LMFDB - Embedded newform 820.2.u.a.201.6

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 = [24] 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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.6
Character	$\chi$	$=$	820.201
Dual form			820.2.u.a.461.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.07771 q^{3} +(0.309017 - 0.951057i) q^{5} +(-2.25264 - 1.63664i) q^{7} +6.47232 q^{9} +(-1.30935 - 4.02977i) q^{11} +(-0.246061 + 0.178774i) q^{13} +(0.951066 - 2.92708i) q^{15} +(-1.50621 - 4.63563i) q^{17} +(6.63495 + 4.82057i) q^{19} +(-6.93298 - 5.03710i) q^{21} +(1.47271 - 1.06999i) q^{23} +(-0.809017 - 0.587785i) q^{25} +10.6868 q^{27} +(-0.727875 + 2.24017i) q^{29} +(1.34569 + 4.14160i) q^{31} +(-4.02981 - 12.4025i) q^{33} +(-2.25264 + 1.63664i) q^{35} +(-1.44758 + 4.45520i) q^{37} +(-0.757304 + 0.550214i) q^{39} +(6.32912 + 0.970675i) q^{41} +(3.39125 - 2.46389i) q^{43} +(2.00006 - 6.15554i) q^{45} +(-2.72993 + 1.98341i) q^{47} +(0.232682 + 0.716122i) q^{49} +(-4.63567 - 14.2671i) q^{51} +(-2.92668 + 9.00740i) q^{53} -4.23715 q^{55} +(20.4205 + 14.8363i) q^{57} +(-7.93983 + 5.76862i) q^{59} +(1.89333 + 1.37558i) q^{61} +(-14.5798 - 10.5928i) q^{63} +(0.0939869 + 0.289262i) q^{65} +(-2.11143 + 6.49831i) q^{67} +(4.53258 - 3.29311i) q^{69} +(1.55188 + 4.77620i) q^{71} -11.5986 q^{73} +(-2.48992 - 1.80903i) q^{75} +(-3.64578 + 11.2206i) q^{77} -11.1197 q^{79} +13.4739 q^{81} +9.74140 q^{83} -4.87419 q^{85} +(-2.24019 + 6.89460i) q^{87} +(4.05088 + 2.94313i) q^{89} +0.846874 q^{91} +(4.14164 + 12.7466i) q^{93} +(6.63495 - 4.82057i) q^{95} +(0.935472 - 2.87909i) q^{97} +(-8.47453 - 26.0819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} - 6 q^{5} + 5 q^{7} + 18 q^{9} - 7 q^{11} - 5 q^{13} + 2 q^{15} + 3 q^{17} - q^{19} + 2 q^{21} + 20 q^{23} - 6 q^{25} + 20 q^{27} - 15 q^{29} - q^{31} - 6 q^{33} + 5 q^{35} + q^{37} + 28 q^{41}+ \cdots + 34 q^{99}+O(q^{100}) $ 24 * q + 2 * q^3 - 6 * q^5 + 5 * q^7 + 18 * q^9 - 7 * q^11 - 5 * q^13 + 2 * q^15 + 3 * q^17 - q^19 + 2 * q^21 + 20 * q^23 - 6 * q^25 + 20 * q^27 - 15 * q^29 - q^31 - 6 * q^33 + 5 * q^35 + q^37 + 28 * q^41 - 4 * q^43 + 3 * q^45 + 3 * q^47 + 3 * q^49 + 37 * q^51 + 29 * q^53 - 12 * q^55 + 17 * q^57 - 4 * q^59 - 14 * q^61 - 10 * q^63 + 5 * q^65 - 14 * q^67 - 26 * q^69 + q^71 - 84 * q^73 - 3 * q^75 + 24 * q^77 + 18 * q^79 - 40 * q^81 - 6 * q^83 - 12 * q^85 + 39 * q^87 + 12 * q^89 - 2 * q^91 - 58 * q^93 - q^95 - 20 * q^97 + 34 * 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
$3$	3.07771			1.77692			0.888459	−	0.458956i	$-0.151776\pi$
$3$	3.07771			1.77692			0.888459	+	0.458956i	$0.151776\pi$
$4$		0			0
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$		0			0
$7$	−2.25264	−	1.63664i	−0.851418	−	0.618591i	0.0741187	−	0.997249i	$-0.476386\pi$
$7$	−2.25264	−	1.63664i	−0.851418	−	0.618591i	−0.925537	+	0.378658i	$0.876386\pi$
$8$		0			0
$9$	6.47232			2.15744
$10$		0			0
$11$	−1.30935	−	4.02977i	−0.394784	−	1.21502i	−0.929130	−	0.369754i	$-0.879442\pi$
$11$	−1.30935	−	4.02977i	−0.394784	−	1.21502i	0.534345	−	0.845266i	$-0.320558\pi$
$12$		0			0
$13$	−0.246061	+	0.178774i	−0.0682450	+	0.0495829i	−0.621385	−	0.783506i	$-0.713430\pi$
$13$	−0.246061	+	0.178774i	−0.0682450	+	0.0495829i	0.553140	+	0.833089i	$0.313430\pi$
$14$		0			0
$15$	0.951066	−	2.92708i	0.245564	−	0.755769i
$16$		0			0
$17$	−1.50621	−	4.63563i	−0.365309	−	1.12430i	−0.949787	−	0.312896i	$-0.898701\pi$
$17$	−1.50621	−	4.63563i	−0.365309	−	1.12430i	0.584479	−	0.811409i	$-0.301299\pi$
$18$		0			0
$19$	6.63495	+	4.82057i	1.52216	+	1.10591i	0.960404	+	0.278613i	$0.0898746\pi$
$19$	6.63495	+	4.82057i	1.52216	+	1.10591i	0.561757	+	0.827302i	$0.310125\pi$
$20$		0			0
$21$	−6.93298	−	5.03710i	−1.51290	−	1.09919i
$22$		0			0
$23$	1.47271	−	1.06999i	0.307081	−	0.223108i	−0.423562	−	0.905867i	$-0.639220\pi$
$23$	1.47271	−	1.06999i	0.307081	−	0.223108i	0.730643	+	0.682760i	$0.239220\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$		0			0
$27$	10.6868			2.05667
$28$		0			0
$29$	−0.727875	+	2.24017i	−0.135163	+	0.415989i	−0.995615	−	0.0935419i	$-0.970181\pi$
$29$	−0.727875	+	2.24017i	−0.135163	+	0.415989i	0.860452	+	0.509531i	$0.170181\pi$
$30$		0			0
$31$	1.34569	+	4.14160i	0.241692	+	0.743853i	0.996163	+	0.0875188i	$0.0278938\pi$
$31$	1.34569	+	4.14160i	0.241692	+	0.743853i	−0.754470	+	0.656334i	$0.772106\pi$
$32$		0			0
$33$	−4.02981	−	12.4025i	−0.701499	−	2.15899i
$34$		0			0
$35$	−2.25264	+	1.63664i	−0.380766	+	0.276642i
$36$		0			0
$37$	−1.44758	+	4.45520i	−0.237981	+	0.732430i	0.758731	+	0.651404i	$0.225820\pi$
$37$	−1.44758	+	4.45520i	−0.237981	+	0.732430i	−0.996712	+	0.0810257i	$0.974180\pi$
$38$		0			0
$39$	−0.757304	+	0.550214i	−0.121266	+	0.0881047i
$40$		0			0
$41$	6.32912	+	0.970675i	0.988443	+	0.151594i
$41$	6.32912	+	0.970675i	0.988443	+	0.151594i
$42$		0			0
$43$	3.39125	−	2.46389i	0.517161	−	0.375740i	−0.298372	−	0.954450i	$-0.596444\pi$
$43$	3.39125	−	2.46389i	0.517161	−	0.375740i	0.815533	+	0.578710i	$0.196444\pi$
$44$		0			0
$45$	2.00006	−	6.15554i	0.298151	−	0.917614i
$46$		0			0
$47$	−2.72993	+	1.98341i	−0.398201	+	0.289310i	−0.768808	−	0.639480i	$-0.779150\pi$
$47$	−2.72993	+	1.98341i	−0.398201	+	0.289310i	0.370607	+	0.928790i	$0.379150\pi$
$48$		0			0
$49$	0.232682	+	0.716122i	0.0332403	+	0.102303i
$50$		0			0
$51$	−4.63567	−	14.2671i	−0.649124	−	1.99780i
$52$		0			0
$53$	−2.92668	+	9.00740i	−0.402011	+	1.23726i	0.521355	+	0.853340i	$0.325427\pi$
$53$	−2.92668	+	9.00740i	−0.402011	+	1.23726i	−0.923366	+	0.383922i	$0.874573\pi$
$54$		0			0
$55$	−4.23715			−0.571337
$56$		0			0
$57$	20.4205	+	14.8363i	2.70476	+	1.96512i
$58$		0			0
$59$	−7.93983	+	5.76862i	−1.03368	+	0.751011i	−0.969041	−	0.246898i	$-0.920589\pi$
$59$	−7.93983	+	5.76862i	−1.03368	+	0.751011i	−0.0646363	+	0.997909i	$0.520589\pi$
$60$		0			0
$61$	1.89333	+	1.37558i	0.242416	+	0.176125i	0.702359	−	0.711823i	$-0.252130\pi$
$61$	1.89333	+	1.37558i	0.242416	+	0.176125i	−0.459943	+	0.887948i	$0.652130\pi$
$62$		0			0
$63$	−14.5798	−	10.5928i	−1.83688	−	1.33457i
$64$		0			0
$65$	0.0939869	+	0.289262i	0.0116576	+	0.0358785i
$66$		0			0
$67$	−2.11143	+	6.49831i	−0.257952	+	0.793895i	0.735282	+	0.677762i	$0.237050\pi$
$67$	−2.11143	+	6.49831i	−0.257952	+	0.793895i	−0.993234	+	0.116133i	$0.962950\pi$
$68$		0			0
$69$	4.53258	−	3.29311i	0.545658	−	0.396444i
$70$		0			0
$71$	1.55188	+	4.77620i	0.184175	+	0.566831i	0.999933	−	0.0115615i	$-0.00368022\pi$
$71$	1.55188	+	4.77620i	0.184175	+	0.566831i	−0.815759	+	0.578393i	$0.803680\pi$
$72$		0			0
$73$	−11.5986			−1.35751			−0.678756	−	0.734363i	$-0.737481\pi$
$73$	−11.5986			−1.35751			−0.678756	+	0.734363i	$0.737481\pi$
$74$		0			0
$75$	−2.48992	−	1.80903i	−0.287511	−	0.208889i
$76$		0			0
$77$	−3.64578	+	11.2206i	−0.415475	+	1.27870i
$78$		0			0
$79$	−11.1197			−1.25107			−0.625533	−	0.780198i	$-0.715118\pi$
$79$	−11.1197			−1.25107			−0.625533	+	0.780198i	$0.715118\pi$
$80$		0			0
$81$	13.4739			1.49710
$82$		0			0
$83$	9.74140			1.06926			0.534629	−	0.845087i	$-0.320452\pi$
$83$	9.74140			1.06926			0.534629	+	0.845087i	$0.320452\pi$
$84$		0			0
$85$	−4.87419			−0.528680
$86$		0			0
$87$	−2.24019	+	6.89460i	−0.240174	+	0.739179i
$88$		0			0
$89$	4.05088	+	2.94313i	0.429392	+	0.311971i	0.781406	−	0.624023i	$-0.214503\pi$
$89$	4.05088	+	2.94313i	0.429392	+	0.311971i	−0.352014	+	0.935995i	$0.614503\pi$
$90$		0			0
$91$	0.846874			0.0887766
$92$		0			0
$93$	4.14164	+	12.7466i	0.429468	+	1.32177i
$94$		0			0
$95$	6.63495	−	4.82057i	0.680731	−	0.494580i
$96$		0			0
$97$	0.935472	−	2.87909i	0.0949828	−	0.292327i	−0.892266	−	0.451509i	$-0.850886\pi$
$97$	0.935472	−	2.87909i	0.0949828	−	0.292327i	0.987249	+	0.159182i	$0.0508858\pi$
$98$		0			0
$99$	−8.47453	−	26.0819i	−0.851723	−	2.62133i
$100$		0			0
$101$	−12.0304	−	8.74058i	−1.19707	−	0.869721i	−0.203075	−	0.979163i	$-0.565093\pi$
$101$	−12.0304	−	8.74058i	−1.19707	−	0.869721i	−0.993993	+	0.109443i	$0.965093\pi$
$102$		0			0
$103$	3.68476	+	2.67713i	0.363070	+	0.263786i	0.754331	−	0.656494i	$-0.227961\pi$
$103$	3.68476	+	2.67713i	0.363070	+	0.263786i	−0.391261	+	0.920280i	$0.627961\pi$
$104$		0			0
$105$	−6.93298	+	5.03710i	−0.676590	+	0.491571i
$106$		0			0
$107$	7.57918	+	5.50660i	0.732707	+	0.532343i	0.890419	−	0.455142i	$-0.150412\pi$
$107$	7.57918	+	5.50660i	0.732707	+	0.532343i	−0.157711	+	0.987485i	$0.550412\pi$
$108$		0			0
$109$	11.1379			1.06682			0.533411	−	0.845856i	$-0.320910\pi$
$109$	11.1379			1.06682			0.533411	+	0.845856i	$0.320910\pi$
$110$		0			0
$111$	−4.45524	+	13.7118i	−0.422872	+	1.30147i
$112$		0			0
$113$	−4.99658	−	15.3779i	−0.470039	−	1.44663i	−0.852534	−	0.522672i	$-0.824935\pi$
$113$	−4.99658	−	15.3779i	−0.470039	−	1.44663i	0.382495	−	0.923958i	$-0.375065\pi$
$114$		0			0
$115$	−0.562525	−	1.73127i	−0.0524558	−	0.161442i
$116$		0			0
$117$	−1.59258	+	1.15708i	−0.147234	+	0.106972i
$118$		0			0
$119$	−4.19391	+	12.9075i	−0.384455	+	1.18323i
$120$		0			0
$121$	−5.62544	+	4.08712i	−0.511403	+	0.371556i
$122$		0			0
$123$	19.4792	+	2.98746i	1.75638	+	0.269370i
$124$		0			0
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$		0			0
$127$	0.582735	−	1.79347i	0.0517093	−	0.159145i	−0.921867	−	0.387506i	$-0.873337\pi$
$127$	0.582735	−	1.79347i	0.0517093	−	0.159145i	0.973577	+	0.228361i	$0.0733366\pi$
$128$		0			0
$129$	10.4373	−	7.58315i	0.918954	−	0.667659i
$130$		0			0
$131$	−3.24008	−	9.97194i	−0.283087	−	0.871252i	−0.986966	−	0.160932i	$-0.948550\pi$
$131$	−3.24008	−	9.97194i	−0.283087	−	0.871252i	0.703879	−	0.710320i	$-0.251450\pi$
$132$		0			0
$133$	−7.05661	−	21.7180i	−0.611886	−	1.88319i
$134$		0			0
$135$	3.30240	−	10.1637i	0.284225	−	0.874756i
$136$		0			0
$137$	18.9115			1.61572			0.807859	−	0.589376i	$-0.200626\pi$
$137$	18.9115			1.61572			0.807859	+	0.589376i	$0.200626\pi$
$138$		0			0
$139$	6.93669	+	5.03980i	0.588362	+	0.427470i	0.841729	−	0.539900i	$-0.181538\pi$
$139$	6.93669	+	5.03980i	0.588362	+	0.427470i	−0.253367	+	0.967370i	$0.581538\pi$
$140$		0			0
$141$	−8.40194	+	6.10437i	−0.707571	+	0.514081i
$142$		0			0
$143$	1.04260	+	0.757490i	0.0871863	+	0.0633445i
$144$		0			0
$145$	1.90560	+	1.38450i	0.158252	+	0.114977i
$146$		0			0
$147$	0.716129	+	2.20402i	0.0590653	+	0.181784i
$148$		0			0
$149$	6.02508	−	18.5433i	0.493594	−	1.51913i	−0.325542	−	0.945527i	$-0.605547\pi$
$149$	6.02508	−	18.5433i	0.493594	−	1.51913i	0.819136	−	0.573599i	$-0.194453\pi$
$150$		0			0
$151$	12.1792	−	8.84873i	0.991132	−	0.720099i	0.0309631	−	0.999521i	$-0.490143\pi$
$151$	12.1792	−	8.84873i	0.991132	−	0.720099i	0.960169	+	0.279421i	$0.0901426\pi$
$152$		0			0
$153$	−9.74865	−	30.0032i	−0.788131	−	2.42562i
$154$		0			0
$155$	4.35473			0.349781
$156$		0			0
$157$	−13.4425	−	9.76658i	−1.07283	−	0.779458i	−0.0964128	−	0.995341i	$-0.530737\pi$
$157$	−13.4425	−	9.76658i	−1.07283	−	0.779458i	−0.976419	+	0.215883i	$0.930737\pi$
$158$		0			0
$159$	−9.00749	+	27.7222i	−0.714340	+	2.19851i
$160$		0			0
$161$	−5.06867			−0.399467
$162$		0			0
$163$	−10.5894			−0.829426			−0.414713	−	0.909952i	$-0.636118\pi$
$163$	−10.5894			−0.829426			−0.414713	+	0.909952i	$0.636118\pi$
$164$		0			0
$165$	−13.0407			−1.01522
$166$		0			0
$167$	12.0754			0.934425			0.467212	−	0.884145i	$-0.345258\pi$
$167$	12.0754			0.934425			0.467212	+	0.884145i	$0.345258\pi$
$168$		0			0
$169$	−3.98864	+	12.2758i	−0.306818	+	0.944289i
$170$		0			0
$171$	42.9435	+	31.2003i	3.28397	+	2.38594i
$172$		0			0
$173$	−26.2006			−1.99199			−0.995996	−	0.0894004i	$-0.971505\pi$
$173$	−26.2006			−1.99199			−0.995996	+	0.0894004i	$0.971505\pi$
$174$		0			0
$175$	0.860432	+	2.64814i	0.0650425	+	0.200180i
$176$		0			0
$177$	−24.4365	+	17.7542i	−1.83676	+	1.33448i
$178$		0			0
$179$	−3.40256	+	10.4720i	−0.254319	+	0.782714i	0.739644	+	0.672998i	$0.234994\pi$
$179$	−3.40256	+	10.4720i	−0.254319	+	0.782714i	−0.993963	+	0.109715i	$0.965006\pi$
$180$		0			0
$181$	6.53226	+	20.1042i	0.485539	+	1.49434i	0.831199	+	0.555975i	$0.187655\pi$
$181$	6.53226	+	20.1042i	0.485539	+	1.49434i	−0.345660	+	0.938360i	$0.612345\pi$
$182$		0			0
$183$	5.82712	+	4.23365i	0.430753	+	0.312961i
$184$		0			0
$185$	3.78982	+	2.75346i	0.278633	+	0.202439i
$186$		0			0
$187$	−16.7083	+	12.1393i	−1.22184	+	0.887715i
$188$		0			0
$189$	−24.0735	−	17.4904i	−1.75109	−	1.27224i
$190$		0			0
$191$	9.06674			0.656047			0.328023	−	0.944670i	$-0.393618\pi$
$191$	9.06674			0.656047			0.328023	+	0.944670i	$0.393618\pi$
$192$		0			0
$193$	−6.97160	+	21.4564i	−0.501827	+	1.54446i	0.304213	+	0.952604i	$0.401607\pi$
$193$	−6.97160	+	21.4564i	−0.501827	+	1.54446i	−0.806040	+	0.591861i	$0.798393\pi$
$194$		0			0
$195$	0.289265	+	0.890265i	0.0207147	+	0.0637532i
$196$		0			0
$197$	−7.93840	−	24.4319i	−0.565587	−	1.74070i	−0.666200	−	0.745773i	$-0.732080\pi$
$197$	−7.93840	−	24.4319i	−0.565587	−	1.74070i	0.100612	−	0.994926i	$-0.467920\pi$
$198$		0			0
$199$	−17.6602	+	12.8309i	−1.25190	+	0.909559i	−0.998331	−	0.0577576i	$-0.981605\pi$
$199$	−17.6602	+	12.8309i	−1.25190	+	0.909559i	−0.253570	+	0.967317i	$0.581605\pi$
$200$		0			0
$201$	−6.49837	+	19.9999i	−0.458360	+	1.41069i
$202$		0			0
$203$	5.30599	−	3.85503i	0.372408	−	0.270570i
$204$		0			0
$205$	2.87897	−	5.71940i	0.201076	−	0.399460i
$206$		0			0
$207$	9.53185	−	6.92529i	0.662509	−	0.481341i
$208$		0			0
$209$	10.7383	−	33.0491i	0.742784	−	2.28605i
$210$		0			0
$211$	−18.5913	+	13.5073i	−1.27988	+	0.929884i	−0.999549	−	0.0300212i	$-0.990443\pi$
$211$	−18.5913	+	13.5073i	−1.27988	+	0.929884i	−0.280326	+	0.959905i	$0.590443\pi$
$212$		0			0
$213$	4.77625	+	14.6998i	0.327263	+	1.00721i
$214$		0			0
$215$	−1.29534	−	3.98666i	−0.0883417	−	0.271888i
$216$		0			0
$217$	3.74695	−	11.5319i	0.254360	−	0.782839i
$218$		0			0
$219$	−35.6971			−2.41219
$220$		0			0
$221$	1.19935	+	0.871376i	0.0806768	+	0.0586151i
$222$		0			0
$223$	7.70014	−	5.59448i	0.515640	−	0.374634i	−0.299319	−	0.954153i	$-0.596760\pi$
$223$	7.70014	−	5.59448i	0.515640	−	0.374634i	0.814959	+	0.579519i	$0.196760\pi$
$224$		0			0
$225$	−5.23621	−	3.80433i	−0.349081	−	0.253622i
$226$		0			0
$227$	19.5957	+	14.2371i	1.30061	+	0.944952i	0.999961	−	0.00878170i	$-0.00279534\pi$
$227$	19.5957	+	14.2371i	1.30061	+	0.944952i	0.300653	+	0.953734i	$0.402795\pi$
$228$		0			0
$229$	8.40300	+	25.8618i	0.555286	+	1.70899i	0.695188	+	0.718828i	$0.255321\pi$
$229$	8.40300	+	25.8618i	0.555286	+	1.70899i	−0.139902	+	0.990165i	$0.544679\pi$
$230$		0			0
$231$	−11.2207	+	34.5336i	−0.738265	+	2.27215i
$232$		0			0
$233$	8.24485	−	5.99024i	0.540138	−	0.392434i	−0.283998	−	0.958825i	$-0.591661\pi$
$233$	8.24485	−	5.99024i	0.540138	−	0.392434i	0.824136	+	0.566391i	$0.191661\pi$
$234$		0			0
$235$	1.04274	+	3.20923i	0.0680209	+	0.209347i
$236$		0			0
$237$	−34.2233			−2.22304
$238$		0			0
$239$	7.39286	+	5.37123i	0.478204	+	0.347436i	0.800630	−	0.599159i	$-0.204498\pi$
$239$	7.39286	+	5.37123i	0.478204	+	0.347436i	−0.322426	+	0.946595i	$0.604498\pi$
$240$		0			0
$241$	6.37345	−	19.6155i	0.410550	−	1.26354i	−0.505621	−	0.862756i	$-0.668737\pi$
$241$	6.37345	−	19.6155i	0.410550	−	1.26354i	0.916171	−	0.400788i	$-0.131263\pi$
$242$		0			0
$243$	9.40851			0.603556
$244$		0			0
$245$	0.752975			0.0481058
$246$		0			0
$247$	−2.49439			−0.158714
$248$		0			0
$249$	29.9812			1.89998
$250$		0			0
$251$	−4.08943	+	12.5860i	−0.258122	+	0.794419i	0.735076	+	0.677985i	$0.237146\pi$
$251$	−4.08943	+	12.5860i	−0.258122	+	0.794419i	−0.993198	+	0.116434i	$0.962854\pi$
$252$		0			0
$253$	−6.24009	−	4.53369i	−0.392311	−	0.285031i
$254$		0			0
$255$	−15.0013			−0.939421
$256$		0			0
$257$	−5.54020	−	17.0510i	−0.345588	−	1.06361i	−0.961268	−	0.275614i	$-0.911119\pi$
$257$	−5.54020	−	17.0510i	−0.345588	−	1.06361i	0.615680	−	0.787996i	$-0.288881\pi$
$258$		0			0
$259$	10.5524	−	7.66679i	0.655696	−	0.476391i
$260$		0			0
$261$	−4.71104	+	14.4991i	−0.291606	+	0.897471i
$262$		0			0
$263$	−6.15396	−	18.9399i	−0.379469	−	1.16789i	−0.940414	−	0.340033i	$-0.889562\pi$
$263$	−6.15396	−	18.9399i	−0.379469	−	1.16789i	0.560944	−	0.827854i	$-0.310438\pi$
$264$		0			0
$265$	7.66215	+	5.56688i	0.470682	+	0.341971i
$266$		0			0
$267$	12.4674	+	9.05812i	0.762994	+	0.554348i
$268$		0			0
$269$	−4.44023	+	3.22602i	−0.270726	+	0.196694i	−0.714862	−	0.699265i	$-0.753511\pi$
$269$	−4.44023	+	3.22602i	−0.270726	+	0.196694i	0.444136	+	0.895959i	$0.353511\pi$
$270$		0			0
$271$	7.83496	+	5.69243i	0.475940	+	0.345790i	0.799752	−	0.600331i	$-0.204965\pi$
$271$	7.83496	+	5.69243i	0.475940	+	0.345790i	−0.323812	+	0.946121i	$0.604965\pi$
$272$		0			0
$273$	2.60644			0.157749
$274$		0			0
$275$	−1.30935	+	4.02977i	−0.0789568	+	0.243004i
$276$		0			0
$277$	−4.05657	−	12.4848i	−0.243736	−	0.750141i	−0.995842	−	0.0910990i	$-0.970962\pi$
$277$	−4.05657	−	12.4848i	−0.243736	−	0.750141i	0.752106	−	0.659042i	$-0.229038\pi$
$278$		0			0
$279$	8.70971	+	26.8057i	0.521437	+	1.60482i
$280$		0			0
$281$	2.21702	−	1.61076i	0.132256	−	0.0960898i	−0.519690	−	0.854355i	$-0.673953\pi$
$281$	2.21702	−	1.61076i	0.132256	−	0.0960898i	0.651947	+	0.758265i	$0.273953\pi$
$282$		0			0
$283$	−7.86200	+	24.1968i	−0.467347	+	1.43835i	0.388659	+	0.921382i	$0.372939\pi$
$283$	−7.86200	+	24.1968i	−0.467347	+	1.43835i	−0.856006	+	0.516966i	$0.827061\pi$
$284$		0			0
$285$	20.4205	−	14.8363i	1.20960	−	0.878828i
$286$		0			0
$287$	−12.6686	−	12.5451i	−0.747803	−	0.740512i
$288$		0			0
$289$	−5.46709	+	3.97208i	−0.321594	+	0.233652i
$290$		0			0
$291$	2.87911	−	8.86100i	0.168777	−	0.519441i
$292$		0			0
$293$	−8.50447	+	6.17886i	−0.496836	+	0.360973i	−0.807807	−	0.589447i	$-0.799346\pi$
$293$	−8.50447	+	6.17886i	−0.496836	+	0.360973i	0.310971	+	0.950419i	$0.399346\pi$
$294$		0			0
$295$	3.03274	+	9.33383i	0.176573	+	0.543437i
$296$		0			0
$297$	−13.9928	−	43.0653i	−0.811942	−	2.49890i
$298$		0			0
$299$	−0.171091	+	0.526564i	−0.00989444	+	0.0304520i
$300$		0			0
$301$	−11.6718			−0.672750
$302$		0			0
$303$	−37.0261	−	26.9010i	−2.12709	−	1.54542i
$304$		0			0
$305$	1.89333	−	1.37558i	0.108412	−	0.0787657i
$306$		0			0
$307$	−21.1203	−	15.3448i	−1.20540	−	0.875772i	−0.210592	−	0.977574i	$-0.567539\pi$
$307$	−21.1203	−	15.3448i	−1.20540	−	0.875772i	−0.994805	+	0.101802i	$0.967539\pi$
$308$		0			0
$309$	11.3406	+	8.23945i	0.645146	+	0.468726i
$310$		0			0
$311$	0.0561245	+	0.172733i	0.00318253	+	0.00979481i	0.952635	−	0.304115i	$-0.0983609\pi$
$311$	0.0561245	+	0.172733i	0.00318253	+	0.00979481i	−0.949453	+	0.313910i	$0.898361\pi$
$312$		0			0
$313$	4.92587	−	15.1603i	0.278427	−	0.856910i	−0.709866	−	0.704337i	$-0.751244\pi$
$313$	4.92587	−	15.1603i	0.278427	−	0.856910i	0.988292	−	0.152572i	$-0.0487557\pi$
$314$		0			0
$315$	−14.5798	+	10.5928i	−0.821479	+	0.596839i
$316$		0			0
$317$	2.49406	+	7.67592i	0.140080	+	0.431123i	0.996346	−	0.0854135i	$-0.0272211\pi$
$317$	2.49406	+	7.67592i	0.140080	+	0.431123i	−0.856265	+	0.516536i	$0.827221\pi$
$318$		0			0
$319$	9.98041			0.558796
$320$		0			0
$321$	23.3266	+	16.9477i	1.30196	+	0.945930i
$322$		0			0
$323$	12.3528	−	38.0179i	0.687326	−	2.11537i
$324$		0			0
$325$	0.304148			0.0168711
$326$		0			0
$327$	34.2794			1.89565
$328$		0			0
$329$	9.39568			0.518001
$330$		0			0
$331$	12.5109			0.687659			0.343829	−	0.939032i	$-0.388276\pi$
$331$	12.5109			0.687659			0.343829	+	0.939032i	$0.388276\pi$
$332$		0			0
$333$	−9.36920	+	28.8354i	−0.513429	+	1.58017i
$334$		0			0
$335$	5.52779	+	4.01617i	0.302015	+	0.219427i
$336$		0			0
$337$	−25.6065			−1.39488			−0.697438	−	0.716645i	$-0.745677\pi$
$337$	−25.6065			−1.39488			−0.697438	+	0.716645i	$0.745677\pi$
$338$		0			0
$339$	−15.3780	−	47.3287i	−0.835220	−	2.57054i
$340$		0			0
$341$	14.9277	−	10.8456i	0.808380	−	0.587323i
$342$		0			0
$343$	−5.37514	+	16.5430i	−0.290230	+	0.893237i
$344$		0			0
$345$	−1.73129	−	5.32837i	−0.0932096	−	0.286870i
$346$		0			0
$347$	2.34086	+	1.70073i	0.125664	+	0.0913000i	0.648842	−	0.760923i	$-0.275254\pi$
$347$	2.34086	+	1.70073i	0.125664	+	0.0913000i	−0.523178	+	0.852223i	$0.675254\pi$
$348$		0			0
$349$	2.48910	+	1.80844i	0.133239	+	0.0968034i	0.652408	−	0.757868i	$-0.273759\pi$
$349$	2.48910	+	1.80844i	0.133239	+	0.0968034i	−0.519170	+	0.854671i	$0.673759\pi$
$350$		0			0
$351$	−2.62960	+	1.91052i	−0.140358	+	0.101976i
$352$		0			0
$353$	−8.19633	−	5.95498i	−0.436247	−	0.316952i	0.347895	−	0.937533i	$-0.386897\pi$
$353$	−8.19633	−	5.95498i	−0.436247	−	0.316952i	−0.784142	+	0.620582i	$0.786897\pi$
$354$		0			0
$355$	5.02200			0.266540
$356$		0			0
$357$	−12.9076	+	39.7256i	−0.683145	+	2.10250i
$358$		0			0
$359$	6.87240	+	21.1511i	0.362711	+	1.11631i	0.951402	+	0.307952i	$0.0996436\pi$
$359$	6.87240	+	21.1511i	0.362711	+	1.11631i	−0.588691	+	0.808358i	$0.700356\pi$
$360$		0			0
$361$	14.9133	+	45.8984i	0.784910	+	2.41570i
$362$		0			0
$363$	−17.3135	+	12.5790i	−0.908722	+	0.660225i
$364$		0			0
$365$	−3.58416	+	11.0309i	−0.187604	+	0.577385i
$366$		0			0
$367$	−13.0049	+	9.44862i	−0.678851	+	0.493214i	−0.872976	−	0.487763i	$-0.837813\pi$
$367$	−13.0049	+	9.44862i	−0.678851	+	0.493214i	0.194125	+	0.980977i	$0.437813\pi$
$368$		0			0
$369$	40.9641	+	6.28251i	2.13251	+	0.327055i
$370$		0			0
$371$	21.3346	−	15.5005i	1.10764	−	0.804747i
$372$		0			0
$373$	9.03110	−	27.7949i	0.467613	−	1.43916i	−0.388054	−	0.921636i	$-0.626853\pi$
$373$	9.03110	−	27.7949i	0.467613	−	1.43916i	0.855667	−	0.517527i	$-0.173147\pi$
$374$		0			0
$375$	−2.48992	+	1.80903i	−0.128579	+	0.0934181i
$376$		0			0
$377$	−0.221382	−	0.681343i	−0.0114017	−	0.0350910i
$378$		0			0
$379$	−0.000967881	−	0.00297883i	−4.97167e−5	−	0.000153012i	0.951032	−	0.309093i	$-0.100026\pi$
$379$	−0.000967881	−	0.00297883i	−4.97167e−5	−	0.000153012i	−0.951081	+	0.308940i	$0.900026\pi$
$380$		0			0
$381$	1.79349	−	5.51980i	0.0918833	−	0.282788i
$382$		0			0
$383$	6.70918			0.342823			0.171411	−	0.985200i	$-0.445167\pi$
$383$	6.70918			0.342823			0.171411	+	0.985200i	$0.445167\pi$
$384$		0			0
$385$	9.54477	+	6.93468i	0.486447	+	0.353424i
$386$		0			0
$387$	21.9493	−	15.9471i	1.11574	−	0.810635i
$388$		0			0
$389$	−17.5285	−	12.7352i	−0.888732	−	0.645702i	0.0468150	−	0.998904i	$-0.485093\pi$
$389$	−17.5285	−	12.7352i	−0.888732	−	0.645702i	−0.935547	+	0.353202i	$0.885093\pi$
$390$		0			0
$391$	−7.17827	−	5.21532i	−0.363021	−	0.263750i
$392$		0			0
$393$	−9.97203	−	30.6908i	−0.503023	−	1.54814i
$394$		0			0
$395$	−3.43618	+	10.5755i	−0.172893	+	0.532110i
$396$		0			0
$397$	27.3601	−	19.8782i	1.37316	−	0.997660i	0.375679	−	0.926750i	$-0.377410\pi$
$397$	27.3601	−	19.8782i	1.37316	−	0.997660i	0.997483	−	0.0709105i	$-0.0225905\pi$
$398$		0			0
$399$	−21.7182	−	66.8418i	−1.08727	−	3.34628i
$400$		0			0
$401$	−27.1311			−1.35486			−0.677431	−	0.735586i	$-0.736907\pi$
$401$	−27.1311			−1.35486			−0.677431	+	0.735586i	$0.736907\pi$
$402$		0			0
$403$	−1.07153	−	0.778511i	−0.0533767	−	0.0387804i
$404$		0			0
$405$	4.16367	−	12.8145i	0.206895	−	0.636756i
$406$		0			0
$407$	19.8488			0.983868
$408$		0			0
$409$	−23.3140			−1.15280			−0.576402	−	0.817166i	$-0.695544\pi$
$409$	−23.3140			−1.15280			−0.576402	+	0.817166i	$0.695544\pi$
$410$		0			0
$411$	58.2041			2.87100
$412$		0			0
$413$	27.3267			1.34466
$414$		0			0
$415$	3.01026	−	9.26462i	0.147768	−	0.454782i
$416$		0			0
$417$	21.3491	+	15.5111i	1.04547	+	0.759580i
$418$		0			0
$419$	27.3546			1.33636			0.668180	−	0.744000i	$-0.267074\pi$
$419$	27.3546			1.33636			0.668180	+	0.744000i	$0.267074\pi$
$420$		0			0
$421$	−6.31508	−	19.4358i	−0.307778	−	0.947244i	−0.978626	−	0.205649i	$-0.934069\pi$
$421$	−6.31508	−	19.4358i	−0.307778	−	0.947244i	0.670847	−	0.741595i	$-0.265931\pi$
$422$		0			0
$423$	−17.6690	+	12.8373i	−0.859095	+	0.624169i
$424$		0			0
$425$	−1.50621	+	4.63563i	−0.0730618	+	0.224861i
$426$		0			0
$427$	−2.01365	−	6.19739i	−0.0974476	−	0.299913i
$428$		0			0
$429$	3.20881	+	2.33134i	0.154923	+	0.112558i
$430$		0			0
$431$	22.3342	+	16.2267i	1.07580	+	0.781615i	0.976946	−	0.213487i	$-0.0684822\pi$
$431$	22.3342	+	16.2267i	1.07580	+	0.781615i	0.0988544	+	0.995102i	$0.468482\pi$
$432$		0			0
$433$	−9.70173	+	7.04872i	−0.466235	+	0.338740i	−0.795972	−	0.605333i	$-0.793040\pi$
$433$	−9.70173	+	7.04872i	−0.466235	+	0.338740i	0.329737	+	0.944073i	$0.393040\pi$
$434$		0			0
$435$	5.86490	+	4.26110i	0.281200	+	0.204304i
$436$		0			0
$437$	14.9293			0.714165
$438$		0			0
$439$	8.93400	−	27.4960i	0.426396	−	1.31231i	−0.475254	−	0.879848i	$-0.657644\pi$
$439$	8.93400	−	27.4960i	0.426396	−	1.31231i	0.901651	−	0.432465i	$-0.142356\pi$
$440$		0			0
$441$	1.50599	+	4.63497i	0.0717139	+	0.220713i
$442$		0			0
$443$	−4.86164	−	14.9626i	−0.230984	−	0.710895i	−0.997629	−	0.0688237i	$-0.978075\pi$
$443$	−4.86164	−	14.9626i	−0.230984	−	0.710895i	0.766645	−	0.642071i	$-0.221925\pi$
$444$		0			0
$445$	4.05088	−	2.94313i	0.192030	−	0.139518i
$446$		0			0
$447$	18.5435	−	57.0710i	0.877076	−	2.69936i
$448$		0			0
$449$	19.3366	−	14.0488i	0.912549	−	0.663006i	−0.0291089	−	0.999576i	$-0.509267\pi$
$449$	19.3366	−	14.0488i	0.912549	−	0.663006i	0.941658	+	0.336570i	$0.109267\pi$
$450$		0			0
$451$	−4.37545	−	26.7758i	−0.206032	−	1.26083i
$452$		0			0
$453$	37.4842	−	27.2338i	1.76116	−	1.27956i
$454$		0			0
$455$	0.261699	−	0.805425i	0.0122686	−	0.0377589i
$456$		0			0
$457$	18.1805	−	13.2089i	0.850450	−	0.617888i	−0.0748200	−	0.997197i	$-0.523838\pi$
$457$	18.1805	−	13.2089i	0.850450	−	0.617888i	0.925270	+	0.379309i	$0.123838\pi$
$458$		0			0
$459$	−16.0965	−	49.5400i	−0.751321	−	2.31233i
$460$		0			0
$461$	−8.72276	−	26.8459i	−0.406259	−	1.25034i	−0.919839	−	0.392296i	$-0.871681\pi$
$461$	−8.72276	−	26.8459i	−0.406259	−	1.25034i	0.513580	−	0.858042i	$-0.328319\pi$
$462$		0			0
$463$	6.67081	−	20.5307i	0.310019	−	0.954140i	−0.667737	−	0.744397i	$-0.732737\pi$
$463$	6.67081	−	20.5307i	0.310019	−	0.954140i	0.977756	−	0.209744i	$-0.0672629\pi$
$464$		0			0
$465$	13.4026			0.621532
$466$		0			0
$467$	24.9375	+	18.1181i	1.15397	+	0.838407i	0.989004	−	0.147892i	$-0.0472488\pi$
$467$	24.9375	+	18.1181i	1.15397	+	0.838407i	0.164965	+	0.986299i	$0.447249\pi$
$468$		0			0
$469$	15.3917	−	11.1827i	0.710721	−	0.516369i
$470$		0			0
$471$	−41.3723	−	30.0587i	−1.90633	−	1.38503i
$472$		0			0
$473$	−14.3692	−	10.4399i	−0.660699	−	0.480026i
$474$		0			0
$475$	−2.53432	−	7.79985i	−0.116283	−	0.357882i
$476$		0			0
$477$	−18.9424	+	58.2988i	−0.867313	+	2.66932i
$478$		0			0
$479$	−13.8328	+	10.0501i	−0.632037	+	0.459202i	−0.857105	−	0.515141i	$-0.827739\pi$
$479$	−13.8328	+	10.0501i	−0.632037	+	0.459202i	0.225068	+	0.974343i	$0.427739\pi$
$480$		0			0
$481$	−0.440279	−	1.35504i	−0.0200750	−	0.0617844i
$482$		0			0
$483$	−15.5999			−0.709820
$484$		0			0
$485$	−2.44910	−	1.77937i	−0.111208	−	0.0807972i
$486$		0			0
$487$	−4.27314	+	13.1514i	−0.193634	+	0.595945i	0.806356	+	0.591431i	$0.201437\pi$
$487$	−4.27314	+	13.1514i	−0.193634	+	0.595945i	−0.999990	+	0.00451388i	$0.998563\pi$
$488$		0			0
$489$	−32.5911			−1.47382
$490$		0			0
$491$	6.71970			0.303256			0.151628	−	0.988438i	$-0.451548\pi$
$491$	6.71970			0.303256			0.151628	+	0.988438i	$0.451548\pi$
$492$		0			0
$493$	11.4809			0.517075
$494$		0			0
$495$	−27.4242			−1.23262
$496$		0			0
$497$	4.32109	−	13.2989i	0.193827	−	0.596539i
$498$		0			0
$499$	−1.13757	−	0.826493i	−0.0509246	−	0.0369989i	0.562032	−	0.827116i	$-0.310020\pi$
$499$	−1.13757	−	0.826493i	−0.0509246	−	0.0369989i	−0.612956	+	0.790117i	$0.710020\pi$
$500$		0			0
$501$	37.1647			1.66040
$502$		0			0
$503$	−0.735820	−	2.26462i	−0.0328086	−	0.100975i	0.933311	−	0.359069i	$-0.116906\pi$
$503$	−0.735820	−	2.26462i	−0.0328086	−	0.100975i	−0.966120	+	0.258094i	$0.916906\pi$
$504$		0			0
$505$	−12.0304	+	8.74058i	−0.535345	+	0.388951i
$506$		0			0
$507$	−12.2759	+	37.7813i	−0.545191	+	1.67792i
$508$		0			0
$509$	6.88691	+	21.1957i	0.305257	+	0.939484i	0.979581	+	0.201049i	$0.0644350\pi$
$509$	6.88691	+	21.1957i	0.305257	+	0.939484i	−0.674324	+	0.738435i	$0.735565\pi$
$510$		0			0
$511$	26.1275	+	18.9827i	1.15581	+	0.839746i
$512$		0			0
$513$	70.9063	+	51.5164i	3.13059	+	2.27451i
$514$		0			0
$515$	3.68476	−	2.67713i	0.162370	−	0.117969i
$516$		0			0
$517$	11.5671	+	8.40401i	0.508721	+	0.369608i
$518$		0			0
$519$	−80.6378			−3.53961
$520$		0			0
$521$	5.41178	−	16.6557i	0.237094	−	0.729702i	−0.759742	−	0.650224i	$-0.774675\pi$
$521$	5.41178	−	16.6557i	0.237094	−	0.729702i	0.996837	−	0.0794772i	$-0.0253251\pi$
$522$		0			0
$523$	−0.927661	−	2.85505i	−0.0405638	−	0.124842i	0.928724	−	0.370772i	$-0.120907\pi$
$523$	−0.927661	−	2.85505i	−0.0405638	−	0.124842i	−0.969288	+	0.245929i	$0.920907\pi$
$524$		0			0
$525$	2.64816	+	8.15021i	0.115575	+	0.355704i
$526$		0			0
$527$	17.1720	−	12.4762i	0.748025	−	0.543472i
$528$		0			0
$529$	−6.08339	+	18.7227i	−0.264495	+	0.814032i
$530$		0			0
$531$	−51.3891	+	37.3364i	−2.23010	+	1.62026i
$532$		0			0
$533$	−1.73088	+	0.892635i	−0.0749727	+	0.0386643i
$534$		0			0
$535$	7.57918	−	5.50660i	0.327677	−	0.238071i
$536$		0			0
$537$	−10.4721	+	32.2298i	−0.451904	+	1.39082i
$538$		0			0
$539$	2.58114	−	1.87531i	0.111178	−	0.0807753i
$540$		0			0
$541$	−9.10114	−	28.0104i	−0.391288	−	1.20426i	−0.931815	−	0.362935i	$-0.881775\pi$
$541$	−9.10114	−	28.0104i	−0.391288	−	1.20426i	0.540526	−	0.841327i	$-0.318225\pi$
$542$		0			0
$543$	20.1044	+	61.8750i	0.862763	+	2.65531i
$544$		0			0
$545$	3.44181	−	10.5928i	0.147431	−	0.453746i
$546$		0			0
$547$	7.00205			0.299386			0.149693	−	0.988733i	$-0.452171\pi$
$547$	7.00205			0.299386			0.149693	+	0.988733i	$0.452171\pi$
$548$		0			0
$549$	12.2542	+	8.90321i	0.522997	+	0.379980i
$550$		0			0
$551$	−15.6283	+	11.3546i	−0.665789	+	0.483724i
$552$		0			0
$553$	25.0487	+	18.1990i	1.06518	+	0.773898i
$554$		0			0
$555$	11.6640	+	8.47437i	0.495108	+	0.359717i
$556$		0			0
$557$	5.28218	+	16.2569i	0.223813	+	0.688826i	0.998410	+	0.0563708i	$0.0179529\pi$
$557$	5.28218	+	16.2569i	0.223813	+	0.688826i	−0.774597	+	0.632456i	$0.782047\pi$
$558$		0			0
$559$	−0.393976	+	1.21253i	−0.0166634	+	0.0512847i
$560$		0			0
$561$	−51.4235	+	37.3614i	−2.17110	+	1.57740i
$562$		0			0
$563$	−2.64600	−	8.14354i	−0.111515	−	0.343209i	0.879689	−	0.475550i	$-0.157751\pi$
$563$	−2.64600	−	8.14354i	−0.111515	−	0.343209i	−0.991204	+	0.132340i	$0.957751\pi$
$564$		0			0
$565$	−16.1693			−0.680246
$566$		0			0
$567$	−30.3519	−	22.0520i	−1.27466	−	0.926095i
$568$		0			0
$569$	2.36095	−	7.26624i	0.0989760	−	0.304617i	−0.889293	−	0.457337i	$-0.848803\pi$
$569$	2.36095	−	7.26624i	0.0989760	−	0.304617i	0.988269	+	0.152720i	$0.0488033\pi$
$570$		0			0
$571$	−3.19866			−0.133860			−0.0669300	−	0.997758i	$-0.521320\pi$
$571$	−3.19866			−0.133860			−0.0669300	+	0.997758i	$0.521320\pi$
$572$		0			0
$573$	27.9048			1.16574
$574$		0			0
$575$	−1.82037			−0.0759147
$576$		0			0
$577$	−23.4296			−0.975386			−0.487693	−	0.873015i	$-0.662161\pi$
$577$	−23.4296			−0.975386			−0.487693	+	0.873015i	$0.662161\pi$
$578$		0			0
$579$	−21.4566	+	66.0366i	−0.891706	+	2.74439i
$580$		0			0
$581$	−21.9439	−	15.9431i	−0.910385	−	0.661433i
$582$		0			0
$583$	40.1298			1.66201
$584$		0			0
$585$	0.608313	+	1.87219i	0.0251506	+	0.0774057i
$586$		0			0
$587$	6.42994	−	4.67163i	0.265392	−	0.192819i	−0.447129	−	0.894470i	$-0.647553\pi$
$587$	6.42994	−	4.67163i	0.265392	−	0.192819i	0.712521	+	0.701651i	$0.247553\pi$
$588$		0			0
$589$	−11.0363	+	33.9663i	−0.454743	+	1.39955i
$590$		0			0
$591$	−24.4321	−	75.1943i	−1.00500	−	3.09308i
$592$		0			0
$593$	−6.54840	−	4.75769i	−0.268911	−	0.195375i	0.445155	−	0.895453i	$-0.353148\pi$
$593$	−6.54840	−	4.75769i	−0.268911	−	0.195375i	−0.714066	+	0.700078i	$0.753148\pi$
$594$		0			0
$595$	10.9798	+	7.97728i	0.450128	+	0.327037i
$596$		0			0
$597$	−54.3531	+	39.4899i	−2.22453	+	1.61621i
$598$		0			0
$599$	7.22036	+	5.24590i	0.295016	+	0.214342i	0.725440	−	0.688285i	$-0.241636\pi$
$599$	7.22036	+	5.24590i	0.295016	+	0.214342i	−0.430424	+	0.902627i	$0.641636\pi$
$600$		0			0
$601$	−47.4325			−1.93481			−0.967405	−	0.253232i	$-0.918506\pi$
$601$	−47.4325			−1.93481			−0.967405	+	0.253232i	$0.918506\pi$
$602$		0			0
$603$	−13.6658	+	42.0591i	−0.556516	+	1.71278i
$604$		0			0
$605$	2.14873	+	6.61310i	0.0873581	+	0.268861i
$606$		0			0
$607$	−9.44749	−	29.0764i	−0.383462	−	1.18017i	−0.937590	−	0.347742i	$-0.886948\pi$
$607$	−9.44749	−	29.0764i	−0.383462	−	1.18017i	0.554129	−	0.832431i	$-0.313052\pi$
$608$		0			0
$609$	16.3303	−	11.8647i	0.661738	−	0.480781i
$610$		0			0
$611$	0.317147	−	0.976079i	0.0128304	−	0.0394879i
$612$		0			0
$613$	−1.12817	+	0.819660i	−0.0455662	+	0.0331058i	−0.610335	−	0.792143i	$-0.708965\pi$
$613$	−1.12817	+	0.819660i	−0.0455662	+	0.0331058i	0.564769	+	0.825249i	$0.308965\pi$
$614$		0			0
$615$	8.86065	−	17.6027i	0.357296	−	0.709808i
$616$		0			0
$617$	−14.4969	+	10.5326i	−0.583624	+	0.424028i	−0.840029	−	0.542542i	$-0.817462\pi$
$617$	−14.4969	+	10.5326i	−0.583624	+	0.424028i	0.256405	+	0.966570i	$0.417462\pi$
$618$		0			0
$619$	−10.0254	+	30.8549i	−0.402954	+	1.24016i	0.519638	+	0.854387i	$0.326067\pi$
$619$	−10.0254	+	30.8549i	−0.402954	+	1.24016i	−0.922592	+	0.385778i	$0.873933\pi$
$620$		0			0
$621$	15.7386	−	11.4347i	0.631566	−	0.458860i
$622$		0			0
$623$	−4.30832	−	13.2596i	−0.172609	−	0.531236i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$		0			0
$627$	33.0494	−	101.716i	1.31987	−	4.06213i
$628$		0			0
$629$	22.8330			0.910411
$630$		0			0
$631$	−15.7009	−	11.4073i	−0.625041	−	0.454119i	0.229637	−	0.973276i	$-0.426246\pi$
$631$	−15.7009	−	11.4073i	−0.625041	−	0.454119i	−0.854679	+	0.519157i	$0.826246\pi$
$632$		0			0
$633$	−57.2186	+	41.5717i	−2.27423	+	1.65233i
$634$		0			0
$635$	−1.52562	−	1.10843i	−0.0605424	−	0.0439866i
$636$		0			0
$637$	−0.185278	−	0.134612i	−0.00734097	−	0.00533353i
$638$		0			0
$639$	10.0443	+	30.9131i	0.397345	+	1.22290i
$640$		0			0
$641$	−5.92707	+	18.2416i	−0.234105	+	0.720502i	0.763134	+	0.646241i	$0.223660\pi$
$641$	−5.92707	+	18.2416i	−0.234105	+	0.720502i	−0.997239	+	0.0742610i	$0.976340\pi$
$642$		0			0
$643$	5.94343	−	4.31816i	0.234386	−	0.170292i	−0.464392	−	0.885630i	$-0.653727\pi$
$643$	5.94343	−	4.31816i	0.234386	−	0.170292i	0.698779	+	0.715338i	$0.253727\pi$
$644$		0			0
$645$	−3.98670	−	12.2698i	−0.156976	−	0.483122i
$646$		0			0
$647$	−45.8536			−1.80269			−0.901346	−	0.433100i	$-0.857420\pi$
$647$	−45.8536			−1.80269			−0.901346	+	0.433100i	$0.857420\pi$
$648$		0			0
$649$	33.6422	+	24.4425i	1.32057	+	0.959453i
$650$		0			0
$651$	11.5320	−	35.4920i	0.451976	−	1.39104i
$652$		0			0
$653$	35.9680			1.40754			0.703768	−	0.710430i	$-0.251499\pi$
$653$	35.9680			1.40754			0.703768	+	0.710430i	$0.251499\pi$
$654$		0			0
$655$	−10.4851			−0.409687
$656$		0			0
$657$	−75.0698			−2.92875
$658$		0			0
$659$	19.7307			0.768598			0.384299	−	0.923209i	$-0.374443\pi$
$659$	19.7307			0.768598			0.384299	+	0.923209i	$0.374443\pi$
$660$		0			0
$661$	13.6490	−	42.0072i	0.530883	−	1.63389i	−0.221497	−	0.975161i	$-0.571094\pi$
$661$	13.6490	−	42.0072i	0.530883	−	1.63389i	0.752380	−	0.658729i	$-0.228906\pi$
$662$		0			0
$663$	3.69124	+	2.68185i	0.143356	+	0.104154i
$664$		0			0
$665$	−22.8357			−0.885530
$666$		0			0
$667$	1.32500	+	4.07794i	0.0513043	+	0.157898i
$668$		0			0
$669$	23.6988	−	17.2182i	0.916250	−	0.665694i
$670$		0			0
$671$	3.06425	−	9.43080i	0.118294	−	0.364072i
$672$		0			0
$673$	1.42086	+	4.37296i	0.0547702	+	0.168565i	0.974700	−	0.223519i	$-0.0717543\pi$
$673$	1.42086	+	4.37296i	0.0547702	+	0.168565i	−0.919929	+	0.392084i	$0.871754\pi$
$674$		0			0
$675$	−8.64580	−	6.28154i	−0.332777	−	0.241777i
$676$		0			0
$677$	−3.97875	−	2.89073i	−0.152916	−	0.111100i	0.508697	−	0.860946i	$-0.330128\pi$
$677$	−3.97875	−	2.89073i	−0.152916	−	0.111100i	−0.661612	+	0.749846i	$0.730128\pi$
$678$		0			0
$679$	−6.81931	+	4.95452i	−0.261701	+	0.190137i
$680$		0			0
$681$	60.3100	+	43.8178i	2.31109	+	1.67910i
$682$		0			0
$683$	−8.72847			−0.333986			−0.166993	−	0.985958i	$-0.553406\pi$
$683$	−8.72847			−0.333986			−0.166993	+	0.985958i	$0.553406\pi$
$684$		0			0
$685$	5.84397	−	17.9859i	0.223287	−	0.687206i
$686$		0			0
$687$	25.8620	+	79.5951i	0.986697	+	3.03674i
$688$		0			0
$689$	−0.890144	−	2.73958i	−0.0339118	−	0.104370i
$690$		0			0
$691$	10.6534	−	7.74014i	0.405274	−	0.294449i	−0.366412	−	0.930453i	$-0.619414\pi$
$691$	10.6534	−	7.74014i	0.405274	−	0.294449i	0.771686	+	0.636004i	$0.219414\pi$
$692$		0			0
$693$	−23.5966	+	72.6230i	−0.896362	+	2.75872i
$694$		0			0
$695$	6.93669	−	5.03980i	0.263124	−	0.191171i
$696$		0			0
$697$	−5.03328	−	30.8015i	−0.190649	−	1.16669i
$698$		0			0
$699$	25.3753	−	18.4362i	0.959782	−	0.697322i
$700$		0			0
$701$	10.9948	−	33.8384i	0.415267	−	1.27806i	−0.496746	−	0.867896i	$-0.665472\pi$
$701$	10.9948	−	33.8384i	0.415267	−	1.27806i	0.912012	−	0.410163i	$-0.134528\pi$
$702$		0			0
$703$	−31.0812	+	22.5818i	−1.17225	+	0.851689i
$704$		0			0
$705$	3.20926	+	9.87708i	0.120868	+	0.371992i
$706$		0			0
$707$	12.7949	+	39.3788i	0.481203	+	1.48099i
$708$		0			0
$709$	−8.05324	+	24.7853i	−0.302446	+	0.930832i	0.678172	+	0.734903i	$0.262772\pi$
$709$	−8.05324	+	24.7853i	−0.302446	+	0.930832i	−0.980618	+	0.195929i	$0.937228\pi$
$710$		0			0
$711$	−71.9703			−2.69910
$712$		0			0
$713$	6.41326	+	4.65951i	0.240179	+	0.174500i
$714$		0			0
$715$	1.04260	−	0.757490i	0.0389909	−	0.0283285i
$716$		0			0
$717$	22.7531	+	16.5311i	0.849730	+	0.617365i
$718$		0			0
$719$	−36.9230	−	26.8261i	−1.37700	−	1.00045i	−0.997154	−	0.0753951i	$-0.975978\pi$
$719$	−36.9230	−	26.8261i	−1.37700	−	1.00045i	−0.379842	−	0.925051i	$-0.624022\pi$
$720$		0			0
$721$	−3.91893	−	12.0612i	−0.145949	−	0.449184i
$722$		0			0
$723$	19.6157	−	60.3708i	0.729514	−	2.24521i
$724$		0			0
$725$	1.90560	−	1.38450i	0.0707723	−	0.0514191i
$726$		0			0
$727$	−12.6490	−	38.9297i	−0.469127	−	1.44382i	−0.853718	−	0.520736i	$-0.825658\pi$
$727$	−12.6490	−	38.9297i	−0.469127	−	1.44382i	0.384591	−	0.923087i	$-0.374342\pi$
$728$		0			0
$729$	−11.4651			−0.424633
$730$		0			0
$731$	−16.5296	−	12.0095i	−0.611370	−	0.444186i
$732$		0			0
$733$	0.804354	−	2.47555i	0.0297095	−	0.0914364i	−0.935102	−	0.354378i	$-0.884693\pi$
$733$	0.804354	−	2.47555i	0.0297095	−	0.0914364i	0.964812	+	0.262942i	$0.0846926\pi$
$734$		0			0
$735$	2.31744			0.0854801
$736$		0			0
$737$	28.9513			1.06643
$738$		0			0
$739$	38.1728			1.40421			0.702104	−	0.712074i	$-0.252244\pi$
$739$	38.1728			1.40421			0.702104	+	0.712074i	$0.252244\pi$
$740$		0			0
$741$	−7.67702			−0.282022
$742$		0			0
$743$	−0.275409	+	0.847621i	−0.0101038	+	0.0310962i	−0.955981	−	0.293428i	$-0.905204\pi$
$743$	−0.275409	+	0.847621i	−0.0101038	+	0.0310962i	0.945878	+	0.324524i	$0.105204\pi$
$744$		0			0
$745$	−15.7739	−	11.4604i	−0.577910	−	0.419876i
$746$		0			0
$747$	63.0494			2.30686
$748$		0			0
$749$	−8.06086	−	24.8088i	−0.294537	−	0.906493i
$750$		0			0
$751$	−25.1444	+	18.2685i	−0.917533	+	0.666627i	−0.942909	−	0.333051i	$-0.891922\pi$
$751$	−25.1444	+	18.2685i	−0.917533	+	0.666627i	0.0253760	+	0.999678i	$0.491922\pi$
$752$		0			0
$753$	−12.5861	+	38.7360i	−0.458663	+	1.41162i
$754$		0			0
$755$	−4.65205	−	14.3175i	−0.169306	−	0.521069i
$756$		0			0
$757$	19.2078	+	13.9553i	0.698118	+	0.507212i	0.879319	−	0.476234i	$-0.157998\pi$
$757$	19.2078	+	13.9553i	0.698118	+	0.507212i	−0.181201	+	0.983446i	$0.557998\pi$
$758$		0			0
$759$	−19.2052	−	13.9534i	−0.697105	−	0.506476i
$760$		0			0
$761$	18.1163	−	13.1623i	0.656716	−	0.477132i	−0.208837	−	0.977951i	$-0.566968\pi$
$761$	18.1163	−	13.1623i	0.656716	−	0.477132i	0.865552	+	0.500819i	$0.166968\pi$
$762$		0			0
$763$	−25.0898	−	18.2288i	−0.908311	−	0.659927i
$764$		0			0
$765$	−31.5473			−1.14059
$766$		0			0
$767$	0.922403	−	2.83886i	0.0333060	−	0.102505i
$768$		0			0
$769$	10.7310	+	33.0268i	0.386971	+	1.19098i	0.935040	+	0.354542i	$0.115363\pi$
$769$	10.7310	+	33.0268i	0.386971	+	1.19098i	−0.548068	+	0.836433i	$0.684637\pi$
$770$		0			0
$771$	−17.0511	−	52.4780i	−0.614082	−	1.88995i
$772$		0			0
$773$	−2.60896	+	1.89552i	−0.0938377	+	0.0681771i	−0.633715	−	0.773567i	$-0.718471\pi$
$773$	−2.60896	+	1.89552i	−0.0938377	+	0.0681771i	0.539877	+	0.841744i	$0.318471\pi$
$774$		0			0
$775$	1.34569	−	4.14160i	0.0483385	−	0.148771i
$776$		0			0
$777$	32.4773	−	23.5962i	1.16512	−	0.846508i
$778$		0			0
$779$	37.3142	+	36.9504i	1.33692	+	1.32388i
$780$		0			0
$781$	17.2150	−	12.5075i	0.616002	−	0.447552i
$782$		0			0
$783$	−7.77865	+	23.9402i	−0.277986	+	0.855554i
$784$		0			0
$785$	−13.4425	+	9.76658i	−0.479785	+	0.348584i
$786$		0			0
$787$	−2.66964	−	8.21632i	−0.0951625	−	0.292880i	0.892133	−	0.451772i	$-0.149208\pi$
$787$	−2.66964	−	8.21632i	−0.0951625	−	0.292880i	−0.987296	+	0.158892i	$0.949208\pi$
$788$		0			0
$789$	−18.9401	−	58.2917i	−0.674286	−	2.07524i
$790$		0			0
$791$	−13.9126	+	42.8184i	−0.494674	+	1.52245i
$792$		0			0
$793$	−0.711792			−0.0252765
$794$		0			0
$795$	23.5819	+	17.1333i	0.836364	+	0.607654i
$796$		0			0
$797$	−19.1309	+	13.8994i	−0.677650	+	0.492341i	−0.872577	−	0.488476i	$-0.837553\pi$
$797$	−19.1309	+	13.8994i	−0.677650	+	0.492341i	0.194927	+	0.980818i	$0.437553\pi$
$798$		0			0
$799$	13.3062	+	9.66752i	0.470739	+	0.342012i
$800$		0			0
$801$	26.2185	+	19.0489i	0.926387	+	0.673059i
$802$		0			0
$803$	15.1866	+	46.7396i	0.535924	+	1.64941i
$804$		0			0
$805$	−1.56630	+	4.82059i	−0.0552050	+	0.169903i
$806$		0			0
$807$	−13.6658	+	9.92875i	−0.481057	+	0.349509i
$808$		0			0
$809$	−5.59320	−	17.2141i	−0.196647	−	0.605216i	−0.999953	−	0.00965047i	$-0.996928\pi$
$809$	−5.59320	−	17.2141i	−0.196647	−	0.605216i	0.803307	−	0.595565i	$-0.203072\pi$
$810$		0			0
$811$	−28.1652			−0.989015			−0.494507	−	0.869173i	$-0.664652\pi$
$811$	−28.1652			−0.989015			−0.494507	+	0.869173i	$0.664652\pi$
$812$		0			0
$813$	24.1137	+	17.5197i	0.845706	+	0.614441i
$814$		0			0
$815$	−3.27230	+	10.0711i	−0.114624	+	0.352776i
$816$		0			0
$817$	34.3781			1.20274
$818$		0			0
$819$	5.48124			0.191530
$820$		0			0
$821$	−13.2112			−0.461075			−0.230537	−	0.973063i	$-0.574048\pi$
$821$	−13.2112			−0.461075			−0.230537	+	0.973063i	$0.574048\pi$
$822$		0			0
$823$	−26.2174			−0.913883			−0.456941	−	0.889497i	$-0.651055\pi$
$823$	−26.2174			−0.913883			−0.456941	+	0.889497i	$0.651055\pi$
$824$		0			0
$825$	−4.02981	+	12.4025i	−0.140300	+	0.431798i
$826$		0			0
$827$	−36.3449	−	26.4061i	−1.26384	−	0.918231i	−0.264898	−	0.964277i	$-0.585338\pi$
$827$	−36.3449	−	26.4061i	−1.26384	−	0.918231i	−0.998939	+	0.0460452i	$0.985338\pi$
$828$		0			0
$829$	34.6541			1.20359			0.601793	−	0.798652i	$-0.294453\pi$
$829$	34.6541			1.20359			0.601793	+	0.798652i	$0.294453\pi$
$830$		0			0
$831$	−12.4849	−	38.4247i	−0.433098	−	1.33294i
$832$		0			0
$833$	2.96921	−	2.15726i	0.102877	−	0.0747445i
$834$		0			0
$835$	3.73151	−	11.4844i	0.129134	−	0.397435i
$836$		0			0
$837$	14.3811	+	44.2604i	0.497083	+	1.52986i
$838$		0			0
$839$	−0.473730	−	0.344185i	−0.0163550	−	0.0118826i	0.579578	−	0.814917i	$-0.303218\pi$
$839$	−0.473730	−	0.344185i	−0.0163550	−	0.0118826i	−0.595933	+	0.803034i	$0.703218\pi$
$840$		0			0
$841$	18.9729	+	13.7846i	0.654239	+	0.475332i
$842$		0			0
$843$	6.82335	−	4.95745i	0.235009	−	0.170744i
$844$		0			0
$845$	10.4424	+	7.58683i	0.359229	+	0.260995i
$846$		0			0
$847$	19.3612			0.665260
$848$		0			0
$849$	−24.1970	+	74.4707i	−0.830438	+	2.55583i
$850$		0			0
$851$	2.63513	+	8.11010i	0.0903312	+	0.278011i
$852$		0			0
$853$	5.55872	+	17.1080i	0.190327	+	0.585766i	0.999999	−	0.00111623i	$-0.000355306\pi$
$853$	5.55872	+	17.1080i	0.190327	+	0.585766i	−0.809673	+	0.586882i	$0.800355\pi$
$854$		0			0
$855$	42.9435	−	31.2003i	1.46864	−	1.06703i
$856$		0			0
$857$	−1.99426	+	6.13770i	−0.0681226	+	0.209660i	−0.979323	−	0.202304i	$-0.935157\pi$
$857$	−1.99426	+	6.13770i	−0.0681226	+	0.209660i	0.911200	+	0.411964i	$0.135157\pi$
$858$		0			0
$859$	−6.07954	+	4.41704i	−0.207431	+	0.150708i	−0.686651	−	0.726988i	$-0.740920\pi$
$859$	−6.07954	+	4.41704i	−0.207431	+	0.150708i	0.479220	+	0.877695i	$0.340920\pi$
$860$		0			0
$861$	−38.9903	−	38.6101i	−1.32879	−	1.31583i
$862$		0			0
$863$	9.25479	−	6.72400i	0.315037	−	0.228888i	−0.419018	−	0.907978i	$-0.637626\pi$
$863$	9.25479	−	6.72400i	0.315037	−	0.228888i	0.734055	+	0.679090i	$0.237626\pi$
$864$		0			0
$865$	−8.09642	+	24.9182i	−0.275286	+	0.847245i
$866$		0			0
$867$	−16.8261	+	12.2249i	−0.571446	+	0.415180i
$868$		0			0
$869$	14.5596	+	44.8098i	0.493901	+	1.52007i
$870$		0			0
$871$	−0.642186	−	1.97645i	−0.0217597	−	0.0669693i
$872$		0			0
$873$	6.05467	−	18.6344i	0.204920	−	0.630678i
$874$		0			0
$875$	2.78442			0.0941305
$876$		0			0
$877$	−12.1985	−	8.86272i	−0.411914	−	0.299273i	0.362462	−	0.931998i	$-0.381936\pi$
$877$	−12.1985	−	8.86272i	−0.411914	−	0.299273i	−0.774376	+	0.632726i	$0.781936\pi$
$878$		0			0
$879$	−26.1743	+	19.0168i	−0.882838	+	0.641419i
$880$		0			0
$881$	−31.4425	−	22.8443i	−1.05932	−	0.769645i	−0.0853615	−	0.996350i	$-0.527205\pi$
$881$	−31.4425	−	22.8443i	−1.05932	−	0.769645i	−0.973963	+	0.226706i	$0.927205\pi$
$882$		0			0
$883$	−0.0602632	−	0.0437838i	−0.00202802	−	0.00147344i	0.586771	−	0.809753i	$-0.300399\pi$
$883$	−0.0602632	−	0.0437838i	−0.00202802	−	0.00147344i	−0.588799	+	0.808280i	$0.700399\pi$
$884$		0			0
$885$	9.33392	+	28.7268i	0.313756	+	0.965642i
$886$		0			0
$887$	−2.39871	+	7.38247i	−0.0805408	+	0.247879i	−0.983217	−	0.182442i	$-0.941600\pi$
$887$	−2.39871	+	7.38247i	−0.0805408	+	0.247879i	0.902676	+	0.430321i	$0.141600\pi$
$888$		0			0
$889$	−4.24796	+	3.08632i	−0.142472	+	0.103512i
$890$		0			0
$891$	−17.6421	−	54.2968i	−0.591033	−	1.81901i
$892$		0			0
$893$	−27.6741			−0.926079
$894$		0			0
$895$	8.90801	+	6.47205i	0.297762	+	0.216337i
$896$		0			0
$897$	−0.526569	+	1.62061i	−0.0175816	+	0.0541106i
$898$		0			0
$899$	−10.2574			−0.342103
$900$		0			0
$901$	46.1631			1.53792
$902$		0			0
$903$	−35.9224			−1.19542
$904$		0			0
$905$	21.1388			0.702679
$906$		0			0
$907$	1.19400	−	3.67474i	0.0396460	−	0.122018i	−0.929275	−	0.369389i	$-0.879567\pi$
$907$	1.19400	−	3.67474i	0.0396460	−	0.122018i	0.968921	+	0.247372i	$0.0795669\pi$
$908$		0			0
$909$	−77.8644	−	56.5718i	−2.58260	−	1.87637i
$910$		0			0
$911$	40.6015			1.34519			0.672595	−	0.740011i	$-0.265180\pi$
$911$	40.6015			1.34519			0.672595	+	0.740011i	$0.265180\pi$
$912$		0			0
$913$	−12.7549	−	39.2556i	−0.422126	−	1.29917i
$914$		0			0
$915$	5.82712	−	4.23365i	0.192639	−	0.139960i
$916$		0			0
$917$	−9.02173	+	27.7660i	−0.297924	+	0.916915i
$918$		0			0
$919$	14.3212	+	44.0761i	0.472412	+	1.45393i	0.849416	+	0.527723i	$0.176954\pi$
$919$	14.3212	+	44.0761i	0.472412	+	1.45393i	−0.377004	+	0.926211i	$0.623046\pi$
$920$		0			0
$921$	−65.0021	−	47.2268i	−2.14189	−	1.55617i
$922$		0			0
$923$	−1.23572	−	0.897801i	−0.0406741	−	0.0295515i
$924$		0			0
$925$	3.78982	−	2.75346i	0.124608	−	0.0905333i
$926$		0			0
$927$	23.8489	+	17.3273i	0.783301	+	0.569102i
$928$		0			0
$929$	26.8683			0.881520			0.440760	−	0.897625i	$-0.354709\pi$
$929$	26.8683			0.881520			0.440760	+	0.897625i	$0.354709\pi$
$930$		0			0
$931$	−1.90828	+	5.87309i	−0.0625415	+	0.192483i
$932$		0			0
$933$	0.172735	+	0.531624i	0.00565509	+	0.0174046i
$934$		0			0
$935$	6.38202	+	19.6418i	0.208714	+	0.642357i
$936$		0			0
$937$	−12.9387	+	9.40051i	−0.422689	+	0.307101i	−0.778719	−	0.627373i	$-0.784130\pi$
$937$	−12.9387	+	9.40051i	−0.422689	+	0.307101i	0.356030	+	0.934475i	$0.384130\pi$
$938$		0			0
$939$	15.1604	−	46.6590i	0.494742	−	1.52266i
$940$		0			0
$941$	23.6374	−	17.1736i	0.770556	−	0.559842i	−0.131574	−	0.991306i	$-0.542003\pi$
$941$	23.6374	−	17.1736i	0.770556	−	0.559842i	0.902130	+	0.431465i	$0.142003\pi$
$942$		0			0
$943$	10.3596	−	5.34255i	0.337354	−	0.173978i
$944$		0			0
$945$	−24.0735	+	17.4904i	−0.783111	+	0.568963i
$946$		0			0
$947$	3.75626	−	11.5606i	0.122062	−	0.375668i	−0.871292	−	0.490764i	$-0.836718\pi$
$947$	3.75626	−	11.5606i	0.122062	−	0.375668i	0.993354	+	0.115096i	$0.0367176\pi$
$948$		0			0
$949$	2.85396	−	2.07352i	0.0926434	−	0.0673094i
$950$		0			0
$951$	7.67600	+	23.6243i	0.248911	+	0.766070i
$952$		0			0
$953$	1.78570	+	5.49581i	0.0578444	+	0.178027i	0.975804	−	0.218647i	$-0.0701644\pi$
$953$	1.78570	+	5.49581i	0.0578444	+	0.178027i	−0.917960	+	0.396674i	$0.870164\pi$
$954$		0			0
$955$	2.80178	−	8.62299i	0.0906634	−	0.279033i
$956$		0			0
$957$	30.7168			0.992934
$958$		0			0
$959$	−42.6008	−	30.9513i	−1.37565	−	0.999469i
$960$		0			0
$961$	9.73757	−	7.07476i	0.314115	−	0.228218i
$962$		0			0
$963$	49.0549	+	35.6405i	1.58077	+	1.14850i
$964$		0			0
$965$	18.2519	+	13.2608i	0.587549	+	0.426880i
$966$		0			0
$967$	8.23352	+	25.3402i	0.264772	+	0.814885i	0.991746	+	0.128219i	$0.0409262\pi$
$967$	8.23352	+	25.3402i	0.264772	+	0.814885i	−0.726974	+	0.686665i	$0.759074\pi$
$968$		0			0
$969$	38.0183	−	117.008i	1.22132	−	3.75885i
$970$		0			0
$971$	26.5635	−	19.2995i	0.852462	−	0.619350i	−0.0733619	−	0.997305i	$-0.523373\pi$
$971$	26.5635	−	19.2995i	0.852462	−	0.619350i	0.925824	+	0.377956i	$0.123373\pi$
$972$		0			0
$973$	−7.37754	−	22.7057i	−0.236513	−	0.727912i
$974$		0			0
$975$	0.936080			0.0299785
$976$		0			0
$977$	−43.6030	−	31.6794i	−1.39498	−	1.01351i	−0.995298	−	0.0968621i	$-0.969119\pi$
$977$	−43.6030	−	31.6794i	−1.39498	−	1.01351i	−0.399685	−	0.916652i	$-0.630881\pi$
$978$		0			0
$979$	6.55612	−	20.1777i	0.209535	−	0.644881i
$980$		0			0
$981$	72.0883			2.30160
$982$		0			0
$983$	−19.6789			−0.627660			−0.313830	−	0.949479i	$-0.601612\pi$
$983$	−19.6789			−0.627660			−0.313830	+	0.949479i	$0.601612\pi$
$984$		0			0
$985$	−25.6892			−0.818526
$986$		0			0
$987$	28.9172			0.920445
$988$		0			0
$989$	2.35801	−	7.25719i	0.0749802	−	0.230765i
$990$		0			0
$991$	−33.7404	−	24.5138i	−1.07180	−	0.778707i	−0.0955635	−	0.995423i	$-0.530465\pi$
$991$	−33.7404	−	24.5138i	−1.07180	−	0.778707i	−0.976235	+	0.216716i	$0.930465\pi$
$992$		0			0
$993$	38.5048			1.22191
$994$		0			0
$995$	6.74561	+	20.7609i	0.213850	+	0.658163i
$996$		0			0
$997$	3.14703	−	2.28645i	0.0996674	−	0.0724126i	−0.536835	−	0.843687i	$-0.680380\pi$
$997$	3.14703	−	2.28645i	0.0996674	−	0.0724126i	0.636503	+	0.771274i	$0.280380\pi$
$998$		0			0
$999$	−15.4700	+	47.6117i	−0.489449	+	1.50637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.u.a.201.6	✓	24
41.10	even	5	inner	820.2.u.a.461.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.u.a.201.6	✓	24	1.1	even	1	trivial
820.2.u.a.461.6	yes	24	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)

\(f(q)\)	\(=\)	\(q+3.07771 q^{3} +(0.309017 - 0.951057i) q^{5} +(-2.25264 - 1.63664i) q^{7} +6.47232 q^{9} +(-1.30935 - 4.02977i) q^{11} +(-0.246061 + 0.178774i) q^{13} +(0.951066 - 2.92708i) q^{15} +(-1.50621 - 4.63563i) q^{17} +(6.63495 + 4.82057i) q^{19} +(-6.93298 - 5.03710i) q^{21} +(1.47271 - 1.06999i) q^{23} +(-0.809017 - 0.587785i) q^{25} +10.6868 q^{27} +(-0.727875 + 2.24017i) q^{29} +(1.34569 + 4.14160i) q^{31} +(-4.02981 - 12.4025i) q^{33} +(-2.25264 + 1.63664i) q^{35} +(-1.44758 + 4.45520i) q^{37} +(-0.757304 + 0.550214i) q^{39} +(6.32912 + 0.970675i) q^{41} +(3.39125 - 2.46389i) q^{43} +(2.00006 - 6.15554i) q^{45} +(-2.72993 + 1.98341i) q^{47} +(0.232682 + 0.716122i) q^{49} +(-4.63567 - 14.2671i) q^{51} +(-2.92668 + 9.00740i) q^{53} -4.23715 q^{55} +(20.4205 + 14.8363i) q^{57} +(-7.93983 + 5.76862i) q^{59} +(1.89333 + 1.37558i) q^{61} +(-14.5798 - 10.5928i) q^{63} +(0.0939869 + 0.289262i) q^{65} +(-2.11143 + 6.49831i) q^{67} +(4.53258 - 3.29311i) q^{69} +(1.55188 + 4.77620i) q^{71} -11.5986 q^{73} +(-2.48992 - 1.80903i) q^{75} +(-3.64578 + 11.2206i) q^{77} -11.1197 q^{79} +13.4739 q^{81} +9.74140 q^{83} -4.87419 q^{85} +(-2.24019 + 6.89460i) q^{87} +(4.05088 + 2.94313i) q^{89} +0.846874 q^{91} +(4.14164 + 12.7466i) q^{93} +(6.63495 - 4.82057i) q^{95} +(0.935472 - 2.87909i) q^{97} +(-8.47453 - 26.0819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 6 q^{5} + 5 q^{7} + 18 q^{9} - 7 q^{11} - 5 q^{13} + 2 q^{15} + 3 q^{17} - q^{19} + 2 q^{21} + 20 q^{23} - 6 q^{25} + 20 q^{27} - 15 q^{29} - q^{31} - 6 q^{33} + 5 q^{35} + q^{37} + 28 q^{41}+ \cdots + 34 q^{99}+O(q^{100}) \) 24 * q + 2 * q^3 - 6 * q^5 + 5 * q^7 + 18 * q^9 - 7 * q^11 - 5 * q^13 + 2 * q^15 + 3 * q^17 - q^19 + 2 * q^21 + 20 * q^23 - 6 * q^25 + 20 * q^27 - 15 * q^29 - q^31 - 6 * q^33 + 5 * q^35 + q^37 + 28 * q^41 - 4 * q^43 + 3 * q^45 + 3 * q^47 + 3 * q^49 + 37 * q^51 + 29 * q^53 - 12 * q^55 + 17 * q^57 - 4 * q^59 - 14 * q^61 - 10 * q^63 + 5 * q^65 - 14 * q^67 - 26 * q^69 + q^71 - 84 * q^73 - 3 * q^75 + 24 * q^77 + 18 * q^79 - 40 * q^81 - 6 * q^83 - 12 * q^85 + 39 * q^87 + 12 * q^89 - 2 * q^91 - 58 * q^93 - q^95 - 20 * q^97 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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