LMFDB - Embedded newform 2646.2.e.r.1549.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2646,2,Mod(1549,2646)] 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([2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2646.1549"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [8,-8,0,8,0,0,0,-8,0,0,16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == 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			1549.4
Root			$1.72286 + 0.178197i$ of defining polynomial
Character	$\chi$	$=$	2646.1549
Dual form			2646.2.e.r.2125.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.72286 + 2.98408i) q^{5} -1.00000 q^{8} +(-1.72286 - 2.98408i) q^{10} +(2.00000 - 3.46410i) q^{11} +(-2.12132 + 3.67423i) q^{13} +1.00000 q^{16} +(-0.707107 - 1.22474i) q^{17} +(-3.13707 + 5.43357i) q^{19} +(1.72286 + 2.98408i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(-4.37298 - 7.57423i) q^{23} +(-3.43649 + 5.95218i) q^{25} +(2.12132 - 3.67423i) q^{26} +(0.563508 + 0.976025i) q^{29} -5.47723 q^{31} -1.00000 q^{32} +(0.707107 + 1.22474i) q^{34} +(-2.87298 + 4.97615i) q^{37} +(3.13707 - 5.43357i) q^{38} +(-1.72286 - 2.98408i) q^{40} +(-2.82843 + 4.89898i) q^{41} +(-0.563508 - 0.976025i) q^{43} +(2.00000 - 3.46410i) q^{44} +(4.37298 + 7.57423i) q^{46} -4.06301 q^{47} +(3.43649 - 5.95218i) q^{50} +(-2.12132 + 3.67423i) q^{52} +(6.30948 + 10.9283i) q^{53} +13.7829 q^{55} +(-0.563508 - 0.976025i) q^{58} -8.30565 q^{59} -6.27415 q^{61} +5.47723 q^{62} +1.00000 q^{64} -14.6190 q^{65} -6.87298 q^{67} +(-0.707107 - 1.22474i) q^{68} +9.87298 q^{71} +(2.21113 + 3.82980i) q^{73} +(2.87298 - 4.97615i) q^{74} +(-3.13707 + 5.43357i) q^{76} -1.87298 q^{79} +(1.72286 + 2.98408i) q^{80} +(2.82843 - 4.89898i) q^{82} +(1.32440 + 2.29393i) q^{83} +(2.43649 - 4.22013i) q^{85} +(0.563508 + 0.976025i) q^{86} +(-2.00000 + 3.46410i) q^{88} +(-3.53553 + 6.12372i) q^{89} +(-4.37298 - 7.57423i) q^{92} +4.06301 q^{94} -21.6190 q^{95} +(7.50873 + 13.0055i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + 16 q^{11} + 8 q^{16} - 16 q^{22} - 4 q^{23} - 12 q^{25} + 20 q^{29} - 8 q^{32} + 8 q^{37} - 20 q^{43} + 16 q^{44} + 4 q^{46} + 12 q^{50} + 4 q^{53} - 20 q^{58} + 8 q^{64}+ \cdots - 80 q^{95}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 + 16 * q^11 + 8 * q^16 - 16 * q^22 - 4 * q^23 - 12 * q^25 + 20 * q^29 - 8 * q^32 + 8 * q^37 - 20 * q^43 + 16 * q^44 + 4 * q^46 + 12 * q^50 + 4 * q^53 - 20 * q^58 + 8 * q^64 - 24 * q^65 - 24 * q^67 + 48 * q^71 - 8 * q^74 + 16 * q^79 + 4 * q^85 + 20 * q^86 - 16 * q^88 - 4 * q^92 - 80 * q^95

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	1.72286	+	2.98408i	0.770486	+	1.33452i	0.937297	+	0.348532i	$0.113320\pi$
$5$	1.72286	+	2.98408i	0.770486	+	1.33452i	−0.166810	+	0.985989i	$0.553347\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.72286	−	2.98408i	−0.544816	−	0.943649i
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$		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
$16$	1.00000			0.250000
$17$	−0.707107	−	1.22474i	−0.171499	−	0.297044i	0.767445	−	0.641114i	$-0.221528\pi$
$17$	−0.707107	−	1.22474i	−0.171499	−	0.297044i	−0.938944	+	0.344070i	$0.888194\pi$
$18$		0			0
$19$	−3.13707	+	5.43357i	−0.719694	+	1.24655i	0.241427	+	0.970419i	$0.422385\pi$
$19$	−3.13707	+	5.43357i	−0.719694	+	1.24655i	−0.961121	+	0.276128i	$0.910949\pi$
$20$	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	−0.811477	−	0.584384i	$-0.801336\pi$
$23$	−4.37298	−	7.57423i	−0.911830	−	1.57934i	−0.100353	−	0.994952i	$-0.531997\pi$
$24$		0			0
$25$	−3.43649	+	5.95218i	−0.687298	+	1.19044i
$26$	2.12132	−	3.67423i	0.416025	−	0.720577i
$27$		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
$31$	−5.47723			−0.983739			−0.491869	−	0.870669i	$-0.663686\pi$
$31$	−5.47723			−0.983739			−0.491869	+	0.870669i	$0.663686\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	0.707107	+	1.22474i	0.121268	+	0.210042i
$35$		0			0
$36$		0			0
$37$	−2.87298	+	4.97615i	−0.472316	+	0.818075i	−0.999498	−	0.0316775i	$-0.989915\pi$
$37$	−2.87298	+	4.97615i	−0.472316	+	0.818075i	0.527183	+	0.849752i	$0.323248\pi$
$38$	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	$0.860721\pi$
$44$	2.00000	−	3.46410i	0.301511	−	0.522233i
$45$		0			0
$46$	4.37298	+	7.57423i	0.644761	+	1.11676i
$47$	−4.06301			−0.592651			−0.296326	−	0.955087i	$-0.595761\pi$
$47$	−4.06301			−0.592651			−0.296326	+	0.955087i	$0.595761\pi$
$48$		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
$53$	6.30948	+	10.9283i	0.866673	+	1.50112i	0.865376	+	0.501123i	$0.167079\pi$
$53$	6.30948	+	10.9283i	0.866673	+	1.50112i	0.00129674	+	0.999999i	$0.499587\pi$
$54$		0			0
$55$	13.7829			1.85848
$56$		0			0
$57$		0			0
$58$	−0.563508	−	0.976025i	−0.0739923	−	0.128158i
$59$	−8.30565			−1.08130			−0.540652	−	0.841246i	$-0.681822\pi$
$59$	−8.30565			−1.08130			−0.540652	+	0.841246i	$0.681822\pi$
$60$		0			0
$61$	−6.27415			−0.803322			−0.401661	−	0.915788i	$-0.631567\pi$
$61$	−6.27415			−0.803322			−0.401661	+	0.915788i	$0.631567\pi$
$62$	5.47723			0.695608
$63$		0			0
$64$	1.00000			0.125000
$65$	−14.6190			−1.81326
$66$		0			0
$67$	−6.87298			−0.839669			−0.419834	−	0.907601i	$-0.637912\pi$
$67$	−6.87298			−0.839669			−0.419834	+	0.907601i	$0.637912\pi$
$68$	−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
$73$	2.21113	+	3.82980i	0.258794	+	0.448244i	0.965919	−	0.258844i	$-0.0833417\pi$
$73$	2.21113	+	3.82980i	0.258794	+	0.448244i	−0.707125	+	0.707088i	$0.750008\pi$
$74$	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
$79$	−1.87298			−0.210727			−0.105364	−	0.994434i	$-0.533601\pi$
$79$	−1.87298			−0.210727			−0.105364	+	0.994434i	$0.533601\pi$
$80$	1.72286	+	2.98408i	0.192622	+	0.333630i
$81$		0			0
$82$	2.82843	−	4.89898i	0.312348	−	0.541002i
$83$	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
$89$	−3.53553	+	6.12372i	−0.374766	+	0.649113i	−0.990292	−	0.139003i	$-0.955610\pi$
$89$	−3.53553	+	6.12372i	−0.374766	+	0.649113i	0.615526	+	0.788116i	$0.288944\pi$
$90$		0			0
$91$		0			0
$92$	−4.37298	−	7.57423i	−0.455915	−	0.789668i
$93$		0			0
$94$	4.06301			0.419068
$95$	−21.6190			−2.21806
$96$		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
$100$	−3.43649	+	5.95218i	−0.343649	+	0.595218i
$101$	6.67261	−	11.5573i	0.663949	−	1.14999i	−0.315620	−	0.948886i	$-0.602212\pi$
$101$	6.67261	−	11.5573i	0.663949	−	1.14999i	0.979569	−	0.201108i	$-0.0644542\pi$
$102$		0			0
$103$	1.94169	+	3.36311i	0.191321	+	0.331377i	0.945688	−	0.325075i	$-0.105390\pi$
$103$	1.94169	+	3.36311i	0.191321	+	0.331377i	−0.754368	+	0.656452i	$0.772056\pi$
$104$	2.12132	−	3.67423i	0.208013	−	0.360288i
$105$		0			0
$106$	−6.30948	−	10.9283i	−0.612830	−	1.06145i
$107$	0.127017	−	0.219999i	0.0122792	−	0.0212681i	−0.859821	−	0.510596i	$-0.829425\pi$
$107$	0.127017	−	0.219999i	0.0122792	−	0.0212681i	0.872100	+	0.489328i	$0.162758\pi$
$108$		0			0
$109$	−8.43649	−	14.6124i	−0.808069	−	1.39962i	−0.914199	−	0.405265i	$-0.867179\pi$
$109$	−8.43649	−	14.6124i	−0.808069	−	1.39962i	0.106130	−	0.994352i	$-0.466154\pi$
$110$	−13.7829			−1.31415
$111$		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
$116$	0.563508	+	0.976025i	0.0523204	+	0.0906217i
$117$		0			0
$118$	8.30565			0.764597
$119$		0			0
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	6.27415			0.568035
$123$		0			0
$124$	−5.47723			−0.491869
$125$	−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	$0.510537\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	14.6190			1.28217
$131$	−6.67261	−	11.5573i	−0.582988	−	1.00977i	−0.995123	−	0.0986425i	$-0.968550\pi$
$131$	−6.67261	−	11.5573i	−0.582988	−	1.00977i	0.412135	−	0.911123i	$-0.364783\pi$
$132$		0			0
$133$		0			0
$134$	6.87298			0.593735
$135$		0			0
$136$	0.707107	+	1.22474i	0.0606339	+	0.105021i
$137$	−7.74597	+	13.4164i	−0.661783	+	1.14624i	0.318364	+	0.947968i	$0.396866\pi$
$137$	−7.74597	+	13.4164i	−0.661783	+	1.14624i	−0.980147	+	0.198273i	$0.936467\pi$
$138$		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
$142$	−9.87298			−0.828522
$143$	8.48528	+	14.6969i	0.709575	+	1.22902i
$144$		0			0
$145$	−1.94169	+	3.36311i	−0.161249	+	0.279291i
$146$	−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	−0.984306	−	0.176469i	$-0.943532\pi$
$149$	−7.87298	−	13.6364i	−0.644980	−	1.11714i	0.339326	−	0.940669i	$-0.389801\pi$
$150$		0			0
$151$	−5.50000	+	9.52628i	−0.447584	+	0.775238i	−0.998228	−	0.0595022i	$-0.981049\pi$
$151$	−5.50000	+	9.52628i	−0.447584	+	0.775238i	0.550645	+	0.834740i	$0.314382\pi$
$152$	3.13707	−	5.43357i	0.254450	−	0.440721i
$153$		0			0
$154$		0			0
$155$	−9.43649	−	16.3445i	−0.757957	−	1.31282i
$156$		0			0
$157$	−11.9310			−0.952198			−0.476099	−	0.879392i	$-0.657950\pi$
$157$	−11.9310			−0.952198			−0.476099	+	0.879392i	$0.657950\pi$
$158$	1.87298			0.149007
$159$		0			0
$160$	−1.72286	−	2.98408i	−0.136204	−	0.235912i
$161$		0			0
$162$		0			0
$163$	−5.00000	+	8.66025i	−0.391630	+	0.678323i	−0.992665	−	0.120900i	$-0.961422\pi$
$163$	−5.00000	+	8.66025i	−0.391630	+	0.678323i	0.601035	+	0.799223i	$0.294755\pi$
$164$	−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
$170$	−2.43649	+	4.22013i	−0.186870	+	0.323669i
$171$		0			0
$172$	−0.563508	−	0.976025i	−0.0429671	−	0.0744212i
$173$	12.7279			0.967686			0.483843	−	0.875155i	$-0.339241\pi$
$173$	12.7279			0.967686			0.483843	+	0.875155i	$0.339241\pi$
$174$		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
$179$	−3.43649	−	5.95218i	−0.256855	−	0.444887i	0.708542	−	0.705668i	$-0.249353\pi$
$179$	−3.43649	−	5.95218i	−0.256855	−	0.444887i	−0.965398	+	0.260782i	$0.916020\pi$
$180$		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
$185$	−19.7990			−1.45565
$186$		0			0
$187$	−5.65685			−0.413670
$188$	−4.06301			−0.296326
$189$		0			0
$190$	21.6190			1.56840
$191$	6.12702			0.443335			0.221668	−	0.975122i	$-0.428850\pi$
$191$	6.12702			0.443335			0.221668	+	0.975122i	$0.428850\pi$
$192$		0			0
$193$	23.8730			1.71841			0.859207	−	0.511627i	$-0.170957\pi$
$193$	23.8730			1.71841			0.859207	+	0.511627i	$0.170957\pi$
$194$	−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
$199$	6.09452	+	10.5560i	0.432029	+	0.748296i	0.997048	−	0.0767818i	$-0.0244645\pi$
$199$	6.09452	+	10.5560i	0.432029	+	0.748296i	−0.565019	+	0.825078i	$0.691131\pi$
$200$	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
$205$	−19.4919			−1.36138
$206$	−1.94169	−	3.36311i	−0.135284	−	0.234319i
$207$		0			0
$208$	−2.12132	+	3.67423i	−0.147087	+	0.254762i
$209$	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
$215$	1.94169	−	3.36311i	0.132422	−	0.229362i
$216$		0			0
$217$		0			0
$218$	8.43649	+	14.6124i	0.571391	+	0.989679i
$219$		0			0
$220$	13.7829			0.929241
$221$	6.00000			0.403604
$222$		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
$226$	−1.93649	+	3.35410i	−0.128814	+	0.223112i
$227$	−5.16858	+	8.95224i	−0.343051	+	0.594181i	−0.984998	−	0.172568i	$-0.944794\pi$
$227$	−5.16858	+	8.95224i	−0.343051	+	0.594181i	0.641947	+	0.766749i	$0.278127\pi$
$228$		0			0
$229$	6.67261	+	11.5573i	0.440938	+	0.763728i	0.997759	−	0.0669049i	$-0.0213124\pi$
$229$	6.67261	+	11.5573i	0.440938	+	0.763728i	−0.556821	+	0.830632i	$0.687979\pi$
$230$	−15.0681	+	26.0987i	−0.993559	+	1.72090i
$231$		0			0
$232$	−0.563508	−	0.976025i	−0.0369961	−	0.0640792i
$233$	3.62702	−	6.28218i	0.237614	−	0.411559i	−0.722415	−	0.691459i	$-0.756968\pi$
$233$	3.62702	−	6.28218i	0.237614	−	0.411559i	0.960029	+	0.279900i	$0.0903014\pi$
$234$		0			0
$235$	−7.00000	−	12.1244i	−0.456630	−	0.790906i
$236$	−8.30565			−0.540652
$237$		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	0.178666	+	0.983910i	$0.442822\pi$
$241$	−11.8412	+	20.5095i	−0.762758	+	1.32114i	−0.941424	+	0.337226i	$0.890511\pi$
$242$	2.50000	+	4.33013i	0.160706	+	0.278351i
$243$		0			0
$244$	−6.27415			−0.401661
$245$		0			0
$246$		0			0
$247$	−13.3095	−	23.0527i	−0.846862	−	1.46681i
$248$	5.47723			0.347804
$249$		0			0
$250$	6.45378			0.408173
$251$	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
$254$	0.745967			0.0468061
$255$		0			0
$256$	1.00000			0.0625000
$257$	−1.50403	−	2.60505i	−0.0938187	−	0.162499i	0.815296	−	0.579044i	$-0.196574\pi$
$257$	−1.50403	−	2.60505i	−0.0938187	−	0.162499i	−0.909115	+	0.416545i	$0.863241\pi$
$258$		0			0
$259$		0			0
$260$	−14.6190			−0.906629
$261$		0			0
$262$	6.67261	+	11.5573i	0.412235	+	0.714012i
$263$	−8.80948	+	15.2585i	−0.543216	+	0.940877i	0.455501	+	0.890235i	$0.349460\pi$
$263$	−8.80948	+	15.2585i	−0.543216	+	0.940877i	−0.998717	+	0.0506418i	$0.983873\pi$
$264$		0			0
$265$	−21.7407	+	37.6560i	−1.33552	+	2.31319i
$266$		0			0
$267$		0			0
$268$	−6.87298			−0.419834
$269$	1.01575	+	1.75934i	0.0619316	+	0.107269i	0.895329	−	0.445406i	$-0.146941\pi$
$269$	1.01575	+	1.75934i	0.0619316	+	0.107269i	−0.833397	+	0.552674i	$0.813607\pi$
$270$		0			0
$271$	3.53553	−	6.12372i	0.214768	−	0.371990i	−0.738433	−	0.674327i	$-0.764434\pi$
$271$	3.53553	−	6.12372i	0.214768	−	0.371990i	0.953201	+	0.302338i	$0.0977670\pi$
$272$	−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	−0.997007	−	0.0773089i	$-0.975367\pi$
$277$	−7.18246	+	12.4404i	−0.431552	+	0.747470i	0.565455	+	0.824779i	$0.308701\pi$
$278$	−9.93870	+	17.2143i	−0.596084	+	1.03245i
$279$		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
$283$	−5.03956			−0.299571			−0.149785	−	0.988719i	$-0.547858\pi$
$283$	−5.03956			−0.299571			−0.149785	+	0.988719i	$0.547858\pi$
$284$	9.87298			0.585854
$285$		0			0
$286$	−8.48528	−	14.6969i	−0.501745	−	0.869048i
$287$		0			0
$288$		0			0
$289$	7.50000	−	12.9904i	0.441176	−	0.764140i
$290$	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
$296$	2.87298	−	4.97615i	0.166989	−	0.289233i
$297$		0			0
$298$	7.87298	+	13.6364i	0.456070	+	0.789936i
$299$	37.1060			2.14590
$300$		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
$305$	−10.8095	−	18.7226i	−0.618949	−	1.07205i
$306$		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
$311$	−1.41421			−0.0801927			−0.0400963	−	0.999196i	$-0.512766\pi$
$311$	−1.41421			−0.0801927			−0.0400963	+	0.999196i	$0.512766\pi$
$312$		0			0
$313$	−15.7360			−0.889450			−0.444725	−	0.895667i	$-0.646699\pi$
$313$	−15.7360			−0.889450			−0.444725	+	0.895667i	$0.646699\pi$
$314$	11.9310			0.673305
$315$		0			0
$316$	−1.87298			−0.105364
$317$	−24.6190			−1.38274			−0.691369	−	0.722502i	$-0.742992\pi$
$317$	−24.6190			−1.38274			−0.691369	+	0.722502i	$0.742992\pi$
$318$		0			0
$319$	4.50807			0.252403
$320$	1.72286	+	2.98408i	0.0963108	+	0.166815i
$321$		0			0
$322$		0			0
$323$	8.87298			0.493706
$324$		0			0
$325$	−14.5798	−	25.2530i	−0.808742	−	1.40078i
$326$	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
$331$	20.3649			1.11936			0.559679	−	0.828710i	$-0.310925\pi$
$331$	20.3649			1.11936			0.559679	+	0.828710i	$0.310925\pi$
$332$	1.32440	+	2.29393i	0.0726859	+	0.125896i
$333$		0			0
$334$	4.77012	−	8.26209i	0.261009	−	0.452081i
$335$	−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
$341$	−10.9545	+	18.9737i	−0.593217	+	1.02748i
$342$		0			0
$343$		0			0
$344$	0.563508	+	0.976025i	0.0303823	+	0.0526237i
$345$		0			0
$346$	−12.7279			−0.684257
$347$	−7.74597			−0.415825			−0.207913	−	0.978147i	$-0.566667\pi$
$347$	−7.74597			−0.415825			−0.207913	+	0.978147i	$0.566667\pi$
$348$		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
$352$	−2.00000	+	3.46410i	−0.106600	+	0.184637i
$353$	−1.94169	+	3.36311i	−0.103346	+	0.179000i	−0.913061	−	0.407823i	$-0.866288\pi$
$353$	−1.94169	+	3.36311i	−0.103346	+	0.179000i	0.809715	+	0.586823i	$0.199622\pi$
$354$		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
$359$	9.11895	−	15.7945i	0.481280	−	0.833601i	−0.518489	−	0.855084i	$-0.673505\pi$
$359$	9.11895	−	15.7945i	0.481280	−	0.833601i	0.999769	+	0.0214830i	$0.00683878\pi$
$360$		0			0
$361$	−10.1825	−	17.6365i	−0.535919	−	0.928239i
$362$	−13.3452			−0.701409
$363$		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	−0.761969	−	0.647613i	$-0.775767\pi$
$367$	3.44572	−	5.96816i	0.179865	−	0.311535i	0.941834	+	0.336078i	$0.109101\pi$
$368$	−4.37298	−	7.57423i	−0.227958	−	0.394834i
$369$		0			0
$370$	19.7990			1.02930
$371$		0			0
$372$		0			0
$373$	0.563508	+	0.976025i	0.0291774	+	0.0505367i	0.880245	−	0.474519i	$-0.157378\pi$
$373$	0.563508	+	0.976025i	0.0291774	+	0.0505367i	−0.851068	+	0.525055i	$0.824045\pi$
$374$	5.65685			0.292509
$375$		0			0
$376$	4.06301			0.209534
$377$	−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	$0.263220\pi$
$380$	−21.6190			−1.10903
$381$		0			0
$382$	−6.12702			−0.313485
$383$	6.45378	+	11.1783i	0.329773	+	0.571183i	0.982467	−	0.186439i	$-0.0596946\pi$
$383$	6.45378	+	11.1783i	0.329773	+	0.571183i	−0.652694	+	0.757622i	$0.726361\pi$
$384$		0			0
$385$		0			0
$386$	−23.8730			−1.21510
$387$		0			0
$388$	7.50873	+	13.0055i	0.381198	+	0.660254i
$389$	6.56351	−	11.3683i	0.332783	−	0.576397i	−0.650273	−	0.759700i	$-0.725346\pi$
$389$	6.56351	−	11.3683i	0.332783	−	0.576397i	0.983056	+	0.183303i	$0.0586790\pi$
$390$		0			0
$391$	−6.18433	+	10.7116i	−0.312755	+	0.541708i
$392$		0			0
$393$		0			0
$394$	16.6190			0.837251
$395$	−3.22689	−	5.58913i	−0.162362	−	0.281220i
$396$		0			0
$397$	3.53553	−	6.12372i	0.177443	−	0.307341i	−0.763561	−	0.645736i	$-0.776551\pi$
$397$	3.53553	−	6.12372i	0.177443	−	0.307341i	0.941004	+	0.338395i	$0.109884\pi$
$398$	−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	0.813615	−	0.581405i	$-0.197497\pi$
$401$	−1.93649	−	3.35410i	−0.0967038	−	0.167496i	−0.910318	+	0.413909i	$0.864163\pi$
$402$		0			0
$403$	11.6190	−	20.1246i	0.578781	−	1.00248i
$404$	6.67261	−	11.5573i	0.331975	−	0.574997i
$405$		0			0
$406$		0			0
$407$	11.4919	+	19.9046i	0.569634	+	0.986635i
$408$		0			0
$409$	−23.1435			−1.14437			−0.572186	−	0.820124i	$-0.693904\pi$
$409$	−23.1435			−1.14437			−0.572186	+	0.820124i	$0.693904\pi$
$410$	19.4919			0.962638
$411$		0			0
$412$	1.94169	+	3.36311i	0.0956603	+	0.165688i
$413$		0			0
$414$		0			0
$415$	−4.56351	+	7.90423i	−0.224014	+	0.388003i
$416$	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	$0.731766\pi$
$422$	10.3095	−	17.8565i	0.501857	−	0.869243i
$423$		0			0
$424$	−6.30948	−	10.9283i	−0.306415	−	0.530727i
$425$	9.71987			0.471483
$426$		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
$431$	−10.7460	−	18.6126i	−0.517615	−	0.896535i	−0.999791	−	0.0204609i	$-0.993487\pi$
$431$	−10.7460	−	18.6126i	−0.517615	−	0.896535i	0.482176	−	0.876075i	$-0.339847\pi$
$432$		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
$437$	54.8735			2.62495
$438$		0			0
$439$	10.9545			0.522827			0.261414	−	0.965227i	$-0.415811\pi$
$439$	10.9545			0.522827			0.261414	+	0.965227i	$0.415811\pi$
$440$	−13.7829			−0.657073
$441$		0			0
$442$	−6.00000			−0.285391
$443$	14.3649			0.682498			0.341249	−	0.939973i	$-0.389150\pi$
$443$	14.3649			0.682498			0.341249	+	0.939973i	$0.389150\pi$
$444$		0			0
$445$	−24.3649			−1.15501
$446$	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
$451$	11.3137	+	19.5959i	0.532742	+	0.922736i
$452$	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
$457$	26.1270			1.22217			0.611085	−	0.791565i	$-0.290733\pi$
$457$	26.1270			1.22217			0.611085	+	0.791565i	$0.290733\pi$
$458$	−6.67261	−	11.5573i	−0.311790	−	0.540037i
$459$		0			0
$460$	15.0681	−	26.0987i	0.702553	−	1.21686i
$461$	−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
$467$	−3.09787	+	5.36567i	−0.143352	+	0.248294i	−0.928757	−	0.370689i	$-0.879122\pi$
$467$	−3.09787	+	5.36567i	−0.143352	+	0.248294i	0.785405	+	0.618983i	$0.212455\pi$
$468$		0			0
$469$		0			0
$470$	7.00000	+	12.1244i	0.322886	+	0.559255i
$471$		0			0
$472$	8.30565			0.382299
$473$	−4.50807			−0.207281
$474$		0			0
$475$	−21.5611	−	37.3448i	−0.989289	−	1.71350i
$476$		0			0
$477$		0			0
$478$	7.50000	−	12.9904i	0.343042	−	0.594166i
$479$	−1.94169	+	3.36311i	−0.0887182	+	0.153664i	−0.906970	−	0.421196i	$-0.861610\pi$
$479$	−1.94169	+	3.36311i	−0.0887182	+	0.153664i	0.818251	+	0.574861i	$0.194944\pi$
$480$		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
$485$	−25.8730	+	44.8133i	−1.17483	+	2.03487i
$486$		0			0
$487$	0.245967	+	0.426027i	0.0111458	+	0.0193051i	0.871545	−	0.490316i	$-0.163119\pi$
$487$	0.245967	+	0.426027i	0.0111458	+	0.0193051i	−0.860399	+	0.509622i	$0.829785\pi$
$488$	6.27415			0.284017
$489$		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
$494$	13.3095	+	23.0527i	0.598822	+	1.03719i
$495$		0			0
$496$	−5.47723			−0.245935
$497$		0			0
$498$		0			0
$499$	14.8730	+	25.7608i	0.665806	+	1.15321i	0.979066	+	0.203543i	$0.0652456\pi$
$499$	14.8730	+	25.7608i	0.665806	+	1.15321i	−0.313260	+	0.949667i	$0.601421\pi$
$500$	−6.45378			−0.288622
$501$		0			0
$502$	−9.46183			−0.422302
$503$	−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
$506$	34.9839			1.55522
$507$		0			0
$508$	−0.745967			−0.0330969
$509$	−11.4035	−	19.7515i	−0.505452	−	0.875469i	−0.999980	−	0.00630722i	$-0.997992\pi$
$509$	−11.4035	−	19.7515i	−0.505452	−	0.875469i	0.494528	−	0.869162i	$-0.335341\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	1.50403	+	2.60505i	0.0663398	+	0.114904i
$515$	−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
$520$	14.6190			0.641083
$521$	−0.707107	−	1.22474i	−0.0309789	−	0.0536570i	0.850120	−	0.526589i	$-0.176529\pi$
$521$	−0.707107	−	1.22474i	−0.0309789	−	0.0536570i	−0.881099	+	0.472931i	$0.843196\pi$
$522$		0			0
$523$	9.14178	−	15.8340i	0.399742	−	0.692373i	−0.593952	−	0.804501i	$-0.702433\pi$
$523$	9.14178	−	15.8340i	0.399742	−	0.692373i	0.993694	+	0.112127i	$0.0357664\pi$
$524$	−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
$530$	21.7407	−	37.6560i	0.944355	−	1.63567i
$531$		0			0
$532$		0			0
$533$	−12.0000	−	20.7846i	−0.519778	−	0.900281i
$534$		0			0
$535$	0.875328			0.0378437
$536$	6.87298			0.296868
$537$		0			0
$538$	−1.01575	−	1.75934i	−0.0437922	−	0.0758504i
$539$		0			0
$540$		0			0
$541$	19.0554	−	33.0050i	0.819257	−	1.41900i	−0.0869727	−	0.996211i	$-0.527719\pi$
$541$	19.0554	−	33.0050i	0.819257	−	1.41900i	0.906230	−	0.422785i	$-0.138947\pi$
$542$	−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	$0.584216\pi$
$548$	−7.74597	+	13.4164i	−0.330891	+	0.573121i
$549$		0			0
$550$	−13.7460	−	23.8087i	−0.586130	−	1.01521i
$551$	−7.07107			−0.301238
$552$		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
$557$	13.3095	+	23.0527i	0.563941	+	0.976774i	0.997147	+	0.0754792i	$0.0240486\pi$
$557$	13.3095	+	23.0527i	0.563941	+	0.976774i	−0.433207	+	0.901295i	$0.642618\pi$
$558$		0			0
$559$	4.78153			0.202237
$560$		0			0
$561$		0			0
$562$	−4.37298	−	7.57423i	−0.184463	−	0.319500i
$563$	−21.6509			−0.912475			−0.456238	−	0.889858i	$-0.650803\pi$
$563$	−21.6509			−0.912475			−0.456238	+	0.889858i	$0.650803\pi$
$564$		0			0
$565$	13.3452			0.561437
$566$	5.03956			0.211829
$567$		0			0
$568$	−9.87298			−0.414261
$569$	23.4919			0.984833			0.492417	−	0.870360i	$-0.336114\pi$
$569$	23.4919			0.984833			0.492417	+	0.870360i	$0.336114\pi$
$570$		0			0
$571$	31.4919			1.31790			0.658948	−	0.752188i	$-0.271002\pi$
$571$	31.4919			1.31790			0.658948	+	0.752188i	$0.271002\pi$
$572$	8.48528	+	14.6969i	0.354787	+	0.614510i
$573$		0			0
$574$		0			0
$575$	60.1109			2.50680
$576$		0			0
$577$	12.1106	+	20.9762i	0.504172	+	0.873252i	0.999988	+	0.00482425i	$0.00153561\pi$
$577$	12.1106	+	20.9762i	0.504172	+	0.873252i	−0.495816	+	0.868427i	$0.665131\pi$
$578$	−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
$583$	50.4758			2.09049
$584$	−2.21113	−	3.82980i	−0.0914974	−	0.158478i
$585$		0			0
$586$	−0.398461	+	0.690154i	−0.0164603	+	0.0285100i
$587$	−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
$593$	−16.8807	+	29.2383i	−0.693209	+	1.20067i	0.277571	+	0.960705i	$0.410470\pi$
$593$	−16.8807	+	29.2383i	−0.693209	+	1.20067i	−0.970781	+	0.239969i	$0.922863\pi$
$594$		0			0
$595$		0			0
$596$	−7.87298	−	13.6364i	−0.322490	−	0.558569i
$597$		0			0
$598$	−37.1060			−1.51738
$599$	45.2379			1.84837			0.924185	−	0.381945i	$-0.124745\pi$
$599$	45.2379			1.84837			0.924185	+	0.381945i	$0.124745\pi$
$600$		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
$604$	−5.50000	+	9.52628i	−0.223792	+	0.387619i
$605$	8.61430	−	14.9204i	0.350221	−	0.606601i
$606$		0			0
$607$	13.3452	+	23.1146i	0.541666	+	0.938192i	0.998809	+	0.0487991i	$0.0155394\pi$
$607$	13.3452	+	23.1146i	0.541666	+	0.938192i	−0.457143	+	0.889393i	$0.651127\pi$
$608$	3.13707	−	5.43357i	0.127225	−	0.220360i
$609$		0			0
$610$	10.8095	+	18.7226i	0.437663	+	0.758054i
$611$	8.61895	−	14.9285i	0.348685	−	0.603941i
$612$		0			0
$613$	−13.3095	−	23.0527i	−0.537565	−	0.931089i	−0.999034	−	0.0439334i	$-0.986011\pi$
$613$	−13.3095	−	23.0527i	−0.537565	−	0.931089i	0.461470	−	0.887156i	$-0.347322\pi$
$614$	14.2205			0.573894
$615$		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	0.180238	+	0.983623i	$0.442313\pi$
$619$	−18.9515	+	32.8249i	−0.761723	+	1.31934i	−0.941962	+	0.335721i	$0.891020\pi$
$620$	−9.43649	−	16.3445i	−0.378979	−	0.656410i
$621$		0			0
$622$	1.41421			0.0567048
$623$		0			0
$624$		0			0
$625$	6.06351	+	10.5023i	0.242540	+	0.420092i
$626$	15.7360			0.628936
$627$		0			0
$628$	−11.9310			−0.476099
$629$	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	$0.527793\pi$
$632$	1.87298			0.0745033
$633$		0			0
$634$	24.6190			0.977743
$635$	−1.28520	−	2.22602i	−0.0510014	−	0.0883371i
$636$		0			0
$637$		0			0
$638$	−4.50807			−0.178476
$639$		0			0
$640$	−1.72286	−	2.98408i	−0.0681020	−	0.117956i
$641$	8.55544	−	14.8185i	0.337920	−	0.585294i	−0.646122	−	0.763234i	$-0.723610\pi$
$641$	8.55544	−	14.8185i	0.337920	−	0.585294i	0.984041	+	0.177941i	$0.0569435\pi$
$642$		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
$646$	−8.87298			−0.349103
$647$	2.73861	+	4.74342i	0.107666	+	0.186483i	0.914824	−	0.403852i	$-0.132329\pi$
$647$	2.73861	+	4.74342i	0.107666	+	0.186483i	−0.807158	+	0.590335i	$0.798996\pi$
$648$		0			0
$649$	−16.6113	+	28.7716i	−0.652051	+	1.12939i
$650$	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	0.688463	−	0.725272i	$-0.258286\pi$
$653$	−7.25403	−	12.5644i	−0.283872	−	0.491681i	−0.972335	+	0.233590i	$0.924952\pi$
$654$		0			0
$655$	22.9919	−	39.8232i	0.898369	−	1.55602i
$656$	−2.82843	+	4.89898i	−0.110432	+	0.191273i
$657$		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
$661$	46.2086			1.79730			0.898652	−	0.438661i	$-0.144547\pi$
$661$	46.2086			1.79730			0.898652	+	0.438661i	$0.144547\pi$
$662$	−20.3649			−0.791505
$663$		0			0
$664$	−1.32440	−	2.29393i	−0.0513967	−	0.0890216i
$665$		0			0
$666$		0			0
$667$	4.92843	−	8.53628i	0.190829	−	0.330526i
$668$	−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	$0.921818\pi$
$674$	7.87298	−	13.6364i	0.303256	−	0.525255i
$675$		0			0
$676$	−2.50000	−	4.33013i	−0.0961538	−	0.166543i
$677$	12.7279			0.489174			0.244587	−	0.969627i	$-0.421348\pi$
$677$	12.7279			0.489174			0.244587	+	0.969627i	$0.421348\pi$
$678$		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
$683$	3.87298	+	6.70820i	0.148196	+	0.256682i	0.930561	−	0.366138i	$-0.119320\pi$
$683$	3.87298	+	6.70820i	0.148196	+	0.256682i	−0.782365	+	0.622820i	$0.785987\pi$
$684$		0			0
$685$	−53.3809			−2.03958
$686$		0			0
$687$		0			0
$688$	−0.563508	−	0.976025i	−0.0214836	−	0.0372106i
$689$	−53.5377			−2.03962
$690$		0			0
$691$	−17.0490			−0.648573			−0.324287	−	0.945959i	$-0.605124\pi$
$691$	−17.0490			−0.648573			−0.324287	+	0.945959i	$0.605124\pi$
$692$	12.7279			0.483843
$693$		0			0
$694$	7.74597			0.294033
$695$	68.4919			2.59805
$696$		0			0
$697$	8.00000			0.303022
$698$	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
$703$	−18.0255	−	31.2211i	−0.679845	−	1.17753i
$704$	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
$709$	−52.7298			−1.98031			−0.990155	−	0.139974i	$-0.955298\pi$
$709$	−52.7298			−1.98031			−0.990155	+	0.139974i	$0.955298\pi$
$710$	−17.0098	−	29.4618i	−0.638365	−	1.10568i
$711$		0			0
$712$	3.53553	−	6.12372i	0.132500	−	0.229496i
$713$	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
$719$	11.7514	−	20.3540i	0.438252	−	0.759075i	−0.559303	−	0.828964i	$-0.688931\pi$
$719$	11.7514	−	20.3540i	0.438252	−	0.759075i	0.997555	+	0.0698884i	$0.0222643\pi$
$720$		0			0
$721$		0			0
$722$	10.1825	+	17.6365i	0.378952	+	0.656364i
$723$		0			0
$724$	13.3452			0.495971
$725$	−7.74597			−0.287678
$726$		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
$730$	7.61895	−	13.1964i	0.281990	−	0.488421i
$731$	−0.796921	+	1.38031i	−0.0294752	+	0.0510525i
$732$		0			0
$733$	−18.5138	−	32.0668i	−0.683823	−	1.18442i	−0.973805	−	0.227384i	$-0.926983\pi$
$733$	−18.5138	−	32.0668i	−0.683823	−	1.18442i	0.289983	−	0.957032i	$-0.406350\pi$
$734$	−3.44572	+	5.96816i	−0.127184	+	0.220289i
$735$		0			0
$736$	4.37298	+	7.57423i	0.161190	+	0.279190i
$737$	−13.7460	+	23.8087i	−0.506339	+	0.877005i
$738$		0			0
$739$	15.0000	+	25.9808i	0.551784	+	0.955718i	0.998146	+	0.0608653i	$0.0193860\pi$
$739$	15.0000	+	25.9808i	0.551784	+	0.955718i	−0.446362	+	0.894852i	$0.647281\pi$
$740$	−19.7990			−0.727825
$741$		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
$746$	−0.563508	−	0.976025i	−0.0206315	−	0.0357348i
$747$		0			0
$748$	−5.65685			−0.206835
$749$		0			0
$750$		0			0
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	0.959906	−	0.280321i	$-0.0904408\pi$
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	−0.722718	+	0.691143i	$0.757107\pi$
$752$	−4.06301			−0.148163
$753$		0			0
$754$	4.78153			0.174133
$755$	−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	$0.307841\pi$
$758$	−26.3649			−0.957617
$759$		0			0
$760$	21.6190			0.784202
$761$	15.2869	+	26.4777i	0.554150	+	0.959816i	0.997969	+	0.0636995i	$0.0202899\pi$
$761$	15.2869	+	26.4777i	0.554150	+	0.959816i	−0.443819	+	0.896116i	$0.646377\pi$
$762$		0			0
$763$		0			0
$764$	6.12702			0.221668
$765$		0			0
$766$	−6.45378	−	11.1783i	−0.233184	−	0.403887i
$767$	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
$772$	23.8730			0.859207
$773$	1.01575	+	1.75934i	0.0365341	+	0.0632789i	0.883714	−	0.468027i	$-0.155035\pi$
$773$	1.01575	+	1.75934i	0.0365341	+	0.0632789i	−0.847180	+	0.531306i	$0.821702\pi$
$774$		0			0
$775$	18.8224	−	32.6014i	0.676122	−	1.17108i
$776$	−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
$782$	6.18433	−	10.7116i	0.221151	−	0.383045i
$783$		0			0
$784$		0			0
$785$	−20.5554	−	35.6031i	−0.733655	−	1.27073i
$786$		0			0
$787$	−12.3687			−0.440895			−0.220448	−	0.975399i	$-0.570752\pi$
$787$	−12.3687			−0.440895			−0.220448	+	0.975399i	$0.570752\pi$
$788$	−16.6190			−0.592026
$789$		0			0
$790$	3.22689	+	5.58913i	0.114808	+	0.198852i
$791$		0			0
$792$		0			0
$793$	13.3095	−	23.0527i	0.472633	−	0.818625i
$794$	−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
$800$	3.43649	−	5.95218i	0.121498	−	0.210441i
$801$		0			0
$802$	1.93649	+	3.35410i	0.0683799	+	0.118437i
$803$	17.6891			0.624234
$804$		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
$809$	23.3649	+	40.4692i	0.821467	+	1.42282i	0.904590	+	0.426283i	$0.140177\pi$
$809$	23.3649	+	40.4692i	0.821467	+	1.42282i	−0.0831232	+	0.996539i	$0.526490\pi$
$810$		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
$815$	−34.4572			−1.20698
$816$		0			0
$817$	7.07107			0.247385
$818$	23.1435			0.809193
$819$		0			0
$820$	−19.4919			−0.680688
$821$	9.49193			0.331271			0.165635	−	0.986187i	$-0.447033\pi$
$821$	9.49193			0.331271			0.165635	+	0.986187i	$0.447033\pi$
$822$		0			0
$823$	−6.25403			−0.218002			−0.109001	−	0.994042i	$-0.534765\pi$
$823$	−6.25403			−0.218002			−0.109001	+	0.994042i	$0.534765\pi$
$824$	−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
$829$	−5.30900	−	9.19547i	−0.184389	−	0.319372i	0.758981	−	0.651113i	$-0.225697\pi$
$829$	−5.30900	−	9.19547i	−0.184389	−	0.319372i	−0.943371	+	0.331741i	$0.892364\pi$
$830$	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
$835$	−32.8730			−1.13762
$836$	12.5483	+	21.7343i	0.433992	+	0.751696i
$837$		0			0
$838$	−15.6854	+	27.1679i	−0.541842	+	0.938498i
$839$	−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
$845$	8.61430	−	14.9204i	0.296341	−	0.513277i
$846$		0			0
$847$		0			0
$848$	6.30948	+	10.9283i	0.216668	+	0.375280i
$849$		0			0
$850$	−9.71987			−0.333389
$851$	50.2540			1.72269
$852$		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
$856$	−0.127017	+	0.219999i	−0.00434134	+	0.00751942i
$857$	−12.9076	+	22.3565i	−0.440914	+	0.763685i	−0.997758	−	0.0669325i	$-0.978679\pi$
$857$	−12.9076	+	22.3565i	−0.440914	+	0.763685i	0.556844	+	0.830617i	$0.312012\pi$
$858$		0			0
$859$	15.2869	+	26.4777i	0.521583	+	0.903407i	0.999685	+	0.0251033i	$0.00799146\pi$
$859$	15.2869	+	26.4777i	0.521583	+	0.903407i	−0.478102	+	0.878304i	$0.658675\pi$
$860$	1.94169	−	3.36311i	0.0662111	−	0.114681i
$861$		0			0
$862$	10.7460	+	18.6126i	0.366009	+	0.633946i
$863$	−21.9365	+	37.9951i	−0.746727	+	1.29337i	0.202657	+	0.979250i	$0.435042\pi$
$863$	−21.9365	+	37.9951i	−0.746727	+	1.29337i	−0.949384	+	0.314119i	$0.898291\pi$
$864$		0			0
$865$	21.9284	+	37.9811i	0.745589	+	1.29140i
$866$	−29.6985			−1.00920
$867$		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
$872$	8.43649	+	14.6124i	0.285696	+	0.494839i
$873$		0			0
$874$	−54.8735			−1.85612
$875$		0			0
$876$		0			0
$877$	−15.5635	−	26.9568i	−0.525542	−	0.910266i	−0.999557	−	0.0297493i	$-0.990529\pi$
$877$	−15.5635	−	26.9568i	−0.525542	−	0.910266i	0.474015	−	0.880517i	$-0.342804\pi$
$878$	−10.9545			−0.369695
$879$		0			0
$880$	13.7829			0.464621
$881$	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	$0.296280\pi$
$884$	6.00000			0.201802
$885$		0			0
$886$	−14.3649			−0.482599
$887$	−3.88338	−	6.72622i	−0.130391	−	0.225844i	0.793436	−	0.608653i	$-0.208290\pi$
$887$	−3.88338	−	6.72622i	−0.130391	−	0.225844i	−0.923827	+	0.382809i	$0.874957\pi$
$888$		0			0
$889$		0			0
$890$	24.3649			0.816714
$891$		0			0
$892$	−11.2239	−	19.4404i	−0.375804	−	0.650911i
$893$	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
$898$	9.00000			0.300334
$899$	−3.08646	−	5.34591i	−0.102939	−	0.178296i
$900$		0			0
$901$	8.92295	−	15.4550i	0.297266	−	0.514881i
$902$	−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	−0.978169	−	0.207810i	$-0.933366\pi$
$907$	−9.30948	+	16.1245i	−0.309116	+	0.535405i	0.669053	+	0.743215i	$0.266700\pi$
$908$	−5.16858	+	8.95224i	−0.171525	+	0.297091i
$909$		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
$913$	10.5952			0.350650
$914$	−26.1270			−0.864205
$915$		0			0
$916$	6.67261	+	11.5573i	0.220469	+	0.381864i
$917$		0			0
$918$		0			0
$919$	0.317542	−	0.549998i	0.0104747	−	0.0181428i	−0.860741	−	0.509044i	$-0.829999\pi$
$919$	0.317542	−	0.549998i	0.0104747	−	0.0181428i	0.871215	+	0.490901i	$0.163332\pi$
$920$	−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
$926$	−0.809475	+	1.40205i	−0.0266010	+	0.0460743i
$927$		0			0
$928$	−0.563508	−	0.976025i	−0.0184981	−	0.0320396i
$929$	−54.4358			−1.78598			−0.892991	−	0.450075i	$-0.851397\pi$
$929$	−54.4358			−1.78598			−0.892991	+	0.450075i	$0.851397\pi$
$930$		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
$935$	−9.74597	−	16.8805i	−0.318727	−	0.552052i
$936$		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
$941$	25.7139			0.838249			0.419124	−	0.907929i	$-0.362337\pi$
$941$	25.7139			0.838249			0.419124	+	0.907929i	$0.362337\pi$
$942$		0			0
$943$	49.4747			1.61112
$944$	−8.30565			−0.270326
$945$		0			0
$946$	4.50807			0.146570
$947$	57.6028			1.87184			0.935920	−	0.352213i	$-0.114571\pi$
$947$	57.6028			1.87184			0.935920	+	0.352213i	$0.114571\pi$
$948$		0			0
$949$	−18.7621			−0.609044
$950$	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
$955$	10.5560	+	18.2835i	0.341584	+	0.591641i
$956$	−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
$961$	−1.00000			−0.0322581
$962$	12.1890	+	21.1120i	0.392990	+	0.680679i
$963$		0			0
$964$	−11.8412	+	20.5095i	−0.381379	+	0.660568i
$965$	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
$971$	−0.746310	+	1.29265i	−0.0239502	+	0.0414830i	−0.877752	−	0.479115i	$-0.840958\pi$
$971$	−0.746310	+	1.29265i	−0.0239502	+	0.0414830i	0.853802	+	0.520598i	$0.174291\pi$
$972$		0			0
$973$		0			0
$974$	−0.245967	−	0.426027i	−0.00788128	−	0.0136508i
$975$		0			0
$976$	−6.27415			−0.200831
$977$	−45.4919			−1.45542			−0.727708	−	0.685887i	$-0.759414\pi$
$977$	−45.4919			−1.45542			−0.727708	+	0.685887i	$0.759414\pi$
$978$		0			0
$979$	14.1421	+	24.4949i	0.451985	+	0.782860i
$980$		0			0
$981$		0			0
$982$	−0.872983	+	1.51205i	−0.0278580	+	0.0482515i
$983$	4.94975	−	8.57321i	0.157872	−	0.273443i	−0.776229	−	0.630451i	$-0.782870\pi$
$983$	4.94975	−	8.57321i	0.157872	−	0.273443i	0.934101	+	0.357008i	$0.116203\pi$
$984$		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
$989$	−4.92843	+	8.53628i	−0.156715	+	0.271438i
$990$		0			0
$991$	5.87298	+	10.1723i	0.186561	+	0.323134i	0.944102	−	0.329655i	$-0.106932\pi$
$991$	5.87298	+	10.1723i	0.186561	+	0.323134i	−0.757540	+	0.652789i	$0.773599\pi$
$992$	5.47723			0.173902
$993$		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	−0.996836	−	0.0794898i	$-0.974671\pi$
$997$	−13.5640	+	23.4936i	−0.429578	+	0.744050i	0.567258	+	0.823540i	$0.308004\pi$
$998$	−14.8730	−	25.7608i	−0.470796	−	0.815443i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.t.373.2		8	3.2	odd	2
882.2.e.t.373.3		8	21.20	even	2
882.2.e.t.655.2		8	63.11	odd	6
882.2.e.t.655.3		8	63.38	even	6
882.2.f.p.295.2	✓	8	63.2	odd	6
882.2.f.p.295.3	yes	8	63.47	even	6
882.2.f.p.589.1	yes	8	21.2	odd	6
882.2.f.p.589.4	yes	8	21.5	even	6
882.2.h.r.67.1		8	21.17	even	6
882.2.h.r.67.4		8	21.11	odd	6
882.2.h.r.79.1		8	63.20	even	6
882.2.h.r.79.4		8	9.2	odd	6
2646.2.e.r.1549.1		8	7.6	odd	2	inner
2646.2.e.r.1549.4		8	1.1	even	1	trivial
2646.2.e.r.2125.1		8	63.52	odd	6	inner
2646.2.e.r.2125.4		8	63.25	even	3	inner
2646.2.f.s.883.1		8	63.61	odd	6
2646.2.f.s.883.4		8	63.16	even	3
2646.2.f.s.1765.1		8	7.5	odd	6
2646.2.f.s.1765.4		8	7.2	even	3
2646.2.h.s.361.1		8	7.4	even	3
2646.2.h.s.361.4		8	7.3	odd	6
2646.2.h.s.667.1		8	9.7	even	3
2646.2.h.s.667.4		8	63.34	odd	6
7938.2.a.cd.1.1		4	63.58	even	3
7938.2.a.cd.1.4		4	63.40	odd	6
7938.2.a.cu.1.1		4	63.5	even	6
7938.2.a.cu.1.4		4	63.23	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.72286 + 2.98408i) q^{5} -1.00000 q^{8} +(-1.72286 - 2.98408i) q^{10} +(2.00000 - 3.46410i) q^{11} +(-2.12132 + 3.67423i) q^{13} +1.00000 q^{16} +(-0.707107 - 1.22474i) q^{17} +(-3.13707 + 5.43357i) q^{19} +(1.72286 + 2.98408i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(-4.37298 - 7.57423i) q^{23} +(-3.43649 + 5.95218i) q^{25} +(2.12132 - 3.67423i) q^{26} +(0.563508 + 0.976025i) q^{29} -5.47723 q^{31} -1.00000 q^{32} +(0.707107 + 1.22474i) q^{34} +(-2.87298 + 4.97615i) q^{37} +(3.13707 - 5.43357i) q^{38} +(-1.72286 - 2.98408i) q^{40} +(-2.82843 + 4.89898i) q^{41} +(-0.563508 - 0.976025i) q^{43} +(2.00000 - 3.46410i) q^{44} +(4.37298 + 7.57423i) q^{46} -4.06301 q^{47} +(3.43649 - 5.95218i) q^{50} +(-2.12132 + 3.67423i) q^{52} +(6.30948 + 10.9283i) q^{53} +13.7829 q^{55} +(-0.563508 - 0.976025i) q^{58} -8.30565 q^{59} -6.27415 q^{61} +5.47723 q^{62} +1.00000 q^{64} -14.6190 q^{65} -6.87298 q^{67} +(-0.707107 - 1.22474i) q^{68} +9.87298 q^{71} +(2.21113 + 3.82980i) q^{73} +(2.87298 - 4.97615i) q^{74} +(-3.13707 + 5.43357i) q^{76} -1.87298 q^{79} +(1.72286 + 2.98408i) q^{80} +(2.82843 - 4.89898i) q^{82} +(1.32440 + 2.29393i) q^{83} +(2.43649 - 4.22013i) q^{85} +(0.563508 + 0.976025i) q^{86} +(-2.00000 + 3.46410i) q^{88} +(-3.53553 + 6.12372i) q^{89} +(-4.37298 - 7.57423i) q^{92} +4.06301 q^{94} -21.6190 q^{95} +(7.50873 + 13.0055i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + 16 q^{11} + 8 q^{16} - 16 q^{22} - 4 q^{23} - 12 q^{25} + 20 q^{29} - 8 q^{32} + 8 q^{37} - 20 q^{43} + 16 q^{44} + 4 q^{46} + 12 q^{50} + 4 q^{53} - 20 q^{58} + 8 q^{64}+ \cdots - 80 q^{95}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 + 16 * q^11 + 8 * q^16 - 16 * q^22 - 4 * q^23 - 12 * q^25 + 20 * q^29 - 8 * q^32 + 8 * q^37 - 20 * q^43 + 16 * q^44 + 4 * q^46 + 12 * q^50 + 4 * q^53 - 20 * q^58 + 8 * q^64 - 24 * q^65 - 24 * q^67 + 48 * q^71 - 8 * q^74 + 16 * q^79 + 4 * q^85 + 20 * q^86 - 16 * q^88 - 4 * q^92 - 80 * q^95

Introduction

L-functions

Modular forms

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Fields

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Database

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