LMFDB - Embedded newform 728.2.h.a.27.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(27,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.27"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,1,0,1,0,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			27.13
Character	$\chi$	$=$	728.27
Dual form			728.2.h.a.27.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.879218 - 1.10769i) q^{2} +1.92788i q^{3} +(-0.453951 + 1.94780i) q^{4} -2.16680 q^{5} +(2.13549 - 1.69503i) q^{6} +(1.74001 - 1.99308i) q^{7} +(2.55668 - 1.20971i) q^{8} -0.716713 q^{9} +(1.90509 + 2.40014i) q^{10} -5.04203 q^{11} +(-3.75512 - 0.875162i) q^{12} -1.00000 q^{13} +(-3.73756 - 0.175035i) q^{14} -4.17733i q^{15} +(-3.58786 - 1.76841i) q^{16} +0.687834i q^{17} +(0.630147 + 0.793895i) q^{18} -1.09617i q^{19} +(0.983622 - 4.22050i) q^{20} +(3.84242 + 3.35452i) q^{21} +(4.43304 + 5.58500i) q^{22} -3.80258i q^{23} +(2.33216 + 4.92897i) q^{24} -0.304972 q^{25} +(0.879218 + 1.10769i) q^{26} +4.40190i q^{27} +(3.09225 + 4.29395i) q^{28} -6.62535i q^{29} +(-4.62718 + 3.67278i) q^{30} +8.65921 q^{31} +(1.19566 + 5.52905i) q^{32} -9.72042i q^{33} +(0.761906 - 0.604756i) q^{34} +(-3.77025 + 4.31861i) q^{35} +(0.325352 - 1.39601i) q^{36} -9.25001i q^{37} +(-1.21422 + 0.963776i) q^{38} -1.92788i q^{39} +(-5.53982 + 2.62119i) q^{40} -6.30848i q^{41} +(0.337445 - 7.20556i) q^{42} -3.27423 q^{43} +(2.28883 - 9.82087i) q^{44} +1.55297 q^{45} +(-4.21208 + 3.34330i) q^{46} -2.09029 q^{47} +(3.40928 - 6.91695i) q^{48} +(-0.944747 - 6.93595i) q^{49} +(0.268137 + 0.337814i) q^{50} -1.32606 q^{51} +(0.453951 - 1.94780i) q^{52} -2.89312i q^{53} +(4.87594 - 3.87023i) q^{54} +10.9251 q^{55} +(2.03760 - 7.20057i) q^{56} +2.11329 q^{57} +(-7.33883 + 5.82513i) q^{58} -11.6482i q^{59} +(8.13660 + 1.89630i) q^{60} -1.96479 q^{61} +(-7.61334 - 9.59172i) q^{62} +(-1.24709 + 1.42847i) q^{63} +(5.07323 - 6.18566i) q^{64} +2.16680 q^{65} +(-10.7672 + 8.54637i) q^{66} +13.5558 q^{67} +(-1.33976 - 0.312243i) q^{68} +7.33091 q^{69} +(8.09855 + 0.379265i) q^{70} +5.07363i q^{71} +(-1.83241 + 0.867011i) q^{72} +2.08832i q^{73} +(-10.2461 + 8.13278i) q^{74} -0.587948i q^{75} +(2.13513 + 0.497609i) q^{76} +(-8.77317 + 10.0492i) q^{77} +(-2.13549 + 1.69503i) q^{78} -0.772654i q^{79} +(7.77417 + 3.83180i) q^{80} -10.6365 q^{81} +(-6.98783 + 5.54653i) q^{82} -5.41871i q^{83} +(-8.27821 + 5.96148i) q^{84} -1.49040i q^{85} +(2.87876 + 3.62683i) q^{86} +12.7729 q^{87} +(-12.8909 + 6.09937i) q^{88} +3.65311i q^{89} +(-1.36540 - 1.72021i) q^{90} +(-1.74001 + 1.99308i) q^{91} +(7.40667 + 1.72618i) q^{92} +16.6939i q^{93} +(1.83782 + 2.31539i) q^{94} +2.37519i q^{95} +(-10.6593 + 2.30508i) q^{96} +2.48774i q^{97} +(-6.85224 + 7.14470i) q^{98} +3.61369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + q^{4} - 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} + 10 q^{12} - 48 q^{13} + 10 q^{14} + 5 q^{16} - 15 q^{18} - 22 q^{20} - 6 q^{22} + 48 q^{25} - q^{26} + 4 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) $ 48 * q + q^2 + q^4 - 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 + 10 * q^12 - 48 * q^13 + 10 * q^14 + 5 * q^16 - 15 * q^18 - 22 * q^20 - 6 * q^22 + 48 * q^25 - q^26 + 4 * q^28 - 26 * q^30 - 19 * q^32 + 36 * q^34 + 12 * q^35 - 5 * q^36 - 10 * q^38 - 48 * q^40 + 3 * q^42 - 4 * q^43 - 30 * q^44 + 24 * q^45 + 2 * q^46 + 48 * q^48 + 11 * q^50 - 40 * q^51 - q^52 + 62 * q^54 + 10 * q^56 + 2 * q^58 + 18 * q^60 - 36 * q^62 + 20 * q^63 - 11 * q^64 + 32 * q^66 - 4 * q^67 + 62 * q^68 - 11 * q^70 + 13 * q^72 - 44 * q^74 - 48 * q^76 - 20 * q^77 + 10 * q^78 + 32 * q^80 + 64 * q^81 - 50 * q^82 + 21 * q^84 + 2 * q^86 - 40 * q^87 - 66 * q^88 + 74 * q^90 - 24 * q^92 - 26 * q^94 - 84 * q^96 - 6 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.879218	−	1.10769i	−0.621701	−	0.783255i
$2$	−0.879218	−	1.10769i	−0.621701	−	0.783255i
$3$			1.92788i			1.11306i	0.830827	+	0.556530i	$0.187868\pi$
$3$			1.92788i			1.11306i	−0.830827	+	0.556530i	$0.812132\pi$
$4$	−0.453951	+	1.94780i	−0.226975	+	0.973900i
$5$	−2.16680			−0.969023			−0.484512	−	0.874785i	$-0.661003\pi$
$5$	−2.16680			−0.969023			−0.484512	+	0.874785i	$0.661003\pi$
$6$	2.13549	−	1.69503i	0.871810	−	0.691991i
$7$	1.74001	−	1.99308i	0.657661	−	0.753314i
$7$	1.74001	−	1.99308i	0.657661	−	0.753314i
$8$	2.55668	−	1.20971i	0.903923	−	0.427695i
$9$	−0.716713			−0.238904
$10$	1.90509	+	2.40014i	0.602443	+	0.758992i
$11$	−5.04203			−1.52023			−0.760115	−	0.649789i	$-0.774857\pi$
$11$	−5.04203			−1.52023			−0.760115	+	0.649789i	$0.774857\pi$
$12$	−3.75512	−	0.875162i	−1.08401	−	0.252638i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−3.73756	−	0.175035i	−0.998905	−	0.0467799i
$15$		−	4.17733i		−	1.07858i
$16$	−3.58786	−	1.76841i	−0.896964	−	0.442103i
$17$			0.687834i			0.166824i	0.996515	+	0.0834121i	$0.0265818\pi$
$17$			0.687834i			0.166824i	−0.996515	+	0.0834121i	$0.973418\pi$
$18$	0.630147	+	0.793895i	0.148527	+	0.187123i
$19$		−	1.09617i		−	0.251479i	−0.992063	−	0.125740i	$-0.959870\pi$
$19$		−	1.09617i		−	0.251479i	0.992063	−	0.125740i	$-0.0401304\pi$
$20$	0.983622	−	4.22050i	0.219944	−	0.943732i
$21$	3.84242	+	3.35452i	0.838484	+	0.732017i
$22$	4.43304	+	5.58500i	0.945128	+	1.19073i
$23$		−	3.80258i		−	0.792892i	−0.918058	−	0.396446i	$-0.870243\pi$
$23$		−	3.80258i		−	0.792892i	0.918058	−	0.396446i	$-0.129757\pi$
$24$	2.33216	+	4.92897i	0.476051	+	1.00612i
$25$	−0.304972			−0.0609943
$26$	0.879218	+	1.10769i	0.172429	+	0.217236i
$27$			4.40190i			0.847146i
$28$	3.09225	+	4.29395i	0.584380	+	0.811480i
$29$		−	6.62535i		−	1.23030i	−0.788411	−	0.615148i	$-0.789096\pi$
$29$		−	6.62535i		−	1.23030i	0.788411	−	0.615148i	$-0.210904\pi$
$30$	−4.62718	+	3.67278i	−0.844804	+	0.670555i
$31$	8.65921			1.55524			0.777620	−	0.628734i	$-0.216427\pi$
$31$	8.65921			1.55524			0.777620	+	0.628734i	$0.216427\pi$
$32$	1.19566	+	5.52905i	0.211364	+	0.977407i
$33$		−	9.72042i		−	1.69211i
$34$	0.761906	−	0.604756i	0.130666	−	0.103715i
$35$	−3.77025	+	4.31861i	−0.637289	+	0.729979i
$36$	0.325352	−	1.39601i	0.0542254	−	0.232669i
$37$		−	9.25001i		−	1.52069i	−0.649518	−	0.760346i	$-0.725029\pi$
$37$		−	9.25001i		−	1.52069i	0.649518	−	0.760346i	$-0.274971\pi$
$38$	−1.21422	+	0.963776i	−0.196972	+	0.156345i
$39$		−	1.92788i		−	0.308708i
$40$	−5.53982	+	2.62119i	−0.875922	+	0.414447i
$41$		−	6.30848i		−	0.985218i	−0.870251	−	0.492609i	$-0.836043\pi$
$41$		−	6.30848i		−	0.985218i	0.870251	−	0.492609i	$-0.163957\pi$
$42$	0.337445	−	7.20556i	0.0520689	−	1.11184i
$43$	−3.27423			−0.499315			−0.249657	−	0.968334i	$-0.580318\pi$
$43$	−3.27423			−0.499315			−0.249657	+	0.968334i	$0.580318\pi$
$44$	2.28883	−	9.82087i	0.345055	−	1.48055i
$45$	1.55297			0.231504
$46$	−4.21208	+	3.34330i	−0.621037	+	0.492942i
$47$	−2.09029			−0.304900			−0.152450	−	0.988311i	$-0.548716\pi$
$47$	−2.09029			−0.304900			−0.152450	+	0.988311i	$0.548716\pi$
$48$	3.40928	−	6.91695i	0.492088	−	0.998376i
$49$	−0.944747	−	6.93595i	−0.134964	−	0.990851i
$50$	0.268137	+	0.337814i	0.0379202	+	0.0477741i
$51$	−1.32606			−0.185685
$52$	0.453951	−	1.94780i	0.0629517	−	0.270111i
$53$		−	2.89312i		−	0.397400i	−0.980060	−	0.198700i	$-0.936328\pi$
$53$		−	2.89312i		−	0.397400i	0.980060	−	0.198700i	$-0.0636720\pi$
$54$	4.87594	−	3.87023i	0.663531	−	0.526671i
$55$	10.9251			1.47314
$56$	2.03760	−	7.20057i	0.272286	−	0.962216i
$57$	2.11329			0.279912
$58$	−7.33883	+	5.82513i	−0.963635	+	0.764877i
$59$		−	11.6482i		−	1.51647i	−0.651980	−	0.758236i	$-0.726061\pi$
$59$		−	11.6482i		−	1.51647i	0.651980	−	0.758236i	$-0.273939\pi$
$60$	8.13660	+	1.89630i	1.05043	+	0.244812i
$61$	−1.96479			−0.251566			−0.125783	−	0.992058i	$-0.540144\pi$
$61$	−1.96479			−0.251566			−0.125783	+	0.992058i	$0.540144\pi$
$62$	−7.61334	−	9.59172i	−0.966895	−	1.21815i
$63$	−1.24709	+	1.42847i	−0.157118	+	0.179970i
$64$	5.07323	−	6.18566i	0.634153	−	0.773207i
$65$	2.16680			0.268759
$66$	−10.7672	+	8.54637i	−1.32535	+	1.05199i
$67$	13.5558			1.65611			0.828053	−	0.560650i	$-0.189449\pi$
$67$	13.5558			1.65611			0.828053	+	0.560650i	$0.189449\pi$
$68$	−1.33976	−	0.312243i	−0.162470	−	0.0378650i
$69$	7.33091			0.882537
$70$	8.09855	+	0.379265i	0.967962	+	0.0453308i
$71$			5.07363i			0.602129i	0.953604	+	0.301064i	$0.0973419\pi$
$71$			5.07363i			0.602129i	−0.953604	+	0.301064i	$0.902658\pi$
$72$	−1.83241	+	0.867011i	−0.215951	+	0.102178i
$73$			2.08832i			0.244420i	0.992504	+	0.122210i	$0.0389981\pi$
$73$			2.08832i			0.244420i	−0.992504	+	0.122210i	$0.961002\pi$
$74$	−10.2461	+	8.13278i	−1.19109	+	0.945416i
$75$		−	0.587948i		−	0.0678904i
$76$	2.13513	+	0.497609i	0.244916	+	0.0570797i
$77$	−8.77317	+	10.0492i	−0.999796	+	1.14521i
$78$	−2.13549	+	1.69503i	−0.241797	+	0.191924i
$79$		−	0.772654i		−	0.0869303i	−0.999055	−	0.0434652i	$-0.986160\pi$
$79$		−	0.772654i		−	0.0869303i	0.999055	−	0.0434652i	$-0.0138398\pi$
$80$	7.77417	+	3.83180i	0.869179	+	0.428408i
$81$	−10.6365			−1.18183
$82$	−6.98783	+	5.54653i	−0.771677	+	0.612511i
$83$		−	5.41871i		−	0.594781i	−0.954756	−	0.297390i	$-0.903884\pi$
$83$		−	5.41871i		−	0.594781i	0.954756	−	0.297390i	$-0.0961163\pi$
$84$	−8.27821	+	5.96148i	−0.903227	+	0.650450i
$85$		−	1.49040i		−	0.161656i
$86$	2.87876	+	3.62683i	0.310425	+	0.391091i
$87$	12.7729			1.36939
$88$	−12.8909	+	6.09937i	−1.37417	+	0.650195i
$89$			3.65311i			0.387229i	0.981078	+	0.193615i	$0.0620212\pi$
$89$			3.65311i			0.387229i	−0.981078	+	0.193615i	$0.937979\pi$
$90$	−1.36540	−	1.72021i	−0.143926	−	0.181326i
$91$	−1.74001	+	1.99308i	−0.182402	+	0.208932i
$92$	7.40667	+	1.72618i	0.772198	+	0.179967i
$93$			16.6939i			1.73108i
$94$	1.83782	+	2.31539i	0.189557	+	0.238815i
$95$			2.37519i			0.243689i
$96$	−10.6593	+	2.30508i	−1.08791	+	0.235261i
$97$			2.48774i			0.252592i	0.991993	+	0.126296i	$0.0403088\pi$
$97$			2.48774i			0.252592i	−0.991993	+	0.126296i	$0.959691\pi$
$98$	−6.85224	+	7.14470i	−0.692181	+	0.721724i
$99$	3.61369			0.363189
$100$	0.138442	−	0.594024i	0.0138442	−	0.0594024i
$101$	−17.2080			−1.71226			−0.856131	−	0.516759i	$-0.827138\pi$
$101$	−17.2080			−1.71226			−0.856131	+	0.516759i	$0.827138\pi$
$102$	1.16590	+	1.46886i	0.115441	+	0.145439i
$103$	−7.58040			−0.746919			−0.373460	−	0.927646i	$-0.621829\pi$
$103$	−7.58040			−0.746919			−0.373460	+	0.927646i	$0.621829\pi$
$104$	−2.55668	+	1.20971i	−0.250703	+	0.118621i
$105$	−8.32576	−	7.26858i	−0.812511	−	0.709341i
$106$	−3.20468	+	2.54368i	−0.311266	+	0.247064i
$107$	3.55104			0.343292			0.171646	−	0.985159i	$-0.445092\pi$
$107$	3.55104			0.343292			0.171646	+	0.985159i	$0.445092\pi$
$108$	−8.57402	−	1.99825i	−0.825036	−	0.192281i
$109$		−	8.44828i		−	0.809199i	−0.914494	−	0.404599i	$-0.867411\pi$
$109$		−	8.44828i		−	0.809199i	0.914494	−	0.404599i	$-0.132589\pi$
$110$	−9.60553	−	12.1016i	−0.915851	−	1.15384i
$111$	17.8329			1.69262
$112$	−9.76749	+	4.07384i	−0.922941	+	0.384942i
$113$	−15.2181			−1.43159			−0.715797	−	0.698308i	$-0.753936\pi$
$113$	−15.2181			−1.43159			−0.715797	+	0.698308i	$0.753936\pi$
$114$	−1.85804	−	2.34087i	−0.174022	−	0.219242i
$115$			8.23943i			0.768331i
$116$	12.9049	+	3.00758i	1.19819	+	0.279247i
$117$	0.716713			0.0662601
$118$	−12.9026	+	10.2413i	−1.18778	+	0.942793i
$119$	1.37091	+	1.19684i	0.125671	+	0.109714i
$120$	−5.05334	−	10.6801i	−0.461304	−	0.974955i
$121$	14.4221			1.31110
$122$	1.72748	+	2.17638i	0.156399	+	0.197040i
$123$	12.1620			1.09661
$124$	−3.93086	+	16.8664i	−0.353002	+	1.51465i
$125$	11.4948			1.02813
$126$	2.67876	+	0.125449i	0.238643	+	0.0111759i
$127$		−	4.05535i		−	0.359854i	−0.983680	−	0.179927i	$-0.942414\pi$
$127$		−	4.05535i		−	0.359854i	0.983680	−	0.179927i	$-0.0575862\pi$
$128$	−11.3123	−	0.181015i	−0.999872	−	0.0159996i
$129$		−	6.31231i		−	0.555768i
$130$	−1.90509	−	2.40014i	−0.167088	−	0.210506i
$131$			12.3281i			1.07711i	0.842591	+	0.538554i	$0.181029\pi$
$131$			12.3281i			1.07711i	−0.842591	+	0.538554i	$0.818971\pi$
$132$	18.9334	+	4.41259i	1.64794	+	0.384067i
$133$	−2.18476	−	1.90735i	−0.189443	−	0.165388i
$134$	−11.9185	−	15.0156i	−1.02960	−	1.29715i
$135$		−	9.53804i		−	0.820904i
$136$	0.832076	+	1.75857i	0.0713499	+	0.150796i
$137$	−10.0410			−0.857859			−0.428929	−	0.903338i	$-0.641109\pi$
$137$	−10.0410			−0.857859			−0.428929	+	0.903338i	$0.641109\pi$
$138$	−6.44547	−	8.12037i	−0.548674	−	0.691251i
$139$			22.5954i			1.91651i	0.285909	+	0.958257i	$0.407705\pi$
$139$			22.5954i			1.91651i	−0.285909	+	0.958257i	$0.592295\pi$
$140$	−6.70029	−	9.30414i	−0.566278	−	0.786343i
$141$		−	4.02983i		−	0.339373i
$142$	5.62000	−	4.46083i	0.471620	−	0.374344i
$143$	5.04203			0.421636
$144$	2.57146	+	1.26744i	0.214289	+	0.105620i
$145$			14.3558i			1.19219i
$146$	2.31321	−	1.83609i	0.191443	−	0.151956i
$147$	13.3717	−	1.82136i	1.10288	−	0.150223i
$148$	18.0172	+	4.19905i	1.48100	+	0.345160i
$149$		−	0.279812i		−	0.0229231i	−0.999934	−	0.0114615i	$-0.996352\pi$
$149$		−	0.279812i		−	0.0229231i	0.999934	−	0.0114615i	$-0.00364840\pi$
$150$	−0.651264	+	0.516934i	−0.0531755	+	0.0422075i
$151$		−	19.0561i		−	1.55076i	−0.631493	−	0.775382i	$-0.717557\pi$
$151$		−	19.0561i		−	1.55076i	0.631493	−	0.775382i	$-0.282443\pi$
$152$	−1.32605	−	2.80257i	−0.107557	−	0.227318i
$153$		−	0.492979i		−	0.0398550i
$154$	18.8449	+	0.882529i	1.51857	+	0.0711163i
$155$	−18.7628			−1.50706
$156$	3.75512	+	0.875162i	0.300650	+	0.0700690i
$157$	12.5958			1.00525			0.502626	−	0.864504i	$-0.332367\pi$
$157$	12.5958			1.00525			0.502626	+	0.864504i	$0.332367\pi$
$158$	−0.855860	+	0.679331i	−0.0680886	+	0.0540447i
$159$	5.57758			0.442331
$160$	−2.59075	−	11.9804i	−0.204817	−	0.947130i
$161$	−7.57885	−	6.61652i	−0.597297	−	0.521454i
$162$	9.35177	+	11.7819i	0.734744	+	0.925673i
$163$	14.7205			1.15300			0.576498	−	0.817099i	$-0.304419\pi$
$163$	14.7205			1.15300			0.576498	+	0.817099i	$0.304419\pi$
$164$	12.2877	+	2.86374i	0.959505	+	0.223620i
$165$			21.0622i			1.63969i
$166$	−6.00225	+	4.76423i	−0.465865	+	0.369776i
$167$	−6.51701			−0.504302			−0.252151	−	0.967688i	$-0.581138\pi$
$167$	−6.51701			−0.504302			−0.252151	+	0.967688i	$0.581138\pi$
$168$	13.8818	+	3.92825i	1.07101	+	0.303071i
$169$	1.00000			0.0769231
$170$	−1.65090	+	1.31039i	−0.126618	+	0.100502i
$171$			0.785642i			0.0600795i
$172$	1.48634	−	6.37754i	0.113332	−	0.486283i
$173$	−21.8519			−1.66137			−0.830686	−	0.556742i	$-0.812051\pi$
$173$	−21.8519			−1.66137			−0.830686	+	0.556742i	$0.812051\pi$
$174$	−11.2301	−	14.1484i	−0.851354	−	1.07258i
$175$	−0.530653	+	0.607833i	−0.0401136	+	0.0459479i
$176$	18.0901	+	8.91639i	1.36359	+	0.672098i
$177$	22.4564			1.68793
$178$	4.04652	−	3.21188i	0.303299	−	0.240741i
$179$	12.9272			0.966228			0.483114	−	0.875557i	$-0.339506\pi$
$179$	12.9272			0.966228			0.483114	+	0.875557i	$0.339506\pi$
$180$	−0.704974	+	3.02488i	−0.0525457	+	0.225462i
$181$	−9.89018			−0.735132			−0.367566	−	0.929998i	$-0.619809\pi$
$181$	−9.89018			−0.735132			−0.367566	+	0.929998i	$0.619809\pi$
$182$	3.73756	+	0.175035i	0.277046	+	0.0129744i
$183$		−	3.78788i		−	0.280008i
$184$	−4.60000	−	9.72198i	−0.339116	−	0.716714i
$185$			20.0429i			1.47359i
$186$	18.4917	−	14.6776i	1.35587	−	1.07621i
$187$		−	3.46808i		−	0.253611i
$188$	0.948890	−	4.07147i	0.0692049	−	0.296943i
$189$	8.77334	+	7.65934i	0.638167	+	0.557135i
$190$	2.63097	−	2.08831i	0.190871	−	0.151502i
$191$			13.5574i			0.980978i	0.871448	+	0.490489i	$0.163182\pi$
$191$			13.5574i			0.980978i	−0.871448	+	0.490489i	$0.836818\pi$
$192$	11.9252	+	9.78056i	0.860627	+	0.705851i
$193$	−23.1425			−1.66584			−0.832919	−	0.553396i	$-0.813332\pi$
$193$	−23.1425			−1.66584			−0.832919	+	0.553396i	$0.813332\pi$
$194$	2.75564	−	2.18726i	0.197843	−	0.157036i
$195$			4.17733i			0.299145i
$196$	13.9387	+	1.30840i	0.995623	+	0.0934575i
$197$		−	0.809664i		−	0.0576862i	−0.999584	−	0.0288431i	$-0.990818\pi$
$197$		−	0.809664i		−	0.0576862i	0.999584	−	0.0288431i	$-0.00918232\pi$
$198$	−3.17722	−	4.00284i	−0.225795	−	0.284470i
$199$	−13.7274			−0.973109			−0.486554	−	0.873650i	$-0.661746\pi$
$199$	−13.7274			−0.973109			−0.486554	+	0.873650i	$0.661746\pi$
$200$	−0.779715	+	0.368926i	−0.0551342	+	0.0260870i
$201$			26.1339i			1.84335i
$202$	15.1296	+	19.0611i	1.06452	+	1.34114i
$203$	−13.2049	−	11.5282i	−0.926800	−	0.809118i
$204$	0.601966	−	2.58290i	0.0421460	−	0.180839i
$205$			13.6692i			0.954699i
$206$	6.66483	+	8.39673i	0.464361	+	0.585028i
$207$			2.72536i			0.189425i
$208$	3.58786	+	1.76841i	0.248773	+	0.122617i
$209$			5.52694i			0.382306i
$210$	−0.731177	+	15.6130i	−0.0504560	+	1.07740i
$211$	22.1210			1.52288			0.761438	−	0.648238i	$-0.224494\pi$
$211$	22.1210			1.52288			0.761438	+	0.648238i	$0.224494\pi$
$212$	5.63522	+	1.31333i	0.387028	+	0.0902001i
$213$	−9.78134			−0.670206
$214$	−3.12214	−	3.93345i	−0.213425	−	0.268885i
$215$	7.09460			0.483848
$216$	5.32500	+	11.2542i	0.362320	+	0.765755i
$217$	15.0671	−	17.2585i	1.02282	−	1.17158i
$218$	−9.35807	+	7.42789i	−0.633809	+	0.503080i
$219$	−4.02603			−0.272054
$220$	−4.95945	+	21.2799i	−0.334366	+	1.43469i
$221$		−	0.687834i		−	0.0462687i
$222$	−15.6790	−	19.7533i	−1.05231	−	1.32575i
$223$	−10.5227			−0.704650			−0.352325	−	0.935878i	$-0.614609\pi$
$223$	−10.5227			−0.704650			−0.352325	+	0.935878i	$0.614609\pi$
$224$	13.1003	+	7.23755i	0.875301	+	0.483579i
$225$	0.218577			0.0145718
$226$	13.3800	+	16.8569i	0.890024	+	1.12130i
$227$		−	15.9121i		−	1.05612i	−0.849206	−	0.528062i	$-0.822919\pi$
$227$		−	15.9121i		−	1.05612i	0.849206	−	0.528062i	$-0.177081\pi$
$228$	−0.959329	+	4.11627i	−0.0635331	+	0.272606i
$229$	−10.2718			−0.678779			−0.339390	−	0.940646i	$-0.610221\pi$
$229$	−10.2718			−0.678779			−0.339390	+	0.940646i	$0.610221\pi$
$230$	9.12673	−	7.24426i	0.601799	−	0.477672i
$231$	−19.3736	−	16.9136i	−1.27469	−	1.11283i
$232$	−8.01472	−	16.9389i	−0.526192	−	1.11209i
$233$	−4.62581			−0.303047			−0.151524	−	0.988454i	$-0.548418\pi$
$233$	−4.62581			−0.303047			−0.151524	+	0.988454i	$0.548418\pi$
$234$	−0.630147	−	0.793895i	−0.0411940	−	0.0518985i
$235$	4.52925			0.295456
$236$	22.6885	+	5.28773i	1.47689	+	0.344202i
$237$	1.48958			0.0967588
$238$	0.120395	−	2.57082i	0.00780403	−	0.166642i
$239$			5.81217i			0.375958i	0.982173	+	0.187979i	$0.0601937\pi$
$239$			5.81217i			0.375958i	−0.982173	+	0.187979i	$0.939806\pi$
$240$	−7.38724	+	14.9877i	−0.476844	+	0.967449i
$241$			0.550538i			0.0354633i	0.999843	+	0.0177316i	$0.00564445\pi$
$241$			0.550538i			0.0354633i	−0.999843	+	0.0177316i	$0.994356\pi$
$242$	−12.6801	−	15.9752i	−0.815111	−	1.02692i
$243$		−	7.30010i		−	0.468302i
$244$	0.891920	−	3.82703i	0.0570993	−	0.245000i
$245$	2.04708	+	15.0288i	0.130783	+	0.960157i
$246$	−10.6930	−	13.4717i	−0.681762	−	0.858923i
$247$			1.09617i			0.0697479i
$248$	22.1388	−	10.4751i	1.40582	−	0.665169i
$249$	10.4466			0.662027
$250$	−10.1065	−	12.7327i	−0.639188	−	0.805286i
$251$			26.0984i			1.64731i	0.567088	+	0.823657i	$0.308070\pi$
$251$			26.0984i			1.64731i	−0.567088	+	0.823657i	$0.691930\pi$
$252$	−2.21625	−	3.07753i	−0.139611	−	0.193866i
$253$			19.1727i			1.20538i
$254$	−4.49207	+	3.56554i	−0.281857	+	0.223722i
$255$	2.87331			0.179933
$256$	9.74544	+	12.6896i	0.609090	+	0.793101i
$257$		−	23.7161i		−	1.47937i	−0.672952	−	0.739686i	$-0.734974\pi$
$257$		−	23.7161i		−	1.47937i	0.672952	−	0.739686i	$-0.265026\pi$
$258$	−6.99208	+	5.54990i	−0.435308	+	0.345521i
$259$	−18.4360	−	16.0951i	−1.14556	−	1.00010i
$260$	−0.983622	+	4.22050i	−0.0610016	+	0.261744i
$261$			4.74847i			0.293923i
$262$	13.6557	−	10.8391i	0.843649	−	0.669639i
$263$		−	15.7303i		−	0.969970i	−0.874522	−	0.484985i	$-0.838825\pi$
$263$		−	15.7303i		−	0.969970i	0.874522	−	0.484985i	$-0.161175\pi$
$264$	−11.7588	−	24.8520i	−0.723707	−	1.52953i
$265$			6.26881i			0.385090i
$266$	−0.191868	+	4.09702i	−0.0117642	+	0.251204i
$267$	−7.04276			−0.431010
$268$	−6.15367	+	26.4040i	−0.375895	+	1.61288i
$269$	26.9053			1.64045			0.820223	−	0.572043i	$-0.193849\pi$
$269$	26.9053			1.64045			0.820223	+	0.572043i	$0.193849\pi$
$270$	−10.5652	+	8.38602i	−0.642977	+	0.510357i
$271$	−23.7291			−1.44144			−0.720720	−	0.693226i	$-0.756189\pi$
$271$	−23.7291			−1.44144			−0.720720	+	0.693226i	$0.756189\pi$
$272$	1.21637	−	2.46785i	0.0737535	−	0.149635i
$273$	−3.84242	−	3.35452i	−0.232554	−	0.203025i
$274$	8.82821	+	11.1223i	0.533332	+	0.671922i
$275$	1.53768			0.0927254
$276$	−3.32787	+	14.2791i	−0.200314	+	0.859504i
$277$		−	29.3334i		−	1.76248i	−0.472673	−	0.881238i	$-0.656711\pi$
$277$		−	29.3334i		−	1.76248i	0.472673	−	0.881238i	$-0.343289\pi$
$278$	25.0286	−	19.8663i	1.50112	−	1.19150i
$279$	−6.20617			−0.371554
$280$	−4.41508	+	15.6022i	−0.263851	+	0.932410i
$281$	9.82013			0.585820			0.292910	−	0.956140i	$-0.405376\pi$
$281$	9.82013			0.585820			0.292910	+	0.956140i	$0.405376\pi$
$282$	−4.46380	+	3.54310i	−0.265815	+	0.210988i
$283$			18.2222i			1.08320i	0.840637	+	0.541599i	$0.182181\pi$
$283$			18.2222i			1.08320i	−0.840637	+	0.541599i	$0.817819\pi$
$284$	−9.88242	−	2.30318i	−0.586414	−	0.136669i
$285$	−4.57908			−0.271241
$286$	−4.43304	−	5.58500i	−0.262131	−	0.330248i
$287$	−12.5733	−	10.9768i	−0.742179	−	0.647940i
$288$	−0.856943	−	3.96274i	−0.0504959	−	0.233507i
$289$	16.5269			0.972170
$290$	15.9018	−	12.6219i	0.933785	−	0.741183i
$291$	−4.79606			−0.281150
$292$	−4.06764	−	0.947997i	−0.238041	−	0.0554773i
$293$	−10.0394			−0.586508			−0.293254	−	0.956034i	$-0.594738\pi$
$293$	−10.0394			−0.586508			−0.293254	+	0.956034i	$0.594738\pi$
$294$	−13.7741	−	13.2103i	−0.803323	−	0.770440i
$295$			25.2394i			1.46950i
$296$	−11.1898	−	23.6493i	−0.650393	−	1.37459i
$297$		−	22.1945i		−	1.28786i
$298$	−0.309944	+	0.246015i	−0.0179546	+	0.0142513i
$299$			3.80258i			0.219909i
$300$	1.14521	+	0.266900i	0.0661185	+	0.0154095i
$301$	−5.69718	+	6.52580i	−0.328380	+	0.376141i
$302$	−21.1082	+	16.7545i	−1.21464	+	0.964111i
$303$		−	33.1750i		−	1.90585i
$304$	−1.93849	+	3.93291i	−0.111180	+	0.225568i
$305$	4.25732			0.243773
$306$	−0.546068	+	0.433436i	−0.0312166	+	0.0247779i
$307$		−	3.94497i		−	0.225151i	−0.993643	−	0.112576i	$-0.964090\pi$
$307$		−	3.94497i		−	0.225151i	0.993643	−	0.112576i	$-0.0359101\pi$
$308$	−15.5912	−	21.6502i	−0.888391	−	1.23364i
$309$		−	14.6141i		−	0.831367i
$310$	16.4966	+	20.7834i	0.936944	+	1.18042i
$311$	17.3290			0.982640			0.491320	−	0.870979i	$-0.336515\pi$
$311$	17.3290			0.982640			0.491320	+	0.870979i	$0.336515\pi$
$312$	−2.33216	−	4.92897i	−0.132033	−	0.279048i
$313$			10.1877i			0.575844i	0.957654	+	0.287922i	$0.0929645\pi$
$313$			10.1877i			0.575844i	−0.957654	+	0.287922i	$0.907036\pi$
$314$	−11.0744	−	13.9522i	−0.624966	−	0.787368i
$315$	2.70219	−	3.09520i	0.152251	−	0.174395i
$316$	1.50498	+	0.350747i	0.0846615	+	0.0197311i
$317$			5.12951i			0.288102i	0.989570	+	0.144051i	$0.0460130\pi$
$317$			5.12951i			0.288102i	−0.989570	+	0.144051i	$0.953987\pi$
$318$	−4.90391	−	6.17822i	−0.274997	−	0.346458i
$319$			33.4052i			1.87033i
$320$	−10.9927	+	13.4031i	−0.614509	+	0.749256i
$321$			6.84596i			0.382105i
$322$	−0.665583	+	14.2124i	−0.0370915	+	0.792024i
$323$	0.753985			0.0419529
$324$	4.82843	−	20.7177i	0.268246	−	1.15098i
$325$	0.304972			0.0169168
$326$	−12.9425	−	16.3057i	−0.716818	−	0.903089i
$327$	16.2873			0.900688
$328$	−7.63140	−	16.1288i	−0.421373	−	0.890562i
$329$	−3.63712	+	4.16612i	−0.200521	+	0.229686i
$330$	23.3304	−	18.5183i	1.28430	−	1.01940i
$331$	−10.6345			−0.584527			−0.292263	−	0.956338i	$-0.594408\pi$
$331$	−10.6345			−0.584527			−0.292263	+	0.956338i	$0.594408\pi$
$332$	10.5546	+	2.45983i	0.579257	+	0.135001i
$333$			6.62960i			0.363300i
$334$	5.72988	+	7.21883i	0.313525	+	0.394997i
$335$	−29.3727			−1.60480
$336$	−7.85387	−	18.8305i	−0.428463	−	1.02729i
$337$	−19.4556			−1.05981			−0.529906	−	0.848057i	$-0.677773\pi$
$337$	−19.4556			−1.05981			−0.529906	+	0.848057i	$0.677773\pi$
$338$	−0.879218	−	1.10769i	−0.0478232	−	0.0602504i
$339$		−	29.3386i		−	1.59345i
$340$	2.90300	+	0.676568i	0.157437	+	0.0366921i
$341$	−43.6600			−2.36432
$342$	0.870247	−	0.690750i	0.0470576	−	0.0373515i
$343$	−15.4678	−	10.1857i	−0.835182	−	0.549974i
$344$	−8.37115	+	3.96085i	−0.451342	+	0.213555i
$345$	−15.8846			−0.855199
$346$	19.2126	+	24.2051i	1.03288	+	1.30128i
$347$	27.4986			1.47620			0.738102	−	0.674690i	$-0.235723\pi$
$347$	27.4986			1.47620			0.738102	+	0.674690i	$0.235723\pi$
$348$	−5.79825	+	24.8790i	−0.310819	+	1.33365i
$349$	23.0163			1.23203			0.616017	−	0.787733i	$-0.288745\pi$
$349$	23.0163			1.23203			0.616017	+	0.787733i	$0.288745\pi$
$350$	1.13985	+	0.0533806i	0.0609275	+	0.00285331i
$351$		−	4.40190i		−	0.234956i
$352$	−6.02854	−	27.8776i	−0.321322	−	1.48588i
$353$		−	32.6293i		−	1.73668i	−0.495967	−	0.868342i	$-0.665186\pi$
$353$		−	32.6293i		−	1.73668i	0.495967	−	0.868342i	$-0.334814\pi$
$354$	−19.7441	−	24.8747i	−1.04939	−	1.32208i
$355$		−	10.9935i		−	0.583477i
$356$	−7.11554	−	1.65833i	−0.377123	−	0.0878916i
$357$	−2.30735	+	2.64294i	−0.122118	+	0.139879i
$358$	−11.3659	−	14.3194i	−0.600705	−	0.756802i
$359$		−	14.0579i		−	0.741947i	−0.928643	−	0.370973i	$-0.879024\pi$
$359$		−	14.0579i		−	0.741947i	0.928643	−	0.370973i	$-0.120976\pi$
$360$	3.97046	−	1.87864i	0.209262	−	0.0990131i
$361$	17.7984			0.936758
$362$	8.69563	+	10.9553i	0.457032	+	0.575795i
$363$			27.8040i			1.45933i
$364$	−3.09225	−	4.29395i	−0.162078	−	0.225064i
$365$		−	4.52498i		−	0.236849i
$366$	−4.19580	+	3.33037i	−0.219318	+	0.174081i
$367$	−13.8941			−0.725266			−0.362633	−	0.931932i	$-0.618122\pi$
$367$	−13.8941			−0.725266			−0.362633	+	0.931932i	$0.618122\pi$
$368$	−6.72453	+	13.6431i	−0.350540	+	0.711196i
$369$			4.52137i			0.235373i
$370$	22.2013	−	17.6221i	1.15419	−	0.916130i
$371$	−5.76622	−	5.03405i	−0.299367	−	0.261355i
$372$	−32.5164	−	7.57822i	−1.68590	−	0.392912i
$373$		−	9.46915i		−	0.490294i	−0.969486	−	0.245147i	$-0.921164\pi$
$373$		−	9.46915i		−	0.490294i	0.969486	−	0.245147i	$-0.0788362\pi$
$374$	−3.84155	+	3.04920i	−0.198642	+	0.157670i
$375$			22.1606i			1.14437i
$376$	−5.34421	+	2.52864i	−0.275607	+	0.130405i
$377$			6.62535i			0.341223i
$378$	0.770484	−	16.4524i	0.0396294	−	0.846218i
$379$	−29.3716			−1.50872			−0.754359	−	0.656462i	$-0.772052\pi$
$379$	−29.3716			−1.50872			−0.754359	+	0.656462i	$0.772052\pi$
$380$	−4.62640	−	1.07822i	−0.237329	−	0.0553115i
$381$	7.81822			0.400540
$382$	15.0174	−	11.9199i	0.768355	−	0.609875i
$383$	23.8795			1.22019			0.610093	−	0.792330i	$-0.291132\pi$
$383$	23.8795			1.22019			0.610093	+	0.792330i	$0.291132\pi$
$384$	0.348975	−	21.8087i	0.0178085	−	1.11292i
$385$	19.0097	−	21.7746i	0.968825	−	1.10973i
$386$	20.3473	+	25.6348i	1.03565	+	1.30477i
$387$	2.34668			0.119288
$388$	−4.84562	−	1.12931i	−0.245999	−	0.0573321i
$389$			24.2232i			1.22816i	0.789242	+	0.614082i	$0.210474\pi$
$389$			24.2232i			1.22816i	−0.789242	+	0.614082i	$0.789526\pi$
$390$	4.62718	−	3.67278i	0.234306	−	0.185979i
$391$	2.61554			0.132274
$392$	−10.8059	−	16.5901i	−0.545779	−	0.837929i
$393$	−23.7670			−1.19889
$394$	−0.896857	+	0.711872i	−0.0451830	+	0.0358636i
$395$			1.67419i			0.0842375i
$396$	−1.64044	+	7.03874i	−0.0824351	+	0.353710i
$397$	−24.1030			−1.20969			−0.604847	−	0.796342i	$-0.706766\pi$
$397$	−24.1030			−1.20969			−0.604847	+	0.796342i	$0.706766\pi$
$398$	12.0694	+	15.2057i	0.604983	+	0.762192i
$399$	3.67714	−	4.21196i	0.184087	−	0.210862i
$400$	1.09419	+	0.539315i	0.0547097	+	0.0269658i
$401$	−21.2274			−1.06004			−0.530022	−	0.847984i	$-0.677817\pi$
$401$	−21.2274			−1.06004			−0.530022	+	0.847984i	$0.677817\pi$
$402$	28.9483	−	22.9774i	1.44381	−	1.14601i
$403$	−8.65921			−0.431346
$404$	7.81160	−	33.5178i	0.388642	−	1.66757i
$405$	23.0471			1.14522
$406$	−1.15967	+	24.7627i	−0.0575532	+	1.22895i
$407$			46.6388i			2.31180i
$408$	−3.39031	+	1.60414i	−0.167845	+	0.0794168i
$409$			15.1763i			0.750420i	0.926940	+	0.375210i	$0.122429\pi$
$409$			15.1763i			0.750420i	−0.926940	+	0.375210i	$0.877571\pi$
$410$	15.1412	−	12.0182i	0.747773	−	0.593538i
$411$		−	19.3578i		−	0.954849i
$412$	3.44113	−	14.7651i	0.169532	−	0.727425i
$413$	−23.2159	−	20.2680i	−1.14238	−	0.997325i
$414$	3.01885	−	2.39618i	0.148368	−	0.117766i
$415$			11.7413i			0.576356i
$416$	−1.19566	−	5.52905i	−0.0586219	−	0.271084i
$417$	−43.5611			−2.13320
$418$	6.12213	−	4.85939i	0.299443	−	0.237680i
$419$			22.3917i			1.09391i	0.837163	+	0.546953i	$0.184212\pi$
$419$			22.3917i			1.09391i	−0.837163	+	0.546953i	$0.815788\pi$
$420$	17.9372	−	12.9173i	0.875248	−	0.630301i
$421$			6.95017i			0.338731i	0.985553	+	0.169365i	$0.0541718\pi$
$421$			6.95017i			0.338731i	−0.985553	+	0.169365i	$0.945828\pi$
$422$	−19.4492	−	24.5032i	−0.946773	−	1.19280i
$423$	1.49814			0.0728420
$424$	−3.49982	−	7.39678i	−0.169966	−	0.359219i
$425$		−	0.209770i		−	0.0101753i
$426$	8.59993	+	10.8347i	0.416668	+	0.524942i
$427$	−3.41876	+	3.91599i	−0.165445	+	0.189508i
$428$	−1.61200	+	6.91671i	−0.0779188	+	0.334332i
$429$			9.72042i			0.469306i
$430$	−6.23770	−	7.85861i	−0.300809	−	0.378976i
$431$			17.5920i			0.847378i	0.905808	+	0.423689i	$0.139265\pi$
$431$			17.5920i			0.847378i	−0.905808	+	0.423689i	$0.860735\pi$
$432$	7.78437	−	15.7934i	0.374526	−	0.759860i
$433$			12.7562i			0.613025i	0.951867	+	0.306512i	$0.0991620\pi$
$433$			12.7562i			0.613025i	−0.951867	+	0.306512i	$0.900838\pi$
$434$	−32.3643	−	1.51566i	−1.55354	−	0.0727541i
$435$	−27.6763			−1.32698
$436$	16.4556	+	3.83511i	0.788079	+	0.183668i
$437$	−4.16829			−0.199396
$438$	3.53976	+	4.45960i	0.169136	+	0.213088i
$439$	39.8195			1.90048			0.950240	−	0.311518i	$-0.100838\pi$
$439$	39.8195			1.90048			0.950240	+	0.311518i	$0.100838\pi$
$440$	27.9319	−	13.2161i	1.33160	−	0.630054i
$441$	0.677112	+	4.97109i	0.0322434	+	0.236718i
$442$	−0.761906	+	0.604756i	−0.0362402	+	0.0287653i
$443$	−2.94265			−0.139810			−0.0699049	−	0.997554i	$-0.522270\pi$
$443$	−2.94265			−0.139810			−0.0699049	+	0.997554i	$0.522270\pi$
$444$	−8.09526	+	34.7349i	−0.384184	+	1.64845i
$445$		−	7.91557i		−	0.375234i
$446$	9.25172	+	11.6558i	0.438081	+	0.551920i
$447$	0.539443			0.0255148
$448$	−3.50107	−	20.8744i	−0.165410	−	0.986225i
$449$	12.7756			0.602918			0.301459	−	0.953479i	$-0.402526\pi$
$449$	12.7756			0.602918			0.301459	+	0.953479i	$0.402526\pi$
$450$	−0.192177	−	0.242115i	−0.00905931	−	0.0114134i
$451$			31.8075i			1.49776i
$452$	6.90825	−	29.6417i	0.324937	−	1.39423i
$453$	36.7378			1.72609
$454$	−17.6257	+	13.9902i	−0.827215	+	0.656594i
$455$	3.77025	−	4.31861i	0.176752	−	0.202460i
$456$	5.40300	−	2.55646i	0.253019	−	0.119717i
$457$	−6.05610			−0.283293			−0.141646	−	0.989917i	$-0.545240\pi$
$457$	−6.05610			−0.283293			−0.141646	+	0.989917i	$0.545240\pi$
$458$	9.03115	+	11.3780i	0.421998	+	0.531657i
$459$	−3.02777			−0.141324
$460$	−16.0488	−	3.74030i	−0.748278	−	0.174392i
$461$	13.5455			0.630878			0.315439	−	0.948946i	$-0.397848\pi$
$461$	13.5455			0.630878			0.315439	+	0.948946i	$0.397848\pi$
$462$	−1.70141	+	36.3307i	−0.0791567	+	1.69026i
$463$			24.3379i			1.13108i	0.824721	+	0.565539i	$0.191332\pi$
$463$			24.3379i			1.13108i	−0.824721	+	0.565539i	$0.808668\pi$
$464$	−11.7164	+	23.7708i	−0.543918	+	1.10353i
$465$		−	36.1724i		−	1.67745i
$466$	4.06710	+	5.12396i	0.188405	+	0.237363i
$467$		−	29.3776i		−	1.35943i	−0.733476	−	0.679716i	$-0.762103\pi$
$467$		−	29.3776i		−	1.35943i	0.733476	−	0.679716i	$-0.237897\pi$
$468$	−0.325352	+	1.39601i	−0.0150394	+	0.0645308i
$469$	23.5872	−	27.0178i	1.08916	−	1.24757i
$470$	−3.98220	−	5.01700i	−0.183685	−	0.231417i
$471$			24.2831i			1.11891i
$472$	−14.0909	−	29.7808i	−0.648588	−	1.37077i
$473$	16.5088			0.759073
$474$	−1.30967	−	1.64999i	−0.0601550	−	0.0757867i
$475$			0.334302i			0.0153388i
$476$	−2.95352	+	2.12695i	−0.135375	+	0.0974887i
$477$			2.07353i			0.0949406i
$478$	6.43808	−	5.11017i	0.294471	−	0.233734i
$479$	−2.86853			−0.131066			−0.0655332	−	0.997850i	$-0.520875\pi$
$479$	−2.86853			−0.131066			−0.0655332	+	0.997850i	$0.520875\pi$
$480$	23.0967	−	4.99465i	1.05421	−	0.227974i
$481$			9.25001i			0.421764i
$482$	0.609825	−	0.484043i	0.0277768	−	0.0220476i
$483$	12.7558	−	14.6111i	0.580410	−	0.664828i
$484$	−6.54691	+	28.0913i	−0.297587	+	1.27688i
$485$		−	5.39044i		−	0.244767i
$486$	−8.08624	+	6.41838i	−0.366799	+	0.291144i
$487$			24.5884i			1.11421i	0.830443	+	0.557104i	$0.188088\pi$
$487$			24.5884i			1.11421i	−0.830443	+	0.557104i	$0.811912\pi$
$488$	−5.02335	+	2.37682i	−0.227396	+	0.107594i
$489$			28.3792i			1.28335i
$490$	14.8474	−	15.4812i	0.670739	−	0.699367i
$491$	40.7235			1.83783			0.918913	−	0.394460i	$-0.129068\pi$
$491$	40.7235			1.83783			0.918913	+	0.394460i	$0.129068\pi$
$492$	−5.52094	+	23.6891i	−0.248903	+	1.06799i
$493$	4.55714			0.205243
$494$	1.21422	−	0.963776i	0.0546303	−	0.0433623i
$495$	−7.83014			−0.351939
$496$	−31.0680	−	15.3131i	−1.39500	−	0.687577i
$497$	10.1122	+	8.82815i	0.453592	+	0.395997i
$498$	−9.18485	−	11.5716i	−0.411583	−	0.518536i
$499$	−37.7172			−1.68845			−0.844226	−	0.535987i	$-0.819940\pi$
$499$	−37.7172			−1.68845			−0.844226	+	0.535987i	$0.819940\pi$
$500$	−5.21808	+	22.3896i	−0.233360	+	1.00129i
$501$		−	12.5640i		−	0.561318i
$502$	28.9089	−	22.9462i	1.29027	−	1.02414i
$503$	−2.68750			−0.119830			−0.0599148	−	0.998203i	$-0.519083\pi$
$503$	−2.68750			−0.119830			−0.0599148	+	0.998203i	$0.519083\pi$
$504$	−1.46038	+	5.16074i	−0.0650503	+	0.229878i
$505$	37.2864			1.65922
$506$	21.2374	−	16.8570i	0.944118	−	0.749385i
$507$			1.92788i			0.0856201i
$508$	7.89902	+	1.84093i	0.350462	+	0.0816781i
$509$	−5.67996			−0.251760			−0.125880	−	0.992045i	$-0.540175\pi$
$509$	−5.67996			−0.251760			−0.125880	+	0.992045i	$0.540175\pi$
$510$	−2.52626	−	3.18273i	−0.111865	−	0.140934i
$511$	4.16220	+	3.63370i	0.184125	+	0.160745i
$512$	5.48779	−	21.9519i	0.242528	−	0.970144i
$513$	4.82524			0.213040
$514$	−26.2701	+	20.8517i	−1.15873	+	0.919728i
$515$	16.4252			0.723782
$516$	12.2951	+	2.86548i	0.541263	+	0.126146i
$517$	10.5393			0.463519
$518$	−1.61907	+	34.5725i	−0.0711379	+	1.51903i
$519$		−	42.1279i		−	1.84921i
$520$	5.53982	−	2.62119i	0.242937	−	0.114947i
$521$		−	18.1395i		−	0.794706i	−0.917666	−	0.397353i	$-0.869929\pi$
$521$		−	18.1395i		−	0.794706i	0.917666	−	0.397353i	$-0.130071\pi$
$522$	5.25983	−	4.17494i	0.230217	−	0.182732i
$523$		−	26.7276i		−	1.16872i	−0.811496	−	0.584358i	$-0.801346\pi$
$523$		−	26.7276i		−	1.16872i	0.811496	−	0.584358i	$-0.198654\pi$
$524$	−24.0126	−	5.59633i	−1.04900	−	0.244477i
$525$	−1.17183	−	1.02303i	−0.0511428	−	0.0446489i
$526$	−17.4243	+	13.8303i	−0.759734	+	0.603032i
$527$			5.95610i			0.259452i
$528$	−17.1897	+	34.8755i	−0.748086	+	1.51776i
$529$	8.54040			0.371322
$530$	6.94390	−	5.51165i	0.301624	−	0.239411i
$531$			8.34845i			0.362292i
$532$	4.70691	−	3.38964i	0.204071	−	0.146960i
$533$			6.30848i			0.273250i
$534$	6.19212	+	7.80119i	0.267959	+	0.337590i
$535$	−7.69439			−0.332658
$536$	34.6579	−	16.3985i	1.49699	−	0.708309i
$537$			24.9222i			1.07547i
$538$	−23.6556	−	29.8027i	−1.01987	−	1.28489i
$539$	4.76344	+	34.9713i	0.205176	+	1.50632i
$540$	18.5782	+	4.32980i	0.799479	+	0.186325i
$541$		−	32.6687i		−	1.40454i	−0.711912	−	0.702268i	$-0.752171\pi$
$541$		−	32.6687i		−	1.40454i	0.711912	−	0.702268i	$-0.247829\pi$
$542$	20.8631	+	26.2845i	0.896145	+	1.12901i
$543$		−	19.0671i		−	0.818246i
$544$	−3.80307	+	0.822414i	−0.163055	+	0.0352607i
$545$			18.3058i			0.784132i
$546$	−0.337445	+	7.20556i	−0.0144413	+	0.308370i
$547$	33.9785			1.45281			0.726407	−	0.687265i	$-0.241189\pi$
$547$	33.9785			1.45281			0.726407	+	0.687265i	$0.241189\pi$
$548$	4.55811	−	19.5578i	0.194713	−	0.835469i
$549$	1.40819			0.0601002
$550$	−1.35195	−	1.70327i	−0.0576475	−	0.0726276i
$551$	−7.26253			−0.309394
$552$	18.7428	−	8.86824i	0.797746	−	0.377457i
$553$	−1.53996	−	1.34442i	−0.0654858	−	0.0571707i
$554$	−32.4923	+	25.7905i	−1.38047	+	1.09573i
$555$	−38.6403			−1.64019
$556$	−44.0113	−	10.2572i	−1.86649	−	0.435002i
$557$		−	12.1520i		−	0.514899i	−0.966292	−	0.257449i	$-0.917118\pi$
$557$		−	12.1520i		−	0.514899i	0.966292	−	0.257449i	$-0.0828821\pi$
$558$	5.45658	+	6.87451i	0.230995	+	0.291021i
$559$	3.27423			0.138485
$560$	21.1642	−	8.82720i	0.894351	−	0.373017i
$561$	6.68603			0.282284
$562$	−8.63404	−	10.8777i	−0.364205	−	0.458846i
$563$		−	35.0006i		−	1.47510i	−0.675293	−	0.737549i	$-0.735983\pi$
$563$		−	35.0006i		−	1.47510i	0.675293	−	0.737549i	$-0.264017\pi$
$564$	7.84930	+	1.82934i	0.330515	+	0.0770293i
$565$	32.9745			1.38725
$566$	20.1846	−	16.0213i	0.848420	−	0.673426i
$567$	−18.5075	+	21.1993i	−0.777243	+	0.890288i
$568$	6.13759	+	12.9716i	0.257528	+	0.544278i
$569$	41.2142			1.72779			0.863894	−	0.503673i	$-0.168018\pi$
$569$	41.2142			1.72779			0.863894	+	0.503673i	$0.168018\pi$
$570$	4.02601	+	5.07219i	0.168631	+	0.212451i
$571$	−19.0805			−0.798496			−0.399248	−	0.916843i	$-0.630729\pi$
$571$	−19.0805			−0.798496			−0.399248	+	0.916843i	$0.630729\pi$
$572$	−2.28883	+	9.82087i	−0.0957010	+	0.410631i
$573$	−26.1370			−1.09189
$574$	−1.10420	+	23.5783i	−0.0460885	+	0.984140i
$575$			1.15968i			0.0483619i
$576$	−3.63605	+	4.43334i	−0.151502	+	0.184723i
$577$			14.5431i			0.605438i	0.953080	+	0.302719i	$0.0978944\pi$
$577$			14.5431i			0.605438i	−0.953080	+	0.302719i	$0.902106\pi$
$578$	−14.5307	−	18.3067i	−0.604399	−	0.761456i
$579$		−	44.6160i		−	1.85418i
$580$	−27.9623	−	6.51684i	−1.16107	−	0.270597i
$581$	−10.7999	−	9.42860i	−0.448057	−	0.391164i
$582$	4.21678	+	5.31254i	0.174791	+	0.220212i
$583$			14.5872i			0.604140i
$584$	2.52626	+	5.33918i	0.104537	+	0.220937i
$585$	−1.55297			−0.0642076
$586$	8.82683	+	11.1205i	0.364633	+	0.459385i
$587$			21.4770i			0.886451i	0.896410	+	0.443226i	$0.146166\pi$
$587$			21.4770i			0.886451i	−0.896410	+	0.443226i	$0.853834\pi$
$588$	−2.52244	+	26.8722i	−0.104024	+	1.10819i
$589$		−	9.49200i		−	0.391111i
$590$	27.9574	−	22.1910i	1.15099	−	0.913588i
$591$	1.56093			0.0642083
$592$	−16.3578	+	33.1877i	−0.672303	+	1.36401i
$593$			3.89623i			0.159999i	0.996795	+	0.0799994i	$0.0254919\pi$
$593$			3.89623i			0.159999i	−0.996795	+	0.0799994i	$0.974508\pi$
$594$	−24.5846	+	19.5138i	−1.00872	+	0.800661i
$595$	−2.97049	−	2.59331i	−0.121778	−	0.106315i
$596$	0.545017	+	0.127021i	0.0223248	+	0.00520297i
$597$		−	26.4647i		−	1.08313i
$598$	4.21208	−	3.34330i	0.172245	−	0.136718i
$599$			36.2640i			1.48171i	0.671667	+	0.740853i	$0.265578\pi$
$599$			36.2640i			1.48171i	−0.671667	+	0.740853i	$0.734422\pi$
$600$	−0.711244	−	1.50319i	−0.0290364	−	0.0613677i
$601$		−	25.1481i		−	1.02581i	−0.858445	−	0.512906i	$-0.828569\pi$
$601$		−	25.1481i		−	1.02581i	0.858445	−	0.512906i	$-0.171431\pi$
$602$	12.2376	+	0.573103i	0.498768	+	0.0233579i
$603$	−9.71562			−0.395651
$604$	37.1175	+	8.65053i	1.51029	+	0.351985i
$605$	−31.2498			−1.27048
$606$	−36.7475	+	29.1680i	−1.49277	+	1.18487i
$607$	15.8233			0.642247			0.321123	−	0.947037i	$-0.395940\pi$
$607$	15.8233			0.642247			0.321123	+	0.947037i	$0.395940\pi$
$608$	6.06080	−	1.31065i	0.245798	−	0.0531538i
$609$	22.2249	−	25.4574i	0.900598	−	1.03158i
$610$	−3.74311	−	4.71579i	−0.151554	−	0.190937i
$611$	2.09029			0.0845642
$612$	0.960225	+	0.223788i	0.0388148	+	0.00904611i
$613$		−	12.6133i		−	0.509447i	−0.967014	−	0.254723i	$-0.918016\pi$
$613$		−	12.6133i		−	0.509447i	0.967014	−	0.254723i	$-0.0819844\pi$
$614$	−4.36980	+	3.46849i	−0.176351	+	0.139977i
$615$	−26.3526			−1.06264
$616$	−10.2737	+	36.3055i	−0.413937	+	1.46279i
$617$	33.7479			1.35864			0.679319	−	0.733843i	$-0.262275\pi$
$617$	33.7479			1.35864			0.679319	+	0.733843i	$0.262275\pi$
$618$	−16.1879	+	12.8490i	−0.651172	+	0.516862i
$619$		−	47.3965i		−	1.90502i	−0.304500	−	0.952512i	$-0.598489\pi$
$619$		−	47.3965i		−	1.90502i	0.304500	−	0.952512i	$-0.401511\pi$
$620$	8.51739	−	36.5462i	0.342067	−	1.46773i
$621$	16.7386			0.671695
$622$	−15.2360	−	19.1952i	−0.610908	−	0.769657i
$623$	7.28095	+	6.35645i	0.291705	+	0.254666i
$624$	−3.40928	+	6.91695i	−0.136481	+	0.276900i
$625$	−23.3821			−0.935285
$626$	11.2848	−	8.95724i	0.451033	−	0.358003i
$627$	−10.6553			−0.425530
$628$	−5.71786	+	24.5341i	−0.228168	+	0.979016i
$629$	6.36247			0.253688
$630$	−5.80434	−	0.271824i	−0.231250	−	0.0108297i
$631$		−	10.6781i		−	0.425088i	−0.977151	−	0.212544i	$-0.931825\pi$
$631$		−	10.6781i		−	0.425088i	0.977151	−	0.212544i	$-0.0681749\pi$
$632$	−0.934683	−	1.97543i	−0.0371797	−	0.0785783i
$633$			42.6467i			1.69505i
$634$	5.68191	−	4.50996i	0.225657	−	0.179113i
$635$			8.78714i			0.348707i
$636$	−2.53195	+	10.8640i	−0.100398	+	0.430786i
$637$	0.944747	+	6.93595i	0.0374322	+	0.274812i
$638$	37.0026	−	29.3705i	1.46495	−	1.16279i
$639$		−	3.63633i		−	0.143851i
$640$	24.5114	+	0.392224i	0.968899	+	0.0155040i
$641$	28.3033			1.11791			0.558956	−	0.829197i	$-0.311202\pi$
$641$	28.3033			1.11791			0.558956	+	0.829197i	$0.311202\pi$
$642$	7.58320	−	6.01910i	0.299285	−	0.237555i
$643$		−	13.4258i		−	0.529462i	−0.964322	−	0.264731i	$-0.914717\pi$
$643$		−	13.4258i		−	0.529462i	0.964322	−	0.264731i	$-0.0852831\pi$
$644$	16.3281	−	11.7585i	0.643416	−	0.463350i
$645$			13.6775i			0.538552i
$646$	−0.662917	−	0.835181i	−0.0260821	−	0.0328598i
$647$	17.7213			0.696698			0.348349	−	0.937365i	$-0.386742\pi$
$647$	17.7213			0.696698			0.348349	+	0.937365i	$0.386742\pi$
$648$	−27.1940	+	12.8670i	−1.06828	+	0.505463i
$649$			58.7308i			2.30539i
$650$	−0.268137	−	0.337814i	−0.0105172	−	0.0132501i
$651$	33.2723	+	29.0475i	1.30404	+	1.13846i
$652$	−6.68237	+	28.6725i	−0.261702	+	1.12290i
$653$			18.2377i			0.713695i	0.934163	+	0.356847i	$0.116148\pi$
$653$			18.2377i			0.713695i	−0.934163	+	0.356847i	$0.883852\pi$
$654$	−14.3201	−	18.0412i	−0.559958	−	0.705468i
$655$		−	26.7125i		−	1.04374i
$656$	−11.1560	+	22.6339i	−0.435568	+	0.883706i
$657$		−	1.49673i		−	0.0583930i
$658$	7.81260	+	0.365873i	0.304567	+	0.0142632i
$659$	11.1172			0.433064			0.216532	−	0.976276i	$-0.430525\pi$
$659$	11.1172			0.433064			0.216532	+	0.976276i	$0.430525\pi$
$660$	−41.0250	−	9.56121i	−1.59690	−	0.372170i
$661$	10.0383			0.390444			0.195222	−	0.980759i	$-0.437457\pi$
$661$	10.0383			0.390444			0.195222	+	0.980759i	$0.437457\pi$
$662$	9.35007	+	11.7798i	0.363401	+	0.457833i
$663$	1.32606			0.0514999
$664$	−6.55504	−	13.8539i	−0.254385	−	0.537636i
$665$	4.73395	+	4.13285i	0.183575	+	0.160265i
$666$	7.34354	−	5.82887i	0.284556	−	0.225864i
$667$	−25.1934			−0.975493
$668$	2.95841	−	12.6938i	0.114464	−	0.491140i
$669$		−	20.2864i		−	0.784318i
$670$	25.8250	+	32.5359i	0.997709	+	1.25697i
$671$	9.90655			0.382438
$672$	−13.9531	+	25.2558i	−0.538253	+	0.974263i
$673$	18.9917			0.732077			0.366039	−	0.930600i	$-0.380714\pi$
$673$	18.9917			0.732077			0.366039	+	0.930600i	$0.380714\pi$
$674$	17.1057	+	21.5507i	0.658886	+	0.830102i
$675$		−	1.34245i		−	0.0516711i
$676$	−0.453951	+	1.94780i	−0.0174597	+	0.0749154i
$677$	−11.8708			−0.456231			−0.228115	−	0.973634i	$-0.573256\pi$
$677$	−11.8708			−0.456231			−0.228115	+	0.973634i	$0.573256\pi$
$678$	−32.4980	+	25.7950i	−1.24808	+	0.990650i
$679$	4.95826	+	4.32868i	0.190281	+	0.166120i
$680$	−1.80294	−	3.81047i	−0.0691397	−	0.146125i
$681$	30.6766			1.17553
$682$	38.3867	+	48.3617i	1.46990	+	1.85187i
$683$	24.1203			0.922937			0.461469	−	0.887156i	$-0.347323\pi$
$683$	24.1203			0.922937			0.461469	+	0.887156i	$0.347323\pi$
$684$	−1.53027	−	0.356643i	−0.0585115	−	0.0136366i
$685$	21.7568			0.831285
$686$	2.31702	+	26.0889i	0.0884641	+	0.996079i
$687$		−	19.8028i		−	0.755523i
$688$	11.7475	+	5.79018i	0.447868	+	0.220749i
$689$			2.89312i			0.110219i
$690$	13.9660	+	17.5952i	0.531678	+	0.669839i
$691$			15.6365i			0.594842i	0.954746	+	0.297421i	$0.0961265\pi$
$691$			15.6365i			0.594842i	−0.954746	+	0.297421i	$0.903874\pi$
$692$	9.91970	−	42.5632i	0.377091	−	1.61801i
$693$	6.28784	−	7.20237i	0.238855	−	0.273596i
$694$	−24.1773	−	30.4599i	−0.917757	−	1.15624i
$695$		−	48.9597i		−	1.85715i
$696$	32.6561	−	15.4514i	1.23783	−	0.585684i
$697$	4.33918			0.164358
$698$	−20.2364	−	25.4949i	−0.765957	−	0.964997i
$699$		−	8.91800i		−	0.337310i
$700$	−0.943048	−	1.30953i	−0.0356439	−	0.0494957i
$701$		−	6.05523i		−	0.228703i	−0.993440	−	0.114351i	$-0.963521\pi$
$701$		−	6.05523i		−	0.228703i	0.993440	−	0.114351i	$-0.0364790\pi$
$702$	−4.87594	+	3.87023i	−0.184030	+	0.146072i
$703$	−10.1396			−0.382423
$704$	−25.5794	+	31.1883i	−0.964058	+	1.17545i
$705$			8.73184i			0.328860i
$706$	−36.1431	+	28.6883i	−1.36027	+	1.07970i
$707$	−29.9421	+	34.2970i	−1.12609	+	1.28987i
$708$	−10.1941	+	43.7406i	−0.383118	+	1.64387i
$709$		−	10.6349i		−	0.399401i	−0.979857	−	0.199701i	$-0.936003\pi$
$709$		−	10.6349i		−	0.399401i	0.979857	−	0.199701i	$-0.0639969\pi$
$710$	−12.1774	+	9.66572i	−0.457011	+	0.362748i
$711$			0.553771i			0.0207680i
$712$	4.41919	+	9.33984i	0.165616	+	0.350025i
$713$		−	32.9273i		−	1.23314i
$714$	4.95623	+	0.232106i	0.185482	+	0.00868636i
$715$	−10.9251			−0.408575
$716$	−5.86834	+	25.1797i	−0.219310	+	0.941010i
$717$	−11.2052			−0.418464
$718$	−15.5718	+	12.3599i	−0.581133	+	0.461269i
$719$	6.21956			0.231950			0.115975	−	0.993252i	$-0.463001\pi$
$719$	6.21956			0.231950			0.115975	+	0.993252i	$0.463001\pi$
$720$	−5.57185	−	2.74630i	−0.207651	−	0.102349i
$721$	−13.1900	+	15.1084i	−0.491220	+	0.562665i
$722$	−15.6487	−	19.7151i	−0.582384	−	0.733720i
$723$	−1.06137			−0.0394728
$724$	4.48966	−	19.2641i	0.166857	−	0.715945i
$725$			2.02054i			0.0750411i
$726$	30.7982	−	24.4458i	1.14303	−	0.907268i
$727$	−26.7235			−0.991118			−0.495559	−	0.868574i	$-0.665037\pi$
$727$	−26.7235			−0.991118			−0.495559	+	0.868574i	$0.665037\pi$
$728$	−2.03760	+	7.20057i	−0.0755186	+	0.266871i
$729$	−17.8357			−0.660581
$730$	−5.01228	+	3.97845i	−0.185513	+	0.147249i
$731$		−	2.25212i		−	0.0832978i
$732$	7.37804	+	1.71951i	0.272700	+	0.0635550i
$733$	21.9273			0.809905			0.404953	−	0.914338i	$-0.367288\pi$
$733$	21.9273			0.809905			0.404953	+	0.914338i	$0.367288\pi$
$734$	12.2159	+	15.3904i	0.450899	+	0.568068i
$735$	−28.9738	+	3.94652i	−1.06871	+	0.145569i
$736$	21.0246	−	4.54658i	0.774979	−	0.167589i
$737$	−68.3488			−2.51766
$738$	5.00827	−	3.97527i	0.184357	−	0.146332i
$739$	−29.1929			−1.07388			−0.536938	−	0.843621i	$-0.680419\pi$
$739$	−29.1929			−1.07388			−0.536938	+	0.843621i	$0.680419\pi$
$740$	−39.0397	−	9.09851i	−1.43513	−	0.334468i
$741$	−2.11329			−0.0776336
$742$	−0.506396	+	10.8132i	−0.0185904	+	0.396965i
$743$		−	43.4204i		−	1.59294i	−0.604678	−	0.796470i	$-0.706698\pi$
$743$		−	43.4204i		−	1.59294i	0.604678	−	0.796470i	$-0.293302\pi$
$744$	20.1947	+	42.6810i	0.740374	+	1.56476i
$745$			0.606296i			0.0222130i
$746$	−10.4889	+	8.32545i	−0.384025	+	0.304816i
$747$			3.88366i			0.142096i
$748$	6.75513	+	1.57434i	0.246992	+	0.0575635i
$749$	6.17883	−	7.07751i	0.225770	−	0.258606i
$750$	24.5471	−	19.4840i	0.896332	−	0.711455i
$751$		−	11.5694i		−	0.422174i	−0.977467	−	0.211087i	$-0.932300\pi$
$751$		−	11.5694i		−	0.422174i	0.977467	−	0.211087i	$-0.0677003\pi$
$752$	7.49967	+	3.69650i	0.273485	+	0.134797i
$753$	−50.3145			−1.83356
$754$	7.33883	−	5.82513i	0.267264	−	0.212139i
$755$			41.2908i			1.50273i
$756$	−18.9015	+	13.6118i	−0.687442	+	0.495055i
$757$		−	3.36324i		−	0.122239i	−0.998130	−	0.0611196i	$-0.980533\pi$
$757$		−	3.36324i		−	0.122239i	0.998130	−	0.0611196i	$-0.0194671\pi$
$758$	25.8241	+	32.5346i	0.937972	+	1.18171i
$759$	−36.9627			−1.34166
$760$	2.87328	+	6.07260i	0.104225	+	0.220276i
$761$			28.7317i			1.04152i	0.853702	+	0.520761i	$0.174352\pi$
$761$			28.7317i			1.04152i	−0.853702	+	0.520761i	$0.825648\pi$
$762$	−6.87392	−	8.66016i	−0.249016	−	0.313724i
$763$	−16.8381	−	14.7001i	−0.609581	−	0.532179i
$764$	−26.4071	−	6.15439i	−0.955374	−	0.222658i
$765$			1.06819i			0.0386204i
$766$	−20.9953	−	26.4511i	−0.758591	−	0.955716i
$767$			11.6482i			0.420594i
$768$	−24.4640	+	18.7880i	−0.882770	+	0.677954i
$769$		−	32.7273i		−	1.18018i	−0.807338	−	0.590089i	$-0.799093\pi$
$769$		−	32.7273i		−	1.18018i	0.807338	−	0.590089i	$-0.200907\pi$
$770$	−40.8331	−	1.91227i	−1.47152	−	0.0689133i
$771$	45.7218			1.64663
$772$	10.5056	−	45.0771i	0.378104	−	1.62236i
$773$	1.68151			0.0604796			0.0302398	−	0.999543i	$-0.490373\pi$
$773$	1.68151			0.0604796			0.0302398	+	0.999543i	$0.490373\pi$
$774$	−2.06324	−	2.59939i	−0.0741618	−	0.0934332i
$775$	−2.64081			−0.0948609
$776$	3.00943	+	6.36035i	0.108032	+	0.228323i
$777$	31.0294	−	35.5424i	1.11317	−	1.27508i
$778$	26.8318	−	21.2975i	0.961966	−	0.763551i
$779$	−6.91518			−0.247762
$780$	−8.13660	−	1.89630i	−0.291337	−	0.0678985i
$781$		−	25.5814i		−	0.915374i
$782$	−2.29963	−	2.89721i	−0.0822346	−	0.103604i
$783$	29.1641			1.04224
$784$	−8.87601	+	26.5559i	−0.317000	+	0.948425i
$785$	−27.2925			−0.974113
$786$	20.8964	+	26.3264i	0.745349	+	0.939033i
$787$		−	5.75339i		−	0.205086i	−0.994729	−	0.102543i	$-0.967302\pi$
$787$		−	5.75339i		−	0.205086i	0.994729	−	0.102543i	$-0.0326979\pi$
$788$	1.57707	+	0.367548i	0.0561806	+	0.0130934i
$789$	30.3260			1.07964
$790$	1.85448	−	1.47198i	0.0659794	−	0.0523706i
$791$	−26.4795	+	30.3308i	−0.941504	+	1.07844i
$792$	9.23904	−	4.37150i	0.328295	−	0.155334i
$793$	1.96479			0.0697719
$794$	21.1918	+	26.6986i	0.752068	+	0.947499i
$795$	−12.0855			−0.428629
$796$	6.23156	−	26.7382i	0.220872	−	0.947711i
$797$	0.563854			0.0199727			0.00998636	−	0.999950i	$-0.496821\pi$
$797$	0.563854			0.0199727			0.00998636	+	0.999950i	$0.496821\pi$
$798$	−7.89855	−	0.369899i	−0.279605	−	0.0130943i
$799$		−	1.43777i		−	0.0508648i
$800$	−0.364642	−	1.68620i	−0.0128920	−	0.0596163i
$801$		−	2.61823i		−	0.0925107i
$802$	18.6635	+	23.5133i	0.659031	+	0.830285i
$803$		−	10.5294i		−	0.371574i
$804$	−50.9037	−	11.8635i	−1.79524	−	0.418394i
$805$	16.4219	+	14.3367i	0.578794	+	0.505301i
$806$	7.61334	+	9.59172i	0.268168	+	0.337854i
$807$			51.8702i			1.82592i
$808$	−43.9954	+	20.8166i	−1.54775	+	0.732327i
$809$	−40.0661			−1.40865			−0.704325	−	0.709878i	$-0.748750\pi$
$809$	−40.0661			−1.40865			−0.704325	+	0.709878i	$0.748750\pi$
$810$	−20.2634	−	25.5290i	−0.711984	−	0.896998i
$811$		−	10.3867i		−	0.364728i	−0.983231	−	0.182364i	$-0.941625\pi$
$811$		−	10.3867i		−	0.364728i	0.983231	−	0.182364i	$-0.0583749\pi$
$812$	28.4489	−	20.4872i	0.998361	−	0.718961i
$813$		−	45.7468i		−	1.60441i
$814$	51.6613	−	41.0057i	1.81073	−	1.43725i
$815$	−31.8963			−1.11728
$816$	4.75771	+	2.34502i	0.166553	+	0.0820921i
$817$			3.58912i			0.125567i
$818$	16.8106	−	13.3433i	0.587770	−	0.466537i
$819$	1.24709	−	1.42847i	0.0435767	−	0.0499147i
$820$	−26.6249	−	6.20515i	−0.929782	−	0.216693i
$821$			25.9082i			0.904202i	0.891967	+	0.452101i	$0.149325\pi$
$821$			25.9082i			0.904202i	−0.891967	+	0.452101i	$0.850675\pi$
$822$	−21.4424	+	17.0197i	−0.747890	+	0.593631i
$823$		−	32.7107i		−	1.14022i	−0.821567	−	0.570112i	$-0.806900\pi$
$823$		−	32.7107i		−	1.14022i	0.821567	−	0.570112i	$-0.193100\pi$
$824$	−19.3807	+	9.17005i	−0.675158	+	0.319454i
$825$			2.96445i			0.103209i
$826$	−2.03885	+	43.5360i	−0.0709405	+	1.51481i
$827$	−9.60694			−0.334066			−0.167033	−	0.985951i	$-0.553419\pi$
$827$	−9.60694			−0.334066			−0.167033	+	0.985951i	$0.553419\pi$
$828$	−5.30845	−	1.23718i	−0.184481	−	0.0429949i
$829$	55.6806			1.93387			0.966934	−	0.255027i	$-0.0820843\pi$
$829$	55.6806			1.93387			0.966934	+	0.255027i	$0.0820843\pi$
$830$	13.0057	−	10.3231i	0.451434	−	0.358321i
$831$	56.5513			1.96174
$832$	−5.07323	+	6.18566i	−0.175882	+	0.214449i
$833$	4.77078	−	0.649829i	0.165298	−	0.0225152i
$834$	38.2997	+	48.2522i	1.32621	+	1.67084i
$835$	14.1211			0.488680
$836$	−10.7654	−	2.50896i	−0.372328	−	0.0867742i
$837$			38.1170i			1.31752i
$838$	24.8031	−	19.6872i	0.856807	−	0.680083i
$839$	26.2179			0.905142			0.452571	−	0.891728i	$-0.350507\pi$
$839$	26.2179			0.905142			0.452571	+	0.891728i	$0.350507\pi$
$840$	−30.0791	−	8.51173i	−1.03783	−	0.293683i
$841$	−14.8953			−0.513630
$842$	7.69863	−	6.11072i	0.265312	−	0.210589i
$843$			18.9320i			0.652053i
$844$	−10.0419	+	43.0874i	−0.345655	+	1.48313i
$845$	−2.16680			−0.0745402
$846$	−1.31719	−	1.65947i	−0.0452860	−	0.0570538i
$847$	25.0945	−	28.7444i	0.862258	−	0.987668i
$848$	−5.11622	+	10.3801i	−0.175692	+	0.356454i
$849$	−35.1302			−1.20567
$850$	−0.232360	+	0.184433i	−0.00796987	+	0.00632601i
$851$	−35.1739			−1.20575
$852$	4.44025	−	19.0521i	0.152120	−	0.652714i
$853$	−29.3901			−1.00630			−0.503149	−	0.864200i	$-0.667825\pi$
$853$	−29.3901			−1.00630			−0.503149	+	0.864200i	$0.667825\pi$
$854$	7.34354	+	0.343907i	0.251291	+	0.0117682i
$855$		−	1.70233i		−	0.0582184i
$856$	9.07887	−	4.29571i	0.310309	−	0.146824i
$857$			22.3255i			0.762624i	0.924446	+	0.381312i	$0.124528\pi$
$857$			22.3255i			0.762624i	−0.924446	+	0.381312i	$0.875472\pi$
$858$	10.7672	−	8.54637i	0.367586	−	0.291768i
$859$		−	15.7351i		−	0.536873i	−0.963297	−	0.268437i	$-0.913493\pi$
$859$		−	15.7351i		−	0.536873i	0.963297	−	0.268437i	$-0.0865070\pi$
$860$	−3.22060	+	13.8189i	−0.109822	+	0.471219i
$861$	21.1619	−	24.2398i	0.721196	−	0.826090i
$862$	19.4865	−	15.4672i	0.663712	−	0.526816i
$863$		−	31.8109i		−	1.08286i	−0.840747	−	0.541428i	$-0.817884\pi$
$863$		−	31.8109i		−	1.08286i	0.840747	−	0.541428i	$-0.182116\pi$
$864$	−24.3383	+	5.26316i	−0.828007	+	0.179056i
$865$	47.3488			1.60991
$866$	14.1299	−	11.2155i	0.480154	−	0.381118i
$867$			31.8618i			1.08208i
$868$	26.7764	+	37.1822i	0.908851	+	1.26205i
$869$			3.89574i			0.132154i
$870$	24.3335	+	30.6567i	0.824982	+	1.03936i
$871$	−13.5558			−0.459321
$872$	−10.2199	−	21.5996i	−0.346091	−	0.731453i
$873$		−	1.78299i		−	0.0603452i
$874$	3.66483	+	4.61717i	0.123965	+	0.156178i
$875$	20.0011	−	22.9101i	0.676160	−	0.774503i
$876$	1.82762	−	7.84191i	0.0617496	−	0.264954i
$877$			4.71862i			0.159337i	0.996821	+	0.0796683i	$0.0253861\pi$
$877$			4.71862i			0.159337i	−0.996821	+	0.0796683i	$0.974614\pi$
$878$	−35.0100	−	44.1076i	−1.18153	−	1.48856i
$879$		−	19.3548i		−	0.652820i
$880$	−39.1976	−	19.3200i	−1.32135	−	0.651279i
$881$		−	34.3311i		−	1.15665i	−0.815808	−	0.578323i	$-0.803707\pi$
$881$		−	34.3311i		−	1.15665i	0.815808	−	0.578323i	$-0.196293\pi$
$882$	4.91109	−	5.12070i	0.165365	−	0.172423i
$883$	13.7434			0.462503			0.231252	−	0.972894i	$-0.425718\pi$
$883$	13.7434			0.462503			0.231252	+	0.972894i	$0.425718\pi$
$884$	1.33976	+	0.312243i	0.0450611	+	0.0105019i
$885$	−48.6585			−1.63564
$886$	2.58723	+	3.25955i	0.0869199	+	0.109507i
$887$	−23.5082			−0.789328			−0.394664	−	0.918825i	$-0.629139\pi$
$887$	−23.5082			−0.789328			−0.394664	+	0.918825i	$0.629139\pi$
$888$	45.5930	−	21.5725i	1.53000	−	0.723927i
$889$	−8.08264	−	7.05634i	−0.271083	−	0.236662i
$890$	−8.76799	+	6.95952i	−0.293904	+	0.233283i
$891$	53.6294			1.79665
$892$	4.77677	−	20.4961i	0.159938	−	0.686259i
$893$			2.29132i			0.0766762i
$894$	−0.474288	−	0.597535i	−0.0158626	−	0.0199846i
$895$	−28.0108			−0.936297
$896$	−20.0442	+	22.2313i	−0.669630	+	0.742695i
$897$	−7.33091			−0.244772
$898$	−11.2325	−	14.1514i	−0.374835	−	0.472238i
$899$		−	57.3703i		−	1.91341i
$900$	−0.0992233	+	0.425745i	−0.00330744	+	0.0141915i
$901$	1.98998			0.0662960
$902$	35.2329	−	27.9658i	1.17313	−	0.931158i
$903$	−12.5809	−	10.9835i	−0.418668	−	0.365507i
$904$	−38.9077	+	18.4094i	−1.29405	+	0.612286i
$905$	21.4301			0.712359
$906$	−32.3006	−	40.6941i	−1.07311	−	1.35197i
$907$	−36.4422			−1.21004			−0.605021	−	0.796209i	$-0.706835\pi$
$907$	−36.4422			−1.21004			−0.605021	+	0.796209i	$0.706835\pi$
$908$	30.9937	+	7.22333i	1.02856	+	0.239714i
$909$	12.3332			0.409067
$910$	−8.09855	−	0.379265i	−0.268464	−	0.0125725i
$911$			9.46472i			0.313580i	0.987632	+	0.156790i	$0.0501146\pi$
$911$			9.46472i			0.313580i	−0.987632	+	0.156790i	$0.949885\pi$
$912$	−7.58218	−	3.73717i	−0.251071	−	0.123750i
$913$			27.3213i			0.904203i
$914$	5.32464	+	6.70828i	0.176123	+	0.221890i
$915$			8.20759i			0.271335i
$916$	4.66289	−	20.0074i	0.154066	−	0.661063i
$917$	24.5708	+	21.4509i	0.811400	+	0.708372i
$918$	2.66207	+	3.35383i	0.0878615	+	0.110693i
$919$			43.3424i			1.42973i	0.699261	+	0.714867i	$0.253513\pi$
$919$			43.3424i			1.42973i	−0.699261	+	0.714867i	$0.746487\pi$
$920$	9.96728	+	21.0656i	0.328612	+	0.694512i
$921$	7.60542			0.250607
$922$	−11.9095	−	15.0042i	−0.392217	−	0.494138i
$923$		−	5.07363i		−	0.167001i
$924$	41.7390	−	30.0579i	1.37311	−	0.988834i
$925$			2.82099i			0.0927536i
$926$	26.9588	−	21.3983i	0.885923	−	0.703193i
$927$	5.43297			0.178442
$928$	36.6319	−	7.92165i	1.20250	−	0.260041i
$929$		−	39.0336i		−	1.28065i	−0.768104	−	0.640325i	$-0.778799\pi$
$929$		−	39.0336i		−	1.28065i	0.768104	−	0.640325i	$-0.221201\pi$
$930$	−40.0678	+	31.8034i	−1.31387	+	1.04288i
$931$	−7.60301	+	1.03561i	−0.249179	+	0.0339406i
$932$	2.09989	−	9.01017i	0.0687843	−	0.295138i
$933$			33.4083i			1.09374i
$934$	−32.5412	+	25.8293i	−1.06478	+	0.845160i
$935$			7.51464i			0.245755i
$936$	1.83241	−	0.867011i	0.0598940	−	0.0283391i
$937$			53.0178i			1.73202i	0.500030	+	0.866008i	$0.333322\pi$
$937$			53.0178i			1.73202i	−0.500030	+	0.866008i	$0.666678\pi$
$938$	−50.6657	−	2.37273i	−1.65429	−	0.0774725i
$939$	−19.6407			−0.640950
$940$	−2.05606	+	8.82207i	−0.0670612	+	0.287744i
$941$	−16.8743			−0.550087			−0.275044	−	0.961432i	$-0.588692\pi$
$941$	−16.8743			−0.550087			−0.275044	+	0.961432i	$0.588692\pi$
$942$	26.8981	−	21.3502i	0.876389	−	0.695626i
$943$	−23.9885			−0.781172
$944$	−20.5989	+	41.7922i	−0.670437	+	1.36022i
$945$	−19.0101	−	16.5963i	−0.618398	−	0.539876i
$946$	−14.5148	−	18.2866i	−0.471917	−	0.594548i
$947$	−8.43947			−0.274246			−0.137123	−	0.990554i	$-0.543786\pi$
$947$	−8.43947			−0.274246			−0.137123	+	0.990554i	$0.543786\pi$
$948$	−0.676197	+	2.90141i	−0.0219619	+	0.0942334i
$949$		−	2.08832i		−	0.0677899i
$950$	0.370302	−	0.293924i	0.0120142	−	0.00953616i
$951$	−9.88907			−0.320675
$952$	4.95279	+	1.40153i	0.160521	+	0.0454239i
$953$	−18.5496			−0.600880			−0.300440	−	0.953801i	$-0.597134\pi$
$953$	−18.5496			−0.600880			−0.300440	+	0.953801i	$0.597134\pi$
$954$	2.29683	−	1.82309i	0.0743627	−	0.0590247i
$955$		−	29.3761i		−	0.950590i
$956$	−11.3210	−	2.63844i	−0.366146	−	0.0853333i
$957$	−64.4012			−2.08179
$958$	2.52206	+	3.17744i	0.0814841	+	0.102658i
$959$	−17.4714	+	20.0125i	−0.564180	+	0.646237i
$960$	−25.8395	−	21.1925i	−0.833967	−	0.683986i
$961$	43.9820			1.41877
$962$	10.2461	−	8.13278i	0.330349	−	0.262211i
$963$	−2.54507			−0.0820138
$964$	−1.07234	−	0.249917i	−0.0345377	−	0.00804929i
$965$	50.1453			1.61423
$966$	−27.3997	−	1.28316i	−0.881571	−	0.0412851i
$967$		−	7.56789i		−	0.243367i	−0.992569	−	0.121683i	$-0.961171\pi$
$967$		−	7.56789i		−	0.243367i	0.992569	−	0.121683i	$-0.0388293\pi$
$968$	36.8726	−	17.4465i	1.18513	−	0.560750i
$969$			1.45359i			0.0466961i
$970$	−5.97093	+	4.73937i	−0.191715	+	0.152172i
$971$			4.56757i			0.146580i	0.997311	+	0.0732901i	$0.0233499\pi$
$971$			4.56757i			0.146580i	−0.997311	+	0.0732901i	$0.976650\pi$
$972$	14.2191	+	3.31389i	0.456079	+	0.106293i
$973$	45.0344	+	39.3161i	1.44374	+	1.26042i
$974$	27.2363	−	21.6186i	0.872709	−	0.692704i
$975$			0.587948i			0.0188294i
$976$	7.04940	+	3.47457i	0.225646	+	0.111218i
$977$	35.0513			1.12139			0.560696	−	0.828022i	$-0.310534\pi$
$977$	35.0513			1.12139			0.560696	+	0.828022i	$0.310534\pi$
$978$	31.4354	−	24.9515i	1.00519	−	0.797863i
$979$		−	18.4191i		−	0.588677i
$980$	−30.2025	−	2.83505i	−0.964782	−	0.0905624i
$981$			6.05499i			0.193321i
$982$	−35.8048	−	45.1090i	−1.14258	−	1.43949i
$983$	17.4575			0.556809			0.278404	−	0.960464i	$-0.410195\pi$
$983$	17.4575			0.556809			0.278404	+	0.960464i	$0.410195\pi$
$984$	31.0943	−	14.7124i	0.991249	−	0.469014i
$985$			1.75438i			0.0558993i
$986$	−4.00672	−	5.04789i	−0.127600	−	0.160758i
$987$	−8.03178	−	7.01193i	−0.255654	−	0.223192i
$988$	−2.13513	−	0.497609i	−0.0679275	−	0.0158311i
$989$			12.4505i			0.395903i
$990$	6.88440	+	8.67337i	0.218801	+	0.275658i
$991$		−	11.0252i		−	0.350227i	−0.984548	−	0.175114i	$-0.943971\pi$
$991$		−	11.0252i		−	0.350227i	0.984548	−	0.175114i	$-0.0560292\pi$
$992$	10.3535	+	47.8772i	0.328723	+	1.52010i
$993$		−	20.5021i		−	0.650614i
$994$	0.888060	−	18.9630i	0.0281676	−	0.601470i
$995$	29.7445			0.942965
$996$	−4.74225	+	20.3479i	−0.150264	+	0.644749i
$997$	−5.72166			−0.181207			−0.0906033	−	0.995887i	$-0.528880\pi$
$997$	−5.72166			−0.181207			−0.0906033	+	0.995887i	$0.528880\pi$
$998$	33.1616	+	41.7789i	1.04971	+	1.32249i
$999$	40.7176			1.28825

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.h.a.27.13	✓	48
4.3	odd	2		2912.2.h.a.2575.11		48
7.6	odd	2		728.2.h.b.27.13	yes	48
8.3	odd	2		728.2.h.b.27.14	yes	48
8.5	even	2		2912.2.h.b.2575.11		48
28.27	even	2		2912.2.h.b.2575.38		48
56.13	odd	2		2912.2.h.a.2575.38		48
56.27	even	2	inner	728.2.h.a.27.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.h.a.27.13	✓	48	1.1	even	1	trivial
728.2.h.a.27.14	yes	48	56.27	even	2	inner
728.2.h.b.27.13	yes	48	7.6	odd	2
728.2.h.b.27.14	yes	48	8.3	odd	2
2912.2.h.a.2575.11		48	4.3	odd	2
2912.2.h.a.2575.38		48	56.13	odd	2
2912.2.h.b.2575.11		48	8.5	even	2
2912.2.h.b.2575.38		48	28.27	even	2

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.879218 - 1.10769i) q^{2} +1.92788i q^{3} +(-0.453951 + 1.94780i) q^{4} -2.16680 q^{5} +(2.13549 - 1.69503i) q^{6} +(1.74001 - 1.99308i) q^{7} +(2.55668 - 1.20971i) q^{8} -0.716713 q^{9} +(1.90509 + 2.40014i) q^{10} -5.04203 q^{11} +(-3.75512 - 0.875162i) q^{12} -1.00000 q^{13} +(-3.73756 - 0.175035i) q^{14} -4.17733i q^{15} +(-3.58786 - 1.76841i) q^{16} +0.687834i q^{17} +(0.630147 + 0.793895i) q^{18} -1.09617i q^{19} +(0.983622 - 4.22050i) q^{20} +(3.84242 + 3.35452i) q^{21} +(4.43304 + 5.58500i) q^{22} -3.80258i q^{23} +(2.33216 + 4.92897i) q^{24} -0.304972 q^{25} +(0.879218 + 1.10769i) q^{26} +4.40190i q^{27} +(3.09225 + 4.29395i) q^{28} -6.62535i q^{29} +(-4.62718 + 3.67278i) q^{30} +8.65921 q^{31} +(1.19566 + 5.52905i) q^{32} -9.72042i q^{33} +(0.761906 - 0.604756i) q^{34} +(-3.77025 + 4.31861i) q^{35} +(0.325352 - 1.39601i) q^{36} -9.25001i q^{37} +(-1.21422 + 0.963776i) q^{38} -1.92788i q^{39} +(-5.53982 + 2.62119i) q^{40} -6.30848i q^{41} +(0.337445 - 7.20556i) q^{42} -3.27423 q^{43} +(2.28883 - 9.82087i) q^{44} +1.55297 q^{45} +(-4.21208 + 3.34330i) q^{46} -2.09029 q^{47} +(3.40928 - 6.91695i) q^{48} +(-0.944747 - 6.93595i) q^{49} +(0.268137 + 0.337814i) q^{50} -1.32606 q^{51} +(0.453951 - 1.94780i) q^{52} -2.89312i q^{53} +(4.87594 - 3.87023i) q^{54} +10.9251 q^{55} +(2.03760 - 7.20057i) q^{56} +2.11329 q^{57} +(-7.33883 + 5.82513i) q^{58} -11.6482i q^{59} +(8.13660 + 1.89630i) q^{60} -1.96479 q^{61} +(-7.61334 - 9.59172i) q^{62} +(-1.24709 + 1.42847i) q^{63} +(5.07323 - 6.18566i) q^{64} +2.16680 q^{65} +(-10.7672 + 8.54637i) q^{66} +13.5558 q^{67} +(-1.33976 - 0.312243i) q^{68} +7.33091 q^{69} +(8.09855 + 0.379265i) q^{70} +5.07363i q^{71} +(-1.83241 + 0.867011i) q^{72} +2.08832i q^{73} +(-10.2461 + 8.13278i) q^{74} -0.587948i q^{75} +(2.13513 + 0.497609i) q^{76} +(-8.77317 + 10.0492i) q^{77} +(-2.13549 + 1.69503i) q^{78} -0.772654i q^{79} +(7.77417 + 3.83180i) q^{80} -10.6365 q^{81} +(-6.98783 + 5.54653i) q^{82} -5.41871i q^{83} +(-8.27821 + 5.96148i) q^{84} -1.49040i q^{85} +(2.87876 + 3.62683i) q^{86} +12.7729 q^{87} +(-12.8909 + 6.09937i) q^{88} +3.65311i q^{89} +(-1.36540 - 1.72021i) q^{90} +(-1.74001 + 1.99308i) q^{91} +(7.40667 + 1.72618i) q^{92} +16.6939i q^{93} +(1.83782 + 2.31539i) q^{94} +2.37519i q^{95} +(-10.6593 + 2.30508i) q^{96} +2.48774i q^{97} +(-6.85224 + 7.14470i) q^{98} +3.61369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + q^{4} - 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} + 10 q^{12} - 48 q^{13} + 10 q^{14} + 5 q^{16} - 15 q^{18} - 22 q^{20} - 6 q^{22} + 48 q^{25} - q^{26} + 4 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) \) 48 * q + q^2 + q^4 - 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 + 10 * q^12 - 48 * q^13 + 10 * q^14 + 5 * q^16 - 15 * q^18 - 22 * q^20 - 6 * q^22 + 48 * q^25 - q^26 + 4 * q^28 - 26 * q^30 - 19 * q^32 + 36 * q^34 + 12 * q^35 - 5 * q^36 - 10 * q^38 - 48 * q^40 + 3 * q^42 - 4 * q^43 - 30 * q^44 + 24 * q^45 + 2 * q^46 + 48 * q^48 + 11 * q^50 - 40 * q^51 - q^52 + 62 * q^54 + 10 * q^56 + 2 * q^58 + 18 * q^60 - 36 * q^62 + 20 * q^63 - 11 * q^64 + 32 * q^66 - 4 * q^67 + 62 * q^68 - 11 * q^70 + 13 * q^72 - 44 * q^74 - 48 * q^76 - 20 * q^77 + 10 * q^78 + 32 * q^80 + 64 * q^81 - 50 * q^82 + 21 * q^84 + 2 * q^86 - 40 * q^87 - 66 * q^88 + 74 * q^90 - 24 * q^92 - 26 * q^94 - 84 * q^96 - 6 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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