LMFDB - Embedded newform 728.2.h.a.27.14

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

$q$-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	$-0.812132\pi$
$3$		−	1.92788i		−	1.11306i	0.830827	−	0.556530i	$-0.187868\pi$
$4$	−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	$-0.973418\pi$
$17$		−	0.687834i		−	0.166824i	0.996515	−	0.0834121i	$-0.0265818\pi$
$18$	0.630147	−	0.793895i	0.148527	−	0.187123i
$19$			1.09617i			0.251479i	0.992063	+	0.125740i	$0.0401304\pi$
$19$			1.09617i			0.251479i	−0.992063	+	0.125740i	$0.959870\pi$
$20$	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	$0.129757\pi$
$23$			3.80258i			0.792892i	−0.918058	+	0.396446i	$0.870243\pi$
$24$	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	$0.210904\pi$
$29$			6.62535i			1.23030i	−0.788411	+	0.615148i	$0.789096\pi$
$30$	−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	$0.274971\pi$
$37$			9.25001i			1.52069i	−0.649518	+	0.760346i	$0.725029\pi$
$38$	−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	$0.163957\pi$
$41$			6.30848i			0.985218i	−0.870251	+	0.492609i	$0.836043\pi$
$42$	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	$0.0636720\pi$
$53$			2.89312i			0.397400i	−0.980060	+	0.198700i	$0.936328\pi$
$54$	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	$0.273939\pi$
$59$			11.6482i			1.51647i	−0.651980	+	0.758236i	$0.726061\pi$
$60$	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	$-0.902658\pi$
$71$		−	5.07363i		−	0.602129i	0.953604	−	0.301064i	$-0.0973419\pi$
$72$	−1.83241	−	0.867011i	−0.215951	−	0.102178i
$73$		−	2.08832i		−	0.244420i	−0.992504	−	0.122210i	$-0.961002\pi$
$73$		−	2.08832i		−	0.244420i	0.992504	−	0.122210i	$-0.0389981\pi$
$74$	−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	$0.0138398\pi$
$79$			0.772654i			0.0869303i	−0.999055	+	0.0434652i	$0.986160\pi$
$80$	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	$0.0961163\pi$
$83$			5.41871i			0.594781i	−0.954756	+	0.297390i	$0.903884\pi$
$84$	−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	$-0.937979\pi$
$89$		−	3.65311i		−	0.387229i	0.981078	−	0.193615i	$-0.0620212\pi$
$90$	−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	$-0.959691\pi$
$97$		−	2.48774i		−	0.252592i	0.991993	−	0.126296i	$-0.0403088\pi$
$98$	−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	$0.132589\pi$
$109$			8.44828i			0.809199i	−0.914494	+	0.404599i	$0.867411\pi$
$110$	−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	$0.0575862\pi$
$127$			4.05535i			0.359854i	−0.983680	+	0.179927i	$0.942414\pi$
$128$	−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	$-0.818971\pi$
$131$		−	12.3281i		−	1.07711i	0.842591	−	0.538554i	$-0.181029\pi$
$132$	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	$-0.592295\pi$
$139$		−	22.5954i		−	1.91651i	0.285909	−	0.958257i	$-0.407705\pi$
$140$	−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	$0.00364840\pi$
$149$			0.279812i			0.0229231i	−0.999934	+	0.0114615i	$0.996352\pi$
$150$	−0.651264	−	0.516934i	−0.0531755	−	0.0422075i
$151$			19.0561i			1.55076i	0.631493	+	0.775382i	$0.282443\pi$
$151$			19.0561i			1.55076i	−0.631493	+	0.775382i	$0.717557\pi$
$152$	−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	$-0.836818\pi$
$191$		−	13.5574i		−	0.980978i	0.871448	−	0.490489i	$-0.163182\pi$
$192$	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	$0.00918232\pi$
$197$			0.809664i			0.0576862i	−0.999584	+	0.0288431i	$0.990818\pi$
$198$	−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	$0.177081\pi$
$227$			15.9121i			1.05612i	−0.849206	+	0.528062i	$0.822919\pi$
$228$	−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	$-0.939806\pi$
$239$		−	5.81217i		−	0.375958i	0.982173	−	0.187979i	$-0.0601937\pi$
$240$	−7.38724	−	14.9877i	−0.476844	−	0.967449i
$241$		−	0.550538i		−	0.0354633i	−0.999843	−	0.0177316i	$-0.994356\pi$
$241$		−	0.550538i		−	0.0354633i	0.999843	−	0.0177316i	$-0.00564445\pi$
$242$	−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	$-0.691930\pi$
$251$		−	26.0984i		−	1.64731i	0.567088	−	0.823657i	$-0.308070\pi$
$252$	−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	$0.265026\pi$
$257$			23.7161i			1.47937i	−0.672952	+	0.739686i	$0.734974\pi$
$258$	−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	$0.161175\pi$
$263$			15.7303i			0.969970i	−0.874522	+	0.484985i	$0.838825\pi$
$264$	−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	$0.343289\pi$
$277$			29.3334i			1.76248i	−0.472673	+	0.881238i	$0.656711\pi$
$278$	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	$-0.817819\pi$
$283$		−	18.2222i		−	1.08320i	0.840637	−	0.541599i	$-0.182181\pi$
$284$	−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	$0.0359101\pi$
$307$			3.94497i			0.225151i	−0.993643	+	0.112576i	$0.964090\pi$
$308$	−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	$-0.907036\pi$
$313$		−	10.1877i		−	0.575844i	0.957654	−	0.287922i	$-0.0929645\pi$
$314$	−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	$-0.953987\pi$
$317$		−	5.12951i		−	0.288102i	0.989570	−	0.144051i	$-0.0460130\pi$
$318$	−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	$0.334814\pi$
$353$			32.6293i			1.73668i	−0.495967	+	0.868342i	$0.665186\pi$
$354$	−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	$0.120976\pi$
$359$			14.0579i			0.741947i	−0.928643	+	0.370973i	$0.879024\pi$
$360$	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	$0.0788362\pi$
$373$			9.46915i			0.490294i	−0.969486	+	0.245147i	$0.921164\pi$
$374$	−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	$-0.789526\pi$
$389$		−	24.2232i		−	1.22816i	0.789242	−	0.614082i	$-0.210474\pi$
$390$	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	$-0.877571\pi$
$409$		−	15.1763i		−	0.750420i	0.926940	−	0.375210i	$-0.122429\pi$
$410$	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	$-0.815788\pi$
$419$		−	22.3917i		−	1.09391i	0.837163	−	0.546953i	$-0.184212\pi$
$420$	17.9372	+	12.9173i	0.875248	+	0.630301i
$421$		−	6.95017i		−	0.338731i	−0.985553	−	0.169365i	$-0.945828\pi$
$421$		−	6.95017i		−	0.338731i	0.985553	−	0.169365i	$-0.0541718\pi$
$422$	−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	$-0.860735\pi$
$431$		−	17.5920i		−	0.847378i	0.905808	−	0.423689i	$-0.139265\pi$
$432$	7.78437	+	15.7934i	0.374526	+	0.759860i
$433$		−	12.7562i		−	0.613025i	−0.951867	−	0.306512i	$-0.900838\pi$
$433$		−	12.7562i		−	0.613025i	0.951867	−	0.306512i	$-0.0991620\pi$
$434$	−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	$-0.808668\pi$
$463$		−	24.3379i		−	1.13108i	0.824721	−	0.565539i	$-0.191332\pi$
$464$	−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	$0.237897\pi$
$467$			29.3776i			1.35943i	−0.733476	+	0.679716i	$0.762103\pi$
$468$	−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	$-0.811912\pi$
$487$		−	24.5884i		−	1.11421i	0.830443	−	0.557104i	$-0.188088\pi$
$488$	−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	$0.130071\pi$
$521$			18.1395i			0.794706i	−0.917666	+	0.397353i	$0.869929\pi$
$522$	5.25983	+	4.17494i	0.230217	+	0.182732i
$523$			26.7276i			1.16872i	0.811496	+	0.584358i	$0.198654\pi$
$523$			26.7276i			1.16872i	−0.811496	+	0.584358i	$0.801346\pi$
$524$	−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	$0.247829\pi$
$541$			32.6687i			1.40454i	−0.711912	+	0.702268i	$0.752171\pi$
$542$	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	$0.0828821\pi$
$557$			12.1520i			0.514899i	−0.966292	+	0.257449i	$0.917118\pi$
$558$	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	$0.264017\pi$
$563$			35.0006i			1.47510i	−0.675293	+	0.737549i	$0.735983\pi$
$564$	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	$-0.902106\pi$
$577$		−	14.5431i		−	0.605438i	0.953080	−	0.302719i	$-0.0978944\pi$
$578$	−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	$-0.853834\pi$
$587$		−	21.4770i		−	0.886451i	0.896410	−	0.443226i	$-0.146166\pi$
$588$	−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	$-0.974508\pi$
$593$		−	3.89623i		−	0.159999i	0.996795	−	0.0799994i	$-0.0254919\pi$
$594$	−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	$-0.734422\pi$
$599$		−	36.2640i		−	1.48171i	0.671667	−	0.740853i	$-0.265578\pi$
$600$	−0.711244	+	1.50319i	−0.0290364	+	0.0613677i
$601$			25.1481i			1.02581i	0.858445	+	0.512906i	$0.171431\pi$
$601$			25.1481i			1.02581i	−0.858445	+	0.512906i	$0.828569\pi$
$602$	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	$0.0819844\pi$
$613$			12.6133i			0.509447i	−0.967014	+	0.254723i	$0.918016\pi$
$614$	−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	$0.401511\pi$
$619$			47.3965i			1.90502i	−0.304500	+	0.952512i	$0.598489\pi$
$620$	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	$0.0681749\pi$
$631$			10.6781i			0.425088i	−0.977151	+	0.212544i	$0.931825\pi$
$632$	−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	$0.0852831\pi$
$643$			13.4258i			0.529462i	−0.964322	+	0.264731i	$0.914717\pi$
$644$	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	$-0.883852\pi$
$653$		−	18.2377i		−	0.713695i	0.934163	−	0.356847i	$-0.116148\pi$
$654$	−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	$-0.903874\pi$
$691$		−	15.6365i		−	0.594842i	0.954746	−	0.297421i	$-0.0961265\pi$
$692$	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	$0.0364790\pi$
$701$			6.05523i			0.228703i	−0.993440	+	0.114351i	$0.963521\pi$
$702$	−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	$0.0639969\pi$
$709$			10.6349i			0.399401i	−0.979857	+	0.199701i	$0.936003\pi$
$710$	−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	$0.293302\pi$
$743$			43.4204i			1.59294i	−0.604678	+	0.796470i	$0.706698\pi$
$744$	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	$0.0677003\pi$
$751$			11.5694i			0.422174i	−0.977467	+	0.211087i	$0.932300\pi$
$752$	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	$0.0194671\pi$
$757$			3.36324i			0.122239i	−0.998130	+	0.0611196i	$0.980533\pi$
$758$	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	$-0.825648\pi$
$761$		−	28.7317i		−	1.04152i	0.853702	−	0.520761i	$-0.174352\pi$
$762$	−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	$0.200907\pi$
$769$			32.7273i			1.18018i	−0.807338	+	0.590089i	$0.799093\pi$
$770$	−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	$0.0326979\pi$
$787$			5.75339i			0.205086i	−0.994729	+	0.102543i	$0.967302\pi$
$788$	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	$0.0583749\pi$
$811$			10.3867i			0.364728i	−0.983231	+	0.182364i	$0.941625\pi$
$812$	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	$-0.850675\pi$
$821$		−	25.9082i		−	0.904202i	0.891967	−	0.452101i	$-0.149325\pi$
$822$	−21.4424	−	17.0197i	−0.747890	−	0.593631i
$823$			32.7107i			1.14022i	0.821567	+	0.570112i	$0.193100\pi$
$823$			32.7107i			1.14022i	−0.821567	+	0.570112i	$0.806900\pi$
$824$	−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	$-0.875472\pi$
$857$		−	22.3255i		−	0.762624i	0.924446	−	0.381312i	$-0.124528\pi$
$858$	10.7672	+	8.54637i	0.367586	+	0.291768i
$859$			15.7351i			0.536873i	0.963297	+	0.268437i	$0.0865070\pi$
$859$			15.7351i			0.536873i	−0.963297	+	0.268437i	$0.913493\pi$
$860$	−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	$0.182116\pi$
$863$			31.8109i			1.08286i	−0.840747	+	0.541428i	$0.817884\pi$
$864$	−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	$-0.974614\pi$
$877$		−	4.71862i		−	0.159337i	0.996821	−	0.0796683i	$-0.0253861\pi$
$878$	−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	$0.196293\pi$
$881$			34.3311i			1.15665i	−0.815808	+	0.578323i	$0.803707\pi$
$882$	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	$-0.949885\pi$
$911$		−	9.46472i		−	0.313580i	0.987632	−	0.156790i	$-0.0501146\pi$
$912$	−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	$-0.746487\pi$
$919$		−	43.3424i		−	1.42973i	0.699261	−	0.714867i	$-0.253513\pi$
$920$	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	$0.221201\pi$
$929$			39.0336i			1.28065i	−0.768104	+	0.640325i	$0.778799\pi$
$930$	−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	$-0.666678\pi$
$937$		−	53.0178i		−	1.73202i	0.500030	−	0.866008i	$-0.333322\pi$
$938$	−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	$0.0388293\pi$
$967$			7.56789i			0.243367i	−0.992569	+	0.121683i	$0.961171\pi$
$968$	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	$-0.976650\pi$
$971$		−	4.56757i		−	0.146580i	0.997311	−	0.0732901i	$-0.0233499\pi$
$972$	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	$0.0560292\pi$
$991$			11.0252i			0.350227i	−0.984548	+	0.175114i	$0.943971\pi$
$992$	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.27.14	yes	48
4.3	odd	2		2912.2.h.a.2575.38		48
7.6	odd	2		728.2.h.b.27.14	yes	48
8.3	odd	2		728.2.h.b.27.13	yes	48
8.5	even	2		2912.2.h.b.2575.38		48
28.27	even	2		2912.2.h.b.2575.11		48
56.13	odd	2		2912.2.h.a.2575.11		48
56.27	even	2	inner	728.2.h.a.27.13	✓	48

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