LMFDB - Embedded newform 637.2.bc.a.411.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(31,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("637.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bc (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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			411.4
Character	$\chi$	$=$	637.411
Dual form			637.2.bc.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.550552 - 0.147520i) q^{2} +(1.06729 - 0.616199i) q^{3} +(-1.45071 + 0.837565i) q^{4} +(0.377817 + 1.41003i) q^{5} +(0.496696 - 0.496696i) q^{6} +(-1.48119 + 1.48119i) q^{8} +(-0.740597 + 1.28275i) q^{9} +O(q^{10})$	\(q+(0.550552 - 0.147520i) q^{2} +(1.06729 - 0.616199i) q^{3} +(-1.45071 + 0.837565i) q^{4} +(0.377817 + 1.41003i) q^{5} +(0.496696 - 0.496696i) q^{6} +(-1.48119 + 1.48119i) q^{8} +(-0.740597 + 1.28275i) q^{9} +(0.416015 + 0.720559i) q^{10} +(0.815474 + 0.218506i) q^{11} +(-1.03221 + 1.78785i) q^{12} +(-3.59334 + 0.296512i) q^{13} +(1.27210 + 1.27210i) q^{15} +(1.07816 - 1.86743i) q^{16} +(3.67402 + 6.36359i) q^{17} +(-0.218506 + 0.815474i) q^{18} +(1.31525 + 4.90859i) q^{19} +(-1.72909 - 1.72909i) q^{20} +0.481194 q^{22} +(-3.84826 - 2.22179i) q^{23} +(-0.668151 + 2.49357i) q^{24} +(2.48469 - 1.43453i) q^{25} +(-1.93458 + 0.693334i) q^{26} +5.52262i q^{27} -3.54420 q^{29} +(0.888016 + 0.512696i) q^{30} +(1.73652 + 0.465299i) q^{31} +(1.40241 - 5.23387i) q^{32} +(1.00499 - 0.269286i) q^{33} +(2.96149 + 2.96149i) q^{34} -2.48119i q^{36} +(1.05570 + 3.93993i) q^{37} +(1.44823 + 2.50841i) q^{38} +(-3.65242 + 2.53068i) q^{39} +(-2.64815 - 1.52891i) q^{40} +(1.23240 - 1.23240i) q^{41} -8.66291i q^{43} +(-1.36603 + 0.366025i) q^{44} +(-2.08853 - 0.559620i) q^{45} +(-2.44642 - 0.655517i) q^{46} +(-3.44553 + 0.923226i) q^{47} -2.65745i q^{48} +(1.15633 - 1.15633i) q^{50} +(7.84247 + 4.52785i) q^{51} +(4.96453 - 3.43981i) q^{52} +(4.89692 + 8.48172i) q^{53} +(0.814696 + 3.04049i) q^{54} +1.23240i q^{55} +(4.42842 + 4.42842i) q^{57} +(-1.95126 + 0.522840i) q^{58} +(-0.398865 + 1.48858i) q^{59} +(-2.91091 - 0.779975i) q^{60} +(6.15660 + 3.55452i) q^{61} +1.02469 q^{62} +1.22425i q^{64} +(-1.77571 - 4.95469i) q^{65} +(0.513573 - 0.296512i) q^{66} +(3.20948 - 11.9779i) q^{67} +(-10.6598 - 6.15446i) q^{68} -5.47626 q^{69} +(-1.46604 - 1.46604i) q^{71} +(-0.803037 - 2.99697i) q^{72} +(-0.0380142 + 0.141871i) q^{73} +(1.16243 + 2.01340i) q^{74} +(1.76792 - 3.06212i) q^{75} +(-6.01931 - 6.01931i) q^{76} +(-1.63752 + 1.93207i) q^{78} +(2.39938 - 4.15586i) q^{79} +(3.04049 + 0.814696i) q^{80} +(1.18124 + 2.04597i) q^{81} +(0.496696 - 0.860302i) q^{82} +(12.3165 - 12.3165i) q^{83} +(-7.58475 + 7.58475i) q^{85} +(-1.27795 - 4.76938i) q^{86} +(-3.78268 + 2.18393i) q^{87} +(-1.53152 + 0.884226i) q^{88} +(9.41214 - 2.52198i) q^{89} -1.23240 q^{90} +7.44358 q^{92} +(2.14009 - 0.573434i) q^{93} +(-1.76075 + 1.01657i) q^{94} +(-6.42434 + 3.70910i) q^{95} +(-1.72833 - 6.45021i) q^{96} +(-6.05814 + 6.05814i) q^{97} +(-0.884226 + 0.884226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9	$ 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9} + 8 q^{11} - 8 q^{15} - 16 q^{16} + 8 q^{18} - 32 q^{22} - 8 q^{29} + 16 q^{32} - 12 q^{37} - 40 q^{39} - 12 q^{44} - 24 q^{46} - 56 q^{50} + 12 q^{53} - 16 q^{57} + 44 q^{58} - 44 q^{60} + 40 q^{65} - 60 q^{67} + 28 q^{72} + 48 q^{74} + 88 q^{78} + 4 q^{79} + 92 q^{81} + 24 q^{85} - 36 q^{86} + 48 q^{92} + 28 q^{93} + 24 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9 + 8 * q^11 - 8 * q^15 - 16 * q^16 + 8 * q^18 - 32 * q^22 - 8 * q^29 + 16 * q^32 - 12 * q^37 - 40 * q^39 - 12 * q^44 - 24 * q^46 - 56 * q^50 + 12 * q^53 - 16 * q^57 + 44 * q^58 - 44 * q^60 + 40 * q^65 - 60 * q^67 + 28 * q^72 + 48 * q^74 + 88 * q^78 + 4 * q^79 + 92 * q^81 + 24 * q^85 - 36 * q^86 + 48 * q^92 + 28 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.550552	−	0.147520i	0.389299	−	0.104312i	−0.0588601	−	0.998266i	$-0.518747\pi$
$2$	0.550552	−	0.147520i	0.389299	−	0.104312i	0.448159	+	0.893954i	$0.352080\pi$
$3$	1.06729	−	0.616199i	0.616199	−	0.355763i	−0.159189	−	0.987248i	$-0.550888\pi$
$3$	1.06729	−	0.616199i	0.616199	−	0.355763i	0.775388	+	0.631485i	$0.217554\pi$
$4$	−1.45071	+	0.837565i	−0.725353	+	0.418783i
$5$	0.377817	+	1.41003i	0.168965	+	0.630585i	0.997501	+	0.0706498i	$0.0225073\pi$
$5$	0.377817	+	1.41003i	0.168965	+	0.630585i	−0.828536	+	0.559935i	$0.810826\pi$
$6$	0.496696	−	0.496696i	0.202775	−	0.202775i
$7$		0			0
$7$		0			0
$8$	−1.48119	+	1.48119i	−0.523681	+	0.523681i
$9$	−0.740597	+	1.28275i	−0.246866	+	0.427584i
$10$	0.416015	+	0.720559i	0.131556	+	0.227861i
$11$	0.815474	+	0.218506i	0.245875	+	0.0658819i	0.379652	−	0.925130i	$-0.376044\pi$
$11$	0.815474	+	0.218506i	0.245875	+	0.0658819i	−0.133777	+	0.991011i	$0.542711\pi$
$12$	−1.03221	+	1.78785i	−0.297975	+	0.516107i
$13$	−3.59334	+	0.296512i	−0.996613	+	0.0822375i
$13$	−3.59334	+	0.296512i	−0.996613	+	0.0822375i
$14$		0			0
$15$	1.27210	+	1.27210i	0.328455	+	0.328455i
$16$	1.07816	−	1.86743i	0.269541	−	0.466858i
$17$	3.67402	+	6.36359i	0.891080	+	1.54340i	0.838582	+	0.544776i	$0.183385\pi$
$17$	3.67402	+	6.36359i	0.891080	+	1.54340i	0.0524987	+	0.998621i	$0.483281\pi$
$18$	−0.218506	+	0.815474i	−0.0515023	+	0.192209i
$19$	1.31525	+	4.90859i	0.301740	+	1.12611i	0.935716	+	0.352755i	$0.114755\pi$
$19$	1.31525	+	4.90859i	0.301740	+	1.12611i	−0.633976	+	0.773353i	$0.718578\pi$
$20$	−1.72909	−	1.72909i	−0.386637	−	0.386637i
$21$		0			0
$22$	0.481194			0.102591
$23$	−3.84826	−	2.22179i	−0.802417	−	0.463276i	0.0418988	−	0.999122i	$-0.486659\pi$
$23$	−3.84826	−	2.22179i	−0.802417	−	0.463276i	−0.844316	+	0.535846i	$0.819993\pi$
$24$	−0.668151	+	2.49357i	−0.136386	+	0.508998i
$25$	2.48469	−	1.43453i	0.496937	−	0.286907i
$26$	−1.93458	+	0.693334i	−0.379402	+	0.135974i
$27$			5.52262i			1.06283i
$28$		0			0
$29$	−3.54420			−0.658141			−0.329071	−	0.944305i	$-0.606735\pi$
$29$	−3.54420			−0.658141			−0.329071	+	0.944305i	$0.606735\pi$
$30$	0.888016	+	0.512696i	0.162129	+	0.0936051i
$31$	1.73652	+	0.465299i	0.311888	+	0.0835702i	0.411368	−	0.911469i	$-0.365051\pi$
$31$	1.73652	+	0.465299i	0.311888	+	0.0835702i	−0.0994796	+	0.995040i	$0.531718\pi$
$32$	1.40241	−	5.23387i	0.247913	−	0.925226i
$33$	1.00499	−	0.269286i	0.174946	−	0.0468767i
$34$	2.96149	+	2.96149i	0.507892	+	0.507892i
$35$		0			0
$36$		−	2.48119i		−	0.413532i
$37$	1.05570	+	3.93993i	0.173556	+	0.647720i	0.996793	+	0.0800221i	$0.0254991\pi$
$37$	1.05570	+	3.93993i	0.173556	+	0.647720i	−0.823237	+	0.567698i	$0.807834\pi$
$38$	1.44823	+	2.50841i	0.234934	+	0.406917i
$39$	−3.65242	+	2.53068i	−0.584855	+	0.405232i
$40$	−2.64815	−	1.52891i	−0.418709	−	0.241742i
$41$	1.23240	−	1.23240i	0.192468	−	0.192468i	−0.604294	−	0.796762i	$-0.706545\pi$
$41$	1.23240	−	1.23240i	0.192468	−	0.192468i	0.796762	+	0.604294i	$0.206545\pi$
$42$		0			0
$43$		−	8.66291i		−	1.32108i	−0.750790	−	0.660541i	$-0.770327\pi$
$43$		−	8.66291i		−	1.32108i	0.750790	−	0.660541i	$-0.229673\pi$
$44$	−1.36603	+	0.366025i	−0.205936	+	0.0551804i
$45$	−2.08853	−	0.559620i	−0.311340	−	0.0834232i
$46$	−2.44642	−	0.655517i	−0.360705	−	0.0966507i
$47$	−3.44553	+	0.923226i	−0.502582	+	0.134666i	−0.501198	−	0.865333i	$-0.667107\pi$
$47$	−3.44553	+	0.923226i	−0.502582	+	0.134666i	−0.00138385	+	0.999999i	$0.500440\pi$
$48$		−	2.65745i		−	0.383570i
$49$		0			0
$50$	1.15633	−	1.15633i	0.163529	−	0.163529i
$51$	7.84247	+	4.52785i	1.09817	+	0.634027i
$52$	4.96453	−	3.43981i	0.688456	−	0.477015i
$53$	4.89692	+	8.48172i	0.672644	+	1.16505i	0.977152	+	0.212544i	$0.0681748\pi$
$53$	4.89692	+	8.48172i	0.672644	+	1.16505i	−0.304508	+	0.952510i	$0.598492\pi$
$54$	0.814696	+	3.04049i	0.110866	+	0.413758i
$55$			1.23240i			0.166177i
$56$		0			0
$57$	4.42842	+	4.42842i	0.586559	+	0.586559i
$58$	−1.95126	+	0.522840i	−0.256214	+	0.0686522i
$59$	−0.398865	+	1.48858i	−0.0519278	+	0.193797i	−0.987017	−	0.160615i	$-0.948652\pi$
$59$	−0.398865	+	1.48858i	−0.0519278	+	0.193797i	0.935089	+	0.354412i	$0.115319\pi$
$60$	−2.91091	−	0.779975i	−0.375797	−	0.100694i
$61$	6.15660	+	3.55452i	0.788272	+	0.455109i	0.839354	−	0.543585i	$-0.182934\pi$
$61$	6.15660	+	3.55452i	0.788272	+	0.455109i	−0.0510818	+	0.998694i	$0.516267\pi$
$62$	1.02469			0.130135
$63$		0			0
$64$			1.22425i			0.153032i
$65$	−1.77571	−	4.95469i	−0.220250	−	0.614554i
$66$	0.513573	−	0.296512i	0.0632165	−	0.0364980i
$67$	3.20948	−	11.9779i	0.392100	−	1.46334i	−0.434564	−	0.900641i	$-0.643098\pi$
$67$	3.20948	−	11.9779i	0.392100	−	1.46334i	0.826664	−	0.562696i	$-0.190236\pi$
$68$	−10.6598	−	6.15446i	−1.29270	−	0.746338i
$69$	−5.47626			−0.659265
$70$		0			0
$71$	−1.46604	−	1.46604i	−0.173986	−	0.173986i	0.614742	−	0.788728i	$-0.289260\pi$
$71$	−1.46604	−	1.46604i	−0.173986	−	0.173986i	−0.788728	+	0.614742i	$0.789260\pi$
$72$	−0.803037	−	2.99697i	−0.0946388	−	0.353197i
$73$	−0.0380142	+	0.141871i	−0.00444922	+	0.0166047i	−0.968115	−	0.250507i	$-0.919403\pi$
$73$	−0.0380142	+	0.141871i	−0.00444922	+	0.0166047i	0.963666	+	0.267112i	$0.0860693\pi$
$74$	1.16243	+	2.01340i	0.135130	+	0.234052i
$75$	1.76792	−	3.06212i	0.204141	−	0.353583i
$76$	−6.01931	−	6.01931i	−0.690462	−	0.690462i
$77$		0			0
$78$	−1.63752	+	1.93207i	−0.185413	+	0.218764i
$79$	2.39938	−	4.15586i	0.269952	−	0.467570i	−0.698897	−	0.715222i	$-0.746326\pi$
$79$	2.39938	−	4.15586i	0.269952	−	0.467570i	0.968849	+	0.247652i	$0.0796589\pi$
$80$	3.04049	+	0.814696i	0.339937	+	0.0910857i
$81$	1.18124	+	2.04597i	0.131249	+	0.227330i
$82$	0.496696	−	0.860302i	0.0548509	−	0.0950045i
$83$	12.3165	−	12.3165i	1.35191	−	1.35191i	0.468379	−	0.883528i	$-0.344838\pi$
$83$	12.3165	−	12.3165i	1.35191	−	1.35191i	0.883528	−	0.468379i	$-0.155162\pi$
$84$		0			0
$85$	−7.58475	+	7.58475i	−0.822682	+	0.822682i
$86$	−1.27795	−	4.76938i	−0.137805	−	0.514295i
$87$	−3.78268	+	2.18393i	−0.405546	+	0.234142i
$88$	−1.53152	+	0.884226i	−0.163261	+	0.0942588i
$89$	9.41214	−	2.52198i	0.997685	−	0.267329i	0.277210	−	0.960809i	$-0.410590\pi$
$89$	9.41214	−	2.52198i	0.997685	−	0.267329i	0.720475	+	0.693481i	$0.243924\pi$
$90$	−1.23240			−0.129906
$91$		0			0
$92$	7.44358			0.776047
$93$	2.14009	−	0.573434i	0.221916	−	0.0594623i
$94$	−1.76075	+	1.01657i	−0.181607	+	0.104851i
$95$	−6.42434	+	3.70910i	−0.659124	+	0.380545i
$96$	−1.72833	−	6.45021i	−0.176397	−	0.658322i
$97$	−6.05814	+	6.05814i	−0.615110	+	0.615110i	−0.944273	−	0.329163i	$-0.893234\pi$
$97$	−6.05814	+	6.05814i	−0.615110	+	0.615110i	0.329163	+	0.944273i	$0.393234\pi$
$98$		0			0
$99$	−0.884226	+	0.884226i	−0.0888681	+	0.0888681i
$100$	−2.40303	+	4.16217i	−0.240303	+	0.416217i
$101$	−6.43533	−	11.1463i	−0.640339	−	1.10910i	−0.985357	−	0.170504i	$-0.945461\pi$
$101$	−6.43533	−	11.1463i	−0.640339	−	1.10910i	0.345018	−	0.938596i	$-0.387873\pi$
$102$	4.98564	+	1.33590i	0.493651	+	0.132274i
$103$	3.05782	−	5.29630i	0.301296	−	0.521860i	−0.675134	−	0.737695i	$-0.735914\pi$
$103$	3.05782	−	5.29630i	0.301296	−	0.521860i	0.976430	+	0.215835i	$0.0692475\pi$
$104$	4.88324	−	5.76162i	0.478841	−	0.564974i
$105$		0			0
$106$	3.94723	+	3.94723i	0.383389	+	0.383389i
$107$	−4.43453	+	7.68084i	−0.428703	+	0.742535i	−0.996758	−	0.0804555i	$-0.974362\pi$
$107$	−4.43453	+	7.68084i	−0.428703	+	0.742535i	0.568056	+	0.822990i	$0.307696\pi$
$108$	−4.62555	−	8.01169i	−0.445094	−	0.770925i
$109$	−1.68261	+	6.27958i	−0.161165	+	0.601474i	0.837334	+	0.546692i	$0.184113\pi$
$109$	−1.68261	+	6.27958i	−0.161165	+	0.601474i	−0.998498	+	0.0547823i	$0.982554\pi$
$110$	0.181803	+	0.678499i	0.0173343	+	0.0646923i
$111$	3.55452	+	3.55452i	0.337380	+	0.337380i
$112$		0			0
$113$	1.60720			0.151193			0.0755964	−	0.997138i	$-0.475914\pi$
$113$	1.60720			0.151193			0.0755964	+	0.997138i	$0.475914\pi$
$114$	3.09136	+	1.78480i	0.289532	+	0.167161i
$115$	1.67886	−	6.26559i	0.156554	−	0.584269i
$116$	5.14159	−	2.96850i	0.477385	−	0.275618i
$117$	2.28087	−	4.82896i	0.210866	−	0.446437i
$118$			0.878382i			0.0808617i
$119$		0			0
$120$	−3.76845			−0.344011
$121$	−8.90903	−	5.14363i	−0.809912	−	0.467603i
$122$	3.91389	+	1.04872i	0.354347	+	0.0949469i
$123$	0.555921	−	2.07473i	0.0501258	−	0.187072i
$124$	−2.90890	+	0.779437i	−0.261227	+	0.0699955i
$125$	8.12256	+	8.12256i	0.726504	+	0.726504i
$126$		0			0
$127$		−	1.54912i		−	0.137462i	−0.997635	−	0.0687312i	$-0.978105\pi$
$127$		−	1.54912i		−	0.137462i	0.997635	−	0.0687312i	$-0.0218951\pi$
$128$	2.98542	+	11.1417i	0.263877	+	0.984801i
$129$	−5.33808	−	9.24582i	−0.469992	−	0.814049i
$130$	−1.70854	−	2.46586i	−0.149849	−	0.216270i
$131$	4.60284	+	2.65745i	0.402152	+	0.232183i	0.687412	−	0.726268i	$-0.258747\pi$
$131$	4.60284	+	2.65745i	0.402152	+	0.232183i	−0.285260	+	0.958450i	$0.592080\pi$
$132$	−1.23240	+	1.23240i	−0.107267	+	0.107267i
$133$		0			0
$134$		−	7.06793i		−	0.610576i
$135$	−7.78706	+	2.08654i	−0.670203	+	0.179580i
$136$	−14.8676	−	3.98377i	−1.27489	−	0.341606i
$137$	−17.3699	−	4.65426i	−1.48401	−	0.397640i	−0.576303	−	0.817236i	$-0.695505\pi$
$137$	−17.3699	−	4.65426i	−1.48401	−	0.397640i	−0.907711	+	0.419595i	$0.862172\pi$
$138$	−3.01497	+	0.807858i	−0.256651	+	0.0687694i
$139$			6.94767i			0.589294i	0.955606	+	0.294647i	$0.0952020\pi$
$139$			6.94767i			0.589294i	−0.955606	+	0.294647i	$0.904798\pi$
$140$		0			0
$141$	−3.10848	+	3.10848i	−0.261781	+	0.261781i
$142$	−1.02340	−	0.590859i	−0.0858816	−	0.0495838i
$143$	−2.99506	−	0.543367i	−0.250460	−	0.0454386i
$144$	1.59697	+	2.76603i	0.133081	+	0.230503i
$145$	−1.33906	−	4.99743i	−0.111203	−	0.415014i
$146$			0.0837150i			0.00692831i
$147$		0			0
$148$	−4.83146	−	4.83146i	−0.397143	−	0.397143i
$149$	14.9789	−	4.01359i	1.22712	−	0.328806i	0.413663	−	0.910430i	$-0.364249\pi$
$149$	14.9789	−	4.01359i	1.22712	−	0.328806i	0.813458	+	0.581624i	$0.197583\pi$
$150$	0.521606	−	1.94666i	0.0425889	−	0.158944i
$151$	−8.38899	−	2.24782i	−0.682686	−	0.182925i	−0.0992236	−	0.995065i	$-0.531636\pi$
$151$	−8.38899	−	2.24782i	−0.682686	−	0.182925i	−0.583463	+	0.812140i	$0.698303\pi$
$152$	−9.21872	−	5.32243i	−0.747737	−	0.431706i
$153$	−10.8839			−0.879909
$154$		0			0
$155$			2.62435i			0.210793i
$156$	3.17898	−	6.73040i	0.254522	−	0.538864i
$157$	−8.39856	+	4.84891i	−0.670278	+	0.386985i	−0.796182	−	0.605057i	$-0.793150\pi$
$157$	−8.39856	+	4.84891i	−0.670278	+	0.386985i	0.125904	+	0.992042i	$0.459817\pi$
$158$	0.707914	−	2.64197i	0.0563186	−	0.210184i
$159$	10.4529	+	6.03496i	0.828965	+	0.478603i
$160$	7.90977			0.625322
$161$		0			0
$162$	0.952155	+	0.952155i	0.0748083	+	0.0748083i
$163$	−1.98139	−	7.39466i	−0.155195	−	0.579194i	−0.999089	−	0.0426843i	$-0.986409\pi$
$163$	−1.98139	−	7.39466i	−0.155195	−	0.579194i	0.843894	−	0.536510i	$-0.180258\pi$
$164$	−0.755633	+	2.82006i	−0.0590050	+	0.220210i
$165$	0.759403	+	1.31532i	0.0591194	+	0.102398i
$166$	4.96392	−	8.59776i	0.385275	−	0.667316i
$167$	8.90824	+	8.90824i	0.689340	+	0.689340i	0.962086	−	0.272746i	$-0.0879318\pi$
$167$	8.90824	+	8.90824i	0.689340	+	0.689340i	−0.272746	+	0.962086i	$0.587932\pi$
$168$		0			0
$169$	12.8242	−	2.13093i	0.986474	−	0.163918i
$170$	−3.05689	+	5.29470i	−0.234453	+	0.406085i
$171$	−7.27058	−	1.94815i	−0.555995	−	0.148978i
$172$	7.25576	+	12.5673i	0.553246	+	0.958251i
$173$	−3.57769	+	6.19674i	−0.272007	+	0.471130i	−0.969376	−	0.245583i	$-0.921021\pi$
$173$	−3.57769	+	6.19674i	−0.272007	+	0.471130i	0.697369	+	0.716712i	$0.254354\pi$
$174$	−1.76039	+	1.76039i	−0.133455	+	0.133455i
$175$		0			0
$176$	1.28726	−	1.28726i	0.0970307	−	0.0970307i
$177$	0.491560	+	1.83453i	0.0369479	+	0.137892i
$178$	4.80983	−	2.77696i	0.360512	−	0.208142i
$179$	11.9615	−	6.90597i	0.894044	−	0.516177i	0.0187809	−	0.999824i	$-0.494022\pi$
$179$	11.9615	−	6.90597i	0.894044	−	0.516177i	0.875263	+	0.483647i	$0.160688\pi$
$180$	3.49856	−	0.937436i	0.260767	−	0.0698724i
$181$	−4.56052			−0.338981			−0.169490	−	0.985532i	$-0.554212\pi$
$181$	−4.56052			−0.338981			−0.169490	+	0.985532i	$0.554212\pi$
$182$		0			0
$183$	8.76116			0.647643
$184$	8.99092	−	2.40911i	0.662819	−	0.177602i
$185$	−5.15656	+	2.97714i	−0.379118	+	0.218884i
$186$	1.09363	−	0.631410i	0.0801892	−	0.0462972i
$187$	1.60559	+	5.99213i	0.117412	+	0.438188i
$188$	4.22518	−	4.22518i	0.308153	−	0.308153i
$189$		0			0
$190$	−2.98977	+	2.98977i	−0.216900	+	0.216900i
$191$	−1.85272	+	3.20901i	−0.134058	+	0.232196i	−0.925237	−	0.379389i	$-0.876134\pi$
$191$	−1.85272	+	3.20901i	−0.134058	+	0.232196i	0.791179	+	0.611585i	$0.209468\pi$
$192$	0.754384	+	1.30663i	0.0544430	+	0.0942980i
$193$	23.2918	+	6.24102i	1.67658	+	0.449238i	0.966873	−	0.255258i	$-0.0821603\pi$
$193$	23.2918	+	6.24102i	1.67658	+	0.449238i	0.709708	+	0.704496i	$0.248827\pi$
$194$	−2.44162	+	4.22901i	−0.175298	+	0.303625i
$195$	−4.94827	−	4.19389i	−0.354353	−	0.300331i
$196$		0			0
$197$	−8.01810	−	8.01810i	−0.571266	−	0.571266i	0.361216	−	0.932482i	$-0.382362\pi$
$197$	−8.01810	−	8.01810i	−0.571266	−	0.571266i	−0.932482	+	0.361216i	$0.882362\pi$
$198$	−0.356371	+	0.617253i	−0.0253262	+	0.0438663i
$199$	2.28779	+	3.96257i	0.162177	+	0.280899i	0.935649	−	0.352931i	$-0.114815\pi$
$199$	2.28779	+	3.96257i	0.162177	+	0.280899i	−0.773472	+	0.633830i	$0.781482\pi$
$200$	−1.55548	+	5.80512i	−0.109989	+	0.410484i
$201$	−3.95535	−	14.7616i	−0.278989	−	1.04120i
$202$	−5.18728	−	5.18728i	−0.364976	−	0.364976i
$203$		0			0
$204$	−15.1695			−1.06208
$205$	2.20334	+	1.27210i	0.153888	+	0.0888473i
$206$	0.902178	−	3.36697i	0.0628577	−	0.234588i
$207$	5.70001	−	3.29090i	0.396178	−	0.228734i
$208$	−3.32049	+	7.03000i	−0.230234	+	0.487443i
$209$			4.29022i			0.296761i
$210$		0			0
$211$	−0.594028			−0.0408946			−0.0204473	−	0.999791i	$-0.506509\pi$
$211$	−0.594028			−0.0408946			−0.0204473	+	0.999791i	$0.506509\pi$
$212$	−14.2080	−	8.20299i	−0.975809	−	0.563383i
$213$	−2.46805	−	0.661313i	−0.169108	−	0.0453124i
$214$	−1.30836	+	4.88288i	−0.0894379	+	0.333787i
$215$	12.2150	−	3.27299i	0.833054	−	0.223216i
$216$	−8.18007	−	8.18007i	−0.556583	−	0.556583i
$217$		0			0
$218$			3.70545i			0.250965i
$219$	0.0468486	+	0.174841i	0.00316574	+	0.0118147i
$220$	−1.03221	−	1.78785i	−0.0695919	−	0.120537i
$221$	−15.0889	−	21.7771i	−1.01499	−	1.46489i
$222$	2.48131	+	1.43258i	0.166534	+	0.0961486i
$223$	2.85764	−	2.85764i	0.191361	−	0.191361i	−0.604923	−	0.796284i	$-0.706796\pi$
$223$	2.85764	−	2.85764i	0.191361	−	0.191361i	0.796284	+	0.604923i	$0.206796\pi$
$224$		0			0
$225$			4.24965i			0.283310i
$226$	0.884848	−	0.237094i	0.0588592	−	0.0157713i
$227$	26.8519	+	7.19495i	1.78222	+	0.477545i	0.990986	−	0.133963i	$-0.0427704\pi$
$227$	26.8519	+	7.19495i	1.78222	+	0.477545i	0.791238	+	0.611509i	$0.209437\pi$
$228$	−10.1334	−	2.71525i	−0.671103	−	0.179822i
$229$	18.0397	−	4.83373i	1.19210	−	0.319422i	0.392383	−	0.919802i	$-0.371651\pi$
$229$	18.0397	−	4.83373i	1.19210	−	0.319422i	0.799715	+	0.600380i	$0.204984\pi$
$230$		−	3.69720i		−	0.243786i
$231$		0			0
$232$	5.24965	−	5.24965i	0.344656	−	0.344656i
$233$	14.0506	+	8.11213i	0.920486	+	0.531443i	0.883790	−	0.467883i	$-0.154983\pi$
$233$	14.0506	+	8.11213i	0.920486	+	0.531443i	0.0366962	+	0.999326i	$0.488317\pi$
$234$	0.543367	−	2.99506i	0.0355210	−	0.195793i
$235$	−2.60356	−	4.50949i	−0.169837	−	0.294167i
$236$	−0.668151	−	2.49357i	−0.0434929	−	0.162318i
$237$		−	5.91400i		−	0.384155i
$238$		0			0
$239$	−0.843675	−	0.843675i	−0.0545728	−	0.0545728i	0.679294	−	0.733867i	$-0.262286\pi$
$239$	−0.843675	−	0.843675i	−0.0545728	−	0.0545728i	−0.733867	+	0.679294i	$0.762286\pi$
$240$	3.74709	−	1.00403i	0.241874	−	0.0648098i
$241$	5.59895	−	20.8956i	0.360660	−	1.34600i	−0.512549	−	0.858658i	$-0.671299\pi$
$241$	5.59895	−	20.8956i	0.360660	−	1.34600i	0.873210	−	0.487345i	$-0.162035\pi$
$242$	−5.66367	−	1.51757i	−0.364074	−	0.0975534i
$243$	−11.8267	−	6.82817i	−0.758685	−	0.438027i
$244$	−11.9086			−0.762367
$245$		0			0
$246$		−	1.22425i		−	0.0780556i
$247$	−6.18160	−	17.2482i	−0.393326	−	1.09748i
$248$	−3.26132	+	1.88293i	−0.207094	+	0.119566i
$249$	5.55582	−	20.7346i	0.352086	−	1.31400i
$250$	5.67013	+	3.27365i	0.358610	+	0.207044i
$251$	27.4367			1.73179			0.865893	−	0.500229i	$-0.166751\pi$
$251$	27.4367			1.73179			0.865893	+	0.500229i	$0.166751\pi$
$252$		0			0
$253$	−2.65268	−	2.65268i	−0.166772	−	0.166772i
$254$	−0.228526	−	0.852872i	−0.0143390	−	0.0535139i
$255$	−3.42140	+	12.7688i	−0.214256	+	0.799615i
$256$	2.06300	+	3.57323i	0.128938	+	0.223327i
$257$	−10.2864	+	17.8165i	−0.641645	+	1.11136i	0.343420	+	0.939182i	$0.388414\pi$
$257$	−10.2864	+	17.8165i	−0.641645	+	1.11136i	−0.985065	+	0.172180i	$0.944919\pi$
$258$	−4.30283	−	4.30283i	−0.267883	−	0.267883i
$259$		0			0
$260$	6.72592	+	5.70052i	0.417124	+	0.353531i
$261$	2.62482	−	4.54633i	0.162472	−	0.281411i
$262$	2.92613	+	0.784054i	0.180777	+	0.0484390i
$263$	11.9284	+	20.6606i	0.735538	+	1.27399i	0.954487	+	0.298253i	$0.0964039\pi$
$263$	11.9284	+	20.6606i	0.735538	+	1.27399i	−0.218949	+	0.975736i	$0.570263\pi$
$264$	−1.08972	+	1.88745i	−0.0670675	+	0.116164i
$265$	−10.1093	+	10.1093i	−0.621012	+	0.621012i
$266$		0			0
$267$	8.49143	−	8.49143i	0.519667	−	0.519667i
$268$	5.37629	+	20.0646i	0.328409	+	1.22564i
$269$	−0.959903	+	0.554200i	−0.0585263	+	0.0337902i	−0.528978	−	0.848636i	$-0.677424\pi$
$269$	−0.959903	+	0.554200i	−0.0585263	+	0.0337902i	0.470451	+	0.882426i	$0.344091\pi$
$270$	−3.97937	+	2.29749i	−0.242177	+	0.139821i
$271$	−28.5354	+	7.64604i	−1.73340	+	0.464464i	−0.980962	−	0.194198i	$-0.937790\pi$
$271$	−28.5354	+	7.64604i	−1.73340	+	0.464464i	−0.752440	+	0.658661i	$0.771123\pi$
$272$	15.8448			0.960730
$273$		0			0
$274$	−10.2496			−0.619204
$275$	2.33965	−	0.626907i	0.141086	−	0.0378039i
$276$	7.94445	−	4.58673i	0.478200	−	0.276089i
$277$	−22.3664	+	12.9133i	−1.34387	+	0.775883i	−0.987373	−	0.158414i	$-0.949362\pi$
$277$	−22.3664	+	12.9133i	−1.34387	+	0.775883i	−0.356496	+	0.934297i	$0.616029\pi$
$278$	1.02492	+	3.82505i	0.0614706	+	0.229411i
$279$	−1.88293	+	1.88293i	−0.112728	+	0.112728i
$280$		0			0
$281$	12.0782	−	12.0782i	0.720523	−	0.720523i	−0.248189	−	0.968712i	$-0.579835\pi$
$281$	12.0782	−	12.0782i	0.720523	−	0.720523i	0.968712	+	0.248189i	$0.0798354\pi$
$282$	−1.25282	+	2.16994i	−0.0746041	+	0.129218i
$283$	7.68337	+	13.3080i	0.456729	+	0.791078i	0.998786	−	0.0492639i	$-0.0156875\pi$
$283$	7.68337	+	13.3080i	0.456729	+	0.791078i	−0.542057	+	0.840342i	$0.682354\pi$
$284$	3.35469	+	0.898886i	0.199064	+	0.0533391i
$285$	−4.57108	+	7.91735i	−0.270768	+	0.468983i
$286$	−1.72909	+	0.142680i	−0.102243	+	0.00843683i
$287$		0			0
$288$	5.67513	+	5.67513i	0.334410	+	0.334410i
$289$	−18.4968	+	32.0375i	−1.08805	+	1.88456i
$290$	−1.47444	−	2.55380i	−0.0865821	−	0.149965i
$291$	−2.73276	+	10.1988i	−0.160197	+	0.597864i
$292$	−0.0636787	−	0.237652i	−0.00372651	−	0.0139075i
$293$	−9.78662	−	9.78662i	−0.571741	−	0.571741i	0.360874	−	0.932615i	$-0.382478\pi$
$293$	−9.78662	−	9.78662i	−0.571741	−	0.571741i	−0.932615	+	0.360874i	$0.882478\pi$
$294$		0			0
$295$	−2.24965			−0.130979
$296$	−7.39949	−	4.27210i	−0.430087	−	0.248311i
$297$	−1.20672	+	4.50355i	−0.0700211	+	0.261322i
$298$	7.65458	−	4.41938i	0.443418	−	0.256008i
$299$	14.4869	+	6.84260i	0.837797	+	0.395718i
$300$			5.92298i			0.341964i
$301$		0			0
$302$	−4.95017			−0.284850
$303$	−13.7367	−	7.93089i	−0.789153	−	0.455618i
$304$	10.5845	+	2.83611i	0.607064	+	0.162662i
$305$	−2.68591	+	10.0240i	−0.153795	+	0.573970i
$306$	−5.99213	+	1.60559i	−0.342547	+	0.0917853i
$307$	−8.14125	−	8.14125i	−0.464645	−	0.464645i	0.435529	−	0.900175i	$-0.356561\pi$
$307$	−8.14125	−	8.14125i	−0.464645	−	0.464645i	−0.900175	+	0.435529i	$0.856561\pi$
$308$		0			0
$309$		−	7.53690i		−	0.428759i
$310$	0.387143	+	1.44484i	0.0219882	+	0.0820613i
$311$	16.2406	+	28.1296i	0.920922	+	1.59508i	0.797992	+	0.602668i	$0.205896\pi$
$311$	16.2406	+	28.1296i	0.920922	+	1.59508i	0.122930	+	0.992415i	$0.460771\pi$
$312$	1.66152	−	9.15836i	0.0940650	−	0.518490i
$313$	−17.0907	−	9.86730i	−0.966022	−	0.557733i	−0.0680008	−	0.997685i	$-0.521662\pi$
$313$	−17.0907	−	9.86730i	−0.966022	−	0.557733i	−0.898021	+	0.439952i	$0.854995\pi$
$314$	−3.90853	+	3.90853i	−0.220571	+	0.220571i
$315$		0			0
$316$			8.03857i			0.452205i
$317$	11.0904	−	2.97166i	0.622897	−	0.166905i	0.0664527	−	0.997790i	$-0.478832\pi$
$317$	11.0904	−	2.97166i	0.622897	−	0.166905i	0.556445	+	0.830885i	$0.312165\pi$
$318$	6.64511	+	1.78055i	0.372639	+	0.0998484i
$319$	−2.89020	−	0.774427i	−0.161820	−	0.0433596i
$320$	−1.72624	+	0.462543i	−0.0964995	+	0.0258570i
$321$			10.9302i			0.610066i
$322$		0			0
$323$	−26.4040	+	26.4040i	−1.46916	+	1.46916i
$324$	−3.42726	−	1.97873i	−0.190404	−	0.109930i
$325$	−8.50296	+	5.89150i	−0.471659	+	0.326802i
$326$	−2.18172	−	3.77885i	−0.120834	−	0.209291i
$327$	2.07364	+	7.73894i	0.114673	+	0.427964i
$328$			3.65084i			0.201584i
$329$		0			0
$330$	0.612127	+	0.612127i	0.0336965	+	0.0336965i
$331$	1.10110	−	0.295040i	0.0605221	−	0.0162168i	−0.228431	−	0.973560i	$-0.573360\pi$
$331$	1.10110	−	0.295040i	0.0605221	−	0.0162168i	0.288953	+	0.957343i	$0.406693\pi$
$332$	−7.55172	+	28.1834i	−0.414454	+	1.54676i
$333$	−5.83580	−	1.56370i	−0.319800	−	0.0856901i
$334$	6.21859	+	3.59030i	0.340266	+	0.196453i
$335$	18.1018			0.989009
$336$		0			0
$337$			26.6058i			1.44931i	0.689112	+	0.724655i	$0.258001\pi$
$337$			26.6058i			1.44931i	−0.689112	+	0.724655i	$0.741999\pi$
$338$	6.74601	−	3.06501i	0.366934	−	0.166714i
$339$	1.71535	−	0.990357i	0.0931649	−	0.0537888i
$340$	4.65052	−	17.3560i	0.252210	−	0.941259i
$341$	1.31442	+	0.758879i	0.0711797	+	0.0410956i
$342$	−4.29022			−0.231988
$343$		0			0
$344$	12.8315	+	12.8315i	0.691826	+	0.691826i
$345$	−2.06902	−	7.72170i	−0.111392	−	0.415722i
$346$	−1.05556	+	3.93941i	−0.0567473	+	0.211784i
$347$	10.1036	+	17.4999i	0.542387	+	0.939442i	0.998766	+	0.0496568i	$0.0158128\pi$
$347$	10.1036	+	17.4999i	0.542387	+	0.939442i	−0.456379	+	0.889785i	$0.650854\pi$
$348$	3.65837	−	6.33649i	0.196109	−	0.339671i
$349$	−2.31459	−	2.31459i	−0.123897	−	0.123897i	0.642439	−	0.766336i	$-0.277922\pi$
$349$	−2.31459	−	2.31459i	−0.123897	−	0.123897i	−0.766336	+	0.642439i	$0.777922\pi$
$350$		0			0
$351$	−1.63752	−	19.8446i	−0.0874043	−	1.05923i
$352$	2.28726	−	3.96165i	0.121911	−	0.211156i
$353$	14.6727	+	3.93155i	0.780951	+	0.209255i	0.627204	−	0.778855i	$-0.284199\pi$
$353$	14.6727	+	3.93155i	0.780951	+	0.209255i	0.153747	+	0.988110i	$0.450866\pi$
$354$	0.541259	+	0.937487i	0.0287676	+	0.0498269i
$355$	1.51326	−	2.62105i	0.0803157	−	0.139111i
$356$	−11.5419	+	11.5419i	−0.611721	+	0.611721i
$357$		0			0
$358$	5.56665	−	5.56665i	0.294207	−	0.294207i
$359$	−6.21241	−	23.1850i	−0.327879	−	1.22366i	−0.911386	−	0.411552i	$-0.864987\pi$
$359$	−6.21241	−	23.1850i	−0.327879	−	1.22366i	0.583508	−	0.812107i	$-0.301680\pi$
$360$	3.92242	−	2.26461i	0.206730	−	0.119356i
$361$	−5.90990	+	3.41208i	−0.311047	+	0.179583i
$362$	−2.51080	+	0.672767i	−0.131965	+	0.0353599i
$363$	−12.6780			−0.665422
$364$		0			0
$365$	−0.214405			−0.0112225
$366$	4.82347	−	1.29244i	0.252127	−	0.0675572i
$367$	−8.48512	+	4.89889i	−0.442920	+	0.255720i	−0.704835	−	0.709371i	$-0.748979\pi$
$367$	−8.48512	+	4.89889i	−0.442920	+	0.255720i	0.261916	+	0.965091i	$0.415646\pi$
$368$	−8.29809	+	4.79090i	−0.432568	+	0.249743i
$369$	0.668151	+	2.49357i	0.0347825	+	0.129810i
$370$	−2.39976	+	2.39976i	−0.124758	+	0.124758i
$371$		0			0
$372$	−2.62435	+	2.62435i	−0.136066	+	0.136066i
$373$	2.98366	−	5.16784i	0.154488	−	0.267581i	−0.778385	−	0.627788i	$-0.783961\pi$
$373$	2.98366	−	5.16784i	0.154488	−	0.267581i	0.932872	+	0.360207i	$0.117294\pi$
$374$	1.76792	+	3.06212i	0.0914168	+	0.158339i
$375$	13.6742	+	3.66400i	0.706134	+	0.189208i
$376$	3.73602	−	6.47097i	0.192670	−	0.333715i
$377$	12.7355	−	1.05090i	0.655912	−	0.0541239i
$378$		0			0
$379$	2.14117	+	2.14117i	0.109984	+	0.109984i	0.759957	−	0.649973i	$-0.225220\pi$
$379$	2.14117	+	2.14117i	0.109984	+	0.109984i	−0.649973	+	0.759957i	$0.725220\pi$
$380$	6.21322	−	10.7616i	0.318731	−	0.552059i
$381$	−0.954568	−	1.65336i	−0.0489040	−	0.0847042i
$382$	−0.546627	+	2.04004i	−0.0279679	+	0.104378i
$383$	1.06569	+	3.97721i	0.0544542	+	0.203226i	0.987793	−	0.155770i	$-0.0497859\pi$
$383$	1.06569	+	3.97721i	0.0544542	+	0.203226i	−0.933339	+	0.358996i	$0.883119\pi$
$384$	10.0518	+	10.0518i	0.512956	+	0.512956i
$385$		0			0
$386$	13.7440			0.699552
$387$	11.1124	+	6.41573i	0.564873	+	0.326130i
$388$	3.71449	−	13.8627i	0.188575	−	0.703770i
$389$	15.1066	−	8.72179i	0.765934	−	0.442212i	−0.0654880	−	0.997853i	$-0.520860\pi$
$389$	15.1066	−	8.72179i	0.765934	−	0.442212i	0.831422	+	0.555641i	$0.187527\pi$
$390$	−3.34296	−	1.57898i	−0.169277	−	0.0799550i
$391$		−	32.6516i		−	1.65126i
$392$		0			0
$393$	6.55008			0.330408
$394$	−5.59721	−	3.23155i	−0.281983	−	0.162803i
$395$	6.76641	+	1.81305i	0.340455	+	0.0912247i
$396$	0.542155	−	2.02335i	0.0272443	−	0.101677i
$397$	−13.9157	+	3.72870i	−0.698408	+	0.187138i	−0.590518	−	0.807025i	$-0.701076\pi$
$397$	−13.9157	+	3.72870i	−0.698408	+	0.187138i	−0.107891	+	0.994163i	$0.534410\pi$
$398$	1.84410	+	1.84410i	0.0924365	+	0.0924365i
$399$		0			0
$400$		−	6.18664i		−	0.309332i
$401$	5.70816	+	21.3031i	0.285052	+	1.06383i	0.948801	+	0.315873i	$0.102297\pi$
$401$	5.70816	+	21.3031i	0.285052	+	1.06383i	−0.663749	+	0.747955i	$0.731036\pi$
$402$	−4.35525	−	7.54352i	−0.217220	−	0.376236i
$403$	−6.37787	−	1.15708i	−0.317704	−	0.0576382i
$404$	18.6715	+	10.7800i	0.928944	+	0.536326i
$405$	−2.43859	+	2.43859i	−0.121174	+	0.121174i
$406$		0			0
$407$			3.44358i			0.170692i
$408$	−18.3229	+	4.90960i	−0.907117	+	0.243061i
$409$	−2.45777	−	0.658557i	−0.121529	−	0.0325635i	0.197542	−	0.980294i	$-0.436704\pi$
$409$	−2.45777	−	0.658557i	−0.121529	−	0.0325635i	−0.319071	+	0.947731i	$0.603371\pi$
$410$	1.40071	+	0.375320i	0.0691763	+	0.0185357i
$411$	−21.4067	+	5.73591i	−1.05591	+	0.282931i
$412$			10.2445i			0.504710i
$413$		0			0
$414$	2.65268	−	2.65268i	0.130372	−	0.130372i
$415$	22.0199	+	12.7132i	1.08092	+	0.624067i
$416$	−3.48743	+	19.2229i	−0.170985	+	0.942479i
$417$	4.28115	+	7.41517i	0.209649	+	0.363122i
$418$	0.632892	+	2.36199i	0.0309558	+	0.115529i
$419$			16.5064i			0.806392i	0.915114	+	0.403196i	$0.132101\pi$
$419$			16.5064i			0.806392i	−0.915114	+	0.403196i	$0.867899\pi$
$420$		0			0
$421$	−8.53492	−	8.53492i	−0.415967	−	0.415967i	0.467844	−	0.883811i	$-0.345031\pi$
$421$	−8.53492	−	8.53492i	−0.415967	−	0.415967i	−0.883811	+	0.467844i	$0.845031\pi$
$422$	−0.327043	+	0.0876310i	−0.0159202	+	0.00426581i
$423$	1.36748	−	5.10350i	0.0664890	−	0.248140i
$424$	−19.8164	−	5.30978i	−0.962368	−	0.257866i
$425$	18.2576	+	10.5410i	0.885622	+	0.511314i
$426$	−1.45635			−0.0705602
$427$		0			0
$428$		−	14.8568i		−	0.718133i
$429$	−3.53142	+	1.26563i	−0.170498	+	0.0611050i
$430$	6.24214	−	3.60390i	0.301023	−	0.173796i
$431$	8.86042	−	33.0675i	0.426791	−	1.59281i	−0.333189	−	0.942860i	$-0.608125\pi$
$431$	8.86042	−	33.0675i	0.426791	−	1.59281i	0.759980	−	0.649947i	$-0.225209\pi$
$432$	10.3131	+	5.95428i	0.496190	+	0.286475i
$433$	−35.8708			−1.72384			−0.861920	−	0.507044i	$-0.830738\pi$
$433$	−35.8708			−1.72384			−0.861920	+	0.507044i	$0.830738\pi$
$434$		0			0
$435$	−4.50857	−	4.50857i	−0.216169	−	0.216169i
$436$	−2.81859	−	10.5191i	−0.134986	−	0.503774i
$437$	5.84444	−	21.8117i	0.279577	−	1.04340i
$438$	0.0515851	+	0.0893481i	0.00246483	+	0.00426922i
$439$	−5.26493	+	9.11912i	−0.251281	+	0.435232i	−0.963879	−	0.266341i	$-0.914185\pi$
$439$	−5.26493	+	9.11912i	−0.251281	+	0.435232i	0.712598	+	0.701573i	$0.247519\pi$
$440$	−1.82542	−	1.82542i	−0.0870236	−	0.0870236i
$441$		0			0
$442$	−11.5198	−	9.76353i	−0.547939	−	0.464404i
$443$	−6.43089	+	11.1386i	−0.305541	+	0.529212i	−0.977382	−	0.211484i	$-0.932171\pi$
$443$	−6.43089	+	11.1386i	−0.305541	+	0.529212i	0.671841	+	0.740695i	$0.265504\pi$
$444$	−8.13370	−	2.17942i	−0.386008	−	0.103431i
$445$	7.11213	+	12.3186i	0.337147	+	0.583956i
$446$	1.15172	−	1.99483i	0.0545354	−	0.0944581i
$447$	13.5137	−	13.5137i	0.639174	−	0.639174i
$448$		0			0
$449$	9.65069	−	9.65069i	0.455444	−	0.455444i	−0.441712	−	0.897157i	$-0.645629\pi$
$449$	9.65069	−	9.65069i	0.455444	−	0.455444i	0.897157	+	0.441712i	$0.145629\pi$
$450$	0.626907	+	2.33965i	0.0295527	+	0.110292i
$451$	1.27427	−	0.735703i	0.0600032	−	0.0346429i
$452$	−2.33158	+	1.34614i	−0.109668	+	0.0633170i
$453$	−10.3386	+	2.77021i	−0.485749	+	0.130156i
$454$	15.8448			0.743631
$455$		0			0
$456$	−13.1187			−0.614340
$457$	30.2187	−	8.09709i	1.41357	−	0.378766i	0.530374	−	0.847764i	$-0.322052\pi$
$457$	30.2187	−	8.09709i	1.41357	−	0.378766i	0.883199	+	0.468998i	$0.155385\pi$
$458$	9.21872	−	5.32243i	0.430763	−	0.248701i
$459$	−35.1437	+	20.2902i	−1.64037	+	0.947065i
$460$	2.81231	+	10.4957i	0.131125	+	0.489364i
$461$	0.593023	−	0.593023i	0.0276198	−	0.0276198i	−0.693162	−	0.720782i	$-0.743783\pi$
$461$	0.593023	−	0.593023i	0.0276198	−	0.0276198i	0.720782	+	0.693162i	$0.243783\pi$
$462$		0			0
$463$	2.47096	−	2.47096i	0.114835	−	0.114835i	−0.647354	−	0.762189i	$-0.724124\pi$
$463$	2.47096	−	2.47096i	0.114835	−	0.114835i	0.762189	+	0.647354i	$0.224124\pi$
$464$	−3.82122	+	6.61855i	−0.177396	+	0.307259i
$465$	1.61712	+	2.80093i	0.0749921	+	0.129890i
$466$	8.93229	+	2.39340i	0.413780	+	0.110872i
$467$	6.69302	−	11.5926i	0.309716	−	0.536444i	−0.668584	−	0.743636i	$-0.733099\pi$
$467$	6.69302	−	11.5926i	0.309716	−	0.536444i	0.978300	+	0.207193i	$0.0664327\pi$
$468$	0.735703	+	8.91577i	0.0340079	+	0.412132i
$469$		0			0
$470$	−2.09863	−	2.09863i	−0.0968026	−	0.0968026i
$471$	−5.97579	+	10.3504i	−0.275350	+	0.476920i
$472$	−1.61409	−	2.79568i	−0.0742943	−	0.128681i
$473$	1.89289	−	7.06438i	0.0870354	−	0.324820i
$474$	−0.872432	−	3.25596i	−0.0400721	−	0.149551i
$475$	10.3095	+	10.3095i	0.473034	+	0.473034i
$476$		0			0
$477$	−14.5066			−0.664211
$478$	−0.588945	−	0.340028i	−0.0269377	−	0.0155525i
$479$	−3.24235	+	12.1006i	−0.148147	+	0.552891i	0.851448	+	0.524438i	$0.175725\pi$
$479$	−3.24235	+	12.1006i	−0.148147	+	0.552891i	−0.999595	+	0.0284528i	$0.990942\pi$
$480$	8.44200	−	4.87399i	0.385323	−	0.222466i
$481$	−4.96172	−	13.8445i	−0.226235	−	0.631253i
$482$		−	12.3301i		−	0.561619i
$483$		0			0
$484$	17.2325			0.783296
$485$	−10.8310	−	6.25329i	−0.491811	−	0.283947i
$486$	−7.51852	−	2.01458i	−0.341047	−	0.0913832i
$487$	6.58132	−	24.5618i	0.298228	−	1.11300i	−0.640392	−	0.768048i	$-0.721228\pi$
$487$	6.58132	−	24.5618i	0.298228	−	1.11300i	0.938620	−	0.344953i	$-0.112105\pi$
$488$	−14.3841	+	3.85419i	−0.651135	+	0.174471i
$489$	−6.67130	−	6.67130i	−0.301687	−	0.301687i
$490$		0			0
$491$			19.4944i			0.879769i	0.898054	+	0.439884i	$0.144981\pi$
$491$			19.4944i			0.879769i	−0.898054	+	0.439884i	$0.855019\pi$
$492$	0.931241	+	3.47544i	0.0419836	+	0.156685i
$493$	−13.0215	−	22.5538i	−0.586457	−	1.01577i
$494$	−5.94775	−	8.58414i	−0.267602	−	0.386219i
$495$	−1.58086	−	0.912711i	−0.0710544	−	0.0410233i
$496$	2.74117	−	2.74117i	0.123082	−	0.123082i
$497$		0			0
$498$		−	12.2351i		−	0.548266i
$499$	−13.9539	+	3.73894i	−0.624663	+	0.167378i	−0.557247	−	0.830347i	$-0.688142\pi$
$499$	−13.9539	+	3.73894i	−0.624663	+	0.167378i	−0.0674163	+	0.997725i	$0.521476\pi$
$500$	−18.5866	−	4.98027i	−0.831219	−	0.222725i
$501$	14.9969	+	4.01841i	0.670013	+	0.179529i
$502$	15.1053	−	4.04745i	0.674182	−	0.180647i
$503$		−	31.8196i		−	1.41877i	−0.704824	−	0.709383i	$-0.748974\pi$
$503$		−	31.8196i		−	1.41877i	0.704824	−	0.709383i	$-0.251026\pi$
$504$		0			0
$505$	13.2853	−	13.2853i	0.591187	−	0.591187i
$506$	−1.85176	−	1.06911i	−0.0823207	−	0.0475279i
$507$	12.3740	−	10.1766i	0.549549	−	0.451957i
$508$	1.29749	+	2.24732i	0.0575669	+	0.0997088i
$509$	−4.98303	−	18.5969i	−0.220869	−	0.824294i	−0.984018	−	0.178071i	$-0.943014\pi$
$509$	−4.98303	−	18.5969i	−0.220869	−	0.824294i	0.763149	−	0.646223i	$-0.223652\pi$
$510$			7.53462i			0.333639i
$511$		0			0
$512$	−14.6497	−	14.6497i	−0.647433	−	0.647433i
$513$	−27.1083	+	7.26364i	−1.19686	+	0.320697i
$514$	−3.03488	+	11.3263i	−0.133863	+	0.499583i
$515$	8.62324	+	2.31059i	0.379985	+	0.101817i
$516$	15.4880	+	8.94198i	0.681820	+	0.393649i
$517$	−3.01147			−0.132444
$518$		0			0
$519$			8.81828i			0.387080i
$520$	9.96904	+	4.70868i	0.437171	+	0.206489i
$521$	18.7711	−	10.8375i	0.822378	−	0.474800i	−0.0288576	−	0.999584i	$-0.509187\pi$
$521$	18.7711	−	10.8375i	0.822378	−	0.474800i	0.851236	+	0.524783i	$0.175854\pi$
$522$	0.774427	−	2.89020i	0.0338958	−	0.126501i
$523$	−7.59772	−	4.38655i	−0.332225	−	0.191810i	0.324603	−	0.945850i	$-0.394769\pi$
$523$	−7.59772	−	4.38655i	−0.332225	−	0.191810i	−0.656829	+	0.754040i	$0.728102\pi$
$524$	−8.90316			−0.388936
$525$		0			0
$526$	9.61507	+	9.61507i	0.419237	+	0.419237i
$527$	3.41904	+	12.7600i	0.148936	+	0.555835i
$528$	0.580668	−	2.16708i	0.0252703	−	0.0943101i
$529$	−1.62729	−	2.81854i	−0.0707515	−	0.122545i
$530$	−4.07439	+	7.05705i	−0.176980	+	0.306538i
$531$	−1.61409	−	1.61409i	−0.0700453	−	0.0700453i
$532$		0			0
$533$	−4.06300	+	4.79384i	−0.175988	+	0.207644i
$534$	3.42231	−	5.92762i	0.148098	−	0.256513i
$535$	−12.5057	−	3.35088i	−0.540667	−	0.144871i
$536$	12.9878	+	22.4955i	0.560987	+	0.971657i
$537$	8.51091	−	14.7413i	0.367273	−	0.636135i
$538$	−0.446720	+	0.446720i	−0.0192595	+	0.0192595i
$539$		0			0
$540$	9.54912	−	9.54912i	0.410929	−	0.410929i
$541$	−8.52300	−	31.8083i	−0.366432	−	1.36754i	−0.865469	−	0.500963i	$-0.832979\pi$
$541$	−8.52300	−	31.8083i	−0.366432	−	1.36754i	0.499036	−	0.866581i	$-0.333688\pi$
$542$	−14.5823	+	8.41908i	−0.626362	+	0.361630i
$543$	−4.86739	+	2.81019i	−0.208880	+	0.120597i
$544$	38.4586	−	10.3050i	1.64890	−	0.441822i
$545$	−9.49011			−0.406512
$546$		0			0
$547$	−15.1744			−0.648812			−0.324406	−	0.945918i	$-0.605164\pi$
$547$	−15.1744			−0.648812			−0.324406	+	0.945918i	$0.605164\pi$
$548$	29.0969	−	7.79650i	1.24296	−	0.333050i
$549$	−9.11912	+	5.26493i	−0.389195	+	0.224702i
$550$	1.19562	−	0.690289i	0.0509813	−	0.0294340i
$551$	−4.66152	−	17.3970i	−0.198587	−	0.741138i
$552$	8.11141	−	8.11141i	0.345245	−	0.345245i
$553$		0			0
$554$	−10.4089	+	10.4089i	−0.442232	+	0.442232i
$555$	−3.66902	+	6.35493i	−0.155741	+	0.269752i
$556$	−5.81913	−	10.0790i	−0.246786	−	0.427446i
$557$	−11.5521	−	3.09539i	−0.489480	−	0.131156i	0.00563336	−	0.999984i	$-0.498207\pi$
$557$	−11.5521	−	3.09539i	−0.489480	−	0.131156i	−0.495113	+	0.868828i	$0.664874\pi$
$558$	−0.758879	+	1.31442i	−0.0321259	+	0.0556437i
$559$	2.56865	+	31.1288i	0.108642	+	1.31661i
$560$		0			0
$561$	5.40597	+	5.40597i	0.228240	+	0.228240i
$562$	4.86788	−	8.43142i	0.205339	−	0.355658i
$563$	−3.17429	−	5.49803i	−0.133780	−	0.231714i	0.791351	−	0.611363i	$-0.209378\pi$
$563$	−3.17429	−	5.49803i	−0.133780	−	0.231714i	−0.925131	+	0.379648i	$0.876045\pi$
$564$	1.90593	−	7.11305i	0.0802543	−	0.299513i
$565$	0.607228	+	2.26620i	0.0255463	+	0.0953400i
$566$	6.19329	+	6.19329i	0.260323	+	0.260323i
$567$		0			0
$568$	4.34297			0.182227
$569$	−31.7087	−	18.3070i	−1.32930	−	0.767470i	−0.344106	−	0.938931i	$-0.611818\pi$
$569$	−31.7087	−	18.3070i	−1.32930	−	0.767470i	−0.985191	+	0.171461i	$0.945151\pi$
$570$	−1.34865	+	5.03323i	−0.0564888	+	0.210819i
$571$	−16.2874	+	9.40351i	−0.681605	+	0.393525i	−0.800459	−	0.599387i	$-0.795411\pi$
$571$	−16.2874	+	9.40351i	−0.681605	+	0.393525i	0.118855	+	0.992912i	$0.462078\pi$
$572$	4.80006	−	1.72030i	0.200701	−	0.0719292i
$573$			4.56659i			0.190772i
$574$		0			0
$575$	−12.7489			−0.531668
$576$	−1.57041	−	0.906679i	−0.0654339	−	0.0377783i
$577$	−42.8134	−	11.4718i	−1.78234	−	0.477578i	−0.791336	−	0.611381i	$-0.790614\pi$
$577$	−42.8134	−	11.4718i	−1.78234	−	0.477578i	−0.991008	+	0.133803i	$0.957281\pi$
$578$	−5.45730	+	20.3669i	−0.226994	+	0.847152i
$579$	28.7048	−	7.69142i	1.19293	−	0.319645i
$580$	6.12825	+	6.12825i	0.254462	+	0.254462i
$581$		0			0
$582$			6.01810i			0.249458i
$583$	2.14001	+	7.98662i	0.0886301	+	0.330772i
$584$	−0.153832	−	0.266445i	−0.00636561	−	0.0110256i
$585$	7.67073	+	1.39163i	0.317146	+	0.0575368i
$586$	−6.83176	−	3.94432i	−0.282218	−	0.162938i
$587$	3.36694	−	3.36694i	0.138969	−	0.138969i	−0.634200	−	0.773169i	$-0.718671\pi$
$587$	3.36694	−	3.36694i	0.138969	−	0.138969i	0.773169	+	0.634200i	$0.218671\pi$
$588$		0			0
$589$			9.13586i			0.376436i
$590$	−1.23855	+	0.331867i	−0.0509901	+	0.0136628i
$591$	−13.4984	−	3.61688i	−0.555249	−	0.148778i
$592$	8.49576	+	2.27643i	0.349174	+	0.0935608i
$593$	−14.5942	+	3.91050i	−0.599312	+	0.160585i	−0.545705	−	0.837977i	$-0.683738\pi$
$593$	−14.5942	+	3.91050i	−0.599312	+	0.160585i	−0.0536061	+	0.998562i	$0.517072\pi$
$594$			2.65745i			0.109037i
$595$		0			0
$596$	−18.3684	+	18.3684i	−0.752397	+	0.752397i
$597$	4.88346	+	2.81947i	0.199867	+	0.115393i
$598$	8.98519	+	1.63010i	0.367432	+	0.0666598i
$599$	6.42184	+	11.1229i	0.262389	+	0.454471i	0.966876	−	0.255245i	$-0.0821563\pi$
$599$	6.42184	+	11.1229i	0.262389	+	0.454471i	−0.704487	+	0.709717i	$0.748823\pi$
$600$	1.91697	+	7.15423i	0.0782599	+	0.292070i
$601$		−	19.5732i		−	0.798409i	−0.916862	−	0.399205i	$-0.869286\pi$
$601$		−	19.5732i		−	0.798409i	0.916862	−	0.399205i	$-0.130714\pi$
$602$		0			0
$603$	12.9878	+	12.9878i	0.528903	+	0.528903i
$604$	14.0527	−	3.76540i	0.571794	−	0.153212i
$605$	3.88670	−	14.5054i	0.158017	−	0.589726i
$606$	−8.73272	−	2.33993i	−0.354743	−	0.0950530i
$607$	−36.3561	−	20.9902i	−1.47565	−	0.851965i	−0.476024	−	0.879432i	$-0.657923\pi$
$607$	−36.3561	−	20.9902i	−1.47565	−	0.851965i	−0.999623	+	0.0274668i	$0.991256\pi$
$608$	27.5354			1.11671
$609$		0			0
$610$			5.91493i			0.239488i
$611$	12.1072	−	4.33910i	0.489805	−	0.175541i
$612$	15.7893	−	9.11595i	0.638245	−	0.368491i
$613$	7.50326	−	28.0026i	0.303054	−	1.13101i	−0.631554	−	0.775332i	$-0.717582\pi$
$613$	7.50326	−	28.0026i	0.303054	−	1.13101i	0.934608	−	0.355680i	$-0.115751\pi$
$614$	−5.68317	−	3.28118i	−0.229354	−	0.132418i
$615$	3.13547			0.126434
$616$		0			0
$617$	8.21440	+	8.21440i	0.330699	+	0.330699i	0.852852	−	0.522153i	$-0.174871\pi$
$617$	8.21440	+	8.21440i	0.330699	+	0.330699i	−0.522153	+	0.852852i	$0.674871\pi$
$618$	−1.11184	−	4.14945i	−0.0447249	−	0.166916i
$619$	9.77190	−	36.4692i	0.392766	−	1.46582i	−0.432786	−	0.901497i	$-0.642469\pi$
$619$	9.77190	−	36.4692i	0.392766	−	1.46582i	0.825552	−	0.564326i	$-0.190864\pi$
$620$	−2.19806	−	3.80715i	−0.0882763	−	0.152899i
$621$	12.2701	−	21.2524i	0.492382	−	0.852831i
$622$	13.0910	+	13.0910i	0.524900	+	0.524900i
$623$		0			0
$624$	0.787965	+	9.54912i	0.0315438	+	0.382271i
$625$	−1.21156	+	2.09848i	−0.0484623	+	0.0839392i
$626$	−10.8649	−	2.91125i	−0.434250	−	0.116357i
$627$	2.64363	+	4.57890i	0.105576	+	0.182864i
$628$	8.12256	−	14.0687i	0.324126	−	0.561402i
$629$	−21.1934	+	21.1934i	−0.845036	+	0.845036i
$630$		0			0
$631$	5.13093	−	5.13093i	0.204259	−	0.204259i	−0.597563	−	0.801822i	$-0.703864\pi$
$631$	5.13093	−	5.13093i	0.204259	−	0.204259i	0.801822	+	0.597563i	$0.203864\pi$
$632$	2.60168	+	9.70959i	0.103489	+	0.386227i
$633$	−0.634000	+	0.366040i	−0.0251992	+	0.0145488i
$634$	5.66744	−	3.27210i	0.225083	−	0.129952i
$635$	2.18431	−	0.585284i	0.0866817	−	0.0232263i
$636$	−20.2187			−0.801723
$637$		0			0
$638$	−1.70545			−0.0675193
$639$	2.96630	−	0.794818i	0.117345	−	0.0314425i
$640$	−14.5823	+	8.41908i	−0.576415	+	0.332793i
$641$	−14.1471	+	8.16784i	−0.558777	+	0.322610i	−0.752655	−	0.658416i	$-0.771227\pi$
$641$	−14.1471	+	8.16784i	−0.558777	+	0.322610i	0.193877	+	0.981026i	$0.437894\pi$
$642$	1.61242	+	6.01765i	0.0636373	+	0.237498i
$643$	28.1910	−	28.1910i	1.11175	−	1.11175i	0.118832	−	0.992914i	$-0.462085\pi$
$643$	28.1910	−	28.1910i	1.11175	−	1.11175i	0.992914	−	0.118832i	$-0.0379150\pi$
$644$		0			0
$645$	11.0201	−	11.0201i	0.433915	−	0.433915i
$646$	−10.6416	+	18.4319i	−0.418690	+	0.725192i
$647$	−5.55694	−	9.62491i	−0.218466	−	0.378394i	0.735873	−	0.677119i	$-0.236772\pi$
$647$	−5.55694	−	9.62491i	−0.218466	−	0.378394i	−0.954339	+	0.298725i	$0.903439\pi$
$648$	−4.78012	−	1.28083i	−0.187781	−	0.0503158i
$649$	−0.650527	+	1.12675i	−0.0255354	+	0.0442287i
$650$	−3.81220	+	4.49793i	−0.149527	+	0.176423i
$651$		0			0
$652$	9.06793	+	9.06793i	0.355127	+	0.355127i
$653$	−2.47825	+	4.29246i	−0.0969816	+	0.167977i	−0.910434	−	0.413655i	$-0.864252\pi$
$653$	−2.47825	+	4.29246i	−0.0969816	+	0.167977i	0.813452	+	0.581632i	$0.197585\pi$
$654$	2.28329	+	3.95478i	0.0892839	+	0.154644i
$655$	−2.00806	+	7.49418i	−0.0784614	+	0.292822i
$656$	−0.972695	−	3.63015i	−0.0379774	−	0.141733i
$657$	−0.153832	−	0.153832i	−0.00600155	−	0.00600155i
$658$		0			0
$659$	26.1514			1.01871			0.509357	−	0.860555i	$-0.329883\pi$
$659$	26.1514			1.01871			0.509357	+	0.860555i	$0.329883\pi$
$660$	−2.20334	−	1.27210i	−0.0857649	−	0.0495164i
$661$	−8.15894	+	30.4496i	−0.317346	+	1.18435i	0.604439	+	0.796651i	$0.293397\pi$
$661$	−8.15894	+	30.4496i	−0.317346	+	1.18435i	−0.921785	+	0.387701i	$0.873269\pi$
$662$	0.562690	−	0.324869i	0.0218696	−	0.0126264i
$663$	−29.5232	−	13.9447i	−1.14659	−	0.541568i
$664$			36.4861i			1.41594i
$665$		0			0
$666$	−3.44358			−0.133436
$667$	13.6390	+	7.87447i	0.528103	+	0.304901i
$668$	−20.3845	−	5.46200i	−0.788699	−	0.211331i
$669$	1.28905	−	4.81079i	0.0498375	−	0.185996i
$670$	9.96600	−	2.67038i	0.385020	−	0.103166i
$671$	4.24387	+	4.24387i	0.163833	+	0.163833i
$672$		0			0
$673$			1.38550i			0.0534072i	0.999643	+	0.0267036i	$0.00850104\pi$
$673$			1.38550i			0.0534072i	−0.999643	+	0.0267036i	$0.991499\pi$
$674$	3.92488	+	14.6479i	0.151181	+	0.564214i
$675$	7.92238	+	13.7220i	0.304933	+	0.528159i
$676$	−16.8193	+	13.8324i	−0.646896	+	0.532017i
$677$	−12.2861	−	7.09338i	−0.472193	−	0.272621i	0.244964	−	0.969532i	$-0.421224\pi$
$677$	−12.2861	−	7.09338i	−0.472193	−	0.272621i	−0.717157	+	0.696911i	$0.754557\pi$
$678$	0.798290	−	0.798290i	0.0306582	−	0.0306582i
$679$		0			0
$680$		−	22.4690i		−	0.861646i
$681$	33.0923	−	8.86704i	1.26810	−	0.339786i
$682$	0.835604	+	0.223899i	0.0319969	+	0.00857355i
$683$	−37.2764	−	9.98818i	−1.42634	−	0.382187i	−0.538613	−	0.842554i	$-0.681051\pi$
$683$	−37.2764	−	9.98818i	−1.42634	−	0.382187i	−0.887729	+	0.460367i	$0.847718\pi$
$684$	12.1792	−	3.26340i	0.465682	−	0.124779i
$685$		−	26.2506i		−	1.00298i
$686$		0			0
$687$	16.2750	−	16.2750i	0.620931	−	0.620931i
$688$	−16.1774	−	9.34003i	−0.616758	−	0.356085i
$689$	−20.1112	−	29.0257i	−0.766177	−	1.10579i
$690$	−2.27821	−	3.94597i	−0.0867299	−	0.150221i
$691$	5.92730	+	22.1210i	0.225485	+	0.841522i	0.982210	+	0.187788i	$0.0601318\pi$
$691$	5.92730	+	22.1210i	0.225485	+	0.841522i	−0.756724	+	0.653734i	$0.773201\pi$
$692$		−	11.9862i		−	0.455647i
$693$		0			0
$694$	8.14411	+	8.14411i	0.309146	+	0.309146i
$695$	−9.79643	+	2.62495i	−0.371600	+	0.0995698i
$696$	2.36806	−	8.83771i	0.0897610	−	0.334993i
$697$	12.3703	+	3.31462i	0.468560	+	0.125550i
$698$	−1.61575	−	0.932852i	−0.0611569	−	0.0353090i
$699$	19.9947			0.756271
$700$		0			0
$701$		−	15.2981i		−	0.577800i	−0.957359	−	0.288900i	$-0.906711\pi$
$701$		−	15.2981i		−	0.577800i	0.957359	−	0.288900i	$-0.0932895\pi$
$702$	−3.82902	−	10.6839i	−0.144517	−	0.403239i
$703$	−17.9510	+	10.3640i	−0.677034	+	0.390886i
$704$	−0.267506	+	0.998347i	−0.0100820	+	0.0376266i
$705$	−5.55749	−	3.20862i	−0.209307	−	0.120844i
$706$	8.65808			0.325851
$707$		0			0
$708$	−2.24965	−	2.24965i	−0.0845469	−	0.0845469i
$709$	−1.00330	−	3.74438i	−0.0376798	−	0.140623i	0.944523	−	0.328444i	$-0.106524\pi$
$709$	−1.00330	−	3.74438i	−0.0376798	−	0.140623i	−0.982203	+	0.187821i	$0.939858\pi$
$710$	0.446473	−	1.66626i	0.0167558	−	0.0625336i
$711$	3.55395	+	6.15563i	0.133284	+	0.230854i
$712$	−10.2057	+	17.6767i	−0.382474	+	0.662464i
$713$	−5.64878	−	5.64878i	−0.211548	−	0.211548i
$714$		0			0
$715$	−0.365420	−	4.42842i	−0.0136659	−	0.165614i
$716$	−11.5684	+	20.0371i	−0.432332	+	0.748820i
$717$	−1.42032	−	0.380573i	−0.0530427	−	0.0142127i
$718$	−6.84051	−	11.8481i	−0.255285	−	0.442167i
$719$	2.99728	−	5.19144i	0.111780	−	0.193608i	−0.804708	−	0.593671i	$-0.797678\pi$
$719$	2.99728	−	5.19144i	0.111780	−	0.193608i	0.916488	+	0.400062i	$0.131012\pi$
$720$	−3.29683	+	3.29683i	−0.122865	+	0.122865i
$721$		0			0
$722$	−2.75035	+	2.75035i	−0.102358	+	0.102358i
$723$	−6.90014	−	25.7517i	−0.256619	−	0.957715i
$724$	6.61597	−	3.81973i	0.245881	−	0.141959i
$725$	−8.80622	+	5.08427i	−0.327055	+	0.188825i
$726$	−6.97989	+	1.87026i	−0.259048	+	0.0694117i
$727$	14.6184			0.542168			0.271084	−	0.962556i	$-0.412618\pi$
$727$	14.6184			0.542168			0.271084	+	0.962556i	$0.412618\pi$
$728$		0			0
$729$	−23.9175			−0.885833
$730$	−0.118041	+	0.0316289i	−0.00436889	+	0.00117064i
$731$	55.1272	−	31.8277i	2.03895	−	1.17719i
$732$	−12.7099	+	7.33804i	−0.469770	+	0.271222i
$733$	−10.2738	−	38.3423i	−0.379471	−	1.41621i	−0.846701	−	0.532069i	$-0.821415\pi$
$733$	−10.2738	−	38.3423i	−0.379471	−	1.41621i	0.467230	−	0.884136i	$-0.345252\pi$
$734$	−3.94881	+	3.94881i	−0.145753	+	0.145753i
$735$		0			0
$736$	−17.0254	+	17.0254i	−0.627564	+	0.627564i
$737$	5.23449	−	9.06640i	0.192815	−	0.333965i
$738$	0.735703	+	1.27427i	0.0270816	+	0.0469067i
$739$	22.6799	+	6.07706i	0.834294	+	0.223548i	0.650586	−	0.759432i	$-0.274523\pi$
$739$	22.6799	+	6.07706i	0.834294	+	0.223548i	0.183708	+	0.982981i	$0.441190\pi$
$740$	4.98710	−	8.63791i	0.183329	−	0.317536i
$741$	−17.2259	−	14.5997i	−0.632809	−	0.536335i
$742$		0			0
$743$	−2.87636	−	2.87636i	−0.105523	−	0.105523i	0.652374	−	0.757897i	$-0.273773\pi$
$743$	−2.87636	−	2.87636i	−0.105523	−	0.105523i	−0.757897	+	0.652374i	$0.773773\pi$
$744$	−2.32051	+	4.01925i	−0.0850742	+	0.147353i
$745$	11.3186	+	19.6043i	0.414680	+	0.718247i
$746$	0.880297	−	3.28531i	0.0322300	−	0.120284i
$747$	6.67742	+	24.9205i	0.244314	+	0.911793i
$748$	−7.34804	−	7.34804i	−0.268671	−	0.268671i
$749$		0			0
$750$	8.06888			0.294634
$751$	39.7885	+	22.9719i	1.45190	+	0.838257i	0.998590	−	0.0530936i	$-0.0169082\pi$
$751$	39.7885	+	22.9719i	1.45190	+	0.838257i	0.453314	+	0.891351i	$0.350242\pi$
$752$	−1.99078	+	7.42968i	−0.0725961	+	0.270932i
$753$	29.2828	−	16.9064i	1.06713	−	0.616105i
$754$	6.85652	−	2.45731i	0.249700	−	0.0894900i
$755$		−	12.6780i		−	0.461400i
$756$		0			0
$757$	−24.7889			−0.900969			−0.450484	−	0.892784i	$-0.648749\pi$
$757$	−24.7889			−0.900969			−0.450484	+	0.892784i	$0.648749\pi$
$758$	1.49469	+	0.862958i	0.0542895	+	0.0313440i
$759$	−4.46575	−	1.19659i	−0.162096	−	0.0434336i
$760$	4.02181	−	15.0096i	0.145886	−	0.544455i
$761$	−14.8146	+	3.96956i	−0.537029	+	0.143897i	−0.517132	−	0.855905i	$-0.673000\pi$
$761$	−14.8146	+	3.96956i	−0.537029	+	0.143897i	−0.0198970	+	0.999802i	$0.506334\pi$
$762$	−0.769443	−	0.769443i	−0.0278740	−	0.0278740i
$763$		0			0
$764$		−	6.20711i		−	0.224565i
$765$	−4.11211	−	15.3466i	−0.148674	−	0.554857i
$766$	1.17343	+	2.03245i	0.0423979	+	0.0734353i
$767$	0.991874	−	5.46725i	0.0358145	−	0.197411i
$768$	4.40364	+	2.54244i	0.158903	+	0.0917425i
$769$	−4.63670	+	4.63670i	−0.167204	+	0.167204i	−0.785749	−	0.618545i	$-0.787722\pi$
$769$	−4.63670	+	4.63670i	−0.167204	+	0.167204i	0.618545	+	0.785749i	$0.287722\pi$
$770$		0			0
$771$			25.3538i			0.913094i
$772$	−39.0168	+	10.4545i	−1.40425	+	0.376267i
$773$	7.76446	+	2.08048i	0.279268	+	0.0748297i	0.395734	−	0.918365i	$-0.370490\pi$
$773$	7.76446	+	2.08048i	0.279268	+	0.0748297i	−0.116466	+	0.993195i	$0.537157\pi$
$774$	7.06438	+	1.89289i	0.253924	+	0.0680387i
$775$	4.98219	−	1.33498i	0.178966	−	0.0479537i
$776$		−	17.9466i		−	0.644244i
$777$		0			0
$778$	7.03032	−	7.03032i	0.252049	−	0.252049i
$779$	7.67026	+	4.42842i	0.274815	+	0.158665i
$780$	10.6911	+	1.93960i	0.382805	+	0.0694487i
$781$	−0.875177	−	1.51585i	−0.0313163	−	0.0542414i
$782$	−4.81676	−	17.9764i	−0.172247	−	0.642835i
$783$		−	19.5732i		−	0.699491i
$784$		0			0
$785$	−10.0102	−	10.0102i	−0.357281	−	0.357281i
$786$	3.60616	−	0.966266i	0.128627	−	0.0344656i
$787$	−3.16854	+	11.8252i	−0.112946	+	0.421522i	−0.999125	−	0.0418220i	$-0.986684\pi$
$787$	−3.16854	+	11.8252i	−0.112946	+	0.421522i	0.886179	+	0.463344i	$0.153350\pi$
$788$	18.3476	+	4.91622i	0.653606	+	0.175133i
$789$	25.4621	+	14.7006i	0.906476	+	0.523354i
$790$	3.99272			0.142055
$791$		0			0
$792$		−	2.61942i		−	0.0930771i
$793$	−23.1767	−	10.9471i	−0.823029	−	0.388742i
$794$	−7.11125	+	4.10568i	−0.252369	+	0.145705i
$795$	−4.56022	+	17.0190i	−0.161734	+	0.603600i
$796$	−6.63782	−	3.83235i	−0.235271	−	0.135834i
$797$	−28.1163			−0.995931			−0.497966	−	0.867197i	$-0.665919\pi$
$797$	−28.1163			−0.995931			−0.497966	+	0.867197i	$0.665919\pi$
$798$		0			0
$799$	−18.5340	−	18.5340i	−0.655685	−	0.655685i
$800$	−4.02361	−	15.0163i	−0.142256	−	0.530907i
$801$	−3.73554	+	13.9412i	−0.131989	+	0.492588i
$802$	6.28527	+	10.8864i	0.221941	+	0.384413i
$803$	−0.0619991	+	0.107386i	−0.00218790	+	0.00378956i
$804$	18.1018	+	18.1018i	0.638403	+	0.638403i
$805$		0			0
$806$	−3.68204	+	0.303831i	−0.129694	+	0.0107020i
$807$	−0.682995	+	1.18298i	−0.0240426	+	0.0416430i
$808$	26.0418	+	6.97789i	0.916148	+	0.245481i
$809$	−0.343675	−	0.595262i	−0.0120830	−	0.0209283i	0.859921	−	0.510428i	$-0.170513\pi$
$809$	−0.343675	−	0.595262i	−0.0120830	−	0.0209283i	−0.872004	+	0.489499i	$0.837180\pi$
$810$	−0.982828	+	1.70231i	−0.0345330	+	0.0598130i
$811$	−0.354016	+	0.354016i	−0.0124312	+	0.0124312i	−0.713295	−	0.700864i	$-0.752798\pi$
$811$	−0.354016	+	0.354016i	−0.0124312	+	0.0124312i	0.700864	+	0.713295i	$0.252798\pi$
$812$		0			0
$813$	−25.7440	+	25.7440i	−0.902882	+	0.902882i
$814$	0.507997	+	1.89587i	0.0178053	+	0.0664502i
$815$	9.67809	−	5.58765i	0.339009	−	0.195727i
$816$	16.9109	−	9.76353i	0.592001	−	0.341792i
$817$	42.5227	−	11.3939i	1.48768	−	0.398623i
$818$	−1.45028			−0.0507078
$819$		0			0
$820$	−4.26187			−0.148831
$821$	−28.5189	+	7.64163i	−0.995318	+	0.266695i	−0.719483	−	0.694510i	$-0.755621\pi$
$821$	−28.5189	+	7.64163i	−0.995318	+	0.266695i	−0.275835	+	0.961205i	$0.588954\pi$
$822$	−10.9393	+	6.31582i	−0.381553	+	0.220290i
$823$	8.97295	−	5.18053i	0.312777	−	0.180582i	−0.335391	−	0.942079i	$-0.608869\pi$
$823$	8.97295	−	5.18053i	0.312777	−	0.180582i	0.648169	+	0.761497i	$0.275535\pi$
$824$	3.31562	+	12.3741i	0.115505	+	0.431071i
$825$	2.11078	−	2.11078i	0.0734880	−	0.0734880i
$826$		0			0
$827$	33.3235	−	33.3235i	1.15877	−	1.15877i	0.174030	−	0.984740i	$-0.444321\pi$
$827$	33.3235	−	33.3235i	1.15877	−	1.15877i	0.984740	−	0.174030i	$-0.0556789\pi$
$828$	−5.51270	+	9.54827i	−0.191579	+	0.331825i
$829$	9.93234	+	17.2033i	0.344964	+	0.597496i	0.985347	−	0.170560i	$-0.0545577\pi$
$829$	9.93234	+	17.2033i	0.344964	+	0.597496i	−0.640383	+	0.768056i	$0.721224\pi$
$830$	13.9986	+	3.75090i	0.485897	+	0.130196i
$831$	−15.9143	+	27.5644i	−0.552061	+	0.956197i
$832$	−0.363005	−	4.39916i	−0.0125849	−	0.152513i
$833$		0			0
$834$	3.45088	+	3.45088i	0.119494	+	0.119494i
$835$	−9.19521	+	15.9266i	−0.318214	+	0.551162i
$836$	−3.59334	−	6.22384i	−0.124278	−	0.215256i
$837$	−2.56967	+	9.59014i	−0.0888208	+	0.331484i
$838$	2.43503	+	9.08765i	0.0841166	+	0.313928i
$839$	−16.2048	−	16.2048i	−0.559453	−	0.559453i	0.369698	−	0.929152i	$-0.379461\pi$
$839$	−16.2048	−	16.2048i	−0.559453	−	0.559453i	−0.929152	+	0.369698i	$0.879461\pi$
$840$		0			0
$841$	−16.4387			−0.566850
$842$	−5.95798	−	3.43984i	−0.205326	−	0.118545i
$843$	5.44833	−	20.3334i	0.187650	−	0.700321i
$844$	0.861761	−	0.497538i	0.0296630	−	0.0171260i
$845$	7.84986	+	17.2774i	0.270043	+	0.594359i
$846$		−	3.01147i		−	0.103536i
$847$		0			0
$848$	21.1187			0.725220
$849$	16.4007	+	9.46898i	0.562872	+	0.324974i
$850$	11.6067	+	3.11002i	0.398108	+	0.106673i
$851$	4.69109	−	17.5074i	0.160809	−	0.600146i
$852$	4.13431	−	1.10779i	0.141639	−	0.0379521i
$853$	−12.4778	−	12.4778i	−0.427232	−	0.427232i	0.460452	−	0.887684i	$-0.347687\pi$
$853$	−12.4778	−	12.4778i	−0.427232	−	0.427232i	−0.887684	+	0.460452i	$0.847687\pi$
$854$		0			0
$855$		−	10.9878i		−	0.375774i
$856$	−4.80841	−	17.9452i	−0.164348	−	0.613355i
$857$	−13.6250	−	23.5993i	−0.465422	−	0.806135i	0.533798	−	0.845612i	$-0.320764\pi$
$857$	−13.6250	−	23.5993i	−0.465422	−	0.806135i	−0.999220	+	0.0394767i	$0.987431\pi$
$858$	−1.75752	+	1.21775i	−0.0600008	+	0.0415732i
$859$	19.7310	+	11.3917i	0.673214	+	0.388680i	0.797293	−	0.603592i	$-0.206264\pi$
$859$	19.7310	+	11.3917i	0.673214	+	0.388680i	−0.124079	+	0.992272i	$0.539598\pi$
$860$	−14.9790	+	14.9790i	−0.510779	+	0.510779i
$861$		0			0
$862$		−	19.5125i		−	0.664597i
$863$	28.8487	−	7.72999i	0.982021	−	0.263132i	0.268126	−	0.963384i	$-0.413596\pi$
$863$	28.8487	−	7.72999i	0.982021	−	0.263132i	0.713896	+	0.700252i	$0.246929\pi$
$864$	28.9046	+	7.74497i	0.983356	+	0.263489i
$865$	−10.0893	−	2.70342i	−0.343047	−	0.0919191i
$866$	−19.7487	+	5.29165i	−0.671089	+	0.179818i
$867$			45.5909i			1.54835i
$868$		0			0
$869$	2.86471	−	2.86471i	0.0971787	−	0.0971787i
$870$	−3.14730	−	1.81710i	−0.106704	−	0.0616054i
$871$	−7.98114	+	43.9924i	−0.270431	+	1.49063i
$872$	−6.80900	−	11.7935i	−0.230582	−	0.399380i
$873$	−3.28445	−	12.2577i	−0.111162	−	0.414861i
$874$		−	12.8707i		−	0.435356i
$875$		0			0
$876$	−0.214405	−	0.214405i	−0.00724406	−	0.00724406i
$877$	−19.1865	+	5.14100i	−0.647881	+	0.173599i	−0.567771	−	0.823187i	$-0.692194\pi$
$877$	−19.1865	+	5.14100i	−0.647881	+	0.173599i	−0.0801105	+	0.996786i	$0.525527\pi$
$878$	−1.55336	+	5.79723i	−0.0524235	+	0.195647i
$879$	−16.4757	−	4.41464i	−0.555710	−	0.148902i
$880$	2.30142	+	1.32873i	0.0775809	+	0.0447913i
$881$	−13.3800			−0.450782			−0.225391	−	0.974268i	$-0.572366\pi$
$881$	−13.3800			−0.450782			−0.225391	+	0.974268i	$0.572366\pi$
$882$		0			0
$883$			1.63893i			0.0551545i	0.999620	+	0.0275773i	$0.00877923\pi$
$883$			1.63893i			0.0551545i	−0.999620	+	0.0275773i	$0.991221\pi$
$884$	40.1293	+	18.9543i	1.34969	+	0.637502i
$885$	−2.40102	+	1.38623i	−0.0807094	+	0.0465976i
$886$	−1.89737	+	7.08107i	−0.0637433	+	0.237893i
$887$	−18.5501	−	10.7099i	−0.622851	−	0.359603i	0.155127	−	0.987895i	$-0.450421\pi$
$887$	−18.5501	−	10.7099i	−0.622851	−	0.359603i	−0.777978	+	0.628291i	$0.783755\pi$
$888$	−10.5299			−0.353359
$889$		0			0
$890$	5.73283	+	5.73283i	0.192165	+	0.192165i
$891$	0.516215	+	1.92654i	0.0172939	+	0.0645416i
$892$	−1.75213	+	6.53905i	−0.0586657	+	0.218943i
$893$	−9.06348	−	15.6984i	−0.303298	−	0.525327i
$894$	5.44643	−	9.43349i	0.182156	−	0.315503i
$895$	14.2569	+	14.2569i	0.476555	+	0.476555i
$896$		0			0
$897$	19.6781	−	1.62378i	0.657032	−	0.0542163i
$898$	3.88954	−	6.73687i	0.129795	−	0.224812i
$899$	−6.15457	−	1.64911i	−0.205267	−	0.0550010i
$900$	−3.55936	−	6.16499i	−0.118645	−	0.205500i
$901$	−35.9828	+	62.3240i	−1.19876	+	2.07631i
$902$	0.593023	−	0.593023i	0.0197455	−	0.0197455i
$903$		0			0
$904$	−2.38058	+	2.38058i	−0.0791769	+	0.0791769i
$905$	−1.72304	−	6.43047i	−0.0572758	−	0.213756i
$906$	−5.28326	+	3.05029i	−0.175524	+	0.101339i
$907$	−2.25159	+	1.29995i	−0.0747627	+	0.0431643i	−0.536915	−	0.843636i	$-0.680411\pi$
$907$	−2.25159	+	1.29995i	−0.0747627	+	0.0431643i	0.462153	+	0.886800i	$0.347077\pi$
$908$	−44.9805	+	12.0525i	−1.49273	+	0.399976i
$909$	19.0639			0.632311
$910$		0			0
$911$	41.2579			1.36694			0.683468	−	0.729981i	$-0.260471\pi$
$911$	41.2579			1.36694			0.683468	+	0.729981i	$0.260471\pi$
$912$	13.0443	−	3.49522i	0.431941	−	0.115738i
$913$	12.7350	−	7.35253i	0.421466	−	0.243333i
$914$	15.4425	−	8.91573i	0.510792	−	0.294906i
$915$	3.31011	+	12.3535i	0.109429	+	0.408394i
$916$	−22.1218	+	22.1218i	−0.730924	+	0.730924i
$917$		0			0
$918$	−16.3552	+	16.3552i	−0.539802	+	0.539802i
$919$	24.1520	−	41.8324i	0.796700	−	1.37992i	−0.125054	−	0.992150i	$-0.539910\pi$
$919$	24.1520	−	41.8324i	0.796700	−	1.37992i	0.921754	−	0.387775i	$-0.126756\pi$
$920$	6.79384	+	11.7673i	0.223986	+	0.387955i
$921$	−13.7057	−	3.67243i	−0.451618	−	0.121011i
$922$	0.239007	−	0.413972i	0.00787128	−	0.0136335i
$923$	5.70266	+	4.83327i	0.187705	+	0.159089i
$924$		0			0
$925$	8.27504	+	8.27504i	0.272082	+	0.272082i
$926$	0.995875	−	1.72491i	0.0327265	−	0.0566840i
$927$	4.52923	+	7.84485i	0.148759	+	0.257659i
$928$	−4.97042	+	18.5499i	−0.163162	+	0.608929i
$929$	7.02052	+	26.2009i	0.230336	+	0.859624i	0.980196	+	0.198029i	$0.0634539\pi$
$929$	7.02052	+	26.2009i	0.230336	+	0.859624i	−0.749861	+	0.661596i	$0.769879\pi$
$930$	1.30350	+	1.30350i	0.0427435	+	0.0427435i
$931$		0			0
$932$	−27.1777			−0.890237
$933$	34.6669	+	20.0149i	1.13494	+	0.655259i
$934$	1.97471	−	7.36970i	0.0646143	−	0.241144i
$935$	−7.84247	+	4.52785i	−0.256476	+	0.148077i
$936$	3.77422	+	10.5310i	0.123364	+	0.344217i
$937$			2.66644i			0.0871088i	0.999051	+	0.0435544i	$0.0138682\pi$
$937$			2.66644i			0.0871088i	−0.999051	+	0.0435544i	$0.986132\pi$
$938$		0			0
$939$	−24.3209			−0.793683
$940$	7.55399	+	4.36130i	0.246384	+	0.142250i
$941$	43.6215	+	11.6883i	1.42202	+	0.381029i	0.886200	−	0.463303i	$-0.153336\pi$
$941$	43.6215	+	11.6883i	1.42202	+	0.381029i	0.535820	+	0.844332i	$0.320003\pi$
$942$	−1.76310	+	6.57996i	−0.0574448	+	0.214387i
$943$	−7.48072	+	2.00445i	−0.243606	+	0.0652739i
$944$	2.34979	+	2.34979i	0.0764791	+	0.0764791i
$945$		0			0
$946$		−	4.16854i		−	0.135531i
$947$	−3.08574	−	11.5162i	−0.100273	−	0.374225i	0.897493	−	0.441029i	$-0.145386\pi$
$947$	−3.08574	−	11.5162i	−0.100273	−	0.374225i	−0.997766	+	0.0668042i	$0.978720\pi$
$948$	4.95336	+	8.57947i	0.160878	+	0.278648i
$949$	0.0945314	−	0.521061i	0.00306862	−	0.0169144i
$950$	7.19679	+	4.15507i	0.233495	+	0.134808i
$951$	10.0055	−	10.0055i	0.324450	−	0.324450i
$952$		0			0
$953$		−	20.8846i		−	0.676519i	−0.941053	−	0.338259i	$-0.890162\pi$
$953$		−	20.8846i		−	0.676519i	0.941053	−	0.338259i	$-0.109838\pi$
$954$	−7.98662	+	2.14001i	−0.258577	+	0.0692854i
$955$	−5.22480	−	1.39998i	−0.169070	−	0.0453023i
$956$	1.93056	+	0.517291i	0.0624387	+	0.0167304i
$957$	−3.56188	+	0.954403i	−0.115139	+	0.0308515i
$958$			7.14032i			0.230693i
$959$		0			0
$960$	−1.55737	+	1.55737i	−0.0502640	+	0.0502640i
$961$	−24.0478	−	13.8840i	−0.775735	−	0.447871i
$962$	−4.77402	−	6.89014i	−0.153920	−	0.222147i
$963$	−6.56841	−	11.3768i	−0.211664	−	0.366613i
$964$	9.37898	+	35.0028i	0.302077	+	1.12737i
$965$			35.2001i			1.13313i
$966$		0			0
$967$	20.9628	+	20.9628i	0.674117	+	0.674117i	0.958663	−	0.284545i	$-0.0918426\pi$
$967$	20.9628	+	20.9628i	0.674117	+	0.674117i	−0.284545	+	0.958663i	$0.591843\pi$
$968$	20.8147	−	5.57729i	0.669010	−	0.179261i
$969$	−11.9106	+	44.4508i	−0.382622	+	1.42796i
$970$	−6.88552	−	1.84497i	−0.221081	−	0.0592384i
$971$	11.0608	+	6.38594i	0.354957	+	0.204935i	0.666866	−	0.745177i	$-0.267635\pi$
$971$	11.0608	+	6.38594i	0.354957	+	0.204935i	−0.311909	+	0.950112i	$0.600969\pi$
$972$	22.8761			0.733753
$973$		0			0
$974$		−	14.4934i		−	0.464399i
$975$	−5.44477	+	11.5274i	−0.174372	+	0.369174i
$976$	13.2756	−	7.66469i	0.424943	−	0.245341i
$977$	−10.1836	+	38.0058i	−0.325803	+	1.21591i	0.587699	+	0.809079i	$0.300034\pi$
$977$	−10.1836	+	38.0058i	−0.325803	+	1.21591i	−0.913502	+	0.406834i	$0.866633\pi$
$978$	−4.65704	−	2.68875i	−0.148916	−	0.0859766i
$979$	8.22642			0.262918
$980$		0			0
$981$	−6.80900	−	6.80900i	−0.217395	−	0.217395i
$982$	2.87581	+	10.7327i	0.0917707	+	0.342493i
$983$	−13.1392	+	49.0362i	−0.419076	+	1.56401i	0.357453	+	0.933931i	$0.383645\pi$
$983$	−13.1392	+	49.0362i	−0.419076	+	1.56401i	−0.776529	+	0.630082i	$0.783021\pi$
$984$	2.24965	+	3.89650i	0.0717161	+	0.124216i
$985$	8.27640	−	14.3351i	0.263708	−	0.456755i
$986$	−10.4961	−	10.4961i	−0.334264	−	0.334264i
$987$		0			0
$988$	23.4142	+	19.8446i	0.744906	+	0.631342i
$989$	−19.2472	+	33.3371i	−0.612025	+	1.06006i
$990$	−1.00499	−	0.269286i	−0.0319406	−	0.00855847i
$991$	4.34709	+	7.52938i	0.138090	+	0.239179i	0.926774	−	0.375620i	$-0.122570\pi$
$991$	4.34709	+	7.52938i	0.138090	+	0.239179i	−0.788684	+	0.614799i	$0.789237\pi$
$992$	4.87063	−	8.43618i	0.154643	−	0.267849i
$993$	0.993391	−	0.993391i	0.0315243	−	0.0315243i
$994$		0			0
$995$	−4.72298	+	4.72298i	−0.149728	+	0.149728i
$996$	9.30672	+	34.7332i	0.294895	+	1.10056i
$997$	23.0079	−	13.2836i	0.728668	−	0.420697i	−0.0892664	−	0.996008i	$-0.528452\pi$
$997$	23.0079	−	13.2836i	0.728668	−	0.420697i	0.817935	+	0.575311i	$0.195119\pi$
$998$	−7.13078	+	4.11696i	−0.225721	+	0.130320i
$999$	−21.7587	+	5.83023i	−0.688415	+	0.184460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bc.a.411.4		24
7.2	even	3		91.2.i.a.34.4	yes	12
7.3	odd	6	inner	637.2.bc.a.619.4		24
7.4	even	3	inner	637.2.bc.a.619.3		24
7.5	odd	6		91.2.i.a.34.3	✓	12
7.6	odd	2	inner	637.2.bc.a.411.3		24
13.5	odd	4	inner	637.2.bc.a.460.4		24
21.2	odd	6		819.2.y.h.307.3		12
21.5	even	6		819.2.y.h.307.4		12
91.5	even	12		91.2.i.a.83.3	yes	12
91.18	odd	12	inner	637.2.bc.a.31.3		24
91.31	even	12	inner	637.2.bc.a.31.4		24
91.44	odd	12		91.2.i.a.83.4	yes	12
91.83	even	4	inner	637.2.bc.a.460.3		24
273.5	odd	12		819.2.y.h.811.3		12
273.44	even	12		819.2.y.h.811.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.3	✓	12	7.5	odd	6
91.2.i.a.34.4	yes	12	7.2	even	3
91.2.i.a.83.3	yes	12	91.5	even	12
91.2.i.a.83.4	yes	12	91.44	odd	12
637.2.bc.a.31.3		24	91.18	odd	12	inner
637.2.bc.a.31.4		24	91.31	even	12	inner
637.2.bc.a.411.3		24	7.6	odd	2	inner
637.2.bc.a.411.4		24	1.1	even	1	trivial
637.2.bc.a.460.3		24	91.83	even	4	inner
637.2.bc.a.460.4		24	13.5	odd	4	inner
637.2.bc.a.619.3		24	7.4	even	3	inner
637.2.bc.a.619.4		24	7.3	odd	6	inner
819.2.y.h.307.3		12	21.2	odd	6
819.2.y.h.307.4		12	21.5	even	6
819.2.y.h.811.3		12	273.5	odd	12
819.2.y.h.811.4		12	273.44	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.550552 - 0.147520i) q^{2} +(1.06729 - 0.616199i) q^{3} +(-1.45071 + 0.837565i) q^{4} +(0.377817 + 1.41003i) q^{5} +(0.496696 - 0.496696i) q^{6} +(-1.48119 + 1.48119i) q^{8} +(-0.740597 + 1.28275i) q^{9} +O(q^{10})\)	\(q+(0.550552 - 0.147520i) q^{2} +(1.06729 - 0.616199i) q^{3} +(-1.45071 + 0.837565i) q^{4} +(0.377817 + 1.41003i) q^{5} +(0.496696 - 0.496696i) q^{6} +(-1.48119 + 1.48119i) q^{8} +(-0.740597 + 1.28275i) q^{9} +(0.416015 + 0.720559i) q^{10} +(0.815474 + 0.218506i) q^{11} +(-1.03221 + 1.78785i) q^{12} +(-3.59334 + 0.296512i) q^{13} +(1.27210 + 1.27210i) q^{15} +(1.07816 - 1.86743i) q^{16} +(3.67402 + 6.36359i) q^{17} +(-0.218506 + 0.815474i) q^{18} +(1.31525 + 4.90859i) q^{19} +(-1.72909 - 1.72909i) q^{20} +0.481194 q^{22} +(-3.84826 - 2.22179i) q^{23} +(-0.668151 + 2.49357i) q^{24} +(2.48469 - 1.43453i) q^{25} +(-1.93458 + 0.693334i) q^{26} +5.52262i q^{27} -3.54420 q^{29} +(0.888016 + 0.512696i) q^{30} +(1.73652 + 0.465299i) q^{31} +(1.40241 - 5.23387i) q^{32} +(1.00499 - 0.269286i) q^{33} +(2.96149 + 2.96149i) q^{34} -2.48119i q^{36} +(1.05570 + 3.93993i) q^{37} +(1.44823 + 2.50841i) q^{38} +(-3.65242 + 2.53068i) q^{39} +(-2.64815 - 1.52891i) q^{40} +(1.23240 - 1.23240i) q^{41} -8.66291i q^{43} +(-1.36603 + 0.366025i) q^{44} +(-2.08853 - 0.559620i) q^{45} +(-2.44642 - 0.655517i) q^{46} +(-3.44553 + 0.923226i) q^{47} -2.65745i q^{48} +(1.15633 - 1.15633i) q^{50} +(7.84247 + 4.52785i) q^{51} +(4.96453 - 3.43981i) q^{52} +(4.89692 + 8.48172i) q^{53} +(0.814696 + 3.04049i) q^{54} +1.23240i q^{55} +(4.42842 + 4.42842i) q^{57} +(-1.95126 + 0.522840i) q^{58} +(-0.398865 + 1.48858i) q^{59} +(-2.91091 - 0.779975i) q^{60} +(6.15660 + 3.55452i) q^{61} +1.02469 q^{62} +1.22425i q^{64} +(-1.77571 - 4.95469i) q^{65} +(0.513573 - 0.296512i) q^{66} +(3.20948 - 11.9779i) q^{67} +(-10.6598 - 6.15446i) q^{68} -5.47626 q^{69} +(-1.46604 - 1.46604i) q^{71} +(-0.803037 - 2.99697i) q^{72} +(-0.0380142 + 0.141871i) q^{73} +(1.16243 + 2.01340i) q^{74} +(1.76792 - 3.06212i) q^{75} +(-6.01931 - 6.01931i) q^{76} +(-1.63752 + 1.93207i) q^{78} +(2.39938 - 4.15586i) q^{79} +(3.04049 + 0.814696i) q^{80} +(1.18124 + 2.04597i) q^{81} +(0.496696 - 0.860302i) q^{82} +(12.3165 - 12.3165i) q^{83} +(-7.58475 + 7.58475i) q^{85} +(-1.27795 - 4.76938i) q^{86} +(-3.78268 + 2.18393i) q^{87} +(-1.53152 + 0.884226i) q^{88} +(9.41214 - 2.52198i) q^{89} -1.23240 q^{90} +7.44358 q^{92} +(2.14009 - 0.573434i) q^{93} +(-1.76075 + 1.01657i) q^{94} +(-6.42434 + 3.70910i) q^{95} +(-1.72833 - 6.45021i) q^{96} +(-6.05814 + 6.05814i) q^{97} +(-0.884226 + 0.884226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9	\( 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9} + 8 q^{11} - 8 q^{15} - 16 q^{16} + 8 q^{18} - 32 q^{22} - 8 q^{29} + 16 q^{32} - 12 q^{37} - 40 q^{39} - 12 q^{44} - 24 q^{46} - 56 q^{50} + 12 q^{53} - 16 q^{57} + 44 q^{58} - 44 q^{60} + 40 q^{65} - 60 q^{67} + 28 q^{72} + 48 q^{74} + 88 q^{78} + 4 q^{79} + 92 q^{81} + 24 q^{85} - 36 q^{86} + 48 q^{92} + 28 q^{93} + 24 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9 + 8 * q^11 - 8 * q^15 - 16 * q^16 + 8 * q^18 - 32 * q^22 - 8 * q^29 + 16 * q^32 - 12 * q^37 - 40 * q^39 - 12 * q^44 - 24 * q^46 - 56 * q^50 + 12 * q^53 - 16 * q^57 + 44 * q^58 - 44 * q^60 + 40 * q^65 - 60 * q^67 + 28 * q^72 + 48 * q^74 + 88 * q^78 + 4 * q^79 + 92 * q^81 + 24 * q^85 - 36 * q^86 + 48 * q^92 + 28 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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