LMFDB - Embedded newform 637.2.bc.a.460.4

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			460.4
Character	$\chi$	$=$	637.460
Dual form			637.2.bc.a.619.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.147520 - 0.550552i) q^{2} +(1.06729 - 0.616199i) q^{3} +(1.45071 - 0.837565i) q^{4} +(1.41003 - 0.377817i) q^{5} +(-0.496696 - 0.496696i) q^{6} +(-1.48119 - 1.48119i) q^{8} +(-0.740597 + 1.28275i) q^{9} +O(q^{10})$	\(q+(-0.147520 - 0.550552i) q^{2} +(1.06729 - 0.616199i) q^{3} +(1.45071 - 0.837565i) q^{4} +(1.41003 - 0.377817i) 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} +(-0.218506 + 0.815474i) 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} +(0.815474 + 0.218506i) q^{18} +(4.90859 - 1.31525i) q^{19} +(1.72909 - 1.72909i) q^{20} +0.481194 q^{22} +(3.84826 + 2.22179i) q^{23} +(-2.49357 - 0.668151i) q^{24} +(-2.48469 + 1.43453i) q^{25} +(-0.366844 - 2.02206i) q^{26} +5.52262i q^{27} -3.54420 q^{29} +(-0.888016 - 0.512696i) q^{30} +(0.465299 - 1.73652i) q^{31} +(-5.23387 - 1.40241i) q^{32} +(0.269286 + 1.00499i) q^{33} +(-2.96149 + 2.96149i) q^{34} +2.48119i q^{36} +(-3.93993 + 1.05570i) q^{37} +(-1.44823 - 2.50841i) q^{38} +(4.01784 - 1.89775i) q^{39} +(-2.64815 - 1.52891i) q^{40} +(-1.23240 - 1.23240i) q^{41} +8.66291i q^{43} +(0.366025 + 1.36603i) q^{44} +(-0.559620 + 2.08853i) q^{45} +(0.655517 - 2.44642i) q^{46} +(-0.923226 - 3.44553i) q^{47} -2.65745i q^{48} +(1.15633 + 1.15633i) q^{50} +(-7.84247 - 4.52785i) q^{51} +(5.46122 - 2.57951i) q^{52} +(4.89692 + 8.48172i) q^{53} +(3.04049 - 0.814696i) q^{54} +1.23240i q^{55} +(4.42842 - 4.42842i) q^{57} +(0.522840 + 1.95126i) q^{58} +(-1.48858 - 0.398865i) q^{59} +(0.779975 - 2.91091i) q^{60} +(6.15660 + 3.55452i) q^{61} -1.02469 q^{62} -1.22425i q^{64} +(5.17875 - 0.939533i) q^{65} +(0.513573 - 0.296512i) q^{66} +(-11.9779 - 3.20948i) q^{67} +(-10.6598 - 6.15446i) q^{68} +5.47626 q^{69} +(-1.46604 + 1.46604i) q^{71} +(2.99697 - 0.803037i) q^{72} +(-0.141871 - 0.0380142i) 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} +(0.814696 - 3.04049i) 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} +(4.76938 - 1.27795i) q^{86} +(-3.78268 + 2.18393i) q^{87} +(1.53152 - 0.884226i) q^{88} +(2.52198 + 9.41214i) q^{89} +1.23240 q^{90} +7.44358 q^{92} +(-0.573434 - 2.14009i) q^{93} +(-1.76075 + 1.01657i) q^{94} +(6.42434 - 3.70910i) q^{95} +(-6.45021 + 1.72833i) 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.147520	−	0.550552i	−0.104312	−	0.389299i	0.893954	−	0.448159i	$-0.147920\pi$
$2$	−0.147520	−	0.550552i	−0.104312	−	0.389299i	−0.998266	+	0.0588601i	$0.981253\pi$
$3$	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
$5$	1.41003	−	0.377817i	0.630585	−	0.168965i	0.0706498	−	0.997501i	$-0.477493\pi$
$5$	1.41003	−	0.377817i	0.630585	−	0.168965i	0.559935	+	0.828536i	$0.310826\pi$
$6$	−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
$11$	−0.218506	+	0.815474i	−0.0658819	+	0.245875i	−0.991011	−	0.133777i	$-0.957289\pi$
$11$	−0.218506	+	0.815474i	−0.0658819	+	0.245875i	0.925130	+	0.379652i	$0.123956\pi$
$12$	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	$-0.816615\pi$
$17$	−3.67402	−	6.36359i	−0.891080	−	1.54340i	−0.0524987	−	0.998621i	$-0.516719\pi$
$18$	0.815474	+	0.218506i	0.192209	+	0.0515023i
$19$	4.90859	−	1.31525i	1.12611	−	0.301740i	0.352755	−	0.935716i	$-0.385245\pi$
$19$	4.90859	−	1.31525i	1.12611	−	0.301740i	0.773353	+	0.633976i	$0.218578\pi$
$20$	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	0.844316	−	0.535846i	$-0.180007\pi$
$23$	3.84826	+	2.22179i	0.802417	+	0.463276i	−0.0418988	+	0.999122i	$0.513341\pi$
$24$	−2.49357	−	0.668151i	−0.508998	−	0.136386i
$25$	−2.48469	+	1.43453i	−0.496937	+	0.286907i
$26$	−0.366844	−	2.02206i	−0.0719440	−	0.396558i
$27$			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
$31$	0.465299	−	1.73652i	0.0835702	−	0.311888i	−0.911469	−	0.411368i	$-0.865051\pi$
$31$	0.465299	−	1.73652i	0.0835702	−	0.311888i	0.995040	+	0.0994796i	$0.0317178\pi$
$32$	−5.23387	−	1.40241i	−0.925226	−	0.247913i
$33$	0.269286	+	1.00499i	0.0468767	+	0.174946i
$34$	−2.96149	+	2.96149i	−0.507892	+	0.507892i
$35$		0			0
$36$			2.48119i			0.413532i
$37$	−3.93993	+	1.05570i	−0.647720	+	0.173556i	−0.567698	−	0.823237i	$-0.692166\pi$
$37$	−3.93993	+	1.05570i	−0.647720	+	0.173556i	−0.0800221	+	0.996793i	$0.525499\pi$
$38$	−1.44823	−	2.50841i	−0.234934	−	0.406917i
$39$	4.01784	−	1.89775i	0.643369	−	0.303883i
$40$	−2.64815	−	1.52891i	−0.418709	−	0.241742i
$41$	−1.23240	−	1.23240i	−0.192468	−	0.192468i	0.604294	−	0.796762i	$-0.293455\pi$
$41$	−1.23240	−	1.23240i	−0.192468	−	0.192468i	−0.796762	+	0.604294i	$0.793455\pi$
$42$		0			0
$43$			8.66291i			1.32108i	0.750790	+	0.660541i	$0.229673\pi$
$43$			8.66291i			1.32108i	−0.750790	+	0.660541i	$0.770327\pi$
$44$	0.366025	+	1.36603i	0.0551804	+	0.205936i
$45$	−0.559620	+	2.08853i	−0.0834232	+	0.311340i
$46$	0.655517	−	2.44642i	0.0966507	−	0.360705i
$47$	−0.923226	−	3.44553i	−0.134666	−	0.502582i	−0.999999	−	0.00138385i	$-0.999560\pi$
$47$	−0.923226	−	3.44553i	−0.134666	−	0.502582i	0.865333	−	0.501198i	$-0.167107\pi$
$48$		−	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
$52$	5.46122	−	2.57951i	0.757336	−	0.357713i
$53$	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	$0.598492\pi$
$54$	3.04049	−	0.814696i	0.413758	−	0.110866i
$55$			1.23240i			0.166177i
$56$		0			0
$57$	4.42842	−	4.42842i	0.586559	−	0.586559i
$58$	0.522840	+	1.95126i	0.0686522	+	0.256214i
$59$	−1.48858	−	0.398865i	−0.193797	−	0.0519278i	0.160615	−	0.987017i	$-0.448652\pi$
$59$	−1.48858	−	0.398865i	−0.193797	−	0.0519278i	−0.354412	+	0.935089i	$0.615319\pi$
$60$	0.779975	−	2.91091i	0.100694	−	0.375797i
$61$	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
$65$	5.17875	−	0.939533i	0.642344	−	0.116535i
$66$	0.513573	−	0.296512i	0.0632165	−	0.0364980i
$67$	−11.9779	−	3.20948i	−1.46334	−	0.392100i	−0.562696	−	0.826664i	$-0.690236\pi$
$67$	−11.9779	−	3.20948i	−1.46334	−	0.392100i	−0.900641	+	0.434564i	$0.856902\pi$
$68$	−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	−0.788728	−	0.614742i	$-0.789260\pi$
$71$	−1.46604	+	1.46604i	−0.173986	+	0.173986i	0.614742	+	0.788728i	$0.289260\pi$
$72$	2.99697	−	0.803037i	0.353197	−	0.0946388i
$73$	−0.141871	−	0.0380142i	−0.0166047	−	0.00444922i	0.250507	−	0.968115i	$-0.419403\pi$
$73$	−0.141871	−	0.0380142i	−0.0166047	−	0.00444922i	−0.267112	+	0.963666i	$0.586069\pi$
$74$	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	$0.0796589\pi$
$80$	0.814696	−	3.04049i	0.0910857	−	0.339937i
$81$	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	−0.883528	−	0.468379i	$-0.844838\pi$
$83$	−12.3165	−	12.3165i	−1.35191	−	1.35191i	−0.468379	−	0.883528i	$-0.655162\pi$
$84$		0			0
$85$	−7.58475	−	7.58475i	−0.822682	−	0.822682i
$86$	4.76938	−	1.27795i	0.514295	−	0.137805i
$87$	−3.78268	+	2.18393i	−0.405546	+	0.234142i
$88$	1.53152	−	0.884226i	0.163261	−	0.0942588i
$89$	2.52198	+	9.41214i	0.267329	+	0.997685i	0.960809	+	0.277210i	$0.0894096\pi$
$89$	2.52198	+	9.41214i	0.267329	+	0.997685i	−0.693481	+	0.720475i	$0.743924\pi$
$90$	1.23240			0.129906
$91$		0			0
$92$	7.44358			0.776047
$93$	−0.573434	−	2.14009i	−0.0594623	−	0.221916i
$94$	−1.76075	+	1.01657i	−0.181607	+	0.104851i
$95$	6.42434	−	3.70910i	0.659124	−	0.380545i
$96$	−6.45021	+	1.72833i	−0.658322	+	0.176397i
$97$	6.05814	+	6.05814i	0.615110	+	0.615110i	0.944273	−	0.329163i	$-0.106766\pi$
$97$	6.05814	+	6.05814i	0.615110	+	0.615110i	−0.329163	+	0.944273i	$0.606766\pi$
$98$		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	$0.0545395\pi$
$101$	6.43533	+	11.1463i	0.640339	+	1.10910i	−0.345018	+	0.938596i	$0.612127\pi$
$102$	−1.33590	+	4.98564i	−0.132274	+	0.493651i
$103$	−3.05782	+	5.29630i	−0.301296	+	0.521860i	−0.976430	−	0.215835i	$-0.930753\pi$
$103$	−3.05782	+	5.29630i	−0.301296	+	0.521860i	0.675134	+	0.737695i	$0.264086\pi$
$104$	−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
$109$	6.27958	+	1.68261i	0.601474	+	0.161165i	0.546692	−	0.837334i	$-0.315887\pi$
$109$	6.27958	+	1.68261i	0.601474	+	0.161165i	0.0547823	+	0.998498i	$0.482554\pi$
$110$	0.678499	−	0.181803i	0.0646923	−	0.0173343i
$111$	−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
$115$	6.26559	+	1.67886i	0.584269	+	0.156554i
$116$	−5.14159	+	2.96850i	−0.477385	+	0.275618i
$117$	−3.04157	+	4.38977i	−0.281193	+	0.405834i
$118$			0.878382i			0.0808617i
$119$		0			0
$120$	−3.76845			−0.344011
$121$	8.90903	+	5.14363i	0.809912	+	0.467603i
$122$	1.04872	−	3.91389i	0.0949469	−	0.354347i
$123$	−2.07473	−	0.555921i	−0.187072	−	0.0501258i
$124$	−0.779437	−	2.90890i	−0.0699955	−	0.261227i
$125$	−8.12256	+	8.12256i	−0.726504	+	0.726504i
$126$		0			0
$127$			1.54912i			0.137462i	0.997635	+	0.0687312i	$0.0218951\pi$
$127$			1.54912i			0.137462i	−0.997635	+	0.0687312i	$0.978105\pi$
$128$	−11.1417	+	2.98542i	−0.984801	+	0.263877i
$129$	5.33808	+	9.24582i	0.469992	+	0.814049i
$130$	−1.28123	−	2.71257i	−0.112371	−	0.237908i
$131$	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
$135$	2.08654	+	7.78706i	0.179580	+	0.670203i
$136$	−3.98377	+	14.8676i	−0.341606	+	1.27489i
$137$	4.65426	−	17.3699i	0.397640	−	1.48401i	−0.419595	−	0.907711i	$-0.637828\pi$
$137$	4.65426	−	17.3699i	0.397640	−	1.48401i	0.817236	−	0.576303i	$-0.195505\pi$
$138$	−0.807858	−	3.01497i	−0.0687694	−	0.256651i
$139$			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
$143$	−1.02696	+	2.86548i	−0.0858789	+	0.239624i
$144$	1.59697	+	2.76603i	0.133081	+	0.230503i
$145$	−4.99743	+	1.33906i	−0.415014	+	0.111203i
$146$			0.0837150i			0.00692831i
$147$		0			0
$148$	−4.83146	+	4.83146i	−0.397143	+	0.397143i
$149$	−4.01359	−	14.9789i	−0.328806	−	1.22712i	−0.910430	−	0.413663i	$-0.864249\pi$
$149$	−4.01359	−	14.9789i	−0.328806	−	1.22712i	0.581624	−	0.813458i	$-0.302417\pi$
$150$	1.94666	+	0.521606i	0.158944	+	0.0425889i
$151$	2.24782	−	8.38899i	0.182925	−	0.682686i	−0.812140	−	0.583463i	$-0.801697\pi$
$151$	2.24782	−	8.38899i	0.182925	−	0.682686i	0.995065	−	0.0992236i	$-0.0316359\pi$
$152$	−9.21872	−	5.32243i	−0.747737	−	0.431706i
$153$	10.8839			0.879909
$154$		0			0
$155$		−	2.62435i		−	0.210793i
$156$	4.23921	−	6.11828i	0.339409	−	0.489854i
$157$	−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	$0.459817\pi$
$158$	−2.64197	−	0.707914i	−0.210184	−	0.0563186i
$159$	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
$163$	7.39466	−	1.98139i	0.579194	−	0.155195i	0.0426843	−	0.999089i	$-0.486409\pi$
$163$	7.39466	−	1.98139i	0.579194	−	0.155195i	0.536510	+	0.843894i	$0.319742\pi$
$164$	−2.82006	−	0.755633i	−0.220210	−	0.0590050i
$165$	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	$-0.912068\pi$
$167$	−8.90824	+	8.90824i	−0.689340	+	0.689340i	0.272746	+	0.962086i	$0.412068\pi$
$168$		0			0
$169$	12.8242	+	2.13093i	0.986474	+	0.163918i
$170$	−3.05689	+	5.29470i	−0.234453	+	0.406085i
$171$	−1.94815	+	7.27058i	−0.148978	+	0.555995i
$172$	7.25576	+	12.5673i	0.553246	+	0.958251i
$173$	3.57769	−	6.19674i	0.272007	−	0.471130i	−0.697369	−	0.716712i	$-0.745646\pi$
$173$	3.57769	−	6.19674i	0.272007	−	0.471130i	0.969376	+	0.245583i	$0.0789793\pi$
$174$	1.76039	+	1.76039i	0.133455	+	0.133455i
$175$		0			0
$176$	1.28726	+	1.28726i	0.0970307	+	0.0970307i
$177$	−1.83453	+	0.491560i	−0.137892	+	0.0369479i
$178$	4.80983	−	2.77696i	0.360512	−	0.208142i
$179$	−11.9615	+	6.90597i	−0.894044	+	0.516177i	−0.875263	−	0.483647i	$-0.839312\pi$
$179$	−11.9615	+	6.90597i	−0.894044	+	0.516177i	−0.0187809	+	0.999824i	$0.505978\pi$
$180$	0.937436	+	3.49856i	0.0698724	+	0.260767i
$181$	4.56052			0.338981			0.169490	−	0.985532i	$-0.445788\pi$
$181$	4.56052			0.338981			0.169490	+	0.985532i	$0.445788\pi$
$182$		0			0
$183$	8.76116			0.647643
$184$	−2.40911	−	8.99092i	−0.177602	−	0.662819i
$185$	−5.15656	+	2.97714i	−0.379118	+	0.218884i
$186$	−1.09363	+	0.631410i	−0.0801892	+	0.0462972i
$187$	5.99213	−	1.60559i	0.438188	−	0.117412i
$188$	−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
$193$	−6.24102	+	23.2918i	−0.449238	+	1.67658i	0.255258	+	0.966873i	$0.417840\pi$
$193$	−6.24102	+	23.2918i	−0.449238	+	1.67658i	−0.704496	+	0.709708i	$0.748827\pi$
$194$	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	−0.932482	−	0.361216i	$-0.882362\pi$
$197$	−8.01810	+	8.01810i	−0.571266	+	0.571266i	0.361216	+	0.932482i	$0.382362\pi$
$198$	−0.356371	+	0.617253i	−0.0253262	+	0.0438663i
$199$	−2.28779	−	3.96257i	−0.162177	−	0.280899i	0.773472	−	0.633830i	$-0.218518\pi$
$199$	−2.28779	−	3.96257i	−0.162177	−	0.280899i	−0.935649	+	0.352931i	$0.885185\pi$
$200$	5.80512	+	1.55548i	0.410484	+	0.109989i
$201$	−14.7616	+	3.95535i	−1.04120	+	0.278989i
$202$	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
$206$	3.36697	+	0.902178i	0.234588	+	0.0628577i
$207$	−5.70001	+	3.29090i	−0.396178	+	0.228734i
$208$	4.42792	−	6.39063i	0.307021	−	0.443110i
$209$			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
$213$	−0.661313	+	2.46805i	−0.0453124	+	0.169108i
$214$	4.88288	+	1.30836i	0.333787	+	0.0894379i
$215$	3.27299	+	12.2150i	0.223216	+	0.833054i
$216$	8.18007	−	8.18007i	0.556583	−	0.556583i
$217$		0			0
$218$		−	3.70545i		−	0.250965i
$219$	−0.174841	+	0.0468486i	−0.0118147	+	0.00316574i
$220$	1.03221	+	1.78785i	0.0695919	+	0.120537i
$221$	−11.3151	−	23.9559i	−0.761137	−	1.61145i
$222$	2.48131	+	1.43258i	0.166534	+	0.0961486i
$223$	−2.85764	−	2.85764i	−0.191361	−	0.191361i	0.604923	−	0.796284i	$-0.293204\pi$
$223$	−2.85764	−	2.85764i	−0.191361	−	0.191361i	−0.796284	+	0.604923i	$0.793204\pi$
$224$		0			0
$225$		−	4.24965i		−	0.283310i
$226$	−0.237094	−	0.884848i	−0.0157713	−	0.0588592i
$227$	7.19495	−	26.8519i	0.477545	−	1.78222i	−0.133963	−	0.990986i	$-0.542770\pi$
$227$	7.19495	−	26.8519i	0.477545	−	1.78222i	0.611509	−	0.791238i	$-0.290563\pi$
$228$	2.71525	−	10.1334i	0.179822	−	0.671103i
$229$	4.83373	+	18.0397i	0.319422	+	1.19210i	0.919802	+	0.392383i	$0.128349\pi$
$229$	4.83373	+	18.0397i	0.319422	+	1.19210i	−0.600380	+	0.799715i	$0.704984\pi$
$230$		−	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	−0.0366962	−	0.999326i	$-0.511683\pi$
$233$	−14.0506	−	8.11213i	−0.920486	−	0.531443i	−0.883790	+	0.467883i	$0.845017\pi$
$234$	2.86548	+	1.02696i	0.187323	+	0.0671346i
$235$	−2.60356	−	4.50949i	−0.169837	−	0.294167i
$236$	−2.49357	+	0.668151i	−0.162318	+	0.0434929i
$237$		−	5.91400i		−	0.384155i
$238$		0			0
$239$	−0.843675	+	0.843675i	−0.0545728	+	0.0545728i	−0.733867	−	0.679294i	$-0.762286\pi$
$239$	−0.843675	+	0.843675i	−0.0545728	+	0.0545728i	0.679294	+	0.733867i	$0.262286\pi$
$240$	−1.00403	−	3.74709i	−0.0648098	−	0.241874i
$241$	20.8956	+	5.59895i	1.34600	+	0.360660i	0.858658	−	0.512549i	$-0.171299\pi$
$241$	20.8956	+	5.59895i	1.34600	+	0.360660i	0.487345	+	0.873210i	$0.337965\pi$
$242$	1.51757	−	5.66367i	0.0975534	−	0.364074i
$243$	−11.8267	−	6.82817i	−0.758685	−	0.438027i
$244$	11.9086			0.762367
$245$		0			0
$246$			1.22425i			0.0780556i
$247$	18.0282	−	3.27070i	1.14711	−	0.208109i
$248$	−3.26132	+	1.88293i	−0.207094	+	0.119566i
$249$	−20.7346	−	5.55582i	−1.31400	−	0.352086i
$250$	5.67013	+	3.27365i	0.358610	+	0.207044i
$251$	−27.4367			−1.73179			−0.865893	−	0.500229i	$-0.833249\pi$
$251$	−27.4367			−1.73179			−0.865893	+	0.500229i	$0.833249\pi$
$252$		0			0
$253$	−2.65268	+	2.65268i	−0.166772	+	0.166772i
$254$	0.852872	−	0.228526i	0.0535139	−	0.0143390i
$255$	−12.7688	−	3.42140i	−0.799615	−	0.214256i
$256$	2.06300	+	3.57323i	0.128938	+	0.223327i
$257$	10.2864	−	17.8165i	0.641645	−	1.11136i	−0.343420	−	0.939182i	$-0.611586\pi$
$257$	10.2864	−	17.8165i	0.641645	−	1.11136i	0.985065	−	0.172180i	$-0.0550811\pi$
$258$	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
$262$	0.784054	−	2.92613i	0.0484390	−	0.180777i
$263$	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
$268$	−20.0646	+	5.37629i	−1.22564	+	0.328409i
$269$	−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
$271$	−7.64604	−	28.5354i	−0.464464	−	1.73340i	−0.658661	−	0.752440i	$-0.728877\pi$
$271$	−7.64604	−	28.5354i	−0.464464	−	1.73340i	0.194198	−	0.980962i	$-0.437790\pi$
$272$	−15.8448			−0.960730
$273$		0			0
$274$	−10.2496			−0.619204
$275$	−0.626907	−	2.33965i	−0.0378039	−	0.141086i
$276$	7.94445	−	4.58673i	0.478200	−	0.276089i
$277$	22.3664	−	12.9133i	1.34387	−	0.775883i	0.356496	−	0.934297i	$-0.383971\pi$
$277$	22.3664	−	12.9133i	1.34387	−	0.775883i	0.987373	+	0.158414i	$0.0506380\pi$
$278$	3.82505	−	1.02492i	0.229411	−	0.0614706i
$279$	1.88293	+	1.88293i	0.112728	+	0.112728i
$280$		0			0
$281$	12.0782	+	12.0782i	0.720523	+	0.720523i	0.968712	−	0.248189i	$-0.0798354\pi$
$281$	12.0782	+	12.0782i	0.720523	+	0.720523i	−0.248189	+	0.968712i	$0.579835\pi$
$282$	−1.25282	+	2.16994i	−0.0746041	+	0.129218i
$283$	−7.68337	−	13.3080i	−0.456729	−	0.791078i	0.542057	−	0.840342i	$-0.317646\pi$
$283$	−7.68337	−	13.3080i	−0.456729	−	0.791078i	−0.998786	+	0.0492639i	$0.984312\pi$
$284$	−0.898886	+	3.35469i	−0.0533391	+	0.199064i
$285$	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
$291$	10.1988	+	2.73276i	0.597864	+	0.160197i
$292$	−0.237652	+	0.0636787i	−0.0139075	+	0.00372651i
$293$	9.78662	−	9.78662i	0.571741	−	0.571741i	−0.360874	−	0.932615i	$-0.617522\pi$
$293$	9.78662	−	9.78662i	0.571741	−	0.571741i	0.932615	+	0.360874i	$0.117522\pi$
$294$		0			0
$295$	−2.24965			−0.130979
$296$	7.39949	+	4.27210i	0.430087	+	0.248311i
$297$	−4.50355	−	1.20672i	−0.261322	−	0.0700211i
$298$	−7.65458	+	4.41938i	−0.443418	+	0.256008i
$299$	13.1693	+	9.12470i	0.761600	+	0.527695i
$300$			5.92298i			0.341964i
$301$		0			0
$302$	−4.95017			−0.284850
$303$	13.7367	+	7.93089i	0.789153	+	0.455618i
$304$	2.83611	−	10.5845i	0.162662	−	0.607064i
$305$	10.0240	+	2.68591i	0.573970	+	0.153795i
$306$	−1.60559	−	5.99213i	−0.0917853	−	0.342547i
$307$	8.14125	−	8.14125i	0.464645	−	0.464645i	−0.435529	−	0.900175i	$-0.643439\pi$
$307$	8.14125	−	8.14125i	0.464645	−	0.464645i	0.900175	+	0.435529i	$0.143439\pi$
$308$		0			0
$309$			7.53690i			0.428759i
$310$	−1.44484	+	0.387143i	−0.0820613	+	0.0219882i
$311$	−16.2406	−	28.1296i	−0.920922	−	1.59508i	−0.797992	−	0.602668i	$-0.794104\pi$
$311$	−16.2406	−	28.1296i	−0.920922	−	1.59508i	−0.122930	−	0.992415i	$-0.539229\pi$
$312$	−8.76213	−	3.14026i	−0.496058	−	0.177782i
$313$	−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
$317$	−2.97166	−	11.0904i	−0.166905	−	0.622897i	−0.997790	−	0.0664527i	$-0.978832\pi$
$317$	−2.97166	−	11.0904i	−0.166905	−	0.622897i	0.830885	−	0.556445i	$-0.187835\pi$
$318$	1.78055	−	6.64511i	0.0998484	−	0.372639i
$319$	0.774427	−	2.89020i	0.0433596	−	0.161820i
$320$	−0.462543	−	1.72624i	−0.0258570	−	0.0964995i
$321$			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
$325$	−9.35367	+	4.41803i	−0.518848	+	0.245068i
$326$	−2.18172	−	3.77885i	−0.120834	−	0.209291i
$327$	7.73894	−	2.07364i	0.427964	−	0.114673i
$328$			3.65084i			0.201584i
$329$		0			0
$330$	0.612127	−	0.612127i	0.0336965	−	0.0336965i
$331$	−0.295040	−	1.10110i	−0.0162168	−	0.0605221i	0.957343	−	0.288953i	$-0.0933072\pi$
$331$	−0.295040	−	1.10110i	−0.0162168	−	0.0605221i	−0.973560	+	0.228431i	$0.926640\pi$
$332$	−28.1834	−	7.55172i	−1.54676	−	0.414454i
$333$	1.56370	−	5.83580i	0.0856901	−	0.319800i
$334$	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	$-0.741999\pi$
$337$		−	26.6058i		−	1.44931i	0.689112	−	0.724655i	$-0.258001\pi$
$338$	−0.718630	−	7.37472i	−0.0390883	−	0.401132i
$339$	1.71535	−	0.990357i	0.0931649	−	0.0537888i
$340$	−17.3560	−	4.65052i	−0.941259	−	0.252210i
$341$	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
$345$	7.72170	−	2.06902i	0.415722	−	0.111392i
$346$	−3.93941	−	1.05556i	−0.211784	−	0.0567473i
$347$	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	$-0.722078\pi$
$349$	2.31459	−	2.31459i	0.123897	−	0.123897i	0.766336	+	0.642439i	$0.222078\pi$
$350$		0			0
$351$	−1.63752	+	19.8446i	−0.0874043	+	1.05923i
$352$	2.28726	−	3.96165i	0.121911	−	0.211156i
$353$	3.93155	−	14.6727i	0.209255	−	0.780951i	−0.778855	−	0.627204i	$-0.784199\pi$
$353$	3.93155	−	14.6727i	0.209255	−	0.780951i	0.988110	−	0.153747i	$-0.0491341\pi$
$354$	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
$359$	23.1850	−	6.21241i	1.22366	−	0.327879i	0.411552	−	0.911386i	$-0.364987\pi$
$359$	23.1850	−	6.21241i	1.22366	−	0.327879i	0.812107	+	0.583508i	$0.198320\pi$
$360$	3.92242	−	2.26461i	0.206730	−	0.119356i
$361$	5.90990	−	3.41208i	0.311047	−	0.179583i
$362$	−0.672767	−	2.51080i	−0.0353599	−	0.131965i
$363$	12.6780			0.665422
$364$		0			0
$365$	−0.214405			−0.0112225
$366$	−1.29244	−	4.82347i	−0.0675572	−	0.252127i
$367$	−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
$369$	2.49357	−	0.668151i	0.129810	−	0.0347825i
$370$	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
$375$	−3.66400	+	13.6742i	−0.189208	+	0.706134i
$376$	−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	−0.649973	−	0.759957i	$-0.725220\pi$
$379$	2.14117	−	2.14117i	0.109984	−	0.109984i	0.759957	+	0.649973i	$0.225220\pi$
$380$	6.21322	−	10.7616i	0.318731	−	0.552059i
$381$	0.954568	+	1.65336i	0.0489040	+	0.0847042i
$382$	2.04004	+	0.546627i	0.104378	+	0.0279679i
$383$	3.97721	−	1.06569i	0.203226	−	0.0544542i	−0.155770	−	0.987793i	$-0.549786\pi$
$383$	3.97721	−	1.06569i	0.203226	−	0.0544542i	0.358996	+	0.933339i	$0.383119\pi$
$384$	−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
$388$	13.8627	+	3.71449i	0.703770	+	0.188575i
$389$	−15.1066	+	8.72179i	−0.765934	+	0.442212i	−0.831422	−	0.555641i	$-0.812473\pi$
$389$	−15.1066	+	8.72179i	−0.765934	+	0.442212i	0.0654880	+	0.997853i	$0.479140\pi$
$390$	−3.03892	−	2.10560i	−0.153882	−	0.106621i
$391$		−	32.6516i		−	1.65126i
$392$		0			0
$393$	6.55008			0.330408
$394$	5.59721	+	3.23155i	0.281983	+	0.162803i
$395$	1.81305	−	6.76641i	0.0912247	−	0.340455i
$396$	−2.02335	−	0.542155i	−0.101677	−	0.0272443i
$397$	−3.72870	−	13.9157i	−0.187138	−	0.698408i	−0.994163	−	0.107891i	$-0.965590\pi$
$397$	−3.72870	−	13.9157i	−0.187138	−	0.698408i	0.807025	−	0.590518i	$-0.201076\pi$
$398$	−1.84410	+	1.84410i	−0.0924365	+	0.0924365i
$399$		0			0
$400$			6.18664i			0.309332i
$401$	−21.3031	+	5.70816i	−1.06383	+	0.285052i	−0.747955	−	0.663749i	$-0.768964\pi$
$401$	−21.3031	+	5.70816i	−1.06383	+	0.285052i	−0.315873	+	0.948801i	$0.602297\pi$
$402$	4.35525	+	7.54352i	0.217220	+	0.376236i
$403$	2.18688	−	6.10194i	0.108936	−	0.303959i
$404$	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
$408$	4.90960	+	18.3229i	0.243061	+	0.907117i
$409$	−0.658557	+	2.45777i	−0.0325635	+	0.121529i	−0.980294	−	0.197542i	$-0.936704\pi$
$409$	−0.658557	+	2.45777i	−0.0325635	+	0.121529i	0.947731	+	0.319071i	$0.103371\pi$
$410$	−0.375320	+	1.40071i	−0.0185357	+	0.0691763i
$411$	−5.73591	−	21.4067i	−0.282931	−	1.05591i
$412$			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
$416$	−18.3912	−	6.59124i	−0.901704	−	0.323162i
$417$	4.28115	+	7.41517i	0.209649	+	0.363122i
$418$	2.36199	−	0.632892i	0.115529	−	0.0309558i
$419$			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	−0.883811	−	0.467844i	$-0.845031\pi$
$421$	−8.53492	+	8.53492i	−0.415967	+	0.415967i	0.467844	+	0.883811i	$0.345031\pi$
$422$	0.0876310	+	0.327043i	0.00426581	+	0.0159202i
$423$	5.10350	+	1.36748i	0.248140	+	0.0664890i
$424$	5.30978	−	19.8164i	0.257866	−	0.962368i
$425$	18.2576	+	10.5410i	0.885622	+	0.511314i
$426$	1.45635			0.0705602
$427$		0			0
$428$			14.8568i			0.718133i
$429$	0.669645	+	3.69111i	0.0323307	+	0.178208i
$430$	6.24214	−	3.60390i	0.301023	−	0.173796i
$431$	−33.0675	−	8.86042i	−1.59281	−	0.426791i	−0.649947	−	0.759980i	$-0.725209\pi$
$431$	−33.0675	−	8.86042i	−1.59281	−	0.426791i	−0.942860	+	0.333189i	$0.891875\pi$
$432$	10.3131	+	5.95428i	0.496190	+	0.286475i
$433$	35.8708			1.72384			0.861920	−	0.507044i	$-0.169262\pi$
$433$	35.8708			1.72384			0.861920	+	0.507044i	$0.169262\pi$
$434$		0			0
$435$	−4.50857	+	4.50857i	−0.216169	+	0.216169i
$436$	10.5191	−	2.81859i	0.503774	−	0.134986i
$437$	21.8117	+	5.84444i	1.04340	+	0.279577i
$438$	0.0515851	+	0.0893481i	0.00246483	+	0.00426922i
$439$	5.26493	−	9.11912i	0.251281	−	0.435232i	−0.712598	−	0.701573i	$-0.752481\pi$
$439$	5.26493	−	9.11912i	0.251281	−	0.435232i	0.963879	+	0.266341i	$0.0858147\pi$
$440$	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	$0.265504\pi$
$444$	−2.17942	+	8.13370i	−0.103431	+	0.386008i
$445$	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	0.897157	−	0.441712i	$-0.145629\pi$
$449$	9.65069	+	9.65069i	0.455444	+	0.455444i	−0.441712	+	0.897157i	$0.645629\pi$
$450$	−2.33965	+	0.626907i	−0.110292	+	0.0295527i
$451$	1.27427	−	0.735703i	0.0600032	−	0.0346429i
$452$	2.33158	−	1.34614i	0.109668	−	0.0633170i
$453$	−2.77021	−	10.3386i	−0.130156	−	0.485749i
$454$	−15.8448			−0.743631
$455$		0			0
$456$	−13.1187			−0.614340
$457$	−8.09709	−	30.2187i	−0.378766	−	1.41357i	−0.847764	−	0.530374i	$-0.822052\pi$
$457$	−8.09709	−	30.2187i	−0.378766	−	1.41357i	0.468998	−	0.883199i	$-0.344615\pi$
$458$	9.21872	−	5.32243i	0.430763	−	0.248701i
$459$	35.1437	−	20.2902i	1.64037	−	0.947065i
$460$	10.4957	−	2.81231i	0.489364	−	0.131125i
$461$	−0.593023	−	0.593023i	−0.0276198	−	0.0276198i	0.693162	−	0.720782i	$-0.256217\pi$
$461$	−0.593023	−	0.593023i	−0.0276198	−	0.0276198i	−0.720782	+	0.693162i	$0.756217\pi$
$462$		0			0
$463$	2.47096	+	2.47096i	0.114835	+	0.114835i	0.762189	−	0.647354i	$-0.224124\pi$
$463$	2.47096	+	2.47096i	0.114835	+	0.114835i	−0.647354	+	0.762189i	$0.724124\pi$
$464$	−3.82122	+	6.61855i	−0.177396	+	0.307259i
$465$	−1.61712	−	2.80093i	−0.0749921	−	0.129890i
$466$	−2.39340	+	8.93229i	−0.110872	+	0.413780i
$467$	−6.69302	+	11.5926i	−0.309716	+	0.536444i	−0.978300	−	0.207193i	$-0.933567\pi$
$467$	−6.69302	+	11.5926i	−0.309716	+	0.536444i	0.668584	+	0.743636i	$0.266901\pi$
$468$	−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
$473$	−7.06438	−	1.89289i	−0.324820	−	0.0870354i
$474$	−3.25596	+	0.872432i	−0.149551	+	0.0400721i
$475$	−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
$479$	−12.1006	−	3.24235i	−0.552891	−	0.148147i	−0.0284528	−	0.999595i	$-0.509058\pi$
$479$	−12.1006	−	3.24235i	−0.552891	−	0.148147i	−0.524438	+	0.851448i	$0.675725\pi$
$480$	−8.44200	+	4.87399i	−0.385323	+	0.222466i
$481$	−14.4705	+	2.62525i	−0.659799	+	0.119701i
$482$		−	12.3301i		−	0.561619i
$483$		0			0
$484$	17.2325			0.783296
$485$	10.8310	+	6.25329i	0.491811	+	0.283947i
$486$	−2.01458	+	7.51852i	−0.0913832	+	0.341047i
$487$	−24.5618	−	6.58132i	−1.11300	−	0.298228i	−0.344953	−	0.938620i	$-0.612105\pi$
$487$	−24.5618	−	6.58132i	−1.11300	−	0.298228i	−0.768048	+	0.640392i	$0.778772\pi$
$488$	−3.85419	−	14.3841i	−0.174471	−	0.651135i
$489$	6.67130	−	6.67130i	0.301687	−	0.301687i
$490$		0			0
$491$		−	19.4944i		−	0.879769i	−0.898054	−	0.439884i	$-0.855019\pi$
$491$		−	19.4944i		−	0.879769i	0.898054	−	0.439884i	$-0.144981\pi$
$492$	−3.47544	+	0.931241i	−0.156685	+	0.0419836i
$493$	13.0215	+	22.5538i	0.586457	+	1.01577i
$494$	−4.46021	−	9.44297i	−0.200674	−	0.424859i
$495$	−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
$499$	3.73894	+	13.9539i	0.167378	+	0.624663i	0.997725	+	0.0674163i	$0.0214756\pi$
$499$	3.73894	+	13.9539i	0.167378	+	0.624663i	−0.830347	+	0.557247i	$0.811858\pi$
$500$	−4.98027	+	18.5866i	−0.222725	+	0.831219i
$501$	−4.01841	+	14.9969i	−0.179529	+	0.670013i
$502$	4.04745	+	15.1053i	0.180647	+	0.674182i
$503$		−	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
$507$	15.0002	−	5.62792i	0.666180	−	0.249945i
$508$	1.29749	+	2.24732i	0.0575669	+	0.0997088i
$509$	−18.5969	+	4.98303i	−0.824294	+	0.220869i	−0.646223	−	0.763149i	$-0.723652\pi$
$509$	−18.5969	+	4.98303i	−0.824294	+	0.220869i	−0.178071	+	0.984018i	$0.556986\pi$
$510$			7.53462i			0.333639i
$511$		0			0
$512$	−14.6497	+	14.6497i	−0.647433	+	0.647433i
$513$	7.26364	+	27.1083i	0.320697	+	1.19686i
$514$	−11.3263	−	3.03488i	−0.499583	−	0.133863i
$515$	−2.31059	+	8.62324i	−0.101817	+	0.379985i
$516$	15.4880	+	8.94198i	0.681820	+	0.393649i
$517$	3.01147			0.132444
$518$		0			0
$519$		−	8.81828i		−	0.387080i
$520$	−9.06236	−	6.27910i	−0.397411	−	0.275357i
$521$	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	$0.175854\pi$
$522$	−2.89020	−	0.774427i	−0.126501	−	0.0338958i
$523$	−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
$527$	−12.7600	+	3.41904i	−0.555835	+	0.148936i
$528$	2.16708	+	0.580668i	0.0943101	+	0.0252703i
$529$	−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
$535$	−3.35088	+	12.5057i	−0.144871	+	0.540667i
$536$	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
$541$	31.8083	−	8.52300i	1.36754	−	0.366432i	0.500963	−	0.865469i	$-0.332979\pi$
$541$	31.8083	−	8.52300i	1.36754	−	0.366432i	0.866581	+	0.499036i	$0.166312\pi$
$542$	−14.5823	+	8.41908i	−0.626362	+	0.361630i
$543$	4.86739	−	2.81019i	0.208880	−	0.120597i
$544$	10.3050	+	38.4586i	0.441822	+	1.64890i
$545$	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	$0.605164\pi$
$548$	−7.79650	−	29.0969i	−0.333050	−	1.24296i
$549$	−9.11912	+	5.26493i	−0.389195	+	0.224702i
$550$	−1.19562	+	0.690289i	−0.0509813	+	0.0294340i
$551$	−17.3970	+	4.66152i	−0.741138	+	0.198587i
$552$	−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
$557$	3.09539	−	11.5521i	0.131156	−	0.489480i	−0.868828	−	0.495113i	$-0.835126\pi$
$557$	3.09539	−	11.5521i	0.131156	−	0.489480i	0.999984	+	0.00563336i	$0.00179316\pi$
$558$	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	0.925131	−	0.379648i	$-0.123955\pi$
$563$	3.17429	+	5.49803i	0.133780	+	0.231714i	−0.791351	+	0.611363i	$0.790622\pi$
$564$	−7.11305	−	1.90593i	−0.299513	−	0.0802543i
$565$	2.26620	−	0.607228i	0.0953400	−	0.0255463i
$566$	−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	0.985191	−	0.171461i	$-0.0548486\pi$
$569$	31.7087	+	18.3070i	1.32930	+	0.767470i	0.344106	+	0.938931i	$0.388182\pi$
$570$	−5.03323	−	1.34865i	−0.210819	−	0.0564888i
$571$	16.2874	−	9.40351i	0.681605	−	0.393525i	−0.118855	−	0.992912i	$-0.537922\pi$
$571$	16.2874	−	9.40351i	0.681605	−	0.393525i	0.800459	+	0.599387i	$0.204589\pi$
$572$	0.910211	+	5.01712i	0.0380578	+	0.209776i
$573$			4.56659i			0.190772i
$574$		0			0
$575$	−12.7489			−0.531668
$576$	1.57041	+	0.906679i	0.0654339	+	0.0377783i
$577$	−11.4718	+	42.8134i	−0.477578	+	1.78234i	0.133803	+	0.991008i	$0.457281\pi$
$577$	−11.4718	+	42.8134i	−0.477578	+	1.78234i	−0.611381	+	0.791336i	$0.709386\pi$
$578$	20.3669	+	5.45730i	0.847152	+	0.226994i
$579$	7.69142	+	28.7048i	0.319645	+	1.19293i
$580$	−6.12825	+	6.12825i	−0.254462	+	0.254462i
$581$		0			0
$582$		−	6.01810i		−	0.249458i
$583$	−7.98662	+	2.14001i	−0.330772	+	0.0886301i
$584$	0.153832	+	0.266445i	0.00636561	+	0.0110256i
$585$	−2.63018	+	7.33886i	−0.108744	+	0.303425i
$586$	−6.83176	−	3.94432i	−0.282218	−	0.162938i
$587$	−3.36694	−	3.36694i	−0.138969	−	0.138969i	0.634200	−	0.773169i	$-0.281329\pi$
$587$	−3.36694	−	3.36694i	−0.138969	−	0.138969i	−0.773169	+	0.634200i	$0.781329\pi$
$588$		0			0
$589$		−	9.13586i		−	0.376436i
$590$	0.331867	+	1.23855i	0.0136628	+	0.0509901i
$591$	−3.61688	+	13.4984i	−0.148778	+	0.555249i
$592$	−2.27643	+	8.49576i	−0.0935608	+	0.349174i
$593$	−3.91050	−	14.5942i	−0.160585	−	0.599312i	−0.998562	−	0.0536061i	$-0.982928\pi$
$593$	−3.91050	−	14.5942i	−0.160585	−	0.599312i	0.837977	−	0.545705i	$-0.183738\pi$
$594$			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
$598$	3.08089	−	8.59645i	0.125987	−	0.351535i
$599$	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	$0.748823\pi$
$600$	7.15423	−	1.91697i	0.292070	−	0.0782599i
$601$		−	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
$604$	−3.76540	−	14.0527i	−0.153212	−	0.571794i
$605$	14.5054	+	3.88670i	0.589726	+	0.158017i
$606$	2.33993	−	8.73272i	0.0950530	−	0.354743i
$607$	−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
$611$	−2.29583	−	12.6547i	−0.0928792	−	0.511954i
$612$	15.7893	−	9.11595i	0.638245	−	0.368491i
$613$	−28.0026	−	7.50326i	−1.13101	−	0.303054i	−0.355680	−	0.934608i	$-0.615751\pi$
$613$	−28.0026	−	7.50326i	−1.13101	−	0.303054i	−0.775332	+	0.631554i	$0.782418\pi$
$614$	−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	−0.522153	−	0.852852i	$-0.674871\pi$
$617$	8.21440	−	8.21440i	0.330699	−	0.330699i	0.852852	+	0.522153i	$0.174871\pi$
$618$	4.14945	−	1.11184i	0.166916	−	0.0447249i
$619$	36.4692	+	9.77190i	1.46582	+	0.392766i	0.901497	−	0.432786i	$-0.142469\pi$
$619$	36.4692	+	9.77190i	1.46582	+	0.392766i	0.564326	+	0.825552i	$0.309136\pi$
$620$	−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
$626$	−2.91125	+	10.8649i	−0.116357	+	0.434250i
$627$	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	0.801822	−	0.597563i	$-0.203864\pi$
$631$	5.13093	+	5.13093i	0.204259	+	0.204259i	−0.597563	+	0.801822i	$0.703864\pi$
$632$	−9.70959	+	2.60168i	−0.386227	+	0.103489i
$633$	−0.634000	+	0.366040i	−0.0251992	+	0.0145488i
$634$	−5.66744	+	3.27210i	−0.225083	+	0.129952i
$635$	0.585284	+	2.18431i	0.0232263	+	0.0866817i
$636$	20.2187			0.801723
$637$		0			0
$638$	−1.70545			−0.0675193
$639$	−0.794818	−	2.96630i	−0.0314425	−	0.117345i
$640$	−14.5823	+	8.41908i	−0.576415	+	0.332793i
$641$	14.1471	−	8.16784i	0.558777	−	0.322610i	−0.193877	−	0.981026i	$-0.562106\pi$
$641$	14.1471	−	8.16784i	0.558777	−	0.322610i	0.752655	+	0.658416i	$0.228773\pi$
$642$	6.01765	−	1.61242i	0.237498	−	0.0636373i
$643$	−28.1910	−	28.1910i	−1.11175	−	1.11175i	−0.992914	−	0.118832i	$-0.962085\pi$
$643$	−28.1910	−	28.1910i	−1.11175	−	1.11175i	−0.118832	−	0.992914i	$-0.537915\pi$
$644$		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	0.954339	−	0.298725i	$-0.0965614\pi$
$647$	5.55694	+	9.62491i	0.218466	+	0.378394i	−0.735873	+	0.677119i	$0.763228\pi$
$648$	1.28083	−	4.78012i	0.0503158	−	0.187781i
$649$	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
$655$	7.49418	+	2.00806i	0.292822	+	0.0784614i
$656$	−3.63015	+	0.972695i	−0.141733	+	0.0379774i
$657$	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
$661$	−30.4496	−	8.15894i	−1.18435	−	0.317346i	−0.387701	−	0.921785i	$-0.626731\pi$
$661$	−30.4496	−	8.15894i	−1.18435	−	0.317346i	−0.796651	+	0.604439i	$0.793397\pi$
$662$	−0.562690	+	0.324869i	−0.0218696	+	0.0126264i
$663$	−26.8381	−	18.5955i	−1.04231	−	0.722189i
$664$			36.4861i			1.41594i
$665$		0			0
$666$	−3.44358			−0.133436
$667$	−13.6390	−	7.87447i	−0.528103	−	0.304901i
$668$	−5.46200	+	20.3845i	−0.211331	+	0.788699i
$669$	−4.81079	−	1.28905i	−0.185996	−	0.0498375i
$670$	2.67038	+	9.96600i	0.103166	+	0.385020i
$671$	−4.24387	+	4.24387i	−0.163833	+	0.163833i
$672$		0			0
$673$		−	1.38550i		−	0.0534072i	−0.999643	−	0.0267036i	$-0.991499\pi$
$673$		−	1.38550i		−	0.0534072i	0.999643	−	0.0267036i	$-0.00850104\pi$
$674$	−14.6479	+	3.92488i	−0.564214	+	0.151181i
$675$	−7.92238	−	13.7220i	−0.304933	−	0.528159i
$676$	20.3889	−	7.64972i	0.784188	−	0.294220i
$677$	−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
$681$	−8.86704	−	33.0923i	−0.339786	−	1.26810i
$682$	0.223899	−	0.835604i	0.00857355	−	0.0319969i
$683$	9.98818	−	37.2764i	0.382187	−	1.42634i	−0.460367	−	0.887729i	$-0.652282\pi$
$683$	9.98818	−	37.2764i	0.382187	−	1.42634i	0.842554	−	0.538613i	$-0.181051\pi$
$684$	3.26340	+	12.1792i	0.124779	+	0.465682i
$685$		−	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
$689$	15.0814	+	31.9297i	0.574555	+	1.21642i
$690$	−2.27821	−	3.94597i	−0.0867299	−	0.150221i
$691$	22.1210	−	5.92730i	0.841522	−	0.225485i	0.187788	−	0.982210i	$-0.439868\pi$
$691$	22.1210	−	5.92730i	0.841522	−	0.225485i	0.653734	+	0.756724i	$0.273201\pi$
$692$		−	11.9862i		−	0.455647i
$693$		0			0
$694$	8.14411	−	8.14411i	0.309146	−	0.309146i
$695$	2.62495	+	9.79643i	0.0995698	+	0.371600i
$696$	8.83771	+	2.36806i	0.334993	+	0.0897610i
$697$	−3.31462	+	12.3703i	−0.125550	+	0.468560i
$698$	−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	$0.0932895\pi$
$701$			15.2981i			0.577800i	−0.957359	+	0.288900i	$0.906711\pi$
$702$	11.1671	−	2.02594i	0.421473	−	0.0764641i
$703$	−17.9510	+	10.3640i	−0.677034	+	0.390886i
$704$	0.998347	+	0.267506i	0.0376266	+	0.0100820i
$705$	−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
$709$	3.74438	−	1.00330i	0.140623	−	0.0376798i	−0.187821	−	0.982203i	$-0.560142\pi$
$709$	3.74438	−	1.00330i	0.140623	−	0.0376798i	0.328444	+	0.944523i	$0.393476\pi$
$710$	1.66626	+	0.446473i	0.0625336	+	0.0167558i
$711$	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
$717$	−0.380573	+	1.42032i	−0.0142127	+	0.0530427i
$718$	−6.84051	−	11.8481i	−0.255285	−	0.442167i
$719$	−2.99728	+	5.19144i	−0.111780	+	0.193608i	−0.916488	−	0.400062i	$-0.868988\pi$
$719$	−2.99728	+	5.19144i	−0.111780	+	0.193608i	0.804708	+	0.593671i	$0.202322\pi$
$720$	3.29683	+	3.29683i	0.122865	+	0.122865i
$721$		0			0
$722$	−2.75035	−	2.75035i	−0.102358	−	0.102358i
$723$	25.7517	−	6.90014i	0.957715	−	0.256619i
$724$	6.61597	−	3.81973i	0.245881	−	0.141959i
$725$	8.80622	−	5.08427i	0.327055	−	0.188825i
$726$	−1.87026	−	6.97989i	−0.0694117	−	0.259048i
$727$	−14.6184			−0.542168			−0.271084	−	0.962556i	$-0.587382\pi$
$727$	−14.6184			−0.542168			−0.271084	+	0.962556i	$0.587382\pi$
$728$		0			0
$729$	−23.9175			−0.885833
$730$	0.0316289	+	0.118041i	0.00117064	+	0.00436889i
$731$	55.1272	−	31.8277i	2.03895	−	1.17719i
$732$	12.7099	−	7.33804i	0.469770	−	0.271222i
$733$	−38.3423	+	10.2738i	−1.41621	+	0.379471i	−0.884136	−	0.467230i	$-0.845252\pi$
$733$	−38.3423	+	10.2738i	−1.41621	+	0.379471i	−0.532069	+	0.846701i	$0.678585\pi$
$734$	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
$739$	−6.07706	+	22.6799i	−0.223548	+	0.834294i	0.759432	+	0.650586i	$0.225477\pi$
$739$	−6.07706	+	22.6799i	−0.223548	+	0.834294i	−0.982981	+	0.183708i	$0.941190\pi$
$740$	−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	−0.757897	−	0.652374i	$-0.773773\pi$
$743$	−2.87636	+	2.87636i	−0.105523	+	0.105523i	0.652374	+	0.757897i	$0.273773\pi$
$744$	−2.32051	+	4.01925i	−0.0850742	+	0.147353i
$745$	−11.3186	−	19.6043i	−0.414680	−	0.718247i
$746$	−3.28531	−	0.880297i	−0.120284	−	0.0322300i
$747$	24.9205	−	6.67742i	0.911793	−	0.244314i
$748$	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	−0.453314	−	0.891351i	$-0.649758\pi$
$751$	−39.7885	−	22.9719i	−1.45190	−	0.838257i	−0.998590	+	0.0530936i	$0.983092\pi$
$752$	−7.42968	−	1.99078i	−0.270932	−	0.0725961i
$753$	−29.2828	+	16.9064i	−1.06713	+	0.616105i
$754$	1.30017	+	7.16658i	0.0473493	+	0.260991i
$755$		−	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
$759$	−1.19659	+	4.46575i	−0.0434336	+	0.162096i
$760$	−15.0096	−	4.02181i	−0.544455	−	0.145886i
$761$	−3.96956	−	14.8146i	−0.143897	−	0.537029i	−0.999802	−	0.0198970i	$-0.993666\pi$
$761$	−3.96956	−	14.8146i	−0.143897	−	0.537029i	0.855905	−	0.517132i	$-0.173000\pi$
$762$	0.769443	−	0.769443i	0.0278740	−	0.0278740i
$763$		0			0
$764$			6.20711i			0.224565i
$765$	15.3466	−	4.11211i	0.554857	−	0.148674i
$766$	−1.17343	−	2.03245i	−0.0423979	−	0.0734353i
$767$	−5.23072	−	1.87464i	−0.188870	−	0.0676893i
$768$	4.40364	+	2.54244i	0.158903	+	0.0917425i
$769$	4.63670	+	4.63670i	0.167204	+	0.167204i	0.785749	−	0.618545i	$-0.212278\pi$
$769$	4.63670	+	4.63670i	0.167204	+	0.167204i	−0.618545	+	0.785749i	$0.712278\pi$
$770$		0			0
$771$		−	25.3538i		−	0.913094i
$772$	10.4545	+	39.0168i	0.376267	+	1.40425i
$773$	2.08048	−	7.76446i	0.0748297	−	0.279268i	−0.918365	−	0.395734i	$-0.870490\pi$
$773$	2.08048	−	7.76446i	0.0748297	−	0.279268i	0.993195	+	0.116466i	$0.0371567\pi$
$774$	−1.89289	+	7.06438i	−0.0680387	+	0.253924i
$775$	1.33498	+	4.98219i	0.0479537	+	0.178966i
$776$		−	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
$780$	3.66583	−	10.2286i	0.131258	−	0.366243i
$781$	−0.875177	−	1.51585i	−0.0313163	−	0.0542414i
$782$	−17.9764	+	4.81676i	−0.642835	+	0.172247i
$783$		−	19.5732i		−	0.699491i
$784$		0			0
$785$	−10.0102	+	10.0102i	−0.357281	+	0.357281i
$786$	−0.966266	−	3.60616i	−0.0344656	−	0.128627i
$787$	−11.8252	−	3.16854i	−0.421522	−	0.112946i	0.0418220	−	0.999125i	$-0.486684\pi$
$787$	−11.8252	−	3.16854i	−0.421522	−	0.112946i	−0.463344	+	0.886179i	$0.653350\pi$
$788$	−4.91622	+	18.3476i	−0.175133	+	0.653606i
$789$	25.4621	+	14.7006i	0.906476	+	0.523354i
$790$	−3.99272			−0.142055
$791$		0			0
$792$			2.61942i			0.0930771i
$793$	21.0688	+	14.5981i	0.748175	+	0.518393i
$794$	−7.11125	+	4.10568i	−0.252369	+	0.145705i
$795$	17.0190	+	4.56022i	0.603600	+	0.161734i
$796$	−6.63782	−	3.83235i	−0.235271	−	0.135834i
$797$	28.1163			0.995931			0.497966	−	0.867197i	$-0.334081\pi$
$797$	28.1163			0.995931			0.497966	+	0.867197i	$0.334081\pi$
$798$		0			0
$799$	−18.5340	+	18.5340i	−0.655685	+	0.655685i
$800$	15.0163	−	4.02361i	0.530907	−	0.142256i
$801$	−13.9412	−	3.73554i	−0.492588	−	0.131989i
$802$	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
$808$	6.97789	−	26.0418i	0.245481	−	0.916148i
$809$	−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	$-0.247202\pi$
$811$	0.354016	+	0.354016i	0.0124312	+	0.0124312i	−0.700864	+	0.713295i	$0.747202\pi$
$812$		0			0
$813$	−25.7440	−	25.7440i	−0.902882	−	0.902882i
$814$	−1.89587	+	0.507997i	−0.0664502	+	0.0178053i
$815$	9.67809	−	5.58765i	0.339009	−	0.195727i
$816$	−16.9109	+	9.76353i	−0.592001	+	0.341792i
$817$	11.3939	+	42.5227i	0.398623	+	1.48768i
$818$	1.45028			0.0507078
$819$		0			0
$820$	−4.26187			−0.148831
$821$	7.64163	+	28.5189i	0.266695	+	0.995318i	0.961205	+	0.275835i	$0.0889544\pi$
$821$	7.64163	+	28.5189i	0.266695	+	0.995318i	−0.694510	+	0.719483i	$0.744379\pi$
$822$	−10.9393	+	6.31582i	−0.381553	+	0.220290i
$823$	−8.97295	+	5.18053i	−0.312777	+	0.180582i	−0.648169	−	0.761497i	$-0.724465\pi$
$823$	−8.97295	+	5.18053i	−0.312777	+	0.180582i	0.335391	+	0.942079i	$0.391131\pi$
$824$	12.3741	−	3.31562i	0.431071	−	0.115505i
$825$	−2.11078	−	2.11078i	−0.0734880	−	0.0734880i
$826$		0			0
$827$	33.3235	+	33.3235i	1.15877	+	1.15877i	0.984740	+	0.174030i	$0.0556789\pi$
$827$	33.3235	+	33.3235i	1.15877	+	1.15877i	0.174030	+	0.984740i	$0.444321\pi$
$828$	−5.51270	+	9.54827i	−0.191579	+	0.331825i
$829$	−9.93234	−	17.2033i	−0.344964	−	0.597496i	0.640383	−	0.768056i	$-0.278776\pi$
$829$	−9.93234	−	17.2033i	−0.344964	−	0.597496i	−0.985347	+	0.170560i	$0.945442\pi$
$830$	−3.75090	+	13.9986i	−0.130196	+	0.485897i
$831$	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
$837$	9.59014	+	2.56967i	0.331484	+	0.0888208i
$838$	9.08765	−	2.43503i	0.313928	−	0.0841166i
$839$	16.2048	−	16.2048i	0.559453	−	0.559453i	−0.369698	−	0.929152i	$-0.620539\pi$
$839$	16.2048	−	16.2048i	0.559453	−	0.559453i	0.929152	+	0.369698i	$0.120539\pi$
$840$		0			0
$841$	−16.4387			−0.566850
$842$	5.95798	+	3.43984i	0.205326	+	0.118545i
$843$	20.3334	+	5.44833i	0.700321	+	0.187650i
$844$	−0.861761	+	0.497538i	−0.0296630	+	0.0171260i
$845$	18.8876	−	1.84050i	0.649752	−	0.0633152i
$846$		−	3.01147i		−	0.103536i
$847$		0			0
$848$	21.1187			0.725220
$849$	−16.4007	−	9.46898i	−0.562872	−	0.324974i
$850$	3.11002	−	11.6067i	0.106673	−	0.398108i
$851$	−17.5074	−	4.69109i	−0.600146	−	0.160809i
$852$	1.10779	+	4.13431i	0.0379521	+	0.141639i
$853$	12.4778	−	12.4778i	0.427232	−	0.427232i	−0.460452	−	0.887684i	$-0.652313\pi$
$853$	12.4778	−	12.4778i	0.427232	−	0.427232i	0.887684	+	0.460452i	$0.152313\pi$
$854$		0			0
$855$			10.9878i			0.375774i
$856$	17.9452	−	4.80841i	0.613355	−	0.164348i
$857$	13.6250	+	23.5993i	0.465422	+	0.806135i	0.999220	−	0.0394767i	$-0.0125691\pi$
$857$	13.6250	+	23.5993i	0.465422	+	0.806135i	−0.533798	+	0.845612i	$0.679236\pi$
$858$	1.93336	−	0.913186i	0.0660039	−	0.0311757i
$859$	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
$863$	−7.72999	−	28.8487i	−0.263132	−	0.982021i	−0.963384	−	0.268126i	$-0.913596\pi$
$863$	−7.72999	−	28.8487i	−0.263132	−	0.982021i	0.700252	−	0.713896i	$-0.253071\pi$
$864$	7.74497	−	28.9046i	0.263489	−	0.983356i
$865$	2.70342	−	10.0893i	0.0919191	−	0.343047i
$866$	−5.29165	−	19.7487i	−0.179818	−	0.671089i
$867$			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
$871$	−42.0891	−	15.0843i	−1.42613	−	0.511113i
$872$	−6.80900	−	11.7935i	−0.230582	−	0.399380i
$873$	−12.2577	+	3.28445i	−0.414861	+	0.111162i
$874$		−	12.8707i		−	0.435356i
$875$		0			0
$876$	−0.214405	+	0.214405i	−0.00724406	+	0.00724406i
$877$	5.14100	+	19.1865i	0.173599	+	0.647881i	0.996786	+	0.0801105i	$0.0255273\pi$
$877$	5.14100	+	19.1865i	0.173599	+	0.647881i	−0.823187	+	0.567771i	$0.807806\pi$
$878$	−5.79723	−	1.55336i	−0.195647	−	0.0524235i
$879$	4.41464	−	16.4757i	0.148902	−	0.555710i
$880$	2.30142	+	1.32873i	0.0775809	+	0.0447913i
$881$	13.3800			0.450782			0.225391	−	0.974268i	$-0.427634\pi$
$881$	13.3800			0.450782			0.225391	+	0.974268i	$0.427634\pi$
$882$		0			0
$883$		−	1.63893i		−	0.0551545i	−0.999620	−	0.0275773i	$-0.991221\pi$
$883$		−	1.63893i		−	0.0551545i	0.999620	−	0.0275773i	$-0.00877923\pi$
$884$	−36.4795	−	25.2758i	−1.22694	−	0.850118i
$885$	−2.40102	+	1.38623i	−0.0807094	+	0.0465976i
$886$	7.08107	+	1.89737i	0.237893	+	0.0637433i
$887$	−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
$891$	−1.92654	+	0.516215i	−0.0645416	+	0.0172939i
$892$	−6.53905	−	1.75213i	−0.218943	−	0.0586657i
$893$	−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
$899$	−1.64911	+	6.15457i	−0.0550010	+	0.205267i
$900$	−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
$905$	6.43047	−	1.72304i	0.213756	−	0.0572758i
$906$	−5.28326	+	3.05029i	−0.175524	+	0.101339i
$907$	2.25159	−	1.29995i	0.0747627	−	0.0431643i	−0.462153	−	0.886800i	$-0.652923\pi$
$907$	2.25159	−	1.29995i	0.0747627	−	0.0431643i	0.536915	+	0.843636i	$0.319589\pi$
$908$	−12.0525	−	44.9805i	−0.399976	−	1.49273i
$909$	−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	$0.260471\pi$
$912$	−3.49522	−	13.0443i	−0.115738	−	0.431941i
$913$	12.7350	−	7.35253i	0.421466	−	0.243333i
$914$	−15.4425	+	8.91573i	−0.510792	+	0.294906i
$915$	12.3535	−	3.31011i	0.408394	−	0.109429i
$916$	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
$921$	3.67243	−	13.7057i	0.121011	−	0.451618i
$922$	−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
$928$	18.5499	+	4.97042i	0.608929	+	0.163162i
$929$	26.2009	−	7.02052i	0.859624	−	0.230336i	0.198029	−	0.980196i	$-0.436546\pi$
$929$	26.2009	−	7.02052i	0.859624	−	0.230336i	0.661596	+	0.749861i	$0.269879\pi$
$930$	−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
$934$	7.36970	+	1.97471i	0.241144	+	0.0646143i
$935$	7.84247	−	4.52785i	0.256476	−	0.148077i
$936$	11.0072	−	1.99694i	0.359783	−	0.0652722i
$937$			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
$941$	11.6883	−	43.6215i	0.381029	−	1.42202i	−0.463303	−	0.886200i	$-0.653336\pi$
$941$	11.6883	−	43.6215i	0.381029	−	1.42202i	0.844332	−	0.535820i	$-0.179997\pi$
$942$	6.57996	+	1.76310i	0.214387	+	0.0574448i
$943$	−2.00445	−	7.48072i	−0.0652739	−	0.243606i
$944$	−2.34979	+	2.34979i	−0.0764791	+	0.0764791i
$945$		0			0
$946$			4.16854i			0.135531i
$947$	11.5162	−	3.08574i	0.374225	−	0.100273i	−0.0668042	−	0.997766i	$-0.521280\pi$
$947$	11.5162	−	3.08574i	0.374225	−	0.100273i	0.441029	+	0.897493i	$0.354614\pi$
$948$	−4.95336	−	8.57947i	−0.160878	−	0.278648i
$949$	−0.498518	−	0.178664i	−0.0161826	−	0.00579968i
$950$	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	$0.109838\pi$
$953$			20.8846i			0.676519i	−0.941053	+	0.338259i	$0.890162\pi$
$954$	2.14001	+	7.98662i	0.0692854	+	0.258577i
$955$	−1.39998	+	5.22480i	−0.0453023	+	0.169070i
$956$	−0.517291	+	1.93056i	−0.0167304	+	0.0624387i
$957$	−0.954403	−	3.56188i	−0.0308515	−	0.115139i
$958$			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
$962$	3.58003	+	7.57949i	0.115425	+	0.244372i
$963$	−6.56841	−	11.3768i	−0.211664	−	0.366613i
$964$	35.0028	−	9.37898i	1.12737	−	0.302077i
$965$			35.2001i			1.13313i
$966$		0			0
$967$	20.9628	−	20.9628i	0.674117	−	0.674117i	−0.284545	−	0.958663i	$-0.591843\pi$
$967$	20.9628	−	20.9628i	0.674117	−	0.674117i	0.958663	+	0.284545i	$0.0918426\pi$
$968$	−5.57729	−	20.8147i	−0.179261	−	0.669010i
$969$	−44.4508	−	11.9106i	−1.42796	−	0.382622i
$970$	1.84497	−	6.88552i	0.0592384	−	0.221081i
$971$	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
$975$	−7.26068	+	10.4790i	−0.232528	+	0.335598i
$976$	13.2756	−	7.66469i	0.424943	−	0.245341i
$977$	38.0058	+	10.1836i	1.21591	+	0.325803i	0.809079	−	0.587699i	$-0.199966\pi$
$977$	38.0058	+	10.1836i	1.21591	+	0.325803i	0.406834	+	0.913502i	$0.366633\pi$
$978$	−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
$982$	−10.7327	+	2.87581i	−0.342493	+	0.0917707i
$983$	−49.0362	−	13.1392i	−1.56401	−	0.419076i	−0.630082	−	0.776529i	$-0.716979\pi$
$983$	−49.0362	−	13.1392i	−1.56401	−	0.419076i	−0.933931	+	0.357453i	$0.883645\pi$
$984$	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
$990$	−0.269286	+	1.00499i	−0.00855847	+	0.0319406i
$991$	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
$996$	−34.7332	+	9.30672i	−1.10056	+	0.294895i
$997$	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
$999$	−5.83023	−	21.7587i	−0.184460	−	0.688415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bc.a.460.4		24
7.2	even	3		91.2.i.a.83.4	yes	12
7.3	odd	6	inner	637.2.bc.a.31.4		24
7.4	even	3	inner	637.2.bc.a.31.3		24
7.5	odd	6		91.2.i.a.83.3	yes	12
7.6	odd	2	inner	637.2.bc.a.460.3		24
13.8	odd	4	inner	637.2.bc.a.411.4		24
21.2	odd	6		819.2.y.h.811.4		12
21.5	even	6		819.2.y.h.811.3		12
91.34	even	4	inner	637.2.bc.a.411.3		24
91.47	even	12		91.2.i.a.34.3	✓	12
91.60	odd	12	inner	637.2.bc.a.619.3		24
91.73	even	12	inner	637.2.bc.a.619.4		24
91.86	odd	12		91.2.i.a.34.4	yes	12
273.47	odd	12		819.2.y.h.307.4		12
273.86	even	12		819.2.y.h.307.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.3	✓	12	91.47	even	12
91.2.i.a.34.4	yes	12	91.86	odd	12
91.2.i.a.83.3	yes	12	7.5	odd	6
91.2.i.a.83.4	yes	12	7.2	even	3
637.2.bc.a.31.3		24	7.4	even	3	inner
637.2.bc.a.31.4		24	7.3	odd	6	inner
637.2.bc.a.411.3		24	91.34	even	4	inner
637.2.bc.a.411.4		24	13.8	odd	4	inner
637.2.bc.a.460.3		24	7.6	odd	2	inner
637.2.bc.a.460.4		24	1.1	even	1	trivial
637.2.bc.a.619.3		24	91.60	odd	12	inner
637.2.bc.a.619.4		24	91.73	even	12	inner
819.2.y.h.307.3		12	273.86	even	12
819.2.y.h.307.4		12	273.47	odd	12
819.2.y.h.811.3		12	21.5	even	6
819.2.y.h.811.4		12	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.147520 - 0.550552i) q^{2} +(1.06729 - 0.616199i) q^{3} +(1.45071 - 0.837565i) q^{4} +(1.41003 - 0.377817i) q^{5} +(-0.496696 - 0.496696i) q^{6} +(-1.48119 - 1.48119i) q^{8} +(-0.740597 + 1.28275i) q^{9} +O(q^{10})\)	\(q+(-0.147520 - 0.550552i) q^{2} +(1.06729 - 0.616199i) q^{3} +(1.45071 - 0.837565i) q^{4} +(1.41003 - 0.377817i) 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} +(-0.218506 + 0.815474i) 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} +(0.815474 + 0.218506i) q^{18} +(4.90859 - 1.31525i) q^{19} +(1.72909 - 1.72909i) q^{20} +0.481194 q^{22} +(3.84826 + 2.22179i) q^{23} +(-2.49357 - 0.668151i) q^{24} +(-2.48469 + 1.43453i) q^{25} +(-0.366844 - 2.02206i) q^{26} +5.52262i q^{27} -3.54420 q^{29} +(-0.888016 - 0.512696i) q^{30} +(0.465299 - 1.73652i) q^{31} +(-5.23387 - 1.40241i) q^{32} +(0.269286 + 1.00499i) q^{33} +(-2.96149 + 2.96149i) q^{34} +2.48119i q^{36} +(-3.93993 + 1.05570i) q^{37} +(-1.44823 - 2.50841i) q^{38} +(4.01784 - 1.89775i) q^{39} +(-2.64815 - 1.52891i) q^{40} +(-1.23240 - 1.23240i) q^{41} +8.66291i q^{43} +(0.366025 + 1.36603i) q^{44} +(-0.559620 + 2.08853i) q^{45} +(0.655517 - 2.44642i) q^{46} +(-0.923226 - 3.44553i) q^{47} -2.65745i q^{48} +(1.15633 + 1.15633i) q^{50} +(-7.84247 - 4.52785i) q^{51} +(5.46122 - 2.57951i) q^{52} +(4.89692 + 8.48172i) q^{53} +(3.04049 - 0.814696i) q^{54} +1.23240i q^{55} +(4.42842 - 4.42842i) q^{57} +(0.522840 + 1.95126i) q^{58} +(-1.48858 - 0.398865i) q^{59} +(0.779975 - 2.91091i) q^{60} +(6.15660 + 3.55452i) q^{61} -1.02469 q^{62} -1.22425i q^{64} +(5.17875 - 0.939533i) q^{65} +(0.513573 - 0.296512i) q^{66} +(-11.9779 - 3.20948i) q^{67} +(-10.6598 - 6.15446i) q^{68} +5.47626 q^{69} +(-1.46604 + 1.46604i) q^{71} +(2.99697 - 0.803037i) q^{72} +(-0.141871 - 0.0380142i) 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} +(0.814696 - 3.04049i) 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} +(4.76938 - 1.27795i) q^{86} +(-3.78268 + 2.18393i) q^{87} +(1.53152 - 0.884226i) q^{88} +(2.52198 + 9.41214i) q^{89} +1.23240 q^{90} +7.44358 q^{92} +(-0.573434 - 2.14009i) q^{93} +(-1.76075 + 1.01657i) q^{94} +(6.42434 - 3.70910i) q^{95} +(-6.45021 + 1.72833i) 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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