LMFDB - Embedded newform 336.2.s.d.155.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.1
Character	$\chi$	$=$	336.155
Dual form			336.2.s.d.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33839 - 0.456860i) q^{2} +(-1.70974 + 0.277087i) q^{3} +(1.58256 + 1.22291i) q^{4} +(-0.459458 + 0.459458i) q^{5} +(2.41489 + 0.410265i) q^{6} +1.00000 q^{7} +(-1.55938 - 2.35973i) q^{8} +(2.84645 - 0.947494i) q^{9} +O(q^{10})$	\(q+(-1.33839 - 0.456860i) q^{2} +(-1.70974 + 0.277087i) q^{3} +(1.58256 + 1.22291i) q^{4} +(-0.459458 + 0.459458i) q^{5} +(2.41489 + 0.410265i) q^{6} +1.00000 q^{7} +(-1.55938 - 2.35973i) q^{8} +(2.84645 - 0.947494i) q^{9} +(0.824840 - 0.405024i) q^{10} +(-1.43432 - 1.43432i) q^{11} +(-3.04462 - 1.65236i) q^{12} +(-1.18426 + 1.18426i) q^{13} +(-1.33839 - 0.456860i) q^{14} +(0.658245 - 0.912864i) q^{15} +(1.00898 + 3.87065i) q^{16} +7.20845i q^{17} +(-4.24252 - 0.0323143i) q^{18} +(-2.23529 - 2.23529i) q^{19} +(-1.28899 + 0.165243i) q^{20} +(-1.70974 + 0.277087i) q^{21} +(1.26440 + 2.57497i) q^{22} -0.540517i q^{23} +(3.31998 + 3.60246i) q^{24} +4.57780i q^{25} +(2.12603 - 1.04395i) q^{26} +(-4.60416 + 2.40868i) q^{27} +(1.58256 + 1.22291i) q^{28} +(4.14139 + 4.14139i) q^{29} +(-1.29804 + 0.921040i) q^{30} +10.4187i q^{31} +(0.417944 - 5.64139i) q^{32} +(2.84976 + 2.05490i) q^{33} +(3.29325 - 9.64770i) q^{34} +(-0.459458 + 0.459458i) q^{35} +(5.66337 + 1.98149i) q^{36} +(-1.36361 - 1.36361i) q^{37} +(1.97047 + 4.01290i) q^{38} +(1.69663 - 2.35292i) q^{39} +(1.80067 + 0.367731i) q^{40} +2.16181 q^{41} +(2.41489 + 0.410265i) q^{42} +(-6.40813 + 6.40813i) q^{43} +(-0.515851 - 4.02395i) q^{44} +(-0.872488 + 1.74315i) q^{45} +(-0.246940 + 0.723420i) q^{46} -7.63641 q^{47} +(-2.79760 - 6.33825i) q^{48} +1.00000 q^{49} +(2.09141 - 6.12686i) q^{50} +(-1.99736 - 12.3246i) q^{51} +(-3.32239 + 0.425914i) q^{52} +(-2.29189 + 2.29189i) q^{53} +(7.26257 - 1.12030i) q^{54} +1.31802 q^{55} +(-1.55938 - 2.35973i) q^{56} +(4.44114 + 3.20240i) q^{57} +(-3.65075 - 7.43482i) q^{58} +(6.32068 + 6.32068i) q^{59} +(2.15806 - 0.639685i) q^{60} +(0.637183 - 0.637183i) q^{61} +(4.75989 - 13.9442i) q^{62} +(2.84645 - 0.947494i) q^{63} +(-3.13670 + 7.35942i) q^{64} -1.08823i q^{65} +(-2.87528 - 4.05219i) q^{66} +(-2.14006 - 2.14006i) q^{67} +(-8.81529 + 11.4078i) q^{68} +(0.149770 + 0.924145i) q^{69} +(0.824840 - 0.405024i) q^{70} -14.6958i q^{71} +(-6.67451 - 5.23936i) q^{72} -0.233482i q^{73} +(1.20206 + 2.44801i) q^{74} +(-1.26845 - 7.82686i) q^{75} +(-0.803915 - 6.27103i) q^{76} +(-1.43432 - 1.43432i) q^{77} +(-3.34570 + 2.37399i) q^{78} -4.93151i q^{79} +(-2.24198 - 1.31482i) q^{80} +(7.20451 - 5.39398i) q^{81} +(-2.89334 - 0.987644i) q^{82} +(-1.76156 + 1.76156i) q^{83} +(-3.04462 - 1.65236i) q^{84} +(-3.31198 - 3.31198i) q^{85} +(11.5042 - 5.64894i) q^{86} +(-8.22824 - 5.93319i) q^{87} +(-1.14798 + 5.62128i) q^{88} +7.79085 q^{89} +(1.96410 - 1.93441i) q^{90} +(-1.18426 + 1.18426i) q^{91} +(0.661004 - 0.855399i) q^{92} +(-2.88688 - 17.8133i) q^{93} +(10.2205 + 3.48877i) q^{94} +2.05404 q^{95} +(0.848578 + 9.76114i) q^{96} -10.0585 q^{97} +(-1.33839 - 0.456860i) q^{98} +(-5.44174 - 2.72371i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) $ 48 * q + 6 * q^6 + 48 * q^7	$ 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) $ 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.33839	−	0.456860i	−0.946382	−	0.323049i
$2$	−1.33839	−	0.456860i	−0.946382	−	0.323049i
$3$	−1.70974	+	0.277087i	−0.987121	+	0.159976i
$3$	−1.70974	+	0.277087i	−0.987121	+	0.159976i
$4$	1.58256	+	1.22291i	0.791279	+	0.611455i
$5$	−0.459458	+	0.459458i	−0.205476	+	0.205476i	−0.802341	−	0.596866i	$-0.796413\pi$
$5$	−0.459458	+	0.459458i	−0.205476	+	0.205476i	0.596866	+	0.802341i	$0.296413\pi$
$6$	2.41489	+	0.410265i	0.985874	+	0.167490i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−1.55938	−	2.35973i	−0.551322	−	0.834292i
$9$	2.84645	−	0.947494i	0.948815	−	0.315831i
$10$	0.824840	−	0.405024i	0.260837	−	0.128080i
$11$	−1.43432	−	1.43432i	−0.432465	−	0.432465i	0.457001	−	0.889466i	$-0.348924\pi$
$11$	−1.43432	−	1.43432i	−0.432465	−	0.432465i	−0.889466	+	0.457001i	$0.848924\pi$
$12$	−3.04462	−	1.65236i	−0.878906	−	0.476995i
$13$	−1.18426	+	1.18426i	−0.328454	+	0.328454i	−0.851998	−	0.523545i	$-0.824609\pi$
$13$	−1.18426	+	1.18426i	−0.328454	+	0.328454i	0.523545	+	0.851998i	$0.324609\pi$
$14$	−1.33839	−	0.456860i	−0.357699	−	0.122101i
$15$	0.658245	−	0.912864i	0.169958	−	0.235701i
$16$	1.00898	+	3.87065i	0.252245	+	0.967663i
$17$			7.20845i			1.74831i	0.485650	+	0.874153i	$0.338583\pi$
$17$			7.20845i			1.74831i	−0.485650	+	0.874153i	$0.661417\pi$
$18$	−4.24252	−	0.0323143i	−0.999971	−	0.00761655i
$19$	−2.23529	−	2.23529i	−0.512811	−	0.512811i	0.402576	−	0.915387i	$-0.368115\pi$
$19$	−2.23529	−	2.23529i	−0.512811	−	0.512811i	−0.915387	+	0.402576i	$0.868115\pi$
$20$	−1.28899	+	0.165243i	−0.288228	+	0.0369494i
$21$	−1.70974	+	0.277087i	−0.373097	+	0.0604652i
$22$	1.26440	+	2.57497i	0.269570	+	0.548985i
$23$		−	0.540517i		−	0.112706i	−0.998411	−	0.0563528i	$-0.982053\pi$
$23$		−	0.540517i		−	0.112706i	0.998411	−	0.0563528i	$-0.0179471\pi$
$24$	3.31998	+	3.60246i	0.677689	+	0.735349i
$25$			4.57780i			0.915559i
$26$	2.12603	−	1.04395i	0.416949	−	0.204736i
$27$	−4.60416	+	2.40868i	−0.886070	+	0.463551i
$28$	1.58256	+	1.22291i	0.299075	+	0.231108i
$29$	4.14139	+	4.14139i	0.769037	+	0.769037i	0.977937	−	0.208900i	$-0.0669883\pi$
$29$	4.14139	+	4.14139i	0.769037	+	0.769037i	−0.208900	+	0.977937i	$0.566988\pi$
$30$	−1.29804	+	0.921040i	−0.236988	+	0.168158i
$31$			10.4187i			1.87125i	0.352992	+	0.935626i	$0.385164\pi$
$31$			10.4187i			1.87125i	−0.352992	+	0.935626i	$0.614836\pi$
$32$	0.417944	−	5.64139i	0.0738827	−	0.997267i
$33$	2.84976	+	2.05490i	0.496079	+	0.357711i
$34$	3.29325	−	9.64770i	0.564788	−	1.65457i
$35$	−0.459458	+	0.459458i	−0.0776625	+	0.0776625i
$36$	5.66337	+	1.98149i	0.943894	+	0.330248i
$37$	−1.36361	−	1.36361i	−0.224176	−	0.224176i	0.586078	−	0.810254i	$-0.300671\pi$
$37$	−1.36361	−	1.36361i	−0.224176	−	0.224176i	−0.810254	+	0.586078i	$0.800671\pi$
$38$	1.97047	+	4.01290i	0.319652	+	0.650978i
$39$	1.69663	−	2.35292i	0.271679	−	0.376768i
$40$	1.80067	+	0.367731i	0.284710	+	0.0581434i
$41$	2.16181			0.337618			0.168809	−	0.985649i	$-0.446008\pi$
$41$	2.16181			0.337618			0.168809	+	0.985649i	$0.446008\pi$
$42$	2.41489	+	0.410265i	0.372625	+	0.0633052i
$43$	−6.40813	+	6.40813i	−0.977231	+	0.977231i	−0.999746	−	0.0225153i	$-0.992833\pi$
$43$	−6.40813	+	6.40813i	−0.977231	+	0.977231i	0.0225153	+	0.999746i	$0.492833\pi$
$44$	−0.515851	−	4.02395i	−0.0777674	−	0.606634i
$45$	−0.872488	+	1.74315i	−0.130063	+	0.259854i
$46$	−0.246940	+	0.723420i	−0.0364094	+	0.106663i
$47$	−7.63641			−1.11388			−0.556942	−	0.830551i	$-0.688026\pi$
$47$	−7.63641			−1.11388			−0.556942	+	0.830551i	$0.688026\pi$
$48$	−2.79760	−	6.33825i	−0.403799	−	0.914848i
$49$	1.00000			0.142857
$50$	2.09141	−	6.12686i	0.295770	−	0.866469i
$51$	−1.99736	−	12.3246i	−0.279687	−	1.72579i
$52$	−3.32239	+	0.425914i	−0.460733	+	0.0590637i
$53$	−2.29189	+	2.29189i	−0.314816	+	0.314816i	−0.846772	−	0.531956i	$-0.821457\pi$
$53$	−2.29189	+	2.29189i	−0.314816	+	0.314816i	0.531956	+	0.846772i	$0.321457\pi$
$54$	7.26257	−	1.12030i	0.988311	−	0.152453i
$55$	1.31802			0.177722
$56$	−1.55938	−	2.35973i	−0.208380	−	0.315333i
$57$	4.44114	+	3.20240i	0.588243	+	0.424169i
$58$	−3.65075	−	7.43482i	−0.479367	−	0.976240i
$59$	6.32068	+	6.32068i	0.822882	+	0.822882i	0.986520	−	0.163638i	$-0.0523230\pi$
$59$	6.32068	+	6.32068i	0.822882	+	0.822882i	−0.163638	+	0.986520i	$0.552323\pi$
$60$	2.15806	−	0.639685i	0.278605	−	0.0825830i
$61$	0.637183	−	0.637183i	0.0815829	−	0.0815829i	−0.665138	−	0.746721i	$-0.731627\pi$
$61$	0.637183	−	0.637183i	0.0815829	−	0.0815829i	0.746721	+	0.665138i	$0.231627\pi$
$62$	4.75989	−	13.9442i	0.604506	−	1.77092i
$63$	2.84645	−	0.947494i	0.358618	−	0.119373i
$64$	−3.13670	+	7.35942i	−0.392087	+	0.919928i
$65$		−	1.08823i		−	0.134978i
$66$	−2.87528	−	4.05219i	−0.353923	−	0.498790i
$67$	−2.14006	−	2.14006i	−0.261450	−	0.261450i	0.564193	−	0.825643i	$-0.309187\pi$
$67$	−2.14006	−	2.14006i	−0.261450	−	0.261450i	−0.825643	+	0.564193i	$0.809187\pi$
$68$	−8.81529	+	11.4078i	−1.06901	+	1.38340i
$69$	0.149770	+	0.924145i	0.0180302	+	0.111254i
$70$	0.824840	−	0.405024i	0.0985872	−	0.0484097i
$71$		−	14.6958i		−	1.74408i	−0.489438	−	0.872038i	$-0.662798\pi$
$71$		−	14.6958i		−	1.74408i	0.489438	−	0.872038i	$-0.337202\pi$
$72$	−6.67451	−	5.23936i	−0.786599	−	0.617464i
$73$		−	0.233482i		−	0.0273270i	−0.999907	−	0.0136635i	$-0.995651\pi$
$73$		−	0.233482i		−	0.0273270i	0.999907	−	0.0136635i	$-0.00434936\pi$
$74$	1.20206	+	2.44801i	0.139736	+	0.284576i
$75$	−1.26845	−	7.82686i	−0.146468	−	0.903768i
$76$	−0.803915	−	6.27103i	−0.0922154	−	0.719337i
$77$	−1.43432	−	1.43432i	−0.163456	−	0.163456i
$78$	−3.34570	+	2.37399i	−0.378826	+	0.268801i
$79$		−	4.93151i		−	0.554838i	−0.960749	−	0.277419i	$-0.910521\pi$
$79$		−	4.93151i		−	0.554838i	0.960749	−	0.277419i	$-0.0894790\pi$
$80$	−2.24198	−	1.31482i	−0.250662	−	0.147001i
$81$	7.20451	−	5.39398i	0.800501	−	0.599331i
$82$	−2.89334	−	0.987644i	−0.319515	−	0.109067i
$83$	−1.76156	+	1.76156i	−0.193356	+	0.193356i	−0.797145	−	0.603789i	$-0.793657\pi$
$83$	−1.76156	+	1.76156i	−0.193356	+	0.193356i	0.603789	+	0.797145i	$0.293657\pi$
$84$	−3.04462	−	1.65236i	−0.332195	−	0.180287i
$85$	−3.31198	−	3.31198i	−0.359235	−	0.359235i
$86$	11.5042	−	5.64894i	1.24053	−	0.609141i
$87$	−8.22824	−	5.93319i	−0.882160	−	0.636105i
$88$	−1.14798	+	5.62128i	−0.122375	+	0.599230i
$89$	7.79085			0.825829			0.412914	−	0.910770i	$-0.364511\pi$
$89$	7.79085			0.825829			0.412914	+	0.910770i	$0.364511\pi$
$90$	1.96410	−	1.93441i	0.207035	−	0.203905i
$91$	−1.18426	+	1.18426i	−0.124144	+	0.124144i
$92$	0.661004	−	0.855399i	0.0689144	−	0.0891815i
$93$	−2.88688	−	17.8133i	−0.299356	−	1.84715i
$94$	10.2205	+	3.48877i	1.05416	+	0.359839i
$95$	2.05404			0.210740
$96$	0.848578	+	9.76114i	0.0866076	+	0.996243i
$97$	−10.0585			−1.02128			−0.510641	−	0.859794i	$-0.670592\pi$
$97$	−10.0585			−1.02128			−0.510641	+	0.859794i	$0.670592\pi$
$98$	−1.33839	−	0.456860i	−0.135197	−	0.0461498i
$99$	−5.44174	−	2.72371i	−0.546916	−	0.273744i
$100$	−5.59824	+	7.24463i	−0.559824	+	0.724463i
$101$	−6.01152	+	6.01152i	−0.598169	+	0.598169i	−0.939825	−	0.341656i	$-0.889012\pi$
$101$	−6.01152	+	6.01152i	−0.598169	+	0.598169i	0.341656	+	0.939825i	$0.389012\pi$
$102$	−2.95737	+	17.4076i	−0.292823	+	1.72361i
$103$	16.5787			1.63355			0.816775	−	0.576956i	$-0.195760\pi$
$103$	16.5787			1.63355			0.816775	+	0.576956i	$0.195760\pi$
$104$	4.64123	+	0.947831i	0.455110	+	0.0929425i
$105$	0.658245	−	0.912864i	0.0642382	−	0.0890864i
$106$	4.11451	−	2.02037i	0.399637	−	0.196235i
$107$	8.62700	+	8.62700i	0.834004	+	0.834004i	0.988062	−	0.154058i	$-0.0492343\pi$
$107$	8.62700	+	8.62700i	0.834004	+	0.834004i	−0.154058	+	0.988062i	$0.549234\pi$
$108$	−10.2319	−	1.81859i	−0.984570	−	0.174994i
$109$	11.8092	−	11.8092i	1.13111	−	1.13111i	0.141120	−	0.989992i	$-0.454930\pi$
$109$	11.8092	−	11.8092i	1.13111	−	1.13111i	0.989992	−	0.141120i	$-0.0450705\pi$
$110$	−1.76402	−	0.602152i	−0.168193	−	0.0574129i
$111$	2.70926	+	1.95358i	0.257151	+	0.185426i
$112$	1.00898	+	3.87065i	0.0953395	+	0.365742i
$113$			14.6863i			1.38157i	0.723058	+	0.690787i	$0.242736\pi$
$113$			14.6863i			1.38157i	−0.723058	+	0.690787i	$0.757264\pi$
$114$	−4.48091	−	6.31503i	−0.419676	−	0.591457i
$115$	0.248345	+	0.248345i	0.0231582	+	0.0231582i
$116$	1.48944	+	11.6185i	0.138291	+	1.07875i
$117$	−2.24885	+	4.49300i	−0.207906	+	0.415378i
$118$	−5.57184	−	11.3472i	−0.512930	−	1.04459i
$119$			7.20845i			0.660798i
$120$	−3.18057	−	0.129786i	−0.290345	−	0.0118478i
$121$		−	6.88543i		−	0.625948i
$122$	−1.14390	+	0.561694i	−0.103564	+	0.0508533i
$123$	−3.69614	+	0.599008i	−0.333270	+	0.0540107i
$124$	−12.7411	+	16.4882i	−1.14419	+	1.48068i
$125$	−4.40059	−	4.40059i	−0.393601	−	0.393601i
$126$	−4.24252	−	0.0323143i	−0.377954	−	0.00287878i
$127$		−	4.43597i		−	0.393628i	−0.980441	−	0.196814i	$-0.936940\pi$
$127$		−	4.43597i		−	0.393628i	0.980441	−	0.196814i	$-0.0630596\pi$
$128$	7.56034	−	8.41672i	0.668246	−	0.743940i
$129$	9.18066	−	12.7319i	0.808312	−	1.12098i
$130$	−0.497169	+	1.45647i	−0.0436046	+	0.127741i
$131$	−3.16188	+	3.16188i	−0.276255	+	0.276255i	−0.831612	−	0.555357i	$-0.812582\pi$
$131$	−3.16188	+	3.16188i	−0.276255	+	0.276255i	0.555357	+	0.831612i	$0.312582\pi$
$132$	1.99696	+	6.73699i	0.173813	+	0.586380i
$133$	−2.23529	−	2.23529i	−0.193824	−	0.193824i
$134$	1.88652	+	3.84193i	0.162970	+	0.331893i
$135$	1.00873	−	3.22210i	0.0868173	−	0.277314i
$136$	17.0100	−	11.2407i	1.45860	−	0.963880i
$137$	−14.2398			−1.21659			−0.608295	−	0.793711i	$-0.708146\pi$
$137$	−14.2398			−1.21659			−0.608295	+	0.793711i	$0.708146\pi$
$138$	0.221755	−	1.30529i	0.0188770	−	0.111113i
$139$	−5.47134	+	5.47134i	−0.464073	+	0.464073i	−0.899988	−	0.435915i	$-0.856425\pi$
$139$	−5.47134	+	5.47134i	−0.464073	+	0.464073i	0.435915	+	0.899988i	$0.356425\pi$
$140$	−1.28899	+	0.165243i	−0.108940	+	0.0139655i
$141$	13.0563	−	2.11595i	1.09954	−	0.178195i
$142$	−6.71395	+	19.6687i	−0.563422	+	1.65056i
$143$	3.39722			0.284089
$144$	6.53942	+	10.0616i	0.544952	+	0.838467i
$145$	−3.80559			−0.316037
$146$	−0.106668	+	0.312489i	−0.00882794	+	0.0258618i
$147$	−1.70974	+	0.277087i	−0.141017	+	0.0228537i
$148$	−0.490418	−	3.82556i	−0.0403121	−	0.314459i
$149$	4.22703	−	4.22703i	0.346292	−	0.346292i	−0.512435	−	0.858726i	$-0.671256\pi$
$149$	4.22703	−	4.22703i	0.346292	−	0.346292i	0.858726	+	0.512435i	$0.171256\pi$
$150$	−1.87811	+	11.0549i	−0.153347	+	0.902626i
$151$	16.2738			1.32434			0.662170	−	0.749353i	$-0.269636\pi$
$151$	16.2738			1.32434			0.662170	+	0.749353i	$0.269636\pi$
$152$	−1.78904	+	8.76035i	−0.145110	+	0.710558i
$153$	6.82996	+	20.5185i	0.552170	+	1.65882i
$154$	1.26440	+	2.57497i	0.101888	+	0.207497i
$155$	−4.78695	−	4.78695i	−0.384497	−	0.384497i
$156$	5.56243	−	1.64879i	0.445351	−	0.132009i
$157$	3.18084	−	3.18084i	0.253859	−	0.253859i	−0.568692	−	0.822551i	$-0.692550\pi$
$157$	3.18084	−	3.18084i	0.253859	−	0.253859i	0.822551	+	0.568692i	$0.192550\pi$
$158$	−2.25301	+	6.60026i	−0.179240	+	0.525089i
$159$	3.28350	−	4.55360i	0.260398	−	0.361124i
$160$	2.39995	+	2.78401i	0.189733	+	0.220095i
$161$		−	0.540517i		−	0.0425987i
$162$	−12.1067	+	3.92778i	−0.951193	+	0.308595i
$163$	14.7921	+	14.7921i	1.15861	+	1.15861i	0.984775	+	0.173836i	$0.0556161\pi$
$163$	14.7921	+	14.7921i	1.15861	+	1.15861i	0.173836	+	0.984775i	$0.444384\pi$
$164$	3.42119	+	2.64370i	0.267150	+	0.206438i
$165$	−2.25348	+	0.365206i	−0.175433	+	0.0284313i
$166$	3.16243	−	1.55286i	0.245452	−	0.120525i
$167$		−	6.21188i		−	0.480689i	−0.970688	−	0.240345i	$-0.922740\pi$
$167$		−	6.21188i		−	0.480689i	0.970688	−	0.240345i	$-0.0772605\pi$
$168$	3.31998	+	3.60246i	0.256142	+	0.277936i
$169$			10.1951i			0.784236i
$170$	2.91960	+	5.94582i	0.223923	+	0.456023i
$171$	−8.48055	−	4.24471i	−0.648524	−	0.324601i
$172$	−17.9778	+	2.30467i	−1.37080	+	0.175729i
$173$	−1.75745	−	1.75745i	−0.133617	−	0.133617i	0.637135	−	0.770752i	$-0.280119\pi$
$173$	−1.75745	−	1.75745i	−0.133617	−	0.133617i	−0.770752	+	0.637135i	$0.780119\pi$
$174$	8.30193	+	11.7001i	0.629368	+	0.886979i
$175$			4.57780i			0.346049i
$176$	4.10457	−	6.99898i	0.309394	−	0.527568i
$177$	−12.5581	−	9.05536i	−0.943925	−	0.680643i
$178$	−10.4272	−	3.55933i	−0.781550	−	0.266783i
$179$	−6.35744	+	6.35744i	−0.475177	+	0.475177i	−0.903585	−	0.428408i	$-0.859075\pi$
$179$	−6.35744	+	6.35744i	−0.475177	+	0.475177i	0.428408	+	0.903585i	$0.359075\pi$
$180$	−3.51249	+	1.69167i	−0.261805	+	0.126090i
$181$	−9.95720	−	9.95720i	−0.740113	−	0.740113i	0.232487	−	0.972600i	$-0.425314\pi$
$181$	−9.95720	−	9.95720i	−0.740113	−	0.740113i	−0.972600	+	0.232487i	$0.925314\pi$
$182$	2.12603	−	1.04395i	0.157592	−	0.0773830i
$183$	−0.912864	+	1.26597i	−0.0674809	+	0.0935835i
$184$	−1.27548	+	0.842868i	−0.0940293	+	0.0621371i
$185$	1.25304			0.0921254
$186$	−4.27442	+	25.1600i	−0.313416	+	1.84482i
$187$	10.3393	−	10.3393i	0.756081	−	0.756081i
$188$	−12.0851	−	9.33865i	−0.881394	−	0.681091i
$189$	−4.60416	+	2.40868i	−0.334903	+	0.175206i
$190$	−2.74910	−	0.938410i	−0.199441	−	0.0680794i
$191$	−6.17129			−0.446539			−0.223269	−	0.974757i	$-0.571673\pi$
$191$	−6.17129			−0.446539			−0.223269	+	0.974757i	$0.571673\pi$
$192$	3.32375	−	13.4519i	0.239871	−	0.970805i
$193$	17.5110			1.26047			0.630234	−	0.776405i	$-0.282959\pi$
$193$	17.5110			1.26047			0.630234	+	0.776405i	$0.282959\pi$
$194$	13.4621	+	4.59531i	0.966524	+	0.329924i
$195$	0.301534	+	1.86060i	0.0215933	+	0.133240i
$196$	1.58256	+	1.22291i	0.113040	+	0.0873508i
$197$	8.25450	−	8.25450i	0.588109	−	0.588109i	−0.349010	−	0.937119i	$-0.613482\pi$
$197$	8.25450	−	8.25450i	0.588109	−	0.588109i	0.937119	+	0.349010i	$0.113482\pi$
$198$	6.03880	+	6.13150i	0.429159	+	0.435746i
$199$	−8.91908			−0.632257			−0.316128	−	0.948716i	$-0.602383\pi$
$199$	−8.91908			−0.632257			−0.316128	+	0.948716i	$0.602383\pi$
$200$	10.8024	−	7.13850i	0.763844	−	0.504768i
$201$	4.25193	+	3.06597i	0.299908	+	0.216257i
$202$	10.7922	−	5.29932i	0.759334	−	0.372859i
$203$	4.14139	+	4.14139i	0.290669	+	0.290669i
$204$	11.9109	−	21.9470i	0.833933	−	1.53660i
$205$	−0.993260	+	0.993260i	−0.0693723	+	0.0693723i
$206$	−22.1887	−	7.57415i	−1.54596	−	0.527716i
$207$	−0.512136	−	1.53855i	−0.0355959	−	0.106937i
$208$	−5.77874	−	3.38896i	−0.400683	−	0.234982i
$209$			6.41226i			0.443545i
$210$	−1.29804	+	0.921040i	−0.0895731	+	0.0635578i
$211$	−3.36181	−	3.36181i	−0.231436	−	0.231436i	0.581856	−	0.813292i	$-0.302327\pi$
$211$	−3.36181	−	3.36181i	−0.231436	−	0.231436i	−0.813292	+	0.581856i	$0.802327\pi$
$212$	−6.42984	+	0.824273i	−0.441603	+	0.0566113i
$213$	4.07202	+	25.1261i	0.279010	+	1.72161i
$214$	−7.60493	−	15.4876i	−0.519862	−	1.05871i
$215$		−	5.88853i		−	0.401595i
$216$	12.8635	+	7.10854i	0.875248	+	0.483675i
$217$			10.4187i			0.707267i
$218$	−21.2004	+	10.4101i	−1.43587	+	0.705060i
$219$	0.0646946	+	0.399194i	0.00437166	+	0.0269750i
$220$	2.08585	+	1.61182i	0.140628	+	0.108669i
$221$	−8.53665	−	8.53665i	−0.574238	−	0.574238i
$222$	−2.73352	−	3.85240i	−0.183462	−	0.258556i
$223$		−	22.5878i		−	1.51259i	−0.654231	−	0.756295i	$-0.727007\pi$
$223$		−	22.5878i		−	1.51259i	0.654231	−	0.756295i	$-0.272993\pi$
$224$	0.417944	−	5.64139i	0.0279250	−	0.376931i
$225$	4.33743	+	13.0305i	0.289162	+	0.868697i
$226$	6.70960	−	19.6560i	0.446316	−	1.30750i
$227$	−13.6329	+	13.6329i	−0.904847	+	0.904847i	−0.995851	−	0.0910037i	$-0.970992\pi$
$227$	−13.6329	+	13.6329i	−0.904847	+	0.904847i	0.0910037	+	0.995851i	$0.470992\pi$
$228$	3.11211	+	10.4991i	0.206104	+	0.695320i
$229$	−4.15041	−	4.15041i	−0.274267	−	0.274267i	0.556549	−	0.830815i	$-0.312125\pi$
$229$	−4.15041	−	4.15041i	−0.274267	−	0.274267i	−0.830815	+	0.556549i	$0.812125\pi$
$230$	−0.218922	−	0.445840i	−0.0144353	−	0.0293978i
$231$	2.84976	+	2.05490i	0.187500	+	0.135202i
$232$	3.31460	−	16.2306i	0.217614	−	1.06559i
$233$	−3.93645			−0.257886			−0.128943	−	0.991652i	$-0.541158\pi$
$233$	−3.93645			−0.257886			−0.128943	+	0.991652i	$0.541158\pi$
$234$	5.06250	−	4.98596i	0.330946	−	0.325942i
$235$	3.50861	−	3.50861i	0.228876	−	0.228876i
$236$	2.27321	+	17.7325i	0.147974	+	1.15428i
$237$	1.36645	+	8.43161i	0.0887608	+	0.547692i
$238$	3.29325	−	9.64770i	0.213470	−	0.625367i
$239$	−16.3555			−1.05795			−0.528976	−	0.848637i	$-0.677424\pi$
$239$	−16.3555			−1.05795			−0.528976	+	0.848637i	$0.677424\pi$
$240$	4.19754	+	1.62678i	0.270950	+	0.105008i
$241$	−24.3675			−1.56965			−0.784826	−	0.619716i	$-0.787248\pi$
$241$	−24.3675			−1.56965			−0.784826	+	0.619716i	$0.787248\pi$
$242$	−3.14568	+	9.21536i	−0.202212	+	0.592386i
$243$	−10.8233	+	11.2186i	−0.694313	+	0.719673i
$244$	1.78760	−	0.229161i	0.114439	−	0.0146705i
$245$	−0.459458	+	0.459458i	−0.0293537	+	0.0293537i
$246$	5.22053	+	0.886913i	0.332849	+	0.0565475i
$247$	5.29431			0.336869
$248$	24.5854	−	16.2467i	1.56117	−	1.03166i
$249$	2.52371	−	3.49991i	0.159933	−	0.221798i
$250$	3.87924	+	7.90015i	0.245345	+	0.499649i
$251$	18.5928	+	18.5928i	1.17357	+	1.17357i	0.981353	+	0.192213i	$0.0615664\pi$
$251$	18.5928	+	18.5928i	1.17357	+	1.17357i	0.192213	+	0.981353i	$0.438434\pi$
$252$	5.66337	+	1.98149i	0.356759	+	0.124822i
$253$	−0.775276	+	0.775276i	−0.0487412	+	0.0487412i
$254$	−2.02662	+	5.93704i	−0.127161	+	0.372523i
$255$	6.58034	+	4.74493i	0.412077	+	0.297139i
$256$	−13.9639	+	7.81081i	−0.872745	+	0.488176i
$257$		−	29.3016i		−	1.82778i	−0.405961	−	0.913890i	$-0.633063\pi$
$257$		−	29.3016i		−	1.82778i	0.405961	−	0.913890i	$-0.366937\pi$
$258$	−18.1040	+	12.8459i	−1.12710	+	0.799750i
$259$	−1.36361	−	1.36361i	−0.0847305	−	0.0847305i
$260$	1.33081	−	1.72219i	0.0825333	−	0.106806i
$261$	15.7122	+	7.86430i	0.972560	+	0.486788i
$262$	5.67636	−	2.78728i	0.350687	−	0.172199i
$263$		−	14.8023i		−	0.912747i	−0.889788	−	0.456373i	$-0.849148\pi$
$263$		−	14.8023i		−	0.912747i	0.889788	−	0.456373i	$-0.150852\pi$
$264$	0.405164	−	9.92903i	0.0249361	−	0.611089i
$265$		−	2.10606i		−	0.129374i
$266$	1.97047	+	4.01290i	0.120817	+	0.246046i
$267$	−13.3204	+	2.15874i	−0.815193	+	0.132113i
$268$	−0.769666	−	6.00387i	−0.0470148	−	0.366745i
$269$	13.8770	+	13.8770i	0.846095	+	0.846095i	0.989643	−	0.143548i	$-0.0458512\pi$
$269$	13.8770	+	13.8770i	0.846095	+	0.846095i	−0.143548	+	0.989643i	$0.545851\pi$
$270$	−2.82212	+	3.85157i	−0.171748	+	0.234399i
$271$			20.1033i			1.22119i	0.791943	+	0.610595i	$0.209070\pi$
$271$			20.1033i			1.22119i	−0.791943	+	0.610595i	$0.790930\pi$
$272$	−27.9014	+	7.27317i	−1.69177	+	0.441001i
$273$	1.69663	−	2.35292i	0.102685	−	0.142405i
$274$	19.0584	+	6.50561i	1.15136	+	0.393018i
$275$	6.56605	−	6.56605i	0.395948	−	0.395948i
$276$	−0.893127	+	1.64567i	−0.0537599	+	0.0990576i
$277$	−19.8547	−	19.8547i	−1.19295	−	1.19295i	−0.976234	−	0.216719i	$-0.930464\pi$
$277$	−19.8547	−	19.8547i	−1.19295	−	1.19295i	−0.216719	−	0.976234i	$-0.569536\pi$
$278$	9.82240	−	4.82313i	0.589108	−	0.289272i
$279$	9.87165	+	29.6563i	0.591000	+	1.77547i
$280$	1.80067	+	0.367731i	0.107610	+	0.0219762i
$281$	1.87453			0.111825			0.0559126	−	0.998436i	$-0.482193\pi$
$281$	1.87453			0.111825			0.0559126	+	0.998436i	$0.482193\pi$
$282$	−18.4411	−	3.13295i	−1.09815	−	0.186564i
$283$	17.9733	−	17.9733i	1.06840	−	1.06840i	0.0709207	−	0.997482i	$-0.477406\pi$
$283$	17.9733	−	17.9733i	1.06840	−	1.06840i	0.997482	−	0.0709207i	$-0.0225937\pi$
$284$	17.9717	−	23.2570i	1.06642	−	1.38005i
$285$	−3.51189	+	0.569147i	−0.208026	+	0.0337134i
$286$	−4.54679	−	1.55205i	−0.268857	−	0.0917748i
$287$	2.16181			0.127608
$288$	−4.15553	−	16.4539i	−0.244867	−	0.969557i
$289$	−34.9618			−2.05657
$290$	5.09335	+	1.73862i	0.299092	+	0.102095i
$291$	17.1974	−	2.78707i	1.00813	−	0.163381i
$292$	0.285527	−	0.369498i	0.0167092	−	0.0216232i
$293$	17.4851	−	17.4851i	1.02149	−	1.02149i	0.0217268	−	0.999764i	$-0.493084\pi$
$293$	17.4851	−	17.4851i	1.02149	−	1.02149i	0.999764	−	0.0217268i	$-0.00691641\pi$
$294$	2.41489	+	0.410265i	0.140839	+	0.0239271i
$295$	−5.80817			−0.338165
$296$	−1.09138	+	5.34413i	−0.0634350	+	0.310621i
$297$	10.0587	+	3.14902i	0.583664	+	0.182725i
$298$	−7.58856	+	3.72624i	−0.439593	+	0.215855i
$299$	0.640110	+	0.640110i	0.0370185	+	0.0370185i
$300$	7.56416	−	13.9377i	0.436717	−	0.804691i
$301$	−6.40813	+	6.40813i	−0.369359	+	0.369359i
$302$	−21.7806	−	7.43483i	−1.25333	−	0.427827i
$303$	8.61245	−	11.9439i	0.494772	−	0.686158i
$304$	6.39667	−	10.9074i	0.366874	−	0.625582i
$305$			0.585517i			0.0335266i
$306$	0.232936	−	30.5820i	0.0133161	−	1.74826i
$307$	1.90363	+	1.90363i	0.108646	+	0.108646i	0.759340	−	0.650694i	$-0.225522\pi$
$307$	1.90363	+	1.90363i	0.108646	+	0.108646i	−0.650694	+	0.759340i	$0.725522\pi$
$308$	−0.515851	−	4.02395i	−0.0293933	−	0.229286i
$309$	−28.3454	+	4.59374i	−1.61251	+	0.261329i
$310$	4.21982	+	8.59376i	0.239670	+	0.488093i
$311$		−	3.81852i		−	0.216529i	−0.994122	−	0.108264i	$-0.965471\pi$
$311$		−	3.81852i		−	0.216529i	0.994122	−	0.108264i	$-0.0345293\pi$
$312$	−8.19795	−	0.334525i	−0.464117	−	0.0189388i
$313$			2.80396i			0.158489i	0.996855	+	0.0792446i	$0.0252508\pi$
$313$			2.80396i			0.158489i	−0.996855	+	0.0792446i	$0.974749\pi$
$314$	−5.71040	+	2.80400i	−0.322257	+	0.158239i
$315$	−0.872488	+	1.74315i	−0.0491591	+	0.0982157i
$316$	6.03079	−	7.80440i	0.339259	−	0.439032i
$317$	−12.6164	−	12.6164i	−0.708609	−	0.708609i	0.257633	−	0.966243i	$-0.417057\pi$
$317$	−12.6164	−	12.6164i	−0.708609	−	0.708609i	−0.966243	+	0.257633i	$0.917057\pi$
$318$	−6.47495	+	4.59438i	−0.363097	+	0.257640i
$319$		−	11.8802i		−	0.665163i
$320$	−1.94016	−	4.82252i	−0.108458	−	0.269587i
$321$	−17.1404	−	12.3595i	−0.956683	−	0.689842i
$322$	−0.246940	+	0.723420i	−0.0137615	+	0.0403146i
$323$	16.1130	−	16.1130i	0.896550	−	0.896550i
$324$	17.9979	+	0.274188i	0.999884	+	0.0152327i
$325$	−5.42129	−	5.42129i	−0.300719	−	0.300719i
$326$	−13.0397	−	26.5556i	−0.722201	−	1.47078i
$327$	−16.9185	+	23.4628i	−0.935594	+	1.29750i
$328$	−3.37107	−	5.10130i	−0.186136	−	0.281672i
$329$	−7.63641			−0.421009
$330$	3.18288	+	0.540738i	0.175212	+	0.0297667i
$331$	−3.56268	+	3.56268i	−0.195823	+	0.195823i	−0.798207	−	0.602384i	$-0.794218\pi$
$331$	−3.56268	+	3.56268i	−0.195823	+	0.195823i	0.602384	+	0.798207i	$0.294218\pi$
$332$	−4.94199	+	0.633539i	−0.271227	+	0.0347700i
$333$	−5.17345	−	2.58943i	−0.283503	−	0.141900i
$334$	−2.83796	+	8.31389i	−0.155286	+	0.454916i
$335$	1.96653			0.107443
$336$	−2.79760	−	6.33825i	−0.152622	−	0.345780i
$337$	20.7354			1.12953			0.564765	−	0.825252i	$-0.308967\pi$
$337$	20.7354			1.12953			0.564765	+	0.825252i	$0.308967\pi$
$338$	4.65772	−	13.6450i	0.253347	−	0.742187i
$339$	−4.06939	−	25.1099i	−0.221019	−	1.36378i
$340$	−1.19114	−	9.29165i	−0.0645988	−	0.503911i
$341$	14.9438	−	14.9438i	0.809252	−	0.809252i
$342$	9.41102	+	9.55549i	0.508890	+	0.516702i
$343$	1.00000			0.0539949
$344$	25.1142	+	5.12881i	1.35407	+	0.276527i
$345$	−0.493418	−	0.355793i	−0.0265648	−	0.0191552i
$346$	1.54924	+	3.15506i	0.0832877	+	0.169617i
$347$	0.00985354	+	0.00985354i	0.000528966	+	0.000528966i	0.707371	−	0.706842i	$-0.249881\pi$
$347$	0.00985354	+	0.00985354i	0.000528966	+	0.000528966i	−0.706842	+	0.707371i	$0.749881\pi$
$348$	−5.76590	−	19.4520i	−0.309085	−	1.04274i
$349$	0.770588	−	0.770588i	0.0412486	−	0.0412486i	−0.686182	−	0.727430i	$-0.740714\pi$
$349$	0.770588	−	0.770588i	0.0412486	−	0.0412486i	0.727430	+	0.686182i	$0.240714\pi$
$350$	2.09141	−	6.12686i	0.111791	−	0.327495i
$351$	2.60000	−	8.30500i	0.138778	−	0.443288i
$352$	−8.69106	+	7.49212i	−0.463235	+	0.399331i
$353$		−	2.34275i		−	0.124692i	−0.998055	−	0.0623460i	$-0.980142\pi$
$353$		−	2.34275i		−	0.124692i	0.998055	−	0.0623460i	$-0.0198582\pi$
$354$	12.6706	+	17.8569i	0.673433	+	0.949082i
$355$	6.75212	+	6.75212i	0.358365	+	0.358365i
$356$	12.3295	+	9.52752i	0.653461	+	0.504957i
$357$	−1.99736	−	12.3246i	−0.105712	−	0.652287i
$358$	11.4132	−	5.60425i	0.603205	−	0.296194i
$359$			14.4079i			0.760420i	0.924900	+	0.380210i	$0.124148\pi$
$359$			14.4079i			0.760420i	−0.924900	+	0.380210i	$0.875852\pi$
$360$	5.47392	−	0.659392i	0.288501	−	0.0347530i
$361$		−	9.00696i		−	0.474051i
$362$	8.77754	+	17.8756i	0.461337	+	0.939522i
$363$	1.90786	+	11.7723i	0.100137	+	0.617886i
$364$	−3.32239	+	0.425914i	−0.174141	+	0.0223240i
$365$	0.107275	+	0.107275i	0.00561503	+	0.00561503i
$366$	1.80014	−	1.27731i	0.0940947	−	0.0667661i
$367$			27.8523i			1.45388i	0.686703	+	0.726938i	$0.259057\pi$
$367$			27.8523i			1.45388i	−0.686703	+	0.726938i	$0.740943\pi$
$368$	2.09215	−	0.545370i	0.109061	−	0.0284294i
$369$	6.15347	−	2.04830i	0.320337	−	0.106630i
$370$	−1.67705	−	0.572464i	−0.0871859	−	0.0297610i
$371$	−2.29189	+	2.29189i	−0.118989	+	0.118989i
$372$	17.2154	−	31.7210i	0.892578	−	1.64466i
$373$	21.3363	+	21.3363i	1.10475	+	1.10475i	0.993829	+	0.110924i	$0.0353810\pi$
$373$	21.3363	+	21.3363i	1.10475	+	1.10475i	0.110924	+	0.993829i	$0.464619\pi$
$374$	−18.5615	+	9.11433i	−0.959793	+	0.471291i
$375$	8.74323	+	6.30454i	0.451498	+	0.325565i
$376$	11.9080	+	18.0199i	0.614110	+	0.929306i
$377$	−9.80894			−0.505186
$378$	7.26257	−	1.12030i	0.373546	−	0.0576218i
$379$	−24.6296	+	24.6296i	−1.26514	+	1.26514i	−0.316567	+	0.948570i	$0.602530\pi$
$379$	−24.6296	+	24.6296i	−1.26514	+	1.26514i	−0.948570	+	0.316567i	$0.897470\pi$
$380$	3.25064	+	2.51191i	0.166754	+	0.128858i
$381$	1.22915	+	7.58436i	0.0629711	+	0.388559i
$382$	8.25957	+	2.81942i	0.422596	+	0.144254i
$383$	20.0598			1.02501			0.512503	−	0.858685i	$-0.328718\pi$
$383$	20.0598			1.02501			0.512503	+	0.858685i	$0.328718\pi$
$384$	−10.5941	+	16.4853i	−0.540627	+	0.841262i
$385$	1.31802			0.0671727
$386$	−23.4365	−	8.00007i	−1.19289	−	0.407193i
$387$	−12.1687	+	24.3121i	−0.618572	+	1.23585i
$388$	−15.9181	−	12.3006i	−0.808119	−	0.624469i
$389$	9.20544	−	9.20544i	0.466735	−	0.466735i	−0.434120	−	0.900855i	$-0.642941\pi$
$389$	9.20544	−	9.20544i	0.466735	−	0.466735i	0.900855	+	0.434120i	$0.142941\pi$
$390$	0.446463	−	2.62796i	0.0226075	−	0.133072i
$391$	3.89629			0.197044
$392$	−1.55938	−	2.35973i	−0.0787603	−	0.119185i
$393$	4.52989	−	6.28213i	0.228503	−	0.316891i
$394$	−14.8189	+	7.27656i	−0.746564	+	0.366588i
$395$	2.26582	+	2.26582i	0.114006	+	0.114006i
$396$	−5.28101	−	10.9652i	−0.265381	−	0.551022i
$397$	−25.2512	+	25.2512i	−1.26732	+	1.26732i	−0.319852	+	0.947468i	$0.603633\pi$
$397$	−25.2512	+	25.2512i	−1.26732	+	1.26732i	−0.947468	+	0.319852i	$0.896367\pi$
$398$	11.9372	+	4.07477i	0.598357	+	0.204250i
$399$	4.44114	+	3.20240i	0.222335	+	0.160321i
$400$	−17.7191	+	4.61890i	−0.885953	+	0.230945i
$401$			32.1746i			1.60673i	0.595490	+	0.803363i	$0.296958\pi$
$401$			32.1746i			1.60673i	−0.595490	+	0.803363i	$0.703042\pi$
$402$	−4.29001	−	6.04599i	−0.213966	−	0.301547i
$403$	−12.3384	−	12.3384i	−0.614620	−	0.614620i
$404$	−16.8651	+	2.16203i	−0.839072	+	0.107565i
$405$	−0.831862	+	5.78847i	−0.0413356	+	0.287632i
$406$	−3.65075	−	7.43482i	−0.181184	−	0.368984i
$407$			3.91172i			0.193897i
$408$	−25.9682	+	23.9319i	−1.28562	+	1.18481i
$409$		−	37.8980i		−	1.87393i	−0.349417	−	0.936967i	$-0.613620\pi$
$409$		−	37.8980i		−	1.87393i	0.349417	−	0.936967i	$-0.386380\pi$
$410$	1.78315	−	0.875585i	0.0880633	−	0.0432421i
$411$	24.3464	−	3.94566i	1.20092	−	0.194625i
$412$	26.2368	+	20.2743i	1.29259	+	0.998843i
$413$	6.32068	+	6.32068i	0.311020	+	0.311020i
$414$	−0.0174664	+	2.29315i	−0.000858427	+	0.112702i
$415$		−	1.61872i		−	0.0794599i
$416$	6.18590	+	7.17581i	0.303289	+	0.351823i
$417$	7.83855	−	10.8706i	0.383855	−	0.532336i
$418$	2.92951	−	8.58209i	0.143287	−	0.419764i
$419$	−4.83167	+	4.83167i	−0.236043	+	0.236043i	−0.815209	−	0.579167i	$-0.803378\pi$
$419$	−4.83167	+	4.83167i	−0.236043	+	0.236043i	0.579167	+	0.815209i	$0.303378\pi$
$420$	2.15806	−	0.639685i	0.105303	−	0.0312135i
$421$	24.5684	+	24.5684i	1.19739	+	1.19739i	0.974945	+	0.222444i	$0.0714035\pi$
$421$	24.5684	+	24.5684i	1.19739	+	1.19739i	0.222444	+	0.974945i	$0.428597\pi$
$422$	2.96352	+	6.03527i	0.144262	+	0.293792i
$423$	−21.7366	+	7.23545i	−1.05687	+	0.351800i
$424$	8.98218	+	1.83434i	0.436213	+	0.0890834i
$425$	−32.9988			−1.60068
$426$	6.02919	−	35.4888i	0.292115	−	1.71944i
$427$	0.637183	−	0.637183i	0.0308354	−	0.0308354i
$428$	3.10268	+	24.2028i	0.149973	+	1.16989i
$429$	−5.80837	+	0.941323i	−0.280431	+	0.0454475i
$430$	−2.69024	+	7.88113i	−0.129735	+	0.380062i
$431$	4.29534			0.206899			0.103450	−	0.994635i	$-0.467012\pi$
$431$	4.29534			0.206899			0.103450	+	0.994635i	$0.467012\pi$
$432$	−13.9687	−	15.3908i	−0.672068	−	0.740489i
$433$	−1.69551			−0.0814809			−0.0407404	−	0.999170i	$-0.512972\pi$
$433$	−1.69551			−0.0814809			−0.0407404	+	0.999170i	$0.512972\pi$
$434$	4.75989	−	13.9442i	0.228482	−	0.669345i
$435$	6.50658	−	1.05448i	0.311967	−	0.0505583i
$436$	33.1302	−	4.24713i	1.58665	−	0.203401i
$437$	−1.20821	+	1.20821i	−0.0577966	+	0.0577966i
$438$	0.0957892	−	0.563832i	0.00457699	−	0.0269409i
$439$	6.92612			0.330565			0.165283	−	0.986246i	$-0.447146\pi$
$439$	6.92612			0.330565			0.165283	+	0.986246i	$0.447146\pi$
$440$	−2.05529	−	3.11018i	−0.0979822	−	0.148272i
$441$	2.84645	−	0.947494i	0.135545	−	0.0451188i
$442$	7.52529	+	15.3254i	0.357941	+	0.728955i
$443$	24.7883	+	24.7883i	1.17773	+	1.17773i	0.980322	+	0.197404i	$0.0632510\pi$
$443$	24.7883	+	24.7883i	1.17773	+	1.17773i	0.197404	+	0.980322i	$0.436749\pi$
$444$	1.89850	+	6.40484i	0.0900988	+	0.303960i
$445$	−3.57957	+	3.57957i	−0.169688	+	0.169688i
$446$	−10.3195	+	30.2312i	−0.488640	+	1.43149i
$447$	−6.05588	+	8.39839i	−0.286433	+	0.397230i
$448$	−3.13670	+	7.35942i	−0.148195	+	0.347700i
$449$			7.33520i			0.346169i	0.984907	+	0.173085i	$0.0553734\pi$
$449$			7.33520i			0.346169i	−0.984907	+	0.173085i	$0.944627\pi$
$450$	0.147928	−	19.4214i	0.00697340	−	0.915533i
$451$	−3.10074	−	3.10074i	−0.146008	−	0.146008i
$452$	−17.9601	+	23.2420i	−0.844771	+	1.09321i
$453$	−27.8240	+	4.50924i	−1.30728	+	0.211863i
$454$	24.4744	−	12.0178i	1.14864	−	0.564021i
$455$		−	1.08823i		−	0.0510171i
$456$	0.631418	−	15.4737i	0.0295689	−	0.724621i
$457$			9.97328i			0.466531i	0.972413	+	0.233265i	$0.0749411\pi$
$457$			9.97328i			0.466531i	−0.972413	+	0.233265i	$0.925059\pi$
$458$	3.65869	+	7.45100i	0.170960	+	0.348163i
$459$	−17.3629	−	33.1888i	−0.810430	−	1.54912i
$460$	0.0893164	+	0.696723i	0.00416440	+	0.0324849i
$461$	−11.6080	−	11.6080i	−0.540638	−	0.540638i	0.383078	−	0.923716i	$-0.374864\pi$
$461$	−11.6080	−	11.6080i	−0.540638	−	0.540638i	−0.923716	+	0.383078i	$0.874864\pi$
$462$	−2.87528	−	4.05219i	−0.133770	−	0.188525i
$463$			16.8223i			0.781801i	0.920433	+	0.390900i	$0.127836\pi$
$463$			16.8223i			0.781801i	−0.920433	+	0.390900i	$0.872164\pi$
$464$	−11.8513	+	20.2085i	−0.550184	+	0.938155i
$465$	9.51086	+	6.85806i	0.441055	+	0.318035i
$466$	5.26850	+	1.79841i	0.244058	+	0.0833096i
$467$	14.4026	−	14.4026i	0.666474	−	0.666474i	−0.290424	−	0.956898i	$-0.593796\pi$
$467$	14.4026	−	14.4026i	0.666474	−	0.666474i	0.956898	+	0.290424i	$0.0937962\pi$
$468$	−9.05346	+	4.36029i	−0.418497	+	0.201554i
$469$	−2.14006	−	2.14006i	−0.0988187	−	0.0988187i
$470$	−6.29882	+	3.09293i	−0.290543	+	0.142666i
$471$	−4.55706	+	6.31980i	−0.209978	+	0.291201i
$472$	5.05881	−	24.7714i	0.232851	−	1.14020i
$473$	18.3827			0.845237
$474$	2.02322	−	11.9090i	0.0929297	−	0.547000i
$475$	10.2327	−	10.2327i	0.469509	−	0.469509i
$476$	−8.81529	+	11.4078i	−0.404048	+	0.522875i
$477$	−4.35220	+	8.69531i	−0.199273	+	0.398131i
$478$	21.8900	+	7.47220i	1.00123	+	0.341770i
$479$	4.11467			0.188004			0.0940021	−	0.995572i	$-0.470034\pi$
$479$	4.11467			0.188004			0.0940021	+	0.995572i	$0.470034\pi$
$480$	−4.87472	−	4.09495i	−0.222499	−	0.186908i
$481$	3.22972			0.147263
$482$	32.6132	+	11.1326i	1.48549	+	0.507074i
$483$	0.149770	+	0.924145i	0.00681477	+	0.0420500i
$484$	8.42026	−	10.8966i	0.382739	−	0.495299i
$485$	4.62144	−	4.62144i	0.209849	−	0.209849i
$486$	19.6110	−	10.0701i	0.889575	−	0.456789i
$487$	−25.8876			−1.17308			−0.586540	−	0.809920i	$-0.699510\pi$
$487$	−25.8876			−1.17308			−0.586540	+	0.809920i	$0.699510\pi$
$488$	−2.49719	−	0.509975i	−0.113042	−	0.0230855i
$489$	−29.3895	−	21.1921i	−1.32904	−	0.958339i
$490$	0.824840	−	0.405024i	0.0372625	−	0.0182971i
$491$	−19.4155	−	19.4155i	−0.876207	−	0.876207i	0.116933	−	0.993140i	$-0.462694\pi$
$491$	−19.4155	−	19.4155i	−0.876207	−	0.876207i	−0.993140	+	0.116933i	$0.962694\pi$
$492$	−6.58189	−	3.57208i	−0.296734	−	0.161042i
$493$	−29.8530	+	29.8530i	−1.34451	+	1.34451i
$494$	−7.08584	−	2.41876i	−0.318807	−	0.108825i
$495$	3.75168	−	1.24882i	0.168626	−	0.0561302i
$496$	−40.3272	+	10.5122i	−1.81074	+	0.472014i
$497$		−	14.6958i		−	0.659199i
$498$	−4.97667	+	3.53126i	−0.223010	+	0.158239i
$499$	18.9116	+	18.9116i	0.846599	+	0.846599i	0.989707	−	0.143108i	$-0.0457097\pi$
$499$	18.9116	+	18.9116i	0.846599	+	0.846599i	−0.143108	+	0.989707i	$0.545710\pi$
$500$	−1.58266	−	12.3457i	−0.0707787	−	0.552118i
$501$	1.72123	+	10.6207i	0.0768988	+	0.474498i
$502$	−16.3900	−	33.3786i	−0.731523	−	1.48976i
$503$			6.29527i			0.280692i	0.990102	+	0.140346i	$0.0448215\pi$
$503$			6.29527i			0.280692i	−0.990102	+	0.140346i	$0.955178\pi$
$504$	−6.67451	−	5.23936i	−0.297306	−	0.233380i
$505$		−	5.52408i		−	0.245818i
$506$	1.39181	−	0.683427i	0.0618736	−	0.0303820i
$507$	−2.82492	−	17.4310i	−0.125459	−	0.774136i
$508$	5.42479	−	7.02017i	0.240686	−	0.311470i
$509$	−9.53952	−	9.53952i	−0.422832	−	0.422832i	0.463346	−	0.886178i	$-0.346649\pi$
$509$	−9.53952	−	9.53952i	−0.422832	−	0.422832i	−0.886178	+	0.463346i	$0.846649\pi$
$510$	−6.63927	−	9.35684i	−0.293992	−	0.414328i
$511$		−	0.233482i		−	0.0103286i
$512$	22.2576	−	4.07433i	0.983655	−	0.180062i
$513$	15.6757	+	4.90751i	0.692100	+	0.216672i
$514$	−13.3867	+	39.2168i	−0.590462	+	1.72978i
$515$	−7.61722	+	7.61722i	−0.335655	+	0.335655i
$516$	30.0989	−	8.92180i	1.32503	−	0.392760i
$517$	10.9531	+	10.9531i	0.481716	+	0.481716i
$518$	1.20206	+	2.44801i	0.0528154	+	0.107560i
$519$	3.49176	+	2.51783i	0.153271	+	0.110520i
$520$	−2.56794	+	1.69696i	−0.112612	+	0.0744167i
$521$	10.4082			0.455991			0.227995	−	0.973662i	$-0.426783\pi$
$521$	10.4082			0.455991			0.227995	+	0.973662i	$0.426783\pi$
$522$	−17.4361	−	17.7038i	−0.763157	−	0.774872i
$523$	13.2569	−	13.2569i	0.579685	−	0.579685i	−0.355131	−	0.934816i	$-0.615564\pi$
$523$	13.2569	−	13.2569i	0.579685	−	0.579685i	0.934816	+	0.355131i	$0.115564\pi$
$524$	−8.87057	+	1.13716i	−0.387512	+	0.0496772i
$525$	−1.26845	−	7.82686i	−0.0553595	−	0.341592i
$526$	−6.76256	+	19.8112i	−0.294862	+	0.863807i
$527$	−75.1027			−3.27152
$528$	−5.07844	+	13.1038i	−0.221011	+	0.570269i
$529$	22.7078			0.987297
$530$	−0.962173	+	2.81872i	−0.0417941	+	0.122437i
$531$	23.9803	+	12.0027i	1.04065	+	0.520871i
$532$	−0.803915	−	6.27103i	−0.0348541	−	0.271884i
$533$	−2.56014	+	2.56014i	−0.110892	+	0.110892i
$534$	18.8140	+	3.19631i	0.814163	+	0.138318i
$535$	−7.92748			−0.342735
$536$	−1.71282	+	8.38713i	−0.0739824	+	0.362269i
$537$	9.10803	−	12.6311i	0.393040	−	0.545074i
$538$	−12.2329	−	24.9126i	−0.527399	−	1.07406i
$539$	−1.43432	−	1.43432i	−0.0617807	−	0.0617807i
$540$	5.53671	−	3.86558i	0.238262	−	0.166348i
$541$	10.4371	−	10.4371i	0.448725	−	0.448725i	−0.446206	−	0.894930i	$-0.647225\pi$
$541$	10.4371	−	10.4371i	0.448725	−	0.448725i	0.894930	+	0.446206i	$0.147225\pi$
$542$	9.18441	−	26.9060i	0.394504	−	1.15571i
$543$	19.7833	+	14.2653i	0.848981	+	0.612181i
$544$	40.6657	+	3.01273i	1.74353	+	0.129170i
$545$			10.8516i			0.464832i
$546$	−3.34570	+	2.37399i	−0.143183	+	0.101597i
$547$	0.334525	+	0.334525i	0.0143032	+	0.0143032i	0.714222	−	0.699919i	$-0.246781\pi$
$547$	0.334525	+	0.334525i	0.0143032	+	0.0143032i	−0.699919	+	0.714222i	$0.746781\pi$
$548$	−22.5353	−	17.4140i	−0.962662	−	0.743891i
$549$	1.20998	−	2.41743i	0.0516407	−	0.103174i
$550$	−11.7877	+	5.78815i	−0.502628	+	0.246807i
$551$		−	18.5144i		−	0.788741i
$552$	1.94719	−	1.79451i	0.0828779	−	0.0763792i
$553$		−	4.93151i		−	0.209709i
$554$	17.5024	+	35.6441i	0.743608	+	1.51437i
$555$	−2.14238	+	0.347201i	−0.0909389	+	0.0147379i
$556$	−15.3497	+	1.96775i	−0.650971	+	0.0834512i
$557$	22.8719	+	22.8719i	0.969113	+	0.969113i	0.999537	−	0.0304239i	$-0.00968571\pi$
$557$	22.8719	+	22.8719i	0.969113	+	0.969113i	−0.0304239	+	0.999537i	$0.509686\pi$
$558$	0.336673	−	44.2015i	0.0142525	−	1.87120i
$559$		−	15.1777i		−	0.641950i
$560$	−2.24198	−	1.31482i	−0.0947411	−	0.0555612i
$561$	−14.8126	+	20.5424i	−0.625389	+	0.867299i
$562$	−2.50885	−	0.856398i	−0.105829	−	0.0361250i
$563$	23.5403	−	23.5403i	0.992106	−	0.992106i	−0.00786281	−	0.999969i	$-0.502503\pi$
$563$	23.5403	−	23.5403i	0.992106	−	0.992106i	0.999969	+	0.00786281i	$0.00250284\pi$
$564$	23.2500	+	12.6181i	0.979000	+	0.531317i
$565$	−6.74775	−	6.74775i	−0.283880	−	0.283880i
$566$	−32.2665	+	15.8440i	−1.35626	+	0.665971i
$567$	7.20451	−	5.39398i	0.302561	−	0.226526i
$568$	−34.6783	+	22.9163i	−1.45507	+	0.961548i
$569$	−31.9154			−1.33797			−0.668983	−	0.743278i	$-0.733270\pi$
$569$	−31.9154			−1.33797			−0.668983	+	0.743278i	$0.733270\pi$
$570$	4.96028	+	0.842701i	0.207763	+	0.0352968i
$571$	−2.02190	+	2.02190i	−0.0846137	+	0.0846137i	−0.748147	−	0.663533i	$-0.769056\pi$
$571$	−2.02190	+	2.02190i	−0.0846137	+	0.0846137i	0.663533	+	0.748147i	$0.269056\pi$
$572$	5.37629	+	4.15449i	0.224794	+	0.173708i
$573$	10.5513	−	1.70998i	0.440788	−	0.0714355i
$574$	−2.89334	−	0.987644i	−0.120766	−	0.0412235i
$575$	2.47438			0.103189
$576$	−1.95543	+	23.9202i	−0.0814763	+	0.996675i
$577$	43.1754			1.79742			0.898708	−	0.438548i	$-0.144507\pi$
$577$	43.1754			1.79742			0.898708	+	0.438548i	$0.144507\pi$
$578$	46.7924	+	15.9726i	1.94631	+	0.664374i
$579$	−29.9393	+	4.85206i	−1.24424	+	0.201645i
$580$	−6.02256	−	4.65389i	−0.250073	−	0.193242i
$581$	−1.76156	+	1.76156i	−0.0730817	+	0.0730817i
$582$	−24.2901	−	4.12663i	−1.00686	−	0.171054i
$583$	6.57464			0.272294
$584$	−0.550955	+	0.364086i	−0.0227987	+	0.0150660i
$585$	−1.03109	−	3.09759i	−0.0426304	−	0.128070i
$586$	−31.3901	+	15.4136i	−1.29671	+	0.636729i
$587$	−11.8925	−	11.8925i	−0.490854	−	0.490854i	0.417721	−	0.908575i	$-0.362829\pi$
$587$	−11.8925	−	11.8925i	−0.490854	−	0.490854i	−0.908575	+	0.417721i	$0.862829\pi$
$588$	−3.04462	−	1.65236i	−0.125558	−	0.0681421i
$589$	23.2888	−	23.2888i	0.959598	−	0.959598i
$590$	7.77357	+	2.65352i	0.320033	+	0.109244i
$591$	−11.8259	+	16.4003i	−0.486451	+	0.674618i
$592$	3.90221	−	6.65391i	0.160380	−	0.273474i
$593$		−	36.6876i		−	1.50658i	−0.657688	−	0.753291i	$-0.728465\pi$
$593$		−	36.6876i		−	1.50658i	0.657688	−	0.753291i	$-0.271535\pi$
$594$	−12.0238	−	8.81002i	−0.493340	−	0.361479i
$595$	−3.31198	−	3.31198i	−0.135778	−	0.135778i
$596$	11.8588	−	1.52024i	0.485755	−	0.0622714i
$597$	15.2493	−	2.47136i	0.624114	−	0.101146i
$598$	−0.564274	−	1.14916i	−0.0230749	−	0.0469925i
$599$			14.1269i			0.577211i	0.957448	+	0.288606i	$0.0931916\pi$
$599$			14.1269i			0.577211i	−0.957448	+	0.288606i	$0.906808\pi$
$600$	−16.4913	+	15.1982i	−0.673256	+	0.620464i
$601$		−	6.81447i		−	0.277968i	−0.990295	−	0.138984i	$-0.955616\pi$
$601$		−	6.81447i		−	0.277968i	0.990295	−	0.138984i	$-0.0443836\pi$
$602$	11.5042	−	5.64894i	0.468875	−	0.230234i
$603$	−8.11926	−	4.06387i	−0.330642	−	0.165494i
$604$	25.7542	+	19.9014i	1.04792	+	0.809775i
$605$	3.16356	+	3.16356i	0.128617	+	0.128617i
$606$	−16.9835	+	12.0508i	−0.689906	+	0.489532i
$607$			5.05289i			0.205091i	0.994728	+	0.102545i	$0.0326987\pi$
$607$			5.05289i			0.205091i	−0.994728	+	0.102545i	$0.967301\pi$
$608$	−13.5444	+	11.6759i	−0.549297	+	0.473521i
$609$	−8.22824	−	5.93319i	−0.333425	−	0.240425i
$610$	0.267499	−	0.783648i	0.0108307	−	0.0317290i
$611$	9.04347	−	9.04347i	0.365860	−	0.365860i
$612$	−14.2834	+	40.8241i	−0.577374	+	1.65022i
$613$	24.4036	+	24.4036i	0.985651	+	0.985651i	0.999898	−	0.0142478i	$-0.00453537\pi$
$613$	24.4036	+	24.4036i	0.985651	+	0.985651i	−0.0142478	+	0.999898i	$0.504535\pi$
$614$	−1.67810	−	3.41748i	−0.0677225	−	0.137918i
$615$	1.42300	−	1.97344i	0.0573809	−	0.0795767i
$616$	−1.14798	+	5.62128i	−0.0462532	+	0.226488i
$617$	−10.5641			−0.425294			−0.212647	−	0.977129i	$-0.568208\pi$
$617$	−10.5641			−0.425294			−0.212647	+	0.977129i	$0.568208\pi$
$618$	40.0358	+	6.80166i	1.61047	+	0.273603i
$619$	10.2400	−	10.2400i	0.411581	−	0.411581i	−0.470708	−	0.882289i	$-0.656001\pi$
$619$	10.2400	−	10.2400i	0.411581	−	0.411581i	0.882289	+	0.470708i	$0.156001\pi$
$620$	−1.72161	−	13.4296i	−0.0691416	−	0.539347i
$621$	1.30193	+	2.48862i	0.0522448	+	0.0998650i
$622$	−1.74453	+	5.11066i	−0.0699493	+	0.204919i
$623$	7.79085			0.312134
$624$	10.8192	+	4.19304i	0.433114	+	0.167856i
$625$	−18.8452			−0.753809
$626$	1.28102	−	3.75278i	0.0511997	−	0.149991i
$627$	−1.77675	−	10.9633i	−0.0709566	−	0.437833i
$628$	8.92376	−	1.14398i	0.356097	−	0.0456498i
$629$	9.82951	−	9.82951i	0.391928	−	0.391928i
$630$	1.96410	−	1.93441i	0.0782518	−	0.0770688i
$631$	−28.8196			−1.14729			−0.573645	−	0.819104i	$-0.694471\pi$
$631$	−28.8196			−1.14729			−0.573645	+	0.819104i	$0.694471\pi$
$632$	−11.6371	+	7.69007i	−0.462897	+	0.305895i
$633$	6.67934	+	4.81631i	0.265480	+	0.191431i
$634$	11.1217	+	22.6496i	0.441700	+	0.899531i
$635$	2.03814	+	2.03814i	0.0808811	+	0.0808811i
$636$	10.7650	−	3.19092i	0.426859	−	0.126528i
$637$	−1.18426	+	1.18426i	−0.0469219	+	0.0469219i
$638$	−5.42759	+	15.9003i	−0.214880	+	0.629499i
$639$	−13.9242	−	41.8309i	−0.550834	−	1.65481i
$640$	0.393472	+	7.34079i	0.0155533	+	0.290170i
$641$			33.6392i			1.32867i	0.747435	+	0.664335i	$0.231285\pi$
$641$			33.6392i			1.32867i	−0.747435	+	0.664335i	$0.768715\pi$
$642$	17.2939	+	24.3726i	0.682535	+	0.961909i
$643$	2.90938	+	2.90938i	0.114735	+	0.114735i	0.762143	−	0.647409i	$-0.224147\pi$
$643$	2.90938	+	2.90938i	0.114735	+	0.114735i	−0.647409	+	0.762143i	$0.724147\pi$
$644$	0.661004	−	0.855399i	0.0260472	−	0.0337074i
$645$	1.63163	+	10.0679i	0.0642455	+	0.396422i
$646$	−28.9268	+	14.2040i	−1.13811	+	0.558850i
$647$		−	29.6246i		−	1.16466i	−0.812952	−	0.582331i	$-0.802141\pi$
$647$		−	29.6246i		−	1.16466i	0.812952	−	0.582331i	$-0.197859\pi$
$648$	−23.9629	−	8.58950i	−0.941352	−	0.337427i
$649$		−	18.1318i		−	0.711736i
$650$	4.77901	+	9.73254i	0.187448	+	0.381742i
$651$	−2.88688	−	17.8133i	−0.113146	−	0.698158i
$652$	5.31995	+	41.4989i	0.208345	+	1.62522i
$653$	20.6380	+	20.6380i	0.807627	+	0.807627i	0.984274	−	0.176647i	$-0.0565251\pi$
$653$	20.6380	+	20.6380i	0.807627	+	0.807627i	−0.176647	+	0.984274i	$0.556525\pi$
$654$	33.3627	−	23.6729i	1.30458	−	0.925685i
$655$		−	2.90550i		−	0.113527i
$656$	2.18122	+	8.36761i	0.0851623	+	0.326700i
$657$	−0.221222	−	0.664593i	−0.00863071	−	0.0259282i
$658$	10.2205	+	3.48877i	0.398435	+	0.136006i
$659$	23.8523	−	23.8523i	0.929153	−	0.929153i	−0.0684985	−	0.997651i	$-0.521821\pi$
$659$	23.8523	−	23.8523i	0.929153	−	0.929153i	0.997651	+	0.0684985i	$0.0218208\pi$
$660$	−4.01288	−	2.17785i	−0.156201	−	0.0847725i
$661$	−11.8802	−	11.8802i	−0.462085	−	0.462085i	0.437254	−	0.899338i	$-0.355951\pi$
$661$	−11.8802	−	11.8802i	−0.462085	−	0.462085i	−0.899338	+	0.437254i	$0.855951\pi$
$662$	6.39590	−	3.14060i	0.248584	−	0.122063i
$663$	16.9609	+	12.2301i	0.658706	+	0.474978i
$664$	6.90374	+	1.40988i	0.267917	+	0.0547139i
$665$	2.05404			0.0796523
$666$	5.74107	+	5.82920i	0.222462	+	0.225877i
$667$	2.23849	−	2.23849i	0.0866747	−	0.0866747i
$668$	7.59657	−	9.83065i	0.293920	−	0.380359i
$669$	6.25877	+	38.6193i	0.241978	+	1.49311i
$670$	−2.63198	−	0.898430i	−0.101682	−	0.0347094i
$671$	−1.82785			−0.0705635
$672$	0.848578	+	9.76114i	0.0327346	+	0.376544i
$673$	13.0244			0.502052			0.251026	−	0.967980i	$-0.419232\pi$
$673$	13.0244			0.502052			0.251026	+	0.967980i	$0.419232\pi$
$674$	−27.7520	−	9.47317i	−1.06897	−	0.364893i
$675$	−11.0265	−	21.0769i	−0.424409	−	0.811250i
$676$	−12.4677	+	16.1343i	−0.479526	+	0.620550i
$677$	21.3792	−	21.3792i	0.821668	−	0.821668i	−0.164679	−	0.986347i	$-0.552659\pi$
$677$	21.3792	−	21.3792i	0.821668	−	0.821668i	0.986347	+	0.164679i	$0.0526588\pi$
$678$	−6.02528	+	35.4659i	−0.231400	+	1.36206i
$679$	−10.0585			−0.386009
$680$	−2.65077	+	12.9800i	−0.101653	+	0.497761i
$681$	19.5313	−	27.0862i	0.748439	−	1.03795i
$682$	−26.8278	+	13.1733i	−1.02729	+	0.504434i
$683$	−14.3476	−	14.3476i	−0.548996	−	0.548996i	0.377154	−	0.926150i	$-0.376903\pi$
$683$	−14.3476	−	14.3476i	−0.548996	−	0.548996i	−0.926150	+	0.377154i	$0.876903\pi$
$684$	−8.23007	−	17.0885i	−0.314685	−	0.653394i
$685$	6.54260	−	6.54260i	0.249980	−	0.249980i
$686$	−1.33839	−	0.456860i	−0.0510998	−	0.0174430i
$687$	8.24615	+	5.94611i	0.314610	+	0.226858i
$688$	−31.2693	−	18.3380i	−1.19213	−	0.699130i
$689$		−	5.42838i		−	0.206805i
$690$	0.497837	+	0.701611i	0.0189523	+	0.0267099i
$691$	−6.59157	−	6.59157i	−0.250755	−	0.250755i	0.570525	−	0.821280i	$-0.306740\pi$
$691$	−6.59157	−	6.59157i	−0.250755	−	0.250755i	−0.821280	+	0.570525i	$0.806740\pi$
$692$	−0.632063	−	4.93048i	−0.0240274	−	0.187429i
$693$	−5.44174	−	2.72371i	−0.206715	−	0.103465i
$694$	−0.00868616	−	0.0176895i	−0.000329722	−	0.000671486i
$695$		−	5.02769i		−	0.190711i
$696$	−1.16985	+	28.6685i	−0.0443430	+	1.08668i
$697$			15.5833i			0.590259i
$698$	−1.38340	+	0.679294i	−0.0523623	+	0.0257116i
$699$	6.73032	−	1.09074i	0.254564	−	0.0412555i
$700$	−5.59824	+	7.24463i	−0.211593	+	0.273821i
$701$	27.9140	+	27.9140i	1.05430	+	1.05430i	0.998439	+	0.0558581i	$0.0177894\pi$
$701$	27.9140	+	27.9140i	1.05430	+	1.05430i	0.0558581	+	0.998439i	$0.482211\pi$
$702$	−7.27403	+	9.92746i	−0.274541	+	0.374688i
$703$			6.09612i			0.229920i
$704$	15.0548	−	6.05676i	0.567401	−	0.228273i
$705$	−5.02663	+	6.97101i	−0.189314	+	0.262543i
$706$	−1.07031	+	3.13550i	−0.0402816	+	0.118006i
$707$	−6.01152	+	6.01152i	−0.226087	+	0.226087i
$708$	−8.80004	−	29.6881i	−0.330726	−	1.11575i
$709$	7.14776	+	7.14776i	0.268440	+	0.268440i	0.828471	−	0.560031i	$-0.189211\pi$
$709$	7.14776	+	7.14776i	0.268440	+	0.268440i	−0.560031	+	0.828471i	$0.689211\pi$
$710$	−5.95217	−	12.1217i	−0.223381	−	0.454920i
$711$	−4.67257	−	14.0373i	−0.175235	−	0.526439i
$712$	−12.1489	−	18.3843i	−0.455298	−	0.688982i
$713$	5.63148			0.210901
$714$	−2.95737	+	17.4076i	−0.110677	+	0.651463i
$715$	−1.56088	+	1.56088i	−0.0583735	+	0.0583735i
$716$	−17.8356	+	2.28643i	−0.666547	+	0.0854480i
$717$	27.9638	−	4.53190i	1.04433	−	0.169247i
$718$	6.58240	−	19.2833i	0.245653	−	0.719648i
$719$	16.0695			0.599292			0.299646	−	0.954050i	$-0.403131\pi$
$719$	16.0695			0.599292			0.299646	+	0.954050i	$0.403131\pi$
$720$	−7.62747	−	1.61829i	−0.284259	−	0.0603103i
$721$	16.5787			0.617424
$722$	−4.11492	+	12.0548i	−0.153141	+	0.448633i
$723$	41.6623	−	6.75192i	1.54944	−	0.251107i
$724$	−3.58108	−	27.9346i	−0.133090	−	1.03818i
$725$	−18.9585	+	18.9585i	−0.704099	+	0.704099i
$726$	2.82485	−	16.6275i	0.104840	−	0.617106i
$727$	−14.7667			−0.547667			−0.273833	−	0.961777i	$-0.588292\pi$
$727$	−14.7667			−0.547667			−0.273833	+	0.961777i	$0.588292\pi$
$728$	4.64123	+	0.947831i	0.172015	+	0.0351290i
$729$	15.3965	−	22.1799i	0.570240	−	0.821478i
$730$	−0.0945657	−	0.192585i	−0.00350003	−	0.00712789i
$731$	−46.1927	−	46.1927i	−1.70850	−	1.70850i
$732$	−2.99283	+	0.887125i	−0.110618	+	0.0327891i
$733$	14.1137	−	14.1137i	0.521303	−	0.521303i	−0.396662	−	0.917965i	$-0.629831\pi$
$733$	14.1137	−	14.1137i	0.521303	−	0.521303i	0.917965	+	0.396662i	$0.129831\pi$
$734$	12.7246	−	37.2771i	0.469673	−	1.37592i
$735$	0.658245	−	0.912864i	0.0242797	−	0.0336715i
$736$	−3.04927	−	0.225906i	−0.112397	−	0.00832699i
$737$			6.13908i			0.226136i
$738$	−9.17151	−	0.0698573i	−0.337608	−	0.00257148i
$739$	−6.96635	−	6.96635i	−0.256261	−	0.256261i	0.567270	−	0.823532i	$-0.307999\pi$
$739$	−6.96635	−	6.96635i	−0.256261	−	0.256261i	−0.823532	+	0.567270i	$0.807999\pi$
$740$	1.98301	+	1.53236i	0.0728969	+	0.0563306i
$741$	−9.05192	+	1.46698i	−0.332530	+	0.0538910i
$742$	4.11451	−	2.02037i	0.151049	−	0.0741700i
$743$		−	26.0074i		−	0.954117i	−0.878871	−	0.477059i	$-0.841703\pi$
$743$		−	26.0074i		−	0.954117i	0.878871	−	0.477059i	$-0.158297\pi$
$744$	−37.5329	+	34.5899i	−1.37602	+	1.26813i
$745$			3.88428i			0.142309i
$746$	−18.8085	−	38.3040i	−0.688629	−	1.40241i
$747$	−3.34511	+	6.68324i	−0.122391	+	0.244527i
$748$	29.0065	−	3.71848i	1.06058	−	0.135961i
$749$	8.62700	+	8.62700i	0.315224	+	0.315224i
$750$	−8.82153	−	12.4323i	−0.322117	−	0.453965i
$751$		−	24.2030i		−	0.883181i	−0.897217	−	0.441590i	$-0.854414\pi$
$751$		−	24.2030i		−	0.883181i	0.897217	−	0.441590i	$-0.145586\pi$
$752$	−7.70497	−	29.5579i	−0.280971	−	1.07787i
$753$	−36.9407	−	26.6371i	−1.34619	−	0.970709i
$754$	13.1282	+	4.48131i	0.478099	+	0.163200i
$755$	−7.47711	+	7.47711i	−0.272120	+	0.272120i
$756$	−10.2319	−	1.81859i	−0.372132	−	0.0661415i
$757$	10.9658	+	10.9658i	0.398560	+	0.398560i	0.877725	−	0.479165i	$-0.159060\pi$
$757$	10.9658	+	10.9658i	0.398560	+	0.398560i	−0.479165	+	0.877725i	$0.659060\pi$
$758$	44.2162	−	21.7116i	1.60600	−	0.788603i
$759$	1.11071	−	1.54034i	0.0403160	−	0.0559109i
$760$	−3.20302	−	4.84699i	−0.116186	−	0.175819i
$761$	−15.7528			−0.571040			−0.285520	−	0.958373i	$-0.592166\pi$
$761$	−15.7528			−0.571040			−0.285520	+	0.958373i	$0.592166\pi$
$762$	1.81992	−	10.7124i	0.0659287	−	0.388068i
$763$	11.8092	−	11.8092i	0.427520	−	0.427520i
$764$	−9.76642	−	7.54694i	−0.353337	−	0.273039i
$765$	−12.5654	−	6.28929i	−0.454305	−	0.227390i
$766$	−26.8477	−	9.16451i	−0.970048	−	0.331127i
$767$	−14.9706			−0.540557
$768$	21.7105	−	17.2237i	0.783409	−	0.621507i
$769$	−12.6179			−0.455012			−0.227506	−	0.973777i	$-0.573057\pi$
$769$	−12.6179			−0.455012			−0.227506	+	0.973777i	$0.573057\pi$
$770$	−1.76402	−	0.602152i	−0.0635710	−	0.0217001i
$771$	8.11907	+	50.0981i	0.292401	+	1.80424i
$772$	27.7122	+	21.4144i	0.997382	+	0.770720i
$773$	−3.02531	+	3.02531i	−0.108813	+	0.108813i	−0.759417	−	0.650604i	$-0.774516\pi$
$773$	−3.02531	+	3.02531i	−0.108813	+	0.108813i	0.650604	+	0.759417i	$0.274516\pi$
$774$	27.3937	−	26.9795i	0.984646	−	0.969760i
$775$	−47.6947			−1.71324
$776$	15.6849	+	23.7353i	0.563056	+	0.852048i
$777$	2.70926	+	1.95358i	0.0971941	+	0.0700844i
$778$	−16.5260	+	8.11484i	−0.592487	+	0.290931i
$779$	−4.83227	−	4.83227i	−0.173134	−	0.173134i
$780$	−1.79815	+	3.31325i	−0.0643840	+	0.118633i
$781$	−21.0786	+	21.0786i	−0.754252	+	0.754252i
$782$	−5.21474	−	1.78006i	−0.186479	−	0.0636548i
$783$	−29.0429	−	9.09231i	−1.03791	−	0.324933i
$784$	1.00898	+	3.87065i	0.0360349	+	0.138238i
$785$			2.92293i			0.104324i
$786$	−8.93280	+	6.33839i	−0.318623	+	0.226083i
$787$	21.7502	+	21.7502i	0.775311	+	0.775311i	0.979029	−	0.203719i	$-0.0653028\pi$
$787$	21.7502	+	21.7502i	0.775311	+	0.775311i	−0.203719	+	0.979029i	$0.565303\pi$
$788$	23.1578	−	2.96871i	0.824961	−	0.105756i
$789$	4.10151	+	25.3081i	0.146018	+	0.900991i
$790$	−1.99738	−	4.06770i	−0.0710636	−	0.144722i
$791$			14.6863i			0.522186i
$792$	2.05847	+	17.0884i	0.0731447	+	0.607208i
$793$			1.50918i			0.0535924i
$794$	45.3321	−	22.2596i	1.60877	−	0.789963i
$795$	0.583560	+	3.60082i	0.0206967	+	0.127708i
$796$	−14.1150	−	10.9072i	−0.500292	−	0.386597i
$797$	−35.4008	−	35.4008i	−1.25396	−	1.25396i	−0.953930	−	0.300030i	$-0.903003\pi$
$797$	−35.4008	−	35.4008i	−1.25396	−	1.25396i	−0.300030	−	0.953930i	$-0.596997\pi$
$798$	−4.48091	−	6.31503i	−0.158623	−	0.223550i
$799$		−	55.0467i		−	1.94741i
$800$	25.8252	+	1.91326i	0.913057	+	0.0676440i
$801$	22.1762	−	7.38178i	0.783559	−	0.260822i
$802$	14.6993	−	43.0621i	0.519051	−	1.52058i
$803$	−0.334888	+	0.334888i	−0.0118180	+	0.0118180i
$804$	2.97952	+	10.0518i	0.105080	+	0.354500i
$805$	0.248345	+	0.248345i	0.00875299	+	0.00875299i
$806$	10.8766	+	22.1505i	0.383113	+	0.780218i
$807$	−27.5712	−	19.8810i	−0.970553	−	0.699843i
$808$	23.5598	+	4.81138i	0.828832	+	0.169264i
$809$	8.99677			0.316310			0.158155	−	0.987414i	$-0.449445\pi$
$809$	8.99677			0.316310			0.158155	+	0.987414i	$0.449445\pi$
$810$	3.75788	−	7.36717i	0.132038	−	0.258856i
$811$	−20.1943	+	20.1943i	−0.709119	+	0.709119i	−0.966350	−	0.257231i	$-0.917190\pi$
$811$	−20.1943	+	20.1943i	−0.709119	+	0.709119i	0.257231	+	0.966350i	$0.417190\pi$
$812$	1.48944	+	11.6185i	0.0522691	+	0.407731i
$813$	−5.57037	−	34.3716i	−0.195361	−	1.20546i
$814$	1.78711	−	5.23539i	0.0626380	−	0.183500i
$815$	−13.5927			−0.476133
$816$	45.6890	−	20.1664i	1.59943	−	0.705964i
$817$	28.6481			1.00227
$818$	−17.3141	+	50.7222i	−0.605372	+	1.77346i
$819$	−2.24885	+	4.49300i	−0.0785810	+	0.156998i
$820$	−2.78656	+	0.357223i	−0.0973108	+	0.0124748i
$821$	19.3687	−	19.3687i	0.675974	−	0.675974i	−0.283113	−	0.959087i	$-0.591367\pi$
$821$	19.3687	−	19.3687i	0.675974	−	0.675974i	0.959087	+	0.283113i	$0.0913672\pi$
$822$	−34.3876	−	5.84210i	−1.19940	−	0.203766i
$823$	−29.7220			−1.03604			−0.518022	−	0.855368i	$-0.673331\pi$
$823$	−29.7220			−1.03604			−0.518022	+	0.855368i	$0.673331\pi$
$824$	−25.8524	−	39.1214i	−0.900613	−	1.36286i
$825$	−9.40689	+	13.0456i	−0.327506	+	0.454190i
$826$	−5.57184	−	11.3472i	−0.193869	−	0.394819i
$827$	30.0621	+	30.0621i	1.04536	+	1.04536i	0.998921	+	0.0464408i	$0.0147879\pi$
$827$	30.0621	+	30.0621i	1.04536	+	1.04536i	0.0464408	+	0.998921i	$0.485212\pi$
$828$	1.07103	−	3.06114i	0.0372207	−	0.106382i
$829$	8.43540	−	8.43540i	0.292973	−	0.292973i	−0.545280	−	0.838254i	$-0.683577\pi$
$829$	8.43540	−	8.43540i	0.292973	−	0.292973i	0.838254	+	0.545280i	$0.183577\pi$
$830$	−0.739529	+	2.16648i	−0.0256694	+	0.0751995i
$831$	39.4479	+	28.4450i	1.36843	+	0.986745i
$832$	−5.00079	−	12.4301i	−0.173371	−	0.430936i
$833$			7.20845i			0.249758i
$834$	−15.4574	+	10.9680i	−0.535244	+	0.379790i
$835$	2.85409	+	2.85409i	0.0987700	+	0.0987700i
$836$	−7.84162	+	10.1478i	−0.271208	+	0.350968i
$837$	−25.0953	−	47.9693i	−0.867422	−	1.65806i
$838$	8.67405	−	4.25925i	0.299640	−	0.147133i
$839$		−	11.9278i		−	0.411792i	−0.978574	−	0.205896i	$-0.933989\pi$
$839$		−	11.9278i		−	0.411792i	0.978574	−	0.205896i	$-0.0660109\pi$
$840$	−3.18057	−	0.129786i	−0.109740	−	0.00447805i
$841$			5.30225i			0.182836i
$842$	−21.6577	−	44.1063i	−0.746373	−	1.52000i
$843$	−3.20497	+	0.519407i	−0.110385	+	0.0178893i
$844$	−1.20906	−	9.43144i	−0.0416177	−	0.324644i
$845$	−4.68421	−	4.68421i	−0.161142	−	0.161142i
$846$	32.3976	+	0.246765i	1.11385	+	0.00848396i
$847$		−	6.88543i		−	0.236586i
$848$	−11.1836	−	6.55866i	−0.384046	−	0.225225i
$849$	−25.7496	+	35.7099i	−0.883724	+	1.22556i
$850$	44.1652	+	15.0758i	1.51485	+	0.517097i
$851$	−0.737053	+	0.737053i	−0.0252659	+	0.0252659i
$852$	−24.2828	+	44.7433i	−0.831915	+	1.53288i
$853$	35.5832	+	35.5832i	1.21835	+	1.21835i	0.968211	+	0.250136i	$0.0804752\pi$
$853$	35.5832	+	35.5832i	1.21835	+	1.21835i	0.250136	+	0.968211i	$0.419525\pi$
$854$	−1.14390	+	0.561694i	−0.0391435	+	0.0192208i
$855$	5.84672	−	1.94619i	0.199954	−	0.0665584i
$856$	6.90470	−	33.8102i	0.235998	−	1.15561i
$857$	−8.13947			−0.278039			−0.139019	−	0.990290i	$-0.544395\pi$
$857$	−8.13947			−0.278039			−0.139019	+	0.990290i	$0.544395\pi$
$858$	8.20389	+	1.39376i	0.280076	+	0.0475821i
$859$	−13.9483	+	13.9483i	−0.475912	+	0.475912i	−0.903821	−	0.427910i	$-0.859250\pi$
$859$	−13.9483	+	13.9483i	−0.475912	+	0.475912i	0.427910	+	0.903821i	$0.359250\pi$
$860$	7.20115	−	9.31894i	0.245557	−	0.317773i
$861$	−3.69614	+	0.599008i	−0.125964	+	0.0204141i
$862$	−5.74883	−	1.96237i	−0.195806	−	0.0668386i
$863$	41.5365			1.41392			0.706959	−	0.707254i	$-0.250066\pi$
$863$	41.5365			1.41392			0.706959	+	0.707254i	$0.250066\pi$
$864$	11.6641	+	26.9805i	0.396819	+	0.917897i
$865$	1.61495			0.0549100
$866$	2.26924	+	0.774609i	0.0771120	+	0.0263223i
$867$	59.7757	−	9.68744i	2.03009	−	0.329003i
$868$	−12.7411	+	16.4882i	−0.432462	+	0.559646i
$869$	−7.07338	+	7.07338i	−0.239948	+	0.239948i
$870$	−9.19007	−	1.56130i	−0.311573	−	0.0529330i
$871$	5.06876			0.171748
$872$	−46.2814	−	9.45158i	−1.56729	−	0.320071i
$873$	−28.6309	+	9.53034i	−0.969009	+	0.322553i
$874$	2.16904	−	1.06507i	0.0733688	−	0.0360265i
$875$	−4.40059	−	4.40059i	−0.148767	−	0.148767i
$876$	−0.385795	+	0.710863i	−0.0130348	+	0.0240178i
$877$	31.1750	−	31.1750i	1.05270	−	1.05270i	0.0541722	−	0.998532i	$-0.482748\pi$
$877$	31.1750	−	31.1750i	1.05270	−	1.05270i	0.998532	−	0.0541722i	$-0.0172520\pi$
$878$	−9.26982	−	3.16427i	−0.312841	−	0.106789i
$879$	−25.0502	+	34.7399i	−0.844921	+	1.17175i
$880$	1.32986	+	5.10161i	0.0448295	+	0.171975i
$881$			15.8809i			0.535041i	0.963552	+	0.267521i	$0.0862044\pi$
$881$			15.8809i			0.535041i	−0.963552	+	0.267521i	$0.913796\pi$
$882$	−4.24252	−	0.0323143i	−0.142853	−	0.00108808i
$883$	−20.2365	−	20.2365i	−0.681014	−	0.681014i	0.279215	−	0.960229i	$-0.409926\pi$
$883$	−20.2365	−	20.2365i	−0.681014	−	0.681014i	−0.960229	+	0.279215i	$0.909926\pi$
$884$	−3.07018	−	23.9493i	−0.103261	−	0.805503i
$885$	9.93048	−	1.60936i	0.333809	−	0.0540982i
$886$	−21.8515	−	44.5011i	−0.734116	−	1.49504i
$887$			48.4641i			1.62727i	0.581379	+	0.813633i	$0.302513\pi$
$887$			48.4641i			1.62727i	−0.581379	+	0.813633i	$0.697487\pi$
$888$	0.385188	−	9.43950i	0.0129261	−	0.316769i
$889$		−	4.43597i		−	0.148777i
$890$	6.42620	−	3.15548i	0.215407	−	0.105772i
$891$	−18.0703	−	2.59689i	−0.605379	−	0.0869990i
$892$	27.6228	−	35.7465i	0.924881	−	1.19688i
$893$	17.0696	+	17.0696i	0.571212	+	0.571212i
$894$	11.9420	−	8.47360i	0.399400	−	0.283400i
$895$		−	5.84195i		−	0.195275i
$896$	7.56034	−	8.41672i	0.252573	−	0.281183i
$897$	−1.27179	−	0.917059i	−0.0424638	−	0.0306197i
$898$	3.35116	−	9.81733i	0.111830	−	0.327609i
$899$	−43.1479	+	43.1479i	−1.43906	+	1.43906i
$900$	−9.07084	+	25.9257i	−0.302361	+	0.864191i
$901$	−16.5210	−	16.5210i	−0.550395	−	0.550395i
$902$	2.73338	+	5.56658i	0.0910116	+	0.185347i
$903$	9.18066	−	12.7319i	0.305513	−	0.423690i
$904$	34.6559	−	22.9015i	1.15264	−	0.761693i
$905$	9.14983			0.304151
$906$	39.2993	+	6.67655i	1.30563	+	0.221814i
$907$	−16.8309	+	16.8309i	−0.558861	+	0.558861i	−0.928983	−	0.370122i	$-0.879316\pi$
$907$	−16.8309	+	16.8309i	−0.558861	+	0.558861i	0.370122	+	0.928983i	$0.379316\pi$
$908$	−38.2467	+	4.90303i	−1.26926	+	0.162713i
$909$	−11.4156	+	22.8074i	−0.378631	+	0.756472i
$910$	−0.497169	+	1.45647i	−0.0164810	+	0.0482817i
$911$	−2.53307			−0.0839242			−0.0419621	−	0.999119i	$-0.513361\pi$
$911$	−2.53307			−0.0839242			−0.0419621	+	0.999119i	$0.513361\pi$
$912$	−7.91438	+	20.4213i	−0.262071	+	0.676216i
$913$	5.05329			0.167239
$914$	4.55640	−	13.3481i	0.150712	−	0.441516i
$915$	−0.162239	−	1.00108i	−0.00536345	−	0.0330948i
$916$	−1.49268	−	11.6438i	−0.0493196	−	0.384723i
$917$	−3.16188	+	3.16188i	−0.104415	+	0.104415i
$918$	8.07560	+	52.3519i	0.266534	+	1.72787i
$919$	34.0974			1.12477			0.562384	−	0.826876i	$-0.309884\pi$
$919$	34.0974			1.12477			0.562384	+	0.826876i	$0.309884\pi$
$920$	0.198765	−	0.973290i	0.00655309	−	0.0320884i
$921$	−3.78218	−	2.72724i	−0.124627	−	0.0898658i
$922$	10.2328	+	20.8392i	0.336998	+	0.686303i
$923$	17.4037	+	17.4037i	0.572848	+	0.572848i
$924$	1.99696	+	6.73699i	0.0656950	+	0.221631i
$925$	6.24232	−	6.24232i	0.205246	−	0.205246i
$926$	7.68546	−	22.5148i	0.252560	−	0.739882i
$927$	47.1904	−	15.7082i	1.54994	−	0.515926i
$928$	25.0941	−	21.6324i	0.823754	−	0.710117i
$929$		−	10.3387i		−	0.339201i	−0.985513	−	0.169600i	$-0.945752\pi$
$929$		−	10.3387i		−	0.339201i	0.985513	−	0.169600i	$-0.0542477\pi$
$930$	−9.59603	−	13.5239i	−0.314666	−	0.443465i
$931$	−2.23529	−	2.23529i	−0.0732587	−	0.0732587i
$932$	−6.22966	−	4.81393i	−0.204059	−	0.157686i
$933$	1.05806	+	6.52870i	0.0346394	+	0.213740i
$934$	−25.8563	+	12.6963i	−0.846043	+	0.415436i
$935$			9.50090i			0.310713i
$936$	14.1091	−	1.69959i	0.461170	−	0.0555528i
$937$			12.2190i			0.399178i	0.979880	+	0.199589i	$0.0639606\pi$
$937$			12.2190i			0.399178i	−0.979880	+	0.199589i	$0.936039\pi$
$938$	1.88652	+	3.84193i	0.0615970	+	0.125444i
$939$	−0.776939	−	4.79405i	−0.0253545	−	0.156448i
$940$	9.84329	−	1.26186i	0.321053	−	0.0411573i
$941$	−8.49227	−	8.49227i	−0.276840	−	0.276840i	0.555006	−	0.831846i	$-0.312716\pi$
$941$	−8.49227	−	8.49227i	−0.276840	−	0.276840i	−0.831846	+	0.555006i	$0.812716\pi$
$942$	8.98637	−	6.37639i	0.292792	−	0.207754i
$943$		−	1.16849i		−	0.0380514i
$944$	−18.0877	+	30.8426i	−0.588705	+	1.00384i
$945$	1.00873	−	3.22210i	0.0328139	−	0.104815i
$946$	−24.6031	−	8.39831i	−0.799917	−	0.273053i
$947$	−6.61991	+	6.61991i	−0.215118	+	0.215118i	−0.806437	−	0.591319i	$-0.798607\pi$
$947$	−6.61991	+	6.61991i	−0.215118	+	0.215118i	0.591319	+	0.806437i	$0.298607\pi$
$948$	−8.14862	+	15.0146i	−0.264655	+	0.487650i
$949$	0.276502	+	0.276502i	0.00897564	+	0.00897564i
$950$	−18.3702	+	9.02040i	−0.596009	+	0.292660i
$951$	25.0667	+	18.0750i	0.812844	+	0.586123i
$952$	17.0100	−	11.2407i	0.551298	−	0.364313i
$953$	−40.5837			−1.31463			−0.657317	−	0.753614i	$-0.728309\pi$
$953$	−40.5837			−1.31463			−0.657317	+	0.753614i	$0.728309\pi$
$954$	9.79746	−	9.64934i	0.317205	−	0.312409i
$955$	2.83545	−	2.83545i	0.0917529	−	0.0917529i
$956$	−25.8836	−	20.0014i	−0.837135	−	0.646891i
$957$	3.29184	+	20.3121i	0.106410	+	0.656597i
$958$	−5.50703	−	1.87983i	−0.177924	−	0.0607346i
$959$	−14.2398			−0.459828
$960$	4.65344	+	7.70769i	0.150189	+	0.248764i
$961$	−77.5492			−2.50159
$962$	−4.32262	−	1.47553i	−0.139367	−	0.0475731i
$963$	32.7303	+	16.3823i	1.05472	+	0.527911i
$964$	−38.5630	−	29.7993i	−1.24203	−	0.959772i
$965$	−8.04556	+	8.04556i	−0.258996	+	0.258996i
$966$	0.221755	−	1.30529i	0.00713484	−	0.0419969i
$967$	−30.2460			−0.972646			−0.486323	−	0.873779i	$-0.661662\pi$
$967$	−30.2460			−0.972646			−0.486323	+	0.873779i	$0.661662\pi$
$968$	−16.2478	+	10.7370i	−0.522223	+	0.345099i
$969$	−23.0844	+	32.0137i	−0.741577	+	1.02843i
$970$	−8.29663	+	4.07392i	−0.266389	+	0.130806i
$971$	7.00612	+	7.00612i	0.224837	+	0.224837i	0.810532	−	0.585695i	$-0.199178\pi$
$971$	7.00612	+	7.00612i	0.224837	+	0.224837i	−0.585695	+	0.810532i	$0.699178\pi$
$972$	−30.8478	+	4.51819i	−0.989443	+	0.144921i
$973$	−5.47134	+	5.47134i	−0.175403	+	0.175403i
$974$	34.6477	+	11.8270i	1.11018	+	0.378962i
$975$	10.7712	+	7.76684i	0.344954	+	0.248738i
$976$	3.10922	+	1.82341i	0.0995236	+	0.0583659i
$977$			31.7366i			1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$977$			31.7366i			1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$978$	29.6527	+	41.7901i	0.948188	+	1.33630i
$979$	−11.1746	−	11.1746i	−0.357142	−	0.357142i
$980$	−1.28899	+	0.165243i	−0.0411754	+	0.00527848i
$981$	22.4250	−	44.8033i	0.715976	−	1.43046i
$982$	17.1152	+	34.8555i	0.546169	+	1.11228i
$983$			8.56246i			0.273100i	0.990633	+	0.136550i	$0.0436014\pi$
$983$			8.56246i			0.273100i	−0.990633	+	0.136550i	$0.956399\pi$
$984$	7.17717	+	7.78783i	0.228800	+	0.248267i
$985$			7.58519i			0.241684i
$986$	53.5935	−	26.3162i	1.70677	−	0.838080i
$987$	13.0563	−	2.11595i	0.415587	−	0.0673513i
$988$	8.37855	+	6.47447i	0.266557	+	0.205980i
$989$	3.46370	+	3.46370i	0.110139	+	0.110139i
$990$	−5.59174	−	0.0425909i	−0.177717	−	0.00135363i
$991$			50.7710i			1.61279i	0.591374	+	0.806397i	$0.298586\pi$
$991$			50.7710i			1.61279i	−0.591374	+	0.806397i	$0.701414\pi$
$992$	58.7760	+	4.35443i	1.86614	+	0.138253i
$993$	5.10410	−	7.07845i	0.161974	−	0.224628i
$994$	−6.71395	+	19.6687i	−0.212953	+	0.623854i
$995$	4.09794	−	4.09794i	0.129913	−	0.129913i
$996$	8.27400	−	2.45255i	0.262172	−	0.0777120i
$997$	−18.1206	−	18.1206i	−0.573886	−	0.573886i	0.359326	−	0.933212i	$-0.383006\pi$
$997$	−18.1206	−	18.1206i	−0.573886	−	0.573886i	−0.933212	+	0.359326i	$0.883006\pi$
$998$	−16.6711	−	33.9510i	−0.527713	−	1.07470i
$999$	9.56277	+	2.99376i	0.302553	+	0.0947185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.d.155.1	✓	48
3.2	odd	2	inner	336.2.s.d.155.24	yes	48
4.3	odd	2		1344.2.s.d.911.23		48
12.11	even	2		1344.2.s.d.911.12		48
16.3	odd	4	inner	336.2.s.d.323.24	yes	48
16.13	even	4		1344.2.s.d.239.12		48
48.29	odd	4		1344.2.s.d.239.23		48
48.35	even	4	inner	336.2.s.d.323.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.d.155.1	✓	48	1.1	even	1	trivial
336.2.s.d.155.24	yes	48	3.2	odd	2	inner
336.2.s.d.323.1	yes	48	48.35	even	4	inner
336.2.s.d.323.24	yes	48	16.3	odd	4	inner
1344.2.s.d.239.12		48	16.13	even	4
1344.2.s.d.239.23		48	48.29	odd	4
1344.2.s.d.911.12		48	12.11	even	2
1344.2.s.d.911.23		48	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33839 - 0.456860i) q^{2} +(-1.70974 + 0.277087i) q^{3} +(1.58256 + 1.22291i) q^{4} +(-0.459458 + 0.459458i) q^{5} +(2.41489 + 0.410265i) q^{6} +1.00000 q^{7} +(-1.55938 - 2.35973i) q^{8} +(2.84645 - 0.947494i) q^{9} +O(q^{10})\)	\(q+(-1.33839 - 0.456860i) q^{2} +(-1.70974 + 0.277087i) q^{3} +(1.58256 + 1.22291i) q^{4} +(-0.459458 + 0.459458i) q^{5} +(2.41489 + 0.410265i) q^{6} +1.00000 q^{7} +(-1.55938 - 2.35973i) q^{8} +(2.84645 - 0.947494i) q^{9} +(0.824840 - 0.405024i) q^{10} +(-1.43432 - 1.43432i) q^{11} +(-3.04462 - 1.65236i) q^{12} +(-1.18426 + 1.18426i) q^{13} +(-1.33839 - 0.456860i) q^{14} +(0.658245 - 0.912864i) q^{15} +(1.00898 + 3.87065i) q^{16} +7.20845i q^{17} +(-4.24252 - 0.0323143i) q^{18} +(-2.23529 - 2.23529i) q^{19} +(-1.28899 + 0.165243i) q^{20} +(-1.70974 + 0.277087i) q^{21} +(1.26440 + 2.57497i) q^{22} -0.540517i q^{23} +(3.31998 + 3.60246i) q^{24} +4.57780i q^{25} +(2.12603 - 1.04395i) q^{26} +(-4.60416 + 2.40868i) q^{27} +(1.58256 + 1.22291i) q^{28} +(4.14139 + 4.14139i) q^{29} +(-1.29804 + 0.921040i) q^{30} +10.4187i q^{31} +(0.417944 - 5.64139i) q^{32} +(2.84976 + 2.05490i) q^{33} +(3.29325 - 9.64770i) q^{34} +(-0.459458 + 0.459458i) q^{35} +(5.66337 + 1.98149i) q^{36} +(-1.36361 - 1.36361i) q^{37} +(1.97047 + 4.01290i) q^{38} +(1.69663 - 2.35292i) q^{39} +(1.80067 + 0.367731i) q^{40} +2.16181 q^{41} +(2.41489 + 0.410265i) q^{42} +(-6.40813 + 6.40813i) q^{43} +(-0.515851 - 4.02395i) q^{44} +(-0.872488 + 1.74315i) q^{45} +(-0.246940 + 0.723420i) q^{46} -7.63641 q^{47} +(-2.79760 - 6.33825i) q^{48} +1.00000 q^{49} +(2.09141 - 6.12686i) q^{50} +(-1.99736 - 12.3246i) q^{51} +(-3.32239 + 0.425914i) q^{52} +(-2.29189 + 2.29189i) q^{53} +(7.26257 - 1.12030i) q^{54} +1.31802 q^{55} +(-1.55938 - 2.35973i) q^{56} +(4.44114 + 3.20240i) q^{57} +(-3.65075 - 7.43482i) q^{58} +(6.32068 + 6.32068i) q^{59} +(2.15806 - 0.639685i) q^{60} +(0.637183 - 0.637183i) q^{61} +(4.75989 - 13.9442i) q^{62} +(2.84645 - 0.947494i) q^{63} +(-3.13670 + 7.35942i) q^{64} -1.08823i q^{65} +(-2.87528 - 4.05219i) q^{66} +(-2.14006 - 2.14006i) q^{67} +(-8.81529 + 11.4078i) q^{68} +(0.149770 + 0.924145i) q^{69} +(0.824840 - 0.405024i) q^{70} -14.6958i q^{71} +(-6.67451 - 5.23936i) q^{72} -0.233482i q^{73} +(1.20206 + 2.44801i) q^{74} +(-1.26845 - 7.82686i) q^{75} +(-0.803915 - 6.27103i) q^{76} +(-1.43432 - 1.43432i) q^{77} +(-3.34570 + 2.37399i) q^{78} -4.93151i q^{79} +(-2.24198 - 1.31482i) q^{80} +(7.20451 - 5.39398i) q^{81} +(-2.89334 - 0.987644i) q^{82} +(-1.76156 + 1.76156i) q^{83} +(-3.04462 - 1.65236i) q^{84} +(-3.31198 - 3.31198i) q^{85} +(11.5042 - 5.64894i) q^{86} +(-8.22824 - 5.93319i) q^{87} +(-1.14798 + 5.62128i) q^{88} +7.79085 q^{89} +(1.96410 - 1.93441i) q^{90} +(-1.18426 + 1.18426i) q^{91} +(0.661004 - 0.855399i) q^{92} +(-2.88688 - 17.8133i) q^{93} +(10.2205 + 3.48877i) q^{94} +2.05404 q^{95} +(0.848578 + 9.76114i) q^{96} -10.0585 q^{97} +(-1.33839 - 0.456860i) q^{98} +(-5.44174 - 2.72371i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) \) 48 * q + 6 * q^6 + 48 * q^7	\( 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) \) 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * q^99

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