LMFDB - Embedded newform 585.2.bt.b.571.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			571.3
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.26372 + 1.30696i) q^{2} +(-0.538321 - 1.64627i) q^{3} +(2.41629 - 4.18514i) q^{4} +(0.866025 + 0.500000i) q^{5} +(3.37022 + 3.02314i) q^{6} +(3.14827 - 1.81766i) q^{7} +7.40414i q^{8} +(-2.42042 + 1.77245i) q^{9} +O(q^{10})$	\(q+(-2.26372 + 1.30696i) q^{2} +(-0.538321 - 1.64627i) q^{3} +(2.41629 - 4.18514i) q^{4} +(0.866025 + 0.500000i) q^{5} +(3.37022 + 3.02314i) q^{6} +(3.14827 - 1.81766i) q^{7} +7.40414i q^{8} +(-2.42042 + 1.77245i) q^{9} -2.61392 q^{10} +(-5.33710 + 3.08138i) q^{11} +(-8.19061 - 1.72492i) q^{12} +(0.233392 + 3.59799i) q^{13} +(-4.75121 + 8.22933i) q^{14} +(0.356936 - 1.69487i) q^{15} +(-4.84434 - 8.39063i) q^{16} +2.59963 q^{17} +(3.16264 - 7.17572i) q^{18} +6.95618i q^{19} +(4.18514 - 2.41629i) q^{20} +(-4.68714 - 4.20443i) q^{21} +(8.05447 - 13.9508i) q^{22} +(1.37773 - 2.38631i) q^{23} +(12.1892 - 3.98581i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-5.23076 - 7.83981i) q^{26} +(4.22089 + 3.03052i) q^{27} -17.5679i q^{28} +(2.36365 + 4.09396i) q^{29} +(1.40713 + 4.30322i) q^{30} +(-4.56322 - 2.63457i) q^{31} +(9.10811 + 5.25857i) q^{32} +(7.94585 + 7.12754i) q^{33} +(-5.88483 + 3.39761i) q^{34} +3.63531 q^{35} +(1.56949 + 14.4125i) q^{36} +2.85385i q^{37} +(-9.09145 - 15.7469i) q^{38} +(5.79763 - 2.32110i) q^{39} +(-3.70207 + 6.41217i) q^{40} +(0.632395 + 0.365113i) q^{41} +(16.1054 + 3.39175i) q^{42} +(2.01702 + 3.49359i) q^{43} +29.7820i q^{44} +(-2.98237 + 0.324773i) q^{45} +7.20258i q^{46} +(-0.0766416 + 0.0442490i) q^{47} +(-11.2055 + 12.4919i) q^{48} +(3.10774 - 5.38277i) q^{49} +(-2.26372 - 1.30696i) q^{50} +(-1.39943 - 4.27969i) q^{51} +(15.6220 + 7.71701i) q^{52} +1.07708 q^{53} +(-13.5157 - 1.34372i) q^{54} -6.16275 q^{55} +(13.4582 + 23.3102i) q^{56} +(11.4518 - 3.74466i) q^{57} +(-10.7013 - 6.17839i) q^{58} +(5.43841 + 3.13987i) q^{59} +(-6.23082 - 5.58913i) q^{60} +(2.61102 + 4.52242i) q^{61} +13.7731 q^{62} +(-4.39844 + 9.97963i) q^{63} -8.11361 q^{64} +(-1.59687 + 3.23265i) q^{65} +(-27.3026 - 5.74986i) q^{66} +(-10.5075 - 6.06651i) q^{67} +(6.28145 - 10.8798i) q^{68} +(-4.67017 - 0.983525i) q^{69} +(-8.22933 + 4.75121i) q^{70} -4.49697i q^{71} +(-13.1234 - 17.9211i) q^{72} +11.8579i q^{73} +(-3.72987 - 6.46032i) q^{74} +(1.15655 - 1.28934i) q^{75} +(29.1126 + 16.8082i) q^{76} +(-11.2018 + 19.4020i) q^{77} +(-10.0906 + 12.8316i) q^{78} +(-2.01822 - 3.49566i) q^{79} -9.68867i q^{80} +(2.71687 - 8.58013i) q^{81} -1.90875 q^{82} +(12.4976 - 7.21548i) q^{83} +(-28.9216 + 9.45719i) q^{84} +(2.25134 + 1.29981i) q^{85} +(-9.13195 - 5.27234i) q^{86} +(5.46737 - 6.09507i) q^{87} +(-22.8149 - 39.5166i) q^{88} +6.71820i q^{89} +(6.32679 - 4.63303i) q^{90} +(7.27469 + 10.9032i) q^{91} +(-6.65801 - 11.5320i) q^{92} +(-1.88075 + 8.93054i) q^{93} +(0.115663 - 0.200335i) q^{94} +(-3.47809 + 6.02423i) q^{95} +(3.75394 - 17.8252i) q^{96} +(12.5186 - 7.22764i) q^{97} +16.2468i q^{98} +(7.45645 - 16.9179i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−2.26372	+	1.30696i	−1.60069	+	0.924160i	−0.609344	+	0.792906i	$0.708567\pi$
$2$	−2.26372	+	1.30696i	−1.60069	+	0.924160i	−0.991349	+	0.131255i	$0.958099\pi$
$3$	−0.538321	−	1.64627i	−0.310800	−	0.950475i
$3$	−0.538321	−	1.64627i	−0.310800	−	0.950475i
$4$	2.41629	−	4.18514i	1.20815	−	2.09257i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	3.37022	+	3.02314i	1.37589	+	1.23419i
$7$	3.14827	−	1.81766i	1.18993	−	0.687009i	0.231643	−	0.972801i	$-0.425590\pi$
$7$	3.14827	−	1.81766i	1.18993	−	0.687009i	0.958292	+	0.285792i	$0.0922566\pi$
$8$			7.40414i			2.61776i
$9$	−2.42042	+	1.77245i	−0.806807	+	0.590815i
$10$	−2.61392			−0.826594
$11$	−5.33710	+	3.08138i	−1.60920	+	0.929070i	−0.619645	+	0.784882i	$0.712724\pi$
$11$	−5.33710	+	3.08138i	−1.60920	+	0.929070i	−0.989550	+	0.144188i	$0.953943\pi$
$12$	−8.19061	−	1.72492i	−2.36443	−	0.497942i
$13$	0.233392	+	3.59799i	0.0647312	+	0.997903i
$13$	0.233392	+	3.59799i	0.0647312	+	0.997903i
$14$	−4.75121	+	8.22933i	−1.26981	+	2.19938i
$15$	0.356936	−	1.69487i	0.0921604	−	0.437615i
$16$	−4.84434	−	8.39063i	−1.21108	−	2.09766i
$17$	2.59963			0.630502			0.315251	−	0.949008i	$-0.397911\pi$
$17$	2.59963			0.630502			0.315251	+	0.949008i	$0.397911\pi$
$18$	3.16264	−	7.17572i	0.745442	−	1.69133i
$19$			6.95618i			1.59586i	0.602752	+	0.797929i	$0.294071\pi$
$19$			6.95618i			1.59586i	−0.602752	+	0.797929i	$0.705929\pi$
$20$	4.18514	−	2.41629i	0.935825	−	0.540299i
$21$	−4.68714	−	4.20443i	−1.02282	−	0.917481i
$22$	8.05447	−	13.9508i	1.71722	−	2.97431i
$23$	1.37773	−	2.38631i	0.287277	−	0.497579i	−0.685881	−	0.727713i	$-0.740583\pi$
$23$	1.37773	−	2.38631i	0.287277	−	0.497579i	0.973159	+	0.230134i	$0.0739165\pi$
$24$	12.1892	−	3.98581i	2.48811	−	0.813599i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−5.23076	−	7.83981i	−1.02584	−	1.53751i
$27$	4.22089	+	3.03052i	0.812311	+	0.583225i
$28$		−	17.5679i		−	3.32003i
$29$	2.36365	+	4.09396i	0.438919	+	0.760229i	0.997606	−	0.0691488i	$-0.0220283\pi$
$29$	2.36365	+	4.09396i	0.438919	+	0.760229i	−0.558688	+	0.829378i	$0.688695\pi$
$30$	1.40713	+	4.30322i	0.256905	+	0.785657i
$31$	−4.56322	−	2.63457i	−0.819578	−	0.473184i	0.0306930	−	0.999529i	$-0.490229\pi$
$31$	−4.56322	−	2.63457i	−0.819578	−	0.473184i	−0.850271	+	0.526345i	$0.823562\pi$
$32$	9.10811	+	5.25857i	1.61010	+	0.929592i
$33$	7.94585	+	7.12754i	1.38320	+	1.24075i
$34$	−5.88483	+	3.39761i	−1.00924	+	0.582685i
$35$	3.63531			0.614480
$36$	1.56949	+	14.4125i	0.261582	+	2.40209i
$37$			2.85385i			0.469170i	0.972096	+	0.234585i	$0.0753731\pi$
$37$			2.85385i			0.469170i	−0.972096	+	0.234585i	$0.924627\pi$
$38$	−9.09145	−	15.7469i	−1.47483	−	2.55448i
$39$	5.79763	−	2.32110i	0.928363	−	0.371674i
$40$	−3.70207	+	6.41217i	−0.585349	+	1.01385i
$41$	0.632395	+	0.365113i	0.0987635	+	0.0570211i	0.548568	−	0.836106i	$-0.315173\pi$
$41$	0.632395	+	0.365113i	0.0987635	+	0.0570211i	−0.449805	+	0.893127i	$0.648506\pi$
$42$	16.1054	+	3.39175i	2.48512	+	0.523359i
$43$	2.01702	+	3.49359i	0.307593	+	0.532767i	0.977835	−	0.209376i	$-0.0671431\pi$
$43$	2.01702	+	3.49359i	0.307593	+	0.532767i	−0.670242	+	0.742142i	$0.733810\pi$
$44$			29.7820i			4.48980i
$45$	−2.98237	+	0.324773i	−0.444585	+	0.0484144i
$46$			7.20258i			1.06196i
$47$	−0.0766416	+	0.0442490i	−0.0111793	+	0.00645439i	−0.505579	−	0.862780i	$-0.668721\pi$
$47$	−0.0766416	+	0.0442490i	−0.0111793	+	0.00645439i	0.494400	+	0.869235i	$0.335388\pi$
$48$	−11.2055	+	12.4919i	−1.61737	+	1.80306i
$49$	3.10774	−	5.38277i	0.443963	−	0.768967i
$50$	−2.26372	−	1.30696i	−0.320139	−	0.184832i
$51$	−1.39943	−	4.27969i	−0.195960	−	0.599277i
$52$	15.6220	+	7.71701i	2.16638	+	1.07016i
$53$	1.07708			0.147949			0.0739744	−	0.997260i	$-0.476432\pi$
$53$	1.07708			0.147949			0.0739744	+	0.997260i	$0.476432\pi$
$54$	−13.5157	−	1.34372i	−1.83925	−	0.182858i
$55$	−6.16275			−0.830985
$56$	13.4582	+	23.3102i	1.79842	+	3.11496i
$57$	11.4518	−	3.74466i	1.51682	−	0.495992i
$58$	−10.7013	−	6.17839i	−1.40515	−	0.811262i
$59$	5.43841	+	3.13987i	0.708021	+	0.408776i	0.810328	−	0.585977i	$-0.199289\pi$
$59$	5.43841	+	3.13987i	0.708021	+	0.408776i	−0.102307	+	0.994753i	$0.532622\pi$
$60$	−6.23082	−	5.58913i	−0.804395	−	0.721554i
$61$	2.61102	+	4.52242i	0.334307	+	0.579036i	0.983351	−	0.181714i	$-0.0581645\pi$
$61$	2.61102	+	4.52242i	0.334307	+	0.579036i	−0.649045	+	0.760750i	$0.724831\pi$
$62$	13.7731			1.74919
$63$	−4.39844	+	9.97963i	−0.554152	+	1.25732i
$64$	−8.11361			−1.01420
$65$	−1.59687	+	3.23265i	−0.198068	+	0.400960i
$66$	−27.3026	−	5.74986i	−3.36072	−	0.707759i
$67$	−10.5075	−	6.06651i	−1.28370	−	0.741142i	−0.306173	−	0.951976i	$-0.599049\pi$
$67$	−10.5075	−	6.06651i	−1.28370	−	0.741142i	−0.977522	+	0.210834i	$0.932382\pi$
$68$	6.28145	−	10.8798i	0.761738	−	1.31937i
$69$	−4.67017	−	0.983525i	−0.562223	−	0.118403i
$70$	−8.22933	+	4.75121i	−0.983593	+	0.567878i
$71$		−	4.49697i		−	0.533693i	−0.963739	−	0.266846i	$-0.914018\pi$
$71$		−	4.49697i		−	0.533693i	0.963739	−	0.266846i	$-0.0859816\pi$
$72$	−13.1234	−	17.9211i	−1.54661	−	2.11203i
$73$			11.8579i			1.38786i	0.720042	+	0.693930i	$0.244122\pi$
$73$			11.8579i			1.38786i	−0.720042	+	0.693930i	$0.755878\pi$
$74$	−3.72987	−	6.46032i	−0.433588	−	0.750997i
$75$	1.15655	−	1.28934i	0.133547	−	0.148880i
$76$	29.1126	+	16.8082i	3.33944	+	1.92803i
$77$	−11.2018	+	19.4020i	−1.27656	+	2.21106i
$78$	−10.0906	+	12.8316i	−1.14254	+	1.45289i
$79$	−2.01822	−	3.49566i	−0.227068	−	0.393293i	0.729870	−	0.683586i	$-0.239581\pi$
$79$	−2.01822	−	3.49566i	−0.227068	−	0.393293i	−0.956938	+	0.290293i	$0.906247\pi$
$80$		−	9.68867i		−	1.08323i
$81$	2.71687	−	8.58013i	0.301874	−	0.953348i
$82$	−1.90875			−0.210787
$83$	12.4976	−	7.21548i	1.37179	−	0.792001i	0.380634	−	0.924726i	$-0.375706\pi$
$83$	12.4976	−	7.21548i	1.37179	−	0.792001i	0.991153	+	0.132724i	$0.0423725\pi$
$84$	−28.9216	+	9.45719i	−3.15560	+	1.03186i
$85$	2.25134	+	1.29981i	0.244192	+	0.140985i
$86$	−9.13195	−	5.27234i	−0.984724	−	0.568531i
$87$	5.46737	−	6.09507i	0.586163	−	0.653461i
$88$	−22.8149	−	39.5166i	−2.43208	−	4.21249i
$89$			6.71820i			0.712127i	0.934462	+	0.356064i	$0.115881\pi$
$89$			6.71820i			0.712127i	−0.934462	+	0.356064i	$0.884119\pi$
$90$	6.32679	−	4.63303i	0.666902	−	0.488365i
$91$	7.27469	+	10.9032i	0.762594	+	1.14297i
$92$	−6.65801	−	11.5320i	−0.694146	−	1.20230i
$93$	−1.88075	+	8.93054i	−0.195024	+	0.926054i
$94$	0.115663	−	0.200335i	0.0119298	−	0.0206630i
$95$	−3.47809	+	6.02423i	−0.356845	+	0.618073i
$96$	3.75394	−	17.8252i	0.383135	−	1.81928i
$97$	12.5186	−	7.22764i	1.27108	−	0.733856i	0.295885	−	0.955223i	$-0.404385\pi$
$97$	12.5186	−	7.22764i	1.27108	−	0.733856i	0.975190	+	0.221367i	$0.0710520\pi$
$98$			16.2468i			1.64117i
$99$	7.45645	−	16.9179i	0.749401	−	1.70032i
$100$	4.83258			0.483258
$101$	5.68748	+	9.85100i	0.565925	+	0.980211i	0.996963	+	0.0778773i	$0.0248142\pi$
$101$	5.68748	+	9.85100i	0.565925	+	0.980211i	−0.431038	+	0.902334i	$0.641852\pi$
$102$	8.76132	+	7.85902i	0.867500	+	0.778159i
$103$	−5.52903	+	9.57656i	−0.544791	+	0.943606i	0.453829	+	0.891089i	$0.350058\pi$
$103$	−5.52903	+	9.57656i	−0.544791	+	0.943606i	−0.998620	+	0.0525172i	$0.983276\pi$
$104$	−26.6400	+	1.72806i	−2.61227	+	0.169451i
$105$	−1.95697	−	5.98471i	−0.190980	−	0.584048i
$106$	−2.43822	+	1.40771i	−0.236821	+	0.136729i
$107$	−2.96594			−0.286728			−0.143364	−	0.989670i	$-0.545792\pi$
$107$	−2.96594			−0.286728			−0.143364	+	0.989670i	$0.545792\pi$
$108$	22.8821	−	10.3424i	2.20183	−	0.995197i
$109$			4.42434i			0.423775i	0.977294	+	0.211887i	$0.0679610\pi$
$109$			4.42434i			0.423775i	−0.977294	+	0.211887i	$0.932039\pi$
$110$	13.9508	−	8.05447i	1.33015	−	0.767964i
$111$	4.69821	−	1.53629i	0.445934	−	0.145818i
$112$	−30.5026	−	17.6107i	−2.88222	−	1.66405i
$113$	−2.57928	+	4.46745i	−0.242638	+	0.420262i	−0.961465	−	0.274927i	$-0.911346\pi$
$113$	−2.57928	+	4.46745i	−0.242638	+	0.420262i	0.718827	+	0.695189i	$0.244679\pi$
$114$	−21.0295	+	23.4439i	−1.96959	+	2.19572i
$115$	2.38631	−	1.37773i	0.222524	−	0.128474i
$116$	22.8450			2.12111
$117$	−6.94215	−	8.29497i	−0.641802	−	0.766870i
$118$	−16.4147			−1.51110
$119$	8.18433	−	4.72522i	0.750256	−	0.433161i
$120$	12.5491	+	2.64280i	1.14557	+	0.241254i
$121$	13.4897	−	23.3649i	1.22634	−	2.12408i
$122$	−11.8212	−	6.82500i	−1.07025	−	0.617906i
$123$	0.260644	−	1.23764i	0.0235015	−	0.111594i
$124$	−22.0521	+	12.7318i	−1.98034	+	1.14335i
$125$			1.00000i			0.0894427i
$126$	−3.08613	−	28.3397i	−0.274934	−	2.52470i
$127$	16.0536			1.42453			0.712263	−	0.701913i	$-0.247670\pi$
$127$	16.0536			1.42453			0.712263	+	0.701913i	$0.247670\pi$
$128$	0.150750	−	0.0870357i	0.0133246	−	0.00769294i
$129$	4.66558	−	5.20124i	0.410782	−	0.457943i
$130$	−0.610067	−	9.40486i	−0.0535064	−	0.824861i
$131$	0.462103	−	0.800387i	0.0403742	−	0.0699301i	−0.845132	−	0.534557i	$-0.820478\pi$
$131$	0.462103	−	0.800387i	0.0403742	−	0.0699301i	0.885506	+	0.464627i	$0.153812\pi$
$132$	49.0292	−	16.0323i	4.26745	−	1.39543i
$133$	12.6439	+	21.8999i	1.09637	+	1.89897i
$134$	31.7147			2.73974
$135$	2.14014	+	4.73496i	0.184194	+	0.407520i
$136$			19.2480i			1.65050i
$137$	6.99169	−	4.03665i	0.597340	−	0.344875i	−0.170654	−	0.985331i	$-0.554588\pi$
$137$	6.99169	−	4.03665i	0.597340	−	0.344875i	0.767995	+	0.640456i	$0.221255\pi$
$138$	11.8574	−	3.87730i	1.00937	−	0.330058i
$139$	−4.29105	+	7.43232i	−0.363962	+	0.630402i	−0.988609	−	0.150506i	$-0.951910\pi$
$139$	−4.29105	+	7.43232i	−0.363962	+	0.630402i	0.624647	+	0.780908i	$0.285243\pi$
$140$	8.78397	−	15.2143i	0.742381	−	1.28584i
$141$	0.114104	+	0.102353i	0.00960927	+	0.00861965i
$142$	5.87737	+	10.1799i	0.493218	+	0.854278i
$143$	−12.3324	−	18.4837i	−1.03129	−	1.54568i
$144$	26.5973	+	11.7225i	2.21644	+	0.976878i
$145$			4.72730i			0.392581i
$146$	−15.4978	−	26.8429i	−1.28261	−	2.22154i
$147$	−10.5345	−	2.21853i	−0.868868	−	0.182981i
$148$	11.9437	+	6.89573i	0.981770	+	0.566825i
$149$	−13.1652	−	7.60091i	−1.07853	−	0.622691i	−0.148032	−	0.988983i	$-0.547294\pi$
$149$	−13.1652	−	7.60091i	−1.07853	−	0.622691i	−0.930500	+	0.366291i	$0.880627\pi$
$150$	−0.933002	+	4.43026i	−0.0761793	+	0.361730i
$151$	−3.77135	+	2.17739i	−0.306908	+	0.177194i	−0.645542	−	0.763725i	$-0.723369\pi$
$151$	−3.77135	+	2.17739i	−0.306908	+	0.177194i	0.338634	+	0.940918i	$0.390035\pi$
$152$	−51.5045			−4.17757
$153$	−6.29219	+	4.60770i	−0.508693	+	0.372510i
$154$		−	58.5610i		−	4.71898i
$155$	−2.63457	−	4.56322i	−0.211614	−	0.366526i
$156$	4.29463	−	29.8723i	0.343845	−	2.39170i
$157$	−1.81156	+	3.13771i	−0.144578	+	0.250416i	−0.929215	−	0.369539i	$-0.879516\pi$
$157$	−1.81156	+	3.13771i	−0.144578	+	0.250416i	0.784637	+	0.619955i	$0.212849\pi$
$158$	9.13738	+	5.27547i	0.726931	+	0.419694i
$159$	−0.579817	−	1.77317i	−0.0459825	−	0.140622i
$160$	5.25857	+	9.10811i	0.415726	+	0.720059i
$161$		−	10.0170i		−	0.789449i
$162$	5.06365	+	22.9739i	0.397838	+	1.80500i
$163$		−	21.3381i		−	1.67133i	−0.549238	−	0.835666i	$-0.685082\pi$
$163$		−	21.3381i		−	1.67133i	0.549238	−	0.835666i	$-0.314918\pi$
$164$	3.05610	−	1.76444i	0.238641	−	0.137780i
$165$	3.31754	+	10.1456i	0.258270	+	0.789831i
$166$	−18.8607	+	32.6677i	−1.46387	+	2.53550i
$167$	−15.4532	−	8.92193i	−1.19581	−	0.690400i	−0.236190	−	0.971707i	$-0.575899\pi$
$167$	−15.4532	−	8.92193i	−1.19581	−	0.690400i	−0.959618	+	0.281307i	$0.909232\pi$
$168$	31.1302	−	34.7042i	2.40174	−	2.67749i
$169$	−12.8911	+	1.67948i	−0.991620	+	0.129191i
$170$	−6.79522			−0.521169
$171$	−12.3295	−	16.8369i	−0.942857	−	1.28755i
$172$	19.4948			1.48647
$173$	1.03325	+	1.78964i	0.0785563	+	0.136064i	0.902627	−	0.430423i	$-0.141636\pi$
$173$	1.03325	+	1.78964i	0.0785563	+	0.136064i	−0.824071	+	0.566487i	$0.808302\pi$
$174$	−4.41058	+	20.9432i	−0.334365	+	1.58770i
$175$	3.14827	+	1.81766i	0.237987	+	0.137402i
$176$	51.7094	+	29.8544i	3.89774	+	2.25036i
$177$	2.24146	−	10.6434i	0.168479	−	0.800004i
$178$	−8.78042	−	15.2081i	−0.658120	−	1.13990i
$179$	3.29091			0.245974			0.122987	−	0.992408i	$-0.460753\pi$
$179$	3.29091			0.245974			0.122987	+	0.992408i	$0.460753\pi$
$180$	−5.84705	+	13.2664i	−0.435813	+	0.988817i
$181$	−3.13408			−0.232954			−0.116477	−	0.993193i	$-0.537160\pi$
$181$	−3.13408			−0.232954			−0.116477	+	0.993193i	$0.537160\pi$
$182$	−30.7179	−	15.1741i	−2.27697	−	1.12478i
$183$	6.03956	−	6.73296i	0.446457	−	0.497715i
$184$	17.6685	+	10.2009i	1.30254	+	0.752023i
$185$	−1.42692	+	2.47151i	−0.104910	+	0.181709i
$186$	−7.41437	−	22.6743i	−0.543648	−	1.66256i
$187$	−13.8745	+	8.01042i	−1.01460	+	0.585780i
$188$			0.427674i			0.0311913i
$189$	18.7970	+	1.86878i	1.36728	+	0.135934i
$190$		−	18.1829i		−	1.31913i
$191$	−2.32532	−	4.02758i	−0.168255	−	0.291425i	0.769552	−	0.638584i	$-0.220480\pi$
$191$	−2.32532	−	4.02758i	−0.168255	−	0.291425i	−0.937806	+	0.347159i	$0.887146\pi$
$192$	4.36773	+	13.3572i	0.315214	+	0.963974i
$193$	22.2078	+	12.8217i	1.59855	+	0.922925i	0.991767	+	0.128059i	$0.0408747\pi$
$193$	22.2078	+	12.8217i	1.59855	+	0.922925i	0.606786	+	0.794865i	$0.292459\pi$
$194$	−18.8925	+	32.7227i	−1.35640	+	2.34936i
$195$	6.18144	+	0.888682i	0.442662	+	0.0636398i
$196$	−15.0184	−	26.0127i	−1.07274	−	1.85805i
$197$		−	0.692184i		−	0.0493161i	−0.999696	−	0.0246580i	$-0.992150\pi$
$197$		−	0.692184i		−	0.0493161i	0.999696	−	0.0246580i	$-0.00784969\pi$
$198$	5.23175	+	48.0428i	0.371805	+	3.41425i
$199$	20.3639			1.44356			0.721779	−	0.692124i	$-0.243325\pi$
$199$	20.3639			1.44356			0.721779	+	0.692124i	$0.243325\pi$
$200$	−6.41217	+	3.70207i	−0.453409	+	0.261776i
$201$	−4.33071	+	20.5639i	−0.305465	+	1.45047i
$202$	−25.7497	−	14.8666i	−1.81174	−	1.04601i
$203$	14.8828	+	8.59260i	1.04457	+	0.603082i
$204$	−21.2925	−	4.48415i	−1.49078	−	0.313953i
$205$	0.365113	+	0.632395i	0.0255006	+	0.0441684i
$206$		−	28.9049i		−	2.01390i
$207$	0.894903	+	8.21782i	0.0622000	+	0.571178i
$208$	29.0588	−	19.3882i	2.01486	−	1.34433i
$209$	−21.4346	−	37.1258i	−1.48266	−	2.56805i
$210$	12.2518	+	10.9900i	0.845455	+	0.758385i
$211$	−9.20685	+	15.9467i	−0.633826	+	1.09782i	0.352937	+	0.935647i	$0.385183\pi$
$211$	−9.20685	+	15.9467i	−0.633826	+	1.09782i	−0.986763	+	0.162171i	$0.948150\pi$
$212$	2.60255	−	4.50774i	0.178744	−	0.309593i
$213$	−7.40324	+	2.42082i	−0.507262	+	0.165872i
$214$	6.71405	−	3.87636i	0.458963	−	0.264983i
$215$			4.03404i			0.275120i
$216$	−22.4384	+	31.2521i	−1.52674	+	2.12643i
$217$	−19.1550			−1.30033
$218$	−5.78244	−	10.0155i	−0.391636	−	0.678333i
$219$	19.5213	−	6.38335i	1.31913	−	0.431347i
$220$	−14.8910	+	25.7920i	−1.00395	+	1.73889i
$221$	0.606731	+	9.35343i	0.0408131	+	0.629180i
$222$	−8.62757	+	9.61810i	−0.579045	+	0.645525i
$223$	−5.41236	+	3.12483i	−0.362439	+	0.209254i	−0.670150	−	0.742226i	$-0.733770\pi$
$223$	−5.41236	+	3.12483i	−0.362439	+	0.209254i	0.307711	+	0.951480i	$0.400437\pi$
$224$	38.2331			2.55455
$225$	−2.74519	−	1.20992i	−0.183013	−	0.0806615i
$226$		−	13.4841i		−	0.896947i
$227$	−0.760752	+	0.439221i	−0.0504929	+	0.0291521i	−0.525034	−	0.851081i	$-0.675947\pi$
$227$	−0.760752	+	0.439221i	−0.0504929	+	0.0291521i	0.474541	+	0.880233i	$0.342614\pi$
$228$	11.9989	−	56.9754i	0.794644	−	3.77329i
$229$	1.63328	+	0.942977i	0.107931	+	0.0623137i	0.552994	−	0.833186i	$-0.313485\pi$
$229$	1.63328	+	0.942977i	0.107931	+	0.0623137i	−0.445063	+	0.895499i	$0.646819\pi$
$230$	−3.60129	+	6.23761i	−0.237462	+	0.411296i
$231$	37.9711	+	7.99662i	2.49832	+	0.526139i
$232$	−30.3122	+	17.5008i	−1.99010	+	1.14898i
$233$	−14.3979			−0.943241			−0.471620	−	0.881802i	$-0.656331\pi$
$233$	−14.3979			−0.943241			−0.471620	+	0.881802i	$0.656331\pi$
$234$	26.5563	+	9.70440i	1.73604	+	0.634396i
$235$	−0.0884981			−0.00577298
$236$	26.2816	−	15.1737i	1.71078	−	0.987722i
$237$	−4.66836	+	5.20433i	−0.303242	+	0.338058i
$238$	−12.3514	+	21.3932i	−0.800620	+	1.38671i
$239$	7.36485	+	4.25210i	0.476393	+	0.275045i	0.718912	−	0.695101i	$-0.244640\pi$
$239$	7.36485	+	4.25210i	0.476393	+	0.275045i	−0.242519	+	0.970147i	$0.577974\pi$
$240$	−15.9502	+	5.21562i	−1.02958	+	0.336667i
$241$	−12.2554	+	7.07566i	−0.789440	+	0.455783i	−0.839765	−	0.542950i	$-0.817307\pi$
$241$	−12.2554	+	7.07566i	−0.789440	+	0.455783i	0.0503254	+	0.998733i	$0.483974\pi$
$242$			70.5223i			4.53334i
$243$	−15.5878	+	0.146163i	−0.999956	+	0.00937638i
$244$	25.2359			1.61556
$245$	5.38277	−	3.10774i	0.343892	−	0.198546i
$246$	1.02752	+	3.14233i	0.0655125	+	0.200348i
$247$	−25.0283	+	1.62351i	−1.59251	+	0.103302i
$248$	19.5068	−	33.7867i	1.23868	−	2.14546i
$249$	−18.6063	−	16.6902i	−1.17913	−	1.05770i
$250$	−1.30696	−	2.26372i	−0.0826594	−	0.143170i
$251$	8.57844			0.541467			0.270733	−	0.962654i	$-0.412734\pi$
$251$	8.57844			0.541467			0.270733	+	0.962654i	$0.412734\pi$
$252$	31.1382	+	42.5218i	1.96152	+	2.67862i
$253$			16.9813i			1.06760i
$254$	−36.3408	+	20.9814i	−2.28023	+	1.31649i
$255$	0.927900	−	4.40604i	0.0581073	−	0.275917i
$256$	7.88611	−	13.6591i	0.492882	−	0.853696i
$257$	−9.22785	+	15.9831i	−0.575617	+	0.996998i	0.420357	+	0.907359i	$0.361905\pi$
$257$	−9.22785	+	15.9831i	−0.575617	+	0.996998i	−0.995974	+	0.0896395i	$0.971429\pi$
$258$	−3.76377	+	17.8719i	−0.234322	+	1.11266i
$259$	5.18731	+	8.98469i	0.322324	+	0.558281i
$260$	9.67056	+	14.4941i	0.599743	+	0.898888i
$261$	−12.9773	−	5.71966i	−0.803278	−	0.354038i
$262$			2.41580i			0.149249i
$263$	4.84647	+	8.39433i	0.298846	+	0.517616i	0.975872	−	0.218342i	$-0.0700650\pi$
$263$	4.84647	+	8.39433i	0.298846	+	0.517616i	−0.677026	+	0.735959i	$0.736732\pi$
$264$	−52.7733	+	58.8322i	−3.24797	+	3.62087i
$265$	0.932782	+	0.538542i	0.0573004	+	0.0330824i
$266$	−57.2447	−	33.0503i	−3.50990	−	2.02644i
$267$	11.0600	−	3.61655i	0.676860	−	0.221329i
$268$	−50.7783	+	29.3169i	−3.10178	+	1.79081i
$269$	−29.0023			−1.76830			−0.884151	−	0.467202i	$-0.845262\pi$
$269$	−29.0023			−1.76830			−0.884151	+	0.467202i	$0.845262\pi$
$270$	−11.0331	−	7.92155i	−0.671452	−	0.482090i
$271$		−	0.879845i		−	0.0534468i	−0.999643	−	0.0267234i	$-0.991493\pi$
$271$		−	0.879845i		−	0.0534468i	0.999643	−	0.0267234i	$-0.00850733\pi$
$272$	−12.5935	−	21.8125i	−0.763591	−	1.32258i
$273$	14.0335	−	17.8455i	0.849349	−	1.08006i
$274$	−10.5515	+	18.2757i	−0.637439	+	1.10408i
$275$	−5.33710	−	3.08138i	−0.321839	−	0.185814i
$276$	−15.4007	+	17.1688i	−0.927012	+	1.03344i
$277$	−9.68065	−	16.7674i	−0.581654	−	1.00745i	−0.995284	−	0.0970085i	$-0.969073\pi$
$277$	−9.68065	−	16.7674i	−0.581654	−	1.00745i	0.413630	−	0.910445i	$-0.364261\pi$
$278$		−	22.4329i		−	1.34544i
$279$	15.7145	−	1.71128i	0.940805	−	0.102452i
$280$			26.9163i			1.60856i
$281$	8.50247	−	4.90891i	0.507215	−	0.292841i	−0.224473	−	0.974480i	$-0.572066\pi$
$281$	8.50247	−	4.90891i	0.507215	−	0.292841i	0.731688	+	0.681640i	$0.238733\pi$
$282$	−0.392070	−	0.0825689i	−0.0233474	−	0.00491690i
$283$	8.76830	−	15.1871i	0.521221	−	0.902781i	−0.478474	−	0.878102i	$-0.658810\pi$
$283$	8.76830	−	15.1871i	0.521221	−	0.902781i	0.999695	−	0.0246799i	$-0.00785665\pi$
$284$	−18.8205	−	10.8660i	−1.11679	−	0.644778i
$285$	11.7898	+	2.48291i	0.698370	+	0.147075i
$286$	52.0745	+	25.7239i	3.07923	+	1.52109i
$287$	2.65460			0.156696
$288$	−31.3660	+	3.41569i	−1.84826	+	0.201271i
$289$	−10.2419			−0.602467
$290$	−6.17839	−	10.7013i	−0.362808	−	0.628401i
$291$	−18.6377	−	16.7183i	−1.09256	−	0.980044i
$292$	49.6269	+	28.6521i	2.90419	+	1.67674i
$293$	−12.7264	−	7.34761i	−0.743486	−	0.429252i	0.0798491	−	0.996807i	$-0.474556\pi$
$293$	−12.7264	−	7.34761i	−0.743486	−	0.429252i	−0.823336	+	0.567555i	$0.807889\pi$
$294$	26.7466	−	8.74599i	1.55989	−	0.510076i
$295$	3.13987	+	5.43841i	0.182810	+	0.316637i
$296$	−21.1303			−1.22817
$297$	−31.8655	−	3.16805i	−1.84902	−	0.183829i
$298$	39.7364			2.30187
$299$	8.90745	+	4.40013i	0.515131	+	0.254466i
$300$	−2.60148	−	7.95574i	−0.150197	−	0.459325i
$301$	12.7003	+	7.33250i	0.732031	+	0.422638i
$302$	5.69153	−	9.85802i	0.327511	−	0.567265i
$303$	13.1557	−	14.6661i	0.755777	−	0.842548i
$304$	58.3668	−	33.6981i	3.34756	−	1.93272i
$305$			5.22204i			0.299013i
$306$	8.22168	−	18.6542i	0.470002	−	1.06639i
$307$		−	18.6900i		−	1.06669i	−0.845897	−	0.533346i	$-0.820934\pi$
$307$		−	18.6900i		−	1.06669i	0.845897	−	0.533346i	$-0.179066\pi$
$308$	54.1334	+	93.7618i	3.08454	+	5.34257i
$309$	18.7420	+	3.94702i	1.06620	+	0.224538i
$310$	11.9279	+	6.88657i	0.677458	+	0.391131i
$311$	−5.21390	+	9.03074i	−0.295653	+	0.512087i	−0.975137	−	0.221604i	$-0.928871\pi$
$311$	−5.21390	+	9.03074i	−0.295653	+	0.512087i	0.679483	+	0.733691i	$0.262204\pi$
$312$	17.1858	+	42.9264i	0.972952	+	2.43023i
$313$	−11.3410	−	19.6431i	−0.641030	−	1.11030i	−0.985203	−	0.171390i	$-0.945174\pi$
$313$	−11.3410	−	19.6431i	−0.641030	−	1.11030i	0.344174	−	0.938906i	$-0.388159\pi$
$314$		−	9.47053i		−	0.534453i
$315$	−8.79898	+	6.44339i	−0.495766	+	0.363044i
$316$	−19.5064			−1.09732
$317$	8.53451	−	4.92740i	0.479346	−	0.276750i	−0.240798	−	0.970575i	$-0.577409\pi$
$317$	8.53451	−	4.92740i	0.479346	−	0.276750i	0.720144	+	0.693825i	$0.244076\pi$
$318$	3.63001	+	3.25617i	0.203561	+	0.182597i
$319$	−25.2301	−	14.5666i	−1.41261	−	0.815572i
$320$	−7.02660	−	4.05681i	−0.392799	−	0.226782i
$321$	1.59663	+	4.88274i	0.0891150	+	0.272528i
$322$	13.0918	+	22.6757i	0.729577	+	1.26367i
$323$			18.0835i			1.00619i
$324$	−29.3443	−	32.1025i	−1.63024	−	1.78347i
$325$	−2.99925	+	2.00112i	−0.166369	+	0.111002i
$326$	27.8881	+	48.3036i	1.54458	+	2.67529i
$327$	7.28366	−	2.38172i	0.402788	−	0.131709i
$328$	−2.70335	+	4.68234i	−0.149268	+	0.258539i
$329$	−0.160859	+	0.278616i	−0.00886844	+	0.0153606i
$330$	−20.7698	−	18.6308i	−1.14334	−	1.02559i
$331$	19.1056	−	11.0306i	1.05014	−	0.606299i	0.127452	−	0.991845i	$-0.459320\pi$
$331$	19.1056	−	11.0306i	1.05014	−	0.606299i	0.922689	+	0.385546i	$0.125987\pi$
$332$		−	69.7387i		−	3.82741i
$333$	−5.05829	−	6.90751i	−0.277193	−	0.378529i
$334$	46.6424			2.55216
$335$	−6.06651	−	10.5075i	−0.331449	−	0.574086i
$336$	−12.5718	+	59.6957i	−0.685845	+	3.25667i
$337$	6.75696	−	11.7034i	0.368075	−	0.637525i	−0.621190	−	0.783660i	$-0.713350\pi$
$337$	6.75696	−	11.7034i	0.368075	−	0.637525i	0.989265	+	0.146136i	$0.0466837\pi$
$338$	26.9867	−	20.6500i	1.46789	−	1.12321i
$339$	8.74311	+	1.84128i	0.474861	+	0.100004i
$340$	10.8798	−	6.28145i	0.590040	−	0.340660i
$341$	32.4724			1.75848
$342$	49.9156	+	21.9999i	2.69913	+	1.18962i
$343$			2.85196i			0.153991i
$344$	−25.8670	+	14.9343i	−1.39465	+	0.805204i
$345$	−3.55272	−	3.18684i	−0.191272	−	0.171574i
$346$	−4.67797	−	2.70083i	−0.251489	−	0.145197i
$347$	18.4529	−	31.9613i	0.990602	−	1.71577i	0.376849	−	0.926275i	$-0.377008\pi$
$347$	18.4529	−	31.9613i	0.990602	−	1.71577i	0.613753	−	0.789498i	$-0.289659\pi$
$348$	−12.2980	−	37.6091i	−0.659241	−	2.01606i
$349$	6.39554	−	3.69247i	0.342345	−	0.197653i	−0.318963	−	0.947767i	$-0.603335\pi$
$349$	6.39554	−	3.69247i	0.342345	−	0.197653i	0.661309	+	0.750114i	$0.270001\pi$
$350$	−9.50241			−0.507925
$351$	−9.91867	+	15.8940i	−0.529419	+	0.848360i
$352$	−64.8145			−3.45462
$353$	2.80259	−	1.61808i	0.149167	−	0.0861216i	−0.423559	−	0.905869i	$-0.639219\pi$
$353$	2.80259	−	1.61808i	0.149167	−	0.0861216i	0.572726	+	0.819747i	$0.305886\pi$
$354$	8.83640	+	27.0231i	0.469649	+	1.43626i
$355$	2.24849	−	3.89449i	0.119337	−	0.206698i
$356$	28.1166	+	16.2331i	1.49018	+	0.860353i
$357$	−12.1848	−	10.9299i	−0.644888	−	0.578474i
$358$	−7.44970	+	4.30109i	−0.393729	+	0.227320i
$359$		−	0.845505i		−	0.0446241i	−0.999751	−	0.0223120i	$-0.992897\pi$
$359$		−	0.845505i		−	0.0446241i	0.999751	−	0.0223120i	$-0.00710273\pi$
$360$	−2.40467	−	22.0819i	−0.126737	−	1.16382i
$361$	−29.3885			−1.54676
$362$	7.09469	−	4.09612i	0.372888	−	0.215287i
$363$	−45.7268	−	9.62995i	−2.40004	−	0.505441i
$364$	63.2092	−	4.10021i	3.31306	−	0.214909i
$365$	−5.92894	+	10.2692i	−0.310335	+	0.537516i
$366$	−4.87217	+	23.1350i	−0.254673	+	1.20929i
$367$	−16.7452	−	29.0035i	−0.874091	−	1.51397i	−0.857728	−	0.514104i	$-0.828125\pi$
$367$	−16.7452	−	29.0035i	−0.874091	−	1.51397i	−0.0163626	−	0.999866i	$-0.505209\pi$
$368$	−26.6968			−1.39167
$369$	−2.17781	+	0.237158i	−0.113372	+	0.0123460i
$370$		−	7.45973i		−	0.387813i
$371$	3.39095	−	1.95777i	0.176050	−	0.101642i
$372$	32.8311	+	29.4500i	1.70221	+	1.52691i
$373$	−5.49791	+	9.52266i	−0.284671	+	0.493065i	−0.972529	−	0.232780i	$-0.925218\pi$
$373$	−5.49791	+	9.52266i	−0.284671	+	0.493065i	0.687858	+	0.725845i	$0.258551\pi$
$374$	20.9386	−	36.2667i	1.08271	−	1.87531i
$375$	1.64627	−	0.538321i	0.0850131	−	0.0277988i
$376$	−0.327626	−	0.567465i	−0.0168960	−	0.0292648i
$377$	−14.1784	+	9.45988i	−0.730223	+	0.487209i
$378$	−44.9935	+	20.3365i	−2.31422	+	1.04600i
$379$			24.2400i			1.24512i	0.782571	+	0.622562i	$0.213908\pi$
$379$			24.2400i			1.24512i	−0.782571	+	0.622562i	$0.786092\pi$
$380$	16.8082	+	29.1126i	0.862240	+	1.49344i
$381$	−8.64199	−	26.4286i	−0.442742	−	1.35398i
$382$	10.5278	+	6.07821i	0.538648	+	0.310988i
$383$	−1.46047	−	0.843202i	−0.0746265	−	0.0430856i	0.462222	−	0.886764i	$-0.347052\pi$
$383$	−1.46047	−	0.843202i	−0.0746265	−	0.0430856i	−0.536849	+	0.843678i	$0.680385\pi$
$384$	−0.224436	−	0.201323i	−0.0114532	−	0.0102737i
$385$	−19.4020	+	11.2018i	−0.988818	+	0.570894i
$386$	−67.0297			−3.41172
$387$	−11.0742	−	4.88088i	−0.562935	−	0.248109i
$388$		−	69.8563i		−	3.54642i
$389$	11.6835	+	20.2364i	0.592376	+	1.02602i	0.993911	+	0.110182i	$0.0351432\pi$
$389$	11.6835	+	20.2364i	0.592376	+	1.02602i	−0.401536	+	0.915843i	$0.631523\pi$
$390$	−15.1545	+	6.06717i	−0.767380	+	0.307223i
$391$	3.58159	−	6.20350i	0.181129	−	0.313725i
$392$	39.8548	+	23.0102i	2.01297	+	1.16219i
$393$	−1.56641	−	0.329883i	−0.0790151	−	0.0166404i
$394$	0.904657	+	1.56691i	0.0455759	+	0.0789399i
$395$		−	4.03644i		−	0.203096i
$396$	−52.7870	−	72.0849i	−2.65264	−	3.62240i
$397$			31.2323i			1.56751i	0.621073	+	0.783753i	$0.286697\pi$
$397$			31.2323i			1.56751i	−0.621073	+	0.783753i	$0.713303\pi$
$398$	−46.0982	+	26.6148i	−2.31069	+	1.33408i
$399$	29.2468	−	32.6046i	1.46417	−	1.63227i
$400$	4.84434	−	8.39063i	0.242217	−	0.419532i
$401$	3.68676	+	2.12855i	0.184108	+	0.106295i	0.589221	−	0.807972i	$-0.299435\pi$
$401$	3.68676	+	2.12855i	0.184108	+	0.106295i	−0.405113	+	0.914266i	$0.632768\pi$
$402$	−17.0727	−	52.2111i	−0.851510	−	2.60405i
$403$	8.41415	−	17.0333i	0.419139	−	0.848489i
$404$	54.9704			2.73488
$405$	6.64294	−	6.07218i	0.330090	−	0.301729i
$406$	−44.9207			−2.22938
$407$	−8.79378	−	15.2313i	−0.435891	−	0.754986i
$408$	31.6874	−	10.3616i	1.56876	−	0.512976i
$409$	−19.0629	−	11.0060i	−0.942600	−	0.544210i	−0.0518255	−	0.998656i	$-0.516504\pi$
$409$	−19.0629	−	11.0060i	−0.942600	−	0.544210i	−0.890774	+	0.454446i	$0.849837\pi$
$410$	−1.65303	−	0.954377i	−0.0816373	−	0.0471333i
$411$	−10.4092	−	9.33720i	−0.513448	−	0.460570i
$412$	26.7195	+	46.2795i	1.31637	+	2.28003i
$413$	22.8288			1.12333
$414$	−12.7662	−	17.4333i	−0.627423	−	0.856798i
$415$	14.4310			0.708388
$416$	−16.7945	+	33.9982i	−0.823419	+	1.66690i
$417$	14.5456	+	3.06326i	0.712301	+	0.150009i
$418$	97.0439	+	56.0283i	4.74657	+	2.74044i
$419$	−12.0760	+	20.9163i	−0.589954	+	1.02183i	0.404284	+	0.914633i	$0.367521\pi$
$419$	−12.0760	+	20.9163i	−0.589954	+	1.02183i	−0.994238	+	0.107196i	$0.965813\pi$
$420$	−29.7754	−	6.27062i	−1.45289	−	0.305975i
$421$	−10.0225	+	5.78650i	−0.488467	+	0.282017i	−0.723938	−	0.689865i	$-0.757670\pi$
$421$	−10.0225	+	5.78650i	−0.488467	+	0.282017i	0.235471	+	0.971881i	$0.424337\pi$
$422$		−	48.1319i		−	2.34303i
$423$	0.107076	−	0.242944i	0.00520620	−	0.0118124i
$424$			7.97488i			0.387294i
$425$	1.29981	+	2.25134i	0.0630502	+	0.109206i
$426$	13.5950	−	15.1558i	0.658678	−	0.734301i
$427$	16.4404	+	9.49187i	0.795607	+	0.459344i
$428$	−7.16656	+	12.4128i	−0.346409	+	0.599998i
$429$	−23.7903	+	30.2526i	−1.14861	+	1.46061i
$430$	−5.27234	−	9.13195i	−0.254255	−	0.440382i
$431$			11.7078i			0.563946i	0.959422	+	0.281973i	$0.0909888\pi$
$431$			11.7078i			0.563946i	−0.959422	+	0.281973i	$0.909011\pi$
$432$	4.98060	−	50.0968i	0.239629	−	2.41028i
$433$	7.62497			0.366433			0.183216	−	0.983073i	$-0.441349\pi$
$433$	7.62497			0.366433			0.183216	+	0.983073i	$0.441349\pi$
$434$	43.3616	−	25.0348i	2.08142	−	1.20171i
$435$	7.78242	−	2.54481i	0.373138	−	0.122014i
$436$	18.5165	+	10.6905i	0.886778	+	0.511981i
$437$	16.5996	+	9.58377i	0.794065	+	0.458454i
$438$	−35.8480	+	39.9637i	−1.71288	+	1.90954i
$439$	−13.6599	−	23.6596i	−0.651951	−	1.12921i	−0.982649	−	0.185475i	$-0.940618\pi$
$439$	−13.6599	−	23.6596i	−0.651951	−	1.12921i	0.330698	−	0.943737i	$-0.392716\pi$
$440$		−	45.6299i		−	2.17532i
$441$	2.01862	+	18.5369i	0.0961249	+	0.882708i
$442$	−13.5980	−	20.3806i	−0.646792	−	0.969406i
$443$	6.74417	+	11.6812i	0.320425	+	0.554993i	0.980576	−	0.196141i	$-0.0628409\pi$
$443$	6.74417	+	11.6812i	0.320425	+	0.554993i	−0.660151	+	0.751133i	$0.729508\pi$
$444$	4.92266	−	23.3748i	0.233619	−	1.10932i
$445$	−3.35910	+	5.81813i	−0.159237	+	0.275806i
$446$	8.16806	−	14.1475i	0.386769	−	0.669903i
$447$	−5.42608	+	25.7652i	−0.256645	+	1.21865i
$448$	−25.5439	+	14.7478i	−1.20683	+	0.696766i
$449$			30.7327i			1.45037i	0.688555	+	0.725184i	$0.258245\pi$
$449$			30.7327i			1.45037i	−0.688555	+	0.725184i	$0.741755\pi$
$450$	7.79567	−	0.848932i	0.367492	−	0.0400190i
$451$	−4.50021			−0.211906
$452$	12.4646	+	21.5893i	0.586285	+	1.01547i
$453$	5.61478	+	5.03653i	0.263805	+	0.236637i
$454$	1.14809	−	1.98855i	0.0538824	−	0.0933271i
$455$	0.848451	+	13.0798i	0.0397760	+	0.613191i
$456$	27.7260	+	84.7904i	1.29839	+	3.97068i
$457$	2.64079	−	1.52466i	0.123531	−	0.0713206i	−0.436961	−	0.899480i	$-0.643945\pi$
$457$	2.64079	−	1.52466i	0.123531	−	0.0713206i	0.560492	+	0.828160i	$0.310612\pi$
$458$	−4.92974			−0.230351
$459$	10.9727	+	7.87823i	0.512164	+	0.367724i
$460$		−	13.3160i		−	0.620863i
$461$	27.0821	−	15.6358i	1.26134	−	0.728234i	0.288005	−	0.957629i	$-0.407008\pi$
$461$	27.0821	−	15.6358i	1.26134	−	0.728234i	0.973333	+	0.229395i	$0.0736748\pi$
$462$	−96.4073	+	31.5246i	−4.48527	+	1.46666i
$463$	17.3013	+	9.98890i	0.804059	+	0.464224i	0.844888	−	0.534942i	$-0.179667\pi$
$463$	17.3013	+	9.98890i	0.804059	+	0.464224i	−0.0408295	+	0.999166i	$0.513000\pi$
$464$	22.9006	−	39.6650i	1.06313	−	1.84140i
$465$	−6.09405	+	6.79370i	−0.282605	+	0.315050i
$466$	32.5929	−	18.8175i	1.50984	−	0.871706i
$467$	31.4527			1.45546			0.727730	−	0.685864i	$-0.240575\pi$
$467$	31.4527			1.45546			0.727730	+	0.685864i	$0.240575\pi$
$468$	−51.4898	+	9.01079i	−2.38012	+	0.416524i
$469$	−44.1073			−2.03668
$470$	0.200335	−	0.115663i	0.00924076	−	0.00533516i
$471$	6.14072	+	1.29322i	0.282949	+	0.0595884i
$472$	−23.2480	+	40.2668i	−1.07008	+	1.85343i
$473$	−21.5301	−	12.4304i	−0.989955	−	0.571551i
$474$	3.76601	−	17.8825i	0.172979	−	0.821371i
$475$	−6.02423	+	3.47809i	−0.276411	+	0.159586i
$476$		−	45.6701i		−	2.09328i
$477$	−2.60700	+	1.90907i	−0.119366	+	0.0874105i
$478$	−22.2293			−1.01674
$479$	14.5340	−	8.39124i	0.664077	−	0.383405i	−0.129751	−	0.991547i	$-0.541418\pi$
$479$	14.5340	−	8.39124i	0.664077	−	0.383405i	0.793829	+	0.608141i	$0.208085\pi$
$480$	12.1636	−	13.5601i	0.555191	−	0.618932i
$481$	−10.2681	+	0.666064i	−0.468186	+	0.0303699i
$482$	18.4952	−	32.0346i	0.842434	−	1.45914i
$483$	−16.4907	+	5.39236i	−0.750352	+	0.245361i
$484$	−65.1903	−	112.913i	−2.96319	−	5.13240i
$485$	14.4553			0.656381
$486$	35.0953	−	20.7035i	1.59196	−	0.939129i
$487$		−	0.618958i		−	0.0280477i	−0.999902	−	0.0140238i	$-0.995536\pi$
$487$		−	0.618958i		−	0.0280477i	0.999902	−	0.0140238i	$-0.00446407\pi$
$488$	−33.4846	+	19.3324i	−1.51578	+	0.875135i
$489$	−35.1284	+	11.4868i	−1.58856	+	0.519450i
$490$	−8.12339	+	14.0701i	−0.366977	+	0.635623i
$491$	12.4718	−	21.6018i	0.562844	−	0.974875i	−0.434403	−	0.900719i	$-0.643040\pi$
$491$	12.4718	−	21.6018i	0.562844	−	0.974875i	0.997247	−	0.0741557i	$-0.0236262\pi$
$492$	−4.54991	−	4.08133i	−0.205126	−	0.184001i
$493$	6.14460	+	10.6428i	0.276739	+	0.479326i
$494$	54.5352	−	36.3861i	2.45365	−	1.63709i
$495$	14.9164	−	10.9231i	0.670444	−	0.490959i
$496$			51.0510i			2.29226i
$497$	−8.17395	−	14.1577i	−0.366652	−	0.635060i
$498$	63.9330	+	13.4641i	2.86490	+	0.603341i
$499$	−23.3837	−	13.5006i	−1.04680	−	0.604370i	−0.125048	−	0.992151i	$-0.539908\pi$
$499$	−23.3837	−	13.5006i	−1.04680	−	0.604370i	−0.921752	+	0.387781i	$0.873242\pi$
$500$	4.18514	+	2.41629i	0.187165	+	0.108060i
$501$	−6.36911	+	30.2431i	−0.284551	+	1.35116i
$502$	−19.4192	+	11.2117i	−0.866722	+	0.500402i
$503$	−2.15400			−0.0960420			−0.0480210	−	0.998846i	$-0.515291\pi$
$503$	−2.15400			−0.0960420			−0.0480210	+	0.998846i	$0.515291\pi$
$504$	−73.8906	−	32.5667i	−3.29135	−	1.45064i
$505$			11.3750i			0.506179i
$506$	−22.1938	−	38.4409i	−0.986636	−	1.70890i
$507$	9.70441	+	20.3181i	0.430988	+	0.902358i
$508$	38.7901	−	67.1865i	1.72103	−	2.98092i
$509$	3.67565	+	2.12214i	0.162921	+	0.0940622i	0.579243	−	0.815155i	$-0.303348\pi$
$509$	3.67565	+	2.12214i	0.162921	+	0.0940622i	−0.416323	+	0.909217i	$0.636681\pi$
$510$	3.65801	+	11.1868i	0.161979	+	0.495359i
$511$	21.5535	+	37.3318i	0.953473	+	1.65146i
$512$			41.5755i			1.83739i
$513$	−21.0809	+	29.3613i	−0.930743	+	1.29633i
$514$		−	48.2417i		−	2.12785i
$515$	−9.57656	+	5.52903i	−0.421993	+	0.243638i
$516$	−10.4945	−	32.0938i	−0.461994	−	1.41285i
$517$	0.272696	−	0.472323i	0.0119931	−	0.0207727i
$518$	−23.4853	−	13.5592i	−1.03188	−	0.595758i
$519$	2.39001	−	2.66441i	0.104910	−	0.116954i
$520$	−23.9350	−	11.8235i	−1.04962	−	0.518493i
$521$	34.7429			1.52211			0.761057	−	0.648685i	$-0.224681\pi$
$521$	34.7429			1.52211			0.761057	+	0.648685i	$0.224681\pi$
$522$	36.8525	−	4.01315i	1.61299	−	0.175651i
$523$	21.9550			0.960023			0.480012	−	0.877262i	$-0.340632\pi$
$523$	21.9550			0.960023			0.480012	+	0.877262i	$0.340632\pi$
$524$	−2.23315	−	3.86793i	−0.0975557	−	0.168971i
$525$	1.29757	−	6.16139i	0.0566307	−	0.268905i
$526$	−21.9421	−	12.6683i	−0.956721	−	0.552363i
$527$	−11.8627	−	6.84891i	−0.516746	−	0.298343i
$528$	21.3122	−	101.199i	0.927496	−	4.40412i
$529$	7.70370	+	13.3432i	0.334943	+	0.580139i
$530$	−2.81541			−0.122294
$531$	−18.7285	+	2.03949i	−0.812747	+	0.0885064i
$532$	122.206			5.29829
$533$	−1.16608	+	2.36056i	−0.0505085	+	0.102247i
$534$	−20.3100	+	22.6418i	−0.878901	+	0.979807i
$535$	−2.56858	−	1.48297i	−0.111049	−	0.0641143i
$536$	44.9173	−	77.7990i	1.94013	−	3.36040i
$537$	−1.77157	−	5.41773i	−0.0764487	−	0.233792i
$538$	65.6531	−	37.9048i	2.83051	−	1.63419i
$539$			38.3045i			1.64989i
$540$	24.9876	+	2.48426i	1.07530	+	0.106905i
$541$		−	30.3700i		−	1.30571i	−0.757483	−	0.652854i	$-0.773571\pi$
$541$		−	30.3700i		−	1.30571i	0.757483	−	0.652854i	$-0.226429\pi$
$542$	1.14992	+	1.99172i	0.0493934	+	0.0855519i
$543$	1.68714	+	5.15955i	0.0724022	+	0.221417i
$544$	23.6777	+	13.6703i	1.01517	+	0.586110i
$545$	−2.21217	+	3.83159i	−0.0947589	+	0.164127i
$546$	−8.44462	+	58.7386i	−0.361397	+	2.51378i
$547$	3.69703	+	6.40344i	0.158073	+	0.273791i	0.934174	−	0.356818i	$-0.116138\pi$
$547$	3.69703	+	6.40344i	0.158073	+	0.273791i	−0.776100	+	0.630609i	$0.782805\pi$
$548$		−	39.0149i		−	1.66663i
$549$	−14.3355	−	6.31826i	−0.611825	−	0.269657i
$550$	16.1089			0.686887
$551$	−28.4783	+	16.4420i	−1.21322	+	0.700451i
$552$	7.28216	−	34.5786i	0.309949	−	1.47176i
$553$	−12.7078	−	7.33686i	−0.540392	−	0.311995i
$554$	43.8286	+	25.3044i	1.86210	+	1.07508i
$555$	4.83691	+	1.01864i	0.205316	+	0.0432389i
$556$	20.7369	+	35.9173i	0.879439	+	1.52323i
$557$		−	16.6062i		−	0.703627i	−0.936070	−	0.351813i	$-0.885565\pi$
$557$		−	16.6062i		−	0.703627i	0.936070	−	0.351813i	$-0.114435\pi$
$558$	−33.3368	+	24.4121i	−1.41126	+	1.03345i
$559$	−12.0991	+	8.07260i	−0.511739	+	0.341435i
$560$	−17.6107	−	30.5026i	−0.744186	−	1.28897i
$561$	20.6563	+	18.5290i	0.872108	+	0.782293i
$562$	−12.8315	+	22.2248i	−0.541264	+	0.937496i
$563$	−20.7656	+	35.9670i	−0.875164	+	1.51583i	−0.0185768	+	0.999827i	$0.505914\pi$
$563$	−20.7656	+	35.9670i	−0.875164	+	1.51583i	−0.856588	+	0.516002i	$0.827420\pi$
$564$	0.704068	−	0.230226i	0.0296466	−	0.00969427i
$565$	−4.46745	+	2.57928i	−0.187947	+	0.108511i
$566$			45.8393i			1.92677i
$567$	−7.04228	−	31.9509i	−0.295748	−	1.34181i
$568$	33.2962			1.39708
$569$	1.05781	+	1.83218i	0.0443456	+	0.0768088i	0.887346	−	0.461104i	$-0.152546\pi$
$569$	1.05781	+	1.83218i	0.0443456	+	0.0768088i	−0.843001	+	0.537913i	$0.819213\pi$
$570$	−29.9340	+	9.78824i	−1.25380	+	0.409984i
$571$	10.4408	−	18.0840i	0.436935	−	0.756793i	−0.560517	−	0.828143i	$-0.689397\pi$
$571$	10.4408	−	18.0840i	0.436935	−	0.756793i	0.997451	+	0.0713500i	$0.0227307\pi$
$572$	−107.155	+	6.95087i	−4.48039	+	0.290630i
$573$	−5.37872	+	5.99625i	−0.224699	+	0.250497i
$574$	−6.00928	+	3.46946i	−0.250822	+	0.144812i
$575$	2.75547			0.114911
$576$	19.6384	−	14.3809i	0.818265	−	0.599206i
$577$			6.64046i			0.276446i	0.990401	+	0.138223i	$0.0441391\pi$
$577$			6.64046i			0.276446i	−0.990401	+	0.138223i	$0.955861\pi$
$578$	23.1849	−	13.3858i	0.964365	−	0.556776i
$579$	9.15303	−	43.4622i	0.380387	−	1.80623i
$580$	19.7844	+	11.4225i	0.821502	+	0.474294i
$581$	26.2305	−	45.4326i	1.08822	−	1.88486i
$582$	64.0408	+	13.4868i	2.65457	+	0.559046i
$583$	−5.74850	+	3.31890i	−0.238079	+	0.137455i
$584$	−87.7974			−3.63308
$585$	−1.86459	−	10.6547i	−0.0770913	−	0.440519i
$586$	38.4121			1.58679
$587$	−30.0109	+	17.3268i	−1.23868	+	0.715153i	−0.968825	−	0.247747i	$-0.920310\pi$
$587$	−30.0109	+	17.3268i	−1.23868	+	0.715153i	−0.269857	+	0.962900i	$0.586976\pi$
$588$	−34.7392	+	38.7276i	−1.43262	+	1.59710i
$589$	18.3266	−	31.7426i	0.755133	−	1.30793i
$590$	−14.2156	−	8.20737i	−0.585246	−	0.337892i
$591$	−1.13952	+	0.372617i	−0.0468737	+	0.0153274i
$592$	23.9456	−	13.8250i	0.984158	−	0.568204i
$593$		−	7.20317i		−	0.295799i	−0.989002	−	0.147899i	$-0.952749\pi$
$593$		−	7.20317i		−	0.295799i	0.989002	−	0.147899i	$-0.0472512\pi$
$594$	76.2751	−	34.4753i	3.12961	−	1.41454i
$595$	9.45045			0.387431
$596$	−63.6217	+	36.7320i	−2.60605	+	1.50460i
$597$	−10.9623	−	33.5245i	−0.448658	−	1.37207i
$598$	−25.9148	+	1.68102i	−1.05973	+	0.0687421i
$599$	−22.7142	+	39.3422i	−0.928078	+	1.60748i	−0.141544	+	0.989932i	$0.545207\pi$
$599$	−22.7142	+	39.3422i	−0.928078	+	1.60748i	−0.786534	+	0.617547i	$0.788127\pi$
$600$	9.54642	+	8.56327i	0.389731	+	0.349594i
$601$	−4.07239	−	7.05359i	−0.166116	−	0.287722i	0.770935	−	0.636914i	$-0.219789\pi$
$601$	−4.07239	−	7.05359i	−0.166116	−	0.287722i	−0.937051	+	0.349192i	$0.886456\pi$
$602$	−38.3332			−1.56234
$603$	36.1851	−	3.94048i	1.47357	−	0.160469i
$604$			21.0448i			0.856302i
$605$	23.3649	−	13.4897i	0.949919	−	0.548436i
$606$	−10.6129	+	50.3941i	−0.431118	+	2.04712i
$607$	−8.74616	+	15.1488i	−0.354996	+	0.614871i	−0.987117	−	0.159999i	$-0.948851\pi$
$607$	−8.74616	+	15.1488i	−0.354996	+	0.614871i	0.632122	+	0.774869i	$0.282184\pi$
$608$	−36.5795	+	63.3576i	−1.48350	+	2.56949i
$609$	6.13401	−	29.1267i	0.248563	−	1.18027i
$610$	−6.82500	−	11.8212i	−0.276336	−	0.478628i
$611$	−0.177095	−	0.265428i	−0.00716450	−	0.0107381i
$612$	4.08010	+	37.4672i	0.164928	+	1.51452i
$613$			5.29610i			0.213907i	0.994264	+	0.106954i	$0.0341097\pi$
$613$			5.29610i			0.213907i	−0.994264	+	0.106954i	$0.965890\pi$
$614$	24.4270	+	42.3089i	0.985795	+	1.70745i
$615$	0.844546	−	0.941508i	0.0340554	−	0.0379652i
$616$	−143.655	−	82.9394i	−5.78803	−	3.34172i
$617$	8.54310	+	4.93236i	0.343932	+	0.198569i	0.662010	−	0.749495i	$-0.269704\pi$
$617$	8.54310	+	4.93236i	0.343932	+	0.198569i	−0.318077	+	0.948065i	$0.603037\pi$
$618$	−47.5853	+	15.5601i	−1.91416	+	0.625919i
$619$	−9.15285	+	5.28440i	−0.367884	+	0.212398i	−0.672534	−	0.740067i	$-0.734794\pi$
$619$	−9.15285	+	5.28440i	−0.367884	+	0.212398i	0.304650	+	0.952464i	$0.401461\pi$
$620$	−25.4636			−1.02264
$621$	13.0470	−	5.89708i	0.523559	−	0.236642i
$622$		−	27.2575i		−	1.09292i
$623$	12.2114	+	21.1507i	0.489238	+	0.847385i
$624$	−47.5612	−	37.4016i	−1.90397	−	1.49726i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	51.3456	+	29.6444i	2.05218	+	1.18483i
$627$	−49.5805	+	55.2728i	−1.98005	+	2.20738i
$628$	8.75449	+	15.1632i	0.349342	+	0.605079i
$629$			7.41894i			0.295813i
$630$	11.4972	−	26.0860i	0.458059	−	1.03929i
$631$		−	33.9884i		−	1.35306i	−0.736416	−	0.676529i	$-0.763483\pi$
$631$		−	33.9884i		−	1.35306i	0.736416	−	0.676529i	$-0.236517\pi$
$632$	25.8824	−	14.9432i	1.02955	−	0.594408i
$633$	31.2089	+	6.57251i	1.24044	+	0.261234i
$634$	−12.8798	+	22.3085i	−0.511524	+	0.885985i
$635$	13.9028	+	8.02679i	0.551716	+	0.318534i
$636$	−8.82198	−	1.85789i	−0.349814	−	0.0736699i
$637$	20.0925	+	9.92533i	0.796092	+	0.393256i
$638$	76.1518			3.01488
$639$	7.97065	+	10.8846i	0.315314	+	0.430587i
$640$	0.174071			0.00688078
$641$	−2.29674	−	3.97808i	−0.0907160	−	0.157125i	0.817097	−	0.576501i	$-0.195582\pi$
$641$	−2.29674	−	3.97808i	−0.0907160	−	0.157125i	−0.907813	+	0.419376i	$0.862249\pi$
$642$	−9.99586	−	8.96643i	−0.394505	−	0.353877i
$643$	−8.28480	−	4.78323i	−0.326721	−	0.188632i	0.327664	−	0.944794i	$-0.393739\pi$
$643$	−8.28480	−	4.78323i	−0.326721	−	0.188632i	−0.654384	+	0.756162i	$0.727072\pi$
$644$	−41.9225	−	24.2039i	−1.65198	−	0.953769i
$645$	6.64113	−	2.17161i	0.261494	−	0.0855072i
$646$	−23.6344	−	40.9359i	−0.929882	−	1.61060i
$647$	−33.0237			−1.29829			−0.649147	−	0.760663i	$-0.724874\pi$
$647$	−33.0237			−1.29829			−0.649147	+	0.760663i	$0.724874\pi$
$648$	63.5285	+	20.1161i	2.49563	+	0.790234i
$649$	−38.7005			−1.51913
$650$	4.17410	−	8.44988i	0.163721	−	0.331432i
$651$	10.3115	+	31.5343i	0.404141	+	1.23593i
$652$	−89.3030	−	51.5591i	−3.49738	−	2.01921i
$653$	4.99775	−	8.65636i	0.195577	−	0.338749i	−0.751512	−	0.659719i	$-0.770675\pi$
$653$	4.99775	−	8.65636i	0.195577	−	0.338749i	0.947090	+	0.320969i	$0.104009\pi$
$654$	−13.3754	+	14.9110i	−0.523019	+	0.583066i
$655$	0.800387	−	0.462103i	0.0312737	−	0.0180559i
$656$		−	7.07493i		−	0.276229i
$657$	−21.0175	−	28.7011i	−0.819969	−	1.11974i
$658$		−	0.840945i		−	0.0327835i
$659$	−11.6181	−	20.1231i	−0.452575	−	0.783883i	0.545970	−	0.837805i	$-0.316161\pi$
$659$	−11.6181	−	20.1231i	−0.452575	−	0.783883i	−0.998545	+	0.0539217i	$0.982828\pi$
$660$	50.4767	+	10.6303i	1.96480	+	0.413782i
$661$	−13.3047	−	7.68148i	−0.517494	−	0.298775i	0.218415	−	0.975856i	$-0.429911\pi$
$661$	−13.3047	−	7.68148i	−0.517494	−	0.298775i	−0.735909	+	0.677081i	$0.763245\pi$
$662$	−28.8332	+	49.9406i	−1.12064	+	1.94100i
$663$	15.0717	−	6.03399i	0.585335	−	0.234341i
$664$	53.4244	+	92.5338i	2.07327	+	3.59101i
$665$			25.2879i			0.980622i
$666$	20.4784	+	9.02570i	0.793522	+	0.349739i
$667$	13.0259			0.504366
$668$	−74.6790	+	43.1159i	−2.88942	+	1.66821i
$669$	8.05791	+	7.22806i	0.311537	+	0.279453i
$670$	27.4658	+	15.8574i	1.06110	+	0.612623i
$671$	−27.8705	−	16.0911i	−1.07593	−	0.621189i
$672$	−20.5817	−	62.9420i	−0.793955	−	2.42804i
$673$	5.89215	+	10.2055i	0.227126	+	0.393393i	0.956955	−	0.290236i	$-0.0937338\pi$
$673$	5.89215	+	10.2055i	0.227126	+	0.393393i	−0.729829	+	0.683629i	$0.760400\pi$
$674$			35.3243i			1.36064i
$675$	−0.514064	+	5.17066i	−0.0197863	+	0.199019i
$676$	−24.1197	+	58.0090i	−0.927680	+	2.23111i
$677$	−10.6971	−	18.5280i	−0.411125	−	0.712089i	0.583888	−	0.811834i	$-0.301531\pi$
$677$	−10.6971	−	18.5280i	−0.411125	−	0.712089i	−0.995013	+	0.0997450i	$0.968197\pi$
$678$	−22.1984	+	7.25876i	−0.852526	+	0.278771i
$679$	26.2747	−	45.5092i	1.00833	−	1.74648i
$680$	−9.62400	+	16.6693i	−0.369063	+	0.639237i
$681$	1.13261	+	1.01596i	0.0434015	+	0.0389318i
$682$	−73.5086	+	42.4402i	−2.81479	+	1.62512i
$683$			3.62401i			0.138669i	0.997593	+	0.0693344i	$0.0220876\pi$
$683$			3.62401i			0.138669i	−0.997593	+	0.0693344i	$0.977912\pi$
$684$	−100.256	+	10.9177i	−3.83339	+	0.417448i
$685$	8.07331			0.308465
$686$	−3.72740	−	6.45604i	−0.142313	−	0.246493i
$687$	0.673165	−	3.19646i	0.0256828	−	0.121952i
$688$	19.5423	−	33.8482i	0.745042	−	1.29045i
$689$	0.251382	+	3.87534i	0.00957691	+	0.147639i
$690$	12.2075	+	2.57086i	0.464730	+	0.0978709i
$691$	20.4725	−	11.8198i	0.778812	−	0.449647i	−0.0571970	−	0.998363i	$-0.518216\pi$
$691$	20.4725	−	11.8198i	0.778812	−	0.449647i	0.836009	+	0.548715i	$0.184883\pi$
$692$	9.98650			0.379630
$693$	−7.27606	−	66.8155i	−0.276395	−	2.53811i
$694$			96.4687i			3.66190i
$695$	−7.43232	+	4.29105i	−0.281924	+	0.162769i
$696$	45.1288	+	40.4811i	1.71060	+	1.53443i
$697$	1.64399	+	0.949159i	0.0622706	+	0.0359519i
$698$	−9.65181	+	16.7174i	−0.365326	+	0.632764i
$699$	7.75072	+	23.7029i	0.293159	+	0.896527i
$700$	15.2143	−	8.78397i	0.575045	−	0.332003i
$701$	−26.1353			−0.987118			−0.493559	−	0.869712i	$-0.664304\pi$
$701$	−26.1353			−0.987118			−0.493559	+	0.869712i	$0.664304\pi$
$702$	1.68025	−	48.9430i	0.0634170	−	1.84723i
$703$	−19.8519			−0.748728
$704$	43.3032	−	25.0011i	1.63205	−	0.942264i
$705$	0.0476404	+	0.145692i	0.00179424	+	0.00548707i
$706$	−4.22953	+	7.32576i	−0.159180	+	0.275708i
$707$	35.8114	+	20.6757i	1.34683	+	0.777592i
$708$	−39.1279	−	35.0983i	−1.47052	−	1.31907i
$709$	21.0571	−	12.1573i	0.790816	−	0.456578i	−0.0494339	−	0.998777i	$-0.515742\pi$
$709$	21.0571	−	12.1573i	0.790816	−	0.456578i	0.840250	+	0.542200i	$0.182408\pi$
$710$			11.7547i			0.441147i
$711$	11.0808	+	4.88378i	0.415563	+	0.183156i
$712$	−49.7425			−1.86418
$713$	−12.5738	+	7.25949i	−0.470892	+	0.271870i
$714$	41.8680	+	8.81729i	1.56687	+	0.329979i
$715$	−1.43833	−	22.1735i	−0.0537907	−	0.829242i
$716$	7.95179	−	13.7729i	0.297172	−	0.514718i
$717$	3.03545	−	14.4135i	0.113361	−	0.538283i
$718$	1.10504	+	1.91399i	0.0412398	+	0.0714294i
$719$	24.1353			0.900094			0.450047	−	0.893005i	$-0.351407\pi$
$719$	24.1353			0.900094			0.450047	+	0.893005i	$0.351407\pi$
$720$	17.1726	+	23.4507i	0.639987	+	0.873954i
$721$			40.1995i			1.49711i
$722$	66.5273	−	38.4095i	2.47589	−	1.42945i
$723$	18.2458	+	16.3667i	0.678569	+	0.608686i
$724$	−7.57285	+	13.1166i	−0.281443	+	0.487473i
$725$	−2.36365	+	4.09396i	−0.0877837	+	0.152046i
$726$	116.099	−	37.9636i	4.30883	−	1.40896i
$727$	−4.56624	−	7.90895i	−0.169352	−	0.293327i	0.768840	−	0.639441i	$-0.220834\pi$
$727$	−4.56624	−	7.90895i	−0.169352	−	0.293327i	−0.938192	+	0.346114i	$0.887501\pi$
$728$	−80.7290	+	53.8628i	−2.99201	+	1.99629i
$729$	8.63185	+	25.5830i	0.319698	+	0.947519i
$730$		−	30.9956i		−	1.14720i
$731$	5.24350	+	9.08202i	0.193938	+	0.335911i
$732$	−13.5850	−	41.5452i	−0.502117	−	1.53555i
$733$	2.50974	+	1.44900i	0.0926995	+	0.0535201i	0.545633	−	0.838024i	$-0.316289\pi$
$733$	2.50974	+	1.44900i	0.0926995	+	0.0535201i	−0.452934	+	0.891544i	$0.649623\pi$
$734$	75.8128	+	43.7705i	2.79830	+	1.61560i
$735$	−8.01385	−	7.18853i	−0.295595	−	0.265153i
$736$	25.0971	−	14.4898i	0.925091	−	0.534102i
$737$	74.7727			2.75429
$738$	4.61999	−	3.38317i	0.170064	−	0.124536i
$739$			26.2975i			0.967370i	0.875242	+	0.483685i	$0.160702\pi$
$739$			26.2975i			0.967370i	−0.875242	+	0.483685i	$0.839298\pi$
$740$	6.89573	+	11.9437i	0.253492	+	0.439061i
$741$	16.1460	+	40.3293i	0.593138	+	1.48154i
$742$	−5.11745	+	8.86368i	−0.187867	+	0.325396i
$743$	−42.4713	−	24.5208i	−1.55812	−	0.899582i	−0.997437	−	0.0715523i	$-0.977205\pi$
$743$	−42.4713	−	24.5208i	−1.55812	−	0.899582i	−0.560685	−	0.828030i	$-0.689462\pi$
$744$	−66.1230	−	13.9253i	−2.42419	−	0.510527i
$745$	−7.60091	−	13.1652i	−0.278476	−	0.482334i
$746$		−	28.7422i		−	1.05233i
$747$	−17.4603	+	39.6158i	−0.638840	+	1.44946i
$748$			77.4220i			2.83083i
$749$	−9.33757	+	5.39105i	−0.341187	+	0.196985i
$750$	−3.02314	+	3.37022i	−0.110389	+	0.123063i
$751$	−5.50119	+	9.52833i	−0.200741	+	0.347694i	−0.948767	−	0.315975i	$-0.897668\pi$
$751$	−5.50119	+	9.52833i	−0.200741	+	0.347694i	0.748026	+	0.663669i	$0.231002\pi$
$752$	0.742555	+	0.428714i	0.0270782	+	0.0156336i
$753$	−4.61796	−	14.1224i	−0.168288	−	0.514651i
$754$	19.7322	−	39.9451i	0.718604	−	1.45471i
$755$	−4.35478			−0.158487
$756$	53.2400	−	74.1523i	1.93632	−	2.69689i
$757$	−44.9925			−1.63528			−0.817639	−	0.575731i	$-0.804718\pi$
$757$	−44.9925			−1.63528			−0.817639	+	0.575731i	$0.804718\pi$
$758$	−31.6807	−	54.8725i	−1.15069	−	1.99306i
$759$	27.9558	−	9.14138i	1.01473	−	0.331811i
$760$	−44.6042	−	25.7523i	−1.61797	−	0.934133i
$761$	1.61915	+	0.934817i	0.0586941	+	0.0338871i	0.529060	−	0.848584i	$-0.322545\pi$
$761$	1.61915	+	0.934817i	0.0586941	+	0.0338871i	−0.470366	+	0.882472i	$0.655878\pi$
$762$	54.1041	+	48.5322i	1.95999	+	1.75814i
$763$	8.04192	+	13.9290i	0.291137	+	0.504264i
$764$	−22.4746			−0.813103
$765$	−7.75304	+	0.844289i	−0.280312	+	0.0305253i
$766$	4.40813			0.159272
$767$	−10.0279	+	20.3002i	−0.362088	+	0.732997i
$768$	−26.7319	−	5.62967i	−0.964605	−	0.203143i
$769$	−33.3273	−	19.2415i	−1.20181	−	0.693867i	−0.240854	−	0.970561i	$-0.577428\pi$
$769$	−33.3273	−	19.2415i	−1.20181	−	0.693867i	−0.960958	+	0.276695i	$0.910761\pi$
$770$	29.2805	−	50.7153i	1.05520	−	1.82765i
$771$	31.2801	+	6.58750i	1.12652	+	0.237243i
$772$	107.321	−	61.9618i	3.86257	−	2.23005i
$773$		−	3.60526i		−	0.129672i	−0.997896	−	0.0648360i	$-0.979348\pi$
$773$		−	3.60526i		−	0.129672i	0.997896	−	0.0648360i	$-0.0206524\pi$
$774$	31.4481	−	3.42463i	1.13038	−	0.123096i
$775$		−	5.26915i		−	0.189273i
$776$	53.5145	+	92.6898i	1.92106	+	3.32737i
$777$	11.9988	−	13.3764i	0.430454	−	0.479875i
$778$	−52.8963	−	30.5397i	−1.89642	−	1.09490i
$779$	−2.53979	+	4.39905i	−0.0909976	+	0.157612i
$780$	18.6554	−	23.7229i	0.667971	−	0.849415i
$781$	13.8569	+	24.0008i	0.495838	+	0.858816i
$782$			18.7240i			0.669569i
$783$	−2.43014	+	24.4433i	−0.0868460	+	0.873531i
$784$	−60.2198			−2.15071
$785$	−3.13771	+	1.81156i	−0.111990	+	0.0646572i
$786$	3.97707	−	1.30048i	0.141857	−	0.0463865i
$787$	32.3184	+	18.6590i	1.15203	+	0.665123i	0.949380	−	0.314130i	$-0.101713\pi$
$787$	32.3184	+	18.6590i	1.15203	+	0.665123i	0.202646	+	0.979252i	$0.435046\pi$
$788$	−2.89688	−	1.67252i	−0.103197	−	0.0595809i
$789$	11.2104	−	12.4974i	0.399100	−	0.444921i
$790$	5.27547	+	9.13738i	0.187693	+	0.325094i
$791$			18.7530i			0.666779i
$792$	125.263	+	55.2086i	4.45102	+	1.96175i
$793$	−15.6622	+	10.4499i	−0.556182	+	0.371087i
$794$	−40.8194	−	70.7013i	−1.44863	−	2.50910i
$795$	0.384450	−	1.82552i	0.0136350	−	0.0647446i
$796$	49.2051	−	85.2257i	1.74403	−	3.02074i
$797$	20.1585	−	34.9156i	0.714051	−	1.23677i	−0.249274	−	0.968433i	$-0.580192\pi$
$797$	20.1585	−	34.9156i	0.714051	−	1.23677i	0.963324	−	0.268339i	$-0.0864748\pi$
$798$	−23.5936	+	112.032i	−0.835206	+	3.96589i
$799$	−0.199239	+	0.115031i	−0.00704859	+	0.00406950i
$800$			10.5171i			0.371837i
$801$	−11.9076	−	16.2609i	−0.420736	−	0.574549i
$802$	−11.1277			−0.392934
$803$	−36.5386	−	63.2867i	−1.28942	−	2.23334i
$804$	75.5986	+	67.8130i	2.66616	+	2.39158i
$805$	5.00849	−	8.67496i	0.176526	−	0.305752i
$806$	3.21453	+	49.5556i	0.113227	+	1.74552i
$807$	15.6126	+	47.7457i	0.549588	+	1.68073i
$808$	−72.9382	+	42.1109i	−2.56596	+	1.48146i
$809$	10.7012			0.376233			0.188116	−	0.982147i	$-0.439762\pi$
$809$	10.7012			0.376233			0.188116	+	0.982147i	$0.439762\pi$
$810$	−7.10168	+	22.4278i	−0.249528	+	0.788032i
$811$			23.4695i			0.824127i	0.911155	+	0.412063i	$0.135192\pi$
$811$			23.4695i			0.824127i	−0.911155	+	0.412063i	$0.864808\pi$
$812$	71.9224	−	41.5244i	2.52398	−	1.45722i
$813$	−1.44846	+	0.473639i	−0.0507998	+	0.0166113i
$814$	39.8133	+	22.9862i	1.39546	+	0.805667i
$815$	10.6691	−	18.4794i	0.373721	−	0.647304i
$816$	−29.1300	+	32.4744i	−1.01975	+	1.13683i
$817$	−24.3020	+	14.0308i	−0.850220	+	0.490875i
$818$	57.5375			2.01175
$819$	−36.9332	−	13.4964i	−1.29055	−	0.471602i
$820$	3.52888			0.123234
$821$	−16.7724	+	9.68355i	−0.585361	+	0.337958i	−0.763261	−	0.646090i	$-0.776403\pi$
$821$	−16.7724	+	9.68355i	−0.585361	+	0.337958i	0.177900	+	0.984049i	$0.443070\pi$
$822$	35.7669	+	7.53241i	1.24751	+	0.262723i
$823$	−4.10145	+	7.10391i	−0.142967	+	0.247627i	−0.928613	−	0.371050i	$-0.878998\pi$
$823$	−4.10145	+	7.10391i	−0.142967	+	0.247627i	0.785645	+	0.618677i	$0.212331\pi$
$824$	−70.9062	−	40.9377i	−2.47013	−	1.42613i
$825$	−2.19971	+	10.4451i	−0.0765840	+	0.363651i
$826$	−51.6780	+	29.8363i	−1.79811	+	1.03814i
$827$		−	42.2668i		−	1.46976i	−0.678196	−	0.734881i	$-0.737238\pi$
$827$		−	42.2668i		−	1.46976i	0.678196	−	0.734881i	$-0.262762\pi$
$828$	36.5551	+	16.1114i	1.27038	+	0.559908i
$829$	−7.14490			−0.248153			−0.124076	−	0.992273i	$-0.539597\pi$
$829$	−7.14490			−0.248153			−0.124076	+	0.992273i	$0.539597\pi$
$830$	−32.6677	+	18.8607i	−1.13391	+	0.654664i
$831$	−22.3923	+	24.9632i	−0.776782	+	0.865964i
$832$	−1.89365	−	29.1927i	−0.0656505	−	1.01207i
$833$	8.07897	−	13.9932i	0.279920	−	0.484835i
$834$	−36.9307	+	12.0761i	−1.27881	+	0.418162i
$835$	−8.92193	−	15.4532i	−0.308756	−	0.534781i
$836$	−207.169			−7.16509
$837$	−11.2767	−	24.9492i	−0.389780	−	0.862370i
$838$		−	63.1317i		−	2.18085i
$839$	19.6736	−	11.3586i	0.679209	−	0.392142i	−0.120348	−	0.992732i	$-0.538401\pi$
$839$	19.6736	−	11.3586i	0.679209	−	0.392142i	0.799557	+	0.600590i	$0.205068\pi$
$840$	44.3116	−	14.4896i	1.52890	−	0.499940i
$841$	3.32633	−	5.76137i	0.114701	−	0.198668i
$842$	15.1254	−	26.1980i	0.521257	−	0.902844i
$843$	−12.6585	−	11.3548i	−0.435980	−	0.391081i
$844$	44.4928	+	77.0638i	1.53151	+	2.65265i
$845$	−12.0037	−	4.99105i	−0.412941	−	0.171698i
$846$	0.0751288	+	0.689902i	0.00258298	+	0.0237193i
$847$		−	98.0788i		−	3.37003i
$848$	−5.21776	−	9.03742i	−0.179178	−	0.310346i
$849$	−29.7223	−	6.25944i	−1.02007	−	0.214823i
$850$	−5.88483	−	3.39761i	−0.201848	−	0.116537i
$851$	6.81015	+	3.93184i	0.233449	+	0.134782i
$852$	−7.75693	+	36.8330i	−0.265748	+	1.26188i
$853$	26.9717	−	15.5721i	0.923495	−	0.533180i	0.0387467	−	0.999249i	$-0.487663\pi$
$853$	26.9717	−	15.5721i	0.923495	−	0.533180i	0.884748	+	0.466069i	$0.154330\pi$
$854$	−49.6220			−1.69803
$855$	−2.25918	−	20.7459i	−0.0772624	−	0.709495i
$856$		−	21.9602i		−	0.750584i
$857$	11.0565	+	19.1505i	0.377684	+	0.654169i	0.990725	−	0.135883i	$-0.0433871\pi$
$857$	11.0565	+	19.1505i	0.377684	+	0.654169i	−0.613041	+	0.790051i	$0.710054\pi$
$858$	14.3157	−	99.5765i	0.488731	−	3.39949i
$859$	6.76817	−	11.7228i	0.230927	−	0.399977i	−0.727154	−	0.686474i	$-0.759158\pi$
$859$	6.76817	−	11.7228i	0.230927	−	0.399977i	0.958081	+	0.286497i	$0.0924909\pi$
$860$	16.8830	+	9.74742i	0.575707	+	0.332384i
$861$	−1.42903	−	4.37019i	−0.0487012	−	0.148936i
$862$	−15.3017	−	26.5032i	−0.521176	−	0.902704i
$863$		−	33.2446i		−	1.13166i	−0.824522	−	0.565830i	$-0.808556\pi$
$863$		−	33.2446i		−	1.13166i	0.824522	−	0.565830i	$-0.191444\pi$
$864$	22.5081	+	49.7982i	0.765742	+	1.69417i
$865$			2.06649i			0.0702629i
$866$	−17.2608	+	9.96553i	−0.586546	+	0.338643i
$867$	5.51346	+	16.8610i	0.187247	+	0.572630i
$868$	−46.2840	+	80.1663i	−1.57098	+	2.72102i
$869$	21.5429	+	12.4378i	0.730793	+	0.421923i
$870$	−14.2913	+	15.9320i	−0.484519	+	0.540147i
$871$	19.3749	−	39.2217i	0.656492	−	1.32898i
$872$	−32.7584			−1.10934
$873$	−17.4898	+	39.6826i	−0.591939	+	1.34305i
$874$	−50.1024			−1.69474
$875$	1.81766	+	3.14827i	0.0614480	+	0.106431i
$876$	20.4539	−	97.1233i	0.691074	−	3.28149i
$877$	48.2100	+	27.8340i	1.62794	+	0.939889i	0.984708	+	0.174213i	$0.0557382\pi$
$877$	48.2100	+	27.8340i	1.62794	+	0.939889i	0.643227	+	0.765675i	$0.277595\pi$
$878$	61.8443	+	35.7058i	2.08715	+	1.20501i
$879$	−5.24525	+	24.9065i	−0.176918	+	0.840077i
$880$	29.8544	+	51.7094i	1.00639	+	1.74312i
$881$	34.8543			1.17427			0.587135	−	0.809489i	$-0.300256\pi$
$881$	34.8543			1.17427			0.587135	+	0.809489i	$0.300256\pi$
$882$	−28.7965	−	39.3240i	−0.969630	−	1.32411i
$883$	25.4385			0.856074			0.428037	−	0.903761i	$-0.359205\pi$
$883$	25.4385			0.856074			0.428037	+	0.903761i	$0.359205\pi$
$884$	40.6114	+	20.0613i	1.36591	+	0.674736i
$885$	7.26285	−	8.09669i	0.244138	−	0.272167i
$886$	−30.5338	−	17.6287i	−1.02580	−	0.592249i
$887$	22.7848	−	39.4644i	0.765038	−	1.32508i	−0.175189	−	0.984535i	$-0.556054\pi$
$887$	22.7848	−	39.4644i	0.765038	−	1.32508i	0.940227	−	0.340549i	$-0.110613\pi$
$888$	11.3749	+	34.7862i	0.381716	+	1.16735i
$889$	50.5410	−	29.1799i	1.69509	−	0.978662i
$890$		−	17.5608i		−	0.588640i
$891$	11.9384	+	54.1647i	0.399952	+	1.81459i
$892$			30.2020i			1.01124i
$893$	−0.307804	−	0.533133i	−0.0103003	−	0.0178406i
$894$	−21.3909	−	65.4168i	−0.715420	−	2.18787i
$895$	2.85001	+	1.64545i	0.0952654	+	0.0550015i
$896$	0.316402	−	0.548024i	0.0105702	−	0.0183082i
$897$	2.44874	−	17.0328i	0.0817609	−	0.568708i
$898$	−40.1665	−	69.5704i	−1.34037	−	2.32159i
$899$		−	24.9088i		−	0.830756i
$900$	−11.6969	+	8.56549i	−0.389896	+	0.285516i
$901$	2.80002			0.0932821
$902$	10.1872	−	5.88159i	0.339197	−	0.195836i
$903$	5.23447	−	24.8553i	0.174192	−	0.827134i
$904$	−33.0776	−	19.0974i	−1.10014	−	0.635169i
$905$	−2.71419	−	1.56704i	−0.0902229	−	0.0520902i
$906$	−19.2928	−	4.06302i	−0.640962	−	0.134985i
$907$	2.42779	+	4.20505i	0.0806133	+	0.139626i	0.903514	−	0.428560i	$-0.140979\pi$
$907$	2.42779	+	4.20505i	0.0806133	+	0.139626i	−0.822900	+	0.568186i	$0.807645\pi$
$908$			4.24514i			0.140880i
$909$	−31.2265	−	13.7628i	−1.03572	−	0.456484i
$910$	−19.0154	−	28.5002i	−0.630356	−	0.944771i
$911$	4.89229	+	8.47370i	0.162089	+	0.280746i	0.935618	−	0.353015i	$-0.114844\pi$
$911$	4.89229	+	8.47370i	0.162089	+	0.280746i	−0.773529	+	0.633761i	$0.781510\pi$
$912$	−86.8963	−	77.9472i	−2.87742	−	2.58109i
$913$	−44.4672	+	77.0194i	−1.47165	+	2.54897i
$914$	−3.98534	+	6.90281i	−0.131823	+	0.228325i
$915$	8.59690	−	2.81114i	0.284205	−	0.0929333i
$916$	7.89298	−	4.55701i	0.260791	−	0.150568i
$917$		−	3.35978i		−	0.110950i
$918$	−35.1358	−	3.49318i	−1.15965	−	0.115292i
$919$	−12.6553			−0.417461			−0.208731	−	0.977973i	$-0.566933\pi$
$919$	−12.6553			−0.417461			−0.208731	+	0.977973i	$0.566933\pi$
$920$	10.2009	+	17.6685i	0.336315	+	0.582514i
$921$	−30.7688	+	10.0612i	−1.01386	+	0.331528i
$922$	−40.8709	+	70.7904i	−1.34601	+	2.33136i
$923$	16.1801	−	1.04956i	0.532573	−	0.0345466i
$924$	125.216	−	139.592i	4.11931	−	4.59225i
$925$	−2.47151	+	1.42692i	−0.0812626	+	0.0469170i
$926$	−52.2204			−1.71607
$927$	−3.59136	−	32.9792i	−0.117956	−	1.08318i
$928$			49.7176i			1.63206i
$929$	16.3696	−	9.45102i	0.537071	−	0.310078i	−0.206820	−	0.978379i	$-0.566312\pi$
$929$	16.3696	−	9.45102i	0.537071	−	0.310078i	0.743891	+	0.668301i	$0.232978\pi$
$930$	4.91613	−	23.3437i	0.161206	−	0.765471i
$931$	37.4435	+	21.6180i	1.22716	+	0.708502i
$932$	−34.7896	+	60.2574i	−1.13957	+	1.97380i
$933$	17.6738	+	3.72206i	0.578615	+	0.121855i
$934$	−71.2003	+	41.1075i	−2.32974	+	1.34508i
$935$	−16.0208			−0.523938
$936$	61.4171	−	51.4006i	2.00748	−	1.68008i
$937$	46.6926			1.52538			0.762690	−	0.646764i	$-0.223878\pi$
$937$	46.6926			1.52538			0.762690	+	0.646764i	$0.223878\pi$
$938$	99.8466	−	57.6465i	3.26011	−	1.88222i
$939$	−26.2329	+	29.2446i	−0.856077	+	0.954363i
$940$	−0.213837	+	0.370377i	−0.00697459	+	0.0120804i
$941$	1.71877	+	0.992332i	0.0560303	+	0.0323491i	0.527753	−	0.849398i	$-0.323034\pi$
$941$	1.71877	+	0.992332i	0.0560303	+	0.0323491i	−0.471723	+	0.881747i	$0.656368\pi$
$942$	−15.5911	+	5.09819i	−0.507984	+	0.166108i
$943$	1.74254	−	1.00606i	0.0567451	−	0.0327618i
$944$		−	60.8423i		−	1.98025i
$945$	15.3443	+	11.0169i	0.499149	+	0.358380i
$946$	64.9842			2.11282
$947$	48.7544	−	28.1484i	1.58431	−	0.914699i	0.590085	−	0.807341i	$-0.299094\pi$
$947$	48.7544	−	28.1484i	1.58431	−	0.914699i	0.994220	−	0.107358i	$-0.0342390\pi$
$948$	10.5007	+	32.1129i	0.341048	+	1.04298i
$949$	−42.6645	+	2.76753i	−1.38495	+	0.0898379i
$950$	9.09145	−	15.7469i	0.294966	−	0.510895i
$951$	−12.7061	−	11.3976i	−0.412025	−	0.369592i
$952$	34.9862	+	60.5979i	1.13391	+	1.96399i
$953$	17.5769			0.569373			0.284687	−	0.958621i	$-0.408110\pi$
$953$	17.5769			0.569373			0.284687	+	0.958621i	$0.408110\pi$
$954$	3.40643	−	7.72885i	0.110287	−	0.250231i
$955$		−	4.65065i		−	0.150491i
$956$	35.5912	−	20.5486i	1.15110	−	0.664589i
$957$	−10.3987	+	49.3770i	−0.336141	+	1.59613i
$958$	−21.9340	+	37.9908i	−0.708656	+	1.22743i
$959$	14.6745	−	25.4170i	0.473864	−	0.820756i
$960$	−2.89604	+	13.7516i	−0.0934693	+	0.443829i
$961$	−1.61804	−	2.80252i	−0.0521947	−	0.0904040i
$962$	22.3736	−	14.9278i	0.721355	−	0.481292i
$963$	7.17881	−	5.25696i	0.231334	−	0.169403i
$964$			68.3874i			2.20261i
$965$	12.8217	+	22.2078i	0.412744	+	0.714894i
$966$	30.2827	−	33.7595i	0.974330	−	1.08619i
$967$	−15.6472	−	9.03392i	−0.503180	−	0.290511i	0.226846	−	0.973931i	$-0.427159\pi$
$967$	−15.6472	−	9.03392i	−0.503180	−	0.290511i	−0.730026	+	0.683420i	$0.760492\pi$
$968$	172.997	+	99.8800i	5.56034	+	3.21026i
$969$	29.7703	−	9.73472i	0.956360	−	0.312724i
$970$	−32.7227	+	18.8925i	−1.05066	+	0.606601i
$971$	−16.5151			−0.529995			−0.264997	−	0.964249i	$-0.585371\pi$
$971$	−16.5151			−0.529995			−0.264997	+	0.964249i	$0.585371\pi$
$972$	−37.0529	+	65.5901i	−1.18847	+	2.10380i
$973$			31.1986i			1.00018i
$974$	0.808954	+	1.40115i	0.0259206	+	0.0448957i
$975$	4.90895	+	3.86034i	0.157212	+	0.123630i
$976$	25.2973	−	43.8162i	0.809747	−	1.40252i
$977$	36.0683	+	20.8241i	1.15393	+	0.666221i	0.949841	−	0.312732i	$-0.101244\pi$
$977$	36.0683	+	20.8241i	1.15393	+	0.666221i	0.204087	+	0.978953i	$0.434578\pi$
$978$	64.5081	−	71.9142i	2.06274	−	2.29956i
$979$	−20.7013	−	35.8557i	−0.661616	−	1.14595i
$980$		−	30.0368i		−	0.959491i
$981$	−7.84190	−	10.7088i	−0.250373	−	0.341904i
$982$			65.2005i			2.08063i
$983$	44.3790	−	25.6222i	1.41547	−	0.817222i	0.419573	−	0.907722i	$-0.362180\pi$
$983$	44.3790	−	25.6222i	1.41547	−	0.817222i	0.995896	+	0.0904998i	$0.0288465\pi$
$984$	9.16368	+	1.92985i	0.292127	+	0.0615212i
$985$	0.346092	−	0.599449i	0.0110274	−	0.0191000i
$986$	−27.8193	−	16.0615i	−0.885948	−	0.511503i
$987$	0.545271	+	0.114833i	0.0173562	+	0.00365516i
$988$	−53.6809	+	108.670i	−1.70782	+	3.45724i
$989$	11.1157			0.353458
$990$	−19.4906	+	44.2222i	−0.619451	+	1.40547i
$991$	−38.6466			−1.22765			−0.613825	−	0.789442i	$-0.710370\pi$
$991$	−38.6466			−1.22765			−0.613825	+	0.789442i	$0.710370\pi$
$992$	−27.7082	−	47.9920i	−0.879735	−	1.52375i
$993$	−28.4444	−	25.5150i	−0.902656	−	0.809695i
$994$	37.0071	+	21.3661i	1.17379	+	0.677690i
$995$	17.6356	+	10.1819i	0.559088	+	0.322789i
$996$	−114.809	+	37.5419i	−3.63786	+	1.18956i
$997$	−13.6860	−	23.7049i	−0.433441	−	0.750742i	0.563726	−	0.825962i	$-0.309367\pi$
$997$	−13.6860	−	23.7049i	−0.433441	−	0.750742i	−0.997167	+	0.0752200i	$0.976034\pi$
$998$	70.5790			2.23414
$999$	−8.64866	+	12.0458i	−0.273631	+	0.381112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.571.3	yes	108
9.7	even	3	inner	585.2.bt.b.376.52	yes	108
13.12	even	2	inner	585.2.bt.b.571.52	yes	108
117.25	even	6	inner	585.2.bt.b.376.3	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.3	✓	108	117.25	even	6	inner
585.2.bt.b.376.52	yes	108	9.7	even	3	inner
585.2.bt.b.571.3	yes	108	1.1	even	1	trivial
585.2.bt.b.571.52	yes	108	13.12	even	2	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.26372 + 1.30696i) q^{2} +(-0.538321 - 1.64627i) q^{3} +(2.41629 - 4.18514i) q^{4} +(0.866025 + 0.500000i) q^{5} +(3.37022 + 3.02314i) q^{6} +(3.14827 - 1.81766i) q^{7} +7.40414i q^{8} +(-2.42042 + 1.77245i) q^{9} +O(q^{10})\)	\(q+(-2.26372 + 1.30696i) q^{2} +(-0.538321 - 1.64627i) q^{3} +(2.41629 - 4.18514i) q^{4} +(0.866025 + 0.500000i) q^{5} +(3.37022 + 3.02314i) q^{6} +(3.14827 - 1.81766i) q^{7} +7.40414i q^{8} +(-2.42042 + 1.77245i) q^{9} -2.61392 q^{10} +(-5.33710 + 3.08138i) q^{11} +(-8.19061 - 1.72492i) q^{12} +(0.233392 + 3.59799i) q^{13} +(-4.75121 + 8.22933i) q^{14} +(0.356936 - 1.69487i) q^{15} +(-4.84434 - 8.39063i) q^{16} +2.59963 q^{17} +(3.16264 - 7.17572i) q^{18} +6.95618i q^{19} +(4.18514 - 2.41629i) q^{20} +(-4.68714 - 4.20443i) q^{21} +(8.05447 - 13.9508i) q^{22} +(1.37773 - 2.38631i) q^{23} +(12.1892 - 3.98581i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-5.23076 - 7.83981i) q^{26} +(4.22089 + 3.03052i) q^{27} -17.5679i q^{28} +(2.36365 + 4.09396i) q^{29} +(1.40713 + 4.30322i) q^{30} +(-4.56322 - 2.63457i) q^{31} +(9.10811 + 5.25857i) q^{32} +(7.94585 + 7.12754i) q^{33} +(-5.88483 + 3.39761i) q^{34} +3.63531 q^{35} +(1.56949 + 14.4125i) q^{36} +2.85385i q^{37} +(-9.09145 - 15.7469i) q^{38} +(5.79763 - 2.32110i) q^{39} +(-3.70207 + 6.41217i) q^{40} +(0.632395 + 0.365113i) q^{41} +(16.1054 + 3.39175i) q^{42} +(2.01702 + 3.49359i) q^{43} +29.7820i q^{44} +(-2.98237 + 0.324773i) q^{45} +7.20258i q^{46} +(-0.0766416 + 0.0442490i) q^{47} +(-11.2055 + 12.4919i) q^{48} +(3.10774 - 5.38277i) q^{49} +(-2.26372 - 1.30696i) q^{50} +(-1.39943 - 4.27969i) q^{51} +(15.6220 + 7.71701i) q^{52} +1.07708 q^{53} +(-13.5157 - 1.34372i) q^{54} -6.16275 q^{55} +(13.4582 + 23.3102i) q^{56} +(11.4518 - 3.74466i) q^{57} +(-10.7013 - 6.17839i) q^{58} +(5.43841 + 3.13987i) q^{59} +(-6.23082 - 5.58913i) q^{60} +(2.61102 + 4.52242i) q^{61} +13.7731 q^{62} +(-4.39844 + 9.97963i) q^{63} -8.11361 q^{64} +(-1.59687 + 3.23265i) q^{65} +(-27.3026 - 5.74986i) q^{66} +(-10.5075 - 6.06651i) q^{67} +(6.28145 - 10.8798i) q^{68} +(-4.67017 - 0.983525i) q^{69} +(-8.22933 + 4.75121i) q^{70} -4.49697i q^{71} +(-13.1234 - 17.9211i) q^{72} +11.8579i q^{73} +(-3.72987 - 6.46032i) q^{74} +(1.15655 - 1.28934i) q^{75} +(29.1126 + 16.8082i) q^{76} +(-11.2018 + 19.4020i) q^{77} +(-10.0906 + 12.8316i) q^{78} +(-2.01822 - 3.49566i) q^{79} -9.68867i q^{80} +(2.71687 - 8.58013i) q^{81} -1.90875 q^{82} +(12.4976 - 7.21548i) q^{83} +(-28.9216 + 9.45719i) q^{84} +(2.25134 + 1.29981i) q^{85} +(-9.13195 - 5.27234i) q^{86} +(5.46737 - 6.09507i) q^{87} +(-22.8149 - 39.5166i) q^{88} +6.71820i q^{89} +(6.32679 - 4.63303i) q^{90} +(7.27469 + 10.9032i) q^{91} +(-6.65801 - 11.5320i) q^{92} +(-1.88075 + 8.93054i) q^{93} +(0.115663 - 0.200335i) q^{94} +(-3.47809 + 6.02423i) q^{95} +(3.75394 - 17.8252i) q^{96} +(12.5186 - 7.22764i) q^{97} +16.2468i q^{98} +(7.45645 - 16.9179i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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