LMFDB - Embedded newform 456.2.bf.c.65.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(65,456)] 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("456.65"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 6 x^{14} + 5 x^{13} + 21 x^{12} - 4 x^{11} - 94 x^{10} - 6 x^{9} + 364 x^{8} + \cdots + 6561 $ x^16 - x^15 - 6x^14 + 5x^13 + 21x^12 - 4x^11 - 94x^10 - 6x^9 + 364x^8 - 18x^7 - 846x^6 - 108x^5 + 1701x^4 + 1215x^3 - 4374x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.5
Root			$-0.809132 - 1.53144i$ of defining polynomial
Character	$\chi$	$=$	456.65
Dual form			456.2.bf.c.449.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809132 + 1.53144i) q^{3} +(-3.15813 - 1.82335i) q^{5} +1.32651 q^{7} +(-1.69061 + 2.47827i) q^{9} +5.22390i q^{11} +(-5.77665 + 3.33515i) q^{13} +(0.237002 - 6.31182i) q^{15} +(4.40043 + 2.54059i) q^{17} +(-3.57090 + 2.49973i) q^{19} +(1.07332 + 2.03146i) q^{21} +(2.14693 - 1.23953i) q^{23} +(4.14920 + 7.18663i) q^{25} +(-5.16325 - 0.583820i) q^{27} +(0.559525 + 0.969126i) q^{29} -0.304339i q^{31} +(-8.00009 + 4.22682i) q^{33} +(-4.18928 - 2.41868i) q^{35} -4.66495i q^{37} +(-9.78165 - 6.14801i) q^{39} +(2.16072 - 3.74248i) q^{41} +(4.93321 - 8.54458i) q^{43} +(9.85793 - 4.74414i) q^{45} +(-7.04877 + 4.06961i) q^{47} -5.24038 q^{49} +(-0.330230 + 8.79466i) q^{51} +(0.391014 + 0.677256i) q^{53} +(9.52499 - 16.4978i) q^{55} +(-6.71752 - 3.44601i) q^{57} +(2.58526 - 4.47781i) q^{59} +(7.21726 + 12.5007i) q^{61} +(-2.24261 + 3.28744i) q^{63} +24.3246 q^{65} +(3.10845 - 1.79467i) q^{67} +(3.63541 + 2.28495i) q^{69} +(2.10867 - 3.65233i) q^{71} +(-4.88122 + 8.45453i) q^{73} +(-7.64863 + 12.1692i) q^{75} +6.92954i q^{77} +(4.31234 + 2.48973i) q^{79} +(-3.28367 - 8.37959i) q^{81} +5.31583i q^{83} +(-9.26476 - 16.0470i) q^{85} +(-1.03143 + 1.64103i) q^{87} +(0.227250 + 0.393608i) q^{89} +(-7.66276 + 4.42410i) q^{91} +(0.466076 - 0.246250i) q^{93} +(15.8353 - 1.38348i) q^{95} +(9.45642 + 5.45967i) q^{97} +(-12.9462 - 8.83159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{3} - 3 q^{5} + 13 q^{9} - 3 q^{13} + 15 q^{15} + 3 q^{17} + 11 q^{19} - 6 q^{21} + 3 q^{23} + 11 q^{25} - 4 q^{27} - 5 q^{29} + q^{33} - 24 q^{35} - 9 q^{39} - 6 q^{41} + 13 q^{43} + 33 q^{45}+ \cdots - 35 q^{99}+O(q^{100}) $ 16 * q - q^3 - 3 * q^5 + 13 * q^9 - 3 * q^13 + 15 * q^15 + 3 * q^17 + 11 * q^19 - 6 * q^21 + 3 * q^23 + 11 * q^25 - 4 * q^27 - 5 * q^29 + q^33 - 24 * q^35 - 9 * q^39 - 6 * q^41 + 13 * q^43 + 33 * q^45 - 27 * q^47 + 8 * q^49 + 15 * q^51 + 7 * q^53 - 12 * q^55 + 23 * q^57 + 10 * q^59 - q^61 - 8 * q^63 + 30 * q^65 - 24 * q^67 + 41 * q^69 - 27 * q^71 + 2 * q^73 - 21 * q^75 - 21 * q^79 - 7 * q^81 - 5 * q^85 - 23 * q^87 - 25 * q^89 - 78 * q^91 - 56 * q^93 - 13 * q^95 - 60 * q^97 - 35 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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
$3$	0.809132	+	1.53144i	0.467152	+	0.884177i
$3$	0.809132	+	1.53144i	0.467152	+	0.884177i
$4$		0			0
$5$	−3.15813	−	1.82335i	−1.41236	−	0.815426i	−0.416750	−	0.909021i	$-0.636831\pi$
$5$	−3.15813	−	1.82335i	−1.41236	−	0.815426i	−0.995610	+	0.0935948i	$0.970164\pi$
$6$		0			0
$7$	1.32651			0.501372			0.250686	−	0.968068i	$-0.419344\pi$
$7$	1.32651			0.501372			0.250686	+	0.968068i	$0.419344\pi$
$8$		0			0
$9$	−1.69061	+	2.47827i	−0.563537	+	0.826091i
$10$		0			0
$11$			5.22390i			1.57507i	0.616273	+	0.787533i	$0.288642\pi$
$11$			5.22390i			1.57507i	−0.616273	+	0.787533i	$0.711358\pi$
$12$		0			0
$13$	−5.77665	+	3.33515i	−1.60215	+	0.925004i	−0.611099	+	0.791554i	$0.709272\pi$
$13$	−5.77665	+	3.33515i	−1.60215	+	0.925004i	−0.991056	+	0.133450i	$0.957394\pi$
$14$		0			0
$15$	0.237002	−	6.31182i	0.0611937	−	1.62970i
$16$		0			0
$17$	4.40043	+	2.54059i	1.06726	+	0.616183i	0.927432	−	0.373992i	$-0.122011\pi$
$17$	4.40043	+	2.54059i	1.06726	+	0.616183i	0.139829	+	0.990176i	$0.455345\pi$
$18$		0			0
$19$	−3.57090	+	2.49973i	−0.819221	+	0.573478i
$19$	−3.57090	+	2.49973i	−0.819221	+	0.573478i
$20$		0			0
$21$	1.07332	+	2.03146i	0.234217	+	0.443302i
$22$		0			0
$23$	2.14693	−	1.23953i	0.447665	−	0.258460i	−0.259178	−	0.965829i	$-0.583452\pi$
$23$	2.14693	−	1.23953i	0.447665	−	0.258460i	0.706844	+	0.707370i	$0.250118\pi$
$24$		0			0
$25$	4.14920	+	7.18663i	0.829841	+	1.43733i
$26$		0			0
$27$	−5.16325	−	0.583820i	−0.993668	−	0.112356i
$28$		0			0
$29$	0.559525	+	0.969126i	0.103901	+	0.179962i	0.913289	−	0.407313i	$-0.133534\pi$
$29$	0.559525	+	0.969126i	0.103901	+	0.179962i	−0.809388	+	0.587275i	$0.800201\pi$
$30$		0			0
$31$		−	0.304339i		−	0.0546608i	−0.999626	−	0.0273304i	$-0.991299\pi$
$31$		−	0.304339i		−	0.0546608i	0.999626	−	0.0273304i	$-0.00870062\pi$
$32$		0			0
$33$	−8.00009	+	4.22682i	−1.39264	+	0.735796i
$34$		0			0
$35$	−4.18928	−	2.41868i	−0.708118	−	0.408832i
$36$		0			0
$37$		−	4.66495i		−	0.766913i	−0.923559	−	0.383456i	$-0.874734\pi$
$37$		−	4.66495i		−	0.766913i	0.923559	−	0.383456i	$-0.125266\pi$
$38$		0			0
$39$	−9.78165	−	6.14801i	−1.56632	−	0.984470i
$40$		0			0
$41$	2.16072	−	3.74248i	0.337448	−	0.584477i	−0.646504	−	0.762911i	$-0.723770\pi$
$41$	2.16072	−	3.74248i	0.337448	−	0.584477i	0.983952	+	0.178434i	$0.0571030\pi$
$42$		0			0
$43$	4.93321	−	8.54458i	0.752308	−	1.30304i	−0.194393	−	0.980924i	$-0.562274\pi$
$43$	4.93321	−	8.54458i	0.752308	−	1.30304i	0.946701	−	0.322112i	$-0.104393\pi$
$44$		0			0
$45$	9.85793	−	4.74414i	1.46953	−	0.707214i
$46$		0			0
$47$	−7.04877	+	4.06961i	−1.02817	+	0.593614i	−0.916460	−	0.400127i	$-0.868966\pi$
$47$	−7.04877	+	4.06961i	−1.02817	+	0.593614i	−0.111710	+	0.993741i	$0.535633\pi$
$48$		0			0
$49$	−5.24038			−0.748626
$50$		0			0
$51$	−0.330230	+	8.79466i	−0.0462415	+	1.23150i
$52$		0			0
$53$	0.391014	+	0.677256i	0.0537099	+	0.0930282i	0.891630	−	0.452764i	$-0.149562\pi$
$53$	0.391014	+	0.677256i	0.0537099	+	0.0930282i	−0.837920	+	0.545792i	$0.816229\pi$
$54$		0			0
$55$	9.52499	−	16.4978i	1.28435	−	2.22456i
$56$		0			0
$57$	−6.71752	−	3.44601i	−0.889757	−	0.456435i
$58$		0			0
$59$	2.58526	−	4.47781i	0.336573	−	0.582961i	−0.647213	−	0.762309i	$-0.724066\pi$
$59$	2.58526	−	4.47781i	0.336573	−	0.582961i	0.983786	+	0.179348i	$0.0573989\pi$
$60$		0			0
$61$	7.21726	+	12.5007i	0.924076	+	1.60055i	0.793041	+	0.609169i	$0.208497\pi$
$61$	7.21726	+	12.5007i	0.924076	+	1.60055i	0.131035	+	0.991378i	$0.458170\pi$
$62$		0			0
$63$	−2.24261	+	3.28744i	−0.282542	+	0.414179i
$64$		0			0
$65$	24.3246			3.01709
$66$		0			0
$67$	3.10845	−	1.79467i	0.379758	−	0.219253i	−0.297955	−	0.954580i	$-0.596305\pi$
$67$	3.10845	−	1.79467i	0.379758	−	0.219253i	0.677713	+	0.735327i	$0.262971\pi$
$68$		0			0
$69$	3.63541	+	2.28495i	0.437652	+	0.275075i
$70$		0			0
$71$	2.10867	−	3.65233i	0.250253	−	0.433451i	−0.713342	−	0.700816i	$-0.752819\pi$
$71$	2.10867	−	3.65233i	0.250253	−	0.433451i	0.963595	+	0.267364i	$0.0861528\pi$
$72$		0			0
$73$	−4.88122	+	8.45453i	−0.571304	+	0.989527i	0.425128	+	0.905133i	$0.360229\pi$
$73$	−4.88122	+	8.45453i	−0.571304	+	0.989527i	−0.996432	+	0.0843944i	$0.973104\pi$
$74$		0			0
$75$	−7.64863	+	12.1692i	−0.883188	+	1.40518i
$76$		0			0
$77$			6.92954i			0.789694i
$78$		0			0
$79$	4.31234	+	2.48973i	0.485176	+	0.280117i	0.722571	−	0.691297i	$-0.242960\pi$
$79$	4.31234	+	2.48973i	0.485176	+	0.280117i	−0.237395	+	0.971413i	$0.576294\pi$
$80$		0			0
$81$	−3.28367	−	8.37959i	−0.364852	−	0.931066i
$82$		0			0
$83$			5.31583i			0.583488i	0.956496	+	0.291744i	$0.0942356\pi$
$83$			5.31583i			0.583488i	−0.956496	+	0.291744i	$0.905764\pi$
$84$		0			0
$85$	−9.26476	−	16.0470i	−1.00490	−	1.74055i
$86$		0			0
$87$	−1.03143	+	1.64103i	−0.110581	+	0.175937i
$88$		0			0
$89$	0.227250	+	0.393608i	0.0240884	+	0.0417224i	0.877818	−	0.478994i	$-0.158998\pi$
$89$	0.227250	+	0.393608i	0.0240884	+	0.0417224i	−0.853730	+	0.520716i	$0.825665\pi$
$90$		0			0
$91$	−7.66276	+	4.42410i	−0.803276	+	0.463772i
$92$		0			0
$93$	0.466076	−	0.246250i	0.0483298	−	0.0255349i
$94$		0			0
$95$	15.8353	−	1.38348i	1.62466	−	0.141942i
$96$		0			0
$97$	9.45642	+	5.45967i	0.960154	+	0.554345i	0.896220	−	0.443609i	$-0.146302\pi$
$97$	9.45642	+	5.45967i	0.960154	+	0.554345i	0.0639336	+	0.997954i	$0.479635\pi$
$98$		0			0
$99$	−12.9462	−	8.83159i	−1.30115	−	0.887608i
$100$		0			0
$101$	−2.03309	+	1.17381i	−0.202300	+	0.116798i	−0.597728	−	0.801699i	$-0.703930\pi$
$101$	−2.03309	+	1.17381i	−0.202300	+	0.116798i	0.395428	+	0.918497i	$0.370596\pi$
$102$		0			0
$103$			0.991616i			0.0977068i	0.998806	+	0.0488534i	$0.0155567\pi$
$103$			0.991616i			0.0977068i	−0.998806	+	0.0488534i	$0.984443\pi$
$104$		0			0
$105$	0.314385	−	8.37267i	0.0306808	−	0.817089i
$106$		0			0
$107$	17.3827			1.68045			0.840224	−	0.542239i	$-0.182423\pi$
$107$	17.3827			1.68045			0.840224	+	0.542239i	$0.182423\pi$
$108$		0			0
$109$	−0.553359	−	0.319482i	−0.0530021	−	0.0306008i	0.473265	−	0.880920i	$-0.343075\pi$
$109$	−0.553359	−	0.319482i	−0.0530021	−	0.0306008i	−0.526267	+	0.850319i	$0.676409\pi$
$110$		0			0
$111$	7.14408	−	3.77456i	0.678086	−	0.358265i
$112$		0			0
$113$	0.180146			0.0169467			0.00847334	−	0.999964i	$-0.497303\pi$
$113$	0.180146			0.0169467			0.00847334	+	0.999964i	$0.497303\pi$
$114$		0			0
$115$	−9.04038			−0.843020
$116$		0			0
$117$	1.50066	−	19.9546i	0.138736	−	1.84480i
$118$		0			0
$119$	5.83720	+	3.37011i	0.535095	+	0.308937i
$120$		0			0
$121$	−16.2891			−1.48083
$122$		0			0
$123$	7.47969	+	0.280854i	0.674421	+	0.0253238i
$124$		0			0
$125$		−	12.0283i		−	1.07584i
$126$		0			0
$127$	11.6355	−	6.71777i	1.03249	−	0.596106i	0.114790	−	0.993390i	$-0.463381\pi$
$127$	11.6355	−	6.71777i	1.03249	−	0.596106i	0.917696	+	0.397284i	$0.130047\pi$
$128$		0			0
$129$	17.0771	+	0.641228i	1.50356	+	0.0564570i
$130$		0			0
$131$	6.84055	+	3.94939i	0.597661	+	0.345060i	0.768121	−	0.640305i	$-0.221192\pi$
$131$	6.84055	+	3.94939i	0.597661	+	0.345060i	−0.170460	+	0.985365i	$0.554525\pi$
$132$		0			0
$133$	−4.73683	+	3.31591i	−0.410735	+	0.287526i
$134$		0			0
$135$	15.2417	+	11.2582i	1.31180	+	0.968951i
$136$		0			0
$137$	−13.4033	+	7.73838i	−1.14512	+	0.661135i	−0.947693	−	0.319183i	$-0.896592\pi$
$137$	−13.4033	+	7.73838i	−1.14512	+	0.661135i	−0.197426	+	0.980318i	$0.563258\pi$
$138$		0			0
$139$	−4.38454	−	7.59424i	−0.371892	−	0.644135i	0.617965	−	0.786206i	$-0.287957\pi$
$139$	−4.38454	−	7.59424i	−0.371892	−	0.644135i	−0.989857	+	0.142070i	$0.954624\pi$
$140$		0			0
$141$	−11.9358	−	7.50192i	−1.00517	−	0.631775i
$142$		0			0
$143$	−17.4225	−	30.1766i	−1.45694	−	2.52350i
$144$		0			0
$145$		−	4.08084i		−	0.338895i
$146$		0			0
$147$	−4.24016	−	8.02532i	−0.349722	−	0.661918i
$148$		0			0
$149$	−5.20172	−	3.00321i	−0.426141	−	0.246033i	0.271560	−	0.962421i	$-0.412460\pi$
$149$	−5.20172	−	3.00321i	−0.426141	−	0.246033i	−0.697701	+	0.716389i	$0.745794\pi$
$150$		0			0
$151$		−	0.321176i		−	0.0261369i	−0.999915	−	0.0130685i	$-0.995840\pi$
$151$		−	0.321176i		−	0.0261369i	0.999915	−	0.0130685i	$-0.00415994\pi$
$152$		0			0
$153$	−13.7357	+	6.61031i	−1.11046	+	0.534412i
$154$		0			0
$155$	−0.554915	+	0.961142i	−0.0445719	+	0.0772008i
$156$		0			0
$157$	0.746362	−	1.29274i	0.0595662	−	0.103172i	−0.834705	−	0.550698i	$-0.814362\pi$
$157$	0.746362	−	1.29274i	0.0595662	−	0.103172i	0.894271	+	0.447526i	$0.147695\pi$
$158$		0			0
$159$	−0.720794	+	1.14680i	−0.0571627	+	0.0909474i
$160$		0			0
$161$	2.84791	−	1.64424i	0.224447	−	0.129585i
$162$		0			0
$163$	−15.8647			−1.24262			−0.621311	−	0.783564i	$-0.713400\pi$
$163$	−15.8647			−1.24262			−0.621311	+	0.783564i	$0.713400\pi$
$164$		0			0
$165$	32.9723	+	1.23808i	2.56689	+	0.0963840i
$166$		0			0
$167$	4.05882	+	7.03008i	0.314081	+	0.544004i	0.979242	−	0.202696i	$-0.0649704\pi$
$167$	4.05882	+	7.03008i	0.314081	+	0.544004i	−0.665161	+	0.746700i	$0.731637\pi$
$168$		0			0
$169$	15.7465	−	27.2737i	1.21127	−	2.09797i
$170$		0			0
$171$	−0.158007	−	13.0757i	−0.0120831	−	0.999927i
$172$		0			0
$173$	1.21215	−	2.09950i	0.0921579	−	0.159622i	−0.816261	−	0.577683i	$-0.803957\pi$
$173$	1.21215	−	2.09950i	0.0921579	−	0.159622i	0.908419	+	0.418061i	$0.137290\pi$
$174$		0			0
$175$	5.50395	+	9.53311i	0.416059	+	0.720636i
$176$		0			0
$177$	8.94931	+	0.336037i	0.672671	+	0.0252581i
$178$		0			0
$179$	−3.79105			−0.283357			−0.141678	−	0.989913i	$-0.545250\pi$
$179$	−3.79105			−0.283357			−0.141678	+	0.989913i	$0.545250\pi$
$180$		0			0
$181$	−16.0677	+	9.27671i	−1.19431	+	0.689533i	−0.959280	−	0.282456i	$-0.908851\pi$
$181$	−16.0677	+	9.27671i	−1.19431	+	0.689533i	−0.235026	+	0.971989i	$0.575517\pi$
$182$		0			0
$183$	−13.3043	+	21.1675i	−0.983482	+	1.56475i
$184$		0			0
$185$	−8.50583	+	14.7325i	−0.625361	+	1.08316i
$186$		0			0
$187$	−13.2718	+	22.9874i	−0.970529	+	1.68101i
$188$		0			0
$189$	−6.84909	−	0.774441i	−0.498198	−	0.0563323i
$190$		0			0
$191$		−	3.59262i		−	0.259953i	−0.991517	−	0.129976i	$-0.958510\pi$
$191$		−	3.59262i		−	0.259953i	0.991517	−	0.129976i	$-0.0414902\pi$
$192$		0			0
$193$	6.33759	+	3.65901i	0.456189	+	0.263381i	0.710441	−	0.703757i	$-0.248496\pi$
$193$	6.33759	+	3.65901i	0.456189	+	0.263381i	−0.254251	+	0.967138i	$0.581829\pi$
$194$		0			0
$195$	19.6818	+	37.2516i	1.40944	+	2.66764i
$196$		0			0
$197$			21.3146i			1.51860i	0.650741	+	0.759300i	$0.274458\pi$
$197$			21.3146i			1.51860i	−0.650741	+	0.759300i	$0.725542\pi$
$198$		0			0
$199$	5.93321	+	10.2766i	0.420594	+	0.728491i	0.995998	−	0.0893789i	$-0.0284882\pi$
$199$	5.93321	+	10.2766i	0.420594	+	0.728491i	−0.575403	+	0.817870i	$0.695155\pi$
$200$		0			0
$201$	5.26357	+	3.30829i	0.371264	+	0.233348i
$202$		0			0
$203$	0.742214	+	1.28555i	0.0520932	+	0.0902280i
$204$		0			0
$205$	−13.6477	+	7.87950i	−0.953196	+	0.550328i
$206$		0			0
$207$	−0.557730	+	7.41623i	−0.0387649	+	0.515464i
$208$		0			0
$209$	−13.0583	−	18.6540i	−0.903265	−	1.29033i
$210$		0			0
$211$	6.26479	+	3.61698i	0.431286	+	0.249003i	0.699894	−	0.714246i	$-0.253230\pi$
$211$	6.26479	+	3.61698i	0.431286	+	0.249003i	−0.268608	+	0.963250i	$0.586564\pi$
$212$		0			0
$213$	7.29951	+	0.274089i	0.500154	+	0.0187803i
$214$		0			0
$215$	−31.1595	+	17.9899i	−2.12506	+	1.22690i
$216$		0			0
$217$		−	0.403707i		−	0.0274054i
$218$		0			0
$219$	−16.8971	−	0.634470i	−1.14180	−	0.0428735i
$220$		0			0
$221$	−33.8930			−2.27989
$222$		0			0
$223$	14.7806	+	8.53358i	0.989782	+	0.571451i	0.905209	−	0.424966i	$-0.139714\pi$
$223$	14.7806	+	8.53358i	0.989782	+	0.571451i	0.0845731	+	0.996417i	$0.473047\pi$
$224$		0			0
$225$	−24.8251	−	1.86695i	−1.65501	−	0.124463i
$226$		0			0
$227$	10.7482			0.713381			0.356690	−	0.934223i	$-0.383905\pi$
$227$	10.7482			0.713381			0.356690	+	0.934223i	$0.383905\pi$
$228$		0			0
$229$	16.9808			1.12212			0.561061	−	0.827775i	$-0.310393\pi$
$229$	16.9808			1.12212			0.561061	+	0.827775i	$0.310393\pi$
$230$		0			0
$231$	−10.6122	+	5.60691i	−0.698229	+	0.368908i
$232$		0			0
$233$	−14.1267	−	8.15608i	−0.925474	−	0.534322i	−0.0400964	−	0.999196i	$-0.512767\pi$
$233$	−14.1267	−	8.15608i	−0.925474	−	0.534322i	−0.885377	+	0.464873i	$0.846100\pi$
$234$		0			0
$235$	29.6813			1.93619
$236$		0			0
$237$	−0.323619	+	8.61861i	−0.0210213	+	0.559839i
$238$		0			0
$239$		−	0.792303i		−	0.0512498i	−0.999672	−	0.0256249i	$-0.991842\pi$
$239$		−	0.792303i		−	0.0512498i	0.999672	−	0.0256249i	$-0.00815755\pi$
$240$		0			0
$241$	5.78713	−	3.34120i	0.372782	−	0.215226i	−0.301891	−	0.953342i	$-0.597618\pi$
$241$	5.78713	−	3.34120i	0.372782	−	0.215226i	0.674673	+	0.738117i	$0.264285\pi$
$242$		0			0
$243$	10.1759	−	11.8089i	0.652785	−	0.757543i
$244$		0			0
$245$	16.5498	+	9.55504i	1.05733	+	0.610449i
$246$		0			0
$247$	12.2909	−	26.3496i	0.782050	−	1.67658i
$248$		0			0
$249$	−8.14087	+	4.30121i	−0.515907	+	0.272578i
$250$		0			0
$251$	0.609130	−	0.351681i	0.0384479	−	0.0221979i	−0.480653	−	0.876911i	$-0.659600\pi$
$251$	0.609130	−	0.351681i	0.0384479	−	0.0221979i	0.519101	+	0.854713i	$0.326267\pi$
$252$		0			0
$253$	6.47518	+	11.2153i	0.407091	+	0.705102i
$254$		0			0
$255$	17.0786	−	27.1726i	1.06951	−	1.70161i
$256$		0			0
$257$	10.5433	+	18.2615i	0.657672	+	1.13912i	0.981217	+	0.192908i	$0.0617918\pi$
$257$	10.5433	+	18.2615i	0.657672	+	1.13912i	−0.323545	+	0.946213i	$0.604875\pi$
$258$		0			0
$259$		−	6.18808i		−	0.384509i
$260$		0			0
$261$	−3.34770	−	0.251760i	−0.207217	−	0.0155835i
$262$		0			0
$263$	−2.53267	−	1.46224i	−0.156171	−	0.0901655i	0.419878	−	0.907581i	$-0.362073\pi$
$263$	−2.53267	−	1.46224i	−0.156171	−	0.0901655i	−0.576049	+	0.817415i	$0.695406\pi$
$264$		0			0
$265$		−	2.85182i		−	0.175186i
$266$		0			0
$267$	−0.418912	+	0.666500i	−0.0256370	+	0.0407892i
$268$		0			0
$269$	10.4795	−	18.1511i	0.638948	−	1.10669i	−0.346716	−	0.937970i	$-0.612703\pi$
$269$	10.4795	−	18.1511i	0.638948	−	1.10669i	0.985664	−	0.168721i	$-0.0539635\pi$
$270$		0			0
$271$	−6.71324	+	11.6277i	−0.407800	+	0.706330i	−0.994643	−	0.103370i	$-0.967037\pi$
$271$	−6.71324	+	11.6277i	−0.407800	+	0.706330i	0.586843	+	0.809701i	$0.300371\pi$
$272$		0			0
$273$	−12.9754	−	8.15538i	−0.785308	−	0.493586i
$274$		0			0
$275$	−37.5422	+	21.6750i	−2.26388	+	1.30705i
$276$		0			0
$277$	5.81486			0.349381			0.174691	−	0.984623i	$-0.444107\pi$
$277$	5.81486			0.349381			0.174691	+	0.984623i	$0.444107\pi$
$278$		0			0
$279$	0.754234	+	0.514518i	0.0451548	+	0.0308034i
$280$		0			0
$281$	−13.6509	−	23.6440i	−0.814342	−	1.41048i	−0.909799	−	0.415049i	$-0.863765\pi$
$281$	−13.6509	−	23.6440i	−0.814342	−	1.41048i	0.0954570	−	0.995434i	$-0.469569\pi$
$282$		0			0
$283$	−1.45532	+	2.52070i	−0.0865100	+	0.149840i	−0.906034	−	0.423206i	$-0.860905\pi$
$283$	−1.45532	+	2.52070i	−0.0865100	+	0.149840i	0.819524	+	0.573045i	$0.194238\pi$
$284$		0			0
$285$	14.9315	+	23.1313i	0.884468	+	1.37018i
$286$		0			0
$287$	2.86621	−	4.96442i	0.169187	−	0.293041i
$288$		0			0
$289$	4.40918	+	7.63693i	0.259364	+	0.449231i
$290$		0			0
$291$	−0.709657	+	18.8995i	−0.0416008	+	1.10791i
$292$		0			0
$293$	−10.4657			−0.611416			−0.305708	−	0.952125i	$-0.598893\pi$
$293$	−10.4657			−0.611416			−0.305708	+	0.952125i	$0.598893\pi$
$294$		0			0
$295$	−16.3292	+	9.42768i	−0.950724	+	0.548901i
$296$		0			0
$297$	3.04982	−	26.9723i	0.176968	−	1.56509i
$298$		0			0
$299$	−8.26803	+	14.3207i	−0.478153	+	0.828185i
$300$		0			0
$301$	6.54394	−	11.3344i	0.377187	−	0.653306i
$302$		0			0
$303$	−3.44265	−	2.16379i	−0.197775	−	0.124307i
$304$		0			0
$305$		−	52.6384i		−	3.01406i
$306$		0			0
$307$	−8.49577	−	4.90503i	−0.484879	−	0.279945i	0.237568	−	0.971371i	$-0.423650\pi$
$307$	−8.49577	−	4.90503i	−0.484879	−	0.279945i	−0.722448	+	0.691426i	$0.756983\pi$
$308$		0			0
$309$	−1.51860	+	0.802348i	−0.0863901	+	0.0456440i
$310$		0			0
$311$		−	9.42922i		−	0.534682i	−0.963602	−	0.267341i	$-0.913855\pi$
$311$		−	9.42922i		−	0.534682i	0.963602	−	0.267341i	$-0.0861450\pi$
$312$		0			0
$313$	11.1942	+	19.3890i	0.632736	+	1.09593i	0.986990	+	0.160782i	$0.0514016\pi$
$313$	11.1942	+	19.3890i	0.632736	+	1.09593i	−0.354254	+	0.935149i	$0.615265\pi$
$314$		0			0
$315$	13.0766	−	6.29313i	0.736784	−	0.354578i
$316$		0			0
$317$	9.24221	+	16.0080i	0.519094	+	0.899098i	0.999754	+	0.0221905i	$0.00706403\pi$
$317$	9.24221	+	16.0080i	0.519094	+	0.899098i	−0.480659	+	0.876907i	$0.659603\pi$
$318$		0			0
$319$	−5.06262	+	2.92290i	−0.283452	+	0.163651i
$320$		0			0
$321$	14.0649	+	26.6205i	0.785026	+	1.48581i
$322$		0			0
$323$	−22.0643	+	1.92770i	−1.22769	+	0.107260i
$324$		0			0
$325$	−47.9370	−	27.6764i	−2.65907	−	1.53521i
$326$		0			0
$327$	0.0415268	−	1.10594i	0.00229644	−	0.0611585i
$328$		0			0
$329$	−9.35025	+	5.39837i	−0.515496	+	0.297622i
$330$		0			0
$331$		−	13.3307i		−	0.732723i	−0.930473	−	0.366361i	$-0.880603\pi$
$331$		−	13.3307i		−	0.732723i	0.930473	−	0.366361i	$-0.119397\pi$
$332$		0			0
$333$	11.5610	+	7.88661i	0.633539	+	0.432184i
$334$		0			0
$335$	−13.0892			−0.715140
$336$		0			0
$337$	25.8098	+	14.9013i	1.40595	+	0.811725i	0.994994	−	0.0999311i	$-0.0318622\pi$
$337$	25.8098	+	14.9013i	1.40595	+	0.811725i	0.410954	+	0.911656i	$0.365196\pi$
$338$		0			0
$339$	0.145762	+	0.275882i	0.00791668	+	0.0149839i
$340$		0			0
$341$	1.58983			0.0860944
$342$		0			0
$343$	−16.2369			−0.876713
$344$		0			0
$345$	−7.31486	−	13.8448i	−0.393819	−	0.745378i
$346$		0			0
$347$	22.9416	+	13.2454i	1.23157	+	0.711048i	0.967357	−	0.253416i	$-0.0815543\pi$
$347$	22.9416	+	13.2454i	1.23157	+	0.711048i	0.264214	+	0.964464i	$0.414888\pi$
$348$		0			0
$349$	−15.1446			−0.810673			−0.405337	−	0.914168i	$-0.632846\pi$
$349$	−15.1446			−0.810673			−0.405337	+	0.914168i	$0.632846\pi$
$350$		0			0
$351$	31.7734	−	13.8477i	1.69594	−	0.739135i
$352$		0			0
$353$			18.2589i			0.971822i	0.874008	+	0.485911i	$0.161512\pi$
$353$			18.2589i			0.971822i	−0.874008	+	0.485911i	$0.838488\pi$
$354$		0			0
$355$	−13.3189	+	7.68969i	−0.706896	+	0.408126i
$356$		0			0
$357$	−0.438052	+	11.6662i	−0.0231842	+	0.617439i
$358$		0			0
$359$	15.7764	+	9.10850i	0.832645	+	0.480728i	0.854758	−	0.519027i	$-0.173706\pi$
$359$	15.7764	+	9.10850i	0.832645	+	0.480728i	−0.0221122	+	0.999755i	$0.507039\pi$
$360$		0			0
$361$	6.50269	−	17.8526i	0.342247	−	0.939610i
$362$		0			0
$363$	−13.1801	−	24.9458i	−0.691774	−	1.30932i
$364$		0			0
$365$	30.8311	−	17.8003i	1.61377	−	0.931713i
$366$		0			0
$367$	−17.5938	−	30.4734i	−0.918389	−	1.59070i	−0.801862	−	0.597510i	$-0.796157\pi$
$367$	−17.5938	−	30.4734i	−0.918389	−	1.59070i	−0.116528	−	0.993187i	$-0.537176\pi$
$368$		0			0
$369$	5.62194	+	11.6819i	0.292667	+	0.608137i
$370$		0			0
$371$	0.518682	+	0.898384i	0.0269286	+	0.0466418i
$372$		0			0
$373$			16.7168i			0.865561i	0.901499	+	0.432781i	$0.142468\pi$
$373$			16.7168i			0.865561i	−0.901499	+	0.432781i	$0.857532\pi$
$374$		0			0
$375$	18.4206	−	9.73247i	0.951235	−	0.502583i
$376$		0			0
$377$	−6.46436	−	3.73220i	−0.332932	−	0.192218i
$378$		0			0
$379$			5.67816i			0.291668i	0.989309	+	0.145834i	$0.0465865\pi$
$379$			5.67816i			0.291668i	−0.989309	+	0.145834i	$0.953414\pi$
$380$		0			0
$381$	19.7025	+	12.3835i	1.00939	+	0.634427i
$382$		0			0
$383$	14.7085	−	25.4760i	0.751572	−	1.30176i	−0.195489	−	0.980706i	$-0.562629\pi$
$383$	14.7085	−	25.4760i	0.751572	−	1.30176i	0.947061	−	0.321055i	$-0.104037\pi$
$384$		0			0
$385$	12.6350	−	21.8844i	0.643938	−	1.11533i
$386$		0			0
$387$	12.8356	+	26.6714i	0.652472	+	1.35578i
$388$		0			0
$389$	−3.46815	+	2.00234i	−0.175842	+	0.101523i	−0.585338	−	0.810790i	$-0.699038\pi$
$389$	−3.46815	+	2.00234i	−0.175842	+	0.101523i	0.409495	+	0.912312i	$0.365705\pi$
$390$		0			0
$391$	12.5965			0.637034
$392$		0			0
$393$	−0.513349	+	13.6715i	−0.0258950	+	0.689634i
$394$		0			0
$395$	−9.07929	−	15.7258i	−0.456829	−	0.791251i
$396$		0			0
$397$	1.81538	−	3.14434i	0.0911115	−	0.157810i	−0.816868	−	0.576825i	$-0.804291\pi$
$397$	1.81538	−	3.14434i	0.0911115	−	0.157810i	0.907979	+	0.419015i	$0.137625\pi$
$398$		0			0
$399$	−8.91083	−	4.57115i	−0.446100	−	0.228844i
$400$		0			0
$401$	−4.34004	+	7.51717i	−0.216731	+	0.375390i	−0.953807	−	0.300421i	$-0.902873\pi$
$401$	−4.34004	+	7.51717i	−0.216731	+	0.375390i	0.737075	+	0.675810i	$0.236206\pi$
$402$		0			0
$403$	1.01501	+	1.75806i	0.0505615	+	0.0875751i
$404$		0			0
$405$	−4.90866	+	32.4511i	−0.243914	+	1.61251i
$406$		0			0
$407$	24.3692			1.20794
$408$		0			0
$409$	−29.6462	+	17.1162i	−1.46591	+	0.846344i	−0.999274	−	0.0381058i	$-0.987868\pi$
$409$	−29.6462	+	17.1162i	−1.46591	+	0.846344i	−0.466636	+	0.884449i	$0.654534\pi$
$410$		0			0
$411$	−22.6959	−	14.2649i	−1.11951	−	0.703637i
$412$		0			0
$413$	3.42937	−	5.93984i	0.168748	−	0.292281i
$414$		0			0
$415$	9.69262	−	16.7881i	0.475792	−	0.824096i
$416$		0			0
$417$	8.08245	−	12.8594i	0.395799	−	0.629727i
$418$		0			0
$419$		−	15.5987i		−	0.762048i	−0.924565	−	0.381024i	$-0.875571\pi$
$419$		−	15.5987i		−	0.762048i	0.924565	−	0.381024i	$-0.124429\pi$
$420$		0			0
$421$	−10.8879	−	6.28611i	−0.530642	−	0.306366i	0.210636	−	0.977565i	$-0.432447\pi$
$421$	−10.8879	−	6.28611i	−0.530642	−	0.306366i	−0.741278	+	0.671198i	$0.765780\pi$
$422$		0			0
$423$	1.83113	−	24.3489i	0.0890327	−	1.18388i
$424$		0			0
$425$			42.1657i			2.04534i
$426$		0			0
$427$	9.57375	+	16.5822i	0.463306	+	0.802470i
$428$		0			0
$429$	32.1166	−	51.0984i	1.55060	−	2.46705i
$430$		0			0
$431$	−10.2769	−	17.8001i	−0.495022	−	0.857403i	0.504962	−	0.863142i	$-0.331507\pi$
$431$	−10.2769	−	17.8001i	−0.495022	−	0.857403i	−0.999984	+	0.00573880i	$0.998173\pi$
$432$		0			0
$433$	−1.74254	+	1.00605i	−0.0837410	+	0.0483479i	−0.541286	−	0.840839i	$-0.682062\pi$
$433$	−1.74254	+	1.00605i	−0.0837410	+	0.0483479i	0.457545	+	0.889187i	$0.348729\pi$
$434$		0			0
$435$	6.24955	−	3.30194i	0.299643	−	0.158316i
$436$		0			0
$437$	−4.56798	+	9.79298i	−0.218516	+	0.468462i
$438$		0			0
$439$	−10.1428	−	5.85597i	−0.484091	−	0.279490i	0.238029	−	0.971258i	$-0.423499\pi$
$439$	−10.1428	−	5.85597i	−0.484091	−	0.279490i	−0.722120	+	0.691768i	$0.756832\pi$
$440$		0			0
$441$	8.85945	−	12.9871i	0.421878	−	0.618433i
$442$		0			0
$443$	2.76113	−	1.59414i	0.131185	−	0.0757397i	−0.432971	−	0.901408i	$-0.642535\pi$
$443$	2.76113	−	1.59414i	0.131185	−	0.0757397i	0.564156	+	0.825668i	$0.309202\pi$
$444$		0			0
$445$		−	1.65742i		−	0.0785694i
$446$		0			0
$447$	0.390363	−	10.3961i	0.0184635	−	0.491719i
$448$		0			0
$449$	−23.4658			−1.10742			−0.553709	−	0.832710i	$-0.686788\pi$
$449$	−23.4658			−1.10742			−0.553709	+	0.832710i	$0.686788\pi$
$450$		0			0
$451$	19.5503	+	11.2874i	0.920589	+	0.531503i
$452$		0			0
$453$	0.491861	−	0.259874i	0.0231096	−	0.0122099i
$454$		0			0
$455$	32.2667			1.51269
$456$		0			0
$457$	3.31468			0.155054			0.0775270	−	0.996990i	$-0.475298\pi$
$457$	3.31468			0.155054			0.0775270	+	0.996990i	$0.475298\pi$
$458$		0			0
$459$	−21.2373	−	15.6868i	−0.991271	−	0.732195i
$460$		0			0
$461$	15.9430	+	9.20470i	0.742540	+	0.428706i	0.822992	−	0.568053i	$-0.192303\pi$
$461$	15.9430	+	9.20470i	0.742540	+	0.428706i	−0.0804520	+	0.996758i	$0.525636\pi$
$462$		0			0
$463$	19.1970			0.892162			0.446081	−	0.894992i	$-0.352819\pi$
$463$	19.1970			0.892162			0.446081	+	0.894992i	$0.352819\pi$
$464$		0			0
$465$	−1.92093	−	0.0721289i	−0.0890810	−	0.00334490i
$466$		0			0
$467$		−	17.3740i		−	0.803972i	−0.915646	−	0.401986i	$-0.868320\pi$
$467$		−	17.3740i		−	0.803972i	0.915646	−	0.401986i	$-0.131680\pi$
$468$		0			0
$469$	4.12338	−	2.38064i	0.190400	−	0.109928i
$470$		0			0
$471$	2.58365	+	0.0970135i	0.119049	+	0.00447014i
$472$		0			0
$473$	44.6360	+	25.7706i	2.05237	+	1.18493i
$474$		0			0
$475$	−32.7810	−	15.2909i	−1.50410	−	0.701593i
$476$		0			0
$477$	−2.33948	−	0.175938i	−0.107117	−	0.00805564i
$478$		0			0
$479$	−21.1329	+	12.2011i	−0.965589	+	0.557483i	−0.897889	−	0.440223i	$-0.854900\pi$
$479$	−21.1329	+	12.2011i	−0.965589	+	0.557483i	−0.0677004	+	0.997706i	$0.521566\pi$
$480$		0			0
$481$	15.5583	+	26.9478i	0.709398	+	1.22871i
$482$		0			0
$483$	4.82240	+	3.03100i	0.219427	+	0.137915i
$484$		0			0
$485$	−19.9098	−	34.4847i	−0.904055	−	1.56587i
$486$		0			0
$487$			6.87512i			0.311541i	0.987793	+	0.155771i	$0.0497861\pi$
$487$			6.87512i			0.311541i	−0.987793	+	0.155771i	$0.950214\pi$
$488$		0			0
$489$	−12.8367	−	24.2959i	−0.580494	−	1.09870i
$490$		0			0
$491$	−4.89360	−	2.82532i	−0.220845	−	0.127505i	0.385496	−	0.922709i	$-0.374030\pi$
$491$	−4.89360	−	2.82532i	−0.220845	−	0.127505i	−0.606342	+	0.795204i	$0.707364\pi$
$492$		0			0
$493$			5.68609i			0.256089i
$494$		0			0
$495$	24.7829	+	51.4969i	1.11391	+	2.31461i
$496$		0			0
$497$	2.79717	−	4.84484i	0.125470	−	0.217321i
$498$		0			0
$499$	−0.775921	+	1.34393i	−0.0347350	+	0.0601628i	−0.882870	−	0.469617i	$-0.844392\pi$
$499$	−0.775921	+	1.34393i	−0.0347350	+	0.0601628i	0.848135	+	0.529780i	$0.177725\pi$
$500$		0			0
$501$	−7.48202	+	11.9041i	−0.334272	+	0.531836i
$502$		0			0
$503$	−34.2917	+	19.7983i	−1.52899	+	0.882765i	−0.529589	+	0.848255i	$0.677654\pi$
$503$	−34.2917	+	19.7983i	−1.52899	+	0.882765i	−0.999404	+	0.0345100i	$0.989013\pi$
$504$		0			0
$505$	8.56104			0.380961
$506$		0			0
$507$	54.5089	+	2.04675i	2.42083	+	0.0908995i
$508$		0			0
$509$	−12.5606	−	21.7555i	−0.556737	−	0.964296i	−0.997766	−	0.0668036i	$-0.978720\pi$
$509$	−12.5606	−	21.7555i	−0.556737	−	0.964296i	0.441029	−	0.897493i	$-0.354613\pi$
$510$		0			0
$511$	−6.47497	+	11.2150i	−0.286436	+	0.496122i
$512$		0			0
$513$	19.8969	−	10.8220i	0.878468	−	0.477802i
$514$		0			0
$515$	1.80806	−	3.13165i	0.0796727	−	0.137997i
$516$		0			0
$517$	−21.2592	−	36.8221i	−0.934981	−	1.61943i
$518$		0			0
$519$	4.19605	+	0.157557i	0.184186	+	0.00691599i
$520$		0			0
$521$	27.8194			1.21879			0.609395	−	0.792867i	$-0.291413\pi$
$521$	27.8194			1.21879			0.609395	+	0.792867i	$0.291413\pi$
$522$		0			0
$523$	28.3513	−	16.3686i	1.23972	−	0.715750i	0.270679	−	0.962670i	$-0.412752\pi$
$523$	28.3513	−	16.3686i	1.23972	−	0.715750i	0.969036	+	0.246920i	$0.0794184\pi$
$524$		0			0
$525$	−10.1460	+	16.1425i	−0.442806	+	0.704517i
$526$		0			0
$527$	0.773199	−	1.33922i	0.0336811	−	0.0583373i
$528$		0			0
$529$	−8.42713	+	14.5962i	−0.366397	+	0.634618i
$530$		0			0
$531$	6.72655	+	13.9772i	0.291907	+	0.606560i
$532$		0			0
$533$			28.8253i			1.24856i
$534$		0			0
$535$	−54.8969	−	31.6947i	−2.37340	−	1.37028i
$536$		0			0
$537$	−3.06746	−	5.80577i	−0.132371	−	0.250537i
$538$		0			0
$539$		−	27.3752i		−	1.17913i
$540$		0			0
$541$	6.11682	+	10.5946i	0.262982	+	0.455499i	0.967033	−	0.254651i	$-0.0819605\pi$
$541$	6.11682	+	10.5946i	0.262982	+	0.455499i	−0.704051	+	0.710150i	$0.748627\pi$
$542$		0			0
$543$	−27.2076	−	17.1007i	−1.16759	−	0.733861i
$544$		0			0
$545$	1.16505	+	2.01793i	0.0499054	+	0.0864387i
$546$		0			0
$547$	18.8221	−	10.8669i	0.804774	−	0.464637i	−0.0403636	−	0.999185i	$-0.512852\pi$
$547$	18.8221	−	10.8669i	0.804774	−	0.464637i	0.845138	+	0.534548i	$0.179518\pi$
$548$		0			0
$549$	−43.1816	−	3.24743i	−1.84295	−	0.138597i
$550$		0			0
$551$	−4.42056	−	2.06199i	−0.188322	−	0.0878438i
$552$		0			0
$553$	5.72035	+	3.30264i	0.243254	+	0.140443i
$554$		0			0
$555$	−29.4443	−	1.10560i	−1.24984	−	0.0469302i
$556$		0			0
$557$	34.5030	−	19.9203i	1.46194	−	0.844051i	0.462838	−	0.886443i	$-0.346831\pi$
$557$	34.5030	−	19.9203i	1.46194	−	0.844051i	0.999101	+	0.0423915i	$0.0134977\pi$
$558$		0			0
$559$			65.8121i			2.78355i
$560$		0			0
$561$	−45.9424	−	1.72509i	−1.93969	−	0.0728333i
$562$		0			0
$563$	19.8969			0.838554			0.419277	−	0.907858i	$-0.362284\pi$
$563$	19.8969			0.838554			0.419277	+	0.907858i	$0.362284\pi$
$564$		0			0
$565$	−0.568924	−	0.328468i	−0.0239348	−	0.0138188i
$566$		0			0
$567$	−4.35580	−	11.1156i	−0.182927	−	0.466811i
$568$		0			0
$569$	−27.5093			−1.15325			−0.576625	−	0.817009i	$-0.695631\pi$
$569$	−27.5093			−1.15325			−0.576625	+	0.817009i	$0.695631\pi$
$570$		0			0
$571$	23.6597			0.990128			0.495064	−	0.868856i	$-0.335145\pi$
$571$	23.6597			0.990128			0.495064	+	0.868856i	$0.335145\pi$
$572$		0			0
$573$	5.50188	−	2.90690i	0.229844	−	0.121438i
$574$		0			0
$575$	17.8161	+	10.2861i	0.742982	+	0.428961i
$576$		0			0
$577$	33.6172			1.39950			0.699751	−	0.714387i	$-0.253294\pi$
$577$	33.6172			1.39950			0.699751	+	0.714387i	$0.253294\pi$
$578$		0			0
$579$	−0.475604	+	12.6662i	−0.0197654	+	0.526391i
$580$		0			0
$581$			7.05149i			0.292545i
$582$		0			0
$583$	−3.53792	+	2.04262i	−0.146526	+	0.0845965i
$584$		0			0
$585$	−41.1234	+	60.2829i	−1.70024	+	2.49239i
$586$		0			0
$587$	10.2731	+	5.93120i	0.424018	+	0.244807i	0.696795	−	0.717271i	$-0.254609\pi$
$587$	10.2731	+	5.93120i	0.424018	+	0.244807i	−0.272777	+	0.962077i	$0.587942\pi$
$588$		0			0
$589$	0.760765	+	1.08676i	0.0313468	+	0.0447793i
$590$		0			0
$591$	−32.6420	+	17.2463i	−1.34271	+	0.709418i
$592$		0			0
$593$	−9.01249	+	5.20336i	−0.370099	+	0.213677i	−0.673502	−	0.739186i	$-0.735211\pi$
$593$	−9.01249	+	5.20336i	−0.370099	+	0.213677i	0.303403	+	0.952862i	$0.401877\pi$
$594$		0			0
$595$	−12.2898	−	21.2865i	−0.503831	−	0.872661i
$596$		0			0
$597$	−10.9373	+	17.4015i	−0.447633	+	0.712196i
$598$		0			0
$599$	18.0611	+	31.2828i	0.737958	+	1.27818i	0.953413	+	0.301668i	$0.0975433\pi$
$599$	18.0611	+	31.2828i	0.737958	+	1.27818i	−0.215455	+	0.976514i	$0.569123\pi$
$600$		0			0
$601$		−	32.2619i		−	1.31599i	−0.753021	−	0.657996i	$-0.771404\pi$
$601$		−	32.2619i		−	1.31599i	0.753021	−	0.657996i	$-0.228596\pi$
$602$		0			0
$603$	−0.807515	+	10.7377i	−0.0328846	+	0.437272i
$604$		0			0
$605$	51.4433	+	29.7008i	2.09147	+	1.20751i
$606$		0			0
$607$			25.8372i			1.04870i	0.851503	+	0.524350i	$0.175692\pi$
$607$			25.8372i			1.04870i	−0.851503	+	0.524350i	$0.824308\pi$
$608$		0			0
$609$	−1.36820	+	2.17684i	−0.0554421	+	0.0882098i
$610$		0			0
$611$	27.1455	−	47.0174i	1.09819	−	1.90212i
$612$		0			0
$613$	3.88258	−	6.72483i	0.156816	−	0.271613i	−0.776903	−	0.629621i	$-0.783210\pi$
$613$	3.88258	−	6.72483i	0.156816	−	0.271613i	0.933719	+	0.358007i	$0.116544\pi$
$614$		0			0
$615$	−23.1098	−	14.5251i	−0.931875	−	0.585707i
$616$		0			0
$617$	−7.34239	+	4.23913i	−0.295594	+	0.170661i	−0.640462	−	0.767990i	$-0.721257\pi$
$617$	−7.34239	+	4.23913i	−0.295594	+	0.170661i	0.344868	+	0.938651i	$0.387924\pi$
$618$		0			0
$619$	−22.4134			−0.900872			−0.450436	−	0.892809i	$-0.648731\pi$
$619$	−22.4134			−0.900872			−0.450436	+	0.892809i	$0.648731\pi$
$620$		0			0
$621$	−11.8088	+	5.14658i	−0.473870	+	0.206525i
$622$		0			0
$623$	0.301448	+	0.522124i	0.0120773	+	0.0209185i
$624$		0			0
$625$	−1.18576	+	2.05379i	−0.0474302	+	0.0821516i
$626$		0			0
$627$	18.0016	−	35.0916i	0.718915	−	1.40143i
$628$		0			0
$629$	11.8517	−	20.5278i	0.472559	−	0.818496i
$630$		0			0
$631$	−8.49576	−	14.7151i	−0.338211	−	0.585798i	0.645885	−	0.763434i	$-0.276488\pi$
$631$	−8.49576	−	14.7151i	−0.338211	−	0.585798i	−0.984096	+	0.177636i	$0.943155\pi$
$632$		0			0
$633$	−0.470141	+	12.5208i	−0.0186864	+	0.497656i
$634$		0			0
$635$	−48.9954			−1.94432
$636$		0			0
$637$	30.2718	−	17.4775i	1.19941	−	0.692482i
$638$		0			0
$639$	5.48651	+	11.4005i	0.217043	+	0.450998i
$640$		0			0
$641$	−6.38034	+	11.0511i	−0.252008	+	0.436491i	−0.964079	−	0.265617i	$-0.914424\pi$
$641$	−6.38034	+	11.0511i	−0.252008	+	0.436491i	0.712070	+	0.702108i	$0.247758\pi$
$642$		0			0
$643$	18.3192	−	31.7298i	0.722438	−	1.25130i	−0.237582	−	0.971368i	$-0.576355\pi$
$643$	18.3192	−	31.7298i	0.722438	−	1.25130i	0.960020	−	0.279932i	$-0.0903118\pi$
$644$		0			0
$645$	−52.7626	−	33.1626i	−2.07753	−	1.30578i
$646$		0			0
$647$			8.57536i			0.337132i	0.985690	+	0.168566i	$0.0539137\pi$
$647$			8.57536i			0.337132i	−0.985690	+	0.168566i	$0.946086\pi$
$648$		0			0
$649$	23.3916	+	13.5052i	0.918202	+	0.530124i
$650$		0			0
$651$	0.618253	−	0.326652i	0.0242312	−	0.0128025i
$652$		0			0
$653$			8.60841i			0.336873i	0.985713	+	0.168436i	$0.0538718\pi$
$653$			8.60841i			0.336873i	−0.985713	+	0.168436i	$0.946128\pi$
$654$		0			0
$655$	−14.4022	−	24.9454i	−0.562742	−	0.974698i
$656$		0			0
$657$	−12.7004	−	26.3903i	−0.495488	−	1.02958i
$658$		0			0
$659$	14.6656	+	25.4016i	0.571292	+	0.989507i	0.996434	+	0.0843799i	$0.0268909\pi$
$659$	14.6656	+	25.4016i	0.571292	+	0.989507i	−0.425142	+	0.905127i	$0.639776\pi$
$660$		0			0
$661$	−21.6602	+	12.5055i	−0.842484	+	0.486408i	−0.858108	−	0.513469i	$-0.828360\pi$
$661$	−21.6602	+	12.5055i	−0.842484	+	0.486408i	0.0156237	+	0.999878i	$0.495027\pi$
$662$		0			0
$663$	−27.4239	−	51.9050i	−1.06506	−	2.01582i
$664$		0			0
$665$	21.0056	−	1.83520i	0.814562	−	0.0711660i
$666$		0			0
$667$	2.40252	+	1.38710i	0.0930259	+	0.0537085i
$668$		0			0
$669$	−1.10921	+	29.5404i	−0.0428845	+	1.14210i
$670$		0			0
$671$	−65.3022	+	37.7023i	−2.52097	+	1.45548i
$672$		0			0
$673$		−	35.5191i		−	1.36916i	−0.728938	−	0.684580i	$-0.759986\pi$
$673$		−	35.5191i		−	1.36916i	0.728938	−	0.684580i	$-0.240014\pi$
$674$		0			0
$675$	−17.2277	−	39.5288i	−0.663094	−	1.52146i
$676$		0			0
$677$	−31.8988			−1.22597			−0.612985	−	0.790095i	$-0.710031\pi$
$677$	−31.8988			−1.22597			−0.612985	+	0.790095i	$0.710031\pi$
$678$		0			0
$679$	12.5440	+	7.24228i	0.481395	+	0.277933i
$680$		0			0
$681$	8.69668	+	16.4602i	0.333258	+	0.630755i
$682$		0			0
$683$	4.68720			0.179351			0.0896753	−	0.995971i	$-0.471417\pi$
$683$	4.68720			0.179351			0.0896753	+	0.995971i	$0.471417\pi$
$684$		0			0
$685$	56.4391			2.15643
$686$		0			0
$687$	13.7397	+	26.0050i	0.524202	+	0.992154i
$688$		0			0
$689$	−4.51750	−	2.60818i	−0.172103	−	0.0993637i
$690$		0			0
$691$	−11.0315			−0.419658			−0.209829	−	0.977738i	$-0.567291\pi$
$691$	−11.0315			−0.419658			−0.209829	+	0.977738i	$0.567291\pi$
$692$		0			0
$693$	−17.1733	−	11.7152i	−0.652359	−	0.445022i
$694$		0			0
$695$			31.9782i			1.21300i
$696$		0			0
$697$	19.0162	−	10.9790i	0.720290	−	0.415860i
$698$		0			0
$699$	1.06014	−	28.2336i	0.0400982	−	1.06789i
$700$		0			0
$701$	−39.0004	−	22.5169i	−1.47302	−	0.850451i	−0.473485	−	0.880802i	$-0.657004\pi$
$701$	−39.0004	−	22.5169i	−1.47302	−	0.850451i	−0.999539	+	0.0303510i	$0.990338\pi$
$702$		0			0
$703$	11.6611	+	16.6581i	0.439807	+	0.628271i
$704$		0			0
$705$	24.0161	+	45.4551i	0.904498	+	1.71194i
$706$		0			0
$707$	−2.69691	+	1.55706i	−0.101428	+	0.0585594i
$708$		0			0
$709$	1.35288	+	2.34326i	0.0508085	+	0.0880028i	0.890311	−	0.455353i	$-0.150487\pi$
$709$	1.35288	+	2.34326i	0.0508085	+	0.0880028i	−0.839503	+	0.543356i	$0.817154\pi$
$710$		0			0
$711$	−13.4607	+	6.47798i	−0.504816	+	0.242943i
$712$		0			0
$713$	−0.377237	−	0.653393i	−0.0141276	−	0.0244698i
$714$		0			0
$715$			127.069i			4.75212i
$716$		0			0
$717$	1.21336	−	0.641077i	0.0453139	−	0.0239415i
$718$		0			0
$719$	−26.3955	−	15.2394i	−0.984385	−	0.568335i	−0.0807942	−	0.996731i	$-0.525746\pi$
$719$	−26.3955	−	15.2394i	−0.984385	−	0.568335i	−0.903591	+	0.428396i	$0.859079\pi$
$720$		0			0
$721$			1.31538i			0.0489875i
$722$		0			0
$723$	9.79939	+	6.15916i	0.364443	+	0.229062i
$724$		0			0
$725$	−4.64317	+	8.04220i	−0.172443	+	0.298680i
$726$		0			0
$727$	−21.6844	+	37.5584i	−0.804228	+	1.39296i	0.112583	+	0.993642i	$0.464088\pi$
$727$	−21.6844	+	37.5584i	−0.804228	+	1.39296i	−0.916811	+	0.399322i	$0.869246\pi$
$728$		0			0
$729$	26.3183	+	6.02881i	0.974752	+	0.223289i
$730$		0			0
$731$	43.4165	−	25.0665i	1.60582	−	0.927119i
$732$		0			0
$733$	−50.9747			−1.88279			−0.941396	−	0.337302i	$-0.890486\pi$
$733$	−50.9747			−1.88279			−0.941396	+	0.337302i	$0.890486\pi$
$734$		0			0
$735$	−1.24198	+	33.0763i	−0.0458112	+	1.22004i
$736$		0			0
$737$	9.37516	+	16.2383i	0.345338	+	0.598144i
$738$		0			0
$739$	−14.2112	+	24.6146i	−0.522768	+	0.905461i	0.476881	+	0.878968i	$0.341767\pi$
$739$	−14.2112	+	24.6146i	−0.522768	+	0.905461i	−0.999649	+	0.0264934i	$0.991566\pi$
$740$		0			0
$741$	50.2977	−	2.49755i	1.84773	−	0.0917499i
$742$		0			0
$743$	26.1097	−	45.2234i	0.957873	−	1.65908i	0.230221	−	0.973138i	$-0.426055\pi$
$743$	26.1097	−	45.2234i	0.957873	−	1.65908i	0.727652	−	0.685947i	$-0.240612\pi$
$744$		0			0
$745$	10.9518	+	18.9691i	0.401243	+	0.694974i
$746$		0			0
$747$	−13.1741	−	8.98701i	−0.482014	−	0.328817i
$748$		0			0
$749$	23.0583			0.842530
$750$		0			0
$751$	16.5106	−	9.53241i	0.602481	−	0.347843i	−0.167536	−	0.985866i	$-0.553581\pi$
$751$	16.5106	−	9.53241i	0.602481	−	0.347843i	0.770017	+	0.638023i	$0.220248\pi$
$752$		0			0
$753$	1.03144	+	0.648288i	0.0375879	+	0.0236249i
$754$		0			0
$755$	−0.585615	+	1.01432i	−0.0213127	+	0.0369147i
$756$		0			0
$757$	−8.96773	+	15.5326i	−0.325938	+	0.564541i	−0.981702	−	0.190425i	$-0.939013\pi$
$757$	−8.96773	+	15.5326i	−0.325938	+	0.564541i	0.655764	+	0.754966i	$0.272347\pi$
$758$		0			0
$759$	−11.9363	+	18.9910i	−0.433261	+	0.689331i
$760$		0			0
$761$		−	25.5990i		−	0.927964i	−0.885845	−	0.463982i	$-0.846420\pi$
$761$		−	25.5990i		−	0.927964i	0.885845	−	0.463982i	$-0.153580\pi$
$762$		0			0
$763$	−0.734034	−	0.423795i	−0.0265738	−	0.0153424i
$764$		0			0
$765$	55.4320	+	4.16870i	2.00415	+	0.150720i
$766$		0			0
$767$			34.4890i			1.24532i
$768$		0			0
$769$	11.7113	+	20.2845i	0.422319	+	0.731478i	0.996166	−	0.0874846i	$-0.0278828\pi$
$769$	11.7113	+	20.2845i	0.422319	+	0.731478i	−0.573847	+	0.818963i	$0.694550\pi$
$770$		0			0
$771$	−19.4355	+	30.9223i	−0.699951	+	1.11364i
$772$		0			0
$773$	−12.8380	−	22.2360i	−0.461749	−	0.799774i	0.537299	−	0.843392i	$-0.319445\pi$
$773$	−12.8380	−	22.2360i	−0.461749	−	0.799774i	−0.999048	+	0.0436184i	$0.986111\pi$
$774$		0			0
$775$	2.18717	−	1.26276i	0.0785654	−	0.0453598i
$776$		0			0
$777$	9.47667	−	5.00698i	0.339974	−	0.179624i
$778$		0			0
$779$	1.63947	+	18.7652i	0.0587400	+	0.672335i
$780$		0			0
$781$	19.0794	+	11.0155i	0.682714	+	0.394165i
$782$		0			0
$783$	−2.32317	−	5.33050i	−0.0830234	−	0.190497i
$784$		0			0
$785$	−4.71422	+	2.72176i	−0.168258	+	0.0971437i
$786$		0			0
$787$		−	48.3999i		−	1.72527i	−0.505827	−	0.862635i	$-0.668813\pi$
$787$		−	48.3999i		−	1.72527i	0.505827	−	0.862635i	$-0.331187\pi$
$788$		0			0
$789$	0.190064	−	5.06178i	0.00676647	−	0.180204i
$790$		0			0
$791$	0.238964			0.00849659
$792$		0			0
$793$	−83.3832	−	48.1413i	−2.96102	−	1.70955i
$794$		0			0
$795$	4.36739	−	2.30750i	0.154895	−	0.0818385i
$796$		0			0
$797$	28.2387			1.00027			0.500133	−	0.865949i	$-0.333284\pi$
$797$	28.2387			1.00027			0.500133	+	0.865949i	$0.333284\pi$
$798$		0			0
$799$	−41.3568			−1.46310
$800$		0			0
$801$	−1.35966	−	0.102252i	−0.0480412	−	0.00361289i
$802$		0			0
$803$	−44.1656	−	25.4990i	−1.55857	−	0.899841i
$804$		0			0
$805$	−11.9921			−0.422667
$806$		0			0
$807$	36.2766	+	1.36215i	1.27700	+	0.0479499i
$808$		0			0
$809$			21.6359i			0.760679i	0.924847	+	0.380340i	$0.124193\pi$
$809$			21.6359i			0.760679i	−0.924847	+	0.380340i	$0.875807\pi$
$810$		0			0
$811$	20.8163	−	12.0183i	0.730958	−	0.422019i	−0.0878147	−	0.996137i	$-0.527988\pi$
$811$	20.8163	−	12.0183i	0.730958	−	0.422019i	0.818772	+	0.574118i	$0.194655\pi$
$812$		0			0
$813$	−23.2390	−	0.872598i	−0.815026	−	0.0306033i
$814$		0			0
$815$	50.1030	+	28.9270i	1.75503	+	1.01327i
$816$		0			0
$817$	3.74312	+	42.8436i	0.130955	+	1.49891i
$818$		0			0
$819$	1.99064	−	26.4699i	0.0695585	−	0.924931i
$820$		0			0
$821$	26.0781	−	15.0562i	0.910134	−	0.525466i	0.0296595	−	0.999560i	$-0.490558\pi$
$821$	26.0781	−	15.0562i	0.910134	−	0.525466i	0.880474	+	0.474094i	$0.157224\pi$
$822$		0			0
$823$	25.7676	+	44.6309i	0.898204	+	1.55573i	0.829789	+	0.558077i	$0.188461\pi$
$823$	25.7676	+	44.6309i	0.898204	+	1.55573i	0.0684145	+	0.997657i	$0.478206\pi$
$824$		0			0
$825$	−63.5706	−	39.9557i	−2.21324	−	1.39108i
$826$		0			0
$827$	27.8954	+	48.3162i	0.970017	+	1.68012i	0.695485	+	0.718540i	$0.255189\pi$
$827$	27.8954	+	48.3162i	0.970017	+	1.68012i	0.274531	+	0.961578i	$0.411477\pi$
$828$		0			0
$829$			14.7161i			0.511111i	0.966794	+	0.255556i	$0.0822584\pi$
$829$			14.7161i			0.511111i	−0.966794	+	0.255556i	$0.917742\pi$
$830$		0			0
$831$	4.70499	+	8.90511i	0.163214	+	0.308915i
$832$		0			0
$833$	−23.0599	−	13.3137i	−0.798979	−	0.461291i
$834$		0			0
$835$		−	29.6026i		−	1.02444i
$836$		0			0
$837$	−0.177679	+	1.57138i	−0.00614148	+	0.0543147i
$838$		0			0
$839$	−5.71764	+	9.90324i	−0.197395	+	0.341898i	−0.947683	−	0.319213i	$-0.896581\pi$
$839$	−5.71764	+	9.90324i	−0.197395	+	0.341898i	0.750288	+	0.661111i	$0.229915\pi$
$840$		0			0
$841$	13.8739	−	24.0302i	0.478409	−	0.828629i
$842$		0			0
$843$	25.1640	−	40.0366i	0.866694	−	1.37893i
$844$		0			0
$845$	−99.4588	+	57.4226i	−3.42149	+	1.97540i
$846$		0			0
$847$	−21.6077			−0.742448
$848$		0			0
$849$	−5.03784	−	0.189166i	−0.172898	−	0.00649214i
$850$		0			0
$851$	−5.78234	−	10.0153i	−0.198216	−	0.343320i
$852$		0			0
$853$	7.10018	−	12.2979i	0.243105	−	0.421071i	−0.718492	−	0.695535i	$-0.755167\pi$
$853$	7.10018	−	12.2979i	0.243105	−	0.421071i	0.961597	+	0.274464i	$0.0885006\pi$
$854$		0			0
$855$	−23.3426	+	41.5830i	−0.798301	+	1.42211i
$856$		0			0
$857$	26.7454	−	46.3243i	0.913604	−	1.58241i	0.104671	−	0.994507i	$-0.466621\pi$
$857$	26.7454	−	46.3243i	0.913604	−	1.58241i	0.808933	−	0.587902i	$-0.200046\pi$
$858$		0			0
$859$	−2.59167	−	4.48890i	−0.0884266	−	0.153159i	0.818420	−	0.574621i	$-0.194851\pi$
$859$	−2.59167	−	4.48890i	−0.0884266	−	0.153159i	−0.906846	+	0.421462i	$0.861517\pi$
$860$		0			0
$861$	9.92185	+	0.372555i	0.338136	+	0.0126966i
$862$		0			0
$863$	38.4263			1.30804			0.654022	−	0.756475i	$-0.273080\pi$
$863$	38.4263			1.30804			0.654022	+	0.756475i	$0.273080\pi$
$864$		0			0
$865$	−7.65625	+	4.42034i	−0.260320	+	0.150296i
$866$		0			0
$867$	−8.12788	+	12.9317i	−0.276037	+	0.439183i
$868$		0			0
$869$	−13.0061	+	22.5272i	−0.441202	+	0.764184i
$870$		0			0
$871$	−11.9710	+	20.7343i	−0.405621	+	0.702556i
$872$		0			0
$873$	−29.5177	+	14.2054i	−0.999022	+	0.480780i
$874$		0			0
$875$		−	15.9556i		−	0.539398i
$876$		0			0
$877$	−43.3245	−	25.0134i	−1.46296	−	0.844642i	−0.463816	−	0.885932i	$-0.653520\pi$
$877$	−43.3245	−	25.0134i	−1.46296	−	0.844642i	−0.999147	+	0.0412898i	$0.986853\pi$
$878$		0			0
$879$	−8.46817	−	16.0277i	−0.285624	−	0.540599i
$880$		0			0
$881$		−	22.3822i		−	0.754076i	−0.926198	−	0.377038i	$-0.876943\pi$
$881$		−	22.3822i		−	0.754076i	0.926198	−	0.377038i	$-0.123057\pi$
$882$		0			0
$883$	−2.38436	−	4.12984i	−0.0802402	−	0.138980i	0.823113	−	0.567878i	$-0.192235\pi$
$883$	−2.38436	−	4.12984i	−0.0802402	−	0.138980i	−0.903353	+	0.428898i	$0.858902\pi$
$884$		0			0
$885$	−27.6504	−	17.3790i	−0.929458	−	0.584188i
$886$		0			0
$887$	−1.96367	−	3.40117i	−0.0659335	−	0.114200i	0.831174	−	0.556012i	$-0.187669\pi$
$887$	−1.96367	−	3.40117i	−0.0659335	−	0.114200i	−0.897108	+	0.441812i	$0.854336\pi$
$888$		0			0
$889$	15.4346	−	8.91117i	0.517660	−	0.298871i
$890$		0			0
$891$	43.7742	−	17.1535i	1.46649	−	0.574665i
$892$		0			0
$893$	14.9975	−	32.1522i	0.501874	−	1.07593i
$894$		0			0
$895$	11.9727	+	6.91241i	0.400202	+	0.231056i
$896$		0			0
$897$	−28.6211	−	1.07469i	−0.955632	−	0.0358830i
$898$		0			0
$899$	0.294942	−	0.170285i	0.00983688	−	0.00567932i
$900$		0			0
$901$			3.97362i			0.132380i
$902$		0			0
$903$	22.6529	+	0.850593i	0.753842	+	0.0283060i
$904$		0			0
$905$	67.6588			2.24905
$906$		0			0
$907$	−28.4180	−	16.4072i	−0.943605	−	0.544791i	−0.0525167	−	0.998620i	$-0.516724\pi$
$907$	−28.4180	−	16.4072i	−0.943605	−	0.544791i	−0.891089	+	0.453829i	$0.850058\pi$
$908$		0			0
$909$	0.528158	−	7.02301i	0.0175179	−	0.232938i
$910$		0			0
$911$	51.8536			1.71799			0.858993	−	0.511988i	$-0.171091\pi$
$911$	51.8536			1.71799			0.858993	+	0.511988i	$0.171091\pi$
$912$		0			0
$913$	−27.7694			−0.919032
$914$		0			0
$915$	80.6124	−	42.5914i	2.66497	−	1.40803i
$916$		0			0
$917$	9.07403	+	5.23889i	0.299651	+	0.173004i
$918$		0			0
$919$	39.8042			1.31302			0.656510	−	0.754317i	$-0.272032\pi$
$919$	39.8042			1.31302			0.656510	+	0.754317i	$0.272032\pi$
$920$		0			0
$921$	0.637565	−	16.9796i	0.0210085	−	0.559496i
$922$		0			0
$923$			28.1310i			0.925942i
$924$		0			0
$925$	33.5253	−	19.3558i	1.10230	−	0.636415i
$926$		0			0
$927$	−2.45749	−	1.67644i	−0.0807147	−	0.0550614i
$928$		0			0
$929$	−9.94317	−	5.74069i	−0.326225	−	0.188346i	0.327939	−	0.944699i	$-0.393646\pi$
$929$	−9.94317	−	5.74069i	−0.326225	−	0.188346i	−0.654164	+	0.756353i	$0.726979\pi$
$930$		0			0
$931$	18.7129	−	13.0995i	0.613290	−	0.429320i
$932$		0			0
$933$	14.4403	−	7.62948i	0.472753	−	0.249778i
$934$		0			0
$935$	83.8281	−	48.3982i	2.74147	−	1.58279i
$936$		0			0
$937$	−15.0634	−	26.0906i	−0.492101	−	0.852344i	0.507857	−	0.861441i	$-0.330438\pi$
$937$	−15.0634	−	26.0906i	−0.492101	−	0.852344i	−0.999959	+	0.00909679i	$0.997104\pi$
$938$		0			0
$939$	−20.6355	+	32.8316i	−0.673413	+	1.07142i
$940$		0			0
$941$	−7.64125	−	13.2350i	−0.249098	−	0.431450i	0.714178	−	0.699964i	$-0.246801\pi$
$941$	−7.64125	−	13.2350i	−0.249098	−	0.431450i	−0.963276	+	0.268514i	$0.913467\pi$
$942$		0			0
$943$		−	10.7131i		−	0.348867i
$944$		0			0
$945$	20.2182	+	14.9341i	0.657700	+	0.485805i
$946$		0			0
$947$	16.8743	+	9.74235i	0.548340	+	0.316584i	0.748452	−	0.663189i	$-0.230797\pi$
$947$	16.8743	+	9.74235i	0.548340	+	0.316584i	−0.200112	+	0.979773i	$0.564131\pi$
$948$		0			0
$949$		−	65.1185i		−	2.11383i
$950$		0			0
$951$	−17.0371	+	27.1065i	−0.552465	+	0.878987i
$952$		0			0
$953$	−20.5555	+	35.6031i	−0.665857	+	1.15330i	0.313195	+	0.949689i	$0.398601\pi$
$953$	−20.5555	+	35.6031i	−0.665857	+	1.15330i	−0.979052	+	0.203610i	$0.934733\pi$
$954$		0			0
$955$	−6.55060	+	11.3460i	−0.211972	+	0.367147i
$956$		0			0
$957$	−8.57257	−	5.38808i	−0.277112	−	0.174172i
$958$		0			0
$959$	−17.7795	+	10.2650i	−0.574131	+	0.331475i
$960$		0			0
$961$	30.9074			0.997012
$962$		0			0
$963$	−29.3874	+	43.0791i	−0.946995	+	1.38820i
$964$		0			0
$965$	−13.3433	−	23.1113i	−0.429536	−	0.743978i
$966$		0			0
$967$	5.21929	−	9.04007i	0.167841	−	0.290709i	−0.769820	−	0.638262i	$-0.779654\pi$
$967$	5.21929	−	9.04007i	0.167841	−	0.290709i	0.937661	+	0.347552i	$0.112987\pi$
$968$		0			0
$969$	−20.8051	−	32.2304i	−0.668355	−	1.03539i
$970$		0			0
$971$	−17.3621	+	30.0720i	−0.557176	+	0.965057i	0.440555	+	0.897726i	$0.354782\pi$
$971$	−17.3621	+	30.0720i	−0.557176	+	0.965057i	−0.997731	+	0.0673314i	$0.978552\pi$
$972$		0			0
$973$	−5.81612	−	10.0738i	−0.186456	−	0.322952i
$974$		0			0
$975$	3.59743	−	95.8065i	0.115210	−	3.06826i
$976$		0			0
$977$	29.5411			0.945102			0.472551	−	0.881303i	$-0.343333\pi$
$977$	29.5411			0.945102			0.472551	+	0.881303i	$0.343333\pi$
$978$		0			0
$979$	−2.05617	+	1.18713i	−0.0657155	+	0.0379409i
$980$		0			0
$981$	1.72728	−	0.831254i	0.0551477	−	0.0265399i
$982$		0			0
$983$	6.08349	−	10.5369i	0.194033	−	0.336075i	−0.752550	−	0.658535i	$-0.771176\pi$
$983$	6.08349	−	10.5369i	0.194033	−	0.336075i	0.946583	+	0.322460i	$0.104510\pi$
$984$		0			0
$985$	38.8639	−	67.3142i	1.23831	−	2.14481i
$986$		0			0
$987$	−15.8329	−	9.95134i	−0.503965	−	0.316755i
$988$		0			0
$989$		−	24.4595i		−	0.777765i
$990$		0			0
$991$	−35.0709	−	20.2482i	−1.11406	−	0.643205i	−0.174185	−	0.984713i	$-0.555729\pi$
$991$	−35.0709	−	20.2482i	−1.11406	−	0.643205i	−0.939879	+	0.341508i	$0.889062\pi$
$992$		0			0
$993$	20.4152	−	10.7863i	0.647857	−	0.342293i
$994$		0			0
$995$		−	43.2733i		−	1.37186i
$996$		0			0
$997$	0.0891873	+	0.154477i	0.00282459	+	0.00489233i	0.867434	−	0.497552i	$-0.165768\pi$
$997$	0.0891873	+	0.154477i	0.00282459	+	0.00489233i	−0.864610	+	0.502444i	$0.832434\pi$
$998$		0			0
$999$	−2.72349	+	24.0863i	−0.0861674	+	0.762057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bf.c.65.5	✓	16
3.2	odd	2		456.2.bf.d.65.8	yes	16
4.3	odd	2		912.2.bn.o.65.4		16
12.11	even	2		912.2.bn.n.65.1		16
19.12	odd	6		456.2.bf.d.449.8	yes	16
57.50	even	6	inner	456.2.bf.c.449.5	yes	16
76.31	even	6		912.2.bn.n.449.1		16
228.107	odd	6		912.2.bn.o.449.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bf.c.65.5	✓	16	1.1	even	1	trivial
456.2.bf.c.449.5	yes	16	57.50	even	6	inner
456.2.bf.d.65.8	yes	16	3.2	odd	2
456.2.bf.d.449.8	yes	16	19.12	odd	6
912.2.bn.n.65.1		16	12.11	even	2
912.2.bn.n.449.1		16	76.31	even	6
912.2.bn.o.65.4		16	4.3	odd	2
912.2.bn.o.449.4		16	228.107	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809132 + 1.53144i) q^{3} +(-3.15813 - 1.82335i) q^{5} +1.32651 q^{7} +(-1.69061 + 2.47827i) q^{9} +5.22390i q^{11} +(-5.77665 + 3.33515i) q^{13} +(0.237002 - 6.31182i) q^{15} +(4.40043 + 2.54059i) q^{17} +(-3.57090 + 2.49973i) q^{19} +(1.07332 + 2.03146i) q^{21} +(2.14693 - 1.23953i) q^{23} +(4.14920 + 7.18663i) q^{25} +(-5.16325 - 0.583820i) q^{27} +(0.559525 + 0.969126i) q^{29} -0.304339i q^{31} +(-8.00009 + 4.22682i) q^{33} +(-4.18928 - 2.41868i) q^{35} -4.66495i q^{37} +(-9.78165 - 6.14801i) q^{39} +(2.16072 - 3.74248i) q^{41} +(4.93321 - 8.54458i) q^{43} +(9.85793 - 4.74414i) q^{45} +(-7.04877 + 4.06961i) q^{47} -5.24038 q^{49} +(-0.330230 + 8.79466i) q^{51} +(0.391014 + 0.677256i) q^{53} +(9.52499 - 16.4978i) q^{55} +(-6.71752 - 3.44601i) q^{57} +(2.58526 - 4.47781i) q^{59} +(7.21726 + 12.5007i) q^{61} +(-2.24261 + 3.28744i) q^{63} +24.3246 q^{65} +(3.10845 - 1.79467i) q^{67} +(3.63541 + 2.28495i) q^{69} +(2.10867 - 3.65233i) q^{71} +(-4.88122 + 8.45453i) q^{73} +(-7.64863 + 12.1692i) q^{75} +6.92954i q^{77} +(4.31234 + 2.48973i) q^{79} +(-3.28367 - 8.37959i) q^{81} +5.31583i q^{83} +(-9.26476 - 16.0470i) q^{85} +(-1.03143 + 1.64103i) q^{87} +(0.227250 + 0.393608i) q^{89} +(-7.66276 + 4.42410i) q^{91} +(0.466076 - 0.246250i) q^{93} +(15.8353 - 1.38348i) q^{95} +(9.45642 + 5.45967i) q^{97} +(-12.9462 - 8.83159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} - 3 q^{5} + 13 q^{9} - 3 q^{13} + 15 q^{15} + 3 q^{17} + 11 q^{19} - 6 q^{21} + 3 q^{23} + 11 q^{25} - 4 q^{27} - 5 q^{29} + q^{33} - 24 q^{35} - 9 q^{39} - 6 q^{41} + 13 q^{43} + 33 q^{45}+ \cdots - 35 q^{99}+O(q^{100}) \) 16 * q - q^3 - 3 * q^5 + 13 * q^9 - 3 * q^13 + 15 * q^15 + 3 * q^17 + 11 * q^19 - 6 * q^21 + 3 * q^23 + 11 * q^25 - 4 * q^27 - 5 * q^29 + q^33 - 24 * q^35 - 9 * q^39 - 6 * q^41 + 13 * q^43 + 33 * q^45 - 27 * q^47 + 8 * q^49 + 15 * q^51 + 7 * q^53 - 12 * q^55 + 23 * q^57 + 10 * q^59 - q^61 - 8 * q^63 + 30 * q^65 - 24 * q^67 + 41 * q^69 - 27 * q^71 + 2 * q^73 - 21 * q^75 - 21 * q^79 - 7 * q^81 - 5 * q^85 - 23 * q^87 - 25 * q^89 - 78 * q^91 - 56 * q^93 - 13 * q^95 - 60 * q^97 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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