LMFDB - Embedded newform 888.2.br.a.569.31

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)

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")

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);

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			569.31
Character	$\chi$	$=$	888.569
Dual form			888.2.br.a.785.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.31619 + 1.12590i) q^{3} +(0.299949 - 1.11942i) q^{5} +(0.728081 + 1.26107i) q^{7} +(0.464686 + 2.96379i) q^{9} +2.75595 q^{11} +(5.87134 + 1.57322i) q^{13} +(1.65515 - 1.13566i) q^{15} +(-4.20756 + 1.12741i) q^{17} +(-5.86193 - 1.57070i) q^{19} +(-0.461557 + 2.47956i) q^{21} +(-4.77233 - 4.77233i) q^{23} +(3.16699 + 1.82846i) q^{25} +(-2.72533 + 4.42409i) q^{27} +(3.63333 - 3.63333i) q^{29} +(4.56339 + 4.56339i) q^{31} +(3.62734 + 3.10293i) q^{33} +(1.63006 - 0.436774i) q^{35} +(6.04893 + 0.640631i) q^{37} +(5.95647 + 8.68120i) q^{39} +(1.37162 + 2.37572i) q^{41} +(2.55190 - 2.55190i) q^{43} +(3.45712 + 0.368805i) q^{45} +9.51426i q^{47} +(2.43980 - 4.22585i) q^{49} +(-6.80729 - 3.25342i) q^{51} +(-7.21838 - 4.16753i) q^{53} +(0.826644 - 3.08508i) q^{55} +(-5.94693 - 8.66730i) q^{57} +(3.55732 - 0.953181i) q^{59} +(-3.66715 + 13.6860i) q^{61} +(-3.39923 + 2.74389i) q^{63} +(3.52220 - 6.10063i) q^{65} +(4.17797 - 2.41215i) q^{67} +(-0.908090 - 11.6544i) q^{69} +(-8.53196 + 4.92593i) q^{71} -4.05969i q^{73} +(2.10967 + 5.97231i) q^{75} +(2.00656 + 3.47546i) q^{77} +(-12.9500 - 3.46994i) q^{79} +(-8.56813 + 2.75447i) q^{81} +(-3.62264 - 2.09153i) q^{83} +5.04822i q^{85} +(8.87291 - 0.691359i) q^{87} +(-2.69541 - 10.0594i) q^{89} +(2.29086 + 8.54962i) q^{91} +(0.868332 + 11.1442i) q^{93} +(-3.51656 + 6.09086i) q^{95} +(1.19949 - 1.19949i) q^{97} +(1.28065 + 8.16807i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.31619	+	1.12590i	0.759900	+	0.650040i
$3$	1.31619	+	1.12590i	0.759900	+	0.650040i
$4$		0			0
$5$	0.299949	−	1.11942i	0.134141	−	0.500622i	−0.865859	−	0.500289i	$-0.833227\pi$
$5$	0.299949	−	1.11942i	0.134141	−	0.500622i	1.00000		0.000333270i	$-0.000106083\pi$
$6$		0			0
$7$	0.728081	+	1.26107i	0.275189	+	0.476641i	0.970183	−	0.242375i	$-0.0779263\pi$
$7$	0.728081	+	1.26107i	0.275189	+	0.476641i	−0.694994	+	0.719016i	$0.744593\pi$
$8$		0			0
$9$	0.464686	+	2.96379i	0.154895	+	0.987931i
$10$		0			0
$11$	2.75595			0.830950			0.415475	−	0.909604i	$-0.363615\pi$
$11$	2.75595			0.830950			0.415475	+	0.909604i	$0.363615\pi$
$12$		0			0
$13$	5.87134	+	1.57322i	1.62842	+	0.436333i	0.953459	−	0.301524i	$-0.0974953\pi$
$13$	5.87134	+	1.57322i	1.62842	+	0.436333i	0.674957	+	0.737857i	$0.264162\pi$
$14$		0			0
$15$	1.65515	−	1.13566i	0.427358	−	0.293225i
$16$		0			0
$17$	−4.20756	+	1.12741i	−1.02048	+	0.273438i	−0.730004	−	0.683443i	$-0.760482\pi$
$17$	−4.20756	+	1.12741i	−1.02048	+	0.273438i	−0.290480	+	0.956881i	$0.593815\pi$
$18$		0			0
$19$	−5.86193	−	1.57070i	−1.34482	−	0.360343i	−0.486600	−	0.873625i	$-0.661763\pi$
$19$	−5.86193	−	1.57070i	−1.34482	−	0.360343i	−0.858220	+	0.513282i	$0.828430\pi$
$20$		0			0
$21$	−0.461557	+	2.47956i	−0.100720	+	0.541083i
$22$		0			0
$23$	−4.77233	−	4.77233i	−0.995099	−	0.995099i	0.00488889	−	0.999988i	$-0.498444\pi$
$23$	−4.77233	−	4.77233i	−0.995099	−	0.995099i	−0.999988	+	0.00488889i	$0.998444\pi$
$24$		0			0
$25$	3.16699	+	1.82846i	0.633397	+	0.365692i
$26$		0			0
$27$	−2.72533	+	4.42409i	−0.524490	+	0.851417i
$28$		0			0
$29$	3.63333	−	3.63333i	0.674693	−	0.674693i	−0.284101	−	0.958794i	$-0.591695\pi$
$29$	3.63333	−	3.63333i	0.674693	−	0.674693i	0.958794	+	0.284101i	$0.0916953\pi$
$30$		0			0
$31$	4.56339	+	4.56339i	0.819608	+	0.819608i	0.986051	−	0.166443i	$-0.0532281\pi$
$31$	4.56339	+	4.56339i	0.819608	+	0.819608i	−0.166443	+	0.986051i	$0.553228\pi$
$32$		0			0
$33$	3.62734	+	3.10293i	0.631439	+	0.540151i
$34$		0			0
$35$	1.63006	−	0.436774i	0.275531	−	0.0738283i
$36$		0			0
$37$	6.04893	+	0.640631i	0.994438	+	0.105319i
$37$	6.04893	+	0.640631i	0.994438	+	0.105319i
$38$		0			0
$39$	5.95647	+	8.68120i	0.953799	+	1.39011i
$40$		0			0
$41$	1.37162	+	2.37572i	0.214212	+	0.371025i	0.953028	−	0.302881i	$-0.0979484\pi$
$41$	1.37162	+	2.37572i	0.214212	+	0.371025i	−0.738817	+	0.673906i	$0.764615\pi$
$42$		0			0
$43$	2.55190	−	2.55190i	0.389161	−	0.389161i	−0.485227	−	0.874388i	$-0.661263\pi$
$43$	2.55190	−	2.55190i	0.389161	−	0.389161i	0.874388	+	0.485227i	$0.161263\pi$
$44$		0			0
$45$	3.45712	+	0.368805i	0.515358	+	0.0549782i
$46$		0			0
$47$			9.51426i			1.38780i	0.720072	+	0.693899i	$0.244109\pi$
$47$			9.51426i			1.38780i	−0.720072	+	0.693899i	$0.755891\pi$
$48$		0			0
$49$	2.43980	−	4.22585i	0.348542	−	0.603693i
$50$		0			0
$51$	−6.80729	−	3.25342i	−0.953211	−	0.455570i
$52$		0			0
$53$	−7.21838	−	4.16753i	−0.991521	−	0.572455i	−0.0857922	−	0.996313i	$-0.527342\pi$
$53$	−7.21838	−	4.16753i	−0.991521	−	0.572455i	−0.905728	+	0.423858i	$0.860675\pi$
$54$		0			0
$55$	0.826644	−	3.08508i	0.111465	−	0.415992i
$56$		0			0
$57$	−5.94693	−	8.66730i	−0.787691	−	1.14801i
$58$		0			0
$59$	3.55732	−	0.953181i	0.463123	−	0.124094i	−0.0197100	−	0.999806i	$-0.506274\pi$
$59$	3.55732	−	0.953181i	0.463123	−	0.124094i	0.482833	+	0.875712i	$0.339608\pi$
$60$		0			0
$61$	−3.66715	+	13.6860i	−0.469531	+	1.75231i	0.171883	+	0.985117i	$0.445015\pi$
$61$	−3.66715	+	13.6860i	−0.469531	+	1.75231i	−0.641414	+	0.767195i	$0.721652\pi$
$62$		0			0
$63$	−3.39923	+	2.74389i	−0.428263	+	0.345697i
$64$		0			0
$65$	3.52220	−	6.10063i	0.436875	−	0.756690i
$66$		0			0
$67$	4.17797	−	2.41215i	0.510420	−	0.294691i	−0.222586	−	0.974913i	$-0.571450\pi$
$67$	4.17797	−	2.41215i	0.510420	−	0.294691i	0.733006	+	0.680222i	$0.238116\pi$
$68$		0			0
$69$	−0.908090	−	11.6544i	−0.109321	−	1.40303i
$70$		0			0
$71$	−8.53196	+	4.92593i	−1.01256	+	0.584600i	−0.911939	−	0.410325i	$-0.865415\pi$
$71$	−8.53196	+	4.92593i	−1.01256	+	0.584600i	−0.100618	+	0.994925i	$0.532082\pi$
$72$		0			0
$73$		−	4.05969i		−	0.475151i	−0.971369	−	0.237576i	$-0.923647\pi$
$73$		−	4.05969i		−	0.475151i	0.971369	−	0.237576i	$-0.0763527\pi$
$74$		0			0
$75$	2.10967	+	5.97231i	0.243604	+	0.689623i
$76$		0			0
$77$	2.00656	+	3.47546i	0.228668	+	0.396065i
$78$		0			0
$79$	−12.9500	−	3.46994i	−1.45699	−	0.390398i	−0.558539	−	0.829478i	$-0.688638\pi$
$79$	−12.9500	−	3.46994i	−1.45699	−	0.390398i	−0.898448	+	0.439080i	$0.855304\pi$
$80$		0			0
$81$	−8.56813	+	2.75447i	−0.952015	+	0.306052i
$82$		0			0
$83$	−3.62264	−	2.09153i	−0.397636	−	0.229575i	0.287827	−	0.957682i	$-0.407067\pi$
$83$	−3.62264	−	2.09153i	−0.397636	−	0.229575i	−0.685463	+	0.728107i	$0.740400\pi$
$84$		0			0
$85$			5.04822i			0.547556i
$86$		0			0
$87$	8.87291	−	0.691359i	0.951276	−	0.0741215i
$88$		0			0
$89$	−2.69541	−	10.0594i	−0.285713	−	1.06630i	−0.948317	−	0.317326i	$-0.897215\pi$
$89$	−2.69541	−	10.0594i	−0.285713	−	1.06630i	0.662604	−	0.748970i	$-0.269451\pi$
$90$		0			0
$91$	2.29086	+	8.54962i	0.240148	+	0.896244i
$92$		0			0
$93$	0.868332	+	11.1442i	0.0900419	+	1.15560i
$94$		0			0
$95$	−3.51656	+	6.09086i	−0.360792	+	0.624909i
$96$		0			0
$97$	1.19949	−	1.19949i	0.121790	−	0.121790i	−0.643585	−	0.765375i	$-0.722554\pi$
$97$	1.19949	−	1.19949i	0.121790	−	0.121790i	0.765375	+	0.643585i	$0.222554\pi$
$98$		0			0
$99$	1.28065	+	8.16807i	0.128710	+	0.820922i
$100$		0			0
$101$	13.8035			1.37350			0.686749	−	0.726895i	$-0.259037\pi$
$101$	13.8035			1.37350			0.686749	+	0.726895i	$0.259037\pi$
$102$		0			0
$103$	5.19197	+	5.19197i	0.511580	+	0.511580i	0.915010	−	0.403431i	$-0.132182\pi$
$103$	5.19197	+	5.19197i	0.511580	+	0.511580i	−0.403431	+	0.915010i	$0.632182\pi$
$104$		0			0
$105$	2.63723	+	1.26042i	0.257367	+	0.123004i
$106$		0			0
$107$	−2.13166	+	1.23072i	−0.206076	+	0.118978i	−0.599486	−	0.800385i	$-0.704628\pi$
$107$	−2.13166	+	1.23072i	−0.206076	+	0.118978i	0.393411	+	0.919363i	$0.371295\pi$
$108$		0			0
$109$	−4.63156	−	17.2852i	−0.443623	−	1.65562i	−0.719547	−	0.694444i	$-0.755650\pi$
$109$	−4.63156	−	17.2852i	−0.443623	−	1.65562i	0.275923	−	0.961180i	$-0.411016\pi$
$110$		0			0
$111$	7.24023	+	7.65370i	0.687212	+	0.726457i
$112$		0			0
$113$	−3.61208	−	13.4805i	−0.339796	−	1.26813i	−0.898576	−	0.438818i	$-0.855397\pi$
$113$	−3.61208	−	13.4805i	−0.339796	−	1.26813i	0.558780	−	0.829316i	$-0.311270\pi$
$114$		0			0
$115$	−6.77372	+	3.91081i	−0.631652	+	0.364685i
$116$		0			0
$117$	−1.93437	+	18.1325i	−0.178832	+	1.67635i
$118$		0			0
$119$	−4.48520	−	4.48520i	−0.411158	−	0.411158i
$120$		0			0
$121$	−3.40473			−0.309521
$122$		0			0
$123$	−0.869521	+	4.67121i	−0.0784021	+	0.421188i
$124$		0			0
$125$	7.09413	−	7.09413i	0.634519	−	0.634519i
$126$		0			0
$127$	−1.67594	+	2.90282i	−0.148716	+	0.257583i	−0.930753	−	0.365648i	$-0.880847\pi$
$127$	−1.67594	+	2.90282i	−0.148716	+	0.257583i	0.782037	+	0.623232i	$0.214181\pi$
$128$		0			0
$129$	6.23196	−	0.485581i	0.548693	−	0.0427530i
$130$		0			0
$131$	−4.51073	−	16.8343i	−0.394104	−	1.47082i	−0.823301	−	0.567605i	$-0.807870\pi$
$131$	−4.51073	−	16.8343i	−0.394104	−	1.47082i	0.429197	−	0.903211i	$-0.358797\pi$
$132$		0			0
$133$	−2.28720	−	8.53593i	−0.198325	−	0.740159i
$134$		0			0
$135$	4.13498	+	4.37780i	0.355882	+	0.376781i
$136$		0			0
$137$		−	16.6140i		−	1.41943i	−0.704488	−	0.709716i	$-0.748823\pi$
$137$		−	16.6140i		−	1.41943i	0.704488	−	0.709716i	$-0.251177\pi$
$138$		0			0
$139$	−14.1171	−	8.15051i	−1.19740	−	0.691317i	−0.237423	−	0.971406i	$-0.576303\pi$
$139$	−14.1171	−	8.15051i	−1.19740	−	0.691317i	−0.959974	+	0.280089i	$0.909636\pi$
$140$		0			0
$141$	−10.7121	+	12.5225i	−0.902124	+	1.05459i
$142$		0			0
$143$	16.1811	+	4.33572i	1.35313	+	0.362571i
$144$		0			0
$145$	−2.97743	−	5.15705i	−0.247262	−	0.428270i
$146$		0			0
$147$	7.96912	−	2.81503i	0.657282	−	0.232180i
$148$		0			0
$149$			0.655054i			0.0536641i	0.999640	+	0.0268321i	$0.00854193\pi$
$149$			0.655054i			0.0536641i	−0.999640	+	0.0268321i	$0.991458\pi$
$150$		0			0
$151$	7.85567	−	4.53547i	0.639285	−	0.369091i	−0.145054	−	0.989424i	$-0.546336\pi$
$151$	7.85567	−	4.53547i	0.639285	−	0.369091i	0.784339	+	0.620332i	$0.213002\pi$
$152$		0			0
$153$	−5.29662	−	11.9465i	−0.428206	−	0.965814i
$154$		0			0
$155$	6.47715	−	3.73958i	0.520257	−	0.300371i
$156$		0			0
$157$	0.639227	−	1.10717i	0.0510158	−	0.0883620i	−0.839390	−	0.543530i	$-0.817087\pi$
$157$	0.639227	−	1.10717i	0.0510158	−	0.0883620i	0.890406	+	0.455168i	$0.150421\pi$
$158$		0			0
$159$	−4.80849	−	13.6124i	−0.381338	−	1.07954i
$160$		0			0
$161$	2.54361	−	9.49290i	0.200465	−	0.748145i
$162$		0			0
$163$	−19.4378	+	5.20834i	−1.52248	+	0.407948i	−0.920559	−	0.390604i	$-0.872266\pi$
$163$	−19.4378	+	5.20834i	−1.52248	+	0.407948i	−0.601925	+	0.798552i	$0.705600\pi$
$164$		0			0
$165$	4.56152	−	3.12981i	0.355114	−	0.243656i
$166$		0			0
$167$	4.04336	−	15.0900i	0.312884	−	1.16770i	−0.613059	−	0.790038i	$-0.710061\pi$
$167$	4.04336	−	15.0900i	0.312884	−	1.16770i	0.925943	−	0.377663i	$-0.123272\pi$
$168$		0			0
$169$	20.7393	+	11.9738i	1.59533	+	0.921063i
$170$		0			0
$171$	1.93127	−	18.1034i	0.147688	−	1.38440i
$172$		0			0
$173$	−7.04460	+	12.2016i	−0.535591	+	0.927670i	0.463544	+	0.886074i	$0.346578\pi$
$173$	−7.04460	+	12.2016i	−0.535591	+	0.927670i	−0.999135	+	0.0415962i	$0.986756\pi$
$174$		0			0
$175$			5.32507i			0.402537i
$176$		0			0
$177$	5.75528	+	2.75063i	0.432593	+	0.206750i
$178$		0			0
$179$	−8.65000	+	8.65000i	−0.646531	+	0.646531i	−0.952153	−	0.305622i	$-0.901136\pi$
$179$	−8.65000	+	8.65000i	−0.646531	+	0.646531i	0.305622	+	0.952153i	$0.401136\pi$
$180$		0			0
$181$	−2.96839	−	5.14140i	−0.220639	−	0.382157i	0.734363	−	0.678757i	$-0.237481\pi$
$181$	−2.96839	−	5.14140i	−0.220639	−	0.382157i	−0.955002	+	0.296599i	$0.904147\pi$
$182$		0			0
$183$	−20.2358	+	13.8845i	−1.49587	+	1.02637i
$184$		0			0
$185$	2.53151	−	6.57917i	0.186120	−	0.483710i
$186$		0			0
$187$	−11.5958	+	3.10710i	−0.847972	+	0.227213i
$188$		0			0
$189$	−7.56337	−	0.215742i	−0.550154	−	0.0156930i
$190$		0			0
$191$	0.204551	+	0.204551i	0.0148008	+	0.0148008i	0.714468	−	0.699668i	$-0.246669\pi$
$191$	0.204551	+	0.204551i	0.0148008	+	0.0148008i	−0.699668	+	0.714468i	$0.746669\pi$
$192$		0			0
$193$	14.2178	−	14.2178i	1.02342	−	1.02342i	0.0236988	−	0.999719i	$-0.492456\pi$
$193$	14.2178	−	14.2178i	1.02342	−	1.02342i	0.999719	−	0.0236988i	$-0.00754428\pi$
$194$		0			0
$195$	11.5046	−	4.06391i	0.823861	−	0.291022i
$196$		0			0
$197$	21.0553	+	12.1563i	1.50013	+	0.866100i	1.00000		0.000148355i	$4.72228e-5\pi$
$197$	21.0553	+	12.1563i	1.50013	+	0.866100i	0.500128	+	0.865951i	$0.333286\pi$
$198$		0			0
$199$	3.82586	+	3.82586i	0.271208	+	0.271208i	0.829586	−	0.558378i	$-0.188576\pi$
$199$	3.82586	+	3.82586i	0.271208	+	0.271208i	−0.558378	+	0.829586i	$0.688576\pi$
$200$		0			0
$201$	8.21483	+	1.52915i	0.579430	+	0.107858i
$202$		0			0
$203$	7.22726	+	1.93654i	0.507254	+	0.135918i
$204$		0			0
$205$	3.07086	−	0.822834i	0.214478	−	0.0574692i
$206$		0			0
$207$	11.9266	−	16.3618i	0.828953	−	1.13723i
$208$		0			0
$209$	−16.1552	−	4.32877i	−1.11748	−	0.299428i
$210$		0			0
$211$	−19.1417			−1.31777			−0.658884	−	0.752245i	$-0.728971\pi$
$211$	−19.1417			−1.31777			−0.658884	+	0.752245i	$0.728971\pi$
$212$		0			0
$213$	−16.7758	−	3.12272i	−1.14946	−	0.213965i
$214$		0			0
$215$	−2.09122	−	3.62210i	−0.142620	−	0.247025i
$216$		0			0
$217$	−2.43225	+	9.07728i	−0.165112	+	0.616206i
$218$		0			0
$219$	4.57082	−	5.34331i	0.308867	−	0.361067i
$220$		0			0
$221$	−26.4777			−1.78108
$222$		0			0
$223$	−0.0487611			−0.00326528			−0.00163264	−	0.999999i	$-0.500520\pi$
$223$	−0.0487611			−0.00326528			−0.00163264	+	0.999999i	$0.500520\pi$
$224$		0			0
$225$	−3.94752	+	10.2359i	−0.263168	+	0.682396i
$226$		0			0
$227$	−5.82975	+	21.7569i	−0.386934	+	1.44406i	0.448161	+	0.893953i	$0.352079\pi$
$227$	−5.82975	+	21.7569i	−0.386934	+	1.44406i	−0.835095	+	0.550106i	$0.814587\pi$
$228$		0			0
$229$	2.91902	+	5.05588i	0.192894	+	0.334102i	0.946208	−	0.323559i	$-0.104879\pi$
$229$	2.91902	+	5.05588i	0.192894	+	0.334102i	−0.753314	+	0.657661i	$0.771546\pi$
$230$		0			0
$231$	−1.27203	+	6.83353i	−0.0836933	+	0.449613i
$232$		0			0
$233$	6.67585			0.437350			0.218675	−	0.975798i	$-0.429827\pi$
$233$	6.67585			0.437350			0.218675	+	0.975798i	$0.429827\pi$
$234$		0			0
$235$	10.6505	+	2.85379i	0.694762	+	0.186161i
$236$		0			0
$237$	−13.1378	−	19.1475i	−0.853389	−	1.24376i
$238$		0			0
$239$	15.4713	−	4.14553i	1.00076	−	0.268152i	0.278994	−	0.960293i	$-0.409999\pi$
$239$	15.4713	−	4.14553i	1.00076	−	0.268152i	0.721762	+	0.692141i	$0.243332\pi$
$240$		0			0
$241$	−11.1211	−	2.97989i	−0.716373	−	0.191952i	−0.117820	−	0.993035i	$-0.537591\pi$
$241$	−11.1211	−	2.97989i	−0.716373	−	0.191952i	−0.598553	+	0.801083i	$0.704257\pi$
$242$		0			0
$243$	−14.3785	−	6.02149i	−0.922382	−	0.386279i
$244$		0			0
$245$	−3.99871	−	3.99871i	−0.255468	−	0.255468i
$246$		0			0
$247$	−31.9463	−	18.4442i	−2.03270	−	1.17358i
$248$		0			0
$249$	−2.41320	−	6.83158i	−0.152930	−	0.432934i
$250$		0			0
$251$	8.54565	−	8.54565i	0.539396	−	0.539396i	−0.383955	−	0.923352i	$-0.625438\pi$
$251$	8.54565	−	8.54565i	0.539396	−	0.539396i	0.923352	+	0.383955i	$0.125438\pi$
$252$		0			0
$253$	−13.1523	−	13.1523i	−0.826878	−	0.826878i
$254$		0			0
$255$	−5.68380	+	6.64439i	−0.355933	+	0.416088i
$256$		0			0
$257$	9.67555	−	2.59256i	0.603544	−	0.161719i	0.0559083	−	0.998436i	$-0.482195\pi$
$257$	9.67555	−	2.59256i	0.603544	−	0.161719i	0.547636	+	0.836717i	$0.315528\pi$
$258$		0			0
$259$	3.59623	+	8.09458i	0.223459	+	0.502973i
$260$		0			0
$261$	12.4568	+	9.08008i	0.771057	+	0.562043i
$262$		0			0
$263$	−10.7533	−	18.6253i	−0.663078	−	1.14848i	−0.979803	−	0.199967i	$-0.935917\pi$
$263$	−10.7533	−	18.6253i	−0.663078	−	1.14848i	0.316725	−	0.948517i	$-0.397417\pi$
$264$		0			0
$265$	−6.83038	+	6.83038i	−0.419587	+	0.419587i
$266$		0			0
$267$	7.77826	−	16.2748i	0.476022	−	0.996003i
$268$		0			0
$269$			16.0152i			0.976461i	0.872715	+	0.488231i	$0.162358\pi$
$269$			16.0152i			0.976461i	−0.872715	+	0.488231i	$0.837642\pi$
$270$		0			0
$271$	0.434608	−	0.752762i	0.0264005	−	0.0457271i	−0.852523	−	0.522689i	$-0.824929\pi$
$271$	0.434608	−	0.752762i	0.0264005	−	0.0457271i	0.878924	+	0.476962i	$0.158262\pi$
$272$		0			0
$273$	−6.61084	+	13.8322i	−0.400106	+	0.837161i
$274$		0			0
$275$	8.72806	+	5.03915i	0.526322	+	0.303872i
$276$		0			0
$277$	0.0637437	−	0.237895i	0.00382999	−	0.0142937i	−0.963984	−	0.265959i	$-0.914311\pi$
$277$	0.0637437	−	0.237895i	0.00382999	−	0.0142937i	0.967814	+	0.251665i	$0.0809781\pi$
$278$		0			0
$279$	−11.4044	+	15.6455i	−0.682763	+	0.936670i
$280$		0			0
$281$	−30.8486	+	8.26585i	−1.84027	+	0.493099i	−0.998880	−	0.0473251i	$-0.984930\pi$
$281$	−30.8486	+	8.26585i	−1.84027	+	0.493099i	−0.841392	+	0.540425i	$0.818264\pi$
$282$		0			0
$283$	6.14133	−	22.9198i	0.365064	−	1.36244i	−0.502269	−	0.864711i	$-0.667501\pi$
$283$	6.14133	−	22.9198i	0.365064	−	1.36244i	0.867334	−	0.497727i	$-0.165832\pi$
$284$		0			0
$285$	−11.4862	+	4.05740i	−0.680382	+	0.240339i
$286$		0			0
$287$	−1.99731	+	3.45944i	−0.117897	+	0.204204i
$288$		0			0
$289$	1.71010	−	0.987329i	0.100594	−	0.0580782i
$290$		0			0
$291$	2.92926	−	0.228242i	0.171716	−	0.0133798i
$292$		0			0
$293$	−7.97345	+	4.60348i	−0.465814	+	0.268938i	−0.714486	−	0.699650i	$-0.753339\pi$
$293$	−7.97345	+	4.60348i	−0.465814	+	0.268938i	0.248672	+	0.968588i	$0.420006\pi$
$294$		0			0
$295$		−	4.26806i		−	0.248496i
$296$		0			0
$297$	−7.51087	+	12.1926i	−0.435825	+	0.707485i
$298$		0			0
$299$	−20.5120	−	35.5279i	−1.18624	−	2.05463i
$300$		0			0
$301$	5.07612	+	1.36014i	0.292583	+	0.0783973i
$302$		0			0
$303$	18.1679	+	15.5414i	1.04372	+	0.892829i
$304$		0			0
$305$	14.2205	+	8.21020i	0.814263	+	0.470115i
$306$		0			0
$307$			15.7611i			0.899534i	0.893146	+	0.449767i	$0.148493\pi$
$307$			15.7611i			0.899534i	−0.893146	+	0.449767i	$0.851507\pi$
$308$		0			0
$309$	0.987940	+	12.6792i	0.0562019	+	0.721297i
$310$		0			0
$311$	−1.68494	−	6.28828i	−0.0955441	−	0.356576i	0.901557	−	0.432660i	$-0.142425\pi$
$311$	−1.68494	−	6.28828i	−0.0955441	−	0.356576i	−0.997101	+	0.0760842i	$0.975758\pi$
$312$		0			0
$313$	−4.99393	−	18.6376i	−0.282274	−	1.05346i	−0.950809	−	0.309779i	$-0.899745\pi$
$313$	−4.99393	−	18.6376i	−0.282274	−	1.05346i	0.668535	−	0.743681i	$-0.266922\pi$
$314$		0			0
$315$	2.05198	+	4.62821i	0.115616	+	0.260770i
$316$		0			0
$317$	−0.743066	+	1.28703i	−0.0417348	+	0.0722867i	−0.886138	−	0.463421i	$-0.846622\pi$
$317$	−0.743066	+	1.28703i	−0.0417348	+	0.0722867i	0.844403	+	0.535708i	$0.179955\pi$
$318$		0			0
$319$	10.0133	−	10.0133i	0.560636	−	0.560636i
$320$		0			0
$321$	−4.19133	−	0.780194i	−0.233937	−	0.0435462i
$322$		0			0
$323$	26.4353			1.47090
$324$		0			0
$325$	15.7179	+	15.7179i	0.871871	+	0.871871i
$326$		0			0
$327$	13.3655	−	27.9652i	0.739113	−	1.54648i
$328$		0			0
$329$	−11.9982	+	6.92716i	−0.661481	+	0.381907i
$330$		0			0
$331$	−0.00920539	−	0.0343550i	−0.000505974	−	0.00188832i	0.965672	−	0.259763i	$-0.0836445\pi$
$331$	−0.00920539	−	0.0343550i	−0.000505974	−	0.00188832i	−0.966178	+	0.257875i	$0.916978\pi$
$332$		0			0
$333$	0.912159	+	18.2255i	0.0499860	+	0.998750i
$334$		0			0
$335$	−1.44705	−	5.40045i	−0.0790605	−	0.295058i
$336$		0			0
$337$	17.4353	−	10.0663i	0.949763	−	0.548346i	0.0567558	−	0.998388i	$-0.481924\pi$
$337$	17.4353	−	10.0663i	0.949763	−	0.548346i	0.893007	+	0.450042i	$0.148591\pi$
$338$		0			0
$339$	10.4235	−	21.8096i	0.566128	−	1.18454i
$340$		0			0
$341$	12.5765	+	12.5765i	0.681054	+	0.681054i
$342$		0			0
$343$	17.2986			0.934037
$344$		0			0
$345$	−13.3187	−	2.47920i	−0.717052	−	0.133476i
$346$		0			0
$347$	−11.9532	+	11.9532i	−0.641680	+	0.641680i	−0.950968	−	0.309289i	$-0.899909\pi$
$347$	−11.9532	+	11.9532i	−0.641680	+	0.641680i	0.309289	+	0.950968i	$0.399909\pi$
$348$		0			0
$349$	−3.67961	+	6.37327i	−0.196965	+	0.341154i	−0.947543	−	0.319628i	$-0.896442\pi$
$349$	−3.67961	+	6.37327i	−0.196965	+	0.341154i	0.750578	+	0.660782i	$0.229775\pi$
$350$		0			0
$351$	−22.9614	+	21.6878i	−1.22559	+	1.15761i
$352$		0			0
$353$	2.51375	+	9.38143i	0.133793	+	0.499323i	1.00000		0.000362611i	$-0.000115423\pi$
$353$	2.51375	+	9.38143i	0.133793	+	0.499323i	−0.866207	+	0.499686i	$0.833449\pi$
$354$		0			0
$355$	2.95505	+	11.0284i	0.156838	+	0.585327i
$356$		0			0
$357$	−0.853455	−	10.9533i	−0.0451696	−	0.579708i
$358$		0			0
$359$			0.471933i			0.0249077i	0.999922	+	0.0124538i	$0.00396428\pi$
$359$			0.471933i			0.0249077i	−0.999922	+	0.0124538i	$0.996036\pi$
$360$		0			0
$361$	15.4407	+	8.91469i	0.812668	+	0.469194i
$362$		0			0
$363$	−4.48126	−	3.83340i	−0.235205	−	0.201201i
$364$		0			0
$365$	−4.54452	−	1.21770i	−0.237871	−	0.0637374i
$366$		0			0
$367$	−10.8147	−	18.7317i	−0.564525	−	0.977785i	−0.997094	−	0.0761845i	$-0.975726\pi$
$367$	−10.8147	−	18.7317i	−0.564525	−	0.977785i	0.432569	−	0.901601i	$-0.357607\pi$
$368$		0			0
$369$	−6.40377	+	5.16917i	−0.333367	+	0.269096i
$370$		0			0
$371$		−	12.1372i		−	0.630133i
$372$		0			0
$373$	−10.0864	+	5.82336i	−0.522252	+	0.301522i	−0.737856	−	0.674959i	$-0.764161\pi$
$373$	−10.0864	+	5.82336i	−0.522252	+	0.301522i	0.215604	+	0.976481i	$0.430828\pi$
$374$		0			0
$375$	17.3245	−	1.34989i	0.894633	−	0.0697080i
$376$		0			0
$377$	27.0485	−	15.6165i	1.39307	−	0.804290i
$378$		0			0
$379$	1.84124	−	3.18912i	0.0945781	−	0.163814i	−0.814854	−	0.579666i	$-0.803183\pi$
$379$	1.84124	−	3.18912i	0.0945781	−	0.163814i	0.909432	+	0.415852i	$0.136516\pi$
$380$		0			0
$381$	−5.47414	+	1.93370i	−0.280449	+	0.0990662i
$382$		0			0
$383$	−5.02898	+	18.7684i	−0.256969	+	0.959022i	0.710015	+	0.704186i	$0.248688\pi$
$383$	−5.02898	+	18.7684i	−0.256969	+	0.959022i	−0.966984	+	0.254835i	$0.917979\pi$
$384$		0			0
$385$	4.49238	−	1.20373i	0.228953	−	0.0613477i
$386$		0			0
$387$	8.74913	+	6.37746i	0.444743	+	0.324185i
$388$		0			0
$389$	−5.17085	+	19.2979i	−0.262173	+	0.978442i	0.701785	+	0.712388i	$0.252386\pi$
$389$	−5.17085	+	19.2979i	−0.262173	+	0.978442i	−0.963958	+	0.266054i	$0.914280\pi$
$390$		0			0
$391$	25.4603	+	14.6995i	1.28758	+	0.743385i
$392$		0			0
$393$	13.0168	−	27.2356i	0.656610	−	1.37386i
$394$		0			0
$395$	−7.76866	+	13.4557i	−0.390884	+	0.677031i
$396$		0			0
$397$		−	12.0231i		−	0.603421i	−0.953400	−	0.301711i	$-0.902442\pi$
$397$		−	12.0231i		−	0.603421i	0.953400	−	0.301711i	$-0.0975576\pi$
$398$		0			0
$399$	6.60025	−	13.8100i	0.330426	−	0.691366i
$400$		0			0
$401$	2.14231	−	2.14231i	0.106982	−	0.106982i	−0.651590	−	0.758572i	$-0.725898\pi$
$401$	2.14231	−	2.14231i	0.106982	−	0.106982i	0.758572	+	0.651590i	$0.225898\pi$
$402$		0			0
$403$	19.6140	+	33.9724i	0.977041	+	1.69229i
$404$		0			0
$405$	0.513417	+	10.4176i	0.0255119	+	0.517654i
$406$		0			0
$407$	16.6706	+	1.76555i	0.826329	+	0.0875150i
$408$		0			0
$409$	−19.8672	+	5.32340i	−0.982370	+	0.263225i	−0.714043	−	0.700102i	$-0.753138\pi$
$409$	−19.8672	+	5.32340i	−0.982370	+	0.263225i	−0.268328	+	0.963328i	$0.586471\pi$
$410$		0			0
$411$	18.7058	−	21.8671i	0.922687	−	1.07863i
$412$		0			0
$413$	3.79205	+	3.79205i	0.186594	+	0.186594i
$414$		0			0
$415$	−3.42792	+	3.42792i	−0.168270	+	0.168270i
$416$		0			0
$417$	−9.40404	−	26.6221i	−0.460518	−	1.30369i
$418$		0			0
$419$	11.0727	+	6.39284i	0.540938	+	0.312311i	0.745459	−	0.666552i	$-0.232230\pi$
$419$	11.0727	+	6.39284i	0.540938	+	0.312311i	−0.204521	+	0.978862i	$0.565564\pi$
$420$		0			0
$421$	24.4715	+	24.4715i	1.19267	+	1.19267i	0.976315	+	0.216352i	$0.0694160\pi$
$421$	24.4715	+	24.4715i	1.19267	+	1.19267i	0.216352	+	0.976315i	$0.430584\pi$
$422$		0			0
$423$	−28.1983	+	4.42115i	−1.37105	+	0.214964i
$424$		0			0
$425$	−15.3867	−	4.12286i	−0.746366	−	0.199988i
$426$		0			0
$427$	−19.9290	+	5.33997i	−0.964434	+	0.258419i
$428$		0			0
$429$	16.4158	+	23.9250i	0.792560	+	1.15511i
$430$		0			0
$431$	1.05875	+	0.283691i	0.0509982	+	0.0136649i	0.284228	−	0.958757i	$-0.408263\pi$
$431$	1.05875	+	0.283691i	0.0509982	+	0.0136649i	−0.233230	+	0.972422i	$0.574929\pi$
$432$		0			0
$433$	14.8597			0.714110			0.357055	−	0.934083i	$-0.383781\pi$
$433$	14.8597			0.714110			0.357055	+	0.934083i	$0.383781\pi$
$434$		0			0
$435$	1.88750	−	10.1399i	0.0904985	−	0.486172i
$436$		0			0
$437$	20.4792	+	35.4710i	0.979652	+	1.69681i
$438$		0			0
$439$	6.43004	−	23.9972i	0.306889	−	1.14533i	−0.624418	−	0.781091i	$-0.714664\pi$
$439$	6.43004	−	23.9972i	0.306889	−	1.14533i	0.931307	−	0.364235i	$-0.118670\pi$
$440$		0			0
$441$	13.6583	+	5.26735i	0.650394	+	0.250826i
$442$		0			0
$443$	−15.8643			−0.753736			−0.376868	−	0.926267i	$-0.622999\pi$
$443$	−15.8643			−0.753736			−0.376868	+	0.926267i	$0.622999\pi$
$444$		0			0
$445$	−12.0692			−0.572137
$446$		0			0
$447$	−0.737527	+	0.862172i	−0.0348838	+	0.0407793i
$448$		0			0
$449$	−7.66110	+	28.5916i	−0.361550	+	1.34932i	0.510489	+	0.859884i	$0.329464\pi$
$449$	−7.66110	+	28.5916i	−0.361550	+	1.34932i	−0.872039	+	0.489437i	$0.837202\pi$
$450$		0			0
$451$	3.78013	+	6.54737i	0.177999	+	0.308304i
$452$		0			0
$453$	15.4460	+	2.87520i	0.725717	+	0.135088i
$454$		0			0
$455$	10.2578			0.480893
$456$		0			0
$457$	−13.3240	−	3.57015i	−0.623270	−	0.167005i	−0.0666562	−	0.997776i	$-0.521233\pi$
$457$	−13.3240	−	3.57015i	−0.623270	−	0.167005i	−0.556614	+	0.830771i	$0.687900\pi$
$458$		0			0
$459$	6.47922	−	21.6872i	0.302424	−	1.01227i
$460$		0			0
$461$	5.11343	−	1.37014i	0.238156	−	0.0638138i	−0.137767	−	0.990465i	$-0.543992\pi$
$461$	5.11343	−	1.37014i	0.238156	−	0.0638138i	0.375923	+	0.926651i	$0.377326\pi$
$462$		0			0
$463$	8.95268	+	2.39886i	0.416066	+	0.111485i	0.460778	−	0.887515i	$-0.347570\pi$
$463$	8.95268	+	2.39886i	0.416066	+	0.111485i	−0.0447120	+	0.999000i	$0.514237\pi$
$464$		0			0
$465$	12.7355	+	2.37065i	0.590596	+	0.109936i
$466$		0			0
$467$	22.1447	+	22.1447i	1.02473	+	1.02473i	0.999686	+	0.0250480i	$0.00797385\pi$
$467$	22.1447	+	22.1447i	1.02473	+	1.02473i	0.0250480	+	0.999686i	$0.492026\pi$
$468$		0			0
$469$	6.08380	+	3.51249i	0.280924	+	0.162192i
$470$		0			0
$471$	2.08791	−	0.737538i	0.0962058	−	0.0339839i
$472$		0			0
$473$	7.03290	−	7.03290i	0.323373	−	0.323373i
$474$		0			0
$475$	−15.6927	−	15.6927i	−0.720030	−	0.720030i
$476$		0			0
$477$	8.99742	−	23.3304i	0.411964	−	1.06822i
$478$		0			0
$479$	−8.13565	+	2.17994i	−0.371727	+	0.0996040i	−0.439846	−	0.898073i	$-0.644967\pi$
$479$	−8.13565	+	2.17994i	−0.371727	+	0.0996040i	0.0681187	+	0.997677i	$0.478300\pi$
$480$		0			0
$481$	34.5075	+	13.2777i	1.57341	+	0.605409i
$482$		0			0
$483$	14.0359	−	9.63055i	0.638658	−	0.438205i
$484$		0			0
$485$	−0.982954	−	1.70253i	−0.0446336	−	0.0773077i
$486$		0			0
$487$	−10.3305	+	10.3305i	−0.468121	+	0.468121i	−0.901305	−	0.433184i	$-0.857390\pi$
$487$	−10.3305	+	10.3305i	−0.468121	+	0.468121i	0.433184	+	0.901305i	$0.357390\pi$
$488$		0			0
$489$	−31.4478	−	15.0299i	−1.42212	−	0.679676i
$490$		0			0
$491$		−	2.87456i		−	0.129727i	−0.997894	−	0.0648635i	$-0.979339\pi$
$491$		−	2.87456i		−	0.129727i	0.997894	−	0.0648635i	$-0.0206612\pi$
$492$		0			0
$493$	−11.1912	+	19.3837i	−0.504027	+	0.873000i
$494$		0			0
$495$	9.52767	+	1.01641i	0.428237	+	0.0456842i
$496$		0			0
$497$	−12.4239	−	7.17295i	−0.557289	−	0.321751i
$498$		0			0
$499$	−1.80413	+	6.73310i	−0.0807639	+	0.301415i	−0.994478	−	0.104942i	$-0.966534\pi$
$499$	−1.80413	+	6.73310i	−0.0807639	+	0.301415i	0.913714	+	0.406357i	$0.133201\pi$
$500$		0			0
$501$	22.3117	−	15.3088i	0.996813	−	0.683948i
$502$		0			0
$503$	8.50208	−	2.27813i	0.379089	−	0.101577i	−0.0642425	−	0.997934i	$-0.520463\pi$
$503$	8.50208	−	2.27813i	0.379089	−	0.101577i	0.443332	+	0.896358i	$0.353796\pi$
$504$		0			0
$505$	4.14034	−	15.4520i	0.184243	−	0.687603i
$506$		0			0
$507$	13.8153	+	39.1101i	0.613561	+	1.73694i
$508$		0			0
$509$	−8.91630	+	15.4435i	−0.395208	+	0.684520i	−0.993128	−	0.117036i	$-0.962661\pi$
$509$	−8.91630	+	15.4435i	−0.395208	+	0.684520i	0.597920	+	0.801556i	$0.295994\pi$
$510$		0			0
$511$	5.11957	−	2.95579i	0.226477	−	0.130756i
$512$		0			0
$513$	22.9246	−	21.6531i	1.01215	−	0.956006i
$514$		0			0
$515$	7.36934	−	4.25469i	0.324732	−	0.187484i
$516$		0			0
$517$			26.2208i			1.15319i
$518$		0			0
$519$	−23.0098	+	8.12803i	−1.01002	+	0.356781i
$520$		0			0
$521$	8.33125	+	14.4302i	0.364999	+	0.632196i	0.988776	−	0.149406i	$-0.0477361\pi$
$521$	8.33125	+	14.4302i	0.364999	+	0.632196i	−0.623777	+	0.781602i	$0.714403\pi$
$522$		0			0
$523$	32.7428	+	8.77340i	1.43174	+	0.383634i	0.889633	−	0.456675i	$-0.150960\pi$
$523$	32.7428	+	8.77340i	1.43174	+	0.383634i	0.542107	+	0.840309i	$0.317627\pi$
$524$		0			0
$525$	−5.99551	+	7.00878i	−0.261665	+	0.305888i
$526$		0			0
$527$	−24.3456	−	14.0559i	−1.06051	−	0.612285i
$528$		0			0
$529$			22.5502i			0.980445i
$530$		0			0
$531$	4.47807	+	10.1002i	0.194332	+	0.438312i
$532$		0			0
$533$	4.31573	+	16.1065i	0.186935	+	0.697651i
$534$		0			0
$535$	0.738304	+	2.75539i	0.0319197	+	0.119126i
$536$		0			0
$537$	−21.1241	+	1.64594i	−0.911570	+	0.0710277i
$538$		0			0
$539$	6.72396	−	11.6462i	0.289621	−	0.501639i
$540$		0			0
$541$	5.59188	−	5.59188i	0.240414	−	0.240414i	−0.576607	−	0.817021i	$-0.695624\pi$
$541$	5.59188	−	5.59188i	0.240414	−	0.240414i	0.817021	+	0.576607i	$0.195624\pi$
$542$		0			0
$543$	1.88177	−	10.1092i	0.0807544	−	0.433825i
$544$		0			0
$545$	−20.7387			−0.888350
$546$		0			0
$547$	20.0312	+	20.0312i	0.856471	+	0.856471i	0.990921	−	0.134449i	$-0.0429265\pi$
$547$	20.0312	+	20.0312i	0.856471	+	0.856471i	−0.134449	+	0.990921i	$0.542926\pi$
$548$		0			0
$549$	−42.2665	−	4.50898i	−1.80389	−	0.192439i
$550$		0			0
$551$	−27.0052	+	15.5915i	−1.15046	+	0.664219i
$552$		0			0
$553$	−5.05279	−	18.8573i	−0.214867	−	0.801893i
$554$		0			0
$555$	10.7394	−	5.80917i	0.455864	−	0.246585i
$556$		0			0
$557$	0.574982	+	2.14586i	0.0243628	+	0.0909231i	0.977037	−	0.213071i	$-0.0683465\pi$
$557$	0.574982	+	2.14586i	0.0243628	+	0.0909231i	−0.952674	+	0.303994i	$0.901680\pi$
$558$		0			0
$559$	18.9977	−	10.9684i	0.803519	−	0.463912i
$560$		0			0
$561$	−18.7606	−	8.96627i	−0.792072	−	0.378556i
$562$		0			0
$563$	0.564925	+	0.564925i	0.0238087	+	0.0238087i	0.718911	−	0.695102i	$-0.244641\pi$
$563$	0.564925	+	0.564925i	0.0238087	+	0.0238087i	−0.695102	+	0.718911i	$0.744641\pi$
$564$		0			0
$565$	−16.1738			−0.680436
$566$		0			0
$567$	−9.71188	−	8.79957i	−0.407861	−	0.369547i
$568$		0			0
$569$	−3.02257	+	3.02257i	−0.126713	+	0.126713i	−0.767619	−	0.640906i	$-0.778559\pi$
$569$	−3.02257	+	3.02257i	−0.126713	+	0.126713i	0.640906	+	0.767619i	$0.278559\pi$
$570$		0			0
$571$	−18.8036	+	32.5688i	−0.786907	+	1.36296i	0.140946	+	0.990017i	$0.454986\pi$
$571$	−18.8036	+	32.5688i	−0.786907	+	1.36296i	−0.927853	+	0.372946i	$0.878348\pi$
$572$		0			0
$573$	0.0389225	+	0.499531i	0.00162601	+	0.0208682i
$574$		0			0
$575$	−6.38788	−	23.8399i	−0.266393	−	0.994193i
$576$		0			0
$577$	−5.36446	−	20.0204i	−0.223325	−	0.833461i	−0.983069	−	0.183238i	$-0.941342\pi$
$577$	−5.36446	−	20.0204i	−0.223325	−	0.833461i	0.759743	−	0.650223i	$-0.225325\pi$
$578$		0			0
$579$	34.7211	−	2.70539i	1.44296	−	0.112432i
$580$		0			0
$581$		−	6.09122i		−	0.252706i
$582$		0			0
$583$	−19.8935	−	11.4855i	−0.823905	−	0.475682i
$584$		0			0
$585$	19.7177	+	7.60420i	0.815228	+	0.314395i
$586$		0			0
$587$	−30.9958	−	8.30530i	−1.27933	−	0.342796i	−0.445734	−	0.895165i	$-0.647057\pi$
$587$	−30.9958	−	8.30530i	−1.27933	−	0.342796i	−0.833600	+	0.552369i	$0.813724\pi$
$588$		0			0
$589$	−19.5826	−	33.9180i	−0.806885	−	1.39757i
$590$		0			0
$591$	14.0259	+	39.7061i	0.576948	+	1.63329i
$592$		0			0
$593$			27.0051i			1.10897i	0.832195	+	0.554483i	$0.187084\pi$
$593$			27.0051i			1.10897i	−0.832195	+	0.554483i	$0.812916\pi$
$594$		0			0
$595$	−6.36617	+	3.67551i	−0.260988	+	0.150681i
$596$		0			0
$597$	0.727994	+	9.34308i	0.0297948	+	0.382387i
$598$		0			0
$599$	12.6022	−	7.27587i	0.514911	−	0.297284i	−0.219939	−	0.975514i	$-0.570586\pi$
$599$	12.6022	−	7.27587i	0.514911	−	0.297284i	0.734850	+	0.678230i	$0.237252\pi$
$600$		0			0
$601$	−1.23429	+	2.13786i	−0.0503479	+	0.0872052i	−0.890101	−	0.455763i	$-0.849366\pi$
$601$	−1.23429	+	2.13786i	−0.0503479	+	0.0872052i	0.839753	+	0.542968i	$0.182700\pi$
$602$		0			0
$603$	9.09057	+	11.2617i	0.370196	+	0.458614i
$604$		0			0
$605$	−1.02125	+	3.81134i	−0.0415196	+	0.154953i
$606$		0			0
$607$	29.9723	−	8.03106i	1.21654	−	0.325971i	0.407214	−	0.913333i	$-0.366500\pi$
$607$	29.9723	−	8.03106i	1.21654	−	0.325971i	0.809324	+	0.587362i	$0.199834\pi$
$608$		0			0
$609$	7.33206	+	10.6860i	0.297110	+	0.433020i
$610$		0			0
$611$	−14.9680	+	55.8615i	−0.605542	+	2.25991i
$612$		0			0
$613$	−24.4057	−	14.0907i	−0.985738	−	0.569116i	−0.0817406	−	0.996654i	$-0.526048\pi$
$613$	−24.4057	−	14.0907i	−0.985738	−	0.569116i	−0.903998	+	0.427537i	$0.859381\pi$
$614$		0			0
$615$	4.96825	+	2.37449i	0.200339	+	0.0957485i
$616$		0			0
$617$	19.9279	−	34.5162i	0.802269	−	1.38957i	−0.115850	−	0.993267i	$-0.536959\pi$
$617$	19.9279	−	34.5162i	0.802269	−	1.38957i	0.918119	−	0.396304i	$-0.129707\pi$
$618$		0			0
$619$			19.9060i			0.800090i	0.916495	+	0.400045i	$0.131006\pi$
$619$			19.9060i			0.800090i	−0.916495	+	0.400045i	$0.868994\pi$
$620$		0			0
$621$	34.1194	−	8.10705i	1.36916	−	0.325325i
$622$		0			0
$623$	10.7232	−	10.7232i	0.429615	−	0.429615i
$624$		0			0
$625$	3.32883	+	5.76570i	0.133153	+	0.230628i
$626$		0			0
$627$	−16.3895	−	23.8867i	−0.654532	−	0.953941i
$628$		0			0
$629$	−26.1735	+	4.12415i	−1.04361	+	0.164441i
$630$		0			0
$631$	−2.62266	+	0.702739i	−0.104406	+	0.0279756i	−0.310644	−	0.950526i	$-0.600545\pi$
$631$	−2.62266	+	0.702739i	−0.104406	+	0.0279756i	0.206238	+	0.978502i	$0.433878\pi$
$632$		0			0
$633$	−25.1940	−	21.5517i	−1.00137	−	0.856602i
$634$		0			0
$635$	2.74679	+	2.74679i	0.109003	+	0.109003i
$636$		0			0
$637$	20.9731	−	20.9731i	0.830983	−	0.830983i
$638$		0			0
$639$	−18.5641	−	22.9979i	−0.734385	−	0.909785i
$640$		0			0
$641$	26.6897	+	15.4093i	1.05418	+	0.608631i	0.923817	−	0.382835i	$-0.125052\pi$
$641$	26.6897	+	15.4093i	1.05418	+	0.608631i	0.130363	+	0.991466i	$0.458386\pi$
$642$		0			0
$643$	−0.162574	−	0.162574i	−0.00641130	−	0.00641130i	0.703894	−	0.710305i	$-0.251443\pi$
$643$	−0.162574	−	0.162574i	−0.00641130	−	0.00641130i	−0.710305	+	0.703894i	$0.751443\pi$
$644$		0			0
$645$	1.32570	−	7.12186i	0.0521993	−	0.280423i
$646$		0			0
$647$	−14.5541	−	3.89976i	−0.572181	−	0.153315i	−0.0388844	−	0.999244i	$-0.512380\pi$
$647$	−14.5541	−	3.89976i	−0.572181	−	0.153315i	−0.533297	+	0.845928i	$0.679047\pi$
$648$		0			0
$649$	9.80380	−	2.62692i	0.384833	−	0.103116i
$650$		0			0
$651$	−13.4214	+	9.20891i	−0.526027	+	0.360925i
$652$		0			0
$653$	−0.616720	−	0.165250i	−0.0241341	−	0.00646672i	0.246732	−	0.969084i	$-0.420643\pi$
$653$	−0.616720	−	0.165250i	−0.0241341	−	0.00646672i	−0.270866	+	0.962617i	$0.587310\pi$
$654$		0			0
$655$	−20.1977			−0.789188
$656$		0			0
$657$	12.0321	−	1.88648i	0.469417	−	0.0735988i
$658$		0			0
$659$	13.2733	+	22.9901i	0.517056	+	0.895567i	0.999804	+	0.0198077i	$0.00630539\pi$
$659$	13.2733	+	22.9901i	0.517056	+	0.895567i	−0.482748	+	0.875759i	$0.660361\pi$
$660$		0			0
$661$	12.1071	−	45.1842i	0.470911	−	1.75746i	−0.165598	−	0.986193i	$-0.552955\pi$
$661$	12.1071	−	45.1842i	0.470911	−	1.75746i	0.636509	−	0.771269i	$-0.280378\pi$
$662$		0			0
$663$	−34.8496	−	29.8113i	−1.35344	−	1.15778i
$664$		0			0
$665$	−10.2414			−0.397143
$666$		0			0
$667$	−34.6789			−1.34277
$668$		0			0
$669$	−0.0641786	−	0.0549002i	−0.00248129	−	0.00212256i
$670$		0			0
$671$	−10.1065	+	37.7179i	−0.390157	+	1.45609i
$672$		0			0
$673$	11.5103	+	19.9363i	0.443688	+	0.768490i	0.997960	−	0.0638458i	$-0.0203366\pi$
$673$	11.5103	+	19.9363i	0.443688	+	0.768490i	−0.554272	+	0.832336i	$0.687003\pi$
$674$		0			0
$675$	−16.7203	+	9.02788i	−0.643566	+	0.347483i
$676$		0			0
$677$	9.09136			0.349409			0.174705	−	0.984621i	$-0.444103\pi$
$677$	9.09136			0.349409			0.174705	+	0.984621i	$0.444103\pi$
$678$		0			0
$679$	2.38597	+	0.639320i	0.0915653	+	0.0245348i
$680$		0			0
$681$	−32.1692	+	22.0724i	−1.23273	+	0.845817i
$682$		0			0
$683$	−4.60343	+	1.23348i	−0.176145	+	0.0471980i	−0.345814	−	0.938303i	$-0.612397\pi$
$683$	−4.60343	+	1.23348i	−0.176145	+	0.0471980i	0.169668	+	0.985501i	$0.445730\pi$
$684$		0			0
$685$	−18.5981	−	4.98336i	−0.710598	−	0.190404i
$686$		0			0
$687$	−1.85047	+	9.94101i	−0.0705998	+	0.379273i
$688$		0			0
$689$	−35.8251	−	35.8251i	−1.36483	−	1.36483i
$690$		0			0
$691$	8.20631	+	4.73792i	0.312183	+	0.180239i	0.647903	−	0.761723i	$-0.275646\pi$
$691$	8.20631	+	4.73792i	0.312183	+	0.180239i	−0.335720	+	0.941962i	$0.608980\pi$
$692$		0			0
$693$	−9.36812	+	7.56201i	−0.355865	+	0.287257i
$694$		0			0
$695$	−13.3583	+	13.3583i	−0.506709	+	0.506709i
$696$		0			0
$697$	−8.44962	−	8.44962i	−0.320052	−	0.320052i
$698$		0			0
$699$	8.78666	+	7.51636i	0.332342	+	0.284295i
$700$		0			0
$701$	19.1267	−	5.12497i	0.722404	−	0.193568i	0.121160	−	0.992633i	$-0.461339\pi$
$701$	19.1267	−	5.12497i	0.722404	−	0.193568i	0.601244	+	0.799065i	$0.294672\pi$
$702$		0			0
$703$	−34.4522	−	13.2564i	−1.29939	−	0.499975i
$704$		0			0
$705$	10.8049	+	15.7475i	0.406937	+	0.593087i
$706$		0			0
$707$	10.0501	+	17.4072i	0.377971	+	0.654665i
$708$		0			0
$709$	3.62196	−	3.62196i	0.136026	−	0.136026i	−0.635816	−	0.771841i	$-0.719336\pi$
$709$	3.62196	−	3.62196i	0.136026	−	0.136026i	0.771841	+	0.635816i	$0.219336\pi$
$710$		0			0
$711$	4.26649	−	39.9935i	0.160006	−	1.49987i
$712$		0			0
$713$		−	43.5559i		−	1.63118i
$714$		0			0
$715$	9.70702	−	16.8130i	0.363022	−	0.628772i
$716$		0			0
$717$	25.0306	+	11.9629i	0.934784	+	0.446763i
$718$		0			0
$719$	19.7388	+	11.3962i	0.736133	+	0.425007i	0.820662	−	0.571414i	$-0.193605\pi$
$719$	19.7388	+	11.3962i	0.736133	+	0.425007i	−0.0845286	+	0.996421i	$0.526938\pi$
$720$		0			0
$721$	−2.76728	+	10.3276i	−0.103059	+	0.384621i
$722$		0			0
$723$	−11.2824	−	16.4434i	−0.419595	−	0.611535i
$724$		0			0
$725$	18.1501	−	4.86331i	0.674078	−	0.180619i
$726$		0			0
$727$	10.6984	−	39.9269i	0.396781	−	1.48081i	−0.421945	−	0.906622i	$-0.638652\pi$
$727$	10.6984	−	39.9269i	0.396781	−	1.48081i	0.818726	−	0.574185i	$-0.194681\pi$
$728$		0			0
$729$	−12.1452	−	24.1142i	−0.449821	−	0.893119i
$730$		0			0
$731$	−7.86023	+	13.6143i	−0.290721	+	0.503544i
$732$		0			0
$733$	31.9467	−	18.4445i	1.17998	−	0.681262i	0.223970	−	0.974596i	$-0.428098\pi$
$733$	31.9467	−	18.4445i	1.17998	−	0.681262i	0.956010	+	0.293334i	$0.0947649\pi$
$734$		0			0
$735$	−0.760883	−	9.76519i	−0.0280656	−	0.360194i
$736$		0			0
$737$	11.5143	−	6.64777i	0.424134	−	0.244874i
$738$		0			0
$739$		−	36.3141i		−	1.33584i	−0.744235	−	0.667918i	$-0.767186\pi$
$739$		−	36.3141i		−	1.33584i	0.744235	−	0.667918i	$-0.232814\pi$
$740$		0			0
$741$	−21.2809	−	60.2445i	−0.781773	−	2.21314i
$742$		0			0
$743$	10.4342	+	18.0726i	0.382795	+	0.663021i	0.991461	−	0.130406i	$-0.0416281\pi$
$743$	10.4342	+	18.0726i	0.382795	+	0.663021i	−0.608665	+	0.793427i	$0.708295\pi$
$744$		0			0
$745$	0.733283	+	0.196483i	0.0268654	+	0.00719857i
$746$		0			0
$747$	4.51547	−	11.7086i	0.165212	−	0.428397i
$748$		0			0
$749$	−3.10405	−	1.79212i	−0.113419	−	0.0654827i
$750$		0			0
$751$			23.1736i			0.845618i	0.906219	+	0.422809i	$0.138956\pi$
$751$			23.1736i			0.845618i	−0.906219	+	0.422809i	$0.861044\pi$
$752$		0			0
$753$	20.8692	−	1.62609i	0.760517	−	0.0592579i
$754$		0			0
$755$	−2.72082	−	10.1542i	−0.0990207	−	0.369550i
$756$		0			0
$757$	8.33389	+	31.1025i	0.302900	+	1.13044i	0.934738	+	0.355338i	$0.115634\pi$
$757$	8.33389	+	31.1025i	0.302900	+	1.13044i	−0.631837	+	0.775101i	$0.717699\pi$
$758$		0			0
$759$	−2.50265	−	32.1191i	−0.0908405	−	1.16585i
$760$		0			0
$761$	−13.7558	+	23.8257i	−0.498646	+	0.863680i	−0.999999	−	0.00156274i	$-0.999503\pi$
$761$	−13.7558	+	23.8257i	−0.498646	+	0.863680i	0.501353	+	0.865243i	$0.332836\pi$
$762$		0			0
$763$	18.4258	−	18.4258i	0.667058	−	0.667058i
$764$		0			0
$765$	−14.9619	+	2.34584i	−0.540947	+	0.0848139i
$766$		0			0
$767$	22.3858			0.808304
$768$		0			0
$769$	−21.6007	−	21.6007i	−0.778942	−	0.778942i	0.200709	−	0.979651i	$-0.435675\pi$
$769$	−21.6007	−	21.6007i	−0.778942	−	0.778942i	−0.979651	+	0.200709i	$0.935675\pi$
$770$		0			0
$771$	15.6538	+	7.48145i	0.563757	+	0.269438i
$772$		0			0
$773$	14.1200	−	8.15219i	0.507862	−	0.293214i	−0.224093	−	0.974568i	$-0.571942\pi$
$773$	14.1200	−	8.15219i	0.507862	−	0.293214i	0.731954	+	0.681354i	$0.238608\pi$
$774$		0			0
$775$	6.10821	+	22.7961i	0.219413	+	0.818862i
$776$		0			0
$777$	−4.38041	+	14.7030i	−0.157146	+	0.527466i
$778$		0			0
$779$	−4.30882	−	16.0807i	−0.154380	−	0.576152i
$780$		0			0
$781$	−23.5137	+	13.5756i	−0.841385	+	0.485774i
$782$		0			0
$783$	6.17217	+	25.9762i	0.220575	+	0.928314i
$784$		0			0
$785$	−1.04766	−	1.04766i	−0.0373926	−	0.0373926i
$786$		0			0
$787$	−6.40828			−0.228431			−0.114215	−	0.993456i	$-0.536435\pi$
$787$	−6.40828			−0.228431			−0.114215	+	0.993456i	$0.536435\pi$
$788$		0			0
$789$	6.81691	−	36.6215i	0.242688	−	1.30376i
$790$		0			0
$791$	14.3700	−	14.3700i	0.510937	−	0.510937i
$792$		0			0
$793$	−43.0622	+	74.5859i	−1.52918	+	2.64862i
$794$		0			0
$795$	−16.6804	+	1.29970i	−0.591593	+	0.0460957i
$796$		0			0
$797$	8.38483	+	31.2926i	0.297006	+	1.10844i	0.939611	+	0.342244i	$0.111187\pi$
$797$	8.38483	+	31.2926i	0.297006	+	1.10844i	−0.642605	+	0.766197i	$0.722147\pi$
$798$		0			0
$799$	−10.7265	−	40.0319i	−0.379477	−	1.41623i
$800$		0			0
$801$	28.5615	−	12.6631i	1.00917	−	0.447429i
$802$		0			0
$803$		−	11.1883i		−	0.394827i
$804$		0			0
$805$	−9.86363	−	5.69477i	−0.347647	−	0.200714i
$806$		0			0
$807$	−18.0315	+	21.0789i	−0.634739	+	0.742013i
$808$		0			0
$809$	48.9886	+	13.1264i	1.72235	+	0.461501i	0.978397	−	0.206735i	$-0.0662838\pi$
$809$	48.9886	+	13.1264i	1.72235	+	0.461501i	0.743949	+	0.668236i	$0.232950\pi$
$810$		0			0
$811$	−11.4450	−	19.8233i	−0.401887	−	0.696089i	0.592066	−	0.805889i	$-0.298312\pi$
$811$	−11.4450	−	19.8233i	−0.401887	−	0.696089i	−0.993954	+	0.109800i	$0.964979\pi$
$812$		0			0
$813$	1.41956	−	0.501449i	0.0497862	−	0.0175866i
$814$		0			0
$815$			23.3214i			0.816912i
$816$		0			0
$817$	−18.9673	+	10.9508i	−0.663583	+	0.383120i
$818$		0			0
$819$	−24.2748	+	10.7625i	−0.848229	+	0.376074i
$820$		0			0
$821$	−42.8282	+	24.7269i	−1.49471	+	0.862973i	−0.999982	−	0.00607199i	$-0.998067\pi$
$821$	−42.8282	+	24.7269i	−1.49471	+	0.862973i	−0.494732	+	0.869045i	$0.664734\pi$
$822$		0			0
$823$	−22.2288	+	38.5014i	−0.774846	+	1.34207i	0.160034	+	0.987111i	$0.448839\pi$
$823$	−22.2288	+	38.5014i	−0.774846	+	1.34207i	−0.934881	+	0.354962i	$0.884494\pi$
$824$		0			0
$825$	5.81415	+	16.4594i	0.202423	+	0.573042i
$826$		0			0
$827$	8.23934	−	30.7496i	0.286510	−	1.06927i	−0.661219	−	0.750193i	$-0.729961\pi$
$827$	8.23934	−	30.7496i	0.286510	−	1.06927i	0.947729	−	0.319077i	$-0.103373\pi$
$828$		0			0
$829$	−20.5414	+	5.50404i	−0.713431	+	0.191163i	−0.597239	−	0.802063i	$-0.703736\pi$
$829$	−20.5414	+	5.50404i	−0.713431	+	0.191163i	−0.116192	+	0.993227i	$0.537069\pi$
$830$		0			0
$831$	0.351745	−	0.241344i	0.0122019	−	0.00837214i
$832$		0			0
$833$	−5.50132	+	20.5312i	−0.190609	+	0.711364i
$834$		0			0
$835$	−15.6793	−	9.05247i	−0.542606	−	0.313274i
$836$		0			0
$837$	−32.6256	+	7.75211i	−1.12770	+	0.267952i
$838$		0			0
$839$	12.2733	−	21.2581i	0.423723	−	0.733910i	−0.572577	−	0.819851i	$-0.694056\pi$
$839$	12.2733	−	21.2581i	0.423723	−	0.733910i	0.996300	+	0.0859412i	$0.0273897\pi$
$840$		0			0
$841$			2.59780i			0.0895794i
$842$		0			0
$843$	−49.9090	−	23.8531i	−1.71896	−	0.821545i
$844$		0			0
$845$	19.6245	−	19.6245i	0.675103	−	0.675103i
$846$		0			0
$847$	−2.47892	−	4.29362i	−0.0851768	−	0.147531i
$848$		0			0
$849$	33.8885	−	23.2521i	1.16305	−	0.798010i
$850$		0			0
$851$	−25.8102	−	31.9248i	−0.884762	−	1.09437i
$852$		0			0
$853$	−1.56522	+	0.419400i	−0.0535922	+	0.0143600i	−0.285516	−	0.958374i	$-0.592165\pi$
$853$	−1.56522	+	0.419400i	−0.0535922	+	0.0143600i	0.231923	+	0.972734i	$0.425498\pi$
$854$		0			0
$855$	−19.6862	−	7.59202i	−0.673252	−	0.259642i
$856$		0			0
$857$	14.3353	+	14.3353i	0.489683	+	0.489683i	0.908206	−	0.418523i	$-0.137452\pi$
$857$	14.3353	+	14.3353i	0.489683	+	0.489683i	−0.418523	+	0.908206i	$0.637452\pi$
$858$		0			0
$859$	−14.2311	+	14.2311i	−0.485560	+	0.485560i	−0.906902	−	0.421342i	$-0.861559\pi$
$859$	−14.2311	+	14.2311i	−0.485560	+	0.485560i	0.421342	+	0.906902i	$0.361559\pi$
$860$		0			0
$861$	−6.52382	+	2.30449i	−0.222331	+	0.0785367i
$862$		0			0
$863$	21.6342	+	12.4905i	0.736438	+	0.425183i	0.820773	−	0.571255i	$-0.193543\pi$
$863$	21.6342	+	12.4905i	0.736438	+	0.425183i	−0.0843346	+	0.996437i	$0.526876\pi$
$864$		0			0
$865$	11.5457	+	11.5457i	0.392567	+	0.392567i
$866$		0			0
$867$	3.36245	+	0.625903i	0.114195	+	0.0212568i
$868$		0			0
$869$	−35.6895	−	9.56298i	−1.21068	−	0.324402i
$870$		0			0
$871$	28.3251	−	7.58969i	0.959760	−	0.257167i
$872$		0			0
$873$	4.11243	+	2.99766i	0.139185	+	0.101455i
$874$		0			0
$875$	14.1113	+	3.78112i	0.477050	+	0.127825i
$876$		0			0
$877$	−24.1599			−0.815821			−0.407911	−	0.913022i	$-0.633742\pi$
$877$	−24.1599			−0.815821			−0.407911	+	0.913022i	$0.633742\pi$
$878$		0			0
$879$	−15.6776	−	2.91831i	−0.528793	−	0.0984321i
$880$		0			0
$881$	7.49794	+	12.9868i	0.252612	+	0.437537i	0.964244	−	0.265015i	$-0.0853770\pi$
$881$	7.49794	+	12.9868i	0.252612	+	0.437537i	−0.711632	+	0.702552i	$0.752044\pi$
$882$		0			0
$883$	11.6471	−	43.4675i	0.391956	−	1.46280i	−0.434948	−	0.900456i	$-0.643233\pi$
$883$	11.6471	−	43.4675i	0.391956	−	1.46280i	0.826904	−	0.562343i	$-0.190100\pi$
$884$		0			0
$885$	4.80541	−	5.61755i	0.161532	−	0.188832i
$886$		0			0
$887$	−20.6820			−0.694435			−0.347217	−	0.937785i	$-0.612873\pi$
$887$	−20.6820			−0.694435			−0.347217	+	0.937785i	$0.612873\pi$
$888$		0			0
$889$	−4.88089			−0.163700
$890$		0			0
$891$	−23.6134	+	7.59118i	−0.791077	+	0.254314i
$892$		0			0
$893$	14.9441	−	55.7720i	0.500084	−	1.86634i
$894$		0			0
$895$	7.08846	+	12.2776i	0.236941	+	0.410394i
$896$		0			0
$897$	13.0033	−	69.8558i	0.434168	−	2.33242i
$898$		0			0
$899$	33.1606			1.10597
$900$		0			0
$901$	35.0703	+	9.39707i	1.16836	+	0.313062i
$902$		0			0
$903$	5.14973	+	7.50542i	0.171372	+	0.249765i
$904$		0			0
$905$	−6.64578	+	1.78073i	−0.220913	+	0.0591935i
$906$		0			0
$907$	47.4379	+	12.7109i	1.57515	+	0.422060i	0.937420	−	0.348200i	$-0.113207\pi$
$907$	47.4379	+	12.7109i	1.57515	+	0.422060i	0.637729	+	0.770260i	$0.279874\pi$
$908$		0			0
$909$	6.41429	+	40.9107i	0.212749	+	1.35692i
$910$		0			0
$911$	21.8406	+	21.8406i	0.723612	+	0.723612i	0.969339	−	0.245727i	$-0.0790267\pi$
$911$	21.8406	+	21.8406i	0.723612	+	0.723612i	−0.245727	+	0.969339i	$0.579027\pi$
$912$		0			0
$913$	−9.98381	−	5.76416i	−0.330416	−	0.190766i
$914$		0			0
$915$	9.47290	+	26.8170i	0.313165	+	0.886544i
$916$		0			0
$917$	17.9451	−	17.9451i	0.592598	−	0.592598i
$918$		0			0
$919$	22.0408	+	22.0408i	0.727060	+	0.727060i	0.970033	−	0.242973i	$-0.0781227\pi$
$919$	22.0408	+	22.0408i	0.727060	+	0.727060i	−0.242973	+	0.970033i	$0.578123\pi$
$920$		0			0
$921$	−17.7455	+	20.7445i	−0.584733	+	0.683556i
$922$		0			0
$923$	−57.8436	+	15.4991i	−1.90395	+	0.510161i
$924$		0			0
$925$	17.9855	+	13.0891i	0.591360	+	0.430367i
$926$		0			0
$927$	−12.9753	+	17.8005i	−0.426164	+	0.584647i
$928$		0			0
$929$	−11.4551	−	19.8408i	−0.375830	−	0.650957i	0.614621	−	0.788823i	$-0.289309\pi$
$929$	−11.4551	−	19.8408i	−0.375830	−	0.650957i	−0.990451	+	0.137866i	$0.955976\pi$
$930$		0			0
$931$	−20.9395	+	20.9395i	−0.686263	+	0.686263i
$932$		0			0
$933$	4.86230	−	10.1736i	0.159184	−	0.333069i
$934$		0			0
$935$			13.9126i			0.454992i
$936$		0			0
$937$	19.6435	−	34.0235i	0.641724	−	1.11150i	−0.343323	−	0.939217i	$-0.611553\pi$
$937$	19.6435	−	34.0235i	0.641724	−	1.11150i	0.985048	−	0.172282i	$-0.0551140\pi$
$938$		0			0
$939$	14.4112	−	30.1532i	0.470292	−	0.984013i
$940$		0			0
$941$	−28.8358	−	16.6483i	−0.940020	−	0.542721i	−0.0500532	−	0.998747i	$-0.515939\pi$
$941$	−28.8358	−	16.6483i	−0.940020	−	0.542721i	−0.889967	+	0.456026i	$0.849272\pi$
$942$		0			0
$943$	4.79189	−	17.8836i	0.156045	−	0.582369i
$944$		0			0
$945$	−2.51013	+	8.40191i	−0.0816546	+	0.273314i
$946$		0			0
$947$	−11.8152	+	3.16587i	−0.383943	+	0.102877i	−0.445627	−	0.895219i	$-0.647019\pi$
$947$	−11.8152	+	3.16587i	−0.383943	+	0.102877i	0.0616847	+	0.998096i	$0.480353\pi$
$948$		0			0
$949$	6.38679	−	23.8358i	0.207324	−	0.773744i
$950$		0			0
$951$	−2.42708	+	0.857348i	−0.0787035	+	0.0278014i
$952$		0			0
$953$	6.10941	−	10.5818i	0.197903	−	0.342779i	−0.749945	−	0.661500i	$-0.769920\pi$
$953$	6.10941	−	10.5818i	0.197903	−	0.342779i	0.947848	+	0.318721i	$0.103253\pi$
$954$		0			0
$955$	0.290334	−	0.167625i	0.00939499	−	0.00542420i
$956$		0			0
$957$	24.4533	−	1.90535i	0.790464	−	0.0615913i
$958$		0			0
$959$	20.9515	−	12.0964i	0.676559	−	0.390612i
$960$		0			0
$961$			10.6490i			0.343516i
$962$		0			0
$963$	−4.63814	−	5.74591i	−0.149462	−	0.185159i
$964$		0			0
$965$	−11.6511	−	20.1803i	−0.375063	−	0.649628i
$966$		0			0
$967$	−1.02433	−	0.274467i	−0.0329401	−	0.00882627i	0.242311	−	0.970199i	$-0.422094\pi$
$967$	−1.02433	−	0.274467i	−0.0329401	−	0.00882627i	−0.275251	+	0.961372i	$0.588761\pi$
$968$		0			0
$969$	34.7937	+	29.7636i	1.11774	+	0.956144i
$970$		0			0
$971$	41.0340	+	23.6910i	1.31685	+	0.760281i	0.983220	−	0.182425i	$-0.0583946\pi$
$971$	41.0340	+	23.6910i	1.31685	+	0.760281i	0.333625	+	0.942706i	$0.391728\pi$
$972$		0			0
$973$		−	23.7369i		−	0.760971i
$974$		0			0
$975$	2.99083	+	38.3844i	0.0957834	+	1.22929i
$976$		0			0
$977$	−9.57052	−	35.7177i	−0.306188	−	1.14271i	−0.931918	−	0.362669i	$-0.881865\pi$
$977$	−9.57052	−	35.7177i	−0.306188	−	1.14271i	0.625730	−	0.780040i	$-0.284801\pi$
$978$		0			0
$979$	−7.42842	−	27.7233i	−0.237413	−	0.886039i
$980$		0			0
$981$	49.0776	−	21.7592i	1.56693	−	0.694718i
$982$		0			0
$983$	−3.80100	+	6.58353i	−0.121233	+	0.209982i	−0.920254	−	0.391321i	$-0.872018\pi$
$983$	−3.80100	+	6.58353i	−0.121233	+	0.209982i	0.799021	+	0.601303i	$0.205352\pi$
$984$		0			0
$985$	19.9236	−	19.9236i	0.634817	−	0.634817i
$986$		0			0
$987$	−23.5911	−	4.39137i	−0.750914	−	0.139779i
$988$		0			0
$989$	−24.3570			−0.774507
$990$		0			0
$991$	13.9848	+	13.9848i	0.444241	+	0.444241i	0.893434	−	0.449193i	$-0.148289\pi$
$991$	13.9848	+	13.9848i	0.444241	+	0.444241i	−0.449193	+	0.893434i	$0.648289\pi$
$992$		0			0
$993$	0.0265644	−	0.0555819i	0.000842995	−	0.00176384i
$994$		0			0
$995$	5.43032	−	3.13520i	0.172153	−	0.0993924i
$996$		0			0
$997$	3.94065	+	14.7067i	0.124802	+	0.465766i	0.999833	−	0.0183010i	$-0.00582572\pi$
$997$	3.94065	+	14.7067i	0.124802	+	0.465766i	−0.875031	+	0.484067i	$0.839159\pi$
$998$		0			0
$999$	−19.3195	+	25.0151i	−0.611243	+	0.791443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.br.a.569.31	yes	152
3.2	odd	2	inner	888.2.br.a.569.18	✓	152
37.8	odd	12	inner	888.2.br.a.785.18	yes	152
111.8	even	12	inner	888.2.br.a.785.31	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.br.a.569.18	✓	152	3.2	odd	2	inner
888.2.br.a.569.31	yes	152	1.1	even	1	trivial
888.2.br.a.785.18	yes	152	37.8	odd	12	inner
888.2.br.a.785.31	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)

\(f(q)\)	\(=\)	\(q+(1.31619 + 1.12590i) q^{3} +(0.299949 - 1.11942i) q^{5} +(0.728081 + 1.26107i) q^{7} +(0.464686 + 2.96379i) q^{9} +2.75595 q^{11} +(5.87134 + 1.57322i) q^{13} +(1.65515 - 1.13566i) q^{15} +(-4.20756 + 1.12741i) q^{17} +(-5.86193 - 1.57070i) q^{19} +(-0.461557 + 2.47956i) q^{21} +(-4.77233 - 4.77233i) q^{23} +(3.16699 + 1.82846i) q^{25} +(-2.72533 + 4.42409i) q^{27} +(3.63333 - 3.63333i) q^{29} +(4.56339 + 4.56339i) q^{31} +(3.62734 + 3.10293i) q^{33} +(1.63006 - 0.436774i) q^{35} +(6.04893 + 0.640631i) q^{37} +(5.95647 + 8.68120i) q^{39} +(1.37162 + 2.37572i) q^{41} +(2.55190 - 2.55190i) q^{43} +(3.45712 + 0.368805i) q^{45} +9.51426i q^{47} +(2.43980 - 4.22585i) q^{49} +(-6.80729 - 3.25342i) q^{51} +(-7.21838 - 4.16753i) q^{53} +(0.826644 - 3.08508i) q^{55} +(-5.94693 - 8.66730i) q^{57} +(3.55732 - 0.953181i) q^{59} +(-3.66715 + 13.6860i) q^{61} +(-3.39923 + 2.74389i) q^{63} +(3.52220 - 6.10063i) q^{65} +(4.17797 - 2.41215i) q^{67} +(-0.908090 - 11.6544i) q^{69} +(-8.53196 + 4.92593i) q^{71} -4.05969i q^{73} +(2.10967 + 5.97231i) q^{75} +(2.00656 + 3.47546i) q^{77} +(-12.9500 - 3.46994i) q^{79} +(-8.56813 + 2.75447i) q^{81} +(-3.62264 - 2.09153i) q^{83} +5.04822i q^{85} +(8.87291 - 0.691359i) q^{87} +(-2.69541 - 10.0594i) q^{89} +(2.29086 + 8.54962i) q^{91} +(0.868332 + 11.1442i) q^{93} +(-3.51656 + 6.09086i) q^{95} +(1.19949 - 1.19949i) q^{97} +(1.28065 + 8.16807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) \) 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

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Representations

Groups

Database

Properties

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