LMFDB - Embedded newform 170.2.r.a.23.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [170,2,Mod(23,170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("170.23"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(170, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([12, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.r (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	170.23
Dual form			170.2.r.a.37.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.923880 + 0.382683i) q^{2} +(2.33925 + 1.56304i) q^{3} +(0.707107 - 0.707107i) q^{4} +(0.438207 + 2.19271i) q^{5} +(-2.75933 - 0.548865i) q^{6} +(-1.27851 - 0.254312i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(1.88095 + 4.54102i) q^{9} +(-1.24396 - 1.85810i) q^{10} +(1.14054 - 5.73386i) q^{11} +(2.75933 - 0.548865i) q^{12} -5.33794 q^{13} +(1.27851 - 0.254312i) q^{14} +(-2.40221 + 5.81423i) q^{15} -1.00000i q^{16} +(3.93717 - 1.22423i) q^{17} +(-3.47555 - 3.47555i) q^{18} +(0.311731 - 0.752584i) q^{19} +(1.86034 + 1.24062i) q^{20} +(-2.59326 - 2.59326i) q^{21} +(1.14054 + 5.73386i) q^{22} +(3.88994 + 5.82170i) q^{23} +(-2.33925 + 1.56304i) q^{24} +(-4.61595 + 1.92172i) q^{25} +(4.93161 - 2.04274i) q^{26} +(-1.05117 + 5.28458i) q^{27} +(-1.08387 + 0.724218i) q^{28} +(1.17050 - 1.75178i) q^{29} +(-0.00565639 - 6.29093i) q^{30} +(0.301321 + 1.51484i) q^{31} +(0.382683 + 0.923880i) q^{32} +(11.6302 - 11.6302i) q^{33} +(-3.16897 + 2.63773i) q^{34} +(-0.00262084 - 2.91484i) q^{35} +(4.54102 + 1.88095i) q^{36} +(3.87014 - 5.79208i) q^{37} +0.814591i q^{38} +(-12.4868 - 8.34339i) q^{39} +(-2.19349 - 0.434263i) q^{40} +(-4.40455 - 6.59188i) q^{41} +(3.38825 + 1.40346i) q^{42} +(-1.31384 - 0.544211i) q^{43} +(-3.24797 - 4.86093i) q^{44} +(-9.13290 + 6.11429i) q^{45} +(-5.82170 - 3.88994i) q^{46} +0.109944i q^{47} +(1.56304 - 2.33925i) q^{48} +(-4.89724 - 2.02850i) q^{49} +(3.52917 - 3.54189i) q^{50} +(11.1235 + 3.29016i) q^{51} +(-3.77449 + 3.77449i) q^{52} +(0.379151 + 0.915351i) q^{53} +(-1.05117 - 5.28458i) q^{54} +(13.0725 - 0.0117539i) q^{55} +(0.724218 - 1.08387i) q^{56} +(1.90553 - 1.27324i) q^{57} +(-0.411026 + 2.06637i) q^{58} +(5.08359 - 2.10569i) q^{59} +(2.41266 + 5.80990i) q^{60} +(-4.82682 + 3.22518i) q^{61} +(-0.858089 - 1.28422i) q^{62} +(-1.24998 - 6.28410i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(-2.33912 - 11.7045i) q^{65} +(-6.29423 + 15.1956i) q^{66} +(4.12405 + 4.12405i) q^{67} +(1.91834 - 3.64966i) q^{68} +19.6985i q^{69} +(1.11788 + 2.69196i) q^{70} +(-5.38952 + 1.07204i) q^{71} -4.91517 q^{72} +(-8.02579 + 1.59643i) q^{73} +(-1.35901 + 6.83222i) q^{74} +(-13.8016 - 2.71951i) q^{75} +(-0.311731 - 0.752584i) q^{76} +(-2.91637 + 7.04075i) q^{77} +(14.7291 + 2.92981i) q^{78} +(5.01247 + 0.997043i) q^{79} +(2.19271 - 0.438207i) q^{80} +(-0.292298 + 0.292298i) q^{81} +(6.59188 + 4.40455i) q^{82} +(-2.38399 + 0.987480i) q^{83} -3.66742 q^{84} +(4.40967 + 8.09659i) q^{85} +1.42209 q^{86} +(5.47620 - 2.26832i) q^{87} +(4.86093 + 3.24797i) q^{88} +(-0.779290 + 0.779290i) q^{89} +(6.09786 - 9.14388i) q^{90} +(6.82461 + 1.35750i) q^{91} +(6.86717 + 1.36596i) q^{92} +(-1.66289 + 4.01457i) q^{93} +(-0.0420738 - 0.101575i) q^{94} +(1.78680 + 0.353747i) q^{95} +(-0.548865 + 2.75933i) q^{96} +(-14.7649 + 2.93692i) q^{97} +5.30073 q^{98} +(28.1829 - 5.60592i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{10} - 48 q^{15} + 16 q^{18} - 24 q^{25} + 8 q^{26} + 24 q^{27} - 8 q^{28} - 8 q^{29} - 16 q^{30} - 16 q^{31} + 64 q^{33} + 24 q^{34} + 32 q^{35} - 32 q^{37} - 32 q^{39} + 16 q^{41} - 24 q^{42}+ \cdots - 64 q^{99}+O(q^{100}) $ 32 * q - 8 * q^10 - 48 * q^15 + 16 * q^18 - 24 * q^25 + 8 * q^26 + 24 * q^27 - 8 * q^28 - 8 * q^29 - 16 * q^30 - 16 * q^31 + 64 * q^33 + 24 * q^34 + 32 * q^35 - 32 * q^37 - 32 * q^39 + 16 * q^41 - 24 * q^42 - 16 * q^43 - 16 * q^44 - 24 * q^45 - 16 * q^49 - 32 * q^50 + 32 * q^51 - 16 * q^52 + 16 * q^53 + 24 * q^54 - 8 * q^55 + 8 * q^56 - 24 * q^57 - 16 * q^58 - 64 * q^59 + 40 * q^60 - 24 * q^61 - 40 * q^62 - 24 * q^63 + 32 * q^65 + 16 * q^67 + 40 * q^70 + 8 * q^71 - 16 * q^72 + 32 * q^73 + 8 * q^74 - 56 * q^75 + 24 * q^77 + 32 * q^78 + 72 * q^79 + 8 * q^80 + 48 * q^81 + 48 * q^82 + 16 * q^83 + 8 * q^85 - 64 * q^86 + 40 * q^87 + 32 * q^88 + 16 * q^89 + 24 * q^90 + 48 * q^91 + 24 * q^92 - 8 * q^93 + 8 * q^94 + 56 * q^95 - 48 * q^97 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.923880	+	0.382683i	−0.653281	+	0.270598i
$2$	−0.923880	+	0.382683i	−0.653281	+	0.270598i
$3$	2.33925	+	1.56304i	1.35057	+	0.902419i	0.999425	−	0.0339033i	$-0.0107938\pi$
$3$	2.33925	+	1.56304i	1.35057	+	0.902419i	0.351141	+	0.936323i	$0.385794\pi$
$4$	0.707107	−	0.707107i	0.353553	−	0.353553i
$5$	0.438207	+	2.19271i	0.195972	+	0.980609i
$5$	0.438207	+	2.19271i	0.195972	+	0.980609i
$6$	−2.75933	−	0.548865i	−1.12649	−	0.224073i
$7$	−1.27851	−	0.254312i	−0.483232	−	0.0961208i	−0.0525381	−	0.998619i	$-0.516731\pi$
$7$	−1.27851	−	0.254312i	−0.483232	−	0.0961208i	−0.430694	+	0.902498i	$0.641731\pi$
$8$	−0.382683	+	0.923880i	−0.135299	+	0.326641i
$9$	1.88095	+	4.54102i	0.626984	+	1.51367i
$10$	−1.24396	−	1.85810i	−0.393376	−	0.587584i
$11$	1.14054	−	5.73386i	0.343884	−	1.72882i	−0.291450	−	0.956586i	$-0.594138\pi$
$11$	1.14054	−	5.73386i	0.343884	−	1.72882i	0.635335	−	0.772237i	$-0.280862\pi$
$12$	2.75933	−	0.548865i	0.796551	−	0.158444i
$13$	−5.33794			−1.48048			−0.740239	−	0.672344i	$-0.765288\pi$
$13$	−5.33794			−1.48048			−0.740239	+	0.672344i	$0.765288\pi$
$14$	1.27851	−	0.254312i	0.341696	−	0.0679677i
$15$	−2.40221	+	5.81423i	−0.620248	+	1.50123i
$16$		−	1.00000i		−	0.250000i
$17$	3.93717	−	1.22423i	0.954903	−	0.296919i
$17$	3.93717	−	1.22423i	0.954903	−	0.296919i
$18$	−3.47555	−	3.47555i	−0.819195	−	0.819195i
$19$	0.311731	−	0.752584i	0.0715159	−	0.172655i	−0.884080	−	0.467336i	$-0.845214\pi$
$19$	0.311731	−	0.752584i	0.0715159	−	0.172655i	0.955595	+	0.294682i	$0.0952137\pi$
$20$	1.86034	+	1.24062i	0.415984	+	0.277411i
$21$	−2.59326	−	2.59326i	−0.565895	−	0.565895i
$22$	1.14054	+	5.73386i	0.243163	+	1.22246i
$23$	3.88994	+	5.82170i	0.811108	+	1.21391i	0.973839	+	0.227239i	$0.0729697\pi$
$23$	3.88994	+	5.82170i	0.811108	+	1.21391i	−0.162731	+	0.986670i	$0.552030\pi$
$24$	−2.33925	+	1.56304i	−0.477497	+	0.319053i
$25$	−4.61595	+	1.92172i	−0.923190	+	0.384344i
$26$	4.93161	−	2.04274i	0.967168	−	0.400614i
$27$	−1.05117	+	5.28458i	−0.202298	+	1.01702i
$28$	−1.08387	+	0.724218i	−0.204832	+	0.136864i
$29$	1.17050	−	1.75178i	0.217357	−	0.325298i	−0.706727	−	0.707486i	$-0.749829\pi$
$29$	1.17050	−	1.75178i	0.217357	−	0.325298i	0.924085	+	0.382188i	$0.124829\pi$
$30$	−0.00565639	−	6.29093i	−0.00103271	−	1.14856i
$31$	0.301321	+	1.51484i	0.0541188	+	0.272074i	0.998365	−	0.0571677i	$-0.0182070\pi$
$31$	0.301321	+	1.51484i	0.0541188	+	0.272074i	−0.944246	+	0.329241i	$0.893207\pi$
$32$	0.382683	+	0.923880i	0.0676495	+	0.163320i
$33$	11.6302	−	11.6302i	2.02456	−	2.02456i
$34$	−3.16897	+	2.63773i	−0.543475	+	0.452366i
$35$	−0.00262084	−	2.91484i	−0.000443002	−	0.492699i
$36$	4.54102	+	1.88095i	0.756837	+	0.313492i
$37$	3.87014	−	5.79208i	0.636248	−	0.952212i	−0.363539	−	0.931579i	$-0.618432\pi$
$37$	3.87014	−	5.79208i	0.636248	−	0.952212i	0.999787	−	0.0206333i	$-0.00656823\pi$
$38$			0.814591i			0.132144i
$39$	−12.4868	−	8.34339i	−1.99948	−	1.33601i
$40$	−2.19349	−	0.434263i	−0.346822	−	0.0686630i
$41$	−4.40455	−	6.59188i	−0.687876	−	1.02948i	−0.996920	−	0.0784311i	$-0.975009\pi$
$41$	−4.40455	−	6.59188i	−0.687876	−	1.02948i	0.309044	−	0.951048i	$-0.399991\pi$
$42$	3.38825	+	1.40346i	0.522819	+	0.216559i
$43$	−1.31384	−	0.544211i	−0.200359	−	0.0829914i	0.280248	−	0.959928i	$-0.409583\pi$
$43$	−1.31384	−	0.544211i	−0.200359	−	0.0829914i	−0.480607	+	0.876936i	$0.659583\pi$
$44$	−3.24797	−	4.86093i	−0.489650	−	0.732813i
$45$	−9.13290	+	6.11429i	−1.36145	+	0.911465i
$46$	−5.82170	−	3.88994i	−0.858363	−	0.573540i
$47$			0.109944i			0.0160370i	0.999968	+	0.00801850i	$0.00255240\pi$
$47$			0.109944i			0.0160370i	−0.999968	+	0.00801850i	$0.997448\pi$
$48$	1.56304	−	2.33925i	0.225605	−	0.337642i
$49$	−4.89724	−	2.02850i	−0.699606	−	0.289786i
$50$	3.52917	−	3.54189i	0.499100	−	0.500898i
$51$	11.1235	+	3.29016i	1.55760	+	0.460715i
$52$	−3.77449	+	3.77449i	−0.523428	+	0.523428i
$53$	0.379151	+	0.915351i	0.0520804	+	0.125733i	0.947778	−	0.318930i	$-0.103323\pi$
$53$	0.379151	+	0.915351i	0.0520804	+	0.125733i	−0.895698	+	0.444663i	$0.853323\pi$
$54$	−1.05117	−	5.28458i	−0.143046	−	0.719141i
$55$	13.0725	−	0.0117539i	1.76269	−	0.00158490i
$56$	0.724218	−	1.08387i	0.0967778	−	0.144838i
$57$	1.90553	−	1.27324i	0.252394	−	0.168644i
$58$	−0.411026	+	2.06637i	−0.0539704	+	0.271328i
$59$	5.08359	−	2.10569i	0.661827	−	0.274138i	−0.0263799	−	0.999652i	$-0.508398\pi$
$59$	5.08359	−	2.10569i	0.661827	−	0.274138i	0.688207	+	0.725514i	$0.258398\pi$
$60$	2.41266	+	5.80990i	0.311473	+	0.750055i
$61$	−4.82682	+	3.22518i	−0.618011	+	0.412942i	−0.824785	−	0.565447i	$-0.808704\pi$
$61$	−4.82682	+	3.22518i	−0.618011	+	0.412942i	0.206774	+	0.978389i	$0.433704\pi$
$62$	−0.858089	−	1.28422i	−0.108977	−	0.163096i
$63$	−1.24998	−	6.28410i	−0.157483	−	0.791722i
$64$	−0.707107	−	0.707107i	−0.0883883	−	0.0883883i
$65$	−2.33912	−	11.7045i	−0.290132	−	1.45177i
$66$	−6.29423	+	15.1956i	−0.774766	+	1.87045i
$67$	4.12405	+	4.12405i	0.503833	+	0.503833i	0.912627	−	0.408794i	$-0.134050\pi$
$67$	4.12405	+	4.12405i	0.503833	+	0.503833i	−0.408794	+	0.912627i	$0.634050\pi$
$68$	1.91834	−	3.64966i	0.232633	−	0.442586i
$69$			19.6985i			2.37142i
$70$	1.11788	+	2.69196i	0.133613	+	0.321751i
$71$	−5.38952	+	1.07204i	−0.639618	+	0.127228i	−0.504237	−	0.863566i	$-0.668226\pi$
$71$	−5.38952	+	1.07204i	−0.639618	+	0.127228i	−0.135382	+	0.990794i	$0.543226\pi$
$72$	−4.91517			−0.579258
$73$	−8.02579	+	1.59643i	−0.939348	+	0.186848i	−0.640940	−	0.767591i	$-0.721455\pi$
$73$	−8.02579	+	1.59643i	−0.939348	+	0.186848i	−0.298407	+	0.954439i	$0.596455\pi$
$74$	−1.35901	+	6.83222i	−0.157982	+	0.794230i
$75$	−13.8016	−	2.71951i	−1.59367	−	0.314022i
$76$	−0.311731	−	0.752584i	−0.0357580	−	0.0863273i
$77$	−2.91637	+	7.04075i	−0.332352	+	0.802368i
$78$	14.7291	+	2.92981i	1.66775	+	0.331736i
$79$	5.01247	+	0.997043i	0.563947	+	0.112176i	0.468828	−	0.883290i	$-0.344677\pi$
$79$	5.01247	+	0.997043i	0.563947	+	0.112176i	0.0951198	+	0.995466i	$0.469677\pi$
$80$	2.19271	−	0.438207i	0.245152	−	0.0489930i
$81$	−0.292298	+	0.292298i	−0.0324776	+	0.0324776i
$82$	6.59188	+	4.40455i	0.727952	+	0.486402i
$83$	−2.38399	+	0.987480i	−0.261677	+	0.108390i	−0.509665	−	0.860373i	$-0.670231\pi$
$83$	−2.38399	+	0.987480i	−0.261677	+	0.108390i	0.247988	+	0.968763i	$0.420231\pi$
$84$	−3.66742			−0.400148
$85$	4.40967	+	8.09659i	0.478296	+	0.878199i
$86$	1.42209			0.153348
$87$	5.47620	−	2.26832i	0.587110	−	0.243189i
$88$	4.86093	+	3.24797i	0.518177	+	0.346235i
$89$	−0.779290	+	0.779290i	−0.0826045	+	0.0826045i	−0.747202	−	0.664597i	$-0.768603\pi$
$89$	−0.779290	+	0.779290i	−0.0826045	+	0.0826045i	0.664597	+	0.747202i	$0.268603\pi$
$90$	6.09786	−	9.14388i	0.642771	−	0.963849i
$91$	6.82461	+	1.35750i	0.715414	+	0.142305i
$92$	6.86717	+	1.36596i	0.715952	+	0.142412i
$93$	−1.66289	+	4.01457i	−0.172434	+	0.416291i
$94$	−0.0420738	−	0.101575i	−0.00433958	−	0.0104767i
$95$	1.78680	+	0.353747i	0.183322	+	0.0362937i
$96$	−0.548865	+	2.75933i	−0.0560183	+	0.281623i
$97$	−14.7649	+	2.93692i	−1.49915	+	0.298199i	−0.875389	−	0.483418i	$-0.839395\pi$
$97$	−14.7649	+	2.93692i	−1.49915	+	0.298199i	−0.623758	+	0.781617i	$0.714395\pi$
$98$	5.30073			0.535455
$99$	28.1829	−	5.60592i	2.83249	−	0.563416i
$100$	−1.90511	+	4.62283i	−0.190511	+	0.462283i
$101$			6.75581i			0.672228i	0.941821	+	0.336114i	$0.109113\pi$
$101$			6.75581i			0.672228i	−0.941821	+	0.336114i	$0.890887\pi$
$102$	−11.5359	+	1.21708i	−1.14222	+	0.120508i
$103$	−4.75400	−	4.75400i	−0.468426	−	0.468426i	0.432978	−	0.901404i	$-0.357463\pi$
$103$	−4.75400	−	4.75400i	−0.468426	−	0.468426i	−0.901404	+	0.432978i	$0.857463\pi$
$104$	2.04274	−	4.93161i	0.200307	−	0.483584i
$105$	4.54988	−	6.82264i	0.444023	−	0.665822i
$106$	−0.700579	−	0.700579i	−0.0680463	−	0.0680463i
$107$	3.26275	+	16.4030i	0.315422	+	1.58573i	0.735033	+	0.678031i	$0.237166\pi$
$107$	3.26275	+	16.4030i	0.315422	+	1.58573i	−0.419611	+	0.907704i	$0.637834\pi$
$108$	2.99348	+	4.48005i	0.288047	+	0.431093i
$109$	2.02154	−	1.35075i	0.193628	−	0.129378i	−0.454977	−	0.890503i	$-0.650353\pi$
$109$	2.02154	−	1.35075i	0.193628	−	0.129378i	0.648605	+	0.761125i	$0.275353\pi$
$110$	−12.0729	+	5.01348i	−1.15111	+	0.478016i
$111$	18.1065	−	7.49994i	1.71859	−	0.711863i
$112$	−0.254312	+	1.27851i	−0.0240302	+	0.120808i
$113$	−9.40688	+	6.28548i	−0.884925	+	0.591288i	−0.912838	−	0.408322i	$-0.866114\pi$
$113$	−9.40688	+	6.28548i	−0.884925	+	0.591288i	0.0279127	+	0.999610i	$0.491114\pi$
$114$	−1.27324	+	1.90553i	−0.119249	+	0.178469i
$115$	−11.0607	+	11.0806i	−1.03142	+	1.03327i
$116$	−0.411026	−	2.06637i	−0.0381628	−	0.191858i
$117$	−10.0404	−	24.2397i	−0.928236	−	2.24096i
$118$	−3.89081	+	3.89081i	−0.358178	+	0.358178i
$119$	−5.34504	+	0.563921i	−0.489979	+	0.0516945i
$120$	−4.45236	−	4.44436i	−0.406443	−	0.405713i
$121$	−21.4136	−	8.86981i	−1.94669	−	0.806347i
$122$	3.22518	−	4.82682i	0.291994	−	0.437000i
$123$		−	22.3045i		−	2.01113i
$124$	1.28422	+	0.858089i	0.115326	+	0.0770587i
$125$	−6.23652	−	9.27932i	−0.557811	−	0.829968i
$126$	3.55966	+	5.32740i	0.317119	+	0.474603i
$127$	−3.29207	−	1.36362i	−0.292124	−	0.121002i	0.231809	−	0.972761i	$-0.425536\pi$
$127$	−3.29207	−	1.36362i	−0.292124	−	0.121002i	−0.523933	+	0.851760i	$0.675536\pi$
$128$	0.923880	+	0.382683i	0.0816602	+	0.0338248i
$129$	−2.22278	−	3.32663i	−0.195705	−	0.292893i
$130$	6.64020	+	9.91845i	0.582384	+	0.869905i
$131$	9.80467	+	6.55127i	0.856638	+	0.572387i	0.904503	−	0.426467i	$-0.140242\pi$
$131$	9.80467	+	6.55127i	0.856638	+	0.572387i	−0.0478655	+	0.998854i	$0.515242\pi$
$132$		−	16.4476i		−	1.43158i
$133$	−0.589942	+	0.882911i	−0.0511545	+	0.0765581i
$134$	−5.38834	−	2.23192i	−0.465481	−	0.192809i
$135$	−12.0482	+	0.0108329i	−1.03694	+	0.000932351i
$136$	−0.375650	+	4.10596i	−0.0322117	+	0.352083i
$137$	9.59397	−	9.59397i	0.819668	−	0.819668i	−0.166391	−	0.986060i	$-0.553212\pi$
$137$	9.59397	−	9.59397i	0.819668	−	0.819668i	0.986060	+	0.166391i	$0.0532115\pi$
$138$	−7.53830	−	18.1991i	−0.641703	−	1.54921i
$139$	−2.01112	−	10.1106i	−0.170581	−	0.857570i	−0.967381	−	0.253326i	$-0.918475\pi$
$139$	−2.01112	−	10.1106i	−0.170581	−	0.857570i	0.796800	−	0.604244i	$-0.206525\pi$
$140$	−2.06296	−	2.05925i	−0.174352	−	0.174039i
$141$	−0.171847	+	0.257187i	−0.0144721	+	0.0216590i
$142$	4.56901	−	3.05292i	0.383423	−	0.256195i
$143$	−6.08810	+	30.6070i	−0.509113	+	2.55948i
$144$	4.54102	−	1.88095i	0.378419	−	0.156746i
$145$	4.35408	+	1.79893i	0.361586	+	0.149393i
$146$	6.80394	−	4.54625i	0.563098	−	0.376250i
$147$	−8.28524	−	12.3997i	−0.683355	−	1.02271i
$148$	−1.35901	−	6.83222i	−0.111710	−	0.561605i
$149$	13.6274	+	13.6274i	1.11640	+	1.11640i	0.992265	+	0.124139i	$0.0396170\pi$
$149$	13.6274	+	13.6274i	1.11640	+	1.11640i	0.124139	+	0.992265i	$0.460383\pi$
$150$	13.7917	−	2.76913i	1.12609	−	0.226099i
$151$	3.26423	−	7.88055i	0.265639	−	0.641310i	−0.733629	−	0.679550i	$-0.762175\pi$
$151$	3.26423	−	7.88055i	0.265639	−	0.641310i	0.999269	+	0.0382398i	$0.0121751\pi$
$152$	0.576003	+	0.576003i	0.0467200	+	0.0467200i
$153$	12.9649	+	15.5760i	1.04815	+	1.25925i
$154$		−	7.62085i		−	0.614106i
$155$	−3.18957	+	1.32452i	−0.256192	+	0.106388i
$156$	−14.7291	+	2.92981i	−1.17928	+	0.234572i
$157$	−0.880010			−0.0702324			−0.0351162	−	0.999383i	$-0.511180\pi$
$157$	−0.880010			−0.0702324			−0.0351162	+	0.999383i	$0.511180\pi$
$158$	−5.01247	+	0.997043i	−0.398771	+	0.0793205i
$159$	−0.543799	+	2.73386i	−0.0431260	+	0.216809i
$160$	−1.85810	+	1.24396i	−0.146896	+	0.0983440i
$161$	−3.49280	−	8.43237i	−0.275271	−	0.664564i
$162$	0.158191	−	0.381906i	0.0124286	−	0.0300054i
$163$	6.68221	+	1.32917i	0.523391	+	0.104109i	0.449713	−	0.893173i	$-0.351526\pi$
$163$	6.68221	+	1.32917i	0.523391	+	0.104109i	0.0736779	+	0.997282i	$0.476526\pi$
$164$	−7.77565	−	1.54667i	−0.607177	−	0.120775i
$165$	30.5981	+	20.4053i	2.38206	+	1.58855i
$166$	1.82463	−	1.82463i	0.141618	−	0.141618i
$167$	−11.1600	−	7.45689i	−0.863589	−	0.577032i	0.0429863	−	0.999076i	$-0.486313\pi$
$167$	−11.1600	−	7.45689i	−0.863589	−	0.577032i	−0.906575	+	0.422044i	$0.861313\pi$
$168$	3.38825	−	1.40346i	0.261409	−	0.108279i
$169$	15.4936			1.19181
$170$	−7.17243	−	5.79277i	−0.550101	−	0.444285i
$171$	4.00385			0.306182
$172$	−1.31384	+	0.544211i	−0.100180	+	0.0414957i
$173$	−19.6568	−	13.1343i	−1.49448	−	0.998580i	−0.990895	−	0.134635i	$-0.957014\pi$
$173$	−19.6568	−	13.1343i	−1.49448	−	0.998580i	−0.503585	−	0.863945i	$-0.667986\pi$
$174$	−4.19130	+	4.19130i	−0.317742	+	0.317742i
$175$	6.39026	−	1.28305i	0.483058	−	0.0969896i
$176$	−5.73386	−	1.14054i	−0.432206	−	0.0859711i
$177$	15.1831	+	3.02010i	1.14123	+	0.227005i
$178$	0.421748	−	1.01819i	0.0316114	−	0.0763166i
$179$	9.49226	+	22.9163i	0.709485	+	1.71285i	0.701284	+	0.712882i	$0.252610\pi$
$179$	9.49226	+	22.9163i	0.709485	+	1.71285i	0.00820077	+	0.999966i	$0.497390\pi$
$180$	−2.13448	+	10.7814i	−0.159094	+	0.803597i
$181$	−1.10723	+	5.56640i	−0.0822995	+	0.413747i	0.917570	+	0.397575i	$0.130148\pi$
$181$	−1.10723	+	5.56640i	−0.0822995	+	0.413747i	−0.999869	+	0.0161726i	$0.994852\pi$
$182$	−6.82461	+	1.35750i	−0.505874	+	0.100625i
$183$	−16.3322			−1.20731
$184$	−6.86717	+	1.36596i	−0.506254	+	0.100700i
$185$	14.3963	+	5.94797i	1.05844	+	0.437304i
$186$		−	4.34534i		−	0.318616i
$187$	−2.52907	−	23.9714i	−0.184944	−	1.75296i
$188$	0.0777423	+	0.0777423i	0.00566994	+	0.00566994i
$189$	2.68786	−	6.48908i	0.195513	−	0.472011i
$190$	−1.78616	+	0.356960i	−0.129582	+	0.0258966i
$191$	−0.202904	−	0.202904i	−0.0146816	−	0.0146816i	0.699728	−	0.714409i	$-0.253305\pi$
$191$	−0.202904	−	0.202904i	−0.0146816	−	0.0146816i	−0.714409	+	0.699728i	$0.753305\pi$
$192$	−0.548865	−	2.75933i	−0.0396109	−	0.199138i
$193$	13.6206	+	20.3846i	0.980429	+	1.46732i	0.881479	+	0.472223i	$0.156548\pi$
$193$	13.6206	+	20.3846i	0.980429	+	1.46732i	0.0989501	+	0.995092i	$0.468452\pi$
$194$	12.5171	−	8.36364i	0.898673	−	0.600474i
$195$	12.8228	−	31.0360i	0.918263	−	2.22253i
$196$	−4.89724	+	2.02850i	−0.349803	+	0.144893i
$197$	0.490864	−	2.46774i	0.0349726	−	0.175819i	−0.959351	−	0.282215i	$-0.908931\pi$
$197$	0.490864	−	2.46774i	0.0349726	−	0.175819i	0.994324	+	0.106396i	$0.0339310\pi$
$198$	−23.8923	+	15.9643i	−1.69795	+	1.13453i
$199$	−7.18214	+	10.7488i	−0.509128	+	0.761964i	−0.993614	−	0.112835i	$-0.964007\pi$
$199$	−7.18214	+	10.7488i	−0.509128	+	0.761964i	0.484485	+	0.874799i	$0.339007\pi$
$200$	−0.00899134	−	4.99999i	−0.000635784	−	0.353553i
$201$	3.20114	+	16.0932i	0.225791	+	1.13513i
$202$	−2.58533	−	6.24155i	−0.181904	−	0.439154i
$203$	−1.94200	+	1.94200i	−0.136302	+	0.136302i
$204$	10.1920	−	5.53902i	0.713584	−	0.387809i
$205$	12.5240	−	12.5465i	0.874712	−	0.876287i
$206$	6.21141	+	2.57285i	0.432769	+	0.179259i
$207$	−19.1197	+	28.6146i	−1.32891	+	1.98886i
$208$			5.33794i			0.370119i
$209$	−3.95967	−	2.64577i	−0.273896	−	0.183012i
$210$	−1.59263	+	8.04446i	−0.109902	+	0.555121i
$211$	7.92328	+	11.8580i	0.545461	+	0.816340i	0.997119	−	0.0758509i	$-0.0241673\pi$
$211$	7.92328	+	11.8580i	0.545461	+	0.816340i	−0.451658	+	0.892191i	$0.649167\pi$
$212$	0.915351	+	0.379151i	0.0628666	+	0.0260402i
$213$	−14.2831	−	5.91624i	−0.978660	−	0.405374i
$214$	−9.29153	−	13.9058i	−0.635156	−	0.950578i
$215$	0.617562	−	3.11935i	0.0421174	−	0.212738i
$216$	−4.48005	−	2.99348i	−0.304829	−	0.203680i
$217$		−	2.01337i		−	0.136677i
$218$	−1.35075	+	2.02154i	−0.0914842	+	0.136916i
$219$	−21.2696	−	8.81016i	−1.43727	−	0.595335i
$220$	9.23532	−	9.25195i	0.622645	−	0.623766i
$221$	−21.0163	+	6.53485i	−1.41371	+	0.439581i
$222$	−13.8581	+	13.8581i	−0.930094	+	0.930094i
$223$	−5.22346	−	12.6106i	−0.349789	−	0.844465i	−0.996644	−	0.0818526i	$-0.973916\pi$
$223$	−5.22346	−	12.6106i	−0.349789	−	0.844465i	0.646856	−	0.762613i	$-0.276084\pi$
$224$	−0.254312	−	1.27851i	−0.0169919	−	0.0854241i
$225$	−17.4090	−	17.3465i	−1.16060	−	1.15643i
$226$	6.28548	−	9.40688i	0.418104	−	0.625737i
$227$	−6.55814	+	4.38201i	−0.435279	+	0.290844i	−0.753840	−	0.657058i	$-0.771801\pi$
$227$	−6.55814	+	4.38201i	−0.435279	+	0.290844i	0.318561	+	0.947902i	$0.396801\pi$
$228$	0.447101	−	2.24773i	0.0296100	−	0.148859i
$229$	−9.79199	+	4.05598i	−0.647073	+	0.268026i	−0.681987	−	0.731364i	$-0.738884\pi$
$229$	−9.79199	+	4.05598i	−0.647073	+	0.268026i	0.0349144	+	0.999390i	$0.488884\pi$
$230$	5.97839	−	14.4699i	0.394204	−	0.954117i
$231$	−17.8271	+	11.9117i	−1.17294	+	0.783730i
$232$	1.17050	+	1.75178i	0.0768474	+	0.115010i
$233$	0.465778	+	2.34162i	0.0305141	+	0.153405i	0.993038	−	0.117790i	$-0.0375811\pi$
$233$	0.465778	+	2.34162i	0.0305141	+	0.153405i	−0.962524	+	0.271195i	$0.912581\pi$
$234$	18.5523	+	18.5523i	1.21280	+	1.21280i
$235$	−0.241076	+	0.0481783i	−0.0157260	+	0.00314281i
$236$	2.10569	−	5.08359i	0.137069	−	0.330914i
$237$	10.1670	+	10.1670i	0.660418	+	0.660418i
$238$	4.72237	−	2.56645i	0.306106	−	0.166359i
$239$		−	10.4783i		−	0.677786i	−0.940825	−	0.338893i	$-0.889947\pi$
$239$		−	10.4783i		−	0.677786i	0.940825	−	0.338893i	$-0.110053\pi$
$240$	5.81423	+	2.40221i	0.375307	+	0.155062i
$241$	6.35785	−	1.26466i	0.409545	−	0.0814636i	0.0139818	−	0.999902i	$-0.495549\pi$
$241$	6.35785	−	1.26466i	0.409545	−	0.0814636i	0.395564	+	0.918439i	$0.370549\pi$
$242$	23.1779			1.48993
$243$	14.7131	−	2.92662i	0.943847	−	0.187743i
$244$	−1.13253	+	5.69362i	−0.0725029	+	0.364497i
$245$	2.30191	−	11.6271i	0.147064	−	0.742830i
$246$	8.53557	+	20.6067i	0.544208	+	1.31384i
$247$	−1.66400	+	4.01725i	−0.105878	+	0.255611i
$248$	−1.51484	−	0.301321i	−0.0961926	−	0.0191339i
$249$	−7.12021	−	1.41630i	−0.451225	−	0.0897542i
$250$	9.31283	+	6.18637i	0.588995	+	0.391260i
$251$	15.4336	−	15.4336i	0.974160	−	0.974160i	−0.0255144	−	0.999674i	$-0.508122\pi$
$251$	15.4336	−	15.4336i	0.974160	−	0.974160i	0.999674	+	0.0255144i	$0.00812236\pi$
$252$	−5.32740	−	3.55966i	−0.335595	−	0.224237i
$253$	37.8174	−	15.6645i	2.37756	−	0.984818i
$254$	3.56331			0.223582
$255$	−2.33996	+	25.8324i	−0.146534	+	1.61769i
$256$	−1.00000			−0.0625000
$257$	8.96619	−	3.71392i	0.559296	−	0.231668i	−0.0850837	−	0.996374i	$-0.527116\pi$
$257$	8.96619	−	3.71392i	0.559296	−	0.231668i	0.644379	+	0.764706i	$0.277116\pi$
$258$	3.32663	+	2.22278i	0.207107	+	0.138384i
$259$	−6.42102	+	6.42102i	−0.398983	+	0.398983i
$260$	−9.93037	−	6.62236i	−0.615856	−	0.410701i
$261$	10.1566	+	2.02026i	0.628675	+	0.125051i
$262$	−11.5654	−	2.30050i	−0.714512	−	0.142125i
$263$	−6.13000	+	14.7991i	−0.377992	+	0.912553i	0.614350	+	0.789033i	$0.289418\pi$
$263$	−6.13000	+	14.7991i	−0.377992	+	0.912553i	−0.992342	+	0.123520i	$0.960582\pi$
$264$	6.29423	+	15.1956i	0.387383	+	0.935226i
$265$	−1.84095	+	1.23248i	−0.113089	+	0.0757107i
$266$	0.207160	−	1.04146i	0.0127018	−	0.0638563i
$267$	−3.04101	+	0.604895i	−0.186107	+	0.0370189i
$268$	5.83229			0.356264
$269$	−16.1671	+	3.21583i	−0.985724	+	0.196073i	−0.661531	−	0.749918i	$-0.730093\pi$
$269$	−16.1671	+	3.21583i	−0.985724	+	0.196073i	−0.324194	+	0.945991i	$0.605093\pi$
$270$	11.1269	−	4.62065i	0.677163	−	0.281204i
$271$			5.17301i			0.314238i	0.987580	+	0.157119i	$0.0502206\pi$
$271$			5.17301i			0.314238i	−0.987580	+	0.157119i	$0.949779\pi$
$272$	−1.22423	−	3.93717i	−0.0742297	−	0.238726i
$273$	13.8426	+	13.8426i	0.837795	+	0.837795i
$274$	−5.19222	+	12.5351i	−0.313673	+	0.757275i
$275$	5.75422	+	28.6590i	0.346993	+	1.72820i
$276$	13.9290	+	13.9290i	0.838425	+	0.838425i
$277$	−4.03287	−	20.2746i	−0.242312	−	1.21818i	−0.889886	−	0.456182i	$-0.849217\pi$
$277$	−4.03287	−	20.2746i	−0.242312	−	1.21818i	0.647575	−	0.762002i	$-0.275783\pi$
$278$	5.72719	+	8.57135i	0.343494	+	0.514076i
$279$	−6.31216	+	4.21765i	−0.377899	+	0.252504i
$280$	2.69397	+	1.11304i	0.160995	+	0.0665169i
$281$	−1.20815	+	0.500433i	−0.0720724	+	0.0298534i	−0.418428	−	0.908250i	$-0.637419\pi$
$281$	−1.20815	+	0.500433i	−0.0720724	+	0.0298534i	0.346356	+	0.938103i	$0.387419\pi$
$282$	0.0603445	−	0.303372i	0.00359347	−	0.0180656i
$283$	3.79127	−	2.53325i	0.225368	−	0.150586i	−0.437761	−	0.899091i	$-0.644228\pi$
$283$	3.79127	−	2.53325i	0.225368	−	0.150586i	0.663128	+	0.748506i	$0.269228\pi$
$284$	−3.05292	+	4.56901i	−0.181157	+	0.271121i
$285$	3.62685	+	3.62034i	0.214836	+	0.214450i
$286$	−6.08810	−	30.6070i	−0.359997	−	1.80983i
$287$	3.95488	+	9.54792i	0.233449	+	0.563596i
$288$	−3.47555	+	3.47555i	−0.204799	+	0.204799i
$289$	14.0025	−	9.63997i	0.823679	−	0.567057i
$290$	−4.71106	+	0.00423588i	−0.276643	+	0.000248739i
$291$	−39.1293	−	16.2079i	−2.29380	−	0.950122i
$292$	−4.54625	+	6.80394i	−0.266049	+	0.398170i
$293$		−	31.2813i		−	1.82747i	−0.406310	−	0.913735i	$-0.633185\pi$
$293$		−	31.2813i		−	1.82747i	0.406310	−	0.913735i	$-0.366815\pi$
$294$	12.3997	+	8.28524i	0.723167	+	0.483205i
$295$	6.84484	+	10.2241i	0.398522	+	0.595271i
$296$	3.87014	+	5.79208i	0.224948	+	0.336658i
$297$	29.1022	+	12.0545i	1.68868	+	0.699474i
$298$	−17.8051	−	7.37512i	−1.03142	−	0.427229i
$299$	−20.7642	−	31.0759i	−1.20083	−	1.79716i
$300$	−11.6822	+	7.83620i	−0.674471	+	0.452423i
$301$	1.54136	+	1.02991i	0.0888426	+	0.0593628i
$302$			8.52985i			0.490838i
$303$	−10.5596	+	15.8035i	−0.606631	+	0.907888i
$304$	−0.752584	−	0.311731i	−0.0431637	−	0.0178790i
$305$	−9.18703	−	9.17052i	−0.526048	−	0.525102i
$306$	−17.9387	−	9.42895i	−1.02549	−	0.539017i
$307$	−12.1175	+	12.1175i	−0.691579	+	0.691579i	−0.962579	−	0.271000i	$-0.912646\pi$
$307$	−12.1175	+	12.1175i	−0.691579	+	0.691579i	0.271000	+	0.962579i	$0.412646\pi$
$308$	2.91637	+	7.04075i	0.166176	+	0.401184i
$309$	−3.69012	−	18.5515i	−0.209924	−	1.05536i
$310$	2.43990	−	2.44430i	0.138577	−	0.138827i
$311$	−3.04967	+	4.56416i	−0.172931	+	0.258810i	−0.907804	−	0.419396i	$-0.862242\pi$
$311$	−3.04967	+	4.56416i	−0.172931	+	0.258810i	0.734872	+	0.678205i	$0.237242\pi$
$312$	12.4868	−	8.34339i	0.706924	−	0.472351i
$313$	1.25044	−	6.28639i	0.0706791	−	0.355328i	−0.929220	−	0.369527i	$-0.879520\pi$
$313$	1.25044	−	6.28639i	0.0706791	−	0.355328i	0.999899	+	0.0141989i	$0.00451980\pi$
$314$	0.813023	−	0.336765i	0.0458815	−	0.0190048i
$315$	13.2314	−	5.49459i	0.745508	−	0.309585i
$316$	4.24937	−	2.83934i	0.239046	−	0.159725i
$317$	10.7218	+	16.0464i	0.602199	+	0.901254i	0.999868	−	0.0162752i	$-0.00518078\pi$
$317$	10.7218	+	16.0464i	0.602199	+	0.901254i	−0.397669	+	0.917529i	$0.630181\pi$
$318$	−0.543799	−	2.73386i	−0.0304947	−	0.153307i
$319$	−8.70947	−	8.70947i	−0.487637	−	0.487637i
$320$	1.24062	−	1.86034i	0.0693528	−	0.103996i
$321$	−18.0060	+	43.4704i	−1.00500	+	2.42628i
$322$	6.45386	+	6.45386i	0.359659	+	0.359659i
$323$	0.306001	−	3.34468i	0.0170263	−	0.186103i
$324$			0.413372i			0.0229651i
$325$	24.6396	−	10.2580i	1.36676	−	0.569013i
$326$	−6.68221	+	1.32917i	−0.370093	+	0.0736161i
$327$	6.84014			0.378261
$328$	7.77565	−	1.54667i	0.429339	−	0.0854008i
$329$	0.0279601	−	0.140565i	0.00154149	−	0.00774959i
$330$	−36.0777	−	7.14259i	−1.98601	−	0.393187i
$331$	−5.53455	−	13.3616i	−0.304207	−	0.734420i	−0.999871	−	0.0160529i	$-0.994890\pi$
$331$	−5.53455	−	13.3616i	−0.304207	−	0.734420i	0.695665	−	0.718367i	$-0.255110\pi$
$332$	−0.987480	+	2.38399i	−0.0541950	+	0.130838i
$333$	33.5815	+	6.67978i	1.84026	+	0.366050i
$334$	13.1642	+	2.61851i	0.720310	+	0.143279i
$335$	−7.23566	+	10.8500i	−0.395326	+	0.592801i
$336$	−2.59326	+	2.59326i	−0.141474	+	0.141474i
$337$	−7.15312	−	4.77956i	−0.389655	−	0.260359i	0.345276	−	0.938501i	$-0.387785\pi$
$337$	−7.15312	−	4.77956i	−0.389655	−	0.260359i	−0.734931	+	0.678142i	$0.762785\pi$
$338$	−14.3142	+	5.92913i	−0.778590	+	0.322502i
$339$	−31.8295			−1.72874
$340$	8.84326	+	2.60705i	0.479593	+	0.141387i
$341$	9.02956			0.488978
$342$	−3.69908	+	1.53221i	−0.200023	+	0.0828523i
$343$	13.3324	+	8.90842i	0.719881	+	0.481009i
$344$	1.00557	−	1.00557i	0.0542168	−	0.0542168i
$345$	−43.1931	+	8.63203i	−2.32544	+	0.464733i
$346$	23.1868	+	4.61214i	1.24653	+	0.247950i
$347$	33.4249	+	6.64863i	1.79434	+	0.356917i	0.975993	−	0.217802i	$-0.0698888\pi$
$347$	33.4249	+	6.64863i	1.79434	+	0.356917i	0.818350	+	0.574720i	$0.194889\pi$
$348$	2.26832	−	5.47620i	0.121595	−	0.293555i
$349$	2.62113	+	6.32796i	0.140306	+	0.338728i	0.978376	−	0.206834i	$-0.0663161\pi$
$349$	2.62113	+	6.32796i	0.140306	+	0.338728i	−0.838070	+	0.545562i	$0.816316\pi$
$350$	−5.41283	+	3.63083i	−0.289328	+	0.194076i
$351$	5.61108	−	28.2088i	0.299497	−	1.50567i
$352$	5.73386	−	1.14054i	0.305616	−	0.0607907i
$353$	−23.7210			−1.26254			−0.631270	−	0.775563i	$-0.717466\pi$
$353$	−23.7210			−1.26254			−0.631270	+	0.775563i	$0.717466\pi$
$354$	−15.1831	+	3.02010i	−0.806971	+	0.160516i
$355$	−4.71240	−	11.3479i	−0.250108	−	0.602283i
$356$			1.10208i			0.0584102i
$357$	−13.3848	−	7.03535i	−0.708400	−	0.372350i
$358$	−17.5394	−	17.5394i	−0.926987	−	0.926987i
$359$	10.0001	−	24.1423i	0.527783	−	1.27418i	−0.405189	−	0.914233i	$-0.632794\pi$
$359$	10.0001	−	24.1423i	0.527783	−	1.27418i	0.932972	−	0.359948i	$-0.117206\pi$
$360$	−2.15386	−	10.7775i	−0.113518	−	0.568026i
$361$	12.9658	+	12.9658i	0.682412	+	0.682412i
$362$	−1.10723	−	5.56640i	−0.0581945	−	0.292564i
$363$	−36.2280	−	54.2190i	−1.90147	−	2.84576i
$364$	5.78563	−	3.86583i	0.303249	−	0.202625i
$365$	−7.01746	−	16.8987i	−0.367311	−	0.884516i
$366$	15.0890	−	6.25006i	0.788714	−	0.326696i
$367$	2.97569	−	14.9598i	0.155330	−	0.780894i	−0.822052	−	0.569412i	$-0.807171\pi$
$367$	2.97569	−	14.9598i	0.155330	−	0.780894i	0.977382	−	0.211482i	$-0.0678291\pi$
$368$	5.82170	−	3.88994i	0.303477	−	0.202777i
$369$	21.6491	−	32.4002i	1.12701	−	1.68669i
$370$	−15.5766	+	0.0140055i	−0.809790	+	0.000728110i
$371$	−0.251964	−	1.26671i	−0.0130813	−	0.0657643i
$372$	1.66289	+	4.01457i	0.0862168	+	0.208146i
$373$	−3.61554	+	3.61554i	−0.187206	+	0.187206i	−0.794487	−	0.607281i	$-0.792260\pi$
$373$	−3.61554	+	3.61554i	−0.187206	+	0.187206i	0.607281	+	0.794487i	$0.292260\pi$
$374$	11.5100	+	21.1789i	0.595169	+	1.09513i
$375$	−0.0848458	−	31.4546i	−0.00438142	−	1.62431i
$376$	−0.101575	−	0.0420738i	−0.00523834	−	0.00216979i
$377$	−6.24808	+	9.35091i	−0.321792	+	0.481596i
$378$			7.02373i			0.361261i
$379$	20.5807	+	13.7516i	1.05716	+	0.706372i	0.957437	−	0.288643i	$-0.0932042\pi$
$379$	20.5807	+	13.7516i	1.05716	+	0.706372i	0.0997236	+	0.995015i	$0.468204\pi$
$380$	1.51360	−	1.01332i	0.0776458	−	0.0519823i
$381$	−5.56959	−	8.33548i	−0.285339	−	0.427039i
$382$	0.265107	+	0.109811i	0.0135641	+	0.00561842i
$383$	15.5006	+	6.42058i	0.792046	+	0.328076i	0.741766	−	0.670659i	$-0.233989\pi$
$383$	15.5006	+	6.42058i	0.792046	+	0.328076i	0.0502803	+	0.998735i	$0.483989\pi$
$384$	1.56304	+	2.33925i	0.0797634	+	0.119374i
$385$	−16.7163	−	3.30946i	−0.851941	−	0.168665i
$386$	−20.3846	−	13.6206i	−1.03755	−	0.693268i
$387$		−	6.98982i		−	0.355313i
$388$	−8.36364	+	12.5171i	−0.424599	+	0.635458i
$389$	10.3937	+	4.30522i	0.526983	+	0.218283i	0.630281	−	0.776367i	$-0.282940\pi$
$389$	10.3937	+	4.30522i	0.526983	+	0.218283i	−0.103298	+	0.994650i	$0.532940\pi$
$390$	0.0301935	+	33.5806i	0.00152891	+	1.70042i
$391$	22.4424	+	18.1588i	1.13496	+	0.918332i
$392$	3.74819	−	3.74819i	0.189312	−	0.189312i
$393$	12.6957	+	30.6501i	0.640413	+	1.54609i
$394$	0.490864	+	2.46774i	0.0247294	+	0.124323i
$395$	0.0102751	+	11.4278i	0.000516998	+	0.574995i
$396$	15.9643	−	23.8923i	0.802237	−	1.20063i
$397$	−31.0249	+	20.7302i	−1.55710	+	1.04042i	−0.583508	+	0.812107i	$0.698320\pi$
$397$	−31.0249	+	20.7302i	−1.55710	+	1.04042i	−0.973588	+	0.228311i	$0.926680\pi$
$398$	2.52203	−	12.6791i	0.126418	−	0.635546i
$399$	−2.76004	+	1.14325i	−0.138175	+	0.0572339i
$400$	1.92172	+	4.61595i	0.0960860	+	0.230797i
$401$	−3.29578	+	2.20217i	−0.164583	+	0.109971i	−0.635134	−	0.772402i	$-0.719055\pi$
$401$	−3.29578	+	2.20217i	−0.164583	+	0.109971i	0.470551	+	0.882373i	$0.344055\pi$
$402$	−9.11608	−	13.6432i	−0.454669	−	0.680460i
$403$	−1.60843	−	8.08613i	−0.0801217	−	0.402799i
$404$	4.77708	+	4.77708i	0.237668	+	0.237668i
$405$	−0.769012	−	0.512838i	−0.0382125	−	0.0254831i
$406$	1.05100	−	2.53735i	0.0521604	−	0.125926i
$407$	−28.7969	−	28.7969i	−1.42741	−	1.42741i
$408$	−7.29650	+	9.01770i	−0.361230	+	0.446443i
$409$		−	0.304764i		−	0.0150696i	−0.999972	−	0.00753480i	$-0.997602\pi$
$409$		−	0.304764i		−	0.0150696i	0.999972	−	0.00753480i	$-0.00239842\pi$
$410$	−6.76930	+	16.3842i	−0.334312	+	0.809157i
$411$	37.4384	−	7.44696i	1.84670	−	0.367332i
$412$	−6.72318			−0.331227
$413$	−7.03493	+	1.39933i	−0.346166	+	0.0688568i
$414$	6.71394	−	33.7533i	0.329972	−	1.65888i
$415$	−3.20994	−	4.79467i	−0.157570	−	0.235361i
$416$	−2.04274	−	4.93161i	−0.100154	−	0.241792i
$417$	11.0987	−	26.7947i	0.543506	−	1.31214i
$418$	4.67075	+	0.929070i	0.228454	+	0.0454423i
$419$	35.8559	+	7.13218i	1.75168	+	0.348430i	0.963641	−	0.267201i	$-0.0860988\pi$
$419$	35.8559	+	7.13218i	1.75168	+	0.348430i	0.788035	+	0.615631i	$0.211099\pi$
$420$	−1.60709	−	8.04159i	−0.0784179	−	0.392389i
$421$	15.7246	−	15.7246i	0.766371	−	0.766371i	−0.211095	−	0.977466i	$-0.567703\pi$
$421$	15.7246	−	15.7246i	0.766371	−	0.766371i	0.977466	+	0.211095i	$0.0677029\pi$
$422$	−11.8580	−	7.92328i	−0.577240	−	0.385699i
$423$	−0.499259	+	0.206800i	−0.0242748	+	0.0100550i
$424$	−0.990769			−0.0481160
$425$	−15.8211	+	13.2171i	−0.767438	+	0.641124i
$426$	15.4599			0.749034
$427$	6.99134	−	2.89591i	0.338335	−	0.140143i
$428$	13.9058	+	9.29153i	0.672160	+	0.449123i
$429$	−62.0814	+	62.0814i	−2.99732	+	2.99732i
$430$	0.623171	+	3.11823i	0.0300520	+	0.150375i
$431$	−34.8166	−	6.92546i	−1.67706	−	0.333588i	−0.737336	−	0.675526i	$-0.763916\pi$
$431$	−34.8166	−	6.92546i	−1.67706	−	0.333588i	−0.939722	+	0.341939i	$0.888916\pi$
$432$	5.28458	+	1.05117i	0.254255	+	0.0505744i
$433$	−1.80184	+	4.35002i	−0.0865907	+	0.209048i	−0.961243	−	0.275702i	$-0.911090\pi$
$433$	−1.80184	+	4.35002i	−0.0865907	+	0.209048i	0.874652	+	0.484751i	$0.161090\pi$
$434$	0.770484	+	1.86011i	0.0369844	+	0.0892883i
$435$	7.37347	+	11.0137i	0.353531	+	0.528068i
$436$	0.474319	−	2.38457i	0.0227158	−	0.114200i
$437$	5.59393	−	1.11270i	0.267594	−	0.0532278i
$438$	23.0220			1.10004
$439$	16.6816	−	3.31818i	0.796170	−	0.158368i	0.219787	−	0.975548i	$-0.429464\pi$
$439$	16.6816	−	3.31818i	0.796170	−	0.158368i	0.576383	+	0.817180i	$0.304464\pi$
$440$	−4.99176	+	12.0819i	−0.237973	+	0.575981i
$441$		−	26.0540i		−	1.24067i
$442$	16.9158	−	14.0800i	0.804602	−	0.669718i
$443$	8.08098	+	8.08098i	0.383939	+	0.383939i	0.872519	−	0.488580i	$-0.162485\pi$
$443$	8.08098	+	8.08098i	0.383939	+	0.383939i	−0.488580	+	0.872519i	$0.662485\pi$
$444$	7.49994	−	18.1065i	0.355931	−	0.859295i
$445$	−2.05025	−	1.36727i	−0.0971910	−	0.0648146i
$446$	9.65170	+	9.65170i	0.457021	+	0.457021i
$447$	10.5778	+	53.1782i	0.500313	+	2.51524i
$448$	0.724218	+	1.08387i	0.0342161	+	0.0512080i
$449$	−9.49028	+	6.34120i	−0.447874	+	0.299260i	−0.758978	−	0.651116i	$-0.774301\pi$
$449$	−9.49028	+	6.34120i	−0.447874	+	0.299260i	0.311104	+	0.950376i	$0.399301\pi$
$450$	22.7220	+	9.36392i	1.07112	+	0.441419i
$451$	−42.8205	+	17.7368i	−2.01634	+	0.835194i
$452$	−2.20717	+	11.0962i	−0.103816	+	0.521920i
$453$	19.9534	−	13.3325i	0.937494	−	0.626414i
$454$	4.38201	−	6.55814i	0.205658	−	0.307789i
$455$	0.0139899	+	15.5593i	0.000655855	+	0.729429i
$456$	0.447101	+	2.24773i	0.0209374	+	0.105260i
$457$	3.07536	+	7.42458i	0.143859	+	0.347307i	0.979342	−	0.202209i	$-0.0648121\pi$
$457$	3.07536	+	7.42458i	0.143859	+	0.347307i	−0.835483	+	0.549516i	$0.814812\pi$
$458$	7.49447	−	7.49447i	0.350193	−	0.350193i
$459$	2.33090	+	22.0932i	0.108797	+	1.03122i
$460$	0.0140771	+	15.6563i	0.000656348	+	0.729978i
$461$	32.2280	+	13.3493i	1.50101	+	0.621737i	0.973679	−	0.227924i	$-0.0731939\pi$
$461$	32.2280	+	13.3493i	1.50101	+	0.621737i	0.527328	+	0.849662i	$0.323194\pi$
$462$	11.9117	−	17.8271i	0.554181	−	0.829390i
$463$		−	39.0872i		−	1.81654i	−0.418386	−	0.908269i	$-0.637404\pi$
$463$		−	39.0872i		−	1.81654i	0.418386	−	0.908269i	$-0.362596\pi$
$464$	−1.75178	−	1.17050i	−0.0813245	−	0.0543393i
$465$	−9.53147	−	1.88702i	−0.442012	−	0.0875085i
$466$	−1.32642	−	1.98513i	−0.0614454	−	0.0919595i
$467$	15.5971	+	6.46053i	0.721748	+	0.298958i	0.713156	−	0.701005i	$-0.247265\pi$
$467$	15.5971	+	6.46053i	0.721748	+	0.298958i	0.00859198	+	0.999963i	$0.497265\pi$
$468$	−24.2397	−	10.0404i	−1.12048	−	0.464118i
$469$	−4.22385	−	6.32144i	−0.195039	−	0.291897i
$470$	0.204288	−	0.136767i	0.00942309	−	0.00630857i
$471$	−2.05856	−	1.37549i	−0.0948535	−	0.0633791i
$472$			5.50244i			0.253270i
$473$	−4.61891	+	6.91269i	−0.212378	+	0.317846i
$474$	−13.2838	−	5.50235i	−0.610147	−	0.252731i
$475$	0.00732427	+	4.07295i	0.000336060	+	0.186880i
$476$	−3.38077	+	4.17827i	−0.154957	+	0.191511i
$477$	−3.44347	+	3.44347i	−0.157665	+	0.157665i
$478$	4.00988	+	9.68071i	0.183408	+	0.442785i
$479$	1.23929	+	6.23034i	0.0566247	+	0.284672i	0.998714	−	0.0506892i	$-0.0161418\pi$
$479$	1.23929	+	6.23034i	0.0566247	+	0.284672i	−0.942090	+	0.335361i	$0.891142\pi$
$480$	−6.29093	+	0.00565639i	−0.287140	+	0.000258178i
$481$	−20.6586	+	30.9178i	−0.941950	+	1.40973i
$482$	−5.38993	+	3.60143i	−0.245504	+	0.164041i
$483$	5.00957	−	25.1848i	0.227943	−	1.14595i
$484$	−21.4136	+	8.86981i	−0.973346	+	0.403173i
$485$	−12.9099	−	31.0881i	−0.586208	−	1.41164i
$486$	−12.4732	+	8.33431i	−0.565795	+	0.378052i
$487$	−15.0153	−	22.4720i	−0.680407	−	1.01830i	−0.997552	−	0.0699246i	$-0.977724\pi$
$487$	−15.0153	−	22.4720i	−0.680407	−	1.01830i	0.317145	−	0.948377i	$-0.397276\pi$
$488$	−1.13253	−	5.69362i	−0.0512673	−	0.257738i
$489$	13.5538	+	13.5538i	0.612924	+	0.612924i
$490$	2.32282	+	11.6230i	0.104934	+	0.525072i
$491$	−0.0788074	+	0.190258i	−0.00355653	+	0.00858621i	−0.925648	−	0.378386i	$-0.876479\pi$
$491$	−0.0788074	+	0.190258i	−0.00355653	+	0.00858621i	0.922091	+	0.386972i	$0.126479\pi$
$492$	−15.7717	−	15.7717i	−0.711042	−	0.711042i
$493$	2.46389	−	8.33002i	0.110968	−	0.375165i
$494$		−	4.34824i		−	0.195636i
$495$	24.6421	+	59.3403i	1.10758	+	2.66715i
$496$	1.51484	−	0.301321i	0.0680184	−	0.0135297i
$497$	7.16319			0.321313
$498$	7.12021	−	1.41630i	0.319064	−	0.0634658i
$499$	4.34370	−	21.8373i	0.194451	−	0.977570i	−0.753086	−	0.657923i	$-0.771435\pi$
$499$	4.34370	−	21.8373i	0.194451	−	0.977570i	0.947536	−	0.319648i	$-0.103565\pi$
$500$	−10.9714	−	2.15159i	−0.490654	−	0.0962220i
$501$	−14.4507	−	34.8871i	−0.645609	−	1.55864i
$502$	−8.35260	+	20.1650i	−0.372795	+	0.900007i
$503$	1.59744	+	0.317750i	0.0712262	+	0.0141678i	0.230575	−	0.973055i	$-0.425939\pi$
$503$	1.59744	+	0.317750i	0.0712262	+	0.0141678i	−0.159349	+	0.987222i	$0.550939\pi$
$504$	6.28410	+	1.24998i	0.279916	+	0.0556787i
$505$	−14.8135	+	2.96044i	−0.659193	+	0.131738i
$506$	−28.9442	+	28.9442i	−1.28673	+	1.28673i
$507$	36.2433	+	24.2170i	1.60962	+	1.07552i
$508$	−3.29207	+	1.36362i	−0.146062	+	0.0605009i
$509$	35.1547			1.55820			0.779102	−	0.626897i	$-0.215675\pi$
$509$	35.1547			1.55820			0.779102	+	0.626897i	$0.215675\pi$
$510$	−7.72380	−	24.7615i	−0.342015	−	1.09646i
$511$	10.6671			0.471883
$512$	0.923880	−	0.382683i	0.0408301	−	0.0169124i
$513$	3.64941	+	2.43846i	0.161126	+	0.107661i
$514$	−6.86243	+	6.86243i	−0.302689	+	0.302689i
$515$	8.34091	−	12.5074i	0.367544	−	0.551141i
$516$	−3.92402	−	0.780537i	−0.172746	−	0.0343612i
$517$	0.630404	+	0.125395i	0.0277251	+	0.00551487i
$518$	3.47503	−	8.38946i	0.152684	−	0.368612i
$519$	−25.4529	−	61.4487i	−1.11726	−	2.69730i
$520$	11.7087	+	2.31807i	0.513462	+	0.101654i
$521$	6.77862	−	34.0784i	0.296977	−	1.49300i	−0.487653	−	0.873038i	$-0.662147\pi$
$521$	6.77862	−	34.0784i	0.296977	−	1.49300i	0.784629	−	0.619965i	$-0.212853\pi$
$522$	−10.1566	+	2.02026i	−0.444540	+	0.0884246i
$523$	−0.224643			−0.00982294			−0.00491147	−	0.999988i	$-0.501563\pi$
$523$	−0.224643			−0.00982294			−0.00491147	+	0.999988i	$0.501563\pi$
$524$	11.5654	−	2.30050i	0.505237	−	0.100498i
$525$	16.9539	+	6.98683i	0.739927	+	0.304930i
$526$		−	16.0185i		−	0.698438i
$527$	3.04086	+	5.59530i	0.132462	+	0.243735i
$528$	−11.6302	−	11.6302i	−0.506140	−	0.506140i
$529$	−9.95889	+	24.0429i	−0.432995	+	1.04534i
$530$	1.22917	−	1.84317i	0.0533917	−	0.0800620i
$531$	19.1240	+	19.1240i	0.829911	+	0.829911i
$532$	0.207160	+	1.04146i	0.00898153	+	0.0451532i
$533$	23.5112	+	35.1871i	1.01838	+	1.52412i
$534$	2.57804	−	1.72259i	0.111563	−	0.0745439i
$535$	−34.5372	+	14.3422i	−1.49317	+	0.620066i
$536$	−5.38834	+	2.23192i	−0.232741	+	0.0964043i
$537$	−13.6143	+	68.4438i	−0.587501	+	2.95357i
$538$	13.7058	−	9.15792i	0.590899	−	0.394826i
$539$	−17.2166	+	25.7665i	−0.741572	+	1.10984i
$540$	−8.51170	+	8.52702i	−0.366285	+	0.366944i
$541$	6.22565	+	31.2985i	0.267662	+	1.34563i	0.847457	+	0.530864i	$0.178132\pi$
$541$	6.22565	+	31.2985i	0.267662	+	1.34563i	−0.579796	+	0.814762i	$0.696868\pi$
$542$	−1.97962	−	4.77923i	−0.0850321	−	0.205286i
$543$	−11.2906	+	11.2906i	−0.484525	+	0.484525i
$544$	2.63773	+	3.16897i	0.113092	+	0.135869i
$545$	3.84765	+	3.84074i	0.164815	+	0.164519i
$546$	−18.0863	−	7.49159i	−0.774022	−	0.320610i
$547$	−3.82638	+	5.72658i	−0.163604	+	0.244851i	−0.904209	−	0.427090i	$-0.859539\pi$
$547$	−3.82638	+	5.72658i	−0.163604	+	0.244851i	0.740605	+	0.671940i	$0.234539\pi$
$548$		−	13.5679i		−	0.579593i
$549$	−23.7246	−	15.8523i	−1.01254	−	0.676559i
$550$	−16.2835	−	24.2754i	−0.694332	−	1.03511i
$551$	−0.953483	−	1.42699i	−0.0406197	−	0.0607917i
$552$	−18.1991	−	7.53830i	−0.774604	−	0.320851i
$553$	−6.15494	−	2.54946i	−0.261735	−	0.108414i
$554$	11.4847	+	17.1880i	0.487936	+	0.730248i
$555$	24.3796	+	36.4157i	1.03486	+	1.54576i
$556$	−8.57135	−	5.72719i	−0.363506	−	0.242887i
$557$			33.2286i			1.40794i	0.710228	+	0.703971i	$0.248592\pi$
$557$			33.2286i			1.40794i	−0.710228	+	0.703971i	$0.751408\pi$
$558$	4.21765	−	6.31216i	0.178548	−	0.267215i
$559$	7.01321	+	2.90496i	0.296627	+	0.122867i
$560$	−2.91484	+	0.00262084i	−0.123175	+	0.000110751i
$561$	31.5521	−	60.0281i	1.33213	−	2.53439i
$562$	0.924680	−	0.924680i	0.0390053	−	0.0390053i
$563$	8.49755	+	20.5149i	0.358129	+	0.864600i	0.995563	+	0.0940950i	$0.0299958\pi$
$563$	8.49755	+	20.5149i	0.358129	+	0.864600i	−0.637434	+	0.770505i	$0.720004\pi$
$564$	0.0603445	+	0.303372i	0.00254096	+	0.0127743i
$565$	−17.9044	−	17.8722i	−0.753243	−	0.751890i
$566$	−2.53325	+	3.79127i	−0.106480	+	0.159359i
$567$	0.448041	−	0.299372i	0.0188160	−	0.0125724i
$568$	1.07204	−	5.38952i	0.0449819	−	0.226139i
$569$	13.2905	−	5.50510i	0.557166	−	0.230786i	−0.0862883	−	0.996270i	$-0.527501\pi$
$569$	13.2905	−	5.50510i	0.557166	−	0.230786i	0.643454	+	0.765484i	$0.277501\pi$
$570$	−4.73622	−	1.95682i	−0.198378	−	0.0819621i
$571$	17.4454	−	11.6566i	0.730068	−	0.487816i	−0.134133	−	0.990963i	$-0.542825\pi$
$571$	17.4454	−	11.6566i	0.730068	−	0.487816i	0.864200	+	0.503148i	$0.167825\pi$
$572$	17.3375	+	25.9473i	0.724915	+	1.08491i
$573$	−0.157497	−	0.791791i	−0.00657953	−	0.0330775i
$574$	−7.30766	−	7.30766i	−0.305016	−	0.305016i
$575$	−29.1434	−	19.3973i	−1.21537	−	0.808924i
$576$	1.88095	−	4.54102i	0.0783731	−	0.189209i
$577$	13.0297	+	13.0297i	0.542435	+	0.542435i	0.924242	−	0.381807i	$-0.124698\pi$
$577$	13.0297	+	13.0297i	0.542435	+	0.542435i	−0.381807	+	0.924242i	$0.624698\pi$
$578$	−9.24760	+	14.2647i	−0.384650	+	0.593334i
$579$			68.9741i			2.86646i
$580$	4.35083	−	1.80676i	0.180659	−	0.0750216i
$581$	3.29908	−	0.656228i	0.136869	−	0.0272249i
$582$	42.3532			1.75560
$583$	5.68093	−	1.13001i	0.235280	−	0.0468001i
$584$	1.59643	−	8.02579i	0.0660607	−	0.332110i
$585$	48.7508	−	32.6377i	2.01560	−	1.34940i
$586$	11.9708	+	28.9001i	0.494510	+	1.19385i
$587$	8.94250	−	21.5891i	0.369096	−	0.891077i	−0.624803	−	0.780783i	$-0.714821\pi$
$587$	8.94250	−	21.5891i	0.369096	−	0.891077i	0.993899	−	0.110295i	$-0.0351795\pi$
$588$	−14.6265	−	2.90939i	−0.603186	−	0.119981i
$589$	1.23398	+	0.245453i	0.0508452	+	0.0101137i
$590$	−10.2364	−	6.82644i	−0.421426	−	0.281040i
$591$	5.00542	−	5.00542i	0.205895	−	0.205895i
$592$	−5.79208	−	3.87014i	−0.238053	−	0.159062i
$593$	−25.7677	+	10.6733i	−1.05815	+	0.438301i	−0.842795	−	0.538234i	$-0.819092\pi$
$593$	−25.7677	+	10.6733i	−1.05815	+	0.438301i	−0.215357	+	0.976535i	$0.569092\pi$
$594$	−31.4999			−1.29246
$595$	−3.57875	−	11.4730i	−0.146714	−	0.470348i
$596$	19.2721			0.789417
$597$	−33.6016	+	13.9182i	−1.37522	+	0.569636i
$598$	31.0759	+	20.7642i	1.27079	+	0.849113i
$599$	6.03820	−	6.03820i	0.246714	−	0.246714i	−0.572907	−	0.819621i	$-0.694184\pi$
$599$	6.03820	−	6.03820i	0.246714	−	0.246714i	0.819621	+	0.572907i	$0.194184\pi$
$600$	7.79414	−	11.7103i	0.318194	−	0.478070i
$601$	−1.21570	−	0.241819i	−0.0495896	−	0.00986398i	0.170233	−	0.985404i	$-0.445548\pi$
$601$	−1.21570	−	0.241819i	−0.0495896	−	0.00986398i	−0.219823	+	0.975540i	$0.570548\pi$
$602$	−1.81816	−	0.361655i	−0.0741027	−	0.0147399i
$603$	−10.9703	+	26.4846i	−0.446744	+	1.07854i
$604$	−3.26423	−	7.88055i	−0.132820	−	0.320655i
$605$	10.0653	−	50.8407i	0.409214	−	2.06697i
$606$	3.70803	−	18.6415i	0.150628	−	0.757260i
$607$	35.7149	−	7.10414i	1.44962	−	0.288348i	0.593381	−	0.804922i	$-0.297793\pi$
$607$	35.7149	−	7.10414i	1.44962	−	0.288348i	0.856243	+	0.516574i	$0.172793\pi$
$608$	0.814591			0.0330360
$609$	−7.57824	+	1.50741i	−0.307086	+	0.0610832i
$610$	11.9971	+	4.95673i	0.485749	+	0.200692i
$611$		−	0.586875i		−	0.0237424i
$612$	20.1815	+	1.84638i	0.815788	+	0.0746355i
$613$	−1.67709	−	1.67709i	−0.0677372	−	0.0677372i	0.672427	−	0.740164i	$-0.265252\pi$
$613$	−1.67709	−	1.67709i	−0.0677372	−	0.0677372i	−0.740164	+	0.672427i	$0.765252\pi$
$614$	6.55792	−	15.8322i	0.264656	−	0.638936i
$615$	48.9074	−	9.77400i	1.97213	−	0.394126i
$616$	−5.38876	−	5.38876i	−0.217119	−	0.217119i
$617$	−1.85351	−	9.31821i	−0.0746194	−	0.375137i	0.925373	−	0.379058i	$-0.123752\pi$
$617$	−1.85351	−	9.31821i	−0.0746194	−	0.375137i	−0.999992	+	0.00392093i	$0.998752\pi$
$618$	10.5086	+	15.7272i	0.422717	+	0.632640i
$619$	−33.6978	+	22.5162i	−1.35443	+	0.905001i	−0.999553	−	0.0299118i	$-0.990477\pi$
$619$	−33.6978	+	22.5162i	−1.35443	+	0.905001i	−0.354877	+	0.934913i	$0.615477\pi$
$620$	−1.31879	+	3.19195i	−0.0529637	+	0.128192i
$621$	−34.8543	+	14.4371i	−1.39865	+	0.579341i
$622$	1.07090	−	5.38379i	0.0429393	−	0.215870i
$623$	1.19451	−	0.798148i	0.0478571	−	0.0319771i
$624$	−8.34339	+	12.4868i	−0.334003	+	0.499871i
$625$	17.6140	−	17.7411i	0.704559	−	0.709645i
$626$	1.25044	+	6.28639i	0.0499777	+	0.251255i
$627$	−5.12723	−	12.3782i	−0.204762	−	0.494338i
$628$	−0.622261	+	0.622261i	−0.0248309	+	0.0248309i
$629$	8.14658	−	27.5423i	0.324825	−	1.09818i
$630$	−10.1216	+	10.1398i	−0.403253	+	0.403979i
$631$	−12.6410	−	5.23609i	−0.503232	−	0.208446i	0.116602	−	0.993179i	$-0.462800\pi$
$631$	−12.6410	−	5.23609i	−0.503232	−	0.208446i	−0.619834	+	0.784733i	$0.712800\pi$
$632$	−2.83934	+	4.24937i	−0.112943	+	0.169031i
$633$			40.1233i			1.59476i
$634$	−16.0464	−	10.7218i	−0.637283	−	0.425819i
$635$	1.54742	−	7.81610i	0.0614073	−	0.310173i
$636$	1.54861	+	2.31766i	0.0614063	+	0.0919010i
$637$	26.1412	+	10.8280i	1.03575	+	0.429022i
$638$	11.3795	+	4.71353i	0.450518	+	0.186611i
$639$	−15.0056	−	22.4575i	−0.593613	−	0.888404i
$640$	−0.434263	+	2.19349i	−0.0171658	+	0.0867055i
$641$	−28.3365	−	18.9339i	−1.11923	−	0.747843i	−0.148711	−	0.988881i	$-0.547512\pi$
$641$	−28.3365	−	18.9339i	−1.11923	−	0.747843i	−0.970516	+	0.241038i	$0.922512\pi$
$642$		−	47.0520i		−	1.85700i
$643$	6.38975	−	9.56293i	0.251987	−	0.377125i	−0.683813	−	0.729658i	$-0.739679\pi$
$643$	6.38975	−	9.56293i	0.251987	−	0.377125i	0.935800	+	0.352532i	$0.114679\pi$
$644$	−8.43237	−	3.49280i	−0.332282	−	0.137636i
$645$	6.32029	−	6.33167i	0.248861	−	0.249309i
$646$	0.997245	+	3.20718i	0.0392361	+	0.126185i
$647$	22.0524	−	22.0524i	0.866968	−	0.866968i	−0.125168	−	0.992136i	$-0.539947\pi$
$647$	22.0524	−	22.0524i	0.866968	−	0.866968i	0.992136	+	0.125168i	$0.0399469\pi$
$648$	−0.158191	−	0.381906i	−0.00621432	−	0.0150027i
$649$	−6.27573	−	31.5502i	−0.246344	−	1.23845i
$650$	−18.8385	+	18.9064i	−0.738906	+	0.741569i
$651$	3.14697	−	4.70978i	0.123340	−	0.184591i
$652$	5.66490	−	3.78517i	0.221855	−	0.148239i
$653$	9.02163	−	45.3548i	0.353044	−	1.77487i	−0.241088	−	0.970503i	$-0.577504\pi$
$653$	9.02163	−	45.3548i	0.353044	−	1.77487i	0.594132	−	0.804368i	$-0.297496\pi$
$654$	−6.31947	+	2.61761i	−0.247111	+	0.102357i
$655$	−10.0686	+	24.3696i	−0.393411	+	0.952199i
$656$	−6.59188	+	4.40455i	−0.257370	+	0.171969i
$657$	−22.3456	−	33.4425i	−0.871783	−	1.30472i
$658$	0.0279601	+	0.140565i	0.00109000	+	0.00547979i
$659$	−26.4734	−	26.4734i	−1.03126	−	1.03126i	−0.999495	−	0.0317611i	$-0.989888\pi$
$659$	−26.4734	−	26.4734i	−1.03126	−	1.03126i	−0.0317611	−	0.999495i	$-0.510112\pi$
$660$	36.0648	−	7.20746i	1.40382	−	0.280550i
$661$	−3.99375	+	9.64176i	−0.155339	+	0.375021i	−0.982320	−	0.187208i	$-0.940056\pi$
$661$	−3.99375	+	9.64176i	−0.155339	+	0.375021i	0.826981	+	0.562229i	$0.190056\pi$
$662$	10.2265	+	10.2265i	0.397465	+	0.397465i
$663$	−59.3767	−	17.5627i	−2.30600	−	0.682077i
$664$		−	2.58041i		−	0.100139i
$665$	−2.19448	−	0.906674i	−0.0850984	−	0.0351593i
$666$	−33.5815	+	6.67978i	−1.30126	+	0.258836i
$667$	14.7516			0.571182
$668$	−13.1642	+	2.61851i	−0.509336	+	0.101313i
$669$	7.49177	−	37.6637i	0.289649	−	1.45616i
$670$	2.53275	−	12.7931i	0.0978487	−	0.494241i
$671$	12.9876	+	31.3547i	0.501379	+	1.21044i
$672$	1.40346	−	3.38825i	0.0541397	−	0.130705i
$673$	−9.10724	−	1.81154i	−0.351058	−	0.0698299i	0.0164114	−	0.999865i	$-0.494776\pi$
$673$	−9.10724	−	1.81154i	−0.351058	−	0.0698299i	−0.367470	+	0.930035i	$0.619776\pi$
$674$	8.43768	+	1.67836i	0.325007	+	0.0646480i
$675$	−5.30335	−	26.4134i	−0.204126	−	1.01665i
$676$	10.9556	−	10.9556i	0.421370	−	0.421370i
$677$	−31.7217	−	21.1958i	−1.21916	−	0.814619i	−0.231749	−	0.972776i	$-0.574445\pi$
$677$	−31.7217	−	21.1958i	−1.21916	−	0.814619i	−0.987414	+	0.158157i	$0.949445\pi$
$678$	29.4066	−	12.1806i	1.12935	−	0.467794i
$679$	19.6240			0.753099
$680$	−9.16778	+	0.975568i	−0.351568	+	0.0374113i
$681$	−22.1904			−0.850336
$682$	−8.34222	+	3.45546i	−0.319440	+	0.132316i
$683$	−22.6804	−	15.1546i	−0.867842	−	0.579874i	0.0399935	−	0.999200i	$-0.487266\pi$
$683$	−22.6804	−	15.1546i	−0.867842	−	0.579874i	−0.907836	+	0.419326i	$0.862266\pi$
$684$	2.83115	−	2.83115i	0.108252	−	0.108252i
$685$	25.2409	+	16.8326i	0.964407	+	0.643142i
$686$	−15.7266	−	3.12822i	−0.600445	−	0.119436i
$687$	−29.2455	−	5.81730i	−1.11579	−	0.221944i
$688$	−0.544211	+	1.31384i	−0.0207479	+	0.0500898i
$689$	−2.02388	−	4.88609i	−0.0771038	−	0.186145i
$690$	36.6019	−	24.5043i	1.39341	−	0.932861i
$691$	−5.53015	+	27.8020i	−0.210377	+	1.05764i	0.720821	+	0.693122i	$0.243765\pi$
$691$	−5.53015	+	27.8020i	−0.210377	+	1.05764i	−0.931198	+	0.364515i	$0.881235\pi$
$692$	−23.1868	+	4.61214i	−0.881430	+	0.175327i
$693$	−37.4578			−1.42290
$694$	−33.4249	+	6.64863i	−1.26879	+	0.252378i
$695$	21.2883	−	8.84034i	0.807512	−	0.335333i
$696$			5.92740i			0.224677i
$697$	−25.4114	−	20.5612i	−0.962526	−	0.778809i
$698$	−4.84321	−	4.84321i	−0.183318	−	0.183318i
$699$	−2.57047	+	6.20567i	−0.0972242	+	0.234720i
$700$	3.61134	−	5.42585i	0.136496	−	0.205078i
$701$	−2.93942	−	2.93942i	−0.111020	−	0.111020i	0.649414	−	0.760435i	$-0.275014\pi$
$701$	−2.93942	−	2.93942i	−0.111020	−	0.111020i	−0.760435	+	0.649414i	$0.775014\pi$
$702$	5.61108	+	28.2088i	0.211776	+	1.06467i
$703$	−3.15259	−	4.71818i	−0.118902	−	0.177949i
$704$	−4.86093	+	3.24797i	−0.183203	+	0.122412i
$705$	−0.639240	−	0.264109i	−0.0240752	−	0.00994692i
$706$	21.9153	−	9.07762i	0.824794	−	0.341641i
$707$	1.71808	−	8.63737i	0.0646151	−	0.324842i
$708$	12.8716	−	8.60051i	0.483744	−	0.323227i
$709$	−9.66796	+	14.4691i	−0.363088	+	0.543399i	−0.967369	−	0.253372i	$-0.918460\pi$
$709$	−9.66796	+	14.4691i	−0.363088	+	0.543399i	0.604281	+	0.796771i	$0.293460\pi$
$710$	8.69634	+	8.68071i	0.326368	+	0.325781i
$711$	4.90063	+	24.6371i	0.183788	+	0.923965i
$712$	−0.421748	−	1.01819i	−0.0158057	−	0.0381583i
$713$	−7.64684	+	7.64684i	−0.286377	+	0.286377i
$714$	15.0583	+	1.37767i	0.563542	+	0.0515578i
$715$	−69.7800	+	0.0627416i	−2.60963	+	0.00234640i
$716$	22.9163	+	9.49226i	0.856424	+	0.354742i
$717$	16.3780	−	24.5114i	0.611647	−	0.915395i
$718$			26.1314i			0.975216i
$719$	−7.89793	−	5.27723i	−0.294543	−	0.196807i	0.399515	−	0.916727i	$-0.369179\pi$
$719$	−7.89793	−	5.27723i	−0.294543	−	0.196807i	−0.694058	+	0.719919i	$0.744179\pi$
$720$	6.11429	+	9.13290i	0.227866	+	0.340363i
$721$	4.86905	+	7.28705i	0.181333	+	0.271384i
$722$	−16.9407	−	7.01705i	−0.630466	−	0.261148i
$723$	16.8493	+	6.97921i	0.626632	+	0.259560i
$724$	3.15311	+	4.71897i	0.117185	+	0.175379i
$725$	−2.03655	+	10.3355i	−0.0756355	+	0.383852i
$726$	54.2190	+	36.2280i	2.01225	+	1.34455i
$727$		−	11.5433i		−	0.428116i	−0.976821	−	0.214058i	$-0.931332\pi$
$727$		−	11.5433i		−	0.428116i	0.976821	−	0.214058i	$-0.0686681\pi$
$728$	−3.86583	+	5.78563i	−0.143277	+	0.214430i
$729$	40.1378	+	16.6256i	1.48658	+	0.615764i
$730$	12.9501	+	12.9269i	0.479306	+	0.478445i
$731$	−5.83905	−	0.534208i	−0.215965	−	0.0197584i
$732$	−11.5486	+	11.5486i	−0.426849	+	0.426849i
$733$	1.12997	+	2.72799i	0.0417363	+	0.100760i	0.943373	−	0.331734i	$-0.107634\pi$
$733$	1.12997	+	2.72799i	0.0417363	+	0.100760i	−0.901637	+	0.432494i	$0.857634\pi$
$734$	2.97569	+	14.9598i	0.109835	+	0.552176i
$735$	23.5584	−	23.6008i	0.868964	−	0.870528i
$736$	−3.88994	+	5.82170i	−0.143385	+	0.214591i
$737$	28.3504	−	18.9431i	1.04430	−	0.697778i
$738$	−7.60216	+	38.2186i	−0.279839	+	1.40685i
$739$	9.10333	−	3.77072i	0.334871	−	0.138708i	−0.208911	−	0.977935i	$-0.566992\pi$
$739$	9.10333	−	3.77072i	0.334871	−	0.138708i	0.543782	+	0.839226i	$0.316992\pi$
$740$	14.3856	−	5.97385i	0.528823	−	0.219603i
$741$	−10.1716	+	6.79645i	−0.373663	+	0.249674i
$742$	0.717533	+	1.07386i	0.0263415	+	0.0394228i
$743$	0.496966	+	2.49842i	0.0182319	+	0.0916580i	0.988830	−	0.149048i	$-0.0476210\pi$
$743$	0.496966	+	2.49842i	0.0182319	+	0.0916580i	−0.970598	+	0.240706i	$0.922621\pi$
$744$	−3.07262	−	3.07262i	−0.112648	−	0.112648i
$745$	−23.9094	+	35.8527i	−0.875972	+	1.31354i
$746$	1.95672	−	4.72394i	0.0716406	−	0.172956i
$747$	−8.96834	−	8.96834i	−0.328134	−	0.328134i
$748$	−18.7387	−	15.1620i	−0.685154	−	0.554379i
$749$		−	21.8011i		−	0.796596i
$750$	12.1155	+	29.0277i	0.442396	+	1.05994i
$751$	−28.9085	+	5.75025i	−1.05489	+	0.209830i	−0.691921	−	0.721973i	$-0.743235\pi$
$751$	−28.9085	+	5.75025i	−1.05489	+	0.209830i	−0.362964	+	0.931803i	$0.618235\pi$
$752$	0.109944			0.00400925
$753$	60.2263	−	11.9798i	2.19477	−	0.436567i
$754$	2.19403	−	11.0302i	0.0799020	−	0.401694i
$755$	18.7102	+	3.70420i	0.680933	+	0.134810i
$756$	−2.68786	−	6.48908i	−0.0977566	−	0.236005i
$757$	−3.97997	+	9.60850i	−0.144655	+	0.349227i	−0.979556	−	0.201173i	$-0.935525\pi$
$757$	−3.97997	+	9.60850i	−0.144655	+	0.349227i	0.834901	+	0.550400i	$0.185525\pi$
$758$	−24.2766	−	4.82892i	−0.881766	−	0.175394i
$759$	112.949	+	22.4669i	4.09977	+	0.815495i
$760$	−1.01060	+	1.51542i	−0.0366583	+	0.0549699i
$761$	−0.842952	+	0.842952i	−0.0305570	+	0.0305570i	−0.722220	−	0.691663i	$-0.756878\pi$
$761$	−0.842952	+	0.842952i	−0.0305570	+	0.0305570i	0.691663	+	0.722220i	$0.256878\pi$
$762$	8.33548	+	5.56959i	0.301962	+	0.201765i
$763$	−2.92807	+	1.21285i	−0.106003	+	0.0439080i
$764$	−0.286950			−0.0103815
$765$	−28.4724	+	35.2537i	−1.02942	+	1.27460i
$766$	−16.7778			−0.606206
$767$	−27.1359	+	11.2401i	−0.979820	+	0.405855i
$768$	−2.33925	−	1.56304i	−0.0844104	−	0.0564012i
$769$	−5.06321	+	5.06321i	−0.182584	+	0.182584i	−0.792481	−	0.609897i	$-0.791211\pi$
$769$	−5.06321	+	5.06321i	−0.182584	+	0.182584i	0.609897	+	0.792481i	$0.291211\pi$
$770$	16.7103	−	3.33951i	0.602198	−	0.120348i
$771$	26.7791	+	5.32670i	0.964427	+	0.191837i
$772$	24.0453	+	4.78290i	0.865408	+	0.172140i
$773$	−0.443463	+	1.07061i	−0.0159502	+	0.0385073i	−0.931654	−	0.363347i	$-0.881634\pi$
$773$	−0.443463	+	1.07061i	−0.0159502	+	0.0385073i	0.915704	+	0.401854i	$0.131634\pi$
$774$	2.67489	+	6.45775i	0.0961469	+	0.232119i
$775$	−4.30199	−	6.41338i	−0.154532	−	0.230375i
$776$	2.93692	−	14.7649i	0.105429	−	0.530029i
$777$	−25.0566	+	4.98407i	−0.898902	+	0.178803i
$778$	−11.2501			−0.403335
$779$	−6.33398	+	1.25991i	−0.226938	+	0.0451409i
$780$	−12.8786	−	31.0129i	−0.461129	−	1.11044i
$781$			32.1254i			1.14954i
$782$	−27.6832	−	8.18824i	−0.989948	−	0.292811i
$783$	8.02705	+	8.02705i	0.286863	+	0.286863i
$784$	−2.02850	+	4.89724i	−0.0724465	+	0.174901i
$785$	−0.385626	−	1.92961i	−0.0137636	−	0.0688706i
$786$	−23.4586	−	23.4586i	−0.836740	−	0.836740i
$787$	−7.24294	−	36.4127i	−0.258183	−	1.29797i	−0.864453	−	0.502714i	$-0.832335\pi$
$787$	−7.24294	−	36.4127i	−0.258183	−	1.29797i	0.606270	−	0.795259i	$-0.292665\pi$
$788$	−1.39786	−	2.09205i	−0.0497968	−	0.0745261i
$789$	−37.4712	+	25.0374i	−1.33401	+	0.891356i
$790$	−4.38273	−	10.5540i	−0.155930	−	0.375494i
$791$	13.6253	−	5.64377i	0.484459	−	0.200669i
$792$	−5.60592	+	28.1829i	−0.199198	+	1.00143i
$793$	25.7653	−	17.2158i	0.914951	−	0.611351i
$794$	20.7302	−	31.0249i	0.735687	−	1.10103i
$795$	−6.23286	+	0.00560418i	−0.221057	+	0.000198760i
$796$	2.52203	+	12.6791i	0.0893911	+	0.449399i
$797$	−0.0157219	−	0.0379559i	−0.000556897	−	0.00134447i	0.923601	−	0.383356i	$-0.125232\pi$
$797$	−0.0157219	−	0.0379559i	−0.000556897	−	0.00134447i	−0.924158	+	0.382011i	$0.875232\pi$
$798$	2.11245	−	2.11245i	0.0747797	−	0.0747797i
$799$	0.134597	+	0.432868i	0.00476169	+	0.0153138i
$800$	−3.54189	−	3.52917i	−0.125225	−	0.124775i
$801$	−5.00458	−	2.07296i	−0.176828	−	0.0732446i
$802$	2.20217	−	3.29578i	0.0777614	−	0.116378i
$803$			47.8395i			1.68822i
$804$	13.6432	+	9.11608i	0.481158	+	0.321500i
$805$	16.9592	−	11.3538i	0.597732	−	0.400170i
$806$	4.58043	+	6.85509i	0.161339	+	0.241460i
$807$	−42.8453	−	17.7471i	−1.50823	−	0.624727i
$808$	−6.24155	−	2.58533i	−0.219577	−	0.0909518i
$809$	21.2673	+	31.8287i	0.747717	+	1.11904i	0.988904	+	0.148559i	$0.0474635\pi$
$809$	21.2673	+	31.8287i	0.747717	+	1.11904i	−0.241186	+	0.970479i	$0.577537\pi$
$810$	0.906729	+	0.179512i	0.0318592	+	0.00630742i
$811$	−3.94173	−	2.63378i	−0.138413	−	0.0924845i	0.484436	−	0.874827i	$-0.339025\pi$
$811$	−3.94173	−	2.63378i	−0.138413	−	0.0924845i	−0.622849	+	0.782342i	$0.714025\pi$
$812$			2.74641i			0.0963799i
$813$	−8.08560	+	12.1009i	−0.283574	+	0.424399i
$814$	37.6250	+	15.5848i	1.31876	+	0.546246i
$815$	0.0136979	+	15.2346i	0.000479818	+	0.533644i
$816$	3.29016	−	11.1235i	0.115179	−	0.389401i
$817$	−0.819129	+	0.819129i	−0.0286577	+	0.0286577i
$818$	0.116628	+	0.281565i	0.00407780	+	0.00984469i
$819$	6.67234	+	33.5441i	0.233150	+	1.17213i
$820$	−0.0159394	−	17.7275i	−0.000556629	−	0.619072i
$821$	24.1132	−	36.0879i	0.841555	−	1.25948i	−0.122151	−	0.992512i	$-0.538979\pi$
$821$	24.1132	−	36.0879i	0.841555	−	1.25948i	0.963706	−	0.266965i	$-0.0860208\pi$
$822$	−31.7388	+	21.2072i	−1.10702	+	0.739685i
$823$	−6.32657	+	31.8058i	−0.220531	+	1.10868i	0.698837	+	0.715281i	$0.253701\pi$
$823$	−6.32657	+	31.8058i	−0.220531	+	1.10868i	−0.919367	+	0.393401i	$0.871299\pi$
$824$	6.21141	−	2.57285i	0.216385	−	0.0896294i
$825$	−31.3345	+	76.0346i	−1.09093	+	2.64718i
$826$	5.96393	−	3.98497i	0.207512	−	0.138655i
$827$	−24.8130	−	37.1352i	−0.862832	−	1.29132i	−0.955311	−	0.295604i	$-0.904479\pi$
$827$	−24.8130	−	37.1352i	−0.862832	−	1.29132i	0.0924789	−	0.995715i	$-0.470521\pi$
$828$	6.71394	+	33.7533i	0.233326	+	1.17301i
$829$	24.9924	+	24.9924i	0.868024	+	0.868024i	0.992253	−	0.124230i	$-0.0396460\pi$
$829$	24.9924	+	24.9924i	0.868024	+	0.868024i	−0.124230	+	0.992253i	$0.539646\pi$
$830$	4.80044	+	3.20131i	0.166626	+	0.111119i
$831$	22.2561	−	53.7309i	0.772055	−	1.86390i
$832$	3.77449	+	3.77449i	0.130857	+	0.130857i
$833$	−21.7646	−	1.99122i	−0.754098	−	0.0689917i
$834$			29.0023i			1.00427i
$835$	11.4604	−	27.7384i	0.396603	−	0.959926i
$836$	−4.67075	+	0.929070i	−0.161541	+	0.0321326i
$837$	−8.32205			−0.287652
$838$	−35.8559	+	7.13218i	−1.23862	+	0.246377i
$839$	−9.26094	+	46.5579i	−0.319723	+	1.60736i	0.402314	+	0.915502i	$0.368206\pi$
$839$	−9.26094	+	46.5579i	−0.319723	+	1.60736i	−0.722037	+	0.691855i	$0.756794\pi$
$840$	4.56214	+	6.81445i	0.157409	+	0.235121i
$841$	9.39915	+	22.6916i	0.324109	+	0.782468i
$842$	−8.51010	+	20.5452i	−0.293277	+	0.708034i
$843$	−3.60837	−	0.717749i	−0.124279	−	0.0247206i
$844$	13.9875	+	2.78229i	0.481470	+	0.0957702i
$845$	6.78939	+	33.9729i	0.233562	+	1.16870i
$846$	0.382116	−	0.382116i	0.0131374	−	0.0131374i
$847$	25.1219	+	16.7859i	0.863197	+	0.576770i
$848$	0.915351	−	0.379151i	0.0314333	−	0.0130201i
$849$	12.8283			0.440265
$850$	9.55885	−	18.2655i	0.327866	−	0.626501i
$851$	48.7744			1.67196
$852$	−14.2831	+	5.91624i	−0.489330	+	0.202687i
$853$	−16.1374	−	10.7826i	−0.552533	−	0.369191i	0.247740	−	0.968827i	$-0.420312\pi$
$853$	−16.1374	−	10.7826i	−0.552533	−	0.369191i	−0.800273	+	0.599636i	$0.795312\pi$
$854$	−5.35094	+	5.35094i	−0.183106	+	0.183106i
$855$	1.75452	+	8.77929i	0.0600032	+	0.300245i
$856$	−16.4030	−	3.26275i	−0.560642	−	0.111519i
$857$	12.8130	+	2.54865i	0.437682	+	0.0870604i	0.409013	−	0.912529i	$-0.365873\pi$
$857$	12.8130	+	2.54865i	0.437682	+	0.0870604i	0.0286691	+	0.999589i	$0.490873\pi$
$858$	33.5982	−	81.1133i	1.14702	−	2.76916i
$859$	−8.74774	−	21.1189i	−0.298469	−	0.720568i	−0.999969	−	0.00789846i	$-0.997486\pi$
$859$	−8.74774	−	21.1189i	−0.298469	−	0.720568i	0.701500	−	0.712670i	$-0.252514\pi$
$860$	−1.76903	−	2.64240i	−0.0603235	−	0.0901050i
$861$	−5.67230	+	28.5166i	−0.193312	+	0.971843i
$862$	34.8166	−	6.92546i	1.18586	−	0.235882i
$863$	48.9670			1.66686			0.833429	−	0.552627i	$-0.186375\pi$
$863$	48.9670			1.66686			0.833429	+	0.552627i	$0.186375\pi$
$864$	−5.28458	+	1.05117i	−0.179785	+	0.0357615i
$865$	20.1859	−	48.8572i	0.686341	−	1.66120i
$866$		−	4.70842i		−	0.159999i
$867$	47.8230	−	0.663809i	1.62416	−	0.0225441i
$868$	−1.42367	−	1.42367i	−0.0483225	−	0.0483225i
$869$	11.4338	−	27.6036i	0.387865	−	0.936390i
$870$	−11.0270	−	7.35365i	−0.373849	−	0.249312i
$871$	−22.0139	−	22.0139i	−0.745914	−	0.745914i
$872$	0.474319	+	2.38457i	0.0160625	+	0.0807516i
$873$	−41.1087	−	61.5235i	−1.39132	−	2.08226i
$874$	−4.74231	+	3.16871i	−0.160411	+	0.107183i
$875$	5.61362	+	13.4497i	0.189775	+	0.454684i
$876$	−21.2696	+	8.81016i	−0.718633	+	0.297668i
$877$	−1.88944	+	9.49886i	−0.0638019	+	0.320754i	−0.999485	−	0.0320876i	$-0.989784\pi$
$877$	−1.88944	+	9.49886i	−0.0638019	+	0.320754i	0.935683	+	0.352841i	$0.114784\pi$
$878$	−14.1420	+	9.44938i	−0.477269	+	0.318901i
$879$	48.8937	−	73.1747i	1.64915	−	2.46812i
$880$	−0.0117539	−	13.0725i	−0.000396224	−	0.440673i
$881$	−3.65125	−	18.3561i	−0.123014	−	0.618431i	−0.992273	−	0.124075i	$-0.960404\pi$
$881$	−3.65125	−	18.3561i	−0.123014	−	0.618431i	0.869259	−	0.494356i	$-0.164596\pi$
$882$	9.97043	+	24.0708i	0.335722	+	0.810505i
$883$	−19.9922	+	19.9922i	−0.672793	+	0.672793i	−0.958359	−	0.285566i	$-0.907818\pi$
$883$	−19.9922	+	19.9922i	−0.672793	+	0.672793i	0.285566	+	0.958359i	$0.407818\pi$
$884$	−10.2400	+	19.4816i	−0.344407	+	0.655238i
$885$	0.0311240	+	34.6155i	0.00104622	+	1.16359i
$886$	−10.5583	−	4.37340i	−0.354713	−	0.146927i
$887$	−29.6178	+	44.3262i	−0.994469	+	1.48833i	−0.126341	+	0.991987i	$0.540323\pi$
$887$	−29.6178	+	44.3262i	−0.994469	+	1.48833i	−0.868128	+	0.496340i	$0.834677\pi$
$888$			19.5983i			0.657676i
$889$	3.86217	+	2.58062i	0.129533	+	0.0865511i
$890$	2.41741	+	0.478594i	0.0810318	+	0.0160425i
$891$	1.34262	+	2.00937i	0.0449795	+	0.0673165i
$892$	−12.6106	−	5.22346i	−0.422233	−	0.174894i
$893$	0.0827422	+	0.0342730i	0.00276886	+	0.00114690i
$894$	−30.1230	−	45.0823i	−1.00746	−	1.50778i
$895$	−46.0893	+	30.8559i	−1.54060	+	1.03140i
$896$	−1.08387	−	0.724218i	−0.0362095	−	0.0241944i
$897$		−	105.150i		−	3.51084i
$898$	6.34120	−	9.49028i	0.211609	−	0.316695i
$899$	3.00637	+	1.24528i	0.100268	+	0.0415324i
$900$	−24.5758	+	0.0441939i	−0.819193	+	0.00147313i
$901$	2.61338	+	3.13972i	0.0870642	+	0.104599i
$902$	32.7734	−	32.7734i	1.09123	−	1.09123i
$903$	1.99585	+	4.81841i	0.0664178	+	0.160347i
$904$	−2.20717	−	11.0962i	−0.0734093	−	0.369053i
$905$	−12.6907	+	0.0114106i	−0.421853	+	0.000379303i
$906$	−13.3325	+	19.9534i	−0.442941	+	0.662909i
$907$	−28.6777	+	19.1618i	−0.952226	+	0.636257i	−0.931583	−	0.363530i	$-0.881572\pi$
$907$	−28.6777	+	19.1618i	−0.952226	+	0.636257i	−0.0206435	+	0.999787i	$0.506572\pi$
$908$	−1.53876	+	7.73585i	−0.0510654	+	0.256723i
$909$	−30.6783	+	12.7074i	−1.01753	+	0.421476i
$910$	−5.96720	−	14.3695i	−0.197811	−	0.476345i
$911$	−16.3825	+	10.9464i	−0.542777	+	0.362672i	−0.796532	−	0.604597i	$-0.793334\pi$
$911$	−16.3825	+	10.9464i	−0.542777	+	0.362672i	0.253755	+	0.967269i	$0.418334\pi$
$912$	−1.27324	−	1.90553i	−0.0421610	−	0.0630985i
$913$	2.94305	+	14.7957i	0.0974007	+	0.489666i
$914$	−5.68253	−	5.68253i	−0.187961	−	0.187961i
$915$	−7.15689	−	35.8118i	−0.236599	−	1.18390i
$916$	−4.05598	+	9.79199i	−0.134013	+	0.323537i
$917$	−10.8693	−	10.8693i	−0.358936	−	0.358936i
$918$	−10.6082	−	19.5194i	−0.350121	−	0.644237i
$919$			7.48557i			0.246926i	0.992349	+	0.123463i	$0.0394001\pi$
$919$			7.48557i			0.246926i	−0.992349	+	0.123463i	$0.960600\pi$
$920$	−6.00440	−	14.4591i	−0.197959	−	0.476703i
$921$	−47.2857	+	9.40572i	−1.55812	+	0.309929i
$922$	−34.8833			−1.14882
$923$	28.7689	−	5.72249i	0.946941	−	0.188358i
$924$	−4.18282	+	21.0285i	−0.137605	+	0.691786i
$925$	−6.73363	+	34.1733i	−0.221400	+	1.12361i
$926$	14.9580	+	36.1119i	0.491552	+	1.18671i
$927$	12.6460	−	30.5301i	0.415349	−	1.00274i
$928$	2.06637	+	0.411026i	0.0678319	+	0.0134926i
$929$	−23.3245	−	4.63954i	−0.765253	−	0.152218i	−0.202995	−	0.979180i	$-0.565067\pi$
$929$	−23.3245	−	4.63954i	−0.765253	−	0.152218i	−0.562258	+	0.826962i	$0.690067\pi$
$930$	9.52806	−	1.90416i	0.312438	−	0.0624398i
$931$	−3.05324	+	3.05324i	−0.100066	+	0.100066i
$932$	1.98513	+	1.32642i	0.0650252	+	0.0434484i
$933$	−14.2679	+	5.90995i	−0.467110	+	0.193483i
$934$	−16.8822			−0.552402
$935$	51.4541	−	16.0499i	1.68273	−	0.524889i
$936$	26.2369			0.857579
$937$	−27.2845	+	11.3016i	−0.891345	+	0.369207i	−0.780886	−	0.624674i	$-0.785232\pi$
$937$	−27.2845	+	11.3016i	−0.891345	+	0.369207i	−0.110459	+	0.993881i	$0.535232\pi$
$938$	6.32144	+	4.22385i	0.206402	+	0.137914i
$939$	12.7510	−	12.7510i	0.416112	−	0.416112i
$940$	−0.136399	+	0.204533i	−0.00444884	+	0.00667114i
$941$	1.26326	+	0.251277i	0.0411810	+	0.00819140i	0.215638	−	0.976473i	$-0.430817\pi$
$941$	1.26326	+	0.251277i	0.0411810	+	0.00819140i	−0.174457	+	0.984665i	$0.555817\pi$
$942$	2.42824	+	0.483007i	0.0791163	+	0.0157372i
$943$	21.2425	−	51.2840i	0.691752	−	1.67004i
$944$	−2.10569	−	5.08359i	−0.0685345	−	0.165457i
$945$	15.4065	+	3.05015i	0.501173	+	0.0992212i
$946$	1.62195	−	8.15407i	0.0527340	−	0.265112i
$947$	36.8415	−	7.32823i	1.19719	−	0.238136i	0.444052	−	0.896001i	$-0.353540\pi$
$947$	36.8415	−	7.32823i	1.19719	−	0.238136i	0.753136	+	0.657865i	$0.228540\pi$
$948$	14.3783			0.466986
$949$	42.8412	−	8.52164i	1.39068	−	0.276624i
$950$	−1.56542	−	3.76011i	−0.0507888	−	0.121994i
$951$			54.2951i			1.76064i
$952$	1.52447	−	5.15398i	0.0494082	−	0.167041i
$953$	25.9594	+	25.9594i	0.840908	+	0.840908i	0.988977	−	0.148069i	$-0.0473056\pi$
$953$	25.9594	+	25.9594i	0.840908	+	0.840908i	−0.148069	+	0.988977i	$0.547306\pi$
$954$	1.86359	−	4.49910i	0.0603360	−	0.145664i
$955$	0.355996	−	0.533825i	0.0115198	−	0.0172742i
$956$	−7.40929	−	7.40929i	−0.239634	−	0.239634i
$957$	−6.76041	−	33.9869i	−0.218533	−	1.09864i
$958$	−3.52921	−	5.28183i	−0.114023	−	0.170648i
$959$	−14.7059	+	9.82614i	−0.474877	+	0.317303i
$960$	5.80990	−	2.41266i	0.187514	−	0.0778683i
$961$	26.4363	−	10.9503i	0.852784	−	0.353235i
$962$	7.25433	−	36.4700i	0.233889	−	1.17584i
$963$	−68.3492	+	45.6695i	−2.20252	+	1.47168i
$964$	3.60143	−	5.38993i	0.115994	−	0.173598i
$965$	−38.7289	+	38.7986i	−1.24673	+	1.24897i
$966$	5.00957	+	25.1848i	0.161180	+	0.810307i
$967$	9.00902	+	21.7497i	0.289711	+	0.699423i	0.999990	−	0.00449664i	$-0.00143133\pi$
$967$	9.00902	+	21.7497i	0.289711	+	0.699423i	−0.710279	+	0.703920i	$0.751431\pi$
$968$	16.3893	−	16.3893i	0.526771	−	0.526771i
$969$	5.94366	−	7.34574i	0.190938	−	0.235979i
$970$	23.8241	+	23.7813i	0.764946	+	0.763571i
$971$	−16.1076	−	6.67199i	−0.516918	−	0.214114i	0.108945	−	0.994048i	$-0.465253\pi$
$971$	−16.1076	−	6.67199i	−0.516918	−	0.214114i	−0.625862	+	0.779933i	$0.715253\pi$
$972$	8.33431	−	12.4732i	0.267323	−	0.400078i
$973$			13.4380i			0.430801i
$974$	22.4720	+	15.0153i	0.720048	+	0.481121i
$975$	73.6719	+	14.5166i	2.35939	+	0.464903i
$976$	3.22518	+	4.82682i	0.103235	+	0.154503i
$977$	−11.9048	−	4.93111i	−0.380867	−	0.157760i	0.184032	−	0.982920i	$-0.441085\pi$
$977$	−11.9048	−	4.93111i	−0.380867	−	0.157760i	−0.564899	+	0.825160i	$0.691085\pi$
$978$	−17.7089	−	7.33526i	−0.566268	−	0.234556i
$979$	3.57953	+	5.35714i	0.114402	+	0.171215i
$980$	−6.59392	−	9.84932i	−0.210635	−	0.314625i
$981$	9.93619	+	6.63915i	0.317238	+	0.211972i
$982$		−	0.205934i		−	0.00657160i
$983$	18.1782	−	27.2056i	0.579795	−	0.867724i	−0.419402	−	0.907801i	$-0.637760\pi$
$983$	18.1782	−	27.2056i	0.579795	−	0.867724i	0.999197	+	0.0400767i	$0.0127602\pi$
$984$	20.6067	+	8.53557i	0.656918	+	0.272104i
$985$	5.62613	−	0.00505865i	0.179264	−	0.000161182i
$986$	0.911426	+	8.63883i	0.0290257	+	0.275116i
$987$	0.285114	−	0.285114i	0.00907526	−	0.00907526i
$988$	1.66400	+	4.01725i	0.0529388	+	0.127806i
$989$	−1.94253	−	9.76574i	−0.0617688	−	0.310533i
$990$	−45.4749	−	45.3932i	−1.44529	−	1.44269i
$991$	2.85767	−	4.27680i	0.0907767	−	0.135857i	−0.783302	−	0.621642i	$-0.786466\pi$
$991$	2.85767	−	4.27680i	0.0907767	−	0.135857i	0.874079	+	0.485785i	$0.161466\pi$
$992$	−1.28422	+	0.858089i	−0.0407741	+	0.0272444i
$993$	7.93796	−	39.9068i	0.251903	−	1.26640i
$994$	−6.61793	+	2.74124i	−0.209908	+	0.0869467i
$995$	−26.7163	−	11.0381i	−0.846965	−	0.349932i
$996$	−6.03622	+	4.03327i	−0.191265	+	0.127799i
$997$	28.9665	+	43.3514i	0.917378	+	1.37295i	0.927828	+	0.373007i	$0.121673\pi$
$997$	28.9665	+	43.3514i	0.917378	+	1.37295i	−0.0104506	+	0.999945i	$0.503327\pi$
$998$	4.34370	+	21.8373i	0.137498	+	0.691247i
$999$	26.5406	+	26.5406i	0.839706	+	0.839706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.r.a.23.4	yes	32
5.2	odd	4		170.2.o.a.57.4	yes	32
5.3	odd	4		850.2.s.c.57.1		32
5.4	even	2		850.2.v.c.193.1		32
17.3	odd	16		170.2.o.a.3.4	✓	32
85.3	even	16		850.2.v.c.207.1		32
85.37	even	16	inner	170.2.r.a.37.4	yes	32
85.54	odd	16		850.2.s.c.343.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.a.3.4	✓	32	17.3	odd	16
170.2.o.a.57.4	yes	32	5.2	odd	4
170.2.r.a.23.4	yes	32	1.1	even	1	trivial
170.2.r.a.37.4	yes	32	85.37	even	16	inner
850.2.s.c.57.1		32	5.3	odd	4
850.2.s.c.343.1		32	85.54	odd	16
850.2.v.c.193.1		32	5.4	even	2
850.2.v.c.207.1		32	85.3	even	16

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 + 0.382683i) q^{2} +(2.33925 + 1.56304i) q^{3} +(0.707107 - 0.707107i) q^{4} +(0.438207 + 2.19271i) q^{5} +(-2.75933 - 0.548865i) q^{6} +(-1.27851 - 0.254312i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(1.88095 + 4.54102i) q^{9} +(-1.24396 - 1.85810i) q^{10} +(1.14054 - 5.73386i) q^{11} +(2.75933 - 0.548865i) q^{12} -5.33794 q^{13} +(1.27851 - 0.254312i) q^{14} +(-2.40221 + 5.81423i) q^{15} -1.00000i q^{16} +(3.93717 - 1.22423i) q^{17} +(-3.47555 - 3.47555i) q^{18} +(0.311731 - 0.752584i) q^{19} +(1.86034 + 1.24062i) q^{20} +(-2.59326 - 2.59326i) q^{21} +(1.14054 + 5.73386i) q^{22} +(3.88994 + 5.82170i) q^{23} +(-2.33925 + 1.56304i) q^{24} +(-4.61595 + 1.92172i) q^{25} +(4.93161 - 2.04274i) q^{26} +(-1.05117 + 5.28458i) q^{27} +(-1.08387 + 0.724218i) q^{28} +(1.17050 - 1.75178i) q^{29} +(-0.00565639 - 6.29093i) q^{30} +(0.301321 + 1.51484i) q^{31} +(0.382683 + 0.923880i) q^{32} +(11.6302 - 11.6302i) q^{33} +(-3.16897 + 2.63773i) q^{34} +(-0.00262084 - 2.91484i) q^{35} +(4.54102 + 1.88095i) q^{36} +(3.87014 - 5.79208i) q^{37} +0.814591i q^{38} +(-12.4868 - 8.34339i) q^{39} +(-2.19349 - 0.434263i) q^{40} +(-4.40455 - 6.59188i) q^{41} +(3.38825 + 1.40346i) q^{42} +(-1.31384 - 0.544211i) q^{43} +(-3.24797 - 4.86093i) q^{44} +(-9.13290 + 6.11429i) q^{45} +(-5.82170 - 3.88994i) q^{46} +0.109944i q^{47} +(1.56304 - 2.33925i) q^{48} +(-4.89724 - 2.02850i) q^{49} +(3.52917 - 3.54189i) q^{50} +(11.1235 + 3.29016i) q^{51} +(-3.77449 + 3.77449i) q^{52} +(0.379151 + 0.915351i) q^{53} +(-1.05117 - 5.28458i) q^{54} +(13.0725 - 0.0117539i) q^{55} +(0.724218 - 1.08387i) q^{56} +(1.90553 - 1.27324i) q^{57} +(-0.411026 + 2.06637i) q^{58} +(5.08359 - 2.10569i) q^{59} +(2.41266 + 5.80990i) q^{60} +(-4.82682 + 3.22518i) q^{61} +(-0.858089 - 1.28422i) q^{62} +(-1.24998 - 6.28410i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(-2.33912 - 11.7045i) q^{65} +(-6.29423 + 15.1956i) q^{66} +(4.12405 + 4.12405i) q^{67} +(1.91834 - 3.64966i) q^{68} +19.6985i q^{69} +(1.11788 + 2.69196i) q^{70} +(-5.38952 + 1.07204i) q^{71} -4.91517 q^{72} +(-8.02579 + 1.59643i) q^{73} +(-1.35901 + 6.83222i) q^{74} +(-13.8016 - 2.71951i) q^{75} +(-0.311731 - 0.752584i) q^{76} +(-2.91637 + 7.04075i) q^{77} +(14.7291 + 2.92981i) q^{78} +(5.01247 + 0.997043i) q^{79} +(2.19271 - 0.438207i) q^{80} +(-0.292298 + 0.292298i) q^{81} +(6.59188 + 4.40455i) q^{82} +(-2.38399 + 0.987480i) q^{83} -3.66742 q^{84} +(4.40967 + 8.09659i) q^{85} +1.42209 q^{86} +(5.47620 - 2.26832i) q^{87} +(4.86093 + 3.24797i) q^{88} +(-0.779290 + 0.779290i) q^{89} +(6.09786 - 9.14388i) q^{90} +(6.82461 + 1.35750i) q^{91} +(6.86717 + 1.36596i) q^{92} +(-1.66289 + 4.01457i) q^{93} +(-0.0420738 - 0.101575i) q^{94} +(1.78680 + 0.353747i) q^{95} +(-0.548865 + 2.75933i) q^{96} +(-14.7649 + 2.93692i) q^{97} +5.30073 q^{98} +(28.1829 - 5.60592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{10} - 48 q^{15} + 16 q^{18} - 24 q^{25} + 8 q^{26} + 24 q^{27} - 8 q^{28} - 8 q^{29} - 16 q^{30} - 16 q^{31} + 64 q^{33} + 24 q^{34} + 32 q^{35} - 32 q^{37} - 32 q^{39} + 16 q^{41} - 24 q^{42}+ \cdots - 64 q^{99}+O(q^{100}) \) 32 * q - 8 * q^10 - 48 * q^15 + 16 * q^18 - 24 * q^25 + 8 * q^26 + 24 * q^27 - 8 * q^28 - 8 * q^29 - 16 * q^30 - 16 * q^31 + 64 * q^33 + 24 * q^34 + 32 * q^35 - 32 * q^37 - 32 * q^39 + 16 * q^41 - 24 * q^42 - 16 * q^43 - 16 * q^44 - 24 * q^45 - 16 * q^49 - 32 * q^50 + 32 * q^51 - 16 * q^52 + 16 * q^53 + 24 * q^54 - 8 * q^55 + 8 * q^56 - 24 * q^57 - 16 * q^58 - 64 * q^59 + 40 * q^60 - 24 * q^61 - 40 * q^62 - 24 * q^63 + 32 * q^65 + 16 * q^67 + 40 * q^70 + 8 * q^71 - 16 * q^72 + 32 * q^73 + 8 * q^74 - 56 * q^75 + 24 * q^77 + 32 * q^78 + 72 * q^79 + 8 * q^80 + 48 * q^81 + 48 * q^82 + 16 * q^83 + 8 * q^85 - 64 * q^86 + 40 * q^87 + 32 * q^88 + 16 * q^89 + 24 * q^90 + 48 * q^91 + 24 * q^92 - 8 * q^93 + 8 * q^94 + 56 * q^95 - 48 * q^97 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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