LMFDB - Embedded newform 273.2.bh.a.131.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(131,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("273.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.14
Character	$\chi$	$=$	273.131
Dual form			273.2.bh.a.248.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.636389 - 0.367419i) q^{2} +(1.70069 - 0.328105i) q^{3} +(-0.730006 - 1.26441i) q^{4} +(1.03100 - 1.78574i) q^{5} +(-1.20285 - 0.416064i) q^{6} +(-0.617429 - 2.57270i) q^{7} +2.54255i q^{8} +(2.78469 - 1.11601i) q^{9} +O(q^{10})$	\(q+(-0.636389 - 0.367419i) q^{2} +(1.70069 - 0.328105i) q^{3} +(-0.730006 - 1.26441i) q^{4} +(1.03100 - 1.78574i) q^{5} +(-1.20285 - 0.416064i) q^{6} +(-0.617429 - 2.57270i) q^{7} +2.54255i q^{8} +(2.78469 - 1.11601i) q^{9} +(-1.31223 + 0.757615i) q^{10} +(-4.03218 + 2.32798i) q^{11} +(-1.65637 - 1.91085i) q^{12} +1.00000i q^{13} +(-0.552334 + 1.86409i) q^{14} +(1.16750 - 3.37526i) q^{15} +(-0.525831 + 0.910766i) q^{16} +(-2.37277 - 4.10975i) q^{17} +(-2.18219 - 0.312934i) q^{18} +(2.18124 + 1.25934i) q^{19} -3.01053 q^{20} +(-1.89417 - 4.17278i) q^{21} +3.42138 q^{22} +(6.58248 + 3.80040i) q^{23} +(0.834223 + 4.32409i) q^{24} +(0.374097 + 0.647955i) q^{25} +(0.367419 - 0.636389i) q^{26} +(4.36973 - 2.81166i) q^{27} +(-2.80221 + 2.65877i) q^{28} -7.76916i q^{29} +(-1.98312 + 1.71902i) q^{30} +(4.49527 - 2.59534i) q^{31} +(5.07309 - 2.92895i) q^{32} +(-6.09367 + 5.28215i) q^{33} +3.48720i q^{34} +(-5.23073 - 1.54988i) q^{35} +(-3.44394 - 2.70630i) q^{36} +(-2.73320 + 4.73405i) q^{37} +(-0.925409 - 1.60286i) q^{38} +(0.328105 + 1.70069i) q^{39} +(4.54032 + 2.62136i) q^{40} -3.99239 q^{41} +(-0.327732 + 3.35147i) q^{42} +8.41855 q^{43} +(5.88704 + 3.39888i) q^{44} +(0.878108 - 6.12333i) q^{45} +(-2.79268 - 4.83706i) q^{46} +(1.09516 - 1.89686i) q^{47} +(-0.595449 + 1.72146i) q^{48} +(-6.23756 + 3.17692i) q^{49} -0.549801i q^{50} +(-5.38377 - 6.21090i) q^{51} +(1.26441 - 0.730006i) q^{52} +(-0.754260 + 0.435472i) q^{53} +(-3.81391 + 0.183783i) q^{54} +9.60055i q^{55} +(6.54122 - 1.56984i) q^{56} +(4.12280 + 1.42607i) q^{57} +(-2.85454 + 4.94420i) q^{58} +(0.620058 + 1.07397i) q^{59} +(-5.11998 + 0.987770i) q^{60} +(9.38648 + 5.41929i) q^{61} -3.81431 q^{62} +(-4.59051 - 6.47512i) q^{63} -2.20129 q^{64} +(1.78574 + 1.03100i) q^{65} +(5.81871 - 1.12257i) q^{66} +(-2.06791 - 3.58172i) q^{67} +(-3.46427 + 6.00029i) q^{68} +(12.4417 + 4.30356i) q^{69} +(2.75932 + 2.90819i) q^{70} +15.1751i q^{71} +(2.83751 + 7.08022i) q^{72} +(-6.04087 + 3.48770i) q^{73} +(3.47876 - 2.00846i) q^{74} +(0.848820 + 0.979227i) q^{75} -3.67729i q^{76} +(8.47878 + 8.93623i) q^{77} +(0.416064 - 1.20285i) q^{78} +(-3.36228 + 5.82364i) q^{79} +(1.08426 + 1.87799i) q^{80} +(6.50905 - 6.21549i) q^{81} +(2.54071 + 1.46688i) q^{82} +0.428315 q^{83} +(-3.89334 + 5.44116i) q^{84} -9.78524 q^{85} +(-5.35747 - 3.09314i) q^{86} +(-2.54910 - 13.2129i) q^{87} +(-5.91901 - 10.2520i) q^{88} +(-1.97328 + 3.41782i) q^{89} +(-2.80865 + 3.57418i) q^{90} +(2.57270 - 0.617429i) q^{91} -11.0973i q^{92} +(6.79351 - 5.88879i) q^{93} +(-1.39389 + 0.804762i) q^{94} +(4.49769 - 2.59674i) q^{95} +(7.66675 - 6.64574i) q^{96} +1.05407i q^{97} +(5.13677 + 0.270045i) q^{98} +(-8.63034 + 10.9827i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.636389	−	0.367419i	−0.449995	−	0.259805i	0.257833	−	0.966189i	$-0.416991\pi$
$2$	−0.636389	−	0.367419i	−0.449995	−	0.259805i	−0.707828	+	0.706385i	$0.750325\pi$
$3$	1.70069	−	0.328105i	0.981894	−	0.189431i
$3$	1.70069	−	0.328105i	0.981894	−	0.189431i
$4$	−0.730006	−	1.26441i	−0.365003	−	0.632204i
$5$	1.03100	−	1.78574i	0.461075	−	0.798606i	−0.537940	−	0.842983i	$-0.680797\pi$
$5$	1.03100	−	1.78574i	0.461075	−	0.798606i	0.999015	+	0.0443777i	$0.0141305\pi$
$6$	−1.20285	−	0.416064i	−0.491062	−	0.169857i
$7$	−0.617429	−	2.57270i	−0.233366	−	0.972389i
$7$	−0.617429	−	2.57270i	−0.233366	−	0.972389i
$8$			2.54255i			0.898927i
$9$	2.78469	−	1.11601i	0.928231	−	0.372003i
$10$	−1.31223	+	0.757615i	−0.414963	+	0.239579i
$11$	−4.03218	+	2.32798i	−1.21575	+	0.701913i	−0.964006	−	0.265882i	$-0.914337\pi$
$11$	−4.03218	+	2.32798i	−1.21575	+	0.701913i	−0.251743	+	0.967794i	$0.581004\pi$
$12$	−1.65637	−	1.91085i	−0.478154	−	0.551614i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−0.552334	+	1.86409i	−0.147618	+	0.498199i
$15$	1.16750	−	3.37526i	0.301446	−	0.871488i
$16$	−0.525831	+	0.910766i	−0.131458	+	0.227692i
$17$	−2.37277	−	4.10975i	−0.575480	−	0.996761i	−0.995989	−	0.0894726i	$-0.971482\pi$
$17$	−2.37277	−	4.10975i	−0.575480	−	0.996761i	0.420509	−	0.907288i	$-0.361851\pi$
$18$	−2.18219	−	0.312934i	−0.514347	−	0.0737593i
$19$	2.18124	+	1.25934i	0.500410	+	0.288912i	0.728883	−	0.684639i	$-0.240040\pi$
$19$	2.18124	+	1.25934i	0.500410	+	0.288912i	−0.228473	+	0.973550i	$0.573373\pi$
$20$	−3.01053			−0.673176
$21$	−1.89417	−	4.17278i	−0.413342	−	0.910576i
$22$	3.42138			0.729440
$23$	6.58248	+	3.80040i	1.37254	+	0.792438i	0.991248	−	0.132016i	$-0.0421449\pi$
$23$	6.58248	+	3.80040i	1.37254	+	0.792438i	0.381295	+	0.924453i	$0.375478\pi$
$24$	0.834223	+	4.32409i	0.170285	+	0.882651i
$25$	0.374097	+	0.647955i	0.0748194	+	0.129591i
$26$	0.367419	−	0.636389i	0.0720568	−	0.124806i
$27$	4.36973	−	2.81166i	0.840956	−	0.541104i
$28$	−2.80221	+	2.65877i	−0.529569	+	0.502460i
$29$		−	7.76916i		−	1.44270i	−0.692573	−	0.721348i	$-0.743523\pi$
$29$		−	7.76916i		−	1.44270i	0.692573	−	0.721348i	$-0.256477\pi$
$30$	−1.98312	+	1.71902i	−0.362066	+	0.313848i
$31$	4.49527	−	2.59534i	0.807374	−	0.466137i	−0.0386694	−	0.999252i	$-0.512312\pi$
$31$	4.49527	−	2.59534i	0.807374	−	0.466137i	0.846043	+	0.533115i	$0.178979\pi$
$32$	5.07309	−	2.92895i	0.896804	−	0.517770i
$33$	−6.09367	+	5.28215i	−1.06077	+	0.919505i
$34$			3.48720i			0.598050i
$35$	−5.23073	−	1.54988i	−0.884155	−	0.261977i
$36$	−3.44394	−	2.70630i	−0.573989	−	0.451049i
$37$	−2.73320	+	4.73405i	−0.449336	+	0.778272i	−0.998343	−	0.0575453i	$-0.981673\pi$
$37$	−2.73320	+	4.73405i	−0.449336	+	0.778272i	0.549007	+	0.835818i	$0.315006\pi$
$38$	−0.925409	−	1.60286i	−0.150121	−	0.260017i
$39$	0.328105	+	1.70069i	0.0525388	+	0.272328i
$40$	4.54032	+	2.62136i	0.717888	+	0.414473i
$41$	−3.99239			−0.623506			−0.311753	−	0.950163i	$-0.600916\pi$
$41$	−3.99239			−0.623506			−0.311753	+	0.950163i	$0.600916\pi$
$42$	−0.327732	+	3.35147i	−0.0505701	+	0.517142i
$43$	8.41855			1.28382			0.641908	−	0.766781i	$-0.278143\pi$
$43$	8.41855			1.28382			0.641908	+	0.766781i	$0.278143\pi$
$44$	5.88704	+	3.39888i	0.887504	+	0.512401i
$45$	0.878108	−	6.12333i	0.130901	−	0.912812i
$46$	−2.79268	−	4.83706i	−0.411758	−	0.713186i
$47$	1.09516	−	1.89686i	0.159745	−	0.276686i	−0.775032	−	0.631922i	$-0.782266\pi$
$47$	1.09516	−	1.89686i	0.159745	−	0.276686i	0.934777	+	0.355236i	$0.115600\pi$
$48$	−0.595449	+	1.72146i	−0.0859457	+	0.248471i
$49$	−6.23756	+	3.17692i	−0.891080	+	0.453845i
$50$		−	0.549801i		−	0.0777536i
$51$	−5.38377	−	6.21090i	−0.753878	−	0.869699i
$52$	1.26441	−	0.730006i	0.175342	−	0.101234i
$53$	−0.754260	+	0.435472i	−0.103606	+	0.0598167i	−0.550907	−	0.834566i	$-0.685718\pi$
$53$	−0.754260	+	0.435472i	−0.103606	+	0.0598167i	0.447302	+	0.894383i	$0.352385\pi$
$54$	−3.81391	+	0.183783i	−0.519007	+	0.0250097i
$55$			9.60055i			1.29454i
$56$	6.54122	−	1.56984i	0.874107	−	0.209779i
$57$	4.12280	+	1.42607i	0.546078	+	0.188887i
$58$	−2.85454	+	4.94420i	−0.374819	+	0.649206i
$59$	0.620058	+	1.07397i	0.0807247	+	0.139819i	0.903561	−	0.428459i	$-0.140943\pi$
$59$	0.620058	+	1.07397i	0.0807247	+	0.139819i	−0.822837	+	0.568278i	$0.807610\pi$
$60$	−5.11998	+	0.987770i	−0.660987	+	0.127521i
$61$	9.38648	+	5.41929i	1.20182	+	0.693869i	0.960959	−	0.276692i	$-0.0892380\pi$
$61$	9.38648	+	5.41929i	1.20182	+	0.693869i	0.240857	+	0.970561i	$0.422571\pi$
$62$	−3.81431			−0.484418
$63$	−4.59051	−	6.47512i	−0.578350	−	0.815789i
$64$	−2.20129			−0.275161
$65$	1.78574	+	1.03100i	0.221493	+	0.127879i
$66$	5.81871	−	1.12257i	0.716233	−	0.138179i
$67$	−2.06791	−	3.58172i	−0.252635	−	0.437576i	0.711616	−	0.702569i	$-0.247964\pi$
$67$	−2.06791	−	3.58172i	−0.252635	−	0.437576i	−0.964250	+	0.264993i	$0.914630\pi$
$68$	−3.46427	+	6.00029i	−0.420104	+	0.727642i
$69$	12.4417	+	4.30356i	1.49780	+	0.518087i
$70$	2.75932	+	2.90819i	0.329802	+	0.347596i
$71$			15.1751i			1.80095i	0.434906	+	0.900476i	$0.356782\pi$
$71$			15.1751i			1.80095i	−0.434906	+	0.900476i	$0.643218\pi$
$72$	2.83751	+	7.08022i	0.334404	+	0.834412i
$73$	−6.04087	+	3.48770i	−0.707031	+	0.408204i	−0.809961	−	0.586484i	$-0.800512\pi$
$73$	−6.04087	+	3.48770i	−0.707031	+	0.408204i	0.102930	+	0.994689i	$0.467178\pi$
$74$	3.47876	−	2.00846i	0.404397	−	0.233479i
$75$	0.848820	+	0.979227i	0.0980133	+	0.113071i
$76$		−	3.67729i		−	0.421815i
$77$	8.47878	+	8.93623i	0.966247	+	1.01838i
$78$	0.416064	−	1.20285i	0.0471100	−	0.136196i
$79$	−3.36228	+	5.82364i	−0.378286	+	0.655211i	−0.990813	−	0.135239i	$-0.956820\pi$
$79$	−3.36228	+	5.82364i	−0.378286	+	0.655211i	0.612527	+	0.790450i	$0.290153\pi$
$80$	1.08426	+	1.87799i	0.121224	+	0.209966i
$81$	6.50905	−	6.21549i	0.723227	−	0.690610i
$82$	2.54071	+	1.46688i	0.280575	+	0.161990i
$83$	0.428315			0.0470137			0.0235068	−	0.999724i	$-0.492517\pi$
$83$	0.428315			0.0470137			0.0235068	+	0.999724i	$0.492517\pi$
$84$	−3.89334	+	5.44116i	−0.424799	+	0.593680i
$85$	−9.78524			−1.06136
$86$	−5.35747	−	3.09314i	−0.577711	−	0.333541i
$87$	−2.54910	−	13.2129i	−0.273292	−	1.41657i
$88$	−5.91901	−	10.2520i	−0.630968	−	1.09287i
$89$	−1.97328	+	3.41782i	−0.209167	+	0.362288i	−0.951452	−	0.307796i	$-0.900409\pi$
$89$	−1.97328	+	3.41782i	−0.209167	+	0.362288i	0.742285	+	0.670084i	$0.233742\pi$
$90$	−2.80865	+	3.57418i	−0.296057	+	0.376752i
$91$	2.57270	−	0.617429i	0.269692	−	0.0647241i
$92$		−	11.0973i		−	1.15697i
$93$	6.79351	−	5.88879i	0.704454	−	0.610639i
$94$	−1.39389	+	0.804762i	−0.143769	+	0.0830049i
$95$	4.49769	−	2.59674i	0.461453	−	0.266420i
$96$	7.66675	−	6.64574i	0.782485	−	0.678278i
$97$			1.05407i			0.107024i	0.998567	+	0.0535121i	$0.0170416\pi$
$97$			1.05407i			0.107024i	−0.998567	+	0.0535121i	$0.982958\pi$
$98$	5.13677	+	0.270045i	0.518893	+	0.0272787i
$99$	−8.63034	+	10.9827i	−0.867382	+	1.10380i
$100$	0.546186	−	0.946022i	0.0546186	−	0.0946022i
$101$	1.57162	+	2.72213i	0.156382	+	0.270862i	0.933562	−	0.358417i	$-0.116683\pi$
$101$	1.57162	+	2.72213i	0.156382	+	0.270862i	−0.777179	+	0.629279i	$0.783350\pi$
$102$	1.14417	+	5.93064i	0.113289	+	0.587221i
$103$	11.9982	+	6.92714i	1.18221	+	0.682552i	0.956526	−	0.291648i	$-0.0942036\pi$
$103$	11.9982	+	6.92714i	1.18221	+	0.682552i	0.225688	+	0.974200i	$0.427537\pi$
$104$	−2.54255			−0.249318
$105$	−9.40437	−	0.919631i	−0.917773	−	0.0897468i
$106$	0.640003			0.0621626
$107$	−4.60916	−	2.66110i	−0.445584	−	0.257258i	0.260379	−	0.965506i	$-0.416152\pi$
$107$	−4.60916	−	2.66110i	−0.445584	−	0.257258i	−0.705963	+	0.708248i	$0.749486\pi$
$108$	−6.74502	−	3.47260i	−0.649040	−	0.334151i
$109$	−4.52220	−	7.83269i	−0.433148	−	0.750235i	0.563994	−	0.825779i	$-0.309264\pi$
$109$	−4.52220	−	7.83269i	−0.433148	−	0.750235i	−0.997142	+	0.0755437i	$0.975931\pi$
$110$	3.52743	−	6.10968i	0.336327	−	0.582535i
$111$	−3.09507	+	8.94792i	−0.293771	+	0.849299i
$112$	2.66779	+	0.790472i	0.252083	+	0.0746926i
$113$		−	1.79902i		−	0.169238i	−0.996413	−	0.0846188i	$-0.973033\pi$
$113$		−	1.79902i		−	0.169238i	0.996413	−	0.0846188i	$-0.0269672\pi$
$114$	−2.09974	−	2.42233i	−0.196659	−	0.226872i
$115$	13.5730	−	7.83639i	1.26569	−	0.730747i
$116$	−9.82338	+	5.67153i	−0.912078	+	0.526589i
$117$	1.11601	+	2.78469i	0.103175	+	0.257445i
$118$		−	0.911285i		−	0.0838906i
$119$	−9.10814	+	8.64189i	−0.834942	+	0.792201i
$120$	8.58176	+	2.96841i	0.783404	+	0.270978i
$121$	5.33899	−	9.24740i	0.485363	−	0.840673i
$122$	−3.98230	−	6.89755i	−0.360541	−	0.624475i
$123$	−6.78982	+	1.30992i	−0.612217	+	0.118112i
$124$	−6.56314	−	3.78923i	−0.589388	−	0.340283i
$125$	11.8527			1.06014
$126$	0.542262	+	5.80734i	0.0483086	+	0.517359i
$127$	−21.7797			−1.93263			−0.966316	−	0.257359i	$-0.917148\pi$
$127$	−21.7797			−1.93263			−0.966316	+	0.257359i	$0.917148\pi$
$128$	−8.74531	−	5.04911i	−0.772983	−	0.446282i
$129$	14.3173	−	2.76217i	1.26057	−	0.243195i
$130$	−0.757615	−	1.31223i	−0.0664472	−	0.115090i
$131$	9.46302	−	16.3904i	0.826788	−	1.43204i	−0.0737576	−	0.997276i	$-0.523499\pi$
$131$	9.46302	−	16.3904i	0.826788	−	1.43204i	0.900545	−	0.434762i	$-0.143168\pi$
$132$	11.1272	+	3.84888i	0.968500	+	0.335002i
$133$	1.89314	−	6.38921i	0.164156	−	0.554015i
$134$			3.03915i			0.262543i
$135$	−0.515704	−	10.7020i	−0.0443848	−	0.921082i
$136$	10.4492	−	6.03287i	0.896015	−	0.517315i
$137$	−15.9230	+	9.19313i	−1.36039	+	0.785422i	−0.989676	−	0.143325i	$-0.954221\pi$
$137$	−15.9230	+	9.19313i	−1.36039	+	0.785422i	−0.370715	+	0.928747i	$0.620887\pi$
$138$	−6.33654	−	7.31005i	−0.539402	−	0.622273i
$139$		−	4.10030i		−	0.347783i	−0.984765	−	0.173892i	$-0.944366\pi$
$139$		−	4.10030i		−	0.347783i	0.984765	−	0.173892i	$-0.0556342\pi$
$140$	1.85879	+	7.74520i	0.157096	+	0.654589i
$141$	1.24015	−	3.58531i	0.104439	−	0.301937i
$142$	5.57562	−	9.65725i	0.467895	−	0.810419i
$143$	−2.32798	−	4.03218i	−0.194676	−	0.337188i
$144$	−0.447855	+	3.12304i	−0.0373213	+	0.260253i
$145$	−13.8737	−	8.00996i	−1.15215	−	0.665191i
$146$	5.12579			0.424213
$147$	−9.56580	+	7.44953i	−0.788974	+	0.614427i
$148$	7.98102			0.656036
$149$	−13.6539	−	7.88308i	−1.11857	−	0.645807i	−0.177535	−	0.984114i	$-0.556812\pi$
$149$	−13.6539	−	7.88308i	−1.11857	−	0.645807i	−0.941036	+	0.338307i	$0.890146\pi$
$150$	−0.180392	−	0.935042i	−0.0147290	−	0.0763458i
$151$	−7.18429	−	12.4435i	−0.584649	−	1.01264i	−0.994919	−	0.100678i	$-0.967899\pi$
$151$	−7.18429	−	12.4435i	−0.584649	−	1.01264i	0.410270	−	0.911964i	$-0.365434\pi$
$152$	−3.20193	+	5.54590i	−0.259711	+	0.449832i
$153$	−11.1939	−	8.79637i	−0.904977	−	0.711144i
$154$	−2.11246	−	8.80218i	−0.170227	−	0.709300i
$155$		−	10.7031i		−	0.859697i
$156$	1.91085	−	1.65637i	0.152990	−	0.132616i
$157$	−6.99731	+	4.03990i	−0.558446	+	0.322419i	−0.752521	−	0.658568i	$-0.771163\pi$
$157$	−6.99731	+	4.03990i	−0.558446	+	0.322419i	0.194076	+	0.980987i	$0.437829\pi$
$158$	4.27944	−	2.47073i	0.340454	−	0.196561i
$159$	−1.13988	+	0.988079i	−0.0903985	+	0.0783598i
$160$		−	12.0789i		−	0.954924i
$161$	5.71307	−	19.2812i	0.450253	−	1.51957i
$162$	−6.42597	+	1.56392i	−0.504872	+	0.122873i
$163$	−3.27936	+	5.68001i	−0.256859	+	0.444893i	−0.965399	−	0.260778i	$-0.916021\pi$
$163$	−3.27936	+	5.68001i	−0.256859	+	0.444893i	0.708540	+	0.705671i	$0.249354\pi$
$164$	2.91447	+	5.04801i	0.227582	+	0.394183i
$165$	3.14999	+	16.3276i	0.245226	+	1.27110i
$166$	−0.272575	−	0.157371i	−0.0211559	−	0.0122144i
$167$	16.9314			1.31019			0.655097	−	0.755545i	$-0.272628\pi$
$167$	16.9314			1.31019			0.655097	+	0.755545i	$0.272628\pi$
$168$	10.6095	−	4.81602i	0.818541	−	0.371564i
$169$	−1.00000			−0.0769231
$170$	6.22722	+	3.59529i	0.477606	+	0.275746i
$171$	7.47950	+	1.07259i	0.571972	+	0.0820229i
$172$	−6.14559	−	10.6445i	−0.468597	−	0.811634i
$173$	−10.0883	+	17.4734i	−0.766998	+	1.32848i	0.172185	+	0.985065i	$0.444917\pi$
$173$	−10.0883	+	17.4734i	−0.766998	+	1.32848i	−0.939184	+	0.343415i	$0.888416\pi$
$174$	−3.23247	+	9.34514i	−0.245053	+	0.708454i
$175$	1.43601	−	1.36250i	0.108552	−	0.102996i
$176$		−	4.89650i		−	0.369088i
$177$	1.40690	+	1.62305i	0.105749	+	0.121996i
$178$	2.51155	−	1.45004i	0.188248	−	0.108685i
$179$	5.57825	−	3.22061i	0.416938	−	0.240719i	−0.276828	−	0.960919i	$-0.589283\pi$
$179$	5.57825	−	3.22061i	0.416938	−	0.240719i	0.693766	+	0.720200i	$0.255950\pi$
$180$	−8.38341	+	3.35978i	−0.624863	+	0.250423i
$181$			3.91701i			0.291149i	0.989347	+	0.145574i	$0.0465030\pi$
$181$			3.91701i			0.291149i	−0.989347	+	0.145574i	$0.953497\pi$
$182$	−1.86409	−	0.552334i	−0.138176	−	0.0409417i
$183$	17.7416	+	6.13678i	1.31150	+	0.453644i
$184$	−9.66270	+	16.7363i	−0.712344	+	1.23382i
$185$	5.63584	+	9.76156i	0.414355	+	0.717684i
$186$	−6.48697	+	1.25150i	−0.475648	+	0.0917641i
$187$	19.1348	+	11.0475i	1.39928	+	0.807874i
$188$	−3.19788			−0.233229
$189$	−9.93155	−	9.50601i	−0.722414	−	0.691461i
$190$	−3.81637			−0.276869
$191$	18.5943	+	10.7354i	1.34544	+	0.776788i	0.987599	−	0.156997i	$-0.0501812\pi$
$191$	18.5943	+	10.7354i	1.34544	+	0.776788i	0.357836	+	0.933784i	$0.383515\pi$
$192$	−3.74370	+	0.722252i	−0.270179	+	0.0521241i
$193$	0.891272	+	1.54373i	0.0641552	+	0.111120i	0.896319	−	0.443410i	$-0.146231\pi$
$193$	0.891272	+	1.54373i	0.0641552	+	0.111120i	−0.832164	+	0.554530i	$0.812898\pi$
$194$	0.387284	−	0.670795i	0.0278054	−	0.0481603i
$195$	3.37526	+	1.16750i	0.241707	+	0.0836061i
$196$	8.57038	+	5.56765i	0.612170	+	0.397690i
$197$			5.88943i			0.419604i	0.977744	+	0.209802i	$0.0672820\pi$
$197$			5.88943i			0.419604i	−0.977744	+	0.209802i	$0.932718\pi$
$198$	9.52749	−	3.81829i	0.677090	−	0.271354i
$199$	−3.58920	+	2.07223i	−0.254432	+	0.146896i	−0.621792	−	0.783183i	$-0.713595\pi$
$199$	−3.58920	+	2.07223i	−0.254432	+	0.146896i	0.367360	+	0.930079i	$0.380262\pi$
$200$	−1.64746	+	0.951160i	−0.116493	+	0.0672572i
$201$	−4.69204	−	5.41290i	−0.330951	−	0.381797i
$202$		−	2.30978i		−	0.162515i
$203$	−19.9877	+	4.79690i	−1.40286	+	0.336677i
$204$	−3.92292	+	11.3413i	−0.274660	+	0.794048i
$205$	−4.11613	+	7.12935i	−0.287483	+	0.497936i
$206$	−5.09033	−	8.81671i	−0.354660	−	0.614289i
$207$	22.5715	+	3.23683i	1.56883	+	0.224976i
$208$	−0.910766	−	0.525831i	−0.0631503	−	0.0364598i
$209$	−11.7268			−0.811163
$210$	5.64695	+	4.04059i	0.389676	+	0.278827i
$211$	5.18433			0.356904			0.178452	−	0.983949i	$-0.442891\pi$
$211$	5.18433			0.356904			0.178452	+	0.983949i	$0.442891\pi$
$212$	1.10123	+	0.635795i	0.0756327	+	0.0436666i
$213$	4.97902	+	25.8081i	0.341157	+	1.76834i
$214$	1.95548	+	3.38699i	0.133674	+	0.231530i
$215$	8.67948	−	15.0333i	0.591936	−	1.02526i
$216$	7.14878	+	11.1103i	0.486413	+	0.755958i
$217$	−9.45254	−	9.96253i	−0.641680	−	0.676300i
$218$			6.64618i			0.450136i
$219$	−9.12932	+	7.91353i	−0.616902	+	0.534747i
$220$	12.1390	−	7.00846i	0.818412	−	0.472510i
$221$	4.10975	−	2.37277i	0.276452	−	0.159609i
$222$	5.25730	−	4.55717i	0.352847	−	0.305857i
$223$			18.7302i			1.25427i	0.778912	+	0.627134i	$0.215772\pi$
$223$			18.7302i			1.25427i	−0.778912	+	0.627134i	$0.784228\pi$
$224$	−10.6676	−	11.2431i	−0.712758	−	0.751213i
$225$	1.76487	+	1.38686i	0.117658	+	0.0924573i
$226$	−0.660995	+	1.14488i	−0.0439687	+	0.0761560i
$227$	3.51302	+	6.08472i	0.233167	+	0.403857i	0.958738	−	0.284290i	$-0.0917578\pi$
$227$	3.51302	+	6.08472i	0.233167	+	0.403857i	−0.725571	+	0.688147i	$0.758424\pi$
$228$	−1.20654	−	6.25394i	−0.0799050	−	0.414177i
$229$	−11.3143	−	6.53230i	−0.747668	−	0.431667i	0.0771824	−	0.997017i	$-0.475408\pi$
$229$	−11.3143	−	6.53230i	−0.747668	−	0.431667i	−0.824851	+	0.565350i	$0.808741\pi$
$230$	−11.5170			−0.759405
$231$	17.3518	+	12.4158i	1.14166	+	0.816901i
$232$	19.7535			1.29688
$233$	−3.53934	−	2.04344i	−0.231870	−	0.133870i	0.379564	−	0.925165i	$-0.376074\pi$
$233$	−3.53934	−	2.04344i	−0.231870	−	0.133870i	−0.611434	+	0.791295i	$0.709407\pi$
$234$	0.312934	−	2.18219i	0.0204572	−	0.142654i
$235$	−2.25820	−	3.91132i	−0.147309	−	0.255146i
$236$	0.905293	−	1.56801i	0.0589296	−	0.102069i
$237$	−3.80743	+	11.0074i	−0.247319	+	0.715007i
$238$	8.97151	−	2.15310i	0.581537	−	0.139565i
$239$		−	5.55543i		−	0.359351i	−0.983726	−	0.179676i	$-0.942495\pi$
$239$		−	5.55543i		−	0.359351i	0.983726	−	0.179676i	$-0.0575048\pi$
$240$	2.46017	+	2.83813i	0.158803	+	0.183201i
$241$	−0.872052	+	0.503480i	−0.0561738	+	0.0324320i	−0.527824	−	0.849354i	$-0.676992\pi$
$241$	−0.872052	+	0.503480i	−0.0561738	+	0.0324320i	0.471650	+	0.881786i	$0.343659\pi$
$242$	−6.79534	+	3.92329i	−0.436821	+	0.252199i
$243$	9.03054	−	12.7063i	0.579309	−	0.815108i
$244$		−	15.8245i		−	1.01306i
$245$	−0.757760	+	14.4140i	−0.0484115	+	0.920879i
$246$	4.80225	+	1.66109i	0.306180	+	0.105907i
$247$	−1.25934	+	2.18124i	−0.0801297	+	0.138789i
$248$	6.59879	+	11.4294i	0.419023	+	0.725770i
$249$	0.728431	−	0.140532i	0.0461625	−	0.00890587i
$250$	−7.54294	−	4.35492i	−0.477057	−	0.275429i
$251$	−12.6703			−0.799742			−0.399871	−	0.916571i	$-0.630945\pi$
$251$	−12.6703			−0.799742			−0.399871	+	0.916571i	$0.630945\pi$
$252$	−4.83610	+	10.5312i	−0.304646	+	0.663401i
$253$	−35.3890			−2.22489
$254$	13.8603	+	8.00226i	0.869674	+	0.502107i
$255$	−16.6417	+	3.21059i	−1.04214	+	0.201055i
$256$	5.91156	+	10.2391i	0.369473	+	0.639945i
$257$	0.188757	−	0.326936i	0.0117743	−	0.0203937i	−0.860078	−	0.510162i	$-0.829585\pi$
$257$	0.188757	−	0.326936i	0.0117743	−	0.0203937i	0.871853	+	0.489768i	$0.162919\pi$
$258$	−10.1263	−	3.50265i	−0.630434	−	0.218066i
$259$	13.8668	+	4.10877i	0.861643	+	0.255307i
$260$		−	3.01053i		−	0.186705i
$261$	−8.67045	−	21.6347i	−0.536687	−	1.33916i
$262$	−12.0443	+	6.95379i	−0.744100	+	0.429606i
$263$	1.15919	−	0.669257i	0.0714786	−	0.0412682i	−0.463835	−	0.885922i	$-0.653527\pi$
$263$	1.15919	−	0.669257i	0.0714786	−	0.0412682i	0.535313	+	0.844654i	$0.320194\pi$
$264$	−13.4301	−	15.4935i	−0.826568	−	0.953556i
$265$			1.79588i			0.110320i
$266$	−3.55229	+	3.37045i	−0.217805	+	0.206655i
$267$	−2.23453	+	6.46010i	−0.136751	+	0.395352i
$268$	−3.01917	+	5.22935i	−0.184425	+	0.319434i
$269$	−2.81642	−	4.87819i	−0.171720	−	0.297428i	0.767301	−	0.641287i	$-0.221599\pi$
$269$	−2.81642	−	4.87819i	−0.171720	−	0.297428i	−0.939021	+	0.343859i	$0.888266\pi$
$270$	−3.60393	+	7.00011i	−0.219328	+	0.426013i
$271$	17.1317	+	9.89099i	1.04068	+	0.600835i	0.920025	−	0.391860i	$-0.128168\pi$
$271$	17.1317	+	9.89099i	1.04068	+	0.600835i	0.120652	+	0.992695i	$0.461502\pi$
$272$	4.99070			0.302605
$273$	4.17278	−	1.89417i	0.252548	−	0.114640i
$274$	13.5109			0.816225
$275$	−3.01685	−	1.74178i	−0.181923	−	0.105033i
$276$	−3.64106	−	18.8730i	−0.219166	−	1.13602i
$277$	−3.57358	−	6.18963i	−0.214716	−	0.371899i	0.738469	−	0.674288i	$-0.235549\pi$
$277$	−3.57358	−	6.18963i	−0.214716	−	0.371899i	−0.953185	+	0.302389i	$0.902216\pi$
$278$	−1.50653	+	2.60939i	−0.0903556	+	0.156501i
$279$	9.62151	−	12.2440i	0.576025	−	0.733029i
$280$	3.94064	−	13.2994i	0.235498	−	0.794791i
$281$		−	20.7294i		−	1.23661i	−0.785938	−	0.618305i	$-0.787820\pi$
$281$		−	20.7294i		−	1.23661i	0.785938	−	0.618305i	$-0.212180\pi$
$282$	−2.10653	+	1.82599i	−0.125442	+	0.108736i
$283$	−27.7297	+	16.0097i	−1.64836	+	0.951679i	−0.670632	+	0.741790i	$0.733977\pi$
$283$	−27.7297	+	16.0097i	−1.64836	+	0.951679i	−0.977725	+	0.209889i	$0.932690\pi$
$284$	19.1875	−	11.0779i	1.13857	−	0.657353i
$285$	6.79717	−	5.89196i	0.402630	−	0.349010i
$286$			3.42138i			0.202310i
$287$	2.46502	+	10.2712i	0.145505	+	0.606291i
$288$	10.8583	−	13.8179i	0.639830	−	0.814225i
$289$	−2.76003	+	4.78052i	−0.162355	+	0.281207i
$290$	5.88603	+	10.1949i	0.345639	+	0.598665i
$291$	0.345844	+	1.79264i	0.0202737	+	0.105086i
$292$	8.81975	+	5.09208i	0.516137	+	0.297992i
$293$	12.7694			0.745995			0.372997	−	0.927832i	$-0.378330\pi$
$293$	12.7694			0.745995			0.372997	+	0.927832i	$0.378330\pi$
$294$	8.82467	−	1.22614i	0.514665	−	0.0715098i
$295$	2.55711			0.148881
$296$	−12.0365	−	6.94930i	−0.699610	−	0.403920i
$297$	−11.0741	+	21.5098i	−0.642583	+	1.24812i
$298$	5.79279	+	10.0334i	0.335567	+	0.581220i
$299$	−3.80040	+	6.58248i	−0.219783	+	0.380675i
$300$	0.618499	−	1.78810i	0.0357090	−	0.103236i
$301$	−5.19786	−	21.6584i	−0.299599	−	1.24837i
$302$			10.5586i			0.607578i
$303$	3.56599	+	4.11384i	0.204861	+	0.236334i
$304$	−2.29392	+	1.32440i	−0.131566	+	0.0759594i
$305$	19.3548	−	11.1745i	1.10826	−	0.639851i
$306$	3.89175	+	9.71078i	0.222476	+	0.555128i
$307$		−	8.91757i		−	0.508953i	−0.967079	−	0.254476i	$-0.918097\pi$
$307$		−	8.91757i		−	0.508953i	0.967079	−	0.254476i	$-0.0819031\pi$
$308$	5.10947	−	17.2441i	0.291139	−	0.982576i
$309$	22.6780	+	7.84427i	1.29011	+	0.446245i
$310$	−3.93254	+	6.81136i	−0.223353	+	0.386859i
$311$	−9.55334	−	16.5469i	−0.541720	−	0.938287i	−0.998805	−	0.0488641i	$-0.984440\pi$
$311$	−9.55334	−	16.5469i	−0.541720	−	0.938287i	0.457085	−	0.889423i	$-0.348893\pi$
$312$	−4.32409	+	0.834223i	−0.244803	+	0.0472286i
$313$	−10.2120	−	5.89590i	−0.577217	−	0.333256i	0.182810	−	0.983148i	$-0.441481\pi$
$313$	−10.2120	−	5.89590i	−0.577217	−	0.333256i	−0.760027	+	0.649892i	$0.774814\pi$
$314$	5.93734			0.335064
$315$	−16.2957	+	1.52161i	−0.918156	+	0.0857332i
$316$	9.81795			0.552303
$317$	−6.69962	−	3.86803i	−0.376288	−	0.217250i	0.299914	−	0.953966i	$-0.403042\pi$
$317$	−6.69962	−	3.86803i	−0.376288	−	0.217250i	−0.676202	+	0.736716i	$0.736375\pi$
$318$	1.08845	−	0.209988i	0.0610371	−	0.0117755i
$319$	18.0864	+	31.3266i	1.01265	+	1.75396i
$320$	−2.26952	+	3.93092i	−0.126870	+	0.219745i
$321$	−8.71187	−	3.01342i	−0.486249	−	0.168193i
$322$	−10.7200	+	10.1713i	−0.597403	+	0.566822i
$323$		−	11.9524i		−	0.665052i
$324$	−12.6106	−	3.69274i	−0.700587	−	0.205152i
$325$	−0.647955	+	0.374097i	−0.0359421	+	0.0207512i
$326$	4.17389	−	2.40980i	0.231171	−	0.133466i
$327$	−10.2608	−	11.8372i	−0.567424	−	0.654599i
$328$		−	10.1508i		−	0.560487i
$329$	−5.55624	−	1.64633i	−0.306326	−	0.0907649i
$330$	3.99444	−	11.5480i	0.219887	−	0.635699i
$331$	7.76302	−	13.4459i	0.426694	−	0.739056i	−0.569883	−	0.821726i	$-0.693011\pi$
$331$	7.76302	−	13.4459i	0.426694	−	0.739056i	0.996577	+	0.0826699i	$0.0263447\pi$
$332$	−0.312673	−	0.541565i	−0.0171601	−	0.0297223i
$333$	−2.32789	+	16.2332i	−0.127568	+	0.889571i
$334$	−10.7750	−	6.22093i	−0.589580	−	0.340394i
$335$	−8.52800			−0.465935
$336$	4.79644	+	0.469033i	0.261667	+	0.0255878i
$337$	−23.0346			−1.25478			−0.627388	−	0.778707i	$-0.715876\pi$
$337$	−23.0346			−1.25478			−0.627388	+	0.778707i	$0.715876\pi$
$338$	0.636389	+	0.367419i	0.0346150	+	0.0199850i
$339$	−0.590267	−	3.05958i	−0.0320589	−	0.166173i
$340$	7.14329	+	12.3725i	0.387399	+	0.670995i
$341$	−12.0838	+	20.9298i	−0.654375	+	1.13341i
$342$	−4.36578	−	3.43070i	−0.236074	−	0.185511i
$343$	12.0245	+	14.0859i	0.649262	+	0.760565i
$344$			21.4046i			1.15406i
$345$	20.5123	−	17.7806i	1.10435	−	0.957277i
$346$	12.8401	−	7.41326i	0.690290	−	0.398539i
$347$	−0.673331	+	0.388748i	−0.0361463	+	0.0208691i	−0.517964	−	0.855402i	$-0.673310\pi$
$347$	−0.673331	+	0.388748i	−0.0361463	+	0.0208691i	0.481818	+	0.876271i	$0.339977\pi$
$348$	−14.8457	+	12.8686i	−0.795812	+	0.689830i
$349$			3.92987i			0.210361i	0.994453	+	0.105181i	$0.0335421\pi$
$349$			3.92987i			0.210361i	−0.994453	+	0.105181i	$0.966458\pi$
$350$	−1.41447	+	0.339463i	−0.0756068	+	0.0181451i
$351$	2.81166	+	4.36973i	0.150075	+	0.233239i
$352$	−13.6371	+	23.6201i	−0.726859	+	1.25896i
$353$	6.10732	+	10.5782i	0.325060	+	0.563020i	0.981524	−	0.191337i	$-0.0612822\pi$
$353$	6.10732	+	10.5782i	0.325060	+	0.563020i	−0.656465	+	0.754357i	$0.727949\pi$
$354$	−0.298997	−	1.54981i	−0.0158915	−	0.0823717i
$355$	27.0987	+	15.6454i	1.43825	+	0.830374i
$356$	5.76203			0.305387
$357$	−12.6547	+	17.6856i	−0.669756	+	0.936021i
$358$	−4.73325			−0.250160
$359$	13.7332	+	7.92887i	0.724811	+	0.418470i	0.816521	−	0.577316i	$-0.195900\pi$
$359$	13.7332	+	7.92887i	0.724811	+	0.418470i	−0.0917100	+	0.995786i	$0.529233\pi$
$360$	15.5689	+	2.23263i	0.820552	+	0.117670i
$361$	−6.32814	−	10.9607i	−0.333060	−	0.576877i
$362$	1.43918	−	2.49274i	0.0756418	−	0.131015i
$363$	6.04585	−	17.4787i	0.317325	−	0.917395i
$364$	−2.65877	−	2.80221i	−0.139357	−	0.146876i
$365$			14.3832i			0.752851i
$366$	−9.03578	−	10.4240i	−0.472308	−	0.544870i
$367$	−29.3459	+	16.9429i	−1.53184	+	0.884410i	−0.532566	+	0.846388i	$0.678772\pi$
$367$	−29.3459	+	16.9429i	−1.53184	+	0.884410i	−0.999277	+	0.0380219i	$0.987894\pi$
$368$	−6.92255	+	3.99674i	−0.360863	+	0.208344i
$369$	−11.1176	+	4.45554i	−0.578758	+	0.231946i
$370$		−	8.28286i		−	0.430605i
$371$	1.58604	+	1.67161i	0.0823431	+	0.0867857i
$372$	−12.4051	−	4.29091i	−0.643177	−	0.222473i
$373$	−4.76469	+	8.25268i	−0.246706	+	0.427307i	−0.962610	−	0.270891i	$-0.912682\pi$
$373$	−4.76469	+	8.25268i	−0.246706	+	0.427307i	0.715904	+	0.698199i	$0.246015\pi$
$374$	−8.11813	−	14.0610i	−0.419779	−	0.727078i
$375$	20.1578	−	3.88894i	1.04094	−	0.200824i
$376$	4.82287	+	2.78449i	0.248721	+	0.143599i
$377$	7.76916			0.400132
$378$	2.82764	+	9.69856i	0.145438	+	0.498840i
$379$	−16.1971			−0.831987			−0.415993	−	0.909368i	$-0.636566\pi$
$379$	−16.1971			−0.831987			−0.415993	+	0.909368i	$0.636566\pi$
$380$	−6.56668	−	3.79127i	−0.336864	−	0.194488i
$381$	−37.0404	+	7.14601i	−1.89764	+	0.366101i
$382$	−7.88880	−	13.6638i	−0.403626	−	0.699101i
$383$	4.88802	−	8.46629i	0.249766	−	0.432607i	−0.713695	−	0.700457i	$-0.752980\pi$
$383$	4.88802	−	8.46629i	0.249766	−	0.432607i	0.963461	+	0.267849i	$0.0863130\pi$
$384$	−16.5297	−	5.71759i	−0.843528	−	0.291774i
$385$	24.6993	−	5.92766i	1.25879	−	0.302101i
$386$		−	1.30988i		−	0.0666712i
$387$	23.4431	−	9.39518i	1.19168	−	0.477584i
$388$	1.33277	−	0.769475i	0.0676611	−	0.0390642i
$389$	6.83358	−	3.94537i	0.346476	−	0.200038i	−0.316656	−	0.948540i	$-0.602560\pi$
$389$	6.83358	−	3.94537i	0.346476	−	0.200038i	0.663132	+	0.748502i	$0.269227\pi$
$390$	−1.71902	−	1.98312i	−0.0870458	−	0.100419i
$391$		−	36.0698i		−	1.82413i
$392$	−8.07747	−	15.8593i	−0.407974	−	0.801016i
$393$	10.7159	−	30.9799i	0.540545	−	1.56273i
$394$	2.16389	−	3.74797i	0.109015	−	0.188820i
$395$	6.93299	+	12.0083i	0.348837	+	0.604203i
$396$	20.1868	+	2.89486i	1.01442	+	0.145472i
$397$	−6.87226	−	3.96770i	−0.344909	−	0.199133i	0.317532	−	0.948248i	$-0.397146\pi$
$397$	−6.87226	−	3.96770i	−0.344909	−	0.199133i	−0.662441	+	0.749114i	$0.730479\pi$
$398$	3.04550			0.152657
$399$	1.12331	−	11.4872i	0.0562357	−	0.575080i
$400$	−0.786847			−0.0393424
$401$	13.2464	+	7.64780i	0.661493	+	0.381913i	0.792846	−	0.609423i	$-0.208599\pi$
$401$	13.2464	+	7.64780i	0.661493	+	0.381913i	−0.131353	+	0.991336i	$0.541932\pi$
$402$	0.997160	+	5.16866i	0.0497338	+	0.257789i
$403$	2.59534	+	4.49527i	0.129283	+	0.223925i
$404$	2.29459	−	3.97435i	0.114160	−	0.197731i
$405$	−4.38843	−	18.0316i	−0.218063	−	0.895997i
$406$	14.4824	+	4.29117i	0.718750	+	0.212967i
$407$		−	25.4514i		−	1.26158i
$408$	15.7915	−	13.6885i	0.781796	−	0.677682i
$409$	27.6073	−	15.9391i	1.36509	−	0.788136i	0.374794	−	0.927108i	$-0.377713\pi$
$409$	27.6073	−	15.9391i	1.36509	−	0.788136i	0.990296	+	0.138972i	$0.0443799\pi$
$410$	5.23892	−	3.02469i	0.258732	−	0.149379i
$411$	−24.0637	+	20.8591i	−1.18698	+	1.02890i
$412$		−	20.2274i		−	0.996534i
$413$	2.38017	−	2.25833i	0.117120	−	0.111125i
$414$	−13.1750	−	10.3531i	−0.647514	−	0.508826i
$415$	0.441591	−	0.764858i	0.0216769	−	0.0375454i
$416$	2.92895	+	5.07309i	0.143604	+	0.248729i
$417$	−1.34533	−	6.97334i	−0.0658811	−	0.341486i
$418$	7.46283	+	4.30867i	0.365019	+	0.210744i
$419$	10.4315			0.509613			0.254806	−	0.966992i	$-0.417988\pi$
$419$	10.4315			0.509613			0.254806	+	0.966992i	$0.417988\pi$
$420$	5.70246	+	12.5623i	0.278252	+	0.612977i
$421$	26.3649			1.28495			0.642474	−	0.766307i	$-0.277908\pi$
$421$	26.3649			1.28495			0.642474	+	0.766307i	$0.277908\pi$
$422$	−3.29925	−	1.90482i	−0.160605	−	0.0927254i
$423$	0.932754	−	6.50439i	0.0453521	−	0.316254i
$424$	−1.10721	−	1.91774i	−0.0537708	−	0.0931338i
$425$	1.77529	−	3.07489i	0.0861141	−	0.149154i
$426$	6.31381	−	18.2534i	0.305905	−	0.884379i
$427$	8.14671	−	27.4946i	0.394247	−	1.33056i
$428$			7.77048i			0.375600i
$429$	−5.28215	−	6.09367i	−0.255025	−	0.294205i
$430$	−11.0470	+	6.37802i	−0.532736	+	0.307575i
$431$	−34.4553	+	19.8928i	−1.65965	+	0.958202i	−0.686780	+	0.726865i	$0.740976\pi$
$431$	−34.4553	+	19.8928i	−1.65965	+	0.958202i	−0.972874	+	0.231336i	$0.925690\pi$
$432$	0.263021	+	5.45826i	0.0126546	+	0.262611i
$433$			7.06996i			0.339761i	0.985465	+	0.169880i	$0.0543381\pi$
$433$			7.06996i			0.339761i	−0.985465	+	0.169880i	$0.945662\pi$
$434$	2.35507	+	9.81308i	0.113047	+	0.471043i
$435$	−26.2229	−	9.07045i	−1.25729	−	0.434895i
$436$	−6.60247	+	11.4358i	−0.316201	+	0.547676i
$437$	9.57196	+	16.5791i	0.457889	+	0.793087i
$438$	8.71738	−	1.68180i	0.416533	−	0.0803593i
$439$	29.5539	+	17.0630i	1.41053	+	0.814371i	0.995438	−	0.0954077i	$-0.0304155\pi$
$439$	29.5539	+	17.0630i	1.41053	+	0.814371i	0.415094	+	0.909779i	$0.363749\pi$
$440$	−24.4099			−1.16370
$441$	−13.8242	+	15.8079i	−0.658297	+	0.752758i
$442$	−3.48720			−0.165869
$443$	−14.4159	−	8.32305i	−0.684922	−	0.395440i	0.116785	−	0.993157i	$-0.462741\pi$
$443$	−14.4159	−	8.32305i	−0.684922	−	0.395440i	−0.801707	+	0.597717i	$0.796075\pi$
$444$	13.5732	−	2.61861i	0.644158	−	0.124274i
$445$	4.06889	+	7.04752i	0.192884	+	0.334084i
$446$	6.88183	−	11.9197i	0.325864	−	0.564414i
$447$	−25.8075	−	8.92677i	−1.22065	−	0.422222i
$448$	1.35914	+	5.66325i	0.0642132	+	0.267563i
$449$		−	1.73022i		−	0.0816542i	−0.999166	−	0.0408271i	$-0.987001\pi$
$449$		−	1.73022i		−	0.0816542i	0.999166	−	0.0408271i	$-0.0129993\pi$
$450$	−0.613583	−	1.53103i	−0.0289246	−	0.0721734i
$451$	16.0980	−	9.29420i	0.758027	−	0.437647i
$452$	−2.27470	+	1.31330i	−0.106993	+	0.0617723i
$453$	−16.3010	−	18.8054i	−0.765889	−	0.883556i
$454$		−	5.16300i		−	0.242311i
$455$	1.54988	−	5.23073i	0.0726593	−	0.245220i
$456$	−3.62585	+	10.4824i	−0.169796	+	0.490884i
$457$	7.97775	−	13.8179i	0.373183	−	0.646372i	−0.616870	−	0.787065i	$-0.711600\pi$
$457$	7.97775	−	13.8179i	0.373183	−	0.646372i	0.990053	+	0.140693i	$0.0449329\pi$
$458$	4.80018	+	8.31416i	0.224298	+	0.388495i
$459$	−21.9236	−	11.2871i	−1.02330	−	0.526837i
$460$	−19.8168	−	11.4412i	−0.923962	−	0.533450i
$461$	−25.4124			−1.18357			−0.591786	−	0.806095i	$-0.701577\pi$
$461$	−25.4124			−1.18357			−0.591786	+	0.806095i	$0.701577\pi$
$462$	−6.48068	−	14.2767i	−0.301508	−	0.664211i
$463$	16.6866			0.775491			0.387745	−	0.921767i	$-0.373254\pi$
$463$	16.6866			0.775491			0.387745	+	0.921767i	$0.373254\pi$
$464$	7.07589	+	4.08526i	0.328490	+	0.189654i
$465$	−3.51175	−	18.2027i	−0.162854	−	0.844132i
$466$	1.50160	+	2.60084i	0.0695602	+	0.120482i
$467$	−9.86961	+	17.0947i	−0.456711	+	0.791047i	−0.998785	−	0.0492843i	$-0.984306\pi$
$467$	−9.86961	+	17.0947i	−0.456711	+	0.791047i	0.542074	+	0.840331i	$0.317639\pi$
$468$	2.70630	−	3.44394i	0.125099	−	0.159196i
$469$	−7.93790	+	7.53155i	−0.366538	+	0.347775i
$470$			3.31882i			0.153086i
$471$	−10.5747	+	9.16646i	−0.487258	+	0.422368i
$472$	−2.73063	+	1.57653i	−0.125687	+	0.0725656i
$473$	−33.9451	+	19.5982i	−1.56080	+	0.901127i
$474$	6.46733	−	5.60606i	0.297055	−	0.257495i
$475$			1.88446i			0.0864647i
$476$	17.5759	+	5.20777i	0.805589	+	0.238698i
$477$	−1.61439	+	2.05442i	−0.0739179	+	0.0940653i
$478$	−2.04117	+	3.53541i	−0.0933611	+	0.161706i
$479$	−3.87793	−	6.71677i	−0.177187	−	0.306897i	0.763729	−	0.645537i	$-0.223366\pi$
$479$	−3.87793	−	6.71677i	−0.177187	−	0.306897i	−0.940916	+	0.338640i	$0.890033\pi$
$480$	−3.96316	−	20.5425i	−0.180893	−	0.937634i
$481$	−4.73405	−	2.73320i	−0.215854	−	0.124623i
$482$	0.739952			0.0337039
$483$	3.38989	−	34.6659i	0.154245	−	1.57735i
$484$	−15.5900			−0.708636
$485$	1.88228	+	1.08674i	0.0854701	+	0.0493462i
$486$	−10.4155	+	4.76814i	−0.472455	+	0.216287i
$487$	14.0500	+	24.3353i	0.636665	+	1.10274i	0.986160	+	0.165798i	$0.0530200\pi$
$487$	14.0500	+	24.3353i	0.636665	+	1.10274i	−0.349494	+	0.936938i	$0.613647\pi$
$488$	−13.7788	+	23.8656i	−0.623738	+	1.08035i
$489$	−3.71353	+	10.7359i	−0.167932	+	0.485495i
$490$	5.77822	−	8.89451i	0.261033	−	0.401813i
$491$			11.3088i			0.510361i	0.966893	+	0.255180i	$0.0821348\pi$
$491$			11.3088i			0.510361i	−0.966893	+	0.255180i	$0.917865\pi$
$492$	6.61288	+	7.62885i	0.298132	+	0.343935i
$493$	−31.9293	+	18.4344i	−1.43802	+	0.830243i
$494$	1.60286	−	0.925409i	0.0721159	−	0.0416361i
$495$	10.7143	+	26.7346i	0.481572	+	1.20163i
$496$			5.45885i			0.245110i
$497$	39.0409	−	9.36954i	1.75123	−	0.420281i
$498$	−0.515200	−	0.178207i	−0.0230867	−	0.00798562i
$499$	8.78073	−	15.2087i	0.393079	−	0.680834i	−0.599775	−	0.800169i	$-0.704743\pi$
$499$	8.78073	−	15.2087i	0.393079	−	0.680834i	0.992854	+	0.119335i	$0.0380764\pi$
$500$	−8.65256	−	14.9867i	−0.386954	−	0.670225i
$501$	28.7951	−	5.55528i	1.28647	−	0.248192i
$502$	8.06323	+	4.65531i	0.359880	+	0.207777i
$503$	−9.97447			−0.444739			−0.222370	−	0.974962i	$-0.571379\pi$
$503$	−9.97447			−0.444739			−0.222370	+	0.974962i	$0.571379\pi$
$504$	16.4633	−	11.6716i	0.733335	−	0.519894i
$505$	6.48134			0.288416
$506$	22.5212	+	13.0026i	1.00119	+	0.578036i
$507$	−1.70069	+	0.328105i	−0.0755303	+	0.0145716i
$508$	15.8993	+	27.5384i	0.705417	+	1.22182i
$509$	16.7654	−	29.0385i	0.743112	−	1.28711i	−0.207960	−	0.978137i	$-0.566682\pi$
$509$	16.7654	−	29.0385i	0.743112	−	1.28711i	0.951072	−	0.308970i	$-0.0999844\pi$
$510$	11.7702	+	4.07129i	0.521193	+	0.180280i
$511$	12.7026	+	13.3879i	0.561930	+	0.592248i
$512$			11.5083i			0.508602i
$513$	13.0722	−	0.629921i	0.577154	−	0.0278117i
$514$	−0.240245	+	0.138706i	−0.0105968	+	0.00611804i
$515$	24.7401	−	14.2837i	1.09018	−	0.629415i
$516$	−13.9443	−	16.0866i	−0.613862	−	0.708171i
$517$			10.1980i			0.448508i
$518$	−7.31505	−	7.70972i	−0.321405	−	0.338745i
$519$	−11.4239	+	33.0269i	−0.501455	+	1.44972i
$520$	−2.62136	+	4.54032i	−0.114954	+	0.199106i
$521$	−9.33352	−	16.1661i	−0.408909	−	0.708251i	0.585859	−	0.810413i	$-0.300757\pi$
$521$	−9.33352	−	16.1661i	−0.408909	−	0.708251i	−0.994768	+	0.102162i	$0.967424\pi$
$522$	−2.43124	+	16.9538i	−0.106412	+	0.742047i
$523$	4.77202	+	2.75513i	0.208666	+	0.120473i	0.600691	−	0.799481i	$-0.294892\pi$
$523$	4.77202	+	2.75513i	0.208666	+	0.120473i	−0.392025	+	0.919954i	$0.628225\pi$
$524$	−27.6323			−1.20712
$525$	1.99517	−	2.78836i	0.0870764	−	0.121694i
$526$	−0.983592			−0.0428866
$527$	−21.3324	−	12.3163i	−0.929255	−	0.536506i
$528$	−1.60657	−	8.32743i	−0.0699168	−	0.362405i
$529$	17.3861	+	30.1135i	0.755915	+	1.30928i
$530$	0.659840	−	1.14288i	0.0286616	−	0.0496434i
$531$	2.92524	+	2.29869i	0.126944	+	0.0997549i
$532$	−9.46057	+	2.27047i	−0.410168	+	0.0984373i
$533$		−	3.99239i		−	0.172930i
$534$	3.79560	−	3.29012i	0.164251	−	0.142378i
$535$	−9.50404	+	5.48716i	−0.410896	+	0.237231i
$536$	9.10669	−	5.25775i	0.393349	−	0.227100i
$537$	8.43018	−	7.30751i	0.363789	−	0.315342i
$538$			4.13923i			0.178455i
$539$	17.7552	−	27.3308i	0.764770	−	1.17722i
$540$	−13.1552	+	8.46459i	−0.566111	+	0.364258i
$541$	14.8303	−	25.6868i	0.637604	−	1.10436i	−0.348353	−	0.937364i	$-0.613259\pi$
$541$	14.8303	−	25.6868i	0.637604	−	1.10436i	0.985957	−	0.167000i	$-0.0534079\pi$
$542$	−7.26828	−	12.5890i	−0.312199	−	0.540745i
$543$	1.28519	+	6.66161i	0.0551527	+	0.285877i
$544$	−24.0745	−	13.8994i	−1.03219	−	0.595933i
$545$	−18.6495			−0.798856
$546$	−3.35147	−	0.327732i	−0.143430	−	0.0140256i
$547$	−24.0771			−1.02946			−0.514732	−	0.857351i	$-0.672109\pi$
$547$	−24.0771			−1.02946			−0.514732	+	0.857351i	$0.672109\pi$
$548$	23.2477	+	13.4221i	0.993094	+	0.573363i
$549$	32.1865	+	4.61566i	1.37369	+	0.196992i
$550$	1.27993	+	2.21690i	0.0545763	+	0.0945289i
$551$	9.78398	−	16.9464i	0.416812	−	0.721939i
$552$	−10.9420	+	31.6336i	−0.465723	+	1.34642i
$553$	17.0585	+	5.05445i	0.725399	+	0.214937i
$554$			5.25201i			0.223137i
$555$	12.7876	+	14.7522i	0.542805	+	0.626198i
$556$	−5.18446	+	2.99325i	−0.219870	+	0.126942i
$557$	−4.56402	+	2.63504i	−0.193384	+	0.111650i	−0.593566	−	0.804786i	$-0.702280\pi$
$557$	−4.56402	+	2.63504i	−0.193384	+	0.111650i	0.400182	+	0.916436i	$0.368947\pi$
$558$	−10.6217	+	4.25681i	−0.449652	+	0.180205i
$559$			8.41855i			0.356067i
$560$	4.16206	−	3.94900i	0.175879	−	0.166876i
$561$	36.1672	+	12.5101i	1.52698	+	0.528179i
$562$	−7.61637	+	13.1919i	−0.321277	+	0.556468i
$563$	20.0280	+	34.6895i	0.844080	+	1.46199i	0.886418	+	0.462886i	$0.153186\pi$
$563$	20.0280	+	34.6895i	0.844080	+	1.46199i	−0.0423382	+	0.999103i	$0.513481\pi$
$564$	−5.43861	+	1.04924i	−0.229007	+	0.0441810i
$565$	−3.21258	−	1.85478i	−0.135154	−	0.0780313i
$566$	23.5291			0.989003
$567$	−20.0095	−	12.9082i	−0.840318	−	0.542093i
$568$	−38.5834			−1.61892
$569$	−34.0119	−	19.6368i	−1.42585	−	0.823217i	−0.429064	−	0.903274i	$-0.641156\pi$
$569$	−34.0119	−	19.6368i	−1.42585	−	0.823217i	−0.996790	+	0.0800571i	$0.974490\pi$
$570$	−6.49046	+	1.25217i	−0.271856	+	0.0524476i
$571$	−14.4504	−	25.0288i	−0.604730	−	1.04742i	−0.992094	−	0.125496i	$-0.959948\pi$
$571$	−14.4504	−	25.0288i	−0.604730	−	1.04742i	0.387364	−	0.921927i	$-0.373386\pi$
$572$	−3.39888	+	5.88704i	−0.142114	+	0.246149i
$573$	35.1455	+	12.1567i	1.46822	+	0.507855i
$574$	2.20513	−	7.44218i	0.0920405	−	0.310631i
$575$			5.68687i			0.237159i
$576$	−6.12991	+	2.45666i	−0.255413	+	0.102361i
$577$	−39.5105	+	22.8114i	−1.64484	+	0.949650i	−0.665765	+	0.746162i	$0.731895\pi$
$577$	−39.5105	+	22.8114i	−1.64484	+	0.949650i	−0.979077	+	0.203489i	$0.934772\pi$
$578$	3.51291	−	2.02818i	0.146118	−	0.0843611i
$579$	2.02228	+	2.33297i	0.0840432	+	0.0969551i
$580$			23.3893i			0.971188i
$581$	−0.264454	−	1.10193i	−0.0109714	−	0.0457156i
$582$	0.438559	−	1.26788i	0.0181788	−	0.0525555i
$583$	2.02754	−	3.51180i	0.0839722	−	0.145444i
$584$	−8.86765	−	15.3592i	−0.366946	−	0.635569i
$585$	6.12333	+	0.878108i	0.253169	+	0.0363053i
$586$	−8.12628	−	4.69171i	−0.335694	−	0.193813i
$587$	30.7583			1.26953			0.634765	−	0.772705i	$-0.281097\pi$
$587$	30.7583			1.26953			0.634765	+	0.772705i	$0.281097\pi$
$588$	16.4023	+	6.65687i	0.676421	+	0.274525i
$589$	13.0736			0.538690
$590$	−1.62732	−	0.939531i	−0.0669955	−	0.0386799i
$591$	1.93235	+	10.0161i	0.0794863	+	0.412007i
$592$	−2.87441	−	4.97862i	−0.118137	−	0.204620i
$593$	14.6499	−	25.3743i	0.601598	−	1.04200i	−0.390981	−	0.920399i	$-0.627864\pi$
$593$	14.6499	−	25.3743i	0.601598	−	1.04200i	0.992579	−	0.121600i	$-0.0388025\pi$
$594$	14.9505	−	9.61975i	0.613427	−	0.394703i
$595$	6.04169	+	25.1745i	0.247685	+	1.03205i
$596$			23.0188i			0.942887i
$597$	−5.42422	+	4.70185i	−0.221998	+	0.192434i
$598$	4.83706	−	2.79268i	0.197802	−	0.114201i
$599$	5.79676	−	3.34676i	0.236849	−	0.136745i	−0.376879	−	0.926263i	$-0.623003\pi$
$599$	5.79676	−	3.34676i	0.236849	−	0.136745i	0.613728	+	0.789518i	$0.289669\pi$
$600$	−2.48973	+	2.15817i	−0.101643	+	0.0881068i
$601$			8.33430i			0.339963i	0.985447	+	0.169982i	$0.0543708\pi$
$601$			8.33430i			0.339963i	−0.985447	+	0.169982i	$0.945629\pi$
$602$	−4.64985	+	15.6929i	−0.189514	+	0.639597i
$603$	−9.75571	−	7.66618i	−0.397283	−	0.312191i
$604$	−10.4891	+	18.1677i	−0.426797	+	0.739235i
$605$	−11.0089	−	19.0681i	−0.447577	−	0.775227i
$606$	−0.757849	−	3.92822i	−0.0307855	−	0.159573i
$607$	−2.40836	−	1.39047i	−0.0977522	−	0.0564372i	0.450327	−	0.892864i	$-0.351307\pi$
$607$	−2.40836	−	1.39047i	−0.0977522	−	0.0564372i	−0.548079	+	0.836426i	$0.684641\pi$
$608$	14.7541			0.598359
$609$	−32.4190	+	14.7161i	−1.31368	+	0.596327i
$610$	−16.4229			−0.664945
$611$	1.89686	+	1.09516i	0.0767389	+	0.0443052i
$612$	−2.95055	+	20.5751i	−0.119269	+	0.831700i
$613$	−15.1361	−	26.2166i	−0.611343	−	1.05888i	−0.991014	−	0.133756i	$-0.957296\pi$
$613$	−15.1361	−	26.2166i	−0.611343	−	1.05888i	0.379671	−	0.925122i	$-0.376037\pi$
$614$	−3.27649	+	5.67504i	−0.132228	+	0.229026i
$615$	−4.66109	+	13.4753i	−0.187953	+	0.543378i
$616$	−22.7208	+	21.5577i	−0.915447	+	0.868585i
$617$			5.44826i			0.219339i	0.993968	+	0.109669i	$0.0349792\pi$
$617$			5.44826i			0.219339i	−0.993968	+	0.109669i	$0.965021\pi$
$618$	−11.5499	−	13.3243i	−0.464604	−	0.535983i
$619$	20.2706	−	11.7032i	0.814743	−	0.470392i	−0.0338575	−	0.999427i	$-0.510779\pi$
$619$	20.2706	−	11.7032i	0.814743	−	0.470392i	0.848600	+	0.529035i	$0.177446\pi$
$620$	−13.5331	+	7.81336i	−0.543504	+	0.313792i
$621$	39.4491	−	1.90096i	1.58304	−	0.0762829i
$622$			14.0403i			0.562966i
$623$	10.0114	+	2.96639i	0.401098	+	0.118846i
$624$	−1.72146	−	0.595449i	−0.0689135	−	0.0238370i
$625$	10.3496	−	17.9261i	0.413985	−	0.717043i
$626$	4.33254	+	7.50417i	0.173163	+	0.299927i
$627$	−19.9437	+	3.84764i	−0.796476	+	0.153660i
$628$	10.2162	+	5.89830i	0.407669	+	0.235368i
$629$	25.9410			1.03434
$630$	10.9294	+	5.01900i	0.435439	+	0.199962i
$631$	−10.9370			−0.435395			−0.217697	−	0.976016i	$-0.569855\pi$
$631$	−10.9370			−0.435395			−0.217697	+	0.976016i	$0.569855\pi$
$632$	−14.8069	−	8.54877i	−0.588987	−	0.340052i
$633$	8.81695	−	1.70101i	0.350442	−	0.0676089i
$634$	2.84238	+	4.92314i	0.112885	+	0.195523i
$635$	−22.4547	+	38.8927i	−0.891088	+	1.54341i
$636$	2.08146	+	0.719971i	0.0825351	+	0.0285487i
$637$	−3.17692	−	6.23756i	−0.125874	−	0.247141i
$638$		−	26.5812i		−	1.05236i
$639$	16.9355	+	42.2580i	0.669960	+	1.67170i
$640$	−18.0327	+	10.4112i	−0.712807	+	0.411539i
$641$	−0.779616	+	0.450111i	−0.0307930	+	0.0177783i	−0.515317	−	0.856999i	$-0.672326\pi$
$641$	−0.779616	+	0.450111i	−0.0307930	+	0.0177783i	0.484524	+	0.874778i	$0.338993\pi$
$642$	4.43695	+	5.11861i	0.175112	+	0.202016i
$643$		−	29.8005i		−	1.17522i	−0.809145	−	0.587609i	$-0.800069\pi$
$643$		−	29.8005i		−	1.17522i	0.809145	−	0.587609i	$-0.199931\pi$
$644$	−28.5499	+	6.85177i	−1.12502	+	0.269998i
$645$	9.82861	−	28.4148i	0.387001	−	1.11883i
$646$	−4.39156	+	7.60640i	−0.172783	+	0.299270i
$647$	20.1220	+	34.8522i	0.791076	+	1.37018i	0.925301	+	0.379232i	$0.123812\pi$
$647$	20.1220	+	34.8522i	0.791076	+	1.37018i	−0.134226	+	0.990951i	$0.542855\pi$
$648$	15.8032	+	16.5496i	0.620808	+	0.650129i
$649$	−5.00038	−	2.88697i	−0.196282	−	0.113323i
$650$	0.549801			0.0215650
$651$	−19.3446	−	13.8417i	−0.758175	−	0.542501i
$652$	9.57581			0.375018
$653$	−27.1070	−	15.6502i	−1.06078	−	0.612441i	−0.135131	−	0.990828i	$-0.543146\pi$
$653$	−27.1070	−	15.6502i	−1.06078	−	0.612441i	−0.925648	+	0.378387i	$0.876479\pi$
$654$	2.18064	+	11.3031i	0.0852699	+	0.441986i
$655$	−19.5127	−	33.7969i	−0.762423	−	1.32055i
$656$	2.09932	−	3.63613i	0.0819648	−	0.141967i
$657$	−12.9297	+	16.4538i	−0.504435	+	0.641926i
$658$	2.93104	+	3.08917i	0.114264	+	0.120429i
$659$			18.7698i			0.731167i	0.930779	+	0.365583i	$0.119130\pi$
$659$			18.7698i			0.731167i	−0.930779	+	0.365583i	$0.880870\pi$
$660$	18.3452	−	15.9021i	0.714086	−	0.618988i
$661$	30.2517	−	17.4659i	1.17666	−	0.679343i	0.221418	−	0.975179i	$-0.428932\pi$
$661$	30.2517	−	17.4659i	1.17666	−	0.679343i	0.955239	+	0.295836i	$0.0955982\pi$
$662$	−9.88060	+	5.70457i	−0.384020	+	0.221714i
$663$	6.21090	−	5.38377i	0.241211	−	0.209088i
$664$			1.08901i			0.0422619i
$665$	−9.45764	−	9.96789i	−0.366751	−	0.386538i
$666$	7.44582	−	9.47528i	0.288520	−	0.367160i
$667$	29.5259	−	51.1403i	1.14325	−	1.98016i
$668$	−12.3600	−	21.4082i	−0.478225	−	0.828309i
$669$	6.14547	+	31.8543i	0.237598	+	1.23156i
$670$	5.42712	+	3.13335i	0.209668	+	0.121052i
$671$	−50.4640			−1.94814
$672$	−21.8312	−	15.6210i	−0.842156	−	0.602592i
$673$	41.4021			1.59593			0.797967	−	0.602701i	$-0.205909\pi$
$673$	41.4021			1.59593			0.797967	+	0.602701i	$0.205909\pi$
$674$	14.6590	+	8.46336i	0.564642	+	0.325996i
$675$	3.45653	+	1.77956i	0.133042	+	0.0684952i
$676$	0.730006	+	1.26441i	0.0280772	+	0.0486311i
$677$	−20.5028	+	35.5118i	−0.787986	+	1.36483i	0.139214	+	0.990262i	$0.455543\pi$
$677$	−20.5028	+	35.5118i	−0.787986	+	1.36483i	−0.927199	+	0.374569i	$0.877791\pi$
$678$	−0.748508	+	2.16396i	−0.0287463	+	0.0831062i
$679$	2.71179	−	0.650811i	0.104069	−	0.0249758i
$680$		−	24.8795i		−	0.954084i
$681$	7.97098	+	9.19559i	0.305449	+	0.352376i
$682$	15.3800	−	8.87965i	0.588931	−	0.340019i
$683$	22.4638	−	12.9695i	0.859552	−	0.496263i	−0.00431004	−	0.999991i	$-0.501372\pi$
$683$	22.4638	−	12.9695i	0.859552	−	0.496263i	0.863862	+	0.503728i	$0.168039\pi$
$684$	−4.10390	−	10.2401i	−0.156916	−	0.391542i
$685$			37.9123i			1.44855i
$686$	−2.47685	−	13.3821i	−0.0945665	−	0.510931i
$687$	−21.3854	−	7.39715i	−0.815902	−	0.282219i
$688$	−4.42673	+	7.66733i	−0.168768	+	0.292314i
$689$	−0.435472	−	0.754260i	−0.0165902	−	0.0287350i
$690$	−19.5868	+	3.77877i	−0.745656	+	0.143855i
$691$	13.0873	+	7.55597i	0.497865	+	0.287443i	0.727832	−	0.685756i	$-0.240528\pi$
$691$	13.0873	+	7.55597i	0.497865	+	0.287443i	−0.229966	+	0.973199i	$0.573862\pi$
$692$	29.4581			1.11983
$693$	33.5837	+	15.4223i	1.27574	+	0.585843i
$694$	0.571334			0.0216875
$695$	−7.32206	−	4.22739i	−0.277742	−	0.160354i
$696$	33.5945	−	6.48121i	1.27340	−	0.245670i
$697$	9.47300	+	16.4077i	0.358816	+	0.621487i
$698$	1.44391	−	2.50093i	0.0546528	−	0.0946614i
$699$	−6.68979	−	2.31398i	−0.253031	−	0.0875229i
$700$	−2.77106	−	0.821071i	−0.104736	−	0.0310336i
$701$			36.3652i			1.37349i	0.726896	+	0.686747i	$0.240962\pi$
$701$			36.3652i			1.37349i	−0.726896	+	0.686747i	$0.759038\pi$
$702$	−0.183783	−	3.81391i	−0.00693645	−	0.143947i
$703$	−11.9235	+	6.88404i	−0.449704	+	0.259637i
$704$	8.87598	−	5.12455i	0.334526	−	0.193139i
$705$	−5.12382	−	5.91101i	−0.192974	−	0.222622i
$706$		−	8.97579i		−	0.337808i
$707$	6.03286	−	5.72404i	0.226889	−	0.215275i
$708$	1.02515	−	2.96374i	0.0385275	−	0.111384i
$709$	5.76936	−	9.99282i	0.216673	−	0.375288i	−0.737116	−	0.675766i	$-0.763813\pi$
$709$	5.76936	−	9.99282i	0.216673	−	0.375288i	0.953789	+	0.300478i	$0.0971462\pi$
$710$	−11.4969	−	19.9132i	−0.431470	−	0.747328i
$711$	−2.86369	+	19.9694i	−0.107397	+	0.748911i
$712$	−8.68998	−	5.01716i	−0.325671	−	0.188026i
$713$	39.4533			1.47754
$714$	14.5513	−	6.60535i	0.544569	−	0.247199i
$715$	−9.60055			−0.359040
$716$	−8.14432	−	4.70213i	−0.304368	−	0.175727i
$717$	−1.82276	−	9.44807i	−0.0680724	−	0.352845i
$718$	−5.82644	−	10.0917i	−0.217441	−	0.376618i
$719$	8.60057	−	14.8966i	0.320747	−	0.555550i	−0.659895	−	0.751357i	$-0.729399\pi$
$719$	8.60057	−	14.8966i	0.320747	−	0.555550i	0.980642	+	0.195807i	$0.0627328\pi$
$720$	5.11519	+	4.01959i	0.190632	+	0.149801i
$721$	10.4134	−	35.1447i	0.387817	−	1.30886i
$722$			9.30032i			0.346122i
$723$	−1.31790	+	1.14239i	−0.0490131	+	0.0424858i
$724$	4.95269	−	2.85944i	0.184065	−	0.106270i
$725$	5.03406	−	2.90642i	0.186960	−	0.107942i
$726$	−10.2695	+	8.90189i	−0.381138	+	0.330380i
$727$		−	15.2492i		−	0.565563i	−0.959184	−	0.282781i	$-0.908743\pi$
$727$		−	15.2492i		−	0.565563i	0.959184	−	0.282781i	$-0.0912571\pi$
$728$	1.56984	+	6.54122i	0.0581823	+	0.242434i
$729$	11.1892	−	24.5724i	0.414413	−	0.910089i
$730$	5.28467	−	9.15331i	0.195594	−	0.338779i
$731$	−19.9752	−	34.5981i	−0.738811	−	1.27966i
$732$	−5.19208	−	26.9125i	−0.191905	−	0.994715i
$733$	−32.7659	−	18.9174i	−1.21024	−	0.698730i	−0.247425	−	0.968907i	$-0.579584\pi$
$733$	−32.7659	−	18.9174i	−1.21024	−	0.698730i	−0.962811	+	0.270177i	$0.912918\pi$
$734$	24.9005			0.919095
$735$	3.44060	+	24.7624i	0.126908	+	0.913376i
$736$	44.5247			1.64120
$737$	16.6763	+	9.62809i	0.614281	+	0.354655i
$738$	8.71215	+	1.24936i	0.320699	+	0.0459894i
$739$	−8.24744	−	14.2850i	−0.303387	−	0.525482i	0.673514	−	0.739175i	$-0.264784\pi$
$739$	−8.24744	−	14.2850i	−0.303387	−	0.525482i	−0.976901	+	0.213693i	$0.931451\pi$
$740$	8.22840	−	14.2520i	0.302482	−	0.523914i
$741$	−1.42607	+	4.12280i	−0.0523879	+	0.151455i
$742$	−0.395156	−	1.64654i	−0.0145066	−	0.0604462i
$743$			26.5033i			0.972313i	0.873872	+	0.486157i	$0.161602\pi$
$743$			26.5033i			0.972313i	−0.873872	+	0.486157i	$0.838398\pi$
$744$	14.9725	+	17.2728i	0.548920	+	0.633253i
$745$	−28.1542	+	16.2548i	−1.03149	+	0.595531i
$746$	6.06438	−	3.50127i	0.222033	−	0.128191i
$747$	1.19273	−	0.478004i	0.0436396	−	0.0174892i
$748$		−	32.2590i		−	1.17951i
$749$	−4.00038	+	13.5010i	−0.146171	+	0.493317i
$750$	−14.2571	−	4.93149i	−0.520595	−	0.180073i
$751$	−9.61311	+	16.6504i	−0.350787	+	0.607582i	−0.986388	−	0.164437i	$-0.947419\pi$
$751$	−9.61311	+	16.6504i	−0.350787	+	0.607582i	0.635600	+	0.772018i	$0.280753\pi$
$752$	1.15173	+	1.99486i	0.0419994	+	0.0727451i
$753$	−21.5482	+	4.15718i	−0.785262	+	0.151496i
$754$	−4.94420	−	2.85454i	−0.180057	−	0.103956i
$755$	−29.6279			−1.07827
$756$	−4.76938	+	19.4970i	−0.173461	+	0.709098i
$757$	22.7314			0.826188			0.413094	−	0.910688i	$-0.364448\pi$
$757$	22.7314			0.826188			0.413094	+	0.910688i	$0.364448\pi$
$758$	10.3076	+	5.95111i	0.374390	+	0.216154i
$759$	−60.1858	+	11.6113i	−2.18460	+	0.421464i
$760$	6.60234	+	11.4356i	0.239492	+	0.414813i
$761$	5.34960	−	9.26578i	0.193923	−	0.335884i	−0.752624	−	0.658451i	$-0.771212\pi$
$761$	5.34960	−	9.26578i	0.193923	−	0.335884i	0.946547	+	0.322566i	$0.104545\pi$
$762$	26.1977	+	9.06173i	0.949042	+	0.328272i
$763$	−17.3590	+	16.4704i	−0.628438	+	0.596268i
$764$		−	31.3477i		−	1.13412i
$765$	−27.2489	+	10.9204i	−0.985186	+	0.394829i
$766$	−6.22136	+	3.59190i	−0.224787	+	0.129781i
$767$	−1.07397	+	0.620058i	−0.0387789	+	0.0223890i
$768$	13.4132	+	15.4740i	0.484009	+	0.558369i
$769$			26.1381i			0.942564i	0.881983	+	0.471282i	$0.156209\pi$
$769$			26.1381i			0.942564i	−0.881983	+	0.471282i	$0.843791\pi$
$770$	−17.8963	−	5.30271i	−0.644938	−	0.191096i
$771$	0.213747	−	0.617949i	0.00769791	−	0.0222549i
$772$	1.30127	−	2.25386i	0.0468337	−	0.0811183i
$773$	−10.3464	−	17.9205i	−0.372134	−	0.644555i	0.617760	−	0.786367i	$-0.288040\pi$
$773$	−10.3464	−	17.9205i	−0.372134	−	0.644555i	−0.989894	+	0.141812i	$0.954707\pi$
$774$	−18.3709	−	2.63445i	−0.660328	−	0.0946934i
$775$	3.36333	+	1.94182i	0.120814	+	0.0697522i
$776$	−2.68001			−0.0962069
$777$	24.9313	+	2.43797i	0.894405	+	0.0874617i
$778$	−5.79841			−0.207883
$779$	−8.70834	−	5.02776i	−0.312009	−	0.180138i
$780$	−0.987770	−	5.11998i	−0.0353679	−	0.183325i
$781$	−35.3273	−	61.1887i	−1.26411	−	2.18950i
$782$	−13.2527	+	22.9544i	−0.473917	+	0.820848i
$783$	−21.8442	−	33.9491i	−0.780648	−	1.21324i
$784$	0.386475	−	7.35149i	0.0138027	−	0.262553i
$785$			16.6605i			0.594637i
$786$	−18.2021	+	15.7780i	−0.649247	+	0.562784i
$787$	33.8184	−	19.5251i	1.20550	−	0.695993i	0.243723	−	0.969845i	$-0.421631\pi$
$787$	33.8184	−	19.5251i	1.20550	−	0.695993i	0.961772	+	0.273852i	$0.0882978\pi$
$788$	7.44664	−	4.29932i	0.265276	−	0.153157i
$789$	1.75183	−	1.51853i	0.0623669	−	0.0540613i
$790$		−	10.1893i		−	0.362518i
$791$	−4.62834	+	1.11077i	−0.164565	+	0.0394943i
$792$	−27.9240	−	21.9431i	−0.992235	−	0.779713i
$793$	−5.41929	+	9.38648i	−0.192445	+	0.333324i
$794$	2.91562	+	5.05000i	0.103471	+	0.179218i
$795$	0.589236	+	3.05423i	0.0208981	+	0.108322i
$796$	5.24028	+	3.02548i	0.185737	+	0.107235i
$797$	40.8704			1.44770			0.723851	−	0.689956i	$-0.242370\pi$
$797$	40.8704			1.44770			0.723851	+	0.689956i	$0.242370\pi$
$798$	−4.93548	+	6.89761i	−0.174714	+	0.244173i
$799$	−10.3942			−0.367720
$800$	3.79565	+	2.19142i	0.134197	+	0.0774785i
$801$	−1.68066	+	11.7198i	−0.0593832	+	0.414098i
$802$	−5.61990	−	9.73395i	−0.198446	−	0.343718i
$803$	16.2386	−	28.1261i	0.573047	−	0.992547i
$804$	−3.41889	+	9.88411i	−0.120575	+	0.348586i
$805$	−28.5410	−	30.0809i	−1.00594	−	1.06021i
$806$		−	3.81431i		−	0.134353i
$807$	−6.39042	−	7.37221i	−0.224954	−	0.259514i
$808$	−6.92115	+	3.99593i	−0.243485	+	0.140576i
$809$	−15.8249	+	9.13651i	−0.556374	+	0.321223i	−0.751689	−	0.659518i	$-0.770760\pi$
$809$	−15.8249	+	9.13651i	−0.556374	+	0.321223i	0.195315	+	0.980741i	$0.437427\pi$
$810$	−3.83240	+	13.0875i	−0.134657	+	0.459847i
$811$		−	9.04495i		−	0.317611i	−0.987310	−	0.158806i	$-0.949236\pi$
$811$		−	9.04495i		−	0.317611i	0.987310	−	0.158806i	$-0.0507643\pi$
$812$	20.6564	+	21.7708i	0.724897	+	0.764007i
$813$	32.3810	+	11.2005i	1.13565	+	0.392819i
$814$	−9.35132	+	16.1970i	−0.327764	+	0.567703i
$815$	6.76201	+	11.7121i	0.236863	+	0.410258i
$816$	8.48763	−	1.63747i	0.297126	−	0.0573230i
$817$	18.3628	+	10.6018i	0.642434	+	0.370910i
$818$	−23.4253			−0.819045
$819$	6.47512	−	4.59051i	0.226259	−	0.160405i
$820$	12.0192			0.419729
$821$	−6.01699	−	3.47391i	−0.209994	−	0.121240i	0.391314	−	0.920257i	$-0.372021\pi$
$821$	−6.01699	−	3.47391i	−0.209994	−	0.121240i	−0.601309	+	0.799017i	$0.705354\pi$
$822$	22.9779	−	4.43300i	0.801446	−	0.154619i
$823$	−14.6613	−	25.3941i	−0.511060	−	0.885182i	−0.999918	−	0.0128187i	$-0.995920\pi$
$823$	−14.6613	−	25.3941i	−0.511060	−	0.885182i	0.488858	−	0.872364i	$-0.337414\pi$
$824$	−17.6126	+	30.5059i	−0.613564	+	1.06272i
$825$	−5.70222	−	1.97238i	−0.198526	−	0.0686696i
$826$	−2.34446	+	0.562654i	−0.0815743	+	0.0195772i
$827$			15.1080i			0.525355i	0.964884	+	0.262678i	$0.0846056\pi$
$827$			15.1080i			0.525355i	−0.964884	+	0.262678i	$0.915394\pi$
$828$	−12.3846	−	30.9025i	−0.430396	−	1.07394i
$829$	39.6529	−	22.8936i	1.37720	−	0.795128i	0.385379	−	0.922758i	$-0.374071\pi$
$829$	39.6529	−	22.8936i	1.37720	−	0.795128i	0.991822	+	0.127631i	$0.0407372\pi$
$830$	−0.562047	+	0.324498i	−0.0195089	+	0.0112635i
$831$	−8.10840	−	9.35413i	−0.281277	−	0.324491i
$832$		−	2.20129i		−	0.0763158i
$833$	27.8566	+	18.0967i	0.965175	+	0.627015i
$834$	−1.70599	+	4.93206i	−0.0590735	+	0.170783i
$835$	17.4562	−	30.2351i	0.604098	−	1.04633i
$836$	8.56067	+	14.8275i	0.296077	+	0.512820i
$837$	12.3459	−	23.9801i	0.426737	−	0.828874i
$838$	−6.63850	−	3.83274i	−0.229323	−	0.132400i
$839$	−1.25874			−0.0434566			−0.0217283	−	0.999764i	$-0.506917\pi$
$839$	−1.25874			−0.0434566			−0.0217283	+	0.999764i	$0.506917\pi$
$840$	2.33821	−	23.9111i	0.0806758	−	0.825011i
$841$	−31.3598			−1.08137
$842$	−16.7784	−	9.68699i	−0.578220	−	0.333836i
$843$	−6.80141	−	35.2542i	−0.234253	−	1.21422i
$844$	−3.78460	−	6.55511i	−0.130271	−	0.225636i
$845$	−1.03100	+	1.78574i	−0.0354673	+	0.0614312i
$846$	−2.98343	+	3.79661i	−0.102573	+	0.130530i
$847$	−27.0872	−	8.02600i	−0.930728	−	0.275777i
$848$		−	0.915939i		−	0.0314535i
$849$	−41.9067	+	36.3258i	−1.43823	+	1.24670i
$850$	−2.25955	+	1.30455i	−0.0775018	+	0.0447457i
$851$	−35.9825	+	20.7745i	−1.23346	+	0.712141i
$852$	28.9973	−	25.1356i	0.993431	−	0.861132i
$853$			4.17642i			0.142998i	0.997441	+	0.0714990i	$0.0227783\pi$
$853$			4.17642i			0.142998i	−0.997441	+	0.0714990i	$0.977222\pi$
$854$	−15.2865	+	14.5040i	−0.523094	+	0.496317i
$855$	9.62670	−	12.2506i	0.329226	−	0.418961i
$856$	6.76598	−	11.7190i	0.231256	−	0.400548i
$857$	8.88711	+	15.3929i	0.303578	+	0.525812i	0.976944	−	0.213497i	$-0.0684854\pi$
$857$	8.88711	+	15.3929i	0.303578	+	0.525812i	−0.673366	+	0.739309i	$0.735152\pi$
$858$	1.12257	+	5.81871i	0.0383239	+	0.198647i
$859$	−40.3464	−	23.2940i	−1.37660	−	0.794781i	−0.384853	−	0.922978i	$-0.625748\pi$
$859$	−40.3464	−	23.2940i	−1.37660	−	0.794781i	−0.991749	+	0.128196i	$0.959081\pi$
$860$	−25.3443			−0.864234
$861$	7.56226	+	16.6594i	0.257721	+	0.567750i
$862$	29.2360			0.995781
$863$	4.00076	+	2.30984i	0.136187	+	0.0786278i	0.566546	−	0.824030i	$-0.308279\pi$
$863$	4.00076	+	2.30984i	0.136187	+	0.0786278i	−0.430358	+	0.902658i	$0.641613\pi$
$864$	13.9329	−	27.0625i	0.474005	−	0.920686i
$865$	20.8020	+	36.0300i	0.707288	+	1.22506i
$866$	2.59764	−	4.49924i	0.0882714	−	0.152891i
$867$	−3.12545	+	9.03576i	−0.106146	+	0.306870i
$868$	−5.69628	+	19.2246i	−0.193344	+	0.652525i
$869$		−	31.3093i		−	1.06210i
$870$	13.3553	+	15.4071i	0.452787	+	0.522351i
$871$	3.58172	−	2.06791i	0.121362	−	0.0700683i
$872$	19.9150	−	11.4979i	0.674407	−	0.389369i
$873$	1.17635	+	2.93525i	0.0398133	+	0.0993432i
$874$		−	14.0677i		−	0.475847i
$875$	−7.31821	−	30.4935i	−0.247401	−	1.03087i
$876$	16.6704	+	5.76626i	0.563241	+	0.194824i
$877$	−6.22455	+	10.7812i	−0.210188	+	0.364056i	−0.951773	−	0.306802i	$-0.900741\pi$
$877$	−6.22455	+	10.7812i	−0.210188	+	0.364056i	0.741585	+	0.670859i	$0.234074\pi$
$878$	−12.5385	−	21.7174i	−0.423155	−	0.732925i
$879$	21.7168	−	4.18969i	0.732488	−	0.141315i
$880$	−8.74386	−	5.04827i	−0.294755	−	0.170177i
$881$	6.59254			0.222108			0.111054	−	0.993814i	$-0.464577\pi$
$881$	6.59254			0.222108			0.111054	+	0.993814i	$0.464577\pi$
$882$	14.6057	−	4.98070i	0.491800	−	0.167709i
$883$	0.690401			0.0232338			0.0116169	−	0.999933i	$-0.496302\pi$
$883$	0.690401			0.0232338			0.0116169	+	0.999933i	$0.496302\pi$
$884$	−6.00029	−	3.46427i	−0.201812	−	0.116516i
$885$	4.34885	−	0.839000i	0.146185	−	0.0282027i
$886$	6.11610	+	10.5934i	0.205474	+	0.355892i
$887$	7.49599	−	12.9834i	0.251691	−	0.435941i	−0.712301	−	0.701874i	$-0.752347\pi$
$887$	7.49599	−	12.9834i	0.251691	−	0.435941i	0.963991	+	0.265933i	$0.0856801\pi$
$888$	−22.7505	−	7.86936i	−0.763458	−	0.264079i
$889$	13.4474	+	56.0325i	0.451011	+	1.87927i
$890$		−	5.97995i		−	0.200448i
$891$	−11.7761	+	40.2149i	−0.394514	+	1.34725i
$892$	23.6826	−	13.6732i	0.792953	−	0.457811i
$893$	4.77758	−	2.75834i	0.159876	−	0.0923043i
$894$	13.1438	+	15.1631i	0.439593	+	0.507129i
$895$		−	13.2817i		−	0.443959i
$896$	−7.59023	+	25.6165i	−0.253572	+	0.855788i
$897$	−4.30356	+	12.4417i	−0.143692	+	0.415416i
$898$	−0.635717	+	1.10109i	−0.0212141	+	0.0367440i
$899$	−20.1636	−	34.9244i	−0.672494	−	1.16479i
$900$	0.465192	−	3.24393i	0.0155064	−	0.108131i
$901$	3.57936	+	2.06655i	0.119246	+	0.0688466i
$902$	−13.6595			−0.454811
$903$	−15.9462	−	35.1288i	−0.530655	−	1.16901i
$904$	4.57410			0.152132
$905$	6.99474	+	4.03842i	0.232513	+	0.134241i
$906$	3.46432	+	17.9569i	0.115094	+	0.596577i
$907$	−25.7175	−	44.5440i	−0.853935	−	1.47906i	−0.877630	−	0.479339i	$-0.840876\pi$
$907$	−25.7175	−	44.5440i	−0.853935	−	1.47906i	0.0236952	−	0.999719i	$-0.492457\pi$
$908$	5.12905	−	8.88377i	0.170213	−	0.294818i
$909$	7.41441	+	5.82636i	0.245921	+	0.193248i
$910$	−2.90819	+	2.75932i	−0.0964057	+	0.0914707i
$911$			13.9187i			0.461148i	0.973055	+	0.230574i	$0.0740603\pi$
$911$			13.9187i			0.461148i	−0.973055	+	0.230574i	$0.925940\pi$
$912$	−3.46671	+	3.00504i	−0.114794	+	0.0995067i
$913$	−1.72704	+	0.997110i	−0.0571568	+	0.0329995i
$914$	−10.1539	+	5.86235i	−0.335861	+	0.193909i
$915$	29.2502	−	25.3548i	0.966981	−	0.838205i
$916$			19.0745i			0.630239i
$917$	−48.0104	−	14.2256i	−1.58544	−	0.469770i
$918$	9.80481	+	15.2381i	0.323607	+	0.502933i
$919$	−11.5043	+	19.9261i	−0.379493	+	0.657300i	−0.990988	−	0.133947i	$-0.957235\pi$
$919$	−11.5043	+	19.9261i	−0.379493	+	0.657300i	0.611496	+	0.791248i	$0.290568\pi$
$920$	19.9244	+	34.5101i	0.656888	+	1.13776i
$921$	−2.92590	−	15.1660i	−0.0964116	−	0.499738i
$922$	16.1721	+	9.33699i	0.532601	+	0.307497i
$923$	−15.1751			−0.499494
$924$	3.03175	−	31.0034i	0.0997371	−	1.01994i
$925$	−4.08993			−0.134476
$926$	−10.6191	−	6.13096i	−0.348967	−	0.201476i
$927$	41.1420	+	5.89991i	1.35128	+	0.193778i
$928$	−22.7555	−	39.4136i	−0.746985	−	1.29382i
$929$	−19.8373	+	34.3591i	−0.650839	+	1.12729i	0.332080	+	0.943251i	$0.392250\pi$
$929$	−19.8373	+	34.3591i	−0.650839	+	1.12729i	−0.982920	+	0.184036i	$0.941084\pi$
$930$	−4.45319	+	12.8743i	−0.146026	+	0.422165i
$931$	−17.6064	−	0.925586i	−0.577026	−	0.0303349i
$932$			5.96690i			0.195452i
$933$	−21.6764	−	25.0066i	−0.709653	−	0.818680i
$934$	12.5618	−	7.25256i	0.411035	−	0.237311i
$935$	39.4559	−	22.7799i	1.29034	−	0.744981i
$936$	−7.08022	+	2.83751i	−0.231424	+	0.0927469i
$937$			20.9722i			0.685132i	0.939494	+	0.342566i	$0.111296\pi$
$937$			20.9722i			0.685132i	−0.939494	+	0.342566i	$0.888704\pi$
$938$	7.81882	−	1.87646i	0.255294	−	0.0612686i
$939$	−19.3019	−	6.67650i	−0.629895	−	0.217879i
$940$	−3.29700	+	5.71057i	−0.107536	+	0.186258i
$941$	26.8322	+	46.4747i	0.874704	+	1.51503i	0.857078	+	0.515187i	$0.172278\pi$
$941$	26.8322	+	46.4747i	0.874704	+	1.51503i	0.0176266	+	0.999845i	$0.494389\pi$
$942$	10.0976	−	1.94807i	0.328997	−	0.0634716i
$943$	−26.2798	−	15.1727i	−0.855789	−	0.494090i
$944$	−1.30418			−0.0424476
$945$	−27.2146	+	7.93448i	−0.885292	+	0.258109i
$946$	28.8030			0.936468
$947$	−42.5660	−	24.5755i	−1.38321	−	0.798595i	−0.390670	−	0.920531i	$-0.627757\pi$
$947$	−42.5660	−	24.5755i	−1.38321	−	0.798595i	−0.992538	+	0.121936i	$0.961090\pi$
$948$	16.6973	−	3.22132i	0.542303	−	0.104623i
$949$	−3.48770	−	6.04087i	−0.113215	−	0.196095i
$950$	0.692385	−	1.19925i	0.0224639	−	0.0389087i
$951$	−12.6631	−	4.38014i	−0.410629	−	0.142036i
$952$	−21.9724	−	23.1579i	−0.712131	−	0.750552i
$953$		−	1.87614i		−	0.0607740i	−0.999538	−	0.0303870i	$-0.990326\pi$
$953$		−	1.87614i		−	0.0607740i	0.999538	−	0.0303870i	$-0.00967398\pi$
$954$	1.78221	−	0.714249i	0.0577013	−	0.0231247i
$955$	38.3413	−	22.1363i	1.24069	−	0.716315i
$956$	−7.02433	+	4.05550i	−0.227183	+	0.131164i
$957$	41.0379	+	47.3427i	1.32657	+	1.53037i
$958$			5.69930i			0.184136i
$959$	33.4825	+	35.2889i	1.08120	+	1.13954i
$960$	−2.56999	+	7.42991i	−0.0829461	+	0.239799i
$961$	−2.02839	+	3.51328i	−0.0654320	+	0.113332i
$962$	2.00846	+	3.47876i	0.0647554	+	0.112160i
$963$	−15.8049	−	2.26648i	−0.509306	−	0.0730364i
$964$	1.27321	+	0.735087i	0.0410072	+	0.0236755i
$965$	3.67559			0.118321
$966$	−14.8942	+	20.8155i	−0.479213	+	0.669726i
$967$	34.2062			1.10000			0.549999	−	0.835165i	$-0.314628\pi$
$967$	34.2062			1.10000			0.549999	+	0.835165i	$0.314628\pi$
$968$	23.5120	+	13.5746i	0.755704	+	0.436306i
$969$	−3.92165	−	20.3274i	−0.125982	−	0.653010i
$970$	−0.798576	−	1.38317i	−0.0256407	−	0.0444110i
$971$	14.8988	−	25.8055i	0.478126	−	0.828138i	−0.521560	−	0.853215i	$-0.674650\pi$
$971$	14.8988	−	25.8055i	0.478126	−	0.828138i	0.999686	+	0.0250766i	$0.00798296\pi$
$972$	−22.6583	−	2.14262i	−0.726764	−	0.0687247i
$973$	−10.5488	+	2.53165i	−0.338180	+	0.0811608i
$974$		−	20.6489i		−	0.661634i
$975$	−0.979227	+	0.848820i	−0.0313604	+	0.0271840i
$976$	−9.87141	+	5.69926i	−0.315976	+	0.182429i
$977$	30.9432	−	17.8651i	0.989961	−	0.571554i	0.0846984	−	0.996407i	$-0.473007\pi$
$977$	30.9432	−	17.8651i	0.989961	−	0.571554i	0.905263	+	0.424852i	$0.139674\pi$
$978$	6.30783	−	5.46779i	0.201702	−	0.174841i
$979$		−	18.3750i		−	0.587269i
$980$	18.7784	−	9.56422i	0.599854	−	0.305518i
$981$	−21.3343	−	16.7648i	−0.681152	−	0.535259i
$982$	4.15508	−	7.19681i	0.132594	−	0.229660i
$983$	3.50824	+	6.07645i	0.111895	+	0.193809i	0.916534	−	0.399956i	$-0.130974\pi$
$983$	3.50824	+	6.07645i	0.111895	+	0.193809i	−0.804639	+	0.593764i	$0.797641\pi$
$984$	−3.33054	−	17.2634i	−0.106174	−	0.550339i
$985$	10.5170	+	6.07197i	0.335098	+	0.193469i
$986$	27.0926			0.862804
$987$	−9.98962	−	0.976860i	−0.317973	−	0.0310938i
$988$	3.67729			0.116990
$989$	55.4149	+	31.9938i	1.76209	+	1.01734i
$990$	3.00434	−	20.9502i	0.0954842	−	0.665842i
$991$	28.5584	+	49.4646i	0.907188	+	1.57130i	0.817953	+	0.575286i	$0.195109\pi$
$991$	28.5584	+	49.4646i	0.907188	+	1.57130i	0.0892356	+	0.996011i	$0.471558\pi$
$992$	15.2033	−	26.3328i	0.482704	−	0.836068i
$993$	8.79081	−	25.4145i	0.278968	−	0.806504i
$994$	−28.2878	−	8.38172i	−0.897233	−	0.265852i
$995$			8.54583i			0.270921i
$996$	−0.709450	−	0.818445i	−0.0224798	−	0.0259334i
$997$	18.3969	−	10.6214i	0.582634	−	0.336384i	−0.179545	−	0.983750i	$-0.557463\pi$
$997$	18.3969	−	10.6214i	0.582634	−	0.336384i	0.762180	+	0.647366i	$0.224129\pi$
$998$	−11.1759	+	6.45242i	−0.353767	+	0.204248i
$999$	1.36715	+	28.3714i	0.0432547	+	0.897630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bh.a.131.14	✓	64
3.2	odd	2	inner	273.2.bh.a.131.19	yes	64
7.3	odd	6	inner	273.2.bh.a.248.19	yes	64
21.17	even	6	inner	273.2.bh.a.248.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bh.a.131.14	✓	64	1.1	even	1	trivial
273.2.bh.a.131.19	yes	64	3.2	odd	2	inner
273.2.bh.a.248.14	yes	64	21.17	even	6	inner
273.2.bh.a.248.19	yes	64	7.3	odd	6	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.636389 - 0.367419i) q^{2} +(1.70069 - 0.328105i) q^{3} +(-0.730006 - 1.26441i) q^{4} +(1.03100 - 1.78574i) q^{5} +(-1.20285 - 0.416064i) q^{6} +(-0.617429 - 2.57270i) q^{7} +2.54255i q^{8} +(2.78469 - 1.11601i) q^{9} +O(q^{10})\)	\(q+(-0.636389 - 0.367419i) q^{2} +(1.70069 - 0.328105i) q^{3} +(-0.730006 - 1.26441i) q^{4} +(1.03100 - 1.78574i) q^{5} +(-1.20285 - 0.416064i) q^{6} +(-0.617429 - 2.57270i) q^{7} +2.54255i q^{8} +(2.78469 - 1.11601i) q^{9} +(-1.31223 + 0.757615i) q^{10} +(-4.03218 + 2.32798i) q^{11} +(-1.65637 - 1.91085i) q^{12} +1.00000i q^{13} +(-0.552334 + 1.86409i) q^{14} +(1.16750 - 3.37526i) q^{15} +(-0.525831 + 0.910766i) q^{16} +(-2.37277 - 4.10975i) q^{17} +(-2.18219 - 0.312934i) q^{18} +(2.18124 + 1.25934i) q^{19} -3.01053 q^{20} +(-1.89417 - 4.17278i) q^{21} +3.42138 q^{22} +(6.58248 + 3.80040i) q^{23} +(0.834223 + 4.32409i) q^{24} +(0.374097 + 0.647955i) q^{25} +(0.367419 - 0.636389i) q^{26} +(4.36973 - 2.81166i) q^{27} +(-2.80221 + 2.65877i) q^{28} -7.76916i q^{29} +(-1.98312 + 1.71902i) q^{30} +(4.49527 - 2.59534i) q^{31} +(5.07309 - 2.92895i) q^{32} +(-6.09367 + 5.28215i) q^{33} +3.48720i q^{34} +(-5.23073 - 1.54988i) q^{35} +(-3.44394 - 2.70630i) q^{36} +(-2.73320 + 4.73405i) q^{37} +(-0.925409 - 1.60286i) q^{38} +(0.328105 + 1.70069i) q^{39} +(4.54032 + 2.62136i) q^{40} -3.99239 q^{41} +(-0.327732 + 3.35147i) q^{42} +8.41855 q^{43} +(5.88704 + 3.39888i) q^{44} +(0.878108 - 6.12333i) q^{45} +(-2.79268 - 4.83706i) q^{46} +(1.09516 - 1.89686i) q^{47} +(-0.595449 + 1.72146i) q^{48} +(-6.23756 + 3.17692i) q^{49} -0.549801i q^{50} +(-5.38377 - 6.21090i) q^{51} +(1.26441 - 0.730006i) q^{52} +(-0.754260 + 0.435472i) q^{53} +(-3.81391 + 0.183783i) q^{54} +9.60055i q^{55} +(6.54122 - 1.56984i) q^{56} +(4.12280 + 1.42607i) q^{57} +(-2.85454 + 4.94420i) q^{58} +(0.620058 + 1.07397i) q^{59} +(-5.11998 + 0.987770i) q^{60} +(9.38648 + 5.41929i) q^{61} -3.81431 q^{62} +(-4.59051 - 6.47512i) q^{63} -2.20129 q^{64} +(1.78574 + 1.03100i) q^{65} +(5.81871 - 1.12257i) q^{66} +(-2.06791 - 3.58172i) q^{67} +(-3.46427 + 6.00029i) q^{68} +(12.4417 + 4.30356i) q^{69} +(2.75932 + 2.90819i) q^{70} +15.1751i q^{71} +(2.83751 + 7.08022i) q^{72} +(-6.04087 + 3.48770i) q^{73} +(3.47876 - 2.00846i) q^{74} +(0.848820 + 0.979227i) q^{75} -3.67729i q^{76} +(8.47878 + 8.93623i) q^{77} +(0.416064 - 1.20285i) q^{78} +(-3.36228 + 5.82364i) q^{79} +(1.08426 + 1.87799i) q^{80} +(6.50905 - 6.21549i) q^{81} +(2.54071 + 1.46688i) q^{82} +0.428315 q^{83} +(-3.89334 + 5.44116i) q^{84} -9.78524 q^{85} +(-5.35747 - 3.09314i) q^{86} +(-2.54910 - 13.2129i) q^{87} +(-5.91901 - 10.2520i) q^{88} +(-1.97328 + 3.41782i) q^{89} +(-2.80865 + 3.57418i) q^{90} +(2.57270 - 0.617429i) q^{91} -11.0973i q^{92} +(6.79351 - 5.88879i) q^{93} +(-1.39389 + 0.804762i) q^{94} +(4.49769 - 2.59674i) q^{95} +(7.66675 - 6.64574i) q^{96} +1.05407i q^{97} +(5.13677 + 0.270045i) q^{98} +(-8.63034 + 10.9827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

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