LMFDB - Embedded newform 1056.2.y.e.961.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1056,2,Mod(97,1056)] 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("1056.97"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1056, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1056 = 2^{5} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1056.y (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-3,0,0,0,-4,0,-3,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$8.43220245345$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 8 x^{10} - 12 x^{9} + 41 x^{8} - 6 x^{7} + 104 x^{6} + 48 x^{5} + 248 x^{4} + \cdots + 16 $ x^12 - 3x^11 + 8x^10 - 12x^9 + 41x^8 - 6x^7 + 104x^6 + 48x^5 + 248x^4 - 176x^3 + 248x^2 - 96*x + 16
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			961.1
Root			$0.228458 - 0.165984i$ of defining polynomial
Character	$\chi$	$=$	1056.961
Dual form			1056.2.y.e.289.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 - 0.951057i) q^{3} +(-1.02076 + 0.741628i) q^{5} +(0.167822 + 0.516504i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-0.493296 + 3.27973i) q^{11} +(2.16155 + 1.57046i) q^{13} +(0.389897 + 1.19998i) q^{15} +(3.76244 - 2.73357i) q^{17} +(0.283418 - 0.872271i) q^{19} +0.543084 q^{21} -7.92887 q^{23} +(-1.05314 + 3.24123i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(3.02965 + 9.32431i) q^{29} +(2.67170 + 1.94110i) q^{31} +(2.96678 + 1.48265i) q^{33} +(-0.554361 - 0.402766i) q^{35} +(2.34049 + 7.20329i) q^{37} +(2.16155 - 1.57046i) q^{39} +(-0.361835 + 1.11361i) q^{41} +10.2437 q^{43} +1.26173 q^{45} +(-1.28895 + 3.96699i) q^{47} +(5.42451 - 3.94114i) q^{49} +(-1.43712 - 4.42301i) q^{51} +(8.03756 + 5.83963i) q^{53} +(-1.92881 - 3.71368i) q^{55} +(-0.741998 - 0.539093i) q^{57} +(-2.62633 - 8.08300i) q^{59} +(-0.129722 + 0.0942488i) q^{61} +(0.167822 - 0.516504i) q^{63} -3.37112 q^{65} +2.62665 q^{67} +(-2.45016 + 7.54080i) q^{69} +(2.17617 - 1.58108i) q^{71} +(-1.89612 - 5.83567i) q^{73} +(2.75715 + 2.00319i) q^{75} +(-1.77678 + 0.295623i) q^{77} +(-3.36840 - 2.44729i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-10.8346 + 7.87178i) q^{83} +(-1.81327 + 5.58067i) q^{85} +9.80416 q^{87} +2.70577 q^{89} +(-0.448390 + 1.38000i) q^{91} +(2.67170 - 1.94110i) q^{93} +(0.357598 + 1.10057i) q^{95} +(6.61605 + 4.80684i) q^{97} +(2.32686 - 2.36341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 4 q^{7} - 3 q^{9} + 2 q^{11} - 10 q^{13} + 5 q^{15} + 12 q^{17} + 8 q^{19} + 6 q^{21} - 24 q^{23} - 7 q^{25} - 3 q^{27} + 7 q^{29} + 31 q^{31} - 3 q^{33} + 17 q^{35} + 2 q^{37} - 10 q^{39}+ \cdots - 3 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 4 * q^7 - 3 * q^9 + 2 * q^11 - 10 * q^13 + 5 * q^15 + 12 * q^17 + 8 * q^19 + 6 * q^21 - 24 * q^23 - 7 * q^25 - 3 * q^27 + 7 * q^29 + 31 * q^31 - 3 * q^33 + 17 * q^35 + 2 * q^37 - 10 * q^39 + 22 * q^41 - 40 * q^43 - 10 * q^45 + 18 * q^47 - 17 * q^49 - 8 * q^51 + 9 * q^53 - 2 * q^57 + 30 * q^59 + 12 * q^61 - 4 * q^63 - 52 * q^65 - 16 * q^67 + 6 * q^69 + 30 * q^71 + 5 * q^73 + 8 * q^75 - 14 * q^77 - 16 * q^79 - 3 * q^81 - 36 * q^83 + 30 * q^85 + 2 * q^87 - 36 * q^89 + 12 * q^91 + 31 * q^93 - 70 * q^95 + 64 * q^97 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1056\mathbb{Z}\right)^\times$.

$n$	$133$	$353$	$673$	$991$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$		0			0
$5$	−1.02076	+	0.741628i	−0.456499	+	0.331666i	−0.792157	−	0.610318i	$-0.791042\pi$
$5$	−1.02076	+	0.741628i	−0.456499	+	0.331666i	0.335657	+	0.941984i	$0.391042\pi$
$6$		0			0
$7$	0.167822	+	0.516504i	0.0634308	+	0.195220i	0.977750	−	0.209775i	$-0.0672732\pi$
$7$	0.167822	+	0.516504i	0.0634308	+	0.195220i	−0.914319	+	0.404995i	$0.867273\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	−0.493296	+	3.27973i	−0.148734	+	0.988877i
$11$	−0.493296	+	3.27973i	−0.148734	+	0.988877i
$12$		0			0
$13$	2.16155	+	1.57046i	0.599505	+	0.435566i	0.845703	−	0.533654i	$-0.179181\pi$
$13$	2.16155	+	1.57046i	0.599505	+	0.435566i	−0.246198	+	0.969220i	$0.579181\pi$
$14$		0			0
$15$	0.389897	+	1.19998i	0.100671	+	0.309833i
$16$		0			0
$17$	3.76244	−	2.73357i	0.912526	−	0.662989i	−0.0291265	−	0.999576i	$-0.509273\pi$
$17$	3.76244	−	2.73357i	0.912526	−	0.662989i	0.941652	+	0.336587i	$0.109273\pi$
$18$		0			0
$19$	0.283418	−	0.872271i	0.0650206	−	0.200113i	−0.913268	−	0.407358i	$-0.866450\pi$
$19$	0.283418	−	0.872271i	0.0650206	−	0.200113i	0.978289	+	0.207246i	$0.0664500\pi$
$20$		0			0
$21$	0.543084			0.118511
$22$		0			0
$23$	−7.92887			−1.65328			−0.826642	−	0.562728i	$-0.809752\pi$
$23$	−7.92887			−1.65328			−0.826642	+	0.562728i	$0.809752\pi$
$24$		0			0
$25$	−1.05314	+	3.24123i	−0.210628	+	0.648246i
$26$		0			0
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$		0			0
$29$	3.02965	+	9.32431i	0.562592	+	1.73148i	0.674999	+	0.737818i	$0.264144\pi$
$29$	3.02965	+	9.32431i	0.562592	+	1.73148i	−0.112407	+	0.993662i	$0.535856\pi$
$30$		0			0
$31$	2.67170	+	1.94110i	0.479852	+	0.348633i	0.801268	−	0.598305i	$-0.204159\pi$
$31$	2.67170	+	1.94110i	0.479852	+	0.348633i	−0.321417	+	0.946938i	$0.604159\pi$
$32$		0			0
$33$	2.96678	+	1.48265i	0.516449	+	0.258096i
$34$		0			0
$35$	−0.554361	−	0.402766i	−0.0937040	−	0.0680800i
$36$		0			0
$37$	2.34049	+	7.20329i	0.384774	+	1.18421i	0.936644	+	0.350283i	$0.113915\pi$
$37$	2.34049	+	7.20329i	0.384774	+	1.18421i	−0.551870	+	0.833930i	$0.686085\pi$
$38$		0			0
$39$	2.16155	−	1.57046i	0.346125	−	0.251474i
$40$		0			0
$41$	−0.361835	+	1.11361i	−0.0565091	+	0.173917i	−0.975327	−	0.220764i	$-0.929145\pi$
$41$	−0.361835	+	1.11361i	−0.0565091	+	0.173917i	0.918818	+	0.394681i	$0.129145\pi$
$42$		0			0
$43$	10.2437			1.56216			0.781078	−	0.624433i	$-0.214670\pi$
$43$	10.2437			1.56216			0.781078	+	0.624433i	$0.214670\pi$
$44$		0			0
$45$	1.26173			0.188088
$46$		0			0
$47$	−1.28895	+	3.96699i	−0.188013	+	0.578645i	−0.999987	−	0.00504873i	$-0.998393\pi$
$47$	−1.28895	+	3.96699i	−0.188013	+	0.578645i	0.811974	+	0.583693i	$0.198393\pi$
$48$		0			0
$49$	5.42451	−	3.94114i	0.774930	−	0.563019i
$50$		0			0
$51$	−1.43712	−	4.42301i	−0.201238	−	0.619346i
$52$		0			0
$53$	8.03756	+	5.83963i	1.10404	+	0.802134i	0.981715	−	0.190355i	$-0.0609640\pi$
$53$	8.03756	+	5.83963i	1.10404	+	0.802134i	0.122328	+	0.992490i	$0.460964\pi$
$54$		0			0
$55$	−1.92881	−	3.71368i	−0.260080	−	0.500752i
$56$		0			0
$57$	−0.741998	−	0.539093i	−0.0982800	−	0.0714046i
$58$		0			0
$59$	−2.62633	−	8.08300i	−0.341919	−	1.05232i	−0.963213	−	0.268740i	$-0.913393\pi$
$59$	−2.62633	−	8.08300i	−0.341919	−	1.05232i	0.621294	−	0.783578i	$-0.286607\pi$
$60$		0			0
$61$	−0.129722	+	0.0942488i	−0.0166092	+	0.0120673i	−0.596059	−	0.802941i	$-0.703268\pi$
$61$	−0.129722	+	0.0942488i	−0.0166092	+	0.0120673i	0.579450	+	0.815008i	$0.303268\pi$
$62$		0			0
$63$	0.167822	−	0.516504i	0.0211436	−	0.0650733i
$64$		0			0
$65$	−3.37112			−0.418136
$66$		0			0
$67$	2.62665			0.320896			0.160448	−	0.987044i	$-0.448706\pi$
$67$	2.62665			0.320896			0.160448	+	0.987044i	$0.448706\pi$
$68$		0			0
$69$	−2.45016	+	7.54080i	−0.294964	+	0.907806i
$70$		0			0
$71$	2.17617	−	1.58108i	0.258263	−	0.187639i	−0.451118	−	0.892464i	$-0.648975\pi$
$71$	2.17617	−	1.58108i	0.258263	−	0.187639i	0.709381	+	0.704825i	$0.248975\pi$
$72$		0			0
$73$	−1.89612	−	5.83567i	−0.221924	−	0.683013i	−0.998589	−	0.0530990i	$-0.983090\pi$
$73$	−1.89612	−	5.83567i	−0.221924	−	0.683013i	0.776665	−	0.629914i	$-0.216910\pi$
$74$		0			0
$75$	2.75715	+	2.00319i	0.318369	+	0.231308i
$76$		0			0
$77$	−1.77678	+	0.295623i	−0.202483	+	0.0336894i
$78$		0			0
$79$	−3.36840	−	2.44729i	−0.378975	−	0.275341i	0.381948	−	0.924184i	$-0.375253\pi$
$79$	−3.36840	−	2.44729i	−0.378975	−	0.275341i	−0.760923	+	0.648843i	$0.775253\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	−10.8346	+	7.87178i	−1.18925	+	0.864041i	−0.993185	−	0.116550i	$-0.962816\pi$
$83$	−10.8346	+	7.87178i	−1.18925	+	0.864041i	−0.196065	+	0.980591i	$0.562816\pi$
$84$		0			0
$85$	−1.81327	+	5.58067i	−0.196677	+	0.605308i
$86$		0			0
$87$	9.80416			1.05112
$88$		0			0
$89$	2.70577			0.286811			0.143406	−	0.989664i	$-0.454195\pi$
$89$	2.70577			0.286811			0.143406	+	0.989664i	$0.454195\pi$
$90$		0			0
$91$	−0.448390	+	1.38000i	−0.0470041	+	0.144664i
$92$		0			0
$93$	2.67170	−	1.94110i	0.277042	−	0.201283i
$94$		0			0
$95$	0.357598	+	1.10057i	0.0366888	+	0.112916i
$96$		0			0
$97$	6.61605	+	4.80684i	0.671758	+	0.488061i	0.870613	−	0.491968i	$-0.163722\pi$
$97$	6.61605	+	4.80684i	0.671758	+	0.488061i	−0.198855	+	0.980029i	$0.563722\pi$
$98$		0			0
$99$	2.32686	−	2.36341i	0.233859	−	0.237532i
$100$		0			0
$101$	−0.138091	−	0.100329i	−0.0137405	−	0.00998307i	0.580894	−	0.813979i	$-0.302703\pi$
$101$	−0.138091	−	0.100329i	−0.0137405	−	0.00998307i	−0.594634	+	0.803996i	$0.702703\pi$
$102$		0			0
$103$	−2.59832	−	7.99682i	−0.256021	−	0.787950i	−0.993627	−	0.112719i	$-0.964044\pi$
$103$	−2.59832	−	7.99682i	−0.256021	−	0.787950i	0.737606	−	0.675231i	$-0.235956\pi$
$104$		0			0
$105$	−0.554361	+	0.402766i	−0.0541000	+	0.0393060i
$106$		0			0
$107$	−3.52470	+	10.8479i	−0.340746	+	1.04871i	0.623077	+	0.782161i	$0.285882\pi$
$107$	−3.52470	+	10.8479i	−0.340746	+	1.04871i	−0.963822	+	0.266546i	$0.914118\pi$
$108$		0			0
$109$	7.77469			0.744680			0.372340	−	0.928096i	$-0.378556\pi$
$109$	7.77469			0.744680			0.372340	+	0.928096i	$0.378556\pi$
$110$		0			0
$111$	7.57398			0.718891
$112$		0			0
$113$	2.09234	−	6.43957i	0.196831	−	0.605784i	−0.803119	−	0.595818i	$-0.796828\pi$
$113$	2.09234	−	6.43957i	0.196831	−	0.605784i	0.999950	−	0.00996568i	$-0.00317223\pi$
$114$		0			0
$115$	8.09350	−	5.88028i	0.754723	−	0.548339i
$116$		0			0
$117$	−0.825637	−	2.54105i	−0.0763302	−	0.234920i
$118$		0			0
$119$	2.04332	+	1.48456i	0.187311	+	0.136089i
$120$		0			0
$121$	−10.5133	−	3.23576i	−0.955756	−	0.294160i
$122$		0			0
$123$	0.947295	+	0.688250i	0.0854147	+	0.0620574i
$124$		0			0
$125$	−3.27827	−	10.0895i	−0.293217	−	0.902429i
$126$		0			0
$127$	0.415737	−	0.302051i	0.0368907	−	0.0268027i	−0.569187	−	0.822208i	$-0.692742\pi$
$127$	0.415737	−	0.302051i	0.0368907	−	0.0268027i	0.606078	+	0.795405i	$0.292742\pi$
$128$		0			0
$129$	3.16549	−	9.74238i	0.278706	−	0.857769i
$130$		0			0
$131$	−15.5023			−1.35445			−0.677223	−	0.735778i	$-0.736817\pi$
$131$	−15.5023			−1.35445			−0.677223	+	0.735778i	$0.736817\pi$
$132$		0			0
$133$	0.498095			0.0431903
$134$		0			0
$135$	0.389897	−	1.19998i	0.0335570	−	0.103278i
$136$		0			0
$137$	−0.843932	+	0.613153i	−0.0721020	+	0.0523852i	−0.623252	−	0.782021i	$-0.714189\pi$
$137$	−0.843932	+	0.613153i	−0.0721020	+	0.0523852i	0.551150	+	0.834406i	$0.314189\pi$
$138$		0			0
$139$	−4.67943	−	14.4018i	−0.396904	−	1.22154i	−0.927469	−	0.373900i	$-0.878020\pi$
$139$	−4.67943	−	14.4018i	−0.396904	−	1.22154i	0.530565	−	0.847644i	$-0.321980\pi$
$140$		0			0
$141$	3.37452	+	2.45173i	0.284186	+	0.206473i
$142$		0			0
$143$	−6.21696	+	6.31460i	−0.519888	+	0.528053i
$144$		0			0
$145$	−10.0077	−	7.27104i	−0.831097	−	0.603827i
$146$		0			0
$147$	−2.07198	−	6.37689i	−0.170894	−	0.525957i
$148$		0			0
$149$	−1.83247	+	1.33137i	−0.150122	+	0.109070i	−0.660311	−	0.750992i	$-0.729575\pi$
$149$	−1.83247	+	1.33137i	−0.150122	+	0.109070i	0.510189	+	0.860062i	$0.329575\pi$
$150$		0			0
$151$	−3.87322	+	11.9205i	−0.315198	+	0.970079i	0.660475	+	0.750848i	$0.270355\pi$
$151$	−3.87322	+	11.9205i	−0.315198	+	0.970079i	−0.975673	+	0.219231i	$0.929645\pi$
$152$		0			0
$153$	−4.65063			−0.375981
$154$		0			0
$155$	−4.16675			−0.334682
$156$		0			0
$157$	−3.07582	+	9.46641i	−0.245478	+	0.755502i	0.750080	+	0.661347i	$0.230015\pi$
$157$	−3.07582	+	9.46641i	−0.245478	+	0.755502i	−0.995558	+	0.0941550i	$0.969985\pi$
$158$		0			0
$159$	8.03756	−	5.83963i	0.637420	−	0.463113i
$160$		0			0
$161$	−1.33064	−	4.09529i	−0.104869	−	0.322754i
$162$		0			0
$163$	18.1128	+	13.1597i	1.41871	+	1.03075i	0.991984	+	0.126367i	$0.0403316\pi$
$163$	18.1128	+	13.1597i	1.41871	+	1.03075i	0.426722	+	0.904383i	$0.359668\pi$
$164$		0			0
$165$	−4.12795	+	0.686814i	−0.321360	+	0.0534684i
$166$		0			0
$167$	−1.29744	−	0.942643i	−0.100399	−	0.0729439i	0.536453	−	0.843930i	$-0.319764\pi$
$167$	−1.29744	−	0.942643i	−0.100399	−	0.0729439i	−0.636852	+	0.770986i	$0.719764\pi$
$168$		0			0
$169$	−1.81127	−	5.57451i	−0.139328	−	0.428808i
$170$		0			0
$171$	−0.741998	+	0.539093i	−0.0567420	+	0.0412255i
$172$		0			0
$173$	−0.675640	+	2.07941i	−0.0513680	+	0.158094i	−0.973450	−	0.228901i	$-0.926487\pi$
$173$	−0.675640	+	2.07941i	−0.0513680	+	0.158094i	0.922082	+	0.386995i	$0.126487\pi$
$174$		0			0
$175$	−1.85085			−0.139911
$176$		0			0
$177$	−8.49897			−0.638822
$178$		0			0
$179$	−3.19934	+	9.84656i	−0.239130	+	0.735966i	0.757417	+	0.652932i	$0.226461\pi$
$179$	−3.19934	+	9.84656i	−0.239130	+	0.735966i	−0.996547	+	0.0830346i	$0.973539\pi$
$180$		0			0
$181$	−6.97412	+	5.06700i	−0.518382	+	0.376627i	−0.815994	−	0.578060i	$-0.803810\pi$
$181$	−6.97412	+	5.06700i	−0.518382	+	0.376627i	0.297612	+	0.954687i	$0.403810\pi$
$182$		0			0
$183$	0.0495495	+	0.152498i	0.00366281	+	0.0112730i
$184$		0			0
$185$	−7.73125	−	5.61708i	−0.568413	−	0.412976i
$186$		0			0
$187$	7.10940	+	13.6883i	0.519891	+	1.00099i
$188$		0			0
$189$	−0.439364	−	0.319217i	−0.0319590	−	0.0232196i
$190$		0			0
$191$	−1.04765	−	3.22432i	−0.0758050	−	0.233304i	0.905973	−	0.423336i	$-0.139141\pi$
$191$	−1.04765	−	3.22432i	−0.0758050	−	0.233304i	−0.981778	+	0.190032i	$0.939141\pi$
$192$		0			0
$193$	16.2259	−	11.7888i	1.16797	−	0.848579i	0.177205	−	0.984174i	$-0.443294\pi$
$193$	16.2259	−	11.7888i	1.16797	−	0.848579i	0.990764	+	0.135595i	$0.0432945\pi$
$194$		0			0
$195$	−1.04173	+	3.20613i	−0.0746002	+	0.229596i
$196$		0			0
$197$	−22.2953			−1.58847			−0.794237	−	0.607608i	$-0.792129\pi$
$197$	−22.2953			−1.58847			−0.794237	+	0.607608i	$0.792129\pi$
$198$		0			0
$199$	−16.1481			−1.14471			−0.572353	−	0.820008i	$-0.693969\pi$
$199$	−16.1481			−1.14471			−0.572353	+	0.820008i	$0.693969\pi$
$200$		0			0
$201$	0.811679	−	2.49809i	0.0572514	−	0.176202i
$202$		0			0
$203$	−4.30760	+	3.12965i	−0.302334	+	0.219658i
$204$		0			0
$205$	−0.456539	−	1.40508i	−0.0318861	−	0.0981352i
$206$		0			0
$207$	6.41459	+	4.66047i	0.445845	+	0.323925i
$208$		0			0
$209$	2.72101	+	1.35982i	0.188216	+	0.0940610i
$210$		0			0
$211$	3.83447	+	2.78591i	0.263976	+	0.191790i	0.711898	−	0.702283i	$-0.247836\pi$
$211$	3.83447	+	2.78591i	0.263976	+	0.191790i	−0.447922	+	0.894073i	$0.647836\pi$
$212$		0			0
$213$	−0.831221	−	2.55824i	−0.0569543	−	0.175287i
$214$		0			0
$215$	−10.4564	+	7.59705i	−0.713124	+	0.518115i
$216$		0			0
$217$	−0.554217	+	1.70570i	−0.0376227	+	0.115791i
$218$		0			0
$219$	−6.13598			−0.414631
$220$		0			0
$221$	12.4256			0.835840
$222$		0			0
$223$	8.68148	−	26.7188i	0.581355	−	1.78923i	−0.0320852	−	0.999485i	$-0.510215\pi$
$223$	8.68148	−	26.7188i	0.581355	−	1.78923i	0.613440	−	0.789741i	$-0.289785\pi$
$224$		0			0
$225$	2.75715	−	2.00319i	0.183810	−	0.133546i
$226$		0			0
$227$	−7.19753	−	22.1517i	−0.477717	−	1.47026i	−0.842258	−	0.539074i	$-0.818774\pi$
$227$	−7.19753	−	22.1517i	−0.477717	−	1.47026i	0.364541	−	0.931187i	$-0.381226\pi$
$228$		0			0
$229$	−14.3592	−	10.4326i	−0.948882	−	0.689403i	0.00166043	−	0.999999i	$-0.499471\pi$
$229$	−14.3592	−	10.4326i	−0.948882	−	0.689403i	−0.950542	+	0.310596i	$0.899471\pi$
$230$		0			0
$231$	−0.267901	+	1.78117i	−0.0176266	+	0.117192i
$232$		0			0
$233$	−18.9468	−	13.7656i	−1.24124	−	0.901816i	−0.243563	−	0.969885i	$-0.578316\pi$
$233$	−18.9468	−	13.7656i	−1.24124	−	0.901816i	−0.997681	+	0.0680686i	$0.978316\pi$
$234$		0			0
$235$	−1.62631	−	5.00528i	−0.106089	−	0.326508i
$236$		0			0
$237$	−3.36840	+	2.44729i	−0.218801	+	0.158968i
$238$		0			0
$239$	−6.56017	+	20.1901i	−0.424342	+	1.30599i	0.479280	+	0.877662i	$0.340898\pi$
$239$	−6.56017	+	20.1901i	−0.424342	+	1.30599i	−0.903623	+	0.428330i	$0.859102\pi$
$240$		0			0
$241$	−1.23192			−0.0793551			−0.0396776	−	0.999213i	$-0.512633\pi$
$241$	−1.23192			−0.0793551			−0.0396776	+	0.999213i	$0.512633\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−2.61428	+	8.04594i	−0.167020	+	0.514036i
$246$		0			0
$247$	1.98248	−	1.44036i	0.126142	−	0.0916479i
$248$		0			0
$249$	4.13844	+	12.7368i	0.262263	+	0.807163i
$250$		0			0
$251$	11.7203	+	8.51526i	0.739776	+	0.537479i	0.892641	−	0.450769i	$-0.148850\pi$
$251$	11.7203	+	8.51526i	0.739776	+	0.537479i	−0.152865	+	0.988247i	$0.548850\pi$
$252$		0			0
$253$	3.91128	−	26.0046i	0.245900	−	1.63489i
$254$		0			0
$255$	4.74720	+	3.44904i	0.297281	+	0.215987i
$256$		0			0
$257$	1.84528	+	5.67919i	0.115105	+	0.354258i	0.991969	−	0.126481i	$-0.0403683\pi$
$257$	1.84528	+	5.67919i	0.115105	+	0.354258i	−0.876864	+	0.480739i	$0.840368\pi$
$258$		0			0
$259$	−3.32774	+	2.41774i	−0.206776	+	0.150231i
$260$		0			0
$261$	3.02965	−	9.32431i	0.187531	−	0.577160i
$262$		0			0
$263$	26.1883			1.61484			0.807421	−	0.589976i	$-0.200863\pi$
$263$	26.1883			1.61484			0.807421	+	0.589976i	$0.200863\pi$
$264$		0			0
$265$	−12.5353			−0.770036
$266$		0			0
$267$	0.836129	−	2.57334i	0.0511703	−	0.157486i
$268$		0			0
$269$	17.1974	−	12.4947i	1.04855	−	0.761813i	0.0766102	−	0.997061i	$-0.475590\pi$
$269$	17.1974	−	12.4947i	1.04855	−	0.761813i	0.971935	+	0.235248i	$0.0755903\pi$
$270$		0			0
$271$	−0.330382	−	1.01681i	−0.0200693	−	0.0617669i	0.940520	−	0.339737i	$-0.110338\pi$
$271$	−0.330382	−	1.01681i	−0.0200693	−	0.0617669i	−0.960590	+	0.277971i	$0.910338\pi$
$272$		0			0
$273$	1.17390	+	0.852889i	0.0710478	+	0.0516192i
$274$		0			0
$275$	−10.1109	−	5.05290i	−0.609708	−	0.304701i
$276$		0			0
$277$	−13.1821	−	9.57736i	−0.792036	−	0.575448i	0.116531	−	0.993187i	$-0.462823\pi$
$277$	−13.1821	−	9.57736i	−0.792036	−	0.575448i	−0.908567	+	0.417739i	$0.862823\pi$
$278$		0			0
$279$	−1.02050	−	3.14077i	−0.0610957	−	0.188033i
$280$		0			0
$281$	4.39076	−	3.19008i	0.261931	−	0.190304i	−0.449067	−	0.893498i	$-0.648244\pi$
$281$	4.39076	−	3.19008i	0.261931	−	0.190304i	0.710998	+	0.703194i	$0.248244\pi$
$282$		0			0
$283$	0.0223882	−	0.0689037i	0.00133084	−	0.00409590i	−0.950389	−	0.311064i	$-0.899315\pi$
$283$	0.0223882	−	0.0689037i	0.00133084	−	0.00409590i	0.951720	+	0.306968i	$0.0993146\pi$
$284$		0			0
$285$	1.15721			0.0685473
$286$		0			0
$287$	−0.635909			−0.0375365
$288$		0			0
$289$	1.43025	−	4.40185i	0.0841323	−	0.258933i
$290$		0			0
$291$	6.61605	−	4.80684i	0.387840	−	0.281782i
$292$		0			0
$293$	−0.984643	−	3.03042i	−0.0575234	−	0.177039i	0.918166	−	0.396195i	$-0.129670\pi$
$293$	−0.984643	−	3.03042i	−0.0575234	−	0.177039i	−0.975690	+	0.219156i	$0.929670\pi$
$294$		0			0
$295$	8.67545	+	6.30308i	0.505104	+	0.366980i
$296$		0			0
$297$	−1.52869	−	2.94331i	−0.0887039	−	0.170788i
$298$		0			0
$299$	−17.1386	−	12.4519i	−0.991152	−	0.720114i
$300$		0			0
$301$	1.71913	+	5.29093i	0.0990889	+	0.304964i
$302$		0			0
$303$	−0.138091	+	0.100329i	−0.00793309	+	0.00576373i
$304$		0			0
$305$	0.0625183	−	0.192411i	0.00357979	−	0.0110175i
$306$		0			0
$307$	11.6868			0.666999			0.333500	−	0.942750i	$-0.391770\pi$
$307$	11.6868			0.666999			0.333500	+	0.942750i	$0.391770\pi$
$308$		0			0
$309$	−8.40836			−0.478335
$310$		0			0
$311$	7.83003	−	24.0984i	0.444000	−	1.36649i	−0.439576	−	0.898206i	$-0.644871\pi$
$311$	7.83003	−	24.0984i	0.444000	−	1.36649i	0.883576	−	0.468287i	$-0.155129\pi$
$312$		0			0
$313$	−23.1045	+	16.7864i	−1.30595	+	0.948825i	−0.999995	−	0.00322282i	$-0.998974\pi$
$313$	−23.1045	+	16.7864i	−1.30595	+	0.948825i	−0.305950	+	0.952047i	$0.598974\pi$
$314$		0			0
$315$	0.211747	+	0.651690i	0.0119306	+	0.0367186i
$316$		0			0
$317$	−17.6882	−	12.8512i	−0.993466	−	0.721795i	−0.0327884	−	0.999462i	$-0.510439\pi$
$317$	−17.6882	−	12.8512i	−0.993466	−	0.721795i	−0.960677	+	0.277667i	$0.910439\pi$
$318$		0			0
$319$	−32.0758	+	5.33681i	−1.79590	+	0.298804i
$320$		0			0
$321$	9.22778	+	6.70438i	0.515045	+	0.374202i
$322$		0			0
$323$	−1.31807	−	4.05661i	−0.0733396	−	0.225716i
$324$		0			0
$325$	−7.36661	+	5.35216i	−0.408626	+	0.296884i
$326$		0			0
$327$	2.40251	−	7.39417i	0.132859	−	0.408898i
$328$		0			0
$329$	−2.26528			−0.124889
$330$		0			0
$331$	34.2835			1.88439			0.942196	−	0.335061i	$-0.108757\pi$
$331$	34.2835			1.88439			0.942196	+	0.335061i	$0.108757\pi$
$332$		0			0
$333$	2.34049	−	7.20329i	0.128258	−	0.394738i
$334$		0			0
$335$	−2.68119	+	1.94800i	−0.146489	+	0.106430i
$336$		0			0
$337$	−3.50378	−	10.7835i	−0.190863	−	0.587416i	0.809137	−	0.587620i	$-0.199935\pi$
$337$	−3.50378	−	10.7835i	−0.190863	−	0.587416i	−1.00000		0.000204246i	$0.999935\pi$
$338$		0			0
$339$	−5.47783	−	3.97988i	−0.297515	−	0.216157i
$340$		0			0
$341$	−7.68424	+	7.80493i	−0.416125	+	0.422661i
$342$		0			0
$343$	6.02151	+	4.37488i	0.325131	+	0.236222i
$344$		0			0
$345$	−3.09144	−	9.51449i	−0.166438	−	0.512243i
$346$		0			0
$347$	−11.2220	+	8.15328i	−0.602430	+	0.437691i	−0.846741	−	0.532006i	$-0.821438\pi$
$347$	−11.2220	+	8.15328i	−0.602430	+	0.437691i	0.244311	+	0.969697i	$0.421438\pi$
$348$		0			0
$349$	6.25040	−	19.2367i	0.334576	−	1.02972i	−0.632354	−	0.774679i	$-0.717911\pi$
$349$	6.25040	−	19.2367i	0.334576	−	1.02972i	0.966931	−	0.255040i	$-0.0820886\pi$
$350$		0			0
$351$	−2.67182			−0.142611
$352$		0			0
$353$	7.38396			0.393008			0.196504	−	0.980503i	$-0.437041\pi$
$353$	7.38396			0.393008			0.196504	+	0.980503i	$0.437041\pi$
$354$		0			0
$355$	−1.04878	+	3.22781i	−0.0556634	+	0.171314i
$356$		0			0
$357$	2.04332	−	1.48456i	0.108144	−	0.0785712i
$358$		0			0
$359$	−1.57534	−	4.84841i	−0.0831435	−	0.255889i	0.900839	−	0.434153i	$-0.142952\pi$
$359$	−1.57534	−	4.84841i	−0.0831435	−	0.255889i	−0.983983	+	0.178263i	$0.942952\pi$
$360$		0			0
$361$	14.6908	+	10.6735i	0.773200	+	0.561762i
$362$		0			0
$363$	−6.32618	+	8.99886i	−0.332039	+	0.472317i
$364$		0			0
$365$	6.26339	+	4.55062i	0.327841	+	0.238190i
$366$		0			0
$367$	−5.71986	−	17.6039i	−0.298574	−	0.918917i	−0.981997	−	0.188894i	$-0.939510\pi$
$367$	−5.71986	−	17.6039i	−0.298574	−	0.918917i	0.683423	−	0.730022i	$-0.260490\pi$
$368$		0			0
$369$	0.947295	−	0.688250i	0.0493142	−	0.0358289i
$370$		0			0
$371$	−1.66731	+	5.13145i	−0.0865623	+	0.266411i
$372$		0			0
$373$	12.4317			0.643690			0.321845	−	0.946792i	$-0.395697\pi$
$373$	12.4317			0.643690			0.321845	+	0.946792i	$0.395697\pi$
$374$		0			0
$375$	−10.6087			−0.547830
$376$		0			0
$377$	−8.09468	+	24.9129i	−0.416897	+	1.28308i
$378$		0			0
$379$	24.9720	−	18.1432i	1.28272	−	0.931954i	0.283093	−	0.959093i	$-0.408640\pi$
$379$	24.9720	−	18.1432i	1.28272	−	0.931954i	0.999632	+	0.0271386i	$0.00863953\pi$
$380$		0			0
$381$	−0.158797	−	0.488728i	−0.00813544	−	0.0250383i
$382$		0			0
$383$	30.6757	+	22.2872i	1.56746	+	1.13882i	0.929541	+	0.368719i	$0.120204\pi$
$383$	30.6757	+	22.2872i	1.56746	+	1.13882i	0.637917	+	0.770105i	$0.279796\pi$
$384$		0			0
$385$	1.59443	−	1.61947i	0.0812597	−	0.0825360i
$386$		0			0
$387$	−8.28737	−	6.02112i	−0.421270	−	0.306071i
$388$		0			0
$389$	−8.99871	−	27.6952i	−0.456253	−	1.40420i	−0.869658	−	0.493654i	$-0.835661\pi$
$389$	−8.99871	−	27.6952i	−0.456253	−	1.40420i	0.413406	−	0.910547i	$-0.364339\pi$
$390$		0			0
$391$	−29.8319	+	21.6741i	−1.50866	+	1.09611i
$392$		0			0
$393$	−4.79049	+	14.7436i	−0.241648	+	0.743717i
$394$		0			0
$395$	5.25332			0.264323
$396$		0			0
$397$	12.4889			0.626800			0.313400	−	0.949621i	$-0.398532\pi$
$397$	12.4889			0.626800			0.313400	+	0.949621i	$0.398532\pi$
$398$		0			0
$399$	0.153920	−	0.473716i	0.00770563	−	0.0237155i
$400$		0			0
$401$	15.1991	−	11.0428i	0.759007	−	0.551451i	−0.139599	−	0.990208i	$-0.544581\pi$
$401$	15.1991	−	11.0428i	0.759007	−	0.551451i	0.898606	+	0.438757i	$0.144581\pi$
$402$		0			0
$403$	2.72659	+	8.39157i	0.135821	+	0.418014i
$404$		0			0
$405$	−1.02076	−	0.741628i	−0.0507222	−	0.0368518i
$406$		0			0
$407$	−24.7794	+	4.12283i	−1.22827	+	0.204361i
$408$		0			0
$409$	30.3265	+	22.0335i	1.49955	+	1.08949i	0.970561	+	0.240857i	$0.0774284\pi$
$409$	30.3265	+	22.0335i	1.49955	+	1.08949i	0.528988	+	0.848629i	$0.322572\pi$
$410$		0			0
$411$	0.322354	+	0.992102i	0.0159005	+	0.0489368i
$412$		0			0
$413$	3.73414	−	2.71301i	0.183745	−	0.133499i
$414$		0			0
$415$	5.22161	−	16.0705i	0.256319	−	0.788868i
$416$		0			0
$417$	−15.1429			−0.741553
$418$		0			0
$419$	16.7087			0.816272			0.408136	−	0.912921i	$-0.366179\pi$
$419$	16.7087			0.816272			0.408136	+	0.912921i	$0.366179\pi$
$420$		0			0
$421$	1.42450	−	4.38416i	0.0694259	−	0.213671i	−0.910324	−	0.413897i	$-0.864168\pi$
$421$	1.42450	−	4.38416i	0.0694259	−	0.213671i	0.979750	+	0.200226i	$0.0641675\pi$
$422$		0			0
$423$	3.37452	−	2.45173i	0.164075	−	0.119207i
$424$		0			0
$425$	4.89776	+	15.0738i	0.237576	+	0.731185i
$426$		0			0
$427$	−0.0704501	−	0.0511850i	−0.00340932	−	0.00247702i
$428$		0			0
$429$	4.08440	+	7.86400i	0.197197	+	0.379677i
$430$		0			0
$431$	4.49014	+	3.26228i	0.216282	+	0.157138i	0.690652	−	0.723188i	$-0.257324\pi$
$431$	4.49014	+	3.26228i	0.216282	+	0.157138i	−0.474369	+	0.880326i	$0.657324\pi$
$432$		0			0
$433$	8.78642	+	27.0418i	0.422249	+	1.29955i	0.905604	+	0.424123i	$0.139418\pi$
$433$	8.78642	+	27.0418i	0.422249	+	1.29955i	−0.483356	+	0.875424i	$0.660582\pi$
$434$		0			0
$435$	−10.0077	+	7.27104i	−0.479834	+	0.348620i
$436$		0			0
$437$	−2.24719	+	6.91612i	−0.107497	+	0.330843i
$438$		0			0
$439$	20.2313			0.965588			0.482794	−	0.875734i	$-0.339622\pi$
$439$	20.2313			0.965588			0.482794	+	0.875734i	$0.339622\pi$
$440$		0			0
$441$	−6.70506			−0.319289
$442$		0			0
$443$	−0.0735632	+	0.226404i	−0.00349509	+	0.0107568i	−0.952789	−	0.303634i	$-0.901800\pi$
$443$	−0.0735632	+	0.226404i	−0.00349509	+	0.0107568i	0.949294	+	0.314390i	$0.101800\pi$
$444$		0			0
$445$	−2.76195	+	2.00668i	−0.130929	+	0.0951256i
$446$		0			0
$447$	0.699943	+	2.15420i	0.0331061	+	0.101890i
$448$		0			0
$449$	9.40124	+	6.83040i	0.443672	+	0.322347i	0.787092	−	0.616835i	$-0.211586\pi$
$449$	9.40124	+	6.83040i	0.443672	+	0.322347i	−0.343420	+	0.939182i	$0.611586\pi$
$450$		0			0
$451$	−3.47386	−	1.73606i	−0.163578	−	0.0817480i
$452$		0			0
$453$	10.1402	+	7.36729i	0.476429	+	0.346146i
$454$		0			0
$455$	−0.565749	−	1.74120i	−0.0265227	−	0.0816286i
$456$		0			0
$457$	−17.6473	+	12.8215i	−0.825506	+	0.599765i	−0.918284	−	0.395922i	$-0.870425\pi$
$457$	−17.6473	+	12.8215i	−0.825506	+	0.599765i	0.0927784	+	0.995687i	$0.470425\pi$
$458$		0			0
$459$	−1.43712	+	4.42301i	−0.0670792	+	0.206449i
$460$		0			0
$461$	24.7325			1.15191			0.575954	−	0.817482i	$-0.304631\pi$
$461$	24.7325			1.15191			0.575954	+	0.817482i	$0.304631\pi$
$462$		0			0
$463$	−38.5025			−1.78936			−0.894681	−	0.446705i	$-0.852597\pi$
$463$	−38.5025			−1.78936			−0.894681	+	0.446705i	$0.852597\pi$
$464$		0			0
$465$	−1.28760	+	3.96282i	−0.0597109	+	0.183771i
$466$		0			0
$467$	28.6985	−	20.8506i	1.32801	−	0.964853i	0.328211	−	0.944604i	$-0.393554\pi$
$467$	28.6985	−	20.8506i	1.32801	−	0.964853i	0.999795	−	0.0202484i	$-0.00644570\pi$
$468$		0			0
$469$	0.440810	+	1.35667i	0.0203547	+	0.0626454i
$470$		0			0
$471$	8.05261	+	5.85057i	0.371045	+	0.269580i
$472$		0			0
$473$	−5.05320	+	33.5968i	−0.232346	+	1.54478i
$474$		0			0
$475$	2.52875	+	1.83724i	0.116027	+	0.0842986i
$476$		0			0
$477$	−3.07007	−	9.44872i	−0.140569	−	0.432627i
$478$		0			0
$479$	1.06209	−	0.771652i	0.0485280	−	0.0352577i	−0.563257	−	0.826282i	$-0.690452\pi$
$479$	1.06209	−	0.771652i	0.0485280	−	0.0352577i	0.611785	+	0.791024i	$0.290452\pi$
$480$		0			0
$481$	−6.25337	+	19.2459i	−0.285129	+	0.877537i
$482$		0			0
$483$	−4.30604			−0.195932
$484$		0			0
$485$	−10.3183			−0.468530
$486$		0			0
$487$	−6.67061	+	20.5300i	−0.302274	+	0.930305i	0.678406	+	0.734687i	$0.262671\pi$
$487$	−6.67061	+	20.5300i	−0.302274	+	0.930305i	−0.980680	+	0.195618i	$0.937329\pi$
$488$		0			0
$489$	18.1128	−	13.1597i	0.819090	−	0.595104i
$490$		0			0
$491$	−11.1012	−	34.1659i	−0.500990	−	1.54189i	−0.807410	−	0.589991i	$-0.799131\pi$
$491$	−11.1012	−	34.1659i	−0.500990	−	1.54189i	0.306420	−	0.951896i	$-0.400869\pi$
$492$		0			0
$493$	36.8876	+	26.8004i	1.66133	+	1.20703i
$494$		0			0
$495$	−0.622408	+	4.13815i	−0.0279752	+	0.185996i
$496$		0			0
$497$	1.18184	+	0.858657i	0.0530128	+	0.0385160i
$498$		0			0
$499$	−1.70033	−	5.23309i	−0.0761174	−	0.234265i	0.905757	−	0.423797i	$-0.139303\pi$
$499$	−1.70033	−	5.23309i	−0.0761174	−	0.234265i	−0.981875	+	0.189532i	$0.939303\pi$
$500$		0			0
$501$	−1.29744	+	0.942643i	−0.0579652	+	0.0421142i
$502$		0			0
$503$	6.58030	−	20.2521i	0.293401	−	0.902995i	−0.690353	−	0.723473i	$-0.742545\pi$
$503$	6.58030	−	20.2521i	0.293401	−	0.902995i	0.983754	−	0.179522i	$-0.0574553\pi$
$504$		0			0
$505$	0.215364			0.00958359
$506$		0			0
$507$	−5.86138			−0.260313
$508$		0			0
$509$	9.68204	−	29.7983i	0.429149	−	1.32078i	−0.469816	−	0.882764i	$-0.655680\pi$
$509$	9.68204	−	29.7983i	0.429149	−	1.32078i	0.898965	−	0.438020i	$-0.144320\pi$
$510$		0			0
$511$	2.69593	−	1.95871i	0.119261	−	0.0866482i
$512$		0			0
$513$	0.283418	+	0.872271i	0.0125132	+	0.0385117i
$514$		0			0
$515$	8.58295	+	6.23588i	0.378210	+	0.274786i
$516$		0			0
$517$	−12.3748	−	6.18432i	−0.544244	−	0.271986i
$518$		0			0
$519$	1.76885	+	1.28514i	0.0776439	+	0.0564116i
$520$		0			0
$521$	7.06997	+	21.7591i	0.309741	+	0.953285i	0.977865	+	0.209236i	$0.0670975\pi$
$521$	7.06997	+	21.7591i	0.309741	+	0.953285i	−0.668124	+	0.744050i	$0.732902\pi$
$522$		0			0
$523$	−20.7468	+	15.0735i	−0.907196	+	0.659116i	−0.940304	−	0.340335i	$-0.889459\pi$
$523$	−20.7468	+	15.0735i	−0.907196	+	0.659116i	0.0331081	+	0.999452i	$0.489459\pi$
$524$		0			0
$525$	−0.571943	+	1.76026i	−0.0249616	+	0.0768240i
$526$		0			0
$527$	15.3583			0.669017
$528$		0			0
$529$	39.8670			1.73335
$530$		0			0
$531$	−2.62633	+	8.08300i	−0.113973	+	0.350773i
$532$		0			0
$533$	−2.53100	+	1.83888i	−0.109630	+	0.0796507i
$534$		0			0
$535$	−4.44723	−	13.6872i	−0.192271	−	0.591748i
$536$		0			0
$537$	8.37598	+	6.08551i	0.361450	+	0.262609i
$538$		0			0
$539$	10.2500	+	19.7351i	0.441498	+	0.850051i
$540$		0			0
$541$	−31.1941	−	22.6638i	−1.34114	−	0.974395i	−0.999401	−	0.0345992i	$-0.988985\pi$
$541$	−31.1941	−	22.6638i	−1.34114	−	0.974395i	−0.341738	−	0.939795i	$-0.611015\pi$
$542$		0			0
$543$	2.66388	+	8.19857i	0.114318	+	0.351834i
$544$		0			0
$545$	−7.93612	+	5.76593i	−0.339946	+	0.246985i
$546$		0			0
$547$	−12.9738	+	39.9291i	−0.554718	+	1.70725i	0.141970	+	0.989871i	$0.454656\pi$
$547$	−12.9738	+	39.9291i	−0.554718	+	1.70725i	−0.696688	+	0.717374i	$0.745344\pi$
$548$		0			0
$549$	0.160346			0.00684338
$550$		0			0
$551$	8.99198			0.383071
$552$		0			0
$553$	0.698740	−	2.15050i	0.0297134	−	0.0914485i
$554$		0			0
$555$	−7.73125	+	5.61708i	−0.328173	+	0.238432i
$556$		0			0
$557$	8.12732	+	25.0133i	0.344366	+	1.05985i	0.961922	+	0.273322i	$0.0881226\pi$
$557$	8.12732	+	25.0133i	0.344366	+	1.05985i	−0.617557	+	0.786526i	$0.711877\pi$
$558$		0			0
$559$	22.1423	+	16.0874i	0.936521	+	0.680422i
$560$		0			0
$561$	15.2152	−	2.53153i	0.642388	−	0.106881i
$562$		0			0
$563$	14.0239	+	10.1889i	0.591035	+	0.429412i	0.842686	−	0.538406i	$-0.180973\pi$
$563$	14.0239	+	10.1889i	0.591035	+	0.429412i	−0.251650	+	0.967818i	$0.580973\pi$
$564$		0			0
$565$	2.63998	+	8.12503i	0.111065	+	0.341822i
$566$		0			0
$567$	−0.439364	+	0.319217i	−0.0184516	+	0.0134058i
$568$		0			0
$569$	1.60157	−	4.92913i	0.0671414	−	0.206640i	−0.911857	−	0.410508i	$-0.865351\pi$
$569$	1.60157	−	4.92913i	0.0671414	−	0.206640i	0.978998	+	0.203868i	$0.0653514\pi$
$570$		0			0
$571$	−44.0308			−1.84263			−0.921316	−	0.388815i	$-0.872885\pi$
$571$	−44.0308			−1.84263			−0.921316	+	0.388815i	$0.872885\pi$
$572$		0			0
$573$	−3.39025			−0.141630
$574$		0			0
$575$	8.35020	−	25.6993i	0.348227	−	1.07173i
$576$		0			0
$577$	−21.3772	+	15.5314i	−0.889942	+	0.646581i	−0.935863	−	0.352364i	$-0.885378\pi$
$577$	−21.3772	+	15.5314i	−0.889942	+	0.646581i	0.0459206	+	0.998945i	$0.485378\pi$
$578$		0			0
$579$	−6.19776	−	19.0747i	−0.257570	−	0.792719i
$580$		0			0
$581$	−5.88409	−	4.27504i	−0.244113	−	0.177359i
$582$		0			0
$583$	−23.1173	+	23.4804i	−0.957422	+	0.972458i
$584$		0			0
$585$	2.72730	+	1.98150i	0.112760	+	0.0819248i
$586$		0			0
$587$	6.42363	+	19.7699i	0.265132	+	0.815991i	0.991663	+	0.128858i	$0.0411312\pi$
$587$	6.42363	+	19.7699i	0.265132	+	0.815991i	−0.726531	+	0.687133i	$0.758869\pi$
$588$		0			0
$589$	2.45038	−	1.78030i	0.100966	−	0.0733561i
$590$		0			0
$591$	−6.88963	+	21.2041i	−0.283401	+	0.872220i
$592$		0			0
$593$	38.8090			1.59370			0.796848	−	0.604180i	$-0.206499\pi$
$593$	38.8090			1.59370			0.796848	+	0.604180i	$0.206499\pi$
$594$		0			0
$595$	−3.18674			−0.130644
$596$		0			0
$597$	−4.99002	+	15.3577i	−0.204228	+	0.628549i
$598$		0			0
$599$	27.2171	−	19.7744i	1.11206	−	0.807961i	0.129075	−	0.991635i	$-0.458799\pi$
$599$	27.2171	−	19.7744i	1.11206	−	0.807961i	0.982987	+	0.183674i	$0.0587991\pi$
$600$		0			0
$601$	−9.69734	−	29.8454i	−0.395563	−	1.21742i	−0.928522	−	0.371277i	$-0.878920\pi$
$601$	−9.69734	−	29.8454i	−0.395563	−	1.21742i	0.532959	−	0.846141i	$-0.321080\pi$
$602$		0			0
$603$	−2.12500	−	1.54391i	−0.0865368	−	0.0628727i
$604$		0			0
$605$	13.1313	−	4.49403i	0.533865	−	0.182708i
$606$		0			0
$607$	−35.5367	−	25.8189i	−1.44239	−	1.04796i	−0.987537	−	0.157389i	$-0.949692\pi$
$607$	−35.5367	−	25.8189i	−1.44239	−	1.04796i	−0.454852	−	0.890567i	$-0.650308\pi$
$608$		0			0
$609$	1.64536	+	5.06388i	0.0666732	+	0.205199i
$610$		0			0
$611$	−9.01611	+	6.55059i	−0.364753	+	0.265008i
$612$		0			0
$613$	−4.01487	+	12.3565i	−0.162159	+	0.499075i	−0.998816	−	0.0486531i	$-0.984507\pi$
$613$	−4.01487	+	12.3565i	−0.162159	+	0.499075i	0.836656	+	0.547728i	$0.184507\pi$
$614$		0			0
$615$	−1.47739			−0.0595741
$616$		0			0
$617$	−21.4961			−0.865401			−0.432701	−	0.901538i	$-0.642439\pi$
$617$	−21.4961			−0.865401			−0.432701	+	0.901538i	$0.642439\pi$
$618$		0			0
$619$	2.35958	−	7.26205i	0.0948396	−	0.291886i	−0.892372	−	0.451300i	$-0.850960\pi$
$619$	2.35958	−	7.26205i	0.0948396	−	0.291886i	0.987212	+	0.159414i	$0.0509604\pi$
$620$		0			0
$621$	6.41459	−	4.66047i	0.257409	−	0.187018i
$622$		0			0
$623$	0.454088	+	1.39754i	0.0181927	+	0.0559913i
$624$		0			0
$625$	−2.95680	−	2.14824i	−0.118272	−	0.0859295i
$626$		0			0
$627$	2.13411	−	2.16762i	0.0852280	−	0.0865666i
$628$		0			0
$629$	28.4967	+	20.7040i	1.13624	+	0.825524i
$630$		0			0
$631$	4.76280	+	14.6584i	0.189604	+	0.583541i	0.999997	−	0.00234540i	$-0.000746564\pi$
$631$	4.76280	+	14.6584i	0.189604	+	0.583541i	−0.810393	+	0.585886i	$0.800747\pi$
$632$		0			0
$633$	3.83447	−	2.78591i	0.152407	−	0.110730i
$634$		0			0
$635$	−0.200360	+	0.616645i	−0.00795105	+	0.0244708i
$636$		0			0
$637$	17.9147			0.709806
$638$		0			0
$639$	−2.68989			−0.106410
$640$		0			0
$641$	2.73861	−	8.42856i	0.108168	−	0.332908i	−0.882293	−	0.470701i	$-0.844001\pi$
$641$	2.73861	−	8.42856i	0.108168	−	0.332908i	0.990461	+	0.137793i	$0.0440009\pi$
$642$		0			0
$643$	−7.14036	+	5.18777i	−0.281588	+	0.204586i	−0.719610	−	0.694379i	$-0.755679\pi$
$643$	−7.14036	+	5.18777i	−0.281588	+	0.204586i	0.438022	+	0.898964i	$0.355679\pi$
$644$		0			0
$645$	3.99401	+	12.2923i	0.157264	+	0.484008i
$646$		0			0
$647$	11.9448	+	8.67838i	0.469597	+	0.341182i	0.797284	−	0.603604i	$-0.206269\pi$
$647$	11.9448	+	8.67838i	0.469597	+	0.341182i	−0.327687	+	0.944786i	$0.606269\pi$
$648$		0			0
$649$	27.8057	−	4.62634i	1.09147	−	0.181600i
$650$		0			0
$651$	1.45096	+	1.05418i	0.0568675	+	0.0413167i
$652$		0			0
$653$	2.12825	+	6.55008i	0.0832849	+	0.256325i	0.984024	−	0.178036i	$-0.0569744\pi$
$653$	2.12825	+	6.55008i	0.0832849	+	0.256325i	−0.900739	+	0.434361i	$0.856974\pi$
$654$		0			0
$655$	15.8242	−	11.4970i	0.618304	−	0.449224i
$656$		0			0
$657$	−1.89612	+	5.83567i	−0.0739748	+	0.227671i
$658$		0			0
$659$	4.45910			0.173702			0.0868509	−	0.996221i	$-0.472320\pi$
$659$	4.45910			0.173702			0.0868509	+	0.996221i	$0.472320\pi$
$660$		0			0
$661$	26.6538			1.03671			0.518356	−	0.855165i	$-0.326544\pi$
$661$	26.6538			1.03671			0.518356	+	0.855165i	$0.326544\pi$
$662$		0			0
$663$	3.83974	−	11.8175i	0.149123	−	0.458953i
$664$		0			0
$665$	−0.508437	+	0.369401i	−0.0197164	+	0.0143248i
$666$		0			0
$667$	−24.0217	−	73.9312i	−0.930125	−	2.86263i
$668$		0			0
$669$	−22.7284	−	16.5132i	−0.878731	−	0.638435i
$670$		0			0
$671$	−0.245120	−	0.471947i	−0.00946273	−	0.0182193i
$672$		0			0
$673$	−3.36374	−	2.44390i	−0.129663	−	0.0942055i	0.521064	−	0.853518i	$-0.325535\pi$
$673$	−3.36374	−	2.44390i	−0.129663	−	0.0942055i	−0.650726	+	0.759312i	$0.725535\pi$
$674$		0			0
$675$	−1.05314	−	3.24123i	−0.0405353	−	0.124755i
$676$		0			0
$677$	−6.06506	+	4.40653i	−0.233099	+	0.169357i	−0.698203	−	0.715899i	$-0.746017\pi$
$677$	−6.06506	+	4.40653i	−0.233099	+	0.169357i	0.465104	+	0.885256i	$0.346017\pi$
$678$		0			0
$679$	−1.37243	+	4.22391i	−0.0526691	+	0.162099i
$680$		0			0
$681$	−23.2917			−0.892540
$682$		0			0
$683$	15.9932			0.611962			0.305981	−	0.952038i	$-0.401016\pi$
$683$	15.9932			0.611962			0.305981	+	0.952038i	$0.401016\pi$
$684$		0			0
$685$	0.406724	−	1.25177i	0.0155401	−	0.0478276i
$686$		0			0
$687$	−14.3592	+	10.4326i	−0.547837	+	0.398027i
$688$		0			0
$689$	8.20268	+	25.2453i	0.312497	+	0.961768i
$690$		0			0
$691$	22.0240	+	16.0014i	0.837831	+	0.608720i	0.921764	−	0.387751i	$-0.126748\pi$
$691$	22.0240	+	16.0014i	0.837831	+	0.608720i	−0.0839326	+	0.996471i	$0.526748\pi$
$692$		0			0
$693$	1.61121	+	0.805201i	0.0612048	+	0.0305871i
$694$		0			0
$695$	15.4574	+	11.2304i	0.586332	+	0.425995i
$696$		0			0
$697$	1.68276	+	5.17900i	0.0637391	+	0.196169i
$698$		0			0
$699$	−18.9468	+	13.7656i	−0.716632	+	0.520664i
$700$		0			0
$701$	2.23858	−	6.88964i	0.0845500	−	0.260218i	−0.899840	−	0.436221i	$-0.856317\pi$
$701$	2.23858	−	6.88964i	0.0845500	−	0.260218i	0.984390	+	0.176003i	$0.0563167\pi$
$702$		0			0
$703$	6.94656			0.261994
$704$		0			0
$705$	−5.26286			−0.198211
$706$		0			0
$707$	0.0286455	−	0.0881616i	0.00107732	−	0.00331566i
$708$		0			0
$709$	−22.4505	+	16.3112i	−0.843145	+	0.612581i	−0.923247	−	0.384206i	$-0.874475\pi$
$709$	−22.4505	+	16.3112i	−0.843145	+	0.612581i	0.0801023	+	0.996787i	$0.474475\pi$
$710$		0			0
$711$	1.28661	+	3.95979i	0.0482518	+	0.148504i
$712$		0			0
$713$	−21.1836	−	15.3908i	−0.793331	−	0.576389i
$714$		0			0
$715$	1.66296	−	11.0564i	0.0621912	−	0.413486i
$716$		0			0
$717$	17.1748	+	12.4782i	0.641403	+	0.466007i
$718$		0			0
$719$	−9.13018	−	28.0998i	−0.340498	−	1.04795i	−0.963950	−	0.266084i	$-0.914270\pi$
$719$	−9.13018	−	28.0998i	−0.340498	−	1.04795i	0.623452	−	0.781862i	$-0.285730\pi$
$720$		0			0
$721$	3.69433	−	2.68409i	0.137584	−	0.0999607i
$722$		0			0
$723$	−0.380685	+	1.17163i	−0.0141578	+	0.0435733i
$724$		0			0
$725$	−33.4129			−1.24092
$726$		0			0
$727$	35.9365			1.33281			0.666406	−	0.745589i	$-0.267832\pi$
$727$	35.9365			1.33281			0.666406	+	0.745589i	$0.267832\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	38.5415	−	28.0020i	1.42551	−	1.03569i
$732$		0			0
$733$	−12.6573	−	38.9552i	−0.467508	−	1.43884i	−0.855801	−	0.517305i	$-0.826935\pi$
$733$	−12.6573	−	38.9552i	−0.467508	−	1.43884i	0.388293	−	0.921536i	$-0.373065\pi$
$734$		0			0
$735$	6.84428	+	4.97266i	0.252455	+	0.183419i
$736$		0			0
$737$	−1.29571	+	8.61471i	−0.0477283	+	0.317327i
$738$		0			0
$739$	20.7506	+	15.0762i	0.763322	+	0.554586i	0.899927	−	0.436040i	$-0.143619\pi$
$739$	20.7506	+	15.0762i	0.763322	+	0.554586i	−0.136606	+	0.990625i	$0.543619\pi$
$740$		0			0
$741$	−0.757242	−	2.33055i	−0.0278180	−	0.0856149i
$742$		0			0
$743$	−2.36606	+	1.71904i	−0.0868023	+	0.0630655i	−0.630340	−	0.776319i	$-0.717084\pi$
$743$	−2.36606	+	1.71904i	−0.0868023	+	0.0630655i	0.543538	+	0.839385i	$0.317084\pi$
$744$		0			0
$745$	0.883141	−	2.71803i	0.0323558	−	0.0995809i
$746$		0			0
$747$	13.3923			0.489998
$748$		0			0
$749$	−6.19451			−0.226342
$750$		0			0
$751$	5.62802	−	17.3213i	0.205370	−	0.632062i	−0.794328	−	0.607488i	$-0.792177\pi$
$751$	5.62802	−	17.3213i	0.205370	−	0.632062i	0.999698	−	0.0245739i	$-0.00782291\pi$
$752$		0			0
$753$	11.7203	−	8.51526i	0.427110	−	0.310313i
$754$		0			0
$755$	−4.88697	−	15.0405i	−0.177855	−	0.547381i
$756$		0			0
$757$	−13.0694	−	9.49549i	−0.475016	−	0.345119i	0.324377	−	0.945928i	$-0.394845\pi$
$757$	−13.0694	−	9.49549i	−0.475016	−	0.345119i	−0.799393	+	0.600809i	$0.794845\pi$
$758$		0			0
$759$	−23.5232	−	11.7557i	−0.853838	−	0.426705i
$760$		0			0
$761$	10.5978	+	7.69976i	0.384171	+	0.279116i	0.763063	−	0.646325i	$-0.223695\pi$
$761$	10.5978	+	7.69976i	0.384171	+	0.279116i	−0.378892	+	0.925441i	$0.623695\pi$
$762$		0			0
$763$	1.30476	+	4.01565i	0.0472357	+	0.145376i
$764$		0			0
$765$	4.74720	−	3.44904i	0.171635	−	0.124700i
$766$		0			0
$767$	7.01707	−	21.5963i	0.253372	−	0.779798i
$768$		0			0
$769$	20.2660			0.730812			0.365406	−	0.930848i	$-0.380930\pi$
$769$	20.2660			0.730812			0.365406	+	0.930848i	$0.380930\pi$
$770$		0			0
$771$	5.97145			0.215057
$772$		0			0
$773$	4.03968	−	12.4329i	0.145297	−	0.447179i	−0.851752	−	0.523945i	$-0.824460\pi$
$773$	4.03968	−	12.4329i	0.145297	−	0.447179i	0.997049	+	0.0767663i	$0.0244595\pi$
$774$		0			0
$775$	−9.10523	+	6.61534i	−0.327070	+	0.237630i
$776$		0			0
$777$	1.27108	+	3.91199i	0.0455998	+	0.140342i
$778$		0			0
$779$	0.868821	+	0.631236i	0.0311288	+	0.0226164i
$780$		0			0
$781$	4.11202	+	7.91718i	0.147140	+	0.283299i
$782$		0			0
$783$	−7.93173	−	5.76274i	−0.283457	−	0.205944i
$784$		0			0
$785$	−3.88087	−	11.9441i	−0.138514	−	0.426303i
$786$		0			0
$787$	−36.8800	+	26.7949i	−1.31463	+	0.955136i	−0.314649	+	0.949208i	$0.601887\pi$
$787$	−36.8800	+	26.7949i	−1.31463	+	0.955136i	−0.999982	+	0.00592778i	$0.998113\pi$
$788$		0			0
$789$	8.09264	−	24.9066i	0.288106	−	0.886698i
$790$		0			0
$791$	3.67720			0.130746
$792$		0			0
$793$	−0.428414			−0.0152134
$794$		0			0
$795$	−3.87361	+	11.9218i	−0.137383	+	0.422821i
$796$		0			0
$797$	−19.8237	+	14.4027i	−0.702190	+	0.510171i	−0.880645	−	0.473777i	$-0.842890\pi$
$797$	−19.8237	+	14.4027i	−0.702190	+	0.510171i	0.178454	+	0.983948i	$0.442890\pi$
$798$		0			0
$799$	5.99444	+	18.4490i	0.212068	+	0.652679i
$800$		0			0
$801$	−2.18901	−	1.59041i	−0.0773450	−	0.0561945i
$802$		0			0
$803$	20.0748	−	3.34007i	0.708424	−	0.117869i
$804$		0			0
$805$	4.39545	+	3.19348i	0.154919	+	0.112556i
$806$		0			0
$807$	−6.56883	−	20.2168i	−0.231234	−	0.711665i
$808$		0			0
$809$	21.8891	−	15.9034i	0.769581	−	0.559133i	−0.132253	−	0.991216i	$-0.542221\pi$
$809$	21.8891	−	15.9034i	0.769581	−	0.559133i	0.901834	+	0.432083i	$0.142221\pi$
$810$		0			0
$811$	−5.81313	+	17.8910i	−0.204127	+	0.628237i	0.795621	+	0.605794i	$0.207144\pi$
$811$	−5.81313	+	17.8910i	−0.204127	+	0.628237i	−0.999748	+	0.0224432i	$0.992856\pi$
$812$		0			0
$813$	−1.06914			−0.0374963
$814$		0			0
$815$	−28.2485			−0.989503
$816$		0			0
$817$	2.90326	−	8.93532i	0.101572	−	0.312607i
$818$		0			0
$819$	1.17390	−	0.852889i	0.0410194	−	0.0298024i
$820$		0			0
$821$	0.472048	+	1.45281i	0.0164746	+	0.0507035i	0.958956	−	0.283555i	$-0.0915140\pi$
$821$	0.472048	+	1.45281i	0.0164746	+	0.0507035i	−0.942481	+	0.334259i	$0.891514\pi$
$822$		0			0
$823$	1.87252	+	1.36047i	0.0652720	+	0.0474229i	0.619943	−	0.784647i	$-0.287156\pi$
$823$	1.87252	+	1.36047i	0.0652720	+	0.0474229i	−0.554671	+	0.832070i	$0.687156\pi$
$824$		0			0
$825$	−7.93002	+	8.05457i	−0.276088	+	0.280424i
$826$		0			0
$827$	16.8428	+	12.2370i	0.585680	+	0.425522i	0.840767	−	0.541396i	$-0.182104\pi$
$827$	16.8428	+	12.2370i	0.585680	+	0.425522i	−0.255087	+	0.966918i	$0.582104\pi$
$828$		0			0
$829$	8.58521	+	26.4226i	0.298177	+	0.917694i	0.982136	+	0.188173i	$0.0602567\pi$
$829$	8.58521	+	26.4226i	0.298177	+	0.917694i	−0.683959	+	0.729520i	$0.739743\pi$
$830$		0			0
$831$	−13.1821	+	9.57736i	−0.457282	+	0.332235i
$832$		0			0
$833$	9.63601	−	29.6566i	0.333868	−	1.02754i
$834$		0			0
$835$	2.02347			0.0700250
$836$		0			0
$837$	−3.30240			−0.114148
$838$		0			0
$839$	4.73552	−	14.5744i	0.163488	−	0.503165i	−0.835433	−	0.549592i	$-0.814783\pi$
$839$	4.73552	−	14.5744i	0.163488	−	0.503165i	0.998922	+	0.0464265i	$0.0147833\pi$
$840$		0			0
$841$	−54.3025	+	39.4530i	−1.87250	+	1.36045i
$842$		0			0
$843$	−1.67712	−	5.16165i	−0.0577631	−	0.177777i
$844$		0			0
$845$	5.98309	+	4.34697i	0.205825	+	0.149540i
$846$		0			0
$847$	−0.0930872	−	5.97320i	−0.00319851	−	0.205242i
$848$		0			0
$849$	−0.0586130	−	0.0425848i	−0.00201159	−	0.00146151i
$850$		0			0
$851$	−18.5574	−	57.1139i	−0.636141	−	1.95784i
$852$		0			0
$853$	−16.0505	+	11.6614i	−0.549558	+	0.399278i	−0.827623	−	0.561285i	$-0.810307\pi$
$853$	−16.0505	+	11.6614i	−0.549558	+	0.399278i	0.278064	+	0.960562i	$0.410307\pi$
$854$		0			0
$855$	0.357598	−	1.10057i	0.0122296	−	0.0376388i
$856$		0			0
$857$	−19.0643			−0.651225			−0.325613	−	0.945503i	$-0.605571\pi$
$857$	−19.0643			−0.651225			−0.325613	+	0.945503i	$0.605571\pi$
$858$		0			0
$859$	−39.6848			−1.35403			−0.677014	−	0.735970i	$-0.736726\pi$
$859$	−39.6848			−1.35403			−0.677014	+	0.735970i	$0.736726\pi$
$860$		0			0
$861$	−0.196507	+	0.604785i	−0.00669693	+	0.0206110i
$862$		0			0
$863$	−2.98630	+	2.16967i	−0.101655	+	0.0738565i	−0.637451	−	0.770491i	$-0.720011\pi$
$863$	−2.98630	+	2.16967i	−0.101655	+	0.0738565i	0.535797	+	0.844347i	$0.320011\pi$
$864$		0			0
$865$	−0.852478	−	2.62366i	−0.0289851	−	0.0892070i
$866$		0			0
$867$	−3.74444	−	2.72050i	−0.127168	−	0.0923929i
$868$		0			0
$869$	9.68807	−	9.84022i	0.328645	−	0.333807i
$870$		0			0
$871$	5.67762	+	4.12504i	0.192379	+	0.139771i
$872$		0			0
$873$	−2.52711	−	7.77763i	−0.0855296	−	0.263233i
$874$		0			0
$875$	4.66108	−	3.38647i	0.157573	−	0.114484i
$876$		0			0
$877$	−9.19166	+	28.2890i	−0.310380	+	0.955252i	0.667234	+	0.744848i	$0.267478\pi$
$877$	−9.19166	+	28.2890i	−0.310380	+	0.955252i	−0.977614	+	0.210404i	$0.932522\pi$
$878$		0			0
$879$	−3.18637			−0.107474
$880$		0			0
$881$	−52.9912			−1.78532			−0.892660	−	0.450731i	$-0.851163\pi$
$881$	−52.9912			−1.78532			−0.892660	+	0.450731i	$0.851163\pi$
$882$		0			0
$883$	−2.24579	+	6.91183i	−0.0755768	+	0.232602i	−0.981707	−	0.190397i	$-0.939022\pi$
$883$	−2.24579	+	6.91183i	−0.0755768	+	0.232602i	0.906130	+	0.422999i	$0.139022\pi$
$884$		0			0
$885$	8.67545	−	6.30308i	0.291622	−	0.211876i
$886$		0			0
$887$	16.9828	+	52.2677i	0.570227	+	1.75498i	0.651885	+	0.758318i	$0.273979\pi$
$887$	16.9828	+	52.2677i	0.570227	+	1.75498i	−0.0816575	+	0.996660i	$0.526021\pi$
$888$		0			0
$889$	0.225780	+	0.164039i	0.00757242	+	0.00550169i
$890$		0			0
$891$	−3.27165	+	0.544342i	−0.109604	+	0.0182361i
$892$		0			0
$893$	3.09498	+	2.24863i	0.103569	+	0.0752476i
$894$		0			0
$895$	−4.03672	−	12.4237i	−0.134933	−	0.415280i
$896$		0			0
$897$	−17.1386	+	12.4519i	−0.572242	+	0.415758i
$898$		0			0
$899$	−10.0051	+	30.7926i	−0.333690	+	1.02699i
$900$		0			0
$901$	46.2039			1.53927
$902$		0			0
$903$	5.56321			0.185132
$904$		0			0
$905$	3.36110	−	10.3444i	0.111727	−	0.343860i
$906$		0			0
$907$	18.9567	−	13.7728i	0.629447	−	0.457320i	−0.226762	−	0.973950i	$-0.572814\pi$
$907$	18.9567	−	13.7728i	0.629447	−	0.457320i	0.856209	+	0.516630i	$0.172814\pi$
$908$		0			0
$909$	0.0527459	+	0.162335i	0.00174947	+	0.00538432i
$910$		0			0
$911$	33.4577	+	24.3085i	1.10850	+	0.805376i	0.982427	−	0.186645i	$-0.0597613\pi$
$911$	33.4577	+	24.3085i	1.10850	+	0.805376i	0.126077	+	0.992020i	$0.459761\pi$
$912$		0			0
$913$	−20.4727	−	39.4177i	−0.677548	−	1.30453i
$914$		0			0
$915$	−0.163675	−	0.118917i	−0.00541093	−	0.00393127i
$916$		0			0
$917$	−2.60164	−	8.00702i	−0.0859136	−	0.264415i
$918$		0			0
$919$	−8.99997	+	6.53886i	−0.296882	+	0.215697i	−0.726247	−	0.687434i	$-0.758737\pi$
$919$	−8.99997	+	6.53886i	−0.296882	+	0.215697i	0.429365	+	0.903131i	$0.358737\pi$
$920$		0			0
$921$	3.61141	−	11.1148i	0.119000	−	0.366244i
$922$		0			0
$923$	7.18689			0.236559
$924$		0			0
$925$	−25.8124			−0.848705
$926$		0			0
$927$	−2.59832	+	7.99682i	−0.0853402	+	0.262650i
$928$		0			0
$929$	39.2999	−	28.5531i	1.28939	−	0.936795i	0.289595	−	0.957149i	$-0.406479\pi$
$929$	39.2999	−	28.5531i	1.28939	−	0.936795i	0.999793	+	0.0203537i	$0.00647925\pi$
$930$		0			0
$931$	−1.90033	−	5.84863i	−0.0622810	−	0.191681i
$932$		0			0
$933$	−20.4993	−	14.8936i	−0.671117	−	0.487595i
$934$		0			0
$935$	−17.4086	−	8.69996i	−0.569323	−	0.284519i
$936$		0			0
$937$	−34.9622	−	25.4015i	−1.14217	−	0.829832i	−0.154746	−	0.987954i	$-0.549456\pi$
$937$	−34.9622	−	25.4015i	−1.14217	−	0.829832i	−0.987420	+	0.158122i	$0.949456\pi$
$938$		0			0
$939$	8.82514	+	27.1610i	0.287998	+	0.886366i
$940$		0			0
$941$	0.459262	−	0.333673i	0.0149715	−	0.0108774i	−0.580274	−	0.814421i	$-0.697055\pi$
$941$	0.459262	−	0.333673i	0.0149715	−	0.0108774i	0.595246	+	0.803544i	$0.297055\pi$
$942$		0			0
$943$	2.86894	−	8.82969i	0.0934255	−	0.287534i
$944$		0			0
$945$	0.685227			0.0222904
$946$		0			0
$947$	23.5465			0.765159			0.382579	−	0.923923i	$-0.375036\pi$
$947$	23.5465			0.765159			0.382579	+	0.923923i	$0.375036\pi$
$948$		0			0
$949$	5.06610	−	15.5918i	0.164452	−	0.506133i
$950$		0			0
$951$	−17.6882	+	12.8512i	−0.573578	+	0.416729i
$952$		0			0
$953$	−14.9261	−	45.9378i	−0.483504	−	1.48807i	−0.834136	−	0.551559i	$-0.814033\pi$
$953$	−14.9261	−	45.9378i	−0.483504	−	1.48807i	0.350632	−	0.936513i	$-0.385967\pi$
$954$		0			0
$955$	3.46065	+	2.51431i	0.111984	+	0.0813611i
$956$		0			0
$957$	−4.83635	+	32.1550i	−0.156337	+	1.03942i
$958$		0			0
$959$	−0.458326	−	0.332993i	−0.0148001	−	0.0107529i
$960$		0			0
$961$	−6.20943	−	19.1107i	−0.200304	−	0.616473i
$962$		0			0
$963$	9.22778	−	6.70438i	0.297361	−	0.216045i
$964$		0			0
$965$	−7.81992	+	24.0672i	−0.251732	+	0.774752i
$966$		0			0
$967$	27.7356			0.891916			0.445958	−	0.895054i	$-0.352863\pi$
$967$	27.7356			0.891916			0.445958	+	0.895054i	$0.352863\pi$
$968$		0			0
$969$	−4.26537			−0.137024
$970$		0			0
$971$	−3.08190	+	9.48510i	−0.0989028	+	0.304391i	−0.988251	−	0.152839i	$-0.951158\pi$
$971$	−3.08190	+	9.48510i	−0.0989028	+	0.304391i	0.889348	+	0.457230i	$0.151158\pi$
$972$		0			0
$973$	6.65327	−	4.83388i	0.213294	−	0.154967i
$974$		0			0
$975$	2.81380	+	8.65997i	0.0901136	+	0.277341i
$976$		0			0
$977$	−21.0418	−	15.2877i	−0.673186	−	0.489098i	0.197904	−	0.980221i	$-0.436587\pi$
$977$	−21.0418	−	15.2877i	−0.673186	−	0.489098i	−0.871090	+	0.491123i	$0.836587\pi$
$978$		0			0
$979$	−1.33475	+	8.87421i	−0.0426587	+	0.283621i
$980$		0			0
$981$	−6.28985	−	4.56985i	−0.200820	−	0.145904i
$982$		0			0
$983$	−12.5154	−	38.5184i	−0.399179	−	1.22855i	−0.925659	−	0.378359i	$-0.876488\pi$
$983$	−12.5154	−	38.5184i	−0.399179	−	1.22855i	0.526480	−	0.850188i	$-0.323512\pi$
$984$		0			0
$985$	22.7582	−	16.5348i	0.725138	−	0.526843i
$986$		0			0
$987$	−0.700009	+	2.15441i	−0.0222815	+	0.0685755i
$988$		0			0
$989$	−81.2213			−2.58269
$990$		0			0
$991$	−25.5128			−0.810441			−0.405221	−	0.914219i	$-0.632805\pi$
$991$	−25.5128			−0.810441			−0.405221	+	0.914219i	$0.632805\pi$
$992$		0			0
$993$	10.5942	−	32.6056i	0.336196	−	1.03471i
$994$		0			0
$995$	16.4834	−	11.9759i	0.522557	−	0.379660i
$996$		0			0
$997$	−13.5397	−	41.6709i	−0.428806	−	1.31973i	−0.899302	−	0.437328i	$-0.855925\pi$
$997$	−13.5397	−	41.6709i	−0.428806	−	1.31973i	0.470496	−	0.882402i	$-0.344075\pi$
$998$		0			0
$999$	−6.12748	−	4.45188i	−0.193865	−	0.140851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1056.2.y.e.961.1	yes	12
4.3	odd	2		1056.2.y.j.961.1	yes	12
11.3	even	5	inner	1056.2.y.e.289.1	✓	12
44.3	odd	10		1056.2.y.j.289.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1056.2.y.e.289.1	✓	12	11.3	even	5	inner
1056.2.y.e.961.1	yes	12	1.1	even	1	trivial
1056.2.y.j.289.1	yes	12	44.3	odd	10
1056.2.y.j.961.1	yes	12	4.3	odd	2

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:	\( N \)	\(=\)	\( 1056 = 2^{5} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1056.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{3} +(-1.02076 + 0.741628i) q^{5} +(0.167822 + 0.516504i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-0.493296 + 3.27973i) q^{11} +(2.16155 + 1.57046i) q^{13} +(0.389897 + 1.19998i) q^{15} +(3.76244 - 2.73357i) q^{17} +(0.283418 - 0.872271i) q^{19} +0.543084 q^{21} -7.92887 q^{23} +(-1.05314 + 3.24123i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(3.02965 + 9.32431i) q^{29} +(2.67170 + 1.94110i) q^{31} +(2.96678 + 1.48265i) q^{33} +(-0.554361 - 0.402766i) q^{35} +(2.34049 + 7.20329i) q^{37} +(2.16155 - 1.57046i) q^{39} +(-0.361835 + 1.11361i) q^{41} +10.2437 q^{43} +1.26173 q^{45} +(-1.28895 + 3.96699i) q^{47} +(5.42451 - 3.94114i) q^{49} +(-1.43712 - 4.42301i) q^{51} +(8.03756 + 5.83963i) q^{53} +(-1.92881 - 3.71368i) q^{55} +(-0.741998 - 0.539093i) q^{57} +(-2.62633 - 8.08300i) q^{59} +(-0.129722 + 0.0942488i) q^{61} +(0.167822 - 0.516504i) q^{63} -3.37112 q^{65} +2.62665 q^{67} +(-2.45016 + 7.54080i) q^{69} +(2.17617 - 1.58108i) q^{71} +(-1.89612 - 5.83567i) q^{73} +(2.75715 + 2.00319i) q^{75} +(-1.77678 + 0.295623i) q^{77} +(-3.36840 - 2.44729i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-10.8346 + 7.87178i) q^{83} +(-1.81327 + 5.58067i) q^{85} +9.80416 q^{87} +2.70577 q^{89} +(-0.448390 + 1.38000i) q^{91} +(2.67170 - 1.94110i) q^{93} +(0.357598 + 1.10057i) q^{95} +(6.61605 + 4.80684i) q^{97} +(2.32686 - 2.36341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 4 q^{7} - 3 q^{9} + 2 q^{11} - 10 q^{13} + 5 q^{15} + 12 q^{17} + 8 q^{19} + 6 q^{21} - 24 q^{23} - 7 q^{25} - 3 q^{27} + 7 q^{29} + 31 q^{31} - 3 q^{33} + 17 q^{35} + 2 q^{37} - 10 q^{39}+ \cdots - 3 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 4 * q^7 - 3 * q^9 + 2 * q^11 - 10 * q^13 + 5 * q^15 + 12 * q^17 + 8 * q^19 + 6 * q^21 - 24 * q^23 - 7 * q^25 - 3 * q^27 + 7 * q^29 + 31 * q^31 - 3 * q^33 + 17 * q^35 + 2 * q^37 - 10 * q^39 + 22 * q^41 - 40 * q^43 - 10 * q^45 + 18 * q^47 - 17 * q^49 - 8 * q^51 + 9 * q^53 - 2 * q^57 + 30 * q^59 + 12 * q^61 - 4 * q^63 - 52 * q^65 - 16 * q^67 + 6 * q^69 + 30 * q^71 + 5 * q^73 + 8 * q^75 - 14 * q^77 - 16 * q^79 - 3 * q^81 - 36 * q^83 + 30 * q^85 + 2 * q^87 - 36 * q^89 + 12 * q^91 + 31 * q^93 - 70 * q^95 + 64 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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