LMFDB - Embedded newform 1056.2.y.f.289.3

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,-3,0,0,0,0,0,-3,0,6] 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} - x^{11} + 4 x^{10} - 44 x^{9} + 108 x^{8} - 177 x^{7} + 639 x^{6} - 1146 x^{5} + 1207 x^{4} + \cdots + 3911 $ x^12 - x^11 + 4x^10 - 44x^9 + 108x^8 - 177x^7 + 639x^6 - 1146x^5 + 1207x^4 - 2363x^3 + 3313x^2 - 191x + 3911
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			289.3
Root			$-2.03004 - 2.89346i$ of defining polynomial
Character	$\chi$	$=$	1056.289
Dual form			1056.2.y.f.961.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 + 0.951057i) q^{3} +(2.62854 + 1.90975i) q^{5} +(0.345109 - 1.06214i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(3.28219 - 0.476705i) q^{11} +(2.68293 - 1.94926i) q^{13} +(-1.00401 + 3.09003i) q^{15} +(3.19018 + 2.31780i) q^{17} +(-1.93354 - 5.95084i) q^{19} +1.11680 q^{21} +0.811018 q^{23} +(1.71701 + 5.28440i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(0.250914 - 0.772235i) q^{29} +(-1.51953 + 1.10400i) q^{31} +(1.46762 + 2.97424i) q^{33} +(2.93555 - 2.13280i) q^{35} +(-1.59821 + 4.91878i) q^{37} +(2.68293 + 1.94926i) q^{39} +(-0.0363881 - 0.111991i) q^{41} -0.605048 q^{43} -3.24905 q^{45} +(-1.73634 - 5.34390i) q^{47} +(4.65408 + 3.38139i) q^{49} +(-1.21854 + 3.75028i) q^{51} +(-8.84026 + 6.42282i) q^{53} +(9.53774 + 5.01511i) q^{55} +(5.06208 - 3.67782i) q^{57} +(-1.44934 + 4.46060i) q^{59} +(-6.44984 - 4.68608i) q^{61} +(0.345109 + 1.06214i) q^{63} +10.7748 q^{65} -5.27560 q^{67} +(0.250618 + 0.771324i) q^{69} +(-10.6725 - 7.75405i) q^{71} +(-0.635354 + 1.95542i) q^{73} +(-4.49518 + 3.26594i) q^{75} +(0.626388 - 3.65065i) q^{77} +(-14.0249 + 10.1897i) q^{79} +(0.309017 - 0.951057i) q^{81} +(11.4242 + 8.30017i) q^{83} +(3.95910 + 12.1849i) q^{85} +0.811976 q^{87} +13.1623 q^{89} +(-1.14448 - 3.52234i) q^{91} +(-1.51953 - 1.10400i) q^{93} +(6.28219 - 19.3346i) q^{95} +(10.1943 - 7.40659i) q^{97} +(-2.37515 + 2.31488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 3 q^{9} + 6 q^{11} + 6 q^{13} - 5 q^{15} + 8 q^{19} + 10 q^{21} + 8 q^{23} + 9 q^{25} - 3 q^{27} + 5 q^{29} - 11 q^{31} + q^{33} + 9 q^{35} - 6 q^{37} + 6 q^{39} - 10 q^{41} - 16 q^{43}+ \cdots + q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 3 * q^9 + 6 * q^11 + 6 * q^13 - 5 * q^15 + 8 * q^19 + 10 * q^21 + 8 * q^23 + 9 * q^25 - 3 * q^27 + 5 * q^29 - 11 * q^31 + q^33 + 9 * q^35 - 6 * q^37 + 6 * q^39 - 10 * q^41 - 16 * q^43 + 10 * q^45 - 6 * q^47 + 15 * q^49 - 17 * q^53 + 4 * q^55 - 2 * q^57 - 14 * q^59 - 44 * q^61 + 20 * q^65 + 48 * q^67 - 2 * q^69 - 10 * q^71 - 3 * q^73 - 16 * q^75 + 34 * q^77 - 4 * q^79 - 3 * q^81 + 20 * q^83 - 10 * q^85 - 10 * q^87 + 44 * q^89 - 80 * q^91 - 11 * q^93 + 42 * q^95 - 16 * q^97 + q^99

Character values

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

$n$	$133$	$353$	$673$	$991$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$		0			0
$5$	2.62854	+	1.90975i	1.17552	+	0.854064i	0.991659	−	0.128888i	$-0.0411409\pi$
$5$	2.62854	+	1.90975i	1.17552	+	0.854064i	0.183859	+	0.982953i	$0.441141\pi$
$6$		0			0
$7$	0.345109	−	1.06214i	0.130439	−	0.401450i	−0.864414	−	0.502781i	$-0.832310\pi$
$7$	0.345109	−	1.06214i	0.130439	−	0.401450i	0.994853	+	0.101331i	$0.0323101\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	3.28219	−	0.476705i	0.989617	−	0.143732i
$11$	3.28219	−	0.476705i	0.989617	−	0.143732i
$12$		0			0
$13$	2.68293	−	1.94926i	0.744110	−	0.540627i	−0.149886	−	0.988703i	$-0.547891\pi$
$13$	2.68293	−	1.94926i	0.744110	−	0.540627i	0.893995	+	0.448076i	$0.147891\pi$
$14$		0			0
$15$	−1.00401	+	3.09003i	−0.259235	+	0.797843i
$16$		0			0
$17$	3.19018	+	2.31780i	0.773731	+	0.562149i	0.903091	−	0.429449i	$-0.141292\pi$
$17$	3.19018	+	2.31780i	0.773731	+	0.562149i	−0.129360	+	0.991598i	$0.541292\pi$
$18$		0			0
$19$	−1.93354	−	5.95084i	−0.443585	−	1.36522i	−0.884028	−	0.467434i	$-0.845178\pi$
$19$	−1.93354	−	5.95084i	−0.443585	−	1.36522i	0.440442	−	0.897781i	$-0.354822\pi$
$20$		0			0
$21$	1.11680			0.243705
$22$		0			0
$23$	0.811018			0.169109			0.0845545	−	0.996419i	$-0.473053\pi$
$23$	0.811018			0.169109			0.0845545	+	0.996419i	$0.473053\pi$
$24$		0			0
$25$	1.71701	+	5.28440i	0.343401	+	1.05688i
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$		0			0
$29$	0.250914	−	0.772235i	0.0465936	−	0.143400i	−0.925053	−	0.379838i	$-0.875980\pi$
$29$	0.250914	−	0.772235i	0.0465936	−	0.143400i	0.971647	+	0.236437i	$0.0759798\pi$
$30$		0			0
$31$	−1.51953	+	1.10400i	−0.272916	+	0.198285i	−0.715822	−	0.698283i	$-0.753948\pi$
$31$	−1.51953	+	1.10400i	−0.272916	+	0.198285i	0.442906	+	0.896568i	$0.353948\pi$
$32$		0			0
$33$	1.46762	+	2.97424i	0.255481	+	0.517748i
$34$		0			0
$35$	2.93555	−	2.13280i	0.496198	−	0.360509i
$36$		0			0
$37$	−1.59821	+	4.91878i	−0.262744	+	0.808642i	0.729461	+	0.684023i	$0.239771\pi$
$37$	−1.59821	+	4.91878i	−0.262744	+	0.808642i	−0.992205	+	0.124620i	$0.960229\pi$
$38$		0			0
$39$	2.68293	+	1.94926i	0.429612	+	0.312131i
$40$		0			0
$41$	−0.0363881	−	0.111991i	−0.00568286	−	0.0174900i	0.948175	−	0.317749i	$-0.102927\pi$
$41$	−0.0363881	−	0.111991i	−0.00568286	−	0.0174900i	−0.953858	+	0.300259i	$0.902927\pi$
$42$		0			0
$43$	−0.605048			−0.0922690			−0.0461345	−	0.998935i	$-0.514690\pi$
$43$	−0.605048			−0.0922690			−0.0461345	+	0.998935i	$0.514690\pi$
$44$		0			0
$45$	−3.24905			−0.484340
$46$		0			0
$47$	−1.73634	−	5.34390i	−0.253271	−	0.779488i	−0.994165	−	0.107866i	$-0.965598\pi$
$47$	−1.73634	−	5.34390i	−0.253271	−	0.779488i	0.740895	−	0.671621i	$-0.234402\pi$
$48$		0			0
$49$	4.65408	+	3.38139i	0.664869	+	0.483056i
$50$		0			0
$51$	−1.21854	+	3.75028i	−0.170630	+	0.525144i
$52$		0			0
$53$	−8.84026	+	6.42282i	−1.21430	+	0.882243i	−0.995614	−	0.0935521i	$-0.970178\pi$
$53$	−8.84026	+	6.42282i	−1.21430	+	0.882243i	−0.218688	+	0.975795i	$0.570178\pi$
$54$		0			0
$55$	9.53774	+	5.01511i	1.28607	+	0.676237i
$56$		0			0
$57$	5.06208	−	3.67782i	0.670489	−	0.487139i
$58$		0			0
$59$	−1.44934	+	4.46060i	−0.188688	+	0.580721i	−0.999992	−	0.00390262i	$-0.998758\pi$
$59$	−1.44934	+	4.46060i	−0.188688	+	0.580721i	0.811305	+	0.584623i	$0.198758\pi$
$60$		0			0
$61$	−6.44984	−	4.68608i	−0.825817	−	0.599991i	0.0925559	−	0.995707i	$-0.470496\pi$
$61$	−6.44984	−	4.68608i	−0.825817	−	0.599991i	−0.918373	+	0.395716i	$0.870496\pi$
$62$		0			0
$63$	0.345109	+	1.06214i	0.0434797	+	0.133817i
$64$		0			0
$65$	10.7748			1.33645
$66$		0			0
$67$	−5.27560			−0.644518			−0.322259	−	0.946652i	$-0.604442\pi$
$67$	−5.27560			−0.644518			−0.322259	+	0.946652i	$0.604442\pi$
$68$		0			0
$69$	0.250618	+	0.771324i	0.0301709	+	0.0928565i
$70$		0			0
$71$	−10.6725	−	7.75405i	−1.26660	−	0.920237i	−0.267536	−	0.963548i	$-0.586209\pi$
$71$	−10.6725	−	7.75405i	−1.26660	−	0.920237i	−0.999062	+	0.0433112i	$0.986209\pi$
$72$		0			0
$73$	−0.635354	+	1.95542i	−0.0743626	+	0.228864i	−0.981328	−	0.192340i	$-0.938392\pi$
$73$	−0.635354	+	1.95542i	−0.0743626	+	0.228864i	0.906966	+	0.421204i	$0.138392\pi$
$74$		0			0
$75$	−4.49518	+	3.26594i	−0.519059	+	0.377118i
$76$		0			0
$77$	0.626388	−	3.65065i	0.0713835	−	0.416030i
$78$		0			0
$79$	−14.0249	+	10.1897i	−1.57792	+	1.14643i	−0.658889	+	0.752241i	$0.728973\pi$
$79$	−14.0249	+	10.1897i	−1.57792	+	1.14643i	−0.919031	+	0.394185i	$0.871027\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	11.4242	+	8.30017i	1.25397	+	0.911063i	0.998445	−	0.0557400i	$-0.0177518\pi$
$83$	11.4242	+	8.30017i	1.25397	+	0.911063i	0.255525	+	0.966803i	$0.417752\pi$
$84$		0			0
$85$	3.95910	+	12.1849i	0.429425	+	1.32163i
$86$		0			0
$87$	0.811976			0.0870529
$88$		0			0
$89$	13.1623			1.39520			0.697598	−	0.716490i	$-0.254252\pi$
$89$	13.1623			1.39520			0.697598	+	0.716490i	$0.254252\pi$
$90$		0			0
$91$	−1.14448	−	3.52234i	−0.119974	−	0.369242i
$92$		0			0
$93$	−1.51953	−	1.10400i	−0.157568	−	0.114480i
$94$		0			0
$95$	6.28219	−	19.3346i	0.644539	−	1.98369i
$96$		0			0
$97$	10.1943	−	7.40659i	1.03507	−	0.752025i	0.0657562	−	0.997836i	$-0.479054\pi$
$97$	10.1943	−	7.40659i	1.03507	−	0.752025i	0.969318	+	0.245810i	$0.0790540\pi$
$98$		0			0
$99$	−2.37515	+	2.31488i	−0.238711	+	0.232655i
$100$		0			0
$101$	−3.71490	+	2.69904i	−0.369647	+	0.268564i	−0.757064	−	0.653340i	$-0.773367\pi$
$101$	−3.71490	+	2.69904i	−0.369647	+	0.268564i	0.387418	+	0.921904i	$0.373367\pi$
$102$		0			0
$103$	−3.43629	+	10.5758i	−0.338588	+	1.04207i	0.626339	+	0.779550i	$0.284552\pi$
$103$	−3.43629	+	10.5758i	−0.338588	+	1.04207i	−0.964928	+	0.262516i	$0.915448\pi$
$104$		0			0
$105$	2.93555	+	2.13280i	0.286480	+	0.208140i
$106$		0			0
$107$	−4.89884	−	15.0771i	−0.473589	−	1.45756i	−0.847852	−	0.530233i	$-0.822104\pi$
$107$	−4.89884	−	15.0771i	−0.473589	−	1.45756i	0.374263	−	0.927323i	$-0.377896\pi$
$108$		0			0
$109$	−0.104093			−0.00997029			−0.00498514	−	0.999988i	$-0.501587\pi$
$109$	−0.104093			−0.00997029			−0.00498514	+	0.999988i	$0.501587\pi$
$110$		0			0
$111$	−5.17191			−0.490896
$112$		0			0
$113$	3.77865	+	11.6295i	0.355466	+	1.09401i	0.955739	+	0.294216i	$0.0950585\pi$
$113$	3.77865	+	11.6295i	0.355466	+	1.09401i	−0.600273	+	0.799795i	$0.704941\pi$
$114$		0			0
$115$	2.13179	+	1.54884i	0.198791	+	0.144430i
$116$		0			0
$117$	−1.02479	+	3.15397i	−0.0947415	+	0.291584i
$118$		0			0
$119$	3.56278	−	2.58851i	0.326599	−	0.237288i
$120$		0			0
$121$	10.5455	−	3.12927i	0.958682	−	0.284479i
$122$		0			0
$123$	0.0952652	−	0.0692142i	0.00858977	−	0.00624084i
$124$		0			0
$125$	−0.558581	+	1.71914i	−0.0499610	+	0.153764i
$126$		0			0
$127$	11.6044	+	8.43108i	1.02972	+	0.748138i	0.968253	−	0.249971i	$-0.0804211\pi$
$127$	11.6044	+	8.43108i	1.02972	+	0.748138i	0.0614700	+	0.998109i	$0.480421\pi$
$128$		0			0
$129$	−0.186970	−	0.575435i	−0.0164618	−	0.0506642i
$130$		0			0
$131$	15.1652			1.32499			0.662496	−	0.749065i	$-0.269497\pi$
$131$	15.1652			1.32499			0.662496	+	0.749065i	$0.269497\pi$
$132$		0			0
$133$	−6.98789			−0.605927
$134$		0			0
$135$	−1.00401	−	3.09003i	−0.0864117	−	0.265948i
$136$		0			0
$137$	−12.5187	−	9.09537i	−1.06954	−	0.777070i	−0.0937145	−	0.995599i	$-0.529874\pi$
$137$	−12.5187	−	9.09537i	−1.06954	−	0.777070i	−0.975830	+	0.218529i	$0.929874\pi$
$138$		0			0
$139$	0.625174	−	1.92409i	0.0530266	−	0.163199i	−0.921036	−	0.389477i	$-0.872656\pi$
$139$	0.625174	−	1.92409i	0.0530266	−	0.163199i	0.974063	+	0.226278i	$0.0726558\pi$
$140$		0			0
$141$	4.54579	−	3.30271i	0.382825	−	0.278138i
$142$		0			0
$143$	7.87664	−	7.67680i	0.658678	−	0.641966i
$144$		0			0
$145$	2.13431	−	1.55067i	0.177245	−	0.128776i
$146$		0			0
$147$	−1.77770	+	5.47120i	−0.146622	+	0.451257i
$148$		0			0
$149$	−10.1679	−	7.38740i	−0.832986	−	0.605200i	0.0874165	−	0.996172i	$-0.472139\pi$
$149$	−10.1679	−	7.38740i	−0.832986	−	0.605200i	−0.920403	+	0.390972i	$0.872139\pi$
$150$		0			0
$151$	5.46991	+	16.8347i	0.445135	+	1.36998i	0.882336	+	0.470621i	$0.155970\pi$
$151$	5.46991	+	16.8347i	0.445135	+	1.36998i	−0.437201	+	0.899364i	$0.644030\pi$
$152$		0			0
$153$	−3.94327			−0.318795
$154$		0			0
$155$	−6.10251			−0.490166
$156$		0			0
$157$	−3.44051	−	10.5888i	−0.274583	−	0.845078i	−0.989330	−	0.145695i	$-0.953458\pi$
$157$	−3.44051	−	10.5888i	−0.274583	−	0.845078i	0.714747	−	0.699383i	$-0.246542\pi$
$158$		0			0
$159$	−8.84026	−	6.42282i	−0.701078	−	0.509363i
$160$		0			0
$161$	0.279890	−	0.861413i	0.0220584	−	0.0678888i
$162$		0			0
$163$	−20.5866	+	14.9570i	−1.61246	+	1.17152i	−0.757506	+	0.652828i	$0.773582\pi$
$163$	−20.5866	+	14.9570i	−1.61246	+	1.17152i	−0.854959	+	0.518696i	$0.826418\pi$
$164$		0			0
$165$	−1.82232	+	10.6207i	−0.141868	+	0.826819i
$166$		0			0
$167$	5.75586	−	4.18188i	0.445402	−	0.323603i	−0.342376	−	0.939563i	$-0.611232\pi$
$167$	5.75586	−	4.18188i	0.445402	−	0.323603i	0.787778	+	0.615960i	$0.211232\pi$
$168$		0			0
$169$	−0.618745	+	1.90430i	−0.0475957	+	0.146485i
$170$		0			0
$171$	5.06208	+	3.67782i	0.387107	+	0.281250i
$172$		0			0
$173$	−6.92575	−	21.3153i	−0.526555	−	1.62057i	−0.761220	−	0.648494i	$-0.775399\pi$
$173$	−6.92575	−	21.3153i	−0.526555	−	1.62057i	0.234665	−	0.972076i	$-0.424601\pi$
$174$		0			0
$175$	6.20531			0.469078
$176$		0			0
$177$	−4.69015			−0.352534
$178$		0			0
$179$	−7.73260	−	23.7985i	−0.577962	−	1.77878i	−0.625865	−	0.779931i	$-0.715254\pi$
$179$	−7.73260	−	23.7985i	−0.577962	−	1.77878i	0.0479034	−	0.998852i	$-0.484746\pi$
$180$		0			0
$181$	−18.6967	−	13.5840i	−1.38972	−	1.00969i	−0.995897	−	0.0904992i	$-0.971154\pi$
$181$	−18.6967	−	13.5840i	−1.38972	−	1.00969i	−0.393819	−	0.919188i	$-0.628846\pi$
$182$		0			0
$183$	2.46362	−	7.58224i	0.182116	−	0.560495i
$184$		0			0
$185$	−13.5946	+	9.87703i	−0.999492	+	0.726174i
$186$		0			0
$187$	11.5757	+	6.08668i	0.846496	+	0.445102i
$188$		0			0
$189$	−0.903508	+	0.656437i	−0.0657205	+	0.0477488i
$190$		0			0
$191$	5.46312	−	16.8138i	0.395298	−	1.21660i	−0.533432	−	0.845843i	$-0.679098\pi$
$191$	5.46312	−	16.8138i	0.395298	−	1.21660i	0.928729	−	0.370758i	$-0.120902\pi$
$192$		0			0
$193$	−13.5823	−	9.86811i	−0.977674	−	0.710322i	−0.0204868	−	0.999790i	$-0.506522\pi$
$193$	−13.5823	−	9.86811i	−0.977674	−	0.710322i	−0.957188	+	0.289468i	$0.906522\pi$
$194$		0			0
$195$	3.32959	+	10.2474i	0.238437	+	0.733832i
$196$		0			0
$197$	−1.12635			−0.0802492			−0.0401246	−	0.999195i	$-0.512775\pi$
$197$	−1.12635			−0.0802492			−0.0401246	+	0.999195i	$0.512775\pi$
$198$		0			0
$199$	−5.52912			−0.391949			−0.195975	−	0.980609i	$-0.562787\pi$
$199$	−5.52912			−0.391949			−0.195975	+	0.980609i	$0.562787\pi$
$200$		0			0
$201$	−1.63025	−	5.01740i	−0.114989	−	0.353900i
$202$		0			0
$203$	−0.733626	−	0.533011i	−0.0514905	−	0.0374100i
$204$		0			0
$205$	0.118227	−	0.363865i	0.00825732	−	0.0254134i
$206$		0			0
$207$	−0.656128	+	0.476705i	−0.0456040	+	0.0331333i
$208$		0			0
$209$	−9.18304	−	18.6100i	−0.635204	−	1.28728i
$210$		0			0
$211$	7.93602	−	5.76585i	0.546338	−	0.396938i	−0.280096	−	0.959972i	$-0.590366\pi$
$211$	7.93602	−	5.76585i	0.546338	−	0.396938i	0.826433	+	0.563034i	$0.190366\pi$
$212$		0			0
$213$	4.07655	−	12.5463i	0.279320	−	0.859660i
$214$		0			0
$215$	−1.59039	−	1.15549i	−0.108464	−	0.0788037i
$216$		0			0
$217$	0.648199	+	1.99495i	0.0440026	+	0.135426i
$218$		0			0
$219$	−2.05605			−0.138935
$220$		0			0
$221$	13.0770			0.879654
$222$		0			0
$223$	1.06393	+	3.27445i	0.0712461	+	0.219273i	0.980339	−	0.197320i	$-0.0632239\pi$
$223$	1.06393	+	3.27445i	0.0712461	+	0.219273i	−0.909093	+	0.416593i	$0.863224\pi$
$224$		0			0
$225$	−4.49518	−	3.26594i	−0.299679	−	0.217729i
$226$		0			0
$227$	2.14619	−	6.60531i	0.142448	−	0.438410i	−0.854226	−	0.519902i	$-0.825969\pi$
$227$	2.14619	−	6.60531i	0.142448	−	0.438410i	0.996674	+	0.0814922i	$0.0259686\pi$
$228$		0			0
$229$	−10.7934	+	7.84183i	−0.713245	+	0.518203i	−0.884219	−	0.467073i	$-0.845309\pi$
$229$	−10.7934	+	7.84183i	−0.713245	+	0.518203i	0.170974	+	0.985276i	$0.445309\pi$
$230$		0			0
$231$	3.66554	−	0.532382i	0.241175	−	0.0350282i
$232$		0			0
$233$	−12.7033	+	9.22952i	−0.832223	+	0.604646i	−0.920187	−	0.391478i	$-0.871964\pi$
$233$	−12.7033	+	9.22952i	−0.832223	+	0.604646i	0.0879641	+	0.996124i	$0.471964\pi$
$234$		0			0
$235$	5.64145	−	17.3626i	0.368008	−	1.13261i
$236$		0			0
$237$	−14.0249	−	10.1897i	−0.911012	−	0.661889i
$238$		0			0
$239$	7.44550	+	22.9149i	0.481609	+	1.48224i	0.836832	+	0.547459i	$0.184405\pi$
$239$	7.44550	+	22.9149i	0.481609	+	1.48224i	−0.355223	+	0.934782i	$0.615595\pi$
$240$		0			0
$241$	−13.6736			−0.880792			−0.440396	−	0.897804i	$-0.645162\pi$
$241$	−13.6736			−0.880792			−0.440396	+	0.897804i	$0.645162\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	5.77585	+	17.7762i	0.369005	+	1.13568i
$246$		0			0
$247$	−16.7873	−	12.1967i	−1.06815	−	0.776056i
$248$		0			0
$249$	−4.36366	+	13.4300i	−0.276536	+	0.851089i
$250$		0			0
$251$	−19.7941	+	14.3813i	−1.24939	+	0.907737i	−0.998187	−	0.0601968i	$-0.980827\pi$
$251$	−19.7941	+	14.3813i	−1.24939	+	0.907737i	−0.251206	+	0.967934i	$0.580827\pi$
$252$		0			0
$253$	2.66191	−	0.386616i	0.167353	−	0.0243064i
$254$		0			0
$255$	−10.3651	+	7.53065i	−0.649085	+	0.471588i
$256$		0			0
$257$	5.31967	−	16.3722i	0.331832	−	1.02127i	−0.636430	−	0.771334i	$-0.719590\pi$
$257$	5.31967	−	16.3722i	0.331832	−	1.02127i	0.968262	−	0.249938i	$-0.0804104\pi$
$258$		0			0
$259$	4.67286	+	3.39503i	0.290357	+	0.210957i
$260$		0			0
$261$	0.250914	+	0.772235i	0.0155312	+	0.0478001i
$262$		0			0
$263$	1.51375			0.0933417			0.0466708	−	0.998910i	$-0.485139\pi$
$263$	1.51375			0.0933417			0.0466708	+	0.998910i	$0.485139\pi$
$264$		0			0
$265$	−35.5029			−2.18093
$266$		0			0
$267$	4.06736	+	12.5180i	0.248918	+	0.766092i
$268$		0			0
$269$	−2.53286	−	1.84023i	−0.154431	−	0.112201i	0.507886	−	0.861424i	$-0.330427\pi$
$269$	−2.53286	−	1.84023i	−0.154431	−	0.112201i	−0.662318	+	0.749223i	$0.730427\pi$
$270$		0			0
$271$	0.160308	−	0.493377i	0.00973801	−	0.0299705i	−0.946069	−	0.323964i	$-0.894984\pi$
$271$	0.160308	−	0.493377i	0.00973801	−	0.0299705i	0.955807	+	0.293993i	$0.0949844\pi$
$272$		0			0
$273$	2.99628	−	2.17693i	0.181343	−	0.131754i
$274$		0			0
$275$	8.15463	+	16.5259i	0.491743	+	0.996549i
$276$		0			0
$277$	23.2755	−	16.9106i	1.39849	−	1.01606i	0.403613	−	0.914930i	$-0.367754\pi$
$277$	23.2755	−	16.9106i	1.39849	−	1.01606i	0.994873	−	0.101130i	$-0.0322458\pi$
$278$		0			0
$279$	0.580409	−	1.78632i	0.0347482	−	0.106944i
$280$		0			0
$281$	17.6750	+	12.8416i	1.05440	+	0.766068i	0.973045	−	0.230617i	$-0.0740745\pi$
$281$	17.6750	+	12.8416i	1.05440	+	0.766068i	0.0813573	+	0.996685i	$0.474075\pi$
$282$		0			0
$283$	−4.99249	−	15.3653i	−0.296773	−	0.913372i	−0.982620	−	0.185627i	$-0.940568\pi$
$283$	−4.99249	−	15.3653i	−0.296773	−	0.913372i	0.685848	−	0.727745i	$-0.259432\pi$
$284$		0			0
$285$	20.3296			1.20422
$286$		0			0
$287$	−0.131508			−0.00776265
$288$		0			0
$289$	−0.448255	−	1.37959i	−0.0263679	−	0.0811521i
$290$		0			0
$291$	10.1943	+	7.40659i	0.597600	+	0.434182i
$292$		0			0
$293$	3.16632	−	9.74494i	0.184979	−	0.569306i	−0.814969	−	0.579504i	$-0.803246\pi$
$293$	3.16632	−	9.74494i	0.184979	−	0.569306i	0.999948	+	0.0101984i	$0.00324631\pi$
$294$		0			0
$295$	−12.3283	+	8.95700i	−0.717779	+	0.521497i
$296$		0			0
$297$	−2.93555	−	1.54356i	−0.170338	−	0.0895664i
$298$		0			0
$299$	2.17590	−	1.58089i	0.125836	−	0.0914250i
$300$		0			0
$301$	−0.208808	+	0.642644i	−0.0120355	+	0.0370414i
$302$		0			0
$303$	−3.71490	−	2.69904i	−0.213416	−	0.155056i
$304$		0			0
$305$	−8.00443	−	24.6351i	−0.458332	−	1.41060i
$306$		0			0
$307$	−25.3070			−1.44435			−0.722173	−	0.691713i	$-0.756856\pi$
$307$	−25.3070			−1.44435			−0.722173	+	0.691713i	$0.756856\pi$
$308$		0			0
$309$	−11.1201			−0.632599
$310$		0			0
$311$	6.11677	+	18.8255i	0.346850	+	1.06749i	0.960586	+	0.277983i	$0.0896660\pi$
$311$	6.11677	+	18.8255i	0.346850	+	1.06749i	−0.613736	+	0.789512i	$0.710334\pi$
$312$		0			0
$313$	23.8493	+	17.3276i	1.34804	+	0.979411i	0.999106	+	0.0422649i	$0.0134574\pi$
$313$	23.8493	+	17.3276i	1.34804	+	0.979411i	0.348937	+	0.937146i	$0.386543\pi$
$314$		0			0
$315$	−1.12128	+	3.45094i	−0.0631769	+	0.194438i
$316$		0			0
$317$	9.57482	−	6.95651i	0.537775	−	0.390717i	−0.285483	−	0.958384i	$-0.592154\pi$
$317$	9.57482	−	6.95651i	0.537775	−	0.390717i	0.823258	+	0.567667i	$0.192154\pi$
$318$		0			0
$319$	0.455420	−	2.65423i	0.0254986	−	0.148608i
$320$		0			0
$321$	12.8253	−	9.31815i	0.715840	−	0.520088i
$322$		0			0
$323$	7.62449	−	23.4658i	0.424238	−	1.30567i
$324$		0			0
$325$	14.9073	+	10.8308i	0.826906	+	0.600783i
$326$		0			0
$327$	−0.0321665	−	0.0989982i	−0.00177881	−	0.00547461i
$328$		0			0
$329$	−6.27518			−0.345962
$330$		0			0
$331$	24.2951			1.33538			0.667689	−	0.744440i	$-0.267284\pi$
$331$	24.2951			1.33538			0.667689	+	0.744440i	$0.267284\pi$
$332$		0			0
$333$	−1.59821	−	4.91878i	−0.0875812	−	0.269547i
$334$		0			0
$335$	−13.8671	−	10.0751i	−0.757642	−	0.550459i
$336$		0			0
$337$	7.25270	−	22.3215i	0.395080	−	1.21593i	−0.533820	−	0.845598i	$-0.679244\pi$
$337$	7.25270	−	22.3215i	0.395080	−	1.21593i	0.928899	−	0.370332i	$-0.120756\pi$
$338$		0			0
$339$	−9.89264	+	7.18743i	−0.537295	+	0.390367i
$340$		0			0
$341$	−4.46110	+	4.34791i	−0.241582	+	0.235453i
$342$		0			0
$343$	11.5222	−	8.37138i	0.622142	−	0.452012i
$344$		0			0
$345$	−0.814273	+	2.50607i	−0.0438390	+	0.134922i
$346$		0			0
$347$	16.4029	+	11.9174i	0.880554	+	0.639760i	0.933398	−	0.358843i	$-0.116829\pi$
$347$	16.4029	+	11.9174i	0.880554	+	0.639760i	−0.0528442	+	0.998603i	$0.516829\pi$
$348$		0			0
$349$	1.57004	+	4.83210i	0.0840425	+	0.258656i	0.984243	−	0.176818i	$-0.0565805\pi$
$349$	1.57004	+	4.83210i	0.0840425	+	0.258656i	−0.900201	+	0.435475i	$0.856581\pi$
$350$		0			0
$351$	−3.31628			−0.177010
$352$		0			0
$353$	3.10388			0.165203			0.0826015	−	0.996583i	$-0.473677\pi$
$353$	3.10388			0.165203			0.0826015	+	0.996583i	$0.473677\pi$
$354$		0			0
$355$	−13.2449	−	40.7637i	−0.702967	−	2.16351i
$356$		0			0
$357$	3.56278	+	2.58851i	0.188562	+	0.136999i
$358$		0			0
$359$	5.01860	−	15.4457i	0.264872	−	0.815191i	−0.726851	−	0.686795i	$-0.759017\pi$
$359$	5.01860	−	15.4457i	0.264872	−	0.815191i	0.991723	−	0.128396i	$-0.0409829\pi$
$360$		0			0
$361$	−16.3025	+	11.8445i	−0.858028	+	0.623394i
$362$		0			0
$363$	6.23485	+	9.06237i	0.327245	+	0.475651i
$364$		0			0
$365$	−5.40441	+	3.92653i	−0.282880	+	0.205524i
$366$		0			0
$367$	0.621004	−	1.91125i	0.0324161	−	0.0997666i	−0.933539	−	0.358475i	$-0.883297\pi$
$367$	0.621004	−	1.91125i	0.0324161	−	0.0997666i	0.965955	+	0.258708i	$0.0832968\pi$
$368$		0			0
$369$	0.0952652	+	0.0692142i	0.00495931	+	0.00360315i
$370$		0			0
$371$	3.77106	+	11.6061i	0.195784	+	0.602561i
$372$		0			0
$373$	−5.48175			−0.283834			−0.141917	−	0.989879i	$-0.545327\pi$
$373$	−5.48175			−0.283834			−0.141917	+	0.989879i	$0.545327\pi$
$374$		0			0
$375$	−1.80761			−0.0933444
$376$		0			0
$377$	−0.832101	−	2.56094i	−0.0428554	−	0.131895i
$378$		0			0
$379$	−12.3686	−	8.98634i	−0.635334	−	0.461597i	0.222910	−	0.974839i	$-0.428444\pi$
$379$	−12.3686	−	8.98634i	−0.635334	−	0.461597i	−0.858244	+	0.513242i	$0.828444\pi$
$380$		0			0
$381$	−4.43248	+	13.6418i	−0.227083	+	0.698890i
$382$		0			0
$383$	−8.45103	+	6.14003i	−0.431827	+	0.313741i	−0.782379	−	0.622802i	$-0.785994\pi$
$383$	−8.45103	+	6.14003i	−0.431827	+	0.313741i	0.350552	+	0.936543i	$0.385994\pi$
$384$		0			0
$385$	8.61829	−	8.39963i	0.439229	−	0.428085i
$386$		0			0
$387$	0.489494	−	0.355639i	0.0248824	−	0.0180781i
$388$		0			0
$389$	−6.82197	+	20.9959i	−0.345888	+	1.06453i	0.615219	+	0.788356i	$0.289068\pi$
$389$	−6.82197	+	20.9959i	−0.345888	+	1.06453i	−0.961107	+	0.276177i	$0.910932\pi$
$390$		0			0
$391$	2.58729	+	1.87978i	0.130845	+	0.0950644i
$392$		0			0
$393$	4.68631	+	14.4230i	0.236393	+	0.727544i
$394$		0			0
$395$	−56.3245			−2.83400
$396$		0			0
$397$	−0.959507			−0.0481563			−0.0240781	−	0.999710i	$-0.507665\pi$
$397$	−0.959507			−0.0481563			−0.0240781	+	0.999710i	$0.507665\pi$
$398$		0			0
$399$	−2.15938	−	6.64588i	−0.108104	−	0.332710i
$400$		0			0
$401$	−8.82120	−	6.40897i	−0.440510	−	0.320049i	0.345328	−	0.938482i	$-0.387768\pi$
$401$	−8.82120	−	6.40897i	−0.440510	−	0.320049i	−0.785837	+	0.618433i	$0.787768\pi$
$402$		0			0
$403$	−1.92480	+	5.92392i	−0.0958810	+	0.295091i
$404$		0			0
$405$	2.62854	−	1.90975i	0.130613	−	0.0948960i
$406$		0			0
$407$	−2.90081	+	16.9062i	−0.143788	+	0.838010i
$408$		0			0
$409$	−3.70138	+	2.68921i	−0.183021	+	0.132973i	−0.675524	−	0.737338i	$-0.736082\pi$
$409$	−3.70138	+	2.68921i	−0.183021	+	0.132973i	0.492502	+	0.870311i	$0.336082\pi$
$410$		0			0
$411$	4.78172	−	14.7166i	0.235865	−	0.725917i
$412$		0			0
$413$	4.23759	+	3.07879i	0.208518	+	0.151497i
$414$		0			0
$415$	14.1778	+	43.6347i	0.695959	+	2.14194i
$416$		0			0
$417$	2.02311			0.0990720
$418$		0			0
$419$	23.0003			1.12364			0.561819	−	0.827260i	$-0.310102\pi$
$419$	23.0003			1.12364			0.561819	+	0.827260i	$0.310102\pi$
$420$		0			0
$421$	−2.44065	−	7.51154i	−0.118950	−	0.366090i	0.873800	−	0.486285i	$-0.161648\pi$
$421$	−2.44065	−	7.51154i	−0.118950	−	0.366090i	−0.992750	+	0.120194i	$0.961648\pi$
$422$		0			0
$423$	4.54579	+	3.30271i	0.221024	+	0.160583i
$424$		0			0
$425$	−6.77063	+	20.8378i	−0.328424	+	1.01078i
$426$		0			0
$427$	−7.20316	+	5.23340i	−0.348585	+	0.253262i
$428$		0			0
$429$	9.73508	+	5.11887i	0.470014	+	0.247141i
$430$		0			0
$431$	−6.60738	+	4.80054i	−0.318266	+	0.231234i	−0.735435	−	0.677595i	$-0.763022\pi$
$431$	−6.60738	+	4.80054i	−0.318266	+	0.231234i	0.417169	+	0.908829i	$0.363022\pi$
$432$		0			0
$433$	5.02582	−	15.4679i	0.241525	−	0.743339i	−0.754663	−	0.656112i	$-0.772200\pi$
$433$	5.02582	−	15.4679i	0.241525	−	0.743339i	0.996189	−	0.0872263i	$-0.0278003\pi$
$434$		0			0
$435$	2.13431	+	1.55067i	0.102332	+	0.0743488i
$436$		0			0
$437$	−1.56814	−	4.82624i	−0.0750143	−	0.230870i
$438$		0			0
$439$	−27.5051			−1.31275			−0.656374	−	0.754436i	$-0.727911\pi$
$439$	−27.5051			−1.31275			−0.656374	+	0.754436i	$0.727911\pi$
$440$		0			0
$441$	−5.75276			−0.273941
$442$		0			0
$443$	4.60511	+	14.1731i	0.218795	+	0.673383i	0.998862	+	0.0476871i	$0.0151850\pi$
$443$	4.60511	+	14.1731i	0.218795	+	0.673383i	−0.780067	+	0.625696i	$0.784815\pi$
$444$		0			0
$445$	34.5975	+	25.1366i	1.64008	+	1.19159i
$446$		0			0
$447$	3.88379	−	11.9531i	0.183697	−	0.565361i
$448$		0			0
$449$	1.99197	−	1.44725i	0.0940071	−	0.0683001i	−0.539789	−	0.841800i	$-0.681496\pi$
$449$	1.99197	−	1.44725i	0.0940071	−	0.0683001i	0.633796	+	0.773500i	$0.281496\pi$
$450$		0			0
$451$	−0.172819	−	0.350229i	−0.00813773	−	0.0164916i
$452$		0			0
$453$	−14.3204	+	10.4044i	−0.672832	+	0.488841i
$454$		0			0
$455$	3.71847	−	11.4443i	0.174325	−	0.536516i
$456$		0			0
$457$	−2.75543	−	2.00193i	−0.128893	−	0.0936465i	0.521471	−	0.853269i	$-0.325384\pi$
$457$	−2.75543	−	2.00193i	−0.128893	−	0.0936465i	−0.650364	+	0.759623i	$0.725384\pi$
$458$		0			0
$459$	−1.21854	−	3.75028i	−0.0568765	−	0.175048i
$460$		0			0
$461$	−9.22511			−0.429656			−0.214828	−	0.976652i	$-0.568919\pi$
$461$	−9.22511			−0.429656			−0.214828	+	0.976652i	$0.568919\pi$
$462$		0			0
$463$	16.1334			0.749784			0.374892	−	0.927069i	$-0.377680\pi$
$463$	16.1334			0.749784			0.374892	+	0.927069i	$0.377680\pi$
$464$		0			0
$465$	−1.88578	−	5.80383i	−0.0874509	−	0.269146i
$466$		0			0
$467$	14.1151	+	10.2552i	0.653167	+	0.474553i	0.864348	−	0.502893i	$-0.167731\pi$
$467$	14.1151	+	10.2552i	0.653167	+	0.474553i	−0.211182	+	0.977447i	$0.567731\pi$
$468$		0			0
$469$	−1.82066	+	5.60341i	−0.0840703	+	0.258742i
$470$		0			0
$471$	9.00737	−	6.54424i	0.415038	−	0.301543i
$472$		0			0
$473$	−1.98588	+	0.288429i	−0.0913110	+	0.0132620i
$474$		0			0
$475$	28.1267	−	20.4352i	1.29054	−	0.937633i
$476$		0			0
$477$	3.37668	−	10.3923i	0.154607	−	0.475833i
$478$		0			0
$479$	4.86072	+	3.53152i	0.222092	+	0.161359i	0.693268	−	0.720680i	$-0.256170\pi$
$479$	4.86072	+	3.53152i	0.222092	+	0.161359i	−0.471176	+	0.882039i	$0.656170\pi$
$480$		0			0
$481$	5.30010	+	16.3120i	0.241664	+	0.743765i
$482$		0			0
$483$	0.905743			0.0412127
$484$		0			0
$485$	40.9408			1.85903
$486$		0			0
$487$	6.91810	+	21.2917i	0.313489	+	0.964820i	0.976372	+	0.216097i	$0.0693327\pi$
$487$	6.91810	+	21.2917i	0.313489	+	0.964820i	−0.662883	+	0.748723i	$0.730667\pi$
$488$		0			0
$489$	−20.5866	−	14.9570i	−0.930957	−	0.676380i
$490$		0			0
$491$	0.878233	−	2.70292i	0.0396341	−	0.121981i	−0.929282	−	0.369372i	$-0.879573\pi$
$491$	0.878233	−	2.70292i	0.0396341	−	0.121981i	0.968916	+	0.247390i	$0.0795730\pi$
$492$		0			0
$493$	2.59035	−	1.88200i	0.116663	−	0.0847608i
$494$		0			0
$495$	−10.6640	+	1.54884i	−0.479311	+	0.0696151i
$496$		0			0
$497$	−11.9191	+	8.65970i	−0.534643	+	0.388441i
$498$		0			0
$499$	11.9319	−	36.7227i	0.534147	−	1.64393i	−0.211339	−	0.977413i	$-0.567783\pi$
$499$	11.9319	−	36.7227i	0.534147	−	1.64393i	0.745486	−	0.666521i	$-0.232217\pi$
$500$		0			0
$501$	5.75586	+	4.18188i	0.257153	+	0.186832i
$502$		0			0
$503$	3.82688	+	11.7779i	0.170632	+	0.525152i	0.999407	−	0.0344301i	$-0.0109616\pi$
$503$	3.82688	+	11.7779i	0.170632	+	0.525152i	−0.828775	+	0.559582i	$0.810962\pi$
$504$		0			0
$505$	−14.9192			−0.663898
$506$		0			0
$507$	−2.00230			−0.0889253
$508$		0			0
$509$	13.0120	+	40.0469i	0.576748	+	1.77505i	0.630148	+	0.776475i	$0.282994\pi$
$509$	13.0120	+	40.0469i	0.576748	+	1.77505i	−0.0533993	+	0.998573i	$0.517006\pi$
$510$		0			0
$511$	1.85766	+	1.34967i	0.0821779	+	0.0597057i
$512$		0			0
$513$	−1.93354	+	5.95084i	−0.0853680	+	0.262736i
$514$		0			0
$515$	−29.2296	+	21.2365i	−1.28801	+	0.935793i
$516$		0			0
$517$	−8.24645	−	16.7120i	−0.362678	−	0.734991i
$518$		0			0
$519$	18.1319	−	13.1736i	0.795900	−	0.578255i
$520$		0			0
$521$	−7.77071	+	23.9158i	−0.340441	+	1.04777i	0.623538	+	0.781793i	$0.285694\pi$
$521$	−7.77071	+	23.9158i	−0.340441	+	1.04777i	−0.963979	+	0.265977i	$0.914306\pi$
$522$		0			0
$523$	14.5631	+	10.5807i	0.636798	+	0.462661i	0.858749	−	0.512397i	$-0.171242\pi$
$523$	14.5631	+	10.5807i	0.636798	+	0.462661i	−0.221951	+	0.975058i	$0.571242\pi$
$524$		0			0
$525$	1.91755	+	5.90160i	0.0836886	+	0.257567i
$526$		0			0
$527$	−7.40643			−0.322629
$528$		0			0
$529$	−22.3422			−0.971402
$530$		0			0
$531$	−1.44934	−	4.46060i	−0.0628959	−	0.193574i
$532$		0			0
$533$	−0.315926	−	0.229534i	−0.0136843	−	0.00994220i
$534$		0			0
$535$	15.9166	−	48.9862i	0.688134	−	2.11786i
$536$		0			0
$537$	20.2442	−	14.7083i	0.873602	−	0.634709i
$538$		0			0
$539$	16.8875	+	8.87973i	0.727396	+	0.382477i
$540$		0			0
$541$	34.5019	−	25.0671i	1.48335	−	1.07772i	0.506896	−	0.862007i	$-0.330793\pi$
$541$	34.5019	−	25.0671i	1.48335	−	1.07772i	0.976457	−	0.215712i	$-0.0692073\pi$
$542$		0			0
$543$	7.14151	−	21.9793i	0.306471	−	0.943222i
$544$		0			0
$545$	−0.273612	−	0.198791i	−0.0117203	−	0.00851527i
$546$		0			0
$547$	5.02532	+	15.4663i	0.214867	+	0.661293i	0.999163	+	0.0409061i	$0.0130244\pi$
$547$	5.02532	+	15.4663i	0.214867	+	0.661293i	−0.784296	+	0.620387i	$0.786976\pi$
$548$		0			0
$549$	7.97244			0.340255
$550$		0			0
$551$	−5.08060			−0.216441
$552$		0			0
$553$	5.98270	+	18.4129i	0.254410	+	0.782995i
$554$		0			0
$555$	−13.5946	−	9.87703i	−0.577057	−	0.419257i
$556$		0			0
$557$	13.1209	−	40.3819i	0.555949	−	1.71103i	−0.137475	−	0.990505i	$-0.543899\pi$
$557$	13.1209	−	40.3819i	0.555949	−	1.71103i	0.693424	−	0.720530i	$-0.256101\pi$
$558$		0			0
$559$	−1.62330	+	1.17940i	−0.0686583	+	0.0498831i
$560$		0			0
$561$	−2.21170	+	12.8900i	−0.0933780	+	0.544216i
$562$		0			0
$563$	−13.8274	+	10.0462i	−0.582755	+	0.423396i	−0.839716	−	0.543026i	$-0.817279\pi$
$563$	−13.8274	+	10.0462i	−0.582755	+	0.423396i	0.256962	+	0.966422i	$0.417279\pi$
$564$		0			0
$565$	−12.2770	+	37.7849i	−0.516499	+	1.58962i
$566$		0			0
$567$	−0.903508	−	0.656437i	−0.0379438	−	0.0275678i
$568$		0			0
$569$	3.72771	+	11.4727i	0.156274	+	0.480961i	0.998288	−	0.0584945i	$-0.0186300\pi$
$569$	3.72771	+	11.4727i	0.156274	+	0.480961i	−0.842014	+	0.539456i	$0.818630\pi$
$570$		0			0
$571$	−22.2050			−0.929252			−0.464626	−	0.885507i	$-0.653811\pi$
$571$	−22.2050			−0.929252			−0.464626	+	0.885507i	$0.653811\pi$
$572$		0			0
$573$	17.6790			0.738553
$574$		0			0
$575$	1.39252	+	4.28575i	0.0580723	+	0.178728i
$576$		0			0
$577$	20.4466	+	14.8553i	0.851204	+	0.618436i	0.925478	−	0.378802i	$-0.123664\pi$
$577$	20.4466	+	14.8553i	0.851204	+	0.618436i	−0.0742736	+	0.997238i	$0.523664\pi$
$578$		0			0
$579$	5.18797	−	15.9669i	0.215605	−	0.663563i
$580$		0			0
$581$	12.7585	−	9.26961i	0.529313	−	0.384568i
$582$		0			0
$583$	−25.9536	+	25.2951i	−1.07489	+	1.04762i
$584$		0			0
$585$	−8.71697	+	6.33325i	−0.360402	+	0.261848i
$586$		0			0
$587$	2.08186	−	6.40731i	0.0859276	−	0.264458i	−0.898856	−	0.438245i	$-0.855600\pi$
$587$	2.08186	−	6.40731i	0.0859276	−	0.264458i	0.984783	+	0.173787i	$0.0556003\pi$
$588$		0			0
$589$	9.50782	+	6.90784i	0.391763	+	0.284632i
$590$		0			0
$591$	−0.348062	−	1.07122i	−0.0143173	−	0.0440643i
$592$		0			0
$593$	18.9123			0.776635			0.388317	−	0.921526i	$-0.373056\pi$
$593$	18.9123			0.776635			0.388317	+	0.921526i	$0.373056\pi$
$594$		0			0
$595$	14.3083			0.586583
$596$		0			0
$597$	−1.70859	−	5.25851i	−0.0699280	−	0.215216i
$598$		0			0
$599$	−32.6725	−	23.7380i	−1.33496	−	0.969908i	−0.999613	−	0.0278150i	$-0.991145\pi$
$599$	−32.6725	−	23.7380i	−1.33496	−	0.969908i	−0.335351	−	0.942093i	$-0.608855\pi$
$600$		0			0
$601$	−1.16622	+	3.58925i	−0.0475710	+	0.146409i	−0.972021	−	0.234896i	$-0.924525\pi$
$601$	−1.16622	+	3.58925i	−0.0475710	+	0.146409i	0.924449	+	0.381305i	$0.124525\pi$
$602$		0			0
$603$	4.26805	−	3.10092i	0.173809	−	0.126279i
$604$		0			0
$605$	33.6954	+	11.9138i	1.36991	+	0.484366i
$606$		0			0
$607$	10.4015	−	7.55715i	0.422185	−	0.306735i	−0.356332	−	0.934360i	$-0.615973\pi$
$607$	10.4015	−	7.55715i	0.422185	−	0.306735i	0.778516	+	0.627624i	$0.215973\pi$
$608$		0			0
$609$	0.280220	−	0.862429i	0.0113551	−	0.0349474i
$610$		0			0
$611$	−15.0751	−	10.9527i	−0.609874	−	0.443099i
$612$		0			0
$613$	14.0108	+	43.1208i	0.565891	+	1.74163i	0.665290	+	0.746585i	$0.268308\pi$
$613$	14.0108	+	43.1208i	0.565891	+	1.74163i	−0.0993999	+	0.995048i	$0.531692\pi$
$614$		0			0
$615$	0.382590			0.0154275
$616$		0			0
$617$	35.7946			1.44104			0.720519	−	0.693435i	$-0.243904\pi$
$617$	35.7946			1.44104			0.720519	+	0.693435i	$0.243904\pi$
$618$		0			0
$619$	8.76431	+	26.9738i	0.352267	+	1.08417i	0.957577	+	0.288177i	$0.0930492\pi$
$619$	8.76431	+	26.9738i	0.352267	+	1.08417i	−0.605310	+	0.795990i	$0.706951\pi$
$620$		0			0
$621$	−0.656128	−	0.476705i	−0.0263295	−	0.0191295i
$622$		0			0
$623$	4.54241	−	13.9801i	0.181988	−	0.560101i
$624$		0			0
$625$	17.7245	−	12.8776i	0.708981	−	0.515105i
$626$		0			0
$627$	14.8615	−	14.4844i	0.593510	−	0.578452i
$628$		0			0
$629$	−16.4993	+	11.9874i	−0.657870	+	0.477971i
$630$		0			0
$631$	4.87511	−	15.0041i	0.194075	−	0.597302i	−0.805911	−	0.592037i	$-0.798324\pi$
$631$	4.87511	−	15.0041i	0.194075	−	0.597302i	0.999986	−	0.00526533i	$-0.00167602\pi$
$632$		0			0
$633$	7.93602	+	5.76585i	0.315428	+	0.229172i
$634$		0			0
$635$	14.4014	+	44.3229i	0.571501	+	1.75890i
$636$		0			0
$637$	19.0778			0.755889
$638$		0			0
$639$	13.1920			0.521867
$640$		0			0
$641$	−3.40525	−	10.4803i	−0.134499	−	0.413946i	0.861013	−	0.508584i	$-0.169831\pi$
$641$	−3.40525	−	10.4803i	−0.134499	−	0.413946i	−0.995512	+	0.0946378i	$0.969831\pi$
$642$		0			0
$643$	−13.4462	−	9.76920i	−0.530265	−	0.385260i	0.290192	−	0.956968i	$-0.406281\pi$
$643$	−13.4462	−	9.76920i	−0.530265	−	0.385260i	−0.820457	+	0.571709i	$0.806281\pi$
$644$		0			0
$645$	0.607476	−	1.86962i	0.0239194	−	0.0736162i
$646$		0			0
$647$	−23.9629	+	17.4100i	−0.942077	+	0.684459i	−0.948920	−	0.315518i	$-0.897822\pi$
$647$	−23.9629	+	17.4100i	−0.942077	+	0.684459i	0.00684270	+	0.999977i	$0.497822\pi$
$648$		0			0
$649$	−2.63061	+	15.3314i	−0.103260	+	0.601811i
$650$		0			0
$651$	−1.69701	+	1.23295i	−0.0665110	+	0.0483230i
$652$		0			0
$653$	7.75351	−	23.8628i	0.303418	−	0.933825i	−0.676845	−	0.736126i	$-0.736653\pi$
$653$	7.75351	−	23.8628i	0.303418	−	0.933825i	0.980263	−	0.197699i	$-0.0633469\pi$
$654$		0			0
$655$	39.8624	+	28.9617i	1.55755	+	1.13163i
$656$		0			0
$657$	−0.635354	−	1.95542i	−0.0247875	−	0.0762882i
$658$		0			0
$659$	−4.35903			−0.169804			−0.0849018	−	0.996389i	$-0.527058\pi$
$659$	−4.35903			−0.169804			−0.0849018	+	0.996389i	$0.527058\pi$
$660$		0			0
$661$	11.4920			0.446987			0.223493	−	0.974705i	$-0.428254\pi$
$661$	11.4920			0.446987			0.223493	+	0.974705i	$0.428254\pi$
$662$		0			0
$663$	4.04101	+	12.4370i	0.156940	+	0.483012i
$664$		0			0
$665$	−18.3679	−	13.3451i	−0.712278	−	0.517500i
$666$		0			0
$667$	0.203496	−	0.626297i	0.00787940	−	0.0242503i
$668$		0			0
$669$	−2.78541	+	2.02372i	−0.107690	+	0.0782415i
$670$		0			0
$671$	−23.4034	−	12.3059i	−0.903480	−	0.475065i
$672$		0			0
$673$	−21.5880	+	15.6846i	−0.832157	+	0.604598i	−0.920169	−	0.391522i	$-0.871949\pi$
$673$	−21.5880	+	15.6846i	−0.832157	+	0.604598i	0.0880116	+	0.996119i	$0.471949\pi$
$674$		0			0
$675$	1.71701	−	5.28440i	0.0660876	−	0.203397i
$676$		0			0
$677$	17.6500	+	12.8235i	0.678344	+	0.492846i	0.872808	−	0.488064i	$-0.162297\pi$
$677$	17.6500	+	12.8235i	0.678344	+	0.492846i	−0.194464	+	0.980910i	$0.562297\pi$
$678$		0			0
$679$	−4.34867	−	13.3838i	−0.166887	−	0.513624i
$680$		0			0
$681$	6.94523			0.266142
$682$		0			0
$683$	27.1072			1.03723			0.518614	−	0.855009i	$-0.326448\pi$
$683$	27.1072			1.03723			0.518614	+	0.855009i	$0.326448\pi$
$684$		0			0
$685$	−15.5361	−	47.8151i	−0.593602	−	1.82692i
$686$		0			0
$687$	−10.7934	−	7.84183i	−0.411792	−	0.299185i
$688$		0			0
$689$	−11.1980	+	34.4639i	−0.426610	+	1.31297i
$690$		0			0
$691$	−37.9445	+	27.5683i	−1.44348	+	1.04875i	−0.456174	+	0.889891i	$0.650781\pi$
$691$	−37.9445	+	27.5683i	−1.44348	+	1.04875i	−0.987302	+	0.158856i	$0.949219\pi$
$692$		0			0
$693$	1.63904	+	3.32162i	0.0622619	+	0.126178i
$694$		0			0
$695$	5.31782	−	3.86362i	0.201716	−	0.146555i
$696$		0			0
$697$	0.143488	−	0.441611i	0.00543500	−	0.0167272i
$698$		0			0
$699$	−12.7033	−	9.22952i	−0.480484	−	0.349092i
$700$		0			0
$701$	0.437693	+	1.34708i	0.0165315	+	0.0508786i	0.958982	−	0.283467i	$-0.0914847\pi$
$701$	0.437693	+	1.34708i	0.0165315	+	0.0508786i	−0.942450	+	0.334346i	$0.891485\pi$
$702$		0			0
$703$	32.3610			1.22052
$704$		0			0
$705$	18.2561			0.687566
$706$		0			0
$707$	1.58470	+	4.87720i	0.0595987	+	0.183426i
$708$		0			0
$709$	32.7422	+	23.7886i	1.22966	+	0.893398i	0.996864	−	0.0791279i	$-0.0252136\pi$
$709$	32.7422	+	23.7886i	1.22966	+	0.893398i	0.232793	+	0.972526i	$0.425214\pi$
$710$		0			0
$711$	5.35702	−	16.4872i	0.200904	−	0.618319i
$712$		0			0
$713$	−1.23237	+	0.895367i	−0.0461525	+	0.0335318i
$714$		0			0
$715$	35.3648	−	5.13638i	1.32257	−	0.192090i
$716$		0			0
$717$	−19.4926	+	14.1622i	−0.727963	+	0.528896i
$718$		0			0
$719$	−3.85521	+	11.8651i	−0.143775	+	0.442494i	−0.996851	−	0.0792919i	$-0.974734\pi$
$719$	−3.85521	+	11.8651i	−0.143775	+	0.442494i	0.853076	+	0.521786i	$0.174734\pi$
$720$		0			0
$721$	10.0471	+	7.29963i	0.374173	+	0.271852i
$722$		0			0
$723$	−4.22536	−	13.0043i	−0.157143	−	0.483636i
$724$		0			0
$725$	4.51162			0.167557
$726$		0			0
$727$	−16.3245			−0.605442			−0.302721	−	0.953079i	$-0.597895\pi$
$727$	−16.3245			−0.605442			−0.302721	+	0.953079i	$0.597895\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−1.93021	−	1.40238i	−0.0713914	−	0.0518689i
$732$		0			0
$733$	4.83249	−	14.8729i	0.178492	−	0.549342i	−0.821284	−	0.570520i	$-0.806742\pi$
$733$	4.83249	−	14.8729i	0.178492	−	0.549342i	0.999776	+	0.0211781i	$0.00674171\pi$
$734$		0			0
$735$	−15.1214	+	10.9863i	−0.557760	+	0.405236i
$736$		0			0
$737$	−17.3155	+	2.51490i	−0.637825	+	0.0926377i
$738$		0			0
$739$	−32.7572	+	23.7995i	−1.20499	+	0.875480i	−0.994767	−	0.102172i	$-0.967421\pi$
$739$	−32.7572	+	23.7995i	−1.20499	+	0.875480i	−0.210228	+	0.977652i	$0.567421\pi$
$740$		0			0
$741$	6.41217	−	19.7346i	0.235557	−	0.724970i
$742$		0			0
$743$	27.3034	+	19.8371i	1.00167	+	0.727752i	0.962445	−	0.271478i	$-0.0875125\pi$
$743$	27.3034	+	19.8371i	1.00167	+	0.727752i	0.0392206	+	0.999231i	$0.487512\pi$
$744$		0			0
$745$	−12.6186	−	38.8362i	−0.462311	−	1.42285i
$746$		0			0
$747$	−14.1211			−0.516664
$748$		0			0
$749$	−17.7046			−0.646910
$750$		0			0
$751$	−3.29519	−	10.1415i	−0.120243	−	0.370070i	0.872761	−	0.488147i	$-0.162327\pi$
$751$	−3.29519	−	10.1415i	−0.120243	−	0.370070i	−0.993004	+	0.118077i	$0.962327\pi$
$752$		0			0
$753$	−19.7941	−	14.3813i	−0.721337	−	0.524082i
$754$		0			0
$755$	−17.7720	+	54.6967i	−0.646790	+	1.99062i
$756$		0			0
$757$	−12.5856	+	9.14400i	−0.457433	+	0.332344i	−0.792523	−	0.609841i	$-0.791233\pi$
$757$	−12.5856	+	9.14400i	−0.457433	+	0.332344i	0.335090	+	0.942186i	$0.391233\pi$
$758$		0			0
$759$	1.19027	+	2.41216i	0.0432041	+	0.0875559i
$760$		0			0
$761$	6.61906	−	4.80903i	0.239941	−	0.174327i	−0.461316	−	0.887236i	$-0.652623\pi$
$761$	6.61906	−	4.80903i	0.239941	−	0.174327i	0.701257	+	0.712909i	$0.252623\pi$
$762$		0			0
$763$	−0.0359234	+	0.110561i	−0.00130051	+	0.00400257i
$764$		0			0
$765$	−10.3651	−	7.53065i	−0.374749	−	0.272271i
$766$		0			0
$767$	4.80641	+	14.7926i	0.173549	+	0.534130i
$768$		0			0
$769$	−31.2236			−1.12595			−0.562975	−	0.826474i	$-0.690343\pi$
$769$	−31.2236			−1.12595			−0.562975	+	0.826474i	$0.690343\pi$
$770$		0			0
$771$	17.2148			0.619976
$772$		0			0
$773$	−3.44712	−	10.6092i	−0.123984	−	0.381585i	0.869730	−	0.493527i	$-0.164293\pi$
$773$	−3.44712	−	10.6092i	−0.123984	−	0.381585i	−0.993715	+	0.111943i	$0.964293\pi$
$774$		0			0
$775$	−8.44304	−	6.13423i	−0.303283	−	0.220348i
$776$		0			0
$777$	−1.78487	+	5.49328i	−0.0640320	+	0.197070i
$778$		0			0
$779$	−0.596082	+	0.433079i	−0.0213568	+	0.0155167i
$780$		0			0
$781$	−38.7257	−	20.3626i	−1.38571	−	0.728631i
$782$		0			0
$783$	−0.656902	+	0.477267i	−0.0234758	+	0.0170561i
$784$		0			0
$785$	11.1784	−	34.4036i	0.398974	−	1.22792i
$786$		0			0
$787$	−39.6481	−	28.8061i	−1.41330	−	1.02683i	−0.992832	−	0.119520i	$-0.961864\pi$
$787$	−39.6481	−	28.8061i	−1.41330	−	1.02683i	−0.420472	−	0.907305i	$-0.638136\pi$
$788$		0			0
$789$	0.467774	+	1.43966i	0.0166532	+	0.0512532i
$790$		0			0
$791$	13.6562			0.485557
$792$		0			0
$793$	−26.4388			−0.938870
$794$		0			0
$795$	−10.9710	−	33.7653i	−0.389102	−	1.19753i
$796$		0			0
$797$	−27.8223	−	20.2141i	−0.985516	−	0.716019i	−0.0265815	−	0.999647i	$-0.508462\pi$
$797$	−27.8223	−	20.2141i	−0.985516	−	0.716019i	−0.958935	+	0.283627i	$0.908462\pi$
$798$		0			0
$799$	6.84686	−	21.0725i	0.242224	−	0.745490i
$800$		0			0
$801$	−10.6485	+	7.73658i	−0.376246	+	0.273358i
$802$		0			0
$803$	−1.15319	+	6.72093i	−0.0406953	+	0.237176i
$804$		0			0
$805$	2.38078	−	1.72974i	0.0839115	−	0.0609653i
$806$		0			0
$807$	0.967468	−	2.97756i	0.0340565	−	0.104815i
$808$		0			0
$809$	−3.83283	−	2.78471i	−0.134755	−	0.0979053i	0.518366	−	0.855159i	$-0.326541\pi$
$809$	−3.83283	−	2.78471i	−0.134755	−	0.0979053i	−0.653121	+	0.757254i	$0.726541\pi$
$810$		0			0
$811$	0.439870	+	1.35378i	0.0154459	+	0.0475377i	0.958482	−	0.285152i	$-0.0920440\pi$
$811$	0.439870	+	1.35378i	0.0154459	+	0.0475377i	−0.943036	+	0.332689i	$0.892044\pi$
$812$		0			0
$813$	0.518767			0.0181940
$814$		0			0
$815$	−82.6767			−2.89604
$816$		0			0
$817$	1.16989	+	3.60054i	0.0409292	+	0.125967i
$818$		0			0
$819$	2.99628	+	2.17693i	0.104699	+	0.0760680i
$820$		0			0
$821$	−9.17379	+	28.2340i	−0.320168	+	0.985374i	0.653407	+	0.757007i	$0.273339\pi$
$821$	−9.17379	+	28.2340i	−0.320168	+	0.985374i	−0.973575	+	0.228368i	$0.926661\pi$
$822$		0			0
$823$	−6.83410	+	4.96526i	−0.238222	+	0.173078i	−0.700491	−	0.713662i	$-0.747035\pi$
$823$	−6.83410	+	4.96526i	−0.238222	+	0.173078i	0.462269	+	0.886740i	$0.347035\pi$
$824$		0			0
$825$	−13.1971	+	12.8623i	−0.459465	+	0.447808i
$826$		0			0
$827$	4.66210	−	3.38721i	0.162117	−	0.117785i	−0.503769	−	0.863838i	$-0.668054\pi$
$827$	4.66210	−	3.38721i	0.162117	−	0.117785i	0.665886	+	0.746054i	$0.268054\pi$
$828$		0			0
$829$	−12.8466	+	39.5376i	−0.446179	+	1.37320i	0.435006	+	0.900427i	$0.356746\pi$
$829$	−12.8466	+	39.5376i	−0.446179	+	1.37320i	−0.881185	+	0.472771i	$0.843254\pi$
$830$		0			0
$831$	23.2755	+	16.9106i	0.807417	+	0.586622i
$832$		0			0
$833$	7.00997	+	21.5745i	0.242881	+	0.747511i
$834$		0			0
$835$	23.1158			0.799956
$836$		0			0
$837$	1.87824			0.0649216
$838$		0			0
$839$	5.15925	+	15.8785i	0.178117	+	0.548188i	0.999762	−	0.0218113i	$-0.00694331\pi$
$839$	5.15925	+	15.8785i	0.178117	+	0.548188i	−0.821645	+	0.570000i	$0.806943\pi$
$840$		0			0
$841$	22.9281	+	16.6582i	0.790624	+	0.574422i
$842$		0			0
$843$	−6.75125	+	20.7782i	−0.232525	+	0.715639i
$844$		0			0
$845$	−5.26312	+	3.82388i	−0.181057	+	0.131546i
$846$		0			0
$847$	0.315640	−	12.2807i	0.0108455	−	0.421970i
$848$		0			0
$849$	13.0705	−	9.49628i	0.448579	−	0.325911i
$850$		0			0
$851$	−1.29618	+	3.98922i	−0.0444323	+	0.136749i
$852$		0			0
$853$	−33.7963	−	24.5545i	−1.15716	−	0.840729i	−0.167747	−	0.985830i	$-0.553649\pi$
$853$	−33.7963	−	24.5545i	−1.15716	−	0.840729i	−0.989417	+	0.145101i	$0.953649\pi$
$854$		0			0
$855$	6.28219	+	19.3346i	0.214846	+	0.661229i
$856$		0			0
$857$	13.1283			0.448455			0.224227	−	0.974537i	$-0.428014\pi$
$857$	13.1283			0.448455			0.224227	+	0.974537i	$0.428014\pi$
$858$		0			0
$859$	2.12782			0.0726003			0.0363002	−	0.999341i	$-0.488443\pi$
$859$	2.12782			0.0726003			0.0363002	+	0.999341i	$0.488443\pi$
$860$		0			0
$861$	−0.0406381	−	0.125071i	−0.00138494	−	0.00426241i
$862$		0			0
$863$	25.9579	+	18.8596i	0.883619	+	0.641987i	0.934206	−	0.356733i	$-0.116109\pi$
$863$	25.9579	+	18.8596i	0.883619	+	0.641987i	−0.0505875	+	0.998720i	$0.516109\pi$
$864$		0			0
$865$	22.5021	−	69.2545i	0.765096	−	2.35472i
$866$		0			0
$867$	1.17355	−	0.852631i	0.0398557	−	0.0289569i
$868$		0			0
$869$	−41.1747	+	40.1301i	−1.39676	+	1.36132i
$870$		0			0
$871$	−14.1541	+	10.2835i	−0.479592	+	0.348444i
$872$		0			0
$873$	−3.89388	+	11.9841i	−0.131788	+	0.405601i
$874$		0			0
$875$	1.63319	+	1.18658i	0.0552118	+	0.0401137i
$876$		0			0
$877$	−16.6145	−	51.1342i	−0.561032	−	1.72668i	−0.679456	−	0.733716i	$-0.737784\pi$
$877$	−16.6145	−	51.1342i	−0.561032	−	1.72668i	0.118424	−	0.992963i	$-0.462216\pi$
$878$		0			0
$879$	10.2464			0.345604
$880$		0			0
$881$	−1.24849			−0.0420629			−0.0210314	−	0.999779i	$-0.506695\pi$
$881$	−1.24849			−0.0420629			−0.0210314	+	0.999779i	$0.506695\pi$
$882$		0			0
$883$	−12.7992	−	39.3920i	−0.430728	−	1.32565i	−0.897401	−	0.441216i	$-0.854547\pi$
$883$	−12.7992	−	39.3920i	−0.430728	−	1.32565i	0.466673	−	0.884430i	$-0.345453\pi$
$884$		0			0
$885$	−12.3283	−	8.95700i	−0.414410	−	0.301086i
$886$		0			0
$887$	11.7972	−	36.3080i	0.396111	−	1.21910i	−0.531982	−	0.846756i	$-0.678552\pi$
$887$	11.7972	−	36.3080i	0.396111	−	1.21910i	0.928093	−	0.372349i	$-0.121448\pi$
$888$		0			0
$889$	12.9598	−	9.41581i	0.434656	−	0.315796i
$890$		0			0
$891$	0.560879	−	3.26886i	0.0187901	−	0.109511i
$892$		0			0
$893$	−28.4434	+	20.6653i	−0.951821	+	0.691539i
$894$		0			0
$895$	25.1236	−	77.3226i	0.839790	−	2.58461i
$896$		0			0
$897$	2.17590	+	1.58089i	0.0726512	+	0.0527842i
$898$		0			0
$899$	0.471278	+	1.45044i	0.0157180	+	0.0483750i
$900$		0			0
$901$	−43.0888			−1.43550
$902$		0			0
$903$	−0.675716			−0.0224864
$904$		0			0
$905$	−23.2031	−	71.4119i	−0.771298	−	2.37381i
$906$		0			0
$907$	13.1002	+	9.51783i	0.434984	+	0.316034i	0.783639	−	0.621217i	$-0.213361\pi$
$907$	13.1002	+	9.51783i	0.434984	+	0.316034i	−0.348655	+	0.937251i	$0.613361\pi$
$908$		0			0
$909$	1.41897	−	4.36713i	0.0470642	−	0.144849i
$910$		0			0
$911$	−44.1658	+	32.0883i	−1.46328	+	1.06313i	−0.480784	+	0.876839i	$0.659648\pi$
$911$	−44.1658	+	32.0883i	−1.46328	+	1.06313i	−0.982494	+	0.186294i	$0.940352\pi$
$912$		0			0
$913$	41.4531	+	21.7968i	1.37190	+	0.721367i
$914$		0			0
$915$	20.9559	−	15.2253i	0.692779	−	0.503334i
$916$		0			0
$917$	5.23366	−	16.1076i	0.172831	−	0.531918i
$918$		0			0
$919$	−12.1111	−	8.79921i	−0.399507	−	0.290259i	0.369833	−	0.929098i	$-0.379415\pi$
$919$	−12.1111	−	8.79921i	−0.399507	−	0.290259i	−0.769340	+	0.638839i	$0.779415\pi$
$920$		0			0
$921$	−7.82029	−	24.0684i	−0.257687	−	0.793080i
$922$		0			0
$923$	−43.7483			−1.43999
$924$		0			0
$925$	−28.7369			−0.944864
$926$		0			0
$927$	−3.43629	−	10.5758i	−0.112863	−	0.347356i
$928$		0			0
$929$	17.3130	+	12.5786i	0.568022	+	0.412692i	0.834386	−	0.551180i	$-0.185822\pi$
$929$	17.3130	+	12.5786i	0.568022	+	0.412692i	−0.266364	+	0.963872i	$0.585822\pi$
$930$		0			0
$931$	11.1232	−	34.2338i	0.364549	−	1.12197i
$932$		0			0
$933$	−16.0139	+	11.6348i	−0.524272	+	0.380906i
$934$		0			0
$935$	18.8031	+	38.1056i	0.614926	+	1.24619i
$936$		0			0
$937$	44.5506	−	32.3679i	1.45540	−	1.05741i	0.470873	−	0.882201i	$-0.343939\pi$
$937$	44.5506	−	32.3679i	1.45540	−	1.05741i	0.984531	−	0.175212i	$-0.0560610\pi$
$938$		0			0
$939$	−9.10963	+	28.0366i	−0.297282	+	0.914939i
$940$		0			0
$941$	−13.6377	−	9.90835i	−0.444575	−	0.323003i	0.342875	−	0.939381i	$-0.388599\pi$
$941$	−13.6377	−	9.90835i	−0.444575	−	0.323003i	−0.787450	+	0.616378i	$0.788599\pi$
$942$		0			0
$943$	−0.0295114	−	0.0908267i	−0.000961023	−	0.00295773i
$944$		0			0
$945$	−3.62853			−0.118036
$946$		0			0
$947$	43.1436			1.40198			0.700989	−	0.713172i	$-0.252742\pi$
$947$	43.1436			1.40198			0.700989	+	0.713172i	$0.252742\pi$
$948$		0			0
$949$	2.10701	+	6.48471i	0.0683965	+	0.210503i
$950$		0			0
$951$	9.57482	+	6.95651i	0.310485	+	0.225580i
$952$		0			0
$953$	3.36126	−	10.3449i	0.108882	−	0.335104i	−0.881740	−	0.471735i	$-0.843628\pi$
$953$	3.36126	−	10.3449i	0.108882	−	0.335104i	0.990622	+	0.136632i	$0.0436277\pi$
$954$		0			0
$955$	46.4701	−	33.7625i	1.50374	−	1.09253i
$956$		0			0
$957$	2.66506	−	0.387073i	0.0861490	−	0.0125123i
$958$		0			0
$959$	−13.9808	+	10.1577i	−0.451465	+	0.328009i
$960$		0			0
$961$	−8.48938	+	26.1276i	−0.273851	+	0.842826i
$962$		0			0
$963$	12.8253	+	9.31815i	0.413290	+	0.300273i
$964$		0			0
$965$	−16.8560	−	51.8774i	−0.542614	−	1.66999i
$966$		0			0
$967$	−5.69152			−0.183027			−0.0915135	−	0.995804i	$-0.529170\pi$
$967$	−5.69152			−0.183027			−0.0915135	+	0.995804i	$0.529170\pi$
$968$		0			0
$969$	24.6734			0.792623
$970$		0			0
$971$	−14.6985	−	45.2374i	−0.471698	−	1.45174i	−0.850360	−	0.526202i	$-0.823616\pi$
$971$	−14.6985	−	45.2374i	−0.471698	−	1.45174i	0.378662	−	0.925535i	$-0.376384\pi$
$972$		0			0
$973$	−1.82789	−	1.32804i	−0.0585996	−	0.0425751i
$974$		0			0
$975$	−5.69407	+	17.5245i	−0.182356	+	0.561235i
$976$		0			0
$977$	4.83562	−	3.51328i	0.154705	−	0.112400i	−0.507740	−	0.861510i	$-0.669519\pi$
$977$	4.83562	−	3.51328i	0.154705	−	0.112400i	0.662445	+	0.749111i	$0.269519\pi$
$978$		0			0
$979$	43.2010	−	6.27451i	1.38071	−	0.200534i
$980$		0			0
$981$	0.0842129	−	0.0611842i	0.00268871	−	0.00195346i
$982$		0			0
$983$	−11.4661	+	35.2891i	−0.365712	+	1.12555i	0.583822	+	0.811882i	$0.301557\pi$
$983$	−11.4661	+	35.2891i	−0.365712	+	1.12555i	−0.949534	+	0.313665i	$0.898443\pi$
$984$		0			0
$985$	−2.96066	−	2.15104i	−0.0943345	−	0.0685380i
$986$		0			0
$987$	−1.93914	−	5.96805i	−0.0617234	−	0.189965i
$988$		0			0
$989$	−0.490705			−0.0156035
$990$		0			0
$991$	−33.5152			−1.06465			−0.532323	−	0.846542i	$-0.678681\pi$
$991$	−33.5152			−1.06465			−0.532323	+	0.846542i	$0.678681\pi$
$992$		0			0
$993$	7.50759	+	23.1060i	0.238246	+	0.733247i
$994$		0			0
$995$	−14.5335	−	10.5592i	−0.460743	−	0.334750i
$996$		0			0
$997$	0.575741	−	1.77195i	0.0182339	−	0.0561182i	−0.941526	−	0.336942i	$-0.890608\pi$
$997$	0.575741	−	1.77195i	0.0182339	−	0.0561182i	0.959759	+	0.280823i	$0.0906075\pi$
$998$		0			0
$999$	4.18416	−	3.03997i	0.132381	−	0.0961805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1056.2.y.f.289.3	✓	12
4.3	odd	2		1056.2.y.i.289.3	yes	12
11.4	even	5	inner	1056.2.y.f.961.3	yes	12
44.15	odd	10		1056.2.y.i.961.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1056.2.y.f.289.3	✓	12	1.1	even	1	trivial
1056.2.y.f.961.3	yes	12	11.4	even	5	inner
1056.2.y.i.289.3	yes	12	4.3	odd	2
1056.2.y.i.961.3	yes	12	44.15	odd	10

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)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{3} +(2.62854 + 1.90975i) q^{5} +(0.345109 - 1.06214i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(3.28219 - 0.476705i) q^{11} +(2.68293 - 1.94926i) q^{13} +(-1.00401 + 3.09003i) q^{15} +(3.19018 + 2.31780i) q^{17} +(-1.93354 - 5.95084i) q^{19} +1.11680 q^{21} +0.811018 q^{23} +(1.71701 + 5.28440i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(0.250914 - 0.772235i) q^{29} +(-1.51953 + 1.10400i) q^{31} +(1.46762 + 2.97424i) q^{33} +(2.93555 - 2.13280i) q^{35} +(-1.59821 + 4.91878i) q^{37} +(2.68293 + 1.94926i) q^{39} +(-0.0363881 - 0.111991i) q^{41} -0.605048 q^{43} -3.24905 q^{45} +(-1.73634 - 5.34390i) q^{47} +(4.65408 + 3.38139i) q^{49} +(-1.21854 + 3.75028i) q^{51} +(-8.84026 + 6.42282i) q^{53} +(9.53774 + 5.01511i) q^{55} +(5.06208 - 3.67782i) q^{57} +(-1.44934 + 4.46060i) q^{59} +(-6.44984 - 4.68608i) q^{61} +(0.345109 + 1.06214i) q^{63} +10.7748 q^{65} -5.27560 q^{67} +(0.250618 + 0.771324i) q^{69} +(-10.6725 - 7.75405i) q^{71} +(-0.635354 + 1.95542i) q^{73} +(-4.49518 + 3.26594i) q^{75} +(0.626388 - 3.65065i) q^{77} +(-14.0249 + 10.1897i) q^{79} +(0.309017 - 0.951057i) q^{81} +(11.4242 + 8.30017i) q^{83} +(3.95910 + 12.1849i) q^{85} +0.811976 q^{87} +13.1623 q^{89} +(-1.14448 - 3.52234i) q^{91} +(-1.51953 - 1.10400i) q^{93} +(6.28219 - 19.3346i) q^{95} +(10.1943 - 7.40659i) q^{97} +(-2.37515 + 2.31488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 3 q^{9} + 6 q^{11} + 6 q^{13} - 5 q^{15} + 8 q^{19} + 10 q^{21} + 8 q^{23} + 9 q^{25} - 3 q^{27} + 5 q^{29} - 11 q^{31} + q^{33} + 9 q^{35} - 6 q^{37} + 6 q^{39} - 10 q^{41} - 16 q^{43}+ \cdots + q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 3 * q^9 + 6 * q^11 + 6 * q^13 - 5 * q^15 + 8 * q^19 + 10 * q^21 + 8 * q^23 + 9 * q^25 - 3 * q^27 + 5 * q^29 - 11 * q^31 + q^33 + 9 * q^35 - 6 * q^37 + 6 * q^39 - 10 * q^41 - 16 * q^43 + 10 * q^45 - 6 * q^47 + 15 * q^49 - 17 * q^53 + 4 * q^55 - 2 * q^57 - 14 * q^59 - 44 * q^61 + 20 * q^65 + 48 * q^67 - 2 * q^69 - 10 * q^71 - 3 * q^73 - 16 * q^75 + 34 * q^77 - 4 * q^79 - 3 * q^81 + 20 * q^83 - 10 * q^85 - 10 * q^87 + 44 * q^89 - 80 * q^91 - 11 * q^93 + 42 * q^95 - 16 * q^97 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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