LMFDB - Embedded newform 728.2.h.b.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.b.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} +(-0.677869 - 3.67974i) 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} +(4.67200 + 2.48443i) 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} +(7.09409 - 1.30685i) 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} +(-6.85968 + 2.99078i) 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} +(-1.46881 - 7.97327i) 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} +(-4.78967 + 9.00705i) 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} +(8.51352 + 5.05173i) 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} - 6 q^{14} + 5 q^{16} - 15 q^{18} + 22 q^{20} - 6 q^{22} + 48 q^{25} + q^{26} - 26 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 - 6 * q^14 + 5 * q^16 - 15 * q^18 + 22 * q^20 - 6 * q^22 + 48 * q^25 + q^26 - 26 * q^28 - 26 * q^30 - 19 * q^32 - 36 * q^34 + 12 * q^35 - 5 * q^36 + 10 * q^38 + 48 * q^40 + 39 * 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 - 14 * 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 - 37 * 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 - 45 * q^84 + 2 * q^86 + 40 * q^87 - 66 * q^88 - 74 * q^90 - 24 * q^92 + 26 * q^94 + 84 * q^96 - 20 * 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	$-0.338997\pi$
$5$	2.16680			0.969023			0.484512	+	0.874785i	$0.338997\pi$
$6$	−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
$14$	−0.677869	−	3.67974i	−0.181168	−	0.983452i
$15$			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	$0.129757\pi$
$23$			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
$28$	4.67200	+	2.48443i	0.882926	+	0.469513i
$29$			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	$-0.783573\pi$
$31$	−8.65921			−1.55524			−0.777620	+	0.628734i	$0.783573\pi$
$32$	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	$-0.836043\pi$
$41$		−	6.30848i		−	0.985218i	0.870251	−	0.492609i	$-0.163957\pi$
$42$	7.09409	−	1.30685i	1.09464	−	0.201651i
$43$	−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	$-0.451284\pi$
$47$	2.09029			0.304900			0.152450	+	0.988311i	$0.451284\pi$
$48$	−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
$56$	−6.85968	+	2.99078i	−0.916664	+	0.399659i
$57$	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	$-0.459856\pi$
$61$	1.96479			0.251566			0.125783	+	0.992058i	$0.459856\pi$
$62$	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
$70$	−1.46881	−	7.97327i	−0.175556	−	0.952988i
$71$		−	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	$0.0389981\pi$
$73$			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	$0.0138398\pi$
$79$			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	$-0.903884\pi$
$83$		−	5.41871i		−	0.594781i	0.954756	−	0.297390i	$-0.0961163\pi$
$84$	−4.78967	+	9.00705i	−0.522596	+	0.982750i
$85$			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	$0.959691\pi$
$98$	8.51352	+	5.05173i	0.859995	+	0.510302i
$99$	3.61369			0.363189
$100$	0.138442	+	0.594024i	0.0138442	+	0.0594024i
$101$	17.2080			1.71226			0.856131	−	0.516759i	$-0.172862\pi$
$101$	17.2080			1.71226			0.856131	+	0.516759i	$0.172862\pi$
$102$	1.16590	−	1.46886i	0.115441	−	0.145439i
$103$	7.58040			0.746919			0.373460	−	0.927646i	$-0.378171\pi$
$103$	7.58040			0.746919			0.373460	+	0.927646i	$0.378171\pi$
$104$	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
$112$	2.71831	−	10.2279i	0.256856	−	0.966450i
$113$	−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
$126$	0.485837	+	2.63732i	0.0432818	+	0.234951i
$127$			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	$0.181029\pi$
$131$			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	$0.592295\pi$
$140$	10.1233	+	5.38326i	0.855575	+	0.454969i
$141$			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
$154$	3.41783	+	18.5534i	0.275417	+	1.49507i
$155$	−18.7628			−1.50706
$156$	3.75512	−	0.875162i	0.300650	−	0.0700690i
$157$	−12.5958			−1.00525			−0.502626	−	0.864504i	$-0.667633\pi$
$157$	−12.5958			−1.00525			−0.502626	+	0.864504i	$0.667633\pi$
$158$	−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	$-0.418862\pi$
$167$	6.51701			0.504302			0.252151	+	0.967688i	$0.418862\pi$
$168$	−5.76585	−	13.2246i	−0.444845	−	1.02030i
$169$	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	$-0.187949\pi$
$173$	21.8519			1.66137			0.830686	+	0.556742i	$0.187949\pi$
$174$	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	$-0.380191\pi$
$181$	9.89018			0.735132			0.367566	+	0.929998i	$0.380191\pi$
$182$	−0.677869	−	3.67974i	−0.0502470	−	0.272761i
$183$			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
$196$	−13.0810	+	4.98876i	−0.934356	+	0.356340i
$197$			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	$-0.338254\pi$
$199$	13.7274			0.973109			0.486554	+	0.873650i	$0.338254\pi$
$200$	−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
$210$	15.3715	−	2.83168i	1.06073	−	0.195404i
$211$	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	$-0.385391\pi$
$223$	10.5227			0.704650			0.352325	+	0.935878i	$0.385391\pi$
$224$	8.93939	+	12.0036i	0.597288	+	0.802027i
$225$	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	$-0.389779\pi$
$229$	10.2718			0.678779			0.339390	+	0.940646i	$0.389779\pi$
$230$	−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
$238$	2.53105	−	0.466261i	0.164064	−	0.0302232i
$239$		−	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	$0.00564445\pi$
$241$			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	$0.691930\pi$
$252$	−3.34848	−	1.78062i	−0.210935	−	0.112169i
$253$		−	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	$0.161175\pi$
$263$			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
$266$	−4.03363	+	0.743062i	−0.247318	+	0.0455600i
$267$	−7.04276			−0.431010
$268$	−6.15367	−	26.4040i	−0.375895	−	1.61288i
$269$	−26.9053			−1.64045			−0.820223	−	0.572043i	$-0.806151\pi$
$269$	−26.9053			−1.64045			−0.820223	+	0.572043i	$0.806151\pi$
$270$	−10.5652	−	8.38602i	−0.642977	−	0.510357i
$271$	23.7291			1.44144			0.720720	−	0.693226i	$-0.243811\pi$
$271$	23.7291			1.44144			0.720720	+	0.693226i	$0.243811\pi$
$272$	−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
$280$	−14.8636	+	6.48042i	−0.888268	+	0.387279i
$281$	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	$-0.405262\pi$
$293$	10.0394			0.586508			0.293254	+	0.956034i	$0.405262\pi$
$294$	−9.73912	+	16.4130i	−0.567997	+	0.957227i
$295$		−	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	$-0.0359101\pi$
$308$	−23.5564	−	12.5266i	−1.34225	−	0.713767i
$309$			14.6141i			0.831367i
$310$	16.4966	−	20.7834i	0.936944	−	1.18042i
$311$	−17.3290			−0.982640			−0.491320	−	0.870979i	$-0.663485\pi$
$311$	−17.3290			−0.982640			−0.491320	+	0.870979i	$0.663485\pi$
$312$	−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	$-0.953987\pi$
$317$		−	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
$322$	13.9925	−	2.57765i	0.779772	−	0.143647i
$323$	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
$336$	19.7182	+	5.24057i	1.07572	+	0.285896i
$337$	−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	$-0.711255\pi$
$349$	−23.0163			−1.23203			−0.616017	+	0.787733i	$0.711255\pi$
$350$	0.206731	+	1.12222i	0.0110502	+	0.0599850i
$351$			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	$0.120976\pi$
$359$			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
$364$	4.67200	+	2.48443i	0.244880	+	0.130219i
$365$			4.52498i			0.236849i
$366$	−4.19580	−	3.33037i	−0.219318	−	0.174081i
$367$	13.8941			0.725266			0.362633	−	0.931932i	$-0.381878\pi$
$367$	13.8941			0.725266			0.362633	+	0.931932i	$0.381878\pi$
$368$	−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
$378$	16.1978	−	2.98391i	0.833127	−	0.153476i
$379$	−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	$-0.708868\pi$
$383$	−23.8795			−1.22019			−0.610093	+	0.792330i	$0.708868\pi$
$384$	−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
$392$	5.97504	−	18.8759i	0.301785	−	0.953376i
$393$	−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	$-0.293234\pi$
$397$	24.1030			1.20969			0.604847	+	0.796342i	$0.293234\pi$
$398$	−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
$406$	24.3796	−	4.49112i	1.20994	−	0.222890i
$407$		−	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	$0.815788\pi$
$420$	−10.3783	+	19.5165i	−0.506408	+	0.952307i
$421$		−	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	$0.0991620\pi$
$433$			12.7562i			0.613025i	−0.951867	+	0.306512i	$0.900838\pi$
$434$	5.86981	+	31.8637i	0.281760	+	1.52951i
$435$	−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	$-0.899162\pi$
$439$	−39.8195			−1.90048			−0.950240	+	0.311518i	$0.899162\pi$
$440$	−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
$448$	−21.1560	−	0.651741i	−0.999526	−	0.0307919i
$449$	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	$-0.602152\pi$
$461$	−13.5455			−0.630878			−0.315439	+	0.948946i	$0.602152\pi$
$462$	−35.7686	+	6.58917i	−1.66411	+	0.306556i
$463$		−	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	$-0.762103\pi$
$467$		−	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
$476$	−1.70887	+	3.21356i	−0.0783261	+	0.147293i
$477$		−	2.07353i		−	0.0949406i
$478$	6.43808	+	5.11017i	0.294471	+	0.233734i
$479$	2.86853			0.131066			0.0655332	−	0.997850i	$-0.479125\pi$
$479$	2.86853			0.131066			0.0655332	+	0.997850i	$0.479125\pi$
$480$	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
$490$	18.4471	+	10.9461i	0.833355	+	0.494494i
$491$	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	$-0.480917\pi$
$503$	2.68750			0.119830			0.0599148	+	0.998203i	$0.480917\pi$
$504$	4.91642	−	2.14353i	0.218995	−	0.0954803i
$505$	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	$-0.459825\pi$
$509$	5.67996			0.251760			0.125880	+	0.992045i	$0.459825\pi$
$510$	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
$518$	34.0376	−	6.27029i	1.49553	−	0.275501i
$519$			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
$532$	2.72336	−	5.12133i	0.118073	−	0.222038i
$533$		−	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
$546$	7.09409	−	1.30685i	0.303599	−	0.0559279i
$547$	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
$560$	5.89004	−	22.1619i	0.248899	−	0.936512i
$561$	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
$574$	−23.2136	+	4.27632i	−0.968915	+	0.178490i
$575$		−	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	$0.853834\pi$
$588$	−9.61772	−	25.2185i	−0.396628	−	1.04000i
$589$			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	$-0.734422\pi$
$599$		−	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	$-0.828569\pi$
$601$		−	25.1481i		−	1.02581i	0.858445	−	0.512906i	$-0.171431\pi$
$602$	2.21950	+	12.0483i	0.0904599	+	0.491052i
$603$	−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	$-0.604060\pi$
$607$	−15.8233			−0.642247			−0.321123	+	0.947037i	$0.604060\pi$
$608$	−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
$616$	34.5867	−	15.0796i	1.39354	−	0.607574i
$617$	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
$630$	1.05271	+	5.71454i	0.0419411	+	0.227673i
$631$			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	$-0.914717\pi$
$643$		−	13.4258i		−	0.529462i	0.964322	−	0.264731i	$-0.0852831\pi$
$644$	−9.44723	+	17.7657i	−0.372273	+	0.700065i
$645$		−	13.6775i		−	0.538552i
$646$	−0.662917	+	0.835181i	−0.0260821	+	0.0328598i
$647$	−17.7213			−0.696698			−0.348349	−	0.937365i	$-0.613258\pi$
$647$	−17.7213			−0.696698			−0.348349	+	0.937365i	$0.613258\pi$
$648$	−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
$658$	−1.41694	−	7.69173i	−0.0552382	−	0.299855i
$659$	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	$-0.562543\pi$
$661$	−10.0383			−0.390444			−0.195222	+	0.980759i	$0.562543\pi$
$662$	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
$672$	−23.1415	+	17.2341i	−0.892704	+	0.664818i
$673$	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	$-0.426744\pi$
$677$	11.8708			0.456231			0.228115	+	0.973634i	$0.426744\pi$
$678$	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
$686$	−24.8821	+	8.17809i	−0.950003	+	0.312241i
$687$			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
$700$	−1.42483	−	0.757680i	−0.0538535	−	0.0286376i
$701$			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
$714$	0.898894	+	4.87955i	0.0336403	+	0.182613i
$715$	−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	$-0.536999\pi$
$719$	−6.21956			−0.231950			−0.115975	+	0.993252i	$0.536999\pi$
$720$	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	$-0.334963\pi$
$727$	26.7235			0.991118			0.495559	+	0.868574i	$0.334963\pi$
$728$	−6.85968	+	2.99078i	−0.254237	+	0.110845i
$729$	−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	$-0.632712\pi$
$733$	−21.9273			−0.809905			−0.404953	+	0.914338i	$0.632712\pi$
$734$	−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
$742$	10.6459	−	1.96115i	0.390824	−	0.0719962i
$743$			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
$756$	−10.9362	+	20.5657i	−0.397746	+	0.747967i
$757$			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	$0.174352\pi$
$761$			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	$-0.200907\pi$
$770$	7.40577	+	40.2015i	0.266885	+	1.44876i
$771$	45.7218			1.64663
$772$	10.5056	+	45.0771i	0.378104	+	1.62236i
$773$	−1.68151			−0.0604796			−0.0302398	−	0.999543i	$-0.509627\pi$
$773$	−1.68151			−0.0604796			−0.0302398	+	0.999543i	$0.509627\pi$
$774$	−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
$784$	15.6552	+	23.2145i	0.559116	+	0.829090i
$785$	−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	$-0.503179\pi$
$797$	−0.563854			−0.0199727			−0.00998636	+	0.999950i	$0.503179\pi$
$798$	−1.43253	−	7.77635i	−0.0507111	−	0.275280i
$799$			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	$-0.0583749\pi$
$812$	−16.4602	+	30.9537i	−0.577640	+	1.08626i
$813$			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
$826$	−42.8625	+	7.89598i	−1.49138	+	0.274736i
$827$	−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	$-0.917916\pi$
$829$	−55.6806			−1.93387			−0.966934	+	0.255027i	$0.917916\pi$
$830$	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	$-0.649493\pi$
$839$	−26.2179			−0.905142			−0.452571	+	0.891728i	$0.649493\pi$
$840$	−12.4934	−	28.6552i	−0.431065	−	0.988697i
$841$	−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	$-0.332175\pi$
$853$	29.3901			1.00630			0.503149	+	0.864200i	$0.332175\pi$
$854$	−1.33187	−	7.22993i	−0.0455757	−	0.247403i
$855$			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	$0.182116\pi$
$863$			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
$868$	−40.4559	−	21.5132i	−1.37316	−	0.730205i
$869$		−	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	$-0.803707\pi$
$881$		−	34.3311i		−	1.15665i	0.815808	−	0.578323i	$-0.196293\pi$
$882$	−6.10175	−	3.62064i	−0.205457	−	0.121913i
$883$	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	$-0.370861\pi$
$887$	23.5082			0.789328			0.394664	+	0.918825i	$0.370861\pi$
$888$	−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
$896$	19.3226	−	22.8612i	0.645524	−	0.763740i
$897$	−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
$910$	−1.46881	−	7.97327i	−0.0486905	−	0.264311i
$911$		−	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
$924$	24.1497	−	45.4138i	0.794466	−	1.49401i
$925$		−	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	$0.666678\pi$
$938$	−9.18905	−	49.8819i	−0.300033	−	1.62870i
$939$	−19.6407			−0.640950
$940$	−2.05606	−	8.82207i	−0.0670612	−	0.287744i
$941$	16.8743			0.550087			0.275044	−	0.961432i	$-0.411308\pi$
$941$	16.8743			0.550087			0.275044	+	0.961432i	$0.411308\pi$
$942$	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
$952$	−2.05716	−	4.71832i	−0.0666728	−	0.152922i
$953$	−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
$966$	4.96939	+	26.9758i	0.159888	+	0.867933i
$967$			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	$0.0233499\pi$
$971$			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
$980$	−28.3439	+	10.8097i	−0.905413	+	0.345302i
$981$		−	6.05499i		−	0.193321i
$982$	−35.8048	+	45.1090i	−1.14258	+	1.43949i
$983$	−17.4575			−0.556809			−0.278404	−	0.960464i	$-0.589805\pi$
$983$	−17.4575			−0.556809			−0.278404	+	0.960464i	$0.589805\pi$
$984$	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
$994$	−18.6696	+	3.43925i	−0.592165	+	0.109086i
$995$	29.7445			0.942965
$996$	−4.74225	−	20.3479i	−0.150264	−	0.644749i
$997$	5.72166			0.181207			0.0906033	−	0.995887i	$-0.471120\pi$
$997$	5.72166			0.181207			0.0906033	+	0.995887i	$0.471120\pi$
$998$	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.b.27.14	yes	48
4.3	odd	2		2912.2.h.b.2575.11		48
7.6	odd	2		728.2.h.a.27.14	yes	48
8.3	odd	2		728.2.h.a.27.13	✓	48
8.5	even	2		2912.2.h.a.2575.11		48
28.27	even	2		2912.2.h.a.2575.38		48
56.13	odd	2		2912.2.h.b.2575.38		48
56.27	even	2	inner	728.2.h.b.27.13	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.h.a.27.13	✓	48	8.3	odd	2
728.2.h.a.27.14	yes	48	7.6	odd	2
728.2.h.b.27.13	yes	48	56.27	even	2	inner
728.2.h.b.27.14	yes	48	1.1	even	1	trivial
2912.2.h.a.2575.11		48	8.5	even	2
2912.2.h.a.2575.38		48	28.27	even	2
2912.2.h.b.2575.11		48	4.3	odd	2
2912.2.h.b.2575.38		48	56.13	odd	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} +(-0.677869 - 3.67974i) 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} +(4.67200 + 2.48443i) 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} +(7.09409 - 1.30685i) 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} +(-6.85968 + 2.99078i) 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} +(-1.46881 - 7.97327i) 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} +(-4.78967 + 9.00705i) 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} +(8.51352 + 5.05173i) q^{98} +3.61369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + q^{4} + 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} - 10 q^{12} + 48 q^{13} - 6 q^{14} + 5 q^{16} - 15 q^{18} + 22 q^{20} - 6 q^{22} + 48 q^{25} + q^{26} - 26 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) \) 48 * q + q^2 + q^4 + 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 - 10 * q^12 + 48 * q^13 - 6 * q^14 + 5 * q^16 - 15 * q^18 + 22 * q^20 - 6 * q^22 + 48 * q^25 + q^26 - 26 * q^28 - 26 * q^30 - 19 * q^32 - 36 * q^34 + 12 * q^35 - 5 * q^36 + 10 * q^38 + 48 * q^40 + 39 * 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 - 14 * 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 - 37 * 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 - 45 * q^84 + 2 * q^86 + 40 * q^87 - 66 * q^88 - 74 * q^90 - 24 * q^92 + 26 * q^94 + 84 * q^96 - 20 * 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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