LMFDB - Embedded newform 2970.2.t.a.2771.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2970,2,Mod(791,2970)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2970, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2970.791"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2970 = 2 \cdot 3^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2970.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$23.7155694003$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 990)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2771.9
Character	$\chi$	$=$	2970.2771
Dual form			2970.2.t.a.791.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.93804 - 1.11893i) q^{7} +1.00000 q^{8} +1.00000i q^{10} +(-3.16557 + 0.989540i) q^{11} +(2.70110 + 1.55948i) q^{13} +(-1.93804 - 1.11893i) q^{14} +(-0.500000 - 0.866025i) q^{16} -3.53311 q^{17} +0.649165i q^{19} +(0.866025 - 0.500000i) q^{20} +(2.43975 + 2.24669i) q^{22} +(-1.72813 - 0.997734i) q^{23} +(0.500000 + 0.866025i) q^{25} -3.11896i q^{26} +2.23785i q^{28} +(0.0531702 + 0.0920935i) q^{29} +(4.17649 - 7.23389i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.76655 + 3.05976i) q^{34} -2.23785 q^{35} -3.00315 q^{37} +(0.562194 - 0.324583i) q^{38} +(-0.866025 - 0.500000i) q^{40} +(1.38401 - 2.39717i) q^{41} +(-10.0170 + 5.78333i) q^{43} +(0.725816 - 3.23623i) q^{44} +1.99547i q^{46} +(-5.60838 + 3.23800i) q^{47} +(-0.996003 + 1.72513i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.70110 + 1.55948i) q^{52} -3.95259i q^{53} +(3.23623 + 0.725816i) q^{55} +(1.93804 - 1.11893i) q^{56} +(0.0531702 - 0.0920935i) q^{58} +(2.80361 + 1.61866i) q^{59} +(-11.4068 + 6.58570i) q^{61} -8.35297 q^{62} +1.00000 q^{64} +(-1.55948 - 2.70110i) q^{65} +(4.91487 - 8.51280i) q^{67} +(1.76655 - 3.05976i) q^{68} +(1.11893 + 1.93804i) q^{70} -1.16465i q^{71} -1.40361i q^{73} +(1.50157 + 2.60080i) q^{74} +(-0.562194 - 0.324583i) q^{76} +(-5.02777 + 5.45981i) q^{77} +(-2.59056 + 1.49566i) q^{79} +1.00000i q^{80} -2.76801 q^{82} +(-4.91742 - 8.51723i) q^{83} +(3.05976 + 1.76655i) q^{85} +(10.0170 + 5.78333i) q^{86} +(-3.16557 + 0.989540i) q^{88} -0.269039i q^{89} +6.97979 q^{91} +(1.72813 - 0.997734i) q^{92} +(5.60838 + 3.23800i) q^{94} +(0.324583 - 0.562194i) q^{95} +(-2.53151 - 4.38471i) q^{97} +1.99201 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} + 12 q^{11} - 24 q^{13} - 24 q^{16} - 12 q^{17} - 6 q^{22} - 36 q^{23} + 24 q^{25} - 24 q^{32} + 6 q^{34} + 6 q^{38} - 6 q^{41} - 30 q^{43} - 6 q^{44} + 24 q^{49} + 24 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) $ 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 + 12 * q^11 - 24 * q^13 - 24 * q^16 - 12 * q^17 - 6 * q^22 - 36 * q^23 + 24 * q^25 - 24 * q^32 + 6 * q^34 + 6 * q^38 - 6 * q^41 - 30 * q^43 - 6 * q^44 + 24 * q^49 + 24 * q^50 + 24 * q^52 + 54 * q^59 + 48 * q^64 - 6 * q^67 + 6 * q^68 - 6 * q^76 + 18 * q^77 + 12 * q^82 + 36 * q^83 + 30 * q^86 + 12 * q^88 + 24 * q^91 + 36 * q^92 + 6 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2970\mathbb{Z}\right)^\times$.

$n$	$541$	$1541$	$2377$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$		0			0
$7$	1.93804	−	1.11893i	0.732510	−	0.422915i	−0.0868297	−	0.996223i	$-0.527674\pi$
$7$	1.93804	−	1.11893i	0.732510	−	0.422915i	0.819340	+	0.573308i	$0.194340\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$			1.00000i			0.316228i
$11$	−3.16557	+	0.989540i	−0.954454	+	0.298358i
$11$	−3.16557	+	0.989540i	−0.954454	+	0.298358i
$12$		0			0
$13$	2.70110	+	1.55948i	0.749151	+	0.432522i	0.825387	−	0.564567i	$-0.190957\pi$
$13$	2.70110	+	1.55948i	0.749151	+	0.432522i	−0.0762361	+	0.997090i	$0.524290\pi$
$14$	−1.93804	−	1.11893i	−0.517963	−	0.299046i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.53311			−0.856905			−0.428452	−	0.903564i	$-0.640941\pi$
$17$	−3.53311			−0.856905			−0.428452	+	0.903564i	$0.640941\pi$
$18$		0			0
$19$			0.649165i			0.148929i	0.997224	+	0.0744644i	$0.0237247\pi$
$19$			0.649165i			0.148929i	−0.997224	+	0.0744644i	$0.976275\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$		0			0
$22$	2.43975	+	2.24669i	0.520156	+	0.478996i
$23$	−1.72813	−	0.997734i	−0.360339	−	0.208042i	0.308890	−	0.951098i	$-0.400042\pi$
$23$	−1.72813	−	0.997734i	−0.360339	−	0.208042i	−0.669230	+	0.743056i	$0.733376\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		−	3.11896i		−	0.611679i
$27$		0			0
$28$			2.23785i			0.422915i
$29$	0.0531702	+	0.0920935i	0.00987346	+	0.0171013i	0.870920	−	0.491425i	$-0.163524\pi$
$29$	0.0531702	+	0.0920935i	0.00987346	+	0.0171013i	−0.861046	+	0.508526i	$0.830190\pi$
$30$		0			0
$31$	4.17649	−	7.23389i	0.750119	−	1.29924i	−0.197646	−	0.980274i	$-0.563330\pi$
$31$	4.17649	−	7.23389i	0.750119	−	1.29924i	0.947765	−	0.318971i	$-0.103337\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	1.76655	+	3.05976i	0.302962	+	0.524745i
$35$	−2.23785			−0.378267
$36$		0			0
$37$	−3.00315			−0.493715			−0.246857	−	0.969052i	$-0.579398\pi$
$37$	−3.00315			−0.493715			−0.246857	+	0.969052i	$0.579398\pi$
$38$	0.562194	−	0.324583i	0.0911998	−	0.0526543i
$39$		0			0
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	1.38401	−	2.39717i	0.216146	−	0.374375i	−0.737481	−	0.675368i	$-0.763985\pi$
$41$	1.38401	−	2.39717i	0.216146	−	0.374375i	0.953626	+	0.300993i	$0.0973181\pi$
$42$		0			0
$43$	−10.0170	+	5.78333i	−1.52758	+	0.881950i	−0.528119	+	0.849170i	$0.677103\pi$
$43$	−10.0170	+	5.78333i	−1.52758	+	0.881950i	−0.999463	+	0.0327798i	$0.989564\pi$
$44$	0.725816	−	3.23623i	0.109421	−	0.487880i
$45$		0			0
$46$			1.99547i			0.294216i
$47$	−5.60838	+	3.23800i	−0.818067	+	0.472311i	−0.849749	−	0.527187i	$-0.823247\pi$
$47$	−5.60838	+	3.23800i	−0.818067	+	0.472311i	0.0316824	+	0.999498i	$0.489913\pi$
$48$		0			0
$49$	−0.996003	+	1.72513i	−0.142286	+	0.246447i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$		0			0
$52$	−2.70110	+	1.55948i	−0.374575	+	0.216261i
$53$		−	3.95259i		−	0.542930i	−0.962448	−	0.271465i	$-0.912492\pi$
$53$		−	3.95259i		−	0.542930i	0.962448	−	0.271465i	$-0.0875082\pi$
$54$		0			0
$55$	3.23623	+	0.725816i	0.436373	+	0.0978691i
$56$	1.93804	−	1.11893i	0.258981	−	0.149523i
$57$		0			0
$58$	0.0531702	−	0.0920935i	0.00698159	−	0.0120925i
$59$	2.80361	+	1.61866i	0.364998	+	0.210732i	0.671271	−	0.741212i	$-0.265749\pi$
$59$	2.80361	+	1.61866i	0.364998	+	0.210732i	−0.306273	+	0.951944i	$0.599082\pi$
$60$		0			0
$61$	−11.4068	+	6.58570i	−1.46049	+	0.843212i	−0.999034	−	0.0439524i	$-0.986005\pi$
$61$	−11.4068	+	6.58570i	−1.46049	+	0.843212i	−0.461453	+	0.887165i	$0.652672\pi$
$62$	−8.35297			−1.06083
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.55948	−	2.70110i	−0.193430	−	0.335030i
$66$		0			0
$67$	4.91487	−	8.51280i	0.600447	−	1.04000i	−0.392307	−	0.919834i	$-0.628323\pi$
$67$	4.91487	−	8.51280i	0.600447	−	1.04000i	0.992753	−	0.120170i	$-0.0383439\pi$
$68$	1.76655	−	3.05976i	0.214226	−	0.371051i
$69$		0			0
$70$	1.11893	+	1.93804i	0.133737	+	0.231640i
$71$		−	1.16465i		−	0.138219i	−0.997609	−	0.0691095i	$-0.977984\pi$
$71$		−	1.16465i		−	0.138219i	0.997609	−	0.0691095i	$-0.0220158\pi$
$72$		0			0
$73$		−	1.40361i		−	0.164280i	−0.996621	−	0.0821400i	$-0.973825\pi$
$73$		−	1.40361i		−	0.164280i	0.996621	−	0.0821400i	$-0.0261755\pi$
$74$	1.50157	+	2.60080i	0.174554	+	0.302337i
$75$		0			0
$76$	−0.562194	−	0.324583i	−0.0644880	−	0.0372322i
$77$	−5.02777	+	5.45981i	−0.572967	+	0.622203i
$78$		0			0
$79$	−2.59056	+	1.49566i	−0.291461	+	0.168275i	−0.638601	−	0.769538i	$-0.720486\pi$
$79$	−2.59056	+	1.49566i	−0.291461	+	0.168275i	0.347140	+	0.937813i	$0.387153\pi$
$80$			1.00000i			0.111803i
$81$		0			0
$82$	−2.76801			−0.305676
$83$	−4.91742	−	8.51723i	−0.539757	−	0.934887i	−0.998917	−	0.0465331i	$-0.985183\pi$
$83$	−4.91742	−	8.51723i	−0.539757	−	0.934887i	0.459159	−	0.888354i	$-0.348151\pi$
$84$		0			0
$85$	3.05976	+	1.76655i	0.331878	+	0.191610i
$86$	10.0170	+	5.78333i	1.08016	+	0.623633i
$87$		0			0
$88$	−3.16557	+	0.989540i	−0.337451	+	0.105485i
$89$		−	0.269039i		−	0.0285181i	−0.999898	−	0.0142590i	$-0.995461\pi$
$89$		−	0.269039i		−	0.0285181i	0.999898	−	0.0142590i	$-0.00453894\pi$
$90$		0			0
$91$	6.97979			0.731681
$92$	1.72813	−	0.997734i	0.180170	−	0.104021i
$93$		0			0
$94$	5.60838	+	3.23800i	0.578461	+	0.333974i
$95$	0.324583	−	0.562194i	0.0333015	−	0.0576798i
$96$		0			0
$97$	−2.53151	−	4.38471i	−0.257036	−	0.445200i	0.708410	−	0.705801i	$-0.249413\pi$
$97$	−2.53151	−	4.38471i	−0.257036	−	0.445200i	−0.965447	+	0.260601i	$0.916079\pi$
$98$	1.99201			0.201223
$99$		0			0
$100$	−1.00000			−0.100000
$101$	0.625489	+	1.08338i	0.0622385	+	0.107800i	0.895466	−	0.445131i	$-0.146843\pi$
$101$	0.625489	+	1.08338i	0.0622385	+	0.107800i	−0.833227	+	0.552931i	$0.813509\pi$
$102$		0			0
$103$	4.34798	−	7.53091i	0.428419	−	0.742043i	−0.568314	−	0.822812i	$-0.692404\pi$
$103$	4.34798	−	7.53091i	0.428419	−	0.742043i	0.996733	+	0.0807686i	$0.0257375\pi$
$104$	2.70110	+	1.55948i	0.264865	+	0.152920i
$105$		0			0
$106$	−3.42305	+	1.97630i	−0.332476	+	0.191955i
$107$	−7.47916			−0.723038			−0.361519	−	0.932365i	$-0.617742\pi$
$107$	−7.47916			−0.723038			−0.361519	+	0.932365i	$0.617742\pi$
$108$		0			0
$109$			11.4060i			1.09249i	0.837624	+	0.546247i	$0.183944\pi$
$109$			11.4060i			1.09249i	−0.837624	+	0.546247i	$0.816056\pi$
$110$	−0.989540	−	3.16557i	−0.0943489	−	0.301825i
$111$		0			0
$112$	−1.93804	−	1.11893i	−0.183127	−	0.105729i
$113$	−11.2536	−	6.49729i	−1.05865	−	0.611214i	−0.133594	−	0.991036i	$-0.542652\pi$
$113$	−11.2536	−	6.49729i	−1.05865	−	0.611214i	−0.925059	+	0.379822i	$0.875985\pi$
$114$		0			0
$115$	0.997734	+	1.72813i	0.0930392	+	0.161149i
$116$	−0.106340			−0.00987346
$117$		0			0
$118$		−	3.23733i		−	0.298020i
$119$	−6.84730	+	3.95329i	−0.627691	+	0.362398i
$120$		0			0
$121$	9.04162	−	6.26491i	0.821966	−	0.569537i
$122$	11.4068	+	6.58570i	1.03272	+	0.596241i
$123$		0			0
$124$	4.17649	+	7.23389i	0.375059	+	0.649622i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			3.47665i			0.308503i	0.988032	+	0.154251i	$0.0492965\pi$
$127$			3.47665i			0.308503i	−0.988032	+	0.154251i	$0.950703\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.55948	+	2.70110i	−0.136776	+	0.236902i
$131$	−1.86412	+	3.22874i	−0.162869	+	0.282097i	−0.935896	−	0.352276i	$-0.885408\pi$
$131$	−1.86412	+	3.22874i	−0.162869	+	0.282097i	0.773028	+	0.634372i	$0.218741\pi$
$132$		0			0
$133$	0.726369	+	1.25811i	0.0629842	+	0.109092i
$134$	−9.82974			−0.849160
$135$		0			0
$136$	−3.53311			−0.302962
$137$	−2.31644	+	1.33740i	−0.197907	+	0.114262i	−0.595679	−	0.803223i	$-0.703117\pi$
$137$	−2.31644	+	1.33740i	−0.197907	+	0.114262i	0.397772	+	0.917484i	$0.369784\pi$
$138$		0			0
$139$	−6.75836	−	3.90194i	−0.573237	−	0.330958i	0.185204	−	0.982700i	$-0.440705\pi$
$139$	−6.75836	−	3.90194i	−0.573237	−	0.330958i	−0.758441	+	0.651742i	$0.774039\pi$
$140$	1.11893	−	1.93804i	0.0945666	−	0.163794i
$141$		0			0
$142$	−1.00862	+	0.582327i	−0.0846415	+	0.0488678i
$143$	−10.0937	−	2.26380i	−0.844077	−	0.189308i
$144$		0			0
$145$		−	0.106340i		−	0.00883109i
$146$	−1.21556	+	0.701804i	−0.100601	+	0.0580817i
$147$		0			0
$148$	1.50157	−	2.60080i	0.123429	−	0.213785i
$149$	−0.0324085	+	0.0561333i	−0.00265501	+	0.00459862i	−0.867350	−	0.497699i	$-0.834178\pi$
$149$	−0.0324085	+	0.0561333i	−0.00265501	+	0.00459862i	0.864695	+	0.502298i	$0.167512\pi$
$150$		0			0
$151$	−12.7926	+	7.38583i	−1.04105	+	0.601050i	−0.920130	−	0.391612i	$-0.871918\pi$
$151$	−12.7926	+	7.38583i	−1.04105	+	0.601050i	−0.120919	+	0.992662i	$0.538584\pi$
$152$			0.649165i			0.0526543i
$153$		0			0
$154$	7.24222	+	1.62427i	0.583594	+	0.130888i
$155$	−7.23389	+	4.17649i	−0.581040	+	0.335463i
$156$		0			0
$157$	−4.61431	+	7.99222i	−0.368262	+	0.637849i	−0.989294	−	0.145937i	$-0.953380\pi$
$157$	−4.61431	+	7.99222i	−0.368262	+	0.637849i	0.621032	+	0.783785i	$0.286714\pi$
$158$	2.59056	+	1.49566i	0.206094	+	0.118988i
$159$		0			0
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	−4.46557			−0.351936
$162$		0			0
$163$	−1.69270			−0.132582			−0.0662912	−	0.997800i	$-0.521117\pi$
$163$	−1.69270			−0.132582			−0.0662912	+	0.997800i	$0.521117\pi$
$164$	1.38401	+	2.39717i	0.108073	+	0.187188i
$165$		0			0
$166$	−4.91742	+	8.51723i	−0.381666	+	0.661065i
$167$	−8.19719	+	14.1980i	−0.634318	+	1.09867i	0.352341	+	0.935872i	$0.385386\pi$
$167$	−8.19719	+	14.1980i	−0.634318	+	1.09867i	−0.986659	+	0.162799i	$0.947948\pi$
$168$		0			0
$169$	−1.63603	−	2.83369i	−0.125849	−	0.217976i
$170$		−	3.53311i		−	0.270977i
$171$		0			0
$172$		−	11.5667i		−	0.881950i
$173$	10.2188	+	17.6995i	0.776923	+	1.34567i	0.933707	+	0.358037i	$0.116554\pi$
$173$	10.2188	+	17.6995i	0.776923	+	1.34567i	−0.156784	+	0.987633i	$0.550113\pi$
$174$		0			0
$175$	1.93804	+	1.11893i	0.146502	+	0.0845830i
$176$	2.43975	+	2.24669i	0.183903	+	0.169351i
$177$		0			0
$178$	−0.232994	+	0.134519i	−0.0174637	+	0.0100827i
$179$			20.0246i			1.49671i	0.663297	+	0.748356i	$0.269156\pi$
$179$			20.0246i			1.49671i	−0.663297	+	0.748356i	$0.730844\pi$
$180$		0			0
$181$	−22.3978			−1.66482			−0.832408	−	0.554163i	$-0.813038\pi$
$181$	−22.3978			−1.66482			−0.832408	+	0.554163i	$0.813038\pi$
$182$	−3.48989	−	6.04467i	−0.258688	−	0.448061i
$183$		0			0
$184$	−1.72813	−	0.997734i	−0.127399	−	0.0735539i
$185$	2.60080	+	1.50157i	0.191215	+	0.110398i
$186$		0			0
$187$	11.1843	−	3.49615i	0.817876	−	0.255664i
$188$		−	6.47601i		−	0.472311i
$189$		0			0
$190$	−0.649165			−0.0470954
$191$	−1.37544	+	0.794110i	−0.0995233	+	0.0574598i	−0.548936	−	0.835865i	$-0.684967\pi$
$191$	−1.37544	+	0.794110i	−0.0995233	+	0.0574598i	0.449412	+	0.893324i	$0.351633\pi$
$192$		0			0
$193$	22.3683	+	12.9144i	1.61011	+	0.929596i	0.989344	+	0.145597i	$0.0465104\pi$
$193$	22.3683	+	12.9144i	1.61011	+	0.929596i	0.620763	+	0.783998i	$0.286823\pi$
$194$	−2.53151	+	4.38471i	−0.181752	+	0.314804i
$195$		0			0
$196$	−0.996003	−	1.72513i	−0.0711430	−	0.123223i
$197$	−20.0332			−1.42730			−0.713652	−	0.700500i	$-0.752960\pi$
$197$	−20.0332			−1.42730			−0.713652	+	0.700500i	$0.752960\pi$
$198$		0			0
$199$	1.63362			0.115804			0.0579022	−	0.998322i	$-0.481559\pi$
$199$	1.63362			0.115804			0.0579022	+	0.998322i	$0.481559\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	0.625489	−	1.08338i	0.0440092	−	0.0762262i
$203$	0.206092	+	0.118987i	0.0144648	+	0.00835127i
$204$		0			0
$205$	−2.39717	+	1.38401i	−0.167426	+	0.0966633i
$206$	−8.69595			−0.605876
$207$		0			0
$208$		−	3.11896i		−	0.216261i
$209$	−0.642375	−	2.05498i	−0.0444340	−	0.142146i
$210$		0			0
$211$	−13.8809	−	8.01412i	−0.955598	−	0.551715i	−0.0607823	−	0.998151i	$-0.519360\pi$
$211$	−13.8809	−	8.01412i	−0.955598	−	0.551715i	−0.894815	+	0.446437i	$0.852693\pi$
$212$	3.42305	+	1.97630i	0.235096	+	0.135733i
$213$		0			0
$214$	3.73958	+	6.47714i	0.255632	+	0.442768i
$215$	11.5667			0.788840
$216$		0			0
$217$		−	18.6927i		−	1.26895i
$218$	9.87786	−	5.70298i	0.669013	−	0.386255i
$219$		0			0
$220$	−2.24669	+	2.43975i	−0.151472	+	0.164488i
$221$	−9.54329	−	5.50982i	−0.641951	−	0.370630i
$222$		0			0
$223$	−4.23876	−	7.34175i	−0.283848	−	0.491640i	0.688481	−	0.725255i	$-0.258278\pi$
$223$	−4.23876	−	7.34175i	−0.283848	−	0.491640i	−0.972329	+	0.233615i	$0.924945\pi$
$224$			2.23785i			0.149523i
$225$		0			0
$226$			12.9946i			0.864387i
$227$	3.63551	+	6.29688i	0.241297	+	0.417939i	0.961084	−	0.276256i	$-0.0890938\pi$
$227$	3.63551	+	6.29688i	0.241297	+	0.417939i	−0.719787	+	0.694195i	$0.755761\pi$
$228$		0			0
$229$	−7.10018	+	12.2979i	−0.469193	+	0.812667i	−0.999380	−	0.0352143i	$-0.988789\pi$
$229$	−7.10018	+	12.2979i	−0.469193	+	0.812667i	0.530186	+	0.847881i	$0.322122\pi$
$230$	0.997734	−	1.72813i	0.0657886	−	0.113949i
$231$		0			0
$232$	0.0531702	+	0.0920935i	0.00349080	+	0.00604623i
$233$	1.86696			0.122308			0.0611542	−	0.998128i	$-0.480522\pi$
$233$	1.86696			0.122308			0.0611542	+	0.998128i	$0.480522\pi$
$234$		0			0
$235$	6.47601			0.422448
$236$	−2.80361	+	1.61866i	−0.182499	+	0.105366i
$237$		0			0
$238$	6.84730	+	3.95329i	0.443845	+	0.256254i
$239$	−12.8822	+	22.3127i	−0.833282	+	1.44329i	0.0621388	+	0.998068i	$0.480208\pi$
$239$	−12.8822	+	22.3127i	−0.833282	+	1.44329i	−0.895421	+	0.445220i	$0.853125\pi$
$240$		0			0
$241$	−26.3093	+	15.1897i	−1.69473	+	0.978454i	−0.744134	+	0.668031i	$0.767137\pi$
$241$	−26.3093	+	15.1897i	−1.69473	+	0.978454i	−0.950598	+	0.310423i	$0.899529\pi$
$242$	−9.94638	−	4.69782i	−0.639378	−	0.301987i
$243$		0			0
$244$		−	13.1714i		−	0.843212i
$245$	1.72513	−	0.996003i	0.110214	−	0.0636323i
$246$		0			0
$247$	−1.01236	+	1.75346i	−0.0644150	+	0.111570i
$248$	4.17649	−	7.23389i	0.265207	−	0.459352i
$249$		0			0
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$			0.648202i			0.0409141i	0.999791	+	0.0204571i	$0.00651214\pi$
$251$			0.648202i			0.0409141i	−0.999791	+	0.0204571i	$0.993488\pi$
$252$		0			0
$253$	6.45780	+	1.44834i	0.405998	+	0.0910566i
$254$	3.01086	−	1.73832i	0.188918	−	0.109072i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.78451	−	1.03029i	−0.111315	−	0.0642677i	0.443309	−	0.896369i	$-0.353804\pi$
$257$	−1.78451	−	1.03029i	−0.111315	−	0.0642677i	−0.554624	+	0.832101i	$0.687138\pi$
$258$		0			0
$259$	−5.82022	+	3.36031i	−0.361651	+	0.208799i
$260$	3.11896			0.193430
$261$		0			0
$262$	3.72823			0.230331
$263$	4.15995	+	7.20525i	0.256514	+	0.444295i	0.965306	−	0.261123i	$-0.0840928\pi$
$263$	4.15995	+	7.20525i	0.256514	+	0.444295i	−0.708792	+	0.705418i	$0.750759\pi$
$264$		0			0
$265$	−1.97630	+	3.42305i	−0.121403	+	0.210276i
$266$	0.726369	−	1.25811i	0.0445365	−	0.0771395i
$267$		0			0
$268$	4.91487	+	8.51280i	0.300223	+	0.520002i
$269$		−	7.13974i		−	0.435318i	−0.976025	−	0.217659i	$-0.930158\pi$
$269$		−	7.13974i		−	0.435318i	0.976025	−	0.217659i	$-0.0698420\pi$
$270$		0			0
$271$		−	25.6730i		−	1.55952i	−0.626076	−	0.779762i	$-0.715340\pi$
$271$		−	25.6730i		−	1.55952i	0.626076	−	0.779762i	$-0.284660\pi$
$272$	1.76655	+	3.05976i	0.107113	+	0.185525i
$273$		0			0
$274$	2.31644	+	1.33740i	0.139942	+	0.0807953i
$275$	−2.43975	−	2.24669i	−0.147122	−	0.135481i
$276$		0			0
$277$	−15.8621	+	9.15799i	−0.953061	+	0.550250i	−0.894031	−	0.448006i	$-0.852134\pi$
$277$	−15.8621	+	9.15799i	−0.953061	+	0.550250i	−0.0590307	+	0.998256i	$0.518801\pi$
$278$			7.80388i			0.468046i
$279$		0			0
$280$	−2.23785			−0.133737
$281$	−11.3351	−	19.6330i	−0.676196	−	1.17121i	−0.976118	−	0.217242i	$-0.930294\pi$
$281$	−11.3351	−	19.6330i	−0.676196	−	1.17121i	0.299922	−	0.953964i	$-0.403039\pi$
$282$		0			0
$283$	25.3797	+	14.6530i	1.50867	+	0.871029i	0.999949	+	0.0100962i	$0.00321379\pi$
$283$	25.3797	+	14.6530i	1.50867	+	0.871029i	0.508718	+	0.860933i	$0.330120\pi$
$284$	1.00862	+	0.582327i	0.0598506	+	0.0345547i
$285$		0			0
$286$	3.08634	+	9.87329i	0.182499	+	0.583820i
$287$		−	6.19442i		−	0.365645i
$288$		0			0
$289$	−4.51715			−0.265715
$290$	−0.0920935	+	0.0531702i	−0.00540792	+	0.00312226i
$291$		0			0
$292$	1.21556	+	0.701804i	0.0711353	+	0.0410700i
$293$	10.2552	−	17.7625i	0.599113	−	1.03769i	−0.393839	−	0.919179i	$-0.628853\pi$
$293$	10.2552	−	17.7625i	0.599113	−	1.03769i	0.992952	−	0.118515i	$-0.0378133\pi$
$294$		0			0
$295$	−1.61866	−	2.80361i	−0.0942422	−	0.163232i
$296$	−3.00315			−0.174554
$297$		0			0
$298$	0.0648171			0.00375475
$299$	−3.11190	−	5.38996i	−0.179966	−	0.311710i
$300$		0			0
$301$	−12.9423	+	22.4166i	−0.745979	+	1.29207i
$302$	12.7926	+	7.38583i	0.736133	+	0.425007i
$303$		0			0
$304$	0.562194	−	0.324583i	0.0322440	−	0.0186161i
$305$	13.1714			0.754192
$306$		0			0
$307$		−	21.7811i		−	1.24311i	−0.783369	−	0.621557i	$-0.786500\pi$
$307$		−	21.7811i		−	1.24311i	0.783369	−	0.621557i	$-0.213500\pi$
$308$	−2.21445	−	7.08408i	−0.126180	−	0.403653i
$309$		0			0
$310$	7.23389	+	4.17649i	0.410857	+	0.237208i
$311$	1.76080	+	1.01660i	0.0998460	+	0.0576461i	0.549092	−	0.835762i	$-0.314974\pi$
$311$	1.76080	+	1.01660i	0.0998460	+	0.0576461i	−0.449246	+	0.893408i	$0.648307\pi$
$312$		0			0
$313$	−12.2823	−	21.2735i	−0.694235	−	1.20245i	−0.970438	−	0.241352i	$-0.922409\pi$
$313$	−12.2823	−	21.2735i	−0.694235	−	1.20245i	0.276202	−	0.961100i	$-0.410924\pi$
$314$	9.22862			0.520801
$315$		0			0
$316$		−	2.99132i		−	0.168275i
$317$	−15.0163	+	8.66967i	−0.843400	+	0.486937i	−0.858418	−	0.512950i	$-0.828553\pi$
$317$	−15.0163	+	8.66967i	−0.843400	+	0.486937i	0.0150187	+	0.999887i	$0.495219\pi$
$318$		0			0
$319$	−0.259444	−	0.238914i	−0.0145261	−	0.0133766i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$		0			0
$322$	2.23278	+	3.86730i	0.124428	+	0.215516i
$323$		−	2.29357i		−	0.127618i
$324$		0			0
$325$			3.11896i			0.173009i
$326$	0.846349	+	1.46592i	0.0468749	+	0.0811898i
$327$		0			0
$328$	1.38401	−	2.39717i	0.0764190	−	0.132362i
$329$	−7.24618	+	12.5508i	−0.399495	+	0.691945i
$330$		0			0
$331$	8.70296	+	15.0740i	0.478358	+	0.828541i	0.999692	−	0.0248121i	$-0.00789874\pi$
$331$	8.70296	+	15.0740i	0.478358	+	0.828541i	−0.521334	+	0.853353i	$0.674565\pi$
$332$	9.83485			0.539757
$333$		0			0
$334$	16.3944			0.897061
$335$	−8.51280	+	4.91487i	−0.465104	+	0.268528i
$336$		0			0
$337$	−12.1230	−	6.99923i	−0.660383	−	0.381272i	0.132040	−	0.991244i	$-0.457847\pi$
$337$	−12.1230	−	6.99923i	−0.660383	−	0.381272i	−0.792423	+	0.609972i	$0.791181\pi$
$338$	−1.63603	+	2.83369i	−0.0889884	+	0.154132i
$339$		0			0
$340$	−3.05976	+	1.76655i	−0.165939	+	0.0958048i
$341$	−6.06272	+	27.0321i	−0.328315	+	1.46387i
$342$		0			0
$343$			20.1228i			1.08653i
$344$	−10.0170	+	5.78333i	−0.540082	+	0.311816i
$345$		0			0
$346$	10.2188	−	17.6995i	0.549368	−	0.951533i
$347$	13.0830	−	22.6604i	0.702332	−	1.21648i	−0.265314	−	0.964162i	$-0.585475\pi$
$347$	13.0830	−	22.6604i	0.702332	−	1.21648i	0.967646	−	0.252313i	$-0.0811912\pi$
$348$		0			0
$349$	27.7358	−	16.0132i	1.48466	−	0.857170i	0.484814	−	0.874618i	$-0.338887\pi$
$349$	27.7358	−	16.0132i	1.48466	−	0.857170i	0.999848	+	0.0174479i	$0.00555413\pi$
$350$		−	2.23785i		−	0.119618i
$351$		0			0
$352$	0.725816	−	3.23623i	0.0386861	−	0.172492i
$353$	20.2217	−	11.6750i	1.07629	−	0.621397i	0.146398	−	0.989226i	$-0.453232\pi$
$353$	20.2217	−	11.6750i	1.07629	−	0.621397i	0.929894	+	0.367829i	$0.119899\pi$
$354$		0			0
$355$	−0.582327	+	1.00862i	−0.0309067	+	0.0535320i
$356$	0.232994	+	0.134519i	0.0123487	+	0.00712952i
$357$		0			0
$358$	17.3418	−	10.0123i	0.916545	−	0.529168i
$359$	18.2033			0.960731			0.480366	−	0.877068i	$-0.340504\pi$
$359$	18.2033			0.960731			0.480366	+	0.877068i	$0.340504\pi$
$360$		0			0
$361$	18.5786			0.977820
$362$	11.1989	+	19.3971i	0.588602	+	1.01949i
$363$		0			0
$364$	−3.48989	+	6.04467i	−0.182920	+	0.316827i
$365$	−0.701804	+	1.21556i	−0.0367341	+	0.0636253i
$366$		0			0
$367$	−10.7997	−	18.7057i	−0.563741	−	0.976428i	−0.997166	−	0.0752382i	$-0.976028\pi$
$367$	−10.7997	−	18.7057i	−0.563741	−	0.976428i	0.433425	−	0.901190i	$-0.357305\pi$
$368$			1.99547i			0.104021i
$369$		0			0
$370$		−	3.00315i		−	0.156126i
$371$	−4.42266	−	7.66028i	−0.229613	−	0.397702i
$372$		0			0
$373$	5.03375	+	2.90624i	0.260638	+	0.150479i	0.624626	−	0.780924i	$-0.285252\pi$
$373$	5.03375	+	2.90624i	0.260638	+	0.150479i	−0.363988	+	0.931404i	$0.618585\pi$
$374$	−8.61990	−	7.93780i	−0.445724	−	0.410454i
$375$		0			0
$376$	−5.60838	+	3.23800i	−0.289230	+	0.166987i
$377$			0.331672i			0.0170820i
$378$		0			0
$379$	−35.6346			−1.83043			−0.915213	−	0.402970i	$-0.867978\pi$
$379$	−35.6346			−1.83043			−0.915213	+	0.402970i	$0.867978\pi$
$380$	0.324583	+	0.562194i	0.0166507	+	0.0288399i
$381$		0			0
$382$	1.37544	+	0.794110i	0.0703736	+	0.0406302i
$383$	24.4144	+	14.0957i	1.24752	+	0.720254i	0.970614	−	0.240644i	$-0.0773585\pi$
$383$	24.4144	+	14.0957i	1.24752	+	0.720254i	0.276903	+	0.960898i	$0.410692\pi$
$384$		0			0
$385$	7.08408	−	2.21445i	0.361038	−	0.112859i
$386$		−	25.8287i		−	1.31465i
$387$		0			0
$388$	5.06302			0.257036
$389$	1.82484	−	1.05357i	0.0925229	−	0.0534181i	−0.453025	−	0.891498i	$-0.649655\pi$
$389$	1.82484	−	1.05357i	0.0925229	−	0.0534181i	0.545548	+	0.838080i	$0.316322\pi$
$390$		0			0
$391$	6.10566	+	3.52510i	0.308776	+	0.178272i
$392$	−0.996003	+	1.72513i	−0.0503057	+	0.0871321i
$393$		0			0
$394$	10.0166	+	17.3492i	0.504628	+	0.874042i
$395$	2.99132			0.150510
$396$		0			0
$397$	10.4728			0.525615			0.262808	−	0.964848i	$-0.415352\pi$
$397$	10.4728			0.525615			0.262808	+	0.964848i	$0.415352\pi$
$398$	−0.816811	−	1.41476i	−0.0409430	−	0.0709154i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	21.0553	+	12.1563i	1.05145	+	0.607055i	0.923055	−	0.384668i	$-0.125684\pi$
$401$	21.0553	+	12.1563i	1.05145	+	0.607055i	0.128396	+	0.991723i	$0.459017\pi$
$402$		0			0
$403$	22.5622	−	13.0263i	1.12390	−	0.648887i
$404$	−1.25098			−0.0622385
$405$		0			0
$406$		−	0.237974i		−	0.0118105i
$407$	9.50667	−	2.97174i	0.471228	−	0.147304i
$408$		0			0
$409$	26.4890	+	15.2934i	1.30980	+	0.756212i	0.982062	−	0.188557i	$-0.0603810\pi$
$409$	26.4890	+	15.2934i	1.30980	+	0.756212i	0.327736	+	0.944769i	$0.393714\pi$
$410$	2.39717	+	1.38401i	0.118388	+	0.0683513i
$411$		0			0
$412$	4.34798	+	7.53091i	0.214209	+	0.371022i
$413$	7.24466			0.356487
$414$		0			0
$415$			9.83485i			0.482774i
$416$	−2.70110	+	1.55948i	−0.132432	+	0.0764599i
$417$		0			0
$418$	−1.45847	+	1.58380i	−0.0713363	+	0.0774662i
$419$	−17.5066	−	10.1075i	−0.855255	−	0.493782i	0.00716547	−	0.999974i	$-0.497719\pi$
$419$	−17.5066	−	10.1075i	−0.855255	−	0.493782i	−0.862420	+	0.506193i	$0.831052\pi$
$420$		0			0
$421$	−4.03827	−	6.99449i	−0.196813	−	0.340891i	0.750680	−	0.660666i	$-0.229726\pi$
$421$	−4.03827	−	6.99449i	−0.196813	−	0.340891i	−0.947493	+	0.319775i	$0.896393\pi$
$422$			16.0282i			0.780242i
$423$		0			0
$424$		−	3.95259i		−	0.191955i
$425$	−1.76655	−	3.05976i	−0.0856905	−	0.148420i
$426$		0			0
$427$	−14.7378	+	25.5267i	−0.713214	+	1.23532i
$428$	3.73958	−	6.47714i	0.180759	−	0.313084i
$429$		0			0
$430$	−5.78333	−	10.0170i	−0.278897	−	0.483064i
$431$	17.0692			0.822197			0.411098	−	0.911591i	$-0.365145\pi$
$431$	17.0692			0.822197			0.411098	+	0.911591i	$0.365145\pi$
$432$		0			0
$433$	−40.2925			−1.93634			−0.968168	−	0.250303i	$-0.919470\pi$
$433$	−40.2925			−1.93634			−0.968168	+	0.250303i	$0.919470\pi$
$434$	−16.1884	+	9.34637i	−0.777067	+	0.448640i
$435$		0			0
$436$	−9.87786	−	5.70298i	−0.473063	−	0.273123i
$437$	0.647694	−	1.12184i	0.0309834	−	0.0536649i
$438$		0			0
$439$	−18.7045	+	10.7991i	−0.892719	+	0.515411i	−0.874831	−	0.484429i	$-0.839028\pi$
$439$	−18.7045	+	10.7991i	−0.892719	+	0.515411i	−0.0178880	+	0.999840i	$0.505694\pi$
$440$	3.23623	+	0.725816i	0.154281	+	0.0346019i
$441$		0			0
$442$			11.0196i			0.524151i
$443$	14.2248	−	8.21271i	0.675842	−	0.390198i	−0.122445	−	0.992475i	$-0.539073\pi$
$443$	14.2248	−	8.21271i	0.675842	−	0.390198i	0.798287	+	0.602278i	$0.205740\pi$
$444$		0			0
$445$	−0.134519	+	0.232994i	−0.00637683	+	0.0110450i
$446$	−4.23876	+	7.34175i	−0.200711	+	0.347642i
$447$		0			0
$448$	1.93804	−	1.11893i	0.0915637	−	0.0528644i
$449$			22.2449i			1.04980i	0.851163	+	0.524901i	$0.175898\pi$
$449$			22.2449i			1.04980i	−0.851163	+	0.524901i	$0.824102\pi$
$450$		0			0
$451$	−2.00907	+	8.95794i	−0.0946034	+	0.421813i
$452$	11.2536	−	6.49729i	0.529327	−	0.305607i
$453$		0			0
$454$	3.63551	−	6.29688i	0.170623	−	0.295527i
$455$	−6.04467	−	3.48989i	−0.283379	−	0.163609i
$456$		0			0
$457$	−9.07476	+	5.23932i	−0.424500	+	0.245085i	−0.697001	−	0.717071i	$-0.745483\pi$
$457$	−9.07476	+	5.23932i	−0.424500	+	0.245085i	0.272501	+	0.962155i	$0.412149\pi$
$458$	14.2004			0.663540
$459$		0			0
$460$	−1.99547			−0.0930392
$461$	13.9519	+	24.1654i	0.649804	+	1.12549i	0.983169	+	0.182696i	$0.0584825\pi$
$461$	13.9519	+	24.1654i	0.649804	+	1.12549i	−0.333365	+	0.942798i	$0.608184\pi$
$462$		0			0
$463$	20.7852	−	36.0010i	0.965970	−	1.67311i	0.258983	−	0.965882i	$-0.416613\pi$
$463$	20.7852	−	36.0010i	0.965970	−	1.67311i	0.706986	−	0.707227i	$-0.250054\pi$
$464$	0.0531702	−	0.0920935i	0.00246837	−	0.00427533i
$465$		0			0
$466$	−0.933478	−	1.61683i	−0.0432425	−	0.0748983i
$467$		−	34.8128i		−	1.61095i	−0.592632	−	0.805473i	$-0.701911\pi$
$467$		−	34.8128i		−	1.61095i	0.592632	−	0.805473i	$-0.298089\pi$
$468$		0			0
$469$		−	21.9975i		−	1.01575i
$470$	−3.23800	−	5.60838i	−0.149358	−	0.258696i
$471$		0			0
$472$	2.80361	+	1.61866i	0.129046	+	0.0745050i
$473$	25.9867	−	28.2198i	1.19487	−	1.29755i
$474$		0			0
$475$	−0.562194	+	0.324583i	−0.0257952	+	0.0148929i
$476$		−	7.90658i		−	0.362398i
$477$		0			0
$478$	25.7645			1.17844
$479$	−18.0153	−	31.2034i	−0.823139	−	1.42572i	−0.903333	−	0.428939i	$-0.858887\pi$
$479$	−18.0153	−	31.2034i	−0.823139	−	1.42572i	0.0801944	−	0.996779i	$-0.474446\pi$
$480$		0			0
$481$	−8.11181	−	4.68336i	−0.369867	−	0.213543i
$482$	26.3093	+	15.1897i	1.19836	+	0.691872i
$483$		0			0
$484$	0.904760	+	10.9627i	0.0411255	+	0.498306i
$485$			5.06302i			0.229900i
$486$		0			0
$487$	23.2302			1.05266			0.526331	−	0.850280i	$-0.323567\pi$
$487$	23.2302			1.05266			0.526331	+	0.850280i	$0.323567\pi$
$488$	−11.4068	+	6.58570i	−0.516360	+	0.298121i
$489$		0			0
$490$	−1.72513	−	0.996003i	−0.0779333	−	0.0449948i
$491$	−14.0156	+	24.2757i	−0.632514	+	1.09555i	0.354521	+	0.935048i	$0.384644\pi$
$491$	−14.0156	+	24.2757i	−0.632514	+	1.09555i	−0.987036	+	0.160499i	$0.948690\pi$
$492$		0			0
$493$	−0.187856	−	0.325376i	−0.00846061	−	0.0146542i
$494$	2.02472			0.0910966
$495$		0			0
$496$	−8.35297			−0.375059
$497$	−1.30316	−	2.25714i	−0.0584549	−	0.101247i
$498$		0			0
$499$	9.73187	−	16.8561i	0.435658	−	0.754582i	−0.561691	−	0.827347i	$-0.689849\pi$
$499$	9.73187	−	16.8561i	0.435658	−	0.754582i	0.997349	+	0.0727649i	$0.0231823\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$		0			0
$502$	0.561359	−	0.324101i	0.0250547	−	0.0144653i
$503$	25.6161			1.14217			0.571083	−	0.820892i	$-0.306523\pi$
$503$	25.6161			1.14217			0.571083	+	0.820892i	$0.306523\pi$
$504$		0			0
$505$		−	1.25098i		−	0.0556678i
$506$	−1.97460	−	6.31679i	−0.0877815	−	0.280815i
$507$		0			0
$508$	−3.01086	−	1.73832i	−0.133586	−	0.0771256i
$509$	6.65944	+	3.84483i	0.295175	+	0.170419i	0.640273	−	0.768147i	$-0.278821\pi$
$509$	6.65944	+	3.84483i	0.295175	+	0.170419i	−0.345098	+	0.938566i	$0.612154\pi$
$510$		0			0
$511$	−1.57054	−	2.72025i	−0.0694764	−	0.120337i
$512$	1.00000			0.0441942
$513$		0			0
$514$			2.06058i			0.0908883i
$515$	−7.53091	+	4.34798i	−0.331852	+	0.191595i
$516$		0			0
$517$	14.5496	−	15.7998i	0.639890	−	0.694876i
$518$	5.82022	+	3.36031i	0.255726	+	0.147643i
$519$		0			0
$520$	−1.55948	−	2.70110i	−0.0683878	−	0.118451i
$521$			9.19977i			0.403049i	0.979483	+	0.201525i	$0.0645896\pi$
$521$			9.19977i			0.403049i	−0.979483	+	0.201525i	$0.935410\pi$
$522$		0			0
$523$		−	19.8490i		−	0.867937i	−0.900928	−	0.433968i	$-0.857113\pi$
$523$		−	19.8490i		−	0.867937i	0.900928	−	0.433968i	$-0.142887\pi$
$524$	−1.86412	−	3.22874i	−0.0814343	−	0.141048i
$525$		0			0
$526$	4.15995	−	7.20525i	0.181383	−	0.314164i
$527$	−14.7560	+	25.5581i	−0.642780	+	1.11333i
$528$		0			0
$529$	−9.50905	−	16.4702i	−0.413437	−	0.716094i
$530$	3.95259			0.171690
$531$		0			0
$532$	−1.45274			−0.0629842
$533$	7.47669	−	4.31667i	0.323851	−	0.186976i
$534$		0			0
$535$	6.47714	+	3.73958i	0.280031	+	0.161676i
$536$	4.91487	−	8.51280i	0.212290	−	0.367697i
$537$		0			0
$538$	−6.18320	+	3.56987i	−0.266577	+	0.153908i
$539$	1.44583	−	6.44659i	0.0622763	−	0.277674i
$540$		0			0
$541$		−	21.7443i		−	0.934859i	−0.884030	−	0.467429i	$-0.845180\pi$
$541$		−	21.7443i		−	0.934859i	0.884030	−	0.467429i	$-0.154820\pi$
$542$	−22.2335	+	12.8365i	−0.955009	+	0.551375i
$543$		0			0
$544$	1.76655	−	3.05976i	0.0757404	−	0.131186i
$545$	5.70298	−	9.87786i	0.244289	−	0.423121i
$546$		0			0
$547$	−19.2159	+	11.0943i	−0.821611	+	0.474357i	−0.850972	−	0.525211i	$-0.823986\pi$
$547$	−19.2159	+	11.0943i	−0.821611	+	0.474357i	0.0293606	+	0.999569i	$0.490653\pi$
$548$		−	2.67480i		−	0.114262i
$549$		0			0
$550$	−0.725816	+	3.23623i	−0.0309489	+	0.137993i
$551$	−0.0597839	+	0.0345163i	−0.00254688	+	0.00147044i
$552$		0			0
$553$	−3.34707	+	5.79730i	−0.142332	+	0.246526i
$554$	15.8621	+	9.15799i	0.673916	+	0.389086i
$555$		0			0
$556$	6.75836	−	3.90194i	0.286618	−	0.165479i
$557$	−10.9699			−0.464808			−0.232404	−	0.972619i	$-0.574659\pi$
$557$	−10.9699			−0.464808			−0.232404	+	0.972619i	$0.574659\pi$
$558$		0			0
$559$	−36.0760			−1.52585
$560$	1.11893	+	1.93804i	0.0472833	+	0.0818971i
$561$		0			0
$562$	−11.3351	+	19.6330i	−0.478143	+	0.828168i
$563$	11.9763	−	20.7435i	0.504740	−	0.874236i	−0.495245	−	0.868754i	$-0.664922\pi$
$563$	11.9763	−	20.7435i	0.504740	−	0.874236i	0.999985	−	0.00548240i	$-0.00174511\pi$
$564$		0			0
$565$	6.49729	+	11.2536i	0.273343	+	0.473444i
$566$		−	29.3060i		−	1.23182i
$567$		0			0
$568$		−	1.16465i		−	0.0488678i
$569$	7.37244	+	12.7694i	0.309069	+	0.535322i	0.978159	−	0.207859i	$-0.0666494\pi$
$569$	7.37244	+	12.7694i	0.309069	+	0.535322i	−0.669090	+	0.743181i	$0.733316\pi$
$570$		0			0
$571$	−16.8538	−	9.73053i	−0.705309	−	0.407210i	0.104013	−	0.994576i	$-0.466832\pi$
$571$	−16.8538	−	9.73053i	−0.705309	−	0.407210i	−0.809322	+	0.587366i	$0.800165\pi$
$572$	7.00735	−	7.60949i	0.292992	−	0.318169i
$573$		0			0
$574$	−5.36452	+	3.09721i	−0.223911	+	0.129275i
$575$		−	1.99547i		−	0.0832168i
$576$		0			0
$577$	−30.7153			−1.27869			−0.639347	−	0.768919i	$-0.720795\pi$
$577$	−30.7153			−1.27869			−0.639347	+	0.768919i	$0.720795\pi$
$578$	2.25857	+	3.91197i	0.0939443	+	0.162716i
$579$		0			0
$580$	0.0920935	+	0.0531702i	0.00382397	+	0.00220777i
$581$	−19.0603	−	11.0045i	−0.790755	−	0.456543i
$582$		0			0
$583$	3.91125	+	12.5122i	0.161987	+	0.518202i
$584$		−	1.40361i		−	0.0580817i
$585$		0			0
$586$	−20.5103			−0.847274
$587$	16.3401	−	9.43395i	0.674427	−	0.389381i	−0.123325	−	0.992366i	$-0.539356\pi$
$587$	16.3401	−	9.43395i	0.674427	−	0.389381i	0.797752	+	0.602986i	$0.206022\pi$
$588$		0			0
$589$	4.69599	+	2.71123i	0.193495	+	0.111714i
$590$	−1.61866	+	2.80361i	−0.0666393	+	0.115423i
$591$		0			0
$592$	1.50157	+	2.60080i	0.0617143	+	0.106892i
$593$	17.7380			0.728413			0.364206	−	0.931318i	$-0.381340\pi$
$593$	17.7380			0.728413			0.364206	+	0.931318i	$0.381340\pi$
$594$		0			0
$595$	7.90658			0.324138
$596$	−0.0324085	−	0.0561333i	−0.00132751	−	0.00229931i
$597$		0			0
$598$	−3.11190	+	5.38996i	−0.127255	+	0.220412i
$599$	−31.6791	−	18.2899i	−1.29437	−	0.747306i	−0.314946	−	0.949109i	$-0.601987\pi$
$599$	−31.6791	−	18.2899i	−1.29437	−	0.747306i	−0.979426	+	0.201803i	$0.935320\pi$
$600$		0			0
$601$	18.8025	−	10.8556i	0.766971	−	0.442811i	−0.0648219	−	0.997897i	$-0.520648\pi$
$601$	18.8025	−	10.8556i	0.766971	−	0.442811i	0.831793	+	0.555086i	$0.187315\pi$
$602$	25.8845			1.05497
$603$		0			0
$604$		−	14.7717i		−	0.601050i
$605$	−10.9627	+	0.904760i	−0.445698	+	0.0367837i
$606$		0			0
$607$	2.44027	+	1.40889i	0.0990475	+	0.0571851i	0.548706	−	0.836016i	$-0.315121\pi$
$607$	2.44027	+	1.40889i	0.0990475	+	0.0571851i	−0.449658	+	0.893201i	$0.648454\pi$
$608$	−0.562194	−	0.324583i	−0.0228000	−	0.0131636i
$609$		0			0
$610$	−6.58570	−	11.4068i	−0.266647	−	0.461846i
$611$	−20.1984			−0.817141
$612$		0			0
$613$			2.12088i			0.0856617i	0.999082	+	0.0428308i	$0.0136377\pi$
$613$			2.12088i			0.0856617i	−0.999082	+	0.0428308i	$0.986362\pi$
$614$	−18.8630	+	10.8906i	−0.761249	+	0.439507i
$615$		0			0
$616$	−5.02777	+	5.45981i	−0.202575	+	0.219982i
$617$	−38.0414	−	21.9632i	−1.53149	−	0.884206i	−0.999293	−	0.0375859i	$-0.988033\pi$
$617$	−38.0414	−	21.9632i	−1.53149	−	0.884206i	−0.532197	−	0.846620i	$-0.678633\pi$
$618$		0			0
$619$	12.8087	+	22.1853i	0.514825	+	0.891703i	0.999852	+	0.0172042i	$0.00547653\pi$
$619$	12.8087	+	22.1853i	0.514825	+	0.891703i	−0.485027	+	0.874499i	$0.661190\pi$
$620$		−	8.35297i		−	0.335463i
$621$		0			0
$622$		−	2.03320i		−	0.0815239i
$623$	−0.301035	−	0.521408i	−0.0120607	−	0.0208898i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−12.2823	+	21.2735i	−0.490899	+	0.850261i
$627$		0			0
$628$	−4.61431	−	7.99222i	−0.184131	−	0.318924i
$629$	10.6104			0.423066
$630$		0			0
$631$	20.1742			0.803122			0.401561	−	0.915832i	$-0.368468\pi$
$631$	20.1742			0.803122			0.401561	+	0.915832i	$0.368468\pi$
$632$	−2.59056	+	1.49566i	−0.103047	+	0.0594942i
$633$		0			0
$634$	15.0163	+	8.66967i	0.596374	+	0.344316i
$635$	1.73832	−	3.01086i	0.0689833	−	0.119483i
$636$		0			0
$637$	−5.38061	+	3.10650i	−0.213187	+	0.123084i
$638$	−0.0771836	+	0.344142i	−0.00305573	+	0.0136247i
$639$		0			0
$640$			1.00000i			0.0395285i
$641$	15.9881	−	9.23075i	0.631493	−	0.364593i	−0.149837	−	0.988711i	$-0.547875\pi$
$641$	15.9881	−	9.23075i	0.631493	−	0.364593i	0.781330	+	0.624118i	$0.214542\pi$
$642$		0			0
$643$	10.0429	−	17.3949i	0.396054	−	0.685986i	−0.597181	−	0.802107i	$-0.703713\pi$
$643$	10.0429	−	17.3949i	0.396054	−	0.685986i	0.993235	+	0.116120i	$0.0370459\pi$
$644$	2.23278	−	3.86730i	0.0879840	−	0.152393i
$645$		0			0
$646$	−1.98629	+	1.14679i	−0.0781496	+	0.0451197i
$647$		−	3.97837i		−	0.156406i	−0.996937	−	0.0782030i	$-0.975082\pi$
$647$		−	3.97837i		−	0.156406i	0.996937	−	0.0782030i	$-0.0249182\pi$
$648$		0			0
$649$	−10.4767	−	2.34970i	−0.411248	−	0.0922339i
$650$	2.70110	−	1.55948i	0.105946	−	0.0611679i
$651$		0			0
$652$	0.846349	−	1.46592i	0.0331456	−	0.0574098i
$653$	−36.6216	−	21.1435i	−1.43311	−	0.827409i	−0.435757	−	0.900064i	$-0.643519\pi$
$653$	−36.6216	−	21.1435i	−1.43311	−	0.827409i	−0.997357	+	0.0726555i	$0.976853\pi$
$654$		0			0
$655$	3.22874	−	1.86412i	0.126157	−	0.0728370i
$656$	−2.76801			−0.108073
$657$		0			0
$658$	14.4924			0.564971
$659$	11.5514	+	20.0076i	0.449978	+	0.779384i	0.998384	−	0.0568277i	$-0.0180986\pi$
$659$	11.5514	+	20.0076i	0.449978	+	0.779384i	−0.548406	+	0.836212i	$0.684765\pi$
$660$		0			0
$661$	−8.61084	+	14.9144i	−0.334923	+	0.580104i	−0.983470	−	0.181071i	$-0.942044\pi$
$661$	−8.61084	+	14.9144i	−0.334923	+	0.580104i	0.648547	+	0.761175i	$0.275377\pi$
$662$	8.70296	−	15.0740i	0.338250	−	0.585867i
$663$		0			0
$664$	−4.91742	−	8.51723i	−0.190833	−	0.330532i
$665$		−	1.45274i		−	0.0563348i
$666$		0			0
$667$		−	0.212199i		−	0.00821638i
$668$	−8.19719	−	14.1980i	−0.317159	−	0.549335i
$669$		0			0
$670$	8.51280	+	4.91487i	0.328878	+	0.189878i
$671$	29.5921	−	32.1349i	1.14239	−	1.24055i
$672$		0			0
$673$	−10.9871	+	6.34342i	−0.423522	+	0.244521i	−0.696583	−	0.717476i	$-0.745297\pi$
$673$	−10.9871	+	6.34342i	−0.423522	+	0.244521i	0.273061	+	0.961997i	$0.411964\pi$
$674$			13.9985i			0.539200i
$675$		0			0
$676$	3.27206			0.125849
$677$	4.74555	+	8.21953i	0.182386	+	0.315902i	0.942693	−	0.333662i	$-0.108285\pi$
$677$	4.74555	+	8.21953i	0.182386	+	0.315902i	−0.760306	+	0.649565i	$0.774951\pi$
$678$		0			0
$679$	−9.81234	−	5.66516i	−0.376563	−	0.217409i
$680$	3.05976	+	1.76655i	0.117336	+	0.0677443i
$681$		0			0
$682$	26.4419	−	8.26560i	1.01251	−	0.316506i
$683$			27.3499i			1.04651i	0.852175	+	0.523257i	$0.175283\pi$
$683$			27.3499i			1.04651i	−0.852175	+	0.523257i	$0.824717\pi$
$684$		0			0
$685$	2.67480			0.102199
$686$	17.4269	−	10.0614i	0.665361	−	0.384146i
$687$		0			0
$688$	10.0170	+	5.78333i	0.381896	+	0.220487i
$689$	6.16400	−	10.6764i	0.234830	−	0.406737i
$690$		0			0
$691$	18.0682	+	31.2950i	0.687346	+	1.19052i	0.972693	+	0.232093i	$0.0745575\pi$
$691$	18.0682	+	31.2950i	0.687346	+	1.19052i	−0.285348	+	0.958424i	$0.592109\pi$
$692$	−20.4377			−0.776923
$693$		0			0
$694$	−26.1660			−0.993248
$695$	3.90194	+	6.75836i	0.148009	+	0.256359i
$696$		0			0
$697$	−4.88985	+	8.46946i	−0.185216	+	0.320804i
$698$	−27.7358	−	16.0132i	−1.04981	−	0.606110i
$699$		0			0
$700$	−1.93804	+	1.11893i	−0.0732510	+	0.0422915i
$701$	8.65997			0.327083			0.163541	−	0.986536i	$-0.447708\pi$
$701$	8.65997			0.327083			0.163541	+	0.986536i	$0.447708\pi$
$702$		0			0
$703$		−	1.94954i		−	0.0735283i
$704$	−3.16557	+	0.989540i	−0.119307	+	0.0372947i
$705$		0			0
$706$	−20.2217	−	11.6750i	−0.761053	−	0.439394i
$707$	2.42444	+	1.39975i	0.0911806	+	0.0526431i
$708$		0			0
$709$	14.0217	+	24.2864i	0.526598	+	0.912094i	0.999520	+	0.0309898i	$0.00986594\pi$
$709$	14.0217	+	24.2864i	0.526598	+	0.912094i	−0.472922	+	0.881104i	$0.656801\pi$
$710$	1.16465			0.0437087
$711$		0			0
$712$		−	0.269039i		−	0.0100827i
$713$	−14.4350	+	8.33405i	−0.540595	+	0.312112i
$714$		0			0
$715$	7.60949	+	7.00735i	0.284579	+	0.262060i
$716$	−17.3418	−	10.0123i	−0.648095	−	0.374178i
$717$		0			0
$718$	−9.10163	−	15.7645i	−0.339670	−	0.588325i
$719$		−	25.5223i		−	0.951820i	−0.879494	−	0.475910i	$-0.842119\pi$
$719$		−	25.5223i		−	0.951820i	0.879494	−	0.475910i	$-0.157881\pi$
$720$		0			0
$721$		−	19.4603i		−	0.724739i
$722$	−9.28929	−	16.0895i	−0.345712	−	0.598790i
$723$		0			0
$724$	11.1989	−	19.3971i	0.416204	−	0.720887i
$725$	−0.0531702	+	0.0920935i	−0.00197469	+	0.00342027i
$726$		0			0
$727$	−22.7537	−	39.4106i	−0.843889	−	1.46166i	−0.886582	−	0.462571i	$-0.846927\pi$
$727$	−22.7537	−	39.4106i	−0.843889	−	1.46166i	0.0426928	−	0.999088i	$-0.486406\pi$
$728$	6.97979			0.258688
$729$		0			0
$730$	1.40361			0.0519499
$731$	35.3912	−	20.4331i	1.30899	−	0.755747i
$732$		0			0
$733$	−1.96896	−	1.13678i	−0.0727253	−	0.0419880i	0.463196	−	0.886256i	$-0.346702\pi$
$733$	−1.96896	−	1.13678i	−0.0727253	−	0.0419880i	−0.535922	+	0.844268i	$0.680036\pi$
$734$	−10.7997	+	18.7057i	−0.398625	+	0.690439i
$735$		0			0
$736$	1.72813	−	0.997734i	0.0636996	−	0.0367770i
$737$	−7.13458	+	31.8113i	−0.262806	+	1.17178i
$738$		0			0
$739$			2.04843i			0.0753526i	0.999290	+	0.0376763i	$0.0119956\pi$
$739$			2.04843i			0.0753526i	−0.999290	+	0.0376763i	$0.988004\pi$
$740$	−2.60080	+	1.50157i	−0.0956074	+	0.0551990i
$741$		0			0
$742$	−4.42266	+	7.66028i	−0.162361	+	0.281218i
$743$	23.2197	−	40.2176i	0.851847	−	1.47544i	−0.0276930	−	0.999616i	$-0.508816\pi$
$743$	23.2197	−	40.2176i	0.851847	−	1.47544i	0.879540	−	0.475825i	$-0.157851\pi$
$744$		0			0
$745$	0.0561333	−	0.0324085i	0.00205656	−	0.00118736i
$746$		−	5.81248i		−	0.212810i
$747$		0			0
$748$	−2.56439	+	11.4340i	−0.0937633	+	0.418067i
$749$	−14.4949	+	8.36864i	−0.529632	+	0.305783i
$750$		0			0
$751$	3.66422	−	6.34662i	0.133709	−	0.231592i	−0.791394	−	0.611306i	$-0.790644\pi$
$751$	3.66422	−	6.34662i	0.133709	−	0.231592i	0.925104	+	0.379715i	$0.123978\pi$
$752$	5.60838	+	3.23800i	0.204517	+	0.118078i
$753$		0			0
$754$	0.287236	−	0.165836i	0.0104605	−	0.00603939i
$755$	14.7717			0.537596
$756$		0			0
$757$	32.5935			1.18463			0.592315	−	0.805706i	$-0.298214\pi$
$757$	32.5935			1.18463			0.592315	+	0.805706i	$0.298214\pi$
$758$	17.8173	+	30.8605i	0.647153	+	1.12090i
$759$		0			0
$760$	0.324583	−	0.562194i	0.0117738	−	0.0203929i
$761$	−26.8972	+	46.5873i	−0.975023	+	1.68879i	−0.295165	+	0.955446i	$0.595375\pi$
$761$	−26.8972	+	46.5873i	−0.975023	+	1.68879i	−0.679858	+	0.733343i	$0.737959\pi$
$762$		0			0
$763$	12.7624	+	22.1052i	0.462032	+	0.800262i
$764$		−	1.58822i		−	0.0574598i
$765$		0			0
$766$		−	28.1913i		−	1.01859i
$767$	5.04855	+	8.74435i	0.182293	+	0.315740i
$768$		0			0
$769$	−46.7234	−	26.9758i	−1.68489	−	0.972771i	−0.958329	−	0.285668i	$-0.907784\pi$
$769$	−46.7234	−	26.9758i	−1.68489	−	0.972771i	−0.726560	−	0.687103i	$-0.758882\pi$
$770$	−5.45981	−	5.02777i	−0.196758	−	0.181188i
$771$		0			0
$772$	−22.3683	+	12.9144i	−0.805053	+	0.464798i
$773$		−	19.9741i		−	0.718417i	−0.933257	−	0.359209i	$-0.883047\pi$
$773$		−	19.9741i		−	0.718417i	0.933257	−	0.359209i	$-0.116953\pi$
$774$		0			0
$775$	8.35297			0.300048
$776$	−2.53151	−	4.38471i	−0.0908760	−	0.157402i
$777$		0			0
$778$	−1.82484	−	1.05357i	−0.0654236	−	0.0377723i
$779$	1.55616	+	0.898450i	0.0557552	+	0.0321903i
$780$		0			0
$781$	1.15247	+	3.68679i	0.0412387	+	0.131924i
$782$		−	7.05021i		−	0.252115i
$783$		0			0
$784$	1.99201			0.0711430
$785$	7.99222	−	4.61431i	0.285255	−	0.164692i
$786$		0			0
$787$	33.9688	+	19.6119i	1.21086	+	0.699088i	0.962946	−	0.269696i	$-0.0869231\pi$
$787$	33.9688	+	19.6119i	1.21086	+	0.699088i	0.247910	+	0.968783i	$0.420256\pi$
$788$	10.0166	−	17.3492i	0.356826	−	0.618041i
$789$		0			0
$790$	−1.49566	−	2.59056i	−0.0532133	−	0.0921681i
$791$	−29.0800			−1.03397
$792$		0			0
$793$	−41.0811			−1.45883
$794$	−5.23641	−	9.06972i	−0.185833	−	0.321872i
$795$		0			0
$796$	−0.816811	+	1.41476i	−0.0289511	+	0.0501448i
$797$	−28.2733	−	16.3236i	−1.00149	−	0.578212i	−0.0928024	−	0.995685i	$-0.529582\pi$
$797$	−28.2733	−	16.3236i	−1.00149	−	0.578212i	−0.908689	+	0.417473i	$0.862916\pi$
$798$		0			0
$799$	19.8150	−	11.4402i	0.701005	−	0.404726i
$800$	−1.00000			−0.0353553
$801$		0			0
$802$		−	24.3125i		−	0.858506i
$803$	1.38893	+	4.44322i	0.0490142	+	0.156798i
$804$		0			0
$805$	3.86730	+	2.23278i	0.136304	+	0.0786953i
$806$	−22.5622	−	13.0263i	−0.794721	−	0.458832i
$807$		0			0
$808$	0.625489	+	1.08338i	0.0220046	+	0.0381131i
$809$	0.748177			0.0263045			0.0131523	−	0.999914i	$-0.495813\pi$
$809$	0.748177			0.0263045			0.0131523	+	0.999914i	$0.495813\pi$
$810$		0			0
$811$		−	26.0618i		−	0.915155i	−0.889170	−	0.457577i	$-0.848717\pi$
$811$		−	26.0618i		−	0.915155i	0.889170	−	0.457577i	$-0.151283\pi$
$812$	−0.206092	+	0.118987i	−0.00723241	+	0.00417563i
$813$		0			0
$814$	−7.32693	−	6.74715i	−0.256809	−	0.236487i
$815$	1.46592	+	0.846349i	0.0513489	+	0.0296463i
$816$		0			0
$817$	−3.75434	−	6.50270i	−0.131348	−	0.227501i
$818$		−	30.5869i		−	1.06945i
$819$		0			0
$820$		−	2.76801i		−	0.0966633i
$821$	8.01351	+	13.8798i	0.279673	+	0.484409i	0.971304	−	0.237843i	$-0.0764405\pi$
$821$	8.01351	+	13.8798i	0.279673	+	0.484409i	−0.691630	+	0.722252i	$0.743107\pi$
$822$		0			0
$823$	21.2864	−	36.8691i	0.741997	−	1.28518i	−0.209587	−	0.977790i	$-0.567212\pi$
$823$	21.2864	−	36.8691i	0.741997	−	1.28518i	0.951585	−	0.307387i	$-0.0994546\pi$
$824$	4.34798	−	7.53091i	0.151469	−	0.262352i
$825$		0			0
$826$	−3.62233	−	6.27406i	−0.126037	−	0.218303i
$827$	26.1822			0.910444			0.455222	−	0.890378i	$-0.349560\pi$
$827$	26.1822			0.910444			0.455222	+	0.890378i	$0.349560\pi$
$828$		0			0
$829$	32.5134			1.12924			0.564618	−	0.825353i	$-0.309024\pi$
$829$	32.5134			1.12924			0.564618	+	0.825353i	$0.309024\pi$
$830$	8.51723	−	4.91742i	0.295637	−	0.170686i
$831$		0			0
$832$	2.70110	+	1.55948i	0.0936439	+	0.0540653i
$833$	3.51898	−	6.09506i	0.121926	−	0.211181i
$834$		0			0
$835$	14.1980	−	8.19719i	0.491340	−	0.283676i
$836$	2.10085	+	0.471175i	0.0726594	+	0.0162959i
$837$		0			0
$838$			20.2149i			0.698313i
$839$	44.5464	−	25.7189i	1.53791	−	0.887915i	0.538953	−	0.842336i	$-0.318820\pi$
$839$	44.5464	−	25.7189i	1.53791	−	0.887915i	0.998961	−	0.0455791i	$-0.0145133\pi$
$840$		0			0
$841$	14.4943	−	25.1049i	0.499805	−	0.865688i
$842$	−4.03827	+	6.99449i	−0.139168	+	0.241046i
$843$		0			0
$844$	13.8809	−	8.01412i	0.477799	−	0.275857i
$845$			3.27206i			0.112562i
$846$		0			0
$847$	10.5130	−	22.2586i	0.361232	−	0.764813i
$848$	−3.42305	+	1.97630i	−0.117548	+	0.0678663i
$849$		0			0
$850$	−1.76655	+	3.05976i	−0.0605923	+	0.104949i
$851$	5.18982	+	2.99634i	0.177905	+	0.102713i
$852$		0			0
$853$	24.8106	−	14.3244i	0.849498	−	0.490458i	−0.0109834	−	0.999940i	$-0.503496\pi$
$853$	24.8106	−	14.3244i	0.849498	−	0.490458i	0.860481	+	0.509482i	$0.170163\pi$
$854$	29.4757			1.00864
$855$		0			0
$856$	−7.47916			−0.255632
$857$	13.3156	+	23.0633i	0.454852	+	0.787826i	0.998680	−	0.0513704i	$-0.0163589\pi$
$857$	13.3156	+	23.0633i	0.454852	+	0.787826i	−0.543828	+	0.839197i	$0.683026\pi$
$858$		0			0
$859$	21.2715	−	36.8433i	0.725773	−	1.25708i	−0.232882	−	0.972505i	$-0.574815\pi$
$859$	21.2715	−	36.8433i	0.725773	−	1.25708i	0.958655	−	0.284571i	$-0.0918512\pi$
$860$	−5.78333	+	10.0170i	−0.197210	+	0.341578i
$861$		0			0
$862$	−8.53462	−	14.7824i	−0.290690	−	0.503491i
$863$		−	18.5594i		−	0.631770i	−0.948797	−	0.315885i	$-0.897699\pi$
$863$		−	18.5594i		−	0.631770i	0.948797	−	0.315885i	$-0.102301\pi$
$864$		0			0
$865$		−	20.4377i		−	0.694901i
$866$	20.1463	+	34.8943i	0.684598	+	1.18576i
$867$		0			0
$868$	16.1884	+	9.34637i	0.549470	+	0.317236i
$869$	6.72058	−	7.29808i	0.227980	−	0.247570i
$870$		0			0
$871$	26.5511	−	15.3293i	0.899650	−	0.519413i
$872$			11.4060i			0.386255i
$873$		0			0
$874$	−1.29539			−0.0438172
$875$	−1.11893	−	1.93804i	−0.0378267	−	0.0655177i
$876$		0			0
$877$	−37.5715	−	21.6919i	−1.26870	−	0.732484i	−0.293957	−	0.955819i	$-0.594972\pi$
$877$	−37.5715	−	21.6919i	−1.26870	−	0.732484i	−0.974742	+	0.223335i	$0.928306\pi$
$878$	18.7045	+	10.7991i	0.631248	+	0.364451i
$879$		0			0
$880$	−0.989540	−	3.16557i	−0.0333574	−	0.106711i
$881$			54.3837i			1.83223i	0.400913	+	0.916116i	$0.368693\pi$
$881$			54.3837i			1.83223i	−0.400913	+	0.916116i	$0.631307\pi$
$882$		0			0
$883$	22.5423			0.758607			0.379304	−	0.925272i	$-0.376164\pi$
$883$	22.5423			0.758607			0.379304	+	0.925272i	$0.376164\pi$
$884$	9.54329	−	5.50982i	0.320975	−	0.185315i
$885$		0			0
$886$	−14.2248	−	8.21271i	−0.477892	−	0.275911i
$887$	8.42281	−	14.5887i	0.282810	−	0.489842i	−0.689266	−	0.724509i	$-0.742067\pi$
$887$	8.42281	−	14.5887i	0.282810	−	0.489842i	0.972076	+	0.234667i	$0.0754000\pi$
$888$		0			0
$889$	3.89012	+	6.73788i	0.130470	+	0.225981i
$890$	0.269039			0.00901820
$891$		0			0
$892$	8.47752			0.283848
$893$	−2.10200	−	3.64077i	−0.0703407	−	0.121834i
$894$		0			0
$895$	10.0123	−	17.3418i	0.334675	−	0.579674i
$896$	−1.93804	−	1.11893i	−0.0647453	−	0.0373807i
$897$		0			0
$898$	19.2646	−	11.1224i	0.642870	−	0.371161i
$899$	0.888258			0.0296251
$900$		0			0
$901$			13.9649i			0.465239i
$902$	8.76233	−	2.73906i	0.291754	−	0.0912008i
$903$		0			0
$904$	−11.2536	−	6.49729i	−0.374290	−	0.216097i
$905$	19.3971	+	11.1989i	0.644781	+	0.372264i
$906$		0			0
$907$	6.38593	+	11.0608i	0.212041	+	0.367266i	0.952353	−	0.304997i	$-0.0986555\pi$
$907$	6.38593	+	11.0608i	0.212041	+	0.367266i	−0.740312	+	0.672264i	$0.765322\pi$
$908$	−7.27102			−0.241297
$909$		0			0
$910$			6.97979i			0.231378i
$911$	3.35433	−	1.93662i	0.111134	−	0.0641632i	−0.443403	−	0.896323i	$-0.646229\pi$
$911$	3.35433	−	1.93662i	0.111134	−	0.0641632i	0.554537	+	0.832159i	$0.312896\pi$
$912$		0			0
$913$	23.9946	+	22.0959i	0.794104	+	0.731266i
$914$	9.07476	+	5.23932i	0.300166	+	0.173301i
$915$		0			0
$916$	−7.10018	−	12.2979i	−0.234597	−	0.406333i
$917$			8.34324i			0.275518i
$918$		0			0
$919$		−	21.9222i		−	0.723147i	−0.932344	−	0.361573i	$-0.882240\pi$
$919$		−	21.9222i		−	0.723147i	0.932344	−	0.361573i	$-0.117760\pi$
$920$	0.997734	+	1.72813i	0.0328943	+	0.0569746i
$921$		0			0
$922$	13.9519	−	24.1654i	0.459481	−	0.795845i
$923$	1.81626	−	3.14585i	0.0597828	−	0.103547i
$924$		0			0
$925$	−1.50157	−	2.60080i	−0.0493715	−	0.0855139i
$926$	−41.5704			−1.36609
$927$		0			0
$928$	−0.106340			−0.00349080
$929$	16.3628	−	9.44708i	0.536847	−	0.309949i	−0.206953	−	0.978351i	$-0.566355\pi$
$929$	16.3628	−	9.44708i	0.536847	−	0.309949i	0.743800	+	0.668402i	$0.233021\pi$
$930$		0			0
$931$	−1.11989	−	0.646570i	−0.0367030	−	0.0211905i
$932$	−0.933478	+	1.61683i	−0.0305771	+	0.0529611i
$933$		0			0
$934$	−30.1488	+	17.4064i	−0.986499	+	0.569556i
$935$	−11.4340	−	2.56439i	−0.373930	−	0.0838644i
$936$		0			0
$937$			19.5862i			0.639854i	0.947442	+	0.319927i	$0.103658\pi$
$937$			19.5862i			0.639854i	−0.947442	+	0.319927i	$0.896342\pi$
$938$	−19.0504	+	10.9988i	−0.622018	+	0.359122i
$939$		0			0
$940$	−3.23800	+	5.60838i	−0.105612	+	0.182925i
$941$	−26.7009	+	46.2473i	−0.870424	+	1.50762i	−0.00886483	+	0.999961i	$0.502822\pi$
$941$	−26.7009	+	46.2473i	−0.870424	+	1.50762i	−0.861559	+	0.507658i	$0.830512\pi$
$942$		0			0
$943$	−4.78348	+	2.76174i	−0.155772	+	0.0899347i
$944$		−	3.23733i		−	0.105366i
$945$		0			0
$946$	−37.4324	−	8.39527i	−1.21703	−	0.272954i
$947$	25.8265	−	14.9109i	0.839248	−	0.484540i	−0.0177602	−	0.999842i	$-0.505654\pi$
$947$	25.8265	−	14.9109i	0.839248	−	0.484540i	0.857009	+	0.515302i	$0.172320\pi$
$948$		0			0
$949$	2.18890	−	3.79129i	0.0710548	−	0.123070i
$950$	0.562194	+	0.324583i	0.0182400	+	0.0105309i
$951$		0			0
$952$	−6.84730	+	3.95329i	−0.221922	+	0.128127i
$953$	1.51910			0.0492084			0.0246042	−	0.999697i	$-0.492167\pi$
$953$	1.51910			0.0492084			0.0246042	+	0.999697i	$0.492167\pi$
$954$		0			0
$955$	1.58822			0.0513936
$956$	−12.8822	−	22.3127i	−0.416641	−	0.721644i
$957$		0			0
$958$	−18.0153	+	31.2034i	−0.582047	+	1.00814i
$959$	−2.99291	+	5.18387i	−0.0966460	+	0.167396i
$960$		0			0
$961$	−19.3861	−	33.5777i	−0.625357	−	1.08315i
$962$			9.36671i			0.301995i
$963$		0			0
$964$		−	30.3794i		−	0.978454i
$965$	−12.9144	−	22.3683i	−0.415728	−	0.720062i
$966$		0			0
$967$	13.6284	+	7.86838i	0.438261	+	0.253030i	0.702860	−	0.711329i	$-0.251906\pi$
$967$	13.6284	+	7.86838i	0.438261	+	0.253030i	−0.264599	+	0.964359i	$0.585240\pi$
$968$	9.04162	−	6.26491i	0.290609	−	0.201362i
$969$		0			0
$970$	4.38471	−	2.53151i	0.140784	−	0.0812819i
$971$			18.6803i			0.599480i	0.954021	+	0.299740i	$0.0969000\pi$
$971$			18.6803i			0.599480i	−0.954021	+	0.299740i	$0.903100\pi$
$972$		0			0
$973$	−17.4640			−0.559869
$974$	−11.6151	−	20.1179i	−0.372172	−	0.644621i
$975$		0			0
$976$	11.4068	+	6.58570i	0.365122	+	0.210803i
$977$	−41.0917	−	23.7243i	−1.31464	−	0.759007i	−0.331779	−	0.943357i	$-0.607649\pi$
$977$	−41.0917	−	23.7243i	−1.31464	−	0.759007i	−0.982861	+	0.184350i	$0.940982\pi$
$978$		0			0
$979$	0.266225	+	0.851660i	0.00850858	+	0.0272192i
$980$			1.99201i			0.0636323i
$981$		0			0
$982$	28.0312			0.894511
$983$	−15.3785	+	8.87879i	−0.490498	+	0.283189i	−0.724781	−	0.688979i	$-0.758059\pi$
$983$	−15.3785	+	8.87879i	−0.490498	+	0.283189i	0.234283	+	0.972168i	$0.424726\pi$
$984$		0			0
$985$	17.3492	+	10.0166i	0.552793	+	0.319155i
$986$	−0.187856	+	0.325376i	−0.00598256	+	0.0103621i
$987$		0			0
$988$	−1.01236	−	1.75346i	−0.0322075	−	0.0557850i
$989$	23.0809			0.733930
$990$		0			0
$991$	19.1821			0.609338			0.304669	−	0.952458i	$-0.401454\pi$
$991$	19.1821			0.609338			0.304669	+	0.952458i	$0.401454\pi$
$992$	4.17649	+	7.23389i	0.132604	+	0.229676i
$993$		0			0
$994$	−1.30316	+	2.25714i	−0.0413338	+	0.0715923i
$995$	−1.41476	−	0.816811i	−0.0448508	−	0.0258946i
$996$		0			0
$997$	−4.14157	+	2.39114i	−0.131165	+	0.0757280i	−0.564147	−	0.825675i	$-0.690795\pi$
$997$	−4.14157	+	2.39114i	−0.131165	+	0.0757280i	0.432982	+	0.901403i	$0.357461\pi$
$998$	−19.4637			−0.616114
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2970.2.t.a.2771.9		48
3.2	odd	2		990.2.t.b.131.8	yes	48
9.2	odd	6		2970.2.t.b.791.9		48
9.7	even	3		990.2.t.a.461.8	yes	48
11.10	odd	2		2970.2.t.b.2771.9		48
33.32	even	2		990.2.t.a.131.8	✓	48
99.43	odd	6		990.2.t.b.461.8	yes	48
99.65	even	6	inner	2970.2.t.a.791.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.8	✓	48	33.32	even	2
990.2.t.a.461.8	yes	48	9.7	even	3
990.2.t.b.131.8	yes	48	3.2	odd	2
990.2.t.b.461.8	yes	48	99.43	odd	6
2970.2.t.a.791.9		48	99.65	even	6	inner
2970.2.t.a.2771.9		48	1.1	even	1	trivial
2970.2.t.b.791.9		48	9.2	odd	6
2970.2.t.b.2771.9		48	11.10	odd	2

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:	\( N \)	\(=\)	\( 2970 = 2 \cdot 3^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2970.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.93804 - 1.11893i) q^{7} +1.00000 q^{8} +1.00000i q^{10} +(-3.16557 + 0.989540i) q^{11} +(2.70110 + 1.55948i) q^{13} +(-1.93804 - 1.11893i) q^{14} +(-0.500000 - 0.866025i) q^{16} -3.53311 q^{17} +0.649165i q^{19} +(0.866025 - 0.500000i) q^{20} +(2.43975 + 2.24669i) q^{22} +(-1.72813 - 0.997734i) q^{23} +(0.500000 + 0.866025i) q^{25} -3.11896i q^{26} +2.23785i q^{28} +(0.0531702 + 0.0920935i) q^{29} +(4.17649 - 7.23389i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.76655 + 3.05976i) q^{34} -2.23785 q^{35} -3.00315 q^{37} +(0.562194 - 0.324583i) q^{38} +(-0.866025 - 0.500000i) q^{40} +(1.38401 - 2.39717i) q^{41} +(-10.0170 + 5.78333i) q^{43} +(0.725816 - 3.23623i) q^{44} +1.99547i q^{46} +(-5.60838 + 3.23800i) q^{47} +(-0.996003 + 1.72513i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.70110 + 1.55948i) q^{52} -3.95259i q^{53} +(3.23623 + 0.725816i) q^{55} +(1.93804 - 1.11893i) q^{56} +(0.0531702 - 0.0920935i) q^{58} +(2.80361 + 1.61866i) q^{59} +(-11.4068 + 6.58570i) q^{61} -8.35297 q^{62} +1.00000 q^{64} +(-1.55948 - 2.70110i) q^{65} +(4.91487 - 8.51280i) q^{67} +(1.76655 - 3.05976i) q^{68} +(1.11893 + 1.93804i) q^{70} -1.16465i q^{71} -1.40361i q^{73} +(1.50157 + 2.60080i) q^{74} +(-0.562194 - 0.324583i) q^{76} +(-5.02777 + 5.45981i) q^{77} +(-2.59056 + 1.49566i) q^{79} +1.00000i q^{80} -2.76801 q^{82} +(-4.91742 - 8.51723i) q^{83} +(3.05976 + 1.76655i) q^{85} +(10.0170 + 5.78333i) q^{86} +(-3.16557 + 0.989540i) q^{88} -0.269039i q^{89} +6.97979 q^{91} +(1.72813 - 0.997734i) q^{92} +(5.60838 + 3.23800i) q^{94} +(0.324583 - 0.562194i) q^{95} +(-2.53151 - 4.38471i) q^{97} +1.99201 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} + 12 q^{11} - 24 q^{13} - 24 q^{16} - 12 q^{17} - 6 q^{22} - 36 q^{23} + 24 q^{25} - 24 q^{32} + 6 q^{34} + 6 q^{38} - 6 q^{41} - 30 q^{43} - 6 q^{44} + 24 q^{49} + 24 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) \) 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 + 12 * q^11 - 24 * q^13 - 24 * q^16 - 12 * q^17 - 6 * q^22 - 36 * q^23 + 24 * q^25 - 24 * q^32 + 6 * q^34 + 6 * q^38 - 6 * q^41 - 30 * q^43 - 6 * q^44 + 24 * q^49 + 24 * q^50 + 24 * q^52 + 54 * q^59 + 48 * q^64 - 6 * q^67 + 6 * q^68 - 6 * q^76 + 18 * q^77 + 12 * q^82 + 36 * q^83 + 30 * q^86 + 12 * q^88 + 24 * q^91 + 36 * q^92 + 6 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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