LMFDB - Embedded newform 1323.2.h.c.802.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1323,2,Mod(226,1323)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1323.226"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1323, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-6,0,6,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.3
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	1323.802
Dual form			1323.2.h.c.226.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.879385 q^{2} -1.22668 q^{4} +(0.673648 - 1.16679i) q^{5} -2.83750 q^{8} +(0.592396 - 1.02606i) q^{10} +(0.826352 + 1.43128i) q^{11} +(1.68479 + 2.91815i) q^{13} -0.0418891 q^{16} +(0.233956 - 0.405223i) q^{17} +(1.61334 + 2.79439i) q^{19} +(-0.826352 + 1.43128i) q^{20} +(0.726682 + 1.25865i) q^{22} +(4.47178 - 7.74535i) q^{23} +(1.59240 + 2.75811i) q^{25} +(1.48158 + 2.56617i) q^{26} +(3.13429 - 5.42874i) q^{29} +9.23442 q^{31} +5.63816 q^{32} +(0.205737 - 0.356347i) q^{34} +(-4.61721 - 7.99724i) q^{37} +(1.41875 + 2.45734i) q^{38} +(-1.91147 + 3.31077i) q^{40} +(1.70574 + 2.95442i) q^{41} +(2.20574 - 3.82045i) q^{43} +(-1.01367 - 1.75573i) q^{44} +(3.93242 - 6.81115i) q^{46} -9.35504 q^{47} +(1.40033 + 2.42544i) q^{50} +(-2.06670 - 3.57964i) q^{52} +(-0.286989 + 0.497079i) q^{53} +2.22668 q^{55} +(2.75624 - 4.77396i) q^{58} +10.3969 q^{59} +7.63816 q^{61} +8.12061 q^{62} +5.04189 q^{64} +4.53983 q^{65} +0.596267 q^{67} +(-0.286989 + 0.497079i) q^{68} +0.554378 q^{71} +(-1.02481 + 1.77503i) q^{73} +(-4.06031 - 7.03266i) q^{74} +(-1.97906 - 3.42782i) q^{76} -2.40373 q^{79} +(-0.0282185 + 0.0488759i) q^{80} +(1.50000 + 2.59808i) q^{82} +(-7.52481 + 13.0334i) q^{83} +(-0.315207 - 0.545955i) q^{85} +(1.93969 - 3.35965i) q^{86} +(-2.34477 - 4.06126i) q^{88} +(4.54323 + 7.86911i) q^{89} +(-5.48545 + 9.50108i) q^{92} -8.22668 q^{94} +4.34730 q^{95} +(0.949493 - 1.64457i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 6 q^{16} + 6 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} - 3 q^{26} + 9 q^{29} - 6 q^{31} - 9 q^{34} + 3 q^{37} + 6 q^{38}+ \cdots + 3 q^{97}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 + 3 * q^5 - 12 * q^8 + 6 * q^11 + 3 * q^13 + 6 * q^16 + 6 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 - 3 * q^26 + 9 * q^29 - 6 * q^31 - 9 * q^34 + 3 * q^37 + 6 * q^38 + 9 * q^40 + 3 * q^43 + 15 * q^44 - 6 * q^47 - 6 * q^50 + 21 * q^52 + 6 * q^53 + 9 * q^58 + 6 * q^59 + 12 * q^61 + 60 * q^62 + 24 * q^64 - 30 * q^65 - 24 * q^67 + 6 * q^68 - 18 * q^71 + 21 * q^73 - 30 * q^74 - 15 * q^76 - 42 * q^79 - 15 * q^80 + 9 * q^82 - 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 + 12 * q^89 + 3 * q^92 - 36 * q^94 + 24 * q^95 + 3 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.879385			0.621819			0.310910	−	0.950439i	$-0.399366\pi$
$2$	0.879385			0.621819			0.310910	+	0.950439i	$0.399366\pi$
$3$		0			0
$3$		0			0
$4$	−1.22668			−0.613341
$5$	0.673648	−	1.16679i	0.301265	−	0.521806i	−0.675158	−	0.737673i	$-0.735925\pi$
$5$	0.673648	−	1.16679i	0.301265	−	0.521806i	0.976423	+	0.215867i	$0.0692579\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−2.83750			−1.00321
$9$		0			0
$10$	0.592396	−	1.02606i	0.187332	−	0.324469i
$11$	0.826352	+	1.43128i	0.249154	+	0.431548i	0.963291	−	0.268458i	$-0.0865140\pi$
$11$	0.826352	+	1.43128i	0.249154	+	0.431548i	−0.714137	+	0.700006i	$0.753181\pi$
$12$		0			0
$13$	1.68479	+	2.91815i	0.467277	+	0.809348i	0.999301	−	0.0373813i	$-0.0119016\pi$
$13$	1.68479	+	2.91815i	0.467277	+	0.809348i	−0.532024	+	0.846729i	$0.678568\pi$
$14$		0			0
$15$		0			0
$16$	−0.0418891			−0.0104723
$17$	0.233956	−	0.405223i	0.0567426	−	0.0982810i	−0.836259	−	0.548335i	$-0.815262\pi$
$17$	0.233956	−	0.405223i	0.0567426	−	0.0982810i	0.893001	+	0.450054i	$0.148595\pi$
$18$		0			0
$19$	1.61334	+	2.79439i	0.370126	+	0.641077i	0.989585	−	0.143953i	$-0.0459813\pi$
$19$	1.61334	+	2.79439i	0.370126	+	0.641077i	−0.619459	+	0.785029i	$0.712648\pi$
$20$	−0.826352	+	1.43128i	−0.184778	+	0.320045i
$21$		0			0
$22$	0.726682	+	1.25865i	0.154929	+	0.268345i
$23$	4.47178	−	7.74535i	0.932431	−	1.61502i	0.153279	−	0.988183i	$-0.451017\pi$
$23$	4.47178	−	7.74535i	0.932431	−	1.61502i	0.779152	−	0.626835i	$-0.215650\pi$
$24$		0			0
$25$	1.59240	+	2.75811i	0.318479	+	0.551622i
$26$	1.48158	+	2.56617i	0.290562	+	0.503268i
$27$		0			0
$28$		0			0
$29$	3.13429	−	5.42874i	0.582022	−	1.00809i	−0.413217	−	0.910632i	$-0.635595\pi$
$29$	3.13429	−	5.42874i	0.582022	−	1.00809i	0.995239	−	0.0974595i	$-0.0310717\pi$
$30$		0			0
$31$	9.23442			1.65855			0.829276	−	0.558840i	$-0.188753\pi$
$31$	9.23442			1.65855			0.829276	+	0.558840i	$0.188753\pi$
$32$	5.63816			0.996695
$33$		0			0
$34$	0.205737	−	0.356347i	0.0352836	−	0.0611130i
$35$		0			0
$36$		0			0
$37$	−4.61721	−	7.99724i	−0.759065	−	1.31474i	−0.943328	−	0.331862i	$-0.892323\pi$
$37$	−4.61721	−	7.99724i	−0.759065	−	1.31474i	0.184263	−	0.982877i	$-0.441010\pi$
$38$	1.41875	+	2.45734i	0.230151	+	0.398634i
$39$		0			0
$40$	−1.91147	+	3.31077i	−0.302231	+	0.523479i
$41$	1.70574	+	2.95442i	0.266391	+	0.461403i	0.967927	−	0.251231i	$-0.0808353\pi$
$41$	1.70574	+	2.95442i	0.266391	+	0.461403i	−0.701536	+	0.712634i	$0.747502\pi$
$42$		0			0
$43$	2.20574	−	3.82045i	0.336372	−	0.582613i	−0.647376	−	0.762171i	$-0.724133\pi$
$43$	2.20574	−	3.82045i	0.336372	−	0.582613i	0.983747	+	0.179558i	$0.0574668\pi$
$44$	−1.01367	−	1.75573i	−0.152817	−	0.264686i
$45$		0			0
$46$	3.93242	−	6.81115i	0.579803	−	1.00425i
$47$	−9.35504			−1.36457			−0.682286	−	0.731085i	$-0.739014\pi$
$47$	−9.35504			−1.36457			−0.682286	+	0.731085i	$0.739014\pi$
$48$		0			0
$49$		0			0
$50$	1.40033	+	2.42544i	0.198037	+	0.343009i
$51$		0			0
$52$	−2.06670	−	3.57964i	−0.286600	−	0.496406i
$53$	−0.286989	+	0.497079i	−0.0394210	+	0.0682791i	−0.885063	−	0.465472i	$-0.845885\pi$
$53$	−0.286989	+	0.497079i	−0.0394210	+	0.0682791i	0.845642	+	0.533751i	$0.179218\pi$
$54$		0			0
$55$	2.22668			0.300246
$56$		0			0
$57$		0			0
$58$	2.75624	−	4.77396i	0.361913	−	0.626851i
$59$	10.3969			1.35356			0.676782	−	0.736183i	$-0.263374\pi$
$59$	10.3969			1.35356			0.676782	+	0.736183i	$0.263374\pi$
$60$		0			0
$61$	7.63816			0.977966			0.488983	−	0.872293i	$-0.337368\pi$
$61$	7.63816			0.977966			0.488983	+	0.872293i	$0.337368\pi$
$62$	8.12061			1.03132
$63$		0			0
$64$	5.04189			0.630236
$65$	4.53983			0.563097
$66$		0			0
$67$	0.596267			0.0728456			0.0364228	−	0.999336i	$-0.488404\pi$
$67$	0.596267			0.0728456			0.0364228	+	0.999336i	$0.488404\pi$
$68$	−0.286989	+	0.497079i	−0.0348025	+	0.0602797i
$69$		0			0
$70$		0			0
$71$	0.554378			0.0657925			0.0328963	−	0.999459i	$-0.489527\pi$
$71$	0.554378			0.0657925			0.0328963	+	0.999459i	$0.489527\pi$
$72$		0			0
$73$	−1.02481	+	1.77503i	−0.119946	+	0.207752i	−0.919746	−	0.392514i	$-0.871605\pi$
$73$	−1.02481	+	1.77503i	−0.119946	+	0.207752i	0.799800	+	0.600266i	$0.204939\pi$
$74$	−4.06031	−	7.03266i	−0.472001	−	0.817530i
$75$		0			0
$76$	−1.97906	−	3.42782i	−0.227013	−	0.393198i
$77$		0			0
$78$		0			0
$79$	−2.40373			−0.270441			−0.135221	−	0.990816i	$-0.543174\pi$
$79$	−2.40373			−0.270441			−0.135221	+	0.990816i	$0.543174\pi$
$80$	−0.0282185	+	0.0488759i	−0.00315492	+	0.00546449i
$81$		0			0
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$	−7.52481	+	13.0334i	−0.825956	+	1.43060i	0.0752309	+	0.997166i	$0.476031\pi$
$83$	−7.52481	+	13.0334i	−0.825956	+	1.43060i	−0.901187	+	0.433431i	$0.857303\pi$
$84$		0			0
$85$	−0.315207	−	0.545955i	−0.0341891	−	0.0592172i
$86$	1.93969	−	3.35965i	0.209162	−	0.362280i
$87$		0			0
$88$	−2.34477	−	4.06126i	−0.249953	−	0.432932i
$89$	4.54323	+	7.86911i	0.481582	+	0.834124i	0.999777	−	0.0211385i	$-0.00672911\pi$
$89$	4.54323	+	7.86911i	0.481582	+	0.834124i	−0.518195	+	0.855263i	$0.673396\pi$
$90$		0			0
$91$		0			0
$92$	−5.48545	+	9.50108i	−0.571898	+	0.990556i
$93$		0			0
$94$	−8.22668			−0.848517
$95$	4.34730			0.446023
$96$		0			0
$97$	0.949493	−	1.64457i	0.0964064	−	0.166981i	−0.813788	−	0.581161i	$-0.802598\pi$
$97$	0.949493	−	1.64457i	0.0964064	−	0.166981i	0.910195	+	0.414181i	$0.135932\pi$
$98$		0			0
$99$		0			0
$100$	−1.95336	−	3.38332i	−0.195336	−	0.338332i
$101$	−0.854570	−	1.48016i	−0.0850329	−	0.147281i	0.820372	−	0.571830i	$-0.193766\pi$
$101$	−0.854570	−	1.48016i	−0.0850329	−	0.147281i	−0.905405	+	0.424548i	$0.860433\pi$
$102$		0			0
$103$	1.81908	−	3.15074i	0.179239	−	0.310451i	−0.762381	−	0.647128i	$-0.775970\pi$
$103$	1.81908	−	3.15074i	0.179239	−	0.310451i	0.941620	+	0.336677i	$0.109303\pi$
$104$	−4.78059	−	8.28023i	−0.468776	−	0.811943i
$105$		0			0
$106$	−0.252374	+	0.437124i	−0.0245127	+	0.0424573i
$107$	3.56418	+	6.17334i	0.344562	+	0.596799i	0.985274	−	0.170982i	$-0.0546941\pi$
$107$	3.56418	+	6.17334i	0.344562	+	0.596799i	−0.640712	+	0.767781i	$0.721361\pi$
$108$		0			0
$109$	−0.201867	+	0.349643i	−0.0193353	+	0.0334898i	−0.875531	−	0.483162i	$-0.839488\pi$
$109$	−0.201867	+	0.349643i	−0.0193353	+	0.0334898i	0.856196	+	0.516651i	$0.172822\pi$
$110$	1.95811			0.186699
$111$		0			0
$112$		0			0
$113$	7.18479	+	12.4444i	0.675888	+	1.17067i	0.976208	+	0.216835i	$0.0695732\pi$
$113$	7.18479	+	12.4444i	0.675888	+	1.17067i	−0.300320	+	0.953839i	$0.597093\pi$
$114$		0			0
$115$	−6.02481	−	10.4353i	−0.561817	−	0.973095i
$116$	−3.84477	+	6.65934i	−0.356978	+	0.618304i
$117$		0			0
$118$	9.14290			0.841672
$119$		0			0
$120$		0			0
$121$	4.13429	−	7.16079i	0.375844	−	0.650981i
$122$	6.71688			0.608118
$123$		0			0
$124$	−11.3277			−1.01726
$125$	11.0273			0.986315
$126$		0			0
$127$	−20.7716			−1.84318			−0.921589	−	0.388167i	$-0.873108\pi$
$127$	−20.7716			−1.84318			−0.921589	+	0.388167i	$0.873108\pi$
$128$	−6.84255			−0.604802
$129$		0			0
$130$	3.99226			0.350144
$131$	−3.58260	+	6.20524i	−0.313013	+	0.542154i	−0.979013	−	0.203797i	$-0.934672\pi$
$131$	−3.58260	+	6.20524i	−0.313013	+	0.542154i	0.666000	+	0.745952i	$0.268005\pi$
$132$		0			0
$133$		0			0
$134$	0.524348			0.0452968
$135$		0			0
$136$	−0.663848	+	1.14982i	−0.0569245	+	0.0985961i
$137$	1.28446	+	2.22475i	0.109739	+	0.190074i	0.915665	−	0.401943i	$-0.131665\pi$
$137$	1.28446	+	2.22475i	0.109739	+	0.190074i	−0.805925	+	0.592017i	$0.798332\pi$
$138$		0			0
$139$	3.06670	+	5.31169i	0.260114	+	0.450531i	0.966272	−	0.257523i	$-0.0829064\pi$
$139$	3.06670	+	5.31169i	0.260114	+	0.450531i	−0.706158	+	0.708055i	$0.749573\pi$
$140$		0			0
$141$		0			0
$142$	0.487511			0.0409111
$143$	−2.78446	+	4.82283i	−0.232848	+	0.403305i
$144$		0			0
$145$	−4.22281	−	7.31412i	−0.350685	−	0.607405i
$146$	−0.901207	+	1.56094i	−0.0745844	+	0.129184i
$147$		0			0
$148$	5.66385	+	9.81007i	0.465565	+	0.806383i
$149$	0.215537	−	0.373321i	0.0176575	−	0.0305837i	−0.857062	−	0.515214i	$-0.827712\pi$
$149$	0.215537	−	0.373321i	0.0176575	−	0.0305837i	0.874719	+	0.484630i	$0.161046\pi$
$150$		0			0
$151$	1.23530	+	2.13960i	0.100527	+	0.174118i	0.911902	−	0.410408i	$-0.134614\pi$
$151$	1.23530	+	2.13960i	0.100527	+	0.174118i	−0.811375	+	0.584526i	$0.801280\pi$
$152$	−4.57785	−	7.92907i	−0.371313	−	0.643132i
$153$		0			0
$154$		0			0
$155$	6.22075	−	10.7747i	0.499663	−	0.865441i
$156$		0			0
$157$	10.1334			0.808734			0.404367	−	0.914597i	$-0.367492\pi$
$157$	10.1334			0.808734			0.404367	+	0.914597i	$0.367492\pi$
$158$	−2.11381			−0.168166
$159$		0			0
$160$	3.79813	−	6.57856i	0.300269	−	0.520081i
$161$		0			0
$162$		0			0
$163$	1.29813	+	2.24843i	0.101678	+	0.176111i	0.912376	−	0.409353i	$-0.134246\pi$
$163$	1.29813	+	2.24843i	0.101678	+	0.176111i	−0.810698	+	0.585464i	$0.800912\pi$
$164$	−2.09240	−	3.62414i	−0.163389	−	0.282998i
$165$		0			0
$166$	−6.61721	+	11.4613i	−0.513595	+	0.889573i
$167$	−11.5915	−	20.0771i	−0.896979	−	1.55361i	−0.831337	−	0.555769i	$-0.812424\pi$
$167$	−11.5915	−	20.0771i	−0.896979	−	1.55361i	−0.0656422	−	0.997843i	$-0.520910\pi$
$168$		0			0
$169$	0.822948	−	1.42539i	0.0633037	−	0.109645i
$170$	−0.277189	−	0.480105i	−0.0212594	−	0.0368224i
$171$		0			0
$172$	−2.70574	+	4.68647i	−0.206311	+	0.357340i
$173$	4.75196			0.361285			0.180643	−	0.983549i	$-0.442182\pi$
$173$	4.75196			0.361285			0.180643	+	0.983549i	$0.442182\pi$
$174$		0			0
$175$		0			0
$176$	−0.0346151	−	0.0599551i	−0.00260921	−	0.00451929i
$177$		0			0
$178$	3.99525	+	6.91998i	0.299457	+	0.518674i
$179$	−4.26604	+	7.38901i	−0.318859	+	0.552280i	−0.980250	−	0.197761i	$-0.936633\pi$
$179$	−4.26604	+	7.38901i	−0.318859	+	0.552280i	0.661391	+	0.750041i	$0.269966\pi$
$180$		0			0
$181$	−17.2344			−1.28102			−0.640512	−	0.767948i	$-0.721278\pi$
$181$	−17.2344			−1.28102			−0.640512	+	0.767948i	$0.721278\pi$
$182$		0			0
$183$		0			0
$184$	−12.6887	+	21.9774i	−0.935421	+	1.62020i
$185$	−12.4415			−0.914718
$186$		0			0
$187$	0.773318			0.0565506
$188$	11.4757			0.836948
$189$		0			0
$190$	3.82295			0.277346
$191$	−12.9094			−0.934092			−0.467046	−	0.884233i	$-0.654682\pi$
$191$	−12.9094			−0.934092			−0.467046	+	0.884233i	$0.654682\pi$
$192$		0			0
$193$	−0.638156			−0.0459355			−0.0229677	−	0.999736i	$-0.507311\pi$
$193$	−0.638156			−0.0459355			−0.0229677	+	0.999736i	$0.507311\pi$
$194$	0.834970	−	1.44621i	0.0599473	−	0.103832i
$195$		0			0
$196$		0			0
$197$	−11.4456			−0.815467			−0.407733	−	0.913101i	$-0.633681\pi$
$197$	−11.4456			−0.815467			−0.407733	+	0.913101i	$0.633681\pi$
$198$		0			0
$199$	1.81908	−	3.15074i	0.128951	−	0.223350i	−0.794319	−	0.607500i	$-0.792172\pi$
$199$	1.81908	−	3.15074i	0.128951	−	0.223350i	0.923270	+	0.384151i	$0.125506\pi$
$200$	−4.51842	−	7.82613i	−0.319500	−	0.553391i
$201$		0			0
$202$	−0.751497	−	1.30163i	−0.0528751	−	0.0915824i
$203$		0			0
$204$		0			0
$205$	4.59627			0.321017
$206$	1.59967	−	2.77071i	0.111454	−	0.193045i
$207$		0			0
$208$	−0.0705744	−	0.122238i	−0.00489345	−	0.00847571i
$209$	−2.66637	+	4.61830i	−0.184437	+	0.319454i
$210$		0			0
$211$	−2.91147	−	5.04282i	−0.200434	−	0.347162i	0.748234	−	0.663435i	$-0.230902\pi$
$211$	−2.91147	−	5.04282i	−0.200434	−	0.347162i	−0.948668	+	0.316273i	$0.897569\pi$
$212$	0.352044	−	0.609758i	0.0241785	−	0.0418784i
$213$		0			0
$214$	3.13429	+	5.42874i	0.214255	+	0.371101i
$215$	−2.97178	−	5.14728i	−0.202674	−	0.351041i
$216$		0			0
$217$		0			0
$218$	−0.177519	+	0.307471i	−0.0120231	+	0.0208246i
$219$		0			0
$220$	−2.73143			−0.184153
$221$	1.57667			0.106058
$222$		0			0
$223$	−3.54189	+	6.13473i	−0.237182	+	0.410812i	−0.959905	−	0.280327i	$-0.909557\pi$
$223$	−3.54189	+	6.13473i	−0.237182	+	0.410812i	0.722722	+	0.691139i	$0.242891\pi$
$224$		0			0
$225$		0			0
$226$	6.31820	+	10.9434i	0.420280	+	0.727947i
$227$	−5.97178	−	10.3434i	−0.396361	−	0.686517i	0.596913	−	0.802306i	$-0.296394\pi$
$227$	−5.97178	−	10.3434i	−0.396361	−	0.686517i	−0.993274	+	0.115789i	$0.963060\pi$
$228$		0			0
$229$	8.77631	−	15.2010i	0.579955	−	1.00451i	−0.415529	−	0.909580i	$-0.636403\pi$
$229$	8.77631	−	15.2010i	0.579955	−	1.00451i	0.995484	−	0.0949315i	$-0.0302632\pi$
$230$	−5.29813	−	9.17664i	−0.349349	−	0.605089i
$231$		0			0
$232$	−8.89352	+	15.4040i	−0.583888	+	1.01132i
$233$	8.12701	+	14.0764i	0.532418	+	0.922175i	0.999284	+	0.0378470i	$0.0120499\pi$
$233$	8.12701	+	14.0764i	0.532418	+	0.922175i	−0.466865	+	0.884328i	$0.654617\pi$
$234$		0			0
$235$	−6.30200	+	10.9154i	−0.411097	+	0.712042i
$236$	−12.7537			−0.830196
$237$		0			0
$238$		0			0
$239$	−7.54963	−	13.0763i	−0.488345	−	0.845838i	0.511565	−	0.859244i	$-0.329066\pi$
$239$	−7.54963	−	13.0763i	−0.488345	−	0.845838i	−0.999910	+	0.0134062i	$0.995733\pi$
$240$		0			0
$241$	7.81908	+	13.5430i	0.503671	+	0.872384i	0.999991	+	0.00424420i	$0.00135097\pi$
$241$	7.81908	+	13.5430i	0.503671	+	0.872384i	−0.496320	+	0.868140i	$0.665316\pi$
$242$	3.63563	−	6.29710i	0.233707	−	0.404793i
$243$		0			0
$244$	−9.36959			−0.599826
$245$		0			0
$246$		0			0
$247$	−5.43629	+	9.41593i	−0.345903	+	0.599121i
$248$	−26.2026			−1.66387
$249$		0			0
$250$	9.69728			0.613310
$251$	−19.0651			−1.20338			−0.601690	−	0.798730i	$-0.705506\pi$
$251$	−19.0651			−1.20338			−0.601690	+	0.798730i	$0.705506\pi$
$252$		0			0
$253$	14.7811			0.929277
$254$	−18.2662			−1.14612
$255$		0			0
$256$	−16.1010			−1.00631
$257$	13.2909	−	23.0204i	0.829061	−	1.43598i	−0.0697146	−	0.997567i	$-0.522209\pi$
$257$	13.2909	−	23.0204i	0.829061	−	1.43598i	0.898776	−	0.438409i	$-0.144458\pi$
$258$		0			0
$259$		0			0
$260$	−5.56893			−0.345370
$261$		0			0
$262$	−3.15048	+	5.45680i	−0.194637	+	0.337122i
$263$	−0.367059	−	0.635765i	−0.0226338	−	0.0392029i	0.854487	−	0.519473i	$-0.173872\pi$
$263$	−0.367059	−	0.635765i	−0.0226338	−	0.0392029i	−0.877120	+	0.480270i	$0.840539\pi$
$264$		0			0
$265$	0.386659	+	0.669713i	0.0237523	+	0.0411402i
$266$		0			0
$267$		0			0
$268$	−0.731429			−0.0446792
$269$	−10.4251	+	18.0569i	−0.635632	+	1.10095i	0.350749	+	0.936470i	$0.385927\pi$
$269$	−10.4251	+	18.0569i	−0.635632	+	1.10095i	−0.986381	+	0.164478i	$0.947406\pi$
$270$		0			0
$271$	−3.47906	−	6.02590i	−0.211338	−	0.366047i	0.740796	−	0.671730i	$-0.234449\pi$
$271$	−3.47906	−	6.02590i	−0.211338	−	0.366047i	−0.952133	+	0.305683i	$0.901115\pi$
$272$	−0.00980018	+	0.0169744i	−0.000594223	+	0.00102922i
$273$		0			0
$274$	1.12954	+	1.95642i	0.0682379	+	0.118191i
$275$	−2.63176	+	4.55834i	−0.158701	+	0.274878i
$276$		0			0
$277$	−8.93629	−	15.4781i	−0.536930	−	0.929989i	−0.999067	−	0.0431811i	$-0.986251\pi$
$277$	−8.93629	−	15.4781i	−0.536930	−	0.929989i	0.462138	−	0.886808i	$-0.347083\pi$
$278$	2.69681	+	4.67102i	0.161744	+	0.280149i
$279$		0			0
$280$		0			0
$281$	11.1552	−	19.3214i	0.665465	−	1.15262i	−0.313694	−	0.949524i	$-0.601567\pi$
$281$	11.1552	−	19.3214i	0.665465	−	1.15262i	0.979159	−	0.203095i	$-0.0651001\pi$
$282$		0			0
$283$	−18.5945			−1.10533			−0.552665	−	0.833404i	$-0.686389\pi$
$283$	−18.5945			−1.10533			−0.552665	+	0.833404i	$0.686389\pi$
$284$	−0.680045			−0.0403532
$285$		0			0
$286$	−2.44862	+	4.24113i	−0.144790	+	0.250783i
$287$		0			0
$288$		0			0
$289$	8.39053	+	14.5328i	0.493561	+	0.854872i
$290$	−3.71348	−	6.43193i	−0.218063	−	0.377696i
$291$		0			0
$292$	1.25712	−	2.17740i	0.0735675	−	0.127423i
$293$	6.54576	+	11.3376i	0.382407	+	0.662349i	0.991406	−	0.130822i	$-0.0417618\pi$
$293$	6.54576	+	11.3376i	0.382407	+	0.662349i	−0.608998	+	0.793171i	$0.708428\pi$
$294$		0			0
$295$	7.00387	−	12.1311i	0.407781	−	0.706298i
$296$	13.1013	+	22.6922i	0.761499	+	1.31895i
$297$		0			0
$298$	0.189540	−	0.328293i	0.0109798	−	0.0190175i
$299$	30.1361			1.74282
$300$		0			0
$301$		0			0
$302$	1.08630	+	1.88153i	0.0625098	+	0.108270i
$303$		0			0
$304$	−0.0675813	−	0.117054i	−0.00387606	−	0.00671353i
$305$	5.14543	−	8.91215i	0.294626	−	0.510308i
$306$		0			0
$307$	6.31046			0.360157			0.180078	−	0.983652i	$-0.442365\pi$
$307$	6.31046			0.360157			0.180078	+	0.983652i	$0.442365\pi$
$308$		0			0
$309$		0			0
$310$	5.47044	−	9.47508i	0.310700	−	0.538148i
$311$	9.52435			0.540076			0.270038	−	0.962850i	$-0.412964\pi$
$311$	9.52435			0.540076			0.270038	+	0.962850i	$0.412964\pi$
$312$		0			0
$313$	−17.6287			−0.996431			−0.498215	−	0.867053i	$-0.666011\pi$
$313$	−17.6287			−0.996431			−0.498215	+	0.867053i	$0.666011\pi$
$314$	8.91117			0.502886
$315$		0			0
$316$	2.94862			0.165873
$317$	−8.07697			−0.453648			−0.226824	−	0.973936i	$-0.572834\pi$
$317$	−8.07697			−0.453648			−0.226824	+	0.973936i	$0.572834\pi$
$318$		0			0
$319$	10.3601			0.580054
$320$	3.39646	−	5.88284i	0.189868	−	0.328861i
$321$		0			0
$322$		0			0
$323$	1.50980			0.0840075
$324$		0			0
$325$	−5.36571	+	9.29369i	−0.297636	+	0.515521i
$326$	1.14156	+	1.97724i	0.0632251	+	0.109509i
$327$		0			0
$328$	−4.84002	−	8.38316i	−0.267246	−	0.462883i
$329$		0			0
$330$		0			0
$331$	23.0496			1.26692			0.633461	−	0.773775i	$-0.281634\pi$
$331$	23.0496			1.26692			0.633461	+	0.773775i	$0.281634\pi$
$332$	9.23055	−	15.9878i	0.506592	−	0.877444i
$333$		0			0
$334$	−10.1934	−	17.6555i	−0.557759	−	0.966066i
$335$	0.401674	−	0.695720i	0.0219458	−	0.0380112i
$336$		0			0
$337$	−14.5116	−	25.1348i	−0.790498	−	1.36918i	−0.925659	−	0.378359i	$-0.876489\pi$
$337$	−14.5116	−	25.1348i	−0.790498	−	1.36918i	0.135161	−	0.990824i	$-0.456845\pi$
$338$	0.723689	−	1.25347i	0.0393635	−	0.0681795i
$339$		0			0
$340$	0.386659	+	0.669713i	0.0209695	+	0.0363203i
$341$	7.63088	+	13.2171i	0.413235	+	0.715745i
$342$		0			0
$343$		0			0
$344$	−6.25877	+	10.8405i	−0.337450	+	0.584481i
$345$		0			0
$346$	4.17881			0.224654
$347$	−12.9463			−0.694991			−0.347496	−	0.937682i	$-0.612968\pi$
$347$	−12.9463			−0.694991			−0.347496	+	0.937682i	$0.612968\pi$
$348$		0			0
$349$	−0.731429	+	1.26687i	−0.0391525	+	0.0678141i	−0.884938	−	0.465710i	$-0.845799\pi$
$349$	−0.731429	+	1.26687i	−0.0391525	+	0.0678141i	0.845785	+	0.533524i	$0.179132\pi$
$350$		0			0
$351$		0			0
$352$	4.65910	+	8.06980i	0.248331	+	0.430122i
$353$	7.16637	+	12.4125i	0.381428	+	0.660652i	0.991267	−	0.131873i	$-0.0420992\pi$
$353$	7.16637	+	12.4125i	0.381428	+	0.660652i	−0.609839	+	0.792525i	$0.708766\pi$
$354$		0			0
$355$	0.373455	−	0.646844i	0.0198210	−	0.0343309i
$356$	−5.57310	−	9.65289i	−0.295374	−	0.511602i
$357$		0			0
$358$	−3.75150	+	6.49778i	−0.198273	+	0.343418i
$359$	−10.4684	−	18.1318i	−0.552500	−	0.956958i	−0.998093	−	0.0617224i	$-0.980341\pi$
$359$	−10.4684	−	18.1318i	−0.552500	−	0.956958i	0.445593	−	0.895235i	$-0.352993\pi$
$360$		0			0
$361$	4.29426	−	7.43788i	0.226014	−	0.391467i
$362$	−15.1557			−0.796566
$363$		0			0
$364$		0			0
$365$	1.38073	+	2.39149i	0.0722707	+	0.125176i
$366$		0			0
$367$	6.02869	+	10.4420i	0.314695	+	0.545067i	0.979373	−	0.202063i	$-0.0647645\pi$
$367$	6.02869	+	10.4420i	0.314695	+	0.545067i	−0.664678	+	0.747130i	$0.731431\pi$
$368$	−0.187319	+	0.324446i	−0.00976466	+	0.0169129i
$369$		0			0
$370$	−10.9409			−0.568789
$371$		0			0
$372$		0			0
$373$	0.390530	−	0.676417i	0.0202209	−	0.0350235i	−0.855738	−	0.517410i	$-0.826896\pi$
$373$	0.390530	−	0.676417i	0.0202209	−	0.0350235i	0.875959	+	0.482386i	$0.160230\pi$
$374$	0.680045			0.0351643
$375$		0			0
$376$	26.5449			1.36895
$377$	21.1225			1.08786
$378$		0			0
$379$	−6.92396			−0.355660			−0.177830	−	0.984061i	$-0.556908\pi$
$379$	−6.92396			−0.355660			−0.177830	+	0.984061i	$0.556908\pi$
$380$	−5.33275			−0.273564
$381$		0			0
$382$	−11.3523			−0.580837
$383$	3.86618	−	6.69642i	0.197553	−	0.342171i	−0.750182	−	0.661232i	$-0.770034\pi$
$383$	3.86618	−	6.69642i	0.197553	−	0.342171i	0.947734	+	0.319061i	$0.103367\pi$
$384$		0			0
$385$		0			0
$386$	−0.561185			−0.0285636
$387$		0			0
$388$	−1.16473	+	2.01736i	−0.0591300	+	0.102416i
$389$	2.69981	+	4.67620i	0.136886	+	0.237093i	0.926316	−	0.376747i	$-0.122957\pi$
$389$	2.69981	+	4.67620i	0.136886	+	0.237093i	−0.789431	+	0.613840i	$0.789624\pi$
$390$		0			0
$391$	−2.09240	−	3.62414i	−0.105817	−	0.183280i
$392$		0			0
$393$		0			0
$394$	−10.0651			−0.507073
$395$	−1.61927	+	2.80466i	−0.0814743	+	0.141118i
$396$		0			0
$397$	14.6172	+	25.3178i	0.733617	+	1.27066i	0.955328	+	0.295549i	$0.0955026\pi$
$397$	14.6172	+	25.3178i	0.733617	+	1.27066i	−0.221711	+	0.975112i	$0.571164\pi$
$398$	1.59967	−	2.77071i	0.0801842	−	0.138883i
$399$		0			0
$400$	−0.0667040	−	0.115535i	−0.00333520	−	0.00577674i
$401$	−13.6989	+	23.7272i	−0.684092	+	1.18488i	0.289629	+	0.957139i	$0.406468\pi$
$401$	−13.6989	+	23.7272i	−0.684092	+	1.18488i	−0.973721	+	0.227743i	$0.926865\pi$
$402$		0			0
$403$	15.5581	+	26.9474i	0.775003	+	1.34235i
$404$	1.04829	+	1.81568i	0.0521542	+	0.0903337i
$405$		0			0
$406$		0			0
$407$	7.63088	−	13.2171i	0.378249	−	0.655146i
$408$		0			0
$409$	−9.02498			−0.446256			−0.223128	−	0.974789i	$-0.571627\pi$
$409$	−9.02498			−0.446256			−0.223128	+	0.974789i	$0.571627\pi$
$410$	4.04189			0.199615
$411$		0			0
$412$	−2.23143	+	3.86495i	−0.109935	+	0.190412i
$413$		0			0
$414$		0			0
$415$	10.1382	+	17.5598i	0.497662	+	0.861977i
$416$	9.49912	+	16.4530i	0.465733	+	0.806673i
$417$		0			0
$418$	−2.34477	+	4.06126i	−0.114686	+	0.198643i
$419$	0.0876485	+	0.151812i	0.00428191	+	0.00741649i	0.868158	−	0.496287i	$-0.165304\pi$
$419$	0.0876485	+	0.151812i	0.00428191	+	0.00741649i	−0.863877	+	0.503704i	$0.831970\pi$
$420$		0			0
$421$	12.3525	−	21.3952i	0.602025	−	1.04274i	−0.390490	−	0.920607i	$-0.627694\pi$
$421$	12.3525	−	21.3952i	0.602025	−	1.04274i	0.992514	−	0.122130i	$-0.0389724\pi$
$422$	−2.56031	−	4.43458i	−0.124634	−	0.215872i
$423$		0			0
$424$	0.814330	−	1.41046i	0.0395474	−	0.0684980i
$425$	1.49020			0.0722853
$426$		0			0
$427$		0			0
$428$	−4.37211	−	7.57272i	−0.211334	−	0.366041i
$429$		0			0
$430$	−2.61334	−	4.52644i	−0.126026	−	0.218284i
$431$	−14.6596	+	25.3911i	−0.706126	+	1.22305i	0.260157	+	0.965566i	$0.416226\pi$
$431$	−14.6596	+	25.3911i	−0.706126	+	1.22305i	−0.966283	+	0.257481i	$0.917108\pi$
$432$		0			0
$433$	19.6554			0.944578			0.472289	−	0.881444i	$-0.343428\pi$
$433$	19.6554			0.944578			0.472289	+	0.881444i	$0.343428\pi$
$434$		0			0
$435$		0			0
$436$	0.247626	−	0.428901i	0.0118591	−	0.0205406i
$437$	28.8580			1.38047
$438$		0			0
$439$	−21.9299			−1.04666			−0.523330	−	0.852130i	$-0.675310\pi$
$439$	−21.9299			−1.04666			−0.523330	+	0.852130i	$0.675310\pi$
$440$	−6.31820			−0.301208
$441$		0			0
$442$	1.38650			0.0659489
$443$	18.7101			0.888942			0.444471	−	0.895793i	$-0.353392\pi$
$443$	18.7101			0.888942			0.444471	+	0.895793i	$0.353392\pi$
$444$		0			0
$445$	12.2422			0.580334
$446$	−3.11468	+	5.39479i	−0.147485	+	0.255451i
$447$		0			0
$448$		0			0
$449$	−6.68004			−0.315251			−0.157625	−	0.987499i	$-0.550384\pi$
$449$	−6.68004			−0.315251			−0.157625	+	0.987499i	$0.550384\pi$
$450$		0			0
$451$	−2.81908	+	4.88279i	−0.132745	+	0.229921i
$452$	−8.81345	−	15.2653i	−0.414550	−	0.718022i
$453$		0			0
$454$	−5.25150	−	9.09586i	−0.246465	−	0.426890i
$455$		0			0
$456$		0			0
$457$	−19.4287			−0.908837			−0.454418	−	0.890788i	$-0.650153\pi$
$457$	−19.4287			−0.908837			−0.454418	+	0.890788i	$0.650153\pi$
$458$	7.71776	−	13.3676i	0.360627	−	0.624625i
$459$		0			0
$460$	7.39053	+	12.8008i	0.344585	+	0.596839i
$461$	−0.482926	+	0.836452i	−0.0224921	+	0.0389575i	−0.877052	−	0.480395i	$-0.840493\pi$
$461$	−0.482926	+	0.836452i	−0.0224921	+	0.0389575i	0.854560	+	0.519352i	$0.173827\pi$
$462$		0			0
$463$	0.222811	+	0.385920i	0.0103549	+	0.0179352i	0.871156	−	0.491006i	$-0.163371\pi$
$463$	0.222811	+	0.385920i	0.0103549	+	0.0179352i	−0.860802	+	0.508941i	$0.830037\pi$
$464$	−0.131292	+	0.227405i	−0.00609509	+	0.0105570i
$465$		0			0
$466$	7.14677	+	12.3786i	0.331068	+	0.573426i
$467$	−17.1074	−	29.6309i	−0.791637	−	1.37115i	−0.924953	−	0.380081i	$-0.875896\pi$
$467$	−17.1074	−	29.6309i	−0.791637	−	1.37115i	0.133317	−	0.991074i	$-0.457437\pi$
$468$		0			0
$469$		0			0
$470$	−5.54189	+	9.59883i	−0.255628	+	0.442761i
$471$		0			0
$472$	−29.5012			−1.35790
$473$	7.29086			0.335234
$474$		0			0
$475$	−5.13816	+	8.89955i	−0.235755	+	0.408339i
$476$		0			0
$477$		0			0
$478$	−6.63903	−	11.4991i	−0.303662	−	0.525959i
$479$	−10.8965	−	18.8732i	−0.497872	−	0.862339i	0.502125	−	0.864795i	$-0.332552\pi$
$479$	−10.8965	−	18.8732i	−0.497872	−	0.862339i	−0.999997	+	0.00245553i	$0.999218\pi$
$480$		0			0
$481$	15.5581	−	26.9474i	0.709388	−	1.22870i
$482$	6.87598	+	11.9095i	0.313192	+	0.542465i
$483$		0			0
$484$	−5.07145	+	8.78401i	−0.230521	+	0.399273i
$485$	−1.27925	−	2.21572i	−0.0580877	−	0.100611i
$486$		0			0
$487$	−9.69640	+	16.7947i	−0.439386	+	0.761039i	−0.997642	−	0.0686297i	$-0.978137\pi$
$487$	−9.69640	+	16.7947i	−0.439386	+	0.761039i	0.558256	+	0.829669i	$0.311471\pi$
$488$	−21.6732			−0.981101
$489$		0			0
$490$		0			0
$491$	13.0783	+	22.6523i	0.590216	+	1.02228i	0.994203	+	0.107519i	$0.0342908\pi$
$491$	13.0783	+	22.6523i	0.590216	+	1.02228i	−0.403987	+	0.914765i	$0.632376\pi$
$492$		0			0
$493$	−1.46657	−	2.54017i	−0.0660509	−	0.114403i
$494$	−4.78059	+	8.28023i	−0.215089	+	0.372545i
$495$		0			0
$496$	−0.386821			−0.0173688
$497$		0			0
$498$		0			0
$499$	7.15064	−	12.3853i	0.320107	−	0.554441i	−0.660403	−	0.750911i	$-0.729615\pi$
$499$	7.15064	−	12.3853i	0.320107	−	0.554441i	0.980510	+	0.196470i	$0.0629479\pi$
$500$	−13.5270			−0.604947
$501$		0			0
$502$	−16.7656			−0.748284
$503$	−18.7033			−0.833937			−0.416969	−	0.908921i	$-0.636908\pi$
$503$	−18.7033			−0.833937			−0.416969	+	0.908921i	$0.636908\pi$
$504$		0			0
$505$	−2.30272			−0.102470
$506$	12.9982			0.577842
$507$		0			0
$508$	25.4801			1.13050
$509$	−12.8045	+	22.1781i	−0.567551	+	0.983027i	0.429257	+	0.903183i	$0.358776\pi$
$509$	−12.8045	+	22.1781i	−0.567551	+	0.983027i	−0.996807	+	0.0798442i	$0.974558\pi$
$510$		0			0
$511$		0			0
$512$	−0.473897			−0.0209435
$513$		0			0
$514$	11.6878	−	20.2438i	0.515526	−	0.892917i
$515$	−2.45084	−	4.24497i	−0.107997	−	0.187056i
$516$		0			0
$517$	−7.73055	−	13.3897i	−0.339989	−	0.588879i
$518$		0			0
$519$		0			0
$520$	−12.8817			−0.564902
$521$	−10.6061	+	18.3702i	−0.464660	+	0.804815i	−0.999186	−	0.0403370i	$-0.987157\pi$
$521$	−10.6061	+	18.3702i	−0.464660	+	0.804815i	0.534526	+	0.845152i	$0.320490\pi$
$522$		0			0
$523$	−10.4029	−	18.0183i	−0.454885	−	0.787884i	0.543796	−	0.839217i	$-0.316986\pi$
$523$	−10.4029	−	18.0183i	−0.454885	−	0.787884i	−0.998682	+	0.0513330i	$0.983653\pi$
$524$	4.39470	−	7.61185i	0.191984	−	0.332525i
$525$		0			0
$526$	−0.322786	−	0.559082i	−0.0140741	−	0.0243771i
$527$	2.16044	−	3.74200i	0.0941104	−	0.163004i
$528$		0			0
$529$	−28.4937	−	49.3525i	−1.23885	−	2.14576i
$530$	0.340022	+	0.588936i	0.0147696	+	0.0255817i
$531$		0			0
$532$		0			0
$533$	−5.74763	+	9.95518i	−0.248957	+	0.431207i
$534$		0			0
$535$	9.60401			0.415217
$536$	−1.69190			−0.0730791
$537$		0			0
$538$	−9.16772	+	15.8790i	−0.395248	+	0.684590i
$539$		0			0
$540$		0			0
$541$	−13.3648	−	23.1486i	−0.574599	−	0.995235i	−0.996085	−	0.0884001i	$-0.971825\pi$
$541$	−13.3648	−	23.1486i	−0.574599	−	0.995235i	0.421486	−	0.906835i	$-0.361509\pi$
$542$	−3.05943	−	5.29909i	−0.131414	−	0.227615i
$543$		0			0
$544$	1.31908	−	2.28471i	0.0565550	−	0.0979561i
$545$	0.271974	+	0.471073i	0.0116501	+	0.0201786i
$546$		0			0
$547$	−18.3812	+	31.8372i	−0.785923	+	1.36126i	0.142523	+	0.989792i	$0.454479\pi$
$547$	−18.3812	+	31.8372i	−0.785923	+	1.36126i	−0.928446	+	0.371467i	$0.878855\pi$
$548$	−1.57563	−	2.72907i	−0.0673074	−	0.116580i
$549$		0			0
$550$	−2.31433	+	4.00854i	−0.0986834	+	0.170925i
$551$	20.2267			0.861686
$552$		0			0
$553$		0			0
$554$	−7.85844	−	13.6112i	−0.333873	−	0.578285i
$555$		0			0
$556$	−3.76187	−	6.51575i	−0.159539	−	0.276329i
$557$	16.1694	−	28.0062i	0.685118	−	1.18666i	−0.288282	−	0.957546i	$-0.593084\pi$
$557$	16.1694	−	28.0062i	0.685118	−	1.18666i	0.973400	−	0.229114i	$-0.0735827\pi$
$558$		0			0
$559$	14.8648			0.628716
$560$		0			0
$561$		0			0
$562$	9.80974	−	16.9910i	0.413799	−	0.716721i
$563$	17.7419			0.747730			0.373865	−	0.927483i	$-0.378032\pi$
$563$	17.7419			0.747730			0.373865	+	0.927483i	$0.378032\pi$
$564$		0			0
$565$	19.3601			0.814485
$566$	−16.3517			−0.687315
$567$		0			0
$568$	−1.57304			−0.0660035
$569$	26.6013			1.11519			0.557593	−	0.830115i	$-0.311725\pi$
$569$	26.6013			1.11519			0.557593	+	0.830115i	$0.311725\pi$
$570$		0			0
$571$	−10.0172			−0.419208			−0.209604	−	0.977786i	$-0.567218\pi$
$571$	−10.0172			−0.419208			−0.209604	+	0.977786i	$0.567218\pi$
$572$	3.41565	−	5.91608i	0.142815	−	0.247364i
$573$		0			0
$574$		0			0
$575$	28.4834			1.18784
$576$		0			0
$577$	16.4572	−	28.5048i	0.685124	−	1.18667i	−0.288274	−	0.957548i	$-0.593082\pi$
$577$	16.4572	−	28.5048i	0.685124	−	1.18667i	0.973398	−	0.229121i	$-0.0735852\pi$
$578$	7.37851	+	12.7800i	0.306905	+	0.531576i
$579$		0			0
$580$	5.18004	+	8.97210i	0.215090	+	0.372546i
$581$		0			0
$582$		0			0
$583$	−0.948615			−0.0392876
$584$	2.90791	−	5.03665i	0.120330	−	0.208418i
$585$		0			0
$586$	5.75624	+	9.97011i	0.237788	+	0.411861i
$587$	−7.53643	+	13.0535i	−0.311062	+	0.538774i	−0.978592	−	0.205808i	$-0.934018\pi$
$587$	−7.53643	+	13.0535i	−0.311062	+	0.538774i	0.667531	+	0.744582i	$0.267351\pi$
$588$		0			0
$589$	14.8983	+	25.8046i	0.613873	+	1.06326i
$590$	6.15910	−	10.6679i	0.253566	−	0.439189i
$591$		0			0
$592$	0.193411	+	0.334997i	0.00794913	+	0.0137683i
$593$	20.5005	+	35.5079i	0.841853	+	1.45813i	0.888326	+	0.459213i	$0.151869\pi$
$593$	20.5005	+	35.5079i	0.841853	+	1.45813i	−0.0464729	+	0.998920i	$0.514798\pi$
$594$		0			0
$595$		0			0
$596$	−0.264396	+	0.457947i	−0.0108301	+	0.0187582i
$597$		0			0
$598$	26.5012			1.08372
$599$	−6.07367			−0.248164			−0.124082	−	0.992272i	$-0.539599\pi$
$599$	−6.07367			−0.248164			−0.124082	+	0.992272i	$0.539599\pi$
$600$		0			0
$601$	7.06758	−	12.2414i	0.288293	−	0.499338i	−0.685110	−	0.728440i	$-0.740246\pi$
$601$	7.06758	−	12.2414i	0.288293	−	0.499338i	0.973402	+	0.229102i	$0.0735791\pi$
$602$		0			0
$603$		0			0
$604$	−1.51532	−	2.62461i	−0.0616575	−	0.106794i
$605$	−5.57011	−	9.64771i	−0.226457	−	0.392235i
$606$		0			0
$607$	−23.0449	+	39.9149i	−0.935363	+	1.62010i	−0.161377	+	0.986893i	$0.551594\pi$
$607$	−23.0449	+	39.9149i	−0.935363	+	1.62010i	−0.773986	+	0.633203i	$0.781740\pi$
$608$	9.09627	+	15.7552i	0.368902	+	0.638958i
$609$		0			0
$610$	4.52481	−	7.83721i	0.183204	−	0.317319i
$611$	−15.7613	−	27.2994i	−0.637634	−	1.10441i
$612$		0			0
$613$	13.2469	−	22.9443i	0.535038	−	0.926712i	−0.464124	−	0.885770i	$-0.653631\pi$
$613$	13.2469	−	22.9443i	0.535038	−	0.926712i	0.999162	−	0.0409421i	$-0.0130359\pi$
$614$	5.54933			0.223953
$615$		0			0
$616$		0			0
$617$	−1.12495	−	1.94847i	−0.0452889	−	0.0784426i	0.842492	−	0.538708i	$-0.181087\pi$
$617$	−1.12495	−	1.94847i	−0.0452889	−	0.0784426i	−0.887781	+	0.460266i	$0.847754\pi$
$618$		0			0
$619$	−3.09539	−	5.36137i	−0.124414	−	0.215492i	0.797090	−	0.603861i	$-0.206372\pi$
$619$	−3.09539	−	5.36137i	−0.124414	−	0.215492i	−0.921504	+	0.388369i	$0.873038\pi$
$620$	−7.63088	+	13.2171i	−0.306464	+	0.530811i
$621$		0			0
$622$	8.37557			0.335830
$623$		0			0
$624$		0			0
$625$	−0.533433	+	0.923933i	−0.0213373	+	0.0369573i
$626$	−15.5024			−0.619600
$627$		0			0
$628$	−12.4305			−0.496030
$629$	−4.32089			−0.172285
$630$		0			0
$631$	26.1661			1.04166			0.520829	−	0.853661i	$-0.325623\pi$
$631$	26.1661			1.04166			0.520829	+	0.853661i	$0.325623\pi$
$632$	6.82058			0.271308
$633$		0			0
$634$	−7.10277			−0.282087
$635$	−13.9927	+	24.2361i	−0.555284	+	0.961781i
$636$		0			0
$637$		0			0
$638$	9.11051			0.360689
$639$		0			0
$640$	−4.60947	+	7.98384i	−0.182205	+	0.315589i
$641$	2.44444	+	4.23389i	0.0965496	+	0.167229i	0.910254	−	0.414050i	$-0.135886\pi$
$641$	2.44444	+	4.23389i	0.0965496	+	0.167229i	−0.813705	+	0.581278i	$0.802553\pi$
$642$		0			0
$643$	20.1839	+	34.9596i	0.795976	+	1.37867i	0.922218	+	0.386671i	$0.126375\pi$
$643$	20.1839	+	34.9596i	0.795976	+	1.37867i	−0.126242	+	0.992000i	$0.540291\pi$
$644$		0			0
$645$		0			0
$646$	1.32770			0.0522375
$647$	−1.14038	+	1.97519i	−0.0448329	+	0.0776528i	−0.887571	−	0.460671i	$-0.847609\pi$
$647$	−1.14038	+	1.97519i	−0.0448329	+	0.0776528i	0.842738	+	0.538324i	$0.180942\pi$
$648$		0			0
$649$	8.59152	+	14.8809i	0.337247	+	0.584128i
$650$	−4.71853	+	8.17273i	−0.185076	+	0.320561i
$651$		0			0
$652$	−1.59240	−	2.75811i	−0.0623631	−	0.108016i
$653$	11.7396	−	20.3336i	0.459407	−	0.795717i	−0.539522	−	0.841971i	$-0.681395\pi$
$653$	11.7396	−	20.3336i	0.459407	−	0.795717i	0.998930	+	0.0462542i	$0.0147284\pi$
$654$		0			0
$655$	4.82682	+	8.36030i	0.188599	+	0.326664i
$656$	−0.0714517	−	0.123758i	−0.00278972	−	0.00483194i
$657$		0			0
$658$		0			0
$659$	−23.9812	+	41.5366i	−0.934174	+	1.61804i	−0.158073	+	0.987427i	$0.550528\pi$
$659$	−23.9812	+	41.5366i	−0.934174	+	1.61804i	−0.776101	+	0.630609i	$0.782805\pi$
$660$		0			0
$661$	29.3090			1.13999			0.569995	−	0.821648i	$-0.306945\pi$
$661$	29.3090			1.13999			0.569995	+	0.821648i	$0.306945\pi$
$662$	20.2695			0.787797
$663$		0			0
$664$	21.3516	−	36.9821i	0.828604	−	1.43518i
$665$		0			0
$666$		0			0
$667$	−28.0317	−	48.5523i	−1.08539	−	1.87995i
$668$	14.2191	+	24.6282i	0.550154	+	0.952894i
$669$		0			0
$670$	0.353226	−	0.611806i	0.0136463	−	0.0236361i
$671$	6.31180	+	10.9324i	0.243664	+	0.422039i
$672$		0			0
$673$	−13.1591	+	22.7922i	−0.507246	+	0.878576i	0.492719	+	0.870189i	$0.336003\pi$
$673$	−13.1591	+	22.7922i	−0.507246	+	0.878576i	−0.999965	+	0.00838731i	$0.997330\pi$
$674$	−12.7613	−	22.1032i	−0.491547	−	0.851384i
$675$		0			0
$676$	−1.00950	+	1.74850i	−0.0388267	+	0.0672499i
$677$	−35.8907			−1.37939			−0.689697	−	0.724098i	$-0.742256\pi$
$677$	−35.8907			−1.37939			−0.689697	+	0.724098i	$0.742256\pi$
$678$		0			0
$679$		0			0
$680$	0.894400	+	1.54915i	0.0342987	+	0.0594070i
$681$		0			0
$682$	6.71048	+	11.6229i	0.256958	+	0.445064i
$683$	17.5321	−	30.3665i	0.670847	−	1.16194i	−0.306818	−	0.951768i	$-0.599264\pi$
$683$	17.5321	−	30.3665i	0.670847	−	1.16194i	0.977664	−	0.210172i	$-0.0674025\pi$
$684$		0			0
$685$	3.46110			0.132242
$686$		0			0
$687$		0			0
$688$	−0.0923963	+	0.160035i	−0.00352257	+	0.00610128i
$689$	−1.93407			−0.0736821
$690$		0			0
$691$	2.06687			0.0786273			0.0393136	−	0.999227i	$-0.487483\pi$
$691$	2.06687			0.0786273			0.0393136	+	0.999227i	$0.487483\pi$
$692$	−5.82915			−0.221591
$693$		0			0
$694$	−11.3847			−0.432159
$695$	8.26352			0.313453
$696$		0			0
$697$	1.59627			0.0604629
$698$	−0.643208	+	1.11407i	−0.0243458	+	0.0421681i
$699$		0			0
$700$		0			0
$701$	7.36009			0.277987			0.138993	−	0.990293i	$-0.455613\pi$
$701$	7.36009			0.277987			0.138993	+	0.990293i	$0.455613\pi$
$702$		0			0
$703$	14.8983	−	25.8046i	0.561899	−	0.973237i
$704$	4.16637	+	7.21637i	0.157026	+	0.271977i
$705$		0			0
$706$	6.30200	+	10.9154i	0.237179	+	0.410806i
$707$		0			0
$708$		0			0
$709$	9.10876			0.342086			0.171043	−	0.985264i	$-0.445286\pi$
$709$	9.10876			0.342086			0.171043	+	0.985264i	$0.445286\pi$
$710$	0.328411	−	0.568825i	0.0123251	−	0.0213476i
$711$		0			0
$712$	−12.8914	−	22.3286i	−0.483126	−	0.836799i
$713$	41.2943	−	71.5239i	1.54648	−	2.67859i
$714$		0			0
$715$	3.75150	+	6.49778i	0.140298	+	0.243003i
$716$	5.23308	−	9.06396i	0.195569	−	0.338736i
$717$		0			0
$718$	−9.20574	−	15.9448i	−0.343555	−	0.595055i
$719$	−12.9768	−	22.4765i	−0.483954	−	0.838233i	0.515876	−	0.856663i	$-0.327467\pi$
$719$	−12.9768	−	22.4765i	−0.483954	−	0.838233i	−0.999830	+	0.0184300i	$0.994133\pi$
$720$		0			0
$721$		0			0
$722$	3.77631	−	6.54076i	0.140540	−	0.243422i
$723$		0			0
$724$	21.1411			0.785705
$725$	19.9641			0.741448
$726$		0			0
$727$	5.08007	−	8.79894i	0.188409	−	0.326335i	−0.756311	−	0.654213i	$-0.773000\pi$
$727$	5.08007	−	8.79894i	0.188409	−	0.326335i	0.944720	+	0.327878i	$0.106333\pi$
$728$		0			0
$729$		0			0
$730$	1.21419	+	2.10304i	0.0449393	+	0.0778372i
$731$	−1.03209	−	1.78763i	−0.0381732	−	0.0661179i
$732$		0			0
$733$	−20.3307	+	35.2138i	−0.750931	+	1.30065i	0.196441	+	0.980516i	$0.437062\pi$
$733$	−20.3307	+	35.2138i	−0.750931	+	1.30065i	−0.947372	+	0.320135i	$0.896272\pi$
$734$	5.30154	+	9.18253i	0.195683	+	0.338933i
$735$		0			0
$736$	25.2126	−	43.6695i	0.929349	−	1.60968i
$737$	0.492726	+	0.853427i	0.0181498	+	0.0314364i
$738$		0			0
$739$	12.6809	−	21.9640i	0.466475	−	0.807959i	−0.532791	−	0.846247i	$-0.678857\pi$
$739$	12.6809	−	21.9640i	0.466475	−	0.807959i	0.999267	+	0.0382877i	$0.0121903\pi$
$740$	15.2618			0.561034
$741$		0			0
$742$		0			0
$743$	−11.2221	−	19.4372i	−0.411699	−	0.713083i	0.583377	−	0.812202i	$-0.301731\pi$
$743$	−11.2221	−	19.4372i	−0.411699	−	0.713083i	−0.995076	+	0.0991184i	$0.968398\pi$
$744$		0			0
$745$	−0.290393	−	0.502975i	−0.0106392	−	0.0184276i
$746$	0.343426	−	0.594831i	0.0125737	−	0.0217783i
$747$		0			0
$748$	−0.948615			−0.0346848
$749$		0			0
$750$		0			0
$751$	−12.1086	+	20.9727i	−0.441849	+	0.765305i	−0.997827	−	0.0658924i	$-0.979011\pi$
$751$	−12.1086	+	20.9727i	−0.441849	+	0.765305i	0.555978	+	0.831197i	$0.312344\pi$
$752$	0.391874			0.0142902
$753$		0			0
$754$	18.5748			0.676454
$755$	3.32863			0.121141
$756$		0			0
$757$	9.11793			0.331397			0.165698	−	0.986176i	$-0.447012\pi$
$757$	9.11793			0.331397			0.165698	+	0.986176i	$0.447012\pi$
$758$	−6.08883			−0.221156
$759$		0			0
$760$	−12.3354			−0.447453
$761$	−9.13610	+	15.8242i	−0.331183	+	0.573626i	−0.982744	−	0.184970i	$-0.940781\pi$
$761$	−9.13610	+	15.8242i	−0.331183	+	0.573626i	0.651561	+	0.758596i	$0.274114\pi$
$762$		0			0
$763$		0			0
$764$	15.8357			0.572917
$765$		0			0
$766$	3.39986	−	5.88874i	0.122842	−	0.212769i
$767$	17.5167	+	30.3398i	0.632490	+	1.09550i
$768$		0			0
$769$	−9.26470	−	16.0469i	−0.334094	−	0.578667i	0.649217	−	0.760604i	$-0.275097\pi$
$769$	−9.26470	−	16.0469i	−0.334094	−	0.578667i	−0.983310	+	0.181936i	$0.941764\pi$
$770$		0			0
$771$		0			0
$772$	0.782814			0.0281741
$773$	−1.48040	+	2.56413i	−0.0532463	+	0.0922253i	−0.891420	−	0.453178i	$-0.850290\pi$
$773$	−1.48040	+	2.56413i	−0.0532463	+	0.0922253i	0.838174	+	0.545403i	$0.183624\pi$
$774$		0			0
$775$	14.7049	+	25.4696i	0.528214	+	0.914894i
$776$	−2.69418	+	4.66646i	−0.0967155	+	0.167516i
$777$		0			0
$778$	2.37417	+	4.11218i	0.0851181	+	0.147429i
$779$	−5.50387	+	9.53298i	−0.197197	+	0.341555i
$780$		0			0
$781$	0.458111	+	0.793471i	0.0163925	+	0.0283926i
$782$	−1.84002	−	3.18701i	−0.0657991	−	0.113967i
$783$		0			0
$784$		0			0
$785$	6.82635	−	11.8236i	0.243643	−	0.422002i
$786$		0			0
$787$	−33.4020			−1.19065			−0.595326	−	0.803484i	$-0.702977\pi$
$787$	−33.4020			−1.19065			−0.595326	+	0.803484i	$0.702977\pi$
$788$	14.0401			0.500159
$789$		0			0
$790$	−1.42396	+	2.46638i	−0.0506623	+	0.0877497i
$791$		0			0
$792$		0			0
$793$	12.8687	+	22.2893i	0.456981	+	0.791515i
$794$	12.8542	+	22.2641i	0.456177	+	0.790122i
$795$		0			0
$796$	−2.23143	+	3.86495i	−0.0790909	+	0.136989i
$797$	24.6755	+	42.7391i	0.874050	+	1.51390i	0.857772	+	0.514031i	$0.171848\pi$
$797$	24.6755	+	42.7391i	0.874050	+	1.51390i	0.0162779	+	0.999868i	$0.494818\pi$
$798$		0			0
$799$	−2.18866	+	3.79088i	−0.0774293	+	0.134112i
$800$	8.97818	+	15.5507i	0.317427	+	0.549799i
$801$		0			0
$802$	−12.0466	+	20.8654i	−0.425382	+	0.736782i
$803$	−3.38743			−0.119540
$804$		0			0
$805$		0			0
$806$	13.6816	+	23.6971i	0.481912	+	0.834696i
$807$		0			0
$808$	2.42484	+	4.19995i	0.0853056	+	0.147754i
$809$	9.91400	−	17.1716i	0.348558	−	0.603720i	−0.637436	−	0.770503i	$-0.720005\pi$
$809$	9.91400	−	17.1716i	0.348558	−	0.603720i	0.985993	+	0.166784i	$0.0533382\pi$
$810$		0			0
$811$	−23.8557			−0.837686			−0.418843	−	0.908059i	$-0.637564\pi$
$811$	−23.8557			−0.837686			−0.418843	+	0.908059i	$0.637564\pi$
$812$		0			0
$813$		0			0
$814$	6.71048	−	11.6229i	0.235202	−	0.407382i
$815$	3.49794			0.122528
$816$		0			0
$817$	14.2344			0.497999
$818$	−7.93643			−0.277491
$819$		0			0
$820$	−5.63816			−0.196893
$821$	50.9427			1.77791			0.888957	−	0.457991i	$-0.151431\pi$
$821$	50.9427			1.77791			0.888957	+	0.457991i	$0.151431\pi$
$822$		0			0
$823$	13.6149			0.474587			0.237293	−	0.971438i	$-0.423740\pi$
$823$	13.6149			0.474587			0.237293	+	0.971438i	$0.423740\pi$
$824$	−5.16163	+	8.94020i	−0.179814	+	0.311447i
$825$		0			0
$826$		0			0
$827$	−36.2158			−1.25935			−0.629673	−	0.776861i	$-0.716811\pi$
$827$	−36.2158			−1.25935			−0.629673	+	0.776861i	$0.716811\pi$
$828$		0			0
$829$	−12.6630	+	21.9329i	−0.439803	+	0.761761i	−0.997674	−	0.0681664i	$-0.978285\pi$
$829$	−12.6630	+	21.9329i	−0.439803	+	0.761761i	0.557871	+	0.829928i	$0.311618\pi$
$830$	8.91534	+	15.4418i	0.309456	+	0.535994i
$831$		0			0
$832$	8.49454	+	14.7130i	0.294495	+	0.510080i
$833$		0			0
$834$		0			0
$835$	−31.2344			−1.08091
$836$	3.27079	−	5.66518i	0.113123	−	0.195934i
$837$		0			0
$838$	0.0770768	+	0.133501i	0.00266257	+	0.00461171i
$839$	4.35710	−	7.54671i	0.150424	−	0.260541i	−0.780960	−	0.624582i	$-0.785270\pi$
$839$	4.35710	−	7.54671i	0.150424	−	0.260541i	0.931383	+	0.364040i	$0.118603\pi$
$840$		0			0
$841$	−5.14749	−	8.91571i	−0.177500	−	0.307438i
$842$	10.8626	−	18.8146i	0.374350	−	0.648394i
$843$		0			0
$844$	3.57145	+	6.18594i	0.122934	+	0.212929i
$845$	−1.10876	−	1.92042i	−0.0381423	−	0.0660645i
$846$		0			0
$847$		0			0
$848$	0.0120217	−	0.0208222i	0.000412827	−	0.000715037i
$849$		0			0
$850$	1.31046			0.0449484
$851$	−82.5886			−2.83110
$852$		0			0
$853$	5.99067	−	10.3761i	0.205117	−	0.355272i	−0.745053	−	0.667005i	$-0.767576\pi$
$853$	5.99067	−	10.3761i	0.205117	−	0.355272i	0.950170	+	0.311733i	$0.100909\pi$
$854$		0			0
$855$		0			0
$856$	−10.1133	−	17.5168i	−0.345667	−	0.598713i
$857$	3.25015	+	5.62943i	0.111023	+	0.192298i	0.916183	−	0.400760i	$-0.131254\pi$
$857$	3.25015	+	5.62943i	0.111023	+	0.192298i	−0.805160	+	0.593058i	$0.797921\pi$
$858$		0			0
$859$	26.7763	−	46.3779i	0.913596	−	1.58239i	0.104652	−	0.994509i	$-0.466627\pi$
$859$	26.7763	−	46.3779i	0.913596	−	1.58239i	0.808944	−	0.587886i	$-0.200040\pi$
$860$	3.64543	+	6.31407i	0.124308	+	0.215308i
$861$		0			0
$862$	−12.8914	+	22.3286i	−0.439083	+	0.760514i
$863$	1.84982	+	3.20399i	0.0629687	+	0.109065i	0.895791	−	0.444475i	$-0.146610\pi$
$863$	1.84982	+	3.20399i	0.0629687	+	0.109065i	−0.832822	+	0.553540i	$0.813277\pi$
$864$		0			0
$865$	3.20115	−	5.54456i	0.108842	−	0.188521i
$866$	17.2847			0.587357
$867$		0			0
$868$		0			0
$869$	−1.98633	−	3.44042i	−0.0673816	−	0.116708i
$870$		0			0
$871$	1.00459	+	1.73999i	0.0340391	+	0.0589574i
$872$	0.572796	−	0.992112i	0.0193973	−	0.0335971i
$873$		0			0
$874$	25.3773			0.858401
$875$		0			0
$876$		0			0
$877$	5.89440	−	10.2094i	0.199040	−	0.344747i	−0.749178	−	0.662369i	$-0.769551\pi$
$877$	5.89440	−	10.2094i	0.199040	−	0.344747i	0.948217	+	0.317622i	$0.102884\pi$
$878$	−19.2849			−0.650833
$879$		0			0
$880$	−0.0932736			−0.00314425
$881$	−49.4858			−1.66722			−0.833609	−	0.552355i	$-0.813729\pi$
$881$	−49.4858			−1.66722			−0.833609	+	0.552355i	$0.813729\pi$
$882$		0			0
$883$	−21.5357			−0.724734			−0.362367	−	0.932035i	$-0.618031\pi$
$883$	−21.5357			−0.724734			−0.362367	+	0.932035i	$0.618031\pi$
$884$	−1.93407			−0.0650497
$885$		0			0
$886$	16.4534			0.552762
$887$	5.94238	−	10.2925i	0.199526	−	0.345589i	−0.748849	−	0.662741i	$-0.769393\pi$
$887$	5.94238	−	10.2925i	0.199526	−	0.345589i	0.948375	+	0.317152i	$0.102727\pi$
$888$		0			0
$889$		0			0
$890$	10.7656			0.360863
$891$		0			0
$892$	4.34477	−	7.52536i	0.145474	−	0.251968i
$893$	−15.0929	−	26.1416i	−0.505063	−	0.874795i
$894$		0			0
$895$	5.74763	+	9.95518i	0.192122	+	0.332765i
$896$		0			0
$897$		0			0
$898$	−5.87433			−0.196029
$899$	28.9433	−	50.1313i	0.965314	−	1.67197i
$900$		0			0
$901$	0.134285	+	0.232589i	0.00447369	+	0.00774866i
$902$	−2.47906	+	4.29385i	−0.0825435	+	0.142970i
$903$		0			0
$904$	−20.3868	−	35.3110i	−0.678056	−	1.17443i
$905$	−11.6099	+	20.1090i	−0.385927	+	0.668446i
$906$		0			0
$907$	13.0107	+	22.5353i	0.432014	+	0.748271i	0.997047	−	0.0767980i	$-0.0244697\pi$
$907$	13.0107	+	22.5353i	0.432014	+	0.748271i	−0.565032	+	0.825069i	$0.691136\pi$
$908$	7.32547	+	12.6881i	0.243104	+	0.421069i
$909$		0			0
$910$		0			0
$911$	−2.01636	+	3.49244i	−0.0668050	+	0.115710i	−0.897493	−	0.441028i	$-0.854614\pi$
$911$	−2.01636	+	3.49244i	−0.0668050	+	0.115710i	0.830688	+	0.556738i	$0.187947\pi$
$912$		0			0
$913$	−24.8726			−0.823162
$914$	−17.0853			−0.565132
$915$		0			0
$916$	−10.7657	+	18.6468i	−0.355710	+	0.616108i
$917$		0			0
$918$		0			0
$919$	−13.7135	−	23.7524i	−0.452366	−	0.783521i	0.546167	−	0.837677i	$-0.316087\pi$
$919$	−13.7135	−	23.7524i	−0.452366	−	0.783521i	−0.998532	+	0.0541559i	$0.982753\pi$
$920$	17.0954	+	29.6101i	0.563618	+	0.976216i
$921$		0			0
$922$	−0.424678	+	0.735564i	−0.0139860	+	0.0242245i
$923$	0.934011	+	1.61775i	0.0307434	+	0.0532491i
$924$		0			0
$925$	14.7049	−	25.4696i	0.483493	−	0.837434i
$926$	0.195937	+	0.339373i	0.00643889	+	0.0111525i
$927$		0			0
$928$	17.6716	−	30.6081i	0.580098	−	1.00476i
$929$	−7.67675			−0.251866			−0.125933	−	0.992039i	$-0.540192\pi$
$929$	−7.67675			−0.251866			−0.125933	+	0.992039i	$0.540192\pi$
$930$		0			0
$931$		0			0
$932$	−9.96926	−	17.2673i	−0.326554	−	0.565608i
$933$		0			0
$934$	−15.0440	−	26.0570i	−0.492255	−	0.852610i
$935$	0.520945	−	0.902302i	0.0170367	−	0.0295084i
$936$		0			0
$937$	−2.02465			−0.0661425			−0.0330713	−	0.999453i	$-0.510529\pi$
$937$	−2.02465			−0.0661425			−0.0330713	+	0.999453i	$0.510529\pi$
$938$		0			0
$939$		0			0
$940$	7.73055	−	13.3897i	0.252143	−	0.436724i
$941$	6.13928			0.200135			0.100067	−	0.994981i	$-0.468094\pi$
$941$	6.13928			0.200135			0.100067	+	0.994981i	$0.468094\pi$
$942$		0			0
$943$	30.5107			0.993566
$944$	−0.435518			−0.0141749
$945$		0			0
$946$	6.41147			0.208455
$947$	−5.56448			−0.180821			−0.0904107	−	0.995905i	$-0.528818\pi$
$947$	−5.56448			−0.180821			−0.0904107	+	0.995905i	$0.528818\pi$
$948$		0			0
$949$	−6.90640			−0.224191
$950$	−4.51842	+	7.82613i	−0.146597	+	0.253913i
$951$		0			0
$952$		0			0
$953$	8.72018			0.282474			0.141237	−	0.989976i	$-0.454892\pi$
$953$	8.72018			0.282474			0.141237	+	0.989976i	$0.454892\pi$
$954$		0			0
$955$	−8.69640	+	15.0626i	−0.281409	+	0.487415i
$956$	9.26099	+	16.0405i	0.299522	+	0.518787i
$957$		0			0
$958$	−9.58219	−	16.5968i	−0.309586	−	0.536219i
$959$		0			0
$960$		0			0
$961$	54.2746			1.75079
$962$	13.6816	−	23.6971i	0.441111	−	0.764027i
$963$		0			0
$964$	−9.59152	−	16.6130i	−0.308922	−	0.535069i
$965$	−0.429892	+	0.744596i	−0.0138387	+	0.0239694i
$966$		0			0
$967$	28.8849	+	50.0301i	0.928876	+	1.60886i	0.785206	+	0.619235i	$0.212557\pi$
$967$	28.8849	+	50.0301i	0.928876	+	1.60886i	0.143670	+	0.989626i	$0.454110\pi$
$968$	−11.7310	+	20.3187i	−0.377049	+	0.653068i
$969$		0			0
$970$	−1.12495	−	1.94847i	−0.0361200	−	0.0625617i
$971$	−15.3596	−	26.6036i	−0.492914	−	0.853752i	0.507053	−	0.861915i	$-0.330735\pi$
$971$	−15.3596	−	26.6036i	−0.492914	−	0.853752i	−0.999967	+	0.00816326i	$0.997402\pi$
$972$		0			0
$973$		0			0
$974$	−8.52687	+	14.7690i	−0.273219	+	0.473229i
$975$		0			0
$976$	−0.319955			−0.0102415
$977$	−10.3000			−0.329527			−0.164764	−	0.986333i	$-0.552686\pi$
$977$	−10.3000			−0.329527			−0.164764	+	0.986333i	$0.552686\pi$
$978$		0			0
$979$	−7.50862	+	13.0053i	−0.239976	+	0.415651i
$980$		0			0
$981$		0			0
$982$	11.5009	+	19.9201i	0.367008	+	0.635676i
$983$	6.84817	+	11.8614i	0.218423	+	0.378319i	0.954326	−	0.298767i	$-0.0965755\pi$
$983$	6.84817	+	11.8614i	0.218423	+	0.378319i	−0.735903	+	0.677087i	$0.763242\pi$
$984$		0			0
$985$	−7.71032	+	13.3547i	−0.245671	+	0.425515i
$986$	−1.28968	−	2.23379i	−0.0410717	−	0.0711383i
$987$		0			0
$988$	6.66860	−	11.5503i	0.212156	−	0.367465i
$989$	−19.7271	−	34.1684i	−0.627287	−	1.08649i
$990$		0			0
$991$	−28.9907	+	50.2133i	−0.920919	+	1.59508i	−0.122922	+	0.992416i	$0.539227\pi$
$991$	−28.9907	+	50.2133i	−0.920919	+	1.59508i	−0.797997	+	0.602662i	$0.794107\pi$
$992$	52.0651			1.65307
$993$		0			0
$994$		0			0
$995$	−2.45084	−	4.24497i	−0.0776968	−	0.134575i
$996$		0			0
$997$	−8.10876	−	14.0448i	−0.256807	−	0.444803i	0.708578	−	0.705633i	$-0.249337\pi$
$997$	−8.10876	−	14.0448i	−0.256807	−	0.444803i	−0.965385	+	0.260830i	$0.916004\pi$
$998$	6.28817	−	10.8914i	0.199049	−	0.344762i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.c.802.3		6
3.2	odd	2		441.2.h.d.214.1		6
7.2	even	3		1323.2.g.d.667.1		6
7.3	odd	6		1323.2.f.d.883.1		6
7.4	even	3		189.2.f.b.127.1		6
7.5	odd	6		1323.2.g.e.667.1		6
7.6	odd	2		1323.2.h.b.802.3		6
9.4	even	3		1323.2.g.d.361.1		6
9.5	odd	6		441.2.g.c.67.3		6
21.2	odd	6		441.2.g.c.79.3		6
21.5	even	6		441.2.g.b.79.3		6
21.11	odd	6		63.2.f.a.43.3	yes	6
21.17	even	6		441.2.f.c.295.3		6
21.20	even	2		441.2.h.e.214.1		6
28.11	odd	6		3024.2.r.k.2017.2		6
63.4	even	3		189.2.f.b.64.1		6
63.5	even	6		441.2.h.e.373.1		6
63.11	odd	6		567.2.a.h.1.1		3
63.13	odd	6		1323.2.g.e.361.1		6
63.23	odd	6		441.2.h.d.373.1		6
63.25	even	3		567.2.a.c.1.3		3
63.31	odd	6		1323.2.f.d.442.1		6
63.32	odd	6		63.2.f.a.22.3	✓	6
63.38	even	6		3969.2.a.q.1.1		3
63.40	odd	6		1323.2.h.b.226.3		6
63.41	even	6		441.2.g.b.67.3		6
63.52	odd	6		3969.2.a.l.1.3		3
63.58	even	3	inner	1323.2.h.c.226.3		6
63.59	even	6		441.2.f.c.148.3		6
84.11	even	6		1008.2.r.h.673.2		6
252.11	even	6		9072.2.a.ca.1.2		3
252.67	odd	6		3024.2.r.k.1009.2		6
252.95	even	6		1008.2.r.h.337.2		6
252.151	odd	6		9072.2.a.bs.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.3	✓	6	63.32	odd	6
63.2.f.a.43.3	yes	6	21.11	odd	6
189.2.f.b.64.1		6	63.4	even	3
189.2.f.b.127.1		6	7.4	even	3
441.2.f.c.148.3		6	63.59	even	6
441.2.f.c.295.3		6	21.17	even	6
441.2.g.b.67.3		6	63.41	even	6
441.2.g.b.79.3		6	21.5	even	6
441.2.g.c.67.3		6	9.5	odd	6
441.2.g.c.79.3		6	21.2	odd	6
441.2.h.d.214.1		6	3.2	odd	2
441.2.h.d.373.1		6	63.23	odd	6
441.2.h.e.214.1		6	21.20	even	2
441.2.h.e.373.1		6	63.5	even	6
567.2.a.c.1.3		3	63.25	even	3
567.2.a.h.1.1		3	63.11	odd	6
1008.2.r.h.337.2		6	252.95	even	6
1008.2.r.h.673.2		6	84.11	even	6
1323.2.f.d.442.1		6	63.31	odd	6
1323.2.f.d.883.1		6	7.3	odd	6
1323.2.g.d.361.1		6	9.4	even	3
1323.2.g.d.667.1		6	7.2	even	3
1323.2.g.e.361.1		6	63.13	odd	6
1323.2.g.e.667.1		6	7.5	odd	6
1323.2.h.b.226.3		6	63.40	odd	6
1323.2.h.b.802.3		6	7.6	odd	2
1323.2.h.c.226.3		6	63.58	even	3	inner
1323.2.h.c.802.3		6	1.1	even	1	trivial
3024.2.r.k.1009.2		6	252.67	odd	6
3024.2.r.k.2017.2		6	28.11	odd	6
3969.2.a.l.1.3		3	63.52	odd	6
3969.2.a.q.1.1		3	63.38	even	6
9072.2.a.bs.1.2		3	252.151	odd	6
9072.2.a.ca.1.2		3	252.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.879385 q^{2} -1.22668 q^{4} +(0.673648 - 1.16679i) q^{5} -2.83750 q^{8} +(0.592396 - 1.02606i) q^{10} +(0.826352 + 1.43128i) q^{11} +(1.68479 + 2.91815i) q^{13} -0.0418891 q^{16} +(0.233956 - 0.405223i) q^{17} +(1.61334 + 2.79439i) q^{19} +(-0.826352 + 1.43128i) q^{20} +(0.726682 + 1.25865i) q^{22} +(4.47178 - 7.74535i) q^{23} +(1.59240 + 2.75811i) q^{25} +(1.48158 + 2.56617i) q^{26} +(3.13429 - 5.42874i) q^{29} +9.23442 q^{31} +5.63816 q^{32} +(0.205737 - 0.356347i) q^{34} +(-4.61721 - 7.99724i) q^{37} +(1.41875 + 2.45734i) q^{38} +(-1.91147 + 3.31077i) q^{40} +(1.70574 + 2.95442i) q^{41} +(2.20574 - 3.82045i) q^{43} +(-1.01367 - 1.75573i) q^{44} +(3.93242 - 6.81115i) q^{46} -9.35504 q^{47} +(1.40033 + 2.42544i) q^{50} +(-2.06670 - 3.57964i) q^{52} +(-0.286989 + 0.497079i) q^{53} +2.22668 q^{55} +(2.75624 - 4.77396i) q^{58} +10.3969 q^{59} +7.63816 q^{61} +8.12061 q^{62} +5.04189 q^{64} +4.53983 q^{65} +0.596267 q^{67} +(-0.286989 + 0.497079i) q^{68} +0.554378 q^{71} +(-1.02481 + 1.77503i) q^{73} +(-4.06031 - 7.03266i) q^{74} +(-1.97906 - 3.42782i) q^{76} -2.40373 q^{79} +(-0.0282185 + 0.0488759i) q^{80} +(1.50000 + 2.59808i) q^{82} +(-7.52481 + 13.0334i) q^{83} +(-0.315207 - 0.545955i) q^{85} +(1.93969 - 3.35965i) q^{86} +(-2.34477 - 4.06126i) q^{88} +(4.54323 + 7.86911i) q^{89} +(-5.48545 + 9.50108i) q^{92} -8.22668 q^{94} +4.34730 q^{95} +(0.949493 - 1.64457i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 6 q^{16} + 6 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} - 3 q^{26} + 9 q^{29} - 6 q^{31} - 9 q^{34} + 3 q^{37} + 6 q^{38}+ \cdots + 3 q^{97}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 + 3 * q^5 - 12 * q^8 + 6 * q^11 + 3 * q^13 + 6 * q^16 + 6 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 - 3 * q^26 + 9 * q^29 - 6 * q^31 - 9 * q^34 + 3 * q^37 + 6 * q^38 + 9 * q^40 + 3 * q^43 + 15 * q^44 - 6 * q^47 - 6 * q^50 + 21 * q^52 + 6 * q^53 + 9 * q^58 + 6 * q^59 + 12 * q^61 + 60 * q^62 + 24 * q^64 - 30 * q^65 - 24 * q^67 + 6 * q^68 - 18 * q^71 + 21 * q^73 - 30 * q^74 - 15 * q^76 - 42 * q^79 - 15 * q^80 + 9 * q^82 - 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 + 12 * q^89 + 3 * q^92 - 36 * q^94 + 24 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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