LMFDB - Embedded newform 820.2.u.b.201.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(141,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.141"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.u (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.3
Character	$\chi$	$=$	820.201
Dual form			820.2.u.b.461.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.435978 q^{3} +(-0.309017 + 0.951057i) q^{5} +(0.796401 + 0.578619i) q^{7} -2.80992 q^{9} +(0.0342651 + 0.105457i) q^{11} +(3.64575 - 2.64879i) q^{13} +(0.134725 - 0.414640i) q^{15} +(1.66518 + 5.12489i) q^{17} +(2.64615 + 1.92254i) q^{19} +(-0.347213 - 0.252265i) q^{21} +(-6.02118 + 4.37464i) q^{23} +(-0.809017 - 0.587785i) q^{25} +2.53300 q^{27} +(-2.75258 + 8.47156i) q^{29} +(0.443306 + 1.36435i) q^{31} +(-0.0149388 - 0.0459769i) q^{33} +(-0.796401 + 0.578619i) q^{35} +(0.347760 - 1.07029i) q^{37} +(-1.58947 + 1.15481i) q^{39} +(3.55812 + 5.32351i) q^{41} +(-7.97924 + 5.79726i) q^{43} +(0.868314 - 2.67240i) q^{45} +(1.79015 - 1.30062i) q^{47} +(-1.86366 - 5.73577i) q^{49} +(-0.725980 - 2.23434i) q^{51} +(0.0174207 - 0.0536153i) q^{53} -0.110884 q^{55} +(-1.15366 - 0.838184i) q^{57} +(7.66208 - 5.56683i) q^{59} +(11.6116 + 8.43629i) q^{61} +(-2.23783 - 1.62588i) q^{63} +(1.39255 + 4.28584i) q^{65} +(-3.36029 + 10.3419i) q^{67} +(2.62510 - 1.90725i) q^{69} +(1.96678 + 6.05313i) q^{71} -0.130566 q^{73} +(0.352714 + 0.256261i) q^{75} +(-0.0337307 + 0.103812i) q^{77} -10.9095 q^{79} +7.32544 q^{81} -2.84830 q^{83} -5.38863 q^{85} +(1.20006 - 3.69341i) q^{87} +(8.89837 + 6.46505i) q^{89} +4.43612 q^{91} +(-0.193272 - 0.594829i) q^{93} +(-2.64615 + 1.92254i) q^{95} +(0.463798 - 1.42742i) q^{97} +(-0.0962822 - 0.296326i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.435978			−0.251712			−0.125856	−	0.992049i	$-0.540168\pi$
$3$	−0.435978			−0.251712			−0.125856	+	0.992049i	$0.540168\pi$
$4$		0			0
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$		0			0
$7$	0.796401	+	0.578619i	0.301011	+	0.218697i	0.728030	−	0.685545i	$-0.240436\pi$
$7$	0.796401	+	0.578619i	0.301011	+	0.218697i	−0.427019	+	0.904243i	$0.640436\pi$
$8$		0			0
$9$	−2.80992			−0.936641
$10$		0			0
$11$	0.0342651	+	0.105457i	0.0103313	+	0.0317965i	0.956089	−	0.293076i	$-0.0946788\pi$
$11$	0.0342651	+	0.105457i	0.0103313	+	0.0317965i	−0.945758	+	0.324872i	$0.894679\pi$
$12$		0			0
$13$	3.64575	−	2.64879i	1.01115	−	0.734643i	0.0466992	−	0.998909i	$-0.485130\pi$
$13$	3.64575	−	2.64879i	1.01115	−	0.734643i	0.964450	+	0.264266i	$0.0851298\pi$
$14$		0			0
$15$	0.134725	−	0.414640i	0.0347857	−	0.107060i
$16$		0			0
$17$	1.66518	+	5.12489i	0.403865	+	1.24297i	0.921839	+	0.387572i	$0.126686\pi$
$17$	1.66518	+	5.12489i	0.403865	+	1.24297i	−0.517975	+	0.855396i	$0.673314\pi$
$18$		0			0
$19$	2.64615	+	1.92254i	0.607068	+	0.441061i	0.848381	−	0.529387i	$-0.177578\pi$
$19$	2.64615	+	1.92254i	0.607068	+	0.441061i	−0.241313	+	0.970447i	$0.577578\pi$
$20$		0			0
$21$	−0.347213	−	0.252265i	−0.0757681	−	0.0550488i
$22$		0			0
$23$	−6.02118	+	4.37464i	−1.25550	+	0.912176i	−0.998528	−	0.0542418i	$-0.982726\pi$
$23$	−6.02118	+	4.37464i	−1.25550	+	0.912176i	−0.256975	+	0.966418i	$0.582726\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$		0			0
$27$	2.53300			0.487476
$28$		0			0
$29$	−2.75258	+	8.47156i	−0.511141	+	1.57313i	0.279055	+	0.960275i	$0.409979\pi$
$29$	−2.75258	+	8.47156i	−0.511141	+	1.57313i	−0.790196	+	0.612854i	$0.790021\pi$
$30$		0			0
$31$	0.443306	+	1.36435i	0.0796201	+	0.245045i	0.982941	−	0.183919i	$-0.0588785\pi$
$31$	0.443306	+	1.36435i	0.0796201	+	0.245045i	−0.903321	+	0.428965i	$0.858878\pi$
$32$		0			0
$33$	−0.0149388	−	0.0459769i	−0.00260051	−	0.00800356i
$34$		0			0
$35$	−0.796401	+	0.578619i	−0.134616	+	0.0978045i
$36$		0			0
$37$	0.347760	−	1.07029i	0.0571714	−	0.175955i	−0.918393	−	0.395670i	$-0.870513\pi$
$37$	0.347760	−	1.07029i	0.0571714	−	0.175955i	0.975564	+	0.219714i	$0.0705125\pi$
$38$		0			0
$39$	−1.58947	+	1.15481i	−0.254518	+	0.184918i
$40$		0			0
$41$	3.55812	+	5.32351i	0.555685	+	0.831393i
$41$	3.55812	+	5.32351i	0.555685	+	0.831393i
$42$		0			0
$43$	−7.97924	+	5.79726i	−1.21682	+	0.884074i	−0.995832	−	0.0912021i	$-0.970929\pi$
$43$	−7.97924	+	5.79726i	−1.21682	+	0.884074i	−0.220991	+	0.975276i	$0.570929\pi$
$44$		0			0
$45$	0.868314	−	2.67240i	0.129441	−	0.398377i
$46$		0			0
$47$	1.79015	−	1.30062i	0.261121	−	0.189715i	−0.449520	−	0.893270i	$-0.648405\pi$
$47$	1.79015	−	1.30062i	0.261121	−	0.189715i	0.710641	+	0.703555i	$0.248405\pi$
$48$		0			0
$49$	−1.86366	−	5.73577i	−0.266238	−	0.819396i
$50$		0			0
$51$	−0.725980	−	2.23434i	−0.101658	−	0.312870i
$52$		0			0
$53$	0.0174207	−	0.0536153i	0.00239291	−	0.00736463i	−0.949853	−	0.312697i	$-0.898768\pi$
$53$	0.0174207	−	0.0536153i	0.00239291	−	0.00736463i	0.952246	+	0.305332i	$0.0987676\pi$
$54$		0			0
$55$	−0.110884			−0.0149516
$56$		0			0
$57$	−1.15366	−	0.838184i	−0.152806	−	0.111020i
$58$		0			0
$59$	7.66208	−	5.56683i	0.997518	−	0.724739i	0.0359634	−	0.999353i	$-0.488550\pi$
$59$	7.66208	−	5.56683i	0.997518	−	0.724739i	0.961555	+	0.274614i	$0.0885500\pi$
$60$		0			0
$61$	11.6116	+	8.43629i	1.48671	+	1.08016i	0.975318	+	0.220807i	$0.0708691\pi$
$61$	11.6116	+	8.43629i	1.48671	+	1.08016i	0.511390	+	0.859349i	$0.329131\pi$
$62$		0			0
$63$	−2.23783	−	1.62588i	−0.281940	−	0.204841i
$64$		0			0
$65$	1.39255	+	4.28584i	0.172725	+	0.531592i
$66$		0			0
$67$	−3.36029	+	10.3419i	−0.410525	+	1.26347i	0.505668	+	0.862728i	$0.331246\pi$
$67$	−3.36029	+	10.3419i	−0.410525	+	1.26347i	−0.916193	+	0.400738i	$0.868754\pi$
$68$		0			0
$69$	2.62510	−	1.90725i	0.316025	−	0.229606i
$70$		0			0
$71$	1.96678	+	6.05313i	0.233414	+	0.718375i	0.997328	+	0.0730564i	$0.0232753\pi$
$71$	1.96678	+	6.05313i	0.233414	+	0.718375i	−0.763914	+	0.645318i	$0.776725\pi$
$72$		0			0
$73$	−0.130566			−0.0152815			−0.00764077	−	0.999971i	$-0.502432\pi$
$73$	−0.130566			−0.0152815			−0.00764077	+	0.999971i	$0.502432\pi$
$74$		0			0
$75$	0.352714	+	0.256261i	0.0407279	+	0.0295905i
$76$		0			0
$77$	−0.0337307	+	0.103812i	−0.00384397	+	0.0118305i
$78$		0			0
$79$	−10.9095			−1.22742			−0.613708	−	0.789533i	$-0.710323\pi$
$79$	−10.9095			−1.22742			−0.613708	+	0.789533i	$0.710323\pi$
$80$		0			0
$81$	7.32544			0.813938
$82$		0			0
$83$	−2.84830			−0.312642			−0.156321	−	0.987706i	$-0.549963\pi$
$83$	−2.84830			−0.312642			−0.156321	+	0.987706i	$0.549963\pi$
$84$		0			0
$85$	−5.38863			−0.584479
$86$		0			0
$87$	1.20006	−	3.69341i	0.128660	−	0.395976i
$88$		0			0
$89$	8.89837	+	6.46505i	0.943226	+	0.685294i	0.949195	−	0.314688i	$-0.101900\pi$
$89$	8.89837	+	6.46505i	0.943226	+	0.685294i	−0.00596914	+	0.999982i	$0.501900\pi$
$90$		0			0
$91$	4.43612			0.465032
$92$		0			0
$93$	−0.193272	−	0.594829i	−0.0200413	−	0.0616809i
$94$		0			0
$95$	−2.64615	+	1.92254i	−0.271489	+	0.197248i
$96$		0			0
$97$	0.463798	−	1.42742i	0.0470916	−	0.144933i	−0.924746	−	0.380585i	$-0.875723\pi$
$97$	0.463798	−	1.42742i	0.0470916	−	0.144933i	0.971837	+	0.235652i	$0.0757226\pi$
$98$		0			0
$99$	−0.0962822	−	0.296326i	−0.00967673	−	0.0297819i
$100$		0			0
$101$	0.0747393	+	0.0543013i	0.00743684	+	0.00540318i	0.591497	−	0.806307i	$-0.298537\pi$
$101$	0.0747393	+	0.0543013i	0.00743684	+	0.00540318i	−0.584061	+	0.811710i	$0.698537\pi$
$102$		0			0
$103$	−9.24854	−	6.71945i	−0.911285	−	0.662087i	0.0300544	−	0.999548i	$-0.490432\pi$
$103$	−9.24854	−	6.71945i	−0.911285	−	0.662087i	−0.941340	+	0.337461i	$0.890432\pi$
$104$		0			0
$105$	0.347213	−	0.252265i	0.0338845	−	0.0246186i
$106$		0			0
$107$	−15.7872	−	11.4701i	−1.52620	−	1.10885i	−0.958302	−	0.285757i	$-0.907755\pi$
$107$	−15.7872	−	11.4701i	−1.52620	−	1.10885i	−0.567903	−	0.823096i	$-0.692245\pi$
$108$		0			0
$109$	11.1064			1.06380			0.531901	−	0.846806i	$-0.321478\pi$
$109$	11.1064			1.06380			0.531901	+	0.846806i	$0.321478\pi$
$110$		0			0
$111$	−0.151616	+	0.466625i	−0.0143907	+	0.0442901i
$112$		0			0
$113$	−3.16903	−	9.75328i	−0.298117	−	0.917511i	−0.982156	−	0.188066i	$-0.939778\pi$
$113$	−3.16903	−	9.75328i	−0.298117	−	0.917511i	0.684039	−	0.729445i	$-0.260222\pi$
$114$		0			0
$115$	−2.29989	−	7.07832i	−0.214466	−	0.660057i
$116$		0			0
$117$	−10.2443	+	7.44290i	−0.947084	+	0.688097i
$118$		0			0
$119$	−1.63921	+	5.04497i	−0.150266	+	0.462471i
$120$		0			0
$121$	8.88924	−	6.45841i	0.808113	−	0.587128i
$122$		0			0
$123$	−1.55126	−	2.32093i	−0.139872	−	0.209272i
$124$		0			0
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$		0			0
$127$	5.58416	−	17.1863i	0.495514	−	1.52504i	−0.320640	−	0.947201i	$-0.603898\pi$
$127$	5.58416	−	17.1863i	0.495514	−	1.52504i	0.816154	−	0.577835i	$-0.196102\pi$
$128$		0			0
$129$	3.47877	−	2.52748i	0.306289	−	0.222532i
$130$		0			0
$131$	−1.23387	−	3.79748i	−0.107804	−	0.331787i	0.882574	−	0.470173i	$-0.155809\pi$
$131$	−1.23387	−	3.79748i	−0.107804	−	0.331787i	−0.990378	+	0.138386i	$0.955809\pi$
$132$		0			0
$133$	0.994976	+	3.06222i	0.0862754	+	0.265528i
$134$		0			0
$135$	−0.782740	+	2.40902i	−0.0673675	+	0.207336i
$136$		0			0
$137$	21.7141			1.85516			0.927581	−	0.373621i	$-0.121884\pi$
$137$	21.7141			1.85516			0.927581	+	0.373621i	$0.121884\pi$
$138$		0			0
$139$	−6.42301	−	4.66659i	−0.544793	−	0.395815i	0.281069	−	0.959687i	$-0.409311\pi$
$139$	−6.42301	−	4.66659i	−0.544793	−	0.395815i	−0.825862	+	0.563872i	$0.809311\pi$
$140$		0			0
$141$	−0.780468	+	0.567043i	−0.0657272	+	0.0477536i
$142$		0			0
$143$	0.404256	+	0.293709i	0.0338055	+	0.0245612i
$144$		0			0
$145$	−7.20634	−	5.23571i	−0.598454	−	0.434802i
$146$		0			0
$147$	0.812517	+	2.50067i	0.0670153	+	0.206252i
$148$		0			0
$149$	1.01947	−	3.13761i	0.0835182	−	0.257043i	−0.900574	−	0.434704i	$-0.856853\pi$
$149$	1.01947	−	3.13761i	0.0835182	−	0.257043i	0.984092	+	0.177661i	$0.0568531\pi$
$150$		0			0
$151$	9.98663	−	7.25571i	0.812700	−	0.590461i	−0.101912	−	0.994793i	$-0.532496\pi$
$151$	9.98663	−	7.25571i	0.812700	−	0.590461i	0.914612	+	0.404332i	$0.132496\pi$
$152$		0			0
$153$	−4.67902	−	14.4005i	−0.378276	−	1.16421i
$154$		0			0
$155$	−1.43457			−0.115227
$156$		0			0
$157$	7.12964	+	5.17999i	0.569007	+	0.413408i	0.834745	−	0.550637i	$-0.185615\pi$
$157$	7.12964	+	5.17999i	0.569007	+	0.413408i	−0.265737	+	0.964046i	$0.585615\pi$
$158$		0			0
$159$	−0.00759503	+	0.0233751i	−0.000602325	+	0.00185377i
$160$		0			0
$161$	−7.32653			−0.577411
$162$		0			0
$163$	−9.74773			−0.763501			−0.381751	−	0.924265i	$-0.624679\pi$
$163$	−9.74773			−0.763501			−0.381751	+	0.924265i	$0.624679\pi$
$164$		0			0
$165$	0.0483430			0.00376350
$166$		0			0
$167$	6.16980			0.477434			0.238717	−	0.971089i	$-0.423273\pi$
$167$	6.16980			0.477434			0.238717	+	0.971089i	$0.423273\pi$
$168$		0			0
$169$	2.25817	−	6.94993i	0.173705	−	0.534610i
$170$		0			0
$171$	−7.43547	−	5.40218i	−0.568605	−	0.413115i
$172$		0			0
$173$	−20.4914			−1.55793			−0.778965	−	0.627067i	$-0.784255\pi$
$173$	−20.4914			−1.55793			−0.778965	+	0.627067i	$0.784255\pi$
$174$		0			0
$175$	−0.304198	−	0.936225i	−0.0229952	−	0.0707720i
$176$		0			0
$177$	−3.34050	+	2.42701i	−0.251087	+	0.182426i
$178$		0			0
$179$	−3.46687	+	10.6699i	−0.259126	+	0.797507i	0.733863	+	0.679297i	$0.237715\pi$
$179$	−3.46687	+	10.6699i	−0.259126	+	0.797507i	−0.992989	+	0.118209i	$0.962285\pi$
$180$		0			0
$181$	−6.77182	−	20.8415i	−0.503346	−	1.54914i	−0.803534	−	0.595258i	$-0.797050\pi$
$181$	−6.77182	−	20.8415i	−0.503346	−	1.54914i	0.300189	−	0.953880i	$-0.402950\pi$
$182$		0			0
$183$	−5.06238	−	3.67804i	−0.374222	−	0.271888i
$184$		0			0
$185$	0.910447	+	0.661479i	0.0669374	+	0.0486329i
$186$		0			0
$187$	−0.483398	+	0.351209i	−0.0353496	+	0.0256830i
$188$		0			0
$189$	2.01728	+	1.46564i	0.146736	+	0.106610i
$190$		0			0
$191$	12.3513			0.893708			0.446854	−	0.894607i	$-0.352544\pi$
$191$	12.3513			0.893708			0.446854	+	0.894607i	$0.352544\pi$
$192$		0			0
$193$	−2.10033	+	6.46415i	−0.151185	+	0.465300i	−0.997754	−	0.0669786i	$-0.978664\pi$
$193$	−2.10033	+	6.46415i	−0.151185	+	0.465300i	0.846569	+	0.532279i	$0.178664\pi$
$194$		0			0
$195$	−0.607122	−	1.86853i	−0.0434769	−	0.133808i
$196$		0			0
$197$	7.75108	+	23.8554i	0.552241	+	1.69962i	0.703119	+	0.711072i	$0.251790\pi$
$197$	7.75108	+	23.8554i	0.552241	+	1.69962i	−0.150878	+	0.988552i	$0.548210\pi$
$198$		0			0
$199$	10.1753	−	7.39278i	0.721307	−	0.524060i	−0.165495	−	0.986211i	$-0.552922\pi$
$199$	10.1753	−	7.39278i	0.721307	−	0.524060i	0.886801	+	0.462151i	$0.152922\pi$
$200$		0			0
$201$	1.46501	−	4.50885i	0.103334	−	0.318030i
$202$		0			0
$203$	−7.09396	+	5.15406i	−0.497898	+	0.361744i
$204$		0			0
$205$	−6.16248	+	1.73891i	−0.430406	+	0.121451i
$206$		0			0
$207$	16.9191	−	12.2924i	1.17596	−	0.854382i
$208$		0			0
$209$	−0.112075	+	0.344931i	−0.00775237	+	0.0238594i
$210$		0			0
$211$	−7.63557	+	5.54757i	−0.525655	+	0.381910i	−0.818730	−	0.574179i	$-0.805321\pi$
$211$	−7.63557	+	5.54757i	−0.525655	+	0.381910i	0.293075	+	0.956089i	$0.405321\pi$
$212$		0			0
$213$	−0.857474	−	2.63903i	−0.0587531	−	0.180824i
$214$		0			0
$215$	−3.04780	−	9.38016i	−0.207858	−	0.639722i
$216$		0			0
$217$	−0.436393	+	1.34308i	−0.0296243	+	0.0911741i
$218$		0			0
$219$	0.0569237			0.00384655
$220$		0			0
$221$	19.6456	+	14.2733i	1.32150	+	0.960129i
$222$		0			0
$223$	10.0080	−	7.27124i	0.670185	−	0.486918i	−0.199902	−	0.979816i	$-0.564062\pi$
$223$	10.0080	−	7.27124i	0.670185	−	0.486918i	0.870087	+	0.492898i	$0.164062\pi$
$224$		0			0
$225$	2.27328	+	1.65163i	0.151552	+	0.110109i
$226$		0			0
$227$	1.87638	+	1.36327i	0.124539	+	0.0904832i	0.648311	−	0.761375i	$-0.275476\pi$
$227$	1.87638	+	1.36327i	0.124539	+	0.0904832i	−0.523772	+	0.851859i	$0.675476\pi$
$228$		0			0
$229$	−5.78994	−	17.8196i	−0.382610	−	1.17755i	−0.938199	−	0.346096i	$-0.887507\pi$
$229$	−5.78994	−	17.8196i	−0.382610	−	1.17755i	0.555589	−	0.831457i	$-0.312493\pi$
$230$		0			0
$231$	0.0147059	−	0.0452600i	0.000967574	−	0.00297789i
$232$		0			0
$233$	−0.0728639	+	0.0529388i	−0.00477348	+	0.00346813i	−0.590169	−	0.807279i	$-0.700939\pi$
$233$	−0.0728639	+	0.0529388i	−0.00477348	+	0.00346813i	0.585396	+	0.810748i	$0.300939\pi$
$234$		0			0
$235$	0.683778	+	2.10445i	0.0446048	+	0.137279i
$236$		0			0
$237$	4.75631			0.308955
$238$		0			0
$239$	−21.7255	−	15.7845i	−1.40530	−	1.02101i	−0.993984	−	0.109521i	$-0.965068\pi$
$239$	−21.7255	−	15.7845i	−1.40530	−	1.02101i	−0.411319	−	0.911492i	$-0.634932\pi$
$240$		0			0
$241$	−5.15590	+	15.8682i	−0.332121	+	1.02216i	0.636003	+	0.771687i	$0.280587\pi$
$241$	−5.15590	+	15.8682i	−0.332121	+	1.02216i	−0.968123	+	0.250475i	$0.919413\pi$
$242$		0			0
$243$	−10.7927			−0.692354
$244$		0			0
$245$	6.03095			0.385303
$246$		0			0
$247$	14.7396			0.937858
$248$		0			0
$249$	1.24180			0.0786957
$250$		0			0
$251$	−2.65400	+	8.16819i	−0.167519	+	0.515571i	−0.999213	−	0.0396632i	$-0.987372\pi$
$251$	−2.65400	+	8.16819i	−0.167519	+	0.515571i	0.831694	+	0.555235i	$0.187372\pi$
$252$		0			0
$253$	−0.667653	−	0.485078i	−0.0419750	−	0.0304966i
$254$		0			0
$255$	2.34932			0.147120
$256$		0			0
$257$	−5.19980	−	16.0033i	−0.324354	−	0.998260i	−0.971731	−	0.236090i	$-0.924134\pi$
$257$	−5.19980	−	16.0033i	−0.324354	−	0.998260i	0.647377	−	0.762170i	$-0.275866\pi$
$258$		0			0
$259$	0.896249	−	0.651163i	0.0556902	−	0.0404613i
$260$		0			0
$261$	7.73453	−	23.8044i	0.478755	−	1.47346i
$262$		0			0
$263$	−7.59003	−	23.3597i	−0.468021	−	1.44042i	−0.855143	−	0.518393i	$-0.826531\pi$
$263$	−7.59003	−	23.3597i	−0.468021	−	1.44042i	0.387121	−	0.922029i	$-0.373469\pi$
$264$		0			0
$265$	0.0456079	+	0.0331361i	0.00280167	+	0.00203553i
$266$		0			0
$267$	−3.87950	−	2.81862i	−0.237421	−	0.172497i
$268$		0			0
$269$	10.1922	−	7.40510i	0.621432	−	0.451497i	−0.231989	−	0.972718i	$-0.574523\pi$
$269$	10.1922	−	7.40510i	0.621432	−	0.451497i	0.853422	+	0.521221i	$0.174523\pi$
$270$		0			0
$271$	26.1340	+	18.9874i	1.58753	+	1.15341i	0.907366	+	0.420342i	$0.138090\pi$
$271$	26.1340	+	18.9874i	1.58753	+	1.15341i	0.680160	+	0.733063i	$0.261910\pi$
$272$		0			0
$273$	−1.93405			−0.117054
$274$		0			0
$275$	0.0342651	−	0.105457i	0.00206626	−	0.00635930i
$276$		0			0
$277$	−7.47352	−	23.0011i	−0.449041	−	1.38200i	−0.877991	−	0.478677i	$-0.841117\pi$
$277$	−7.47352	−	23.0011i	−0.449041	−	1.38200i	0.428951	−	0.903328i	$-0.358883\pi$
$278$		0			0
$279$	−1.24566	−	3.83373i	−0.0745754	−	0.229520i
$280$		0			0
$281$	5.07720	−	3.68880i	0.302880	−	0.220055i	−0.425955	−	0.904744i	$-0.640062\pi$
$281$	5.07720	−	3.68880i	0.302880	−	0.220055i	0.728836	+	0.684689i	$0.240062\pi$
$282$		0			0
$283$	−2.39112	+	7.35912i	−0.142138	+	0.437455i	−0.996632	−	0.0820064i	$-0.973867\pi$
$283$	−2.39112	+	7.35912i	−0.142138	+	0.437455i	0.854494	+	0.519461i	$0.173867\pi$
$284$		0			0
$285$	1.15366	−	0.838184i	0.0683370	−	0.0496498i
$286$		0			0
$287$	−0.246599	+	6.29845i	−0.0145563	+	0.371786i
$288$		0			0
$289$	−9.73837	+	7.07534i	−0.572845	+	0.416196i
$290$		0			0
$291$	−0.202206	+	0.622325i	−0.0118535	+	0.0364814i
$292$		0			0
$293$	−4.50920	+	3.27612i	−0.263430	+	0.191393i	−0.711658	−	0.702526i	$-0.752055\pi$
$293$	−4.50920	+	3.27612i	−0.263430	+	0.191393i	0.448228	+	0.893919i	$0.352055\pi$
$294$		0			0
$295$	2.92665	+	9.00732i	0.170396	+	0.524426i
$296$		0			0
$297$	0.0867934	+	0.267123i	0.00503626	+	0.0155000i
$298$		0			0
$299$	−10.3642	+	31.8977i	−0.599377	+	1.84469i
$300$		0			0
$301$	−9.70908			−0.559622
$302$		0			0
$303$	−0.0325847	−	0.0236742i	−0.00187194	−	0.00136004i
$304$		0			0
$305$	−11.6116	+	8.43629i	−0.664876	+	0.483060i
$306$		0			0
$307$	−15.7405	−	11.4362i	−0.898360	−	0.652697i	0.0396840	−	0.999212i	$-0.487365\pi$
$307$	−15.7405	−	11.4362i	−0.898360	−	0.652697i	−0.938044	+	0.346515i	$0.887365\pi$
$308$		0			0
$309$	4.03216	+	2.92953i	0.229381	+	0.166655i
$310$		0			0
$311$	8.50365	+	26.1715i	0.482198	+	1.48405i	0.835999	+	0.548732i	$0.184889\pi$
$311$	8.50365	+	26.1715i	0.482198	+	1.48405i	−0.353801	+	0.935321i	$0.615111\pi$
$312$		0			0
$313$	−1.40341	+	4.31924i	−0.0793252	+	0.244138i	−0.982853	−	0.184392i	$-0.940968\pi$
$313$	−1.40341	+	4.31924i	−0.0793252	+	0.244138i	0.903528	+	0.428530i	$0.140968\pi$
$314$		0			0
$315$	2.23783	−	1.62588i	0.126087	−	0.0916077i
$316$		0			0
$317$	6.03604	+	18.5770i	0.339018	+	1.04339i	0.964709	+	0.263319i	$0.0848171\pi$
$317$	6.03604	+	18.5770i	0.339018	+	1.04339i	−0.625691	+	0.780071i	$0.715183\pi$
$318$		0			0
$319$	−0.987703			−0.0553007
$320$		0			0
$321$	6.88287	+	5.00069i	0.384164	+	0.279112i
$322$		0			0
$323$	−5.44649	+	16.7626i	−0.303051	+	0.932694i
$324$		0			0
$325$	−4.50639			−0.249970
$326$		0			0
$327$	−4.84216			−0.267772
$328$		0			0
$329$	2.17825			0.120091
$330$		0			0
$331$	−2.12384			−0.116737			−0.0583684	−	0.998295i	$-0.518590\pi$
$331$	−2.12384			−0.116737			−0.0583684	+	0.998295i	$0.518590\pi$
$332$		0			0
$333$	−0.977179	+	3.00745i	−0.0535491	+	0.164807i
$334$		0			0
$335$	−8.79736	−	6.39166i	−0.480651	−	0.349214i
$336$		0			0
$337$	−15.2219			−0.829192			−0.414596	−	0.910005i	$-0.636077\pi$
$337$	−15.2219			−0.829192			−0.414596	+	0.910005i	$0.636077\pi$
$338$		0			0
$339$	1.38163	+	4.25221i	0.0750397	+	0.230949i
$340$		0			0
$341$	−0.128691	+	0.0934994i	−0.00696900	+	0.00506328i
$342$		0			0
$343$	3.96399	−	12.1999i	0.214035	−	0.658733i
$344$		0			0
$345$	1.00270	+	3.08599i	0.0539835	+	0.166144i
$346$		0			0
$347$	18.4412	+	13.3983i	0.989977	+	0.719261i	0.959916	−	0.280287i	$-0.0904297\pi$
$347$	18.4412	+	13.3983i	0.989977	+	0.719261i	0.0300613	+	0.999548i	$0.490430\pi$
$348$		0			0
$349$	28.2196	+	20.5027i	1.51056	+	1.09748i	0.965929	+	0.258807i	$0.0833295\pi$
$349$	28.2196	+	20.5027i	1.51056	+	1.09748i	0.544629	+	0.838677i	$0.316670\pi$
$350$		0			0
$351$	9.23468	−	6.70939i	0.492911	−	0.358121i
$352$		0			0
$353$	15.8670	+	11.5280i	0.844514	+	0.613575i	0.923628	−	0.383290i	$-0.125209\pi$
$353$	15.8670	+	11.5280i	0.844514	+	0.613575i	−0.0791140	+	0.996866i	$0.525209\pi$
$354$		0			0
$355$	−6.36464			−0.337800
$356$		0			0
$357$	0.714659	−	2.19950i	0.0378238	−	0.116410i
$358$		0			0
$359$	1.65486	+	5.09312i	0.0873399	+	0.268805i	0.985182	−	0.171513i	$-0.0548657\pi$
$359$	1.65486	+	5.09312i	0.0873399	+	0.268805i	−0.897842	+	0.440318i	$0.854866\pi$
$360$		0			0
$361$	−2.56538	−	7.89544i	−0.135020	−	0.415549i
$362$		0			0
$363$	−3.87551	+	2.81572i	−0.203412	+	0.147787i
$364$		0			0
$365$	0.0403470	−	0.124175i	0.00211186	−	0.00649963i
$366$		0			0
$367$	−10.0423	+	7.29614i	−0.524202	+	0.380855i	−0.818185	−	0.574956i	$-0.805019\pi$
$367$	−10.0423	+	7.29614i	−0.524202	+	0.380855i	0.293982	+	0.955811i	$0.405019\pi$
$368$		0			0
$369$	−9.99804	−	14.9587i	−0.520477	−	0.778717i
$370$		0			0
$371$	0.0448967	−	0.0326194i	0.00233092	−	0.00169351i
$372$		0			0
$373$	7.95813	−	24.4926i	0.412056	−	1.26818i	−0.502801	−	0.864402i	$-0.667697\pi$
$373$	7.95813	−	24.4926i	0.412056	−	1.26818i	0.914857	−	0.403777i	$-0.132303\pi$
$374$		0			0
$375$	−0.352714	+	0.256261i	−0.0182141	+	0.0132333i
$376$		0			0
$377$	12.4042	+	38.1762i	0.638849	+	1.96617i
$378$		0			0
$379$	9.20897	+	28.3423i	0.473033	+	1.45585i	0.848592	+	0.529047i	$0.177451\pi$
$379$	9.20897	+	28.3423i	0.473033	+	1.45585i	−0.375559	+	0.926798i	$0.622549\pi$
$380$		0			0
$381$	−2.43457	+	7.49284i	−0.124727	+	0.383870i
$382$		0			0
$383$	−3.80812			−0.194586			−0.0972929	−	0.995256i	$-0.531018\pi$
$383$	−3.80812			−0.194586			−0.0972929	+	0.995256i	$0.531018\pi$
$384$		0			0
$385$	−0.0883082	−	0.0641597i	−0.00450060	−	0.00326988i
$386$		0			0
$387$	22.4211	−	16.2899i	1.13973	−	0.828060i
$388$		0			0
$389$	−3.87455	−	2.81502i	−0.196447	−	0.142727i	0.485213	−	0.874396i	$-0.338742\pi$
$389$	−3.87455	−	2.81502i	−0.196447	−	0.142727i	−0.681661	+	0.731668i	$0.738742\pi$
$390$		0			0
$391$	−32.4459	−	23.5733i	−1.64086	−	1.19215i
$392$		0			0
$393$	0.537942	+	1.65562i	0.0271356	+	0.0835148i
$394$		0			0
$395$	3.37122	−	10.3756i	0.169625	−	0.522051i
$396$		0			0
$397$	−8.00201	+	5.81380i	−0.401609	+	0.291786i	−0.770196	−	0.637807i	$-0.779842\pi$
$397$	−8.00201	+	5.81380i	−0.401609	+	0.291786i	0.368587	+	0.929593i	$0.379842\pi$
$398$		0			0
$399$	−0.433788	−	1.33506i	−0.0217166	−	0.0668367i
$400$		0			0
$401$	3.82103			0.190813			0.0954065	−	0.995438i	$-0.469585\pi$
$401$	3.82103			0.190813			0.0954065	+	0.995438i	$0.469585\pi$
$402$		0			0
$403$	5.23007	+	3.79987i	0.260529	+	0.189285i
$404$		0			0
$405$	−2.26368	+	6.96691i	−0.112483	+	0.346188i
$406$		0			0
$407$	0.124786			0.00618542
$408$		0			0
$409$	16.2992			0.805943			0.402972	−	0.915212i	$-0.367977\pi$
$409$	16.2992			0.805943			0.402972	+	0.915212i	$0.367977\pi$
$410$		0			0
$411$	−9.46688			−0.466967
$412$		0			0
$413$	9.32316			0.458763
$414$		0			0
$415$	0.880173	−	2.70890i	0.0432060	−	0.132974i
$416$		0			0
$417$	2.80029	+	2.03453i	0.137131	+	0.0996314i
$418$		0			0
$419$	−29.8156			−1.45659			−0.728294	−	0.685264i	$-0.759687\pi$
$419$	−29.8156			−1.45659			−0.728294	+	0.685264i	$0.759687\pi$
$420$		0			0
$421$	3.03992	+	9.35590i	0.148157	+	0.455979i	0.997403	−	0.0720171i	$-0.0229436\pi$
$421$	3.03992	+	9.35590i	0.148157	+	0.455979i	−0.849247	+	0.527996i	$0.822944\pi$
$422$		0			0
$423$	−5.03020	+	3.65465i	−0.244576	+	0.177695i
$424$		0			0
$425$	1.66518	−	5.12489i	0.0807729	−	0.248594i
$426$		0			0
$427$	4.36605	+	13.4373i	0.211288	+	0.650278i
$428$		0			0
$429$	−0.176247	−	0.128051i	−0.00850926	−	0.00618234i
$430$		0			0
$431$	−17.5600	−	12.7581i	−0.845837	−	0.614536i	0.0781583	−	0.996941i	$-0.475096\pi$
$431$	−17.5600	−	12.7581i	−0.845837	−	0.614536i	−0.923995	+	0.382405i	$0.875096\pi$
$432$		0			0
$433$	5.78016	−	4.19953i	0.277777	−	0.201817i	−0.440170	−	0.897914i	$-0.645082\pi$
$433$	5.78016	−	4.19953i	0.277777	−	0.201817i	0.717947	+	0.696098i	$0.245082\pi$
$434$		0			0
$435$	3.14181	+	2.28266i	0.150638	+	0.109445i
$436$		0			0
$437$	−24.3433			−1.16450
$438$		0			0
$439$	4.48283	−	13.7967i	0.213954	−	0.658483i	−0.785272	−	0.619151i	$-0.787477\pi$
$439$	4.48283	−	13.7967i	0.213954	−	0.658483i	0.999226	−	0.0393320i	$-0.0125230\pi$
$440$		0			0
$441$	5.23675	+	16.1171i	0.249369	+	0.767480i
$442$		0			0
$443$	12.4673	+	38.3704i	0.592340	+	1.82303i	0.567546	+	0.823341i	$0.307893\pi$
$443$	12.4673	+	38.3704i	0.592340	+	1.82303i	0.0247933	+	0.999693i	$0.492107\pi$
$444$		0			0
$445$	−8.89837	+	6.46505i	−0.421823	+	0.306473i
$446$		0			0
$447$	−0.444466	+	1.36793i	−0.0210225	+	0.0647007i
$448$		0			0
$449$	−11.8880	+	8.63711i	−0.561028	+	0.407610i	−0.831835	−	0.555023i	$-0.812709\pi$
$449$	−11.8880	+	8.63711i	−0.561028	+	0.407610i	0.270807	+	0.962634i	$0.412709\pi$
$450$		0			0
$451$	−0.439483	+	0.557639i	−0.0206944	+	0.0262582i
$452$		0			0
$453$	−4.35395	+	3.16333i	−0.204566	+	0.148626i
$454$		0			0
$455$	−1.37084	+	4.21900i	−0.0642658	+	0.197790i
$456$		0			0
$457$	−4.24686	+	3.08552i	−0.198660	+	0.144335i	−0.682668	−	0.730729i	$-0.739180\pi$
$457$	−4.24686	+	3.08552i	−0.198660	+	0.144335i	0.484008	+	0.875063i	$0.339180\pi$
$458$		0			0
$459$	4.21789	+	12.9813i	0.196874	+	0.605917i
$460$		0			0
$461$	1.80273	+	5.54824i	0.0839616	+	0.258407i	0.984220	−	0.176948i	$-0.0566226\pi$
$461$	1.80273	+	5.54824i	0.0839616	+	0.258407i	−0.900259	+	0.435356i	$0.856623\pi$
$462$		0			0
$463$	5.01463	−	15.4334i	0.233050	−	0.717253i	−0.764324	−	0.644832i	$-0.776927\pi$
$463$	5.01463	−	15.4334i	0.233050	−	0.717253i	0.997374	−	0.0724212i	$-0.0230726\pi$
$464$		0			0
$465$	0.625440			0.0290041
$466$		0			0
$467$	2.53495	+	1.84175i	0.117303	+	0.0852259i	0.644890	−	0.764275i	$-0.276903\pi$
$467$	2.53495	+	1.84175i	0.117303	+	0.0852259i	−0.527587	+	0.849501i	$0.676903\pi$
$468$		0			0
$469$	−8.66017	+	6.29198i	−0.399890	+	0.290537i
$470$		0			0
$471$	−3.10837	−	2.25836i	−0.143226	−	0.104060i
$472$		0			0
$473$	−0.884771	−	0.642824i	−0.0406818	−	0.0295571i
$474$		0			0
$475$	−1.01074	−	3.11073i	−0.0463758	−	0.142730i
$476$		0			0
$477$	−0.0489508	+	0.150655i	−0.00224130	+	0.00689802i
$478$		0			0
$479$	27.9414	−	20.3006i	1.27667	−	0.927558i	0.277227	−	0.960805i	$-0.410585\pi$
$479$	27.9414	−	20.3006i	1.27667	−	0.927558i	0.999447	+	0.0332468i	$0.0105848\pi$
$480$		0			0
$481$	−1.56714	−	4.82317i	−0.0714556	−	0.219918i
$482$		0			0
$483$	3.19420			0.145341
$484$		0			0
$485$	1.21424	+	0.882196i	0.0551358	+	0.0400585i
$486$		0			0
$487$	8.00922	−	24.6498i	0.362932	−	1.11699i	−0.588334	−	0.808618i	$-0.700216\pi$
$487$	8.00922	−	24.6498i	0.362932	−	1.11699i	0.951266	−	0.308372i	$-0.0997842\pi$
$488$		0			0
$489$	4.24980			0.192182
$490$		0			0
$491$	41.6531			1.87978			0.939890	−	0.341478i	$-0.110927\pi$
$491$	41.6531			1.87978			0.939890	+	0.341478i	$0.110927\pi$
$492$		0			0
$493$	−47.9993			−2.16178
$494$		0			0
$495$	0.311576			0.0140043
$496$		0			0
$497$	−1.93611	+	5.95874i	−0.0868465	+	0.267286i
$498$		0			0
$499$	29.7231	+	21.5951i	1.33059	+	0.966730i	0.999734	+	0.0230487i	$0.00733728\pi$
$499$	29.7231	+	21.5951i	1.33059	+	0.966730i	0.330856	+	0.943681i	$0.392663\pi$
$500$		0			0
$501$	−2.68990			−0.120176
$502$		0			0
$503$	1.69973	+	5.23122i	0.0757871	+	0.233249i	0.981772	−	0.190061i	$-0.0608684\pi$
$503$	1.69973	+	5.23122i	0.0757871	+	0.233249i	−0.905985	+	0.423309i	$0.860868\pi$
$504$		0			0
$505$	−0.0747393	+	0.0543013i	−0.00332585	+	0.00241637i
$506$		0			0
$507$	−0.984512	+	3.03002i	−0.0437237	+	0.134568i
$508$		0			0
$509$	−2.95347	−	9.08984i	−0.130910	−	0.402900i	0.864021	−	0.503455i	$-0.167938\pi$
$509$	−2.95347	−	9.08984i	−0.130910	−	0.402900i	−0.994931	+	0.100555i	$0.967938\pi$
$510$		0			0
$511$	−0.103983	−	0.0755478i	−0.00459992	−	0.00334204i
$512$		0			0
$513$	6.70269	+	4.86979i	0.295931	+	0.215006i
$514$		0			0
$515$	9.24854	−	6.71945i	0.407539	−	0.296095i
$516$		0			0
$517$	0.198500	+	0.144218i	0.00873000	+	0.00634272i
$518$		0			0
$519$	8.93379			0.392150
$520$		0			0
$521$	3.68717	−	11.3479i	0.161538	−	0.497162i	−0.837227	−	0.546856i	$-0.815824\pi$
$521$	3.68717	−	11.3479i	0.161538	−	0.497162i	0.998765	+	0.0496936i	$0.0158245\pi$
$522$		0			0
$523$	7.61594	+	23.4395i	0.333022	+	1.02494i	0.967688	+	0.252150i	$0.0811375\pi$
$523$	7.61594	+	23.4395i	0.333022	+	1.02494i	−0.634666	+	0.772786i	$0.718862\pi$
$524$		0			0
$525$	0.132624	+	0.408174i	0.00578817	+	0.0178142i
$526$		0			0
$527$	−6.25398	+	4.54378i	−0.272428	+	0.197930i
$528$		0			0
$529$	10.0097	−	30.8067i	0.435205	−	1.33942i
$530$		0			0
$531$	−21.5299	+	15.6424i	−0.934316	+	0.678821i
$532$		0			0
$533$	27.0729	+	9.98348i	1.17266	+	0.432433i
$534$		0			0
$535$	15.7872	−	11.4701i	0.682540	−	0.495894i
$536$		0			0
$537$	1.51148	−	4.65185i	0.0652250	−	0.200742i
$538$		0			0
$539$	0.541019	−	0.393073i	0.0233033	−	0.0169309i
$540$		0			0
$541$	7.47716	+	23.0123i	0.321468	+	0.989378i	0.973010	+	0.230765i	$0.0741228\pi$
$541$	7.47716	+	23.0123i	0.321468	+	0.989378i	−0.651541	+	0.758613i	$0.725877\pi$
$542$		0			0
$543$	2.95236	+	9.08645i	0.126698	+	0.389937i
$544$		0			0
$545$	−3.43207	+	10.5628i	−0.147014	+	0.452462i
$546$		0			0
$547$	−12.5343			−0.535930			−0.267965	−	0.963429i	$-0.586351\pi$
$547$	−12.5343			−0.535930			−0.267965	+	0.963429i	$0.586351\pi$
$548$		0			0
$549$	−32.6276	−	23.7053i	−1.39251	−	1.01172i
$550$		0			0
$551$	−23.5706	+	17.1251i	−1.00414	+	0.729552i
$552$		0			0
$553$	−8.68834	−	6.31245i	−0.369466	−	0.268433i
$554$		0			0
$555$	−0.396935	−	0.288390i	−0.0168489	−	0.0122415i
$556$		0			0
$557$	−8.58681	−	26.4275i	−0.363835	−	1.11977i	−0.950707	−	0.310089i	$-0.899641\pi$
$557$	−8.58681	−	26.4275i	−0.363835	−	1.11977i	0.586872	−	0.809679i	$-0.300359\pi$
$558$		0			0
$559$	−13.7346	+	42.2707i	−0.580911	+	1.78786i
$560$		0			0
$561$	0.210751	−	0.153119i	0.00889791	−	0.00646471i
$562$		0			0
$563$	11.4608	+	35.2727i	0.483014	+	1.48657i	0.834836	+	0.550498i	$0.185562\pi$
$563$	11.4608	+	35.2727i	0.483014	+	1.48657i	−0.351822	+	0.936067i	$0.614438\pi$
$564$		0			0
$565$	10.2552			0.431440
$566$		0			0
$567$	5.83399	+	4.23864i	0.245004	+	0.178006i
$568$		0			0
$569$	−0.983838	+	3.02794i	−0.0412446	+	0.126938i	−0.969559	−	0.244859i	$-0.921258\pi$
$569$	−0.983838	+	3.02794i	−0.0412446	+	0.126938i	0.928314	+	0.371797i	$0.121258\pi$
$570$		0			0
$571$	−14.2902			−0.598025			−0.299012	−	0.954249i	$-0.596657\pi$
$571$	−14.2902			−0.598025			−0.299012	+	0.954249i	$0.596657\pi$
$572$		0			0
$573$	−5.38489			−0.224957
$574$		0			0
$575$	7.44259			0.310377
$576$		0			0
$577$	−1.91141			−0.0795730			−0.0397865	−	0.999208i	$-0.512668\pi$
$577$	−1.91141			−0.0795730			−0.0397865	+	0.999208i	$0.512668\pi$
$578$		0			0
$579$	0.915698	−	2.81823i	0.0380551	−	0.117122i
$580$		0			0
$581$	−2.26839	−	1.64808i	−0.0941087	−	0.0683739i
$582$		0			0
$583$	0.00625103			0.000258891
$584$		0			0
$585$	−3.91297	−	12.0429i	−0.161781	−	0.497911i
$586$		0			0
$587$	10.3182	−	7.49663i	0.425879	−	0.309419i	−0.354120	−	0.935200i	$-0.615220\pi$
$587$	10.3182	−	7.49663i	0.425879	−	0.309419i	0.779999	+	0.625781i	$0.215220\pi$
$588$		0			0
$589$	−1.44997	+	4.46256i	−0.0597451	+	0.183876i
$590$		0			0
$591$	−3.37930	−	10.4004i	−0.139006	−	0.427816i
$592$		0			0
$593$	−16.9542	−	12.3180i	−0.696227	−	0.505839i	0.182474	−	0.983211i	$-0.441589\pi$
$593$	−16.9542	−	12.3180i	−0.696227	−	0.505839i	−0.878701	+	0.477372i	$0.841589\pi$
$594$		0			0
$595$	−4.29151	−	3.11796i	−0.175935	−	0.127824i
$596$		0			0
$597$	−4.43620	+	3.22309i	−0.181562	+	0.131912i
$598$		0			0
$599$	16.6234	+	12.0776i	0.679215	+	0.493479i	0.873097	−	0.487546i	$-0.162108\pi$
$599$	16.6234	+	12.0776i	0.679215	+	0.493479i	−0.193882	+	0.981025i	$0.562108\pi$
$600$		0			0
$601$	−21.8199			−0.890050			−0.445025	−	0.895518i	$-0.646805\pi$
$601$	−21.8199			−0.890050			−0.445025	+	0.895518i	$0.646805\pi$
$602$		0			0
$603$	9.44217	−	29.0600i	0.384515	−	1.18341i
$604$		0			0
$605$	3.39539	+	10.4499i	0.138042	+	0.424850i
$606$		0			0
$607$	8.68802	+	26.7390i	0.352636	+	1.08530i	0.957368	+	0.288872i	$0.0932802\pi$
$607$	8.68802	+	26.7390i	0.352636	+	1.08530i	−0.604732	+	0.796429i	$0.706720\pi$
$608$		0			0
$609$	3.09281	−	2.24706i	0.125327	−	0.0910554i
$610$		0			0
$611$	3.08137	−	9.48349i	0.124659	−	0.383661i
$612$		0			0
$613$	21.9860	−	15.9737i	0.888005	−	0.645173i	−0.0473524	−	0.998878i	$-0.515078\pi$
$613$	21.9860	−	15.9737i	0.888005	−	0.645173i	0.935357	+	0.353705i	$0.115078\pi$
$614$		0			0
$615$	2.68671	−	0.758128i	0.108338	−	0.0305707i
$616$		0			0
$617$	−25.2332	+	18.3330i	−1.01585	+	0.738059i	−0.965428	−	0.260668i	$-0.916057\pi$
$617$	−25.2332	+	18.3330i	−1.01585	+	0.738059i	−0.0504234	+	0.998728i	$0.516057\pi$
$618$		0			0
$619$	4.30978	−	13.2641i	0.173225	−	0.533131i	−0.826323	−	0.563196i	$-0.809571\pi$
$619$	4.30978	−	13.2641i	0.173225	−	0.533131i	0.999548	+	0.0300652i	$0.00957150\pi$
$620$		0			0
$621$	−15.2516	+	11.0810i	−0.612027	+	0.444664i
$622$		0			0
$623$	3.34587	+	10.2975i	0.134050	+	0.412562i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$		0			0
$627$	0.0488621	−	0.150382i	0.00195137	−	0.00600569i
$628$		0			0
$629$	6.06422			0.241796
$630$		0			0
$631$	0.816013	+	0.592868i	0.0324850	+	0.0236017i	0.603909	−	0.797053i	$-0.293609\pi$
$631$	0.816013	+	0.592868i	0.0324850	+	0.0236017i	−0.571424	+	0.820655i	$0.693609\pi$
$632$		0			0
$633$	3.32894	−	2.41862i	0.132314	−	0.0961314i
$634$		0			0
$635$	14.6195	+	10.6217i	0.580158	+	0.421510i
$636$		0			0
$637$	−21.9873	−	15.9747i	−0.871169	−	0.632941i
$638$		0			0
$639$	−5.52651	−	17.0088i	−0.218625	−	0.672859i
$640$		0			0
$641$	10.7099	−	32.9616i	0.423015	−	1.30191i	−0.481868	−	0.876244i	$-0.660041\pi$
$641$	10.7099	−	32.9616i	0.423015	−	1.30191i	0.904883	−	0.425661i	$-0.139959\pi$
$642$		0			0
$643$	39.3215	−	28.5687i	1.55069	−	1.12664i	0.607528	−	0.794298i	$-0.292161\pi$
$643$	39.3215	−	28.5687i	1.55069	−	1.12664i	0.943159	−	0.332342i	$-0.107839\pi$
$644$		0			0
$645$	1.32877	+	4.08954i	0.0523204	+	0.161026i
$646$		0			0
$647$	22.2774			0.875817			0.437908	−	0.899020i	$-0.355719\pi$
$647$	22.2774			0.875817			0.437908	+	0.899020i	$0.355719\pi$
$648$		0			0
$649$	0.849603	+	0.617273i	0.0333498	+	0.0242301i
$650$		0			0
$651$	0.190258	−	0.585553i	0.00745678	−	0.0229496i
$652$		0			0
$653$	6.88646			0.269488			0.134744	−	0.990880i	$-0.456979\pi$
$653$	6.88646			0.269488			0.134744	+	0.990880i	$0.456979\pi$
$654$		0			0
$655$	3.99290			0.156016
$656$		0			0
$657$	0.366879			0.0143133
$658$		0			0
$659$	−47.1488			−1.83666			−0.918329	−	0.395818i	$-0.870461\pi$
$659$	−47.1488			−1.83666			−0.918329	+	0.395818i	$0.870461\pi$
$660$		0			0
$661$	2.09407	−	6.44489i	0.0814500	−	0.250677i	−0.902036	−	0.431660i	$-0.857928\pi$
$661$	2.09407	−	6.44489i	0.0814500	−	0.250677i	0.983486	+	0.180983i	$0.0579279\pi$
$662$		0			0
$663$	−8.56504	−	6.22287i	−0.332639	−	0.241676i
$664$		0			0
$665$	−3.21981			−0.124859
$666$		0			0
$667$	−20.4863	−	63.0503i	−0.793233	−	2.44132i
$668$		0			0
$669$	−4.36327	+	3.17010i	−0.168694	+	0.122563i
$670$		0			0
$671$	−0.491795	+	1.51359i	−0.0189855	+	0.0584315i
$672$		0			0
$673$	8.52908	+	26.2498i	0.328772	+	1.01186i	0.969709	+	0.244263i	$0.0785459\pi$
$673$	8.52908	+	26.2498i	0.328772	+	1.01186i	−0.640937	+	0.767593i	$0.721454\pi$
$674$		0			0
$675$	−2.04924	−	1.48886i	−0.0788752	−	0.0573062i
$676$		0			0
$677$	2.70107	+	1.96244i	0.103811	+	0.0754228i	0.638480	−	0.769639i	$-0.279564\pi$
$677$	2.70107	+	1.96244i	0.103811	+	0.0754228i	−0.534669	+	0.845062i	$0.679564\pi$
$678$		0			0
$679$	1.19530	−	0.868439i	0.0458716	−	0.0333276i
$680$		0			0
$681$	−0.818058	−	0.594354i	−0.0313481	−	0.0227757i
$682$		0			0
$683$	−23.7792			−0.909888			−0.454944	−	0.890520i	$-0.650341\pi$
$683$	−23.7792			−0.909888			−0.454944	+	0.890520i	$0.650341\pi$
$684$		0			0
$685$	−6.71003	+	20.6514i	−0.256377	+	0.789048i
$686$		0			0
$687$	2.52429	+	7.76895i	0.0963075	+	0.296404i
$688$		0			0
$689$	−0.0785044	−	0.241612i	−0.00299078	−	0.00920468i
$690$		0			0
$691$	−3.36656	+	2.44595i	−0.128070	+	0.0930483i	−0.649976	−	0.759955i	$-0.725221\pi$
$691$	−3.36656	+	2.44595i	−0.128070	+	0.0930483i	0.521906	+	0.853003i	$0.325221\pi$
$692$		0			0
$693$	0.0947807	−	0.291705i	0.00360042	−	0.0110810i
$694$		0			0
$695$	6.42301	−	4.66659i	0.243639	−	0.177014i
$696$		0			0
$697$	−21.3575	+	27.0995i	−0.808974	+	1.02647i
$698$		0			0
$699$	0.0317671	−	0.0230801i	0.00120154	−	0.000872971i
$700$		0			0
$701$	0.000132870	0	0.000408931i	5.01842e−6	0	1.54451e-5i	−0.951054	−	0.309025i	$-0.899997\pi$
$701$	0.000132870	0	0.000408931i	5.01842e−6	0	1.54451e-5i	0.951059	+	0.309009i	$0.0999974\pi$
$702$		0			0
$703$	2.97791	−	2.16358i	0.112314	−	0.0816008i
$704$		0			0
$705$	−0.298112	−	0.917495i	−0.0112276	−	0.0345549i
$706$		0			0
$707$	0.0281027	+	0.0864911i	0.00105691	+	0.00325283i
$708$		0			0
$709$	9.44853	−	29.0796i	0.354847	−	1.09211i	−0.601251	−	0.799060i	$-0.705331\pi$
$709$	9.44853	−	29.0796i	0.354847	−	1.09211i	0.956098	−	0.293047i	$-0.0946692\pi$
$710$		0			0
$711$	30.6549			1.14965
$712$		0			0
$713$	−8.63779	−	6.27572i	−0.323488	−	0.235028i
$714$		0			0
$715$	−0.404256	+	0.293709i	−0.0151183	+	0.0109841i
$716$		0			0
$717$	9.47182	+	6.88168i	0.353732	+	0.257001i
$718$		0			0
$719$	−33.4758	−	24.3216i	−1.24844	−	0.907042i	−0.250307	−	0.968167i	$-0.580531\pi$
$719$	−33.4758	−	24.3216i	−1.24844	−	0.907042i	−0.998130	+	0.0611242i	$0.980531\pi$
$720$		0			0
$721$	−3.47754	−	10.7028i	−0.129510	−	0.398592i
$722$		0			0
$723$	2.24786	−	6.91819i	0.0835987	−	0.257290i
$724$		0			0
$725$	7.20634	−	5.23571i	0.267637	−	0.194449i
$726$		0			0
$727$	−5.11486	−	15.7419i	−0.189700	−	0.583835i	0.810298	−	0.586018i	$-0.199305\pi$
$727$	−5.11486	−	15.7419i	−0.189700	−	0.583835i	−0.999998	+	0.00218265i	$0.999305\pi$
$728$		0			0
$729$	−17.2709			−0.639664
$730$		0			0
$731$	−42.9972	−	31.2393i	−1.59031	−	1.15543i
$732$		0			0
$733$	2.53508	−	7.80218i	0.0936354	−	0.288180i	−0.893260	−	0.449540i	$-0.851588\pi$
$733$	2.53508	−	7.80218i	0.0936354	−	0.288180i	0.986896	+	0.161360i	$0.0515879\pi$
$734$		0			0
$735$	−2.62936			−0.0969854
$736$		0			0
$737$	−1.20577			−0.0444151
$738$		0			0
$739$	−3.03056			−0.111481			−0.0557406	−	0.998445i	$-0.517752\pi$
$739$	−3.03056			−0.111481			−0.0557406	+	0.998445i	$0.517752\pi$
$740$		0			0
$741$	−6.42614			−0.236070
$742$		0			0
$743$	11.7609	−	36.1964i	0.431467	−	1.32792i	−0.465197	−	0.885207i	$-0.654017\pi$
$743$	11.7609	−	36.1964i	0.431467	−	1.32792i	0.896664	−	0.442712i	$-0.145983\pi$
$744$		0			0
$745$	2.66901	+	1.93915i	0.0977848	+	0.0710449i
$746$		0			0
$747$	8.00351			0.292833
$748$		0			0
$749$	−5.93613	−	18.2695i	−0.216902	−	0.667554i
$750$		0			0
$751$	40.5164	−	29.4369i	1.47846	−	1.07417i	0.500416	−	0.865785i	$-0.333180\pi$
$751$	40.5164	−	29.4369i	1.47846	−	1.07417i	0.978047	−	0.208382i	$-0.0668197\pi$
$752$		0			0
$753$	1.15709	−	3.56115i	0.0421666	−	0.129775i
$754$		0			0
$755$	3.81455	+	11.7400i	0.138826	+	0.427262i
$756$		0			0
$757$	7.31272	+	5.31300i	0.265785	+	0.193104i	0.712694	−	0.701475i	$-0.247475\pi$
$757$	7.31272	+	5.31300i	0.265785	+	0.193104i	−0.446908	+	0.894580i	$0.647475\pi$
$758$		0			0
$759$	0.291082	+	0.211483i	0.0105656	+	0.00767636i
$760$		0			0
$761$	−19.9175	+	14.4709i	−0.722011	+	0.524571i	−0.887026	−	0.461720i	$-0.847233\pi$
$761$	−19.9175	+	14.4709i	−0.722011	+	0.524571i	0.165015	+	0.986291i	$0.447233\pi$
$762$		0			0
$763$	8.84516	+	6.42639i	0.320216	+	0.232651i
$764$		0			0
$765$	15.1416			0.547447
$766$		0			0
$767$	13.1887	−	40.5905i	0.476215	−	1.46564i
$768$		0			0
$769$	−9.51098	−	29.2718i	−0.342975	−	1.05557i	−0.962659	−	0.270716i	$-0.912739\pi$
$769$	−9.51098	−	29.2718i	−0.342975	−	1.05557i	0.619685	−	0.784851i	$-0.287261\pi$
$770$		0			0
$771$	2.26700	+	6.97710i	0.0816439	+	0.251274i
$772$		0			0
$773$	23.9265	−	17.3836i	0.860575	−	0.625244i	−0.0674664	−	0.997722i	$-0.521492\pi$
$773$	23.9265	−	17.3836i	0.860575	−	0.625244i	0.928041	+	0.372477i	$0.121492\pi$
$774$		0			0
$775$	0.443306	−	1.36435i	0.0159240	−	0.0490091i
$776$		0			0
$777$	−0.390745	+	0.283893i	−0.0140179	+	0.0101846i
$778$		0			0
$779$	−0.819357	+	20.9274i	−0.0293565	+	0.749802i
$780$		0			0
$781$	−0.570954	+	0.414822i	−0.0204303	+	0.0148435i
$782$		0			0
$783$	−6.97227	+	21.4584i	−0.249169	+	0.766862i
$784$		0			0
$785$	−7.12964	+	5.17999i	−0.254468	+	0.184882i
$786$		0			0
$787$	−4.70317	−	14.4749i	−0.167650	−	0.515973i	0.831572	−	0.555417i	$-0.187441\pi$
$787$	−4.70317	−	14.4749i	−0.167650	−	0.515973i	−0.999222	+	0.0394438i	$0.987441\pi$
$788$		0			0
$789$	3.30909	+	10.1843i	0.117807	+	0.362571i
$790$		0			0
$791$	3.11961	−	9.60118i	0.110921	−	0.341379i
$792$		0			0
$793$	64.6788			2.29681
$794$		0			0
$795$	−0.0198841	−	0.0144466i	−0.000705215	−	0.000512368i
$796$		0			0
$797$	15.4847	−	11.2503i	0.548496	−	0.398506i	−0.278734	−	0.960368i	$-0.589915\pi$
$797$	15.4847	−	11.2503i	0.548496	−	0.398506i	0.827231	+	0.561862i	$0.189915\pi$
$798$		0			0
$799$	9.64647	+	7.00857i	0.341268	+	0.247945i
$800$		0			0
$801$	−25.0038	−	18.1663i	−0.883464	−	0.641874i
$802$		0			0
$803$	−0.00447384	−	0.0137691i	−0.000157878	−	0.000485900i
$804$		0			0
$805$	2.26402	−	6.96794i	0.0797963	−	0.245588i
$806$		0			0
$807$	−4.44360	+	3.22846i	−0.156422	+	0.113647i
$808$		0			0
$809$	8.57892	+	26.4032i	0.301619	+	0.928288i	0.980917	+	0.194425i	$0.0622842\pi$
$809$	8.57892	+	26.4032i	0.301619	+	0.928288i	−0.679298	+	0.733862i	$0.737716\pi$
$810$		0			0
$811$	15.9671			0.560681			0.280340	−	0.959901i	$-0.409553\pi$
$811$	15.9671			0.560681			0.280340	+	0.959901i	$0.409553\pi$
$812$		0			0
$813$	−11.3938	−	8.27811i	−0.399599	−	0.290326i
$814$		0			0
$815$	3.01221	−	9.27064i	0.105513	−	0.324736i
$816$		0			0
$817$	−32.2597			−1.12862
$818$		0			0
$819$	−12.4652			−0.435568
$820$		0			0
$821$	−39.5005			−1.37858			−0.689289	−	0.724486i	$-0.742077\pi$
$821$	−39.5005			−1.37858			−0.689289	+	0.724486i	$0.742077\pi$
$822$		0			0
$823$	26.4527			0.922084			0.461042	−	0.887378i	$-0.347476\pi$
$823$	26.4527			0.922084			0.461042	+	0.887378i	$0.347476\pi$
$824$		0			0
$825$	−0.0149388	+	0.0459769i	−0.000520103	+	0.00160071i
$826$		0			0
$827$	−7.44247	−	5.40727i	−0.258800	−	0.188029i	0.450818	−	0.892616i	$-0.351132\pi$
$827$	−7.44247	−	5.40727i	−0.258800	−	0.188029i	−0.709618	+	0.704587i	$0.751132\pi$
$828$		0			0
$829$	−5.12587			−0.178029			−0.0890144	−	0.996030i	$-0.528372\pi$
$829$	−5.12587			−0.178029			−0.0890144	+	0.996030i	$0.528372\pi$
$830$		0			0
$831$	3.25829	+	10.0280i	0.113029	+	0.347867i
$832$		0			0
$833$	26.2918	−	19.1021i	0.910958	−	0.661850i
$834$		0			0
$835$	−1.90657	+	5.86783i	−0.0659797	+	0.203065i
$836$		0			0
$837$	1.12289	+	3.45591i	0.0388129	+	0.119454i
$838$		0			0
$839$	4.60558	+	3.34615i	0.159002	+	0.115522i	0.664441	−	0.747340i	$-0.268670\pi$
$839$	4.60558	+	3.34615i	0.159002	+	0.115522i	−0.505439	+	0.862862i	$0.668670\pi$
$840$		0			0
$841$	−40.7292	−	29.5915i	−1.40445	−	1.02040i
$842$		0			0
$843$	−2.21355	+	1.60824i	−0.0762386	+	0.0553906i
$844$		0			0
$845$	5.91196	+	4.29529i	0.203378	+	0.147763i
$846$		0			0
$847$	10.8164			0.371654
$848$		0			0
$849$	1.04248	−	3.20842i	0.0357777	−	0.110113i
$850$		0			0
$851$	2.58823	+	7.96576i	0.0887235	+	0.273063i
$852$		0			0
$853$	9.42030	+	28.9927i	0.322545	+	0.992691i	0.972537	+	0.232750i	$0.0747723\pi$
$853$	9.42030	+	28.9927i	0.322545	+	0.992691i	−0.649992	+	0.759941i	$0.725228\pi$
$854$		0			0
$855$	7.43547	−	5.40218i	0.254288	−	0.184751i
$856$		0			0
$857$	−4.74436	+	14.6016i	−0.162064	+	0.498782i	−0.998808	−	0.0488124i	$-0.984456\pi$
$857$	−4.74436	+	14.6016i	−0.162064	+	0.498782i	0.836744	+	0.547595i	$0.184456\pi$
$858$		0			0
$859$	2.52808	−	1.83676i	0.0862570	−	0.0626694i	−0.543821	−	0.839201i	$-0.683023\pi$
$859$	2.52808	−	1.83676i	0.0862570	−	0.0626694i	0.630078	+	0.776532i	$0.283023\pi$
$860$		0			0
$861$	0.107512	−	2.74598i	0.00366399	−	0.0935829i
$862$		0			0
$863$	−22.0631	+	16.0298i	−0.751038	+	0.545661i	−0.896148	−	0.443755i	$-0.853646\pi$
$863$	−22.0631	+	16.0298i	−0.751038	+	0.545661i	0.145111	+	0.989415i	$0.453646\pi$
$864$		0			0
$865$	6.33218	−	19.4884i	0.215301	−	0.662627i
$866$		0			0
$867$	4.24571	−	3.08469i	0.144192	−	0.104762i
$868$		0			0
$869$	−0.373815	−	1.15048i	−0.0126808	−	0.0390275i
$870$		0			0
$871$	15.1428	+	46.6048i	0.513094	+	1.57914i
$872$		0			0
$873$	−1.30324	+	4.01095i	−0.0441079	+	0.135750i
$874$		0			0
$875$	0.984406			0.0332790
$876$		0			0
$877$	−41.0301	−	29.8101i	−1.38549	−	1.00661i	−0.996344	−	0.0854374i	$-0.972771\pi$
$877$	−41.0301	−	29.8101i	−1.38549	−	1.00661i	−0.389143	−	0.921177i	$-0.627229\pi$
$878$		0			0
$879$	1.96591	−	1.42832i	0.0663085	−	0.0481760i
$880$		0			0
$881$	−19.8506	−	14.4223i	−0.668782	−	0.485899i	0.200835	−	0.979625i	$-0.435635\pi$
$881$	−19.8506	−	14.4223i	−0.668782	−	0.485899i	−0.869617	+	0.493726i	$0.835635\pi$
$882$		0			0
$883$	8.87140	+	6.44545i	0.298547	+	0.216907i	0.726966	−	0.686673i	$-0.240930\pi$
$883$	8.87140	+	6.44545i	0.298547	+	0.216907i	−0.428420	+	0.903580i	$0.640930\pi$
$884$		0			0
$885$	−1.27596	−	3.92699i	−0.0428908	−	0.132004i
$886$		0			0
$887$	5.50387	−	16.9392i	0.184802	−	0.568762i	−0.815143	−	0.579260i	$-0.803342\pi$
$887$	5.50387	−	16.9392i	0.184802	−	0.568762i	0.999945	+	0.0104979i	$0.00334164\pi$
$888$		0			0
$889$	14.3915	−	10.4561i	0.482677	−	0.350685i
$890$		0			0
$891$	0.251007	+	0.772519i	0.00840904	+	0.0258804i
$892$		0			0
$893$	7.23751			0.242194
$894$		0			0
$895$	−9.07637	−	6.59437i	−0.303390	−	0.220425i
$896$		0			0
$897$	4.51856	−	13.9067i	0.150870	−	0.464331i
$898$		0			0
$899$	−12.7784			−0.426185
$900$		0			0
$901$	0.303781			0.0101204
$902$		0			0
$903$	4.23295			0.140864
$904$		0			0
$905$	21.9141			0.728448
$906$		0			0
$907$	−6.70151	+	20.6251i	−0.222520	+	0.684846i	0.776014	+	0.630716i	$0.217239\pi$
$907$	−6.70151	+	20.6251i	−0.222520	+	0.684846i	−0.998534	+	0.0541302i	$0.982761\pi$
$908$		0			0
$909$	−0.210012	−	0.152582i	−0.00696565	−	0.00506084i
$910$		0			0
$911$	−12.6754			−0.419956			−0.209978	−	0.977706i	$-0.567339\pi$
$911$	−12.6754			−0.419956			−0.209978	+	0.977706i	$0.567339\pi$
$912$		0			0
$913$	−0.0975972	−	0.300373i	−0.00323000	−	0.00994091i
$914$		0			0
$915$	5.06238	−	3.67804i	0.167357	−	0.121592i
$916$		0			0
$917$	1.21463	−	3.73826i	0.0401107	−	0.123448i
$918$		0			0
$919$	5.06143	+	15.5775i	0.166961	+	0.513853i	0.999175	−	0.0406006i	$-0.0129271\pi$
$919$	5.06143	+	15.5775i	0.166961	+	0.513853i	−0.832214	+	0.554454i	$0.812927\pi$
$920$		0			0
$921$	6.86253	+	4.98592i	0.226128	+	0.164292i
$922$		0			0
$923$	23.2039	+	16.8586i	0.763765	+	0.554908i
$924$		0			0
$925$	−0.910447	+	0.661479i	−0.0299353	+	0.0217493i
$926$		0			0
$927$	25.9877	+	18.8811i	0.853547	+	0.620138i
$928$		0			0
$929$	−12.4140			−0.407289			−0.203645	−	0.979045i	$-0.565279\pi$
$929$	−12.4140			−0.407289			−0.203645	+	0.979045i	$0.565279\pi$
$930$		0			0
$931$	6.09571	−	18.7607i	0.199779	−	0.614856i
$932$		0			0
$933$	−3.70740	−	11.4102i	−0.121375	−	0.373554i
$934$		0			0
$935$	−0.184642	−	0.568268i	−0.00603843	−	0.0185844i
$936$		0			0
$937$	−23.1344	+	16.8081i	−0.755769	+	0.549098i	−0.897610	−	0.440791i	$-0.854698\pi$
$937$	−23.1344	+	16.8081i	−0.755769	+	0.549098i	0.141841	+	0.989889i	$0.454698\pi$
$938$		0			0
$939$	0.611854	−	1.88309i	0.0199671	−	0.0614524i
$940$		0			0
$941$	0.716841	−	0.520815i	0.0233683	−	0.0169781i	−0.576040	−	0.817422i	$-0.695403\pi$
$941$	0.716841	−	0.520815i	0.0233683	−	0.0169781i	0.599408	+	0.800444i	$0.295403\pi$
$942$		0			0
$943$	−44.7125	−	16.4883i	−1.45604	−	0.536934i
$944$		0			0
$945$	−2.01728	+	1.46564i	−0.0656222	+	0.0476773i
$946$		0			0
$947$	11.4993	−	35.3913i	0.373678	−	1.15006i	−0.570688	−	0.821167i	$-0.693323\pi$
$947$	11.4993	−	35.3913i	0.373678	−	1.15006i	0.944366	−	0.328896i	$-0.106677\pi$
$948$		0			0
$949$	−0.476009	+	0.345841i	−0.0154519	+	0.0112265i
$950$		0			0
$951$	−2.63158	−	8.09918i	−0.0853349	−	0.262634i
$952$		0			0
$953$	−3.18358	−	9.79805i	−0.103126	−	0.317390i	0.886160	−	0.463380i	$-0.153363\pi$
$953$	−3.18358	−	9.79805i	−0.103126	−	0.317390i	−0.989286	+	0.145990i	$0.953363\pi$
$954$		0			0
$955$	−3.81676	+	11.7468i	−0.123507	+	0.380117i
$956$		0			0
$957$	0.430617			0.0139199
$958$		0			0
$959$	17.2931	+	12.5642i	0.558425	+	0.405719i
$960$		0			0
$961$	23.4146	−	17.0117i	0.755309	−	0.548764i
$962$		0			0
$963$	44.3608	+	32.2300i	1.42951	+	1.03860i
$964$		0			0
$965$	−5.49874	−	3.99507i	−0.177011	−	0.128606i
$966$		0			0
$967$	−10.2328	−	31.4933i	−0.329065	−	1.01276i	−0.969572	−	0.244805i	$-0.921276\pi$
$967$	−10.2328	−	31.4933i	−0.329065	−	1.01276i	0.640508	−	0.767952i	$-0.278724\pi$
$968$		0			0
$969$	2.37455	−	7.30811i	0.0762815	−	0.234770i
$970$		0			0
$971$	−28.5684	+	20.7561i	−0.916802	+	0.666096i	−0.942726	−	0.333568i	$-0.891747\pi$
$971$	−28.5684	+	20.7561i	−0.916802	+	0.666096i	0.0259239	+	0.999664i	$0.491747\pi$
$972$		0			0
$973$	−2.41511	−	7.43295i	−0.0774250	−	0.238290i
$974$		0			0
$975$	1.96469			0.0629204
$976$		0			0
$977$	−22.9814	−	16.6970i	−0.735241	−	0.534184i	0.155976	−	0.987761i	$-0.450148\pi$
$977$	−22.9814	−	16.6970i	−0.735241	−	0.534184i	−0.891217	+	0.453577i	$0.850148\pi$
$978$		0			0
$979$	−0.376881	+	1.15992i	−0.0120452	+	0.0370713i
$980$		0			0
$981$	−31.2082			−0.996401
$982$		0			0
$983$	−2.11892			−0.0675829			−0.0337915	−	0.999429i	$-0.510758\pi$
$983$	−2.11892			−0.0675829			−0.0337915	+	0.999429i	$0.510758\pi$
$984$		0			0
$985$	−25.0830			−0.799211
$986$		0			0
$987$	−0.949667			−0.0302282
$988$		0			0
$989$	22.6835	−	69.8127i	0.721294	−	2.21991i
$990$		0			0
$991$	−35.5643	−	25.8390i	−1.12974	−	0.820803i	−0.144081	−	0.989566i	$-0.546023\pi$
$991$	−35.5643	−	25.8390i	−1.12974	−	0.820803i	−0.985657	+	0.168763i	$0.946023\pi$
$992$		0			0
$993$	0.925947			0.0293840
$994$		0			0
$995$	3.88661	+	11.9618i	0.123214	+	0.379214i
$996$		0			0
$997$	−24.3916	+	17.7215i	−0.772489	+	0.561246i	−0.902716	−	0.430238i	$-0.858430\pi$
$997$	−24.3916	+	17.7215i	−0.772489	+	0.561246i	0.130226	+	0.991484i	$0.458430\pi$
$998$		0			0
$999$	0.880875	−	2.71106i	0.0278697	−	0.0857740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.u.b.201.3	✓	32
41.10	even	5	inner	820.2.u.b.461.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.u.b.201.3	✓	32	1.1	even	1	trivial
820.2.u.b.461.3	yes	32	41.10	even	5	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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.u (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-0.435978 q^{3} +(-0.309017 + 0.951057i) q^{5} +(0.796401 + 0.578619i) q^{7} -2.80992 q^{9} +(0.0342651 + 0.105457i) q^{11} +(3.64575 - 2.64879i) q^{13} +(0.134725 - 0.414640i) q^{15} +(1.66518 + 5.12489i) q^{17} +(2.64615 + 1.92254i) q^{19} +(-0.347213 - 0.252265i) q^{21} +(-6.02118 + 4.37464i) q^{23} +(-0.809017 - 0.587785i) q^{25} +2.53300 q^{27} +(-2.75258 + 8.47156i) q^{29} +(0.443306 + 1.36435i) q^{31} +(-0.0149388 - 0.0459769i) q^{33} +(-0.796401 + 0.578619i) q^{35} +(0.347760 - 1.07029i) q^{37} +(-1.58947 + 1.15481i) q^{39} +(3.55812 + 5.32351i) q^{41} +(-7.97924 + 5.79726i) q^{43} +(0.868314 - 2.67240i) q^{45} +(1.79015 - 1.30062i) q^{47} +(-1.86366 - 5.73577i) q^{49} +(-0.725980 - 2.23434i) q^{51} +(0.0174207 - 0.0536153i) q^{53} -0.110884 q^{55} +(-1.15366 - 0.838184i) q^{57} +(7.66208 - 5.56683i) q^{59} +(11.6116 + 8.43629i) q^{61} +(-2.23783 - 1.62588i) q^{63} +(1.39255 + 4.28584i) q^{65} +(-3.36029 + 10.3419i) q^{67} +(2.62510 - 1.90725i) q^{69} +(1.96678 + 6.05313i) q^{71} -0.130566 q^{73} +(0.352714 + 0.256261i) q^{75} +(-0.0337307 + 0.103812i) q^{77} -10.9095 q^{79} +7.32544 q^{81} -2.84830 q^{83} -5.38863 q^{85} +(1.20006 - 3.69341i) q^{87} +(8.89837 + 6.46505i) q^{89} +4.43612 q^{91} +(-0.193272 - 0.594829i) q^{93} +(-2.64615 + 1.92254i) q^{95} +(0.463798 - 1.42742i) q^{97} +(-0.0962822 - 0.296326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more