LMFDB - Embedded newform 588.2.n.f.275.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(263,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.263"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,4,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.11
Character	$\chi$	$=$	588.275
Dual form			588.2.n.f.263.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36159 + 0.382199i) q^{2} +(-0.683917 - 1.59131i) q^{3} +(1.70785 + 1.04079i) q^{4} +(1.97228 + 1.13870i) q^{5} +(-0.323018 - 2.42810i) q^{6} +(1.92760 + 2.06987i) q^{8} +(-2.06452 + 2.17664i) q^{9} +(2.25023 + 2.30424i) q^{10} +(2.15917 + 3.73979i) q^{11} +(0.488197 - 3.42953i) q^{12} -0.406728 q^{13} +(0.463141 - 3.91729i) q^{15} +(1.83349 + 3.55504i) q^{16} +(3.73979 - 2.15917i) q^{17} +(-3.64293 + 2.17464i) q^{18} +(-4.70065 - 2.71392i) q^{19} +(2.18321 + 3.99747i) q^{20} +(1.51056 + 5.91729i) q^{22} +(0.581371 - 1.00696i) q^{23} +(1.97548 - 4.48302i) q^{24} +(0.0932716 + 0.161551i) q^{25} +(-0.553797 - 0.155451i) q^{26} +(4.87566 + 1.79664i) q^{27} -3.72469i q^{29} +(2.12779 - 5.15672i) q^{30} +(-5.05289 + 2.91729i) q^{31} +(1.13773 + 5.54126i) q^{32} +(4.47446 - 5.99360i) q^{33} +(5.91729 - 1.51056i) q^{34} +(-5.79132 + 1.56864i) q^{36} +(3.91729 - 6.78494i) q^{37} +(-5.36310 - 5.49183i) q^{38} +(0.278168 + 0.647230i) q^{39} +(1.44481 + 6.27733i) q^{40} +2.56195i q^{41} -11.0211i q^{43} +(-0.204820 + 8.63424i) q^{44} +(-6.55035 + 1.94210i) q^{45} +(1.17645 - 1.14887i) q^{46} +(1.16274 - 2.01393i) q^{47} +(4.40320 - 5.34900i) q^{48} +(0.0652529 + 0.255614i) q^{50} +(-5.99360 - 4.47446i) q^{51} +(-0.694631 - 0.423321i) q^{52} +(-4.74675 + 2.74054i) q^{53} +(5.95198 + 4.30975i) q^{54} +9.83457i q^{55} +(-1.10383 + 9.33627i) q^{57} +(1.42357 - 5.07150i) q^{58} +(1.95653 + 3.38881i) q^{59} +(4.86807 - 6.20810i) q^{60} +(-5.22448 + 9.04906i) q^{61} +(-7.99494 + 2.04094i) q^{62} +(-0.568736 + 7.97976i) q^{64} +(-0.802184 - 0.463141i) q^{65} +(8.38312 - 6.45069i) q^{66} +(-6.78494 + 3.91729i) q^{67} +(8.63424 + 0.204820i) q^{68} +(-2.00000 - 0.236460i) q^{69} +4.88743 q^{71} +(-8.48493 - 0.0775907i) q^{72} +(-1.40673 - 2.43653i) q^{73} +(7.92693 - 7.74112i) q^{74} +(0.193287 - 0.258911i) q^{75} +(-5.20336 - 9.52738i) q^{76} +(0.131381 + 0.987576i) q^{78} +(-3.46410 - 2.00000i) q^{79} +(-0.431948 + 9.09935i) q^{80} +(-0.475549 - 8.98743i) q^{81} +(-0.979172 + 3.48832i) q^{82} -0.641735 q^{83} +9.83457 q^{85} +(4.21225 - 15.0062i) q^{86} +(-5.92712 + 2.54738i) q^{87} +(-3.57888 + 11.6780i) q^{88} +(-12.1218 - 6.99851i) q^{89} +(-9.66116 + 0.140802i) q^{90} +(2.04094 - 1.11466i) q^{92} +(8.09805 + 6.04551i) q^{93} +(2.35290 - 2.29775i) q^{94} +(-6.18068 - 10.7053i) q^{95} +(8.03973 - 5.60024i) q^{96} -2.00000 q^{97} +(-12.5978 - 3.02112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} - 12 q^{6} + 4 q^{9} - 4 q^{10} + 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} - 2 q^{24} + 12 q^{25} - 20 q^{30} + 16 q^{33} + 64 q^{34} - 40 q^{36} + 16 q^{37} - 20 q^{40} - 24 q^{45} + 92 q^{48}+ \cdots - 48 q^{97}+O(q^{100}) $ 24 * q + 4 * q^4 - 12 * q^6 + 4 * q^9 - 4 * q^10 + 6 * q^12 - 4 * q^16 + 8 * q^18 - 32 * q^22 - 2 * q^24 + 12 * q^25 - 20 * q^30 + 16 * q^33 + 64 * q^34 - 40 * q^36 + 16 * q^37 - 20 * q^40 - 24 * q^45 + 92 * q^48 + 28 * q^52 - 10 * q^54 + 32 * q^57 + 32 * q^58 - 28 * q^60 + 16 * q^61 + 40 * q^64 + 12 * q^66 - 48 * q^69 + 32 * q^72 - 24 * q^73 - 120 * q^76 + 40 * q^78 - 28 * q^81 - 8 * q^82 + 80 * q^85 + 56 * q^88 - 160 * q^90 - 24 * q^93 + 34 * q^96 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.36159	+	0.382199i	0.962789	+	0.270255i
$2$	1.36159	+	0.382199i	0.962789	+	0.270255i
$3$	−0.683917	−	1.59131i	−0.394860	−	0.918742i
$3$	−0.683917	−	1.59131i	−0.394860	−	0.918742i
$4$	1.70785	+	1.04079i	0.853924	+	0.520397i
$5$	1.97228	+	1.13870i	0.882033	+	0.509242i	0.871328	−	0.490701i	$-0.163259\pi$
$5$	1.97228	+	1.13870i	0.882033	+	0.509242i	0.0107045	+	0.999943i	$0.496593\pi$
$6$	−0.323018	−	2.42810i	−0.131872	−	0.991267i
$7$		0			0
$7$		0			0
$8$	1.92760	+	2.06987i	0.681509	+	0.731810i
$9$	−2.06452	+	2.17664i	−0.688172	+	0.725548i
$10$	2.25023	+	2.30424i	0.711586	+	0.728666i
$11$	2.15917	+	3.73979i	0.651014	+	1.12759i	0.982877	+	0.184261i	$0.0589893\pi$
$11$	2.15917	+	3.73979i	0.651014	+	1.12759i	−0.331864	+	0.943327i	$0.607677\pi$
$12$	0.488197	−	3.42953i	0.140930	−	0.990020i
$13$	−0.406728			−0.112806			−0.0564031	−	0.998408i	$-0.517963\pi$
$13$	−0.406728			−0.112806			−0.0564031	+	0.998408i	$0.517963\pi$
$14$		0			0
$15$	0.463141	−	3.91729i	0.119583	−	1.01144i
$16$	1.83349	+	3.55504i	0.458373	+	0.888760i
$17$	3.73979	−	2.15917i	0.907032	−	0.523675i	0.0275570	−	0.999620i	$-0.491227\pi$
$17$	3.73979	−	2.15917i	0.907032	−	0.523675i	0.879475	+	0.475945i	$0.157894\pi$
$18$	−3.64293	+	2.17464i	−0.858647	+	0.512567i
$19$	−4.70065	−	2.71392i	−1.07840	−	0.622616i	−0.147938	−	0.988997i	$-0.547264\pi$
$19$	−4.70065	−	2.71392i	−1.07840	−	0.622616i	−0.930465	+	0.366380i	$0.880597\pi$
$20$	2.18321	+	3.99747i	0.488181	+	0.893861i
$21$		0			0
$22$	1.51056	+	5.91729i	0.322052	+	1.26157i
$23$	0.581371	−	1.00696i	0.121224	−	0.209967i	−0.799026	−	0.601296i	$-0.794651\pi$
$23$	0.581371	−	1.00696i	0.121224	−	0.209967i	0.920251	+	0.391329i	$0.127985\pi$
$24$	1.97548	−	4.48302i	0.403244	−	0.915092i
$25$	0.0932716	+	0.161551i	0.0186543	+	0.0323102i
$26$	−0.553797	−	0.155451i	−0.108609	−	0.0304865i
$27$	4.87566	+	1.79664i	0.938322	+	0.345763i
$28$		0			0
$29$		−	3.72469i		−	0.691657i	−0.938298	−	0.345829i	$-0.887598\pi$
$29$		−	3.72469i		−	0.691657i	0.938298	−	0.345829i	$-0.112402\pi$
$30$	2.12779	−	5.15672i	0.388479	−	0.941484i
$31$	−5.05289	+	2.91729i	−0.907525	+	0.523960i	−0.879634	−	0.475651i	$-0.842213\pi$
$31$	−5.05289	+	2.91729i	−0.907525	+	0.523960i	−0.0278913	+	0.999611i	$0.508879\pi$
$32$	1.13773	+	5.54126i	0.201125	+	0.979566i
$33$	4.47446	−	5.99360i	0.778904	−	1.04335i
$34$	5.91729	−	1.51056i	1.01481	−	0.259058i
$35$		0			0
$36$	−5.79132	+	1.56864i	−0.965220	+	0.261440i
$37$	3.91729	−	6.78494i	0.643998	−	1.11544i	−0.340534	−	0.940232i	$-0.610608\pi$
$37$	3.91729	−	6.78494i	0.643998	−	1.11544i	0.984532	−	0.175205i	$-0.0560588\pi$
$38$	−5.36310	−	5.49183i	−0.870009	−	0.890892i
$39$	0.278168	+	0.647230i	0.0445426	+	0.103640i
$40$	1.44481	+	6.27733i	0.228445	+	0.992533i
$41$			2.56195i			0.400109i	0.979785	+	0.200054i	$0.0641119\pi$
$41$			2.56195i			0.400109i	−0.979785	+	0.200054i	$0.935888\pi$
$42$		0			0
$43$		−	11.0211i		−	1.68070i	−0.542041	−	0.840352i	$-0.682348\pi$
$43$		−	11.0211i		−	1.68070i	0.542041	−	0.840352i	$-0.317652\pi$
$44$	−0.204820	+	8.63424i	−0.0308777	+	1.30166i
$45$	−6.55035	+	1.94210i	−0.976469	+	0.289511i
$46$	1.17645	−	1.14887i	0.173458	−	0.169392i
$47$	1.16274	−	2.01393i	0.169603	−	0.293762i	−0.768677	−	0.639637i	$-0.779085\pi$
$47$	1.16274	−	2.01393i	0.169603	−	0.293762i	0.938281	+	0.345875i	$0.112418\pi$
$48$	4.40320	−	5.34900i	0.635547	−	0.772062i
$49$		0			0
$50$	0.0652529	+	0.255614i	0.00922816	+	0.0361493i
$51$	−5.99360	−	4.47446i	−0.839272	−	0.626550i
$52$	−0.694631	−	0.423321i	−0.0963279	−	0.0587040i
$53$	−4.74675	+	2.74054i	−0.652017	+	0.376442i	−0.789228	−	0.614100i	$-0.789519\pi$
$53$	−4.74675	+	2.74054i	−0.652017	+	0.376442i	0.137212	+	0.990542i	$0.456186\pi$
$54$	5.95198	+	4.30975i	0.809962	+	0.586483i
$55$			9.83457i			1.32609i
$56$		0			0
$57$	−1.10383	+	9.33627i	−0.146206	+	1.23662i
$58$	1.42357	−	5.07150i	0.186924	−	0.665920i
$59$	1.95653	+	3.38881i	0.254719	+	0.441186i	0.964819	−	0.262915i	$-0.0846838\pi$
$59$	1.95653	+	3.38881i	0.254719	+	0.441186i	−0.710100	+	0.704100i	$0.751350\pi$
$60$	4.86807	−	6.20810i	0.628464	−	0.801462i
$61$	−5.22448	+	9.04906i	−0.668926	+	1.15861i	0.309279	+	0.950971i	$0.399912\pi$
$61$	−5.22448	+	9.04906i	−0.668926	+	1.15861i	−0.978205	+	0.207642i	$0.933421\pi$
$62$	−7.99494	+	2.04094i	−1.01536	+	0.259199i
$63$		0			0
$64$	−0.568736	+	7.97976i	−0.0710920	+	0.997470i
$65$	−0.802184	−	0.463141i	−0.0994987	−	0.0574456i
$66$	8.38312	−	6.45069i	1.03189	−	0.794025i
$67$	−6.78494	+	3.91729i	−0.828912	+	0.478573i	−0.853480	−	0.521126i	$-0.825512\pi$
$67$	−6.78494	+	3.91729i	−0.828912	+	0.478573i	0.0245679	+	0.999698i	$0.492179\pi$
$68$	8.63424	+	0.204820i	1.04706	+	0.0248380i
$69$	−2.00000	−	0.236460i	−0.240772	−	0.0284665i
$70$		0			0
$71$	4.88743			0.580031			0.290016	−	0.957022i	$-0.406339\pi$
$71$	4.88743			0.580031			0.290016	+	0.957022i	$0.406339\pi$
$72$	−8.48493	−	0.0775907i	−0.999958	−	0.00914415i
$73$	−1.40673	−	2.43653i	−0.164645	−	0.285174i	0.771884	−	0.635763i	$-0.219315\pi$
$73$	−1.40673	−	2.43653i	−0.164645	−	0.285174i	−0.936529	+	0.350590i	$0.885981\pi$
$74$	7.92693	−	7.74112i	0.921486	−	0.899886i
$75$	0.193287	−	0.258911i	0.0223189	−	0.0298965i
$76$	−5.20336	−	9.52738i	−0.596867	−	1.09287i
$77$		0			0
$78$	0.131381	+	0.987576i	0.0148759	+	0.111821i
$79$	−3.46410	−	2.00000i	−0.389742	−	0.225018i	0.292306	−	0.956325i	$-0.405577\pi$
$79$	−3.46410	−	2.00000i	−0.389742	−	0.225018i	−0.682048	+	0.731307i	$0.738911\pi$
$80$	−0.431948	+	9.09935i	−0.0482933	+	1.01734i
$81$	−0.475549	−	8.98743i	−0.0528388	−	0.998603i
$82$	−0.979172	+	3.48832i	−0.108131	+	0.385220i
$83$	−0.641735			−0.0704395			−0.0352198	−	0.999380i	$-0.511213\pi$
$83$	−0.641735			−0.0704395			−0.0352198	+	0.999380i	$0.511213\pi$
$84$		0			0
$85$	9.83457			1.06671
$86$	4.21225	−	15.0062i	0.454219	−	1.61816i
$87$	−5.92712	+	2.54738i	−0.635454	+	0.273108i
$88$	−3.57888	+	11.6780i	−0.381509	+	1.24488i
$89$	−12.1218	−	6.99851i	−1.28491	−	0.741841i	−0.307165	−	0.951656i	$-0.599380\pi$
$89$	−12.1218	−	6.99851i	−1.28491	−	0.741841i	−0.977741	+	0.209815i	$0.932714\pi$
$90$	−9.66116	+	0.140802i	−1.01838	+	0.0148419i
$91$		0			0
$92$	2.04094	−	1.11466i	0.212782	−	0.116211i
$93$	8.09805	+	6.04551i	0.839729	+	0.626891i
$94$	2.35290	−	2.29775i	0.242683	−	0.236994i
$95$	−6.18068	−	10.7053i	−0.634124	−	1.09834i
$96$	8.03973	−	5.60024i	0.820552	−	0.571573i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	−12.5978	−	3.02112i	−1.26613	−	0.303633i
$100$	−0.00884778	+	0.372981i	−0.000884778	+	0.0372981i
$101$	7.52122	−	4.34238i	0.748390	−	0.432083i	−0.0767221	−	0.997053i	$-0.524445\pi$
$101$	7.52122	−	4.34238i	0.748390	−	0.432083i	0.825112	+	0.564970i	$0.191112\pi$
$102$	−6.45069	−	8.38312i	−0.638714	−	0.830053i
$103$	−9.22146	−	5.32401i	−0.908618	−	0.524591i	−0.0286316	−	0.999590i	$-0.509115\pi$
$103$	−9.22146	−	5.32401i	−0.908618	−	0.524591i	−0.879986	+	0.474999i	$0.842448\pi$
$104$	−0.784009	−	0.841876i	−0.0768784	−	0.0825527i
$105$		0			0
$106$	−7.51056	+	1.91729i	−0.729490	+	0.186223i
$107$	−4.20011	+	7.27480i	−0.406040	+	0.703281i	−0.994442	−	0.105287i	$-0.966424\pi$
$107$	−4.20011	+	7.27480i	−0.406040	+	0.703281i	0.588402	+	0.808568i	$0.299757\pi$
$108$	6.45697	+	8.14295i	0.621322	+	0.783555i
$109$	5.24130	+	9.07820i	0.502026	+	0.869534i	0.999997	+	0.00234046i	$0.000744993\pi$
$109$	5.24130	+	9.07820i	0.502026	+	0.869534i	−0.497972	+	0.867193i	$0.665922\pi$
$110$	−3.75876	+	13.3906i	−0.358384	+	1.27675i
$111$	−13.4760	−	1.59327i	−1.27909	−	0.151227i
$112$		0			0
$113$		−	9.56296i		−	0.899607i	−0.893128	−	0.449804i	$-0.851494\pi$
$113$		−	9.56296i		−	0.899607i	0.893128	−	0.449804i	$-0.148506\pi$
$114$	−5.07127	+	12.2903i	−0.474968	+	1.15109i
$115$	2.29326	−	1.32401i	0.213848	−	0.123465i
$116$	3.87664	−	6.36121i	0.359937	−	0.590623i
$117$	0.839697	−	0.885303i	0.0776300	−	0.0818463i
$118$	1.36879	+	5.36195i	0.126008	+	0.493608i
$119$		0			0
$120$	9.00103	−	6.59231i	0.821678	−	0.601793i
$121$	−3.82401	+	6.62339i	−0.347638	+	0.602126i
$122$	−10.5721	+	10.3243i	−0.957156	+	0.934720i
$123$	4.07684	−	1.75216i	0.367597	−	0.157987i
$124$	−11.6659	−	0.276735i	−1.04763	−	0.0248515i
$125$		−	10.9622i		−	0.980485i
$126$		0			0
$127$			6.20766i			0.550841i	0.961324	+	0.275420i	$0.0888170\pi$
$127$			6.20766i			0.550841i	−0.961324	+	0.275420i	$0.911183\pi$
$128$	−3.82424	+	10.6478i	−0.338018	+	0.941140i
$129$	−17.5380	+	7.53753i	−1.54413	+	0.663642i
$130$	−0.915233	−	0.937202i	−0.0802713	−	0.0821980i
$131$	−7.20115	+	12.4728i	−0.629167	+	1.08975i	0.358552	+	0.933510i	$0.383271\pi$
$131$	−7.20115	+	12.4728i	−0.629167	+	1.08975i	−0.987719	+	0.156240i	$0.950063\pi$
$132$	13.8798	−	5.57917i	1.20808	−	0.485605i
$133$		0			0
$134$	−10.7355	+	2.74054i	−0.927404	+	0.236747i
$135$	7.57037	+	9.09539i	0.651554	+	0.782807i
$136$	11.6780	+	3.57888i	1.00138	+	0.306886i
$137$	−2.01393	+	1.16274i	−0.172062	+	0.0993398i	−0.583558	−	0.812072i	$-0.698340\pi$
$137$	−2.01393	+	1.16274i	−0.172062	+	0.0993398i	0.411496	+	0.911412i	$0.365006\pi$
$138$	−2.63280	−	1.08636i	−0.224119	−	0.0924770i
$139$		−	9.22019i		−	0.782046i	−0.920381	−	0.391023i	$-0.872121\pi$
$139$		−	9.22019i		−	0.782046i	0.920381	−	0.391023i	$-0.127879\pi$
$140$		0			0
$141$	−4.00000	−	0.472921i	−0.336861	−	0.0398271i
$142$	6.65467	+	1.86797i	0.558448	+	0.156757i
$143$	−0.878195	−	1.52108i	−0.0734384	−	0.127199i
$144$	−11.5233	−	3.34857i	−0.960277	−	0.279048i
$145$	4.24130	−	7.34615i	0.352221	−	0.610064i
$146$	−0.984149	−	3.85520i	−0.0814488	−	0.319058i
$147$		0			0
$148$	13.7519	−	7.51056i	1.13040	−	0.617364i
$149$	−15.0594	−	8.69454i	−1.23371	−	0.712284i	−0.265911	−	0.963998i	$-0.585673\pi$
$149$	−15.0594	−	8.69454i	−1.23371	−	0.712284i	−0.967802	+	0.251713i	$0.919006\pi$
$150$	0.362133	−	0.278656i	0.0295681	−	0.0227522i
$151$	3.60737	−	2.08271i	0.293563	−	0.169489i	−0.345984	−	0.938240i	$-0.612455\pi$
$151$	3.60737	−	2.08271i	0.293563	−	0.169489i	0.639548	+	0.768751i	$0.279122\pi$
$152$	−3.44349	−	14.9611i	−0.279304	−	1.21350i
$153$	−3.02112	+	12.5978i	−0.244243	+	1.01847i
$154$		0			0
$155$	−13.2876			−1.06729
$156$	−0.198564	+	1.39489i	−0.0158978	+	0.111680i
$157$	9.63121	+	16.6817i	0.768654	+	1.33135i	0.938293	+	0.345842i	$0.112407\pi$
$157$	9.63121	+	16.6817i	0.768654	+	1.33135i	−0.169639	+	0.985506i	$0.554260\pi$
$158$	−3.95229	−	4.04715i	−0.314427	−	0.321974i
$159$	7.60742	+	5.67924i	0.603308	+	0.450393i
$160$	−4.06589	+	12.2245i	−0.321437	+	0.966430i
$161$		0			0
$162$	2.78748	−	12.4189i	0.219005	−	0.975724i
$163$	7.48941	+	4.32401i	0.586616	+	0.338683i	0.763758	−	0.645502i	$-0.223352\pi$
$163$	7.48941	+	4.32401i	0.586616	+	0.338683i	−0.177142	+	0.984185i	$0.556685\pi$
$164$	−2.66646	+	4.37542i	−0.208216	+	0.341663i
$165$	15.6498	−	6.72603i	1.21834	−	0.523621i
$166$	−0.873779	−	0.245270i	−0.0678184	−	0.0190367i
$167$	1.75639			0.135914			0.0679568	−	0.997688i	$-0.478352\pi$
$167$	1.75639			0.135914			0.0679568	+	0.997688i	$0.478352\pi$
$168$		0			0
$169$	−12.8346			−0.987275
$170$	13.3906	+	3.75876i	1.02702	+	0.288284i
$171$	15.6118	−	4.62870i	1.19386	−	0.353966i
$172$	11.4707	−	18.8224i	0.874634	−	1.43519i
$173$	6.81927	+	3.93711i	0.518459	+	0.299333i	0.736304	−	0.676651i	$-0.236569\pi$
$173$	6.81927	+	3.93711i	0.518459	+	0.299333i	−0.217845	+	0.975983i	$0.569903\pi$
$174$	−9.04391	+	1.20314i	−0.685617	+	0.0912100i
$175$		0			0
$176$	−9.33627	+	14.5328i	−0.703748	+	1.09545i
$177$	4.05453	−	5.43111i	0.304757	−	0.408227i
$178$	−13.8301	−	14.1620i	−1.03661	−	1.06149i
$179$	−4.67303	−	8.09392i	−0.349278	−	0.604968i	0.636843	−	0.770993i	$-0.280240\pi$
$179$	−4.67303	−	8.09392i	−0.349278	−	0.604968i	−0.986121	+	0.166026i	$0.946907\pi$
$180$	−13.2083	−	3.50076i	−0.984491	−	0.260932i
$181$	16.8893			1.25537			0.627687	−	0.778466i	$-0.284002\pi$
$181$	16.8893			1.25537			0.627687	+	0.778466i	$0.284002\pi$
$182$		0			0
$183$	17.9729	+	2.12494i	1.32860	+	0.157080i
$184$	3.20494	−	0.737659i	0.236271	−	0.0543809i
$185$	15.4520	−	8.92122i	1.13605	−	0.655901i
$186$	8.71563	+	11.3266i	0.639061	+	0.830504i
$187$	16.1497	+	9.32401i	1.18098	+	0.681839i
$188$	4.08188	−	2.22931i	0.297701	−	0.162589i
$189$		0			0
$190$	−4.32401	−	16.9384i	−0.313697	−	1.22884i
$191$	10.1541	−	17.5874i	0.734725	−	1.27258i	−0.220118	−	0.975473i	$-0.570644\pi$
$191$	10.1541	−	17.5874i	0.734725	−	1.27258i	0.954844	−	0.297108i	$-0.0960223\pi$
$192$	13.0872	−	4.55246i	0.944488	−	0.328545i
$193$	−3.42784	−	5.93720i	−0.246742	−	0.427369i	0.715878	−	0.698225i	$-0.246027\pi$
$193$	−3.42784	−	5.93720i	−0.246742	−	0.427369i	−0.962620	+	0.270856i	$0.912693\pi$
$194$	−2.72318	−	0.764397i	−0.195513	−	0.0548805i
$195$	−0.188373	+	1.59327i	−0.0134897	+	0.114097i
$196$		0			0
$197$			1.96830i			0.140235i	0.997539	+	0.0701177i	$0.0223375\pi$
$197$			1.96830i			0.140235i	−0.997539	+	0.0701177i	$0.977662\pi$
$198$	−15.9984	−	8.92839i	−1.13696	−	0.634513i
$199$	5.51925	−	3.18654i	0.391250	−	0.225888i	−0.291452	−	0.956586i	$-0.594138\pi$
$199$	5.51925	−	3.18654i	0.391250	−	0.225888i	0.682701	+	0.730697i	$0.260805\pi$
$200$	−0.154600	+	0.504466i	−0.0109319	+	0.0356711i
$201$	10.8739	+	8.11782i	0.766988	+	0.572587i
$202$	11.9005	−	3.03794i	0.837314	−	0.213748i
$203$		0			0
$204$	−5.57917	−	13.8798i	−0.390620	−	0.971781i
$205$	−2.91729	+	5.05289i	−0.203752	+	0.352909i
$206$	−10.5210	−	10.7735i	−0.733034	−	0.750629i
$207$	0.991553	+	3.34433i	0.0689177	+	0.232447i
$208$	−0.745734	−	1.44594i	−0.0517073	−	0.100258i
$209$		−	23.4393i		−	1.62133i
$210$		0			0
$211$			25.1306i			1.73006i	0.501717	+	0.865032i	$0.332702\pi$
$211$			25.1306i			1.73006i	−0.501717	+	0.865032i	$0.667298\pi$
$212$	−10.9591	−	0.259969i	−0.752672	−	0.0178547i
$213$	−3.34260	−	7.77740i	−0.229031	−	0.532899i
$214$	−8.49923	+	8.30001i	−0.580996	+	0.567377i
$215$	12.5497	−	21.7368i	0.855885	−	1.48244i
$216$	5.67951	+	13.5552i	0.386442	+	0.922314i
$217$		0			0
$218$	3.66682	+	14.3640i	0.248349	+	0.972852i
$219$	−2.91517	+	3.90492i	−0.196989	+	0.263870i
$220$	−10.2358	+	16.7960i	−0.690095	+	1.13238i
$221$	−1.52108	+	0.878195i	−0.102319	+	0.0590738i
$222$	−17.7398	−	7.31989i	−1.19062	−	0.491279i
$223$		−	9.22877i		−	0.618004i	−0.951061	−	0.309002i	$-0.900005\pi$
$223$		−	9.22877i		−	0.618004i	0.951061	−	0.309002i	$-0.0999950\pi$
$224$		0			0
$225$	−0.544200	−	0.130506i	−0.0362800	−	0.00870039i
$226$	3.65495	−	13.0208i	0.243123	−	0.866132i
$227$	9.76310	+	16.9102i	0.647999	+	1.12237i	0.983600	+	0.180364i	$0.0577274\pi$
$227$	9.76310	+	16.9102i	0.647999	+	1.12237i	−0.335601	+	0.942004i	$0.608939\pi$
$228$	−11.6023	+	14.7961i	−0.768382	+	0.979895i
$229$	−1.01682	+	1.76119i	−0.0671934	+	0.116382i	−0.897665	−	0.440679i	$-0.854738\pi$
$229$	−1.01682	+	1.76119i	−0.0671934	+	0.116382i	0.830471	+	0.557061i	$0.188071\pi$
$230$	3.62851	−	0.926283i	0.239257	−	0.0610773i
$231$		0			0
$232$	7.70963	−	7.17970i	0.506162	−	0.471370i
$233$	2.83305	+	1.63566i	0.185599	+	0.107156i	0.589921	−	0.807461i	$-0.299159\pi$
$233$	2.83305	+	1.63566i	0.185599	+	0.107156i	−0.404321	+	0.914617i	$0.632492\pi$
$234$	1.48168	−	0.884487i	0.0968607	−	0.0578207i
$235$	4.58652	−	2.64803i	0.299192	−	0.172738i
$236$	−0.185597	+	7.82392i	−0.0120814	+	0.509294i
$237$	−0.813457	+	6.88028i	−0.0528397	+	0.446922i
$238$		0			0
$239$	24.5058			1.58515			0.792575	−	0.609775i	$-0.208740\pi$
$239$	24.5058			1.58515			0.792575	+	0.609775i	$0.208740\pi$
$240$	14.7753	−	5.53583i	0.953740	−	0.357336i
$241$	−9.20766	−	15.9481i	−0.593117	−	1.02731i	−0.993810	−	0.111097i	$-0.964564\pi$
$241$	−9.20766	−	15.9481i	−0.593117	−	1.02731i	0.400692	−	0.916213i	$-0.368770\pi$
$242$	−7.73818	+	7.55680i	−0.497429	+	0.485769i
$243$	−13.9765	+	6.90340i	−0.896594	+	0.442853i
$244$	−18.3408	+	10.0168i	−1.17415	+	0.641261i
$245$		0			0
$246$	6.22066	−	0.827555i	0.396615	−	0.0527630i
$247$	1.91189	+	1.10383i	0.121651	+	0.0702350i
$248$	−15.7783	−	4.83547i	−1.00193	−	0.307053i
$249$	0.438893	+	1.02120i	0.0278137	+	0.0647157i
$250$	4.18972	−	14.9260i	0.264981	−	0.944000i
$251$	15.4443			0.974837			0.487418	−	0.873169i	$-0.337939\pi$
$251$	15.4443			0.974837			0.487418	+	0.873169i	$0.337939\pi$
$252$		0			0
$253$	5.02112			0.315675
$254$	−2.37256	+	8.45228i	−0.148868	+	0.530343i
$255$	−6.72603	−	15.6498i	−0.421200	−	0.980030i
$256$	−9.27660	+	13.0363i	−0.579788	+	0.814768i
$257$	7.76765	+	4.48465i	0.484533	+	0.279745i	0.722303	−	0.691576i	$-0.243083\pi$
$257$	7.76765	+	4.48465i	0.484533	+	0.279745i	−0.237771	+	0.971321i	$0.576417\pi$
$258$	−26.7603	+	3.56002i	−1.66603	+	0.221637i
$259$		0			0
$260$	−0.887974	−	1.62588i	−0.0550698	−	0.100833i
$261$	8.10732	+	7.68968i	0.501830	+	0.475979i
$262$	−14.5721	+	14.2305i	−0.900266	+	0.879163i
$263$	9.68119	+	16.7683i	0.596967	+	1.03398i	0.993266	+	0.115856i	$0.0369612\pi$
$263$	9.68119	+	16.7683i	0.596967	+	1.03398i	−0.396299	+	0.918122i	$0.629705\pi$
$264$	21.0309	−	2.29170i	1.29437	−	0.141044i
$265$	−12.4826			−0.766800
$266$		0			0
$267$	−2.84649	+	24.0759i	−0.174203	+	1.47342i
$268$	−15.6647	−	0.371595i	−0.956876	−	0.0226988i
$269$	0.0416451	−	0.0240438i	0.00253914	−	0.00146598i	−0.498730	−	0.866757i	$-0.666200\pi$
$269$	0.0416451	−	0.0240438i	0.00253914	−	0.00146598i	0.501269	+	0.865291i	$0.332867\pi$
$270$	6.83149	+	15.2776i	0.415751	+	0.929763i
$271$	17.2138	+	9.93840i	1.04566	+	0.603715i	0.921433	−	0.388538i	$-0.127020\pi$
$271$	17.2138	+	9.93840i	1.04566	+	0.603715i	0.124232	+	0.992253i	$0.460353\pi$
$272$	14.5328	+	9.33627i	0.881181	+	0.566095i
$273$		0			0
$274$	−3.18654	+	0.813457i	−0.192506	+	0.0491427i
$275$	−0.402778	+	0.697632i	−0.0242884	+	0.0420688i
$276$	−3.16959	−	2.48543i	−0.190787	−	0.149605i
$277$	−5.13747	−	8.89836i	−0.308681	−	0.534651i	0.669393	−	0.742908i	$-0.266554\pi$
$277$	−5.13747	−	8.89836i	−0.308681	−	0.534651i	−0.978074	+	0.208257i	$0.933221\pi$
$278$	3.52394	−	12.5541i	0.211352	−	0.752945i
$279$	4.08188	−	17.0211i	0.244376	−	1.01903i
$280$		0			0
$281$		−	6.78411i		−	0.404706i	−0.979313	−	0.202353i	$-0.935141\pi$
$281$		−	6.78411i		−	0.404706i	0.979313	−	0.202353i	$-0.0648588\pi$
$282$	−5.26561	−	2.17272i	−0.313562	−	0.129383i
$283$	−4.70065	+	2.71392i	−0.279425	+	0.161326i	−0.633163	−	0.774019i	$-0.718244\pi$
$283$	−4.70065	+	2.71392i	−0.279425	+	0.161326i	0.353738	+	0.935344i	$0.384910\pi$
$284$	8.34699	+	5.08681i	0.495303	+	0.301847i
$285$	−12.8083	+	17.1569i	−0.758697	+	1.01628i
$286$	−0.614387	−	2.40673i	−0.0363294	−	0.142313i
$287$		0			0
$288$	−14.4102	−	8.96358i	−0.849130	−	0.528184i
$289$	0.824014	−	1.42723i	0.0484714	−	0.0839550i
$290$	8.58259	−	8.38141i	0.503987	−	0.492174i
$291$	1.36783	+	3.18261i	0.0801838	+	0.186568i
$292$	0.133443	−	5.62533i	0.00780915	−	0.329198i
$293$			28.1874i			1.64673i	0.567515	+	0.823363i	$0.307905\pi$
$293$			28.1874i			1.64673i	−0.567515	+	0.823363i	$0.692095\pi$
$294$		0			0
$295$			8.91160i			0.518853i
$296$	21.5949	−	4.97035i	1.25518	−	0.288896i
$297$	3.80834	+	22.1132i	0.220982	+	1.28314i
$298$	−17.1817	−	17.5941i	−0.995306	−	1.01920i
$299$	−0.236460	+	0.409561i	−0.0136749	+	0.0236855i
$300$	0.599579	−	0.241009i	0.0346167	−	0.0139146i
$301$		0			0
$302$	5.70776	−	1.45707i	0.328445	−	0.0838450i
$303$	−12.0540	−	8.99875i	−0.692481	−	0.516965i
$304$	1.02949	−	21.6870i	0.0590450	−	1.24383i
$305$	−20.6083	+	11.8982i	−1.18003	+	0.681290i
$306$	−8.92839	+	15.9984i	−0.510402	+	0.914567i
$307$		−	2.24130i		−	0.127918i	−0.997953	−	0.0639589i	$-0.979627\pi$
$307$		−	2.24130i		−	0.127918i	0.997953	−	0.0639589i	$-0.0203727\pi$
$308$		0			0
$309$	−2.16543	+	18.3154i	−0.123187	+	1.04192i
$310$	−18.0923	−	5.07852i	−1.02757	−	0.288440i
$311$	−13.2396	−	22.9316i	−0.750746	−	1.30033i	−0.947461	−	0.319870i	$-0.896361\pi$
$311$	−13.2396	−	22.9316i	−0.750746	−	1.30033i	0.196715	−	0.980461i	$-0.436973\pi$
$312$	−0.803486	+	1.82337i	−0.0454884	+	0.103228i
$313$	−0.220185	+	0.381372i	−0.0124456	+	0.0215564i	−0.872181	−	0.489183i	$-0.837295\pi$
$313$	−0.220185	+	0.381372i	−0.0124456	+	0.0215564i	0.859736	+	0.510739i	$0.170628\pi$
$314$	6.73801	+	26.3947i	0.380248	+	1.48954i
$315$		0			0
$316$	−3.83457	−	7.02112i	−0.215712	−	0.394969i
$317$	−10.2124	−	5.89613i	−0.573586	−	0.331160i	0.184995	−	0.982740i	$-0.440773\pi$
$317$	−10.2124	−	5.89613i	−0.573586	−	0.331160i	−0.758580	+	0.651580i	$0.774107\pi$
$318$	8.18759	+	10.6403i	0.459137	+	0.596681i
$319$	13.9296	−	8.04223i	0.779905	−	0.450278i
$320$	−10.2083	+	15.0907i	−0.570659	+	0.843598i
$321$	14.4490	+	1.70830i	0.806462	+	0.0953482i
$322$		0			0
$323$	−23.4393			−1.30419
$324$	8.54190	−	15.8441i	0.474550	−	0.880229i
$325$	−0.0379362	−	0.0657074i	−0.00210432	−	0.00364479i
$326$	8.54487	+	8.74997i	0.473257	+	0.484616i
$327$	10.8616	−	14.5492i	0.600647	−	0.804575i
$328$	−5.30290	+	4.93840i	−0.292804	+	0.272678i
$329$		0			0
$330$	23.8793	−	3.17675i	1.31451	−	0.174874i
$331$	1.13427	+	0.654870i	0.0623451	+	0.0359949i	0.530849	−	0.847467i	$-0.321873\pi$
$331$	1.13427	+	0.654870i	0.0623451	+	0.0359949i	−0.468503	+	0.883462i	$0.655207\pi$
$332$	−1.09599	−	0.667914i	−0.0601500	−	0.0366565i
$333$	6.68109	+	22.5341i	0.366121	+	1.23486i
$334$	2.39148	+	0.671290i	0.130856	+	0.0367313i
$335$	−17.8424			−0.974837
$336$		0			0
$337$	−15.4615			−0.842241			−0.421120	−	0.907005i	$-0.638363\pi$
$337$	−15.4615			−0.842241			−0.421120	+	0.907005i	$0.638363\pi$
$338$	−17.4754	−	4.90535i	−0.950537	−	0.266816i
$339$	−15.2176	+	6.54027i	−0.826506	+	0.355218i
$340$	16.7960	+	10.2358i	0.910889	+	0.555112i
$341$	−21.8201	−	12.5978i	−1.18162	−	0.682210i
$342$	23.0259	−	0.335582i	1.24510	−	0.0181462i
$343$		0			0
$344$	22.8123	−	21.2443i	1.22996	−	1.14541i
$345$	−3.67531	−	2.74377i	−0.197872	−	0.147719i
$346$	7.78028	+	7.96703i	0.418271	+	0.428310i
$347$	13.8307	+	23.9555i	0.742471	+	1.28600i	0.951367	+	0.308060i	$0.0996798\pi$
$347$	13.8307	+	23.9555i	0.742471	+	1.28600i	−0.208896	+	0.977938i	$0.566987\pi$
$348$	−12.7739	−	1.81838i	−0.684754	−	0.0974756i
$349$	−18.9316			−1.01338			−0.506692	−	0.862127i	$-0.669132\pi$
$349$	−18.9316			−1.01338			−0.506692	+	0.862127i	$0.669132\pi$
$350$		0			0
$351$	−1.98307	−	0.730743i	−0.105849	−	0.0390042i
$352$	−18.2666	+	16.2194i	−0.973612	+	0.864497i
$353$	1.72586	−	0.996425i	0.0918582	−	0.0530344i	−0.453367	−	0.891324i	$-0.649777\pi$
$353$	1.72586	−	0.996425i	0.0918582	−	0.0530344i	0.545225	+	0.838289i	$0.316444\pi$
$354$	7.59637	−	5.84530i	0.403742	−	0.310674i
$355$	9.63941	+	5.56531i	0.511607	+	0.295376i
$356$	−13.4182	−	24.5687i	−0.711161	−	1.30214i
$357$		0			0
$358$	−3.26926	−	12.8066i	−0.172786	−	0.676851i
$359$	−1.17502	+	2.03519i	−0.0620151	+	0.107413i	−0.895366	−	0.445331i	$-0.853086\pi$
$359$	−1.17502	+	2.03519i	−0.0620151	+	0.107413i	0.833351	+	0.552744i	$0.186419\pi$
$360$	−16.6463	−	9.81481i	−0.877339	−	0.517286i
$361$	5.23074	+	9.05991i	0.275302	+	0.476837i
$362$	22.9963	+	6.45508i	1.20866	+	0.339271i
$363$	13.1551	+	1.55534i	0.690466	+	0.0816339i
$364$		0			0
$365$		−	6.40736i		−	0.335377i
$366$	23.6596	+	9.76253i	1.23671	+	0.510296i
$367$	29.6129	−	17.0970i	1.54578	−	0.892455i	0.547321	−	0.836923i	$-0.315648\pi$
$367$	29.6129	−	17.0970i	1.54578	−	0.892455i	0.998457	−	0.0555330i	$-0.0176858\pi$
$368$	4.64574	+	0.220534i	0.242176	+	0.0114962i
$369$	−5.57644	−	5.28918i	−0.290298	−	0.275344i
$370$	24.4490	−	6.24130i	1.27104	−	0.324470i
$371$		0			0
$372$	7.53811	+	18.7532i	0.390833	+	0.972310i
$373$	8.83457	−	15.3019i	0.457437	−	0.792304i	−0.541388	−	0.840773i	$-0.682101\pi$
$373$	8.83457	−	15.3019i	0.457437	−	0.792304i	0.998825	+	0.0484692i	$0.0154343\pi$
$374$	18.4256	+	18.8679i	0.952764	+	0.975633i
$375$	−17.4442	+	7.49720i	−0.900813	+	0.387154i
$376$	6.40988	−	1.47532i	0.330564	−	0.0760837i
$377$			1.51494i			0.0780232i
$378$		0			0
$379$		−	5.39420i		−	0.277082i	−0.990357	−	0.138541i	$-0.955759\pi$
$379$		−	5.39420i		−	0.277082i	0.990357	−	0.138541i	$-0.0442412\pi$
$380$	0.586302	−	24.7158i	0.0300767	−	1.26789i
$381$	9.87829	−	4.24552i	0.506080	−	0.217505i
$382$	20.5476	−	20.0660i	1.05131	−	1.02666i
$383$	0.926283	−	1.60437i	0.0473308	−	0.0819794i	−0.841389	−	0.540429i	$-0.818262\pi$
$383$	0.926283	−	1.60437i	0.0473308	−	0.0819794i	0.888720	+	0.458450i	$0.151595\pi$
$384$	19.5593	−	1.19666i	0.998134	−	0.0610669i
$385$		0			0
$386$	−2.39812	−	9.39414i	−0.122061	−	0.478149i
$387$	23.9890	+	22.7533i	1.21943	+	1.15661i
$388$	−3.41570	−	2.08159i	−0.173406	−	0.105677i
$389$	−4.66346	+	2.69245i	−0.236447	+	0.136513i	−0.613543	−	0.789662i	$-0.710256\pi$
$389$	−4.66346	+	2.69245i	−0.236447	+	0.136513i	0.377096	+	0.926174i	$0.376923\pi$
$390$	−0.865432	+	2.09739i	−0.0438229	+	0.106205i
$391$		−	5.02112i		−	0.253929i
$392$		0			0
$393$	24.7730	+	2.92891i	1.24963	+	0.147744i
$394$	−0.752281	+	2.68001i	−0.0378994	+	0.135017i
$395$	−4.55480	−	7.88914i	−0.229177	−	0.396946i
$396$	−18.3708	−	18.2714i	−0.923168	−	0.918170i
$397$	10.8178	−	18.7369i	0.542927	−	0.940378i	−0.455807	−	0.890079i	$-0.650649\pi$
$397$	10.8178	−	18.7369i	0.542927	−	0.940378i	0.998734	−	0.0502990i	$-0.0160174\pi$
$398$	8.73285	−	2.22931i	0.437738	−	0.111745i
$399$		0			0
$400$	−0.403308	+	0.627787i	−0.0201654	+	0.0313893i
$401$	33.1440	+	19.1357i	1.65513	+	0.955591i	0.974914	+	0.222580i	$0.0714480\pi$
$401$	33.1440	+	19.1357i	1.65513	+	0.955591i	0.680217	+	0.733010i	$0.261885\pi$
$402$	11.7032	+	15.2091i	0.583703	+	0.758563i
$403$	2.05515	−	1.18654i	0.102374	−	0.0591059i
$404$	17.3646	+	0.411920i	0.863923	+	0.0204938i
$405$	9.29606	−	18.2673i	0.461925	−	0.907708i
$406$		0			0
$407$	33.8323			1.67701
$408$	−2.29170	−	21.0309i	−0.113456	−	1.04119i
$409$	−2.38561	−	4.13200i	−0.117961	−	0.204314i	0.800999	−	0.598666i	$-0.204302\pi$
$409$	−2.38561	−	4.13200i	−0.117961	−	0.204314i	−0.918960	+	0.394352i	$0.870969\pi$
$410$	−5.90335	+	5.76497i	−0.291546	+	0.284712i
$411$	3.22764	+	2.40956i	0.159208	+	0.118855i
$412$	−10.2077	−	18.6903i	−0.502895	−	0.920803i
$413$		0			0
$414$	0.0718878	+	4.93258i	0.00353309	+	0.242423i
$415$	−1.26568	−	0.730743i	−0.0621300	−	0.0358708i
$416$	−0.462749	−	2.25379i	−0.0226881	−	0.110501i
$417$	−14.6721	+	6.30584i	−0.718498	+	0.308798i
$418$	8.95845	−	31.9146i	0.438172	−	1.56100i
$419$	8.33257			0.407072			0.203536	−	0.979067i	$-0.434757\pi$
$419$	8.33257			0.407072			0.203536	+	0.979067i	$0.434757\pi$
$420$		0			0
$421$	−20.7325			−1.01044			−0.505220	−	0.862991i	$-0.668589\pi$
$421$	−20.7325			−1.01044			−0.505220	+	0.862991i	$0.668589\pi$
$422$	−9.60489	+	34.2176i	−0.467559	+	1.66569i
$423$	1.98311	+	6.68867i	0.0964219	+	0.325214i
$424$	−14.8224	−	4.54251i	−0.719839	−	0.220604i
$425$	0.697632	+	0.402778i	0.0338401	+	0.0195376i
$426$	−1.57873	−	11.8672i	−0.0764897	−	0.574966i
$427$		0			0
$428$	−14.7447	+	8.05280i	−0.712713	+	0.389247i
$429$	−1.81989	+	2.43777i	−0.0878651	+	0.117697i
$430$	25.3953	−	24.8001i	1.22467	−	1.19597i
$431$	−17.4975	−	30.3066i	−0.842826	−	1.45982i	−0.887496	−	0.460816i	$-0.847557\pi$
$431$	−17.4975	−	30.3066i	−0.842826	−	1.45982i	0.0446692	−	0.999002i	$-0.485777\pi$
$432$	2.55239	+	20.6273i	0.122802	+	0.992431i
$433$	17.3383			0.833225			0.416612	−	0.909084i	$-0.363217\pi$
$433$	17.3383			0.833225			0.416612	+	0.909084i	$0.363217\pi$
$434$		0			0
$435$	−14.5907	−	1.72506i	−0.699569	−	0.0827102i
$436$	−0.497192	+	20.9593i	−0.0238112	+	1.00377i
$437$	−5.46565	+	3.15559i	−0.261457	+	0.150953i
$438$	−5.46172	+	4.20272i	−0.260971	+	0.200814i
$439$	−28.8352	−	16.6480i	−1.37623	−	0.794567i	−0.384527	−	0.923114i	$-0.625635\pi$
$439$	−28.8352	−	16.6480i	−1.37623	−	0.794567i	−0.991703	+	0.128547i	$0.958969\pi$
$440$	−20.3563	+	18.9571i	−0.970449	+	0.903744i
$441$		0			0
$442$	−2.40673	+	0.614387i	−0.114476	+	0.0292234i
$443$	−4.43657	+	7.68436i	−0.210788	+	0.365095i	−0.951961	−	0.306218i	$-0.900936\pi$
$443$	−4.43657	+	7.68436i	−0.210788	+	0.365095i	0.741174	+	0.671313i	$0.234270\pi$
$444$	−21.3567	−	16.7468i	−1.01355	−	0.794769i
$445$	−15.9384	−	27.6061i	−0.755553	−	1.30866i
$446$	3.52722	−	12.5658i	0.167019	−	0.595008i
$447$	−3.53632	+	29.9104i	−0.167262	+	1.41472i
$448$		0			0
$449$			26.3829i			1.24509i	0.782585	+	0.622544i	$0.213901\pi$
$449$			26.3829i			1.24509i	−0.782585	+	0.622544i	$0.786099\pi$
$450$	−0.691097	−	0.385688i	−0.0325786	−	0.0181815i
$451$	−9.58114	+	5.53167i	−0.451158	+	0.260476i
$452$	9.95307	−	16.3321i	0.468153	−	0.768196i
$453$	−5.78138	−	4.31602i	−0.271633	−	0.202785i
$454$	6.83028	+	26.7562i	0.320561	+	1.25573i
$455$		0			0
$456$	−21.4526	+	15.7118i	−1.00461	+	0.735772i
$457$	−15.1249	+	26.1972i	−0.707515	+	1.22545i	0.258261	+	0.966075i	$0.416851\pi$
$457$	−15.1249	+	26.1972i	−0.707515	+	1.22545i	−0.965776	+	0.259377i	$0.916483\pi$
$458$	−2.05761	+	2.00938i	−0.0961460	+	0.0938923i
$459$	22.1132	−	3.80834i	1.03216	−	0.177758i
$460$	5.29457	+	0.125597i	0.246861	+	0.00585597i
$461$			1.56302i			0.0727973i	0.999337	+	0.0363987i	$0.0115886\pi$
$461$			1.56302i			0.0727973i	−0.999337	+	0.0363987i	$0.988411\pi$
$462$		0			0
$463$		−	33.2961i		−	1.54740i	−0.633553	−	0.773700i	$-0.718404\pi$
$463$		−	33.2961i		−	1.54740i	0.633553	−	0.773700i	$-0.281596\pi$
$464$	13.2414	−	6.82919i	0.614717	−	0.317037i
$465$	9.08764	+	21.1447i	0.421429	+	0.980563i
$466$	3.23230	+	3.30989i	0.149734	+	0.153328i
$467$	−8.64844	+	14.9795i	−0.400202	+	0.693170i	−0.993750	−	0.111628i	$-0.964393\pi$
$467$	−8.64844	+	14.9795i	−0.400202	+	0.693170i	0.593548	+	0.804799i	$0.297727\pi$
$468$	2.35549	−	0.638010i	0.108883	−	0.0294920i
$469$		0			0
$470$	7.25703	−	1.85257i	0.334742	−	0.0854525i
$471$	19.9588	−	26.7351i	0.919654	−	1.23189i
$472$	−3.24300	+	10.5820i	−0.149271	+	0.487077i
$473$	41.2166	−	23.7964i	1.89514	−	1.09416i
$474$	−3.73723	+	9.05721i	−0.171657	+	0.416012i
$475$		−	1.01253i		−	0.0464579i
$476$		0			0
$477$	3.83457	−	15.9899i	0.175573	−	0.732126i
$478$	33.3669	+	9.36609i	1.52616	+	0.428395i
$479$	8.30404	+	14.3830i	0.379421	+	0.657177i	0.990978	−	0.134024i	$-0.0427898\pi$
$479$	8.30404	+	14.3830i	0.379421	+	0.657177i	−0.611557	+	0.791200i	$0.709456\pi$
$480$	22.2336	−	1.89044i	1.01482	−	0.0862865i
$481$	−1.59327	+	2.75963i	−0.0726469	+	0.125828i
$482$	−6.44169	−	25.2340i	−0.293411	−	1.14938i
$483$		0			0
$484$	−13.4244	+	7.33173i	−0.610201	+	0.333260i
$485$	−3.94457	−	2.27740i	−0.179114	−	0.103411i
$486$	−21.6687	+	4.05778i	−0.982914	+	0.184065i
$487$	−21.0010	+	12.1249i	−0.951647	+	0.549434i	−0.893592	−	0.448880i	$-0.851823\pi$
$487$	−21.0010	+	12.1249i	−0.951647	+	0.549434i	−0.0580548	+	0.998313i	$0.518490\pi$
$488$	−28.8011	+	6.62895i	−1.30376	+	0.300079i
$489$	1.75870	−	14.8752i	0.0795311	−	0.672681i
$490$		0			0
$491$	−20.3082			−0.916497			−0.458248	−	0.888824i	$-0.651523\pi$
$491$	−20.3082			−0.916497			−0.458248	+	0.888824i	$0.651523\pi$
$492$	8.78627	+	1.25074i	0.396115	+	0.0563875i
$493$	−8.04223	−	13.9296i	−0.362204	−	0.627355i
$494$	2.18132	+	2.23368i	0.0981424	+	0.100498i
$495$	−21.4064	−	20.3036i	−0.962144	−	0.912580i
$496$	−19.6355	−	12.6144i	−0.881660	−	0.566403i
$497$		0			0
$498$	0.207292	+	1.55819i	0.00928898	+	0.0698244i
$499$	−9.12662	−	5.26926i	−0.408564	−	0.235884i	0.281609	−	0.959529i	$-0.409132\pi$
$499$	−9.12662	−	5.26926i	−0.408564	−	0.235884i	−0.690172	+	0.723645i	$0.742465\pi$
$500$	11.4094	−	18.7217i	0.510242	−	0.837260i
$501$	−1.20122	−	2.79496i	−0.0536668	−	0.124869i
$502$	21.0288	+	5.90279i	0.938562	+	0.263455i
$503$	−27.6664			−1.23358			−0.616792	−	0.787126i	$-0.711568\pi$
$503$	−27.6664			−1.23358			−0.616792	+	0.787126i	$0.711568\pi$
$504$		0			0
$505$	19.7787			0.880139
$506$	6.83669	+	1.91906i	0.303928	+	0.0853127i
$507$	8.77778	+	20.4237i	0.389835	+	0.907050i
$508$	−6.46090	+	10.6017i	−0.286656	+	0.470376i
$509$	24.4110	+	14.0937i	1.08200	+	0.624693i	0.931435	−	0.363908i	$-0.118558\pi$
$509$	24.4110	+	14.0937i	1.08200	+	0.624693i	0.150564	+	0.988600i	$0.451891\pi$
$510$	−3.17675	−	23.8793i	−0.140669	−	1.05739i
$511$		0			0
$512$	−17.6134	+	14.2046i	−0.778408	+	0.627758i
$513$	−18.0429	−	21.6775i	−0.796612	−	0.957086i
$514$	8.86232	+	9.07504i	0.390900	+	0.400283i
$515$	−12.1249	−	21.0009i	−0.534287	−	0.925412i
$516$	−37.7972	−	5.38048i	−1.66393	−	0.236862i
$517$	10.0422			0.441657
$518$		0			0
$519$	1.60133	−	13.5442i	0.0702907	−	0.594524i
$520$	−0.587645	−	2.55317i	−0.0257700	−	0.111964i
$521$	−20.7962	+	12.0067i	−0.911097	+	0.526022i	−0.880784	−	0.473519i	$-0.842984\pi$
$521$	−20.7962	+	12.0067i	−0.911097	+	0.526022i	−0.0303127	+	0.999540i	$0.509650\pi$
$522$	8.09985	+	13.5688i	0.354521	+	0.593890i
$523$	−2.40739	−	1.38991i	−0.105268	−	0.0607764i	0.446442	−	0.894813i	$-0.352691\pi$
$523$	−2.40739	−	1.38991i	−0.105268	−	0.0607764i	−0.551710	+	0.834036i	$0.686024\pi$
$524$	−25.2801	+	13.8067i	−1.10436	+	0.603147i
$525$		0			0
$526$	6.77297	+	26.5317i	0.295316	+	1.15684i
$527$	−12.5978	+	21.8201i	−0.548770	+	0.950497i
$528$	29.5114	+	4.91765i	1.28432	+	0.214013i
$529$	10.8240	+	18.7477i	0.470609	+	0.815119i
$530$	−16.9962	−	4.77083i	−0.738266	−	0.207232i
$531$	−11.4155	−	2.73758i	−0.495391	−	0.118801i
$532$		0			0
$533$		−	1.04202i		−	0.0451347i
$534$	−13.0775	+	31.6935i	−0.565920	+	1.37151i
$535$	−16.5676	+	9.56531i	−0.716280	+	0.413545i
$536$	−21.1869	−	6.49300i	−0.915135	−	0.280455i
$537$	−9.68395	+	12.9718i	−0.417893	+	0.559774i
$538$	0.0658929	−	0.0168211i	0.00284085	−	0.000725208i
$539$		0			0
$540$	3.46261	+	23.4128i	0.149007	+	1.00752i
$541$	−4.15859	+	7.20288i	−0.178792	+	0.309676i	−0.941467	−	0.337105i	$-0.890552\pi$
$541$	−4.15859	+	7.20288i	−0.178792	+	0.309676i	0.762675	+	0.646782i	$0.223885\pi$
$542$	19.6397	+	20.1111i	0.843597	+	0.863846i
$543$	−11.5509	−	26.8761i	−0.495696	−	1.15336i
$544$	16.2194	+	18.2666i	0.695401	+	0.783173i
$545$			23.8731i			1.02261i
$546$		0			0
$547$		−	15.4364i		−	0.660014i	−0.943978	−	0.330007i	$-0.892949\pi$
$547$		−	15.4364i		−	0.660014i	0.943978	−	0.330007i	$-0.107051\pi$
$548$	−4.64966	−	0.110298i	−0.198624	−	0.00471171i
$549$	−8.91056	−	30.0538i	−0.380293	−	1.28266i
$550$	−0.815052	+	0.795947i	−0.0347539	+	0.0339393i
$551$	−10.1085	+	17.5085i	−0.430637	+	0.745886i
$552$	−3.36575	−	4.59554i	−0.143256	−	0.195599i
$553$		0			0
$554$	−3.59418	−	14.0794i	−0.152702	−	0.598178i
$555$	−24.7643	−	18.4875i	−1.05119	−	0.784751i
$556$	9.59632	−	15.7467i	0.406975	−	0.667808i
$557$	11.6502	−	6.72624i	0.493634	−	0.285000i	−0.232447	−	0.972609i	$-0.574673\pi$
$557$	11.6502	−	6.72624i	0.493634	−	0.285000i	0.726081	+	0.687609i	$0.241340\pi$
$558$	12.0633	−	21.6157i	0.510679	−	0.915064i
$559$			4.48260i			0.189594i
$560$		0			0
$561$	3.79234	−	32.0759i	0.160113	−	1.35425i
$562$	2.59288	−	9.23717i	0.109374	−	0.389646i
$563$	17.0006	+	29.4458i	0.716488	+	1.24099i	0.962383	+	0.271698i	$0.0875851\pi$
$563$	17.0006	+	29.4458i	0.716488	+	1.24099i	−0.245894	+	0.969297i	$0.579082\pi$
$564$	−6.33918	−	4.97085i	−0.266928	−	0.209311i
$565$	10.8893	−	18.8609i	0.458118	−	0.793483i
$566$	−7.43761	+	1.89866i	−0.312626	+	0.0798068i
$567$		0			0
$568$	9.42100	+	10.1164i	0.395296	+	0.424473i
$569$	−23.0318	−	13.2974i	−0.965544	−	0.557457i	−0.0676690	−	0.997708i	$-0.521556\pi$
$569$	−23.0318	−	13.2974i	−0.965544	−	0.557457i	−0.897875	+	0.440251i	$0.854890\pi$
$570$	−23.9969	+	18.4653i	−1.00512	+	0.773426i
$571$	7.12974	−	4.11636i	0.298370	−	0.172264i	−0.343340	−	0.939211i	$-0.611558\pi$
$571$	7.12974	−	4.11636i	0.298370	−	0.172264i	0.641711	+	0.766947i	$0.278225\pi$
$572$	0.0833059	−	3.51179i	0.00348320	−	0.146835i
$573$	−34.9316	−	4.12996i	−1.45929	−	0.172532i
$574$		0			0
$575$	0.216902			0.00904543
$576$	−16.1949	−	17.7123i	−0.674788	−	0.738011i
$577$	−0.792342	−	1.37238i	−0.0329856	−	0.0571328i	0.849061	−	0.528294i	$-0.177168\pi$
$577$	−0.792342	−	1.37238i	−0.0329856	−	0.0571328i	−0.882047	+	0.471162i	$0.843835\pi$
$578$	1.66746	−	1.62837i	0.0693570	−	0.0677313i
$579$	−7.10355	+	9.51530i	−0.295213	+	0.395442i
$580$	14.8893	−	8.13179i	0.618246	−	0.337654i
$581$		0			0
$582$	0.646037	+	4.85620i	0.0267791	+	0.201296i
$583$	−20.4981	−	11.8346i	−0.848944	−	0.490138i
$584$	2.33169	−	7.60839i	0.0964859	−	0.314837i
$585$	2.66422	−	0.789906i	0.110152	−	0.0326586i
$586$	−10.7732	+	38.3797i	−0.445036	+	1.58545i
$587$	30.8651			1.27394			0.636969	−	0.770889i	$-0.280188\pi$
$587$	30.8651			1.27394			0.636969	+	0.770889i	$0.280188\pi$
$588$		0			0
$589$	31.6691			1.30490
$590$	−3.40600	+	12.1339i	−0.140223	+	0.499546i
$591$	3.13217	−	1.34615i	0.128840	−	0.0553733i
$592$	31.3030	+	1.48596i	1.28655	+	0.0610727i
$593$	5.58714	+	3.22574i	0.229436	+	0.132465i	0.610312	−	0.792161i	$-0.291044\pi$
$593$	5.58714	+	3.22574i	0.229436	+	0.132465i	−0.380876	+	0.924626i	$0.624377\pi$
$594$	−3.26624	+	31.5646i	−0.134015	+	1.29511i
$595$		0			0
$596$	−16.6699	−	30.5227i	−0.682826	−	1.25026i
$597$	−8.84548	−	6.60350i	−0.362021	−	0.270263i
$598$	−0.478495	+	0.467279i	−0.0195671	+	0.0191085i
$599$	6.40487	+	11.0936i	0.261696	+	0.453270i	0.966693	−	0.255940i	$-0.0823850\pi$
$599$	6.40487	+	11.0936i	0.261696	+	0.453270i	−0.704997	+	0.709210i	$0.749052\pi$
$600$	0.908493	−	0.0989965i	0.0370891	−	0.00404152i
$601$	−37.2710			−1.52032			−0.760158	−	0.649738i	$-0.774878\pi$
$601$	−37.2710			−1.52032			−0.760158	+	0.649738i	$0.774878\pi$
$602$		0			0
$603$	5.48108	−	22.8557i	0.223207	−	0.930756i
$604$	8.32851	+	0.197567i	0.338882	+	0.00803889i
$605$	−15.0841	+	8.70880i	−0.613256	+	0.354063i
$606$	−12.9732	−	16.8596i	−0.527001	−	0.684874i
$607$	18.0250	+	10.4067i	0.731611	+	0.422396i	0.819011	−	0.573777i	$-0.194522\pi$
$607$	18.0250	+	10.4067i	0.731611	+	0.422396i	−0.0873999	+	0.996173i	$0.527856\pi$
$608$	9.69046	−	29.1352i	0.393000	−	1.18159i
$609$		0			0
$610$	−32.6075	+	8.32401i	−1.32024	+	0.337029i
$611$	−0.472921	+	0.819123i	−0.0191323	+	0.0331382i
$612$	−18.2714	+	18.3708i	−0.738576	+	0.742596i
$613$	−9.61439	−	16.6526i	−0.388321	−	0.672592i	0.603902	−	0.797058i	$-0.293612\pi$
$613$	−9.61439	−	16.6526i	−0.388321	−	0.672592i	−0.992224	+	0.124466i	$0.960278\pi$
$614$	0.856622	−	3.05173i	0.0345704	−	0.123158i
$615$	10.0359	+	1.18654i	0.404686	+	0.0478460i
$616$		0			0
$617$		−	29.3933i		−	1.18333i	−0.806185	−	0.591664i	$-0.798471\pi$
$617$		−	29.3933i		−	1.18333i	0.806185	−	0.591664i	$-0.201529\pi$
$618$	−9.94853	+	24.1104i	−0.400188	+	0.969861i
$619$	−17.2548	+	9.96206i	−0.693529	+	0.400409i	−0.804933	−	0.593366i	$-0.797799\pi$
$619$	−17.2548	+	9.96206i	−0.693529	+	0.400409i	0.111404	+	0.993775i	$0.464465\pi$
$620$	−22.6933	−	13.8297i	−0.911384	−	0.555414i
$621$	4.64372	−	3.86511i	0.186346	−	0.155102i
$622$	−9.26242	−	36.2835i	−0.371389	−	1.45484i
$623$		0			0
$624$	−1.79091	+	2.17559i	−0.0716937	+	0.0870933i
$625$	12.9490	−	22.4283i	0.517958	−	0.897130i
$626$	−0.445562	+	0.435118i	−0.0178082	+	0.0173908i
$627$	−37.2990	+	16.0305i	−1.48958	+	0.640196i
$628$	−0.913620	+	38.5140i	−0.0364574	+	1.53688i
$629$		−	33.8323i		−	1.34898i
$630$		0			0
$631$		−	17.6269i		−	0.701716i	−0.936429	−	0.350858i	$-0.885890\pi$
$631$		−	17.6269i		−	0.701716i	0.936429	−	0.350858i	$-0.114110\pi$
$632$	−2.53765	−	11.0254i	−0.100942	−	0.438568i
$633$	39.9905	−	17.1873i	1.58948	−	0.683132i
$634$	−11.6516	−	11.9313i	−0.462744	−	0.473851i
$635$	−7.06866	+	12.2433i	−0.280511	+	0.485859i
$636$	7.08141	+	17.6171i	0.280796	+	0.698561i
$637$		0			0
$638$	22.0401	−	5.62636i	0.872574	−	0.222750i
$639$	−10.0902	+	10.6382i	−0.399161	+	0.420840i
$640$	−19.6671	+	16.6458i	−0.777410	+	0.657983i
$641$	19.0040	−	10.9719i	0.750611	−	0.433365i	−0.0753036	−	0.997161i	$-0.523993\pi$
$641$	19.0040	−	10.9719i	0.750611	−	0.433365i	0.825915	+	0.563795i	$0.190659\pi$
$642$	19.0206	+	7.84838i	0.750684	+	0.309751i
$643$			49.5796i			1.95523i	0.210406	+	0.977614i	$0.432521\pi$
$643$			49.5796i			1.95523i	−0.210406	+	0.977614i	$0.567479\pi$
$644$		0			0
$645$	−43.1729	−	5.10433i	−1.69993	−	0.200983i
$646$	−31.9146	−	8.95845i	−1.25566	−	0.352465i
$647$	−11.9561	−	20.7086i	−0.470042	−	0.814137i	0.529371	−	0.848391i	$-0.322428\pi$
$647$	−11.9561	−	20.7086i	−0.470042	−	0.814137i	−0.999413	+	0.0342534i	$0.989095\pi$
$648$	17.6862	−	18.3085i	0.694778	−	0.719225i
$649$	−8.44896	+	14.6340i	−0.331651	+	0.574436i
$650$	−0.0265402	−	0.103966i	−0.00104099	−	0.00407787i
$651$		0			0
$652$	8.29037	+	15.1797i	0.324676	+	0.594483i
$653$	40.4145	+	23.3333i	1.58154	+	0.913103i	0.994635	+	0.103447i	$0.0329872\pi$
$653$	40.4145	+	23.3333i	1.58154	+	0.913103i	0.586905	+	0.809656i	$0.300346\pi$
$654$	20.3497	−	15.6588i	0.795737	−	0.612308i
$655$	−28.4054	+	16.3999i	−1.10989	+	0.640797i
$656$	−9.10782	+	4.69731i	−0.355601	+	0.183399i
$657$	8.20766	+	1.96830i	0.320211	+	0.0767907i
$658$		0			0
$659$	−30.4598			−1.18655			−0.593273	−	0.805001i	$-0.702165\pi$
$659$	−30.4598			−1.18655			−0.593273	+	0.805001i	$0.702165\pi$
$660$	33.7279	+	4.80121i	1.31286	+	0.186887i
$661$	24.6523	+	42.6991i	0.958864	+	1.66080i	0.725266	+	0.688468i	$0.241717\pi$
$661$	24.6523	+	42.6991i	0.958864	+	1.66080i	0.233598	+	0.972333i	$0.424950\pi$
$662$	1.29412	+	1.32518i	0.0502973	+	0.0515046i
$663$	2.43777	+	1.81989i	0.0946751	+	0.0706787i
$664$	−1.23701	−	1.32831i	−0.0480052	−	0.0515484i
$665$		0			0
$666$	0.484380	+	33.2357i	0.0187694	+	1.28786i
$667$	−3.75063	−	2.16543i	−0.145225	−	0.0838457i
$668$	2.99965	+	1.82804i	0.116060	+	0.0707290i
$669$	−14.6858	+	6.31171i	−0.567786	+	0.244025i
$670$	−24.2941	−	6.81935i	−0.938562	−	0.263455i
$671$	−45.1221			−1.74192
$672$		0			0
$673$	−19.4364			−0.749219			−0.374610	−	0.927183i	$-0.622223\pi$
$673$	−19.4364			−0.749219			−0.374610	+	0.927183i	$0.622223\pi$
$674$	−21.0522	−	5.90936i	−0.810900	−	0.227620i
$675$	0.164512	+	0.955244i	0.00633208	+	0.0367674i
$676$	−21.9195	−	13.3582i	−0.843058	−	0.513775i
$677$	8.63274	+	4.98411i	0.331783	+	0.191555i	0.656633	−	0.754211i	$-0.271980\pi$
$677$	8.63274	+	4.98411i	0.331783	+	0.191555i	−0.324849	+	0.945766i	$0.605314\pi$
$678$	−23.2198	+	3.08901i	−0.891751	+	0.118633i
$679$		0			0
$680$	18.9571	+	20.3563i	0.726971	+	0.780628i
$681$	20.2321	−	27.1012i	0.775297	−	1.03852i
$682$	−24.8951	−	25.4927i	−0.953282	−	0.976164i
$683$	14.8051	+	25.6431i	0.566501	+	0.981208i	0.996908	+	0.0785732i	$0.0250364\pi$
$683$	14.8051	+	25.6431i	0.566501	+	0.981208i	−0.430408	+	0.902635i	$0.641630\pi$
$684$	31.4801	+	8.34356i	1.20367	+	0.319024i
$685$	−5.29606			−0.202352
$686$		0			0
$687$	3.49801	+	0.413570i	0.133457	+	0.0157787i
$688$	39.1805	−	20.2071i	1.49374	−	0.770390i
$689$	1.93064	−	1.11466i	0.0735515	−	0.0424650i
$690$	−3.95560	−	5.14058i	−0.150587	−	0.195699i
$691$	−38.2440	−	22.0802i	−1.45487	−	0.839969i	−0.456117	−	0.889920i	$-0.650760\pi$
$691$	−38.2440	−	22.0802i	−1.45487	−	0.839969i	−0.998752	+	0.0499504i	$0.984094\pi$
$692$	7.54856	+	13.8214i	0.286953	+	0.525412i
$693$		0			0
$694$	9.67599	+	37.9036i	0.367295	+	1.43880i
$695$	10.4990	−	18.1848i	0.398250	−	0.689790i
$696$	−16.6979	−	7.35807i	−0.632930	−	0.278907i
$697$	5.53167	+	9.58114i	0.209527	+	0.362911i
$698$	−25.7770	−	7.23561i	−0.975674	−	0.273872i
$699$	0.665271	−	5.62691i	0.0251629	−	0.212829i
$700$		0			0
$701$			38.2714i			1.44549i	0.691115	+	0.722745i	$0.257120\pi$
$701$			38.2714i			1.44549i	−0.691115	+	0.722745i	$0.742880\pi$
$702$	−2.42084	−	1.75290i	−0.0913687	−	0.0661589i
$703$	−36.8276	+	21.2624i	−1.38898	+	0.801927i
$704$	−31.0706	+	15.1027i	−1.17102	+	0.569204i
$705$	−7.35062	−	5.48753i	−0.276841	−	0.206672i
$706$	2.73074	−	0.697101i	0.102773	−	0.0262357i
$707$		0			0
$708$	12.5772	−	5.05557i	0.472680	−	0.190000i
$709$	−3.44896	+	5.97377i	−0.129528	+	0.224350i	−0.923494	−	0.383613i	$-0.874680\pi$
$709$	−3.44896	+	5.97377i	−0.129528	+	0.224350i	0.793966	+	0.607963i	$0.208013\pi$
$710$	10.9979	+	11.2618i	0.412742	+	0.422649i
$711$	11.5050	−	3.41108i	0.431470	−	0.127926i
$712$	−8.87989	−	38.5808i	−0.332788	−	1.44588i
$713$			6.78411i			0.254067i
$714$		0			0
$715$		−	4.00000i		−	0.149592i
$716$	0.443285	−	18.6869i	0.0165663	−	0.698360i
$717$	−16.7599	−	38.9963i	−0.625912	−	1.45634i
$718$	−2.37774	+	2.32200i	−0.0887365	+	0.0866564i
$719$	14.1178	−	24.4527i	0.526503	−	0.911930i	−0.473020	−	0.881052i	$-0.656836\pi$
$719$	14.1178	−	24.4527i	0.526503	−	0.911930i	0.999523	−	0.0308787i	$-0.00983056\pi$
$720$	−18.9143	−	19.7259i	−0.704893	−	0.735142i
$721$		0			0
$722$	3.65944	+	14.3351i	0.136190	+	0.533496i
$723$	−19.0811	+	25.5594i	−0.709634	+	0.950565i
$724$	28.8444	+	17.5783i	1.07199	+	0.653293i
$725$	0.601728	−	0.347408i	0.0223476	−	0.0129024i
$726$	17.3175	+	7.14561i	0.642711	+	0.265198i
$727$			27.3942i			1.01599i	0.861359	+	0.507997i	$0.169614\pi$
$727$			27.3942i			1.01599i	−0.861359	+	0.507997i	$0.830386\pi$
$728$		0			0
$729$	20.5442	+	17.5196i	0.760896	+	0.648874i
$730$	2.44888	−	8.72419i	0.0906373	−	0.322897i
$731$	−23.7964	−	41.2166i	−0.880143	−	1.52445i
$732$	28.4834	+	22.3352i	1.05278	+	0.825534i
$733$	14.8514	−	25.7234i	0.548549	−	0.950114i	−0.449826	−	0.893116i	$-0.648514\pi$
$733$	14.8514	−	25.7234i	0.548549	−	0.950114i	0.998374	−	0.0569978i	$-0.0181528\pi$
$734$	46.8550	−	11.9611i	1.72945	−	0.441492i
$735$		0			0
$736$	6.24130	+	2.07587i	0.230057	+	0.0765177i
$737$	−29.2996	−	16.9162i	−1.07927	−	0.623115i
$738$	−5.57131	−	9.33299i	−0.205083	−	0.343552i
$739$	23.7606	−	13.7182i	0.874050	−	0.504633i	0.00535770	−	0.999986i	$-0.498295\pi$
$739$	23.7606	−	13.7182i	0.874050	−	0.504633i	0.868692	+	0.495353i	$0.164961\pi$
$740$	35.6748	+	0.846271i	1.31143	+	0.0311095i
$741$	0.448959	−	3.79733i	0.0164929	−	0.139498i
$742$		0			0
$743$	2.30093			0.0844131			0.0422065	−	0.999109i	$-0.486561\pi$
$743$	2.30093			0.0844131			0.0422065	+	0.999109i	$0.486561\pi$
$744$	3.09635	+	28.4152i	0.113518	+	1.04175i
$745$	−19.8009	−	34.2962i	−0.725450	−	1.25652i
$746$	17.8774	−	17.4584i	0.654539	−	0.639196i
$747$	1.32487	−	1.39683i	0.0484745	−	0.0511072i
$748$	17.8768	+	32.7325i	0.653641	+	1.19682i
$749$		0			0
$750$	−26.6172	+	3.54098i	−0.971922	+	0.129298i
$751$	16.8176	+	9.70963i	0.613682	+	0.354309i	0.774405	−	0.632690i	$-0.218049\pi$
$751$	16.8176	+	9.70963i	0.613682	+	0.354309i	−0.160723	+	0.987000i	$0.551383\pi$
$752$	9.29148	+	0.441069i	0.338825	+	0.0160841i
$753$	−10.5626	−	24.5766i	−0.384924	−	0.895623i
$754$	−0.579007	+	2.06272i	−0.0210862	+	0.0751199i
$755$	9.48634			0.345243
$756$		0			0
$757$	13.9327			0.506393			0.253197	−	0.967415i	$-0.418518\pi$
$757$	13.9327			0.506393			0.253197	+	0.967415i	$0.418518\pi$
$758$	2.06166	−	7.34468i	0.0748827	−	0.266771i
$759$	−3.43402	−	7.99014i	−0.124647	−	0.290024i
$760$	10.2446	−	33.4286i	0.371612	−	1.21258i
$761$	−10.7265	−	6.19296i	−0.388836	−	0.224495i	0.292820	−	0.956168i	$-0.405406\pi$
$761$	−10.7265	−	6.19296i	−0.388836	−	0.224495i	−0.681656	+	0.731673i	$0.738740\pi$
$762$	15.0728	−	2.00519i	0.546030	−	0.0726403i
$763$		0			0
$764$	35.6466	−	19.4683i	1.28965	−	0.704339i
$765$	−20.3036	+	21.4064i	−0.734079	+	0.773948i
$766$	1.87440	−	1.83047i	0.0677249	−	0.0661374i
$767$	−0.795777	−	1.37833i	−0.0287338	−	0.0497685i
$768$	27.0891	+	5.84619i	0.977496	+	0.210956i
$769$	45.0074			1.62301			0.811505	−	0.584346i	$-0.198649\pi$
$769$	45.0074			1.62301			0.811505	+	0.584346i	$0.198649\pi$
$770$		0			0
$771$	1.82404	−	15.4278i	0.0656911	−	0.555620i
$772$	0.325167	−	13.7075i	0.0117030	−	0.493344i
$773$	−44.5842	+	25.7407i	−1.60358	+	0.925828i	−0.612819	+	0.790223i	$0.709965\pi$
$773$	−44.5842	+	25.7407i	−1.60358	+	0.925828i	−0.990763	+	0.135605i	$0.956702\pi$
$774$	23.9669	+	40.1492i	0.861474	+	1.44313i
$775$	−0.942582	−	0.544200i	−0.0338585	−	0.0195482i
$776$	−3.85520	−	4.13974i	−0.138393	−	0.148608i
$777$		0			0
$778$	−7.37877	+	1.88364i	−0.264542	+	0.0675319i
$779$	6.95292	−	12.0428i	0.249114	−	0.431479i
$780$	−1.97998	+	2.52501i	−0.0708947	+	0.0904098i
$781$	10.5528	+	18.2780i	0.377608	+	0.654037i
$782$	1.91906	−	6.83669i	0.0686255	−	0.244480i
$783$	6.69191	−	18.1603i	0.239149	−	0.648997i
$784$		0			0
$785$			43.8682i			1.56572i
$786$	32.6112	+	13.4562i	1.16320	+	0.479966i
$787$	35.6977	−	20.6101i	1.27249	−	0.734670i	0.297031	−	0.954868i	$-0.404003\pi$
$787$	35.6977	−	20.6101i	1.27249	−	0.734670i	0.975455	+	0.220197i	$0.0706701\pi$
$788$	−2.04859	+	3.36156i	−0.0729782	+	0.119750i
$789$	20.0624	−	26.8739i	0.714240	−	0.956735i
$790$	−3.18654	−	12.4826i	−0.113372	−	0.444111i
$791$		0			0
$792$	−18.0302	−	31.8994i	−0.640676	−	1.13349i
$793$	2.12494	−	3.68051i	0.0754590	−	0.130699i
$794$	21.8905	−	21.3774i	0.776866	−	0.758656i
$795$	8.53706	+	19.8636i	0.302778	+	0.704491i
$796$	12.7426	+	0.302277i	0.451649	+	0.0107139i
$797$			37.0164i			1.31119i	0.755113	+	0.655595i	$0.227582\pi$
$797$			37.0164i			1.31119i	−0.755113	+	0.655595i	$0.772418\pi$
$798$		0			0
$799$		−	10.0422i		−	0.355269i
$800$	−0.789078	+	0.700644i	−0.0278981	+	0.0247715i
$801$	40.2589	−	11.9362i	1.42248	−	0.421747i
$802$	37.8149	+	38.7225i	1.33529	+	1.36734i
$803$	6.07473	−	10.5217i	0.214372	−	0.371304i
$804$	10.1221	+	25.1815i	0.356977	+	0.888085i
$805$		0			0
$806$	3.25177	−	0.830108i	0.114539	−	0.0292393i
$807$	−0.0667428	−	0.0498261i	−0.00234946	−	0.00175396i
$808$	23.4861	+	7.19760i	0.826237	+	0.253211i
$809$	−45.3040	+	26.1563i	−1.59280	+	0.919605i	−0.599979	+	0.800016i	$0.704825\pi$
$809$	−45.3040	+	26.1563i	−1.59280	+	0.919605i	−0.992823	+	0.119589i	$0.961842\pi$
$810$	19.6391	−	21.3196i	0.690049	−	0.749094i
$811$		−	25.3719i		−	0.890929i	−0.895300	−	0.445464i	$-0.853039\pi$
$811$		−	25.3719i		−	0.890929i	0.895300	−	0.445464i	$-0.146961\pi$
$812$		0			0
$813$	4.04223	−	34.1895i	0.141767	−	1.19908i
$814$	46.0657	+	12.9307i	1.61460	+	0.453219i
$815$	9.84750	+	17.0564i	0.344943	+	0.597459i
$816$	4.91765	−	29.5114i	0.172152	−	1.03311i
$817$	−29.9104	+	51.8064i	−1.04643	+	1.81248i
$818$	−1.66898	−	6.53787i	−0.0583545	−	0.228591i
$819$		0			0
$820$	−10.2413	+	5.59327i	−0.357642	+	0.195326i
$821$	25.1716	+	14.5328i	0.878493	+	0.507198i	0.870161	−	0.492767i	$-0.164014\pi$
$821$	25.1716	+	14.5328i	0.878493	+	0.507198i	0.00833206	+	0.999965i	$0.497348\pi$
$822$	3.47379	+	4.51443i	0.121162	+	0.157459i
$823$	24.7981	−	14.3172i	0.864406	−	0.499065i	−0.00107900	−	0.999999i	$-0.500343\pi$
$823$	24.7981	−	14.3172i	0.864406	−	0.499065i	0.865485	+	0.500934i	$0.167010\pi$
$824$	−6.75524	−	29.3498i	−0.235330	−	1.02245i
$825$	1.38561	+	0.163821i	0.0482409	+	0.00570352i
$826$		0			0
$827$	−4.88743			−0.169953			−0.0849763	−	0.996383i	$-0.527081\pi$
$827$	−4.88743			−0.169953			−0.0849763	+	0.996383i	$0.527081\pi$
$828$	−1.78734	+	6.74362i	−0.0621144	+	0.234357i
$829$	19.4658	+	33.7157i	0.676074	+	1.17100i	0.976154	+	0.217081i	$0.0696536\pi$
$829$	19.4658	+	33.7157i	0.676074	+	1.17100i	−0.300079	+	0.953914i	$0.597013\pi$
$830$	−1.44405	−	1.47871i	−0.0501238	−	0.0513269i
$831$	−10.6464	+	14.2610i	−0.369320	+	0.494710i
$832$	0.231321	−	3.24559i	0.00801961	−	0.112521i
$833$		0			0
$834$	−22.3875	+	2.97829i	−0.775216	+	0.103130i
$835$	3.46410	+	2.00000i	0.119880	+	0.0692129i
$836$	24.3954	−	40.0307i	0.843734	−	1.38449i
$837$	−29.8775	+	5.14551i	−1.03272	+	0.177855i
$838$	11.3455	+	3.18469i	0.391925	+	0.110013i
$839$	49.3493			1.70373			0.851863	−	0.523765i	$-0.175473\pi$
$839$	49.3493			1.70373			0.851863	+	0.523765i	$0.175473\pi$
$840$		0			0
$841$	15.1267			0.521610
$842$	−28.2291	−	7.92393i	−0.972840	−	0.273077i
$843$	−10.7956	+	4.63976i	−0.371820	+	0.159802i
$844$	−26.1558	+	42.9193i	−0.900321	+	1.47734i
$845$	−25.3134	−	14.6147i	−0.870809	−	0.502762i
$846$	0.143776	+	9.86515i	0.00494310	+	0.339171i
$847$		0			0
$848$	−18.4459	−	11.8501i	−0.633434	−	0.406935i
$849$	7.53354	+	5.62408i	0.258550	+	0.193018i
$850$	0.795947	+	0.815052i	0.0273008	+	0.0279561i
$851$	−4.55480	−	7.88914i	−0.156136	−	0.270436i
$852$	2.38603	−	16.7616i	0.0817441	−	0.574242i
$853$	36.4912			1.24943			0.624717	−	0.780851i	$-0.285214\pi$
$853$	36.4912			1.24943			0.624717	+	0.780851i	$0.285214\pi$
$854$		0			0
$855$	36.0616	+	8.64803i	1.23328	+	0.295756i
$856$	−23.1540	+	5.32920i	−0.791388	+	0.182148i
$857$	−31.5609	+	18.2217i	−1.07810	+	0.622441i	−0.930383	−	0.366589i	$-0.880526\pi$
$857$	−31.5609	+	18.2217i	−1.07810	+	0.622441i	−0.147716	+	0.989030i	$0.547192\pi$
$858$	−3.40965	+	2.62368i	−0.116404	+	0.0895709i
$859$	−10.2782	−	5.93411i	−0.350687	−	0.202469i	0.314301	−	0.949323i	$-0.398230\pi$
$859$	−10.2782	−	5.93411i	−0.350687	−	0.202469i	−0.664988	+	0.746854i	$0.731563\pi$
$860$	44.0566	−	24.0614i	1.50232	−	0.820488i
$861$		0			0
$862$	−12.2413	−	47.9527i	−0.416940	−	1.63327i
$863$	8.16126	−	14.1357i	0.277812	−	0.481185i	−0.693028	−	0.720910i	$-0.743724\pi$
$863$	8.16126	−	14.1357i	0.277812	−	0.481185i	0.970841	+	0.239725i	$0.0770573\pi$
$864$	−4.40842	+	29.0614i	−0.149977	+	0.988689i
$865$	8.96636	+	15.5302i	0.304865	+	0.528042i
$866$	23.6076	+	6.62667i	0.802220	+	0.225183i
$867$	−2.83473	−	0.335150i	−0.0962723	−	0.0113823i
$868$		0			0
$869$		−	17.2733i		−	0.585958i
$870$	−19.2072	−	7.92535i	−0.651184	−	0.268695i
$871$	2.75963	−	1.59327i	0.0935064	−	0.0539859i
$872$	−8.68759	+	28.3479i	−0.294199	+	0.959982i
$873$	4.12903	−	4.35329i	0.139747	−	0.147336i
$874$	−8.64803	+	2.20766i	−0.292524	+	0.0746752i
$875$		0			0
$876$	−9.04289	+	3.63491i	−0.305531	+	0.122812i
$877$	−3.40673	+	5.90063i	−0.115037	+	0.199250i	−0.917795	−	0.397056i	$-0.870032\pi$
$877$	−3.40673	+	5.90063i	−0.115037	+	0.199250i	0.802758	+	0.596306i	$0.203365\pi$
$878$	−32.8989	−	33.6886i	−1.11028	−	1.13693i
$879$	44.8548	−	19.2778i	1.51292	−	0.650226i
$880$	−34.9623	+	18.0316i	−1.17858	+	0.607846i
$881$		−	10.1075i		−	0.340530i	−0.985398	−	0.170265i	$-0.945538\pi$
$881$		−	10.1075i		−	0.340530i	0.985398	−	0.170265i	$-0.0544624\pi$
$882$		0			0
$883$			29.4615i			0.991458i	0.868477	+	0.495729i	$0.165099\pi$
$883$			29.4615i			0.991458i	−0.868477	+	0.495729i	$0.834901\pi$
$884$	−3.51179	−	0.0833059i	−0.118114	−	0.00280188i
$885$	14.1811	−	6.09479i	0.476692	−	0.204874i
$886$	−8.97773	+	8.76729i	−0.301613	+	0.294543i
$887$	22.2334	−	38.5094i	0.746525	−	1.29302i	−0.202954	−	0.979188i	$-0.565054\pi$
$887$	22.2334	−	38.5094i	0.746525	−	1.29302i	0.949479	−	0.313831i	$-0.101613\pi$
$888$	−22.6785	−	30.9648i	−0.761040	−	1.03911i
$889$		0			0
$890$	−11.1505	−	43.6798i	−0.373767	−	1.46415i
$891$	32.5843	−	21.1838i	1.09161	−	0.709685i
$892$	9.60526	−	15.7613i	0.321608	−	0.527729i
$893$	−10.9313	+	6.31119i	−0.365802	+	0.211196i
$894$	−16.2467	+	39.3742i	−0.543372	+	1.31687i
$895$		−	21.2847i		−	0.711469i
$896$		0			0
$897$	0.813457	+	0.0961751i	0.0271605	+	0.00321119i
$898$	−10.0835	+	35.9227i	−0.336491	+	1.19876i
$899$	10.8660	+	18.8204i	0.362401	+	0.627697i
$900$	−0.793581	−	0.789284i	−0.0264527	−	0.0263095i
$901$	−11.8346	+	20.4981i	−0.394267	+	0.682890i
$902$	−15.1598	+	3.86997i	−0.504765	+	0.128856i
$903$		0			0
$904$	19.7941	−	18.4335i	0.658342	−	0.613090i
$905$	33.3106	+	19.2319i	1.10728	+	0.639289i
$906$	−6.22228	−	8.08628i	−0.206721	−	0.268649i
$907$	−48.4273	+	27.9595i	−1.60800	+	0.928380i	−0.618186	+	0.786032i	$0.712132\pi$
$907$	−48.4273	+	27.9595i	−1.60800	+	0.928380i	−0.989817	+	0.142348i	$0.954535\pi$
$908$	−0.926131	+	39.0414i	−0.0307347	+	1.29563i
$909$	−6.07587	+	25.3359i	−0.201524	+	0.840340i
$910$		0			0
$911$	7.71538			0.255622			0.127811	−	0.991799i	$-0.459205\pi$
$911$	7.71538			0.255622			0.127811	+	0.991799i	$0.459205\pi$
$912$	−35.2147	+	13.1938i	−1.16607	+	0.436892i
$913$	−1.38561	−	2.39995i	−0.0458571	−	0.0794268i
$914$	−30.6065	+	29.8890i	−1.01237	+	0.988642i
$915$	33.0281	+	24.6568i	1.09188	+	0.815128i
$916$	−3.56961	+	1.94954i	−0.117943	+	0.0644145i
$917$		0			0
$918$	31.5646	+	3.26624i	1.04179	+	0.107802i
$919$	8.69683	+	5.02112i	0.286882	+	0.165631i	0.636535	−	0.771248i	$-0.280367\pi$
$919$	8.69683	+	5.02112i	0.286882	+	0.165631i	−0.349653	+	0.936879i	$0.613700\pi$
$920$	7.16102	+	2.19459i	0.236092	+	0.0723534i
$921$	−3.56660	+	1.53286i	−0.117523	+	0.0505095i
$922$	−0.597386	+	2.12820i	−0.0196738	+	0.0700884i
$923$	−1.98786			−0.0654311
$924$		0			0
$925$	1.46149			0.0480534
$926$	12.7257	−	45.3355i	0.418193	−	1.48982i
$927$	30.6263	−	9.08032i	1.00590	−	0.298237i
$928$	20.6395	−	4.23770i	0.677524	−	0.139109i
$929$	−2.71156	−	1.56552i	−0.0889635	−	0.0513631i	0.454858	−	0.890564i	$-0.349690\pi$
$929$	−2.71156	−	1.56552i	−0.0889635	−	0.0513631i	−0.543822	+	0.839201i	$0.683023\pi$
$930$	4.29215	+	32.2637i	0.140745	+	1.05797i
$931$		0			0
$932$	3.13603	+	5.74209i	0.102724	+	0.188088i
$933$	−27.4364	+	36.7515i	−0.898229	+	1.20319i
$934$	−17.5008	+	17.0906i	−0.572643	+	0.559220i
$935$	21.2345	+	36.7792i	0.694442	+	1.20281i
$936$	3.45106	+	0.0315583i	0.112801	+	0.00103152i
$937$	−47.0325			−1.53648			−0.768242	−	0.640159i	$-0.778868\pi$
$937$	−47.0325			−1.53648			−0.768242	+	0.640159i	$0.778868\pi$
$938$		0			0
$939$	0.757468	+	0.0895556i	0.0247190	+	0.00292254i
$940$	10.5891	+	0.251193i	0.345380	+	0.00819302i
$941$	19.2716	−	11.1265i	0.628238	−	0.362713i	−0.151832	−	0.988406i	$-0.548517\pi$
$941$	19.2716	−	11.1265i	0.628238	−	0.362713i	0.780069	+	0.625693i	$0.215184\pi$
$942$	37.3938	−	28.7740i	1.21836	−	0.937508i
$943$	2.57979	+	1.48944i	0.0840095	+	0.0485029i
$944$	−8.46007	+	13.1689i	−0.275352	+	0.428611i
$945$		0			0
$946$	65.2151	−	16.6480i	2.12033	−	0.541274i
$947$	−16.9667	+	29.3873i	−0.551345	+	0.954958i	0.446833	+	0.894617i	$0.352552\pi$
$947$	−16.9667	+	29.3873i	−0.551345	+	0.954958i	−0.998178	+	0.0603402i	$0.980781\pi$
$948$	−8.55022	+	10.9038i	−0.277698	+	0.354140i
$949$	0.572156	+	0.991004i	0.0185730	+	0.0321694i
$950$	0.386986	−	1.37865i	0.0125555	−	0.0447292i
$951$	−2.39812	+	20.2835i	−0.0777645	+	0.657739i
$952$		0			0
$953$			20.2641i			0.656419i	0.944605	+	0.328209i	$0.106445\pi$
$953$			20.2641i			0.656419i	−0.944605	+	0.328209i	$0.893555\pi$
$954$	11.3324	−	20.3061i	0.366901	−	0.657433i
$955$	40.0536	−	23.1249i	1.29610	−	0.748306i
$956$	41.8522	+	25.5055i	1.35360	+	0.824908i
$957$	−22.3243	−	16.6660i	−0.721642	−	0.538735i
$958$	5.80952	+	22.7575i	0.187697	+	0.735263i
$959$		0			0
$960$	30.9956	+	5.92366i	1.00038	+	0.191185i
$961$	1.52112	−	2.63465i	0.0490682	−	0.0849887i
$962$	−3.22411	+	3.14853i	−0.103949	+	0.101513i
$963$	−7.16345	−	24.1611i	−0.230839	−	0.778579i
$964$	0.873442	−	36.8203i	0.0281317	−	1.18590i
$965$		−	15.6131i		−	0.502604i
$966$		0			0
$967$			43.5882i			1.40170i	0.713308	+	0.700851i	$0.247196\pi$
$967$			43.5882i			1.40170i	−0.713308	+	0.700851i	$0.752804\pi$
$968$	−21.0807	+	4.85201i	−0.677560	+	0.155949i
$969$	16.0305	+	37.2990i	0.514974	+	1.19822i
$970$	−4.50046	−	4.60849i	−0.144501	−	0.147970i
$971$	1.83580	−	3.17971i	0.0589138	−	0.102042i	−0.835064	−	0.550152i	$-0.814570\pi$
$971$	1.83580	−	3.17971i	0.0589138	−	0.102042i	0.893978	+	0.448111i	$0.147903\pi$
$972$	−31.0548	−	2.75673i	−0.996083	−	0.0884221i
$973$		0			0
$974$	−33.2289	+	8.48263i	−1.06472	+	0.271801i
$975$	−0.0786155	+	0.105307i	−0.00251771	+	0.00337251i
$976$	−41.7488	−	1.98183i	−1.33635	−	0.0634367i
$977$	29.5088	−	17.0369i	0.944069	−	0.545058i	0.0528352	−	0.998603i	$-0.483174\pi$
$977$	29.5088	−	17.0369i	0.944069	−	0.545058i	0.891233	+	0.453545i	$0.149841\pi$
$978$	8.07991	−	19.5818i	0.258367	−	0.626156i
$979$		−	60.4439i		−	1.93179i
$980$		0			0
$981$	−30.5807	−	7.33364i	−0.976368	−	0.234145i
$982$	−27.6514	−	7.76177i	−0.882393	−	0.247688i
$983$	−27.1404	−	47.0086i	−0.865645	−	1.49934i	−0.866406	−	0.499341i	$-0.833576\pi$
$983$	−27.1404	−	47.0086i	−0.865645	−	1.49934i	0.000761201	−	1.00000i	$-0.499758\pi$
$984$	11.4853	+	5.06109i	0.366137	+	0.161342i
$985$	−2.24130	+	3.88205i	−0.0714138	+	0.123692i
$986$	−5.62636	−	22.0401i	−0.179180	−	0.701898i
$987$		0			0
$988$	2.11636	+	3.87506i	0.0673303	+	0.123282i
$989$	−11.0979	−	6.40736i	−0.352892	−	0.203742i
$990$	−21.3866	−	35.8267i	−0.679712	−	1.13865i
$991$	−9.09990	+	5.25383i	−0.289068	+	0.166893i	−0.637521	−	0.770433i	$-0.720040\pi$
$991$	−9.09990	+	5.25383i	−0.289068	+	0.166893i	0.348454	+	0.937326i	$0.386707\pi$
$992$	−21.9143	−	24.6803i	−0.695779	−	0.783599i
$993$	0.266354	−	2.25285i	0.00845250	−	0.0714919i
$994$		0			0
$995$	14.5141			0.460127
$996$	−0.313293	+	2.20085i	−0.00992708	+	0.0697365i
$997$	−10.7282	−	18.5818i	−0.339765	−	0.588491i	0.644623	−	0.764501i	$-0.277014\pi$
$997$	−10.7282	−	18.5818i	−0.339765	−	0.588491i	−0.984388	+	0.176010i	$0.943681\pi$
$998$	−10.4128	−	10.6627i	−0.329612	−	0.337523i
$999$	31.2894	−	26.0431i	0.989954	−	0.823969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.f.275.11		24
3.2	odd	2	inner	588.2.n.f.275.2		24
4.3	odd	2	inner	588.2.n.f.275.9		24
7.2	even	3		84.2.e.a.71.5	✓	12
7.3	odd	6		588.2.n.g.263.4		24
7.4	even	3	inner	588.2.n.f.263.4		24
7.5	odd	6		588.2.e.c.491.5		12
7.6	odd	2		588.2.n.g.275.11		24
12.11	even	2	inner	588.2.n.f.275.4		24
21.2	odd	6		84.2.e.a.71.8	yes	12
21.5	even	6		588.2.e.c.491.8		12
21.11	odd	6	inner	588.2.n.f.263.9		24
21.17	even	6		588.2.n.g.263.9		24
21.20	even	2		588.2.n.g.275.2		24
28.3	even	6		588.2.n.g.263.2		24
28.11	odd	6	inner	588.2.n.f.263.2		24
28.19	even	6		588.2.e.c.491.7		12
28.23	odd	6		84.2.e.a.71.7	yes	12
28.27	even	2		588.2.n.g.275.9		24
56.37	even	6		1344.2.h.h.575.1		12
56.51	odd	6		1344.2.h.h.575.12		12
84.11	even	6	inner	588.2.n.f.263.11		24
84.23	even	6		84.2.e.a.71.6	yes	12
84.47	odd	6		588.2.e.c.491.6		12
84.59	odd	6		588.2.n.g.263.11		24
84.83	odd	2		588.2.n.g.275.4		24
168.107	even	6		1344.2.h.h.575.2		12
168.149	odd	6		1344.2.h.h.575.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.5	✓	12	7.2	even	3
84.2.e.a.71.6	yes	12	84.23	even	6
84.2.e.a.71.7	yes	12	28.23	odd	6
84.2.e.a.71.8	yes	12	21.2	odd	6
588.2.e.c.491.5		12	7.5	odd	6
588.2.e.c.491.6		12	84.47	odd	6
588.2.e.c.491.7		12	28.19	even	6
588.2.e.c.491.8		12	21.5	even	6
588.2.n.f.263.2		24	28.11	odd	6	inner
588.2.n.f.263.4		24	7.4	even	3	inner
588.2.n.f.263.9		24	21.11	odd	6	inner
588.2.n.f.263.11		24	84.11	even	6	inner
588.2.n.f.275.2		24	3.2	odd	2	inner
588.2.n.f.275.4		24	12.11	even	2	inner
588.2.n.f.275.9		24	4.3	odd	2	inner
588.2.n.f.275.11		24	1.1	even	1	trivial
588.2.n.g.263.2		24	28.3	even	6
588.2.n.g.263.4		24	7.3	odd	6
588.2.n.g.263.9		24	21.17	even	6
588.2.n.g.263.11		24	84.59	odd	6
588.2.n.g.275.2		24	21.20	even	2
588.2.n.g.275.4		24	84.83	odd	2
588.2.n.g.275.9		24	28.27	even	2
588.2.n.g.275.11		24	7.6	odd	2
1344.2.h.h.575.1		12	56.37	even	6
1344.2.h.h.575.2		12	168.107	even	6
1344.2.h.h.575.11		12	168.149	odd	6
1344.2.h.h.575.12		12	56.51	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36159 + 0.382199i) q^{2} +(-0.683917 - 1.59131i) q^{3} +(1.70785 + 1.04079i) q^{4} +(1.97228 + 1.13870i) q^{5} +(-0.323018 - 2.42810i) q^{6} +(1.92760 + 2.06987i) q^{8} +(-2.06452 + 2.17664i) q^{9} +(2.25023 + 2.30424i) q^{10} +(2.15917 + 3.73979i) q^{11} +(0.488197 - 3.42953i) q^{12} -0.406728 q^{13} +(0.463141 - 3.91729i) q^{15} +(1.83349 + 3.55504i) q^{16} +(3.73979 - 2.15917i) q^{17} +(-3.64293 + 2.17464i) q^{18} +(-4.70065 - 2.71392i) q^{19} +(2.18321 + 3.99747i) q^{20} +(1.51056 + 5.91729i) q^{22} +(0.581371 - 1.00696i) q^{23} +(1.97548 - 4.48302i) q^{24} +(0.0932716 + 0.161551i) q^{25} +(-0.553797 - 0.155451i) q^{26} +(4.87566 + 1.79664i) q^{27} -3.72469i q^{29} +(2.12779 - 5.15672i) q^{30} +(-5.05289 + 2.91729i) q^{31} +(1.13773 + 5.54126i) q^{32} +(4.47446 - 5.99360i) q^{33} +(5.91729 - 1.51056i) q^{34} +(-5.79132 + 1.56864i) q^{36} +(3.91729 - 6.78494i) q^{37} +(-5.36310 - 5.49183i) q^{38} +(0.278168 + 0.647230i) q^{39} +(1.44481 + 6.27733i) q^{40} +2.56195i q^{41} -11.0211i q^{43} +(-0.204820 + 8.63424i) q^{44} +(-6.55035 + 1.94210i) q^{45} +(1.17645 - 1.14887i) q^{46} +(1.16274 - 2.01393i) q^{47} +(4.40320 - 5.34900i) q^{48} +(0.0652529 + 0.255614i) q^{50} +(-5.99360 - 4.47446i) q^{51} +(-0.694631 - 0.423321i) q^{52} +(-4.74675 + 2.74054i) q^{53} +(5.95198 + 4.30975i) q^{54} +9.83457i q^{55} +(-1.10383 + 9.33627i) q^{57} +(1.42357 - 5.07150i) q^{58} +(1.95653 + 3.38881i) q^{59} +(4.86807 - 6.20810i) q^{60} +(-5.22448 + 9.04906i) q^{61} +(-7.99494 + 2.04094i) q^{62} +(-0.568736 + 7.97976i) q^{64} +(-0.802184 - 0.463141i) q^{65} +(8.38312 - 6.45069i) q^{66} +(-6.78494 + 3.91729i) q^{67} +(8.63424 + 0.204820i) q^{68} +(-2.00000 - 0.236460i) q^{69} +4.88743 q^{71} +(-8.48493 - 0.0775907i) q^{72} +(-1.40673 - 2.43653i) q^{73} +(7.92693 - 7.74112i) q^{74} +(0.193287 - 0.258911i) q^{75} +(-5.20336 - 9.52738i) q^{76} +(0.131381 + 0.987576i) q^{78} +(-3.46410 - 2.00000i) q^{79} +(-0.431948 + 9.09935i) q^{80} +(-0.475549 - 8.98743i) q^{81} +(-0.979172 + 3.48832i) q^{82} -0.641735 q^{83} +9.83457 q^{85} +(4.21225 - 15.0062i) q^{86} +(-5.92712 + 2.54738i) q^{87} +(-3.57888 + 11.6780i) q^{88} +(-12.1218 - 6.99851i) q^{89} +(-9.66116 + 0.140802i) q^{90} +(2.04094 - 1.11466i) q^{92} +(8.09805 + 6.04551i) q^{93} +(2.35290 - 2.29775i) q^{94} +(-6.18068 - 10.7053i) q^{95} +(8.03973 - 5.60024i) q^{96} -2.00000 q^{97} +(-12.5978 - 3.02112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} - 12 q^{6} + 4 q^{9} - 4 q^{10} + 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} - 2 q^{24} + 12 q^{25} - 20 q^{30} + 16 q^{33} + 64 q^{34} - 40 q^{36} + 16 q^{37} - 20 q^{40} - 24 q^{45} + 92 q^{48}+ \cdots - 48 q^{97}+O(q^{100}) \) 24 * q + 4 * q^4 - 12 * q^6 + 4 * q^9 - 4 * q^10 + 6 * q^12 - 4 * q^16 + 8 * q^18 - 32 * q^22 - 2 * q^24 + 12 * q^25 - 20 * q^30 + 16 * q^33 + 64 * q^34 - 40 * q^36 + 16 * q^37 - 20 * q^40 - 24 * q^45 + 92 * q^48 + 28 * q^52 - 10 * q^54 + 32 * q^57 + 32 * q^58 - 28 * q^60 + 16 * q^61 + 40 * q^64 + 12 * q^66 - 48 * q^69 + 32 * q^72 - 24 * q^73 - 120 * q^76 + 40 * q^78 - 28 * q^81 - 8 * q^82 + 80 * q^85 + 56 * q^88 - 160 * q^90 - 24 * q^93 + 34 * q^96 - 48 * q^97

Introduction

L-functions

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