LMFDB - Embedded newform 820.2.y.a.413.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(137,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.137"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.y (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			413.9
Character	$\chi$	$=$	820.413
Dual form			820.2.y.a.137.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.629944 + 0.260931i) q^{3} +(-1.47443 + 1.68109i) q^{5} +(1.11716 + 2.69706i) q^{7} +(-1.79258 + 1.79258i) q^{9} +(-4.93128 - 2.04260i) q^{11} +(3.82604 - 1.58480i) q^{13} +(0.490161 - 1.44372i) q^{15} +(-5.47789 - 2.26902i) q^{17} +(2.03983 - 0.844926i) q^{19} +(-1.40750 - 1.40750i) q^{21} +(-1.25809 + 1.25809i) q^{23} +(-0.652104 - 4.95729i) q^{25} +(1.44428 - 3.48680i) q^{27} +(2.14163 + 0.887091i) q^{29} -4.47182i q^{31} +3.63941 q^{33} +(-6.18117 - 2.09859i) q^{35} +(5.22748 - 5.22748i) q^{37} +(-1.99667 + 1.99667i) q^{39} +(-5.92303 + 2.43263i) q^{41} -8.17602 q^{43} +(-0.370445 - 5.65650i) q^{45} +(-9.28679 - 3.84671i) q^{47} +(-1.07634 + 1.07634i) q^{49} +4.04282 q^{51} +(3.57694 + 8.63550i) q^{53} +(10.7046 - 5.27823i) q^{55} +(-1.06451 + 1.06451i) q^{57} +6.46953i q^{59} +(-7.01064 + 7.01064i) q^{61} +(-6.83728 - 2.83209i) q^{63} +(-2.97705 + 8.76857i) q^{65} +(-6.41247 - 2.65613i) q^{67} +(0.464251 - 1.12080i) q^{69} +(2.83148 - 6.83579i) q^{71} -9.24517 q^{73} +(1.70430 + 2.95266i) q^{75} -15.5819i q^{77} +(-4.47929 + 10.8140i) q^{79} -5.03191i q^{81} +(-3.73755 - 3.73755i) q^{83} +(11.8912 - 5.86330i) q^{85} -1.58058 q^{87} +(-2.29242 - 0.949551i) q^{89} +(8.54858 + 8.54858i) q^{91} +(1.16684 + 2.81700i) q^{93} +(-1.58720 + 4.67492i) q^{95} +(1.24039 - 2.99457i) q^{97} +(12.5012 - 5.17817i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.629944	+	0.260931i	−0.363699	+	0.150649i	−0.557046	−	0.830481i	$-0.688065\pi$
$3$	−0.629944	+	0.260931i	−0.363699	+	0.150649i	0.193348	+	0.981130i	$0.438065\pi$
$4$		0			0
$5$	−1.47443	+	1.68109i	−0.659386	+	0.751805i
$5$	−1.47443	+	1.68109i	−0.659386	+	0.751805i
$6$		0			0
$7$	1.11716	+	2.69706i	0.422246	+	1.01939i	0.981683	+	0.190520i	$0.0610174\pi$
$7$	1.11716	+	2.69706i	0.422246	+	1.01939i	−0.559437	+	0.828873i	$0.688983\pi$
$8$		0			0
$9$	−1.79258	+	1.79258i	−0.597525	+	0.597525i
$10$		0			0
$11$	−4.93128	−	2.04260i	−1.48684	−	0.615868i	−0.516211	−	0.856462i	$-0.672658\pi$
$11$	−4.93128	−	2.04260i	−1.48684	−	0.615868i	−0.970626	+	0.240594i	$0.922658\pi$
$12$		0			0
$13$	3.82604	−	1.58480i	1.06115	−	0.439543i	0.217291	−	0.976107i	$-0.430278\pi$
$13$	3.82604	−	1.58480i	1.06115	−	0.439543i	0.843860	+	0.536563i	$0.180278\pi$
$14$		0			0
$15$	0.490161	−	1.44372i	0.126559	−	0.372766i
$16$		0			0
$17$	−5.47789	−	2.26902i	−1.32858	−	0.550317i	−0.398332	−	0.917241i	$-0.630411\pi$
$17$	−5.47789	−	2.26902i	−1.32858	−	0.550317i	−0.930251	+	0.366924i	$0.880411\pi$
$18$		0			0
$19$	2.03983	−	0.844926i	0.467969	−	0.193839i	−0.136222	−	0.990678i	$-0.543496\pi$
$19$	2.03983	−	0.844926i	0.467969	−	0.193839i	0.604192	+	0.796839i	$0.293496\pi$
$20$		0			0
$21$	−1.40750	−	1.40750i	−0.307141	−	0.307141i
$22$		0			0
$23$	−1.25809	+	1.25809i	−0.262330	+	0.262330i	−0.826000	−	0.563670i	$-0.809389\pi$
$23$	−1.25809	+	1.25809i	−0.262330	+	0.262330i	0.563670	+	0.826000i	$0.309389\pi$
$24$		0			0
$25$	−0.652104	−	4.95729i	−0.130421	−	0.991459i
$26$		0			0
$27$	1.44428	−	3.48680i	0.277951	−	0.671034i
$28$		0			0
$29$	2.14163	+	0.887091i	0.397690	+	0.164729i	0.572560	−	0.819863i	$-0.305950\pi$
$29$	2.14163	+	0.887091i	0.397690	+	0.164729i	−0.174870	+	0.984592i	$0.555950\pi$
$30$		0			0
$31$		−	4.47182i		−	0.803162i	−0.915823	−	0.401581i	$-0.868461\pi$
$31$		−	4.47182i		−	0.803162i	0.915823	−	0.401581i	$-0.131539\pi$
$32$		0			0
$33$	3.63941			0.633540
$34$		0			0
$35$	−6.18117	−	2.09859i	−1.04481	−	0.354726i
$36$		0			0
$37$	5.22748	−	5.22748i	0.859393	−	0.859393i	−0.131874	−	0.991267i	$-0.542099\pi$
$37$	5.22748	−	5.22748i	0.859393	−	0.859393i	0.991267	+	0.131874i	$0.0420993\pi$
$38$		0			0
$39$	−1.99667	+	1.99667i	−0.319723	+	0.319723i
$40$		0			0
$41$	−5.92303	+	2.43263i	−0.925022	+	0.379913i
$41$	−5.92303	+	2.43263i	−0.925022	+	0.379913i
$42$		0			0
$43$	−8.17602			−1.24683			−0.623415	−	0.781891i	$-0.714255\pi$
$43$	−8.17602			−1.24683			−0.623415	+	0.781891i	$0.714255\pi$
$44$		0			0
$45$	−0.370445	−	5.65650i	−0.0552227	−	0.843222i
$46$		0			0
$47$	−9.28679	−	3.84671i	−1.35462	−	0.561101i	−0.417043	−	0.908887i	$-0.636934\pi$
$47$	−9.28679	−	3.84671i	−1.35462	−	0.561101i	−0.937574	+	0.347786i	$0.886934\pi$
$48$		0			0
$49$	−1.07634	+	1.07634i	−0.153763	+	0.153763i
$50$		0			0
$51$	4.04282			0.566109
$52$		0			0
$53$	3.57694	+	8.63550i	0.491330	+	1.18618i	0.954043	+	0.299669i	$0.0968761\pi$
$53$	3.57694	+	8.63550i	0.491330	+	1.18618i	−0.462713	+	0.886508i	$0.653124\pi$
$54$		0			0
$55$	10.7046	−	5.27823i	1.44341	−	0.711716i
$56$		0			0
$57$	−1.06451	+	1.06451i	−0.140998	+	0.140998i
$58$		0			0
$59$			6.46953i			0.842261i	0.907000	+	0.421131i	$0.138367\pi$
$59$			6.46953i			0.842261i	−0.907000	+	0.421131i	$0.861633\pi$
$60$		0			0
$61$	−7.01064	+	7.01064i	−0.897620	+	0.897620i	−0.995225	−	0.0976052i	$-0.968882\pi$
$61$	−7.01064	+	7.01064i	−0.897620	+	0.897620i	0.0976052	+	0.995225i	$0.468882\pi$
$62$		0			0
$63$	−6.83728	−	2.83209i	−0.861416	−	0.356810i
$64$		0			0
$65$	−2.97705	+	8.76857i	−0.369257	+	1.08761i
$66$		0			0
$67$	−6.41247	−	2.65613i	−0.783408	−	0.324498i	−0.0451181	−	0.998982i	$-0.514366\pi$
$67$	−6.41247	−	2.65613i	−0.783408	−	0.324498i	−0.738290	+	0.674483i	$0.764366\pi$
$68$		0			0
$69$	0.464251	−	1.12080i	0.0558892	−	0.134929i
$70$		0			0
$71$	2.83148	−	6.83579i	0.336035	−	0.811259i	−0.662054	−	0.749456i	$-0.730315\pi$
$71$	2.83148	−	6.83579i	0.336035	−	0.811259i	0.998088	−	0.0618030i	$-0.0196851\pi$
$72$		0			0
$73$	−9.24517			−1.08207			−0.541033	−	0.841002i	$-0.681966\pi$
$73$	−9.24517			−1.08207			−0.541033	+	0.841002i	$0.681966\pi$
$74$		0			0
$75$	1.70430	+	2.95266i	0.196796	+	0.340944i
$76$		0			0
$77$		−	15.5819i		−	1.77572i
$78$		0			0
$79$	−4.47929	+	10.8140i	−0.503959	+	1.21666i	0.443352	+	0.896348i	$0.353789\pi$
$79$	−4.47929	+	10.8140i	−0.503959	+	1.21666i	−0.947310	+	0.320317i	$0.896211\pi$
$80$		0			0
$81$		−	5.03191i		−	0.559101i
$82$		0			0
$83$	−3.73755	−	3.73755i	−0.410250	−	0.410250i	0.471576	−	0.881825i	$-0.343685\pi$
$83$	−3.73755	−	3.73755i	−0.410250	−	0.410250i	−0.881825	+	0.471576i	$0.843685\pi$
$84$		0			0
$85$	11.8912	−	5.86330i	1.28978	−	0.635964i
$86$		0			0
$87$	−1.58058			−0.169456
$88$		0			0
$89$	−2.29242	−	0.949551i	−0.242996	−	0.100652i	0.257862	−	0.966182i	$-0.416982\pi$
$89$	−2.29242	−	0.949551i	−0.242996	−	0.100652i	−0.500858	+	0.865530i	$0.666982\pi$
$90$		0			0
$91$	8.54858	+	8.54858i	0.896135	+	0.896135i
$92$		0			0
$93$	1.16684	+	2.81700i	0.120995	+	0.292109i
$94$		0			0
$95$	−1.58720	+	4.67492i	−0.162843	+	0.479636i
$96$		0			0
$97$	1.24039	−	2.99457i	0.125943	−	0.304053i	−0.848314	−	0.529493i	$-0.822382\pi$
$97$	1.24039	−	2.99457i	0.125943	−	0.304053i	0.974257	+	0.225440i	$0.0723821\pi$
$98$		0			0
$99$	12.5012	−	5.17817i	1.25642	−	0.520426i
$100$		0			0
$101$	7.55108	+	18.2299i	0.751361	+	1.81395i	0.551617	+	0.834098i	$0.314011\pi$
$101$	7.55108	+	18.2299i	0.751361	+	1.81395i	0.199744	+	0.979848i	$0.435989\pi$
$102$		0			0
$103$		−	7.52744i		−	0.741701i	−0.928693	−	0.370850i	$-0.879066\pi$
$103$		−	7.52744i		−	0.741701i	0.928693	−	0.370850i	$-0.120934\pi$
$104$		0			0
$105$	4.44138	−	0.290866i	0.433434	−	0.0283856i
$106$		0			0
$107$	−10.5225	−	10.5225i	−1.01725	−	1.01725i	−0.999849	−	0.0173986i	$-0.994462\pi$
$107$	−10.5225	−	10.5225i	−1.01725	−	1.01725i	−0.0173986	−	0.999849i	$-0.505538\pi$
$108$		0			0
$109$	3.85967	+	9.31806i	0.369689	+	0.892508i	0.993801	+	0.111173i	$0.0354608\pi$
$109$	3.85967	+	9.31806i	0.369689	+	0.892508i	−0.624112	+	0.781335i	$0.714539\pi$
$110$		0			0
$111$	−1.92901	+	4.65704i	−0.183093	+	0.442027i
$112$		0			0
$113$	1.42119	−	1.42119i	0.133694	−	0.133694i	−0.637093	−	0.770787i	$-0.719863\pi$
$113$	1.42119	−	1.42119i	0.133694	−	0.133694i	0.770787	+	0.637093i	$0.219863\pi$
$114$		0			0
$115$	−0.259991	−	3.96992i	−0.0242442	−	0.370197i
$116$		0			0
$117$	−4.01759	+	9.69933i	−0.371427	+	0.896703i
$118$		0			0
$119$		−	17.3090i		−	1.58672i
$120$		0			0
$121$	12.3671	+	12.3671i	1.12428	+	1.12428i
$122$		0			0
$123$	3.09643	−	3.07793i	0.279196	−	0.277527i
$124$		0			0
$125$	9.29512	+	6.21295i	0.831381	+	0.555703i
$126$		0			0
$127$	−1.73499	−	1.73499i	−0.153955	−	0.153955i	0.625927	−	0.779882i	$-0.284721\pi$
$127$	−1.73499	−	1.73499i	−0.153955	−	0.153955i	−0.779882	+	0.625927i	$0.784721\pi$
$128$		0			0
$129$	5.15044	−	2.13338i	0.453471	−	0.187834i
$130$		0			0
$131$	9.88634	+	9.88634i	0.863774	+	0.863774i	0.991774	−	0.128000i	$-0.0408558\pi$
$131$	9.88634	+	9.88634i	0.863774	+	0.863774i	−0.128000	+	0.991774i	$0.540856\pi$
$132$		0			0
$133$	4.55763	+	4.55763i	0.395197	+	0.395197i
$134$		0			0
$135$	3.73212	+	7.56900i	0.321209	+	0.651436i
$136$		0			0
$137$	14.3318	+	5.93641i	1.22444	+	0.507182i	0.898820	−	0.438317i	$-0.144425\pi$
$137$	14.3318	+	5.93641i	1.22444	+	0.507182i	0.325625	+	0.945499i	$0.394425\pi$
$138$		0			0
$139$			8.41617i			0.713850i	0.934133	+	0.356925i	$0.116175\pi$
$139$			8.41617i			0.713850i	−0.934133	+	0.356925i	$0.883825\pi$
$140$		0			0
$141$	6.85389			0.577202
$142$		0			0
$143$	−22.1044			−1.84846
$144$		0			0
$145$	−4.64896	+	2.29231i	−0.386075	+	0.190366i
$146$		0			0
$147$	0.397184	−	0.958887i	0.0327592	−	0.0790877i
$148$		0			0
$149$	16.1318	−	6.68202i	1.32157	−	0.547413i	0.393332	−	0.919397i	$-0.371322\pi$
$149$	16.1318	−	6.68202i	1.32157	−	0.547413i	0.928239	+	0.371984i	$0.121322\pi$
$150$		0			0
$151$	−21.5502	−	8.92638i	−1.75373	−	0.726419i	−0.997387	−	0.0722425i	$-0.976984\pi$
$151$	−21.5502	−	8.92638i	−1.75373	−	0.726419i	−0.756342	−	0.654176i	$-0.773016\pi$
$152$		0			0
$153$	13.8869	−	5.75215i	1.12269	−	0.465034i
$154$		0			0
$155$	7.51751	+	6.59339i	0.603821	+	0.529594i
$156$		0			0
$157$	−3.41389	+	1.41408i	−0.272458	+	0.112856i	−0.514729	−	0.857353i	$-0.672108\pi$
$157$	−3.41389	+	1.41408i	−0.272458	+	0.112856i	0.242271	+	0.970209i	$0.422108\pi$
$158$		0			0
$159$	−4.50655	−	4.50655i	−0.357392	−	0.357392i
$160$		0			0
$161$	−4.79863	−	1.98766i	−0.378185	−	0.156649i
$162$		0			0
$163$	−12.9746	+	12.9746i	−1.01625	+	1.01625i	−0.0163799	+	0.999866i	$0.505214\pi$
$163$	−12.9746	+	12.9746i	−1.01625	+	1.01625i	−0.999866	+	0.0163799i	$0.994786\pi$
$164$		0			0
$165$	−5.36606	+	6.11816i	−0.417747	+	0.476298i
$166$		0			0
$167$	−1.42392	−	3.43766i	−0.110187	−	0.266014i	0.859162	−	0.511704i	$-0.170985\pi$
$167$	−1.42392	−	3.43766i	−0.110187	−	0.266014i	−0.969348	+	0.245690i	$0.920985\pi$
$168$		0			0
$169$	2.93458	−	2.93458i	0.225737	−	0.225737i
$170$		0			0
$171$	−2.14196	+	5.17114i	−0.163800	+	0.395447i
$172$		0			0
$173$		−	3.52458i		−	0.267969i	−0.990983	−	0.133985i	$-0.957223\pi$
$173$		−	3.52458i		−	0.267969i	0.990983	−	0.133985i	$-0.0427773\pi$
$174$		0			0
$175$	12.6416	−	7.29685i	0.955616	−	0.551590i
$176$		0			0
$177$	−1.68810	−	4.07545i	−0.126886	−	0.306329i
$178$		0			0
$179$	−8.23706	−	19.8860i	−0.615666	−	1.48635i	−0.856690	−	0.515831i	$-0.827483\pi$
$179$	−8.23706	−	19.8860i	−0.615666	−	1.48635i	0.241024	−	0.970519i	$-0.422517\pi$
$180$		0			0
$181$	−0.120741	−	0.291494i	−0.00897458	−	0.0216665i	0.919329	−	0.393490i	$-0.128733\pi$
$181$	−0.120741	−	0.291494i	−0.00897458	−	0.0216665i	−0.928303	+	0.371824i	$0.878733\pi$
$182$		0			0
$183$	2.58702	−	6.24561i	0.191238	−	0.461689i
$184$		0			0
$185$	1.08029	+	16.4954i	0.0794242	+	1.21277i
$186$		0			0
$187$	22.3783	+	22.3783i	1.63646	+	1.63646i
$188$		0			0
$189$	11.0176			0.801411
$190$		0			0
$191$	−11.7909	+	4.88396i	−0.853161	+	0.353391i	−0.766029	−	0.642806i	$-0.777770\pi$
$191$	−11.7909	+	4.88396i	−0.853161	+	0.353391i	−0.0871322	+	0.996197i	$0.527770\pi$
$192$		0			0
$193$	−20.2143	+	8.37304i	−1.45506	+	0.602705i	−0.963396	−	0.268082i	$-0.913610\pi$
$193$	−20.2143	+	8.37304i	−1.45506	+	0.602705i	−0.491661	+	0.870787i	$0.663610\pi$
$194$		0			0
$195$	−0.412621	−	6.30052i	−0.0295484	−	0.451189i
$196$		0			0
$197$			1.77134i			0.126203i	0.998007	+	0.0631013i	$0.0200991\pi$
$197$			1.77134i			0.126203i	−0.998007	+	0.0631013i	$0.979901\pi$
$198$		0			0
$199$	−1.97801	−	4.77533i	−0.140217	−	0.338514i	0.838134	−	0.545464i	$-0.183646\pi$
$199$	−1.97801	−	4.77533i	−0.140217	−	0.338514i	−0.978352	+	0.206950i	$0.933646\pi$
$200$		0			0
$201$	4.73257			0.333810
$202$		0			0
$203$			6.76712i			0.474959i
$204$		0			0
$205$	4.64364	−	13.5439i	0.324326	−	0.945945i
$206$		0			0
$207$		−	4.51044i		−	0.313497i
$208$		0			0
$209$	−11.7848			−0.815173
$210$		0			0
$211$	3.60618	+	8.70609i	0.248260	+	0.599352i	0.998056	−	0.0623163i	$-0.0198488\pi$
$211$	3.60618	+	8.70609i	0.248260	+	0.599352i	−0.749797	+	0.661668i	$0.769849\pi$
$212$		0			0
$213$			5.04499i			0.345677i
$214$		0			0
$215$	12.0550	−	13.7446i	0.822142	−	0.937373i
$216$		0			0
$217$	12.0608	−	4.99573i	0.818738	−	0.339132i
$218$		0			0
$219$	5.82394	−	2.41236i	0.393546	−	0.163012i
$220$		0			0
$221$	−24.5545			−1.65172
$222$		0			0
$223$	7.51336	+	7.51336i	0.503132	+	0.503132i	0.912410	−	0.409278i	$-0.134219\pi$
$223$	7.51336	+	7.51336i	0.503132	+	0.503132i	−0.409278	+	0.912410i	$0.634219\pi$
$224$		0			0
$225$	10.0553	+	7.71738i	0.670351	+	0.514492i
$226$		0			0
$227$	2.26373	−	5.46513i	0.150249	−	0.362733i	−0.830778	−	0.556604i	$-0.812104\pi$
$227$	2.26373	−	5.46513i	0.150249	−	0.362733i	0.981027	+	0.193871i	$0.0621042\pi$
$228$		0			0
$229$	8.50510	+	20.5331i	0.562033	+	1.35687i	0.908138	+	0.418671i	$0.137504\pi$
$229$	8.50510	+	20.5331i	0.562033	+	1.35687i	−0.346105	+	0.938196i	$0.612496\pi$
$230$		0			0
$231$	4.06580	+	9.81571i	0.267510	+	0.645826i
$232$		0			0
$233$	7.55544	+	18.2405i	0.494973	+	1.19497i	0.952160	+	0.305601i	$0.0988573\pi$
$233$	7.55544	+	18.2405i	0.494973	+	1.19497i	−0.457186	+	0.889371i	$0.651143\pi$
$234$		0			0
$235$	20.1594	−	9.94018i	1.31505	−	0.648426i
$236$		0			0
$237$		−	7.98097i		−	0.518420i
$238$		0			0
$239$	−2.45895	+	5.93643i	−0.159056	+	0.383996i	−0.983237	−	0.182331i	$-0.941636\pi$
$239$	−2.45895	+	5.93643i	−0.159056	+	0.383996i	0.824181	+	0.566326i	$0.191636\pi$
$240$		0			0
$241$	11.8098	−	11.8098i	0.760736	−	0.760736i	−0.215720	−	0.976455i	$-0.569210\pi$
$241$	11.8098	−	11.8098i	0.760736	−	0.760736i	0.976455	+	0.215720i	$0.0692097\pi$
$242$		0			0
$243$	5.64582	+	13.6302i	0.362179	+	0.874378i
$244$		0			0
$245$	−0.222432	−	3.39642i	−0.0142106	−	0.216989i
$246$		0			0
$247$	6.46543	−	6.46543i	0.411386	−	0.411386i
$248$		0			0
$249$	3.32969	+	1.37920i	0.211011	+	0.0874035i
$250$		0			0
$251$	10.9614	+	10.9614i	0.691876	+	0.691876i	0.962644	−	0.270769i	$-0.0872779\pi$
$251$	10.9614	+	10.9614i	0.691876	+	0.691876i	−0.270769	+	0.962644i	$0.587278\pi$
$252$		0			0
$253$	8.77376	−	3.63421i	0.551602	−	0.228481i
$254$		0			0
$255$	−5.96087	+	6.79634i	−0.373284	+	0.425603i
$256$		0			0
$257$	5.60896	−	2.32331i	0.349878	−	0.144924i	−0.200822	−	0.979628i	$-0.564361\pi$
$257$	5.60896	−	2.32331i	0.349878	−	0.144924i	0.550699	+	0.834704i	$0.314361\pi$
$258$		0			0
$259$	19.9388	+	8.25891i	1.23893	+	0.513184i
$260$		0			0
$261$	−5.42921	+	2.24885i	−0.336060	+	0.139200i
$262$		0			0
$263$	1.59517	−	3.85107i	0.0983621	−	0.237467i	−0.867037	−	0.498244i	$-0.833979\pi$
$263$	1.59517	−	3.85107i	0.0983621	−	0.237467i	0.965399	+	0.260776i	$0.0839785\pi$
$264$		0			0
$265$	−19.7910	−	6.71930i	−1.21575	−	0.412763i
$266$		0			0
$267$	1.69186			0.103540
$268$		0			0
$269$	−27.5212			−1.67800			−0.838998	−	0.544135i	$-0.816858\pi$
$269$	−27.5212			−1.67800			−0.838998	+	0.544135i	$0.816858\pi$
$270$		0			0
$271$		−	9.95672i		−	0.604828i	−0.953177	−	0.302414i	$-0.902208\pi$
$271$		−	9.95672i		−	0.604828i	0.953177	−	0.302414i	$-0.0977924\pi$
$272$		0			0
$273$	−7.61572	−	3.15454i	−0.460925	−	0.190921i
$274$		0			0
$275$	−6.91007	+	25.7778i	−0.416693	+	1.55446i
$276$		0			0
$277$	−14.1069	−	14.1069i	−0.847602	−	0.847602i	0.142231	−	0.989833i	$-0.454572\pi$
$277$	−14.1069	−	14.1069i	−0.847602	−	0.847602i	−0.989833	+	0.142231i	$0.954572\pi$
$278$		0			0
$279$	8.01607	+	8.01607i	0.479910	+	0.479910i
$280$		0			0
$281$	−0.0587371	+	0.0243297i	−0.00350396	+	0.00145139i	−0.384435	−	0.923152i	$-0.625604\pi$
$281$	−0.0587371	+	0.0243297i	−0.00350396	+	0.00145139i	0.380931	+	0.924604i	$0.375604\pi$
$282$		0			0
$283$	−6.07128	−	6.07128i	−0.360900	−	0.360900i	0.503244	−	0.864144i	$-0.332140\pi$
$283$	−6.07128	−	6.07128i	−0.360900	−	0.360900i	−0.864144	+	0.503244i	$0.832140\pi$
$284$		0			0
$285$	−0.219987	−	3.35909i	−0.0130309	−	0.198975i
$286$		0			0
$287$	−13.1779	−	13.2571i	−0.777868	−	0.782544i
$288$		0			0
$289$	12.8380	+	12.8380i	0.755178	+	0.755178i
$290$		0			0
$291$			2.21007i			0.129557i
$292$		0			0
$293$	−9.96804	+	24.0650i	−0.582339	+	1.40589i	0.308348	+	0.951274i	$0.400224\pi$
$293$	−9.96804	+	24.0650i	−0.582339	+	1.40589i	−0.890687	+	0.454617i	$0.849776\pi$
$294$		0			0
$295$	−10.8758	−	9.53888i	−0.633216	−	0.555375i
$296$		0			0
$297$	−14.2443	+	14.2443i	−0.826537	+	0.826537i
$298$		0			0
$299$	−2.81968	+	6.80731i	−0.163066	+	0.393677i
$300$		0			0
$301$	−9.13391	−	22.0512i	−0.526470	−	1.27101i
$302$		0			0
$303$	−9.51353	−	9.51353i	−0.546538	−	0.546538i
$304$		0			0
$305$	−1.44878	−	22.1222i	−0.0829571	−	1.26671i
$306$		0			0
$307$		−	6.03298i		−	0.344321i	−0.985069	−	0.172160i	$-0.944925\pi$
$307$		−	6.03298i		−	0.344321i	0.985069	−	0.172160i	$-0.0550747\pi$
$308$		0			0
$309$	1.96415	+	4.74187i	0.111736	+	0.269755i
$310$		0			0
$311$	−15.7187	+	6.51088i	−0.891323	+	0.369198i	−0.780878	−	0.624684i	$-0.785228\pi$
$311$	−15.7187	+	6.51088i	−0.891323	+	0.369198i	−0.110445	+	0.993882i	$0.535228\pi$
$312$		0			0
$313$	10.1010	−	24.3859i	0.570941	−	1.37837i	−0.329814	−	0.944046i	$-0.606986\pi$
$313$	10.1010	−	24.3859i	0.570941	−	1.37837i	0.900755	−	0.434328i	$-0.143014\pi$
$314$		0			0
$315$	14.8421	−	7.31833i	0.836257	−	0.412341i
$316$		0			0
$317$	−8.38833	−	20.2512i	−0.471136	−	1.13742i	−0.963662	−	0.267125i	$-0.913926\pi$
$317$	−8.38833	−	20.2512i	−0.471136	−	1.13742i	0.492526	−	0.870298i	$-0.336074\pi$
$318$		0			0
$319$	−8.74899	−	8.74899i	−0.489849	−	0.489849i
$320$		0			0
$321$	9.37423	+	3.88293i	0.523218	+	0.216724i
$322$		0			0
$323$	−13.0911			−0.728409
$324$		0			0
$325$	−10.3513	−	17.9333i	−0.574185	−	0.994762i
$326$		0			0
$327$	−4.86275	−	4.86275i	−0.268911	−	0.268911i
$328$		0			0
$329$		−	29.3444i		−	1.61781i
$330$		0			0
$331$	−5.39319	+	13.0203i	−0.296436	+	0.715661i	0.703551	+	0.710645i	$0.251597\pi$
$331$	−5.39319	+	13.0203i	−0.296436	+	0.715661i	−0.999987	+	0.00501596i	$0.998403\pi$
$332$		0			0
$333$			18.7413i			1.02702i
$334$		0			0
$335$	13.9199	−	6.86364i	0.760528	−	0.375000i
$336$		0			0
$337$	−6.94993			−0.378587			−0.189293	−	0.981921i	$-0.560620\pi$
$337$	−6.94993			−0.378587			−0.189293	+	0.981921i	$0.560620\pi$
$338$		0			0
$339$	−0.524438	+	1.26611i	−0.0284836	+	0.0687654i
$340$		0			0
$341$	−9.13414	+	22.0518i	−0.494642	+	1.19417i
$342$		0			0
$343$	14.7740	+	6.11960i	0.797722	+	0.330427i
$344$		0			0
$345$	1.19966	+	2.43299i	0.0645874	+	0.130988i
$346$		0			0
$347$	−2.89541	−	1.19932i	−0.155434	−	0.0643828i	0.303610	−	0.952796i	$-0.401808\pi$
$347$	−2.89541	−	1.19932i	−0.155434	−	0.0643828i	−0.459044	+	0.888414i	$0.651808\pi$
$348$		0			0
$349$	5.52723	−	5.52723i	0.295866	−	0.295866i	−0.543526	−	0.839392i	$-0.682911\pi$
$349$	5.52723	−	5.52723i	0.295866	−	0.295866i	0.839392	+	0.543526i	$0.182911\pi$
$350$		0			0
$351$		−	15.6295i		−	0.834240i
$352$		0			0
$353$	4.68350	−	4.68350i	0.249278	−	0.249278i	−0.571396	−	0.820674i	$-0.693598\pi$
$353$	4.68350	−	4.68350i	0.249278	−	0.249278i	0.820674	+	0.571396i	$0.193598\pi$
$354$		0			0
$355$	7.31674	+	14.8389i	0.388332	+	0.787565i
$356$		0			0
$357$	4.51648	+	10.9037i	0.239037	+	0.577087i
$358$		0			0
$359$	−4.29520			−0.226692			−0.113346	−	0.993556i	$-0.536157\pi$
$359$	−4.29520			−0.226692			−0.113346	+	0.993556i	$0.536157\pi$
$360$		0			0
$361$	−9.98802	+	9.98802i	−0.525685	+	0.525685i
$362$		0			0
$363$	−11.0176	−	4.56362i	−0.578272	−	0.239528i
$364$		0			0
$365$	13.6314	−	15.5419i	0.713498	−	0.813502i
$366$		0			0
$367$	−13.7090			−0.715603			−0.357801	−	0.933798i	$-0.616473\pi$
$367$	−13.7090			−0.715603			−0.357801	+	0.933798i	$0.616473\pi$
$368$		0			0
$369$	6.25681	−	14.9782i	0.325717	−	0.779732i
$370$		0			0
$371$	−19.2944	+	19.2944i	−1.00172	+	1.00172i
$372$		0			0
$373$	−1.15360	+	1.15360i	−0.0597312	+	0.0597312i	−0.736341	−	0.676610i	$-0.763448\pi$
$373$	−1.15360	+	1.15360i	−0.0597312	+	0.0597312i	0.676610	+	0.736341i	$0.263448\pi$
$374$		0			0
$375$	−7.47656	−	1.48842i	−0.386088	−	0.0768617i
$376$		0			0
$377$	9.59980			0.494415
$378$		0			0
$379$			23.5487i			1.20961i	0.796372	+	0.604807i	$0.206750\pi$
$379$			23.5487i			1.20961i	−0.796372	+	0.604807i	$0.793250\pi$
$380$		0			0
$381$	1.54566	+	0.640233i	0.0791865	+	0.0328001i
$382$		0			0
$383$	8.29010	−	20.0141i	0.423604	−	1.02267i	−0.557671	−	0.830062i	$-0.688305\pi$
$383$	8.29010	−	20.0141i	0.423604	−	1.02267i	0.981275	−	0.192610i	$-0.0616951\pi$
$384$		0			0
$385$	26.1945	+	22.9744i	1.33499	+	1.17088i
$386$		0			0
$387$	14.6561	−	14.6561i	0.745013	−	0.745013i
$388$		0			0
$389$	−0.972002	−	0.972002i	−0.0492824	−	0.0492824i	0.682036	−	0.731319i	$-0.261095\pi$
$389$	−0.972002	−	0.972002i	−0.0492824	−	0.0492824i	−0.731319	+	0.682036i	$0.761095\pi$
$390$		0			0
$391$	9.74630	−	4.03705i	0.492891	−	0.204162i
$392$		0			0
$393$	−8.80751	−	3.64819i	−0.444280	−	0.184027i
$394$		0			0
$395$	−11.5748	−	23.4745i	−0.582391	−	1.18113i
$396$		0			0
$397$	−12.9242	+	5.35339i	−0.648649	+	0.268679i	−0.682653	−	0.730743i	$-0.739174\pi$
$397$	−12.9242	+	5.35339i	−0.648649	+	0.268679i	0.0340045	+	0.999422i	$0.489174\pi$
$398$		0			0
$399$	−4.06028	−	1.68182i	−0.203268	−	0.0841965i
$400$		0			0
$401$	14.0094	−	14.0094i	0.699594	−	0.699594i	−0.264729	−	0.964323i	$-0.585283\pi$
$401$	14.0094	−	14.0094i	0.699594	−	0.699594i	0.964323	+	0.264729i	$0.0852825\pi$
$402$		0			0
$403$	−7.08692	−	17.1093i	−0.353025	−	0.852277i
$404$		0			0
$405$	8.45908	+	7.41921i	0.420335	+	0.368663i
$406$		0			0
$407$	−36.4558	+	15.1005i	−1.80705	+	0.748504i
$408$		0			0
$409$	6.87677			0.340034			0.170017	−	0.985441i	$-0.445618\pi$
$409$	6.87677			0.340034			0.170017	+	0.985441i	$0.445618\pi$
$410$		0			0
$411$	−10.5772			−0.521735
$412$		0			0
$413$	−17.4487	+	7.22750i	−0.858595	+	0.355642i
$414$		0			0
$415$	11.7939	−	0.772384i	0.578940	−	0.0379148i
$416$		0			0
$417$	−2.19604	−	5.30172i	−0.107541	−	0.259626i
$418$		0			0
$419$	4.67681	−	4.67681i	0.228477	−	0.228477i	−0.583579	−	0.812056i	$-0.698348\pi$
$419$	4.67681	−	4.67681i	0.228477	−	0.228477i	0.812056	+	0.583579i	$0.198348\pi$
$420$		0			0
$421$	−25.3445	−	10.4980i	−1.23522	−	0.511643i	−0.332999	−	0.942927i	$-0.608061\pi$
$421$	−25.3445	−	10.4980i	−1.23522	−	0.511643i	−0.902216	+	0.431284i	$0.858061\pi$
$422$		0			0
$423$	23.5428	−	9.75175i	1.14469	−	0.474146i
$424$		0			0
$425$	−7.67603	+	28.6351i	−0.372342	+	1.38901i
$426$		0			0
$427$	−26.7401	−	11.0761i	−1.29404	−	0.536011i
$428$		0			0
$429$	13.9245	−	5.76772i	0.672282	−	0.278468i
$430$		0			0
$431$	6.84272	+	6.84272i	0.329602	+	0.329602i	0.852435	−	0.522833i	$-0.175125\pi$
$431$	6.84272	+	6.84272i	0.329602	+	0.329602i	−0.522833	+	0.852435i	$0.675125\pi$
$432$		0			0
$433$	9.21154	−	9.21154i	0.442679	−	0.442679i	−0.450233	−	0.892911i	$-0.648659\pi$
$433$	9.21154	−	9.21154i	0.442679	−	0.442679i	0.892911	+	0.450233i	$0.148659\pi$
$434$		0			0
$435$	2.33045	−	2.65709i	0.111737	−	0.127398i
$436$		0			0
$437$	−1.50330	+	3.62928i	−0.0719124	+	0.173612i
$438$		0			0
$439$	−15.2992	−	6.33714i	−0.730192	−	0.302455i	−0.0135610	−	0.999908i	$-0.504317\pi$
$439$	−15.2992	−	6.33714i	−0.730192	−	0.302455i	−0.716631	+	0.697453i	$0.754317\pi$
$440$		0			0
$441$		−	3.85885i		−	0.183755i
$442$		0			0
$443$	−12.7927			−0.607798			−0.303899	−	0.952704i	$-0.598289\pi$
$443$	−12.7927			−0.607798			−0.303899	+	0.952704i	$0.598289\pi$
$444$		0			0
$445$	4.97629	−	2.45371i	0.235899	−	0.116317i
$446$		0			0
$447$	−8.41860	+	8.41860i	−0.398186	+	0.398186i
$448$		0			0
$449$	−22.0850	+	22.0850i	−1.04226	+	1.04226i	−0.0431881	+	0.999067i	$0.513751\pi$
$449$	−22.0850	+	22.0850i	−1.04226	+	1.04226i	−0.999067	+	0.0431881i	$0.986249\pi$
$450$		0			0
$451$	34.1770	+	0.102428i	1.60933	+	0.00482313i
$452$		0			0
$453$	15.9046			0.747263
$454$		0			0
$455$	−26.9752	+	1.76661i	−1.26462	+	0.0828199i
$456$		0			0
$457$	−36.9239	−	15.2944i	−1.72723	−	0.715440i	−0.999565	−	0.0295035i	$-0.990607\pi$
$457$	−36.9239	−	15.2944i	−1.72723	−	0.715440i	−0.727661	−	0.685937i	$-0.759393\pi$
$458$		0			0
$459$	−15.8232	+	15.8232i	−0.738563	+	0.738563i
$460$		0			0
$461$	−8.44773			−0.393450			−0.196725	−	0.980459i	$-0.563031\pi$
$461$	−8.44773			−0.393450			−0.196725	+	0.980459i	$0.563031\pi$
$462$		0			0
$463$	1.10490	+	2.66747i	0.0513491	+	0.123968i	0.947472	−	0.319837i	$-0.103628\pi$
$463$	1.10490	+	2.66747i	0.0513491	+	0.123968i	−0.896123	+	0.443805i	$0.853628\pi$
$464$		0			0
$465$	−6.45604	−	2.19191i	−0.299392	−	0.101647i
$466$		0			0
$467$	26.1310	−	26.1310i	1.20920	−	1.20920i	0.237912	−	0.971287i	$-0.423537\pi$
$467$	26.1310	−	26.1310i	1.20920	−	1.20920i	0.971287	−	0.237912i	$-0.0764630\pi$
$468$		0			0
$469$		−	20.2621i		−	0.935619i
$470$		0			0
$471$	1.78158	−	1.78158i	0.0820910	−	0.0820910i
$472$		0			0
$473$	40.3182	+	16.7003i	1.85383	+	0.767883i
$474$		0			0
$475$	−5.51873	−	9.56106i	−0.253217	−	0.438692i
$476$		0			0
$477$	−21.8917	−	9.06785i	−1.00235	−	0.415188i
$478$		0			0
$479$	−13.9507	+	33.6799i	−0.637423	+	1.53887i	0.192679	+	0.981262i	$0.438283\pi$
$479$	−13.9507	+	33.6799i	−0.637423	+	1.53887i	−0.830101	+	0.557613i	$0.811717\pi$
$480$		0			0
$481$	11.7160	−	28.2850i	0.534206	−	1.28969i
$482$		0			0
$483$	3.54151			0.161144
$484$		0			0
$485$	3.20526	+	6.50050i	0.145543	+	0.295172i
$486$		0			0
$487$			44.0001i			1.99383i	0.0784700	+	0.996916i	$0.474997\pi$
$487$			44.0001i			1.99383i	−0.0784700	+	0.996916i	$0.525003\pi$
$488$		0			0
$489$	4.78778	−	11.5587i	0.216511	−	0.522703i
$490$		0			0
$491$		−	41.6965i		−	1.88173i	−0.338775	−	0.940867i	$-0.610012\pi$
$491$		−	41.6965i		−	1.88173i	0.338775	−	0.940867i	$-0.389988\pi$
$492$		0			0
$493$	−9.71878	−	9.71878i	−0.437712	−	0.437712i
$494$		0			0
$495$	−9.72722	+	28.6505i	−0.437206	+	1.28774i
$496$		0			0
$497$	21.5998			0.968882
$498$		0			0
$499$	−20.2670	−	8.39486i	−0.907275	−	0.375806i	−0.120262	−	0.992742i	$-0.538373\pi$
$499$	−20.2670	−	8.39486i	−0.907275	−	0.375806i	−0.787013	+	0.616937i	$0.788373\pi$
$500$		0			0
$501$	1.79399	+	1.79399i	0.0801493	+	0.0801493i
$502$		0			0
$503$	12.1919	+	29.4338i	0.543609	+	1.31239i	0.922160	+	0.386808i	$0.126423\pi$
$503$	12.1919	+	29.4338i	0.543609	+	1.31239i	−0.378551	+	0.925581i	$0.623577\pi$
$504$		0			0
$505$	−41.7796	−	14.1848i	−1.85917	−	0.631213i
$506$		0			0
$507$	−1.08290	+	2.61435i	−0.0480932	+	0.116107i
$508$		0			0
$509$	18.0169	−	7.46284i	0.798585	−	0.330785i	0.0541954	−	0.998530i	$-0.482741\pi$
$509$	18.0169	−	7.46284i	0.798585	−	0.330785i	0.744390	+	0.667746i	$0.232741\pi$
$510$		0			0
$511$	−10.3283	−	24.9348i	−0.456898	−	1.10305i
$512$		0			0
$513$		−	8.33278i		−	0.367901i
$514$		0			0
$515$	12.6543	+	11.0987i	0.557614	+	0.489067i
$516$		0			0
$517$	37.9384	+	37.9384i	1.66853	+	1.66853i
$518$		0			0
$519$	0.919675	+	2.22029i	0.0403693	+	0.0974600i
$520$		0			0
$521$	7.17995	−	17.3339i	0.314559	−	0.759413i	−0.684965	−	0.728576i	$-0.740183\pi$
$521$	7.17995	−	17.3339i	0.314559	−	0.759413i	0.999524	−	0.0308375i	$-0.00981744\pi$
$522$		0			0
$523$	4.72022	−	4.72022i	0.206401	−	0.206401i	−0.596335	−	0.802736i	$-0.703377\pi$
$523$	4.72022	−	4.72022i	0.206401	−	0.206401i	0.802736	+	0.596335i	$0.203377\pi$
$524$		0			0
$525$	−6.05954	+	7.89520i	−0.264460	+	0.344575i
$526$		0			0
$527$	−10.1466	+	24.4961i	−0.441994	+	1.06707i
$528$		0			0
$529$			19.8344i			0.862366i
$530$		0			0
$531$	−11.5971	−	11.5971i	−0.503272	−	0.503272i
$532$		0			0
$533$	−18.8065	+	18.6941i	−0.814601	+	0.809732i
$534$		0			0
$535$	33.2039	−	2.17453i	1.43553	−	0.0940130i
$536$		0			0
$537$	10.3778	+	10.3778i	0.447834	+	0.447834i
$538$		0			0
$539$	7.50628	−	3.10920i	0.323319	−	0.133923i
$540$		0			0
$541$	24.0987	+	24.0987i	1.03608	+	1.03608i	0.999324	+	0.0367594i	$0.0117035\pi$
$541$	24.0987	+	24.0987i	1.03608	+	1.03608i	0.0367594	+	0.999324i	$0.488296\pi$
$542$		0			0
$543$	0.152120	+	0.152120i	0.00652808	+	0.00652808i
$544$		0			0
$545$	−21.3553	−	7.25040i	−0.914759	−	0.310573i
$546$		0			0
$547$	26.6712	+	11.0476i	1.14038	+	0.472361i	0.871297	−	0.490756i	$-0.163279\pi$
$547$	26.6712	+	11.0476i	1.14038	+	0.472361i	0.269083	+	0.963117i	$0.413279\pi$
$548$		0			0
$549$		−	25.1342i		−	1.07270i
$550$		0			0
$551$	5.11808			0.218038
$552$		0			0
$553$	−34.1700			−1.45305
$554$		0			0
$555$	−4.98469	−	10.1093i	−0.211588	−	0.429116i
$556$		0			0
$557$	7.94258	−	19.1751i	0.336538	−	0.812475i	−0.661505	−	0.749941i	$-0.730082\pi$
$557$	7.94258	−	19.1751i	0.336538	−	0.812475i	0.998043	−	0.0625339i	$-0.0199181\pi$
$558$		0			0
$559$	−31.2817	+	12.9573i	−1.32308	+	0.548036i
$560$		0			0
$561$	−19.9363	−	8.25788i	−0.841711	−	0.348648i
$562$		0			0
$563$	−4.10473	+	1.70024i	−0.172994	+	0.0716564i	−0.467499	−	0.883993i	$-0.654845\pi$
$563$	−4.10473	+	1.70024i	−0.172994	+	0.0716564i	0.294506	+	0.955650i	$0.404845\pi$
$564$		0			0
$565$	0.293697	+	4.48460i	0.0123559	+	0.188668i
$566$		0			0
$567$	13.5714	−	5.62144i	0.569944	−	0.236078i
$568$		0			0
$569$	−28.6633	−	28.6633i	−1.20163	−	1.20163i	−0.973671	−	0.227958i	$-0.926795\pi$
$569$	−28.6633	−	28.6633i	−1.20163	−	1.20163i	−0.227958	−	0.973671i	$-0.573205\pi$
$570$		0			0
$571$	28.2335	+	11.6947i	1.18154	+	0.489408i	0.884990	−	0.465610i	$-0.154165\pi$
$571$	28.2335	+	11.6947i	1.18154	+	0.489408i	0.296546	+	0.955019i	$0.404165\pi$
$572$		0			0
$573$	6.15325	−	6.15325i	0.257056	−	0.257056i
$574$		0			0
$575$	7.05712	+	5.41631i	0.294302	+	0.225876i
$576$		0			0
$577$	2.22221	+	5.36488i	0.0925116	+	0.223343i	0.963362	−	0.268206i	$-0.0864309\pi$
$577$	2.22221	+	5.36488i	0.0925116	+	0.223343i	−0.870850	+	0.491549i	$0.836431\pi$
$578$		0			0
$579$	10.5491	−	10.5491i	0.438406	−	0.438406i
$580$		0			0
$581$	5.90496	−	14.2558i	0.244979	−	0.591432i
$582$		0			0
$583$		−	49.8903i		−	2.06625i
$584$		0			0
$585$	−10.3817	−	21.0549i	−0.429232	−	0.870513i
$586$		0			0
$587$	11.2391	+	27.1336i	0.463888	+	1.11993i	0.966788	+	0.255580i	$0.0822666\pi$
$587$	11.2391	+	27.1336i	0.463888	+	1.11993i	−0.502900	+	0.864345i	$0.667733\pi$
$588$		0			0
$589$	−3.77835	−	9.12175i	−0.155684	−	0.375855i
$590$		0			0
$591$	−0.462198	−	1.11584i	−0.0190123	−	0.0458997i
$592$		0			0
$593$	2.21417	−	5.34547i	0.0909250	−	0.219512i	−0.871874	−	0.489730i	$-0.837096\pi$
$593$	2.21417	−	5.34547i	0.0909250	−	0.219512i	0.962799	+	0.270217i	$0.0870955\pi$
$594$		0			0
$595$	29.0980	+	25.5210i	1.19290	+	1.04626i
$596$		0			0
$597$	2.49207	+	2.49207i	0.101994	+	0.101994i
$598$		0			0
$599$	−16.0048			−0.653939			−0.326969	−	0.945035i	$-0.606027\pi$
$599$	−16.0048			−0.653939			−0.326969	+	0.945035i	$0.606027\pi$
$600$		0			0
$601$	−40.7546	+	16.8811i	−1.66242	+	0.688595i	−0.998258	−	0.0589970i	$-0.981210\pi$
$601$	−40.7546	+	16.8811i	−1.66242	+	0.688595i	−0.664158	+	0.747592i	$0.731210\pi$
$602$		0			0
$603$	16.2562	−	6.73352i	0.662002	−	0.274210i
$604$		0			0
$605$	−39.0246	+	2.55573i	−1.58658	+	0.103905i
$606$		0			0
$607$		−	27.0326i		−	1.09722i	−0.836078	−	0.548611i	$-0.815157\pi$
$607$		−	27.0326i		−	1.09722i	0.836078	−	0.548611i	$-0.184843\pi$
$608$		0			0
$609$	−1.76575	−	4.26291i	−0.0715520	−	0.172742i
$610$		0			0
$611$	−41.6278			−1.68408
$612$		0			0
$613$		−	10.6802i		−	0.431369i	−0.976463	−	0.215684i	$-0.930802\pi$
$613$		−	10.6802i		−	0.431369i	0.976463	−	0.215684i	$-0.0691982\pi$
$614$		0			0
$615$	0.608786	+	9.74356i	0.0245486	+	0.392898i
$616$		0			0
$617$		−	4.58652i		−	0.184647i	−0.995729	−	0.0923233i	$-0.970571\pi$
$617$		−	4.58652i		−	0.184647i	0.995729	−	0.0923233i	$-0.0294293\pi$
$618$		0			0
$619$	33.3987			1.34241			0.671203	−	0.741274i	$-0.265778\pi$
$619$	33.3987			1.34241			0.671203	+	0.741274i	$0.265778\pi$
$620$		0			0
$621$	2.56967	+	6.20373i	0.103117	+	0.248947i
$622$		0			0
$623$		−	7.24359i		−	0.290208i
$624$		0			0
$625$	−24.1495	+	6.46534i	−0.965981	+	0.258614i
$626$		0			0
$627$	7.42378	−	3.07503i	0.296477	−	0.122805i
$628$		0			0
$629$	−40.4968	+	16.7743i	−1.61471	+	0.668836i
$630$		0			0
$631$	36.4236			1.45000			0.725001	−	0.688748i	$-0.241839\pi$
$631$	36.4236			1.45000			0.725001	+	0.688748i	$0.241839\pi$
$632$		0			0
$633$	−4.54339	−	4.54339i	−0.180583	−	0.180583i
$634$		0			0
$635$	5.47479	−	0.358544i	0.217260	−	0.0142284i
$636$		0			0
$637$	−2.41234	+	5.82391i	−0.0955805	+	0.230752i
$638$		0			0
$639$	7.17804	+	17.3293i	0.283959	+	0.685537i
$640$		0			0
$641$	6.38735	+	15.4204i	0.252285	+	0.609071i	0.998388	−	0.0567605i	$-0.0180772\pi$
$641$	6.38735	+	15.4204i	0.252285	+	0.609071i	−0.746103	+	0.665831i	$0.768077\pi$
$642$		0			0
$643$	−1.70053	−	4.10545i	−0.0670624	−	0.161903i	0.886795	−	0.462163i	$-0.152927\pi$
$643$	−1.70053	−	4.10545i	−0.0670624	−	0.161903i	−0.953857	+	0.300260i	$0.902927\pi$
$644$		0			0
$645$	−4.00757	+	11.8038i	−0.157798	+	0.464776i
$646$		0			0
$647$			13.5335i			0.532057i	0.963965	+	0.266029i	$0.0857116\pi$
$647$			13.5335i			0.532057i	−0.963965	+	0.266029i	$0.914288\pi$
$648$		0			0
$649$	13.2147	−	31.9031i	0.518722	−	1.25230i
$650$		0			0
$651$	−6.29406	+	6.29406i	−0.246684	+	0.246684i
$652$		0			0
$653$	−4.56532	−	11.0217i	−0.178655	−	0.431311i	0.809030	−	0.587767i	$-0.199993\pi$
$653$	−4.56532	−	11.0217i	−0.178655	−	0.431311i	−0.987685	+	0.156456i	$0.949993\pi$
$654$		0			0
$655$	−31.1965	+	2.04306i	−1.21895	+	0.0798291i
$656$		0			0
$657$	16.5727	−	16.5727i	0.646561	−	0.646561i
$658$		0			0
$659$	39.9509	+	16.5482i	1.55627	+	0.644626i	0.984435	−	0.175746i	$-0.0562339\pi$
$659$	39.9509	+	16.5482i	1.55627	+	0.644626i	0.571830	+	0.820372i	$0.306234\pi$
$660$		0			0
$661$	18.5260	+	18.5260i	0.720576	+	0.720576i	0.968723	−	0.248146i	$-0.0798214\pi$
$661$	18.5260	+	18.5260i	0.720576	+	0.720576i	−0.248146	+	0.968723i	$0.579821\pi$
$662$		0			0
$663$	15.4680	−	6.40705i	0.600727	−	0.248829i
$664$		0			0
$665$	−14.3817	+	0.941858i	−0.557698	+	0.0365237i
$666$		0			0
$667$	−3.81040	+	1.57832i	−0.147539	+	0.0611127i
$668$		0			0
$669$	−6.69347	−	2.77253i	−0.258784	−	0.107192i
$670$		0			0
$671$	48.8913	−	20.2515i	1.88743	−	0.781799i
$672$		0			0
$673$	−13.1423	+	31.7282i	−0.506597	+	1.22303i	0.439234	+	0.898373i	$0.355250\pi$
$673$	−13.1423	+	31.7282i	−0.506597	+	1.22303i	−0.945831	+	0.324660i	$0.894750\pi$
$674$		0			0
$675$	−18.2269	−	4.88596i	−0.701553	−	0.188061i
$676$		0			0
$677$	26.2051			1.00714			0.503571	−	0.863954i	$-0.332019\pi$
$677$	26.2051			1.00714			0.503571	+	0.863954i	$0.332019\pi$
$678$		0			0
$679$	9.46226			0.363128
$680$		0			0
$681$			4.03340i			0.154560i
$682$		0			0
$683$	−36.2588	−	15.0189i	−1.38740	−	0.574681i	−0.440953	−	0.897530i	$-0.645360\pi$
$683$	−36.2588	−	15.0189i	−1.38740	−	0.574681i	−0.946451	+	0.322849i	$0.895360\pi$
$684$		0			0
$685$	−31.1108	+	15.3401i	−1.18868	+	0.586115i
$686$		0			0
$687$	−10.7155	−	10.7155i	−0.408821	−	0.408821i
$688$		0			0
$689$	27.3710	+	27.3710i	1.04275	+	1.04275i
$690$		0			0
$691$	36.5236	−	15.1286i	1.38942	−	0.575518i	0.442439	−	0.896799i	$-0.354113\pi$
$691$	36.5236	−	15.1286i	1.38942	−	0.575518i	0.946984	+	0.321281i	$0.104113\pi$
$692$		0			0
$693$	27.9317	+	27.9317i	1.06104	+	1.06104i
$694$		0			0
$695$	−14.1483	−	12.4091i	−0.536676	−	0.470703i
$696$		0			0
$697$	37.9654	+	0.113781i	1.43804	+	0.00430977i
$698$		0			0
$699$	−9.51902	−	9.51902i	−0.360042	−	0.360042i
$700$		0			0
$701$		−	30.1161i		−	1.13747i	−0.822520	−	0.568736i	$-0.807433\pi$
$701$		−	30.1161i		−	1.13747i	0.822520	−	0.568736i	$-0.192567\pi$
$702$		0			0
$703$	6.24635	−	15.0800i	0.235585	−	0.568754i
$704$		0			0
$705$	−10.1056	+	11.5220i	−0.380599	+	0.433943i
$706$		0			0
$707$	−40.7315	+	40.7315i	−1.53186	+	1.53186i
$708$		0			0
$709$	−2.39229	+	5.77550i	−0.0898443	+	0.216903i	−0.962414	−	0.271586i	$-0.912452\pi$
$709$	−2.39229	+	5.77550i	−0.0898443	+	0.216903i	0.872570	+	0.488489i	$0.162452\pi$
$710$		0			0
$711$	−11.3554	−	27.4143i	−0.425860	−	1.02812i
$712$		0			0
$713$	5.62594	+	5.62594i	0.210693	+	0.210693i
$714$		0			0
$715$	32.5914	−	37.1593i	1.21885	−	1.38968i
$716$		0			0
$717$		−	4.38124i		−	0.163620i
$718$		0			0
$719$	4.60753	+	11.1236i	0.171832	+	0.414839i	0.986211	−	0.165495i	$-0.0529221\pi$
$719$	4.60753	+	11.1236i	0.171832	+	0.414839i	−0.814379	+	0.580334i	$0.802922\pi$
$720$		0			0
$721$	20.3020	−	8.40935i	0.756084	−	0.313180i
$722$		0			0
$723$	−4.35797	+	10.5211i	−0.162074	+	0.391282i
$724$		0			0
$725$	3.00101	−	11.1952i	0.111455	−	0.415778i
$726$		0			0
$727$	0.243814	+	0.588620i	0.00904257	+	0.0218307i	0.928336	−	0.371741i	$-0.121239\pi$
$727$	0.243814	+	0.588620i	0.00904257	+	0.0218307i	−0.919294	+	0.393572i	$0.871239\pi$
$728$		0			0
$729$	3.56119	+	3.56119i	0.131896	+	0.131896i
$730$		0			0
$731$	44.7873	+	18.5515i	1.65652	+	0.686152i
$732$		0			0
$733$	41.4163			1.52975			0.764874	−	0.644180i	$-0.222801\pi$
$733$	41.4163			1.52975			0.764874	+	0.644180i	$0.222801\pi$
$734$		0			0
$735$	1.02635	+	2.08151i	0.0378576	+	0.0767778i
$736$		0			0
$737$	26.1963	+	26.1963i	0.964952	+	0.964952i
$738$		0			0
$739$			2.43305i			0.0895012i	0.998998	+	0.0447506i	$0.0142493\pi$
$739$			2.43305i			0.0895012i	−0.998998	+	0.0447506i	$0.985751\pi$
$740$		0			0
$741$	−2.38583	+	5.75990i	−0.0876456	+	0.211595i
$742$		0			0
$743$		−	12.4645i		−	0.457278i	−0.973511	−	0.228639i	$-0.926572\pi$
$743$		−	12.4645i		−	0.457278i	0.973511	−	0.228639i	$-0.0734276\pi$
$744$		0			0
$745$	−12.5522	+	36.9712i	−0.459878	+	1.35452i
$746$		0			0
$747$	13.3997			0.490269
$748$		0			0
$749$	16.6245	−	40.1351i	0.607446	−	1.46650i
$750$		0			0
$751$	−3.05534	+	7.37623i	−0.111491	+	0.269163i	−0.969770	−	0.244020i	$-0.921534\pi$
$751$	−3.05534	+	7.37623i	−0.111491	+	0.269163i	0.858279	+	0.513183i	$0.171534\pi$
$752$		0			0
$753$	−9.76522	−	4.04489i	−0.355864	−	0.147404i
$754$		0			0
$755$	46.7803	−	23.0664i	1.70251	−	0.839472i
$756$		0			0
$757$	3.83740	+	1.58950i	0.139473	+	0.0577715i	0.451328	−	0.892358i	$-0.350950\pi$
$757$	3.83740	+	1.58950i	0.139473	+	0.0577715i	−0.311855	+	0.950130i	$0.600950\pi$
$758$		0			0
$759$	−4.57870	+	4.57870i	−0.166196	+	0.166196i
$760$		0			0
$761$			36.3882i			1.31907i	0.751673	+	0.659536i	$0.229247\pi$
$761$			36.3882i			1.31907i	−0.751673	+	0.659536i	$0.770753\pi$
$762$		0			0
$763$	−20.8195	+	20.8195i	−0.753717	+	0.753717i
$764$		0			0
$765$	−10.8054	+	31.8263i	−0.390672	+	1.15068i
$766$		0			0
$767$	10.2529	+	24.7527i	0.370210	+	0.893767i
$768$		0			0
$769$	28.0948			1.01313			0.506563	−	0.862203i	$-0.330916\pi$
$769$	28.0948			1.01313			0.506563	+	0.862203i	$0.330916\pi$
$770$		0			0
$771$	−2.92711	+	2.92711i	−0.105417	+	0.105417i
$772$		0			0
$773$	−5.00353	−	2.07253i	−0.179964	−	0.0745437i	0.290882	−	0.956759i	$-0.406051\pi$
$773$	−5.00353	−	2.07253i	−0.179964	−	0.0745437i	−0.470846	+	0.882215i	$0.656051\pi$
$774$		0			0
$775$	−22.1681	+	2.91609i	−0.796302	+	0.104749i
$776$		0			0
$777$	−14.7153			−0.527909
$778$		0			0
$779$	−10.0266	+	9.96667i	−0.359240	+	0.357093i
$780$		0			0
$781$	−27.9256	+	27.9256i	−0.999257	+	0.999257i
$782$		0			0
$783$	6.18621	−	6.18621i	0.221077	−	0.221077i
$784$		0			0
$785$	2.65636	−	7.82401i	0.0948095	−	0.279251i
$786$		0			0
$787$	39.6517			1.41343			0.706715	−	0.707498i	$-0.250176\pi$
$787$	39.6517			1.41343			0.706715	+	0.707498i	$0.250176\pi$
$788$		0			0
$789$			2.84219i			0.101185i
$790$		0			0
$791$	5.42074	+	2.24534i	0.192739	+	0.0798352i
$792$		0			0
$793$	−15.7125	+	37.9334i	−0.557968	+	1.34705i
$794$		0			0
$795$	14.2205	−	0.931301i	0.504349	−	0.0330298i
$796$		0			0
$797$	26.3466	−	26.3466i	0.933243	−	0.933243i	−0.0646643	−	0.997907i	$-0.520598\pi$
$797$	26.3466	−	26.3466i	0.933243	−	0.933243i	0.997907	+	0.0646643i	$0.0205977\pi$
$798$		0			0
$799$	42.1438	+	42.1438i	1.49094	+	1.49094i
$800$		0			0
$801$	5.81147	−	2.40719i	0.205338	−	0.0850539i
$802$		0			0
$803$	45.5905	+	18.8842i	1.60885	+	0.666409i
$804$		0			0
$805$	10.4167	−	5.13624i	0.367139	−	0.181029i
$806$		0			0
$807$	17.3368	−	7.18114i	0.610284	−	0.252788i
$808$		0			0
$809$	−34.1675	−	14.1526i	−1.20127	−	0.497581i	−0.309858	−	0.950783i	$-0.600282\pi$
$809$	−34.1675	−	14.1526i	−1.20127	−	0.497581i	−0.891408	+	0.453202i	$0.850282\pi$
$810$		0			0
$811$	−8.39412	+	8.39412i	−0.294757	+	0.294757i	−0.838956	−	0.544199i	$-0.816834\pi$
$811$	−8.39412	+	8.39412i	−0.294757	+	0.294757i	0.544199	+	0.838956i	$0.316834\pi$
$812$		0			0
$813$	2.59802	+	6.27218i	0.0911166	+	0.219975i
$814$		0			0
$815$	−2.68126	−	40.9414i	−0.0939204	−	1.43412i
$816$		0			0
$817$	−16.6777	+	6.90812i	−0.583478	+	0.241685i
$818$		0			0
$819$	−30.6480			−1.07093
$820$		0			0
$821$	−13.7255			−0.479025			−0.239512	−	0.970893i	$-0.576988\pi$
$821$	−13.7255			−0.479025			−0.239512	+	0.970893i	$0.576988\pi$
$822$		0			0
$823$	−35.2678	+	14.6084i	−1.22936	+	0.509216i	−0.900373	−	0.435119i	$-0.856706\pi$
$823$	−35.2678	+	14.6084i	−1.22936	+	0.509216i	−0.328984	+	0.944335i	$0.606706\pi$
$824$		0			0
$825$	−2.37327	−	18.0416i	−0.0826268	−	0.628129i
$826$		0			0
$827$	12.3562	+	29.8305i	0.429668	+	1.03731i	0.979393	+	0.201964i	$0.0647324\pi$
$827$	12.3562	+	29.8305i	0.429668	+	1.03731i	−0.549725	+	0.835345i	$0.685268\pi$
$828$		0			0
$829$	−2.87754	+	2.87754i	−0.0999411	+	0.0999411i	−0.755309	−	0.655368i	$-0.772513\pi$
$829$	−2.87754	+	2.87754i	−0.0999411	+	0.0999411i	0.655368	+	0.755309i	$0.272513\pi$
$830$		0			0
$831$	12.5675	+	5.20563i	0.435962	+	0.180581i
$832$		0			0
$833$	8.33832	−	3.45385i	0.288906	−	0.119669i
$834$		0			0
$835$	7.87847	+	2.67485i	0.272646	+	0.0925669i
$836$		0			0
$837$	−15.5923	−	6.45855i	−0.538949	−	0.223240i
$838$		0			0
$839$	−38.8371	+	16.0868i	−1.34080	+	0.555379i	−0.933718	−	0.358010i	$-0.883455\pi$
$839$	−38.8371	+	16.0868i	−1.34080	+	0.555379i	−0.407087	+	0.913389i	$0.633455\pi$
$840$		0			0
$841$	−16.7065	−	16.7065i	−0.576085	−	0.576085i
$842$		0			0
$843$	0.0306527	−	0.0306527i	0.00105574	−	0.00105574i
$844$		0			0
$845$	0.606447	+	9.26013i	0.0208624	+	0.318558i
$846$		0			0
$847$	−19.5388	+	47.1709i	−0.671361	+	1.62081i
$848$		0			0
$849$	5.40876	+	2.24038i	0.185628	+	0.0768897i
$850$		0			0
$851$			13.1533i			0.450888i
$852$		0			0
$853$	48.3911			1.65688			0.828439	−	0.560079i	$-0.189229\pi$
$853$	48.3911			1.65688			0.828439	+	0.560079i	$0.189229\pi$
$854$		0			0
$855$	−5.53497	−	11.2253i	−0.189292	−	0.383898i
$856$		0			0
$857$	23.9140	−	23.9140i	0.816887	−	0.816887i	−0.168769	−	0.985656i	$-0.553979\pi$
$857$	23.9140	−	23.9140i	0.816887	−	0.816887i	0.985656	+	0.168769i	$0.0539792\pi$
$858$		0			0
$859$	1.66780	−	1.66780i	0.0569047	−	0.0569047i	−0.678082	−	0.734986i	$-0.737188\pi$
$859$	1.66780	−	1.66780i	0.0569047	−	0.0569047i	0.734986	+	0.678082i	$0.237188\pi$
$860$		0			0
$861$	11.7606	+	4.91273i	0.400799	+	0.167425i
$862$		0			0
$863$	3.14104			0.106922			0.0534612	−	0.998570i	$-0.482975\pi$
$863$	3.14104			0.106922			0.0534612	+	0.998570i	$0.482975\pi$
$864$		0			0
$865$	5.92513	+	5.19676i	0.201461	+	0.176695i
$866$		0			0
$867$	−11.4371	−	4.73740i	−0.388424	−	0.160890i
$868$		0			0
$869$	44.1772	−	44.1772i	1.49861	−	1.49861i
$870$		0			0
$871$	−28.7438			−0.973946
$872$		0			0
$873$	3.14450	+	7.59150i	0.106425	+	0.256933i
$874$		0			0
$875$	−6.37256	+	32.0104i	−0.215432	+	1.08215i
$876$		0			0
$877$	9.94805	−	9.94805i	0.335922	−	0.335922i	−0.518908	−	0.854830i	$-0.673661\pi$
$877$	9.94805	−	9.94805i	0.335922	−	0.335922i	0.854830	+	0.518908i	$0.173661\pi$
$878$		0			0
$879$		−	17.7606i		−	0.599049i
$880$		0			0
$881$	−13.2174	+	13.2174i	−0.445304	+	0.445304i	−0.893790	−	0.448486i	$-0.851963\pi$
$881$	−13.2174	+	13.2174i	−0.445304	+	0.445304i	0.448486	+	0.893790i	$0.351963\pi$
$882$		0			0
$883$	5.89830	+	2.44316i	0.198494	+	0.0822188i	0.479716	−	0.877424i	$-0.340740\pi$
$883$	5.89830	+	2.44316i	0.198494	+	0.0822188i	−0.281222	+	0.959643i	$0.590740\pi$
$884$		0			0
$885$	9.34017	+	3.17111i	0.313966	+	0.106596i
$886$		0			0
$887$	−20.7028	−	8.57540i	−0.695133	−	0.287934i	0.00700379	−	0.999975i	$-0.497771\pi$
$887$	−20.7028	−	8.57540i	−0.695133	−	0.287934i	−0.702137	+	0.712042i	$0.747771\pi$
$888$		0			0
$889$	2.74111	−	6.61763i	0.0919339	−	0.221948i
$890$		0			0
$891$	−10.2782	+	24.8137i	−0.344332	+	0.831292i
$892$		0			0
$893$	−22.1937			−0.742683
$894$		0			0
$895$	45.5751	+	15.4734i	1.52341	+	0.517217i
$896$		0			0
$897$		−	5.02397i		−	0.167745i
$898$		0			0
$899$	3.96691	−	9.57697i	0.132304	−	0.319410i
$900$		0			0
$901$		−	55.4204i		−	1.84632i
$902$		0			0
$903$	11.5077	+	11.5077i	0.382953	+	0.382953i
$904$		0			0
$905$	0.668050	+	0.226812i	0.0222067	+	0.00753948i
$906$		0			0
$907$	9.87759			0.327980			0.163990	−	0.986462i	$-0.447564\pi$
$907$	9.87759			0.327980			0.163990	+	0.986462i	$0.447564\pi$
$908$		0			0
$909$	−46.2144	−	19.1426i	−1.53284	−	0.634921i
$910$		0			0
$911$	10.6968	+	10.6968i	0.354402	+	0.354402i	0.861744	−	0.507343i	$-0.169372\pi$
$911$	10.6968	+	10.6968i	0.354402	+	0.354402i	−0.507343	+	0.861744i	$0.669372\pi$
$912$		0			0
$913$	10.7966	+	26.0652i	0.357314	+	0.862633i
$914$		0			0
$915$	6.68503	+	13.5577i	0.221000	+	0.448204i
$916$		0			0
$917$	−15.6194	+	37.7087i	−0.515800	+	1.24525i
$918$		0			0
$919$	−5.08272	+	2.10533i	−0.167663	+	0.0694484i	−0.464936	−	0.885344i	$-0.653923\pi$
$919$	−5.08272	+	2.10533i	−0.167663	+	0.0694484i	0.297273	+	0.954792i	$0.403923\pi$
$920$		0			0
$921$	1.57420	+	3.80044i	0.0518715	+	0.125229i
$922$		0			0
$923$		−	30.6413i		−	1.00857i
$924$		0			0
$925$	−29.3230	−	22.5053i	−0.964135	−	0.739970i
$926$		0			0
$927$	13.4935	+	13.4935i	0.443185	+	0.443185i
$928$		0			0
$929$	13.1045	+	31.6370i	0.429943	+	1.03798i	0.979305	+	0.202390i	$0.0648710\pi$
$929$	13.1045	+	31.6370i	0.429943	+	1.03798i	−0.549362	+	0.835585i	$0.685129\pi$
$930$		0			0
$931$	−1.28613	+	3.10499i	−0.0421511	+	0.101762i
$932$		0			0
$933$	8.20298	−	8.20298i	0.268554	−	0.268554i
$934$		0			0
$935$	−70.6151	+	4.62459i	−2.30936	+	0.151240i
$936$		0			0
$937$	−15.3699	+	37.1063i	−0.502113	+	1.21221i	0.446217	+	0.894925i	$0.352771\pi$
$937$	−15.3699	+	37.1063i	−0.502113	+	1.21221i	−0.948331	+	0.317284i	$0.897229\pi$
$938$		0			0
$939$			17.9974i			0.587324i
$940$		0			0
$941$	−29.6241	−	29.6241i	−0.965718	−	0.965718i	0.0337133	−	0.999432i	$-0.489267\pi$
$941$	−29.6241	−	29.6241i	−0.965718	−	0.965718i	−0.999432	+	0.0337133i	$0.989267\pi$
$942$		0			0
$943$	4.39124	−	10.5122i	0.142998	−	0.342323i
$944$		0			0
$945$	−16.2447	+	18.5215i	−0.528439	+	0.602505i
$946$		0			0
$947$	−24.9593	−	24.9593i	−0.811069	−	0.811069i	0.173725	−	0.984794i	$-0.444420\pi$
$947$	−24.9593	−	24.9593i	−0.811069	−	0.811069i	−0.984794	+	0.173725i	$0.944420\pi$
$948$		0			0
$949$	−35.3724	+	14.6517i	−1.14824	+	0.475615i
$950$		0			0
$951$	10.5684	+	10.5684i	0.342703	+	0.342703i
$952$		0			0
$953$	−20.0819	−	20.0819i	−0.650516	−	0.650516i	0.302601	−	0.953117i	$-0.402145\pi$
$953$	−20.0819	−	20.0819i	−0.650516	−	0.650516i	−0.953117	+	0.302601i	$0.902145\pi$
$954$		0			0
$955$	9.17455	−	27.0226i	0.296881	−	0.874432i
$956$		0			0
$957$	7.79426	+	3.22849i	0.251953	+	0.104362i
$958$		0			0
$959$			45.2855i			1.46235i
$960$		0			0
$961$	11.0029			0.354931
$962$		0			0
$963$	37.7247			1.21566
$964$		0			0
$965$	15.7288	−	46.3275i	0.506328	−	1.49133i
$966$		0			0
$967$	9.00105	−	21.7305i	0.289454	−	0.698804i	−0.710534	−	0.703663i	$-0.751547\pi$
$967$	9.00105	−	21.7305i	0.289454	−	0.698804i	0.999988	+	0.00485856i	$0.00154654\pi$
$968$		0			0
$969$	8.24668	−	3.41588i	0.264921	−	0.109734i
$970$		0			0
$971$	−43.0140	−	17.8170i	−1.38038	−	0.571774i	−0.435800	−	0.900044i	$-0.643534\pi$
$971$	−43.0140	−	17.8170i	−1.38038	−	0.571774i	−0.944584	+	0.328270i	$0.893534\pi$
$972$		0			0
$973$	−22.6989	+	9.40220i	−0.727694	+	0.301421i
$974$		0			0
$975$	11.2001	+	8.59603i	0.358690	+	0.275293i
$976$		0			0
$977$	31.3775	−	12.9970i	1.00385	−	0.415810i	0.180645	−	0.983548i	$-0.442181\pi$
$977$	31.3775	−	12.9970i	1.00385	−	0.415810i	0.823209	+	0.567738i	$0.192181\pi$
$978$		0			0
$979$	9.36500	+	9.36500i	0.299307	+	0.299307i
$980$		0			0
$981$	−23.6221	−	9.78458i	−0.754195	−	0.312398i
$982$		0			0
$983$	7.65639	−	7.65639i	0.244201	−	0.244201i	−0.574385	−	0.818586i	$-0.694759\pi$
$983$	7.65639	−	7.65639i	0.244201	−	0.244201i	0.818586	+	0.574385i	$0.194759\pi$
$984$		0			0
$985$	−2.97777	−	2.61171i	−0.0948797	−	0.0832161i
$986$		0			0
$987$	7.65688	+	18.4854i	0.243721	+	0.588395i
$988$		0			0
$989$	10.2862	−	10.2862i	0.327081	−	0.327081i
$990$		0			0
$991$	9.54859	−	23.0523i	0.303321	−	0.732282i	−0.696570	−	0.717489i	$-0.745291\pi$
$991$	9.54859	−	23.0523i	0.303321	−	0.732282i	0.999891	−	0.0147925i	$-0.00470878\pi$
$992$		0			0
$993$		−	9.60932i		−	0.304943i
$994$		0			0
$995$	10.9442	+	3.71570i	0.346954	+	0.117795i
$996$		0			0
$997$	9.19795	+	22.2058i	0.291302	+	0.703265i	0.999997	−	0.00224932i	$-0.000715982\pi$
$997$	9.19795	+	22.2058i	0.291302	+	0.703265i	−0.708696	+	0.705514i	$0.750716\pi$
$998$		0			0
$999$	−10.6772	−	25.7771i	−0.337812	−	0.815551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.y.a.413.9	yes	84
5.2	odd	4		820.2.x.a.577.13	✓	84
41.14	odd	8		820.2.x.a.793.13	yes	84
205.137	even	8	inner	820.2.y.a.137.9	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.577.13	✓	84	5.2	odd	4
820.2.x.a.793.13	yes	84	41.14	odd	8
820.2.y.a.137.9	yes	84	205.137	even	8	inner
820.2.y.a.413.9	yes	84	1.1	even	1	trivial

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.y (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.629944 + 0.260931i) q^{3} +(-1.47443 + 1.68109i) q^{5} +(1.11716 + 2.69706i) q^{7} +(-1.79258 + 1.79258i) q^{9} +(-4.93128 - 2.04260i) q^{11} +(3.82604 - 1.58480i) q^{13} +(0.490161 - 1.44372i) q^{15} +(-5.47789 - 2.26902i) q^{17} +(2.03983 - 0.844926i) q^{19} +(-1.40750 - 1.40750i) q^{21} +(-1.25809 + 1.25809i) q^{23} +(-0.652104 - 4.95729i) q^{25} +(1.44428 - 3.48680i) q^{27} +(2.14163 + 0.887091i) q^{29} -4.47182i q^{31} +3.63941 q^{33} +(-6.18117 - 2.09859i) q^{35} +(5.22748 - 5.22748i) q^{37} +(-1.99667 + 1.99667i) q^{39} +(-5.92303 + 2.43263i) q^{41} -8.17602 q^{43} +(-0.370445 - 5.65650i) q^{45} +(-9.28679 - 3.84671i) q^{47} +(-1.07634 + 1.07634i) q^{49} +4.04282 q^{51} +(3.57694 + 8.63550i) q^{53} +(10.7046 - 5.27823i) q^{55} +(-1.06451 + 1.06451i) q^{57} +6.46953i q^{59} +(-7.01064 + 7.01064i) q^{61} +(-6.83728 - 2.83209i) q^{63} +(-2.97705 + 8.76857i) q^{65} +(-6.41247 - 2.65613i) q^{67} +(0.464251 - 1.12080i) q^{69} +(2.83148 - 6.83579i) q^{71} -9.24517 q^{73} +(1.70430 + 2.95266i) q^{75} -15.5819i q^{77} +(-4.47929 + 10.8140i) q^{79} -5.03191i q^{81} +(-3.73755 - 3.73755i) q^{83} +(11.8912 - 5.86330i) q^{85} -1.58058 q^{87} +(-2.29242 - 0.949551i) q^{89} +(8.54858 + 8.54858i) q^{91} +(1.16684 + 2.81700i) q^{93} +(-1.58720 + 4.67492i) q^{95} +(1.24039 - 2.99457i) q^{97} +(12.5012 - 5.17817i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more