LMFDB - Embedded newform 570.2.bb.b.71.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(41,570)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 13]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("570.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.6
Character	$\chi$	$=$	570.71
Dual form			570.2.bb.b.281.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-0.936498 + 1.45704i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(-0.381683 + 1.68947i) q^{6} +(0.199417 + 0.345401i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.24594 - 2.72903i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-0.936498 + 1.45704i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(-0.381683 + 1.68947i) q^{6} +(0.199417 + 0.345401i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.24594 - 2.72903i) q^{9} +(0.342020 - 0.939693i) q^{10} +(1.04385 + 0.602667i) q^{11} +(0.219169 + 1.71813i) q^{12} +(5.94640 - 1.04851i) q^{13} +(0.305525 + 0.256366i) q^{14} +(0.514190 + 1.65397i) q^{15} +(0.173648 - 0.984808i) q^{16} +(2.60171 + 7.14815i) q^{17} +(-2.10419 - 2.13832i) q^{18} +(-0.407328 - 4.33983i) q^{19} -1.00000i q^{20} +(-0.690017 - 0.0329079i) q^{21} +(1.18702 + 0.209304i) q^{22} +(-0.580645 - 0.691985i) q^{23} +(0.793586 + 1.53955i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(5.22918 - 3.01907i) q^{26} +(5.14314 + 0.740344i) q^{27} +(0.374782 + 0.136409i) q^{28} +(8.41934 + 3.06439i) q^{29} +(1.04887 + 1.37836i) q^{30} +(-8.69322 + 5.01903i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-1.85567 + 0.956536i) q^{33} +(4.88962 + 5.82722i) q^{34} +(0.392775 + 0.0692569i) q^{35} +(-2.70864 - 1.28968i) q^{36} -2.95480i q^{37} +(-1.86707 - 3.93879i) q^{38} +(-4.04107 + 9.64609i) q^{39} +(-0.342020 - 0.939693i) q^{40} +(-1.28067 + 7.26306i) q^{41} +(-0.659659 + 0.205076i) q^{42} +(-2.64638 - 2.22057i) q^{43} +(1.18702 - 0.209304i) q^{44} +(-2.89144 - 0.799742i) q^{45} +(-0.782300 - 0.451661i) q^{46} +(2.32122 - 6.37750i) q^{47} +(1.27229 + 1.17528i) q^{48} +(3.42047 - 5.92442i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-12.8516 - 2.90342i) q^{51} +(3.88124 - 4.62548i) q^{52} +(-1.26980 + 1.06549i) q^{53} +(5.08618 - 1.06336i) q^{54} +(1.13264 - 0.412248i) q^{55} +0.398834 q^{56} +(6.70477 + 3.47074i) q^{57} +8.95967 q^{58} +(1.71773 - 0.625203i) q^{59} +(1.45704 + 0.936498i) q^{60} +(-3.85349 + 3.23346i) q^{61} +(-6.45234 + 7.68961i) q^{62} +(0.694148 - 0.974566i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.01907 - 5.22918i) q^{65} +(-1.41661 + 1.53353i) q^{66} +(2.62828 - 7.22115i) q^{67} +(6.58777 + 3.80345i) q^{68} +(1.55202 - 0.197981i) q^{69} +(0.392775 - 0.0692569i) q^{70} +(-4.35941 - 3.65798i) q^{71} +(-2.98638 - 0.285499i) q^{72} +(1.57158 - 8.91285i) q^{73} +(-1.01060 - 2.77660i) q^{74} +(1.59753 + 0.669258i) q^{75} +(-3.10162 - 3.06267i) q^{76} +0.480728i q^{77} +(-0.498207 + 10.4465i) q^{78} +(-12.3197 - 2.17230i) q^{79} +(-0.642788 - 0.766044i) q^{80} +(-5.89525 + 6.80044i) q^{81} +(1.28067 + 7.26306i) q^{82} +(-14.3878 + 8.30678i) q^{83} +(-0.549737 + 0.418326i) q^{84} +(7.14815 + 2.60171i) q^{85} +(-3.24626 - 1.18154i) q^{86} +(-12.3496 + 9.39753i) q^{87} +(1.04385 - 0.602667i) q^{88} +(-0.549214 - 3.11475i) q^{89} +(-2.99059 + 0.237419i) q^{90} +(1.54797 + 1.84480i) q^{91} +(-0.889599 - 0.156860i) q^{92} +(0.828242 - 17.3667i) q^{93} -6.78679i q^{94} +(-3.58632 - 2.47755i) q^{95} +(1.59753 + 0.669258i) q^{96} +(-3.27059 - 8.98586i) q^{97} +(1.18792 - 6.73700i) q^{98} +(0.344122 - 3.59959i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) $ 84 * q - 6 * q^6 + 42 * q^8	$ 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) $ 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$1$

Coefficient data

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

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

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

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−0.936498	+	1.45704i	−0.540687	+	0.841224i
$3$	−0.936498	+	1.45704i	−0.540687	+	0.841224i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.642788	−	0.766044i	0.287463	−	0.342585i
$5$	0.642788	−	0.766044i	0.287463	−	0.342585i
$6$	−0.381683	+	1.68947i	−0.155821	+	0.689724i
$7$	0.199417	+	0.345401i	0.0753726	+	0.130549i	0.901248	−	0.433303i	$-0.142652\pi$
$7$	0.199417	+	0.345401i	0.0753726	+	0.130549i	−0.825876	+	0.563852i	$0.809319\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−1.24594	−	2.72903i	−0.415314	−	0.909678i
$10$	0.342020	−	0.939693i	0.108156	−	0.297157i
$11$	1.04385	+	0.602667i	0.314732	+	0.181711i	0.649042	−	0.760752i	$-0.275170\pi$
$11$	1.04385	+	0.602667i	0.314732	+	0.181711i	−0.334310	+	0.942463i	$0.608503\pi$
$12$	0.219169	+	1.71813i	0.0632688	+	0.495981i
$13$	5.94640	−	1.04851i	1.64924	−	0.290805i	0.729687	−	0.683781i	$-0.239666\pi$
$13$	5.94640	−	1.04851i	1.64924	−	0.290805i	0.919549	+	0.392977i	$0.128555\pi$
$14$	0.305525	+	0.256366i	0.0816549	+	0.0685166i
$15$	0.514190	+	1.65397i	0.132763	+	0.427053i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	2.60171	+	7.14815i	0.631008	+	1.73368i	0.678285	+	0.734799i	$0.262723\pi$
$17$	2.60171	+	7.14815i	0.631008	+	1.73368i	−0.0472773	+	0.998882i	$0.515054\pi$
$18$	−2.10419	−	2.13832i	−0.495962	−	0.504006i
$19$	−0.407328	−	4.33983i	−0.0934475	−	0.995624i
$19$	−0.407328	−	4.33983i	−0.0934475	−	0.995624i
$20$		−	1.00000i		−	0.223607i
$21$	−0.690017	−	0.0329079i	−0.150574	−	0.00718109i
$22$	1.18702	+	0.209304i	0.253074	+	0.0446238i
$23$	−0.580645	−	0.691985i	−0.121073	−	0.144289i	0.702103	−	0.712075i	$-0.252244\pi$
$23$	−0.580645	−	0.691985i	−0.121073	−	0.144289i	−0.823176	+	0.567786i	$0.807800\pi$
$24$	0.793586	+	1.53955i	0.161990	+	0.314260i
$25$	−0.173648	−	0.984808i	−0.0347296	−	0.196962i
$26$	5.22918	−	3.01907i	1.02553	−	0.592088i
$27$	5.14314	+	0.740344i	0.989798	+	0.142479i
$28$	0.374782	+	0.136409i	0.0708271	+	0.0257789i
$29$	8.41934	+	3.06439i	1.56343	+	0.569042i	0.971519	−	0.236960i	$-0.0761511\pi$
$29$	8.41934	+	3.06439i	1.56343	+	0.569042i	0.591912	+	0.806003i	$0.298373\pi$
$30$	1.04887	+	1.37836i	0.191497	+	0.251653i
$31$	−8.69322	+	5.01903i	−1.56135	+	0.901445i	−0.564227	+	0.825619i	$0.690826\pi$
$31$	−8.69322	+	5.01903i	−1.56135	+	0.901445i	−0.997121	+	0.0758256i	$0.975841\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−1.85567	+	0.956536i	−0.323031	+	0.166512i
$34$	4.88962	+	5.82722i	0.838563	+	0.999361i
$35$	0.392775	+	0.0692569i	0.0663911	+	0.0117065i
$36$	−2.70864	−	1.28968i	−0.451439	−	0.214947i
$37$		−	2.95480i		−	0.485766i	−0.970056	−	0.242883i	$-0.921907\pi$
$37$		−	2.95480i		−	0.485766i	0.970056	−	0.242883i	$-0.0780931\pi$
$38$	−1.86707	−	3.93879i	−0.302879	−	0.638956i
$39$	−4.04107	+	9.64609i	−0.647089	+	1.54461i
$40$	−0.342020	−	0.939693i	−0.0540781	−	0.148578i
$41$	−1.28067	+	7.26306i	−0.200008	+	1.13430i	0.705097	+	0.709111i	$0.250903\pi$
$41$	−1.28067	+	7.26306i	−0.200008	+	1.13430i	−0.905105	+	0.425189i	$0.860208\pi$
$42$	−0.659659	+	0.205076i	−0.101788	+	0.0316440i
$43$	−2.64638	−	2.22057i	−0.403569	−	0.338634i	0.418302	−	0.908308i	$-0.362625\pi$
$43$	−2.64638	−	2.22057i	−0.403569	−	0.338634i	−0.821871	+	0.569673i	$0.807070\pi$
$44$	1.18702	−	0.209304i	0.178950	−	0.0315538i
$45$	−2.89144	−	0.799742i	−0.431030	−	0.119218i
$46$	−0.782300	−	0.451661i	−0.115344	−	0.0665938i
$47$	2.32122	−	6.37750i	0.338585	−	0.930254i	−0.647212	−	0.762310i	$-0.724065\pi$
$47$	2.32122	−	6.37750i	0.338585	−	0.930254i	0.985797	−	0.167944i	$-0.0537127\pi$
$48$	1.27229	+	1.17528i	0.183639	+	0.169638i
$49$	3.42047	−	5.92442i	0.488638	−	0.846346i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−12.8516	−	2.90342i	−1.79959	−	0.406560i
$52$	3.88124	−	4.62548i	0.538231	−	0.641439i
$53$	−1.26980	+	1.06549i	−0.174420	+	0.146356i	−0.725819	−	0.687886i	$-0.758539\pi$
$53$	−1.26980	+	1.06549i	−0.174420	+	0.146356i	0.551399	+	0.834242i	$0.314094\pi$
$54$	5.08618	−	1.06336i	0.692142	−	0.144705i
$55$	1.13264	−	0.412248i	0.152726	−	0.0555876i
$56$	0.398834			0.0532965
$57$	6.70477	+	3.47074i	0.888068	+	0.459711i
$58$	8.95967			1.17646
$59$	1.71773	−	0.625203i	0.223629	−	0.0813944i	−0.227776	−	0.973714i	$-0.573145\pi$
$59$	1.71773	−	0.625203i	0.223629	−	0.0813944i	0.451405	+	0.892319i	$0.350923\pi$
$60$	1.45704	+	0.936498i	0.188103	+	0.120901i
$61$	−3.85349	+	3.23346i	−0.493389	+	0.414003i	−0.855239	−	0.518234i	$-0.826590\pi$
$61$	−3.85349	+	3.23346i	−0.493389	+	0.414003i	0.361850	+	0.932236i	$0.382145\pi$
$62$	−6.45234	+	7.68961i	−0.819449	+	0.976581i
$63$	0.694148	−	0.974566i	0.0874544	−	0.122784i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	3.01907	−	5.22918i	0.374469	−	0.648600i
$66$	−1.41661	+	1.53353i	−0.174372	+	0.188764i
$67$	2.62828	−	7.22115i	0.321096	−	0.882203i	−0.669182	−	0.743099i	$-0.733355\pi$
$67$	2.62828	−	7.22115i	0.321096	−	0.882203i	0.990278	−	0.139105i	$-0.0444225\pi$
$68$	6.58777	+	3.80345i	0.798884	+	0.461236i
$69$	1.55202	−	0.197981i	0.186842	−	0.0238341i
$70$	0.392775	−	0.0692569i	0.0469456	−	0.00827778i
$71$	−4.35941	−	3.65798i	−0.517367	−	0.434123i	0.346345	−	0.938107i	$-0.387422\pi$
$71$	−4.35941	−	3.65798i	−0.517367	−	0.434123i	−0.863713	+	0.503984i	$0.831867\pi$
$72$	−2.98638	−	0.285499i	−0.351949	−	0.0336464i
$73$	1.57158	−	8.91285i	0.183939	−	1.04317i	−0.743372	−	0.668878i	$-0.766775\pi$
$73$	1.57158	−	8.91285i	0.183939	−	1.04317i	0.927311	−	0.374292i	$-0.122114\pi$
$74$	−1.01060	−	2.77660i	−0.117480	−	0.322773i
$75$	1.59753	+	0.669258i	0.184467	+	0.0772792i
$76$	−3.10162	−	3.06267i	−0.355780	−	0.351313i
$77$			0.480728i			0.0547841i
$78$	−0.498207	+	10.4465i	−0.0564109	+	1.18283i
$79$	−12.3197	−	2.17230i	−1.38608	−	0.244403i	−0.569666	−	0.821876i	$-0.692928\pi$
$79$	−12.3197	−	2.17230i	−1.38608	−	0.244403i	−0.816410	+	0.577473i	$0.804039\pi$
$80$	−0.642788	−	0.766044i	−0.0718658	−	0.0856464i
$81$	−5.89525	+	6.80044i	−0.655028	+	0.755604i
$82$	1.28067	+	7.26306i	0.141427	+	0.802071i
$83$	−14.3878	+	8.30678i	−1.57926	+	0.911787i	−0.584299	+	0.811538i	$0.698631\pi$
$83$	−14.3878	+	8.30678i	−1.57926	+	0.911787i	−0.994962	+	0.100249i	$0.968036\pi$
$84$	−0.549737	+	0.418326i	−0.0599812	+	0.0456431i
$85$	7.14815	+	2.60171i	0.775325	+	0.282195i
$86$	−3.24626	−	1.18154i	−0.350054	−	0.127409i
$87$	−12.3496	+	9.39753i	−1.32402	+	1.00752i
$88$	1.04385	−	0.602667i	0.111275	−	0.0642445i
$89$	−0.549214	−	3.11475i	−0.0582165	−	0.330162i	0.941765	−	0.336272i	$-0.109166\pi$
$89$	−0.549214	−	3.11475i	−0.0582165	−	0.330162i	−0.999981	+	0.00610996i	$0.998055\pi$
$90$	−2.99059	+	0.237419i	−0.315236	+	0.0250261i
$91$	1.54797	+	1.84480i	0.162272	+	0.193388i
$92$	−0.889599	−	0.156860i	−0.0927471	−	0.0163538i
$93$	0.828242	−	17.3667i	0.0858847	−	1.80084i
$94$		−	6.78679i		−	0.700004i
$95$	−3.58632	−	2.47755i	−0.367949	−	0.254192i
$96$	1.59753	+	0.669258i	0.163047	+	0.0683058i
$97$	−3.27059	−	8.98586i	−0.332078	−	0.912376i	−0.987571	−	0.157175i	$-0.949761\pi$
$97$	−3.27059	−	8.98586i	−0.332078	−	0.912376i	0.655493	−	0.755201i	$-0.272461\pi$
$98$	1.18792	−	6.73700i	0.119998	−	0.680540i
$99$	0.344122	−	3.59959i	0.0345855	−	0.361772i
$100$	−0.766044	−	0.642788i	−0.0766044	−	0.0642788i
$101$	−14.1996	+	2.50377i	−1.41291	+	0.249134i	−0.827438	−	0.561558i	$-0.810202\pi$
$101$	−14.1996	+	2.50377i	−1.41291	+	0.249134i	−0.585473	+	0.810692i	$0.699091\pi$
$102$	−13.0696	+	1.66720i	−1.29409	+	0.165077i
$103$	16.1061	+	9.29887i	1.58698	+	0.916245i	0.993801	+	0.111177i	$0.0354620\pi$
$103$	16.1061	+	9.29887i	1.58698	+	0.916245i	0.593182	+	0.805068i	$0.297871\pi$
$104$	2.06516	−	5.67399i	0.202506	−	0.556381i
$105$	−0.468743	+	0.507431i	−0.0457447	+	0.0495202i
$106$	−0.828801	+	1.43553i	−0.0805003	+	0.139431i
$107$	1.97816	+	3.42628i	0.191236	+	0.331231i	0.945660	−	0.325156i	$-0.105417\pi$
$107$	1.97816	+	3.42628i	0.191236	+	0.331231i	−0.754424	+	0.656388i	$0.772084\pi$
$108$	4.41576	−	2.73881i	0.424907	−	0.263542i
$109$	−7.89536	+	9.40933i	−0.756239	+	0.901250i	−0.997604	−	0.0691843i	$-0.977960\pi$
$109$	−7.89536	+	9.40933i	−0.756239	+	0.901250i	0.241365	+	0.970434i	$0.422405\pi$
$110$	0.923339	−	0.774773i	0.0880369	−	0.0738718i
$111$	4.30527	+	2.76716i	0.408638	+	0.262647i
$112$	0.374782	−	0.136409i	0.0354135	−	0.0128895i
$113$	−1.98328			−0.186571			−0.0932856	−	0.995639i	$-0.529737\pi$
$113$	−1.98328			−0.186571			−0.0932856	+	0.995639i	$0.529737\pi$
$114$	7.48749	+	0.968266i	0.701267	+	0.0906864i
$115$	−0.903323			−0.0842353
$116$	8.41934	−	3.06439i	0.781716	−	0.284521i
$117$	−10.2703	−	14.9216i	−0.949490	−	1.37950i
$118$	1.40031	−	1.17500i	0.128909	−	0.108167i
$119$	−1.95015	+	2.32410i	−0.178770	+	0.213050i
$120$	1.68947	+	0.381683i	0.154227	+	0.0348427i
$121$	−4.77359	−	8.26809i	−0.433962	−	0.751645i
$122$	−2.51519	+	4.35643i	−0.227714	+	0.394413i
$123$	−9.38324	−	8.66784i	−0.846058	−	0.781553i
$124$	−3.43322	+	9.43270i	−0.308312	+	0.847081i
$125$	−0.866025	−	0.500000i	−0.0774597	−	0.0447214i
$126$	0.318964	−	1.15320i	0.0284156	−	0.102736i
$127$	−8.72354	+	1.53820i	−0.774089	+	0.136493i	−0.546720	−	0.837316i	$-0.684124\pi$
$127$	−8.72354	+	1.53820i	−0.774089	+	0.136493i	−0.227370	+	0.973809i	$0.573013\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	5.71380	−	1.77632i	0.503072	−	0.156396i
$130$	1.04851	−	5.94640i	0.0919605	−	0.521534i
$131$	−0.624238	−	1.71508i	−0.0545399	−	0.149847i	0.909431	−	0.415855i	$-0.136518\pi$
$131$	−0.624238	−	1.71508i	−0.0545399	−	0.149847i	−0.963971	+	0.266008i	$0.914295\pi$
$132$	−0.806679	+	1.92555i	−0.0702124	+	0.167598i
$133$	1.41775	−	1.00613i	0.122935	−	0.0872423i
$134$		−	7.68458i		−	0.663847i
$135$	3.87308	−	3.46399i	0.333342	−	0.298133i
$136$	7.49133	+	1.32092i	0.642377	+	0.113268i
$137$	−4.47056	−	5.32780i	−0.381946	−	0.455185i	0.540482	−	0.841356i	$-0.318242\pi$
$137$	−4.47056	−	5.32780i	−0.381946	−	0.455185i	−0.922427	+	0.386171i	$0.873798\pi$
$138$	1.39071	−	0.716864i	0.118385	−	0.0610236i
$139$	1.96084	+	11.1205i	0.166317	+	0.943229i	0.947696	+	0.319173i	$0.103405\pi$
$139$	1.96084	+	11.1205i	0.166317	+	0.943229i	−0.781380	+	0.624056i	$0.785484\pi$
$140$	0.345401	−	0.199417i	0.0291917	−	0.0168538i
$141$	7.11847	+	9.35463i	0.599483	+	0.787802i
$142$	−5.34761	−	1.94637i	−0.448762	−	0.163336i
$143$	6.83905	+	2.48921i	0.571910	+	0.208158i
$144$	−2.90393	+	0.753122i	−0.241994	+	0.0627602i
$145$	7.75930	−	4.47983i	0.644375	−	0.372030i
$146$	−1.57158	−	8.91285i	−0.130065	−	0.737633i
$147$	5.42887	+	10.5320i	0.447766	+	0.868662i
$148$	−1.89931	−	2.26351i	−0.156122	−	0.186059i
$149$	−21.7871	−	3.84165i	−1.78487	−	0.314720i	−0.819007	−	0.573783i	$-0.805475\pi$
$149$	−21.7871	−	3.84165i	−1.78487	−	0.314720i	−0.965861	+	0.259063i	$0.916586\pi$
$150$	1.73008	+	0.0825101i	0.141261	+	0.00673692i
$151$		−	7.92494i		−	0.644922i	−0.946583	−	0.322461i	$-0.895490\pi$
$151$		−	7.92494i		−	0.644922i	0.946583	−	0.322461i	$-0.104510\pi$
$152$	−3.96206	−	1.81716i	−0.321366	−	0.147391i
$153$	16.2660	−	16.0063i	1.31502	−	1.29404i
$154$	0.164419	+	0.451737i	0.0132492	+	0.0364020i
$155$	−1.74309	+	9.88557i	−0.140009	+	0.794028i
$156$	3.10475	+	9.98688i	0.248579	+	0.799591i
$157$	6.69379	+	5.61676i	0.534222	+	0.448266i	0.869557	−	0.493833i	$-0.164405\pi$
$157$	6.69379	+	5.61676i	0.534222	+	0.448266i	−0.335334	+	0.942099i	$0.608849\pi$
$158$	−12.3197	+	2.17230i	−0.980104	+	0.172819i
$159$	−0.363296	−	2.84797i	−0.0288112	−	0.225859i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	0.123222	−	0.338549i	0.00971123	−	0.0266814i
$162$	−3.21384	+	8.40662i	−0.252503	+	0.660486i
$163$	−9.86611	+	17.0886i	−0.772773	+	1.33848i	0.163264	+	0.986582i	$0.447798\pi$
$163$	−9.86611	+	17.0886i	−0.772773	+	1.33848i	−0.936037	+	0.351900i	$0.885536\pi$
$164$	3.68755	+	6.38703i	0.287950	+	0.498743i
$165$	−0.460055	+	2.03638i	−0.0358152	+	0.158532i
$166$	−10.6790	+	12.7267i	−0.828850	+	0.987785i
$167$	8.77626	−	7.36416i	0.679128	−	0.569856i	−0.236624	−	0.971601i	$-0.576041\pi$
$167$	8.77626	−	7.36416i	0.679128	−	0.569856i	0.915751	+	0.401746i	$0.131596\pi$
$168$	−0.373508	+	0.581118i	−0.0288167	+	0.0448343i
$169$	22.0443	−	8.02348i	1.69572	−	0.617191i
$170$	7.60690			0.583423
$171$	−11.3360	+	6.51879i	−0.866887	+	0.498504i
$172$	−3.45460			−0.263411
$173$	15.7924	−	5.74797i	1.20068	−	0.437010i	0.337216	−	0.941427i	$-0.390515\pi$
$173$	15.7924	−	5.74797i	1.20068	−	0.437010i	0.863460	+	0.504417i	$0.168293\pi$
$174$	−8.39071	+	13.0546i	−0.636098	+	0.989668i
$175$	0.305525	−	0.256366i	0.0230955	−	0.0193794i
$176$	0.774773	−	0.923339i	0.0584007	−	0.0695993i
$177$	−0.697704	+	3.08831i	−0.0524427	+	0.232131i
$178$	−1.58140	−	2.73906i	−0.118531	−	0.205301i
$179$	4.45910	−	7.72338i	0.333288	−	0.577273i	−0.649866	−	0.760049i	$-0.725175\pi$
$179$	4.45910	−	7.72338i	0.333288	−	0.577273i	0.983155	+	0.182776i	$0.0585084\pi$
$180$	−2.72903	+	1.24594i	−0.203410	+	0.0928671i
$181$	−3.68150	+	10.1148i	−0.273644	+	0.751831i	0.724404	+	0.689376i	$0.242115\pi$
$181$	−3.68150	+	10.1148i	−0.273644	+	0.751831i	−0.998048	+	0.0624548i	$0.980107\pi$
$182$	2.08558	+	1.20411i	0.154593	+	0.0892544i
$183$	−1.10250	−	8.64283i	−0.0814995	−	0.638897i
$184$	−0.889599	+	0.156860i	−0.0655821	+	0.0115639i
$185$	−2.26351	−	1.89931i	−0.166416	−	0.139640i
$186$	−5.16147	−	16.6026i	−0.378457	−	1.21736i
$187$	−1.59215	+	9.02956i	−0.116430	+	0.660307i
$188$	−2.32122	−	6.37750i	−0.169292	−	0.465127i
$189$	0.769915	+	1.92408i	0.0560031	+	0.139956i
$190$	−4.21742	−	1.10154i	−0.305964	−	0.0799144i
$191$			23.0358i			1.66681i	0.552661	+	0.833406i	$0.313613\pi$
$191$			23.0358i			1.66681i	−0.552661	+	0.833406i	$0.686387\pi$
$192$	1.73008	+	0.0825101i	0.124858	+	0.00595466i
$193$	14.1721	+	2.49893i	1.02013	+	0.179877i	0.658608	−	0.752486i	$-0.271146\pi$
$193$	14.1721	+	2.49893i	1.02013	+	0.179877i	0.361523	+	0.932363i	$0.382257\pi$
$194$	−6.14669	−	7.32534i	−0.441307	−	0.525929i
$195$	4.79178	+	9.29603i	0.343147	+	0.665702i
$196$	−1.18792	−	6.73700i	−0.0848511	−	0.481214i
$197$	−15.9309	+	9.19771i	−1.13503	+	0.655310i	−0.945195	−	0.326506i	$-0.894129\pi$
$197$	−15.9309	+	9.19771i	−1.13503	+	0.655310i	−0.189835	+	0.981816i	$0.560795\pi$
$198$	−0.907764	−	3.50020i	−0.0645119	−	0.248749i
$199$	6.96454	+	2.53488i	0.493703	+	0.179693i	0.576860	−	0.816843i	$-0.304278\pi$
$199$	6.96454	+	2.53488i	0.493703	+	0.179693i	−0.0831566	+	0.996536i	$0.526500\pi$
$200$	−0.939693	−	0.342020i	−0.0664463	−	0.0241845i
$201$	8.06013	+	10.5921i	0.568518	+	0.747110i
$202$	−12.4869	+	7.20931i	−0.878575	+	0.507245i
$203$	0.620519	+	3.51914i	0.0435519	+	0.246995i
$204$	−11.7112	+	6.03673i	−0.819949	+	0.422656i
$205$	4.74063	+	5.64966i	0.331100	+	0.394589i
$206$	18.3152	+	3.22946i	1.27608	+	0.225007i
$207$	−1.16500	+	2.44677i	−0.0809732	+	0.170062i
$208$		−	6.03814i		−	0.418669i
$209$	2.19028	−	4.77561i	0.151505	−	0.330336i
$210$	−0.266923	+	0.637149i	−0.0184194	+	0.0439674i
$211$	−0.385422	−	1.05894i	−0.0265335	−	0.0729002i	0.925719	−	0.378213i	$-0.123461\pi$
$211$	−0.385422	−	1.05894i	−0.0265335	−	0.0729002i	−0.952252	+	0.305313i	$0.901239\pi$
$212$	−0.287840	+	1.63242i	−0.0197689	+	0.112115i
$213$	9.41242	−	2.92616i	0.644928	−	0.200497i
$214$	3.03072	+	2.54308i	0.207176	+	0.173841i
$215$	−3.40212	+	0.599885i	−0.232022	+	0.0409118i
$216$	3.21273	−	4.08392i	0.218598	−	0.277875i
$217$	−3.46716	−	2.00176i	−0.235366	−	0.135889i
$218$	−4.20103	+	11.5422i	−0.284530	+	0.781740i
$219$	11.5146	+	10.6367i	0.778086	+	0.718763i
$220$	0.602667	−	1.04385i	0.0406318	−	0.0703763i
$221$	22.9657	+	39.7778i	1.54484	+	2.67575i
$222$	4.99205	+	1.12780i	0.335045	+	0.0756927i
$223$	14.9082	−	17.7669i	0.998325	−	1.18976i	0.0165207	−	0.999864i	$-0.494741\pi$
$223$	14.9082	−	17.7669i	0.998325	−	1.18976i	0.981805	−	0.189894i	$-0.0608145\pi$
$224$	0.305525	−	0.256366i	0.0204137	−	0.0171292i
$225$	−2.47122	+	1.70091i	−0.164748	+	0.113394i
$226$	−1.86367	+	0.678322i	−0.123970	+	0.0451213i
$227$	11.2307			0.745410			0.372705	−	0.927950i	$-0.378430\pi$
$227$	11.2307			0.745410			0.372705	+	0.927950i	$0.378430\pi$
$228$	7.36710	−	1.65100i	0.487898	−	0.109340i
$229$	−6.16852			−0.407627			−0.203814	−	0.979010i	$-0.565334\pi$
$229$	−6.16852			−0.407627			−0.203814	+	0.979010i	$0.565334\pi$
$230$	−0.848846	+	0.308955i	−0.0559712	+	0.0203719i
$231$	−0.700442	−	0.450201i	−0.0460857	−	0.0296211i
$232$	6.86351	−	5.75916i	0.450611	−	0.378108i
$233$	−9.21841	+	10.9861i	−0.603918	+	0.719721i	−0.978217	−	0.207587i	$-0.933439\pi$
$233$	−9.21841	+	10.9861i	−0.603918	+	0.719721i	0.374299	+	0.927308i	$0.377883\pi$
$234$	−14.7544	−	10.5090i	−0.964525	−	0.686996i
$235$	−3.39340	−	5.87754i	−0.221361	−	0.383408i
$236$	0.913985	−	1.58307i	0.0594954	−	0.103049i
$237$	14.7025	−	15.9160i	0.955031	−	1.03385i
$238$	−1.03765	+	2.85093i	−0.0672610	+	0.184798i
$239$	−9.77122	−	5.64142i	−0.632048	−	0.364913i	0.149497	−	0.988762i	$-0.452235\pi$
$239$	−9.77122	−	5.64142i	−0.632048	−	0.364913i	−0.781545	+	0.623849i	$0.785568\pi$
$240$	1.71813	−	0.219169i	0.110905	−	0.0141473i
$241$	17.0118	−	2.99964i	1.09583	−	0.193224i	0.403622	−	0.914926i	$-0.367751\pi$
$241$	17.0118	−	2.99964i	1.09583	−	0.193224i	0.692204	+	0.721702i	$0.256640\pi$
$242$	−7.31356	−	6.13680i	−0.470133	−	0.394489i
$243$	−4.38763	−	14.9582i	−0.281467	−	0.959571i
$244$	−0.873516	+	4.95395i	−0.0559211	+	0.317144i
$245$	−2.33974	−	6.42837i	−0.149480	−	0.410694i
$246$	−11.7819	−	4.93585i	−0.751189	−	0.314698i
$247$	−6.97250	−	25.3793i	−0.443649	−	1.61484i
$248$			10.0381i			0.637418i
$249$	1.37079	−	28.7428i	0.0868700	−	1.82150i
$250$	−0.984808	−	0.173648i	−0.0622847	−	0.0109825i
$251$	−3.89921	−	4.64689i	−0.246116	−	0.293309i	0.628817	−	0.777553i	$-0.283539\pi$
$251$	−3.89921	−	4.64689i	−0.246116	−	0.293309i	−0.874933	+	0.484244i	$0.839095\pi$
$252$	−0.0946907	−	1.19275i	−0.00596495	−	0.0751362i
$253$	−0.189069	−	1.07226i	−0.0118867	−	0.0674126i
$254$	−7.67136	+	4.42906i	−0.481344	+	0.277904i
$255$	−10.4850	+	7.97865i	−0.656598	+	0.499643i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−0.617564	−	0.224775i	−0.0385226	−	0.0140211i	0.322687	−	0.946506i	$-0.395414\pi$
$257$	−0.617564	−	0.224775i	−0.0385226	−	0.0140211i	−0.361210	+	0.932485i	$0.617636\pi$
$258$	4.76168	−	3.62343i	0.296449	−	0.225585i
$259$	1.02059	−	0.589238i	0.0634163	−	0.0366134i
$260$	−1.04851	−	5.94640i	−0.0650259	−	0.368780i
$261$	−2.12719	−	26.7947i	−0.131670	−	1.65855i
$262$	−1.17318	−	1.39815i	−0.0724795	−	0.0863777i
$263$	2.15547	+	0.380067i	0.132912	+	0.0234360i	0.239708	−	0.970845i	$-0.422948\pi$
$263$	2.15547	+	0.380067i	0.132912	+	0.0234360i	−0.106796	+	0.994281i	$0.534059\pi$
$264$	−0.0994522	+	2.08533i	−0.00612086	+	0.128343i
$265$			1.65760i			0.101826i
$266$	0.988134	−	1.43035i	0.0605864	−	0.0877004i
$267$	5.05265	+	2.11673i	0.309217	+	0.129541i
$268$	−2.62828	−	7.22115i	−0.160548	−	0.441102i
$269$	4.46063	−	25.2975i	0.271969	−	1.54241i	−0.476458	−	0.879197i	$-0.658080\pi$
$269$	4.46063	−	25.2975i	0.271969	−	1.54241i	0.748427	−	0.663217i	$-0.230809\pi$
$270$	2.45475	−	4.57976i	0.149392	−	0.278715i
$271$	−3.89897	−	3.27162i	−0.236845	−	0.198737i	0.516638	−	0.856204i	$-0.327183\pi$
$271$	−3.89897	−	3.27162i	−0.236845	−	0.198737i	−0.753483	+	0.657467i	$0.771628\pi$
$272$	7.49133	−	1.32092i	0.454229	−	0.0800928i
$273$	−4.13762	+	0.527807i	−0.250420	+	0.0319443i
$274$	−6.02317	−	3.47748i	−0.363873	−	0.210082i
$275$	0.412248	−	1.13264i	0.0248595	−	0.0683009i
$276$	1.06166	−	1.14928i	0.0639044	−	0.0691788i
$277$	0.946003	−	1.63853i	0.0568398	−	0.0984495i	−0.836205	−	0.548416i	$-0.815231\pi$
$277$	0.946003	−	1.63853i	0.0568398	−	0.0984495i	0.893045	+	0.449967i	$0.148564\pi$
$278$	5.64603	+	9.77921i	0.338626	+	0.586518i
$279$	24.5284	+	17.4707i	1.46847	+	1.04594i
$280$	0.256366	−	0.305525i	0.0153208	−	0.0182586i
$281$	12.6119	−	10.5827i	0.752364	−	0.631308i	−0.183763	−	0.982971i	$-0.558828\pi$
$281$	12.6119	−	10.5827i	0.752364	−	0.631308i	0.936127	+	0.351663i	$0.114384\pi$
$282$	9.88865	+	6.35582i	0.588860	+	0.378484i
$283$	−14.5372	+	5.29109i	−0.864144	+	0.314523i	−0.735793	−	0.677206i	$-0.763191\pi$
$283$	−14.5372	+	5.29109i	−0.864144	+	0.314523i	−0.128351	+	0.991729i	$0.540968\pi$
$284$	−5.69081			−0.337688
$285$	6.96849	−	2.90520i	0.412778	−	0.172089i
$286$	7.27797			0.430355
$287$	−2.76405	+	1.00603i	−0.163157	+	0.0593843i
$288$	−2.47122	+	1.70091i	−0.145618	+	0.100227i
$289$	−31.3043	+	26.2675i	−1.84143	+	1.54514i
$290$	5.75916	−	6.86351i	0.338190	−	0.403039i
$291$	16.1557	+	3.64986i	0.947062	+	0.213959i
$292$	−4.52517	−	7.83783i	−0.264816	−	0.458674i
$293$	−9.43651	+	16.3445i	−0.551287	+	0.954857i	0.446895	+	0.894586i	$0.352530\pi$
$293$	−9.43651	+	16.3445i	−0.551287	+	0.954857i	−0.998182	+	0.0602705i	$0.980804\pi$
$294$	8.70361	+	8.04003i	0.507605	+	0.468904i
$295$	0.625203	−	1.71773i	0.0364007	−	0.100010i
$296$	−2.55893	−	1.47740i	−0.148735	−	0.0858721i
$297$	4.92248	+	3.87241i	0.285631	+	0.224700i
$298$	−21.7871	+	3.84165i	−1.26209	+	0.222541i
$299$	−4.17830	−	3.50601i	−0.241637	−	0.202758i
$300$	1.65397	−	0.514190i	0.0954919	−	0.0296867i
$301$	0.239255	−	1.35688i	0.0137904	−	0.0782093i
$302$	−2.71049	−	7.44700i	−0.155971	−	0.428527i
$303$	9.64978	−	23.0341i	0.554365	−	1.32328i
$304$	−4.34463	−	0.352463i	−0.249181	−	0.0202151i
$305$			5.03038i			0.288039i
$306$	9.81050	−	20.6043i	0.560829	−	1.17787i
$307$	−2.60904	−	0.460044i	−0.148906	−	0.0262561i	0.0986983	−	0.995117i	$-0.468532\pi$
$307$	−2.60904	−	0.460044i	−0.148906	−	0.0262561i	−0.247604	+	0.968861i	$0.579643\pi$
$308$	0.309006	+	0.368259i	0.0176073	+	0.0209835i
$309$	−28.6322	+	14.7589i	−1.62883	+	0.839605i
$310$	1.74309	+	9.88557i	0.0990010	+	0.561462i
$311$	−8.90527	+	5.14146i	−0.504971	+	0.291545i	−0.730764	−	0.682630i	$-0.760836\pi$
$311$	−8.90527	+	5.14146i	−0.504971	+	0.291545i	0.225793	+	0.974175i	$0.427503\pi$
$312$	6.33322	+	8.32271i	0.358548	+	0.471181i
$313$	11.8203	+	4.30223i	0.668121	+	0.243176i	0.653739	−	0.756720i	$-0.273200\pi$
$313$	11.8203	+	4.30223i	0.668121	+	0.243176i	0.0143823	+	0.999897i	$0.495422\pi$
$314$	8.21115	+	2.98861i	0.463382	+	0.168657i
$315$	−0.300371	−	1.15819i	−0.0169240	−	0.0652564i
$316$	−10.8338	+	6.25488i	−0.609447	+	0.351865i
$317$	−0.918674	−	5.21006i	−0.0515979	−	0.292626i	0.948079	−	0.318034i	$-0.103023\pi$
$317$	−0.918674	−	5.21006i	−0.0515979	−	0.292626i	−0.999677	+	0.0254080i	$0.991912\pi$
$318$	−1.31545	−	2.55196i	−0.0737668	−	0.143107i
$319$	6.94171	+	8.27281i	0.388661	+	0.463189i
$320$	−0.984808	−	0.173648i	−0.0550524	−	0.00970723i
$321$	−6.84478	−	0.326437i	−0.382039	−	0.0182199i
$322$		−	0.360276i		−	0.0200774i
$323$	29.9620	−	14.2026i	1.66713	−	0.790255i
$324$	−0.144788	+	8.99884i	−0.00804375	+	0.499935i
$325$	−2.06516	−	5.67399i	−0.114555	−	0.314736i
$326$	−3.42646	+	19.4324i	−0.189774	+	1.07626i
$327$	−6.31579	−	20.3157i	−0.349264	−	1.12346i
$328$	5.64966	+	4.74063i	0.311950	+	0.261757i
$329$	2.66568	−	0.470032i	0.146964	−	0.0259137i
$330$	0.264172	+	2.07092i	0.0145422	+	0.114000i
$331$	18.6376	+	10.7604i	1.02442	+	0.591446i	0.915380	−	0.402592i	$-0.131890\pi$
$331$	18.6376	+	10.7604i	1.02442	+	0.591446i	0.109035	+	0.994038i	$0.465224\pi$
$332$	−5.68217	+	15.6116i	−0.311850	+	0.856800i
$333$	−8.06375	+	3.68151i	−0.441891	+	0.201745i
$334$	5.72830	−	9.92170i	0.313439	−	0.542891i
$335$	−3.84229	−	6.65504i	−0.209927	−	0.363604i
$336$	−0.152228	+	0.673820i	−0.00830473	+	0.0367599i
$337$	−7.08715	+	8.44614i	−0.386062	+	0.460091i	−0.923718	−	0.383074i	$-0.874866\pi$
$337$	−7.08715	+	8.44614i	−0.386062	+	0.460091i	0.537656	+	0.843164i	$0.319310\pi$
$338$	17.9707	−	15.0792i	0.977478	−	0.820201i
$339$	1.85734	−	2.88972i	0.100877	−	0.156948i
$340$	7.14815	−	2.60171i	0.387663	−	0.141098i
$341$	−12.0992			−0.655209
$342$	−8.42282	+	10.0028i	−0.455454	+	0.540890i
$343$	5.52024			0.298065
$344$	−3.24626	+	1.18154i	−0.175027	+	0.0637045i
$345$	0.845960	−	1.31618i	0.0455449	−	0.0708607i
$346$	12.8741	−	10.8027i	0.692116	−	0.580754i
$347$	1.07786	−	1.28455i	0.0578628	−	0.0689582i	−0.736337	−	0.676615i	$-0.763446\pi$
$347$	1.07786	−	1.28455i	0.0578628	−	0.0689582i	0.794199	+	0.607657i	$0.207890\pi$
$348$	−3.41975	+	15.1371i	−0.183318	+	0.811435i
$349$	−2.78562	−	4.82483i	−0.149111	−	0.258267i	0.781788	−	0.623544i	$-0.214308\pi$
$349$	−2.78562	−	4.82483i	−0.149111	−	0.258267i	−0.930899	+	0.365277i	$0.880974\pi$
$350$	0.199417	−	0.345401i	0.0106593	−	0.0184624i
$351$	31.3594	−	0.990255i	1.67384	−	0.0528559i
$352$	0.412248	−	1.13264i	0.0219729	−	0.0603701i
$353$	7.47805	+	4.31746i	0.398017	+	0.229795i	0.685628	−	0.727952i	$-0.259528\pi$
$353$	7.47805	+	4.31746i	0.398017	+	0.229795i	−0.287611	+	0.957747i	$0.592861\pi$
$354$	0.400635	+	3.14069i	0.0212935	+	0.166926i
$355$	−5.60436	+	0.988199i	−0.297448	+	0.0524482i
$356$	−2.42284	−	2.03301i	−0.128410	−	0.107749i
$357$	−1.56000	−	5.01796i	−0.0825637	−	0.265579i
$358$	1.54863	−	8.78270i	0.0818475	−	0.464180i
$359$	6.96474	+	19.1355i	0.367585	+	1.00993i	0.976277	+	0.216525i	$0.0694722\pi$
$359$	6.96474	+	19.1355i	0.367585	+	1.00993i	−0.608692	+	0.793406i	$0.708306\pi$
$360$	−2.13832	+	2.10419i	−0.112699	+	0.110900i
$361$	−18.6682	+	3.53547i	−0.982535	+	0.186077i
$362$			10.7640i			0.565743i
$363$	16.5174	+	0.787738i	0.866939	+	0.0413455i
$364$	2.37163	+	0.418182i	0.124307	+	0.0219187i
$365$	−5.81745	−	6.93297i	−0.304499	−	0.362888i
$366$	−3.99204	−	7.74453i	−0.208667	−	0.404813i
$367$	−0.522790	−	2.96489i	−0.0272894	−	0.154766i	0.968118	−	0.250494i	$-0.0805931\pi$
$367$	−0.522790	−	2.96489i	−0.0272894	−	0.154766i	−0.995407	+	0.0957283i	$0.969482\pi$
$368$	−0.782300	+	0.451661i	−0.0407802	+	0.0235445i
$369$	21.4168	−	5.55436i	1.11491	−	0.289148i
$370$	−2.77660	−	1.01060i	−0.144349	−	0.0525386i
$371$	−0.621239	−	0.226112i	−0.0322531	−	0.0117392i
$372$	−10.5286	−	13.8361i	−0.545884	−	0.717366i
$373$	10.3071	−	5.95080i	0.533681	−	0.308121i	−0.208833	−	0.977951i	$-0.566967\pi$
$373$	10.3071	−	5.95080i	0.533681	−	0.308121i	0.742514	+	0.669830i	$0.233633\pi$
$374$	1.59215	+	9.02956i	0.0823283	+	0.466907i
$375$	1.53955	−	0.793586i	0.0795021	−	0.0409806i
$376$	−4.36247	−	5.19899i	−0.224977	−	0.268117i
$377$	53.2778	+	9.39432i	2.74395	+	0.483832i
$378$	1.38156	+	1.54472i	0.0710597	+	0.0794518i
$379$			15.0398i			0.772545i	0.922385	+	0.386273i	$0.126238\pi$
$379$			15.0398i			0.772545i	−0.922385	+	0.386273i	$0.873762\pi$
$380$	−4.33983	+	0.407328i	−0.222628	+	0.0208955i
$381$	5.92837	−	14.1511i	0.303719	−	0.724982i
$382$	7.87871	+	21.6466i	0.403110	+	1.10754i
$383$	−0.601336	+	3.41035i	−0.0307269	+	0.174261i	−0.996309	−	0.0858369i	$-0.972644\pi$
$383$	−0.601336	+	3.41035i	−0.0307269	+	0.174261i	0.965582	+	0.260098i	$0.0837547\pi$
$384$	1.65397	−	0.514190i	0.0844037	−	0.0262396i
$385$	0.368259	+	0.309006i	0.0187682	+	0.0157484i
$386$	14.1721	−	2.49893i	0.721342	−	0.127192i
$387$	−2.76279	+	9.98876i	−0.140440	+	0.507757i
$388$	−8.28141	−	4.78128i	−0.420425	−	0.242733i
$389$	8.96565	−	24.6329i	0.454576	−	1.24894i	−0.474895	−	0.880043i	$-0.657514\pi$
$389$	8.96565	−	24.6329i	0.454576	−	1.24894i	0.929471	−	0.368895i	$-0.120264\pi$
$390$	7.68223	+	7.09652i	0.389005	+	0.359346i
$391$	3.43574	−	5.95088i	0.173753	−	0.300949i
$392$	−3.42047	−	5.92442i	−0.172760	−	0.299228i
$393$	3.08354	+	0.696628i	0.155544	+	0.0351402i
$394$	−11.8244	+	14.0917i	−0.595702	+	0.709930i
$395$	−9.58304	+	8.04112i	−0.482175	+	0.404593i
$396$	−2.05016	−	2.97864i	−0.103024	−	0.149682i
$397$	1.88320	−	0.685431i	0.0945153	−	0.0344008i	−0.294330	−	0.955704i	$-0.595096\pi$
$397$	1.88320	−	0.685431i	0.0945153	−	0.0344008i	0.388845	+	0.921303i	$0.372874\pi$
$398$	7.41151			0.371505
$399$	0.138249	+	3.00796i	0.00692111	+	0.150586i
$400$	−1.00000			−0.0500000
$401$	−22.6953	+	8.26041i	−1.13335	+	0.412505i	−0.839507	−	0.543349i	$-0.817156\pi$
$401$	−22.6953	+	8.26041i	−1.13335	+	0.412505i	−0.293842	+	0.955854i	$0.594934\pi$
$402$	11.1968	+	7.19660i	0.558444	+	0.358934i
$403$	−46.4309	+	38.9601i	−2.31289	+	1.94074i
$404$	−9.26811	+	11.0453i	−0.461106	+	0.549525i
$405$	1.42004	+	8.88726i	0.0705625	+	0.441612i
$406$	1.78671	+	3.09468i	0.0886730	+	0.153586i
$407$	1.78076	−	3.08436i	0.0882689	−	0.152886i
$408$	−8.94026	+	9.67814i	−0.442609	+	0.479140i
$409$	2.46749	−	6.77938i	0.122010	−	0.335219i	−0.863619	−	0.504145i	$-0.831808\pi$
$409$	2.46749	−	6.77938i	0.122010	−	0.335219i	0.985629	+	0.168926i	$0.0540300\pi$
$410$	6.38703	+	3.68755i	0.315433	+	0.182115i
$411$	11.9495	−	1.52431i	0.589426	−	0.0751888i
$412$	18.3152	−	3.22946i	0.902325	−	0.159104i
$413$	0.558490	+	0.468629i	0.0274815	+	0.0230597i
$414$	−0.257898	+	2.69767i	−0.0126750	+	0.132583i
$415$	−2.88491	+	16.3612i	−0.141615	+	0.803137i
$416$	−2.06516	−	5.67399i	−0.101253	−	0.278190i
$417$	−18.0394	−	7.55730i	−0.883392	−	0.370082i
$418$	0.424835	−	5.23672i	0.0207794	−	0.256136i
$419$		−	3.86416i		−	0.188777i	−0.995535	−	0.0943884i	$-0.969910\pi$
$419$		−	3.86416i		−	0.188777i	0.995535	−	0.0943884i	$-0.0300895\pi$
$420$	−0.0329079	+	0.690017i	−0.00160574	+	0.0336694i
$421$	−18.0485	−	3.18244i	−0.879631	−	0.155103i	−0.284447	−	0.958692i	$-0.591810\pi$
$421$	−18.0485	−	3.18244i	−0.879631	−	0.155103i	−0.595184	+	0.803589i	$0.702921\pi$
$422$	−0.724356	−	0.863254i	−0.0352611	−	0.0420225i
$423$	−20.2965	+	1.61131i	−0.986851	+	0.0783446i
$424$	0.287840	+	1.63242i	0.0139787	+	0.0792773i
$425$	6.58777	−	3.80345i	0.319554	−	0.184494i
$426$	7.84398	−	5.96892i	0.380042	−	0.289195i
$427$	−1.88529	−	0.686191i	−0.0912357	−	0.0332071i
$428$	3.71773	+	1.35314i	0.179703	+	0.0654067i
$429$	−10.0316	+	7.63365i	−0.484332	+	0.368556i
$430$	−2.99177	+	1.72730i	−0.144276	+	0.0832978i
$431$	1.77457	+	10.0641i	0.0854781	+	0.484770i	0.997252	+	0.0740787i	$0.0236016\pi$
$431$	1.77457	+	10.0641i	0.0854781	+	0.484770i	−0.911774	+	0.410692i	$0.865287\pi$
$432$	1.62219	−	4.93644i	0.0780478	−	0.237505i
$433$	−4.05087	−	4.82764i	−0.194673	−	0.232002i	0.659874	−	0.751376i	$-0.270610\pi$
$433$	−4.05087	−	4.82764i	−0.194673	−	0.232002i	−0.854547	+	0.519374i	$0.826165\pi$
$434$	−3.94270	−	0.695205i	−0.189256	−	0.0333709i
$435$	−0.739264	+	15.5010i	−0.0354450	+	0.743215i
$436$			12.2830i			0.588249i
$437$	−2.76658	+	2.80176i	−0.132344	+	0.134026i
$438$	14.4582	+	6.05702i	0.690839	+	0.289415i
$439$	−6.51092	−	17.8886i	−0.310749	−	0.853777i	−0.992506	−	0.122198i	$-0.961006\pi$
$439$	−6.51092	−	17.8886i	−0.310749	−	0.853777i	0.681756	−	0.731579i	$-0.261216\pi$
$440$	0.209304	−	1.18702i	0.00997818	−	0.0565890i
$441$	−20.4296	−	1.95308i	−0.972840	−	0.0930038i
$442$	35.1856	+	29.5242i	1.67361	+	1.40432i
$443$	4.55836	−	0.803762i	0.216574	−	0.0381879i	−0.0643081	−	0.997930i	$-0.520484\pi$
$443$	4.55836	−	0.803762i	0.216574	−	0.0381879i	0.280882	+	0.959742i	$0.409373\pi$
$444$	5.07672	−	0.647601i	0.240931	−	0.0307338i
$445$	−2.73906	−	1.58140i	−0.129844	−	0.0749654i
$446$	7.93247	−	21.7943i	0.375614	−	1.03199i
$447$	26.0010	−	28.1470i	1.22981	−	1.33131i
$448$	0.199417	−	0.345401i	0.00942158	−	0.0163186i
$449$	−3.29018	−	5.69875i	−0.155273	−	0.268941i	0.777885	−	0.628406i	$-0.216292\pi$
$449$	−3.29018	−	5.69875i	−0.155273	−	0.268941i	−0.933158	+	0.359465i	$0.882959\pi$
$450$	−1.74044	+	2.44354i	−0.0820452	+	0.115189i
$451$	−5.71404	+	6.80972i	−0.269064	+	0.320657i
$452$	−1.51928	+	1.27483i	−0.0714609	+	0.0599628i
$453$	11.5470	+	7.42169i	0.542524	+	0.348701i
$454$	10.5534	−	3.84114i	0.495297	−	0.180273i
$455$	2.40822			0.112899
$456$	6.35814	−	4.07113i	0.297747	−	0.190648i
$457$	27.9271			1.30637			0.653187	−	0.757197i	$-0.273432\pi$
$457$	27.9271			1.30637			0.653187	+	0.757197i	$0.273432\pi$
$458$	−5.79652	+	2.10976i	−0.270853	+	0.0985826i
$459$	8.08888	+	38.6901i	0.377557	+	1.80590i
$460$	−0.691985	+	0.580645i	−0.0322640	+	0.0270727i
$461$	9.24403	−	11.0166i	0.430537	−	0.513094i	−0.506540	−	0.862216i	$-0.669076\pi$
$461$	9.24403	−	11.0166i	0.430537	−	0.513094i	0.937077	+	0.349122i	$0.113520\pi$
$462$	−0.812178	−	0.183486i	−0.0377859	−	0.00853653i
$463$	−6.97807	−	12.0864i	−0.324298	−	0.561701i	0.657072	−	0.753828i	$-0.271795\pi$
$463$	−6.97807	−	12.0864i	−0.324298	−	0.561701i	−0.981370	+	0.192127i	$0.938461\pi$
$464$	4.47983	−	7.75930i	0.207971	−	0.360217i
$465$	−12.7713	−	11.7976i	−0.592254	−	0.547099i
$466$	−4.90501	+	13.4764i	−0.227220	+	0.624283i
$467$	27.9781	+	16.1532i	1.29467	+	0.747479i	0.979479	−	0.201548i	$-0.0645973\pi$
$467$	27.9781	+	16.1532i	1.29467	+	0.747479i	0.315193	+	0.949027i	$0.397931\pi$
$468$	−17.4589	−	4.82895i	−0.807038	−	0.223218i
$469$	3.01831	−	0.532210i	0.139373	−	0.0245752i
$470$	−5.19899	−	4.36247i	−0.239811	−	0.201226i
$471$	−14.4526	+	4.49305i	−0.665939	+	0.207029i
$472$	0.317424	−	1.80020i	0.0146106	−	0.0828609i
$473$	−1.42415	−	3.91283i	−0.0654826	−	0.179912i
$474$	8.37226	−	19.9847i	0.384551	−	0.917927i
$475$	−4.20316	+	1.15474i	−0.192854	+	0.0529832i
$476$			3.03389i			0.139058i
$477$	4.48984	+	2.13778i	0.205576	+	0.0978824i
$478$	−11.1114	−	1.95924i	−0.508225	−	0.0896137i
$479$	−25.0076	−	29.8029i	−1.14263	−	1.36173i	−0.922379	−	0.386286i	$-0.873758\pi$
$479$	−25.0076	−	29.8029i	−1.14263	−	1.36173i	−0.220248	−	0.975444i	$-0.570687\pi$
$480$	1.53955	−	0.793586i	0.0702706	−	0.0362221i
$481$	−3.09814	−	17.5704i	−0.141263	−	0.801142i
$482$	14.9599	−	8.63712i	0.681406	−	0.393410i
$483$	0.377883	+	0.496589i	0.0171943	+	0.0225956i
$484$	−8.97141	−	3.26532i	−0.407791	−	0.148424i
$485$	−8.98586	−	3.27059i	−0.408027	−	0.148510i
$486$	−9.23904	−	12.5555i	−0.419091	−	0.569528i
$487$	−13.3322	+	7.69736i	−0.604141	+	0.348801i	−0.770669	−	0.637236i	$-0.780078\pi$
$487$	−13.3322	+	7.69736i	−0.604141	+	0.348801i	0.166528	+	0.986037i	$0.446744\pi$
$488$	0.873516	+	4.95395i	0.0395422	+	0.224255i
$489$	−15.6592	−	30.3788i	−0.708134	−	1.37378i
$490$	−4.39727	−	5.24046i	−0.198648	−	0.236740i
$491$	−28.8280	−	5.08315i	−1.30099	−	0.229399i	−0.520119	−	0.854094i	$-0.674112\pi$
$491$	−28.8280	−	5.08315i	−1.30099	−	0.229399i	−0.780869	+	0.624695i	$0.785223\pi$
$492$	−12.7596	−	0.608521i	−0.575245	−	0.0274342i
$493$			68.1553i			3.06956i
$494$	−15.2322	−	21.4640i	−0.685330	−	0.965710i
$495$	−2.53625	−	2.57738i	−0.113996	−	0.115845i
$496$	3.43322	+	9.43270i	0.154156	+	0.423541i
$497$	0.394128	−	2.23521i	0.0176790	−	0.100263i
$498$	−8.54251	−	27.4783i	−0.382799	−	1.23133i
$499$	4.59089	+	3.85221i	0.205517	+	0.172449i	0.739736	−	0.672897i	$-0.234950\pi$
$499$	4.59089	+	3.85221i	0.205517	+	0.172449i	−0.534220	+	0.845346i	$0.679395\pi$
$500$	−0.984808	+	0.173648i	−0.0440419	+	0.00776578i
$501$	2.51094	+	19.6839i	0.112180	+	0.879412i
$502$	−5.25339	−	3.03304i	−0.234470	−	0.135371i
$503$	0.536927	−	1.47519i	0.0239404	−	0.0657757i	−0.927147	−	0.374698i	$-0.877746\pi$
$503$	0.536927	−	1.47519i	0.0239404	−	0.0657757i	0.951087	+	0.308923i	$0.0999685\pi$
$504$	−0.496925	−	1.08843i	−0.0221348	−	0.0484826i
$505$	−7.20931	+	12.4869i	−0.320810	+	0.555660i
$506$	−0.544403	−	0.942933i	−0.0242016	−	0.0419185i
$507$	−8.95393	+	39.6335i	−0.397658	+	1.76019i
$508$	−5.69389	+	6.78571i	−0.252625	+	0.301067i
$509$	13.2571	−	11.1241i	0.587613	−	0.493066i	−0.299824	−	0.953994i	$-0.596928\pi$
$509$	13.2571	−	11.1241i	0.587613	−	0.493066i	0.887437	+	0.460929i	$0.152484\pi$
$510$	−7.12385	+	11.0836i	−0.315449	+	0.490789i
$511$	3.39190	−	1.23455i	0.150049	−	0.0546134i
$512$	−1.00000			−0.0441942
$513$	1.11802	−	22.6219i	0.0493617	−	0.998781i
$514$	−0.657197			−0.0289877
$515$	17.4762	−	6.36080i	0.770092	−	0.280290i
$516$	3.23523	−	5.03350i	0.142423	−	0.221587i
$517$	6.26651	−	5.25823i	0.275601	−	0.231257i
$518$	0.757509	−	0.902764i	0.0332830	−	0.0396652i
$519$	−6.41454	+	28.3932i	−0.281567	+	1.24632i
$520$	−3.01907	−	5.22918i	−0.132395	−	0.229315i
$521$	−9.37747	+	16.2423i	−0.410835	+	0.711586i	−0.994981	−	0.100062i	$-0.968096\pi$
$521$	−9.37747	+	16.2423i	−0.410835	+	0.711586i	0.584147	+	0.811648i	$0.301429\pi$
$522$	−11.1632	−	24.4512i	−0.488602	−	1.07020i
$523$	−6.27446	+	17.2389i	−0.274363	+	0.753806i	0.723612	+	0.690207i	$0.242480\pi$
$523$	−6.27446	+	17.2389i	−0.274363	+	0.753806i	−0.997975	+	0.0635999i	$0.979742\pi$
$524$	−1.58063	−	0.912575i	−0.0690500	−	0.0398660i
$525$	0.0874123	+	0.685249i	0.00381498	+	0.0299067i
$526$	2.15547	−	0.380067i	0.0939829	−	0.0165717i
$527$	−58.4941	−	49.0823i	−2.54804	−	2.13806i
$528$	0.619770	+	1.99358i	0.0269720	+	0.0867596i
$529$	3.85221	−	21.8470i	0.167488	−	0.949869i
$530$	0.566933	+	1.55764i	0.0246260	+	0.0676594i
$531$	−3.84639	−	3.90878i	−0.166919	−	0.169626i
$532$	0.439334	−	1.68205i	0.0190475	−	0.0729261i
$533$			44.5319i			1.92889i
$534$	5.47190	+	0.260963i	0.236792	+	0.0112930i
$535$	3.89622	+	0.687009i	0.168448	+	0.0297020i
$536$	−4.93956	−	5.88673i	−0.213356	−	0.254268i
$537$	7.07736	+	13.7300i	0.305410	+	0.592494i
$538$	−4.46063	−	25.2975i	−0.192311	−	1.09065i
$539$	7.14090	−	4.12280i	0.307580	−	0.177582i
$540$	0.740344	−	5.14314i	0.0318593	−	0.221326i
$541$	−26.1501	−	9.51787i	−1.12428	−	0.409205i	−0.288069	−	0.957610i	$-0.593013\pi$
$541$	−26.1501	−	9.51787i	−1.12428	−	0.409205i	−0.836213	+	0.548404i	$0.815236\pi$
$542$	−4.78279	−	1.74079i	−0.205438	−	0.0747735i
$543$	−11.2900	−	14.8366i	−0.484502	−	0.636701i
$544$	6.58777	−	3.80345i	0.282448	−	0.163072i
$545$	2.13292	+	12.0964i	0.0913643	+	0.518153i
$546$	−3.70757	+	1.91113i	−0.158670	+	0.0817887i
$547$	−2.23691	−	2.66584i	−0.0956432	−	0.113983i	0.716100	−	0.697998i	$-0.245925\pi$
$547$	−2.23691	−	2.66584i	−0.0956432	−	0.113983i	−0.811743	+	0.584015i	$0.801481\pi$
$548$	−6.84929	−	1.20772i	−0.292587	−	0.0515910i
$549$	13.6255	+	6.48760i	0.581521	+	0.276884i
$550$		−	1.20533i		−	0.0513956i
$551$	9.86947	−	37.7867i	0.420454	−	1.60977i
$552$	0.604556	−	1.44308i	0.0257316	−	0.0614217i
$553$	−1.70645	−	4.68843i	−0.0725656	−	0.199372i
$554$	0.328544	−	1.86326i	0.0139585	−	0.0791625i
$555$	4.88714	−	1.51933i	0.207448	−	0.0644918i
$556$	8.65022	+	7.25839i	0.366851	+	0.307824i
$557$	−30.5741	+	5.39104i	−1.29547	+	0.228426i	−0.778535	−	0.627601i	$-0.784037\pi$
$557$	−30.5741	+	5.39104i	−1.29547	+	0.228426i	−0.516931	+	0.856027i	$0.672926\pi$
$558$	29.0244	+	8.02786i	1.22870	+	0.339846i
$559$	−18.0647	−	10.4297i	−0.764057	−	0.441128i
$560$	0.136409	−	0.374782i	0.00576435	−	0.0158374i
$561$	−11.6654	−	10.7760i	−0.492513	−	0.454963i
$562$	8.23184	−	14.2580i	0.347239	−	0.601436i
$563$	−1.90959	−	3.30751i	−0.0804798	−	0.139395i	0.822976	−	0.568076i	$-0.192312\pi$
$563$	−1.90959	−	3.30751i	−0.0804798	−	0.139395i	−0.903456	+	0.428681i	$0.858979\pi$
$564$	11.4661	+	2.59040i	0.482810	+	0.109076i
$565$	−1.27483	+	1.51928i	−0.0536324	+	0.0639166i
$566$	−11.8508	+	9.94400i	−0.498126	+	0.417977i
$567$	−3.52449	−	0.680100i	−0.148015	−	0.0285615i
$568$	−5.34761	+	1.94637i	−0.224381	+	0.0816680i
$569$	19.4113			0.813765			0.406882	−	0.913481i	$-0.366616\pi$
$569$	19.4113			0.813765			0.406882	+	0.913481i	$0.366616\pi$
$570$	5.55460	−	5.11336i	0.232657	−	0.214175i
$571$	11.0240			0.461340			0.230670	−	0.973032i	$-0.425908\pi$
$571$	11.0240			0.461340			0.230670	+	0.973032i	$0.425908\pi$
$572$	6.83905	−	2.48921i	0.285955	−	0.104079i
$573$	−33.5641	−	21.5730i	−1.40216	−	0.901225i
$574$	−2.25328	+	1.89072i	−0.0940500	+	0.0789173i
$575$	−0.580645	+	0.691985i	−0.0242146	+	0.0288578i
$576$	−1.74044	+	2.44354i	−0.0725184	+	0.101814i
$577$	−11.6675	−	20.2087i	−0.485725	−	0.841300i	0.514141	−	0.857706i	$-0.328111\pi$
$577$	−11.6675	−	20.2087i	−0.485725	−	0.841300i	−0.999865	+	0.0164059i	$0.994778\pi$
$578$	−20.4325	+	35.3901i	−0.849878	+	1.47203i
$579$	−16.9132	+	18.3091i	−0.702889	+	0.760901i
$580$	3.06439	−	8.41934i	0.127242	−	0.349594i
$581$	−5.73833	−	3.31303i	−0.238066	−	0.137448i
$582$	16.4297	−	2.09582i	0.681033	−	0.0868745i
$583$	−1.96761	+	0.346943i	−0.0814901	+	0.0143689i
$584$	−6.93297	−	5.81745i	−0.286888	−	0.240728i
$585$	−18.0322	−	1.72388i	−0.745539	−	0.0712737i
$586$	−3.27727	+	18.5863i	−0.135383	+	0.767793i
$587$	−1.87592	−	5.15405i	−0.0774275	−	0.212730i	0.894940	−	0.446187i	$-0.147218\pi$
$587$	−1.87592	−	5.15405i	−0.0774275	−	0.212730i	−0.972367	+	0.233457i	$0.924996\pi$
$588$	10.9286	+	4.57835i	0.450687	+	0.188808i
$589$	25.3227	+	35.6827i	1.04340	+	1.47028i
$590$		−	1.82797i		−	0.0752563i
$591$	1.51781	−	31.8256i	0.0624343	−	1.30913i
$592$	−2.90991	−	0.513095i	−0.119596	−	0.0210881i
$593$	11.0167	+	13.1291i	0.452400	+	0.539149i	0.943245	−	0.332097i	$-0.107756\pi$
$593$	11.0167	+	13.1291i	0.452400	+	0.539149i	−0.490845	+	0.871247i	$0.663312\pi$
$594$	5.95006	+	1.95528i	0.244134	+	0.0802263i
$595$	0.526830	+	2.98780i	0.0215979	+	0.122488i
$596$	−19.1592	+	11.0616i	−0.784793	+	0.453101i
$597$	−10.2157	+	7.77371i	−0.418101	+	0.318157i
$598$	−5.12545	−	1.86551i	−0.209595	−	0.0762864i
$599$	1.93692	+	0.704981i	0.0791404	+	0.0288047i	0.381287	−	0.924457i	$-0.375481\pi$
$599$	1.93692	+	0.704981i	0.0791404	+	0.0288047i	−0.302147	+	0.953261i	$0.597703\pi$
$600$	1.37836	−	1.04887i	0.0562712	−	0.0428200i
$601$	25.4749	−	14.7079i	1.03914	−	0.599949i	0.119552	−	0.992828i	$-0.461854\pi$
$601$	25.4749	−	14.7079i	1.03914	−	0.599949i	0.919590	+	0.392878i	$0.128521\pi$
$602$	−0.239255	−	1.35688i	−0.00975130	−	0.0553024i
$603$	−22.9814	+	1.82446i	−0.935877	+	0.0742979i
$604$	−5.09405	−	6.07085i	−0.207274	−	0.247019i
$605$	−9.40213	−	1.65785i	−0.382251	−	0.0674011i
$606$	1.18968	−	24.9454i	0.0483276	−	1.01334i
$607$			17.1253i			0.695095i	0.937662	+	0.347547i	$0.112985\pi$
$607$			17.1253i			0.695095i	−0.937662	+	0.347547i	$0.887015\pi$
$608$	−4.20316	+	1.15474i	−0.170461	+	0.0468310i
$609$	−5.70864	−	2.39154i	−0.231326	−	0.0969102i
$610$	1.72049	+	4.72701i	0.0696606	+	0.191391i
$611$	7.11603	−	40.3570i	0.287884	−	1.63267i
$612$	2.17176	−	22.7171i	0.0877883	−	0.918285i
$613$	−12.8893	−	10.8154i	−0.520595	−	0.436831i	0.344244	−	0.938880i	$-0.388135\pi$
$613$	−12.8893	−	10.8154i	−0.520595	−	0.436831i	−0.864839	+	0.502049i	$0.832580\pi$
$614$	−2.60904	+	0.460044i	−0.105292	+	0.0185659i
$615$	−12.6714	+	1.61640i	−0.510959	+	0.0651794i
$616$	0.416323	+	0.240364i	0.0167741	+	0.00968455i
$617$	−7.05425	+	19.3814i	−0.283993	+	0.780265i	0.712883	+	0.701283i	$0.247389\pi$
$617$	−7.05425	+	19.3814i	−0.283993	+	0.780265i	−0.996876	+	0.0789819i	$0.974833\pi$
$618$	−21.8576	+	23.6616i	−0.879242	+	0.951810i
$619$	6.11219	−	10.5866i	0.245670	−	0.425512i	−0.716650	−	0.697433i	$-0.754326\pi$
$619$	6.11219	−	10.5866i	0.245670	−	0.425512i	0.962320	+	0.271921i	$0.0876588\pi$
$620$	5.01903	+	8.69322i	0.201569	+	0.349128i
$621$	−2.47403	−	3.98885i	−0.0992794	−	0.160067i
$622$	−6.60973	+	7.87717i	−0.265026	+	0.315846i
$623$	0.966312	−	0.810832i	0.0387145	−	0.0324853i
$624$	8.79782	+	5.65470i	0.352195	+	0.226369i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	12.5789			0.502753
$627$	4.90707	+	7.66368i	0.195969	+	0.306058i
$628$	8.73812			0.348689
$629$	21.1213	−	7.68754i	0.842163	−	0.306522i
$630$	−0.678380	−	0.985607i	−0.0270273	−	0.0392675i
$631$	11.5845	−	9.72056i	0.461172	−	0.386969i	−0.382390	−	0.924001i	$-0.624899\pi$
$631$	11.5845	−	9.72056i	0.461172	−	0.386969i	0.843562	+	0.537032i	$0.180454\pi$
$632$	−8.04112	+	9.58304i	−0.319859	+	0.381193i
$633$	1.90386	+	0.430117i	0.0756717	+	0.0170956i
$634$	−2.64522	−	4.58165i	−0.105055	−	0.181961i
$635$	−4.42906	+	7.67136i	−0.175762	+	0.304428i
$636$	−2.10894	−	1.94815i	−0.0836250	−	0.0772493i
$637$	14.1276	−	38.8154i	0.559758	−	1.53792i
$638$	9.35255	+	5.39970i	0.370271	+	0.213776i
$639$	−4.55118	+	16.4546i	−0.180042	+	0.650935i
$640$	−0.984808	+	0.173648i	−0.0389279	+	0.00686405i
$641$	9.47696	+	7.95211i	0.374317	+	0.314090i	0.810467	−	0.585785i	$-0.199214\pi$
$641$	9.47696	+	7.95211i	0.374317	+	0.314090i	−0.436149	+	0.899874i	$0.643658\pi$
$642$	−6.54364	+	2.03430i	−0.258257	+	0.0802875i
$643$	6.91444	−	39.2137i	0.272679	−	1.54644i	−0.473561	−	0.880761i	$-0.657032\pi$
$643$	6.91444	−	39.2137i	0.272679	−	1.54644i	0.746240	−	0.665677i	$-0.231857\pi$
$644$	−0.123222	−	0.338549i	−0.00485561	−	0.0133407i
$645$	2.31202	−	5.51882i	0.0910356	−	0.217303i
$646$	23.2974	−	23.5937i	0.916626	−	0.928281i
$647$		−	12.5741i		−	0.494340i	−0.968972	−	0.247170i	$-0.920499\pi$
$647$		−	12.5741i		−	0.494340i	0.968972	−	0.247170i	$-0.0795006\pi$
$648$	2.94173	+	8.50566i	0.115562	+	0.334134i
$649$	2.16984	+	0.382601i	0.0851737	+	0.0150184i
$650$	−3.88124	−	4.62548i	−0.152235	−	0.181426i
$651$	6.16364	−	3.17714i	0.241572	−	0.124522i
$652$	3.42646	+	19.4324i	0.134191	+	0.761033i
$653$	−37.8752	+	21.8673i	−1.48217	+	0.855732i	−0.999795	−	0.0202318i	$-0.993560\pi$
$653$	−37.8752	+	21.8673i	−1.48217	+	0.855732i	−0.482376	+	0.875964i	$0.660226\pi$
$654$	−12.8833	−	16.9304i	−0.503776	−	0.662030i
$655$	−1.71508	−	0.624238i	−0.0670137	−	0.0243910i
$656$	6.93033	+	2.52244i	0.270584	+	0.0984845i
$657$	−26.2816	+	6.81602i	−1.02534	+	0.265918i
$658$	2.34416	−	1.35340i	0.0913850	−	0.0527612i
$659$	2.62536	+	14.8891i	0.102269	+	0.579998i	0.992276	+	0.124050i	$0.0395885\pi$
$659$	2.62536	+	14.8891i	0.102269	+	0.579998i	−0.890007	+	0.455948i	$0.849300\pi$
$660$	0.956536	+	1.85567i	0.0372331	+	0.0722320i
$661$	13.8730	+	16.5331i	0.539595	+	0.643065i	0.965097	−	0.261893i	$-0.0843467\pi$
$661$	13.8730	+	16.5331i	0.539595	+	0.643065i	−0.425502	+	0.904958i	$0.639902\pi$
$662$	21.1939	+	3.73706i	0.823724	+	0.145245i
$663$	−79.4654	−	3.78981i	−3.08618	−	0.147184i
$664$			16.6136i			0.644731i
$665$	0.140574	−	1.73279i	0.00545123	−	0.0671946i
$666$	−6.31829	+	6.21745i	−0.244829	+	0.240921i
$667$	−2.76813	−	7.60538i	−0.107182	−	0.294481i
$668$	1.98942	−	11.2825i	0.0769729	−	0.436535i
$669$	11.9256	+	38.3605i	0.461070	+	1.48310i
$670$	−5.88673	−	4.93956i	−0.227424	−	0.190832i
$671$	−5.97117	+	1.05288i	−0.230514	+	0.0406459i
$672$	0.0874123	+	0.685249i	0.00337200	+	0.0264340i
$673$	−7.76037	−	4.48045i	−0.299140	−	0.172709i	0.342916	−	0.939366i	$-0.388585\pi$
$673$	−7.76037	−	4.48045i	−0.299140	−	0.172709i	−0.642057	+	0.766657i	$0.721919\pi$
$674$	−3.77100	+	10.3607i	−0.145253	+	0.399080i
$675$	−0.164000	−	5.19356i	−0.00631237	−	0.199900i
$676$	11.7295	−	20.3162i	0.451136	−	0.781391i
$677$	7.90024	+	13.6836i	0.303631	+	0.525904i	0.976956	−	0.213443i	$-0.0684677\pi$
$677$	7.90024	+	13.6836i	0.303631	+	0.525904i	−0.673325	+	0.739347i	$0.735134\pi$
$678$	0.756983	−	3.35070i	0.0290718	−	0.128683i
$679$	2.45151	−	2.92160i	0.0940804	−	0.112121i
$680$	5.82722	−	4.88962i	0.223464	−	0.187508i
$681$	−10.5176	+	16.3636i	−0.403034	+	0.627056i
$682$	−11.3695	+	4.13818i	−0.435362	+	0.158459i
$683$	−12.1531			−0.465025			−0.232512	−	0.972593i	$-0.574695\pi$
$683$	−12.1531			−0.465025			−0.232512	+	0.972593i	$0.574695\pi$
$684$	−4.49370	+	12.2803i	−0.171821	+	0.469550i
$685$	−6.95495			−0.265735
$686$	5.18733	−	1.88803i	0.198053	−	0.0720854i
$687$	5.77681	−	8.98780i	0.220399	−	0.342906i
$688$	−2.64638	+	2.22057i	−0.100892	+	0.0846586i
$689$	−6.43355	+	7.66721i	−0.245099	+	0.292097i
$690$	0.344783	−	1.52614i	0.0131256	−	0.0580991i
$691$	19.6216	+	33.9855i	0.746439	+	1.29287i	0.949519	+	0.313709i	$0.101572\pi$
$691$	19.6216	+	33.9855i	0.746439	+	1.29287i	−0.203080	+	0.979162i	$0.565095\pi$
$692$	8.40298	−	14.5544i	0.319433	−	0.553275i
$693$	1.31192	−	0.598960i	0.0498359	−	0.0227526i
$694$	0.573519	−	1.57573i	0.0217705	−	0.0598140i
$695$	9.77921	+	5.64603i	0.370946	+	0.214166i
$696$	1.96369	+	15.3939i	0.0744333	+	0.583503i
$697$	−55.2494	+	9.74196i	−2.09272	+	0.369003i
$698$	−4.26781	−	3.58112i	−0.161539	−	0.135547i
$699$	−7.37414	−	23.7200i	−0.278916	−	0.897174i
$700$	0.0692569	−	0.392775i	0.00261766	−	0.0148455i
$701$	−2.63968	−	7.25247i	−0.0996995	−	0.273922i	0.879808	−	0.475329i	$-0.157671\pi$
$701$	−2.63968	−	7.25247i	−0.0996995	−	0.273922i	−0.979508	+	0.201407i	$0.935449\pi$
$702$	29.1296	−	11.6561i	1.09942	−	0.439931i
$703$	−12.8233	+	1.20357i	−0.483640	+	0.0453936i
$704$		−	1.20533i		−	0.0454277i
$705$	11.7417	+	0.559979i	0.442219	+	0.0210900i
$706$	8.50373	+	1.49944i	0.320042	+	0.0564321i
$707$	−3.69644	−	4.40525i	−0.139019	−	0.165676i
$708$	1.45065	+	2.81426i	0.0545188	+	0.105766i
$709$	−8.52321	−	48.3375i	−0.320096	−	1.81535i	−0.542107	−	0.840310i	$-0.682373\pi$
$709$	−8.52321	−	48.3375i	−0.320096	−	1.81535i	0.222011	−	0.975044i	$-0.428738\pi$
$710$	−4.92839	+	2.84541i	−0.184959	+	0.106786i
$711$	9.42138	+	36.3275i	0.353329	+	1.36239i
$712$	−2.97206	−	1.08174i	−0.111382	−	0.0405399i
$713$	8.52077	+	3.10131i	0.319105	+	0.116145i
$714$	−3.18216	−	4.18179i	−0.119089	−	0.156500i
$715$	6.30291	−	3.63898i	0.235715	−	0.136090i
$716$	−1.54863	−	8.78270i	−0.0578749	−	0.328225i
$717$	17.3705	−	8.95390i	0.648714	−	0.334390i
$718$	13.0894	+	15.5994i	0.488493	+	0.582163i
$719$	9.25885	+	1.63259i	0.345297	+	0.0608851i	0.343607	−	0.939113i	$-0.388351\pi$
$719$	9.25885	+	1.63259i	0.345297	+	0.0608851i	0.00168954	+	0.999999i	$0.499462\pi$
$720$	−1.28968	+	2.70864i	−0.0480637	+	0.100945i
$721$			7.41742i			0.276239i
$722$	−16.3331	+	9.70714i	−0.607856	+	0.361262i
$723$	−11.5609	+	27.5961i	−0.429955	+	1.02631i
$724$	3.68150	+	10.1148i	0.136822	+	0.375915i
$725$	1.55583	−	8.82355i	0.0577821	−	0.327699i
$726$	15.7907	−	4.90906i	0.586048	−	0.182192i
$727$	7.36110	+	6.17670i	0.273008	+	0.229081i	0.769004	−	0.639244i	$-0.220753\pi$
$727$	7.36110	+	6.17670i	0.273008	+	0.229081i	−0.495996	+	0.868325i	$0.665197\pi$
$728$	2.37163	−	0.418182i	0.0878985	−	0.0154989i
$729$	25.9038	+	7.61539i	0.959399	+	0.282051i
$730$	−7.83783	−	4.52517i	−0.290091	−	0.167484i
$731$	8.98788	−	24.6940i	0.332429	−	0.913340i
$732$	−6.40007	−	5.91212i	−0.236554	−	0.218518i
$733$	1.66893	−	2.89068i	0.0616434	−	0.106770i	−0.833557	−	0.552434i	$-0.813699\pi$
$733$	1.66893	−	2.89068i	0.0616434	−	0.106770i	0.895200	+	0.445664i	$0.147033\pi$
$734$	−1.50531	−	2.60728i	−0.0555621	−	0.0962364i
$735$	11.5576	+	2.61106i	0.426307	+	0.0963106i
$736$	−0.580645	+	0.691985i	−0.0214028	+	0.0255069i
$737$	7.09548	−	5.95381i	0.261365	−	0.219311i
$738$	18.2255	−	12.5444i	0.670890	−	0.461764i
$739$	26.4929	−	9.64262i	0.974556	−	0.354710i	0.194835	−	0.980836i	$-0.437583\pi$
$739$	26.4929	−	9.64262i	0.974556	−	0.354710i	0.779721	+	0.626127i	$0.215361\pi$
$740$	−2.95480			−0.108621
$741$	43.5084	+	13.6084i	1.59832	+	0.499918i
$742$	−0.661109			−0.0242701
$743$	−27.0476	+	9.84451i	−0.992279	+	0.361160i	−0.786602	−	0.617460i	$-0.788162\pi$
$743$	−27.0476	+	9.84451i	−0.992279	+	0.361160i	−0.205677	+	0.978620i	$0.565940\pi$
$744$	−14.6259	−	9.40063i	−0.536211	−	0.344644i
$745$	−16.9473	+	14.2205i	−0.620903	+	0.520999i
$746$	7.65021	−	9.11716i	0.280094	−	0.333803i
$747$	40.5958	+	28.9149i	1.48532	+	1.05794i
$748$	4.58443	+	7.94046i	0.167623	+	0.290332i
$749$	−0.788960	+	1.36652i	−0.0288280	+	0.0499315i
$750$	1.17528	−	1.27229i	0.0429153	−	0.0464573i
$751$	16.6424	−	45.7246i	0.607289	−	1.66851i	−0.128834	−	0.991666i	$-0.541123\pi$
$751$	16.6424	−	45.7246i	0.607289	−	1.66851i	0.736123	−	0.676847i	$-0.236654\pi$
$752$	−5.87754	−	3.39340i	−0.214332	−	0.123744i
$753$	10.4223	−	1.32950i	0.379810	−	0.0484497i
$754$	53.2778	−	9.39432i	1.94026	−	0.342121i
$755$	−6.07085	−	5.09405i	−0.220941	−	0.185391i
$756$	1.82656	+	0.979040i	0.0664315	+	0.0356073i
$757$	0.709067	−	4.02132i	0.0257715	−	0.146157i	−0.969207	−	0.246248i	$-0.920802\pi$
$757$	0.709067	−	4.02132i	0.0257715	−	0.146157i	0.994978	+	0.100091i	$0.0319133\pi$
$758$	5.14393	+	14.1328i	0.186836	+	0.513328i
$759$	1.73940	+	0.728691i	0.0631361	+	0.0264498i
$760$	−3.93879	+	1.86707i	−0.142875	+	0.0677258i
$761$			51.7615i			1.87635i	0.346160	+	0.938176i	$0.387485\pi$
$761$			51.7615i			1.87635i	−0.346160	+	0.938176i	$0.612515\pi$
$762$	0.730885	−	15.3253i	0.0264772	−	0.555177i
$763$	−4.82446	−	0.850682i	−0.174657	−	0.0307968i
$764$	14.8071	+	17.6465i	0.535703	+	0.638426i
$765$	−1.80602	−	22.7491i	−0.0652968	−	0.822496i
$766$	0.601336	+	3.41035i	0.0217272	+	0.123221i
$767$	9.55878	−	5.51877i	0.345148	−	0.199271i
$768$	1.37836	−	1.04887i	0.0497372	−	0.0378479i
$769$	−26.0549	−	9.48323i	−0.939565	−	0.341974i	−0.173571	−	0.984821i	$-0.555531\pi$
$769$	−26.0549	−	9.48323i	−0.939565	−	0.341974i	−0.765994	+	0.642847i	$0.777753\pi$
$770$	0.451737	+	0.164419i	0.0162795	+	0.00592524i
$771$	0.905853	−	0.689315i	0.0326235	−	0.0248251i
$772$	12.4627	−	7.19537i	0.448544	−	0.258967i
$773$	0.389808	+	2.21071i	0.0140204	+	0.0795137i	0.991015	−	0.133750i	$-0.0427018\pi$
$773$	0.389808	+	2.21071i	0.0140204	+	0.0795137i	−0.976995	+	0.213263i	$0.931591\pi$
$774$	0.820186	+	10.3313i	0.0294810	+	0.371351i
$775$	6.45234	+	7.68961i	0.231775	+	0.276219i
$776$	−9.41728	−	1.66052i	−0.338061	−	0.0596092i
$777$	−0.0972361	+	2.03886i	−0.00348833	+	0.0731437i
$778$		−	26.2138i		−	0.939810i
$779$	32.0421	+	2.59945i	1.14803	+	0.0931349i
$780$	9.64609	+	4.04107i	0.345385	+	0.144694i
$781$	−2.34603	−	6.44566i	−0.0839475	−	0.230644i
$782$	1.19322	−	6.76709i	0.0426695	−	0.241991i
$783$	41.0331	+	21.9938i	1.46640	+	0.785994i
$784$	−5.24046	−	4.39727i	−0.187159	−	0.157045i
$785$	8.60537	−	1.51736i	0.307139	−	0.0541569i
$786$	3.13584	−	0.400017i	0.111852	−	0.0142681i
$787$	23.0410	+	13.3028i	0.821324	+	0.474192i	0.850873	−	0.525371i	$-0.176074\pi$
$787$	23.0410	+	13.3028i	0.821324	+	0.474192i	−0.0295485	+	0.999563i	$0.509407\pi$
$788$	−6.29161	+	17.2860i	−0.224129	+	0.615790i
$789$	−2.57237	+	2.78468i	−0.0915787	+	0.0991371i
$790$	−6.25488	+	10.8338i	−0.222539	+	0.385448i
$791$	−0.395500	−	0.685026i	−0.0140624	−	0.0243567i
$792$	−2.94527	−	2.09781i	−0.104656	−	0.0745425i
$793$	−19.5241	+	23.2679i	−0.693321	+	0.826268i
$794$	1.53520	−	1.28819i	0.0544823	−	0.0457161i
$795$	−2.41520	−	1.55234i	−0.0856582	−	0.0550559i
$796$	6.96454	−	2.53488i	0.246852	−	0.0898466i
$797$	32.7568			1.16031			0.580153	−	0.814507i	$-0.302993\pi$
$797$	32.7568			1.16031			0.580153	+	0.814507i	$0.302993\pi$
$798$	1.15869	+	2.77927i	0.0410173	+	0.0983852i
$799$	51.6265			1.82641
$800$	−0.939693	+	0.342020i	−0.0332232	+	0.0120922i
$801$	−7.81596	+	5.37962i	−0.276163	+	0.190079i
$802$	−18.5014	+	15.5245i	−0.653306	+	0.548189i
$803$	7.01197	−	8.35654i	0.247447	−	0.294896i
$804$	12.9829	+	2.93307i	0.457871	+	0.103441i
$805$	−0.180138	−	0.312008i	−0.00634903	−	0.0109968i
$806$	−30.3056	+	52.4909i	−1.06747	+	1.84891i
$807$	32.6821	+	30.1904i	1.15046	+	1.06275i
$808$	−4.93146	+	13.5491i	−0.173488	+	0.476655i
$809$	−7.96919	−	4.60101i	−0.280182	−	0.161763i	0.353324	−	0.935501i	$-0.385051\pi$
$809$	−7.96919	−	4.60101i	−0.280182	−	0.161763i	−0.633506	+	0.773738i	$0.718385\pi$
$810$	4.37403	+	7.86561i	0.153688	+	0.276369i
$811$	−36.5094	+	6.43760i	−1.28202	+	0.226055i	−0.772837	−	0.634604i	$-0.781163\pi$
$811$	−36.5094	+	6.43760i	−1.28202	+	0.226055i	−0.509182	+	0.860659i	$0.670052\pi$
$812$	2.73740	+	2.29695i	0.0960640	+	0.0806072i
$813$	8.41826	−	2.61709i	0.295241	−	0.0917854i
$814$	0.618451	−	3.50741i	0.0216767	−	0.122935i
$815$	6.74882	+	18.5422i	0.236401	+	0.649506i
$816$	−5.09098	+	12.1522i	−0.178220	+	0.425413i
$817$	−8.55896	+	12.3893i	−0.299440	+	0.433447i
$818$		−	7.21446i		−	0.252248i
$819$	3.10584	−	6.52298i	0.108527	−	0.227931i
$820$	7.26306	+	1.28067i	0.253637	+	0.0447231i
$821$	13.4288	+	16.0038i	0.468667	+	0.558536i	0.947659	−	0.319284i	$-0.103442\pi$
$821$	13.4288	+	16.0038i	0.468667	+	0.558536i	−0.478992	+	0.877819i	$0.658998\pi$
$822$	10.7075	−	5.51936i	0.373467	−	0.192510i
$823$	−2.94276	−	16.6892i	−0.102578	−	0.581750i	−0.992160	−	0.124974i	$-0.960115\pi$
$823$	−2.94276	−	16.6892i	−0.102578	−	0.581750i	0.889582	−	0.456776i	$-0.150996\pi$
$824$	16.1061	−	9.29887i	0.561083	−	0.323942i
$825$	1.26424	+	1.66138i	0.0440151	+	0.0578419i
$826$	0.685090	+	0.249352i	0.0238373	+	0.00867607i
$827$	−35.7234	−	13.0023i	−1.24222	−	0.452133i	−0.364457	−	0.931220i	$-0.618745\pi$
$827$	−35.7234	−	13.0023i	−1.24222	−	0.452133i	−0.877767	+	0.479088i	$0.840968\pi$
$828$	0.680312	+	2.62319i	0.0236425	+	0.0911620i
$829$	−33.6996	+	19.4565i	−1.17044	+	0.675751i	−0.953783	−	0.300497i	$-0.902847\pi$
$829$	−33.6996	+	19.4565i	−1.17044	+	0.675751i	−0.216653	+	0.976249i	$0.569514\pi$
$830$	2.88491	+	16.3612i	0.100137	+	0.567904i
$831$	1.50147	+	2.91284i	0.0520854	+	0.101045i
$832$	−3.88124	−	4.62548i	−0.134558	−	0.160360i
$833$	51.2477	+	9.03635i	1.77563	+	0.313091i
$834$	−19.5362	−	0.931709i	−0.676484	−	0.0322624i
$835$		−	11.4566i		−	0.396472i
$836$	−1.39185	−	5.06621i	−0.0481382	−	0.175219i
$837$	−48.4263	+	19.3776i	−1.67386	+	0.669788i
$838$	−1.32162	−	3.63113i	−0.0456547	−	0.125435i
$839$	6.49747	−	36.8490i	0.224317	−	1.27217i	−0.639668	−	0.768651i	$-0.720928\pi$
$839$	6.49747	−	36.8490i	0.224317	−	1.27217i	0.863986	−	0.503516i	$-0.167961\pi$
$840$	0.205076	+	0.659659i	0.00707581	+	0.0227604i
$841$	39.2795	+	32.9594i	1.35446	+	1.13653i
$842$	−18.0485	+	3.18244i	−0.621993	+	0.109674i
$843$	3.60834	+	28.2867i	0.124278	+	0.974246i
$844$	−0.975922	−	0.563449i	−0.0335926	−	0.0193947i
$845$	8.02348	−	22.0443i	0.276016	−	0.758348i
$846$	−18.5214	+	8.45596i	−0.636779	+	0.290722i
$847$	1.90387	−	3.29760i	0.0654177	−	0.113307i
$848$	0.828801	+	1.43553i	0.0284611	+	0.0492961i
$849$	5.90467	−	26.1363i	0.202648	−	0.896997i
$850$	4.88962	−	5.82722i	0.167713	−	0.199872i
$851$	−2.04468	+	1.71569i	−0.0700906	+	0.0588130i
$852$	5.32943	−	8.29175i	0.182583	−	0.284071i
$853$	18.2086	−	6.62738i	0.623450	−	0.226917i	−0.0109278	−	0.999940i	$-0.503479\pi$
$853$	18.2086	−	6.62738i	0.623450	−	0.226917i	0.634378	+	0.773023i	$0.281256\pi$
$854$	−2.00629			−0.0686537
$855$	−2.29297	+	12.8741i	−0.0784181	+	0.440285i
$856$	3.95633			0.135225
$857$	−19.2681	+	7.01302i	−0.658187	+	0.239560i	−0.649453	−	0.760402i	$-0.725002\pi$
$857$	−19.2681	+	7.01302i	−0.658187	+	0.239560i	−0.00873331	+	0.999962i	$0.502780\pi$
$858$	−6.81580	+	10.6043i	−0.232688	+	0.362025i
$859$	−14.7052	+	12.3391i	−0.501735	+	0.421006i	−0.858210	−	0.513299i	$-0.828423\pi$
$859$	−14.7052	+	12.3391i	−0.501735	+	0.421006i	0.356475	+	0.934305i	$0.383979\pi$
$860$	−2.22057	+	2.64638i	−0.0757210	+	0.0902407i
$861$	1.12270	−	4.96949i	0.0382615	−	0.169360i
$862$	5.10967	+	8.85021i	0.174036	+	0.301440i
$863$	15.3894	−	26.6552i	0.523860	−	0.907352i	−0.475754	−	0.879578i	$-0.657825\pi$
$863$	15.3894	−	26.6552i	0.523860	−	0.907352i	0.999614	−	0.0277739i	$-0.00884185\pi$
$864$	−0.164000	−	5.19356i	−0.00557940	−	0.176689i
$865$	5.74797	−	15.7924i	0.195437	−	0.536959i
$866$	−5.45773	−	3.15102i	−0.185461	−	0.107076i
$867$	−8.95634	−	70.2112i	−0.304173	−	2.38450i
$868$	−3.94270	+	0.695205i	−0.133824	+	0.0235968i
$869$	−11.5508	−	9.69223i	−0.391833	−	0.328787i
$870$	4.60697	+	14.8190i	0.156191	+	0.502411i
$871$	8.05737	−	45.6956i	0.273014	−	1.54834i
$872$	4.20103	+	11.5422i	0.142265	+	0.390870i
$873$	−20.4478	+	20.1214i	−0.692052	+	0.681006i
$874$	−1.64148	+	3.57902i	−0.0555238	+	0.121062i
$875$		−	0.398834i		−	0.0134831i
$876$	15.6579	+	0.746745i	0.529030	+	0.0252302i
$877$	53.9707	+	9.51648i	1.82246	+	0.321349i	0.977089	−	0.212831i	$-0.0682685\pi$
$877$	53.9707	+	9.51648i	1.82246	+	0.321349i	0.845371	+	0.534180i	$0.179380\pi$
$878$	−12.2365	−	14.5829i	−0.412963	−	0.492150i
$879$	−14.9774	−	29.0560i	−0.505174	−	0.980034i
$880$	−0.209304	−	1.18702i	−0.00705564	−	0.0400145i
$881$	17.9307	−	10.3523i	0.604102	−	0.348778i	−0.166552	−	0.986033i	$-0.553263\pi$
$881$	17.9307	−	10.3523i	0.604102	−	0.348778i	0.770654	+	0.637254i	$0.219930\pi$
$882$	−19.8656	+	5.15206i	−0.668909	+	0.173479i
$883$	48.0785	+	17.4991i	1.61797	+	0.588893i	0.982994	−	0.183638i	$-0.0587874\pi$
$883$	48.0785	+	17.4991i	1.61797	+	0.588893i	0.634977	+	0.772531i	$0.281010\pi$
$884$	43.1615	+	15.7095i	1.45168	+	0.528368i
$885$	1.91730	+	2.51960i	0.0644495	+	0.0846953i
$886$	4.00855	−	2.31434i	0.134670	−	0.0777518i
$887$	5.23121	+	29.6677i	0.175647	+	0.996144i	0.937394	+	0.348270i	$0.113231\pi$
$887$	5.23121	+	29.6677i	0.175647	+	0.996144i	−0.761747	+	0.647874i	$0.775658\pi$
$888$	4.54907	−	2.34489i	0.152657	−	0.0786893i
$889$	−2.27092	−	2.70638i	−0.0761642	−	0.0907689i
$890$	−3.11475	−	0.549214i	−0.104406	−	0.0184097i
$891$	−10.2522	+	3.54576i	−0.343460	+	0.118788i
$892$		−	23.1930i		−	0.776559i
$893$	−28.6227	−	7.47595i	−0.957823	−	0.250173i
$894$	14.8061	−	35.3424i	0.495191	−	1.18203i
$895$	−3.05020	−	8.38036i	−0.101957	−	0.280125i
$896$	0.0692569	−	0.392775i	0.00231371	−	0.0131217i
$897$	9.02138	−	2.80459i	0.301215	−	0.0936425i
$898$	−5.04084	−	4.22977i	−0.168215	−	0.141149i
$899$	−88.5714	+	15.6175i	−2.95402	+	0.520874i
$900$	−0.799742	+	2.89144i	−0.0266581	+	0.0963813i
$901$	−10.9199	−	6.30461i	−0.363795	−	0.210037i
$902$	−3.04038	+	8.35336i	−0.101233	+	0.278137i
$903$	1.75297	+	1.61932i	0.0583352	+	0.0538876i
$904$	−0.991640	+	1.71757i	−0.0329814	+	0.0571255i
$905$	5.38200	+	9.32189i	0.178904	+	0.309870i
$906$	13.3890	+	3.02481i	0.444818	+	0.100493i
$907$	20.2829	−	24.1722i	0.673483	−	0.802626i	−0.315770	−	0.948836i	$-0.602263\pi$
$907$	20.2829	−	24.1722i	0.673483	−	0.802626i	0.989254	+	0.146209i	$0.0467074\pi$
$908$	8.60324	−	7.21897i	0.285508	−	0.239570i
$909$	24.5247	+	35.6316i	0.813434	+	1.18182i
$910$	2.26298	−	0.823658i	0.0750172	−	0.0273040i
$911$	25.9992			0.861393			0.430696	−	0.902497i	$-0.358268\pi$
$911$	25.9992			0.861393			0.430696	+	0.902497i	$0.358268\pi$
$912$	4.58229	−	6.00022i	0.151735	−	0.198687i
$913$	−20.0249			−0.662727
$914$	26.2429	−	9.55162i	0.868037	−	0.315940i
$915$	−7.32947	−	4.71094i	−0.242305	−	0.155739i
$916$	−4.72536	+	3.96505i	−0.156130	+	0.131009i
$917$	0.467906	−	0.557629i	0.0154516	−	0.0184145i
$918$	20.8339	+	33.5902i	0.687620	+	1.10864i
$919$	9.68133	+	16.7685i	0.319357	+	0.553143i	0.980354	−	0.197245i	$-0.0631996\pi$
$919$	9.68133	+	16.7685i	0.319357	+	0.553143i	−0.660997	+	0.750389i	$0.729866\pi$
$920$	−0.451661	+	0.782300i	−0.0148908	+	0.0257917i
$921$	3.11366	−	3.37065i	0.102599	−	0.111067i
$922$	4.91864	−	13.5139i	0.161987	−	0.445055i
$923$	−29.7583	−	17.1809i	−0.979506	−	0.565518i
$924$	−0.825953	+	0.105361i	−0.0271719	+	0.00346612i
$925$	−2.90991	+	0.513095i	−0.0956772	+	0.0168705i
$926$	−10.6910	−	8.97083i	−0.351329	−	0.294800i
$927$	5.30964	−	55.5400i	0.174391	−	1.82417i
$928$	1.55583	−	8.82355i	0.0510726	−	0.289647i
$929$	6.41252	+	17.6183i	0.210388	+	0.578036i	0.999336	−	0.0364232i	$-0.0115964\pi$
$929$	6.41252	+	17.6183i	0.210388	+	0.578036i	−0.788949	+	0.614459i	$0.789374\pi$
$930$	−16.0361	−	6.71806i	−0.525844	−	0.220294i
$931$	−27.1042	−	12.4310i	−0.888304	−	0.407411i
$932$			14.3413i			0.469765i
$933$	0.848445	−	17.7903i	0.0277768	−	0.582429i
$934$	31.8155	+	5.60993i	1.04104	+	0.183563i
$935$	5.89362	+	7.02375i	0.192742	+	0.229701i
$936$	−18.0576	+	1.43357i	−0.590231	+	0.0468576i
$937$	7.69823	+	43.6589i	0.251490	+	1.42627i	0.804923	+	0.593379i	$0.202206\pi$
$937$	7.69823	+	43.6589i	0.251490	+	1.42627i	−0.553433	+	0.832894i	$0.686682\pi$
$938$	2.65426	−	1.53244i	0.0866647	−	0.0500359i
$939$	−17.3382	+	13.1936i	−0.565810	+	0.430557i
$940$	−6.37750	−	2.32122i	−0.208011	−	0.0757099i
$941$	−0.140754	−	0.0512302i	−0.00458845	−	0.00167006i	0.339725	−	0.940525i	$-0.389666\pi$
$941$	−0.140754	−	0.0512302i	−0.00458845	−	0.00167006i	−0.344313	+	0.938855i	$0.611888\pi$
$942$	−12.0443	+	9.16516i	−0.392423	+	0.298617i
$943$	5.76955	−	3.33105i	0.187882	−	0.108474i
$944$	−0.317424	−	1.80020i	−0.0103313	−	0.0585915i
$945$	1.96882	+	0.646987i	0.0640458	+	0.0210465i
$946$	−2.67653	−	3.18977i	−0.0870216	−	0.103708i
$947$	31.8460	+	5.61530i	1.03485	+	0.182473i	0.665176	−	0.746687i	$-0.268357\pi$
$947$	31.8460	+	5.61530i	1.03485	+	0.182473i	0.369679	+	0.929160i	$0.379468\pi$
$948$	1.03218	−	21.6429i	0.0335237	−	0.702930i
$949$		−	54.6472i		−	1.77392i
$950$	−3.55473	+	2.52267i	−0.115331	+	0.0818462i
$951$	8.45161	+	3.54066i	0.274062	+	0.114814i
$952$	1.03765	+	2.85093i	0.0336305	+	0.0923991i
$953$	−1.80963	+	10.2629i	−0.0586196	+	0.332448i	−0.999988	−	0.00493265i	$-0.998430\pi$
$953$	−1.80963	+	10.2629i	−0.0586196	+	0.332448i	0.941368	+	0.337381i	$0.109541\pi$
$954$	4.95024	+	0.473244i	0.160270	+	0.0153218i
$955$	17.6465	+	14.8071i	0.571026	+	0.479148i
$956$	−11.1114	+	1.95924i	−0.359369	+	0.0633665i
$957$	−18.5547	+	2.36690i	−0.599790	+	0.0765109i
$958$	−33.6927	−	19.4525i	−1.08856	−	0.628481i
$959$	0.948721	−	2.60659i	0.0306358	−	0.0841712i
$960$	1.17528	−	1.27229i	0.0379321	−	0.0410628i
$961$	34.8814	−	60.4163i	1.12521	−	1.94891i
$962$	−8.92074	−	15.4512i	−0.287616	−	0.498166i
$963$	6.88576	−	9.66743i	0.221890	−	0.311529i
$964$	11.1037	−	13.2328i	0.357625	−	0.426201i
$965$	11.0239	−	9.25019i	0.354873	−	0.297774i
$966$	0.524937	+	0.337398i	0.0168896	+	0.0108556i
$967$	−8.78715	+	3.19826i	−0.282576	+	0.102849i	−0.479420	−	0.877586i	$-0.659153\pi$
$967$	−8.78715	+	3.19826i	−0.282576	+	0.102849i	0.196844	+	0.980435i	$0.436931\pi$
$968$	−9.54717			−0.306858
$969$	−7.36550	+	56.9566i	−0.236614	+	1.82971i
$970$	−9.56255			−0.307035
$971$	18.1378	−	6.60161i	0.582069	−	0.211856i	−0.0341689	−	0.999416i	$-0.510878\pi$
$971$	18.1378	−	6.60161i	0.582069	−	0.211856i	0.616237	+	0.787560i	$0.288656\pi$
$972$	−12.9761	−	8.63835i	−0.416208	−	0.277075i
$973$	−3.45000	+	2.89490i	−0.110602	+	0.0928061i
$974$	−9.89554	+	11.7930i	−0.317074	+	0.377874i
$975$	10.2013	+	2.30465i	0.326702	+	0.0738079i
$976$	2.51519	+	4.35643i	0.0805092	+	0.139446i
$977$	17.5706	−	30.4332i	0.562135	−	0.973646i	−0.435175	−	0.900346i	$-0.643314\pi$
$977$	17.5706	−	30.4332i	0.562135	−	0.973646i	0.997310	−	0.0733000i	$-0.0233530\pi$
$978$	−25.1050	−	23.1909i	−0.802770	−	0.741565i
$979$	1.30386	−	3.58232i	0.0416715	−	0.114491i
$980$	−5.92442	−	3.42047i	−0.189249	−	0.109263i
$981$	35.5155	+	9.82323i	1.13392	+	0.313632i
$982$	−28.8280	+	5.08315i	−0.919937	+	0.162210i
$983$	2.03983	+	1.71162i	0.0650606	+	0.0545923i	0.674738	−	0.738057i	$-0.264257\pi$
$983$	2.03983	+	1.71162i	0.0650606	+	0.0545923i	−0.609677	+	0.792650i	$0.708701\pi$
$984$	−12.1982	+	3.79220i	−0.388864	+	0.120891i
$985$	−3.19433	+	18.1160i	−0.101780	+	0.577222i
$986$	23.3105	+	64.0450i	0.742357	+	2.03961i
$987$	−1.81155	+	4.32420i	−0.0576623	+	0.137641i
$988$	−21.6547	−	14.9598i	−0.688928	−	0.475935i
$989$			3.12062i			0.0992299i
$990$	−3.26481	−	1.55450i	−0.103762	−	0.0494053i
$991$	28.3197	+	4.99353i	0.899605	+	0.158625i	0.604280	−	0.796772i	$-0.293461\pi$
$991$	28.3197	+	4.99353i	0.899605	+	0.158625i	0.295325	+	0.955397i	$0.404572\pi$
$992$	6.45234	+	7.68961i	0.204862	+	0.244145i
$993$	−33.1325	+	17.0786i	−1.05143	+	0.541975i
$994$	−0.394128	−	2.23521i	−0.0125010	−	0.0708965i
$995$	6.41855	−	3.70575i	0.203482	−	0.117480i
$996$	−17.4255	−	22.8994i	−0.552147	−	0.725596i
$997$	34.8295	+	12.6769i	1.10306	+	0.401481i	0.828444	−	0.560072i	$-0.189227\pi$
$997$	34.8295	+	12.6769i	1.10306	+	0.401481i	0.274617	+	0.961554i	$0.411449\pi$
$998$	5.63156	+	2.04972i	0.178264	+	0.0648828i
$999$	2.18757	−	15.1969i	0.0692116	−	0.480810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.b.71.6	yes	84
3.2	odd	2		570.2.bb.a.71.7	✓	84
19.15	odd	18		570.2.bb.a.281.7	yes	84
57.53	even	18	inner	570.2.bb.b.281.6	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.71.7	✓	84	3.2	odd	2
570.2.bb.a.281.7	yes	84	19.15	odd	18
570.2.bb.b.71.6	yes	84	1.1	even	1	trivial
570.2.bb.b.281.6	yes	84	57.53	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.936498 + 1.45704i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(-0.381683 + 1.68947i) q^{6} +(0.199417 + 0.345401i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.24594 - 2.72903i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.936498 + 1.45704i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(-0.381683 + 1.68947i) q^{6} +(0.199417 + 0.345401i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.24594 - 2.72903i) q^{9} +(0.342020 - 0.939693i) q^{10} +(1.04385 + 0.602667i) q^{11} +(0.219169 + 1.71813i) q^{12} +(5.94640 - 1.04851i) q^{13} +(0.305525 + 0.256366i) q^{14} +(0.514190 + 1.65397i) q^{15} +(0.173648 - 0.984808i) q^{16} +(2.60171 + 7.14815i) q^{17} +(-2.10419 - 2.13832i) q^{18} +(-0.407328 - 4.33983i) q^{19} -1.00000i q^{20} +(-0.690017 - 0.0329079i) q^{21} +(1.18702 + 0.209304i) q^{22} +(-0.580645 - 0.691985i) q^{23} +(0.793586 + 1.53955i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(5.22918 - 3.01907i) q^{26} +(5.14314 + 0.740344i) q^{27} +(0.374782 + 0.136409i) q^{28} +(8.41934 + 3.06439i) q^{29} +(1.04887 + 1.37836i) q^{30} +(-8.69322 + 5.01903i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-1.85567 + 0.956536i) q^{33} +(4.88962 + 5.82722i) q^{34} +(0.392775 + 0.0692569i) q^{35} +(-2.70864 - 1.28968i) q^{36} -2.95480i q^{37} +(-1.86707 - 3.93879i) q^{38} +(-4.04107 + 9.64609i) q^{39} +(-0.342020 - 0.939693i) q^{40} +(-1.28067 + 7.26306i) q^{41} +(-0.659659 + 0.205076i) q^{42} +(-2.64638 - 2.22057i) q^{43} +(1.18702 - 0.209304i) q^{44} +(-2.89144 - 0.799742i) q^{45} +(-0.782300 - 0.451661i) q^{46} +(2.32122 - 6.37750i) q^{47} +(1.27229 + 1.17528i) q^{48} +(3.42047 - 5.92442i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-12.8516 - 2.90342i) q^{51} +(3.88124 - 4.62548i) q^{52} +(-1.26980 + 1.06549i) q^{53} +(5.08618 - 1.06336i) q^{54} +(1.13264 - 0.412248i) q^{55} +0.398834 q^{56} +(6.70477 + 3.47074i) q^{57} +8.95967 q^{58} +(1.71773 - 0.625203i) q^{59} +(1.45704 + 0.936498i) q^{60} +(-3.85349 + 3.23346i) q^{61} +(-6.45234 + 7.68961i) q^{62} +(0.694148 - 0.974566i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.01907 - 5.22918i) q^{65} +(-1.41661 + 1.53353i) q^{66} +(2.62828 - 7.22115i) q^{67} +(6.58777 + 3.80345i) q^{68} +(1.55202 - 0.197981i) q^{69} +(0.392775 - 0.0692569i) q^{70} +(-4.35941 - 3.65798i) q^{71} +(-2.98638 - 0.285499i) q^{72} +(1.57158 - 8.91285i) q^{73} +(-1.01060 - 2.77660i) q^{74} +(1.59753 + 0.669258i) q^{75} +(-3.10162 - 3.06267i) q^{76} +0.480728i q^{77} +(-0.498207 + 10.4465i) q^{78} +(-12.3197 - 2.17230i) q^{79} +(-0.642788 - 0.766044i) q^{80} +(-5.89525 + 6.80044i) q^{81} +(1.28067 + 7.26306i) q^{82} +(-14.3878 + 8.30678i) q^{83} +(-0.549737 + 0.418326i) q^{84} +(7.14815 + 2.60171i) q^{85} +(-3.24626 - 1.18154i) q^{86} +(-12.3496 + 9.39753i) q^{87} +(1.04385 - 0.602667i) q^{88} +(-0.549214 - 3.11475i) q^{89} +(-2.99059 + 0.237419i) q^{90} +(1.54797 + 1.84480i) q^{91} +(-0.889599 - 0.156860i) q^{92} +(0.828242 - 17.3667i) q^{93} -6.78679i q^{94} +(-3.58632 - 2.47755i) q^{95} +(1.59753 + 0.669258i) q^{96} +(-3.27059 - 8.98586i) q^{97} +(1.18792 - 6.73700i) q^{98} +(0.344122 - 3.59959i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) \) 84 * q - 6 * q^6 + 42 * q^8	\( 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) \) 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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