LMFDB - Embedded newform 784.2.x.p.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.1
Character	$\chi$	$=$	784.165
Dual form			784.2.x.p.765.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40346 - 0.174081i) q^{2} +(-0.548135 - 2.04567i) q^{3} +(1.93939 + 0.488631i) q^{4} +(0.207992 - 0.776238i) q^{5} +(0.413172 + 2.96643i) q^{6} +(-2.63679 - 1.02339i) q^{8} +(-1.28622 + 0.742602i) q^{9} +O(q^{10})$	\(q+(-1.40346 - 0.174081i) q^{2} +(-0.548135 - 2.04567i) q^{3} +(1.93939 + 0.488631i) q^{4} +(0.207992 - 0.776238i) q^{5} +(0.413172 + 2.96643i) q^{6} +(-2.63679 - 1.02339i) q^{8} +(-1.28622 + 0.742602i) q^{9} +(-0.427037 + 1.05321i) q^{10} +(4.56933 - 1.22435i) q^{11} +(-0.0634710 - 4.23518i) q^{12} +(-0.658150 + 0.658150i) q^{13} -1.70193 q^{15} +(3.52248 + 1.89529i) q^{16} +(1.75927 - 3.04715i) q^{17} +(1.93444 - 0.818304i) q^{18} +(-4.39209 - 1.17686i) q^{19} +(0.782673 - 1.40380i) q^{20} +(-6.62600 + 0.922888i) q^{22} +(2.06245 - 1.19075i) q^{23} +(-0.648187 + 5.95495i) q^{24} +(3.77084 + 2.17710i) q^{25} +(1.03826 - 0.809114i) q^{26} +(-2.26846 - 2.26846i) q^{27} +(4.06282 - 4.06282i) q^{29} +(2.38859 + 0.296274i) q^{30} +(4.95223 - 8.57752i) q^{31} +(-4.61372 - 3.27317i) q^{32} +(-5.00922 - 8.67622i) q^{33} +(-2.99951 + 3.97029i) q^{34} +(-2.85735 + 0.811707i) q^{36} +(-2.12056 + 7.91402i) q^{37} +(5.95925 + 2.41625i) q^{38} +(1.70711 + 0.985600i) q^{39} +(-1.34282 + 1.83392i) q^{40} +3.75281i q^{41} +(-6.04279 - 6.04279i) q^{43} +(9.45998 - 0.141773i) q^{44} +(0.308911 + 1.15287i) q^{45} +(-3.10185 + 1.31214i) q^{46} +(5.12882 + 8.88338i) q^{47} +(1.94635 - 8.24469i) q^{48} +(-4.91323 - 3.71190i) q^{50} +(-7.19776 - 1.92863i) q^{51} +(-1.59800 + 0.954817i) q^{52} +(-12.1874 + 3.26561i) q^{53} +(2.78879 + 3.57858i) q^{54} -3.80155i q^{55} +9.62984i q^{57} +(-6.40925 + 4.99473i) q^{58} +(3.30200 - 0.884769i) q^{59} +(-3.30071 - 0.831618i) q^{60} +(-6.44729 - 1.72755i) q^{61} +(-8.44344 + 11.1761i) q^{62} +(5.90536 + 5.39691i) q^{64} +(0.373991 + 0.647771i) q^{65} +(5.51986 + 13.0487i) q^{66} +(-2.10001 - 7.83735i) q^{67} +(4.90085 - 5.04998i) q^{68} +(-3.56639 - 3.56639i) q^{69} +1.91187i q^{71} +(4.15148 - 0.641785i) q^{72} +(-12.1692 - 7.02587i) q^{73} +(4.35380 - 10.7379i) q^{74} +(2.38668 - 8.90723i) q^{75} +(-7.94294 - 4.42850i) q^{76} +(-2.22428 - 1.68042i) q^{78} +(-2.33048 - 4.03650i) q^{79} +(2.20385 - 2.34008i) q^{80} +(-5.62489 + 9.74260i) q^{81} +(0.653294 - 5.26692i) q^{82} +(9.13749 - 9.13749i) q^{83} +(-1.99940 - 1.99940i) q^{85} +(7.42887 + 9.53274i) q^{86} +(-10.5381 - 6.08420i) q^{87} +(-13.3014 - 1.44783i) q^{88} +(0.158841 - 0.0917070i) q^{89} +(-0.232851 - 1.67178i) q^{90} +(4.58173 - 1.30156i) q^{92} +(-20.2612 - 5.42898i) q^{93} +(-5.65166 - 13.3603i) q^{94} +(-1.82704 + 3.16453i) q^{95} +(-4.16687 + 11.2323i) q^{96} -9.26984 q^{97} +(-4.96798 + 4.96798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{4}+O(q^{10}) $ 96 * q + 4 * q^4	$ 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) $ 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.40346	−	0.174081i	−0.992395	−	0.123094i
$2$	−1.40346	−	0.174081i	−0.992395	−	0.123094i
$3$	−0.548135	−	2.04567i	−0.316466	−	1.18107i	−0.922617	−	0.385717i	$-0.873954\pi$
$3$	−0.548135	−	2.04567i	−0.316466	−	1.18107i	0.606151	−	0.795349i	$-0.292713\pi$
$4$	1.93939	+	0.488631i	0.969696	+	0.244316i
$5$	0.207992	−	0.776238i	0.0930170	−	0.347144i	−0.903694	−	0.428178i	$-0.859156\pi$
$5$	0.207992	−	0.776238i	0.0930170	−	0.347144i	0.996711	+	0.0810339i	$0.0258222\pi$
$6$	0.413172	+	2.96643i	0.168677	+	1.21104i
$7$		0			0
$7$		0			0
$8$	−2.63679	−	1.02339i	−0.932247	−	0.361821i
$9$	−1.28622	+	0.742602i	−0.428742	+	0.247534i
$10$	−0.427037	+	1.05321i	−0.135041	+	0.333054i
$11$	4.56933	−	1.22435i	1.37771	−	0.369155i	0.507418	−	0.861700i	$-0.330600\pi$
$11$	4.56933	−	1.22435i	1.37771	−	0.369155i	0.870287	+	0.492545i	$0.163933\pi$
$12$	−0.0634710	−	4.23518i	−0.0183225	−	1.22259i
$13$	−0.658150	+	0.658150i	−0.182538	+	0.182538i	−0.792461	−	0.609923i	$-0.791200\pi$
$13$	−0.658150	+	0.658150i	−0.182538	+	0.182538i	0.609923	+	0.792461i	$0.291200\pi$
$14$		0			0
$15$	−1.70193			−0.439437
$16$	3.52248	+	1.89529i	0.880620	+	0.473824i
$17$	1.75927	−	3.04715i	0.426686	−	0.739042i	−0.569890	−	0.821721i	$-0.693014\pi$
$17$	1.75927	−	3.04715i	0.426686	−	0.739042i	0.996576	+	0.0826792i	$0.0263477\pi$
$18$	1.93444	−	0.818304i	0.455951	−	0.192876i
$19$	−4.39209	−	1.17686i	−1.00762	−	0.269990i	−0.282983	−	0.959125i	$-0.591324\pi$
$19$	−4.39209	−	1.17686i	−1.00762	−	0.269990i	−0.724633	+	0.689135i	$0.757991\pi$
$20$	0.782673	−	1.40380i	0.175011	−	0.313899i
$21$		0			0
$22$	−6.62600	+	0.922888i	−1.41267	+	0.196760i
$23$	2.06245	−	1.19075i	0.430050	−	0.248290i	−0.269318	−	0.963051i	$-0.586798\pi$
$23$	2.06245	−	1.19075i	0.430050	−	0.248290i	0.699368	+	0.714762i	$0.253465\pi$
$24$	−0.648187	+	5.95495i	−0.132311	+	1.21555i
$25$	3.77084	+	2.17710i	0.754168	+	0.435419i
$26$	1.03826	−	0.809114i	0.203619	−	0.158680i
$27$	−2.26846	−	2.26846i	−0.436564	−	0.436564i
$28$		0			0
$29$	4.06282	−	4.06282i	0.754446	−	0.754446i	−0.220860	−	0.975306i	$-0.570886\pi$
$29$	4.06282	−	4.06282i	0.754446	−	0.754446i	0.975306	+	0.220860i	$0.0708863\pi$
$30$	2.38859	+	0.296274i	0.436095	+	0.0540921i
$31$	4.95223	−	8.57752i	0.889447	−	1.54057i	0.0489170	−	0.998803i	$-0.484423\pi$
$31$	4.95223	−	8.57752i	0.889447	−	1.54057i	0.840530	−	0.541765i	$-0.182244\pi$
$32$	−4.61372	−	3.27317i	−0.815598	−	0.578619i
$33$	−5.00922	−	8.67622i	−0.871993	−	1.51034i
$34$	−2.99951	+	3.97029i	−0.514412	+	0.680899i
$35$		0			0
$36$	−2.85735	+	0.811707i	−0.476225	+	0.135284i
$37$	−2.12056	+	7.91402i	−0.348617	+	1.30106i	0.539712	+	0.841850i	$0.318533\pi$
$37$	−2.12056	+	7.91402i	−0.348617	+	1.30106i	−0.888329	+	0.459208i	$0.848133\pi$
$38$	5.95925	+	2.41625i	0.966718	+	0.391968i
$39$	1.70711	+	0.985600i	0.273356	+	0.157822i
$40$	−1.34282	+	1.83392i	−0.212319	+	0.289969i
$41$			3.75281i			0.586091i	0.956098	+	0.293046i	$0.0946687\pi$
$41$			3.75281i			0.586091i	−0.956098	+	0.293046i	$0.905331\pi$
$42$		0			0
$43$	−6.04279	−	6.04279i	−0.921517	−	0.921517i	0.0756198	−	0.997137i	$-0.475906\pi$
$43$	−6.04279	−	6.04279i	−0.921517	−	0.921517i	−0.997137	+	0.0756198i	$0.975906\pi$
$44$	9.45998	−	0.141773i	1.42615	−	0.0213731i
$45$	0.308911	+	1.15287i	0.0460498	+	0.171860i
$46$	−3.10185	+	1.31214i	−0.457343	+	0.193465i
$47$	5.12882	+	8.88338i	0.748115	+	1.29577i	0.948725	+	0.316103i	$0.102374\pi$
$47$	5.12882	+	8.88338i	0.748115	+	1.29577i	−0.200610	+	0.979671i	$0.564292\pi$
$48$	1.94635	−	8.24469i	0.280931	−	1.19002i
$49$		0			0
$50$	−4.91323	−	3.71190i	−0.694835	−	0.524942i
$51$	−7.19776	−	1.92863i	−1.00789	−	0.270063i
$52$	−1.59800	+	0.954817i	−0.221603	+	0.132409i
$53$	−12.1874	+	3.26561i	−1.67407	+	0.448566i	−0.966204	−	0.257778i	$-0.917010\pi$
$53$	−12.1874	+	3.26561i	−1.67407	+	0.448566i	−0.707868	+	0.706345i	$0.750343\pi$
$54$	2.78879	+	3.57858i	0.379506	+	0.486983i
$55$		−	3.80155i		−	0.512600i
$56$		0			0
$57$			9.62984i			1.27550i
$58$	−6.40925	+	4.99473i	−0.841576	+	0.655841i
$59$	3.30200	−	0.884769i	0.429884	−	0.115187i	−0.0373877	−	0.999301i	$-0.511904\pi$
$59$	3.30200	−	0.884769i	0.429884	−	0.115187i	0.467272	+	0.884114i	$0.345237\pi$
$60$	−3.30071	−	0.831618i	−0.426120	−	0.107361i
$61$	−6.44729	−	1.72755i	−0.825491	−	0.221190i	−0.178745	−	0.983895i	$-0.557204\pi$
$61$	−6.44729	−	1.72755i	−0.825491	−	0.221190i	−0.646745	+	0.762706i	$0.723870\pi$
$62$	−8.44344	+	11.1761i	−1.07232	+	1.41937i
$63$		0			0
$64$	5.90536	+	5.39691i	0.738171	+	0.674614i
$65$	0.373991	+	0.647771i	0.0463878	+	0.0803461i
$66$	5.51986	+	13.0487i	0.679448	+	1.60619i
$67$	−2.10001	−	7.83735i	−0.256557	−	0.957485i	−0.967217	−	0.253950i	$-0.918270\pi$
$67$	−2.10001	−	7.83735i	−0.256557	−	0.957485i	0.710660	−	0.703536i	$-0.248396\pi$
$68$	4.90085	−	5.04998i	0.594315	−	0.612399i
$69$	−3.56639	−	3.56639i	−0.429343	−	0.429343i
$70$		0			0
$71$			1.91187i			0.226897i	0.993544	+	0.113448i	$0.0361896\pi$
$71$			1.91187i			0.226897i	−0.993544	+	0.113448i	$0.963810\pi$
$72$	4.15148	−	0.641785i	0.489256	−	0.0756351i
$73$	−12.1692	−	7.02587i	−1.42429	−	0.822316i	−0.427630	−	0.903954i	$-0.640651\pi$
$73$	−12.1692	−	7.02587i	−1.42429	−	0.822316i	−0.996662	+	0.0816382i	$0.973985\pi$
$74$	4.35380	−	10.7379i	0.506118	−	1.24825i
$75$	2.38668	−	8.90723i	0.275591	−	1.02852i
$76$	−7.94294	−	4.42850i	−0.911118	−	0.507984i
$77$		0			0
$78$	−2.22428	−	1.68042i	−0.251850	−	0.190271i
$79$	−2.33048	−	4.03650i	−0.262199	−	0.454142i	0.704627	−	0.709578i	$-0.251114\pi$
$79$	−2.33048	−	4.03650i	−0.262199	−	0.454142i	−0.966826	+	0.255436i	$0.917781\pi$
$80$	2.20385	−	2.34008i	0.246398	−	0.261628i
$81$	−5.62489	+	9.74260i	−0.624988	+	1.08251i
$82$	0.653294	−	5.26692i	0.0721443	−	0.581634i
$83$	9.13749	−	9.13749i	1.00297	−	1.00297i	0.00297439	−	0.999996i	$-0.499053\pi$
$83$	9.13749	−	9.13749i	1.00297	−	1.00297i	0.999996	−	0.00297439i	$-0.000946780\pi$
$84$		0			0
$85$	−1.99940	−	1.99940i	−0.216865	−	0.216865i
$86$	7.42887	+	9.53274i	0.801076	+	1.02794i
$87$	−10.5381	−	6.08420i	−1.12981	−	0.652294i
$88$	−13.3014	−	1.44783i	−1.41793	−	0.154339i
$89$	0.158841	−	0.0917070i	0.0168371	−	0.00972093i	−0.491558	−	0.870845i	$-0.663572\pi$
$89$	0.158841	−	0.0917070i	0.0168371	−	0.00972093i	0.508395	+	0.861124i	$0.330239\pi$
$90$	−0.232851	−	1.67178i	−0.0245446	−	0.176222i
$91$		0			0
$92$	4.58173	−	1.30156i	0.477679	−	0.135697i
$93$	−20.2612	−	5.42898i	−2.10099	−	0.562959i
$94$	−5.65166	−	13.3603i	−0.582924	−	1.37801i
$95$	−1.82704	+	3.16453i	−0.187451	+	0.324674i
$96$	−4.16687	+	11.2323i	−0.425279	+	1.14639i
$97$	−9.26984			−0.941210			−0.470605	−	0.882344i	$-0.655964\pi$
$97$	−9.26984			−0.941210			−0.470605	+	0.882344i	$0.655964\pi$
$98$		0			0
$99$	−4.96798	+	4.96798i	−0.499301	+	0.499301i
$100$	6.24934	+	6.06479i	0.624934	+	0.606479i
$101$	1.10437	−	0.295916i	0.109889	−	0.0294447i	−0.203455	−	0.979084i	$-0.565217\pi$
$101$	1.10437	−	0.295916i	0.109889	−	0.0294447i	0.313345	+	0.949640i	$0.398551\pi$
$102$	9.76602	+	3.95975i	0.966980	+	0.392074i
$103$	−7.44930	+	4.30086i	−0.734001	+	0.423776i	−0.819884	−	0.572529i	$-0.805962\pi$
$103$	−7.44930	+	4.30086i	−0.734001	+	0.423776i	0.0858829	+	0.996305i	$0.472629\pi$
$104$	2.40895	−	1.06186i	0.236217	−	0.104124i
$105$		0			0
$106$	17.6730	−	2.46155i	1.71656	−	0.239087i
$107$	0.986478	−	3.68159i	0.0953664	−	0.355912i	−0.901708	−	0.432345i	$-0.857686\pi$
$107$	0.986478	−	3.68159i	0.0953664	−	0.355912i	0.997075	+	0.0764325i	$0.0243530\pi$
$108$	−3.29098	−	5.50786i	−0.316675	−	0.529994i
$109$	2.99305	+	11.1702i	0.286682	+	1.06991i	0.947602	+	0.319455i	$0.103500\pi$
$109$	2.99305	+	11.1702i	0.286682	+	1.06991i	−0.660920	+	0.750457i	$0.729834\pi$
$110$	−0.661777	+	5.33531i	−0.0630980	+	0.508702i
$111$	17.3518			1.64696
$112$		0			0
$113$	4.00658			0.376907			0.188454	−	0.982082i	$-0.439652\pi$
$113$	4.00658			0.376907			0.188454	+	0.982082i	$0.439652\pi$
$114$	1.67637	−	13.5151i	0.157007	−	1.26580i
$115$	−0.495336	−	1.84862i	−0.0461903	−	0.172385i
$116$	9.86461	−	5.89417i	0.915906	−	0.547260i
$117$	0.357785	−	1.33527i	0.0330772	−	0.123446i
$118$	−4.78824	+	0.666920i	−0.440794	+	0.0613949i
$119$		0			0
$120$	4.48765	+	1.74173i	0.409664	+	0.158998i
$121$	9.85348	−	5.68891i	0.895771	−	0.517174i
$122$	8.74777	+	3.54689i	0.791986	+	0.321120i
$123$	7.67701	−	2.05705i	0.692212	−	0.185478i
$124$	13.7956	−	14.2153i	1.23888	−	1.27658i
$125$	5.31548	−	5.31548i	0.475431	−	0.475431i
$126$		0			0
$127$	−1.74284			−0.154652			−0.0773259	−	0.997006i	$-0.524638\pi$
$127$	−1.74284			−0.154652			−0.0773259	+	0.997006i	$0.524638\pi$
$128$	−7.34843	−	8.60236i	−0.649516	−	0.760348i
$129$	−9.04927	+	15.6738i	−0.796744	+	1.38000i
$130$	−0.412116	−	0.974225i	−0.0361449	−	0.0854451i
$131$	−8.00923	−	2.14607i	−0.699770	−	0.187503i	−0.108642	−	0.994081i	$-0.534650\pi$
$131$	−8.00923	−	2.14607i	−0.699770	−	0.187503i	−0.591127	+	0.806578i	$0.701317\pi$
$132$	−5.47536	−	19.2743i	−0.476569	−	1.67761i
$133$		0			0
$134$	1.58295	+	11.3650i	0.136746	+	0.981784i
$135$	−2.23268	+	1.28904i	−0.192159	+	0.110943i
$136$	−7.75724	+	6.23429i	−0.665178	+	0.534586i
$137$	12.8412	+	7.41389i	1.09710	+	0.633411i	0.935458	−	0.353438i	$-0.114987\pi$
$137$	12.8412	+	7.41389i	1.09710	+	0.633411i	0.161643	+	0.986849i	$0.448321\pi$
$138$	4.38444	+	5.62612i	0.373228	+	0.478927i
$139$	7.93463	+	7.93463i	0.673007	+	0.673007i	0.958408	−	0.285401i	$-0.0921269\pi$
$139$	7.93463	+	7.93463i	0.673007	+	0.673007i	−0.285401	+	0.958408i	$0.592127\pi$
$140$		0			0
$141$	15.3611	−	15.3611i	1.29364	−	1.29364i
$142$	0.332820	−	2.68322i	0.0279296	−	0.225171i
$143$	−2.20150	+	3.81311i	−0.184099	+	0.318868i
$144$	−5.93815	+	0.178025i	−0.494846	+	0.0148354i
$145$	−2.30868	−	3.99875i	−0.191725	−	0.332078i
$146$	15.8558	+	11.9789i	1.31224	+	0.991384i
$147$		0			0
$148$	−7.97963	+	14.3122i	−0.655921	+	1.17646i
$149$	3.21006	−	11.9801i	0.262978	−	0.981448i	−0.700498	−	0.713654i	$-0.747039\pi$
$149$	3.21006	−	11.9801i	0.262978	−	0.981448i	0.963476	−	0.267794i	$-0.0862945\pi$
$150$	−4.90019	+	12.0854i	−0.400099	+	0.986773i
$151$	4.16136	+	2.40256i	0.338647	+	0.195518i	0.659673	−	0.751552i	$-0.270695\pi$
$151$	4.16136	+	2.40256i	0.338647	+	0.195518i	−0.321027	+	0.947070i	$0.604028\pi$
$152$	10.3767	+	7.59794i	0.841659	+	0.616274i
$153$			5.22575i			0.422477i
$154$		0			0
$155$	−5.62817	−	5.62817i	−0.452066	−	0.452066i
$156$	2.82916	+	2.74561i	0.226514	+	0.219825i
$157$	2.39898	+	8.95313i	0.191460	+	0.714537i	0.993155	+	0.116804i	$0.0372651\pi$
$157$	2.39898	+	8.95313i	0.191460	+	0.714537i	−0.801695	+	0.597733i	$0.796068\pi$
$158$	2.56805	+	6.07075i	0.204303	+	0.482963i
$159$	13.3607	+	23.1414i	1.05957	+	1.83523i
$160$	−3.50037	+	2.90055i	−0.276729	+	0.229309i
$161$		0			0
$162$	9.59030	−	12.6941i	0.753485	−	0.997346i
$163$	2.04796	+	0.548750i	0.160409	+	0.0429814i	0.338130	−	0.941100i	$-0.390206\pi$
$163$	2.04796	+	0.548750i	0.160409	+	0.0429814i	−0.177721	+	0.984081i	$0.556872\pi$
$164$	−1.83374	+	7.27817i	−0.143191	+	0.568330i
$165$	−7.77670	+	2.08376i	−0.605415	+	0.162220i
$166$	−14.4148	+	11.2334i	−1.11880	+	0.871883i
$167$			10.3049i			0.797414i	0.917078	+	0.398707i	$0.130541\pi$
$167$			10.3049i			0.797414i	−0.917078	+	0.398707i	$0.869459\pi$
$168$		0			0
$169$			12.1337i			0.933360i
$170$	2.45801	+	3.15413i	0.188521	+	0.241911i
$171$	6.52316	−	1.74787i	0.498838	−	0.133663i
$172$	−8.76664	−	14.6720i	−0.668450	−	1.11873i
$173$	23.4210	+	6.27563i	1.78066	+	0.477128i	0.990705	−	0.136031i	$-0.0434347\pi$
$173$	23.4210	+	6.27563i	1.78066	+	0.477128i	0.789960	+	0.613159i	$0.210101\pi$
$174$	13.7307	+	10.3734i	1.04092	+	0.786406i
$175$		0			0
$176$	18.4159	+	4.34749i	1.38815	+	0.327704i
$177$	−3.61988	−	6.26982i	−0.272087	−	0.471269i
$178$	−0.238892	+	0.101056i	−0.0179057	+	0.00757445i
$179$	−5.59688	−	20.8878i	−0.418330	−	1.56123i	−0.778070	−	0.628178i	$-0.783801\pi$
$179$	−5.59688	−	20.8878i	−0.418330	−	1.56123i	0.359739	−	0.933053i	$-0.382866\pi$
$180$	0.0357702	+	2.38681i	0.00266615	+	0.177903i
$181$	−2.90147	−	2.90147i	−0.215664	−	0.215664i	0.591004	−	0.806669i	$-0.298732\pi$
$181$	−2.90147	−	2.90147i	−0.215664	−	0.215664i	−0.806669	+	0.591004i	$0.798732\pi$
$182$		0			0
$183$			14.1359i			1.04496i
$184$	−6.65685	+	1.02910i	−0.490750	+	0.0758660i
$185$	5.70211	+	3.29211i	0.419227	+	0.242041i
$186$	27.4907	+	11.1464i	2.01572	+	0.817297i
$187$	4.30792	−	16.0774i	0.315026	−	1.17569i
$188$	5.60609	+	19.7345i	0.408866	+	1.43928i
$189$		0			0
$190$	3.11507	−	4.12324i	0.225991	−	0.299131i
$191$	1.80789	+	3.13135i	0.130814	+	0.226577i	0.923991	−	0.382415i	$-0.124908\pi$
$191$	1.80789	+	3.13135i	0.130814	+	0.226577i	−0.793176	+	0.608992i	$0.791574\pi$
$192$	7.80335	−	15.0386i	0.563158	−	1.08532i
$193$	2.74388	−	4.75253i	0.197509	−	0.342095i	−0.750211	−	0.661198i	$-0.770048\pi$
$193$	2.74388	−	4.75253i	0.197509	−	0.342095i	0.947720	+	0.319103i	$0.103382\pi$
$194$	13.0098	+	1.61371i	0.934052	+	0.115857i
$195$	1.12013	−	1.12013i	0.0802139	−	0.0802139i
$196$		0			0
$197$	−3.42910	−	3.42910i	−0.244313	−	0.244313i	0.574319	−	0.818632i	$-0.305267\pi$
$197$	−3.42910	−	3.42910i	−0.244313	−	0.244313i	−0.818632	+	0.574319i	$0.805267\pi$
$198$	7.83719	−	6.10752i	0.556965	−	0.434043i
$199$	2.29905	+	1.32736i	0.162975	+	0.0940937i	0.579269	−	0.815136i	$-0.303338\pi$
$199$	2.29905	+	1.32736i	0.162975	+	0.0940937i	−0.416294	+	0.909230i	$0.636671\pi$
$200$	−7.71492	−	9.59958i	−0.545528	−	0.678793i
$201$	−14.8815	+	8.59185i	−1.04966	+	0.606023i
$202$	−1.60145	+	0.223055i	−0.112678	+	0.0156941i
$203$		0			0
$204$	−13.0169	−	7.25743i	−0.911365	−	0.508122i
$205$	2.91308	+	0.780557i	0.203458	+	0.0545165i
$206$	11.2035	−	4.73929i	0.780584	−	0.330202i
$207$	−1.76851	+	3.06316i	−0.122920	+	0.212904i
$208$	−3.56571	+	1.07093i	−0.247237	+	0.0742557i
$209$	−21.5098			−1.48786
$210$		0			0
$211$	4.71786	−	4.71786i	0.324791	−	0.324791i	−0.525811	−	0.850602i	$-0.676238\pi$
$211$	4.71786	−	4.71786i	0.324791	−	0.324791i	0.850602	+	0.525811i	$0.176238\pi$
$212$	−25.2319	+	0.378140i	−1.73293	+	0.0259707i
$213$	3.91104	−	1.04796i	0.267980	−	0.0718050i
$214$	−2.02538	+	4.99523i	−0.138452	+	0.341467i
$215$	−5.94750	+	3.43379i	−0.405616	+	0.234183i
$216$	3.65995	+	8.30295i	0.249028	+	0.564944i
$217$		0			0
$218$	−2.25610	−	16.1980i	−0.152802	−	1.09706i
$219$	−7.70224	+	28.7452i	−0.520469	+	1.94242i
$220$	1.85755	−	7.37269i	0.125236	−	0.497066i
$221$	0.847615	+	3.16334i	0.0570167	+	0.212789i
$222$	−24.3525	−	3.02062i	−1.63444	−	0.202731i
$223$	25.4486			1.70416			0.852082	−	0.523408i	$-0.175340\pi$
$223$	25.4486			1.70416			0.852082	+	0.523408i	$0.175340\pi$
$224$		0			0
$225$	−6.46687			−0.431124
$226$	−5.62307	−	0.697470i	−0.374041	−	0.0463950i
$227$	−0.696176	−	2.59817i	−0.0462068	−	0.172446i	0.938966	−	0.344009i	$-0.111785\pi$
$227$	−0.696176	−	2.59817i	−0.0462068	−	0.172446i	−0.985173	+	0.171563i	$0.945118\pi$
$228$	−4.70544	+	18.6760i	−0.311625	+	1.23685i
$229$	−5.06138	+	18.8893i	−0.334466	+	1.24824i	0.569982	+	0.821657i	$0.306950\pi$
$229$	−5.06138	+	18.8893i	−0.334466	+	1.24824i	−0.904447	+	0.426585i	$0.859716\pi$
$230$	0.373374	+	2.68069i	0.0246195	+	0.176759i
$231$		0			0
$232$	−14.8706	+	6.55498i	−0.976305	+	0.430356i
$233$	15.9354	−	9.20030i	1.04396	−	0.602732i	0.123009	−	0.992406i	$-0.460745\pi$
$233$	15.9354	−	9.20030i	1.04396	−	0.602732i	0.920953	+	0.389674i	$0.127412\pi$
$234$	−0.734582	+	1.81171i	−0.0480211	+	0.118435i
$235$	7.96238	−	2.13351i	0.519408	−	0.139175i
$236$	6.83620	−	0.102451i	0.444999	−	0.00666901i
$237$	−6.97992	+	6.97992i	−0.453395	+	0.453395i
$238$		0			0
$239$	27.3287			1.76775			0.883874	−	0.467725i	$-0.154926\pi$
$239$	27.3287			1.76775			0.883874	+	0.467725i	$0.154926\pi$
$240$	−5.99502	−	3.22566i	−0.386977	−	0.208216i
$241$	10.7757	−	18.6640i	0.694123	−	1.20226i	−0.276353	−	0.961056i	$-0.589126\pi$
$241$	10.7757	−	18.6640i	0.694123	−	1.20226i	0.970476	−	0.241199i	$-0.0775408\pi$
$242$	−14.8193	+	6.26884i	−0.952619	+	0.402976i
$243$	13.7170	+	3.67546i	0.879946	+	0.235781i
$244$	−11.6597	−	6.50073i	−0.746435	−	0.416167i
$245$		0			0
$246$	−11.1325	+	1.55056i	−0.709779	+	0.0988600i
$247$	3.66520	−	2.11611i	0.233211	−	0.134645i
$248$	−21.8361	+	17.5491i	−1.38660	+	1.11437i
$249$	−23.7008	−	13.6837i	−1.50198	−	0.867168i
$250$	−8.38538	+	6.53473i	−0.530338	+	0.413293i
$251$	−3.96408	−	3.96408i	−0.250211	−	0.250211i	0.570846	−	0.821057i	$-0.306615\pi$
$251$	−3.96408	−	3.96408i	−0.250211	−	0.250211i	−0.821057	+	0.570846i	$0.806615\pi$
$252$		0			0
$253$	7.96611	−	7.96611i	0.500825	−	0.500825i
$254$	2.44600	+	0.303395i	0.153476	+	0.0190367i
$255$	−2.99416	+	5.18604i	−0.187502	+	0.324762i
$256$	8.81571	+	13.3523i	0.550982	+	0.834517i
$257$	−1.60859	−	2.78615i	−0.100341	−	0.173795i	0.811484	−	0.584374i	$-0.198660\pi$
$257$	−1.60859	−	2.78615i	−0.100341	−	0.173795i	−0.911825	+	0.410579i	$0.865327\pi$
$258$	15.4288	−	20.4222i	0.960555	−	1.27143i
$259$		0			0
$260$	0.408793	+	1.43903i	0.0253523	+	0.0892446i
$261$	−2.20864	+	8.24275i	−0.136711	+	0.510213i
$262$	10.8670	+	4.40617i	0.671367	+	0.272214i
$263$	−15.9834	−	9.22803i	−0.985580	−	0.569025i	−0.0816300	−	0.996663i	$-0.526013\pi$
$263$	−15.9834	−	9.22803i	−0.985580	−	0.569025i	−0.903950	+	0.427638i	$0.859346\pi$
$264$	4.32916	+	28.0038i	0.266441	+	1.72351i
$265$			10.1396i			0.622869i
$266$		0			0
$267$	−0.274668	−	0.274668i	−0.0168094	−	0.0168094i
$268$	−0.243170	−	16.2258i	−0.0148540	−	0.991150i
$269$	6.98276	+	26.0600i	0.425746	+	1.58891i	0.762287	+	0.647239i	$0.224076\pi$
$269$	6.98276	+	26.0600i	0.425746	+	1.58891i	−0.336541	+	0.941669i	$0.609257\pi$
$270$	3.35788	−	1.42045i	0.204354	−	0.0864456i
$271$	4.01460	+	6.95349i	0.243870	+	0.422394i	0.961813	−	0.273707i	$-0.0882498\pi$
$271$	4.01460	+	6.95349i	0.243870	+	0.422394i	−0.717944	+	0.696101i	$0.754916\pi$
$272$	11.9722	−	7.39917i	0.725923	−	0.448641i
$273$		0			0
$274$	−16.7315	−	12.6405i	−1.01079	−	0.763641i
$275$	19.8958	+	5.33105i	1.19976	+	0.321474i
$276$	−5.17397	−	8.65927i	−0.311436	−	0.521227i
$277$	28.4754	−	7.62997i	1.71092	−	0.458440i	0.735272	−	0.677772i	$-0.237054\pi$
$277$	28.4754	−	7.62997i	1.71092	−	0.458440i	0.975650	+	0.219332i	$0.0703877\pi$
$278$	−9.75466	−	12.5172i	−0.585046	−	0.750732i
$279$			14.7102i			0.880674i
$280$		0			0
$281$		−	8.30834i		−	0.495634i	−0.968807	−	0.247817i	$-0.920287\pi$
$281$		−	8.30834i		−	0.495634i	0.968807	−	0.247817i	$-0.0797132\pi$
$282$	−24.2328	+	18.8846i	−1.44304	+	1.12456i
$283$	11.2742	−	3.02092i	0.670183	−	0.179575i	0.0923455	−	0.995727i	$-0.470564\pi$
$283$	11.2742	−	3.02092i	0.670183	−	0.179575i	0.577837	+	0.816152i	$0.303897\pi$
$284$	−0.934197	+	3.70785i	−0.0554344	+	0.220021i
$285$	7.47505	+	2.00293i	0.442784	+	0.118644i
$286$	3.75350	−	4.96830i	0.221949	−	0.293782i
$287$		0			0
$288$	8.36494	+	0.783869i	0.492909	+	0.0461899i
$289$	2.30993	+	4.00092i	0.135878	+	0.235348i
$290$	2.54403	+	6.01397i	0.149390	+	0.353153i
$291$	5.08112	+	18.9630i	0.297861	+	1.11163i
$292$	−20.1677	−	19.5721i	−1.18023	−	1.14537i
$293$	−19.8534	−	19.8534i	−1.15985	−	1.15985i	−0.984509	−	0.175337i	$-0.943899\pi$
$293$	−19.8534	−	19.8534i	−1.15985	−	1.15985i	−0.175337	−	0.984509i	$-0.556101\pi$
$294$		0			0
$295$		−	2.74717i		−	0.159946i
$296$	13.6906	−	18.6975i	0.795748	−	1.08677i
$297$	−13.1427	−	7.58794i	−0.762617	−	0.440297i
$298$	−6.59069	+	16.2548i	−0.381789	+	0.941613i
$299$	−0.573704	+	2.14109i	−0.0331782	+	0.123823i
$300$	8.98107	−	16.1084i	0.518522	−	0.930019i
$301$		0			0
$302$	−5.42205	−	4.09631i	−0.312004	−	0.235716i
$303$	−1.21069	−	2.09698i	−0.0695523	−	0.120468i
$304$	−13.2406	−	12.4698i	−0.759398	−	0.715190i
$305$	−2.68197	+	4.64532i	−0.153569	+	0.265990i
$306$	0.909705	−	7.33413i	0.0520044	−	0.419264i
$307$	−8.22502	+	8.22502i	−0.469427	+	0.469427i	−0.901729	−	0.432302i	$-0.857701\pi$
$307$	−8.22502	+	8.22502i	−0.469427	+	0.469427i	0.432302	+	0.901729i	$0.357701\pi$
$308$		0			0
$309$	12.8813	+	12.8813i	0.732794	+	0.732794i
$310$	6.91915	+	8.87866i	0.392981	+	0.504274i
$311$	16.2031	+	9.35488i	0.918796	+	0.530467i	0.883251	−	0.468901i	$-0.155350\pi$
$311$	16.2031	+	9.35488i	0.918796	+	0.530467i	0.0355449	+	0.999368i	$0.488683\pi$
$312$	−3.49265	−	4.34585i	−0.197732	−	0.246036i
$313$	−24.8251	+	14.3328i	−1.40320	+	0.810136i	−0.994719	−	0.102633i	$-0.967273\pi$
$313$	−24.8251	+	14.3328i	−1.40320	+	0.810136i	−0.408477	+	0.912769i	$0.633940\pi$
$314$	−1.80830	−	12.9830i	−0.102048	−	0.732671i
$315$		0			0
$316$	−2.54734	−	8.96710i	−0.143299	−	0.504439i
$317$	4.83476	+	1.29547i	0.271547	+	0.0727608i	0.392023	−	0.919955i	$-0.371775\pi$
$317$	4.83476	+	1.29547i	0.271547	+	0.0727608i	−0.120476	+	0.992716i	$0.538442\pi$
$318$	−14.7227	−	34.8039i	−0.825609	−	1.95170i
$319$	13.5900	−	23.5386i	0.760896	−	1.31791i
$320$	5.41756	−	3.46145i	0.302851	−	0.193501i
$321$	−8.07202			−0.450536
$322$		0			0
$323$	−11.3129	+	11.3129i	−0.629469	+	0.629469i
$324$	−15.6694	+	16.1462i	−0.870522	+	0.897012i
$325$	−3.91463	+	1.04892i	−0.217145	+	0.0581838i
$326$	−2.77870	−	1.12666i	−0.153898	−	0.0623999i
$327$	21.2099	−	12.2456i	1.17291	−	0.677181i
$328$	3.84057	−	9.89540i	0.212060	−	0.546382i
$329$		0			0
$330$	11.2770	−	1.57069i	0.620779	−	0.0864638i
$331$	−4.75517	+	17.7465i	−0.261368	+	0.975437i	0.703069	+	0.711122i	$0.251813\pi$
$331$	−4.75517	+	17.7465i	−0.261368	+	0.975437i	−0.964436	+	0.264315i	$0.914854\pi$
$332$	22.1860	−	13.2563i	1.21762	−	0.727534i
$333$	−3.14946	−	11.7539i	−0.172589	−	0.644112i
$334$	1.79388	−	14.4624i	0.0981569	−	0.791350i
$335$	−6.52044			−0.356250
$336$		0			0
$337$	−13.7900			−0.751188			−0.375594	−	0.926784i	$-0.622561\pi$
$337$	−13.7900			−0.751188			−0.375594	+	0.926784i	$0.622561\pi$
$338$	2.11224	−	17.0291i	0.114891	−	0.926262i
$339$	−2.19615	−	8.19613i	−0.119278	−	0.445153i
$340$	−2.90065	−	4.85458i	−0.157310	−	0.263277i
$341$	12.1265	−	45.2568i	0.656688	−	2.45079i
$342$	−9.45925	+	1.31751i	−0.511498	+	0.0712428i
$343$		0			0
$344$	9.74949	+	22.1177i	0.525657	+	1.19251i
$345$	−3.51015	+	2.02658i	−0.188980	+	0.109108i
$346$	−31.7779	−	12.8847i	−1.70839	−	0.692688i
$347$	−11.7471	+	3.14763i	−0.630619	+	0.168974i	−0.559951	−	0.828526i	$-0.689180\pi$
$347$	−11.7471	+	3.14763i	−0.630619	+	0.168974i	−0.0706683	+	0.997500i	$0.522513\pi$
$348$	−17.4646	−	16.9489i	−0.936203	−	0.908556i
$349$	2.67727	−	2.67727i	0.143311	−	0.143311i	−0.631811	−	0.775122i	$-0.717688\pi$
$349$	2.67727	−	2.67727i	0.143311	−	0.143311i	0.775122	+	0.631811i	$0.217688\pi$
$350$		0			0
$351$	2.98597			0.159379
$352$	−25.0891	−	9.30738i	−1.33725	−	0.496085i
$353$	−1.39107	+	2.40941i	−0.0740393	+	0.128240i	−0.900668	−	0.434508i	$-0.856922\pi$
$353$	−1.39107	+	2.40941i	−0.0740393	+	0.128240i	0.826629	+	0.562748i	$0.190256\pi$
$354$	3.98890	+	9.42959i	0.212008	+	0.501177i
$355$	1.48406	+	0.397653i	0.0787659	+	0.0211053i
$356$	0.352866	−	0.100241i	0.0187019	−	0.00531276i
$357$		0			0
$358$	4.21881	+	30.2895i	0.222971	+	1.60085i
$359$	17.5060	−	10.1071i	0.923929	−	0.533431i	0.0390425	−	0.999238i	$-0.487569\pi$
$359$	17.5060	−	10.1071i	0.923929	−	0.533431i	0.884886	+	0.465807i	$0.154236\pi$
$360$	0.365297	−	3.35602i	0.0192529	−	0.176878i
$361$	1.45101	+	0.837739i	0.0763687	+	0.0440915i
$362$	3.56700	+	4.57718i	0.187477	+	0.240571i
$363$	−17.0386	−	17.0386i	−0.894297	−	0.894297i
$364$		0			0
$365$	−7.98484	+	7.98484i	−0.417946	+	0.417946i
$366$	2.46080	−	19.8392i	0.128628	−	1.03701i
$367$	−11.0728	+	19.1786i	−0.577995	+	1.00112i	0.417714	+	0.908579i	$0.362831\pi$
$367$	−11.0728	+	19.1786i	−0.577995	+	1.00112i	−0.995709	+	0.0925384i	$0.970502\pi$
$368$	9.52176	−	0.285462i	0.496356	−	0.0148807i
$369$	−2.78685	−	4.82696i	−0.145077	−	0.251282i
$370$	−7.42958	−	5.61298i	−0.386245	−	0.291805i
$371$		0			0
$372$	−36.6417	−	20.4292i	−1.89978	−	1.05920i
$373$	1.52059	−	5.67492i	0.0787331	−	0.293836i	−0.915321	−	0.402726i	$-0.868063\pi$
$373$	1.52059	−	5.67492i	0.0787331	−	0.293836i	0.994054	+	0.108890i	$0.0347295\pi$
$374$	−8.84476	+	21.8140i	−0.457352	+	1.12798i
$375$	−13.7873	−	7.96010i	−0.711973	−	0.411058i
$376$	−4.43253	−	28.6724i	−0.228590	−	1.47867i
$377$			5.34788i			0.275430i
$378$		0			0
$379$	−25.5714	−	25.5714i	−1.31352	−	1.31352i	−0.918805	−	0.394712i	$-0.870844\pi$
$379$	−25.5714	−	25.5714i	−1.31352	−	1.31352i	−0.394712	−	0.918805i	$-0.629156\pi$
$380$	−5.08964	+	5.24452i	−0.261093	+	0.269038i
$381$	0.955310	+	3.56527i	0.0489420	+	0.182654i
$382$	−1.99219	−	4.70944i	−0.101929	−	0.240956i
$383$	−12.4264	−	21.5232i	−0.634961	−	1.09978i	−0.986523	−	0.163620i	$-0.947683\pi$
$383$	−12.4264	−	21.5232i	−0.634961	−	1.09978i	0.351563	−	0.936164i	$-0.385650\pi$
$384$	−13.5696	+	19.7477i	−0.692472	+	1.00775i
$385$		0			0
$386$	−4.67824	+	6.19233i	−0.238116	+	0.315181i
$387$	12.2598	+	3.28500i	0.623199	+	0.166986i
$388$	−17.9779	−	4.52954i	−0.912687	−	0.229952i
$389$	−8.77896	+	2.35232i	−0.445111	+	0.119267i	−0.474411	−	0.880304i	$-0.657339\pi$
$389$	−8.77896	+	2.35232i	−0.445111	+	0.119267i	0.0292999	+	0.999571i	$0.490672\pi$
$390$	−1.76704	+	1.37706i	−0.0894777	+	0.0697300i
$391$		−	8.37944i		−	0.423767i
$392$		0			0
$393$			17.5605i			0.885812i
$394$	4.21565	+	5.40953i	0.212381	+	0.272528i
$395$	−3.61801	+	0.969443i	−0.182042	+	0.0487780i
$396$	−12.0624	+	7.20735i	−0.606157	+	0.362183i
$397$	33.5464	+	8.98874i	1.68365	+	0.451132i	0.968738	−	0.248086i	$-0.0798015\pi$
$397$	33.5464	+	8.98874i	1.68365	+	0.451132i	0.714909	+	0.699218i	$0.246468\pi$
$398$	−2.99555	−	2.26311i	−0.150153	−	0.113439i
$399$		0			0
$400$	9.15647	+	14.8156i	0.457824	+	0.740782i
$401$	14.0889	+	24.4026i	0.703564	+	1.21861i	0.967207	+	0.253989i	$0.0817426\pi$
$401$	14.0889	+	24.4026i	0.703564	+	1.21861i	−0.263643	+	0.964620i	$0.584924\pi$
$402$	22.3813	−	9.46772i	1.11628	−	0.472207i
$403$	2.38598	+	8.90460i	0.118854	+	0.443570i
$404$	2.28640	−	0.0342654i	0.113753	−	0.00170477i
$405$	6.39264	+	6.39264i	0.317653	+	0.317653i
$406$		0			0
$407$			38.7581i			1.92117i
$408$	17.0053	+	12.4515i	0.841887	+	0.616441i
$409$	23.0721	+	13.3207i	1.14084	+	0.658666i	0.946639	−	0.322295i	$-0.104454\pi$
$409$	23.0721	+	13.3207i	1.14084	+	0.658666i	0.194204	+	0.980961i	$0.437788\pi$
$410$	−3.95250	−	1.60259i	−0.195200	−	0.0791463i
$411$	8.12762	−	30.3327i	0.400906	−	1.49620i
$412$	−16.5486	+	4.70108i	−0.815293	+	0.231606i
$413$		0			0
$414$	3.01527	−	3.99115i	0.148193	−	0.196154i
$415$	−5.19234	−	8.99340i	−0.254882	−	0.441469i
$416$	5.19075	−	0.882284i	0.254497	−	0.0432575i
$417$	11.8824	−	20.5809i	0.581882	−	1.00785i
$418$	30.1881	+	3.74445i	1.47655	+	0.183147i
$419$	−17.4967	+	17.4967i	−0.854770	+	0.854770i	−0.990716	−	0.135946i	$-0.956593\pi$
$419$	−17.4967	+	17.4967i	−0.854770	+	0.854770i	0.135946	+	0.990716i	$0.456593\pi$
$420$		0			0
$421$	−15.5401	−	15.5401i	−0.757379	−	0.757379i	0.218466	−	0.975845i	$-0.429895\pi$
$421$	−15.5401	−	15.5401i	−0.757379	−	0.757379i	−0.975845	+	0.218466i	$0.929895\pi$
$422$	−7.44261	+	5.80003i	−0.362301	+	0.282341i
$423$	−13.1936	−	7.61735i	−0.641496	−	0.370368i
$424$	35.4777	+	3.86169i	1.72295	+	0.187540i
$425$	13.2679	−	7.66020i	0.643586	−	0.371575i
$426$	−5.67141	+	0.789930i	−0.274781	+	0.0382722i
$427$		0			0
$428$	3.71211	−	6.65801i	0.179431	−	0.321827i
$429$	9.00707	+	2.41344i	0.434865	+	0.116522i
$430$	8.94483	−	3.78384i	0.431358	−	0.182473i
$431$	0.383883	−	0.664905i	0.0184910	−	0.0320274i	−0.856632	−	0.515928i	$-0.827447\pi$
$431$	0.383883	−	0.664905i	0.0184910	−	0.0320274i	0.875123	+	0.483901i	$0.160780\pi$
$432$	−3.69119	−	12.2900i	−0.177593	−	0.591302i
$433$	23.9515			1.15103			0.575517	−	0.817790i	$-0.304801\pi$
$433$	23.9515			1.15103			0.575517	+	0.817790i	$0.304801\pi$
$434$		0			0
$435$	−6.91464	+	6.91464i	−0.331532	+	0.331532i
$436$	0.346578	+	23.1259i	0.0165981	+	1.10753i
$437$	−10.4598	+	2.80270i	−0.500361	+	0.134071i
$438$	15.8138	−	39.0018i	0.755611	−	1.86358i
$439$	−31.9026	+	18.4190i	−1.52263	+	0.879090i	−0.522987	+	0.852341i	$0.675182\pi$
$439$	−31.9026	+	18.4190i	−1.52263	+	0.879090i	−0.999642	+	0.0267498i	$0.991484\pi$
$440$	−3.89045	+	10.0239i	−0.185470	+	0.477870i
$441$		0			0
$442$	−0.638914	−	4.58717i	−0.0303900	−	0.218190i
$443$	3.53635	−	13.1978i	0.168017	−	0.627048i	−0.829619	−	0.558330i	$-0.811442\pi$
$443$	3.53635	−	13.1978i	0.168017	−	0.627048i	0.997636	−	0.0687181i	$-0.0218909\pi$
$444$	33.6519	+	8.47864i	1.59705	+	0.402378i
$445$	−0.0381487	−	0.142373i	−0.00180842	−	0.00674913i
$446$	−35.7160	−	4.43012i	−1.69120	−	0.209772i
$447$	−26.2668			−1.24238
$448$		0			0
$449$	−11.3673			−0.536458			−0.268229	−	0.963355i	$-0.586438\pi$
$449$	−11.3673			−0.536458			−0.268229	+	0.963355i	$0.586438\pi$
$450$	9.07598	+	1.12576i	0.427846	+	0.0530688i
$451$	4.59475	+	17.1478i	0.216358	+	0.807461i
$452$	7.77033	+	1.95774i	0.365486	+	0.0920844i
$453$	2.63385	−	9.82968i	0.123749	−	0.461839i
$454$	0.524763	+	3.76761i	0.0246283	+	0.176823i
$455$		0			0
$456$	9.85503	−	25.3919i	0.461504	−	1.18908i
$457$	2.59459	−	1.49798i	0.121370	−	0.0700728i	−0.438086	−	0.898933i	$-0.644344\pi$
$457$	2.59459	−	1.49798i	0.121370	−	0.0700728i	0.559456	+	0.828860i	$0.311010\pi$
$458$	10.3917	−	25.6293i	0.485573	−	1.19758i
$459$	−10.9031	+	2.92149i	−0.508915	+	0.136363i
$460$	−0.0573572	−	3.82723i	−0.00267429	−	0.178446i
$461$	16.9109	−	16.9109i	0.787618	−	0.787618i	−0.193485	−	0.981103i	$-0.561979\pi$
$461$	16.9109	−	16.9109i	0.787618	−	0.787618i	0.981103	+	0.193485i	$0.0619792\pi$
$462$		0			0
$463$	−4.62269			−0.214835			−0.107417	−	0.994214i	$-0.534258\pi$
$463$	−4.62269			−0.214835			−0.107417	+	0.994214i	$0.534258\pi$
$464$	22.0114	−	6.61095i	1.02185	−	0.306905i
$465$	−8.42837	+	14.5984i	−0.390856	+	0.676983i
$466$	−23.9663	+	10.1382i	−1.11022	+	0.469643i
$467$	7.28591	+	1.95225i	0.337152	+	0.0903395i	0.423423	−	0.905932i	$-0.360828\pi$
$467$	7.28591	+	1.95225i	0.337152	+	0.0903395i	−0.0862712	+	0.996272i	$0.527495\pi$
$468$	1.34634	−	2.41479i	0.0622346	−	0.111624i
$469$		0			0
$470$	−11.5463	+	1.60820i	−0.532590	+	0.0741806i
$471$	17.0002	−	9.81504i	0.783326	−	0.452253i
$472$	−9.61216	−	1.04627i	−0.442435	−	0.0481584i
$473$	−35.0100	−	20.2130i	−1.60976	−	0.929396i
$474$	11.0111	−	8.58096i	0.505757	−	0.394137i
$475$	−13.9998	−	13.9998i	−0.642353	−	0.642353i
$476$		0			0
$477$	13.2507	−	13.2507i	0.606709	−	0.606709i
$478$	−38.3547	−	4.75741i	−1.75430	−	0.217599i
$479$	−13.8193	+	23.9357i	−0.631420	+	1.09365i	0.355842	+	0.934546i	$0.384194\pi$
$479$	−13.8193	+	23.9357i	−0.631420	+	1.09365i	−0.987262	+	0.159105i	$0.949139\pi$
$480$	7.85224	+	5.57071i	0.358404	+	0.254267i
$481$	−3.81297	−	6.60425i	−0.173856	−	0.301128i
$482$	−18.3723	+	24.3183i	−0.836834	+	1.10767i
$483$		0			0
$484$	21.8895	−	6.21830i	0.994979	−	0.282650i
$485$	−1.92806	+	7.19561i	−0.0875486	+	0.326736i
$486$	−18.6114	−	7.54623i	−0.844231	−	0.342304i
$487$	24.6948	+	14.2575i	1.11903	+	0.646071i	0.941152	−	0.337982i	$-0.109744\pi$
$487$	24.6948	+	14.2575i	1.11903	+	0.646071i	0.177875	+	0.984053i	$0.443078\pi$
$488$	15.2322	+	11.1532i	0.689530	+	0.504883i
$489$		−	4.49024i		−	0.203055i
$490$		0			0
$491$	−6.06201	−	6.06201i	−0.273575	−	0.273575i	0.556963	−	0.830537i	$-0.311967\pi$
$491$	−6.06201	−	6.06201i	−0.273575	−	0.273575i	−0.830537	+	0.556963i	$0.811967\pi$
$492$	15.8939	−	0.238195i	0.716550	−	0.0107386i
$493$	−5.23240	−	19.5276i	−0.235655	−	0.879478i
$494$	−5.51233	+	2.33182i	−0.248012	+	0.104914i
$495$	2.82304	+	4.88964i	0.126886	+	0.219773i
$496$	33.7011	−	20.8282i	1.51322	−	0.935213i
$497$		0			0
$498$	30.8811	+	23.3304i	1.38381	+	1.04546i
$499$	8.21984	+	2.20250i	0.367971	+	0.0985974i	0.438066	−	0.898943i	$-0.355664\pi$
$499$	8.21984	+	2.20250i	0.367971	+	0.0985974i	−0.0700953	+	0.997540i	$0.522330\pi$
$500$	12.9061	−	7.71149i	0.577179	−	0.344868i
$501$	21.0803	−	5.64845i	0.941799	−	0.252354i
$502$	4.87335	+	6.25350i	0.217508	+	0.279107i
$503$		−	7.12677i		−	0.317767i	−0.987297	−	0.158884i	$-0.949211\pi$
$503$		−	7.12677i		−	0.317767i	0.987297	−	0.158884i	$-0.0507894\pi$
$504$		0			0
$505$		−	0.918804i		−	0.0408863i
$506$	−12.5669	+	9.79335i	−0.558665	+	0.435368i
$507$	24.8215	−	6.65089i	1.10236	−	0.295376i
$508$	−3.38005	−	0.851605i	−0.149965	−	0.0377839i
$509$	6.13630	+	1.64422i	0.271987	+	0.0728787i	0.392235	−	0.919865i	$-0.371702\pi$
$509$	6.13630	+	1.64422i	0.271987	+	0.0728787i	−0.120248	+	0.992744i	$0.538369\pi$
$510$	5.10497	−	6.75716i	0.226052	−	0.299212i
$511$		0			0
$512$	−10.0481	−	20.2740i	−0.444068	−	0.895993i
$513$	7.29362	+	12.6329i	0.322021	+	0.557757i
$514$	1.77257	+	4.19027i	0.0781846	+	0.184825i
$515$	1.78909	+	6.67698i	0.0788368	+	0.294223i
$516$	−25.2088	+	25.9759i	−1.10976	+	1.14352i
$517$	34.3116	+	34.3116i	1.50902	+	1.50902i
$518$		0			0
$519$		−	51.3514i		−	2.25408i
$520$	−0.323217	−	2.09078i	−0.0141740	−	0.0916866i
$521$	9.12679	+	5.26935i	0.399852	+	0.230855i	0.686420	−	0.727205i	$-0.259181\pi$
$521$	9.12679	+	5.26935i	0.399852	+	0.230855i	−0.286568	+	0.958060i	$0.592515\pi$
$522$	4.53464	−	11.1839i	0.198476	−	0.489505i
$523$	−4.78001	+	17.8393i	−0.209015	+	0.780056i	0.779173	+	0.626809i	$0.215640\pi$
$523$	−4.78001	+	17.8393i	−0.209015	+	0.780056i	−0.988188	+	0.153247i	$0.951027\pi$
$524$	−14.4844	−	8.07562i	−0.632754	−	0.352785i
$525$		0			0
$526$	20.8256	+	15.7336i	0.908041	+	0.686017i
$527$	−17.4246	−	30.1804i	−0.759029	−	1.31468i
$528$	−1.20087	−	40.0558i	−0.0522611	−	1.74320i
$529$	−8.66421	+	15.0068i	−0.376705	+	0.652472i
$530$	1.76511	−	14.2305i	0.0766714	−	0.618132i
$531$	−3.59008	+	3.59008i	−0.155796	+	0.155796i
$532$		0			0
$533$	−2.46991	−	2.46991i	−0.106984	−	0.106984i
$534$	0.337671	+	0.433300i	0.0146125	+	0.0187507i
$535$	−2.65261	−	1.53148i	−0.114682	−	0.0662118i
$536$	−2.48333	+	22.8146i	−0.107264	+	0.985441i
$537$	−39.6617	+	22.8987i	−1.71153	+	0.988152i
$538$	−5.26346	−	37.7897i	−0.226924	−	1.62923i
$539$		0			0
$540$	−4.95991	+	1.40899i	−0.213441	+	0.0606335i
$541$	−11.5287	−	3.08911i	−0.495658	−	0.132811i	0.00232623	−	0.999997i	$-0.499260\pi$
$541$	−11.5287	−	3.08911i	−0.495658	−	0.132811i	−0.497984	+	0.867186i	$0.665926\pi$
$542$	−4.42385	−	10.4578i	−0.190021	−	0.449201i
$543$	−4.34504	+	7.52583i	−0.186464	+	0.322964i
$544$	−18.0906	+	8.30029i	−0.775628	+	0.355872i
$545$	9.29327			0.398080
$546$		0			0
$547$	−3.42607	+	3.42607i	−0.146488	+	0.146488i	−0.776547	−	0.630059i	$-0.783031\pi$
$547$	−3.42607	+	3.42607i	−0.146488	+	0.146488i	0.630059	+	0.776547i	$0.283031\pi$
$548$	21.2815	+	20.6531i	0.909102	+	0.882255i
$549$	9.57554	−	2.56576i	0.408674	−	0.109504i
$550$	−26.9948	−	10.9454i	−1.15106	−	0.466713i
$551$	−22.6256	+	13.0629i	−0.963884	+	0.556499i
$552$	5.75404	+	13.0536i	0.244908	+	0.555599i
$553$		0			0
$554$	−41.2923	+	5.75131i	−1.75434	+	0.244350i
$555$	3.60904	−	13.4691i	0.153195	−	0.571733i
$556$	11.5112	+	19.2655i	0.488186	+	0.817038i
$557$	11.1966	+	41.7862i	0.474415	+	1.77054i	0.623614	+	0.781733i	$0.285664\pi$
$557$	11.1966	+	41.7862i	0.474415	+	1.77054i	−0.149199	+	0.988807i	$0.547670\pi$
$558$	2.56076	−	20.6451i	0.108406	−	0.873976i
$559$	7.95412			0.336423
$560$		0			0
$561$	−35.2503			−1.48827
$562$	−1.44633	+	11.6604i	−0.0610096	+	0.491865i
$563$	0.954457	+	3.56208i	0.0402255	+	0.150124i	0.983118	−	0.182974i	$-0.0585726\pi$
$563$	0.954457	+	3.56208i	0.0402255	+	0.150124i	−0.942892	+	0.333098i	$0.891906\pi$
$564$	37.2972	−	22.2853i	1.57050	−	0.938382i
$565$	0.833339	−	3.11006i	0.0350588	−	0.130841i
$566$	−16.3488	+	2.27710i	−0.687190	+	0.0957138i
$567$		0			0
$568$	1.95657	−	5.04119i	0.0820960	−	0.211524i
$569$	−24.7377	+	14.2823i	−1.03706	+	0.598745i	−0.918998	−	0.394262i	$-0.871000\pi$
$569$	−24.7377	+	14.2823i	−1.03706	+	0.598745i	−0.118059	+	0.993007i	$0.537667\pi$
$570$	−10.1422	−	4.11230i	−0.424812	−	0.172245i
$571$	1.33666	−	0.358158i	0.0559376	−	0.0149884i	−0.230742	−	0.973015i	$-0.574115\pi$
$571$	1.33666	−	0.358158i	0.0559376	−	0.0149884i	0.286679	+	0.958027i	$0.407449\pi$
$572$	−6.13277	+	6.31939i	−0.256424	+	0.264227i
$573$	5.41474	−	5.41474i	0.226204	−	0.226204i
$574$		0			0
$575$	10.3696			0.432440
$576$	−11.6034	−	2.55631i	−0.483474	−	0.106513i
$577$	14.0887	−	24.4023i	0.586520	−	1.01588i	−0.408164	−	0.912908i	$-0.633831\pi$
$577$	14.0887	−	24.4023i	0.586520	−	1.01588i	0.994684	−	0.102973i	$-0.0328357\pi$
$578$	−2.54541	−	6.01724i	−0.105875	−	0.250284i
$579$	−11.2261	−	3.00803i	−0.466541	−	0.125009i
$580$	−2.52352	−	8.88323i	−0.104783	−	0.368856i
$581$		0			0
$582$	−3.83004	−	27.4983i	−0.158760	−	1.13984i
$583$	−51.6902	+	29.8433i	−2.14079	+	1.23598i
$584$	24.8974	+	30.9795i	1.03026	+	1.28194i
$585$	−0.962072	−	0.555453i	−0.0397768	−	0.0229651i
$586$	24.4073	+	31.3195i	1.00825	+	1.29379i
$587$	6.78098	+	6.78098i	0.279881	+	0.279881i	0.833062	−	0.553180i	$-0.186586\pi$
$587$	6.78098	+	6.78098i	0.279881	+	0.279881i	−0.553180	+	0.833062i	$0.686586\pi$
$588$		0			0
$589$	−31.8452	+	31.8452i	−1.31216	+	1.31216i
$590$	−0.478230	+	3.85553i	−0.0196884	+	0.158730i
$591$	−5.13518	+	8.89439i	−0.211233	+	0.365866i
$592$	−22.4690	+	23.8579i	−0.923471	+	0.980554i
$593$	15.1244	+	26.1962i	0.621085	+	1.07575i	0.989284	+	0.146003i	$0.0466410\pi$
$593$	15.1244	+	26.1962i	0.621085	+	1.07575i	−0.368199	+	0.929747i	$0.620026\pi$
$594$	17.1243	+	12.9373i	0.702619	+	0.530822i
$595$		0			0
$596$	12.0794	−	21.6656i	0.494792	−	0.887456i
$597$	1.45514	−	5.43065i	0.0595549	−	0.222262i
$598$	1.17789	−	2.90507i	0.0481677	−	0.118797i
$599$	−6.63353	−	3.82987i	−0.271039	−	0.156484i	0.358321	−	0.933599i	$-0.383349\pi$
$599$	−6.63353	−	3.82987i	−0.271039	−	0.156484i	−0.629360	+	0.777114i	$0.716683\pi$
$600$	−15.4087	+	21.0440i	−0.629058	+	0.859119i
$601$			22.2096i			0.905948i	0.891524	+	0.452974i	$0.149637\pi$
$601$			22.2096i			0.905948i	−0.891524	+	0.452974i	$0.850363\pi$
$602$		0			0
$603$	8.52112	+	8.52112i	0.347007	+	0.347007i
$604$	6.89654	+	6.69288i	0.280616	+	0.272329i
$605$	−2.36650	−	8.83190i	−0.0962119	−	0.359068i
$606$	1.33411	+	3.15378i	0.0541945	+	0.128113i
$607$	−4.81558	−	8.34082i	−0.195458	−	0.338543i	0.751592	−	0.659628i	$-0.229286\pi$
$607$	−4.81558	−	8.34082i	−0.195458	−	0.338543i	−0.947051	+	0.321084i	$0.895953\pi$
$608$	16.4118	+	19.8057i	0.665588	+	0.803229i
$609$		0			0
$610$	4.57270	−	6.05263i	0.185143	−	0.245064i
$611$	−9.22212	−	2.47106i	−0.373087	−	0.0999684i
$612$	−2.55347	+	10.1348i	−0.103218	+	0.409674i
$613$	4.15155	−	1.11240i	0.167679	−	0.0449296i	−0.174003	−	0.984745i	$-0.555670\pi$
$613$	4.15155	−	1.11240i	0.167679	−	0.0449296i	0.341682	+	0.939816i	$0.389003\pi$
$614$	12.9753	−	10.1117i	0.523640	−	0.408073i
$615$		−	6.38704i		−	0.257550i
$616$		0			0
$617$			3.88970i			0.156593i	0.996930	+	0.0782967i	$0.0249481\pi$
$617$			3.88970i			0.156593i	−0.996930	+	0.0782967i	$0.975052\pi$
$618$	−15.8360	−	20.3208i	−0.637018	−	0.817423i
$619$	−11.1601	+	2.99033i	−0.448562	+	0.120192i	−0.476026	−	0.879431i	$-0.657923\pi$
$619$	−11.1601	+	2.99033i	−0.448562	+	0.120192i	0.0274647	+	0.999623i	$0.491257\pi$
$620$	−8.16513	−	13.6653i	−0.327919	−	0.548813i
$621$	−7.37974	−	1.97740i	−0.296139	−	0.0793502i
$622$	−21.1119	−	15.9499i	−0.846511	−	0.639531i
$623$		0			0
$624$	4.14525	+	6.70723i	0.165943	+	0.268504i
$625$	7.86498	+	13.6225i	0.314599	+	0.544902i
$626$	37.3360	−	15.7939i	1.49225	−	0.631250i
$627$	11.7903	+	44.0019i	0.470858	+	1.75727i
$628$	0.277789	+	18.5358i	0.0110850	+	0.739660i
$629$	20.3846	+	20.3846i	0.812786	+	0.812786i
$630$		0			0
$631$		−	21.9788i		−	0.874963i	−0.899227	−	0.437482i	$-0.855871\pi$
$631$		−	21.9788i		−	0.874963i	0.899227	−	0.437482i	$-0.144129\pi$
$632$	2.01409	+	13.0284i	0.0801161	+	0.518242i
$633$	−12.2372	−	7.06515i	−0.486385	−	0.280814i
$634$	−6.55986	−	2.65978i	−0.260525	−	0.105633i
$635$	−0.362497	+	1.35286i	−0.0143853	+	0.0536865i
$636$	14.6040	+	51.4087i	0.579087	+	2.03849i
$637$		0			0
$638$	−23.1707	+	30.6697i	−0.917337	+	1.21423i
$639$	−1.41975	−	2.45909i	−0.0561646	−	0.0972800i
$640$	−8.20590	+	3.91491i	−0.324367	+	0.154750i
$641$	14.2449	−	24.6729i	0.562639	−	0.974519i	−0.434626	−	0.900611i	$-0.643119\pi$
$641$	14.2449	−	24.6729i	0.562639	−	0.974519i	0.997265	−	0.0739082i	$-0.0235472\pi$
$642$	11.3287	+	1.40519i	0.447110	+	0.0554583i
$643$	0.490002	−	0.490002i	0.0193238	−	0.0193238i	−0.697379	−	0.716703i	$-0.745650\pi$
$643$	0.490002	−	0.490002i	0.0193238	−	0.0193238i	0.716703	+	0.697379i	$0.245650\pi$
$644$		0			0
$645$	10.2844	+	10.2844i	0.404949	+	0.404949i
$646$	17.8466	−	13.9079i	0.702166	−	0.547198i
$647$	14.5019	+	8.37265i	0.570127	+	0.329163i	0.757200	−	0.653183i	$-0.226567\pi$
$647$	14.5019	+	8.37265i	0.570127	+	0.329163i	−0.187073	+	0.982346i	$0.559900\pi$
$648$	24.8021	−	19.9328i	0.974319	−	0.783034i
$649$	14.0047	−	8.08560i	0.549731	−	0.317388i
$650$	5.67662	−	0.790656i	0.222655	−	0.0310121i
$651$		0			0
$652$	3.70366	+	2.06494i	0.145047	+	0.0808692i
$653$	−1.72333	−	0.461765i	−0.0674392	−	0.0180703i	0.224942	−	0.974372i	$-0.427781\pi$
$653$	−1.72333	−	0.461765i	−0.0674392	−	0.0180703i	−0.292381	+	0.956302i	$0.594447\pi$
$654$	−31.8990	+	13.4939i	−1.24735	+	0.527652i
$655$	−3.33172	+	5.77071i	−0.130181	+	0.225480i
$656$	−7.11269	+	13.2192i	−0.277704	+	0.516123i
$657$	20.8697			0.814204
$658$		0			0
$659$	17.8258	−	17.8258i	0.694394	−	0.694394i	−0.268802	−	0.963196i	$-0.586628\pi$
$659$	17.8258	−	17.8258i	0.694394	−	0.694394i	0.963196	+	0.268802i	$0.0866276\pi$
$660$	−16.1002	+	0.241288i	−0.626701	+	0.00939211i
$661$	−14.5809	+	3.90694i	−0.567131	+	0.151962i	−0.530980	−	0.847384i	$-0.678176\pi$
$661$	−14.5809	+	3.90694i	−0.567131	+	0.151962i	−0.0361505	+	0.999346i	$0.511510\pi$
$662$	9.76302	−	24.0787i	0.379450	−	0.935846i
$663$	6.00654	−	3.46787i	0.233274	−	0.134681i
$664$	−33.4449	+	14.7425i	−1.29791	+	0.572120i
$665$		0			0
$666$	2.37400	+	17.0444i	0.0919905	+	0.660458i
$667$	3.54153	−	13.2172i	0.137128	−	0.511770i
$668$	−5.03528	+	19.9852i	−0.194821	+	0.773249i
$669$	−13.9493	−	52.0593i	−0.539310	−	2.01273i
$670$	9.15117	+	1.13509i	0.353541	+	0.0438522i
$671$	−31.5749			−1.21894
$672$		0			0
$673$	45.7500			1.76353			0.881767	−	0.471686i	$-0.156354\pi$
$673$	45.7500			1.76353			0.881767	+	0.471686i	$0.156354\pi$
$674$	19.3537	+	2.40058i	0.745476	+	0.0924668i
$675$	−3.61534	−	13.4926i	−0.139154	−	0.519332i
$676$	−5.92890	+	23.5320i	−0.228034	+	0.905075i
$677$	−1.67994	+	6.26961i	−0.0645652	+	0.240961i	−0.990665	−	0.136317i	$-0.956473\pi$
$677$	−1.67994	+	6.26961i	−0.0645652	+	0.240961i	0.926100	+	0.377278i	$0.123140\pi$
$678$	1.65541	+	11.8852i	0.0635756	+	0.456450i
$679$		0			0
$680$	3.22584	+	7.31815i	0.123705	+	0.280638i
$681$	−4.93338	+	2.84829i	−0.189048	+	0.109147i
$682$	−24.8974	+	61.4050i	−0.953371	+	2.35132i
$683$	−32.2981	+	8.65425i	−1.23585	+	0.331146i	−0.816856	−	0.576842i	$-0.804285\pi$
$683$	−32.2981	+	8.65425i	−1.23585	+	0.331146i	−0.418997	+	0.907988i	$0.637618\pi$
$684$	13.5050	−	0.202394i	0.516377	−	0.00773873i
$685$	8.42583	−	8.42583i	0.321934	−	0.321934i
$686$		0			0
$687$	41.4156			1.58010
$688$	−9.83273	−	32.7385i	−0.374869	−	1.24814i
$689$	5.87189	−	10.1704i	0.223701	−	0.387462i
$690$	5.27914	−	2.23318i	0.200973	−	0.0850156i
$691$	24.4879	+	6.56150i	0.931562	+	0.249611i	0.692521	−	0.721398i	$-0.256500\pi$
$691$	24.4879	+	6.56150i	0.931562	+	0.249611i	0.239042	+	0.971009i	$0.423167\pi$
$692$	42.3560	+	23.6151i	1.61013	+	0.897713i
$693$		0			0
$694$	17.0345	−	2.37262i	0.646623	−	0.0900634i
$695$	7.80951	−	4.50882i	0.296232	−	0.171029i
$696$	21.5604	+	26.8273i	0.817245	+	1.01689i
$697$	11.4354	+	6.60222i	0.433146	+	0.250077i
$698$	−4.22350	+	3.29137i	−0.159862	+	0.124580i
$699$	−27.5555	−	27.5555i	−1.04224	−	1.04224i
$700$		0			0
$701$	17.9702	−	17.9702i	0.678723	−	0.678723i	−0.280988	−	0.959711i	$-0.590662\pi$
$701$	17.9702	−	17.9702i	0.678723	−	0.678723i	0.959711	+	0.280988i	$0.0906621\pi$
$702$	−4.19068	−	0.519800i	−0.158167	−	0.0196186i
$703$	18.6274	−	32.2635i	0.702544	−	1.21684i
$704$	33.5913	+	17.4301i	1.26602	+	0.656920i
$705$	−8.72891	−	15.1189i	−0.328750	−	0.569411i
$706$	2.37175	−	3.13935i	0.0892618	−	0.118151i
$707$		0			0
$708$	−3.95674	−	13.9284i	−0.148703	−	0.523462i
$709$	−1.44949	+	5.40955i	−0.0544366	+	0.203160i	−0.987788	−	0.155804i	$-0.950203\pi$
$709$	−1.44949	+	5.40955i	−0.0544366	+	0.203160i	0.933351	+	0.358964i	$0.116870\pi$
$710$	−2.01360	−	0.816438i	−0.0755689	−	0.0306404i
$711$	5.99503	+	3.46123i	0.224831	+	0.129806i
$712$	−0.512683	+	0.0792568i	−0.0192136	+	0.00297027i
$713$		−	23.5876i		−	0.883362i
$714$		0			0
$715$	2.50199	+	2.50199i	0.0935689	+	0.0935689i
$716$	−0.648088	−	43.2445i	−0.0242202	−	1.61612i
$717$	−14.9798	−	55.9054i	−0.559432	−	2.08783i
$718$	−26.3283	+	11.1374i	−0.982565	+	0.415644i
$719$	10.1603	+	17.5982i	0.378916	+	0.656302i	0.990905	−	0.134565i	$-0.0429636\pi$
$719$	10.1603	+	17.5982i	0.378916	+	0.656302i	−0.611989	+	0.790866i	$0.709630\pi$
$720$	−1.09690	+	4.64645i	−0.0408791	+	0.173163i
$721$		0			0
$722$	−1.89059	−	1.42832i	−0.0703606	−	0.0531567i
$723$	−44.0869	−	11.8131i	−1.63961	−	0.439332i
$724$	−4.20933	−	7.04483i	−0.156439	−	0.261819i
$725$	24.1654	−	6.47509i	0.897479	−	0.240479i
$726$	20.9469	+	26.8791i	0.777413	+	0.997578i
$727$			17.0650i			0.632904i	0.948609	+	0.316452i	$0.102492\pi$
$727$			17.0650i			0.632904i	−0.948609	+	0.316452i	$0.897508\pi$
$728$		0			0
$729$			3.67428i			0.136085i
$730$	12.5964	−	9.81638i	0.466214	−	0.363321i
$731$	−29.0442	+	7.78236i	−1.07424	+	0.287841i
$732$	−6.90726	+	27.4151i	−0.255300	+	1.01329i
$733$	−2.51934	−	0.675055i	−0.0930539	−	0.0249337i	0.211992	−	0.977271i	$-0.432005\pi$
$733$	−2.51934	−	0.675055i	−0.0930539	−	0.0249337i	−0.305046	+	0.952338i	$0.598672\pi$
$734$	18.8788	−	24.9889i	0.696831	−	0.922356i
$735$		0			0
$736$	−13.4131	−	1.25693i	−0.494413	−	0.0463309i
$737$	−19.1913	−	33.2403i	−0.706921	−	1.22442i
$738$	3.07094	+	7.25958i	0.113043	+	0.267229i
$739$	−5.79671	−	21.6336i	−0.213235	−	0.795806i	−0.986780	−	0.162064i	$-0.948185\pi$
$739$	−5.79671	−	21.6336i	−0.213235	−	0.795806i	0.773545	−	0.633742i	$-0.218482\pi$
$740$	9.44999	+	9.17093i	0.347389	+	0.337130i
$741$	−6.33787	−	6.33787i	−0.232828	−	0.232828i
$742$		0			0
$743$			46.3700i			1.70115i	0.525854	+	0.850575i	$0.323746\pi$
$743$			46.3700i			1.70115i	−0.525854	+	0.850575i	$0.676254\pi$
$744$	47.8688	+	35.0502i	1.75495	+	1.28500i
$745$	−8.63174	−	4.98354i	−0.316243	−	0.182583i
$746$	−3.12198	+	7.69980i	−0.114304	+	0.281910i
$747$	−4.96735	+	18.5384i	−0.181746	+	0.678284i
$748$	16.2107	−	29.0754i	0.592720	−	1.06310i
$749$		0			0
$750$	17.9642	+	13.5718i	0.655960	+	0.495572i
$751$	−4.69302	−	8.12854i	−0.171251	−	0.296615i	0.767607	−	0.640921i	$-0.221447\pi$
$751$	−4.69302	−	8.12854i	−0.171251	−	0.296615i	−0.938857	+	0.344306i	$0.888114\pi$
$752$	1.22954	+	41.0121i	0.0448367	+	1.49556i
$753$	−5.93634	+	10.2820i	−0.216332	+	0.374699i
$754$	0.930965	−	7.50553i	0.0339037	−	0.273335i
$755$	2.73049	−	2.73049i	0.0993728	−	0.0993728i
$756$		0			0
$757$	7.28329	+	7.28329i	0.264716	+	0.264716i	0.826967	−	0.562251i	$-0.190065\pi$
$757$	7.28329	+	7.28329i	0.264716	+	0.264716i	−0.562251	+	0.826967i	$0.690065\pi$
$758$	31.4370	+	40.3400i	1.14184	+	1.46521i
$759$	−20.6625	−	11.9295i	−0.750001	−	0.433013i
$760$	8.05608	−	6.47445i	0.292225	−	0.234853i
$761$	22.1654	−	12.7972i	0.803494	−	0.463898i	−0.0411972	−	0.999151i	$-0.513117\pi$
$761$	22.1654	−	12.7972i	0.803494	−	0.463898i	0.844692	+	0.535253i	$0.179784\pi$
$762$	−0.720092	−	5.17000i	−0.0260862	−	0.187289i
$763$		0			0
$764$	1.97612	+	6.95631i	0.0714937	+	0.251671i
$765$	4.05643	+	1.08692i	0.146661	+	0.0392976i
$766$	13.6932	+	32.3701i	0.494755	+	1.16958i
$767$	−1.59090	+	2.75552i	−0.0574441	+	0.0994961i
$768$	22.4821	−	25.3529i	0.811253	−	0.914842i
$769$	40.0755			1.44516			0.722580	−	0.691287i	$-0.242956\pi$
$769$	40.0755			1.44516			0.722580	+	0.691287i	$0.242956\pi$
$770$		0			0
$771$	−4.81782	+	4.81782i	−0.173509	+	0.173509i
$772$	7.64369	−	7.87628i	0.275102	−	0.283474i
$773$	35.4059	−	9.48698i	1.27346	−	0.341223i	0.442105	−	0.896963i	$-0.354232\pi$
$773$	35.4059	−	9.48698i	1.27346	−	0.341223i	0.831356	+	0.555740i	$0.187565\pi$
$774$	−16.6342	−	6.74455i	−0.597905	−	0.242428i
$775$	37.3482	−	21.5630i	1.34159	−	0.774565i
$776$	24.4427	+	9.48662i	0.877441	+	0.340550i
$777$		0			0
$778$	12.7304	−	1.77313i	0.456407	−	0.0635696i
$779$	4.41653	−	16.4827i	0.158239	−	0.590554i
$780$	2.71969	−	1.62503i	0.0973806	−	0.0581856i
$781$	2.34079	+	8.73594i	0.0837600	+	0.312597i
$782$	−1.45870	+	11.7602i	−0.0521631	+	0.420544i
$783$	−18.4326			−0.658728
$784$		0			0
$785$	7.44873			0.265857
$786$	3.05696	−	24.6455i	0.109038	−	0.879076i
$787$	5.46554	+	20.3977i	0.194825	+	0.727098i	0.992312	+	0.123761i	$0.0394958\pi$
$787$	5.46554	+	20.3977i	0.194825	+	0.727098i	−0.797487	+	0.603337i	$0.793838\pi$
$788$	−4.97479	−	8.32592i	−0.177220	−	0.296599i
$789$	−10.1164	+	37.7550i	−0.360154	+	1.34411i
$790$	5.24649	−	0.730745i	0.186662	−	0.0259987i
$791$		0			0
$792$	18.1837	−	8.01539i	0.646130	−	0.284814i
$793$	5.38026	−	3.10630i	0.191059	−	0.110308i
$794$	−45.5162	−	18.4551i	−1.61531	−	0.654948i
$795$	20.7422	−	5.55785i	0.735650	−	0.197117i
$796$	3.81017	+	3.69765i	0.135048	+	0.131060i
$797$	14.1690	−	14.1690i	0.501893	−	0.501893i	−0.410133	−	0.912026i	$-0.634518\pi$
$797$	14.1690	−	14.1690i	0.501893	−	0.501893i	0.912026	+	0.410133i	$0.134518\pi$
$798$		0			0
$799$	36.0919			1.27684
$800$	−10.2716	−	22.3871i	−0.363156	−	0.791503i
$801$	−0.136204	+	0.235912i	−0.00481252	+	0.00833553i
$802$	−15.5251	−	36.7007i	−0.548210	−	1.29595i
$803$	−64.2070	−	17.2042i	−2.26582	−	0.607124i
$804$	−33.0594	+	9.39139i	−1.16591	+	0.331209i
$805$		0			0
$806$	−1.79850	−	12.9126i	−0.0633495	−	0.454827i
$807$	49.4826	−	28.5688i	1.74187	−	1.00567i
$808$	−3.21484	−	0.349930i	−0.113098	−	0.0123105i
$809$	28.4891	+	16.4482i	1.00162	+	0.578288i	0.908728	−	0.417388i	$-0.137055\pi$
$809$	28.4891	+	16.4482i	1.00162	+	0.578288i	0.0928952	+	0.995676i	$0.470388\pi$
$810$	−7.85897	−	10.0846i	−0.276136	−	0.354338i
$811$	27.0410	+	27.0410i	0.949540	+	0.949540i	0.998787	−	0.0492471i	$-0.0156822\pi$
$811$	27.0410	+	27.0410i	0.949540	+	0.949540i	−0.0492471	+	0.998787i	$0.515682\pi$
$812$		0			0
$813$	12.0240	−	12.0240i	0.421699	−	0.421699i
$814$	6.74705	−	54.3954i	0.236484	−	1.90656i
$815$	0.851921	−	1.47557i	0.0298415	−	0.0516870i
$816$	−21.6986	−	20.4355i	−0.759604	−	0.715384i
$817$	19.4290	+	33.6520i	0.679735	+	1.17733i
$818$	−30.0619	−	22.7115i	−1.05109	−	0.794088i
$819$		0			0
$820$	5.26819	+	2.93723i	0.183973	+	0.102572i
$821$	−4.35690	+	16.2602i	−0.152057	+	0.567484i	0.847283	+	0.531142i	$0.178237\pi$
$821$	−4.35690	+	16.2602i	−0.152057	+	0.567484i	−0.999339	+	0.0363415i	$0.988430\pi$
$822$	−16.6871	+	41.1558i	−0.582031	+	1.43547i
$823$	11.4767	+	6.62608i	0.400053	+	0.230971i	0.686507	−	0.727123i	$-0.259143\pi$
$823$	11.4767	+	6.62608i	0.400053	+	0.230971i	−0.286454	+	0.958094i	$0.592476\pi$
$824$	24.0437	−	3.71697i	0.837602	−	0.129487i
$825$		−	43.6222i		−	1.51873i
$826$		0			0
$827$	29.8245	+	29.8245i	1.03710	+	1.03710i	0.999285	+	0.0378135i	$0.0120393\pi$
$827$	29.8245	+	29.8245i	1.03710	+	1.03710i	0.0378135	+	0.999285i	$0.487961\pi$
$828$	−4.92659	+	5.07651i	−0.171211	+	0.176421i
$829$	9.96287	+	37.1819i	0.346025	+	1.29138i	0.891411	+	0.453197i	$0.149716\pi$
$829$	9.96287	+	37.1819i	0.346025	+	1.29138i	−0.545386	+	0.838185i	$0.683617\pi$
$830$	5.72166	+	13.5258i	0.198602	+	0.469486i
$831$	−31.2167	−	54.0690i	−1.08290	−	1.87563i
$832$	−7.43859	+	0.334638i	−0.257887	+	0.0116015i
$833$		0			0
$834$	−20.2591	+	26.8159i	−0.701517	+	0.928558i
$835$	7.99903	+	2.14333i	0.276818	+	0.0741731i
$836$	−41.7159	−	10.5104i	−1.44278	−	0.363509i
$837$	−30.6916	+	8.22380i	−1.06086	+	0.284256i
$838$	27.6017	−	21.5100i	0.953486	−	0.743052i
$839$			9.84258i			0.339804i	0.985461	+	0.169902i	$0.0543450\pi$
$839$			9.84258i			0.339804i	−0.985461	+	0.169902i	$0.945655\pi$
$840$		0			0
$841$		−	4.01293i		−	0.138377i
$842$	19.1047	+	24.5152i	0.658390	+	0.844848i
$843$	−16.9961	+	4.55409i	−0.585377	+	0.156851i
$844$	11.4551	−	6.84448i	0.394300	−	0.235597i
$845$	9.41863	+	2.52371i	0.324011	+	0.0868184i
$846$	17.1907	+	12.9874i	0.591028	+	0.446516i
$847$		0			0
$848$	−49.1193	−	11.5957i	−1.68676	−	0.398199i
$849$	−12.3596	−	21.4074i	−0.424180	−	0.734701i
$850$	−19.9544	+	8.44109i	−0.684430	+	0.289527i
$851$	5.05013	+	18.8473i	0.173116	+	0.646078i
$852$	8.09710	−	0.121348i	0.277402	−	0.00415731i
$853$	−16.9924	−	16.9924i	−0.581810	−	0.581810i	0.353590	−	0.935400i	$-0.384961\pi$
$853$	−16.9924	−	16.9924i	−0.581810	−	0.581810i	−0.935400	+	0.353590i	$0.884961\pi$
$854$		0			0
$855$		−	5.42707i		−	0.185602i
$856$	−6.36882	+	8.69804i	−0.217682	+	0.297293i
$857$	−40.2292	−	23.2264i	−1.37420	−	0.793397i	−0.382750	−	0.923852i	$-0.625023\pi$
$857$	−40.2292	−	23.2264i	−1.37420	−	0.793397i	−0.991454	+	0.130455i	$0.958356\pi$
$858$	−12.2209	−	4.95512i	−0.417215	−	0.169165i
$859$	2.70009	−	10.0769i	0.0921259	−	0.343819i	−0.904442	−	0.426596i	$-0.859713\pi$
$859$	2.70009	−	10.0769i	0.0921259	−	0.343819i	0.996568	+	0.0827778i	$0.0263792\pi$
$860$	−13.2124	+	3.75333i	−0.450539	+	0.127987i
$861$		0			0
$862$	−0.654512	+	0.866340i	−0.0222928	+	0.0295077i
$863$	17.9220	+	31.0417i	0.610071	+	1.05667i	0.991228	+	0.132163i	$0.0421922\pi$
$863$	17.9220	+	31.0417i	0.610071	+	1.05667i	−0.381157	+	0.924510i	$0.624474\pi$
$864$	3.04098	+	17.8910i	0.103456	+	0.608666i
$865$	9.74278	−	16.8750i	0.331264	−	0.573767i
$866$	−33.6149	−	4.16950i	−1.14228	−	0.141685i
$867$	6.91839	−	6.91839i	0.234961	−	0.234961i
$868$		0			0
$869$	−15.5908	−	15.5908i	−0.528882	−	0.528882i
$870$	10.9081	−	8.50070i	0.369820	−	0.288201i
$871$	6.54027	+	3.77603i	0.221609	+	0.127946i
$872$	3.53937	−	32.5166i	0.119858	−	1.10115i
$873$	11.9231	−	6.88381i	0.403536	−	0.232982i
$874$	15.1678	−	2.11261i	0.513059	−	0.0714602i
$875$		0			0
$876$	−28.9835	+	51.9846i	−0.979260	+	1.75640i
$877$	−6.19451	−	1.65982i	−0.209174	−	0.0560480i	0.152710	−	0.988271i	$-0.451200\pi$
$877$	−6.19451	−	1.65982i	−0.209174	−	0.0560480i	−0.361884	+	0.932223i	$0.617866\pi$
$878$	47.9804	−	20.2966i	1.61926	−	0.684978i
$879$	−29.7310	+	51.4957i	−1.00280	+	1.73691i
$880$	7.20505	−	13.3909i	0.242882	−	0.451406i
$881$	−37.6372			−1.26803			−0.634014	−	0.773321i	$-0.718594\pi$
$881$	−37.6372			−1.26803			−0.634014	+	0.773321i	$0.718594\pi$
$882$		0			0
$883$	36.3793	−	36.3793i	1.22426	−	1.22426i	0.258161	−	0.966102i	$-0.416884\pi$
$883$	36.3793	−	36.3793i	1.22426	−	1.22426i	0.966102	−	0.258161i	$-0.0831163\pi$
$884$	0.0981491	+	6.54913i	0.00330111	+	0.220271i
$885$	−5.61978	+	1.50582i	−0.188907	+	0.0506175i
$886$	−7.26061	+	17.9070i	−0.243925	+	0.601597i
$887$	−19.2102	+	11.0910i	−0.645014	+	0.372399i	−0.786543	−	0.617535i	$-0.788131\pi$
$887$	−19.2102	+	11.0910i	−0.645014	+	0.372399i	0.141529	+	0.989934i	$0.454798\pi$
$888$	−45.7531	−	17.7576i	−1.53537	−	0.595906i
$889$		0			0
$890$	0.0287557	+	0.206456i	0.000963894	+	0.00692041i
$891$	−13.7737	+	51.4040i	−0.461435	+	1.72210i
$892$	49.3548	+	12.4350i	1.65252	+	0.416354i
$893$	−12.0718	−	45.0525i	−0.403967	−	1.50763i
$894$	36.8644	+	4.57256i	1.23293	+	0.152929i
$895$	−17.3781			−0.580884
$896$		0			0
$897$	4.69443			0.156743
$898$	15.9536	+	1.97884i	0.532378	+	0.0660347i
$899$	−14.7289	−	54.9689i	−0.491235	−	1.83331i
$900$	−12.5418	−	3.15991i	−0.418059	−	0.105330i
$901$	−11.4902	+	42.8820i	−0.382794	+	1.42861i
$902$	−3.46343	−	24.8662i	−0.115319	−	0.827952i
$903$		0			0
$904$	−10.5645	−	4.10028i	−0.351371	−	0.136373i
$905$	−2.85571	+	1.64875i	−0.0949271	+	0.0548062i
$906$	−5.40767	+	13.3370i	−0.179658	+	0.443094i
$907$	−8.44631	+	2.26318i	−0.280455	+	0.0751477i	−0.396305	−	0.918119i	$-0.629708\pi$
$907$	−8.44631	+	2.26318i	−0.280455	+	0.0751477i	0.115850	+	0.993267i	$0.463041\pi$
$908$	−0.0806134	−	5.37903i	−0.00267525	−	0.178509i
$909$	−1.20072	+	1.20072i	−0.0398255	+	0.0398255i
$910$		0			0
$911$	−36.5239			−1.21009			−0.605045	−	0.796192i	$-0.706845\pi$
$911$	−36.5239			−1.21009			−0.605045	+	0.796192i	$0.706845\pi$
$912$	−18.2514	+	33.9209i	−0.604364	+	1.12323i
$913$	30.5647	−	52.9397i	1.01155	−	1.75205i
$914$	−3.90216	+	1.65069i	−0.129072	+	0.0546000i
$915$	10.9729	+	2.94017i	0.362751	+	0.0971989i
$916$	−19.0459	+	34.1607i	−0.629295	+	1.12870i
$917$		0			0
$918$	15.8107	−	2.20216i	0.521830	−	0.0726820i
$919$	−44.9513	+	25.9526i	−1.48281	+	0.856098i	−0.999809	−	0.0195244i	$-0.993785\pi$
$919$	−44.9513	+	25.9526i	−1.48281	+	0.856098i	−0.482996	+	0.875623i	$0.660451\pi$
$920$	−0.585751	+	5.38135i	−0.0193116	+	0.177418i
$921$	21.3341	+	12.3172i	0.702982	+	0.405867i
$922$	−26.6776	+	20.7898i	−0.878579	+	0.684677i
$923$	−1.25829	−	1.25829i	−0.0414172	−	0.0414172i
$924$		0			0
$925$	−25.2259	+	25.2259i	−0.829422	+	0.829422i
$926$	6.48775	+	0.804723i	0.213201	+	0.0264448i
$927$	6.38765	−	11.0637i	0.209798	−	0.363381i
$928$	−32.0429	+	5.44642i	−1.05186	+	0.178787i
$929$	−8.84548	−	15.3208i	−0.290211	−	0.502660i	0.683649	−	0.729811i	$-0.260392\pi$
$929$	−8.84548	−	15.3208i	−0.290211	−	0.502660i	−0.973859	+	0.227151i	$0.927059\pi$
$930$	14.3702	−	19.0210i	0.471216	−	0.623722i
$931$		0			0
$932$	35.4005	−	10.0565i	1.15958	−	0.329410i
$933$	10.2555	−	38.2740i	0.335749	−	1.25303i
$934$	−9.88562	−	4.00824i	−0.323467	−	0.131154i
$935$	−11.5839	−	6.68795i	−0.378833	−	0.218719i
$936$	−2.30990	+	3.15468i	−0.0755015	+	0.103114i
$937$			25.8059i			0.843044i	0.906818	+	0.421522i	$0.138504\pi$
$937$			25.8059i			0.843044i	−0.906818	+	0.421522i	$0.861496\pi$
$938$		0			0
$939$	42.9276	+	42.9276i	1.40089	+	1.40089i
$940$	16.4847	−	0.247049i	0.537670	−	0.00805785i
$941$	−3.59745	−	13.4259i	−0.117273	−	0.437670i	0.882173	−	0.470925i	$-0.156080\pi$
$941$	−3.59745	−	13.4259i	−0.117273	−	0.437670i	−0.999447	+	0.0332541i	$0.989413\pi$
$942$	−25.5676	+	10.8156i	−0.833038	+	0.352391i
$943$	4.46868	+	7.73998i	0.145520	+	0.252048i
$944$	13.3081	+	3.14169i	0.433143	+	0.102253i
$945$		0			0
$946$	45.6164	+	34.4627i	1.48312	+	1.12048i
$947$	−30.5294	−	8.18033i	−0.992073	−	0.265825i	−0.273952	−	0.961743i	$-0.588331\pi$
$947$	−30.5294	−	8.18033i	−0.992073	−	0.265825i	−0.718121	+	0.695918i	$0.754998\pi$
$948$	−16.9474	+	10.1262i	−0.550426	+	0.328884i
$949$	12.6332	−	3.38505i	0.410091	−	0.109884i
$950$	17.2110	+	22.0852i	0.558398	+	0.716538i
$951$		−	10.6004i		−	0.343741i
$952$		0			0
$953$		−	35.5679i		−	1.15216i	−0.817394	−	0.576078i	$-0.804582\pi$
$953$		−	35.5679i		−	1.15216i	0.817394	−	0.576078i	$-0.195418\pi$
$954$	−20.9035	+	16.2901i	−0.676777	+	0.527413i
$955$	2.80670	−	0.752054i	0.0908228	−	0.0243359i
$956$	53.0011	+	13.3537i	1.71418	+	0.431888i
$957$	−55.6014	−	14.8984i	−1.79734	−	0.481595i
$958$	23.5616	−	31.1871i	0.761240	−	1.00761i
$959$		0			0
$960$	−10.0505	−	9.18518i	−0.324380	−	0.296451i
$961$	−33.5492	−	58.1089i	−1.08223	−	1.87448i
$962$	4.20167	+	9.93256i	0.135467	+	0.320239i
$963$	1.46512	+	5.46791i	0.0472129	+	0.176201i
$964$	30.0181	−	30.9315i	0.966818	−	0.996237i
$965$	−3.11839	−	3.11839i	−0.100385	−	0.100385i
$966$		0			0
$967$		−	14.0321i		−	0.451242i	−0.974215	−	0.225621i	$-0.927559\pi$
$967$		−	14.0321i		−	0.451242i	0.974215	−	0.225621i	$-0.0724411\pi$
$968$	−31.8035	+	4.91657i	−1.02220	+	0.158025i
$969$	29.3435	+	16.9415i	0.942650	+	0.544239i
$970$	3.95857	−	9.76310i	0.127102	−	0.313474i
$971$	−3.36637	+	12.5635i	−0.108032	+	0.403181i	−0.998671	−	0.0515292i	$-0.983590\pi$
$971$	−3.36637	+	12.5635i	−0.108032	+	0.403181i	0.890639	+	0.454710i	$0.150257\pi$
$972$	24.8067	+	13.8307i	0.795675	+	0.443620i
$973$		0			0
$974$	−32.1761	−	24.3088i	−1.03099	−	0.778903i
$975$	4.29149	+	7.43308i	0.137438	+	0.238049i
$976$	−19.4362	−	18.3048i	−0.622138	−	0.585921i
$977$	2.14248	−	3.71088i	0.0685440	−	0.118722i	−0.829717	−	0.558185i	$-0.811498\pi$
$977$	2.14248	−	3.71088i	0.0685440	−	0.118722i	0.898261	+	0.439463i	$0.144831\pi$
$978$	−0.781665	+	6.30186i	−0.0249949	+	0.201511i
$979$	0.613517	−	0.613517i	0.0196081	−	0.0196081i
$980$		0			0
$981$	−12.1447	−	12.1447i	−0.387752	−	0.387752i
$982$	7.45250	+	9.56306i	0.237819	+	0.305170i
$983$	−17.7428	−	10.2438i	−0.565908	−	0.326727i	0.189606	−	0.981860i	$-0.439279\pi$
$983$	−17.7428	−	10.2438i	−0.565908	−	0.326727i	−0.755513	+	0.655133i	$0.772612\pi$
$984$	−22.3478	−	2.43252i	−0.712423	−	0.0775461i
$985$	−3.37502	+	1.94857i	−0.107537	+	0.0620866i
$986$	3.94407	+	28.3170i	0.125605	+	0.901798i
$987$		0			0
$988$	8.14226	−	2.31302i	0.259040	−	0.0735871i
$989$	−19.6584	−	5.26746i	−0.625101	−	0.167495i
$990$	−3.11082	−	7.35385i	−0.0988683	−	0.233721i
$991$	−21.4774	+	37.1999i	−0.682252	+	1.18169i	0.292040	+	0.956406i	$0.405666\pi$
$991$	−21.4774	+	37.1999i	−0.682252	+	1.18169i	−0.974292	+	0.225289i	$0.927668\pi$
$992$	−50.9238	+	23.3648i	−1.61683	+	0.741832i
$993$	38.9099			1.23477
$994$		0			0
$995$	1.50853	−	1.50853i	0.0478236	−	0.0478236i
$996$	−39.2789	−	38.1190i	−1.24460	−	1.20785i
$997$	−29.3244	+	7.85746i	−0.928714	+	0.248848i	−0.691306	−	0.722562i	$-0.742964\pi$
$997$	−29.3244	+	7.85746i	−0.928714	+	0.248848i	−0.237408	+	0.971410i	$0.576298\pi$
$998$	−11.1528	−	4.52204i	−0.353035	−	0.143143i
$999$	22.7630	−	13.1422i	0.720189	−	0.415802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.p.165.1		96
7.2	even	3	inner	784.2.x.p.373.16		96
7.3	odd	6		784.2.m.l.197.18	yes	48
7.4	even	3		784.2.m.l.197.17	✓	48
7.5	odd	6	inner	784.2.x.p.373.15		96
7.6	odd	2	inner	784.2.x.p.165.2		96
16.13	even	4	inner	784.2.x.p.557.16		96
112.13	odd	4	inner	784.2.x.p.557.15		96
112.45	odd	12		784.2.m.l.589.18	yes	48
112.61	odd	12	inner	784.2.x.p.765.2		96
112.93	even	12	inner	784.2.x.p.765.1		96
112.109	even	12		784.2.m.l.589.17	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.l.197.17	✓	48	7.4	even	3
784.2.m.l.197.18	yes	48	7.3	odd	6
784.2.m.l.589.17	yes	48	112.109	even	12
784.2.m.l.589.18	yes	48	112.45	odd	12
784.2.x.p.165.1		96	1.1	even	1	trivial
784.2.x.p.165.2		96	7.6	odd	2	inner
784.2.x.p.373.15		96	7.5	odd	6	inner
784.2.x.p.373.16		96	7.2	even	3	inner
784.2.x.p.557.15		96	112.13	odd	4	inner
784.2.x.p.557.16		96	16.13	even	4	inner
784.2.x.p.765.1		96	112.93	even	12	inner
784.2.x.p.765.2		96	112.61	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40346 - 0.174081i) q^{2} +(-0.548135 - 2.04567i) q^{3} +(1.93939 + 0.488631i) q^{4} +(0.207992 - 0.776238i) q^{5} +(0.413172 + 2.96643i) q^{6} +(-2.63679 - 1.02339i) q^{8} +(-1.28622 + 0.742602i) q^{9} +O(q^{10})\)	\(q+(-1.40346 - 0.174081i) q^{2} +(-0.548135 - 2.04567i) q^{3} +(1.93939 + 0.488631i) q^{4} +(0.207992 - 0.776238i) q^{5} +(0.413172 + 2.96643i) q^{6} +(-2.63679 - 1.02339i) q^{8} +(-1.28622 + 0.742602i) q^{9} +(-0.427037 + 1.05321i) q^{10} +(4.56933 - 1.22435i) q^{11} +(-0.0634710 - 4.23518i) q^{12} +(-0.658150 + 0.658150i) q^{13} -1.70193 q^{15} +(3.52248 + 1.89529i) q^{16} +(1.75927 - 3.04715i) q^{17} +(1.93444 - 0.818304i) q^{18} +(-4.39209 - 1.17686i) q^{19} +(0.782673 - 1.40380i) q^{20} +(-6.62600 + 0.922888i) q^{22} +(2.06245 - 1.19075i) q^{23} +(-0.648187 + 5.95495i) q^{24} +(3.77084 + 2.17710i) q^{25} +(1.03826 - 0.809114i) q^{26} +(-2.26846 - 2.26846i) q^{27} +(4.06282 - 4.06282i) q^{29} +(2.38859 + 0.296274i) q^{30} +(4.95223 - 8.57752i) q^{31} +(-4.61372 - 3.27317i) q^{32} +(-5.00922 - 8.67622i) q^{33} +(-2.99951 + 3.97029i) q^{34} +(-2.85735 + 0.811707i) q^{36} +(-2.12056 + 7.91402i) q^{37} +(5.95925 + 2.41625i) q^{38} +(1.70711 + 0.985600i) q^{39} +(-1.34282 + 1.83392i) q^{40} +3.75281i q^{41} +(-6.04279 - 6.04279i) q^{43} +(9.45998 - 0.141773i) q^{44} +(0.308911 + 1.15287i) q^{45} +(-3.10185 + 1.31214i) q^{46} +(5.12882 + 8.88338i) q^{47} +(1.94635 - 8.24469i) q^{48} +(-4.91323 - 3.71190i) q^{50} +(-7.19776 - 1.92863i) q^{51} +(-1.59800 + 0.954817i) q^{52} +(-12.1874 + 3.26561i) q^{53} +(2.78879 + 3.57858i) q^{54} -3.80155i q^{55} +9.62984i q^{57} +(-6.40925 + 4.99473i) q^{58} +(3.30200 - 0.884769i) q^{59} +(-3.30071 - 0.831618i) q^{60} +(-6.44729 - 1.72755i) q^{61} +(-8.44344 + 11.1761i) q^{62} +(5.90536 + 5.39691i) q^{64} +(0.373991 + 0.647771i) q^{65} +(5.51986 + 13.0487i) q^{66} +(-2.10001 - 7.83735i) q^{67} +(4.90085 - 5.04998i) q^{68} +(-3.56639 - 3.56639i) q^{69} +1.91187i q^{71} +(4.15148 - 0.641785i) q^{72} +(-12.1692 - 7.02587i) q^{73} +(4.35380 - 10.7379i) q^{74} +(2.38668 - 8.90723i) q^{75} +(-7.94294 - 4.42850i) q^{76} +(-2.22428 - 1.68042i) q^{78} +(-2.33048 - 4.03650i) q^{79} +(2.20385 - 2.34008i) q^{80} +(-5.62489 + 9.74260i) q^{81} +(0.653294 - 5.26692i) q^{82} +(9.13749 - 9.13749i) q^{83} +(-1.99940 - 1.99940i) q^{85} +(7.42887 + 9.53274i) q^{86} +(-10.5381 - 6.08420i) q^{87} +(-13.3014 - 1.44783i) q^{88} +(0.158841 - 0.0917070i) q^{89} +(-0.232851 - 1.67178i) q^{90} +(4.58173 - 1.30156i) q^{92} +(-20.2612 - 5.42898i) q^{93} +(-5.65166 - 13.3603i) q^{94} +(-1.82704 + 3.16453i) q^{95} +(-4.16687 + 11.2323i) q^{96} -9.26984 q^{97} +(-4.96798 + 4.96798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{4}+O(q^{10}) \) 96 * q + 4 * q^4	\( 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) \) 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more