LMFDB - Embedded newform 220.2.m.b.141.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(81,220)] 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("220.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.m (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25$ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.1
Root			$-0.762262 + 2.34600i$ of defining polynomial
Character	$\chi$	$=$	220.141
Dual form			220.2.m.b.181.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.686611 + 0.498852i) q^{3} +(0.309017 + 0.951057i) q^{5} +(0.762262 + 0.553816i) q^{7} +(-0.704470 + 2.16813i) q^{9} +(3.28679 - 0.443888i) q^{11} +(-1.40919 + 4.33705i) q^{13} +(-0.686611 - 0.498852i) q^{15} +(0.759560 + 2.33769i) q^{17} +(1.84433 - 1.33998i) q^{19} -0.799650 q^{21} +0.329578 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-1.38467 - 4.26157i) q^{27} +(1.08914 + 0.791305i) q^{29} +(1.49730 - 4.60821i) q^{31} +(-2.03531 + 1.94440i) q^{33} +(-0.291158 + 0.896093i) q^{35} +(-5.07332 - 3.68598i) q^{37} +(-1.19598 - 3.68084i) q^{39} +(8.84266 - 6.42457i) q^{41} -12.4713 q^{43} -2.27971 q^{45} +(7.81335 - 5.67673i) q^{47} +(-1.88879 - 5.81309i) q^{49} +(-1.68768 - 1.22617i) q^{51} +(-1.70869 + 5.25879i) q^{53} +(1.43784 + 2.98875i) q^{55} +(-0.597882 + 1.84009i) q^{57} +(-1.62511 - 1.18071i) q^{59} +(0.321724 + 0.990166i) q^{61} +(-1.73774 + 1.26254i) q^{63} -4.56024 q^{65} +9.08143 q^{67} +(-0.226292 + 0.164411i) q^{69} +(-2.51786 - 7.74917i) q^{71} +(1.12511 + 0.817439i) q^{73} +(0.262262 - 0.807160i) q^{75} +(2.75122 + 1.48191i) q^{77} +(-2.23774 + 6.88705i) q^{79} +(-2.45636 - 1.78465i) q^{81} +(-0.443240 - 1.36415i) q^{83} +(-1.98855 + 1.44477i) q^{85} -1.14256 q^{87} +16.5037 q^{89} +(-3.47610 + 2.52553i) q^{91} +(1.27075 + 3.91098i) q^{93} +(1.84433 + 1.33998i) q^{95} +(-1.98974 + 6.12380i) q^{97} +(-1.35303 + 7.43890i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 5 q^{3} - 2 q^{5} - q^{7} + 3 q^{9} + 5 q^{11} + 4 q^{13} + 5 q^{15} + 9 q^{17} - 7 q^{19} - 28 q^{21} - 10 q^{23} - 2 q^{25} - 10 q^{27} - q^{29} + 22 q^{31} + q^{33} + 4 q^{35} + 4 q^{37} + 27 q^{39}+ \cdots + 60 q^{99}+O(q^{100})$ 8 * q + 5 * q^3 - 2 * q^5 - q^7 + 3 * q^9 + 5 * q^11 + 4 * q^13 + 5 * q^15 + 9 * q^17 - 7 * q^19 - 28 * q^21 - 10 * q^23 - 2 * q^25 - 10 * q^27 - q^29 + 22 * q^31 + q^33 + 4 * q^35 + 4 * q^37 + 27 * q^39 + 24 * q^41 - 22 * q^43 + 8 * q^45 - 6 * q^47 - 27 * q^49 - 47 * q^51 - q^53 - 5 * q^55 - 25 * q^57 - 9 * q^59 + 22 * q^61 - 21 * q^63 - 26 * q^65 - 2 * q^67 + 11 * q^69 - 22 * q^71 + 5 * q^73 - 5 * q^75 + 16 * q^77 - 25 * q^79 - 28 * q^81 + 33 * q^83 + 4 * q^85 + 14 * q^87 + 8 * q^89 + 14 * q^91 + 31 * q^93 - 7 * q^95 + 20 * q^97 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$ .

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$	−0.686611	+	0.498852i	−0.396415	+	0.288012i	−0.768079	−	0.640355i	$-0.778787\pi$
$3$	−0.686611	+	0.498852i	−0.396415	+	0.288012i	0.371664	+	0.928367i	$0.378787\pi$
$4$		0			0
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$6$		0			0
$7$	0.762262	+	0.553816i	0.288108	+	0.209323i	0.722446	−	0.691427i	$-0.243018\pi$
$7$	0.762262	+	0.553816i	0.288108	+	0.209323i	−0.434338	+	0.900750i	$0.643018\pi$
$8$		0			0
$9$	−0.704470	+	2.16813i	−0.234823	+	0.722712i
$10$		0			0
$11$	3.28679	−	0.443888i	0.991003	−	0.133837i
$11$	3.28679	−	0.443888i	0.991003	−	0.133837i
$12$		0			0
$13$	−1.40919	+	4.33705i	−0.390840	+	1.20288i	0.541315	+	0.840820i	$0.317927\pi$
$13$	−1.40919	+	4.33705i	−0.390840	+	1.20288i	−0.932155	+	0.362061i	$0.882073\pi$
$14$		0			0
$15$	−0.686611	−	0.498852i	−0.177282	−	0.128803i
$16$		0			0
$17$	0.759560	+	2.33769i	0.184220	+	0.566972i	0.999934	−	0.0114839i	$-0.00365551\pi$
$17$	0.759560	+	2.33769i	0.184220	+	0.566972i	−0.815714	+	0.578456i	$0.803656\pi$
$18$		0			0
$19$	1.84433	−	1.33998i	0.423117	−	0.307413i	−0.355774	−	0.934572i	$-0.615783\pi$
$19$	1.84433	−	1.33998i	0.423117	−	0.307413i	0.778891	+	0.627159i	$0.215783\pi$
$20$		0			0
$21$	−0.799650			−0.174498
$22$		0			0
$23$	0.329578			0.0687217			0.0343609	−	0.999409i	$-0.489060\pi$
$23$	0.329578			0.0687217			0.0343609	+	0.999409i	$0.489060\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	−1.38467	−	4.26157i	−0.266479	−	0.820140i
$28$		0			0
$29$	1.08914	+	0.791305i	0.202248	+	0.146942i	0.684299	−	0.729201i	$-0.260108\pi$
$29$	1.08914	+	0.791305i	0.202248	+	0.146942i	−0.482051	+	0.876143i	$0.660108\pi$
$30$		0			0
$31$	1.49730	−	4.60821i	0.268923	−	0.827659i	−0.721841	−	0.692059i	$-0.756704\pi$
$31$	1.49730	−	4.60821i	0.268923	−	0.827659i	0.990764	−	0.135600i	$-0.0432962\pi$
$32$		0			0
$33$	−2.03531	+	1.94440i	−0.354302	+	0.338476i
$34$		0			0
$35$	−0.291158	+	0.896093i	−0.0492147	+	0.151467i
$36$		0			0
$37$	−5.07332	−	3.68598i	−0.834049	−	0.605972i	0.0866532	−	0.996239i	$-0.472383\pi$
$37$	−5.07332	−	3.68598i	−0.834049	−	0.605972i	−0.920702	+	0.390267i	$0.872383\pi$
$38$		0			0
$39$	−1.19598	−	3.68084i	−0.191510	−	0.589407i
$40$		0			0
$41$	8.84266	−	6.42457i	1.38099	−	1.00335i	0.384204	−	0.923248i	$-0.374476\pi$
$41$	8.84266	−	6.42457i	1.38099	−	1.00335i	0.996787	−	0.0801003i	$-0.0255241\pi$
$42$		0			0
$43$	−12.4713			−1.90186			−0.950929	−	0.309409i	$-0.899869\pi$
$43$	−12.4713			−1.90186			−0.950929	+	0.309409i	$0.899869\pi$
$44$		0			0
$45$	−2.27971			−0.339839
$46$		0			0
$47$	7.81335	−	5.67673i	1.13969	−	0.828036i	0.152618	−	0.988285i	$-0.451230\pi$
$47$	7.81335	−	5.67673i	1.13969	−	0.828036i	0.987077	+	0.160249i	$0.0512297\pi$
$48$		0			0
$49$	−1.88879	−	5.81309i	−0.269827	−	0.830441i
$50$		0			0
$51$	−1.68768	−	1.22617i	−0.236323	−	0.171698i
$52$		0			0
$53$	−1.70869	+	5.25879i	−0.234706	+	0.722351i	0.762454	+	0.647042i	$0.223994\pi$
$53$	−1.70869	+	5.25879i	−0.234706	+	0.722351i	−0.997160	+	0.0753087i	$0.976006\pi$
$54$		0			0
$55$	1.43784	+	2.98875i	0.193878	+	0.403003i
$56$		0			0
$57$	−0.597882	+	1.84009i	−0.0791914	+	0.243726i
$58$		0			0
$59$	−1.62511	−	1.18071i	−0.211571	−	0.153715i	0.476953	−	0.878929i	$-0.341741\pi$
$59$	−1.62511	−	1.18071i	−0.211571	−	0.153715i	−0.688524	+	0.725213i	$0.741741\pi$
$60$		0			0
$61$	0.321724	+	0.990166i	0.0411926	+	0.126778i	0.969538	−	0.244941i	$-0.0787686\pi$
$61$	0.321724	+	0.990166i	0.0411926	+	0.126778i	−0.928345	+	0.371719i	$0.878769\pi$
$62$		0			0
$63$	−1.73774	+	1.26254i	−0.218934	+	0.159065i
$64$		0			0
$65$	−4.56024			−0.565628
$66$		0			0
$67$	9.08143			1.10947			0.554736	−	0.832026i	$-0.312819\pi$
$67$	9.08143			1.10947			0.554736	+	0.832026i	$0.312819\pi$
$68$		0			0
$69$	−0.226292	+	0.164411i	−0.0272423	+	0.0197927i
$70$		0			0
$71$	−2.51786	−	7.74917i	−0.298815	−	0.919658i	−0.981913	−	0.189331i	$-0.939368\pi$
$71$	−2.51786	−	7.74917i	−0.298815	−	0.919658i	0.683098	−	0.730326i	$-0.260632\pi$
$72$		0			0
$73$	1.12511	+	0.817439i	0.131684	+	0.0956740i	0.651677	−	0.758496i	$-0.274066\pi$
$73$	1.12511	+	0.817439i	0.131684	+	0.0956740i	−0.519993	+	0.854170i	$0.674066\pi$
$74$		0			0
$75$	0.262262	−	0.807160i	0.0302834	−	0.0932028i
$76$		0			0
$77$	2.75122	+	1.48191i	0.313531	+	0.168880i
$78$		0			0
$79$	−2.23774	+	6.88705i	−0.251765	+	0.774854i	0.742685	+	0.669641i	$0.233552\pi$
$79$	−2.23774	+	6.88705i	−0.251765	+	0.774854i	−0.994450	+	0.105212i	$0.966448\pi$
$80$		0			0
$81$	−2.45636	−	1.78465i	−0.272928	−	0.198294i
$82$		0			0
$83$	−0.443240	−	1.36415i	−0.0486519	−	0.149735i	0.923779	−	0.382926i	$-0.125083\pi$
$83$	−0.443240	−	1.36415i	−0.0486519	−	0.149735i	−0.972431	+	0.233190i	$0.925083\pi$
$84$		0			0
$85$	−1.98855	+	1.44477i	−0.215689	+	0.156707i
$86$		0			0
$87$	−1.14256			−0.122495
$88$		0			0
$89$	16.5037			1.74939			0.874694	−	0.484675i	$-0.161062\pi$
$89$	16.5037			1.74939			0.874694	+	0.484675i	$0.161062\pi$
$90$		0			0
$91$	−3.47610	+	2.52553i	−0.364394	+	0.264748i
$92$		0			0
$93$	1.27075	+	3.91098i	0.131771	+	0.405549i
$94$		0			0
$95$	1.84433	+	1.33998i	0.189224	+	0.137479i
$96$		0			0
$97$	−1.98974	+	6.12380i	−0.202028	+	0.621777i	0.797795	+	0.602929i	$0.206000\pi$
$97$	−1.98974	+	6.12380i	−0.202028	+	0.621777i	−0.999822	+	0.0188481i	$0.994000\pi$
$98$		0			0
$99$	−1.35303	+	7.43890i	−0.135985	+	0.747638i
$100$		0			0
$101$	−4.05983	+	12.4949i	−0.403968	+	1.24329i	0.517785	+	0.855511i	$0.326757\pi$
$101$	−4.05983	+	12.4949i	−0.403968	+	1.24329i	−0.921753	+	0.387776i	$0.873243\pi$
$102$		0			0
$103$	0.724251	+	0.526199i	0.0713626	+	0.0518480i	0.622895	−	0.782306i	$-0.285957\pi$
$103$	0.724251	+	0.526199i	0.0713626	+	0.0518480i	−0.551532	+	0.834154i	$0.685957\pi$
$104$		0			0
$105$	−0.247105	−	0.760512i	−0.0241150	−	0.0742184i
$106$		0			0
$107$	3.27371	−	2.37849i	0.316481	−	0.229937i	−0.418191	−	0.908359i	$-0.637336\pi$
$107$	3.27371	−	2.37849i	0.316481	−	0.229937i	0.734673	+	0.678422i	$0.237336\pi$
$108$		0			0
$109$	−5.97843			−0.572630			−0.286315	−	0.958136i	$-0.592430\pi$
$109$	−5.97843			−0.572630			−0.286315	+	0.958136i	$0.592430\pi$
$110$		0			0
$111$	5.32216			0.505157
$112$		0			0
$113$	10.1658	−	7.38590i	0.956320	−	0.694807i	0.00402683	−	0.999992i	$-0.498718\pi$
$113$	10.1658	−	7.38590i	0.956320	−	0.694807i	0.952293	+	0.305185i	$0.0987182\pi$
$114$		0			0
$115$	0.101845	+	0.313447i	0.00949711	+	0.0292291i
$116$		0			0
$117$	−8.41057	−	6.11064i	−0.777558	−	0.564929i
$118$		0			0
$119$	−0.715663	+	2.20259i	−0.0656047	+	0.201911i
$120$		0			0
$121$	10.6059	−	2.91793i	0.964175	−	0.265267i
$122$		0			0
$123$	−2.86656	+	8.82235i	−0.258469	+	0.795485i
$124$		0			0
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$		0			0
$127$	3.63548	+	11.1889i	0.322597	+	0.992852i	0.972514	+	0.232846i	$0.0748038\pi$
$127$	3.63548	+	11.1889i	0.322597	+	0.992852i	−0.649917	+	0.760006i	$0.725196\pi$
$128$		0			0
$129$	8.56294	−	6.22134i	0.753925	−	0.547759i
$130$		0			0
$131$	7.89441			0.689737			0.344869	−	0.938651i	$-0.387923\pi$
$131$	7.89441			0.689737			0.344869	+	0.938651i	$0.387923\pi$
$132$		0			0
$133$	2.14796			0.186252
$134$		0			0
$135$	3.62511	−	2.63380i	0.312000	−	0.226681i
$136$		0			0
$137$	−2.57961	−	7.93924i	−0.220391	−	0.678295i	−0.998727	−	0.0504461i	$-0.983936\pi$
$137$	−2.57961	−	7.93924i	−0.220391	−	0.678295i	0.778335	−	0.627849i	$-0.216064\pi$
$138$		0			0
$139$	−7.40686	−	5.38140i	−0.628242	−	0.456444i	0.227549	−	0.973767i	$-0.426929\pi$
$139$	−7.40686	−	5.38140i	−0.628242	−	0.456444i	−0.855791	+	0.517322i	$0.826929\pi$
$140$		0			0
$141$	−2.53288	+	7.79541i	−0.213307	+	0.656492i
$142$		0			0
$143$	−2.70655	+	14.8805i	−0.226333	+	1.24437i
$144$		0			0
$145$	−0.416014	+	1.28036i	−0.0345481	+	0.106328i
$146$		0			0
$147$	4.19673	+	3.04911i	0.346141	+	0.251486i
$148$		0			0
$149$	3.92394	+	12.0766i	0.321462	+	0.989357i	0.973013	+	0.230752i	$0.0741187\pi$
$149$	3.92394	+	12.0766i	0.321462	+	0.989357i	−0.651551	+	0.758605i	$0.725881\pi$
$150$		0			0
$151$	−12.1177	+	8.80406i	−0.986128	+	0.716464i	−0.959070	−	0.283170i	$-0.908614\pi$
$151$	−12.1177	+	8.80406i	−0.986128	+	0.716464i	−0.0270582	+	0.999634i	$0.508614\pi$
$152$		0			0
$153$	−5.60350			−0.453016
$154$		0			0
$155$	4.84536			0.389189
$156$		0			0
$157$	−11.8231	+	8.59000i	−0.943588	+	0.685557i	−0.949282	−	0.314427i	$-0.898188\pi$
$157$	−11.8231	+	8.59000i	−0.943588	+	0.685557i	0.00569346	+	0.999984i	$0.498188\pi$
$158$		0			0
$159$	−1.45016	−	4.46313i	−0.115005	−	0.353949i
$160$		0			0
$161$	0.251225	+	0.182525i	0.0197993	+	0.0143850i
$162$		0			0
$163$	6.21384	−	19.1242i	0.486705	−	1.49792i	−0.342791	−	0.939412i	$-0.611372\pi$
$163$	6.21384	−	19.1242i	0.486705	−	1.49792i	0.829496	−	0.558513i	$-0.188628\pi$
$164$		0			0
$165$	−2.47818	−	1.33484i	−0.192926	−	0.103917i
$166$		0			0
$167$	1.06357	−	3.27332i	0.0823013	−	0.253297i	−0.901435	−	0.432913i	$-0.857486\pi$
$167$	1.06357	−	3.27332i	0.0823013	−	0.253297i	0.983737	+	0.179616i	$0.0574856\pi$
$168$		0			0
$169$	−6.30694	−	4.58226i	−0.485149	−	0.352481i
$170$		0			0
$171$	1.60599	+	4.94272i	0.122813	+	0.377980i
$172$		0			0
$173$	12.3730	−	8.98951i	0.940701	−	0.683459i	−0.00788813	−	0.999969i	$-0.502511\pi$
$173$	12.3730	−	8.98951i	0.940701	−	0.683459i	0.948589	+	0.316509i	$0.102511\pi$
$174$		0			0
$175$	−0.942208			−0.0712242
$176$		0			0
$177$	1.70482			0.128142
$178$		0			0
$179$	−4.04508	+	2.93893i	−0.302344	+	0.219666i	−0.728604	−	0.684935i	$-0.759831\pi$
$179$	−4.04508	+	2.93893i	−0.302344	+	0.219666i	0.426261	+	0.904600i	$0.359831\pi$
$180$		0			0
$181$	−7.92291	−	24.3842i	−0.588905	−	1.81246i	−0.582988	−	0.812481i	$-0.698116\pi$
$181$	−7.92291	−	24.3842i	−0.588905	−	1.81246i	−0.00591755	−	0.999982i	$-0.501884\pi$
$182$		0			0
$183$	−0.714846	−	0.519366i	−0.0528429	−	0.0383926i
$184$		0			0
$185$	1.93784	−	5.96404i	0.142473	−	0.438485i
$186$		0			0
$187$	3.53418	+	7.34631i	0.258445	+	0.537216i
$188$		0			0
$189$	1.30464	−	4.01528i	0.0948990	−	0.292069i
$190$		0			0
$191$	−3.63548	−	2.64133i	−0.263054	−	0.191120i	0.448438	−	0.893814i	$-0.351980\pi$
$191$	−3.63548	−	2.64133i	−0.263054	−	0.191120i	−0.711493	+	0.702694i	$0.751980\pi$
$192$		0			0
$193$	−7.47562	−	23.0076i	−0.538107	−	1.65612i	−0.736839	−	0.676068i	$-0.763682\pi$
$193$	−7.47562	−	23.0076i	−0.538107	−	1.65612i	0.198732	−	0.980054i	$-0.436318\pi$
$194$		0			0
$195$	3.13111	−	2.27489i	0.224224	−	0.162908i
$196$		0			0
$197$	−11.5021			−0.819493			−0.409747	−	0.912199i	$-0.634383\pi$
$197$	−11.5021			−0.819493			−0.409747	+	0.912199i	$0.634383\pi$
$198$		0			0
$199$	−11.1210			−0.788346			−0.394173	−	0.919036i	$-0.628969\pi$
$199$	−11.1210			−0.788346			−0.394173	+	0.919036i	$0.628969\pi$
$200$		0			0
$201$	−6.23541	+	4.53029i	−0.439812	+	0.319542i
$202$		0			0
$203$	0.391971	+	1.20636i	0.0275110	+	0.0846701i
$204$		0			0
$205$	8.84266	+	6.42457i	0.617598	+	0.448711i
$206$		0			0
$207$	−0.232178	+	0.714569i	−0.0161375	+	0.0496660i
$208$		0			0
$209$	5.46710	−	5.22291i	0.378167	−	0.361276i
$210$		0			0
$211$	−5.65011	+	17.3893i	−0.388970	+	1.19713i	0.544589	+	0.838703i	$0.316686\pi$
$211$	−5.65011	+	17.3893i	−0.388970	+	1.19713i	−0.933559	+	0.358423i	$0.883314\pi$
$212$		0			0
$213$	5.59448	+	4.06463i	0.383327	+	0.278504i
$214$		0			0
$215$	−3.85385	−	11.8609i	−0.262830	−	0.808909i
$216$		0			0
$217$	3.69343	−	2.68344i	0.250727	−	0.182163i
$218$		0			0
$219$	−1.18029			−0.0797568
$220$		0			0
$221$	−11.2090			−0.754000
$222$		0			0
$223$	20.8931	−	15.1797i	1.39910	−	1.01651i	0.404308	−	0.914623i	$-0.367512\pi$
$223$	20.8931	−	15.1797i	1.39910	−	1.01651i	0.994796	−	0.101886i	$-0.0324877\pi$
$224$		0			0
$225$	−0.704470	−	2.16813i	−0.0469647	−	0.144542i
$226$		0			0
$227$	−18.7633	−	13.6323i	−1.24536	−	0.904808i	−0.247418	−	0.968909i	$-0.579582\pi$
$227$	−18.7633	−	13.6323i	−1.24536	−	0.904808i	−0.997943	+	0.0641012i	$0.979582\pi$
$228$		0			0
$229$	3.08618	−	9.49829i	0.203941	−	0.627665i	−0.795815	−	0.605540i	$-0.792957\pi$
$229$	3.08618	−	9.49829i	0.203941	−	0.627665i	0.999755	−	0.0221245i	$-0.00704303\pi$
$230$		0			0
$231$	−2.62828	+	0.354955i	−0.172928	+	0.0233543i
$232$		0			0
$233$	7.06302	−	21.7377i	0.462714	−	1.42409i	−0.399122	−	0.916898i	$-0.630685\pi$
$233$	7.06302	−	21.7377i	0.462714	−	1.42409i	0.861835	−	0.507188i	$-0.169315\pi$
$234$		0			0
$235$	7.81335	+	5.67673i	0.509687	+	0.370309i
$236$		0			0
$237$	−1.89916	−	5.84502i	−0.123364	−	0.379675i
$238$		0			0
$239$	−15.6493	+	11.3699i	−1.01227	+	0.735458i	−0.964684	−	0.263409i	$-0.915153\pi$
$239$	−15.6493	+	11.3699i	−1.01227	+	0.735458i	−0.0475874	+	0.998867i	$0.515153\pi$
$240$		0			0
$241$	9.52407			0.613499			0.306750	−	0.951790i	$-0.400759\pi$
$241$	9.52407			0.613499			0.306750	+	0.951790i	$0.400759\pi$
$242$		0			0
$243$	16.0195			1.02765
$244$		0			0
$245$	4.94491	−	3.59269i	0.315919	−	0.229528i
$246$		0			0
$247$	3.21255	+	9.88722i	0.204410	+	0.629109i
$248$		0			0
$249$	0.984843	+	0.715531i	0.0624119	+	0.0453449i
$250$		0			0
$251$	−1.50914	+	4.64465i	−0.0952560	+	0.293168i	−0.987320	−	0.158741i	$-0.949257\pi$
$251$	−1.50914	+	4.64465i	−0.0952560	+	0.293168i	0.892064	+	0.451908i	$0.149257\pi$
$252$		0			0
$253$	1.08325	−	0.146296i	0.0681035	−	0.00919754i
$254$		0			0
$255$	0.644637	−	1.98399i	0.0403687	−	0.124242i
$256$		0			0
$257$	−10.3965	−	7.55349i	−0.648515	−	0.471174i	0.214250	−	0.976779i	$-0.431269\pi$
$257$	−10.3965	−	7.55349i	−0.648515	−	0.471174i	−0.862765	+	0.505605i	$0.831269\pi$
$258$		0			0
$259$	−1.82584	−	5.61937i	−0.113452	−	0.349171i
$260$		0			0
$261$	−2.48292	+	1.80395i	−0.153689	+	0.111662i
$262$		0			0
$263$	−20.6566			−1.27374			−0.636869	−	0.770972i	$-0.719771\pi$
$263$	−20.6566			−1.27374			−0.636869	+	0.770972i	$0.719771\pi$
$264$		0			0
$265$	−5.52942			−0.339670
$266$		0			0
$267$	−11.3316	+	8.23290i	−0.693484	+	0.503845i
$268$		0			0
$269$	5.49936	+	16.9253i	0.335302	+	1.03195i	0.966573	+	0.256391i	$0.0825335\pi$
$269$	5.49936	+	16.9253i	0.335302	+	1.03195i	−0.631271	+	0.775562i	$0.717466\pi$
$270$		0			0
$271$	4.25453	+	3.09109i	0.258444	+	0.187771i	0.709461	−	0.704745i	$-0.248939\pi$
$271$	4.25453	+	3.09109i	0.258444	+	0.187771i	−0.451017	+	0.892515i	$0.648939\pi$
$272$		0			0
$273$	1.12686	−	3.46812i	0.0682007	−	0.209900i
$274$		0			0
$275$	−2.39815	+	2.29104i	−0.144614	+	0.138155i
$276$		0			0
$277$	−6.66619	+	20.5164i	−0.400533	+	1.23271i	0.524036	+	0.851696i	$0.324426\pi$
$277$	−6.66619	+	20.5164i	−0.400533	+	1.23271i	−0.924568	+	0.381016i	$0.875574\pi$
$278$		0			0
$279$	8.93642	+	6.49269i	0.535009	+	0.388707i
$280$		0			0
$281$	7.40576	+	22.7926i	0.441790	+	1.35969i	0.885966	+	0.463751i	$0.153497\pi$
$281$	7.40576	+	22.7926i	0.441790	+	1.35969i	−0.444175	+	0.895940i	$0.646503\pi$
$282$		0			0
$283$	−7.10455	+	5.16176i	−0.422321	+	0.306835i	−0.778571	−	0.627556i	$-0.784055\pi$
$283$	−7.10455	+	5.16176i	−0.422321	+	0.306835i	0.356250	+	0.934391i	$0.384055\pi$
$284$		0			0
$285$	−1.93479			−0.114607
$286$		0			0
$287$	10.2984			0.607898
$288$		0			0
$289$	8.86545	−	6.44113i	0.521497	−	0.378890i
$290$		0			0
$291$	−1.68869	−	5.19725i	−0.0989927	−	0.304668i
$292$		0			0
$293$	23.1853	+	16.8451i	1.35450	+	0.984100i	0.998774	+	0.0495096i	$0.0157658\pi$
$293$	23.1853	+	16.8451i	1.35450	+	0.984100i	0.355724	+	0.934591i	$0.384234\pi$
$294$		0			0
$295$	0.620736	−	1.91043i	0.0361407	−	0.111229i
$296$		0			0
$297$	−6.44277	−	13.3922i	−0.373847	−	0.777096i
$298$		0			0
$299$	−0.464439	+	1.42939i	−0.0268592	+	0.0826640i
$300$		0			0
$301$	−9.50641	−	6.90681i	−0.547941	−	0.398102i
$302$		0			0
$303$	−3.44557	−	10.6044i	−0.197943	−	0.609206i
$304$		0			0
$305$	−0.842285	+	0.611956i	−0.0482291	+	0.0350405i
$306$		0			0
$307$	34.3848			1.96244			0.981221	−	0.192885i	$-0.0617846\pi$
$307$	34.3848			1.96244			0.981221	+	0.192885i	$0.0617846\pi$
$308$		0			0
$309$	−0.759774			−0.0432221
$310$		0			0
$311$	−22.6729	+	16.4728i	−1.28566	+	0.934086i	−0.999708	−	0.0241576i	$-0.992310\pi$
$311$	−22.6729	+	16.4728i	−1.28566	+	0.934086i	−0.285952	+	0.958244i	$0.592310\pi$
$312$		0			0
$313$	7.87062	+	24.2233i	0.444874	+	1.36918i	0.882622	+	0.470083i	$0.155776\pi$
$313$	7.87062	+	24.2233i	0.444874	+	1.36918i	−0.437749	+	0.899097i	$0.644224\pi$
$314$		0			0
$315$	−1.73774	−	1.26254i	−0.0979104	−	0.0711361i
$316$		0			0
$317$	−4.65875	+	14.3381i	−0.261661	+	0.805311i	0.730782	+	0.682610i	$0.239155\pi$
$317$	−4.65875	+	14.3381i	−0.261661	+	0.805311i	−0.992444	+	0.122700i	$0.960845\pi$
$318$		0			0
$319$	3.93101	+	2.11739i	0.220095	+	0.118551i
$320$		0			0
$321$	−1.06125	+	3.26619i	−0.0592332	+	0.182301i
$322$		0			0
$323$	4.53333	+	3.29366i	0.252241	+	0.183264i
$324$		0			0
$325$	−1.40919	−	4.33705i	−0.0781679	−	0.240576i
$326$		0			0
$327$	4.10486	−	2.98235i	0.226999	−	0.164924i
$328$		0			0
$329$	9.09968			0.501682
$330$		0			0
$331$	−12.8112			−0.704167			−0.352084	−	0.935969i	$-0.614527\pi$
$331$	−12.8112			−0.704167			−0.352084	+	0.935969i	$0.614527\pi$
$332$		0			0
$333$	11.5657	−	8.40298i	0.633797	−	0.460480i
$334$		0			0
$335$	2.80631	+	8.63695i	0.153325	+	0.471887i
$336$		0			0
$337$	16.6043	+	12.0637i	0.904495	+	0.657154i	0.939617	−	0.342229i	$-0.111182\pi$
$337$	16.6043	+	12.0637i	0.904495	+	0.657154i	−0.0351217	+	0.999383i	$0.511182\pi$
$338$		0			0
$339$	−3.29549	+	10.1425i	−0.178987	+	0.550864i
$340$		0			0
$341$	2.87577	−	15.8108i	0.155732	−	0.856205i
$342$		0			0
$343$	3.81774	−	11.7498i	0.206138	−	0.634429i
$344$		0			0
$345$	−0.226292	−	0.164411i	−0.0121831	−	0.00885157i
$346$		0			0
$347$	2.59715	+	7.99320i	0.139422	+	0.429097i	0.996252	−	0.0865026i	$-0.0275691\pi$
$347$	2.59715	+	7.99320i	0.139422	+	0.429097i	−0.856829	+	0.515600i	$0.827569\pi$
$348$		0			0
$349$	2.20976	−	1.60548i	0.118286	−	0.0859395i	−0.527070	−	0.849822i	$-0.676709\pi$
$349$	2.20976	−	1.60548i	0.118286	−	0.0859395i	0.645355	+	0.763883i	$0.276709\pi$
$350$		0			0
$351$	20.4339			1.09068
$352$		0			0
$353$	−14.0021			−0.745255			−0.372627	−	0.927981i	$-0.621543\pi$
$353$	−14.0021			−0.745255			−0.372627	+	0.927981i	$0.621543\pi$
$354$		0			0
$355$	6.59184	−	4.78925i	0.349859	−	0.254187i
$356$		0			0
$357$	−0.607382	−	1.86933i	−0.0321461	−	0.0989354i
$358$		0			0
$359$	−8.71166	−	6.32939i	−0.459784	−	0.334053i	0.333663	−	0.942693i	$-0.391715\pi$
$359$	−8.71166	−	6.32939i	−0.459784	−	0.334053i	−0.793447	+	0.608640i	$0.791715\pi$
$360$		0			0
$361$	−4.26533	+	13.1274i	−0.224491	+	0.690913i
$362$		0			0
$363$	−5.82653	+	7.29427i	−0.305813	+	0.382850i
$364$		0			0
$365$	−0.429753	+	1.32264i	−0.0224943	+	0.0692303i
$366$		0			0
$367$	18.9540	+	13.7709i	0.989393	+	0.718836i	0.959788	−	0.280725i	$-0.0905750\pi$
$367$	18.9540	+	13.7709i	0.989393	+	0.718836i	0.0296051	+	0.999562i	$0.490575\pi$
$368$		0			0
$369$	7.69994	+	23.6980i	0.400843	+	1.23367i
$370$		0			0
$371$	−4.21487	+	3.06228i	−0.218825	+	0.158986i
$372$		0			0
$373$	−14.7156			−0.761946			−0.380973	−	0.924586i	$-0.624411\pi$
$373$	−14.7156			−0.761946			−0.380973	+	0.924586i	$0.624411\pi$
$374$		0			0
$375$	0.848698			0.0438266
$376$		0			0
$377$	−4.96673	+	3.60854i	−0.255800	+	0.185849i
$378$		0			0
$379$	−6.97516	−	21.4673i	−0.358290	−	1.10270i	−0.954077	−	0.299561i	$-0.903160\pi$
$379$	−6.97516	−	21.4673i	−0.358290	−	1.10270i	0.595787	−	0.803142i	$-0.296840\pi$
$380$		0			0
$381$	−8.07775	−	5.86883i	−0.413836	−	0.300669i
$382$		0			0
$383$	5.77885	−	17.7855i	0.295285	−	0.908794i	−0.687840	−	0.725862i	$-0.741441\pi$
$383$	5.77885	−	17.7855i	0.295285	−	0.908794i	0.983126	−	0.182932i	$-0.0585589\pi$
$384$		0			0
$385$	−0.559210	+	3.07451i	−0.0285000	+	0.156691i
$386$		0			0
$387$	8.78567	−	27.0395i	0.446601	−	1.37450i
$388$		0			0
$389$	−6.67054	−	4.84643i	−0.338210	−	0.245724i	0.405696	−	0.914008i	$-0.367029\pi$
$389$	−6.67054	−	4.84643i	−0.338210	−	0.245724i	−0.743906	+	0.668284i	$0.767029\pi$
$390$		0			0
$391$	0.250334	+	0.770449i	0.0126599	+	0.0389633i
$392$		0			0
$393$	−5.42039	+	3.93814i	−0.273422	+	0.198653i
$394$		0			0
$395$	−7.24147			−0.364358
$396$		0			0
$397$	−22.4624			−1.12736			−0.563678	−	0.825994i	$-0.690614\pi$
$397$	−22.4624			−1.12736			−0.563678	+	0.825994i	$0.690614\pi$
$398$		0			0
$399$	−1.47481	+	1.07152i	−0.0738331	+	0.0536429i
$400$		0			0
$401$	2.59699	+	7.99272i	0.129688	+	0.399137i	0.994726	−	0.102568i	$-0.0327061\pi$
$401$	2.59699	+	7.99272i	0.129688	+	0.399137i	−0.865038	+	0.501706i	$0.832706\pi$
$402$		0			0
$403$	17.8760	+	12.9877i	0.890469	+	0.646964i
$404$		0			0
$405$	0.938244	−	2.88762i	0.0466217	−	0.143487i
$406$		0			0
$407$	−18.3111	−	9.86305i	−0.907647	−	0.488893i
$408$		0			0
$409$	6.53339	−	20.1077i	0.323055	−	0.994262i	−0.649256	−	0.760570i	$-0.724919\pi$
$409$	6.53339	−	20.1077i	0.323055	−	0.994262i	0.972311	−	0.233691i	$-0.0750805\pi$
$410$		0			0
$411$	5.73170	+	4.16432i	0.282724	+	0.205411i
$412$		0			0
$413$	−0.584862	−	1.80002i	−0.0287792	−	0.0885732i
$414$		0			0
$415$	1.16042	−	0.843092i	0.0569626	−	0.0413858i
$416$		0			0
$417$	7.77015			0.380506
$418$		0			0
$419$	−9.73051			−0.475367			−0.237683	−	0.971343i	$-0.576388\pi$
$419$	−9.73051			−0.475367			−0.237683	+	0.971343i	$0.576388\pi$
$420$		0			0
$421$	−24.4847	+	17.7892i	−1.19331	+	0.866993i	−0.993610	−	0.112864i	$-0.963998\pi$
$421$	−24.4847	+	17.7892i	−1.19331	+	0.866993i	−0.199702	+	0.979857i	$0.563998\pi$
$422$		0			0
$423$	6.80365	+	20.9395i	0.330805	+	1.01811i
$424$		0			0
$425$	−1.98855	−	1.44477i	−0.0964590	−	0.0700816i
$426$		0			0
$427$	−0.303131	+	0.932942i	−0.0146695	+	0.0451482i
$428$		0			0
$429$	−5.56481	−	11.5673i	−0.268671	−	0.558473i
$430$		0			0
$431$	10.5456	−	32.4561i	0.507964	−	1.56335i	−0.287765	−	0.957701i	$-0.592912\pi$
$431$	10.5456	−	32.4561i	0.507964	−	1.56335i	0.795729	−	0.605652i	$-0.207088\pi$
$432$		0			0
$433$	−6.15731	−	4.47354i	−0.295901	−	0.214985i	0.429922	−	0.902866i	$-0.358541\pi$
$433$	−6.15731	−	4.47354i	−0.295901	−	0.214985i	−0.725823	+	0.687881i	$0.758541\pi$
$434$		0			0
$435$	−0.353070	−	1.08664i	−0.0169284	−	0.0521003i
$436$		0			0
$437$	0.607849	−	0.441628i	0.0290774	−	0.0211259i
$438$		0			0
$439$	11.9039			0.568142			0.284071	−	0.958803i	$-0.408315\pi$
$439$	11.9039			0.568142			0.284071	+	0.958803i	$0.408315\pi$
$440$		0			0
$441$	13.9342			0.663531
$442$		0			0
$443$	0.469025	−	0.340767i	0.0222841	−	0.0161903i	−0.576587	−	0.817035i	$-0.695616\pi$
$443$	0.469025	−	0.340767i	0.0222841	−	0.0161903i	0.598872	+	0.800845i	$0.295616\pi$
$444$		0			0
$445$	5.09992	+	15.6959i	0.241760	+	0.744059i
$446$		0			0
$447$	−8.71868	−	6.33449i	−0.412379	−	0.299611i
$448$		0			0
$449$	−10.4366	+	32.1207i	−0.492536	+	1.51587i	0.328226	+	0.944599i	$0.393549\pi$
$449$	−10.4366	+	32.1207i	−0.492536	+	1.51587i	−0.820762	+	0.571270i	$0.806451\pi$
$450$		0			0
$451$	26.2121	−	25.0413i	1.23428	−	1.17915i
$452$		0			0
$453$	3.92825	−	12.0899i	0.184565	−	0.568034i
$454$		0			0
$455$	−3.47610	−	2.52553i	−0.162962	−	0.118399i
$456$		0			0
$457$	3.02760	+	9.31798i	0.141625	+	0.435877i	0.996562	−	0.0828556i	$-0.0264040\pi$
$457$	3.02760	+	9.31798i	0.141625	+	0.435877i	−0.854937	+	0.518733i	$0.826404\pi$
$458$		0			0
$459$	8.91047	−	6.47384i	0.415905	−	0.302173i
$460$		0			0
$461$	20.7030			0.964235			0.482117	−	0.876107i	$-0.339868\pi$
$461$	20.7030			0.964235			0.482117	+	0.876107i	$0.339868\pi$
$462$		0			0
$463$	−29.9244			−1.39071			−0.695353	−	0.718669i	$-0.744752\pi$
$463$	−29.9244			−1.39071			−0.695353	+	0.718669i	$0.744752\pi$
$464$		0			0
$465$	−3.32688	+	2.41712i	−0.154280	+	0.112091i
$466$		0			0
$467$	−9.12293	−	28.0775i	−0.422159	−	1.29927i	−0.905689	−	0.423944i	$-0.860645\pi$
$467$	−9.12293	−	28.0775i	−0.422159	−	1.29927i	0.483530	−	0.875328i	$-0.339355\pi$
$468$		0			0
$469$	6.92243	+	5.02944i	0.319648	+	0.232238i
$470$		0			0
$471$	3.83275	−	11.7960i	0.176604	−	0.543530i
$472$		0			0
$473$	−40.9906	+	5.53587i	−1.88475	+	0.254540i
$474$		0			0
$475$	−0.704470	+	2.16813i	−0.0323233	+	0.0994809i
$476$		0			0
$477$	−10.1981	−	7.40932i	−0.466937	−	0.339250i
$478$		0			0
$479$	−6.26391	−	19.2783i	−0.286205	−	0.880849i	−0.986035	−	0.166539i	$-0.946741\pi$
$479$	−6.26391	−	19.2783i	−0.286205	−	0.880849i	0.699830	−	0.714310i	$-0.253259\pi$
$480$		0			0
$481$	23.1356	−	16.8090i	1.05489	−	0.766423i
$482$		0			0
$483$	−0.263547			−0.0119918
$484$		0			0
$485$	−6.43894			−0.292377
$486$		0			0
$487$	3.07876	−	2.23685i	0.139512	−	0.101361i	−0.515840	−	0.856685i	$-0.672520\pi$
$487$	3.07876	−	2.23685i	0.139512	−	0.101361i	0.655352	+	0.755323i	$0.272520\pi$
$488$		0			0
$489$	5.27367	+	16.2307i	0.238484	+	0.733977i
$490$		0			0
$491$	−34.7675	−	25.2601i	−1.56904	−	1.13997i	−0.928072	−	0.372400i	$-0.878535\pi$
$491$	−34.7675	−	25.2601i	−1.56904	−	1.13997i	−0.640964	−	0.767571i	$-0.721465\pi$
$492$		0			0
$493$	−1.02256	+	3.14711i	−0.0460536	+	0.141738i
$494$		0			0
$495$	−7.49293	+	1.01194i	−0.336782	+	0.0454832i
$496$		0			0
$497$	2.37235	−	7.30133i	0.106414	−	0.327509i
$498$		0			0
$499$	4.75867	+	3.45738i	0.213027	+	0.154773i	0.689182	−	0.724588i	$-0.257970\pi$
$499$	4.75867	+	3.45738i	0.213027	+	0.154773i	−0.476155	+	0.879361i	$0.657970\pi$
$500$		0			0
$501$	0.902647	+	2.77806i	0.0403273	+	0.124115i
$502$		0			0
$503$	−24.6768	+	17.9288i	−1.10029	+	0.799404i	−0.981106	−	0.193469i	$-0.938026\pi$
$503$	−24.6768	+	17.9288i	−1.10029	+	0.799404i	−0.119179	+	0.992873i	$0.538026\pi$
$504$		0			0
$505$	−13.1379			−0.584629
$506$		0			0
$507$	6.61628			0.293839
$508$		0			0
$509$	13.6522	−	9.91890i	0.605123	−	0.439648i	−0.242571	−	0.970134i	$-0.577991\pi$
$509$	13.6522	−	9.91890i	0.605123	−	0.439648i	0.847694	+	0.530486i	$0.177991\pi$
$510$		0			0
$511$	0.404917	+	1.24621i	0.0179125	+	0.0551289i
$512$		0			0
$513$	−8.26420	−	6.00429i	−0.364873	−	0.265096i
$514$		0			0
$515$	−0.276639	+	0.851408i	−0.0121902	+	0.0375175i
$516$		0			0
$517$	23.1610	−	22.1265i	1.01862	−	0.973121i
$518$		0			0
$519$	−4.01100	+	12.3446i	−0.176063	+	0.541867i
$520$		0			0
$521$	−1.34854	−	0.979773i	−0.0590807	−	0.0429246i	0.557853	−	0.829940i	$-0.311625\pi$
$521$	−1.34854	−	0.979773i	−0.0590807	−	0.0429246i	−0.616934	+	0.787015i	$0.711625\pi$
$522$		0			0
$523$	−10.4720	−	32.2294i	−0.457908	−	1.40930i	−0.867687	−	0.497110i	$-0.834394\pi$
$523$	−10.4720	−	32.2294i	−0.457908	−	1.40930i	0.409780	−	0.912185i	$-0.365606\pi$
$524$		0			0
$525$	0.646930	−	0.470022i	0.0282343	−	0.0205135i
$526$		0			0
$527$	11.9098			0.518800
$528$		0			0
$529$	−22.8914			−0.995277
$530$		0			0
$531$	3.70478	−	2.69168i	0.160774	−	0.116809i
$532$		0			0
$533$	15.4026	+	47.4045i	0.667163	+	2.05332i
$534$		0			0
$535$	3.27371	+	2.37849i	0.141535	+	0.102831i
$536$		0			0
$537$	1.31131	−	4.03580i	0.0565872	−	0.174158i
$538$		0			0
$539$	−8.78840	−	18.2680i	−0.378543	−	0.786857i
$540$		0			0
$541$	9.05402	−	27.8654i	0.389263	−	1.19803i	−0.544078	−	0.839035i	$-0.683120\pi$
$541$	9.05402	−	27.8654i	0.389263	−	1.19803i	0.933340	−	0.358993i	$-0.116880\pi$
$542$		0			0
$543$	17.6041	+	12.7901i	0.755463	+	0.548876i
$544$		0			0
$545$	−1.84744	−	5.68583i	−0.0791355	−	0.243554i
$546$		0			0
$547$	−29.8639	+	21.6974i	−1.27689	+	0.927714i	−0.999454	−	0.0330304i	$-0.989484\pi$
$547$	−29.8639	+	21.6974i	−1.27689	+	0.927714i	−0.277435	+	0.960745i	$0.589484\pi$
$548$		0			0
$549$	−2.37346			−0.101297
$550$		0			0
$551$	3.06906			0.130746
$552$		0			0
$553$	−5.51990	+	4.01044i	−0.234730	+	0.170541i
$554$		0			0
$555$	1.64464	+	5.06167i	0.0698109	+	0.214856i
$556$		0			0
$557$	13.7246	+	9.97149i	0.581529	+	0.422506i	0.839275	−	0.543707i	$-0.182980\pi$
$557$	13.7246	+	9.97149i	0.581529	+	0.422506i	−0.257746	+	0.966213i	$0.582980\pi$
$558$		0			0
$559$	17.5745	−	54.0887i	0.743321	−	2.28771i
$560$		0			0
$561$	−6.09133	−	3.28102i	−0.257176	−	0.138525i
$562$		0			0
$563$	0.385700	−	1.18706i	0.0162553	−	0.0500287i	−0.942600	−	0.333924i	$-0.891627\pi$
$563$	0.385700	−	1.18706i	0.0162553	−	0.0500287i	0.958855	+	0.283896i	$0.0916270\pi$
$564$		0			0
$565$	10.1658	+	7.38590i	0.427679	+	0.310727i
$566$		0			0
$567$	−0.884021	−	2.72074i	−0.0371254	−	0.114260i
$568$		0			0
$569$	−17.8719	+	12.9847i	−0.749228	+	0.544346i	−0.895588	−	0.444885i	$-0.853244\pi$
$569$	−17.8719	+	12.9847i	−0.749228	+	0.544346i	0.146359	+	0.989232i	$0.453244\pi$
$570$		0			0
$571$	43.8975			1.83705			0.918527	−	0.395358i	$-0.129379\pi$
$571$	43.8975			1.83705			0.918527	+	0.395358i	$0.129379\pi$
$572$		0			0
$573$	3.81380			0.159324
$574$		0			0
$575$	−0.266634	+	0.193721i	−0.0111194	+	0.00807872i
$576$		0			0
$577$	5.60251	+	17.2428i	0.233236	+	0.717826i	0.997351	+	0.0727454i	$0.0231761\pi$
$577$	5.60251	+	17.2428i	0.233236	+	0.717826i	−0.764115	+	0.645080i	$0.776824\pi$
$578$		0			0
$579$	16.6102	+	12.0680i	0.690297	+	0.501530i
$580$		0			0
$581$	0.417624	−	1.28531i	0.0173260	−	0.0533238i
$582$		0			0
$583$	−3.28177	+	18.0430i	−0.135917	+	0.747265i
$584$		0			0
$585$	3.21255	−	9.88722i	0.132823	−	0.408786i
$586$		0			0
$587$	−15.3792	−	11.1736i	−0.634766	−	0.461184i	0.223282	−	0.974754i	$-0.428323\pi$
$587$	−15.3792	−	11.1736i	−0.634766	−	0.461184i	−0.858048	+	0.513570i	$0.828323\pi$
$588$		0			0
$589$	−3.41341	−	10.5054i	−0.140647	−	0.432867i
$590$		0			0
$591$	7.89749	−	5.73786i	0.324859	−	0.236024i
$592$		0			0
$593$	−42.6545			−1.75161			−0.875804	−	0.482666i	$-0.839668\pi$
$593$	−42.6545			−1.75161			−0.875804	+	0.482666i	$0.839668\pi$
$594$		0			0
$595$	−2.31593			−0.0949441
$596$		0			0
$597$	7.63579	−	5.54773i	0.312512	−	0.227053i
$598$		0			0
$599$	8.27674	+	25.4732i	0.338178	+	1.04081i	0.965135	+	0.261752i	$0.0843002\pi$
$599$	8.27674	+	25.4732i	0.338178	+	1.04081i	−0.626957	+	0.779054i	$0.715700\pi$
$600$		0			0
$601$	11.8373	+	8.60028i	0.482853	+	0.350813i	0.802429	−	0.596748i	$-0.203541\pi$
$601$	11.8373	+	8.60028i	0.482853	+	0.350813i	−0.319576	+	0.947560i	$0.603541\pi$
$602$		0			0
$603$	−6.39759	+	19.6898i	−0.260530	+	0.801829i
$604$		0			0
$605$	6.05253	+	9.18514i	0.246070	+	0.373429i
$606$		0			0
$607$	0.310627	−	0.956013i	0.0126080	−	0.0388034i	−0.944555	−	0.328354i	$-0.893506\pi$
$607$	0.310627	−	0.956013i	0.0126080	−	0.0388034i	0.957163	+	0.289551i	$0.0935060\pi$
$608$		0			0
$609$	−0.870929	−	0.632767i	−0.0352918	−	0.0256410i
$610$		0			0
$611$	13.6097	+	41.8865i	0.550591	+	1.69455i
$612$		0			0
$613$	0.213546	−	0.155150i	0.00862505	−	0.00626647i	−0.583464	−	0.812139i	$-0.698303\pi$
$613$	0.213546	−	0.155150i	0.00862505	−	0.00626647i	0.592089	+	0.805872i	$0.298303\pi$
$614$		0			0
$615$	−9.27637			−0.374059
$616$		0			0
$617$	−5.14458			−0.207113			−0.103556	−	0.994624i	$-0.533022\pi$
$617$	−5.14458			−0.207113			−0.103556	+	0.994624i	$0.533022\pi$
$618$		0			0
$619$	−38.2308	+	27.7763i	−1.53663	+	1.11643i	−0.584221	+	0.811595i	$0.698600\pi$
$619$	−38.2308	+	27.7763i	−1.53663	+	1.11643i	−0.952407	+	0.304830i	$0.901400\pi$
$620$		0			0
$621$	−0.456356	−	1.40452i	−0.0183129	−	0.0563614i
$622$		0			0
$623$	12.5801	+	9.14001i	0.504013	+	0.366187i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$		0			0
$627$	−1.14831	+	6.31338i	−0.0458593	+	0.252132i
$628$		0			0
$629$	4.76318	−	14.6595i	0.189920	−	0.584514i
$630$		0			0
$631$	0.995219	+	0.723069i	0.0396190	+	0.0287849i	0.607419	−	0.794382i	$-0.292205\pi$
$631$	0.995219	+	0.723069i	0.0396190	+	0.0287849i	−0.567799	+	0.823167i	$0.692205\pi$
$632$		0			0
$633$	−4.79524	−	14.7582i	−0.190594	−	0.586587i
$634$		0			0
$635$	−9.51782	+	6.91510i	−0.377703	+	0.274417i
$636$		0			0
$637$	27.8733			1.10438
$638$		0			0
$639$	18.5750			0.734816
$640$		0			0
$641$	5.04917	−	3.66843i	0.199430	−	0.144894i	−0.483588	−	0.875296i	$-0.660667\pi$
$641$	5.04917	−	3.66843i	0.199430	−	0.144894i	0.683018	+	0.730401i	$0.260667\pi$
$642$		0			0
$643$	1.42934	+	4.39907i	0.0563678	+	0.173482i	0.975277	−	0.220988i	$-0.0709281\pi$
$643$	1.42934	+	4.39907i	0.0563678	+	0.173482i	−0.918909	+	0.394470i	$0.870928\pi$
$644$		0			0
$645$	8.56294	+	6.22134i	0.337166	+	0.244965i
$646$		0			0
$647$	−2.98239	+	9.17886i	−0.117250	+	0.360858i	−0.992410	−	0.122976i	$-0.960756\pi$
$647$	−2.98239	+	9.17886i	−0.117250	+	0.360858i	0.875160	+	0.483834i	$0.160756\pi$
$648$		0			0
$649$	−5.86549	−	3.15938i	−0.230240	−	0.124016i
$650$		0			0
$651$	−1.19731	+	3.68495i	−0.0469264	+	0.144425i
$652$		0			0
$653$	24.0319	+	17.4602i	0.940442	+	0.683271i	0.948527	−	0.316696i	$-0.102574\pi$
$653$	24.0319	+	17.4602i	0.940442	+	0.683271i	−0.00808493	+	0.999967i	$0.502574\pi$
$654$		0			0
$655$	2.43951	+	7.50803i	0.0953194	+	0.293363i
$656$		0			0
$657$	−2.56492	+	1.86353i	−0.100067	+	0.0727030i
$658$		0			0
$659$	43.3285			1.68784			0.843920	−	0.536469i	$-0.180242\pi$
$659$	43.3285			1.68784			0.843920	+	0.536469i	$0.180242\pi$
$660$		0			0
$661$	−9.88967			−0.384664			−0.192332	−	0.981330i	$-0.561605\pi$
$661$	−9.88967			−0.384664			−0.192332	+	0.981330i	$0.561605\pi$
$662$		0			0
$663$	7.69623	−	5.59164i	0.298897	−	0.217161i
$664$		0			0
$665$	0.663757	+	2.04283i	0.0257394	+	0.0792177i
$666$		0			0
$667$	0.358956	+	0.260797i	0.0138988	+	0.0100981i
$668$		0			0
$669$	−6.77299	+	20.8451i	−0.261859	+	0.805919i
$670$		0			0
$671$	1.49696	+	3.11165i	0.0577896	+	0.120124i
$672$		0			0
$673$	−8.63603	+	26.5790i	−0.332895	+	1.02454i	0.634855	+	0.772631i	$0.281060\pi$
$673$	−8.63603	+	26.5790i	−0.332895	+	1.02454i	−0.967750	+	0.251913i	$0.918940\pi$
$674$		0			0
$675$	3.62511	+	2.63380i	0.139530	+	0.101375i
$676$		0			0
$677$	−0.813531	−	2.50379i	−0.0312665	−	0.0962285i	0.934205	−	0.356736i	$-0.116110\pi$
$677$	−0.813531	−	2.50379i	−0.0312665	−	0.0962285i	−0.965472	+	0.260507i	$0.916110\pi$
$678$		0			0
$679$	−4.90816	+	3.56599i	−0.188358	+	0.136850i
$680$		0			0
$681$	19.6836			0.754276
$682$		0			0
$683$	−24.4582			−0.935868			−0.467934	−	0.883763i	$-0.655001\pi$
$683$	−24.4582			−0.935868			−0.467934	+	0.883763i	$0.655001\pi$
$684$		0			0
$685$	6.75352	−	4.90672i	0.258039	−	0.187476i
$686$		0			0
$687$	2.61924	+	8.06118i	0.0999301	+	0.307553i
$688$		0			0
$689$	−20.3998	−	14.8213i	−0.777169	−	0.564647i
$690$		0			0
$691$	−0.404553	+	1.24509i	−0.0153899	+	0.0473653i	−0.958457	−	0.285239i	$-0.907927\pi$
$691$	−0.404553	+	1.24509i	−0.0153899	+	0.0473653i	0.943067	+	0.332604i	$0.107927\pi$
$692$		0			0
$693$	−5.15115	+	4.92106i	−0.195676	+	0.186936i
$694$		0			0
$695$	2.82917	−	8.70729i	0.107316	−	0.330286i
$696$		0			0
$697$	21.7351	+	15.7915i	0.823277	+	0.598146i
$698$		0			0
$699$	5.99437	+	18.4488i	0.226728	+	0.697796i
$700$		0			0
$701$	−0.215878	+	0.156844i	−0.00815359	+	0.00592393i	−0.591855	−	0.806045i	$-0.701604\pi$
$701$	−0.215878	+	0.156844i	−0.00815359	+	0.00592393i	0.583701	+	0.811969i	$0.301604\pi$
$702$		0			0
$703$	−14.2960			−0.539184
$704$		0			0
$705$	−8.19658			−0.308701
$706$		0			0
$707$	−10.0145	+	7.27597i	−0.376635	+	0.273641i
$708$		0			0
$709$	−8.97210	−	27.6133i	−0.336954	−	1.03704i	−0.965751	−	0.259469i	$-0.916452\pi$
$709$	−8.97210	−	27.6133i	−0.336954	−	1.03704i	0.628797	−	0.777569i	$-0.283548\pi$
$710$		0			0
$711$	−13.3556	−	9.70344i	−0.500875	−	0.363907i
$712$		0			0
$713$	0.493476	−	1.51876i	0.0184808	−	0.0568781i
$714$		0			0
$715$	−14.9885	+	2.02424i	−0.560540	+	0.0757022i
$716$		0			0
$717$	5.07311	−	15.6134i	0.189459	−	0.583094i
$718$		0			0
$719$	37.7429	+	27.4218i	1.40757	+	1.02266i	0.993670	+	0.112340i	$0.0358346\pi$
$719$	37.7429	+	27.4218i	1.40757	+	1.02266i	0.413903	+	0.910321i	$0.364165\pi$
$720$		0			0
$721$	0.260652	+	0.802204i	0.00970718	+	0.0298756i
$722$		0			0
$723$	−6.53933	+	4.75110i	−0.243200	+	0.176695i
$724$		0			0
$725$	−1.34625			−0.0499984
$726$		0			0
$727$	−28.9126			−1.07231			−0.536154	−	0.844120i	$-0.680123\pi$
$727$	−28.9126			−1.07231			−0.536154	+	0.844120i	$0.680123\pi$
$728$		0			0
$729$	−3.63008	+	2.63741i	−0.134447	+	0.0976818i
$730$		0			0
$731$	−9.47271	−	29.1540i	−0.350361	−	1.07830i
$732$		0			0
$733$	25.3784	+	18.4385i	0.937371	+	0.681040i	0.947786	−	0.318906i	$-0.103315\pi$
$733$	25.3784	+	18.4385i	0.937371	+	0.681040i	−0.0104153	+	0.999946i	$0.503315\pi$
$734$		0			0
$735$	−1.60301	+	4.93356i	−0.0591279	+	0.181977i
$736$		0			0
$737$	29.8487	−	4.03114i	1.09949	−	0.148489i
$738$		0			0
$739$	−3.43117	+	10.5601i	−0.126218	+	0.388458i	−0.994121	−	0.108275i	$-0.965467\pi$
$739$	−3.43117	+	10.5601i	−0.126218	+	0.388458i	0.867903	+	0.496733i	$0.165467\pi$
$740$		0			0
$741$	−7.13803	−	5.18608i	−0.262222	−	0.190516i
$742$		0			0
$743$	−3.54691	−	10.9163i	−0.130124	−	0.400479i	0.864676	−	0.502330i	$-0.167524\pi$
$743$	−3.54691	−	10.9163i	−0.130124	−	0.400479i	−0.994800	+	0.101851i	$0.967524\pi$
$744$		0			0
$745$	−10.2730	+	7.46378i	−0.376374	+	0.273452i
$746$		0			0
$747$	3.26991			0.119640
$748$		0			0
$749$	3.81267			0.139312
$750$		0			0
$751$	−9.51030	+	6.90964i	−0.347036	+	0.252136i	−0.747624	−	0.664122i	$-0.768806\pi$
$751$	−9.51030	+	6.90964i	−0.347036	+	0.252136i	0.400589	+	0.916258i	$0.368806\pi$
$752$		0			0
$753$	−1.28080	−	3.94190i	−0.0466750	−	0.143651i
$754$		0			0
$755$	−12.1177	−	8.80406i	−0.441010	−	0.320412i
$756$		0			0
$757$	13.7801	−	42.4108i	0.500846	−	1.54145i	−0.306797	−	0.951775i	$-0.599257\pi$
$757$	13.7801	−	42.4108i	0.500846	−	1.54145i	0.807643	−	0.589671i	$-0.200743\pi$
$758$		0			0
$759$	−0.670793	+	0.640831i	−0.0243482	+	0.0232607i
$760$		0			0
$761$	0.436560	−	1.34359i	0.0158253	−	0.0487052i	−0.942832	−	0.333268i	$-0.891849\pi$
$761$	0.436560	−	1.34359i	0.0158253	−	0.0487052i	0.958657	+	0.284563i	$0.0918485\pi$
$762$		0			0
$763$	−4.55713	−	3.31095i	−0.164979	−	0.119864i
$764$		0			0
$765$	−1.73158	−	5.32925i	−0.0626053	−	0.192679i
$766$		0			0
$767$	7.41089	−	5.38432i	0.267592	−	0.194417i
$768$		0			0
$769$	−7.86871			−0.283753			−0.141876	−	0.989884i	$-0.545314\pi$
$769$	−7.86871			−0.283753			−0.141876	+	0.989884i	$0.545314\pi$
$770$		0			0
$771$	10.9064			0.392785
$772$		0			0
$773$	21.9016	−	15.9124i	0.787746	−	0.572331i	−0.119548	−	0.992828i	$-0.538145\pi$
$773$	21.9016	−	15.9124i	0.787746	−	0.572331i	0.907294	+	0.420498i	$0.138145\pi$
$774$		0			0
$775$	1.49730	+	4.60821i	0.0537845	+	0.165532i
$776$		0			0
$777$	4.05688	+	2.94749i	0.145540	+	0.105741i
$778$		0			0
$779$	7.69994	−	23.6980i	0.275879	−	0.849068i
$780$		0			0
$781$	−11.7154	−	24.3522i	−0.419211	−	0.871391i
$782$		0			0
$783$	1.86411	−	5.73713i	0.0666178	−	0.205028i
$784$		0			0
$785$	−11.8231	−	8.59000i	−0.421985	−	0.306590i
$786$		0			0
$787$	9.28963	+	28.5905i	0.331140	+	1.01914i	0.968593	+	0.248653i	$0.0799880\pi$
$787$	9.28963	+	28.5905i	0.331140	+	1.01914i	−0.637453	+	0.770489i	$0.720012\pi$
$788$		0			0
$789$	14.1830	−	10.3046i	0.504929	−	0.366852i
$790$		0			0
$791$	11.8394			0.420962
$792$		0			0
$793$	−4.74777			−0.168598
$794$		0			0
$795$	3.79656	−	2.75836i	0.134650	−	0.0978291i
$796$		0			0
$797$	−11.0801	−	34.1012i	−0.392479	−	1.20793i	−0.930908	−	0.365254i	$-0.880982\pi$
$797$	−11.0801	−	34.1012i	−0.392479	−	1.20793i	0.538429	−	0.842671i	$-0.319018\pi$
$798$		0			0
$799$	19.2051	+	13.9533i	0.679428	+	0.493634i
$800$		0			0
$801$	−11.6264	+	35.7822i	−0.410797	+	1.26430i
$802$		0			0
$803$	4.06084	+	2.18732i	0.143304	+	0.0771890i
$804$		0			0
$805$	−0.0959593	+	0.295332i	−0.00338212	+	0.0104091i
$806$		0			0
$807$	−12.2191	−	8.87773i	−0.430134	−	0.312511i
$808$		0			0
$809$	−4.28457	−	13.1865i	−0.150637	−	0.463614i	0.847055	−	0.531505i	$-0.178373\pi$
$809$	−4.28457	−	13.1865i	−0.150637	−	0.463614i	−0.997693	+	0.0678905i	$0.978373\pi$
$810$		0			0
$811$	−26.8947	+	19.5401i	−0.944401	+	0.686147i	−0.949476	−	0.313840i	$-0.898385\pi$
$811$	−26.8947	+	19.5401i	−0.944401	+	0.686147i	0.00507517	+	0.999987i	$0.498385\pi$
$812$		0			0
$813$	−4.46320			−0.156531
$814$		0			0
$815$	20.1084			0.704367
$816$		0			0
$817$	−23.0012	+	16.7113i	−0.804709	+	0.584655i
$818$		0			0
$819$	−3.02689	−	9.31581i	−0.105768	−	0.325521i
$820$		0			0
$821$	−15.2385	−	11.0714i	−0.531827	−	0.386395i	0.289214	−	0.957264i	$-0.406606\pi$
$821$	−15.2385	−	11.0714i	−0.531827	−	0.386395i	−0.821041	+	0.570870i	$0.806606\pi$
$822$		0			0
$823$	16.1196	−	49.6110i	0.561894	−	1.72933i	−0.115111	−	0.993353i	$-0.536722\pi$
$823$	16.1196	−	49.6110i	0.561894	−	1.72933i	0.677005	−	0.735978i	$-0.263278\pi$
$824$		0			0
$825$	0.503711	−	2.76938i	0.0175370	−	0.0964173i
$826$		0			0
$827$	−3.81680	+	11.7469i	−0.132723	+	0.408480i	−0.995229	−	0.0975673i	$-0.968894\pi$
$827$	−3.81680	+	11.7469i	−0.132723	+	0.408480i	0.862506	+	0.506047i	$0.168894\pi$
$828$		0			0
$829$	−22.4628	−	16.3201i	−0.780164	−	0.566822i	0.124864	−	0.992174i	$-0.460150\pi$
$829$	−22.4628	−	16.3201i	−0.780164	−	0.566822i	−0.905028	+	0.425352i	$0.860150\pi$
$830$		0			0
$831$	−5.65758	−	17.4122i	−0.196259	−	0.604024i
$832$		0			0
$833$	12.1545	−	8.83078i	0.421129	−	0.305968i
$834$		0			0
$835$	3.44178			0.119108
$836$		0			0
$837$	−21.7115			−0.750458
$838$		0			0
$839$	−8.75012	+	6.35733i	−0.302088	+	0.219479i	−0.728494	−	0.685052i	$-0.759779\pi$
$839$	−8.75012	+	6.35733i	−0.302088	+	0.219479i	0.426406	+	0.904532i	$0.359779\pi$
$840$		0			0
$841$	−8.40144	−	25.8570i	−0.289705	−	0.891619i
$842$		0			0
$843$	−16.4550	−	11.9553i	−0.566740	−	0.411761i
$844$		0			0
$845$	2.40904	−	7.41425i	0.0828734	−	0.255058i
$846$		0			0
$847$	9.70049	+	3.64950i	0.333313	+	0.125398i
$848$		0			0
$849$	2.30311	−	7.08824i	0.0790424	−	0.243268i
$850$		0			0
$851$	−1.67205	−	1.21482i	−0.0573173	−	0.0416434i
$852$		0			0
$853$	−6.39884	−	19.6936i	−0.219092	−	0.674296i	−0.998838	−	0.0481996i	$-0.984652\pi$
$853$	−6.39884	−	19.6936i	−0.219092	−	0.674296i	0.779746	−	0.626096i	$-0.215348\pi$
$854$		0			0
$855$	−4.20453	+	3.05477i	−0.143792	+	0.104471i
$856$		0			0
$857$	10.9041			0.372478			0.186239	−	0.982504i	$-0.440370\pi$
$857$	10.9041			0.372478			0.186239	+	0.982504i	$0.440370\pi$
$858$		0			0
$859$	−1.13276			−0.0386493			−0.0193246	−	0.999813i	$-0.506152\pi$
$859$	−1.13276			−0.0386493			−0.0193246	+	0.999813i	$0.506152\pi$
$860$		0			0
$861$	−7.07103	+	5.13740i	−0.240980	+	0.175082i
$862$		0			0
$863$	8.24306	+	25.3695i	0.280597	+	0.863589i	0.987684	+	0.156462i	$0.0500089\pi$
$863$	8.24306	+	25.3695i	0.280597	+	0.863589i	−0.707087	+	0.707127i	$0.749991\pi$
$864$		0			0
$865$	12.3730	+	8.98951i	0.420694	+	0.305652i
$866$		0			0
$867$	−2.87395	+	8.84509i	−0.0976043	+	0.300395i
$868$		0			0
$869$	−4.29789	+	23.6296i	−0.145796	+	0.801578i
$870$		0			0
$871$	−12.7975	+	39.3866i	−0.433626	+	1.33456i
$872$		0			0
$873$	−11.8755	−	8.62806i	−0.401925	−	0.292016i
$874$		0			0
$875$	−0.291158	−	0.896093i	−0.00984294	−	0.0302935i
$876$		0			0
$877$	13.4997	−	9.80813i	0.455854	−	0.331197i	−0.336049	−	0.941845i	$-0.609091\pi$
$877$	13.4997	−	9.80813i	0.455854	−	0.331197i	0.791903	+	0.610648i	$0.209091\pi$
$878$		0			0
$879$	−24.3225			−0.820377
$880$		0			0
$881$	31.5034			1.06138			0.530689	−	0.847567i	$-0.321933\pi$
$881$	31.5034			1.06138			0.530689	+	0.847567i	$0.321933\pi$
$882$		0			0
$883$	19.6191	−	14.2541i	0.660236	−	0.479690i	−0.206507	−	0.978445i	$-0.566209\pi$
$883$	19.6191	−	14.2541i	0.660236	−	0.479690i	0.866743	+	0.498756i	$0.166209\pi$
$884$		0			0
$885$	0.526817	+	1.62138i	0.0177088	+	0.0545020i
$886$		0			0
$887$	−40.3969	−	29.3501i	−1.35639	−	0.985478i	−0.998665	−	0.0516529i	$-0.983551\pi$
$887$	−40.3969	−	29.3501i	−1.35639	−	0.985478i	−0.357729	−	0.933825i	$-0.616449\pi$
$888$		0			0
$889$	−3.42538	+	10.5422i	−0.114884	+	0.353575i
$890$		0			0
$891$	−8.86570	−	4.77541i	−0.297012	−	0.159982i
$892$		0			0
$893$	6.80365	−	20.9395i	0.227676	−	0.700713i
$894$		0			0
$895$	−4.04508	−	2.93893i	−0.135212	−	0.0982375i
$896$		0			0
$897$	−0.394168	−	1.21312i	−0.0131609	−	0.0405050i
$898$		0			0
$899$	5.27726	−	3.83416i	0.176007	−	0.127876i
$900$		0			0
$901$	−13.5913			−0.452790
$902$		0			0
$903$	9.97268			0.331870
$904$		0			0
$905$	20.7424	−	15.0703i	0.689502	−	0.500953i
$906$		0			0
$907$	2.32700	+	7.16176i	0.0772666	+	0.237802i	0.982228	−	0.187691i	$-0.0601005\pi$
$907$	2.32700	+	7.16176i	0.0772666	+	0.237802i	−0.904961	+	0.425494i	$0.860100\pi$
$908$		0			0
$909$	−24.2306	−	17.6045i	−0.803677	−	0.583905i
$910$		0			0
$911$	−15.2789	+	47.0236i	−0.506212	+	1.55796i	0.292510	+	0.956262i	$0.405509\pi$
$911$	−15.2789	+	47.0236i	−0.506212	+	1.55796i	−0.798723	+	0.601699i	$0.794491\pi$
$912$		0			0
$913$	−2.06237	−	4.28693i	−0.0682543	−	0.141877i
$914$		0			0
$915$	0.273047	−	0.840351i	0.00902665	−	0.0277812i
$916$		0			0
$917$	6.01761	+	4.37205i	0.198719	+	0.144378i
$918$		0			0
$919$	−8.31031	−	25.5765i	−0.274132	−	0.843691i	−0.989448	−	0.144890i	$-0.953717\pi$
$919$	−8.31031	−	25.5765i	−0.274132	−	0.843691i	0.715316	−	0.698801i	$-0.246283\pi$
$920$		0			0
$921$	−23.6090	+	17.1529i	−0.777942	+	0.565208i
$922$		0			0
$923$	37.1567			1.22303
$924$		0			0
$925$	6.27097			0.206188
$926$		0			0
$927$	−1.65108	+	1.19958i	−0.0542287	+	0.0393995i
$928$		0			0
$929$	4.06864	+	12.5220i	0.133488	+	0.410833i	0.995352	−	0.0963066i	$-0.0307029\pi$
$929$	4.06864	+	12.5220i	0.133488	+	0.410833i	−0.861864	+	0.507139i	$0.830703\pi$
$930$		0			0
$931$	−11.2730	−	8.19029i	−0.369457	−	0.268426i
$932$		0			0
$933$	7.34994	−	22.6208i	0.240626	−	0.740572i
$934$		0			0
$935$	−5.89464	+	5.63134i	−0.192775	+	0.184165i
$936$		0			0
$937$	−11.4905	+	35.3640i	−0.375377	+	1.15529i	0.567847	+	0.823134i	$0.307777\pi$
$937$	−11.4905	+	35.3640i	−0.375377	+	1.15529i	−0.943224	+	0.332158i	$0.892223\pi$
$938$		0			0
$939$	−17.4879	−	12.7057i	−0.570695	−	0.414634i
$940$		0			0
$941$	4.63203	+	14.2559i	0.151000	+	0.464729i	0.997734	−	0.0672872i	$-0.0214344\pi$
$941$	4.63203	+	14.2559i	0.151000	+	0.464729i	−0.846734	+	0.532017i	$0.821434\pi$
$942$		0			0
$943$	2.91434	−	2.11739i	0.0949041	−	0.0689519i
$944$		0			0
$945$	4.22192			0.137339
$946$		0			0
$947$	41.0601			1.33428			0.667138	−	0.744934i	$-0.267519\pi$
$947$	41.0601			1.33428			0.667138	+	0.744934i	$0.267519\pi$
$948$		0			0
$949$	−5.13076	+	3.72772i	−0.166552	+	0.121007i
$950$		0			0
$951$	−3.95387	−	12.1688i	−0.128213	−	0.394599i
$952$		0			0
$953$	−20.1508	−	14.6404i	−0.652749	−	0.474250i	0.211457	−	0.977387i	$-0.432179\pi$
$953$	−20.1508	−	14.6404i	−0.652749	−	0.474250i	−0.864207	+	0.503137i	$0.832179\pi$
$954$		0			0
$955$	1.38863	−	4.27377i	0.0449351	−	0.138296i
$956$		0			0
$957$	−3.75534	+	0.507168i	−0.121393	+	0.0163944i
$958$		0			0
$959$	2.43053	−	7.48041i	0.0784860	−	0.241555i
$960$		0			0
$961$	6.08584	+	4.42162i	0.196317	+	0.142633i
$962$		0			0
$963$	2.85066	+	8.77341i	0.0918611	+	0.282719i
$964$		0			0
$965$	19.5714	−	14.2195i	0.630026	−	0.457741i
$966$		0			0
$967$	−56.7325			−1.82439			−0.912197	−	0.409752i	$-0.865615\pi$
$967$	−56.7325			−1.82439			−0.912197	+	0.409752i	$0.865615\pi$
$968$		0			0
$969$	−4.75568			−0.152775
$970$		0			0
$971$	0.852314	−	0.619242i	0.0273521	−	0.0198724i	−0.574025	−	0.818838i	$-0.694619\pi$
$971$	0.852314	−	0.619242i	0.0273521	−	0.0198724i	0.601377	+	0.798965i	$0.294619\pi$
$972$		0			0
$973$	−2.66566	−	8.20407i	−0.0854573	−	0.263011i
$974$		0			0
$975$	3.13111	+	2.27489i	0.100276	+	0.0728547i
$976$		0			0
$977$	7.17033	−	22.0680i	0.229399	−	0.706018i	−0.768416	−	0.639950i	$-0.778955\pi$
$977$	7.17033	−	22.0680i	0.229399	−	0.706018i	0.997815	−	0.0660672i	$-0.0210452\pi$
$978$		0			0
$979$	54.2441	−	7.32580i	1.73365	−	0.234134i
$980$		0			0
$981$	4.21162	−	12.9620i	0.134467	−	0.413846i
$982$		0			0
$983$	11.0190	+	8.00580i	0.351453	+	0.255345i	0.749478	−	0.662029i	$-0.230304\pi$
$983$	11.0190	+	8.00580i	0.351453	+	0.255345i	−0.398025	+	0.917374i	$0.630304\pi$
$984$		0			0
$985$	−3.55436	−	10.9392i	−0.113251	−	0.348551i
$986$		0			0
$987$	−6.24794	+	4.53940i	−0.198874	+	0.144491i
$988$		0			0
$989$	−4.11027			−0.130699
$990$		0			0
$991$	0.947848			0.0301094			0.0150547	−	0.999887i	$-0.495208\pi$
$991$	0.947848			0.0301094			0.0150547	+	0.999887i	$0.495208\pi$
$992$		0			0
$993$	8.79631	−	6.39089i	0.279142	−	0.202809i
$994$		0			0
$995$	−3.43657	−	10.5767i	−0.108947	−	0.335304i
$996$		0			0
$997$	40.6527	+	29.5359i	1.28749	+	0.935413i	0.999751	−	0.0222975i	$-0.00709809\pi$
$997$	40.6527	+	29.5359i	1.28749	+	0.935413i	0.287734	+	0.957710i	$0.407098\pi$
$998$		0			0
$999$	−8.68321	+	26.7242i	−0.274725	+	0.845515i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.m.b.141.1	✓	8
3.2	odd	2		1980.2.z.d.361.2		8
4.3	odd	2		880.2.bo.c.801.2		8
5.2	odd	4		1100.2.cb.b.449.3		16
5.3	odd	4		1100.2.cb.b.449.2		16
5.4	even	2		1100.2.n.b.801.2		8
11.4	even	5		2420.2.a.k.1.3		4
11.5	even	5	inner	220.2.m.b.181.1	yes	8
11.7	odd	10		2420.2.a.l.1.3		4
33.5	odd	10		1980.2.z.d.181.2		8
44.7	even	10		9680.2.a.co.1.2		4
44.15	odd	10		9680.2.a.cp.1.2		4
44.27	odd	10		880.2.bo.c.401.2		8
55.27	odd	20		1100.2.cb.b.49.2		16
55.38	odd	20		1100.2.cb.b.49.3		16
55.49	even	10		1100.2.n.b.401.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.m.b.141.1	✓	8	1.1	even	1	trivial
220.2.m.b.181.1	yes	8	11.5	even	5	inner
880.2.bo.c.401.2		8	44.27	odd	10
880.2.bo.c.801.2		8	4.3	odd	2
1100.2.n.b.401.2		8	55.49	even	10
1100.2.n.b.801.2		8	5.4	even	2
1100.2.cb.b.49.2		16	55.27	odd	20
1100.2.cb.b.49.3		16	55.38	odd	20
1100.2.cb.b.449.2		16	5.3	odd	4
1100.2.cb.b.449.3		16	5.2	odd	4
1980.2.z.d.181.2		8	33.5	odd	10
1980.2.z.d.361.2		8	3.2	odd	2
2420.2.a.k.1.3		4	11.4	even	5
2420.2.a.l.1.3		4	11.7	odd	10
9680.2.a.co.1.2		4	44.7	even	10
9680.2.a.cp.1.2		4	44.15	odd	10

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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	220.2.m.b.141.1

Level	$220$
Weight	$2$
Character	220.141
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$