LMFDB - Embedded newform 888.2.br.a.569.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [888,2,Mod(473,888)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("888.473"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(888, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 6, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.br (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			569.17
Character	$\chi$	$=$	888.569
Dual form			888.2.br.a.785.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.350286 + 1.69626i) q^{3} +(0.557275 - 2.07978i) q^{5} +(1.90625 + 3.30173i) q^{7} +(-2.75460 - 1.18835i) q^{9} +2.70521 q^{11} +(0.737048 + 0.197491i) q^{13} +(3.33264 + 1.67380i) q^{15} +(0.554152 - 0.148484i) q^{17} +(-2.06065 - 0.552149i) q^{19} +(-6.26832 + 2.07695i) q^{21} +(4.13412 + 4.13412i) q^{23} +(0.315207 + 0.181985i) q^{25} +(2.98065 - 4.25625i) q^{27} +(1.48612 - 1.48612i) q^{29} +(0.369408 + 0.369408i) q^{31} +(-0.947598 + 4.58874i) q^{33} +(7.92916 - 2.12461i) q^{35} +(-1.29198 + 5.94397i) q^{37} +(-0.593175 + 1.18105i) q^{39} +(1.11956 + 1.93913i) q^{41} +(-5.18129 + 5.18129i) q^{43} +(-4.00658 + 5.06671i) q^{45} +1.34429i q^{47} +(-3.76760 + 6.52568i) q^{49} +(0.0577567 + 0.991997i) q^{51} +(0.415147 + 0.239685i) q^{53} +(1.50755 - 5.62624i) q^{55} +(1.65840 - 3.30198i) q^{57} +(12.4806 - 3.34417i) q^{59} +(0.788533 - 2.94285i) q^{61} +(-1.32735 - 11.3602i) q^{63} +(0.821477 - 1.42284i) q^{65} +(-2.47617 + 1.42962i) q^{67} +(-8.46067 + 5.56442i) q^{69} +(-5.44141 + 3.14160i) q^{71} +14.3331i q^{73} +(-0.419107 + 0.470927i) q^{75} +(5.15682 + 8.93187i) q^{77} +(-10.2736 - 2.75281i) q^{79} +(6.17563 + 6.54687i) q^{81} +(4.79474 + 2.76824i) q^{83} -1.23526i q^{85} +(2.00028 + 3.04141i) q^{87} +(-3.12906 - 11.6778i) q^{89} +(0.752937 + 2.81000i) q^{91} +(-0.756010 + 0.497213i) q^{93} +(-2.29669 + 3.97799i) q^{95} +(0.215187 - 0.215187i) q^{97} +(-7.45177 - 3.21475i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) $ 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Character values

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

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$-1$

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
$3$	−0.350286	+	1.69626i	−0.202238	+	0.979336i
$3$	−0.350286	+	1.69626i	−0.202238	+	0.979336i
$4$		0			0
$5$	0.557275	−	2.07978i	0.249221	−	0.930105i	−0.721994	−	0.691899i	$-0.756774\pi$
$5$	0.557275	−	2.07978i	0.249221	−	0.930105i	0.971215	−	0.238205i	$-0.0765592\pi$
$6$		0			0
$7$	1.90625	+	3.30173i	0.720496	+	1.24794i	0.960801	+	0.277238i	$0.0894191\pi$
$7$	1.90625	+	3.30173i	0.720496	+	1.24794i	−0.240305	+	0.970697i	$0.577248\pi$
$8$		0			0
$9$	−2.75460	−	1.18835i	−0.918200	−	0.396118i
$10$		0			0
$11$	2.70521			0.815652			0.407826	−	0.913060i	$-0.366287\pi$
$11$	2.70521			0.815652			0.407826	+	0.913060i	$0.366287\pi$
$12$		0			0
$13$	0.737048	+	0.197491i	0.204420	+	0.0547743i	0.359576	−	0.933116i	$-0.382921\pi$
$13$	0.737048	+	0.197491i	0.204420	+	0.0547743i	−0.155156	+	0.987890i	$0.549588\pi$
$14$		0			0
$15$	3.33264	+	1.67380i	0.860484	+	0.432173i
$16$		0			0
$17$	0.554152	−	0.148484i	0.134401	−	0.0360128i	−0.190991	−	0.981592i	$-0.561170\pi$
$17$	0.554152	−	0.148484i	0.134401	−	0.0360128i	0.325393	+	0.945579i	$0.394504\pi$
$18$		0			0
$19$	−2.06065	−	0.552149i	−0.472745	−	0.126672i	0.0145776	−	0.999894i	$-0.495360\pi$
$19$	−2.06065	−	0.552149i	−0.472745	−	0.126672i	−0.487322	+	0.873222i	$0.662026\pi$
$20$		0			0
$21$	−6.26832	+	2.07695i	−1.36786	+	0.453228i
$22$		0			0
$23$	4.13412	+	4.13412i	0.862023	+	0.862023i	0.991573	−	0.129550i	$-0.0413532\pi$
$23$	4.13412	+	4.13412i	0.862023	+	0.862023i	−0.129550	+	0.991573i	$0.541353\pi$
$24$		0			0
$25$	0.315207	+	0.181985i	0.0630415	+	0.0363970i
$26$		0			0
$27$	2.98065	−	4.25625i	0.573627	−	0.819116i
$28$		0			0
$29$	1.48612	−	1.48612i	0.275965	−	0.275965i	−0.555531	−	0.831496i	$-0.687485\pi$
$29$	1.48612	−	1.48612i	0.275965	−	0.275965i	0.831496	+	0.555531i	$0.187485\pi$
$30$		0			0
$31$	0.369408	+	0.369408i	0.0663476	+	0.0663476i	0.739502	−	0.673154i	$-0.235061\pi$
$31$	0.369408	+	0.369408i	0.0663476	+	0.0663476i	−0.673154	+	0.739502i	$0.735061\pi$
$32$		0			0
$33$	−0.947598	+	4.58874i	−0.164956	+	0.798798i
$34$		0			0
$35$	7.92916	−	2.12461i	1.34027	−	0.359125i
$36$		0			0
$37$	−1.29198	+	5.94397i	−0.212400	+	0.977183i
$37$	−1.29198	+	5.94397i	−0.212400	+	0.977183i
$38$		0			0
$39$	−0.593175	+	1.18105i	−0.0949840	+	0.189119i
$40$		0			0
$41$	1.11956	+	1.93913i	0.174845	+	0.302841i	0.940108	−	0.340877i	$-0.110724\pi$
$41$	1.11956	+	1.93913i	0.174845	+	0.302841i	−0.765262	+	0.643719i	$0.777391\pi$
$42$		0			0
$43$	−5.18129	+	5.18129i	−0.790140	+	0.790140i	−0.981517	−	0.191377i	$-0.938705\pi$
$43$	−5.18129	+	5.18129i	−0.790140	+	0.790140i	0.191377	+	0.981517i	$0.438705\pi$
$44$		0			0
$45$	−4.00658	+	5.06671i	−0.597265	+	0.755301i
$46$		0			0
$47$			1.34429i			0.196084i	0.995182	+	0.0980421i	$0.0312580\pi$
$47$			1.34429i			0.196084i	−0.995182	+	0.0980421i	$0.968742\pi$
$48$		0			0
$49$	−3.76760	+	6.52568i	−0.538229	+	0.932239i
$50$		0			0
$51$	0.0577567	+	0.991997i	0.00808756	+	0.138907i
$52$		0			0
$53$	0.415147	+	0.239685i	0.0570248	+	0.0329233i	0.528241	−	0.849094i	$-0.322852\pi$
$53$	0.415147	+	0.239685i	0.0570248	+	0.0329233i	−0.471217	+	0.882018i	$0.656185\pi$
$54$		0			0
$55$	1.50755	−	5.62624i	0.203277	−	0.758642i
$56$		0			0
$57$	1.65840	−	3.30198i	0.219661	−	0.437358i
$58$		0			0
$59$	12.4806	−	3.34417i	1.62484	−	0.435374i	0.672419	−	0.740171i	$-0.265255\pi$
$59$	12.4806	−	3.34417i	1.62484	−	0.435374i	0.952417	+	0.304797i	$0.0985887\pi$
$60$		0			0
$61$	0.788533	−	2.94285i	0.100961	−	0.376793i	−0.896894	−	0.442245i	$-0.854182\pi$
$61$	0.788533	−	2.94285i	0.100961	−	0.376793i	0.997856	+	0.0654520i	$0.0208489\pi$
$62$		0			0
$63$	−1.32735	−	11.3602i	−0.167230	−	1.43126i
$64$		0			0
$65$	0.821477	−	1.42284i	0.101892	−	0.176481i
$66$		0			0
$67$	−2.47617	+	1.42962i	−0.302512	+	0.174655i	−0.643571	−	0.765387i	$-0.722548\pi$
$67$	−2.47617	+	1.42962i	−0.302512	+	0.174655i	0.341059	+	0.940042i	$0.389214\pi$
$68$		0			0
$69$	−8.46067	+	5.56442i	−1.01854	+	0.669877i
$70$		0			0
$71$	−5.44141	+	3.14160i	−0.645777	+	0.372839i	−0.786836	−	0.617162i	$-0.788282\pi$
$71$	−5.44141	+	3.14160i	−0.645777	+	0.372839i	0.141060	+	0.990001i	$0.454949\pi$
$72$		0			0
$73$			14.3331i			1.67756i	0.544469	+	0.838781i	$0.316731\pi$
$73$			14.3331i			1.67756i	−0.544469	+	0.838781i	$0.683269\pi$
$74$		0			0
$75$	−0.419107	+	0.470927i	−0.0483943	+	0.0543780i
$76$		0			0
$77$	5.15682	+	8.93187i	0.587674	+	1.01788i
$78$		0			0
$79$	−10.2736	−	2.75281i	−1.15587	−	0.309716i	−0.370557	−	0.928810i	$-0.620833\pi$
$79$	−10.2736	−	2.75281i	−1.15587	−	0.309716i	−0.785317	+	0.619094i	$0.787500\pi$
$80$		0			0
$81$	6.17563	+	6.54687i	0.686181	+	0.727430i
$82$		0			0
$83$	4.79474	+	2.76824i	0.526291	+	0.303854i	0.739505	−	0.673151i	$-0.235060\pi$
$83$	4.79474	+	2.76824i	0.526291	+	0.303854i	−0.213214	+	0.977006i	$0.568393\pi$
$84$		0			0
$85$		−	1.23526i		−	0.133983i
$86$		0			0
$87$	2.00028	+	3.04141i	0.214452	+	0.326074i
$88$		0			0
$89$	−3.12906	−	11.6778i	−0.331680	−	1.23785i	−0.907424	−	0.420217i	$-0.861954\pi$
$89$	−3.12906	−	11.6778i	−0.331680	−	1.23785i	0.575744	−	0.817630i	$-0.304713\pi$
$90$		0			0
$91$	0.752937	+	2.81000i	0.0789293	+	0.294568i
$92$		0			0
$93$	−0.756010	+	0.497213i	−0.0783946	+	0.0515586i
$94$		0			0
$95$	−2.29669	+	3.97799i	−0.235636	+	0.408133i
$96$		0			0
$97$	0.215187	−	0.215187i	0.0218489	−	0.0218489i	−0.696098	−	0.717947i	$-0.745082\pi$
$97$	0.215187	−	0.215187i	0.0218489	−	0.0218489i	0.717947	+	0.696098i	$0.245082\pi$
$98$		0			0
$99$	−7.45177	−	3.21475i	−0.748931	−	0.323094i
$100$		0			0
$101$	−2.38449			−0.237266			−0.118633	−	0.992938i	$-0.537851\pi$
$101$	−2.38449			−0.237266			−0.118633	+	0.992938i	$0.537851\pi$
$102$		0			0
$103$	5.73644	+	5.73644i	0.565228	+	0.565228i	0.930788	−	0.365560i	$-0.119122\pi$
$103$	5.73644	+	5.73644i	0.565228	+	0.565228i	−0.365560	+	0.930788i	$0.619122\pi$
$104$		0			0
$105$	0.826421	+	14.1942i	0.0806504	+	1.38521i
$106$		0			0
$107$	−7.24666	+	4.18386i	−0.700561	+	0.404469i	−0.807556	−	0.589790i	$-0.799210\pi$
$107$	−7.24666	+	4.18386i	−0.700561	+	0.404469i	0.106995	+	0.994260i	$0.465877\pi$
$108$		0			0
$109$	−4.47610	−	16.7050i	−0.428732	−	1.60005i	−0.755635	−	0.654993i	$-0.772672\pi$
$109$	−4.47610	−	16.7050i	−0.428732	−	1.60005i	0.326903	−	0.945058i	$-0.393995\pi$
$110$		0			0
$111$	−9.62996	−	4.27362i	−0.914035	−	0.405634i
$112$		0			0
$113$	3.60146	+	13.4408i	0.338796	+	1.26441i	0.899694	+	0.436521i	$0.143789\pi$
$113$	3.60146	+	13.4408i	0.338796	+	1.26441i	−0.560898	+	0.827885i	$0.689544\pi$
$114$		0			0
$115$	10.9019	−	6.29421i	1.01661	−	0.586938i
$116$		0			0
$117$	−1.79558	−	1.41988i	−0.166002	−	0.131268i
$118$		0			0
$119$	1.54661	+	1.54661i	0.141777	+	0.141777i
$120$		0			0
$121$	−3.68183			−0.334712
$122$		0			0
$123$	−3.68144	+	1.21981i	−0.331944	+	0.109987i
$124$		0			0
$125$	8.16666	−	8.16666i	0.730448	−	0.730448i
$126$		0			0
$127$	9.83451	−	17.0339i	0.872672	−	1.51151i	0.0134499	−	0.999910i	$-0.495719\pi$
$127$	9.83451	−	17.0339i	0.872672	−	1.51151i	0.859222	−	0.511603i	$-0.170948\pi$
$128$		0			0
$129$	−6.97389	−	10.6038i	−0.614017	−	0.933609i
$130$		0			0
$131$	−1.34334	−	5.01341i	−0.117368	−	0.438023i	0.882085	−	0.471090i	$-0.156139\pi$
$131$	−1.34334	−	5.01341i	−0.117368	−	0.438023i	−0.999453	+	0.0330667i	$0.989473\pi$
$132$		0			0
$133$	−2.10507	−	7.85623i	−0.182533	−	0.681221i
$134$		0			0
$135$	−7.19102	−	8.57100i	−0.618904	−	0.737674i
$136$		0			0
$137$		−	12.7696i		−	1.09098i	−0.838118	−	0.545488i	$-0.816344\pi$
$137$		−	12.7696i		−	1.09098i	0.838118	−	0.545488i	$-0.183656\pi$
$138$		0			0
$139$	5.25005	+	3.03112i	0.445303	+	0.257096i	0.705845	−	0.708367i	$-0.250568\pi$
$139$	5.25005	+	3.03112i	0.445303	+	0.257096i	−0.260541	+	0.965463i	$0.583901\pi$
$140$		0			0
$141$	−2.28026	−	0.470885i	−0.192032	−	0.0396556i
$142$		0			0
$143$	1.99387	+	0.534256i	0.166736	+	0.0446767i
$144$		0			0
$145$	−2.26262	−	3.91898i	−0.187900	−	0.325453i
$146$		0			0
$147$	−9.74951	−	8.67669i	−0.804126	−	0.715641i
$148$		0			0
$149$		−	4.38215i		−	0.359000i	−0.983758	−	0.179500i	$-0.942552\pi$
$149$		−	4.38215i		−	0.359000i	0.983758	−	0.179500i	$-0.0574480\pi$
$150$		0			0
$151$	−7.35098	+	4.24409i	−0.598215	+	0.345379i	−0.768339	−	0.640043i	$-0.778916\pi$
$151$	−7.35098	+	4.24409i	−0.598215	+	0.345379i	0.170124	+	0.985423i	$0.445583\pi$
$152$		0			0
$153$	−1.70292	−	0.249513i	−0.137673	−	0.0201719i
$154$		0			0
$155$	0.974147	−	0.562424i	0.0782454	−	0.0451750i
$156$		0			0
$157$	8.04292	−	13.9307i	0.641895	−	1.11179i	−0.343115	−	0.939293i	$-0.611482\pi$
$157$	8.04292	−	13.9307i	0.641895	−	1.11179i	0.985009	−	0.172500i	$-0.0551846\pi$
$158$		0			0
$159$	−0.551989	+	0.620239i	−0.0437755	+	0.0491881i
$160$		0			0
$161$	−5.76905	+	21.5304i	−0.454665	+	1.69683i
$162$		0			0
$163$	20.8950	−	5.59881i	1.63663	−	0.438533i	0.680801	−	0.732468i	$-0.261632\pi$
$163$	20.8950	−	5.59881i	1.63663	−	0.438533i	0.955825	+	0.293936i	$0.0949651\pi$
$164$		0			0
$165$	9.01549	+	4.52798i	0.701855	+	0.352503i
$166$		0			0
$167$	4.70514	−	17.5598i	0.364095	−	1.35882i	−0.504549	−	0.863383i	$-0.668341\pi$
$167$	4.70514	−	17.5598i	0.364095	−	1.35882i	0.868644	−	0.495437i	$-0.164992\pi$
$168$		0			0
$169$	−10.7541	−	6.20888i	−0.827238	−	0.477606i
$170$		0			0
$171$	5.02011	+	3.96972i	0.383897	+	0.303572i
$172$		0			0
$173$	6.08785	−	10.5445i	0.462851	−	0.801681i	−0.536251	−	0.844059i	$-0.680160\pi$
$173$	6.08785	−	10.5445i	0.462851	−	0.801681i	0.999102	+	0.0423775i	$0.0134932\pi$
$174$		0			0
$175$			1.38764i			0.104896i
$176$		0			0
$177$	1.30080	+	22.3418i	0.0977739	+	1.67931i
$178$		0			0
$179$	15.4730	−	15.4730i	1.15651	−	1.15651i	0.171289	−	0.985221i	$-0.445207\pi$
$179$	15.4730	−	15.4730i	1.15651	−	1.15651i	0.985221	−	0.171289i	$-0.0547931\pi$
$180$		0			0
$181$	−10.1627	−	17.6022i	−0.755384	−	1.30836i	−0.945183	−	0.326541i	$-0.894117\pi$
$181$	−10.1627	−	17.6022i	−0.755384	−	1.30836i	0.189799	−	0.981823i	$-0.439216\pi$
$182$		0			0
$183$	4.71562	+	2.36840i	0.348589	+	0.175077i
$184$		0			0
$185$	11.6422	+	5.99945i	0.855948	+	0.441088i
$186$		0			0
$187$	1.49910	−	0.401682i	0.109625	−	0.0293739i
$188$		0			0
$189$	19.7349	+	1.72781i	1.43550	+	0.125680i
$190$		0			0
$191$	−8.15152	−	8.15152i	−0.589823	−	0.589823i	0.347760	−	0.937584i	$-0.386942\pi$
$191$	−8.15152	−	8.15152i	−0.589823	−	0.589823i	−0.937584	+	0.347760i	$0.886942\pi$
$192$		0			0
$193$	5.27878	−	5.27878i	0.379975	−	0.379975i	−0.491118	−	0.871093i	$-0.663412\pi$
$193$	5.27878	−	5.27878i	0.379975	−	0.379975i	0.871093	+	0.491118i	$0.163412\pi$
$194$		0			0
$195$	2.12575	+	1.89184i	0.152228	+	0.135477i
$196$		0			0
$197$	−15.1620	−	8.75378i	−1.08025	−	0.623681i	−0.149284	−	0.988794i	$-0.547697\pi$
$197$	−15.1620	−	8.75378i	−1.08025	−	0.623681i	−0.930963	+	0.365113i	$0.881030\pi$
$198$		0			0
$199$	14.8274	+	14.8274i	1.05109	+	1.05109i	0.998623	+	0.0524668i	$0.0167084\pi$
$199$	14.8274	+	14.8274i	1.05109	+	1.05109i	0.0524668	+	0.998623i	$0.483292\pi$
$200$		0			0
$201$	−1.55763	−	4.70100i	−0.109867	−	0.331583i
$202$		0			0
$203$	7.73968	+	2.07384i	0.543219	+	0.145555i
$204$		0			0
$205$	4.65686	−	1.24780i	0.325249	−	0.0871503i
$206$		0			0
$207$	−6.47505	−	16.3006i	−0.450047	−	1.13297i
$208$		0			0
$209$	−5.57449	−	1.49368i	−0.385595	−	0.103320i
$210$		0			0
$211$	17.8600			1.22953			0.614765	−	0.788710i	$-0.289251\pi$
$211$	17.8600			1.22953			0.614765	+	0.788710i	$0.289251\pi$
$212$		0			0
$213$	−3.42292	−	10.3305i	−0.234535	−	0.707835i
$214$		0			0
$215$	7.88853	+	13.6633i	0.537994	+	0.931832i
$216$		0			0
$217$	−0.515499	+	1.92387i	−0.0349943	+	0.130601i
$218$		0			0
$219$	−24.3127	−	5.02068i	−1.64290	−	0.339266i
$220$		0			0
$221$	0.437761			0.0294470
$222$		0			0
$223$	−25.8852			−1.73340			−0.866702	−	0.498827i	$-0.833764\pi$
$223$	−25.8852			−1.73340			−0.866702	+	0.498827i	$0.833764\pi$
$224$		0			0
$225$	−0.652008	−	0.875874i	−0.0434672	−	0.0583916i
$226$		0			0
$227$	4.32519	−	16.1418i	0.287073	−	1.07137i	−0.660239	−	0.751056i	$-0.729545\pi$
$227$	4.32519	−	16.1418i	0.287073	−	1.07137i	0.947311	−	0.320314i	$-0.103788\pi$
$228$		0			0
$229$	5.30968	+	9.19664i	0.350874	+	0.607731i	0.986403	−	0.164346i	$-0.0525513\pi$
$229$	5.30968	+	9.19664i	0.350874	+	0.607731i	−0.635529	+	0.772077i	$0.719218\pi$
$230$		0			0
$231$	−16.9571	+	5.61860i	−1.11570	+	0.369676i
$232$		0			0
$233$	−26.3676			−1.72740			−0.863701	−	0.504005i	$-0.831859\pi$
$233$	−26.3676			−1.72740			−0.863701	+	0.504005i	$0.831859\pi$
$234$		0			0
$235$	2.79582	+	0.749136i	0.182379	+	0.0488683i
$236$		0			0
$237$	8.26820	−	16.4625i	0.537077	−	1.06935i
$238$		0			0
$239$	−3.62256	+	0.970662i	−0.234324	+	0.0627869i	−0.374070	−	0.927400i	$-0.622038\pi$
$239$	−3.62256	+	0.970662i	−0.234324	+	0.0627869i	0.139746	+	0.990187i	$0.455371\pi$
$240$		0			0
$241$	−3.84948	−	1.03147i	−0.247967	−	0.0664425i	0.132695	−	0.991157i	$-0.457637\pi$
$241$	−3.84948	−	1.03147i	−0.247967	−	0.0664425i	−0.380662	+	0.924714i	$0.624304\pi$
$242$		0			0
$243$	−13.2684	+	8.18220i	−0.851171	+	0.524889i
$244$		0			0
$245$	11.4724	+	11.4724i	0.732943	+	0.732943i
$246$		0			0
$247$	−1.40975	−	0.813920i	−0.0897003	−	0.0517885i
$248$		0			0
$249$	−6.37519	+	7.16345i	−0.404011	+	0.453965i
$250$		0			0
$251$	−17.9014	+	17.9014i	−1.12993	+	1.12993i	−0.139739	+	0.990188i	$0.544627\pi$
$251$	−17.9014	+	17.9014i	−1.12993	+	1.12993i	−0.990188	+	0.139739i	$0.955373\pi$
$252$		0			0
$253$	11.1837	+	11.1837i	0.703111	+	0.703111i
$254$		0			0
$255$	2.09532	+	0.432694i	0.131214	+	0.0270963i
$256$		0			0
$257$	−18.5669	+	4.97498i	−1.15817	+	0.310331i	−0.786235	−	0.617928i	$-0.787972\pi$
$257$	−18.5669	+	4.97498i	−1.15817	+	0.310331i	−0.371935	+	0.928259i	$0.621306\pi$
$258$		0			0
$259$	−22.0882	+	7.06495i	−1.37249	+	0.438995i
$260$		0			0
$261$	−5.85970	+	2.32763i	−0.362706	+	0.144077i
$262$		0			0
$263$	−13.0462	−	22.5967i	−0.804464	−	1.39337i	−0.916652	−	0.399685i	$-0.869119\pi$
$263$	−13.0462	−	22.5967i	−0.804464	−	1.39337i	0.112188	−	0.993687i	$-0.464214\pi$
$264$		0			0
$265$	0.729843	−	0.729843i	0.0448339	−	0.0448339i
$266$		0			0
$267$	20.9047	−	1.21713i	1.27935	−	0.0744869i
$268$		0			0
$269$		−	4.22158i		−	0.257395i	−0.991684	−	0.128697i	$-0.958920\pi$
$269$		−	4.22158i		−	0.257395i	0.991684	−	0.128697i	$-0.0410795\pi$
$270$		0			0
$271$	−12.7510	+	22.0854i	−0.774568	+	1.34159i	0.160468	+	0.987041i	$0.448700\pi$
$271$	−12.7510	+	22.0854i	−0.774568	+	1.34159i	−0.935037	+	0.354551i	$0.884634\pi$
$272$		0			0
$273$	−5.03024	+	0.292874i	−0.304444	+	0.0177255i
$274$		0			0
$275$	0.852703	+	0.492308i	0.0514199	+	0.0296873i
$276$		0			0
$277$	2.88639	−	10.7722i	0.173426	−	0.647236i	−0.823388	−	0.567479i	$-0.807919\pi$
$277$	2.88639	−	10.7722i	0.173426	−	0.647236i	0.996814	−	0.0797573i	$-0.0254145\pi$
$278$		0			0
$279$	−0.578583	−	1.45656i	−0.0346389	−	0.0872018i
$280$		0			0
$281$	15.6420	−	4.19125i	0.933122	−	0.250029i	0.239936	−	0.970789i	$-0.422873\pi$
$281$	15.6420	−	4.19125i	0.933122	−	0.250029i	0.693185	+	0.720759i	$0.256207\pi$
$282$		0			0
$283$	−5.79096	+	21.6121i	−0.344237	+	1.28471i	0.549265	+	0.835648i	$0.314908\pi$
$283$	−5.79096	+	21.6121i	−0.344237	+	1.28471i	−0.893501	+	0.449060i	$0.851759\pi$
$284$		0			0
$285$	−5.94320	−	5.28922i	−0.352045	−	0.313307i
$286$		0			0
$287$	−4.26832	+	7.39295i	−0.251951	+	0.436392i
$288$		0			0
$289$	−14.4374	+	8.33543i	−0.849259	+	0.490320i
$290$		0			0
$291$	0.289636	+	0.440390i	0.0169788	+	0.0258161i
$292$		0			0
$293$	14.9950	−	8.65737i	0.876018	−	0.505769i	0.00667446	−	0.999978i	$-0.497875\pi$
$293$	14.9950	−	8.65737i	0.876018	−	0.505769i	0.869343	+	0.494209i	$0.164542\pi$
$294$		0			0
$295$		−	27.8205i		−	1.61977i
$296$		0			0
$297$	8.06330	−	11.5141i	0.467880	−	0.668114i
$298$		0			0
$299$	2.23059	+	3.86350i	0.128998	+	0.223432i
$300$		0			0
$301$	−26.9841	−	7.23036i	−1.55534	−	0.416751i
$302$		0			0
$303$	0.835254	−	4.04472i	0.0479841	−	0.232363i
$304$		0			0
$305$	−5.68103	−	3.27995i	−0.325295	−	0.187809i
$306$		0			0
$307$		−	2.82163i		−	0.161039i	−0.996753	−	0.0805196i	$-0.974342\pi$
$307$		−	2.82163i		−	0.161039i	0.996753	−	0.0805196i	$-0.0256579\pi$
$308$		0			0
$309$	−11.7399	+	7.72110i	−0.667859	+	0.439238i
$310$		0			0
$311$	0.0473655	+	0.176770i	0.00268585	+	0.0100237i	0.967256	−	0.253804i	$-0.0816817\pi$
$311$	0.0473655	+	0.176770i	0.00268585	+	0.0100237i	−0.964570	+	0.263827i	$0.915015\pi$
$312$		0			0
$313$	3.12831	+	11.6750i	0.176823	+	0.659911i	0.996234	+	0.0867049i	$0.0276337\pi$
$313$	3.12831	+	11.6750i	0.176823	+	0.659911i	−0.819412	+	0.573206i	$0.805700\pi$
$314$		0			0
$315$	−24.3665	−	3.57019i	−1.37289	−	0.201157i
$316$		0			0
$317$	−6.21877	+	10.7712i	−0.349281	+	0.604973i	−0.986122	−	0.166023i	$-0.946908\pi$
$317$	−6.21877	+	10.7712i	−0.349281	+	0.604973i	0.636841	+	0.770995i	$0.280241\pi$
$318$		0			0
$319$	4.02027	−	4.02027i	0.225092	−	0.225092i
$320$		0			0
$321$	−4.55851	−	13.7578i	−0.254431	−	0.767884i
$322$		0			0
$323$	−1.22390			−0.0680994
$324$		0			0
$325$	0.196383	+	0.196383i	0.0108933	+	0.0108933i
$326$		0			0
$327$	29.9040	−	1.74109i	1.65369	−	0.0962824i
$328$		0			0
$329$	−4.43846	+	2.56255i	−0.244700	+	0.141278i
$330$		0			0
$331$	8.61140	+	32.1382i	0.473325	+	1.76647i	0.627693	+	0.778461i	$0.283999\pi$
$331$	8.61140	+	32.1382i	0.473325	+	1.76647i	−0.154368	+	0.988013i	$0.549334\pi$
$332$		0			0
$333$	10.6224	−	14.8379i	0.582105	−	0.813114i
$334$		0			0
$335$	1.59338	+	5.94657i	0.0870556	+	0.324896i
$336$		0			0
$337$	27.9700	−	16.1485i	1.52362	−	0.879665i	0.524014	−	0.851709i	$-0.324434\pi$
$337$	27.9700	−	16.1485i	1.52362	−	0.879665i	0.999609	−	0.0279552i	$-0.00889957\pi$
$338$		0			0
$339$	−24.0607	+	1.40088i	−1.30680	+	0.0760851i
$340$		0			0
$341$	0.999326	+	0.999326i	0.0541165	+	0.0541165i
$342$		0			0
$343$	−2.04046			−0.110175
$344$		0			0
$345$	6.85783	+	20.6972i	0.369213	+	1.11430i
$346$		0			0
$347$	−6.82848	+	6.82848i	−0.366572	+	0.366572i	−0.866225	−	0.499653i	$-0.833461\pi$
$347$	−6.82848	+	6.82848i	−0.366572	+	0.366572i	0.499653	+	0.866225i	$0.333461\pi$
$348$		0			0
$349$	9.81677	−	17.0031i	0.525480	−	0.910157i	−0.474080	−	0.880482i	$-0.657219\pi$
$349$	9.81677	−	17.0031i	0.525480	−	0.910157i	0.999560	−	0.0296755i	$-0.00944739\pi$
$350$		0			0
$351$	3.03746	−	2.54841i	0.162128	−	0.136024i
$352$		0			0
$353$	−0.682597	−	2.54749i	−0.0363310	−	0.135589i	0.945378	−	0.325975i	$-0.105693\pi$
$353$	−0.682597	−	2.54749i	−0.0363310	−	0.135589i	−0.981709	+	0.190386i	$0.939026\pi$
$354$		0			0
$355$	3.50147	+	13.0677i	0.185839	+	0.693559i
$356$		0			0
$357$	−3.16521	+	2.08169i	−0.167520	+	0.110175i
$358$		0			0
$359$			10.3090i			0.544089i	0.962285	+	0.272045i	$0.0876999\pi$
$359$			10.3090i			0.544089i	−0.962285	+	0.272045i	$0.912300\pi$
$360$		0			0
$361$	−12.5131	−	7.22443i	−0.658583	−	0.380233i
$362$		0			0
$363$	1.28969	−	6.24534i	0.0676914	−	0.327795i
$364$		0			0
$365$	29.8096	+	7.98747i	1.56031	+	0.418083i
$366$		0			0
$367$	9.04410	+	15.6648i	0.472098	+	0.817698i	0.999490	−	0.0319241i	$-0.0101635\pi$
$367$	9.04410	+	15.6648i	0.472098	+	0.817698i	−0.527392	+	0.849622i	$0.676830\pi$
$368$		0			0
$369$	−0.779560	−	6.67196i	−0.0405823	−	0.347328i
$370$		0			0
$371$			1.82760i			0.0948844i
$372$		0			0
$373$	10.0643	−	5.81064i	0.521111	−	0.300863i	−0.216278	−	0.976332i	$-0.569392\pi$
$373$	10.0643	−	5.81064i	0.521111	−	0.300863i	0.737389	+	0.675468i	$0.236059\pi$
$374$		0			0
$375$	10.9921	+	16.7135i	0.567630	+	0.863079i
$376$		0			0
$377$	1.38884	−	0.801846i	0.0715288	−	0.0412972i
$378$		0			0
$379$	−3.05369	+	5.28914i	−0.156857	+	0.271685i	−0.933734	−	0.357968i	$-0.883470\pi$
$379$	−3.05369	+	5.28914i	−0.156857	+	0.271685i	0.776876	+	0.629653i	$0.216803\pi$
$380$		0			0
$381$	25.4490	+	22.6486i	1.30379	+	1.16032i
$382$		0			0
$383$	−1.13067	+	4.21971i	−0.0577745	+	0.215617i	−0.988778	−	0.149393i	$-0.952268\pi$
$383$	−1.13067	+	4.21971i	−0.0577745	+	0.215617i	0.931003	+	0.365011i	$0.118935\pi$
$384$		0			0
$385$	21.4501	−	5.74753i	1.09320	−	0.292921i
$386$		0			0
$387$	20.4296	−	8.11518i	1.03849	−	0.412518i
$388$		0			0
$389$	6.88906	−	25.7103i	0.349289	−	1.30357i	−0.538231	−	0.842797i	$-0.680907\pi$
$389$	6.88906	−	25.7103i	0.349289	−	1.30357i	0.887520	−	0.460769i	$-0.152426\pi$
$390$		0			0
$391$	2.90478	+	1.67708i	0.146901	+	0.0848134i
$392$		0			0
$393$	8.97459	−	0.522524i	0.452708	−	0.0263579i
$394$		0			0
$395$	−11.4505	+	19.8328i	−0.576136	+	0.997897i
$396$		0			0
$397$			25.1748i			1.26349i	0.775178	+	0.631743i	$0.217660\pi$
$397$			25.1748i			1.26349i	−0.775178	+	0.631743i	$0.782340\pi$
$398$		0			0
$399$	14.0636	−	0.818819i	0.704060	−	0.0409922i
$400$		0			0
$401$	2.57603	−	2.57603i	0.128641	−	0.128641i	−0.639855	−	0.768496i	$-0.721006\pi$
$401$	2.57603	−	2.57603i	0.128641	−	0.128641i	0.768496	+	0.639855i	$0.221006\pi$
$402$		0			0
$403$	0.199316	+	0.345226i	0.00992865	+	0.0171969i
$404$		0			0
$405$	17.0576	−	9.19554i	0.847597	−	0.456930i
$406$		0			0
$407$	−3.49507	+	16.0797i	−0.173244	+	0.797041i
$408$		0			0
$409$	7.21772	−	1.93398i	0.356893	−	0.0956293i	−0.0759173	−	0.997114i	$-0.524189\pi$
$409$	7.21772	−	1.93398i	0.356893	−	0.0956293i	0.432811	+	0.901485i	$0.357522\pi$
$410$		0			0
$411$	21.6605	+	4.47300i	1.06843	+	0.220637i
$412$		0			0
$413$	34.8327	+	34.8327i	1.71401	+	1.71401i
$414$		0			0
$415$	8.42932	−	8.42932i	0.413779	−	0.413779i
$416$		0			0
$417$	−6.98058	+	7.84369i	−0.341841	+	0.384107i
$418$		0			0
$419$	−22.6734	−	13.0905i	−1.10767	−	0.639514i	−0.169445	−	0.985540i	$-0.554198\pi$
$419$	−22.6734	−	13.0905i	−1.10767	−	0.639514i	−0.938225	+	0.346026i	$0.887531\pi$
$420$		0			0
$421$	−15.5296	−	15.5296i	−0.756868	−	0.756868i	0.218883	−	0.975751i	$-0.429759\pi$
$421$	−15.5296	−	15.5296i	−0.756868	−	0.756868i	−0.975751	+	0.218883i	$0.929759\pi$
$422$		0			0
$423$	1.59749	−	3.70297i	0.0776724	−	0.180044i
$424$		0			0
$425$	0.201695	+	0.0540439i	0.00978363	+	0.00262152i
$426$		0			0
$427$	11.2196	−	3.00629i	0.542955	−	0.145484i
$428$		0			0
$429$	−1.60466	+	3.19498i	−0.0774739	+	0.154255i
$430$		0			0
$431$	30.1733	+	8.08490i	1.45339	+	0.389436i	0.897203	−	0.441618i	$-0.145595\pi$
$431$	30.1733	+	8.08490i	1.45339	+	0.389436i	0.556191	+	0.831054i	$0.312262\pi$
$432$		0			0
$433$	4.32635			0.207911			0.103955	−	0.994582i	$-0.466850\pi$
$433$	4.32635			0.207911			0.103955	+	0.994582i	$0.466850\pi$
$434$		0			0
$435$	7.44017	−	2.46523i	0.356729	−	0.118199i
$436$		0			0
$437$	−6.23631	−	10.8016i	−0.298323	−	0.516711i
$438$		0			0
$439$	−2.84602	+	10.6215i	−0.135833	+	0.506936i	0.864160	+	0.503217i	$0.167850\pi$
$439$	−2.84602	+	10.6215i	−0.135833	+	0.506936i	−0.999993	+	0.00371867i	$0.998816\pi$
$440$		0			0
$441$	18.1330	−	13.4984i	0.863478	−	0.642780i
$442$		0			0
$443$	−38.1169			−1.81099			−0.905493	−	0.424361i	$-0.860499\pi$
$443$	−38.1169			−1.81099			−0.905493	+	0.424361i	$0.860499\pi$
$444$		0			0
$445$	−26.0310			−1.23399
$446$		0			0
$447$	7.43327	+	1.53501i	0.351582	+	0.0726034i
$448$		0			0
$449$	−8.03325	+	29.9805i	−0.379113	+	1.41487i	0.468129	+	0.883660i	$0.344928\pi$
$449$	−8.03325	+	29.9805i	−0.379113	+	1.41487i	−0.847242	+	0.531207i	$0.821739\pi$
$450$		0			0
$451$	3.02864	+	5.24576i	0.142613	+	0.247013i
$452$		0			0
$453$	−4.62414	−	13.9558i	−0.217261	−	0.655702i
$454$		0			0
$455$	6.26377			0.293650
$456$		0			0
$457$	−0.367921	−	0.0985842i	−0.0172106	−	0.00461157i	0.250203	−	0.968193i	$-0.419502\pi$
$457$	−0.367921	−	0.0985842i	−0.0172106	−	0.00461157i	−0.267414	+	0.963582i	$0.586169\pi$
$458$		0			0
$459$	1.01975	−	2.80119i	0.0475977	−	0.130748i
$460$		0			0
$461$	4.95511	−	1.32772i	0.230782	−	0.0618379i	−0.141574	−	0.989928i	$-0.545216\pi$
$461$	4.95511	−	1.32772i	0.230782	−	0.0618379i	0.372357	+	0.928090i	$0.378550\pi$
$462$		0			0
$463$	−34.6268	−	9.27823i	−1.60925	−	0.431196i	−0.661428	−	0.750009i	$-0.730049\pi$
$463$	−34.6268	−	9.27823i	−1.60925	−	0.431196i	−0.947818	+	0.318813i	$0.896716\pi$
$464$		0			0
$465$	0.612787	+	1.84942i	0.0284173	+	0.0857646i
$466$		0			0
$467$	−4.14129	−	4.14129i	−0.191636	−	0.191636i	0.604767	−	0.796403i	$-0.293266\pi$
$467$	−4.14129	−	4.14129i	−0.191636	−	0.191636i	−0.796403	+	0.604767i	$0.793266\pi$
$468$		0			0
$469$	−9.44041	−	5.45042i	−0.435918	−	0.251677i
$470$		0			0
$471$	20.8128	+	18.5226i	0.959005	+	0.853477i
$472$		0			0
$473$	−14.0165	+	14.0165i	−0.644479	+	0.644479i
$474$		0			0
$475$	−0.549048	−	0.549048i	−0.0251921	−	0.0251921i
$476$		0			0
$477$	−0.858733	−	1.15358i	−0.0393187	−	0.0528187i
$478$		0			0
$479$	8.47115	−	2.26984i	0.387057	−	0.103712i	−0.0600427	−	0.998196i	$-0.519124\pi$
$479$	8.47115	−	2.26984i	0.387057	−	0.103712i	0.447099	+	0.894484i	$0.352457\pi$
$480$		0			0
$481$	−2.12613	+	4.12584i	−0.0969433	+	0.188122i
$482$		0			0
$483$	−34.5004	−	17.3276i	−1.56982	−	0.788434i
$484$		0			0
$485$	−0.327623	−	0.567459i	−0.0148766	−	0.0257670i
$486$		0			0
$487$	16.9721	−	16.9721i	0.769081	−	0.769081i	−0.208864	−	0.977945i	$-0.566977\pi$
$487$	16.9721	−	16.9721i	0.769081	−	0.769081i	0.977945	+	0.208864i	$0.0669766\pi$
$488$		0			0
$489$	2.17780	+	37.4046i	0.0984833	+	1.69150i
$490$		0			0
$491$		−	38.2408i		−	1.72578i	−0.505391	−	0.862891i	$-0.668652\pi$
$491$		−	38.2408i		−	1.72578i	0.505391	−	0.862891i	$-0.331348\pi$
$492$		0			0
$493$	0.602870	−	1.04420i	0.0271519	−	0.0470285i
$494$		0			0
$495$	−10.8386	+	13.7065i	−0.487161	+	0.616063i
$496$		0			0
$497$	−20.7454	−	11.9774i	−0.930559	−	0.537259i
$498$		0			0
$499$	1.26453	−	4.71928i	0.0566080	−	0.211264i	−0.931829	−	0.362899i	$-0.881787\pi$
$499$	1.26453	−	4.71928i	0.0566080	−	0.211264i	0.988437	+	0.151635i	$0.0484538\pi$
$500$		0			0
$501$	28.1379	+	14.1321i	1.25711	+	0.631376i
$502$		0			0
$503$	−24.0280	+	6.43830i	−1.07136	+	0.287069i	−0.751051	−	0.660244i	$-0.770453\pi$
$503$	−24.0280	+	6.43830i	−1.07136	+	0.287069i	−0.320307	+	0.947314i	$0.603786\pi$
$504$		0			0
$505$	−1.32882	+	4.95921i	−0.0591316	+	0.220682i
$506$		0			0
$507$	14.2989	−	16.0669i	0.635036	−	0.713554i
$508$		0			0
$509$	16.5803	−	28.7179i	0.734909	−	1.27290i	−0.219854	−	0.975533i	$-0.570558\pi$
$509$	16.5803	−	28.7179i	0.734909	−	1.27290i	0.954763	−	0.297367i	$-0.0961085\pi$
$510$		0			0
$511$	−47.3240	+	27.3225i	−2.09349	+	1.20868i
$512$		0			0
$513$	−8.49216	+	7.12487i	−0.374938	+	0.314571i
$514$		0			0
$515$	15.1273	−	8.73374i	0.666588	−	0.384855i
$516$		0			0
$517$			3.63658i			0.159936i
$518$		0			0
$519$	15.7537	+	14.0202i	0.691510	+	0.615417i
$520$		0			0
$521$	2.27342	+	3.93768i	0.0996004	+	0.172513i	0.911519	−	0.411257i	$-0.134910\pi$
$521$	2.27342	+	3.93768i	0.0996004	+	0.172513i	−0.811919	+	0.583770i	$0.801577\pi$
$522$		0			0
$523$	−21.5556	−	5.77580i	−0.942559	−	0.252558i	−0.245357	−	0.969433i	$-0.578905\pi$
$523$	−21.5556	−	5.77580i	−0.942559	−	0.252558i	−0.697202	+	0.716875i	$0.745572\pi$
$524$		0			0
$525$	−2.35380	−	0.486071i	−0.102728	−	0.0212139i
$526$		0			0
$527$	0.259559	+	0.149856i	0.0113066	+	0.00652785i
$528$		0			0
$529$			11.1819i			0.486168i
$530$		0			0
$531$	−38.3531	−	5.61952i	−1.66438	−	0.243867i
$532$		0			0
$533$	0.442206	+	1.65034i	0.0191541	+	0.0714840i
$534$		0			0
$535$	4.66312	+	17.4030i	0.201604	+	0.752397i
$536$		0			0
$537$	20.8263	+	31.6663i	0.898722	+	1.36650i
$538$		0			0
$539$	−10.1922	+	17.6533i	−0.439007	+	0.760383i
$540$		0			0
$541$	2.88877	−	2.88877i	0.124198	−	0.124198i	−0.642276	−	0.766474i	$-0.722010\pi$
$541$	2.88877	−	2.88877i	0.124198	−	0.124198i	0.766474	+	0.642276i	$0.222010\pi$
$542$		0			0
$543$	33.4178	−	11.0727i	1.43410	−	0.475175i
$544$		0			0
$545$	−37.2371			−1.59506
$546$		0			0
$547$	8.95410	+	8.95410i	0.382850	+	0.382850i	0.872128	−	0.489278i	$-0.162740\pi$
$547$	8.95410	+	8.95410i	0.382850	+	0.382850i	−0.489278	+	0.872128i	$0.662740\pi$
$548$		0			0
$549$	−5.66923	+	7.16930i	−0.241957	+	0.305978i
$550$		0			0
$551$	−3.88293	+	2.24181i	−0.165418	+	0.0955043i
$552$		0			0
$553$	−10.4951	−	39.1683i	−0.446298	−	1.66561i
$554$		0			0
$555$	−14.2547	+	17.6466i	−0.605079	+	0.749056i
$556$		0			0
$557$	−0.625587	−	2.33472i	−0.0265070	−	0.0989254i	0.951405	−	0.307942i	$-0.0996403\pi$
$557$	−0.625587	−	2.33472i	−0.0265070	−	0.0989254i	−0.977912	+	0.209017i	$0.932974\pi$
$558$		0			0
$559$	−4.84212	+	2.79560i	−0.204800	+	0.118241i
$560$		0			0
$561$	0.156244	+	2.68356i	0.00659663	+	0.113300i
$562$		0			0
$563$	2.76272	+	2.76272i	0.116435	+	0.116435i	0.762924	−	0.646489i	$-0.223763\pi$
$563$	2.76272	+	2.76272i	0.116435	+	0.116435i	−0.646489	+	0.762924i	$0.723763\pi$
$564$		0			0
$565$	29.9609			1.26046
$566$		0			0
$567$	−9.84367	+	32.8703i	−0.413395	+	1.38042i
$568$		0			0
$569$	22.4734	−	22.4734i	0.942135	−	0.942135i	−0.0562797	−	0.998415i	$-0.517924\pi$
$569$	22.4734	−	22.4734i	0.942135	−	0.942135i	0.998415	+	0.0562797i	$0.0179238\pi$
$570$		0			0
$571$	1.85572	−	3.21420i	0.0776595	−	0.134510i	−0.824580	−	0.565745i	$-0.808589\pi$
$571$	1.85572	−	3.21420i	0.0776595	−	0.134510i	0.902240	+	0.431235i	$0.141922\pi$
$572$		0			0
$573$	16.6825	−	10.9717i	0.696920	−	0.458351i
$574$		0			0
$575$	0.550757	+	2.05545i	0.0229682	+	0.0857183i
$576$		0			0
$577$	9.48223	+	35.3882i	0.394750	+	1.47323i	0.822205	+	0.569192i	$0.192744\pi$
$577$	9.48223	+	35.3882i	0.394750	+	1.47323i	−0.427454	+	0.904037i	$0.640590\pi$
$578$		0			0
$579$	7.10510	+	10.8033i	0.295278	+	0.448969i
$580$		0			0
$581$			21.1079i			0.875703i
$582$		0			0
$583$	1.12306	+	0.648399i	0.0465124	+	0.0268539i
$584$		0			0
$585$	−3.95367	+	2.94315i	−0.163464	+	0.121684i
$586$		0			0
$587$	11.0572	+	2.96278i	0.456381	+	0.122287i	0.479684	−	0.877442i	$-0.340751\pi$
$587$	11.0572	+	2.96278i	0.456381	+	0.122287i	−0.0233027	+	0.999728i	$0.507418\pi$
$588$		0			0
$589$	−0.557251	−	0.965186i	−0.0229611	−	0.0397698i
$590$		0			0
$591$	20.1597	−	22.6524i	0.829260	−	0.931793i
$592$		0			0
$593$		−	7.80685i		−	0.320589i	−0.987069	−	0.160294i	$-0.948756\pi$
$593$		−	7.80685i		−	0.320589i	0.987069	−	0.160294i	$-0.0512444\pi$
$594$		0			0
$595$	4.07849	−	2.35472i	0.167202	−	0.0965339i
$596$		0			0
$597$	−30.3450	+	19.9574i	−1.24194	+	0.816800i
$598$		0			0
$599$	−37.8861	+	21.8735i	−1.54798	+	0.893728i	−0.549687	+	0.835371i	$0.685253\pi$
$599$	−37.8861	+	21.8735i	−1.54798	+	0.893728i	−0.998296	+	0.0583578i	$0.981414\pi$
$600$		0			0
$601$	−6.72804	+	11.6533i	−0.274443	+	0.475348i	−0.969994	−	0.243128i	$-0.921827\pi$
$601$	−6.72804	+	11.6533i	−0.274443	+	0.475348i	0.695552	+	0.718476i	$0.255160\pi$
$602$		0			0
$603$	8.51974	−	0.995458i	0.346951	−	0.0405382i
$604$		0			0
$605$	−2.05179	+	7.65739i	−0.0834171	+	0.311317i
$606$		0			0
$607$	22.2333	−	5.95740i	0.902422	−	0.241803i	0.222366	−	0.974963i	$-0.428622\pi$
$607$	22.2333	−	5.95740i	0.902422	−	0.241803i	0.680056	+	0.733160i	$0.261955\pi$
$608$		0			0
$609$	−6.22888	+	12.4021i	−0.252407	+	0.502558i
$610$		0			0
$611$	−0.265485	+	0.990803i	−0.0107404	+	0.0400836i
$612$		0			0
$613$	−26.3900	−	15.2363i	−1.06588	−	0.615388i	−0.138829	−	0.990316i	$-0.544334\pi$
$613$	−26.3900	−	15.2363i	−1.06588	−	0.615388i	−0.927054	+	0.374928i	$0.877667\pi$
$614$		0			0
$615$	0.485363	+	8.33634i	0.0195717	+	0.336153i
$616$		0			0
$617$	8.51897	−	14.7553i	0.342961	−	0.594026i	−0.642020	−	0.766688i	$-0.721904\pi$
$617$	8.51897	−	14.7553i	0.342961	−	0.594026i	0.984981	+	0.172662i	$0.0552368\pi$
$618$		0			0
$619$			21.1165i			0.848744i	0.905488	+	0.424372i	$0.139505\pi$
$619$			21.1165i			0.848744i	−0.905488	+	0.424372i	$0.860495\pi$
$620$		0			0
$621$	29.9182	−	5.27348i	1.20058	−	0.211617i
$622$		0			0
$623$	32.5922	−	32.5922i	1.30578	−	1.30578i
$624$		0			0
$625$	−11.5238	−	19.9599i	−0.460953	−	0.798395i
$626$		0			0
$627$	4.48633	−	8.93257i	0.179167	−	0.356732i
$628$		0			0
$629$	0.166636	+	3.48570i	0.00664421	+	0.138984i
$630$		0			0
$631$	−4.08463	+	1.09447i	−0.162606	+	0.0435703i	−0.339204	−	0.940713i	$-0.610158\pi$
$631$	−4.08463	+	1.09447i	−0.162606	+	0.0435703i	0.176597	+	0.984283i	$0.443491\pi$
$632$		0			0
$633$	−6.25610	+	30.2951i	−0.248658	+	1.20412i
$634$		0			0
$635$	−29.9462	−	29.9462i	−1.18838	−	1.18838i
$636$		0			0
$637$	−4.06567	+	4.06567i	−0.161088	+	0.161088i
$638$		0			0
$639$	18.7222	−	2.18753i	0.740640	−	0.0865374i
$640$		0			0
$641$	37.6527	+	21.7388i	1.48719	+	0.858630i	0.999893	−	0.0146055i	$-0.00464923\pi$
$641$	37.6527	+	21.7388i	1.48719	+	0.858630i	0.487298	+	0.873236i	$0.337983\pi$
$642$		0			0
$643$	−0.0304529	−	0.0304529i	−0.00120094	−	0.00120094i	0.706506	−	0.707707i	$-0.250270\pi$
$643$	−0.0304529	−	0.0304529i	−0.00120094	−	0.00120094i	−0.707707	+	0.706506i	$0.750270\pi$
$644$		0			0
$645$	−25.9398	+	8.59493i	−1.02138	+	0.338425i
$646$		0			0
$647$	−5.14937	−	1.37977i	−0.202443	−	0.0542444i	0.156173	−	0.987730i	$-0.450084\pi$
$647$	−5.14937	−	1.37977i	−0.202443	−	0.0542444i	−0.358615	+	0.933485i	$0.616751\pi$
$648$		0			0
$649$	33.7627	−	9.04668i	1.32530	−	0.355113i
$650$		0			0
$651$	−3.08281	−	1.54832i	−0.120825	−	0.0606836i
$652$		0			0
$653$	12.0727	+	3.23487i	0.472441	+	0.126590i	0.487181	−	0.873301i	$-0.338025\pi$
$653$	12.0727	+	3.23487i	0.472441	+	0.126590i	−0.0147396	+	0.999891i	$0.504692\pi$
$654$		0			0
$655$	−11.1754			−0.436658
$656$		0			0
$657$	17.0328	−	39.4819i	0.664512	−	1.54034i
$658$		0			0
$659$	4.98746	+	8.63853i	0.194284	+	0.336509i	0.946665	−	0.322218i	$-0.104428\pi$
$659$	4.98746	+	8.63853i	0.194284	+	0.336509i	−0.752382	+	0.658727i	$0.771095\pi$
$660$		0			0
$661$	−5.70231	+	21.2813i	−0.221794	+	0.827747i	0.761869	+	0.647731i	$0.224282\pi$
$661$	−5.70231	+	21.2813i	−0.221794	+	0.827747i	−0.983664	+	0.180016i	$0.942385\pi$
$662$		0			0
$663$	−0.153342	+	0.742556i	−0.00595529	+	0.0288385i
$664$		0			0
$665$	−17.5123			−0.679098
$666$		0			0
$667$	12.2876			0.475777
$668$		0			0
$669$	9.06724	−	43.9081i	0.350560	−	1.69758i
$670$		0			0
$671$	2.13315	−	7.96102i	0.0823493	−	0.307332i
$672$		0			0
$673$	20.0857	+	34.7894i	0.774245	+	1.34103i	0.935218	+	0.354073i	$0.115204\pi$
$673$	20.0857	+	34.7894i	0.774245	+	1.34103i	−0.160972	+	0.986959i	$0.551463\pi$
$674$		0			0
$675$	1.71410	−	0.799168i	0.0659757	−	0.0307600i
$676$		0			0
$677$	−26.0209			−1.00006			−0.500032	−	0.866007i	$-0.666678\pi$
$677$	−26.0209			−1.00006			−0.500032	+	0.866007i	$0.666678\pi$
$678$		0			0
$679$	1.12069	+	0.300288i	0.0430081	+	0.0115240i
$680$		0			0
$681$	25.8657	+	12.9909i	0.991175	+	0.497812i
$682$		0			0
$683$	−37.3180	+	9.99932i	−1.42793	+	0.382613i	−0.888291	−	0.459281i	$-0.848107\pi$
$683$	−37.3180	+	9.99932i	−1.42793	+	0.382613i	−0.539642	+	0.841895i	$0.681440\pi$
$684$		0			0
$685$	−26.5578	−	7.11615i	−1.01472	−	0.271894i
$686$		0			0
$687$	−17.4598	+	5.78515i	−0.666133	+	0.220717i
$688$		0			0
$689$	0.258647	+	0.258647i	0.00985368	+	0.00985368i
$690$		0			0
$691$	−9.90110	−	5.71640i	−0.376656	−	0.217462i	0.299707	−	0.954031i	$-0.403111\pi$
$691$	−9.90110	−	5.71640i	−0.376656	−	0.217462i	−0.676362	+	0.736569i	$0.736445\pi$
$692$		0			0
$693$	−3.59075	−	30.7318i	−0.136401	−	1.16741i
$694$		0			0
$695$	9.22977	−	9.22977i	0.350105	−	0.350105i
$696$		0			0
$697$	0.908335	+	0.908335i	0.0344056	+	0.0344056i
$698$		0			0
$699$	9.23622	−	44.7264i	0.349346	−	1.69171i
$700$		0			0
$701$	−16.8314	+	4.50995i	−0.635712	+	0.170338i	−0.562260	−	0.826960i	$-0.690068\pi$
$701$	−16.8314	+	4.50995i	−0.635712	+	0.170338i	−0.0734516	+	0.997299i	$0.523401\pi$
$702$		0			0
$703$	5.94427	−	11.5351i	0.224192	−	0.435053i
$704$		0			0
$705$	−2.25007	+	4.48002i	−0.0847424	+	0.168727i
$706$		0			0
$707$	−4.54544	−	7.87294i	−0.170949	−	0.296092i
$708$		0			0
$709$	−9.66349	+	9.66349i	−0.362920	+	0.362920i	−0.864887	−	0.501967i	$-0.832610\pi$
$709$	−9.66349	+	9.66349i	−0.362920	+	0.362920i	0.501967	+	0.864887i	$0.332610\pi$
$710$		0			0
$711$	25.0284	+	19.7916i	0.938640	+	0.742243i
$712$		0			0
$713$			3.05435i			0.114386i
$714$		0			0
$715$	2.22227	−	3.84908i	0.0831081	−	0.143947i
$716$		0			0
$717$	−0.377563	−	6.48481i	−0.0141003	−	0.242180i
$718$		0			0
$719$	0.428771	+	0.247551i	0.0159905	+	0.00923210i	0.507974	−	0.861372i	$-0.330395\pi$
$719$	0.428771	+	0.247551i	0.0159905	+	0.00923210i	−0.491983	+	0.870605i	$0.663728\pi$
$720$		0			0
$721$	−8.00505	+	29.8753i	−0.298124	+	1.11261i
$722$		0			0
$723$	3.09805	−	6.16841i	0.115218	−	0.229406i
$724$		0			0
$725$	0.738888	−	0.197984i	0.0274416	−	0.00735296i
$726$		0			0
$727$	13.5199	−	50.4571i	0.501427	−	1.87135i	0.0108727	−	0.999941i	$-0.496539\pi$
$727$	13.5199	−	50.4571i	0.501427	−	1.87135i	0.490554	−	0.871411i	$-0.336794\pi$
$728$		0			0
$729$	−9.23140	−	25.3728i	−0.341904	−	0.939735i
$730$		0			0
$731$	−2.10188	+	3.64056i	−0.0777409	+	0.134651i
$732$		0			0
$733$	−31.0179	+	17.9082i	−1.14567	+	0.661453i	−0.947829	−	0.318781i	$-0.896727\pi$
$733$	−31.0179	+	17.9082i	−1.14567	+	0.661453i	−0.197842	+	0.980234i	$0.563393\pi$
$734$		0			0
$735$	−23.4787	+	15.4415i	−0.866026	+	0.569569i
$736$		0			0
$737$	−6.69856	+	3.86742i	−0.246745	+	0.142458i
$738$		0			0
$739$		−	21.7053i		−	0.798444i	−0.916854	−	0.399222i	$-0.869280\pi$
$739$		−	21.7053i		−	0.798444i	0.916854	−	0.399222i	$-0.130720\pi$
$740$		0			0
$741$	1.87444	−	2.10620i	0.0688592	−	0.0773732i
$742$		0			0
$743$	−9.08901	−	15.7426i	−0.333443	−	0.577541i	0.649741	−	0.760155i	$-0.274877\pi$
$743$	−9.08901	−	15.7426i	−0.333443	−	0.577541i	−0.983185	+	0.182615i	$0.941544\pi$
$744$		0			0
$745$	−9.11391	−	2.44206i	−0.333908	−	0.0894703i
$746$		0			0
$747$	−9.91793	−	13.3232i	−0.362878	−	0.487472i
$748$		0			0
$749$	−27.6279	−	15.9510i	−1.00950	−	0.582837i
$750$		0			0
$751$		−	13.1087i		−	0.478342i	−0.970977	−	0.239171i	$-0.923124\pi$
$751$		−	13.1087i		−	0.478342i	0.970977	−	0.239171i	$-0.0768757\pi$
$752$		0			0
$753$	−24.0949	−	36.6361i	−0.878065	−	1.33509i
$754$		0			0
$755$	4.73025	+	17.6535i	0.172151	+	0.642478i
$756$		0			0
$757$	−7.75169	−	28.9297i	−0.281740	−	1.05147i	−0.951189	−	0.308610i	$-0.900136\pi$
$757$	−7.75169	−	28.9297i	−0.281740	−	1.05147i	0.669449	−	0.742858i	$-0.266530\pi$
$758$		0			0
$759$	−22.8879	+	15.0529i	−0.830778	+	0.546387i
$760$		0			0
$761$	9.51049	−	16.4727i	0.344755	−	0.597133i	−0.640554	−	0.767913i	$-0.721295\pi$
$761$	9.51049	−	16.4727i	0.344755	−	0.597133i	0.985309	+	0.170780i	$0.0546287\pi$
$762$		0			0
$763$	46.6228	−	46.6228i	1.68786	−	1.68786i
$764$		0			0
$765$	−1.46792	+	3.40264i	−0.0530729	+	0.123023i
$766$		0			0
$767$	9.85925			0.355997
$768$		0			0
$769$	−14.7047	−	14.7047i	−0.530267	−	0.530267i	0.390385	−	0.920652i	$-0.372342\pi$
$769$	−14.7047	−	14.7047i	−0.530267	−	0.530267i	−0.920652	+	0.390385i	$0.872342\pi$
$770$		0			0
$771$	−1.93514	−	33.2369i	−0.0696924	−	1.19700i
$772$		0			0
$773$	−44.2120	+	25.5258i	−1.59019	+	0.918099i	−0.596921	+	0.802300i	$0.703610\pi$
$773$	−44.2120	+	25.5258i	−1.59019	+	0.918099i	−0.993273	+	0.115799i	$0.963057\pi$
$774$		0			0
$775$	0.0492133	+	0.183667i	0.00176780	+	0.00659750i
$776$		0			0
$777$	−4.24681	−	39.9421i	−0.152353	−	1.43292i
$778$		0			0
$779$	−1.23632	−	4.61402i	−0.0442959	−	0.165315i
$780$		0			0
$781$	−14.7202	+	8.49870i	−0.526729	+	0.304107i
$782$		0			0
$783$	−1.89569	−	10.7549i	−0.0677466	−	0.384349i
$784$		0			0
$785$	−24.4907	−	24.4907i	−0.874111	−	0.874111i
$786$		0			0
$787$	38.2063			1.36191			0.680953	−	0.732327i	$-0.261566\pi$
$787$	38.2063			1.36191			0.680953	+	0.732327i	$0.261566\pi$
$788$		0			0
$789$	42.8998	−	14.2145i	1.52727	−	0.506048i
$790$		0			0
$791$	−37.5126	+	37.5126i	−1.33380	+	1.33380i
$792$		0			0
$793$	1.16237	−	2.01329i	0.0412771	−	0.0714940i
$794$		0			0
$795$	0.982349	+	1.49366i	0.0348403	+	0.0529746i
$796$		0			0
$797$	−5.38267	−	20.0884i	−0.190664	−	0.711567i	−0.993347	−	0.115161i	$-0.963262\pi$
$797$	−5.38267	−	20.0884i	−0.190664	−	0.711567i	0.802683	−	0.596406i	$-0.203405\pi$
$798$		0			0
$799$	0.199606	+	0.744938i	0.00706154	+	0.0263540i
$800$		0			0
$801$	−5.25806	+	35.8862i	−0.185785	+	1.26798i
$802$		0			0
$803$			38.7740i			1.36831i
$804$		0			0
$805$	41.5635	+	23.9967i	1.46492	+	0.845773i
$806$		0			0
$807$	7.16091	+	1.47876i	0.252076	+	0.0520549i
$808$		0			0
$809$	43.1204	+	11.5541i	1.51603	+	0.406219i	0.918433	−	0.395576i	$-0.129455\pi$
$809$	43.1204	+	11.5541i	1.51603	+	0.406219i	0.597598	+	0.801796i	$0.296122\pi$
$810$		0			0
$811$	19.6567	+	34.0464i	0.690241	+	1.19553i	0.971759	+	0.235976i	$0.0758286\pi$
$811$	19.6567	+	34.0464i	0.690241	+	1.19553i	−0.281518	+	0.959556i	$0.590838\pi$
$812$		0			0
$813$	−32.9961	−	29.3652i	−1.15722	−	1.02988i
$814$		0			0
$815$		−	46.5771i		−	1.63153i
$816$		0			0
$817$	13.5377	−	7.81597i	0.473623	−	0.273446i
$818$		0			0
$819$	1.26523	−	8.63518i	0.0442108	−	0.301738i
$820$		0			0
$821$	−26.8684	+	15.5125i	−0.937713	+	0.541389i	−0.889243	−	0.457436i	$-0.848768\pi$
$821$	−26.8684	+	15.5125i	−0.937713	+	0.541389i	−0.0484704	+	0.998825i	$0.515435\pi$
$822$		0			0
$823$	7.08841	−	12.2775i	0.247086	−	0.427966i	−0.715630	−	0.698480i	$-0.753860\pi$
$823$	7.08841	−	12.2775i	0.247086	−	0.427966i	0.962716	+	0.270514i	$0.0871935\pi$
$824$		0			0
$825$	−1.13377	+	1.27396i	−0.0394729	+	0.0443535i
$826$		0			0
$827$	−4.39269	+	16.3937i	−0.152749	+	0.570066i	0.846539	+	0.532327i	$0.178682\pi$
$827$	−4.39269	+	16.3937i	−0.152749	+	0.570066i	−0.999288	+	0.0377390i	$0.987984\pi$
$828$		0			0
$829$	31.8785	−	8.54182i	1.10719	−	0.296670i	0.341499	−	0.939882i	$-0.389065\pi$
$829$	31.8785	−	8.54182i	1.10719	−	0.296670i	0.765688	+	0.643212i	$0.222399\pi$
$830$		0			0
$831$	17.2613	+	8.66941i	0.598789	+	0.300738i
$832$		0			0
$833$	−1.11886	+	4.17564i	−0.0387662	+	0.144677i
$834$		0			0
$835$	−33.8985	−	19.5713i	−1.17311	−	0.677293i
$836$		0			0
$837$	2.67337	−	0.471216i	0.0924051	−	0.0162876i
$838$		0			0
$839$	−11.0490	+	19.1374i	−0.381452	+	0.660695i	−0.991270	−	0.131847i	$-0.957909\pi$
$839$	−11.0490	+	19.1374i	−0.381452	+	0.660695i	0.609818	+	0.792542i	$0.291243\pi$
$840$		0			0
$841$			24.5829i			0.847686i
$842$		0			0
$843$	1.63029	+	28.0010i	0.0561502	+	0.964405i
$844$		0			0
$845$	−18.9061	+	18.9061i	−0.650389	+	0.650389i
$846$		0			0
$847$	−7.01850	−	12.1564i	−0.241158	−	0.417699i
$848$		0			0
$849$	−34.6313	−	17.3934i	−1.18854	−	0.596940i
$850$		0			0
$851$	−29.9143	+	19.2319i	−1.02545	+	0.659261i
$852$		0			0
$853$	52.1734	−	13.9798i	1.78638	−	0.478660i	0.794660	−	0.607055i	$-0.207649\pi$
$853$	52.1734	−	13.9798i	1.78638	−	0.478660i	0.991723	+	0.128396i	$0.0409827\pi$
$854$		0			0
$855$	11.0537	−	8.22848i	0.378029	−	0.281408i
$856$		0			0
$857$	−20.7919	−	20.7919i	−0.710237	−	0.710237i	0.256347	−	0.966585i	$-0.417481\pi$
$857$	−20.7919	−	20.7919i	−0.710237	−	0.710237i	−0.966585	+	0.256347i	$0.917481\pi$
$858$		0			0
$859$	−6.23621	+	6.23621i	−0.212777	+	0.212777i	−0.805446	−	0.592669i	$-0.798074\pi$
$859$	−6.23621	+	6.23621i	−0.212777	+	0.212777i	0.592669	+	0.805446i	$0.298074\pi$
$860$		0			0
$861$	−11.0452	−	9.82983i	−0.376420	−	0.335000i
$862$		0			0
$863$	32.4080	+	18.7108i	1.10318	+	0.636922i	0.937055	−	0.349182i	$-0.113541\pi$
$863$	32.4080	+	18.7108i	1.10318	+	0.636922i	0.166127	+	0.986104i	$0.446874\pi$
$864$		0			0
$865$	−18.5375	−	18.5375i	−0.630295	−	0.630295i
$866$		0			0
$867$	−9.08185	−	27.4094i	−0.308436	−	0.930871i
$868$		0			0
$869$	−27.7924	−	7.44694i	−0.942791	−	0.252620i
$870$		0			0
$871$	−2.10739	+	0.564674i	−0.0714063	+	0.0191333i
$872$		0			0
$873$	−0.848472	+	0.337036i	−0.0287164	+	0.0114069i
$874$		0			0
$875$	42.5318	+	11.3964i	1.43784	+	0.385267i
$876$		0			0
$877$	−25.6171			−0.865027			−0.432513	−	0.901628i	$-0.642373\pi$
$877$	−25.6171			−0.865027			−0.432513	+	0.901628i	$0.642373\pi$
$878$		0			0
$879$	9.43261	+	28.4680i	0.318154	+	0.960202i
$880$		0			0
$881$	20.2599	+	35.0911i	0.682572	+	1.18225i	0.974193	+	0.225716i	$0.0724720\pi$
$881$	20.2599	+	35.0911i	0.682572	+	1.18225i	−0.291621	+	0.956534i	$0.594195\pi$
$882$		0			0
$883$	−3.29281	+	12.2889i	−0.110812	+	0.413556i	−0.998940	−	0.0460410i	$-0.985339\pi$
$883$	−3.29281	+	12.2889i	−0.110812	+	0.413556i	0.888128	+	0.459597i	$0.152006\pi$
$884$		0			0
$885$	47.1908	+	9.74514i	1.58630	+	0.327579i
$886$		0			0
$887$	35.6590			1.19731			0.598655	−	0.801007i	$-0.295702\pi$
$887$	35.6590			1.19731			0.598655	+	0.801007i	$0.295702\pi$
$888$		0			0
$889$	74.9883			2.51503
$890$		0			0
$891$	16.7064	+	17.7107i	0.559685	+	0.593330i
$892$		0			0
$893$	0.742245	−	2.77010i	0.0248383	−	0.0926978i
$894$		0			0
$895$	−23.5578	−	40.8032i	−0.787449	−	1.36390i
$896$		0			0
$897$	−7.33484	+	2.43033i	−0.244903	+	0.0811465i
$898$		0			0
$899$	1.09797			0.0366193
$900$		0			0
$901$	0.265644	+	0.0711790i	0.00884988	+	0.00237132i
$902$		0			0
$903$	21.7167	−	43.2393i	0.722687	−	1.43891i
$904$		0			0
$905$	−42.2721	+	11.3268i	−1.40517	+	0.376515i
$906$		0			0
$907$	43.3896	+	11.6262i	1.44073	+	0.386042i	0.892789	−	0.450475i	$-0.148745\pi$
$907$	43.3896	+	11.6262i	1.44073	+	0.386042i	0.547940	+	0.836517i	$0.315412\pi$
$908$		0			0
$909$	6.56832	+	2.83362i	0.217857	+	0.0939851i
$910$		0			0
$911$	−33.8502	−	33.8502i	−1.12151	−	1.12151i	−0.991515	−	0.129992i	$-0.958505\pi$
$911$	−33.8502	−	33.8502i	−1.12151	−	1.12151i	−0.129992	−	0.991515i	$-0.541495\pi$
$912$		0			0
$913$	12.9708	+	7.48868i	0.429270	+	0.247839i
$914$		0			0
$915$	7.55363	−	8.48759i	0.249715	−	0.280591i
$916$		0			0
$917$	13.9922	−	13.9922i	0.462062	−	0.462062i
$918$		0			0
$919$	−29.1574	−	29.1574i	−0.961812	−	0.961812i	0.0374849	−	0.999297i	$-0.488065\pi$
$919$	−29.1574	−	29.1574i	−0.961812	−	0.961812i	−0.999297	+	0.0374849i	$0.988065\pi$
$920$		0			0
$921$	4.78622	+	0.988379i	0.157711	+	0.0325682i
$922$		0			0
$923$	−4.63102	+	1.24088i	−0.152432	+	0.0408440i
$924$		0			0
$925$	−1.48896	+	1.63846i	−0.0489566	+	0.0538723i
$926$		0			0
$927$	−8.98468	−	22.6185i	−0.295095	−	0.742889i
$928$		0			0
$929$	−12.1939	−	21.1204i	−0.400069	−	0.692939i	0.593665	−	0.804712i	$-0.297680\pi$
$929$	−12.1939	−	21.1204i	−0.400069	−	0.692939i	−0.993734	+	0.111773i	$0.964347\pi$
$930$		0			0
$931$	11.3668	−	11.3668i	0.372533	−	0.372533i
$932$		0			0
$933$	−0.316440	+	0.0184240i	−0.0103598	+	0.000603174i
$934$		0			0
$935$		−	3.34164i		−	0.109283i
$936$		0			0
$937$	−12.5493	+	21.7360i	−0.409967	+	0.710084i	−0.994886	−	0.101008i	$-0.967793\pi$
$937$	−12.5493	+	21.7360i	−0.409967	+	0.710084i	0.584918	+	0.811092i	$0.301127\pi$
$938$		0			0
$939$	−20.8997	+	1.21683i	−0.682035	+	0.0397099i
$940$		0			0
$941$	−41.2185	−	23.7975i	−1.34369	−	0.775777i	−0.356339	−	0.934357i	$-0.615975\pi$
$941$	−41.2185	−	23.7975i	−1.34369	−	0.775777i	−0.987346	+	0.158580i	$0.949309\pi$
$942$		0			0
$943$	−3.38821	+	12.6450i	−0.110335	+	0.411777i
$944$		0			0
$945$	14.5912	−	40.0813i	0.474652	−	1.30384i
$946$		0			0
$947$	20.4547	−	5.48081i	0.664687	−	0.178102i	0.0893269	−	0.996002i	$-0.471528\pi$
$947$	20.4547	−	5.48081i	0.664687	−	0.178102i	0.575361	+	0.817900i	$0.304862\pi$
$948$		0			0
$949$	−2.83066	+	10.5642i	−0.0918872	+	0.342928i
$950$		0			0
$951$	−16.0925	−	14.3217i	−0.521834	−	0.464412i
$952$		0			0
$953$	−1.26786	+	2.19600i	−0.0410701	+	0.0711355i	−0.885830	−	0.464010i	$-0.846410\pi$
$953$	−1.26786	+	2.19600i	−0.0410701	+	0.0711355i	0.844760	+	0.535146i	$0.179743\pi$
$954$		0			0
$955$	−21.4960	+	12.4107i	−0.695594	+	0.401601i
$956$		0			0
$957$	5.41118	+	8.22767i	0.174919	+	0.265963i
$958$		0			0
$959$	42.1616	−	24.3420i	1.36147	−	0.786044i
$960$		0			0
$961$		−	30.7271i		−	0.991196i
$962$		0			0
$963$	24.9336	−	2.91327i	0.803473	−	0.0938788i
$964$		0			0
$965$	−8.03696	−	13.9204i	−0.258719	−	0.448114i
$966$		0			0
$967$	−14.2720	−	3.82418i	−0.458958	−	0.122977i	0.0219301	−	0.999760i	$-0.493019\pi$
$967$	−14.2720	−	3.82418i	−0.458958	−	0.122977i	−0.480888	+	0.876782i	$0.659686\pi$
$968$		0			0
$969$	0.428714	−	2.07605i	0.0137723	−	0.0666922i
$970$		0			0
$971$	45.4278	+	26.2278i	1.45785	+	0.841689i	0.998905	−	0.0467766i	$-0.0148949\pi$
$971$	45.4278	+	26.2278i	1.45785	+	0.841689i	0.458943	+	0.888466i	$0.348228\pi$
$972$		0			0
$973$			23.1123i			0.740947i
$974$		0			0
$975$	−0.401906	+	0.264326i	−0.0128713	+	0.00846520i
$976$		0			0
$977$	−4.88999	−	18.2497i	−0.156445	−	0.583859i	−0.998977	−	0.0452140i	$-0.985603\pi$
$977$	−4.88999	−	18.2497i	−0.156445	−	0.583859i	0.842533	−	0.538645i	$-0.181064\pi$
$978$		0			0
$979$	−8.46478	−	31.5910i	−0.270536	−	1.00965i
$980$		0			0
$981$	−7.52161	+	51.3348i	−0.240147	+	1.63899i
$982$		0			0
$983$	13.9935	−	24.2375i	0.446324	−	0.773056i	−0.551819	−	0.833964i	$-0.686066\pi$
$983$	13.9935	−	24.2375i	0.446324	−	0.773056i	0.998143	+	0.0609077i	$0.0193995\pi$
$984$		0			0
$985$	−26.6553	+	26.6553i	−0.849309	+	0.849309i
$986$		0			0
$987$	−2.79202	−	8.42642i	−0.0888709	−	0.268216i
$988$		0			0
$989$	−42.8402			−1.36224
$990$		0			0
$991$	−2.82365	−	2.82365i	−0.0896962	−	0.0896962i	0.660835	−	0.750531i	$-0.270202\pi$
$991$	−2.82365	−	2.82365i	−0.0896962	−	0.0896962i	−0.750531	+	0.660835i	$0.770202\pi$
$992$		0			0
$993$	−57.5312	+	3.34962i	−1.82570	+	0.106297i
$994$		0			0
$995$	39.1007	−	22.5748i	1.23958	−	0.715670i
$996$		0			0
$997$	0.191959	+	0.716402i	0.00607941	+	0.0226887i	0.968899	−	0.247457i	$-0.0795949\pi$
$997$	0.191959	+	0.716402i	0.00607941	+	0.0226887i	−0.962820	+	0.270146i	$0.912928\pi$
$998$		0			0
$999$	21.4481	+	23.2159i	0.678588	+	0.734519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.br.a.569.17	yes	152
3.2	odd	2	inner	888.2.br.a.569.4	✓	152
37.8	odd	12	inner	888.2.br.a.785.4	yes	152
111.8	even	12	inner	888.2.br.a.785.17	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.br.a.569.4	✓	152	3.2	odd	2	inner
888.2.br.a.569.17	yes	152	1.1	even	1	trivial
888.2.br.a.785.4	yes	152	37.8	odd	12	inner
888.2.br.a.785.17	yes	152	111.8	even	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.350286 + 1.69626i) q^{3} +(0.557275 - 2.07978i) q^{5} +(1.90625 + 3.30173i) q^{7} +(-2.75460 - 1.18835i) q^{9} +2.70521 q^{11} +(0.737048 + 0.197491i) q^{13} +(3.33264 + 1.67380i) q^{15} +(0.554152 - 0.148484i) q^{17} +(-2.06065 - 0.552149i) q^{19} +(-6.26832 + 2.07695i) q^{21} +(4.13412 + 4.13412i) q^{23} +(0.315207 + 0.181985i) q^{25} +(2.98065 - 4.25625i) q^{27} +(1.48612 - 1.48612i) q^{29} +(0.369408 + 0.369408i) q^{31} +(-0.947598 + 4.58874i) q^{33} +(7.92916 - 2.12461i) q^{35} +(-1.29198 + 5.94397i) q^{37} +(-0.593175 + 1.18105i) q^{39} +(1.11956 + 1.93913i) q^{41} +(-5.18129 + 5.18129i) q^{43} +(-4.00658 + 5.06671i) q^{45} +1.34429i q^{47} +(-3.76760 + 6.52568i) q^{49} +(0.0577567 + 0.991997i) q^{51} +(0.415147 + 0.239685i) q^{53} +(1.50755 - 5.62624i) q^{55} +(1.65840 - 3.30198i) q^{57} +(12.4806 - 3.34417i) q^{59} +(0.788533 - 2.94285i) q^{61} +(-1.32735 - 11.3602i) q^{63} +(0.821477 - 1.42284i) q^{65} +(-2.47617 + 1.42962i) q^{67} +(-8.46067 + 5.56442i) q^{69} +(-5.44141 + 3.14160i) q^{71} +14.3331i q^{73} +(-0.419107 + 0.470927i) q^{75} +(5.15682 + 8.93187i) q^{77} +(-10.2736 - 2.75281i) q^{79} +(6.17563 + 6.54687i) q^{81} +(4.79474 + 2.76824i) q^{83} -1.23526i q^{85} +(2.00028 + 3.04141i) q^{87} +(-3.12906 - 11.6778i) q^{89} +(0.752937 + 2.81000i) q^{91} +(-0.756010 + 0.497213i) q^{93} +(-2.29669 + 3.97799i) q^{95} +(0.215187 - 0.215187i) q^{97} +(-7.45177 - 3.21475i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) \) 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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