LMFDB - Embedded newform 510.2.bd.a.7.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [510,2,Mod(7,510)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(510, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 4, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("510.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.bd (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			7.8
Character	$\chi$	$=$	510.7
Dual form			510.2.bd.a.73.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.923880 - 0.382683i) q^{2} +(0.195090 + 0.980785i) q^{3} +(0.707107 - 0.707107i) q^{4} +(2.19965 - 0.401940i) q^{5} +(0.555570 + 0.831470i) q^{6} +(1.83348 - 1.22509i) q^{7} +(0.382683 - 0.923880i) q^{8} +(-0.923880 + 0.382683i) q^{9} +(1.87839 - 1.21311i) q^{10} +(0.466386 - 0.311629i) q^{11} +(0.831470 + 0.555570i) q^{12} +1.12943i q^{13} +(1.22509 - 1.83348i) q^{14} +(0.823346 + 2.07897i) q^{15} -1.00000i q^{16} +(-3.97314 + 1.10188i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-6.75006 - 2.79597i) q^{19} +(1.27117 - 1.83960i) q^{20} +(1.55924 + 1.55924i) q^{21} +(0.311629 - 0.466386i) q^{22} +(4.76128 + 0.947078i) q^{23} +(0.980785 + 0.195090i) q^{24} +(4.67689 - 1.76825i) q^{25} +(0.432213 + 1.04345i) q^{26} +(-0.555570 - 0.831470i) q^{27} +(0.430195 - 2.16273i) q^{28} +(0.0390941 + 0.196540i) q^{29} +(1.55626 + 1.60563i) q^{30} +(7.43375 + 4.96707i) q^{31} +(-0.382683 - 0.923880i) q^{32} +(0.396628 + 0.396628i) q^{33} +(-3.24904 + 2.53846i) q^{34} +(3.54059 - 3.43171i) q^{35} +(-0.382683 + 0.923880i) q^{36} +(-3.03334 + 0.603368i) q^{37} -7.30622 q^{38} +(-1.10772 + 0.220340i) q^{39} +(0.470424 - 2.18602i) q^{40} +(-1.10160 + 5.53813i) q^{41} +(2.03725 + 0.843857i) q^{42} +(-5.84859 - 2.42256i) q^{43} +(0.109430 - 0.550139i) q^{44} +(-1.87839 + 1.21311i) q^{45} +(4.76128 - 0.947078i) q^{46} +1.61812 q^{47} +(0.980785 - 0.195090i) q^{48} +(-0.817990 + 1.97480i) q^{49} +(3.64420 - 3.42342i) q^{50} +(-1.85582 - 3.68184i) q^{51} +(0.798625 + 0.798625i) q^{52} +(2.07650 + 5.01310i) q^{53} +(-0.831470 - 0.555570i) q^{54} +(0.900627 - 0.872932i) q^{55} +(-0.430195 - 2.16273i) q^{56} +(1.42537 - 7.16583i) q^{57} +(0.111331 + 0.166618i) q^{58} +(-1.25681 - 3.03421i) q^{59} +(2.05224 + 0.887857i) q^{60} +(-6.28194 - 1.24956i) q^{61} +(8.76871 + 1.74420i) q^{62} +(-1.22509 + 1.83348i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(0.453962 + 2.48434i) q^{65} +(0.518220 + 0.214654i) q^{66} +(2.06000 - 2.06000i) q^{67} +(-2.03029 + 3.58858i) q^{68} +4.85456i q^{69} +(1.95782 - 4.52542i) q^{70} +(-4.60670 + 6.89441i) q^{71} +1.00000i q^{72} +(-13.3669 - 8.93145i) q^{73} +(-2.57154 + 1.71825i) q^{74} +(2.64669 + 4.24205i) q^{75} +(-6.75006 + 2.79597i) q^{76} +(0.473334 - 1.14273i) q^{77} +(-0.939084 + 0.627476i) q^{78} +(-7.98431 - 11.9494i) q^{79} +(-0.401940 - 2.19965i) q^{80} +(0.707107 - 0.707107i) q^{81} +(1.10160 + 5.53813i) q^{82} +(9.33675 - 3.86741i) q^{83} +2.20511 q^{84} +(-8.29662 + 4.02070i) q^{85} -6.33047 q^{86} +(-0.185136 + 0.0766859i) q^{87} +(-0.109430 - 0.550139i) q^{88} +(-11.5229 + 11.5229i) q^{89} +(-1.27117 + 1.83960i) q^{90} +(1.38365 + 2.07078i) q^{91} +(4.03642 - 2.69705i) q^{92} +(-3.42138 + 8.25994i) q^{93} +(1.49495 - 0.619229i) q^{94} +(-15.9716 - 3.43702i) q^{95} +(0.831470 - 0.555570i) q^{96} +(-13.0448 - 8.71624i) q^{97} +2.13751i q^{98} +(-0.311629 + 0.466386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 16 q^{15} + 16 q^{20} + 16 q^{25} - 16 q^{28} + 32 q^{29} + 16 q^{31} + 16 q^{33} + 32 q^{35} - 16 q^{37} - 16 q^{40} + 48 q^{41} + 16 q^{44} + 32 q^{47} - 64 q^{49} - 16 q^{50} + 32 q^{51} + 16 q^{52}+ \cdots - 80 q^{97}+O(q^{100}) $ 64 * q - 16 * q^15 + 16 * q^20 + 16 * q^25 - 16 * q^28 + 32 * q^29 + 16 * q^31 + 16 * q^33 + 32 * q^35 - 16 * q^37 - 16 * q^40 + 48 * q^41 + 16 * q^44 + 32 * q^47 - 64 * q^49 - 16 * q^50 + 32 * q^51 + 16 * q^52 + 80 * q^53 - 16 * q^55 + 16 * q^56 - 32 * q^57 + 64 * q^59 - 48 * q^61 + 32 * q^65 + 16 * q^67 - 48 * q^68 - 64 * q^71 + 16 * q^73 + 48 * q^74 - 32 * q^75 - 80 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 48 * q^82 - 32 * q^83 - 16 * q^85 - 64 * q^86 - 32 * q^87 - 16 * q^88 - 32 * q^89 - 16 * q^90 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 112 * q^95 - 80 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	0.923880	−	0.382683i	0.653281	−	0.270598i
$2$	0.923880	−	0.382683i	0.653281	−	0.270598i
$3$	0.195090	+	0.980785i	0.112635	+	0.566257i
$3$	0.195090	+	0.980785i	0.112635	+	0.566257i
$4$	0.707107	−	0.707107i	0.353553	−	0.353553i
$5$	2.19965	−	0.401940i	0.983712	−	0.179753i
$5$	2.19965	−	0.401940i	0.983712	−	0.179753i
$6$	0.555570	+	0.831470i	0.226811	+	0.339446i
$7$	1.83348	−	1.22509i	0.692989	−	0.463041i	−0.158537	−	0.987353i	$-0.550678\pi$
$7$	1.83348	−	1.22509i	0.692989	−	0.463041i	0.851526	+	0.524312i	$0.175678\pi$
$8$	0.382683	−	0.923880i	0.135299	−	0.326641i
$9$	−0.923880	+	0.382683i	−0.307960	+	0.127561i
$10$	1.87839	−	1.21311i	0.594000	−	0.383620i
$11$	0.466386	−	0.311629i	0.140621	−	0.0939596i	−0.483270	−	0.875471i	$-0.660551\pi$
$11$	0.466386	−	0.311629i	0.140621	−	0.0939596i	0.623891	+	0.781512i	$0.285551\pi$
$12$	0.831470	+	0.555570i	0.240025	+	0.160379i
$13$			1.12943i			0.313247i	0.987658	+	0.156623i	$0.0500608\pi$
$13$			1.12943i			0.313247i	−0.987658	+	0.156623i	$0.949939\pi$
$14$	1.22509	−	1.83348i	0.327419	−	0.490018i
$15$	0.823346	+	2.07897i	0.212587	+	0.536787i
$16$		−	1.00000i		−	0.250000i
$17$	−3.97314	+	1.10188i	−0.963629	+	0.267244i
$17$	−3.97314	+	1.10188i	−0.963629	+	0.267244i
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−6.75006	−	2.79597i	−1.54857	−	0.641439i	−0.565514	−	0.824739i	$-0.691322\pi$
$19$	−6.75006	−	2.79597i	−1.54857	−	0.641439i	−0.983057	+	0.183300i	$0.941322\pi$
$20$	1.27117	−	1.83960i	0.284242	−	0.411347i
$21$	1.55924	+	1.55924i	0.340255	+	0.340255i
$22$	0.311629	−	0.466386i	0.0664395	−	0.0994337i
$23$	4.76128	+	0.947078i	0.992796	+	0.197479i	0.664656	−	0.747150i	$-0.268578\pi$
$23$	4.76128	+	0.947078i	0.992796	+	0.197479i	0.328140	+	0.944629i	$0.393578\pi$
$24$	0.980785	+	0.195090i	0.200202	+	0.0398226i
$25$	4.67689	−	1.76825i	0.935378	−	0.353650i
$26$	0.432213	+	1.04345i	0.0847639	+	0.204638i
$27$	−0.555570	−	0.831470i	−0.106920	−	0.160016i
$28$	0.430195	−	2.16273i	0.0812991	−	0.408718i
$29$	0.0390941	+	0.196540i	0.00725960	+	0.0364965i	0.984245	−	0.176808i	$-0.0565773\pi$
$29$	0.0390941	+	0.196540i	0.00725960	+	0.0364965i	−0.976986	+	0.213305i	$0.931577\pi$
$30$	1.55626	+	1.60563i	0.284133	+	0.293147i
$31$	7.43375	+	4.96707i	1.33514	+	0.892113i	0.998768	−	0.0496161i	$-0.0157998\pi$
$31$	7.43375	+	4.96707i	1.33514	+	0.892113i	0.336373	+	0.941729i	$0.390800\pi$
$32$	−0.382683	−	0.923880i	−0.0676495	−	0.163320i
$33$	0.396628	+	0.396628i	0.0690441	+	0.0690441i
$34$	−3.24904	+	2.53846i	−0.557205	+	0.435342i
$35$	3.54059	−	3.43171i	0.598469	−	0.580066i
$36$	−0.382683	+	0.923880i	−0.0637806	+	0.153980i
$37$	−3.03334	+	0.603368i	−0.498677	+	0.0991931i	−0.438019	−	0.898965i	$-0.644320\pi$
$37$	−3.03334	+	0.603368i	−0.498677	+	0.0991931i	−0.0606580	+	0.998159i	$0.519320\pi$
$38$	−7.30622			−1.18522
$39$	−1.10772	+	0.220340i	−0.177378	+	0.0352827i
$40$	0.470424	−	2.18602i	0.0743806	−	0.345641i
$41$	−1.10160	+	5.53813i	−0.172041	+	0.864910i	0.794276	+	0.607557i	$0.207850\pi$
$41$	−1.10160	+	5.53813i	−0.172041	+	0.864910i	−0.966317	+	0.257353i	$0.917150\pi$
$42$	2.03725	+	0.843857i	0.314355	+	0.130210i
$43$	−5.84859	−	2.42256i	−0.891901	−	0.369438i	−0.110801	−	0.993843i	$-0.535342\pi$
$43$	−5.84859	−	2.42256i	−0.891901	−	0.369438i	−0.781101	+	0.624405i	$0.785342\pi$
$44$	0.109430	−	0.550139i	0.0164971	−	0.0829366i
$45$	−1.87839	+	1.21311i	−0.280014	+	0.180840i
$46$	4.76128	−	0.947078i	0.702013	−	0.139639i
$47$	1.61812			0.236028			0.118014	−	0.993012i	$-0.462347\pi$
$47$	1.61812			0.236028			0.118014	+	0.993012i	$0.462347\pi$
$48$	0.980785	−	0.195090i	0.141564	−	0.0281589i
$49$	−0.817990	+	1.97480i	−0.116856	+	0.282115i
$50$	3.64420	−	3.42342i	0.515368	−	0.484145i
$51$	−1.85582	−	3.68184i	−0.259867	−	0.515560i
$52$	0.798625	+	0.798625i	0.110749	+	0.110749i
$53$	2.07650	+	5.01310i	0.285229	+	0.688603i	0.999942	−	0.0108152i	$-0.00344266\pi$
$53$	2.07650	+	5.01310i	0.285229	+	0.688603i	−0.714713	+	0.699418i	$0.753443\pi$
$54$	−0.831470	−	0.555570i	−0.113149	−	0.0756035i
$55$	0.900627	−	0.872932i	0.121441	−	0.117706i
$56$	−0.430195	−	2.16273i	−0.0574872	−	0.289008i
$57$	1.42537	−	7.16583i	0.188795	−	0.949137i
$58$	0.111331	+	0.166618i	0.0146184	+	0.0218780i
$59$	−1.25681	−	3.03421i	−0.163623	−	0.395020i	0.820709	−	0.571346i	$-0.193579\pi$
$59$	−1.25681	−	3.03421i	−0.163623	−	0.395020i	−0.984332	+	0.176326i	$0.943579\pi$
$60$	2.05224	+	0.887857i	0.264944	+	0.114622i
$61$	−6.28194	−	1.24956i	−0.804320	−	0.159989i	−0.224224	−	0.974538i	$-0.571985\pi$
$61$	−6.28194	−	1.24956i	−0.804320	−	0.159989i	−0.580096	+	0.814548i	$0.696985\pi$
$62$	8.76871	+	1.74420i	1.11363	+	0.221514i
$63$	−1.22509	+	1.83348i	−0.154347	+	0.230996i
$64$	−0.707107	−	0.707107i	−0.0883883	−	0.0883883i
$65$	0.453962	+	2.48434i	0.0563070	+	0.308144i
$66$	0.518220	+	0.214654i	0.0637885	+	0.0264220i
$67$	2.06000	−	2.06000i	0.251669	−	0.251669i	−0.569986	−	0.821655i	$-0.693051\pi$
$67$	2.06000	−	2.06000i	0.251669	−	0.251669i	0.821655	+	0.569986i	$0.193051\pi$
$68$	−2.03029	+	3.58858i	−0.246209	+	0.435179i
$69$			4.85456i			0.584421i
$70$	1.95782	−	4.52542i	0.234004	−	0.540891i
$71$	−4.60670	+	6.89441i	−0.546714	+	0.818216i	−0.997217	−	0.0745596i	$-0.976245\pi$
$71$	−4.60670	+	6.89441i	−0.546714	+	0.818216i	0.450502	+	0.892775i	$0.351245\pi$
$72$			1.00000i			0.117851i
$73$	−13.3669	−	8.93145i	−1.56447	−	1.04535i	−0.970572	−	0.240810i	$-0.922587\pi$
$73$	−13.3669	−	8.93145i	−1.56447	−	1.04535i	−0.593901	−	0.804538i	$-0.702413\pi$
$74$	−2.57154	+	1.71825i	−0.298935	+	0.199742i
$75$	2.64669	+	4.24205i	0.305614	+	0.489830i
$76$	−6.75006	+	2.79597i	−0.774285	+	0.320720i
$77$	0.473334	−	1.14273i	0.0539414	−	0.130226i
$78$	−0.939084	+	0.627476i	−0.106330	+	0.0710476i
$79$	−7.98431	−	11.9494i	−0.898305	−	1.34441i	−0.938523	−	0.345217i	$-0.887805\pi$
$79$	−7.98431	−	11.9494i	−0.898305	−	1.34441i	0.0402183	−	0.999191i	$-0.487195\pi$
$80$	−0.401940	−	2.19965i	−0.0449382	−	0.245928i
$81$	0.707107	−	0.707107i	0.0785674	−	0.0785674i
$82$	1.10160	+	5.53813i	0.121652	+	0.611584i
$83$	9.33675	−	3.86741i	1.02484	−	0.424503i	0.193993	−	0.981003i	$-0.437856\pi$
$83$	9.33675	−	3.86741i	1.02484	−	0.424503i	0.830848	+	0.556500i	$0.187856\pi$
$84$	2.20511			0.240597
$85$	−8.29662	+	4.02070i	−0.899895	+	0.436106i
$86$	−6.33047			−0.682632
$87$	−0.185136	+	0.0766859i	−0.0198487	+	0.00822159i
$88$	−0.109430	−	0.550139i	−0.0116652	−	0.0586450i
$89$	−11.5229	+	11.5229i	−1.22143	+	1.22143i	−0.254306	+	0.967124i	$0.581847\pi$
$89$	−11.5229	+	11.5229i	−1.22143	+	1.22143i	−0.967124	+	0.254306i	$0.918153\pi$
$90$	−1.27117	+	1.83960i	−0.133993	+	0.193911i
$91$	1.38365	+	2.07078i	0.145046	+	0.217077i
$92$	4.03642	−	2.69705i	0.420826	−	0.281187i
$93$	−3.42138	+	8.25994i	−0.354781	+	0.856516i
$94$	1.49495	−	0.619229i	0.154192	−	0.0638686i
$95$	−15.9716	−	3.43702i	−1.63865	−	0.352631i
$96$	0.831470	−	0.555570i	0.0848615	−	0.0567026i
$97$	−13.0448	−	8.71624i	−1.32450	−	0.885000i	−0.326314	−	0.945261i	$-0.605807\pi$
$97$	−13.0448	−	8.71624i	−1.32450	−	0.885000i	−0.998183	+	0.0602612i	$0.980807\pi$
$98$			2.13751i			0.215921i
$99$	−0.311629	+	0.466386i	−0.0313199	+	0.0468735i
$100$	2.05672	−	4.55740i	0.205672	−	0.455740i
$101$			7.90649i			0.786725i	0.919383	+	0.393363i	$0.128688\pi$
$101$			7.90649i			0.786725i	−0.919383	+	0.393363i	$0.871312\pi$
$102$	−3.12354	−	2.69138i	−0.309276	−	0.266486i
$103$	7.16852	−	7.16852i	0.706335	−	0.706335i	−0.259427	−	0.965763i	$-0.583534\pi$
$103$	7.16852	−	7.16852i	0.706335	−	0.706335i	0.965763	+	0.259427i	$0.0835338\pi$
$104$	1.04345	+	0.432213i	0.102319	+	0.0423819i
$105$	4.05651	+	2.80306i	0.395875	+	0.273551i
$106$	3.83686	+	3.83686i	0.372669	+	0.372669i
$107$	5.24023	−	7.84255i	0.506592	−	0.758168i	−0.486729	−	0.873553i	$-0.661810\pi$
$107$	5.24023	−	7.84255i	0.506592	−	0.758168i	0.993321	+	0.115385i	$0.0368101\pi$
$108$	−0.980785	−	0.195090i	−0.0943761	−	0.0187726i
$109$	11.7275	+	2.33275i	1.12329	+	0.223437i	0.721582	−	0.692329i	$-0.243415\pi$
$109$	11.7275	+	2.33275i	1.12329	+	0.223437i	0.401712	+	0.915766i	$0.368415\pi$
$110$	0.498014	−	1.15114i	0.0474838	−	0.109757i
$111$	−1.18355	−	2.85734i	−0.112338	−	0.271207i
$112$	−1.22509	−	1.83348i	−0.115760	−	0.173247i
$113$	−0.660137	+	3.31874i	−0.0621005	+	0.312200i	−0.999334	−	0.0365033i	$-0.988378\pi$
$113$	−0.660137	+	3.31874i	−0.0621005	+	0.312200i	0.937233	+	0.348704i	$0.113378\pi$
$114$	−1.42537	−	7.16583i	−0.133498	−	0.671141i
$115$	10.8538	+	0.169487i	1.01212	+	0.0158048i
$116$	0.166618	+	0.111331i	0.0154701	+	0.0103368i
$117$	−0.432213	−	1.04345i	−0.0399581	−	0.0964673i
$118$	−2.32228	−	2.32228i	−0.213783	−	0.213783i
$119$	−5.93477	+	6.88773i	−0.544040	+	0.631397i
$120$	2.23580	+	0.0349130i	0.204099	+	0.00318710i
$121$	−4.08911	+	9.87200i	−0.371738	+	0.897454i
$122$	−6.28194	+	1.24956i	−0.568740	+	0.113129i
$123$	−5.64662			−0.509139
$124$	8.76871	−	1.74420i	0.787453	−	0.156634i
$125$	9.57677	−	5.76936i	0.856572	−	0.516027i
$126$	−0.430195	+	2.16273i	−0.0383248	+	0.192672i
$127$	−11.2700	−	4.66821i	−1.00006	−	0.414236i	−0.178238	−	0.983987i	$-0.557040\pi$
$127$	−11.2700	−	4.66821i	−1.00006	−	0.414236i	−0.821817	+	0.569751i	$0.807040\pi$
$128$	−0.923880	−	0.382683i	−0.0816602	−	0.0338248i
$129$	1.23501	−	6.20883i	0.108737	−	0.546657i
$130$	1.37012	+	2.12151i	0.120168	+	0.186068i
$131$	−0.397519	+	0.0790714i	−0.0347314	+	0.00690850i	−0.212425	−	0.977177i	$-0.568136\pi$
$131$	−0.397519	+	0.0790714i	−0.0347314	+	0.00690850i	0.177694	+	0.984086i	$0.443136\pi$
$132$	0.560917			0.0488216
$133$	−15.8014	+	3.14310i	−1.37016	+	0.272541i
$134$	1.11486	−	2.69152i	0.0963095	−	0.232512i
$135$	−1.55626	−	1.60563i	−0.133941	−	0.138191i
$136$	−0.502456	+	4.09238i	−0.0430853	+	0.350918i
$137$	13.1176	+	13.1176i	1.12071	+	1.12071i	0.991634	+	0.129080i	$0.0412024\pi$
$137$	13.1176	+	13.1176i	1.12071	+	1.12071i	0.129080	+	0.991634i	$0.458798\pi$
$138$	1.85776	+	4.48503i	0.158143	+	0.381791i
$139$	−8.01190	−	5.35338i	−0.679561	−	0.454068i	0.167284	−	0.985909i	$-0.446500\pi$
$139$	−8.01190	−	5.35338i	−0.679561	−	0.454068i	−0.846844	+	0.531841i	$0.821500\pi$
$140$	0.0769868	−	4.93016i	0.00650657	−	0.416675i
$141$	0.315680	+	1.58703i	0.0265851	+	0.133652i
$142$	−1.61766	+	8.13251i	−0.135751	+	0.682465i
$143$	0.351962	+	0.526748i	0.0294325	+	0.0440489i
$144$	0.382683	+	0.923880i	0.0318903	+	0.0769900i
$145$	0.164990	+	0.416604i	0.0137017	+	0.0345971i
$146$	−15.7673	−	3.13631i	−1.30491	−	0.259563i
$147$	−2.09644	−	0.417008i	−0.172911	−	0.0343942i
$148$	−1.71825	+	2.57154i	−0.141239	+	0.211379i
$149$	2.84066	+	2.84066i	0.232716	+	0.232716i	0.813825	−	0.581110i	$-0.197381\pi$
$149$	2.84066	+	2.84066i	0.232716	+	0.232716i	−0.581110	+	0.813825i	$0.697381\pi$
$150$	4.06859	+	2.90630i	0.332199	+	0.237299i
$151$	11.3138	+	4.68633i	0.920704	+	0.381368i	0.792145	−	0.610334i	$-0.208965\pi$
$151$	11.3138	+	4.68633i	0.920704	+	0.381368i	0.128560	+	0.991702i	$0.458965\pi$
$152$	−5.16627	+	5.16627i	−0.419040	+	0.419040i
$153$	3.24904	−	2.53846i	0.262669	−	0.205222i
$154$		−	1.23688i		−	0.0996707i
$155$	18.3481	+	7.93788i	1.47375	+	0.637586i
$156$	−0.627476	+	0.939084i	−0.0502383	+	0.0751869i
$157$		−	9.63912i		−	0.769285i	−0.923066	−	0.384643i	$-0.874325\pi$
$157$		−	9.63912i		−	0.769285i	0.923066	−	0.384643i	$-0.125675\pi$
$158$	−11.9494	−	7.98431i	−0.950640	−	0.635197i
$159$	−4.51167	+	3.01460i	−0.357799	+	0.239074i
$160$	−1.21311	−	1.87839i	−0.0959049	−	0.148500i
$161$	9.88996	−	4.09656i	0.779438	−	0.322854i
$162$	0.382683	−	0.923880i	0.0300665	−	0.0725868i
$163$	5.90776	−	3.94744i	0.462731	−	0.309187i	−0.302263	−	0.953225i	$-0.597742\pi$
$163$	5.90776	−	3.94744i	0.462731	−	0.309187i	0.764994	+	0.644037i	$0.222742\pi$
$164$	3.13710	+	4.69500i	0.244966	+	0.366618i
$165$	1.03186	+	0.713021i	0.0803304	+	0.0555086i
$166$	7.14604	−	7.14604i	0.554640	−	0.554640i
$167$	0.320149	+	1.60950i	0.0247739	+	0.124547i	0.991193	−	0.132423i	$-0.0422759\pi$
$167$	0.320149	+	1.60950i	0.0247739	+	0.124547i	−0.966419	+	0.256970i	$0.917276\pi$
$168$	2.03725	−	0.843857i	0.157177	−	0.0651050i
$169$	11.7244			0.901877
$170$	−6.12643	+	6.88962i	−0.469875	+	0.528410i
$171$	7.30622			0.558720
$172$	−5.84859	+	2.42256i	−0.445951	+	0.184719i
$173$	−0.410039	−	2.06141i	−0.0311747	−	0.156726i	0.962062	−	0.272830i	$-0.0879595\pi$
$173$	−0.410039	−	2.06141i	−0.0311747	−	0.156726i	−0.993237	+	0.116104i	$0.962959\pi$
$174$	−0.141697	+	0.141697i	−0.0107420	+	0.0107420i
$175$	6.40870	−	8.97166i	0.484452	−	0.678194i
$176$	−0.311629	−	0.466386i	−0.0234899	−	0.0351551i
$177$	2.73071	−	1.82460i	0.205253	−	0.137146i
$178$	−6.23617	+	15.0555i	−0.467421	+	1.12845i
$179$	−0.172756	+	0.0715578i	−0.0129124	+	0.00534848i	−0.389130	−	0.921183i	$-0.627224\pi$
$179$	−0.172756	+	0.0715578i	−0.0129124	+	0.00534848i	0.376218	+	0.926531i	$0.377224\pi$
$180$	−0.470424	+	2.18602i	−0.0350633	+	0.162937i
$181$	2.13211	−	1.42463i	0.158478	−	0.105892i	−0.473803	−	0.880631i	$-0.657119\pi$
$181$	2.13211	−	1.42463i	0.158478	−	0.105892i	0.632281	+	0.774739i	$0.282119\pi$
$182$	2.07078	+	1.38365i	0.153496	+	0.102563i
$183$		−	6.40501i		−	0.473472i
$184$	2.69705	−	4.03642i	0.198829	−	0.297569i
$185$	−6.42975	+	2.54642i	−0.472725	+	0.187216i
$186$			8.94050i			0.655549i
$187$	−1.50964	+	1.75204i	−0.110396	+	0.128122i
$188$	1.14419	−	1.14419i	0.0834483	−	0.0834483i
$189$	−2.03725	−	0.843857i	−0.148188	−	0.0613816i
$190$	−16.0711	+	2.93666i	−1.16592	+	0.213048i
$191$	12.0014	+	12.0014i	0.868393	+	0.868393i	0.992294	−	0.123902i	$-0.0395408\pi$
$191$	12.0014	+	12.0014i	0.868393	+	0.868393i	−0.123902	+	0.992294i	$0.539541\pi$
$192$	0.555570	−	0.831470i	0.0400948	−	0.0600062i
$193$	2.09082	+	0.415891i	0.150501	+	0.0299365i	0.269766	−	0.962926i	$-0.413054\pi$
$193$	2.09082	+	0.415891i	0.150501	+	0.0299365i	−0.119265	+	0.992862i	$0.538054\pi$
$194$	−15.3874	−	3.06074i	−1.10475	−	0.219748i
$195$	−2.34804	+	0.929909i	−0.168147	+	0.0665922i
$196$	0.817990	+	1.97480i	0.0584279	+	0.141057i
$197$	−5.85067	−	8.75615i	−0.416843	−	0.623850i	0.562321	−	0.826919i	$-0.309908\pi$
$197$	−5.85067	−	8.75615i	−0.416843	−	0.623850i	−0.979164	+	0.203069i	$0.934908\pi$
$198$	−0.109430	+	0.550139i	−0.00777682	+	0.0390967i
$199$	3.73665	+	18.7854i	0.264884	+	1.33166i	0.852587	+	0.522585i	$0.175032\pi$
$199$	3.73665	+	18.7854i	0.264884	+	1.33166i	−0.587704	+	0.809076i	$0.699968\pi$
$200$	0.156117	−	4.99756i	0.0110391	−	0.353381i
$201$	2.42230	+	1.61853i	0.170856	+	0.114162i
$202$	3.02568	+	7.30465i	0.212886	+	0.513953i
$203$	0.312457	+	0.312457i	0.0219302	+	0.0219302i
$204$	−3.91572	−	1.29118i	−0.274155	−	0.0904010i
$205$	−0.197140	+	12.6247i	−0.0137689	+	0.881747i
$206$	3.87958	−	9.36612i	0.270303	−	0.652569i
$207$	−4.76128	+	0.947078i	−0.330932	+	0.0658265i
$208$	1.12943			0.0783116
$209$	−4.01944	+	0.799516i	−0.278030	+	0.0553036i
$210$	4.82041	+	1.03733i	0.332640	+	0.0715829i
$211$	−0.897713	+	4.51311i	−0.0618011	+	0.310695i	−0.999305	−	0.0372800i	$-0.988131\pi$
$211$	−0.897713	+	4.51311i	−0.0618011	+	0.310695i	0.937504	+	0.347975i	$0.113131\pi$
$212$	5.01310	+	2.07650i	0.344301	+	0.142614i
$213$	−7.66066	−	3.17315i	−0.524899	−	0.217420i
$214$	1.84012	−	9.25092i	0.125788	−	0.632380i
$215$	−13.8386	−	2.97800i	−0.943781	−	0.203098i
$216$	−0.980785	+	0.195090i	−0.0667340	+	0.0132742i
$217$	19.7147			1.33832
$218$	11.7275	−	2.33275i	0.794289	−	0.157994i
$219$	6.15209	−	14.8525i	0.415720	−	1.00364i
$220$	0.0195833	−	1.25410i	0.00132030	−	0.0845511i
$221$	−1.24449	−	4.48737i	−0.0837132	−	0.301853i
$222$	−2.18691	−	2.18691i	−0.146776	−	0.146776i
$223$	−10.1154	−	24.4207i	−0.677376	−	1.63533i	−0.768777	−	0.639517i	$-0.779134\pi$
$223$	−10.1154	−	24.4207i	−0.677376	−	1.63533i	0.0914004	−	0.995814i	$-0.470866\pi$
$224$	−1.83348	−	1.22509i	−0.122504	−	0.0818548i
$225$	−3.64420	+	3.42342i	−0.242947	+	0.228228i
$226$	0.660137	+	3.31874i	0.0439117	+	0.220759i
$227$	−0.792779	+	3.98557i	−0.0526186	+	0.264532i	−0.998135	−	0.0610424i	$-0.980558\pi$
$227$	−0.792779	+	3.98557i	−0.0526186	+	0.264532i	0.945517	+	0.325574i	$0.105558\pi$
$228$	−4.05912	−	6.07490i	−0.268822	−	0.402320i
$229$	0.637547	+	1.53917i	0.0421303	+	0.101712i	0.943544	−	0.331247i	$-0.107469\pi$
$229$	0.637547	+	1.53917i	0.0421303	+	0.101712i	−0.901414	+	0.432959i	$0.857469\pi$
$230$	10.0925	−	3.99699i	0.665478	−	0.263553i
$231$	1.21311	+	0.241304i	0.0798171	+	0.0158766i
$232$	0.196540	+	0.0390941i	0.0129035	+	0.00256666i
$233$	6.51076	−	9.74404i	0.426534	−	0.638353i	−0.554501	−	0.832183i	$-0.687091\pi$
$233$	6.51076	−	9.74404i	0.426534	−	0.638353i	0.981035	+	0.193830i	$0.0620909\pi$
$234$	−0.798625	−	0.798625i	−0.0522078	−	0.0522078i
$235$	3.55930	−	0.650388i	0.232183	−	0.0424267i
$236$	−3.03421	−	1.25681i	−0.197510	−	0.0818113i
$237$	10.1621	−	10.1621i	0.660099	−	0.660099i
$238$	−2.84720	+	8.63457i	−0.184556	+	0.559696i
$239$			7.09449i			0.458905i	0.973320	+	0.229452i	$0.0736935\pi$
$239$			7.09449i			0.458905i	−0.973320	+	0.229452i	$0.926306\pi$
$240$	2.07897	−	0.823346i	0.134197	−	0.0531468i
$241$	3.43623	−	5.14268i	0.221347	−	0.331269i	−0.704131	−	0.710070i	$-0.748663\pi$
$241$	3.43623	−	5.14268i	0.221347	−	0.331269i	0.925478	+	0.378800i	$0.123663\pi$
$242$			10.6854i			0.686882i
$243$	0.831470	+	0.555570i	0.0533388	+	0.0356398i
$244$	−5.32557	+	3.55843i	−0.340935	+	0.227805i
$245$	−1.00554	+	4.67265i	−0.0642414	+	0.298525i
$246$	−5.21680	+	2.16087i	−0.332611	+	0.137772i
$247$	3.15784	−	7.62370i	0.200929	−	0.485084i
$248$	7.43375	−	4.96707i	0.472044	−	0.315409i
$249$	5.61460	+	8.40285i	0.355811	+	0.532509i
$250$	6.63995	−	8.99506i	0.419947	−	0.568898i
$251$	17.7424	−	17.7424i	1.11989	−	1.11989i	0.128137	−	0.991757i	$-0.459100\pi$
$251$	17.7424	−	17.7424i	1.11989	−	1.11989i	0.991757	−	0.128137i	$-0.0408997\pi$
$252$	0.430195	+	2.16273i	0.0270997	+	0.136239i
$253$	2.51573	−	1.04205i	0.158163	−	0.0655131i
$254$	−12.1986			−0.765409
$255$	−5.56204	−	7.35281i	−0.348308	−	0.460451i
$256$	−1.00000			−0.0625000
$257$	−6.13258	+	2.54020i	−0.382540	+	0.158453i	−0.565663	−	0.824637i	$-0.691379\pi$
$257$	−6.13258	+	2.54020i	−0.382540	+	0.158453i	0.183123	+	0.983090i	$0.441379\pi$
$258$	−1.23501	−	6.20883i	−0.0768885	−	0.386545i
$259$	−4.82237	+	4.82237i	−0.299648	+	0.299648i
$260$	2.07769	+	1.43569i	0.128853	+	0.0890379i
$261$	−0.111331	−	0.166618i	−0.00689120	−	0.0103134i
$262$	−0.337000	+	0.225176i	−0.0208199	+	0.0139114i
$263$	10.1366	−	24.4719i	0.625048	−	1.50900i	−0.220659	−	0.975351i	$-0.570821\pi$
$263$	10.1366	−	24.4719i	0.625048	−	1.50900i	0.845707	−	0.533648i	$-0.179179\pi$
$264$	0.518220	−	0.214654i	0.0318942	−	0.0132110i
$265$	6.58252	+	10.1924i	0.404361	+	0.626116i
$266$	−13.3958	+	8.95078i	−0.821348	+	0.548807i
$267$	−13.5495	−	9.05352i	−0.829219	−	0.554066i
$268$		−	2.91328i		−	0.177957i
$269$	−9.93828	+	14.8737i	−0.605947	+	0.906864i	−0.999925	−	0.0122557i	$-0.996099\pi$
$269$	−9.93828	+	14.8737i	−0.605947	+	0.906864i	0.393977	+	0.919120i	$0.371099\pi$
$270$	−2.05224	−	0.887857i	−0.124896	−	0.0540333i
$271$			11.3842i			0.691543i	0.938319	+	0.345771i	$0.112383\pi$
$271$			11.3842i			0.691543i	−0.938319	+	0.345771i	$0.887617\pi$
$272$	1.10188	+	3.97314i	0.0668110	+	0.240907i
$273$	−1.76105	+	1.76105i	−0.106584	+	0.106584i
$274$	17.1390	+	7.09921i	1.03540	+	0.428879i
$275$	1.63020	−	2.28214i	0.0983045	−	0.137618i
$276$	3.43269	+	3.43269i	0.206624	+	0.206624i
$277$	13.1121	−	19.6236i	0.787829	−	1.17907i	−0.192422	−	0.981312i	$-0.561634\pi$
$277$	13.1121	−	19.6236i	0.787829	−	1.17907i	0.980251	−	0.197757i	$-0.0633658\pi$
$278$	−9.45068	−	1.87986i	−0.566814	−	0.112746i
$279$	−8.76871	−	1.74420i	−0.524969	−	0.104423i
$280$	−1.81557	−	4.58434i	−0.108501	−	0.273967i
$281$	0.647218	+	1.56252i	0.0386098	+	0.0932123i	0.942008	−	0.335590i	$-0.108936\pi$
$281$	0.647218	+	1.56252i	0.0386098	+	0.0932123i	−0.903398	+	0.428802i	$0.858936\pi$
$282$	0.898981	+	1.34542i	0.0535335	+	0.0801186i
$283$	2.12865	−	10.7015i	0.126535	−	0.636136i	−0.864511	−	0.502615i	$-0.832371\pi$
$283$	2.12865	−	10.7015i	0.126535	−	0.636136i	0.991046	−	0.133522i	$-0.0426285\pi$
$284$	1.61766	+	8.13251i	0.0959903	+	0.482576i
$285$	0.255082	−	16.3352i	0.0151097	−	0.967614i
$286$	0.526748	+	0.351962i	0.0311473	+	0.0208119i
$287$	4.76494	+	11.5036i	0.281266	+	0.679036i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	14.5717	−	8.75582i	0.857161	−	0.515048i
$290$	0.311859	+	0.321753i	0.0183130	+	0.0188940i
$291$	6.00385	−	14.4946i	0.351952	−	0.849687i
$292$	−15.7673	+	3.13631i	−0.922711	+	0.183539i
$293$	16.8757			0.985891			0.492945	−	0.870060i	$-0.335920\pi$
$293$	16.8757			0.985891			0.492945	+	0.870060i	$0.335920\pi$
$294$	−2.09644	+	0.417008i	−0.122267	+	0.0243204i
$295$	−3.98410	−	6.16902i	−0.231964	−	0.359174i
$296$	−0.603368	+	3.03334i	−0.0350701	+	0.176309i
$297$	−0.518220	−	0.214654i	−0.0300702	−	0.0124555i
$298$	3.71150	+	1.53735i	0.215001	+	0.0890565i
$299$	−1.06965	+	5.37752i	−0.0618597	+	0.310990i
$300$	4.87108	+	1.12809i	0.281232	+	0.0651305i
$301$	−13.6911	+	2.72333i	−0.789143	+	0.156970i
$302$	12.2460			0.704677
$303$	−7.75457	+	1.54248i	−0.445488	+	0.0886132i
$304$	−2.79597	+	6.75006i	−0.160360	+	0.387143i
$305$	−14.3203	−	0.223618i	−0.819977	−	0.0128043i
$306$	2.03029	−	3.58858i	0.116064	−	0.205145i
$307$	−3.83123	−	3.83123i	−0.218660	−	0.218660i	0.589274	−	0.807933i	$-0.299414\pi$
$307$	−3.83123	−	3.83123i	−0.218660	−	0.218660i	−0.807933	+	0.589274i	$0.799414\pi$
$308$	−0.473334	−	1.14273i	−0.0269707	−	0.0651130i
$309$	8.42929	+	5.63227i	0.479525	+	0.320409i
$310$	19.9891	+	0.312139i	1.13531	+	0.0177283i
$311$	−5.77903	−	29.0531i	−0.327699	−	1.64745i	−0.696216	−	0.717832i	$-0.745135\pi$
$311$	−5.77903	−	29.0531i	−0.327699	−	1.64745i	0.368518	−	0.929621i	$-0.379865\pi$
$312$	−0.220340	+	1.10772i	−0.0124743	+	0.0627126i
$313$	11.5286	+	17.2537i	0.651632	+	0.975237i	0.999292	+	0.0376160i	$0.0119764\pi$
$313$	11.5286	+	17.2537i	0.651632	+	0.975237i	−0.347660	+	0.937621i	$0.613024\pi$
$314$	−3.68873	−	8.90538i	−0.208167	−	0.502560i
$315$	−1.95782	+	4.52542i	−0.110311	+	0.254978i
$316$	−14.0952	−	2.80372i	−0.792919	−	0.157721i
$317$	−8.24904	−	1.64084i	−0.463312	−	0.0921585i	−0.0420856	−	0.999114i	$-0.513400\pi$
$317$	−8.24904	−	1.64084i	−0.463312	−	0.0921585i	−0.421226	+	0.906956i	$0.638400\pi$
$318$	−3.01460	+	4.51167i	−0.169051	+	0.253002i
$319$	0.0794803	+	0.0794803i	0.00445004	+	0.00445004i
$320$	−1.83960	−	1.27117i	−0.102837	−	0.0710606i
$321$	8.71418	+	3.60953i	0.486378	+	0.201464i
$322$	7.56945	−	7.56945i	0.421829	−	0.421829i
$323$	29.8998	+	3.67105i	1.66367	+	0.204263i
$324$		−	1.00000i		−	0.0555556i
$325$	1.99711	+	5.28220i	0.110780	+	0.293004i
$326$	3.94744	−	5.90776i	0.218628	−	0.327201i
$327$			11.9573i			0.661240i
$328$	4.69500	+	3.13710i	0.259238	+	0.173217i
$329$	2.96679	−	1.98235i	0.163565	−	0.109290i
$330$	1.22618	+	0.263869i	0.0674989	+	0.0145255i
$331$	−27.6572	+	11.4560i	−1.52018	+	0.629677i	−0.977627	−	0.210347i	$-0.932541\pi$
$331$	−27.6572	+	11.4560i	−1.52018	+	0.629677i	−0.542549	+	0.840024i	$0.682541\pi$
$332$	3.86741	−	9.33675i	0.212252	−	0.512421i
$333$	2.57154	−	1.71825i	0.140919	−	0.0941594i
$334$	0.911707	+	1.36447i	0.0498864	+	0.0746602i
$335$	3.70327	−	5.35926i	0.202331	−	0.292808i
$336$	1.55924	−	1.55924i	0.0850638	−	0.0850638i
$337$	7.12294	+	35.8094i	0.388011	+	1.95066i	0.297291	+	0.954787i	$0.403917\pi$
$337$	7.12294	+	35.8094i	0.388011	+	1.95066i	0.0907198	+	0.995876i	$0.471083\pi$
$338$	10.8319	−	4.48673i	0.589179	−	0.244046i
$339$	−3.38375			−0.183780
$340$	−3.02353	+	8.70966i	−0.163974	+	0.472348i
$341$	5.01488			0.271571
$342$	6.75006	−	2.79597i	0.365002	−	0.151189i
$343$	3.93091	+	19.7620i	0.212249	+	1.06705i
$344$	−4.47632	+	4.47632i	−0.241347	+	0.241347i
$345$	1.95124	+	10.6783i	0.105051	+	0.574901i
$346$	−1.16769	−	1.74758i	−0.0627755	−	0.0939502i
$347$	13.1296	−	8.77290i	0.704832	−	0.470954i	−0.150782	−	0.988567i	$-0.548179\pi$
$347$	13.1296	−	8.77290i	0.704832	−	0.470954i	0.855615	+	0.517613i	$0.173179\pi$
$348$	−0.0766859	+	0.185136i	−0.00411080	+	0.00992434i
$349$	20.2993	−	8.40823i	1.08660	−	0.450082i	0.233777	−	0.972290i	$-0.424891\pi$
$349$	20.2993	−	8.40823i	1.08660	−	0.450082i	0.852818	+	0.522208i	$0.174891\pi$
$350$	2.48756	−	10.7412i	0.132966	−	0.574143i
$351$	0.939084	−	0.627476i	0.0501246	−	0.0334922i
$352$	−0.466386	−	0.311629i	−0.0248584	−	0.0166099i
$353$		−	12.5847i		−	0.669815i	−0.942251	−	0.334907i	$-0.891295\pi$
$353$		−	12.5847i		−	0.669815i	0.942251	−	0.334907i	$-0.108705\pi$
$354$	1.82460	−	2.73071i	0.0969766	−	0.145136i
$355$	−7.36196	+	17.0169i	−0.390732	+	0.903162i
$356$			16.2959i			0.863681i
$357$	−7.91320	−	4.47701i	−0.418811	−	0.236949i
$358$	−0.132222	+	0.132222i	−0.00698813	+	0.00698813i
$359$	13.0379	+	5.40049i	0.688116	+	0.285027i	0.699215	−	0.714912i	$-0.253533\pi$
$359$	13.0379	+	5.40049i	0.688116	+	0.285027i	−0.0110992	+	0.999938i	$0.503533\pi$
$360$	0.401940	+	2.19965i	0.0211841	+	0.115932i
$361$	24.3109	+	24.3109i	1.27952	+	1.27952i
$362$	1.42463	−	2.13211i	0.0748768	−	0.112061i
$363$	−10.4801	−	2.08461i	−0.550060	−	0.109414i
$364$	2.44265	+	0.485873i	0.128030	+	0.0254667i
$365$	−32.9923	−	14.2734i	−1.72690	−	0.747102i
$366$	−2.45109	−	5.91746i	−0.128121	−	0.309310i
$367$	2.98048	+	4.46060i	0.155580	+	0.232841i	0.901069	−	0.433677i	$-0.142784\pi$
$367$	2.98048	+	4.46060i	0.155580	+	0.232841i	−0.745489	+	0.666518i	$0.767784\pi$
$368$	0.947078	−	4.76128i	0.0493699	−	0.248199i
$369$	−1.10160	−	5.53813i	−0.0573471	−	0.288303i
$370$	−4.96584	+	4.81314i	−0.258162	+	0.250223i
$371$	9.94871	+	6.64752i	0.516512	+	0.345122i
$372$	3.42138	+	8.25994i	0.177390	+	0.428258i
$373$	1.96553	+	1.96553i	0.101771	+	0.101771i	0.756159	−	0.654388i	$-0.227074\pi$
$373$	1.96553	+	1.96553i	0.101771	+	0.101771i	−0.654388	+	0.756159i	$0.727074\pi$
$374$	−0.724248	+	2.19639i	−0.0374500	+	0.113573i
$375$	7.52683	+	8.26721i	0.388684	+	0.426917i
$376$	0.619229	−	1.49495i	0.0319343	−	0.0770962i
$377$	−0.221977	+	0.0441539i	−0.0114324	+	0.00227404i
$378$	−2.20511			−0.113418
$379$	13.7661	−	2.73825i	0.707116	−	0.140654i	0.171585	−	0.985169i	$-0.445111\pi$
$379$	13.7661	−	2.73825i	0.707116	−	0.140654i	0.535532	+	0.844515i	$0.320111\pi$
$380$	−13.7239	+	8.86326i	−0.704023	+	0.454676i
$381$	2.37983	−	11.9642i	0.121922	−	0.612946i
$382$	15.6806	+	6.49512i	0.802290	+	0.332319i
$383$	17.1136	+	7.08869i	0.874464	+	0.362215i	0.774347	−	0.632761i	$-0.218078\pi$
$383$	17.1136	+	7.08869i	0.874464	+	0.362215i	0.100117	+	0.994976i	$0.468078\pi$
$384$	0.195090	−	0.980785i	0.00995566	−	0.0500505i
$385$	0.581859	−	2.70385i	0.0296543	−	0.137801i
$386$	2.09082	−	0.415891i	0.106420	−	0.0211683i
$387$	6.33047			0.321796
$388$	−15.3874	+	3.06074i	−0.781175	+	0.155385i
$389$	−2.09273	+	5.05229i	−0.106106	+	0.256161i	−0.968011	−	0.250907i	$-0.919271\pi$
$389$	−2.09273	+	5.05229i	−0.106106	+	0.256161i	0.861906	+	0.507069i	$0.169271\pi$
$390$	−1.81344	+	1.75768i	−0.0918273	+	0.0890036i
$391$	−19.9608	+	1.48346i	−1.00946	+	0.0750219i
$392$	1.51145	+	1.51145i	0.0763397	+	0.0763397i
$393$	−0.155104	−	0.374454i	−0.00782397	−	0.0188887i
$394$	−8.75615	−	5.85067i	−0.441128	−	0.294753i
$395$	−22.3656	−	23.0752i	−1.12533	−	1.16104i
$396$	0.109430	+	0.550139i	0.00549904	+	0.0276455i
$397$	−5.23837	+	26.3351i	−0.262906	+	1.32172i	0.593257	+	0.805013i	$0.297842\pi$
$397$	−5.23837	+	26.3351i	−0.262906	+	1.32172i	−0.856163	+	0.516705i	$0.827158\pi$
$398$	10.6411	+	15.9255i	0.533389	+	0.798272i
$399$	−6.16540	−	14.8846i	−0.308656	−	0.745162i
$400$	−1.76825	−	4.67689i	−0.0884126	−	0.233844i
$401$	−35.2056	−	7.00283i	−1.75808	−	0.349705i	−0.792515	−	0.609852i	$-0.791229\pi$
$401$	−35.2056	−	7.00283i	−1.75808	−	0.349705i	−0.965569	+	0.260147i	$0.916229\pi$
$402$	2.85730	+	0.568352i	0.142509	+	0.0283468i
$403$	−5.60994	+	8.39587i	−0.279451	+	0.418228i
$404$	5.59073	+	5.59073i	0.278149	+	0.278149i
$405$	1.27117	−	1.83960i	0.0631650	−	0.0914104i
$406$	0.408245	+	0.169100i	0.0202608	+	0.00839232i
$407$	−1.22668	+	1.22668i	−0.0608041	+	0.0608041i
$408$	−4.11177	+	0.305581i	−0.203563	+	0.0151285i
$409$			9.77686i			0.483435i	0.970347	+	0.241717i	$0.0777107\pi$
$409$			9.77686i			0.483435i	−0.970347	+	0.241717i	$0.922289\pi$
$410$	4.64913	+	11.7391i	0.229604	+	0.579755i
$411$	−10.3065	+	15.4247i	−0.508380	+	0.760844i
$412$		−	10.1378i		−	0.499454i
$413$	−6.02151	−	4.02344i	−0.296299	−	0.197981i
$414$	−4.03642	+	2.69705i	−0.198379	+	0.132553i
$415$	18.9831	−	12.2597i	0.931843	−	0.601807i
$416$	1.04345	−	0.432213i	0.0511595	−	0.0211910i
$417$	3.68747	−	8.90235i	0.180576	−	0.435950i
$418$	−3.40751	+	2.27683i	−0.166667	+	0.111363i
$419$	−18.1755	−	27.2016i	−0.887932	−	1.32888i	−0.943824	−	0.330447i	$-0.892800\pi$
$419$	−18.1755	−	27.2016i	−0.887932	−	1.32888i	0.0558925	−	0.998437i	$-0.482200\pi$
$420$	4.85045	−	0.886320i	0.236678	−	0.0432480i
$421$	25.7559	−	25.7559i	1.25527	−	1.25527i	0.301938	−	0.953328i	$-0.402366\pi$
$421$	25.7559	−	25.7559i	1.25527	−	1.25527i	0.953328	−	0.301938i	$-0.0976335\pi$
$422$	0.897713	+	4.51311i	0.0437000	+	0.219695i
$423$	−1.49495	+	0.619229i	−0.0726870	+	0.0301079i
$424$	5.42614			0.263517
$425$	−16.6336	+	12.1789i	−0.806846	+	0.590762i
$426$	−8.29183			−0.401741
$427$	−13.0486	+	5.40491i	−0.631467	+	0.261562i
$428$	−1.84012	−	9.25092i	−0.0889457	−	0.447160i
$429$	−0.447962	+	0.447962i	−0.0216278	+	0.0216278i
$430$	−13.9248	+	2.54447i	−0.671513	+	0.122705i
$431$	−6.37653	−	9.54315i	−0.307146	−	0.459677i	0.645499	−	0.763761i	$-0.276650\pi$
$431$	−6.37653	−	9.54315i	−0.307146	−	0.459677i	−0.952645	+	0.304084i	$0.901650\pi$
$432$	−0.831470	+	0.555570i	−0.0400041	+	0.0267299i
$433$	−8.53701	+	20.6102i	−0.410263	+	0.990462i	0.574804	+	0.818291i	$0.305078\pi$
$433$	−8.53701	+	20.6102i	−0.410263	+	0.990462i	−0.985067	+	0.172171i	$0.944922\pi$
$434$	18.2140	−	7.54450i	0.874302	−	0.362148i
$435$	−0.376411	+	0.243096i	−0.0180475	+	0.0116555i
$436$	9.94213	−	6.64312i	0.476142	−	0.318148i
$437$	−29.4910	−	19.7052i	−1.41074	−	0.942629i
$438$		−	16.0762i		−	0.768150i
$439$	−9.09707	+	13.6147i	−0.434179	+	0.649795i	−0.982454	−	0.186503i	$-0.940285\pi$
$439$	−9.09707	+	13.6147i	−0.434179	+	0.649795i	0.548275	+	0.836298i	$0.315285\pi$
$440$	−0.461829	−	1.16613i	−0.0220168	−	0.0555930i
$441$		−	2.13751i		−	0.101786i
$442$	−2.86700	−	3.66955i	−0.136369	−	0.174543i
$443$	9.80059	−	9.80059i	0.465640	−	0.465640i	−0.434859	−	0.900499i	$-0.643202\pi$
$443$	9.80059	−	9.80059i	0.465640	−	0.465640i	0.900499	+	0.434859i	$0.143202\pi$
$444$	−2.85734	−	1.18355i	−0.135603	−	0.0561688i
$445$	−20.7149	+	29.9779i	−0.981979	+	1.42109i
$446$	−18.6908	−	18.6908i	−0.885035	−	0.885035i
$447$	−2.23189	+	3.34026i	−0.105565	+	0.157989i
$448$	−2.16273	−	0.430195i	−0.102180	−	0.0203248i
$449$	−5.04341	−	1.00320i	−0.238013	−	0.0473438i	0.0746422	−	0.997210i	$-0.476219\pi$
$449$	−5.04341	−	1.00320i	−0.238013	−	0.0473438i	−0.312655	+	0.949867i	$0.601219\pi$
$450$	−2.05672	+	4.55740i	−0.0969546	+	0.214838i
$451$	1.21207	+	2.92619i	0.0570741	+	0.137789i
$452$	1.87991	+	2.81349i	0.0884236	+	0.132335i
$453$	−2.38907	+	12.0107i	−0.112248	+	0.564311i
$454$	0.792779	+	3.98557i	0.0372070	+	0.187052i
$455$	3.87587	+	3.99884i	0.181704	+	0.187468i
$456$	−6.07490	−	4.05912i	−0.284483	−	0.190086i
$457$	−9.25474	−	22.3429i	−0.432918	−	1.04516i	−0.978342	−	0.206997i	$-0.933631\pi$
$457$	−9.25474	−	22.3429i	−0.432918	−	1.04516i	0.545423	−	0.838161i	$-0.316369\pi$
$458$	1.17803	+	1.17803i	0.0550459	+	0.0550459i
$459$	3.12354	+	2.69138i	0.145794	+	0.125623i
$460$	7.79465	−	7.55496i	0.363427	−	0.352252i
$461$	−1.78695	+	4.31408i	−0.0832266	+	0.200927i	−0.960014	−	0.279951i	$-0.909682\pi$
$461$	−1.78695	+	4.31408i	−0.0832266	+	0.200927i	0.876788	+	0.480878i	$0.159682\pi$
$462$	1.21311	−	0.241304i	0.0564392	−	0.0112265i
$463$	16.4990			0.766773			0.383387	−	0.923588i	$-0.374758\pi$
$463$	16.4990			0.766773			0.383387	+	0.923588i	$0.374758\pi$
$464$	0.196540	−	0.0390941i	0.00912412	−	0.00181490i
$465$	−4.20583	+	19.5441i	−0.195040	+	0.906338i
$466$	2.28628	−	11.4939i	0.105910	−	0.532444i
$467$	19.6642	+	8.14517i	0.909950	+	0.376914i	0.788037	−	0.615627i	$-0.211097\pi$
$467$	19.6642	+	8.14517i	0.909950	+	0.376914i	0.121912	+	0.992541i	$0.461097\pi$
$468$	−1.04345	−	0.432213i	−0.0482337	−	0.0199790i
$469$	1.25328	−	6.30065i	0.0578709	−	0.290937i
$470$	3.03947	−	1.96297i	0.140200	−	0.0905448i
$471$	9.45390	−	1.88050i	0.435613	−	0.0866488i
$472$	−3.28420			−0.151168
$473$	−3.48264	+	0.692740i	−0.160132	+	0.0318522i
$474$	5.49969	−	13.2774i	0.252609	−	0.609852i
$475$	−36.5133	−	1.14062i	−1.67534	−	0.0523353i
$476$	0.673838	+	9.06688i	0.0308853	+	0.415580i
$477$	−3.83686	−	3.83686i	−0.175678	−	0.175678i
$478$	2.71495	+	6.55446i	0.124179	+	0.299794i
$479$	23.0933	+	15.4305i	1.05516	+	0.705036i	0.956986	−	0.290133i	$-0.0936996\pi$
$479$	23.0933	+	15.4305i	1.05516	+	0.705036i	0.0981749	+	0.995169i	$0.468700\pi$
$480$	1.60563	−	1.55626i	0.0732868	−	0.0710332i
$481$	−0.681460	−	3.42593i	−0.0310719	−	0.156209i
$482$	1.20664	−	6.06621i	0.0549611	−	0.276308i
$483$	5.94728	+	8.90073i	0.270611	+	0.404997i
$484$	4.08911	+	9.87200i	0.185869	+	0.448727i
$485$	−32.1973	−	13.9294i	−1.46200	−	0.632503i
$486$	0.980785	+	0.195090i	0.0444893	+	0.00884948i
$487$	−12.9031	−	2.56658i	−0.584693	−	0.116303i	−0.106124	−	0.994353i	$-0.533844\pi$
$487$	−12.9031	−	2.56658i	−0.584693	−	0.116303i	−0.478569	+	0.878050i	$0.658844\pi$
$488$	−3.55843	+	5.32557i	−0.161083	+	0.241077i
$489$	5.02414	+	5.02414i	0.227199	+	0.227199i
$490$	0.859151	+	4.70177i	0.0388125	+	0.212404i
$491$	−36.8458	−	15.2620i	−1.66283	−	0.688765i	−0.664538	−	0.747254i	$-0.731372\pi$
$491$	−36.8458	−	15.2620i	−1.66283	−	0.688765i	−0.998288	+	0.0584891i	$0.981372\pi$
$492$	−3.99277	+	3.99277i	−0.180008	+	0.180008i
$493$	−0.371889	−	0.737803i	−0.0167490	−	0.0332290i
$494$		−	8.25183i		−	0.371268i
$495$	−0.498014	+	1.15114i	−0.0223841	+	0.0517399i
$496$	4.96707	−	7.43375i	0.223028	−	0.333785i
$497$			18.2844i			0.820166i
$498$	8.40285	+	5.61460i	0.376541	+	0.251596i
$499$	10.8214	−	7.23062i	0.484432	−	0.323687i	−0.289259	−	0.957251i	$-0.593409\pi$
$499$	10.8214	−	7.23062i	0.484432	−	0.323687i	0.773690	+	0.633564i	$0.218409\pi$
$500$	2.69225	−	10.8514i	0.120401	−	0.485287i
$501$	−1.51611	+	0.627994i	−0.0677349	+	0.0280567i
$502$	9.60214	−	23.1816i	0.428565	−	1.03465i
$503$	−17.4868	+	11.6843i	−0.779698	+	0.520977i	−0.880567	−	0.473922i	$-0.842838\pi$
$503$	−17.4868	+	11.6843i	−0.779698	+	0.520977i	0.100869	+	0.994900i	$0.467838\pi$
$504$	1.22509	+	1.83348i	0.0545699	+	0.0816696i
$505$	3.17793	+	17.3915i	0.141416	+	0.773911i
$506$	1.92546	−	1.92546i	0.0855970	−	0.0855970i
$507$	2.28732	+	11.4991i	0.101583	+	0.510694i
$508$	−11.2700	+	4.66821i	−0.500028	+	0.207118i
$509$	25.7829			1.14281			0.571404	−	0.820669i	$-0.306399\pi$
$509$	25.7829			1.14281			0.571404	+	0.820669i	$0.306399\pi$
$510$	−7.95245	−	4.66461i	−0.352140	−	0.206552i
$511$	−35.4497			−1.56820
$512$	−0.923880	+	0.382683i	−0.0408301	+	0.0169124i
$513$	1.42537	+	7.16583i	0.0629317	+	0.316379i
$514$	−4.69368	+	4.69368i	−0.207029	+	0.207029i
$515$	12.8869	−	18.6495i	0.567864	−	0.821796i
$516$	−3.51702	−	5.26359i	−0.154828	−	0.231717i
$517$	0.754669	−	0.504254i	0.0331903	−	0.0221771i
$518$	−2.60985	+	6.30074i	−0.114670	+	0.276838i
$519$	1.94180	−	0.804321i	0.0852356	−	0.0353058i
$520$	2.46895	+	0.531309i	0.108271	+	0.0232995i
$521$	−3.02274	+	2.01973i	−0.132428	+	0.0884859i	−0.620020	−	0.784586i	$-0.712876\pi$
$521$	−3.02274	+	2.01973i	−0.132428	+	0.0884859i	0.487592	+	0.873072i	$0.337876\pi$
$522$	−0.166618	−	0.111331i	−0.00729268	−	0.00487281i
$523$			17.7854i			0.777703i	0.921300	+	0.388851i	$0.127128\pi$
$523$			17.7854i			0.777703i	−0.921300	+	0.388851i	$0.872872\pi$
$524$	−0.225176	+	0.337000i	−0.00983687	+	0.0147219i
$525$	10.0496	+	4.53528i	0.438598	+	0.197936i
$526$		−	26.4881i		−	1.15494i
$527$	−35.0085	−	11.5438i	−1.52499	−	0.502857i
$528$	0.396628	−	0.396628i	0.0172610	−	0.0172610i
$529$	0.523630	+	0.216895i	0.0227665	+	0.00943020i
$530$	9.98193	+	6.89755i	0.433587	+	0.299611i
$531$	2.32228	+	2.32228i	0.100778	+	0.100778i
$532$	−8.95078	+	13.3958i	−0.388065	+	0.580781i
$533$	−6.25491	−	1.24418i	−0.270930	−	0.0538913i
$534$	−15.9828	−	3.17917i	−0.691643	−	0.137576i
$535$	8.37441	−	19.3571i	0.362057	−	0.836880i
$536$	−1.11486	−	2.69152i	−0.0481548	−	0.116256i
$537$	−0.103886	−	0.155476i	−0.00448301	−	0.00670929i
$538$	−3.48986	+	17.5447i	−0.150458	+	0.756406i
$539$	0.233907	+	1.17593i	0.0100751	+	0.0506509i
$540$	−2.23580	−	0.0349130i	−0.0962133	−	0.00150241i
$541$	−10.1573	−	6.78689i	−0.436696	−	0.291791i	0.317723	−	0.948183i	$-0.397082\pi$
$541$	−10.1573	−	6.78689i	−0.436696	−	0.291791i	−0.754420	+	0.656392i	$0.772082\pi$
$542$	4.35656	+	10.5177i	0.187130	+	0.451772i
$543$	1.81321	+	1.81321i	0.0778122	+	0.0778122i
$544$	2.53846	+	3.24904i	0.108835	+	0.139301i
$545$	26.7341	+	0.417465i	1.14516	+	0.0178822i
$546$	−0.953074	+	2.30093i	−0.0407878	+	0.0984705i
$547$	28.9090	−	5.75036i	1.23606	−	0.245868i	0.466546	−	0.884497i	$-0.345498\pi$
$547$	28.9090	−	5.75036i	1.23606	−	0.245868i	0.769515	+	0.638629i	$0.220498\pi$
$548$	18.5511			0.792465
$549$	6.28194	−	1.24956i	0.268107	−	0.0533297i
$550$	0.632767	−	2.73227i	0.0269813	−	0.116504i
$551$	0.285630	−	1.43596i	0.0121683	−	0.0611740i
$552$	4.48503	+	1.85776i	0.190896	+	0.0790715i
$553$	−29.2781	−	12.1274i	−1.24503	−	0.515709i
$554$	4.60435	−	23.1476i	0.195620	−	0.983449i
$555$	−3.75187	−	5.80942i	−0.159258	−	0.246596i
$556$	−9.45068	+	1.87986i	−0.400798	+	0.0797237i
$557$	−29.0139			−1.22936			−0.614679	−	0.788778i	$-0.710714\pi$
$557$	−29.0139			−1.22936			−0.614679	+	0.788778i	$0.710714\pi$
$558$	−8.76871	+	1.74420i	−0.371209	+	0.0738381i
$559$	2.73611	−	6.60555i	0.115725	−	0.279385i
$560$	−3.43171	−	3.54059i	−0.145016	−	0.149617i
$561$	−2.01290	−	1.13883i	−0.0849845	−	0.0480813i
$562$	1.19590	+	1.19590i	0.0504461	+	0.0504461i
$563$	7.82005	+	18.8793i	0.329576	+	0.795667i	0.998624	+	0.0524473i	$0.0167022\pi$
$563$	7.82005	+	18.8793i	0.329576	+	0.795667i	−0.669048	+	0.743219i	$0.733298\pi$
$564$	1.34542	+	0.898981i	0.0566524	+	0.0378539i
$565$	−0.118137	+	7.56538i	−0.00497006	+	0.318278i
$566$	−2.12865	−	10.7015i	−0.0894740	−	0.449816i
$567$	0.430195	−	2.16273i	0.0180665	−	0.0908263i
$568$	4.60670	+	6.89441i	0.193293	+	0.289283i
$569$	−0.572101	−	1.38118i	−0.0239837	−	0.0579019i	0.911434	−	0.411446i	$-0.134976\pi$
$569$	−0.572101	−	1.38118i	−0.0239837	−	0.0579019i	−0.935418	+	0.353545i	$0.884976\pi$
$570$	−6.01555	−	15.1894i	−0.251964	−	0.636213i
$571$	−4.26761	−	0.848881i	−0.178594	−	0.0355246i	0.104983	−	0.994474i	$-0.466521\pi$
$571$	−4.26761	−	0.848881i	−0.178594	−	0.0355246i	−0.283577	+	0.958949i	$0.591521\pi$
$572$	0.621342	+	0.123593i	0.0259796	+	0.00516766i
$573$	−9.42946	+	14.1122i	−0.393921	+	0.589545i
$574$	8.80447	+	8.80447i	0.367491	+	0.367491i
$575$	23.9427	−	3.98977i	0.998478	−	0.166385i
$576$	0.923880	+	0.382683i	0.0384950	+	0.0159451i
$577$	−4.13492	+	4.13492i	−0.172139	+	0.172139i	−0.787919	−	0.615779i	$-0.788841\pi$
$577$	−4.13492	+	4.13492i	−0.172139	+	0.172139i	0.615779	+	0.787919i	$0.288841\pi$
$578$	10.1118	−	13.6657i	0.420597	−	0.568418i
$579$			2.13179i			0.0885940i
$580$	0.411249	+	0.177918i	0.0170762	+	0.00738763i
$581$	12.3808	−	18.5292i	0.513642	−	0.768719i
$582$		−	15.6888i		−	0.650323i
$583$	2.53068	+	1.69094i	0.104810	+	0.0700317i
$584$	−13.3669	+	8.93145i	−0.553125	+	0.369586i
$585$	−1.37012	−	2.12151i	−0.0566475	−	0.0877135i
$586$	15.5911	−	6.45806i	0.644064	−	0.266780i
$587$	−14.6630	+	35.3997i	−0.605208	+	1.46110i	0.262949	+	0.964810i	$0.415305\pi$
$587$	−14.6630	+	35.3997i	−0.605208	+	1.46110i	−0.868156	+	0.496291i	$0.834695\pi$
$588$	−1.77728	+	1.18754i	−0.0732936	+	0.0489732i
$589$	−36.2905	−	54.3126i	−1.49532	−	2.23791i
$590$	−6.04161	−	4.17478i	−0.248729	−	0.171873i
$591$	7.44649	−	7.44649i	0.306308	−	0.306308i
$592$	0.603368	+	3.03334i	0.0247983	+	0.124669i
$593$	−23.1923	+	9.60657i	−0.952394	+	0.394495i	−0.804130	−	0.594453i	$-0.797369\pi$
$593$	−23.1923	+	9.60657i	−0.952394	+	0.394495i	−0.148264	+	0.988948i	$0.547369\pi$
$594$	−0.560917			−0.0230147
$595$	−10.2860	+	17.5360i	−0.421683	+	0.718905i
$596$	4.01730			0.164555
$597$	−17.6955	+	7.32970i	−0.724227	+	0.299984i
$598$	1.06965	+	5.37752i	0.0437414	+	0.219903i
$599$	−28.1390	+	28.1390i	−1.14973	+	1.14973i	−0.163121	+	0.986606i	$0.552156\pi$
$599$	−28.1390	+	28.1390i	−1.14973	+	1.14973i	−0.986606	+	0.163121i	$0.947844\pi$
$600$	4.93199	−	0.821859i	0.201348	−	0.0335523i
$601$	23.2584	+	34.8087i	0.948732	+	1.41988i	0.907181	+	0.420741i	$0.138230\pi$
$601$	23.2584	+	34.8087i	0.948732	+	1.41988i	0.0415512	+	0.999136i	$0.486770\pi$
$602$	−11.6068	+	7.75540i	−0.473057	+	0.316086i
$603$	−1.11486	+	2.69152i	−0.0454007	+	0.109607i
$604$	11.3138	−	4.68633i	0.460352	−	0.190684i
$605$	−5.02666	+	23.3585i	−0.204363	+	0.949657i
$606$	−6.57401	+	4.39261i	−0.267051	+	0.178438i
$607$	−5.22684	−	3.49247i	−0.212151	−	0.141755i	0.444955	−	0.895553i	$-0.353220\pi$
$607$	−5.22684	−	3.49247i	−0.212151	−	0.141755i	−0.657106	+	0.753798i	$0.728220\pi$
$608$			7.30622i			0.296306i
$609$	−0.245496	+	0.367411i	−0.00994799	+	0.0148882i
$610$	−13.3158	+	5.27354i	−0.539141	+	0.213519i
$611$			1.82755i			0.0739348i
$612$	0.502456	−	4.09238i	0.0203106	−	0.165424i
$613$	−6.18244	+	6.18244i	−0.249706	+	0.249706i	−0.820850	−	0.571144i	$-0.806500\pi$
$613$	−6.18244	+	6.18244i	−0.249706	+	0.249706i	0.571144	+	0.820850i	$0.306500\pi$
$614$	−5.00574	−	2.07345i	−0.202015	−	0.0836774i
$615$	−12.4206	+	2.26960i	−0.500846	+	0.0915193i
$616$	−0.874607	−	0.874607i	−0.0352389	−	0.0352389i
$617$	13.2967	−	19.8999i	0.535305	−	0.801140i	−0.460966	−	0.887418i	$-0.652497\pi$
$617$	13.2967	−	19.8999i	0.535305	−	0.801140i	0.996271	+	0.0862772i	$0.0274971\pi$
$618$	9.94302	+	1.97779i	0.399967	+	0.0795584i
$619$	−40.1948	−	7.99525i	−1.61557	−	0.321356i	−0.697137	−	0.716938i	$-0.745543\pi$
$619$	−40.1948	−	7.99525i	−1.61557	−	0.321356i	−0.918431	+	0.395582i	$0.870543\pi$
$620$	18.5870	−	7.36113i	0.746471	−	0.295630i
$621$	−1.85776	−	4.48503i	−0.0745494	−	0.179978i
$622$	−16.4573	−	24.6301i	−0.659877	−	0.987576i
$623$	−7.01041	+	35.2437i	−0.280866	+	1.41201i
$624$	0.220340	+	1.10772i	0.00882067	+	0.0443445i
$625$	18.7466	−	16.5398i	0.749863	−	0.661593i
$626$	17.2537	+	11.5286i	0.689597	+	0.460774i
$627$	−1.56831	−	3.78623i	−0.0626321	−	0.151207i
$628$	−6.81588	−	6.81588i	−0.271983	−	0.271983i
$629$	11.3870	−	5.73963i	0.454031	−	0.228854i
$630$	−0.0769868	+	4.93016i	−0.00306723	+	0.196422i
$631$	16.9954	−	41.0305i	0.676575	−	1.63340i	−0.0936341	−	0.995607i	$-0.529848\pi$
$631$	16.9954	−	41.0305i	0.676575	−	1.63340i	0.770210	−	0.637791i	$-0.220152\pi$
$632$	−14.0952	+	2.80372i	−0.560678	+	0.111526i
$633$	−4.60153			−0.182894
$634$	−8.24904	+	1.64084i	−0.327611	+	0.0651659i
$635$	−26.6665	−	5.73852i	−1.05823	−	0.227726i
$636$	−1.05859	+	5.32188i	−0.0419758	+	0.211026i
$637$	−2.23040	−	0.923860i	−0.0883715	−	0.0366047i
$638$	0.103846	+	0.0430144i	0.00411130	+	0.00170296i
$639$	1.61766	−	8.13251i	0.0639935	−	0.321717i
$640$	−2.18602	−	0.470424i	−0.0864102	−	0.0185951i
$641$	43.1992	−	8.59286i	1.70627	−	0.339398i	0.756892	−	0.653540i	$-0.226717\pi$
$641$	43.1992	−	8.59286i	1.70627	−	0.339398i	0.949376	+	0.314143i	$0.101717\pi$
$642$	9.43216			0.372258
$643$	30.4817	−	6.06318i	1.20208	−	0.239108i	0.446874	−	0.894597i	$-0.352537\pi$
$643$	30.4817	−	6.06318i	1.20208	−	0.239108i	0.755205	+	0.655488i	$0.227537\pi$
$644$	4.09656	−	9.88996i	0.161427	−	0.389719i
$645$	0.221015	−	14.1536i	0.00870247	−	0.557299i
$646$	29.0286	−	8.05054i	1.14212	−	0.316744i
$647$	16.4072	+	16.4072i	0.645034	+	0.645034i	0.951789	−	0.306754i	$-0.0992430\pi$
$647$	16.4072	+	16.4072i	0.645034	+	0.645034i	−0.306754	+	0.951789i	$0.599243\pi$
$648$	−0.382683	−	0.923880i	−0.0150332	−	0.0362934i
$649$	−1.53170	−	1.02345i	−0.0601246	−	0.0401740i
$650$	3.86650	+	4.11586i	0.151657	+	0.161437i
$651$	3.84615	+	19.3359i	0.150743	+	0.757834i
$652$	1.38616	−	6.96868i	0.0542861	−	0.272914i
$653$	−22.3001	−	33.3745i	−0.872671	−	1.30605i	−0.951023	−	0.309119i	$-0.899966\pi$
$653$	−22.3001	−	33.3745i	−0.872671	−	1.30605i	0.0783519	−	0.996926i	$-0.475034\pi$
$654$	4.57586	+	11.0471i	0.178930	+	0.431976i
$655$	−0.842618	+	0.333708i	−0.0329238	+	0.0130390i
$656$	5.53813	+	1.10160i	0.216227	+	0.0430103i
$657$	15.7673	+	3.13631i	0.615141	+	0.122359i
$658$	1.98235	−	2.96679i	0.0772800	−	0.115658i
$659$	31.4277	+	31.4277i	1.22425	+	1.22425i	0.966107	+	0.258140i	$0.0831097\pi$
$659$	31.4277	+	31.4277i	1.22425	+	1.22425i	0.258140	+	0.966107i	$0.416890\pi$
$660$	1.23382	−	0.225455i	0.0480264	−	0.00877582i
$661$	−16.9008	−	7.00054i	−0.657365	−	0.272289i	0.0289643	−	0.999580i	$-0.490779\pi$
$661$	−16.9008	−	7.00054i	−0.657365	−	0.272289i	−0.686329	+	0.727291i	$0.740779\pi$
$662$	−21.1679	+	21.1679i	−0.822713	+	0.822713i
$663$	4.15836	−	2.09602i	0.161497	−	0.0814026i
$664$		−	10.1060i		−	0.392190i
$665$	−33.4942	+	13.2649i	−1.29885	+	0.514391i
$666$	1.71825	−	2.57154i	0.0665807	−	0.0996451i
$667$			0.972805i			0.0376672i
$668$	1.36447	+	0.911707i	0.0527927	+	0.0352750i
$669$	21.9781	−	14.6853i	0.849721	−	0.567765i
$670$	1.37048	−	6.36850i	0.0529461	−	0.246036i
$671$	−3.31920	+	1.37486i	−0.128136	+	0.0530758i
$672$	0.843857	−	2.03725i	0.0325525	−	0.0785887i
$673$	20.1142	−	13.4399i	0.775347	−	0.518070i	−0.103813	−	0.994597i	$-0.533104\pi$
$673$	20.1142	−	13.4399i	0.775347	−	0.518070i	0.879160	+	0.476527i	$0.158104\pi$
$674$	20.2844	+	30.3578i	0.781326	+	1.16934i
$675$	−4.06859	−	2.90630i	−0.156600	−	0.111864i
$676$	8.29040	−	8.29040i	0.318862	−	0.318862i
$677$	8.47396	+	42.6015i	0.325681	+	1.63731i	0.702975	+	0.711215i	$0.251855\pi$
$677$	8.47396	+	42.6015i	0.325681	+	1.63731i	−0.377294	+	0.926094i	$0.623145\pi$
$678$	−3.12618	+	1.29491i	−0.120060	+	0.0497306i
$679$	−34.5955			−1.32765
$680$	0.539663	+	9.20374i	0.0206951	+	0.352947i
$681$	−4.06365			−0.155719
$682$	4.63314	−	1.91911i	0.177412	−	0.0734865i
$683$	4.86479	+	24.4569i	0.186146	+	0.935819i	0.955048	+	0.296452i	$0.0958035\pi$
$683$	4.86479	+	24.4569i	0.186146	+	0.935819i	−0.768902	+	0.639367i	$0.779197\pi$
$684$	5.16627	−	5.16627i	0.197537	−	0.197537i
$685$	34.1266	+	23.5816i	1.30391	+	0.901008i
$686$	11.1943	+	16.7534i	0.427400	+	0.639649i
$687$	−1.38522	+	0.925575i	−0.0528495	+	0.0353129i
$688$	−2.42256	+	5.84859i	−0.0923594	+	0.222975i
$689$	−5.66193	+	2.34525i	−0.215702	+	0.0893469i
$690$	5.88913	+	9.11877i	0.224195	+	0.347146i
$691$	−11.1608	+	7.45738i	−0.424575	+	0.283692i	−0.749445	−	0.662067i	$-0.769680\pi$
$691$	−11.1608	+	7.45738i	−0.424575	+	0.283692i	0.324870	+	0.945759i	$0.394680\pi$
$692$	−1.74758	−	1.16769i	−0.0664328	−	0.0443890i
$693$			1.23688i			0.0469852i
$694$	8.77290	−	13.1296i	0.333015	−	0.498392i
$695$	−19.7751	−	8.55524i	−0.750112	−	0.324519i
$696$			0.200390i			0.00759576i
$697$	−1.72550	−	23.2176i	−0.0653580	−	0.879429i
$698$	15.5364	−	15.5364i	0.588061	−	0.588061i
$699$	10.8270	+	4.48469i	0.409515	+	0.169627i
$700$	−1.81229	−	10.8756i	−0.0684980	−	0.411058i
$701$	−2.54260	−	2.54260i	−0.0960325	−	0.0960325i	0.657458	−	0.753491i	$-0.271632\pi$
$701$	−2.54260	−	2.54260i	−0.0960325	−	0.0960325i	−0.753491	+	0.657458i	$0.771632\pi$
$702$	0.627476	−	0.939084i	0.0236825	−	0.0354434i
$703$	22.1622	+	4.40834i	0.835864	+	0.166264i
$704$	−0.550139	−	0.109430i	−0.0207342	−	0.00412428i
$705$	1.33228	+	3.36402i	0.0501764	+	0.126696i
$706$	−4.81595	−	11.6267i	−0.181251	−	0.437578i
$707$	9.68617	+	14.4964i	0.364286	+	0.545192i
$708$	0.640716	−	3.22110i	0.0240796	−	0.121056i
$709$	−7.80538	−	39.2403i	−0.293137	−	1.47370i	−0.793864	−	0.608095i	$-0.791934\pi$
$709$	−7.80538	−	39.2403i	−0.293137	−	1.47370i	0.500727	−	0.865605i	$-0.333066\pi$
$710$	−0.289493	+	18.5388i	−0.0108645	+	0.695750i
$711$	11.9494	+	7.98431i	0.448136	+	0.299435i
$712$	6.23617	+	15.0555i	0.233710	+	0.564227i
$713$	30.6900	+	30.6900i	1.14935	+	1.14935i
$714$	−9.02412	−	1.10797i	−0.337719	−	0.0414647i
$715$	0.985913	+	1.01719i	0.0368710	+	0.0380408i
$716$	−0.0715578	+	0.172756i	−0.00267424	+	0.00645619i
$717$	−6.95818	+	1.38407i	−0.259858	+	0.0516889i
$718$	14.1122			0.526661
$719$	14.9343	−	2.97062i	0.556957	−	0.110786i	0.0914172	−	0.995813i	$-0.470860\pi$
$719$	14.9343	−	2.97062i	0.556957	−	0.110786i	0.465539	+	0.885027i	$0.345860\pi$
$720$	1.21311	+	1.87839i	0.0452100	+	0.0700036i
$721$	4.36124	−	21.9254i	0.162421	−	0.816545i
$722$	31.7637	+	13.1570i	1.18212	+	0.489651i
$723$	5.71424	+	2.36692i	0.212515	+	0.0880266i
$724$	0.500263	−	2.51499i	0.0185921	−	0.0934689i
$725$	0.530370	+	0.850065i	0.0196975	+	0.0315706i
$726$	−10.4801	+	2.08461i	−0.388951	+	0.0773672i
$727$	−1.10360			−0.0409301			−0.0204650	−	0.999791i	$-0.506515\pi$
$727$	−1.10360			−0.0409301			−0.0204650	+	0.999791i	$0.506515\pi$
$728$	2.44265	−	0.485873i	0.0905306	−	0.0180077i
$729$	−0.382683	+	0.923880i	−0.0141735	+	0.0342178i
$730$	−35.9431	−	0.561268i	−1.33031	−	0.0207734i
$731$	25.9066	+	3.18078i	0.958192	+	0.117646i
$732$	−4.52902	−	4.52902i	−0.167398	−	0.167398i
$733$	−13.0269	−	31.4498i	−0.481160	−	1.16162i	−0.959058	−	0.283208i	$-0.908601\pi$
$733$	−13.0269	−	31.4498i	−0.481160	−	1.16162i	0.477898	−	0.878415i	$-0.341399\pi$
$734$	4.46060	+	2.98048i	0.164644	+	0.110011i
$735$	−4.77904	−	0.0746269i	−0.176278	−	0.00275265i
$736$	−0.947078	−	4.76128i	−0.0349098	−	0.175503i
$737$	0.318799	−	1.60271i	0.0117431	−	0.0590365i
$738$	−3.13710	−	4.69500i	−0.115478	−	0.172825i
$739$	8.80819	+	21.2648i	0.324014	+	0.782240i	0.999013	+	0.0444208i	$0.0141442\pi$
$739$	8.80819	+	21.2648i	0.324014	+	0.782240i	−0.674999	+	0.737819i	$0.735856\pi$
$740$	−2.74593	+	6.34711i	−0.100942	+	0.233324i
$741$	8.09328	+	1.60985i	0.297314	+	0.0591394i
$742$	11.7353	+	2.33430i	0.430817	+	0.0856948i
$743$	17.4919	−	26.1785i	0.641717	−	0.960398i	−0.357928	−	0.933749i	$-0.616517\pi$
$743$	17.4919	−	26.1785i	0.641717	−	0.960398i	0.999645	−	0.0266484i	$-0.00848346\pi$
$744$	6.32189	+	6.32189i	0.231772	+	0.231772i
$745$	7.39022	+	5.10667i	0.270757	+	0.187094i
$746$	2.56809	+	1.06374i	0.0940244	+	0.0389462i
$747$	−7.14604	+	7.14604i	−0.261460	+	0.261460i
$748$	0.171406	+	2.30636i	0.00626721	+	0.0843289i
$749$		−	20.7989i		−	0.759975i
$750$	10.1176	+	4.75751i	0.369443	+	0.173720i
$751$	7.38621	−	11.0543i	0.269527	−	0.403375i	−0.671874	−	0.740666i	$-0.734510\pi$
$751$	7.38621	−	11.0543i	0.269527	−	0.403375i	0.941401	+	0.337290i	$0.109510\pi$
$752$		−	1.61812i		−	0.0590069i
$753$	20.8629	+	13.9402i	0.760287	+	0.508007i
$754$	−0.188183	+	0.125740i	−0.00685322	+	0.00457917i
$755$	26.7700	+	5.76080i	0.974260	+	0.209657i
$756$	−2.03725	+	0.843857i	−0.0740941	+	0.0306908i
$757$	17.7353	−	42.8168i	0.644600	−	1.55620i	−0.175809	−	0.984424i	$-0.556254\pi$
$757$	17.7353	−	42.8168i	0.644600	−	1.55620i	0.820409	−	0.571777i	$-0.193746\pi$
$758$	11.6703	−	7.79786i	0.423885	−	0.283231i
$759$	1.51282	+	2.26410i	0.0549119	+	0.0821815i
$760$	−9.28745	+	13.4405i	−0.336891	+	0.487539i
$761$	−26.6120	+	26.6120i	−0.964686	+	0.964686i	−0.999397	−	0.0347114i	$-0.988949\pi$
$761$	−26.6120	+	26.6120i	−0.964686	+	0.964686i	0.0347114	+	0.999397i	$0.488949\pi$
$762$	−2.37983	−	11.9642i	−0.0862122	−	0.433418i
$763$	24.3600	−	10.0903i	0.881892	−	0.365292i
$764$	16.9726			0.614046
$765$	6.12643	−	6.88962i	0.221501	−	0.249095i
$766$	18.5236			0.669286
$767$	3.42691	−	1.41947i	0.123739	−	0.0512542i
$768$	−0.195090	−	0.980785i	−0.00703972	−	0.0353910i
$769$	22.9662	−	22.9662i	0.828184	−	0.828184i	−0.159081	−	0.987265i	$-0.550853\pi$
$769$	22.9662	−	22.9662i	0.828184	−	0.828184i	0.987265	+	0.159081i	$0.0508533\pi$
$770$	−0.497152	−	2.72070i	−0.0179161	−	0.0980473i
$771$	−3.68780	−	5.51918i	−0.132813	−	0.198768i
$772$	1.77252	−	1.18436i	0.0637942	−	0.0426259i
$773$	7.82039	−	18.8801i	0.281280	−	0.679070i	−0.718586	−	0.695438i	$-0.755210\pi$
$773$	7.82039	−	18.8801i	0.281280	−	0.679070i	0.999866	+	0.0163681i	$0.00521036\pi$
$774$	5.84859	−	2.42256i	0.210223	−	0.0870773i
$775$	43.5499	+	10.0857i	1.56436	+	0.362289i
$776$	−13.0448	+	8.71624i	−0.468280	+	0.312895i
$777$	−5.67051	−	3.78892i	−0.203429	−	0.135927i
$778$			5.46856i			0.196057i
$779$	22.9203	−	34.3027i	0.821205	−	1.22902i
$780$	−1.00277	+	2.31786i	−0.0359049	+	0.0829927i
$781$			4.65103i			0.166427i
$782$	−17.8737	+	9.00922i	−0.639162	+	0.322169i
$783$	0.141697	−	0.141697i	0.00506384	−	0.00506384i
$784$	1.97480	+	0.817990i	0.0705287	+	0.0292139i
$785$	−3.87435	−	21.2026i	−0.138281	−	0.756755i
$786$	−0.286595	−	0.286595i	−0.0102225	−	0.0102225i
$787$	−29.6368	+	44.3546i	−1.05644	+	1.58107i	−0.270548	+	0.962707i	$0.587205\pi$
$787$	−29.6368	+	44.3546i	−1.05644	+	1.58107i	−0.785891	+	0.618365i	$0.787795\pi$
$788$	−10.3286	−	2.05448i	−0.367941	−	0.0731879i
$789$	25.9792	+	5.16758i	0.924883	+	0.183971i
$790$	−29.4936	−	12.7597i	−1.04933	−	0.453971i
$791$	2.85540	+	6.89356i	0.101526	+	0.245107i
$792$	0.311629	+	0.466386i	0.0110732	+	0.0165723i
$793$	1.41128	−	7.09499i	0.0501160	−	0.251950i
$794$	5.23837	+	26.3351i	0.185903	+	0.934596i
$795$	−8.71240	+	8.44448i	−0.308997	+	0.299495i
$796$	15.9255	+	10.6411i	0.564464	+	0.377163i
$797$	−19.7299	−	47.6323i	−0.698870	−	1.68722i	−0.726096	−	0.687593i	$-0.758667\pi$
$797$	−19.7299	−	47.6323i	−0.698870	−	1.68722i	0.0272260	−	0.999629i	$-0.491333\pi$
$798$	−11.3922	−	11.3922i	−0.403279	−	0.403279i
$799$	−6.42904	+	1.78297i	−0.227443	+	0.0630769i
$800$	−3.42342	−	3.64420i	−0.121036	−	0.128842i
$801$	6.23617	−	15.0555i	0.220344	−	0.531958i
$802$	−35.2056	+	7.00283i	−1.24315	+	0.247279i
$803$	−9.01741			−0.318218
$804$	2.85730	−	0.568352i	0.100769	−	0.0200442i
$805$	20.1079	−	12.9861i	0.708709	−	0.457702i
$806$	−1.96995	+	9.90361i	−0.0693885	+	0.348840i
$807$	−16.5268	−	6.84560i	−0.581769	−	0.240977i
$808$	7.30465	+	3.02568i	0.256977	+	0.106443i
$809$	−5.73722	+	28.8430i	−0.201710	+	1.01406i	0.738703	+	0.674031i	$0.235439\pi$
$809$	−5.73722	+	28.8430i	−0.201710	+	1.01406i	−0.940413	+	0.340034i	$0.889561\pi$
$810$	0.470424	−	2.18602i	0.0165290	−	0.0768091i
$811$	−17.5282	+	3.48657i	−0.615497	+	0.122430i	−0.492986	−	0.870037i	$-0.664095\pi$
$811$	−17.5282	+	3.48657i	−0.615497	+	0.122430i	−0.122511	+	0.992467i	$0.539095\pi$
$812$	0.441881			0.0155070
$813$	−11.1655	+	2.22095i	−0.391591	+	0.0778923i
$814$	−0.663873	+	1.60273i	−0.0232687	+	0.0561757i
$815$	11.4083	−	11.0575i	0.399617	−	0.387328i
$816$	−3.68184	+	1.85582i	−0.128890	+	0.0649669i
$817$	32.7049	+	32.7049i	1.14420	+	1.14420i
$818$	3.74144	+	9.03264i	0.130816	+	0.315819i
$819$	−2.07078	−	1.38365i	−0.0723588	−	0.0483486i
$820$	8.78761	+	9.06641i	0.306877	+	0.316613i
$821$	−10.9299	−	54.9481i	−0.381454	−	1.91770i	−0.396993	−	0.917822i	$-0.629946\pi$
$821$	−10.9299	−	54.9481i	−0.381454	−	1.91770i	0.0155388	−	0.999879i	$-0.495054\pi$
$822$	−3.61914	+	18.1947i	−0.126232	+	0.634612i
$823$	−2.11412	−	3.16401i	−0.0736937	−	0.110290i	0.792792	−	0.609492i	$-0.208627\pi$
$823$	−2.11412	−	3.16401i	−0.0736937	−	0.110290i	−0.866486	+	0.499202i	$0.833627\pi$
$824$	−3.87958	−	9.36612i	−0.135151	−	0.326284i
$825$	2.55632	+	1.15365i	0.0889998	+	0.0401649i
$826$	−7.10286	−	1.41285i	−0.247140	−	0.0491592i
$827$	24.8160	+	4.93620i	0.862936	+	0.171649i	0.606666	−	0.794957i	$-0.292507\pi$
$827$	24.8160	+	4.93620i	0.862936	+	0.171649i	0.256270	+	0.966605i	$0.417507\pi$
$828$	−2.69705	+	4.03642i	−0.0937290	+	0.140275i
$829$	11.3419	+	11.3419i	0.393920	+	0.393920i	0.876082	−	0.482162i	$-0.160148\pi$
$829$	11.3419	+	11.3419i	0.393920	+	0.393920i	−0.482162	+	0.876082i	$0.660148\pi$
$830$	12.8465	−	18.5910i	0.445908	−	0.645304i
$831$	21.8046	+	9.03176i	0.756394	+	0.313308i
$832$	0.798625	−	0.798625i	0.0276873	−	0.0276873i
$833$	1.07401	−	8.74750i	0.0372121	−	0.303083i
$834$		−	9.63583i		−	0.333662i
$835$	1.35113	+	3.41164i	0.0467580	+	0.118065i
$836$	−2.27683	+	3.40751i	−0.0787457	+	0.117851i
$837$		−	8.94050i		−	0.309029i
$838$	−27.2016	−	18.1755i	−0.939663	−	0.627863i
$839$	−4.64900	+	3.10636i	−0.160501	+	0.107243i	−0.633227	−	0.773966i	$-0.718270\pi$
$839$	−4.64900	+	3.10636i	−0.160501	+	0.107243i	0.472726	+	0.881210i	$0.343270\pi$
$840$	4.14205	−	2.67504i	0.142914	−	0.0922976i
$841$	26.7554	−	11.0825i	0.922600	−	0.382154i
$842$	13.9390	−	33.6517i	0.480369	−	1.15971i
$843$	−1.40623	+	0.939615i	−0.0484332	+	0.0323621i
$844$	2.55647	+	3.82603i	0.0879974	+	0.131697i
$845$	25.7895	−	4.71250i	0.887187	−	0.162115i
$846$	−1.14419	+	1.14419i	−0.0393379	+	0.0393379i
$847$	4.59679	+	23.1096i	0.157948	+	0.794056i
$848$	5.01310	−	2.07650i	0.172151	−	0.0713071i
$849$	10.9111			0.374469
$850$	−10.7068	+	17.6172i	−0.367239	+	0.604265i
$851$	−15.0140			−0.514674
$852$	−7.66066	+	3.17315i	−0.262450	+	0.108710i
$853$	−9.16023	−	46.0516i	−0.313640	−	1.57678i	−0.740245	−	0.672337i	$-0.765290\pi$
$853$	−9.16023	−	46.0516i	−0.313640	−	1.57678i	0.426605	−	0.904438i	$-0.359710\pi$
$854$	−9.98698	+	9.98698i	−0.341747	+	0.341747i
$855$	16.0711	−	2.93666i	0.549620	−	0.100432i
$856$	−5.24023	−	7.84255i	−0.179107	−	0.268053i
$857$	18.0259	−	12.0445i	0.615752	−	0.411432i	−0.208205	−	0.978085i	$-0.566762\pi$
$857$	18.0259	−	12.0445i	0.615752	−	0.411432i	0.823957	+	0.566653i	$0.191762\pi$
$858$	−0.242436	+	0.585291i	−0.00827661	+	0.0199815i
$859$	−35.6766	+	14.7777i	−1.21727	+	0.504210i	−0.896541	−	0.442961i	$-0.853928\pi$
$859$	−35.6766	+	14.7777i	−1.21727	+	0.504210i	−0.320730	+	0.947171i	$0.603928\pi$
$860$	−11.8911	+	7.67957i	−0.405483	+	0.261871i
$861$	−10.3530	+	6.91763i	−0.352828	+	0.235752i
$862$	−9.54315	−	6.37653i	−0.325041	−	0.217185i
$863$			42.9670i			1.46261i	0.682049	+	0.731307i	$0.261089\pi$
$863$			42.9670i			1.46261i	−0.682049	+	0.731307i	$0.738911\pi$
$864$	−0.555570	+	0.831470i	−0.0189009	+	0.0282872i
$865$	−1.73050	−	4.36955i	−0.0588388	−	0.148569i
$866$			22.3083i			0.758067i
$867$	11.4304	+	12.5836i	0.388196	+	0.427361i
$868$	13.9404	−	13.9404i	0.473169	−	0.473169i
$869$	−7.44753	−	3.08487i	−0.252640	−	0.104647i
$870$	−0.254730	+	0.368637i	−0.00863615	+	0.0124980i
$871$	2.32662	+	2.32662i	0.0788344	+	0.0788344i
$872$	6.64312	−	9.94213i	0.224964	−	0.336683i
$873$	15.3874	+	3.06074i	0.520783	+	0.103590i
$874$	−34.7870	−	6.91956i	−1.17669	−	0.234058i
$875$	10.4908	−	22.3104i	0.354654	−	0.754229i
$876$	−6.15209	−	14.8525i	−0.207860	−	0.501818i
$877$	3.28151	+	4.91112i	0.110809	+	0.165837i	0.882729	−	0.469882i	$-0.155704\pi$
$877$	3.28151	+	4.91112i	0.110809	+	0.165837i	−0.771920	+	0.635719i	$0.780704\pi$
$878$	−3.19446	+	16.0597i	−0.107808	+	0.541987i
$879$	3.29229	+	16.5515i	0.111046	+	0.558267i
$880$	−0.872932	−	0.900627i	−0.0294265	−	0.0303601i
$881$	13.8863	+	9.27854i	0.467842	+	0.312602i	0.767052	−	0.641585i	$-0.221723\pi$
$881$	13.8863	+	9.27854i	0.467842	+	0.312602i	−0.299210	+	0.954187i	$0.596723\pi$
$882$	−0.817990	−	1.97480i	−0.0275432	−	0.0664951i
$883$	−9.80023	−	9.80023i	−0.329804	−	0.329804i	0.522708	−	0.852512i	$-0.324922\pi$
$883$	−9.80023	−	9.80023i	−0.329804	−	0.329804i	−0.852512	+	0.522708i	$0.824922\pi$
$884$	−4.05304	−	2.29307i	−0.136318	−	0.0771242i
$885$	5.27322	−	5.11107i	0.177257	−	0.171807i
$886$	5.30404	−	12.8051i	0.178193	−	0.430195i
$887$	−9.47636	+	1.88496i	−0.318185	+	0.0632909i	−0.351599	−	0.936151i	$-0.614362\pi$
$887$	−9.47636	+	1.88496i	−0.318185	+	0.0632909i	0.0334141	+	0.999442i	$0.489362\pi$
$888$	−3.09276			−0.103786
$889$	−26.3824	+	5.24778i	−0.884836	+	0.176005i
$890$	−7.66599	+	35.6232i	−0.256964	+	1.19409i
$891$	0.109430	−	0.550139i	0.00366603	−	0.0184304i
$892$	−24.4207	−	10.1154i	−0.817666	−	0.338688i
$893$	−10.9224	−	4.52422i	−0.365505	−	0.151397i
$894$	−0.783736	+	3.94011i	−0.0262121	+	0.131777i
$895$	−0.351240	+	0.226839i	−0.0117407	+	0.00758241i
$896$	−2.16273	+	0.430195i	−0.0722519	+	0.0143718i
$897$	−5.48287			−0.183068
$898$	−5.04341	+	1.00320i	−0.168301	+	0.0334771i
$899$	−0.685610	+	1.65521i	−0.0228664	+	0.0552043i
$900$	−0.156117	+	4.99756i	−0.00520388	+	0.166585i
$901$	−13.7740	−	17.6297i	−0.458879	−	0.587332i
$902$	2.23961	+	2.23961i	0.0745709	+	0.0745709i
$903$	−5.34201	−	12.8968i	−0.177771	−	0.429177i
$904$	2.81349	+	1.87991i	0.0935752	+	0.0625250i
$905$	4.11727	−	3.99066i	0.136863	−	0.132654i
$906$	2.38907	+	12.0107i	0.0793716	+	0.399028i
$907$	3.35673	−	16.8754i	0.111458	−	0.560339i	−0.884188	−	0.467131i	$-0.845288\pi$
$907$	3.35673	−	16.8754i	0.111458	−	0.560339i	0.995647	−	0.0932081i	$-0.0297122\pi$
$908$	2.25764	+	3.37880i	0.0749226	+	0.112130i
$909$	−3.02568	−	7.30465i	−0.100356	−	0.242280i
$910$	5.11112	+	2.21121i	0.169432	+	0.0733010i
$911$	−15.0105	−	2.98578i	−0.497321	−	0.0989232i	−0.0599442	−	0.998202i	$-0.519092\pi$
$911$	−15.0105	−	2.98578i	−0.497321	−	0.0989232i	−0.437376	+	0.899278i	$0.644092\pi$
$912$	−7.16583	−	1.42537i	−0.237284	−	0.0471988i
$913$	3.14933	−	4.71330i	0.104228	−	0.155988i
$914$	−17.1005	−	17.1005i	−0.565635	−	0.565635i
$915$	−2.57443	−	14.0888i	−0.0851080	−	0.465760i
$916$	1.53917	+	0.637547i	0.0508558	+	0.0210651i
$917$	−0.631972	+	0.631972i	−0.0208696	+	0.0208696i
$918$	3.91572	+	1.29118i	0.129238	+	0.0426154i
$919$			21.9450i			0.723900i	0.932197	+	0.361950i	$0.117889\pi$
$919$			21.9450i			0.723900i	−0.932197	+	0.361950i	$0.882111\pi$
$920$	4.31016	−	9.96275i	0.142102	−	0.328462i
$921$	3.01018	−	4.50505i	0.0991887	−	0.148446i
$922$			4.66953i			0.153783i
$923$	−7.78673	−	5.20292i	−0.256303	−	0.171256i
$924$	1.02843	−	0.687174i	0.0338328	−	0.0226064i
$925$	−13.1197	+	8.18559i	−0.431372	+	0.269140i
$926$	15.2431	−	6.31389i	0.500919	−	0.207487i
$927$	−3.87958	+	9.36612i	−0.127422	+	0.307624i
$928$	0.166618	−	0.111331i	0.00546951	−	0.00365461i
$929$	−16.3244	−	24.4312i	−0.535586	−	0.801561i	0.460710	−	0.887551i	$-0.347595\pi$
$929$	−16.3244	−	24.4312i	−0.535586	−	0.801561i	−0.996296	+	0.0859899i	$0.972595\pi$
$930$	3.59354	+	19.6659i	0.117837	+	0.644871i
$931$	11.0430	−	11.0430i	0.361919	−	0.361919i
$932$	−2.28628	−	11.4939i	−0.0748894	−	0.376495i
$933$	27.3675	−	11.3360i	0.895971	−	0.371123i
$934$	21.2844			0.696445
$935$	−2.61646	+	4.46066i	−0.0855674	+	0.145879i
$936$	−1.12943			−0.0369165
$937$	−27.2251	+	11.2770i	−0.889405	+	0.368404i	−0.780137	−	0.625609i	$-0.784851\pi$
$937$	−27.2251	+	11.2770i	−0.889405	+	0.368404i	−0.109268	+	0.994012i	$0.534851\pi$
$938$	−1.25328	−	6.30065i	−0.0409209	−	0.205723i
$939$	−14.6731	+	14.6731i	−0.478837	+	0.478837i
$940$	2.05691	−	2.97670i	0.0670890	−	0.0970892i
$941$	−11.9648	−	17.9066i	−0.390041	−	0.583738i	0.583539	−	0.812085i	$-0.301668\pi$
$941$	−11.9648	−	17.9066i	−0.390041	−	0.583738i	−0.973580	+	0.228348i	$0.926668\pi$
$942$	8.01463	−	5.35521i	0.261131	−	0.174482i
$943$	−10.4901	+	25.3253i	−0.341604	+	0.824705i
$944$	−3.03421	+	1.25681i	−0.0987550	+	0.0409057i
$945$	−4.82041	−	1.03733i	−0.156808	−	0.0337445i
$946$	−2.95244	+	1.97276i	−0.0959920	+	0.0641398i
$947$	−7.21991	−	4.82419i	−0.234616	−	0.156765i	0.432705	−	0.901535i	$-0.357559\pi$
$947$	−7.21991	−	4.82419i	−0.234616	−	0.156765i	−0.667321	+	0.744770i	$0.732559\pi$
$948$		−	14.3714i		−	0.466760i
$949$	10.0874	−	15.0969i	0.327452	−	0.490066i
$950$	−34.1704	+	12.9192i	−1.10863	+	0.419155i
$951$		−	8.41064i		−	0.272734i
$952$	4.09229	+	8.11883i	0.132632	+	0.263133i
$953$	−4.83316	+	4.83316i	−0.156561	+	0.156561i	−0.781041	−	0.624480i	$-0.785311\pi$
$953$	−4.83316	+	4.83316i	−0.156561	+	0.156561i	0.624480	+	0.781041i	$0.285311\pi$
$954$	−5.01310	−	2.07650i	−0.162305	−	0.0672290i
$955$	31.2227	+	21.5750i	1.01034	+	0.698152i
$956$	5.01656	+	5.01656i	0.162247	+	0.162247i
$957$	−0.0624473	+	0.0934590i	−0.00201863	+	0.00302110i
$958$	27.2404	+	5.41846i	0.880099	+	0.175063i
$959$	40.1212	+	7.98059i	1.29558	+	0.257707i
$960$	0.887857	−	2.05224i	0.0286555	−	0.0662359i
$961$	18.7256	+	45.2077i	0.604053	+	1.45831i
$962$	−1.94063	−	2.90436i	−0.0625685	−	0.0936404i
$963$	−1.84012	+	9.25092i	−0.0592971	+	0.298107i
$964$	−1.20664	−	6.06621i	−0.0388634	−	0.195379i
$965$	4.76624	+	0.0744270i	0.153431	+	0.00239589i
$966$	8.90073	+	5.94728i	0.286376	+	0.191351i
$967$	−6.69730	−	16.1687i	−0.215371	−	0.519951i	0.778862	−	0.627195i	$-0.215797\pi$
$967$	−6.69730	−	16.1687i	−0.215371	−	0.519951i	−0.994233	+	0.107245i	$0.965797\pi$
$968$	7.55570	+	7.55570i	0.242849	+	0.242849i
$969$	2.23264	+	30.0415i	0.0717228	+	0.965070i
$970$	−35.0770	−	0.547743i	−1.12625	−	0.0175870i
$971$	22.4721	−	54.2523i	0.721162	−	1.74104i	0.0511494	−	0.998691i	$-0.483712\pi$
$971$	22.4721	−	54.2523i	0.721162	−	1.74104i	0.670013	−	0.742349i	$-0.266288\pi$
$972$	0.980785	−	0.195090i	0.0314587	−	0.00625752i
$973$	−21.2480			−0.681180
$974$	−12.9031	+	2.56658i	−0.413440	+	0.0822384i
$975$	−4.79109	+	2.98924i	−0.153438	+	0.0957324i
$976$	−1.24956	+	6.28194i	−0.0399973	+	0.201080i
$977$	40.7450	+	16.8771i	1.30355	+	0.539947i	0.922995	−	0.384813i	$-0.125734\pi$
$977$	40.7450	+	16.8771i	1.30355	+	0.539947i	0.380552	+	0.924759i	$0.375734\pi$
$978$	6.56435	+	2.71904i	0.209905	+	0.0869454i
$979$	−1.78325	+	8.96502i	−0.0569930	+	0.286523i
$980$	2.59304	+	4.01509i	0.0828317	+	0.128257i
$981$	−11.7275	+	2.33275i	−0.374432	+	0.0744791i
$982$	−39.8816			−1.27267
$983$	−58.5989	+	11.6561i	−1.86902	+	0.371770i	−0.993727	−	0.111830i	$-0.964329\pi$
$983$	−58.5989	+	11.6561i	−1.86902	+	0.371770i	−0.875289	+	0.483601i	$0.839329\pi$
$984$	−2.16087	+	5.21680i	−0.0688860	+	0.166306i
$985$	−16.3889	−	16.9088i	−0.522192	−	0.538760i
$986$	−0.625925	−	0.539325i	−0.0199335	−	0.0171756i
$987$	2.52305	+	2.52305i	0.0803096	+	0.0803096i
$988$	−3.15784	−	7.62370i	−0.100464	−	0.242542i
$989$	−25.5524	−	17.0736i	−0.812520	−	0.542908i
$990$	−0.0195833	+	1.25410i	−0.000622398	+	0.0398578i
$991$	−2.76683	−	13.9098i	−0.0878913	−	0.441859i	−0.999524	−	0.0308533i	$-0.990178\pi$
$991$	−2.76683	−	13.9098i	−0.0878913	−	0.441859i	0.911633	−	0.411006i	$-0.134822\pi$
$992$	1.74420	−	8.76871i	0.0553785	−	0.278407i
$993$	−16.6315	−	24.8908i	−0.527785	−	0.789886i
$994$	6.99712	+	16.8925i	0.221935	+	0.535799i
$995$	15.7699	+	39.8193i	0.499939	+	1.26236i
$996$	9.91184	+	1.97159i	0.314069	+	0.0624721i
$997$	47.6243	+	9.47306i	1.50828	+	0.300015i	0.878870	−	0.477061i	$-0.158298\pi$
$997$	47.6243	+	9.47306i	1.50828	+	0.300015i	0.629406	+	0.777076i	$0.283298\pi$
$998$	7.23062	−	10.8214i	0.228881	−	0.342545i
$999$	2.18691	+	2.18691i	0.0691909	+	0.0691909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.bd.a.7.8	✓	64
5.3	odd	4		510.2.bi.a.313.1	yes	64
17.5	odd	16		510.2.bi.a.277.1	yes	64
85.73	even	16	inner	510.2.bd.a.73.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.bd.a.7.8	✓	64	1.1	even	1	trivial
510.2.bd.a.73.8	yes	64	85.73	even	16	inner
510.2.bi.a.277.1	yes	64	17.5	odd	16
510.2.bi.a.313.1	yes	64	5.3	odd	4

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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 - 0.382683i) q^{2} +(0.195090 + 0.980785i) q^{3} +(0.707107 - 0.707107i) q^{4} +(2.19965 - 0.401940i) q^{5} +(0.555570 + 0.831470i) q^{6} +(1.83348 - 1.22509i) q^{7} +(0.382683 - 0.923880i) q^{8} +(-0.923880 + 0.382683i) q^{9} +(1.87839 - 1.21311i) q^{10} +(0.466386 - 0.311629i) q^{11} +(0.831470 + 0.555570i) q^{12} +1.12943i q^{13} +(1.22509 - 1.83348i) q^{14} +(0.823346 + 2.07897i) q^{15} -1.00000i q^{16} +(-3.97314 + 1.10188i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-6.75006 - 2.79597i) q^{19} +(1.27117 - 1.83960i) q^{20} +(1.55924 + 1.55924i) q^{21} +(0.311629 - 0.466386i) q^{22} +(4.76128 + 0.947078i) q^{23} +(0.980785 + 0.195090i) q^{24} +(4.67689 - 1.76825i) q^{25} +(0.432213 + 1.04345i) q^{26} +(-0.555570 - 0.831470i) q^{27} +(0.430195 - 2.16273i) q^{28} +(0.0390941 + 0.196540i) q^{29} +(1.55626 + 1.60563i) q^{30} +(7.43375 + 4.96707i) q^{31} +(-0.382683 - 0.923880i) q^{32} +(0.396628 + 0.396628i) q^{33} +(-3.24904 + 2.53846i) q^{34} +(3.54059 - 3.43171i) q^{35} +(-0.382683 + 0.923880i) q^{36} +(-3.03334 + 0.603368i) q^{37} -7.30622 q^{38} +(-1.10772 + 0.220340i) q^{39} +(0.470424 - 2.18602i) q^{40} +(-1.10160 + 5.53813i) q^{41} +(2.03725 + 0.843857i) q^{42} +(-5.84859 - 2.42256i) q^{43} +(0.109430 - 0.550139i) q^{44} +(-1.87839 + 1.21311i) q^{45} +(4.76128 - 0.947078i) q^{46} +1.61812 q^{47} +(0.980785 - 0.195090i) q^{48} +(-0.817990 + 1.97480i) q^{49} +(3.64420 - 3.42342i) q^{50} +(-1.85582 - 3.68184i) q^{51} +(0.798625 + 0.798625i) q^{52} +(2.07650 + 5.01310i) q^{53} +(-0.831470 - 0.555570i) q^{54} +(0.900627 - 0.872932i) q^{55} +(-0.430195 - 2.16273i) q^{56} +(1.42537 - 7.16583i) q^{57} +(0.111331 + 0.166618i) q^{58} +(-1.25681 - 3.03421i) q^{59} +(2.05224 + 0.887857i) q^{60} +(-6.28194 - 1.24956i) q^{61} +(8.76871 + 1.74420i) q^{62} +(-1.22509 + 1.83348i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(0.453962 + 2.48434i) q^{65} +(0.518220 + 0.214654i) q^{66} +(2.06000 - 2.06000i) q^{67} +(-2.03029 + 3.58858i) q^{68} +4.85456i q^{69} +(1.95782 - 4.52542i) q^{70} +(-4.60670 + 6.89441i) q^{71} +1.00000i q^{72} +(-13.3669 - 8.93145i) q^{73} +(-2.57154 + 1.71825i) q^{74} +(2.64669 + 4.24205i) q^{75} +(-6.75006 + 2.79597i) q^{76} +(0.473334 - 1.14273i) q^{77} +(-0.939084 + 0.627476i) q^{78} +(-7.98431 - 11.9494i) q^{79} +(-0.401940 - 2.19965i) q^{80} +(0.707107 - 0.707107i) q^{81} +(1.10160 + 5.53813i) q^{82} +(9.33675 - 3.86741i) q^{83} +2.20511 q^{84} +(-8.29662 + 4.02070i) q^{85} -6.33047 q^{86} +(-0.185136 + 0.0766859i) q^{87} +(-0.109430 - 0.550139i) q^{88} +(-11.5229 + 11.5229i) q^{89} +(-1.27117 + 1.83960i) q^{90} +(1.38365 + 2.07078i) q^{91} +(4.03642 - 2.69705i) q^{92} +(-3.42138 + 8.25994i) q^{93} +(1.49495 - 0.619229i) q^{94} +(-15.9716 - 3.43702i) q^{95} +(0.831470 - 0.555570i) q^{96} +(-13.0448 - 8.71624i) q^{97} +2.13751i q^{98} +(-0.311629 + 0.466386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 16 q^{15} + 16 q^{20} + 16 q^{25} - 16 q^{28} + 32 q^{29} + 16 q^{31} + 16 q^{33} + 32 q^{35} - 16 q^{37} - 16 q^{40} + 48 q^{41} + 16 q^{44} + 32 q^{47} - 64 q^{49} - 16 q^{50} + 32 q^{51} + 16 q^{52}+ \cdots - 80 q^{97}+O(q^{100}) \) 64 * q - 16 * q^15 + 16 * q^20 + 16 * q^25 - 16 * q^28 + 32 * q^29 + 16 * q^31 + 16 * q^33 + 32 * q^35 - 16 * q^37 - 16 * q^40 + 48 * q^41 + 16 * q^44 + 32 * q^47 - 64 * q^49 - 16 * q^50 + 32 * q^51 + 16 * q^52 + 80 * q^53 - 16 * q^55 + 16 * q^56 - 32 * q^57 + 64 * q^59 - 48 * q^61 + 32 * q^65 + 16 * q^67 - 48 * q^68 - 64 * q^71 + 16 * q^73 + 48 * q^74 - 32 * q^75 - 80 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 48 * q^82 - 32 * q^83 - 16 * q^85 - 64 * q^86 - 32 * q^87 - 16 * q^88 - 32 * q^89 - 16 * q^90 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 112 * q^95 - 80 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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