LMFDB - Embedded newform 882.2.f.p.295.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(295,882)] 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([4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.295"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,0,-4,0,0,0,8,-16] 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			295.4
Root			$-1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	882.295
Dual form			882.2.f.p.589.3

$q$-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} +(0.707107 + 1.58114i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.01575 - 1.75934i) q^{5} +(-1.72286 - 0.178197i) q^{6} +1.00000 q^{8} +(-2.00000 + 2.23607i) q^{9} +2.03151 q^{10} +(-2.00000 + 3.46410i) q^{11} +(1.01575 - 1.40294i) q^{12} +(2.12132 + 3.67423i) q^{13} +(2.06351 - 2.85008i) q^{15} +(-0.500000 + 0.866025i) q^{16} +1.41421 q^{17} +(-0.936492 - 2.85008i) q^{18} -0.796921 q^{19} +(-1.01575 + 1.75934i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(-3.37298 - 5.84218i) q^{23} +(0.707107 + 1.58114i) q^{24} +(0.436492 - 0.756026i) q^{25} -4.24264 q^{26} +(-4.94975 - 1.58114i) q^{27} +(-4.43649 + 7.68423i) q^{29} +(1.43649 + 3.21209i) q^{30} +(2.73861 + 4.74342i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-6.89144 - 0.712788i) q^{33} +(-0.707107 + 1.22474i) q^{34} +(2.93649 + 0.614017i) q^{36} -9.74597 q^{37} +(0.398461 - 0.690154i) q^{38} +(-4.30948 + 5.95218i) q^{39} +(-1.01575 - 1.75934i) q^{40} +(-2.82843 - 4.89898i) q^{41} +(-4.43649 + 7.68423i) q^{43} +4.00000 q^{44} +(5.96550 + 1.24738i) q^{45} +6.74597 q^{46} +(-3.44572 + 5.96816i) q^{47} +(-1.72286 - 0.178197i) q^{48} +(0.436492 + 0.756026i) q^{50} +(1.00000 + 2.23607i) q^{51} +(2.12132 - 3.67423i) q^{52} -10.6190 q^{53} +(3.84418 - 3.49604i) q^{54} +8.12602 q^{55} +(-0.563508 - 1.26004i) q^{57} +(-4.43649 - 7.68423i) q^{58} +(-1.32440 - 2.29393i) q^{59} +(-3.50000 - 0.362008i) q^{60} +(-0.398461 + 0.690154i) q^{61} -5.47723 q^{62} +1.00000 q^{64} +(4.30948 - 7.46423i) q^{65} +(4.06301 - 5.61177i) q^{66} +(-0.436492 - 0.756026i) q^{67} +(-0.707107 - 1.22474i) q^{68} +(6.85224 - 9.46420i) q^{69} -2.12702 q^{71} +(-2.00000 + 2.23607i) q^{72} +15.3767 q^{73} +(4.87298 - 8.44025i) q^{74} +(1.50403 + 0.155563i) q^{75} +(0.398461 + 0.690154i) q^{76} +(-3.00000 - 6.70820i) q^{78} +(-2.93649 + 5.08615i) q^{79} +2.03151 q^{80} +(-1.00000 - 8.94427i) q^{81} +5.65685 q^{82} +(-4.15283 + 7.19291i) q^{83} +(-1.43649 - 2.48808i) q^{85} +(-4.43649 - 7.68423i) q^{86} +(-15.2869 - 1.58114i) q^{87} +(-2.00000 + 3.46410i) q^{88} +7.07107 q^{89} +(-4.06301 + 4.54259i) q^{90} +(-3.37298 + 5.84218i) q^{92} +(-5.56351 + 7.68423i) q^{93} +(-3.44572 - 5.96816i) q^{94} +(0.809475 + 1.40205i) q^{95} +(1.01575 - 1.40294i) q^{96} +(8.92295 - 15.4550i) q^{97} +(-3.74597 - 11.4003i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{9} - 16 q^{11} + 32 q^{15} - 4 q^{16} + 8 q^{18} - 16 q^{22} + 4 q^{23} - 12 q^{25} - 20 q^{29} - 4 q^{30} - 4 q^{32} + 8 q^{36} - 16 q^{37} + 12 q^{39} - 20 q^{43}+ \cdots + 32 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^9 - 16 * q^11 + 32 * q^15 - 4 * q^16 + 8 * q^18 - 16 * q^22 + 4 * q^23 - 12 * q^25 - 20 * q^29 - 4 * q^30 - 4 * q^32 + 8 * q^36 - 16 * q^37 + 12 * q^39 - 20 * q^43 + 32 * q^44 - 8 * q^46 - 12 * q^50 + 8 * q^51 + 8 * q^53 - 20 * q^57 - 20 * q^58 - 28 * q^60 + 8 * q^64 - 12 * q^65 + 12 * q^67 - 48 * q^71 - 16 * q^72 + 8 * q^74 - 24 * q^78 - 8 * q^79 - 8 * q^81 + 4 * q^85 - 20 * q^86 - 16 * q^88 + 4 * q^92 - 60 * q^93 - 40 * q^95 + 32 * q^99

Character values

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

$n$	$199$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.707107	+	1.58114i	0.408248	+	0.912871i
$3$	0.707107	+	1.58114i	0.408248	+	0.912871i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.01575	−	1.75934i	−0.454259	−	0.786799i	0.544387	−	0.838834i	$-0.316762\pi$
$5$	−1.01575	−	1.75934i	−0.454259	−	0.786799i	−0.998645	+	0.0520355i	$0.983429\pi$
$6$	−1.72286	−	0.178197i	−0.703355	−	0.0727486i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−2.00000	+	2.23607i	−0.666667	+	0.745356i
$10$	2.03151			0.642419
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$	1.01575	−	1.40294i	0.293223	−	0.404994i
$13$	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
$15$	2.06351	−	2.85008i	0.532796	−	0.735889i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.41421			0.342997			0.171499	−	0.985184i	$-0.445139\pi$
$17$	1.41421			0.342997			0.171499	+	0.985184i	$0.445139\pi$
$18$	−0.936492	−	2.85008i	−0.220733	−	0.671771i
$19$	−0.796921			−0.182826			−0.0914131	−	0.995813i	$-0.529138\pi$
$19$	−0.796921			−0.182826			−0.0914131	+	0.995813i	$0.529138\pi$
$20$	−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	−0.967296	−	0.253650i	$-0.918369\pi$
$23$	−3.37298	−	5.84218i	−0.703316	−	1.21818i	0.263980	−	0.964528i	$-0.414965\pi$
$24$	0.707107	+	1.58114i	0.144338	+	0.322749i
$25$	0.436492	−	0.756026i	0.0872983	−	0.151205i
$26$	−4.24264			−0.832050
$27$	−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	$0.858496\pi$
$30$	1.43649	+	3.21209i	0.262266	+	0.586445i
$31$	2.73861	+	4.74342i	0.491869	+	0.851943i	0.999956	−	0.00936313i	$-0.00298042\pi$
$31$	2.73861	+	4.74342i	0.491869	+	0.851943i	−0.508087	+	0.861306i	$0.669647\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−6.89144	−	0.712788i	−1.19965	−	0.124080i
$34$	−0.707107	+	1.22474i	−0.121268	+	0.210042i
$35$		0			0
$36$	2.93649	+	0.614017i	0.489415	+	0.102336i
$37$	−9.74597			−1.60223			−0.801114	−	0.598512i	$-0.795759\pi$
$37$	−9.74597			−1.60223			−0.801114	+	0.598512i	$0.795759\pi$
$38$	0.398461	−	0.690154i	0.0646388	−	0.111958i
$39$	−4.30948	+	5.95218i	−0.690068	+	0.953111i
$40$	−1.01575	−	1.75934i	−0.160605	−	0.278175i
$41$	−2.82843	−	4.89898i	−0.441726	−	0.765092i	0.556092	−	0.831121i	$-0.312300\pi$
$41$	−2.82843	−	4.89898i	−0.441726	−	0.765092i	−0.997818	+	0.0660290i	$0.978967\pi$
$42$		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	$0.930137\pi$
$44$	4.00000			0.603023
$45$	5.96550	+	1.24738i	0.889284	+	0.185948i
$46$	6.74597			0.994639
$47$	−3.44572	+	5.96816i	−0.502610	+	0.870546i	0.497386	+	0.867530i	$0.334293\pi$
$47$	−3.44572	+	5.96816i	−0.502610	+	0.870546i	−0.999995	+	0.00301623i	$0.999040\pi$
$48$	−1.72286	−	0.178197i	−0.248673	−	0.0257205i
$49$		0			0
$50$	0.436492	+	0.756026i	0.0617292	+	0.106918i
$51$	1.00000	+	2.23607i	0.140028	+	0.313112i
$52$	2.12132	−	3.67423i	0.294174	−	0.509525i
$53$	−10.6190			−1.45862			−0.729312	−	0.684181i	$-0.760160\pi$
$53$	−10.6190			−1.45862			−0.729312	+	0.684181i	$0.760160\pi$
$54$	3.84418	−	3.49604i	0.523127	−	0.475750i
$55$	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
$59$	−1.32440	−	2.29393i	−0.172422	−	0.298644i	0.766844	−	0.641833i	$-0.221826\pi$
$59$	−1.32440	−	2.29393i	−0.172422	−	0.298644i	−0.939266	+	0.343190i	$0.888493\pi$
$60$	−3.50000	−	0.362008i	−0.451848	−	0.0467351i
$61$	−0.398461	+	0.690154i	−0.0510176	+	0.0883652i	−0.890406	−	0.455166i	$-0.849580\pi$
$61$	−0.398461	+	0.690154i	−0.0510176	+	0.0883652i	0.839389	+	0.543531i	$0.182913\pi$
$62$	−5.47723			−0.695608
$63$		0			0
$64$	1.00000			0.125000
$65$	4.30948	−	7.46423i	0.534525	−	0.925824i
$66$	4.06301	−	5.61177i	0.500122	−	0.690761i
$67$	−0.436492	−	0.756026i	−0.0533259	−	0.0923632i	0.838130	−	0.545470i	$-0.183649\pi$
$67$	−0.436492	−	0.756026i	−0.0533259	−	0.0923632i	−0.891456	+	0.453107i	$0.850316\pi$
$68$	−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	$0.540283\pi$
$72$	−2.00000	+	2.23607i	−0.235702	+	0.263523i
$73$	15.3767			1.79971			0.899855	−	0.436190i	$-0.143673\pi$
$73$	15.3767			1.79971			0.899855	+	0.436190i	$0.143673\pi$
$74$	4.87298	−	8.44025i	0.566473	−	0.981160i
$75$	1.50403	+	0.155563i	0.173670	+	0.0179629i
$76$	0.398461	+	0.690154i	0.0457066	+	0.0791661i
$77$		0			0
$78$	−3.00000	−	6.70820i	−0.339683	−	0.759555i
$79$	−2.93649	+	5.08615i	−0.330381	+	0.572237i	−0.982587	−	0.185805i	$-0.940511\pi$
$79$	−2.93649	+	5.08615i	−0.330381	+	0.572237i	0.652205	+	0.758042i	$0.273844\pi$
$80$	2.03151			0.227129
$81$	−1.00000	−	8.94427i	−0.111111	−	0.993808i
$82$	5.65685			0.624695
$83$	−4.15283	+	7.19291i	−0.455832	+	0.789524i	−0.998736	−	0.0502709i	$-0.983992\pi$
$83$	−4.15283	+	7.19291i	−0.455832	+	0.789524i	0.542904	+	0.839795i	$0.317325\pi$
$84$		0			0
$85$	−1.43649	−	2.48808i	−0.155809	−	0.269870i
$86$	−4.43649	−	7.68423i	−0.478399	−	0.828612i
$87$	−15.2869	−	1.58114i	−1.63893	−	0.169516i
$88$	−2.00000	+	3.46410i	−0.213201	+	0.369274i
$89$	7.07107			0.749532			0.374766	−	0.927119i	$-0.377723\pi$
$89$	7.07107			0.749532			0.374766	+	0.927119i	$0.377723\pi$
$90$	−4.06301	+	4.54259i	−0.428279	+	0.478831i
$91$		0			0
$92$	−3.37298	+	5.84218i	−0.351658	+	0.609089i
$93$	−5.56351	+	7.68423i	−0.576909	+	0.796817i
$94$	−3.44572	−	5.96816i	−0.355399	−	0.615569i
$95$	0.809475	+	1.40205i	0.0830504	+	0.143847i
$96$	1.01575	−	1.40294i	0.103670	−	0.143187i
$97$	8.92295	−	15.4550i	0.905988	−	1.56922i	0.0864021	−	0.996260i	$-0.472463\pi$
$97$	8.92295	−	15.4550i	0.905988	−	1.56922i	0.819586	−	0.572957i	$-0.194204\pi$
$98$		0			0
$99$	−3.74597	−	11.4003i	−0.376484	−	1.14578i
$100$	−0.872983			−0.0872983
$101$	3.93399	−	6.81388i	0.391447	−	0.678006i	−0.601194	−	0.799103i	$-0.705308\pi$
$101$	3.93399	−	6.81388i	0.391447	−	0.678006i	0.992641	+	0.121097i	$0.0386413\pi$
$102$	−2.43649	−	0.252009i	−0.241249	−	0.0249526i
$103$	9.01276	+	15.6106i	0.888054	+	1.53815i	0.842173	+	0.539207i	$0.181276\pi$
$103$	9.01276	+	15.6106i	0.888054	+	1.53815i	0.0458803	+	0.998947i	$0.485391\pi$
$104$	2.12132	+	3.67423i	0.208013	+	0.360288i
$105$		0			0
$106$	5.30948	−	9.19628i	0.515702	−	0.893222i
$107$	15.7460			1.52222			0.761110	−	0.648623i	$-0.224655\pi$
$107$	15.7460			1.52222			0.761110	+	0.648623i	$0.224655\pi$
$108$	1.10557	+	5.07718i	0.106383	+	0.488552i
$109$	9.12702			0.874210			0.437105	−	0.899411i	$-0.356004\pi$
$109$	9.12702			0.874210			0.437105	+	0.899411i	$0.356004\pi$
$110$	−4.06301	+	7.03734i	−0.387393	+	0.670984i
$111$	−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	$0.775021\pi$
$114$	1.37298	+	0.142009i	0.128592	+	0.0133004i
$115$	−6.85224	+	11.8684i	−0.638974	+	1.10674i
$116$	8.87298			0.823836
$117$	−12.4585	−	2.60505i	−1.15179	−	0.240837i
$118$	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
$122$	−0.398461	−	0.690154i	−0.0360749	−	0.0624836i
$123$	5.74597	−	7.93624i	0.518096	−	0.715586i
$124$	2.73861	−	4.74342i	0.245935	−	0.425971i
$125$	−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	$0.272986\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−15.2869	−	1.58114i	−1.34594	−	0.139212i
$130$	4.30948	+	7.46423i	0.377966	+	0.654656i
$131$	−3.93399	−	6.81388i	−0.343715	−	0.595331i	0.641405	−	0.767203i	$-0.278352\pi$
$131$	−3.93399	−	6.81388i	−0.343715	−	0.595331i	−0.985119	+	0.171871i	$0.945019\pi$
$132$	2.82843	+	6.32456i	0.246183	+	0.550482i
$133$		0			0
$134$	0.872983			0.0754143
$135$	2.24597	+	10.3143i	0.193302	+	0.887715i
$136$	1.41421			0.121268
$137$	−7.74597	+	13.4164i	−0.661783	+	1.14624i	0.318364	+	0.947968i	$0.396866\pi$
$137$	−7.74597	+	13.4164i	−0.661783	+	1.14624i	−0.980147	+	0.198273i	$0.936467\pi$
$138$	4.77012	+	10.6663i	0.406059	+	0.907977i
$139$	9.23159	+	15.9896i	0.783013	+	1.35622i	0.930179	+	0.367107i	$0.119652\pi$
$139$	9.23159	+	15.9896i	0.783013	+	1.35622i	−0.147165	+	0.989112i	$0.547015\pi$
$140$		0			0
$141$	−11.8730	−	1.22803i	−0.999886	−	0.103419i
$142$	1.06351	−	1.84205i	0.0892476	−	0.154581i
$143$	−16.9706			−1.41915
$144$	−0.936492	−	2.85008i	−0.0780410	−	0.237507i
$145$	18.0255			1.49694
$146$	−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	0.871181	−	0.490961i	$-0.163354\pi$
$149$	0.127017	+	0.219999i	0.0104056	+	0.0180230i	−0.860776	+	0.508984i	$0.830021\pi$
$150$	−0.886735	+	1.22474i	−0.0724016	+	0.100000i
$151$	−5.50000	+	9.52628i	−0.447584	+	0.775238i	−0.998228	−	0.0595022i	$-0.981049\pi$
$151$	−5.50000	+	9.52628i	−0.447584	+	0.775238i	0.550645	+	0.834740i	$0.314382\pi$
$152$	−0.796921			−0.0646388
$153$	−2.82843	+	3.16228i	−0.228665	+	0.255655i
$154$		0			0
$155$	5.56351	−	9.63628i	0.446872	−	0.774005i
$156$	7.30948	+	0.756026i	0.585226	+	0.0605305i
$157$	−3.22689	−	5.58913i	−0.257534	−	0.446061i	0.708047	−	0.706165i	$-0.249576\pi$
$157$	−3.22689	−	5.58913i	−0.257534	−	0.446061i	−0.965581	+	0.260104i	$0.916243\pi$
$158$	−2.93649	−	5.08615i	−0.233615	−	0.404633i
$159$	−7.50873	−	16.7900i	−0.595481	−	1.33154i
$160$	−1.01575	+	1.75934i	−0.0803023	+	0.139088i
$161$		0			0
$162$	8.24597	+	3.60611i	0.647864	+	0.283323i
$163$	10.0000			0.783260			0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000			0.783260			0.391630	+	0.920123i	$0.371911\pi$
$164$	−2.82843	+	4.89898i	−0.220863	+	0.382546i
$165$	5.74597	+	12.8484i	0.447323	+	1.00024i
$166$	−4.15283	−	7.19291i	−0.322322	−	0.558278i
$167$	6.18433	+	10.7116i	0.478558	+	0.828887i	0.999698	−	0.0245846i	$-0.00782630\pi$
$167$	6.18433	+	10.7116i	0.478558	+	0.828887i	−0.521140	+	0.853471i	$0.674493\pi$
$168$		0			0
$169$	−2.50000	+	4.33013i	−0.192308	+	0.333087i
$170$	2.87298			0.220348
$171$	1.59384	−	1.78197i	0.121884	−	0.136271i
$172$	8.87298			0.676559
$173$	−6.36396	+	11.0227i	−0.483843	+	0.838041i	−0.999828	−	0.0185571i	$-0.994093\pi$
$173$	−6.36396	+	11.0227i	−0.483843	+	0.838041i	0.515985	+	0.856598i	$0.327426\pi$
$174$	9.01276	−	12.4483i	0.683256	−	0.943702i
$175$		0			0
$176$	−2.00000	−	3.46410i	−0.150756	−	0.261116i
$177$	2.69052	−	3.71611i	0.202232	−	0.279320i
$178$	−3.53553	+	6.12372i	−0.264999	+	0.458993i
$179$	0.872983			0.0652498			0.0326249	−	0.999468i	$-0.489613\pi$
$179$	0.872983			0.0652498			0.0326249	+	0.999468i	$0.489613\pi$
$180$	−1.90249	−	5.78996i	−0.141803	−	0.431558i
$181$	−7.86799			−0.584823			−0.292412	−	0.956293i	$-0.594458\pi$
$181$	−7.86799			−0.584823			−0.292412	+	0.956293i	$0.594458\pi$
$182$		0			0
$183$	−1.37298	−	0.142009i	−0.101494	−	0.0104976i
$184$	−3.37298	−	5.84218i	−0.248660	−	0.430691i
$185$	9.89949	+	17.1464i	0.727825	+	1.26063i
$186$	−3.87298	−	8.66025i	−0.283981	−	0.635001i
$187$	−2.82843	+	4.89898i	−0.206835	+	0.358249i
$188$	6.89144			0.502610
$189$		0			0
$190$	−1.61895			−0.117451
$191$	6.93649	−	12.0144i	0.501907	−	0.869328i	−0.498091	−	0.867125i	$-0.665965\pi$
$191$	6.93649	−	12.0144i	0.501907	−	0.869328i	0.999998	−	0.00220333i	$-0.000701341\pi$
$192$	0.707107	+	1.58114i	0.0510310	+	0.114109i
$193$	−8.06351	−	13.9664i	−0.580424	−	1.00532i	−0.995429	−	0.0955048i	$-0.969553\pi$
$193$	−8.06351	−	13.9664i	−0.580424	−	1.00532i	0.415005	−	0.909819i	$-0.363780\pi$
$194$	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	$0.575768\pi$
$198$	11.7460	+	2.45607i	0.834750	+	0.174545i
$199$	−20.6743			−1.46556			−0.732782	−	0.680464i	$-0.761778\pi$
$199$	−20.6743			−1.46556			−0.732782	+	0.680464i	$0.761778\pi$
$200$	0.436492	−	0.756026i	0.0308646	−	0.0534591i
$201$	0.886735	−	1.22474i	0.0625455	−	0.0863868i
$202$	3.93399	+	6.81388i	0.276795	+	0.479423i
$203$		0			0
$204$	1.43649	−	1.98406i	0.100575	−	0.138912i
$205$	−5.74597	+	9.95231i	−0.401316	+	0.695099i
$206$	−18.0255			−1.25590
$207$	19.8095	+	4.14214i	1.37685	+	0.287898i
$208$	−4.24264			−0.294174
$209$	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
$213$	−1.50403	−	3.36311i	−0.103054	−	0.230436i
$214$	−7.87298	+	13.6364i	−0.538186	+	0.932166i
$215$	18.0255			1.22933
$216$	−4.94975	−	1.58114i	−0.336788	−	0.107583i
$217$		0			0
$218$	−4.56351	+	7.90423i	−0.309080	+	0.535342i
$219$	10.8730	+	24.3127i	0.734728	+	1.64290i
$220$	−4.06301	−	7.03734i	−0.273928	−	0.474458i
$221$	3.00000	+	5.19615i	0.201802	+	0.349531i
$222$	16.7909	+	1.73670i	1.12693	+	0.116560i
$223$	5.74667	−	9.95352i	0.384825	−	0.666537i	−0.606920	−	0.794763i	$-0.707595\pi$
$223$	5.74667	−	9.95352i	0.384825	−	0.666537i	0.991745	+	0.128226i	$0.0409283\pi$
$224$		0			0
$225$	0.817542	+	2.48808i	0.0545028	+	0.165872i
$226$	−3.87298			−0.257627
$227$	3.04726	−	5.27801i	0.202254	−	0.350314i	−0.747001	−	0.664823i	$-0.768507\pi$
$227$	3.04726	−	5.27801i	0.202254	−	0.350314i	0.949254	+	0.314510i	$0.101840\pi$
$228$	−0.809475	+	1.11803i	−0.0536088	+	0.0740436i
$229$	−3.93399	−	6.81388i	−0.259966	−	0.450274i	0.706267	−	0.707946i	$-0.250378\pi$
$229$	−3.93399	−	6.81388i	−0.259966	−	0.450274i	−0.966232	+	0.257672i	$0.917045\pi$
$230$	−6.85224	−	11.8684i	−0.451823	−	0.782580i
$231$		0			0
$232$	−4.43649	+	7.68423i	−0.291270	+	0.504494i
$233$	22.7460			1.49014			0.745069	−	0.666987i	$-0.232417\pi$
$233$	22.7460			1.49014			0.745069	+	0.666987i	$0.232417\pi$
$234$	8.48528	−	9.48683i	0.554700	−	0.620174i
$235$	14.0000			0.913259
$236$	−1.32440	+	2.29393i	−0.0862110	+	0.149322i
$237$	−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	$0.672104\pi$
$240$	1.43649	+	3.21209i	0.0927251	+	0.207340i
$241$	0.886735	−	1.53587i	0.0571197	−	0.0989341i	−0.836052	−	0.548651i	$-0.815142\pi$
$241$	0.886735	−	1.53587i	0.0571197	−	0.0989341i	0.893171	+	0.449717i	$0.148475\pi$
$242$	5.00000			0.321412
$243$	13.4350	−	7.90569i	0.861858	−	0.507151i
$244$	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
$248$	2.73861	+	4.74342i	0.173902	+	0.301207i
$249$	−14.3095	−	1.48004i	−0.906826	−	0.0937939i
$250$	5.96550	−	10.3325i	0.377291	−	0.653488i
$251$	25.8935			1.63438			0.817192	−	0.576366i	$-0.195530\pi$
$251$	25.8935			1.63438			0.817192	+	0.576366i	$0.195530\pi$
$252$		0			0
$253$	26.9839			1.69646
$254$	−7.37298	+	12.7704i	−0.462622	+	0.801285i
$255$	2.91824	−	4.03063i	0.182747	−	0.252408i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.98125	−	12.0919i	−0.435479	−	0.754271i	0.561856	−	0.827235i	$-0.310088\pi$
$257$	−6.98125	−	12.0919i	−0.435479	−	0.754271i	−0.997335	+	0.0729640i	$0.976754\pi$
$258$	9.01276	−	12.4483i	0.561110	−	0.774996i
$259$		0			0
$260$	−8.61895			−0.534525
$261$	−8.30948	−	25.2888i	−0.514344	−	1.56533i
$262$	7.86799			0.486086
$263$	−2.80948	+	4.86615i	−0.173240	+	0.300060i	−0.939551	−	0.342410i	$-0.888757\pi$
$263$	−2.80948	+	4.86615i	−0.173240	+	0.300060i	0.766311	+	0.642470i	$0.222090\pi$
$264$	−6.89144	−	0.712788i	−0.424139	−	0.0438691i
$265$	10.7862	+	18.6823i	0.662593	+	1.14764i
$266$		0			0
$267$	5.00000	+	11.1803i	0.305995	+	0.684226i
$268$	−0.436492	+	0.756026i	−0.0266630	+	0.0461816i
$269$	3.44572			0.210089			0.105045	−	0.994468i	$-0.466501\pi$
$269$	3.44572			0.210089			0.105045	+	0.994468i	$0.466501\pi$
$270$	−10.0554	−	3.21209i	−0.611955	−	0.195482i
$271$	7.07107			0.429537			0.214768	−	0.976665i	$-0.431100\pi$
$271$	7.07107			0.429537			0.214768	+	0.976665i	$0.431100\pi$
$272$	−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
$276$	−11.6224	−	1.20211i	−0.699584	−	0.0723586i
$277$	12.1825	−	21.1006i	0.731973	−	1.26781i	−0.224066	−	0.974574i	$-0.571933\pi$
$277$	12.1825	−	21.1006i	0.731973	−	1.26781i	0.956039	−	0.293240i	$-0.0947336\pi$
$278$	−18.4632			−1.10735
$279$	−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	$0.102178\pi$
$282$	7.00000	−	9.66829i	0.416844	−	0.575738i
$283$	−5.25839	−	9.10781i	−0.312579	−	0.541403i	0.666341	−	0.745647i	$-0.267860\pi$
$283$	−5.25839	−	9.10781i	−0.312579	−	0.541403i	−0.978920	+	0.204244i	$0.934526\pi$
$284$	1.06351	+	1.84205i	0.0631076	+	0.109306i
$285$	−1.64445	+	2.27129i	−0.0974090	+	0.134540i
$286$	8.48528	−	14.6969i	0.501745	−	0.869048i
$287$		0			0
$288$	2.93649	+	0.614017i	0.173034	+	0.0361813i
$289$	−15.0000			−0.882353
$290$	−9.01276	+	15.6106i	−0.529247	+	0.916683i
$291$	30.7460	+	3.18008i	1.80236	+	0.186420i
$292$	−7.68836	−	13.3166i	−0.449927	−	0.779297i
$293$	3.13707	+	5.43357i	0.183270	+	0.317433i	0.942992	−	0.332815i	$-0.107998\pi$
$293$	3.13707	+	5.43357i	0.183270	+	0.317433i	−0.759722	+	0.650248i	$0.774665\pi$
$294$		0			0
$295$	−2.69052	+	4.66013i	−0.156648	+	0.271323i
$296$	−9.74597			−0.566473
$297$	15.3767	−	13.9842i	0.892248	−	0.811443i
$298$	−0.254033			−0.0147158
$299$	14.3104	−	24.7863i	0.827589	−	1.43343i
$300$	−0.617292	−	1.38031i	−0.0356394	−	0.0796921i
$301$		0			0
$302$	−5.50000	−	9.52628i	−0.316489	−	0.548176i
$303$	13.5554	+	1.40205i	0.778740	+	0.0805458i
$304$	0.398461	−	0.690154i	0.0228533	−	0.0395830i
$305$	1.61895			0.0927008
$306$	−1.32440	−	4.03063i	−0.0757109	−	0.230416i
$307$	−24.1200			−1.37660			−0.688302	−	0.725425i	$-0.741643\pi$
$307$	−24.1200			−1.37660			−0.688302	+	0.725425i	$0.741643\pi$
$308$		0			0
$309$	−18.3095	+	25.2888i	−1.04159	+	1.43863i
$310$	5.56351	+	9.63628i	0.315986	+	0.547304i
$311$	0.707107	+	1.22474i	0.0400963	+	0.0694489i	0.885377	−	0.464873i	$-0.153900\pi$
$311$	0.707107	+	1.22474i	0.0400963	+	0.0694489i	−0.845281	+	0.534322i	$0.820567\pi$
$312$	−4.30948	+	5.95218i	−0.243976	+	0.336976i
$313$	−13.3452	+	23.1146i	−0.754316	+	1.30651i	0.191397	+	0.981513i	$0.438698\pi$
$313$	−13.3452	+	23.1146i	−0.754316	+	1.30651i	−0.945714	+	0.325001i	$0.894635\pi$
$314$	6.45378			0.364208
$315$		0			0
$316$	5.87298			0.330381
$317$	−0.690525	+	1.19602i	−0.0387837	+	0.0671754i	−0.884766	−	0.466036i	$-0.845682\pi$
$317$	−0.690525	+	1.19602i	−0.0387837	+	0.0671754i	0.845982	+	0.533212i	$0.179015\pi$
$318$	18.2950	+	1.89226i	1.02593	+	0.106113i
$319$	−17.7460	−	30.7369i	−0.993583	−	1.72094i
$320$	−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
$324$	−7.24597	+	5.33816i	−0.402554	+	0.296565i
$325$	3.70375			0.205447
$326$	−5.00000	+	8.66025i	−0.276924	+	0.479647i
$327$	6.45378	+	14.4311i	0.356895	+	0.798041i
$328$	−2.82843	−	4.89898i	−0.156174	−	0.270501i
$329$		0			0
$330$	−14.0000	−	1.44803i	−0.770675	−	0.0797116i
$331$	9.18246	−	15.9045i	0.504714	−	0.874190i	−0.495272	−	0.868738i	$-0.664931\pi$
$331$	9.18246	−	15.9045i	0.504714	−	0.874190i	0.999985	−	0.00545133i	$-0.00173522\pi$
$332$	8.30565			0.455832
$333$	19.4919	−	21.7926i	1.06815	−	1.19423i
$334$	−12.3687			−0.676783
$335$	−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
$339$	−3.93399	+	5.43357i	−0.213665	+	0.295111i
$340$	−1.43649	+	2.48808i	−0.0779047	+	0.134935i
$341$	−21.9089			−1.18643
$342$	0.746310	+	2.27129i	0.0403558	+	0.122817i
$343$		0			0
$344$	−4.43649	+	7.68423i	−0.239200	+	0.414306i
$345$	−23.6109	−	2.44210i	−1.27117	−	0.131478i
$346$	−6.36396	−	11.0227i	−0.342129	−	0.592584i
$347$	3.87298	+	6.70820i	0.207913	+	0.360115i	0.951057	−	0.309016i	$-0.0999997\pi$
$347$	3.87298	+	6.70820i	0.207913	+	0.360115i	−0.743144	+	0.669131i	$0.766666\pi$
$348$	6.27415	+	14.0294i	0.336330	+	0.752056i
$349$	−8.21584	+	14.2302i	−0.439784	+	0.761728i	−0.997672	−	0.0681880i	$-0.978278\pi$
$349$	−8.21584	+	14.2302i	−0.439784	+	0.761728i	0.557889	+	0.829916i	$0.311612\pi$
$350$		0			0
$351$	−4.69052	−	21.5406i	−0.250362	−	1.14975i
$352$	4.00000			0.213201
$353$	9.01276	−	15.6106i	0.479701	−	0.830866i	−0.520028	−	0.854149i	$-0.674079\pi$
$353$	9.01276	−	15.6106i	0.479701	−	0.830866i	0.999729	+	0.0232830i	$0.00741188\pi$
$354$	1.87298	+	4.18812i	0.0995479	+	0.222596i
$355$	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
$359$	−28.2379			−1.49034			−0.745170	−	0.666875i	$-0.767632\pi$
$359$	−28.2379			−1.49034			−0.745170	+	0.666875i	$0.767632\pi$
$360$	5.96550	+	1.24738i	0.314409	+	0.0657426i
$361$	−18.3649			−0.966575
$362$	3.93399	−	6.81388i	0.206766	−	0.358129i
$363$	5.07877	−	7.01471i	0.266566	−	0.368177i
$364$		0			0
$365$	−15.6190	−	27.0528i	−0.817533	−	1.41601i
$366$	0.809475	−	1.11803i	0.0423119	−	0.0584406i
$367$	2.03151	−	3.51867i	0.106044	−	0.183673i	−0.808120	−	0.589017i	$-0.799515\pi$
$367$	2.03151	−	3.51867i	0.106044	−	0.183673i	0.914164	+	0.405344i	$0.132848\pi$
$368$	6.74597			0.351658
$369$	16.6113	+	3.47340i	0.864750	+	0.180818i
$370$	−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	0.957723	−	0.287692i	$-0.0928880\pi$
$373$	4.43649	+	7.68423i	0.229713	+	0.397874i	−0.728010	+	0.685566i	$0.759555\pi$
$374$	−2.82843	−	4.89898i	−0.146254	−	0.253320i
$375$	−8.43649	−	18.8646i	−0.435659	−	0.974162i
$376$	−3.44572	+	5.96816i	−0.177699	+	0.307784i
$377$	−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	$0.602867\pi$
$380$	0.809475	−	1.40205i	0.0415252	−	0.0719237i
$381$	10.4270	+	23.3154i	0.534190	+	1.19449i
$382$	6.93649	+	12.0144i	0.354902	+	0.614708i
$383$	11.9310	+	20.6651i	0.609646	+	1.05594i	0.991299	+	0.131632i	$0.0420216\pi$
$383$	11.9310	+	20.6651i	0.609646	+	1.05594i	−0.381653	+	0.924306i	$0.624645\pi$
$384$	−1.72286	−	0.178197i	−0.0879193	−	0.00909358i
$385$		0			0
$386$	16.1270			0.820844
$387$	−8.30948	−	25.2888i	−0.422394	−	1.28550i
$388$	−17.8459			−0.905988
$389$	−10.4365	+	18.0765i	−0.529151	+	0.916517i	0.470271	+	0.882522i	$0.344156\pi$
$389$	−10.4365	+	18.0765i	−0.529151	+	0.916517i	−0.999422	+	0.0339945i	$0.989177\pi$
$390$	−8.75472	+	12.0919i	−0.443313	+	0.612296i
$391$	−4.77012	−	8.26209i	−0.241235	−	0.417832i
$392$		0			0
$393$	7.99193	−	11.0383i	0.403140	−	0.556810i
$394$	3.30948	−	5.73218i	0.166729	−	0.288783i
$395$	11.9310			0.600314
$396$	−8.00000	+	8.94427i	−0.402015	+	0.449467i
$397$	7.07107			0.354887			0.177443	−	0.984131i	$-0.443217\pi$
$397$	7.07107			0.354887			0.177443	+	0.984131i	$0.443217\pi$
$398$	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	0.813615	−	0.581405i	$-0.197497\pi$
$401$	−1.93649	−	3.35410i	−0.0967038	−	0.167496i	−0.910318	+	0.413909i	$0.864163\pi$
$402$	0.617292	+	1.38031i	0.0307877	+	0.0688435i
$403$	−11.6190	+	20.1246i	−0.578781	+	1.00248i
$404$	−7.86799			−0.391447
$405$	−14.7202	+	10.8445i	−0.731454	+	0.538868i
$406$		0			0
$407$	19.4919	−	33.7610i	0.966179	−	1.67347i
$408$	1.00000	+	2.23607i	0.0495074	+	0.110702i
$409$	15.8144	+	27.3913i	0.781971	+	1.35441i	0.930792	+	0.365549i	$0.119119\pi$
$409$	15.8144	+	27.3913i	0.781971	+	1.35441i	−0.148821	+	0.988864i	$0.547548\pi$
$410$	−5.74597	−	9.95231i	−0.283773	−	0.491509i
$411$	−26.6904	−	2.76062i	−1.31654	−	0.136171i
$412$	9.01276	−	15.6106i	0.444027	−	0.769077i
$413$		0			0
$414$	−13.4919	+	15.0844i	−0.663092	+	0.741360i
$415$	16.8730			0.828262
$416$	2.12132	−	3.67423i	0.104006	−	0.180144i
$417$	−18.7540	+	25.9028i	−0.918389	+	1.26846i
$418$	1.59384	+	2.76062i	0.0779574	+	0.135026i
$419$	1.99230	+	3.45077i	0.0973304	+	0.168581i	0.910579	−	0.413335i	$-0.135636\pi$
$419$	1.99230	+	3.45077i	0.0973304	+	0.168581i	−0.813248	+	0.581917i	$0.802303\pi$
$420$		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	$0.126794\pi$
$422$	−2.61895			−0.127488
$423$	−6.45378	−	19.6412i	−0.313793	−	0.954987i
$424$	−10.6190			−0.515702
$425$	0.617292	−	1.06918i	0.0299431	−	0.0518629i
$426$	3.66455	+	0.379028i	0.177548	+	0.0183640i
$427$		0			0
$428$	−7.87298	−	13.6364i	−0.380555	−	0.659141i
$429$	−12.0000	−	26.8328i	−0.579365	−	1.29550i
$430$	−9.01276	+	15.6106i	−0.434634	+	0.752808i
$431$	9.49193			0.457210			0.228605	−	0.973519i	$-0.426584\pi$
$431$	9.49193			0.457210			0.228605	+	0.973519i	$0.426584\pi$
$432$	3.84418	−	3.49604i	0.184953	−	0.168203i
$433$	−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
$435$	12.7460	+	28.5008i	0.611122	+	1.36651i
$436$	−4.56351	−	7.90423i	−0.218552	−	0.378544i
$437$	2.68800	+	4.65576i	0.128585	+	0.222715i
$438$	−26.4919	−	2.74009i	−1.26583	−	0.130926i
$439$	−5.47723	+	9.48683i	−0.261414	+	0.452782i	−0.966618	−	0.256223i	$-0.917522\pi$
$439$	−5.47723	+	9.48683i	−0.261414	+	0.452782i	0.705204	+	0.709004i	$0.250855\pi$
$440$	8.12602			0.387393
$441$		0			0
$442$	−6.00000			−0.285391
$443$	−12.1825	+	21.1006i	−0.578806	+	1.00252i	0.416811	+	0.908993i	$0.363148\pi$
$443$	−12.1825	+	21.1006i	−0.578806	+	1.00252i	−0.995617	+	0.0935281i	$0.970185\pi$
$444$	−9.89949	+	13.6730i	−0.469809	+	0.648893i
$445$	−7.18246	−	12.4404i	−0.340481	−	0.589731i
$446$	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	$0.431882\pi$
$450$	−2.56351	−	0.536026i	−0.120845	−	0.0252685i
$451$	22.6274			1.06548
$452$	1.93649	−	3.35410i	0.0910849	−	0.157764i
$453$	−18.9515	−	1.96017i	−0.890417	−	0.0920967i
$454$	3.04726	+	5.27801i	0.143015	+	0.247709i
$455$		0			0
$456$	−0.563508	−	1.26004i	−0.0263887	−	0.0590069i
$457$	−16.9365	+	29.3349i	−0.792256	+	1.37223i	0.132312	+	0.991208i	$0.457760\pi$
$457$	−16.9365	+	29.3349i	−0.792256	+	1.37223i	−0.924567	+	0.381019i	$0.875573\pi$
$458$	7.86799			0.367647
$459$	−7.00000	−	2.23607i	−0.326732	−	0.104371i
$460$	13.7045			0.638974
$461$	4.98895	−	8.64112i	0.232359	−	0.402457i	−0.726143	−	0.687544i	$-0.758689\pi$
$461$	4.98895	−	8.64112i	0.232359	−	0.402457i	0.958502	+	0.285087i	$0.0920224\pi$
$462$		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
$465$	19.1703	+	1.98280i	0.889001	+	0.0919502i
$466$	−11.3730	+	19.6986i	−0.526843	+	0.912519i
$467$	39.0591			1.80744			0.903720	−	0.428125i	$-0.140826\pi$
$467$	39.0591			1.80744			0.903720	+	0.428125i	$0.140826\pi$
$468$	3.97320	+	12.0919i	0.183661	+	0.558948i
$469$		0			0
$470$	−7.00000	+	12.1244i	−0.322886	+	0.559255i
$471$	6.55544	−	9.05427i	0.302059	−	0.417199i
$472$	−1.32440	−	2.29393i	−0.0609604	−	0.105587i
$473$	−17.7460	−	30.7369i	−0.815960	−	1.41328i
$474$	5.96550	−	8.23945i	0.274005	−	0.378451i
$475$	−0.347849	+	0.602493i	−0.0159604	+	0.0276443i
$476$		0			0
$477$	21.2379	−	23.7447i	0.972417	−	1.08719i
$478$	−15.0000			−0.686084
$479$	9.01276	−	15.6106i	0.411803	−	0.713265i	−0.583284	−	0.812269i	$-0.698232\pi$
$479$	9.01276	−	15.6106i	0.411803	−	0.713265i	0.995087	+	0.0990041i	$0.0315657\pi$
$480$	−3.50000	−	0.362008i	−0.159752	−	0.0165233i
$481$	−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
$485$	−36.2540			−1.64621
$486$	0.129018	+	15.5879i	0.00585235	+	0.707083i
$487$	30.4919			1.38172			0.690861	−	0.722988i	$-0.257232\pi$
$487$	30.4919			1.38172			0.690861	+	0.722988i	$0.257232\pi$
$488$	−0.398461	+	0.690154i	−0.0180375	+	0.0312418i
$489$	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	$0.732946\pi$
$492$	−9.74597	−	1.00803i	−0.439382	−	0.0454457i
$493$	−6.27415	+	10.8671i	−0.282573	+	0.489431i
$494$	3.38105			0.152121
$495$	−16.2520	+	18.1703i	−0.730475	+	0.816696i
$496$	−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	0.980290	−	0.197564i	$-0.0633032\pi$
$499$	7.12702	+	12.3444i	0.319049	+	0.552609i	−0.661241	+	0.750174i	$0.729970\pi$
$500$	5.96550	+	10.3325i	0.266785	+	0.462086i
$501$	−12.5635	+	17.3525i	−0.561296	+	0.775253i
$502$	−12.9468	+	22.4244i	−0.577842	+	1.00085i
$503$	18.0255			0.803718			0.401859	−	0.915702i	$-0.368364\pi$
$503$	18.0255			0.803718			0.401859	+	0.915702i	$0.368364\pi$
$504$		0			0
$505$	−15.9839			−0.711273
$506$	−13.4919	+	23.3687i	−0.599790	+	1.03887i
$507$	−8.61430	−	0.890985i	−0.382574	−	0.0395700i
$508$	−7.37298	−	12.7704i	−0.327123	−	0.566594i
$509$	−16.8807	−	29.2383i	−0.748226	−	1.29597i	−0.948672	−	0.316261i	$-0.897573\pi$
$509$	−16.8807	−	29.2383i	−0.748226	−	1.29597i	0.200446	−	0.979705i	$-0.435761\pi$
$510$	2.03151	+	4.54259i	0.0899566	+	0.201149i
$511$		0			0
$512$	1.00000			0.0441942
$513$	3.94456	+	1.26004i	0.174157	+	0.0556323i
$514$	13.9625			0.615860
$515$	18.3095	−	31.7129i	0.806812	−	1.39744i
$516$	6.27415	+	14.0294i	0.276204	+	0.617611i
$517$	−13.7829	−	23.8726i	−0.606170	−	1.04992i
$518$		0			0
$519$	−21.9284	−	2.26808i	−0.962551	−	0.0995575i
$520$	4.30948	−	7.46423i	0.188983	−	0.327328i
$521$	1.41421			0.0619578			0.0309789	−	0.999520i	$-0.490138\pi$
$521$	1.41421			0.0619578			0.0309789	+	0.999520i	$0.490138\pi$
$522$	26.0554	+	5.44816i	1.14042	+	0.238460i
$523$	−31.0115			−1.35604			−0.678019	−	0.735045i	$-0.737161\pi$
$523$	−31.0115			−1.35604			−0.678019	+	0.735045i	$0.737161\pi$
$524$	−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
$528$	4.06301	−	5.61177i	0.176820	−	0.244221i
$529$	−11.2540	+	19.4926i	−0.489306	+	0.847502i
$530$	−21.5725			−0.937048
$531$	7.77817	+	1.62641i	0.337544	+	0.0705800i
$532$		0			0
$533$	12.0000	−	20.7846i	0.519778	−	0.900281i
$534$	−12.1825	−	1.26004i	−0.527187	−	0.0545274i
$535$	−15.9940	−	27.7024i	−0.691481	−	1.19768i
$536$	−0.436492	−	0.756026i	−0.0188536	−	0.0326553i
$537$	0.617292	+	1.38031i	0.0266381	+	0.0595647i
$538$	−1.72286	+	2.98408i	−0.0742778	+	0.128653i
$539$		0			0
$540$	7.80948	−	7.10222i	0.336066	−	0.305631i
$541$	16.1109			0.692661			0.346330	−	0.938113i	$-0.387428\pi$
$541$	16.1109			0.692661			0.346330	+	0.938113i	$0.387428\pi$
$542$	−3.53553	+	6.12372i	−0.151864	+	0.263036i
$543$	−5.56351	−	12.4404i	−0.238753	−	0.533868i
$544$	−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	$0.953949\pi$
$548$	15.4919			0.661783
$549$	−0.746310	−	2.27129i	−0.0318517	−	0.0969364i
$550$	−3.49193			−0.148897
$551$	3.53553	−	6.12372i	0.150619	−	0.260879i
$552$	6.85224	−	9.46420i	0.291651	−	0.402823i
$553$		0			0
$554$	12.1825	+	21.1006i	0.517583	+	0.896480i
$555$	−20.1109	+	27.7768i	−0.853659	+	1.17906i
$556$	9.23159	−	15.9896i	0.391507	−	0.678109i
$557$	3.38105			0.143260			0.0716298	−	0.997431i	$-0.477180\pi$
$557$	3.38105			0.143260			0.0716298	+	0.997431i	$0.477180\pi$
$558$	10.9545	−	12.2474i	0.463739	−	0.518476i
$559$	−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
$563$	2.60960	+	4.51995i	0.109981	+	0.190493i	0.915762	−	0.401720i	$-0.131588\pi$
$563$	2.60960	+	4.51995i	0.109981	+	0.190493i	−0.805781	+	0.592213i	$0.798254\pi$
$564$	4.87298	+	10.8963i	0.205190	+	0.458818i
$565$	3.93399	−	6.81388i	0.165504	−	0.286662i
$566$	10.5168			0.442054
$567$		0			0
$568$	−2.12702			−0.0892476
$569$	−3.74597	+	6.48820i	−0.157039	+	0.272000i	−0.933800	−	0.357796i	$-0.883528\pi$
$569$	−3.74597	+	6.48820i	−0.157039	+	0.272000i	0.776761	+	0.629796i	$0.216862\pi$
$570$	−1.14477	−	2.55978i	−0.0479492	−	0.107218i
$571$	−0.254033	−	0.439999i	−0.0106310	−	0.0184134i	0.860661	−	0.509178i	$-0.170051\pi$
$571$	−0.254033	−	0.439999i	−0.0106310	−	0.0184134i	−0.871292	+	0.490765i	$0.836717\pi$
$572$	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
$576$	−2.00000	+	2.23607i	−0.0833333	+	0.0931695i
$577$	35.1757			1.46438			0.732192	−	0.681098i	$-0.238497\pi$
$577$	35.1757			1.46438			0.732192	+	0.681098i	$0.238497\pi$
$578$	7.50000	−	12.9904i	0.311959	−	0.540329i
$579$	16.3811	−	22.6253i	0.680774	−	0.940274i
$580$	−9.01276	−	15.6106i	−0.374234	−	0.648193i
$581$		0			0
$582$	−18.1270	+	25.0367i	−0.751389	+	1.03781i
$583$	21.2379	−	36.7851i	0.879584	−	1.52348i
$584$	15.3767			0.636293
$585$	8.07157	+	24.5647i	0.333719	+	1.01563i
$586$	−6.27415			−0.259183
$587$	14.8884	−	25.7875i	0.614512	−	1.06437i	−0.375958	−	0.926637i	$-0.622686\pi$
$587$	14.8884	−	25.7875i	0.614512	−	1.06437i	0.990470	−	0.137729i	$-0.0439804\pi$
$588$		0			0
$589$	−2.18246	−	3.78013i	−0.0899266	−	0.155757i
$590$	−2.69052	−	4.66013i	−0.110767	−	0.191854i
$591$	−4.68030	−	10.4655i	−0.192522	−	0.430492i
$592$	4.87298	−	8.44025i	0.200278	−	0.346892i
$593$	22.8070			0.936573			0.468287	−	0.883577i	$-0.344871\pi$
$593$	22.8070			0.936573			0.468287	+	0.883577i	$0.344871\pi$
$594$	4.42227	+	20.3087i	0.181448	+	0.833276i
$595$		0			0
$596$	0.127017	−	0.219999i	0.00520280	−	0.00901152i
$597$	−14.6190	−	32.6890i	−0.598314	−	1.33787i
$598$	14.3104	+	24.7863i	0.585194	+	1.01359i
$599$	−0.618950	−	1.07205i	−0.0252896	−	0.0438029i	0.853104	−	0.521742i	$-0.174717\pi$
$599$	−0.618950	−	1.07205i	−0.0252896	−	0.0438029i	−0.878393	+	0.477939i	$0.841384\pi$
$600$	1.50403	+	0.155563i	0.0614017	+	0.00635083i
$601$	18.8224	−	32.6014i	0.767783	−	1.32984i	−0.170979	−	0.985275i	$-0.554693\pi$
$601$	18.8224	−	32.6014i	0.767783	−	1.32984i	0.938762	−	0.344565i	$-0.111974\pi$
$602$		0			0
$603$	2.56351	+	0.536026i	0.104394	+	0.0218287i
$604$	11.0000			0.447584
$605$	−5.07877	+	8.79668i	−0.206481	+	0.357636i
$606$	−7.99193	+	11.0383i	−0.324650	+	0.448402i
$607$	−7.86799	−	13.6278i	−0.319352	−	0.553134i	0.661001	−	0.750385i	$-0.270132\pi$
$607$	−7.86799	−	13.6278i	−0.319352	−	0.553134i	−0.980353	+	0.197251i	$0.936799\pi$
$608$	0.398461	+	0.690154i	0.0161597	+	0.0279894i
$609$		0			0
$610$	−0.809475	+	1.40205i	−0.0327747	+	0.0567674i
$611$	−29.2379			−1.18284
$612$	4.15283	+	0.868351i	0.167868	+	0.0351010i
$613$	3.38105			0.136559			0.0682797	−	0.997666i	$-0.478249\pi$
$613$	3.38105			0.136559			0.0682797	+	0.997666i	$0.478249\pi$
$614$	12.0600	−	20.8886i	0.486703	−	0.842994i
$615$	−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	$0.644708\pi$
$618$	−12.7460	−	28.5008i	−0.512718	−	1.14647i
$619$	−11.1733	+	19.3527i	−0.449092	+	0.777850i	−0.998327	−	0.0578175i	$-0.981586\pi$
$619$	−11.1733	+	19.3527i	−0.449092	+	0.777850i	0.549235	+	0.835668i	$0.314919\pi$
$620$	−11.1270			−0.446872
$621$	7.45812	+	34.2505i	0.299284	+	1.37442i
$622$	−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
$626$	−13.3452	−	23.1146i	−0.533382	−	0.923845i
$627$	5.49193	+	0.568036i	0.219327	+	0.0226852i
$628$	−3.22689	+	5.58913i	−0.128767	+	0.223031i
$629$	−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	$0.685276\pi$
$632$	−2.93649	+	5.08615i	−0.116807	+	0.202316i
$633$	−2.66021	+	3.67423i	−0.105734	+	0.146038i
$634$	−0.690525	−	1.19602i	−0.0274243	−	0.0475002i
$635$	−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
$639$	4.25403	−	4.75615i	0.168287	−	0.188151i
$640$	2.03151			0.0803023
$641$	18.5554	−	32.1390i	0.732896	−	1.26941i	−0.222744	−	0.974877i	$-0.571502\pi$
$641$	18.5554	−	32.1390i	0.732896	−	1.26941i	0.955640	−	0.294536i	$-0.0951651\pi$
$642$	−27.1281	−	2.80588i	−1.07066	−	0.110739i
$643$	20.1468	+	34.8953i	0.794514	+	1.37614i	0.923147	+	0.384446i	$0.125608\pi$
$643$	20.1468	+	34.8953i	0.794514	+	1.37614i	−0.128634	+	0.991692i	$0.541059\pi$
$644$		0			0
$645$	12.7460	+	28.5008i	0.501872	+	1.12222i
$646$	0.563508	−	0.976025i	0.0221709	−	0.0384012i
$647$	5.47723			0.215332			0.107666	−	0.994187i	$-0.465662\pi$
$647$	5.47723			0.215332			0.107666	+	0.994187i	$0.465662\pi$
$648$	−1.00000	−	8.94427i	−0.0392837	−	0.351364i
$649$	10.5952			0.415898
$650$	−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	0.839732	+	0.543001i	$0.182712\pi$
$653$	22.7460	+	39.3972i	0.890118	+	1.54173i	0.0503861	+	0.998730i	$0.483955\pi$
$654$	−15.7246	−	1.62641i	−0.614879	−	0.0635975i
$655$	−7.99193	+	13.8424i	−0.312271	+	0.540869i
$656$	5.65685			0.220863
$657$	−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	$0.911640\pi$
$660$	8.25403	−	11.4003i	0.321288	−	0.443758i
$661$	−12.4977	−	21.6466i	−0.486104	−	0.841956i	0.513769	−	0.857929i	$-0.328249\pi$
$661$	−12.4977	−	21.6466i	−0.486104	−	0.841956i	−0.999872	+	0.0159726i	$0.994916\pi$
$662$	9.18246	+	15.9045i	0.356886	+	0.618145i
$663$	−6.09452	+	8.41765i	−0.236691	+	0.326914i
$664$	−4.15283	+	7.19291i	−0.161161	+	0.279139i
$665$		0			0
$666$	9.12702	+	27.7768i	0.353665	+	1.07633i
$667$	59.8569			2.31767
$668$	6.18433	−	10.7116i	0.239279	−	0.414443i
$669$	19.8014	+	2.04808i	0.765567	+	0.0791833i
$670$	−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	$-0.0467447\pi$
$674$	0.254033			0.00978500
$675$	−3.35591	+	3.05198i	−0.129169	+	0.117471i
$676$	5.00000			0.192308
$677$	−6.36396	+	11.0227i	−0.244587	+	0.423637i	−0.962015	−	0.272995i	$-0.911986\pi$
$677$	−6.36396	+	11.0227i	−0.244587	+	0.423637i	0.717428	+	0.696632i	$0.245319\pi$
$678$	−2.73861	−	6.12372i	−0.105176	−	0.235180i
$679$		0			0
$680$	−1.43649	−	2.48808i	−0.0550869	−	0.0954134i
$681$	10.5000	+	1.08602i	0.402361	+	0.0416166i
$682$	10.9545	−	18.9737i	0.419468	−	0.726539i
$683$	−7.74597			−0.296391			−0.148196	−	0.988958i	$-0.547347\pi$
$683$	−7.74597			−0.296391			−0.148196	+	0.988958i	$0.547347\pi$
$684$	−2.34015	−	0.489323i	−0.0894780	−	0.0187097i
$685$	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
$689$	−22.5262	−	39.0165i	−0.858180	−	1.48641i
$690$	13.9204	−	19.2266i	0.529939	−	0.731943i
$691$	10.6458	−	18.4391i	0.404986	−	0.701455i	−0.589334	−	0.807889i	$-0.700610\pi$
$691$	10.6458	−	18.4391i	0.404986	−	0.701455i	0.994320	+	0.106434i	$0.0339432\pi$
$692$	12.7279			0.483843
$693$		0			0
$694$	−7.74597			−0.294033
$695$	18.7540	−	32.4829i	0.711381	−	1.23215i
$696$	−15.2869	−	1.58114i	−0.579449	−	0.0599329i
$697$	−4.00000	−	6.92820i	−0.151511	−	0.262424i
$698$	−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	$0.704640\pi$
$702$	21.0000	+	6.70820i	0.792594	+	0.253185i
$703$	7.76677			0.292929
$704$	−2.00000	+	3.46410i	−0.0753778	+	0.130558i
$705$	9.89949	+	22.1359i	0.372837	+	0.833688i
$706$	9.01276	+	15.6106i	0.339200	+	0.587511i
$707$		0			0
$708$	−4.56351	−	0.472008i	−0.171507	−	0.0177391i
$709$	−12.3649	+	21.4167i	−0.464374	+	0.804320i	−0.999173	−	0.0406597i	$-0.987054\pi$
$709$	−12.3649	+	21.4167i	−0.464374	+	0.804320i	0.534799	+	0.844979i	$0.320387\pi$
$710$	−4.32105			−0.162166
$711$	−5.50000	−	16.7385i	−0.206266	−	0.627743i
$712$	7.07107			0.264999
$713$	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
$717$	−15.2363	+	21.0441i	−0.569010	+	0.785907i
$718$	14.1190	−	24.4547i	0.526915	−	0.912643i
$719$	9.36061			0.349092			0.174546	−	0.984649i	$-0.444154\pi$
$719$	9.36061			0.349092			0.174546	+	0.984649i	$0.444154\pi$
$720$	−4.06301	+	4.54259i	−0.151420	+	0.169292i
$721$		0			0
$722$	9.18246	−	15.9045i	0.341736	−	0.591904i
$723$	3.05544	+	0.316027i	0.113633	+	0.0117532i
$724$	3.93399	+	6.81388i	0.146206	+	0.253236i
$725$	3.87298	+	6.70820i	0.143839	+	0.249136i
$726$	3.53553	+	7.90569i	0.131216	+	0.293408i
$727$	−18.1153	+	31.3767i	−0.671861	+	1.16370i	0.305515	+	0.952187i	$0.401171\pi$
$727$	−18.1153	+	31.3767i	−0.671861	+	1.16370i	−0.977376	+	0.211509i	$0.932162\pi$
$728$		0			0
$729$	22.0000	+	15.6525i	0.814815	+	0.579721i
$730$	31.2379			1.15617
$731$	−6.27415	+	10.8671i	−0.232058	+	0.401936i
$732$	0.563508	+	1.26004i	0.0208279	+	0.0465725i
$733$	4.82073	+	8.34975i	0.178058	+	0.308405i	0.941215	−	0.337808i	$-0.109685\pi$
$733$	4.82073	+	8.34975i	0.178058	+	0.308405i	−0.763157	+	0.646213i	$0.776352\pi$
$734$	2.03151	+	3.51867i	0.0749843	+	0.129877i
$735$		0			0
$736$	−3.37298	+	5.84218i	−0.124330	+	0.215346i
$737$	3.49193			0.128627
$738$	−11.3137	+	12.6491i	−0.416463	+	0.465620i
$739$	−30.0000			−1.10357			−0.551784	−	0.833987i	$-0.686053\pi$
$739$	−30.0000			−1.10357			−0.551784	+	0.833987i	$0.686053\pi$
$740$	9.89949	−	17.1464i	0.363913	−	0.630315i
$741$	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	$0.663367\pi$
$744$	−5.56351	+	7.68423i	−0.203968	+	0.281718i
$745$	0.258035	−	0.446930i	0.00945367	−	0.0163742i
$746$	−8.87298			−0.324863
$747$	−7.77817	−	23.6718i	−0.284589	−	0.866106i
$748$	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	0.959906	−	0.280321i	$-0.0904408\pi$
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	−0.722718	+	0.691143i	$0.757107\pi$
$752$	−3.44572	−	5.96816i	−0.125652	−	0.217636i
$753$	18.3095	+	40.9412i	0.667234	+	1.49198i
$754$	18.8224	−	32.6014i	0.685473	−	1.18727i
$755$	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	$0.589312\pi$
$758$	6.18246	−	10.7083i	0.224557	−	0.388944i
$759$	19.0805	+	42.6652i	0.692577	+	1.54865i
$760$	0.809475	+	1.40205i	0.0293627	+	0.0508578i
$761$	−1.14477	−	1.98280i	−0.0414979	−	0.0718765i	0.844530	−	0.535508i	$-0.179880\pi$
$761$	−1.14477	−	1.98280i	−0.0414979	−	0.0718765i	−0.886028	+	0.463631i	$0.846546\pi$
$762$	−25.4052	−	2.62769i	−0.920334	−	0.0951910i
$763$		0			0
$764$	−13.8730			−0.501907
$765$	8.43649	+	1.76406i	0.305022	+	0.0637797i
$766$	−23.8620			−0.862169
$767$	5.61895	−	9.73231i	0.202889	−	0.351413i
$768$	1.01575	−	1.40294i	0.0366528	−	0.0506243i
$769$	−4.85993	−	8.41765i	−0.175254	−	0.303548i	0.764995	−	0.644036i	$-0.222741\pi$
$769$	−4.85993	−	8.41765i	−0.175254	−	0.303548i	−0.940249	+	0.340488i	$0.889408\pi$
$770$		0			0
$771$	14.1825	−	19.5886i	0.510769	−	0.705466i
$772$	−8.06351	+	13.9664i	−0.290212	+	0.502662i
$773$	3.44572			0.123934			0.0619670	−	0.998078i	$-0.480263\pi$
$773$	3.44572			0.123934			0.0619670	+	0.998078i	$0.480263\pi$
$774$	26.0554	+	5.44816i	0.936544	+	0.195830i
$775$	4.78153			0.171758
$776$	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
$780$	−6.09452	−	13.6278i	−0.218219	−	0.487952i
$781$	4.25403	−	7.36820i	0.152221	−	0.263655i
$782$	9.54024			0.341158
$783$	34.1093	−	31.0203i	1.21897	−	1.10857i
$784$		0			0
$785$	−6.55544	+	11.3544i	−0.233974	+	0.405254i
$786$	5.56351	+	12.4404i	0.198444	+	0.443734i
$787$	4.77012	+	8.26209i	0.170036	+	0.294512i	0.938432	−	0.345463i	$-0.112278\pi$
$787$	4.77012	+	8.26209i	0.170036	+	0.294512i	−0.768396	+	0.639975i	$0.778945\pi$
$788$	3.30948	+	5.73218i	0.117895	+	0.204200i
$789$	−9.68066	−	1.00128i	−0.344641	−	0.0356465i
$790$	−5.96550	+	10.3325i	−0.212243	+	0.367616i
$791$		0			0
$792$	−3.74597	−	11.4003i	−0.133107	−	0.405093i
$793$	−3.38105			−0.120065
$794$	−3.53553	+	6.12372i	−0.125471	+	0.217323i
$795$	−21.9123	+	30.2649i	−0.777149	+	1.07339i
$796$	10.3372	+	17.9045i	0.366391	+	0.634608i
$797$	13.0366	+	22.5800i	0.461779	+	0.799825i	0.999050	−	0.0435852i	$-0.0138780\pi$
$797$	13.0366	+	22.5800i	0.461779	+	0.799825i	−0.537271	+	0.843410i	$0.680545\pi$
$798$		0			0
$799$	−4.87298	+	8.44025i	−0.172394	+	0.298595i
$800$	−0.872983			−0.0308646
$801$	−14.1421	+	15.8114i	−0.499688	+	0.558668i
$802$	3.87298			0.136760
$803$	−30.7534	+	53.2665i	−1.08527	+	1.87973i
$804$	−1.50403	−	0.155563i	−0.0530430	−	0.00548628i
$805$		0			0
$806$	−11.6190	−	20.1246i	−0.409260	−	0.708859i
$807$	2.43649	+	5.44816i	0.0857686	+	0.191784i
$808$	3.93399	−	6.81388i	0.138397	−	0.239711i
$809$	−30.7298			−1.08040			−0.540202	−	0.841536i	$-0.681652\pi$
$809$	−30.7298			−1.08040			−0.540202	+	0.841536i	$0.681652\pi$
$810$	−2.03151	−	18.1703i	−0.0713798	−	0.638441i
$811$	−13.9625			−0.490290			−0.245145	−	0.969486i	$-0.578836\pi$
$811$	−13.9625			−0.490290			−0.245145	+	0.969486i	$0.578836\pi$
$812$		0			0
$813$	5.00000	+	11.1803i	0.175358	+	0.392112i
$814$	19.4919	+	33.7610i	0.683192	+	1.18332i
$815$	−10.1575	−	17.5934i	−0.355803	−	0.616268i
$816$	−2.43649	−	0.252009i	−0.0852943	−	0.00882207i
$817$	3.53553	−	6.12372i	0.123693	−	0.214242i
$818$	−31.6288			−1.10587
$819$		0			0
$820$	11.4919			0.401316
$821$	−10.7460	+	18.6126i	−0.375037	+	0.649583i	−0.990333	−	0.138714i	$-0.955703\pi$
$821$	−10.7460	+	18.6126i	−0.375037	+	0.649583i	0.615296	+	0.788296i	$0.289037\pi$
$822$	15.7360	−	21.7343i	0.548855	−	0.758070i
$823$	10.8730	+	18.8326i	0.379008	+	0.656462i	0.990918	−	0.134466i	$-0.0429318\pi$
$823$	10.8730	+	18.8326i	0.379008	+	0.656462i	−0.611910	+	0.790928i	$0.709598\pi$
$824$	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	$0.246398\pi$
$828$	−6.31754	−	19.2266i	−0.219550	−	0.668170i
$829$	−54.4358			−1.89063			−0.945317	−	0.326153i	$-0.894248\pi$
$829$	−54.4358			−1.89063			−0.945317	+	0.326153i	$0.894248\pi$
$830$	−8.43649	+	14.6124i	−0.292835	+	0.507205i
$831$	41.9773	+	4.34175i	1.45618	+	0.150614i
$832$	2.12132	+	3.67423i	0.0735436	+	0.127381i
$833$		0			0
$834$	−13.0554	−	29.1929i	−0.452073	−	1.01087i
$835$	12.5635	−	21.7606i	0.434778	−	0.753058i
$836$	−3.18768			−0.110248
$837$	−6.05544	−	27.8088i	−0.209307	−	0.961214i
$838$	−3.98461			−0.137646
$839$	19.9672	−	34.5842i	0.689345	−	1.19398i	−0.282706	−	0.959207i	$-0.591232\pi$
$839$	19.9672	−	34.5842i	0.689345	−	1.19398i	0.972050	−	0.234773i	$-0.0754348\pi$
$840$		0			0
$841$	−24.8649	−	43.0673i	−0.857411	−	1.48508i
$842$	2.56351	+	4.44013i	0.0883443	+	0.153017i
$843$	11.6224	+	1.20211i	0.400295	+	0.0414029i
$844$	1.30948	−	2.26808i	0.0450740	−	0.0780704i
$845$	10.1575			0.349430
$846$	20.2367	+	4.23146i	0.695750	+	0.145481i
$847$		0			0
$848$	5.30948	−	9.19628i	0.182328	−	0.315802i
$849$	10.6825	−	14.7544i	0.366621	−	0.506371i
$850$	0.617292	+	1.06918i	0.0211730	+	0.0366726i
$851$	32.8730	+	56.9377i	1.12687	+	1.95180i
$852$	−2.16052	+	2.98408i	−0.0740183	+	0.102233i
$853$	22.7564	−	39.4153i	0.779165	−	1.34955i	−0.153258	−	0.988186i	$-0.548976\pi$
$853$	22.7564	−	39.4153i	0.779165	−	1.34955i	0.932423	−	0.361368i	$-0.117690\pi$
$854$		0			0
$855$	−4.75403	−	0.994063i	−0.162585	−	0.0339962i
$856$	15.7460			0.538186
$857$	−23.8620	+	41.3302i	−0.815110	+	1.41181i	0.0941381	+	0.995559i	$0.469990\pi$
$857$	−23.8620	+	41.3302i	−0.815110	+	1.41181i	−0.909249	+	0.416254i	$0.863343\pi$
$858$	29.2379	+	3.02410i	0.998165	+	0.103241i
$859$	1.14477	+	1.98280i	0.0390591	+	0.0676523i	0.884894	−	0.465792i	$-0.154231\pi$
$859$	1.14477	+	1.98280i	0.0390591	+	0.0676523i	−0.845835	+	0.533445i	$0.820897\pi$
$860$	−9.01276	−	15.6106i	−0.307333	−	0.532316i
$861$		0			0
$862$	−4.74597	+	8.22026i	−0.161648	+	0.279983i
$863$	−36.1270			−1.22978			−0.614889	−	0.788614i	$-0.710799\pi$
$863$	−36.1270			−1.22978			−0.614889	+	0.788614i	$0.710799\pi$
$864$	1.10557	+	5.07718i	0.0376122	+	0.172729i
$865$	25.8569			0.879159
$866$	14.8492	−	25.7196i	0.504598	−	0.873989i
$867$	−10.6066	−	23.7171i	−0.360219	−	0.805474i
$868$		0			0
$869$	−11.7460	−	20.3446i	−0.398455	−	0.690144i
$870$	−31.0554	−	3.21209i	−1.05288	−	0.108900i
$871$	1.85188	−	3.20755i	0.0627485	−	0.108684i
$872$	9.12702			0.309080
$873$	16.7125	+	50.8623i	0.565633	+	1.72143i
$874$	−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	−0.981560	−	0.191153i	$-0.938777\pi$
$877$	−19.4365	−	33.6650i	−0.656324	−	1.13679i	0.325237	−	0.945633i	$-0.394556\pi$
$878$	−5.47723	−	9.48683i	−0.184847	−	0.320165i
$879$	−6.37298	+	8.80226i	−0.214955	+	0.296893i
$880$	−4.06301	+	7.03734i	−0.136964	+	0.237229i
$881$	15.7360			0.530159			0.265079	−	0.964227i	$-0.414602\pi$
$881$	15.7360			0.530159			0.265079	+	0.964227i	$0.414602\pi$
$882$		0			0
$883$	4.50807			0.151709			0.0758543	−	0.997119i	$-0.475832\pi$
$883$	4.50807			0.151709			0.0758543	+	0.997119i	$0.475832\pi$
$884$	3.00000	−	5.19615i	0.100901	−	0.174766i
$885$	−9.27079	−	0.958887i	−0.311634	−	0.0322326i
$886$	−12.1825	−	21.1006i	−0.409278	−	0.708890i
$887$	18.0255	+	31.2211i	0.605238	+	1.04830i	0.992014	+	0.126129i	$0.0402553\pi$
$887$	18.0255	+	31.2211i	0.605238	+	1.04830i	−0.386776	+	0.922174i	$0.626411\pi$
$888$	−6.89144	−	15.4097i	−0.231262	−	0.517117i
$889$		0			0
$890$	14.3649			0.481513
$891$	32.9839	+	14.4244i	1.10500	+	0.483237i
$892$	−11.4933			−0.384825
$893$	2.74597	−	4.75615i	0.0918903	−	0.159159i
$894$	−0.179629	−	0.401662i	−0.00600768	−	0.0134336i
$895$	−0.886735	−	1.53587i	−0.0296403	−	0.0513385i
$896$		0			0
$897$	49.3095	+	5.10012i	1.64640	+	0.170288i
$898$	−4.50000	+	7.79423i	−0.150167	+	0.260097i
$899$	−48.5993			−1.62088
$900$	1.74597	−	1.95205i	0.0581989	−	0.0650683i
$901$	−15.0175			−0.500304
$902$	−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
$906$	11.1733	−	15.4324i	0.371207	−	0.512706i
$907$	2.30948	−	4.00013i	0.0766849	−	0.132822i	−0.825133	−	0.564939i	$-0.808900\pi$
$907$	2.30948	−	4.00013i	0.0766849	−	0.132822i	0.901818	+	0.432117i	$0.142233\pi$
$908$	−6.09452			−0.202254
$909$	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	$0.0407921\pi$
$912$	1.37298	+	0.142009i	0.0454640	+	0.00470239i
$913$	−16.6113	−	28.7716i	−0.549754	−	0.952202i
$914$	−16.9365	−	29.3349i	−0.560209	−	0.970311i
$915$	1.14477	+	2.55978i	0.0378449	+	0.0846239i
$916$	−3.93399	+	6.81388i	−0.129983	+	0.225137i
$917$		0			0
$918$	5.43649	−	4.94414i	0.179431	−	0.163181i
$919$	−39.3649			−1.29853			−0.649264	−	0.760563i	$-0.724923\pi$
$919$	−39.3649			−1.29853			−0.649264	+	0.760563i	$0.724923\pi$
$920$	−6.85224	+	11.8684i	−0.225912	+	0.391290i
$921$	−17.0554	−	38.1371i	−0.561996	−	1.25666i
$922$	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
$926$	21.6190			0.710443
$927$	−52.9318	−	11.0680i	−1.73851	−	0.363520i
$928$	8.87298			0.291270
$929$	5.30900	−	9.19547i	0.174183	−	0.301693i	−0.765695	−	0.643203i	$-0.777605\pi$
$929$	5.30900	−	9.19547i	0.174183	−	0.301693i	0.939878	+	0.341510i	$0.110938\pi$
$930$	−11.3023	+	15.6106i	−0.370617	+	0.511890i
$931$		0			0
$932$	−11.3730	−	19.6986i	−0.372534	−	0.645249i
$933$	−1.43649	+	1.98406i	−0.0470286	+	0.0649552i
$934$	−19.5295	+	33.8262i	−0.639026	+	1.10683i
$935$	11.4919			0.375826
$936$	−12.4585	−	2.60505i	−0.407218	−	0.0851488i
$937$	42.4036			1.38526			0.692632	−	0.721291i	$-0.256451\pi$
$937$	42.4036			1.38526			0.692632	+	0.721291i	$0.256451\pi$
$938$		0			0
$939$	−45.9839	−	4.75615i	−1.50063	−	0.155211i
$940$	−7.00000	−	12.1244i	−0.228315	−	0.395453i
$941$	0.836124	+	1.44821i	0.0272569	+	0.0472103i	0.879332	−	0.476209i	$-0.157989\pi$
$941$	0.836124	+	1.44821i	0.0272569	+	0.0472103i	−0.852075	+	0.523419i	$0.824656\pi$
$942$	4.56351	+	10.2043i	0.148687	+	0.332475i
$943$	−19.0805	+	33.0484i	−0.621346	+	1.07620i
$944$	2.64880			0.0862110
$945$		0			0
$946$	35.4919			1.15394
$947$	−13.8014	+	23.9047i	−0.448486	+	0.776800i	−0.998288	−	0.0584952i	$-0.981370\pi$
$947$	−13.8014	+	23.9047i	−0.448486	+	0.776800i	0.549802	+	0.835295i	$0.314703\pi$
$948$	4.15283	+	9.28600i	0.134878	+	0.301595i
$949$	32.6190	+	56.4977i	1.05886	+	1.83399i
$950$	−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	$0.652772\pi$
$954$	9.94456	+	30.2649i	0.321967	+	0.979863i
$955$	−28.1830			−0.911982
$956$	7.50000	−	12.9904i	0.242567	−	0.420139i
$957$	36.0510	−	49.7931i	1.16536	−	1.60958i
$958$	9.01276	+	15.6106i	0.291189	+	0.504354i
$959$		0			0
$960$	2.06351	−	2.85008i	0.0665994	−	0.0919861i
$961$	0.500000	−	0.866025i	0.0161290	−	0.0279363i
$962$	41.3486			1.33313
$963$	−31.4919	+	35.2091i	−1.01481	+	1.13460i
$964$	−1.77347			−0.0571197
$965$	−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
$969$	−0.796921	−	1.78197i	−0.0256008	−	0.0572451i
$970$	18.1270	−	31.3969i	0.582023	−	1.00809i
$971$	−36.8480			−1.18251			−0.591254	−	0.806486i	$-0.701367\pi$
$971$	−36.8480			−1.18251			−0.591254	+	0.806486i	$0.701367\pi$
$972$	−13.5640	−	7.68223i	−0.435067	−	0.246408i
$973$		0			0
$974$	−15.2460	+	26.4068i	−0.488512	+	0.846128i
$975$	2.61895	+	5.85615i	0.0838735	+	0.187547i
$976$	−0.398461	−	0.690154i	−0.0127544	−	0.0220913i
$977$	−7.25403	−	12.5644i	−0.232077	−	0.401969i	0.726342	−	0.687333i	$-0.241219\pi$
$977$	−7.25403	−	12.5644i	−0.232077	−	0.401969i	−0.958419	+	0.285364i	$0.907885\pi$
$978$	−17.2286	−	1.78197i	−0.550910	−	0.0569811i
$979$	−14.1421	+	24.4949i	−0.451985	+	0.782860i
$980$		0			0
$981$	−18.2540	+	20.4086i	−0.582806	+	0.651597i
$982$	−13.7460			−0.438651
$983$	4.94975	−	8.57321i	0.157872	−	0.273443i	−0.776229	−	0.630451i	$-0.782870\pi$
$983$	4.94975	−	8.57321i	0.157872	−	0.273443i	0.934101	+	0.357008i	$0.116203\pi$
$984$	5.74597	−	7.93624i	0.183175	−	0.252998i
$985$	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
$989$	59.8569			1.90334
$990$	−7.60995	−	23.1599i	−0.241860	−	0.736069i
$991$	3.74597			0.118995			0.0594973	−	0.998228i	$-0.481050\pi$
$991$	3.74597			0.118995			0.0594973	+	0.998228i	$0.481050\pi$
$992$	2.73861	−	4.74342i	0.0869510	−	0.150604i
$993$	31.6402	+	3.27257i	1.00407	+	0.103852i
$994$		0			0
$995$	21.0000	+	36.3731i	0.665745	+	1.15310i
$996$	5.87298	+	13.1324i	0.186093	+	0.416116i
$997$	−0.129018	+	0.223465i	−0.00408603	+	0.00707721i	−0.868061	−	0.496457i	$-0.834634\pi$
$997$	−0.129018	+	0.223465i	−0.00408603	+	0.00707721i	0.863975	+	0.503534i	$0.167967\pi$
$998$	−14.2540			−0.451204
$999$	48.2401	+	15.4097i	1.52625	+	0.487542i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.t.373.1		8	63.4	even	3
882.2.e.t.373.4		8	63.31	odd	6
882.2.e.t.655.1		8	7.2	even	3
882.2.e.t.655.4		8	7.5	odd	6
882.2.f.p.295.1	✓	8	7.6	odd	2	inner
882.2.f.p.295.4	yes	8	1.1	even	1	trivial
882.2.f.p.589.2	yes	8	63.13	odd	6	inner
882.2.f.p.589.3	yes	8	9.4	even	3	inner
882.2.h.r.67.2		8	63.40	odd	6
882.2.h.r.67.3		8	63.58	even	3
882.2.h.r.79.2		8	7.3	odd	6
882.2.h.r.79.3		8	7.4	even	3
2646.2.e.r.1549.2		8	63.59	even	6
2646.2.e.r.1549.3		8	63.32	odd	6
2646.2.e.r.2125.2		8	21.5	even	6
2646.2.e.r.2125.3		8	21.2	odd	6
2646.2.f.s.883.2		8	21.20	even	2
2646.2.f.s.883.3		8	3.2	odd	2
2646.2.f.s.1765.2		8	63.41	even	6
2646.2.f.s.1765.3		8	9.5	odd	6
2646.2.h.s.361.2		8	63.23	odd	6
2646.2.h.s.361.3		8	63.5	even	6
2646.2.h.s.667.2		8	21.11	odd	6
2646.2.h.s.667.3		8	21.17	even	6
7938.2.a.cd.1.2		4	9.2	odd	6
7938.2.a.cd.1.3		4	63.20	even	6
7938.2.a.cu.1.2		4	63.34	odd	6
7938.2.a.cu.1.3		4	9.7	even	3

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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.707107 + 1.58114i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.01575 - 1.75934i) q^{5} +(-1.72286 - 0.178197i) q^{6} +1.00000 q^{8} +(-2.00000 + 2.23607i) q^{9} +2.03151 q^{10} +(-2.00000 + 3.46410i) q^{11} +(1.01575 - 1.40294i) q^{12} +(2.12132 + 3.67423i) q^{13} +(2.06351 - 2.85008i) q^{15} +(-0.500000 + 0.866025i) q^{16} +1.41421 q^{17} +(-0.936492 - 2.85008i) q^{18} -0.796921 q^{19} +(-1.01575 + 1.75934i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(-3.37298 - 5.84218i) q^{23} +(0.707107 + 1.58114i) q^{24} +(0.436492 - 0.756026i) q^{25} -4.24264 q^{26} +(-4.94975 - 1.58114i) q^{27} +(-4.43649 + 7.68423i) q^{29} +(1.43649 + 3.21209i) q^{30} +(2.73861 + 4.74342i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-6.89144 - 0.712788i) q^{33} +(-0.707107 + 1.22474i) q^{34} +(2.93649 + 0.614017i) q^{36} -9.74597 q^{37} +(0.398461 - 0.690154i) q^{38} +(-4.30948 + 5.95218i) q^{39} +(-1.01575 - 1.75934i) q^{40} +(-2.82843 - 4.89898i) q^{41} +(-4.43649 + 7.68423i) q^{43} +4.00000 q^{44} +(5.96550 + 1.24738i) q^{45} +6.74597 q^{46} +(-3.44572 + 5.96816i) q^{47} +(-1.72286 - 0.178197i) q^{48} +(0.436492 + 0.756026i) q^{50} +(1.00000 + 2.23607i) q^{51} +(2.12132 - 3.67423i) q^{52} -10.6190 q^{53} +(3.84418 - 3.49604i) q^{54} +8.12602 q^{55} +(-0.563508 - 1.26004i) q^{57} +(-4.43649 - 7.68423i) q^{58} +(-1.32440 - 2.29393i) q^{59} +(-3.50000 - 0.362008i) q^{60} +(-0.398461 + 0.690154i) q^{61} -5.47723 q^{62} +1.00000 q^{64} +(4.30948 - 7.46423i) q^{65} +(4.06301 - 5.61177i) q^{66} +(-0.436492 - 0.756026i) q^{67} +(-0.707107 - 1.22474i) q^{68} +(6.85224 - 9.46420i) q^{69} -2.12702 q^{71} +(-2.00000 + 2.23607i) q^{72} +15.3767 q^{73} +(4.87298 - 8.44025i) q^{74} +(1.50403 + 0.155563i) q^{75} +(0.398461 + 0.690154i) q^{76} +(-3.00000 - 6.70820i) q^{78} +(-2.93649 + 5.08615i) q^{79} +2.03151 q^{80} +(-1.00000 - 8.94427i) q^{81} +5.65685 q^{82} +(-4.15283 + 7.19291i) q^{83} +(-1.43649 - 2.48808i) q^{85} +(-4.43649 - 7.68423i) q^{86} +(-15.2869 - 1.58114i) q^{87} +(-2.00000 + 3.46410i) q^{88} +7.07107 q^{89} +(-4.06301 + 4.54259i) q^{90} +(-3.37298 + 5.84218i) q^{92} +(-5.56351 + 7.68423i) q^{93} +(-3.44572 - 5.96816i) q^{94} +(0.809475 + 1.40205i) q^{95} +(1.01575 - 1.40294i) q^{96} +(8.92295 - 15.4550i) q^{97} +(-3.74597 - 11.4003i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{9} - 16 q^{11} + 32 q^{15} - 4 q^{16} + 8 q^{18} - 16 q^{22} + 4 q^{23} - 12 q^{25} - 20 q^{29} - 4 q^{30} - 4 q^{32} + 8 q^{36} - 16 q^{37} + 12 q^{39} - 20 q^{43}+ \cdots + 32 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^9 - 16 * q^11 + 32 * q^15 - 4 * q^16 + 8 * q^18 - 16 * q^22 + 4 * q^23 - 12 * q^25 - 20 * q^29 - 4 * q^30 - 4 * q^32 + 8 * q^36 - 16 * q^37 + 12 * q^39 - 20 * q^43 + 32 * q^44 - 8 * q^46 - 12 * q^50 + 8 * q^51 + 8 * q^53 - 20 * q^57 - 20 * q^58 - 28 * q^60 + 8 * q^64 - 12 * q^65 + 12 * q^67 - 48 * q^71 - 16 * q^72 + 8 * q^74 - 24 * q^78 - 8 * q^79 - 8 * q^81 + 4 * q^85 - 20 * q^86 - 16 * q^88 + 4 * q^92 - 60 * q^93 - 40 * q^95 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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