LMFDB - Embedded newform 882.2.l.b.509.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(227,882)] 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("882.227"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-16,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.7
Root			$1.27866 + 1.16834i$ of defining polynomial
Character	$\chi$	$=$	882.509
Dual form			882.2.l.b.227.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(1.08509 + 1.35003i) q^{3} -1.00000 q^{4} +(-1.77612 - 3.07634i) q^{5} +(-1.35003 + 1.08509i) q^{6} -1.00000i q^{8} +(-0.645160 + 2.92981i) q^{9} +(3.07634 - 1.77612i) q^{10} +(2.61745 + 1.51119i) q^{11} +(-1.08509 - 1.35003i) q^{12} +(0.888944 + 0.513232i) q^{13} +(2.22589 - 5.73592i) q^{15} +1.00000 q^{16} +(0.809204 + 1.40158i) q^{17} +(-2.92981 - 0.645160i) q^{18} +(7.12643 + 4.11444i) q^{19} +(1.77612 + 3.07634i) q^{20} +(-1.51119 + 2.61745i) q^{22} +(2.90837 - 1.67915i) q^{23} +(1.35003 - 1.08509i) q^{24} +(-3.80924 + 6.59779i) q^{25} +(-0.513232 + 0.888944i) q^{26} +(-4.65538 + 2.30812i) q^{27} +(-3.70319 + 2.13804i) q^{29} +(5.73592 + 2.22589i) q^{30} +5.98576i q^{31} +1.00000i q^{32} +(0.800023 + 5.17341i) q^{33} +(-1.40158 + 0.809204i) q^{34} +(0.645160 - 2.92981i) q^{36} +(2.92323 - 5.06319i) q^{37} +(-4.11444 + 7.12643i) q^{38} +(0.271706 + 1.75700i) q^{39} +(-3.07634 + 1.77612i) q^{40} +(-0.0472226 + 0.0817920i) q^{41} +(3.05899 + 5.29833i) q^{43} +(-2.61745 - 1.51119i) q^{44} +(10.1590 - 3.21897i) q^{45} +(1.67915 + 2.90837i) q^{46} +5.14045 q^{47} +(1.08509 + 1.35003i) q^{48} +(-6.59779 - 3.80924i) q^{50} +(-1.01412 + 2.61329i) q^{51} +(-0.888944 - 0.513232i) q^{52} +(-2.76235 + 1.59484i) q^{53} +(-2.30812 - 4.65538i) q^{54} -10.7362i q^{55} +(2.17819 + 14.0854i) q^{57} +(-2.13804 - 3.70319i) q^{58} +8.84071 q^{59} +(-2.22589 + 5.73592i) q^{60} +4.69034i q^{61} -5.98576 q^{62} -1.00000 q^{64} -3.64626i q^{65} +(-5.17341 + 0.800023i) q^{66} -0.375675 q^{67} +(-0.809204 - 1.40158i) q^{68} +(5.42275 + 2.10436i) q^{69} -13.9868i q^{71} +(2.92981 + 0.645160i) q^{72} +(-1.13546 + 0.655556i) q^{73} +(5.06319 + 2.92323i) q^{74} +(-13.0406 + 2.01662i) q^{75} +(-7.12643 - 4.11444i) q^{76} +(-1.75700 + 0.271706i) q^{78} +0.924134 q^{79} +(-1.77612 - 3.07634i) q^{80} +(-8.16754 - 3.78039i) q^{81} +(-0.0817920 - 0.0472226i) q^{82} +(-5.43209 - 9.40866i) q^{83} +(2.87450 - 4.97877i) q^{85} +(-5.29833 + 3.05899i) q^{86} +(-6.90471 - 2.67945i) q^{87} +(1.51119 - 2.61745i) q^{88} +(2.35495 - 4.07888i) q^{89} +(3.21897 + 10.1590i) q^{90} +(-2.90837 + 1.67915i) q^{92} +(-8.08095 + 6.49509i) q^{93} +5.14045i q^{94} -29.2311i q^{95} +(-1.35003 + 1.08509i) q^{96} +(-13.3330 + 7.69782i) q^{97} +(-6.11615 + 6.69367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 12 q^{11} - 6 q^{13} - 18 q^{15} + 16 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 36 q^{27} + 6 q^{29} - 2 q^{37} - 12 q^{39} + 6 q^{41} - 2 q^{43} - 12 q^{44} + 30 q^{45}+ \cdots + 18 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 12 * q^11 - 6 * q^13 - 18 * q^15 + 16 * q^16 + 18 * q^17 - 12 * q^18 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 36 * q^27 + 6 * q^29 - 2 * q^37 - 12 * q^39 + 6 * q^41 - 2 * q^43 - 12 * q^44 + 30 * q^45 + 6 * q^46 + 36 * q^47 - 12 * q^50 + 6 * q^51 + 6 * q^52 - 36 * q^53 - 18 * q^54 + 6 * q^57 + 6 * q^58 - 60 * q^59 + 18 * q^60 - 36 * q^62 - 16 * q^64 - 24 * q^66 - 28 * q^67 - 18 * q^68 + 42 * q^69 + 12 * q^72 + 18 * q^74 - 60 * q^75 + 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^86 + 24 * q^87 + 24 * q^89 - 18 * q^90 + 6 * q^92 - 42 * q^93 - 6 * q^97 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.08509	+	1.35003i	0.626477	+	0.779440i
$3$	1.08509	+	1.35003i	0.626477	+	0.779440i
$4$	−1.00000			−0.500000
$5$	−1.77612	−	3.07634i	−0.794307	−	1.37578i	−0.923278	−	0.384132i	$-0.874501\pi$
$5$	−1.77612	−	3.07634i	−0.794307	−	1.37578i	0.128971	−	0.991648i	$-0.458833\pi$
$6$	−1.35003	+	1.08509i	−0.551147	+	0.442986i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−0.645160	+	2.92981i	−0.215053	+	0.976602i
$10$	3.07634	−	1.77612i	0.972824	−	0.561660i
$11$	2.61745	+	1.51119i	0.789191	+	0.455639i	0.839678	−	0.543085i	$-0.182744\pi$
$11$	2.61745	+	1.51119i	0.789191	+	0.455639i	−0.0504869	+	0.998725i	$0.516077\pi$
$12$	−1.08509	−	1.35003i	−0.313238	−	0.389720i
$13$	0.888944	+	0.513232i	0.246549	+	0.142345i	0.618183	−	0.786034i	$-0.287869\pi$
$13$	0.888944	+	0.513232i	0.246549	+	0.142345i	−0.371634	+	0.928379i	$0.621202\pi$
$14$		0			0
$15$	2.22589	−	5.73592i	0.574723	−	1.48101i
$16$	1.00000			0.250000
$17$	0.809204	+	1.40158i	0.196261	+	0.339934i	0.947313	−	0.320309i	$-0.103787\pi$
$17$	0.809204	+	1.40158i	0.196261	+	0.339934i	−0.751052	+	0.660243i	$0.770453\pi$
$18$	−2.92981	−	0.645160i	−0.690562	−	0.152066i
$19$	7.12643	+	4.11444i	1.63491	+	0.943918i	0.982547	+	0.186016i	$0.0595575\pi$
$19$	7.12643	+	4.11444i	1.63491	+	0.943918i	0.652368	+	0.757903i	$0.273776\pi$
$20$	1.77612	+	3.07634i	0.397154	+	0.687890i
$21$		0			0
$22$	−1.51119	+	2.61745i	−0.322186	+	0.558042i
$23$	2.90837	−	1.67915i	0.606438	−	0.350127i	−0.165132	−	0.986271i	$-0.552805\pi$
$23$	2.90837	−	1.67915i	0.606438	−	0.350127i	0.771570	+	0.636144i	$0.219472\pi$
$24$	1.35003	−	1.08509i	0.275574	−	0.221493i
$25$	−3.80924	+	6.59779i	−0.761848	+	1.31956i
$26$	−0.513232	+	0.888944i	−0.100653	+	0.174336i
$27$	−4.65538	+	2.30812i	−0.895929	+	0.444198i
$28$		0			0
$29$	−3.70319	+	2.13804i	−0.687666	+	0.397024i	−0.802737	−	0.596333i	$-0.796624\pi$
$29$	−3.70319	+	2.13804i	−0.687666	+	0.397024i	0.115071	+	0.993357i	$0.463290\pi$
$30$	5.73592	+	2.22589i	1.04723	+	0.406391i
$31$			5.98576i			1.07507i	0.843240	+	0.537537i	$0.180645\pi$
$31$			5.98576i			1.07507i	−0.843240	+	0.537537i	$0.819355\pi$
$32$			1.00000i			0.176777i
$33$	0.800023	+	5.17341i	0.139266	+	0.900574i
$34$	−1.40158	+	0.809204i	−0.240369	+	0.138777i
$35$		0			0
$36$	0.645160	−	2.92981i	0.107527	−	0.488301i
$37$	2.92323	−	5.06319i	0.480577	−	0.832384i	−0.519175	−	0.854668i	$-0.673761\pi$
$37$	2.92323	−	5.06319i	0.480577	−	0.832384i	0.999752	+	0.0222846i	$0.00709398\pi$
$38$	−4.11444	+	7.12643i	−0.667451	+	1.15606i
$39$	0.271706	+	1.75700i	0.0435078	+	0.281346i
$40$	−3.07634	+	1.77612i	−0.486412	+	0.280830i
$41$	−0.0472226	+	0.0817920i	−0.00737493	+	0.0127738i	−0.869689	−	0.493600i	$-0.835681\pi$
$41$	−0.0472226	+	0.0817920i	−0.00737493	+	0.0127738i	0.862314	+	0.506373i	$0.169014\pi$
$42$		0			0
$43$	3.05899	+	5.29833i	0.466492	+	0.807988i	0.999267	−	0.0382684i	$-0.0121842\pi$
$43$	3.05899	+	5.29833i	0.466492	+	0.807988i	−0.532775	+	0.846257i	$0.678851\pi$
$44$	−2.61745	−	1.51119i	−0.394595	−	0.227820i
$45$	10.1590	−	3.21897i	1.51441	−	0.479856i
$46$	1.67915	+	2.90837i	0.247577	+	0.428816i
$47$	5.14045			0.749812			0.374906	−	0.927063i	$-0.377675\pi$
$47$	5.14045			0.749812			0.374906	+	0.927063i	$0.377675\pi$
$48$	1.08509	+	1.35003i	0.156619	+	0.194860i
$49$		0			0
$50$	−6.59779	−	3.80924i	−0.933069	−	0.538708i
$51$	−1.01412	+	2.61329i	−0.142005	+	0.365934i
$52$	−0.888944	−	0.513232i	−0.123274	−	0.0711725i
$53$	−2.76235	+	1.59484i	−0.379438	+	0.219068i	−0.677574	−	0.735455i	$-0.736968\pi$
$53$	−2.76235	+	1.59484i	−0.379438	+	0.219068i	0.298136	+	0.954523i	$0.403635\pi$
$54$	−2.30812	−	4.65538i	−0.314095	−	0.633517i
$55$		−	10.7362i		−	1.44767i
$56$		0			0
$57$	2.17819	+	14.0854i	0.288509	+	1.86566i
$58$	−2.13804	−	3.70319i	−0.280738	−	0.486253i
$59$	8.84071			1.15096			0.575481	−	0.817815i	$-0.304815\pi$
$59$	8.84071			1.15096			0.575481	+	0.817815i	$0.304815\pi$
$60$	−2.22589	+	5.73592i	−0.287361	+	0.740505i
$61$			4.69034i			0.600537i	0.953855	+	0.300268i	$0.0970762\pi$
$61$			4.69034i			0.600537i	−0.953855	+	0.300268i	$0.902924\pi$
$62$	−5.98576			−0.760192
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	3.64626i		−	0.452263i
$66$	−5.17341	+	0.800023i	−0.636802	+	0.0984761i
$67$	−0.375675			−0.0458961			−0.0229480	−	0.999737i	$-0.507305\pi$
$67$	−0.375675			−0.0458961			−0.0229480	+	0.999737i	$0.507305\pi$
$68$	−0.809204	−	1.40158i	−0.0981304	−	0.169967i
$69$	5.42275	+	2.10436i	0.652822	+	0.253335i
$70$		0			0
$71$		−	13.9868i		−	1.65993i	−0.557815	−	0.829966i	$-0.688360\pi$
$71$		−	13.9868i		−	1.65993i	0.557815	−	0.829966i	$-0.311640\pi$
$72$	2.92981	+	0.645160i	0.345281	+	0.0760328i
$73$	−1.13546	+	0.655556i	−0.132895	+	0.0767270i	−0.564974	−	0.825109i	$-0.691114\pi$
$73$	−1.13546	+	0.655556i	−0.132895	+	0.0767270i	0.432079	+	0.901836i	$0.357780\pi$
$74$	5.06319	+	2.92323i	0.588584	+	0.339819i
$75$	−13.0406	+	2.01662i	−1.50580	+	0.232859i
$76$	−7.12643	−	4.11444i	−0.817457	−	0.471959i
$77$		0			0
$78$	−1.75700	+	0.271706i	−0.198942	+	0.0307646i
$79$	0.924134			0.103973			0.0519866	−	0.998648i	$-0.483445\pi$
$79$	0.924134			0.103973			0.0519866	+	0.998648i	$0.483445\pi$
$80$	−1.77612	−	3.07634i	−0.198577	−	0.343945i
$81$	−8.16754	−	3.78039i	−0.907504	−	0.420043i
$82$	−0.0817920	−	0.0472226i	−0.00903241	−	0.00521487i
$83$	−5.43209	−	9.40866i	−0.596250	−	1.03273i	−0.993369	−	0.114968i	$-0.963323\pi$
$83$	−5.43209	−	9.40866i	−0.596250	−	1.03273i	0.397119	−	0.917767i	$-0.370010\pi$
$84$		0			0
$85$	2.87450	−	4.97877i	0.311783	−	0.540024i
$86$	−5.29833	+	3.05899i	−0.571334	+	0.329860i
$87$	−6.90471	−	2.67945i	−0.740263	−	0.287268i
$88$	1.51119	−	2.61745i	0.161093	−	0.279021i
$89$	2.35495	−	4.07888i	0.249624	−	0.432361i	−0.713798	−	0.700352i	$-0.753026\pi$
$89$	2.35495	−	4.07888i	0.249624	−	0.432361i	0.963421	+	0.267991i	$0.0863598\pi$
$90$	3.21897	+	10.1590i	0.339310	+	1.07085i
$91$		0			0
$92$	−2.90837	+	1.67915i	−0.303219	+	0.175063i
$93$	−8.08095	+	6.49509i	−0.837956	+	0.673509i
$94$			5.14045i			0.530197i
$95$		−	29.2311i		−	2.99904i
$96$	−1.35003	+	1.08509i	−0.137787	+	0.110747i
$97$	−13.3330	+	7.69782i	−1.35376	+	0.781595i	−0.988774	−	0.149417i	$-0.952260\pi$
$97$	−13.3330	+	7.69782i	−1.35376	+	0.781595i	−0.364988	+	0.931012i	$0.618927\pi$
$98$		0			0
$99$	−6.11615	+	6.69367i	−0.614697	+	0.672739i
$100$	3.80924	−	6.59779i	0.380924	−	0.659779i
$101$	6.85234	−	11.8686i	0.681833	−	1.18097i	−0.292588	−	0.956239i	$-0.594516\pi$
$101$	6.85234	−	11.8686i	0.681833	−	1.18097i	0.974421	−	0.224731i	$-0.0721503\pi$
$102$	−2.61329	−	1.01412i	−0.258755	−	0.100413i
$103$	−2.64014	+	1.52429i	−0.260141	+	0.150192i	−0.624399	−	0.781106i	$-0.714656\pi$
$103$	−2.64014	+	1.52429i	−0.260141	+	0.150192i	0.364258	+	0.931298i	$0.381323\pi$
$104$	0.513232	−	0.888944i	0.0503266	−	0.0871682i
$105$		0			0
$106$	−1.59484	−	2.76235i	−0.154905	−	0.268303i
$107$	−11.3681	−	6.56336i	−1.09899	−	0.634504i	−0.163037	−	0.986620i	$-0.552129\pi$
$107$	−11.3681	−	6.56336i	−1.09899	−	0.634504i	−0.935956	+	0.352116i	$0.885462\pi$
$108$	4.65538	−	2.30812i	0.447964	−	0.222099i
$109$	5.28574	+	9.15516i	0.506282	+	0.876906i	0.999974	+	0.00726875i	$0.00231373\pi$
$109$	5.28574	+	9.15516i	0.506282	+	0.876906i	−0.493692	+	0.869637i	$0.664353\pi$
$110$	10.7362			1.02366
$111$	10.0074	−	1.54756i	0.949863	−	0.146888i
$112$		0			0
$113$	10.6520	+	6.14993i	1.00205	+	0.578537i	0.908856	−	0.417111i	$-0.136957\pi$
$113$	10.6520	+	6.14993i	1.00205	+	0.578537i	0.0931992	+	0.995647i	$0.470291\pi$
$114$	−14.0854	+	2.17819i	−1.31922	+	0.204006i
$115$	−10.3313	−	5.96476i	−0.963396	−	0.556217i
$116$	3.70319	−	2.13804i	0.343833	−	0.198512i
$117$	−2.07718	+	2.27332i	−0.192036	+	0.210168i
$118$			8.84071i			0.813853i
$119$		0			0
$120$	−5.73592	−	2.22589i	−0.523616	−	0.203195i
$121$	−0.932639	−	1.61538i	−0.0847854	−	0.146853i
$122$	−4.69034			−0.424644
$123$	−0.161662	+	0.0249997i	−0.0145766	+	0.00225415i
$124$		−	5.98576i		−	0.537537i
$125$	9.30148			0.831950
$126$		0			0
$127$	0.287164			0.0254817			0.0127408	−	0.999919i	$-0.495944\pi$
$127$	0.287164			0.0254817			0.0127408	+	0.999919i	$0.495944\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−3.83362	+	9.87890i	−0.337532	+	0.869789i
$130$	3.64626			0.319798
$131$	−0.186474	−	0.322983i	−0.0162923	−	0.0282192i	0.857764	−	0.514043i	$-0.171853\pi$
$131$	−0.186474	−	0.322983i	−0.0162923	−	0.0282192i	−0.874057	+	0.485824i	$0.838520\pi$
$132$	−0.800023	−	5.17341i	−0.0696331	−	0.450287i
$133$		0			0
$134$		−	0.375675i		−	0.0324534i
$135$	15.3691	+	10.2220i	1.32276	+	0.879772i
$136$	1.40158	−	0.809204i	0.120185	−	0.0693887i
$137$	6.11607	+	3.53111i	0.522531	+	0.301683i	0.737969	−	0.674834i	$-0.235785\pi$
$137$	6.11607	+	3.53111i	0.522531	+	0.301683i	−0.215439	+	0.976517i	$0.569118\pi$
$138$	−2.10436	+	5.42275i	−0.179135	+	0.461615i
$139$	12.6320	+	7.29308i	1.07143	+	0.618591i	0.928572	−	0.371152i	$-0.121037\pi$
$139$	12.6320	+	7.29308i	1.07143	+	0.618591i	0.142858	+	0.989743i	$0.454371\pi$
$140$		0			0
$141$	5.57785	+	6.93976i	0.469740	+	0.584434i
$142$	13.9868			1.17375
$143$	1.55118	+	2.68672i	0.129716	+	0.224675i
$144$	−0.645160	+	2.92981i	−0.0537633	+	0.244151i
$145$	13.1547	+	7.59485i	1.09244	+	0.630718i
$146$	−0.655556	−	1.13546i	−0.0542542	−	0.0939710i
$147$		0			0
$148$	−2.92323	+	5.06319i	−0.240288	+	0.416192i
$149$	−9.26832	+	5.35107i	−0.759290	+	0.438376i	−0.829041	−	0.559188i	$-0.811113\pi$
$149$	−9.26832	+	5.35107i	−0.759290	+	0.438376i	0.0697505	+	0.997564i	$0.477780\pi$
$150$	−2.01662	−	13.0406i	−0.164656	−	1.06476i
$151$	−8.00065	+	13.8575i	−0.651084	+	1.12771i	0.331777	+	0.943358i	$0.392352\pi$
$151$	−8.00065	+	13.8575i	−0.651084	+	1.12771i	−0.982860	+	0.184352i	$0.940981\pi$
$152$	4.11444	−	7.12643i	0.333726	−	0.578030i
$153$	−4.62843	+	1.46657i	−0.374187	+	0.118565i
$154$		0			0
$155$	18.4142	−	10.6315i	1.47907	−	0.853939i
$156$	−0.271706	−	1.75700i	−0.0217539	−	0.140673i
$157$		−	11.5267i		−	0.919928i	−0.887937	−	0.459964i	$-0.847862\pi$
$157$		−	11.5267i		−	0.919928i	0.887937	−	0.459964i	$-0.152138\pi$
$158$			0.924134i			0.0735202i
$159$	−5.15048	−	1.99870i	−0.408460	−	0.158508i
$160$	3.07634	−	1.77612i	0.243206	−	0.140415i
$161$		0			0
$162$	3.78039	−	8.16754i	0.297015	−	0.641702i
$163$	1.37386	−	2.37960i	0.107609	−	0.186385i	−0.807192	−	0.590289i	$-0.799014\pi$
$163$	1.37386	−	2.37960i	0.107609	−	0.186385i	0.914801	+	0.403904i	$0.132347\pi$
$164$	0.0472226	−	0.0817920i	0.00368747	−	0.00638688i
$165$	14.4942	−	11.6498i	1.12837	−	0.906932i
$166$	9.40866	−	5.43209i	0.730254	−	0.421612i
$167$	2.76946	−	4.79685i	0.214307	−	0.371191i	−0.738751	−	0.673979i	$-0.764584\pi$
$167$	2.76946	−	4.79685i	0.214307	−	0.371191i	0.953058	+	0.302788i	$0.0979173\pi$
$168$		0			0
$169$	−5.97319	−	10.3459i	−0.459476	−	0.795835i
$170$	4.97877	+	2.87450i	0.381854	+	0.220464i
$171$	−16.6522	+	18.2246i	−1.27343	+	1.39367i
$172$	−3.05899	−	5.29833i	−0.233246	−	0.403994i
$173$	−11.2051			−0.851905			−0.425953	−	0.904745i	$-0.640061\pi$
$173$	−11.2051			−0.851905			−0.425953	+	0.904745i	$0.640061\pi$
$174$	2.67945	−	6.90471i	0.203129	−	0.523445i
$175$		0			0
$176$	2.61745	+	1.51119i	0.197298	+	0.113910i
$177$	9.59297	+	11.9352i	0.721052	+	0.897106i
$178$	4.07888	+	2.35495i	0.305725	+	0.176511i
$179$	−2.37445	+	1.37089i	−0.177475	+	0.102465i	−0.586106	−	0.810235i	$-0.699340\pi$
$179$	−2.37445	+	1.37089i	−0.177475	+	0.102465i	0.408631	+	0.912700i	$0.366006\pi$
$180$	−10.1590	+	3.21897i	−0.757204	+	0.239928i
$181$		−	22.2899i		−	1.65679i	−0.560142	−	0.828397i	$-0.689253\pi$
$181$		−	22.2899i		−	1.65679i	0.560142	−	0.828397i	$-0.310747\pi$
$182$		0			0
$183$	−6.33210	+	5.08944i	−0.468082	+	0.376222i
$184$	−1.67915	−	2.90837i	−0.123789	−	0.214408i
$185$	−20.7681			−1.52690
$186$	−6.49509	−	8.08095i	−0.476243	−	0.592524i
$187$			4.89143i			0.357697i
$188$	−5.14045			−0.374906
$189$		0			0
$190$	29.2311			2.12064
$191$		−	5.13264i		−	0.371385i	−0.982608	−	0.185692i	$-0.940547\pi$
$191$		−	5.13264i		−	0.371385i	0.982608	−	0.185692i	$-0.0594528\pi$
$192$	−1.08509	−	1.35003i	−0.0783096	−	0.0974300i
$193$	15.9847			1.15060			0.575302	−	0.817941i	$-0.304884\pi$
$193$	15.9847			1.15060			0.575302	+	0.817941i	$0.304884\pi$
$194$	−7.69782	−	13.3330i	−0.552671	−	0.957254i
$195$	4.92256	−	3.95652i	0.352512	−	0.283332i
$196$		0			0
$197$			4.72572i			0.336694i	0.985728	+	0.168347i	$0.0538428\pi$
$197$			4.72572i			0.336694i	−0.985728	+	0.168347i	$0.946157\pi$
$198$	−6.69367	−	6.11615i	−0.475698	−	0.434656i
$199$	−1.83679	+	1.06047i	−0.130207	+	0.0751749i	−0.563689	−	0.825987i	$-0.690618\pi$
$199$	−1.83679	+	1.06047i	−0.130207	+	0.0751749i	0.433482	+	0.901162i	$0.357285\pi$
$200$	6.59779	+	3.80924i	0.466534	+	0.269354i
$201$	−0.407642	−	0.507173i	−0.0287528	−	0.0357732i
$202$	11.8686	+	6.85234i	0.835072	+	0.482129i
$203$		0			0
$204$	1.01412	−	2.61329i	0.0710025	−	0.182967i
$205$	0.335493			0.0234319
$206$	−1.52429	−	2.64014i	−0.106202	−	0.183947i
$207$	3.04322	+	9.60429i	0.211518	+	0.667544i
$208$	0.888944	+	0.513232i	0.0616372	+	0.0355863i
$209$	12.4354	+	21.5387i	0.860173	+	1.48986i
$210$		0			0
$211$	−13.8079	+	23.9160i	−0.950578	+	1.64645i	−0.206399	+	0.978468i	$0.566174\pi$
$211$	−13.8079	+	23.9160i	−0.950578	+	1.64645i	−0.744179	+	0.667981i	$0.767159\pi$
$212$	2.76235	−	1.59484i	0.189719	−	0.109534i
$213$	18.8826	−	15.1770i	1.29382	−	1.03991i
$214$	6.56336	−	11.3681i	0.448662	−	0.777105i
$215$	10.8663	−	18.8210i	0.741076	−	1.28358i
$216$	2.30812	+	4.65538i	0.157048	+	0.316759i
$217$		0			0
$218$	−9.15516	+	5.28574i	−0.620066	+	0.357995i
$219$	−2.11709	−	0.821562i	−0.143060	−	0.0555160i
$220$			10.7362i			0.723835i
$221$			1.66124i			0.111747i
$222$	1.54756	+	10.0074i	0.103866	+	0.671655i
$223$	17.6209	−	10.1734i	1.17998	−	0.681264i	0.223973	−	0.974595i	$-0.428097\pi$
$223$	17.6209	−	10.1734i	1.17998	−	0.681264i	0.956011	+	0.293331i	$0.0947638\pi$
$224$		0			0
$225$	−16.8727	−	15.4170i	−1.12485	−	1.02780i
$226$	−6.14993	+	10.6520i	−0.409087	+	0.708560i
$227$	2.08000	−	3.60266i	0.138054	−	0.239117i	−0.788706	−	0.614771i	$-0.789248\pi$
$227$	2.08000	−	3.60266i	0.138054	−	0.239117i	0.926760	+	0.375654i	$0.122582\pi$
$228$	−2.17819	−	14.0854i	−0.144254	−	0.932830i
$229$	5.16986	−	2.98482i	0.341634	−	0.197242i	−0.319361	−	0.947633i	$-0.603468\pi$
$229$	5.16986	−	2.98482i	0.341634	−	0.197242i	0.660994	+	0.750391i	$0.270135\pi$
$230$	5.96476	−	10.3313i	0.393305	−	0.681224i
$231$		0			0
$232$	2.13804	+	3.70319i	0.140369	+	0.243126i
$233$	−3.88603	−	2.24360i	−0.254582	−	0.146983i	0.367278	−	0.930111i	$-0.380290\pi$
$233$	−3.88603	−	2.24360i	−0.254582	−	0.146983i	−0.621861	+	0.783128i	$0.713623\pi$
$234$	−2.27332	−	2.07718i	−0.148611	−	0.135790i
$235$	−9.13009	−	15.8138i	−0.595581	−	1.03158i
$236$	−8.84071			−0.575481
$237$	1.00277	+	1.24761i	0.0651368	+	0.0810409i
$238$		0			0
$239$	−3.02944	−	1.74905i	−0.195958	−	0.113136i	0.398811	−	0.917033i	$-0.369423\pi$
$239$	−3.02944	−	1.74905i	−0.195958	−	0.113136i	−0.594769	+	0.803897i	$0.702756\pi$
$240$	2.22589	−	5.73592i	0.143681	−	0.370252i
$241$	−10.0170	−	5.78332i	−0.645252	−	0.372537i	0.141383	−	0.989955i	$-0.454845\pi$
$241$	−10.0170	−	5.78332i	−0.645252	−	0.372537i	−0.786635	+	0.617419i	$0.788179\pi$
$242$	1.61538	−	0.932639i	0.103840	−	0.0599523i
$243$	−3.75888	−	15.1285i	−0.241132	−	0.970492i
$244$		−	4.69034i		−	0.300268i
$245$		0			0
$246$	−0.0249997	−	0.161662i	−0.00159392	−	0.0103072i
$247$	4.22333	+	7.31502i	0.268724	+	0.465444i
$248$	5.98576			0.380096
$249$	6.80766	−	17.5427i	0.431418	−	1.11173i
$250$			9.30148i			0.588277i
$251$	−26.7426			−1.68798			−0.843988	−	0.536361i	$-0.819798\pi$
$251$	−26.7426			−1.68798			−0.843988	+	0.536361i	$0.819798\pi$
$252$		0			0
$253$	10.1500			0.638127
$254$			0.287164i			0.0180183i
$255$	9.84057	−	1.52176i	0.616241	−	0.0952964i
$256$	1.00000			0.0625000
$257$	−2.60614	−	4.51396i	−0.162566	−	0.281573i	0.773222	−	0.634135i	$-0.218644\pi$
$257$	−2.60614	−	4.51396i	−0.162566	−	0.281573i	−0.935788	+	0.352562i	$0.885310\pi$
$258$	−9.87890	−	3.83362i	−0.615034	−	0.238671i
$259$		0			0
$260$			3.64626i			0.226131i
$261$	−3.87489	−	12.2290i	−0.239850	−	0.756957i
$262$	0.322983	−	0.186474i	0.0199540	−	0.0115204i
$263$	−13.0228	−	7.51869i	−0.803018	−	0.463622i	0.0415076	−	0.999138i	$-0.486784\pi$
$263$	−13.0228	−	7.51869i	−0.803018	−	0.463622i	−0.844525	+	0.535516i	$0.820117\pi$
$264$	5.17341	−	0.800023i	0.318401	−	0.0492380i
$265$	9.81255	+	5.66528i	0.602780	+	0.348015i
$266$		0			0
$267$	8.06194	−	1.24671i	0.493383	−	0.0762975i
$268$	0.375675			0.0229480
$269$	11.5657	+	20.0323i	0.705170	+	1.22139i	0.966630	+	0.256177i	$0.0824628\pi$
$269$	11.5657	+	20.0323i	0.705170	+	1.22139i	−0.261460	+	0.965214i	$0.584204\pi$
$270$	−10.2220	+	15.3691i	−0.622092	+	0.935333i
$271$	−8.58661	−	4.95748i	−0.521599	−	0.301146i	0.215989	−	0.976396i	$-0.430702\pi$
$271$	−8.58661	−	4.95748i	−0.521599	−	0.301146i	−0.737589	+	0.675250i	$0.764036\pi$
$272$	0.809204	+	1.40158i	0.0490652	+	0.0849834i
$273$		0			0
$274$	−3.53111	+	6.11607i	−0.213322	+	0.369485i
$275$	−19.9410	+	11.5129i	−1.20249	+	0.694256i
$276$	−5.42275	−	2.10436i	−0.326411	−	0.126668i
$277$	4.29721	−	7.44299i	0.258195	−	0.447206i	−0.707564	−	0.706650i	$-0.750206\pi$
$277$	4.29721	−	7.44299i	0.258195	−	0.447206i	0.965758	+	0.259443i	$0.0835391\pi$
$278$	−7.29308	+	12.6320i	−0.437410	+	0.757616i
$279$	−17.5371	−	3.86177i	−1.04992	−	0.231198i
$280$		0			0
$281$	−17.9508	+	10.3639i	−1.07085	+	0.618258i	−0.928415	−	0.371545i	$-0.878828\pi$
$281$	−17.9508	+	10.3639i	−1.07085	+	0.618258i	−0.142440	+	0.989803i	$0.545495\pi$
$282$	−6.93976	+	5.57785i	−0.413257	+	0.332156i
$283$		−	2.36710i		−	0.140709i	−0.997522	−	0.0703547i	$-0.977587\pi$
$283$		−	2.36710i		−	0.140709i	0.997522	−	0.0703547i	$-0.0224131\pi$
$284$			13.9868i			0.829966i
$285$	39.4628	−	31.7183i	2.33757	−	1.87883i
$286$	−2.68672	+	1.55118i	−0.158869	+	0.0917231i
$287$		0			0
$288$	−2.92981	−	0.645160i	−0.172641	−	0.0380164i
$289$	7.19038	−	12.4541i	0.422963	−	0.732594i
$290$	−7.59485	+	13.1547i	−0.445985	+	0.772468i
$291$	−24.8598	−	9.64714i	−1.45731	−	0.565525i
$292$	1.13546	−	0.655556i	0.0664475	−	0.0383635i
$293$	−8.83774	+	15.3074i	−0.516306	+	0.894268i	0.483515	+	0.875336i	$0.339360\pi$
$293$	−8.83774	+	15.3074i	−0.516306	+	0.894268i	−0.999821	+	0.0189321i	$0.993973\pi$
$294$		0			0
$295$	−15.7022	−	27.1970i	−0.914218	−	1.58347i
$296$	−5.06319	−	2.92323i	−0.294292	−	0.169910i
$297$	−15.6732	−	0.993759i	−0.909453	−	0.0576637i
$298$	−5.35107	−	9.26832i	−0.309979	−	0.536899i
$299$	3.44718			0.199355
$300$	13.0406	−	2.01662i	0.752898	−	0.116429i
$301$		0			0
$302$	−13.8575	−	8.00065i	−0.797411	−	0.460386i
$303$	23.4584	−	3.62764i	1.34765	−	0.208402i
$304$	7.12643	+	4.11444i	0.408729	+	0.235980i
$305$	14.4291	−	8.33063i	0.826206	−	0.477011i
$306$	−1.46657	−	4.62843i	−0.0838381	−	0.264590i
$307$			1.28155i			0.0731422i	0.999331	+	0.0365711i	$0.0116435\pi$
$307$			1.28155i			0.0731422i	−0.999331	+	0.0365711i	$0.988356\pi$
$308$		0			0
$309$	−4.92262	−	1.91028i	−0.280038	−	0.108672i
$310$	10.6315	+	18.4142i	0.603826	+	1.04586i
$311$	−12.5329			−0.710673			−0.355336	−	0.934738i	$-0.615634\pi$
$311$	−12.5329			−0.710673			−0.355336	+	0.934738i	$0.615634\pi$
$312$	1.75700	−	0.271706i	0.0994708	−	0.0153823i
$313$		−	8.75385i		−	0.494797i	−0.968914	−	0.247398i	$-0.920424\pi$
$313$		−	8.75385i		−	0.494797i	0.968914	−	0.247398i	$-0.0795756\pi$
$314$	11.5267			0.650488
$315$		0			0
$316$	−0.924134			−0.0519866
$317$		−	13.6784i		−	0.768256i	−0.923280	−	0.384128i	$-0.874502\pi$
$317$		−	13.6784i		−	0.768256i	0.923280	−	0.384128i	$-0.125498\pi$
$318$	1.99870	−	5.15048i	0.112082	−	0.288825i
$319$	−12.9239			−0.723599
$320$	1.77612	+	3.07634i	0.0992884	+	0.171973i
$321$	−3.47465	−	22.4691i	−0.193936	−	1.25410i
$322$		0			0
$323$			13.3177i			0.741017i
$324$	8.16754	+	3.78039i	0.453752	+	0.210021i
$325$	−6.77240	+	3.91005i	−0.375665	+	0.216890i
$326$	2.37960	+	1.37386i	0.131794	+	0.0760912i
$327$	−6.62424	+	17.0701i	−0.366321	+	0.943977i
$328$	0.0817920	+	0.0472226i	0.00451621	+	0.00260743i
$329$		0			0
$330$	11.6498	+	14.4942i	0.641298	+	0.797880i
$331$	−10.8972			−0.598962			−0.299481	−	0.954102i	$-0.596813\pi$
$331$	−10.8972			−0.598962			−0.299481	+	0.954102i	$0.596813\pi$
$332$	5.43209	+	9.40866i	0.298125	+	0.516367i
$333$	12.9482	+	11.8311i	0.709558	+	0.648339i
$334$	4.79685	+	2.76946i	0.262472	+	0.151538i
$335$	0.667247	+	1.15570i	0.0364556	+	0.0631429i
$336$		0			0
$337$	12.8090	−	22.1858i	0.697749	−	1.20854i	−0.271496	−	0.962440i	$-0.587518\pi$
$337$	12.8090	−	22.1858i	0.697749	−	1.20854i	0.969245	−	0.246098i	$-0.0791484\pi$
$338$	10.3459	−	5.97319i	0.562741	−	0.324898i
$339$	3.25578	+	21.0537i	0.176830	+	1.14348i
$340$	−2.87450	+	4.97877i	−0.155891	+	0.270012i
$341$	−9.04559	+	15.6674i	−0.489846	+	0.848438i
$342$	−18.2246	−	16.6522i	−0.985473	−	0.900448i
$343$		0			0
$344$	5.29833	−	3.05899i	0.285667	−	0.164930i
$345$	−3.15775	−	20.4198i	−0.170008	−	1.09937i
$346$		−	11.2051i		−	0.602388i
$347$			16.7623i			0.899848i	0.893067	+	0.449924i	$0.148549\pi$
$347$			16.7623i			0.899848i	−0.893067	+	0.449924i	$0.851451\pi$
$348$	6.90471	+	2.67945i	0.370131	+	0.143634i
$349$	−14.4455	+	8.34010i	−0.773249	+	0.446435i	−0.834032	−	0.551716i	$-0.813973\pi$
$349$	−14.4455	+	8.34010i	−0.773249	+	0.446435i	0.0607835	+	0.998151i	$0.480640\pi$
$350$		0			0
$351$	−5.32298	−	0.337503i	−0.284119	−	0.0180146i
$352$	−1.51119	+	2.61745i	−0.0805464	+	0.139511i
$353$	17.9568	−	31.1021i	0.955746	−	1.65540i	0.223093	−	0.974797i	$-0.428385\pi$
$353$	17.9568	−	31.1021i	0.955746	−	1.65540i	0.732653	−	0.680603i	$-0.238282\pi$
$354$	−11.9352	+	9.59297i	−0.634350	+	0.509860i
$355$	−43.0282	+	24.8424i	−2.28370	+	1.31850i
$356$	−2.35495	+	4.07888i	−0.124812	+	0.216180i
$357$		0			0
$358$	−1.37089	−	2.37445i	−0.0724538	−	0.125494i
$359$	24.7248	+	14.2749i	1.30493	+	0.753399i	0.981245	−	0.192767i	$-0.0617461\pi$
$359$	24.7248	+	14.2749i	1.30493	+	0.753399i	0.323681	+	0.946166i	$0.395079\pi$
$360$	−3.21897	−	10.1590i	−0.169655	−	0.535424i
$361$	24.3573	+	42.1881i	1.28196	+	2.22043i
$362$	22.2899			1.17153
$363$	1.16881	−	3.01192i	0.0613467	−	0.158085i
$364$		0			0
$365$	4.03342	+	2.32870i	0.211119	+	0.121890i
$366$	−5.08944	−	6.33210i	−0.266029	−	0.330984i
$367$	−0.310665	−	0.179362i	−0.0162166	−	0.00936264i	0.491870	−	0.870669i	$-0.336314\pi$
$367$	−0.310665	−	0.179362i	−0.0162166	−	0.00936264i	−0.508086	+	0.861306i	$0.669647\pi$
$368$	2.90837	−	1.67915i	0.151609	−	0.0875317i
$369$	−0.209169	−	0.191122i	−0.0108889	−	0.00994942i
$370$		−	20.7681i		−	1.07968i
$371$		0			0
$372$	8.08095	−	6.49509i	0.418978	−	0.336755i
$373$	−12.6854	−	21.9718i	−0.656826	−	1.13766i	−0.981433	−	0.191807i	$-0.938565\pi$
$373$	−12.6854	−	21.9718i	−0.656826	−	1.13766i	0.324606	−	0.945849i	$-0.394768\pi$
$374$	−4.89143			−0.252930
$375$	10.0929	+	12.5573i	0.521197	+	0.648455i
$376$		−	5.14045i		−	0.265099i
$377$	−4.38924			−0.226057
$378$		0			0
$379$	26.9063			1.38209			0.691043	−	0.722814i	$-0.257152\pi$
$379$	26.9063			1.38209			0.691043	+	0.722814i	$0.257152\pi$
$380$			29.2311i			1.49952i
$381$	0.311599	+	0.387680i	0.0159637	+	0.0198614i
$382$	5.13264			0.262609
$383$	6.28586	+	10.8874i	0.321192	+	0.556322i	0.980734	−	0.195346i	$-0.0625830\pi$
$383$	6.28586	+	10.8874i	0.321192	+	0.556322i	−0.659542	+	0.751668i	$0.729250\pi$
$384$	1.35003	−	1.08509i	0.0688934	−	0.0553733i
$385$		0			0
$386$			15.9847i			0.813600i
$387$	−17.4966	+	5.54399i	−0.889404	+	0.281817i
$388$	13.3330	−	7.69782i	0.676881	−	0.390798i
$389$	−14.0805	−	8.12937i	−0.713909	−	0.412175i	0.0985980	−	0.995127i	$-0.468564\pi$
$389$	−14.0805	−	8.12937i	−0.713909	−	0.412175i	−0.812507	+	0.582952i	$0.801898\pi$
$390$	3.95652	+	4.92256i	0.200346	+	0.249263i
$391$	4.70694	+	2.71755i	0.238040	+	0.137432i
$392$		0			0
$393$	0.233695	−	0.602212i	0.0117884	−	0.0303776i
$394$	−4.72572			−0.238078
$395$	−1.64138	−	2.84295i	−0.0825866	−	0.143044i
$396$	6.11615	−	6.69367i	0.307348	−	0.336369i
$397$	12.7252	+	7.34692i	0.638662	+	0.368732i	0.784099	−	0.620636i	$-0.213125\pi$
$397$	12.7252	+	7.34692i	0.638662	+	0.368732i	−0.145437	+	0.989368i	$0.546459\pi$
$398$	−1.06047	−	1.83679i	−0.0531567	−	0.0920701i
$399$		0			0
$400$	−3.80924	+	6.59779i	−0.190462	+	0.329890i
$401$	14.4162	−	8.32318i	0.719909	−	0.415640i	−0.0948099	−	0.995495i	$-0.530224\pi$
$401$	14.4162	−	8.32318i	0.719909	−	0.415640i	0.814719	+	0.579855i	$0.196891\pi$
$402$	0.507173	−	0.407642i	0.0252955	−	0.0203313i
$403$	−3.07208	+	5.32101i	−0.153031	+	0.265058i
$404$	−6.85234	+	11.8686i	−0.340917	+	0.590485i
$405$	2.87682	+	31.8405i	0.142950	+	1.58217i
$406$		0			0
$407$	15.3028	−	8.83510i	0.758534	−	0.437940i
$408$	2.61329	+	1.01412i	0.129377	+	0.0502064i
$409$		−	2.80886i		−	0.138889i	−0.997586	−	0.0694446i	$-0.977877\pi$
$409$		−	2.80886i		−	0.138889i	0.997586	−	0.0694446i	$-0.0221227\pi$
$410$			0.335493i			0.0165688i
$411$	1.86938	+	12.0884i	0.0922095	+	0.596279i
$412$	2.64014	−	1.52429i	0.130070	−	0.0750962i
$413$		0			0
$414$	−9.60429	+	3.04322i	−0.472025	+	0.149566i
$415$	−19.2962	+	33.4219i	−0.947211	+	1.64062i
$416$	−0.513232	+	0.888944i	−0.0251633	+	0.0435841i
$417$	3.86096	+	24.9672i	0.189072	+	1.22265i
$418$	−21.5387	+	12.4354i	−1.05349	+	0.608234i
$419$	−7.47362	+	12.9447i	−0.365110	+	0.632390i	−0.988794	−	0.149287i	$-0.952302\pi$
$419$	−7.47362	+	12.9447i	−0.365110	+	0.632390i	0.623684	+	0.781677i	$0.285635\pi$
$420$		0			0
$421$	−7.80336	−	13.5158i	−0.380312	−	0.658720i	0.610794	−	0.791789i	$-0.290850\pi$
$421$	−7.80336	−	13.5158i	−0.380312	−	0.658720i	−0.991107	+	0.133069i	$0.957517\pi$
$422$	−23.9160	−	13.8079i	−1.16421	−	0.672160i
$423$	−3.31641	+	15.0605i	−0.161250	+	0.732268i
$424$	1.59484	+	2.76235i	0.0774524	+	0.134151i
$425$	−12.3298			−0.598083
$426$	15.1770	+	18.8826i	0.735326	+	0.914867i
$427$		0			0
$428$	11.3681	+	6.56336i	0.549496	+	0.317252i
$429$	−1.94398	+	5.00947i	−0.0938563	+	0.241859i
$430$	18.8210	+	10.8663i	0.907629	+	0.524020i
$431$	−14.0087	+	8.08792i	−0.674775	+	0.389581i	−0.797883	−	0.602812i	$-0.794047\pi$
$431$	−14.0087	+	8.08792i	−0.674775	+	0.389581i	0.123109	+	0.992393i	$0.460714\pi$
$432$	−4.65538	+	2.30812i	−0.223982	+	0.111049i
$433$			27.2499i			1.30955i	0.755824	+	0.654774i	$0.227236\pi$
$433$			27.2499i			1.30955i	−0.755824	+	0.654774i	$0.772764\pi$
$434$		0			0
$435$	4.02072	+	26.0003i	0.192779	+	1.24662i
$436$	−5.28574	−	9.15516i	−0.253141	−	0.438453i
$437$	27.6351			1.32197
$438$	0.821562	−	2.11709i	0.0392557	−	0.101159i
$439$		−	33.1347i		−	1.58143i	−0.612182	−	0.790717i	$-0.709708\pi$
$439$		−	33.1347i		−	1.58143i	0.612182	−	0.790717i	$-0.290292\pi$
$440$	−10.7362			−0.511829
$441$		0			0
$442$	−1.66124			−0.0790171
$443$		−	22.2636i		−	1.05777i	−0.848692	−	0.528887i	$-0.822609\pi$
$443$		−	22.2636i		−	1.05777i	0.848692	−	0.528887i	$-0.177391\pi$
$444$	−10.0074	+	1.54756i	−0.474932	+	0.0734442i
$445$	−16.7307			−0.793111
$446$	10.1734	+	17.6209i	0.481727	+	0.834375i
$447$	−17.2811	−	6.70612i	−0.817366	−	0.317188i
$448$		0			0
$449$		−	6.80819i		−	0.321298i	−0.987012	−	0.160649i	$-0.948641\pi$
$449$		−	6.80819i		−	0.321298i	0.987012	−	0.160649i	$-0.0513588\pi$
$450$	15.4170	−	16.8727i	0.726763	−	0.795386i
$451$	−0.247206	+	0.142724i	−0.0116405	+	0.00672062i
$452$	−10.6520	−	6.14993i	−0.501027	−	0.289268i
$453$	−27.3895	+	4.23555i	−1.28687	+	0.199004i
$454$	3.60266	+	2.08000i	0.169081	+	0.0976192i
$455$		0			0
$456$	14.0854	−	2.17819i	0.659611	−	0.102003i
$457$	15.2260			0.712240			0.356120	−	0.934440i	$-0.384099\pi$
$457$	15.2260			0.712240			0.356120	+	0.934440i	$0.384099\pi$
$458$	2.98482	+	5.16986i	0.139471	+	0.241572i
$459$	−7.00218	−	4.65716i	−0.326834	−	0.217378i
$460$	10.3313	+	5.96476i	0.481698	+	0.278108i
$461$	−0.103381	−	0.179060i	−0.00481492	−	0.00833968i	0.863608	−	0.504164i	$-0.168199\pi$
$461$	−0.103381	−	0.179060i	−0.00481492	−	0.00833968i	−0.868423	+	0.495824i	$0.834866\pi$
$462$		0			0
$463$	−7.60217	+	13.1673i	−0.353303	+	0.611938i	−0.986826	−	0.161785i	$-0.948275\pi$
$463$	−7.60217	+	13.1673i	−0.353303	+	0.611938i	0.633523	+	0.773724i	$0.281608\pi$
$464$	−3.70319	+	2.13804i	−0.171916	+	0.0992560i
$465$	34.3339	+	13.3237i	1.59219	+	0.617870i
$466$	2.24360	−	3.88603i	0.103933	−	0.180017i
$467$	−1.15424	+	1.99921i	−0.0534120	+	0.0925123i	−0.891495	−	0.453030i	$-0.850343\pi$
$467$	−1.15424	+	1.99921i	−0.0534120	+	0.0925123i	0.838083	+	0.545542i	$0.183676\pi$
$468$	2.07718	−	2.27332i	0.0960178	−	0.105084i
$469$		0			0
$470$	15.8138	−	9.13009i	0.729435	−	0.421139i
$471$	15.5613	−	12.5075i	0.717029	−	0.576314i
$472$		−	8.84071i		−	0.406927i
$473$			18.4908i			0.850209i
$474$	−1.24761	+	1.00277i	−0.0573045	+	0.0460587i
$475$	−54.2925	+	31.3458i	−2.49111	+	1.43824i
$476$		0			0
$477$	−2.89042	−	9.12207i	−0.132343	−	0.417671i
$478$	1.74905	−	3.02944i	0.0799996	−	0.138563i
$479$	−6.21659	+	10.7674i	−0.284043	+	0.491977i	−0.972377	−	0.233417i	$-0.925009\pi$
$479$	−6.21659	+	10.7674i	−0.284043	+	0.491977i	0.688334	+	0.725394i	$0.258343\pi$
$480$	5.73592	+	2.22589i	0.261808	+	0.101598i
$481$	5.19719	−	3.00060i	0.236971	−	0.136815i
$482$	5.78332	−	10.0170i	0.263423	−	0.456262i
$483$		0			0
$484$	0.932639	+	1.61538i	0.0423927	+	0.0734263i
$485$	47.3622	+	27.3446i	2.15061	+	1.24165i
$486$	15.1285	−	3.75888i	0.686242	−	0.170506i
$487$	−18.6503	−	32.3033i	−0.845128	−	1.46380i	−0.885510	−	0.464620i	$-0.846191\pi$
$487$	−18.6503	−	32.3033i	−0.845128	−	1.46380i	0.0403829	−	0.999184i	$-0.487142\pi$
$488$	4.69034			0.212322
$489$	4.70330	−	0.727325i	0.212690	−	0.0328908i
$490$		0			0
$491$	−11.8191	−	6.82377i	−0.533389	−	0.307952i	0.209006	−	0.977914i	$-0.432977\pi$
$491$	−11.8191	−	6.82377i	−0.533389	−	0.307952i	−0.742396	+	0.669962i	$0.766310\pi$
$492$	0.161662	−	0.0249997i	0.00728830	−	0.00112707i
$493$	−5.99328	−	3.46022i	−0.269924	−	0.155840i
$494$	−7.31502	+	4.22333i	−0.329118	+	0.190017i
$495$	31.4550	+	6.92657i	1.41380	+	0.311326i
$496$			5.98576i			0.268768i
$497$		0			0
$498$	17.5427	+	6.80766i	0.786109	+	0.305059i
$499$	10.5010	+	18.1882i	0.470088	+	0.814216i	0.999415	−	0.0342021i	$-0.0108890\pi$
$499$	10.5010	+	18.1882i	0.470088	+	0.814216i	−0.529327	+	0.848418i	$0.677556\pi$
$500$	−9.30148			−0.415975
$501$	9.48100	−	1.46616i	0.423580	−	0.0655030i
$502$		−	26.7426i		−	1.19358i
$503$	22.3018			0.994388			0.497194	−	0.867639i	$-0.334364\pi$
$503$	22.3018			0.994388			0.497194	+	0.867639i	$0.334364\pi$
$504$		0			0
$505$	−48.6824			−2.16634
$506$			10.1500i			0.451224i
$507$	7.48577	−	19.2902i	0.332455	−	0.856706i
$508$	−0.287164			−0.0127408
$509$	10.9589	+	18.9814i	0.485746	+	0.841337i	0.999866	−	0.0163813i	$-0.00521458\pi$
$509$	10.9589	+	18.9814i	0.485746	+	0.841337i	−0.514120	+	0.857719i	$0.671881\pi$
$510$	1.52176	+	9.84057i	0.0673847	+	0.435748i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−42.6729	−	2.70567i	−1.88405	−	0.119458i
$514$	4.51396	−	2.60614i	0.199102	−	0.114952i
$515$	9.37844	+	5.41465i	0.413264	+	0.238598i
$516$	3.83362	−	9.87890i	0.168766	−	0.434894i
$517$	13.4549	+	7.76818i	0.591745	+	0.341644i
$518$		0			0
$519$	−12.1585	−	15.1272i	−0.533699	−	0.664009i
$520$	−3.64626			−0.159899
$521$	−13.3839	−	23.1816i	−0.586358	−	1.01560i	−0.994705	−	0.102775i	$-0.967228\pi$
$521$	−13.3839	−	23.1816i	−0.586358	−	1.01560i	0.408346	−	0.912827i	$-0.366106\pi$
$522$	12.2290	−	3.87489i	0.535249	−	0.169599i
$523$	−14.8576	−	8.57805i	−0.649678	−	0.375092i	0.138655	−	0.990341i	$-0.455722\pi$
$523$	−14.8576	−	8.57805i	−0.649678	−	0.375092i	−0.788333	+	0.615249i	$0.789055\pi$
$524$	0.186474	+	0.322983i	0.00814617	+	0.0141096i
$525$		0			0
$526$	7.51869	−	13.0228i	0.327831	−	0.567819i
$527$	−8.38954	+	4.84370i	−0.365454	+	0.210995i
$528$	0.800023	+	5.17341i	0.0348165	+	0.225144i
$529$	−5.86091	+	10.1514i	−0.254822	+	0.441365i
$530$	−5.66528	+	9.81255i	−0.246084	+	0.426230i
$531$	−5.70367	+	25.9016i	−0.247518	+	1.12403i
$532$		0			0
$533$	−0.0839566	+	0.0484723i	−0.00363656	+	0.00209957i
$534$	1.24671	+	8.06194i	0.0539505	+	0.348874i
$535$			46.6294i			2.01596i
$536$			0.375675i			0.0162267i
$537$	−4.42724	−	1.71804i	−0.191049	−	0.0741390i
$538$	−20.0323	+	11.5657i	−0.863654	+	0.498631i
$539$		0			0
$540$	−15.3691	−	10.2220i	−0.661381	−	0.439886i
$541$	−14.4091	+	24.9573i	−0.619496	+	1.07300i	0.370081	+	0.928999i	$0.379330\pi$
$541$	−14.4091	+	24.9573i	−0.619496	+	1.07300i	−0.989578	+	0.144000i	$0.954004\pi$
$542$	4.95748	−	8.58661i	0.212942	−	0.368827i
$543$	30.0920	−	24.1865i	1.29137	−	1.03794i
$544$	−1.40158	+	0.809204i	−0.0600924	+	0.0346943i
$545$	18.7763	−	32.5214i	0.804286	−	1.39306i
$546$		0			0
$547$	−16.4045	−	28.4135i	−0.701407	−	1.21487i	−0.967972	−	0.251056i	$-0.919222\pi$
$547$	−16.4045	−	28.4135i	−0.701407	−	1.21487i	0.266565	−	0.963817i	$-0.414111\pi$
$548$	−6.11607	−	3.53111i	−0.261265	−	0.150842i
$549$	−13.7418	−	3.02602i	−0.586485	−	0.129147i
$550$	−11.5129	−	19.9410i	−0.490913	−	0.850286i
$551$	−35.1874			−1.49903
$552$	2.10436	−	5.42275i	0.0895676	−	0.230808i
$553$		0			0
$554$	7.44299	+	4.29721i	0.316223	+	0.182571i
$555$	−22.5353	−	28.0376i	−0.956569	−	1.19013i
$556$	−12.6320	−	7.29308i	−0.535715	−	0.309295i
$557$	−40.0544	+	23.1254i	−1.69716	+	0.979855i	−0.748725	+	0.662880i	$0.769334\pi$
$557$	−40.0544	+	23.1254i	−1.69716	+	0.979855i	−0.948434	+	0.316975i	$0.897333\pi$
$558$	3.86177	−	17.5371i	0.163482	−	0.742405i
$559$			6.27990i			0.265611i
$560$		0			0
$561$	−6.60357	+	5.30764i	−0.278803	+	0.224089i
$562$	−10.3639	−	17.9508i	−0.437174	−	0.757208i
$563$	−1.97727			−0.0833322			−0.0416661	−	0.999132i	$-0.513267\pi$
$563$	−1.97727			−0.0833322			−0.0416661	+	0.999132i	$0.513267\pi$
$564$	−5.57785	−	6.93976i	−0.234870	−	0.292217i
$565$		−	43.6922i		−	1.83814i
$566$	2.36710			0.0994966
$567$		0			0
$568$	−13.9868			−0.586874
$569$			32.9901i			1.38302i	0.722369	+	0.691508i	$0.243053\pi$
$569$			32.9901i			1.38302i	−0.722369	+	0.691508i	$0.756947\pi$
$570$	31.7183	+	39.4628i	1.32853	+	1.65291i
$571$	14.8065			0.619634			0.309817	−	0.950796i	$-0.399732\pi$
$571$	14.8065			0.619634			0.309817	+	0.950796i	$0.399732\pi$
$572$	−1.55118	−	2.68672i	−0.0648580	−	0.112337i
$573$	6.92921	−	5.56937i	0.289472	−	0.232664i
$574$		0			0
$575$			25.5851i			1.06697i
$576$	0.645160	−	2.92981i	0.0268817	−	0.122075i
$577$	15.9505	−	9.20901i	0.664027	−	0.383376i	−0.129783	−	0.991542i	$-0.541428\pi$
$577$	15.9505	−	9.20901i	0.664027	−	0.383376i	0.793810	+	0.608166i	$0.208095\pi$
$578$	12.4541	+	7.19038i	0.518022	+	0.299080i
$579$	17.3448	+	21.5798i	0.720827	+	0.896827i
$580$	−13.1547	−	7.59485i	−0.546218	−	0.315359i
$581$		0			0
$582$	9.64714	−	24.8598i	0.399887	−	1.03047i
$583$	−9.64041			−0.399265
$584$	0.655556	+	1.13546i	0.0271271	+	0.0469855i
$585$	10.6828	+	2.35242i	0.441681	+	0.0972605i
$586$	−15.3074	−	8.83774i	−0.632343	−	0.365084i
$587$	−23.1065	−	40.0216i	−0.953707	−	1.65187i	−0.737301	−	0.675565i	$-0.763900\pi$
$587$	−23.1065	−	40.0216i	−0.953707	−	1.65187i	−0.216406	−	0.976304i	$-0.569433\pi$
$588$		0			0
$589$	−24.6281	+	42.6571i	−1.01478	+	1.75765i
$590$	27.1970	−	15.7022i	1.11968	−	0.646450i
$591$	−6.37986	+	5.12783i	−0.262432	+	0.210931i
$592$	2.92323	−	5.06319i	0.120144	−	0.208096i
$593$	−6.80465	+	11.7860i	−0.279434	+	0.483993i	−0.971244	−	0.238086i	$-0.923480\pi$
$593$	−6.80465	+	11.7860i	−0.279434	+	0.483993i	0.691810	+	0.722079i	$0.256813\pi$
$594$	0.993759	−	15.6732i	0.0407744	−	0.643080i
$595$		0			0
$596$	9.26832	−	5.35107i	0.379645	−	0.219188i
$597$	−3.42476	−	1.32902i	−0.140166	−	0.0543930i
$598$			3.44718i			0.140965i
$599$			23.5806i			0.963477i	0.876315	+	0.481739i	$0.159995\pi$
$599$			23.5806i			0.963477i	−0.876315	+	0.481739i	$0.840005\pi$
$600$	2.01662	+	13.0406i	0.0823280	+	0.532380i
$601$	31.0765	−	17.9420i	1.26764	−	0.731871i	0.293097	−	0.956083i	$-0.405314\pi$
$601$	31.0765	−	17.9420i	1.26764	−	0.731871i	0.974540	+	0.224212i	$0.0719808\pi$
$602$		0			0
$603$	0.242371	−	1.10066i	0.00987010	−	0.0448222i
$604$	8.00065	−	13.8575i	0.325542	−	0.563855i
$605$	−3.31297	+	5.73823i	−0.134691	+	0.233292i
$606$	3.62764	+	23.4584i	0.147363	+	0.952931i
$607$	16.8502	−	9.72845i	0.683928	−	0.394866i	−0.117406	−	0.993084i	$-0.537458\pi$
$607$	16.8502	−	9.72845i	0.683928	−	0.394866i	0.801333	+	0.598218i	$0.204124\pi$
$608$	−4.11444	+	7.12643i	−0.166863	+	0.289015i
$609$		0			0
$610$	8.33063	+	14.4291i	0.337297	+	0.584216i
$611$	4.56958	+	2.63825i	0.184865	+	0.106732i
$612$	4.62843	−	1.46657i	0.187093	−	0.0592825i
$613$	−21.1210	−	36.5827i	−0.853071	−	1.47756i	−0.878423	−	0.477883i	$-0.841404\pi$
$613$	−21.1210	−	36.5827i	−0.853071	−	1.47756i	0.0253526	−	0.999679i	$-0.491929\pi$
$614$	−1.28155			−0.0517193
$615$	0.364040	+	0.452926i	0.0146795	+	0.0182637i
$616$		0			0
$617$	9.63660	+	5.56369i	0.387955	+	0.223986i	0.681274	−	0.732029i	$-0.261426\pi$
$617$	9.63660	+	5.56369i	0.387955	+	0.223986i	−0.293319	+	0.956015i	$0.594760\pi$
$618$	1.91028	−	4.92262i	0.0768428	−	0.198017i
$619$	−8.71387	−	5.03096i	−0.350240	−	0.202211i	0.314551	−	0.949241i	$-0.398146\pi$
$619$	−8.71387	−	5.03096i	−0.350240	−	0.202211i	−0.664791	+	0.747029i	$0.731479\pi$
$620$	−18.4142	+	10.6315i	−0.739533	+	0.426969i
$621$	−9.66391	+	14.5300i	−0.387799	+	0.583067i
$622$		−	12.5329i		−	0.502522i
$623$		0			0
$624$	0.271706	+	1.75700i	0.0108769	+	0.0703365i
$625$	2.52560	+	4.37447i	0.101024	+	0.174979i
$626$	8.75385			0.349874
$627$	−15.5844	+	40.1595i	−0.622380	+	1.60382i
$628$			11.5267i			0.459964i
$629$	9.46198			0.377274
$630$		0			0
$631$	10.3528			0.412139			0.206070	−	0.978537i	$-0.433933\pi$
$631$	10.3528			0.412139			0.206070	+	0.978537i	$0.433933\pi$
$632$		−	0.924134i		−	0.0367601i
$633$	−47.2702	+	7.30994i	−1.87882	+	0.290544i
$634$	13.6784			0.543239
$635$	−0.510039	−	0.883413i	−0.0202403	−	0.0350572i
$636$	5.15048	+	1.99870i	0.204230	+	0.0792538i
$637$		0			0
$638$		−	12.9239i		−	0.511662i
$639$	40.9787	+	9.02374i	1.62109	+	0.356974i
$640$	−3.07634	+	1.77612i	−0.121603	+	0.0702075i
$641$	−23.0678	−	13.3182i	−0.911123	−	0.526037i	−0.0303310	−	0.999540i	$-0.509656\pi$
$641$	−23.0678	−	13.3182i	−0.911123	−	0.526037i	−0.880792	+	0.473503i	$0.842989\pi$
$642$	22.4691	−	3.47465i	0.886783	−	0.137134i
$643$	−40.0493	−	23.1225i	−1.57939	−	0.911861i	−0.994944	−	0.100429i	$-0.967979\pi$
$643$	−40.0493	−	23.1225i	−1.57939	−	0.911861i	−0.584446	−	0.811433i	$-0.698688\pi$
$644$		0			0
$645$	37.1998	−	5.75264i	1.46474	−	0.226510i
$646$	−13.3177			−0.523978
$647$	15.7032	+	27.1987i	0.617355	+	1.06929i	0.989966	+	0.141303i	$0.0451293\pi$
$647$	15.7032	+	27.1987i	0.617355	+	1.06929i	−0.372611	+	0.927988i	$0.621537\pi$
$648$	−3.78039	+	8.16754i	−0.148508	+	0.320851i
$649$	23.1401	+	13.3600i	0.908329	+	0.524424i
$650$	−3.91005	−	6.77240i	−0.153365	−	0.265635i
$651$		0			0
$652$	−1.37386	+	2.37960i	−0.0538046	+	0.0931923i
$653$	39.9639	−	23.0732i	1.56391	−	0.902924i	0.567054	−	0.823681i	$-0.308083\pi$
$653$	39.9639	−	23.0732i	1.56391	−	0.902924i	0.996855	−	0.0792429i	$-0.0252503\pi$
$654$	−17.0701	−	6.62424i	−0.667493	−	0.259028i
$655$	−0.662404	+	1.14732i	−0.0258823	+	0.0448294i
$656$	−0.0472226	+	0.0817920i	−0.00184373	+	0.00319344i
$657$	−1.18810	−	3.74960i	−0.0463522	−	0.146286i
$658$		0			0
$659$	1.18052	−	0.681575i	0.0459867	−	0.0265504i	−0.476830	−	0.878995i	$-0.658214\pi$
$659$	1.18052	−	0.681575i	0.0459867	−	0.0265504i	0.522817	+	0.852445i	$0.324881\pi$
$660$	−14.4942	+	11.6498i	−0.564186	+	0.453466i
$661$			7.20404i			0.280205i	0.990137	+	0.140102i	$0.0447431\pi$
$661$			7.20404i			0.280205i	−0.990137	+	0.140102i	$0.955257\pi$
$662$		−	10.8972i		−	0.423530i
$663$	−2.24272	+	1.80259i	−0.0871001	+	0.0700069i
$664$	−9.40866	+	5.43209i	−0.365127	+	0.210806i
$665$		0			0
$666$	−11.8311	+	12.9482i	−0.458445	+	0.501733i
$667$	−7.18018	+	12.4364i	−0.278018	+	0.481541i
$668$	−2.76946	+	4.79685i	−0.107154	+	0.185596i
$669$	32.8547	+	12.7497i	1.27024	+	0.492931i
$670$	−1.15570	+	0.667247i	−0.0446488	+	0.0257780i
$671$	−7.08797	+	12.2767i	−0.273628	+	0.473938i
$672$		0			0
$673$	19.4709	+	33.7246i	0.750548	+	1.29999i	0.947558	+	0.319585i	$0.103544\pi$
$673$	19.4709	+	33.7246i	0.750548	+	1.29999i	−0.197010	+	0.980402i	$0.563123\pi$
$674$	22.1858	+	12.8090i	0.854565	+	0.493383i
$675$	2.50496	−	39.5074i	0.0964161	−	1.52064i
$676$	5.97319	+	10.3459i	0.229738	+	0.397918i
$677$	−2.41011			−0.0926280			−0.0463140	−	0.998927i	$-0.514747\pi$
$677$	−2.41011			−0.0926280			−0.0463140	+	0.998927i	$0.514747\pi$
$678$	−21.0537	+	3.25578i	−0.808563	+	0.125037i
$679$		0			0
$680$	−4.97877	−	2.87450i	−0.190927	−	0.110232i
$681$	7.12069	−	1.10115i	0.272865	−	0.0421963i
$682$	−15.6674	−	9.04559i	−0.599937	−	0.346374i
$683$	24.5302	−	14.1625i	0.938624	−	0.541915i	0.0490952	−	0.998794i	$-0.484366\pi$
$683$	24.5302	−	14.1625i	0.938624	−	0.541915i	0.889529	+	0.456879i	$0.151033\pi$
$684$	16.6522	−	18.2246i	0.636713	−	0.696834i
$685$		−	25.0868i		−	0.958517i
$686$		0			0
$687$	9.63935	+	3.74066i	0.367764	+	0.142715i
$688$	3.05899	+	5.29833i	0.116623	+	0.201997i
$689$	−3.27410			−0.124733
$690$	20.4198	−	3.15775i	0.777369	−	0.120214i
$691$			3.41022i			0.129731i	0.997894	+	0.0648655i	$0.0206618\pi$
$691$			3.41022i			0.129731i	−0.997894	+	0.0648655i	$0.979338\pi$
$692$	11.2051			0.425953
$693$		0			0
$694$	−16.7623			−0.636289
$695$		−	51.8136i		−	1.96540i
$696$	−2.67945	+	6.90471i	−0.101564	+	0.261722i
$697$	−0.152851			−0.00578964
$698$	−8.34010	−	14.4455i	−0.315678	−	0.546769i
$699$	−1.18776	−	7.68076i	−0.0449254	−	0.290513i
$700$		0			0
$701$		−	51.4943i		−	1.94491i	−0.233087	−	0.972456i	$-0.574883\pi$
$701$		−	51.4943i		−	1.94491i	0.233087	−	0.972456i	$-0.425117\pi$
$702$	0.337503	−	5.32298i	0.0127382	−	0.200903i
$703$	41.6644	−	24.0550i	1.57140	−	0.907251i
$704$	−2.61745	−	1.51119i	−0.0986488	−	0.0569549i
$705$	11.4421	−	29.4853i	0.430934	−	1.11048i
$706$	31.1021	+	17.9568i	1.17054	+	0.675814i
$707$		0			0
$708$	−9.59297	−	11.9352i	−0.360526	−	0.448553i
$709$	10.0844			0.378726			0.189363	−	0.981907i	$-0.439358\pi$
$709$	10.0844			0.378726			0.189363	+	0.981907i	$0.439358\pi$
$710$	−24.8424	−	43.0282i	−0.932317	−	1.61482i
$711$	−0.596214	+	2.70753i	−0.0223598	+	0.101540i
$712$	−4.07888	−	2.35495i	−0.152863	−	0.0882553i
$713$	10.0510	+	17.4088i	0.376412	+	0.651965i
$714$		0			0
$715$	5.51017	−	9.54389i	0.206069	−	0.356921i
$716$	2.37445	−	1.37089i	0.0887375	−	0.0512326i
$717$	−0.925948	−	5.98770i	−0.0345802	−	0.223615i
$718$	−14.2749	+	24.7248i	−0.532734	+	0.922722i
$719$	15.9584	−	27.6408i	0.595148	−	1.03083i	−0.398378	−	0.917221i	$-0.630427\pi$
$719$	15.9584	−	27.6408i	0.595148	−	1.03083i	0.993526	−	0.113605i	$-0.0362399\pi$
$720$	10.1590	−	3.21897i	0.378602	−	0.119964i
$721$		0			0
$722$	−42.1881	+	24.3573i	−1.57008	+	0.906485i
$723$	−3.06170	−	19.7987i	−0.113866	−	0.736321i
$724$			22.2899i			0.828397i
$725$		−	32.5772i		−	1.20989i
$726$	3.01192	+	1.16881i	0.111783	+	0.0433787i
$727$	17.9336	−	10.3540i	0.665120	−	0.384007i	−0.129105	−	0.991631i	$-0.541210\pi$
$727$	17.9336	−	10.3540i	0.665120	−	0.384007i	0.794225	+	0.607624i	$0.207877\pi$
$728$		0			0
$729$	16.3452	−	21.4904i	0.605377	−	0.795939i
$730$	−2.32870	+	4.03342i	−0.0861889	+	0.149284i
$731$	−4.95070	+	8.57487i	−0.183108	+	0.317153i
$732$	6.33210	−	5.08944i	0.234041	−	0.188111i
$733$	−7.69996	+	4.44558i	−0.284405	+	0.164201i	−0.635416	−	0.772170i	$-0.719171\pi$
$733$	−7.69996	+	4.44558i	−0.284405	+	0.164201i	0.351011	+	0.936371i	$0.385838\pi$
$734$	0.179362	−	0.310665i	0.00662038	−	0.0114668i
$735$		0			0
$736$	1.67915	+	2.90837i	0.0618943	+	0.107204i
$737$	−0.983312	−	0.567715i	−0.0362207	−	0.0209121i
$738$	0.191122	−	0.209169i	0.00703530	−	0.00769960i
$739$	−16.3882	−	28.3851i	−0.602848	−	1.04416i	−0.992388	−	0.123154i	$-0.960699\pi$
$739$	−16.3882	−	28.3851i	−0.602848	−	1.04416i	0.389539	−	0.921010i	$-0.372634\pi$
$740$	20.7681			0.763451
$741$	−5.29280	+	13.6391i	−0.194436	+	0.501044i
$742$		0			0
$743$	−6.68055	−	3.85702i	−0.245086	−	0.141500i	0.372426	−	0.928062i	$-0.378526\pi$
$743$	−6.68055	−	3.85702i	−0.245086	−	0.141500i	−0.617512	+	0.786562i	$0.711859\pi$
$744$	6.49509	+	8.08095i	0.238121	+	0.296262i
$745$	32.9234	+	19.0083i	1.20622	+	0.696411i
$746$	21.9718	−	12.6854i	0.804445	−	0.464446i
$747$	31.0701	−	9.84490i	1.13680	−	0.360206i
$748$		−	4.89143i		−	0.178848i
$749$		0			0
$750$	−12.5573	+	10.0929i	−0.458527	+	0.368542i
$751$	−15.3804	−	26.6397i	−0.561239	−	0.972095i	−0.997389	−	0.0722207i	$-0.976991\pi$
$751$	−15.3804	−	26.6397i	−0.561239	−	0.972095i	0.436149	−	0.899874i	$-0.356342\pi$
$752$	5.14045			0.187453
$753$	−29.0181	−	36.1033i	−1.05748	−	1.31568i
$754$		−	4.38924i		−	0.159847i
$755$	56.8406			2.06864
$756$		0			0
$757$	46.4611			1.68866			0.844328	−	0.535827i	$-0.180000\pi$
$757$	46.4611			1.68866			0.844328	+	0.535827i	$0.180000\pi$
$758$			26.9063i			0.977282i
$759$	11.0137	+	13.7028i	0.399772	+	0.497381i
$760$	−29.2311			−1.06032
$761$	18.5959	+	32.2090i	0.674099	+	1.16757i	0.976731	+	0.214467i	$0.0688013\pi$
$761$	18.5959	+	32.2090i	0.674099	+	1.16757i	−0.302632	+	0.953107i	$0.597865\pi$
$762$	−0.387680	+	0.311599i	−0.0140442	+	0.0112880i
$763$		0			0
$764$			5.13264i			0.185692i
$765$	12.7323	+	11.6338i	0.460338	+	0.420622i
$766$	−10.8874	+	6.28586i	−0.393379	+	0.227117i
$767$	7.85890	+	4.53734i	0.283768	+	0.163834i
$768$	1.08509	+	1.35003i	0.0391548	+	0.0487150i
$769$	12.2312	+	7.06166i	0.441067	+	0.254650i	0.704050	−	0.710150i	$-0.251373\pi$
$769$	12.2312	+	7.06166i	0.441067	+	0.254650i	−0.262983	+	0.964800i	$0.584706\pi$
$770$		0			0
$771$	3.26609	−	8.41642i	0.117625	−	0.303110i
$772$	−15.9847			−0.575302
$773$	−15.4728	−	26.7996i	−0.556517	−	0.963915i	−0.997784	−	0.0665393i	$-0.978804\pi$
$773$	−15.4728	−	26.7996i	−0.556517	−	0.963915i	0.441267	−	0.897376i	$-0.354529\pi$
$774$	−5.54399	−	17.4966i	−0.199275	−	0.628904i
$775$	−39.4928	−	22.8012i	−1.41862	−	0.819043i
$776$	7.69782	+	13.3330i	0.276336	+	0.478627i
$777$		0			0
$778$	8.12937	−	14.0805i	0.291452	−	0.504810i
$779$	−0.673057	+	0.388590i	−0.0241148	+	0.0139227i
$780$	−4.92256	+	3.95652i	−0.176256	+	0.141666i
$781$	21.1367	−	36.6098i	0.756330	−	1.31000i
$782$	−2.71755	+	4.70694i	−0.0971794	+	0.168320i
$783$	12.3049	−	18.5008i	0.439742	−	0.661165i
$784$		0			0
$785$	−35.4599	+	20.4728i	−1.26562	+	0.730706i
$786$	0.602212	+	0.233695i	0.0214802	+	0.00833564i
$787$		−	18.3256i		−	0.653237i	−0.945156	−	0.326619i	$-0.894091\pi$
$787$		−	18.3256i		−	0.653237i	0.945156	−	0.326619i	$-0.105909\pi$
$788$		−	4.72572i		−	0.168347i
$789$	−3.98041	−	25.7396i	−0.141706	−	0.916353i
$790$	2.84295	−	1.64138i	0.101148	−	0.0583976i
$791$		0			0
$792$	6.69367	+	6.11615i	0.237849	+	0.217328i
$793$	−2.40723	+	4.16945i	−0.0854834	+	0.148062i
$794$	−7.34692	+	12.7252i	−0.260733	+	0.451602i
$795$	2.99921	+	19.3946i	0.106371	+	0.687854i
$796$	1.83679	−	1.06047i	0.0651034	−	0.0375875i
$797$	1.07681	−	1.86508i	0.0381424	−	0.0660646i	−0.846324	−	0.532668i	$-0.821189\pi$
$797$	1.07681	−	1.86508i	0.0381424	−	0.0660646i	0.884466	+	0.466604i	$0.154523\pi$
$798$		0			0
$799$	4.15968	+	7.20477i	0.147159	+	0.254886i
$800$	−6.59779	−	3.80924i	−0.233267	−	0.134677i
$801$	10.4310	+	9.53107i	0.368562	+	0.336764i
$802$	8.32318	+	14.4162i	0.293902	+	0.509053i
$803$	−3.96266			−0.139839
$804$	0.407642	+	0.507173i	0.0143764	+	0.0178866i
$805$		0			0
$806$	−5.32101	−	3.07208i	−0.187424	−	0.108210i
$807$	−14.4944	+	37.3508i	−0.510228	+	1.31481i
$808$	−11.8686	−	6.85234i	−0.417536	−	0.241064i
$809$	17.0147	−	9.82342i	0.598204	−	0.345373i	−0.170131	−	0.985421i	$-0.554419\pi$
$809$	17.0147	−	9.82342i	0.598204	−	0.345373i	0.768335	+	0.640048i	$0.221086\pi$
$810$	−31.8405	+	2.87682i	−1.11876	+	0.101081i
$811$		−	12.3340i		−	0.433105i	−0.976271	−	0.216552i	$-0.930519\pi$
$811$		−	12.3340i		−	0.433105i	0.976271	−	0.216552i	$-0.0694812\pi$
$812$		0			0
$813$	−2.62450	−	16.9715i	−0.0920452	−	0.595216i
$814$	8.83510	+	15.3028i	0.309670	+	0.536364i
$815$	−9.76061			−0.341899
$816$	−1.01412	+	2.61329i	−0.0355013	+	0.0914836i
$817$			50.3443i			1.76132i
$818$	2.80886			0.0982095
$819$		0			0
$820$	−0.335493			−0.0117159
$821$			22.3738i			0.780853i	0.920634	+	0.390426i	$0.127672\pi$
$821$			22.3738i			0.780853i	−0.920634	+	0.390426i	$0.872328\pi$
$822$	−12.0884	+	1.86938i	−0.421633	+	0.0652020i
$823$	27.0065			0.941388			0.470694	−	0.882297i	$-0.344004\pi$
$823$	27.0065			0.941388			0.470694	+	0.882297i	$0.344004\pi$
$824$	1.52429	+	2.64014i	0.0531010	+	0.0919737i
$825$	−37.1805	−	14.4283i	−1.29446	−	0.502330i
$826$		0			0
$827$			26.3189i			0.915196i	0.889159	+	0.457598i	$0.151290\pi$
$827$			26.3189i			0.915196i	−0.889159	+	0.457598i	$0.848710\pi$
$828$	−3.04322	−	9.60429i	−0.105759	−	0.333772i
$829$	−28.8691	+	16.6676i	−1.00266	+	0.578888i	−0.909035	−	0.416719i	$-0.863180\pi$
$829$	−28.8691	+	16.6676i	−1.00266	+	0.578888i	−0.0936287	+	0.995607i	$0.529847\pi$
$830$	−33.4219	−	19.2962i	−1.16009	−	0.669779i
$831$	14.7111	−	2.27495i	0.510323	−	0.0789172i
$832$	−0.888944	−	0.513232i	−0.0308186	−	0.0177931i
$833$		0			0
$834$	−24.9672	+	3.86096i	−0.864543	+	0.133694i
$835$	−19.6756			−0.680903
$836$	−12.4354	−	21.5387i	−0.430086	−	0.744932i
$837$	−13.8158	−	27.8660i	−0.477545	−	0.963190i
$838$	−12.9447	−	7.47362i	−0.447167	−	0.258172i
$839$	18.6896	+	32.3713i	0.645236	+	1.11758i	0.984247	+	0.176799i	$0.0565743\pi$
$839$	18.6896	+	32.3713i	0.645236	+	1.11758i	−0.339011	+	0.940782i	$0.610092\pi$
$840$		0			0
$841$	−5.35758	+	9.27960i	−0.184744	+	0.319986i
$842$	13.5158	−	7.80336i	0.465786	−	0.268922i
$843$	−33.4698	−	12.9883i	−1.15276	−	0.447342i
$844$	13.8079	−	23.9160i	0.475289	−	0.823224i
$845$	−21.2182	+	36.7511i	−0.729930	+	1.26428i
$846$	−15.0605	−	3.31641i	−0.517792	−	0.114021i
$847$		0			0
$848$	−2.76235	+	1.59484i	−0.0948594	+	0.0547671i
$849$	3.19565	−	2.56852i	0.109675	−	0.0881512i
$850$		−	12.3298i		−	0.422909i
$851$		−	19.6342i		−	0.673052i
$852$	−18.8826	+	15.1770i	−0.646908	+	0.519954i
$853$	4.65798	−	2.68929i	0.159486	−	0.0920795i	−0.418133	−	0.908386i	$-0.637315\pi$
$853$	4.65798	−	2.68929i	0.159486	−	0.0920795i	0.577619	+	0.816306i	$0.303982\pi$
$854$		0			0
$855$	85.6414	+	18.8587i	2.92887	+	0.644954i
$856$	−6.56336	+	11.3681i	−0.224331	+	0.388553i
$857$	−22.7000	+	39.3176i	−0.775418	+	1.34306i	0.159142	+	0.987256i	$0.449127\pi$
$857$	−22.7000	+	39.3176i	−0.775418	+	1.34306i	−0.934559	+	0.355807i	$0.884206\pi$
$858$	−5.00947	−	1.94398i	−0.171020	−	0.0663665i
$859$	−3.36261	+	1.94141i	−0.114731	+	0.0662399i	−0.556267	−	0.831003i	$-0.687767\pi$
$859$	−3.36261	+	1.94141i	−0.114731	+	0.0662399i	0.441536	+	0.897243i	$0.354434\pi$
$860$	−10.8663	+	18.8210i	−0.370538	+	0.641791i
$861$		0			0
$862$	−8.08792	−	14.0087i	−0.275476	−	0.477138i
$863$	−20.3332	−	11.7394i	−0.692152	−	0.399614i	0.112266	−	0.993678i	$-0.464189\pi$
$863$	−20.3332	−	11.7394i	−0.692152	−	0.399614i	−0.804418	+	0.594064i	$0.797522\pi$
$864$	−2.30812	−	4.65538i	−0.0785238	−	0.158379i
$865$	19.9016	+	34.4706i	0.676674	+	1.17203i
$866$	−27.2499			−0.925991
$867$	24.6156	−	3.80660i	0.835990	−	0.129279i
$868$		0			0
$869$	2.41887	+	1.39654i	0.0820547	+	0.0473743i
$870$	−26.0003	+	4.02072i	−0.881492	+	0.136315i
$871$	−0.333955	−	0.192809i	−0.0113156	−	0.00653308i
$872$	9.15516	−	5.28574i	0.310033	−	0.178998i
$873$	−13.9512	−	44.0295i	−0.472177	−	1.49017i
$874$			27.6351i			0.934770i
$875$		0			0
$876$	2.11709	+	0.821562i	0.0715299	+	0.0277580i
$877$	−16.4796	−	28.5434i	−0.556475	−	0.963843i	−0.997787	−	0.0664896i	$-0.978820\pi$
$877$	−16.4796	−	28.5434i	−0.556475	−	0.963843i	0.441312	−	0.897354i	$-0.354513\pi$
$878$	33.1347			1.11824
$879$	−30.2552	+	4.67871i	−1.02048	+	0.157809i
$880$		−	10.7362i		−	0.361918i
$881$	−7.44403			−0.250796			−0.125398	−	0.992107i	$-0.540021\pi$
$881$	−7.44403			−0.250796			−0.125398	+	0.992107i	$0.540021\pi$
$882$		0			0
$883$	−28.2839			−0.951828			−0.475914	−	0.879492i	$-0.657883\pi$
$883$	−28.2839			−0.951828			−0.475914	+	0.879492i	$0.657883\pi$
$884$		−	1.66124i		−	0.0558735i
$885$	19.6785	−	50.7097i	0.661485	−	1.70459i
$886$	22.2636			0.747960
$887$	−6.06377	−	10.5028i	−0.203602	−	0.352648i	0.746085	−	0.665851i	$-0.231931\pi$
$887$	−6.06377	−	10.5028i	−0.203602	−	0.352648i	−0.949686	+	0.313203i	$0.898598\pi$
$888$	−1.54756	−	10.0074i	−0.0519329	−	0.335827i
$889$		0			0
$890$		−	16.7307i		−	0.560814i
$891$	−15.6653	−	22.2376i	−0.524806	−	0.744989i
$892$	−17.6209	+	10.1734i	−0.589992	+	0.340632i
$893$	36.6331	+	21.1501i	1.22588	+	0.707761i
$894$	6.70612	−	17.2811i	0.224286	−	0.577965i
$895$	8.43465	+	4.86975i	0.281939	+	0.162778i
$896$		0			0
$897$	3.74050	+	4.65379i	0.124892	+	0.155385i
$898$	6.80819			0.227192
$899$	−12.7978	−	22.1664i	−0.426830	−	0.739291i
$900$	16.8727	+	15.4170i	0.562423	+	0.513899i
$901$	−4.47061	−	2.58111i	−0.148938	−	0.0859891i
$902$	−0.142724	−	0.247206i	−0.00475220	−	0.00823105i
$903$		0			0
$904$	6.14993	−	10.6520i	0.204544	−	0.354280i
$905$	−68.5712	+	39.5896i	−2.27938	+	1.31600i
$906$	−4.23555	−	27.3895i	−0.140717	−	0.909955i
$907$	23.0890	−	39.9913i	0.766657	−	1.32789i	−0.172709	−	0.984973i	$-0.555252\pi$
$907$	23.0890	−	39.9913i	0.766657	−	1.32789i	0.939366	−	0.342916i	$-0.111415\pi$
$908$	−2.08000	+	3.60266i	−0.0690272	+	0.119559i
$909$	30.3518	+	27.7332i	1.00671	+	0.919851i
$910$		0			0
$911$	−12.7284	+	7.34874i	−0.421710	+	0.243475i	−0.695809	−	0.718227i	$-0.744954\pi$
$911$	−12.7284	+	7.34874i	−0.421710	+	0.243475i	0.274098	+	0.961702i	$0.411621\pi$
$912$	2.17819	+	14.0854i	0.0721272	+	0.466415i
$913$		−	32.8356i		−	1.08670i
$914$			15.2260i			0.503630i
$915$	26.9034	+	10.4402i	0.889400	+	0.345142i
$916$	−5.16986	+	2.98482i	−0.170817	+	0.0986212i
$917$		0			0
$918$	4.65716	−	7.00218i	0.153709	−	0.231106i
$919$	−12.9345	+	22.4033i	−0.426671	+	0.739015i	−0.996575	−	0.0826958i	$-0.973647\pi$
$919$	−12.9345	+	22.4033i	−0.426671	+	0.739015i	0.569904	+	0.821711i	$0.306980\pi$
$920$	−5.96476	+	10.3313i	−0.196652	+	0.340612i
$921$	−1.73014	+	1.39060i	−0.0570099	+	0.0458219i
$922$	0.179060	−	0.103381i	0.00589704	−	0.00340466i
$923$	7.17849	−	12.4335i	0.236283	−	0.409254i
$924$		0			0
$925$	22.2706	+	38.5738i	0.732253	+	1.26830i
$926$	−13.1673	−	7.60217i	−0.432706	−	0.249823i
$927$	−2.76255	−	8.71852i	−0.0907341	−	0.286354i
$928$	−2.13804	−	3.70319i	−0.0701846	−	0.121563i
$929$	−13.1935			−0.432863			−0.216432	−	0.976298i	$-0.569442\pi$
$929$	−13.1935			−0.432863			−0.216432	+	0.976298i	$0.569442\pi$
$930$	−13.3237	+	34.3339i	−0.436900	+	1.12585i
$931$		0			0
$932$	3.88603	+	2.24360i	0.127291	+	0.0734915i
$933$	−13.5993	−	16.9197i	−0.445220	−	0.553927i
$934$	−1.99921	−	1.15424i	−0.0654161	−	0.0377680i
$935$	15.0477	−	8.68779i	0.492112	−	0.284121i
$936$	2.27332	+	2.07718i	0.0743057	+	0.0678948i
$937$		−	8.86021i		−	0.289451i	−0.989472	−	0.144725i	$-0.953770\pi$
$937$		−	8.86021i		−	0.289451i	0.989472	−	0.144725i	$-0.0462298\pi$
$938$		0			0
$939$	11.8180	−	9.49871i	0.385664	−	0.309979i
$940$	9.13009	+	15.8138i	0.297791	+	0.515788i
$941$	4.11839			0.134256			0.0671278	−	0.997744i	$-0.478616\pi$
$941$	4.11839			0.134256			0.0671278	+	0.997744i	$0.478616\pi$
$942$	12.5075	+	15.5613i	0.407516	+	0.507016i
$943$			0.317175i			0.0103287i
$944$	8.84071			0.287741
$945$		0			0
$946$	−18.4908			−0.601189
$947$			24.7681i			0.804854i	0.915452	+	0.402427i	$0.131833\pi$
$947$			24.7681i			0.804854i	−0.915452	+	0.402427i	$0.868167\pi$
$948$	−1.00277	−	1.24761i	−0.0325684	−	0.0405204i
$949$	−1.34581			−0.0436868
$950$	−31.3458	−	54.2925i	−1.01699	−	1.76148i
$951$	18.4662	−	14.8423i	0.598809	−	0.481294i
$952$		0			0
$953$		−	9.62625i		−	0.311825i	−0.987771	−	0.155912i	$-0.950168\pi$
$953$		−	9.62625i		−	0.311825i	0.987771	−	0.155912i	$-0.0498317\pi$
$954$	9.12207	−	2.89042i	0.295338	−	0.0935810i
$955$	−15.7897	+	9.11620i	−0.510944	+	0.294993i
$956$	3.02944	+	1.74905i	0.0979790	+	0.0565682i
$957$	−14.0236	−	17.4476i	−0.453318	−	0.564002i
$958$	−10.7674	−	6.21659i	−0.347880	−	0.200849i
$959$		0			0
$960$	−2.22589	+	5.73592i	−0.0718404	+	0.185126i
$961$	−4.82931			−0.155784
$962$	3.00060	+	5.19719i	0.0967431	+	0.167564i
$963$	26.5636	−	29.0718i	0.856000	−	0.936827i
$964$	10.0170	+	5.78332i	0.322626	+	0.186268i
$965$	−28.3908	−	49.1744i	−0.913933	−	1.58298i
$966$		0			0
$967$	5.05558	−	8.75652i	0.162576	−	0.281591i	−0.773216	−	0.634143i	$-0.781353\pi$
$967$	5.05558	−	8.75652i	0.162576	−	0.281591i	0.935792	+	0.352553i	$0.114686\pi$
$968$	−1.61538	+	0.932639i	−0.0519202	+	0.0299762i
$969$	−17.9793	+	14.4509i	−0.577578	+	0.464230i
$970$	−27.3446	+	47.3622i	−0.877981	+	1.52071i
$971$	12.6574	−	21.9233i	0.406196	−	0.703552i	−0.588264	−	0.808669i	$-0.700188\pi$
$971$	12.6574	−	21.9233i	0.406196	−	0.703552i	0.994460	+	0.105117i	$0.0335216\pi$
$972$	3.75888	+	15.1285i	0.120566	+	0.485246i
$973$		0			0
$974$	32.3033	−	18.6503i	1.03507	−	0.597595i
$975$	−12.6273	−	4.90019i	−0.404399	−	0.156932i
$976$			4.69034i			0.150134i
$977$			9.05294i			0.289629i	0.989459	+	0.144815i	$0.0462586\pi$
$977$			9.05294i			0.289629i	−0.989459	+	0.144815i	$0.953741\pi$
$978$	0.727325	+	4.70330i	0.0232573	+	0.150395i
$979$	12.3279	−	7.11752i	0.394001	−	0.227477i
$980$		0			0
$981$	−30.2330	+	9.57964i	−0.965266	+	0.305855i
$982$	6.82377	−	11.8191i	0.217755	−	0.377163i
$983$	3.19651	−	5.53653i	0.101953	−	0.176588i	−0.810536	−	0.585688i	$-0.800824\pi$
$983$	3.19651	−	5.53653i	0.101953	−	0.176588i	0.912489	+	0.409101i	$0.134158\pi$
$984$	0.0249997	+	0.161662i	0.000796962	+	0.00515361i
$985$	14.5379	−	8.39347i	0.463216	−	0.267438i
$986$	3.46022	−	5.99328i	0.110196	−	0.190865i
$987$		0			0
$988$	−4.22333	−	7.31502i	−0.134362	−	0.232722i
$989$	17.7934	+	10.2730i	0.565797	+	0.326663i
$990$	−6.92657	+	31.4550i	−0.220141	+	0.999706i
$991$	6.92230	+	11.9898i	0.219894	+	0.380868i	0.954775	−	0.297328i	$-0.0960954\pi$
$991$	6.92230	+	11.9898i	0.219894	+	0.380868i	−0.734881	+	0.678196i	$0.762762\pi$
$992$	−5.98576			−0.190048
$993$	−11.8244	−	14.7115i	−0.375236	−	0.466855i
$994$		0			0
$995$	6.52475	+	3.76706i	0.206848	+	0.119424i
$996$	−6.80766	+	17.5427i	−0.215709	+	0.555863i
$997$	5.99391	+	3.46059i	0.189829	+	0.109598i	0.591903	−	0.806010i	$-0.298377\pi$
$997$	5.99391	+	3.46059i	0.189829	+	0.109598i	−0.402073	+	0.915607i	$0.631710\pi$
$998$	−18.1882	+	10.5010i	−0.575737	+	0.332402i
$999$	−1.92233	+	30.3183i	−0.0608197	+	0.959227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.l.b.509.7		16
3.2	odd	2		2646.2.l.a.1097.4		16
7.2	even	3		882.2.m.a.293.5		16
7.3	odd	6		882.2.t.a.815.1		16
7.4	even	3		126.2.t.a.59.4	yes	16
7.5	odd	6		882.2.m.b.293.8		16
7.6	odd	2		126.2.l.a.5.6	✓	16
9.2	odd	6		882.2.t.a.803.1		16
9.7	even	3		2646.2.t.b.1979.8		16
21.2	odd	6		2646.2.m.a.881.4		16
21.5	even	6		2646.2.m.b.881.1		16
21.11	odd	6		378.2.t.a.17.5		16
21.17	even	6		2646.2.t.b.2285.8		16
21.20	even	2		378.2.l.a.341.1		16
28.11	odd	6		1008.2.df.c.689.3		16
28.27	even	2		1008.2.ca.c.257.7		16
63.2	odd	6		882.2.m.b.587.8		16
63.4	even	3		1134.2.k.b.647.5		16
63.11	odd	6		126.2.l.a.101.2	yes	16
63.13	odd	6		1134.2.k.a.971.4		16
63.16	even	3		2646.2.m.b.1763.1		16
63.20	even	6		126.2.t.a.47.4	yes	16
63.25	even	3		378.2.l.a.143.5		16
63.32	odd	6		1134.2.k.a.647.4		16
63.34	odd	6		378.2.t.a.89.5		16
63.38	even	6	inner	882.2.l.b.227.3		16
63.41	even	6		1134.2.k.b.971.5		16
63.47	even	6		882.2.m.a.587.5		16
63.52	odd	6		2646.2.l.a.521.8		16
63.61	odd	6		2646.2.m.a.1763.4		16
84.11	even	6		3024.2.df.c.17.1		16
84.83	odd	2		3024.2.ca.c.2609.1		16
252.11	even	6		1008.2.ca.c.353.7		16
252.83	odd	6		1008.2.df.c.929.3		16
252.151	odd	6		3024.2.ca.c.2033.1		16
252.223	even	6		3024.2.df.c.1601.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.6	✓	16	7.6	odd	2
126.2.l.a.101.2	yes	16	63.11	odd	6
126.2.t.a.47.4	yes	16	63.20	even	6
126.2.t.a.59.4	yes	16	7.4	even	3
378.2.l.a.143.5		16	63.25	even	3
378.2.l.a.341.1		16	21.20	even	2
378.2.t.a.17.5		16	21.11	odd	6
378.2.t.a.89.5		16	63.34	odd	6
882.2.l.b.227.3		16	63.38	even	6	inner
882.2.l.b.509.7		16	1.1	even	1	trivial
882.2.m.a.293.5		16	7.2	even	3
882.2.m.a.587.5		16	63.47	even	6
882.2.m.b.293.8		16	7.5	odd	6
882.2.m.b.587.8		16	63.2	odd	6
882.2.t.a.803.1		16	9.2	odd	6
882.2.t.a.815.1		16	7.3	odd	6
1008.2.ca.c.257.7		16	28.27	even	2
1008.2.ca.c.353.7		16	252.11	even	6
1008.2.df.c.689.3		16	28.11	odd	6
1008.2.df.c.929.3		16	252.83	odd	6
1134.2.k.a.647.4		16	63.32	odd	6
1134.2.k.a.971.4		16	63.13	odd	6
1134.2.k.b.647.5		16	63.4	even	3
1134.2.k.b.971.5		16	63.41	even	6
2646.2.l.a.521.8		16	63.52	odd	6
2646.2.l.a.1097.4		16	3.2	odd	2
2646.2.m.a.881.4		16	21.2	odd	6
2646.2.m.a.1763.4		16	63.61	odd	6
2646.2.m.b.881.1		16	21.5	even	6
2646.2.m.b.1763.1		16	63.16	even	3
2646.2.t.b.1979.8		16	9.7	even	3
2646.2.t.b.2285.8		16	21.17	even	6
3024.2.ca.c.2033.1		16	252.151	odd	6
3024.2.ca.c.2609.1		16	84.83	odd	2
3024.2.df.c.17.1		16	84.11	even	6
3024.2.df.c.1601.1		16	252.223	even	6

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.08509 + 1.35003i) q^{3} -1.00000 q^{4} +(-1.77612 - 3.07634i) q^{5} +(-1.35003 + 1.08509i) q^{6} -1.00000i q^{8} +(-0.645160 + 2.92981i) q^{9} +(3.07634 - 1.77612i) q^{10} +(2.61745 + 1.51119i) q^{11} +(-1.08509 - 1.35003i) q^{12} +(0.888944 + 0.513232i) q^{13} +(2.22589 - 5.73592i) q^{15} +1.00000 q^{16} +(0.809204 + 1.40158i) q^{17} +(-2.92981 - 0.645160i) q^{18} +(7.12643 + 4.11444i) q^{19} +(1.77612 + 3.07634i) q^{20} +(-1.51119 + 2.61745i) q^{22} +(2.90837 - 1.67915i) q^{23} +(1.35003 - 1.08509i) q^{24} +(-3.80924 + 6.59779i) q^{25} +(-0.513232 + 0.888944i) q^{26} +(-4.65538 + 2.30812i) q^{27} +(-3.70319 + 2.13804i) q^{29} +(5.73592 + 2.22589i) q^{30} +5.98576i q^{31} +1.00000i q^{32} +(0.800023 + 5.17341i) q^{33} +(-1.40158 + 0.809204i) q^{34} +(0.645160 - 2.92981i) q^{36} +(2.92323 - 5.06319i) q^{37} +(-4.11444 + 7.12643i) q^{38} +(0.271706 + 1.75700i) q^{39} +(-3.07634 + 1.77612i) q^{40} +(-0.0472226 + 0.0817920i) q^{41} +(3.05899 + 5.29833i) q^{43} +(-2.61745 - 1.51119i) q^{44} +(10.1590 - 3.21897i) q^{45} +(1.67915 + 2.90837i) q^{46} +5.14045 q^{47} +(1.08509 + 1.35003i) q^{48} +(-6.59779 - 3.80924i) q^{50} +(-1.01412 + 2.61329i) q^{51} +(-0.888944 - 0.513232i) q^{52} +(-2.76235 + 1.59484i) q^{53} +(-2.30812 - 4.65538i) q^{54} -10.7362i q^{55} +(2.17819 + 14.0854i) q^{57} +(-2.13804 - 3.70319i) q^{58} +8.84071 q^{59} +(-2.22589 + 5.73592i) q^{60} +4.69034i q^{61} -5.98576 q^{62} -1.00000 q^{64} -3.64626i q^{65} +(-5.17341 + 0.800023i) q^{66} -0.375675 q^{67} +(-0.809204 - 1.40158i) q^{68} +(5.42275 + 2.10436i) q^{69} -13.9868i q^{71} +(2.92981 + 0.645160i) q^{72} +(-1.13546 + 0.655556i) q^{73} +(5.06319 + 2.92323i) q^{74} +(-13.0406 + 2.01662i) q^{75} +(-7.12643 - 4.11444i) q^{76} +(-1.75700 + 0.271706i) q^{78} +0.924134 q^{79} +(-1.77612 - 3.07634i) q^{80} +(-8.16754 - 3.78039i) q^{81} +(-0.0817920 - 0.0472226i) q^{82} +(-5.43209 - 9.40866i) q^{83} +(2.87450 - 4.97877i) q^{85} +(-5.29833 + 3.05899i) q^{86} +(-6.90471 - 2.67945i) q^{87} +(1.51119 - 2.61745i) q^{88} +(2.35495 - 4.07888i) q^{89} +(3.21897 + 10.1590i) q^{90} +(-2.90837 + 1.67915i) q^{92} +(-8.08095 + 6.49509i) q^{93} +5.14045i q^{94} -29.2311i q^{95} +(-1.35003 + 1.08509i) q^{96} +(-13.3330 + 7.69782i) q^{97} +(-6.11615 + 6.69367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 12 q^{11} - 6 q^{13} - 18 q^{15} + 16 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 36 q^{27} + 6 q^{29} - 2 q^{37} - 12 q^{39} + 6 q^{41} - 2 q^{43} - 12 q^{44} + 30 q^{45}+ \cdots + 18 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 12 * q^11 - 6 * q^13 - 18 * q^15 + 16 * q^16 + 18 * q^17 - 12 * q^18 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 36 * q^27 + 6 * q^29 - 2 * q^37 - 12 * q^39 + 6 * q^41 - 2 * q^43 - 12 * q^44 + 30 * q^45 + 6 * q^46 + 36 * q^47 - 12 * q^50 + 6 * q^51 + 6 * q^52 - 36 * q^53 - 18 * q^54 + 6 * q^57 + 6 * q^58 - 60 * q^59 + 18 * q^60 - 36 * q^62 - 16 * q^64 - 24 * q^66 - 28 * q^67 - 18 * q^68 + 42 * q^69 + 12 * q^72 + 18 * q^74 - 60 * q^75 + 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^86 + 24 * q^87 + 24 * q^89 - 18 * q^90 + 6 * q^92 - 42 * q^93 - 6 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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