LMFDB - Embedded newform 143.2.o.a.54.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [143,2,Mod(32,143)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(143, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("143.32"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.o (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			54.3
Character	$\chi$	$=$	143.54
Dual form			143.2.o.a.98.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.434323 + 1.62091i) q^{2} +(-1.48314 - 2.56887i) q^{3} +(-0.706676 - 0.408000i) q^{4} +(-2.16789 + 2.16789i) q^{5} +(4.80807 - 1.28832i) q^{6} +(0.693856 + 2.58950i) q^{7} +(-1.40493 + 1.40493i) q^{8} +(-2.89939 + 5.02189i) q^{9} +(-2.57240 - 4.45553i) q^{10} +(-2.96119 - 1.49377i) q^{11} +2.42048i q^{12} +(0.216719 + 3.59903i) q^{13} -4.49872 q^{14} +(8.78431 + 2.35375i) q^{15} +(-2.48307 - 4.30081i) q^{16} +(0.225766 - 0.391039i) q^{17} +(-6.88078 - 6.88078i) q^{18} +(1.97570 - 0.529386i) q^{19} +(2.41650 - 0.647499i) q^{20} +(5.62301 - 5.62301i) q^{21} +(3.70738 - 4.15106i) q^{22} +(2.14280 - 1.23715i) q^{23} +(5.69276 + 1.52537i) q^{24} -4.39952i q^{25} +(-5.92785 - 1.21186i) q^{26} +8.30193 q^{27} +(0.566186 - 2.11303i) q^{28} +(-6.34231 + 3.66173i) q^{29} +(-7.63045 + 13.2163i) q^{30} +(2.94097 - 2.94097i) q^{31} +(4.21137 - 1.12843i) q^{32} +(0.554568 + 9.82237i) q^{33} +(0.535785 + 0.535785i) q^{34} +(-7.11797 - 4.10956i) q^{35} +(4.09786 - 2.36590i) q^{36} +(-1.56394 + 5.83672i) q^{37} +3.43236i q^{38} +(8.92401 - 5.89458i) q^{39} -6.09145i q^{40} +(2.16676 - 8.08646i) q^{41} +(6.67222 + 11.5566i) q^{42} +(-2.94915 + 5.10808i) q^{43} +(1.48315 + 2.26377i) q^{44} +(-4.60135 - 17.1725i) q^{45} +(1.07464 + 4.01062i) q^{46} +(9.59969 + 9.59969i) q^{47} +(-7.36547 + 12.7574i) q^{48} +(-0.161920 + 0.0934845i) q^{49} +(7.13124 + 1.91081i) q^{50} -1.33937 q^{51} +(1.31525 - 2.63177i) q^{52} +1.80061 q^{53} +(-3.60572 + 13.4567i) q^{54} +(9.65787 - 3.18123i) q^{55} +(-4.61288 - 2.66324i) q^{56} +(-4.29015 - 4.29015i) q^{57} +(-3.18075 - 11.8707i) q^{58} +(0.371900 - 0.0996502i) q^{59} +(-5.24733 - 5.24733i) q^{60} +(1.95356 + 1.12789i) q^{61} +(3.48973 + 6.04438i) q^{62} +(-15.0160 - 4.02351i) q^{63} -2.61592i q^{64} +(-8.27214 - 7.33249i) q^{65} +(-16.1621 - 3.36717i) q^{66} +(-10.8810 - 2.91555i) q^{67} +(-0.319088 + 0.184225i) q^{68} +(-6.35613 - 3.66971i) q^{69} +(9.75275 - 9.75275i) q^{70} +(2.86807 + 10.7038i) q^{71} +(-2.98195 - 11.1288i) q^{72} +(-3.23341 + 3.23341i) q^{73} +(-8.78156 - 5.07004i) q^{74} +(-11.3018 + 6.52509i) q^{75} +(-1.61217 - 0.431979i) q^{76} +(1.81347 - 8.70448i) q^{77} +(5.67870 + 17.0252i) q^{78} -5.08084i q^{79} +(14.7067 + 3.94065i) q^{80} +(-3.61473 - 6.26090i) q^{81} +(12.1664 + 7.02427i) q^{82} +(5.78357 + 5.78357i) q^{83} +(-6.26784 + 1.67946i) q^{84} +(0.358293 + 1.33717i) q^{85} +(-6.99887 - 6.99887i) q^{86} +(18.8130 + 10.8617i) q^{87} +(6.25888 - 2.06163i) q^{88} +(-1.24309 + 4.63928i) q^{89} +29.8336 q^{90} +(-9.16934 + 3.05840i) q^{91} -2.01902 q^{92} +(-11.9168 - 3.19310i) q^{93} +(-19.7296 + 11.3909i) q^{94} +(-3.13544 + 5.43075i) q^{95} +(-9.14482 - 9.14482i) q^{96} +(1.98623 + 7.41270i) q^{97} +(-0.0812049 - 0.303061i) q^{98} +(16.0872 - 10.5398i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 20 q^{9} + 8 q^{11} - 16 q^{14} + 12 q^{15} - 8 q^{16} - 52 q^{20} + 12 q^{22} - 36 q^{26} - 16 q^{27} + 4 q^{31} + 48 q^{33} - 12 q^{34} + 120 q^{36} - 20 q^{37} - 12 q^{42}+ \cdots + 16 q^{99}+O(q^{100}) $ 48 * q - 4 * q^3 - 12 * q^4 - 8 * q^5 - 20 * q^9 + 8 * q^11 - 16 * q^14 + 12 * q^15 - 8 * q^16 - 52 * q^20 + 12 * q^22 - 36 * q^26 - 16 * q^27 + 4 * q^31 + 48 * q^33 - 12 * q^34 + 120 * q^36 - 20 * q^37 - 12 * q^42 + 8 * q^44 + 8 * q^45 + 40 * q^47 - 48 * q^48 - 12 * q^49 + 24 * q^53 + 12 * q^55 - 132 * q^56 + 28 * q^58 - 40 * q^59 + 20 * q^60 - 32 * q^66 - 60 * q^67 - 12 * q^69 + 92 * q^70 - 96 * q^75 + 12 * q^78 + 148 * q^80 + 16 * q^81 + 156 * q^82 - 76 * q^86 - 48 * q^88 + 68 * q^89 - 84 * q^91 + 24 * q^92 + 24 * q^93 + 4 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.434323	+	1.62091i	−0.307113	+	1.14616i	0.623999	+	0.781425i	$0.285507\pi$
$2$	−0.434323	+	1.62091i	−0.307113	+	1.14616i	−0.931112	+	0.364734i	$0.881160\pi$
$3$	−1.48314	−	2.56887i	−0.856289	−	1.48314i	−0.875444	−	0.483320i	$-0.839431\pi$
$3$	−1.48314	−	2.56887i	−0.856289	−	1.48314i	0.0191546	−	0.999817i	$-0.493903\pi$
$4$	−0.706676	−	0.408000i	−0.353338	−	0.204000i
$5$	−2.16789	+	2.16789i	−0.969511	+	0.969511i	−0.999549	−	0.0300377i	$-0.990437\pi$
$5$	−2.16789	+	2.16789i	−0.969511	+	0.969511i	0.0300377	+	0.999549i	$0.490437\pi$
$6$	4.80807	−	1.28832i	1.96289	−	0.525954i
$7$	0.693856	+	2.58950i	0.262253	+	0.978741i	0.963910	+	0.266227i	$0.0857769\pi$
$7$	0.693856	+	2.58950i	0.262253	+	0.978741i	−0.701658	+	0.712514i	$0.747556\pi$
$8$	−1.40493	+	1.40493i	−0.496716	+	0.496716i
$9$	−2.89939	+	5.02189i	−0.966462	+	1.67396i
$10$	−2.57240	−	4.45553i	−0.813465	−	1.40896i
$11$	−2.96119	−	1.49377i	−0.892833	−	0.450387i
$11$	−2.96119	−	1.49377i	−0.892833	−	0.450387i
$12$			2.42048i			0.698732i
$13$	0.216719	+	3.59903i	0.0601070	+	0.998192i
$13$	0.216719	+	3.59903i	0.0601070	+	0.998192i
$14$	−4.49872			−1.20233
$15$	8.78431	+	2.35375i	2.26810	+	0.607735i
$16$	−2.48307	−	4.30081i	−0.620768	−	1.07520i
$17$	0.225766	−	0.391039i	0.0547564	−	0.0948409i	−0.837348	−	0.546670i	$-0.815895\pi$
$17$	0.225766	−	0.391039i	0.0547564	−	0.0948409i	0.892104	+	0.451829i	$0.149228\pi$
$18$	−6.88078	−	6.88078i	−1.62181	−	1.62181i
$19$	1.97570	−	0.529386i	0.453256	−	0.121450i	−0.0249666	−	0.999688i	$-0.507948\pi$
$19$	1.97570	−	0.529386i	0.453256	−	0.121450i	0.478222	+	0.878239i	$0.341281\pi$
$20$	2.41650	−	0.647499i	0.540345	−	0.144785i
$21$	5.62301	−	5.62301i	1.22704	−	1.22704i
$22$	3.70738	−	4.15106i	0.790416	−	0.885010i
$23$	2.14280	−	1.23715i	0.446805	−	0.257963i	−0.259675	−	0.965696i	$-0.583615\pi$
$23$	2.14280	−	1.23715i	0.446805	−	0.257963i	0.706480	+	0.707733i	$0.250282\pi$
$24$	5.69276	+	1.52537i	1.16203	+	0.311365i
$25$		−	4.39952i		−	0.879904i
$26$	−5.92785	−	1.21186i	−1.16255	−	0.237665i
$27$	8.30193			1.59771
$28$	0.566186	−	2.11303i	0.106999	−	0.399326i
$29$	−6.34231	+	3.66173i	−1.17774	+	0.679967i	−0.955490	−	0.295023i	$-0.904673\pi$
$29$	−6.34231	+	3.66173i	−1.17774	+	0.679967i	−0.222247	+	0.974990i	$0.571339\pi$
$30$	−7.63045	+	13.2163i	−1.39312	+	2.41296i
$31$	2.94097	−	2.94097i	0.528213	−	0.528213i	−0.391826	−	0.920039i	$-0.628157\pi$
$31$	2.94097	−	2.94097i	0.528213	−	0.528213i	0.920039	+	0.391826i	$0.128157\pi$
$32$	4.21137	−	1.12843i	0.744472	−	0.199481i
$33$	0.554568	+	9.82237i	0.0965380	+	1.70986i
$34$	0.535785	+	0.535785i	0.0918864	+	0.0918864i
$35$	−7.11797	−	4.10956i	−1.20316	−	0.694643i
$36$	4.09786	−	2.36590i	0.682976	−	0.394316i
$37$	−1.56394	+	5.83672i	−0.257111	+	0.959550i	0.709793	+	0.704410i	$0.248788\pi$
$37$	−1.56394	+	5.83672i	−0.257111	+	0.959550i	−0.966904	+	0.255140i	$0.917878\pi$
$38$			3.43236i			0.556802i
$39$	8.92401	−	5.89458i	1.42899	−	0.943888i
$40$		−	6.09145i		−	0.963143i
$41$	2.16676	−	8.08646i	0.338391	−	1.26289i	−0.561754	−	0.827304i	$-0.689873\pi$
$41$	2.16676	−	8.08646i	0.338391	−	1.26289i	0.900146	−	0.435589i	$-0.143460\pi$
$42$	6.67222	+	11.5566i	1.02955	+	1.78323i
$43$	−2.94915	+	5.10808i	−0.449741	+	0.778975i	−0.998369	−	0.0570921i	$-0.981817\pi$
$43$	−2.94915	+	5.10808i	−0.449741	+	0.778975i	0.548628	+	0.836067i	$0.315150\pi$
$44$	1.48315	+	2.26377i	0.223593	+	0.341277i
$45$	−4.60135	−	17.1725i	−0.685929	−	2.55992i
$46$	1.07464	+	4.01062i	0.158447	+	0.591333i
$47$	9.59969	+	9.59969i	1.40026	+	1.40026i	0.799220	+	0.601038i	$0.205246\pi$
$47$	9.59969	+	9.59969i	1.40026	+	1.40026i	0.601038	+	0.799220i	$0.294754\pi$
$48$	−7.36547	+	12.7574i	−1.06311	+	1.84137i
$49$	−0.161920	+	0.0934845i	−0.0231314	+	0.0133549i
$50$	7.13124	+	1.91081i	1.00851	+	0.270229i
$51$	−1.33937			−0.187549
$52$	1.31525	−	2.63177i	0.182393	−	0.364961i
$53$	1.80061			0.247333			0.123667	−	0.992324i	$-0.460535\pi$
$53$	1.80061			0.247333			0.123667	+	0.992324i	$0.460535\pi$
$54$	−3.60572	+	13.4567i	−0.490676	+	1.83123i
$55$	9.65787	−	3.18123i	1.30227	−	0.428957i
$56$	−4.61288	−	2.66324i	−0.616421	−	0.355891i
$57$	−4.29015	−	4.29015i	−0.568244	−	0.568244i
$58$	−3.18075	−	11.8707i	−0.417653	−	1.55870i
$59$	0.371900	−	0.0996502i	0.0484172	−	0.0129734i	−0.234529	−	0.972109i	$-0.575355\pi$
$59$	0.371900	−	0.0996502i	0.0484172	−	0.0129734i	0.282946	+	0.959136i	$0.408688\pi$
$60$	−5.24733	−	5.24733i	−0.677428	−	0.677428i
$61$	1.95356	+	1.12789i	0.250127	+	0.144411i	0.619823	−	0.784742i	$-0.287205\pi$
$61$	1.95356	+	1.12789i	0.250127	+	0.144411i	−0.369695	+	0.929153i	$0.620538\pi$
$62$	3.48973	+	6.04438i	0.443196	+	0.767637i
$63$	−15.0160	−	4.02351i	−1.89183	−	0.506915i
$64$		−	2.61592i		−	0.326990i
$65$	−8.27214	−	7.33249i	−1.02603	−	0.909484i
$66$	−16.1621	−	3.36717i	−1.98941	−	0.414470i
$67$	−10.8810	−	2.91555i	−1.32932	−	0.356191i	−0.476861	−	0.878979i	$-0.658225\pi$
$67$	−10.8810	−	2.91555i	−1.32932	−	0.356191i	−0.852463	+	0.522788i	$0.824892\pi$
$68$	−0.319088	+	0.184225i	−0.0386950	+	0.0223406i
$69$	−6.35613	−	3.66971i	−0.765188	−	0.441782i
$70$	9.75275	−	9.75275i	1.16568	−	1.16568i
$71$	2.86807	+	10.7038i	0.340377	+	1.27030i	0.897921	+	0.440157i	$0.145077\pi$
$71$	2.86807	+	10.7038i	0.340377	+	1.27030i	−0.557544	+	0.830147i	$0.688256\pi$
$72$	−2.98195	−	11.1288i	−0.351426	−	1.31154i
$73$	−3.23341	+	3.23341i	−0.378442	+	0.378442i	−0.870540	−	0.492098i	$-0.836230\pi$
$73$	−3.23341	+	3.23341i	−0.378442	+	0.378442i	0.492098	+	0.870540i	$0.336230\pi$
$74$	−8.78156	−	5.07004i	−1.02084	−	0.589380i
$75$	−11.3018	+	6.52509i	−1.30502	+	0.753452i
$76$	−1.61217	−	0.431979i	−0.184928	−	0.0495514i
$77$	1.81347	−	8.70448i	0.206664	−	0.991968i
$78$	5.67870	+	17.0252i	0.642987	+	1.92773i
$79$		−	5.08084i		−	0.571639i	−0.958283	−	0.285820i	$-0.907734\pi$
$79$		−	5.08084i		−	0.571639i	0.958283	−	0.285820i	$-0.0922658\pi$
$80$	14.7067	+	3.94065i	1.64426	+	0.440579i
$81$	−3.61473	−	6.26090i	−0.401637	−	0.695655i
$82$	12.1664	+	7.02427i	1.34355	+	0.775701i
$83$	5.78357	+	5.78357i	0.634829	+	0.634829i	0.949275	−	0.314446i	$-0.101819\pi$
$83$	5.78357	+	5.78357i	0.634829	+	0.634829i	−0.314446	+	0.949275i	$0.601819\pi$
$84$	−6.26784	+	1.67946i	−0.683877	+	0.183244i
$85$	0.358293	+	1.33717i	0.0388623	+	0.145036i
$86$	−6.99887	−	6.99887i	−0.754708	−	0.754708i
$87$	18.8130	+	10.8617i	2.01697	+	1.16450i
$88$	6.25888	−	2.06163i	0.667199	−	0.219770i
$89$	−1.24309	+	4.63928i	−0.131767	+	0.491763i	−0.999990	−	0.00441167i	$-0.998596\pi$
$89$	−1.24309	+	4.63928i	−0.131767	+	0.491763i	0.868223	+	0.496175i	$0.165262\pi$
$90$	29.8336			3.14473
$91$	−9.16934	+	3.05840i	−0.961208	+	0.320608i
$92$	−2.01902			−0.210498
$93$	−11.9168	−	3.19310i	−1.23572	−	0.331109i
$94$	−19.7296	+	11.3909i	−2.03496	+	1.17488i
$95$	−3.13544	+	5.43075i	−0.321690	+	0.557183i
$96$	−9.14482	−	9.14482i	−0.933340	−	0.933340i
$97$	1.98623	+	7.41270i	0.201671	+	0.752646i	0.990439	+	0.137955i	$0.0440528\pi$
$97$	1.98623	+	7.41270i	0.201671	+	0.752646i	−0.788768	+	0.614691i	$0.789281\pi$
$98$	−0.0812049	−	0.303061i	−0.00820293	−	0.0306138i
$99$	16.0872	−	10.5398i	1.61682	−	1.05929i
$100$	−1.79500	+	3.10903i	−0.179500	+	0.310903i
$101$	7.16356	+	12.4076i	0.712800	+	1.23461i	0.963802	+	0.266620i	$0.0859068\pi$
$101$	7.16356	+	12.4076i	0.712800	+	1.23461i	−0.251001	+	0.967987i	$0.580760\pi$
$102$	0.581719	−	2.17100i	0.0575987	−	0.214961i
$103$		−	5.86388i		−	0.577785i	−0.957362	−	0.288893i	$-0.906713\pi$
$103$		−	5.86388i		−	0.577785i	0.957362	−	0.288893i	$-0.0932870\pi$
$104$	−5.36084	−	4.75190i	−0.525674	−	0.465962i
$105$			24.3802i			2.37926i
$106$	−0.782048	+	2.91864i	−0.0759592	+	0.283483i
$107$	9.65152	−	5.57231i	0.933048	−	0.538695i	0.0452736	−	0.998975i	$-0.485584\pi$
$107$	9.65152	−	5.57231i	0.933048	−	0.538695i	0.887774	+	0.460279i	$0.152251\pi$
$108$	−5.86678	−	3.38718i	−0.564531	−	0.325932i
$109$	−8.63388	−	8.63388i	−0.826976	−	0.826976i	0.160121	−	0.987097i	$-0.448811\pi$
$109$	−8.63388	−	8.63388i	−0.826976	−	0.826976i	−0.987097	+	0.160121i	$0.948811\pi$
$110$	0.961863	+	17.0363i	0.0917100	+	1.62434i
$111$	17.3133	−	4.63908i	1.64330	−	0.440322i
$112$	9.41406	−	9.41406i	0.889546	−	0.889546i
$113$	−2.01675	+	3.49312i	−0.189720	+	0.328605i	−0.945157	−	0.326617i	$-0.894091\pi$
$113$	−2.01675	+	3.49312i	−0.189720	+	0.328605i	0.755437	+	0.655222i	$0.227425\pi$
$114$	8.81727	−	5.09066i	0.825813	−	0.476784i
$115$	−1.96336	+	7.32736i	−0.183084	+	0.683280i
$116$	5.97595			0.554853
$117$	−18.7023	−	9.34665i	−1.72903	−	0.864098i
$118$			0.646098i			0.0594781i
$119$	1.16925	+	0.313299i	0.107185	+	0.0287200i
$120$	−15.6481	+	9.03446i	−1.42847	+	0.824729i
$121$	6.53733	+	8.84665i	0.594303	+	0.804241i
$122$	−2.67668	+	2.67668i	−0.242335	+	0.242335i
$123$	−23.9867	+	6.42721i	−2.16280	+	0.579522i
$124$	−3.27822	+	0.878398i	−0.294393	+	0.0788824i
$125$	−1.30178	−	1.30178i	−0.116435	−	0.116435i
$126$	13.0435	−	22.5921i	1.16201	−	2.01266i
$127$	0.217110	+	0.376046i	0.0192654	+	0.0333687i	0.875497	−	0.483223i	$-0.160534\pi$
$127$	0.217110	+	0.376046i	0.0192654	+	0.0333687i	−0.856232	+	0.516592i	$0.827201\pi$
$128$	12.6629	+	3.39302i	1.11925	+	0.299903i
$129$	17.4960			1.54043
$130$	15.4781	−	10.2238i	1.35752	−	0.896683i
$131$			4.59551i			0.401512i	0.979641	+	0.200756i	$0.0643398\pi$
$131$			4.59551i			0.401512i	−0.979641	+	0.200756i	$0.935660\pi$
$132$	3.61562	−	7.16750i	0.314700	−	0.623851i
$133$	2.74170	+	4.74876i	0.237735	+	0.411769i
$134$	9.45171	−	16.3708i	0.816504	−	1.41423i
$135$	−17.9977	+	17.9977i	−1.54899	+	1.54899i
$136$	0.232195	+	0.866565i	0.0199106	+	0.0743074i
$137$	−10.2924	+	2.75785i	−0.879343	+	0.235619i	−0.670124	−	0.742250i	$-0.733759\pi$
$137$	−10.2924	+	2.75785i	−0.879343	+	0.235619i	−0.209219	+	0.977869i	$0.567092\pi$
$138$	8.70890	−	8.70890i	0.741351	−	0.741351i
$139$	−1.92441	−	1.11106i	−0.163226	−	0.0942387i	0.416162	−	0.909291i	$-0.363375\pi$
$139$	−1.92441	−	1.11106i	−0.163226	−	0.0942387i	−0.579388	+	0.815052i	$0.696708\pi$
$140$	3.35340	+	5.80826i	0.283414	+	0.490888i
$141$	10.4227	−	38.8980i	0.877748	−	3.27580i
$142$	−18.5956			−1.56051
$143$	4.73436	−	10.9812i	0.395907	−	0.918290i
$144$	28.7975			2.39980
$145$	5.81120	−	21.6877i	0.482594	−	1.80106i
$146$	−3.83674	−	6.64543i	−0.317531	−	0.549980i
$147$	0.480299	+	0.277300i	0.0396144	+	0.0228714i
$148$	3.48658	−	3.48658i	0.286595	−	0.286595i
$149$	7.16978	−	1.92114i	0.587372	−	0.157386i	0.0471199	−	0.998889i	$-0.484996\pi$
$149$	7.16978	−	1.92114i	0.587372	−	0.157386i	0.540252	+	0.841503i	$0.318329\pi$
$150$	−5.66798	−	21.1532i	−0.462789	−	1.72715i
$151$	−13.5910	+	13.5910i	−1.10602	+	1.10602i	−0.112351	+	0.993669i	$0.535838\pi$
$151$	−13.5910	+	13.5910i	−1.10602	+	1.10602i	−0.993669	+	0.112351i	$0.964162\pi$
$152$	−2.03196	+	3.51945i	−0.164813	+	0.285465i
$153$	1.30917	+	2.26755i	0.105840	+	0.183320i
$154$	13.3216	+	6.72003i	1.07348	+	0.541516i
$155$			12.7514i			1.02422i
$156$	−8.71138	+	0.524563i	−0.697468	+	0.0419986i
$157$	9.58510			0.764974			0.382487	−	0.923961i	$-0.375068\pi$
$157$	9.58510			0.764974			0.382487	+	0.923961i	$0.375068\pi$
$158$	8.23561	+	2.20672i	0.655190	+	0.175558i
$159$	−2.67056	−	4.62554i	−0.211789	−	0.366829i
$160$	−6.68347	+	11.5761i	−0.528375	+	0.915172i
$161$	4.69039	+	4.69039i	0.369654	+	0.369654i
$162$	11.7183	−	3.13992i	0.920680	−	0.246695i
$163$	−1.19050	+	0.318993i	−0.0932470	+	0.0249854i	−0.305141	−	0.952307i	$-0.598704\pi$
$163$	−1.19050	+	0.318993i	−0.0932470	+	0.0249854i	0.211894	+	0.977293i	$0.432037\pi$
$164$	−4.83047	+	4.83047i	−0.377197	+	0.377197i
$165$	−22.4961	−	20.0916i	−1.75132	−	1.56413i
$166$	−11.8866	+	6.86274i	−0.922580	+	0.532652i
$167$	−19.5494	−	5.23825i	−1.51278	−	0.405348i	−0.595422	−	0.803413i	$-0.703015\pi$
$167$	−19.5494	−	5.23825i	−1.51278	−	0.405348i	−0.917357	+	0.398065i	$0.869682\pi$
$168$			15.7998i			1.21898i
$169$	−12.9061	+	1.55996i	−0.992774	+	0.119997i
$170$	−2.32305			−0.178170
$171$	−3.06979	+	11.4566i	−0.234753	+	0.876109i
$172$	4.16819	−	2.40651i	0.317821	−	0.183494i
$173$	5.65372	−	9.79254i	0.429845	−	0.744513i	−0.567014	−	0.823708i	$-0.691902\pi$
$173$	5.65372	−	9.79254i	0.429845	−	0.744513i	0.996859	+	0.0791950i	$0.0252350\pi$
$174$	−25.7768	+	25.7768i	−1.95413	+	1.95413i
$175$	11.3926	−	3.05263i	0.861197	−	0.230757i
$176$	0.928460	+	16.4446i	0.0699853	+	1.23956i
$177$	−0.807566	−	0.807566i	−0.0607004	−	0.0607004i
$178$	−6.97997	−	4.02989i	−0.523171	−	0.302053i
$179$	10.8178	−	6.24566i	0.808560	−	0.466822i	−0.0378956	−	0.999282i	$-0.512065\pi$
$179$	10.8178	−	6.24566i	0.808560	−	0.466822i	0.846456	+	0.532459i	$0.178732\pi$
$180$	−3.75470	+	14.0127i	−0.279859	+	1.04445i
$181$		−	3.97606i		−	0.295539i	−0.989022	−	0.147769i	$-0.952791\pi$
$181$		−	3.97606i		−	0.295539i	0.989022	−	0.147769i	$-0.0472093\pi$
$182$	−0.974957	−	16.1910i	−0.0722686	−	1.20016i
$183$		−	6.69124i		−	0.494630i
$184$	−1.27238	+	4.74857i	−0.0938008	+	0.350069i
$185$	−9.26291	−	16.0438i	−0.681023	−	1.17957i
$186$	10.3515	−	17.9293i	0.759007	−	1.31464i
$187$	−1.25266	+	0.820700i	−0.0916034	+	0.0600155i
$188$	−2.86720	−	10.7005i	−0.209112	−	0.780417i
$189$	5.76034	+	21.4979i	0.419003	+	1.56374i
$190$	−7.44098	−	7.44098i	−0.539826	−	0.539826i
$191$	10.1296	−	17.5449i	0.732949	−	1.26950i	−0.222669	−	0.974894i	$-0.571477\pi$
$191$	10.1296	−	17.5449i	0.732949	−	1.26950i	0.955618	−	0.294610i	$-0.0951897\pi$
$192$	−6.71995	+	3.87976i	−0.484971	+	0.279998i
$193$	10.2553	+	2.74791i	0.738195	+	0.197799i	0.608276	−	0.793726i	$-0.291862\pi$
$193$	10.2553	+	2.74791i	0.738195	+	0.197799i	0.129919	+	0.991525i	$0.458528\pi$
$194$	−12.8780			−0.924588
$195$	−6.56749	+	32.1251i	−0.470308	+	2.30053i
$196$	0.152567			0.0108976
$197$	0.442831	−	1.65267i	0.0315504	−	0.117748i	−0.948355	−	0.317212i	$-0.897253\pi$
$197$	0.442831	−	1.65267i	0.0315504	−	0.117748i	0.979905	+	0.199464i	$0.0639201\pi$
$198$	10.0970	+	30.6536i	0.717566	+	2.17845i
$199$	1.34347	+	0.775655i	0.0952363	+	0.0549847i	0.546862	−	0.837223i	$-0.315822\pi$
$199$	1.34347	+	0.775655i	0.0952363	+	0.0549847i	−0.451625	+	0.892208i	$0.649156\pi$
$200$	6.18099	+	6.18099i	0.437062	+	0.437062i
$201$	8.64832	+	32.2760i	0.610005	+	2.27657i
$202$	−23.2230	+	6.22259i	−1.63397	+	0.437820i
$203$	−13.8827	−	13.8827i	−0.974376	−	0.974376i
$204$	0.946501	+	0.546462i	0.0662683	+	0.0382600i
$205$	12.8333	+	22.2279i	0.896315	+	1.55246i
$206$	9.50484	+	2.54682i	0.662234	+	0.177445i
$207$			14.3479i			0.997246i
$208$	14.9406	−	9.86872i	1.03595	−	0.684273i
$209$	−6.64120	−	1.38361i	−0.459381	−	0.0957064i
$210$	−39.5182	−	10.5889i	−2.72701	−	0.730701i
$211$	18.9354	−	10.9324i	1.30357	−	0.752614i	0.322552	−	0.946552i	$-0.395459\pi$
$211$	18.9354	−	10.9324i	1.30357	−	0.752614i	0.981014	+	0.193938i	$0.0621260\pi$
$212$	−1.27245	−	0.734650i	−0.0873923	−	0.0504560i
$213$	23.2428	−	23.2428i	1.59257	−	1.59257i
$214$	4.84036	+	18.0645i	0.330880	+	1.23486i
$215$	−4.68032	−	17.4672i	−0.319195	−	1.19125i
$216$	−11.6636	+	11.6636i	−0.793607	+	0.793607i
$217$	9.65625	+	5.57504i	0.655509	+	0.378458i
$218$	17.7447	−	10.2449i	1.20182	−	0.693872i
$219$	13.1018	+	3.51062i	0.885338	+	0.237226i
$220$	−8.12293	−	1.69231i	−0.547648	−	0.114096i
$221$	1.45629	+	0.727795i	0.0979606	+	0.0489568i
$222$			30.0782i			2.01872i
$223$	1.51263	+	0.405308i	0.101293	+	0.0271414i	0.309110	−	0.951026i	$-0.399969\pi$
$223$	1.51263	+	0.405308i	0.101293	+	0.0271414i	−0.207816	+	0.978168i	$0.566636\pi$
$224$	5.84416	+	10.1224i	0.390479	+	0.676330i
$225$	22.0939	+	12.7559i	1.47293	+	0.850394i
$226$	−4.78613	−	4.78613i	−0.318368	−	0.318368i
$227$	14.9141	−	3.99621i	0.989882	−	0.265238i	0.272681	−	0.962104i	$-0.412090\pi$
$227$	14.9141	−	3.99621i	0.989882	−	0.265238i	0.717201	+	0.696866i	$0.245423\pi$
$228$	1.28137	+	4.78213i	0.0848606	+	0.316704i
$229$	11.4409	+	11.4409i	0.756035	+	0.756035i	0.975598	−	0.219563i	$-0.0704631\pi$
$229$	11.4409	+	11.4409i	0.756035	+	0.756035i	−0.219563	+	0.975598i	$0.570463\pi$
$230$	−11.0243	−	6.36488i	−0.726920	−	0.419688i
$231$	−25.0503	+	8.25136i	−1.64819	+	0.542900i
$232$	3.76601	−	14.0549i	0.247251	−	0.922751i
$233$	−12.7209			−0.833374			−0.416687	−	0.909050i	$-0.636809\pi$
$233$	−12.7209			−0.833374			−0.416687	+	0.909050i	$0.636809\pi$
$234$	23.2729	−	26.2553i	1.52140	−	1.71636i
$235$	−41.6222			−2.71513
$236$	−0.303470	−	0.0813145i	−0.0197542	−	0.00529313i
$237$	−13.0520	+	7.53558i	−0.847819	+	0.489489i
$238$	−1.01566	+	1.75918i	−0.0658355	+	0.114030i
$239$	−8.83513	−	8.83513i	−0.571497	−	0.571497i	0.361049	−	0.932547i	$-0.382419\pi$
$239$	−8.83513	−	8.83513i	−0.571497	−	0.571497i	−0.932547	+	0.361049i	$0.882419\pi$
$240$	−11.6891	−	43.6241i	−0.754525	−	2.81593i
$241$	−0.878491	−	3.27857i	−0.0565886	−	0.211192i	0.931842	−	0.362864i	$-0.118201\pi$
$241$	−0.878491	−	3.27857i	−0.0565886	−	0.211192i	−0.988431	+	0.151672i	$0.951534\pi$
$242$	−17.1790	+	6.75415i	−1.10431	+	0.434173i
$243$	1.73061	−	2.99751i	0.111019	−	0.192290i
$244$	−0.920355	−	1.59410i	−0.0589197	−	0.102052i
$245$	0.148361	−	0.553689i	0.00947841	−	0.0353739i
$246$		−	41.6718i		−	2.65690i
$247$	2.33345	+	6.99587i	0.148474	+	0.445136i
$248$			8.26367i			0.524744i
$249$	6.27940	−	23.4351i	0.397941	−	1.48514i
$250$	2.67547	−	1.54468i	0.169211	−	0.0976943i
$251$	−3.03763	−	1.75378i	−0.191734	−	0.110697i	0.401060	−	0.916052i	$-0.368642\pi$
$251$	−3.03763	−	1.75378i	−0.191734	−	0.110697i	−0.592794	+	0.805354i	$0.701975\pi$
$252$	8.96983	+	8.96983i	0.565046	+	0.565046i
$253$	−8.19325	+	0.462589i	−0.515105	+	0.0290827i
$254$	−0.703834	+	0.188592i	−0.0441625	+	0.0118333i
$255$	2.90361	−	2.90361i	0.181831	−	0.181831i
$256$	−8.38366	+	14.5209i	−0.523979	+	0.907558i
$257$	−9.11143	+	5.26049i	−0.568356	+	0.328140i	−0.756492	−	0.654003i	$-0.773089\pi$
$257$	−9.11143	+	5.26049i	−0.568356	+	0.328140i	0.188137	+	0.982143i	$0.439755\pi$
$258$	−7.59890	+	28.3595i	−0.473087	+	1.76558i
$259$	−16.1994			−1.00658
$260$	2.85407	+	8.55673i	0.177002	+	0.530666i
$261$		−	42.4671i		−	2.62865i
$262$	−7.44893	−	1.99593i	−0.460196	−	0.123309i
$263$	2.92724	−	1.69004i	0.180501	−	0.104212i	−0.407027	−	0.913416i	$-0.633434\pi$
$263$	2.92724	−	1.69004i	0.180501	−	0.104212i	0.587528	+	0.809204i	$0.300101\pi$
$264$	−14.5788	−	13.0206i	−0.897265	−	0.801361i
$265$	−3.90354	+	3.90354i	−0.239792	+	0.239792i
$266$	−8.88811	+	2.38156i	−0.544965	+	0.146023i
$267$	13.7614	−	3.68735i	0.842182	−	0.225662i
$268$	6.49979	+	6.49979i	0.397038	+	0.397038i
$269$	−0.255708	+	0.442899i	−0.0155908	+	0.0270040i	−0.873716	−	0.486437i	$-0.838296\pi$
$269$	−0.255708	+	0.442899i	−0.0155908	+	0.0270040i	0.858125	+	0.513441i	$0.171630\pi$
$270$	−21.3559	−	36.9895i	−1.29968	−	2.25111i
$271$	−6.06974	−	1.62638i	−0.368710	−	0.0987957i	0.0697061	−	0.997568i	$-0.477794\pi$
$271$	−6.06974	−	1.62638i	−0.368710	−	0.0987957i	−0.438417	+	0.898772i	$0.644461\pi$
$272$	−2.24238			−0.135964
$273$	21.4560	+	19.0188i	1.29858	+	1.15107i
$274$		−	17.8810i		−	1.08023i
$275$	−6.57185	+	13.0278i	−0.396297	+	0.785607i
$276$	2.99448	+	5.18660i	0.180247	+	0.312197i
$277$	−14.2430	+	24.6695i	−0.855776	+	1.48225i	0.0201472	+	0.999797i	$0.493587\pi$
$277$	−14.2430	+	24.6695i	−0.855776	+	1.48225i	−0.875923	+	0.482451i	$0.839747\pi$
$278$	2.63675	−	2.63675i	0.158141	−	0.158141i
$279$	6.24220	+	23.2962i	0.373711	+	1.39471i
$280$	15.7738	−	4.22659i	0.942668	−	0.252587i
$281$	12.9152	−	12.9152i	0.770455	−	0.770455i	−0.207731	−	0.978186i	$-0.566608\pi$
$281$	12.9152	−	12.9152i	0.770455	−	0.770455i	0.978186	+	0.207731i	$0.0666079\pi$
$282$	58.5235	+	33.7885i	3.48502	+	2.01208i
$283$	−11.3662	−	19.6868i	−0.675648	−	1.17026i	−0.976279	−	0.216516i	$-0.930531\pi$
$283$	−11.3662	−	19.6868i	−0.675648	−	1.17026i	0.300631	−	0.953740i	$-0.402803\pi$
$284$	2.34034	−	8.73427i	0.138874	−	0.518284i
$285$	18.6012			1.10184
$286$	15.7433	+	12.4434i	0.930919	+	0.735791i
$287$	22.4434			1.32479
$288$	−6.54352	+	24.4208i	−0.385581	+	1.43901i
$289$	8.39806	+	14.5459i	0.494003	+	0.855639i
$290$	32.6300	+	18.8389i	1.91610	+	1.10626i
$291$	16.0964	−	16.0964i	0.943588	−	0.943588i
$292$	3.60421	−	0.965744i	0.210920	−	0.0565159i
$293$	0.0132974	+	0.0496266i	0.000776844	+	0.00289922i	0.966313	−	0.257369i	$-0.0828556\pi$
$293$	0.0132974	+	0.0496266i	0.000776844	+	0.00289922i	−0.965536	+	0.260268i	$0.916189\pi$
$294$	−0.658085	+	0.658085i	−0.0383803	+	0.0383803i
$295$	−0.590208	+	1.02227i	−0.0343632	+	0.0595189i
$296$	−6.00293	−	10.3974i	−0.348913	−	0.604335i
$297$	−24.5836	−	12.4011i	−1.42649	−	0.719587i
$298$			12.4560i			0.721557i
$299$	4.91691	+	7.44389i	0.284352	+	0.430492i
$300$	10.6489			0.614816
$301$	−15.2737	−	4.09257i	−0.880360	−	0.235892i
$302$	−16.1270	−	27.9327i	−0.928002	−	1.60735i
$303$	21.2491	−	36.8045i	1.22073	−	2.11436i
$304$	−7.18258	−	7.18258i	−0.411949	−	0.411949i
$305$	−6.68024	+	1.78996i	−0.382509	+	0.102493i
$306$	−4.24410	+	1.13720i	−0.242619	+	0.0650096i
$307$	−0.852073	+	0.852073i	−0.0486304	+	0.0486304i	−0.731004	−	0.682373i	$-0.760948\pi$
$307$	−0.852073	+	0.852073i	−0.0486304	+	0.0486304i	0.682373	+	0.731004i	$0.260948\pi$
$308$	−4.83296	+	5.41135i	−0.275384	+	0.308341i
$309$	−15.0635	+	8.69693i	−0.856934	+	0.494751i
$310$	−20.6689	−	5.53822i	−1.17392	−	0.314550i
$311$			2.17436i			0.123296i	0.998098	+	0.0616482i	$0.0196357\pi$
$311$			2.17436i			0.123296i	−0.998098	+	0.0616482i	$0.980364\pi$
$312$	−4.25613	+	20.8190i	−0.240956	+	1.17864i
$313$	−13.2192			−0.747195			−0.373597	−	0.927591i	$-0.621876\pi$
$313$	−13.2192			−0.747195			−0.373597	+	0.927591i	$0.621876\pi$
$314$	−4.16303	+	15.5366i	−0.234933	+	0.876783i
$315$	41.2755	−	23.8304i	2.32561	−	1.34269i
$316$	−2.07298	+	3.59051i	−0.116614	+	0.201982i
$317$	−21.7028	+	21.7028i	−1.21895	+	1.21895i	−0.250951	+	0.968000i	$0.580743\pi$
$317$	−21.7028	+	21.7028i	−1.21895	+	1.21895i	−0.968000	+	0.250951i	$0.919257\pi$
$318$	8.65749	−	2.31977i	0.485488	−	0.130086i
$319$	24.2506	−	1.36918i	1.35777	−	0.0766594i
$320$	5.67103	+	5.67103i	0.317020	+	0.317020i
$321$	−28.6290	−	16.5290i	−1.59792	−	0.922558i
$322$	−9.63986	+	5.56558i	−0.537209	+	0.310157i
$323$	0.239035	−	0.892092i	0.0133003	−	0.0496373i
$324$			5.89924i			0.327735i
$325$	15.8340	−	0.953458i	0.878313	−	0.0528883i
$326$		−	2.06824i		−	0.114549i
$327$	−9.37408	+	34.9845i	−0.518388	+	1.93465i
$328$	8.31674	+	14.4050i	0.459215	+	0.795384i
$329$	−18.1976	+	31.5192i	−1.00327	+	1.73771i
$330$	42.3373	−	27.7380i	2.33059	−	1.52693i
$331$	−4.04874	−	15.1101i	−0.222539	−	0.830527i	−0.983376	−	0.181583i	$-0.941878\pi$
$331$	−4.04874	−	15.1101i	−0.222539	−	0.830527i	0.760837	−	0.648943i	$-0.224789\pi$
$332$	−1.72742	−	6.44681i	−0.0948043	−	0.353815i
$333$	−24.7768	−	24.7768i	−1.35776	−	1.35776i
$334$	16.9815	−	29.4128i	0.929187	−	1.60940i
$335$	29.9094	−	17.2682i	1.63413	−	0.943463i
$336$	−38.1458	−	10.2211i	−2.08103	−	0.557609i
$337$	11.0973			0.604510			0.302255	−	0.953227i	$-0.402261\pi$
$337$	11.0973			0.604510			0.302255	+	0.953227i	$0.402261\pi$
$338$	3.07684	−	21.5972i	0.167358	−	1.17473i
$339$	11.9645			0.649821
$340$	0.292367	−	1.09113i	0.0158558	−	0.0591747i
$341$	−13.1019	+	4.31566i	−0.709507	+	0.233706i
$342$	−17.2369	−	9.95174i	−0.932066	−	0.538128i
$343$	12.9151	+	12.9151i	0.697351	+	0.697351i
$344$	−3.03313	−	11.3198i	−0.163536	−	0.610323i
$345$	21.7350	−	5.82386i	1.17017	−	0.313546i
$346$	13.4173	+	13.4173i	0.721320	+	0.721320i
$347$	−24.1972	−	13.9702i	−1.29897	−	0.749962i	−0.318746	−	0.947840i	$-0.603262\pi$
$347$	−24.1972	−	13.9702i	−1.29897	−	0.749962i	−0.980227	+	0.197878i	$0.936595\pi$
$348$	−8.86314	−	15.3514i	−0.475114	−	0.822922i
$349$	11.5508	+	3.09502i	0.618299	+	0.165673i	0.554355	−	0.832281i	$-0.312965\pi$
$349$	11.5508	+	3.09502i	0.618299	+	0.165673i	0.0639448	+	0.997953i	$0.479632\pi$
$350$			19.7922i			1.05794i
$351$	1.79918	+	29.8789i	0.0960333	+	1.59482i
$352$	−14.1563	−	2.94929i	−0.754532	−	0.157198i
$353$	16.4159	+	4.39862i	0.873730	+	0.234115i	0.667700	−	0.744431i	$-0.267279\pi$
$353$	16.4159	+	4.39862i	0.873730	+	0.234115i	0.206030	+	0.978546i	$0.433946\pi$
$354$	1.65974	−	0.958252i	0.0882142	−	0.0509305i
$355$	−29.4223	−	16.9870i	−1.56157	−	0.901575i
$356$	2.77129	−	2.77129i	0.146878	−	0.146878i
$357$	−0.929329	−	3.46830i	−0.0491853	−	0.183562i
$358$	5.42526	+	20.2474i	0.286734	+	1.07011i
$359$	−20.7563	+	20.7563i	−1.09548	+	1.09548i	−0.100544	+	0.994933i	$0.532058\pi$
$359$	−20.7563	+	20.7563i	−1.09548	+	1.09548i	−0.994933	+	0.100544i	$0.967942\pi$
$360$	30.5906	+	17.6615i	1.61227	+	0.930842i
$361$	−12.8314	+	7.40819i	−0.675335	+	0.389905i
$362$	6.44486	+	1.72690i	0.338734	+	0.0907636i
$363$	13.0301	−	29.9143i	0.683905	−	1.57010i
$364$	7.72758	+	1.57979i	0.405035	+	0.0828033i
$365$		−	14.0194i		−	0.733808i
$366$	10.8459	+	2.90616i	0.566925	+	0.151907i
$367$	6.12769	+	10.6135i	0.319863	+	0.554019i	0.980459	−	0.196722i	$-0.0630298\pi$
$367$	6.12769	+	10.6135i	0.319863	+	0.554019i	−0.660596	+	0.750741i	$0.729696\pi$
$368$	−10.6415	−	6.14385i	−0.554724	−	0.320270i
$369$	34.3270	+	34.3270i	1.78699	+	1.78699i
$370$	30.0288	−	8.04619i	1.56112	−	0.418301i
$371$	1.24937	+	4.66270i	0.0648639	+	0.242075i
$372$	7.11854	+	7.11854i	0.369079	+	0.369079i
$373$	3.79170	+	2.18914i	0.196327	+	0.113349i	0.594941	−	0.803769i	$-0.297175\pi$
$373$	3.79170	+	2.18914i	0.196327	+	0.113349i	−0.398614	+	0.917119i	$0.630509\pi$
$374$	−0.786226	−	2.38690i	−0.0406548	−	0.123424i
$375$	−1.41338	+	5.27482i	−0.0729869	+	0.272391i
$376$	−26.9737			−1.39106
$377$	−14.5532	−	22.0326i	−0.749528	−	1.13474i
$378$	−37.3481			−1.92098
$379$	36.6834	+	9.82930i	1.88430	+	0.504897i	0.999221	+	0.0394587i	$0.0125634\pi$
$379$	36.6834	+	9.82930i	1.88430	+	0.504897i	0.885080	+	0.465438i	$0.154103\pi$
$380$	4.43149	−	2.55852i	0.227331	−	0.131249i
$381$	0.644008	−	1.11545i	0.0329935	−	0.0571465i
$382$	24.0393	+	24.0393i	1.22996	+	1.22996i
$383$	−1.49562	−	5.58174i	−0.0764227	−	0.285213i	0.917129	−	0.398590i	$-0.130500\pi$
$383$	−1.49562	−	5.58174i	−0.0764227	−	0.285213i	−0.993552	+	0.113376i	$0.963834\pi$
$384$	−10.0646	−	37.5617i	−0.513608	−	1.91681i
$385$	14.9390	+	22.8018i	0.761360	+	1.16209i
$386$	−8.90824	+	15.4295i	−0.453418	+	0.785343i
$387$	−17.1015	−	29.6206i	−0.869316	−	1.50570i
$388$	1.62076	−	6.04876i	0.0822817	−	0.307079i
$389$			17.0791i			0.865943i	0.901408	+	0.432971i	$0.142535\pi$
$389$			17.0791i			0.865943i	−0.901408	+	0.432971i	$0.857465\pi$
$390$	−49.2197	−	24.5980i	−2.49233	−	1.24557i
$391$		−	1.11722i		−	0.0565005i
$392$	0.0961466	−	0.358824i	0.00485614	−	0.0181233i
$393$	11.8053	−	6.81577i	0.595497	−	0.343810i
$394$	2.48650	+	1.43558i	0.125268	+	0.0723235i
$395$	11.0147	+	11.0147i	0.554211	+	0.554211i
$396$	−15.6686	+	0.884647i	−0.787379	+	0.0444552i
$397$	28.2570	−	7.57145i	1.41818	−	0.380000i	0.533342	−	0.845900i	$-0.320936\pi$
$397$	28.2570	−	7.57145i	1.41818	−	0.380000i	0.884837	+	0.465900i	$0.154269\pi$
$398$	−1.84077	+	1.84077i	−0.0922695	+	0.0922695i
$399$	8.13262	−	14.0861i	0.407140	−	0.705187i
$400$	−18.9215	+	10.9243i	−0.946074	+	0.546216i
$401$	−3.71510	+	13.8650i	−0.185523	+	0.692383i	0.808995	+	0.587816i	$0.200012\pi$
$401$	−3.71510	+	13.8650i	−0.185523	+	0.692383i	−0.994518	+	0.104566i	$0.966654\pi$
$402$	−56.0727			−2.79665
$403$	11.2220	+	9.94727i	0.559007	+	0.495509i
$404$		−	11.6909i		−	0.581645i
$405$	21.4093	+	5.73661i	1.06384	+	0.285054i
$406$	28.5323	−	16.4731i	1.41603	−	0.817547i
$407$	13.3498	−	14.9475i	0.661726	−	0.740919i
$408$	1.88171	−	1.88171i	0.0931587	−	0.0931587i
$409$	13.3991	−	3.59027i	0.662542	−	0.177527i	0.0881488	−	0.996107i	$-0.471905\pi$
$409$	13.3991	−	3.59027i	0.662542	−	0.177527i	0.574393	+	0.818580i	$0.305238\pi$
$410$	−41.6033	+	11.1476i	−2.05464	+	0.550539i
$411$	22.3497	+	22.3497i	1.10243	+	1.10243i
$412$	−2.39246	+	4.14386i	−0.117868	+	0.204153i
$413$	0.516090	+	0.893893i	0.0253951	+	0.0439856i
$414$	−23.2567	−	6.23160i	−1.14300	−	0.306267i
$415$	−25.0763			−1.23095
$416$	4.97395	+	14.9123i	0.243868	+	0.731135i
$417$			6.59140i			0.322782i
$418$	5.12714	−	10.1639i	0.250777	−	0.497131i
$419$	−9.10258	−	15.7661i	−0.444690	−	0.770226i	0.553340	−	0.832955i	$-0.313353\pi$
$419$	−9.10258	−	15.7661i	−0.444690	−	0.770226i	−0.998031	+	0.0627292i	$0.980020\pi$
$420$	9.94710	−	17.2289i	0.485369	−	0.840684i
$421$	−18.1194	+	18.1194i	−0.883087	+	0.883087i	−0.993847	−	0.110760i	$-0.964671\pi$
$421$	−18.1194	+	18.1194i	−0.883087	+	0.883087i	0.110760	+	0.993847i	$0.464671\pi$
$422$	9.49634	+	35.4408i	0.462274	+	1.72523i
$423$	−76.0418	+	20.3753i	−3.69728	+	0.990682i
$424$	−2.52973	+	2.52973i	−0.122854	+	0.122854i
$425$	−1.72038	−	0.993263i	−0.0834508	−	0.0481803i
$426$	27.5798	+	47.7695i	1.33624	+	2.31444i
$427$	−1.56518	+	5.84133i	−0.0757444	+	0.282682i
$428$	−9.09400			−0.439575
$429$	−35.2308	+	4.12460i	−1.70096	+	0.199138i
$430$	30.3456			1.46340
$431$	8.24893	−	30.7854i	0.397337	−	1.48288i	−0.420427	−	0.907326i	$-0.638120\pi$
$431$	8.24893	−	30.7854i	0.397337	−	1.48288i	0.817763	−	0.575554i	$-0.195214\pi$
$432$	−20.6143	−	35.7050i	−0.991805	−	1.71786i
$433$	2.85044	+	1.64570i	0.136983	+	0.0790873i	0.566925	−	0.823769i	$-0.308133\pi$
$433$	2.85044	+	1.64570i	0.136983	+	0.0790873i	−0.429942	+	0.902856i	$0.641466\pi$
$434$	−13.2306	+	13.2306i	−0.635089	+	0.635089i
$435$	−64.3316	+	17.2376i	−3.08446	+	0.826480i
$436$	2.57874	+	9.62398i	0.123499	+	0.460905i
$437$	3.57859	−	3.57859i	0.171187	−	0.171187i
$438$	−11.3808	+	19.7122i	−0.543797	+	0.941883i
$439$	0.148579	+	0.257346i	0.00709128	+	0.0122825i	0.869549	−	0.493846i	$-0.164409\pi$
$439$	0.148579	+	0.257346i	0.00709128	+	0.0122825i	−0.862458	+	0.506129i	$0.831076\pi$
$440$	−9.09920	+	18.0380i	−0.433787	+	0.859927i
$441$		−	1.08419i		−	0.0516281i
$442$	−1.81219	+	2.04442i	−0.0861972	+	0.0972433i
$443$	21.7425			1.03302			0.516508	−	0.856283i	$-0.327232\pi$
$443$	21.7425			1.03302			0.516508	+	0.856283i	$0.327232\pi$
$444$	−14.1276	−	3.78549i	−0.670468	−	0.179651i
$445$	−7.36258	−	12.7524i	−0.349020	−	0.604520i
$446$	−1.31394	+	2.27581i	−0.0622169	+	0.107763i
$447$	−15.5689	−	15.5689i	−0.736385	−	0.736385i
$448$	6.77393	−	1.81507i	0.320038	−	0.0857540i
$449$	−12.5508	+	3.36299i	−0.592311	+	0.158709i	−0.542509	−	0.840050i	$-0.682526\pi$
$449$	−12.5508	+	3.36299i	−0.592311	+	0.158709i	−0.0498018	+	0.998759i	$0.515859\pi$
$450$	−30.2721	+	30.2721i	−1.42704	+	1.42704i
$451$	−18.4955	+	20.7089i	−0.870918	+	0.975146i
$452$	2.85038	−	1.64567i	0.134071	−	0.0774058i
$453$	55.0708	+	14.7562i	2.58745	+	0.693305i
$454$			25.9101i			1.21602i
$455$	13.2479	−	26.5084i	0.621069	−	1.24273i
$456$	12.0547			0.564512
$457$	1.67295	−	6.24352i	0.0782572	−	0.292060i	−0.915695	−	0.401874i	$-0.868359\pi$
$457$	1.67295	−	6.24352i	0.0782572	−	0.292060i	0.993952	+	0.109814i	$0.0350256\pi$
$458$	−23.5137	+	13.5757i	−1.09873	+	0.634349i
$459$	1.87430	−	3.24638i	0.0874847	−	0.151528i
$460$	4.37702	−	4.37702i	0.204080	−	0.204080i
$461$	−31.0375	+	8.31646i	−1.44556	+	0.387336i	−0.894477	−	0.447114i	$-0.852452\pi$
$461$	−31.0375	+	8.31646i	−1.44556	+	0.387336i	−0.551082	+	0.834451i	$0.685785\pi$
$462$	−2.49485	−	44.1881i	−0.116071	−	2.05582i
$463$	−24.1352	−	24.1352i	−1.12166	−	1.12166i	−0.991492	−	0.130167i	$-0.958449\pi$
$463$	−24.1352	−	24.1352i	−1.12166	−	1.12166i	−0.130167	−	0.991492i	$-0.541551\pi$
$464$	31.4968	+	18.1847i	1.46220	+	0.844203i
$465$	32.7567	−	18.9121i	1.51905	−	0.877026i
$466$	5.52498	−	20.6195i	0.255940	−	0.955180i
$467$			0.988294i			0.0457328i	0.999739	+	0.0228664i	$0.00727924\pi$
$467$			0.988294i			0.0457328i	−0.999739	+	0.0228664i	$0.992721\pi$
$468$	9.40303	+	14.2356i	0.434655	+	0.658040i
$469$		−	30.1993i		−	1.39448i
$470$	18.0775	−	67.4660i	0.833851	−	3.11197i
$471$	−14.2160	−	24.6229i	−0.655039	−	1.13456i
$472$	−0.382490	+	0.662492i	−0.0176055	+	0.0304937i
$473$	16.3633	−	10.7207i	0.752384	−	0.492937i
$474$	−6.54575	−	24.4291i	−0.300656	−	1.12206i
$475$	−2.32904	−	8.69211i	−0.106864	−	0.398821i
$476$	−0.698453	−	0.698453i	−0.0320135	−	0.0320135i
$477$	−5.22068	+	9.04248i	−0.239038	+	0.414027i
$478$	18.1583	−	10.4837i	0.830541	−	0.479513i
$479$	27.6299	+	7.40341i	1.26244	+	0.338271i	0.827131	−	0.562009i	$-0.189971\pi$
$479$	27.6299	+	7.40341i	1.26244	+	0.338271i	0.435312	+	0.900280i	$0.356638\pi$
$480$	39.6500			1.80977
$481$	−21.3455	−	4.36376i	−0.973269	−	0.198970i
$482$	5.69584			0.259438
$483$	5.09250	−	19.0055i	0.231717	−	0.864779i
$484$	−1.01034	−	8.91895i	−0.0459247	−	0.405407i
$485$	−20.3759	−	11.7640i	−0.925221	−	0.534176i
$486$	4.10706	+	4.10706i	0.186300	+	0.186300i
$487$	−6.59278	−	24.6046i	−0.298747	−	1.11494i	−0.938196	−	0.346106i	$-0.887504\pi$
$487$	−6.59278	−	24.6046i	−0.298747	−	1.11494i	0.639448	−	0.768834i	$-0.279163\pi$
$488$	−4.32920	+	1.16000i	−0.195974	+	0.0525109i
$489$	2.58512	+	2.58512i	0.116903	+	0.116903i
$490$	0.833046	+	0.480960i	0.0376332	+	0.0217275i
$491$	14.6114	+	25.3077i	0.659404	+	1.14212i	0.980770	+	0.195166i	$0.0625245\pi$
$491$	14.6114	+	25.3077i	0.659404	+	1.14212i	−0.321367	+	0.946955i	$0.604142\pi$
$492$	19.5731	+	5.24460i	0.882423	+	0.236445i
$493$			3.30679i			0.148930i
$494$	−12.3532	+	0.743856i	−0.555795	+	0.0334677i
$495$	−12.0262	+	57.7243i	−0.540535	+	2.59452i
$496$	−19.9512	−	5.34590i	−0.895833	−	0.240038i
$497$	−25.7274	+	14.8537i	−1.15403	+	0.666282i
$498$	35.2589	+	20.3568i	1.57999	+	0.912208i
$499$	−2.64738	+	2.64738i	−0.118513	+	0.118513i	−0.763876	−	0.645363i	$-0.776706\pi$
$499$	−2.64738	+	2.64738i	−0.118513	+	0.118513i	0.645363	+	0.763876i	$0.276706\pi$
$500$	0.388811	+	1.45106i	0.0173882	+	0.0648936i
$501$	15.5381	+	57.9889i	0.694190	+	2.59075i
$502$	4.16204	−	4.16204i	0.185761	−	0.185761i
$503$	25.1971	+	14.5475i	1.12348	+	0.648643i	0.942288	−	0.334804i	$-0.108670\pi$
$503$	25.1971	+	14.5475i	1.12348	+	0.648643i	0.181195	+	0.983447i	$0.442004\pi$
$504$	26.7490	−	15.4436i	1.19150	−	0.687911i
$505$	−42.4283	−	11.3686i	−1.88803	−	0.505897i
$506$	2.80870	−	13.4815i	0.124862	−	0.599325i
$507$	23.1488	+	30.8403i	1.02807	+	1.36967i
$508$		−	0.354324i		−	0.0157206i
$509$	4.04720	+	1.08444i	0.179389	+	0.0480671i	0.347395	−	0.937719i	$-0.387066\pi$
$509$	4.04720	+	1.08444i	0.179389	+	0.0480671i	−0.168006	+	0.985786i	$0.553733\pi$
$510$	3.44540	+	5.96761i	0.152565	+	0.264250i
$511$	−10.6165	−	6.12941i	−0.469644	−	0.271149i
$512$	−1.35618	−	1.35618i	−0.0599351	−	0.0599351i
$513$	16.4021	−	4.39493i	0.724170	−	0.194041i
$514$	−4.56950	−	17.0536i	−0.201552	−	0.752202i
$515$	12.7123	+	12.7123i	0.560169	+	0.560169i
$516$	−12.3640	−	7.13835i	−0.544294	−	0.314248i
$517$	−14.0869	−	42.7662i	−0.619539	−	1.88086i
$518$	7.03575	−	26.2578i	0.309133	−	1.15370i
$519$	−33.5410			−1.47229
$520$	21.9233	−	1.32013i	0.961402	−	0.0578916i
$521$	37.0108			1.62147			0.810736	−	0.585412i	$-0.199067\pi$
$521$	37.0108			1.62147			0.810736	+	0.585412i	$0.199067\pi$
$522$	68.8356	+	18.4444i	3.01285	+	0.807291i
$523$	−6.14967	+	3.55051i	−0.268906	+	0.155253i	−0.628390	−	0.777898i	$-0.716286\pi$
$523$	−6.14967	+	3.55051i	−0.268906	+	0.155253i	0.359484	+	0.933151i	$0.382953\pi$
$524$	1.87497	−	3.24754i	0.0819083	−	0.141869i
$525$	−24.7385	−	24.7385i	−1.07968	−	1.07968i
$526$	1.46805	+	5.47882i	0.0640099	+	0.238888i
$527$	−0.486061	−	1.81400i	−0.0211731	−	0.0790192i
$528$	40.8671	−	26.7747i	1.77851	−	1.16522i
$529$	−8.43894	+	14.6167i	−0.366910	+	0.635507i
$530$	−4.63191	−	8.02270i	−0.201197	−	0.348484i
$531$	−0.577849	+	2.15656i	−0.0250765	+	0.0935869i
$532$		−	4.47444i		−	0.193992i
$533$	29.5730	+	6.04576i	1.28095	+	0.261871i
$534$			23.9075i			1.03458i
$535$	−8.84330	+	33.0036i	−0.382329	+	1.42687i
$536$	19.3831	−	11.1908i	0.837222	−	0.483370i
$537$	−32.0885	−	18.5263i	−1.38472	−	0.799470i
$538$	−0.606842	−	0.606842i	−0.0261628	−	0.0261628i
$539$	0.619120	−	0.0349553i	0.0266674	−	0.00150563i
$540$	20.0616	−	5.37549i	0.863314	−	0.231324i
$541$	−5.78944	+	5.78944i	−0.248908	+	0.248908i	−0.820522	−	0.571615i	$-0.806317\pi$
$541$	−5.78944	+	5.78944i	−0.248908	+	0.248908i	0.571615	+	0.820522i	$0.306317\pi$
$542$	5.27245	−	9.13215i	0.226471	−	0.392260i
$543$	−10.2140	+	5.89705i	−0.438324	+	0.253066i
$544$	0.509524	−	1.90157i	0.0218457	−	0.0815292i
$545$	37.4347			1.60352
$546$	−40.1467	+	26.5181i	−1.71812	+	1.13487i
$547$			11.3494i			0.485265i	0.970118	+	0.242632i	$0.0780109\pi$
$547$			11.3494i			0.485265i	−0.970118	+	0.242632i	$0.921989\pi$
$548$	8.39863	+	2.25041i	0.358772	+	0.0961326i
$549$	−11.3282	+	6.54036i	−0.483477	+	0.279136i
$550$	−18.2627	−	16.3107i	−0.778723	−	0.695490i
$551$	−10.5920	+	10.5920i	−0.451235	+	0.451235i
$552$	14.0856	−	3.77421i	0.599521	−	0.160641i
$553$	13.1569	−	3.52537i	0.559487	−	0.149914i
$554$	−33.8011	−	33.8011i	−1.43607	−	1.43607i
$555$	−27.4763	+	47.5904i	−1.16630	+	2.02010i
$556$	0.906623	+	1.57032i	0.0384494	+	0.0665963i
$557$	33.9317	+	9.09197i	1.43773	+	0.385239i	0.891739	−	0.452550i	$-0.149486\pi$
$557$	33.9317	+	9.09197i	1.43773	+	0.385239i	0.545993	+	0.837790i	$0.316152\pi$
$558$	−40.4723			−1.71333
$559$	−19.0233	−	9.50707i	−0.804599	−	0.402106i
$560$			40.8174i			1.72485i
$561$	3.96613	+	2.00070i	0.167450	+	0.0844698i
$562$	15.3250	+	26.5438i	0.646448	+	1.11968i
$563$	18.2738	−	31.6511i	0.770147	−	1.33393i	−0.167335	−	0.985900i	$-0.553516\pi$
$563$	18.2738	−	31.6511i	0.770147	−	1.33393i	0.937482	−	0.348034i	$-0.113151\pi$
$564$	−23.2358	+	23.2358i	−0.978405	+	0.978405i
$565$	−3.20060	−	11.9448i	−0.134650	−	0.502522i
$566$	36.8471	−	9.87316i	1.54880	−	0.415000i
$567$	13.7045	−	13.7045i	0.575536	−	0.575536i
$568$	−19.0674	−	11.0086i	−0.800051	−	0.461910i
$569$	11.1623	+	19.3337i	0.467950	+	0.810513i	0.999329	−	0.0366211i	$-0.0116595\pi$
$569$	11.1623	+	19.3337i	0.467950	+	0.810513i	−0.531379	+	0.847134i	$0.678326\pi$
$570$	−8.07891	+	30.1509i	−0.338388	+	1.26288i
$571$	31.7969			1.33066			0.665329	−	0.746550i	$-0.268291\pi$
$571$	31.7969			1.33066			0.665329	+	0.746550i	$0.268291\pi$
$572$	−7.82597	+	5.82850i	−0.327220	+	0.243702i
$573$	−60.0940			−2.51046
$574$	−9.74766	+	36.3788i	−0.406859	+	1.51842i
$575$	−5.44285	−	9.42729i	−0.226982	−	0.393145i
$576$	13.1368	+	7.58456i	0.547369	+	0.316023i
$577$	15.3471	−	15.3471i	0.638907	−	0.638907i	−0.311379	−	0.950286i	$-0.600791\pi$
$577$	15.3471	−	15.3471i	0.638907	−	0.638907i	0.950286	+	0.311379i	$0.100791\pi$
$578$	−27.2251	+	7.29494i	−1.13241	+	0.303429i
$579$	−8.15104	−	30.4201i	−0.338746	−	1.26422i
$580$	−12.9552	+	12.9552i	−0.537936	+	0.537936i
$581$	−10.9636	+	18.9895i	−0.454848	+	0.787819i
$582$	19.0999	+	33.0819i	0.791715	+	1.37129i
$583$	−5.33197	−	2.68969i	−0.220827	−	0.111396i
$584$		−	9.08541i		−	0.375957i
$585$	60.8071	−	20.2820i	2.51406	−	0.838558i
$586$	−0.0862159			−0.00356155
$587$	−13.4108	−	3.59342i	−0.553524	−	0.148316i	−0.0287945	−	0.999585i	$-0.509167\pi$
$587$	−13.4108	−	3.59342i	−0.553524	−	0.148316i	−0.524729	+	0.851269i	$0.675834\pi$
$588$	−0.226277	−	0.391923i	−0.00933151	−	0.0161626i
$589$	4.25355	−	7.36736i	0.175264	−	0.303567i
$590$	−1.40067	−	1.40067i	−0.0576647	−	0.0576647i
$591$	−4.90226	+	1.31356i	−0.201652	+	0.0540325i
$592$	28.9860	−	7.76677i	1.19132	−	0.319212i
$593$	8.01765	−	8.01765i	0.329245	−	0.329245i	−0.523054	−	0.852299i	$-0.675207\pi$
$593$	8.01765	−	8.01765i	0.329245	−	0.329245i	0.852299	+	0.523054i	$0.175207\pi$
$594$	30.7784	−	34.4618i	1.26285	−	1.41399i
$595$	−3.21400	+	1.85560i	−0.131761	+	0.0760723i
$596$	−5.85054	−	1.56765i	−0.239647	−	0.0642133i
$597$		−	4.60161i		−	0.188331i
$598$	−14.2014	+	4.73684i	−0.580740	+	0.193704i
$599$	−0.139561			−0.00570233			−0.00285116	−	0.999996i	$-0.500908\pi$
$599$	−0.139561			−0.00570233			−0.00285116	+	0.999996i	$0.500908\pi$
$600$	6.71090	−	25.0454i	0.273971	−	1.02247i
$601$	14.4562	−	8.34627i	0.589679	−	0.340451i	−0.175292	−	0.984517i	$-0.556087\pi$
$601$	14.4562	−	8.34627i	0.589679	−	0.340451i	0.764971	+	0.644065i	$0.222753\pi$
$602$	13.2674	−	22.9798i	0.540739	−	0.936588i
$603$	46.1897	−	46.1897i	1.88099	−	1.88099i
$604$	15.1496	−	4.05931i	0.616427	−	0.165171i
$605$	−33.3508	−	5.00637i	−1.35590	−	0.203538i
$606$	50.4279	+	50.4279i	2.04849	+	2.04849i
$607$	1.54492	+	0.891961i	0.0627064	+	0.0362036i	0.531025	−	0.847356i	$-0.321807\pi$
$607$	1.54492	+	0.891961i	0.0627064	+	0.0362036i	−0.468319	+	0.883559i	$0.655140\pi$
$608$	7.72300	−	4.45888i	0.313209	−	0.180831i
$609$	−15.0729	+	56.2529i	−0.610785	+	2.27948i
$610$		−	11.6055i		−	0.469894i
$611$	−32.4692	+	36.6300i	−1.31356	+	1.48189i
$612$		−	2.13656i		−	0.0863654i
$613$	−7.26468	+	27.1121i	−0.293418	+	1.09505i	0.649048	+	0.760747i	$0.275167\pi$
$613$	−7.26468	+	27.1121i	−0.293418	+	1.09505i	−0.942466	+	0.334302i	$0.891499\pi$
$614$	−1.01106	−	1.75121i	−0.0408032	−	0.0706732i
$615$	38.0670	−	65.9340i	1.53501	−	2.65872i
$616$	9.68135	+	14.7769i	0.390073	+	0.595380i
$617$	−9.35141	−	34.9000i	−0.376474	−	1.40502i	−0.851180	−	0.524875i	$-0.824112\pi$
$617$	−9.35141	−	34.9000i	−0.376474	−	1.40502i	0.474706	−	0.880145i	$-0.342554\pi$
$618$	−7.55455	−	28.1940i	−0.303888	−	1.13413i
$619$	4.01983	+	4.01983i	0.161570	+	0.161570i	0.783262	−	0.621692i	$-0.213554\pi$
$619$	4.01983	+	4.01983i	0.161570	+	0.161570i	−0.621692	+	0.783262i	$0.713554\pi$
$620$	5.20257	−	9.01111i	0.208940	−	0.361895i
$621$	17.7894	−	10.2707i	0.713863	−	0.412149i
$622$	−3.52444	−	0.944372i	−0.141317	−	0.0378659i
$623$	−12.8760			−0.515865
$624$	−47.5104	−	23.7438i	−1.90194	−	0.950513i
$625$	27.6418			1.10567
$626$	5.74141	−	21.4272i	0.229473	−	0.856405i
$627$	6.29549	+	19.1124i	0.251417	+	0.763277i
$628$	−6.77356	−	3.91072i	−0.270295	−	0.156055i
$629$	1.92930	+	1.92930i	0.0769261	+	0.0769261i
$630$	20.7002	+	77.2542i	0.824715	+	3.07788i
$631$	−20.6925	+	5.54454i	−0.823756	+	0.220725i	−0.645988	−	0.763348i	$-0.723554\pi$
$631$	−20.6925	+	5.54454i	−0.823756	+	0.220725i	−0.177768	+	0.984072i	$0.556888\pi$
$632$	7.13820	+	7.13820i	0.283942	+	0.283942i
$633$	−56.1675	−	32.4283i	−2.23246	−	1.28891i
$634$	−25.7524	−	44.6044i	−1.02276	−	1.77147i
$635$	−1.28590	−	0.344556i	−0.0510293	−	0.0136733i
$636$			4.35835i			0.172820i
$637$	−0.371545	−	0.562495i	−0.0147211	−	0.0222869i
$638$	−8.31325	+	39.9028i	−0.329125	+	1.57977i
$639$	−62.0688	−	16.6313i	−2.45540	−	0.657923i
$640$	−34.8075	+	20.0961i	−1.37589	+	0.794370i
$641$	33.3177	+	19.2360i	1.31597	+	0.759777i	0.983078	−	0.183188i	$-0.0586417\pi$
$641$	33.3177	+	19.2360i	1.31597	+	0.759777i	0.332894	+	0.942964i	$0.391975\pi$
$642$	39.2263	−	39.2263i	1.54814	−	1.54814i
$643$	−5.93350	−	22.1441i	−0.233994	−	0.873279i	−0.978600	−	0.205774i	$-0.934029\pi$
$643$	−5.93350	−	22.1441i	−0.233994	−	0.873279i	0.744605	−	0.667505i	$-0.232638\pi$
$644$	−1.40091	−	5.22826i	−0.0552036	−	0.206022i
$645$	−37.9294	+	37.9294i	−1.49347	+	1.49347i
$646$	1.34219	+	0.774911i	0.0528076	+	0.0304885i
$647$	−12.3604	+	7.13629i	−0.485938	+	0.280557i	−0.722888	−	0.690965i	$-0.757186\pi$
$647$	−12.3604	+	7.13629i	−0.485938	+	0.280557i	0.236950	+	0.971522i	$0.423852\pi$
$648$	13.8745	+	3.71767i	0.545043	+	0.146044i
$649$	−1.25012	−	0.260447i	−0.0490716	−	0.0102235i
$650$	−5.33159	+	26.0797i	−0.209122	+	1.02293i
$651$		−	33.0742i		−	1.29628i
$652$	0.971445	+	0.260298i	0.0380447	+	0.0101941i
$653$	11.9727	+	20.7373i	0.468528	+	0.811514i	0.999353	−	0.0359673i	$-0.0114512\pi$
$653$	11.9727	+	20.7373i	0.468528	+	0.811514i	−0.530825	+	0.847481i	$0.678118\pi$
$654$	−52.6356	−	30.3891i	−2.05821	−	1.18831i
$655$	−9.96258	−	9.96258i	−0.389270	−	0.389270i
$656$	−40.1585	+	10.7604i	−1.56793	+	0.420125i
$657$	−6.86291	−	25.6127i	−0.267748	−	0.999248i
$658$	−43.1863	−	43.1863i	−1.68358	−	1.68358i
$659$	13.9122	+	8.03221i	0.541942	+	0.312891i	0.745866	−	0.666096i	$-0.232036\pi$
$659$	13.9122	+	8.03221i	0.541942	+	0.312891i	−0.203923	+	0.978987i	$0.565369\pi$
$660$	7.70009	+	23.3767i	0.299725	+	0.909935i
$661$	5.31487	−	19.8354i	0.206724	−	0.771506i	−0.782193	−	0.623037i	$-0.785899\pi$
$661$	5.31487	−	19.8354i	0.206724	−	0.771506i	0.988917	−	0.148469i	$-0.0474346\pi$
$662$	26.2506			1.02026
$663$	−0.290266	−	4.82043i	−0.0112730	−	0.187210i
$664$	−16.2510			−0.630660
$665$	−16.2385	−	4.35109i	−0.629702	−	0.168728i
$666$	50.9223	−	29.4000i	1.97320	−	1.13923i
$667$	−9.06020	+	15.6927i	−0.350812	+	0.607625i
$668$	11.6779	+	11.6779i	0.451832	+	0.451832i
$669$	−1.20225	−	4.48688i	−0.0464819	−	0.173473i
$670$	14.9999	+	55.9805i	0.579498	+	2.16272i
$671$	−4.10006	−	6.25804i	−0.158281	−	0.241589i
$672$	17.3354	−	30.0258i	0.668727	−	1.15827i
$673$	−3.53947	−	6.13054i	−0.136437	−	0.236315i	0.789709	−	0.613482i	$-0.210232\pi$
$673$	−3.53947	−	6.13054i	−0.136437	−	0.236315i	−0.926145	+	0.377167i	$0.876898\pi$
$674$	−4.81982	+	17.9878i	−0.185652	+	0.692864i
$675$		−	36.5245i		−	1.40583i
$676$	9.75687	+	4.16329i	0.375264	+	0.160126i
$677$		−	44.7375i		−	1.71940i	−0.510796	−	0.859702i	$-0.670649\pi$
$677$		−	44.7375i		−	1.71940i	0.510796	−	0.859702i	$-0.329351\pi$
$678$	−5.19645	+	19.3934i	−0.199568	+	0.744799i
$679$	−17.8171	+	10.2867i	−0.683757	+	0.394767i
$680$	−2.38200	−	1.37525i	−0.0913454	−	0.0527383i
$681$	−32.3854	−	32.3854i	−1.24101	−	1.24101i
$682$	−1.30486	−	23.1114i	−0.0499658	−	0.884982i
$683$	5.43458	−	1.45619i	0.207948	−	0.0557196i	−0.153341	−	0.988173i	$-0.549003\pi$
$683$	5.43458	−	1.45619i	0.207948	−	0.0557196i	0.361289	+	0.932454i	$0.382337\pi$
$684$	6.84364	−	6.84364i	0.261673	−	0.261673i
$685$	16.3342	−	28.2916i	0.624097	−	1.08097i
$686$	−26.5436	+	15.3250i	−1.01344	+	0.585110i
$687$	12.4217	−	46.3585i	0.473919	−	1.76869i
$688$	29.2918			1.11674
$689$	0.390227	+	6.48047i	0.0148665	+	0.246886i
$690$			37.7599i			1.43750i
$691$	−22.5794	−	6.05012i	−0.858960	−	0.230158i	−0.197652	−	0.980272i	$-0.563332\pi$
$691$	−22.5794	−	6.05012i	−0.858960	−	0.230158i	−0.661308	+	0.750115i	$0.729998\pi$
$692$	−7.99070	+	4.61344i	−0.303761	+	0.175377i
$693$	38.4550	+	34.3447i	1.46078	+	1.30465i
$694$	33.1539	−	33.1539i	1.25851	−	1.25851i
$695$	6.58057	−	1.76326i	0.249615	−	0.0668842i
$696$	−41.6908	+	11.1710i	−1.58028	+	0.423436i
$697$	−2.67294	−	2.67294i	−0.101245	−	0.101245i
$698$	−10.0335	+	17.3786i	−0.379775	+	0.657790i
$699$	18.8668	+	32.6783i	0.713609	+	1.23601i
$700$	−9.29633	−	2.49094i	−0.351368	−	0.0941489i
$701$	18.4993			0.698709			0.349354	−	0.936991i	$-0.386401\pi$
$701$	18.4993			0.698709			0.349354	+	0.936991i	$0.386401\pi$
$702$	−49.2126	−	10.0608i	−1.85741	−	0.379719i
$703$			12.3595i			0.466148i
$704$	−3.90757	+	7.74624i	−0.147272	+	0.291947i
$705$	61.7314	+	106.922i	2.32494	+	4.02691i
$706$	−14.2596	+	24.6983i	−0.536667	+	0.929534i
$707$	−27.1592	+	27.1592i	−1.02143	+	1.02143i
$708$	0.241201	+	0.900175i	0.00906489	+	0.0338306i
$709$	18.3100	−	4.90614i	0.687645	−	0.184254i	0.101955	−	0.994789i	$-0.467490\pi$
$709$	18.3100	−	4.90614i	0.687645	−	0.184254i	0.585690	+	0.810535i	$0.300824\pi$
$710$	40.3132	−	40.3132i	1.51293	−	1.51293i
$711$	25.5154	+	14.7313i	0.956902	+	0.552468i
$712$	−4.77139	−	8.26429i	−0.178815	−	0.309718i
$713$	2.66350	−	9.94031i	0.0997488	−	0.372267i
$714$	6.02545			0.225497
$715$	13.5424	+	34.0696i	0.506456	+	1.27413i
$716$	−10.1929			−0.380927
$717$	−9.59258	+	35.8000i	−0.358242	+	1.33698i
$718$	−24.6293	−	42.6592i	−0.919156	−	1.59203i
$719$	−41.2942	−	23.8412i	−1.54001	−	0.889127i	−0.998837	−	0.0482172i	$-0.984646\pi$
$719$	−41.2942	−	23.8412i	−1.54001	−	0.889127i	−0.541176	−	0.840909i	$-0.682021\pi$
$720$	−62.4300	+	62.4300i	−2.32663	+	2.32663i
$721$	15.1845	−	4.06868i	0.565502	−	0.151526i
$722$	−6.43509	−	24.0161i	−0.239489	−	0.893786i
$723$	−7.11930	+	7.11930i	−0.264770	+	0.264770i
$724$	−1.62223	+	2.80979i	−0.0602898	+	0.104425i
$725$	16.1099	+	27.9031i	0.598305	+	1.03630i
$726$	42.8293	+	34.1132i	1.58954	+	1.26606i
$727$			21.7318i			0.805987i	0.915203	+	0.402994i	$0.132030\pi$
$727$			21.7318i			0.805987i	−0.915203	+	0.402994i	$0.867970\pi$
$728$	8.58541	−	17.1791i	0.318196	−	0.636698i
$729$	−31.9553			−1.18353
$730$	22.7242	+	6.08894i	0.841061	+	0.225362i
$731$	1.33164	+	2.30647i	0.0492524	+	0.0853077i
$732$	−2.73002	+	4.72854i	−0.100905	+	0.174772i
$733$	−18.9129	−	18.9129i	−0.698564	−	0.698564i	0.265537	−	0.964101i	$-0.414451\pi$
$733$	−18.9129	−	18.9129i	−0.698564	−	0.698564i	−0.964101	+	0.265537i	$0.914451\pi$
$734$	−19.8649	+	5.32279i	−0.733228	+	0.196468i
$735$	−1.64239	+	0.440078i	−0.0605806	+	0.0162325i
$736$	7.62808	−	7.62808i	0.281175	−	0.281175i
$737$	27.8655	+	24.8871i	1.02644	+	0.916730i
$738$	−70.5502	+	40.7322i	−2.59699	+	1.49937i
$739$	9.84854	+	2.63891i	0.362284	+	0.0970738i	0.435369	−	0.900252i	$-0.356618\pi$
$739$	9.84854	+	2.63891i	0.362284	+	0.0970738i	−0.0730850	+	0.997326i	$0.523284\pi$
$740$			15.1171i			0.555714i
$741$	14.5106	−	16.3701i	0.533061	−	0.601372i
$742$	−8.10046			−0.297377
$743$	2.39547	−	8.94003i	0.0878814	−	0.327978i	−0.907963	−	0.419051i	$-0.862363\pi$
$743$	2.39547	−	8.94003i	0.0878814	−	0.327978i	0.995844	+	0.0910729i	$0.0290296\pi$
$744$	21.2283	−	12.2562i	0.778267	−	0.449333i
$745$	−11.3785	+	19.7081i	−0.416876	+	0.722051i
$746$	−5.19523	+	5.19523i	−0.190211	+	0.190211i
$747$	−45.8133	+	12.2756i	−1.67622	+	0.449142i
$748$	1.22007	−	0.0688848i	0.0446101	−	0.00251868i
$749$	21.1263	+	21.1263i	0.771938	+	0.771938i
$750$	−7.93617	−	4.58195i	−0.289788	−	0.167309i
$751$	0.780318	−	0.450517i	0.0284742	−	0.0164396i	−0.485695	−	0.874128i	$-0.661434\pi$
$751$	0.780318	−	0.450517i	0.0284742	−	0.0164396i	0.514170	+	0.857689i	$0.328100\pi$
$752$	17.4497	−	65.1231i	0.636325	−	2.37480i
$753$			10.4044i			0.379156i
$754$	42.0338	−	14.0202i	1.53078	−	0.510586i
$755$		−	58.9276i		−	2.14460i
$756$	4.70043	−	17.5423i	0.170953	−	0.638006i
$757$	−2.55257	−	4.42118i	−0.0927748	−	0.160691i	0.815903	−	0.578189i	$-0.196240\pi$
$757$	−2.55257	−	4.42118i	−0.0927748	−	0.160691i	−0.908678	+	0.417498i	$0.862907\pi$
$758$	−31.8649	+	55.1916i	−1.15739	+	2.00465i
$759$	13.3400	+	20.3613i	0.484213	+	0.739068i
$760$	−3.22473	−	12.0349i	−0.116973	−	0.436550i
$761$	7.81971	+	29.1835i	0.283464	+	1.05790i	0.949954	+	0.312389i	$0.101129\pi$
$761$	7.81971	+	29.1835i	0.283464	+	1.05790i	−0.666490	+	0.745514i	$0.732204\pi$
$762$	1.52835	+	1.52835i	0.0553663	+	0.0553663i
$763$	16.3668	−	28.3481i	0.592518	−	1.02627i
$764$	−14.3166	+	8.26571i	−0.517957	+	0.299043i
$765$	−7.75393	−	2.07766i	−0.280344	−	0.0751180i
$766$	9.69710			0.350371
$767$	0.439242	+	1.31688i	0.0158601	+	0.0475499i
$768$	49.7365			1.79471
$769$	13.0624	−	48.7497i	0.471044	−	1.75796i	−0.164987	−	0.986296i	$-0.552758\pi$
$769$	13.0624	−	48.7497i	0.471044	−	1.75796i	0.636031	−	0.771663i	$-0.280575\pi$
$770$	−43.4481	+	14.3115i	−1.56576	+	0.515749i
$771$	27.0270	+	15.6040i	0.973354	+	0.561966i
$772$	−6.12605	−	6.12605i	−0.220481	−	0.220481i
$773$	5.12116	+	19.1124i	0.184195	+	0.687426i	0.994801	+	0.101834i	$0.0324711\pi$
$773$	5.12116	+	19.1124i	0.184195	+	0.687426i	−0.810606	+	0.585592i	$0.800862\pi$
$774$	55.4400	−	14.8551i	1.99275	−	0.533956i
$775$	−12.9388	−	12.9388i	−0.464777	−	0.464777i
$776$	−13.2048	−	7.62379i	−0.474025	−	0.273678i
$777$	24.0258	+	41.6140i	0.861922	+	1.49289i
$778$	−27.6837	−	7.41782i	−0.992508	−	0.265942i
$779$		−	17.1234i		−	0.613511i
$780$	17.7481	−	20.0225i	0.635485	−	0.716921i
$781$	7.49602	−	35.9802i	0.268229	−	1.28747i
$782$	1.81092	+	0.485236i	0.0647585	+	0.0173520i
$783$	−52.6534	+	30.3995i	−1.88168	+	1.08639i
$784$	0.804117	+	0.464257i	0.0287185	+	0.0165806i
$785$	−20.7795	+	20.7795i	−0.741651	+	0.741651i
$786$	5.92049	+	22.0956i	0.211177	+	0.788123i
$787$	7.38479	+	27.5604i	0.263239	+	0.982423i	0.963319	+	0.268358i	$0.0864811\pi$
$787$	7.38479	+	27.5604i	0.263239	+	0.982423i	−0.700080	+	0.714065i	$0.746852\pi$
$788$	−0.987225	+	0.987225i	−0.0351684	+	0.0351684i
$789$	−8.68299	−	5.01312i	−0.309122	−	0.178472i
$790$	−22.6379	+	13.0700i	−0.805419	+	0.465009i
$791$	−10.4448	−	2.79867i	−0.371374	−	0.0995093i
$792$	−7.79367	+	37.4089i	−0.276936	+	1.32927i
$793$	−3.63593	+	7.27535i	−0.129116	+	0.258355i
$794$			49.0907i			1.74216i
$795$	15.8172	+	4.23819i	0.560977	+	0.150313i
$796$	−0.632934	−	1.09627i	−0.0224337	−	0.0388564i
$797$	15.0814	+	8.70727i	0.534212	+	0.308427i	0.742730	−	0.669591i	$-0.233531\pi$
$797$	15.0814	+	8.70727i	0.534212	+	0.308427i	−0.208518	+	0.978019i	$0.566864\pi$
$798$	19.3002	+	19.3002i	0.683219	+	0.683219i
$799$	5.92114	−	1.58656i	0.209475	−	0.0561286i
$800$	−4.96456	−	18.5280i	−0.175524	−	0.655063i
$801$	−19.6937	−	19.6937i	−0.695844	−	0.695844i
$802$	−20.8603	−	12.0437i	−0.736604	−	0.425279i
$803$	14.4047	−	4.74480i	0.508331	−	0.167440i
$804$	7.05702	−	26.3372i	0.248882	−	0.928840i
$805$	−20.3365			−0.716768
$806$	−20.9976	+	13.8696i	−0.739610	+	0.488535i
$807$	1.51700			0.0534009
$808$	−27.4961	−	7.36755i	−0.967308	−	0.259189i
$809$	24.0467	−	13.8834i	0.845438	−	0.488114i	−0.0136712	−	0.999907i	$-0.504352\pi$
$809$	24.0467	−	13.8834i	0.845438	−	0.488114i	0.859109	+	0.511793i	$0.171018\pi$
$810$	−18.5971	+	32.2111i	−0.653435	+	1.13178i
$811$	−14.6444	−	14.6444i	−0.514235	−	0.514235i	0.401586	−	0.915821i	$-0.368459\pi$
$811$	−14.6444	−	14.6444i	−0.514235	−	0.514235i	−0.915821	+	0.401586i	$0.868459\pi$
$812$	4.14644	+	15.4747i	0.145512	+	0.543057i
$813$	4.82429	+	18.0045i	0.169195	+	0.631446i
$814$	18.4305	+	28.1309i	0.645987	+	0.985989i
$815$	1.88933	−	3.27241i	0.0661803	−	0.114628i
$816$	3.32575	+	5.76037i	0.116425	+	0.201653i
$817$	−3.12248	+	11.6533i	−0.109242	+	0.407696i
$818$			23.2781i			0.813899i
$819$	11.2265	−	54.9149i	0.392286	−	1.91888i
$820$		−	20.9439i		−	0.731393i
$821$	7.03521	−	26.2557i	0.245530	−	0.916332i	−0.727586	−	0.686017i	$-0.759358\pi$
$821$	7.03521	−	26.2557i	0.245530	−	0.916332i	0.973116	−	0.230315i	$-0.0739757\pi$
$822$	−45.9338	+	26.5199i	−1.60213	+	0.924988i
$823$	37.7299	+	21.7834i	1.31518	+	0.759320i	0.982949	−	0.183878i	$-0.0588651\pi$
$823$	37.7299	+	21.7834i	1.31518	+	0.759320i	0.332232	+	0.943198i	$0.392198\pi$
$824$	8.23831	+	8.23831i	0.286995	+	0.286995i
$825$	43.2137	−	2.43983i	1.50451	−	0.0849441i
$826$	−1.67307	+	0.448299i	−0.0582137	+	0.0155983i
$827$	1.72179	−	1.72179i	0.0598724	−	0.0598724i	−0.676537	−	0.736409i	$-0.736520\pi$
$827$	1.72179	−	1.72179i	0.0598724	−	0.0598724i	0.736409	+	0.676537i	$0.236520\pi$
$828$	5.85392	−	10.1393i	0.203438	−	0.352365i
$829$	45.5705	−	26.3101i	1.58273	−	0.913789i	0.588270	−	0.808665i	$-0.299809\pi$
$829$	45.5705	−	26.3101i	1.58273	−	0.913789i	0.994459	−	0.105124i	$-0.0335240\pi$
$830$	10.8912	−	40.6466i	0.378040	−	1.41086i
$831$	84.4970			2.93117
$832$	9.41478	−	0.566919i	0.326399	−	0.0196544i
$833$			0.0844226i			0.00292507i
$834$	−10.6841	−	2.86280i	−0.369960	−	0.0991305i
$835$	53.7370	−	31.0251i	1.85965	−	1.07367i
$836$	4.12866	+	3.68737i	0.142793	+	0.127530i
$837$	24.4157	−	24.4157i	0.843930	−	0.843930i
$838$	29.5090	−	7.90692i	1.01937	−	0.273140i
$839$	3.11467	−	0.834574i	0.107530	−	0.0288127i	−0.204653	−	0.978835i	$-0.565606\pi$
$839$	3.11467	−	0.834574i	0.107530	−	0.0288127i	0.312183	+	0.950022i	$0.398940\pi$
$840$	−34.2523	−	34.2523i	−1.18182	−	1.18182i
$841$	12.3166	−	21.3330i	0.424710	−	0.735619i
$842$	−21.5004	−	37.2397i	−0.740951	−	1.28337i
$843$	−52.3324	−	14.0224i	−1.80242	−	0.482958i
$844$	−17.8416			−0.614133
$845$	24.5972	−	31.3608i	0.846168	−	1.07884i
$846$		−	132.107i		−	4.54192i
$847$	−18.3725	+	23.0667i	−0.631286	+	0.792583i
$848$	−4.47105	−	7.74409i	−0.153537	−	0.265933i
$849$	−33.7151	+	58.3963i	−1.15710	+	2.00416i
$850$	2.35720	−	2.35720i	0.0808512	−	0.0808512i
$851$	3.86965	+	14.4417i	0.132650	+	0.495057i
$852$	−25.9082	+	6.94209i	−0.887601	+	0.237832i
$853$	0.591192	−	0.591192i	0.0202420	−	0.0202420i	−0.696913	−	0.717155i	$-0.745444\pi$
$853$	0.591192	−	0.591192i	0.0202420	−	0.0202420i	0.717155	+	0.696913i	$0.245444\pi$
$854$	−8.78851	−	5.07405i	−0.300737	−	0.173630i
$855$	−18.1817	−	31.4917i	−0.621802	−	1.07699i
$856$	−5.73099	+	21.3883i	−0.195881	+	0.731039i
$857$	−30.1021			−1.02827			−0.514135	−	0.857710i	$-0.671887\pi$
$857$	−30.1021			−1.02827			−0.514135	+	0.857710i	$0.671887\pi$
$858$	8.61593	−	58.8976i	0.294143	−	2.01073i
$859$	−9.48264			−0.323544			−0.161772	−	0.986828i	$-0.551721\pi$
$859$	−9.48264			−0.323544			−0.161772	+	0.986828i	$0.551721\pi$
$860$	−3.81914	+	14.2532i	−0.130232	+	0.486031i
$861$	−33.2866	−	57.6540i	−1.13440	−	1.96484i
$862$	46.3178	+	26.7416i	1.57759	+	0.910823i
$863$	−18.4177	+	18.4177i	−0.626947	+	0.626947i	−0.947299	−	0.320352i	$-0.896199\pi$
$863$	−18.4177	+	18.4177i	−0.626947	+	0.626947i	0.320352	+	0.947299i	$0.396199\pi$
$864$	34.9625	−	9.36817i	1.18945	−	0.318711i
$865$	8.97250	+	33.4858i	0.305074	+	1.13855i
$866$	−3.90555	+	3.90555i	−0.132716	+	0.132716i
$867$	24.9109	−	43.1470i	0.846020	−	1.46535i
$868$	−4.54923	−	7.87950i	−0.154411	−	0.267448i
$869$	−7.58958	+	15.0454i	−0.257459	+	0.510379i
$870$		−	111.763i		−	3.78911i
$871$	8.13505	−	39.7929i	0.275646	−	1.34833i
$872$	24.2599			0.821544
$873$	−42.9846	−	11.5177i	−1.45481	−	0.389815i
$874$	4.24633	+	7.35486i	0.143634	+	0.248782i
$875$	2.46772	−	4.27422i	0.0834242	−	0.144495i
$876$	−7.82640	−	7.82640i	−0.264430	−	0.264430i
$877$	38.1091	−	10.2113i	1.28685	−	0.344811i	0.450388	−	0.892833i	$-0.351286\pi$
$877$	38.1091	−	10.2113i	1.28685	−	0.344811i	0.836464	+	0.548022i	$0.184619\pi$
$878$	−0.481667	+	0.129062i	−0.0162555	+	0.00435564i
$879$	0.107762	−	0.107762i	0.00363474	−	0.00363474i
$880$	−37.6630	−	33.6374i	−1.26962	−	1.13392i
$881$	27.0602	−	15.6232i	0.911681	−	0.526359i	0.0307091	−	0.999528i	$-0.490223\pi$
$881$	27.0602	−	15.6232i	0.911681	−	0.526359i	0.880972	+	0.473169i	$0.156890\pi$
$882$	1.75738	+	0.470889i	0.0591741	+	0.0158556i
$883$			28.6061i			0.962670i	0.876537	+	0.481335i	$0.159848\pi$
$883$			28.6061i			0.962670i	−0.876537	+	0.481335i	$0.840152\pi$
$884$	−0.732185	−	1.10848i	−0.0246260	−	0.0372823i
$885$	3.50143			0.117699
$886$	−9.44324	+	35.2427i	−0.317252	+	1.18400i
$887$	−11.6957	+	6.75250i	−0.392702	+	0.226727i	−0.683330	−	0.730109i	$-0.739469\pi$
$887$	−11.6957	+	6.75250i	−0.392702	+	0.226727i	0.290628	+	0.956836i	$0.406136\pi$
$888$	−17.8063	+	30.8414i	−0.597541	+	1.03497i
$889$	−0.823129	+	0.823129i	−0.0276069	+	0.0276069i
$890$	23.8682	−	6.39547i	0.800064	−	0.214377i
$891$	1.35161	+	23.9393i	0.0452805	+	0.801996i
$892$	−0.903575	−	0.903575i	−0.0302539	−	0.0302539i
$893$	24.0480	+	13.8841i	0.804736	+	0.464615i
$894$	31.9978	−	18.4739i	1.07017	−	0.617861i
$895$	−9.91191	+	36.9917i	−0.331318	+	1.23650i
$896$			35.1449i			1.17411i
$897$	11.8299	−	23.6712i	0.394990	−	0.790359i
$898$		−	21.8045i		−	0.727624i
$899$	−7.88348	+	29.4216i	−0.262929	+	0.981264i
$900$	−10.4088	−	18.0286i	−0.346960	−	0.600953i
$901$	0.406518	−	0.704110i	0.0135431	−	0.0234573i
$902$	−25.5344	−	38.9739i	−0.850203	−	1.29769i
$903$	12.1397	+	45.3059i	0.403983	+	1.50769i
$904$	−2.07418	−	7.74096i	−0.0689863	−	0.257460i
$905$	8.61968	+	8.61968i	0.286528	+	0.286528i
$906$	−47.8370	+	82.8561i	−1.58928	+	2.75271i
$907$	−25.5565	+	14.7551i	−0.848590	+	0.489934i	−0.860175	−	0.509999i	$-0.829646\pi$
$907$	−25.5565	+	14.7551i	−0.848590	+	0.489934i	0.0115850	+	0.999933i	$0.496312\pi$
$908$	−12.1699	−	3.26091i	−0.403872	−	0.108217i
$909$	−83.0797			−2.75558
$910$	37.2141	+	32.9868i	1.23363	+	1.09350i
$911$	−35.0065			−1.15982			−0.579908	−	0.814682i	$-0.696912\pi$
$911$	−35.0065			−1.15982			−0.579908	+	0.814682i	$0.696912\pi$
$912$	−7.79835	+	29.1039i	−0.258229	+	0.963725i
$913$	−8.48698	−	25.7656i	−0.280878	−	0.852716i
$914$	9.39362	+	5.42341i	0.310713	+	0.179390i
$915$	14.5059	+	14.5059i	0.479550	+	0.479550i
$916$	−3.41713	−	12.7529i	−0.112905	−	0.421367i
$917$	−11.9001	+	3.18862i	−0.392976	+	0.105298i
$918$	4.44805	+	4.44805i	0.146808	+	0.146808i
$919$	−2.40099	−	1.38621i	−0.0792013	−	0.0457269i	0.459876	−	0.887983i	$-0.347894\pi$
$919$	−2.40099	−	1.38621i	−0.0792013	−	0.0457269i	−0.539078	+	0.842256i	$0.681227\pi$
$920$	−7.53602	−	13.0528i	−0.248455	−	0.430337i
$921$	3.45260	+	0.925122i	0.113767	+	0.0304838i
$922$		−	53.9211i		−	1.77580i
$923$	−37.9017	+	12.6420i	−1.24755	+	0.416116i
$924$	21.0690	+	4.38947i	0.693119	+	0.144403i
$925$	25.6787	+	6.88060i	0.844312	+	0.226233i
$926$	49.6036	−	28.6386i	1.63008	−	0.941124i
$927$	29.4477	+	17.0017i	0.967190	+	0.558408i
$928$	−22.5778	+	22.5778i	−0.741152	+	0.741152i
$929$	4.95938	+	18.5086i	0.162712	+	0.607249i	0.998321	+	0.0579244i	$0.0184482\pi$
$929$	4.95938	+	18.5086i	0.162712	+	0.607249i	−0.835609	+	0.549324i	$0.814885\pi$
$930$	16.4279	+	61.3097i	0.538691	+	2.01042i
$931$	−0.270415	+	0.270415i	−0.00886250	+	0.00886250i
$932$	8.98956	+	5.19013i	0.294463	+	0.170008i
$933$	5.58563	−	3.22487i	0.182865	−	0.105577i
$934$	−1.60194	−	0.429239i	−0.0524171	−	0.0140451i
$935$	0.936440	−	4.49482i	0.0306249	−	0.146996i
$936$	39.4067	−	13.1440i	1.28805	−	0.429624i
$937$			54.0596i			1.76605i	0.469326	+	0.883025i	$0.344497\pi$
$937$			54.0596i			1.76605i	−0.469326	+	0.883025i	$0.655503\pi$
$938$	48.9505	+	13.1163i	1.59829	+	0.428261i
$939$	19.6059	+	33.9584i	0.639815	+	1.10819i
$940$	29.4134	+	16.9818i	0.959360	+	0.553887i
$941$	−27.1789	−	27.1789i	−0.886008	−	0.886008i	0.108129	−	0.994137i	$-0.465514\pi$
$941$	−27.1789	−	27.1789i	−0.886008	−	0.886008i	−0.994137	+	0.108129i	$0.965514\pi$
$942$	46.0859	−	12.3487i	1.50156	−	0.402342i
$943$	−5.36120	−	20.0083i	−0.174585	−	0.651559i
$944$	−1.35203	−	1.35203i	−0.0440048	−	0.0440048i
$945$	−59.0929	−	34.1173i	−1.92229	−	1.10984i
$946$	10.2703	+	31.1797i	0.333918	+	1.01374i
$947$	−8.97894	+	33.5099i	−0.291776	+	1.08892i	0.651968	+	0.758247i	$0.273944\pi$
$947$	−8.97894	+	33.5099i	−0.291776	+	1.08892i	−0.943744	+	0.330677i	$0.892723\pi$
$948$	12.2981			0.399422
$949$	−12.3379	−	10.9364i	−0.400505	−	0.355011i
$950$	15.1007			0.489932
$951$	87.9399	+	23.5634i	2.85165	+	0.764096i
$952$	−2.08286	+	1.20254i	−0.0675060	+	0.0389746i
$953$	−7.59525	+	13.1554i	−0.246034	+	0.426144i	−0.962422	−	0.271559i	$-0.912461\pi$
$953$	−7.59525	+	13.1554i	−0.246034	+	0.426144i	0.716388	+	0.697702i	$0.245794\pi$
$954$	−12.3896	−	12.3896i	−0.401129	−	0.401129i
$955$	16.0757	+	59.9952i	0.520197	+	1.94140i
$956$	2.63885	+	9.84831i	0.0853464	+	0.318517i
$957$	−39.4842	−	60.2658i	−1.27634	−	1.94812i
$958$	−24.0006	+	41.5703i	−0.775424	+	1.34307i
$959$	−14.2829	−	24.7388i	−0.461220	−	0.798857i
$960$	6.15722	−	22.9790i	0.198723	−	0.741645i
$961$			13.7014i			0.441982i
$962$	16.3441	−	32.7039i	0.526955	−	1.05442i
$963$			64.6251i			2.08252i
$964$	−0.716848	+	2.67531i	−0.0230881	+	0.0861661i
$965$	−28.1896	+	16.2753i	−0.907456	+	0.523920i
$966$	28.5945	+	16.5090i	0.920012	+	0.531169i
$967$	36.4670	+	36.4670i	1.17270	+	1.17270i	0.981564	+	0.191134i	$0.0612166\pi$
$967$	36.4670	+	36.4670i	1.17270	+	1.17270i	0.191134	+	0.981564i	$0.438783\pi$
$968$	−21.6133	−	3.24443i	−0.694679	−	0.104280i
$969$	−2.64619	+	0.709044i	−0.0850078	+	0.0227778i
$970$	27.9182	−	27.9182i	0.896398	−	0.896398i
$971$	−5.30619	+	9.19059i	−0.170284	+	0.294940i	−0.938519	−	0.345228i	$-0.887802\pi$
$971$	−5.30619	+	9.19059i	−0.170284	+	0.294940i	0.768235	+	0.640168i	$0.221135\pi$
$972$	−2.44597	+	1.41218i	−0.0784544	+	0.0452957i
$973$	1.54183	−	5.75418i	0.0494287	−	0.184471i
$974$	42.7453			1.36965
$975$	−25.9333	−	39.2614i	−0.830530	−	1.25737i
$976$		−	11.2025i		−	0.358583i
$977$	−34.3472	−	9.20331i	−1.09886	−	0.294440i	−0.336562	−	0.941661i	$-0.609264\pi$
$977$	−34.3472	−	9.20331i	−1.09886	−	0.294440i	−0.762302	+	0.647221i	$0.775931\pi$
$978$	−5.31304	+	3.06748i	−0.169892	+	0.0980873i
$979$	10.6110	−	11.8809i	0.339130	−	0.379716i
$980$	−0.330748	+	0.330748i	−0.0105654	+	0.0105654i
$981$	68.3913	−	18.3254i	2.18357	−	0.585085i
$982$	−47.3677	+	12.6921i	−1.51156	+	0.405022i
$983$	29.7630	+	29.7630i	0.949292	+	0.949292i	0.998775	−	0.0494825i	$-0.0157572\pi$
$983$	29.7630	+	29.7630i	0.949292	+	0.949292i	−0.0494825	+	0.998775i	$0.515757\pi$
$984$	24.6697	−	42.7292i	0.786442	−	1.36216i
$985$	2.62279	+	4.54281i	0.0835692	+	0.144746i
$986$	−5.36002	−	1.43621i	−0.170698	−	0.0457383i
$987$	107.958			3.43635
$988$	1.20532	−	5.89586i	0.0383463	−	0.187572i
$989$			14.5941i			0.464066i
$990$	−88.3430	−	44.5644i	−2.80772	−	1.41635i
$991$	−4.81208	−	8.33476i	−0.152861	−	0.264762i	0.779417	−	0.626505i	$-0.215515\pi$
$991$	−4.81208	−	8.33476i	−0.152861	−	0.264762i	−0.932278	+	0.361743i	$0.882182\pi$
$992$	9.06681	−	15.7042i	0.287871	−	0.498608i
$993$	−32.8110	+	32.8110i	−1.04123	+	1.04123i
$994$	−12.9026	−	48.1533i	−0.409247	−	1.52733i
$995$	−4.59404	+	1.23097i	−0.145641	+	0.0390244i
$996$	−13.9990	+	13.9990i	−0.443575	+	0.443575i
$997$	8.15580	+	4.70875i	0.258297	+	0.149128i	0.623557	−	0.781778i	$-0.285687\pi$
$997$	8.15580	+	4.70875i	0.258297	+	0.149128i	−0.365261	+	0.930905i	$0.619020\pi$
$998$	−3.14136	−	5.44100i	−0.0994381	−	0.172232i
$999$	−12.9837	+	48.4560i	−0.410788	+	1.53308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.o.a.54.3	✓	48
11.10	odd	2	inner	143.2.o.a.54.10	yes	48
13.7	odd	12	inner	143.2.o.a.98.10	yes	48
143.98	even	12	inner	143.2.o.a.98.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.o.a.54.3	✓	48	1.1	even	1	trivial
143.2.o.a.54.10	yes	48	11.10	odd	2	inner
143.2.o.a.98.3	yes	48	143.98	even	12	inner
143.2.o.a.98.10	yes	48	13.7	odd	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.434323 + 1.62091i) q^{2} +(-1.48314 - 2.56887i) q^{3} +(-0.706676 - 0.408000i) q^{4} +(-2.16789 + 2.16789i) q^{5} +(4.80807 - 1.28832i) q^{6} +(0.693856 + 2.58950i) q^{7} +(-1.40493 + 1.40493i) q^{8} +(-2.89939 + 5.02189i) q^{9} +(-2.57240 - 4.45553i) q^{10} +(-2.96119 - 1.49377i) q^{11} +2.42048i q^{12} +(0.216719 + 3.59903i) q^{13} -4.49872 q^{14} +(8.78431 + 2.35375i) q^{15} +(-2.48307 - 4.30081i) q^{16} +(0.225766 - 0.391039i) q^{17} +(-6.88078 - 6.88078i) q^{18} +(1.97570 - 0.529386i) q^{19} +(2.41650 - 0.647499i) q^{20} +(5.62301 - 5.62301i) q^{21} +(3.70738 - 4.15106i) q^{22} +(2.14280 - 1.23715i) q^{23} +(5.69276 + 1.52537i) q^{24} -4.39952i q^{25} +(-5.92785 - 1.21186i) q^{26} +8.30193 q^{27} +(0.566186 - 2.11303i) q^{28} +(-6.34231 + 3.66173i) q^{29} +(-7.63045 + 13.2163i) q^{30} +(2.94097 - 2.94097i) q^{31} +(4.21137 - 1.12843i) q^{32} +(0.554568 + 9.82237i) q^{33} +(0.535785 + 0.535785i) q^{34} +(-7.11797 - 4.10956i) q^{35} +(4.09786 - 2.36590i) q^{36} +(-1.56394 + 5.83672i) q^{37} +3.43236i q^{38} +(8.92401 - 5.89458i) q^{39} -6.09145i q^{40} +(2.16676 - 8.08646i) q^{41} +(6.67222 + 11.5566i) q^{42} +(-2.94915 + 5.10808i) q^{43} +(1.48315 + 2.26377i) q^{44} +(-4.60135 - 17.1725i) q^{45} +(1.07464 + 4.01062i) q^{46} +(9.59969 + 9.59969i) q^{47} +(-7.36547 + 12.7574i) q^{48} +(-0.161920 + 0.0934845i) q^{49} +(7.13124 + 1.91081i) q^{50} -1.33937 q^{51} +(1.31525 - 2.63177i) q^{52} +1.80061 q^{53} +(-3.60572 + 13.4567i) q^{54} +(9.65787 - 3.18123i) q^{55} +(-4.61288 - 2.66324i) q^{56} +(-4.29015 - 4.29015i) q^{57} +(-3.18075 - 11.8707i) q^{58} +(0.371900 - 0.0996502i) q^{59} +(-5.24733 - 5.24733i) q^{60} +(1.95356 + 1.12789i) q^{61} +(3.48973 + 6.04438i) q^{62} +(-15.0160 - 4.02351i) q^{63} -2.61592i q^{64} +(-8.27214 - 7.33249i) q^{65} +(-16.1621 - 3.36717i) q^{66} +(-10.8810 - 2.91555i) q^{67} +(-0.319088 + 0.184225i) q^{68} +(-6.35613 - 3.66971i) q^{69} +(9.75275 - 9.75275i) q^{70} +(2.86807 + 10.7038i) q^{71} +(-2.98195 - 11.1288i) q^{72} +(-3.23341 + 3.23341i) q^{73} +(-8.78156 - 5.07004i) q^{74} +(-11.3018 + 6.52509i) q^{75} +(-1.61217 - 0.431979i) q^{76} +(1.81347 - 8.70448i) q^{77} +(5.67870 + 17.0252i) q^{78} -5.08084i q^{79} +(14.7067 + 3.94065i) q^{80} +(-3.61473 - 6.26090i) q^{81} +(12.1664 + 7.02427i) q^{82} +(5.78357 + 5.78357i) q^{83} +(-6.26784 + 1.67946i) q^{84} +(0.358293 + 1.33717i) q^{85} +(-6.99887 - 6.99887i) q^{86} +(18.8130 + 10.8617i) q^{87} +(6.25888 - 2.06163i) q^{88} +(-1.24309 + 4.63928i) q^{89} +29.8336 q^{90} +(-9.16934 + 3.05840i) q^{91} -2.01902 q^{92} +(-11.9168 - 3.19310i) q^{93} +(-19.7296 + 11.3909i) q^{94} +(-3.13544 + 5.43075i) q^{95} +(-9.14482 - 9.14482i) q^{96} +(1.98623 + 7.41270i) q^{97} +(-0.0812049 - 0.303061i) q^{98} +(16.0872 - 10.5398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 20 q^{9} + 8 q^{11} - 16 q^{14} + 12 q^{15} - 8 q^{16} - 52 q^{20} + 12 q^{22} - 36 q^{26} - 16 q^{27} + 4 q^{31} + 48 q^{33} - 12 q^{34} + 120 q^{36} - 20 q^{37} - 12 q^{42}+ \cdots + 16 q^{99}+O(q^{100}) \) 48 * q - 4 * q^3 - 12 * q^4 - 8 * q^5 - 20 * q^9 + 8 * q^11 - 16 * q^14 + 12 * q^15 - 8 * q^16 - 52 * q^20 + 12 * q^22 - 36 * q^26 - 16 * q^27 + 4 * q^31 + 48 * q^33 - 12 * q^34 + 120 * q^36 - 20 * q^37 - 12 * q^42 + 8 * q^44 + 8 * q^45 + 40 * q^47 - 48 * q^48 - 12 * q^49 + 24 * q^53 + 12 * q^55 - 132 * q^56 + 28 * q^58 - 40 * q^59 + 20 * q^60 - 32 * q^66 - 60 * q^67 - 12 * q^69 + 92 * q^70 - 96 * q^75 + 12 * q^78 + 148 * q^80 + 16 * q^81 + 156 * q^82 - 76 * q^86 - 48 * q^88 + 68 * q^89 - 84 * q^91 + 24 * q^92 + 24 * q^93 + 4 * q^97 + 16 * q^99

Introduction

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