LMFDB - Embedded newform 546.2.u.a.425.17

Newspace parameters

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.u (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			425.17
Character	$\chi$	$=$	546.425
Dual form			546.2.u.a.185.17

$q$-expansion

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.62717 - 0.593575i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.76347 - 3.05441i) q^{5} +(-1.11238 + 1.32763i) q^{6} +(1.45770 - 2.20797i) q^{7} +1.00000i q^{8} +(2.29534 - 1.93169i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.62717 - 0.593575i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.76347 - 3.05441i) q^{5} +(-1.11238 + 1.32763i) q^{6} +(1.45770 - 2.20797i) q^{7} +1.00000i q^{8} +(2.29534 - 1.93169i) q^{9} +3.52693i q^{10} +5.58476i q^{11} +(0.299532 - 1.70595i) q^{12} +(1.38855 + 3.32745i) q^{13} +(-0.158422 + 2.64100i) q^{14} +(1.05643 - 6.01678i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.37527 + 2.38204i) q^{17} +(-1.02197 + 2.82056i) q^{18} -7.22955i q^{19} +(-1.76347 - 3.05441i) q^{20} +(1.06133 - 4.45798i) q^{21} +(-2.79238 - 4.83655i) q^{22} +(-3.91643 + 2.26115i) q^{23} +(0.593575 + 1.62717i) q^{24} +(-3.71962 - 6.44257i) q^{25} +(-2.86625 - 2.18738i) q^{26} +(2.58829 - 4.50564i) q^{27} +(-1.18330 - 2.36639i) q^{28} +(-0.473303 - 0.273262i) q^{29} +(2.09350 + 5.73890i) q^{30} +(-1.25106 + 0.722302i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.31498 + 9.08733i) q^{33} -2.75055i q^{34} +(-4.17343 - 8.34609i) q^{35} +(-0.525225 - 2.95367i) q^{36} +(1.35222 + 2.34212i) q^{37} +(3.61478 + 6.26098i) q^{38} +(4.23450 + 4.59010i) q^{39} +(3.05441 + 1.76347i) q^{40} +(-3.63062 + 6.28842i) q^{41} +(1.30986 + 4.39139i) q^{42} +(0.0709937 + 0.122965i) q^{43} +(4.83655 + 2.79238i) q^{44} +(-1.85243 - 10.4174i) q^{45} +(2.26115 - 3.91643i) q^{46} +(1.96371 - 3.40124i) q^{47} +(-1.32763 - 1.11238i) q^{48} +(-2.75022 - 6.43710i) q^{49} +(6.44257 + 3.71962i) q^{50} +(-0.823876 + 4.69231i) q^{51} +(3.57593 + 0.461204i) q^{52} +(-9.33624 + 5.39028i) q^{53} +(0.0112934 + 5.19614i) q^{54} +(17.0582 + 9.84854i) q^{55} +(2.20797 + 1.45770i) q^{56} +(-4.29128 - 11.7637i) q^{57} +0.546524 q^{58} +(3.71440 - 6.43353i) q^{59} +(-4.68247 - 3.92329i) q^{60} +12.4949i q^{61} +(0.722302 - 1.25106i) q^{62} +(-0.919194 - 7.88385i) q^{63} -1.00000 q^{64} +(12.6121 + 1.62663i) q^{65} +(-7.41452 - 6.21237i) q^{66} -10.5200 q^{67} +(1.37527 + 2.38204i) q^{68} +(-5.03052 + 6.00397i) q^{69} +(7.78734 + 5.14121i) q^{70} +(1.01248 - 0.584557i) q^{71} +(1.93169 + 2.29534i) q^{72} +(11.2019 - 6.46743i) q^{73} +(-2.34212 - 1.35222i) q^{74} +(-9.87659 - 8.27526i) q^{75} +(-6.26098 - 3.61478i) q^{76} +(12.3310 + 8.14091i) q^{77} +(-5.96223 - 1.85790i) q^{78} +(-4.47939 + 7.75854i) q^{79} -3.52693 q^{80} +(1.53714 - 8.86776i) q^{81} -7.26124i q^{82} +3.92570 q^{83} +(-3.33006 - 3.14812i) q^{84} +(4.85050 + 8.40131i) q^{85} +(-0.122965 - 0.0709937i) q^{86} +(-0.932345 - 0.163701i) q^{87} -5.58476 q^{88} +(0.677113 + 1.17279i) q^{89} +(6.81294 + 8.09550i) q^{90} +(9.37099 + 1.78455i) q^{91} +4.52231i q^{92} +(-1.60695 + 1.91790i) q^{93} +3.92741i q^{94} +(-22.0820 - 12.7491i) q^{95} +(1.70595 + 0.299532i) q^{96} +(11.1130 - 6.41610i) q^{97} +(5.60031 + 4.19958i) q^{98} +(10.7880 + 12.8189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.62717	−	0.593575i	0.939445	−	0.342701i
$3$	1.62717	−	0.593575i	0.939445	−	0.342701i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.76347	−	3.05441i	0.788646	−	1.36597i	−0.138151	−	0.990411i	$-0.544116\pi$
$5$	1.76347	−	3.05441i	0.788646	−	1.36597i	0.926797	−	0.375563i	$-0.122551\pi$
$6$	−1.11238	+	1.32763i	−0.454127	+	0.542004i
$7$	1.45770	−	2.20797i	0.550959	−	0.834533i
$7$	1.45770	−	2.20797i	0.550959	−	0.834533i
$8$			1.00000i			0.353553i
$9$	2.29534	−	1.93169i	0.765112	−	0.643897i
$10$			3.52693i			1.11531i
$11$			5.58476i			1.68387i	0.539580	+	0.841935i	$0.318583\pi$
$11$			5.58476i			1.68387i	−0.539580	+	0.841935i	$0.681417\pi$
$12$	0.299532	−	1.70595i	0.0864673	−	0.492467i
$13$	1.38855	+	3.32745i	0.385115	+	0.922869i
$13$	1.38855	+	3.32745i	0.385115	+	0.922869i
$14$	−0.158422	+	2.64100i	−0.0423401	+	0.705838i
$15$	1.05643	−	6.01678i	0.272768	−	1.55353i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.37527	+	2.38204i	−0.333553	+	0.577731i	−0.983206	−	0.182500i	$-0.941581\pi$
$17$	−1.37527	+	2.38204i	−0.333553	+	0.577731i	0.649653	+	0.760231i	$0.274914\pi$
$18$	−1.02197	+	2.82056i	−0.240882	+	0.664813i
$19$		−	7.22955i		−	1.65857i	−0.558823	−	0.829287i	$-0.688747\pi$
$19$		−	7.22955i		−	1.65857i	0.558823	−	0.829287i	$-0.311253\pi$
$20$	−1.76347	−	3.05441i	−0.394323	−	0.682987i
$21$	1.06133	−	4.45798i	0.231600	−	0.972811i
$22$	−2.79238	−	4.83655i	−0.595338	−	1.03116i
$23$	−3.91643	+	2.26115i	−0.816632	+	0.471483i	−0.849254	−	0.527985i	$-0.822948\pi$
$23$	−3.91643	+	2.26115i	−0.816632	+	0.471483i	0.0326214	+	0.999468i	$0.489614\pi$
$24$	0.593575	+	1.62717i	0.121163	+	0.332144i
$25$	−3.71962	−	6.44257i	−0.743924	−	1.28851i
$26$	−2.86625	−	2.18738i	−0.562117	−	0.428981i
$27$	2.58829	−	4.50564i	0.498117	−	0.867110i
$28$	−1.18330	−	2.36639i	−0.223624	−	0.447205i
$29$	−0.473303	−	0.273262i	−0.0878902	−	0.0507435i	0.455411	−	0.890281i	$-0.349492\pi$
$29$	−0.473303	−	0.273262i	−0.0878902	−	0.0507435i	−0.543301	+	0.839538i	$0.682826\pi$
$30$	2.09350	+	5.73890i	0.382219	+	1.04778i
$31$	−1.25106	+	0.722302i	−0.224698	+	0.129729i	−0.608124	−	0.793842i	$-0.708077\pi$
$31$	−1.25106	+	0.722302i	−0.224698	+	0.129729i	0.383426	+	0.923572i	$0.374744\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	3.31498	+	9.08733i	0.577063	+	1.58190i
$34$		−	2.75055i		−	0.471715i
$35$	−4.17343	−	8.34609i	−0.705439	−	1.41075i
$36$	−0.525225	−	2.95367i	−0.0875375	−	0.492278i
$37$	1.35222	+	2.34212i	0.222304	+	0.385042i	0.955507	−	0.294968i	$-0.0953090\pi$
$37$	1.35222	+	2.34212i	0.222304	+	0.385042i	−0.733203	+	0.680010i	$0.761976\pi$
$38$	3.61478	+	6.26098i	0.586394	+	1.01566i
$39$	4.23450	+	4.59010i	0.678062	+	0.735005i
$40$	3.05441	+	1.76347i	0.482945	+	0.278828i
$41$	−3.63062	+	6.28842i	−0.567008	+	0.982086i	0.429852	+	0.902899i	$0.358566\pi$
$41$	−3.63062	+	6.28842i	−0.567008	+	0.982086i	−0.996860	+	0.0791869i	$0.974768\pi$
$42$	1.30986	+	4.39139i	0.202115	+	0.677606i
$43$	0.0709937	+	0.122965i	0.0108264	+	0.0187519i	0.871388	−	0.490595i	$-0.163220\pi$
$43$	0.0709937	+	0.122965i	0.0108264	+	0.0187519i	−0.860561	+	0.509347i	$0.829887\pi$
$44$	4.83655	+	2.79238i	0.729137	+	0.420967i
$45$	−1.85243	−	10.4174i	−0.276144	−	1.55293i
$46$	2.26115	−	3.91643i	0.333389	−	0.577446i
$47$	1.96371	−	3.40124i	0.286436	−	0.496122i	−0.686520	−	0.727110i	$-0.740863\pi$
$47$	1.96371	−	3.40124i	0.286436	−	0.496122i	0.972956	+	0.230989i	$0.0741961\pi$
$48$	−1.32763	−	1.11238i	−0.191627	−	0.160558i
$49$	−2.75022	−	6.43710i	−0.392889	−	0.919586i
$50$	6.44257	+	3.71962i	0.911118	+	0.526034i
$51$	−0.823876	+	4.69231i	−0.115366	+	0.657055i
$52$	3.57593	+	0.461204i	0.495893	+	0.0639574i
$53$	−9.33624	+	5.39028i	−1.28243	+	0.740412i	−0.977292	−	0.211896i	$-0.932036\pi$
$53$	−9.33624	+	5.39028i	−1.28243	+	0.740412i	−0.305139	+	0.952308i	$0.598703\pi$
$54$	0.0112934	+	5.19614i	0.00153683	+	0.707105i
$55$	17.0582	+	9.84854i	2.30012	+	1.32798i
$56$	2.20797	+	1.45770i	0.295052	+	0.194793i
$57$	−4.29128	−	11.7637i	−0.568395	−	1.55814i
$58$	0.546524			0.0717621
$59$	3.71440	−	6.43353i	0.483574	−	0.837574i	−0.516248	−	0.856439i	$-0.672672\pi$
$59$	3.71440	−	6.43353i	0.483574	−	0.837574i	0.999822	+	0.0188647i	$0.00600517\pi$
$60$	−4.68247	−	3.92329i	−0.604505	−	0.506494i
$61$			12.4949i			1.59981i	0.600124	+	0.799907i	$0.295118\pi$
$61$			12.4949i			1.59981i	−0.600124	+	0.799907i	$0.704882\pi$
$62$	0.722302	−	1.25106i	0.0917324	−	0.158885i
$63$	−0.919194	−	7.88385i	−0.115808	−	0.993272i
$64$	−1.00000			−0.125000
$65$	12.6121	+	1.62663i	1.56433	+	0.201759i
$66$	−7.41452	−	6.21237i	−0.912664	−	0.764690i
$67$	−10.5200			−1.28522			−0.642608	−	0.766195i	$-0.722148\pi$
$67$	−10.5200			−1.28522			−0.642608	+	0.766195i	$0.722148\pi$
$68$	1.37527	+	2.38204i	0.166776	+	0.288865i
$69$	−5.03052	+	6.00397i	−0.605603	+	0.722793i
$70$	7.78734	+	5.14121i	0.930765	+	0.614492i
$71$	1.01248	−	0.584557i	0.120159	−	0.0693741i	−0.438716	−	0.898626i	$-0.644566\pi$
$71$	1.01248	−	0.584557i	0.120159	−	0.0693741i	0.558875	+	0.829252i	$0.311233\pi$
$72$	1.93169	+	2.29534i	0.227652	+	0.270508i
$73$	11.2019	−	6.46743i	1.31109	−	0.756956i	0.328810	−	0.944396i	$-0.393353\pi$
$73$	11.2019	−	6.46743i	1.31109	−	0.756956i	0.982276	+	0.187441i	$0.0600192\pi$
$74$	−2.34212	−	1.35222i	−0.272266	−	0.157193i
$75$	−9.87659	−	8.27526i	−1.14045	−	0.955545i
$76$	−6.26098	−	3.61478i	−0.718183	−	0.414643i
$77$	12.3310	+	8.14091i	1.40524	+	0.927742i
$78$	−5.96223	−	1.85790i	−0.675090	−	0.210365i
$79$	−4.47939	+	7.75854i	−0.503971	+	0.872904i	0.496018	+	0.868312i	$0.334795\pi$
$79$	−4.47939	+	7.75854i	−0.503971	+	0.872904i	−0.999989	+	0.00459152i	$0.998538\pi$
$80$	−3.52693			−0.394323
$81$	1.53714	−	8.86776i	0.170794	−	0.985307i
$82$		−	7.26124i		−	0.801870i
$83$	3.92570			0.430901			0.215451	−	0.976515i	$-0.430878\pi$
$83$	3.92570			0.430901			0.215451	+	0.976515i	$0.430878\pi$
$84$	−3.33006	−	3.14812i	−0.363339	−	0.343489i
$85$	4.85050	+	8.40131i	0.526110	+	0.911249i
$86$	−0.122965	−	0.0709937i	−0.0132596	−	0.00765544i
$87$	−0.932345	−	0.163701i	−0.0999578	−	0.0175506i
$88$	−5.58476			−0.595338
$89$	0.677113	+	1.17279i	0.0717739	+	0.124316i	0.899679	−	0.436552i	$-0.143801\pi$
$89$	0.677113	+	1.17279i	0.0717739	+	0.124316i	−0.827905	+	0.560868i	$0.810467\pi$
$90$	6.81294	+	8.09550i	0.718147	+	0.853340i
$91$	9.37099	+	1.78455i	0.982346	+	0.187071i
$92$			4.52231i			0.471483i
$93$	−1.60695	+	1.91790i	−0.166633	+	0.198877i
$94$			3.92741i			0.405082i
$95$	−22.0820	−	12.7491i	−2.26557	−	1.30803i
$96$	1.70595	+	0.299532i	0.174113	+	0.0305708i
$97$	11.1130	−	6.41610i	1.12836	−	0.651456i	0.184835	−	0.982770i	$-0.440825\pi$
$97$	11.1130	−	6.41610i	1.12836	−	0.651456i	0.943521	+	0.331313i	$0.107492\pi$
$98$	5.60031	+	4.19958i	0.565717	+	0.424222i
$99$	10.7880	+	12.8189i	1.08424	+	1.28835i
$100$	−7.43924			−0.743924
$101$	−7.73029			−0.769192			−0.384596	−	0.923085i	$-0.625659\pi$
$101$	−7.73029			−0.769192			−0.384596	+	0.923085i	$0.625659\pi$
$102$	−1.63266	−	4.47560i	−0.161657	−	0.443150i
$103$	−2.85313	−	1.64725i	−0.281127	−	0.162309i	0.352807	−	0.935696i	$-0.385227\pi$
$103$	−2.85313	−	1.64725i	−0.281127	−	0.162309i	−0.633933	+	0.773388i	$0.718561\pi$
$104$	−3.32745	+	1.38855i	−0.326283	+	0.136159i
$105$	−11.7449	−	11.1032i	−1.14618	−	1.08356i
$106$	5.39028	−	9.33624i	0.523550	−	0.906815i
$107$	1.30919	−	0.755862i	0.126564	−	0.0730719i	−0.435381	−	0.900246i	$-0.643386\pi$
$107$	1.30919	−	0.755862i	0.126564	−	0.0730719i	0.561945	+	0.827174i	$0.310053\pi$
$108$	−2.60785	−	4.49434i	−0.250941	−	0.432468i
$109$	5.99142	+	10.3775i	0.573874	+	0.993979i	0.996163	+	0.0875181i	$0.0278935\pi$
$109$	5.99142	+	10.3775i	0.573874	+	0.993979i	−0.422289	+	0.906461i	$0.638773\pi$
$110$	−19.6971			−1.87804
$111$	3.59051	+	3.00837i	0.340796	+	0.285542i
$112$	−2.64100	−	0.158422i	−0.249551	−	0.0149695i
$113$	−3.57873	+	2.06618i	−0.336659	+	0.194370i	−0.658793	−	0.752324i	$-0.728933\pi$
$113$	−3.57873	+	2.06618i	−0.336659	+	0.194370i	0.322135	+	0.946694i	$0.395600\pi$
$114$	9.59820	+	8.04201i	0.898954	+	0.753203i
$115$			15.9499i			1.48733i
$116$	−0.473303	+	0.273262i	−0.0439451	+	0.0253717i
$117$	9.61480	+	4.95537i	0.888888	+	0.458124i
$118$			7.42880i			0.683877i
$119$	3.25473	+	6.50886i	0.298361	+	0.596666i
$120$	6.01678	+	1.05643i	0.549255	+	0.0964382i
$121$	−20.1896			−1.83542
$122$	−6.24747	−	10.8209i	−0.565620	−	0.979682i
$123$	−2.17497	+	12.3873i	−0.196111	+	1.11693i
$124$			1.44460i			0.129729i
$125$	−8.60304			−0.769480
$126$	4.73797	+	6.36802i	0.422092	+	0.567308i
$127$	2.29973	−	3.98324i	0.204068	−	0.353456i	−0.745768	−	0.666206i	$-0.767917\pi$
$127$	2.29973	−	3.98324i	0.204068	−	0.353456i	0.949835	+	0.312751i	$0.101250\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	0.188507	+	0.157944i	0.0165971	+	0.0139062i
$130$	−11.7357	+	4.89733i	−1.02929	+	0.429524i
$131$	2.02661	−	3.51018i	0.177065	−	0.306686i	−0.763809	−	0.645443i	$-0.776673\pi$
$131$	2.02661	−	3.51018i	0.177065	−	0.306686i	0.940874	+	0.338756i	$0.110006\pi$
$132$	9.52735	+	1.67281i	0.829249	+	0.145600i
$133$	−15.9626	−	10.5385i	−1.38413	−	0.913806i
$134$	9.11054	−	5.25998i	0.787031	−	0.454393i
$135$	−9.19771	−	15.8512i	−0.791613	−	1.36426i
$136$	−2.38204	−	1.37527i	−0.204259	−	0.117929i
$137$	2.30652	+	1.33167i	0.197060	+	0.113772i	0.595283	−	0.803516i	$-0.297040\pi$
$137$	2.30652	+	1.33167i	0.197060	+	0.113772i	−0.398224	+	0.917288i	$0.630373\pi$
$138$	1.35457	−	7.71485i	0.115309	−	0.656731i
$139$	−12.6149	+	7.28322i	−1.06998	+	0.617755i	−0.928177	−	0.372139i	$-0.878624\pi$
$139$	−12.6149	+	7.28322i	−1.06998	+	0.617755i	−0.141806	+	0.989894i	$0.545291\pi$
$140$	−9.31464	−	0.558744i	−0.787231	−	0.0472225i
$141$	1.17638	−	6.69999i	0.0990694	−	0.564241i
$142$	−0.584557	+	1.01248i	−0.0490549	+	0.0849656i
$143$	−18.5830	+	7.75473i	−1.55399	+	0.648483i
$144$	−2.82056	−	1.02197i	−0.235047	−	0.0851646i
$145$	−1.66931	+	0.963776i	−0.138629	+	0.0800372i
$146$	−6.46743	+	11.2019i	−0.535248	+	0.927077i
$147$	−8.29597	−	8.84177i	−0.684240	−	0.729257i
$148$	2.70444			0.222304
$149$		−	7.06203i		−	0.578544i	−0.957247	−	0.289272i	$-0.906587\pi$
$149$		−	7.06203i		−	0.578544i	0.957247	−	0.289272i	$-0.0934132\pi$
$150$	12.6910	+	2.22829i	1.03622	+	0.181939i
$151$	−0.381853	−	0.661388i	−0.0310747	−	0.0538230i	0.850070	−	0.526670i	$-0.176560\pi$
$151$	−0.381853	−	0.661388i	−0.0310747	−	0.0538230i	−0.881145	+	0.472847i	$0.843226\pi$
$152$	7.22955			0.586394
$153$	1.44466	+	8.12420i	0.116793	+	0.656802i
$154$	−14.7494	−	0.884750i	−1.18854	−	0.0712952i
$155$			5.09502i			0.409242i
$156$	6.09239	−	1.37213i	0.487782	−	0.109858i
$157$	−13.9268	+	8.04062i	−1.11148	+	0.641711i	−0.939211	−	0.343340i	$-0.888442\pi$
$157$	−13.9268	+	8.04062i	−1.11148	+	0.641711i	−0.172265	+	0.985051i	$0.555108\pi$
$158$		−	8.95879i		−	0.712723i
$159$	−11.9921	+	14.3126i	−0.951033	+	1.13507i
$160$	3.05441	−	1.76347i	0.241472	−	0.139414i
$161$	−0.716434	+	11.9434i	−0.0564629	+	0.941274i
$162$	3.10268	+	8.44828i	0.243769	+	0.663759i
$163$	7.19256			0.563365			0.281682	−	0.959508i	$-0.409108\pi$
$163$	7.19256			0.563365			0.281682	+	0.959508i	$0.409108\pi$
$164$	3.63062	+	6.28842i	0.283504	+	0.491043i
$165$	33.6023	+	5.89990i	2.61594	+	0.459306i
$166$	−3.39976	+	1.96285i	−0.263872	+	0.152347i
$167$	−3.75042	+	6.49592i	−0.290216	+	0.502669i	−0.973861	−	0.227146i	$-0.927061\pi$
$167$	−3.75042	+	6.49592i	−0.290216	+	0.502669i	0.683644	+	0.729815i	$0.260394\pi$
$168$	4.45798	+	1.06133i	0.343941	+	0.0818830i
$169$	−9.14385	+	9.24067i	−0.703373	+	0.710821i
$170$	−8.40131	−	4.85050i	−0.644351	−	0.372016i
$171$	−13.9653	−	16.5943i	−1.06795	−	1.26900i
$172$	0.141987			0.0108264
$173$	22.0661			1.67765			0.838827	−	0.544398i	$-0.183242\pi$
$173$	22.0661			1.67765			0.838827	+	0.544398i	$0.183242\pi$
$174$	0.889285	−	0.324403i	0.0674165	−	0.0245929i
$175$	−19.6471	−	1.17854i	−1.48518	−	0.0890894i
$176$	4.83655	−	2.79238i	0.364568	−	0.210484i
$177$	2.22516	−	12.6732i	0.167253	−	0.952576i
$178$	−1.17279	−	0.677113i	−0.0879047	−	0.0507518i
$179$		−	11.1282i		−	0.831761i	−0.909419	−	0.415881i	$-0.863473\pi$
$179$		−	11.1282i		−	0.831761i	0.909419	−	0.415881i	$-0.136527\pi$
$180$	−9.94793	−	3.60443i	−0.741475	−	0.268659i
$181$		−	3.28580i		−	0.244232i	−0.992516	−	0.122116i	$-0.961032\pi$
$181$		−	3.28580i		−	0.244232i	0.992516	−	0.122116i	$-0.0389680\pi$
$182$	−9.00779	+	3.14003i	−0.667702	+	0.232754i
$183$	7.41669	+	20.3313i	0.548257	+	1.50294i
$184$	−2.26115	−	3.91643i	−0.166694	−	0.288723i
$185$	9.53838			0.701276
$186$	0.432704	−	2.46443i	0.0317274	−	0.180701i
$187$	−13.3031	−	7.68058i	−0.972823	−	0.561659i
$188$	−1.96371	−	3.40124i	−0.143218	−	0.248061i
$189$	−6.17534	−	12.2827i	−0.449190	−	0.893436i
$190$	25.4981			1.84983
$191$			2.26934i			0.164204i	0.996624	+	0.0821018i	$0.0261633\pi$
$191$			2.26934i			0.164204i	−0.996624	+	0.0821018i	$0.973837\pi$
$192$	−1.62717	+	0.593575i	−0.117431	+	0.0428376i
$193$	16.0127			1.15262			0.576311	−	0.817231i	$-0.304492\pi$
$193$	16.0127			1.15262			0.576311	+	0.817231i	$0.304492\pi$
$194$	−6.41610	+	11.1130i	−0.460649	+	0.797868i
$195$	21.4875	−	4.83941i	1.53875	−	0.346557i
$196$	−6.94980	−	0.836788i	−0.496415	−	0.0597705i
$197$	20.3601	+	11.7549i	1.45060	+	0.837503i	0.998515	−	0.0544726i	$-0.0173478\pi$
$197$	20.3601	+	11.7549i	1.45060	+	0.837503i	0.452083	+	0.891976i	$0.350681\pi$
$198$	−15.7522	−	5.70749i	−1.11946	−	0.405613i
$199$	3.78078	+	2.18284i	0.268013	+	0.154737i	0.627984	−	0.778226i	$-0.283880\pi$
$199$	3.78078	+	2.18284i	0.268013	+	0.154737i	−0.359972	+	0.932963i	$0.617214\pi$
$200$	6.44257	−	3.71962i	0.455559	−	0.263017i
$201$	−17.1177	+	6.24438i	−1.20739	+	0.440445i
$202$	6.69463	−	3.86514i	0.471032	−	0.271951i
$203$	−1.29329	+	0.646704i	−0.0907710	+	0.0453897i
$204$	3.65172	+	3.05965i	0.255672	+	0.214218i
$205$	12.8050	+	22.1788i	0.894337	+	1.54904i
$206$	3.29451			0.229539
$207$	−4.62168	+	12.7554i	−0.321229	+	0.886564i
$208$	2.18738	−	2.86625i	0.151668	−	0.198738i
$209$	40.3753			2.79282
$210$	15.7230	+	3.74322i	1.08499	+	0.258307i
$211$	2.97744	−	5.15707i	0.204975	−	0.355028i	−0.745150	−	0.666897i	$-0.767622\pi$
$211$	2.97744	−	5.15707i	0.204975	−	0.355028i	0.950125	+	0.311870i	$0.100955\pi$
$212$			10.7806i			0.740412i
$213$	1.30050	−	1.55215i	0.0891086	−	0.106352i
$214$	−0.755862	+	1.30919i	−0.0516697	+	0.0894945i
$215$	0.500779			0.0341529
$216$	4.50564	+	2.58829i	0.306570	+	0.176111i
$217$	−0.228857	+	3.81520i	−0.0155358	+	0.258993i
$218$	−10.3775	−	5.99142i	−0.702850	−	0.405790i
$219$	14.3885	−	17.1728i	0.972283	−	1.16043i
$220$	17.0582	−	9.84854i	1.15006	−	0.663988i
$221$	−9.83577	−	1.26856i	−0.661626	−	0.0853328i
$222$	−4.61366	−	0.810066i	−0.309648	−	0.0543681i
$223$	−7.80461	−	4.50599i	−0.522635	−	0.301744i	0.215377	−	0.976531i	$-0.430902\pi$
$223$	−7.80461	−	4.50599i	−0.522635	−	0.301744i	−0.738012	+	0.674787i	$0.764235\pi$
$224$	2.36639	−	1.18330i	0.158111	−	0.0790628i
$225$	−20.9828	−	7.60272i	−1.39886	−	0.506848i
$226$	2.06618	−	3.57873i	0.137440	−	0.238054i
$227$	−12.6033	+	21.8296i	−0.836511	+	1.44888i	0.0562831	+	0.998415i	$0.482075\pi$
$227$	−12.6033	+	21.8296i	−0.836511	+	1.44888i	−0.892794	+	0.450465i	$0.851258\pi$
$228$	−12.3333	−	2.16548i	−0.816792	−	0.143412i
$229$	−6.18369	−	3.57015i	−0.408630	−	0.235922i	0.281571	−	0.959540i	$-0.409144\pi$
$229$	−6.18369	−	3.57015i	−0.408630	−	0.235922i	−0.690201	+	0.723618i	$0.742478\pi$
$230$	−7.97493	−	13.8130i	−0.525851	−	0.910801i
$231$	24.8968	+	5.92725i	1.63809	+	0.389984i
$232$	0.273262	−	0.473303i	0.0179405	−	0.0310739i
$233$	−18.7499	−	10.8253i	−1.22835	−	0.709187i	−0.261664	−	0.965159i	$-0.584271\pi$
$233$	−18.7499	−	10.8253i	−1.22835	−	0.709187i	−0.966684	+	0.255972i	$0.917605\pi$
$234$	−10.8043	+	0.515927i	−0.706302	+	0.0337272i
$235$	−6.92586	−	11.9959i	−0.451793	−	0.782528i
$236$	−3.71440	−	6.43353i	−0.241787	−	0.418787i
$237$	−2.68344	+	15.2833i	−0.174308	+	0.992756i
$238$	−6.07311	−	4.00947i	−0.393661	−	0.259895i
$239$		−	23.2948i		−	1.50682i	−0.657552	−	0.753409i	$-0.728408\pi$
$239$		−	23.2948i		−	1.50682i	0.657552	−	0.753409i	$-0.271592\pi$
$240$	−5.73890	+	2.09350i	−0.370445	+	0.135135i
$241$	0.810506	+	0.467946i	0.0522093	+	0.0301431i	0.525877	−	0.850560i	$-0.323737\pi$
$241$	0.810506	+	0.467946i	0.0522093	+	0.0301431i	−0.473668	+	0.880703i	$0.657070\pi$
$242$	17.4847	−	10.0948i	1.12396	−	0.648917i
$243$	−2.76250	−	15.3417i	−0.177214	−	0.984172i
$244$	10.8209	+	6.24747i	0.692740	+	0.399953i
$245$	−24.5115	−	2.95129i	−1.56598	−	0.188551i
$246$	−4.31009	−	11.8152i	−0.274802	−	0.753312i
$247$	24.0560	−	10.0386i	1.53065	−	0.638742i
$248$	−0.722302	−	1.25106i	−0.0458662	−	0.0794426i
$249$	6.38776	−	2.33020i	0.404808	−	0.147670i
$250$	7.45045	−	4.30152i	0.471208	−	0.272052i
$251$	−12.4011	−	21.4793i	−0.782748	−	1.35576i	−0.930335	−	0.366711i	$-0.880484\pi$
$251$	−12.4011	−	21.4793i	−0.782748	−	1.35576i	0.147587	−	0.989049i	$-0.452849\pi$
$252$	−7.28721	−	3.14588i	−0.459051	−	0.198172i
$253$	−12.6280	−	21.8723i	−0.793916	−	1.37510i
$254$			4.59945i			0.288595i
$255$	12.8794	+	10.7912i	0.806537	+	0.675770i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.2108	+	24.6139i	0.886448	+	1.53537i	0.844045	+	0.536272i	$0.180168\pi$
$257$	14.2108	+	24.6139i	0.886448	+	1.53537i	0.0424030	+	0.999101i	$0.486499\pi$
$258$	−0.242224	−	0.0425297i	−0.0150802	−	0.00264778i
$259$	7.14245	+	0.428444i	0.443810	+	0.0266222i
$260$	7.71474	−	10.1091i	0.478448	−	0.626937i
$261$	−1.61425	+	0.287048i	−0.0999195	+	0.0177678i
$262$			4.05321i			0.250408i
$263$		−	12.8091i		−	0.789844i	−0.918715	−	0.394922i	$-0.870772\pi$
$263$		−	12.8091i		−	0.789844i	0.918715	−	0.394922i	$-0.129228\pi$
$264$	−9.08733	+	3.31498i	−0.559287	+	0.204023i
$265$			38.0223i			2.33569i
$266$	19.0933	+	1.14532i	1.17068	+	0.0702242i
$267$	1.79792	+	1.50641i	0.110031	+	0.0921910i
$268$	−5.25998	+	9.11054i	−0.321304	+	0.556515i
$269$	−2.73526	+	4.73762i	−0.166772	+	0.288858i	−0.937283	−	0.348569i	$-0.886668\pi$
$269$	−2.73526	+	4.73762i	−0.166772	+	0.288858i	0.770511	+	0.637427i	$0.220001\pi$
$270$	15.8911	+	9.12872i	0.967100	+	0.555556i
$271$	3.90906	−	2.25690i	0.237458	−	0.137097i	−0.376550	−	0.926396i	$-0.622890\pi$
$271$	3.90906	−	2.25690i	0.237458	−	0.137097i	0.614008	+	0.789300i	$0.289556\pi$
$272$	2.75055			0.166776
$273$	16.3074	−	2.65863i	0.986969	−	0.160908i
$274$	−2.66334			−0.160898
$275$	35.9802	−	20.7732i	2.16969	−	1.25267i
$276$	2.68433	+	7.35854i	0.161578	+	0.442932i
$277$	1.38293	−	2.39530i	0.0830922	−	0.143920i	−0.821484	−	0.570231i	$-0.806854\pi$
$277$	1.38293	−	2.39530i	0.0830922	−	0.143920i	0.904577	+	0.426311i	$0.140187\pi$
$278$	7.28322	−	12.6149i	0.436819	−	0.756592i
$279$	−1.47635	+	4.07459i	−0.0883866	+	0.243939i
$280$	8.34609	−	4.17343i	0.498774	−	0.249410i
$281$		−	4.56102i		−	0.272088i	−0.990703	−	0.136044i	$-0.956561\pi$
$281$		−	4.56102i		−	0.272088i	0.990703	−	0.136044i	$-0.0434388\pi$
$282$	2.33121	+	6.39055i	0.138822	+	0.380552i
$283$			10.8625i			0.645711i	0.946448	+	0.322855i	$0.104643\pi$
$283$			10.8625i			0.645711i	−0.946448	+	0.322855i	$0.895357\pi$
$284$		−	1.16911i		−	0.0693741i
$285$	−43.4987	−	7.63750i	−2.57664	−	0.452406i
$286$	12.2160	−	16.0073i	0.722347	−	0.946532i
$287$	8.59226	+	17.1829i	0.507185	+	1.01428i
$288$	2.95367	−	0.525225i	0.174046	−	0.0309492i
$289$	4.71724	+	8.17051i	0.277485	+	0.480618i
$290$	0.963776	−	1.66931i	0.0565949	−	0.0980252i
$291$	14.2743	−	17.0365i	0.836773	−	0.998696i
$292$		−	12.9349i		−	0.756956i
$293$	2.27824	+	3.94604i	0.133096	+	0.230530i	0.924869	−	0.380287i	$-0.124175\pi$
$293$	2.27824	+	3.94604i	0.133096	+	0.230530i	−0.791772	+	0.610816i	$0.790841\pi$
$294$	11.6054	+	3.50921i	0.676841	+	0.204661i
$295$	−13.1004	−	22.6906i	−0.762737	−	1.32110i
$296$	−2.34212	+	1.35222i	−0.136133	+	0.0785963i
$297$	25.1629	+	14.4550i	1.46010	+	0.838763i
$298$	3.53101	+	6.11590i	0.204546	+	0.354284i
$299$	−12.9620	−	9.89200i	−0.749614	−	0.572069i
$300$	−12.1049	+	4.41575i	−0.698876	+	0.254943i
$301$	0.374989	+	0.0224939i	0.0216140	+	0.00129653i
$302$	0.661388	+	0.381853i	0.0380586	+	0.0219731i
$303$	−12.5785	+	4.58851i	−0.722614	+	0.263603i
$304$	−6.26098	+	3.61478i	−0.359092	+	0.207322i
$305$	38.1647	+	22.0344i	2.18530	+	1.26169i
$306$	−5.31321	−	6.31343i	−0.303736	−	0.360915i
$307$		−	14.2501i		−	0.813298i	−0.913584	−	0.406649i	$-0.866697\pi$
$307$		−	14.2501i		−	0.813298i	0.913584	−	0.406649i	$-0.133303\pi$
$308$	13.2157	−	6.60847i	0.753035	−	0.376553i
$309$	−5.62028	−	0.986809i	−0.319727	−	0.0561376i
$310$	−2.54751	−	4.41241i	−0.144689	−	0.250608i
$311$	−9.01815	−	15.6199i	−0.511372	−	0.885723i	−0.999913	−	0.0131816i	$-0.995804\pi$
$311$	−9.01815	−	15.6199i	−0.511372	−	0.885723i	0.488541	−	0.872541i	$-0.337529\pi$
$312$	−4.59010	+	4.23450i	−0.259863	+	0.239731i
$313$	18.1151	+	10.4587i	1.02392	+	0.591163i	0.915238	−	0.402913i	$-0.132002\pi$
$313$	18.1151	+	10.4587i	1.02392	+	0.591163i	0.108686	+	0.994076i	$0.465336\pi$
$314$	8.04062	−	13.9268i	0.453758	−	0.785932i
$315$	−25.7015	−	11.0953i	−1.44812	−	0.625149i
$316$	4.47939	+	7.75854i	0.251986	+	0.436452i
$317$	−12.2233	−	7.05711i	−0.686528	−	0.396367i	0.115782	−	0.993275i	$-0.463063\pi$
$317$	−12.2233	−	7.05711i	−0.686528	−	0.396367i	−0.802310	+	0.596908i	$0.796396\pi$
$318$	3.22912	−	18.3911i	0.181080	−	1.03132i
$319$	1.52610	−	2.64329i	0.0854453	−	0.147996i
$320$	−1.76347	+	3.05441i	−0.0985807	+	0.170747i
$321$	1.68161	−	2.00702i	0.0938583	−	0.112021i
$322$	−5.35126	−	10.7015i	−0.298214	−	0.596373i
$323$	17.2211	+	9.94262i	0.958209	+	0.553222i
$324$	−6.91114	−	5.76509i	−0.383952	−	0.320283i
$325$	16.2725	−	21.3227i	0.902633	−	1.18277i
$326$	−6.22894	+	3.59628i	−0.344989	+	0.199180i
$327$	15.9088	+	13.3295i	0.879761	+	0.737121i
$328$	−6.28842	−	3.63062i	−0.347220	−	0.200468i
$329$	−4.64732	−	9.29378i	−0.256215	−	0.512383i
$330$	−32.0504	+	11.6917i	−1.76432	+	0.643607i
$331$	2.33255			0.128209			0.0641043	−	0.997943i	$-0.479581\pi$
$331$	2.33255			0.128209			0.0641043	+	0.997943i	$0.479581\pi$
$332$	1.96285	−	3.39976i	0.107725	−	0.186586i
$333$	7.62805	+	2.76387i	0.418014	+	0.151459i
$334$		−	7.50084i		−	0.410428i
$335$	−18.5516	+	32.1323i	−1.01358	+	1.75557i
$336$	−4.39139	+	1.30986i	−0.239570	+	0.0714585i
$337$	33.7268			1.83722			0.918609	−	0.395168i	$-0.129313\pi$
$337$	33.7268			1.83722			0.918609	+	0.395168i	$0.129313\pi$
$338$	3.29847	−	12.5746i	0.179413	−	0.683967i
$339$	−4.59675	+	5.48626i	−0.249661	+	0.297973i
$340$	9.70099			0.526110
$341$	−4.03388	−	6.98689i	−0.218447	−	0.378361i
$342$	20.3914	+	7.38842i	1.10264	+	0.399520i
$343$	−18.2219	−	3.31096i	−0.983890	−	0.178775i
$344$	−0.122965	+	0.0709937i	−0.00662981	+	0.00382772i
$345$	9.46744	+	25.9531i	0.509710	+	1.39727i
$346$	−19.1098	+	11.0331i	−1.02735	+	0.593140i
$347$	2.56323	+	1.47988i	0.137602	+	0.0794443i	0.567220	−	0.823566i	$-0.308019\pi$
$347$	2.56323	+	1.47988i	0.137602	+	0.0794443i	−0.429619	+	0.903010i	$0.641352\pi$
$348$	−0.607942	+	0.725584i	−0.0325891	+	0.0388954i
$349$	7.78741	+	4.49606i	0.416851	+	0.240669i	0.693729	−	0.720236i	$-0.255967\pi$
$349$	7.78741	+	4.49606i	0.416851	+	0.240669i	−0.276878	+	0.960905i	$0.589300\pi$
$350$	17.6041	−	8.80289i	0.940981	−	0.470534i
$351$	18.5863	+	2.35609i	0.992061	+	0.125759i
$352$	−2.79238	+	4.83655i	−0.148834	+	0.257789i
$353$	−15.6323			−0.832022			−0.416011	−	0.909360i	$-0.636572\pi$
$353$	−15.6323			−0.832022			−0.416011	+	0.909360i	$0.636572\pi$
$354$	4.40955	+	12.0879i	0.234365	+	0.642464i
$355$		−	4.12338i		−	0.218846i
$356$	1.35423			0.0717739
$357$	9.15949	+	8.65907i	0.484772	+	0.458286i
$358$	5.56410	+	9.63731i	0.294072	+	0.509348i
$359$	−7.17996	−	4.14535i	−0.378944	−	0.218783i	0.298415	−	0.954436i	$-0.403542\pi$
$359$	−7.17996	−	4.14535i	−0.378944	−	0.218783i	−0.677359	+	0.735653i	$0.736875\pi$
$360$	10.4174	−	1.85243i	0.549044	−	0.0976317i
$361$	−33.2665			−1.75087
$362$	1.64290	+	2.84559i	0.0863490	+	0.149561i
$363$	−32.8518	+	11.9840i	−1.72427	+	0.628998i
$364$	6.23096	−	7.22324i	0.326591	−	0.378601i
$365$		−	45.6204i		−	2.38788i
$366$	−16.5887	−	13.8991i	−0.867106	−	0.726519i
$367$			27.4310i			1.43189i	0.698159	+	0.715943i	$0.254003\pi$
$367$			27.4310i			1.43189i	−0.698159	+	0.715943i	$0.745997\pi$
$368$	3.91643	+	2.26115i	0.204158	+	0.117871i
$369$	3.81378	+	21.4473i	0.198538	+	1.11650i
$370$	−8.26048	+	4.76919i	−0.429442	+	0.247939i
$371$	−1.70788	+	28.4715i	−0.0886687	+	1.47817i
$372$	0.857481	+	2.35061i	0.0444583	+	0.121873i
$373$	33.1534			1.71662			0.858308	−	0.513135i	$-0.171516\pi$
$373$	33.1534			1.71662			0.858308	+	0.513135i	$0.171516\pi$
$374$	15.3612			0.794306
$375$	−13.9986	+	5.10655i	−0.722884	+	0.263701i
$376$	3.40124	+	1.96371i	0.175405	+	0.101270i
$377$	0.252059	−	1.95433i	0.0129817	−	0.100653i
$378$	11.4894	+	7.54948i	0.590949	+	0.388303i
$379$	8.65643	−	14.9934i	0.444651	−	0.770158i	−0.553377	−	0.832931i	$-0.686661\pi$
$379$	8.65643	−	14.9934i	0.444651	−	0.770158i	0.998028	+	0.0627730i	$0.0199944\pi$
$380$	−22.0820	+	12.7491i	−1.13278	+	0.654014i
$381$	1.37768	−	7.84646i	0.0705808	−	0.401986i
$382$	−1.13467	−	1.96531i	−0.0580547	−	0.100554i
$383$	−11.9845			−0.612380			−0.306190	−	0.951970i	$-0.599054\pi$
$383$	−11.9845			−0.612380			−0.306190	+	0.951970i	$0.599054\pi$
$384$	1.11238	−	1.32763i	0.0567659	−	0.0677505i
$385$	46.6109	−	23.3076i	2.37551	−	1.18787i
$386$	−13.8674	+	8.00636i	−0.705833	+	0.407513i
$387$	0.400484	+	0.145107i	0.0203577	+	0.00737623i
$388$		−	12.8322i		−	0.651456i
$389$	−6.65966	+	3.84496i	−0.337658	+	0.194947i	−0.659236	−	0.751936i	$-0.729120\pi$
$389$	−6.65966	+	3.84496i	−0.337658	+	0.194947i	0.321578	+	0.946883i	$0.395787\pi$
$390$	−16.1890	+	14.9348i	−0.819761	+	0.756252i
$391$		−	12.4388i		−	0.629058i
$392$	6.43710	−	2.75022i	0.325123	−	0.138907i
$393$	1.21406	−	6.91459i	0.0612415	−	0.348795i
$394$	−23.5098			−1.18441
$395$	15.7985	+	27.3638i	0.794909	+	1.37682i
$396$	16.4955	−	2.93326i	0.828931	−	0.147402i
$397$		−	2.01403i		−	0.101081i	−0.998722	−	0.0505407i	$-0.983906\pi$
$397$		−	2.01403i		−	0.101081i	0.998722	−	0.0505407i	$-0.0160945\pi$
$398$	−4.36567			−0.218831
$399$	−32.2292	−	7.67291i	−1.61348	−	0.384126i
$400$	−3.71962	+	6.44257i	−0.185981	+	0.322129i
$401$	−25.6675	+	14.8191i	−1.28177	+	0.740033i	−0.977173	−	0.212447i	$-0.931857\pi$
$401$	−25.6675	+	14.8191i	−1.28177	+	0.740033i	−0.304602	+	0.952480i	$0.598523\pi$
$402$	11.7022	−	13.9666i	0.583651	−	0.696593i
$403$	−4.14059	−	3.15990i	−0.206257	−	0.157406i
$404$	−3.86514	+	6.69463i	−0.192298	+	0.333070i
$405$	−24.3751	−	20.3331i	−1.21121	−	1.01036i
$406$	0.796668	−	1.20671i	0.0395379	−	0.0598878i
$407$	−13.0802	+	7.55184i	−0.648360	+	0.374331i
$408$	−4.69231	−	0.823876i	−0.232304	−	0.0407879i
$409$	−19.6394	−	11.3388i	−0.971105	−	0.560668i	−0.0715323	−	0.997438i	$-0.522789\pi$
$409$	−19.6394	−	11.3388i	−0.971105	−	0.560668i	−0.899573	+	0.436770i	$0.856122\pi$
$410$	−22.1788	−	12.8050i	−1.09533	−	0.632391i
$411$	4.54354	+	0.797756i	0.224116	+	0.0393504i
$412$	−2.85313	+	1.64725i	−0.140563	+	0.0811544i
$413$	−8.79053	−	17.5794i	−0.432554	−	0.865027i
$414$	−2.37523	−	13.3574i	−0.116736	−	0.656479i
$415$	6.92284	−	11.9907i	0.339829	−	0.588600i
$416$	−0.461204	+	3.57593i	−0.0226124	+	0.175325i
$417$	−16.2034	+	19.3389i	−0.793485	+	0.947031i
$418$	−34.9661	+	20.1877i	−1.71025	+	0.987411i
$419$	−2.01719	+	3.49388i	−0.0985463	+	0.170687i	−0.911083	−	0.412223i	$-0.864753\pi$
$419$	−2.01719	+	3.49388i	−0.0985463	+	0.170687i	0.812537	+	0.582910i	$0.198086\pi$
$420$	−15.4881	+	4.61977i	−0.755743	+	0.225422i
$421$	−7.21848			−0.351807			−0.175904	−	0.984407i	$-0.556285\pi$
$421$	−7.21848			−0.351807			−0.175904	+	0.984407i	$0.556285\pi$
$422$			5.95488i			0.289879i
$423$	−2.06277	−	11.6003i	−0.100295	−	0.564024i
$424$	−5.39028	−	9.33624i	−0.261775	−	0.453408i
$425$	20.4620			0.992552
$426$	−0.350186	+	1.99445i	−0.0169666	+	0.0966316i
$427$	27.5884	+	18.2139i	1.33510	+	0.881431i
$428$		−	1.51172i		−	0.0730719i
$429$	−25.6346	+	23.6487i	−1.23765	+	1.14177i
$430$	−0.433688	+	0.250390i	−0.0209143	+	0.0120749i
$431$		−	18.4030i		−	0.886440i	−0.896413	−	0.443220i	$-0.853836\pi$
$431$		−	18.4030i		−	0.886440i	0.896413	−	0.443220i	$-0.146164\pi$
$432$	−5.19614	+	0.0112934i	−0.249999	+	0.000543352i
$433$	−1.86816	+	1.07858i	−0.0897781	+	0.0518334i	−0.544217	−	0.838945i	$-0.683173\pi$
$433$	−1.86816	+	1.07858i	−0.0897781	+	0.0518334i	0.454439	+	0.890778i	$0.349840\pi$
$434$	−1.70941	−	3.41849i	−0.0820541	−	0.164093i
$435$	−2.14417	+	2.55908i	−0.102805	+	0.122699i
$436$	11.9828			0.573874
$437$	16.3471	+	28.3141i	0.781989	+	1.35444i
$438$	−3.87440	+	22.0663i	−0.185126	+	1.05437i
$439$	−31.1263	+	17.9708i	−1.48558	+	0.857699i	−0.999865	−	0.0164188i	$-0.994773\pi$
$439$	−31.1263	+	17.9708i	−1.48558	+	0.857699i	−0.485713	+	0.874118i	$0.661440\pi$
$440$	−9.84854	+	17.0582i	−0.469511	+	0.813216i
$441$	−18.7472	−	9.46274i	−0.892723	−	0.450606i
$442$	9.15231	−	3.81928i	0.435331	−	0.181665i
$443$	−12.0373	−	6.94972i	−0.571908	−	0.330191i	0.186003	−	0.982549i	$-0.440447\pi$
$443$	−12.0373	−	6.94972i	−0.571908	−	0.330191i	−0.757911	+	0.652358i	$0.773780\pi$
$444$	4.40058	−	1.60529i	0.208842	−	0.0761837i
$445$	4.77626			0.226417
$446$	9.01198			0.426730
$447$	−4.19185	−	11.4911i	−0.198268	−	0.543510i
$448$	−1.45770	+	2.20797i	−0.0688698	+	0.104317i
$449$	7.01192	−	4.04833i	0.330913	−	0.191053i	−0.325333	−	0.945599i	$-0.605477\pi$
$449$	7.01192	−	4.04833i	0.330913	−	0.191053i	0.656246	+	0.754547i	$0.272143\pi$
$450$	21.9730	−	3.90727i	1.03582	−	0.184191i
$451$	−35.1193	−	20.2762i	−1.65370	−	0.954767i
$452$			4.13236i			0.194370i
$453$	−1.01392	−	0.849530i	−0.0476382	−	0.0399144i
$454$		−	25.2066i		−	1.18301i
$455$	21.9762	−	25.4759i	1.03026	−	1.19433i
$456$	11.7637	−	4.29128i	0.550885	−	0.200958i
$457$	7.49317	+	12.9786i	0.350516	+	0.607111i	0.986340	−	0.164723i	$-0.0526730\pi$
$457$	7.49317	+	12.9786i	0.350516	+	0.607111i	−0.635824	+	0.771834i	$0.719340\pi$
$458$	7.14031			0.333645
$459$	7.17302	+	12.3619i	0.334808	+	0.577004i
$460$	13.8130	+	7.97493i	0.644034	+	0.371833i
$461$	−19.1448	−	33.1598i	−0.891662	−	1.54440i	−0.837882	−	0.545851i	$-0.816206\pi$
$461$	−19.1448	−	33.1598i	−0.891662	−	1.54440i	−0.0537801	−	0.998553i	$-0.517127\pi$
$462$	−24.5249	+	7.31523i	−1.14100	+	0.340335i
$463$	−33.6387			−1.56333			−0.781663	−	0.623702i	$-0.785628\pi$
$463$	−33.6387			−1.56333			−0.781663	+	0.623702i	$0.785628\pi$
$464$			0.546524i			0.0253717i
$465$	3.02428	+	8.29044i	0.140247	+	0.384460i
$466$	21.6505			1.00294
$467$	19.5650	−	33.8876i	0.905362	−	1.56813i	0.0849307	−	0.996387i	$-0.472933\pi$
$467$	19.5650	−	33.8876i	0.905362	−	1.56813i	0.820431	−	0.571746i	$-0.193734\pi$
$468$	9.09887	−	5.84898i	0.420595	−	0.270369i
$469$	−15.3349	+	23.2277i	−0.708101	+	1.07255i
$470$	11.9959	+	6.92586i	0.553331	+	0.319466i
$471$	−17.8884	+	21.3500i	−0.824255	+	0.983756i
$472$	6.43353	+	3.71440i	0.296127	+	0.170969i
$473$	−0.686728	+	0.396483i	−0.0315758	+	0.0182303i
$474$	−5.31771	−	14.5774i	−0.244251	−	0.669564i
$475$	−46.5769	+	26.8912i	−2.13710	+	1.23385i
$476$	7.26421	+	0.435748i	0.332954	+	0.0199725i
$477$	−11.0175	+	30.4072i	−0.504455	+	1.39225i
$478$	11.6474	+	20.1739i	0.532741	+	0.922734i
$479$	−8.01010			−0.365991			−0.182996	−	0.983114i	$-0.558579\pi$
$479$	−8.01010			−0.365991			−0.182996	+	0.983114i	$0.558579\pi$
$480$	3.92329	−	4.68247i	0.179073	−	0.213725i
$481$	−5.91565	+	7.75160i	−0.269730	+	0.353443i
$482$	−0.935892			−0.0426287
$483$	5.92357	+	19.8592i	0.269532	+	0.903625i
$484$	−10.0948	+	17.4847i	−0.458854	+	0.794758i
$485$		−	45.2583i		−	2.05507i
$486$	10.0633	+	11.9051i	0.456479	+	0.540025i
$487$	−7.66284	+	13.2724i	−0.347236	+	0.601431i	−0.985757	−	0.168173i	$-0.946213\pi$
$487$	−7.66284	+	13.2724i	−0.347236	+	0.601431i	0.638521	+	0.769604i	$0.279547\pi$
$488$	−12.4949			−0.565620
$489$	11.7035	−	4.26933i	0.529250	−	0.193066i
$490$	22.7032	−	9.69985i	1.02563	−	0.438194i
$491$	13.6930	+	7.90566i	0.617956	+	0.356777i	0.776073	−	0.630643i	$-0.217209\pi$
$491$	13.6930	+	7.90566i	0.617956	+	0.356777i	−0.158116	+	0.987420i	$0.550542\pi$
$492$	9.64027	+	8.07726i	0.434617	+	0.364151i
$493$	1.30184	−	0.751620i	0.0586321	−	0.0338513i
$494$	−15.8138	+	20.7217i	−0.711496	+	0.932313i
$495$	58.1786	−	10.3454i	2.61493	−	0.464991i
$496$	1.25106	+	0.722302i	0.0561744	+	0.0324323i
$497$	0.185214	−	3.08763i	0.00830796	−	0.138499i
$498$	−4.36687	+	5.21189i	−0.195684	+	0.233550i
$499$	9.63442	−	16.6873i	0.431296	−	0.747026i	−0.565689	−	0.824618i	$-0.691390\pi$
$499$	9.63442	−	16.6873i	0.431296	−	0.747026i	0.996985	+	0.0775923i	$0.0247232\pi$
$500$	−4.30152	+	7.45045i	−0.192370	+	0.333194i
$501$	−2.24674	+	12.7961i	−0.100377	+	0.571687i
$502$	21.4793	+	12.4011i	0.958667	+	0.553487i
$503$	12.4057	+	21.4872i	0.553141	+	0.958069i	0.998046	+	0.0624908i	$0.0199044\pi$
$503$	12.4057	+	21.4872i	0.553141	+	0.958069i	−0.444904	+	0.895578i	$0.646762\pi$
$504$	7.88385	−	0.919194i	0.351175	−	0.0409442i
$505$	−13.6321	+	23.6115i	−0.606620	+	1.05070i
$506$	21.8723	+	12.6280i	0.972344	+	0.561383i
$507$	−9.39352	+	20.4637i	−0.417181	+	0.908824i
$508$	−2.29973	−	3.98324i	−0.102034	−	0.176728i
$509$	5.05002	+	8.74690i	0.223838	+	0.387699i	0.955970	−	0.293463i	$-0.0948079\pi$
$509$	5.05002	+	8.74690i	0.223838	+	0.387699i	−0.732132	+	0.681163i	$0.761475\pi$
$510$	−16.5495	−	2.90575i	−0.732822	−	0.128669i
$511$	2.04917	−	34.1610i	0.0906499	−	1.51119i
$512$		−	1.00000i		−	0.0441942i
$513$	−32.5737	−	18.7122i	−1.43817	−	0.826163i
$514$	−24.6139	−	14.2108i	−1.08567	−	0.626813i
$515$	−10.0628	+	5.80975i	−0.443419	+	0.256008i
$516$	0.231037	−	0.0842802i	0.0101708	−	0.00371023i
$517$	18.9951	+	10.9668i	0.835404	+	0.482321i
$518$	−6.39976	+	3.20018i	−0.281189	+	0.140608i
$519$	35.9052	−	13.0979i	1.57606	−	0.574934i
$520$	−1.62663	+	12.6121i	−0.0713326	+	0.553076i
$521$	−7.92535	−	13.7271i	−0.347216	−	0.601395i	0.638538	−	0.769590i	$-0.279540\pi$
$521$	−7.92535	−	13.7271i	−0.347216	−	0.601395i	−0.985754	+	0.168195i	$0.946206\pi$
$522$	1.25446	−	1.05571i	0.0549061	−	0.0462074i
$523$	33.5587	−	19.3751i	1.46742	−	0.847215i	0.468084	−	0.883684i	$-0.344945\pi$
$523$	33.5587	−	19.3751i	1.46742	−	0.847215i	0.999335	+	0.0364696i	$0.0116112\pi$
$524$	−2.02661	−	3.51018i	−0.0885327	−	0.153343i
$525$	−32.6686	+	9.74433i	−1.42577	+	0.425278i
$526$	6.40456	+	11.0930i	0.279252	+	0.483679i
$527$		−	3.97345i		−	0.173086i
$528$	6.21237	−	7.41452i	0.270359	−	0.322676i
$529$	−1.27438	+	2.20728i	−0.0554076	+	0.0959688i
$530$	−19.0111	−	32.9283i	−0.825791	−	1.43031i
$531$	−3.90179	−	21.9422i	−0.169323	−	0.952210i
$532$	−17.1079	+	8.55476i	−0.741723	+	0.370896i
$533$	−25.9657	−	3.34891i	−1.12470	−	0.145057i
$534$	−2.31025	−	0.405634i	−0.0999743	−	0.0175535i
$535$		−	5.33175i		−	0.230511i
$536$		−	10.5200i		−	0.454393i
$537$	−6.60543	−	18.1074i	−0.285045	−	0.781394i
$538$		−	5.47053i		−	0.235851i
$539$	35.9497	−	15.3593i	1.54846	−	0.661574i
$540$	−18.3264	+	0.0398309i	−0.788644	+	0.00171405i
$541$	8.32547	−	14.4201i	0.357940	−	0.619970i	−0.629676	−	0.776857i	$-0.716813\pi$
$541$	8.32547	−	14.4201i	0.357940	−	0.619970i	0.987617	+	0.156887i	$0.0501459\pi$
$542$	−2.25690	+	3.90906i	−0.0969420	+	0.167908i
$543$	−1.95037	−	5.34654i	−0.0836984	−	0.229442i
$544$	−2.38204	+	1.37527i	−0.102129	+	0.0589644i
$545$	42.2627			1.81033
$546$	−12.7933	+	10.4561i	−0.547503	+	0.447482i
$547$	−15.5709			−0.665762			−0.332881	−	0.942969i	$-0.608021\pi$
$547$	−15.5709			−0.665762			−0.332881	+	0.942969i	$0.608021\pi$
$548$	2.30652	−	1.33167i	0.0985298	−	0.0568862i
$549$	24.1364	+	28.6801i	1.03012	+	1.22404i
$550$	−20.7732	+	35.9802i	−0.885772	+	1.53420i
$551$	−1.97556	+	3.42177i	−0.0841618	+	0.145772i
$552$	−6.00397	−	5.03052i	−0.255546	−	0.214113i
$553$	10.6010	+	21.2000i	0.450799	+	0.901514i
$554$			2.76586i			0.117510i
$555$	15.5205	−	5.66175i	0.658810	−	0.240328i
$556$			14.5664i			0.617755i
$557$		−	28.0326i		−	1.18778i	−0.804546	−	0.593890i	$-0.797591\pi$
$557$		−	28.0326i		−	1.18778i	0.804546	−	0.593890i	$-0.202409\pi$
$558$	−0.758741	−	4.26687i	−0.0321201	−	0.180631i
$559$	−0.310580	+	0.406971i	−0.0131361	+	0.0172130i
$560$	−5.14121	+	7.78734i	−0.217256	+	0.329075i
$561$	−26.2054	−	4.60115i	−1.10639	−	0.194261i
$562$	2.28051	+	3.94996i	0.0961975	+	0.166619i
$563$	14.5119	−	25.1354i	0.611605	−	1.05933i	−0.379365	−	0.925247i	$-0.623858\pi$
$563$	14.5119	−	25.1354i	0.611605	−	1.05933i	0.990970	−	0.134084i	$-0.0428092\pi$
$564$	−5.21417	−	4.36877i	−0.219556	−	0.183958i
$565$			14.5746i			0.613156i
$566$	−5.43127	−	9.40723i	−0.228293	−	0.395415i
$567$	−17.3390	−	16.3205i	−0.728170	−	0.685396i
$568$	0.584557	+	1.01248i	0.0245274	+	0.0424828i
$569$	18.1164	−	10.4595i	0.759477	−	0.438484i	−0.0696307	−	0.997573i	$-0.522182\pi$
$569$	18.1164	−	10.4595i	0.759477	−	0.438484i	0.829108	+	0.559088i	$0.188849\pi$
$570$	41.4897	−	15.1351i	1.73781	−	0.633938i
$571$	13.7259	+	23.7740i	0.574412	+	0.994910i	0.996105	+	0.0881718i	$0.0281025\pi$
$571$	13.7259	+	23.7740i	0.574412	+	0.994910i	−0.421694	+	0.906738i	$0.638564\pi$
$572$	−2.57571	+	19.9707i	−0.107696	+	0.835018i
$573$	1.34702	+	3.69259i	0.0562727	+	0.154260i
$574$	−16.0326	−	10.5847i	−0.669187	−	0.441797i
$575$	29.1353	+	16.8213i	1.21503	+	0.701495i
$576$	−2.29534	+	1.93169i	−0.0956390	+	0.0804871i
$577$	12.3366	−	7.12257i	0.513581	−	0.296516i	−0.220723	−	0.975336i	$-0.570842\pi$
$577$	12.3366	−	7.12257i	0.513581	−	0.296516i	0.734305	+	0.678820i	$0.237508\pi$
$578$	−8.17051	−	4.71724i	−0.339848	−	0.196212i
$579$	26.0554	−	9.50476i	1.08282	−	0.395004i
$580$			1.92755i			0.0800372i
$581$	5.72249	−	8.66781i	0.237409	−	0.359601i
$582$	−3.84365	+	21.8912i	−0.159324	+	0.907418i
$583$	−30.1034	−	52.1407i	−1.24676	−	2.15945i
$584$	6.46743	+	11.2019i	0.267624	+	0.463539i
$585$	32.0911	−	20.6289i	1.32680	−	0.852902i
$586$	−3.94604	−	2.27824i	−0.163009	−	0.0941134i
$587$	14.8030	−	25.6395i	0.610983	−	1.05825i	−0.380092	−	0.924949i	$-0.624108\pi$
$587$	14.8030	−	25.6395i	0.610983	−	1.05825i	0.991075	−	0.133305i	$-0.0425591\pi$
$588$	−11.8052	+	2.76364i	−0.486837	+	0.113971i
$589$	5.22192	+	9.04463i	0.215165	+	0.372677i
$590$	22.6906	+	13.1004i	0.934158	+	0.539336i
$591$	40.1067	+	7.04194i	1.64977	+	0.289667i
$592$	1.35222	−	2.34212i	0.0555760	−	0.0962604i
$593$	−11.0829	+	19.1962i	−0.455121	+	0.788292i	−0.998695	−	0.0510687i	$-0.983737\pi$
$593$	−11.0829	+	19.1962i	−0.455121	+	0.788292i	0.543574	+	0.839361i	$0.317071\pi$
$594$	−29.0192	+	0.0630707i	−1.19067	+	0.00258782i
$595$	25.6204	+	1.53685i	1.05033	+	0.0630048i
$596$	−6.11590	−	3.53101i	−0.250517	−	0.144636i
$597$	7.44764	+	1.30766i	0.304812	+	0.0535188i
$598$	16.1715	+	2.08570i	0.661300	+	0.0852908i
$599$	−6.69141	+	3.86329i	−0.273404	+	0.157850i	−0.630433	−	0.776243i	$-0.717123\pi$
$599$	−6.69141	+	3.86329i	−0.273404	+	0.157850i	0.357030	+	0.934093i	$0.383789\pi$
$600$	8.27526	−	9.87659i	0.337836	−	0.403210i
$601$	−30.6255	−	17.6816i	−1.24924	−	0.721249i	−0.278282	−	0.960499i	$-0.589765\pi$
$601$	−30.6255	−	17.6816i	−1.24924	−	0.721249i	−0.970958	+	0.239251i	$0.923098\pi$
$602$	−0.335997	+	0.168014i	−0.0136942	+	0.00684775i
$603$	−24.1468	+	20.3213i	−0.983335	+	0.827547i
$604$	−0.763705			−0.0310747
$605$	−35.6036	+	61.6673i	−1.44749	+	2.50713i
$606$	8.59901	−	10.2630i	0.349311	−	0.416906i
$607$			38.5504i			1.56471i	0.622832	+	0.782356i	$0.285982\pi$
$607$			38.5504i			1.56471i	−0.622832	+	0.782356i	$0.714018\pi$
$608$	3.61478	−	6.26098i	0.146599	−	0.253916i
$609$	−1.72053	+	1.81996i	−0.0697192	+	0.0737484i
$610$	−44.0688			−1.78429
$611$	14.0442	+	1.81134i	0.568166	+	0.0732788i
$612$	7.75809	+	2.81099i	0.313602	+	0.113628i
$613$	−13.3805			−0.540435			−0.270218	−	0.962799i	$-0.587096\pi$
$613$	−13.3805			−0.540435			−0.270218	+	0.962799i	$0.587096\pi$
$614$	7.12507	+	12.3410i	0.287544	+	0.498042i
$615$	34.0006	+	28.4879i	1.37104	+	1.14874i
$616$	−8.14091	+	12.3310i	−0.328006	+	0.496829i
$617$	9.07671	−	5.24044i	0.365415	−	0.210972i	−0.306039	−	0.952019i	$-0.599004\pi$
$617$	9.07671	−	5.24044i	0.365415	−	0.210972i	0.671453	+	0.741047i	$0.265670\pi$
$618$	5.36071	−	1.95554i	0.215639	−	0.0786633i
$619$	3.18142	−	1.83679i	0.127872	−	0.0738269i	−0.434700	−	0.900576i	$-0.643145\pi$
$619$	3.18142	−	1.83679i	0.127872	−	0.0738269i	0.562571	+	0.826749i	$0.309812\pi$
$620$	4.41241	+	2.54751i	0.177207	+	0.102310i
$621$	0.0510720	+	23.4985i	0.00204945	+	0.942964i
$622$	15.6199	+	9.01815i	0.626300	+	0.361595i
$623$	3.57652	+	0.214540i	0.143290	+	0.00859535i
$624$	1.85790	−	5.96223i	0.0743754	−	0.238680i
$625$	3.42694	−	5.93563i	0.137077	−	0.237425i
$626$	−20.9175			−0.836031
$627$	65.6974	−	23.9658i	2.62370	−	0.957102i
$628$			16.0812i			0.641711i
$629$	−7.43870			−0.296600
$630$	27.8058	−	3.24194i	1.10781	−	0.129162i
$631$	−3.19085	−	5.52672i	−0.127026	−	0.220015i	0.795497	−	0.605957i	$-0.207210\pi$
$631$	−3.19085	−	5.52672i	−0.127026	−	0.220015i	−0.922523	+	0.385942i	$0.873876\pi$
$632$	−7.75854	−	4.47939i	−0.308618	−	0.178181i
$633$	1.78367	−	10.1587i	0.0708947	−	0.403774i
$634$	14.1142			0.560548
$635$	−8.11098	−	14.0486i	−0.321874	−	0.557503i
$636$	6.39907	+	17.5418i	0.253740	+	0.695576i
$637$	17.6003	−	18.0895i	0.697349	−	0.716731i
$638$			3.05221i			0.120838i
$639$	1.19480	−	3.29756i	0.0472657	−	0.130449i
$640$		−	3.52693i		−	0.139414i
$641$	−12.0384	−	6.95037i	−0.475488	−	0.274523i	0.243046	−	0.970015i	$-0.421853\pi$
$641$	−12.0384	−	6.95037i	−0.475488	−	0.274523i	−0.718534	+	0.695492i	$0.755187\pi$
$642$	−0.452809	+	2.57893i	−0.0178710	+	0.101782i
$643$	15.1084	−	8.72286i	0.595818	−	0.343996i	−0.171576	−	0.985171i	$-0.554886\pi$
$643$	15.1084	−	8.72286i	0.595818	−	0.343996i	0.767395	+	0.641175i	$0.221553\pi$
$644$	9.98509	+	6.59216i	0.393468	+	0.259768i
$645$	0.814851	−	0.297250i	0.0320847	−	0.0117042i
$646$	−19.8852			−0.782374
$647$	−35.2949			−1.38758			−0.693792	−	0.720175i	$-0.744061\pi$
$647$	−35.2949			−1.38758			−0.693792	+	0.720175i	$0.744061\pi$
$648$	8.86776	+	1.53714i	0.348359	+	0.0603847i
$649$	35.9297	+	20.7440i	1.41037	+	0.814275i
$650$	−3.43101	+	26.6022i	−0.134575	+	1.04343i
$651$	1.89222	+	6.34381i	0.0741620	+	0.248634i
$652$	3.59628	−	6.22894i	0.140841	−	0.243944i
$653$	31.1330	−	17.9747i	1.21833	−	0.703402i	0.253768	−	0.967265i	$-0.418330\pi$
$653$	31.1330	−	17.9747i	1.21833	−	0.703402i	0.964560	+	0.263863i	$0.0849965\pi$
$654$	−20.4422	−	3.58924i	−0.799353	−	0.140350i
$655$	−7.14770	−	12.3802i	−0.279284	−	0.483733i
$656$	7.26124			0.283504
$657$	13.2191	−	36.4836i	0.515726	−	1.42336i
$658$	8.67159	+	5.72499i	0.338054	+	0.223183i
$659$	−8.28033	+	4.78065i	−0.322556	+	0.186228i	−0.652531	−	0.757762i	$-0.726293\pi$
$659$	−8.28033	+	4.78065i	−0.322556	+	0.186228i	0.329975	+	0.943990i	$0.392960\pi$
$660$	21.9106	−	26.1505i	0.852869	−	1.01791i
$661$		−	19.2554i		−	0.748948i	−0.927237	−	0.374474i	$-0.877823\pi$
$661$		−	19.2554i		−	0.748948i	0.927237	−	0.374474i	$-0.122177\pi$
$662$	−2.02005	+	1.16628i	−0.0785114	+	0.0453286i
$663$	−16.7574	+	3.77411i	−0.650804	+	0.146574i
$664$			3.92570i			0.152347i
$665$	−60.3385	+	30.1721i	−2.33983	+	1.17002i
$666$	−7.98802	+	1.42044i	−0.309529	+	0.0550410i
$667$	2.47155			0.0956987
$668$	3.75042	+	6.49592i	0.145108	+	0.251335i
$669$	−15.3740	−	2.69937i	−0.594395	−	0.104364i
$670$		−	37.1031i		−	1.43342i
$671$	−69.7813			−2.69388
$672$	3.14812	−	3.33006i	0.121442	−	0.128460i
$673$	−10.1725	+	17.6192i	−0.392120	+	0.679172i	−0.992729	−	0.120371i	$-0.961592\pi$
$673$	−10.1725	+	17.6192i	−0.392120	+	0.679172i	0.600609	+	0.799543i	$0.294925\pi$
$674$	−29.2083	+	16.8634i	−1.12506	+	0.649555i
$675$	−38.6554	+	0.0840140i	−1.48785	+	0.00323370i
$676$	3.43074	+	12.5391i	0.131951	+	0.482275i
$677$	0.353311	−	0.611953i	0.0135788	−	0.0235193i	−0.859156	−	0.511714i	$-0.829011\pi$
$677$	0.353311	−	0.611953i	0.0135788	−	0.0235193i	0.872735	+	0.488194i	$0.162344\pi$
$678$	1.23777	−	7.04962i	0.0475364	−	0.270739i
$679$	2.03291	−	33.8899i	0.0780158	−	1.30058i
$680$	−8.40131	+	4.85050i	−0.322175	+	0.186008i
$681$	−7.55018	+	43.0013i	−0.289324	+	1.64782i
$682$	6.98689	+	4.03388i	0.267542	+	0.154465i
$683$	−27.7948	−	16.0474i	−1.06354	−	0.614035i	−0.137131	−	0.990553i	$-0.543788\pi$
$683$	−27.7948	−	16.0474i	−1.06354	−	0.614035i	−0.926409	+	0.376518i	$0.877121\pi$
$684$	−21.3537	+	3.79714i	−0.816479	+	0.145187i
$685$	8.13495	−	4.69671i	0.310820	−	0.179452i
$686$	17.4361	−	6.24357i	0.665714	−	0.238381i
$687$	−12.1810	−	2.13875i	−0.464736	−	0.0815983i
$688$	0.0709937	−	0.122965i	0.00270661	−	0.00468798i
$689$	−30.8997	−	23.5812i	−1.17719	−	0.898371i
$690$	−21.1756	−	17.7423i	−0.806141	−	0.675438i
$691$	33.8912	−	19.5671i	1.28928	−	0.744366i	0.310754	−	0.950490i	$-0.399418\pi$
$691$	33.8912	−	19.5671i	1.28928	−	0.744366i	0.978526	+	0.206124i	$0.0660850\pi$
$692$	11.0331	−	19.1098i	0.419414	−	0.726446i
$693$	44.0294	−	5.13348i	1.67254	−	0.195005i
$694$	−2.95977			−0.112351
$695$			51.3749i			1.94876i
$696$	0.163701	−	0.932345i	0.00620508	−	0.0353404i
$697$	−9.98620	−	17.2966i	−0.378254	−	0.655155i
$698$	−8.99213			−0.340357
$699$	−36.9348	−	6.48502i	−1.39700	−	0.245286i
$700$	−10.8442	+	16.4256i	−0.409872	+	0.620829i
$701$			17.9693i			0.678690i	0.940662	+	0.339345i	$0.110205\pi$
$701$			17.9693i			0.678690i	−0.940662	+	0.339345i	$0.889795\pi$
$702$	−17.2742	+	7.25269i	−0.651973	+	0.273735i
$703$	16.9325	−	9.77596i	0.638620	−	0.368707i
$704$		−	5.58476i		−	0.210484i
$705$	−18.3900	−	15.4084i	−0.692608	−	0.580312i
$706$	13.5379	−	7.81614i	0.509507	−	0.294164i
$707$	−11.2684	+	17.0682i	−0.423793	+	0.641916i
$708$	−9.86273	−	8.26364i	−0.370664	−	0.310567i
$709$	−14.1082			−0.529843			−0.264921	−	0.964270i	$-0.585346\pi$
$709$	−14.1082			−0.529843			−0.264921	+	0.964270i	$0.585346\pi$
$710$	2.06169	+	3.57095i	0.0773739	+	0.134015i
$711$	4.70538	+	26.4613i	0.176465	+	0.992375i
$712$	−1.17279	+	0.677113i	−0.0439523	+	0.0253759i
$713$	3.26647	−	5.65769i	0.122330	−	0.211882i
$714$	−12.2619	−	2.91923i	−0.458890	−	0.109249i
$715$	−9.08436	+	70.4354i	−0.339736	+	2.63413i
$716$	−9.63731	−	5.56410i	−0.360163	−	0.207940i
$717$	−13.8272	−	37.9046i	−0.516388	−	1.41557i
$718$	8.29071			0.309406
$719$	−6.22271			−0.232068			−0.116034	−	0.993245i	$-0.537018\pi$
$719$	−6.22271			−0.232068			−0.116034	+	0.993245i	$0.537018\pi$
$720$	−8.09550	+	6.81294i	−0.301701	+	0.253903i
$721$	−7.79608	+	3.89840i	−0.290341	+	0.145184i
$722$	28.8096	−	16.6332i	1.07218	−	0.619025i
$723$	1.59659	+	0.280329i	0.0593778	+	0.0104256i
$724$	−2.84559	−	1.64290i	−0.105755	−	0.0610579i
$725$			4.06572i			0.150997i
$726$	22.4585	−	26.8044i	0.833511	−	0.994803i
$727$		−	28.3604i		−	1.05183i	−0.850537	−	0.525915i	$-0.823723\pi$
$727$		−	28.3604i		−	1.05183i	0.850537	−	0.525915i	$-0.176277\pi$
$728$	−1.78455	+	9.37099i	−0.0661397	+	0.347312i
$729$	−13.6015	−	23.3238i	−0.503760	−	0.863844i
$730$	22.8102	+	39.5084i	0.844243	+	1.46227i
$731$	−0.390543			−0.0144447
$732$	21.3158	+	3.74263i	0.787855	+	0.138332i
$733$	−21.0117	−	12.1311i	−0.776086	−	0.448073i	0.0589554	−	0.998261i	$-0.481223\pi$
$733$	−21.0117	−	12.1311i	−0.776086	−	0.448073i	−0.835041	+	0.550187i	$0.814556\pi$
$734$	−13.7155	−	23.7559i	−0.506248	−	0.876847i
$735$	−41.6361	+	9.74717i	−1.53577	+	0.359530i
$736$	−4.52231			−0.166694
$737$		−	58.7514i		−	2.16414i
$738$	−14.0265	−	16.6670i	−0.516322	−	0.613521i
$739$	−10.9315			−0.402120			−0.201060	−	0.979579i	$-0.564439\pi$
$739$	−10.9315			−0.402120			−0.201060	+	0.979579i	$0.564439\pi$
$740$	4.76919	−	8.26048i	0.175319	−	0.303661i
$741$	33.1844	−	30.6135i	1.21906	−	1.12462i
$742$	−12.7567	−	25.5110i	−0.468312	−	0.936537i
$743$	32.1661	+	18.5711i	1.18006	+	0.681307i	0.956028	−	0.293275i	$-0.0947451\pi$
$743$	32.1661	+	18.5711i	1.18006	+	0.681307i	0.224031	+	0.974582i	$0.428078\pi$
$744$	−1.91790	−	1.60695i	−0.0703138	−	0.0589135i
$745$	−21.5703	−	12.4536i	−0.790276	−	0.456266i
$746$	−28.7117	+	16.5767i	−1.05121	+	0.606916i
$747$	9.01080	−	7.58324i	0.329688	−	0.277456i
$748$	−13.3031	+	7.68058i	−0.486411	+	0.280830i
$749$	0.239491	−	3.99247i	0.00875080	−	0.145882i
$750$	9.56985	−	11.4217i	0.349441	−	0.417061i
$751$	4.68281	+	8.11087i	0.170878	+	0.295970i	0.938727	−	0.344661i	$-0.112006\pi$
$751$	4.68281	+	8.11087i	0.170878	+	0.295970i	−0.767849	+	0.640631i	$0.778673\pi$
$752$	−3.92741			−0.143218
$753$	−32.9282	−	27.5894i	−1.19997	−	1.00541i
$754$	0.758877	+	1.81853i	0.0276367	+	0.0662270i
$755$	−2.69354			−0.0980278
$756$	−13.7248	−	0.793358i	−0.499167	−	0.0288542i
$757$	19.2229	−	33.2950i	0.698667	−	1.21013i	−0.270262	−	0.962787i	$-0.587110\pi$
$757$	19.2229	−	33.2950i	0.698667	−	1.21013i	0.968929	−	0.247340i	$-0.0795564\pi$
$758$			17.3129i			0.628831i
$759$	−33.5307	−	28.0943i	−1.21709	−	1.01976i
$760$	12.7491	−	22.0820i	0.462457	−	0.801000i
$761$	32.4386			1.17590			0.587950	−	0.808898i	$-0.299935\pi$
$761$	32.4386			1.17590			0.587950	+	0.808898i	$0.299935\pi$
$762$	2.73012	+	7.48407i	0.0989019	+	0.271119i
$763$	31.6467	+	1.89835i	1.14569	+	0.0687249i
$764$	1.96531	+	1.13467i	0.0711022	+	0.0410509i
$765$	27.3622	+	9.91417i	0.989284	+	0.358447i
$766$	10.3789	−	5.99225i	0.375004	−	0.216509i
$767$	26.5649	+	3.42619i	0.959202	+	0.123713i
$768$	−0.299532	+	1.70595i	−0.0108084	+	0.0615583i
$769$	−24.3005	−	14.0299i	−0.876299	−	0.505931i	−0.00686245	−	0.999976i	$-0.502184\pi$
$769$	−24.3005	−	14.0299i	−0.876299	−	0.505931i	−0.869436	+	0.494045i	$0.835518\pi$
$770$	−28.7124	+	43.4905i	−1.03472	+	1.56729i
$771$	37.7336	+	31.6157i	1.35894	+	1.13861i
$772$	8.00636	−	13.8674i	0.288155	−	0.499100i
$773$	−4.92641	+	8.53280i	−0.177191	+	0.306903i	−0.940917	−	0.338637i	$-0.890034\pi$
$773$	−4.92641	+	8.53280i	−0.177191	+	0.306903i	0.763726	+	0.645540i	$0.223368\pi$
$774$	−0.419383	+	0.0745753i	−0.0150744

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.62717 - 0.593575i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.76347 - 3.05441i) q^{5} +(-1.11238 + 1.32763i) q^{6} +(1.45770 - 2.20797i) q^{7} +1.00000i q^{8} +(2.29534 - 1.93169i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.62717 - 0.593575i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.76347 - 3.05441i) q^{5} +(-1.11238 + 1.32763i) q^{6} +(1.45770 - 2.20797i) q^{7} +1.00000i q^{8} +(2.29534 - 1.93169i) q^{9} +3.52693i q^{10} +5.58476i q^{11} +(0.299532 - 1.70595i) q^{12} +(1.38855 + 3.32745i) q^{13} +(-0.158422 + 2.64100i) q^{14} +(1.05643 - 6.01678i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.37527 + 2.38204i) q^{17} +(-1.02197 + 2.82056i) q^{18} -7.22955i q^{19} +(-1.76347 - 3.05441i) q^{20} +(1.06133 - 4.45798i) q^{21} +(-2.79238 - 4.83655i) q^{22} +(-3.91643 + 2.26115i) q^{23} +(0.593575 + 1.62717i) q^{24} +(-3.71962 - 6.44257i) q^{25} +(-2.86625 - 2.18738i) q^{26} +(2.58829 - 4.50564i) q^{27} +(-1.18330 - 2.36639i) q^{28} +(-0.473303 - 0.273262i) q^{29} +(2.09350 + 5.73890i) q^{30} +(-1.25106 + 0.722302i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.31498 + 9.08733i) q^{33} -2.75055i q^{34} +(-4.17343 - 8.34609i) q^{35} +(-0.525225 - 2.95367i) q^{36} +(1.35222 + 2.34212i) q^{37} +(3.61478 + 6.26098i) q^{38} +(4.23450 + 4.59010i) q^{39} +(3.05441 + 1.76347i) q^{40} +(-3.63062 + 6.28842i) q^{41} +(1.30986 + 4.39139i) q^{42} +(0.0709937 + 0.122965i) q^{43} +(4.83655 + 2.79238i) q^{44} +(-1.85243 - 10.4174i) q^{45} +(2.26115 - 3.91643i) q^{46} +(1.96371 - 3.40124i) q^{47} +(-1.32763 - 1.11238i) q^{48} +(-2.75022 - 6.43710i) q^{49} +(6.44257 + 3.71962i) q^{50} +(-0.823876 + 4.69231i) q^{51} +(3.57593 + 0.461204i) q^{52} +(-9.33624 + 5.39028i) q^{53} +(0.0112934 + 5.19614i) q^{54} +(17.0582 + 9.84854i) q^{55} +(2.20797 + 1.45770i) q^{56} +(-4.29128 - 11.7637i) q^{57} +0.546524 q^{58} +(3.71440 - 6.43353i) q^{59} +(-4.68247 - 3.92329i) q^{60} +12.4949i q^{61} +(0.722302 - 1.25106i) q^{62} +(-0.919194 - 7.88385i) q^{63} -1.00000 q^{64} +(12.6121 + 1.62663i) q^{65} +(-7.41452 - 6.21237i) q^{66} -10.5200 q^{67} +(1.37527 + 2.38204i) q^{68} +(-5.03052 + 6.00397i) q^{69} +(7.78734 + 5.14121i) q^{70} +(1.01248 - 0.584557i) q^{71} +(1.93169 + 2.29534i) q^{72} +(11.2019 - 6.46743i) q^{73} +(-2.34212 - 1.35222i) q^{74} +(-9.87659 - 8.27526i) q^{75} +(-6.26098 - 3.61478i) q^{76} +(12.3310 + 8.14091i) q^{77} +(-5.96223 - 1.85790i) q^{78} +(-4.47939 + 7.75854i) q^{79} -3.52693 q^{80} +(1.53714 - 8.86776i) q^{81} -7.26124i q^{82} +3.92570 q^{83} +(-3.33006 - 3.14812i) q^{84} +(4.85050 + 8.40131i) q^{85} +(-0.122965 - 0.0709937i) q^{86} +(-0.932345 - 0.163701i) q^{87} -5.58476 q^{88} +(0.677113 + 1.17279i) q^{89} +(6.81294 + 8.09550i) q^{90} +(9.37099 + 1.78455i) q^{91} +4.52231i q^{92} +(-1.60695 + 1.91790i) q^{93} +3.92741i q^{94} +(-22.0820 - 12.7491i) q^{95} +(1.70595 + 0.299532i) q^{96} +(11.1130 - 6.41610i) q^{97} +(5.60031 + 4.19958i) q^{98} +(10.7880 + 12.8189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Introduction

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