LMFDB - Embedded newform 980.2.o.f.31.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(31,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("980.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.o (of order $6$, degree $2$, 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.8
Character	$\chi$	$=$	980.31
Dual form			980.2.o.f.411.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0915727 - 1.41125i) q^{2} +(-1.49907 + 2.59647i) q^{3} +(-1.98323 - 0.258463i) q^{4} +(0.866025 - 0.500000i) q^{5} +(3.52698 + 2.35332i) q^{6} +(-0.546365 + 2.77516i) q^{8} +(-2.99443 - 5.18651i) q^{9} +O(q^{10})$	\(q+(0.0915727 - 1.41125i) q^{2} +(-1.49907 + 2.59647i) q^{3} +(-1.98323 - 0.258463i) q^{4} +(0.866025 - 0.500000i) q^{5} +(3.52698 + 2.35332i) q^{6} +(-0.546365 + 2.77516i) q^{8} +(-2.99443 - 5.18651i) q^{9} +(-0.626319 - 1.26796i) q^{10} +(1.93693 + 1.11828i) q^{11} +(3.64409 - 4.76194i) q^{12} -3.17109i q^{13} +2.99814i q^{15} +(3.86639 + 1.02518i) q^{16} +(2.98390 + 1.72275i) q^{17} +(-7.59365 + 3.75094i) q^{18} +(1.02618 + 1.77739i) q^{19} +(-1.84676 + 0.767779i) q^{20} +(1.75554 - 2.63107i) q^{22} +(2.30481 - 1.33068i) q^{23} +(-6.38656 - 5.57878i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-4.47519 - 0.290385i) q^{26} +8.96105 q^{27} -7.38092 q^{29} +(4.23112 + 0.274548i) q^{30} +(-2.44599 + 4.23658i) q^{31} +(1.80084 - 5.36255i) q^{32} +(-5.80718 + 3.35278i) q^{33} +(2.70447 - 4.05325i) q^{34} +(4.59812 + 11.0600i) q^{36} +(5.59689 + 9.69410i) q^{37} +(2.60230 - 1.28543i) q^{38} +(8.23364 + 4.75369i) q^{39} +(0.914412 + 2.67654i) q^{40} -1.46011i q^{41} +9.95752i q^{43} +(-3.55233 - 2.71844i) q^{44} +(-5.18651 - 2.99443i) q^{45} +(-1.66686 - 3.37451i) q^{46} +(3.06343 + 5.30601i) q^{47} +(-8.45786 + 8.50215i) q^{48} +(-1.17639 - 0.784927i) q^{50} +(-8.94615 + 5.16506i) q^{51} +(-0.819610 + 6.28900i) q^{52} +(-2.32888 + 4.03374i) q^{53} +(0.820587 - 12.6462i) q^{54} +2.23657 q^{55} -6.15325 q^{57} +(-0.675891 + 10.4163i) q^{58} +(-3.55938 + 6.16503i) q^{59} +(0.774910 - 5.94600i) q^{60} +(2.19681 - 1.26833i) q^{61} +(5.75488 + 3.83985i) q^{62} +(-7.40297 - 3.03249i) q^{64} +(-1.58555 - 2.74625i) q^{65} +(4.19981 + 8.50238i) q^{66} +(0.0456998 + 0.0263848i) q^{67} +(-5.47248 - 4.18784i) q^{68} +7.97917i q^{69} +0.212347i q^{71} +(16.0294 - 5.47629i) q^{72} +(12.8816 + 7.43720i) q^{73} +(14.1933 - 7.01088i) q^{74} +(1.49907 + 2.59647i) q^{75} +(-1.57575 - 3.79020i) q^{76} +(7.46261 - 11.1844i) q^{78} +(-0.399413 + 0.230601i) q^{79} +(3.86099 - 1.04536i) q^{80} +(-4.44995 + 7.70755i) q^{81} +(-2.06058 - 0.133707i) q^{82} +10.9174 q^{83} +3.44551 q^{85} +(14.0525 + 0.911837i) q^{86} +(11.0645 - 19.1643i) q^{87} +(-4.16168 + 4.76428i) q^{88} +(-6.07992 + 3.51024i) q^{89} +(-4.70082 + 7.04523i) q^{90} +(-4.91490 + 2.04334i) q^{92} +(-7.33344 - 12.7019i) q^{93} +(7.76862 - 3.83736i) q^{94} +(1.77739 + 1.02618i) q^{95} +(11.2241 + 12.7147i) q^{96} +0.185459i q^{97} -13.3945i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} + 30 q^{12} - 14 q^{16} - 8 q^{22} - 36 q^{24} + 16 q^{25} - 30 q^{26} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} + 60 q^{38} - 18 q^{44} - 12 q^{45} + 2 q^{46} + 4 q^{50} + 36 q^{52} - 8 q^{53} - 12 q^{54} + 48 q^{57} + 2 q^{58} + 14 q^{60} - 24 q^{61} + 4 q^{64} + 4 q^{65} - 24 q^{66} - 60 q^{68} + 4 q^{72} + 72 q^{73} + 38 q^{74} + 120 q^{78} - 36 q^{81} - 42 q^{82} + 28 q^{86} + 4 q^{88} + 60 q^{89} - 4 q^{92} - 8 q^{93} - 18 q^{94} + 60 q^{96}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 + 30 * q^12 - 14 * q^16 - 8 * q^22 - 36 * q^24 + 16 * q^25 - 30 * q^26 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 + 60 * q^38 - 18 * q^44 - 12 * q^45 + 2 * q^46 + 4 * q^50 + 36 * q^52 - 8 * q^53 - 12 * q^54 + 48 * q^57 + 2 * q^58 + 14 * q^60 - 24 * q^61 + 4 * q^64 + 4 * q^65 - 24 * q^66 - 60 * q^68 + 4 * q^72 + 72 * q^73 + 38 * q^74 + 120 * q^78 - 36 * q^81 - 42 * q^82 + 28 * q^86 + 4 * q^88 + 60 * q^89 - 4 * q^92 - 8 * q^93 - 18 * q^94 + 60 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.0915727	−	1.41125i	0.0647517	−	0.997901i
$2$	0.0915727	−	1.41125i	0.0647517	−	0.997901i
$3$	−1.49907	+	2.59647i	−0.865490	+	1.49907i	0.00107081	+	0.999999i	$0.499659\pi$
$3$	−1.49907	+	2.59647i	−0.865490	+	1.49907i	−0.866560	+	0.499072i	$0.833674\pi$
$4$	−1.98323	−	0.258463i	−0.991614	−	0.129232i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	3.52698	+	2.35332i	1.43988	+	0.960741i
$7$		0			0
$7$		0			0
$8$	−0.546365	+	2.77516i	−0.193169	+	0.981165i
$9$	−2.99443	−	5.18651i	−0.998144	−	1.72884i
$10$	−0.626319	−	1.26796i	−0.198059	−	0.400964i
$11$	1.93693	+	1.11828i	0.584005	+	0.337175i	0.762723	−	0.646725i	$-0.223862\pi$
$11$	1.93693	+	1.11828i	0.584005	+	0.337175i	−0.178718	+	0.983900i	$0.557195\pi$
$12$	3.64409	−	4.76194i	1.05196	−	1.37465i
$13$		−	3.17109i		−	0.879502i	−0.898120	−	0.439751i	$-0.855067\pi$
$13$		−	3.17109i		−	0.879502i	0.898120	−	0.439751i	$-0.144933\pi$
$14$		0			0
$15$			2.99814i			0.774117i
$16$	3.86639	+	1.02518i	0.966598	+	0.256296i
$17$	2.98390	+	1.72275i	0.723701	+	0.417829i	0.816113	−	0.577892i	$-0.196124\pi$
$17$	2.98390	+	1.72275i	0.723701	+	0.417829i	−0.0924124	+	0.995721i	$0.529458\pi$
$18$	−7.59365	+	3.75094i	−1.78984	+	0.884104i
$19$	1.02618	+	1.77739i	0.235421	+	0.407761i	0.959395	−	0.282066i	$-0.0910198\pi$
$19$	1.02618	+	1.77739i	0.235421	+	0.407761i	−0.723974	+	0.689827i	$0.757686\pi$
$20$	−1.84676	+	0.767779i	−0.412948	+	0.171681i
$21$		0			0
$22$	1.75554	−	2.63107i	0.374283	−	0.560947i
$23$	2.30481	−	1.33068i	0.480587	−	0.277467i	−0.240074	−	0.970755i	$-0.577172\pi$
$23$	2.30481	−	1.33068i	0.480587	−	0.277467i	0.720661	+	0.693288i	$0.243838\pi$
$24$	−6.38656	−	5.57878i	−1.30365	−	1.13876i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−4.47519	−	0.290385i	−0.877657	−	0.0569493i
$27$	8.96105			1.72455
$28$		0			0
$29$	−7.38092			−1.37060			−0.685301	−	0.728260i	$-0.740329\pi$
$29$	−7.38092			−1.37060			−0.685301	+	0.728260i	$0.740329\pi$
$30$	4.23112	+	0.274548i	0.772493	+	0.0501254i
$31$	−2.44599	+	4.23658i	−0.439313	+	0.760913i	−0.997637	−	0.0687104i	$-0.978112\pi$
$31$	−2.44599	+	4.23658i	−0.439313	+	0.760913i	0.558323	+	0.829623i	$0.311445\pi$
$32$	1.80084	−	5.36255i	0.318347	−	0.947974i
$33$	−5.80718	+	3.35278i	−1.01090	+	0.583643i
$34$	2.70447	−	4.05325i	0.463813	−	0.695127i
$35$		0			0
$36$	4.59812	+	11.0600i	0.766354	+	1.84333i
$37$	5.59689	+	9.69410i	0.920123	+	1.59370i	0.799222	+	0.601036i	$0.205245\pi$
$37$	5.59689	+	9.69410i	0.920123	+	1.59370i	0.120902	+	0.992664i	$0.461421\pi$
$38$	2.60230	−	1.28543i	0.422149	−	0.208524i
$39$	8.23364	+	4.75369i	1.31844	+	0.761200i
$40$	0.914412	+	2.67654i	0.144581	+	0.423198i
$41$		−	1.46011i		−	0.228031i	−0.993479	−	0.114016i	$-0.963629\pi$
$41$		−	1.46011i		−	0.228031i	0.993479	−	0.114016i	$-0.0363714\pi$
$42$		0			0
$43$			9.95752i			1.51851i	0.650794	+	0.759254i	$0.274436\pi$
$43$			9.95752i			1.51851i	−0.650794	+	0.759254i	$0.725564\pi$
$44$	−3.55233	−	2.71844i	−0.535534	−	0.409820i
$45$	−5.18651	−	2.99443i	−0.773159	−	0.446384i
$46$	−1.66686	−	3.37451i	−0.245766	−	0.497545i
$47$	3.06343	+	5.30601i	0.446847	+	0.773962i	0.998179	−	0.0603243i	$-0.0192135\pi$
$47$	3.06343	+	5.30601i	0.446847	+	0.773962i	−0.551332	+	0.834286i	$0.685880\pi$
$48$	−8.45786	+	8.50215i	−1.22079	+	1.22718i
$49$		0			0
$50$	−1.17639	−	0.784927i	−0.166366	−	0.111005i
$51$	−8.94615	+	5.16506i	−1.25271	+	0.723253i
$52$	−0.819610	+	6.28900i	−0.113659	+	0.872127i
$53$	−2.32888	+	4.03374i	−0.319897	+	0.554077i	−0.980466	−	0.196688i	$-0.936982\pi$
$53$	−2.32888	+	4.03374i	−0.319897	+	0.554077i	0.660570	+	0.750765i	$0.270315\pi$
$54$	0.820587	−	12.6462i	0.111668	−	1.72094i
$55$	2.23657			0.301579
$56$		0			0
$57$	−6.15325			−0.815018
$58$	−0.675891	+	10.4163i	−0.0887488	+	1.36773i
$59$	−3.55938	+	6.16503i	−0.463392	+	0.802619i	−0.999127	−	0.0417674i	$-0.986701\pi$
$59$	−3.55938	+	6.16503i	−0.463392	+	0.802619i	0.535735	+	0.844386i	$0.320035\pi$
$60$	0.774910	−	5.94600i	0.100040	−	0.767626i
$61$	2.19681	−	1.26833i	0.281272	−	0.162393i	−0.352727	−	0.935726i	$-0.614746\pi$
$61$	2.19681	−	1.26833i	0.281272	−	0.162393i	0.633999	+	0.773334i	$0.281412\pi$
$62$	5.75488	+	3.83985i	0.730870	+	0.487662i
$63$		0			0
$64$	−7.40297	−	3.03249i	−0.925371	−	0.379062i
$65$	−1.58555	−	2.74625i	−0.196663	−	0.340630i
$66$	4.19981	+	8.50238i	0.516961	+	1.04657i
$67$	0.0456998	+	0.0263848i	0.00558311	+	0.00322341i	0.502789	−	0.864409i	$-0.332307\pi$
$67$	0.0456998	+	0.0263848i	0.00558311	+	0.00322341i	−0.497206	+	0.867633i	$0.665641\pi$
$68$	−5.47248	−	4.18784i	−0.663636	−	0.507850i
$69$			7.97917i			0.960579i
$70$		0			0
$71$			0.212347i			0.0252009i	0.999921	+	0.0126005i	$0.00401095\pi$
$71$			0.212347i			0.0252009i	−0.999921	+	0.0126005i	$0.995989\pi$
$72$	16.0294	−	5.47629i	1.88909	−	0.645387i
$73$	12.8816	+	7.43720i	1.50768	+	0.870459i	0.999960	+	0.00893589i	$0.00284442\pi$
$73$	12.8816	+	7.43720i	1.50768	+	0.870459i	0.507719	+	0.861523i	$0.330489\pi$
$74$	14.1933	−	7.01088i	1.64994	−	0.814998i
$75$	1.49907	+	2.59647i	0.173098	+	0.299814i
$76$	−1.57575	−	3.79020i	−0.180751	−	0.434766i
$77$		0			0
$78$	7.46261	−	11.1844i	0.844974	−	1.26638i
$79$	−0.399413	+	0.230601i	−0.0449375	+	0.0259447i	−0.522300	−	0.852762i	$-0.674926\pi$
$79$	−0.399413	+	0.230601i	−0.0449375	+	0.0259447i	0.477363	+	0.878706i	$0.341593\pi$
$80$	3.86099	−	1.04536i	0.431671	−	0.116875i
$81$	−4.44995	+	7.70755i	−0.494439	+	0.856394i
$82$	−2.06058	−	0.133707i	−0.227553	−	0.0147654i
$83$	10.9174			1.19834			0.599168	−	0.800624i	$-0.295498\pi$
$83$	10.9174			1.19834			0.599168	+	0.800624i	$0.295498\pi$
$84$		0			0
$85$	3.44551			0.373718
$86$	14.0525	+	0.911837i	1.51532	+	0.0983259i
$87$	11.0645	−	19.1643i	1.18624	−	2.05463i
$88$	−4.16168	+	4.76428i	−0.443637	+	0.507874i
$89$	−6.07992	+	3.51024i	−0.644470	+	0.372085i	−0.786334	−	0.617801i	$-0.788024\pi$
$89$	−6.07992	+	3.51024i	−0.644470	+	0.372085i	0.141864	+	0.989886i	$0.454690\pi$
$90$	−4.70082	+	7.04523i	−0.495510	+	0.742633i
$91$		0			0
$92$	−4.91490	+	2.04334i	−0.512414	+	0.213033i
$93$	−7.33344	−	12.7019i	−0.760442	−	1.31712i
$94$	7.76862	−	3.83736i	0.801272	−	0.395794i
$95$	1.77739	+	1.02618i	0.182356	+	0.105284i
$96$	11.2241	+	12.7147i	1.14556	+	1.29769i
$97$			0.185459i			0.0188305i	0.999956	+	0.00941523i	$0.00299701\pi$
$97$			0.185459i			0.0188305i	−0.999956	+	0.00941523i	$0.997003\pi$
$98$		0			0
$99$		−	13.3945i		−	1.34620i
$100$	−1.21545	+	1.58830i	−0.121545	+	0.158830i
$101$	5.41172	+	3.12446i	0.538486	+	0.310895i	0.744465	−	0.667661i	$-0.232705\pi$
$101$	5.41172	+	3.12446i	0.538486	+	0.310895i	−0.205979	+	0.978556i	$0.566038\pi$
$102$	6.46995	+	13.0982i	0.640620	+	1.29691i
$103$	−5.70918	−	9.88858i	−0.562542	−	0.974351i	−0.997274	−	0.0737911i	$-0.976490\pi$
$103$	−5.70918	−	9.88858i	−0.562542	−	0.974351i	0.434732	−	0.900560i	$-0.356843\pi$
$104$	8.80027	+	1.73257i	0.862937	+	0.169893i
$105$		0			0
$106$	5.47934	+	3.65601i	0.532201	+	0.355103i
$107$	−2.25502	+	1.30194i	−0.218001	+	0.125863i	−0.605024	−	0.796207i	$-0.706837\pi$
$107$	−2.25502	+	1.30194i	−0.218001	+	0.125863i	0.387023	+	0.922070i	$0.373503\pi$
$108$	−17.7718	−	2.31610i	−1.71009	−	0.222867i
$109$	−0.500946	+	0.867663i	−0.0479819	+	0.0831071i	−0.889019	−	0.457871i	$-0.848612\pi$
$109$	−0.500946	+	0.867663i	−0.0479819	+	0.0831071i	0.841037	+	0.540978i	$0.181946\pi$
$110$	0.204809	−	3.15635i	0.0195277	−	0.300946i
$111$	−33.5606			−3.18543
$112$		0			0
$113$	14.8588			1.39780			0.698899	−	0.715220i	$-0.253674\pi$
$113$	14.8588			1.39780			0.698899	+	0.715220i	$0.253674\pi$
$114$	−0.563470	+	8.68375i	−0.0527738	+	0.813307i
$115$	1.33068	−	2.30481i	0.124087	−	0.214925i
$116$	14.6381	+	1.90770i	1.35911	+	0.177125i
$117$	−16.4469	+	9.49562i	−1.52052	+	0.877870i
$118$	8.37443	+	5.58771i	0.770929	+	0.514391i
$119$		0			0
$120$	−8.32031	−	1.63808i	−0.759537	−	0.149536i
$121$	−2.99888	−	5.19421i	−0.272626	−	0.472201i
$122$	−1.58875	−	3.21638i	−0.143839	−	0.291197i
$123$	3.79114	+	2.18882i	0.341836	+	0.197359i
$124$	5.94597	−	7.76992i	0.533963	−	0.697759i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	3.02360i		−	0.268301i	−0.990961	−	0.134151i	$-0.957169\pi$
$127$		−	3.02360i		−	0.268301i	0.990961	−	0.134151i	$-0.0428306\pi$
$128$	−4.95750	+	10.1697i	−0.438186	+	0.898885i
$129$	−25.8544	−	14.9270i	−2.27635	−	1.31425i
$130$	−4.02082	+	1.98611i	−0.352649	+	0.174194i
$131$	7.85267	+	13.6012i	0.686091	+	1.18834i	0.973093	+	0.230414i	$0.0740081\pi$
$131$	7.85267	+	13.6012i	0.686091	+	1.18834i	−0.287002	+	0.957930i	$0.592659\pi$
$132$	12.3835	−	5.14838i	1.07785	−	0.448109i
$133$		0			0
$134$	0.0414202	−	0.0620775i	0.00357816	−	0.00536268i
$135$	7.76049	−	4.48052i	0.667917	−	0.385622i
$136$	−6.41120	+	7.33952i	−0.549756	+	0.629359i
$137$	−4.80718	+	8.32628i	−0.410705	+	0.711362i	−0.994967	−	0.100203i	$-0.968051\pi$
$137$	−4.80718	+	8.32628i	−0.410705	+	0.711362i	0.584262	+	0.811565i	$0.301384\pi$
$138$	11.2606	+	0.730674i	0.958563	+	0.0621991i
$139$	−7.49745			−0.635925			−0.317963	−	0.948103i	$-0.602999\pi$
$139$	−7.49745			−0.635925			−0.317963	+	0.948103i	$0.602999\pi$
$140$		0			0
$141$	−18.3692			−1.54697
$142$	0.299673	+	0.0194451i	0.0251480	+	0.00163180i
$143$	3.54618	−	6.14217i	0.296547	−	0.513634i
$144$	−6.26053	−	23.1229i	−0.521711	−	1.92691i
$145$	−6.39206	+	3.69046i	−0.530832	+	0.306476i
$146$	11.6753	−	17.4981i	0.966257	−	1.44815i
$147$		0			0
$148$	−8.59435	−	20.6722i	−0.706451	−	1.69925i
$149$	−3.25066	−	5.63031i	−0.266305	−	0.461253i	0.701600	−	0.712571i	$-0.252469\pi$
$149$	−3.25066	−	5.63031i	−0.266305	−	0.461253i	−0.967905	+	0.251318i	$0.919136\pi$
$150$	3.80153	−	1.87779i	0.310394	−	0.153321i
$151$	−20.5029	−	11.8373i	−1.66850	−	0.963309i	−0.968448	−	0.249217i	$-0.919827\pi$
$151$	−20.5029	−	11.8373i	−1.66850	−	0.963309i	−0.700052	−	0.714092i	$-0.746840\pi$
$152$	−5.49320	+	1.87670i	−0.445557	+	0.152220i
$153$		−	20.6347i		−	1.66821i
$154$		0			0
$155$			4.89199i			0.392934i
$156$	−15.1005	−	11.5558i	−1.20901	−	0.925201i
$157$	−6.78313	−	3.91624i	−0.541353	−	0.312550i	0.204274	−	0.978914i	$-0.434517\pi$
$157$	−6.78313	−	3.91624i	−0.541353	−	0.312550i	−0.745627	+	0.666363i	$0.767850\pi$
$158$	0.288860	+	0.584787i	0.0229805	+	0.0465232i
$159$	−6.98233	−	12.0937i	−0.553734	−	0.959096i
$160$	−1.12170	−	5.54453i	−0.0886783	−	0.438333i
$161$		0			0
$162$	10.4697	+	6.98578i	0.822581	+	0.548855i
$163$	9.39774	−	5.42579i	0.736088	−	0.424980i	−0.0845574	−	0.996419i	$-0.526948\pi$
$163$	9.39774	−	5.42579i	0.736088	−	0.424980i	0.820645	+	0.571438i	$0.193614\pi$
$164$	−0.377386	+	2.89574i	−0.0294689	+	0.226119i
$165$	−3.35278	+	5.80718i	−0.261013	+	0.452088i
$166$	0.999731	−	15.4071i	0.0775942	−	1.19582i
$167$	−11.7476			−0.909058			−0.454529	−	0.890732i	$-0.650192\pi$
$167$	−11.7476			−0.909058			−0.454529	+	0.890732i	$0.650192\pi$
$168$		0			0
$169$	2.94418			0.226476
$170$	0.315514	−	4.86246i	0.0241988	−	0.372933i
$171$	6.14563	−	10.6445i	0.469968	−	0.814009i
$172$	2.57365	−	19.7480i	0.196239	−	1.50577i
$173$	14.2785	−	8.24371i	1.08558	−	0.626758i	0.153181	−	0.988198i	$-0.451048\pi$
$173$	14.2785	−	8.24371i	1.08558	−	0.626758i	0.932395	+	0.361440i	$0.117715\pi$
$174$	−26.0324	−	17.3697i	−1.97351	−	1.31679i
$175$		0			0
$176$	6.34247	+	6.30943i	0.478082	+	0.475591i
$177$	−10.6715	−	18.4836i	−0.802122	−	1.38932i
$178$	4.39706	+	8.90170i	0.329574	+	0.667211i
$179$	7.88914	+	4.55480i	0.589662	+	0.340441i	0.764964	−	0.644073i	$-0.222757\pi$
$179$	7.88914	+	4.55480i	0.589662	+	0.340441i	−0.175302	+	0.984515i	$0.556090\pi$
$180$	9.51208	+	7.27917i	0.708989	+	0.542557i
$181$			16.5755i			1.23205i	0.787728	+	0.616023i	$0.211257\pi$
$181$			16.5755i			1.23205i	−0.787728	+	0.616023i	$0.788743\pi$
$182$		0			0
$183$			7.60525i			0.562196i
$184$	2.43359	+	7.12325i	0.179406	+	0.525133i
$185$	9.69410	+	5.59689i	0.712725	+	0.411492i
$186$	−18.5970	+	9.18614i	−1.36360	+	0.673560i
$187$	3.85305	+	6.67369i	0.281763	+	0.488028i
$188$	−4.70407	−	11.3148i	−0.343080	−	0.825218i
$189$		0			0
$190$	1.61095	−	2.41436i	0.116870	−	0.175156i
$191$	2.59197	−	1.49648i	0.187549	−	0.108281i	−0.403286	−	0.915074i	$-0.632132\pi$
$191$	2.59197	−	1.49648i	0.187549	−	0.108281i	0.590834	+	0.806793i	$0.298799\pi$
$192$	18.9714	−	14.6757i	1.36914	−	1.05912i
$193$	7.35442	−	12.7382i	0.529383	−	0.916918i	−0.470030	−	0.882651i	$-0.655757\pi$
$193$	7.35442	−	12.7382i	0.529383	−	0.916918i	0.999413	−	0.0342676i	$-0.0109098\pi$
$194$	0.261728	+	0.0169829i	0.0187909	+	0.00121930i
$195$	9.50739			0.680838
$196$		0			0
$197$	4.81748			0.343231			0.171616	−	0.985164i	$-0.445101\pi$
$197$	4.81748			0.343231			0.171616	+	0.985164i	$0.445101\pi$
$198$	−18.9029	−	1.22657i	−1.34337	−	0.0871686i
$199$	−0.637180	+	1.10363i	−0.0451685	+	0.0782342i	−0.887726	−	0.460373i	$-0.847716\pi$
$199$	−0.637180	+	1.10363i	−0.0451685	+	0.0782342i	0.842557	+	0.538607i	$0.181049\pi$
$200$	2.13017	+	1.86074i	0.150626	+	0.131574i
$201$	−0.137014	+	0.0791053i	−0.00966425	+	0.00557966i
$202$	4.90494	−	7.35115i	0.345110	−	0.517225i
$203$		0			0
$204$	19.0772	−	7.93125i	1.33567	−	0.555298i
$205$	−0.730057	−	1.26450i	−0.0509894	−	0.0883162i
$206$	−14.4780	+	7.15153i	−1.00873	+	0.498270i
$207$	−13.8032	−	7.96929i	−0.959390	−	0.553904i
$208$	3.25095	−	12.2607i	0.225413	−	0.850126i
$209$			4.59023i			0.317513i
$210$		0			0
$211$		−	3.70986i		−	0.255397i	−0.991813	−	0.127698i	$-0.959241\pi$
$211$		−	3.70986i		−	0.255397i	0.991813	−	0.127698i	$-0.0407590\pi$
$212$	5.66128	−	7.39791i	0.388818	−	0.508090i
$213$	−0.551351	−	0.318323i	−0.0377780	−	0.0218111i
$214$	1.63085	+	3.30161i	0.111483	+	0.225693i
$215$	4.97876	+	8.62347i	0.339549	+	0.588116i
$216$	−4.89600	+	24.8683i	−0.333131	+	1.69207i
$217$		0			0
$218$	1.17861	+	0.786412i	0.0798258	+	0.0532625i
$219$	−38.6209	+	22.2978i	−2.60976	+	1.50675i
$220$	−4.43563	−	0.578071i	−0.299050	−	0.0389735i
$221$	5.46301	−	9.46220i	0.367482	−	0.636497i
$222$	−3.07323	+	47.3622i	−0.206262	+	3.17874i
$223$	−12.9581			−0.867737			−0.433869	−	0.900976i	$-0.642852\pi$
$223$	−12.9581			−0.867737			−0.433869	+	0.900976i	$0.642852\pi$
$224$		0			0
$225$	−5.98886			−0.399258
$226$	1.36066	−	20.9694i	0.0905098	−	1.39487i
$227$	−4.44626	+	7.70115i	−0.295109	+	0.511143i	−0.975010	−	0.222160i	$-0.928689\pi$
$227$	−4.44626	+	7.70115i	−0.295109	+	0.511143i	0.679901	+	0.733304i	$0.262023\pi$
$228$	12.2033	+	1.59039i	0.808183	+	0.105326i
$229$	11.2113	−	6.47287i	0.740866	−	0.427739i	−0.0815180	−	0.996672i	$-0.525977\pi$
$229$	11.2113	−	6.47287i	0.740866	−	0.427739i	0.822384	+	0.568933i	$0.192643\pi$
$230$	−3.13080	−	2.08898i	−0.206439	−	0.137743i
$231$		0			0
$232$	4.03267	−	20.4832i	0.264758	−	1.34479i
$233$	7.60809	+	13.1776i	0.498423	+	0.863294i	0.999998	−	0.00182020i	$-0.000579387\pi$
$233$	7.60809	+	13.1776i	0.498423	+	0.863294i	−0.501576	+	0.865114i	$0.667246\pi$
$234$	11.8946	+	24.0801i	0.777572	+	1.57417i
$235$	5.30601	+	3.06343i	0.346126	+	0.199836i
$236$	8.65250	−	11.3067i	0.563230	−	0.736003i
$237$		−	1.38275i		−	0.0898194i
$238$		0			0
$239$			0.0438513i			0.00283650i	0.999999	+	0.00141825i	$0.000451444\pi$
$239$			0.0438513i			0.00283650i	−0.999999	+	0.00141825i	$0.999549\pi$
$240$	−3.07365	+	11.5920i	−0.198403	+	0.748261i
$241$	−1.99236	−	1.15029i	−0.128339	−	0.0740968i	0.434456	−	0.900693i	$-0.356941\pi$
$241$	−1.99236	−	1.15029i	−0.128339	−	0.0740968i	−0.562795	+	0.826596i	$0.690274\pi$
$242$	−7.60493	+	3.75651i	−0.488863	+	0.241478i
$243$	0.0999675	+	0.173149i	0.00641292	+	0.0111075i
$244$	−4.68458	+	1.94759i	−0.299900	+	0.124682i
$245$		0			0
$246$	3.43612	−	5.14979i	0.219079	−	0.328339i
$247$	5.63627	−	3.25410i	0.358627	−	0.207053i
$248$	−10.4208	−	9.10273i	−0.661720	−	0.578024i
$249$	−16.3659	+	28.3466i	−1.03715	+	1.79639i
$250$	−1.41125	−	0.0915727i	−0.0892550	−	0.00579157i
$251$	6.32409			0.399173			0.199587	−	0.979880i	$-0.436040\pi$
$251$	6.32409			0.399173			0.199587	+	0.979880i	$0.436040\pi$
$252$		0			0
$253$	5.95233			0.374220
$254$	−4.26704	−	0.276879i	−0.267738	−	0.0173729i
$255$	−5.16506	+	8.94615i	−0.323449	+	0.560229i
$256$	13.8980	+	7.92752i	0.868625	+	0.495470i
$257$	12.3334	−	7.12068i	0.769335	−	0.444176i	−0.0633025	−	0.997994i	$-0.520163\pi$
$257$	12.3334	−	7.12068i	0.769335	−	0.444176i	0.832637	+	0.553819i	$0.186830\pi$
$258$	−23.4333	+	35.1200i	−1.45889	+	2.18648i
$259$		0			0
$260$	2.43470	+	5.85624i	0.150993	+	0.363188i
$261$	22.1017	+	38.2812i	1.36806	+	2.36955i
$262$	19.9138	−	9.83654i	1.23028	−	0.607704i
$263$	−10.1744	−	5.87421i	−0.627382	−	0.362219i	0.152355	−	0.988326i	$-0.451314\pi$
$263$	−10.1744	−	5.87421i	−0.627382	−	0.362219i	−0.779738	+	0.626107i	$0.784647\pi$
$264$	−6.13164	−	17.9477i	−0.377376	−	1.10460i
$265$			4.65777i			0.286124i
$266$		0			0
$267$		−	21.0484i		−	1.28814i
$268$	−0.0838136	−	0.0641387i	−0.00511973	−	0.00391790i
$269$	7.35196	+	4.24466i	0.448257	+	0.258801i	0.707094	−	0.707120i	$-0.250006\pi$
$269$	7.35196	+	4.24466i	0.448257	+	0.258801i	−0.258837	+	0.965921i	$0.583339\pi$
$270$	−5.61247	−	11.3623i	−0.341564	−	0.691485i
$271$	−3.98686	−	6.90544i	−0.242184	−	0.419476i	0.719152	−	0.694853i	$-0.244531\pi$
$271$	−3.98686	−	6.90544i	−0.242184	−	0.419476i	−0.961336	+	0.275377i	$0.911197\pi$
$272$	9.77078	+	9.71988i	0.592440	+	0.589354i
$273$		0			0
$274$	11.3102	+	7.54657i	0.683275	+	0.455905i
$275$	1.93693	−	1.11828i	0.116801	−	0.0674351i
$276$	2.06232	−	15.8245i	0.124137	−	0.952524i
$277$	6.79754	−	11.7737i	0.408425	−	0.707412i	−0.586289	−	0.810102i	$-0.699412\pi$
$277$	6.79754	−	11.7737i	0.408425	−	0.707412i	0.994713	+	0.102690i	$0.0327449\pi$
$278$	−0.686562	+	10.5807i	−0.0411772	+	0.634591i
$279$	29.2974			1.75399
$280$		0			0
$281$	9.48286			0.565700			0.282850	−	0.959164i	$-0.408720\pi$
$281$	9.48286			0.565700			0.282850	+	0.959164i	$0.408720\pi$
$282$	−1.68212	+	25.9235i	−0.100169	+	1.54372i
$283$	−10.7746	+	18.6621i	−0.640483	+	1.10935i	0.344842	+	0.938661i	$0.387933\pi$
$283$	−10.7746	+	18.6621i	−0.640483	+	1.10935i	−0.985325	+	0.170689i	$0.945401\pi$
$284$	0.0548838	−	0.421132i	0.00325675	−	0.0249896i
$285$	−5.32887	+	3.07662i	−0.315655	+	0.182244i
$286$	−8.34337	−	5.56699i	−0.493354	−	0.329183i
$287$		0			0
$288$	−33.2054	+	6.71772i	−1.95665	+	0.395845i
$289$	−2.56424	−	4.44140i	−0.150838	−	0.261259i
$290$	4.62281	+	9.35872i	0.271461	+	0.549563i
$291$	−0.481537	−	0.278016i	−0.0282282	−	0.0162976i
$292$	−23.6249	−	18.0791i	−1.38255	−	1.05800i
$293$		−	28.9496i		−	1.69125i	−0.533776	−	0.845626i	$-0.679227\pi$
$293$		−	28.9496i		−	1.69125i	0.533776	−	0.845626i	$-0.320773\pi$
$294$		0			0
$295$			7.11876i			0.414470i
$296$	−29.9606	+	10.2357i	−1.74142	+	0.594940i
$297$	17.3569	+	10.0210i	1.00715	+	0.581477i
$298$	−8.24342	+	4.07190i	−0.477529	+	0.235879i
$299$	−4.21972	−	7.30877i	−0.244033	−	0.422677i
$300$	−2.30191	−	5.53685i	−0.132901	−	0.319670i
$301$		0			0
$302$	−18.5829	+	27.8506i	−1.06933	+	1.60262i
$303$	−16.2251	+	9.36757i	−0.932108	+	0.538153i
$304$	2.14545	+	7.92411i	0.123050	+	0.454479i
$305$	1.26833	−	2.19681i	0.0726242	−	0.125789i
$306$	−29.1206	−	1.88957i	−1.66471	−	0.108020i
$307$	−8.00589			−0.456920			−0.228460	−	0.973553i	$-0.573369\pi$
$307$	−8.00589			−0.456920			−0.228460	+	0.973553i	$0.573369\pi$
$308$		0			0
$309$	34.2339			1.94750
$310$	6.90379	+	0.447972i	0.392109	+	0.0254431i
$311$	6.87633	−	11.9101i	0.389921	−	0.675363i	−0.602518	−	0.798105i	$-0.705836\pi$
$311$	6.87633	−	11.9101i	0.389921	−	0.675363i	0.992438	+	0.122743i	$0.0391691\pi$
$312$	−17.6908	+	20.2524i	−1.00154	+	1.14656i
$313$	−9.21091	+	5.31792i	−0.520631	+	0.300587i	−0.737193	−	0.675682i	$-0.763849\pi$
$313$	−9.21091	+	5.31792i	−0.520631	+	0.300587i	0.216562	+	0.976269i	$0.430516\pi$
$314$	−6.14793	+	9.21404i	−0.346948	+	0.519979i
$315$		0			0
$316$	0.851730	−	0.354102i	0.0479136	−	0.0199198i
$317$	8.49175	+	14.7081i	0.476944	+	0.826091i	0.999651	−	0.0264211i	$-0.00841107\pi$
$317$	8.49175	+	14.7081i	0.476944	+	0.826091i	−0.522707	+	0.852513i	$0.675078\pi$
$318$	−17.7066	+	8.74632i	−0.992939	+	0.490469i
$319$	−14.2963	−	8.25397i	−0.800439	−	0.462133i
$320$	−7.92741	+	1.07527i	−0.443156	+	0.0601094i
$321$		−	7.80679i		−	0.435732i
$322$		0			0
$323$			7.07140i			0.393463i
$324$	10.8174	−	14.1357i	0.600966	−	0.785316i
$325$	−2.74625	−	1.58555i	−0.152334	−	0.0879502i
$326$	−6.79654	−	13.7594i	−0.376426	−	0.762061i
$327$	−1.50191	−	2.60138i	−0.0830557	−	0.143857i
$328$	4.05204	+	0.797755i	0.223737	+	0.0440486i
$329$		0			0
$330$	7.88833	+	5.26337i	0.434239	+	0.289739i
$331$	−7.21415	+	4.16509i	−0.396525	+	0.228934i	−0.684984	−	0.728558i	$-0.740191\pi$
$331$	−7.21415	+	4.16509i	−0.396525	+	0.228934i	0.288458	+	0.957492i	$0.406857\pi$
$332$	−21.6516	−	2.82173i	−1.18829	−	0.154863i
$333$	33.5190	−	58.0567i	1.83683	−	3.18149i
$334$	−1.07576	+	16.5788i	−0.0588630	+	0.907150i
$335$	0.0527695			0.00288311
$336$		0			0
$337$	−27.0772			−1.47499			−0.737495	−	0.675353i	$-0.763991\pi$
$337$	−27.0772			−1.47499			−0.737495	+	0.675353i	$0.763991\pi$
$338$	0.269607	−	4.15496i	0.0146647	−	0.226000i
$339$	−22.2744	+	38.5804i	−1.20978	+	2.09540i
$340$	−6.83323	−	0.890536i	−0.370584	−	0.0482961i
$341$	−9.47541	+	5.47063i	−0.513122	+	0.296251i
$342$	−14.4593	−	9.64775i	−0.781870	−	0.521690i
$343$		0			0
$344$	−27.6337	−	5.44044i	−1.48991	−	0.293329i
$345$	3.98958	+	6.91016i	0.214792	+	0.372031i
$346$	−10.3264	−	20.9054i	−0.555150	−	1.12388i
$347$	24.0514	+	13.8861i	1.29115	+	0.745443i	0.978857	−	0.204544i	$-0.0655713\pi$
$347$	24.0514	+	13.8861i	1.29115	+	0.745443i	0.312288	+	0.949987i	$0.398905\pi$
$348$	−26.8968	+	35.1475i	−1.44182	+	1.88410i
$349$		−	9.64063i		−	0.516051i	−0.966138	−	0.258026i	$-0.916928\pi$
$349$		−	9.64063i		−	0.516051i	0.966138	−	0.258026i	$-0.0830719\pi$
$350$		0			0
$351$		−	28.4163i		−	1.51675i
$352$	9.48495	−	8.37301i	0.505550	−	0.446283i
$353$	14.1283	+	8.15697i	0.751973	+	0.434152i	0.826406	−	0.563074i	$-0.190381\pi$
$353$	14.1283	+	8.15697i	0.751973	+	0.434152i	−0.0744333	+	0.997226i	$0.523715\pi$
$354$	−27.0622	+	13.3676i	−1.43834	+	0.710478i
$355$	0.106173	+	0.183898i	0.00563509	+	0.00976027i
$356$	12.9651	−	5.39018i	0.687151	−	0.285679i
$357$		0			0
$358$	7.15037	−	10.7164i	0.377909	−	0.566380i
$359$	−1.38744	+	0.801040i	−0.0732264	+	0.0422773i	−0.536166	−	0.844112i	$-0.680128\pi$
$359$	−1.38744	+	0.801040i	−0.0732264	+	0.0422773i	0.462940	+	0.886390i	$0.346795\pi$
$360$	11.1437	−	12.7573i	0.587327	−	0.672370i
$361$	7.39392	−	12.8067i	0.389154	−	0.674034i
$362$	23.3921	+	1.51786i	1.22946	+	0.0797771i
$363$	17.9822			0.943818
$364$		0			0
$365$	14.8744			0.778562
$366$	10.7329	+	0.696433i	0.561016	+	0.0364031i
$367$	−0.630259	+	1.09164i	−0.0328993	+	0.0569832i	−0.882006	−	0.471238i	$-0.843807\pi$
$367$	−0.630259	+	1.09164i	−0.0328993	+	0.0569832i	0.849107	+	0.528221i	$0.177141\pi$
$368$	10.2755	−	2.78209i	0.535648	−	0.145027i
$369$	−7.57289	+	4.37221i	−0.394229	+	0.227608i
$370$	8.78631	−	13.1682i	0.456778	−	0.684584i
$371$		0			0
$372$	11.2609	+	27.0862i	0.583851	+	1.40435i
$373$	−4.61372	−	7.99120i	−0.238889	−	0.413768i	0.721507	−	0.692408i	$-0.243450\pi$
$373$	−4.61372	−	7.99120i	−0.238889	−	0.413768i	−0.960396	+	0.278639i	$0.910117\pi$
$374$	9.77105	−	4.82648i	0.505249	−	0.249571i
$375$	2.59647	+	1.49907i	0.134081	+	0.0774117i
$376$	−16.3988	+	5.60247i	−0.845702	+	0.288925i
$377$			23.4056i			1.20545i
$378$		0			0
$379$		−	2.53516i		−	0.130223i	−0.997878	−	0.0651113i	$-0.979260\pi$
$379$		−	2.53516i		−	0.130223i	0.997878	−	0.0651113i	$-0.0207403\pi$
$380$	−3.25974	−	2.49453i	−0.167221	−	0.127967i
$381$	7.85068	+	4.53259i	0.402203	+	0.232212i
$382$	−1.87454	−	3.79495i	−0.0959099	−	0.194166i
$383$	−0.662435	−	1.14737i	−0.0338489	−	0.0586279i	0.848605	−	0.529027i	$-0.177443\pi$
$383$	−0.662435	−	1.14737i	−0.0338489	−	0.0586279i	−0.882454	+	0.470400i	$0.844110\pi$
$384$	−18.9737	−	28.1171i	−0.968248	−	1.43485i
$385$		0			0
$386$	−17.3033	−	11.5454i	−0.880715	−	0.587644i
$387$	51.6448	−	29.8171i	2.62525	−	1.51569i
$388$	0.0479342	−	0.367807i	0.00243349	−	0.0186726i
$389$	−16.1134	+	27.9093i	−0.816983	+	1.41506i	0.0909120	+	0.995859i	$0.471022\pi$
$389$	−16.1134	+	27.9093i	−0.816983	+	1.41506i	−0.907895	+	0.419197i	$0.862312\pi$
$390$	0.870617	−	13.4173i	0.0440854	−	0.679409i
$391$	9.16976			0.463735
$392$		0			0
$393$	−47.0869			−2.37522
$394$	0.441150	−	6.79865i	0.0222248	−	0.342511i
$395$	−0.230601	+	0.399413i	−0.0116028	+	0.0200967i
$396$	−3.46199	+	26.5644i	−0.173971	+	1.33491i
$397$	30.4617	−	17.5871i	1.52883	−	0.882670i	0.529419	−	0.848361i	$-0.322410\pi$
$397$	30.4617	−	17.5871i	1.52883	−	0.882670i	0.999411	−	0.0343095i	$-0.0109232\pi$
$398$	1.49914	+	1.00028i	0.0751452	+	0.0501395i
$399$		0			0
$400$	2.82103	−	2.83580i	0.141052	−	0.141790i
$401$	−15.9623	−	27.6476i	−0.797120	−	1.38065i	−0.921484	−	0.388416i	$-0.873022\pi$
$401$	−15.9623	−	27.6476i	−0.797120	−	1.38065i	0.124364	−	0.992237i	$-0.460311\pi$
$402$	0.0990903	+	0.200605i	0.00494217	+	0.0100053i
$403$	13.4346	+	7.75647i	0.669225	+	0.386377i
$404$	−9.92512	−	7.59524i	−0.493793	−	0.377877i
$405$			8.89991i			0.442240i
$406$		0			0
$407$			25.0357i			1.24097i
$408$	−9.44599	−	27.6490i	−0.467646	−	1.36883i
$409$	−14.2151	−	8.20712i	−0.702894	−	0.405816i	0.105530	−	0.994416i	$-0.466346\pi$
$409$	−14.2151	−	8.20712i	−0.702894	−	0.405816i	−0.808424	+	0.588600i	$0.799679\pi$
$410$	−1.85137	+	0.914496i	−0.0914325	+	0.0451638i
$411$	−14.4126	−	24.9634i	−0.710922	−	1.23135i
$412$	8.76677	+	21.0869i	0.431908	+	1.03888i
$413$		0			0
$414$	−12.5106	+	18.7500i	−0.614864	+	0.921510i
$415$	9.45470	−	5.45868i	0.464113	−	0.267956i
$416$	−17.0051	−	5.71063i	−0.833746	−	0.279987i
$417$	11.2392	−	19.4669i	0.550387	−	0.953298i
$418$	6.47794	+	0.420340i	0.316846	+	0.0205595i
$419$	−11.8654			−0.579665			−0.289832	−	0.957077i	$-0.593600\pi$
$419$	−11.8654			−0.579665			−0.289832	+	0.957077i	$0.593600\pi$
$420$		0			0
$421$	10.3433			0.504101			0.252051	−	0.967714i	$-0.418895\pi$
$421$	10.3433			0.504101			0.252051	+	0.967714i	$0.418895\pi$
$422$	−5.23552	−	0.339721i	−0.254861	−	0.0165374i
$423$	18.3465	−	31.7770i	0.892035	−	1.54505i
$424$	−9.92185	−	8.66691i	−0.481847	−	0.420902i
$425$	2.98390	−	1.72275i	0.144740	−	0.0835658i
$426$	−0.499720	+	0.748942i	−0.0242115	+	0.0362864i
$427$		0			0
$428$	4.80873	−	1.99920i	0.232439	−	0.0966349i
$429$	10.6320	+	18.4151i	0.513316	+	0.889089i
$430$	12.6257	−	6.23658i	0.608868	−	0.300755i
$431$	25.6838	+	14.8286i	1.23715	+	0.714267i	0.968510	−	0.248975i	$-0.0800937\pi$
$431$	25.6838	+	14.8286i	1.23715	+	0.714267i	0.268636	+	0.963242i	$0.413427\pi$
$432$	34.6469	+	9.18671i	1.66695	+	0.441996i
$433$			29.4107i			1.41339i	0.707520	+	0.706693i	$0.249814\pi$
$433$			29.4107i			1.41339i	−0.707520	+	0.706693i	$0.750186\pi$
$434$		0			0
$435$		−	22.1291i		−	1.06101i
$436$	1.21775	−	1.59130i	0.0583196	−	0.0762094i
$437$	4.73029	+	2.73103i	0.226280	+	0.130643i
$438$	27.9311	+	56.5455i	1.33460	+	2.70185i
$439$	4.41191	+	7.64165i	0.210569	+	0.364716i	0.951893	−	0.306432i	$-0.0991351\pi$
$439$	4.41191	+	7.64165i	0.210569	+	0.364716i	−0.741324	+	0.671147i	$0.765802\pi$
$440$	−1.22198	+	6.20682i	−0.0582557	+	0.295899i
$441$		0			0
$442$	−12.8532	−	8.57612i	−0.611366	−	0.407925i
$443$	16.9454	−	9.78342i	0.805099	−	0.464824i	−0.0401518	−	0.999194i	$-0.512784\pi$
$443$	16.9454	−	9.78342i	0.805099	−	0.464824i	0.845251	+	0.534369i	$0.179451\pi$
$444$	66.5583	+	8.67417i	3.15872	+	0.411658i
$445$	−3.51024	+	6.07992i	−0.166402	+	0.288216i
$446$	−1.18661	+	18.2870i	−0.0561874	+	0.865916i
$447$	19.4919			0.921935
$448$		0			0
$449$	5.02309			0.237054			0.118527	−	0.992951i	$-0.462183\pi$
$449$	5.02309			0.237054			0.118527	+	0.992951i	$0.462183\pi$
$450$	−0.548417	+	8.45176i	−0.0258526	+	0.398420i
$451$	1.63282	−	2.82813i	0.0768866	−	0.133171i
$452$	−29.4684	−	3.84045i	−1.38608	−	0.180640i
$453$	61.4705	−	35.4900i	2.88814	−	1.66747i
$454$	10.4611	+	6.97998i	0.490962	+	0.327587i
$455$		0			0
$456$	3.36192	−	17.0762i	0.157436	−	0.799667i
$457$	13.9225	+	24.1144i	0.651265	+	1.12802i	0.982816	+	0.184587i	$0.0590946\pi$
$457$	13.9225	+	24.1144i	0.651265	+	1.12802i	−0.331551	+	0.943437i	$0.607572\pi$
$458$	−8.10816	−	16.4147i	−0.378869	−	0.767008i
$459$	26.7388	+	15.4377i	1.24806	+	0.720569i
$460$	−3.23476	+	4.22704i	−0.150822	+	0.197087i
$461$		−	19.8494i		−	0.924481i	−0.886755	−	0.462240i	$-0.847046\pi$
$461$		−	19.8494i		−	0.924481i	0.886755	−	0.462240i	$-0.152954\pi$
$462$		0			0
$463$		−	35.7118i		−	1.65967i	−0.558012	−	0.829833i	$-0.688436\pi$
$463$		−	35.7118i		−	1.65967i	0.558012	−	0.829833i	$-0.311564\pi$
$464$	−28.5375	−	7.56680i	−1.32482	−	0.351280i
$465$	−12.7019	−	7.33344i	−0.589036	−	0.340080i
$466$	19.2935	−	9.53018i	0.893756	−	0.441477i
$467$	11.3055	+	19.5818i	0.523158	+	0.906136i	0.999637	+	0.0269503i	$0.00857959\pi$
$467$	11.3055	+	19.5818i	0.523158	+	0.906136i	−0.476479	+	0.879186i	$0.658087\pi$
$468$	35.0722	−	14.5811i	1.62121	−	0.674010i
$469$		0			0
$470$	4.80914	−	7.20756i	0.221829	−	0.332460i
$471$	20.3368	−	11.7415i	0.937070	−	0.541018i
$472$	−15.1642	−	13.2462i	−0.697989	−	0.609705i
$473$	−11.1353	+	19.2870i	−0.512003	+	0.886816i
$474$	−1.95140	−	0.126622i	−0.0896309	−	0.00581596i
$475$	2.05235			0.0941684
$476$		0			0
$477$	27.8947			1.27721
$478$	0.0618849	+	0.00401558i	0.00283055	+	0.000183668i
$479$	−4.28200	+	7.41664i	−0.195649	+	0.338875i	−0.947113	−	0.320900i	$-0.896015\pi$
$479$	−4.28200	+	7.41664i	−0.195649	+	0.338875i	0.751464	+	0.659774i	$0.229348\pi$
$480$	16.0777	+	5.39918i	0.733843	+	0.246438i
$481$	30.7409	−	17.7483i	1.40166	−	0.809251i
$482$	−1.80579	+	2.70638i	−0.0822515	+	0.123272i
$483$		0			0
$484$	4.60495	+	11.0764i	0.209316	+	0.503473i
$485$	0.0927293	+	0.160612i	0.00421062	+	0.00729301i
$486$	0.253510	−	0.125223i	0.0114994	−	0.00568023i
$487$	−27.4054	−	15.8225i	−1.24186	−	0.716987i	−0.272386	−	0.962188i	$-0.587813\pi$
$487$	−27.4054	−	15.8225i	−1.24186	−	0.716987i	−0.969472	+	0.245201i	$0.921146\pi$
$488$	2.31955	+	6.78945i	0.105001	+	0.307344i
$489$			32.5346i			1.47126i
$490$		0			0
$491$			35.7781i			1.61464i	0.590113	+	0.807321i	$0.299083\pi$
$491$			35.7781i			1.61464i	−0.590113	+	0.807321i	$0.700917\pi$
$492$	−6.95297	−	5.32079i	−0.313464	−	0.239880i
$493$	−22.0239	−	12.7155i	−0.991906	−	0.572677i
$494$	−4.07621	−	8.25214i	−0.183397	−	0.371281i
$495$	−6.69725	−	11.6000i	−0.301019	−	0.521380i
$496$	−13.8004	+	13.8727i	−0.619658	+	0.622903i
$497$		0			0
$498$	38.5053	+	25.6921i	1.72546	+	1.15129i
$499$	35.7797	−	20.6574i	1.60172	−	0.924752i	0.610574	−	0.791959i	$-0.290939\pi$
$499$	35.7797	−	20.6574i	1.60172	−	0.924752i	0.991144	−	0.132793i	$-0.0423947\pi$
$500$	−0.258463	+	1.98323i	−0.0115588	+	0.0886927i
$501$	17.6105	−	30.5023i	0.786780	−	1.36274i
$502$	0.579114	−	8.92485i	0.0258471	−	0.398336i
$503$	−29.0170			−1.29381			−0.646903	−	0.762572i	$-0.723936\pi$
$503$	−29.0170			−1.29381			−0.646903	+	0.762572i	$0.723936\pi$
$504$		0			0
$505$	6.24891			0.278073
$506$	0.545071	−	8.40021i	0.0242314	−	0.373435i
$507$	−4.41354	+	7.64448i	−0.196012	+	0.339503i
$508$	−0.781489	+	5.99649i	−0.0346730	+	0.266051i
$509$	−17.3474	+	10.0155i	−0.768910	+	0.443931i	−0.832486	−	0.554046i	$-0.813083\pi$
$509$	−17.3474	+	10.0155i	−0.768910	+	0.443931i	0.0635754	+	0.997977i	$0.479750\pi$
$510$	12.1522	+	8.10839i	0.538110	+	0.359046i
$511$		0			0
$512$	12.4604	−	18.8875i	0.550675	−	0.834720i
$513$	9.19562	+	15.9273i	0.405996	+	0.703206i
$514$	−8.91962	−	18.0575i	−0.393428	−	0.796481i
$515$	−9.88858	−	5.70918i	−0.435743	−	0.251576i
$516$	47.4171	+	36.2861i	2.08742	+	1.59741i
$517$			13.7031i			0.602663i
$518$		0			0
$519$			49.4317i			2.16981i
$520$	8.48754	−	2.89968i	0.372203	−	0.127160i
$521$	−18.5712	−	10.7221i	−0.813620	−	0.469743i	0.0345917	−	0.999402i	$-0.488987\pi$
$521$	−18.5712	−	10.7221i	−0.813620	−	0.469743i	−0.848211	+	0.529658i	$0.822320\pi$
$522$	56.0481	−	27.6854i	2.45316	−	1.21176i
$523$	−20.5020	−	35.5105i	−0.896491	−	1.55277i	−0.831949	−	0.554852i	$-0.812775\pi$
$523$	−20.5020	−	35.5105i	−0.896491	−	1.55277i	−0.0645418	−	0.997915i	$-0.520559\pi$
$524$	−12.0582	−	29.0040i	−0.526766	−	1.26704i
$525$		0			0
$526$	−9.22165	+	13.8207i	−0.402083	+	0.602611i
$527$	−14.5972	+	8.42768i	−0.635863	+	0.367116i
$528$	−25.8901	+	7.00973i	−1.12672	+	0.305059i
$529$	−7.95856	+	13.7846i	−0.346024	+	0.599332i
$530$	6.57325	+	0.426524i	0.285524	+	0.0185270i
$531$	42.6333			1.85013
$532$		0			0
$533$	−4.63015			−0.200554
$534$	−29.7045	−	1.92746i	−1.28544	−	0.0834094i
$535$	−1.30194	+	2.25502i	−0.0562876	+	0.0974931i
$536$	−0.0981906	+	0.112408i	−0.00424119	+	0.00485530i
$537$	−23.6528	+	13.6559i	−1.02069	+	0.589297i
$538$	6.66349	−	9.98673i	0.287284	−	0.430559i
$539$		0			0
$540$	−16.5489	+	6.88010i	−0.712151	+	0.296072i
$541$	−1.72641	−	2.99023i	−0.0742242	−	0.128560i	0.826524	−	0.562901i	$-0.190315\pi$
$541$	−1.72641	−	2.99023i	−0.0742242	−	0.128560i	−0.900749	+	0.434341i	$0.856981\pi$
$542$	−10.1104	+	4.99409i	−0.434277	+	0.214514i
$543$	−43.0377	−	24.8479i	−1.84693	−	1.06632i
$544$	14.6119	−	12.8989i	0.626479	−	0.553035i
$545$			1.00189i			0.0429163i
$546$		0			0
$547$			28.2607i			1.20834i	0.796855	+	0.604170i	$0.206495\pi$
$547$			28.2607i			1.20834i	−0.796855	+	0.604170i	$0.793505\pi$
$548$	11.6858	−	15.2704i	0.499191	−	0.652321i
$549$	−13.1564	−	7.59584i	−0.561500	−	0.324182i
$550$	−1.40080	−	2.83588i	−0.0597305	−	0.120922i
$551$	−7.57413	−	13.1188i	−0.322669	−	0.558879i
$552$	−22.1434	−	4.35953i	−0.942487	−	0.185554i
$553$		0			0
$554$	−15.9931	−	10.6711i	−0.679481	−	0.453374i
$555$	−29.0643	+	16.7803i	−1.23371	+	0.712284i
$556$	14.8692	+	1.93781i	0.630593	+	0.0821816i
$557$	−1.03826	+	1.79833i	−0.0439927	+	0.0761976i	−0.887183	−	0.461417i	$-0.847341\pi$
$557$	−1.03826	+	1.79833i	−0.0439927	+	0.0761976i	0.843191	+	0.537615i	$0.180674\pi$
$558$	2.68285	−	41.3459i	0.113574	−	1.75031i
$559$	31.5762			1.33553
$560$		0			0
$561$	−23.1040			−0.975453
$562$	0.868371	−	13.3826i	0.0366300	−	0.564513i
$563$	22.9547	−	39.7588i	0.967426	−	1.67563i	0.264477	−	0.964392i	$-0.414801\pi$
$563$	22.9547	−	39.7588i	0.967426	−	1.67563i	0.702949	−	0.711240i	$-0.251866\pi$
$564$	36.4303	+	4.74776i	1.53399	+	0.199917i
$565$	12.8681	−	7.42940i	0.541365	−	0.312557i
$566$	25.3502	+	16.9145i	1.06555	+	0.710971i
$567$		0			0
$568$	−0.589295	−	0.116019i	−0.0247263	−	0.00486803i
$569$	−3.96413	−	6.86607i	−0.166185	−	0.287840i	0.770891	−	0.636968i	$-0.219811\pi$
$569$	−3.96413	−	6.86607i	−0.166185	−	0.287840i	−0.937075	+	0.349127i	$0.886478\pi$
$570$	3.85389	+	7.80208i	0.161422	+	0.326793i
$571$	−18.3314	−	10.5837i	−0.767147	−	0.442912i	0.0647092	−	0.997904i	$-0.479388\pi$
$571$	−18.3314	−	10.5837i	−0.767147	−	0.442912i	−0.831856	+	0.554992i	$0.812721\pi$
$572$	−8.62041	+	11.2648i	−0.360438	+	0.471003i
$573$			8.97330i			0.374865i
$574$		0			0
$575$		−	2.66137i		−	0.110987i
$576$	6.43964	+	47.4762i	0.268318	+	1.97817i
$577$	−8.94731	−	5.16573i	−0.372481	−	0.215052i	0.302061	−	0.953289i	$-0.402325\pi$
$577$	−8.94731	−	5.16573i	−0.372481	−	0.215052i	−0.674542	+	0.738237i	$0.735659\pi$
$578$	−6.50272	+	3.21207i	−0.270478	+	0.133604i
$579$	22.0496	+	38.1911i	0.916351	+	1.58717i
$580$	13.6308	−	5.66691i	0.565987	−	0.235306i
$581$		0			0
$582$	−0.436444	+	0.654109i	−0.0180912	+	0.0271137i
$583$	−9.02174	+	5.20871i	−0.373642	+	0.215723i
$584$	−27.6774	+	31.6851i	−1.14530	+	1.31114i
$585$	−9.49562	+	16.4469i	−0.392595	+	0.679995i
$586$	−40.8550	−	2.65099i	−1.68770	−	0.109511i
$587$	−20.4660			−0.844722			−0.422361	−	0.906428i	$-0.638799\pi$
$587$	−20.4660			−0.844722			−0.422361	+	0.906428i	$0.638799\pi$
$588$		0			0
$589$	−10.0401			−0.413694
$590$	10.0463	+	0.651884i	0.413601	+	0.0268377i
$591$	−7.22175	+	12.5084i	−0.297063	+	0.514529i
$592$	11.7016	+	43.2191i	0.480931	+	1.77629i
$593$	−38.8389	+	22.4236i	−1.59492	+	0.920828i	−0.602477	+	0.798136i	$0.705819\pi$
$593$	−38.8389	+	22.4236i	−1.59492	+	0.920828i	−0.992445	+	0.122692i	$0.960847\pi$
$594$	15.7315	−	23.5772i	0.645471	−	0.967383i
$595$		0			0
$596$	4.99158	+	12.0064i	0.204463	+	0.491800i
$597$	−1.91036	−	3.30884i	−0.0781857	−	0.135422i
$598$	−10.7009	+	5.28578i	−0.437592	+	0.216152i
$599$	14.1499	+	8.16942i	0.578147	+	0.333793i	0.760397	−	0.649459i	$-0.225005\pi$
$599$	14.1499	+	8.16942i	0.578147	+	0.333793i	−0.182250	+	0.983252i	$0.558338\pi$
$600$	−8.02464	+	2.74154i	−0.327605	+	0.111923i
$601$		−	39.8029i		−	1.62359i	−0.583941	−	0.811796i	$-0.698490\pi$
$601$		−	39.8029i		−	1.62359i	0.583941	−	0.811796i	$-0.301510\pi$
$602$		0			0
$603$		−	0.316030i		−	0.0128697i
$604$	37.6024	+	28.7754i	1.53002	+	1.17085i
$605$	−5.19421	−	2.99888i	−0.211175	−	0.121922i
$606$	11.7342	+	23.7554i	0.476668	+	0.964998i
$607$	4.70373	+	8.14710i	0.190919	+	0.330681i	0.945555	−	0.325463i	$-0.105520\pi$
$607$	4.70373	+	8.14710i	0.190919	+	0.330681i	−0.754636	+	0.656143i	$0.772187\pi$
$608$	11.3793	−	2.30213i	0.461493	−	0.0933636i
$609$		0			0
$610$	−2.98409	−	1.99109i	−0.120822	−	0.0806168i
$611$	16.8259	−	9.71441i	0.680701	−	0.393003i
$612$	−5.33330	+	40.9233i	−0.215586	+	1.65423i
$613$	−6.81796	+	11.8091i	−0.275375	+	0.476963i	−0.970230	−	0.242187i	$-0.922135\pi$
$613$	−6.81796	+	11.8091i	−0.275375	+	0.476963i	0.694855	+	0.719150i	$0.255469\pi$
$614$	−0.733121	+	11.2983i	−0.0295863	+	0.455961i
$615$	4.37763			0.176523
$616$		0			0
$617$	39.1144			1.57469			0.787343	−	0.616515i	$-0.211456\pi$
$617$	39.1144			1.57469			0.787343	+	0.616515i	$0.211456\pi$
$618$	3.13489	−	48.3124i	0.126104	−	1.94341i
$619$	9.50950	−	16.4709i	0.382219	−	0.662023i	−0.609160	−	0.793047i	$-0.708493\pi$
$619$	9.50950	−	16.4709i	0.382219	−	0.662023i	0.991379	+	0.131024i	$0.0418266\pi$
$620$	1.26440	−	9.70193i	0.0507795	−	0.389639i
$621$	20.6535	−	11.9243i	0.828798	−	0.478507i
$622$	−16.1785	−	10.7948i	−0.648697	−	0.432833i
$623$		0			0
$624$	26.9611	+	26.8206i	1.07931	+	1.07368i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	6.66143	+	13.4858i	0.266244	+	0.539002i
$627$	−11.9184	−	6.88108i	−0.475974	−	0.274804i
$628$	12.4403	+	9.52000i	0.496422	+	0.379889i
$629$			38.5683i			1.53782i
$630$		0			0
$631$		−	16.4987i		−	0.656802i	−0.944538	−	0.328401i	$-0.893490\pi$
$631$		−	16.4987i		−	0.656802i	0.944538	−	0.328401i	$-0.106510\pi$
$632$	−0.421729	−	1.23443i	−0.0167755	−	0.0491028i
$633$	9.63252	+	5.56134i	0.382858	+	0.221043i
$634$	21.5344	−	10.6371i	0.855241	−	0.422452i
$635$	−1.51180	−	2.61851i	−0.0599939	−	0.103913i
$636$	10.7218	+	25.7893i	0.425146	+	1.02261i
$637$		0			0
$638$	−12.9575	+	19.4197i	−0.512993	+	0.768835i
$639$	1.10134	−	0.635857i	0.0435682	−	0.0251541i
$640$	0.791535	+	11.2860i	0.0312882	+	0.446118i
$641$	−13.4723	+	23.3347i	−0.532124	+	0.921665i	0.467173	+	0.884166i	$0.345272\pi$
$641$	−13.4723	+	23.3347i	−0.532124	+	0.921665i	−0.999297	+	0.0374991i	$0.988061\pi$
$642$	−11.0173	−	0.714889i	−0.434818	−	0.0282144i
$643$	−43.6730			−1.72229			−0.861147	−	0.508355i	$-0.830254\pi$
$643$	−43.6730			−1.72229			−0.861147	+	0.508355i	$0.830254\pi$
$644$		0			0
$645$	−29.8541			−1.17550
$646$	9.97948	+	0.647547i	0.392637	+	0.0254774i
$647$	14.0540	−	24.3422i	0.552518	−	0.956989i	−0.445574	−	0.895245i	$-0.647000\pi$
$647$	14.0540	−	24.3422i	0.552518	−	0.956989i	0.998092	−	0.0617443i	$-0.0196663\pi$
$648$	−18.9583	−	16.5604i	−0.744754	−	0.650556i
$649$	−13.7885	+	7.96080i	−0.541246	+	0.312489i
$650$	−2.48908	+	3.73043i	−0.0976296	+	0.146320i
$651$		0			0
$652$	−20.0402	+	8.33161i	−0.784836	+	0.326291i
$653$	20.8367	+	36.0902i	0.815403	+	1.41232i	0.909038	+	0.416713i	$0.136818\pi$
$653$	20.8367	+	36.0902i	0.815403	+	1.41232i	−0.0936346	+	0.995607i	$0.529849\pi$
$654$	−3.80872	+	1.88134i	−0.148933	+	0.0735664i
$655$	13.6012	+	7.85267i	0.531444	+	0.306829i
$656$	1.49688	−	5.64538i	0.0584435	−	0.220415i
$657$		−	89.0808i		−	3.47537i
$658$		0			0
$659$		−	47.0951i		−	1.83457i	−0.398236	−	0.917283i	$-0.630378\pi$
$659$		−	47.0951i		−	1.83457i	0.398236	−	0.917283i	$-0.369622\pi$
$660$	8.15027	−	10.6504i	0.317249	−	0.414566i
$661$	10.0792	+	5.81924i	0.392036	+	0.226342i	0.683042	−	0.730379i	$-0.260657\pi$
$661$	10.0792	+	5.81924i	0.392036	+	0.226342i	−0.291006	+	0.956721i	$0.593990\pi$
$662$	5.21735	+	10.5623i	0.202778	+	0.410517i
$663$	16.3789	+	28.3690i	0.636103	+	1.10176i
$664$	−5.96486	+	30.2973i	−0.231481	+	1.17577i
$665$		0			0
$666$	−78.8628	−	52.6200i	−3.05587	−	2.03898i
$667$	−17.0116	+	9.82168i	−0.658693	+	0.380297i
$668$	23.2982	+	3.03633i	0.901435	+	0.117479i
$669$	19.4251	−	33.6452i	0.751017	−	1.30080i
$670$	0.00483225	−	0.0744708i	0.000186686	−	0.00287706i
$671$	5.67340			0.219019
$672$		0			0
$673$	14.9849			0.577626			0.288813	−	0.957385i	$-0.406739\pi$
$673$	14.9849			0.577626			0.288813	+	0.957385i	$0.406739\pi$
$674$	−2.47953	+	38.2126i	−0.0955080	+	1.47189i
$675$	4.48052	−	7.76049i	0.172455	−	0.298702i
$676$	−5.83899	−	0.760963i	−0.224576	−	0.0292678i
$677$	−19.9347	+	11.5093i	−0.766154	+	0.442339i	−0.831501	−	0.555524i	$-0.812518\pi$
$677$	−19.9347	+	11.5093i	−0.766154	+	0.442339i	0.0653470	+	0.997863i	$0.479185\pi$
$678$	52.4067	+	34.9676i	2.01267	+	1.34292i
$679$		0			0
$680$	−1.88250	+	9.56181i	−0.0721907	+	0.366679i
$681$	−13.3305	−	23.0892i	−0.510827	−	0.884779i
$682$	6.85272	+	13.8731i	0.262404	+	0.531228i
$683$	−32.2762	−	18.6347i	−1.23502	−	0.713037i	−0.266945	−	0.963712i	$-0.586014\pi$
$683$	−32.2762	−	18.6347i	−1.23502	−	0.713037i	−0.968071	+	0.250675i	$0.919348\pi$
$684$	−14.9394	+	19.5222i	−0.571223	+	0.746448i
$685$			9.61436i			0.367346i
$686$		0			0
$687$			38.8132i			1.48082i
$688$	−10.2083	+	38.4997i	−0.389187	+	1.46779i
$689$	12.7914	+	7.38510i	0.487312	+	0.281350i
$690$	10.1173	−	4.99750i	0.385158	−	0.190252i
$691$	−13.9969	−	24.2433i	−0.532467	−	0.922260i	−0.999281	−	0.0379044i	$-0.987932\pi$
$691$	−13.9969	−	24.2433i	−0.532467	−	0.922260i	0.466815	−	0.884355i	$-0.345402\pi$
$692$	−30.4483	+	12.6587i	−1.15747	+	0.481211i
$693$		0			0
$694$	21.7991	−	32.6708i	0.827483	−	1.24017i
$695$	−6.49298	+	3.74872i	−0.246293	+	0.142197i
$696$	47.1387	+	41.1765i	1.78679	+	1.56079i
$697$	2.51542	−	4.35683i	0.0952782	−	0.165027i
$698$	−13.6053	−	0.882819i	−0.514968	−	0.0334152i
$699$	−45.6203			−1.72552
$700$		0			0
$701$	29.2334			1.10413			0.552065	−	0.833801i	$-0.313840\pi$
$701$	29.2334			1.10413			0.552065	+	0.833801i	$0.313840\pi$
$702$	−40.1024	−	2.60216i	−1.51357	−	0.0982121i
$703$	−11.4868	+	19.8957i	−0.433233	+	0.750381i
$704$	−10.9478	−	14.1523i	−0.412611	−	0.533386i
$705$	−15.9082	+	9.18460i	−0.599137	+	0.345912i
$706$	12.8053	−	19.1915i	0.481932	−	0.722283i
$707$		0			0
$708$	16.3868	+	39.4155i	0.615852	+	1.48133i
$709$	2.08074	+	3.60395i	0.0781440	+	0.135349i	0.902449	−	0.430796i	$-0.141767\pi$
$709$	2.08074	+	3.60395i	0.0781440	+	0.135349i	−0.824305	+	0.566146i	$0.808434\pi$
$710$	0.269247	−	0.132997i	0.0101047	−	0.00499127i
$711$	2.39203	+	1.38104i	0.0897082	+	0.0517931i
$712$	−6.41962	−	18.7906i	−0.240585	−	0.704207i
$713$			13.0194i			0.487580i
$714$		0			0
$715$		−	7.09236i		−	0.265239i
$716$	−14.4687	−	11.0723i	−0.540722	−	0.413790i
$717$	−0.113858	−	0.0657362i	−0.00425212	−	0.00245496i
$718$	1.00341	+	2.03137i	0.0374470	+	0.0758102i
$719$	−21.1113	−	36.5658i	−0.787318	−	1.36368i	−0.927604	−	0.373564i	$-0.878135\pi$
$719$	−21.1113	−	36.5658i	−0.787318	−	1.36368i	0.140286	−	0.990111i	$-0.455198\pi$
$720$	−16.9832	−	16.8948i	−0.632928	−	0.629631i
$721$		0			0
$722$	−17.3962	−	11.6074i	−0.647421	−	0.431982i
$723$	5.97339	−	3.44874i	0.222153	−	0.128260i
$724$	4.28415	−	32.8730i	0.159219	−	1.22172i
$725$	−3.69046	+	6.39206i	−0.137060	+	0.237395i
$726$	1.64667	−	25.3772i	0.0611138	−	0.941837i
$727$	27.2605			1.01104			0.505519	−	0.862816i	$-0.331301\pi$
$727$	27.2605			1.01104			0.505519	+	0.862816i	$0.331301\pi$
$728$		0			0
$729$	−27.2992			−1.01108
$730$	1.36209	−	20.9914i	0.0504132	−	0.776928i
$731$	−17.1544	+	29.7122i	−0.634477	+	1.09895i
$732$	1.96568	−	15.0830i	0.0726535	−	0.557482i
$733$	−13.2554	+	7.65300i	−0.489599	+	0.282670i	−0.724408	−	0.689372i	$-0.757887\pi$
$733$	−13.2554	+	7.65300i	−0.489599	+	0.282670i	0.234809	+	0.972041i	$0.424553\pi$
$734$	1.48286	+	0.989415i	0.0547333	+	0.0365200i
$735$		0			0
$736$	−2.98526	−	14.7560i	−0.110038	−	0.543915i
$737$	0.0590113	+	0.102211i	0.00217371	+	0.00376498i
$738$	5.47680	+	11.0876i	0.201604	+	0.408140i
$739$	−42.5694	−	24.5774i	−1.56594	−	0.904096i	−0.996635	−	0.0819692i	$-0.973879\pi$
$739$	−42.5694	−	24.5774i	−1.56594	−	0.904096i	−0.569305	−	0.822126i	$-0.692788\pi$
$740$	−17.7790	−	13.6055i	−0.653570	−	0.500148i
$741$			19.5125i			0.716810i
$742$		0			0
$743$		−	35.2067i		−	1.29161i	−0.763503	−	0.645805i	$-0.776522\pi$
$743$		−	35.2067i		−	1.29161i	0.763503	−	0.645805i	$-0.223478\pi$
$744$	39.2564	−	13.4116i	1.43921	−	0.491692i
$745$	−5.63031	−	3.25066i	−0.206279	−	0.119095i
$746$	−11.7000	+	5.77932i	−0.428369	+	0.211596i
$747$	−32.6913	−	56.6229i	−1.19611	−	2.07173i
$748$	−5.91659	−	14.2313i	−0.216332	−	0.520349i
$749$		0			0
$750$	2.35332	−	3.52698i	0.0859313	−	0.128787i
$751$	−0.584292	+	0.337341i	−0.0213211	+	0.0123098i	−0.510623	−	0.859805i	$-0.670585\pi$
$751$	−0.584292	+	0.337341i	−0.0213211	+	0.0123098i	0.489302	+	0.872115i	$0.337252\pi$
$752$	6.40478	+	23.6557i	0.233558	+	0.862635i
$753$	−9.48027	+	16.4203i	−0.345480	+	0.598389i
$754$	33.0310	+	2.14331i	1.20292	+	0.0780548i
$755$	−23.6747			−0.861609
$756$		0			0
$757$	−45.8640			−1.66695			−0.833477	−	0.552553i	$-0.813654\pi$
$757$	−45.8640			−1.66695			−0.833477	+	0.552553i	$0.813654\pi$
$758$	−3.57774	−	0.232152i	−0.129949	−	0.00843214i
$759$	−8.92298	+	15.4550i	−0.323883	+	0.560983i
$760$	−3.81890	+	4.37187i	−0.138526	+	0.158584i
$761$	−18.9229	+	10.9252i	−0.685956	+	0.396037i	−0.802095	−	0.597196i	$-0.796281\pi$
$761$	−18.9229	+	10.9252i	−0.685956	+	0.396037i	0.116139	+	0.993233i	$0.462948\pi$
$762$	7.11551	−	10.6642i	0.257768	−	0.386322i
$763$		0			0
$764$	−5.52726	+	2.29793i	−0.199969	+	0.0831360i
$765$	−10.3173	−	17.8701i	−0.373024	−	0.646097i
$766$	−1.67988	+	0.829791i	−0.0606967	+	0.0299816i
$767$	19.5499	+	11.2871i	0.705905	+	0.407554i
$768$	−41.4177	+	24.2018i	−1.49453	+	0.873307i
$769$			16.0214i			0.577745i	0.957368	+	0.288872i	$0.0932803\pi$
$769$			16.0214i			0.577745i	−0.957368	+	0.288872i	$0.906720\pi$
$770$		0			0
$771$			42.6976i			1.53772i
$772$	−17.8779	+	23.3620i	−0.643439	+	0.840816i
$773$	36.6688	+	21.1707i	1.31888	+	0.761458i	0.983549	−	0.180641i	$-0.0578171\pi$
$773$	36.6688	+	21.1707i	1.31888	+	0.761458i	0.335335	+	0.942099i	$0.391150\pi$
$774$	−37.3500	−	75.6139i	−1.34252	−	2.71789i
$775$	2.44599	+	4.23658i	0.0878627	+	0.152183i
$776$	−0.514676	−	0.101328i	−0.0184758	−	0.00363746i
$777$		0			0
$778$	37.9113	+	25.2957i	1.35919	+	0.906896i
$779$	2.59519	−	1.49833i	0.0929824	−	0.0536834i
$780$	−18.8553	−	2.45731i	−0.675129	−	0.0879858i
$781$	−0.237464	+	0.411299i	−0.00849712	+	0.0147174i
$782$	0.839700	−	12.9408i	0.0300276	−	0.462762i
$783$	−66.1408			−2.36368
$784$		0			0
$785$	−7.83249			−0.279553
$786$	−4.31187	+	66.4511i	−0.153799	+	2.37023i
$787$	−2.19121	+	3.79528i	−0.0781081	+	0.135287i	−0.902434	−	0.430829i	$-0.858221\pi$
$787$	−2.19121	+	3.79528i	−0.0781081	+	0.135287i	0.824326	+	0.566116i	$0.191555\pi$
$788$	−9.55417	−	1.24514i	−0.340353	−	0.0443563i
$789$	30.5044	−	17.6117i	1.08599	−	0.626994i
$790$	0.542554	+	0.362011i	0.0193032	+	0.0128798i
$791$		0			0
$792$	37.1718	+	7.31828i	1.32084	+	0.260044i
$793$	−4.02198	−	6.96627i	−0.142825	−	0.247380i
$794$	−22.0302	−	44.5995i	−0.781824	−	1.58278i
$795$	−12.0937	−	6.98233i	−0.428921	−	0.247638i
$796$	1.54892	−	2.02406i	0.0549001	−	0.0717409i
$797$			53.6019i			1.89868i	0.314255	+	0.949339i	$0.398245\pi$
$797$			53.6019i			1.89868i	−0.314255	+	0.949339i	$0.601755\pi$
$798$		0			0
$799$			21.1101i			0.746822i
$800$	−3.74369	−	4.24085i	−0.132359	−	0.149937i
$801$	36.4118	+	21.0224i	1.28655	+	0.742789i
$802$	−40.4792	+	19.9950i	−1.42937	+	0.706048i
$803$	16.6338	+	28.8106i	0.586995	+	1.01670i
$804$	0.292177	−	0.121471i	0.0103043	−	0.00428394i
$805$		0			0
$806$	12.1765	−	18.2492i	0.428900	−	0.642802i
$807$	−22.0422	+	12.7261i	−0.775924	+	0.447980i
$808$	−11.6276	+	13.3113i	−0.409058	+	0.468289i
$809$	0.754693	−	1.30717i	0.0265336	−	0.0459575i	−0.852454	−	0.522803i	$-0.824886\pi$
$809$	0.754693	−	1.30717i	0.0265336	−	0.0459575i	0.878987	+	0.476845i	$0.158220\pi$
$810$	12.5600	+	0.814989i	0.441312	+	0.0286358i
$811$	43.1894			1.51658			0.758292	−	0.651915i	$-0.226034\pi$
$811$	43.1894			1.51658			0.758292	+	0.651915i	$0.226034\pi$
$812$		0			0
$813$	23.9063			0.838432
$814$	35.3315	+	2.29258i	1.23837	+	0.0803550i
$815$	5.42579	−	9.39774i	0.190057	−	0.329188i
$816$	−39.8845	+	10.7987i	−1.39624	+	0.378031i
$817$	−17.6984	+	10.2182i	−0.619189	+	0.357489i
$818$	−12.8840	+	19.3095i	−0.450478	+	0.675142i
$819$		0			0
$820$	1.12104	+	2.69648i	0.0391486	+	0.0941651i
$821$	4.56478	+	7.90644i	0.159312	+	0.275937i	0.934621	−	0.355646i	$-0.115739\pi$
$821$	4.56478	+	7.90644i	0.159312	+	0.275937i	−0.775309	+	0.631582i	$0.782406\pi$
$822$	−36.5493	+	18.0538i	−1.27480	+	0.629698i
$823$	0.329424	+	0.190193i	0.0114830	+	0.00662972i	0.505731	−	0.862692i	$-0.331223\pi$
$823$	0.329424	+	0.190193i	0.0114830	+	0.00662972i	−0.494248	+	0.869321i	$0.664556\pi$
$824$	30.5616	−	10.4411i	1.06467	−	0.363732i
$825$			6.70555i			0.233457i
$826$		0			0
$827$		−	23.9044i		−	0.831236i	−0.909539	−	0.415618i	$-0.863565\pi$
$827$		−	23.9044i		−	0.831236i	0.909539	−	0.415618i	$-0.136435\pi$
$828$	25.3152	+	19.3725i	0.879763	+	0.673243i
$829$	−35.8241	−	20.6830i	−1.24422	−	0.718352i	−0.274271	−	0.961653i	$-0.588436\pi$
$829$	−35.8241	−	20.6830i	−1.24422	−	0.718352i	−0.969951	+	0.243301i	$0.921770\pi$
$830$	−6.83774	−	13.8428i	−0.237341	−	0.480490i
$831$	20.3800	+	35.2992i	0.706974	+	1.22452i
$832$	−9.61631	+	23.4755i	−0.333386	+	0.813866i
$833$		0			0
$834$	−26.4434	−	17.6439i	−0.915659	−	0.610959i
$835$	−10.1737	+	5.87381i	−0.352076	+	0.203271i
$836$	1.18640	−	9.10347i	0.0410327	−	0.314850i
$837$	−21.9187	+	37.9642i	−0.757620	+	1.31224i
$838$	−1.08655	+	16.7451i	−0.0375343	+	0.578448i
$839$	46.4174			1.60251			0.801253	−	0.598326i	$-0.204167\pi$
$839$	46.4174			1.60251			0.801253	+	0.598326i	$0.204167\pi$
$840$		0			0
$841$	25.4780			0.878551
$842$	0.947163	−	14.5969i	0.0326414	−	0.503043i
$843$	−14.2155	+	24.6219i	−0.489607	+	0.848025i
$844$	−0.958861	+	7.35749i	−0.0330054	+	0.253255i
$845$	2.54974	−	1.47209i	0.0877136	−	0.0506415i
$846$	−43.1651	−	28.8013i	−1.48405	−	0.990208i
$847$		0			0
$848$	−13.1397	+	13.2085i	−0.451219	+	0.453582i
$849$	−32.3038	−	55.9518i	−1.10866	−	1.92026i
$850$	−2.15798	−	4.36877i	−0.0740183	−	0.149847i
$851$	25.7996	+	14.8954i	0.884398	+	0.510608i
$852$	1.01118	+	0.773811i	0.0346425	+	0.0265103i
$853$			10.5928i			0.362692i	0.983419	+	0.181346i	$0.0580454\pi$
$853$			10.5928i			0.362692i	−0.983419	+	0.181346i	$0.941955\pi$
$854$		0			0
$855$		−	12.2913i		−	0.420352i
$856$	−2.38101	−	6.96937i	−0.0813814	−	0.238208i
$857$	0.245410	+	0.141688i	0.00838305	+	0.00483996i	0.504186	−	0.863595i	$-0.331793\pi$
$857$	0.245410	+	0.141688i	0.00838305	+	0.00483996i	−0.495803	+	0.868435i	$0.665126\pi$
$858$	26.9618	−	13.3180i	0.920461	−	0.454669i
$859$	4.93861	+	8.55393i	0.168503	+	0.291856i	0.937894	−	0.346922i	$-0.112773\pi$
$859$	4.93861	+	8.55393i	0.168503	+	0.291856i	−0.769391	+	0.638779i	$0.779440\pi$
$860$	−7.64517	−	18.3891i	−0.260698	−	0.627064i
$861$		0			0
$862$	23.2787	−	34.8883i	0.792875	−	1.18830i
$863$	−28.2007	+	16.2817i	−0.959963	+	0.554235i	−0.896162	−	0.443728i	$-0.853656\pi$
$863$	−28.2007	+	16.2817i	−0.959963	+	0.554235i	−0.0638012	+	0.997963i	$0.520322\pi$
$864$	16.1374	−	48.0541i	0.549006	−	1.63483i
$865$	8.24371	−	14.2785i	0.280295	−	0.485485i
$866$	41.5057	+	2.69321i	1.41042	+	0.0915192i
$867$	15.3759			0.522195
$868$		0			0
$869$	−1.03151			−0.0349916
$870$	−31.2295	−	2.02642i	−1.05878	−	0.0687020i
$871$	0.0836685	−	0.144918i	0.00283500	−	0.00491036i
$872$	−2.13420	−	1.86426i	−0.0722732	−	0.0631319i
$873$	0.961883	−	0.555343i	0.0325548	−	0.0187955i
$874$	4.28733	−	6.42551i	0.145021	−	0.217346i
$875$		0			0
$876$	82.3573	−	34.2396i	2.78260	−	1.15685i
$877$	−19.0353	−	32.9700i	−0.642775	−	1.11332i	−0.984811	−	0.173632i	$-0.944450\pi$
$877$	−19.0353	−	32.9700i	−0.642775	−	1.11332i	0.342036	−	0.939687i	$-0.388884\pi$
$878$	11.1883	−	5.52652i	0.377585	−	0.186511i
$879$	75.1666	+	43.3975i	2.53531	+	1.46376i
$880$	8.64745	+	2.29289i	0.291506	+	0.0772934i
$881$		−	27.7529i		−	0.935019i	−0.883988	−	0.467509i	$-0.845151\pi$
$881$		−	27.7529i		−	0.935019i	0.883988	−	0.467509i	$-0.154849\pi$
$882$		0			0
$883$			44.1707i			1.48646i	0.669034	+	0.743232i	$0.266708\pi$
$883$			44.1707i			1.48646i	−0.669034	+	0.743232i	$0.733292\pi$
$884$	−13.2800	+	17.3537i	−0.446656	+	0.583669i
$885$	−18.4836	−	10.6715i	−0.621321	−	0.358720i
$886$	−12.2551	−	24.8100i	−0.411717	−	0.833508i
$887$	10.0638	+	17.4310i	0.337909	+	0.585275i	0.984039	−	0.177952i	$-0.0569471\pi$
$887$	10.0638	+	17.4310i	0.337909	+	0.585275i	−0.646130	+	0.763227i	$0.723614\pi$
$888$	18.3363	−	93.1358i	0.615326	−	3.12543i
$889$		0			0
$890$	8.25882	+	5.51057i	0.276836	+	0.184715i
$891$	−17.2385	+	9.95263i	−0.577510	+	0.333426i
$892$	25.6988	+	3.34919i	0.860461	+	0.112139i
$893$	−6.28724	+	10.8898i	−0.210394	+	0.364414i
$894$	1.78493	−	27.5079i	0.0596968	−	0.920000i
$895$	9.10959			0.304500
$896$		0			0
$897$	25.3027			0.844831
$898$	0.459978	−	7.08882i	0.0153497	−	0.236557i
$899$	18.0537	−	31.2699i	0.602124	−	1.04291i
$900$	11.8773	+	1.54790i	0.395910	+	0.0515967i
$901$	−13.8983	+	8.02418i	−0.463019	+	0.267324i
$902$	−3.84167	−	2.56329i	−0.127913	−	0.0853483i
$903$		0			0
$904$	−8.11832	+	41.2355i	−0.270011	+	1.37147i
$905$	8.28775	+	14.3548i	0.275494	+	0.477170i
$906$	−44.4561	−	90.0000i	−1.47696	−	2.99005i
$907$	13.0052	+	7.50854i	0.431830	+	0.249317i	0.700126	−	0.714020i	$-0.253127\pi$
$907$	13.0052	+	7.50854i	0.431830	+	0.249317i	−0.268296	+	0.963336i	$0.586461\pi$
$908$	10.8084	−	14.1240i	0.358690	−	0.468720i
$909$		−	37.4239i		−	1.24127i
$910$		0			0
$911$		−	24.0198i		−	0.795811i	−0.917426	−	0.397906i	$-0.869737\pi$
$911$		−	24.0198i		−	0.795811i	0.917426	−	0.397906i	$-0.130263\pi$
$912$	−23.7909	−	6.30821i	−0.787795	−	0.208886i
$913$	21.1461	+	12.2087i	0.699834	+	0.404049i
$914$	35.3063	−	17.4398i	1.16783	−	0.576857i
$915$	3.80262	+	6.58634i	0.125711	+	0.217738i
$916$	−23.9076	+	9.93946i	−0.789931	+	0.328409i
$917$		0			0
$918$	24.2349	−	36.3214i	0.799871	−	1.19878i
$919$	49.7575	−	28.7275i	1.64135	−	0.947632i	0.660992	−	0.750393i	$-0.270136\pi$
$919$	49.7575	−	28.7275i	1.64135	−	0.947632i	0.980355	−	0.197239i	$-0.0631976\pi$
$920$	5.66917	+	4.95212i	0.186907	+	0.163267i
$921$	12.0014	−	20.7870i	0.395459	−	0.684956i
$922$	−28.0124	−	1.81767i	−0.922541	−	0.0598617i
$923$	0.673370			0.0221643
$924$		0			0
$925$	11.1938			0.368049
$926$	−50.3981	−	3.27022i	−1.65618	−	0.107466i
$927$	−34.1915	+	59.2214i	−1.12300	+	1.94509i
$928$	−13.2919	+	39.5806i	−0.436327	+	1.29930i
$929$	−3.45964	+	1.99743i	−0.113507	+	0.0655334i	−0.555679	−	0.831397i	$-0.687542\pi$
$929$	−3.45964	+	1.99743i	−0.113507	+	0.0655334i	0.442172	+	0.896930i	$0.354208\pi$
$930$	−11.5124	+	17.2539i	−0.377507	+	0.565779i
$931$		0			0
$932$	−11.6827	−	28.1006i	−0.382678	−	0.920466i
$933$	20.6162	+	35.7083i	0.674945	+	1.16904i
$934$	28.6700	−	14.1617i	0.938110	−	0.463386i
$935$	6.67369	+	3.85305i	0.218253	+	0.126008i
$936$	−17.3658	−	50.8307i	−0.567619	−	1.66145i
$937$		−	43.2204i		−	1.41195i	−0.708237	−	0.705975i	$-0.750509\pi$
$937$		−	43.2204i		−	1.41195i	0.708237	−	0.705975i	$-0.249491\pi$
$938$		0			0
$939$		−	31.8878i		−	1.04062i
$940$	−9.73126	−	7.44689i	−0.317399	−	0.242891i
$941$	30.6731	+	17.7091i	0.999915	+	0.577301i	0.908223	−	0.418486i	$-0.137439\pi$
$941$	30.6731	+	17.7091i	0.999915	+	0.577301i	0.0916918	+	0.995787i	$0.470773\pi$
$942$	−14.7078	−	29.7754i	−0.479206	−	0.970136i
$943$	−1.94295	−	3.36529i	−0.0632712	−	0.109589i
$944$	−20.0823	+	20.1874i	−0.653622	+	0.657044i
$945$		0			0
$946$	26.1990	+	17.4809i	0.851802	+	0.568352i
$947$	−42.1696	+	24.3466i	−1.37033	+	0.791159i	−0.990969	−	0.134091i	$-0.957188\pi$
$947$	−42.1696	+	24.3466i	−1.37033	+	0.791159i	−0.379358	+	0.925250i	$0.623855\pi$
$948$	−0.357390	+	2.74231i	−0.0116075	+	0.0890662i
$949$	23.5840	−	40.8488i	0.765571	−	1.32601i
$950$	0.187940	−	2.89637i	0.00609756	−	0.0939708i
$951$	−50.9190			−1.65116
$952$		0			0
$953$	−47.5308			−1.53967			−0.769837	−	0.638241i	$-0.779662\pi$
$953$	−47.5308			−1.53967			−0.769837	+	0.638241i	$0.779662\pi$
$954$	2.55440	−	39.3663i	0.0827016	−	1.27453i
$955$	1.49648	−	2.59197i	0.0484248	−	0.0838743i
$956$	0.0113339	−	0.0869671i	0.000366566	−	0.00281272i
$957$	42.8623	−	24.7466i	1.38554	−	0.799943i
$958$	10.0746	+	6.72211i	0.325495	+	0.217182i
$959$		0			0
$960$	9.09185	−	22.1952i	0.293438	−	0.716346i
$961$	3.53423	+	6.12147i	0.114008	+	0.197467i
$962$	−22.2321	−	45.0082i	−0.716792	−	1.45112i
$963$	13.5050	+	7.79713i	0.435193	+	0.251259i
$964$	3.65400	+	2.79624i	0.117688	+	0.0900609i
$965$		−	14.7088i		−	0.473494i
$966$		0			0
$967$		−	29.3643i		−	0.944292i	−0.881520	−	0.472146i	$-0.843479\pi$
$967$		−	29.3643i		−	0.944292i	0.881520	−	0.472146i	$-0.156521\pi$
$968$	16.0532	−	5.48442i	0.515970	−	0.176276i
$969$	−18.3607	−	10.6005i	−0.589829	−	0.340538i
$970$	0.235154	−	0.116156i	0.00755035	−	0.00372955i
$971$	13.3188	+	23.0688i	0.427419	+	0.740312i	0.996643	−	0.0818708i	$-0.0260895\pi$
$971$	13.3188	+	23.0688i	0.427419	+	0.740312i	−0.569224	+	0.822183i	$0.692756\pi$
$972$	−0.153506	−	0.369231i	−0.00492370	−	0.0118431i
$973$		0			0
$974$	−24.8391	+	37.2269i	−0.795895	+	1.19283i
$975$	8.23364	−	4.75369i	0.263687	−	0.152240i
$976$	9.79398	−	2.65172i	0.313498	−	0.0848795i
$977$	−7.73476	+	13.3970i	−0.247457	+	0.428608i	−0.962819	−	0.270146i	$-0.912928\pi$
$977$	−7.73476	+	13.3970i	−0.247457	+	0.428608i	0.715363	+	0.698753i	$0.246261\pi$
$978$	45.9143	+	2.97928i	1.46818	+	0.0952668i
$979$	−15.7018			−0.501832
$980$		0			0
$981$	6.00019			0.191571
$982$	50.4916	+	3.27629i	1.61125	+	0.104551i
$983$	22.0131	−	38.1277i	0.702107	−	1.21609i	−0.265618	−	0.964078i	$-0.585576\pi$
$983$	22.0131	−	38.1277i	0.702107	−	1.21609i	0.967725	−	0.252007i	$-0.0810907\pi$
$984$	−8.14565	+	9.32511i	−0.259674	+	0.297274i
$985$	4.17206	−	2.40874i	0.132933	−	0.0767489i
$986$	−19.9615	+	29.9167i	−0.635703	+	0.952743i
$987$		0			0
$988$	−12.0191	+	4.99686i	−0.382378	+	0.158971i
$989$	13.2503	+	22.9502i	0.421336	+	0.729775i
$990$	−16.9837	+	8.38923i	−0.539778	+	0.266627i
$991$	14.4776	+	8.35865i	0.459896	+	0.265521i	0.712001	−	0.702179i	$-0.247789\pi$
$991$	14.4776	+	8.35865i	0.459896	+	0.265521i	−0.252104	+	0.967700i	$0.581123\pi$
$992$	18.3141	+	20.7462i	0.581472	+	0.658692i
$993$		−	24.9751i		−	0.792560i
$994$		0			0
$995$			1.27436i			0.0403999i
$996$	39.7839	−	51.9877i	1.26060	−	1.64729i
$997$	−23.8844	−	13.7897i	−0.756427	−	0.436723i	0.0715845	−	0.997435i	$-0.477194\pi$
$997$	−23.8844	−	13.7897i	−0.756427	−	0.436723i	−0.828011	+	0.560711i	$0.810528\pi$
$998$	−25.8762	−	52.3856i	−0.819098	−	1.65824i
$999$	50.1540	+	86.8693i	1.58680	+	2.74842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.o.f.31.8		32
4.3	odd	2	inner	980.2.o.f.31.3		32
7.2	even	3		140.2.o.a.131.3	yes	32
7.3	odd	6		980.2.g.a.391.27		32
7.4	even	3		980.2.g.a.391.28		32
7.5	odd	6	inner	980.2.o.f.411.3		32
7.6	odd	2		140.2.o.a.31.8	yes	32
28.3	even	6		980.2.g.a.391.26		32
28.11	odd	6		980.2.g.a.391.25		32
28.19	even	6	inner	980.2.o.f.411.8		32
28.23	odd	6		140.2.o.a.131.8	yes	32
28.27	even	2		140.2.o.a.31.3	✓	32
35.2	odd	12		700.2.t.d.299.6		32
35.9	even	6		700.2.p.c.551.14		32
35.13	even	4		700.2.t.d.199.1		32
35.23	odd	12		700.2.t.c.299.11		32
35.27	even	4		700.2.t.c.199.16		32
35.34	odd	2		700.2.p.c.451.9		32
140.23	even	12		700.2.t.c.299.16		32
140.27	odd	4		700.2.t.c.199.11		32
140.79	odd	6		700.2.p.c.551.9		32
140.83	odd	4		700.2.t.d.199.6		32
140.107	even	12		700.2.t.d.299.1		32
140.139	even	2		700.2.p.c.451.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.3	✓	32	28.27	even	2
140.2.o.a.31.8	yes	32	7.6	odd	2
140.2.o.a.131.3	yes	32	7.2	even	3
140.2.o.a.131.8	yes	32	28.23	odd	6
700.2.p.c.451.9		32	35.34	odd	2
700.2.p.c.451.14		32	140.139	even	2
700.2.p.c.551.9		32	140.79	odd	6
700.2.p.c.551.14		32	35.9	even	6
700.2.t.c.199.11		32	140.27	odd	4
700.2.t.c.199.16		32	35.27	even	4
700.2.t.c.299.11		32	35.23	odd	12
700.2.t.c.299.16		32	140.23	even	12
700.2.t.d.199.1		32	35.13	even	4
700.2.t.d.199.6		32	140.83	odd	4
700.2.t.d.299.1		32	140.107	even	12
700.2.t.d.299.6		32	35.2	odd	12
980.2.g.a.391.25		32	28.11	odd	6
980.2.g.a.391.26		32	28.3	even	6
980.2.g.a.391.27		32	7.3	odd	6
980.2.g.a.391.28		32	7.4	even	3
980.2.o.f.31.3		32	4.3	odd	2	inner
980.2.o.f.31.8		32	1.1	even	1	trivial
980.2.o.f.411.3		32	7.5	odd	6	inner
980.2.o.f.411.8		32	28.19	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0915727 - 1.41125i) q^{2} +(-1.49907 + 2.59647i) q^{3} +(-1.98323 - 0.258463i) q^{4} +(0.866025 - 0.500000i) q^{5} +(3.52698 + 2.35332i) q^{6} +(-0.546365 + 2.77516i) q^{8} +(-2.99443 - 5.18651i) q^{9} +O(q^{10})\)	\(q+(0.0915727 - 1.41125i) q^{2} +(-1.49907 + 2.59647i) q^{3} +(-1.98323 - 0.258463i) q^{4} +(0.866025 - 0.500000i) q^{5} +(3.52698 + 2.35332i) q^{6} +(-0.546365 + 2.77516i) q^{8} +(-2.99443 - 5.18651i) q^{9} +(-0.626319 - 1.26796i) q^{10} +(1.93693 + 1.11828i) q^{11} +(3.64409 - 4.76194i) q^{12} -3.17109i q^{13} +2.99814i q^{15} +(3.86639 + 1.02518i) q^{16} +(2.98390 + 1.72275i) q^{17} +(-7.59365 + 3.75094i) q^{18} +(1.02618 + 1.77739i) q^{19} +(-1.84676 + 0.767779i) q^{20} +(1.75554 - 2.63107i) q^{22} +(2.30481 - 1.33068i) q^{23} +(-6.38656 - 5.57878i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-4.47519 - 0.290385i) q^{26} +8.96105 q^{27} -7.38092 q^{29} +(4.23112 + 0.274548i) q^{30} +(-2.44599 + 4.23658i) q^{31} +(1.80084 - 5.36255i) q^{32} +(-5.80718 + 3.35278i) q^{33} +(2.70447 - 4.05325i) q^{34} +(4.59812 + 11.0600i) q^{36} +(5.59689 + 9.69410i) q^{37} +(2.60230 - 1.28543i) q^{38} +(8.23364 + 4.75369i) q^{39} +(0.914412 + 2.67654i) q^{40} -1.46011i q^{41} +9.95752i q^{43} +(-3.55233 - 2.71844i) q^{44} +(-5.18651 - 2.99443i) q^{45} +(-1.66686 - 3.37451i) q^{46} +(3.06343 + 5.30601i) q^{47} +(-8.45786 + 8.50215i) q^{48} +(-1.17639 - 0.784927i) q^{50} +(-8.94615 + 5.16506i) q^{51} +(-0.819610 + 6.28900i) q^{52} +(-2.32888 + 4.03374i) q^{53} +(0.820587 - 12.6462i) q^{54} +2.23657 q^{55} -6.15325 q^{57} +(-0.675891 + 10.4163i) q^{58} +(-3.55938 + 6.16503i) q^{59} +(0.774910 - 5.94600i) q^{60} +(2.19681 - 1.26833i) q^{61} +(5.75488 + 3.83985i) q^{62} +(-7.40297 - 3.03249i) q^{64} +(-1.58555 - 2.74625i) q^{65} +(4.19981 + 8.50238i) q^{66} +(0.0456998 + 0.0263848i) q^{67} +(-5.47248 - 4.18784i) q^{68} +7.97917i q^{69} +0.212347i q^{71} +(16.0294 - 5.47629i) q^{72} +(12.8816 + 7.43720i) q^{73} +(14.1933 - 7.01088i) q^{74} +(1.49907 + 2.59647i) q^{75} +(-1.57575 - 3.79020i) q^{76} +(7.46261 - 11.1844i) q^{78} +(-0.399413 + 0.230601i) q^{79} +(3.86099 - 1.04536i) q^{80} +(-4.44995 + 7.70755i) q^{81} +(-2.06058 - 0.133707i) q^{82} +10.9174 q^{83} +3.44551 q^{85} +(14.0525 + 0.911837i) q^{86} +(11.0645 - 19.1643i) q^{87} +(-4.16168 + 4.76428i) q^{88} +(-6.07992 + 3.51024i) q^{89} +(-4.70082 + 7.04523i) q^{90} +(-4.91490 + 2.04334i) q^{92} +(-7.33344 - 12.7019i) q^{93} +(7.76862 - 3.83736i) q^{94} +(1.77739 + 1.02618i) q^{95} +(11.2241 + 12.7147i) q^{96} +0.185459i q^{97} -13.3945i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} + 30 q^{12} - 14 q^{16} - 8 q^{22} - 36 q^{24} + 16 q^{25} - 30 q^{26} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} + 60 q^{38} - 18 q^{44} - 12 q^{45} + 2 q^{46} + 4 q^{50} + 36 q^{52} - 8 q^{53} - 12 q^{54} + 48 q^{57} + 2 q^{58} + 14 q^{60} - 24 q^{61} + 4 q^{64} + 4 q^{65} - 24 q^{66} - 60 q^{68} + 4 q^{72} + 72 q^{73} + 38 q^{74} + 120 q^{78} - 36 q^{81} - 42 q^{82} + 28 q^{86} + 4 q^{88} + 60 q^{89} - 4 q^{92} - 8 q^{93} - 18 q^{94} + 60 q^{96}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 + 30 * q^12 - 14 * q^16 - 8 * q^22 - 36 * q^24 + 16 * q^25 - 30 * q^26 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 + 60 * q^38 - 18 * q^44 - 12 * q^45 + 2 * q^46 + 4 * q^50 + 36 * q^52 - 8 * q^53 - 12 * q^54 + 48 * q^57 + 2 * q^58 + 14 * q^60 - 24 * q^61 + 4 * q^64 + 4 * q^65 - 24 * q^66 - 60 * q^68 + 4 * q^72 + 72 * q^73 + 38 * q^74 + 120 * q^78 - 36 * q^81 - 42 * q^82 + 28 * q^86 + 4 * q^88 + 60 * q^89 - 4 * q^92 - 8 * q^93 - 18 * q^94 + 60 * q^96

Introduction

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