LMFDB - Embedded newform 888.2.bo.c.601.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [888,2,Mod(49,888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(888, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 0, 14]))

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

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

chi := DirichletCharacter("888.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.bo (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			601.2
Character	$\chi$	$=$	888.601
Dual form			888.2.bo.c.625.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{3} +(-1.02288 - 0.858301i) q^{5} +(-0.439492 - 0.368778i) q^{7} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{3} +(-1.02288 - 0.858301i) q^{5} +(-0.439492 - 0.368778i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(0.555956 + 0.962944i) q^{11} +(4.43532 - 1.61432i) q^{13} +(-1.02288 + 0.858301i) q^{15} +(-3.29082 - 1.19776i) q^{17} +(0.848742 - 4.81346i) q^{19} +(-0.439492 + 0.368778i) q^{21} +(-0.286858 + 0.496853i) q^{23} +(-0.558631 - 3.16816i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-3.48055 - 6.02849i) q^{29} -6.66526 q^{31} +(1.04486 - 0.380296i) q^{33} +(0.133027 + 0.754433i) q^{35} +(-6.07706 - 0.263284i) q^{37} +(-0.819613 - 4.64826i) q^{39} +(0.000118594 - 4.31647e-5i) q^{41} -1.57061 q^{43} +(0.667640 + 1.15639i) q^{45} +(-2.44015 + 4.22647i) q^{47} +(-1.15838 - 6.56950i) q^{49} +(-1.75101 + 3.03283i) q^{51} +(1.08913 - 0.913891i) q^{53} +(0.257818 - 1.46216i) q^{55} +(-4.59295 - 1.67170i) q^{57} +(-6.37374 + 5.34821i) q^{59} +(8.18466 - 2.97897i) q^{61} +(0.286858 + 0.496853i) q^{63} +(-5.92239 - 2.15557i) q^{65} +(3.03185 + 2.54402i) q^{67} +(0.439492 + 0.368778i) q^{69} +(-0.365286 + 2.07164i) q^{71} +11.2951 q^{73} -3.21703 q^{75} +(0.110774 - 0.628230i) q^{77} +(6.08402 + 5.10510i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-5.49447 - 1.99982i) q^{83} +(2.33808 + 4.04968i) q^{85} +(-6.54129 + 2.38083i) q^{87} +(9.94019 - 8.34081i) q^{89} +(-2.54461 - 0.926163i) q^{91} +(-1.15741 + 6.56400i) q^{93} +(-4.99956 + 4.19513i) q^{95} +(8.73161 - 15.1236i) q^{97} +(-0.193081 - 1.09502i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) $ 24 * q + 3 * q^5 + 15 * q^7	$ 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) $ 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$4$		0			0
$5$	−1.02288	−	0.858301i	−0.457447	−	0.383844i	0.384743	−	0.923024i	$-0.374290\pi$
$5$	−1.02288	−	0.858301i	−0.457447	−	0.383844i	−0.842191	+	0.539180i	$0.818734\pi$
$6$		0			0
$7$	−0.439492	−	0.368778i	−0.166112	−	0.139385i	0.555942	−	0.831221i	$-0.312358\pi$
$7$	−0.439492	−	0.368778i	−0.166112	−	0.139385i	−0.722055	+	0.691836i	$0.756802\pi$
$8$		0			0
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$		0			0
$11$	0.555956	+	0.962944i	0.167627	+	0.290338i	0.937585	−	0.347756i	$-0.113056\pi$
$11$	0.555956	+	0.962944i	0.167627	+	0.290338i	−0.769958	+	0.638094i	$0.779723\pi$
$12$		0			0
$13$	4.43532	−	1.61432i	1.23014	−	0.447733i	0.356492	−	0.934298i	$-0.383973\pi$
$13$	4.43532	−	1.61432i	1.23014	−	0.447733i	0.873644	+	0.486566i	$0.161751\pi$
$14$		0			0
$15$	−1.02288	+	0.858301i	−0.264107	+	0.221612i
$16$		0			0
$17$	−3.29082	−	1.19776i	−0.798140	−	0.290499i	−0.0894245	−	0.995994i	$-0.528503\pi$
$17$	−3.29082	−	1.19776i	−0.798140	−	0.290499i	−0.708715	+	0.705494i	$0.750725\pi$
$18$		0			0
$19$	0.848742	−	4.81346i	0.194715	−	1.10428i	−0.718109	−	0.695930i	$-0.754992\pi$
$19$	0.848742	−	4.81346i	0.194715	−	1.10428i	0.912824	−	0.408353i	$-0.133897\pi$
$20$		0			0
$21$	−0.439492	+	0.368778i	−0.0959050	+	0.0804739i
$22$		0			0
$23$	−0.286858	+	0.496853i	−0.0598140	+	0.103601i	−0.894382	−	0.447304i	$-0.852384\pi$
$23$	−0.286858	+	0.496853i	−0.0598140	+	0.103601i	0.834568	+	0.550905i	$0.185717\pi$
$24$		0			0
$25$	−0.558631	−	3.16816i	−0.111726	−	0.633631i
$26$		0			0
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$		0			0
$29$	−3.48055	−	6.02849i	−0.646322	−	1.11946i	−0.983995	−	0.178198i	$-0.942973\pi$
$29$	−3.48055	−	6.02849i	−0.646322	−	1.11946i	0.337673	−	0.941263i	$-0.390360\pi$
$30$		0			0
$31$	−6.66526			−1.19712			−0.598558	−	0.801079i	$-0.704259\pi$
$31$	−6.66526			−1.19712			−0.598558	+	0.801079i	$0.704259\pi$
$32$		0			0
$33$	1.04486	−	0.380296i	0.181886	−	0.0662011i
$34$		0			0
$35$	0.133027	+	0.754433i	0.0224856	+	0.127522i
$36$		0			0
$37$	−6.07706	−	0.263284i	−0.999063	−	0.0432836i
$37$	−6.07706	−	0.263284i	−0.999063	−	0.0432836i
$38$		0			0
$39$	−0.819613	−	4.64826i	−0.131243	−	0.744317i
$40$		0			0
$41$	0.000118594	0	4.31647e-5i	1.85213e−5	0	6.74119e-6i	−0.342011	−	0.939696i	$-0.611108\pi$
$41$	0.000118594	0	4.31647e-5i	1.85213e−5	0	6.74119e-6i	0.342029	+	0.939689i	$0.388886\pi$
$42$		0			0
$43$	−1.57061			−0.239516			−0.119758	−	0.992803i	$-0.538212\pi$
$43$	−1.57061			−0.239516			−0.119758	+	0.992803i	$0.538212\pi$
$44$		0			0
$45$	0.667640	+	1.15639i	0.0995258	+	0.172384i
$46$		0			0
$47$	−2.44015	+	4.22647i	−0.355933	+	0.616494i	−0.987277	−	0.159009i	$-0.949170\pi$
$47$	−2.44015	+	4.22647i	−0.355933	+	0.616494i	0.631344	+	0.775503i	$0.282503\pi$
$48$		0			0
$49$	−1.15838	−	6.56950i	−0.165483	−	0.938501i
$50$		0			0
$51$	−1.75101	+	3.03283i	−0.245190	+	0.424681i
$52$		0			0
$53$	1.08913	−	0.913891i	0.149604	−	0.125533i	−0.564914	−	0.825150i	$-0.691091\pi$
$53$	1.08913	−	0.913891i	0.149604	−	0.125533i	0.714518	+	0.699617i	$0.246646\pi$
$54$		0			0
$55$	0.257818	−	1.46216i	0.0347641	−	0.197157i
$56$		0			0
$57$	−4.59295	−	1.67170i	−0.608351	−	0.221422i
$58$		0			0
$59$	−6.37374	+	5.34821i	−0.829791	+	0.696277i	−0.955243	−	0.295823i	$-0.904406\pi$
$59$	−6.37374	+	5.34821i	−0.829791	+	0.696277i	0.125452	+	0.992100i	$0.459962\pi$
$60$		0			0
$61$	8.18466	−	2.97897i	1.04794	−	0.381418i	0.240054	−	0.970760i	$-0.422835\pi$
$61$	8.18466	−	2.97897i	1.04794	−	0.381418i	0.807884	+	0.589341i	$0.200613\pi$
$62$		0			0
$63$	0.286858	+	0.496853i	0.0361407	+	0.0625976i
$64$		0			0
$65$	−5.92239	−	2.15557i	−0.734582	−	0.267366i
$66$		0			0
$67$	3.03185	+	2.54402i	0.370399	+	0.310802i	0.808920	−	0.587919i	$-0.200053\pi$
$67$	3.03185	+	2.54402i	0.370399	+	0.310802i	−0.438520	+	0.898721i	$0.644497\pi$
$68$		0			0
$69$	0.439492	+	0.368778i	0.0529086	+	0.0443956i
$70$		0			0
$71$	−0.365286	+	2.07164i	−0.0433514	+	0.245858i	−0.998781	−	0.0493609i	$-0.984282\pi$
$71$	−0.365286	+	2.07164i	−0.0433514	+	0.245858i	0.955430	+	0.295219i	$0.0953927\pi$
$72$		0			0
$73$	11.2951			1.32199			0.660997	−	0.750388i	$-0.270134\pi$
$73$	11.2951			1.32199			0.660997	+	0.750388i	$0.270134\pi$
$74$		0			0
$75$	−3.21703			−0.371471
$76$		0			0
$77$	0.110774	−	0.628230i	0.0126239	−	0.0715935i
$78$		0			0
$79$	6.08402	+	5.10510i	0.684506	+	0.574368i	0.917319	−	0.398153i	$-0.130349\pi$
$79$	6.08402	+	5.10510i	0.684506	+	0.574368i	−0.232813	+	0.972521i	$0.574793\pi$
$80$		0			0
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$		0			0
$83$	−5.49447	−	1.99982i	−0.603097	−	0.219509i	0.0223832	−	0.999749i	$-0.492875\pi$
$83$	−5.49447	−	1.99982i	−0.603097	−	0.219509i	−0.625480	+	0.780240i	$0.715097\pi$
$84$		0			0
$85$	2.33808	+	4.04968i	0.253601	+	0.439249i
$86$		0			0
$87$	−6.54129	+	2.38083i	−0.701300	+	0.255252i
$88$		0			0
$89$	9.94019	−	8.34081i	1.05366	−	0.884124i	0.0601842	−	0.998187i	$-0.480831\pi$
$89$	9.94019	−	8.34081i	1.05366	−	0.884124i	0.993473	+	0.114064i	$0.0363868\pi$
$90$		0			0
$91$	−2.54461	−	0.926163i	−0.266748	−	0.0970883i
$92$		0			0
$93$	−1.15741	+	6.56400i	−0.120018	+	0.680655i
$94$		0			0
$95$	−4.99956	+	4.19513i	−0.512944	+	0.430411i
$96$		0			0
$97$	8.73161	−	15.1236i	0.886561	−	1.53557i	0.0426462	−	0.999090i	$-0.486421\pi$
$97$	8.73161	−	15.1236i	0.886561	−	1.53557i	0.843914	−	0.536478i	$-0.180245\pi$
$98$		0			0
$99$	−0.193081	−	1.09502i	−0.0194054	−	0.110054i
$100$		0			0
$101$	−5.41075	+	9.37169i	−0.538390	+	0.932518i	0.460601	+	0.887607i	$0.347634\pi$
$101$	−5.41075	+	9.37169i	−0.538390	+	0.932518i	−0.998991	+	0.0449109i	$0.985700\pi$
$102$		0			0
$103$	−5.72469	−	9.91546i	−0.564071	−	0.976999i	−0.997135	−	0.0756362i	$-0.975901\pi$
$103$	−5.72469	−	9.91546i	−0.564071	−	0.976999i	0.433065	−	0.901363i	$-0.357432\pi$
$104$		0			0
$105$	0.766071			0.0747609
$106$		0			0
$107$	2.60311	−	0.947456i	0.251653	−	0.0915940i	−0.213114	−	0.977027i	$-0.568361\pi$
$107$	2.60311	−	0.947456i	0.251653	−	0.0915940i	0.464766	+	0.885433i	$0.346138\pi$
$108$		0			0
$109$	1.85069	+	10.4958i	0.177264	+	1.00532i	0.935498	+	0.353333i	$0.114952\pi$
$109$	1.85069	+	10.4958i	0.177264	+	1.00532i	−0.758233	+	0.651983i	$0.773937\pi$
$110$		0			0
$111$	−1.31455	+	5.93902i	−0.124772	+	0.563707i
$112$		0			0
$113$	−2.18502	−	12.3918i	−0.205549	−	1.16573i	−0.896574	−	0.442895i	$-0.853952\pi$
$113$	−2.18502	−	12.3918i	−0.205549	−	1.16573i	0.691025	−	0.722831i	$-0.257160\pi$
$114$		0			0
$115$	0.719871	−	0.262012i	0.0671284	−	0.0244327i
$116$		0			0
$117$	−4.71997			−0.436361
$118$		0			0
$119$	1.00458	+	1.73998i	0.0920897	+	0.159504i
$120$		0			0
$121$	4.88183	−	8.45557i	0.443802	−	0.768688i
$122$		0			0
$123$	−2.19153e−5	0	0.000124288i	−1.97603e−6	0	1.12066e-5i
$124$		0			0
$125$	−5.48601	+	9.50206i	−0.490684	+	0.849890i
$126$		0			0
$127$	3.18236	−	2.67032i	0.282389	−	0.236952i	−0.490580	−	0.871396i	$-0.663215\pi$
$127$	3.18236	−	2.67032i	0.282389	−	0.236952i	0.772969	+	0.634444i	$0.218771\pi$
$128$		0			0
$129$	−0.272734	+	1.54675i	−0.0240129	+	0.136184i
$130$		0			0
$131$	10.6012	+	3.85850i	0.926227	+	0.337119i	0.760713	−	0.649088i	$-0.224849\pi$
$131$	10.6012	+	3.85850i	0.926227	+	0.337119i	0.165514	+	0.986207i	$0.447072\pi$
$132$		0			0
$133$	−2.14811	+	1.80248i	−0.186265	+	0.156295i
$134$		0			0
$135$	1.25475	−	0.456692i	0.107992	−	0.0393058i
$136$		0			0
$137$	−4.08044	−	7.06753i	−0.348615	−	0.603820i	0.637388	−	0.770543i	$-0.280015\pi$
$137$	−4.08044	−	7.06753i	−0.348615	−	0.603820i	−0.986004	+	0.166723i	$0.946681\pi$
$138$		0			0
$139$	14.4472	+	5.25836i	1.22540	+	0.446008i	0.872019	−	0.489472i	$-0.162810\pi$
$139$	14.4472	+	5.25836i	1.22540	+	0.446008i	0.353379	+	0.935480i	$0.385033\pi$
$140$		0			0
$141$	3.73853	+	3.13700i	0.314841	+	0.264183i
$142$		0			0
$143$	4.02034	+	3.37347i	0.336198	+	0.282104i
$144$		0			0
$145$	−1.61406	+	9.15379i	−0.134040	+	0.760181i
$146$		0			0
$147$	−6.67085			−0.550202
$148$		0			0
$149$	10.3714			0.849656			0.424828	−	0.905274i	$-0.360335\pi$
$149$	10.3714			0.849656			0.424828	+	0.905274i	$0.360335\pi$
$150$		0			0
$151$	−0.151656	+	0.860087i	−0.0123416	+	0.0699929i	−0.990357	−	0.138542i	$-0.955758\pi$
$151$	−0.151656	+	0.860087i	−0.0123416	+	0.0699929i	0.978015	+	0.208535i	$0.0668695\pi$
$152$		0			0
$153$	2.68270	+	2.25105i	0.216883	+	0.181987i
$154$		0			0
$155$	6.81778	+	5.72080i	0.547618	+	0.459506i
$156$		0			0
$157$	13.4546	+	4.89707i	1.07379	+	0.390829i	0.817594	−	0.575795i	$-0.195307\pi$
$157$	13.4546	+	4.89707i	1.07379	+	0.390829i	0.256199	+	0.966624i	$0.417530\pi$
$158$		0			0
$159$	−0.710881	−	1.23128i	−0.0563765	−	0.0976470i
$160$		0			0
$161$	0.309300	−	0.112576i	0.0243763	−	0.00887223i
$162$		0			0
$163$	0.210856	−	0.176930i	0.0165156	−	0.0138582i	−0.634492	−	0.772929i	$-0.718791\pi$
$163$	0.210856	−	0.176930i	0.0165156	−	0.0138582i	0.651008	+	0.759071i	$0.274346\pi$
$164$		0			0
$165$	−1.39517	−	0.507802i	−0.108614	−	0.0395323i
$166$		0			0
$167$	0.0934174	−	0.529796i	0.00722885	−	0.0409969i	−0.980980	−	0.194109i	$-0.937818\pi$
$167$	0.0934174	−	0.529796i	0.00722885	−	0.0409969i	0.988209	+	0.153112i	$0.0489296\pi$
$168$		0			0
$169$	7.10742	−	5.96383i	0.546725	−	0.458756i
$170$		0			0
$171$	−2.44386	+	4.23288i	−0.186886	+	0.323697i
$172$		0			0
$173$	0.436266	+	2.47419i	0.0331687	+	0.188109i	0.996890	−	0.0787999i	$-0.0251088\pi$
$173$	0.436266	+	2.47419i	0.0331687	+	0.188109i	−0.963722	+	0.266909i	$0.913998\pi$
$174$		0			0
$175$	−0.922831	+	1.59839i	−0.0697595	+	0.120827i
$176$		0			0
$177$	4.16017	+	7.20562i	0.312697	+	0.541607i
$178$		0			0
$179$	1.65283			0.123538			0.0617692	−	0.998090i	$-0.480326\pi$
$179$	1.65283			0.123538			0.0617692	+	0.998090i	$0.480326\pi$
$180$		0			0
$181$	−6.43940	+	2.34375i	−0.478637	+	0.174210i	−0.570061	−	0.821602i	$-0.693080\pi$
$181$	−6.43940	+	2.34375i	−0.478637	+	0.174210i	0.0914239	+	0.995812i	$0.470858\pi$
$182$		0			0
$183$	−1.51246	−	8.57761i	−0.111805	−	0.634075i
$184$		0			0
$185$	5.99015	+	5.48526i	0.440404	+	0.403284i
$186$		0			0
$187$	−0.676174	−	3.83477i	−0.0494467	−	0.280426i
$188$		0			0
$189$	0.539117	−	0.196222i	0.0392150	−	0.0142731i
$190$		0			0
$191$	−19.9383			−1.44269			−0.721343	−	0.692578i	$-0.756475\pi$
$191$	−19.9383			−1.44269			−0.721343	+	0.692578i	$0.756475\pi$
$192$		0			0
$193$	6.83353	+	11.8360i	0.491889	+	0.851976i	0.999956	−	0.00934108i	$-0.00297340\pi$
$193$	6.83353	+	11.8360i	0.491889	+	0.851976i	−0.508068	+	0.861317i	$0.669640\pi$
$194$		0			0
$195$	−3.15124	+	5.45810i	−0.225665	+	0.390863i
$196$		0			0
$197$	−1.38303	−	7.84356i	−0.0985369	−	0.558831i	−0.993606	−	0.112903i	$-0.963985\pi$
$197$	−1.38303	−	7.84356i	−0.0985369	−	0.558831i	0.895069	−	0.445928i	$-0.147126\pi$
$198$		0			0
$199$	−1.04585	+	1.81146i	−0.0741381	+	0.128411i	−0.900711	−	0.434419i	$-0.856954\pi$
$199$	−1.04585	+	1.81146i	−0.0741381	+	0.128411i	0.826573	+	0.562829i	$0.190287\pi$
$200$		0			0
$201$	3.03185	−	2.54402i	0.213850	−	0.179442i
$202$		0			0
$203$	−0.693497	+	3.93302i	−0.0486740	+	0.276044i
$204$		0			0
$205$	−0.000158356	0	5.76369e-5i	−1.10601e−5	0	4.02553e-6i
$206$		0			0
$207$	0.439492	−	0.368778i	0.0305468	−	0.0256318i
$208$		0			0
$209$	5.10695	−	1.85878i	0.353255	−	0.128574i
$210$		0			0
$211$	−2.65361	−	4.59619i	−0.182682	−	0.316415i	0.760111	−	0.649793i	$-0.225145\pi$
$211$	−2.65361	−	4.59619i	−0.182682	−	0.316415i	−0.942793	+	0.333379i	$0.891811\pi$
$212$		0			0
$213$	1.97673	+	0.719472i	0.135444	+	0.0492974i
$214$		0			0
$215$	1.60655	+	1.34806i	0.109566	+	0.0919368i
$216$		0			0
$217$	2.92933	+	2.45800i	0.198856	+	0.166860i
$218$		0			0
$219$	1.96138	−	11.1235i	0.132538	−	0.751658i
$220$		0			0
$221$	−16.5294			−1.11189
$222$		0			0
$223$	4.88828			0.327343			0.163672	−	0.986515i	$-0.447666\pi$
$223$	4.88828			0.327343			0.163672	+	0.986515i	$0.447666\pi$
$224$		0			0
$225$	−0.558631	+	3.16816i	−0.0372421	+	0.211210i
$226$		0			0
$227$	12.9378	+	10.8561i	0.858711	+	0.720544i	0.961690	−	0.274139i	$-0.0883929\pi$
$227$	12.9378	+	10.8561i	0.858711	+	0.720544i	−0.102979	+	0.994684i	$0.532837\pi$
$228$		0			0
$229$	3.03418	+	2.54598i	0.200504	+	0.168243i	0.737511	−	0.675335i	$-0.236001\pi$
$229$	3.03418	+	2.54598i	0.200504	+	0.168243i	−0.537007	+	0.843578i	$0.680445\pi$
$230$		0			0
$231$	−0.599450	−	0.218182i	−0.0394409	−	0.0143553i
$232$		0			0
$233$	−0.717978	−	1.24358i	−0.0470363	−	0.0814693i	0.841549	−	0.540181i	$-0.181644\pi$
$233$	−0.717978	−	1.24358i	−0.0470363	−	0.0814693i	−0.888585	+	0.458712i	$0.848311\pi$
$234$		0			0
$235$	6.12357	−	2.22880i	0.399458	−	0.145391i
$236$		0			0
$237$	6.08402	−	5.10510i	0.395199	−	0.331612i
$238$		0			0
$239$	22.3200	+	8.12382i	1.44376	+	0.525486i	0.940842	−	0.338846i	$-0.110037\pi$
$239$	22.3200	+	8.12382i	1.44376	+	0.525486i	0.502920	+	0.864333i	$0.332259\pi$
$240$		0			0
$241$	−1.76734	+	10.0231i	−0.113844	+	0.645643i	0.873472	+	0.486875i	$0.161863\pi$
$241$	−1.76734	+	10.0231i	−0.113844	+	0.645643i	−0.987316	+	0.158768i	$0.949248\pi$
$242$		0			0
$243$	0.766044	−	0.642788i	0.0491418	−	0.0412348i
$244$		0			0
$245$	−4.45372	+	7.71408i	−0.284538	+	0.492834i
$246$		0			0
$247$	−4.00604	−	22.7194i	−0.254898	−	1.44560i
$248$		0			0
$249$	−2.92355	+	5.06373i	−0.185272	+	0.320901i
$250$		0			0
$251$	15.0381	+	26.0467i	0.949194	+	1.64405i	0.747129	+	0.664679i	$0.231432\pi$
$251$	15.0381	+	26.0467i	0.949194	+	1.64405i	0.202065	+	0.979372i	$0.435235\pi$
$252$		0			0
$253$	−0.637922			−0.0401058
$254$		0			0
$255$	4.39416	−	1.59934i	0.275173	−	0.100155i
$256$		0			0
$257$	−2.20973	−	12.5320i	−0.137839	−	0.781724i	−0.972841	−	0.231476i	$-0.925644\pi$
$257$	−2.20973	−	12.5320i	−0.137839	−	0.781724i	0.835002	−	0.550248i	$-0.185467\pi$
$258$		0			0
$259$	2.57373	+	2.35680i	0.159924	+	0.146444i
$260$		0			0
$261$	1.20878	+	6.85534i	0.0748217	+	0.424335i
$262$		0			0
$263$	−15.7099	+	5.71793i	−0.968713	+	0.352583i	−0.777442	−	0.628955i	$-0.783483\pi$
$263$	−15.7099	+	5.71793i	−0.968713	+	0.352583i	−0.191271	+	0.981537i	$0.561261\pi$
$264$		0			0
$265$	−1.89845			−0.116621
$266$		0			0
$267$	−6.48800	−	11.2375i	−0.397059	−	0.687726i
$268$		0			0
$269$	−10.8668	+	18.8219i	−0.662562	+	1.14759i	0.317379	+	0.948299i	$0.397197\pi$
$269$	−10.8668	+	18.8219i	−0.662562	+	1.14759i	−0.979940	+	0.199291i	$0.936136\pi$
$270$		0			0
$271$	4.08626	+	23.1743i	0.248223	+	1.40774i	0.812888	+	0.582420i	$0.197894\pi$
$271$	4.08626	+	23.1743i	0.248223	+	1.40774i	−0.564665	+	0.825320i	$0.690995\pi$
$272$		0			0
$273$	−1.35396	+	2.34513i	−0.0819454	+	0.141934i
$274$		0			0
$275$	2.74018	−	2.29929i	0.165239	−	0.138652i
$276$		0			0
$277$	−2.03053	+	11.5157i	−0.122003	+	0.691913i	0.861040	+	0.508537i	$0.169814\pi$
$277$	−2.03053	+	11.5157i	−0.122003	+	0.691913i	−0.983043	+	0.183376i	$0.941297\pi$
$278$		0			0
$279$	6.26330	+	2.27965i	0.374974	+	0.136479i
$280$		0			0
$281$	−6.19016	+	5.19416i	−0.369274	+	0.309858i	−0.808474	−	0.588532i	$-0.799706\pi$
$281$	−6.19016	+	5.19416i	−0.369274	+	0.309858i	0.439200	+	0.898389i	$0.355262\pi$
$282$		0			0
$283$	12.2142	−	4.44559i	0.726057	−	0.264263i	0.0475620	−	0.998868i	$-0.484855\pi$
$283$	12.2142	−	4.44559i	0.726057	−	0.264263i	0.678495	+	0.734605i	$0.262633\pi$
$284$		0			0
$285$	3.26323	+	5.65208i	0.193297	+	0.334800i
$286$		0			0
$287$	−6.80393e−5	0	2.47643e-5i	−4.01623e−6	0	1.46179e-6i
$288$		0			0
$289$	−3.62792	−	3.04418i	−0.213407	−	0.179070i
$290$		0			0
$291$	−13.3776	−	11.2251i	−0.784209	−	0.658029i
$292$		0			0
$293$	−0.749290	+	4.24944i	−0.0437740	+	0.248255i	−0.998841	−	0.0481359i	$-0.984672\pi$
$293$	−0.749290	+	4.24944i	−0.0437740	+	0.248255i	0.955067	+	0.296391i	$0.0957830\pi$
$294$		0			0
$295$	11.1100			0.646847
$296$		0			0
$297$	−1.11191			−0.0645197
$298$		0			0
$299$	−0.470225	+	2.66678i	−0.0271938	+	0.154224i
$300$		0			0
$301$	0.690272	+	0.579207i	0.0397866	+	0.0333849i
$302$		0			0
$303$	8.28975	+	6.95592i	0.476233	+	0.399607i
$304$		0			0
$305$	−10.9288	−	3.97776i	−0.625781	−	0.227766i
$306$		0			0
$307$	2.03444	+	3.52375i	0.116111	+	0.201111i	0.918224	−	0.396063i	$-0.129624\pi$
$307$	2.03444	+	3.52375i	0.116111	+	0.201111i	−0.802112	+	0.597174i	$0.796290\pi$
$308$		0			0
$309$	−10.7589	+	3.91592i	−0.612052	+	0.222769i
$310$		0			0
$311$	15.6197	−	13.1065i	0.885710	−	0.743199i	−0.0816350	−	0.996662i	$-0.526014\pi$
$311$	15.6197	−	13.1065i	0.885710	−	0.743199i	0.967345	+	0.253463i	$0.0815697\pi$
$312$		0			0
$313$	−11.1046	−	4.04174i	−0.627668	−	0.228452i	0.00854795	−	0.999963i	$-0.497279\pi$
$313$	−11.1046	−	4.04174i	−0.627668	−	0.228452i	−0.636216	+	0.771511i	$0.719501\pi$
$314$		0			0
$315$	0.133027	−	0.754433i	0.00749521	−	0.0425075i
$316$		0			0
$317$	4.18872	−	3.51476i	0.235262	−	0.197408i	−0.517533	−	0.855663i	$-0.673150\pi$
$317$	4.18872	−	3.51476i	0.235262	−	0.197408i	0.752795	+	0.658255i	$0.228705\pi$
$318$		0			0
$319$	3.87006	−	6.70314i	0.216682	−	0.375304i
$320$		0			0
$321$	−0.481036	−	2.72809i	−0.0268488	−	0.152267i
$322$		0			0
$323$	−8.55842	+	14.8236i	−0.476203	+	0.824808i
$324$		0			0
$325$	−7.59213	−	13.1500i	−0.421136	−	0.729429i
$326$		0			0
$327$	10.6577			0.589373
$328$		0			0
$329$	2.63105	−	0.957625i	0.145055	−	0.0527956i
$330$		0			0
$331$	−6.00393	−	34.0500i	−0.330006	−	1.87156i	−0.471865	−	0.881671i	$-0.656419\pi$
$331$	−6.00393	−	34.0500i	−0.330006	−	1.87156i	0.141859	−	0.989887i	$-0.454692\pi$
$332$		0			0
$333$	5.62052	+	2.32588i	0.308003	+	0.127458i
$334$		0			0
$335$	−0.917690	−	5.20448i	−0.0501388	−	0.284351i
$336$		0			0
$337$	−6.63327	+	2.41431i	−0.361337	+	0.131516i	−0.516308	−	0.856403i	$-0.672694\pi$
$337$	−6.63327	+	2.41431i	−0.361337	+	0.131516i	0.154971	+	0.987919i	$0.450472\pi$
$338$		0			0
$339$	−12.5830			−0.683415
$340$		0			0
$341$	−3.70559	−	6.41827i	−0.200669	−	0.347569i
$342$		0			0
$343$	−3.92159	+	6.79240i	−0.211746	+	0.366755i
$344$		0			0
$345$	−0.133027	−	0.754433i	−0.00716193	−	0.0406173i
$346$		0			0
$347$	11.9984	−	20.7819i	0.644110	−	1.11563i	−0.340396	−	0.940282i	$-0.610561\pi$
$347$	11.9984	−	20.7819i	0.644110	−	1.11563i	0.984506	−	0.175350i	$-0.0561056\pi$
$348$		0			0
$349$	−8.53763	+	7.16393i	−0.457009	+	0.383476i	−0.842029	−	0.539432i	$-0.818639\pi$
$349$	−8.53763	+	7.16393i	−0.457009	+	0.383476i	0.385020	+	0.922908i	$0.374195\pi$
$350$		0			0
$351$	−0.819613	+	4.64826i	−0.0437477	+	0.248106i
$352$		0			0
$353$	4.59382	+	1.67201i	0.244504	+	0.0889923i	0.461366	−	0.887210i	$-0.347360\pi$
$353$	4.59382	+	1.67201i	0.244504	+	0.0889923i	−0.216861	+	0.976202i	$0.569582\pi$
$354$		0			0
$355$	2.15173	−	1.80552i	0.114202	−	0.0958270i
$356$		0			0
$357$	1.88799	−	0.687174i	0.0999232	−	0.0363691i
$358$		0			0
$359$	−15.6162	−	27.0481i	−0.824193	−	1.42754i	−0.902534	−	0.430618i	$-0.858296\pi$
$359$	−15.6162	−	27.0481i	−0.824193	−	1.42754i	0.0783413	−	0.996927i	$-0.475038\pi$
$360$		0			0
$361$	−4.59485	−	1.67239i	−0.241834	−	0.0880204i
$362$		0			0
$363$	−7.47939	−	6.27595i	−0.392566	−	0.329402i
$364$		0			0
$365$	−11.5536	−	9.69462i	−0.604743	−	0.507439i
$366$		0			0
$367$	−3.29483	+	18.6859i	−0.171988	+	0.975395i	0.769574	+	0.638557i	$0.220469\pi$
$367$	−3.29483	+	18.6859i	−0.171988	+	0.975395i	−0.941563	+	0.336838i	$0.890643\pi$
$368$		0			0
$369$	−0.000126205	0		−6.56997e−6	0
$370$		0			0
$371$	−0.815688			−0.0423484
$372$		0			0
$373$	0.160800	−	0.911942i	0.00832591	−	0.0472186i	−0.980362	−	0.197208i	$-0.936813\pi$
$373$	0.160800	−	0.911942i	0.00832591	−	0.0472186i	0.988688	+	0.149989i	$0.0479238\pi$
$374$		0			0
$375$	8.40506	+	7.05268i	0.434036	+	0.364199i
$376$		0			0
$377$	−25.1693	−	21.1195i	−1.29628	−	1.08771i
$378$		0			0
$379$	−11.1108	−	4.04399i	−0.570722	−	0.207726i	0.0405077	−	0.999179i	$-0.487102\pi$
$379$	−11.1108	−	4.04399i	−0.570722	−	0.207726i	−0.611229	+	0.791454i	$0.709325\pi$
$380$		0			0
$381$	−2.07714	−	3.59771i	−0.106415	−	0.184316i
$382$		0			0
$383$	15.8969	−	5.78600i	0.812294	−	0.295651i	0.0977228	−	0.995214i	$-0.468844\pi$
$383$	15.8969	−	5.78600i	0.812294	−	0.295651i	0.714571	+	0.699563i	$0.246622\pi$
$384$		0			0
$385$	−0.652519	+	0.547529i	−0.0332555	+	0.0279046i
$386$		0			0
$387$	1.47589	+	0.537181i	0.0750238	+	0.0273064i
$388$		0			0
$389$	−1.02430	+	5.80908i	−0.0519339	+	0.294532i	−0.999702	−	0.0244297i	$-0.992223\pi$
$389$	−1.02430	+	5.80908i	−0.0519339	+	0.294532i	0.947768	+	0.318962i	$0.103334\pi$
$390$		0			0
$391$	1.53911	−	1.29146i	0.0778360	−	0.0653121i
$392$		0			0
$393$	5.64076	−	9.77008i	0.284538	−	0.492835i
$394$		0			0
$395$	−1.84153	−	10.4438i	−0.0926574	−	0.525486i
$396$		0			0
$397$	0.0230389	−	0.0399046i	0.00115629	−	0.00200275i	−0.865447	−	0.501001i	$-0.832965\pi$
$397$	0.0230389	−	0.0399046i	0.00115629	−	0.00200275i	0.866603	+	0.498998i	$0.166299\pi$
$398$		0			0
$399$	1.40208	+	2.42847i	0.0701918	+	0.121576i
$400$		0			0
$401$	33.8111			1.68845			0.844223	−	0.535992i	$-0.180062\pi$
$401$	33.8111			1.68845			0.844223	+	0.535992i	$0.180062\pi$
$402$		0			0
$403$	−29.5625	+	10.7599i	−1.47262	+	0.535988i
$404$		0			0
$405$	−0.231869	−	1.31499i	−0.0115217	−	0.0653425i
$406$		0			0
$407$	−3.12505	−	5.99824i	−0.154903	−	0.297322i
$408$		0			0
$409$	1.15666	+	6.55975i	0.0571932	+	0.324359i	0.999959	−	0.00909783i	$-0.00289597\pi$
$409$	1.15666	+	6.55975i	0.0571932	+	0.324359i	−0.942765	+	0.333457i	$0.891785\pi$
$410$		0			0
$411$	−7.66872	+	2.79118i	−0.378270	+	0.137679i
$412$		0			0
$413$	4.77351			0.234889
$414$		0			0
$415$	3.90375	+	6.76150i	0.191628	+	0.331909i
$416$		0			0
$417$	7.68721	−	13.3146i	0.376444	−	0.652021i
$418$		0			0
$419$	3.19655	+	18.1285i	0.156162	+	0.885637i	0.957716	+	0.287715i	$0.0928957\pi$
$419$	3.19655	+	18.1285i	0.156162	+	0.885637i	−0.801554	+	0.597922i	$0.795993\pi$
$420$		0			0
$421$	−13.7222	+	23.7675i	−0.668777	+	1.15836i	0.309469	+	0.950909i	$0.399849\pi$
$421$	−13.7222	+	23.7675i	−0.668777	+	1.15836i	−0.978246	+	0.207446i	$0.933485\pi$
$422$		0			0
$423$	3.73853	−	3.13700i	0.181774	−	0.152526i
$424$		0			0
$425$	−1.95633	+	11.0949i	−0.0948961	+	0.538183i
$426$		0			0
$427$	−4.69567	−	1.70908i	−0.227239	−	0.0827084i
$428$		0			0
$429$	4.02034	−	3.37347i	0.194104	−	0.162873i
$430$		0			0
$431$	−11.7328	+	4.27038i	−0.565148	+	0.205697i	−0.608764	−	0.793351i	$-0.708334\pi$
$431$	−11.7328	+	4.27038i	−0.565148	+	0.205697i	0.0436158	+	0.999048i	$0.486112\pi$
$432$		0			0
$433$	−18.3961	−	31.8630i	−0.884060	−	1.53124i	−0.846787	−	0.531932i	$-0.821466\pi$
$433$	−18.3961	−	31.8630i	−0.884060	−	1.53124i	−0.0372734	−	0.999305i	$-0.511867\pi$
$434$		0			0
$435$	8.73445	+	3.17908i	0.418785	+	0.152425i
$436$		0			0
$437$	2.14811	+	1.80248i	0.102758	+	0.0862243i
$438$		0			0
$439$	−16.6692	−	13.9871i	−0.795577	−	0.667568i	0.151542	−	0.988451i	$-0.451576\pi$
$439$	−16.6692	−	13.9871i	−0.795577	−	0.667568i	−0.947119	+	0.320883i	$0.896021\pi$
$440$		0			0
$441$	−1.15838	+	6.56950i	−0.0551610	+	0.312834i
$442$		0			0
$443$	19.4612			0.924628			0.462314	−	0.886716i	$-0.347019\pi$
$443$	19.4612			0.924628			0.462314	+	0.886716i	$0.347019\pi$
$444$		0			0
$445$	−17.3266			−0.821358
$446$		0			0
$447$	1.80097	−	10.2138i	0.0851830	−	0.483097i
$448$		0			0
$449$	−5.39860	−	4.52997i	−0.254776	−	0.213782i	0.506450	−	0.862269i	$-0.330958\pi$
$449$	−5.39860	−	4.52997i	−0.254776	−	0.213782i	−0.761226	+	0.648487i	$0.775402\pi$
$450$		0			0
$451$	0.000107498	0	9.02017e-5i	5.06189e−6	0	4.24743e-6i
$452$		0			0
$453$	0.820685	+	0.298705i	0.0385592	+	0.0140344i
$454$		0			0
$455$	1.80792	+	3.13140i	0.0847564	+	0.146802i
$456$		0			0
$457$	21.3240	−	7.76130i	0.997495	−	0.363058i	0.208877	−	0.977942i	$-0.433019\pi$
$457$	21.3240	−	7.76130i	0.997495	−	0.363058i	0.788618	+	0.614883i	$0.210797\pi$
$458$		0			0
$459$	2.68270	−	2.25105i	0.125218	−	0.105070i
$460$		0			0
$461$	−37.8426	−	13.7736i	−1.76251	−	0.641500i	−0.762523	−	0.646961i	$-0.776039\pi$
$461$	−37.8426	−	13.7736i	−1.76251	−	0.641500i	−0.999985	+	0.00546102i	$0.998262\pi$
$462$		0			0
$463$	1.75781	−	9.96906i	0.0816925	−	0.463301i	−0.916329	−	0.400427i	$-0.868862\pi$
$463$	1.75781	−	9.96906i	0.0816925	−	0.463301i	0.998021	−	0.0628749i	$-0.0200269\pi$
$464$		0			0
$465$	6.81778	−	5.72080i	0.316167	−	0.265296i
$466$		0			0
$467$	9.09671	−	15.7560i	0.420945	−	0.729099i	−0.575087	−	0.818092i	$-0.695032\pi$
$467$	9.09671	−	15.7560i	0.420945	−	0.729099i	0.996032	+	0.0889935i	$0.0283650\pi$
$468$		0			0
$469$	−0.394295	−	2.23616i	−0.0182068	−	0.103256i
$470$		0			0
$471$	7.15904	−	12.3998i	0.329871	−	0.571354i
$472$		0			0
$473$	−0.873191	−	1.51241i	−0.0401494	−	0.0695407i
$474$		0			0
$475$	−15.7239			−0.721463
$476$		0			0
$477$	−1.33602	+	0.486271i	−0.0611721	+	0.0222648i
$478$		0			0
$479$	−7.05042	−	39.9849i	−0.322142	−	1.82696i	−0.529044	−	0.848595i	$-0.677449\pi$
$479$	−7.05042	−	39.9849i	−0.322142	−	1.82696i	0.206902	−	0.978362i	$-0.433662\pi$
$480$		0			0
$481$	−27.3787	+	8.64260i	−1.24836	+	0.394068i
$482$		0			0
$483$	−0.0571563	−	0.324150i	−0.00260070	−	0.0147493i
$484$		0			0
$485$	−21.9120	+	7.97532i	−0.994973	+	0.362141i
$486$		0			0
$487$	10.3000			0.466739			0.233369	−	0.972388i	$-0.425025\pi$
$487$	10.3000			0.466739			0.233369	+	0.972388i	$0.425025\pi$
$488$		0			0
$489$	−0.137627	−	0.238377i	−0.00622370	−	0.0107798i
$490$		0			0
$491$	16.9425	−	29.3454i	0.764606	−	1.32434i	−0.175848	−	0.984417i	$-0.556267\pi$
$491$	16.9425	−	29.3454i	0.764606	−	1.32434i	0.940454	−	0.339920i	$-0.110400\pi$
$492$		0			0
$493$	4.23317	+	24.0075i	0.190652	+	1.08124i
$494$		0			0
$495$	−0.742356	+	1.28580i	−0.0333664	+	0.0577924i
$496$		0			0
$497$	0.924514	−	0.775759i	0.0414701	−	0.0347976i
$498$		0			0
$499$	3.63077	−	20.5911i	0.162536	−	0.921785i	−0.789034	−	0.614350i	$-0.789418\pi$
$499$	3.63077	−	20.5911i	0.162536	−	0.921785i	0.951569	−	0.307435i	$-0.0994706\pi$
$500$		0			0
$501$	−0.505526	−	0.183996i	−0.0225852	−	0.00822035i
$502$		0			0
$503$	17.4438	−	14.6371i	0.777782	−	0.652636i	−0.164907	−	0.986309i	$-0.552733\pi$
$503$	17.4438	−	14.6371i	0.777782	−	0.652636i	0.942689	+	0.333673i	$0.108288\pi$
$504$		0			0
$505$	13.5783	−	4.94209i	0.604226	−	0.219920i
$506$		0			0
$507$	−4.63904	−	8.03505i	−0.206027	−	0.356849i
$508$		0			0
$509$	41.2455	+	15.0121i	1.82817	+	0.665401i	0.993385	+	0.114830i	$0.0366322\pi$
$509$	41.2455	+	15.0121i	1.82817	+	0.665401i	0.834788	+	0.550571i	$0.185590\pi$
$510$		0			0
$511$	−4.96412	−	4.16539i	−0.219600	−	0.184266i
$512$		0			0
$513$	3.74420	+	3.14176i	0.165311	+	0.138712i
$514$		0			0
$515$	−2.65475	+	15.0559i	−0.116982	+	0.663441i
$516$		0			0
$517$	−5.42647			−0.238656
$518$		0			0
$519$	2.51236			0.110280
$520$		0			0
$521$	−0.502523	+	2.84995i	−0.0220159	+	0.124858i	−0.993835	−	0.110870i	$-0.964636\pi$
$521$	−0.502523	+	2.84995i	−0.0220159	+	0.124858i	0.971819	+	0.235728i	$0.0757475\pi$
$522$		0			0
$523$	−34.1497	−	28.6550i	−1.49326	−	1.25300i	−0.890424	−	0.455132i	$-0.849592\pi$
$523$	−34.1497	−	28.6550i	−1.49326	−	1.25300i	−0.602838	−	0.797864i	$-0.705964\pi$
$524$		0			0
$525$	1.41386	+	1.18637i	0.0617059	+	0.0517774i
$526$		0			0
$527$	21.9341	+	7.98337i	0.955466	+	0.347761i
$528$		0			0
$529$	11.3354	+	19.6335i	0.492845	+	0.853632i
$530$		0			0
$531$	7.81855	−	2.84572i	0.339296	−	0.123494i
$532$		0			0
$533$	0.000456320	0	0.000382898i	1.97654e−5	0	1.65852e-5i
$534$		0			0
$535$	−3.47588	−	1.26512i	−0.150276	−	0.0546958i
$536$		0			0
$537$	0.287011	−	1.62772i	0.0123854	−	0.0702413i
$538$		0			0
$539$	5.68205	−	4.76781i	0.244743	−	0.205364i
$540$		0			0
$541$	−6.87807	+	11.9132i	−0.295711	+	0.512187i	−0.975150	−	0.221545i	$-0.928890\pi$
$541$	−6.87807	+	11.9132i	−0.295711	+	0.512187i	0.679439	+	0.733732i	$0.262223\pi$
$542$		0			0
$543$	1.18995	+	6.74856i	0.0510658	+	0.289608i
$544$		0			0
$545$	7.11552	−	12.3244i	0.304795	−	0.527921i
$546$		0			0
$547$	0.803595	+	1.39187i	0.0343592	+	0.0595120i	0.882694	−	0.469949i	$-0.155728\pi$
$547$	0.803595	+	1.39187i	0.0343592	+	0.0595120i	−0.848334	+	0.529461i	$0.822394\pi$
$548$		0			0
$549$	−8.70993			−0.371731
$550$		0			0
$551$	−31.9719	+	11.6368i	−1.36205	+	0.495746i
$552$		0			0
$553$	−0.791232	−	4.48730i	−0.0336466	−	0.190819i
$554$		0			0
$555$	6.44210	−	4.94664i	0.273452	−	0.209973i
$556$		0			0
$557$	−5.12227	−	29.0499i	−0.217038	−	1.23088i	−0.877335	−	0.479878i	$-0.840681\pi$
$557$	−5.12227	−	29.0499i	−0.217038	−	1.23088i	0.660298	−	0.751004i	$-0.270430\pi$
$558$		0			0
$559$	−6.96616	+	2.53548i	−0.294637	+	0.107239i
$560$		0			0
$561$	−3.89393			−0.164402
$562$		0			0
$563$	9.92512	+	17.1908i	0.418294	+	0.724506i	0.995768	−	0.0919026i	$-0.0292948\pi$
$563$	9.92512	+	17.1908i	0.418294	+	0.724506i	−0.577474	+	0.816409i	$0.695962\pi$
$564$		0			0
$565$	−8.40091	+	14.5508i	−0.353429	+	0.612157i
$566$		0			0
$567$	−0.0996248	−	0.565000i	−0.00418385	−	0.0237278i
$568$		0			0
$569$	12.9278	−	22.3917i	0.541963	−	0.938707i	−0.456828	−	0.889555i	$-0.651015\pi$
$569$	12.9278	−	22.3917i	0.541963	−	0.938707i	0.998791	−	0.0491523i	$-0.0156520\pi$
$570$		0			0
$571$	−27.9268	+	23.4334i	−1.16870	+	0.980656i	−0.999987	−	0.00500883i	$-0.998406\pi$
$571$	−27.9268	+	23.4334i	−1.16870	+	0.980656i	−0.168713	+	0.985665i	$0.553961\pi$
$572$		0			0
$573$	−3.46225	+	19.6354i	−0.144638	+	0.820281i
$574$		0			0
$575$	1.73435	+	0.631253i	0.0723276	+	0.0263251i
$576$		0			0
$577$	−13.3409	+	11.1944i	−0.555390	+	0.466028i	−0.876761	−	0.480926i	$-0.840301\pi$
$577$	−13.3409	+	11.1944i	−0.555390	+	0.466028i	0.321371	+	0.946953i	$0.395856\pi$
$578$		0			0
$579$	12.8428	−	4.67441i	0.533730	−	0.194262i
$580$		0			0
$581$	1.67729	+	2.90515i	0.0695856	+	0.120526i
$582$		0			0
$583$	1.48554	+	0.540691i	0.0615246	+	0.0223931i
$584$		0			0
$585$	4.82797	+	4.05115i	0.199612	+	0.167494i
$586$		0			0
$587$	−12.1642	−	10.2070i	−0.502072	−	0.421288i	0.356257	−	0.934388i	$-0.384053\pi$
$587$	−12.1642	−	10.2070i	−0.502072	−	0.421288i	−0.858329	+	0.513100i	$0.828497\pi$
$588$		0			0
$589$	−5.65709	+	32.0829i	−0.233096	+	1.32195i
$590$		0			0
$591$	−7.96456			−0.327618
$592$		0			0
$593$	−21.6279			−0.888152			−0.444076	−	0.895989i	$-0.646468\pi$
$593$	−21.6279			−0.888152			−0.444076	+	0.895989i	$0.646468\pi$
$594$		0			0
$595$	0.465862	−	2.64203i	0.0190985	−	0.108313i
$596$		0			0
$597$	1.60233	+	1.34451i	0.0655790	+	0.0550273i
$598$		0			0
$599$	−11.4587	−	9.61503i	−0.468191	−	0.392859i	0.377943	−	0.925829i	$-0.376632\pi$
$599$	−11.4587	−	9.61503i	−0.468191	−	0.392859i	−0.846134	+	0.532970i	$0.821076\pi$
$600$		0			0
$601$	23.9718	+	8.72503i	0.977831	+	0.355901i	0.780997	−	0.624535i	$-0.214712\pi$
$601$	23.9718	+	8.72503i	0.977831	+	0.355901i	0.196834	+	0.980437i	$0.436934\pi$
$602$		0			0
$603$	−1.97890	−	3.42755i	−0.0805870	−	0.139581i
$604$		0			0
$605$	−12.2510	+	4.45899i	−0.498072	+	0.181284i
$606$		0			0
$607$	13.7841	−	11.5662i	0.559479	−	0.469458i	−0.318657	−	0.947870i	$-0.603232\pi$
$607$	13.7841	−	11.5662i	0.559479	−	0.469458i	0.878136	+	0.478412i	$0.158787\pi$
$608$		0			0
$609$	3.75284	+	1.36592i	0.152073	+	0.0553500i
$610$		0			0
$611$	−3.99996	+	22.6849i	−0.161821	+	0.917733i
$612$		0			0
$613$	21.0990	−	17.7041i	0.852179	−	0.715063i	−0.108089	−	0.994141i	$-0.534473\pi$
$613$	21.0990	−	17.7041i	0.852179	−	0.715063i	0.960268	+	0.279078i	$0.0900288\pi$
$614$		0			0
$615$	−8.42595e−5	0	0.000145942i	−3.39767e−6	0	5.88494e-6i
$616$		0			0
$617$	−0.900790	−	5.10864i	−0.0362645	−	0.205666i	0.961292	−	0.275532i	$-0.0888540\pi$
$617$	−0.900790	−	5.10864i	−0.0362645	−	0.205666i	−0.997556	+	0.0698659i	$0.977743\pi$
$618$		0			0
$619$	−3.61423	+	6.26004i	−0.145268	+	0.251612i	−0.929473	−	0.368890i	$-0.879738\pi$
$619$	−3.61423	+	6.26004i	−0.145268	+	0.251612i	0.784205	+	0.620502i	$0.213071\pi$
$620$		0			0
$621$	−0.286858	−	0.496853i	−0.0115112	−	0.0199380i
$622$		0			0
$623$	−7.44454			−0.298259
$624$		0			0
$625$	−1.34792	+	0.490602i	−0.0539168	+	0.0196241i
$626$		0			0
$627$	−0.943727	−	5.35214i	−0.0376888	−	0.213744i
$628$		0			0
$629$	19.6831	+	8.14527i	0.784818	+	0.324773i
$630$		0			0
$631$	6.25104	+	35.4514i	0.248850	+	1.41130i	0.811379	+	0.584521i	$0.198718\pi$
$631$	6.25104	+	35.4514i	0.248850	+	1.41130i	−0.562528	+	0.826778i	$0.690171\pi$
$632$		0			0
$633$	−4.98716	+	1.81518i	−0.198222	+	0.0721469i
$634$		0			0
$635$	−5.54712			−0.220131
$636$		0			0
$637$	−15.7431	−	27.2678i	−0.623764	−	1.08039i
$638$		0			0
$639$	1.05180	−	1.82177i	0.0416085	−	0.0720680i
$640$		0			0
$641$	2.05791	+	11.6710i	0.0812824	+	0.460975i	0.998097	+	0.0616624i	$0.0196402\pi$
$641$	2.05791	+	11.6710i	0.0812824	+	0.460975i	−0.916815	+	0.399313i	$0.869249\pi$
$642$		0			0
$643$	−11.8443	+	20.5150i	−0.467095	+	0.809032i	−0.999293	−	0.0375875i	$-0.988033\pi$
$643$	−11.8443	+	20.5150i	−0.467095	+	0.809032i	0.532198	+	0.846620i	$0.321366\pi$
$644$		0			0
$645$	1.60655	−	1.34806i	0.0632580	−	0.0530797i
$646$		0			0
$647$	−1.44791	+	8.21151i	−0.0569233	+	0.322828i	−0.999951	−	0.00988584i	$-0.996853\pi$
$647$	−1.44791	+	8.21151i	−0.0569233	+	0.322828i	0.943028	+	0.332714i	$0.107964\pi$
$648$		0			0
$649$	−8.69354	−	3.16419i	−0.341251	−	0.124205i
$650$		0			0
$651$	2.92933	−	2.45800i	0.114809	−	0.0963366i
$652$		0			0
$653$	41.8595	−	15.2356i	1.63809	−	0.596215i	0.651385	−	0.758747i	$-0.274188\pi$
$653$	41.8595	−	15.2356i	1.63809	−	0.596215i	0.986703	+	0.162532i	$0.0519661\pi$
$654$		0			0
$655$	−7.53198	−	13.0458i	−0.294299	−	0.509741i
$656$		0			0
$657$	−10.6139	−	3.86316i	−0.414089	−	0.150716i
$658$		0			0
$659$	−9.40947	−	7.89548i	−0.366541	−	0.307564i	0.440851	−	0.897580i	$-0.354677\pi$
$659$	−9.40947	−	7.89548i	−0.366541	−	0.307564i	−0.807391	+	0.590016i	$0.799121\pi$
$660$		0			0
$661$	1.71744	+	1.44110i	0.0668005	+	0.0560523i	0.675577	−	0.737290i	$-0.263895\pi$
$661$	1.71744	+	1.44110i	0.0668005	+	0.0560523i	−0.608776	+	0.793342i	$0.708339\pi$
$662$		0			0
$663$	−2.87030	+	16.2783i	−0.111473	+	0.632195i
$664$		0			0
$665$	3.74434			0.145199
$666$		0			0
$667$	3.99369			0.154636
$668$		0			0
$669$	0.848840	−	4.81401i	0.0328181	−	0.186120i
$670$		0			0
$671$	7.41889	+	6.22519i	0.286403	+	0.240321i
$672$		0			0
$673$	−28.3806	−	23.8141i	−1.09399	−	0.917967i	−0.0969845	−	0.995286i	$-0.530920\pi$
$673$	−28.3806	−	23.8141i	−1.09399	−	0.917967i	−0.997006	+	0.0773184i	$0.975364\pi$
$674$		0			0
$675$	3.02302	+	1.10029i	0.116356	+	0.0423501i
$676$		0			0
$677$	17.4629	+	30.2466i	0.671152	+	1.16247i	0.977578	+	0.210575i	$0.0675337\pi$
$677$	17.4629	+	30.2466i	0.671152	+	1.16247i	−0.306425	+	0.951895i	$0.599133\pi$
$678$		0			0
$679$	−9.41471	+	3.42668i	−0.361304	+	0.131504i
$680$		0			0
$681$	12.9378	−	10.8561i	0.495777	−	0.416007i
$682$		0			0
$683$	19.0659	+	6.93944i	0.729538	+	0.265530i	0.679969	−	0.733241i	$-0.261993\pi$
$683$	19.0659	+	6.93944i	0.729538	+	0.265530i	0.0495687	+	0.998771i	$0.484215\pi$
$684$		0			0
$685$	−1.89225	+	10.7315i	−0.0722993	+	0.410030i
$686$		0			0
$687$	3.03418	−	2.54598i	0.115761	−	0.0971350i
$688$		0			0
$689$	3.35533	−	5.81161i	0.127828	−	0.221405i
$690$		0			0
$691$	3.45559	+	19.5976i	0.131457	+	0.745529i	0.977262	+	0.212037i	$0.0680097\pi$
$691$	3.45559	+	19.5976i	0.131457	+	0.745529i	−0.845805	+	0.533493i	$0.820879\pi$
$692$		0			0
$693$	−0.318961	+	0.552456i	−0.0121163	+	0.0209861i
$694$		0			0
$695$	−10.2646	−	17.7788i	−0.389357	−	0.674387i
$696$		0			0
$697$	−0.000441972	0		−1.67409e−5	0
$698$		0			0
$699$	−1.34936	+	0.491126i	−0.0510374	+	0.0185761i
$700$		0			0
$701$	−1.11106	−	6.30114i	−0.0419642	−	0.237991i	0.956610	−	0.291371i	$-0.0941115\pi$
$701$	−1.11106	−	6.30114i	−0.0419642	−	0.237991i	−0.998574	+	0.0533804i	$0.983000\pi$
$702$		0			0
$703$	−6.42516	+	29.0282i	−0.242330	+	1.09482i
$704$		0			0
$705$	−1.13159	−	6.41757i	−0.0426182	−	0.241700i
$706$		0			0
$707$	5.83405	−	2.12342i	0.219412	−	0.0798594i
$708$		0			0
$709$	3.28037			0.123197			0.0615984	−	0.998101i	$-0.480380\pi$
$709$	3.28037			0.123197			0.0615984	+	0.998101i	$0.480380\pi$
$710$		0			0
$711$	−3.97106	−	6.87808i	−0.148926	−	0.257948i
$712$		0			0
$713$	1.91198	−	3.31165i	0.0716044	−	0.124022i
$714$		0			0
$715$	−1.21689	−	6.90133i	−0.0455091	−	0.258095i
$716$		0			0
$717$	11.8762	−	20.5702i	0.443526	−	0.768210i
$718$		0			0
$719$	−30.7191	+	25.7764i	−1.14563	+	0.961296i	−0.999608	−	0.0279860i	$-0.991091\pi$
$719$	−30.7191	+	25.7764i	−1.14563	+	0.961296i	−0.146019	+	0.989282i	$0.546646\pi$
$720$		0			0
$721$	−1.14064	+	6.46890i	−0.0424797	+	0.240915i
$722$		0			0
$723$	9.56391	+	3.48098i	0.355686	+	0.129459i
$724$		0			0
$725$	−17.1548	+	14.3946i	−0.637115	+	0.534603i
$726$		0			0
$727$	38.6054	−	14.0512i	1.43180	−	0.521131i	0.494351	−	0.869263i	$-0.335406\pi$
$727$	38.6054	−	14.0512i	1.43180	−	0.521131i	0.937446	+	0.348131i	$0.113184\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	5.16860	+	1.88121i	0.191167	+	0.0695792i
$732$		0			0
$733$	3.75374	+	3.14976i	0.138647	+	0.116339i	0.709474	−	0.704732i	$-0.248933\pi$
$733$	3.75374	+	3.14976i	0.138647	+	0.116339i	−0.570826	+	0.821071i	$0.693377\pi$
$734$		0			0
$735$	6.82350	+	5.72560i	0.251689	+	0.211192i
$736$		0			0
$737$	−0.764177	+	4.33387i	−0.0281488	+	0.159640i
$738$		0			0
$739$	−15.1802			−0.558412			−0.279206	−	0.960231i	$-0.590071\pi$
$739$	−15.1802			−0.558412			−0.279206	+	0.960231i	$0.590071\pi$
$740$		0			0
$741$	−23.0698			−0.847492
$742$		0			0
$743$	0.633296	−	3.59160i	0.0232334	−	0.131763i	−0.970985	−	0.239141i	$-0.923134\pi$
$743$	0.633296	−	3.59160i	0.0232334	−	0.131763i	0.994218	+	0.107378i	$0.0342454\pi$
$744$		0			0
$745$	−10.6087	−	8.90176i	−0.388673	−	0.326135i
$746$		0			0
$747$	4.47914	+	3.75844i	0.163883	+	0.137514i
$748$		0			0
$749$	−1.49345	−	0.543571i	−0.0545694	−	0.0198616i
$750$		0			0
$751$	15.7108	+	27.2118i	0.573294	+	0.992974i	0.996225	+	0.0868120i	$0.0276679\pi$
$751$	15.7108	+	27.2118i	0.573294	+	0.992974i	−0.422931	+	0.906162i	$0.638999\pi$
$752$		0			0
$753$	28.2623	−	10.2866i	1.02994	−	0.374866i
$754$		0			0
$755$	0.893340	−	0.749601i	0.0325120	−	0.0272808i
$756$		0			0
$757$	−16.8023	−	6.11553i	−0.610689	−	0.222273i	0.0181155	−	0.999836i	$-0.494233\pi$
$757$	−16.8023	−	6.11553i	−0.610689	−	0.222273i	−0.628805	+	0.777563i	$0.716456\pi$
$758$		0			0
$759$	−0.110774	+	0.628230i	−0.00402084	+	0.0228033i
$760$		0			0
$761$	−9.76924	+	8.19737i	−0.354135	+	0.297154i	−0.802448	−	0.596722i	$-0.796469\pi$
$761$	−9.76924	+	8.19737i	−0.354135	+	0.297154i	0.448313	+	0.893877i	$0.352025\pi$
$762$		0			0
$763$	3.05725	−	5.29532i	0.110680	−	0.191703i
$764$		0			0
$765$	−0.812007	−	4.60512i	−0.0293582	−	0.166499i
$766$		0			0
$767$	−19.6358	+	34.0103i	−0.709009	+	1.22804i
$768$		0			0
$769$	10.7531	+	18.6249i	0.387766	+	0.671630i	0.992149	−	0.125064i	$-0.0399136\pi$
$769$	10.7531	+	18.6249i	0.387766	+	0.671630i	−0.604383	+	0.796694i	$0.706580\pi$
$770$		0			0
$771$	−12.7253			−0.458291
$772$		0			0
$773$	39.4945	−	14.3748i	1.42052	−	0.517027i	0.486321	−	0.873780i	$-0.338338\pi$
$773$	39.4945	−	14.3748i	1.42052	−	0.517027i	0.934199	+	0.356753i	$0.116116\pi$
$774$		0			0
$775$	3.72342	+	21.1166i	0.133749	+	0.758530i
$776$		0			0
$777$	2.76791	−	2.12537i	0.0992983	−	0.0762473i
$778$		0			0
$779$	−0.000107116	0	0.000607483i	−3.83781e−6	0	2.17653e-5i
$780$		0			0
$781$	−2.19795	+	0.799990i	−0.0786490	+	0.0286259i
$782$		0			0
$783$	6.96110			0.248769
$784$		0			0
$785$	−9.55932	−	16.5572i	−0.341187	−	0.590953i
$786$		0			0
$787$	−17.4662	+	30.2523i	−0.622602	+	1.07838i	0.366397	+	0.930459i	$0.380591\pi$
$787$	−17.4662	+	30.2523i	−0.622602	+	1.07838i	−0.988999	+	0.147920i	$0.952742\pi$
$788$		0			0
$789$	2.90307	+	16.4641i	0.103352	+	0.586138i
$790$		0			0
$791$	−3.60954	+	6.25190i	−0.128340	+	0.222292i
$792$		0			0
$793$	31.4925	−	26.4254i	1.11833	−	0.938392i
$794$		0			0
$795$	−0.329662	+	1.86961i	−0.0116919	+	0.0663081i
$796$		0			0
$797$	34.6904	+	12.6263i	1.22880	+	0.447245i	0.873185	−	0.487389i	$-0.162050\pi$
$797$	34.6904	+	12.6263i	1.22880	+	0.447245i	0.355611	+	0.934634i	$0.384273\pi$
$798$		0			0
$799$	13.0924	−	10.9858i	0.463175	−	0.388650i
$800$		0			0
$801$	−12.1934	+	4.43805i	−0.430834	+	0.156811i
$802$		0			0
$803$	6.27959	+	10.8766i	0.221602	+	0.383826i
$804$		0			0
$805$	−0.413002	−	0.150320i	−0.0145564	−	0.00529810i
$806$		0			0
$807$	16.6489	+	13.9701i	0.586070	+	0.491771i
$808$		0			0
$809$	32.3229	+	27.1222i	1.13641	+	0.953564i	0.999316	−	0.0369931i	$-0.0117780\pi$
$809$	32.3229	+	27.1222i	1.13641	+	0.953564i	0.137098	+	0.990557i	$0.456222\pi$
$810$		0			0
$811$	−5.71133	+	32.3906i	−0.200552	+	1.13739i	0.703735	+	0.710462i	$0.251514\pi$
$811$	−5.71133	+	32.3906i	−0.200552	+	1.13739i	−0.904287	+	0.426925i	$0.859597\pi$
$812$		0			0
$813$	23.5318			0.825297
$814$		0			0
$815$	−0.367540			−0.0128744
$816$		0			0
$817$	−1.33305	+	7.56007i	−0.0466373	+	0.264494i
$818$		0			0
$819$	2.07439	+	1.74062i	0.0724850	+	0.0608221i
$820$		0			0
$821$	−2.28313	−	1.91577i	−0.0796817	−	0.0668609i	0.602077	−	0.798438i	$-0.294340\pi$
$821$	−2.28313	−	1.91577i	−0.0796817	−	0.0668609i	−0.681759	+	0.731577i	$0.738785\pi$
$822$		0			0
$823$	−7.19638	−	2.61927i	−0.250850	−	0.0913019i	0.213535	−	0.976935i	$-0.431502\pi$
$823$	−7.19638	−	2.61927i	−0.250850	−	0.0913019i	−0.464385	+	0.885634i	$0.653725\pi$
$824$		0			0
$825$	−1.78853	−	3.09782i	−0.0622685	−	0.107852i
$826$		0			0
$827$	41.9521	−	15.2693i	1.45882	−	0.530966i	0.513778	−	0.857923i	$-0.328245\pi$
$827$	41.9521	−	15.2693i	1.45882	−	0.530966i	0.945039	+	0.326957i	$0.106023\pi$
$828$		0			0
$829$	30.0029	−	25.1754i	1.04204	−	0.874378i	0.0498082	−	0.998759i	$-0.484139\pi$
$829$	30.0029	−	25.1754i	1.04204	−	0.874378i	0.992235	+	0.124381i	$0.0396945\pi$
$830$		0			0
$831$	10.9882	+	3.99937i	0.381176	+	0.138737i
$832$		0			0
$833$	−4.05666	+	23.0065i	−0.140555	+	0.797128i
$834$		0			0
$835$	−0.550280	+	0.461740i	−0.0190432	+	0.0159792i
$836$		0			0
$837$	3.33263	−	5.77228i	0.115193	−	0.199519i
$838$		0			0
$839$	−7.73190	−	43.8498i	−0.266935	−	1.51386i	−0.763469	−	0.645845i	$-0.776505\pi$
$839$	−7.73190	−	43.8498i	−0.266935	−	1.51386i	0.496534	−	0.868017i	$-0.334606\pi$
$840$		0			0
$841$	−9.72843	+	16.8501i	−0.335463	+	0.581039i
$842$		0			0
$843$	4.04034	+	6.99807i	0.139157	+	0.241026i
$844$		0			0
$845$	−12.3888			−0.426189
$846$		0			0
$847$	−5.26375	+	1.91585i	−0.180865	+	0.0658293i
$848$		0			0
$849$	−2.25709	−	12.8006i	−0.0774630	−	0.439315i
$850$		0			0
$851$	1.87407	−	2.94388i	0.0642422	−	0.100915i
$852$		0			0
$853$	−5.92586	−	33.6072i	−0.202898	−	1.15069i	−0.900714	−	0.434413i	$-0.856956\pi$
$853$	−5.92586	−	33.6072i	−0.202898	−	1.15069i	0.697816	−	0.716277i	$-0.254155\pi$
$854$		0			0
$855$	6.13287	−	2.23218i	0.209740	−	0.0763390i
$856$		0			0
$857$	−35.2775			−1.20505			−0.602527	−	0.798098i	$-0.705840\pi$
$857$	−35.2775			−1.20505			−0.602527	+	0.798098i	$0.705840\pi$
$858$		0			0
$859$	−8.72796	−	15.1173i	−0.297794	−	0.515794i	0.677837	−	0.735212i	$-0.262918\pi$
$859$	−8.72796	−	15.1173i	−0.297794	−	0.515794i	−0.975631	+	0.219418i	$0.929584\pi$
$860$		0			0
$861$	−3.62029e−5	0	6.27053e-5i	−1.23379e−6	0	2.13699e-6i
$862$		0			0
$863$	−1.00399	−	5.69392i	−0.0341763	−	0.193823i	0.962940	−	0.269717i	$-0.0869302\pi$
$863$	−1.00399	−	5.69392i	−0.0341763	−	0.193823i	−0.997116	+	0.0758936i	$0.975819\pi$
$864$		0			0
$865$	1.67735	−	2.90525i	0.0570316	−	0.0987816i
$866$		0			0
$867$	−3.62792	+	3.04418i	−0.123210	+	0.103386i
$868$		0			0
$869$	−1.53348	+	8.69678i	−0.0520196	+	0.295018i
$870$		0			0
$871$	17.5541	+	6.38917i	0.594798	+	0.216489i
$872$		0			0
$873$	−13.3776	+	11.2251i	−0.452763	+	0.379913i
$874$		0			0
$875$	5.91520	−	2.15296i	0.199970	−	0.0727833i
$876$		0			0
$877$	0.748422	+	1.29631i	0.0252724	+	0.0437731i	0.878385	−	0.477954i	$-0.158621\pi$
$877$	0.748422	+	1.29631i	0.0252724	+	0.0437731i	−0.853113	+	0.521727i	$0.825288\pi$
$878$		0			0
$879$	4.05477	+	1.47581i	0.136764	+	0.0497780i
$880$		0			0
$881$	24.6246	+	20.6625i	0.829625	+	0.696138i	0.955205	−	0.295946i	$-0.0956347\pi$
$881$	24.6246	+	20.6625i	0.829625	+	0.696138i	−0.125580	+	0.992084i	$0.540079\pi$
$882$		0			0
$883$	−12.3983	−	10.4034i	−0.417237	−	0.350104i	0.409874	−	0.912142i	$-0.365573\pi$
$883$	−12.3983	−	10.4034i	−0.417237	−	0.350104i	−0.827111	+	0.562039i	$0.810017\pi$
$884$		0			0
$885$	1.92922	−	10.9412i	0.0648502	−	0.367784i
$886$		0			0
$887$	14.1911			0.476491			0.238246	−	0.971205i	$-0.423428\pi$
$887$	14.1911			0.476491			0.238246	+	0.971205i	$0.423428\pi$
$888$		0			0
$889$	−2.38338			−0.0799358
$890$		0			0
$891$	−0.193081	+	1.09502i	−0.00646847	+	0.0366845i
$892$		0			0
$893$	18.2729	+	15.3327i	0.611478	+	0.513091i
$894$		0			0
$895$	−1.69065	−	1.41863i	−0.0565123	−	0.0474194i
$896$		0			0
$897$	2.54461	+	0.926163i	0.0849622	+	0.0309237i
$898$		0			0
$899$	23.1988	+	40.1814i	0.773722	+	1.34013i
$900$		0			0
$901$	−4.67876	+	1.70293i	−0.155872	+	0.0567328i
$902$		0			0
$903$	0.690272	−	0.579207i	0.0229708	−	0.0192748i
$904$		0			0
$905$	8.59840	+	3.12956i	0.285820	+	0.104030i
$906$		0			0
$907$	−3.48667	+	19.7739i	−0.115773	+	0.656581i	0.870592	+	0.492006i	$0.163736\pi$
$907$	−3.48667	+	19.7739i	−0.115773	+	0.656581i	−0.986365	+	0.164575i	$0.947375\pi$
$908$		0			0
$909$	8.28975	−	6.95592i	0.274954	−	0.230713i
$910$		0			0
$911$	−9.82387	+	17.0154i	−0.325479	+	0.563747i	−0.981609	−	0.190901i	$-0.938859\pi$
$911$	−9.82387	+	17.0154i	−0.325479	+	0.563747i	0.656130	+	0.754648i	$0.272192\pi$
$912$		0			0
$913$	−1.12897	−	6.40268i	−0.0373633	−	0.211898i
$914$		0			0
$915$	−5.81509	+	10.0720i	−0.192241	+	0.332971i
$916$		0			0
$917$	−3.23619	−	5.60525i	−0.106868	−	0.185102i
$918$		0			0
$919$	57.5271			1.89764			0.948822	−	0.315810i	$-0.102276\pi$
$919$	57.5271			1.89764			0.948822	+	0.315810i	$0.102276\pi$
$920$		0			0
$921$	3.82349	−	1.39164i	0.125988	−	0.0458560i
$922$		0			0
$923$	1.72414	+	9.77806i	0.0567506	+	0.321849i
$924$		0			0
$925$	2.56071	+	19.4002i	0.0841957	+	0.637873i
$926$		0			0
$927$	1.98816	+	11.2754i	0.0652999	+	0.370334i
$928$		0			0
$929$	−4.71036	+	1.71443i	−0.154542	+	0.0562486i	−0.418133	−	0.908386i	$-0.637315\pi$
$929$	−4.71036	+	1.71443i	−0.154542	+	0.0562486i	0.263591	+	0.964635i	$0.415093\pi$
$930$		0			0
$931$	−32.6052			−1.06859
$932$		0			0
$933$	−10.1950	−	17.6583i	−0.333770	−	0.578106i
$934$		0			0
$935$	−2.59974	+	4.50288i	−0.0850206	+	0.147260i
$936$		0			0
$937$	−7.36889	−	41.7911i	−0.240731	−	1.36525i	−0.830201	−	0.557464i	$-0.811774\pi$
$937$	−7.36889	−	41.7911i	−0.240731	−	1.36525i	0.589470	−	0.807791i	$-0.299337\pi$
$938$		0			0
$939$	−5.90862	+	10.2340i	−0.192821	+	0.333975i
$940$		0			0
$941$	7.57405	−	6.35538i	0.246907	−	0.207180i	−0.510932	−	0.859621i	$-0.670700\pi$
$941$	7.57405	−	6.35538i	0.246907	−	0.207180i	0.757839	+	0.652442i	$0.226255\pi$
$942$		0			0
$943$	−1.25731e−5	0	7.13059e-5i	−4.09438e−7	0	2.32204e-6i
$944$		0			0
$945$	−0.719871	−	0.262012i	−0.0234174	−	0.00852324i
$946$		0			0
$947$	3.18200	−	2.67002i	0.103401	−	0.0867638i	−0.589621	−	0.807680i	$-0.700723\pi$
$947$	3.18200	−	2.67002i	0.103401	−	0.0867638i	0.693023	+	0.720916i	$0.256279\pi$
$948$		0			0
$949$	50.0975	−	18.2340i	1.62623	−	0.591900i
$950$		0			0
$951$	−2.73400	−	4.73542i	−0.0886559	−	0.153556i
$952$		0			0
$953$	24.7410	+	9.00498i	0.801439	+	0.291700i	0.710083	−	0.704118i	$-0.248658\pi$
$953$	24.7410	+	9.00498i	0.801439	+	0.291700i	0.0913564	+	0.995818i	$0.470880\pi$
$954$		0			0
$955$	20.3946	+	17.1131i	0.659953	+	0.553766i
$956$		0			0
$957$	−5.92928	−	4.97526i	−0.191666	−	0.160827i
$958$		0			0
$959$	−0.813025	+	4.61090i	−0.0262540	+	0.148894i
$960$		0			0
$961$	13.4257			0.433087
$962$		0			0
$963$	−2.77018			−0.0892677
$964$		0			0
$965$	3.16897	−	17.9721i	0.102013	−	0.578542i
$966$		0			0
$967$	−23.1941	−	19.4621i	−0.745870	−	0.625860i	0.188537	−	0.982066i	$-0.439626\pi$
$967$	−23.1941	−	19.4621i	−0.745870	−	0.625860i	−0.934407	+	0.356207i	$0.884070\pi$
$968$		0			0
$969$	13.1123	+	11.0025i	0.421226	+	0.353451i
$970$		0			0
$971$	−30.6099	−	11.1411i	−0.982319	−	0.357535i	−0.199577	−	0.979882i	$-0.563957\pi$
$971$	−30.6099	−	11.1411i	−0.982319	−	0.357535i	−0.782741	+	0.622347i	$0.786179\pi$
$972$		0			0
$973$	−4.41028	−	7.63882i	−0.141387	−	0.244889i
$974$		0			0
$975$	−14.2685	+	5.19333i	−0.456959	+	0.166320i
$976$		0			0
$977$	36.4890	−	30.6179i	1.16739	−	0.979554i	0.167407	−	0.985888i	$-0.446461\pi$
$977$	36.4890	−	30.6179i	1.16739	−	0.979554i	0.999980	+	0.00633423i	$0.00201626\pi$
$978$		0			0
$979$	13.5580	+	4.93472i	0.433317	+	0.157714i
$980$		0			0
$981$	1.85069	−	10.4958i	0.0590881	−	0.335105i
$982$		0			0
$983$	−14.3813	+	12.0673i	−0.458692	+	0.384888i	−0.842649	−	0.538463i	$-0.819005\pi$
$983$	−14.3813	+	12.0673i	−0.458692	+	0.384888i	0.383958	+	0.923351i	$0.374561\pi$
$984$		0			0
$985$	−5.31746	+	9.21011i	−0.169428	+	0.293458i
$986$		0			0
$987$	−0.486199	−	2.75737i	−0.0154759	−	0.0877681i
$988$		0			0
$989$	0.450543	−	0.780363i	0.0143264	−	0.0248141i
$990$		0			0
$991$	24.1727	+	41.8683i	0.767870	+	1.32999i	0.938716	+	0.344692i	$0.112017\pi$
$991$	24.1727	+	41.8683i	0.767870	+	1.32999i	−0.170846	+	0.985298i	$0.554650\pi$
$992$		0			0
$993$	−34.5753			−1.09721
$994$		0			0
$995$	2.62455	−	0.955260i	0.0832040	−	0.0302838i
$996$		0			0
$997$	1.05943	+	6.00830i	0.0335524	+	0.190285i	0.996977	−	0.0776935i	$-0.0247555\pi$
$997$	1.05943	+	6.00830i	0.0335524	+	0.190285i	−0.963425	+	0.267978i	$0.913644\pi$
$998$		0			0
$999$	3.26654	−	5.13125i	0.103349	−	0.162346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.bo.c.601.2	✓	24
37.33	even	9	inner	888.2.bo.c.625.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.bo.c.601.2	✓	24	1.1	even	1	trivial
888.2.bo.c.625.2	yes	24	37.33	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{3} +(-1.02288 - 0.858301i) q^{5} +(-0.439492 - 0.368778i) q^{7} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{3} +(-1.02288 - 0.858301i) q^{5} +(-0.439492 - 0.368778i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(0.555956 + 0.962944i) q^{11} +(4.43532 - 1.61432i) q^{13} +(-1.02288 + 0.858301i) q^{15} +(-3.29082 - 1.19776i) q^{17} +(0.848742 - 4.81346i) q^{19} +(-0.439492 + 0.368778i) q^{21} +(-0.286858 + 0.496853i) q^{23} +(-0.558631 - 3.16816i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-3.48055 - 6.02849i) q^{29} -6.66526 q^{31} +(1.04486 - 0.380296i) q^{33} +(0.133027 + 0.754433i) q^{35} +(-6.07706 - 0.263284i) q^{37} +(-0.819613 - 4.64826i) q^{39} +(0.000118594 - 4.31647e-5i) q^{41} -1.57061 q^{43} +(0.667640 + 1.15639i) q^{45} +(-2.44015 + 4.22647i) q^{47} +(-1.15838 - 6.56950i) q^{49} +(-1.75101 + 3.03283i) q^{51} +(1.08913 - 0.913891i) q^{53} +(0.257818 - 1.46216i) q^{55} +(-4.59295 - 1.67170i) q^{57} +(-6.37374 + 5.34821i) q^{59} +(8.18466 - 2.97897i) q^{61} +(0.286858 + 0.496853i) q^{63} +(-5.92239 - 2.15557i) q^{65} +(3.03185 + 2.54402i) q^{67} +(0.439492 + 0.368778i) q^{69} +(-0.365286 + 2.07164i) q^{71} +11.2951 q^{73} -3.21703 q^{75} +(0.110774 - 0.628230i) q^{77} +(6.08402 + 5.10510i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-5.49447 - 1.99982i) q^{83} +(2.33808 + 4.04968i) q^{85} +(-6.54129 + 2.38083i) q^{87} +(9.94019 - 8.34081i) q^{89} +(-2.54461 - 0.926163i) q^{91} +(-1.15741 + 6.56400i) q^{93} +(-4.99956 + 4.19513i) q^{95} +(8.73161 - 15.1236i) q^{97} +(-0.193081 - 1.09502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) \) 24 * q + 3 * q^5 + 15 * q^7	\( 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) \) 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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