LMFDB - Embedded newform 820.2.bi.a.189.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(189,820)] 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, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.189"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bi (of order $10$, 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:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			189.3
Character	$\chi$	$=$	820.189
Dual form			820.2.bi.a.269.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.59331 q^{3} +(-2.08605 - 0.805227i) q^{5} +(0.600140 + 1.84704i) q^{7} +3.72526 q^{9} +(-1.11720 - 1.53770i) q^{11} +(-1.70506 + 5.24762i) q^{13} +(5.40978 + 2.08820i) q^{15} +(1.07889 - 0.783861i) q^{17} +(-5.58571 + 1.81491i) q^{19} +(-1.55635 - 4.78995i) q^{21} +(-4.82327 - 1.56717i) q^{23} +(3.70322 + 3.35949i) q^{25} -1.88082 q^{27} +(3.26279 - 4.49085i) q^{29} +(6.41418 - 4.66017i) q^{31} +(2.89726 + 3.98773i) q^{33} +(0.235365 - 4.33627i) q^{35} +(6.78119 - 9.33351i) q^{37} +(4.42174 - 13.6087i) q^{39} +(5.28275 - 3.61837i) q^{41} +(1.44108 + 0.468236i) q^{43} +(-7.77108 - 2.99968i) q^{45} +(-1.40246 + 4.31632i) q^{47} +(2.61173 - 1.89753i) q^{49} +(-2.79790 + 2.03279i) q^{51} +(-4.43214 - 3.22014i) q^{53} +(1.09235 + 4.10732i) q^{55} +(14.4855 - 4.70662i) q^{57} +(1.87921 - 5.78361i) q^{59} +(3.75107 + 11.5446i) q^{61} +(2.23568 + 6.88071i) q^{63} +(7.78236 - 9.57385i) q^{65} +(-11.0524 - 8.03004i) q^{67} +(12.5082 + 4.06417i) q^{69} +(-1.78089 - 2.45118i) q^{71} -5.98378i q^{73} +(-9.60360 - 8.71220i) q^{75} +(2.16971 - 2.98636i) q^{77} +7.30155i q^{79} -6.29822 q^{81} -2.17634i q^{83} +(-2.88181 + 0.766421i) q^{85} +(-8.46143 + 11.6462i) q^{87} +(14.5402 - 4.72438i) q^{89} -10.7158 q^{91} +(-16.6340 + 12.0853i) q^{93} +(13.1135 + 0.711776i) q^{95} +(-3.17524 - 2.30695i) q^{97} +(-4.16188 - 5.72833i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) $ 80 * q + 68 * q^9 + 10 * q^15 - 26 * q^21 + 10 * q^25 - 20 * q^29 + 4 * q^31 + 15 * q^35 - 8 * q^39 + 4 * q^41 - 4 * q^45 + 18 * q^49 + 52 * q^51 - 36 * q^59 - 42 * q^61 - 15 * q^65 + 30 * q^69 - 20 * q^75 + 32 * q^81 + 10 * q^89 - 132 * q^91 + 50 * q^95 + 80 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$-1$

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
$3$	−2.59331			−1.49725			−0.748624	−	0.662994i	$-0.769285\pi$
$3$	−2.59331			−1.49725			−0.748624	+	0.662994i	$0.769285\pi$
$4$		0			0
$5$	−2.08605	−	0.805227i	−0.932910	−	0.360109i
$5$	−2.08605	−	0.805227i	−0.932910	−	0.360109i
$6$		0			0
$7$	0.600140	+	1.84704i	0.226832	+	0.698116i	0.998101	+	0.0616064i	$0.0196224\pi$
$7$	0.600140	+	1.84704i	0.226832	+	0.698116i	−0.771269	+	0.636509i	$0.780378\pi$
$8$		0			0
$9$	3.72526			1.24175
$10$		0			0
$11$	−1.11720	−	1.53770i	−0.336850	−	0.463634i	0.606668	−	0.794955i	$-0.292506\pi$
$11$	−1.11720	−	1.53770i	−0.336850	−	0.463634i	−0.943518	+	0.331321i	$0.892506\pi$
$12$		0			0
$13$	−1.70506	+	5.24762i	−0.472898	+	1.45543i	0.375875	+	0.926670i	$0.377342\pi$
$13$	−1.70506	+	5.24762i	−0.472898	+	1.45543i	−0.848772	+	0.528759i	$0.822658\pi$
$14$		0			0
$15$	5.40978	+	2.08820i	1.39680	+	0.539172i
$16$		0			0
$17$	1.07889	−	0.783861i	0.261670	−	0.190114i	−0.449213	−	0.893425i	$-0.648296\pi$
$17$	1.07889	−	0.783861i	0.261670	−	0.190114i	0.710883	+	0.703310i	$0.248296\pi$
$18$		0			0
$19$	−5.58571	+	1.81491i	−1.28145	+	0.416368i	−0.869091	−	0.494653i	$-0.835295\pi$
$19$	−5.58571	+	1.81491i	−1.28145	+	0.416368i	−0.412359	+	0.911021i	$0.635295\pi$
$20$		0			0
$21$	−1.55635	−	4.78995i	−0.339623	−	1.04525i
$22$		0			0
$23$	−4.82327	−	1.56717i	−1.00572	−	0.326779i	−0.240572	−	0.970631i	$-0.577335\pi$
$23$	−4.82327	−	1.56717i	−1.00572	−	0.326779i	−0.765149	+	0.643853i	$0.777335\pi$
$24$		0			0
$25$	3.70322	+	3.35949i	0.740644	+	0.671898i
$26$		0			0
$27$	−1.88082			−0.361965
$28$		0			0
$29$	3.26279	−	4.49085i	0.605885	−	0.833929i	−0.390346	−	0.920668i	$-0.627645\pi$
$29$	3.26279	−	4.49085i	0.605885	−	0.833929i	0.996231	+	0.0867390i	$0.0276446\pi$
$30$		0			0
$31$	6.41418	−	4.66017i	1.15202	−	0.836992i	0.163272	−	0.986581i	$-0.447795\pi$
$31$	6.41418	−	4.66017i	1.15202	−	0.836992i	0.988748	+	0.149589i	$0.0477951\pi$
$32$		0			0
$33$	2.89726	+	3.98773i	0.504348	+	0.694175i
$34$		0			0
$35$	0.235365	−	4.33627i	0.0397839	−	0.732963i
$36$		0			0
$37$	6.78119	−	9.33351i	1.11482	−	1.53442i	0.300705	−	0.953717i	$-0.402778\pi$
$37$	6.78119	−	9.33351i	1.11482	−	1.53442i	0.814116	−	0.580703i	$-0.197222\pi$
$38$		0			0
$39$	4.42174	−	13.6087i	0.708045	−	2.17914i
$40$		0			0
$41$	5.28275	−	3.61837i	0.825026	−	0.565094i
$41$	5.28275	−	3.61837i	0.825026	−	0.565094i
$42$		0			0
$43$	1.44108	+	0.468236i	0.219763	+	0.0714053i	0.416829	−	0.908985i	$-0.363141\pi$
$43$	1.44108	+	0.468236i	0.219763	+	0.0714053i	−0.197066	+	0.980390i	$0.563141\pi$
$44$		0			0
$45$	−7.77108	−	2.99968i	−1.15844	−	0.447166i
$46$		0			0
$47$	−1.40246	+	4.31632i	−0.204569	+	0.629600i	0.795161	+	0.606398i	$0.207386\pi$
$47$	−1.40246	+	4.31632i	−0.204569	+	0.629600i	−0.999731	+	0.0232019i	$0.992614\pi$
$48$		0			0
$49$	2.61173	−	1.89753i	0.373104	−	0.271076i
$50$		0			0
$51$	−2.79790	+	2.03279i	−0.391785	+	0.284648i
$52$		0			0
$53$	−4.43214	−	3.22014i	−0.608801	−	0.442320i	0.240191	−	0.970726i	$-0.422790\pi$
$53$	−4.43214	−	3.22014i	−0.608801	−	0.442320i	−0.848992	+	0.528406i	$0.822790\pi$
$54$		0			0
$55$	1.09235	+	4.10732i	0.147292	+	0.553831i
$56$		0			0
$57$	14.4855	−	4.70662i	1.91865	−	0.623407i
$58$		0			0
$59$	1.87921	−	5.78361i	0.244652	−	0.752962i	−0.751041	−	0.660255i	$-0.770448\pi$
$59$	1.87921	−	5.78361i	0.244652	−	0.752962i	0.995693	−	0.0927065i	$-0.0295518\pi$
$60$		0			0
$61$	3.75107	+	11.5446i	0.480275	+	1.47814i	0.838709	+	0.544580i	$0.183311\pi$
$61$	3.75107	+	11.5446i	0.480275	+	1.47814i	−0.358433	+	0.933555i	$0.616689\pi$
$62$		0			0
$63$	2.23568	+	6.88071i	0.281669	+	0.866888i
$64$		0			0
$65$	7.78236	−	9.57385i	0.965283	−	1.18749i
$66$		0			0
$67$	−11.0524	−	8.03004i	−1.35027	−	0.981026i	−0.998998	−	0.0447505i	$-0.985751\pi$
$67$	−11.0524	−	8.03004i	−1.35027	−	0.981026i	−0.351268	−	0.936275i	$-0.614249\pi$
$68$		0			0
$69$	12.5082	+	4.06417i	1.50581	+	0.489269i
$70$		0			0
$71$	−1.78089	−	2.45118i	−0.211352	−	0.290901i	0.690158	−	0.723658i	$-0.257541\pi$
$71$	−1.78089	−	2.45118i	−0.211352	−	0.290901i	−0.901511	+	0.432757i	$0.857541\pi$
$72$		0			0
$73$		−	5.98378i		−	0.700349i	−0.936685	−	0.350174i	$-0.886122\pi$
$73$		−	5.98378i		−	0.700349i	0.936685	−	0.350174i	$-0.113878\pi$
$74$		0			0
$75$	−9.60360	−	8.71220i	−1.10893	−	1.00600i
$76$		0			0
$77$	2.16971	−	2.98636i	0.247262	−	0.340327i
$78$		0			0
$79$			7.30155i			0.821488i	0.911751	+	0.410744i	$0.134731\pi$
$79$			7.30155i			0.821488i	−0.911751	+	0.410744i	$0.865269\pi$
$80$		0			0
$81$	−6.29822			−0.699802
$82$		0			0
$83$		−	2.17634i		−	0.238884i	−0.992841	−	0.119442i	$-0.961889\pi$
$83$		−	2.17634i		−	0.238884i	0.992841	−	0.119442i	$-0.0381106\pi$
$84$		0			0
$85$	−2.88181	+	0.766421i	−0.312576	+	0.0831300i
$86$		0			0
$87$	−8.46143	+	11.6462i	−0.907161	+	1.24860i
$88$		0			0
$89$	14.5402	−	4.72438i	1.54125	−	0.500784i	0.589531	−	0.807745i	$-0.299312\pi$
$89$	14.5402	−	4.72438i	1.54125	−	0.500784i	0.951722	+	0.306962i	$0.0993124\pi$
$90$		0			0
$91$	−10.7158			−1.12333
$92$		0			0
$93$	−16.6340	+	12.0853i	−1.72486	+	1.25319i
$94$		0			0
$95$	13.1135	+	0.711776i	1.34542	+	0.0730267i
$96$		0			0
$97$	−3.17524	−	2.30695i	−0.322397	−	0.234235i	0.414801	−	0.909912i	$-0.363851\pi$
$97$	−3.17524	−	2.30695i	−0.322397	−	0.234235i	−0.737198	+	0.675677i	$0.763851\pi$
$98$		0			0
$99$	−4.16188	−	5.72833i	−0.418284	−	0.575719i
$100$		0			0
$101$	−3.85449	+	1.25240i	−0.383536	+	0.124618i	−0.494438	−	0.869213i	$-0.664626\pi$
$101$	−3.85449	+	1.25240i	−0.383536	+	0.124618i	0.110902	+	0.993831i	$0.464626\pi$
$102$		0			0
$103$	−2.71395	+	0.881816i	−0.267414	+	0.0868879i	−0.439655	−	0.898167i	$-0.644899\pi$
$103$	−2.71395	+	0.881816i	−0.267414	+	0.0868879i	0.172241	+	0.985055i	$0.444899\pi$
$104$		0			0
$105$	−0.610374	+	11.2453i	−0.0595664	+	1.09743i
$106$		0			0
$107$	17.3433	−	5.63519i	1.67664	−	0.544774i	0.692388	−	0.721525i	$-0.256559\pi$
$107$	17.3433	−	5.63519i	1.67664	−	0.544774i	0.984256	+	0.176751i	$0.0565587\pi$
$108$		0			0
$109$			1.18155i			0.113172i	0.998398	+	0.0565859i	$0.0180215\pi$
$109$			1.18155i			0.113172i	−0.998398	+	0.0565859i	$0.981979\pi$
$110$		0			0
$111$	−17.5857	+	24.2047i	−1.66916	+	2.29741i
$112$		0			0
$113$	8.20205	+	11.2892i	0.771584	+	1.06199i	0.996161	+	0.0875381i	$0.0278999\pi$
$113$	8.20205	+	11.2892i	0.771584	+	1.06199i	−0.224577	+	0.974456i	$0.572100\pi$
$114$		0			0
$115$	8.79965	+	7.15303i	0.820572	+	0.667024i
$116$		0			0
$117$	−6.35178	+	19.5488i	−0.587222	+	1.80728i
$118$		0			0
$119$	2.09531	+	1.52233i	0.192077	+	0.139552i
$120$		0			0
$121$	2.28281	−	7.02577i	0.207528	−	0.638707i
$122$		0			0
$123$	−13.6998	+	9.38355i	−1.23527	+	0.846086i
$124$		0			0
$125$	−5.01995	−	9.99000i	−0.448998	−	0.893533i
$126$		0			0
$127$	0.672166	−	0.925158i	0.0596451	−	0.0820945i	−0.778152	−	0.628075i	$-0.783843\pi$
$127$	0.672166	−	0.925158i	0.0596451	−	0.0820945i	0.837798	+	0.545981i	$0.183843\pi$
$128$		0			0
$129$	−3.73717	−	1.21428i	−0.329040	−	0.106912i
$130$		0			0
$131$	−12.6065	+	9.15919i	−1.10144	+	0.800242i	−0.981294	−	0.192514i	$-0.938336\pi$
$131$	−12.6065	+	9.15919i	−1.10144	+	0.800242i	−0.120145	+	0.992756i	$0.538336\pi$
$132$		0			0
$133$	−6.70441	−	9.22784i	−0.581346	−	0.800155i
$134$		0			0
$135$	3.92350	+	1.51449i	0.337681	+	0.130347i
$136$		0			0
$137$	7.68018			0.656162			0.328081	−	0.944650i	$-0.393598\pi$
$137$	7.68018			0.656162			0.328081	+	0.944650i	$0.393598\pi$
$138$		0			0
$139$	2.59317	+	7.98097i	0.219950	+	0.676937i	0.998765	+	0.0496830i	$0.0158211\pi$
$139$	2.59317	+	7.98097i	0.219950	+	0.676937i	−0.778815	+	0.627254i	$0.784179\pi$
$140$		0			0
$141$	3.63701	−	11.1936i	0.306291	−	0.942667i
$142$		0			0
$143$	9.97417	−	3.24080i	0.834082	−	0.271010i
$144$		0			0
$145$	−10.4225	+	6.74085i	−0.865542	+	0.559797i
$146$		0			0
$147$	−6.77302	+	4.92089i	−0.558629	+	0.405868i
$148$		0			0
$149$	12.6916	−	17.4684i	1.03973	−	1.43107i	0.142350	−	0.989816i	$-0.454534\pi$
$149$	12.6916	−	17.4684i	1.03973	−	1.43107i	0.897383	−	0.441253i	$-0.145466\pi$
$150$		0			0
$151$	4.04686	+	1.31490i	0.329329	+	0.107005i	0.469014	−	0.883191i	$-0.344609\pi$
$151$	4.04686	+	1.31490i	0.329329	+	0.107005i	−0.139686	+	0.990196i	$0.544609\pi$
$152$		0			0
$153$	4.01915	−	2.92009i	0.324929	−	0.236075i
$154$		0			0
$155$	−17.1328	+	4.55649i	−1.37614	+	0.365986i
$156$		0			0
$157$	1.80133	+	5.54391i	0.143762	+	0.442452i	0.996850	−	0.0793144i	$-0.0252731\pi$
$157$	1.80133	+	5.54391i	0.143762	+	0.442452i	−0.853088	+	0.521767i	$0.825273\pi$
$158$		0			0
$159$	11.4939	+	8.35081i	0.911526	+	0.662263i
$160$		0			0
$161$		−	9.84930i		−	0.776233i
$162$		0			0
$163$		−	7.69914i		−	0.603043i	−0.953459	−	0.301521i	$-0.902506\pi$
$163$		−	7.69914i		−	0.603043i	0.953459	−	0.301521i	$-0.0974945\pi$
$164$		0			0
$165$	−2.83280	−	10.6516i	−0.220533	−	0.829223i
$166$		0			0
$167$	−2.13468			−0.165187			−0.0825933	−	0.996583i	$-0.526320\pi$
$167$	−2.13468			−0.165187			−0.0825933	+	0.996583i	$0.526320\pi$
$168$		0			0
$169$	−14.1131	−	10.2538i	−1.08562	−	0.788752i
$170$		0			0
$171$	−20.8082	+	6.76100i	−1.59124	+	0.517027i
$172$		0			0
$173$		−	1.87510i		−	0.142561i	−0.997456	−	0.0712805i	$-0.977291\pi$
$173$		−	1.87510i		−	0.142561i	0.997456	−	0.0712805i	$-0.0227085\pi$
$174$		0			0
$175$	−3.98267	+	8.85616i	−0.301061	+	0.669463i
$176$		0			0
$177$	−4.87337	+	14.9987i	−0.366305	+	1.12737i
$178$		0			0
$179$	−3.65494	+	5.03059i	−0.273183	+	0.376004i	−0.923461	−	0.383692i	$-0.874652\pi$
$179$	−3.65494	+	5.03059i	−0.273183	+	0.376004i	0.650278	+	0.759696i	$0.274652\pi$
$180$		0			0
$181$	13.3904	+	18.4303i	0.995301	+	1.36991i	0.928164	+	0.372171i	$0.121387\pi$
$181$	13.3904	+	18.4303i	0.995301	+	1.36991i	0.0671373	+	0.997744i	$0.478613\pi$
$182$		0			0
$183$	−9.72769	−	29.9388i	−0.719092	−	2.21314i
$184$		0			0
$185$	−21.6615	+	14.0098i	−1.59259	+	1.03002i
$186$		0			0
$187$	−2.41068	−	0.783279i	−0.176287	−	0.0572790i
$188$		0			0
$189$	−1.12876	−	3.47396i	−0.0821051	−	0.252693i
$190$		0			0
$191$		−	9.20965i		−	0.666387i	−0.942859	−	0.333193i	$-0.891874\pi$
$191$		−	9.20965i		−	0.666387i	0.942859	−	0.333193i	$-0.108126\pi$
$192$		0			0
$193$	−15.0601	−	10.9418i	−1.08405	−	0.787607i	−0.105664	−	0.994402i	$-0.533697\pi$
$193$	−15.0601	−	10.9418i	−1.08405	−	0.787607i	−0.978384	+	0.206795i	$0.933697\pi$
$194$		0			0
$195$	−20.1821	+	24.8280i	−1.44527	+	1.77797i
$196$		0			0
$197$	1.41441	+	1.94676i	0.100772	+	0.138701i	0.856425	−	0.516271i	$-0.172680\pi$
$197$	1.41441	+	1.94676i	0.100772	+	0.138701i	−0.755653	+	0.654972i	$0.772680\pi$
$198$		0			0
$199$	9.25534	+	3.00724i	0.656094	+	0.213178i	0.618099	−	0.786100i	$-0.287903\pi$
$199$	9.25534	+	3.00724i	0.656094	+	0.213178i	0.0379947	+	0.999278i	$0.487903\pi$
$200$		0			0
$201$	28.6623	+	20.8244i	2.02168	+	1.46884i
$202$		0			0
$203$	10.2529	+	3.33137i	0.719613	+	0.233816i
$204$		0			0
$205$	−13.9337	+	3.29429i	−0.973171	+	0.230083i
$206$		0			0
$207$	−17.9679	−	5.83813i	−1.24886	−	0.405778i
$208$		0			0
$209$	9.03116	+	6.56152i	0.624698	+	0.453870i
$210$		0			0
$211$	−5.34024	−	1.73515i	−0.367637	−	0.119453i	0.119372	−	0.992850i	$-0.461912\pi$
$211$	−5.34024	−	1.73515i	−0.367637	−	0.119453i	−0.487009	+	0.873397i	$0.661912\pi$
$212$		0			0
$213$	4.61839	+	6.35667i	0.316447	+	0.435552i
$214$		0			0
$215$	−2.62913	−	2.13716i	−0.179305	−	0.145753i
$216$		0			0
$217$	12.4569	+	9.05049i	0.845632	+	0.614388i
$218$		0			0
$219$			15.5178i			1.04860i
$220$		0			0
$221$	2.27384	+	6.99814i	0.152955	+	0.470746i
$222$		0			0
$223$	15.2827	+	4.96565i	1.02340	+	0.332524i	0.772180	−	0.635404i	$-0.219167\pi$
$223$	15.2827	+	4.96565i	1.02340	+	0.332524i	0.251225	+	0.967929i	$0.419167\pi$
$224$		0			0
$225$	13.7955	+	12.5150i	0.919697	+	0.834332i
$226$		0			0
$227$	−3.98985	−	12.2795i	−0.264816	−	0.815019i	−0.991736	−	0.128297i	$-0.959049\pi$
$227$	−3.98985	−	12.2795i	−0.264816	−	0.815019i	0.726920	−	0.686722i	$-0.240951\pi$
$228$		0			0
$229$	−0.616959	−	0.849171i	−0.0407698	−	0.0561148i	0.788145	−	0.615489i	$-0.211041\pi$
$229$	−0.616959	−	0.849171i	−0.0407698	−	0.0561148i	−0.828915	+	0.559374i	$0.811041\pi$
$230$		0			0
$231$	−5.62674	+	7.74455i	−0.370213	+	0.509554i
$232$		0			0
$233$	−0.644015	+	1.98207i	−0.0421908	+	0.129850i	−0.969933	−	0.243371i	$-0.921747\pi$
$233$	−0.644015	+	1.98207i	−0.0421908	+	0.129850i	0.927742	+	0.373221i	$0.121747\pi$
$234$		0			0
$235$	6.40121	−	7.87476i	0.417569	−	0.513693i
$236$		0			0
$237$		−	18.9352i		−	1.22997i
$238$		0			0
$239$	−20.0420	+	6.51204i	−1.29641	+	0.421229i	−0.874331	−	0.485331i	$-0.838699\pi$
$239$	−20.0420	+	6.51204i	−1.29641	+	0.421229i	−0.422078	+	0.906559i	$0.638699\pi$
$240$		0			0
$241$	−17.1197	−	12.4382i	−1.10278	−	0.801213i	−0.121265	−	0.992620i	$-0.538695\pi$
$241$	−17.1197	−	12.4382i	−1.10278	−	0.801213i	−0.981511	+	0.191407i	$0.938695\pi$
$242$		0			0
$243$	21.9757			1.40974
$244$		0			0
$245$	−6.97614	+	1.85531i	−0.445689	+	0.118532i
$246$		0			0
$247$		−	32.4062i		−	2.06196i
$248$		0			0
$249$			5.64392i			0.357669i
$250$		0			0
$251$	11.4821	+	8.34226i	0.724746	+	0.526559i	0.887897	−	0.460042i	$-0.152166\pi$
$251$	11.4821	+	8.34226i	0.724746	+	0.526559i	−0.163151	+	0.986601i	$0.552166\pi$
$252$		0			0
$253$	2.97873	+	9.16759i	0.187271	+	0.576362i
$254$		0			0
$255$	7.47343	−	1.98757i	0.468004	−	0.124466i
$256$		0			0
$257$	5.04588	−	3.66605i	0.314754	−	0.228682i	−0.419180	−	0.907903i	$-0.637682\pi$
$257$	5.04588	−	3.66605i	0.314754	−	0.228682i	0.733933	+	0.679221i	$0.237682\pi$
$258$		0			0
$259$	21.3090	+	6.92373i	1.32408	+	0.430219i
$260$		0			0
$261$	12.1547	−	16.7296i	0.752360	−	1.03553i
$262$		0			0
$263$	16.9236	−	12.2957i	1.04356	−	0.758188i	0.0725797	−	0.997363i	$-0.476877\pi$
$263$	16.9236	−	12.2957i	1.04356	−	0.758188i	0.970977	+	0.239175i	$0.0768768\pi$
$264$		0			0
$265$	6.65272	+	10.2862i	0.408674	+	0.631879i
$266$		0			0
$267$	−37.7071	+	12.2518i	−2.30764	+	0.749797i
$268$		0			0
$269$	2.42620	−	7.46709i	0.147928	−	0.455277i	−0.849448	−	0.527673i	$-0.823065\pi$
$269$	2.42620	−	7.46709i	0.147928	−	0.455277i	0.997376	+	0.0723964i	$0.0230647\pi$
$270$		0			0
$271$	−7.63272	−	23.4911i	−0.463654	−	1.42698i	−0.860667	−	0.509168i	$-0.829953\pi$
$271$	−7.63272	−	23.4911i	−0.463654	−	1.42698i	0.397013	−	0.917813i	$-0.370047\pi$
$272$		0			0
$273$	27.7895			1.68190
$274$		0			0
$275$	1.02864	−	9.44767i	0.0620291	−	0.569716i
$276$		0			0
$277$	−5.45788	−	7.51213i	−0.327932	−	0.451360i	0.612936	−	0.790133i	$-0.289988\pi$
$277$	−5.45788	−	7.51213i	−0.327932	−	0.451360i	−0.940868	+	0.338772i	$0.889988\pi$
$278$		0			0
$279$	23.8945	−	17.3604i	1.43053	−	1.03934i
$280$		0			0
$281$	12.8966	+	4.19035i	0.769345	+	0.249975i	0.667285	−	0.744803i	$-0.267456\pi$
$281$	12.8966	+	4.19035i	0.769345	+	0.249975i	0.102060	+	0.994778i	$0.467456\pi$
$282$		0			0
$283$	12.3164	−	16.9521i	0.732134	−	1.00770i	−0.266899	−	0.963724i	$-0.585999\pi$
$283$	12.3164	−	16.9521i	0.732134	−	1.00770i	0.999033	−	0.0439711i	$-0.0140009\pi$
$284$		0			0
$285$	−34.0073	−	1.84586i	−2.01442	−	0.109339i
$286$		0			0
$287$	9.85366	+	7.58592i	0.581643	+	0.447783i
$288$		0			0
$289$	−4.70372	+	14.4766i	−0.276689	+	0.851562i
$290$		0			0
$291$	8.23439	+	5.98263i	0.482708	+	0.350708i
$292$		0			0
$293$	−9.06631	+	27.9032i	−0.529660	+	1.63012i	0.225254	+	0.974300i	$0.427679\pi$
$293$	−9.06631	+	27.9032i	−0.529660	+	1.63012i	−0.754913	+	0.655825i	$0.772321\pi$
$294$		0			0
$295$	−8.57724	+	10.5517i	−0.499386	+	0.614344i
$296$		0			0
$297$	2.10126	+	2.89214i	0.121928	+	0.167819i
$298$		0			0
$299$	16.4479	−	22.6386i	0.951206	−	1.30922i
$300$		0			0
$301$			2.94274i			0.169617i
$302$		0			0
$303$	9.99588	−	3.24786i	0.574249	−	0.186585i
$304$		0			0
$305$	1.47111	−	27.1031i	0.0842354	−	1.55192i
$306$		0			0
$307$	15.7997	−	5.13364i	0.901737	−	0.292992i	0.178783	−	0.983888i	$-0.442784\pi$
$307$	15.7997	−	5.13364i	0.901737	−	0.292992i	0.722954	+	0.690896i	$0.242784\pi$
$308$		0			0
$309$	7.03812	−	2.28682i	0.400385	−	0.130093i
$310$		0			0
$311$	−0.0852038	−	0.117273i	−0.00483146	−	0.00664994i	0.806594	−	0.591105i	$-0.201308\pi$
$311$	−0.0852038	−	0.117273i	−0.00483146	−	0.00664994i	−0.811426	+	0.584455i	$0.801308\pi$
$312$		0			0
$313$	−21.4450	−	15.5807i	−1.21214	−	0.880673i	−0.216719	−	0.976234i	$-0.569536\pi$
$313$	−21.4450	−	15.5807i	−1.21214	−	0.880673i	−0.995424	+	0.0955607i	$0.969536\pi$
$314$		0			0
$315$	0.876795	−	16.1537i	0.0494018	−	0.910160i
$316$		0			0
$317$	−4.11178	+	2.98739i	−0.230941	+	0.167788i	−0.697238	−	0.716840i	$-0.745588\pi$
$317$	−4.11178	+	2.98739i	−0.230941	+	0.167788i	0.466297	+	0.884628i	$0.345588\pi$
$318$		0			0
$319$	−10.5508			−0.590730
$320$		0			0
$321$	−44.9767	+	14.6138i	−2.51035	+	0.815663i
$322$		0			0
$323$	−4.60374	+	6.33651i	−0.256159	+	0.352573i
$324$		0			0
$325$	−23.9435	+	13.7050i	−1.32815	+	0.760215i
$326$		0			0
$327$		−	3.06412i		−	0.169446i
$328$		0			0
$329$	−8.81409			−0.485936
$330$		0			0
$331$			7.49537i			0.411983i	0.978554	+	0.205991i	$0.0660419\pi$
$331$			7.49537i			0.411983i	−0.978554	+	0.205991i	$0.933958\pi$
$332$		0			0
$333$	25.2617	−	34.7698i	1.38433	−	1.90537i
$334$		0			0
$335$	16.5899	+	25.6508i	0.906401	+	1.40145i
$336$		0			0
$337$			22.8184i			1.24300i	0.783414	+	0.621500i	$0.213476\pi$
$337$			22.8184i			1.24300i	−0.783414	+	0.621500i	$0.786524\pi$
$338$		0			0
$339$	−21.2705	−	29.2763i	−1.15525	−	1.59007i
$340$		0			0
$341$	−14.3319	−	4.65672i	−0.776116	−	0.252175i
$342$		0			0
$343$	16.0705	+	11.6759i	0.867727	+	0.630440i
$344$		0			0
$345$	−22.8202	−	18.5500i	−1.22860	−	0.998700i
$346$		0			0
$347$	−7.09011	−	21.8211i	−0.380617	−	1.17142i	−0.939610	−	0.342246i	$-0.888812\pi$
$347$	−7.09011	−	21.8211i	−0.380617	−	1.17142i	0.558993	−	0.829172i	$-0.311188\pi$
$348$		0			0
$349$	2.47949	+	7.63109i	0.132724	+	0.408483i	0.995229	−	0.0975659i	$-0.0311057\pi$
$349$	2.47949	+	7.63109i	0.132724	+	0.408483i	−0.862505	+	0.506049i	$0.831106\pi$
$350$		0			0
$351$	3.20691	−	9.86986i	0.171172	−	0.526814i
$352$		0			0
$353$	−17.5226	+	5.69345i	−0.932636	+	0.303032i	−0.735640	−	0.677373i	$-0.763118\pi$
$353$	−17.5226	+	5.69345i	−0.932636	+	0.303032i	−0.196996	+	0.980404i	$0.563118\pi$
$354$		0			0
$355$	1.74126	+	6.54730i	0.0924166	+	0.347495i
$356$		0			0
$357$	−5.43379	−	3.94788i	−0.287586	−	0.208944i
$358$		0			0
$359$	16.2363	−	11.7963i	0.856917	−	0.622587i	−0.0701276	−	0.997538i	$-0.522341\pi$
$359$	16.2363	−	11.7963i	0.856917	−	0.622587i	0.927044	+	0.374952i	$0.122341\pi$
$360$		0			0
$361$	12.5349	−	9.10717i	0.659734	−	0.479325i
$362$		0			0
$363$	−5.92004	+	18.2200i	−0.310722	+	0.956303i
$364$		0			0
$365$	−4.81830	+	12.4825i	−0.252202	+	0.653363i
$366$		0			0
$367$	13.9347	+	4.52765i	0.727384	+	0.236341i	0.649222	−	0.760599i	$-0.275095\pi$
$367$	13.9347	+	4.52765i	0.727384	+	0.236341i	0.0781623	+	0.996941i	$0.475095\pi$
$368$		0			0
$369$	19.6796	−	13.4794i	1.02448	−	0.701708i
$370$		0			0
$371$	3.28782	−	10.1189i	0.170695	−	0.525346i
$372$		0			0
$373$	6.24340	−	8.59330i	0.323271	−	0.444944i	−0.616191	−	0.787596i	$-0.711325\pi$
$373$	6.24340	−	8.59330i	0.323271	−	0.444944i	0.939462	+	0.342652i	$0.111325\pi$
$374$		0			0
$375$	13.0183	+	25.9072i	0.672262	+	1.33784i
$376$		0			0
$377$	18.0030	+	24.7790i	0.927203	+	1.27619i
$378$		0			0
$379$	20.1060	−	14.6078i	1.03277	−	0.750354i	0.0639117	−	0.997956i	$-0.479642\pi$
$379$	20.1060	−	14.6078i	1.03277	−	0.750354i	0.968862	+	0.247602i	$0.0796424\pi$
$380$		0			0
$381$	−1.74314	+	2.39922i	−0.0893036	+	0.122916i
$382$		0			0
$383$	0.718225			0.0366996			0.0183498	−	0.999832i	$-0.494159\pi$
$383$	0.718225			0.0366996			0.0183498	+	0.999832i	$0.494159\pi$
$384$		0			0
$385$	−6.93083	+	4.48258i	−0.353228	+	0.228453i
$386$		0			0
$387$	5.36841	+	1.74430i	0.272891	+	0.0886678i
$388$		0			0
$389$	−8.26502	−	25.4371i	−0.419053	−	1.28971i	−0.908575	−	0.417722i	$-0.862829\pi$
$389$	−8.26502	−	25.4371i	−0.419053	−	1.28971i	0.489521	−	0.871991i	$-0.337171\pi$
$390$		0			0
$391$	−6.43223	+	2.08996i	−0.325292	+	0.105694i
$392$		0			0
$393$	32.6927	−	23.7526i	1.64913	−	1.19816i
$394$		0			0
$395$	5.87940	−	15.2314i	0.295825	−	0.766375i
$396$		0			0
$397$	−1.92555	+	5.92625i	−0.0966408	+	0.297430i	−0.987678	−	0.156501i	$-0.949979\pi$
$397$	−1.92555	+	5.92625i	−0.0966408	+	0.297430i	0.891037	+	0.453931i	$0.149979\pi$
$398$		0			0
$399$	17.3866	+	23.9306i	0.870420	+	1.19803i
$400$		0			0
$401$	9.64036			0.481416			0.240708	−	0.970598i	$-0.422620\pi$
$401$	9.64036			0.481416			0.240708	+	0.970598i	$0.422620\pi$
$402$		0			0
$403$	13.5183	+	41.6051i	0.673395	+	2.07250i
$404$		0			0
$405$	13.1384	+	5.07150i	0.652853	+	0.252005i
$406$		0			0
$407$	−21.9281			−1.08694
$408$		0			0
$409$	−11.9323			−0.590014			−0.295007	−	0.955495i	$-0.595322\pi$
$409$	−11.9323			−0.590014			−0.295007	+	0.955495i	$0.595322\pi$
$410$		0			0
$411$	−19.9171			−0.982437
$412$		0			0
$413$	11.8103			0.581149
$414$		0			0
$415$	−1.75245	+	4.53995i	−0.0860242	+	0.222857i
$416$		0			0
$417$	−6.72490	−	20.6971i	−0.329320	−	1.01354i
$418$		0			0
$419$	−4.14082			−0.202292			−0.101146	−	0.994872i	$-0.532251\pi$
$419$	−4.14082			−0.202292			−0.101146	+	0.994872i	$0.532251\pi$
$420$		0			0
$421$	−1.00310	−	1.38065i	−0.0488881	−	0.0672887i	0.783873	−	0.620921i	$-0.213241\pi$
$421$	−1.00310	−	1.38065i	−0.0488881	−	0.0672887i	−0.832761	+	0.553632i	$0.813241\pi$
$422$		0			0
$423$	−5.22452	+	16.0794i	−0.254025	+	0.781808i
$424$		0			0
$425$	6.62874	+	0.721719i	0.321541	+	0.0350085i
$426$		0			0
$427$	−19.0722	+	13.8568i	−0.922968	+	0.670576i
$428$		0			0
$429$	−25.8661	+	8.40441i	−1.24883	+	0.405769i
$430$		0			0
$431$	−7.51728	−	23.1358i	−0.362094	−	1.11441i	−0.951781	−	0.306780i	$-0.900749\pi$
$431$	−7.51728	−	23.1358i	−0.362094	−	1.11441i	0.589686	−	0.807633i	$-0.299251\pi$
$432$		0			0
$433$	−35.2343	−	11.4483i	−1.69325	−	0.550172i	−0.705846	−	0.708365i	$-0.749433\pi$
$433$	−35.2343	−	11.4483i	−1.69325	−	0.550172i	−0.987408	+	0.158194i	$0.949433\pi$
$434$		0			0
$435$	27.0288	−	17.4811i	1.29593	−	0.838155i
$436$		0			0
$437$	29.7857			1.42484
$438$		0			0
$439$	19.9011	−	27.3915i	0.949826	−	1.30732i	−0.00177921	−	0.999998i	$-0.500566\pi$
$439$	19.9011	−	27.3915i	0.949826	−	1.30732i	0.951605	−	0.307324i	$-0.0994337\pi$
$440$		0			0
$441$	9.72936	−	7.06880i	0.463303	−	0.336609i
$442$		0			0
$443$	−24.2123	−	33.3254i	−1.15036	−	1.58334i	−0.741826	−	0.670592i	$-0.766040\pi$
$443$	−24.2123	−	33.3254i	−1.15036	−	1.58334i	−0.408534	−	0.912743i	$-0.633960\pi$
$444$		0			0
$445$	−34.1357	−	1.85282i	−1.61819	−	0.0878323i
$446$		0			0
$447$	−32.9131	+	45.3011i	−1.55674	+	2.14267i
$448$		0			0
$449$	1.66219	−	5.11571i	0.0784438	−	0.241425i	−0.904143	−	0.427230i	$-0.859489\pi$
$449$	1.66219	−	5.11571i	0.0784438	−	0.241425i	0.982587	+	0.185805i	$0.0594893\pi$
$450$		0			0
$451$	−11.4659	−	4.08082i	−0.539907	−	0.192158i
$452$		0			0
$453$	−10.4948	−	3.40995i	−0.493087	−	0.160214i
$454$		0			0
$455$	22.3538	+	8.62869i	1.04796	+	0.404519i
$456$		0			0
$457$	−6.32344	+	19.4616i	−0.295798	+	0.910373i	0.687154	+	0.726512i	$0.258860\pi$
$457$	−6.32344	+	19.4616i	−0.295798	+	0.910373i	−0.982952	+	0.183861i	$0.941140\pi$
$458$		0			0
$459$	−2.02921	+	1.47430i	−0.0947152	+	0.0688146i
$460$		0			0
$461$	29.5083	−	21.4390i	1.37434	−	0.998516i	0.376955	−	0.926232i	$-0.376971\pi$
$461$	29.5083	−	21.4390i	1.37434	−	0.998516i	0.997384	−	0.0722841i	$-0.0230288\pi$
$462$		0			0
$463$	13.8244	+	10.0440i	0.642473	+	0.466784i	0.860699	−	0.509114i	$-0.170027\pi$
$463$	13.8244	+	10.0440i	0.642473	+	0.466784i	−0.218226	+	0.975898i	$0.570027\pi$
$464$		0			0
$465$	44.4307	−	11.8164i	2.06042	−	0.547972i
$466$		0			0
$467$	−2.04607	+	0.664808i	−0.0946808	+	0.0307637i	−0.355974	−	0.934496i	$-0.615851\pi$
$467$	−2.04607	+	0.664808i	−0.0946808	+	0.0307637i	0.261294	+	0.965259i	$0.415851\pi$
$468$		0			0
$469$	8.19882	−	25.2334i	0.378587	−	1.16517i
$470$		0			0
$471$	−4.67140	−	14.3771i	−0.215247	−	0.662461i
$472$		0			0
$473$	−0.889977	−	2.73907i	−0.0409212	−	0.125942i
$474$		0			0
$475$	−26.7823	−	12.0441i	−1.22885	−	0.552623i
$476$		0			0
$477$	−16.5109	−	11.9958i	−0.755981	−	0.549252i
$478$		0			0
$479$	−5.38883	−	1.75094i	−0.246222	−	0.0800023i	0.183306	−	0.983056i	$-0.441320\pi$
$479$	−5.38883	−	1.75094i	−0.246222	−	0.0800023i	−0.429528	+	0.903054i	$0.641320\pi$
$480$		0			0
$481$	37.4164	+	51.4993i	1.70604	+	2.34817i
$482$		0			0
$483$			25.5423i			1.16221i
$484$		0			0
$485$	4.76610	+	7.36920i	0.216417	+	0.334618i
$486$		0			0
$487$	4.37493	−	6.02158i	0.198247	−	0.272864i	−0.698307	−	0.715799i	$-0.746063\pi$
$487$	4.37493	−	6.02158i	0.198247	−	0.272864i	0.896554	+	0.442935i	$0.146063\pi$
$488$		0			0
$489$			19.9663i			0.902905i
$490$		0			0
$491$	−4.58151			−0.206761			−0.103380	−	0.994642i	$-0.532966\pi$
$491$	−4.58151			−0.206761			−0.103380	+	0.994642i	$0.532966\pi$
$492$		0			0
$493$		−	7.40271i		−	0.333401i
$494$		0			0
$495$	4.06928	+	15.3008i	0.182900	+	0.687722i
$496$		0			0
$497$	3.45865	−	4.76042i	0.155141	−	0.213534i
$498$		0			0
$499$	−31.5751	+	10.2594i	−1.41350	+	0.459273i	−0.913530	−	0.406771i	$-0.866655\pi$
$499$	−31.5751	+	10.2594i	−1.41350	+	0.459273i	−0.499967	+	0.866044i	$0.666655\pi$
$500$		0			0
$501$	5.53589			0.247325
$502$		0			0
$503$	−20.8337	+	15.1366i	−0.928928	+	0.674906i	−0.945730	−	0.324953i	$-0.894651\pi$
$503$	−20.8337	+	15.1366i	−0.928928	+	0.674906i	0.0168022	+	0.999859i	$0.494651\pi$
$504$		0			0
$505$	9.04912	+	0.491170i	0.402681	+	0.0218568i
$506$		0			0
$507$	36.5997	+	26.5912i	1.62545	+	1.18096i
$508$		0			0
$509$	−6.15695	−	8.47432i	−0.272902	−	0.375618i	0.650465	−	0.759537i	$-0.274574\pi$
$509$	−6.15695	−	8.47432i	−0.272902	−	0.375618i	−0.923367	+	0.383919i	$0.874574\pi$
$510$		0			0
$511$	11.0523	−	3.59111i	0.488925	−	0.158861i
$512$		0			0
$513$	10.5057	−	3.41352i	0.463840	−	0.150711i
$514$		0			0
$515$	6.37150	+	0.345834i	0.280762	+	0.0152393i
$516$		0			0
$517$	8.20403	−	2.66565i	0.360813	−	0.117235i
$518$		0			0
$519$			4.86271i			0.213449i
$520$		0			0
$521$	−20.0122	+	27.5444i	−0.876751	+	1.20674i	0.100560	+	0.994931i	$0.467937\pi$
$521$	−20.0122	+	27.5444i	−0.876751	+	1.20674i	−0.977310	+	0.211813i	$0.932063\pi$
$522$		0			0
$523$	−19.2093	−	26.4393i	−0.839964	−	1.15611i	−0.985986	−	0.166830i	$-0.946647\pi$
$523$	−19.2093	−	26.4393i	−0.839964	−	1.15611i	0.146022	−	0.989281i	$-0.453353\pi$
$524$		0			0
$525$	10.3283	−	22.9668i	0.450764	−	1.00235i
$526$		0			0
$527$	3.26728	−	10.0556i	0.142325	−	0.438031i
$528$		0			0
$529$	2.20049	+	1.59875i	0.0956733	+	0.0695107i
$530$		0			0
$531$	7.00054	−	21.5454i	0.303798	−	0.934993i
$532$		0			0
$533$	9.98045	+	33.8914i	0.432301	+	1.46800i
$534$		0			0
$535$	−40.7167	−	2.21003i	−1.76034	−	0.0955479i
$536$		0			0
$537$	9.47839	−	13.0459i	0.409023	−	0.562971i
$538$		0			0
$539$	−5.83567	−	1.89612i	−0.251360	−	0.0816718i
$540$		0			0
$541$	8.86425	−	6.44025i	0.381104	−	0.276888i	−0.380697	−	0.924700i	$-0.624316\pi$
$541$	8.86425	−	6.44025i	0.381104	−	0.276888i	0.761800	+	0.647812i	$0.224316\pi$
$542$		0			0
$543$	−34.7255	−	47.7955i	−1.49021	−	2.05110i
$544$		0			0
$545$	0.951414	−	2.46477i	0.0407541	−	0.105579i
$546$		0			0
$547$	40.3334			1.72453			0.862267	−	0.506455i	$-0.169044\pi$
$547$	40.3334			1.72453			0.862267	+	0.506455i	$0.169044\pi$
$548$		0			0
$549$	13.9737	+	43.0067i	0.596384	+	1.83548i
$550$		0			0
$551$	−10.0745	+	31.0062i	−0.429190	+	1.32091i
$552$		0			0
$553$	−13.4863	+	4.38195i	−0.573494	+	0.186339i
$554$		0			0
$555$	56.1750	−	36.3317i	2.38450	−	1.54220i
$556$		0			0
$557$	37.9158	−	27.5474i	1.60654	−	1.16722i	0.733346	−	0.679856i	$-0.237958\pi$
$557$	37.9158	−	27.5474i	1.60654	−	1.16722i	0.873198	−	0.487366i	$-0.162042\pi$
$558$		0			0
$559$	−4.91425	+	6.76389i	−0.207851	+	0.286082i
$560$		0			0
$561$	6.25165	+	2.03129i	0.263945	+	0.0857609i
$562$		0			0
$563$	−1.51935	+	1.10387i	−0.0640330	+	0.0465227i	−0.619341	−	0.785122i	$-0.712600\pi$
$563$	−1.51935	+	1.10387i	−0.0640330	+	0.0465227i	0.555308	+	0.831645i	$0.312600\pi$
$564$		0			0
$565$	−8.01956	−	30.1543i	−0.337386	−	1.26860i
$566$		0			0
$567$	−3.77981	−	11.6331i	−0.158737	−	0.488543i
$568$		0			0
$569$	−16.6138	−	12.0706i	−0.696486	−	0.506027i	0.182300	−	0.983243i	$-0.441646\pi$
$569$	−16.6138	−	12.0706i	−0.696486	−	0.506027i	−0.878786	+	0.477216i	$0.841646\pi$
$570$		0			0
$571$		−	6.06869i		−	0.253967i	−0.991905	−	0.126983i	$-0.959471\pi$
$571$		−	6.06869i		−	0.253967i	0.991905	−	0.126983i	$-0.0405295\pi$
$572$		0			0
$573$			23.8835i			0.997747i
$574$		0			0
$575$	−12.5967	−	22.0073i	−0.525319	−	0.917768i
$576$		0			0
$577$	12.3038			0.512214			0.256107	−	0.966648i	$-0.417560\pi$
$577$	12.3038			0.512214			0.256107	+	0.966648i	$0.417560\pi$
$578$		0			0
$579$	39.0555	+	28.3755i	1.62309	+	1.17924i
$580$		0			0
$581$	4.01978	−	1.30611i	0.166769	−	0.0541864i
$582$		0			0
$583$			10.4128i			0.431256i
$584$		0			0
$585$	28.9913	−	35.6651i	1.19864	−	1.47457i
$586$		0			0
$587$	0.864226	−	2.65982i	0.0356704	−	0.109782i	−0.931636	−	0.363393i	$-0.881618\pi$
$587$	0.864226	−	2.65982i	0.0356704	−	0.109782i	0.967306	+	0.253611i	$0.0816182\pi$
$588$		0			0
$589$	−27.3700	+	37.6715i	−1.12776	+	1.55223i
$590$		0			0
$591$	−3.66800	−	5.04857i	−0.150881	−	0.207670i
$592$		0			0
$593$	−10.2544	−	31.5599i	−0.421099	−	1.29601i	−0.906680	−	0.421819i	$-0.861392\pi$
$593$	−10.2544	−	31.5599i	−0.421099	−	1.29601i	0.485581	−	0.874192i	$-0.338608\pi$
$594$		0			0
$595$	−3.14510	−	4.86286i	−0.128936	−	0.199358i
$596$		0			0
$597$	−24.0020	−	7.79872i	−0.982336	−	0.319180i
$598$		0			0
$599$	11.9521	+	36.7848i	0.488350	+	1.50299i	0.827070	+	0.562099i	$0.190006\pi$
$599$	11.9521	+	36.7848i	0.488350	+	1.50299i	−0.338720	+	0.940887i	$0.609994\pi$
$600$		0			0
$601$		−	45.9356i		−	1.87375i	−0.349661	−	0.936876i	$-0.613703\pi$
$601$		−	45.9356i		−	1.87375i	0.349661	−	0.936876i	$-0.386297\pi$
$602$		0			0
$603$	−41.1731	−	29.9140i	−1.67670	−	1.21819i
$604$		0			0
$605$	−10.4194	+	12.8179i	−0.423609	+	0.521123i
$606$		0			0
$607$	−4.26468	−	5.86982i	−0.173098	−	0.238249i	0.713650	−	0.700503i	$-0.247041\pi$
$607$	−4.26468	−	5.86982i	−0.173098	−	0.238249i	−0.886748	+	0.462254i	$0.847041\pi$
$608$		0			0
$609$	−26.5890	−	8.63928i	−1.07744	−	0.350081i
$610$		0			0
$611$	−20.2591	−	14.7191i	−0.819597	−	0.595472i
$612$		0			0
$613$	33.8491	+	10.9982i	1.36715	+	0.444214i	0.898424	−	0.439129i	$-0.144713\pi$
$613$	33.8491	+	10.9982i	1.36715	+	0.444214i	0.468727	+	0.883343i	$0.344713\pi$
$614$		0			0
$615$	36.1344	−	8.54311i	1.45708	−	0.344492i
$616$		0			0
$617$	−17.5502	−	5.70242i	−0.706546	−	0.229571i	−0.0663657	−	0.997795i	$-0.521140\pi$
$617$	−17.5502	−	5.70242i	−0.706546	−	0.229571i	−0.640180	+	0.768225i	$0.721140\pi$
$618$		0			0
$619$	−12.7474	−	9.26150i	−0.512360	−	0.372251i	0.301358	−	0.953511i	$-0.402560\pi$
$619$	−12.7474	−	9.26150i	−0.512360	−	0.372251i	−0.813718	+	0.581260i	$0.802560\pi$
$620$		0			0
$621$	9.07172	+	2.94758i	0.364036	+	0.118282i
$622$		0			0
$623$	17.4523	+	24.0210i	0.699210	+	0.962380i
$624$		0			0
$625$	2.42765	+	24.8819i	0.0971061	+	0.995274i
$626$		0			0
$627$	−23.4206	−	17.0161i	−0.935329	−	0.679556i
$628$		0			0
$629$		−	15.3854i		−	0.613454i
$630$		0			0
$631$	4.34919	+	13.3854i	0.173139	+	0.532866i	0.999544	−	0.0302103i	$-0.00961771\pi$
$631$	4.34919	+	13.3854i	0.173139	+	0.532866i	−0.826405	+	0.563076i	$0.809618\pi$
$632$		0			0
$633$	13.8489	+	4.49978i	0.550444	+	0.178850i
$634$		0			0
$635$	−2.14714	+	1.38868i	−0.0852065	+	0.0551081i
$636$		0			0
$637$	5.50439	+	16.9408i	0.218092	+	0.671217i
$638$		0			0
$639$	−6.63426	−	9.13128i	−0.262447	−	0.361228i
$640$		0			0
$641$	17.4729	−	24.0494i	0.690139	−	0.949894i	−0.309861	−	0.950782i	$-0.600282\pi$
$641$	17.4729	−	24.0494i	0.690139	−	0.949894i	1.00000		0.000887439i	$0.000282480\pi$
$642$		0			0
$643$	1.89591	−	5.83500i	0.0747672	−	0.230110i	−0.906688	−	0.421802i	$-0.861398\pi$
$643$	1.89591	−	5.83500i	0.0747672	−	0.230110i	0.981455	+	0.191692i	$0.0613976\pi$
$644$		0			0
$645$	6.81816	+	5.54233i	0.268465	+	0.218229i
$646$		0			0
$647$			18.5029i			0.727424i	0.931511	+	0.363712i	$0.118491\pi$
$647$			18.5029i			0.727424i	−0.931511	+	0.363712i	$0.881509\pi$
$648$		0			0
$649$	−10.9929	+	3.57181i	−0.431510	+	0.140206i
$650$		0			0
$651$	−32.3047	−	23.4707i	−1.26612	−	0.919891i
$652$		0			0
$653$	18.6167			0.728526			0.364263	−	0.931296i	$-0.381321\pi$
$653$	18.6167			0.728526			0.364263	+	0.931296i	$0.381321\pi$
$654$		0			0
$655$	33.6731	−	8.95541i	1.31572	−	0.349917i
$656$		0			0
$657$		−	22.2911i		−	0.869660i
$658$		0			0
$659$			33.1407i			1.29098i	0.763769	+	0.645490i	$0.223347\pi$
$659$			33.1407i			1.29098i	−0.763769	+	0.645490i	$0.776653\pi$
$660$		0			0
$661$	6.27385	+	4.55822i	0.244024	+	0.177294i	0.703074	−	0.711116i	$-0.251810\pi$
$661$	6.27385	+	4.55822i	0.244024	+	0.177294i	−0.459050	+	0.888410i	$0.651810\pi$
$662$		0			0
$663$	−5.89676	−	18.1484i	−0.229011	−	0.704824i
$664$		0			0
$665$	6.55525	+	24.6483i	0.254202	+	0.955821i
$666$		0			0
$667$	−22.7753	+	16.5472i	−0.881861	+	0.640710i
$668$		0			0
$669$	−39.6328	−	12.8775i	−1.53229	−	0.497872i
$670$		0			0
$671$	13.5614	−	18.6657i	0.523533	−	0.720582i
$672$		0			0
$673$	−15.6779	+	11.3907i	−0.604340	+	0.439079i	−0.847417	−	0.530928i	$-0.821843\pi$
$673$	−15.6779	+	11.3907i	−0.604340	+	0.439079i	0.243077	+	0.970007i	$0.421843\pi$
$674$		0			0
$675$	−6.96510	−	6.31861i	−0.268087	−	0.243203i
$676$		0			0
$677$	−19.9637	+	6.48661i	−0.767269	+	0.249301i	−0.666395	−	0.745598i	$-0.732164\pi$
$677$	−19.9637	+	6.48661i	−0.767269	+	0.249301i	−0.100873	+	0.994899i	$0.532164\pi$
$678$		0			0
$679$	2.35544	−	7.24929i	0.0903934	−	0.278202i
$680$		0			0
$681$	10.3469	+	31.8446i	0.396495	+	1.22029i
$682$		0			0
$683$	5.02934			0.192442			0.0962211	−	0.995360i	$-0.469324\pi$
$683$	5.02934			0.192442			0.0962211	+	0.995360i	$0.469324\pi$
$684$		0			0
$685$	−16.0212	−	6.18429i	−0.612140	−	0.236290i
$686$		0			0
$687$	1.59997	+	2.20216i	0.0610425	+	0.0840178i
$688$		0			0
$689$	24.4551	−	17.7677i	0.931665	−	0.676895i
$690$		0			0
$691$	33.2696	+	10.8099i	1.26563	+	0.411230i	0.863499	−	0.504351i	$-0.168268\pi$
$691$	33.2696	+	10.8099i	1.26563	+	0.411230i	0.402135	+	0.915580i	$0.368268\pi$
$692$		0			0
$693$	8.08275	−	11.1250i	0.307038	−	0.422602i
$694$		0			0
$695$	1.01700	−	18.7368i	0.0385770	−	0.710727i
$696$		0			0
$697$	2.86322	−	8.04477i	0.108452	−	0.304717i
$698$		0			0
$699$	1.67013	−	5.14013i	0.0631701	−	0.194418i
$700$		0			0
$701$	−37.6337	−	27.3425i	−1.42141	−	1.03271i	−0.991537	−	0.129821i	$-0.958560\pi$
$701$	−37.6337	−	27.3425i	−1.42141	−	1.03271i	−0.429869	−	0.902891i	$-0.641440\pi$
$702$		0			0
$703$	−20.9383	+	64.4415i	−0.789704	+	2.43046i
$704$		0			0
$705$	−16.6003	+	20.4217i	−0.625205	+	0.769126i
$706$		0			0
$707$	−4.62646	−	6.36778i	−0.173996	−	0.239485i
$708$		0			0
$709$	−18.6809	+	25.7121i	−0.701576	+	0.965637i	0.298361	+	0.954453i	$0.403560\pi$
$709$	−18.6809	+	25.7121i	−0.701576	+	0.965637i	−0.999937	+	0.0111841i	$0.996440\pi$
$710$		0			0
$711$			27.2002i			1.02009i
$712$		0			0
$713$	−38.2406	+	12.4251i	−1.43212	+	0.465325i
$714$		0			0
$715$	−23.4162	−	1.27099i	−0.875716	−	0.0475323i
$716$		0			0
$717$	51.9751	−	16.8877i	1.94105	−	0.630684i
$718$		0			0
$719$	27.1017	−	8.80587i	1.01072	−	0.328404i	0.243580	−	0.969881i	$-0.421678\pi$
$719$	27.1017	−	8.80587i	1.01072	−	0.328404i	0.767142	+	0.641477i	$0.221678\pi$
$720$		0			0
$721$	−3.25750	−	4.48357i	−0.121316	−	0.166977i
$722$		0			0
$723$	44.3966	+	32.2560i	1.65113	+	1.19962i
$724$		0			0
$725$	27.1698	−	5.66927i	1.00906	−	0.210551i
$726$		0			0
$727$	37.4995	−	27.2450i	1.39078	−	1.01046i	0.394999	−	0.918682i	$-0.370745\pi$
$727$	37.4995	−	27.2450i	1.39078	−	1.01046i	0.995779	−	0.0917779i	$-0.0292550\pi$
$728$		0			0
$729$	−38.0952			−1.41093
$730$		0			0
$731$	1.92180	−	0.624432i	0.0710805	−	0.0230954i
$732$		0			0
$733$	16.2245	−	22.3311i	0.599264	−	0.824817i	−0.396376	−	0.918088i	$-0.629732\pi$
$733$	16.2245	−	22.3311i	0.599264	−	0.824817i	0.995641	+	0.0932714i	$0.0297324\pi$
$734$		0			0
$735$	18.0913	−	4.81140i	0.667308	−	0.177471i
$736$		0			0
$737$			25.9665i			0.956487i
$738$		0			0
$739$	−13.5824			−0.499636			−0.249818	−	0.968293i	$-0.580371\pi$
$739$	−13.5824			−0.499636			−0.249818	+	0.968293i	$0.580371\pi$
$740$		0			0
$741$			84.0394i			3.08726i
$742$		0			0
$743$	−13.5292	+	18.6213i	−0.496338	+	0.683150i	−0.981541	−	0.191251i	$-0.938746\pi$
$743$	−13.5292	+	18.6213i	−0.496338	+	0.683150i	0.485203	+	0.874401i	$0.338746\pi$
$744$		0			0
$745$	−40.5413	+	26.2204i	−1.48532	+	0.960643i
$746$		0			0
$747$		−	8.10742i		−	0.296635i
$748$		0			0
$749$	20.8169	+	28.6519i	0.760631	+	1.04692i
$750$		0			0
$751$	36.0055	+	11.6989i	1.31386	+	0.426899i	0.880382	−	0.474265i	$-0.157286\pi$
$751$	36.0055	+	11.6989i	1.31386	+	0.426899i	0.433478	+	0.901164i	$0.357286\pi$
$752$		0			0
$753$	−29.7767	−	21.6341i	−1.08512	−	0.788389i
$754$		0			0
$755$	−7.38316	−	6.00160i	−0.268701	−	0.218420i
$756$		0			0
$757$	−4.97055	−	15.2978i	−0.180658	−	0.556007i	0.819189	−	0.573524i	$-0.194424\pi$
$757$	−4.97055	−	15.2978i	−0.180658	−	0.556007i	−0.999847	+	0.0175166i	$0.994424\pi$
$758$		0			0
$759$	−7.72477	−	23.7744i	−0.280392	−	0.862956i
$760$		0			0
$761$	1.68916	−	5.19870i	0.0612320	−	0.188453i	−0.915761	−	0.401723i	$-0.868411\pi$
$761$	1.68916	−	5.19870i	0.0612320	−	0.188453i	0.976993	+	0.213270i	$0.0684115\pi$
$762$		0			0
$763$	−2.18237	+	0.709094i	−0.0790070	+	0.0256709i
$764$		0			0
$765$	−10.7355	+	2.85512i	−0.388142	+	0.103227i
$766$		0			0
$767$	27.1460	+	19.7228i	0.980187	+	0.712147i
$768$		0			0
$769$	−40.5947	+	29.4938i	−1.46388	+	1.06357i	−0.481554	+	0.876417i	$0.659927\pi$
$769$	−40.5947	+	29.4938i	−1.46388	+	1.06357i	−0.982330	+	0.187157i	$0.940073\pi$
$770$		0			0
$771$	−13.0855	+	9.50720i	−0.471264	+	0.342394i
$772$		0			0
$773$	−10.7002	+	32.9318i	−0.384859	+	1.18447i	0.551723	+	0.834027i	$0.313970\pi$
$773$	−10.7002	+	32.9318i	−0.384859	+	1.18447i	−0.936582	+	0.350447i	$0.886030\pi$
$774$		0			0
$775$	39.4089	+	4.29073i	1.41561	+	0.154128i
$776$		0			0
$777$	−55.2610	−	17.9554i	−1.98248	−	0.644145i
$778$		0			0
$779$	−22.9409	+	29.7988i	−0.821943	+	1.06765i
$780$		0			0
$781$	−1.77956	+	5.47693i	−0.0636778	+	0.195980i
$782$		0			0
$783$	−6.13674	+	8.44649i	−0.219309	+	0.301853i
$784$		0			0
$785$	0.706450	−	13.0154i	0.0252143	−	0.464538i
$786$		0			0
$787$	27.3356	+	37.6242i	0.974408	+	1.34116i	0.939788	+	0.341757i	$0.111022\pi$
$787$	27.3356	+	37.6242i	0.974408	+	1.34116i	0.0346195	+	0.999401i	$0.488978\pi$
$788$		0			0
$789$	−43.8883	+	31.8867i	−1.56246	+	1.13520i
$790$		0			0
$791$	−15.9292	+	21.9246i	−0.566375	+	0.779549i
$792$		0			0
$793$	−66.9776			−2.37844
$794$		0			0
$795$	−17.2526	−	26.6754i	−0.611886	−	0.946080i
$796$		0			0
$797$	−44.9082	−	14.5916i	−1.59073	−	0.516859i	−0.625937	−	0.779873i	$-0.715283\pi$
$797$	−44.9082	−	14.5916i	−1.59073	−	0.516859i	−0.964792	+	0.263014i	$0.915283\pi$
$798$		0			0
$799$	1.87029	+	5.75617i	0.0661662	+	0.203639i
$800$		0			0
$801$	54.1659	−	17.5996i	1.91386	−	0.621850i
$802$		0			0
$803$	−9.20126	+	6.68511i	−0.324705	+	0.235912i
$804$		0			0
$805$	−7.93092	+	20.5461i	−0.279528	+	0.724156i
$806$		0			0
$807$	−6.29190	+	19.3645i	−0.221485	+	0.681662i
$808$		0			0
$809$	−2.68928	−	3.70147i	−0.0945499	−	0.130137i	0.759121	−	0.650949i	$-0.225629\pi$
$809$	−2.68928	−	3.70147i	−0.0945499	−	0.130137i	−0.853671	+	0.520813i	$0.825629\pi$
$810$		0			0
$811$	5.89376			0.206958			0.103479	−	0.994632i	$-0.467003\pi$
$811$	5.89376			0.206958			0.103479	+	0.994632i	$0.467003\pi$
$812$		0			0
$813$	19.7940	+	60.9197i	0.694206	+	2.13655i
$814$		0			0
$815$	−6.19955	+	16.0608i	−0.217161	+	0.562585i
$816$		0			0
$817$	−8.89927			−0.311346
$818$		0			0
$819$	−39.9193			−1.39489
$820$		0			0
$821$	29.1465			1.01722			0.508610	−	0.860997i	$-0.330160\pi$
$821$	29.1465			1.01722			0.508610	+	0.860997i	$0.330160\pi$
$822$		0			0
$823$	−50.2335			−1.75103			−0.875514	−	0.483193i	$-0.839477\pi$
$823$	−50.2335			−1.75103			−0.875514	+	0.483193i	$0.839477\pi$
$824$		0			0
$825$	−2.66757	+	24.5008i	−0.0928729	+	0.853007i
$826$		0			0
$827$	4.77688	+	14.7017i	0.166108	+	0.511229i	0.999116	−	0.0420321i	$-0.0133832\pi$
$827$	4.77688	+	14.7017i	0.166108	+	0.511229i	−0.833008	+	0.553261i	$0.813383\pi$
$828$		0			0
$829$	11.6942			0.406157			0.203079	−	0.979162i	$-0.434905\pi$
$829$	11.6942			0.406157			0.203079	+	0.979162i	$0.434905\pi$
$830$		0			0
$831$	14.1540	+	19.4813i	0.490996	+	0.675798i
$832$		0			0
$833$	1.33037	−	4.09446i	0.0460946	−	0.141865i
$834$		0			0
$835$	4.45305	+	1.71890i	0.154104	+	0.0594851i
$836$		0			0
$837$	−12.0639	+	8.76497i	−0.416991	+	0.302962i
$838$		0			0
$839$	−39.6901	+	12.8961i	−1.37025	+	0.445222i	−0.899453	−	0.437017i	$-0.856035\pi$
$839$	−39.6901	+	12.8961i	−1.37025	+	0.445222i	−0.470800	+	0.882240i	$0.656035\pi$
$840$		0			0
$841$	−0.560404	−	1.72475i	−0.0193243	−	0.0594740i
$842$		0			0
$843$	−33.4448	−	10.8669i	−1.15190	−	0.374275i
$844$		0			0
$845$	21.1841	+	32.7542i	0.728754	+	1.12678i
$846$		0			0
$847$	14.3469			0.492965
$848$		0			0
$849$	−31.9402	+	43.9620i	−1.09619	+	1.50877i
$850$		0			0
$851$	−47.3348	+	34.3907i	−1.62261	+	1.17890i
$852$		0			0
$853$	20.6171	+	28.3769i	0.705914	+	0.971608i	0.999875	+	0.0157903i	$0.00502643\pi$
$853$	20.6171	+	28.3769i	0.705914	+	0.971608i	−0.293961	+	0.955817i	$0.594974\pi$
$854$		0			0
$855$	48.8512	+	2.65155i	1.67067	+	0.0906812i
$856$		0			0
$857$	11.2804	−	15.5261i	0.385330	−	0.530362i	−0.571656	−	0.820493i	$-0.693699\pi$
$857$	11.2804	−	15.5261i	0.385330	−	0.530362i	0.956987	+	0.290131i	$0.0936990\pi$
$858$		0			0
$859$	−16.3602	+	50.3514i	−0.558201	+	1.71797i	0.129134	+	0.991627i	$0.458780\pi$
$859$	−16.3602	+	50.3514i	−0.558201	+	1.71797i	−0.687336	+	0.726340i	$0.741220\pi$
$860$		0			0
$861$	−25.5536	−	19.6727i	−0.870864	−	0.670442i
$862$		0			0
$863$	−4.60463	−	1.49614i	−0.156744	−	0.0509291i	0.229594	−	0.973286i	$-0.426260\pi$
$863$	−4.60463	−	1.49614i	−0.156744	−	0.0509291i	−0.386338	+	0.922357i	$0.626260\pi$
$864$		0			0
$865$	−1.50988	+	3.91155i	−0.0513374	+	0.132997i
$866$		0			0
$867$	12.1982	−	37.5422i	0.414273	−	1.27500i
$868$		0			0
$869$	11.2276	−	8.15732i	0.380870	−	0.276718i
$870$		0			0
$871$	60.9836	−	44.3072i	2.06635	−	1.50129i
$872$		0			0
$873$	−11.8286	−	8.59398i	−0.400337	−	0.290862i
$874$		0			0
$875$	15.4393	−	15.2675i	0.521942	−	0.516134i
$876$		0			0
$877$	−3.61858	+	1.17575i	−0.122191	+	0.0397022i	−0.369474	−	0.929241i	$-0.620462\pi$
$877$	−3.61858	+	1.17575i	−0.122191	+	0.0397022i	0.247283	+	0.968943i	$0.420462\pi$
$878$		0			0
$879$	23.5118	−	72.3618i	0.793032	−	2.44070i
$880$		0			0
$881$	−12.0118	−	36.9685i	−0.404688	−	1.24550i	−0.921155	−	0.389195i	$-0.872753\pi$
$881$	−12.0118	−	36.9685i	−0.404688	−	1.24550i	0.516467	−	0.856307i	$-0.327247\pi$
$882$		0			0
$883$	−7.71918	−	23.7572i	−0.259771	−	0.799493i	−0.992852	−	0.119352i	$-0.961918\pi$
$883$	−7.71918	−	23.7572i	−0.259771	−	0.799493i	0.733081	−	0.680141i	$-0.238082\pi$
$884$		0			0
$885$	22.2435	−	27.3639i	0.747706	−	0.919826i
$886$		0			0
$887$	−5.66017	−	4.11236i	−0.190050	−	0.138079i	0.488692	−	0.872457i	$-0.337474\pi$
$887$	−5.66017	−	4.11236i	−0.190050	−	0.138079i	−0.678742	+	0.734377i	$0.737474\pi$
$888$		0			0
$889$	2.11220	+	0.686295i	0.0708408	+	0.0230176i
$890$		0			0
$891$	7.03640	+	9.68477i	0.235728	+	0.324452i
$892$		0			0
$893$		−	26.6550i		−	0.891977i
$894$		0			0
$895$	11.6752	−	7.55101i	0.390257	−	0.252402i
$896$		0			0
$897$	−42.6545	+	58.7089i	−1.42419	+	1.96023i
$898$		0			0
$899$		−	44.0103i		−	1.46782i
$900$		0			0
$901$	−7.30593			−0.243396
$902$		0			0
$903$		−	7.63145i		−	0.253959i
$904$		0			0
$905$	−13.0925	−	49.2289i	−0.435209	−	1.63642i
$906$		0			0
$907$	−3.74361	+	5.15263i	−0.124304	+	0.171090i	−0.866634	−	0.498945i	$-0.833721\pi$
$907$	−3.74361	+	5.15263i	−0.124304	+	0.171090i	0.742329	+	0.670035i	$0.233721\pi$
$908$		0			0
$909$	−14.3590	+	4.66551i	−0.476257	+	0.154745i
$910$		0			0
$911$	−50.7606			−1.68177			−0.840886	−	0.541212i	$-0.817966\pi$
$911$	−50.7606			−1.68177			−0.840886	+	0.541212i	$0.817966\pi$
$912$		0			0
$913$	−3.34655	+	2.43141i	−0.110755	+	0.0804680i
$914$		0			0
$915$	−3.81504	+	70.2868i	−0.126121	+	2.32361i
$916$		0			0
$917$	−24.4831	−	17.7880i	−0.808503	−	0.587412i
$918$		0			0
$919$	−12.6713	−	17.4405i	−0.417987	−	0.575309i	0.547157	−	0.837030i	$-0.315710\pi$
$919$	−12.6713	−	17.4405i	−0.417987	−	0.575309i	−0.965144	+	0.261721i	$0.915710\pi$
$920$		0			0
$921$	−40.9736	+	13.3131i	−1.35013	+	0.438682i
$922$		0			0
$923$	15.8994	−	5.16602i	0.523334	−	0.170042i
$924$		0			0
$925$	56.4681	−	11.7827i	1.85666	−	0.387412i
$926$		0			0
$927$	−10.1102	+	3.28499i	−0.332062	+	0.107893i
$928$		0			0
$929$			30.8851i			1.01331i	0.862150	+	0.506654i	$0.169118\pi$
$929$			30.8851i			1.01331i	−0.862150	+	0.506654i	$0.830882\pi$
$930$		0			0
$931$	−11.1445	+	15.3391i	−0.365247	+	0.502719i
$932$		0			0
$933$	0.220960	+	0.304125i	0.00723390	+	0.00995661i
$934$		0			0
$935$	4.39809	+	3.57511i	0.143833	+	0.116919i
$936$		0			0
$937$	2.93004	−	9.01773i	0.0957202	−	0.294596i	−0.891721	−	0.452586i	$-0.850501\pi$
$937$	2.93004	−	9.01773i	0.0957202	−	0.294596i	0.987441	+	0.157990i	$0.0505014\pi$
$938$		0			0
$939$	55.6135	+	40.4056i	1.81488	+	1.31859i
$940$		0			0
$941$	−1.07874	+	3.32003i	−0.0351660	+	0.108230i	−0.967099	−	0.254401i	$-0.918122\pi$
$941$	−1.07874	+	3.32003i	−0.0351660	+	0.108230i	0.931933	+	0.362631i	$0.118122\pi$
$942$		0			0
$943$	−31.1507	+	9.17337i	−1.01441	+	0.298726i
$944$		0			0
$945$	−0.442680	+	8.15576i	−0.0144004	+	0.265307i
$946$		0			0
$947$	28.4993	−	39.2260i	0.926104	−	1.27467i	−0.0352564	−	0.999378i	$-0.511225\pi$
$947$	28.4993	−	39.2260i	0.926104	−	1.27467i	0.961360	−	0.275294i	$-0.0887752\pi$
$948$		0			0
$949$	31.4006	+	10.2027i	1.01931	+	0.331193i
$950$		0			0
$951$	10.6631	−	7.74722i	0.345776	−	0.251221i
$952$		0			0
$953$	−23.6012	−	32.4842i	−0.764517	−	1.05227i	−0.996825	−	0.0796255i	$-0.974628\pi$
$953$	−23.6012	−	32.4842i	−0.764517	−	1.05227i	0.232308	−	0.972642i	$-0.425372\pi$
$954$		0			0
$955$	−7.41586	+	19.2118i	−0.239972	+	0.621679i
$956$		0			0
$957$	27.3614			0.884470
$958$		0			0
$959$	4.60918	+	14.1856i	0.148838	+	0.458077i
$960$		0			0
$961$	9.84495	−	30.2996i	0.317579	−	0.977408i
$962$		0			0
$963$	64.6084	−	20.9926i	2.08198	−	0.676476i
$964$		0			0
$965$	22.6055	+	34.9519i	0.727696	+	1.12514i
$966$		0			0
$967$	7.70962	−	5.60137i	0.247925	−	0.180128i	−0.456882	−	0.889527i	$-0.651034\pi$
$967$	7.70962	−	5.60137i	0.247925	−	0.180128i	0.704807	+	0.709400i	$0.251034\pi$
$968$		0			0
$969$	11.9389	−	16.4325i	0.383534	−	0.527889i
$970$		0			0
$971$	−31.0351	−	10.0839i	−0.995965	−	0.323609i	−0.234713	−	0.972065i	$-0.575415\pi$
$971$	−31.0351	−	10.0839i	−0.995965	−	0.323609i	−0.761252	+	0.648456i	$0.775415\pi$
$972$		0			0
$973$	−13.1849	+	9.57939i	−0.422689	+	0.307101i
$974$		0			0
$975$	62.0930	−	35.5413i	1.98857	−	1.13823i
$976$		0			0
$977$	−10.3046	−	31.7144i	−0.329674	−	1.01463i	−0.969286	−	0.245935i	$-0.920905\pi$
$977$	−10.3046	−	31.7144i	−0.329674	−	1.01463i	0.639612	−	0.768698i	$-0.279095\pi$
$978$		0			0
$979$	−23.5090	−	17.0803i	−0.751351	−	0.545888i
$980$		0			0
$981$			4.40157i			0.140531i
$982$		0			0
$983$		−	30.9494i		−	0.987131i	−0.869709	−	0.493566i	$-0.835693\pi$
$983$		−	30.9494i		−	0.987131i	0.869709	−	0.493566i	$-0.164307\pi$
$984$		0			0
$985$	−1.38294	−	5.19997i	−0.0440641	−	0.165685i
$986$		0			0
$987$	22.8577			0.727567
$988$		0			0
$989$	−6.21692	−	4.51685i	−0.197686	−	0.143628i
$990$		0			0
$991$	−5.85534	+	1.90251i	−0.186001	+	0.0604354i	−0.400536	−	0.916281i	$-0.631176\pi$
$991$	−5.85534	+	1.90251i	−0.186001	+	0.0604354i	0.214536	+	0.976716i	$0.431176\pi$
$992$		0			0
$993$		−	19.4378i		−	0.616841i
$994$		0			0
$995$	−16.8856	−	13.7259i	−0.535310	−	0.435141i
$996$		0			0
$997$	15.7711	−	48.5384i	0.499475	−	1.53723i	−0.310389	−	0.950610i	$-0.600459\pi$
$997$	15.7711	−	48.5384i	0.499475	−	1.53723i	0.809864	−	0.586617i	$-0.199541\pi$
$998$		0			0
$999$	−12.7542	+	17.5547i	−0.403526	+	0.555406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bi.a.189.3	✓	80
5.4	even	2	inner	820.2.bi.a.189.18	yes	80
41.23	even	10	inner	820.2.bi.a.269.18	yes	80
205.64	even	10	inner	820.2.bi.a.269.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bi.a.189.3	✓	80	1.1	even	1	trivial
820.2.bi.a.189.18	yes	80	5.4	even	2	inner
820.2.bi.a.269.3	yes	80	205.64	even	10	inner
820.2.bi.a.269.18	yes	80	41.23	even	10	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.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-2.59331 q^{3} +(-2.08605 - 0.805227i) q^{5} +(0.600140 + 1.84704i) q^{7} +3.72526 q^{9} +(-1.11720 - 1.53770i) q^{11} +(-1.70506 + 5.24762i) q^{13} +(5.40978 + 2.08820i) q^{15} +(1.07889 - 0.783861i) q^{17} +(-5.58571 + 1.81491i) q^{19} +(-1.55635 - 4.78995i) q^{21} +(-4.82327 - 1.56717i) q^{23} +(3.70322 + 3.35949i) q^{25} -1.88082 q^{27} +(3.26279 - 4.49085i) q^{29} +(6.41418 - 4.66017i) q^{31} +(2.89726 + 3.98773i) q^{33} +(0.235365 - 4.33627i) q^{35} +(6.78119 - 9.33351i) q^{37} +(4.42174 - 13.6087i) q^{39} +(5.28275 - 3.61837i) q^{41} +(1.44108 + 0.468236i) q^{43} +(-7.77108 - 2.99968i) q^{45} +(-1.40246 + 4.31632i) q^{47} +(2.61173 - 1.89753i) q^{49} +(-2.79790 + 2.03279i) q^{51} +(-4.43214 - 3.22014i) q^{53} +(1.09235 + 4.10732i) q^{55} +(14.4855 - 4.70662i) q^{57} +(1.87921 - 5.78361i) q^{59} +(3.75107 + 11.5446i) q^{61} +(2.23568 + 6.88071i) q^{63} +(7.78236 - 9.57385i) q^{65} +(-11.0524 - 8.03004i) q^{67} +(12.5082 + 4.06417i) q^{69} +(-1.78089 - 2.45118i) q^{71} -5.98378i q^{73} +(-9.60360 - 8.71220i) q^{75} +(2.16971 - 2.98636i) q^{77} +7.30155i q^{79} -6.29822 q^{81} -2.17634i q^{83} +(-2.88181 + 0.766421i) q^{85} +(-8.46143 + 11.6462i) q^{87} +(14.5402 - 4.72438i) q^{89} -10.7158 q^{91} +(-16.6340 + 12.0853i) q^{93} +(13.1135 + 0.711776i) q^{95} +(-3.17524 - 2.30695i) q^{97} +(-4.16188 - 5.72833i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) \) 80 * q + 68 * q^9 + 10 * q^15 - 26 * q^21 + 10 * q^25 - 20 * q^29 + 4 * q^31 + 15 * q^35 - 8 * q^39 + 4 * q^41 - 4 * q^45 + 18 * q^49 + 52 * q^51 - 36 * q^59 - 42 * q^61 - 15 * q^65 + 30 * q^69 - 20 * q^75 + 32 * q^81 + 10 * q^89 - 132 * q^91 + 50 * q^95 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more