LMFDB - Embedded newform 819.2.dk.a.43.59

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(43,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 1]))

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

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

chi := DirichletCharacter("819.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dk (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.59
Character	$\chi$	$=$	819.43
Dual form			819.2.dk.a.400.59

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14134 - 0.658952i) q^{2} +(0.489776 - 1.66136i) q^{3} +(-0.131566 + 0.227878i) q^{4} +(-2.75601 + 1.59118i) q^{5} +(-0.535756 - 2.21891i) q^{6} +1.00000i q^{7} +2.98259i q^{8} +(-2.52024 - 1.62739i) q^{9} +O(q^{10})$	\(q+(1.14134 - 0.658952i) q^{2} +(0.489776 - 1.66136i) q^{3} +(-0.131566 + 0.227878i) q^{4} +(-2.75601 + 1.59118i) q^{5} +(-0.535756 - 2.21891i) q^{6} +1.00000i q^{7} +2.98259i q^{8} +(-2.52024 - 1.62739i) q^{9} +(-2.09703 + 3.63216i) q^{10} +(2.60990 - 1.50683i) q^{11} +(0.314150 + 0.330187i) q^{12} +(1.16511 + 3.41211i) q^{13} +(0.658952 + 1.14134i) q^{14} +(1.29370 + 5.35805i) q^{15} +(1.70225 + 2.94838i) q^{16} +(2.51231 + 4.35145i) q^{17} +(-3.94881 - 0.196687i) q^{18} +(-3.84455 + 2.21965i) q^{19} -0.837380i q^{20} +(1.66136 + 0.489776i) q^{21} +(1.98585 - 3.43960i) q^{22} +5.84702 q^{23} +(4.95515 + 1.46080i) q^{24} +(2.56373 - 4.44052i) q^{25} +(3.57820 + 3.12662i) q^{26} +(-3.93804 + 3.38997i) q^{27} +(-0.227878 - 0.131566i) q^{28} +(0.831612 + 1.44039i) q^{29} +(5.00725 + 5.26286i) q^{30} +(3.41567 - 1.97204i) q^{31} +(-1.28031 - 0.739187i) q^{32} +(-1.22511 - 5.07399i) q^{33} +(5.73479 + 3.31098i) q^{34} +(-1.59118 - 2.75601i) q^{35} +(0.702423 - 0.360199i) q^{36} +(1.36441 + 0.787742i) q^{37} +(-2.92529 + 5.06675i) q^{38} +(6.23939 - 0.264496i) q^{39} +(-4.74585 - 8.22005i) q^{40} +10.9939i q^{41} +(2.21891 - 0.535756i) q^{42} -12.3259 q^{43} +0.792986i q^{44} +(9.53528 + 0.474944i) q^{45} +(6.67342 - 3.85290i) q^{46} +(2.33120 + 1.34592i) q^{47} +(5.73205 - 1.38400i) q^{48} -1.00000 q^{49} -6.75750i q^{50} +(8.45979 - 2.04262i) q^{51} +(-0.930834 - 0.183413i) q^{52} -10.0514 q^{53} +(-2.26080 + 6.46407i) q^{54} +(-4.79528 + 8.30566i) q^{55} -2.98259 q^{56} +(1.80467 + 7.47432i) q^{57} +(1.89830 + 1.09598i) q^{58} +(-2.68842 - 1.55216i) q^{59} +(-1.39119 - 0.410129i) q^{60} -4.28112 q^{61} +(2.59896 - 4.50153i) q^{62} +(1.62739 - 2.52024i) q^{63} -8.75735 q^{64} +(-8.64036 - 7.54992i) q^{65} +(-4.74179 - 4.98385i) q^{66} -7.27878i q^{67} -1.32213 q^{68} +(2.86373 - 9.71401i) q^{69} +(-3.63216 - 2.09703i) q^{70} +(14.4362 - 8.33475i) q^{71} +(4.85383 - 7.51683i) q^{72} +1.90227i q^{73} +2.07634 q^{74} +(-6.12164 - 6.43414i) q^{75} -1.16812i q^{76} +(1.50683 + 2.60990i) q^{77} +(6.94697 - 4.41334i) q^{78} +(3.07911 - 5.33317i) q^{79} +(-9.38284 - 5.41719i) q^{80} +(3.70320 + 8.20282i) q^{81} +(7.24447 + 12.5478i) q^{82} +(9.05731 + 5.22924i) q^{83} +(-0.330187 + 0.314150i) q^{84} +(-13.8479 - 7.99509i) q^{85} +(-14.0680 + 8.12218i) q^{86} +(2.80032 - 0.676136i) q^{87} +(4.49424 + 7.78426i) q^{88} +(-0.665908 - 0.384462i) q^{89} +(11.1959 - 5.74122i) q^{90} +(-3.41211 + 1.16511i) q^{91} +(-0.769266 + 1.33241i) q^{92} +(-1.60335 - 6.64052i) q^{93} +3.54758 q^{94} +(7.06375 - 12.2348i) q^{95} +(-1.85512 + 1.76502i) q^{96} +3.94877i q^{97} +(-1.14134 + 0.658952i) q^{98} +(-9.02976 - 0.449764i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 84 q^{4} - 2 q^{9}+O(q^{10}) $ 168 * q + 84 * q^4 - 2 * q^9	$ 168 q + 84 q^{4} - 2 q^{9} + 12 q^{12} + 8 q^{14} - 84 q^{16} + 12 q^{18} - 6 q^{21} + 40 q^{23} - 84 q^{24} + 84 q^{25} + 4 q^{26} - 24 q^{27} + 34 q^{29} + 44 q^{30} + 36 q^{32} + 18 q^{33} + 16 q^{35} + 4 q^{36} - 12 q^{38} - 6 q^{39} - 30 q^{45} - 30 q^{47} - 2 q^{48} - 168 q^{49} - 38 q^{51} + 18 q^{52} - 48 q^{53} + 114 q^{54} + 48 q^{56} - 54 q^{57} + 48 q^{59} + 24 q^{60} + 6 q^{62} - 12 q^{63} - 132 q^{64} - 16 q^{65} - 54 q^{66} - 156 q^{68} - 28 q^{69} + 24 q^{71} + 36 q^{72} - 84 q^{74} + 30 q^{75} - 16 q^{77} + 116 q^{78} - 6 q^{79} - 2 q^{81} - 6 q^{82} + 18 q^{83} - 24 q^{84} + 90 q^{85} - 24 q^{86} + 52 q^{87} + 24 q^{88} - 36 q^{89} - 44 q^{90} - 6 q^{91} + 8 q^{92} - 66 q^{93} + 120 q^{94} - 48 q^{95} - 24 q^{96} + 6 q^{99}+O(q^{100}) $ 168 * q + 84 * q^4 - 2 * q^9 + 12 * q^12 + 8 * q^14 - 84 * q^16 + 12 * q^18 - 6 * q^21 + 40 * q^23 - 84 * q^24 + 84 * q^25 + 4 * q^26 - 24 * q^27 + 34 * q^29 + 44 * q^30 + 36 * q^32 + 18 * q^33 + 16 * q^35 + 4 * q^36 - 12 * q^38 - 6 * q^39 - 30 * q^45 - 30 * q^47 - 2 * q^48 - 168 * q^49 - 38 * q^51 + 18 * q^52 - 48 * q^53 + 114 * q^54 + 48 * q^56 - 54 * q^57 + 48 * q^59 + 24 * q^60 + 6 * q^62 - 12 * q^63 - 132 * q^64 - 16 * q^65 - 54 * q^66 - 156 * q^68 - 28 * q^69 + 24 * q^71 + 36 * q^72 - 84 * q^74 + 30 * q^75 - 16 * q^77 + 116 * q^78 - 6 * q^79 - 2 * q^81 - 6 * q^82 + 18 * q^83 - 24 * q^84 + 90 * q^85 - 24 * q^86 + 52 * q^87 + 24 * q^88 - 36 * q^89 - 44 * q^90 - 6 * q^91 + 8 * q^92 - 66 * q^93 + 120 * q^94 - 48 * q^95 - 24 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	1.14134	−	0.658952i	0.807048	−	0.465949i	−0.0388819	−	0.999244i	$-0.512380\pi$
$2$	1.14134	−	0.658952i	0.807048	−	0.465949i	0.845930	+	0.533295i	$0.179046\pi$
$3$	0.489776	−	1.66136i	0.282773	−	0.959187i
$3$	0.489776	−	1.66136i	0.282773	−	0.959187i
$4$	−0.131566	+	0.227878i	−0.0657828	+	0.113939i
$5$	−2.75601	+	1.59118i	−1.23253	+	0.711599i	−0.967556	−	0.252658i	$-0.918695\pi$
$5$	−2.75601	+	1.59118i	−1.23253	+	0.711599i	−0.264970	+	0.964257i	$0.585362\pi$
$6$	−0.535756	−	2.21891i	−0.218722	−	0.905867i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			2.98259i			1.05450i
$9$	−2.52024	−	1.62739i	−0.840079	−	0.542463i
$10$	−2.09703	+	3.63216i	−0.663138	+	1.14859i
$11$	2.60990	−	1.50683i	0.786914	−	0.454325i	−0.0519607	−	0.998649i	$-0.516547\pi$
$11$	2.60990	−	1.50683i	0.786914	−	0.454325i	0.838875	+	0.544324i	$0.183214\pi$
$12$	0.314150	+	0.330187i	0.0906873	+	0.0953168i
$13$	1.16511	+	3.41211i	0.323143	+	0.946350i
$13$	1.16511	+	3.41211i	0.323143	+	0.946350i
$14$	0.658952	+	1.14134i	0.176112	+	0.305035i
$15$	1.29370	+	5.35805i	0.334032	+	1.38344i
$16$	1.70225	+	2.94838i	0.425562	+	0.737096i
$17$	2.51231	+	4.35145i	0.609325	+	1.05538i	0.991352	+	0.131230i	$0.0418927\pi$
$17$	2.51231	+	4.35145i	0.609325	+	1.05538i	−0.382027	+	0.924151i	$0.624774\pi$
$18$	−3.94881	−	0.196687i	−0.930744	−	0.0463595i
$19$	−3.84455	+	2.21965i	−0.882000	+	0.509223i	−0.871317	−	0.490720i	$-0.836734\pi$
$19$	−3.84455	+	2.21965i	−0.882000	+	0.509223i	−0.0106829	+	0.999943i	$0.503401\pi$
$20$		−	0.837380i		−	0.187244i
$21$	1.66136	+	0.489776i	0.362539	+	0.106878i
$22$	1.98585	−	3.43960i	0.423385	−	0.733324i
$23$	5.84702			1.21919			0.609594	−	0.792714i	$-0.291333\pi$
$23$	5.84702			1.21919			0.609594	+	0.792714i	$0.291333\pi$
$24$	4.95515	+	1.46080i	1.01147	+	0.298185i
$25$	2.56373	−	4.44052i	0.512747	−	0.888103i
$26$	3.57820	+	3.12662i	0.701743	+	0.613181i
$27$	−3.93804	+	3.38997i	−0.757875	+	0.652400i
$28$	−0.227878	−	0.131566i	−0.0430649	−	0.0248635i
$29$	0.831612	+	1.44039i	0.154426	+	0.267474i	0.932850	−	0.360265i	$-0.117314\pi$
$29$	0.831612	+	1.44039i	0.154426	+	0.267474i	−0.778424	+	0.627739i	$0.783980\pi$
$30$	5.00725	+	5.26286i	0.914194	+	0.960863i
$31$	3.41567	−	1.97204i	0.613473	−	0.354189i	−0.160850	−	0.986979i	$-0.551424\pi$
$31$	3.41567	−	1.97204i	0.613473	−	0.354189i	0.774323	+	0.632790i	$0.218090\pi$
$32$	−1.28031	−	0.739187i	−0.226329	−	0.130671i
$33$	−1.22511	−	5.07399i	−0.213265	−	0.883269i
$34$	5.73479	+	3.31098i	0.983508	+	0.567829i
$35$	−1.59118	−	2.75601i	−0.268959	−	0.465851i
$36$	0.702423	−	0.360199i	0.117071	−	0.0600331i
$37$	1.36441	+	0.787742i	0.224307	+	0.129504i	0.607943	−	0.793981i	$-0.291995\pi$
$37$	1.36441	+	0.787742i	0.224307	+	0.129504i	−0.383636	+	0.923485i	$0.625328\pi$
$38$	−2.92529	+	5.06675i	−0.474544	+	0.821935i
$39$	6.23939	−	0.264496i	0.999103	−	0.0423532i
$40$	−4.74585	−	8.22005i	−0.750384	−	1.29970i
$41$			10.9939i			1.71696i	0.512843	+	0.858482i	$0.328592\pi$
$41$			10.9939i			1.71696i	−0.512843	+	0.858482i	$0.671408\pi$
$42$	2.21891	−	0.535756i	0.342386	−	0.0826690i
$43$	−12.3259			−1.87968			−0.939842	−	0.341609i	$-0.889028\pi$
$43$	−12.3259			−1.87968			−0.939842	+	0.341609i	$0.889028\pi$
$44$			0.792986i			0.119547i
$45$	9.53528	+	0.474944i	1.42144	+	0.0708004i
$46$	6.67342	−	3.85290i	0.983943	−	0.568080i
$47$	2.33120	+	1.34592i	0.340040	+	0.196322i	0.660290	−	0.751011i	$-0.270433\pi$
$47$	2.33120	+	1.34592i	0.340040	+	0.196322i	−0.320250	+	0.947333i	$0.603767\pi$
$48$	5.73205	−	1.38400i	0.827350	−	0.199764i
$49$	−1.00000			−0.142857
$50$		−	6.75750i		−	0.955655i
$51$	8.45979	−	2.04262i	1.18461	−	0.286023i
$52$	−0.930834	−	0.183413i	−0.129084	−	0.0254348i
$53$	−10.0514			−1.38067			−0.690333	−	0.723492i	$-0.742536\pi$
$53$	−10.0514			−1.38067			−0.690333	+	0.723492i	$0.742536\pi$
$54$	−2.26080	+	6.46407i	−0.307656	+	0.879649i
$55$	−4.79528	+	8.30566i	−0.646595	+	1.11994i
$56$	−2.98259			−0.398565
$57$	1.80467	+	7.47432i	0.239035	+	0.989998i
$58$	1.89830	+	1.09598i	0.249259	+	0.143910i
$59$	−2.68842	−	1.55216i	−0.350002	−	0.202074i	0.314684	−	0.949196i	$-0.398101\pi$
$59$	−2.68842	−	1.55216i	−0.350002	−	0.202074i	−0.664686	+	0.747123i	$0.731435\pi$
$60$	−1.39119	−	0.410129i	−0.179602	−	0.0529474i
$61$	−4.28112			−0.548142			−0.274071	−	0.961709i	$-0.588370\pi$
$61$	−4.28112			−0.548142			−0.274071	+	0.961709i	$0.588370\pi$
$62$	2.59896	−	4.50153i	0.330068	−	0.571694i
$63$	1.62739	−	2.52024i	0.205032	−	0.317520i
$64$	−8.75735			−1.09467
$65$	−8.64036	−	7.54992i	−1.07170	−	0.936452i
$66$	−4.74179	−	4.98385i	−0.583673	−	0.613469i
$67$		−	7.27878i		−	0.889244i	−0.895718	−	0.444622i	$-0.853338\pi$
$67$		−	7.27878i		−	0.889244i	0.895718	−	0.444622i	$-0.146662\pi$
$68$	−1.32213			−0.160332
$69$	2.86373	−	9.71401i	0.344753	−	1.16943i
$70$	−3.63216	−	2.09703i	−0.434126	−	0.250643i
$71$	14.4362	−	8.33475i	1.71326	−	0.989152i	0.783184	−	0.621790i	$-0.213594\pi$
$71$	14.4362	−	8.33475i	1.71326	−	0.989152i	0.930078	−	0.367363i	$-0.119739\pi$
$72$	4.85383	−	7.51683i	0.572030	−	0.885867i
$73$			1.90227i			0.222644i	0.993784	+	0.111322i	$0.0355085\pi$
$73$			1.90227i			0.222644i	−0.993784	+	0.111322i	$0.964491\pi$
$74$	2.07634			0.241369
$75$	−6.12164	−	6.43414i	−0.706866	−	0.742951i
$76$		−	1.16812i		−	0.133992i
$77$	1.50683	+	2.60990i	0.171719	+	0.297426i
$78$	6.94697	−	4.41334i	0.786589	−	0.499712i
$79$	3.07911	−	5.33317i	0.346426	−	0.600028i	−0.639185	−	0.769053i	$-0.720728\pi$
$79$	3.07911	−	5.33317i	0.346426	−	0.600028i	0.985612	+	0.169024i	$0.0540617\pi$
$80$	−9.38284	−	5.41719i	−1.04903	−	0.605660i
$81$	3.70320	+	8.20282i	0.411467	+	0.911425i
$82$	7.24447	+	12.5478i	0.800018	+	1.38567i
$83$	9.05731	+	5.22924i	0.994169	+	0.573984i	0.906518	−	0.422167i	$-0.138731\pi$
$83$	9.05731	+	5.22924i	0.994169	+	0.573984i	0.0876513	+	0.996151i	$0.472064\pi$
$84$	−0.330187	+	0.314150i	−0.0360264	+	0.0342766i
$85$	−13.8479	−	7.99509i	−1.50202	−	0.867190i
$86$	−14.0680	+	8.12218i	−1.51699	+	0.875837i
$87$	2.80032	−	0.676136i	0.300225	−	0.0724894i
$88$	4.49424	+	7.78426i	0.479088	+	0.829804i
$89$	−0.665908	−	0.384462i	−0.0705861	−	0.0407529i	0.464292	−	0.885682i	$-0.346309\pi$
$89$	−0.665908	−	0.384462i	−0.0705861	−	0.0407529i	−0.534878	+	0.844930i	$0.679642\pi$
$90$	11.1959	−	5.74122i	1.18016	−	0.605178i
$91$	−3.41211	+	1.16511i	−0.357687	+	0.122137i
$92$	−0.769266	+	1.33241i	−0.0802015	+	0.138913i
$93$	−1.60335	−	6.64052i	−0.166260	−	0.688590i
$94$	3.54758			0.365905
$95$	7.06375	−	12.2348i	0.724725	−	1.25526i
$96$	−1.85512	+	1.76502i	−0.189338	+	0.180142i
$97$			3.94877i			0.400937i	0.979700	+	0.200468i	$0.0642464\pi$
$97$			3.94877i			0.400937i	−0.979700	+	0.200468i	$0.935754\pi$
$98$	−1.14134	+	0.658952i	−0.115293	+	0.0665642i
$99$	−9.02976	−	0.449764i	−0.907525	−	0.0452030i
$100$	0.674598	+	1.16844i	0.0674598	+	0.116844i
$101$	3.82167	+	6.61932i	0.380270	+	0.658647i	0.991101	−	0.133114i	$-0.0424977\pi$
$101$	3.82167	+	6.61932i	0.380270	+	0.658647i	−0.610831	+	0.791761i	$0.709164\pi$
$102$	8.30950	−	7.90591i	0.822763	−	0.782802i
$103$	−5.74012	−	9.94218i	−0.565591	−	0.979632i	−0.996994	−	0.0774731i	$-0.975315\pi$
$103$	−5.74012	−	9.94218i	−0.565591	−	0.979632i	0.431404	−	0.902159i	$-0.358019\pi$
$104$	−10.1769	+	3.47504i	−0.997930	+	0.340756i
$105$	−5.35805	+	1.29370i	−0.522892	+	0.126252i
$106$	−11.4720	+	6.62338i	−1.11426	+	0.643320i
$107$	10.0213	−	17.3574i	0.968797	−	1.67801i	0.269749	−	0.962931i	$-0.413059\pi$
$107$	10.0213	−	17.3574i	0.968797	−	1.67801i	0.699048	−	0.715075i	$-0.253607\pi$
$108$	−0.254390	−	1.34340i	−0.0244787	−	0.129268i
$109$			4.36888i			0.418463i	0.977866	+	0.209231i	$0.0670962\pi$
$109$			4.36888i			0.418463i	−0.977866	+	0.209231i	$0.932904\pi$
$110$			12.6394i			1.20512i
$111$	1.97698	−	1.88096i	0.187647	−	0.178533i
$112$	−2.94838	+	1.70225i	−0.278596	+	0.160848i
$113$	1.91682	−	3.32004i	0.180320	−	0.312323i	−0.761670	−	0.647965i	$-0.775620\pi$
$113$	1.91682	−	3.32004i	0.180320	−	0.312323i	0.941989	+	0.335643i	$0.108953\pi$
$114$	6.98496	+	7.34153i	0.654201	+	0.687597i
$115$	−16.1145	+	9.30368i	−1.50268	+	0.867573i
$116$	−0.437646			−0.0406344
$117$	2.61648	−	10.4954i	0.241894	−	0.970303i
$118$	−4.09119			−0.376624
$119$	−4.35145	+	2.51231i	−0.398897	+	0.230303i
$120$	−15.9809	+	3.85858i	−1.45885	+	0.352238i
$121$	−0.958948	+	1.66095i	−0.0871771	+	0.150995i
$122$	−4.88621	+	2.82105i	−0.442377	+	0.255406i
$123$	18.2649	+	5.38457i	1.64689	+	0.485510i
$124$			1.03781i			0.0931981i
$125$			0.405644i			0.0362819i
$126$	0.196687	−	3.94881i	0.0175223	−	0.351788i
$127$	−1.94629	+	3.37108i	−0.172705	+	0.299135i	−0.939365	−	0.342919i	$-0.888584\pi$
$127$	−1.94629	+	3.37108i	−0.172705	+	0.299135i	0.766659	+	0.642054i	$0.221918\pi$
$128$	−7.43448	+	4.29230i	−0.657121	+	0.379389i
$129$	−6.03694	+	20.4778i	−0.531523	+	1.80297i
$130$	−14.8366	−	2.92343i	−1.30126	−	0.256402i
$131$	0.486210	+	0.842141i	0.0424804	+	0.0735782i	0.886484	−	0.462760i	$-0.153141\pi$
$131$	0.486210	+	0.842141i	0.0424804	+	0.0735782i	−0.844003	+	0.536338i	$0.819807\pi$
$132$	1.31744	+	0.388386i	0.114668	+	0.0338046i
$133$	−2.21965	−	3.84455i	−0.192468	−	0.333365i
$134$	−4.79636	−	8.30754i	−0.414343	−	0.717662i
$135$	5.45921	−	15.6089i	0.469854	−	1.34340i
$136$	−12.9786	+	7.49318i	−1.11290	+	0.642535i
$137$		−	5.62631i		−	0.480688i	−0.970688	−	0.240344i	$-0.922740\pi$
$137$		−	5.62631i		−	0.480688i	0.970688	−	0.240344i	$-0.0772602\pi$
$138$	−3.13258	−	12.9740i	−0.266663	−	1.10442i
$139$	6.75454	−	11.6992i	0.572912	−	0.992314i	−0.423352	−	0.905965i	$-0.639147\pi$
$139$	6.75454	−	11.6992i	0.572912	−	0.992314i	0.996265	−	0.0863485i	$-0.0275199\pi$
$140$	0.837380			0.0707715
$141$	3.37782	−	3.21376i	0.284464	−	0.270648i
$142$	10.9844	−	19.0255i	0.921789	−	1.59659i
$143$	8.18228	+	7.14966i	0.684237	+	0.597884i
$144$	0.508095	−	10.2009i	0.0423413	−	0.850071i
$145$	−4.58386	−	2.64649i	−0.380669	−	0.219779i
$146$	1.25351	+	2.17114i	0.103741	+	0.179684i
$147$	−0.489776	+	1.66136i	−0.0403961	+	0.137027i
$148$	−0.359018	+	0.207279i	−0.0295111	+	0.0170383i
$149$	8.47383	+	4.89237i	0.694203	+	0.400799i	0.805185	−	0.593024i	$-0.202066\pi$
$149$	8.47383	+	4.89237i	0.694203	+	0.400799i	−0.110981	+	0.993822i	$0.535399\pi$
$150$	−11.2267	−	3.30967i	−0.916652	−	0.270233i
$151$	13.2487	+	7.64912i	1.07816	+	0.622476i	0.930400	−	0.366547i	$-0.119460\pi$
$151$	13.2487	+	7.64912i	1.07816	+	0.622476i	0.147761	+	0.989023i	$0.452793\pi$
$152$	−6.62031	−	11.4667i	−0.536978	−	0.930073i
$153$	0.749885	−	15.0552i	0.0606246	−	1.21714i
$154$	3.43960	+	1.98585i	0.277171	+	0.160024i
$155$	−6.27576	+	10.8699i	−0.504081	+	0.873094i
$156$	−0.760616	+	1.45662i	−0.0608980	+	0.116623i
$157$	−0.705989	−	1.22281i	−0.0563441	−	0.0975908i	0.836478	−	0.548001i	$-0.184611\pi$
$157$	−0.705989	−	1.22281i	−0.0563441	−	0.0975908i	−0.892822	+	0.450410i	$0.851278\pi$
$158$		−	8.11593i		−	0.645669i
$159$	−4.92293	+	16.6990i	−0.390414	+	1.32432i
$160$	4.70473			0.371942
$161$			5.84702i			0.460810i
$162$	9.63187	+	6.92196i	0.756751	+	0.543841i
$163$	5.70807	−	3.29556i	0.447091	−	0.258128i	−0.259510	−	0.965740i	$-0.583561\pi$
$163$	5.70807	−	3.29556i	0.447091	−	0.258128i	0.706601	+	0.707612i	$0.250228\pi$
$164$	−2.50528	−	1.44642i	−0.195629	−	0.112947i
$165$	11.4501	+	12.0346i	0.891388	+	0.936892i
$166$	13.7833			1.06979
$167$			6.11478i			0.473176i	0.971610	+	0.236588i	$0.0760291\pi$
$167$			6.11478i			0.473176i	−0.971610	+	0.236588i	$0.923971\pi$
$168$	−1.46080	+	4.95515i	−0.112703	+	0.382298i
$169$	−10.2850	+	7.95098i	−0.791157	+	0.611614i
$170$	−21.0735			−1.61627
$171$	13.3014	+	0.662532i	1.01719	+	0.0506651i
$172$	1.62167	−	2.80881i	0.123651	−	0.214169i
$173$	−9.38992			−0.713903			−0.356951	−	0.934123i	$-0.616184\pi$
$173$	−9.38992			−0.713903			−0.356951	+	0.934123i	$0.616184\pi$
$174$	2.75057	−	2.61697i	0.208520	−	0.198392i
$175$	4.44052	+	2.56373i	0.335671	+	0.193800i
$176$	8.88540	+	5.12999i	0.669763	+	0.386688i
$177$	−3.89542	+	3.70622i	−0.292797	+	0.278576i
$178$	−1.01337			−0.0759551
$179$	−12.0595	+	20.8877i	−0.901369	+	1.56122i	−0.0756503	+	0.997134i	$0.524103\pi$
$179$	−12.0595	+	20.8877i	−0.901369	+	1.56122i	−0.825719	+	0.564082i	$0.809230\pi$
$180$	−1.36274	+	2.11040i	−0.101573	+	0.157300i
$181$	12.7142			0.945043			0.472521	−	0.881319i	$-0.343344\pi$
$181$	12.7142			0.945043			0.472521	+	0.881319i	$0.343344\pi$
$182$	−3.12662	+	3.57820i	−0.231761	+	0.265234i
$183$	−2.09679	+	7.11249i	−0.154999	+	0.525771i
$184$			17.4392i			1.28564i
$185$	−5.01377			−0.368620
$186$	−6.20575	−	6.52255i	−0.455028	−	0.478256i
$187$	13.1138	+	7.57123i	0.958973	+	0.553663i
$188$	−0.613411	+	0.354153i	−0.0447376	+	0.0258293i
$189$	−3.38997	−	3.93804i	−0.246584	−	0.286450i
$190$		−	18.6187i		−	1.35074i
$191$	21.0003			1.51953			0.759763	−	0.650200i	$-0.225315\pi$
$191$	21.0003			1.51953			0.759763	+	0.650200i	$0.225315\pi$
$192$	−4.28914	+	14.5491i	−0.309542	+	1.04999i
$193$			0.900017i			0.0647846i	0.999475	+	0.0323923i	$0.0103126\pi$
$193$			0.900017i			0.0647846i	−0.999475	+	0.0323923i	$0.989687\pi$
$194$	2.60205	+	4.50688i	0.186816	+	0.323575i
$195$	−16.7750	+	10.6570i	−1.20128	+	0.763162i
$196$	0.131566	−	0.227878i	0.00939754	−	0.0162770i
$197$	22.0547	+	12.7333i	1.57134	+	0.907211i	0.996006	+	0.0892897i	$0.0284597\pi$
$197$	22.0547	+	12.7333i	1.57134	+	0.907211i	0.575330	+	0.817921i	$0.304874\pi$
$198$	−10.6024	+	5.43685i	−0.753479	+	0.386380i
$199$	−12.3894	−	21.4591i	−0.878263	−	1.52120i	−0.853246	−	0.521509i	$-0.825369\pi$
$199$	−12.3894	−	21.4591i	−0.878263	−	1.52120i	−0.0250175	−	0.999687i	$-0.507964\pi$
$200$	13.2442	+	7.64656i	0.936508	+	0.540693i
$201$	−12.0927	−	3.56497i	−0.852952	−	0.251454i
$202$	8.72362	+	5.03659i	0.613792	+	0.354373i
$203$	−1.44039	+	0.831612i	−0.101096	+	0.0583677i
$204$	−0.647550	+	2.19654i	−0.0453375	+	0.153789i
$205$	−17.4934	−	30.2994i	−1.22179	−	2.11620i
$206$	−13.1028	−	7.56492i	−0.912918	−	0.527073i
$207$	−14.7359	−	9.51538i	−1.02421	−	0.661365i
$208$	−8.07691	+	9.24346i	−0.560033	+	0.640919i
$209$	−6.68926	+	11.5861i	−0.462706	+	0.801430i
$210$	−5.26286	+	5.00725i	−0.363172	+	0.345533i
$211$	−4.14202			−0.285148			−0.142574	−	0.989784i	$-0.545538\pi$
$211$	−4.14202			−0.285148			−0.142574	+	0.989784i	$0.545538\pi$
$212$	1.32242	−	2.29049i	0.0908240	−	0.157312i
$213$	−6.77651	−	28.0659i	−0.464319	−	1.92304i
$214$		−	26.4142i		−	1.80564i
$215$	33.9704	−	19.6128i	2.31676	−	1.33758i
$216$	−10.1109	−	11.7455i	−0.687958	−	0.799182i
$217$	1.97204	+	3.41567i	0.133871	+	0.231871i
$218$	2.87888	+	4.98637i	0.194982	+	0.337719i
$219$	3.16036	+	0.931688i	0.213557	+	0.0629577i
$220$	−1.26179	−	2.18548i	−0.0850696	−	0.147345i
$221$	−11.9205	+	13.6422i	−0.801861	+	0.917674i
$222$	1.01694	−	3.44954i	0.0682525	−	0.231518i
$223$	−21.4281	+	12.3715i	−1.43493	+	0.828457i	−0.997491	−	0.0707913i	$-0.977448\pi$
$223$	−21.4281	+	12.3715i	−1.43493	+	0.828457i	−0.437438	+	0.899248i	$0.644114\pi$
$224$	0.739187	−	1.28031i	0.0493890	−	0.0855443i
$225$	−13.6877	+	7.01896i	−0.912511	+	0.467931i
$226$		−	5.05238i		−	0.336079i
$227$			10.8650i			0.721135i	0.932733	+	0.360568i	$0.117417\pi$
$227$			10.8650i			0.721135i	−0.932733	+	0.360568i	$0.882583\pi$
$228$	−1.94067	−	0.572117i	−0.128524	−	0.0378894i
$229$	12.0034	−	6.93017i	0.793208	−	0.457959i	−0.0478828	−	0.998853i	$-0.515247\pi$
$229$	12.0034	−	6.93017i	0.793208	−	0.457959i	0.841091	+	0.540894i	$0.181914\pi$
$230$	−12.2614	+	21.2373i	−0.808490	+	1.40035i
$231$	5.07399	−	1.22511i	0.333844	−	0.0806066i
$232$	−4.29610	+	2.48035i	−0.282053	+	0.162843i
$233$	11.8790			0.778219			0.389109	−	0.921192i	$-0.372783\pi$
$233$	11.8790			0.778219			0.389109	+	0.921192i	$0.372783\pi$
$234$	−3.92969	−	13.7030i	−0.256892	−	0.895791i
$235$	−8.56641			−0.558811
$236$	0.707406	−	0.408421i	0.0460482	−	0.0265859i
$237$	−7.35224	−	7.72756i	−0.477579	−	0.501959i
$238$	−3.31098	+	5.73479i	−0.214619	+	0.371731i
$239$	15.2349	−	8.79589i	0.985466	−	0.568959i	0.0815501	−	0.996669i	$-0.474013\pi$
$239$	15.2349	−	8.79589i	0.985466	−	0.568959i	0.903916	+	0.427710i	$0.140680\pi$
$240$	−13.5954	+	12.9351i	−0.877579	+	0.834955i
$241$		−	6.05925i		−	0.390310i	−0.980772	−	0.195155i	$-0.937479\pi$
$241$		−	6.05925i		−	0.390310i	0.980772	−	0.195155i	$-0.0625210\pi$
$242$			2.52760i			0.162480i
$243$	15.4416	−	2.13481i	0.990578	−	0.136948i
$244$	0.563248	−	0.975575i	0.0360583	−	0.0624548i
$245$	2.75601	−	1.59118i	0.176075	−	0.101657i
$246$	24.3946	−	5.89007i	1.55534	−	0.375537i
$247$	−12.0530	−	10.5319i	−0.766916	−	0.670129i
$248$	5.88178	+	10.1875i	0.373493	+	0.646910i
$249$	13.1237	−	12.4863i	0.831682	−	0.791287i
$250$	0.267300	+	0.462977i	0.0169055	+	0.0292812i
$251$	−0.0516419	−	0.0894464i	−0.00325961	−	0.00564581i	0.864391	−	0.502820i	$-0.167704\pi$
$251$	−0.0516419	−	0.0894464i	−0.00325961	−	0.00564581i	−0.867651	+	0.497174i	$0.834371\pi$
$252$	0.360199	+	0.702423i	0.0226904	+	0.0442485i
$253$	15.2601	−	8.81044i	0.959397	−	0.553908i
$254$			5.13005i			0.321888i
$255$	−20.0651	+	19.0906i	−1.25653	+	1.19550i
$256$	3.10052	−	5.37026i	0.193782	−	0.335641i
$257$	0.120446			0.00751319			0.00375659	−	0.999993i	$-0.498804\pi$
$257$	0.120446			0.00751319			0.00375659	+	0.999993i	$0.498804\pi$
$258$	6.60368	+	27.3501i	0.411127	+	1.70274i
$259$	−0.787742	+	1.36441i	−0.0489479	+	0.0847803i
$260$	2.85723	−	0.975640i	0.177198	−	0.0605066i
$261$	0.248223	−	4.98349i	0.0153646	−	0.308470i
$262$	1.10986	+	0.640778i	0.0685674	+	0.0395874i
$263$	−12.0484	−	20.8684i	−0.742935	−	1.28680i	−0.951153	−	0.308719i	$-0.900100\pi$
$263$	−12.0484	−	20.8684i	−0.742935	−	1.28680i	0.208218	−	0.978082i	$-0.433234\pi$
$264$	15.1336	−	3.65401i	0.931410	−	0.224889i
$265$	27.7018	−	15.9936i	1.70171	−	0.982480i
$266$	−5.06675	−	2.92529i	−0.310662	−	0.179361i
$267$	−0.964876	+	0.918013i	−0.0590495	+	0.0561815i
$268$	1.65867	+	0.957636i	0.101320	+	0.0584969i
$269$	−5.79878	−	10.0438i	−0.353558	−	0.612380i	0.633312	−	0.773896i	$-0.281695\pi$
$269$	−5.79878	−	10.0438i	−0.353558	−	0.612380i	−0.986870	+	0.161516i	$0.948362\pi$
$270$	−4.05473	−	21.4124i	−0.246763	−	1.30312i
$271$	−14.0325	−	8.10169i	−0.852416	−	0.492143i	0.00904924	−	0.999959i	$-0.497119\pi$
$271$	−14.0325	−	8.10169i	−0.852416	−	0.492143i	−0.861465	+	0.507816i	$0.830453\pi$
$272$	−8.55316	+	14.8145i	−0.518611	+	0.898261i
$273$	0.264496	+	6.23939i	0.0160080	+	0.377625i
$274$	−3.70746	−	6.42152i	−0.223976	−	0.387938i
$275$		−	15.4524i		−	0.931815i
$276$	1.83684	+	1.93061i	0.110565	+	0.116209i
$277$	−22.5153			−1.35281			−0.676405	−	0.736530i	$-0.736463\pi$
$277$	−22.5153			−1.35281			−0.676405	+	0.736530i	$0.736463\pi$
$278$		−	17.8037i		−	1.06779i
$279$	−11.8176	−	0.588623i	−0.707500	−	0.0352399i
$280$	8.22005	−	4.74585i	0.491242	−	0.283619i
$281$	24.5837	+	14.1934i	1.46654	+	0.846709i	0.999300	−	0.0374193i	$-0.0119137\pi$
$281$	24.5837	+	14.1934i	1.46654	+	0.846709i	0.467244	+	0.884129i	$0.345247\pi$
$282$	1.73752	−	5.89381i	0.103468	−	0.350971i
$283$	29.4412			1.75010			0.875048	−	0.484036i	$-0.160829\pi$
$283$	29.4412			1.75010			0.875048	+	0.484036i	$0.160829\pi$
$284$			4.38626i			0.260277i
$285$	−16.8667	−	17.7277i	−0.999098	−	1.05010i
$286$	14.0500	+	2.76844i	0.830795	+	0.163701i
$287$	−10.9939			−0.648952
$288$	2.02374	+	3.94649i	0.119250	+	0.232549i
$289$	−4.12340	+	7.14194i	−0.242553	+	0.420114i
$290$	−6.97565			−0.409624
$291$	6.56033	+	1.93401i	0.384573	+	0.113374i
$292$	−0.433486	−	0.250274i	−0.0253679	−	0.0146462i
$293$	−15.7467	−	9.09137i	−0.919933	−	0.531123i	−0.0363192	−	0.999340i	$-0.511563\pi$
$293$	−15.7467	−	9.09137i	−0.919933	−	0.531123i	−0.883614	+	0.468217i	$0.844897\pi$
$294$	0.535756	+	2.21891i	0.0312459	+	0.129410i
$295$	9.87908			0.575182
$296$	−2.34951	+	4.06947i	−0.136562	+	0.236533i
$297$	−5.16979	+	14.7814i	−0.299981	+	0.857704i
$298$	12.8953			0.747007
$299$	6.81242	+	19.9507i	0.393973	+	1.15378i
$300$	2.27160	−	0.548477i	0.131151	−	0.0316663i
$301$		−	12.3259i		−	0.710454i
$302$	20.1616			1.16017
$303$	12.8688	−	3.10718i	0.739296	−	0.178503i
$304$	−13.0888	−	7.55681i	−0.750693	−	0.433413i
$305$	11.7988	−	6.81206i	0.675599	−	0.390057i
$306$	−9.06477	−	17.6772i	−0.518199	−	1.01054i
$307$			2.14329i			0.122324i	0.998128	+	0.0611620i	$0.0194806\pi$
$307$			2.14329i			0.122324i	−0.998128	+	0.0611620i	$0.980519\pi$
$308$	−0.792986			−0.0451845
$309$	−19.3289	+	4.66697i	−1.09958	+	0.265494i
$310$			16.5417i			0.939504i
$311$	−11.4308	−	19.7987i	−0.648181	−	1.12268i	−0.983557	−	0.180599i	$-0.942196\pi$
$311$	−11.4308	−	19.7987i	−0.648181	−	1.12268i	0.335375	−	0.942085i	$-0.391137\pi$
$312$	0.788882	+	18.6095i	0.0446617	+	1.05356i
$313$	14.6134	−	25.3112i	0.825999	−	1.43067i	−0.0751539	−	0.997172i	$-0.523945\pi$
$313$	14.6134	−	25.3112i	0.825999	−	1.43067i	0.901153	−	0.433501i	$-0.142722\pi$
$314$	−1.61154	−	0.930426i	−0.0909447	−	0.0525070i
$315$	−0.474944	+	9.53528i	−0.0267600	+	0.537252i
$316$	0.810208	+	1.40332i	0.0455778	+	0.0789430i
$317$	8.84591	+	5.10719i	0.496836	+	0.286848i	0.727406	−	0.686207i	$-0.240726\pi$
$317$	8.84591	+	5.10719i	0.496836	+	0.286848i	−0.230570	+	0.973056i	$0.574059\pi$
$318$	5.38510	+	22.3032i	0.301981	+	1.25070i
$319$	4.34085	+	2.50619i	0.243041	+	0.140320i
$320$	24.1354	−	13.9346i	1.34921	−	0.778966i
$321$	−23.9287	−	25.1503i	−1.33557	−	1.40375i
$322$	3.85290	+	6.67342i	0.214714	+	0.371895i
$323$	−19.3174	−	11.1529i	−1.07485	−	0.620564i
$324$	−2.35646	−	0.235330i	−0.130914	−	0.0130739i
$325$	18.1386	+	3.57406i	1.00615	+	0.198253i
$326$	4.34323	−	7.52269i	0.240549	−	0.416643i
$327$	7.25828	+	2.13977i	0.401384	+	0.118330i
$328$	−32.7904			−1.81055
$329$	−1.34592	+	2.33120i	−0.0742029	+	0.128523i
$330$	20.9986	+	6.19049i	1.15594	+	0.340775i
$331$		−	10.2097i		−	0.561176i	−0.959828	−	0.280588i	$-0.909471\pi$
$331$		−	10.2097i		−	0.561176i	0.959828	−	0.280588i	$-0.0905294\pi$
$332$	−2.38326	+	1.37598i	−0.130798	+	0.0755165i
$333$	−2.15667	−	4.20572i	−0.118185	−	0.230472i
$334$	4.02934	+	6.97903i	0.220476	+	0.381875i
$335$	11.5819	+	20.0604i	0.632785	+	1.09602i
$336$	1.38400	+	5.73205i	0.0755035	+	0.312709i
$337$	−0.995268	−	1.72386i	−0.0542157	−	0.0939044i	0.837644	−	0.546217i	$-0.183933\pi$
$337$	−0.995268	−	1.72386i	−0.0542157	−	0.0939044i	−0.891860	+	0.452312i	$0.850599\pi$
$338$	−6.49939	+	15.8521i	−0.353520	+	0.862240i
$339$	−4.57696	−	4.81061i	−0.248586	−	0.261277i
$340$	3.64381	−	2.10376i	0.197614	−	0.114092i
$341$	5.94304	−	10.2937i	0.321834	−	0.557433i
$342$	15.6180	−	8.00882i	0.844524	−	0.433068i
$343$		−	1.00000i		−	0.0539949i
$344$		−	36.7631i		−	1.98213i
$345$	7.56430	+	31.3286i	0.407248	+	1.68668i
$346$	−10.7171	+	6.18751i	−0.576153	+	0.332642i
$347$	−5.81769	+	10.0765i	−0.312310	+	0.540937i	−0.978862	−	0.204522i	$-0.934436\pi$
$347$	−5.81769	+	10.0765i	−0.312310	+	0.540937i	0.666552	+	0.745459i	$0.267769\pi$
$348$	−0.214348	+	0.727087i	−0.0114903	+	0.0389760i
$349$	1.76640	−	1.01983i	0.0945532	−	0.0545903i	−0.451978	−	0.892029i	$-0.649281\pi$
$349$	1.76640	−	1.01983i	0.0945532	−	0.0545903i	0.546531	+	0.837439i	$0.315948\pi$
$350$	6.75750			0.361204
$351$	−16.1552	−	9.48734i	−0.862301	−	0.506397i
$352$	−4.45531			−0.237469
$353$	6.46823	−	3.73444i	0.344269	−	0.198764i	−0.317889	−	0.948128i	$-0.602974\pi$
$353$	6.46823	−	3.73444i	0.344269	−	0.198764i	0.662158	+	0.749364i	$0.269641\pi$
$354$	−2.00377	+	6.79694i	−0.106499	+	0.361253i
$355$	−26.5242	+	45.9413i	−1.40776	+	2.43831i
$356$	0.175221	−	0.101164i	0.00928670	−	0.00536168i
$357$	2.04262	+	8.45979i	0.108107	+	0.447740i
$358$			31.7865i			1.67997i
$359$			17.5376i			0.925601i	0.886462	+	0.462801i	$0.153155\pi$
$359$			17.5376i			0.925601i	−0.886462	+	0.462801i	$0.846845\pi$
$360$	−1.41656	+	28.4398i	−0.0746593	+	1.49891i
$361$	0.353712	−	0.612648i	0.0186164	−	0.0322446i
$362$	14.5113	−	8.37807i	0.762694	−	0.440342i
$363$	2.28976	+	2.40665i	0.120181	+	0.126316i
$364$	0.183413	−	0.930834i	0.00961347	−	0.0487890i
$365$	−3.02687	−	5.24269i	−0.158433	−	0.274415i
$366$	2.29364	+	9.49944i	0.119890	+	0.496544i
$367$	−3.04433	−	5.27293i	−0.158913	−	0.275245i	0.775564	−	0.631269i	$-0.217466\pi$
$367$	−3.04433	−	5.27293i	−0.158913	−	0.275245i	−0.934477	+	0.356024i	$0.884132\pi$
$368$	9.95309	+	17.2393i	0.518841	+	0.898658i
$369$	17.8914	−	27.7073i	0.931390	−	1.44239i
$370$	−5.72240	+	3.30383i	−0.297494	+	0.171758i
$371$		−	10.0514i		−	0.521842i
$372$	1.72418	+	0.508295i	0.0893944	+	0.0263538i
$373$	1.18156	−	2.04652i	0.0611789	−	0.105965i	−0.833814	−	0.552046i	$-0.813847\pi$
$373$	1.18156	−	2.04652i	0.0611789	−	0.105965i	0.894993	+	0.446081i	$0.147181\pi$
$374$	19.9563			1.03192
$375$	0.673921	+	0.198675i	0.0348011	+	0.0102595i
$376$	−4.01432	+	6.95300i	−0.207023	+	0.358574i
$377$	−3.94587	+	4.51577i	−0.203222	+	0.232574i
$378$	−6.46407	−	2.26080i	−0.332476	−	0.116283i
$379$	28.4946	+	16.4514i	1.46367	+	0.845049i	0.999178	−	0.0405288i	$-0.0129042\pi$
$379$	28.4946	+	16.4514i	1.46367	+	0.845049i	0.464490	+	0.885578i	$0.346238\pi$
$380$	1.85869	+	3.21935i	0.0953489	+	0.165149i
$381$	4.64732	+	4.88456i	0.238090	+	0.250244i
$382$	23.9684	−	13.8382i	1.22633	−	0.708022i
$383$	11.3415	+	6.54799i	0.579521	+	0.334587i	0.760943	−	0.648819i	$-0.224737\pi$
$383$	11.3415	+	6.54799i	0.579521	+	0.334587i	−0.181422	+	0.983405i	$0.558070\pi$
$384$	3.48982	+	14.4536i	0.178089	+	0.737583i
$385$	−8.30566	−	4.79528i	−0.423296	−	0.244390i
$386$	0.593068	+	1.02722i	0.0301864	+	0.0522843i
$387$	31.0642	+	20.0591i	1.57908	+	1.01966i
$388$	−0.899838	−	0.519522i	−0.0456823	−	0.0263747i
$389$	7.83826	−	13.5763i	0.397416	−	0.688344i	−0.595991	−	0.802991i	$-0.703240\pi$
$389$	7.83826	−	13.5763i	0.397416	−	0.688344i	0.993406	+	0.114647i	$0.0365738\pi$
$390$	−12.1235	+	23.2171i	−0.613897	+	1.17564i
$391$	14.6895	+	25.4430i	0.742881	+	1.28671i
$392$		−	2.98259i		−	0.150643i
$393$	1.63723	−	0.395310i	0.0825875	−	0.0199407i
$394$	33.5626			1.69086
$395$			19.5977i			0.986067i
$396$	1.29050	−	1.99851i	0.0648499	−	0.100429i
$397$	−17.6213	+	10.1737i	−0.884389	+	0.510602i	−0.872103	−	0.489322i	$-0.837244\pi$
$397$	−17.6213	+	10.1737i	−0.884389	+	0.510602i	−0.0122863	+	0.999925i	$0.503911\pi$
$398$	−28.2810	−	16.3281i	−1.41760	−	0.818452i
$399$	−7.47432	+	1.80467i	−0.374184	+	0.0903467i
$400$	17.4565			0.872823
$401$		−	29.6795i		−	1.48212i	−0.671438	−	0.741061i	$-0.734323\pi$
$401$		−	29.6795i		−	1.48212i	0.671438	−	0.741061i	$-0.265677\pi$
$402$	−16.1510	+	3.89965i	−0.805537	+	0.194497i
$403$	10.7085	+	9.35702i	0.533426	+	0.466106i
$404$	−2.01120			−0.100061
$405$	−23.2583	−	16.7146i	−1.15571	−	0.830555i
$406$	−1.09598	+	1.89830i	−0.0543928	+	0.0942110i
$407$	4.74796			0.235348
$408$	6.09228	+	25.2321i	0.301613	+	1.24917i
$409$	4.38417	+	2.53120i	0.216783	+	0.125160i	0.604460	−	0.796636i	$-0.293389\pi$
$409$	4.38417	+	2.53120i	0.216783	+	0.125160i	−0.387677	+	0.921795i	$0.626722\pi$
$410$	−39.9317	−	23.0546i	−1.97209	−	1.13858i
$411$	−9.34732	−	2.75563i	−0.461070	−	0.135925i
$412$	3.02081			0.148825
$413$	1.55216	−	2.68842i	0.0763767	−	0.132288i
$414$	−23.0888	−	1.15003i	−1.13475	−	0.0565210i
$415$	−33.2827			−1.63379
$416$	1.03049	−	5.22980i	0.0505238	−	0.256412i
$417$	−16.1284	−	16.9517i	−0.789810	−	0.830129i
$418$			17.6316i			0.862390i
$419$	−21.8097			−1.06548			−0.532738	−	0.846280i	$-0.678837\pi$
$419$	−21.8097			−1.06548			−0.532738	+	0.846280i	$0.678837\pi$
$420$	0.410129	−	1.39119i	0.0200122	−	0.0678831i
$421$	−5.84765	−	3.37614i	−0.284997	−	0.164543i	0.350686	−	0.936493i	$-0.385948\pi$
$421$	−5.84765	−	3.37614i	−0.284997	−	0.164543i	−0.635683	+	0.771950i	$0.719282\pi$
$422$	−4.72744	+	2.72939i	−0.230128	+	0.132865i
$423$	−3.68484	−	7.18580i	−0.179163	−	0.349386i
$424$		−	29.9792i		−	1.45592i
$425$	25.7636			1.24972
$426$	−26.2284	−	27.5673i	−1.27077	−	1.33564i
$427$		−	4.28112i		−	0.207178i
$428$	2.63692	+	4.56728i	0.127460	+	0.220768i
$429$	15.8856	−	10.0920i	0.766966	−	0.487246i
$430$	25.8478	−	44.7696i	1.24649	−	2.15898i
$431$	0.787971	+	0.454936i	0.0379552	+	0.0219135i	0.518858	−	0.854861i	$-0.326357\pi$
$431$	0.787971	+	0.454936i	0.0379552	+	0.0219135i	−0.480902	+	0.876774i	$0.659691\pi$
$432$	−16.6984	−	5.84027i	−0.803404	−	0.280990i
$433$	16.4097	+	28.4224i	0.788600	+	1.36590i	0.926825	+	0.375495i	$0.122527\pi$
$433$	16.4097	+	28.4224i	0.788600	+	1.36590i	−0.138224	+	0.990401i	$0.544140\pi$
$434$	4.50153	+	2.59896i	0.216080	+	0.124754i
$435$	−6.64185	+	6.31926i	−0.318452	+	0.302985i
$436$	−0.995572	−	0.574794i	−0.0476793	−	0.0275276i
$437$	−22.4792	+	12.9784i	−1.07532	+	0.620839i
$438$	4.22098	−	1.01915i	0.201686	−	0.0486971i
$439$	6.11000	+	10.5828i	0.291615	+	0.505091i	0.974192	−	0.225722i	$-0.0724742\pi$
$439$	6.11000	+	10.5828i	0.291615	+	0.505091i	−0.682577	+	0.730814i	$0.739141\pi$
$440$	−24.7724	−	14.3023i	−1.18098	−	0.681837i
$441$	2.52024	+	1.62739i	0.120011	+	0.0774948i
$442$	−4.61578	+	23.4254i	−0.219550	+	1.11423i
$443$	−0.0481446	+	0.0833889i	−0.00228742	+	0.00396193i	−0.867167	−	0.498018i	$-0.834061\pi$
$443$	−0.0481446	+	0.0833889i	−0.00228742	+	0.00396193i	0.864879	+	0.501980i	$0.167395\pi$
$444$	0.168527	+	0.697980i	0.00799794	+	0.0331246i
$445$	2.44700			0.115999
$446$	−16.3044	+	28.2401i	−0.772038	+	1.33721i
$447$	12.2783	−	11.6819i	0.580742	−	0.552536i
$448$		−	8.75735i		−	0.413746i
$449$	−24.3354	+	14.0501i	−1.14846	+	0.663063i	−0.948511	−	0.316743i	$-0.897411\pi$
$449$	−24.3354	+	14.0501i	−1.14846	+	0.663063i	−0.199948	+	0.979807i	$0.564077\pi$
$450$	−10.9971	+	17.0305i	−0.518408	+	0.802826i
$451$	16.5660	+	28.6931i	0.780060	+	1.35110i
$452$	0.504376	+	0.873605i	0.0237238	+	0.0410909i
$453$	19.1968	−	18.2644i	0.901945	−	0.858138i
$454$	7.15951	+	12.4006i	0.336012	+	0.581990i
$455$	7.54992	−	8.64036i	0.353946	−	0.405066i
$456$	−22.2928	+	5.38260i	−1.04396	+	0.252063i
$457$	−8.46399	+	4.88669i	−0.395929	+	0.228590i	−0.684726	−	0.728801i	$-0.740078\pi$
$457$	−8.46399	+	4.88669i	−0.395929	+	0.228590i	0.288797	+	0.957390i	$0.406745\pi$
$458$	9.13330	−	15.8193i	0.426771	−	0.739189i
$459$	−24.6448	−	8.61951i	−1.15032	−	0.402324i
$460$		−	4.89618i		−	0.228285i
$461$		−	11.9510i		−	0.556614i	−0.960492	−	0.278307i	$-0.910227\pi$
$461$		−	11.9510i		−	0.556614i	0.960492	−	0.278307i	$-0.0897733\pi$
$462$	4.98385	−	4.74179i	0.231870	−	0.220608i
$463$	−12.9447	+	7.47362i	−0.601591	+	0.347329i	−0.769667	−	0.638445i	$-0.779578\pi$
$463$	−12.9447	+	7.47362i	−0.601591	+	0.347329i	0.168076	+	0.985774i	$0.446244\pi$
$464$	−2.83122	+	4.90382i	−0.131436	+	0.227654i
$465$	14.9852	+	15.7501i	0.694920	+	0.730395i
$466$	13.5579	−	7.82768i	0.628060	−	0.362610i
$467$	28.3039			1.30975			0.654875	−	0.755737i	$-0.272721\pi$
$467$	28.3039			1.30975			0.654875	+	0.755737i	$0.272721\pi$
$468$	2.04744	+	1.97708i	0.0946429	+	0.0913904i
$469$	7.27878			0.336103
$470$	−9.77717	+	5.64485i	−0.450987	+	0.260378i
$471$	−2.37730	+	0.574000i	−0.109540	+	0.0264485i
$472$	4.62945	−	8.01844i	0.213088	−	0.369079i
$473$	−32.1694	+	18.5730i	−1.47915	+	0.853988i
$474$	−13.4835	−	3.97499i	−0.619317	−	0.182577i
$475$			22.7624i			1.04441i
$476$		−	1.32213i		−	0.0605999i
$477$	25.3319	+	16.3575i	1.15987	+	0.748960i
$478$	11.5921	−	20.0782i	0.530212	−	0.918354i
$479$	18.9585	−	10.9457i	0.866236	−	0.500121i	0.000140296	−	1.00000i	$-0.499955\pi$
$479$	18.9585	−	10.9457i	0.866236	−	0.500121i	0.866096	+	0.499878i	$0.166622\pi$
$480$	2.30427	−	7.81625i	0.105175	−	0.356761i
$481$	−1.09818	+	5.57332i	−0.0500726	+	0.254122i
$482$	−3.99275	−	6.91565i	−0.181865	−	0.314999i
$483$	9.71401	+	2.86373i	0.442003	+	0.130304i
$484$	−0.252329	−	0.437047i	−0.0114695	−	0.0198658i
$485$	−6.28321	−	10.8828i	−0.285306	−	0.494165i
$486$	16.2173	−	12.6118i	0.735633	−	0.572083i
$487$	28.5165	−	16.4640i	1.29220	−	0.746054i	0.313159	−	0.949701i	$-0.398613\pi$
$487$	28.5165	−	16.4640i	1.29220	−	0.746054i	0.979045	+	0.203646i	$0.0652793\pi$
$488$		−	12.7688i		−	0.578018i
$489$	−2.67943	−	11.0973i	−0.121168	−	0.501835i
$490$	2.09703	−	3.63216i	0.0947340	−	0.164084i
$491$	−12.2840			−0.554370			−0.277185	−	0.960817i	$-0.589401\pi$
$491$	−12.2840			−0.554370			−0.277185	+	0.960817i	$0.589401\pi$
$492$	−3.63006	+	3.45375i	−0.163656	+	0.155707i
$493$	−4.17853	+	7.23743i	−0.188192	+	0.325957i
$494$	−20.6966	−	4.07809i	−0.931184	−	0.183482i
$495$	25.6018	−	13.1285i	1.15071	−	0.590080i
$496$	11.6287	+	6.71381i	0.522142	+	0.301459i
$497$	8.33475	+	14.4362i	0.373864	+	0.647552i
$498$	6.75072	−	22.8990i	0.302507	−	1.02613i
$499$	−22.9522	+	13.2515i	−1.02748	+	0.593217i	−0.916262	−	0.400579i	$-0.868809\pi$
$499$	−22.9522	+	13.2515i	−1.02748	+	0.593217i	−0.111219	+	0.993796i	$0.535476\pi$
$500$	−0.0924374	−	0.0533688i	−0.00413393	−	0.00238672i
$501$	10.1589	+	2.99487i	0.453864	+	0.133801i
$502$	−0.117882	−	0.0680591i	−0.00526132	−	0.00303762i
$503$	5.68773	+	9.85144i	0.253603	+	0.439254i	0.964515	−	0.264027i	$-0.0850509\pi$
$503$	5.68773	+	9.85144i	0.253603	+	0.439254i	−0.710912	+	0.703281i	$0.751718\pi$
$504$	7.51683	+	4.85383i	0.334826	+	0.216207i
$505$	−21.0651	−	12.1620i	−0.937385	−	0.541200i
$506$	11.6113	−	20.1114i	0.516186	−	0.894060i
$507$	8.17207	+	20.9814i	0.362935	+	0.931815i
$508$	−0.512130	−	0.887035i	−0.0227221	−	0.0393558i
$509$		−	0.516877i		−	0.0229102i	−0.999934	−	0.0114551i	$-0.996354\pi$
$509$		−	0.516877i		−	0.0229102i	0.999934	−	0.0114551i	$-0.00364635\pi$
$510$	−10.3213	+	35.0107i	−0.457035	+	1.55030i
$511$	−1.90227			−0.0841516
$512$		−	25.3416i		−	1.11995i
$513$	7.61543	−	21.7740i	0.336229	−	0.961344i
$514$	0.137469	−	0.0793678i	0.00606350	−	0.00350076i
$515$	31.6397	+	18.2672i	1.39421	+	0.804948i
$516$	−3.87219	−	4.06986i	−0.170464	−	0.179166i
$517$	8.11226			0.356777
$518$			2.07634i			0.0912289i
$519$	−4.59896	+	15.6001i	−0.201872	+	0.684766i
$520$	22.5183	−	25.7706i	0.987493	−	1.13012i
$521$	12.6636			0.554801			0.277401	−	0.960754i	$-0.410527\pi$
$521$	12.6636			0.554801			0.277401	+	0.960754i	$0.410527\pi$
$522$	−3.00057	−	5.85141i	−0.131332	−	0.256109i
$523$	−17.4627	+	30.2462i	−0.763589	+	1.32258i	0.177400	+	0.984139i	$0.443231\pi$
$523$	−17.4627	+	30.2462i	−0.763589	+	1.32258i	−0.940989	+	0.338437i	$0.890102\pi$
$524$	−0.255874			−0.0111779
$525$	6.43414	−	6.12164i	0.280809	−	0.267170i
$526$	−27.5025	−	15.8786i	−1.19917	−	0.692340i
$527$	17.1625	+	9.90875i	0.747608	+	0.431632i
$528$	12.8746	−	12.2493i	0.560296	−	0.533083i
$529$	11.1876			0.486419
$530$	21.0780	−	36.5082i	0.915572	−	1.58582i
$531$	4.24948	+	8.28691i	0.184412	+	0.359621i
$532$	1.16812			0.0506444
$533$	−37.5126	+	12.8091i	−1.62485	+	0.554826i
$534$	−0.496324	+	1.68357i	−0.0214780	+	0.0728552i
$535$			63.7830i			2.75758i
$536$	21.7096			0.937712
$537$	28.7955	+	30.2654i	1.24262	+	1.30605i
$538$	−13.2367	−	7.64223i	−0.570676	−	0.329480i
$539$	−2.60990	+	1.50683i	−0.112416	+	0.0649036i
$540$	2.83869	+	3.29763i	0.122158	+	0.141907i
$541$		−	40.0787i		−	1.72312i	−0.507658	−	0.861559i	$-0.669489\pi$
$541$		−	40.0787i		−	1.72312i	0.507658	−	0.861559i	$-0.330511\pi$
$542$	−21.3545			−0.917254
$543$	6.22714	−	21.1230i	0.267232	−	0.906473i
$544$		−	7.42827i		−	0.318484i
$545$	−6.95169	−	12.0407i	−0.297778	−	0.515766i
$546$	4.41334	+	6.94697i	0.188873	+	0.297303i
$547$	−7.04774	+	12.2070i	−0.301340	+	0.521936i	−0.976440	−	0.215791i	$-0.930767\pi$
$547$	−7.04774	+	12.2070i	−0.301340	+	0.521936i	0.675100	+	0.737726i	$0.264100\pi$
$548$	1.28211	+	0.740228i	0.0547691	+	0.0316210i
$549$	10.7895	+	6.96706i	0.460483	+	0.297347i
$550$	−10.1824	−	17.6364i	−0.434178	−	0.752019i
$551$	−6.39435	−	3.69178i	−0.272408	−	0.157275i
$552$	28.9729	+	8.54133i	1.23317	+	0.363543i
$553$	5.33317	+	3.07911i	0.226789	+	0.130937i
$554$	−25.6975	+	14.8365i	−1.09178	+	0.630341i
$555$	−2.45563	+	8.32968i	−0.104236	+	0.353575i
$556$	1.77733	+	3.07842i	0.0753755	+	0.130554i
$557$	20.0402	+	11.5702i	0.849132	+	0.490246i	0.860358	−	0.509691i	$-0.170240\pi$
$557$	20.0402	+	11.5702i	0.849132	+	0.490246i	−0.0112260	+	0.999937i	$0.503573\pi$
$558$	−13.8757	+	7.11540i	−0.587407	+	0.301219i
$559$	−14.3610	−	42.0574i	−0.607408	−	1.77884i
$560$	5.41719	−	9.38284i	0.228918	−	0.396497i
$561$	19.0013	−	18.0785i	0.802238	−	0.763273i
$562$	37.4111			1.57809
$563$	−14.4328	+	24.9983i	−0.608269	+	1.05355i	0.383257	+	0.923642i	$0.374802\pi$
$563$	−14.4328	+	24.9983i	−0.608269	+	1.05355i	−0.991526	+	0.129911i	$0.958531\pi$
$564$	0.287942	+	1.19255i	0.0121245	+	0.0502155i
$565$			12.2001i			0.513261i
$566$	33.6023	−	19.4003i	1.41241	−	0.815456i
$567$	−8.20282	+	3.70320i	−0.344486	+	0.155520i
$568$	24.8591	+	43.0572i	1.04307	+	1.80664i
$569$	−20.6578	−	35.7804i	−0.866022	−	1.49999i	−0.866029	−	0.499994i	$-0.833335\pi$
$569$	−20.6578	−	35.7804i	−0.866022	−	1.49999i	6.70125e−6	−	1.00000i	$-0.499998\pi$
$570$	−30.9323	−	9.11899i	−1.29561	−	0.381952i
$571$	−7.50268	−	12.9950i	−0.313977	−	0.543825i	0.665242	−	0.746628i	$-0.268328\pi$
$571$	−7.50268	−	12.9950i	−0.313977	−	0.543825i	−0.979220	+	0.202803i	$0.934995\pi$
$572$	−2.70576	+	0.923916i	−0.113133	+	0.0386309i
$573$	10.2854	−	34.8890i	0.429680	−	1.45751i
$574$	−12.5478	+	7.24447i	−0.523735	+	0.302378i
$575$	14.9902	−	25.9638i	0.625134	−	1.08276i
$576$	22.0706	+	14.2516i	0.919609	+	0.593818i
$577$		−	1.98265i		−	0.0825389i	−0.999148	−	0.0412695i	$-0.986860\pi$
$577$		−	1.98265i		−	0.0825389i	0.999148	−	0.0412695i	$-0.0131402\pi$
$578$			10.8685i			0.452069i
$579$	1.49525	+	0.440807i	0.0621406	+	0.0183193i
$580$	1.20616	−	0.696375i	0.0500829	−	0.0289154i
$581$	−5.22924	+	9.05731i	−0.216946	+	0.375761i
$582$	8.76197	−	2.11558i	0.363195	−	0.0876934i
$583$	−26.2331	+	15.1457i	−1.08647	+	0.627271i
$584$	−5.67370			−0.234779
$585$	9.48910	+	33.0888i	0.392326	+	1.36805i
$586$	−23.9631			−0.989906
$587$	19.8184	−	11.4422i	0.817995	−	0.472269i	−0.0317297	−	0.999496i	$-0.510102\pi$
$587$	19.8184	−	11.4422i	0.817995	−	0.472269i	0.849724	+	0.527227i	$0.176768\pi$
$588$	−0.314150	−	0.330187i	−0.0129553	−	0.0136167i
$589$	−8.75448	+	15.1632i	−0.360722	+	0.624789i
$590$	11.2754	−	6.50983i	0.464199	−	0.268006i
$591$	31.9565	−	30.4044i	1.31452	−	1.25067i
$592$			5.36374i			0.220448i
$593$		−	9.26906i		−	0.380635i	−0.981723	−	0.190317i	$-0.939048\pi$
$593$		−	9.26906i		−	0.380635i	0.981723	−	0.190317i	$-0.0609517\pi$
$594$	3.83976	+	20.2772i	0.157547	+	0.831984i
$595$	7.99509	−	13.8479i	0.327767	−	0.567709i
$596$	−2.22973	+	1.28733i	−0.0913332	+	0.0527313i
$597$	−41.7194	+	10.0731i	−1.70746	+	0.412266i
$598$	20.9218	+	18.2814i	0.855557	+	0.747583i
$599$	−23.2862	−	40.3329i	−0.951449	−	1.64796i	−0.742292	−	0.670076i	$-0.766261\pi$
$599$	−23.2862	−	40.3329i	−0.951449	−	1.64796i	−0.209157	−	0.977882i	$-0.567072\pi$
$600$	19.1904	−	18.2583i	0.783445	−	0.745393i
$601$	14.1197	+	24.4560i	0.575954	+	0.997581i	0.995937	+	0.0900493i	$0.0287025\pi$
$601$	14.1197	+	24.4560i	0.575954	+	0.997581i	−0.419984	+	0.907532i	$0.637964\pi$
$602$	−8.12218	−	14.0680i	−0.331035	−	0.573370i
$603$	−11.8454	+	18.3443i	−0.482383	+	0.747036i
$604$	−3.48613	+	2.01272i	−0.141849	+	0.0818964i
$605$		−	6.10345i		−	0.248141i
$606$	12.6402	−	12.0263i	0.513474	−	0.488534i
$607$	−0.597636	+	1.03514i	−0.0242573	+	0.0420149i	−0.877899	−	0.478845i	$-0.841055\pi$
$607$	−0.597636	+	1.03514i	−0.0242573	+	0.0420149i	0.853642	+	0.520860i	$0.174389\pi$
$608$	6.56295			0.266163
$609$	0.676136	+	2.80032i	0.0273984	+	0.113475i
$610$	8.97763	−	15.5497i	0.363494	−	0.629590i
$611$	−1.87632	+	9.52246i	−0.0759079	+	0.385237i
$612$	3.33209	+	2.15163i	0.134692	+	0.0869744i
$613$	24.9425	+	14.4006i	1.00742	+	0.581634i	0.910435	−	0.413652i	$-0.135747\pi$
$613$	24.9425	+	14.4006i	1.00742	+	0.581634i	0.0969848	+	0.995286i	$0.469080\pi$
$614$	1.41232	+	2.44622i	0.0569968	+	0.0987213i
$615$	−58.9061	+	14.2229i	−2.37532	+	0.573521i
$616$	−7.78426	+	4.49424i	−0.313637	+	0.181078i
$617$	7.37810	+	4.25975i	0.297031	+	0.171491i	0.641108	−	0.767450i	$-0.278475\pi$
$617$	7.37810	+	4.25975i	0.297031	+	0.171491i	−0.344077	+	0.938941i	$0.611808\pi$
$618$	−18.9855	+	18.0634i	−0.763710	+	0.726617i
$619$	35.8345	+	20.6891i	1.44031	+	0.831564i	0.997870	−	0.0652332i	$-0.0207791\pi$
$619$	35.8345	+	20.6891i	1.44031	+	0.831564i	0.442441	+	0.896797i	$0.354112\pi$
$620$	−1.65135	−	2.86022i	−0.0663197	−	0.114869i
$621$	−23.0258	+	19.8212i	−0.923992	+	0.795398i
$622$	−26.0928	−	15.0647i	−1.04623	−	0.604039i
$623$	0.384462	−	0.665908i	0.0154032	−	0.0266790i
$624$	11.4008	+	17.9459i	0.456399	+	0.718411i
$625$	12.1732	+	21.0846i	0.486928	+	0.843385i
$626$		−	38.5181i		−	1.53949i
$627$	15.9725	+	16.7879i	0.637881	+	0.670444i
$628$	0.371535			0.0148259
$629$			7.91621i			0.315640i
$630$	5.74122	+	11.1959i	0.228736	+	0.446057i
$631$	25.7356	−	14.8585i	1.02452	−	0.591507i	0.109110	−	0.994030i	$-0.465200\pi$
$631$	25.7356	−	14.8585i	1.02452	−	0.591507i	0.915410	+	0.402523i	$0.131867\pi$
$632$	15.9066	+	9.18370i	0.632732	+	0.365308i
$633$	−2.02866	+	6.88139i	−0.0806321	+	0.273511i
$634$	13.4616			0.534627
$635$		−	12.3876i		−	0.491588i
$636$	−3.15765	−	3.31884i	−0.125209	−	0.131601i
$637$	−1.16511	−	3.41211i	−0.0461634	−	0.135193i
$638$	6.60583			0.261527
$639$	−49.9466	−	2.48779i	−1.97586	−	0.0984155i
$640$	13.6597	−	23.6592i	0.539946	−	0.935214i
$641$	12.1313			0.479157			0.239578	−	0.970877i	$-0.422991\pi$
$641$	12.1313			0.479157			0.239578	+	0.970877i	$0.422991\pi$
$642$	−43.8836	−	12.9371i	−1.73195	−	0.510585i
$643$	−10.1934	−	5.88516i	−0.401988	−	0.232088i	0.285353	−	0.958422i	$-0.407889\pi$
$643$	−10.1934	−	5.88516i	−0.401988	−	0.232088i	−0.687342	+	0.726334i	$0.741222\pi$
$644$	−1.33241	−	0.769266i	−0.0525042	−	0.0303133i
$645$	−15.9460	−	66.0429i	−0.627875	−	2.60044i
$646$	−29.3969			−1.15661
$647$	−7.41386	+	12.8412i	−0.291469	+	0.504839i	−0.974157	−	0.225871i	$-0.927477\pi$
$647$	−7.41386	+	12.8412i	−0.291469	+	0.504839i	0.682688	+	0.730710i	$0.260811\pi$
$648$	−24.4656	+	11.0451i	−0.961101	+	0.433893i
$649$	−9.35533			−0.367229
$650$	23.0574	−	7.87324i	0.904384	−	0.308814i
$651$	6.64052	−	1.60335i	0.260263	−	0.0628404i
$652$			1.73433i			0.0679215i
$653$	−36.8684			−1.44277			−0.721386	−	0.692533i	$-0.756495\pi$
$653$	−36.8684			−1.44277			−0.721386	+	0.692533i	$0.756495\pi$
$654$	9.69416	−	2.34065i	0.379072	−	0.0915268i
$655$	−2.68000	−	1.54730i	−0.104716	−	0.0604580i
$656$	−32.4143	+	18.7144i	−1.26557	+	0.730676i
$657$	3.09574	−	4.79418i	0.120776	−	0.187039i
$658$			3.54758i			0.138299i
$659$	−43.1050			−1.67913			−0.839567	−	0.543256i	$-0.817191\pi$
$659$	−43.1050			−1.67913			−0.839567	+	0.543256i	$0.817191\pi$
$660$	−4.24886	+	1.02589i	−0.165387	+	0.0399326i
$661$		−	45.5975i		−	1.77354i	−0.462213	−	0.886769i	$-0.652944\pi$
$661$		−	45.5975i		−	1.77354i	0.462213	−	0.886769i	$-0.347056\pi$
$662$	−6.72770	−	11.6527i	−0.261479	−	0.452895i
$663$	16.8262	+	26.4859i	0.653477	+	1.02863i
$664$	−15.5967	+	27.0142i	−0.605268	+	1.04836i
$665$	12.2348	+	7.06375i	0.474444	+	0.273920i
$666$	−5.23286	−	3.37901i	−0.202769	−	0.130934i
$667$	4.86245	+	8.42201i	0.188275	+	0.326102i
$668$	−1.39342	−	0.804494i	−0.0539132	−	0.0311268i
$669$	10.0586	+	41.6590i	0.388887	+	1.61063i
$670$	26.4377	+	15.2638i	1.02138	+	0.589692i
$671$	−11.1733	+	6.45091i	−0.431341	+	0.249035i
$672$	−1.76502	−	1.85512i	−0.0680871	−	0.0715629i
$673$	20.3882	+	35.3135i	0.785909	+	1.36123i	0.928455	+	0.371445i	$0.121138\pi$
$673$	20.3882	+	35.3135i	0.785909	+	1.36123i	−0.142546	+	0.989788i	$0.545529\pi$
$674$	−2.27187	−	1.31167i	−0.0875093	−	0.0505235i
$675$	4.95713	+	26.1779i	0.190800	+	1.00759i
$676$	−0.458698	−	3.38981i	−0.0176422	−	0.130377i
$677$	−1.07953	+	1.86981i	−0.0414899	+	0.0718625i	−0.886025	−	0.463638i	$-0.846544\pi$
$677$	−1.07953	+	1.86981i	−0.0414899	+	0.0718625i	0.844535	+	0.535501i	$0.179877\pi$
$678$	−8.39382	−	2.47453i	−0.322363	−	0.0950339i
$679$	−3.94877			−0.151540
$680$	23.8461	−	41.3026i	0.914455	−	1.58388i
$681$	18.0507	+	5.32142i	0.691703	+	0.203917i
$682$		−	15.6647i		−	0.599833i
$683$	16.6819	−	9.63129i	0.638315	−	0.368531i	−0.145650	−	0.989336i	$-0.546527\pi$
$683$	16.6819	−	9.63129i	0.638315	−	0.368531i	0.783965	+	0.620805i	$0.213194\pi$
$684$	−1.90099	+	2.94394i	−0.0726860	+	0.112564i
$685$	8.95249	+	15.5062i	0.342057	+	0.592460i
$686$	−0.658952	−	1.14134i	−0.0251589	−	0.0435765i
$687$	−5.63453	−	23.3362i	−0.214971	−	0.890333i
$688$	−20.9818	−	36.3415i	−0.799923	−	1.38551i
$689$	−11.7110	−	34.2965i	−0.446153	−	1.30659i
$690$	29.2775	+	30.7721i	1.11457	+	1.17147i
$691$	−5.45097	+	3.14712i	−0.207365	+	0.119722i	−0.600086	−	0.799935i	$-0.704867\pi$
$691$	−5.45097	+	3.14712i	−0.207365	+	0.119722i	0.392721	+	0.919658i	$0.371534\pi$
$692$	1.23539	−	2.13976i	0.0469625	−	0.0813414i
$693$	0.449764	−	9.02976i	0.0170851	−	0.343012i
$694$			15.3343i			0.582082i
$695$			42.9909i			1.63074i
$696$	2.01664	+	8.35219i	0.0764404	+	0.316589i
$697$	−47.8395	+	27.6202i	−1.81205	+	1.04619i
$698$	1.34404	−	2.32794i	0.0508726	−	0.0881140i
$699$	5.81805	−	19.7353i	0.220059	−	0.746457i
$700$	−1.16844	+	0.674598i	−0.0441628	+	0.0254974i
$701$	47.8104			1.80577			0.902887	−	0.429878i	$-0.141443\pi$
$701$	47.8104			1.80577			0.902887	+	0.429878i	$0.141443\pi$
$702$	−24.6902	−	0.182761i	−0.931873	−	0.00689787i
$703$	−6.99405			−0.263786
$704$	−22.8558	+	13.1958i	−0.861411	+	0.497336i
$705$	−4.19563	+	14.2319i	−0.158016	+	0.536004i
$706$	4.92163	−	8.52451i	0.185228	−	0.320824i
$707$	−6.61932	+	3.82167i	−0.248945	+	0.143729i
$708$	−0.332064	−	1.37529i	−0.0124797	−	0.0516866i
$709$			13.6993i			0.514487i	0.966347	+	0.257243i	$0.0828142\pi$
$709$			13.6993i			0.514487i	−0.966347	+	0.257243i	$0.917186\pi$
$710$			69.9127i			2.62378i
$711$	−16.4392	+	8.42995i	−0.616519	+	0.316148i
$712$	1.14669	−	1.98613i	0.0429741	−	0.0744333i
$713$	19.9715	−	11.5306i	0.747939	−	0.431823i
$714$	7.90591	+	8.30950i	0.295871	+	0.310975i
$715$	−33.9269	−	6.68501i	−1.26879	−	0.250005i
$716$	−3.17323	−	5.49619i	−0.118589	−	0.205402i
$717$	−7.15144	−	29.6187i	−0.267075	−	1.10613i
$718$	11.5565	+	20.0164i	0.431283	+	0.747004i
$719$	−7.49922	−	12.9890i	−0.279674	−	0.484409i	0.691630	−	0.722252i	$-0.256893\pi$
$719$	−7.49922	−	12.9890i	−0.279674	−	0.484409i	−0.971304	+	0.237843i	$0.923560\pi$
$720$	14.8311	+	28.9221i	0.552723	+	1.07786i
$721$	9.94218	−	5.74012i	0.370266	−	0.213773i
$722$		−	0.932317i		−	0.0346972i
$723$	−10.0666	−	2.96768i	−0.374381	−	0.110369i
$724$	−1.67276	+	2.89730i	−0.0621675	+	0.107677i
$725$	8.52812			0.316726
$726$	4.19926	+	1.23796i	0.155849	+	0.0459450i
$727$	−11.6656	+	20.2054i	−0.432653	+	0.749377i	−0.997101	−	0.0760920i	$-0.975756\pi$
$727$	−11.6656	+	20.2054i	−0.432653	+	0.749377i	0.564448	+	0.825469i	$0.309089\pi$
$728$	−3.47504	−	10.1769i	−0.128794	−	0.377182i
$729$	4.01624	−	26.6996i	0.148750	−	0.988875i
$730$	−6.90935	−	3.98912i	−0.255727	−	0.147644i
$731$	−30.9665	−	53.6356i	−1.14534	−	1.98378i
$732$	−1.34492	−	1.41357i	−0.0497095	−	0.0522471i
$733$	−9.33040	+	5.38691i	−0.344626	+	0.198970i	−0.662316	−	0.749225i	$-0.730426\pi$
$733$	−9.33040	+	5.38691i	−0.344626	+	0.198970i	0.317690	+	0.948195i	$0.397093\pi$
$734$	−6.94922	−	4.01213i	−0.256500	−	0.148090i
$735$	−1.29370	−	5.35805i	−0.0477189	−	0.197635i
$736$	−7.48599	−	4.32204i	−0.275937	−	0.159313i
$737$	−10.9679	−	18.9969i	−0.404006	−	0.699759i
$738$	2.16236	−	43.4130i	0.0795976	−	1.59806i
$739$	−0.855074	−	0.493677i	−0.0314544	−	0.0181602i	0.484190	−	0.874963i	$-0.339114\pi$
$739$	−0.855074	−	0.493677i	−0.0314544	−	0.0181602i	−0.515645	+	0.856802i	$0.672448\pi$
$740$	0.659639	−	1.14253i	0.0242488	−	0.0420002i
$741$	−23.4006	+	14.8662i	−0.859642	+	0.546122i
$742$	−6.62338	−	11.4720i	−0.243152	−	0.421152i
$743$			50.9690i			1.86987i	0.354817	+	0.934936i	$0.384543\pi$
$743$			50.9690i			1.86987i	−0.354817	+	0.934936i	$0.615457\pi$
$744$	19.8059	−	4.78214i	0.726121	−	0.175322i
$745$	−31.1386			−1.14083
$746$		−	3.11437i		−	0.114025i
$747$	−14.3166	−	27.9187i	−0.523816	−	1.02149i
$748$	−3.45064	+	1.99223i	−0.126168	+	0.0728430i
$749$	17.3574	+	10.0213i	0.634226	+	0.366171i
$750$	0.900088	−	0.217326i	0.0328666	−	0.00793563i
$751$	34.4378			1.25665			0.628327	−	0.777949i	$-0.283740\pi$
$751$	34.4378			1.25665			0.628327	+	0.777949i	$0.283740\pi$
$752$			9.16436i			0.334190i
$753$	−0.173896	+	0.0419871i	−0.00633712	+	0.00153010i
$754$	−1.52789	+	7.75415i	−0.0556426	+	0.282390i
$755$	−48.6846			−1.77181
$756$	1.34340	−	0.254390i	0.0488588	−	0.00925207i
$757$	4.69216	−	8.12707i	0.170540	−	0.295383i	−0.768069	−	0.640367i	$-0.778782\pi$
$757$	4.69216	−	8.12707i	0.170540	−	0.295383i	0.938609	+	0.344984i	$0.112116\pi$
$758$	43.3626			1.57500
$759$	−7.16327	−	29.6677i	−0.260010	−	1.07687i
$760$	36.4913	+	21.0683i	1.32368	+	0.764226i
$761$	−7.26747	−	4.19588i	−0.263446	−	0.152100i	0.362460	−	0.931999i	$-0.381937\pi$
$761$	−7.26747	−	4.19588i	−0.263446	−	0.152100i	−0.625905	+	0.779899i	$0.715270\pi$
$762$	8.52286	+	2.51258i	0.308751	+	0.0910210i
$763$	−4.36888			−0.158164
$764$	−2.76291	+	4.78550i	−0.0999586	+	0.173133i
$765$	21.8889	+	42.6855i	0.791395	+	1.54330i
$766$	17.2592			0.623602
$767$	2.16384	−	10.9816i	0.0781316	−	0.396523i
$768$	−7.40337	−	7.78131i	−0.267146	−	0.280784i
$769$			22.3293i			0.805214i	0.915373	+	0.402607i	$0.131896\pi$
$769$			22.3293i			0.805214i	−0.915373	+	0.402607i	$0.868104\pi$
$770$	−12.6394			−0.455493
$771$	0.0589914	−	0.200104i	0.00212452	−	0.00720655i
$772$	−0.205094	−	0.118411i	−0.00738150	−	0.00426171i
$773$	−14.3637	+	8.29289i	−0.516627	+	0.298275i	−0.735553	−	0.677467i	$-0.763078\pi$
$773$	−14.3637	+	8.29289i	−0.516627	+	0.298275i	0.218927	+	0.975741i	$0.429744\pi$
$774$	48.6727	+	2.42434i	1.74951	+	0.0871413i
$775$		−	20.2231i		−	0.726436i
$776$	−11.7775			−0.422789
$777$	1.88096	+	1.97698i	0.0674790	+	0.0709237i
$778$		−	20.6601i		−	0.740702i
$779$	−24.4027	−	42.2667i	−0.874318	−	1.51436i
$780$	−0.221484	−	5.22474i	−0.00793038	−	0.187076i
$781$	25.1180	−	43.5057i	0.898794	−	1.55676i
$782$	33.5314	+	19.3594i	1.19908	+	0.692290i
$783$	−8.15780	−	2.85318i	−0.291536	−	0.101964i
$784$	−1.70225	−	2.94838i	−0.0607946	−	0.105299i
$785$	3.89143	+	2.24672i	0.138891	+	0.0801888i
$786$	1.60815	−	1.53004i	0.0573607	−	0.0545747i
$787$	−44.0360	−	25.4242i	−1.56971	−	0.906274i	−0.996202	−	0.0870759i	$-0.972248\pi$
$787$	−44.0360	−	25.4242i	−1.56971	−	0.906274i	−0.573511	−	0.819198i	$-0.694419\pi$
$788$	−5.80329	+	3.35053i	−0.206734	+	0.119358i
$789$	−40.5710	+	9.79585i	−1.44436	+	0.348742i
$790$	12.9139	+	22.3676i	0.459457	+	0.795803i
$791$	3.32004	+	1.91682i	0.118047	+	0.0681544i
$792$	1.34146	−	26.9321i	0.0476667	−	0.956989i
$793$	−4.98798	−	14.6077i	−0.177128	−	0.518734i
$794$	−13.4079	+	23.2232i	−0.475830	+	0.824161i
$795$	−13.0035	−	53.8559i	−0.461187	−	1.91007i
$796$	6.52009			0.231098
$797$	19.8129	−	34.3170i	0.701809	−	1.21557i	−0.266021	−	0.963967i	$-0.585709\pi$
$797$	19.8129	−	34.3170i	0.701809	−	1.21557i	0.967831	−	0.251602i	$-0.0809575\pi$
$798$	−7.34153	+	6.98496i	−0.259887	+	0.247265i
$799$			13.5255i			0.478496i
$800$	−6.56474	+	3.79016i	−0.232099	+	0.134002i
$801$	1.05258	+	2.05263i	0.0371910	+	0.0725261i
$802$	−19.5573	−	33.8743i	−0.690593	−	1.19614i
$803$	2.86640	+	4.96474i	0.101153	+	0.175202i
$804$	2.40336	−	2.28663i	0.0847599	−	0.0806432i
$805$	−9.30368	−	16.1145i	−0.327912	−	0.567960i
$806$	18.3878	+	3.62316i	0.647682	+	0.127620i
$807$	−19.5264	+	4.71466i	−0.687363	+	0.165964i
$808$	−19.7427	+	11.3985i	−0.694546	+	0.400996i
$809$	−7.69756	+	13.3326i	−0.270632	+	0.468748i	−0.969024	−	0.246967i	$-0.920566\pi$
$809$	−7.69756	+	13.3326i	−0.270632	+	0.468748i	0.698392	+	0.715716i	$0.253899\pi$
$810$	−37.5596	−	3.75093i	−1.31971	−	0.131794i
$811$		−	5.68807i		−	0.199735i	−0.995001	−	0.0998675i	$-0.968158\pi$
$811$		−	5.68807i		−	0.199735i	0.995001	−	0.0998675i	$-0.0318419\pi$
$812$		−	0.437646i		−	0.0153584i
$813$	−20.3326	+	19.3451i	−0.713097	+	0.678462i
$814$	5.41903	−	3.12868i	0.189937	−	0.109660i
$815$	−10.4877	+	18.1652i	−0.367367	+	0.636299i
$816$	20.4231	+	21.4657i	0.714952	+	0.751449i
$817$	47.3876	−	27.3592i	1.65788	−	0.957179i
$818$	6.67175			0.233272
$819$	10.4954	+	2.61648i	0.366740	+	0.0914274i
$820$	9.20610			0.321491
$821$	−8.77414	+	5.06575i	−0.306220	+	0.176796i	−0.645234	−	0.763985i	$-0.723240\pi$
$821$	−8.77414	+	5.06575i	−0.306220	+	0.176796i	0.339014	+	0.940781i	$0.389907\pi$
$822$	−12.4843	+	3.01433i	−0.435439	+	0.105137i
$823$	−22.3127	+	38.6467i	−0.777770	+	1.34714i	0.155454	+	0.987843i	$0.450316\pi$
$823$	−22.3127	+	38.6467i	−0.777770	+	1.34714i	−0.933224	+	0.359294i	$0.883017\pi$
$824$	29.6534	−	17.1204i	1.03303	−	0.596418i
$825$	−25.6720	−	7.56822i	−0.893785	−	0.263492i
$826$		−	4.09119i		−	0.142351i
$827$			15.3574i			0.534031i	0.963692	+	0.267015i	$0.0860374\pi$
$827$			15.3574i			0.534031i	−0.963692	+	0.267015i	$0.913963\pi$
$828$	4.10708	−	2.10609i	0.142731	−	0.0731917i
$829$	19.5633	−	33.8847i	0.679463	−	1.17686i	−0.295680	−	0.955287i	$-0.595546\pi$
$829$	19.5633	−	33.8847i	0.679463	−	1.17686i	0.975143	−	0.221578i	$-0.0711206\pi$
$830$	−37.9869	+	21.9317i	−1.31854	+	0.761261i
$831$	−11.0274	+	37.4060i	−0.382538	+	1.29760i
$832$	−10.2033	−	29.8811i	−0.353735	−	1.03594i
$833$	−2.51231	−	4.35145i	−0.0870464	−	0.150769i
$834$	−29.5783	−	8.71981i	−1.02421	−	0.301942i
$835$	−9.72974	−	16.8524i	−0.336711	−	0.583201i
$836$	−1.76015	−	3.04867i	−0.0608761	−	0.105441i
$837$	−6.76589	+	19.3450i	−0.233863	+	0.668660i
$838$	−24.8923	+	14.3716i	−0.859890	+	0.496458i
$839$		−	24.9178i		−	0.860256i	−0.902768	−	0.430128i	$-0.858468\pi$
$839$		−	24.9178i		−	0.860256i	0.902768	−	0.430128i	$-0.141532\pi$
$840$	−3.85858	−	15.9809i	−0.133134	−	0.551392i
$841$	13.1168	−	22.7190i	0.452305	−	0.783415i
$842$	−8.89886			−0.306675
$843$	35.6210	−	33.8909i	1.22685	−	1.16726i
$844$	0.544947	−	0.943875i	0.0187578	−	0.0324895i
$845$	15.6942	−	38.2784i	0.539897	−	1.31682i
$846$	−8.94075	−	5.77330i	−0.307389	−	0.198490i
$847$	−1.66095	−	0.958948i	−0.0570708	−	0.0329498i
$848$	−17.1100	−	29.6354i	−0.587559	−	1.01768i
$849$	14.4196	−	48.9124i	0.494879	−	1.67867i
$850$	29.4049	−	16.9769i	1.00858	−	0.582304i
$851$	7.97773	+	4.60594i	0.273473	+	0.157890i
$852$	7.28716	+	2.14829i	0.249654	+	0.0735991i
$853$	−39.1598	−	22.6089i	−1.34081	−	0.774114i	−0.353879	−	0.935291i	$-0.615138\pi$
$853$	−39.1598	−	22.6089i	−1.34081	−	0.774114i	−0.986926	+	0.161177i	$0.948471\pi$
$854$	−2.82105	−	4.88621i	−0.0965345	−	0.167203i
$855$	−37.7131	+	19.3391i	−1.28976	+	0.661382i
$856$	51.7700	+	29.8894i	1.76946	+	1.02160i
$857$	−10.2898	+	17.8225i	−0.351495	+	0.608806i	−0.986512	−	0.163692i	$-0.947660\pi$
$857$	−10.2898	+	17.8225i	−0.351495	+	0.608806i	0.635017	+	0.772498i	$0.280993\pi$
$858$	11.4808	−	21.9862i	0.391946	−	0.750598i
$859$	7.83232	+	13.5660i	0.267235	+	0.462865i	0.968147	−	0.250383i	$-0.0805566\pi$
$859$	7.83232	+	13.5660i	0.267235	+	0.462865i	−0.700912	+	0.713248i	$0.747223\pi$
$860$			10.3215i			0.351959i
$861$	−5.38457	+	18.2649i	−0.183506	+	0.622466i
$862$	1.19912			0.0408423
$863$		−	36.9217i		−	1.25683i	−0.777878	−	0.628415i	$-0.783704\pi$
$863$		−	36.9217i		−	1.25683i	0.777878	−	0.628415i	$-0.216296\pi$
$864$	7.54772	−	1.42926i	0.256779	−	0.0486245i
$865$	25.8787	−	14.9411i	0.879904	−	0.508013i
$866$	37.4580	+	21.6264i	1.27288	+	0.734895i
$867$	9.84579	+	10.3484i	0.334381	+	0.351450i
$868$	−1.03781			−0.0352256
$869$		−	18.5587i		−	0.629561i
$870$	−3.41651	+	11.5891i	−0.115830	+	0.392906i
$871$	24.8360	−	8.48058i	0.841536	−	0.287353i
$872$	−13.0306			−0.441271
$873$	6.42619	−	9.95183i	0.217493	−	0.336819i
$874$	−17.1042	+	29.6254i	−0.578559	+	1.00209i
$875$	−0.405644			−0.0137133
$876$	−0.628106	+	0.597599i	−0.0212217	+	0.0201910i
$877$	−29.3150	−	16.9250i	−0.989897	−	0.571517i	−0.0846537	−	0.996410i	$-0.526978\pi$
$877$	−29.3150	−	16.9250i	−0.989897	−	0.571517i	−0.905244	+	0.424893i	$0.860312\pi$
$878$	13.9472	+	8.05240i	0.470694	+	0.271755i
$879$	−22.8164	+	21.7082i	−0.769578	+	0.732201i
$880$	−32.6510			−1.10067
$881$	−11.7589	+	20.3670i	−0.396168	+	0.686183i	−0.993249	−	0.115998i	$-0.962994\pi$
$881$	−11.7589	+	20.3670i	−0.396168	+	0.686183i	0.597082	+	0.802181i	$0.296327\pi$
$882$	3.94881	+	0.196687i	0.132963	+	0.00662279i
$883$	−39.5145			−1.32977			−0.664884	−	0.746947i	$-0.731519\pi$
$883$	−39.5145			−1.32977			−0.664884	+	0.746947i	$0.731519\pi$
$884$	−1.54043	−	4.51127i	−0.0518103	−	0.151730i
$885$	4.83854	−	16.4127i	0.162646	−	0.551707i
$886$			0.126900i			0.00426328i
$887$	24.4521			0.821021			0.410510	−	0.911856i	$-0.365351\pi$
$887$	24.4521			0.821021			0.410510	+	0.911856i	$0.365351\pi$
$888$	5.61012	+	5.89651i	0.188263	+	0.197874i
$889$	−3.37108	−	1.94629i	−0.113062	−	0.0652765i
$890$	2.79285	−	1.61245i	0.0936167	−	0.0540496i
$891$	22.0252	+	15.8285i	0.737872	+	0.530273i
$892$		−	6.51065i		−	0.217993i
$893$	−11.9499			−0.399888
$894$	6.31583	−	21.4238i	0.211233	−	0.716519i
$895$		−	76.7555i		−	2.56565i
$896$	−4.29230	−	7.43448i	−0.143396	−	0.248369i
$897$	36.4819	−	1.54651i	1.21809	−	0.0516366i
$898$	−18.5166	+	32.0717i	−0.617908	+	1.07025i
$899$	5.68103	+	3.27994i	0.189473	+	0.109392i
$900$	0.201357	−	4.04257i	0.00671190	−	0.134752i
$901$	−25.2522	−	43.7381i	−0.841273	−	1.45713i
$902$	37.8147	+	21.8323i	1.25909	+	0.726937i
$903$	−20.4778	−	6.03694i	−0.681458	−	0.200897i
$904$	9.90230	+	5.71710i	0.329346	+	0.190148i
$905$	−35.0406	+	20.2307i	−1.16479	+	0.672492i
$906$	9.87467	−	33.4957i	0.328064	−	1.11282i
$907$	6.60644	+	11.4427i	0.219363	+	0.379948i	0.954614	−	0.297847i	$-0.0962687\pi$
$907$	6.60644	+	11.4427i	0.219363	+	0.379948i	−0.735250	+	0.677796i	$0.762935\pi$
$908$	−2.47590	−	1.42946i	−0.0821655	−	0.0474383i
$909$	1.14071	−	22.9016i	0.0378349	−	0.759598i
$910$	2.92343	−	14.8366i	0.0969107	−	0.491828i
$911$	−20.0446	+	34.7183i	−0.664108	+	1.15027i	0.315419	+	0.948953i	$0.397855\pi$
$911$	−20.0446	+	34.7183i	−0.664108	+	1.15027i	−0.979526	+	0.201316i	$0.935478\pi$
$912$	−18.9652	+	18.0440i	−0.627999	+	0.597497i
$913$	31.5182			1.04310
$914$	−6.44018	+	11.1547i	−0.213022	+	0.368965i
$915$	−5.53850	−	22.9385i	−0.183097	−	0.758323i
$916$			3.64709i			0.120503i
$917$	−0.842141	+	0.486210i	−0.0278099	+	0.0160561i
$918$	−33.8079	+	6.40198i	−1.11583	+	0.211297i
$919$	19.7284	+	34.1705i	0.650779	+	1.12718i	0.982934	+	0.183958i	$0.0588909\pi$
$919$	19.7284	+	34.1705i	0.650779	+	1.12718i	−0.332155	+	0.943225i	$0.607776\pi$
$920$	−27.7491	−	48.0628i	−0.914859	−	1.58458i
$921$	3.56078	+	1.04973i	0.117332	+	0.0345899i
$922$	−7.87514	−	13.6401i	−0.259354	−	0.449214i
$923$	45.2589	+	39.5471i	1.48971	+	1.30171i
$924$	−0.388386	+	1.31744i	−0.0127769	+	0.0433404i
$925$	6.99596	−	4.03912i	0.230026	−	0.132805i
$926$	−9.84951	+	17.0598i	−0.323675	+	0.560621i
$927$	−1.71334	+	34.3981i	−0.0562734	+	1.12978i
$928$		−	2.45887i		−	0.0807162i
$929$		−	3.77968i		−	0.124007i	−0.998076	−	0.0620037i	$-0.980251\pi$
$929$		−	3.77968i		−	0.124007i	0.998076	−	0.0620037i	$-0.0197490\pi$
$930$	27.4817	+	8.10172i	0.901160	+	0.265666i
$931$	3.84455	−	2.21965i	0.126000	−	0.0727462i
$932$	−1.56287	+	2.70696i	−0.0511934	+	0.0886695i
$933$	−38.4914	+	9.29374i	−1.26015	+	0.304263i
$934$	32.3044	−	18.6509i	1.05703	−	0.610277i
$935$	−48.1889			−1.57594
$936$	31.3035	+	7.80389i	1.02319	+	0.255078i
$937$	20.0595			0.655314			0.327657	−	0.944797i	$-0.393741\pi$
$937$	20.0595			0.655314			0.327657	+	0.944797i	$0.393741\pi$
$938$	8.30754	−	4.79636i	0.271251	−	0.156607i
$939$	−34.8937	−	36.6750i	−1.13871	−	1.19684i
$940$	1.12704	−	1.95210i	0.0367601	−	0.0636704i
$941$	32.3393	−	18.6711i	1.05423	−	0.608661i	0.130400	−	0.991461i	$-0.458374\pi$
$941$	32.3393	−	18.6711i	1.05423	−	0.608661i	0.923831	+	0.382801i	$0.125040\pi$
$942$	−2.33507	+	2.22166i	−0.0760807	+	0.0723855i
$943$			64.2818i			2.09330i
$944$		−	10.5686i		−	0.343980i
$945$	15.6089	+	5.45921i	0.507758	+	0.177588i
$946$	−24.4774	+	42.3962i	−0.795830	+	1.37842i
$947$	−19.5104	+	11.2643i	−0.634003	+	0.366042i	−0.782301	−	0.622901i	$-0.785954\pi$
$947$	−19.5104	+	11.2643i	−0.634003	+	0.366042i	0.148298	+	0.988943i	$0.452621\pi$
$948$	2.72824	−	0.658734i	0.0886093	−	0.0213947i
$949$	−6.49077	+	2.21636i	−0.210699	+	0.0719460i
$950$	14.9993	+	25.9796i	0.486642	+	0.842888i
$951$	12.8174	−	12.1949i	0.415633	−	0.395446i
$952$	−7.49318	−	12.9786i	−0.242855	−	0.420638i
$953$	15.6543	+	27.1140i	0.507092	+	0.878309i	0.999966	+	0.00820831i	$0.00261281\pi$
$953$	15.6543	+	27.1140i	0.507092	+	0.878309i	−0.492875	+	0.870100i	$0.664054\pi$
$954$	39.6911	+	1.97698i	1.28505	+	0.0640070i
$955$	−57.8770	+	33.4153i	−1.87285	+	1.08129i
$956$			4.62895i			0.149711i
$957$	6.28973	−	5.98424i	0.203318	−	0.193443i
$958$	14.4254	−	24.9855i	0.466062	−	0.807244i
$959$	5.62631			0.181683
$960$	−11.3294	−	46.9224i	−0.365655	−	1.51441i
$961$	−7.72212	+	13.3751i	−0.249101	+	0.431455i
$962$	2.41916	+	7.08469i	0.0779968	+	0.228420i
$963$	−53.5034	+	27.4363i	−1.72412	+	0.884121i
$964$	1.38077	+	0.797188i	0.0444716	+	0.0256757i
$965$	−1.43209	−	2.48046i	−0.0461007	−	0.0798487i
$966$	12.9740	−	3.13258i	0.417432	−	0.100789i
$967$	16.2894	−	9.40467i	0.523830	−	0.302434i	−0.214670	−	0.976687i	$-0.568868\pi$
$967$	16.2894	−	9.40467i	0.523830	−	0.302434i	0.738500	+	0.674253i	$0.235534\pi$
$968$	−4.95392	−	2.86015i	−0.159225	−	0.0919286i
$969$	−27.9902	+	26.6307i	−0.899175	+	0.855503i
$970$	−14.3425	−	8.28067i	−0.460511	−	0.265876i
$971$	−23.7756	−	41.1805i	−0.762995	−	1.32155i	−0.941300	−	0.337571i	$-0.890395\pi$
$971$	−23.7756	−	41.1805i	−0.762995	−	1.32155i	0.178305	−	0.983975i	$-0.442939\pi$
$972$	−1.54510	+	3.79967i	−0.0495593	+	0.121874i
$973$	11.6992	+	6.75454i	0.375059	+	0.216541i
$974$	21.6979	−	37.5819i	0.695247	−	1.20420i
$975$	14.8216	−	28.3842i	0.474672	−	0.909023i
$976$	−7.28754	−	12.6224i	−0.233269	−	0.404033i
$977$			3.37349i			0.107928i	0.998543	+	0.0539638i	$0.0171856\pi$
$977$			3.37349i			0.107928i	−0.998543	+	0.0539638i	$0.982814\pi$
$978$	−10.3707	−	10.9001i	−0.331618	−	0.348547i
$979$	−2.31727			−0.0740603
$980$			0.837380i			0.0267491i
$981$	7.10987	−	11.0106i	0.227001	−	0.351542i
$982$	−14.0202	+	8.09457i	−0.447403	+	0.258308i
$983$	35.2171	+	20.3326i	1.12325	+	0.648509i	0.942229	−	0.334970i	$-0.108726\pi$
$983$	35.2171	+	20.3326i	1.12325	+	0.648509i	0.181021	+	0.983479i	$0.442060\pi$
$984$	−16.0600	+	54.4766i	−0.511973	+	1.73665i
$985$	−81.0442			−2.58228
$986$			11.0138i			0.350751i
$987$	3.21376	+	3.37782i	0.102295	+	0.107517i
$988$	3.98575	−	1.36099i	0.126804	−	0.0432988i
$989$	−72.0699			−2.29169
$990$	20.5693	−	31.8544i	0.653734	−	1.01240i
$991$	−15.3712	+	26.6236i	−0.488281	+	0.845728i	−0.999909	−	0.0134793i	$-0.995709\pi$
$991$	−15.3712	+	26.6236i	−0.488281	+	0.845728i	0.511628	+	0.859207i	$0.329043\pi$
$992$	−5.83082			−0.185129
$993$	−16.9620	−	5.00047i	−0.538272	−	0.158685i
$994$	19.0255	+	10.9844i	0.603453	+	0.348404i
$995$	68.2908	+	39.4277i	2.16496	+	1.24994i
$996$	1.11873	+	4.63338i	0.0354482	+	0.146814i
$997$	−29.3284			−0.928841			−0.464421	−	0.885615i	$-0.653737\pi$
$997$	−29.3284			−0.928841			−0.464421	+	0.885615i	$0.653737\pi$
$998$	−17.4641	+	30.2488i	−0.552818	+	0.957508i
$999$	−8.04351	+	1.52315i	−0.254485	+	0.0481902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dk.a.43.59	yes	168
9.4	even	3		819.2.bh.a.589.59	✓	168
13.10	even	6		819.2.bh.a.673.26	yes	168
117.49	even	6	inner	819.2.dk.a.400.59	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.bh.a.589.59	✓	168	9.4	even	3
819.2.bh.a.673.26	yes	168	13.10	even	6
819.2.dk.a.43.59	yes	168	1.1	even	1	trivial
819.2.dk.a.400.59	yes	168	117.49	even	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14134 - 0.658952i) q^{2} +(0.489776 - 1.66136i) q^{3} +(-0.131566 + 0.227878i) q^{4} +(-2.75601 + 1.59118i) q^{5} +(-0.535756 - 2.21891i) q^{6} +1.00000i q^{7} +2.98259i q^{8} +(-2.52024 - 1.62739i) q^{9} +O(q^{10})\)	\(q+(1.14134 - 0.658952i) q^{2} +(0.489776 - 1.66136i) q^{3} +(-0.131566 + 0.227878i) q^{4} +(-2.75601 + 1.59118i) q^{5} +(-0.535756 - 2.21891i) q^{6} +1.00000i q^{7} +2.98259i q^{8} +(-2.52024 - 1.62739i) q^{9} +(-2.09703 + 3.63216i) q^{10} +(2.60990 - 1.50683i) q^{11} +(0.314150 + 0.330187i) q^{12} +(1.16511 + 3.41211i) q^{13} +(0.658952 + 1.14134i) q^{14} +(1.29370 + 5.35805i) q^{15} +(1.70225 + 2.94838i) q^{16} +(2.51231 + 4.35145i) q^{17} +(-3.94881 - 0.196687i) q^{18} +(-3.84455 + 2.21965i) q^{19} -0.837380i q^{20} +(1.66136 + 0.489776i) q^{21} +(1.98585 - 3.43960i) q^{22} +5.84702 q^{23} +(4.95515 + 1.46080i) q^{24} +(2.56373 - 4.44052i) q^{25} +(3.57820 + 3.12662i) q^{26} +(-3.93804 + 3.38997i) q^{27} +(-0.227878 - 0.131566i) q^{28} +(0.831612 + 1.44039i) q^{29} +(5.00725 + 5.26286i) q^{30} +(3.41567 - 1.97204i) q^{31} +(-1.28031 - 0.739187i) q^{32} +(-1.22511 - 5.07399i) q^{33} +(5.73479 + 3.31098i) q^{34} +(-1.59118 - 2.75601i) q^{35} +(0.702423 - 0.360199i) q^{36} +(1.36441 + 0.787742i) q^{37} +(-2.92529 + 5.06675i) q^{38} +(6.23939 - 0.264496i) q^{39} +(-4.74585 - 8.22005i) q^{40} +10.9939i q^{41} +(2.21891 - 0.535756i) q^{42} -12.3259 q^{43} +0.792986i q^{44} +(9.53528 + 0.474944i) q^{45} +(6.67342 - 3.85290i) q^{46} +(2.33120 + 1.34592i) q^{47} +(5.73205 - 1.38400i) q^{48} -1.00000 q^{49} -6.75750i q^{50} +(8.45979 - 2.04262i) q^{51} +(-0.930834 - 0.183413i) q^{52} -10.0514 q^{53} +(-2.26080 + 6.46407i) q^{54} +(-4.79528 + 8.30566i) q^{55} -2.98259 q^{56} +(1.80467 + 7.47432i) q^{57} +(1.89830 + 1.09598i) q^{58} +(-2.68842 - 1.55216i) q^{59} +(-1.39119 - 0.410129i) q^{60} -4.28112 q^{61} +(2.59896 - 4.50153i) q^{62} +(1.62739 - 2.52024i) q^{63} -8.75735 q^{64} +(-8.64036 - 7.54992i) q^{65} +(-4.74179 - 4.98385i) q^{66} -7.27878i q^{67} -1.32213 q^{68} +(2.86373 - 9.71401i) q^{69} +(-3.63216 - 2.09703i) q^{70} +(14.4362 - 8.33475i) q^{71} +(4.85383 - 7.51683i) q^{72} +1.90227i q^{73} +2.07634 q^{74} +(-6.12164 - 6.43414i) q^{75} -1.16812i q^{76} +(1.50683 + 2.60990i) q^{77} +(6.94697 - 4.41334i) q^{78} +(3.07911 - 5.33317i) q^{79} +(-9.38284 - 5.41719i) q^{80} +(3.70320 + 8.20282i) q^{81} +(7.24447 + 12.5478i) q^{82} +(9.05731 + 5.22924i) q^{83} +(-0.330187 + 0.314150i) q^{84} +(-13.8479 - 7.99509i) q^{85} +(-14.0680 + 8.12218i) q^{86} +(2.80032 - 0.676136i) q^{87} +(4.49424 + 7.78426i) q^{88} +(-0.665908 - 0.384462i) q^{89} +(11.1959 - 5.74122i) q^{90} +(-3.41211 + 1.16511i) q^{91} +(-0.769266 + 1.33241i) q^{92} +(-1.60335 - 6.64052i) q^{93} +3.54758 q^{94} +(7.06375 - 12.2348i) q^{95} +(-1.85512 + 1.76502i) q^{96} +3.94877i q^{97} +(-1.14134 + 0.658952i) q^{98} +(-9.02976 - 0.449764i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 84 q^{4} - 2 q^{9}+O(q^{10}) \) 168 * q + 84 * q^4 - 2 * q^9	\( 168 q + 84 q^{4} - 2 q^{9} + 12 q^{12} + 8 q^{14} - 84 q^{16} + 12 q^{18} - 6 q^{21} + 40 q^{23} - 84 q^{24} + 84 q^{25} + 4 q^{26} - 24 q^{27} + 34 q^{29} + 44 q^{30} + 36 q^{32} + 18 q^{33} + 16 q^{35} + 4 q^{36} - 12 q^{38} - 6 q^{39} - 30 q^{45} - 30 q^{47} - 2 q^{48} - 168 q^{49} - 38 q^{51} + 18 q^{52} - 48 q^{53} + 114 q^{54} + 48 q^{56} - 54 q^{57} + 48 q^{59} + 24 q^{60} + 6 q^{62} - 12 q^{63} - 132 q^{64} - 16 q^{65} - 54 q^{66} - 156 q^{68} - 28 q^{69} + 24 q^{71} + 36 q^{72} - 84 q^{74} + 30 q^{75} - 16 q^{77} + 116 q^{78} - 6 q^{79} - 2 q^{81} - 6 q^{82} + 18 q^{83} - 24 q^{84} + 90 q^{85} - 24 q^{86} + 52 q^{87} + 24 q^{88} - 36 q^{89} - 44 q^{90} - 6 q^{91} + 8 q^{92} - 66 q^{93} + 120 q^{94} - 48 q^{95} - 24 q^{96} + 6 q^{99}+O(q^{100}) \) 168 * q + 84 * q^4 - 2 * q^9 + 12 * q^12 + 8 * q^14 - 84 * q^16 + 12 * q^18 - 6 * q^21 + 40 * q^23 - 84 * q^24 + 84 * q^25 + 4 * q^26 - 24 * q^27 + 34 * q^29 + 44 * q^30 + 36 * q^32 + 18 * q^33 + 16 * q^35 + 4 * q^36 - 12 * q^38 - 6 * q^39 - 30 * q^45 - 30 * q^47 - 2 * q^48 - 168 * q^49 - 38 * q^51 + 18 * q^52 - 48 * q^53 + 114 * q^54 + 48 * q^56 - 54 * q^57 + 48 * q^59 + 24 * q^60 + 6 * q^62 - 12 * q^63 - 132 * q^64 - 16 * q^65 - 54 * q^66 - 156 * q^68 - 28 * q^69 + 24 * q^71 + 36 * q^72 - 84 * q^74 + 30 * q^75 - 16 * q^77 + 116 * q^78 - 6 * q^79 - 2 * q^81 - 6 * q^82 + 18 * q^83 - 24 * q^84 + 90 * q^85 - 24 * q^86 + 52 * q^87 + 24 * q^88 - 36 * q^89 - 44 * q^90 - 6 * q^91 + 8 * q^92 - 66 * q^93 + 120 * q^94 - 48 * q^95 - 24 * q^96 + 6 * q^99

Introduction

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