373.2		8
21.17	even	6		882.2.e.t.373.3		8
21.20	even	2		882.2.f.p.589.4	yes	8
63.2	odd	6		882.2.e.t.655.2		8
63.11	odd	6		882.2.h.r.79.4		8
63.13	odd	6		7938.2.a.cd.1.4		4
63.16	even	3		2646.2.e.r.2125.4		8
63.20	even	6		882.2.f.p.295.3	yes	8
63.25	even	3		2646.2.h.s.667.1		8
63.34	odd	6	inner	2646.2.f.s.883.1		8
63.38	even	6		882.2.h.r.79.1		8
63.41	even	6		7938.2.a.cu.1.1		4
63.47	even	6		882.2.e.t.655.3		8
63.52	odd	6		2646.2.h.s.667.4		8
63.61	odd	6		2646.2.e.r.2125.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.t.373.2		8	21.11	odd	6
882.2.e.t.373.3		8	21.17	even	6
882.2.e.t.655.2		8	63.2	odd	6
882.2.e.t.655.3		8	63.47	even	6
882.2.f.p.295.2	✓	8	9.2	odd	6
882.2.f.p.295.3	yes	8	63.20	even	6
882.2.f.p.589.1	yes	8	3.2	odd	2
882.2.f.p.589.4	yes	8	21.20	even	2
882.2.h.r.67.1		8	21.5	even	6
882.2.h.r.67.4		8	21.2	odd	6
882.2.h.r.79.1		8	63.38	even	6
882.2.h.r.79.4		8	63.11	odd	6
2646.2.e.r.1549.1		8	7.3	odd	6
2646.2.e.r.1549.4		8	7.4	even	3
2646.2.e.r.2125.1		8	63.61	odd	6
2646.2.e.r.2125.4		8	63.16	even	3
2646.2.f.s.883.1		8	63.34	odd	6	inner
2646.2.f.s.883.4		8	9.7	even	3	inner
2646.2.f.s.1765.1		8	7.6	odd	2	inner
2646.2.f.s.1765.4		8	1.1	even	1	trivial
2646.2.h.s.361.1		8	7.2	even	3
2646.2.h.s.361.4		8	7.5	odd	6
2646.2.h.s.667.1		8	63.25	even	3
2646.2.h.s.667.4		8	63.52	odd	6
7938.2.a.cd.1.1		4	9.4	even	3
7938.2.a.cd.1.4		4	63.13	odd	6
7938.2.a.cu.1.1		4	63.41	even	6
7938.2.a.cu.1.4		4	9.5	odd	6

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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.72286 - 2.98408i) q^{5} -1.00000 q^{8} +3.44572 q^{10} +(2.00000 + 3.46410i) q^{11} +(-2.12132 + 3.67423i) q^{13} +(-0.500000 - 0.866025i) q^{16} +1.41421 q^{17} +6.27415 q^{19} +(1.72286 + 2.98408i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(-4.37298 + 7.57423i) q^{23} +(-3.43649 - 5.95218i) q^{25} -4.24264 q^{26} +(0.563508 + 0.976025i) q^{29} +(2.73861 - 4.74342i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.707107 + 1.22474i) q^{34} +5.74597 q^{37} +(3.13707 + 5.43357i) q^{38} +(-1.72286 + 2.98408i) q^{40} +(-2.82843 + 4.89898i) q^{41} +(-0.563508 - 0.976025i) q^{43} -4.00000 q^{44} -8.74597 q^{46} +(2.03151 + 3.51867i) q^{47} +(3.43649 - 5.95218i) q^{50} +(-2.12132 - 3.67423i) q^{52} -12.6190 q^{53} +13.7829 q^{55} +(-0.563508 + 0.976025i) q^{58} +(4.15283 - 7.19291i) q^{59} +(3.13707 + 5.43357i) q^{61} +5.47723 q^{62} +1.00000 q^{64} +(7.30948 + 12.6604i) q^{65} +(3.43649 - 5.95218i) q^{67} +(-0.707107 + 1.22474i) q^{68} +9.87298 q^{71} -4.42227 q^{73} +(2.87298 + 4.97615i) q^{74} +(-3.13707 + 5.43357i) q^{76} +(0.936492 + 1.62205i) q^{79} -3.44572 q^{80} -5.65685 q^{82} +(1.32440 + 2.29393i) q^{83} +(2.43649 - 4.22013i) q^{85} +(0.563508 - 0.976025i) q^{86} +(-2.00000 - 3.46410i) q^{88} +7.07107 q^{89} +(-4.37298 - 7.57423i) q^{92} +(-2.03151 + 3.51867i) q^{94} +(10.8095 - 18.7226i) q^{95} +(7.50873 + 13.0055i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} + 16 q^{11} - 4 q^{16} - 16 q^{22} - 4 q^{23} - 12 q^{25} + 20 q^{29} + 4 q^{32} - 16 q^{37} - 20 q^{43} - 32 q^{44} - 8 q^{46} + 12 q^{50} - 8 q^{53} - 20 q^{58} + 8 q^{64}+ \cdots + 40 q^{95}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 + 16 * q^11 - 4 * q^16 - 16 * q^22 - 4 * q^23 - 12 * q^25 + 20 * q^29 + 4 * q^32 - 16 * q^37 - 20 * q^43 - 32 * q^44 - 8 * q^46 + 12 * q^50 - 8 * q^53 - 20 * q^58 + 8 * q^64 + 12 * q^65 + 12 * q^67 + 48 * q^71 - 8 * q^74 - 8 * q^79 + 4 * q^85 + 20 * q^86 - 16 * q^88 - 4 * q^92 + 40 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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