LMFDB - Embedded newform 2646.2.h.s.667.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(361,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("2646.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$21.1284163748$
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			667.4
Root			$1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	2646.667
Dual form			2646.2.h.s.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.44572 q^{5} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.44572 q^{5} -1.00000 q^{8} +(1.72286 + 2.98408i) q^{10} -4.00000 q^{11} +(2.12132 + 3.67423i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(0.707107 + 1.22474i) q^{17} +(3.13707 - 5.43357i) q^{19} +(-1.72286 + 2.98408i) q^{20} +(-2.00000 - 3.46410i) q^{22} +8.74597 q^{23} +6.87298 q^{25} +(-2.12132 + 3.67423i) q^{26} +(0.563508 - 0.976025i) q^{29} +(-2.73861 + 4.74342i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.707107 + 1.22474i) q^{34} +(-2.87298 + 4.97615i) q^{37} +6.27415 q^{38} -3.44572 q^{40} +(2.82843 + 4.89898i) q^{41} +(-0.563508 + 0.976025i) q^{43} +(2.00000 - 3.46410i) q^{44} +(4.37298 + 7.57423i) q^{46} +(-2.03151 - 3.51867i) q^{47} +(3.43649 + 5.95218i) q^{50} -4.24264 q^{52} +(6.30948 + 10.9283i) q^{53} -13.7829 q^{55} +1.12702 q^{58} +(-4.15283 + 7.19291i) q^{59} +(-3.13707 - 5.43357i) q^{61} -5.47723 q^{62} +1.00000 q^{64} +(7.30948 + 12.6604i) q^{65} +(3.43649 - 5.95218i) q^{67} -1.41421 q^{68} +9.87298 q^{71} +(-2.21113 - 3.82980i) q^{73} -5.74597 q^{74} +(3.13707 + 5.43357i) q^{76} +(0.936492 + 1.62205i) q^{79} +(-1.72286 - 2.98408i) q^{80} +(-2.82843 + 4.89898i) q^{82} +(-1.32440 + 2.29393i) q^{83} +(2.43649 + 4.22013i) q^{85} -1.12702 q^{86} +4.00000 q^{88} +(3.53553 - 6.12372i) q^{89} +(-4.37298 + 7.57423i) q^{92} +(2.03151 - 3.51867i) q^{94} +(10.8095 - 18.7226i) q^{95} +(-7.50873 + 13.0055i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 32 q^{11} - 4 q^{16} - 16 q^{22} + 8 q^{23} + 24 q^{25} + 20 q^{29} + 4 q^{32} + 8 q^{37} - 20 q^{43} + 16 q^{44} + 4 q^{46} + 12 q^{50} + 4 q^{53} + 40 q^{58} + 8 q^{64} + 12 q^{65} + 12 q^{67} + 48 q^{71} + 16 q^{74} - 8 q^{79} + 4 q^{85} - 40 q^{86} + 32 q^{88} - 4 q^{92} + 40 q^{95}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 32 * q^11 - 4 * q^16 - 16 * q^22 + 8 * q^23 + 24 * q^25 + 20 * q^29 + 4 * q^32 + 8 * q^37 - 20 * q^43 + 16 * q^44 + 4 * q^46 + 12 * q^50 + 4 * q^53 + 40 * q^58 + 8 * q^64 + 12 * q^65 + 12 * q^67 + 48 * q^71 + 16 * q^74 - 8 * q^79 + 4 * q^85 - 40 * q^86 + 32 * q^88 - 4 * q^92 + 40 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	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
$5$	3.44572			1.54097			0.770486	−	0.637457i	$-0.220013\pi$
$5$	3.44572			1.54097			0.770486	+	0.637457i	$0.220013\pi$
$6$		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
$11$	−4.00000			−1.20605			−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000			−1.20605			−0.603023	+	0.797724i	$0.706037\pi$
$12$		0			0
$13$	2.12132	+	3.67423i	0.588348	+	1.01905i	0.994449	+	0.105221i	$0.0335550\pi$
$13$	2.12132	+	3.67423i	0.588348	+	1.01905i	−0.406100	+	0.913828i	$0.633112\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.707107	+	1.22474i	0.171499	+	0.297044i	0.938944	−	0.344070i	$-0.111806\pi$
$17$	0.707107	+	1.22474i	0.171499	+	0.297044i	−0.767445	+	0.641114i	$0.778472\pi$
$18$		0			0
$19$	3.13707	−	5.43357i	0.719694	−	1.24655i	−0.241427	−	0.970419i	$-0.577615\pi$
$19$	3.13707	−	5.43357i	0.719694	−	1.24655i	0.961121	−	0.276128i	$-0.0890512\pi$
$20$	−1.72286	+	2.98408i	−0.385243	+	0.667261i
$21$		0			0
$22$	−2.00000	−	3.46410i	−0.426401	−	0.738549i
$23$	8.74597			1.82366			0.911830	−	0.410568i	$-0.134669\pi$
$23$	8.74597			1.82366			0.911830	+	0.410568i	$0.134669\pi$
$24$		0			0
$25$	6.87298			1.37460
$26$	−2.12132	+	3.67423i	−0.416025	+	0.720577i
$27$		0			0
$28$		0			0
$29$	0.563508	−	0.976025i	0.104641	−	0.181243i	−0.808951	−	0.587877i	$-0.799964\pi$
$29$	0.563508	−	0.976025i	0.104641	−	0.181243i	0.913591	+	0.406633i	$0.133297\pi$
$30$		0			0
$31$	−2.73861	+	4.74342i	−0.491869	+	0.851943i	−0.999956	−	0.00936313i	$-0.997020\pi$
$31$	−2.73861	+	4.74342i	−0.491869	+	0.851943i	0.508087	+	0.861306i	$0.330353\pi$
$32$	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
$37$	−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	$0.323248\pi$
$38$	6.27415			1.01780
$39$		0			0
$40$	−3.44572			−0.544816
$41$	2.82843	+	4.89898i	0.441726	+	0.765092i	0.997818	−	0.0660290i	$-0.0210330\pi$
$41$	2.82843	+	4.89898i	0.441726	+	0.765092i	−0.556092	+	0.831121i	$0.687700\pi$
$42$		0			0
$43$	−0.563508	+	0.976025i	−0.0859342	+	0.148842i	−0.905789	−	0.423729i	$-0.860721\pi$
$43$	−0.563508	+	0.976025i	−0.0859342	+	0.148842i	0.819855	+	0.572572i	$0.194054\pi$
$44$	2.00000	−	3.46410i	0.301511	−	0.522233i
$45$		0			0
$46$	4.37298	+	7.57423i	0.644761	+	1.11676i
$47$	−2.03151	−	3.51867i	−0.296326	−	0.513251i	0.678967	−	0.734169i	$-0.262428\pi$
$47$	−2.03151	−	3.51867i	−0.296326	−	0.513251i	−0.975292	+	0.220918i	$0.929095\pi$
$48$		0			0
$49$		0			0
$50$	3.43649	+	5.95218i	0.485993	+	0.841765i
$51$		0			0
$52$	−4.24264			−0.588348
$53$	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
$58$	1.12702			0.147985
$59$	−4.15283	+	7.19291i	−0.540652	+	0.936437i	0.458215	+	0.888842i	$0.348489\pi$
$59$	−4.15283	+	7.19291i	−0.540652	+	0.936437i	−0.998867	+	0.0475951i	$0.984844\pi$
$60$		0			0
$61$	−3.13707	−	5.43357i	−0.401661	−	0.695697i	0.592265	−	0.805743i	$-0.298234\pi$
$61$	−3.13707	−	5.43357i	−0.401661	−	0.695697i	−0.993927	+	0.110045i	$0.964900\pi$
$62$	−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	$0.0287549\pi$
$68$	−1.41421			−0.171499
$69$		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	0.707125	−	0.707088i	$-0.249992\pi$
$73$	−2.21113	−	3.82980i	−0.258794	−	0.448244i	−0.965919	+	0.258844i	$0.916658\pi$
$74$	−5.74597			−0.667955
$75$		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	$0.799733\pi$
$80$	−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	$-0.879771\pi$
$83$	−1.32440	+	2.29393i	−0.145372	+	0.251791i	0.784140	+	0.620584i	$0.213104\pi$
$84$		0			0
$85$	2.43649	+	4.22013i	0.264275	+	0.457737i
$86$	−1.12702			−0.121529
$87$		0			0
$88$	4.00000			0.426401
$89$	3.53553	−	6.12372i	0.374766	−	0.649113i	−0.615526	−	0.788116i	$-0.711056\pi$
$89$	3.53553	−	6.12372i	0.374766	−	0.649113i	0.990292	+	0.139003i	$0.0443898\pi$
$90$		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	0.179216	+	0.983810i	$0.442644\pi$
$97$	−7.50873	+	13.0055i	−0.762396	+	1.32051i	−0.941612	+	0.336699i	$0.890689\pi$
$98$		0			0
$99$		0			0
$100$	−3.43649	+	5.95218i	−0.343649	+	0.595218i
$101$	13.3452			1.32790			0.663949	−	0.747778i	$-0.268879\pi$
$101$	13.3452			1.32790			0.663949	+	0.747778i	$0.268879\pi$
$102$		0			0
$103$	3.88338			0.382641			0.191321	−	0.981528i	$-0.438723\pi$
$103$	3.88338			0.382641			0.191321	+	0.981528i	$0.438723\pi$
$104$	−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	$-0.466154\pi$
$110$	−6.89144	−	11.9363i	−0.657073	−	1.13808i
$111$		0			0
$112$		0			0
$113$	1.93649	+	3.35410i	0.182170	+	0.315527i	0.942619	−	0.333870i	$-0.108355\pi$
$113$	1.93649	+	3.35410i	0.182170	+	0.315527i	−0.760449	+	0.649397i	$0.775021\pi$
$114$		0			0
$115$	30.1361			2.81021
$116$	0.563508	+	0.976025i	0.0523204	+	0.0906217i
$117$		0			0
$118$	−8.30565			−0.764597
$119$		0			0
$120$		0			0
$121$	5.00000			0.454545
$122$	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
$131$	−13.3452			−1.16598			−0.582988	−	0.812480i	$-0.698117\pi$
$131$	−13.3452			−1.16598			−0.582988	+	0.812480i	$0.698117\pi$
$132$		0			0
$133$		0			0
$134$	6.87298			0.593735
$135$		0			0
$136$	−0.707107	−	1.22474i	−0.0606339	−	0.105021i
$137$	15.4919			1.32357			0.661783	−	0.749696i	$-0.269800\pi$
$137$	15.4919			1.32357			0.661783	+	0.749696i	$0.269800\pi$
$138$		0			0
$139$	−9.93870	−	17.2143i	−0.842989	−	1.46010i	−0.887356	−	0.461085i	$-0.847460\pi$
$139$	−9.93870	−	17.2143i	−0.842989	−	1.46010i	0.0443665	−	0.999015i	$-0.485873\pi$
$140$		0			0
$141$		0			0
$142$	4.93649	+	8.55025i	0.414261	+	0.717521i
$143$	−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
$149$	15.7460			1.28996			0.644980	−	0.764200i	$-0.276866\pi$
$149$	15.7460			1.28996			0.644980	+	0.764200i	$0.276866\pi$
$150$		0			0
$151$	11.0000			0.895167			0.447584	−	0.894242i	$-0.352285\pi$
$151$	11.0000			0.895167			0.447584	+	0.894242i	$0.352285\pi$
$152$	−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
$157$	−5.96550	+	10.3325i	−0.476099	+	0.824627i	−0.999625	−	0.0273823i	$-0.991283\pi$
$157$	−5.96550	+	10.3325i	−0.476099	+	0.824627i	0.523526	+	0.852010i	$0.324616\pi$
$158$	−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
$163$	−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	$0.294755\pi$
$164$	−5.65685			−0.441726
$165$		0			0
$166$	−2.64880			−0.205587
$167$	4.77012	+	8.26209i	0.369123	+	0.639340i	0.989429	−	0.145021i	$-0.0463248\pi$
$167$	4.77012	+	8.26209i	0.369123	+	0.639340i	−0.620306	+	0.784360i	$0.712991\pi$
$168$		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
$173$	6.36396	+	11.0227i	0.483843	+	0.838041i	0.999828	−	0.0185571i	$-0.00590724\pi$
$173$	6.36396	+	11.0227i	0.483843	+	0.838041i	−0.515985	+	0.856598i	$0.672574\pi$
$174$		0			0
$175$		0			0
$176$	2.00000	+	3.46410i	0.150756	+	0.261116i
$177$		0			0
$178$	7.07107			0.529999
$179$	−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	$-0.665188\pi$
$181$	−13.3452			−0.991942			−0.495971	+	0.868339i	$0.665188\pi$
$182$		0			0
$183$		0			0
$184$	−8.74597			−0.644761
$185$	−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	$0.837624\pi$
$194$	−15.0175			−1.07819
$195$		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	0.565019	−	0.825078i	$-0.308869\pi$
$199$	−6.09452	−	10.5560i	−0.432029	−	0.748296i	−0.997048	+	0.0767818i	$0.975536\pi$
$200$	−6.87298			−0.485993
$201$		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
$206$	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	−0.964956	−	0.262412i	$-0.915482\pi$
$211$	−10.3095	−	17.8565i	−0.709734	−	1.22929i	0.255222	−	0.966882i	$-0.417851\pi$
$212$	−12.6190			−0.866673
$213$		0			0
$214$	0.254033			0.0173654
$215$	−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
$220$	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	−0.195436	−	0.980717i	$-0.562612\pi$
$223$	11.2239	−	19.4404i	0.751608	−	1.30182i	0.947043	−	0.321106i	$-0.104055\pi$
$224$		0			0
$225$		0			0
$226$	−1.93649	+	3.35410i	−0.128814	+	0.223112i
$227$	−10.3372			−0.686101			−0.343051	−	0.939317i	$-0.611460\pi$
$227$	−10.3372			−0.686101			−0.343051	+	0.939317i	$0.611460\pi$
$228$		0			0
$229$	13.3452			0.881877			0.440938	−	0.897537i	$-0.354646\pi$
$229$	13.3452			0.881877			0.440938	+	0.897537i	$0.354646\pi$
$230$	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
$236$	−4.15283	−	7.19291i	−0.270326	−	0.468218i
$237$		0			0
$238$		0			0
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	0.514719	−	0.857359i	$-0.327896\pi$
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	−0.999854	+	0.0170808i	$0.994563\pi$
$240$		0			0
$241$	−23.6824			−1.52552			−0.762758	−	0.646684i	$-0.776155\pi$
$241$	−23.6824			−1.52552			−0.762758	+	0.646684i	$0.776155\pi$
$242$	2.50000	+	4.33013i	0.160706	+	0.278351i
$243$		0			0
$244$	6.27415			0.401661
$245$		0			0
$246$		0			0
$247$	26.6190			1.69372
$248$	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	$-0.596524\pi$
$251$	−9.46183			−0.597225			−0.298613	+	0.954374i	$0.596524\pi$
$252$		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
$257$	−3.00806			−0.187637			−0.0938187	−	0.995589i	$-0.529907\pi$
$257$	−3.00806			−0.187637			−0.0938187	+	0.995589i	$0.529907\pi$
$258$		0			0
$259$		0			0
$260$	−14.6190			−0.906629
$261$		0			0
$262$	−6.67261	−	11.5573i	−0.412235	−	0.714012i
$263$	17.6190			1.08643			0.543216	−	0.839593i	$-0.317207\pi$
$263$	17.6190			1.08643			0.543216	+	0.839593i	$0.317207\pi$
$264$		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
$269$	−1.01575	−	1.75934i	−0.0619316	−	0.107269i	0.833397	−	0.552674i	$-0.186393\pi$
$269$	−1.01575	−	1.75934i	−0.0619316	−	0.107269i	−0.895329	+	0.445406i	$0.853059\pi$
$270$		0			0
$271$	−3.53553	+	6.12372i	−0.214768	+	0.371990i	−0.953201	−	0.302338i	$-0.902233\pi$
$271$	−3.53553	+	6.12372i	−0.214768	+	0.371990i	0.738433	+	0.674327i	$0.235566\pi$
$272$	0.707107	−	1.22474i	0.0428746	−	0.0742611i
$273$		0			0
$274$	7.74597	+	13.4164i	0.467951	+	0.810515i
$275$	−27.4919			−1.65783
$276$		0			0
$277$	14.3649			0.863104			0.431552	−	0.902088i	$-0.357966\pi$
$277$	14.3649			0.863104			0.431552	+	0.902088i	$0.357966\pi$
$278$	9.93870	−	17.2143i	0.596084	−	1.03245i
$279$		0			0
$280$		0			0
$281$	4.37298	−	7.57423i	0.260870	−	0.451841i	−0.705603	−	0.708607i	$-0.749324\pi$
$281$	4.37298	−	7.57423i	0.260870	−	0.451841i	0.966473	+	0.256767i	$0.0826572\pi$
$282$		0			0
$283$	−2.51978	+	4.36439i	−0.149785	+	0.259436i	−0.931148	−	0.364641i	$-0.881192\pi$
$283$	−2.51978	+	4.36439i	−0.149785	+	0.259436i	0.781363	+	0.624077i	$0.214525\pi$
$284$	−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
$289$	7.50000	−	12.9904i	0.441176	−	0.764140i
$290$	3.88338			0.228040
$291$		0			0
$292$	4.42227			0.258794
$293$	−0.398461	−	0.690154i	−0.0232783	−	0.0403192i	0.854152	−	0.520024i	$-0.174077\pi$
$293$	−0.398461	−	0.690154i	−0.0232783	−	0.0403192i	−0.877430	+	0.479705i	$0.840744\pi$
$294$		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
$299$	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
$304$	−6.27415			−0.359847
$305$	−10.8095	−	18.7226i	−0.618949	−	1.07205i
$306$		0			0
$307$	14.2205			0.811609			0.405805	−	0.913960i	$-0.366991\pi$
$307$	14.2205			0.811609			0.405805	+	0.913960i	$0.366991\pi$
$308$		0			0
$309$		0			0
$310$	−18.8730			−1.07191
$311$	−0.707107	+	1.22474i	−0.0400963	+	0.0694489i	−0.885377	−	0.464873i	$-0.846100\pi$
$311$	−0.707107	+	1.22474i	−0.0400963	+	0.0694489i	0.845281	+	0.534322i	$0.179433\pi$
$312$		0			0
$313$	−7.86799	−	13.6278i	−0.444725	−	0.770286i	0.553308	−	0.832977i	$-0.313365\pi$
$313$	−7.86799	−	13.6278i	−0.444725	−	0.770286i	−0.998033	+	0.0626904i	$0.980032\pi$
$314$	−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
$320$	3.44572			0.192622
$321$		0			0
$322$		0			0
$323$	8.87298			0.493706
$324$		0			0
$325$	14.5798	+	25.2530i	0.808742	+	1.40078i
$326$	−10.0000			−0.553849
$327$		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	$-0.355742\pi$
$332$	−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	0.567904	−	0.823095i	$-0.307754\pi$
$337$	−7.87298	−	13.6364i	−0.428869	−	0.742822i	−0.996773	+	0.0802722i	$0.974421\pi$
$338$	−5.00000			−0.271964
$339$		0			0
$340$	−4.87298			−0.264275
$341$	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
$346$	−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	$-0.688388\pi$
$349$	8.21584	−	14.2302i	0.439784	−	0.761728i	0.997672	+	0.0681880i	$0.0217218\pi$
$350$		0			0
$351$		0			0
$352$	−2.00000	+	3.46410i	−0.106600	+	0.184637i
$353$	−3.88338			−0.206692			−0.103346	−	0.994645i	$-0.532955\pi$
$353$	−3.88338			−0.206692			−0.103346	+	0.994645i	$0.532955\pi$
$354$		0			0
$355$	34.0195			1.80557
$356$	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
$362$	−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
$367$	6.89144			0.359730			0.179865	−	0.983691i	$-0.442434\pi$
$367$	6.89144			0.359730			0.179865	+	0.983691i	$0.442434\pi$
$368$	−4.37298	−	7.57423i	−0.227958	−	0.394834i
$369$		0			0
$370$	−19.7990			−1.02930
$371$		0			0
$372$		0			0
$373$	−1.12702			−0.0583547			−0.0291774	−	0.999574i	$-0.509289\pi$
$373$	−1.12702			−0.0583547			−0.0291774	+	0.999574i	$0.509289\pi$
$374$	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
$383$	12.9076			0.659545			0.329773	−	0.944060i	$-0.393028\pi$
$383$	12.9076			0.659545			0.329773	+	0.944060i	$0.393028\pi$
$384$		0			0
$385$		0			0
$386$	−23.8730			−1.21510
$387$		0			0
$388$	−7.50873	−	13.0055i	−0.381198	−	0.660254i
$389$	−13.1270			−0.665566			−0.332783	−	0.943003i	$-0.607988\pi$
$389$	−13.1270			−0.665566			−0.332783	+	0.943003i	$0.607988\pi$
$390$		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
$395$	3.22689	+	5.58913i	0.162362	+	0.281220i
$396$		0			0
$397$	−3.53553	+	6.12372i	−0.177443	+	0.307341i	−0.941004	−	0.338395i	$-0.890116\pi$
$397$	−3.53553	+	6.12372i	−0.177443	+	0.307341i	0.763561	+	0.645736i	$0.223449\pi$
$398$	6.09452	−	10.5560i	0.305491	−	0.529125i
$399$		0			0
$400$	−3.43649	−	5.95218i	−0.171825	−	0.297609i
$401$	3.87298			0.193408			0.0967038	−	0.995313i	$-0.469170\pi$
$401$	3.87298			0.193408			0.0967038	+	0.995313i	$0.469170\pi$
$402$		0			0
$403$	−23.2379			−1.15756
$404$	−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
$409$	−11.5717	+	20.0428i	−0.572186	+	0.991055i	0.424155	+	0.905589i	$0.360571\pi$
$409$	−11.5717	+	20.0428i	−0.572186	+	0.991055i	−0.996341	+	0.0854655i	$0.972762\pi$
$410$	−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
$415$	−4.56351	+	7.90423i	−0.224014	+	0.388003i
$416$	4.24264			0.208013
$417$		0			0
$418$	−25.0966			−1.22751
$419$	−15.6854	−	27.1679i	−0.766280	−	1.32724i	−0.939567	−	0.342365i	$-0.888772\pi$
$419$	−15.6854	−	27.1679i	−0.766280	−	1.32724i	0.173287	−	0.984871i	$-0.444561\pi$
$420$		0			0
$421$	6.43649	−	11.1483i	0.313695	−	0.543336i	−0.665464	−	0.746430i	$-0.731766\pi$
$421$	6.43649	−	11.1483i	0.313695	−	0.543336i	0.979159	+	0.203094i	$0.0650996\pi$
$422$	10.3095	−	17.8565i	0.501857	−	0.869243i
$423$		0			0
$424$	−6.30948	−	10.9283i	−0.306415	−	0.530727i
$425$	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
$430$	−3.88338			−0.187273
$431$	−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	$-0.752941\pi$
$433$	−29.6985			−1.42722			−0.713609	+	0.700544i	$0.752941\pi$
$434$		0			0
$435$		0			0
$436$	16.8730			0.808069
$437$	27.4367	−	47.5218i	1.31248	−	2.27328i
$438$		0			0
$439$	5.47723	+	9.48683i	0.261414	+	0.452782i	0.966618	−	0.256223i	$-0.0824780\pi$
$439$	5.47723	+	9.48683i	0.261414	+	0.452782i	−0.705204	+	0.709004i	$0.749145\pi$
$440$	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
$446$	22.4478			1.06293
$447$		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
$452$	−3.87298			−0.182170
$453$		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	$-0.375933\pi$
$458$	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	−0.319996	−	0.947419i	$-0.603682\pi$
$461$	14.1813	−	24.5628i	0.660491	−	1.14400i	0.980487	−	0.196585i	$-0.0629851\pi$
$462$		0			0
$463$	0.809475	+	1.40205i	0.0376195	+	0.0651589i	0.884222	−	0.467067i	$-0.154689\pi$
$463$	0.809475	+	1.40205i	0.0376195	+	0.0651589i	−0.846603	+	0.532226i	$0.821356\pi$
$464$	−1.12702			−0.0523204
$465$		0			0
$466$	7.25403			0.336037
$467$	3.09787	−	5.36567i	0.143352	−	0.248294i	−0.785405	−	0.618983i	$-0.787545\pi$
$467$	3.09787	−	5.36567i	0.143352	−	0.248294i	0.928757	+	0.370689i	$0.120878\pi$
$468$		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
$478$	7.50000	−	12.9904i	0.343042	−	0.594166i
$479$	−3.88338			−0.177436			−0.0887182	−	0.996057i	$-0.528277\pi$
$479$	−3.88338			−0.177436			−0.0887182	+	0.996057i	$0.528277\pi$
$480$		0			0
$481$	−24.3781			−1.11154
$482$	−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	$0.829785\pi$
$488$	3.13707	+	5.43357i	0.142009	+	0.245966i
$489$		0			0
$490$		0			0
$491$	0.872983	+	1.51205i	0.0393972	+	0.0682379i	0.885052	−	0.465493i	$-0.154123\pi$
$491$	0.872983	+	1.51205i	0.0393972	+	0.0682379i	−0.845654	+	0.533731i	$0.820790\pi$
$492$		0			0
$493$	1.59384			0.0717830
$494$	13.3095	+	23.0527i	0.598822	+	1.03719i
$495$		0			0
$496$	5.47723			0.245935
$497$		0			0
$498$		0			0
$499$	−29.7460			−1.33161			−0.665806	−	0.746125i	$-0.731912\pi$
$499$	−29.7460			−1.33161			−0.665806	+	0.746125i	$0.731912\pi$
$500$	−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	$-0.472408\pi$
$503$	3.88338			0.173152			0.0865758	+	0.996245i	$0.472408\pi$
$504$		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
$509$	−22.8070			−1.01090			−0.505452	−	0.862855i	$-0.668674\pi$
$509$	−22.8070			−1.01090			−0.505452	+	0.862855i	$0.668674\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−1.50403	−	2.60505i	−0.0663398	−	0.114904i
$515$	13.3810			0.589640
$516$		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
$521$	0.707107	+	1.22474i	0.0309789	+	0.0536570i	0.881099	−	0.472931i	$-0.156804\pi$
$521$	0.707107	+	1.22474i	0.0309789	+	0.0536570i	−0.850120	+	0.526589i	$0.823471\pi$
$522$		0			0
$523$	−9.14178	+	15.8340i	−0.399742	+	0.692373i	−0.993694	−	0.112127i	$-0.964234\pi$
$523$	−9.14178	+	15.8340i	−0.399742	+	0.692373i	0.593952	+	0.804501i	$0.297567\pi$
$524$	6.67261	−	11.5573i	0.291494	−	0.504883i
$525$		0			0
$526$	8.80948	+	15.2585i	0.384111	+	0.665300i
$527$	−7.74597			−0.337420
$528$		0			0
$529$	53.4919			2.32574
$530$	−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
$535$	0.437664	−	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
$541$	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	$-0.138947\pi$
$542$	−7.07107			−0.303728
$543$		0			0
$544$	1.41421			0.0606339
$545$	−29.0698	−	50.3503i	−1.24521	−	2.15677i
$546$		0			0
$547$	16.4919	−	28.5649i	0.705144	−	1.22135i	−0.261495	−	0.965205i	$-0.584216\pi$
$547$	16.4919	−	28.5649i	0.705144	−	1.22135i	0.966639	−	0.256141i	$-0.0824511\pi$
$548$	−7.74597	+	13.4164i	−0.330891	+	0.573121i
$549$		0			0
$550$	−13.7460	−	23.8087i	−0.586130	−	1.01521i
$551$	−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
$556$	19.8774			0.842989
$557$	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
$562$	8.74597			0.368926
$563$	−10.8254	+	18.7502i	−0.456238	+	0.790227i	−0.998758	−	0.0498156i	$-0.984137\pi$
$563$	−10.8254	+	18.7502i	−0.456238	+	0.790227i	0.542521	+	0.840042i	$0.317470\pi$
$564$		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	$0.937668\pi$
$572$	16.9706			0.709575
$573$		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	$-0.998464\pi$
$577$	−12.1106	−	20.9762i	−0.504172	−	0.873252i	0.495816	−	0.868427i	$-0.334869\pi$
$578$	15.0000			0.623918
$579$		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
$584$	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	$-0.776781\pi$
$587$	4.28184	−	7.41637i	0.176731	−	0.306106i	0.940759	+	0.339076i	$0.110115\pi$
$588$		0			0
$589$	17.1825	+	29.7609i	0.707991	+	1.22628i
$590$	−28.6190			−1.17822
$591$		0			0
$592$	5.74597			0.236158
$593$	16.8807	−	29.2383i	0.693209	−	1.20067i	−0.277571	−	0.960705i	$-0.589530\pi$
$593$	16.8807	−	29.2383i	0.693209	−	1.20067i	0.970781	−	0.239969i	$-0.0771372\pi$
$594$		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	$-0.802242\pi$
$601$	2.39076	−	4.14092i	0.0975213	−	0.168912i	0.910658	+	0.413161i	$0.135575\pi$
$602$		0			0
$603$		0			0
$604$	−5.50000	+	9.52628i	−0.223792	+	0.387619i
$605$	17.2286			0.700442
$606$		0			0
$607$	26.6904			1.08333			0.541666	−	0.840594i	$-0.317794\pi$
$607$	26.6904			1.08333			0.541666	+	0.840594i	$0.317794\pi$
$608$	−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	$-0.347322\pi$
$614$	7.11027	+	12.3154i	0.286947	+	0.497007i
$615$		0			0
$616$		0			0
$617$	−6.12702	−	10.6123i	−0.246664	−	0.427235i	0.715934	−	0.698168i	$-0.246001\pi$
$617$	−6.12702	−	10.6123i	−0.246664	−	0.427235i	−0.962598	+	0.270933i	$0.912668\pi$
$618$		0			0
$619$	−37.9029			−1.52345			−0.761723	−	0.647902i	$-0.775646\pi$
$619$	−37.9029			−1.52345			−0.761723	+	0.647902i	$0.775646\pi$
$620$	−9.43649	−	16.3445i	−0.378979	−	0.656410i
$621$		0			0
$622$	−1.41421			−0.0567048
$623$		0			0
$624$		0			0
$625$	−12.1270			−0.485081
$626$	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
$635$	−2.57039			−0.102003
$636$		0			0
$637$		0			0
$638$	−4.50807			−0.178476
$639$		0			0
$640$	1.72286	+	2.98408i	0.0681020	+	0.117956i
$641$	−17.1109			−0.675839			−0.337920	−	0.941175i	$-0.609723\pi$
$641$	−17.1109			−0.675839			−0.337920	+	0.941175i	$0.609723\pi$
$642$		0			0
$643$	−1.76206	−	3.05198i	−0.0694890	−	0.120358i	0.829187	−	0.558971i	$-0.188804\pi$
$643$	−1.76206	−	3.05198i	−0.0694890	−	0.120358i	−0.898676	+	0.438612i	$0.855470\pi$
$644$		0			0
$645$		0			0
$646$	4.43649	+	7.68423i	0.174551	+	0.302332i
$647$	−2.73861	−	4.74342i	−0.107666	−	0.186483i	0.807158	−	0.590335i	$-0.201004\pi$
$647$	−2.73861	−	4.74342i	−0.107666	−	0.186483i	−0.914824	+	0.403852i	$0.867671\pi$
$648$		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
$653$	14.5081			0.567745			0.283872	−	0.958862i	$-0.408381\pi$
$653$	14.5081			0.567745			0.283872	+	0.958862i	$0.408381\pi$
$654$		0			0
$655$	−45.9839			−1.79674
$656$	2.82843	−	4.89898i	0.110432	−	0.191273i
$657$		0			0
$658$		0			0
$659$	14.5635	−	25.2247i	0.567314	−	0.982616i	−0.429517	−	0.903059i	$-0.641316\pi$
$659$	14.5635	−	25.2247i	0.567314	−	0.982616i	0.996830	−	0.0795572i	$-0.0253506\pi$
$660$		0			0
$661$	23.1043	−	40.0178i	0.898652	−	1.55651i	0.0694345	−	0.997587i	$-0.477881\pi$
$661$	23.1043	−	40.0178i	0.898652	−	1.55651i	0.829218	−	0.558925i	$-0.188786\pi$
$662$	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
$667$	4.92843	−	8.53628i	0.190829	−	0.330526i
$668$	−9.54024			−0.369123
$669$		0			0
$670$	23.6824			0.914930
$671$	12.5483	+	21.7343i	0.484421	+	0.839043i
$672$		0			0
$673$	−7.11895	+	12.3304i	−0.274415	+	0.475301i	−0.969987	−	0.243155i	$-0.921818\pi$
$673$	−7.11895	+	12.3304i	−0.274415	+	0.475301i	0.695572	+	0.718456i	$0.255151\pi$
$674$	7.87298	−	13.6364i	0.303256	−	0.525255i
$675$		0			0
$676$	−2.50000	−	4.33013i	−0.0961538	−	0.166543i
$677$	6.36396	+	11.0227i	0.244587	+	0.423637i	0.962015	−	0.272995i	$-0.0880143\pi$
$677$	6.36396	+	11.0227i	0.244587	+	0.423637i	−0.717428	+	0.696632i	$0.754681\pi$
$678$		0			0
$679$		0			0
$680$	−2.43649	−	4.22013i	−0.0934352	−	0.161834i
$681$		0			0
$682$	21.9089			0.838935
$683$	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
$688$	1.12702			0.0429671
$689$	−26.7688	+	46.3650i	−1.01981	+	1.76637i
$690$		0			0
$691$	−8.52448	−	14.7648i	−0.324287	−	0.561681i	0.657081	−	0.753820i	$-0.271791\pi$
$691$	−8.52448	−	14.7648i	−0.324287	−	0.561681i	−0.981368	+	0.192139i	$0.938458\pi$
$692$	−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
$698$	16.4317			0.621948
$699$		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
$704$	−4.00000			−0.150756
$705$		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	$0.378035\pi$
$710$	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
$716$	6.87298			0.256855
$717$		0			0
$718$	18.2379			0.680632
$719$	−11.7514	+	20.3540i	−0.438252	+	0.759075i	−0.997555	−	0.0698884i	$-0.977736\pi$
$719$	−11.7514	+	20.3540i	−0.438252	+	0.759075i	0.559303	+	0.828964i	$0.311069\pi$
$720$		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	$-0.853223\pi$
$727$	−1.68366	+	2.91618i	−0.0624434	+	0.108155i	0.833114	+	0.553102i	$0.186556\pi$
$728$		0			0
$729$		0			0
$730$	7.61895	−	13.1964i	0.281990	−	0.488421i
$731$	−1.59384			−0.0589504
$732$		0			0
$733$	−37.0276			−1.36765			−0.683823	−	0.729648i	$-0.739684\pi$
$733$	−37.0276			−1.36765			−0.683823	+	0.729648i	$0.739684\pi$
$734$	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	$0.647281\pi$
$740$	−9.89949	−	17.1464i	−0.363913	−	0.630315i
$741$		0			0
$742$		0			0
$743$	−6.12702	−	10.6123i	−0.224778	−	0.389328i	0.731475	−	0.681869i	$-0.238833\pi$
$743$	−6.12702	−	10.6123i	−0.224778	−	0.389328i	−0.956253	+	0.292541i	$0.905499\pi$
$744$		0			0
$745$	54.2562			1.98779
$746$	−0.563508	−	0.976025i	−0.0206315	−	0.0357348i
$747$		0			0
$748$	5.65685			0.206835
$749$		0			0
$750$		0			0
$751$	−13.0000			−0.474377			−0.237188	−	0.971464i	$-0.576226\pi$
$751$	−13.0000			−0.474377			−0.237188	+	0.971464i	$0.576226\pi$
$752$	−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
$761$	30.5738			1.10830			0.554150	−	0.832417i	$-0.313043\pi$
$761$	30.5738			1.10830			0.554150	+	0.832417i	$0.313043\pi$
$762$		0			0
$763$		0			0
$764$	6.12702			0.221668
$765$		0			0
$766$	6.45378	+	11.1783i	0.233184	+	0.403887i
$767$	−35.2379			−1.27237
$768$		0			0
$769$	0.617292	+	1.06918i	0.0222601	+	0.0385557i	0.876941	−	0.480598i	$-0.159580\pi$
$769$	0.617292	+	1.06918i	0.0222601	+	0.0385557i	−0.854681	+	0.519154i	$0.826247\pi$
$770$		0			0
$771$		0			0
$772$	−11.9365	−	20.6746i	−0.429604	−	0.744095i
$773$	−1.01575	−	1.75934i	−0.0365341	−	0.0632789i	0.847180	−	0.531306i	$-0.178298\pi$
$773$	−1.01575	−	1.75934i	−0.0365341	−	0.0632789i	−0.883714	+	0.468027i	$0.844965\pi$
$774$		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
$779$	35.4919			1.27163
$780$		0			0
$781$	−39.4919			−1.41313
$782$	−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
$787$	−6.18433	+	10.7116i	−0.220448	+	0.381827i	−0.954944	−	0.296786i	$-0.904085\pi$
$787$	−6.18433	+	10.7116i	−0.220448	+	0.381827i	0.734496	+	0.678613i	$0.237418\pi$
$788$	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
$793$	13.3095	−	23.0527i	0.472633	−	0.818625i
$794$	−7.07107			−0.250943
$795$		0			0
$796$	12.1890			0.432029
$797$	−10.2980	−	17.8366i	−0.364772	−	0.631804i	0.623967	−	0.781450i	$-0.285520\pi$
$797$	−10.2980	−	17.8366i	−0.364772	−	0.631804i	−0.988740	+	0.149646i	$0.952187\pi$
$798$		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
$803$	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
$808$	−13.3452			−0.469483
$809$	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	$-0.516819\pi$
$811$	−3.00806			−0.105627			−0.0528136	+	0.998604i	$0.516819\pi$
$812$		0			0
$813$		0			0
$814$	22.9839			0.805584
$815$	−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	$0.131902\pi$
$824$	−3.88338			−0.135284
$825$		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	0.943371	−	0.331741i	$-0.107636\pi$
$829$	5.30900	+	9.19547i	0.184389	+	0.319372i	−0.758981	+	0.651113i	$0.774303\pi$
$830$	−9.12702			−0.316803
$831$		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
$836$	−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	$-0.686457\pi$
$839$	12.8961	−	22.3368i	0.445224	−	0.771151i	0.998068	+	0.0621340i	$0.0197906\pi$
$840$		0			0
$841$	13.8649	+	24.0147i	0.478101	+	0.828094i
$842$	12.8730			0.443632
$843$		0			0
$844$	20.6190			0.709734
$845$	−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
$850$	−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	$-0.732896\pi$
$853$	9.06337	−	15.6982i	0.310324	−	0.537497i	0.978432	+	0.206567i	$0.0662292\pi$
$854$		0			0
$855$		0			0
$856$	−0.127017	+	0.219999i	−0.00434134	+	0.00751942i
$857$	−25.8151			−0.881827			−0.440914	−	0.897550i	$-0.645345\pi$
$857$	−25.8151			−0.881827			−0.440914	+	0.897550i	$0.645345\pi$
$858$		0			0
$859$	30.5738			1.04317			0.521583	−	0.853201i	$-0.325342\pi$
$859$	30.5738			1.04317			0.521583	+	0.853201i	$0.325342\pi$
$860$	−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
$866$	−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
$871$	29.1596			0.988035
$872$	8.43649	+	14.6124i	0.285696	+	0.494839i
$873$		0			0
$874$	54.8735			1.85612
$875$		0			0
$876$		0			0
$877$	31.1270			1.05108			0.525542	−	0.850767i	$-0.323862\pi$
$877$	31.1270			1.05108			0.525542	+	0.850767i	$0.323862\pi$
$878$	−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	$-0.648438\pi$
$881$	−26.6904			−0.899223			−0.449612	+	0.893224i	$0.648438\pi$
$882$		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
$887$	−7.76677			−0.260783			−0.130391	−	0.991463i	$-0.541623\pi$
$887$	−7.76677			−0.260783			−0.130391	+	0.991463i	$0.541623\pi$
$888$		0			0
$889$		0			0
$890$	24.3649			0.816714
$891$		0			0
$892$	11.2239	+	19.4404i	0.375804	+	0.650911i
$893$	−25.4919			−0.853055
$894$		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
$899$	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
$905$	−45.9839			−1.52856
$906$		0			0
$907$	18.6190			0.618232			0.309116	−	0.951024i	$-0.399967\pi$
$907$	18.6190			0.618232			0.309116	+	0.951024i	$0.399967\pi$
$908$	5.16858	−	8.95224i	0.171525	−	0.297091i
$909$		0			0
$910$		0			0
$911$	−19.3730	+	33.5550i	−0.641856	+	1.11173i	0.343163	+	0.939276i	$0.388502\pi$
$911$	−19.3730	+	33.5550i	−0.641856	+	1.11173i	−0.985018	+	0.172450i	$0.944832\pi$
$912$		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
$919$	0.317542	−	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	$0.163332\pi$
$920$	−30.1361			−0.993559
$921$		0			0
$922$	28.3627			0.934075
$923$	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
$929$	−27.2179	−	47.1428i	−0.892991	−	1.54671i	−0.836272	−	0.548315i	$-0.815270\pi$
$929$	−27.2179	−	47.1428i	−0.892991	−	1.54671i	−0.0567186	−	0.998390i	$-0.518064\pi$
$930$		0			0
$931$		0			0
$932$	3.62702	+	6.28218i	0.118807	+	0.205780i
$933$		0			0
$934$	6.19574			0.202731
$935$	−9.74597	−	16.8805i	−0.318727	−	0.552052i
$936$		0			0
$937$	−45.2320			−1.47767			−0.738833	−	0.673889i	$-0.764623\pi$
$937$	−45.2320			−1.47767			−0.738833	+	0.673889i	$0.764623\pi$
$938$		0			0
$939$		0			0
$940$	14.0000			0.456630
$941$	12.8569	−	22.2689i	0.419124	−	0.725945i	−0.576727	−	0.816937i	$-0.695670\pi$
$941$	12.8569	−	22.2689i	0.419124	−	0.725945i	0.995852	+	0.0909922i	$0.0290038\pi$
$942$		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
$950$	43.1221			1.39907
$951$		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
$956$	15.0000			0.485135
$957$		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
$962$	−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	−0.687498	−	0.726186i	$-0.741291\pi$
$967$	−30.2460	−	52.3876i	−0.972645	−	1.68467i	−0.285147	−	0.958484i	$-0.592042\pi$
$968$	−5.00000			−0.160706
$969$		0			0
$970$	−51.7460			−1.66146
$971$	0.746310	−	1.29265i	0.0239502	−	0.0414830i	−0.853802	−	0.520598i	$-0.825709\pi$
$971$	0.746310	−	1.29265i	0.0239502	−	0.0414830i	0.877752	+	0.479115i	$0.159042\pi$
$972$		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
$982$	−0.872983	+	1.51205i	−0.0278580	+	0.0482515i
$983$	9.89949			0.315745			0.157872	−	0.987460i	$-0.449537\pi$
$983$	9.89949			0.315745			0.157872	+	0.987460i	$0.449537\pi$
$984$		0			0
$985$	−57.2642			−1.82459
$986$	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	$0.773599\pi$
$992$	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
$997$	−27.1281			−0.859155			−0.429578	−	0.903030i	$-0.641338\pi$
$997$	−27.1281			−0.859155			−0.429578	+	0.903030i	$0.641338\pi$
$998$	−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.h.s.667.4		8
3.2	odd	2		882.2.h.r.79.1		8
7.2	even	3		2646.2.f.s.883.1		8
7.3	odd	6		2646.2.e.r.2125.4		8
7.4	even	3		2646.2.e.r.2125.1		8
7.5	odd	6		2646.2.f.s.883.4		8
7.6	odd	2	inner	2646.2.h.s.667.1		8
9.4	even	3		2646.2.e.r.1549.1		8
9.5	odd	6		882.2.e.t.373.3		8
21.2	odd	6		882.2.f.p.295.3	yes	8
21.5	even	6		882.2.f.p.295.2	✓	8
21.11	odd	6		882.2.e.t.655.3		8
21.17	even	6		882.2.e.t.655.2		8
21.20	even	2		882.2.h.r.79.4		8
63.2	odd	6		7938.2.a.cu.1.1		4
63.4	even	3	inner	2646.2.h.s.361.4		8
63.5	even	6		882.2.f.p.589.1	yes	8
63.13	odd	6		2646.2.e.r.1549.4		8
63.16	even	3		7938.2.a.cd.1.4		4
63.23	odd	6		882.2.f.p.589.4	yes	8
63.31	odd	6	inner	2646.2.h.s.361.1		8
63.32	odd	6		882.2.h.r.67.1		8
63.40	odd	6		2646.2.f.s.1765.4		8
63.41	even	6		882.2.e.t.373.2		8
63.47	even	6		7938.2.a.cu.1.4		4
63.58	even	3		2646.2.f.s.1765.1		8
63.59	even	6		882.2.h.r.67.4		8
63.61	odd	6		7938.2.a.cd.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.t.373.2		8	63.41	even	6
882.2.e.t.373.3		8	9.5	odd	6
882.2.e.t.655.2		8	21.17	even	6
882.2.e.t.655.3		8	21.11	odd	6
882.2.f.p.295.2	✓	8	21.5	even	6
882.2.f.p.295.3	yes	8	21.2	odd	6
882.2.f.p.589.1	yes	8	63.5	even	6
882.2.f.p.589.4	yes	8	63.23	odd	6
882.2.h.r.67.1		8	63.32	odd	6
882.2.h.r.67.4		8	63.59	even	6
882.2.h.r.79.1		8	3.2	odd	2
882.2.h.r.79.4		8	21.20	even	2
2646.2.e.r.1549.1		8	9.4	even	3
2646.2.e.r.1549.4		8	63.13	odd	6
2646.2.e.r.2125.1		8	7.4	even	3
2646.2.e.r.2125.4		8	7.3	odd	6
2646.2.f.s.883.1		8	7.2	even	3
2646.2.f.s.883.4		8	7.5	odd	6
2646.2.f.s.1765.1		8	63.58	even	3
2646.2.f.s.1765.4		8	63.40	odd	6
2646.2.h.s.361.1		8	63.31	odd	6	inner
2646.2.h.s.361.4		8	63.4	even	3	inner
2646.2.h.s.667.1		8	7.6	odd	2	inner
2646.2.h.s.667.4		8	1.1	even	1	trivial
7938.2.a.cd.1.1		4	63.61	odd	6
7938.2.a.cd.1.4		4	63.16	even	3
7938.2.a.cu.1.1		4	63.2	odd	6
7938.2.a.cu.1.4		4	63.47	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.44572 q^{5} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.44572 q^{5} -1.00000 q^{8} +(1.72286 + 2.98408i) q^{10} -4.00000 q^{11} +(2.12132 + 3.67423i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(0.707107 + 1.22474i) q^{17} +(3.13707 - 5.43357i) q^{19} +(-1.72286 + 2.98408i) q^{20} +(-2.00000 - 3.46410i) q^{22} +8.74597 q^{23} +6.87298 q^{25} +(-2.12132 + 3.67423i) q^{26} +(0.563508 - 0.976025i) q^{29} +(-2.73861 + 4.74342i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.707107 + 1.22474i) q^{34} +(-2.87298 + 4.97615i) q^{37} +6.27415 q^{38} -3.44572 q^{40} +(2.82843 + 4.89898i) q^{41} +(-0.563508 + 0.976025i) q^{43} +(2.00000 - 3.46410i) q^{44} +(4.37298 + 7.57423i) q^{46} +(-2.03151 - 3.51867i) q^{47} +(3.43649 + 5.95218i) q^{50} -4.24264 q^{52} +(6.30948 + 10.9283i) q^{53} -13.7829 q^{55} +1.12702 q^{58} +(-4.15283 + 7.19291i) q^{59} +(-3.13707 - 5.43357i) q^{61} -5.47723 q^{62} +1.00000 q^{64} +(7.30948 + 12.6604i) q^{65} +(3.43649 - 5.95218i) q^{67} -1.41421 q^{68} +9.87298 q^{71} +(-2.21113 - 3.82980i) q^{73} -5.74597 q^{74} +(3.13707 + 5.43357i) q^{76} +(0.936492 + 1.62205i) q^{79} +(-1.72286 - 2.98408i) q^{80} +(-2.82843 + 4.89898i) q^{82} +(-1.32440 + 2.29393i) q^{83} +(2.43649 + 4.22013i) q^{85} -1.12702 q^{86} +4.00000 q^{88} +(3.53553 - 6.12372i) q^{89} +(-4.37298 + 7.57423i) q^{92} +(2.03151 - 3.51867i) q^{94} +(10.8095 - 18.7226i) q^{95} +(-7.50873 + 13.0055i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 32 q^{11} - 4 q^{16} - 16 q^{22} + 8 q^{23} + 24 q^{25} + 20 q^{29} + 4 q^{32} + 8 q^{37} - 20 q^{43} + 16 q^{44} + 4 q^{46} + 12 q^{50} + 4 q^{53} + 40 q^{58} + 8 q^{64} + 12 q^{65} + 12 q^{67} + 48 q^{71} + 16 q^{74} - 8 q^{79} + 4 q^{85} - 40 q^{86} + 32 q^{88} - 4 q^{92} + 40 q^{95}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 32 * q^11 - 4 * q^16 - 16 * q^22 + 8 * q^23 + 24 * q^25 + 20 * q^29 + 4 * q^32 + 8 * q^37 - 20 * q^43 + 16 * q^44 + 4 * q^46 + 12 * q^50 + 4 * q^53 + 40 * q^58 + 8 * q^64 + 12 * q^65 + 12 * q^67 + 48 * q^71 + 16 * q^74 - 8 * q^79 + 4 * q^85 - 40 * q^86 + 32 * q^88 - 4 * q^92 + 40 * q^95

Introduction

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