LMFDB - Embedded newform 882.2.e.t.655.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(373,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, 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("882.373"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,0,8,0,0,0,8,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$7.04280545828$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			655.4
Root			$1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	882.655
Dual form			882.2.e.t.373.4

$q$-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} +(1.72286 + 0.178197i) q^{3} +1.00000 q^{4} +(1.01575 - 1.75934i) q^{5} +(1.72286 + 0.178197i) q^{6} +1.00000 q^{8} +(2.93649 + 0.614017i) q^{9} +(1.01575 - 1.75934i) q^{10} +(-2.00000 - 3.46410i) q^{11} +(1.72286 + 0.178197i) q^{12} +(-2.12132 - 3.67423i) q^{13} +(2.06351 - 2.85008i) q^{15} +1.00000 q^{16} +(0.707107 - 1.22474i) q^{17} +(2.93649 + 0.614017i) q^{18} +(-0.398461 - 0.690154i) q^{19} +(1.01575 - 1.75934i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(-3.37298 + 5.84218i) q^{23} +(1.72286 + 0.178197i) q^{24} +(0.436492 + 0.756026i) q^{25} +(-2.12132 - 3.67423i) q^{26} +(4.94975 + 1.58114i) q^{27} +(-4.43649 + 7.68423i) q^{29} +(2.06351 - 2.85008i) q^{30} +5.47723 q^{31} +1.00000 q^{32} +(-2.82843 - 6.32456i) q^{33} +(0.707107 - 1.22474i) q^{34} +(2.93649 + 0.614017i) q^{36} +(4.87298 + 8.44025i) q^{37} +(-0.398461 - 0.690154i) q^{38} +(-3.00000 - 6.70820i) q^{39} +(1.01575 - 1.75934i) q^{40} +(2.82843 + 4.89898i) q^{41} +(-4.43649 + 7.68423i) q^{43} +(-2.00000 - 3.46410i) q^{44} +(4.06301 - 4.54259i) q^{45} +(-3.37298 + 5.84218i) q^{46} -6.89144 q^{47} +(1.72286 + 0.178197i) q^{48} +(0.436492 + 0.756026i) q^{50} +(1.43649 - 1.98406i) q^{51} +(-2.12132 - 3.67423i) q^{52} +(5.30948 - 9.19628i) q^{53} +(4.94975 + 1.58114i) q^{54} -8.12602 q^{55} +(-0.563508 - 1.26004i) q^{57} +(-4.43649 + 7.68423i) q^{58} -2.64880 q^{59} +(2.06351 - 2.85008i) q^{60} -0.796921 q^{61} +5.47723 q^{62} +1.00000 q^{64} -8.61895 q^{65} +(-2.82843 - 6.32456i) q^{66} +0.872983 q^{67} +(0.707107 - 1.22474i) q^{68} +(-6.85224 + 9.46420i) q^{69} -2.12702 q^{71} +(2.93649 + 0.614017i) q^{72} +(7.68836 - 13.3166i) q^{73} +(4.87298 + 8.44025i) q^{74} +(0.617292 + 1.38031i) q^{75} +(-0.398461 - 0.690154i) q^{76} +(-3.00000 - 6.70820i) q^{78} +5.87298 q^{79} +(1.01575 - 1.75934i) q^{80} +(8.24597 + 3.60611i) q^{81} +(2.82843 + 4.89898i) q^{82} +(4.15283 - 7.19291i) q^{83} +(-1.43649 - 2.48808i) q^{85} +(-4.43649 + 7.68423i) q^{86} +(-9.01276 + 12.4483i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(3.53553 + 6.12372i) q^{89} +(4.06301 - 4.54259i) q^{90} +(-3.37298 + 5.84218i) q^{92} +(9.43649 + 0.976025i) q^{93} -6.89144 q^{94} -1.61895 q^{95} +(1.72286 + 0.178197i) q^{96} +(-8.92295 + 15.4550i) q^{97} +(-3.74597 - 11.4003i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} + 8 q^{9} - 16 q^{11} + 32 q^{15} + 8 q^{16} + 8 q^{18} - 16 q^{22} + 4 q^{23} - 12 q^{25} - 20 q^{29} + 32 q^{30} + 8 q^{32} + 8 q^{36} + 8 q^{37} - 24 q^{39} - 20 q^{43}+ \cdots + 32 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 + 8 * q^9 - 16 * q^11 + 32 * q^15 + 8 * q^16 + 8 * q^18 - 16 * q^22 + 4 * q^23 - 12 * q^25 - 20 * q^29 + 32 * q^30 + 8 * q^32 + 8 * q^36 + 8 * q^37 - 24 * q^39 - 20 * q^43 - 16 * q^44 + 4 * q^46 - 12 * q^50 - 4 * q^51 - 4 * q^53 - 20 * q^57 - 20 * q^58 + 32 * q^60 + 8 * q^64 + 24 * q^65 - 24 * q^67 - 48 * q^71 + 8 * q^72 + 8 * q^74 - 24 * q^78 + 16 * q^79 + 4 * q^81 + 4 * q^85 - 20 * q^86 - 16 * q^88 + 4 * q^92 + 60 * q^93 + 80 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$	1.72286	+	0.178197i	0.994694	+	0.102882i
$3$	1.72286	+	0.178197i	0.994694	+	0.102882i
$4$	1.00000			0.500000
$5$	1.01575	−	1.75934i	0.454259	−	0.786799i	−0.544387	−	0.838834i	$-0.683238\pi$
$5$	1.01575	−	1.75934i	0.454259	−	0.786799i	0.998645	+	0.0520355i	$0.0165709\pi$
$6$	1.72286	+	0.178197i	0.703355	+	0.0727486i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	2.93649	+	0.614017i	0.978831	+	0.204672i
$10$	1.01575	−	1.75934i	0.321209	−	0.556351i
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$	1.72286	+	0.178197i	0.497347	+	0.0514410i
$13$	−2.12132	−	3.67423i	−0.588348	−	1.01905i	−0.994449	−	0.105221i	$-0.966445\pi$
$13$	−2.12132	−	3.67423i	−0.588348	−	1.01905i	0.406100	−	0.913828i	$-0.366888\pi$
$14$		0			0
$15$	2.06351	−	2.85008i	0.532796	−	0.735889i
$16$	1.00000			0.250000
$17$	0.707107	−	1.22474i	0.171499	−	0.297044i	−0.767445	−	0.641114i	$-0.778472\pi$
$17$	0.707107	−	1.22474i	0.171499	−	0.297044i	0.938944	+	0.344070i	$0.111806\pi$
$18$	2.93649	+	0.614017i	0.692138	+	0.144725i
$19$	−0.398461	−	0.690154i	−0.0914131	−	0.158332i	0.816693	−	0.577073i	$-0.195805\pi$
$19$	−0.398461	−	0.690154i	−0.0914131	−	0.158332i	−0.908106	+	0.418740i	$0.862472\pi$
$20$	1.01575	−	1.75934i	0.227129	−	0.393399i
$21$		0			0
$22$	−2.00000	−	3.46410i	−0.426401	−	0.738549i
$23$	−3.37298	+	5.84218i	−0.703316	+	1.21818i	0.263980	+	0.964528i	$0.414965\pi$
$23$	−3.37298	+	5.84218i	−0.703316	+	1.21818i	−0.967296	+	0.253650i	$0.918369\pi$
$24$	1.72286	+	0.178197i	0.351677	+	0.0363743i
$25$	0.436492	+	0.756026i	0.0872983	+	0.151205i
$26$	−2.12132	−	3.67423i	−0.416025	−	0.720577i
$27$	4.94975	+	1.58114i	0.952579	+	0.304290i
$28$		0			0
$29$	−4.43649	+	7.68423i	−0.823836	+	1.42693i	0.0789700	+	0.996877i	$0.474837\pi$
$29$	−4.43649	+	7.68423i	−0.823836	+	1.42693i	−0.902806	+	0.430049i	$0.858496\pi$
$30$	2.06351	−	2.85008i	0.376743	−	0.520352i
$31$	5.47723			0.983739			0.491869	−	0.870669i	$-0.336314\pi$
$31$	5.47723			0.983739			0.491869	+	0.870669i	$0.336314\pi$
$32$	1.00000			0.176777
$33$	−2.82843	−	6.32456i	−0.492366	−	1.10096i
$34$	0.707107	−	1.22474i	0.121268	−	0.210042i
$35$		0			0
$36$	2.93649	+	0.614017i	0.489415	+	0.102336i
$37$	4.87298	+	8.44025i	0.801114	+	1.38757i	0.918884	+	0.394528i	$0.129092\pi$
$37$	4.87298	+	8.44025i	0.801114	+	1.38757i	−0.117770	+	0.993041i	$0.537575\pi$
$38$	−0.398461	−	0.690154i	−0.0646388	−	0.111958i
$39$	−3.00000	−	6.70820i	−0.480384	−	1.07417i
$40$	1.01575	−	1.75934i	0.160605	−	0.278175i
$41$	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
$43$	−4.43649	+	7.68423i	−0.676559	+	1.17183i	0.299452	+	0.954111i	$0.403196\pi$
$43$	−4.43649	+	7.68423i	−0.676559	+	1.17183i	−0.976011	+	0.217723i	$0.930137\pi$
$44$	−2.00000	−	3.46410i	−0.301511	−	0.522233i
$45$	4.06301	−	4.54259i	0.605678	−	0.677169i
$46$	−3.37298	+	5.84218i	−0.497319	+	0.861382i
$47$	−6.89144			−1.00522			−0.502610	−	0.864513i	$-0.667627\pi$
$47$	−6.89144			−1.00522			−0.502610	+	0.864513i	$0.667627\pi$
$48$	1.72286	+	0.178197i	0.248673	+	0.0257205i
$49$		0			0
$50$	0.436492	+	0.756026i	0.0617292	+	0.106918i
$51$	1.43649	−	1.98406i	0.201149	−	0.277824i
$52$	−2.12132	−	3.67423i	−0.294174	−	0.509525i
$53$	5.30948	−	9.19628i	0.729312	−	1.26321i	−0.227862	−	0.973694i	$-0.573173\pi$
$53$	5.30948	−	9.19628i	0.729312	−	1.26321i	0.957174	−	0.289513i	$-0.0934933\pi$
$54$	4.94975	+	1.58114i	0.673575	+	0.215166i
$55$	−8.12602			−1.09571
$56$		0			0
$57$	−0.563508	−	1.26004i	−0.0746385	−	0.166897i
$58$	−4.43649	+	7.68423i	−0.582540	+	1.00899i
$59$	−2.64880			−0.344844			−0.172422	−	0.985023i	$-0.555159\pi$
$59$	−2.64880			−0.344844			−0.172422	+	0.985023i	$0.555159\pi$
$60$	2.06351	−	2.85008i	0.266398	−	0.367944i
$61$	−0.796921			−0.102035			−0.0510176	−	0.998698i	$-0.516246\pi$
$61$	−0.796921			−0.102035			−0.0510176	+	0.998698i	$0.516246\pi$
$62$	5.47723			0.695608
$63$		0			0
$64$	1.00000			0.125000
$65$	−8.61895			−1.06905
$66$	−2.82843	−	6.32456i	−0.348155	−	0.778499i
$67$	0.872983			0.106652			0.0533259	−	0.998577i	$-0.483018\pi$
$67$	0.872983			0.106652			0.0533259	+	0.998577i	$0.483018\pi$
$68$	0.707107	−	1.22474i	0.0857493	−	0.148522i
$69$	−6.85224	+	9.46420i	−0.824912	+	1.13936i
$70$		0			0
$71$	−2.12702			−0.252430			−0.126215	−	0.992003i	$-0.540283\pi$
$71$	−2.12702			−0.252430			−0.126215	+	0.992003i	$0.540283\pi$
$72$	2.93649	+	0.614017i	0.346069	+	0.0723626i
$73$	7.68836	−	13.3166i	0.899855	−	1.55859i	0.0721755	−	0.997392i	$-0.477006\pi$
$73$	7.68836	−	13.3166i	0.899855	−	1.55859i	0.827679	−	0.561202i	$-0.189661\pi$
$74$	4.87298	+	8.44025i	0.566473	+	0.981160i
$75$	0.617292	+	1.38031i	0.0712788	+	0.159384i
$76$	−0.398461	−	0.690154i	−0.0457066	−	0.0791661i
$77$		0			0
$78$	−3.00000	−	6.70820i	−0.339683	−	0.759555i
$79$	5.87298			0.660762			0.330381	−	0.943848i	$-0.392823\pi$
$79$	5.87298			0.660762			0.330381	+	0.943848i	$0.392823\pi$
$80$	1.01575	−	1.75934i	0.113565	−	0.196700i
$81$	8.24597	+	3.60611i	0.916219	+	0.400679i
$82$	2.82843	+	4.89898i	0.312348	+	0.541002i
$83$	4.15283	−	7.19291i	0.455832	−	0.789524i	−0.542904	−	0.839795i	$-0.682675\pi$
$83$	4.15283	−	7.19291i	0.455832	−	0.789524i	0.998736	+	0.0502709i	$0.0160085\pi$
$84$		0			0
$85$	−1.43649	−	2.48808i	−0.155809	−	0.269870i
$86$	−4.43649	+	7.68423i	−0.478399	+	0.828612i
$87$	−9.01276	+	12.4483i	−0.966269	+	1.33460i
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	3.53553	+	6.12372i	0.374766	+	0.649113i	0.990292	−	0.139003i	$-0.0443898\pi$
$89$	3.53553	+	6.12372i	0.374766	+	0.649113i	−0.615526	+	0.788116i	$0.711056\pi$
$90$	4.06301	−	4.54259i	0.428279	−	0.478831i
$91$		0			0
$92$	−3.37298	+	5.84218i	−0.351658	+	0.609089i
$93$	9.43649	+	0.976025i	0.978519	+	0.101209i
$94$	−6.89144			−0.710798
$95$	−1.61895			−0.166101
$96$	1.72286	+	0.178197i	0.175839	+	0.0181872i
$97$	−8.92295	+	15.4550i	−0.905988	+	1.56922i	−0.0864021	+	0.996260i	$0.527537\pi$
$97$	−8.92295	+	15.4550i	−0.905988	+	1.56922i	−0.819586	+	0.572957i	$0.805796\pi$
$98$		0			0
$99$	−3.74597	−	11.4003i	−0.376484	−	1.14578i
$100$	0.436492	+	0.756026i	0.0436492	+	0.0756026i
$101$	−3.93399	−	6.81388i	−0.391447	−	0.678006i	0.601194	−	0.799103i	$-0.294692\pi$
$101$	−3.93399	−	6.81388i	−0.391447	−	0.678006i	−0.992641	+	0.121097i	$0.961359\pi$
$102$	1.43649	−	1.98406i	0.142234	−	0.196451i
$103$	−9.01276	+	15.6106i	−0.888054	+	1.53815i	−0.0458803	+	0.998947i	$0.514609\pi$
$103$	−9.01276	+	15.6106i	−0.888054	+	1.53815i	−0.842173	+	0.539207i	$0.818724\pi$
$104$	−2.12132	−	3.67423i	−0.208013	−	0.360288i
$105$		0			0
$106$	5.30948	−	9.19628i	0.515702	−	0.893222i
$107$	−7.87298	−	13.6364i	−0.761110	−	1.31828i	−0.942279	−	0.334829i	$-0.891321\pi$
$107$	−7.87298	−	13.6364i	−0.761110	−	1.31828i	0.181169	−	0.983452i	$-0.442012\pi$
$108$	4.94975	+	1.58114i	0.476290	+	0.152145i
$109$	−4.56351	+	7.90423i	−0.437105	+	0.757088i	−0.997465	−	0.0711614i	$-0.977329\pi$
$109$	−4.56351	+	7.90423i	−0.437105	+	0.757088i	0.560360	+	0.828249i	$0.310663\pi$
$110$	−8.12602			−0.774786
$111$	6.89144	+	15.4097i	0.654106	+	1.46263i
$112$		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	$0.775021\pi$
$114$	−0.563508	−	1.26004i	−0.0527774	−	0.118014i
$115$	6.85224	+	11.8684i	0.638974	+	1.10674i
$116$	−4.43649	+	7.68423i	−0.411918	+	0.713463i
$117$	−3.97320	−	12.0919i	−0.367322	−	1.11790i
$118$	−2.64880			−0.243842
$119$		0			0
$120$	2.06351	−	2.85008i	0.188372	−	0.260176i
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	−0.796921			−0.0721498
$123$	4.00000	+	8.94427i	0.360668	+	0.806478i
$124$	5.47723			0.491869
$125$	11.9310			1.06714
$126$		0			0
$127$	14.7460			1.30849			0.654246	−	0.756281i	$-0.272986\pi$
$127$	14.7460			1.30849			0.654246	+	0.756281i	$0.272986\pi$
$128$	1.00000			0.0883883
$129$	−9.01276	+	12.4483i	−0.793529	+	1.09601i
$130$	−8.61895			−0.755932
$131$	3.93399	−	6.81388i	0.343715	−	0.595331i	−0.641405	−	0.767203i	$-0.721648\pi$
$131$	3.93399	−	6.81388i	0.343715	−	0.595331i	0.985119	+	0.171871i	$0.0549814\pi$
$132$	−2.82843	−	6.32456i	−0.246183	−	0.550482i
$133$		0			0
$134$	0.872983			0.0754143
$135$	7.80948	−	7.10222i	0.672133	−	0.611262i
$136$	0.707107	−	1.22474i	0.0606339	−	0.105021i
$137$	−7.74597	−	13.4164i	−0.661783	−	1.14624i	−0.980147	−	0.198273i	$-0.936467\pi$
$137$	−7.74597	−	13.4164i	−0.661783	−	1.14624i	0.318364	−	0.947968i	$-0.396866\pi$
$138$	−6.85224	+	9.46420i	−0.583301	+	0.805646i
$139$	−9.23159	−	15.9896i	−0.783013	−	1.35622i	−0.930179	−	0.367107i	$-0.880348\pi$
$139$	−9.23159	−	15.9896i	−0.783013	−	1.35622i	0.147165	−	0.989112i	$-0.452985\pi$
$140$		0			0
$141$	−11.8730	−	1.22803i	−0.999886	−	0.103419i
$142$	−2.12702			−0.178495
$143$	−8.48528	+	14.6969i	−0.709575	+	1.22902i
$144$	2.93649	+	0.614017i	0.244708	+	0.0511681i
$145$	9.01276	+	15.6106i	0.748469	+	1.29639i
$146$	7.68836	−	13.3166i	0.636293	−	1.10209i
$147$		0			0
$148$	4.87298	+	8.44025i	0.400557	+	0.693785i
$149$	0.127017	−	0.219999i	0.0104056	−	0.0180230i	−0.860776	−	0.508984i	$-0.830021\pi$
$149$	0.127017	−	0.219999i	0.0104056	−	0.0180230i	0.871181	+	0.490961i	$0.163354\pi$
$150$	0.617292	+	1.38031i	0.0504017	+	0.112702i
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	0.550645	−	0.834740i	$-0.314382\pi$
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	−0.998228	+	0.0595022i	$0.981049\pi$
$152$	−0.398461	−	0.690154i	−0.0323194	−	0.0559789i
$153$	2.82843	−	3.16228i	0.228665	−	0.255655i
$154$		0			0
$155$	5.56351	−	9.63628i	0.446872	−	0.774005i
$156$	−3.00000	−	6.70820i	−0.240192	−	0.537086i
$157$	−6.45378			−0.515067			−0.257534	−	0.966269i	$-0.582910\pi$
$157$	−6.45378			−0.515067			−0.257534	+	0.966269i	$0.582910\pi$
$158$	5.87298			0.467229
$159$	10.7862	−	14.8978i	0.855404	−	1.18147i
$160$	1.01575	−	1.75934i	0.0803023	−	0.139088i
$161$		0			0
$162$	8.24597	+	3.60611i	0.647864	+	0.283323i
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	0.601035	−	0.799223i	$-0.294755\pi$
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	−0.992665	+	0.120900i	$0.961422\pi$
$164$	2.82843	+	4.89898i	0.220863	+	0.382546i
$165$	−14.0000	−	1.44803i	−1.08990	−	0.112729i
$166$	4.15283	−	7.19291i	0.322322	−	0.558278i
$167$	−6.18433	−	10.7116i	−0.478558	−	0.828887i	0.521140	−	0.853471i	$-0.325507\pi$
$167$	−6.18433	−	10.7116i	−0.478558	−	0.828887i	−0.999698	+	0.0245846i	$0.992174\pi$
$168$		0			0
$169$	−2.50000	+	4.33013i	−0.192308	+	0.333087i
$170$	−1.43649	−	2.48808i	−0.110174	−	0.190827i
$171$	−0.746310	−	2.27129i	−0.0570718	−	0.173690i
$172$	−4.43649	+	7.68423i	−0.338279	+	0.585917i
$173$	−12.7279			−0.967686			−0.483843	−	0.875155i	$-0.660759\pi$
$173$	−12.7279			−0.967686			−0.483843	+	0.875155i	$0.660759\pi$
$174$	−9.01276	+	12.4483i	−0.683256	+	0.943702i
$175$		0			0
$176$	−2.00000	−	3.46410i	−0.150756	−	0.261116i
$177$	−4.56351	−	0.472008i	−0.343014	−	0.0354783i
$178$	3.53553	+	6.12372i	0.264999	+	0.458993i
$179$	−0.436492	+	0.756026i	−0.0326249	+	0.0565080i	−0.881877	−	0.471480i	$-0.843720\pi$
$179$	−0.436492	+	0.756026i	−0.0326249	+	0.0565080i	0.849252	+	0.527988i	$0.177053\pi$
$180$	4.06301	−	4.54259i	0.302839	−	0.338584i
$181$	7.86799			0.584823			0.292412	−	0.956293i	$-0.405542\pi$
$181$	7.86799			0.584823			0.292412	+	0.956293i	$0.405542\pi$
$182$		0			0
$183$	−1.37298	−	0.142009i	−0.101494	−	0.0104976i
$184$	−3.37298	+	5.84218i	−0.248660	+	0.430691i
$185$	19.7990			1.45565
$186$	9.43649	+	0.976025i	0.691917	+	0.0715656i
$187$	−5.65685			−0.413670
$188$	−6.89144			−0.502610
$189$		0			0
$190$	−1.61895			−0.117451
$191$	−13.8730			−1.00381			−0.501907	−	0.864922i	$-0.667368\pi$
$191$	−13.8730			−1.00381			−0.501907	+	0.864922i	$0.667368\pi$
$192$	1.72286	+	0.178197i	0.124337	+	0.0128603i
$193$	16.1270			1.16085			0.580424	−	0.814314i	$-0.302887\pi$
$193$	16.1270			1.16085			0.580424	+	0.814314i	$0.302887\pi$
$194$	−8.92295	+	15.4550i	−0.640630	+	1.10960i
$195$	−14.8492	−	1.53587i	−1.06338	−	0.109986i
$196$		0			0
$197$	−6.61895			−0.471581			−0.235790	−	0.971804i	$-0.575768\pi$
$197$	−6.61895			−0.471581			−0.235790	+	0.971804i	$0.575768\pi$
$198$	−3.74597	−	11.4003i	−0.266214	−	0.810187i
$199$	−10.3372	+	17.9045i	−0.732782	+	1.26922i	0.222908	+	0.974839i	$0.428445\pi$
$199$	−10.3372	+	17.9045i	−0.732782	+	1.26922i	−0.955690	+	0.294376i	$0.904888\pi$
$200$	0.436492	+	0.756026i	0.0308646	+	0.0534591i
$201$	1.50403	+	0.155563i	0.106086	+	0.0109726i
$202$	−3.93399	−	6.81388i	−0.276795	−	0.479423i
$203$		0			0
$204$	1.43649	−	1.98406i	0.100575	−	0.138912i
$205$	11.4919			0.802631
$206$	−9.01276	+	15.6106i	−0.627949	+	1.08764i
$207$	−13.4919	+	15.0844i	−0.937754	+	1.04844i
$208$	−2.12132	−	3.67423i	−0.147087	−	0.254762i
$209$	−1.59384	+	2.76062i	−0.110248	+	0.190956i
$210$		0			0
$211$	1.30948	+	2.26808i	0.0901480	+	0.156141i	0.907573	−	0.419894i	$-0.137933\pi$
$211$	1.30948	+	2.26808i	0.0901480	+	0.156141i	−0.817425	+	0.576035i	$0.804599\pi$
$212$	5.30948	−	9.19628i	0.364656	−	0.631603i
$213$	−3.66455	−	0.379028i	−0.251091	−	0.0259706i
$214$	−7.87298	−	13.6364i	−0.538186	−	0.932166i
$215$	9.01276	+	15.6106i	0.614665	+	1.06463i
$216$	4.94975	+	1.58114i	0.336788	+	0.107583i
$217$		0			0
$218$	−4.56351	+	7.90423i	−0.309080	+	0.535342i
$219$	15.6190	−	21.5726i	1.05543	−	1.45774i
$220$	−8.12602			−0.547856
$221$	−6.00000			−0.403604
$222$	6.89144	+	15.4097i	0.462523	+	1.03423i
$223$	−5.74667	+	9.95352i	−0.384825	+	0.666537i	−0.991745	−	0.128226i	$-0.959072\pi$
$223$	−5.74667	+	9.95352i	−0.384825	+	0.666537i	0.606920	+	0.794763i	$0.292405\pi$
$224$		0			0
$225$	0.817542	+	2.48808i	0.0545028	+	0.165872i
$226$	1.93649	+	3.35410i	0.128814	+	0.223112i
$227$	−3.04726	−	5.27801i	−0.202254	−	0.350314i	0.747001	−	0.664823i	$-0.231493\pi$
$227$	−3.04726	−	5.27801i	−0.202254	−	0.350314i	−0.949254	+	0.314510i	$0.898160\pi$
$228$	−0.563508	−	1.26004i	−0.0373193	−	0.0834484i
$229$	3.93399	−	6.81388i	0.259966	−	0.450274i	−0.706267	−	0.707946i	$-0.749622\pi$
$229$	3.93399	−	6.81388i	0.259966	−	0.450274i	0.966232	+	0.257672i	$0.0829554\pi$
$230$	6.85224	+	11.8684i	0.451823	+	0.782580i
$231$		0			0
$232$	−4.43649	+	7.68423i	−0.291270	+	0.504494i
$233$	−11.3730	−	19.6986i	−0.745069	−	1.29050i	−0.950163	−	0.311755i	$-0.899083\pi$
$233$	−11.3730	−	19.6986i	−0.745069	−	1.29050i	0.205094	−	0.978742i	$-0.434250\pi$
$234$	−3.97320	−	12.0919i	−0.259736	−	0.790471i
$235$	−7.00000	+	12.1244i	−0.456630	+	0.790906i
$236$	−2.64880			−0.172422
$237$	10.1183	+	1.04655i	0.657256	+	0.0679806i
$238$		0			0
$239$	7.50000	+	12.9904i	0.485135	+	0.840278i	0.999854	−	0.0170808i	$-0.00543724\pi$
$239$	7.50000	+	12.9904i	0.485135	+	0.840278i	−0.514719	+	0.857359i	$0.672104\pi$
$240$	2.06351	−	2.85008i	0.133199	−	0.183972i
$241$	−0.886735	−	1.53587i	−0.0571197	−	0.0989341i	0.836052	−	0.548651i	$-0.184858\pi$
$241$	−0.886735	−	1.53587i	−0.0571197	−	0.0989341i	−0.893171	+	0.449717i	$0.851525\pi$
$242$	−2.50000	+	4.33013i	−0.160706	+	0.278351i
$243$	13.5640	+	7.68223i	0.870134	+	0.492815i
$244$	−0.796921			−0.0510176
$245$		0			0
$246$	4.00000	+	8.94427i	0.255031	+	0.570266i
$247$	−1.69052	+	2.92808i	−0.107566	+	0.186309i
$248$	5.47723			0.347804
$249$	8.43649	−	11.6523i	0.534641	−	0.738438i
$250$	11.9310			0.754583
$251$	−25.8935			−1.63438			−0.817192	−	0.576366i	$-0.804470\pi$
$251$	−25.8935			−1.63438			−0.817192	+	0.576366i	$0.804470\pi$
$252$		0			0
$253$	26.9839			1.69646
$254$	14.7460			0.925244
$255$	−2.03151	−	4.54259i	−0.127218	−	0.284468i
$256$	1.00000			0.0625000
$257$	6.98125	−	12.0919i	0.435479	−	0.754271i	−0.561856	−	0.827235i	$-0.689912\pi$
$257$	6.98125	−	12.0919i	0.435479	−	0.754271i	0.997335	+	0.0729640i	$0.0232458\pi$
$258$	−9.01276	+	12.4483i	−0.561110	+	0.774996i
$259$		0			0
$260$	−8.61895			−0.534525
$261$	−17.7460	+	19.8406i	−1.09845	+	1.22810i
$262$	3.93399	−	6.81388i	0.243043	−	0.420963i
$263$	−2.80948	−	4.86615i	−0.173240	−	0.300060i	0.766311	−	0.642470i	$-0.222090\pi$
$263$	−2.80948	−	4.86615i	−0.173240	−	0.300060i	−0.939551	+	0.342410i	$0.888757\pi$
$264$	−2.82843	−	6.32456i	−0.174078	−	0.389249i
$265$	−10.7862	−	18.6823i	−0.662593	−	1.14764i
$266$		0			0
$267$	5.00000	+	11.1803i	0.305995	+	0.684226i
$268$	0.872983			0.0533259
$269$	1.72286	−	2.98408i	0.105045	−	0.181943i	−0.808712	−	0.588205i	$-0.799835\pi$
$269$	1.72286	−	2.98408i	0.105045	−	0.181943i	0.913756	+	0.406262i	$0.133168\pi$
$270$	7.80948	−	7.10222i	0.475270	−	0.432227i
$271$	3.53553	+	6.12372i	0.214768	+	0.371990i	0.953201	−	0.302338i	$-0.0977670\pi$
$271$	3.53553	+	6.12372i	0.214768	+	0.371990i	−0.738433	+	0.674327i	$0.764434\pi$
$272$	0.707107	−	1.22474i	0.0428746	−	0.0742611i
$273$		0			0
$274$	−7.74597	−	13.4164i	−0.467951	−	0.810515i
$275$	1.74597	−	3.02410i	0.105286	−	0.182360i
$276$	−6.85224	+	9.46420i	−0.412456	+	0.569678i
$277$	12.1825	+	21.1006i	0.731973	+	1.26781i	0.956039	+	0.293240i	$0.0947336\pi$
$277$	12.1825	+	21.1006i	0.731973	+	1.26781i	−0.224066	+	0.974574i	$0.571933\pi$
$278$	−9.23159	−	15.9896i	−0.553674	−	0.958992i
$279$	16.0838	+	3.36311i	0.962914	+	0.201344i
$280$		0			0
$281$	3.37298	−	5.84218i	0.201215	−	0.348515i	−0.747705	−	0.664031i	$-0.768844\pi$
$281$	3.37298	−	5.84218i	0.201215	−	0.348515i	0.948920	+	0.315516i	$0.102178\pi$
$282$	−11.8730	−	1.22803i	−0.707026	−	0.0731283i
$283$	−10.5168			−0.625158			−0.312579	−	0.949892i	$-0.601193\pi$
$283$	−10.5168			−0.625158			−0.312579	+	0.949892i	$0.601193\pi$
$284$	−2.12702			−0.126215
$285$	−2.78922	−	0.288492i	−0.165219	−	0.0170888i
$286$	−8.48528	+	14.6969i	−0.501745	+	0.869048i
$287$		0			0
$288$	2.93649	+	0.614017i	0.173034	+	0.0361813i
$289$	7.50000	+	12.9904i	0.441176	+	0.764140i
$290$	9.01276	+	15.6106i	0.529247	+	0.916683i
$291$	−18.1270	+	25.0367i	−1.06262	+	1.46768i
$292$	7.68836	−	13.3166i	0.449927	−	0.779297i
$293$	−3.13707	−	5.43357i	−0.183270	−	0.317433i	0.759722	−	0.650248i	$-0.225335\pi$
$293$	−3.13707	−	5.43357i	−0.183270	−	0.317433i	−0.942992	+	0.332815i	$0.892002\pi$
$294$		0			0
$295$	−2.69052	+	4.66013i	−0.156648	+	0.271323i
$296$	4.87298	+	8.44025i	0.283236	+	0.490580i
$297$	−4.42227	−	20.3087i	−0.256606	−	1.17843i
$298$	0.127017	−	0.219999i	0.00735788	−	0.0127442i
$299$	28.6207			1.65518
$300$	0.617292	+	1.38031i	0.0356394	+	0.0796921i
$301$		0			0
$302$	−5.50000	−	9.52628i	−0.316489	−	0.548176i
$303$	−5.56351	−	12.4404i	−0.319615	−	0.714681i
$304$	−0.398461	−	0.690154i	−0.0228533	−	0.0395830i
$305$	−0.809475	+	1.40205i	−0.0463504	+	0.0802813i
$306$	2.82843	−	3.16228i	0.161690	−	0.180775i
$307$	24.1200			1.37660			0.688302	−	0.725425i	$-0.258357\pi$
$307$	24.1200			1.37660			0.688302	+	0.725425i	$0.258357\pi$
$308$		0			0
$309$	−18.3095	+	25.2888i	−1.04159	+	1.43863i
$310$	5.56351	−	9.63628i	0.315986	−	0.547304i
$311$	1.41421			0.0801927			0.0400963	−	0.999196i	$-0.487234\pi$
$311$	1.41421			0.0801927			0.0400963	+	0.999196i	$0.487234\pi$
$312$	−3.00000	−	6.70820i	−0.169842	−	0.379777i
$313$	−26.6904			−1.50863			−0.754316	−	0.656511i	$-0.772031\pi$
$313$	−26.6904			−1.50863			−0.754316	+	0.656511i	$0.772031\pi$
$314$	−6.45378			−0.364208
$315$		0			0
$316$	5.87298			0.330381
$317$	1.38105			0.0775675			0.0387837	−	0.999248i	$-0.487652\pi$
$317$	1.38105			0.0775675			0.0387837	+	0.999248i	$0.487652\pi$
$318$	10.7862	−	14.8978i	0.604862	−	0.835425i
$319$	35.4919			1.98717
$320$	1.01575	−	1.75934i	0.0567823	−	0.0983499i
$321$	−11.1341	−	24.8966i	−0.621444	−	1.38959i
$322$		0			0
$323$	−1.12702			−0.0627089
$324$	8.24597	+	3.60611i	0.458109	+	0.200339i
$325$	1.85188	−	3.20755i	0.102724	−	0.177923i
$326$	−5.00000	−	8.66025i	−0.276924	−	0.479647i
$327$	−9.27079	+	12.8047i	−0.512676	+	0.708100i
$328$	2.82843	+	4.89898i	0.156174	+	0.270501i
$329$		0			0
$330$	−14.0000	−	1.44803i	−0.770675	−	0.0797116i
$331$	−18.3649			−1.00943			−0.504714	−	0.863287i	$-0.668402\pi$
$331$	−18.3649			−1.00943			−0.504714	+	0.863287i	$0.668402\pi$
$332$	4.15283	−	7.19291i	0.227916	−	0.394762i
$333$	9.12702	+	27.7768i	0.500157	+	1.52216i
$334$	−6.18433	−	10.7116i	−0.338392	−	0.586111i
$335$	0.886735	−	1.53587i	0.0484475	−	0.0839136i
$336$		0			0
$337$	−0.127017	−	0.219999i	−0.00691904	−	0.0119841i	0.862545	−	0.505980i	$-0.168869\pi$
$337$	−0.127017	−	0.219999i	−0.00691904	−	0.0119841i	−0.869464	+	0.493996i	$0.835536\pi$
$338$	−2.50000	+	4.33013i	−0.135982	+	0.235528i
$339$	2.73861	+	6.12372i	0.148741	+	0.332595i
$340$	−1.43649	−	2.48808i	−0.0779047	−	0.134935i
$341$	−10.9545	−	18.9737i	−0.593217	−	1.02748i
$342$	−0.746310	−	2.27129i	−0.0403558	−	0.122817i
$343$		0			0
$344$	−4.43649	+	7.68423i	−0.239200	+	0.414306i
$345$	9.69052	+	21.6687i	0.521720	+	1.16660i
$346$	−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	$0.566667\pi$
$348$	−9.01276	+	12.4483i	−0.483135	+	0.667298i
$349$	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
$351$	−4.69052	−	21.5406i	−0.250362	−	1.14975i
$352$	−2.00000	−	3.46410i	−0.106600	−	0.184637i
$353$	−9.01276	−	15.6106i	−0.479701	−	0.830866i	0.520028	−	0.854149i	$-0.325921\pi$
$353$	−9.01276	−	15.6106i	−0.479701	−	0.830866i	−0.999729	+	0.0232830i	$0.992588\pi$
$354$	−4.56351	−	0.472008i	−0.242548	−	0.0250869i
$355$	−2.16052	+	3.74214i	−0.114669	+	0.198612i
$356$	3.53553	+	6.12372i	0.187383	+	0.324557i
$357$		0			0
$358$	−0.436492	+	0.756026i	−0.0230693	+	0.0399572i
$359$	14.1190	+	24.4547i	0.745170	+	1.29067i	0.950115	+	0.311898i	$0.100965\pi$
$359$	14.1190	+	24.4547i	0.745170	+	1.29067i	−0.204946	+	0.978773i	$0.565702\pi$
$360$	4.06301	−	4.54259i	0.214140	−	0.239415i
$361$	9.18246	−	15.9045i	0.483287	−	0.837078i
$362$	7.86799			0.413532
$363$	−5.07877	+	7.01471i	−0.266566	+	0.368177i
$364$		0			0
$365$	−15.6190	−	27.0528i	−0.817533	−	1.41601i
$366$	−1.37298	−	0.142009i	−0.0717670	−	0.00742293i
$367$	−2.03151	−	3.51867i	−0.106044	−	0.183673i	0.808120	−	0.589017i	$-0.200485\pi$
$367$	−2.03151	−	3.51867i	−0.106044	−	0.183673i	−0.914164	+	0.405344i	$0.867152\pi$
$368$	−3.37298	+	5.84218i	−0.175829	+	0.304545i
$369$	5.29760	+	16.1225i	0.275782	+	0.839305i
$370$	19.7990			1.02930
$371$		0			0
$372$	9.43649	+	0.976025i	0.489259	+	0.0506045i
$373$	4.43649	−	7.68423i	0.229713	−	0.397874i	−0.728010	−	0.685566i	$-0.759555\pi$
$373$	4.43649	−	7.68423i	0.229713	−	0.397874i	0.957723	+	0.287692i	$0.0928880\pi$
$374$	−5.65685			−0.292509
$375$	20.5554	+	2.12607i	1.06148	+	0.109790i
$376$	−6.89144			−0.355399
$377$	37.6449			1.93881
$378$		0			0
$379$	−12.3649			−0.635143			−0.317572	−	0.948234i	$-0.602867\pi$
$379$	−12.3649			−0.635143			−0.317572	+	0.948234i	$0.602867\pi$
$380$	−1.61895			−0.0830504
$381$	25.4052	+	2.62769i	1.30155	+	0.134620i
$382$	−13.8730			−0.709804
$383$	−11.9310	+	20.6651i	−0.609646	+	1.05594i	0.381653	+	0.924306i	$0.375355\pi$
$383$	−11.9310	+	20.6651i	−0.609646	+	1.05594i	−0.991299	+	0.131632i	$0.957978\pi$
$384$	1.72286	+	0.178197i	0.0879193	+	0.00909358i
$385$		0			0
$386$	16.1270			0.820844
$387$	−17.7460	+	19.8406i	−0.902078	+	1.00855i
$388$	−8.92295	+	15.4550i	−0.452994	+	0.784608i
$389$	−10.4365	−	18.0765i	−0.529151	−	0.916517i	−0.999422	−	0.0339945i	$-0.989177\pi$
$389$	−10.4365	−	18.0765i	−0.529151	−	0.916517i	0.470271	−	0.882522i	$-0.344156\pi$
$390$	−14.8492	−	1.53587i	−0.751921	−	0.0777718i
$391$	4.77012	+	8.26209i	0.241235	+	0.417832i
$392$		0			0
$393$	7.99193	−	11.0383i	0.403140	−	0.556810i
$394$	−6.61895			−0.333458
$395$	5.96550	−	10.3325i	0.300157	−	0.519887i
$396$	−3.74597	−	11.4003i	−0.188242	−	0.572889i
$397$	3.53553	+	6.12372i	0.177443	+	0.307341i	0.941004	−	0.338395i	$-0.109884\pi$
$397$	3.53553	+	6.12372i	0.177443	+	0.307341i	−0.763561	+	0.645736i	$0.776551\pi$
$398$	−10.3372	+	17.9045i	−0.518155	+	0.897471i
$399$		0			0
$400$	0.436492	+	0.756026i	0.0218246	+	0.0378013i
$401$	−1.93649	+	3.35410i	−0.0967038	+	0.167496i	−0.910318	−	0.413909i	$-0.864163\pi$
$401$	−1.93649	+	3.35410i	−0.0967038	+	0.167496i	0.813615	+	0.581405i	$0.197497\pi$
$402$	1.50403	+	0.155563i	0.0750141	+	0.00775878i
$403$	−11.6190	−	20.1246i	−0.578781	−	1.00248i
$404$	−3.93399	−	6.81388i	−0.195724	−	0.339003i
$405$	14.7202	−	10.8445i	0.731454	−	0.538868i
$406$		0			0
$407$	19.4919	−	33.7610i	0.966179	−	1.67347i
$408$	1.43649	−	1.98406i	0.0711169	−	0.0982256i
$409$	31.6288			1.56394			0.781971	−	0.623315i	$-0.214214\pi$
$409$	31.6288			1.56394			0.781971	+	0.623315i	$0.214214\pi$
$410$	11.4919			0.567546
$411$	−10.9545	−	24.4949i	−0.540343	−	1.20824i
$412$	−9.01276	+	15.6106i	−0.444027	+	0.769077i
$413$		0			0
$414$	−13.4919	+	15.0844i	−0.663092	+	0.741360i
$415$	−8.43649	−	14.6124i	−0.414131	−	0.717296i
$416$	−2.12132	−	3.67423i	−0.104006	−	0.180144i
$417$	−13.0554	−	29.1929i	−0.639328	−	1.42958i
$418$	−1.59384	+	2.76062i	−0.0779574	+	0.135026i
$419$	−1.99230	−	3.45077i	−0.0973304	−	0.168581i	0.813248	−	0.581917i	$-0.197697\pi$
$419$	−1.99230	−	3.45077i	−0.0973304	−	0.168581i	−0.910579	+	0.413335i	$0.864364\pi$
$420$		0			0
$421$	2.56351	−	4.44013i	0.124938	−	0.216399i	−0.796771	−	0.604282i	$-0.793460\pi$
$421$	2.56351	−	4.44013i	0.124938	−	0.216399i	0.921709	+	0.387883i	$0.126794\pi$
$422$	1.30948	+	2.26808i	0.0637442	+	0.110408i
$423$	−20.2367	−	4.23146i	−0.983940	−	0.205741i
$424$	5.30948	−	9.19628i	0.257851	−	0.446611i
$425$	1.23458			0.0598862
$426$	−3.66455	−	0.379028i	−0.177548	−	0.0183640i
$427$		0			0
$428$	−7.87298	−	13.6364i	−0.380555	−	0.659141i
$429$	−17.2379	+	23.8087i	−0.832254	+	1.14950i
$430$	9.01276	+	15.6106i	0.434634	+	0.752808i
$431$	−4.74597	+	8.22026i	−0.228605	+	0.395956i	−0.957395	−	0.288782i	$-0.906750\pi$
$431$	−4.74597	+	8.22026i	−0.228605	+	0.395956i	0.728790	+	0.684737i	$0.240083\pi$
$432$	4.94975	+	1.58114i	0.238145	+	0.0760726i
$433$	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
$435$	12.7460	+	28.5008i	0.611122	+	1.36651i
$436$	−4.56351	+	7.90423i	−0.218552	+	0.378544i
$437$	5.37600			0.257169
$438$	15.6190	−	21.5726i	0.746302	−	1.03078i
$439$	−10.9545			−0.522827			−0.261414	−	0.965227i	$-0.584189\pi$
$439$	−10.9545			−0.522827			−0.261414	+	0.965227i	$0.584189\pi$
$440$	−8.12602			−0.387393
$441$		0			0
$442$	−6.00000			−0.285391
$443$	24.3649			1.15761			0.578806	−	0.815465i	$-0.303519\pi$
$443$	24.3649			1.15761			0.578806	+	0.815465i	$0.303519\pi$
$444$	6.89144	+	15.4097i	0.327053	+	0.731313i
$445$	14.3649			0.680962
$446$	−5.74667	+	9.95352i	−0.272113	+	0.471313i
$447$	0.258035	−	0.356394i	0.0122046	−	0.0168569i
$448$		0			0
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$	0.817542	+	2.48808i	0.0385393	+	0.117289i
$451$	11.3137	−	19.5959i	0.532742	−	0.922736i
$452$	1.93649	+	3.35410i	0.0910849	+	0.157764i
$453$	−7.77817	−	17.3925i	−0.365451	−	0.817172i
$454$	−3.04726	−	5.27801i	−0.143015	−	0.247709i
$455$		0			0
$456$	−0.563508	−	1.26004i	−0.0263887	−	0.0590069i
$457$	33.8730			1.58451			0.792256	−	0.610189i	$-0.208907\pi$
$457$	33.8730			1.58451			0.792256	+	0.610189i	$0.208907\pi$
$458$	3.93399	−	6.81388i	0.183823	−	0.318392i
$459$	5.43649	−	4.94414i	0.253754	−	0.230773i
$460$	6.85224	+	11.8684i	0.319487	+	0.553368i
$461$	−4.98895	+	8.64112i	−0.232359	+	0.402457i	−0.958502	−	0.285087i	$-0.907978\pi$
$461$	−4.98895	+	8.64112i	−0.232359	+	0.402457i	0.726143	+	0.687544i	$0.241311\pi$
$462$		0			0
$463$	−10.8095	−	18.7226i	−0.502359	−	0.870111i	−0.999996	−	0.00272598i	$-0.999132\pi$
$463$	−10.8095	−	18.7226i	−0.502359	−	0.870111i	0.497637	−	0.867385i	$-0.334201\pi$
$464$	−4.43649	+	7.68423i	−0.205959	+	0.356731i
$465$	11.3023	−	15.6106i	0.524132	−	0.723922i
$466$	−11.3730	−	19.6986i	−0.526843	−	0.912519i
$467$	19.5295	+	33.8262i	0.903720	+	1.56529i	0.822627	+	0.568582i	$0.192508\pi$
$467$	19.5295	+	33.8262i	0.903720	+	1.56529i	0.0810929	+	0.996707i	$0.474159\pi$
$468$	−3.97320	−	12.0919i	−0.183661	−	0.558948i
$469$		0			0
$470$	−7.00000	+	12.1244i	−0.322886	+	0.559255i
$471$	−11.1190	−	1.15004i	−0.512334	−	0.0529912i
$472$	−2.64880			−0.121921
$473$	35.4919			1.63192
$474$	10.1183	+	1.04655i	0.464750	+	0.0480695i
$475$	0.347849	−	0.602493i	0.0159604	−	0.0276443i
$476$		0			0
$477$	21.2379	−	23.7447i	0.972417	−	1.08719i
$478$	7.50000	+	12.9904i	0.343042	+	0.594166i
$479$	−9.01276	−	15.6106i	−0.411803	−	0.713265i	0.583284	−	0.812269i	$-0.301768\pi$
$479$	−9.01276	−	15.6106i	−0.411803	−	0.713265i	−0.995087	+	0.0990041i	$0.968434\pi$
$480$	2.06351	−	2.85008i	0.0941858	−	0.130088i
$481$	20.6743	−	35.8090i	0.942668	−	1.63275i
$482$	−0.886735	−	1.53587i	−0.0403897	−	0.0699570i
$483$		0			0
$484$	−2.50000	+	4.33013i	−0.113636	+	0.196824i
$485$	18.1270	+	31.3969i	0.823105	+	1.42566i
$486$	13.5640	+	7.68223i	0.615278	+	0.348473i
$487$	−15.2460	+	26.4068i	−0.690861	+	1.19661i	0.280696	+	0.959797i	$0.409435\pi$
$487$	−15.2460	+	26.4068i	−0.690861	+	1.19661i	−0.971556	+	0.236809i	$0.923898\pi$
$488$	−0.796921			−0.0360749
$489$	−7.07107	−	15.8114i	−0.319765	−	0.715016i
$490$		0			0
$491$	6.87298	+	11.9044i	0.310173	+	0.537236i	0.978400	−	0.206722i	$-0.0662796\pi$
$491$	6.87298	+	11.9044i	0.310173	+	0.537236i	−0.668226	+	0.743958i	$0.732946\pi$
$492$	4.00000	+	8.94427i	0.180334	+	0.403239i
$493$	6.27415	+	10.8671i	0.282573	+	0.489431i
$494$	−1.69052	+	2.92808i	−0.0760603	+	0.131740i
$495$	−23.8620	−	4.98952i	−1.07252	−	0.224262i
$496$	5.47723			0.245935
$497$		0			0
$498$	8.43649	−	11.6523i	0.378048	−	0.522154i
$499$	7.12702	−	12.3444i	0.319049	−	0.552609i	−0.661241	−	0.750174i	$-0.729970\pi$
$499$	7.12702	−	12.3444i	0.319049	−	0.552609i	0.980290	+	0.197564i	$0.0633032\pi$
$500$	11.9310			0.533571
$501$	−8.74597	−	19.5566i	−0.390741	−	0.873723i
$502$	−25.8935			−1.15568
$503$	−18.0255			−0.803718			−0.401859	−	0.915702i	$-0.631636\pi$
$503$	−18.0255			−0.803718			−0.401859	+	0.915702i	$0.631636\pi$
$504$		0			0
$505$	−15.9839			−0.711273
$506$	26.9839			1.19958
$507$	−5.07877	+	7.01471i	−0.225556	+	0.311534i
$508$	14.7460			0.654246
$509$	16.8807	−	29.2383i	0.748226	−	1.29597i	−0.200446	−	0.979705i	$-0.564239\pi$
$509$	16.8807	−	29.2383i	0.748226	−	1.29597i	0.948672	−	0.316261i	$-0.102427\pi$
$510$	−2.03151	−	4.54259i	−0.0899566	−	0.201149i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−0.881050	−	4.04611i	−0.0388993	−	0.178640i
$514$	6.98125	−	12.0919i	0.307930	−	0.533350i
$515$	18.3095	+	31.7129i	0.806812	+	1.39744i
$516$	−9.01276	+	12.4483i	−0.396765	+	0.548005i
$517$	13.7829	+	23.8726i	0.606170	+	1.04992i
$518$		0			0
$519$	−21.9284	−	2.26808i	−0.962551	−	0.0995575i
$520$	−8.61895			−0.377966
$521$	0.707107	−	1.22474i	0.0309789	−	0.0536570i	−0.850120	−	0.526589i	$-0.823471\pi$
$521$	0.707107	−	1.22474i	0.0309789	−	0.0536570i	0.881099	+	0.472931i	$0.156804\pi$
$522$	−17.7460	+	19.8406i	−0.776720	+	0.868399i
$523$	−15.5057	−	26.8567i	−0.678019	−	1.17436i	−0.975577	−	0.219659i	$-0.929506\pi$
$523$	−15.5057	−	26.8567i	−0.678019	−	1.17436i	0.297558	−	0.954704i	$-0.403828\pi$
$524$	3.93399	−	6.81388i	0.171857	−	0.297666i
$525$		0			0
$526$	−2.80948	−	4.86615i	−0.122499	−	0.212174i
$527$	3.87298	−	6.70820i	0.168710	−	0.292214i
$528$	−2.82843	−	6.32456i	−0.123091	−	0.275241i
$529$	−11.2540	−	19.4926i	−0.489306	−	0.847502i
$530$	−10.7862	−	18.6823i	−0.468524	−	0.811507i
$531$	−7.77817	−	1.62641i	−0.337544	−	0.0705800i
$532$		0			0
$533$	12.0000	−	20.7846i	0.519778	−	0.900281i
$534$	5.00000	+	11.1803i	0.216371	+	0.483821i
$535$	−31.9880			−1.38296
$536$	0.872983			0.0377071
$537$	−0.886735	+	1.22474i	−0.0382655	+	0.0528516i
$538$	1.72286	−	2.98408i	0.0742778	−	0.128653i
$539$		0			0
$540$	7.80948	−	7.10222i	0.336066	−	0.305631i
$541$	−8.05544	−	13.9524i	−0.346330	−	0.599862i	0.639264	−	0.768987i	$-0.279239\pi$
$541$	−8.05544	−	13.9524i	−0.346330	−	0.599862i	−0.985595	+	0.169125i	$0.945906\pi$
$542$	3.53553	+	6.12372i	0.151864	+	0.263036i
$543$	13.5554	+	1.40205i	0.581720	+	0.0601678i
$544$	0.707107	−	1.22474i	0.0303170	−	0.0525105i
$545$	9.27079	+	16.0575i	0.397117	+	0.687827i
$546$		0			0
$547$	−14.4919	+	25.1008i	−0.619630	+	1.07323i	0.369923	+	0.929062i	$0.379384\pi$
$547$	−14.4919	+	25.1008i	−0.619630	+	1.07323i	−0.989553	+	0.144169i	$0.953949\pi$
$548$	−7.74597	−	13.4164i	−0.330891	−	0.573121i
$549$	−2.34015	−	0.489323i	−0.0998753	−	0.0208838i
$550$	1.74597	−	3.02410i	0.0744483	−	0.128948i
$551$	7.07107			0.301238
$552$	−6.85224	+	9.46420i	−0.291651	+	0.402823i
$553$		0			0
$554$	12.1825	+	21.1006i	0.517583	+	0.896480i
$555$	34.1109	+	3.52812i	1.44793	+	0.149760i
$556$	−9.23159	−	15.9896i	−0.391507	−	0.678109i
$557$	−1.69052	+	2.92808i	−0.0716298	+	0.124067i	−0.899616	−	0.436682i	$-0.856153\pi$
$557$	−1.69052	+	2.92808i	−0.0716298	+	0.124067i	0.827986	+	0.560749i	$0.189487\pi$
$558$	16.0838	+	3.36311i	0.680883	+	0.142372i
$559$	37.6449			1.59221
$560$		0			0
$561$	−9.74597	−	1.00803i	−0.411475	−	0.0425592i
$562$	3.37298	−	5.84218i	0.142281	−	0.246437i
$563$	5.21919			0.219963			0.109981	−	0.993934i	$-0.464921\pi$
$563$	5.21919			0.219963			0.109981	+	0.993934i	$0.464921\pi$
$564$	−11.8730	−	1.22803i	−0.499943	−	0.0517095i
$565$	7.86799			0.331009
$566$	−10.5168			−0.442054
$567$		0			0
$568$	−2.12702			−0.0892476
$569$	7.49193			0.314078			0.157039	−	0.987592i	$-0.449805\pi$
$569$	7.49193			0.314078			0.157039	+	0.987592i	$0.449805\pi$
$570$	−2.78922	−	0.288492i	−0.116828	−	0.0120836i
$571$	0.508067			0.0212619			0.0106310	−	0.999943i	$-0.496616\pi$
$571$	0.508067			0.0212619			0.0106310	+	0.999943i	$0.496616\pi$
$572$	−8.48528	+	14.6969i	−0.354787	+	0.614510i
$573$	−23.9012	−	2.47212i	−0.998487	−	0.103274i
$574$		0			0
$575$	−5.88912			−0.245593
$576$	2.93649	+	0.614017i	0.122354	+	0.0255840i
$577$	17.5879	−	30.4631i	0.732192	−	1.26819i	−0.223752	−	0.974646i	$-0.571831\pi$
$577$	17.5879	−	30.4631i	0.732192	−	1.26819i	0.955944	−	0.293548i	$-0.0948360\pi$
$578$	7.50000	+	12.9904i	0.311959	+	0.540329i
$579$	27.7846	+	2.87379i	1.15469	+	0.119430i
$580$	9.01276	+	15.6106i	0.374234	+	0.648193i
$581$		0			0
$582$	−18.1270	+	25.0367i	−0.751389	+	1.03781i
$583$	−42.4758			−1.75917
$584$	7.68836	−	13.3166i	0.318147	−	0.551046i
$585$	−25.3095	−	5.29218i	−1.04642	−	0.218805i
$586$	−3.13707	−	5.43357i	−0.129591	−	0.224459i
$587$	−14.8884	+	25.7875i	−0.614512	+	1.06437i	0.375958	+	0.926637i	$0.377314\pi$
$587$	−14.8884	+	25.7875i	−0.614512	+	1.06437i	−0.990470	+	0.137729i	$0.956020\pi$
$588$		0			0
$589$	−2.18246	−	3.78013i	−0.0899266	−	0.155757i
$590$	−2.69052	+	4.66013i	−0.110767	+	0.191854i
$591$	−11.4035	−	1.17948i	−0.469078	−	0.0485172i
$592$	4.87298	+	8.44025i	0.200278	+	0.346892i
$593$	11.4035	+	19.7515i	0.468287	+	0.811096i	0.999343	−	0.0362403i	$-0.0115382\pi$
$593$	11.4035	+	19.7515i	0.468287	+	0.811096i	−0.531057	+	0.847336i	$0.678205\pi$
$594$	−4.42227	−	20.3087i	−0.181448	−	0.833276i
$595$		0			0
$596$	0.127017	−	0.219999i	0.00520280	−	0.00901152i
$597$	−21.0000	+	29.0049i	−0.859473	+	1.18709i
$598$	28.6207			1.17039
$599$	1.23790			0.0505792			0.0252896	−	0.999680i	$-0.491949\pi$
$599$	1.23790			0.0505792			0.0252896	+	0.999680i	$0.491949\pi$
$600$	0.617292	+	1.38031i	0.0252009	+	0.0563508i
$601$	−18.8224	+	32.6014i	−0.767783	+	1.32984i	0.170979	+	0.985275i	$0.445307\pi$
$601$	−18.8224	+	32.6014i	−0.767783	+	1.32984i	−0.938762	+	0.344565i	$0.888026\pi$
$602$		0			0
$603$	2.56351	+	0.536026i	0.104394	+	0.0218287i
$604$	−5.50000	−	9.52628i	−0.223792	−	0.387619i
$605$	5.07877	+	8.79668i	0.206481	+	0.357636i
$606$	−5.56351	−	12.4404i	−0.226002	−	0.505356i
$607$	7.86799	−	13.6278i	0.319352	−	0.553134i	−0.661001	−	0.750385i	$-0.729868\pi$
$607$	7.86799	−	13.6278i	0.319352	−	0.553134i	0.980353	+	0.197251i	$0.0632015\pi$
$608$	−0.398461	−	0.690154i	−0.0161597	−	0.0279894i
$609$		0			0
$610$	−0.809475	+	1.40205i	−0.0327747	+	0.0567674i
$611$	14.6190	+	25.3208i	0.591419	+	1.02437i
$612$	2.82843	−	3.16228i	0.114332	−	0.127827i
$613$	−1.69052	+	2.92808i	−0.0682797	+	0.118264i	−0.898144	−	0.439701i	$-0.855084\pi$
$613$	−1.69052	+	2.92808i	−0.0682797	+	0.118264i	0.829864	+	0.557965i	$0.188418\pi$
$614$	24.1200			0.973405
$615$	19.7990	+	2.04783i	0.798372	+	0.0825764i
$616$		0			0
$617$	13.8730	+	24.0287i	0.558505	+	0.967360i	0.997622	+	0.0689293i	$0.0219583\pi$
$617$	13.8730	+	24.0287i	0.558505	+	0.967360i	−0.439116	+	0.898430i	$0.644708\pi$
$618$	−18.3095	+	25.2888i	−0.736515	+	1.01726i
$619$	11.1733	+	19.3527i	0.449092	+	0.777850i	0.998327	−	0.0578175i	$-0.0184142\pi$
$619$	11.1733	+	19.3527i	0.449092	+	0.777850i	−0.549235	+	0.835668i	$0.685081\pi$
$620$	5.56351	−	9.63628i	0.223436	−	0.387002i
$621$	−25.9327	+	23.5842i	−1.04064	+	0.946399i
$622$	1.41421			0.0567048
$623$		0			0
$624$	−3.00000	−	6.70820i	−0.120096	−	0.268543i
$625$	9.93649	−	17.2105i	0.397460	−	0.688420i
$626$	−26.6904			−1.06676
$627$	−3.23790	+	4.47214i	−0.129309	+	0.178600i
$628$	−6.45378			−0.257534
$629$	13.7829			0.549559
$630$		0			0
$631$	−27.6190			−1.09949			−0.549747	−	0.835332i	$-0.685276\pi$
$631$	−27.6190			−1.09949			−0.549747	+	0.835332i	$0.685276\pi$
$632$	5.87298			0.233615
$633$	1.85188	+	4.14092i	0.0736055	+	0.164587i
$634$	1.38105			0.0548485
$635$	14.9783	−	25.9431i	0.594394	−	1.02952i
$636$	10.7862	−	14.8978i	0.427702	−	0.590735i
$637$		0			0
$638$	35.4919			1.40514
$639$	−6.24597	−	1.30602i	−0.247087	−	0.0516655i
$640$	1.01575	−	1.75934i	0.0401512	−	0.0695439i
$641$	18.5554	+	32.1390i	0.732896	+	1.26941i	0.955640	+	0.294536i	$0.0951651\pi$
$641$	18.5554	+	32.1390i	0.732896	+	1.26941i	−0.222744	+	0.974877i	$0.571502\pi$
$642$	−11.1341	−	24.8966i	−0.439427	−	0.982589i
$643$	−20.1468	−	34.8953i	−0.794514	−	1.37614i	−0.923147	−	0.384446i	$-0.874392\pi$
$643$	−20.1468	−	34.8953i	−0.794514	−	1.37614i	0.128634	−	0.991692i	$-0.458941\pi$
$644$		0			0
$645$	12.7460	+	28.5008i	0.501872	+	1.12222i
$646$	−1.12702			−0.0443419
$647$	2.73861	−	4.74342i	0.107666	−	0.186483i	−0.807158	−	0.590335i	$-0.798996\pi$
$647$	2.73861	−	4.74342i	0.107666	−	0.186483i	0.914824	+	0.403852i	$0.132329\pi$
$648$	8.24597	+	3.60611i	0.323932	+	0.141661i
$649$	5.29760	+	9.17571i	0.207949	+	0.360178i
$650$	1.85188	−	3.20755i	0.0726366	−	0.125810i
$651$		0			0
$652$	−5.00000	−	8.66025i	−0.195815	−	0.339162i
$653$	22.7460	−	39.3972i	0.890118	−	1.54173i	0.0503861	−	0.998730i	$-0.483955\pi$
$653$	22.7460	−	39.3972i	0.890118	−	1.54173i	0.839732	−	0.543001i	$-0.182712\pi$
$654$	−9.27079	+	12.8047i	−0.362517	+	0.500702i
$655$	−7.99193	−	13.8424i	−0.312271	−	0.540869i
$656$	2.82843	+	4.89898i	0.110432	+	0.191273i
$657$	30.7534	−	34.3834i	1.19981	−	1.34142i
$658$		0			0
$659$	−18.4365	+	31.9329i	−0.718184	+	1.24393i	0.243535	+	0.969892i	$0.421693\pi$
$659$	−18.4365	+	31.9329i	−0.718184	+	1.24393i	−0.961719	+	0.274039i	$0.911640\pi$
$660$	−14.0000	−	1.44803i	−0.544949	−	0.0563646i
$661$	−24.9954			−0.972207			−0.486104	−	0.873901i	$-0.661582\pi$
$661$	−24.9954			−0.972207			−0.486104	+	0.873901i	$0.661582\pi$
$662$	−18.3649			−0.713773
$663$	−10.3372	−	1.06918i	−0.401462	−	0.0415236i
$664$	4.15283	−	7.19291i	0.161161	−	0.279139i
$665$		0			0
$666$	9.12702	+	27.7768i	0.353665	+	1.07633i
$667$	−29.9284	−	51.8376i	−1.15883	−	2.00716i
$668$	−6.18433	−	10.7116i	−0.239279	−	0.414443i
$669$	−11.6744	+	16.1245i	−0.451358	+	0.623409i
$670$	0.886735	−	1.53587i	0.0342576	−	0.0593359i
$671$	1.59384	+	2.76062i	0.0615296	+	0.106572i
$672$		0			0
$673$	16.1190	−	27.9188i	0.621340	−	1.07619i	−0.367897	−	0.929867i	$-0.619922\pi$
$673$	16.1190	−	27.9188i	0.621340	−	1.07619i	0.989236	−	0.146326i	$-0.0467447\pi$
$674$	−0.127017	−	0.219999i	−0.00489250	−	0.00847406i
$675$	0.965142	+	4.43229i	0.0371483	+	0.170599i
$676$	−2.50000	+	4.33013i	−0.0961538	+	0.166543i
$677$	−12.7279			−0.489174			−0.244587	−	0.969627i	$-0.578652\pi$
$677$	−12.7279			−0.489174			−0.244587	+	0.969627i	$0.578652\pi$
$678$	2.73861	+	6.12372i	0.105176	+	0.235180i
$679$		0			0
$680$	−1.43649	−	2.48808i	−0.0550869	−	0.0954134i
$681$	−4.30948	−	9.63628i	−0.165139	−	0.369263i
$682$	−10.9545	−	18.9737i	−0.419468	−	0.726539i
$683$	3.87298	−	6.70820i	0.148196	−	0.256682i	−0.782365	−	0.622820i	$-0.785987\pi$
$683$	3.87298	−	6.70820i	0.148196	−	0.256682i	0.930561	+	0.366138i	$0.119320\pi$
$684$	−0.746310	−	2.27129i	−0.0285359	−	0.0868450i
$685$	−31.4720			−1.20248
$686$		0			0
$687$	7.99193	−	11.0383i	0.304911	−	0.421139i
$688$	−4.43649	+	7.68423i	−0.169140	+	0.292958i
$689$	−45.0524			−1.71636
$690$	9.69052	+	21.6687i	0.368912	+	0.824912i
$691$	21.2916			0.809971			0.404986	−	0.914323i	$-0.367277\pi$
$691$	21.2916			0.809971			0.404986	+	0.914323i	$0.367277\pi$
$692$	−12.7279			−0.483843
$693$		0			0
$694$	−7.74597			−0.294033
$695$	−37.5081			−1.42276
$696$	−9.01276	+	12.4483i	−0.341628	+	0.471851i
$697$	8.00000			0.303022
$698$	8.21584	−	14.2302i	0.310974	−	0.538623i
$699$	−16.0838	−	35.9645i	−0.608346	−	1.36030i
$700$		0			0
$701$	−31.7460			−1.19903			−0.599514	−	0.800364i	$-0.704640\pi$
$701$	−31.7460			−1.19903			−0.599514	+	0.800364i	$0.704640\pi$
$702$	−4.69052	−	21.5406i	−0.177032	−	0.812999i
$703$	3.88338	−	6.72622i	0.146465	−	0.253684i
$704$	−2.00000	−	3.46410i	−0.0753778	−	0.130558i
$705$	−14.2205	+	19.6412i	−0.535577	+	0.739730i
$706$	−9.01276	−	15.6106i	−0.339200	−	0.587511i
$707$		0			0
$708$	−4.56351	−	0.472008i	−0.171507	−	0.0177391i
$709$	24.7298			0.928748			0.464374	−	0.885639i	$-0.346279\pi$
$709$	24.7298			0.928748			0.464374	+	0.885639i	$0.346279\pi$
$710$	−2.16052	+	3.74214i	−0.0810830	+	0.140440i
$711$	17.2460	+	3.60611i	0.646774	+	0.135240i
$712$	3.53553	+	6.12372i	0.132500	+	0.229496i
$713$	−18.4746	+	31.9989i	−0.691879	+	1.19837i
$714$		0			0
$715$	17.2379	+	29.8569i	0.644661	+	1.11659i
$716$	−0.436492	+	0.756026i	−0.0163125	+	0.0282540i
$717$	10.6066	+	23.7171i	0.396111	+	0.885731i
$718$	14.1190	+	24.4547i	0.526915	+	0.912643i
$719$	4.68030	+	8.10653i	0.174546	+	0.302322i	0.940004	−	0.341163i	$-0.110821\pi$
$719$	4.68030	+	8.10653i	0.174546	+	0.302322i	−0.765458	+	0.643486i	$0.777488\pi$
$720$	4.06301	−	4.54259i	0.151420	−	0.169292i
$721$		0			0
$722$	9.18246	−	15.9045i	0.341736	−	0.591904i
$723$	−1.25403	−	2.80410i	−0.0466380	−	0.104286i
$724$	7.86799			0.292412
$725$	−7.74597			−0.287678
$726$	−5.07877	+	7.01471i	−0.188491	+	0.260340i
$727$	18.1153	−	31.3767i	0.671861	−	1.16370i	−0.305515	−	0.952187i	$-0.598829\pi$
$727$	18.1153	−	31.3767i	0.671861	−	1.16370i	0.977376	−	0.211509i	$-0.0678379\pi$
$728$		0			0
$729$	22.0000	+	15.6525i	0.814815	+	0.579721i
$730$	−15.6190	−	27.0528i	−0.578083	−	1.00127i
$731$	6.27415	+	10.8671i	0.232058	+	0.401936i
$732$	−1.37298	−	0.142009i	−0.0507469	−	0.00524880i
$733$	−4.82073	+	8.34975i	−0.178058	+	0.308405i	−0.941215	−	0.337808i	$-0.890315\pi$
$733$	−4.82073	+	8.34975i	−0.178058	+	0.308405i	0.763157	+	0.646213i	$0.223648\pi$
$734$	−2.03151	−	3.51867i	−0.0749843	−	0.129877i
$735$		0			0
$736$	−3.37298	+	5.84218i	−0.124330	+	0.215346i
$737$	−1.74597	−	3.02410i	−0.0643135	−	0.111394i
$738$	5.29760	+	16.1225i	0.195007	+	0.593478i
$739$	15.0000	−	25.9808i	0.551784	−	0.955718i	−0.446362	−	0.894852i	$-0.647281\pi$
$739$	15.0000	−	25.9808i	0.551784	−	0.955718i	0.998146	−	0.0608653i	$-0.0193860\pi$
$740$	19.7990			0.727825
$741$	−3.43431	+	4.74342i	−0.126163	+	0.174254i
$742$		0			0
$743$	13.8730	+	24.0287i	0.508950	+	0.881528i	0.999946	+	0.0103660i	$0.00329968\pi$
$743$	13.8730	+	24.0287i	0.508950	+	0.881528i	−0.490996	+	0.871162i	$0.663367\pi$
$744$	9.43649	+	0.976025i	0.345959	+	0.0357828i
$745$	−0.258035	−	0.446930i	−0.00945367	−	0.0163742i
$746$	4.43649	−	7.68423i	0.162432	−	0.281340i
$747$	16.6113	−	18.5720i	0.607776	−	0.679514i
$748$	−5.65685			−0.206835
$749$		0			0
$750$	20.5554	+	2.12607i	0.750579	+	0.0776330i
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	−0.722718	−	0.691143i	$-0.757107\pi$
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	0.959906	+	0.280321i	$0.0904408\pi$
$752$	−6.89144			−0.251305
$753$	−44.6109	−	4.61414i	−1.62571	−	0.168149i
$754$	37.6449			1.37095
$755$	−22.3466			−0.813275
$756$		0			0
$757$	−15.2379			−0.553831			−0.276915	−	0.960894i	$-0.589312\pi$
$757$	−15.2379			−0.553831			−0.276915	+	0.960894i	$0.589312\pi$
$758$	−12.3649			−0.449114
$759$	46.4894	+	4.80844i	1.68746	+	0.174535i
$760$	−1.61895			−0.0587255
$761$	1.14477	−	1.98280i	0.0414979	−	0.0718765i	−0.844530	−	0.535508i	$-0.820120\pi$
$761$	1.14477	−	1.98280i	0.0414979	−	0.0718765i	0.886028	+	0.463631i	$0.153454\pi$
$762$	25.4052	+	2.62769i	0.920334	+	0.0951910i
$763$		0			0
$764$	−13.8730			−0.501907
$765$	−2.69052	−	8.18825i	−0.0972761	−	0.296047i
$766$	−11.9310	+	20.6651i	−0.431085	+	0.746660i
$767$	5.61895	+	9.73231i	0.202889	+	0.351413i
$768$	1.72286	+	0.178197i	0.0621683	+	0.00643013i
$769$	4.85993	+	8.41765i	0.175254	+	0.303548i	0.940249	−	0.340488i	$-0.110592\pi$
$769$	4.85993	+	8.41765i	0.175254	+	0.303548i	−0.764995	+	0.644036i	$0.777259\pi$
$770$		0			0
$771$	14.1825	−	19.5886i	0.510769	−	0.705466i
$772$	16.1270			0.580424
$773$	1.72286	−	2.98408i	0.0619670	−	0.107330i	−0.833378	−	0.552704i	$-0.813596\pi$
$773$	1.72286	−	2.98408i	0.0619670	−	0.107330i	0.895345	+	0.445374i	$0.146929\pi$
$774$	−17.7460	+	19.8406i	−0.637866	+	0.713155i
$775$	2.39076	+	4.14092i	0.0858788	+	0.148746i
$776$	−8.92295	+	15.4550i	−0.320315	+	0.554802i
$777$		0			0
$778$	−10.4365	−	18.0765i	−0.374166	−	0.648075i
$779$	2.25403	−	3.90410i	0.0807591	−	0.139879i
$780$	−14.8492	−	1.53587i	−0.531688	−	0.0549930i
$781$	4.25403	+	7.36820i	0.152221	+	0.263655i
$782$	4.77012	+	8.26209i	0.170579	+	0.295452i
$783$	−34.1093	+	31.0203i	−1.21897	+	1.10857i
$784$		0			0
$785$	−6.55544	+	11.3544i	−0.233974	+	0.405254i
$786$	7.99193	−	11.0383i	0.285063	−	0.393724i
$787$	9.54024			0.340073			0.170036	−	0.985438i	$-0.445611\pi$
$787$	9.54024			0.340073			0.170036	+	0.985438i	$0.445611\pi$
$788$	−6.61895			−0.235790
$789$	−3.97320	−	8.88434i	−0.141450	−	0.316291i
$790$	5.96550	−	10.3325i	0.212243	−	0.367616i
$791$		0			0
$792$	−3.74597	−	11.4003i	−0.133107	−	0.405093i
$793$	1.69052	+	2.92808i	0.0600323	+	0.103979i
$794$	3.53553	+	6.12372i	0.125471	+	0.217323i
$795$	−15.2540	−	34.1091i	−0.541005	−	1.20972i
$796$	−10.3372	+	17.9045i	−0.366391	+	0.634608i
$797$	−13.0366	−	22.5800i	−0.461779	−	0.799825i	0.537271	−	0.843410i	$-0.319455\pi$
$797$	−13.0366	−	22.5800i	−0.461779	−	0.799825i	−0.999050	+	0.0435852i	$0.986122\pi$
$798$		0			0
$799$	−4.87298	+	8.44025i	−0.172394	+	0.298595i
$800$	0.436492	+	0.756026i	0.0154323	+	0.0267295i
$801$	6.62200	+	20.1531i	0.233977	+	0.712076i
$802$	−1.93649	+	3.35410i	−0.0683799	+	0.118437i
$803$	−61.5069			−2.17053
$804$	1.50403	+	0.155563i	0.0530430	+	0.00548628i
$805$		0			0
$806$	−11.6190	−	20.1246i	−0.409260	−	0.708859i
$807$	3.50000	−	4.83414i	0.123206	−	0.170170i
$808$	−3.93399	−	6.81388i	−0.138397	−	0.239711i
$809$	15.3649	−	26.6128i	0.540202	−	0.935657i	−0.458690	−	0.888596i	$-0.651681\pi$
$809$	15.3649	−	26.6128i	0.540202	−	0.935657i	0.998892	−	0.0470606i	$-0.0149854\pi$
$810$	14.7202	−	10.8445i	0.517216	−	0.381037i
$811$	13.9625			0.490290			0.245145	−	0.969486i	$-0.421164\pi$
$811$	13.9625			0.490290			0.245145	+	0.969486i	$0.421164\pi$
$812$		0			0
$813$	5.00000	+	11.1803i	0.175358	+	0.392112i
$814$	19.4919	−	33.7610i	0.683192	−	1.18332i
$815$	−20.3151			−0.711606
$816$	1.43649	−	1.98406i	0.0502873	−	0.0694560i
$817$	7.07107			0.247385
$818$	31.6288			1.10587
$819$		0			0
$820$	11.4919			0.401316
$821$	21.4919			0.750074			0.375037	−	0.927010i	$-0.377630\pi$
$821$	21.4919			0.750074			0.375037	+	0.927010i	$0.377630\pi$
$822$	−10.9545	−	24.4949i	−0.382080	−	0.854358i
$823$	−21.7460			−0.758017			−0.379008	−	0.925393i	$-0.623735\pi$
$823$	−21.7460			−0.758017			−0.379008	+	0.925393i	$0.623735\pi$
$824$	−9.01276	+	15.6106i	−0.313974	+	0.543820i
$825$	3.54694	−	4.89898i	0.123489	−	0.170561i
$826$		0			0
$827$	41.1270			1.43013			0.715063	−	0.699060i	$-0.246398\pi$
$827$	41.1270			1.43013			0.715063	+	0.699060i	$0.246398\pi$
$828$	−13.4919	+	15.0844i	−0.468877	+	0.524221i
$829$	−27.2179	+	47.1428i	−0.945317	+	1.63734i	−0.190202	+	0.981745i	$0.560914\pi$
$829$	−27.2179	+	47.1428i	−0.945317	+	1.63734i	−0.755115	+	0.655592i	$0.772419\pi$
$830$	−8.43649	−	14.6124i	−0.292835	−	0.507205i
$831$	17.2286	+	38.5243i	0.597653	+	1.33639i
$832$	−2.12132	−	3.67423i	−0.0735436	−	0.127381i
$833$		0			0
$834$	−13.0554	−	29.1929i	−0.452073	−	1.01087i
$835$	−25.1270			−0.869556
$836$	−1.59384	+	2.76062i	−0.0551242	+	0.0954779i
$837$	27.1109	+	8.66025i	0.937089	+	0.299342i
$838$	−1.99230	−	3.45077i	−0.0688230	−	0.119205i
$839$	−19.9672	+	34.5842i	−0.689345	+	1.19398i	0.282706	+	0.959207i	$0.408768\pi$
$839$	−19.9672	+	34.5842i	−0.689345	+	1.19398i	−0.972050	+	0.234773i	$0.924565\pi$
$840$		0			0
$841$	−24.8649	−	43.0673i	−0.857411	−	1.48508i
$842$	2.56351	−	4.44013i	0.0883443	−	0.153017i
$843$	6.85224	−	9.46420i	0.236004	−	0.325964i
$844$	1.30948	+	2.26808i	0.0450740	+	0.0780704i
$845$	5.07877	+	8.79668i	0.174715	+	0.302615i
$846$	−20.2367	−	4.23146i	−0.695750	−	0.145481i
$847$		0			0
$848$	5.30948	−	9.19628i	0.182328	−	0.315802i
$849$	−18.1190	−	1.87406i	−0.621841	−	0.0643176i
$850$	1.23458			0.0423459
$851$	−65.7460			−2.25374
$852$	−3.66455	−	0.379028i	−0.125545	−	0.0129853i
$853$	−22.7564	+	39.4153i	−0.779165	+	1.34955i	0.153258	+	0.988186i	$0.451024\pi$
$853$	−22.7564	+	39.4153i	−0.779165	+	1.34955i	−0.932423	+	0.361368i	$0.882310\pi$
$854$		0			0
$855$	−4.75403	−	0.994063i	−0.162585	−	0.0339962i
$856$	−7.87298	−	13.6364i	−0.269093	−	0.466083i
$857$	23.8620	+	41.3302i	0.815110	+	1.41181i	0.909249	+	0.416254i	$0.136657\pi$
$857$	23.8620	+	41.3302i	0.815110	+	1.41181i	−0.0941381	+	0.995559i	$0.530010\pi$
$858$	−17.2379	+	23.8087i	−0.588492	+	0.812816i
$859$	−1.14477	+	1.98280i	−0.0390591	+	0.0676523i	−0.884894	−	0.465792i	$-0.845769\pi$
$859$	−1.14477	+	1.98280i	−0.0390591	+	0.0676523i	0.845835	+	0.533445i	$0.179103\pi$
$860$	9.01276	+	15.6106i	0.307333	+	0.532316i
$861$		0			0
$862$	−4.74597	+	8.22026i	−0.161648	+	0.279983i
$863$	18.0635	+	31.2869i	0.614889	+	1.06502i	0.990404	+	0.138203i	$0.0441325\pi$
$863$	18.0635	+	31.2869i	0.614889	+	1.06502i	−0.375515	+	0.926816i	$0.622534\pi$
$864$	4.94975	+	1.58114i	0.168394	+	0.0537914i
$865$	−12.9284	+	22.3927i	−0.439580	+	0.761374i
$866$	29.6985			1.00920
$867$	10.6066	+	23.7171i	0.360219	+	0.805474i
$868$		0			0
$869$	−11.7460	−	20.3446i	−0.398455	−	0.690144i
$870$	12.7460	+	28.5008i	0.432129	+	0.966269i
$871$	−1.85188	−	3.20755i	−0.0627485	−	0.108684i
$872$	−4.56351	+	7.90423i	−0.154540	+	0.267671i
$873$	−35.6918	+	39.9046i	−1.20798	+	1.35057i
$874$	5.37600			0.181846
$875$		0			0
$876$	15.6190	−	21.5726i	0.527715	−	0.728872i
$877$	−19.4365	+	33.6650i	−0.656324	+	1.13679i	0.325237	+	0.945633i	$0.394556\pi$
$877$	−19.4365	+	33.6650i	−0.656324	+	1.13679i	−0.981560	+	0.191153i	$0.938777\pi$
$878$	−10.9545			−0.369695
$879$	−4.43649	−	9.92030i	−0.149639	−	0.334603i
$880$	−8.12602			−0.273928
$881$	−15.7360			−0.530159			−0.265079	−	0.964227i	$-0.585398\pi$
$881$	−15.7360			−0.530159			−0.265079	+	0.964227i	$0.585398\pi$
$882$		0			0
$883$	4.50807			0.151709			0.0758543	−	0.997119i	$-0.475832\pi$
$883$	4.50807			0.151709			0.0758543	+	0.997119i	$0.475832\pi$
$884$	−6.00000			−0.201802
$885$	−5.46582	+	7.54930i	−0.183731	+	0.253767i
$886$	24.3649			0.818555
$887$	−18.0255	+	31.2211i	−0.605238	+	1.04830i	0.386776	+	0.922174i	$0.373589\pi$
$887$	−18.0255	+	31.2211i	−0.605238	+	1.04830i	−0.992014	+	0.126129i	$0.959745\pi$
$888$	6.89144	+	15.4097i	0.231262	+	0.517117i
$889$		0			0
$890$	14.3649			0.481513
$891$	−4.00000	−	35.7771i	−0.134005	−	1.19858i
$892$	−5.74667	+	9.95352i	−0.192413	+	0.333269i
$893$	2.74597	+	4.75615i	0.0918903	+	0.159159i
$894$	0.258035	−	0.356394i	0.00862998	−	0.0119196i
$895$	0.886735	+	1.53587i	0.0296403	+	0.0513385i
$896$		0			0
$897$	49.3095	+	5.10012i	1.64640	+	0.170288i
$898$	9.00000			0.300334
$899$	−24.2997	+	42.0883i	−0.810439	+	1.40372i
$900$	0.817542	+	2.48808i	0.0272514	+	0.0829359i
$901$	−7.50873	−	13.0055i	−0.250152	−	0.433276i
$902$	11.3137	−	19.5959i	0.376705	−	0.652473i
$903$		0			0
$904$	1.93649	+	3.35410i	0.0644068	+	0.111556i
$905$	7.99193	−	13.8424i	0.265661	−	0.460138i
$906$	−7.77817	−	17.3925i	−0.258413	−	0.577828i
$907$	2.30948	+	4.00013i	0.0766849	+	0.132822i	0.901818	−	0.432117i	$-0.142233\pi$
$907$	2.30948	+	4.00013i	0.0766849	+	0.132822i	−0.825133	+	0.564939i	$0.808900\pi$
$908$	−3.04726	−	5.27801i	−0.101127	−	0.175157i
$909$	−7.36831	−	22.4244i	−0.244391	−	0.743772i
$910$		0			0
$911$	11.6270	−	20.1386i	0.385220	−	0.667221i	−0.606579	−	0.795023i	$-0.707459\pi$
$911$	11.6270	−	20.1386i	0.385220	−	0.667221i	0.991800	+	0.127802i	$0.0407921\pi$
$912$	−0.563508	−	1.26004i	−0.0186596	−	0.0417242i
$913$	−33.2226			−1.09951
$914$	33.8730			1.12042
$915$	−1.64445	+	2.27129i	−0.0543640	+	0.0750866i
$916$	3.93399	−	6.81388i	0.129983	−	0.225137i
$917$		0			0
$918$	5.43649	−	4.94414i	0.179431	−	0.163181i
$919$	19.6825	+	34.0910i	0.649264	+	1.12456i	0.983299	+	0.181998i	$0.0582565\pi$
$919$	19.6825	+	34.0910i	0.649264	+	1.12456i	−0.334034	+	0.942561i	$0.608410\pi$
$920$	6.85224	+	11.8684i	0.225912	+	0.391290i
$921$	41.5554	+	4.29812i	1.36930	+	0.141628i
$922$	−4.98895	+	8.64112i	−0.164302	+	0.284580i
$923$	4.51208	+	7.81516i	0.148517	+	0.257239i
$924$		0			0
$925$	−4.25403	+	7.36820i	−0.139872	+	0.242265i
$926$	−10.8095	−	18.7226i	−0.355221	−	0.615261i
$927$	−36.0510	+	40.3063i	−1.18407	+	1.32383i
$928$	−4.43649	+	7.68423i	−0.145635	+	0.252247i
$929$	10.6180			0.348366			0.174183	−	0.984713i	$-0.444272\pi$
$929$	10.6180			0.348366			0.174183	+	0.984713i	$0.444272\pi$
$930$	11.3023	−	15.6106i	0.370617	−	0.511890i
$931$		0			0
$932$	−11.3730	−	19.6986i	−0.372534	−	0.645249i
$933$	2.43649	+	0.252009i	0.0797672	+	0.00825039i
$934$	19.5295	+	33.8262i	0.639026	+	1.10683i
$935$	−5.74597	+	9.95231i	−0.187913	+	0.325475i
$936$	−3.97320	−	12.0919i	−0.129868	−	0.395236i
$937$	−42.4036			−1.38526			−0.692632	−	0.721291i	$-0.743549\pi$
$937$	−42.4036			−1.38526			−0.692632	+	0.721291i	$0.743549\pi$
$938$		0			0
$939$	−45.9839	−	4.75615i	−1.50063	−	0.155211i
$940$	−7.00000	+	12.1244i	−0.228315	+	0.395453i
$941$	1.67225			0.0545137			0.0272569	−	0.999628i	$-0.491323\pi$
$941$	1.67225			0.0545137			0.0272569	+	0.999628i	$0.491323\pi$
$942$	−11.1190	−	1.15004i	−0.362275	−	0.0374704i
$943$	−38.1610			−1.24269
$944$	−2.64880			−0.0862110
$945$		0			0
$946$	35.4919			1.15394
$947$	27.6028			0.896971			0.448486	−	0.893790i	$-0.351964\pi$
$947$	27.6028			0.896971			0.448486	+	0.893790i	$0.351964\pi$
$948$	10.1183	+	1.04655i	0.328628	+	0.0339903i
$949$	−65.2379			−2.11771
$950$	0.347849	−	0.602493i	0.0112857	−	0.0195475i
$951$	2.37936	+	0.246099i	0.0771559	+	0.00798030i
$952$		0			0
$953$	−28.5081			−0.923467			−0.461733	−	0.887019i	$-0.652772\pi$
$953$	−28.5081			−0.923467			−0.461733	+	0.887019i	$0.652772\pi$
$954$	21.2379	−	23.7447i	0.687602	−	0.768763i
$955$	−14.0915	+	24.4072i	−0.455991	+	0.789800i
$956$	7.50000	+	12.9904i	0.242567	+	0.420139i
$957$	61.1476	+	6.32456i	1.97662	+	0.204444i
$958$	−9.01276	−	15.6106i	−0.291189	−	0.504354i
$959$		0			0
$960$	2.06351	−	2.85008i	0.0665994	−	0.0919861i
$961$	−1.00000			−0.0322581
$962$	20.6743	−	35.8090i	0.666567	−	1.15453i
$963$	−14.7460	−	44.8773i	−0.475182	−	1.44615i
$964$	−0.886735	−	1.53587i	−0.0285598	−	0.0494671i
$965$	16.3811	−	28.3728i	0.527325	−	0.913354i
$966$		0			0
$967$	−14.7540	−	25.5547i	−0.474458	−	0.821785i	0.525114	−	0.851032i	$-0.324022\pi$
$967$	−14.7540	−	25.5547i	−0.474458	−	0.821785i	−0.999572	+	0.0292467i	$0.990689\pi$
$968$	−2.50000	+	4.33013i	−0.0803530	+	0.139176i
$969$	−1.94169	−	0.200831i	−0.0623761	−	0.00645162i
$970$	18.1270	+	31.3969i	0.582023	+	1.00809i
$971$	−18.4240	−	31.9113i	−0.591254	−	1.02408i	−0.994064	−	0.108798i	$-0.965300\pi$
$971$	−18.4240	−	31.9113i	−0.591254	−	1.02408i	0.402810	−	0.915284i	$-0.368033\pi$
$972$	13.5640	+	7.68223i	0.435067	+	0.246408i
$973$		0			0
$974$	−15.2460	+	26.4068i	−0.488512	+	0.846128i
$975$	3.76210	−	5.19615i	0.120484	−	0.166410i
$976$	−0.796921			−0.0255088
$977$	14.5081			0.464154			0.232077	−	0.972697i	$-0.425448\pi$
$977$	14.5081			0.464154			0.232077	+	0.972697i	$0.425448\pi$
$978$	−7.07107	−	15.8114i	−0.226108	−	0.505592i
$979$	14.1421	−	24.4949i	0.451985	−	0.782860i
$980$		0			0
$981$	−18.2540	+	20.4086i	−0.582806	+	0.651597i
$982$	6.87298	+	11.9044i	0.219326	+	0.379883i
$983$	−4.94975	−	8.57321i	−0.157872	−	0.273443i	0.776229	−	0.630451i	$-0.217130\pi$
$983$	−4.94975	−	8.57321i	−0.157872	−	0.273443i	−0.934101	+	0.357008i	$0.883797\pi$
$984$	4.00000	+	8.94427i	0.127515	+	0.285133i
$985$	−6.72322	+	11.6450i	−0.214220	+	0.371039i
$986$	6.27415	+	10.8671i	0.199810	+	0.346080i
$987$		0			0
$988$	−1.69052	+	2.92808i	−0.0537828	+	0.0931545i
$989$	−29.9284	−	51.8376i	−0.951669	−	1.64834i
$990$	−23.8620	−	4.98952i	−0.758384	−	0.158577i
$991$	−1.87298	+	3.24410i	−0.0594973	+	0.103052i	−0.894240	−	0.447588i	$-0.852283\pi$
$991$	−1.87298	+	3.24410i	−0.0594973	+	0.103052i	0.834743	+	0.550640i	$0.185616\pi$
$992$	5.47723			0.173902
$993$	−31.6402	−	3.27257i	−1.00407	−	0.103852i
$994$		0			0
$995$	21.0000	+	36.3731i	0.665745	+	1.15310i
$996$	8.43649	−	11.6523i	0.267320	−	0.369219i
$997$	0.129018	+	0.223465i	0.00408603	+	0.00707721i	0.868061	−	0.496457i	$-0.165366\pi$
$997$	0.129018	+	0.223465i	0.00408603	+	0.00707721i	−0.863975	+	0.503534i	$0.832033\pi$
$998$	7.12702	−	12.3444i	0.225602	−	0.390754i
$999$	10.7748	+	49.4820i	0.340900	+	1.56554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.e.t.655.4		8
3.2	odd	2		2646.2.e.r.2125.2		8
7.2	even	3		882.2.h.r.79.2		8
7.3	odd	6		882.2.f.p.295.4	yes	8
7.4	even	3		882.2.f.p.295.1	✓	8
7.5	odd	6		882.2.h.r.79.3		8
7.6	odd	2	inner	882.2.e.t.655.1		8
9.4	even	3		882.2.h.r.67.2		8
9.5	odd	6		2646.2.h.s.361.3		8
21.2	odd	6		2646.2.h.s.667.3		8
21.5	even	6		2646.2.h.s.667.2		8
21.11	odd	6		2646.2.f.s.883.2		8
21.17	even	6		2646.2.f.s.883.3		8
21.20	even	2		2646.2.e.r.2125.3		8
63.4	even	3		882.2.f.p.589.2	yes	8
63.5	even	6		2646.2.e.r.1549.3		8
63.11	odd	6		7938.2.a.cd.1.3		4
63.13	odd	6		882.2.h.r.67.3		8
63.23	odd	6		2646.2.e.r.1549.2		8
63.25	even	3		7938.2.a.cu.1.2		4
63.31	odd	6		882.2.f.p.589.3	yes	8
63.32	odd	6		2646.2.f.s.1765.2		8
63.38	even	6		7938.2.a.cd.1.2		4
63.40	odd	6	inner	882.2.e.t.373.1		8
63.41	even	6		2646.2.h.s.361.2		8
63.52	odd	6		7938.2.a.cu.1.3		4
63.58	even	3	inner	882.2.e.t.373.4		8
63.59	even	6		2646.2.f.s.1765.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.t.373.1		8	63.40	odd	6	inner
882.2.e.t.373.4		8	63.58	even	3	inner
882.2.e.t.655.1		8	7.6	odd	2	inner
882.2.e.t.655.4		8	1.1	even	1	trivial
882.2.f.p.295.1	✓	8	7.4	even	3
882.2.f.p.295.4	yes	8	7.3	odd	6
882.2.f.p.589.2	yes	8	63.4	even	3
882.2.f.p.589.3	yes	8	63.31	odd	6
882.2.h.r.67.2		8	9.4	even	3
882.2.h.r.67.3		8	63.13	odd	6
882.2.h.r.79.2		8	7.2	even	3
882.2.h.r.79.3		8	7.5	odd	6
2646.2.e.r.1549.2		8	63.23	odd	6
2646.2.e.r.1549.3		8	63.5	even	6
2646.2.e.r.2125.2		8	3.2	odd	2
2646.2.e.r.2125.3		8	21.20	even	2
2646.2.f.s.883.2		8	21.11	odd	6
2646.2.f.s.883.3		8	21.17	even	6
2646.2.f.s.1765.2		8	63.32	odd	6
2646.2.f.s.1765.3		8	63.59	even	6
2646.2.h.s.361.2		8	63.41	even	6
2646.2.h.s.361.3		8	9.5	odd	6
2646.2.h.s.667.2		8	21.5	even	6
2646.2.h.s.667.3		8	21.2	odd	6
7938.2.a.cd.1.2		4	63.38	even	6
7938.2.a.cd.1.3		4	63.11	odd	6
7938.2.a.cu.1.2		4	63.25	even	3
7938.2.a.cu.1.3		4	63.52	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.72286 + 0.178197i) q^{3} +1.00000 q^{4} +(1.01575 - 1.75934i) q^{5} +(1.72286 + 0.178197i) q^{6} +1.00000 q^{8} +(2.93649 + 0.614017i) q^{9} +(1.01575 - 1.75934i) q^{10} +(-2.00000 - 3.46410i) q^{11} +(1.72286 + 0.178197i) q^{12} +(-2.12132 - 3.67423i) q^{13} +(2.06351 - 2.85008i) q^{15} +1.00000 q^{16} +(0.707107 - 1.22474i) q^{17} +(2.93649 + 0.614017i) q^{18} +(-0.398461 - 0.690154i) q^{19} +(1.01575 - 1.75934i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(-3.37298 + 5.84218i) q^{23} +(1.72286 + 0.178197i) q^{24} +(0.436492 + 0.756026i) q^{25} +(-2.12132 - 3.67423i) q^{26} +(4.94975 + 1.58114i) q^{27} +(-4.43649 + 7.68423i) q^{29} +(2.06351 - 2.85008i) q^{30} +5.47723 q^{31} +1.00000 q^{32} +(-2.82843 - 6.32456i) q^{33} +(0.707107 - 1.22474i) q^{34} +(2.93649 + 0.614017i) q^{36} +(4.87298 + 8.44025i) q^{37} +(-0.398461 - 0.690154i) q^{38} +(-3.00000 - 6.70820i) q^{39} +(1.01575 - 1.75934i) q^{40} +(2.82843 + 4.89898i) q^{41} +(-4.43649 + 7.68423i) q^{43} +(-2.00000 - 3.46410i) q^{44} +(4.06301 - 4.54259i) q^{45} +(-3.37298 + 5.84218i) q^{46} -6.89144 q^{47} +(1.72286 + 0.178197i) q^{48} +(0.436492 + 0.756026i) q^{50} +(1.43649 - 1.98406i) q^{51} +(-2.12132 - 3.67423i) q^{52} +(5.30948 - 9.19628i) q^{53} +(4.94975 + 1.58114i) q^{54} -8.12602 q^{55} +(-0.563508 - 1.26004i) q^{57} +(-4.43649 + 7.68423i) q^{58} -2.64880 q^{59} +(2.06351 - 2.85008i) q^{60} -0.796921 q^{61} +5.47723 q^{62} +1.00000 q^{64} -8.61895 q^{65} +(-2.82843 - 6.32456i) q^{66} +0.872983 q^{67} +(0.707107 - 1.22474i) q^{68} +(-6.85224 + 9.46420i) q^{69} -2.12702 q^{71} +(2.93649 + 0.614017i) q^{72} +(7.68836 - 13.3166i) q^{73} +(4.87298 + 8.44025i) q^{74} +(0.617292 + 1.38031i) q^{75} +(-0.398461 - 0.690154i) q^{76} +(-3.00000 - 6.70820i) q^{78} +5.87298 q^{79} +(1.01575 - 1.75934i) q^{80} +(8.24597 + 3.60611i) q^{81} +(2.82843 + 4.89898i) q^{82} +(4.15283 - 7.19291i) q^{83} +(-1.43649 - 2.48808i) q^{85} +(-4.43649 + 7.68423i) q^{86} +(-9.01276 + 12.4483i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(3.53553 + 6.12372i) q^{89} +(4.06301 - 4.54259i) q^{90} +(-3.37298 + 5.84218i) q^{92} +(9.43649 + 0.976025i) q^{93} -6.89144 q^{94} -1.61895 q^{95} +(1.72286 + 0.178197i) q^{96} +(-8.92295 + 15.4550i) q^{97} +(-3.74597 - 11.4003i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} + 8 q^{9} - 16 q^{11} + 32 q^{15} + 8 q^{16} + 8 q^{18} - 16 q^{22} + 4 q^{23} - 12 q^{25} - 20 q^{29} + 32 q^{30} + 8 q^{32} + 8 q^{36} + 8 q^{37} - 24 q^{39} - 20 q^{43}+ \cdots + 32 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 + 8 * q^9 - 16 * q^11 + 32 * q^15 + 8 * q^16 + 8 * q^18 - 16 * q^22 + 4 * q^23 - 12 * q^25 - 20 * q^29 + 32 * q^30 + 8 * q^32 + 8 * q^36 + 8 * q^37 - 24 * q^39 - 20 * q^43 - 16 * q^44 + 4 * q^46 - 12 * q^50 - 4 * q^51 - 4 * q^53 - 20 * q^57 - 20 * q^58 + 32 * q^60 + 8 * q^64 + 24 * q^65 - 24 * q^67 - 48 * q^71 + 8 * q^72 + 8 * q^74 - 24 * q^78 + 16 * q^79 + 4 * q^81 + 4 * q^85 - 20 * q^86 - 16 * q^88 + 4 * q^92 + 60 * q^93 + 80 * q^95 + 32 * q^99

Introduction

L-functions

Modular forms

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