LMFDB - Embedded newform 850.2.v.d.507.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(107,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("850.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.v (of order $16$, degree $8$, 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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			507.2
Character	$\chi$	$=$	850.507
Dual form			850.2.v.d.793.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.923880 + 0.382683i) q^{2} +(-0.530147 - 0.793420i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-0.186163 - 0.935903i) q^{6} +(-0.736366 - 3.70196i) q^{7} +(0.382683 + 0.923880i) q^{8} +(0.799590 - 1.93038i) q^{9} +(-2.74651 + 0.546316i) q^{11} +(0.186163 - 0.935903i) q^{12} -5.74893 q^{13} +(0.736366 - 3.70196i) q^{14} +1.00000i q^{16} +(-3.33833 - 2.41983i) q^{17} +(1.47745 - 1.47745i) q^{18} +(0.119335 + 0.288099i) q^{19} +(-2.54683 + 2.54683i) q^{21} +(-2.74651 - 0.546316i) q^{22} +(3.97327 + 2.65485i) q^{23} +(0.530147 - 0.793420i) q^{24} +(-5.31132 - 2.20002i) q^{26} +(-4.76321 + 0.947462i) q^{27} +(2.09699 - 3.13837i) q^{28} +(0.463177 - 0.309485i) q^{29} +(-5.00121 - 0.994802i) q^{31} +(-0.382683 + 0.923880i) q^{32} +(1.88951 + 1.88951i) q^{33} +(-2.15819 - 3.51315i) q^{34} +(1.93038 - 0.799590i) q^{36} +(8.56427 - 5.72246i) q^{37} +0.311836i q^{38} +(3.04777 + 4.56132i) q^{39} +(-7.70784 - 5.15021i) q^{41} +(-3.32759 + 1.37833i) q^{42} +(8.32027 - 3.44637i) q^{43} +(-2.32838 - 1.55578i) q^{44} +(2.65485 + 3.97327i) q^{46} +5.61274i q^{47} +(0.793420 - 0.530147i) q^{48} +(-6.69512 + 2.77321i) q^{49} +(-0.150134 + 3.93156i) q^{51} +(-4.06511 - 4.06511i) q^{52} +(2.52221 - 6.08916i) q^{53} +(-4.76321 - 0.947462i) q^{54} +(3.13837 - 2.09699i) q^{56} +(0.165319 - 0.247417i) q^{57} +(0.546354 - 0.108677i) q^{58} +(3.14785 + 1.30388i) q^{59} +(5.67092 - 8.48713i) q^{61} +(-4.23982 - 2.83296i) q^{62} +(-7.73498 - 1.53858i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(1.02260 + 2.46877i) q^{66} +(-1.94198 + 1.94198i) q^{67} +(-0.649481 - 4.07163i) q^{68} -4.55993i q^{69} +(0.782371 - 3.93324i) q^{71} +2.08943 q^{72} +(0.167388 - 0.841518i) q^{73} +(10.1022 - 2.00946i) q^{74} +(-0.119335 + 0.288099i) q^{76} +(4.04488 + 9.76520i) q^{77} +(1.07024 + 5.38044i) q^{78} +(-0.872680 - 4.38726i) q^{79} +(-1.15541 - 1.15541i) q^{81} +(-5.15021 - 7.70784i) q^{82} +(1.36475 + 0.565299i) q^{83} -3.60176 q^{84} +9.00580 q^{86} +(-0.491103 - 0.203422i) q^{87} +(-1.55578 - 2.32838i) q^{88} +(7.49831 + 7.49831i) q^{89} +(4.23331 + 21.2823i) q^{91} +(0.932261 + 4.68679i) q^{92} +(1.86208 + 4.49545i) q^{93} +(-2.14790 + 5.18549i) q^{94} +(0.935903 - 0.186163i) q^{96} +(3.04671 - 15.3169i) q^{97} -7.24674 q^{98} +(-1.14149 + 5.73865i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} + 32 q^{33} + 8 q^{34} - 32 q^{39} - 56 q^{41} + 24 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{49} - 32 q^{51} + 16 q^{52} - 16 q^{53}+ \cdots + 160 q^{99}+O(q^{100}) $ 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 + 32 * q^33 + 8 * q^34 - 32 * q^39 - 56 * q^41 + 24 * q^42 - 16 * q^43 + 16 * q^44 + 16 * q^49 - 32 * q^51 + 16 * q^52 - 16 * q^53 - 24 * q^54 - 8 * q^56 + 120 * q^57 - 16 * q^58 + 24 * q^61 + 8 * q^62 + 24 * q^63 - 16 * q^67 + 24 * q^71 - 56 * q^72 - 88 * q^73 + 32 * q^74 - 24 * q^77 - 32 * q^78 - 104 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 + 96 * q^86 - 136 * q^87 - 16 * q^89 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 - 16 * q^97 - 72 * q^98 + 160 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{16}\right)$

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
$3$	−0.530147	−	0.793420i	−0.306080	−	0.458081i	0.646261	−	0.763117i	$-0.276332\pi$
$3$	−0.530147	−	0.793420i	−0.306080	−	0.458081i	−0.952341	+	0.305035i	$0.901332\pi$
$4$	0.707107	+	0.707107i	0.353553	+	0.353553i
$5$		0			0
$5$		0			0
$6$	−0.186163	−	0.935903i	−0.0760006	−	0.382081i
$7$	−0.736366	−	3.70196i	−0.278320	−	1.39921i	−0.826541	−	0.562876i	$-0.809695\pi$
$7$	−0.736366	−	3.70196i	−0.278320	−	1.39921i	0.548221	−	0.836333i	$-0.315305\pi$
$8$	0.382683	+	0.923880i	0.135299	+	0.326641i
$9$	0.799590	−	1.93038i	0.266530	−	0.643460i
$10$		0			0
$11$	−2.74651	+	0.546316i	−0.828105	+	0.164720i	−0.590906	−	0.806741i	$-0.701230\pi$
$11$	−2.74651	+	0.546316i	−0.828105	+	0.164720i	−0.237200	+	0.971461i	$0.576230\pi$
$12$	0.186163	−	0.935903i	0.0537405	−	0.270172i
$13$	−5.74893			−1.59447			−0.797233	−	0.603672i	$-0.793704\pi$
$13$	−5.74893			−1.59447			−0.797233	+	0.603672i	$0.793704\pi$
$14$	0.736366	−	3.70196i	0.196802	−	0.989390i
$15$		0			0
$16$			1.00000i			0.250000i
$17$	−3.33833	−	2.41983i	−0.809664	−	0.586894i
$17$	−3.33833	−	2.41983i	−0.809664	−	0.586894i
$18$	1.47745	−	1.47745i	0.348238	−	0.348238i
$19$	0.119335	+	0.288099i	0.0273772	+	0.0660944i	0.936977	−	0.349391i	$-0.113612\pi$
$19$	0.119335	+	0.288099i	0.0273772	+	0.0660944i	−0.909600	+	0.415486i	$0.863612\pi$
$20$		0			0
$21$	−2.54683	+	2.54683i	−0.555764	+	0.555764i
$22$	−2.74651	−	0.546316i	−0.585559	−	0.116475i
$23$	3.97327	+	2.65485i	0.828484	+	0.553575i	0.895954	−	0.444146i	$-0.146493\pi$
$23$	3.97327	+	2.65485i	0.828484	+	0.553575i	−0.0674705	+	0.997721i	$0.521493\pi$
$24$	0.530147	−	0.793420i	0.108216	−	0.161956i
$25$		0			0
$26$	−5.31132	−	2.20002i	−1.04164	−	0.431459i
$27$	−4.76321	+	0.947462i	−0.916681	+	0.182339i
$28$	2.09699	−	3.13837i	0.396294	−	0.593096i
$29$	0.463177	−	0.309485i	0.0860098	−	0.0574699i	−0.511822	−	0.859092i	$-0.671029\pi$
$29$	0.463177	−	0.309485i	0.0860098	−	0.0574699i	0.597832	+	0.801622i	$0.296029\pi$
$30$		0			0
$31$	−5.00121	−	0.994802i	−0.898244	−	0.178672i	−0.275688	−	0.961247i	$-0.588906\pi$
$31$	−5.00121	−	0.994802i	−0.898244	−	0.178672i	−0.622556	+	0.782575i	$0.713906\pi$
$32$	−0.382683	+	0.923880i	−0.0676495	+	0.163320i
$33$	1.88951	+	1.88951i	0.328922	+	0.328922i
$34$	−2.15819	−	3.51315i	−0.370126	−	0.602500i
$35$		0			0
$36$	1.93038	−	0.799590i	0.321730	−	0.133265i
$37$	8.56427	−	5.72246i	1.40796	−	0.940767i	0.408348	−	0.912826i	$-0.366105\pi$
$37$	8.56427	−	5.72246i	1.40796	−	0.940767i	0.999610	−	0.0279411i	$-0.00889508\pi$
$38$			0.311836i			0.0505865i
$39$	3.04777	+	4.56132i	0.488035	+	0.730395i
$40$		0			0
$41$	−7.70784	−	5.15021i	−1.20376	−	0.804328i	−0.218576	−	0.975820i	$-0.570141\pi$
$41$	−7.70784	−	5.15021i	−1.20376	−	0.804328i	−0.985186	+	0.171492i	$0.945141\pi$
$42$	−3.32759	+	1.37833i	−0.513459	+	0.212682i
$43$	8.32027	−	3.44637i	1.26883	−	0.525566i	0.356221	−	0.934402i	$-0.384065\pi$
$43$	8.32027	−	3.44637i	1.26883	−	0.525566i	0.912608	+	0.408835i	$0.134065\pi$
$44$	−2.32838	−	1.55578i	−0.351017	−	0.234542i
$45$		0			0
$46$	2.65485	+	3.97327i	0.391437	+	0.585827i
$47$			5.61274i			0.818702i	0.912377	+	0.409351i	$0.134245\pi$
$47$			5.61274i			0.818702i	−0.912377	+	0.409351i	$0.865755\pi$
$48$	0.793420	−	0.530147i	0.114520	−	0.0765201i
$49$	−6.69512	+	2.77321i	−0.956445	+	0.396173i
$50$		0			0
$51$	−0.150134	+	3.93156i	−0.0210230	+	0.550529i
$52$	−4.06511	−	4.06511i	−0.563729	−	0.563729i
$53$	2.52221	−	6.08916i	0.346453	−	0.836411i	−0.650580	−	0.759437i	$-0.725474\pi$
$53$	2.52221	−	6.08916i	0.346453	−	0.836411i	0.997033	−	0.0769735i	$-0.0245257\pi$
$54$	−4.76321	−	0.947462i	−0.648191	−	0.128933i
$55$		0			0
$56$	3.13837	−	2.09699i	0.419382	−	0.280222i
$57$	0.165319	−	0.247417i	0.0218970	−	0.0327712i
$58$	0.546354	−	0.108677i	0.0717398	−	0.0142699i
$59$	3.14785	+	1.30388i	0.409815	+	0.169751i	0.578060	−	0.815994i	$-0.303810\pi$
$59$	3.14785	+	1.30388i	0.409815	+	0.169751i	−0.168245	+	0.985745i	$0.553810\pi$
$60$		0			0
$61$	5.67092	−	8.48713i	0.726086	−	1.08667i	−0.266346	−	0.963877i	$-0.585817\pi$
$61$	5.67092	−	8.48713i	0.726086	−	1.08667i	0.992433	−	0.122788i	$-0.0391835\pi$
$62$	−4.23982	−	2.83296i	−0.538458	−	0.359786i
$63$	−7.73498	−	1.53858i	−0.974516	−	0.193843i
$64$	−0.707107	+	0.707107i	−0.0883883	+	0.0883883i
$65$		0			0
$66$	1.02260	+	2.46877i	0.125873	+	0.303884i
$67$	−1.94198	+	1.94198i	−0.237251	+	0.237251i	−0.815711	−	0.578460i	$-0.803654\pi$
$67$	−1.94198	+	1.94198i	−0.237251	+	0.237251i	0.578460	+	0.815711i	$0.303654\pi$
$68$	−0.649481	−	4.07163i	−0.0787611	−	0.493758i
$69$		−	4.55993i		−	0.548952i
$70$		0			0
$71$	0.782371	−	3.93324i	0.0928503	−	0.466790i	−0.906185	−	0.422881i	$-0.861019\pi$
$71$	0.782371	−	3.93324i	0.0928503	−	0.466790i	0.999036	−	0.0439090i	$-0.0139812\pi$
$72$	2.08943			0.246242
$73$	0.167388	−	0.841518i	0.0195913	−	0.0984922i	−0.969752	−	0.244090i	$-0.921511\pi$
$73$	0.167388	−	0.841518i	0.0195913	−	0.0984922i	0.989344	+	0.145598i	$0.0465107\pi$
$74$	10.1022	−	2.00946i	1.17436	−	0.233595i
$75$		0			0
$76$	−0.119335	+	0.288099i	−0.0136886	+	0.0330472i
$77$	4.04488	+	9.76520i	0.460957	+	1.11285i
$78$	1.07024	+	5.38044i	0.121180	+	0.609215i
$79$	−0.872680	−	4.38726i	−0.0981841	−	0.493605i	−0.998317	−	0.0579898i	$-0.981531\pi$
$79$	−0.872680	−	4.38726i	−0.0981841	−	0.493605i	0.900133	−	0.435615i	$-0.143469\pi$
$80$		0			0
$81$	−1.15541	−	1.15541i	−0.128379	−	0.128379i
$82$	−5.15021	−	7.70784i	−0.568746	−	0.851188i
$83$	1.36475	+	0.565299i	0.149801	+	0.0620496i	0.456324	−	0.889814i	$-0.349166\pi$
$83$	1.36475	+	0.565299i	0.149801	+	0.0620496i	−0.306523	+	0.951863i	$0.599166\pi$
$84$	−3.60176			−0.392984
$85$		0			0
$86$	9.00580			0.971120
$87$	−0.491103	−	0.203422i	−0.0526518	−	0.0218091i
$88$	−1.55578	−	2.32838i	−0.165846	−	0.248206i
$89$	7.49831	+	7.49831i	0.794819	+	0.794819i	0.982273	−	0.187454i	$-0.0600236\pi$
$89$	7.49831	+	7.49831i	0.794819	+	0.794819i	−0.187454	+	0.982273i	$0.560024\pi$
$90$		0			0
$91$	4.23331	+	21.2823i	0.443772	+	2.23099i
$92$	0.932261	+	4.68679i	0.0971949	+	0.488632i
$93$	1.86208	+	4.49545i	0.193088	+	0.466157i
$94$	−2.14790	+	5.18549i	−0.221539	+	0.534843i
$95$		0			0
$96$	0.935903	−	0.186163i	0.0955202	−	0.0190002i
$97$	3.04671	−	15.3169i	0.309347	−	1.55519i	−0.443059	−	0.896492i	$-0.646107\pi$
$97$	3.04671	−	15.3169i	0.309347	−	1.55519i	0.752406	−	0.658699i	$-0.228893\pi$
$98$	−7.24674			−0.732031
$99$	−1.14149	+	5.73865i	−0.114724	+	0.576756i
$100$		0			0
$101$			5.19202i			0.516626i	0.966061	+	0.258313i	$0.0831665\pi$
$101$			5.19202i			0.516626i	−0.966061	+	0.258313i	$0.916833\pi$
$102$	−1.64325	+	3.57483i	−0.162706	+	0.353961i
$103$	−10.3087	+	10.3087i	−1.01575	+	1.01575i	−0.0158769	+	0.999874i	$0.505054\pi$
$103$	−10.3087	+	10.3087i	−1.01575	+	1.01575i	−0.999874	+	0.0158769i	$0.994946\pi$
$104$	−2.20002	−	5.31132i	−0.215730	−	0.520818i
$105$		0			0
$106$	4.66044	−	4.66044i	0.452662	−	0.452662i
$107$	14.1573	+	2.81607i	1.36864	+	0.272240i	0.824076	−	0.566479i	$-0.191695\pi$
$107$	14.1573	+	2.81607i	1.36864	+	0.272240i	0.544565	+	0.838719i	$0.316695\pi$
$108$	−4.03806	−	2.69814i	−0.388562	−	0.259629i
$109$	4.51551	−	6.75794i	0.432508	−	0.647293i	−0.549641	−	0.835401i	$-0.685235\pi$
$109$	4.51551	−	6.75794i	0.432508	−	0.647293i	0.982148	+	0.188108i	$0.0602354\pi$
$110$		0			0
$111$	−9.08064	−	3.76132i	−0.861896	−	0.357009i
$112$	3.70196	−	0.736366i	0.349802	−	0.0695800i
$113$	2.35754	−	3.52830i	0.221779	−	0.331915i	−0.703850	−	0.710349i	$-0.748537\pi$
$113$	2.35754	−	3.52830i	0.221779	−	0.331915i	0.925628	+	0.378434i	$0.123537\pi$
$114$	0.247417	−	0.165319i	0.0231727	−	0.0154835i
$115$		0			0
$116$	0.546354	+	0.108677i	0.0507277	+	0.0100904i
$117$	−4.59679	+	11.0976i	−0.424973	+	1.02598i
$118$	2.40926	+	2.40926i	0.221790	+	0.221790i
$119$	−6.49986	+	14.1402i	−0.595842	+	1.29623i
$120$		0			0
$121$	−2.91779	+	1.20859i	−0.265254	+	0.109872i
$122$	8.48713	−	5.67092i	0.768388	−	0.513421i
$123$			8.84592i			0.797610i
$124$	−2.83296	−	4.23982i	−0.254407	−	0.380747i
$125$		0			0
$126$	−6.55740	−	4.38152i	−0.584180	−	0.390336i
$127$	−18.5435	+	7.68099i	−1.64547	+	0.681577i	−0.996833	−	0.0795178i	$-0.974662\pi$
$127$	−18.5435	+	7.68099i	−1.64547	+	0.681577i	−0.648640	+	0.761095i	$0.724662\pi$
$128$	−0.923880	+	0.382683i	−0.0816602	+	0.0338248i
$129$	−7.14538	−	4.77439i	−0.629116	−	0.420362i
$130$		0			0
$131$	9.72499	+	14.5545i	0.849677	+	1.27163i	0.960637	+	0.277806i	$0.0896073\pi$
$131$	9.72499	+	14.5545i	0.849677	+	1.27163i	−0.110960	+	0.993825i	$0.535393\pi$
$132$			2.67218i			0.232583i
$133$	0.978657	−	0.653918i	0.0848603	−	0.0567019i
$134$	−2.53732	+	1.05099i	−0.219191	+	0.0907921i
$135$		0			0
$136$	0.958103	−	4.01024i	0.0821567	−	0.343875i
$137$	−0.812756	−	0.812756i	−0.0694385	−	0.0694385i	0.671535	−	0.740973i	$-0.265635\pi$
$137$	−0.812756	−	0.812756i	−0.0694385	−	0.0694385i	−0.740973	+	0.671535i	$0.765635\pi$
$138$	1.74501	−	4.21283i	0.148545	−	0.358620i
$139$	6.48365	+	1.28968i	0.549936	+	0.109389i	0.462234	−	0.886758i	$-0.347048\pi$
$139$	6.48365	+	1.28968i	0.549936	+	0.109389i	0.0877014	+	0.996147i	$0.472048\pi$
$140$		0			0
$141$	4.45326	−	2.97557i	0.375032	−	0.250588i
$142$	2.22800	−	3.33444i	0.186970	−	0.279820i
$143$	15.7895	−	3.14073i	1.32039	−	0.262641i
$144$	1.93038	+	0.799590i	0.160865	+	0.0666325i
$145$		0			0
$146$	0.476681	−	0.713404i	0.0394504	−	0.0590417i
$147$	5.74971	+	3.84183i	0.474228	+	0.316869i
$148$	10.1022	+	2.00946i	0.830400	+	0.165177i
$149$	−6.06959	+	6.06959i	−0.497240	+	0.497240i	−0.910578	−	0.413338i	$-0.864363\pi$
$149$	−6.06959	+	6.06959i	−0.497240	+	0.497240i	0.413338	+	0.910578i	$0.364363\pi$
$150$		0			0
$151$	−1.69264	−	4.08639i	−0.137745	−	0.332545i	0.839922	−	0.542708i	$-0.182601\pi$
$151$	−1.69264	−	4.08639i	−0.137745	−	0.332545i	−0.977667	+	0.210162i	$0.932601\pi$
$152$	−0.220501	+	0.220501i	−0.0178850	+	0.0178850i
$153$	−7.34048	+	4.50938i	−0.593442	+	0.364562i
$154$			10.5698i			0.851737i
$155$		0			0
$156$	−1.07024	+	5.38044i	−0.0856875	+	0.430780i
$157$	13.3044			1.06181			0.530903	−	0.847432i	$-0.321853\pi$
$157$	13.3044			1.06181			0.530903	+	0.847432i	$0.321853\pi$
$158$	0.872680	−	4.38726i	0.0694267	−	0.349031i
$159$	−6.16841	+	1.22697i	−0.489187	+	0.0973053i
$160$		0			0
$161$	6.90238	−	16.6638i	0.543984	−	1.31329i
$162$	−0.625305	−	1.50962i	−0.0491286	−	0.118607i
$163$	−2.97940	−	14.9784i	−0.233364	−	1.17320i	−0.902710	−	0.430250i	$-0.858425\pi$
$163$	−2.97940	−	14.9784i	−0.233364	−	1.17320i	0.669345	−	0.742951i	$-0.266575\pi$
$164$	−1.80851	−	9.09201i	−0.141221	−	0.709967i
$165$		0			0
$166$	1.04454	+	1.04454i	0.0810717	+	0.0810717i
$167$	−0.262363	−	0.392653i	−0.0203022	−	0.0303844i	0.821180	−	0.570670i	$-0.193316\pi$
$167$	−0.262363	−	0.392653i	−0.0203022	−	0.0303844i	−0.841482	+	0.540285i	$0.818316\pi$
$168$	−3.32759	−	1.37833i	−0.256729	−	0.106341i
$169$	20.0502			1.54232
$170$		0			0
$171$	0.651559			0.0498260
$172$	8.32027	+	3.44637i	0.634415	+	0.262783i
$173$	4.97303	+	7.44267i	0.378093	+	0.565856i	0.970899	−	0.239489i	$-0.0769800\pi$
$173$	4.97303	+	7.44267i	0.378093	+	0.565856i	−0.592806	+	0.805345i	$0.701980\pi$
$174$	−0.375874	−	0.375874i	−0.0284949	−	0.0284949i
$175$		0			0
$176$	−0.546316	−	2.74651i	−0.0411801	−	0.207026i
$177$	−0.634295	−	3.18882i	−0.0476765	−	0.239686i
$178$	4.05806	+	9.79701i	0.304164	+	0.734317i
$179$	2.79239	−	6.74143i	0.208713	−	0.503878i	−0.784508	−	0.620119i	$-0.787084\pi$
$179$	2.79239	−	6.74143i	0.208713	−	0.503878i	0.993221	+	0.116241i	$0.0370844\pi$
$180$		0			0
$181$	−2.13090	+	0.423862i	−0.158389	+	0.0315054i	−0.273648	−	0.961830i	$-0.588230\pi$
$181$	−2.13090	+	0.423862i	−0.158389	+	0.0315054i	0.115259	+	0.993335i	$0.463230\pi$
$182$	−4.23331	+	21.2823i	−0.313794	+	1.57755i
$183$	−9.74028			−0.720022
$184$	−0.932261	+	4.68679i	−0.0687272	+	0.345515i
$185$		0			0
$186$			4.86584i			0.356781i
$187$	10.4908	+	4.82230i	0.767160	+	0.352642i
$188$	−3.96880	+	3.96880i	−0.289455	+	0.289455i
$189$	7.01493	+	16.9355i	0.510261	+	1.23188i
$190$		0			0
$191$	9.99830	−	9.99830i	0.723451	−	0.723451i	−0.245855	−	0.969307i	$-0.579069\pi$
$191$	9.99830	−	9.99830i	0.723451	−	0.723451i	0.969307	+	0.245855i	$0.0790688\pi$
$192$	0.935903	+	0.186163i	0.0675430	+	0.0134351i
$193$	−1.10146	−	0.735974i	−0.0792850	−	0.0529766i	0.515296	−	0.857012i	$-0.327682\pi$
$193$	−1.10146	−	0.735974i	−0.0792850	−	0.0529766i	−0.594581	+	0.804036i	$0.702682\pi$
$194$	8.67631	−	12.9850i	0.622922	−	0.932269i
$195$		0			0
$196$	−6.69512	−	2.77321i	−0.478223	−	0.198086i
$197$	−1.71612	+	0.341358i	−0.122269	+	0.0243208i	−0.255845	−	0.966718i	$-0.582354\pi$
$197$	−1.71612	+	0.341358i	−0.122269	+	0.0243208i	0.133577	+	0.991038i	$0.457354\pi$
$198$	−3.25068	+	4.86499i	−0.231016	+	0.345740i
$199$	−2.83249	+	1.89261i	−0.200790	+	0.134164i	−0.651900	−	0.758305i	$-0.726028\pi$
$199$	−2.83249	+	1.89261i	−0.200790	+	0.134164i	0.451111	+	0.892468i	$0.351028\pi$
$200$		0			0
$201$	2.57035	+	0.511274i	0.181298	+	0.0360625i
$202$	−1.98690	+	4.79680i	−0.139798	+	0.337502i
$203$	−1.48677	−	1.48677i	−0.104351	−	0.104351i
$204$	−2.88619	+	2.67387i	−0.202074	+	0.187208i
$205$		0			0
$206$	−13.4690	+	5.57905i	−0.938431	+	0.388711i
$207$	8.30186	−	5.54713i	0.577019	−	0.385552i
$208$		−	5.74893i		−	0.398617i
$209$	−0.485147	−	0.726074i	−0.0335583	−	0.0502236i
$210$		0			0
$211$	−0.412646	−	0.275721i	−0.0284077	−	0.0189814i	0.541285	−	0.840839i	$-0.317938\pi$
$211$	−0.412646	−	0.275721i	−0.0284077	−	0.0189814i	−0.569693	+	0.821858i	$0.692938\pi$
$212$	6.08916	−	2.52221i	0.418205	−	0.173226i
$213$	−3.53549	+	1.46445i	−0.242247	+	0.100342i
$214$	12.0020	+	8.01948i	0.820440	+	0.548201i
$215$		0			0
$216$	−2.69814	−	4.03806i	−0.183585	−	0.274755i
$217$			19.2468i			1.30656i
$218$	6.75794	−	4.51551i	0.457706	−	0.305829i
$219$	−0.756417	+	0.313318i	−0.0511140	+	0.0211721i
$220$		0			0
$221$	19.1918	+	13.9114i	1.29098	+	0.935782i
$222$	−6.95002	−	6.95002i	−0.466455	−	0.466455i
$223$	−9.42022	+	22.7424i	−0.630824	+	1.52294i	0.207764	+	0.978179i	$0.433381\pi$
$223$	−9.42022	+	22.7424i	−0.630824	+	1.52294i	−0.838588	+	0.544766i	$0.816619\pi$
$224$	3.70196	+	0.736366i	0.247348	+	0.0492005i
$225$		0			0
$226$	3.52830	−	2.35754i	0.234699	−	0.156821i
$227$	13.2991	−	19.9035i	0.882694	−	1.32104i	−0.0636798	−	0.997970i	$-0.520284\pi$
$227$	13.2991	−	19.9035i	0.882694	−	1.32104i	0.946374	−	0.323074i	$-0.104716\pi$
$228$	0.291848	−	0.0580523i	0.0193281	−	0.00384460i
$229$	2.19707	+	0.910057i	0.145187	+	0.0601383i	0.454094	−	0.890954i	$-0.349963\pi$
$229$	2.19707	+	0.910057i	0.145187	+	0.0601383i	−0.308907	+	0.951092i	$0.599963\pi$
$230$		0			0
$231$	5.60353	−	8.38628i	0.368685	−	0.551776i
$232$	0.463177	+	0.309485i	0.0304090	+	0.0203187i
$233$	−10.5416	−	2.09685i	−0.690602	−	0.137369i	−0.162701	−	0.986675i	$-0.552021\pi$
$233$	−10.5416	−	2.09685i	−0.690602	−	0.137369i	−0.527901	+	0.849306i	$0.677021\pi$
$234$	−8.49375	+	8.49375i	−0.555254	+	0.555254i
$235$		0			0
$236$	1.30388	+	3.14785i	0.0848755	+	0.204908i
$237$	−3.01829	+	3.01829i	−0.196059	+	0.196059i
$238$	−11.4163	+	10.5765i	−0.740011	+	0.685572i
$239$		−	20.1117i		−	1.30091i	−0.759543	−	0.650457i	$-0.774577\pi$
$239$		−	20.1117i		−	1.30091i	0.759543	−	0.650457i	$-0.225423\pi$
$240$		0			0
$241$	−0.884741	+	4.44789i	−0.0569912	+	0.286514i	−0.998762	−	0.0497410i	$-0.984160\pi$
$241$	−0.884741	+	4.44789i	−0.0569912	+	0.286514i	0.941771	+	0.336255i	$0.109160\pi$
$242$	−3.15820			−0.203016
$243$	−3.14658	+	15.8189i	−0.201853	+	1.01478i
$244$	10.0112	−	1.99136i	0.640904	−	0.127484i
$245$		0			0
$246$	−3.38519	+	8.17256i	−0.215832	+	0.521064i
$247$	−0.686046	−	1.65626i	−0.0436520	−	0.105385i
$248$	−0.994802	−	5.00121i	−0.0631700	−	0.317577i
$249$	−0.274999	−	1.38251i	−0.0174273	−	0.0876132i
$250$		0			0
$251$	−2.34040	−	2.34040i	−0.147725	−	0.147725i	0.629376	−	0.777101i	$-0.283311\pi$
$251$	−2.34040	−	2.34040i	−0.147725	−	0.147725i	−0.777101	+	0.629376i	$0.783311\pi$
$252$	−4.38152	−	6.55740i	−0.276010	−	0.413077i
$253$	−12.3630	−	5.12094i	−0.777257	−	0.321950i
$254$	−20.0714			−1.25939
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	−13.1832	−	5.46064i	−0.822343	−	0.340626i	−0.0684760	−	0.997653i	$-0.521814\pi$
$257$	−13.1832	−	5.46064i	−0.822343	−	0.340626i	−0.753867	+	0.657027i	$0.771814\pi$
$258$	−4.77439	−	7.14538i	−0.297241	−	0.444852i
$259$	−27.4908	−	27.4908i	−1.70819	−	1.70819i
$260$		0			0
$261$	−0.227072	−	1.14157i	−0.0140554	−	0.0706613i
$262$	3.41496	+	17.1682i	0.210977	+	1.06065i
$263$	2.13884	+	5.16361i	0.131886	+	0.318402i	0.976003	−	0.217758i	$-0.0698744\pi$
$263$	2.13884	+	5.16361i	0.131886	+	0.318402i	−0.844116	+	0.536160i	$0.819874\pi$
$264$	−1.02260	+	2.46877i	−0.0629365	+	0.151942i
$265$		0			0
$266$	1.15440	−	0.229625i	0.0707811	−	0.0140792i
$267$	1.97411	−	9.92451i	0.120813	−	0.607370i
$268$	−2.74638			−0.167762
$269$	1.33070	−	6.68989i	0.0811343	−	0.407890i	−0.918780	−	0.394771i	$-0.870824\pi$
$269$	1.33070	−	6.68989i	0.0811343	−	0.407890i	0.999914	−	0.0131189i	$-0.00417601\pi$
$270$		0			0
$271$			0.568062i			0.0345073i	0.999851	+	0.0172537i	$0.00549229\pi$
$271$			0.568062i			0.0345073i	−0.999851	+	0.0172537i	$0.994508\pi$
$272$	2.41983	−	3.33833i	0.146723	−	0.202416i
$273$	14.6415	−	14.6415i	0.886146	−	0.886146i
$274$	−0.439861	−	1.06192i	−0.0265729	−	0.0641528i
$275$		0			0
$276$	3.22436	−	3.22436i	0.194084	−	0.194084i
$277$	−19.7796	−	3.93441i	−1.18844	−	0.236396i	−0.439013	−	0.898480i	$-0.644672\pi$
$277$	−19.7796	−	3.93441i	−1.18844	−	0.236396i	−0.749429	+	0.662085i	$0.769672\pi$
$278$	5.49657	+	3.67269i	0.329662	+	0.220273i
$279$	−5.91926	+	8.85880i	−0.354377	+	0.530363i
$280$		0			0
$281$	−0.143711	−	0.0595269i	−0.00857306	−	0.00355108i	0.378393	−	0.925645i	$-0.376477\pi$
$281$	−0.143711	−	0.0595269i	−0.00857306	−	0.00355108i	−0.386966	+	0.922094i	$0.626477\pi$
$282$	5.25298	−	1.04488i	0.312810	−	0.0622218i
$283$	−7.66884	+	11.4772i	−0.455865	+	0.682250i	−0.986204	−	0.165535i	$-0.947065\pi$
$283$	−7.66884	+	11.4772i	−0.455865	+	0.682250i	0.530339	+	0.847786i	$0.322065\pi$
$284$	3.33444	−	2.22800i	0.197863	−	0.132208i
$285$		0			0
$286$	15.7895	+	3.14073i	0.933654	+	0.185715i
$287$	−13.3901	+	32.3265i	−0.790392	+	1.90818i
$288$	1.47745	+	1.47745i	0.0870595	+	0.0870595i
$289$	5.28889	+	16.1563i	0.311111	+	0.950373i
$290$		0			0
$291$	−13.7679	+	5.70286i	−0.807089	+	0.334307i
$292$	0.713404	−	0.476681i	0.0417488	−	0.0278957i
$293$		−	23.1984i		−	1.35527i	−0.735400	−	0.677633i	$-0.763006\pi$
$293$		−	23.1984i		−	1.35527i	0.735400	−	0.677633i	$-0.236994\pi$
$294$	3.84183	+	5.74971i	0.224060	+	0.335330i
$295$		0			0
$296$	8.56427	+	5.72246i	0.497788	+	0.332611i
$297$	12.5646	−	5.20444i	0.729073	−	0.301992i
$298$	−7.93030	+	3.28484i	−0.459390	+	0.190286i
$299$	−22.8420	−	15.2626i	−1.32099	−	0.882657i
$300$		0			0
$301$	−18.8851	−	28.2635i	−1.08852	−	1.62908i
$302$		−	4.42307i		−	0.254519i
$303$	4.11946	−	2.75253i	0.236657	−	0.158129i
$304$	−0.288099	+	0.119335i	−0.0165236	+	0.00684430i
$305$		0			0
$306$	−8.50738	+	1.35704i	−0.486335	+	0.0775771i
$307$	−5.80418	−	5.80418i	−0.331262	−	0.331262i	0.521803	−	0.853066i	$-0.325259\pi$
$307$	−5.80418	−	5.80418i	−0.331262	−	0.331262i	−0.853066	+	0.521803i	$0.825259\pi$
$308$	−4.04488	+	9.76520i	−0.230478	+	0.556424i
$309$	13.6443	+	2.71402i	0.776198	+	0.154395i
$310$		0			0
$311$	−19.7609	+	13.2038i	−1.12054	+	0.748721i	−0.970773	−	0.240000i	$-0.922852\pi$
$311$	−19.7609	+	13.2038i	−1.12054	+	0.748721i	−0.149767	+	0.988721i	$0.547852\pi$
$312$	−3.04777	+	4.56132i	−0.172546	+	0.258234i
$313$	0.321242	−	0.0638990i	0.0181577	−	0.00361179i	−0.186003	−	0.982549i	$-0.559553\pi$
$313$	0.321242	−	0.0638990i	0.0181577	−	0.00361179i	0.204161	+	0.978937i	$0.434553\pi$
$314$	12.2917	+	5.09137i	0.693659	+	0.287323i
$315$		0			0
$316$	2.48518	−	3.71934i	0.139802	−	0.209229i
$317$	0.124348	+	0.0830869i	0.00698410	+	0.00466663i	0.559057	−	0.829129i	$-0.311163\pi$
$317$	0.124348	+	0.0830869i	0.00698410	+	0.00466663i	−0.552073	+	0.833796i	$0.686163\pi$
$318$	−6.16841	−	1.22697i	−0.345907	−	0.0688052i
$319$	−1.10305	+	1.10305i	−0.0617587	+	0.0617587i
$320$		0			0
$321$	−5.27113	−	12.7256i	−0.294206	−	0.710276i
$322$	12.7539	−	12.7539i	0.710749	−	0.710749i
$323$	0.298771	−	1.25054i	0.0166241	−	0.0695818i
$324$		−	1.63400i		−	0.0907778i
$325$		0			0
$326$	2.97940	−	14.9784i	0.165013	−	0.829579i
$327$	−7.75577			−0.428895
$328$	1.80851	−	9.09201i	0.0998585	−	0.502022i
$329$	20.7781	−	4.13303i	1.14554	−	0.227861i
$330$		0			0
$331$	−11.8192	+	28.5341i	−0.649643	+	1.56838i	0.163646	+	0.986519i	$0.447674\pi$
$331$	−11.8192	+	28.5341i	−0.649643	+	1.56838i	−0.813290	+	0.581859i	$0.802326\pi$
$332$	0.565299	+	1.36475i	0.0310248	+	0.0749005i
$333$	−4.19863	−	21.1079i	−0.230083	−	1.15671i
$334$	−0.0921295	−	0.463166i	−0.00504110	−	0.0253433i
$335$		0			0
$336$	−2.54683	−	2.54683i	−0.138941	−	0.138941i
$337$	1.83165	+	2.74125i	0.0997761	+	0.149325i	0.877999	−	0.478663i	$-0.158878\pi$
$337$	1.83165	+	2.74125i	0.0997761	+	0.149325i	−0.778223	+	0.627989i	$0.783878\pi$
$338$	18.5240	+	7.67288i	1.00757	+	0.417349i
$339$	−4.04927			−0.219926
$340$		0			0
$341$	14.2794			0.773271
$342$	0.601962	+	0.249341i	0.0325504	+	0.0134828i
$343$	0.517415	+	0.774367i	0.0279378	+	0.0418119i
$344$	6.36806	+	6.36806i	0.343343	+	0.343343i
$345$		0			0
$346$	1.74630	+	8.77923i	0.0938815	+	0.471974i
$347$	−0.502701	−	2.52725i	−0.0269864	−	0.135670i	0.964943	−	0.262458i	$-0.0845331\pi$
$347$	−0.502701	−	2.52725i	−0.0269864	−	0.135670i	−0.991930	+	0.126788i	$0.959533\pi$
$348$	−0.203422	−	0.491103i	−0.0109045	−	0.0263259i
$349$	−2.63485	+	6.36108i	−0.141040	+	0.340501i	−0.978577	−	0.205879i	$-0.933995\pi$
$349$	−2.63485	+	6.36108i	−0.141040	+	0.340501i	0.837537	+	0.546380i	$0.183995\pi$
$350$		0			0
$351$	27.3834	−	5.44689i	1.46162	−	0.290734i
$352$	0.546316	−	2.74651i	0.0291187	−	0.146390i
$353$	25.0889			1.33535			0.667674	−	0.744454i	$-0.267290\pi$
$353$	25.0889			1.33535			0.667674	+	0.744454i	$0.267290\pi$
$354$	0.634295	−	3.18882i	0.0337124	−	0.169484i
$355$		0			0
$356$			10.6042i			0.562022i
$357$	14.6650	−	2.33927i	0.776156	−	0.123808i
$358$	5.15966	−	5.15966i	0.272697	−	0.272697i
$359$	−3.72132	−	8.98407i	−0.196404	−	0.474161i	0.794741	−	0.606949i	$-0.207607\pi$
$359$	−3.72132	−	8.98407i	−0.196404	−	0.474161i	−0.991144	+	0.132788i	$0.957607\pi$
$360$		0			0
$361$	13.3663	−	13.3663i	0.703488	−	0.703488i
$362$	−2.13090	−	0.423862i	−0.111998	−	0.0222777i
$363$	2.50578	+	1.67431i	0.131519	+	0.0878783i
$364$	−12.0555	+	18.0423i	−0.631878	+	0.945672i
$365$		0			0
$366$	−8.99884	−	3.72744i	−0.470377	−	0.194837i
$367$	−15.2095	+	3.02536i	−0.793931	+	0.157923i	−0.575362	−	0.817899i	$-0.695139\pi$
$367$	−15.2095	+	3.02536i	−0.793931	+	0.157923i	−0.218569	+	0.975822i	$0.570139\pi$
$368$	−2.65485	+	3.97327i	−0.138394	+	0.207121i
$369$	−16.1050	+	10.7610i	−0.838392	+	0.560195i
$370$		0			0
$371$	−24.3991	−	4.85328i	−1.26674	−	0.251970i
$372$	−1.86208	+	4.49545i	−0.0965442	+	0.233078i
$373$	−16.1984	−	16.1984i	−0.838724	−	0.838724i	0.149967	−	0.988691i	$-0.452083\pi$
$373$	−16.1984	−	16.1984i	−0.838724	−	0.838724i	−0.988691	+	0.149967i	$0.952083\pi$
$374$	7.84678	+	8.46987i	0.405748	+	0.437966i
$375$		0			0
$376$	−5.18549	+	2.14790i	−0.267421	+	0.110770i
$377$	−2.66277	+	1.77921i	−0.137140	+	0.0916338i
$378$			18.3309i			0.942840i
$379$	12.1871	+	18.2394i	0.626012	+	0.936893i	0.999955	+	0.00944122i	$0.00300528\pi$
$379$	12.1871	+	18.2394i	0.626012	+	0.936893i	−0.373944	+	0.927451i	$0.621995\pi$
$380$		0			0
$381$	15.9250	+	10.6408i	0.815865	+	0.545144i
$382$	13.0634	−	5.41104i	0.668382	−	0.276853i
$383$	23.4891	−	9.72950i	1.20024	−	0.497154i	0.309161	−	0.951010i	$-0.399952\pi$
$383$	23.4891	−	9.72950i	1.20024	−	0.497154i	0.891075	+	0.453855i	$0.149952\pi$
$384$	0.793420	+	0.530147i	0.0404891	+	0.0270539i
$385$		0			0
$386$	−0.735974	−	1.10146i	−0.0374601	−	0.0560630i
$387$		−	18.8170i		−	0.956520i
$388$	12.9850	−	8.67631i	0.659214	−	0.440473i
$389$	−14.6940	+	6.08645i	−0.745015	+	0.308595i	−0.722706	−	0.691156i	$-0.757102\pi$
$389$	−14.6940	+	6.08645i	−0.745015	+	0.308595i	−0.0223090	+	0.999751i	$0.507102\pi$
$390$		0			0
$391$	−6.83980	−	18.4774i	−0.345904	−	0.934442i
$392$	−5.12422	−	5.12422i	−0.258812	−	0.258812i
$393$	6.39215	−	15.4320i	0.322441	−	0.778442i
$394$	−1.71612	−	0.341358i	−0.0864571	−	0.0171974i
$395$		0			0
$396$	−4.86499	+	3.25068i	−0.244475	+	0.163353i
$397$	7.31860	−	10.9531i	0.367310	−	0.549718i	−0.601071	−	0.799196i	$-0.705259\pi$
$397$	7.31860	−	10.9531i	0.367310	−	0.549718i	0.968381	+	0.249478i	$0.0802590\pi$
$398$	−3.34115	+	0.664596i	−0.167477	+	0.0333132i
$399$	−1.03766	−	0.429814i	−0.0519481	−	0.0215176i
$400$		0			0
$401$	2.27205	−	3.40036i	0.113461	−	0.169806i	−0.770393	−	0.637569i	$-0.779940\pi$
$401$	2.27205	−	3.40036i	0.113461	−	0.169806i	0.883854	+	0.467763i	$0.154940\pi$
$402$	2.17903	+	1.45598i	0.108680	+	0.0726179i
$403$	28.7516	+	5.71905i	1.43222	+	0.284886i
$404$	−3.67132	+	3.67132i	−0.182655	+	0.182655i
$405$		0			0
$406$	−0.804633	−	1.94256i	−0.0399333	−	0.0964074i
$407$	−20.3956	+	20.3956i	−1.01097	+	1.01097i
$408$	−3.68974	+	1.36584i	−0.182669	+	0.0676190i
$409$		−	26.3322i		−	1.30204i	−0.759060	−	0.651021i	$-0.774341\pi$
$409$		−	26.3322i		−	1.30204i	0.759060	−	0.651021i	$-0.225659\pi$
$410$		0			0
$411$	−0.213977	+	1.07574i	−0.0105547	+	0.0530622i
$412$	−14.5788			−0.718244
$413$	2.50895	−	12.6133i	0.123457	−	0.620662i
$414$	9.79272	−	1.94789i	0.481286	−	0.0957337i
$415$		0			0
$416$	2.20002	−	5.31132i	0.107865	−	0.260409i
$417$	−2.41403	−	5.82798i	−0.118215	−	0.285397i
$418$	−0.170361	−	0.856462i	−0.00833263	−	0.0418910i
$419$	−1.24149	−	6.24139i	−0.0606508	−	0.304912i	0.938538	−	0.345175i	$-0.112180\pi$
$419$	−1.24149	−	6.24139i	−0.0606508	−	0.304912i	−0.999189	+	0.0402629i	$0.987180\pi$
$420$		0			0
$421$	−16.7929	−	16.7929i	−0.818436	−	0.818436i	0.167445	−	0.985881i	$-0.446448\pi$
$421$	−16.7929	−	16.7929i	−0.818436	−	0.818436i	−0.985881	+	0.167445i	$0.946448\pi$
$422$	−0.275721	−	0.412646i	−0.0134219	−	0.0200873i
$423$	10.8347	+	4.48789i	0.526802	+	0.218209i
$424$	6.59086			0.320081
$425$		0			0
$426$	−3.82678			−0.185408
$427$	−35.5949	−	14.7439i	−1.72256	−	0.713506i
$428$	8.01948	+	12.0020i	0.387636	+	0.580139i
$429$	−10.8627	−	10.8627i	−0.524455	−	0.524455i
$430$		0			0
$431$	4.77925	+	24.0269i	0.230208	+	1.15734i	0.906990	+	0.421152i	$0.138374\pi$
$431$	4.77925	+	24.0269i	0.230208	+	1.15734i	−0.676782	+	0.736184i	$0.736626\pi$
$432$	−0.947462	−	4.76321i	−0.0455848	−	0.229170i
$433$	7.10985	+	17.1647i	0.341678	+	0.824883i	0.997546	+	0.0700080i	$0.0223025\pi$
$433$	7.10985	+	17.1647i	0.341678	+	0.824883i	−0.655869	+	0.754875i	$0.727698\pi$
$434$	−7.36544	+	17.7817i	−0.353552	+	0.853551i
$435$		0			0
$436$	7.97153	−	1.58564i	0.381767	−	0.0759382i
$437$	−0.290713	+	1.46151i	−0.0139067	+	0.0699135i
$438$	−0.818740			−0.0391209
$439$	6.96095	−	34.9950i	0.332228	−	1.67022i	−0.348210	−	0.937417i	$-0.613210\pi$
$439$	6.96095	−	34.9950i	0.332228	−	1.67022i	0.680438	−	0.732806i	$-0.261790\pi$
$440$		0			0
$441$			15.1416i			0.721026i
$442$	12.4073	+	20.1969i	0.590154	+	0.960666i
$443$	19.6949	−	19.6949i	0.935735	−	0.935735i	−0.0623210	−	0.998056i	$-0.519850\pi$
$443$	19.6949	−	19.6949i	0.935735	−	0.935735i	0.998056	+	0.0623210i	$0.0198503\pi$
$444$	−3.76132	−	9.08064i	−0.178505	−	0.430948i
$445$		0			0
$446$	−17.4063	+	17.4063i	−0.824212	+	0.824212i
$447$	8.03351	+	1.59796i	0.379972	+	0.0755811i
$448$	3.13837	+	2.09699i	0.148274	+	0.0990736i
$449$	10.1228	−	15.1498i	0.477724	−	0.714965i	−0.511836	−	0.859083i	$-0.671034\pi$
$449$	10.1228	−	15.1498i	0.477724	−	0.714965i	0.989561	+	0.144118i	$0.0460345\pi$
$450$		0			0
$451$	23.9833	+	9.93422i	1.12933	+	0.467784i
$452$	4.16192	−	0.827857i	0.195760	−	0.0389391i
$453$	−2.34488	+	3.50936i	−0.110172	+	0.164884i
$454$	19.9035	−	13.2991i	0.934120	−	0.624159i
$455$		0			0
$456$	0.291848	+	0.0580523i	0.0136671	+	0.00271855i
$457$	9.80059	−	23.6607i	0.458452	−	1.10680i	−0.510572	−	0.859835i	$-0.670566\pi$
$457$	9.80059	−	23.6607i	0.458452	−	1.10680i	0.969024	−	0.246966i	$-0.0794337\pi$
$458$	1.68157	+	1.68157i	0.0785744	+	0.0785744i
$459$	18.1939	+	8.36320i	0.849217	+	0.390361i
$460$		0			0
$461$	30.2852	−	12.5445i	1.41052	−	0.584257i	0.458061	−	0.888921i	$-0.348544\pi$
$461$	30.2852	−	12.5445i	1.41052	−	0.584257i	0.952460	+	0.304664i	$0.0985441\pi$
$462$	8.38628	−	5.60353i	0.390165	−	0.260700i
$463$			2.18733i			0.101654i	0.998707	+	0.0508269i	$0.0161857\pi$
$463$			2.18733i			0.101654i	−0.998707	+	0.0508269i	$0.983814\pi$
$464$	0.309485	+	0.463177i	0.0143675	+	0.0215024i
$465$		0			0
$466$	−8.93672	−	5.97133i	−0.413986	−	0.276616i
$467$	28.6355	−	11.8612i	1.32509	−	0.548872i	0.395841	−	0.918319i	$-0.370453\pi$
$467$	28.6355	−	11.8612i	1.32509	−	0.548872i	0.929252	+	0.369447i	$0.120453\pi$
$468$	−11.0976	+	4.59679i	−0.512988	+	0.212486i
$469$	8.61916	+	5.75914i	0.397996	+	0.265932i
$470$		0			0
$471$	−7.05328	−	10.5560i	−0.324998	−	0.486394i
$472$			3.40721i			0.156829i
$473$	−20.9689	+	14.0110i	−0.964153	+	0.644226i
$474$	−3.94359	+	1.63349i	−0.181135	+	0.0750285i
$475$		0			0
$476$	−14.5948	+	5.40256i	−0.668950	+	0.247626i
$477$	−9.73767	−	9.73767i	−0.445857	−	0.445857i
$478$	7.69640	−	18.5807i	0.352025	−	0.849863i
$479$	−30.9583	−	6.15799i	−1.41452	−	0.281366i	−0.572100	−	0.820184i	$-0.693871\pi$
$479$	−30.9583	−	6.15799i	−1.41452	−	0.281366i	−0.842422	+	0.538818i	$0.818871\pi$
$480$		0			0
$481$	−49.2354	+	32.8980i	−2.24494	+	1.50002i
$482$	−2.51953	+	3.77074i	−0.114761	+	0.171753i
$483$	−16.8807	+	3.35778i	−0.768098	+	0.152784i
$484$	−2.91779	−	1.20859i	−0.132627	−	0.0549359i
$485$		0			0
$486$	−8.96069	+	13.4106i	−0.406465	+	0.608318i
$487$	−16.7437	−	11.1878i	−0.758732	−	0.506968i	0.115007	−	0.993365i	$-0.463311\pi$
$487$	−16.7437	−	11.1878i	−0.758732	−	0.506968i	−0.873738	+	0.486396i	$0.838311\pi$
$488$	10.0112	+	1.99136i	0.453188	+	0.0901447i
$489$	−10.3047	+	10.3047i	−0.465994	+	0.465994i
$490$		0			0
$491$	9.38490	+	22.6571i	0.423534	+	1.02250i	0.981297	+	0.192502i	$0.0616601\pi$
$491$	9.38490	+	22.6571i	0.423534	+	1.02250i	−0.557762	+	0.830001i	$0.688340\pi$
$492$	−6.25501	+	6.25501i	−0.281998	+	0.281998i
$493$	−2.29514	−	0.0876443i	−0.103368	−	0.00394730i
$494$		−	1.79272i		−	0.0806585i
$495$		0			0
$496$	0.994802	−	5.00121i	0.0446679	−	0.224561i
$497$	−15.1368			−0.678979
$498$	0.274999	−	1.38251i	0.0123230	−	0.0619519i
$499$	36.9936	−	7.35849i	1.65606	−	0.329411i	0.723473	−	0.690353i	$-0.242545\pi$
$499$	36.9936	−	7.35849i	1.65606	−	0.329411i	0.932588	+	0.360942i	$0.117545\pi$
$500$		0			0
$501$	−0.172449	+	0.416328i	−0.00770444	+	0.0186002i
$502$	−1.26662	−	3.05788i	−0.0565319	−	0.136480i
$503$	−1.32307	−	6.65150i	−0.0589926	−	0.296576i	0.940014	−	0.341135i	$-0.110811\pi$
$503$	−1.32307	−	6.65150i	−0.0589926	−	0.296576i	−0.999007	+	0.0445597i	$0.985811\pi$
$504$	−1.53858	−	7.73498i	−0.0685340	−	0.344543i
$505$		0			0
$506$	−9.46225	−	9.46225i	−0.420649	−	0.420649i
$507$	−10.6295	−	15.9082i	−0.472074	−	0.706509i
$508$	−18.5435	−	7.68099i	−0.822737	−	0.340789i
$509$	13.5968			0.602668			0.301334	−	0.953519i	$-0.402568\pi$
$509$	13.5968			0.602668			0.301334	+	0.953519i	$0.402568\pi$
$510$		0			0
$511$	−3.23852			−0.143264
$512$	−0.923880	−	0.382683i	−0.0408301	−	0.0169124i
$513$	−0.841378	−	1.25921i	−0.0371478	−	0.0555956i
$514$	−10.0900	−	10.0900i	−0.445049	−	0.445049i
$515$		0			0
$516$	−1.67654	−	8.42855i	−0.0738057	−	0.371046i
$517$	−3.06633	−	15.4155i	−0.134857	−	0.677971i
$518$	−14.8779	−	35.9184i	−0.653697	−	1.57816i
$519$	3.26873	−	7.89141i	0.143481	−	0.346394i
$520$		0			0
$521$	32.2104	−	6.40706i	1.41117	−	0.280698i	0.570075	−	0.821593i	$-0.306914\pi$
$521$	32.2104	−	6.40706i	1.41117	−	0.280698i	0.841090	+	0.540895i	$0.181914\pi$
$522$	0.227072	−	1.14157i	0.00993867	−	0.0499651i
$523$	−36.5024			−1.59614			−0.798070	−	0.602565i	$-0.794146\pi$
$523$	−36.5024			−1.59614			−0.798070	+	0.602565i	$0.794146\pi$
$524$	−3.41496	+	17.1682i	−0.149183	+	0.749996i
$525$		0			0
$526$			5.58905i			0.243694i
$527$	14.2884	+	15.4230i	0.622414	+	0.671838i
$528$	−1.88951	+	1.88951i	−0.0822305	+	0.0822305i
$529$	−0.0630980	−	0.152332i	−0.00274339	−	0.00662313i
$530$		0			0
$531$	5.03398	−	5.03398i	0.218456	−	0.218456i
$532$	1.15440	+	0.229625i	0.0500498	+	0.00995552i
$533$	44.3118	+	29.6082i	1.91936	+	1.28247i
$534$	5.62179	−	8.41360i	0.243278	−	0.364092i
$535$		0			0
$536$	−2.53732	−	1.05099i	−0.109596	−	0.0453960i
$537$	−6.82916	+	1.35840i	−0.294700	+	0.0586195i
$538$	3.78952	−	5.67141i	0.163378	−	0.244512i
$539$	16.8732	−	11.2743i	0.726780	−	0.485619i
$540$		0			0
$541$	7.08352	+	1.40900i	0.304544	+	0.0605776i	0.344997	−	0.938604i	$-0.387880\pi$
$541$	7.08352	+	1.40900i	0.304544	+	0.0605776i	−0.0404526	+	0.999181i	$0.512880\pi$
$542$	−0.217388	+	0.524821i	−0.00933762	+	0.0225430i
$543$	1.46599	+	1.46599i	0.0629116	+	0.0629116i
$544$	3.51315	−	2.15819i	0.150625	−	0.0925315i
$545$		0			0
$546$	19.1301	−	7.92394i	0.818692	−	0.339113i
$547$	−33.0002	+	22.0501i	−1.41099	+	0.942792i	−0.411481	+	0.911418i	$0.634988\pi$
$547$	−33.0002	+	22.0501i	−1.41099	+	0.942792i	−0.999508	+	0.0313741i	$0.990012\pi$
$548$		−	1.14941i		−	0.0491004i
$549$	−11.8490	−	17.7332i	−0.505702	−	0.756837i
$550$		0			0
$551$	0.144435	+	0.0965085i	0.00615315	+	0.00411140i
$552$	4.21283	−	1.74501i	0.179310	−	0.0742726i
$553$	−15.5988	+	6.46125i	−0.663330	+	0.274760i
$554$	−16.7684	−	11.2043i	−0.712419	−	0.476023i
$555$		0			0
$556$	3.67269	+	5.49657i	0.155757	+	0.233107i
$557$			29.8842i			1.26623i	0.774056	+	0.633117i	$0.218225\pi$
$557$			29.8842i			1.26623i	−0.774056	+	0.633117i	$0.781775\pi$
$558$	−8.85880	+	5.91926i	−0.375023	+	0.250582i
$559$	−47.8326	+	19.8129i	−2.02311	+	0.837998i
$560$		0			0
$561$	−1.73553	−	10.8801i	−0.0732740	−	0.459359i
$562$	−0.109991	−	0.109991i	−0.00463971	−	0.00463971i
$563$	−1.18442	+	2.85945i	−0.0499174	+	0.120511i	−0.946871	−	0.321613i	$-0.895775\pi$
$563$	−1.18442	+	2.85945i	−0.0499174	+	0.120511i	0.896954	+	0.442124i	$0.145775\pi$
$564$	5.25298	+	1.04488i	0.221190	+	0.0439975i
$565$		0			0
$566$	−11.4772	+	7.66884i	−0.482424	+	0.322345i
$567$	−3.42648	+	5.12810i	−0.143899	+	0.215360i
$568$	3.93324	−	0.782371i	0.165035	−	0.0328275i
$569$	22.5622	+	9.34559i	0.945859	+	0.391787i	0.801673	−	0.597763i	$-0.203944\pi$
$569$	22.5622	+	9.34559i	0.945859	+	0.391787i	0.144186	+	0.989551i	$0.453944\pi$
$570$		0			0
$571$	−6.22109	+	9.31052i	−0.260345	+	0.389633i	−0.938497	−	0.345288i	$-0.887781\pi$
$571$	−6.22109	+	9.31052i	−0.260345	+	0.389633i	0.678152	+	0.734922i	$0.262781\pi$
$572$	13.3857	+	8.94404i	0.559685	+	0.373969i
$573$	−13.2334	−	2.63229i	−0.552834	−	0.109965i
$574$	−24.7417	+	24.7417i	−1.03270	+	1.03270i
$575$		0			0
$576$	0.799590	+	1.93038i	0.0333162	+	0.0804325i
$577$	3.62693	−	3.62693i	0.150991	−	0.150991i	−0.627569	−	0.778561i	$-0.715950\pi$
$577$	3.62693	−	3.62693i	0.150991	−	0.150991i	0.778561	+	0.627569i	$0.215950\pi$
$578$	−1.29647	+	16.9505i	−0.0539259	+	0.705048i
$579$			1.26410i			0.0525341i
$580$		0			0
$581$	1.08776	−	5.46852i	0.0451277	−	0.226873i
$582$	−14.9023			−0.617719
$583$	−3.60069	+	18.1019i	−0.149125	+	0.749704i
$584$	0.841518	−	0.167388i	0.0348222	−	0.00692657i
$585$		0			0
$586$	8.87765	−	21.4325i	0.366732	−	0.885370i
$587$	−1.02281	−	2.46929i	−0.0422161	−	0.101919i	0.901365	−	0.433060i	$-0.142566\pi$
$587$	−1.02281	−	2.46929i	−0.0422161	−	0.101919i	−0.943581	+	0.331142i	$0.892566\pi$
$588$	1.34907	+	6.78225i	0.0556348	+	0.279695i
$589$	−0.310215	−	1.55956i	−0.0127822	−	0.0642605i
$590$		0			0
$591$	1.18064	+	1.18064i	0.0485649	+	0.0485649i
$592$	5.72246	+	8.56427i	0.235192	+	0.351989i
$593$	−36.5110	−	15.1234i	−1.49933	−	0.621042i	−0.526004	−	0.850482i	$-0.676310\pi$
$593$	−36.5110	−	15.1234i	−1.49933	−	0.621042i	−0.973323	+	0.229440i	$0.926310\pi$
$594$	13.5998			0.558008
$595$		0			0
$596$	−8.58370			−0.351602
$597$	3.00327	+	1.24400i	0.122916	+	0.0509133i
$598$	−15.2626	−	22.8420i	−0.624133	−	0.934081i
$599$	33.3470	+	33.3470i	1.36252	+	1.36252i	0.870689	+	0.491834i	$0.163673\pi$
$599$	33.3470	+	33.3470i	1.36252	+	1.36252i	0.491834	+	0.870689i	$0.336327\pi$
$600$		0			0
$601$	−5.91062	−	29.7147i	−0.241099	−	1.21209i	−0.891685	−	0.452656i	$-0.850477\pi$
$601$	−5.91062	−	29.7147i	−0.241099	−	1.21209i	0.650586	−	0.759433i	$-0.274523\pi$
$602$	−6.63156	−	33.3391i	−0.270282	−	1.35880i
$603$	2.19598	+	5.30156i	0.0894271	+	0.215896i
$604$	1.69264	−	4.08639i	0.0688724	−	0.166273i
$605$		0			0
$606$	4.85923	−	0.966561i	0.197393	−	0.0392639i
$607$	3.03730	−	15.2695i	0.123280	−	0.619771i	−0.868903	−	0.494982i	$-0.835175\pi$
$607$	3.03730	−	15.2695i	0.123280	−	0.619771i	0.992183	−	0.124789i	$-0.0398254\pi$
$608$	−0.311836			−0.0126466
$609$	−0.391427	+	1.96784i	−0.0158614	+	0.0797408i
$610$		0			0
$611$		−	32.2672i		−	1.30539i
$612$	−8.37911	−	2.00189i	−0.338706	−	0.0809216i
$613$	15.5475	−	15.5475i	0.627957	−	0.627957i	−0.319597	−	0.947554i	$-0.603547\pi$
$613$	15.5475	−	15.5475i	0.627957	−	0.627957i	0.947554	+	0.319597i	$0.103547\pi$
$614$	−3.14120	−	7.58353i	−0.126769	−	0.306046i
$615$		0			0
$616$	−7.47396	+	7.47396i	−0.301134	+	0.301134i
$617$	16.5015	+	3.28236i	0.664327	+	0.132143i	0.515725	−	0.856754i	$-0.327523\pi$
$617$	16.5015	+	3.28236i	0.664327	+	0.132143i	0.148602	+	0.988897i	$0.452523\pi$
$618$	11.5671	+	7.72888i	0.465297	+	0.310901i
$619$	−10.9909	+	16.4491i	−0.441763	+	0.661145i	−0.983812	−	0.179202i	$-0.942649\pi$
$619$	−10.9909	+	16.4491i	−0.441763	+	0.661145i	0.542049	+	0.840347i	$0.317649\pi$
$620$		0			0
$621$	−21.4409	−	8.88111i	−0.860394	−	0.356387i
$622$	−23.3096	+	4.63657i	−0.934631	+	0.185910i
$623$	22.2369	−	33.2799i	0.890904	−	1.33333i
$624$	−4.56132	+	3.04777i	−0.182599	+	0.122009i
$625$		0			0
$626$	0.321242	+	0.0638990i	0.0128394	+	0.00255392i
$627$	−0.318883	+	0.769851i	−0.0127349	+	0.0307449i
$628$	9.40763	+	9.40763i	0.375405	+	0.375405i
$629$	−42.4377	−	1.62057i	−1.69210	−	0.0646163i
$630$		0			0
$631$	−19.6003	+	8.11870i	−0.780275	+	0.323200i	−0.737026	−	0.675864i	$-0.763771\pi$
$631$	−19.6003	+	8.11870i	−0.780275	+	0.323200i	−0.0432484	+	0.999064i	$0.513771\pi$
$632$	3.71934	−	2.48518i	0.147947	−	0.0988552i
$633$			0.473574i			0.0188229i
$634$	0.0830869	+	0.124348i	0.00329980	+	0.00493851i
$635$		0			0
$636$	−5.22932	−	3.49412i	−0.207356	−	0.138551i
$637$	38.4898	−	15.9430i	1.52502	−	0.631684i
$638$	−1.44120	+	0.596964i	−0.0570576	+	0.0236340i
$639$	−6.96708	−	4.65525i	−0.275613	−	0.184159i
$640$		0			0
$641$	3.29442	+	4.93045i	0.130122	+	0.194741i	0.890810	−	0.454377i	$-0.150138\pi$
$641$	3.29442	+	4.93045i	0.130122	+	0.194741i	−0.760688	+	0.649118i	$0.775138\pi$
$642$		−	13.7741i		−	0.543622i
$643$	18.6025	−	12.4298i	0.733612	−	0.490184i	−0.131780	−	0.991279i	$-0.542069\pi$
$643$	18.6025	−	12.4298i	0.733612	−	0.490184i	0.865392	+	0.501095i	$0.167069\pi$
$644$	16.6638	−	6.90238i	0.656647	−	0.271992i
$645$		0			0
$646$	0.754589	−	1.04101i	0.0296889	−	0.0409581i
$647$	25.6959	+	25.6959i	1.01021	+	1.01021i	0.999947	+	0.0102608i	$0.00326617\pi$
$647$	25.6959	+	25.6959i	1.01021	+	1.01021i	0.0102608	+	0.999947i	$0.496734\pi$
$648$	0.625305	−	1.50962i	0.0245643	−	0.0593034i
$649$	−9.35795	−	1.86141i	−0.367332	−	0.0730668i
$650$		0			0
$651$	15.2708	−	10.2036i	0.598510	−	0.399912i
$652$	8.48460	−	12.6981i	0.332283	−	0.497296i
$653$	−33.2017	+	6.60423i	−1.29928	+	0.258443i	−0.795799	−	0.605561i	$-0.792949\pi$
$653$	−33.2017	+	6.60423i	−1.29928	+	0.258443i	−0.503484	+	0.864004i	$0.667949\pi$
$654$	−7.16540	−	2.96800i	−0.280189	−	0.116058i
$655$		0			0
$656$	5.15021	−	7.70784i	0.201082	−	0.300940i
$657$	−1.49061	−	0.995992i	−0.0581541	−	0.0388573i
$658$	20.7781	+	4.13303i	0.810016	+	0.161122i
$659$	30.0602	−	30.0602i	1.17098	−	1.17098i	0.189001	−	0.981977i	$-0.439475\pi$
$659$	30.0602	−	30.0602i	1.17098	−	1.17098i	0.981977	−	0.189001i	$-0.0605250\pi$
$660$		0			0
$661$	−11.8936	−	28.7137i	−0.462608	−	1.11683i	−0.967323	−	0.253548i	$-0.918403\pi$
$661$	−11.8936	−	28.7137i	−0.462608	−	1.11683i	0.504715	−	0.863286i	$-0.331597\pi$
$662$	−21.8391	+	21.8391i	−0.848800	+	0.848800i
$663$	0.863112	−	22.6023i	0.0335205	−	0.877799i
$664$			1.47720i			0.0573263i
$665$		0			0
$666$	4.19863	−	21.1079i	0.162694	−	0.817916i
$667$	2.66196			0.103072
$668$	0.0921295	−	0.463166i	0.00356460	−	0.0179204i
$669$	23.0384	−	4.58262i	0.890716	−	0.177174i
$670$		0			0
$671$	−10.9386	+	26.4081i	−0.422280	+	1.01947i
$672$	−1.37833	−	3.32759i	−0.0531704	−	0.128365i
$673$	6.29309	+	31.6375i	0.242581	+	1.21954i	0.889485	+	0.456964i	$0.151063\pi$
$673$	6.29309	+	31.6375i	0.242581	+	1.21954i	−0.646904	+	0.762571i	$0.723937\pi$
$674$	0.643188	+	3.23353i	0.0247747	+	0.124551i
$675$		0			0
$676$	14.1776	+	14.1776i	0.545293	+	0.545293i
$677$	−11.6902	−	17.4957i	−0.449292	−	0.672413i	0.535819	−	0.844333i	$-0.320003\pi$
$677$	−11.6902	−	17.4957i	−0.449292	−	0.672413i	−0.985111	+	0.171920i	$0.945003\pi$
$678$	−3.74104	−	1.54959i	−0.143674	−	0.0595116i
$679$	−58.9459			−2.26214
$680$		0			0
$681$	−22.8424			−0.875321
$682$	13.1924	+	5.46448i	0.505164	+	0.209246i
$683$	24.8872	+	37.2464i	0.952284	+	1.42519i	0.904566	+	0.426333i	$0.140195\pi$
$683$	24.8872	+	37.2464i	0.952284	+	1.42519i	0.0477178	+	0.998861i	$0.484805\pi$
$684$	0.460722	+	0.460722i	0.0176161	+	0.0176161i
$685$		0			0
$686$	0.181692	+	0.913428i	0.00693704	+	0.0348748i
$687$	−0.442712	−	2.22567i	−0.0168905	−	0.0849144i
$688$	3.44637	+	8.32027i	0.131392	+	0.317207i
$689$	−14.5000	+	35.0062i	−0.552407	+	1.33363i
$690$		0			0
$691$	−15.5942	+	3.10187i	−0.593230	+	0.118001i	−0.482570	−	0.875858i	$-0.660297\pi$
$691$	−15.5942	+	3.10187i	−0.593230	+	0.118001i	−0.110660	+	0.993858i	$0.535297\pi$
$692$	−1.74630	+	8.77923i	−0.0663842	+	0.333736i
$693$	22.0848			0.838932
$694$	0.502701	−	2.52725i	0.0190823	−	0.0959330i
$695$		0			0
$696$		−	0.531566i		−	0.0201490i
$697$	13.2687	+	35.8447i	0.502587	+	1.35772i
$698$	−4.86856	+	4.86856i	−0.184278	+	0.184278i
$699$	3.92490	+	9.47554i	0.148453	+	0.358398i
$700$		0			0
$701$	−18.7261	+	18.7261i	−0.707276	+	0.707276i	−0.965961	−	0.258686i	$-0.916711\pi$
$701$	−18.7261	+	18.7261i	−0.707276	+	0.707276i	0.258686	+	0.965961i	$0.416711\pi$
$702$	27.3834	+	5.44689i	1.03352	+	0.205580i
$703$	2.67065	+	1.78447i	0.100725	+	0.0673026i
$704$	1.55578	−	2.32838i	0.0586355	−	0.0877542i
$705$		0			0
$706$	23.1791	+	9.60111i	0.872358	+	0.361343i
$707$	19.2207	−	3.82323i	0.722867	−	0.143787i
$708$	1.80632	−	2.70335i	0.0678857	−	0.101598i
$709$	−10.9253	+	7.30008i	−0.410310	+	0.274160i	−0.743548	−	0.668682i	$-0.766859\pi$
$709$	−10.9253	+	7.30008i	−0.410310	+	0.274160i	0.333238	+	0.942843i	$0.391859\pi$
$710$		0			0
$711$	−9.16686	−	1.82340i	−0.343784	−	0.0683829i
$712$	−4.05806	+	9.79701i	−0.152082	+	0.367159i
$713$	−17.2301	−	17.2301i	−0.645272	−	0.645272i
$714$	14.4439	+	3.45086i	0.540550	+	0.129145i
$715$		0			0
$716$	6.74143	−	2.79239i	0.251939	−	0.104357i
$717$	−15.9570	+	10.6621i	−0.595925	+	0.398184i
$718$		−	9.72428i		−	0.362907i
$719$	28.8785	+	43.2197i	1.07698	+	1.61182i	0.743064	+	0.669220i	$0.233372\pi$
$719$	28.8785	+	43.2197i	1.07698	+	1.61182i	0.333921	+	0.942601i	$0.391628\pi$
$720$		0			0
$721$	45.7536	+	30.5716i	1.70395	+	1.13854i
$722$	17.4639	−	7.23377i	0.649938	−	0.269213i
$723$	3.99809	−	1.65606i	0.148691	−	0.0615897i
$724$	−1.80649	−	1.20706i	−0.0671376	−	0.0448599i
$725$		0			0
$726$	1.67431	+	2.50578i	0.0621393	+	0.0929981i
$727$		−	1.45820i		−	0.0540815i	−0.999634	−	0.0270407i	$-0.991392\pi$
$727$		−	1.45820i		−	0.0540815i	0.999634	−	0.0270407i	$-0.00860838\pi$
$728$	−18.0423	+	12.0555i	−0.668691	+	0.446805i
$729$	9.69033	−	4.01387i	0.358901	−	0.148662i
$730$		0			0
$731$	−36.1154	−	8.62848i	−1.33578	−	0.319136i
$732$	−6.88741	−	6.88741i	−0.254566	−	0.254566i
$733$	−4.20864	+	10.1606i	−0.155450	+	0.375289i	−0.982348	−	0.187063i	$-0.940103\pi$
$733$	−4.20864	+	10.1606i	−0.155450	+	0.375289i	0.826898	+	0.562351i	$0.190103\pi$
$734$	−15.2095	−	3.02536i	−0.561394	−	0.111668i
$735$		0			0
$736$	−3.97327	+	2.65485i	−0.146457	+	0.0978592i
$737$	4.27275	−	6.39463i	0.157389	−	0.235549i
$738$	−18.9971	+	3.77876i	−0.699293	+	0.139098i
$739$	30.1250	+	12.4782i	1.10817	+	0.459017i	0.860306	−	0.509779i	$-0.170273\pi$
$739$	30.1250	+	12.4782i	1.10817	+	0.459017i	0.247860	+	0.968796i	$0.420273\pi$
$740$		0			0
$741$	−0.950406	+	1.42238i	−0.0349140	+	0.0522526i
$742$	−20.6846	−	13.8210i	−0.759354	−	0.507384i
$743$	−44.2588	−	8.80362i	−1.62370	−	0.322973i	−0.702385	−	0.711797i	$-0.747881\pi$
$743$	−44.2588	−	8.80362i	−1.62370	−	0.322973i	−0.921312	+	0.388824i	$0.872881\pi$
$744$	−3.44067	+	3.44067i	−0.126141	+	0.126141i
$745$		0			0
$746$	−8.76653	−	21.1643i	−0.320966	−	0.774880i
$747$	2.18248	−	2.18248i	0.0798529	−	0.0798529i
$748$	4.00821	+	10.8280i	0.146554	+	0.395910i
$749$		−	54.4835i		−	1.99078i
$750$		0			0
$751$	7.33561	−	36.8786i	0.267680	−	1.34572i	−0.579742	−	0.814800i	$-0.696847\pi$
$751$	7.33561	−	36.8786i	0.267680	−	1.34572i	0.847422	−	0.530919i	$-0.178153\pi$
$752$	−5.61274			−0.204675
$753$	−0.616167	+	3.09768i	−0.0224544	+	0.112886i
$754$	−3.14095	+	0.624774i	−0.114387	+	0.0227529i
$755$		0			0
$756$	−7.01493	+	16.9355i	−0.255131	+	0.615940i
$757$	15.2554	+	36.8299i	0.554469	+	1.33861i	0.914091	+	0.405508i	$0.132905\pi$
$757$	15.2554	+	36.8299i	0.554469	+	1.33861i	−0.359623	+	0.933098i	$0.617095\pi$
$758$	4.27956	+	21.5148i	0.155440	+	0.781452i
$759$	2.49116	+	12.5239i	0.0904235	+	0.454590i
$760$		0			0
$761$	19.4265	+	19.4265i	0.704212	+	0.704212i	0.965312	−	0.261100i	$-0.0840852\pi$
$761$	19.4265	+	19.4265i	0.704212	+	0.704212i	−0.261100	+	0.965312i	$0.584085\pi$
$762$	10.6408	+	15.9250i	0.385475	+	0.576904i
$763$	−28.3427	−	11.7399i	−1.02607	−	0.425014i
$764$	14.1397			0.511557
$765$		0			0
$766$	25.4244			0.918621
$767$	−18.0968	−	7.49593i	−0.653436	−	0.270662i
$768$	0.530147	+	0.793420i	0.0191300	+	0.0286301i
$769$	−6.98576	−	6.98576i	−0.251913	−	0.251913i	0.569842	−	0.821755i	$-0.307005\pi$
$769$	−6.98576	−	6.98576i	−0.251913	−	0.251913i	−0.821755	+	0.569842i	$0.807005\pi$
$770$		0			0
$771$	2.65642	+	13.3547i	0.0956687	+	0.480959i
$772$	−0.258440	−	1.29926i	−0.00930145	−	0.0467615i
$773$	2.37475	+	5.73316i	0.0854140	+	0.206208i	0.960815	−	0.277189i	$-0.0894029\pi$
$773$	2.37475	+	5.73316i	0.0854140	+	0.206208i	−0.875401	+	0.483397i	$0.839403\pi$
$774$	7.20094	−	17.3846i	0.258833	−	0.624877i
$775$		0			0
$776$	15.3169	−	3.04671i	0.549843	−	0.109371i
$777$	−7.23760	+	36.3859i	−0.259647	+	1.30534i
$778$	−15.9047			−0.570209
$779$	0.563960	−	2.83522i	0.0202060	−	0.101582i
$780$		0			0
$781$			11.2301i			0.401846i
$782$	0.751839	−	19.6884i	0.0268857	−	0.704055i
$783$	−1.91298	+	1.91298i	−0.0683645	+	0.0683645i
$784$	−2.77321	−	6.69512i	−0.0990431	−	0.239111i
$785$		0			0
$786$	11.8112	−	11.8112i	0.421290	−	0.421290i
$787$	19.1406	+	3.80730i	0.682288	+	0.135716i	0.524053	−	0.851686i	$-0.324420\pi$
$787$	19.1406	+	3.80730i	0.682288	+	0.135716i	0.158235	+	0.987401i	$0.449420\pi$
$788$	−1.45486	−	0.972106i	−0.0518272	−	0.0346298i
$789$	2.96302	−	4.43447i	0.105486	−	0.157871i
$790$		0			0
$791$	−14.7977	−	6.12939i	−0.526144	−	0.217936i
$792$	−5.73865	+	1.14149i	−0.203914	+	0.0405610i
$793$	−32.6017	+	48.7919i	−1.15772	+	1.73265i
$794$	10.9531	−	7.31860i	0.388709	−	0.259727i
$795$		0			0
$796$	−3.34115	−	0.664596i	−0.118424	−	0.0235560i
$797$	−8.81871	+	21.2903i	−0.312375	+	0.754140i	0.687241	+	0.726429i	$0.258822\pi$
$797$	−8.81871	+	21.2903i	−0.312375	+	0.754140i	−0.999616	+	0.0277102i	$0.991178\pi$
$798$	−0.794193	−	0.794193i	−0.0281141	−	0.0281141i
$799$	13.5818	−	18.7372i	0.480491	−	0.662873i
$800$		0			0
$801$	20.4702	−	8.47902i	0.723278	−	0.299591i
$802$	3.40036	−	2.27205i	0.120071	−	0.0802288i
$803$			2.40269i			0.0847890i
$804$	1.45598	+	2.17903i	0.0513486	+	0.0768486i
$805$		0			0
$806$	24.3744	+	16.2865i	0.858553	+	0.573667i
$807$	−6.01336	+	2.49082i	−0.211680	+	0.0876809i
$808$	−4.79680	+	1.98690i	−0.168751	+	0.0698990i
$809$	−25.3345	−	16.9279i	−0.890712	−	0.595155i	0.0237985	−	0.999717i	$-0.492424\pi$
$809$	−25.3345	−	16.9279i	−0.890712	−	0.595155i	−0.914511	+	0.404562i	$0.867424\pi$
$810$		0			0
$811$	3.76345	+	5.63241i	0.132153	+	0.197781i	0.891644	−	0.452737i	$-0.149552\pi$
$811$	3.76345	+	5.63241i	0.132153	+	0.197781i	−0.759492	+	0.650517i	$0.774552\pi$
$812$		−	2.10261i		−	0.0737871i
$813$	0.450712	−	0.301156i	0.0158072	−	0.0105620i
$814$	−26.6482	+	11.0380i	−0.934018	+	0.386883i
$815$		0			0
$816$	−3.93156	−	0.150134i	−0.137632	−	0.00525576i
$817$	1.98579	+	1.98579i	0.0694740	+	0.0694740i
$818$	10.0769	−	24.3277i	0.352330	−	0.850600i
$819$	44.4679	+	8.84521i	1.55383	+	0.309077i
$820$		0			0
$821$	0.0491354	−	0.0328312i	0.00171484	−	0.00114582i	−0.554713	−	0.832042i	$-0.687172\pi$
$821$	0.0491354	−	0.0328312i	0.00171484	−	0.00114582i	0.556427	+	0.830896i	$0.312172\pi$
$822$	−0.609356	+	0.911966i	−0.0212537	+	0.0318085i
$823$	27.4218	−	5.45454i	0.955866	−	0.190133i	0.307573	−	0.951525i	$-0.400483\pi$
$823$	27.4218	−	5.45454i	0.955866	−	0.190133i	0.648293	+	0.761391i	$0.275483\pi$
$824$	−13.4690	−	5.57905i	−0.469216	−	0.194356i
$825$		0			0
$826$	7.14489	−	10.6931i	0.248602	−	0.372060i
$827$	2.86713	+	1.91575i	0.0996998	+	0.0666173i	0.604421	−	0.796665i	$-0.293405\pi$
$827$	2.86713	+	1.91575i	0.0996998	+	0.0666173i	−0.504721	+	0.863283i	$0.668405\pi$
$828$	9.79272	+	1.94789i	0.340320	+	0.0676939i
$829$	−20.0943	+	20.0943i	−0.697904	+	0.697904i	−0.963958	−	0.266054i	$-0.914280\pi$
$829$	−20.0943	+	20.0943i	−0.697904	+	0.697904i	0.266054	+	0.963958i	$0.414280\pi$
$830$		0			0
$831$	7.36446	+	17.7794i	0.255470	+	0.616760i
$832$	4.06511	−	4.06511i	0.140932	−	0.140932i
$833$	29.0612	+	6.94313i	1.00691	+	0.240565i
$834$		−	6.30816i		−	0.218434i
$835$		0			0
$836$	0.170361	−	0.856462i	0.00589206	−	0.0296214i
$837$	24.7644			0.855981
$838$	1.24149	−	6.24139i	0.0428866	−	0.215605i
$839$	16.6096	−	3.30385i	0.573426	−	0.114062i	0.100145	−	0.994973i	$-0.468069\pi$
$839$	16.6096	−	3.30385i	0.573426	−	0.114062i	0.473281	+	0.880911i	$0.343069\pi$
$840$		0			0
$841$	−10.9791	+	26.5058i	−0.378589	+	0.913994i
$842$	−9.08826	−	21.9410i	−0.313202	−	0.756137i
$843$	0.0289578	+	0.145581i	0.000997361	+	0.00501407i
$844$	−0.0968204	−	0.486749i	−0.00333270	−	0.0167546i
$845$		0			0
$846$	8.29253	+	8.29253i	0.285103	+	0.285103i
$847$	6.62271	+	9.91159i	0.227559	+	0.340566i
$848$	6.08916	+	2.52221i	0.209103	+	0.0866132i
$849$	13.1719			0.452058
$850$		0			0
$851$	49.2205			1.68726
$852$	−3.53549	−	1.46445i	−0.121124	−	0.0501711i
$853$	10.6966	+	16.0086i	0.366245	+	0.548124i	0.968127	−	0.250461i	$-0.0805822\pi$
$853$	10.6966	+	16.0086i	0.366245	+	0.548124i	−0.601882	+	0.798585i	$0.705582\pi$
$854$	−27.2431	−	27.2431i	−0.932241	−	0.932241i
$855$		0			0
$856$	2.81607	+	14.1573i	0.0962512	+	0.483888i
$857$	1.69936	+	8.54328i	0.0580492	+	0.291833i	0.998895	−	0.0470027i	$-0.0149669\pi$
$857$	1.69936	+	8.54328i	0.0580492	+	0.291833i	−0.940846	+	0.338836i	$0.889967\pi$
$858$	−5.87884	−	14.1928i	−0.200700	−	0.484533i
$859$	−19.4345	+	46.9191i	−0.663097	+	1.60086i	0.129826	+	0.991537i	$0.458558\pi$
$859$	−19.4345	+	46.9191i	−0.663097	+	1.60086i	−0.792923	+	0.609321i	$0.791442\pi$
$860$		0			0
$861$	32.7472	−	6.51383i	1.11602	−	0.221991i
$862$	−4.77925	+	24.0269i	−0.162782	+	0.818360i
$863$	−19.7887			−0.673617			−0.336808	−	0.941573i	$-0.609347\pi$
$863$	−19.7887			−0.673617			−0.336808	+	0.941573i	$0.609347\pi$
$864$	0.947462	−	4.76321i	0.0322333	−	0.162048i
$865$		0			0
$866$			18.5789i			0.631338i
$867$	10.0149	−	12.7615i	0.340123	−	0.433405i
$868$	−13.6096	+	13.6096i	−0.461938	+	0.461938i
$869$	4.79365	+	11.5729i	0.162614	+	0.392584i
$870$		0			0
$871$	11.1643	−	11.1643i	0.378289	−	0.378289i
$872$	7.97153	+	1.58564i	0.269950	+	0.0536964i
$873$	−27.1313	−	18.1285i	−0.918254	−	0.613558i
$874$	−0.827879	+	1.23901i	−0.0280034	+	0.0419101i
$875$		0			0
$876$	−0.756417	−	0.313318i	−0.0255570	−	0.0105860i
$877$	1.28871	−	0.256340i	0.0435167	−	0.00865600i	−0.173284	−	0.984872i	$-0.555438\pi$
$877$	1.28871	−	0.256340i	0.0435167	−	0.00865600i	0.216801	+	0.976216i	$0.430438\pi$
$878$	19.8231	−	29.6674i	0.668997	−	1.00123i
$879$	−18.4061	+	12.2986i	−0.620822	+	0.414820i
$880$		0			0
$881$	36.3159	+	7.22367i	1.22351	+	0.243372i	0.764245	−	0.644926i	$-0.223112\pi$
$881$	36.3159	+	7.22367i	1.22351	+	0.243372i	0.459268	+	0.888298i	$0.348112\pi$
$882$	−5.79442	+	13.9890i	−0.195108	+	0.471033i
$883$	8.11148	+	8.11148i	0.272973	+	0.272973i	0.830296	−	0.557323i	$-0.188171\pi$
$883$	8.11148	+	8.11148i	0.272973	+	0.272973i	−0.557323	+	0.830296i	$0.688171\pi$
$884$	3.73382	+	23.4075i	0.125582	+	0.787280i
$885$		0			0
$886$	25.7327	−	10.6588i	0.864507	−	0.358090i
$887$	26.1101	−	17.4462i	0.876692	−	0.585787i	−0.0337466	−	0.999430i	$-0.510744\pi$
$887$	26.1101	−	17.4462i	0.876692	−	0.585787i	0.910439	+	0.413643i	$0.135744\pi$
$888$		−	9.82881i		−	0.329833i
$889$	42.0895	+	62.9914i	1.41164	+	2.11267i
$890$		0			0
$891$	3.80458	+	2.54214i	0.127458	+	0.0851648i
$892$	−22.7424	+	9.42022i	−0.761472	+	0.315412i
$893$	−1.61702	+	0.669793i	−0.0541116	+	0.0224138i
$894$	6.81048	+	4.55062i	0.227776	+	0.152195i
$895$		0			0
$896$	2.09699	+	3.13837i	0.0700556	+	0.104846i
$897$			26.2147i			0.875285i
$898$	15.1498	−	10.1228i	0.505557	−	0.337802i
$899$	−2.62432	+	1.08703i	−0.0875260	+	0.0362544i
$900$		0			0
$901$	−23.1547	+	14.2243i	−0.771395	+	0.473881i
$902$	18.3560	+	18.3560i	0.611189	+	0.611189i
$903$	−12.4130	+	29.9676i	−0.413078	+	0.997260i
$904$	4.16192	+	0.827857i	0.138423	+	0.0275341i
$905$		0			0
$906$	−3.50936	+	2.34488i	−0.116591	+	0.0779033i
$907$	19.1339	−	28.6359i	0.635330	−	0.950839i	−0.364477	−	0.931212i	$-0.618752\pi$
$907$	19.1339	−	28.6359i	0.635330	−	0.950839i	0.999807	−	0.0196268i	$-0.00624782\pi$
$908$	23.4778	−	4.67003i	0.779139	−	0.154980i
$909$	10.0226	+	4.15149i	0.332428	+	0.137696i
$910$		0			0
$911$	6.35786	−	9.51521i	0.210645	−	0.315253i	−0.711069	−	0.703122i	$-0.751789\pi$
$911$	6.35786	−	9.51521i	0.210645	−	0.315253i	0.921714	+	0.387869i	$0.126789\pi$
$912$	0.247417	+	0.165319i	0.00819280	+	0.00547425i
$913$	−4.05714	−	0.807016i	−0.134272	−	0.0267083i
$914$	18.1091	−	18.1091i	0.598997	−	0.598997i
$915$		0			0
$916$	0.910057	+	2.19707i	0.0300691	+	0.0725933i
$917$	46.7190	−	46.7190i	1.54280	−	1.54280i
$918$	13.6085	+	14.6891i	0.449147	+	0.484812i
$919$			19.9181i			0.657036i	0.944498	+	0.328518i	$0.106549\pi$
$919$			19.9181i			0.657036i	−0.944498	+	0.328518i	$0.893451\pi$
$920$		0			0
$921$	−1.52809	+	7.68223i	−0.0503523	+	0.253138i
$922$	32.7804			1.07957
$923$	−4.49779	+	22.6119i	−0.148047	+	0.744281i
$924$	9.89229	−	1.96770i	0.325432	−	0.0647325i
$925$		0			0
$926$	−0.837054	+	2.02083i	−0.0275073	+	0.0664085i
$927$	11.6570	+	28.1426i	0.382867	+	0.924323i
$928$	0.108677	+	0.546354i	0.00356748	+	0.0179350i
$929$	−4.63571	−	23.3053i	−0.152093	−	0.764621i	−0.979251	−	0.202652i	$-0.935044\pi$
$929$	−4.63571	−	23.3053i	−0.152093	−	0.764621i	0.827158	−	0.561969i	$-0.189956\pi$
$930$		0			0
$931$	−1.59792	−	1.59792i	−0.0523696	−	0.0523696i
$932$	−5.97133	−	8.93672i	−0.195597	−	0.292732i
$933$	20.9524	+	8.67876i	0.685950	+	0.284130i
$934$	30.9948			1.01418
$935$		0			0
$936$	−12.0120			−0.392624
$937$	27.0210	+	11.1925i	0.882738	+	0.365642i	0.777558	−	0.628811i	$-0.216458\pi$
$937$	27.0210	+	11.1925i	0.882738	+	0.365642i	0.105180	+	0.994453i	$0.466458\pi$
$938$	5.75914	+	8.61916i	0.188043	+	0.281425i
$939$	−0.221004	−	0.221004i	−0.00721220	−	0.00721220i
$940$		0			0
$941$	6.12322	+	30.7835i	0.199611	+	1.00351i	0.942527	+	0.334129i	$0.108442\pi$
$941$	6.12322	+	30.7835i	0.199611	+	1.00351i	−0.742916	+	0.669385i	$0.766558\pi$
$942$	−2.47678	−	12.4516i	−0.0806979	−	0.405696i
$943$	−16.9523	−	40.9264i	−0.552041	−	1.33275i
$944$	−1.30388	+	3.14785i	−0.0424378	+	0.102454i
$945$		0			0
$946$	−24.7345	+	4.92001i	−0.804190	+	0.159963i
$947$	−3.88070	+	19.5096i	−0.126106	+	0.633977i	0.865095	+	0.501609i	$0.167258\pi$
$947$	−3.88070	+	19.5096i	−0.126106	+	0.633977i	−0.991201	+	0.132369i	$0.957742\pi$
$948$	−4.26851			−0.138635
$949$	−0.962303	+	4.83783i	−0.0312377	+	0.157042i
$950$		0			0
$951$		−	0.142709i		−	0.00462765i
$952$	−15.5513	−	0.593856i	−0.504020	−	0.0192470i
$953$	−9.32003	+	9.32003i	−0.301905	+	0.301905i	−0.841759	−	0.539854i	$-0.818480\pi$
$953$	−9.32003	+	9.32003i	−0.301905	+	0.301905i	0.539854	+	0.841759i	$0.318480\pi$
$954$	−5.26999	−	12.7229i	−0.170622	−	0.411918i
$955$		0			0
$956$	14.2211	−	14.2211i	0.459943	−	0.459943i
$957$	1.45995	+	0.290403i	0.0471936	+	0.00938740i
$958$	−26.2452	−	17.5365i	−0.847944	−	0.566578i
$959$	−2.41031	+	3.60728i	−0.0778328	+	0.116485i
$960$		0			0
$961$	−4.61780	−	1.91276i	−0.148961	−	0.0617018i
$962$	−58.0771	+	11.5523i	−1.87248	+	0.372460i
$963$	16.7561	−	25.0773i	0.539959	−	0.808106i
$964$	−3.77074	+	2.51953i	−0.121447	+	0.0811486i
$965$		0			0
$966$	−16.8807	−	3.35778i	−0.543127	−	0.108035i
$967$	5.70914	−	13.7831i	0.183594	−	0.443234i	−0.805109	−	0.593128i	$-0.797893\pi$
$967$	5.70914	−	13.7831i	0.183594	−	0.443234i	0.988702	+	0.149893i	$0.0478930\pi$
$968$	−2.23318	−	2.23318i	−0.0717772	−	0.0717772i
$969$	−1.15059	+	0.425917i	−0.0369624	+	0.0136824i
$970$		0			0
$971$	−2.84225	+	1.17730i	−0.0912121	+	0.0377813i	−0.427823	−	0.903863i	$-0.640719\pi$
$971$	−2.84225	+	1.17730i	−0.0912121	+	0.0377813i	0.336611	+	0.941644i	$0.390719\pi$
$972$	−13.4106	+	8.96069i	−0.430146	+	0.287414i
$973$		−	24.9519i		−	0.799921i
$974$	−11.1878	−	16.7437i	−0.358481	−	0.536504i
$975$		0			0
$976$	8.48713	+	5.67092i	0.271666	+	0.181522i
$977$	−4.32813	+	1.79277i	−0.138469	+	0.0573558i	−0.450842	−	0.892604i	$-0.648876\pi$
$977$	−4.32813	+	1.79277i	−0.138469	+	0.0573558i	0.312373	+	0.949960i	$0.398876\pi$
$978$	−13.4637	+	5.57685i	−0.430522	+	0.178328i
$979$	−24.6907	−	16.4978i	−0.789117	−	0.527271i
$980$		0			0
$981$	−9.43484	−	14.1202i	−0.301231	−	0.450824i
$982$			24.5239i			0.782590i
$983$	−20.5105	+	13.7047i	−0.654185	+	0.437112i	−0.837868	−	0.545873i	$-0.816198\pi$
$983$	−20.5105	+	13.7047i	−0.654185	+	0.437112i	0.183683	+	0.982986i	$0.441198\pi$
$984$	−8.17256	+	3.38519i	−0.260532	+	0.107916i
$985$		0			0
$986$	−2.08689	−	0.959283i	−0.0664601	−	0.0305498i
$987$	−14.2947	−	14.2947i	−0.455005	−	0.455005i
$988$	0.686046	−	1.65626i	0.0218260	−	0.0526927i
$989$	42.2083	+	8.39575i	1.34215	+	0.266969i
$990$		0			0
$991$	26.8671	−	17.9521i	0.853463	−	0.570266i	−0.0500887	−	0.998745i	$-0.515950\pi$
$991$	26.8671	−	17.9521i	0.853463	−	0.570266i	0.903552	+	0.428479i	$0.140950\pi$
$992$	2.83296	−	4.23982i	0.0899465	−	0.134614i
$993$	28.9055	−	5.74966i	0.917288	−	0.182460i
$994$	−13.9846	−	5.79261i	−0.443564	−	0.183730i
$995$		0			0
$996$	0.783131	−	1.17204i	0.0248144	−	0.0371374i
$997$	−48.8913	−	32.6681i	−1.54840	−	1.03461i	−0.976819	−	0.214066i	$-0.931329\pi$
$997$	−48.8913	−	32.6681i	−1.54840	−	1.03461i	−0.571583	−	0.820544i	$-0.693671\pi$
$998$	36.9936	+	7.35849i	1.17101	+	0.232929i
$999$	−35.3716	+	35.3716i	−1.11911	+	1.11911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.v.d.507.2		40
5.2	odd	4		170.2.o.b.133.2	✓	40
5.3	odd	4		850.2.s.d.643.4		40
5.4	even	2		170.2.r.b.167.4	yes	40
17.11	odd	16		850.2.s.d.657.4		40
85.28	even	16	inner	850.2.v.d.793.2		40
85.62	even	16		170.2.r.b.113.4	yes	40
85.79	odd	16		170.2.o.b.147.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.133.2	✓	40	5.2	odd	4
170.2.o.b.147.2	yes	40	85.79	odd	16
170.2.r.b.113.4	yes	40	85.62	even	16
170.2.r.b.167.4	yes	40	5.4	even	2
850.2.s.d.643.4		40	5.3	odd	4
850.2.s.d.657.4		40	17.11	odd	16
850.2.v.d.507.2		40	1.1	even	1	trivial
850.2.v.d.793.2		40	85.28	even	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.v (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 + 0.382683i) q^{2} +(-0.530147 - 0.793420i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-0.186163 - 0.935903i) q^{6} +(-0.736366 - 3.70196i) q^{7} +(0.382683 + 0.923880i) q^{8} +(0.799590 - 1.93038i) q^{9} +(-2.74651 + 0.546316i) q^{11} +(0.186163 - 0.935903i) q^{12} -5.74893 q^{13} +(0.736366 - 3.70196i) q^{14} +1.00000i q^{16} +(-3.33833 - 2.41983i) q^{17} +(1.47745 - 1.47745i) q^{18} +(0.119335 + 0.288099i) q^{19} +(-2.54683 + 2.54683i) q^{21} +(-2.74651 - 0.546316i) q^{22} +(3.97327 + 2.65485i) q^{23} +(0.530147 - 0.793420i) q^{24} +(-5.31132 - 2.20002i) q^{26} +(-4.76321 + 0.947462i) q^{27} +(2.09699 - 3.13837i) q^{28} +(0.463177 - 0.309485i) q^{29} +(-5.00121 - 0.994802i) q^{31} +(-0.382683 + 0.923880i) q^{32} +(1.88951 + 1.88951i) q^{33} +(-2.15819 - 3.51315i) q^{34} +(1.93038 - 0.799590i) q^{36} +(8.56427 - 5.72246i) q^{37} +0.311836i q^{38} +(3.04777 + 4.56132i) q^{39} +(-7.70784 - 5.15021i) q^{41} +(-3.32759 + 1.37833i) q^{42} +(8.32027 - 3.44637i) q^{43} +(-2.32838 - 1.55578i) q^{44} +(2.65485 + 3.97327i) q^{46} +5.61274i q^{47} +(0.793420 - 0.530147i) q^{48} +(-6.69512 + 2.77321i) q^{49} +(-0.150134 + 3.93156i) q^{51} +(-4.06511 - 4.06511i) q^{52} +(2.52221 - 6.08916i) q^{53} +(-4.76321 - 0.947462i) q^{54} +(3.13837 - 2.09699i) q^{56} +(0.165319 - 0.247417i) q^{57} +(0.546354 - 0.108677i) q^{58} +(3.14785 + 1.30388i) q^{59} +(5.67092 - 8.48713i) q^{61} +(-4.23982 - 2.83296i) q^{62} +(-7.73498 - 1.53858i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(1.02260 + 2.46877i) q^{66} +(-1.94198 + 1.94198i) q^{67} +(-0.649481 - 4.07163i) q^{68} -4.55993i q^{69} +(0.782371 - 3.93324i) q^{71} +2.08943 q^{72} +(0.167388 - 0.841518i) q^{73} +(10.1022 - 2.00946i) q^{74} +(-0.119335 + 0.288099i) q^{76} +(4.04488 + 9.76520i) q^{77} +(1.07024 + 5.38044i) q^{78} +(-0.872680 - 4.38726i) q^{79} +(-1.15541 - 1.15541i) q^{81} +(-5.15021 - 7.70784i) q^{82} +(1.36475 + 0.565299i) q^{83} -3.60176 q^{84} +9.00580 q^{86} +(-0.491103 - 0.203422i) q^{87} +(-1.55578 - 2.32838i) q^{88} +(7.49831 + 7.49831i) q^{89} +(4.23331 + 21.2823i) q^{91} +(0.932261 + 4.68679i) q^{92} +(1.86208 + 4.49545i) q^{93} +(-2.14790 + 5.18549i) q^{94} +(0.935903 - 0.186163i) q^{96} +(3.04671 - 15.3169i) q^{97} -7.24674 q^{98} +(-1.14149 + 5.73865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} + 32 q^{33} + 8 q^{34} - 32 q^{39} - 56 q^{41} + 24 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{49} - 32 q^{51} + 16 q^{52} - 16 q^{53}+ \cdots + 160 q^{99}+O(q^{100}) \) 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 + 32 * q^33 + 8 * q^34 - 32 * q^39 - 56 * q^41 + 24 * q^42 - 16 * q^43 + 16 * q^44 + 16 * q^49 - 32 * q^51 + 16 * q^52 - 16 * q^53 - 24 * q^54 - 8 * q^56 + 120 * q^57 - 16 * q^58 + 24 * q^61 + 8 * q^62 + 24 * q^63 - 16 * q^67 + 24 * q^71 - 56 * q^72 - 88 * q^73 + 32 * q^74 - 24 * q^77 - 32 * q^78 - 104 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 + 96 * q^86 - 136 * q^87 - 16 * q^89 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 - 16 * q^97 - 72 * q^98 + 160 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more