LMFDB - Embedded newform 820.2.u.b.201.1

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			201.1
Character	$\chi$	$=$	820.201
Dual form			820.2.u.b.461.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.30240 q^{3} +(-0.309017 + 0.951057i) q^{5} +(-1.74674 - 1.26908i) q^{7} +7.90585 q^{9} +(-0.472492 - 1.45418i) q^{11} +(1.40906 - 1.02374i) q^{13} +(1.02050 - 3.14077i) q^{15} +(-1.12456 - 3.46103i) q^{17} +(-1.89070 - 1.37367i) q^{19} +(5.76845 + 4.19102i) q^{21} +(0.714482 - 0.519102i) q^{23} +(-0.809017 - 0.587785i) q^{25} -16.2011 q^{27} +(-2.14284 + 6.59498i) q^{29} +(3.00788 + 9.25730i) q^{31} +(1.56036 + 4.80229i) q^{33} +(1.74674 - 1.26908i) q^{35} +(-0.114668 + 0.352911i) q^{37} +(-4.65327 + 3.38080i) q^{39} +(4.79946 + 4.23853i) q^{41} +(0.227859 - 0.165549i) q^{43} +(-2.44304 + 7.51891i) q^{45} +(-2.21228 + 1.60732i) q^{47} +(-0.722579 - 2.22387i) q^{49} +(3.71374 + 11.4297i) q^{51} +(-3.53558 + 10.8814i) q^{53} +1.52902 q^{55} +(6.24384 + 4.53642i) q^{57} +(-4.12440 + 2.99656i) q^{59} +(1.69291 + 1.22997i) q^{61} +(-13.8095 - 10.0332i) q^{63} +(0.538212 + 1.65645i) q^{65} +(-2.29947 + 7.07704i) q^{67} +(-2.35951 + 1.71428i) q^{69} +(-0.299474 - 0.921685i) q^{71} -5.21188 q^{73} +(2.67170 + 1.94110i) q^{75} +(-1.02015 + 3.13971i) q^{77} +12.9080 q^{79} +29.7849 q^{81} -14.4095 q^{83} +3.63915 q^{85} +(7.07651 - 21.7793i) q^{87} +(-13.5939 - 9.87655i) q^{89} -3.76047 q^{91} +(-9.93322 - 30.5713i) q^{93} +(1.89070 - 1.37367i) q^{95} +(-3.95010 + 12.1572i) q^{97} +(-3.73545 - 11.4965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.30240			−1.90664			−0.953321	−	0.301959i	$-0.902359\pi$
$3$	−3.30240			−1.90664			−0.953321	+	0.301959i	$0.902359\pi$
$4$		0			0
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$		0			0
$7$	−1.74674	−	1.26908i	−0.660207	−	0.479668i	0.206526	−	0.978441i	$-0.433784\pi$
$7$	−1.74674	−	1.26908i	−0.660207	−	0.479668i	−0.866733	+	0.498773i	$0.833784\pi$
$8$		0			0
$9$	7.90585			2.63528
$10$		0			0
$11$	−0.472492	−	1.45418i	−0.142462	−	0.438452i	0.854214	−	0.519921i	$-0.174039\pi$
$11$	−0.472492	−	1.45418i	−0.142462	−	0.438452i	−0.996676	+	0.0814692i	$0.974039\pi$
$12$		0			0
$13$	1.40906	−	1.02374i	0.390802	−	0.283934i	−0.374982	−	0.927032i	$-0.622351\pi$
$13$	1.40906	−	1.02374i	0.390802	−	0.283934i	0.765784	+	0.643098i	$0.222351\pi$
$14$		0			0
$15$	1.02050	−	3.14077i	0.263491	−	0.810943i
$16$		0			0
$17$	−1.12456	−	3.46103i	−0.272745	−	0.839424i	−0.989807	−	0.142414i	$-0.954513\pi$
$17$	−1.12456	−	3.46103i	−0.272745	−	0.839424i	0.717062	−	0.697010i	$-0.245487\pi$
$18$		0			0
$19$	−1.89070	−	1.37367i	−0.433756	−	0.315142i	0.349393	−	0.936976i	$-0.386388\pi$
$19$	−1.89070	−	1.37367i	−0.433756	−	0.315142i	−0.783149	+	0.621834i	$0.786388\pi$
$20$		0			0
$21$	5.76845	+	4.19102i	1.25878	+	0.914556i
$22$		0			0
$23$	0.714482	−	0.519102i	0.148980	−	0.108240i	−0.510798	−	0.859700i	$-0.670650\pi$
$23$	0.714482	−	0.519102i	0.148980	−	0.108240i	0.659778	+	0.751460i	$0.270650\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$		0			0
$27$	−16.2011			−3.11790
$28$		0			0
$29$	−2.14284	+	6.59498i	−0.397915	+	1.22466i	0.528753	+	0.848776i	$0.322660\pi$
$29$	−2.14284	+	6.59498i	−0.397915	+	1.22466i	−0.926668	+	0.375881i	$0.877340\pi$
$30$		0			0
$31$	3.00788	+	9.25730i	0.540231	+	1.66266i	0.732066	+	0.681233i	$0.238556\pi$
$31$	3.00788	+	9.25730i	0.540231	+	1.66266i	−0.191835	+	0.981427i	$0.561444\pi$
$32$		0			0
$33$	1.56036	+	4.80229i	0.271623	+	0.835971i
$34$		0			0
$35$	1.74674	−	1.26908i	0.295254	−	0.214514i
$36$		0			0
$37$	−0.114668	+	0.352911i	−0.0188513	+	0.0580182i	−0.960040	−	0.279864i	$-0.909711\pi$
$37$	−0.114668	+	0.352911i	−0.0188513	+	0.0580182i	0.941188	+	0.337882i	$0.109711\pi$
$38$		0			0
$39$	−4.65327	+	3.38080i	−0.745120	+	0.541361i
$40$		0			0
$41$	4.79946	+	4.23853i	0.749550	+	0.661947i
$41$	4.79946	+	4.23853i	0.749550	+	0.661947i
$42$		0			0
$43$	0.227859	−	0.165549i	0.0347481	−	0.0252460i	−0.570276	−	0.821453i	$-0.693164\pi$
$43$	0.227859	−	0.165549i	0.0347481	−	0.0252460i	0.605024	+	0.796207i	$0.293164\pi$
$44$		0			0
$45$	−2.44304	+	7.51891i	−0.364187	+	1.12085i
$46$		0			0
$47$	−2.21228	+	1.60732i	−0.322694	+	0.234451i	−0.737324	−	0.675539i	$-0.763911\pi$
$47$	−2.21228	+	1.60732i	−0.322694	+	0.234451i	0.414630	+	0.909990i	$0.363911\pi$
$48$		0			0
$49$	−0.722579	−	2.22387i	−0.103226	−	0.317696i
$50$		0			0
$51$	3.71374	+	11.4297i	0.520028	+	1.60048i
$52$		0			0
$53$	−3.53558	+	10.8814i	−0.485649	+	1.49468i	0.345389	+	0.938460i	$0.387747\pi$
$53$	−3.53558	+	10.8814i	−0.485649	+	1.49468i	−0.831038	+	0.556216i	$0.812253\pi$
$54$		0			0
$55$	1.52902			0.206173
$56$		0			0
$57$	6.24384	+	4.53642i	0.827017	+	0.600863i
$58$		0			0
$59$	−4.12440	+	2.99656i	−0.536952	+	0.390118i	−0.822952	−	0.568111i	$-0.807674\pi$
$59$	−4.12440	+	2.99656i	−0.536952	+	0.390118i	0.286000	+	0.958230i	$0.407674\pi$
$60$		0			0
$61$	1.69291	+	1.22997i	0.216755	+	0.157482i	0.690865	−	0.722984i	$-0.257230\pi$
$61$	1.69291	+	1.22997i	0.216755	+	0.157482i	−0.474110	+	0.880466i	$0.657230\pi$
$62$		0			0
$63$	−13.8095	−	10.0332i	−1.73983	−	1.26406i
$64$		0			0
$65$	0.538212	+	1.65645i	0.0667570	+	0.205457i
$66$		0			0
$67$	−2.29947	+	7.07704i	−0.280925	+	0.864597i	0.706666	+	0.707547i	$0.250198\pi$
$67$	−2.29947	+	7.07704i	−0.280925	+	0.864597i	−0.987591	+	0.157050i	$0.949802\pi$
$68$		0			0
$69$	−2.35951	+	1.71428i	−0.284051	+	0.206375i
$70$		0			0
$71$	−0.299474	−	0.921685i	−0.0355410	−	0.109384i	0.931712	−	0.363198i	$-0.118315\pi$
$71$	−0.299474	−	0.921685i	−0.0355410	−	0.109384i	−0.967253	+	0.253814i	$0.918315\pi$
$72$		0			0
$73$	−5.21188			−0.610005			−0.305002	−	0.952352i	$-0.598657\pi$
$73$	−5.21188			−0.610005			−0.305002	+	0.952352i	$0.598657\pi$
$74$		0			0
$75$	2.67170	+	1.94110i	0.308501	+	0.224139i
$76$		0			0
$77$	−1.02015	+	3.13971i	−0.116257	+	0.357804i
$78$		0			0
$79$	12.9080			1.45226			0.726131	−	0.687556i	$-0.241317\pi$
$79$	12.9080			1.45226			0.726131	+	0.687556i	$0.241317\pi$
$80$		0			0
$81$	29.7849			3.30943
$82$		0			0
$83$	−14.4095			−1.58164			−0.790822	−	0.612047i	$-0.790346\pi$
$83$	−14.4095			−1.58164			−0.790822	+	0.612047i	$0.790346\pi$
$84$		0			0
$85$	3.63915			0.394721
$86$		0			0
$87$	7.07651	−	21.7793i	0.758682	−	2.33498i
$88$		0			0
$89$	−13.5939	−	9.87655i	−1.44095	−	1.04691i	−0.987843	−	0.155457i	$-0.950315\pi$
$89$	−13.5939	−	9.87655i	−1.44095	−	1.04691i	−0.453109	−	0.891455i	$-0.649685\pi$
$90$		0			0
$91$	−3.76047			−0.394205
$92$		0			0
$93$	−9.93322	−	30.5713i	−1.03003	−	3.17010i
$94$		0			0
$95$	1.89070	−	1.37367i	0.193982	−	0.140936i
$96$		0			0
$97$	−3.95010	+	12.1572i	−0.401072	+	1.23437i	0.523059	+	0.852296i	$0.324791\pi$
$97$	−3.95010	+	12.1572i	−0.401072	+	1.23437i	−0.924131	+	0.382076i	$0.875209\pi$
$98$		0			0
$99$	−3.73545	−	11.4965i	−0.375427	−	1.15545i
$100$		0			0
$101$	5.57573	+	4.05101i	0.554806	+	0.403090i	0.829554	−	0.558426i	$-0.188595\pi$
$101$	5.57573	+	4.05101i	0.554806	+	0.403090i	−0.274748	+	0.961516i	$0.588595\pi$
$102$		0			0
$103$	12.6380	+	9.18205i	1.24526	+	0.904734i	0.997937	−	0.0641994i	$-0.0204494\pi$
$103$	12.6380	+	9.18205i	1.24526	+	0.904734i	0.247322	+	0.968933i	$0.420449\pi$
$104$		0			0
$105$	−5.76845	+	4.19102i	−0.562943	+	0.409002i
$106$		0			0
$107$	15.7137	+	11.4167i	1.51910	+	1.10369i	0.961931	+	0.273292i	$0.0881125\pi$
$107$	15.7137	+	11.4167i	1.51910	+	1.10369i	0.557169	+	0.830399i	$0.311888\pi$
$108$		0			0
$109$	−12.5867			−1.20559			−0.602793	−	0.797898i	$-0.705945\pi$
$109$	−12.5867			−1.20559			−0.602793	+	0.797898i	$0.705945\pi$
$110$		0			0
$111$	0.378679	−	1.16545i	0.0359426	−	0.110620i
$112$		0			0
$113$	4.56119	+	14.0379i	0.429081	+	1.32057i	0.899032	+	0.437882i	$0.144271\pi$
$113$	4.56119	+	14.0379i	0.429081	+	1.32057i	−0.469951	+	0.882692i	$0.655729\pi$
$114$		0			0
$115$	0.272908	+	0.839924i	0.0254488	+	0.0783233i
$116$		0			0
$117$	11.1398	−	8.09353i	1.02987	−	0.748247i
$118$		0			0
$119$	−2.42803	+	7.47270i	−0.222577	+	0.685021i
$120$		0			0
$121$	7.00779	−	5.09146i	0.637072	−	0.462860i
$122$		0			0
$123$	−15.8498	−	13.9973i	−1.42912	−	1.26210i
$124$		0			0
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$		0			0
$127$	3.78591	−	11.6518i	0.335945	−	1.03393i	−0.630309	−	0.776344i	$-0.717072\pi$
$127$	3.78591	−	11.6518i	0.335945	−	1.03393i	0.966255	−	0.257589i	$-0.0829281\pi$
$128$		0			0
$129$	−0.752480	+	0.546709i	−0.0662522	+	0.0481350i
$130$		0			0
$131$	2.77860	+	8.55166i	0.242768	+	0.747162i	0.995996	+	0.0894022i	$0.0284956\pi$
$131$	2.77860	+	8.55166i	0.242768	+	0.747162i	−0.753228	+	0.657759i	$0.771504\pi$
$132$		0			0
$133$	1.55926	+	4.79891i	0.135205	+	0.416118i
$134$		0			0
$135$	5.00640	−	15.4081i	0.430883	−	1.32612i
$136$		0			0
$137$	9.42455			0.805193			0.402597	−	0.915377i	$-0.368108\pi$
$137$	9.42455			0.805193			0.402597	+	0.915377i	$0.368108\pi$
$138$		0			0
$139$	−14.3417	−	10.4198i	−1.21644	−	0.883798i	−0.220644	−	0.975354i	$-0.570816\pi$
$139$	−14.3417	−	10.4198i	−1.21644	−	0.883798i	−0.995800	+	0.0915565i	$0.970816\pi$
$140$		0			0
$141$	7.30584	−	5.30800i	0.615262	−	0.447014i
$142$		0			0
$143$	−2.15447	−	1.56532i	−0.180166	−	0.130898i
$144$		0			0
$145$	−5.61002	−	4.07592i	−0.465887	−	0.338487i
$146$		0			0
$147$	2.38624	+	7.34410i	0.196814	+	0.605732i
$148$		0			0
$149$	0.687223	−	2.11505i	0.0562995	−	0.173272i	−0.918953	−	0.394368i	$-0.870963\pi$
$149$	0.687223	−	2.11505i	0.0562995	−	0.173272i	0.975252	+	0.221096i	$0.0709635\pi$
$150$		0			0
$151$	6.20012	−	4.50465i	0.504559	−	0.366583i	−0.306197	−	0.951968i	$-0.599057\pi$
$151$	6.20012	−	4.50465i	0.504559	−	0.366583i	0.810756	+	0.585385i	$0.199057\pi$
$152$		0			0
$153$	−8.89058	−	27.3624i	−0.718761	−	2.21212i
$154$		0			0
$155$	−9.73370			−0.781830
$156$		0			0
$157$	−10.7856	−	7.83620i	−0.860785	−	0.625397i	0.0673135	−	0.997732i	$-0.478557\pi$
$157$	−10.7856	−	7.83620i	−0.860785	−	0.625397i	−0.928098	+	0.372335i	$0.878557\pi$
$158$		0			0
$159$	11.6759	−	35.9347i	0.925959	−	2.84981i
$160$		0			0
$161$	−1.90680			−0.150277
$162$		0			0
$163$	13.3885			1.04867			0.524336	−	0.851511i	$-0.324314\pi$
$163$	13.3885			1.04867			0.524336	+	0.851511i	$0.324314\pi$
$164$		0			0
$165$	−5.04942			−0.393097
$166$		0			0
$167$	−16.3037			−1.26161			−0.630807	−	0.775940i	$-0.717276\pi$
$167$	−16.3037			−1.26161			−0.630807	+	0.775940i	$0.717276\pi$
$168$		0			0
$169$	−3.07982	+	9.47872i	−0.236909	+	0.729132i
$170$		0			0
$171$	−14.9476	−	10.8600i	−1.14307	−	0.830488i
$172$		0			0
$173$	9.23124			0.701838			0.350919	−	0.936406i	$-0.385869\pi$
$173$	9.23124			0.701838			0.350919	+	0.936406i	$0.385869\pi$
$174$		0			0
$175$	0.667197	+	2.05342i	0.0504353	+	0.155224i
$176$		0			0
$177$	13.6204	−	9.89582i	1.02377	−	0.743816i
$178$		0			0
$179$	−1.32595	+	4.08085i	−0.0991059	+	0.305017i	−0.988302	−	0.152510i	$-0.951264\pi$
$179$	−1.32595	+	4.08085i	−0.0991059	+	0.305017i	0.889196	+	0.457526i	$0.151264\pi$
$180$		0			0
$181$	1.96538	+	6.04881i	0.146085	+	0.449604i	0.997149	−	0.0754582i	$-0.0240419\pi$
$181$	1.96538	+	6.04881i	0.146085	+	0.449604i	−0.851064	+	0.525063i	$0.824042\pi$
$182$		0			0
$183$	−5.59067	−	4.06186i	−0.413274	−	0.300261i
$184$		0			0
$185$	−0.300204	−	0.218111i	−0.0220714	−	0.0160358i
$186$		0			0
$187$	−4.50163	+	3.27062i	−0.329191	+	0.239172i
$188$		0			0
$189$	28.2991	+	20.5605i	2.05846	+	1.49556i
$190$		0			0
$191$	−17.3002			−1.25180			−0.625899	−	0.779904i	$-0.715268\pi$
$191$	−17.3002			−1.25180			−0.625899	+	0.779904i	$0.715268\pi$
$192$		0			0
$193$	5.84997	−	18.0044i	0.421090	−	1.29598i	−0.485598	−	0.874182i	$-0.661398\pi$
$193$	5.84997	−	18.0044i	0.421090	−	1.29598i	0.906689	−	0.421801i	$-0.138602\pi$
$194$		0			0
$195$	−1.77739	−	5.47025i	−0.127282	−	0.391733i
$196$		0			0
$197$	4.54589	+	13.9908i	0.323881	+	0.996804i	0.971943	+	0.235216i	$0.0755798\pi$
$197$	4.54589	+	13.9908i	0.323881	+	0.996804i	−0.648062	+	0.761588i	$0.724420\pi$
$198$		0			0
$199$	2.88066	−	2.09293i	0.204205	−	0.148364i	−0.480983	−	0.876730i	$-0.659720\pi$
$199$	2.88066	−	2.09293i	0.204205	−	0.148364i	0.685188	+	0.728366i	$0.259720\pi$
$200$		0			0
$201$	7.59376	−	23.3712i	0.535623	−	1.64848i
$202$		0			0
$203$	12.1126	−	8.80030i	0.850136	−	0.617660i
$204$		0			0
$205$	−5.51420	+	3.25478i	−0.385128	+	0.227324i
$206$		0			0
$207$	5.64859	−	4.10394i	0.392604	−	0.285243i
$208$		0			0
$209$	−1.10423	+	3.39847i	−0.0763811	+	0.235077i
$210$		0			0
$211$	5.08774	−	3.69646i	0.350254	−	0.254475i	−0.398721	−	0.917072i	$-0.630546\pi$
$211$	5.08774	−	3.69646i	0.350254	−	0.254475i	0.748976	+	0.662597i	$0.230546\pi$
$212$		0			0
$213$	0.988982	+	3.04377i	0.0677639	+	0.208556i
$214$		0			0
$215$	0.0870342	+	0.267864i	0.00593569	+	0.0182682i
$216$		0			0
$217$	6.49429	−	19.9874i	0.440861	−	1.35683i
$218$		0			0
$219$	17.2117			1.16306
$220$		0			0
$221$	−5.12777	−	3.72554i	−0.344931	−	0.250607i
$222$		0			0
$223$	−11.0086	+	7.99821i	−0.737190	+	0.535600i	−0.891830	−	0.452371i	$-0.850578\pi$
$223$	−11.0086	+	7.99821i	−0.737190	+	0.535600i	0.154640	+	0.987971i	$0.450578\pi$
$224$		0			0
$225$	−6.39596	−	4.64694i	−0.426398	−	0.309796i
$226$		0			0
$227$	3.17445	+	2.30638i	0.210696	+	0.153080i	0.688129	−	0.725589i	$-0.258433\pi$
$227$	3.17445	+	2.30638i	0.210696	+	0.153080i	−0.477433	+	0.878668i	$0.658433\pi$
$228$		0			0
$229$	1.15072	+	3.54154i	0.0760415	+	0.234032i	0.981851	−	0.189653i	$-0.0607364\pi$
$229$	1.15072	+	3.54154i	0.0760415	+	0.234032i	−0.905810	+	0.423685i	$0.860736\pi$
$230$		0			0
$231$	3.36896	−	10.3686i	0.221661	−	0.682203i
$232$		0			0
$233$	0.0120704	−	0.00876962i	0.000790755	−	0.000574517i	−0.587390	−	0.809304i	$-0.699844\pi$
$233$	0.0120704	−	0.00876962i	0.000790755	−	0.000574517i	0.588181	+	0.808730i	$0.299844\pi$
$234$		0			0
$235$	−0.845016	−	2.60069i	−0.0551228	−	0.169650i
$236$		0			0
$237$	−42.6273			−2.76894
$238$		0			0
$239$	15.2276	+	11.0635i	0.984993	+	0.715640i	0.958819	−	0.284018i	$-0.0916675\pi$
$239$	15.2276	+	11.0635i	0.984993	+	0.715640i	0.0261744	+	0.999657i	$0.491667\pi$
$240$		0			0
$241$	−0.430412	+	1.32467i	−0.0277253	+	0.0853297i	−0.963962	−	0.266041i	$-0.914284\pi$
$241$	−0.430412	+	1.32467i	−0.0277253	+	0.0853297i	0.936236	+	0.351371i	$0.114284\pi$
$242$		0			0
$243$	−49.7583			−3.19200
$244$		0			0
$245$	2.33831			0.149389
$246$		0			0
$247$	−4.07039			−0.258992
$248$		0			0
$249$	47.5858			3.01563
$250$		0			0
$251$	−7.07655	+	21.7794i	−0.446668	+	1.37470i	0.433976	+	0.900925i	$0.357110\pi$
$251$	−7.07655	+	21.7794i	−0.446668	+	1.37470i	−0.880644	+	0.473779i	$0.842890\pi$
$252$		0			0
$253$	−1.09246	−	0.793715i	−0.0686821	−	0.0499004i
$254$		0			0
$255$	−12.0179			−0.752591
$256$		0			0
$257$	3.66057	+	11.2661i	0.228340	+	0.702758i	0.997935	+	0.0642260i	$0.0204579\pi$
$257$	3.66057	+	11.2661i	0.228340	+	0.702758i	−0.769596	+	0.638532i	$0.779542\pi$
$258$		0			0
$259$	0.648169	−	0.470922i	0.0402752	−	0.0292617i
$260$		0			0
$261$	−16.9410	+	52.1389i	−1.04862	+	3.22732i
$262$		0			0
$263$	8.38938	+	25.8199i	0.517311	+	1.59212i	0.779037	+	0.626978i	$0.215709\pi$
$263$	8.38938	+	25.8199i	0.517311	+	1.59212i	−0.261725	+	0.965142i	$0.584291\pi$
$264$		0			0
$265$	−9.25627	−	6.72508i	−0.568608	−	0.413118i
$266$		0			0
$267$	44.8925	+	32.6163i	2.74738	+	1.99609i
$268$		0			0
$269$	−21.8461	+	15.8721i	−1.33198	+	0.967740i	−0.332281	+	0.943180i	$0.607818\pi$
$269$	−21.8461	+	15.8721i	−1.33198	+	0.967740i	−0.999698	+	0.0245596i	$0.992182\pi$
$270$		0			0
$271$	−1.85459	−	1.34744i	−0.112658	−	0.0818509i	0.530030	−	0.847979i	$-0.322181\pi$
$271$	−1.85459	−	1.34744i	−0.112658	−	0.0818509i	−0.642688	+	0.766128i	$0.722181\pi$
$272$		0			0
$273$	12.4186			0.751607
$274$		0			0
$275$	−0.472492	+	1.45418i	−0.0284923	+	0.0876904i
$276$		0			0
$277$	1.14027	+	3.50940i	0.0685125	+	0.210860i	0.979451	−	0.201683i	$-0.0646409\pi$
$277$	1.14027	+	3.50940i	0.0685125	+	0.210860i	−0.910938	+	0.412542i	$0.864641\pi$
$278$		0			0
$279$	23.7798	+	73.1868i	1.42366	+	4.38158i
$280$		0			0
$281$	−3.56351	+	2.58904i	−0.212581	+	0.154449i	−0.688981	−	0.724780i	$-0.741942\pi$
$281$	−3.56351	+	2.58904i	−0.212581	+	0.154449i	0.476400	+	0.879229i	$0.341942\pi$
$282$		0			0
$283$	−6.67840	+	20.5540i	−0.396989	+	1.22181i	0.530412	+	0.847740i	$0.322037\pi$
$283$	−6.67840	+	20.5540i	−0.396989	+	1.22181i	−0.927401	+	0.374068i	$0.877963\pi$
$284$		0			0
$285$	−6.24384	+	4.53642i	−0.369853	+	0.268714i
$286$		0			0
$287$	−3.00439	−	13.4945i	−0.177343	−	0.796558i
$288$		0			0
$289$	3.03916	−	2.20808i	0.178774	−	0.129887i
$290$		0			0
$291$	13.0448	−	40.1478i	0.764700	−	2.35350i
$292$		0			0
$293$	10.8513	−	7.88391i	0.633938	−	0.460583i	−0.223824	−	0.974629i	$-0.571854\pi$
$293$	10.8513	−	7.88391i	0.633938	−	0.460583i	0.857762	+	0.514047i	$0.171854\pi$
$294$		0			0
$295$	−1.57538	−	4.84853i	−0.0917223	−	0.282292i
$296$		0			0
$297$	7.65488	+	23.5593i	0.444181	+	1.36705i
$298$		0			0
$299$	0.475321	−	1.46289i	0.0274885	−	0.0846010i
$300$		0			0
$301$	−0.608106			−0.0350507
$302$		0			0
$303$	−18.4133	−	13.3780i	−1.05782	−	0.768549i
$304$		0			0
$305$	−1.69291	+	1.22997i	−0.0969358	+	0.0704280i
$306$		0			0
$307$	−8.78398	−	6.38193i	−0.501328	−	0.364236i	0.308196	−	0.951323i	$-0.400275\pi$
$307$	−8.78398	−	6.38193i	−0.501328	−	0.364236i	−0.809524	+	0.587087i	$0.800275\pi$
$308$		0			0
$309$	−41.7357	−	30.3228i	−2.37426	−	1.72500i
$310$		0			0
$311$	8.72777	+	26.8613i	0.494907	+	1.52317i	0.817102	+	0.576493i	$0.195579\pi$
$311$	8.72777	+	26.8613i	0.494907	+	1.52317i	−0.322195	+	0.946673i	$0.604421\pi$
$312$		0			0
$313$	2.85368	−	8.78271i	0.161299	−	0.496428i	−0.837445	−	0.546521i	$-0.815952\pi$
$313$	2.85368	−	8.78271i	0.161299	−	0.496428i	0.998745	+	0.0500930i	$0.0159518\pi$
$314$		0			0
$315$	13.8095	−	10.0332i	0.778076	−	0.565306i
$316$		0			0
$317$	2.90492	+	8.94042i	0.163157	+	0.502144i	0.998896	−	0.0469824i	$-0.0149605\pi$
$317$	2.90492	+	8.94042i	0.163157	+	0.502144i	−0.835739	+	0.549127i	$0.814960\pi$
$318$		0			0
$319$	10.6028			0.593641
$320$		0			0
$321$	−51.8929	−	37.7024i	−2.89638	−	2.10434i
$322$		0			0
$323$	−2.62813	+	8.08854i	−0.146233	+	0.450059i
$324$		0			0
$325$	−1.74169			−0.0966116
$326$		0			0
$327$	41.5662			2.29862
$328$		0			0
$329$	5.90410			0.325504
$330$		0			0
$331$	29.0334			1.59582			0.797910	−	0.602776i	$-0.205939\pi$
$331$	29.0334			1.59582			0.797910	+	0.602776i	$0.205939\pi$
$332$		0			0
$333$	−0.906545	+	2.79006i	−0.0496784	+	0.152894i
$334$		0			0
$335$	−6.02009	−	4.37385i	−0.328912	−	0.238969i
$336$		0			0
$337$	−23.9996			−1.30734			−0.653670	−	0.756780i	$-0.726771\pi$
$337$	−23.9996			−1.30734			−0.653670	+	0.756780i	$0.726771\pi$
$338$		0			0
$339$	−15.0629	−	46.3588i	−0.818103	−	2.51786i
$340$		0			0
$341$	12.0406	−	8.74800i	0.652035	−	0.473731i
$342$		0			0
$343$	−6.23049	+	19.1755i	−0.336415	+	1.03538i
$344$		0			0
$345$	−0.901251	−	2.77377i	−0.0485217	−	0.149335i
$346$		0			0
$347$	16.6450	+	12.0933i	0.893553	+	0.649204i	0.936802	−	0.349860i	$-0.113771\pi$
$347$	16.6450	+	12.0933i	0.893553	+	0.649204i	−0.0432493	+	0.999064i	$0.513771\pi$
$348$		0			0
$349$	−24.1019	−	17.5111i	−1.29015	−	0.937346i	−0.290337	−	0.956924i	$-0.593768\pi$
$349$	−24.1019	−	17.5111i	−1.29015	−	0.937346i	−0.999808	+	0.0195786i	$0.993768\pi$
$350$		0			0
$351$	−22.8282	+	16.5857i	−1.21848	+	0.885278i
$352$		0			0
$353$	−6.19005	−	4.49733i	−0.329463	−	0.239369i	0.410740	−	0.911753i	$-0.365270\pi$
$353$	−6.19005	−	4.49733i	−0.329463	−	0.239369i	−0.740203	+	0.672384i	$0.765270\pi$
$354$		0			0
$355$	0.969117			0.0514354
$356$		0			0
$357$	8.01831	−	24.6778i	0.424374	−	1.30609i
$358$		0			0
$359$	−7.76293	−	23.8919i	−0.409712	−	1.26096i	−0.916896	−	0.399126i	$-0.869314\pi$
$359$	−7.76293	−	23.8919i	−0.409712	−	1.26096i	0.507184	−	0.861838i	$-0.330686\pi$
$360$		0			0
$361$	−4.18356	−	12.8757i	−0.220187	−	0.677667i
$362$		0			0
$363$	−23.1425	+	16.8140i	−1.21467	+	0.882508i
$364$		0			0
$365$	1.61056	−	4.95679i	0.0843006	−	0.259450i
$366$		0			0
$367$	9.62649	−	6.99406i	0.502499	−	0.365087i	−0.307472	−	0.951557i	$-0.599483\pi$
$367$	9.62649	−	6.99406i	0.502499	−	0.365087i	0.809971	+	0.586470i	$0.199483\pi$
$368$		0			0
$369$	37.9438	+	33.5092i	1.97528	+	1.74442i
$370$		0			0
$371$	19.9852	−	14.5201i	1.03758	−	0.753844i
$372$		0			0
$373$	6.57605	−	20.2390i	0.340495	−	1.04794i	−0.623457	−	0.781858i	$-0.714272\pi$
$373$	6.57605	−	20.2390i	0.340495	−	1.04794i	0.963952	−	0.266078i	$-0.0857278\pi$
$374$		0			0
$375$	−2.67170	+	1.94110i	−0.137966	+	0.100238i
$376$		0			0
$377$	3.73216	+	11.4864i	0.192216	+	0.591581i
$378$		0			0
$379$	−3.56511	−	10.9723i	−0.183127	−	0.563608i	0.816784	−	0.576944i	$-0.195755\pi$
$379$	−3.56511	−	10.9723i	−0.183127	−	0.563608i	−0.999911	+	0.0133362i	$0.995755\pi$
$380$		0			0
$381$	−12.5026	+	38.4790i	−0.640527	+	1.97134i
$382$		0			0
$383$	−3.75355			−0.191797			−0.0958987	−	0.995391i	$-0.530572\pi$
$383$	−3.75355			−0.191797			−0.0958987	+	0.995391i	$0.530572\pi$
$384$		0			0
$385$	−2.67080	−	1.94045i	−0.136117	−	0.0988945i
$386$		0			0
$387$	1.80142	−	1.30880i	0.0915711	−	0.0665303i
$388$		0			0
$389$	−1.12975	−	0.820815i	−0.0572808	−	0.0416170i	0.558776	−	0.829318i	$-0.311271\pi$
$389$	−1.12975	−	0.820815i	−0.0572808	−	0.0416170i	−0.616057	+	0.787701i	$0.711271\pi$
$390$		0			0
$391$	−2.60011	−	1.88909i	−0.131493	−	0.0955352i
$392$		0			0
$393$	−9.17605	−	28.2410i	−0.462871	−	1.42457i
$394$		0			0
$395$	−3.98879	+	12.2762i	−0.200698	+	0.617684i
$396$		0			0
$397$	19.1096	−	13.8839i	0.959081	−	0.696813i	0.00614378	−	0.999981i	$-0.498044\pi$
$397$	19.1096	−	13.8839i	0.959081	−	0.696813i	0.952937	+	0.303168i	$0.0980444\pi$
$398$		0			0
$399$	−5.14930	−	15.8479i	−0.257787	−	0.793388i
$400$		0			0
$401$	−18.8000			−0.938827			−0.469414	−	0.882978i	$-0.655535\pi$
$401$	−18.8000			−0.938827			−0.469414	+	0.882978i	$0.655535\pi$
$402$		0			0
$403$	13.7153	+	9.96478i	0.683210	+	0.496381i
$404$		0			0
$405$	−9.20403	+	28.3271i	−0.457352	+	1.40758i
$406$		0			0
$407$	0.567376			0.0281238
$408$		0			0
$409$	21.6983			1.07291			0.536456	−	0.843928i	$-0.319763\pi$
$409$	21.6983			1.07291			0.536456	+	0.843928i	$0.319763\pi$
$410$		0			0
$411$	−31.1236			−1.53522
$412$		0			0
$413$	11.0072			0.541627
$414$		0			0
$415$	4.45277	−	13.7042i	0.218578	−	0.672713i
$416$		0			0
$417$	47.3619	+	34.4104i	2.31932	+	1.68509i
$418$		0			0
$419$	−15.3866			−0.751685			−0.375843	−	0.926683i	$-0.622647\pi$
$419$	−15.3866			−0.751685			−0.375843	+	0.926683i	$0.622647\pi$
$420$		0			0
$421$	−9.55590	−	29.4100i	−0.465726	−	1.43336i	−0.858067	−	0.513538i	$-0.828335\pi$
$421$	−9.55590	−	29.4100i	−0.465726	−	1.43336i	0.392341	−	0.919820i	$-0.371665\pi$
$422$		0			0
$423$	−17.4899	+	12.7072i	−0.850390	+	0.617845i
$424$		0			0
$425$	−1.12456	+	3.46103i	−0.0545491	+	0.167885i
$426$		0			0
$427$	−1.39614	−	4.29689i	−0.0675642	−	0.207941i
$428$		0			0
$429$	7.11493	+	5.16930i	0.343512	+	0.249576i
$430$		0			0
$431$	−2.79875	−	2.03341i	−0.134811	−	0.0979460i	0.518336	−	0.855177i	$-0.326552\pi$
$431$	−2.79875	−	2.03341i	−0.134811	−	0.0979460i	−0.653147	+	0.757231i	$0.726552\pi$
$432$		0			0
$433$	10.3196	−	7.49763i	0.495928	−	0.360313i	−0.311531	−	0.950236i	$-0.600842\pi$
$433$	10.3196	−	7.49763i	0.495928	−	0.360313i	0.807460	+	0.589923i	$0.200842\pi$
$434$		0			0
$435$	18.5265	+	13.4603i	0.888280	+	0.645373i
$436$		0			0
$437$	−2.06395			−0.0987319
$438$		0			0
$439$	−8.50095	+	26.1632i	−0.405728	+	1.24870i	0.514558	+	0.857456i	$0.327956\pi$
$439$	−8.50095	+	26.1632i	−0.405728	+	1.24870i	−0.920286	+	0.391247i	$0.872044\pi$
$440$		0			0
$441$	−5.71260	−	17.5816i	−0.272028	−	0.837217i
$442$		0			0
$443$	2.65221	+	8.16268i	0.126011	+	0.387820i	0.994084	−	0.108616i	$-0.0346417\pi$
$443$	2.65221	+	8.16268i	0.126011	+	0.387820i	−0.868073	+	0.496436i	$0.834642\pi$
$444$		0			0
$445$	13.5939	−	9.87655i	0.644413	−	0.468193i
$446$		0			0
$447$	−2.26949	+	6.98476i	−0.107343	+	0.330368i
$448$		0			0
$449$	−19.4666	+	14.1433i	−0.918685	+	0.667464i	−0.943196	−	0.332236i	$-0.892197\pi$
$449$	−19.4666	+	14.1433i	−0.918685	+	0.667464i	0.0245113	+	0.999700i	$0.492197\pi$
$450$		0			0
$451$	3.89588	−	8.98196i	0.183450	−	0.422944i
$452$		0			0
$453$	−20.4753	+	14.8762i	−0.962013	+	0.698943i
$454$		0			0
$455$	1.16205	−	3.57642i	0.0544778	−	0.167665i
$456$		0			0
$457$	−32.9515	+	23.9406i	−1.54140	+	1.11990i	−0.591958	+	0.805969i	$0.701645\pi$
$457$	−32.9515	+	23.9406i	−1.54140	+	1.11990i	−0.949447	+	0.313927i	$0.898355\pi$
$458$		0			0
$459$	18.2190	+	56.0724i	0.850392	+	2.61724i
$460$		0			0
$461$	−0.834423	−	2.56809i	−0.0388629	−	0.119608i	0.929743	−	0.368209i	$-0.120029\pi$
$461$	−0.834423	−	2.56809i	−0.0388629	−	0.119608i	−0.968606	+	0.248602i	$0.920029\pi$
$462$		0			0
$463$	4.93980	−	15.2031i	0.229572	−	0.706550i	−0.768223	−	0.640182i	$-0.778859\pi$
$463$	4.93980	−	15.2031i	0.229572	−	0.706550i	0.997795	−	0.0663679i	$-0.0211411\pi$
$464$		0			0
$465$	32.1446			1.49067
$466$		0			0
$467$	−4.00501	−	2.90981i	−0.185330	−	0.134650i	0.491252	−	0.871017i	$-0.336539\pi$
$467$	−4.00501	−	2.90981i	−0.185330	−	0.134650i	−0.676582	+	0.736368i	$0.736539\pi$
$468$		0			0
$469$	12.9979	−	9.44355i	0.600189	−	0.436063i
$470$		0			0
$471$	35.6184	+	25.8783i	1.64121	+	1.19241i
$472$		0			0
$473$	−0.348400	−	0.253127i	−0.0160194	−	0.0116388i
$474$		0			0
$475$	0.722182	+	2.22265i	0.0331360	+	0.101982i
$476$		0			0
$477$	−27.9518	+	86.0267i	−1.27982	+	3.93889i
$478$		0			0
$479$	18.6249	−	13.5318i	0.850992	−	0.618282i	−0.0744270	−	0.997226i	$-0.523713\pi$
$479$	18.6249	−	13.5318i	0.850992	−	0.618282i	0.925420	+	0.378944i	$0.123713\pi$
$480$		0			0
$481$	0.199716	+	0.614662i	0.00910625	+	0.0280262i
$482$		0			0
$483$	6.29702			0.286524
$484$		0			0
$485$	−10.3415	−	7.51353i	−0.469583	−	0.341172i
$486$		0			0
$487$	−0.151748	+	0.467033i	−0.00687637	+	0.0211633i	−0.954436	−	0.298416i	$-0.903542\pi$
$487$	−0.151748	+	0.467033i	−0.00687637	+	0.0211633i	0.947559	+	0.319580i	$0.103542\pi$
$488$		0			0
$489$	−44.2143			−1.99944
$490$		0			0
$491$	−32.5978			−1.47112			−0.735560	−	0.677460i	$-0.763081\pi$
$491$	−32.5978			−1.47112			−0.735560	+	0.677460i	$0.763081\pi$
$492$		0			0
$493$	25.2352			1.13654
$494$		0			0
$495$	12.0882			0.543323
$496$		0			0
$497$	−0.646592	+	1.99000i	−0.0290036	+	0.0892639i
$498$		0			0
$499$	−21.6664	−	15.7416i	−0.969921	−	0.704689i	−0.0144874	−	0.999895i	$-0.504612\pi$
$499$	−21.6664	−	15.7416i	−0.969921	−	0.704689i	−0.955434	+	0.295206i	$0.904612\pi$
$500$		0			0
$501$	53.8412			2.40545
$502$		0			0
$503$	−11.5053	−	35.4096i	−0.512995	−	1.57884i	−0.786900	−	0.617080i	$-0.788315\pi$
$503$	−11.5053	−	35.4096i	−0.512995	−	1.57884i	0.273905	−	0.961757i	$-0.411685\pi$
$504$		0			0
$505$	−5.57573	+	4.05101i	−0.248117	+	0.180267i
$506$		0			0
$507$	10.1708	−	31.3025i	0.451701	−	1.39019i
$508$		0			0
$509$	−12.5764	−	38.7062i	−0.557440	−	1.71562i	−0.689411	−	0.724370i	$-0.742131\pi$
$509$	−12.5764	−	38.7062i	−0.557440	−	1.71562i	0.131971	−	0.991254i	$-0.457869\pi$
$510$		0			0
$511$	9.10382	+	6.61431i	0.402729	+	0.292600i
$512$		0			0
$513$	30.6313	+	22.2550i	1.35241	+	0.982580i
$514$		0			0
$515$	−12.6380	+	9.18205i	−0.556897	+	0.404609i
$516$		0			0
$517$	3.38261	+	2.45761i	0.148767	+	0.108086i
$518$		0			0
$519$	−30.4852			−1.33815
$520$		0			0
$521$	−5.03281	+	15.4894i	−0.220492	+	0.678603i	0.778226	+	0.627984i	$0.216120\pi$
$521$	−5.03281	+	15.4894i	−0.220492	+	0.678603i	−0.998718	+	0.0506196i	$0.983880\pi$
$522$		0			0
$523$	7.39916	+	22.7723i	0.323543	+	0.995761i	0.972094	+	0.234591i	$0.0753750\pi$
$523$	7.39916	+	22.7723i	0.323543	+	0.995761i	−0.648552	+	0.761171i	$0.724625\pi$
$524$		0			0
$525$	−2.20335	−	6.78122i	−0.0961621	−	0.295956i
$526$		0			0
$527$	28.6573	−	20.8207i	1.24833	−	0.906966i
$528$		0			0
$529$	−6.86637	+	21.1325i	−0.298538	+	0.918805i
$530$		0			0
$531$	−32.6069	+	23.6903i	−1.41502	+	1.02807i
$532$		0			0
$533$	11.1019	+	1.05893i	0.480876	+	0.0458673i
$534$		0			0
$535$	−15.7137	+	11.4167i	−0.679362	+	0.493586i
$536$		0			0
$537$	4.37881	−	13.4766i	0.188960	−	0.581558i
$538$		0			0
$539$	−2.89250	+	2.10152i	−0.124589	+	0.0905189i
$540$		0			0
$541$	8.75631	+	26.9492i	0.376463	+	1.15864i	0.942486	+	0.334245i	$0.108481\pi$
$541$	8.75631	+	26.9492i	0.376463	+	1.15864i	−0.566023	+	0.824390i	$0.691519\pi$
$542$		0			0
$543$	−6.49046	−	19.9756i	−0.278532	−	0.857234i
$544$		0			0
$545$	3.88950	−	11.9706i	0.166608	−	0.512766i
$546$		0			0
$547$	5.68506			0.243075			0.121538	−	0.992587i	$-0.461217\pi$
$547$	5.68506			0.243075			0.121538	+	0.992587i	$0.461217\pi$
$548$		0			0
$549$	13.3839	+	9.72397i	0.571211	+	0.415009i
$550$		0			0
$551$	13.1108	−	9.52556i	0.558539	−	0.405802i
$552$		0			0
$553$	−22.5469	−	16.3813i	−0.958793	−	0.696604i
$554$		0			0
$555$	0.991394	+	0.720290i	0.0420823	+	0.0305746i
$556$		0			0
$557$	−4.45465	−	13.7100i	−0.188750	−	0.580912i	0.811243	−	0.584709i	$-0.198791\pi$
$557$	−4.45465	−	13.7100i	−0.188750	−	0.580912i	−0.999993	+	0.00379736i	$0.998791\pi$
$558$		0			0
$559$	0.151587	−	0.466536i	0.00641144	−	0.0197324i
$560$		0			0
$561$	14.8662	−	10.8009i	0.627650	−	0.456015i
$562$		0			0
$563$	−1.70470	−	5.24653i	−0.0718445	−	0.221115i	0.908686	−	0.417479i	$-0.137086\pi$
$563$	−1.70470	−	5.24653i	−0.0718445	−	0.221115i	−0.980531	+	0.196365i	$0.937086\pi$
$564$		0			0
$565$	−14.7603			−0.620971
$566$		0			0
$567$	−52.0265	−	37.7995i	−2.18491	−	1.58743i
$568$		0			0
$569$	6.09885	−	18.7703i	0.255677	−	0.786893i	−0.738018	−	0.674781i	$-0.764238\pi$
$569$	6.09885	−	18.7703i	0.255677	−	0.786893i	0.993695	−	0.112113i	$-0.0357618\pi$
$570$		0			0
$571$	−23.9200			−1.00102			−0.500511	−	0.865730i	$-0.666854\pi$
$571$	−23.9200			−1.00102			−0.500511	+	0.865730i	$0.666854\pi$
$572$		0			0
$573$	57.1321			2.38673
$574$		0			0
$575$	−0.883149			−0.0368298
$576$		0			0
$577$	−37.2918			−1.55248			−0.776240	−	0.630438i	$-0.782875\pi$
$577$	−37.2918			−1.55248			−0.776240	+	0.630438i	$0.782875\pi$
$578$		0			0
$579$	−19.3189	+	59.4576i	−0.802868	+	2.47097i
$580$		0			0
$581$	25.1696	+	18.2868i	1.04421	+	0.758664i
$582$		0			0
$583$	17.4941			0.724530
$584$		0			0
$585$	4.25502	+	13.0956i	0.175924	+	0.541437i
$586$		0			0
$587$	19.8838	−	14.4464i	0.820691	−	0.596267i	−0.0962194	−	0.995360i	$-0.530675\pi$
$587$	19.8838	−	14.4464i	0.820691	−	0.596267i	0.916910	+	0.399093i	$0.130675\pi$
$588$		0			0
$589$	7.02951	−	21.6346i	0.289646	−	0.891438i
$590$		0			0
$591$	−15.0123	−	46.2032i	−0.617525	−	1.90055i
$592$		0			0
$593$	24.4257	+	17.7463i	1.00304	+	0.728754i	0.962739	−	0.270434i	$-0.0871671\pi$
$593$	24.4257	+	17.7463i	1.00304	+	0.728754i	0.0403048	+	0.999187i	$0.487167\pi$
$594$		0			0
$595$	−6.35666	−	4.61838i	−0.260597	−	0.189335i
$596$		0			0
$597$	−9.51311	+	6.91168i	−0.389346	+	0.282876i
$598$		0			0
$599$	−18.8428	−	13.6901i	−0.769895	−	0.559361i	0.132035	−	0.991245i	$-0.457849\pi$
$599$	−18.8428	−	13.6901i	−0.769895	−	0.559361i	−0.901929	+	0.431884i	$0.857849\pi$
$600$		0			0
$601$	47.2012			1.92538			0.962688	−	0.270613i	$-0.0872263\pi$
$601$	47.2012			1.92538			0.962688	+	0.270613i	$0.0872263\pi$
$602$		0			0
$603$	−18.1792	+	55.9499i	−0.740316	+	2.27846i
$604$		0			0
$605$	2.67674	+	8.23815i	0.108825	+	0.334929i
$606$		0			0
$607$	−13.7550	−	42.3336i	−0.558299	−	1.71827i	−0.687067	−	0.726594i	$-0.741102\pi$
$607$	−13.7550	−	42.3336i	−0.558299	−	1.71827i	0.128768	−	0.991675i	$-0.458898\pi$
$608$		0			0
$609$	−40.0005	+	29.0621i	−1.62090	+	1.17766i
$610$		0			0
$611$	−1.47176	+	4.52960i	−0.0595409	+	0.183248i
$612$		0			0
$613$	−21.0786	+	15.3145i	−0.851355	+	0.618546i	−0.925519	−	0.378700i	$-0.876371\pi$
$613$	−21.0786	+	15.3145i	−0.851355	+	0.618546i	0.0741641	+	0.997246i	$0.476371\pi$
$614$		0			0
$615$	18.2101	−	10.7486i	0.734302	−	0.433425i
$616$		0			0
$617$	−31.5386	+	22.9142i	−1.26970	+	0.922489i	−0.999191	−	0.0402285i	$-0.987191\pi$
$617$	−31.5386	+	22.9142i	−1.26970	+	0.922489i	−0.270507	+	0.962718i	$0.587191\pi$
$618$		0			0
$619$	7.32585	−	22.5467i	0.294451	−	0.906227i	−0.688954	−	0.724805i	$-0.741930\pi$
$619$	7.32585	−	22.5467i	0.294451	−	0.906227i	0.983405	−	0.181422i	$-0.0580700\pi$
$620$		0			0
$621$	−11.5754	+	8.41000i	−0.464504	+	0.337482i
$622$		0			0
$623$	11.2109	+	34.5036i	0.449155	+	1.38236i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$		0			0
$627$	3.64661	−	11.2231i	0.145631	−	0.448207i
$628$		0			0
$629$	1.35039			0.0538435
$630$		0			0
$631$	38.9150	+	28.2734i	1.54918	+	1.12555i	0.944230	+	0.329286i	$0.106808\pi$
$631$	38.9150	+	28.2734i	1.54918	+	1.12555i	0.604953	+	0.796262i	$0.293192\pi$
$632$		0			0
$633$	−16.8017	+	12.2072i	−0.667809	+	0.485192i
$634$		0			0
$635$	9.91165	+	7.20123i	0.393332	+	0.285772i
$636$		0			0
$637$	−3.29482	−	2.39383i	−0.130545	−	0.0948468i
$638$		0			0
$639$	−2.36759	−	7.28670i	−0.0936605	−	0.288257i
$640$		0			0
$641$	1.80300	−	5.54907i	0.0712144	−	0.219175i	−0.909115	−	0.416546i	$-0.863240\pi$
$641$	1.80300	−	5.54907i	0.0712144	−	0.219175i	0.980329	+	0.197371i	$0.0632404\pi$
$642$		0			0
$643$	33.0871	−	24.0392i	1.30483	−	0.948014i	0.304839	−	0.952404i	$-0.401397\pi$
$643$	33.0871	−	24.0392i	1.30483	−	0.948014i	0.999990	+	0.00438945i	$0.00139721\pi$
$644$		0			0
$645$	−0.287422	−	0.884594i	−0.0113172	−	0.0348308i
$646$		0			0
$647$	−36.1489			−1.42116			−0.710581	−	0.703616i	$-0.751568\pi$
$647$	−36.1489			−1.42116			−0.710581	+	0.703616i	$0.751568\pi$
$648$		0			0
$649$	6.30628	+	4.58178i	0.247543	+	0.179851i
$650$		0			0
$651$	−21.4468	+	66.0063i	−0.840565	+	2.58699i
$652$		0			0
$653$	−4.01574			−0.157148			−0.0785740	−	0.996908i	$-0.525037\pi$
$653$	−4.01574			−0.157148			−0.0785740	+	0.996908i	$0.525037\pi$
$654$		0			0
$655$	−8.99174			−0.351336
$656$		0			0
$657$	−41.2043			−1.60753
$658$		0			0
$659$	−14.8327			−0.577800			−0.288900	−	0.957359i	$-0.593290\pi$
$659$	−14.8327			−0.577800			−0.288900	+	0.957359i	$0.593290\pi$
$660$		0			0
$661$	7.41044	−	22.8070i	0.288233	−	0.887089i	−0.697178	−	0.716898i	$-0.745561\pi$
$661$	7.41044	−	22.8070i	0.288233	−	0.887089i	0.985411	−	0.170191i	$-0.0544386\pi$
$662$		0			0
$663$	16.9339	+	12.3032i	0.657660	+	0.477818i
$664$		0			0
$665$	−5.04587			−0.195670
$666$		0			0
$667$	1.89245	+	5.82435i	0.0732758	+	0.225520i
$668$		0			0
$669$	36.3548	−	26.4133i	1.40556	−	1.02120i
$670$		0			0
$671$	0.988715	−	3.04295i	0.0381689	−	0.117472i
$672$		0			0
$673$	−6.55118	−	20.1625i	−0.252529	−	0.777205i	−0.994306	−	0.106559i	$-0.966017\pi$
$673$	−6.55118	−	20.1625i	−0.252529	−	0.777205i	0.741777	−	0.670647i	$-0.233983\pi$
$674$		0			0
$675$	13.1069	+	9.52275i	0.504486	+	0.366531i
$676$		0			0
$677$	−5.69162	−	4.13520i	−0.218747	−	0.158929i	0.473016	−	0.881054i	$-0.343165\pi$
$677$	−5.69162	−	4.13520i	−0.218747	−	0.158929i	−0.691762	+	0.722125i	$0.743165\pi$
$678$		0			0
$679$	22.3283	−	16.2224i	0.856880	−	0.622560i
$680$		0			0
$681$	−10.4833	−	7.61658i	−0.401722	−	0.291868i
$682$		0			0
$683$	−2.70453			−0.103486			−0.0517430	−	0.998660i	$-0.516478\pi$
$683$	−2.70453			−0.103486			−0.0517430	+	0.998660i	$0.516478\pi$
$684$		0			0
$685$	−2.91235	+	8.96328i	−0.111275	+	0.342469i
$686$		0			0
$687$	−3.80013	−	11.6956i	−0.144984	−	0.446214i
$688$		0			0
$689$	6.15789	+	18.9520i	0.234597	+	0.722015i
$690$		0			0
$691$	−20.1820	+	14.6631i	−0.767758	+	0.557809i	−0.901280	−	0.433237i	$-0.857371\pi$
$691$	−20.1820	+	14.6631i	−0.767758	+	0.557809i	0.133522	+	0.991046i	$0.457371\pi$
$692$		0			0
$693$	−8.06519	+	24.8221i	−0.306371	+	0.942913i
$694$		0			0
$695$	14.3417	−	10.4198i	0.544010	−	0.395246i
$696$		0			0
$697$	9.27242	−	21.3776i	0.351218	−	0.809734i
$698$		0			0
$699$	−0.0398611	+	0.0289608i	−0.00150769	+	0.00109540i
$700$		0			0
$701$	0.246251	−	0.757884i	0.00930079	−	0.0286249i	−0.946298	−	0.323294i	$-0.895210\pi$
$701$	0.246251	−	0.757884i	0.00930079	−	0.0286249i	0.955599	+	0.294670i	$0.0952096\pi$
$702$		0			0
$703$	0.701586	−	0.509732i	0.0264608	−	0.0192249i
$704$		0			0
$705$	2.79058	+	8.58852i	0.105099	+	0.323463i
$706$		0			0
$707$	−4.59831	−	14.1521i	−0.172937	−	0.532246i
$708$		0			0
$709$	−13.8822	+	42.7251i	−0.521358	+	1.60457i	0.250050	+	0.968233i	$0.419553\pi$
$709$	−13.8822	+	42.7251i	−0.521358	+	1.60457i	−0.771408	+	0.636341i	$0.780447\pi$
$710$		0			0
$711$	102.049			3.82712
$712$		0			0
$713$	6.95456	+	5.05278i	0.260450	+	0.189228i
$714$		0			0
$715$	2.15447	−	1.56532i	0.0805727	−	0.0585395i
$716$		0			0
$717$	−50.2877	−	36.5362i	−1.87803	−	1.36447i
$718$		0			0
$719$	4.13794	+	3.00639i	0.154319	+	0.112120i	0.662265	−	0.749269i	$-0.269595\pi$
$719$	4.13794	+	3.00639i	0.154319	+	0.112120i	−0.507946	+	0.861389i	$0.669595\pi$
$720$		0			0
$721$	−10.4226	−	32.0774i	−0.388157	−	1.19462i
$722$		0			0
$723$	1.42139	−	4.37460i	0.0528622	−	0.162693i
$724$		0			0
$725$	5.61002	−	4.07592i	0.208351	−	0.151376i
$726$		0			0
$727$	4.98964	+	15.3565i	0.185055	+	0.569542i	0.999949	−	0.0100681i	$-0.00320484\pi$
$727$	4.98964	+	15.3565i	0.185055	+	0.569542i	−0.814894	+	0.579610i	$0.803205\pi$
$728$		0			0
$729$	74.9673			2.77657
$730$		0			0
$731$	−0.829211	−	0.602457i	−0.0306695	−	0.0222827i
$732$		0			0
$733$	−0.442215	+	1.36100i	−0.0163336	+	0.0502696i	−0.958891	−	0.283774i	$-0.908413\pi$
$733$	−0.442215	+	1.36100i	−0.0163336	+	0.0502696i	0.942558	+	0.334044i	$0.108413\pi$
$734$		0			0
$735$	−7.72205			−0.284832
$736$		0			0
$737$	11.3778			0.419106
$738$		0			0
$739$	41.8742			1.54037			0.770184	−	0.637822i	$-0.220164\pi$
$739$	41.8742			1.54037			0.770184	+	0.637822i	$0.220164\pi$
$740$		0			0
$741$	13.4420			0.493806
$742$		0			0
$743$	−0.527711	+	1.62413i	−0.0193598	+	0.0595835i	−0.960270	−	0.279074i	$-0.909973\pi$
$743$	−0.527711	+	1.62413i	−0.0193598	+	0.0595835i	0.940910	+	0.338657i	$0.109973\pi$
$744$		0			0
$745$	1.79917	+	1.30718i	0.0659166	+	0.0478912i
$746$		0			0
$747$	−113.919			−4.16808
$748$		0			0
$749$	−12.9591	−	39.8840i	−0.473515	−	1.45733i
$750$		0			0
$751$	−17.6645	+	12.8340i	−0.644585	+	0.468319i	−0.861422	−	0.507889i	$-0.830426\pi$
$751$	−17.6645	+	12.8340i	−0.644585	+	0.468319i	0.216837	+	0.976208i	$0.430426\pi$
$752$		0			0
$753$	23.3696	−	71.9243i	0.851636	−	2.62107i
$754$		0			0
$755$	2.36824	+	7.28868i	0.0861889	+	0.265262i
$756$		0			0
$757$	−35.8170	−	26.0226i	−1.30179	−	0.945808i	−0.301821	−	0.953364i	$-0.597595\pi$
$757$	−35.8170	−	26.0226i	−1.30179	−	0.945808i	−0.999971	+	0.00755667i	$0.997595\pi$
$758$		0			0
$759$	3.60772	+	2.62116i	0.130952	+	0.0951423i
$760$		0			0
$761$	−15.8661	+	11.5274i	−0.575145	+	0.417867i	−0.836971	−	0.547248i	$-0.815675\pi$
$761$	−15.8661	+	11.5274i	−0.575145	+	0.417867i	0.261826	+	0.965115i	$0.415675\pi$
$762$		0			0
$763$	21.9857	+	15.9735i	0.795936	+	0.578281i
$764$		0			0
$765$	28.7705			1.04020
$766$		0			0
$767$	−2.74383	+	8.44464i	−0.0990739	+	0.304918i
$768$		0			0
$769$	−3.24291	−	9.98065i	−0.116942	−	0.359911i	0.875405	−	0.483390i	$-0.160595\pi$
$769$	−3.24291	−	9.98065i	−0.116942	−	0.359911i	−0.992347	+	0.123479i	$0.960595\pi$
$770$		0			0
$771$	−12.0887	−	37.2050i	−0.435362	−	1.33991i
$772$		0			0
$773$	−30.6579	+	22.2743i	−1.10269	+	0.801150i	−0.981497	−	0.191479i	$-0.938672\pi$
$773$	−30.6579	+	22.2743i	−1.10269	+	0.801150i	−0.121192	+	0.992629i	$0.538672\pi$
$774$		0			0
$775$	3.00788	−	9.25730i	0.108046	−	0.332532i
$776$		0			0
$777$	−2.14051	+	1.55517i	−0.0767904	+	0.0557915i
$778$		0			0
$779$	−3.25199	−	14.6067i	−0.116514	−	0.523338i
$780$		0			0
$781$	−1.19880	+	0.870978i	−0.0428964	+	0.0311660i
$782$		0			0
$783$	34.7163	−	106.846i	1.24066	−	3.81835i
$784$		0			0
$785$	10.7856	−	7.83620i	0.384955	−	0.279686i
$786$		0			0
$787$	−1.24088	−	3.81902i	−0.0442324	−	0.136133i	0.926501	−	0.376291i	$-0.122801\pi$
$787$	−1.24088	−	3.81902i	−0.0442324	−	0.136133i	−0.970734	+	0.240158i	$0.922801\pi$
$788$		0			0
$789$	−27.7051	−	85.2675i	−0.986327	−	3.03560i
$790$		0			0
$791$	9.84804	−	30.3091i	0.350156	−	1.07767i
$792$		0			0
$793$	3.64458			0.129423
$794$		0			0
$795$	30.5679	+	22.2089i	1.08413	+	0.787668i
$796$		0			0
$797$	40.8885	−	29.7072i	1.44835	−	1.05228i	0.462131	−	0.886811i	$-0.347085\pi$
$797$	40.8885	−	29.7072i	1.44835	−	1.05228i	0.986214	−	0.165473i	$-0.0529152\pi$
$798$		0			0
$799$	8.05081	+	5.84926i	0.284817	+	0.206932i
$800$		0			0
$801$	−107.471	−	78.0825i	−3.79731	−	2.75891i
$802$		0			0
$803$	2.46257	+	7.57902i	0.0869023	+	0.267458i
$804$		0			0
$805$	0.589234	−	1.81348i	0.0207678	−	0.0639166i
$806$		0			0
$807$	72.1445	−	52.4161i	2.53961	−	1.84513i
$808$		0			0
$809$	−0.987386	−	3.03886i	−0.0347147	−	0.106841i	0.932198	−	0.361949i	$-0.117889\pi$
$809$	−0.987386	−	3.03886i	−0.0347147	−	0.106841i	−0.966912	+	0.255109i	$0.917889\pi$
$810$		0			0
$811$	11.9643			0.420124			0.210062	−	0.977688i	$-0.432633\pi$
$811$	11.9643			0.420124			0.210062	+	0.977688i	$0.432633\pi$
$812$		0			0
$813$	6.12459	+	4.44977i	0.214799	+	0.156060i
$814$		0			0
$815$	−4.13729	+	12.7333i	−0.144923	+	0.446027i
$816$		0			0
$817$	−0.658222			−0.0230283
$818$		0			0
$819$	−29.7297			−1.03884
$820$		0			0
$821$	41.0569			1.43289			0.716447	−	0.697641i	$-0.245767\pi$
$821$	41.0569			1.43289			0.716447	+	0.697641i	$0.245767\pi$
$822$		0			0
$823$	51.8741			1.80822			0.904109	−	0.427302i	$-0.140536\pi$
$823$	51.8741			1.80822			0.904109	+	0.427302i	$0.140536\pi$
$824$		0			0
$825$	1.56036	−	4.80229i	0.0543247	−	0.167194i
$826$		0			0
$827$	36.6611	+	26.6359i	1.27483	+	0.926220i	0.999384	−	0.0350960i	$-0.0111737\pi$
$827$	36.6611	+	26.6359i	1.27483	+	0.926220i	0.275448	+	0.961316i	$0.411174\pi$
$828$		0			0
$829$	19.3744			0.672900			0.336450	−	0.941701i	$-0.390774\pi$
$829$	19.3744			0.672900			0.336450	+	0.941701i	$0.390774\pi$
$830$		0			0
$831$	−3.76564	−	11.5895i	−0.130629	−	0.402034i
$832$		0			0
$833$	−6.88430	+	5.00174i	−0.238527	+	0.173300i
$834$		0			0
$835$	5.03811	−	15.5057i	0.174351	−	0.536597i
$836$		0			0
$837$	−48.7309	−	149.978i	−1.68438	−	5.18400i
$838$		0			0
$839$	13.2915	+	9.65683i	0.458873	+	0.333391i	0.793089	−	0.609106i	$-0.208472\pi$
$839$	13.2915	+	9.65683i	0.458873	+	0.333391i	−0.334216	+	0.942496i	$0.608472\pi$
$840$		0			0
$841$	−15.4405	−	11.2182i	−0.532431	−	0.386834i
$842$		0			0
$843$	11.7681	−	8.55004i	0.405316	−	0.294479i
$844$		0			0
$845$	−8.06308	−	5.85817i	−0.277378	−	0.201527i
$846$		0			0
$847$	−18.7023			−0.642619
$848$		0			0
$849$	22.0547	−	67.8775i	0.756917	−	2.32955i
$850$		0			0
$851$	0.101269	+	0.311673i	0.00347144	+	0.0106840i
$852$		0			0
$853$	1.98453	+	6.10774i	0.0679489	+	0.209125i	0.979265	−	0.202581i	$-0.0649330\pi$
$853$	1.98453	+	6.10774i	0.0679489	+	0.209125i	−0.911317	+	0.411706i	$0.864933\pi$
$854$		0			0
$855$	14.9476	−	10.8600i	0.511196	−	0.371406i
$856$		0			0
$857$	−9.41222	+	28.9678i	−0.321515	+	0.989522i	0.651474	+	0.758671i	$0.274151\pi$
$857$	−9.41222	+	28.9678i	−0.321515	+	0.989522i	−0.972989	+	0.230851i	$0.925849\pi$
$858$		0			0
$859$	20.1980	−	14.6747i	0.689148	−	0.500695i	−0.187232	−	0.982316i	$-0.559952\pi$
$859$	20.1980	−	14.6747i	0.689148	−	0.500695i	0.876380	+	0.481621i	$0.159952\pi$
$860$		0			0
$861$	9.92168	+	44.5644i	0.338130	+	1.51875i
$862$		0			0
$863$	16.7062	−	12.1378i	0.568687	−	0.413175i	−0.265941	−	0.963989i	$-0.585683\pi$
$863$	16.7062	−	12.1378i	0.568687	−	0.413175i	0.834628	+	0.550814i	$0.185683\pi$
$864$		0			0
$865$	−2.85261	+	8.77943i	−0.0969916	+	0.298509i
$866$		0			0
$867$	−10.0365	+	7.29197i	−0.340859	+	0.247648i
$868$		0			0
$869$	−6.09892	−	18.7706i	−0.206892	−	0.636747i
$870$		0			0
$871$	4.00496	+	12.3260i	0.135703	+	0.417651i
$872$		0			0
$873$	−31.2289	+	96.1126i	−1.05694	+	3.25292i
$874$		0			0
$875$	−2.15909			−0.0729907
$876$		0			0
$877$	15.2406	+	11.0729i	0.514638	+	0.373906i	0.814580	−	0.580051i	$-0.196967\pi$
$877$	15.2406	+	11.0729i	0.514638	+	0.373906i	−0.299942	+	0.953957i	$0.596967\pi$
$878$		0			0
$879$	−35.8352	+	26.0358i	−1.20869	+	0.878166i
$880$		0			0
$881$	8.44150	+	6.13311i	0.284401	+	0.206630i	0.720835	−	0.693107i	$-0.243759\pi$
$881$	8.44150	+	6.13311i	0.284401	+	0.206630i	−0.436434	+	0.899736i	$0.643759\pi$
$882$		0			0
$883$	−41.5213	−	30.1670i	−1.39730	−	1.01520i	−0.995019	−	0.0996867i	$-0.968216\pi$
$883$	−41.5213	−	30.1670i	−1.39730	−	1.01520i	−0.402285	−	0.915514i	$-0.631784\pi$
$884$		0			0
$885$	5.20254	+	16.0118i	0.174882	+	0.538230i
$886$		0			0
$887$	−10.4581	+	32.1866i	−0.351147	+	1.08072i	0.607063	+	0.794654i	$0.292348\pi$
$887$	−10.4581	+	32.1866i	−0.351147	+	1.08072i	−0.958210	+	0.286066i	$0.907652\pi$
$888$		0			0
$889$	−21.4002	+	15.5481i	−0.717739	+	0.521468i
$890$		0			0
$891$	−14.0731	−	43.3126i	−0.471467	−	1.45103i
$892$		0			0
$893$	6.39068			0.213856
$894$		0			0
$895$	−3.47137	−	2.52210i	−0.116035	−	0.0843046i
$896$		0			0
$897$	−1.56970	+	4.83104i	−0.0524108	+	0.161304i
$898$		0			0
$899$	−67.4971			−2.25115
$900$		0			0
$901$	41.6369			1.38713
$902$		0			0
$903$	2.00821			0.0668290
$904$		0			0
$905$	−6.36009			−0.211417
$906$		0			0
$907$	3.65077	−	11.2359i	0.121222	−	0.373082i	−0.871972	−	0.489556i	$-0.837159\pi$
$907$	3.65077	−	11.2359i	0.121222	−	0.373082i	0.993194	+	0.116474i	$0.0371590\pi$
$908$		0			0
$909$	44.0809	+	32.0266i	1.46207	+	1.06226i
$910$		0			0
$911$	−10.6555			−0.353033			−0.176516	−	0.984298i	$-0.556483\pi$
$911$	−10.6555			−0.353033			−0.176516	+	0.984298i	$0.556483\pi$
$912$		0			0
$913$	6.80835	+	20.9540i	0.225324	+	0.693475i
$914$		0			0
$915$	5.59067	−	4.06186i	0.184822	−	0.134281i
$916$		0			0
$917$	5.99926	−	18.4638i	0.198113	−	0.609729i
$918$		0			0
$919$	6.72826	+	20.7075i	0.221945	+	0.683076i	0.998587	+	0.0531345i	$0.0169212\pi$
$919$	6.72826	+	20.7075i	0.221945	+	0.683076i	−0.776642	+	0.629942i	$0.783079\pi$
$920$		0			0
$921$	29.0082	+	21.0757i	0.955853	+	0.694468i
$922$		0			0
$923$	−1.36554	−	0.992124i	−0.0449473	−	0.0326562i
$924$		0			0
$925$	0.300204	−	0.218111i	0.00987065	−	0.00717144i
$926$		0			0
$927$	99.9141	+	72.5918i	3.28161	+	2.38423i
$928$		0			0
$929$	−47.4688			−1.55740			−0.778700	−	0.627397i	$-0.784120\pi$
$929$	−47.4688			−1.55740			−0.778700	+	0.627397i	$0.784120\pi$
$930$		0			0
$931$	−1.68869	+	5.19725i	−0.0553445	+	0.170333i
$932$		0			0
$933$	−28.8226	−	88.7069i	−0.943610	−	2.90413i
$934$		0			0
$935$	−1.71947	−	5.29198i	−0.0562326	−	0.173066i
$936$		0			0
$937$	−8.65163	+	6.28578i	−0.282636	+	0.205347i	−0.720067	−	0.693905i	$-0.755889\pi$
$937$	−8.65163	+	6.28578i	−0.282636	+	0.205347i	0.437430	+	0.899252i	$0.355889\pi$
$938$		0			0
$939$	−9.42398	+	29.0040i	−0.307540	+	0.946511i
$940$		0			0
$941$	18.0296	−	13.0993i	0.587748	−	0.427024i	−0.253761	−	0.967267i	$-0.581668\pi$
$941$	18.0296	−	13.0993i	0.587748	−	0.427024i	0.841509	+	0.540243i	$0.181668\pi$
$942$		0			0
$943$	5.62936	+	0.536944i	0.183317	+	0.0174853i
$944$		0			0
$945$	−28.2991	+	20.5605i	−0.920570	+	0.668833i
$946$		0			0
$947$	−8.76722	+	26.9827i	−0.284896	+	0.876821i	0.701533	+	0.712637i	$0.252499\pi$
$947$	−8.76722	+	26.9827i	−0.284896	+	0.876821i	−0.986430	+	0.164184i	$0.947501\pi$
$948$		0			0
$949$	−7.34384	+	5.33561i	−0.238391	+	0.173201i
$950$		0			0
$951$	−9.59321	−	29.5249i	−0.311081	−	0.957409i
$952$		0			0
$953$	2.22591	+	6.85064i	0.0721042	+	0.221914i	0.980614	−	0.195950i	$-0.0627789\pi$
$953$	2.22591	+	6.85064i	0.0721042	+	0.221914i	−0.908510	+	0.417864i	$0.862779\pi$
$954$		0			0
$955$	5.34605	−	16.4535i	0.172994	−	0.532421i
$956$		0			0
$957$	−35.0146			−1.13186
$958$		0			0
$959$	−16.4623	−	11.9605i	−0.531594	−	0.386226i
$960$		0			0
$961$	−51.5708	+	37.4684i	−1.66357	+	1.20866i
$962$		0			0
$963$	124.230	+	90.2584i	4.00326	+	2.90854i
$964$		0			0
$965$	15.3154	+	11.1273i	0.493021	+	0.358201i
$966$		0			0
$967$	3.94717	+	12.1482i	0.126933	+	0.390658i	0.994248	−	0.107100i	$-0.0341566\pi$
$967$	3.94717	+	12.1482i	0.126933	+	0.390658i	−0.867316	+	0.497759i	$0.834157\pi$
$968$		0			0
$969$	8.67913	−	26.7116i	0.278814	−	0.858100i
$970$		0			0
$971$	35.2456	−	25.6074i	1.13109	−	0.821782i	0.145233	−	0.989397i	$-0.453607\pi$
$971$	35.2456	−	25.6074i	1.13109	−	0.821782i	0.985852	+	0.167616i	$0.0536067\pi$
$972$		0			0
$973$	11.8276	+	36.4015i	0.379175	+	1.16698i
$974$		0			0
$975$	5.75176			0.184204
$976$		0			0
$977$	6.92773	+	5.03329i	0.221638	+	0.161029i	0.693064	−	0.720877i	$-0.256261\pi$
$977$	6.92773	+	5.03329i	0.221638	+	0.161029i	−0.471426	+	0.881906i	$0.656261\pi$
$978$		0			0
$979$	−7.93928	+	24.4346i	−0.253741	+	0.780933i
$980$		0			0
$981$	−99.5083			−3.17706
$982$		0			0
$983$	−30.1015			−0.960089			−0.480044	−	0.877244i	$-0.659379\pi$
$983$	−30.1015			−0.960089			−0.480044	+	0.877244i	$0.659379\pi$
$984$		0			0
$985$	−14.7108			−0.468725
$986$		0			0
$987$	−19.4977			−0.620619
$988$		0			0
$989$	0.0768642	−	0.236564i	0.00244414	−	0.00752228i
$990$		0			0
$991$	−45.2272	−	32.8595i	−1.43669	−	1.04382i	−0.988722	−	0.149765i	$-0.952148\pi$
$991$	−45.2272	−	32.8595i	−1.43669	−	1.04382i	−0.447967	−	0.894050i	$-0.647852\pi$
$992$		0			0
$993$	−95.8799			−3.04266
$994$		0			0
$995$	1.10032	+	3.38642i	0.0348824	+	0.107357i
$996$		0			0
$997$	24.5313	−	17.8230i	0.776915	−	0.564462i	−0.127137	−	0.991885i	$-0.540579\pi$
$997$	24.5313	−	17.8230i	0.776915	−	0.564462i	0.904051	+	0.427424i	$0.140579\pi$
$998$		0			0
$999$	1.85774	−	5.71753i	0.0587763	−	0.180895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.u.b.201.1	✓	32
41.10	even	5	inner	820.2.u.b.461.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.u.b.201.1	✓	32	1.1	even	1	trivial
820.2.u.b.461.1	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)

\(f(q)\)	\(=\)	\(q-3.30240 q^{3} +(-0.309017 + 0.951057i) q^{5} +(-1.74674 - 1.26908i) q^{7} +7.90585 q^{9} +(-0.472492 - 1.45418i) q^{11} +(1.40906 - 1.02374i) q^{13} +(1.02050 - 3.14077i) q^{15} +(-1.12456 - 3.46103i) q^{17} +(-1.89070 - 1.37367i) q^{19} +(5.76845 + 4.19102i) q^{21} +(0.714482 - 0.519102i) q^{23} +(-0.809017 - 0.587785i) q^{25} -16.2011 q^{27} +(-2.14284 + 6.59498i) q^{29} +(3.00788 + 9.25730i) q^{31} +(1.56036 + 4.80229i) q^{33} +(1.74674 - 1.26908i) q^{35} +(-0.114668 + 0.352911i) q^{37} +(-4.65327 + 3.38080i) q^{39} +(4.79946 + 4.23853i) q^{41} +(0.227859 - 0.165549i) q^{43} +(-2.44304 + 7.51891i) q^{45} +(-2.21228 + 1.60732i) q^{47} +(-0.722579 - 2.22387i) q^{49} +(3.71374 + 11.4297i) q^{51} +(-3.53558 + 10.8814i) q^{53} +1.52902 q^{55} +(6.24384 + 4.53642i) q^{57} +(-4.12440 + 2.99656i) q^{59} +(1.69291 + 1.22997i) q^{61} +(-13.8095 - 10.0332i) q^{63} +(0.538212 + 1.65645i) q^{65} +(-2.29947 + 7.07704i) q^{67} +(-2.35951 + 1.71428i) q^{69} +(-0.299474 - 0.921685i) q^{71} -5.21188 q^{73} +(2.67170 + 1.94110i) q^{75} +(-1.02015 + 3.13971i) q^{77} +12.9080 q^{79} +29.7849 q^{81} -14.4095 q^{83} +3.63915 q^{85} +(7.07651 - 21.7793i) q^{87} +(-13.5939 - 9.87655i) q^{89} -3.76047 q^{91} +(-9.93322 - 30.5713i) q^{93} +(1.89070 - 1.37367i) q^{95} +(-3.95010 + 12.1572i) q^{97} +(-3.73545 - 11.4965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) \) 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

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