LMFDB - Embedded newform 357.2.u.a.127.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(43,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.u (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			127.5
Character	$\chi$	$=$	357.127
Dual form			357.2.u.a.253.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.764267 - 0.764267i) q^{2} +(-0.382683 + 0.923880i) q^{3} +0.831793i q^{4} +(-1.58285 - 0.655638i) q^{5} +(0.413618 + 0.998563i) q^{6} +(0.923880 - 0.382683i) q^{7} +(2.16424 + 2.16424i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-1.71080 + 0.708638i) q^{10} +(2.36262 + 5.70387i) q^{11} +(-0.768476 - 0.318313i) q^{12} +1.23070i q^{13} +(0.413618 - 0.998563i) q^{14} +(1.21146 - 1.21146i) q^{15} +1.64454 q^{16} +(-2.91141 + 2.91953i) q^{17} -1.08084 q^{18} +(3.85915 - 3.85915i) q^{19} +(0.545355 - 1.31660i) q^{20} +1.00000i q^{21} +(6.16495 + 2.55361i) q^{22} +(2.95179 + 7.12624i) q^{23} +(-2.82772 + 1.17128i) q^{24} +(-1.45998 - 1.45998i) q^{25} +(0.940583 + 0.940583i) q^{26} +(0.923880 - 0.382683i) q^{27} +(0.318313 + 0.768476i) q^{28} +(-3.68393 - 1.52593i) q^{29} -1.85176i q^{30} +(1.09798 - 2.65076i) q^{31} +(-3.07163 + 3.07163i) q^{32} -6.17383 q^{33} +(0.00620859 + 4.45640i) q^{34} -1.71327 q^{35} +(0.588166 - 0.588166i) q^{36} +(0.941849 - 2.27382i) q^{37} -5.89883i q^{38} +(-1.13702 - 0.470968i) q^{39} +(-2.00672 - 4.84464i) q^{40} +(9.31001 - 3.85633i) q^{41} +(0.764267 + 0.764267i) q^{42} +(-5.14399 - 5.14399i) q^{43} +(-4.74444 + 1.96521i) q^{44} +(0.655638 + 1.58285i) q^{45} +(7.70230 + 3.19040i) q^{46} -5.99099i q^{47} +(-0.629336 + 1.51935i) q^{48} +(0.707107 - 0.707107i) q^{49} -2.23163 q^{50} +(-1.58315 - 3.80705i) q^{51} -1.02369 q^{52} +(6.56019 - 6.56019i) q^{53} +(0.413618 - 0.998563i) q^{54} -10.5774i q^{55} +(2.82772 + 1.17128i) q^{56} +(2.08855 + 5.04222i) q^{57} +(-3.98173 + 1.64929i) q^{58} +(-7.34731 - 7.34731i) q^{59} +(1.00768 + 1.00768i) q^{60} +(-7.67745 + 3.18010i) q^{61} +(-1.18674 - 2.86504i) q^{62} +(-0.923880 - 0.382683i) q^{63} +7.98415i q^{64} +(0.806894 - 1.94801i) q^{65} +(-4.71845 + 4.71845i) q^{66} +10.9203 q^{67} +(-2.42845 - 2.42169i) q^{68} -7.71339 q^{69} +(-1.30939 + 1.30939i) q^{70} +(-1.37278 + 3.31420i) q^{71} -3.06070i q^{72} +(9.26092 + 3.83600i) q^{73} +(-1.01798 - 2.45763i) q^{74} +(1.90755 - 0.790135i) q^{75} +(3.21001 + 3.21001i) q^{76} +(4.36555 + 4.36555i) q^{77} +(-1.22893 + 0.509040i) q^{78} +(-3.62512 - 8.75181i) q^{79} +(-2.60305 - 1.07822i) q^{80} +1.00000i q^{81} +(4.16806 - 10.0626i) q^{82} +(-2.97117 + 2.97117i) q^{83} -0.831793 q^{84} +(6.52249 - 2.71236i) q^{85} -7.86276 q^{86} +(2.81956 - 2.81956i) q^{87} +(-7.23129 + 17.4579i) q^{88} +6.50588i q^{89} +(1.71080 + 0.708638i) q^{90} +(0.470968 + 1.13702i) q^{91} +(-5.92756 + 2.45527i) q^{92} +(2.02880 + 2.02880i) q^{93} +(-4.57871 - 4.57871i) q^{94} +(-8.63866 + 3.57825i) q^{95} +(-1.66235 - 4.01327i) q^{96} +(-1.20637 - 0.499696i) q^{97} -1.08084i q^{98} +(2.36262 - 5.70387i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{6} - 32 q^{10} + 8 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} + 8 q^{19} - 16 q^{20} - 8 q^{23} - 8 q^{24} + 24 q^{25} - 32 q^{26} + 24 q^{29} + 8 q^{31} - 40 q^{32} + 8 q^{33} - 8 q^{34} - 8 q^{35}+ \cdots + 96 q^{97}+O(q^{100}) $ 32 * q + 8 * q^6 - 32 * q^10 + 8 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 + 8 * q^19 - 16 * q^20 - 8 * q^23 - 8 * q^24 + 24 * q^25 - 32 * q^26 + 24 * q^29 + 8 * q^31 - 40 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^35 - 8 * q^36 + 72 * q^37 - 16 * q^39 + 40 * q^40 + 8 * q^41 - 32 * q^43 - 48 * q^44 + 8 * q^45 + 40 * q^46 + 32 * q^48 + 56 * q^50 - 16 * q^51 - 56 * q^53 + 8 * q^54 + 8 * q^56 + 16 * q^57 - 32 * q^58 - 48 * q^59 - 48 * q^60 + 8 * q^61 - 24 * q^62 + 16 * q^66 + 96 * q^67 - 16 * q^68 + 8 * q^69 - 16 * q^70 + 24 * q^71 - 24 * q^73 - 32 * q^74 - 16 * q^75 - 48 * q^76 - 24 * q^77 - 72 * q^78 - 48 * q^79 + 72 * q^80 + 96 * q^82 - 24 * q^83 + 24 * q^84 - 136 * q^85 - 32 * q^87 + 16 * q^88 + 32 * q^90 + 8 * q^91 + 136 * q^92 + 8 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 + 96 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	0.764267	−	0.764267i	0.540418	−	0.540418i	−0.383233	−	0.923652i	$-0.625189\pi$
$2$	0.764267	−	0.764267i	0.540418	−	0.540418i	0.923652	+	0.383233i	$0.125189\pi$
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$4$			0.831793i			0.415896i
$5$	−1.58285	−	0.655638i	−0.707872	−	0.293210i	−0.000448543	−	1.00000i	$-0.500143\pi$
$5$	−1.58285	−	0.655638i	−0.707872	−	0.293210i	−0.707424	+	0.706790i	$0.750143\pi$
$6$	0.413618	+	0.998563i	0.168859	+	0.407661i
$7$	0.923880	−	0.382683i	0.349194	−	0.144641i
$7$	0.923880	−	0.382683i	0.349194	−	0.144641i
$8$	2.16424	+	2.16424i	0.765176	+	0.765176i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	−1.71080	+	0.708638i	−0.541003	+	0.224091i
$11$	2.36262	+	5.70387i	0.712357	+	1.71978i	0.694026	+	0.719950i	$0.255835\pi$
$11$	2.36262	+	5.70387i	0.712357	+	1.71978i	0.0183315	+	0.999832i	$0.494165\pi$
$12$	−0.768476	−	0.318313i	−0.221840	−	0.0918891i
$13$			1.23070i			0.341335i	0.985329	+	0.170667i	$0.0545924\pi$
$13$			1.23070i			0.341335i	−0.985329	+	0.170667i	$0.945408\pi$
$14$	0.413618	−	0.998563i	0.110544	−	0.266877i
$15$	1.21146	−	1.21146i	0.312798	−	0.312798i
$16$	1.64454			0.411134
$17$	−2.91141	+	2.91953i	−0.706121	+	0.708091i
$17$	−2.91141	+	2.91953i	−0.706121	+	0.708091i
$18$	−1.08084			−0.254756
$19$	3.85915	−	3.85915i	0.885349	−	0.885349i	−0.108723	−	0.994072i	$-0.534676\pi$
$19$	3.85915	−	3.85915i	0.885349	−	0.885349i	0.994072	+	0.108723i	$0.0346762\pi$
$20$	0.545355	−	1.31660i	0.121945	−	0.294402i
$21$			1.00000i			0.218218i
$22$	6.16495	+	2.55361i	1.31437	+	0.544431i
$23$	2.95179	+	7.12624i	0.615490	+	1.48592i	0.856891	+	0.515498i	$0.172393\pi$
$23$	2.95179	+	7.12624i	0.615490	+	1.48592i	−0.241401	+	0.970426i	$0.577607\pi$
$24$	−2.82772	+	1.17128i	−0.577206	+	0.239087i
$25$	−1.45998	−	1.45998i	−0.291996	−	0.291996i
$26$	0.940583	+	0.940583i	0.184464	+	0.184464i
$27$	0.923880	−	0.382683i	0.177801	−	0.0736475i
$28$	0.318313	+	0.768476i	0.0601556	+	0.145228i
$29$	−3.68393	−	1.52593i	−0.684089	−	0.283359i	0.0134460	−	0.999910i	$-0.495720\pi$
$29$	−3.68393	−	1.52593i	−0.684089	−	0.283359i	−0.697535	+	0.716551i	$0.745720\pi$
$30$		−	1.85176i		−	0.338083i
$31$	1.09798	−	2.65076i	0.197203	−	0.476090i	−0.794084	−	0.607808i	$-0.792049\pi$
$31$	1.09798	−	2.65076i	0.197203	−	0.476090i	0.991287	+	0.131717i	$0.0420491\pi$
$32$	−3.07163	+	3.07163i	−0.542992	+	0.542992i
$33$	−6.17383			−1.07473
$34$	0.00620859	+	4.45640i	0.00106476	+	0.764266i
$35$	−1.71327			−0.289595
$36$	0.588166	−	0.588166i	0.0980277	−	0.0980277i
$37$	0.941849	−	2.27382i	0.154839	−	0.373814i	−0.827356	−	0.561678i	$-0.810156\pi$
$37$	0.941849	−	2.27382i	0.154839	−	0.373814i	0.982195	+	0.187863i	$0.0601562\pi$
$38$		−	5.89883i		−	0.956917i
$39$	−1.13702	−	0.470968i	−0.182069	−	0.0754153i
$40$	−2.00672	−	4.84464i	−0.317290	−	0.766005i
$41$	9.31001	−	3.85633i	1.45398	−	0.602258i	0.490837	−	0.871252i	$-0.336691\pi$
$41$	9.31001	−	3.85633i	1.45398	−	0.602258i	0.963142	+	0.268994i	$0.0866911\pi$
$42$	0.764267	+	0.764267i	0.117929	+	0.117929i
$43$	−5.14399	−	5.14399i	−0.784451	−	0.784451i	0.196128	−	0.980578i	$-0.437163\pi$
$43$	−5.14399	−	5.14399i	−0.784451	−	0.784451i	−0.980578	+	0.196128i	$0.937163\pi$
$44$	−4.74444	+	1.96521i	−0.715251	+	0.296267i
$45$	0.655638	+	1.58285i	0.0977368	+	0.235957i
$46$	7.70230	+	3.19040i	1.13564	+	0.470398i
$47$		−	5.99099i		−	0.873876i	−0.899492	−	0.436938i	$-0.856063\pi$
$47$		−	5.99099i		−	0.873876i	0.899492	−	0.436938i	$-0.143937\pi$
$48$	−0.629336	+	1.51935i	−0.0908369	+	0.219300i
$49$	0.707107	−	0.707107i	0.101015	−	0.101015i
$50$	−2.23163			−0.315600
$51$	−1.58315	−	3.80705i	−0.221685	−	0.533094i
$52$	−1.02369			−0.141960
$53$	6.56019	−	6.56019i	0.901112	−	0.901112i	−0.0944208	−	0.995532i	$-0.530100\pi$
$53$	6.56019	−	6.56019i	0.901112	−	0.901112i	0.995532	+	0.0944208i	$0.0300999\pi$
$54$	0.413618	−	0.998563i	0.0562863	−	0.135887i
$55$		−	10.5774i		−	1.42626i
$56$	2.82772	+	1.17128i	0.377870	+	0.156519i
$57$	2.08855	+	5.04222i	0.276636	+	0.667858i
$58$	−3.98173	+	1.64929i	−0.522827	+	0.216562i
$59$	−7.34731	−	7.34731i	−0.956538	−	0.956538i	0.0425558	−	0.999094i	$-0.486450\pi$
$59$	−7.34731	−	7.34731i	−0.956538	−	0.956538i	−0.999094	+	0.0425558i	$0.986450\pi$
$60$	1.00768	+	1.00768i	0.130092	+	0.130092i
$61$	−7.67745	+	3.18010i	−0.982997	+	0.407171i	−0.815535	−	0.578708i	$-0.803557\pi$
$61$	−7.67745	+	3.18010i	−0.982997	+	0.407171i	−0.167462	+	0.985879i	$0.553557\pi$
$62$	−1.18674	−	2.86504i	−0.150716	−	0.363860i
$63$	−0.923880	−	0.382683i	−0.116398	−	0.0482136i
$64$			7.98415i			0.998019i
$65$	0.806894	−	1.94801i	0.100083	−	0.241621i
$66$	−4.71845	+	4.71845i	−0.580801	+	0.580801i
$67$	10.9203			1.33413			0.667064	−	0.745001i	$-0.267551\pi$
$67$	10.9203			1.33413			0.667064	+	0.745001i	$0.267551\pi$
$68$	−2.42845	−	2.42169i	−0.294493	−	0.293673i
$69$	−7.71339			−0.928583
$70$	−1.30939	+	1.30939i	−0.156502	+	0.156502i
$71$	−1.37278	+	3.31420i	−0.162920	+	0.393323i	−0.984166	−	0.177252i	$-0.943279\pi$
$71$	−1.37278	+	3.31420i	−0.162920	+	0.393323i	0.821246	+	0.570574i	$0.193279\pi$
$72$		−	3.06070i		−	0.360707i
$73$	9.26092	+	3.83600i	1.08391	+	0.448970i	0.851879	−	0.523739i	$-0.175463\pi$
$73$	9.26092	+	3.83600i	1.08391	+	0.448970i	0.232030	+	0.972709i	$0.425463\pi$
$74$	−1.01798	−	2.45763i	−0.118338	−	0.285694i
$75$	1.90755	−	0.790135i	0.220265	−	0.0912369i
$76$	3.21001	+	3.21001i	0.368213	+	0.368213i
$77$	4.36555	+	4.36555i	0.497501	+	0.497501i
$78$	−1.22893	+	0.509040i	−0.139149	+	0.0576374i
$79$	−3.62512	−	8.75181i	−0.407858	−	0.984655i	−0.985700	−	0.168507i	$-0.946105\pi$
$79$	−3.62512	−	8.75181i	−0.407858	−	0.984655i	0.577843	−	0.816148i	$-0.303895\pi$
$80$	−2.60305	−	1.07822i	−0.291030	−	0.120549i
$81$			1.00000i			0.111111i
$82$	4.16806	−	10.0626i	0.460286	−	1.11123i
$83$	−2.97117	+	2.97117i	−0.326128	+	0.326128i	−0.851112	−	0.524984i	$-0.824071\pi$
$83$	−2.97117	+	2.97117i	−0.326128	+	0.326128i	0.524984	+	0.851112i	$0.324071\pi$
$84$	−0.831793			−0.0907560
$85$	6.52249	−	2.71236i	0.707463	−	0.294196i
$86$	−7.86276			−0.847863
$87$	2.81956	−	2.81956i	0.302289	−	0.302289i
$88$	−7.23129	+	17.4579i	−0.770858	+	1.86102i
$89$			6.50588i			0.689622i	0.938672	+	0.344811i	$0.112057\pi$
$89$			6.50588i			0.689622i	−0.938672	+	0.344811i	$0.887943\pi$
$90$	1.71080	+	0.708638i	0.180334	+	0.0746970i
$91$	0.470968	+	1.13702i	0.0493709	+	0.119192i
$92$	−5.92756	+	2.45527i	−0.617990	+	0.255980i
$93$	2.02880	+	2.02880i	0.210377	+	0.210377i
$94$	−4.57871	−	4.57871i	−0.472258	−	0.472258i
$95$	−8.63866	+	3.57825i	−0.886307	+	0.367121i
$96$	−1.66235	−	4.01327i	−0.169663	−	0.409603i
$97$	−1.20637	−	0.499696i	−0.122489	−	0.0507364i	0.320597	−	0.947216i	$-0.396116\pi$
$97$	−1.20637	−	0.499696i	−0.122489	−	0.0507364i	−0.443086	+	0.896479i	$0.646116\pi$
$98$		−	1.08084i		−	0.109181i
$99$	2.36262	−	5.70387i	0.237452	−	0.573261i
$100$	1.21440	−	1.21440i	0.121440	−	0.121440i
$101$	−14.7166			−1.46436			−0.732179	−	0.681112i	$-0.761497\pi$
$101$	−14.7166			−1.46436			−0.732179	+	0.681112i	$0.761497\pi$
$102$	−4.11955	−	1.69965i	−0.407896	−	0.168291i
$103$	5.63127			0.554865			0.277433	−	0.960745i	$-0.410516\pi$
$103$	5.63127			0.554865			0.277433	+	0.960745i	$0.410516\pi$
$104$	−2.66354	+	2.66354i	−0.261181	+	0.261181i
$105$	0.655638	−	1.58285i	0.0639837	−	0.154470i
$106$		−	10.0275i		−	0.973954i
$107$	3.93575	+	1.63024i	0.380483	+	0.157601i	0.564724	−	0.825280i	$-0.308983\pi$
$107$	3.93575	+	1.63024i	0.380483	+	0.157601i	−0.184241	+	0.982881i	$0.558983\pi$
$108$	0.318313	+	0.768476i	0.0306297	+	0.0739467i
$109$	10.3038	−	4.26799i	0.986929	−	0.408800i	0.169941	−	0.985454i	$-0.445642\pi$
$109$	10.3038	−	4.26799i	0.986929	−	0.408800i	0.816988	+	0.576655i	$0.195642\pi$
$110$	−8.08396	−	8.08396i	−0.770775	−	0.770775i
$111$	1.74031	+	1.74031i	0.165183	+	0.165183i
$112$	1.51935	−	0.629336i	0.143565	−	0.0594667i
$113$	1.14109	+	2.75483i	0.107344	+	0.259152i	0.968420	−	0.249325i	$-0.0802086\pi$
$113$	1.14109	+	2.75483i	0.107344	+	0.259152i	−0.861075	+	0.508477i	$0.830209\pi$
$114$	5.44981	+	2.25739i	0.510422	+	0.211424i
$115$		−	13.2151i		−	1.23231i
$116$	1.26926	−	3.06427i	0.117848	−	0.284510i
$117$	0.870236	−	0.870236i	0.0804534	−	0.0804534i
$118$	−11.2306			−1.03386
$119$	−1.57254	+	3.81145i	−0.144154	+	0.349395i
$120$	5.24380			0.478691
$121$	−19.1740	+	19.1740i	−1.74309	+	1.74309i
$122$	−3.43717	+	8.29807i	−0.311187	+	0.751272i
$123$			10.0771i			0.908620i
$124$	2.20488	+	0.913292i	0.198004	+	0.0820160i
$125$	4.63190	+	11.1824i	0.414290	+	1.00018i
$126$	−0.998563	+	0.413618i	−0.0889590	+	0.0368480i
$127$	6.32389	+	6.32389i	0.561154	+	0.561154i	0.929635	−	0.368481i	$-0.120122\pi$
$127$	6.32389	+	6.32389i	0.561154	+	0.561154i	−0.368481	+	0.929635i	$0.620122\pi$
$128$	−0.0412292	−	0.0412292i	−0.00364418	−	0.00364418i
$129$	6.72094	−	2.78391i	0.591746	−	0.245109i
$130$	−0.872120	−	2.10548i	−0.0764900	−	0.184663i
$131$	−0.509587	−	0.211078i	−0.0445228	−	0.0184419i	0.360311	−	0.932832i	$-0.382671\pi$
$131$	−0.509587	−	0.211078i	−0.0445228	−	0.0184419i	−0.404834	+	0.914390i	$0.632671\pi$
$132$		−	5.13534i		−	0.446974i
$133$	2.08855	−	5.04222i	0.181101	−	0.437216i
$134$	8.34602	−	8.34602i	0.720987	−	0.720987i
$135$	−1.71327			−0.147454
$136$	−12.6196	+	0.0175814i	−1.08212	+	0.00150760i
$137$	13.0418			1.11423			0.557117	−	0.830434i	$-0.311907\pi$
$137$	13.0418			1.11423			0.557117	+	0.830434i	$0.311907\pi$
$138$	−5.89509	+	5.89509i	−0.501823	+	0.501823i
$139$	−6.14565	+	14.8369i	−0.521267	+	1.25845i	0.415850	+	0.909433i	$0.363484\pi$
$139$	−6.14565	+	14.8369i	−0.521267	+	1.25845i	−0.937117	+	0.349016i	$0.886516\pi$
$140$		−	1.42508i		−	0.120441i
$141$	5.53495	+	2.29265i	0.466127	+	0.193076i
$142$	1.48376	+	3.58210i	0.124514	+	0.300603i
$143$	−7.01976	+	2.90768i	−0.587021	+	0.243152i
$144$	−1.16286	−	1.16286i	−0.0969052	−	0.0969052i
$145$	4.83065	+	4.83065i	0.401164	+	0.401164i
$146$	10.0095	−	4.14609i	0.828395	−	0.343133i
$147$	0.382683	+	0.923880i	0.0315632	+	0.0762003i
$148$	1.89135	+	0.783423i	0.155468	+	0.0643970i
$149$		−	23.0108i		−	1.88512i	−0.334044	−	0.942558i	$-0.608413\pi$
$149$		−	23.0108i		−	1.88512i	0.334044	−	0.942558i	$-0.391587\pi$
$150$	0.854006	−	2.06175i	0.0697293	−	0.168341i
$151$	13.0894	−	13.0894i	1.06520	−	1.06520i	0.0674800	−	0.997721i	$-0.478504\pi$
$151$	13.0894	−	13.0894i	1.06520	−	1.06520i	0.997721	−	0.0674800i	$-0.0214959\pi$
$152$	16.7043			1.35490
$153$	4.12310	−	0.00574424i	0.333333	−	0.000464395i
$154$	6.67290			0.537717
$155$	−3.47588	+	3.47588i	−0.279189	+	0.279189i
$156$	0.391748	−	0.945764i	0.0313650	−	0.0757217i
$157$		−	14.6547i		−	1.16957i	−0.811188	−	0.584786i	$-0.801178\pi$
$157$		−	14.6547i		−	1.16957i	0.811188	−	0.584786i	$-0.198822\pi$
$158$	−9.45927	−	3.91816i	−0.752539	−	0.311712i
$159$	3.55035	+	8.57130i	0.281561	+	0.679749i
$160$	6.87580	−	2.84805i	0.543580	−	0.225158i
$161$	5.45419	+	5.45419i	0.429850	+	0.429850i
$162$	0.764267	+	0.764267i	0.0600465	+	0.0600465i
$163$	−13.0988	+	5.42570i	−1.02598	+	0.424974i	−0.831259	−	0.555886i	$-0.812379\pi$
$163$	−13.0988	+	5.42570i	−1.02598	+	0.424974i	−0.194718	+	0.980859i	$0.562379\pi$
$164$	3.20767	+	7.74400i	0.250477	+	0.604704i
$165$	9.77225	+	4.04780i	0.760768	+	0.315121i
$166$			4.54153i			0.352491i
$167$	7.47951	−	18.0571i	0.578782	−	1.39730i	−0.315125	−	0.949050i	$-0.602046\pi$
$167$	7.47951	−	18.0571i	0.578782	−	1.39730i	0.893907	−	0.448253i	$-0.147954\pi$
$168$	−2.16424	+	2.16424i	−0.166975	+	0.166975i
$169$	11.4854			0.883491
$170$	2.91196	−	7.05788i	0.223337	−	0.541315i
$171$	−5.45766			−0.417357
$172$	4.27873	−	4.27873i	0.326250	−	0.326250i
$173$	−5.41037	+	13.0618i	−0.411343	+	0.993069i	0.573435	+	0.819251i	$0.305610\pi$
$173$	−5.41037	+	13.0618i	−0.411343	+	0.993069i	−0.984778	+	0.173818i	$0.944390\pi$
$174$		−	4.30979i		−	0.326724i
$175$	−1.90755	−	0.790135i	−0.144198	−	0.0597286i
$176$	3.88541	+	9.38022i	0.292874	+	0.707061i
$177$	9.59972	−	3.97634i	0.721559	−	0.298880i
$178$	4.97223	+	4.97223i	0.372684	+	0.372684i
$179$	−1.79479	−	1.79479i	−0.134149	−	0.134149i	0.636844	−	0.770993i	$-0.280240\pi$
$179$	−1.79479	−	1.79479i	−0.134149	−	0.134149i	−0.770993	+	0.636844i	$0.780240\pi$
$180$	−1.31660	+	0.545355i	−0.0981339	+	0.0406484i
$181$	1.52091	+	3.67179i	0.113048	+	0.272922i	0.970270	−	0.242025i	$-0.0778116\pi$
$181$	1.52091	+	3.67179i	0.113048	+	0.272922i	−0.857222	+	0.514947i	$0.827812\pi$
$182$	1.22893	+	0.509040i	0.0910944	+	0.0377325i
$183$		−	8.31001i		−	0.614294i
$184$	−9.03454	+	21.8113i	−0.666035	+	1.60795i
$185$	−2.98161	+	2.98161i	−0.219212	+	0.219212i
$186$	3.10109			0.227383
$187$	−23.5312	−	9.70856i	−1.72077	−	0.709960i
$188$	4.98326			0.363442
$189$	0.707107	−	0.707107i	0.0514344	−	0.0514344i
$190$	−3.86750	+	9.33697i	−0.280578	+	0.677375i
$191$		−	15.4058i		−	1.11473i	−0.830269	−	0.557363i	$-0.811813\pi$
$191$		−	15.4058i		−	1.11473i	0.830269	−	0.557363i	$-0.188187\pi$
$192$	−7.37640	−	3.05540i	−0.532346	−	0.220505i
$193$	3.03104	+	7.31758i	0.218179	+	0.526731i	0.994636	−	0.103440i	$-0.0329850\pi$
$193$	3.03104	+	7.31758i	0.218179	+	0.526731i	−0.776457	+	0.630171i	$0.782985\pi$
$194$	−1.30389	+	0.540089i	−0.0936139	+	0.0387762i
$195$	1.49095	+	1.49095i	0.106769	+	0.106769i
$196$	0.588166	+	0.588166i	0.0420119	+	0.0420119i
$197$	−2.30108	+	0.953139i	−0.163945	+	0.0679084i	−0.463147	−	0.886282i	$-0.653280\pi$
$197$	−2.30108	+	0.953139i	−0.163945	+	0.0679084i	0.299201	+	0.954190i	$0.403280\pi$
$198$	−2.55361	−	6.16495i	−0.181477	−	0.438124i
$199$	−16.6522	−	6.89757i	−1.18044	−	0.488955i	−0.295811	−	0.955246i	$-0.595590\pi$
$199$	−16.6522	−	6.89757i	−1.18044	−	0.488955i	−0.884631	+	0.466291i	$0.845590\pi$
$200$		−	6.31950i		−	0.446856i
$201$	−4.17902	+	10.0890i	−0.294765	+	0.711626i
$202$	−11.2474	+	11.2474i	−0.791366	+	0.791366i
$203$	−3.98746			−0.279865
$204$	3.16668	−	1.31685i	0.221712	−	0.0921981i
$205$	−17.2647			−1.20582
$206$	4.30379	−	4.30379i	0.299859	−	0.299859i
$207$	2.95179	−	7.12624i	0.205163	−	0.495308i
$208$			2.02393i			0.140334i
$209$	31.1298	+	12.8944i	2.15329	+	0.891923i
$210$	−0.708638	−	1.71080i	−0.0489006	−	0.118057i
$211$	5.09644	−	2.11102i	0.350853	−	0.145328i	−0.200295	−	0.979736i	$-0.564190\pi$
$211$	5.09644	−	2.11102i	0.350853	−	0.145328i	0.551148	+	0.834407i	$0.314190\pi$
$212$	5.45672	+	5.45672i	0.374769	+	0.374769i
$213$	−2.53658	−	2.53658i	−0.173803	−	0.173803i
$214$	4.25390	−	1.76202i	0.290791	−	0.120449i
$215$	4.76957	+	11.5148i	0.325282	+	0.785300i
$216$	2.82772	+	1.17128i	0.192402	+	0.0796956i
$217$		−	2.86916i		−	0.194771i
$218$	4.61300	−	11.1368i	0.312432	−	0.754277i
$219$	−7.08800	+	7.08800i	−0.478963	+	0.478963i
$220$	8.79821			0.593175
$221$	−3.59307	−	3.58307i	−0.241696	−	0.241024i
$222$	2.66012			0.178536
$223$	7.51995	−	7.51995i	0.503573	−	0.503573i	−0.408973	−	0.912546i	$-0.634113\pi$
$223$	7.51995	−	7.51995i	0.503573	−	0.503573i	0.912546	+	0.408973i	$0.134113\pi$
$224$	−1.66235	+	4.01327i	−0.111071	+	0.268148i
$225$			2.06472i			0.137648i
$226$	2.97752	+	1.23333i	0.198062	+	0.0820398i
$227$	2.00155	+	4.83217i	0.132847	+	0.320722i	0.976280	−	0.216514i	$-0.0694685\pi$
$227$	2.00155	+	4.83217i	0.132847	+	0.320722i	−0.843432	+	0.537236i	$0.819469\pi$
$228$	−4.19408	+	1.73724i	−0.277760	+	0.115052i
$229$	5.68396	+	5.68396i	0.375607	+	0.375607i	0.869514	−	0.493908i	$-0.164432\pi$
$229$	5.68396	+	5.68396i	0.375607	+	0.375607i	−0.493908	+	0.869514i	$0.664432\pi$
$230$	−10.0998	−	10.0998i	−0.665964	−	0.665964i
$231$	−5.70387	+	2.36262i	−0.375287	+	0.155449i
$232$	−4.67044	−	11.2754i	−0.306629	−	0.740268i
$233$	17.2885	+	7.16114i	1.13261	+	0.469142i	0.868667	−	0.495397i	$-0.164977\pi$
$233$	17.2885	+	7.16114i	1.13261	+	0.469142i	0.263942	+	0.964539i	$0.414977\pi$
$234$		−	1.33019i		−	0.0869569i
$235$	−3.92792	+	9.48284i	−0.256229	+	0.618592i
$236$	6.11144	−	6.11144i	0.397821	−	0.397821i
$237$	9.47289			0.615330
$238$	1.71113	+	4.11480i	0.110916	+	0.266723i
$239$	−5.20254			−0.336524			−0.168262	−	0.985742i	$-0.553816\pi$
$239$	−5.20254			−0.336524			−0.168262	+	0.985742i	$0.553816\pi$
$240$	1.99229	−	1.99229i	0.128602	−	0.128602i
$241$	4.08378	−	9.85912i	0.263059	−	0.635082i	−0.736065	−	0.676910i	$-0.763318\pi$
$241$	4.08378	−	9.85912i	0.263059	−	0.635082i	0.999125	+	0.0418288i	$0.0133184\pi$
$242$			29.3081i			1.88400i
$243$	−0.923880	−	0.382683i	−0.0592669	−	0.0245492i
$244$	−2.64519	−	6.38605i	−0.169341	−	0.408825i
$245$	−1.58285	+	0.655638i	−0.101125	+	0.0418872i
$246$	7.70158	+	7.70158i	0.491035	+	0.491035i
$247$	4.74945	+	4.74945i	0.302200	+	0.302200i
$248$	8.11319	−	3.36059i	0.515188	−	0.213398i
$249$	−1.60799	−	3.88202i	−0.101902	−	0.246013i
$250$	12.0863	+	5.00633i	0.764408	+	0.316628i
$251$			9.54484i			0.602465i	0.953551	+	0.301232i	$0.0973980\pi$
$251$			9.54484i			0.602465i	−0.953551	+	0.301232i	$0.902602\pi$
$252$	0.318313	−	0.768476i	0.0200519	−	0.0484095i
$253$	−33.6732	+	33.6732i	−2.11702	+	2.11702i
$254$	9.66628			0.606516
$255$	0.00984141	+	7.06397i	0.000616293	+	0.442363i
$256$	−16.0313			−1.00196
$257$	−12.9232	+	12.9232i	−0.806127	+	0.806127i	−0.984045	−	0.177919i	$-0.943064\pi$
$257$	−12.9232	+	12.9232i	−0.806127	+	0.806127i	0.177919	+	0.984045i	$0.443064\pi$
$258$	3.00895	−	7.26424i	0.187329	−	0.452252i
$259$		−	2.46117i		−	0.152930i
$260$	1.62034	+	0.671169i	0.100489	+	0.0416241i
$261$	1.52593	+	3.68393i	0.0944530	+	0.228030i
$262$	−0.550780	+	0.228140i	−0.0340273	+	0.0140946i
$263$	−8.73547	−	8.73547i	−0.538652	−	0.538652i	0.384481	−	0.923133i	$-0.374380\pi$
$263$	−8.73547	−	8.73547i	−0.538652	−	0.538652i	−0.923133	+	0.384481i	$0.874380\pi$
$264$	−13.3617	−	13.3617i	−0.822354	−	0.822354i
$265$	−14.6849	+	6.08269i	−0.902087	+	0.373657i
$266$	−2.25739	−	5.44981i	−0.138409	−	0.334149i
$267$	−6.01065	−	2.48969i	−0.367846	−	0.152367i
$268$			9.08343i			0.554859i
$269$	3.60406	−	8.70098i	0.219744	−	0.530508i	−0.775110	−	0.631826i	$-0.782306\pi$
$269$	3.60406	−	8.70098i	0.219744	−	0.530508i	0.994854	+	0.101318i	$0.0323058\pi$
$270$	−1.30939	+	1.30939i	−0.0796870	+	0.0796870i
$271$	18.9261			1.14968			0.574840	−	0.818266i	$-0.305064\pi$
$271$	18.9261			1.14968			0.574840	+	0.818266i	$0.305064\pi$
$272$	−4.78792	+	4.80128i	−0.290310	+	0.291120i
$273$	−1.23070			−0.0744853
$274$	9.96739	−	9.96739i	0.602152	−	0.602152i
$275$	4.87816	−	11.7769i	0.294164	−	0.710174i
$276$		−	6.41594i		−	0.386194i
$277$	−11.6847	−	4.83995i	−0.702064	−	0.290805i	0.00295204	−	0.999996i	$-0.499060\pi$
$277$	−11.6847	−	4.83995i	−0.702064	−	0.290805i	−0.705016	+	0.709191i	$0.749060\pi$
$278$	6.64244	+	16.0363i	0.398387	+	0.961791i
$279$	−2.65076	+	1.09798i	−0.158697	+	0.0657344i
$280$	−3.70793	−	3.70793i	−0.221591	−	0.221591i
$281$	−9.53972	−	9.53972i	−0.569092	−	0.569092i	0.362782	−	0.931874i	$-0.381827\pi$
$281$	−9.53972	−	9.53972i	−0.569092	−	0.569092i	−0.931874	+	0.362782i	$0.881827\pi$
$282$	5.98238	−	2.47798i	0.356245	−	0.147562i
$283$	2.15463	+	5.20173i	0.128079	+	0.309211i	0.974891	−	0.222682i	$-0.0714810\pi$
$283$	2.15463	+	5.20173i	0.128079	+	0.309211i	−0.846812	+	0.531893i	$0.821481\pi$
$284$	−2.75672	−	1.14187i	−0.163581	−	0.0677577i
$285$		−	9.35041i		−	0.553871i
$286$	−3.14272	+	7.58721i	−0.185833	+	0.448641i
$287$	7.12557	−	7.12557i	0.420609	−	0.420609i
$288$	4.34394			0.255969
$289$	−0.0473682	−	16.9999i	−0.00278636	−	0.999996i
$290$	7.38382			0.433593
$291$	0.923318	−	0.923318i	0.0541258	−	0.0541258i
$292$	−3.19076	+	7.70317i	−0.186725	+	0.450794i
$293$			23.5739i			1.37720i	0.725141	+	0.688600i	$0.241775\pi$
$293$			23.5739i			1.37720i	−0.725141	+	0.688600i	$0.758225\pi$
$294$	0.998563	+	0.413618i	0.0582374	+	0.0241227i
$295$	6.81252	+	16.4469i	0.396640	+	0.957574i
$296$	6.95950	−	2.88272i	0.404513	−	0.167555i
$297$	4.36555	+	4.36555i	0.253315	+	0.253315i
$298$	−17.5864	−	17.5864i	−1.01875	−	1.01875i
$299$	−8.77026	+	3.63276i	−0.507197	+	0.210088i
$300$	0.657228	+	1.58669i	0.0379451	+	0.0916076i
$301$	−6.72094	−	2.78391i	−0.387389	−	0.160462i
$302$		−	20.0076i		−	1.15131i
$303$	5.63181	−	13.5964i	0.323539	−	0.781092i
$304$	6.34650	−	6.34650i	0.363997	−	0.363997i
$305$	14.2373			0.815223
$306$	3.14676	−	3.15554i	0.179888	−	0.180390i
$307$	−16.9298			−0.966236			−0.483118	−	0.875555i	$-0.660496\pi$
$307$	−16.9298			−0.966236			−0.483118	+	0.875555i	$0.660496\pi$
$308$	−3.63124	+	3.63124i	−0.206909	+	0.206909i
$309$	−2.15499	+	5.20261i	−0.122593	+	0.295966i
$310$			5.31300i			0.301758i
$311$	−28.5865	−	11.8409i	−1.62099	−	0.671436i	−0.626811	−	0.779171i	$-0.715640\pi$
$311$	−28.5865	−	11.8409i	−1.62099	−	0.671436i	−0.994180	+	0.107735i	$0.965640\pi$
$312$	−1.44150	−	3.48008i	−0.0816086	−	0.197021i
$313$	−25.2609	+	10.4634i	−1.42783	+	0.591426i	−0.956815	−	0.290699i	$-0.906112\pi$
$313$	−25.2609	+	10.4634i	−1.42783	+	0.591426i	−0.471015	+	0.882125i	$0.656112\pi$
$314$	−11.2001	−	11.2001i	−0.632058	−	0.632058i
$315$	1.21146	+	1.21146i	0.0682581	+	0.0682581i
$316$	7.27969	−	3.01535i	0.409514	−	0.169626i
$317$	5.04086	+	12.1697i	0.283123	+	0.683520i	0.999905	−	0.0137777i	$-0.00438571\pi$
$317$	5.04086	+	12.1697i	0.283123	+	0.683520i	−0.716782	+	0.697297i	$0.754386\pi$
$318$	9.26418	+	3.83735i	0.519509	+	0.215188i
$319$		−	24.6179i		−	1.37834i
$320$	5.23472	−	12.6377i	0.292630	−	0.706470i
$321$	−3.01229	+	3.01229i	−0.168130	+	0.168130i
$322$	8.33691			0.464598
$323$	0.0313501	+	22.5025i	0.00174437	+	1.25207i
$324$	−0.831793			−0.0462107
$325$	1.79680	−	1.79680i	0.0996683	−	0.0996683i
$326$	−5.86429	+	14.1577i	−0.324793	+	0.784120i
$327$			11.1528i			0.616751i
$328$	28.4952	+	11.8031i	1.57338	+	0.651717i
$329$	−2.29265	−	5.53495i	−0.126398	−	0.305152i
$330$	10.5622	−	4.37501i	0.581430	−	0.240836i
$331$	−16.4994	−	16.4994i	−0.906887	−	0.906887i	0.0891328	−	0.996020i	$-0.471590\pi$
$331$	−16.4994	−	16.4994i	−0.906887	−	0.906887i	−0.996020	+	0.0891328i	$0.971590\pi$
$332$	−2.47140	−	2.47140i	−0.135636	−	0.135636i
$333$	−2.27382	+	0.941849i	−0.124605	+	0.0516130i
$334$	−8.08413	−	19.5168i	−0.442344	−	1.06791i
$335$	−17.2852	−	7.15977i	−0.944392	−	0.391180i
$336$			1.64454i			0.0897168i
$337$	1.00554	−	2.42759i	0.0547753	−	0.132239i	−0.894123	−	0.447822i	$-0.852200\pi$
$337$	1.00554	−	2.42759i	0.0547753	−	0.132239i	0.948898	+	0.315583i	$0.102200\pi$
$338$	8.77789	−	8.77789i	0.477454	−	0.477454i
$339$	−2.98181			−0.161949
$340$	2.25612	+	5.42536i	0.122355	+	0.294231i
$341$	17.7137			0.959251
$342$	−4.17111	+	4.17111i	−0.225548	+	0.225548i
$343$	0.382683	−	0.923880i	0.0206630	−	0.0498848i
$344$		−	22.2657i		−	1.20049i
$345$	12.2091	+	5.05719i	0.657318	+	0.272270i
$346$	5.84772	+	14.1177i	0.314376	+	0.758970i
$347$	6.36523	−	2.63656i	0.341703	−	0.141538i	−0.205231	−	0.978714i	$-0.565795\pi$
$347$	6.36523	−	2.63656i	0.341703	−	0.141538i	0.546935	+	0.837175i	$0.315795\pi$
$348$	2.34529	+	2.34529i	0.125721	+	0.125721i
$349$	−2.18617	−	2.18617i	−0.117023	−	0.117023i	0.646170	−	0.763193i	$-0.276370\pi$
$349$	−2.18617	−	2.18617i	−0.117023	−	0.117023i	−0.763193	+	0.646170i	$0.776370\pi$
$350$	−2.06175	+	0.854006i	−0.110205	+	0.0456486i
$351$	0.470968	+	1.13702i	0.0251384	+	0.0606896i
$352$	−24.7773	−	10.2631i	−1.32063	−	0.547024i
$353$		−	3.34967i		−	0.178285i	−0.996019	−	0.0891424i	$-0.971587\pi$
$353$		−	3.34967i		−	0.178285i	0.996019	−	0.0891424i	$-0.0284126\pi$
$354$	4.29777	−	10.3757i	0.228424	−	0.551464i
$355$	4.34583	−	4.34583i	0.230653	−	0.230653i
$356$	−5.41154			−0.286811
$357$	−2.91953	−	2.91141i	−0.154518	−	0.154088i
$358$	−2.74339			−0.144993
$359$	14.7391	−	14.7391i	0.777898	−	0.777898i	−0.201575	−	0.979473i	$-0.564606\pi$
$359$	14.7391	−	14.7391i	0.777898	−	0.777898i	0.979473	+	0.201575i	$0.0646059\pi$
$360$	−2.00672	+	4.84464i	−0.105763	+	0.255335i
$361$		−	10.7860i		−	0.567685i
$362$	3.96860	+	1.64385i	0.208585	+	0.0863988i
$363$	−10.3769	−	25.0520i	−0.544646	−	1.31489i
$364$	−0.945764	+	0.391748i	−0.0495715	+	0.0205332i
$365$	−12.1436	−	12.1436i	−0.635627	−	0.635627i
$366$	−6.35106	−	6.35106i	−0.331975	−	0.331975i
$367$	14.3031	−	5.92454i	0.746615	−	0.309258i	0.0232557	−	0.999730i	$-0.492597\pi$
$367$	14.3031	−	5.92454i	0.746615	−	0.309258i	0.723360	+	0.690471i	$0.242597\pi$
$368$	4.85432	+	11.7194i	0.253049	+	0.610914i
$369$	−9.31001	−	3.85633i	−0.484660	−	0.200753i
$370$			4.55749i			0.236933i
$371$	3.55035	−	8.57130i	0.184325	−	0.445000i
$372$	−1.68754	+	1.68754i	−0.0874951	+	0.0874951i
$373$	13.5924			0.703787			0.351893	−	0.936040i	$-0.385538\pi$
$373$	13.5924			0.703787			0.351893	+	0.936040i	$0.385538\pi$
$374$	−25.4041	+	10.5642i	−1.31361	+	0.546261i
$375$	−12.1037			−0.625035
$376$	12.9660	−	12.9660i	0.668669	−	0.668669i
$377$	1.87797	−	4.53382i	0.0967203	−	0.233503i
$378$		−	1.08084i		−	0.0555922i
$379$	−27.5636	−	11.4172i	−1.41585	−	0.586463i	−0.462033	−	0.886862i	$-0.652880\pi$
$379$	−27.5636	−	11.4172i	−1.41585	−	0.586463i	−0.953813	+	0.300399i	$0.902880\pi$
$380$	−2.97636	−	7.18557i	−0.152684	−	0.368612i
$381$	−8.26256	+	3.42246i	−0.423304	+	0.175338i
$382$	−11.7741	−	11.7741i	−0.602418	−	0.602418i
$383$	12.1284	+	12.1284i	0.619735	+	0.619735i	0.945463	−	0.325729i	$-0.105610\pi$
$383$	12.1284	+	12.1284i	0.619735	+	0.619735i	−0.325729	+	0.945463i	$0.605610\pi$
$384$	0.0538685	−	0.0223131i	0.00274897	−	0.00113866i
$385$	−4.04780	−	9.77225i	−0.206295	−	0.498040i
$386$	7.90910	+	3.27606i	0.402563	+	0.166747i
$387$			7.27470i			0.369794i
$388$	0.415643	−	1.00345i	0.0211011	−	0.0509426i
$389$	−18.4139	+	18.4139i	−0.933619	+	0.933619i	−0.997930	−	0.0643106i	$-0.979515\pi$
$389$	−18.4139	+	18.4139i	−0.933619	+	0.933619i	0.0643106	+	0.997930i	$0.479515\pi$
$390$	2.27896			0.115400
$391$	−29.3992	−	12.1296i	−1.48678	−	0.613419i
$392$	3.06070			0.154589
$393$	0.390021	−	0.390021i	0.0196739	−	0.0196739i
$394$	−1.03019	+	2.48709i	−0.0519001	+	0.125298i
$395$			16.2296i			0.816598i
$396$	4.74444	+	1.96521i	0.238417	+	0.0987556i
$397$	−7.95372	−	19.2020i	−0.399186	−	0.963719i	−0.987860	−	0.155349i	$-0.950350\pi$
$397$	−7.95372	−	19.2020i	−0.399186	−	0.963719i	0.588674	−	0.808371i	$-0.299650\pi$
$398$	−17.9983	+	7.45514i	−0.902173	+	0.373692i
$399$	3.85915	+	3.85915i	0.193199	+	0.193199i
$400$	−2.40099	−	2.40099i	−0.120049	−	0.120049i
$401$	−11.6722	+	4.83476i	−0.582880	+	0.241437i	−0.654584	−	0.755989i	$-0.727156\pi$
$401$	−11.6722	+	4.83476i	−0.582880	+	0.241437i	0.0717044	+	0.997426i	$0.477156\pi$
$402$	4.51683	+	10.9046i	0.225279	+	0.543872i
$403$	3.26229	+	1.35128i	0.162506	+	0.0673123i
$404$		−	12.2412i		−	0.609021i
$405$	0.655638	−	1.58285i	0.0325789	−	0.0786525i
$406$	−3.04748	+	3.04748i	−0.151244	+	0.151244i
$407$	15.1948			0.753180
$408$	4.81307	−	11.6657i	0.238282	−	0.577539i
$409$	20.6540			1.02128			0.510638	−	0.859796i	$-0.329409\pi$
$409$	20.6540			1.02128			0.510638	+	0.859796i	$0.329409\pi$
$410$	−13.1948	+	13.1948i	−0.651647	+	0.651647i
$411$	−4.99087	+	12.0490i	−0.246182	+	0.594335i
$412$			4.68405i			0.230767i
$413$	−9.59972	−	3.97634i	−0.472371	−	0.195663i
$414$	−3.19040	−	7.70230i	−0.156799	−	0.378547i
$415$	6.65093	−	2.75491i	0.326481	−	0.135233i
$416$	−3.78025	−	3.78025i	−0.185342	−	0.185342i
$417$	−11.3557	−	11.3557i	−0.556090	−	0.556090i
$418$	33.6462	−	13.9367i	1.64569	−	0.681667i
$419$	−2.60192	−	6.28158i	−0.127112	−	0.306875i	0.847493	−	0.530806i	$-0.178111\pi$
$419$	−2.60192	−	6.28158i	−0.127112	−	0.306875i	−0.974605	+	0.223931i	$0.928111\pi$
$420$	1.31660	+	0.545355i	0.0642437	+	0.0266106i
$421$			31.1895i			1.52008i	0.649875	+	0.760041i	$0.274821\pi$
$421$			31.1895i			1.52008i	−0.649875	+	0.760041i	$0.725179\pi$
$422$	2.28166	−	5.50842i	0.111070	−	0.268146i
$423$	−4.23627	+	4.23627i	−0.205974	+	0.205974i
$424$	28.3957			1.37902
$425$	8.51306	−	0.0118603i	0.412944	−	0.000575307i
$426$	−3.87724			−0.187853
$427$	−5.87606	+	5.87606i	−0.284363	+	0.284363i
$428$	−1.35602	+	3.27373i	−0.0655458	+	0.158242i
$429$		−	7.59813i		−	0.366841i
$430$	12.4456	+	5.15513i	0.600179	+	0.248602i
$431$	−6.77154	−	16.3479i	−0.326173	−	0.787452i	−0.998870	−	0.0475336i	$-0.984864\pi$
$431$	−6.77154	−	16.3479i	−0.326173	−	0.787452i	0.672696	−	0.739919i	$-0.265136\pi$
$432$	1.51935	−	0.629336i	0.0730999	−	0.0302790i
$433$	6.15105	+	6.15105i	0.295601	+	0.295601i	0.839288	−	0.543687i	$-0.182972\pi$
$433$	6.15105	+	6.15105i	0.295601	+	0.295601i	−0.543687	+	0.839288i	$0.682972\pi$
$434$	−2.19280	−	2.19280i	−0.105258	−	0.105258i
$435$	−6.31155	+	2.61433i	−0.302616	+	0.125348i
$436$	3.55009	+	8.57066i	0.170018	+	0.410460i
$437$	38.8926	+	16.1098i	1.86048	+	0.770638i
$438$			10.8342i			0.517680i
$439$	−1.99721	+	4.82169i	−0.0953217	+	0.230127i	−0.964347	−	0.264640i	$-0.914747\pi$
$439$	−1.99721	+	4.82169i	−0.0953217	+	0.230127i	0.869025	+	0.494767i	$0.164747\pi$
$440$	22.8921	−	22.8921i	1.09134	−	1.09134i
$441$	−1.00000			−0.0476190
$442$	−5.48449	+	0.00764091i	−0.260871	+	0.000363441i
$443$	−19.9255			−0.946691			−0.473345	−	0.880877i	$-0.656954\pi$
$443$	−19.9255			−0.946691			−0.473345	+	0.880877i	$0.656954\pi$
$444$	−1.44758	+	1.44758i	−0.0686990	+	0.0686990i
$445$	4.26550	−	10.2978i	0.202204	−	0.488164i
$446$		−	11.4945i		−	0.544280i
$447$	21.2592	+	8.80584i	1.00552	+	0.416502i
$448$	3.05540	+	7.37640i	0.144354	+	0.348502i
$449$	5.77536	−	2.39223i	0.272556	−	0.112896i	−0.242219	−	0.970222i	$-0.577875\pi$
$449$	5.77536	−	2.39223i	0.272556	−	0.112896i	0.514775	+	0.857325i	$0.327875\pi$
$450$	1.57800	+	1.57800i	0.0743875	+	0.0743875i
$451$	43.9920	+	43.9920i	2.07150	+	2.07150i
$452$	−2.29145	+	0.949148i	−0.107781	+	0.0446442i
$453$	7.08393	+	17.1021i	0.332832	+	0.803528i
$454$	5.22278	+	2.16335i	0.245117	+	0.101531i
$455$		−	2.10852i		−	0.0988487i
$456$	−6.39245	+	15.4327i	−0.299354	+	0.722704i
$457$	−28.9628	+	28.9628i	−1.35482	+	1.35482i	−0.474643	+	0.880178i	$0.657423\pi$
$457$	−28.9628	+	28.9628i	−1.35482	+	1.35482i	−0.880178	+	0.474643i	$0.842577\pi$
$458$	8.68813			0.405970
$459$	−1.57254	+	3.81145i	−0.0733997	+	0.177903i
$460$	10.9922			0.512514
$461$	13.6565	−	13.6565i	0.636046	−	0.636046i	−0.313532	−	0.949578i	$-0.601512\pi$
$461$	13.6565	−	13.6565i	0.636046	−	0.636046i	0.949578	+	0.313532i	$0.101512\pi$
$462$	−2.55361	+	6.16495i	−0.118805	+	0.286820i
$463$		−	5.12114i		−	0.238000i	−0.992894	−	0.119000i	$-0.962031\pi$
$463$		−	5.12114i		−	0.238000i	0.992894	−	0.119000i	$-0.0379688\pi$
$464$	−6.05836	−	2.50945i	−0.281252	−	0.116498i
$465$	−1.88113	−	4.54145i	−0.0872354	−	0.210605i
$466$	18.6861	−	7.74002i	0.865615	−	0.358549i
$467$	−9.34379	−	9.34379i	−0.432379	−	0.432379i	0.457058	−	0.889437i	$-0.348903\pi$
$467$	−9.34379	−	9.34379i	−0.432379	−	0.432379i	−0.889437	+	0.457058i	$0.848903\pi$
$468$	0.723856	+	0.723856i	0.0334603	+	0.0334603i
$469$	10.0890	−	4.17902i	0.465869	−	0.192969i
$470$	4.24544	+	10.2494i	0.195828	+	0.472770i
$471$	13.5392	+	5.60811i	0.623852	+	0.258408i
$472$		−	31.8028i		−	1.46384i
$473$	17.1874	−	41.4940i	0.790276	−	1.90789i
$474$	7.23981	−	7.23981i	0.332536	−	0.332536i
$475$	−11.2685			−0.517036
$476$	−3.17033	−	1.30802i	−0.145312	−	0.0599532i
$477$	−9.27751			−0.424788
$478$	−3.97613	+	3.97613i	−0.181864	+	0.181864i
$479$	−6.55595	+	15.8275i	−0.299549	+	0.723176i	0.700406	+	0.713744i	$0.253002\pi$
$479$	−6.55595	+	15.8275i	−0.299549	+	0.723176i	−0.999956	+	0.00943130i	$0.996998\pi$
$480$			7.44231i			0.339694i
$481$	2.79839	+	1.15913i	0.127596	+	0.0528519i
$482$	−4.41390	−	10.6561i	−0.201048	−	0.485372i
$483$	−7.12624	+	2.95179i	−0.324255	+	0.134311i
$484$	−15.9488	−	15.9488i	−0.724945	−	0.724945i
$485$	1.58189	+	1.58189i	0.0718298	+	0.0718298i
$486$	−0.998563	+	0.413618i	−0.0452957	+	0.0187621i
$487$	4.67209	+	11.2794i	0.211713	+	0.511119i	0.993687	−	0.112192i	$-0.0357871\pi$
$487$	4.67209	+	11.2794i	0.211713	+	0.511119i	−0.781974	+	0.623311i	$0.785787\pi$
$488$	−23.4984	−	9.73336i	−1.06372	−	0.440608i
$489$		−	14.1780i		−	0.641153i
$490$	−0.708638	+	1.71080i	−0.0320130	+	0.0772862i
$491$	−20.4446	+	20.4446i	−0.922650	+	0.922650i	−0.997216	−	0.0745659i	$-0.976243\pi$
$491$	−20.4446	+	20.4446i	−0.922650	+	0.922650i	0.0745659	+	0.997216i	$0.476243\pi$
$492$	−8.38204			−0.377892
$493$	15.1805	−	6.31275i	0.683694	−	0.284312i
$494$	7.25969			0.326629
$495$	−7.47935	+	7.47935i	−0.336172	+	0.336172i
$496$	1.80567	−	4.35927i	0.0810769	−	0.195737i
$497$			3.58726i			0.160911i
$498$	−4.19583	−	1.73797i	−0.188020	−	0.0778802i
$499$	10.6892	+	25.8060i	0.478514	+	1.15524i	0.960306	+	0.278949i	$0.0899862\pi$
$499$	10.6892	+	25.8060i	0.478514	+	1.15524i	−0.481792	+	0.876286i	$0.660014\pi$
$500$	−9.30144	+	3.85278i	−0.415973	+	0.172302i
$501$	13.8203	+	13.8203i	0.617447	+	0.617447i
$502$	7.29480	+	7.29480i	0.325583	+	0.325583i
$503$	−21.9215	+	9.08017i	−0.977430	+	0.404865i	−0.813473	−	0.581603i	$-0.802426\pi$
$503$	−21.9215	+	9.08017i	−0.977430	+	0.404865i	−0.163957	+	0.986467i	$0.552426\pi$
$504$	−1.17128	−	2.82772i	−0.0521730	−	0.125957i
$505$	23.2942	+	9.64878i	1.03658	+	0.429365i
$506$			51.4706i			2.28815i
$507$	−4.39526	+	10.6111i	−0.195201	+	0.471256i
$508$	−5.26016	+	5.26016i	−0.233382	+	0.233382i
$509$	−19.6433			−0.870674			−0.435337	−	0.900268i	$-0.643371\pi$
$509$	−19.6433			−0.870674			−0.435337	+	0.900268i	$0.643371\pi$
$510$	5.40628	+	5.39123i	0.239394	+	0.238728i
$511$	10.0239			0.443433
$512$	−12.1698	+	12.1698i	−0.537832	+	0.537832i
$513$	2.08855	−	5.04222i	0.0922119	−	0.222619i
$514$			19.7535i			0.871291i
$515$	−8.91346	−	3.69208i	−0.392774	−	0.162692i
$516$	2.31563	+	5.59043i	0.101940	+	0.246105i
$517$	34.1718	−	14.1544i	1.50288	−	0.622511i
$518$	−1.88099	−	1.88099i	−0.0826459	−	0.0826459i
$519$	−9.99706	−	9.99706i	−0.438822	−	0.438822i
$520$	5.96230	−	2.46966i	0.261464	−	0.108302i
$521$	−2.50151	−	6.03918i	−0.109593	−	0.264581i	0.859563	−	0.511031i	$-0.170736\pi$
$521$	−2.50151	−	6.03918i	−0.109593	−	0.264581i	−0.969156	+	0.246449i	$0.920736\pi$
$522$	3.98173	+	1.64929i	0.174276	+	0.0721873i
$523$			31.0312i			1.35690i	0.734646	+	0.678451i	$0.237348\pi$
$523$			31.0312i			1.35690i	−0.734646	+	0.678451i	$0.762652\pi$
$524$	0.175573	−	0.423870i	0.00766994	−	0.0185169i
$525$	1.45998	−	1.45998i	0.0637187	−	0.0637187i
$526$	−13.3525			−0.582195
$527$	4.54231	+	10.9230i	0.197866	+	0.475815i
$528$	−10.1531			−0.441856
$529$	−25.8068	+	25.8068i	−1.12204	+	1.12204i
$530$	−6.57439	+	15.8720i	−0.285573	+	0.689435i
$531$			10.3907i			0.450916i
$532$	4.19408	+	1.73724i	0.181836	+	0.0753191i
$533$	4.74599	+	11.4578i	0.205571	+	0.496293i
$534$	−6.49653	+	2.69095i	−0.281132	+	0.116449i
$535$	−5.16086	−	5.16086i	−0.223123	−	0.223123i
$536$	23.6342	+	23.6342i	1.02084	+	1.02084i
$537$	2.34500	−	0.971332i	0.101194	−	0.0419161i
$538$	−3.89540	−	9.40434i	−0.167943	−	0.405450i
$539$	5.70387	+	2.36262i	0.245683	+	0.101765i
$540$		−	1.42508i		−	0.0613258i
$541$	−0.603614	+	1.45725i	−0.0259514	+	0.0626522i	−0.936324	−	0.351137i	$-0.885795\pi$
$541$	−0.603614	+	1.45725i	−0.0259514	+	0.0626522i	0.910373	+	0.413789i	$0.135795\pi$
$542$	14.4646	−	14.4646i	0.621308	−	0.621308i
$543$	−3.97432			−0.170554
$544$	−0.0249526	−	17.9105i	−0.00106983	−	0.767906i
$545$	−19.1077			−0.818484
$546$	−0.940583	+	0.940583i	−0.0402532	+	0.0402532i
$547$	4.03670	−	9.74547i	0.172597	−	0.416686i	−0.813783	−	0.581169i	$-0.802596\pi$
$547$	4.03670	−	9.74547i	0.172597	−	0.416686i	0.986380	+	0.164483i	$0.0525955\pi$
$548$			10.8481i			0.463406i
$549$	7.67745	+	3.18010i	0.327666	+	0.135724i
$550$	−5.27249	−	12.7289i	−0.224820	−	0.542763i
$551$	−20.1056	+	8.32803i	−0.856529	+	0.354786i
$552$	−16.6937	−	16.6937i	−0.710529	−	0.710529i
$553$	−6.69834	−	6.69834i	−0.284842	−	0.284842i
$554$	−12.6292	+	5.23120i	−0.536564	+	0.222252i
$555$	−1.61364	−	3.89566i	−0.0684951	−	0.165362i
$556$	−12.3412	−	5.11190i	−0.523385	−	0.216793i
$557$			21.4442i			0.908621i	0.890844	+	0.454310i	$0.150114\pi$
$557$			21.4442i			0.908621i	−0.890844	+	0.454310i	$0.849886\pi$
$558$	−1.18674	+	2.86504i	−0.0502386	+	0.121287i
$559$	6.33071	−	6.33071i	0.267760	−	0.267760i
$560$	−2.81753			−0.119062
$561$	17.9745	−	18.0247i	0.758886	−	0.761004i
$562$	−14.5818			−0.615095
$563$	2.39495	−	2.39495i	0.100935	−	0.100935i	−0.654836	−	0.755771i	$-0.727262\pi$
$563$	2.39495	−	2.39495i	0.100935	−	0.100935i	0.755771	+	0.654836i	$0.227262\pi$
$564$	−1.90701	+	4.60393i	−0.0802997	+	0.193861i
$565$		−	5.10862i		−	0.214921i
$566$	5.62222	+	2.32880i	0.236320	+	0.0978868i
$567$	0.382683	+	0.923880i	0.0160712	+	0.0387993i
$568$	−10.1438	+	4.20169i	−0.425623	+	0.176299i
$569$	−10.3815	−	10.3815i	−0.435215	−	0.435215i	0.455183	−	0.890398i	$-0.349574\pi$
$569$	−10.3815	−	10.3815i	−0.435215	−	0.435215i	−0.890398	+	0.455183i	$0.849574\pi$
$570$	−7.14621	−	7.14621i	−0.299322	−	0.299322i
$571$	7.67666	−	3.17978i	0.321258	−	0.133070i	−0.216226	−	0.976343i	$-0.569375\pi$
$571$	7.67666	−	3.17978i	0.321258	−	0.133070i	0.537484	+	0.843274i	$0.319375\pi$
$572$	−2.41859	−	5.83898i	−0.101126	−	0.244140i
$573$	14.2331	+	5.89555i	0.594597	+	0.246290i
$574$		−	10.8917i		−	0.454610i
$575$	6.09462	−	14.7137i	0.254163	−	0.613604i
$576$	5.64565	−	5.64565i	0.235235	−	0.235235i
$577$	19.4474			0.809605			0.404803	−	0.914404i	$-0.367340\pi$
$577$	19.4474			0.809605			0.404803	+	0.914404i	$0.367340\pi$
$578$	−13.0287	−	12.9563i	−0.541922	−	0.538910i
$579$	−7.92049			−0.329164
$580$	−4.01810	+	4.01810i	−0.166843	+	0.166843i
$581$	−1.60799	+	3.88202i	−0.0667105	+	0.161053i
$582$		−	1.41132i		−	0.0585012i
$583$	52.9177	+	21.9192i	2.19163	+	0.907802i
$584$	11.7409	+	28.3449i	0.485840	+	1.17292i
$585$	−1.94801	+	0.806894i	−0.0805405	+	0.0333610i
$586$	18.0167	+	18.0167i	0.744264	+	0.744264i
$587$	19.3113	+	19.3113i	0.797063	+	0.797063i	0.982631	−	0.185569i	$-0.0594127\pi$
$587$	19.3113	+	19.3113i	0.797063	+	0.797063i	−0.185569	+	0.982631i	$0.559413\pi$
$588$	−0.768476	+	0.318313i	−0.0316914	+	0.0131270i
$589$	−5.99240	−	14.4669i	−0.246912	−	0.596099i
$590$	17.7764	+	7.36322i	0.731842	+	0.303139i
$591$		−	2.49067i		−	0.102453i
$592$	1.54890	−	3.73938i	0.0636595	−	0.153688i
$593$	15.4020	−	15.4020i	0.632483	−	0.632483i	−0.316207	−	0.948690i	$-0.602409\pi$
$593$	15.4020	−	15.4020i	0.632483	−	0.632483i	0.948690	+	0.316207i	$0.102409\pi$
$594$	6.67290			0.273792
$595$	4.98802	−	5.00194i	0.204489	−	0.205059i
$596$	19.1402			0.784012
$597$	12.7450	−	12.7450i	0.521620	−	0.521620i
$598$	−3.92642	+	9.47922i	−0.160563	+	0.387634i
$599$		−	19.4080i		−	0.792988i	−0.918037	−	0.396494i	$-0.870227\pi$
$599$		−	19.4080i		−	0.792988i	0.918037	−	0.396494i	$-0.129773\pi$
$600$	5.83846	+	2.41837i	0.238354	+	0.0987295i
$601$	3.57710	+	8.63589i	0.145913	+	0.352265i	0.979891	−	0.199532i	$-0.0639422\pi$
$601$	3.57710	+	8.63589i	0.145913	+	0.352265i	−0.833978	+	0.551797i	$0.813942\pi$
$602$	−7.26424	+	3.00895i	−0.296068	+	0.122636i
$603$	−7.72182	−	7.72182i	−0.314457	−	0.314457i
$604$	10.8877	+	10.8877i	0.443013	+	0.443013i
$605$	42.9208	−	17.7784i	1.74498	−	0.722794i
$606$	−6.08706	−	14.6955i	−0.247270	−	0.596962i
$607$	14.9218	+	6.18081i	0.605657	+	0.250871i	0.664370	−	0.747404i	$-0.268700\pi$
$607$	14.9218	+	6.18081i	0.605657	+	0.250871i	−0.0587134	+	0.998275i	$0.518700\pi$
$608$			23.7077i			0.961475i
$609$	1.52593	−	3.68393i	0.0618340	−	0.149280i
$610$	10.8811	−	10.8811i	0.440561	−	0.440561i
$611$	7.37311			0.298284
$612$	0.00477802	+	3.42957i	0.000193140	+	0.138632i
$613$	−3.27688			−0.132352			−0.0661760	−	0.997808i	$-0.521080\pi$
$613$	−3.27688			−0.132352			−0.0661760	+	0.997808i	$0.521080\pi$
$614$	−12.9389	+	12.9389i	−0.522172	+	0.522172i
$615$	6.60692	−	15.9505i	0.266417	−	0.643187i
$616$			18.8963i			0.761352i
$617$	−29.2212	−	12.1038i	−1.17640	−	0.487281i	−0.293097	−	0.956083i	$-0.594686\pi$
$617$	−29.2212	−	12.1038i	−1.17640	−	0.487281i	−0.883304	+	0.468802i	$0.844686\pi$
$618$	2.32920	+	5.62317i	0.0936940	+	0.226197i
$619$	40.9212	−	16.9501i	1.64476	−	0.681282i	0.647995	−	0.761644i	$-0.275608\pi$
$619$	40.9212	−	16.9501i	1.64476	−	0.681282i	0.996766	+	0.0803621i	$0.0256077\pi$
$620$	−2.89121	−	2.89121i	−0.116114	−	0.116114i
$621$	5.45419	+	5.45419i	0.218869	+	0.218869i
$622$	−30.8973	+	12.7981i	−1.23887	+	0.513157i
$623$	2.48969	+	6.01065i	0.0997474	+	0.240812i
$624$	−1.86987	−	0.774524i	−0.0748546	−	0.0310058i
$625$		−	10.4133i		−	0.416533i
$626$	−11.3092	+	27.3029i	−0.452008	+	1.09124i
$627$	−23.8257	+	23.8257i	−0.951507	+	0.951507i
$628$	12.1897			0.486421
$629$	3.89640	+	9.36980i	0.155360	+	0.373598i
$630$	1.85176			0.0737759
$631$	5.12683	−	5.12683i	0.204096	−	0.204096i	−0.597656	−	0.801752i	$-0.703901\pi$
$631$	5.12683	−	5.12683i	0.204096	−	0.204096i	0.801752	+	0.597656i	$0.203901\pi$
$632$	11.0954	−	26.7867i	0.441352	−	1.06552i
$633$			5.51635i			0.219255i
$634$	13.1535	+	5.44835i	0.522391	+	0.216382i
$635$	−5.86359	−	14.1560i	−0.232689	−	0.561762i
$636$	−7.12955	+	2.95316i	−0.282705	+	0.117100i
$637$	0.870236	+	0.870236i	0.0344800	+	0.0344800i
$638$	−18.8146	−	18.8146i	−0.744878	−	0.744878i
$639$	3.31420	−	1.37278i	0.131108	−	0.0543065i
$640$	0.0382282	+	0.0922910i	0.00151110	+	0.00364812i
$641$	−36.4095	−	15.0813i	−1.43809	−	0.595676i	−0.478754	−	0.877949i	$-0.658912\pi$
$641$	−36.4095	−	15.0813i	−1.43809	−	0.595676i	−0.959334	+	0.282273i	$0.908912\pi$
$642$			4.60439i			0.181721i
$643$	10.0389	−	24.2361i	0.395896	−	0.955778i	−0.592732	−	0.805399i	$-0.701951\pi$
$643$	10.0389	−	24.2361i	0.395896	−	0.955778i	0.988629	−	0.150378i	$-0.0480492\pi$
$644$	−4.53675	+	4.53675i	−0.178773	+	0.178773i
$645$	−12.4635			−0.490749
$646$	17.2219	+	17.1739i	0.677585	+	0.675699i
$647$	19.0481			0.748856			0.374428	−	0.927256i	$-0.377839\pi$
$647$	19.0481			0.748856			0.374428	+	0.927256i	$0.377839\pi$
$648$	−2.16424	+	2.16424i	−0.0850196	+	0.0850196i
$649$	24.5492	−	59.2670i	0.963641	−	2.32643i
$650$		−	2.74646i		−	0.107725i
$651$	2.65076	+	1.09798i	0.103891	+	0.0430332i
$652$	−4.51306	−	10.8955i	−0.176745	−	0.426700i
$653$	−23.6149	+	9.78160i	−0.924122	+	0.382784i	−0.793445	−	0.608641i	$-0.791715\pi$
$653$	−23.6149	+	9.78160i	−0.924122	+	0.382784i	−0.130676	+	0.991425i	$0.541715\pi$
$654$	8.52371	+	8.52371i	0.333304	+	0.333304i
$655$	0.668209	+	0.668209i	0.0261091	+	0.0261091i
$656$	15.3106	−	6.34187i	0.597780	−	0.247609i
$657$	−3.83600	−	9.26092i	−0.149657	−	0.361303i
$658$	−5.98238	−	2.47798i	−0.233217	−	0.0966018i
$659$		−	0.973671i		−	0.0379288i	−0.999820	−	0.0189644i	$-0.993963\pi$
$659$		−	0.973671i		−	0.0379288i	0.999820	−	0.0189644i	$-0.00603692\pi$
$660$	−3.36693	+	8.12848i	−0.131058	+	0.316401i
$661$	−31.3539	+	31.3539i	−1.21952	+	1.21952i	−0.251725	+	0.967799i	$0.580998\pi$
$661$	−31.3539	+	31.3539i	−1.21952	+	1.21952i	−0.967799	+	0.251725i	$0.919002\pi$
$662$	−25.2198			−0.980196
$663$	4.68534	−	1.94838i	0.181963	−	0.0756689i
$664$	−12.8607			−0.499091
$665$	−6.61174	+	6.61174i	−0.256392	+	0.256392i
$666$	−1.01798	+	2.45763i	−0.0394461	+	0.0952313i
$667$		−	30.7568i		−	1.19091i
$668$	15.0198	+	6.22140i	0.581133	+	0.240713i
$669$	4.06977	+	9.82529i	0.157346	+	0.379868i
$670$	−18.6825	+	7.73854i	−0.721767	+	0.298966i
$671$	−36.2778	−	36.2778i	−1.40049	−	1.40049i
$672$	−3.07163	−	3.07163i	−0.118491	−	0.118491i
$673$	−0.0358530	+	0.0148508i	−0.00138203	+	0.000572457i	−0.383374	−	0.923593i	$-0.625238\pi$
$673$	−0.0358530	+	0.0148508i	−0.00138203	+	0.000572457i	0.381992	+	0.924166i	$0.375238\pi$
$674$	−1.08682	−	2.62383i	−0.0418629	−	0.101066i
$675$	−1.90755	−	0.790135i	−0.0734218	−	0.0304123i
$676$			9.55345i			0.367441i
$677$	1.82438	−	4.40445i	0.0701168	−	0.169277i	−0.884936	−	0.465713i	$-0.845798\pi$
$677$	1.82438	−	4.40445i	0.0701168	−	0.169277i	0.955053	+	0.296436i	$0.0957981\pi$
$678$	−2.27889	+	2.27889i	−0.0875204	+	0.0875204i
$679$	−1.30577			−0.0501108
$680$	19.9865	+	8.24606i	0.766446	+	0.316222i
$681$	−5.23030			−0.200426
$682$	13.5380	−	13.5380i	0.518396	−	0.518396i
$683$	11.2865	−	27.2481i	0.431868	−	1.04262i	−0.546817	−	0.837252i	$-0.684161\pi$
$683$	11.2865	−	27.2481i	0.431868	−	1.04262i	0.978685	−	0.205369i	$-0.0658393\pi$
$684$		−	4.53964i		−	0.173577i
$685$	−20.6432	−	8.55069i	−0.788736	−	0.326705i
$686$	−0.413618	−	0.998563i	−0.0157920	−	0.0381253i
$687$	−7.42646	+	3.07614i	−0.283337	+	0.117362i
$688$	−8.45947	−	8.45947i	−0.322514	−	0.322514i
$689$	8.07363	+	8.07363i	0.307581	+	0.307581i
$690$	13.1961	−	5.46600i	0.502366	−	0.208087i
$691$	−8.64604	−	20.8734i	−0.328911	−	0.794061i	−0.998674	−	0.0514859i	$-0.983604\pi$
$691$	−8.64604	−	20.8734i	−0.328911	−	0.794061i	0.669763	−	0.742575i	$-0.266396\pi$
$692$	−10.8647	−	4.50031i	−0.413014	−	0.171076i
$693$		−	6.17383i		−	0.234524i
$694$	2.84969	−	6.87977i	0.108173	−	0.261153i
$695$	19.4553	−	19.4553i	0.737981	−	0.737981i
$696$	12.2044			0.462608
$697$	−15.8466	+	38.4083i	−0.600231	+	1.45482i
$698$	−3.34163			−0.126482
$699$	−13.2321	+	13.2321i	−0.500482	+	0.500482i
$700$	0.657228	−	1.58669i	0.0248409	−	0.0599712i
$701$		−	35.6863i		−	1.34785i	−0.738799	−	0.673926i	$-0.764607\pi$
$701$		−	35.6863i		−	1.34785i	0.738799	−	0.673926i	$-0.235393\pi$
$702$	1.22893	+	0.509040i	0.0463830	+	0.0192125i
$703$	−5.14029	−	12.4097i	−0.193870	−	0.468043i
$704$	−45.5406	+	18.8635i	−1.71638	+	0.710946i
$705$	−7.25785	−	7.25785i	−0.273347	−	0.273347i
$706$	−2.56004	−	2.56004i	−0.0963484	−	0.0963484i
$707$	−13.5964	+	5.63181i	−0.511345	+	0.211806i
$708$	3.30749	+	7.98498i	0.124303	+	0.300094i
$709$	22.9393	+	9.50177i	0.861504	+	0.356847i	0.769295	−	0.638893i	$-0.220607\pi$
$709$	22.9393	+	9.50177i	0.861504	+	0.356847i	0.0922083	+	0.995740i	$0.470607\pi$
$710$		−	6.64274i		−	0.249298i
$711$	−3.62512	+	8.75181i	−0.135953	+	0.328218i
$712$	−14.0803	+	14.0803i	−0.527682	+	0.527682i
$713$	22.1309			0.828810
$714$	−4.45640	+	0.00620859i	−0.166777	+	0.000232351i
$715$	13.0176			0.486831
$716$	1.49289	−	1.49289i	0.0557920	−	0.0557920i
$717$	1.99093	−	4.80652i	0.0743525	−	0.179503i
$718$		−	22.5292i		−	0.840781i
$719$	3.61525	+	1.49748i	0.134826	+	0.0558467i	0.449076	−	0.893493i	$-0.351753\pi$
$719$	3.61525	+	1.49748i	0.134826	+	0.0558467i	−0.314250	+	0.949340i	$0.601753\pi$
$720$	1.07822	+	2.60305i	0.0401829	+	0.0970101i
$721$	5.20261	−	2.15499i	0.193755	−	0.0802561i
$722$	−8.24339	−	8.24339i	−0.306787	−	0.306787i
$723$	7.54584	+	7.54584i	0.280633	+	0.280633i
$724$	−3.05417	+	1.26508i	−0.113507	+	0.0470163i
$725$	3.15063	+	7.60629i	0.117011	+	0.282491i
$726$	−27.0772	−	11.2157i	−1.00493	−	0.416255i
$727$		−	0.402296i		−	0.0149203i	−0.999972	−	0.00746016i	$-0.997625\pi$
$727$		−	0.402296i		−	0.0149203i	0.999972	−	0.00746016i	$-0.00237467\pi$
$728$	−1.44150	+	3.48008i	−0.0534254	+	0.128980i
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	−18.5619			−0.687008
$731$	29.9943	−	0.0417876i	1.10938	−	0.00154557i
$732$	6.91221			0.255482
$733$	−12.4485	+	12.4485i	−0.459794	+	0.459794i	−0.898588	−	0.438793i	$-0.855406\pi$
$733$	−12.4485	+	12.4485i	−0.459794	+	0.459794i	0.438793	+	0.898588i	$0.355406\pi$
$734$	6.40345	−	15.4593i	0.236356	−	0.570613i
$735$		−	1.71327i		−	0.0631947i
$736$	−30.9559	−	12.8224i	−1.14105	−	0.472639i
$737$	25.8005	+	62.2880i	0.950375	+	2.29441i
$738$	−10.0626	+	4.16806i	−0.370409	+	0.153429i
$739$	19.3971	+	19.3971i	0.713535	+	0.713535i	0.967273	−	0.253738i	$-0.0816600\pi$
$739$	19.3971	+	19.3971i	0.713535	+	0.713535i	−0.253738	+	0.967273i	$0.581660\pi$
$740$	−2.48008	−	2.48008i	−0.0911697	−	0.0911697i
$741$	−6.20546	+	2.57038i	−0.227963	+	0.0944254i
$742$	−3.83735	−	9.26418i	−0.140873	−	0.340099i
$743$	23.1964	+	9.60825i	0.850992	+	0.352493i	0.765178	−	0.643819i	$-0.222651\pi$
$743$	23.1964	+	9.60825i	0.850992	+	0.352493i	0.0858142	+	0.996311i	$0.472651\pi$
$744$			8.78165i			0.321951i
$745$	−15.0867	+	36.4226i	−0.552735	+	1.33442i
$746$	10.3882	−	10.3882i	0.380339	−	0.380339i
$747$	4.20187			0.153738
$748$	8.07551	−	19.5731i	0.295270	−	0.715663i
$749$	4.26003			0.155658
$750$	−9.25049	+	9.25049i	−0.337780	+	0.337780i
$751$	11.3798	−	27.4732i	0.415254	−	1.00251i	−0.568451	−	0.822717i	$-0.692457\pi$
$751$	11.3798	−	27.4732i	0.415254	−	1.00251i	0.983704	−	0.179794i	$-0.0575430\pi$
$752$		−	9.85239i		−	0.359280i
$753$	−8.81828	−	3.65265i	−0.321356	−	0.133110i
$754$	−2.02978	−	4.90031i	−0.0739201	−	0.178459i
$755$	−29.3005	+	12.1367i	−1.06635	+	0.441698i
$756$	0.588166	+	0.588166i	0.0213914	+	0.0213914i
$757$	−25.0477	−	25.0477i	−0.910376	−	0.910376i	0.0859259	−	0.996302i	$-0.472615\pi$
$757$	−25.0477	−	25.0477i	−0.910376	−	0.910376i	−0.996302	+	0.0859259i	$0.972615\pi$
$758$	−29.7917	+	12.3401i	−1.08208	+	0.448214i
$759$	−18.2238	−	43.9962i	−0.661483	−	1.59696i
$760$	−26.4404	−	10.9520i	−0.959093	−	0.397269i
$761$		−	48.7473i		−	1.76709i	−0.468349	−	0.883544i	$-0.655151\pi$
$761$		−	48.7473i		−	1.76709i	0.468349	−	0.883544i	$-0.344849\pi$
$762$	−3.69912	+	8.93047i	−0.134005	+	0.323517i
$763$	7.88622	−	7.88622i	0.285500	−	0.285500i
$764$	12.8144			0.463610
$765$	−6.53002	−	2.69417i	−0.236093	−	0.0974080i
$766$	18.5387			0.669832
$767$	9.04233	−	9.04233i	0.326500	−	0.326500i
$768$	6.13492	−	14.8110i	0.221375	−	0.534447i
$769$			35.1290i			1.26678i	0.773831	+	0.633392i	$0.218338\pi$
$769$			35.1290i			1.26678i	−0.773831	+	0.633392i	$0.781662\pi$
$770$	−10.5622	−	4.37501i	−0.380635	−	0.157664i
$771$	−6.99398	−	16.8850i	−0.251882	−	0.608097i
$772$	−6.08671	+	2.52120i	−0.219065	+	0.0907398i
$773$	−1.19120	−	1.19120i	−0.0428445	−	0.0428445i	0.685360	−	0.728204i	$-0.259645\pi$
$773$	−1.19120	−	1.19120i	−0.0428445	−	0.0428445i	−0.728204	+	0.685360i	$0.759645\pi$
$774$	5.55981	+	5.55981i	0.199843	+	0.199843i
$775$	−5.47308	+	2.26702i	−0.196599	+	0.0814339i
$776$	−1.52942	−	3.69235i	−0.0549030	−	0.132548i
$777$	2.27382	+	0.941849i	0.0815730	+	0.0337886i
$778$			28.1462i			1.00909i
$779$	21.0465	−	50.8108i	0.754070	−	1.82049i
$780$	−1.24016	+	1.24016i	−0.0444048	+	0.0444048i
$781$	−22.1471			−0.792486
$782$	−31.7390	+	13.1986i	−1.13499	+	0.471980i
$783$	−3.98746			−0.142500
$784$	1.16286	−	1.16286i	0.0415308	−	0.0415308i
$785$	−9.60818	+	23.1962i	−0.342931	+	0.827908i
$786$		−	0.596160i		−	0.0212643i
$787$	−46.1727	−	19.1254i	−1.64588	−	0.681745i	−0.649007	−	0.760782i	$-0.724816\pi$
$787$	−46.1727	−	19.1254i	−1.64588	−	0.681745i	−0.996872	+	0.0790369i	$0.974816\pi$
$788$	−0.792814	−	1.91402i	−0.0282428	−	0.0681842i
$789$	11.4134	−	4.72760i	0.406329	−	0.168307i
$790$	12.4037	+	12.4037i	0.441305	+	0.441305i
$791$	2.10845	+	2.10845i	0.0749680	+	0.0749680i
$792$	17.4579	−	7.23129i	0.620338	−	0.256953i
$793$	−3.91375	−	9.44864i	−0.138981	−	0.335531i
$794$	−20.7542	−	8.59667i	−0.736539	−	0.305084i
$795$		−	15.8948i		−	0.563732i
$796$	5.73735	−	13.8512i	0.203355	−	0.490942i
$797$	−0.882281	+	0.882281i	−0.0312520	+	0.0312520i	−0.722560	−	0.691308i	$-0.757035\pi$
$797$	−0.882281	+	0.882281i	−0.0312520	+	0.0312520i	0.691308	+	0.722560i	$0.257035\pi$
$798$	5.89883			0.208816
$799$	17.4909	+	17.4422i	0.618784	+	0.617062i
$800$	8.96902			0.317103
$801$	4.60035	−	4.60035i	0.162545	−	0.162545i
$802$	−5.22559	+	12.6157i	−0.184522	+	0.445475i
$803$			61.8861i			2.18391i
$804$	−8.39199	−	3.47608i	−0.295963	−	0.122592i
$805$	−5.05719	−	12.2091i	−0.178243	−	0.430316i
$806$	3.52600	−	1.46052i	0.124198	−	0.0514445i
$807$	6.65944	+	6.65944i	0.234423	+	0.234423i
$808$	−31.8504	−	31.8504i	−1.12049	−	1.12049i
$809$	37.8185	−	15.6649i	1.32963	−	0.550750i	0.399079	−	0.916917i	$-0.369330\pi$
$809$	37.8185	−	15.6649i	1.32963	−	0.550750i	0.930549	+	0.366167i	$0.119330\pi$
$810$	−0.708638	−	1.71080i	−0.0248990	−	0.0601115i
$811$	14.9164	+	6.17856i	0.523785	+	0.216959i	0.628878	−	0.777504i	$-0.283514\pi$
$811$	14.9164	+	6.17856i	0.523785	+	0.216959i	−0.105094	+	0.994462i	$0.533514\pi$
$812$		−	3.31674i		−	0.116395i
$813$	−7.24272	+	17.4855i	−0.254013	+	0.613242i
$814$	11.6129	−	11.6129i	0.407032	−	0.407032i
$815$	24.2907			0.850867
$816$	−2.60355	−	6.26083i	−0.0911423	−	0.219173i
$817$	−39.7028			−1.38903
$818$	15.7852	−	15.7852i	0.551917	−	0.551917i
$819$	0.470968	−	1.13702i	0.0164570	−	0.0397306i
$820$		−	14.3607i		−	0.501496i
$821$	−32.7728	−	13.5749i	−1.14378	−	0.473769i	−0.271336	−	0.962485i	$-0.587465\pi$
$821$	−32.7728	−	13.5749i	−1.14378	−	0.473769i	−0.872443	+	0.488716i	$0.837465\pi$
$822$	5.39432	+	13.0230i	0.188148	+	0.454230i
$823$	27.8137	−	11.5208i	0.969524	−	0.401590i	0.158989	−	0.987280i	$-0.449176\pi$
$823$	27.8137	−	11.5208i	0.969524	−	0.401590i	0.810535	+	0.585690i	$0.199176\pi$
$824$	12.1874	+	12.1874i	0.424570	+	0.424570i
$825$	9.01366	+	9.01366i	0.313815	+	0.313815i
$826$	−10.3757	+	4.29777i	−0.361018	+	0.149538i
$827$	11.9328	+	28.8083i	0.414944	+	1.00176i	0.983791	+	0.179320i	$0.0573897\pi$
$827$	11.9328	+	28.8083i	0.414944	+	1.00176i	−0.568847	+	0.822443i	$0.692610\pi$
$828$	5.92756	+	2.45527i	0.205997	+	0.0853267i
$829$		−	14.5835i		−	0.506507i	−0.967400	−	0.253254i	$-0.918499\pi$
$829$		−	14.5835i		−	0.506507i	0.967400	−	0.253254i	$-0.0815007\pi$
$830$	2.97760	−	7.18857i	0.103354	−	0.249519i
$831$	8.94307	−	8.94307i	0.310231	−	0.310231i
$832$	−9.82610			−0.340659
$833$	0.00574424	+	4.12310i	0.000199026	+	0.142857i
$834$	−17.3575			−0.601042
$835$	−23.6779	+	23.6779i	−0.819407	+	0.819407i
$836$	−10.7254	+	25.8935i	−0.370947	+	0.895546i
$837$		−	2.86916i		−	0.0991727i
$838$	−6.78936	−	2.81224i	−0.234535	−	0.0971474i
$839$	−5.38193	−	12.9931i	−0.185805	−	0.448572i	0.803339	−	0.595522i	$-0.203055\pi$
$839$	−5.38193	−	12.9931i	−0.185805	−	0.448572i	−0.989144	+	0.146949i	$0.953055\pi$
$840$	4.84464	−	2.00672i	0.167156	−	0.0692382i
$841$	−9.26322	−	9.26322i	−0.319421	−	0.319421i
$842$	23.8371	+	23.8371i	0.821480	+	0.821480i
$843$	12.4642	−	5.16286i	0.429291	−	0.177818i
$844$	1.75593	+	4.23918i	0.0604415	+	0.145919i
$845$	−18.1796	−	7.53025i	−0.625399	−	0.259049i
$846$			6.47528i			0.222625i
$847$	−10.3769	+	25.0520i	−0.356554	+	0.860799i
$848$	10.7885	−	10.7885i	0.370477	−	0.370477i
$849$	−5.63032			−0.193232
$850$	6.49718	−	6.51531i	0.222851	−	0.223473i
$851$	18.9840			0.650761
$852$	2.10991	−	2.10991i	0.0722842	−	0.0722842i
$853$	9.36705	−	22.6141i	0.320722	−	0.774291i	−0.678491	−	0.734609i	$-0.737366\pi$
$853$	9.36705	−	22.6141i	0.320722	−	0.774291i	0.999212	−	0.0396817i	$-0.0126344\pi$
$854$			8.98176i			0.307350i
$855$	8.63866	+	3.57825i	0.295436	+	0.122374i
$856$	4.98969	+	12.0462i	0.170544	+	0.411730i
$857$	−39.4869	+	16.3560i	−1.34885	+	0.558711i	−0.935971	−	0.352077i	$-0.885476\pi$
$857$	−39.4869	+	16.3560i	−1.34885	+	0.558711i	−0.412876	+	0.910787i	$0.635476\pi$
$858$	−5.80700	−	5.80700i	−0.198248	−	0.198248i
$859$	0.174964	+	0.174964i	0.00596969	+	0.00596969i	0.710085	−	0.704116i	$-0.248656\pi$
$859$	0.174964	+	0.174964i	0.00596969	+	0.00596969i	−0.704116	+	0.710085i	$0.748656\pi$
$860$	−9.57790	+	3.96729i	−0.326604	+	0.135284i
$861$	3.85633	+	9.31001i	0.131423	+	0.317284i
$862$	−17.6694	−	7.31892i	−0.601824	−	0.249284i
$863$			22.8588i			0.778123i	0.921212	+	0.389062i	$0.127201\pi$
$863$			22.8588i			0.778123i	−0.921212	+	0.389062i	$0.872799\pi$
$864$	−1.66235	+	4.01327i	−0.0565544	+	0.136534i
$865$	17.1276	−	17.1276i	0.582356	−	0.582356i
$866$	9.40209			0.319496
$867$	15.7240	+	6.46183i	0.534016	+	0.219455i
$868$	2.38655			0.0810047
$869$	41.3544	−	41.3544i	1.40285	−	1.40285i
$870$	−2.82566	+	6.82176i	−0.0957990	+	0.231279i
$871$			13.4396i			0.455384i
$872$	31.5370	+	13.0631i	1.06798	+	0.442371i
$873$	0.499696	+	1.20637i	0.0169121	+	0.0408295i
$874$	42.0365	−	17.4121i	1.42191	−	0.588973i
$875$	8.55864	+	8.55864i	0.289335	+	0.289335i
$876$	−5.89575	−	5.89575i	−0.199199	−	0.199199i
$877$	−23.6677	+	9.80350i	−0.799203	+	0.331041i	−0.744637	−	0.667470i	$-0.767377\pi$
$877$	−23.6677	+	9.80350i	−0.799203	+	0.331041i	−0.0545657	+	0.998510i	$0.517377\pi$
$878$	2.15866	+	5.21146i	0.0728512	+	0.175878i
$879$	−21.7794	−	9.02133i	−0.734602	−	0.304282i
$880$		−	17.3949i		−	0.586382i
$881$	−14.0430	+	33.9029i	−0.473122	+	1.14222i	0.489655	+	0.871916i	$0.337123\pi$
$881$	−14.0430	+	33.9029i	−0.473122	+	1.14222i	−0.962776	+	0.270300i	$0.912877\pi$
$882$	−0.764267	+	0.764267i	−0.0257342	+	0.0257342i
$883$	7.24309			0.243749			0.121875	−	0.992545i	$-0.461109\pi$
$883$	7.24309			0.243749			0.121875	+	0.992545i	$0.461109\pi$
$884$	2.98037	−	2.98869i	0.100241	−	0.100521i
$885$	−17.8020			−0.598407
$886$	−15.2284	+	15.2284i	−0.511609	+	0.511609i
$887$	−3.05592	+	7.37765i	−0.102608	+	0.247717i	−0.966843	−	0.255370i	$-0.917803\pi$
$887$	−3.05592	+	7.37765i	−0.102608	+	0.247717i	0.864235	+	0.503087i	$0.167803\pi$
$888$			7.53291i			0.252788i
$889$	8.26256	+	3.42246i	0.277117	+	0.114786i
$890$	−4.61031	−	11.1303i	−0.154538	−	0.373088i
$891$	−5.70387	+	2.36262i	−0.191087	+	0.0791508i
$892$	6.25504	+	6.25504i	0.209434	+	0.209434i
$893$	−23.1201	−	23.1201i	−0.773685	−	0.773685i
$894$	22.9777	−	9.51767i	0.768489	−	0.318318i
$895$	1.66415	+	4.01761i	0.0556264	+	0.134294i
$896$	−0.0538685	−	0.0223131i	−0.00179962	−	0.000745427i
$897$		−	9.49287i		−	0.316958i
$898$	2.58561	−	6.24222i	0.0862830	−	0.208306i
$899$	−8.08977	+	8.08977i	−0.269809	+	0.269809i
$900$	−1.71742			−0.0572473
$901$	0.0532923	+	38.2521i	0.00177542	+	1.27436i
$902$	67.2433			2.23896
$903$	5.14399	−	5.14399i	0.171181	−	0.171181i
$904$	−3.49253	+	8.43172i	−0.116160	+	0.280435i
$905$		−	6.80906i		−	0.226341i
$906$	18.4846	+	7.65657i	0.614110	+	0.254373i
$907$	−13.7659	−	33.2339i	−0.457090	−	1.10351i	−0.969570	−	0.244813i	$-0.921273\pi$
$907$	−13.7659	−	33.2339i	−0.457090	−	1.10351i	0.512481	−	0.858699i	$-0.328727\pi$
$908$	−4.01936	+	1.66487i	−0.133387	+	0.0552508i
$909$	10.4062	+	10.4062i	0.345153	+	0.345153i
$910$	−1.61147	−	1.61147i	−0.0534197	−	0.0534197i
$911$	−3.51116	+	1.45437i	−0.116330	+	0.0481855i	−0.440089	−	0.897954i	$-0.645053\pi$
$911$	−3.51116	+	1.45437i	−0.116330	+	0.0481855i	0.323759	+	0.946140i	$0.395053\pi$
$912$	3.43470	+	8.29210i	0.113734	+	0.274579i
$913$	−23.9669	−	9.92742i	−0.793189	−	0.328550i
$914$			44.2706i			1.46434i
$915$	−5.44836	+	13.1535i	−0.180117	+	0.434842i
$916$	−4.72788	+	4.72788i	−0.156214	+	0.156214i
$917$	−0.551573			−0.0182145
$918$	1.71113	+	4.11480i	0.0564756	+	0.135809i
$919$	−27.2967			−0.900436			−0.450218	−	0.892919i	$-0.648654\pi$
$919$	−27.2967			−0.900436			−0.450218	+	0.892919i	$0.648654\pi$
$920$	28.6007	−	28.6007i	0.942936	−	0.942936i
$921$	6.47877	−	15.6411i	0.213483	−	0.515393i
$922$		−	20.8744i		−	0.687462i
$923$	−4.07878	−	1.68949i	−0.134255	−	0.0556101i
$924$	−1.96521	−	4.74444i	−0.0646507	−	0.156081i
$925$	−4.69481	+	1.94466i	−0.154365	+	0.0639399i
$926$	−3.91392	−	3.91392i	−0.128619	−	0.128619i
$927$	−3.98191	−	3.98191i	−0.130783	−	0.130783i
$928$	16.0028	−	6.62856i	0.525317	−	0.217593i
$929$	3.44439	+	8.31549i	0.113007	+	0.272822i	0.970257	−	0.242078i	$-0.0778290\pi$
$929$	3.44439	+	8.31549i	0.113007	+	0.272822i	−0.857250	+	0.514900i	$0.827829\pi$
$930$	−4.90857	−	2.03320i	−0.160958	−	0.0666711i
$931$		−	5.45766i		−	0.178867i
$932$	−5.95658	+	14.3805i	−0.195114	+	0.471048i
$933$	21.8792	−	21.8792i	0.716291	−	0.716291i
$934$	−14.2823			−0.467331
$935$	30.8811	+	30.7952i	1.00992	+	1.00711i
$936$	3.76681			0.123122
$937$	−15.5720	+	15.5720i	−0.508715	+	0.508715i	−0.914132	−	0.405417i	$-0.867126\pi$
$937$	−15.5720	+	15.5720i	−0.508715	+	0.508715i	0.405417	+	0.914132i	$0.367126\pi$
$938$	4.51683	−	10.9046i	0.147480	−	0.356048i
$939$		−	27.3422i		−	0.892278i
$940$	−7.88776	−	3.26722i	−0.257270	−	0.106565i
$941$	−22.0195	−	53.1597i	−0.717814	−	1.73296i	−0.679483	−	0.733691i	$-0.737796\pi$
$941$	−22.0195	−	53.1597i	−0.717814	−	1.73296i	−0.0383305	−	0.999265i	$-0.512204\pi$
$942$	14.6336	−	6.06145i	0.476790	−	0.197493i
$943$	54.9623	+	54.9623i	1.78982	+	1.78982i
$944$	−12.0829	−	12.0829i	−0.393265	−	0.393265i
$945$	−1.58285	+	0.655638i	−0.0514901	+	0.0213279i
$946$	−18.5767	−	44.8482i	−0.603981	−	1.45814i
$947$	−45.8667	−	18.9986i	−1.49047	−	0.617372i	−0.519048	−	0.854745i	$-0.673713\pi$
$947$	−45.8667	−	18.9986i	−1.49047	−	0.617372i	−0.971418	+	0.237373i	$0.923713\pi$
$948$			7.87948i			0.255914i
$949$	−4.72096	+	11.3974i	−0.153249	+	0.369976i
$950$	−8.61217	+	8.61217i	−0.279416	+	0.279416i
$951$	−13.1724			−0.427145
$952$	−11.6523	+	4.84555i	−0.377652	+	0.157045i
$953$	29.4215			0.953057			0.476529	−	0.879159i	$-0.341895\pi$
$953$	29.4215			0.953057			0.476529	+	0.879159i	$0.341895\pi$
$954$	−7.09049	+	7.09049i	−0.229563	+	0.229563i
$955$	−10.1006	+	24.3851i	−0.326849	+	0.789083i
$956$		−	4.32744i		−	0.139959i
$957$	22.7440	+	9.42086i	0.735208	+	0.304533i
$958$	7.08591	+	17.1069i	0.228935	+	0.552699i
$959$	12.0490	−	4.99087i	0.389083	−	0.161164i
$960$	9.67250	+	9.67250i	0.312178	+	0.312178i
$961$	16.0993	+	16.0993i	0.519334	+	0.519334i
$962$	3.02461	−	1.25283i	0.0975172	−	0.0403930i
$963$	−1.63024	−	3.93575i	−0.0525338	−	0.126828i
$964$	8.20074	+	3.39686i	0.264128	+	0.109405i
$965$		−	13.5699i		−	0.436830i
$966$	−3.19040	+	7.70230i	−0.102649	+	0.247817i
$967$	−11.3604	+	11.3604i	−0.365325	+	0.365325i	−0.865769	−	0.500444i	$-0.833170\pi$
$967$	−11.3604	+	11.3604i	−0.365325	+	0.365325i	0.500444	+	0.865769i	$0.333170\pi$
$968$	−82.9945			−2.66754
$969$	−20.8016	−	8.58236i	−0.668243	−	0.275705i
$970$	2.41797			0.0776363
$971$	1.13434	−	1.13434i	0.0364027	−	0.0364027i	−0.688671	−	0.725074i	$-0.741806\pi$
$971$	1.13434	−	1.13434i	0.0364027	−	0.0364027i	0.725074	+	0.688671i	$0.241806\pi$
$972$	0.318313	−	0.768476i	0.0102099	−	0.0246489i
$973$			16.0593i			0.514839i
$974$	12.1912	+	5.04976i	0.390631	+	0.161805i
$975$	0.972419	+	2.34763i	0.0311423	+	0.0751842i
$976$	−12.6258	+	5.22979i	−0.404143	+	0.167402i
$977$	31.0297	+	31.0297i	0.992727	+	0.992727i	0.999974	−	0.00724656i	$-0.00230667\pi$
$977$	31.0297	+	31.0297i	0.992727	+	0.992727i	−0.00724656	+	0.999974i	$0.502307\pi$
$978$	−10.8358	−	10.8358i	−0.346491	−	0.346491i
$979$	−37.1087	+	15.3709i	−1.18600	+	0.491257i
$980$	−0.545355	−	1.31660i	−0.0174207	−	0.0420574i
$981$	−10.3038	−	4.26799i	−0.328976	−	0.136267i
$982$			31.2502i			0.997234i
$983$	−3.18503	+	7.68933i	−0.101587	+	0.245252i	−0.966499	−	0.256672i	$-0.917374\pi$
$983$	−3.18503	+	7.68933i	−0.101587	+	0.245252i	0.864912	+	0.501923i	$0.167374\pi$
$984$	−21.8093	+	21.8093i	−0.695254	+	0.695254i
$985$	4.26718			0.135964
$986$	6.77730	−	16.4265i	0.215833	−	0.523128i
$987$	5.99099			0.190695
$988$	−3.95056	+	3.95056i	−0.125684	+	0.125684i
$989$	21.4734	−	51.8413i	0.682813	−	1.64846i
$990$			11.4324i			0.363347i
$991$	1.05615	+	0.437473i	0.0335498	+	0.0138968i	0.399395	−	0.916779i	$-0.369220\pi$
$991$	1.05615	+	0.437473i	0.0335498	+	0.0138968i	−0.365845	+	0.930676i	$0.619220\pi$
$992$	4.76956	+	11.5147i	0.151434	+	0.365593i
$993$	21.5575	−	8.92939i	0.684105	−	0.283366i
$994$	2.74162	+	2.74162i	0.0869590	+	0.0869590i
$995$	21.8356	+	21.8356i	0.692236	+	0.692236i
$996$	3.22904	−	1.33751i	0.102316	−	0.0423806i
$997$	10.6994	+	25.8306i	0.338853	+	0.818063i	0.997826	+	0.0658971i	$0.0209909\pi$
$997$	10.6994	+	25.8306i	0.338853	+	0.818063i	−0.658974	+	0.752166i	$0.729009\pi$
$998$	27.8921	+	11.5533i	0.882908	+	0.365712i
$999$		−	2.46117i		−	0.0778679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.u.a.127.5	✓	32
17.7	odd	16		6069.2.a.bk.1.7		16
17.10	odd	16		6069.2.a.bj.1.7		16
17.15	even	8	inner	357.2.u.a.253.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.u.a.127.5	✓	32	1.1	even	1	trivial
357.2.u.a.253.5	yes	32	17.15	even	8	inner
6069.2.a.bj.1.7		16	17.10	odd	16
6069.2.a.bk.1.7		16	17.7	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.764267 - 0.764267i) q^{2} +(-0.382683 + 0.923880i) q^{3} +0.831793i q^{4} +(-1.58285 - 0.655638i) q^{5} +(0.413618 + 0.998563i) q^{6} +(0.923880 - 0.382683i) q^{7} +(2.16424 + 2.16424i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-1.71080 + 0.708638i) q^{10} +(2.36262 + 5.70387i) q^{11} +(-0.768476 - 0.318313i) q^{12} +1.23070i q^{13} +(0.413618 - 0.998563i) q^{14} +(1.21146 - 1.21146i) q^{15} +1.64454 q^{16} +(-2.91141 + 2.91953i) q^{17} -1.08084 q^{18} +(3.85915 - 3.85915i) q^{19} +(0.545355 - 1.31660i) q^{20} +1.00000i q^{21} +(6.16495 + 2.55361i) q^{22} +(2.95179 + 7.12624i) q^{23} +(-2.82772 + 1.17128i) q^{24} +(-1.45998 - 1.45998i) q^{25} +(0.940583 + 0.940583i) q^{26} +(0.923880 - 0.382683i) q^{27} +(0.318313 + 0.768476i) q^{28} +(-3.68393 - 1.52593i) q^{29} -1.85176i q^{30} +(1.09798 - 2.65076i) q^{31} +(-3.07163 + 3.07163i) q^{32} -6.17383 q^{33} +(0.00620859 + 4.45640i) q^{34} -1.71327 q^{35} +(0.588166 - 0.588166i) q^{36} +(0.941849 - 2.27382i) q^{37} -5.89883i q^{38} +(-1.13702 - 0.470968i) q^{39} +(-2.00672 - 4.84464i) q^{40} +(9.31001 - 3.85633i) q^{41} +(0.764267 + 0.764267i) q^{42} +(-5.14399 - 5.14399i) q^{43} +(-4.74444 + 1.96521i) q^{44} +(0.655638 + 1.58285i) q^{45} +(7.70230 + 3.19040i) q^{46} -5.99099i q^{47} +(-0.629336 + 1.51935i) q^{48} +(0.707107 - 0.707107i) q^{49} -2.23163 q^{50} +(-1.58315 - 3.80705i) q^{51} -1.02369 q^{52} +(6.56019 - 6.56019i) q^{53} +(0.413618 - 0.998563i) q^{54} -10.5774i q^{55} +(2.82772 + 1.17128i) q^{56} +(2.08855 + 5.04222i) q^{57} +(-3.98173 + 1.64929i) q^{58} +(-7.34731 - 7.34731i) q^{59} +(1.00768 + 1.00768i) q^{60} +(-7.67745 + 3.18010i) q^{61} +(-1.18674 - 2.86504i) q^{62} +(-0.923880 - 0.382683i) q^{63} +7.98415i q^{64} +(0.806894 - 1.94801i) q^{65} +(-4.71845 + 4.71845i) q^{66} +10.9203 q^{67} +(-2.42845 - 2.42169i) q^{68} -7.71339 q^{69} +(-1.30939 + 1.30939i) q^{70} +(-1.37278 + 3.31420i) q^{71} -3.06070i q^{72} +(9.26092 + 3.83600i) q^{73} +(-1.01798 - 2.45763i) q^{74} +(1.90755 - 0.790135i) q^{75} +(3.21001 + 3.21001i) q^{76} +(4.36555 + 4.36555i) q^{77} +(-1.22893 + 0.509040i) q^{78} +(-3.62512 - 8.75181i) q^{79} +(-2.60305 - 1.07822i) q^{80} +1.00000i q^{81} +(4.16806 - 10.0626i) q^{82} +(-2.97117 + 2.97117i) q^{83} -0.831793 q^{84} +(6.52249 - 2.71236i) q^{85} -7.86276 q^{86} +(2.81956 - 2.81956i) q^{87} +(-7.23129 + 17.4579i) q^{88} +6.50588i q^{89} +(1.71080 + 0.708638i) q^{90} +(0.470968 + 1.13702i) q^{91} +(-5.92756 + 2.45527i) q^{92} +(2.02880 + 2.02880i) q^{93} +(-4.57871 - 4.57871i) q^{94} +(-8.63866 + 3.57825i) q^{95} +(-1.66235 - 4.01327i) q^{96} +(-1.20637 - 0.499696i) q^{97} -1.08084i q^{98} +(2.36262 - 5.70387i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{6} - 32 q^{10} + 8 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} + 8 q^{19} - 16 q^{20} - 8 q^{23} - 8 q^{24} + 24 q^{25} - 32 q^{26} + 24 q^{29} + 8 q^{31} - 40 q^{32} + 8 q^{33} - 8 q^{34} - 8 q^{35}+ \cdots + 96 q^{97}+O(q^{100}) \) 32 * q + 8 * q^6 - 32 * q^10 + 8 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 + 8 * q^19 - 16 * q^20 - 8 * q^23 - 8 * q^24 + 24 * q^25 - 32 * q^26 + 24 * q^29 + 8 * q^31 - 40 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^35 - 8 * q^36 + 72 * q^37 - 16 * q^39 + 40 * q^40 + 8 * q^41 - 32 * q^43 - 48 * q^44 + 8 * q^45 + 40 * q^46 + 32 * q^48 + 56 * q^50 - 16 * q^51 - 56 * q^53 + 8 * q^54 + 8 * q^56 + 16 * q^57 - 32 * q^58 - 48 * q^59 - 48 * q^60 + 8 * q^61 - 24 * q^62 + 16 * q^66 + 96 * q^67 - 16 * q^68 + 8 * q^69 - 16 * q^70 + 24 * q^71 - 24 * q^73 - 32 * q^74 - 16 * q^75 - 48 * q^76 - 24 * q^77 - 72 * q^78 - 48 * q^79 + 72 * q^80 + 96 * q^82 - 24 * q^83 + 24 * q^84 - 136 * q^85 - 32 * q^87 + 16 * q^88 + 32 * q^90 + 8 * q^91 + 136 * q^92 + 8 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 + 96 * q^97

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