LMFDB - Embedded newform 414.2.p.a.5.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(5,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("414.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.p (of order $66$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	414.5
Dual form			414.2.p.a.83.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.971812 - 0.235759i) q^{2} +(-1.36529 + 1.06582i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-0.463371 - 0.364399i) q^{5} +(-1.07553 + 1.35766i) q^{6} +(0.209188 + 0.148962i) q^{7} +(0.755750 - 0.654861i) q^{8} +(0.728058 - 2.91031i) q^{9} +O(q^{10})$	\(q+(0.971812 - 0.235759i) q^{2} +(-1.36529 + 1.06582i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-0.463371 - 0.364399i) q^{5} +(-1.07553 + 1.35766i) q^{6} +(0.209188 + 0.148962i) q^{7} +(0.755750 - 0.654861i) q^{8} +(0.728058 - 2.91031i) q^{9} +(-0.536220 - 0.244883i) q^{10} +(4.65375 + 4.43734i) q^{11} +(-0.725135 + 1.57295i) q^{12} +(2.30313 + 3.23429i) q^{13} +(0.238411 + 0.0954453i) q^{14} +(1.02102 + 0.00364213i) q^{15} +(0.580057 - 0.814576i) q^{16} +(-0.341450 + 0.219437i) q^{17} +(0.0214025 - 2.99992i) q^{18} +(0.553986 - 0.862020i) q^{19} +(-0.578838 - 0.111562i) q^{20} +(-0.444370 + 0.0195795i) q^{21} +(5.56871 + 3.21510i) q^{22} +(4.05778 + 2.55626i) q^{23} +(-0.333857 + 1.69957i) q^{24} +(-1.09687 - 4.52135i) q^{25} +(3.00072 + 2.60014i) q^{26} +(2.10786 + 4.74941i) q^{27} +(0.254192 + 0.0365474i) q^{28} +(-2.34281 + 4.54442i) q^{29} +(0.993100 - 0.237176i) q^{30} +(-4.08909 + 0.788107i) q^{31} +(0.371662 - 0.928368i) q^{32} +(-11.0831 - 1.09822i) q^{33} +(-0.280091 + 0.293751i) q^{34} +(-0.0426501 - 0.145253i) q^{35} +(-0.686460 - 2.92041i) q^{36} +(2.01101 - 0.289139i) q^{37} +(0.335142 - 0.968328i) q^{38} +(-6.59162 - 1.96104i) q^{39} +(-0.588823 + 0.0280491i) q^{40} +(-3.29846 + 4.19433i) q^{41} +(-0.427228 + 0.123792i) q^{42} +(1.30173 - 6.75404i) q^{43} +(6.16973 + 1.81160i) q^{44} +(-1.39788 + 1.08325i) q^{45} +(4.54606 + 1.52754i) q^{46} +(10.7232 - 6.19104i) q^{47} +(0.0762423 + 1.73037i) q^{48} +(-2.26791 - 6.55268i) q^{49} +(-2.13190 - 4.13531i) q^{50} +(0.232300 - 0.663519i) q^{51} +(3.52914 + 1.81940i) q^{52} +(-4.51077 - 9.87720i) q^{53} +(3.16816 + 4.11859i) q^{54} +(-0.539451 - 3.75196i) q^{55} +(0.255643 - 0.0244110i) q^{56} +(0.162403 + 1.76736i) q^{57} +(-1.20538 + 4.96866i) q^{58} +(-6.73346 + 4.79488i) q^{59} +(0.909190 - 0.464622i) q^{60} +(-0.591956 - 0.204878i) q^{61} +(-3.78802 + 1.72993i) q^{62} +(0.585828 - 0.500350i) q^{63} +(0.142315 - 0.989821i) q^{64} +(0.111370 - 2.33794i) q^{65} +(-11.0296 + 1.54569i) q^{66} +(-1.58647 - 1.66384i) q^{67} +(-0.202941 + 0.351504i) q^{68} +(-8.26457 + 0.834817i) q^{69} +(-0.0756925 - 0.131103i) q^{70} +(0.321673 - 1.09552i) q^{71} +(-1.35562 - 2.67625i) q^{72} +(-2.62993 - 1.69016i) q^{73} +(1.88615 - 0.755101i) q^{74} +(6.31649 + 5.00392i) q^{75} +(0.0974025 - 1.02004i) q^{76} +(0.312513 + 1.62147i) q^{77} +(-6.86814 - 0.351729i) q^{78} +(-0.0537433 - 0.562826i) q^{79} +(-0.565613 + 0.166079i) q^{80} +(-7.93986 - 4.23776i) q^{81} +(-2.21663 + 4.85374i) q^{82} +(2.47978 - 1.95012i) q^{83} +(-0.386000 + 0.221025i) q^{84} +(0.238181 + 0.0227435i) q^{85} +(-0.327285 - 6.87055i) q^{86} +(-1.64490 - 8.70148i) q^{87} +(6.42291 + 0.305961i) q^{88} +(-11.2157 + 12.9436i) q^{89} +(-1.10309 + 1.38228i) q^{90} +1.01965i q^{91} +(4.77804 + 0.412709i) q^{92} +(4.74283 - 5.43423i) q^{93} +(8.96133 - 8.54461i) q^{94} +(-0.570821 + 0.197563i) q^{95} +(0.482044 + 1.66362i) q^{96} +(-4.11218 - 10.2717i) q^{97} +(-3.74883 - 5.83329i) q^{98} +(16.3023 - 10.3132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{22}\right)$

Coefficient data

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

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

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

$2$	0.971812	−	0.235759i	0.687175	−	0.166707i
$2$	0.971812	−	0.235759i	0.687175	−	0.166707i
$3$	−1.36529	+	1.06582i	−0.788253	+	0.615351i
$3$	−1.36529	+	1.06582i	−0.788253	+	0.615351i
$4$	0.888835	−	0.458227i	0.444418	−	0.229113i
$5$	−0.463371	−	0.364399i	−0.207226	−	0.162964i	0.509152	−	0.860676i	$-0.329959\pi$
$5$	−0.463371	−	0.364399i	−0.207226	−	0.162964i	−0.716378	+	0.697712i	$0.754201\pi$
$6$	−1.07553	+	1.35766i	−0.439084	+	0.554261i
$7$	0.209188	+	0.148962i	0.0790657	+	0.0563025i	0.618906	−	0.785465i	$-0.287576\pi$
$7$	0.209188	+	0.148962i	0.0790657	+	0.0563025i	−0.539841	+	0.841767i	$0.681515\pi$
$8$	0.755750	−	0.654861i	0.267198	−	0.231528i
$9$	0.728058	−	2.91031i	0.242686	−	0.970105i
$10$	−0.536220	−	0.244883i	−0.169568	−	0.0774390i
$11$	4.65375	+	4.43734i	1.40316	+	1.33791i	0.871016	+	0.491255i	$0.163462\pi$
$11$	4.65375	+	4.43734i	1.40316	+	1.33791i	0.532143	+	0.846655i	$0.321387\pi$
$12$	−0.725135	+	1.57295i	−0.209329	+	0.454072i
$13$	2.30313	+	3.23429i	0.638773	+	0.897031i	0.999363	−	0.0356937i	$-0.0113641\pi$
$13$	2.30313	+	3.23429i	0.638773	+	0.897031i	−0.360590	+	0.932724i	$0.617425\pi$
$14$	0.238411	+	0.0954453i	0.0637180	+	0.0255088i
$15$	1.02102	+	0.00364213i	0.263627	+	0.000940393i
$16$	0.580057	−	0.814576i	0.145014	−	0.203644i
$17$	−0.341450	+	0.219437i	−0.0828138	+	0.0532212i	−0.581392	−	0.813623i	$-0.697492\pi$
$17$	−0.341450	+	0.219437i	−0.0828138	+	0.0532212i	0.498579	+	0.866844i	$0.333856\pi$
$18$	0.0214025	−	2.99992i	0.00504463	−	0.707089i
$19$	0.553986	−	0.862020i	0.127093	−	0.197761i	−0.771876	−	0.635774i	$-0.780681\pi$
$19$	0.553986	−	0.862020i	0.127093	−	0.197761i	0.898969	+	0.438013i	$0.144318\pi$
$20$	−0.578838	−	0.111562i	−0.129432	−	0.0249460i
$21$	−0.444370	+	0.0195795i	−0.0969696	+	0.00427260i
$22$	5.56871	+	3.21510i	1.18725	+	0.685461i
$23$	4.05778	+	2.55626i	0.846105	+	0.533016i
$23$	4.05778	+	2.55626i	0.846105	+	0.533016i
$24$	−0.333857	+	1.69957i	−0.0681484	+	0.346923i
$25$	−1.09687	−	4.52135i	−0.219374	−	0.904271i
$26$	3.00072	+	2.60014i	0.588489	+	0.509929i
$27$	2.10786	+	4.74941i	0.405657	+	0.914025i
$28$	0.254192	+	0.0365474i	0.0480379	+	0.00690680i
$29$	−2.34281	+	4.54442i	−0.435049	+	0.843877i	0.564777	+	0.825243i	$0.308962\pi$
$29$	−2.34281	+	4.54442i	−0.435049	+	0.843877i	−0.999826	+	0.0186340i	$0.994068\pi$
$30$	0.993100	−	0.237176i	0.181314	−	0.0433022i
$31$	−4.08909	+	0.788107i	−0.734422	+	0.141548i	−0.542730	−	0.839907i	$-0.682609\pi$
$31$	−4.08909	+	0.788107i	−0.734422	+	0.141548i	−0.191692	+	0.981455i	$0.561397\pi$
$32$	0.371662	−	0.928368i	0.0657013	−	0.164114i
$33$	−11.0831	−	1.09822i	−1.92933	−	0.191176i
$34$	−0.280091	+	0.293751i	−0.0480352	+	0.0503778i
$35$	−0.0426501	−	0.145253i	−0.00720918	−	0.0245522i
$36$	−0.686460	−	2.92041i	−0.114410	−	0.486734i
$37$	2.01101	−	0.289139i	0.330607	−	0.0475342i	0.0249875	−	0.999688i	$-0.492045\pi$
$37$	2.01101	−	0.289139i	0.330607	−	0.0475342i	0.305620	+	0.952154i	$0.401136\pi$
$38$	0.335142	−	0.968328i	0.0543671	−	0.157084i
$39$	−6.59162	−	1.96104i	−1.05550	−	0.314018i
$40$	−0.588823	+	0.0280491i	−0.0931012	+	0.00443496i
$41$	−3.29846	+	4.19433i	−0.515133	+	0.655044i	−0.972135	−	0.234421i	$-0.924681\pi$
$41$	−3.29846	+	4.19433i	−0.515133	+	0.655044i	0.457003	+	0.889465i	$0.348923\pi$
$42$	−0.427228	+	0.123792i	−0.0659228	+	0.0191015i
$43$	1.30173	−	6.75404i	0.198513	−	1.02998i	−0.736787	−	0.676125i	$-0.763658\pi$
$43$	1.30173	−	6.75404i	0.198513	−	1.02998i	0.935300	−	0.353856i	$-0.115130\pi$
$44$	6.16973	+	1.81160i	0.930121	+	0.273108i
$45$	−1.39788	+	1.08325i	−0.208383	+	0.161482i
$46$	4.54606	+	1.52754i	0.670279	+	0.225224i
$47$	10.7232	−	6.19104i	1.56414	−	0.903056i	0.567307	−	0.823506i	$-0.307985\pi$
$47$	10.7232	−	6.19104i	1.56414	−	0.903056i	0.996831	−	0.0795495i	$-0.0253482\pi$
$48$	0.0762423	+	1.73037i	0.0110046	+	0.249758i
$49$	−2.26791	−	6.55268i	−0.323987	−	0.936098i
$50$	−2.13190	−	4.13531i	−0.301496	−	0.584821i
$51$	0.232300	−	0.663519i	0.0325285	−	0.0929113i
$52$	3.52914	+	1.81940i	0.489403	+	0.252305i
$53$	−4.51077	−	9.87720i	−0.619601	−	1.35674i	−0.915809	−	0.401614i	$-0.868449\pi$
$53$	−4.51077	−	9.87720i	−0.619601	−	1.35674i	0.296208	−	0.955124i	$-0.404278\pi$
$54$	3.16816	+	4.11859i	0.431131	+	0.560469i
$55$	−0.539451	−	3.75196i	−0.0727395	−	0.505914i
$56$	0.255643	−	0.0244110i	0.0341618	−	0.00326206i
$57$	0.162403	+	1.76736i	0.0215108	+	0.234093i
$58$	−1.20538	+	4.96866i	−0.158275	+	0.652417i
$59$	−6.73346	+	4.79488i	−0.876622	+	0.624240i	−0.927236	−	0.374478i	$-0.877822\pi$
$59$	−6.73346	+	4.79488i	−0.876622	+	0.624240i	0.0506134	+	0.998718i	$0.483882\pi$
$60$	0.909190	−	0.464622i	0.117376	−	0.0599825i
$61$	−0.591956	−	0.204878i	−0.0757922	−	0.0262319i	0.288909	−	0.957357i	$-0.406708\pi$
$61$	−0.591956	−	0.204878i	−0.0757922	−	0.0262319i	−0.364701	+	0.931125i	$0.618829\pi$
$62$	−3.78802	+	1.72993i	−0.481079	+	0.219701i
$63$	0.585828	−	0.500350i	0.0738074	−	0.0630382i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	0.111370	−	2.33794i	0.0138137	−	0.289985i
$66$	−11.0296	+	1.54569i	−1.35766	+	0.190261i
$67$	−1.58647	−	1.66384i	−0.193818	−	0.203270i	0.619653	−	0.784876i	$-0.287273\pi$
$67$	−1.58647	−	1.66384i	−0.193818	−	0.203270i	−0.813471	+	0.581605i	$0.802425\pi$
$68$	−0.202941	+	0.351504i	−0.0246102	+	0.0426262i
$69$	−8.26457	+	0.834817i	−0.994937	+	0.100500i
$70$	−0.0756925	−	0.131103i	−0.00904699	−	0.0156698i
$71$	0.321673	−	1.09552i	0.0381756	−	0.130014i	−0.938200	−	0.346092i	$-0.887508\pi$
$71$	0.321673	−	1.09552i	0.0381756	−	0.130014i	0.976376	+	0.216078i	$0.0693266\pi$
$72$	−1.35562	−	2.67625i	−0.159761	−	0.315399i
$73$	−2.62993	−	1.69016i	−0.307811	−	0.197818i	0.377611	−	0.925964i	$-0.376746\pi$
$73$	−2.62993	−	1.69016i	−0.307811	−	0.197818i	−0.685422	+	0.728146i	$0.740382\pi$
$74$	1.88615	−	0.755101i	0.219261	−	0.0877788i
$75$	6.31649	+	5.00392i	0.729366	+	0.577802i
$76$	0.0974025	−	1.02004i	0.0111728	−	0.117007i
$77$	0.312513	+	1.62147i	0.0356142	+	0.184784i
$78$	−6.86814	−	0.351729i	−0.777664	−	0.0398255i
$79$	−0.0537433	−	0.562826i	−0.00604660	−	0.0633228i	0.991945	−	0.126669i	$-0.0404287\pi$
$79$	−0.0537433	−	0.562826i	−0.00604660	−	0.0633228i	−0.997992	+	0.0633465i	$0.979823\pi$
$80$	−0.565613	+	0.166079i	−0.0632374	+	0.0185682i
$81$	−7.93986	−	4.23776i	−0.882207	−	0.470862i
$82$	−2.21663	+	4.85374i	−0.244786	+	0.536006i
$83$	2.47978	−	1.95012i	0.272191	−	0.214053i	−0.472728	−	0.881209i	$-0.656731\pi$
$83$	2.47978	−	1.95012i	0.272191	−	0.214053i	0.744919	+	0.667155i	$0.232488\pi$
$84$	−0.386000	+	0.221025i	−0.0421161	+	0.0241158i
$85$	0.238181	+	0.0227435i	0.0258343	+	0.00246688i
$86$	−0.327285	−	6.87055i	−0.0352920	−	0.740870i
$87$	−1.64490	−	8.70148i	−0.176352	−	0.932897i
$88$	6.42291	+	0.305961i	0.684685	+	0.0326156i
$89$	−11.2157	+	12.9436i	−1.18886	+	1.37202i	−0.277331	+	0.960774i	$0.589450\pi$
$89$	−11.2157	+	12.9436i	−1.18886	+	1.37202i	−0.911527	+	0.411241i	$0.865095\pi$
$90$	−1.10309	+	1.38228i	−0.116276	+	0.145705i
$91$			1.01965i			0.106889i
$92$	4.77804	+	0.412709i	0.498145	+	0.0430279i
$93$	4.74283	−	5.43423i	0.491809	−	0.563503i
$94$	8.96133	−	8.54461i	0.924291	−	0.881309i
$95$	−0.570821	+	0.197563i	−0.0585650	+	0.0202695i
$96$	0.482044	+	1.66362i	0.0491984	+	0.169793i
$97$	−4.11218	−	10.2717i	−0.417529	−	1.04294i	−0.976839	−	0.213978i	$-0.931358\pi$
$97$	−4.11218	−	10.2717i	−0.417529	−	1.04294i	0.559310	−	0.828959i	$-0.311066\pi$
$98$	−3.74883	−	5.83329i	−0.378689	−	0.589252i
$99$	16.3023	−	10.3132i	1.63844	−	1.03652i
$100$	−3.04674	−	3.51613i	−0.304674	−	0.351613i
$101$	6.77819	+	8.61916i	0.674455	+	0.857639i	0.996009	−	0.0892522i	$-0.0284477\pi$
$101$	6.77819	+	8.61916i	0.674455	+	0.857639i	−0.321554	+	0.946891i	$0.604205\pi$
$102$	0.0693212	−	0.699583i	0.00686382	−	0.0692690i
$103$	−14.9562	−	3.62833i	−1.47368	−	0.357510i	−0.583121	−	0.812386i	$-0.698169\pi$
$103$	−14.9562	−	3.62833i	−1.47368	−	0.357510i	−0.890555	+	0.454876i	$0.849684\pi$
$104$	3.85860	+	0.936086i	0.378367	+	0.0917907i
$105$	0.213043	+	0.152856i	0.0207909	+	0.0149172i
$106$	−6.71225	−	8.53532i	−0.651952	−	0.829024i
$107$	7.23957	+	8.35491i	0.699876	+	0.807700i	0.988736	−	0.149671i	$-0.0478216\pi$
$107$	7.23957	+	8.35491i	0.699876	+	0.807700i	−0.288860	+	0.957371i	$0.593276\pi$
$108$	4.04985	+	3.25557i	0.389697	+	0.313268i
$109$	−6.70063	−	10.4264i	−0.641804	−	0.998667i	−0.997935	−	0.0642307i	$-0.979541\pi$
$109$	−6.70063	−	10.4264i	−0.641804	−	0.998667i	0.356131	−	0.934436i	$-0.384096\pi$
$110$	−1.40880	−	3.51902i	−0.134324	−	0.335525i
$111$	−2.43745	+	2.53813i	−0.231352	+	0.240909i
$112$	0.242682	−	0.0839931i	0.0229313	−	0.00793660i
$113$	−7.34857	+	7.00685i	−0.691295	+	0.659149i	−0.951939	−	0.306286i	$-0.900914\pi$
$113$	−7.34857	+	7.00685i	−0.691295	+	0.659149i	0.260644	+	0.965435i	$0.416065\pi$
$114$	0.574496	+	1.67925i	0.0538065	+	0.157276i
$115$	−0.948760	−	2.66315i	−0.0884724	−	0.248340i
$116$			5.11278i			0.474710i
$117$	11.0896	−	4.34807i	1.02523	−	0.401980i
$118$	−5.41322	+	6.24719i	−0.498328	+	0.575101i
$119$	−0.104115	−	0.00495961i	−0.00954421	−	0.000454647i
$120$	0.774022	−	0.665875i	0.0706582	−	0.0607858i
$121$	1.44399	+	30.3130i	0.131272	+	2.75573i
$122$	−0.623571	−	0.0595438i	−0.0564555	−	0.00539085i
$123$	0.0329677	−	9.24206i	0.00297260	−	0.833328i
$124$	−3.27340	+	2.57423i	−0.293960	+	0.231172i
$125$	−2.36374	+	5.17586i	−0.211419	+	0.462943i
$126$	0.451353	−	0.624361i	0.0402097	−	0.0556225i
$127$	12.8822	−	3.78257i	1.14311	−	0.335649i	0.345265	−	0.938505i	$-0.387789\pi$
$127$	12.8822	−	3.78257i	1.14311	−	0.335649i	0.797850	+	0.602856i	$0.205971\pi$
$128$	−0.0950560	−	0.995472i	−0.00840185	−	0.0879881i
$129$	5.42133	+	10.6087i	0.477322	+	0.934041i
$130$	−0.442959	−	2.29829i	−0.0388501	−	0.201573i
$131$	−0.758280	+	7.94107i	−0.0662512	+	0.693814i	0.899945	+	0.436004i	$0.143607\pi$
$131$	−0.758280	+	7.94107i	−0.0662512	+	0.693814i	−0.966196	+	0.257810i	$0.916999\pi$
$132$	−10.3543	+	4.10245i	−0.901229	+	0.357073i
$133$	0.244296	−	0.0978013i	0.0211831	−	0.00848045i
$134$	−1.93401	−	1.24291i	−0.167073	−	0.107371i
$135$	0.753963	−	2.96884i	0.0648908	−	0.255517i
$136$	−0.114350	+	0.389441i	−0.00980545	+	0.0333943i
$137$	−3.07790	−	5.33107i	−0.262963	−	0.455464i	0.704065	−	0.710135i	$-0.251366\pi$
$137$	−3.07790	−	5.33107i	−0.262963	−	0.455464i	−0.967028	+	0.254671i	$0.918033\pi$
$138$	−7.83479	+	2.75973i	−0.666941	+	0.234924i
$139$	3.74377	−	6.48441i	0.317543	−	0.550000i	−0.662432	−	0.749122i	$-0.730476\pi$
$139$	3.74377	−	6.48441i	0.317543	−	0.550000i	0.979975	+	0.199122i	$0.0638090\pi$
$140$	−0.104468	−	0.109563i	−0.00882913	−	0.00925972i
$141$	−8.04179	+	19.8816i	−0.677241	+	1.67433i
$142$	0.0543275	−	1.14047i	0.00455906	−	0.0957065i
$143$	−3.63347	+	25.2713i	−0.303846	+	2.11330i
$144$	−1.94836	−	2.28121i	−0.162363	−	0.190101i
$145$	2.74157	−	1.25203i	0.227675	−	0.103976i
$146$	−2.95427	−	1.02248i	−0.244497	−	0.0846213i
$147$	10.0803	+	6.52916i	0.831412	+	0.538516i
$148$	1.65496	−	1.17849i	0.136037	−	0.0968716i
$149$	5.13637	−	21.1724i	0.420788	−	1.73451i	−0.228109	−	0.973635i	$-0.573254\pi$
$149$	5.13637	−	21.1724i	0.420788	−	1.73451i	0.648897	−	0.760876i	$-0.275230\pi$
$150$	7.31816	+	3.37369i	0.597525	+	0.275461i
$151$	4.15545	−	0.396797i	0.338166	−	0.0322909i	0.0754080	−	0.997153i	$-0.475974\pi$
$151$	4.15545	−	0.396797i	0.338166	−	0.0322909i	0.262758	+	0.964862i	$0.415368\pi$
$152$	−0.145828	−	1.01425i	−0.0118282	−	0.0822669i
$153$	0.390034	+	1.15349i	0.0315324	+	0.0932541i
$154$	0.685981	+	1.50209i	0.0552779	+	0.121042i
$155$	2.18195	+	1.12487i	0.175259	+	0.0903521i
$156$	−6.75746	+	1.27741i	−0.541030	+	0.102275i
$157$	−1.12217	−	2.17670i	−0.0895587	−	0.173720i	0.839802	−	0.542893i	$-0.182671\pi$
$157$	−1.12217	−	2.17670i	−0.0895587	−	0.173720i	−0.929360	+	0.369174i	$0.879641\pi$
$158$	−0.184920	−	0.534290i	−0.0147114	−	0.0425058i
$159$	16.6858	+	8.67763i	1.32327	+	0.688180i
$160$	−0.510514	+	0.294746i	−0.0403597	+	0.0233017i
$161$	0.468054	+	1.13919i	0.0368878	+	0.0897811i
$162$	−8.71514	−	2.24641i	−0.684726	−	0.176494i
$163$	15.1910	+	4.46049i	1.18985	+	0.349372i	0.815965	−	0.578102i	$-0.196206\pi$
$163$	15.1910	+	4.46049i	1.18985	+	0.349372i	0.373888	+	0.927474i	$0.378025\pi$
$164$	−1.00983	+	5.23951i	−0.0788547	+	0.409137i
$165$	4.73542	+	4.54758i	0.368652	+	0.354028i
$166$	1.95012	−	2.47978i	0.151359	−	0.192468i
$167$	−17.2447	+	0.821468i	−1.33444	+	0.0635671i	−0.702628	−	0.711557i	$-0.747990\pi$
$167$	−17.2447	+	0.821468i	−1.33444	+	0.0635671i	−0.631809	+	0.775124i	$0.717687\pi$
$168$	−0.323011	+	0.305798i	−0.0249208	+	0.0235928i
$169$	−0.904352	+	2.61295i	−0.0695655	+	0.200996i
$170$	0.236829	−	0.0340508i	0.0181639	−	0.00261158i
$171$	−2.10541	−	2.23987i	−0.161005	−	0.171288i
$172$	−1.93785	−	6.59972i	−0.147760	−	0.503224i
$173$	13.8460	−	14.5213i	1.05270	−	1.10403i	0.0583008	−	0.998299i	$-0.481432\pi$
$173$	13.8460	−	14.5213i	1.05270	−	1.10403i	0.994394	−	0.105736i	$-0.0337198\pi$
$174$	−3.64999	−	8.06840i	−0.276705	−	0.611664i
$175$	0.444059	−	1.10921i	0.0335677	−	0.0838481i
$176$	6.31399	−	1.21692i	0.475935	−	0.0917290i
$177$	4.08269	−	13.7231i	0.306874	−	1.03149i
$178$	−7.84795	+	15.2229i	−0.588229	+	1.14100i
$179$	3.96206	+	0.569658i	0.296138	+	0.0425783i	0.288783	−	0.957395i	$-0.406749\pi$
$179$	3.96206	+	0.569658i	0.296138	+	0.0425783i	0.00735572	+	0.999973i	$0.497659\pi$
$180$	−0.746108	+	1.60338i	−0.0556116	+	0.119509i
$181$	−10.8436	−	9.39606i	−0.806001	−	0.698404i	0.150986	−	0.988536i	$-0.451755\pi$
$181$	−10.8436	−	9.39606i	−0.806001	−	0.698404i	−0.956987	+	0.290132i	$0.906301\pi$
$182$	0.240393	+	0.990912i	0.0178191	+	0.0734513i
$183$	1.02656	−	0.351199i	0.0758853	−	0.0259614i
$184$	4.74065	−	0.725391i	0.349486	−	0.0534765i
$185$	−1.03720	−	0.598831i	−0.0762568	−	0.0440269i
$186$	3.32797	−	6.39921i	0.244019	−	0.469213i
$187$	−2.56274	−	0.493927i	−0.187406	−	0.0361195i
$188$	6.69426	−	10.4165i	0.488229	−	0.759699i
$189$	−0.266545	+	1.30751i	−0.0193883	+	0.0951076i
$190$	−0.508153	+	0.326570i	−0.0368653	+	0.0236919i
$191$	0.908844	−	1.27629i	0.0657616	−	0.0923493i	−0.780385	−	0.625299i	$-0.784977\pi$
$191$	0.908844	−	1.27629i	0.0657616	−	0.0923493i	0.846147	+	0.532950i	$0.178916\pi$
$192$	0.860669	+	1.50308i	0.0621135	+	0.108475i
$193$	15.5621	+	6.23012i	1.12018	+	0.448454i	0.856496	−	0.516154i	$-0.172637\pi$
$193$	15.5621	+	6.23012i	1.12018	+	0.448454i	0.263688	+	0.964608i	$0.415061\pi$
$194$	−6.41792	−	9.01271i	−0.460780	−	0.647075i
$195$	2.33976	+	3.31067i	0.167554	+	0.237082i
$196$	−5.01841	−	4.78504i	−0.358458	−	0.341789i
$197$	2.35020	+	1.07330i	0.167445	+	0.0764695i	0.497374	−	0.867536i	$-0.334298\pi$
$197$	2.35020	+	1.07330i	0.167445	+	0.0764695i	−0.329929	+	0.944006i	$0.607025\pi$
$198$	13.4113	−	13.8659i	0.953099	−	0.985409i
$199$	2.50455	−	2.17020i	0.177543	−	0.153842i	−0.561556	−	0.827439i	$-0.689797\pi$
$199$	2.50455	−	2.17020i	0.177543	−	0.153842i	0.739099	+	0.673597i	$0.235252\pi$
$200$	−3.78981	−	2.69871i	−0.267980	−	0.190828i
$201$	3.93935	+	0.580743i	0.277860	+	0.0409624i
$202$	8.61916	+	6.77819i	0.606442	+	0.476911i
$203$	−1.16704	+	0.601649i	−0.0819098	+	0.0422275i
$204$	−0.0975657	−	0.696206i	−0.00683097	−	0.0487441i
$205$	3.05682	−	0.741577i	0.213498	−	0.0517940i
$206$	−15.3900			−1.07227
$207$	10.3938	−	9.94831i	0.722419	−	0.691455i
$208$	3.97052			0.275306
$209$	6.40319	−	1.55340i	0.442918	−	0.107451i
$210$	0.243075	+	0.0983201i	0.0167738	+	0.00678473i
$211$	−17.6094	+	9.07825i	−1.21228	+	0.624973i	−0.941286	−	0.337609i	$-0.890382\pi$
$211$	−17.6094	+	9.07825i	−1.21228	+	0.624973i	−0.270991	+	0.962582i	$0.587352\pi$
$212$	−8.53532	−	6.71225i	−0.586208	−	0.460999i
$213$	0.728446	+	1.83855i	0.0499123	+	0.125975i
$214$	9.00525	+	6.41261i	0.615586	+	0.438357i
$215$	−3.06435	+	2.65528i	−0.208987	+	0.181088i
$216$	4.70322	+	2.20902i	0.320013	+	0.150305i
$217$	−0.972788	−	0.444257i	−0.0660371	−	0.0301582i
$218$	−8.96987	−	8.55275i	−0.607516	−	0.579265i
$219$	5.39204	−	0.495474i	0.364360	−	0.0334810i
$220$	−2.19873	−	3.08769i	−0.148238	−	0.208172i
$221$	−1.49612	−	0.598958i	−0.100640	−	0.0402903i
$222$	−1.77035	+	3.04123i	−0.118818	+	0.204114i
$223$	−8.55794	+	12.0179i	−0.573082	+	0.804781i	−0.994789	−	0.101951i	$-0.967491\pi$
$223$	−8.55794	+	12.0179i	−0.573082	+	0.804781i	0.421708	+	0.906732i	$0.361431\pi$
$224$	0.216039	−	0.138840i	0.0144347	−	0.00927664i
$225$	−13.9571	−	0.0995754i	−0.930476	−	0.00663836i
$226$	−5.48950	+	8.54183i	−0.365156	+	0.568194i
$227$	−18.0902	−	3.48660i	−1.20069	−	0.231414i	−0.450584	−	0.892734i	$-0.648784\pi$
$227$	−18.0902	−	3.48660i	−1.20069	−	0.231414i	−0.750104	+	0.661320i	$0.769996\pi$
$228$	0.954200	+	1.49648i	0.0631935	+	0.0991065i
$229$	−14.8007	−	8.54517i	−0.978056	−	0.564681i	−0.0763732	−	0.997079i	$-0.524334\pi$
$229$	−14.8007	−	8.54517i	−0.978056	−	0.564681i	−0.901683	+	0.432398i	$0.857667\pi$
$230$	−1.54988	−	2.36440i	−0.102196	−	0.155904i
$231$	−2.15487	−	1.88071i	−0.141780	−	0.123741i
$232$	1.20538	+	4.96866i	0.0791373	+	0.326208i
$233$	−2.05853	−	1.78372i	−0.134859	−	0.116856i	0.584820	−	0.811163i	$-0.301165\pi$
$233$	−2.05853	−	1.78372i	−0.134859	−	0.116856i	−0.719678	+	0.694308i	$0.755711\pi$
$234$	9.75192	−	6.83998i	0.637503	−	0.447144i
$235$	−7.22483	−	1.03877i	−0.471296	−	0.0677621i
$236$	−3.78780	+	7.34731i	−0.246565	+	0.478269i
$237$	0.673246	+	0.711142i	0.0437320	+	0.0461936i
$238$	−0.102350	+	0.0197263i	−0.00663433	+	0.00127866i
$239$	5.53330	−	13.8215i	0.357920	−	0.894040i	−0.634699	−	0.772760i	$-0.718876\pi$
$239$	5.53330	−	13.8215i	0.357920	−	0.894040i	0.992618	−	0.121280i	$-0.0387000\pi$
$240$	0.595218	−	0.829587i	0.0384211	−	0.0535496i
$241$	6.00083	−	6.29349i	0.386548	−	0.405399i	−0.501495	−	0.865160i	$-0.667216\pi$
$241$	6.00083	−	6.29349i	0.386548	−	0.405399i	0.888043	+	0.459761i	$0.152065\pi$
$242$	8.54986	+	29.1181i	0.549606	+	1.87178i
$243$	15.3569	−	2.67667i	0.985148	−	0.171709i
$244$	−0.620032	+	0.0891471i	−0.0396935	+	0.00570706i
$245$	−1.33691	+	3.86275i	−0.0854121	+	0.246782i
$246$	−2.14686	−	8.98931i	−0.136879	−	0.573137i
$247$	4.06392	−	0.193588i	0.258581	−	0.0123177i
$248$	−2.57423	+	3.27340i	−0.163464	+	0.207861i
$249$	−1.30715	+	5.30548i	−0.0828375	+	0.336221i
$250$	−1.07685	+	5.58724i	−0.0681061	+	0.353368i
$251$	17.7797	+	5.22059i	1.12225	+	0.329521i	0.789655	−	0.613551i	$-0.210259\pi$
$251$	17.7797	+	5.22059i	1.12225	+	0.329521i	0.332590	+	0.943072i	$0.392078\pi$
$252$	0.291431	−	0.713171i	0.0183584	−	0.0449256i
$253$	7.54091	+	29.9019i	0.474093	+	1.87992i
$254$	11.6273	−	6.71305i	0.729564	−	0.421214i
$255$	−0.349427	+	0.222806i	−0.0218820	+	0.0139526i
$256$	−0.327068	−	0.945001i	−0.0204417	−	0.0590626i
$257$	−2.71464	−	5.26568i	−0.169335	−	0.328464i	0.788864	−	0.614568i	$-0.210670\pi$
$257$	−2.71464	−	5.26568i	−0.169335	−	0.328464i	−0.958198	+	0.286105i	$0.907640\pi$
$258$	7.76960	+	9.03149i	0.483714	+	0.562276i
$259$	0.463750	+	0.239080i	0.0288160	+	0.0148557i
$260$	−0.972315	−	2.12907i	−0.0603004	−	0.132039i
$261$	11.5200	+	10.1269i	0.713069	+	0.626840i
$262$	1.13527	+	7.89599i	0.0701373	+	0.487816i
$263$	15.1997	−	1.45140i	0.937254	−	0.0894969i	0.384763	−	0.923015i	$-0.374283\pi$
$263$	15.1997	−	1.45140i	0.937254	−	0.0894969i	0.552492	+	0.833519i	$0.313677\pi$
$264$	−9.09527	+	6.42794i	−0.559775	+	0.395612i
$265$	−1.50908	+	6.22053i	−0.0927023	+	0.382124i
$266$	0.214352	−	0.152639i	0.0131428	−	0.00935892i
$267$	1.51718	−	29.6257i	0.0928499	−	1.81306i
$268$	−2.17252	−	0.751918i	−0.132708	−	0.0459307i
$269$	22.6545	−	10.3460i	1.38127	−	0.630805i	0.420282	−	0.907394i	$-0.361931\pi$
$269$	22.6545	−	10.3460i	1.38127	−	0.630805i	0.960988	+	0.276589i	$0.0892039\pi$
$270$	0.0327786	−	3.06291i	0.00199484	−	0.186403i
$271$	−1.99777	+	13.8948i	−0.121356	+	0.844047i	0.834667	+	0.550755i	$0.185660\pi$
$271$	−1.99777	+	13.8948i	−0.121356	+	0.844047i	−0.956023	+	0.293293i	$0.905249\pi$
$272$	−0.0193127	+	0.405423i	−0.00117100	+	0.0245824i
$273$	−1.08677	−	1.39213i	−0.0657742	−	0.0842555i
$274$	−4.24798	−	4.45516i	−0.256630	−	0.269146i
$275$	14.9582	−	25.9084i	0.902016	−	1.56234i
$276$	−6.96331	+	4.52906i	−0.419142	+	0.272617i
$277$	0.0807080	+	0.139790i	0.00484927	+	0.00839918i	0.868440	−	0.495795i	$-0.165123\pi$
$277$	0.0807080	+	0.139790i	0.00484927	+	0.00839918i	−0.863591	+	0.504194i	$0.831790\pi$
$278$	2.10949	−	7.18425i	0.126519	−	0.430883i
$279$	−0.683454	+	12.4743i	−0.0409173	+	0.746818i
$280$	−0.127353	−	0.0818449i	−0.00761081	−	0.00489117i
$281$	−15.7975	+	6.32438i	−0.942402	+	0.377281i	−0.791432	−	0.611257i	$-0.790664\pi$
$281$	−15.7975	+	6.32438i	−0.942402	+	0.377281i	−0.150970	+	0.988538i	$0.548240\pi$
$282$	−3.12784	+	21.2171i	−0.186260	+	1.26346i
$283$	1.96045	−	20.5307i	0.116537	−	1.22043i	−0.728246	−	0.685316i	$-0.759664\pi$
$283$	1.96045	−	20.5307i	0.116537	−	1.22043i	0.844782	−	0.535110i	$-0.179730\pi$
$284$	−0.216081	−	1.12113i	−0.0128220	−	0.0665271i
$285$	0.568772	−	0.878123i	0.0336911	−	0.0520155i
$286$	2.42690	+	25.4156i	0.143505	+	1.50286i
$287$	−1.31480	+	0.386059i	−0.0776099	+	0.0227883i
$288$	−2.43125	−	1.75756i	−0.143263	−	0.103565i
$289$	−6.99362	+	15.3139i	−0.411389	+	0.900817i
$290$	2.36911	−	1.86309i	0.139119	−	0.109405i
$291$	16.5622	+	9.64110i	0.970891	+	0.565171i
$292$	−3.11205	−	0.297165i	−0.182119	−	0.0173903i
$293$	0.119445	+	2.50745i	0.00697804	+	0.146487i	0.999667	+	0.0257897i	$0.00821002\pi$
$293$	0.119445	+	2.50745i	0.00697804	+	0.146487i	−0.992689	+	0.120697i	$0.961487\pi$
$294$	11.3355	+	3.96859i	0.661100	+	0.231453i
$295$	4.86734	+	0.231860i	0.283388	+	0.0134994i
$296$	1.33047	−	1.53545i	0.0773321	−	0.0892460i
$297$	−11.2653	+	31.4559i	−0.653682	+	1.82526i
$298$		−	21.7865i		−	1.26206i
$299$	1.07791	+	19.0114i	0.0623371	+	1.09946i
$300$	7.90725	+	1.55327i	0.456525	+	0.0896782i
$301$	1.27840	−	1.21896i	0.0736860	−	0.0702595i
$302$	3.94477	−	1.36530i	0.226996	−	0.0785640i
$303$	−18.4407	−	4.54338i	−1.05939	−	0.261010i
$304$	−0.380837	−	0.951284i	−0.0218425	−	0.0545599i
$305$	0.199638	+	0.310643i	0.0114312	+	0.0177874i
$306$	0.650985	+	1.02902i	0.0372143	+	0.0588252i
$307$	9.14883	+	10.5583i	0.522151	+	0.602595i	0.954168	−	0.299271i	$-0.0967434\pi$
$307$	9.14883	+	10.5583i	0.522151	+	0.602595i	−0.432017	+	0.901866i	$0.642198\pi$
$308$	1.02078	+	1.29802i	0.0581641	+	0.0739616i
$309$	24.2867	−	10.9868i	1.38162	−	0.625020i
$310$	2.38565	+	0.578752i	0.135496	+	0.0328709i
$311$	−32.7255	−	7.93911i	−1.85569	−	0.450186i	−0.857735	−	0.514091i	$-0.828129\pi$
$311$	−32.7255	−	7.93911i	−1.85569	−	0.450186i	−0.997956	+	0.0639057i	$0.979644\pi$
$312$	−6.26582	+	2.83454i	−0.354732	+	0.160474i
$313$	14.8544	+	18.8889i	0.839620	+	1.06766i	0.996788	+	0.0800915i	$0.0255212\pi$
$313$	14.8544	+	18.8889i	0.839620	+	1.06766i	−0.157168	+	0.987572i	$0.550236\pi$
$314$	−1.60371	−	1.85078i	−0.0905027	−	0.104446i
$315$	−0.453783	+	0.0183727i	−0.0255678	+	0.00103518i
$316$	−0.305671	−	0.475633i	−0.0171953	−	0.0267564i
$317$	−9.27516	−	23.1682i	−0.520945	−	1.30126i	−0.922703	−	0.385511i	$-0.874025\pi$
$317$	−9.27516	−	23.1682i	−0.520945	−	1.30126i	0.401758	−	0.915746i	$-0.368399\pi$
$318$	18.2613	+	4.49918i	1.02404	+	0.252302i
$319$	−31.0680	+	10.7527i	−1.73947	+	0.602038i
$320$	−0.426635	+	0.406795i	−0.0238496	+	0.0227406i
$321$	−18.7890	−	3.69084i	−1.04870	−	0.206003i
$322$	0.723435	+	0.996734i	0.0403155	+	0.0555458i
$323$			0.415901i			0.0231414i
$324$	−8.99908	−	0.128412i	−0.499949	−	0.00713400i
$325$	12.0971	−	13.9608i	0.671029	−	0.774408i
$326$	15.8144	+	0.753333i	0.875879	+	0.0417233i
$327$	20.2610	+	7.09342i	1.12043	+	0.392267i
$328$	0.253894	+	5.32989i	0.0140190	+	0.294294i
$329$	3.16540	+	0.302259i	0.174514	+	0.0166641i
$330$	5.67407	+	3.30297i	0.312347	+	0.181822i
$331$	−3.36330	+	2.64493i	−0.184864	+	0.145379i	−0.706302	−	0.707910i	$-0.749638\pi$
$331$	−3.36330	+	2.64493i	−0.184864	+	0.145379i	0.521438	+	0.853289i	$0.325396\pi$
$332$	1.31052	−	2.86964i	0.0719241	−	0.157492i
$333$	0.622644	−	6.06317i	0.0341207	−	0.332260i
$334$	−16.5650	+	4.86391i	−0.906394	+	0.266141i
$335$	0.128822	+	1.34908i	0.00703829	+	0.0737083i
$336$	−0.241811	+	0.373331i	−0.0131919	+	0.0203669i
$337$	0.729770	+	3.78641i	0.0397531	+	0.206259i	0.996375	−	0.0850752i	$-0.0271130\pi$
$337$	0.729770	+	3.78641i	0.0397531	+	0.206259i	−0.956621	+	0.291334i	$0.905901\pi$
$338$	−0.262833	+	2.75251i	−0.0142962	+	0.149717i
$339$	2.56493	−	17.3987i	0.139308	−	0.944966i
$340$	0.222125	−	0.0889255i	0.0120464	−	0.00482266i
$341$	−22.5267	−	14.4770i	−1.21989	−	0.783976i
$342$	−2.57414	−	1.68037i	−0.139193	−	0.0908638i
$343$	1.00814	−	3.43340i	0.0544344	−	0.185386i
$344$	−3.43917	−	5.95682i	−0.185428	−	0.321170i
$345$	4.13377	+	2.62477i	0.222555	+	0.141313i
$346$	10.0322	−	17.3763i	0.539335	−	0.934156i
$347$	−1.17603	−	1.23339i	−0.0631328	−	0.0662118i	0.691410	−	0.722463i	$-0.256990\pi$
$347$	−1.17603	−	1.23339i	−0.0631328	−	0.0662118i	−0.754543	+	0.656251i	$0.772141\pi$
$348$	−5.44930	−	6.98045i	−0.292113	−	0.374191i
$349$	−1.34605	+	28.2570i	−0.0720523	+	1.51256i	0.616487	+	0.787365i	$0.288555\pi$
$349$	−1.34605	+	28.2570i	−0.0720523	+	1.51256i	−0.688539	+	0.725199i	$0.741748\pi$
$350$	0.170037	−	1.18263i	0.00908884	−	0.0632142i
$351$	−10.5063	+	17.7559i	−0.560786	+	0.947741i
$352$	5.84911	−	2.67120i	0.311759	−	0.142375i
$353$	−9.89009	−	3.42300i	−0.526397	−	0.182188i	0.0509280	−	0.998702i	$-0.483782\pi$
$353$	−9.89009	−	3.42300i	−0.526397	−	0.182188i	−0.577325	+	0.816515i	$0.695903\pi$
$354$	0.732265	−	14.2988i	0.0389194	−	0.759971i
$355$	−0.548260	+	0.390414i	−0.0290986	+	0.0207210i
$356$	−4.03779	+	16.6440i	−0.214003	+	0.882131i
$357$	0.147434	−	0.104197i	0.00780302	−	0.00551467i
$358$	3.98468	−	0.380491i	0.210597	−	0.0201096i
$359$	−3.47291	−	24.1546i	−0.183293	−	1.27483i	−0.848910	−	0.528538i	$-0.822741\pi$
$359$	−3.47291	−	24.1546i	−0.183293	−	1.27483i	0.665617	−	0.746294i	$-0.268169\pi$
$360$	−0.347066	+	1.73408i	−0.0182920	+	0.0913942i
$361$	7.45671	+	16.3279i	0.392458	+	0.859364i
$362$	−12.7532	−	6.57472i	−0.670292	−	0.345560i
$363$	−34.2797	−	39.8472i	−1.79922	−	2.09144i
$364$	0.467233	+	0.906305i	0.0244897	+	0.0475033i
$365$	0.602745	+	1.74152i	0.0315491	+	0.0911551i
$366$	0.914821	−	0.583319i	0.0478185	−	0.0304906i
$367$	−15.7089	+	9.06955i	−0.819999	+	0.473426i	−0.850416	−	0.526111i	$-0.823650\pi$
$367$	−15.7089	+	9.06955i	−0.819999	+	0.473426i	0.0304174	+	0.999537i	$0.490316\pi$
$368$	4.43601	−	1.82259i	0.231243	−	0.0950093i
$369$	9.80535	+	12.6533i	0.510446	+	0.658703i
$370$	−1.14915	−	0.337420i	−0.0597413	−	0.0175416i
$371$	0.527731	−	2.73813i	0.0273984	−	0.142157i
$372$	1.72549	−	7.00343i	0.0894624	−	0.363111i
$373$	8.94203	−	11.3707i	0.463001	−	0.588753i	−0.497349	−	0.867550i	$-0.665693\pi$
$373$	8.94203	−	11.3707i	0.463001	−	0.588753i	0.960350	+	0.278797i	$0.0899357\pi$
$374$	−2.60695	+	0.124184i	−0.134802	+	0.00642141i
$375$	−2.28934	−	9.58590i	−0.118221	−	0.495014i
$376$	4.04978	−	11.7011i	0.208851	−	0.603437i
$377$	−20.0938	+	2.88905i	−1.03488	+	0.148793i
$378$	0.0492264	+	1.33350i	0.00253193	+	0.0685877i
$379$	5.26273	+	17.9232i	0.270328	+	0.920654i	0.977023	+	0.213135i	$0.0683674\pi$
$379$	5.26273	+	17.9232i	0.270328	+	0.920654i	−0.706694	+	0.707519i	$0.749814\pi$
$380$	−0.416837	+	0.437166i	−0.0213833	+	0.0224262i
$381$	−13.5565	+	18.8945i	−0.694522	+	0.967993i
$382$	0.582327	−	1.45458i	0.0297945	−	0.0744230i
$383$	2.43154	−	0.468640i	0.124246	−	0.0239464i	−0.126749	−	0.991935i	$-0.540454\pi$
$383$	2.43154	−	0.468640i	0.124246	−	0.0239464i	0.250995	+	0.967988i	$0.419242\pi$
$384$	1.19077	+	1.25780i	0.0607664	+	0.0641868i
$385$	0.446054	−	0.865224i	0.0227330	−	0.0440959i
$386$	16.5922	+	2.38560i	0.844522	+	0.121424i
$387$	−18.7086	−	8.70579i	−0.951013	−	0.442540i
$388$	−8.36183	−	7.24557i	−0.424508	−	0.367838i
$389$	−5.42956	−	22.3810i	−0.275290	−	1.13476i	−0.926630	−	0.375974i	$-0.877308\pi$
$389$	−5.42956	−	22.3810i	−0.275290	−	1.13476i	0.651340	−	0.758786i	$-0.274207\pi$
$390$	3.05433	+	2.66573i	0.154662	+	0.134984i
$391$	−1.94646	+	0.0175916i	−0.0984369	+	0.000889644i
$392$	−6.00506	−	3.46703i	−0.303302	−	0.175111i
$393$	−7.42847	−	11.6501i	−0.374717	−	0.587669i
$394$	2.53699	+	0.488965i	0.127812	+	0.0246337i
$395$	−0.180190	+	0.280381i	−0.00906635	+	0.0141075i
$396$	9.76423	−	16.6369i	0.490671	−	0.836036i
$397$	11.3841	−	7.31609i	0.571349	−	0.367184i	−0.222839	−	0.974855i	$-0.571533\pi$
$397$	11.3841	−	7.31609i	0.571349	−	0.367184i	0.794189	+	0.607671i	$0.207896\pi$
$398$	1.92230	−	2.69950i	0.0963564	−	0.135314i
$399$	−0.229297	+	0.393903i	−0.0114792	+	0.0197198i
$400$	−4.31923	−	1.72916i	−0.215962	−	0.0864580i
$401$	−17.4340	−	24.4827i	−0.870614	−	1.22261i	−0.973677	−	0.227931i	$-0.926804\pi$
$401$	−17.4340	−	24.4827i	−0.870614	−	1.22261i	0.103063	−	0.994675i	$-0.467136\pi$
$402$	3.96522	−	0.364364i	0.197767	−	0.0181728i
$403$	−11.9667	−	11.4102i	−0.596102	−	0.568382i
$404$	9.97422	+	4.55507i	0.496236	+	0.226623i
$405$	2.13487	+	4.85694i	0.106083	+	0.241343i
$406$	−0.992295	+	0.859828i	−0.0492467	+	0.0426726i
$407$	10.6417	+	7.57794i	0.527491	+	0.375625i
$408$	−0.258952	−	0.653579i	−0.0128200	−	0.0323570i
$409$	−17.0044	−	13.3724i	−0.840815	−	0.661225i	0.101910	−	0.994794i	$-0.467505\pi$
$409$	−17.0044	−	13.3724i	−0.840815	−	0.661225i	−0.942726	+	0.333569i	$0.891747\pi$
$410$	2.79582	−	1.44135i	0.138076	−	0.0711830i
$411$	9.88420	+	3.99800i	0.487552	+	0.197207i
$412$	−14.9562	+	3.62833i	−0.736838	+	0.178755i
$413$	−2.12282			−0.104457
$414$	7.75542	−	12.1183i	0.381158	−	0.595583i
$415$	−1.85968			−0.0912881
$416$	3.85860	−	0.936086i	0.189183	−	0.0458954i
$417$	1.79985	+	12.8433i	0.0881392	+	0.628940i
$418$	5.85647	−	3.01922i	0.286449	−	0.147675i
$419$	21.1685	+	16.6471i	1.03415	+	0.813264i	0.982661	−	0.185409i	$-0.0593611\pi$
$419$	21.1685	+	16.6471i	1.03415	+	0.813264i	0.0514882	+	0.998674i	$0.483604\pi$
$420$	0.259403	+	0.0382415i	0.0126576	+	0.00186599i
$421$	−12.5464	−	8.93422i	−0.611472	−	0.435427i	0.231913	−	0.972737i	$-0.425501\pi$
$421$	−12.5464	−	8.93422i	−0.611472	−	0.435427i	−0.843385	+	0.537309i	$0.819441\pi$
$422$	−14.9727	+	12.9739i	−0.728859	+	0.631560i
$423$	−10.2108	−	35.7153i	−0.496464	−	1.73654i
$424$	−9.87720	−	4.51077i	−0.479679	−	0.219062i
$425$	1.36668	+	1.30312i	0.0662935	+	0.0632107i
$426$	1.14137	+	1.61499i	0.0552994	+	0.0782464i
$427$	−0.0933111	−	0.131037i	−0.00451564	−	0.00634133i
$428$	10.2632	+	4.10878i	0.496092	+	0.198605i
$429$	−21.9739	−	38.3755i	−1.06091	−	1.85278i
$430$	−2.35197	+	3.30288i	−0.113422	+	0.159279i
$431$	−12.5635	+	8.07406i	−0.605162	+	0.388914i	−0.807040	−	0.590497i	$-0.798932\pi$
$431$	−12.5635	+	8.07406i	−0.605162	+	0.388914i	0.201878	+	0.979411i	$0.435295\pi$
$432$	5.09144	+	1.03792i	0.244962	+	0.0499370i
$433$	14.1176	−	21.9674i	0.678448	−	1.05569i	−0.315825	−	0.948818i	$-0.602281\pi$
$433$	14.1176	−	21.9674i	0.678448	−	1.05569i	0.994273	−	0.106869i	$-0.0340824\pi$
$434$	−1.05010	−	0.202391i	−0.0504066	−	0.00971508i
$435$	−2.40861	+	4.63142i	−0.115484	+	0.222060i
$436$	−10.7334	−	6.19693i	−0.514037	−	0.296779i
$437$	4.45150	−	2.08175i	0.212944	−	0.0995838i
$438$	5.12323	−	1.75273i	0.244797	−	0.0837486i
$439$	−3.10657	−	12.8055i	−0.148269	−	0.611172i	−0.996650	−	0.0817859i	$-0.973938\pi$
$439$	−3.10657	−	12.8055i	−0.148269	−	0.611172i	0.848381	−	0.529386i	$-0.177578\pi$
$440$	−2.86470	−	2.48228i	−0.136569	−	0.118338i
$441$	−20.7215	+	1.82959i	−0.986740	+	0.0871231i
$442$	−1.59516	−	0.229349i	−0.0758740	−	0.0109090i
$443$	−5.50993	+	10.6878i	−0.261785	+	0.507792i	−0.982694	−	0.185238i	$-0.940694\pi$
$443$	−5.50993	+	10.6878i	−0.261785	+	0.507792i	0.720909	+	0.693030i	$0.243725\pi$
$444$	−1.00345	+	3.37288i	−0.0476216	+	0.160070i
$445$	9.91364	−	1.91070i	0.469952	−	0.0905758i
$446$	−5.48336	+	13.6968i	−0.259645	+	0.648561i
$447$	15.5533	+	34.3810i	0.735646	+	1.62617i
$448$	0.177217	−	0.185859i	0.00837270	−	0.00878104i
$449$	5.63653	+	19.1963i	0.266004	+	0.905928i	0.978845	+	0.204602i	$0.0655900\pi$
$449$	5.63653	+	19.1963i	0.266004	+	0.905928i	−0.712841	+	0.701326i	$0.752592\pi$
$450$	−13.5872	+	3.19375i	−0.640506	+	0.150555i
$451$	−33.9619	+	4.88298i	−1.59920	+	0.229931i
$452$	−3.32095	+	9.59525i	−0.156204	+	0.451322i
$453$	−5.25050	+	4.97070i	−0.246690	+	0.233544i
$454$	−18.4023	+	0.876607i	−0.863660	+	0.0411412i
$455$	0.371561	−	0.472479i	0.0174191	−	0.0221501i
$456$	1.28011	+	1.22933i	0.0599467	+	0.0575687i
$457$	6.59084	−	34.1965i	0.308306	−	1.59965i	−0.415468	−	0.909608i	$-0.636382\pi$
$457$	6.59084	−	34.1965i	0.308306	−	1.59965i	0.723774	−	0.690037i	$-0.242406\pi$
$458$	−16.3981	−	4.81491i	−0.766231	−	0.224986i
$459$	−1.76192	−	1.15915i	−0.0822395	−	0.0541043i
$460$	−2.06362	−	1.93235i	−0.0962166	−	0.0900964i
$461$	10.8080	−	6.24002i	0.503380	−	0.290627i	−0.226728	−	0.973958i	$-0.572803\pi$
$461$	10.8080	−	6.24002i	0.503380	−	0.290627i	0.730108	+	0.683331i	$0.239470\pi$
$462$	−2.53752	−	1.31966i	−0.118056	−	0.0613962i
$463$	−3.93319	−	11.3642i	−0.182791	−	0.528139i	0.815960	−	0.578108i	$-0.196209\pi$
$463$	−3.93319	−	11.3642i	−0.182791	−	0.528139i	−0.998751	+	0.0499691i	$0.984088\pi$
$464$	2.34281	+	4.54442i	0.108762	+	0.210969i
$465$	−4.17792	+	0.789782i	−0.193746	+	0.0366253i
$466$	−2.42103	−	1.24813i	−0.112152	−	0.0578184i
$467$	−7.42203	−	16.2520i	−0.343451	−	0.752052i	0.656547	−	0.754285i	$-0.272016\pi$
$467$	−7.42203	−	16.2520i	−0.343451	−	0.752052i	−0.999998	+	0.00223341i	$0.999289\pi$
$468$	7.86444	−	8.94628i	0.363534	−	0.413542i
$469$	−0.0840211	−	0.584380i	−0.00387973	−	0.0269841i
$470$	−7.26607	+	0.693826i	−0.335159	+	0.0320038i
$471$	3.85206	+	1.77581i	0.177493	+	0.0818250i
$472$	−1.94884	+	8.03321i	−0.0897024	+	0.369758i
$473$	36.0279	−	25.6554i	1.65657	−	1.17964i
$474$	0.821926	+	0.532372i	0.0377523	+	0.0244527i
$475$	−4.50515	−	1.55925i	−0.206710	−	0.0715431i
$476$	−0.0948138	+	0.0433000i	−0.00434578	+	0.00198465i
$477$	−32.0299	+	5.93657i	−1.46655	+	0.271817i
$478$	2.11878	−	14.7364i	0.0969108	−	0.674029i
$479$	−0.134728	+	2.82830i	−0.00615590	+	0.129228i	0.993697	+	0.112096i	$0.0357565\pi$
$479$	−0.134728	+	2.82830i	−0.00615590	+	0.129228i	−0.999853	+	0.0171319i	$0.994546\pi$
$480$	0.382857	−	0.946531i	0.0174749	−	0.0432030i
$481$	5.56676	+	5.83825i	0.253823	+	0.266201i
$482$	4.34793	−	7.53084i	0.198043	−	0.343020i
$483$	−1.85321	−	1.05648i	−0.0843238	−	0.0480713i
$484$	15.1737	+	26.2816i	0.689714	+	1.19462i
$485$	−1.83755	+	6.25810i	−0.0834386	+	0.284166i
$486$	14.2930	−	6.22176i	0.648343	−	0.282225i
$487$	0.421529	+	0.270900i	0.0191013	+	0.0122757i	0.550157	−	0.835061i	$-0.314568\pi$
$487$	0.421529	+	0.270900i	0.0191013	+	0.0122757i	−0.531055	+	0.847337i	$0.678204\pi$
$488$	−0.581537	+	0.232812i	−0.0263249	+	0.0105389i
$489$	−25.4943	+	10.1010i	−1.15289	+	0.456783i
$490$	−0.388547	+	4.06905i	−0.0175528	+	0.183821i
$491$	7.75295	+	40.2261i	0.349886	+	1.81538i	0.549488	+	0.835502i	$0.314823\pi$
$491$	7.75295	+	40.2261i	0.349886	+	1.81538i	−0.199602	+	0.979877i	$0.563965\pi$
$492$	−4.20565	−	8.22977i	−0.189605	−	0.371027i
$493$	−0.197259	−	2.06579i	−0.00888410	−	0.0930385i
$494$	3.90373	−	1.14624i	0.175637	−	0.0515717i
$495$	−11.3121	−	1.16167i	−0.508443	−	0.0522134i
$496$	−1.72993	+	3.78802i	−0.0776762	+	0.170087i
$497$	0.230481	−	0.181252i	0.0103385	−	0.00813028i
$498$	−0.0194912	+	5.46410i	−0.000873422	+	0.244852i
$499$	−1.51099	−	0.144282i	−0.0676413	−	0.00645896i	0.0611805	−	0.998127i	$-0.480513\pi$
$499$	−1.51099	−	0.144282i	−0.0676413	−	0.00645896i	−0.128822	+	0.991668i	$0.541120\pi$
$500$	0.270744	+	5.68362i	0.0121080	+	0.254179i
$501$	22.6686	−	19.5013i	1.01276	−	0.871254i
$502$	18.5093	+	0.881708i	0.826112	+	0.0393525i
$503$	−8.25655	+	9.52857i	−0.368141	+	0.424858i	−0.909351	−	0.416030i	$-0.863421\pi$
$503$	−8.25655	+	9.52857i	−0.368141	+	0.424858i	0.541209	+	0.840888i	$0.317967\pi$
$504$	0.115080	−	0.761776i	0.00512605	−	0.0339322i
$505$		−	6.46384i		−	0.287637i
$506$	14.3780	+	27.2812i	0.639180	+	1.21280i
$507$	−1.55023	−	4.53133i	−0.0688481	−	0.201243i
$508$	9.71693	−	9.26507i	0.431119	−	0.411071i
$509$	6.44001	−	2.22891i	0.285448	−	0.0987946i	−0.180592	−	0.983558i	$-0.557801\pi$
$509$	6.44001	−	2.22891i	0.285448	−	0.0987946i	0.466040	+	0.884763i	$0.345680\pi$
$510$	−0.287049	+	0.298906i	−0.0127107	+	0.0132358i
$511$	−0.298382	−	0.745322i	−0.0131996	−	0.0329711i
$512$	−0.540641	−	0.841254i	−0.0238932	−	0.0371785i
$513$	5.26181	+	0.814098i	0.232315	+	0.0359433i
$514$	−3.87955	−	4.47724i	−0.171120	−	0.197483i
$515$	5.60810	+	7.13128i	0.247123	+	0.314242i
$516$	9.67984	+	6.94516i	0.426131	+	0.305744i
$517$	77.3748	+	18.7709i	3.40294	+	0.825545i
$518$	0.507043	+	0.123007i	0.0222782	+	0.00540463i
$519$	−3.42683	+	34.5832i	−0.150421	+	1.51804i
$520$	−1.44685	−	1.83983i	−0.0634488	−	0.0806817i
$521$	−6.15384	−	7.10191i	−0.269605	−	0.311140i	0.604762	−	0.796406i	$-0.293268\pi$
$521$	−6.15384	−	7.10191i	−0.269605	−	0.311140i	−0.874367	+	0.485266i	$0.838723\pi$
$522$	13.5828	+	7.12551i	0.594502	+	0.311875i
$523$	−2.11713	−	3.29432i	−0.0925756	−	0.144050i	0.791877	−	0.610681i	$-0.209104\pi$
$523$	−2.11713	−	3.29432i	−0.0925756	−	0.144050i	−0.884452	+	0.466630i	$0.845468\pi$
$524$	2.96482	+	7.40576i	0.129519	+	0.323522i
$525$	0.575942	+	1.98768i	0.0251362	+	0.0867495i
$526$	14.4291	−	4.99395i	0.629138	−	0.217747i
$527$	1.22328	−	1.16639i	0.0532869	−	0.0508090i
$528$	−7.32344	+	8.39103i	−0.318712	+	0.365173i
$529$	9.93112	+	20.7454i	0.431788	+	0.901975i
$530$			6.40097i			0.278040i
$531$	9.05225	+	23.0874i	0.392834	+	1.00191i
$532$	0.172324	−	0.198872i	0.00747118	−	0.00862220i
$533$	−21.1625	−	1.00809i	−0.916647	−	0.0436653i
$534$	−5.51010	−	29.1482i	−0.238445	−	1.26137i
$535$	−0.310087	−	6.50952i	−0.0134062	−	0.281431i
$536$	−2.28856	−	0.218531i	−0.0988506	−	0.00943908i
$537$	−6.01653	+	3.44509i	−0.259633	+	0.148667i
$538$	19.5768	−	15.3953i	0.844014	−	0.663740i
$539$	18.5222	−	40.5580i	0.797809	−	1.74696i
$540$	−0.690254	−	2.98430i	−0.0297038	−	0.128424i
$541$	−18.6669	+	5.48109i	−0.802552	+	0.235650i	−0.657187	−	0.753728i	$-0.728254\pi$
$541$	−18.6669	+	5.48109i	−0.802552	+	0.235650i	−0.145365	+	0.989378i	$0.546436\pi$
$542$	1.33436	+	13.9741i	0.0573158	+	0.600239i
$543$	24.8193	+	1.27104i	1.06510	+	0.0545454i
$544$	0.0768137	+	0.398547i	0.00329336	+	0.0170876i
$545$	−0.694487	+	7.27299i	−0.0297485	+	0.311541i
$546$	−1.38434	−	1.09667i	−0.0592443	−	0.0469332i
$547$	−36.9022	+	14.7734i	−1.57782	+	0.631665i	−0.984827	−	0.173540i	$-0.944479\pi$
$547$	−36.9022	+	14.7734i	−1.57782	+	0.631665i	−0.592996	+	0.805205i	$0.702055\pi$
$548$	−5.17858	−	3.32807i	−0.221218	−	0.142168i
$549$	−1.02724	+	1.57361i	−0.0438414	+	0.0671602i
$550$	8.42845	−	28.7047i	0.359390	−	1.22397i
$551$	2.61949	+	4.53709i	0.111594	+	0.193287i
$552$	−5.69925	+	6.04305i	−0.242576	+	0.257209i
$553$	0.0725973	−	0.125742i	0.00308715	−	0.00534710i
$554$	0.111390	+	0.116822i	0.00473250	+	0.00496330i
$555$	2.05434	−	0.287893i	0.0872017	−	0.0122204i
$556$	0.356272	−	7.47907i	0.0151093	−	0.317183i
$557$	−1.95048	+	13.5659i	−0.0826444	+	0.574804i	0.905856	+	0.423586i	$0.139229\pi$
$557$	−1.95048	+	13.5659i	−0.0826444	+	0.574804i	−0.988500	+	0.151218i	$0.951680\pi$
$558$	2.27675	+	12.2838i	0.0963823	+	0.520016i
$559$	24.8426	−	11.3452i	1.05073	−	0.479852i
$560$	−0.143059	−	0.0495132i	−0.00604535	−	0.00209231i
$561$	4.02533	−	2.05706i	0.169950	−	0.0868491i
$562$	−13.8612	+	9.87052i	−0.584699	+	0.416363i
$563$	−5.22736	+	21.5475i	−0.220307	+	0.908117i	0.749061	+	0.662501i	$0.230505\pi$
$563$	−5.22736	+	21.5475i	−0.220307	+	0.908117i	−0.969367	+	0.245615i	$0.921010\pi$
$564$	1.96244	+	21.3564i	0.0826336	+	0.899267i
$565$	5.95841	−	0.568959i	0.250672	−	0.0239363i
$566$	−2.93512	−	20.4142i	−0.123372	−	0.858073i
$567$	−1.02966	−	2.06923i	−0.0432417	−	0.0868994i
$568$	−0.474307	−	1.03859i	−0.0199015	−	0.0435782i
$569$	−1.60905	−	0.829525i	−0.0674550	−	0.0347755i	0.424169	−	0.905583i	$-0.360566\pi$
$569$	−1.60905	−	0.829525i	−0.0674550	−	0.0347755i	−0.491624	+	0.870808i	$0.663597\pi$
$570$	0.345714	−	0.987464i	0.0144804	−	0.0413603i
$571$	18.4233	+	35.7362i	0.770991	+	1.49551i	0.866003	+	0.500038i	$0.166681\pi$
$571$	18.4233	+	35.7362i	0.770991	+	1.49551i	−0.0950124	+	0.995476i	$0.530289\pi$
$572$	8.35044	+	24.1270i	0.349150	+	1.00880i
$573$	0.119458	+	2.71118i	0.00499042	+	0.113261i
$574$	−1.18672	+	0.685151i	−0.0495326	+	0.0285977i
$575$	7.10688	−	21.1505i	0.296378	−	0.882038i
$576$	−2.77708	−	1.13483i	−0.115712	−	0.0472845i
$577$	3.26112	+	0.957551i	0.135762	+	0.0398634i	0.348908	−	0.937157i	$-0.386553\pi$
$577$	3.26112	+	0.957551i	0.135762	+	0.0398634i	−0.213146	+	0.977020i	$0.568371\pi$
$578$	−3.18609	+	16.5310i	−0.132524	+	0.687600i
$579$	−27.8870	+	8.08043i	−1.15895	+	0.335811i
$580$	1.86309	−	2.36911i	0.0773607	−	0.0983721i
$581$	0.809235	−	0.0385486i	0.0335727	−	0.00159927i
$582$	18.3683	+	5.46466i	0.761389	+	0.226517i
$583$	22.8365	−	65.9819i	0.945793	−	2.73269i
$584$	−3.09439	+	0.444906i	−0.128047	+	0.0184103i
$585$	−6.72304	−	2.02627i	−0.277964	−	0.0837761i
$586$	0.707232	+	2.40861i	0.0292155	+	0.0994989i
$587$	−25.4054	+	26.6444i	−1.04859	+	1.09973i	−0.0537255	+	0.998556i	$0.517110\pi$
$587$	−25.4054	+	26.6444i	−1.04859	+	1.09973i	−0.994868	+	0.101178i	$0.967739\pi$
$588$	11.9516	+	1.18428i	0.492876	+	0.0488387i
$589$	−1.58594	+	3.96148i	−0.0653473	+	0.163230i
$590$	4.78480	−	0.922195i	0.196987	−	0.0379662i
$591$	−4.35266	+	1.03952i	−0.179044	+	0.0427600i
$592$	0.930972	−	1.80583i	0.0382627	−	0.0742193i
$593$	23.9665	+	3.44586i	0.984187	+	0.141505i	0.615575	−	0.788079i	$-0.288924\pi$
$593$	23.9665	+	3.44586i	0.984187	+	0.141505i	0.368612	+	0.929583i	$0.379833\pi$
$594$	−3.53179	+	33.2251i	−0.144911	+	1.36324i
$595$	0.0464367	+	0.0402376i	0.00190372	+	0.00164958i
$596$	−5.13637	−	21.1724i	−0.210394	−	0.867256i
$597$	−1.10640	+	5.63236i	−0.0452820	+	0.230517i
$598$	5.52963	+	18.2214i	0.226124	+	0.745128i
$599$	12.5022	+	7.21817i	0.510828	+	0.294927i	0.733174	−	0.680041i	$-0.238038\pi$
$599$	12.5022	+	7.21817i	0.510828	+	0.294927i	−0.222346	+	0.974968i	$0.571371\pi$
$600$	8.05056	−	0.354718i	0.328663	−	0.0144813i
$601$	2.81167	+	0.541905i	0.114690	+	0.0221047i	0.246273	−	0.969200i	$-0.420794\pi$
$601$	2.81167	+	0.541905i	0.114690	+	0.0221047i	−0.131583	+	0.991305i	$0.542006\pi$
$602$	0.954988	−	1.48599i	0.0389224	−	0.0605645i
$603$	−5.99734	+	3.40575i	−0.244230	+	0.138693i
$604$	3.51169	−	2.25682i	0.142889	−	0.0918289i
$605$	10.3769	−	14.5724i	0.421883	−	0.592452i
$606$	−18.9920	−	0.0677471i	−0.771498	−	0.00275204i
$607$	12.5766	+	5.03489i	0.510467	+	0.204360i	0.612574	−	0.790413i	$-0.290134\pi$
$607$	12.5766	+	5.03489i	0.510467	+	0.204360i	−0.102107	+	0.994773i	$0.532558\pi$
$608$	−0.594375	−	0.834683i	−0.0241051	−	0.0338509i
$609$	0.952098	−	2.06528i	0.0385810	−	0.0836892i
$610$	0.267247	+	0.254820i	0.0108205	+	0.0103174i
$611$	44.7205	+	20.4232i	1.80920	+	0.826233i
$612$	0.875235	+	0.846538i	0.0353793	+	0.0342193i
$613$	−7.28596	+	6.31332i	−0.294277	+	0.254993i	−0.789468	−	0.613792i	$-0.789644\pi$
$613$	−7.28596	+	6.31332i	−0.294277	+	0.254993i	0.495191	+	0.868784i	$0.335098\pi$
$614$	11.3802	+	8.10377i	0.459266	+	0.327042i
$615$	−3.38308	+	4.27049i	−0.136419	+	0.172203i
$616$	1.29802	+	1.02078i	0.0522988	+	0.0411282i
$617$	−25.2767	+	13.0311i	−1.01760	+	0.524611i	−0.884524	−	0.466495i	$-0.845517\pi$
$617$	−25.2767	+	13.0311i	−1.01760	+	0.524611i	−0.133079	+	0.991105i	$0.542486\pi$
$618$	21.0119	−	16.4030i	0.845222	−	0.659824i
$619$	29.7974	−	7.22876i	1.19766	−	0.290549i	0.413147	−	0.910664i	$-0.364430\pi$
$619$	29.7974	−	7.22876i	1.19766	−	0.290549i	0.784510	+	0.620116i	$0.212914\pi$
$620$	2.45484			0.0985889
$621$	−3.58750	+	24.6603i	−0.143962	+	0.989583i
$622$	−33.6747			−1.35023
$623$	−4.27429	+	1.03693i	−0.171246	+	0.0415438i
$624$	−5.42093	+	4.23186i	−0.217011	+	0.169410i
$625$	−17.6952	+	9.12249i	−0.707807	+	0.364900i
$626$	18.8889	+	14.8544i	0.754952	+	0.593701i
$627$	−7.08660	+	8.94549i	−0.283012	+	0.357248i
$628$	−1.99484	−	1.42052i	−0.0796029	−	0.0566850i
$629$	−0.623210	+	0.540015i	−0.0248490	+	0.0215318i
$630$	−0.436660	+	0.124838i	−0.0173970	+	0.00497368i
$631$	25.7194	+	11.7456i	1.02387	+	0.467586i	0.855317	−	0.518106i	$-0.173363\pi$
$631$	25.7194	+	11.7456i	1.02387	+	0.467586i	0.168555	+	0.985692i	$0.446090\pi$
$632$	−0.409189	−	0.390161i	−0.0162767	−	0.0155198i
$633$	14.3662	−	31.1629i	0.571004	−	1.23861i
$634$	−14.4758	−	20.3284i	−0.574908	−	0.807346i
$635$	−7.34763	−	2.94155i	−0.291582	−	0.116732i
$636$	18.8073	+	0.0670881i	0.745757	+	0.00266022i
$637$	15.9700	−	22.4267i	0.632755	−	0.888579i
$638$	−27.6572	+	17.7742i	−1.09496	+	0.703687i
$639$	−2.95411	−	1.73377i	−0.116863	−	0.0685869i
$640$	−0.318703	+	0.495912i	−0.0125978	+	0.0196026i
$641$	−10.0628	−	1.93944i	−0.397455	−	0.0766032i	−0.0133928	−	0.999910i	$-0.504263\pi$
$641$	−10.0628	−	1.93944i	−0.397455	−	0.0766032i	−0.384063	+	0.923307i	$0.625475\pi$
$642$	−19.1295	+	0.842869i	−0.754981	+	0.0332654i
$643$	−29.3031	−	16.9182i	−1.15560	−	0.667187i	−0.205356	−	0.978687i	$-0.565835\pi$
$643$	−29.3031	−	16.9182i	−1.15560	−	0.667187i	−0.950246	+	0.311501i	$0.899168\pi$
$644$	0.938032	+	0.798082i	0.0369636	+	0.0314488i
$645$	1.35370	−	6.89128i	0.0533018	−	0.271344i
$646$	0.0980525	+	0.404178i	0.00385782	+	0.0159022i
$647$	4.01021	+	3.47486i	0.157657	+	0.136611i	0.730117	−	0.683322i	$-0.239465\pi$
$647$	4.01021	+	3.47486i	0.157657	+	0.136611i	−0.572460	+	0.819933i	$0.694011\pi$
$648$	−8.77569	+	1.99682i	−0.344742	+	0.0784426i
$649$	−52.6124	−	7.56452i	−2.06522	−	0.296933i
$650$	8.46475	−	16.4193i	0.332015	−	0.644019i
$651$	1.80164	−	0.430274i	0.0706118	−	0.0168638i
$652$	15.5462	−	2.99629i	0.608837	−	0.117344i
$653$	−16.6495	+	41.5885i	−0.651546	+	1.62748i	0.121095	+	0.992641i	$0.461359\pi$
$653$	−16.6495	+	41.5885i	−0.651546	+	1.62748i	−0.772641	+	0.634843i	$0.781065\pi$
$654$	21.3622	+	2.11677i	0.835328	+	0.0827721i
$655$	3.24508	−	3.40335i	0.126796	−	0.132980i
$656$	1.50331	+	5.11979i	0.0586943	+	0.199894i
$657$	−6.83363	+	6.42341i	−0.266605	+	0.250601i
$658$	3.14743	−	0.452532i	0.122700	−	0.0176415i
$659$	−10.8803	+	31.4366i	−0.423837	+	1.22460i	0.507884	+	0.861425i	$0.330428\pi$
$659$	−10.8803	+	31.4366i	−0.423837	+	1.22460i	−0.931722	+	0.363173i	$0.881693\pi$
$660$	6.29283	+	1.87215i	0.244948	+	0.0728733i
$661$	38.5109	−	1.83450i	1.49790	−	0.0713538i	0.717467	−	0.696592i	$-0.245301\pi$
$661$	38.5109	−	1.83450i	1.49790	−	0.0713538i	0.780434	+	0.625238i	$0.214998\pi$
$662$	−2.64493	+	3.36330i	−0.102798	+	0.130719i
$663$	2.68103	−	0.776844i	0.104123	−	0.0301701i
$664$	0.597035	−	3.09771i	0.0231695	−	0.120215i
$665$	−0.148838	−	0.0437029i	−0.00577171	−	0.00169473i
$666$	−0.824355	−	6.03905i	−0.0319431	−	0.234009i
$667$	−21.1233	+	12.4514i	−0.817897	+	0.482121i
$668$	−14.9513	+	8.63214i	−0.578483	+	0.333988i
$669$	−1.12485	−	25.5292i	−0.0434892	−	0.987017i
$670$	0.443249	+	1.28068i	0.0171242	+	0.0494771i
$671$	−1.84570	−	3.58016i	−0.0712525	−	0.138211i
$672$	−0.146979	+	0.419816i	−0.00566983	+	0.0161948i
$673$	19.9760	+	10.2983i	0.770019	+	0.396972i	0.798016	−	0.602636i	$-0.205883\pi$
$673$	19.9760	+	10.2983i	0.770019	+	0.396972i	−0.0279977	+	0.999608i	$0.508913\pi$
$674$	1.60188	+	3.50762i	0.0617021	+	0.135109i
$675$	19.1617	−	14.7398i	0.737536	−	0.567337i
$676$	0.393504	+	2.73688i	0.0151348	+	0.105265i
$677$	49.3613	−	4.71343i	1.89711	−	0.181152i	0.919715	−	0.392586i	$-0.128419\pi$
$677$	49.3613	−	4.71343i	1.89711	−	0.181152i	0.977392	+	0.211434i	$0.0678134\pi$
$678$	−1.60926	−	17.5129i	−0.0618033	−	0.672580i
$679$	0.669881	−	2.76129i	0.0257077	−	0.105968i
$680$	0.194899	−	0.138787i	0.00747402	−	0.00532223i
$681$	28.4145	−	14.5206i	1.08885	−	0.556432i
$682$	−25.3048	−	8.75808i	−0.968971	−	0.335364i
$683$	18.9872	−	8.67114i	0.726523	−	0.331792i	−0.0175902	−	0.999845i	$-0.505599\pi$
$683$	18.9872	−	8.67114i	0.726523	−	0.331792i	0.744114	+	0.668053i	$0.232872\pi$
$684$	−2.89774	−	1.02612i	−0.110798	−	0.0392348i
$685$	−0.516430	+	3.59185i	−0.0197318	+	0.137238i
$686$	0.170265	−	3.57430i	0.00650074	−	0.136467i
$687$	29.3149	−	4.10817i	1.11843	−	0.156736i
$688$	−4.74660	−	4.97809i	−0.180962	−	0.189788i
$689$	21.5569	−	37.3376i	0.821251	−	1.42245i
$690$	4.63606	+	1.57621i	0.176492	+	0.0600053i
$691$	−12.2013	−	21.1333i	−0.464161	−	0.803950i	0.535002	−	0.844851i	$-0.320311\pi$
$691$	−12.2013	−	21.1333i	−0.464161	−	0.803950i	−0.999163	+	0.0409003i	$0.986977\pi$
$692$	5.65280	−	19.2517i	0.214887	−	0.731839i
$693$	4.94653	+	0.271015i	0.187903	+	0.0102950i
$694$	−1.43367	−	0.921361i	−0.0544212	−	0.0349744i
$695$	−4.09767	+	1.64046i	−0.155434	+	0.0622262i
$696$	−6.94139	−	5.49896i	−0.263113	−	0.208438i
$697$	0.205869	−	2.15596i	0.00779784	−	0.0816626i
$698$	5.35374	+	27.7778i	0.202642	+	1.05141i
$699$	4.71162	+	0.241290i	0.178210	+	0.00912644i
$700$	−0.113572	−	1.18938i	−0.00429262	−	0.0449544i
$701$	8.33842	−	2.44838i	0.314938	−	0.0924741i	−0.120444	−	0.992720i	$-0.538432\pi$
$701$	8.33842	−	2.44838i	0.314938	−	0.0924741i	0.435381	+	0.900246i	$0.356614\pi$
$702$	−6.02405	+	19.7324i	−0.227363	+	0.744750i
$703$	0.864827	−	1.89371i	0.0326176	−	0.0714225i
$704$	5.05448	−	3.97488i	0.190498	−	0.149809i
$705$	10.9712	−	6.28213i	0.413198	−	0.236599i
$706$	−10.4183	−	0.994828i	−0.392098	−	0.0374408i
$707$	0.133986	+	2.81272i	0.00503908	+	0.105783i
$708$	−2.65944	−	14.0684i	−0.0999479	−	0.528721i
$709$	29.3048	+	1.39596i	1.10056	+	0.0524264i	0.589993	−	0.807409i	$-0.299131\pi$
$709$	29.3048	+	1.39596i	1.10056	+	0.0524264i	0.510572	+	0.859835i	$0.329434\pi$
$710$	−0.440762	+	0.508666i	−0.0165415	+	0.0190899i
$711$	−1.67713	−	0.253360i	−0.0628972	−	0.00950173i
$712$			17.1268i			0.641854i
$713$	−18.6072	−	7.25479i	−0.696846	−	0.271694i
$714$	0.118713	−	0.136018i	0.00444271	−	0.00509035i
$715$	10.8925	−	10.3860i	0.407357	−	0.388414i
$716$	3.78265	−	1.30919i	0.141364	−	0.0489267i
$717$	7.17666	+	24.7680i	0.268017	+	0.924976i
$718$	−9.06968	−	22.6550i	−0.338477	−	0.845475i
$719$	−12.3368	−	19.1964i	−0.460085	−	0.715907i	0.531257	−	0.847211i	$-0.321720\pi$
$719$	−12.3368	−	19.1964i	−0.460085	−	0.715907i	−0.991342	+	0.131304i	$0.958084\pi$
$720$	0.0715429	+	1.76703i	0.00266625	+	0.0658532i
$721$	−2.58817	−	2.98691i	−0.0963886	−	0.111238i
$722$	11.0960	+	14.1097i	0.412949	+	0.525108i
$723$	−1.48518	+	14.9883i	−0.0552344	+	0.557420i
$724$	−13.9437	−	3.38271i	−0.518215	−	0.125718i
$725$	23.1167	+	5.60805i	0.858532	+	0.208278i
$726$	−42.7077	−	30.6422i	−1.58503	−	1.13724i
$727$	10.3365	+	13.1440i	0.383361	+	0.487483i	0.938989	−	0.343948i	$-0.111764\pi$
$727$	10.3365	+	13.1440i	0.383361	+	0.487483i	−0.555628	+	0.831431i	$0.687522\pi$
$728$	0.667732	+	0.770604i	0.0247478	+	0.0285605i
$729$	−18.1139	+	20.0222i	−0.670885	+	0.741562i
$730$	0.996332	+	1.55032i	0.0368759	+	0.0573800i
$731$	1.03761	+	2.59181i	0.0383772	+	0.0958617i
$732$	0.751511	−	0.782554i	0.0277767	−	0.0289240i
$733$	1.79971	−	0.622887i	0.0664739	−	0.0230069i	−0.293629	−	0.955920i	$-0.594863\pi$
$733$	1.79971	−	0.622887i	0.0664739	−	0.0230069i	0.360103	+	0.932913i	$0.382742\pi$
$734$	−13.1279	+	12.5174i	−0.484559	+	0.462026i
$735$	−2.29172	−	6.69870i	−0.0845312	−	0.247085i
$736$	3.88127	−	2.81705i	0.143065	−	0.103838i
$737$		−	14.7828i		−	0.544531i
$738$	12.5121	+	9.98489i	0.460576	+	0.367549i
$739$	−12.4361	+	14.3520i	−0.457468	+	0.527946i	−0.936883	−	0.349642i	$-0.886303\pi$
$739$	−12.4361	+	14.3520i	−0.457468	+	0.527946i	0.479415	+	0.877588i	$0.340849\pi$
$740$	−1.19630	−	0.0569870i	−0.0439770	−	0.00209488i
$741$	−5.34212	+	4.59571i	−0.196248	+	0.168828i
$742$	−0.132683	−	2.78536i	−0.00487095	−	0.102254i
$743$	1.05337	+	0.100585i	0.0386444	+	0.00369009i	0.114360	−	0.993439i	$-0.463518\pi$
$743$	1.05337	+	0.100585i	0.0386444	+	0.00369009i	−0.0757159	+	0.997129i	$0.524124\pi$
$744$	0.0257291	−	7.21281i	0.000943274	−	0.264434i
$745$	−10.0953	+	7.93900i	−0.369862	+	0.290862i
$746$	6.00922	−	13.1584i	0.220013	−	0.481762i
$747$	−3.87004	−	8.63674i	−0.141597	−	0.316002i
$748$	−2.50418	+	0.735294i	−0.0915620	+	0.0268850i
$749$	0.269867	+	2.82617i	0.00986072	+	0.103266i
$750$	−4.48477	−	8.77595i	−0.163760	−	0.320452i
$751$	−6.26027	−	32.4814i	−0.228441	−	1.18526i	−0.897146	−	0.441734i	$-0.854363\pi$
$751$	−6.26027	−	32.4814i	−0.228441	−	1.18526i	0.668705	−	0.743527i	$-0.266849\pi$
$752$	1.17699	−	12.3260i	0.0429204	−	0.449483i
$753$	−29.8387	+	11.8223i	−1.08738	+	0.430829i
$754$	−18.8462	+	7.54489i	−0.686339	+	0.274769i
$755$	−2.07011	−	1.33038i	−0.0753390	−	0.0484174i
$756$	0.362223	+	1.28430i	0.0131739	+	0.0467096i
$757$	11.4087	−	38.8543i	0.414655	−	1.41218i	−0.442334	−	0.896850i	$-0.645849\pi$
$757$	11.4087	−	38.8543i	0.414655	−	1.41218i	0.856989	−	0.515335i	$-0.172332\pi$
$758$	9.33994	+	16.1773i	0.339242	+	0.587584i
$759$	−42.1656	−	32.7877i	−1.53051	−	1.19012i
$760$	−0.302021	+	0.523116i	−0.0109555	+	0.0189754i
$761$	27.0613	+	28.3811i	0.980971	+	1.02881i	0.999580	+	0.0289860i	$0.00922781\pi$
$761$	27.0613	+	28.3811i	0.980971	+	1.02881i	−0.0186088	+	0.999827i	$0.505924\pi$
$762$	−8.71985	+	21.5579i	−0.315887	+	0.780962i
$763$	0.151445	−	3.17922i	0.00548267	−	0.115095i
$764$	0.222981	−	1.55087i	0.00806719	−	0.0561085i
$765$	0.239600	−	0.676622i	0.00866276	−	0.0244633i
$766$	2.25251	−	1.02869i	0.0813865	−	0.0371680i
$767$	−31.0160	−	10.7348i	−1.11992	−	0.387610i
$768$	1.45374	+	0.941609i	0.0524575	+	0.0339774i
$769$	−24.1033	+	17.1639i	−0.869187	+	0.618945i	−0.925198	−	0.379485i	$-0.876101\pi$
$769$	−24.1033	+	17.1639i	−0.869187	+	0.618945i	0.0560110	+	0.998430i	$0.482162\pi$
$770$	0.229496	−	0.945996i	0.00827047	−	0.0340913i
$771$	9.31855	+	4.29588i	0.335599	+	0.154712i
$772$	16.6869	−	1.59341i	0.600576	−	0.0573481i
$773$	3.75613	+	26.1245i	0.135099	+	0.939631i	0.938767	+	0.344554i	$0.111970\pi$
$773$	3.75613	+	26.1245i	0.135099	+	0.939631i	−0.803668	+	0.595078i	$0.797121\pi$
$774$	−20.2337	−	4.04966i	−0.727287	−	0.145562i
$775$	8.04851	+	17.6238i	0.289111	+	0.633064i
$776$	−9.83434	−	5.06995i	−0.353032	−	0.182001i
$777$	−0.887971	+	0.167859i	−0.0318558	+	0.00602192i
$778$	−10.5530	−	20.4700i	−0.378344	−	0.733885i
$779$	1.78829	+	5.16694i	0.0640723	+	0.185125i
$780$	3.59670	+	1.87050i	0.128783	+	0.0669746i
$781$	6.35818	−	3.67090i	0.227513	−	0.131355i
$782$	−1.88745	+	0.475992i	−0.0674950	+	0.0170214i
$783$	−26.5216	−	1.54800i	−0.947806	−	0.0553210i
$784$	−6.65317	−	1.95355i	−0.237613	−	0.0697696i
$785$	−0.273208	+	1.41754i	−0.00975121	+	0.0505941i
$786$	−9.96568	−	9.57036i	−0.355464	−	0.341363i
$787$	−16.3279	+	20.7626i	−0.582027	+	0.740108i	−0.984512	−	0.175319i	$-0.943904\pi$
$787$	−16.3279	+	20.7626i	−0.582027	+	0.740108i	0.402484	+	0.915427i	$0.368147\pi$
$788$	2.58075	−	0.122936i	0.0919356	−	0.00437943i
$789$	−19.2052	+	18.1817i	−0.683722	+	0.647287i
$790$	−0.109008	+	0.314959i	−0.00387835	+	0.0112057i
$791$	−2.58099	+	0.371090i	−0.0917695	+	0.0131945i
$792$	5.56670	−	18.4699i	0.197804	−	0.656301i
$793$	−0.700715	−	2.38642i	−0.0248831	−	0.0847441i
$794$	9.33832	−	9.79375i	0.331405	−	0.347567i
$795$	−4.56962	−	10.1013i	−0.162068	−	0.358255i
$796$	1.23169	−	3.07660i	0.0436560	−	0.109047i
$797$	8.28522	−	1.59684i	0.293477	−	0.0565631i	−0.0403874	−	0.999184i	$-0.512859\pi$
$797$	8.28522	−	1.59684i	0.293477	−	0.0565631i	0.333865	+	0.942621i	$0.391647\pi$
$798$	−0.129968	+	0.436858i	−0.00460080	+	0.0154646i
$799$	−2.30289	+	4.46699i	−0.0814705	+	0.158031i
$800$	−4.60514	−	0.662120i	−0.162816	−	0.0234095i
$801$	29.5042	+	42.0648i	1.04248	+	1.48629i
$802$	−22.7146	−	19.6823i	−0.802081	−	0.695007i
$803$	−4.73926	−	19.5355i	−0.167245	−	0.689393i
$804$	3.76754	−	1.28893i	0.132871	−	0.0454570i
$805$	0.198239	−	0.698429i	0.00698700	−	0.0246164i
$806$	−14.3194	−	8.26731i	−0.504379	−	0.291203i
$807$	−19.9032	+	38.2709i	−0.700624	+	1.34720i
$808$	10.7670	+	2.07516i	0.378780	+	0.0730039i
$809$	11.9113	−	18.5344i	0.418780	−	0.651634i	−0.566207	−	0.824263i	$-0.691590\pi$
$809$	11.9113	−	18.5344i	0.418780	−	0.651634i	0.984987	+	0.172629i	$0.0552262\pi$
$810$	3.21976	+	4.21671i	0.113131	+	0.148160i
$811$	32.0877	−	20.6215i	1.12675	−	0.724119i	0.161872	−	0.986812i	$-0.448247\pi$
$811$	32.0877	−	20.6215i	1.12675	−	0.724119i	0.964880	+	0.262692i	$0.0846104\pi$
$812$	−0.761611	+	1.06953i	−0.0267273	+	0.0375333i
$813$	−12.0818	−	21.0997i	−0.423726	−	0.739999i
$814$	12.1283	+	4.85545i	0.425098	+	0.170183i
$815$	−5.41369	−	7.60246i	−0.189633	−	0.266302i
$816$	−0.405740	−	0.574105i	−0.0142037	−	0.0200977i
$817$	−5.10097	−	4.86377i	−0.178460	−	0.170162i
$818$	−19.6778	−	8.98654i	−0.688018	−	0.314207i
$819$	2.96752	+	0.742368i	0.103693	+	0.0259404i
$820$	2.37720	−	2.05986i	0.0830155	−	0.0719333i
$821$	13.1732	+	9.38060i	0.459748	+	0.327385i	0.786355	−	0.617775i	$-0.211966\pi$
$821$	13.1732	+	9.38060i	0.459748	+	0.327385i	−0.326607	+	0.945160i	$0.605905\pi$
$822$	10.5481	+	1.55502i	0.367909	+	0.0542375i
$823$	30.3294	+	23.8513i	1.05722	+	0.831405i	0.986115	−	0.166064i	$-0.0531058\pi$
$823$	30.3294	+	23.8513i	1.05722	+	0.831405i	0.0711025	+	0.997469i	$0.477348\pi$
$824$	−13.6792	+	7.05210i	−0.476537	+	0.245672i
$825$	7.19131	+	51.3154i	0.250369	+	1.78657i
$826$	−2.06298	+	0.500473i	−0.0717802	+	0.0174137i
$827$	−49.9867			−1.73821			−0.869104	−	0.494630i	$-0.835304\pi$
$827$	−49.9867			−1.73821			−0.869104	+	0.494630i	$0.835304\pi$
$828$	4.67980	−	13.6051i	0.162634	−	0.472811i
$829$	44.5582			1.54757			0.773785	−	0.633449i	$-0.218361\pi$
$829$	44.5582			1.54757			0.773785	+	0.633449i	$0.218361\pi$
$830$	−1.80726	+	0.438436i	−0.0627309	+	0.0152183i
$831$	−0.259181	−	0.104835i	−0.00899090	−	0.00363668i
$832$	3.52914	−	1.81940i	0.122351	−	0.0630763i
$833$	2.21227	+	1.73975i	0.0766508	+	0.0602788i
$834$	4.77704	+	12.0569i	0.165415	+	0.417498i
$835$	8.29006	+	5.90332i	0.286889	+	0.204293i
$836$	4.97958	−	4.31483i	0.172222	−	0.149231i
$837$	−12.3623	−	17.7596i	−0.427302	−	0.613860i
$838$	24.4965	+	11.1872i	0.846218	+	0.386455i
$839$	34.9972	+	33.3698i	1.20824	+	1.15205i	0.984122	+	0.177491i	$0.0567980\pi$
$839$	34.9972	+	33.3698i	1.20824	+	1.15205i	0.224116	+	0.974562i	$0.428050\pi$
$840$	0.261107	−	0.0239931i	0.00900903	−	0.000827840i
$841$	1.65867	+	2.32928i	0.0571956	+	0.0803200i
$842$	−14.2990	−	5.72447i	−0.492777	−	0.197278i
$843$	14.8276	−	25.4720i	0.510691	−	0.877301i
$844$	−11.4919	+	16.1381i	−0.395568	+	0.555498i
$845$	1.37121	−	0.881223i	0.0471710	−	0.0303150i
$846$	−18.3431	−	32.3013i	−0.630650	−	1.11054i
$847$	−4.21343	+	6.55623i	−0.144775	+	0.225275i
$848$	−10.6622	−	2.05498i	−0.366143	−	0.0705682i
$849$	19.2055	+	30.1200i	0.659130	+	1.03372i
$850$	1.63537	+	0.944184i	0.0560929	+	0.0323852i
$851$	8.89933	+	3.96738i	0.305065	+	0.136000i
$852$	1.48994	+	1.30038i	0.0510445	+	0.0445501i
$853$	6.43832	+	26.5391i	0.220444	+	0.908682i	0.969287	+	0.245934i	$0.0790947\pi$
$853$	6.43832	+	26.5391i	0.220444	+	0.908682i	−0.748843	+	0.662748i	$0.769390\pi$
$854$	−0.121574	−	0.105344i	−0.00416018	−	0.00360481i
$855$	0.159380	+	1.80511i	0.00545067	+	0.0617333i
$856$	10.9426	+	1.57331i	0.374011	+	0.0537746i
$857$	7.49306	−	14.5345i	0.255958	−	0.496489i	−0.725486	−	0.688237i	$-0.758385\pi$
$857$	7.49306	−	14.5345i	0.255958	−	0.496489i	0.981444	+	0.191747i	$0.0614154\pi$
$858$	−30.4019	−	32.1132i	−1.03790	−	1.09633i
$859$	−54.6728	+	10.5373i	−1.86541	+	0.359529i	−0.991874	−	0.127226i	$-0.959393\pi$
$859$	−54.6728	+	10.5373i	−1.86541	+	0.359529i	−0.873539	+	0.486755i	$0.838181\pi$
$860$	−1.50699	+	3.76427i	−0.0513878	+	0.128361i
$861$	1.38361	−	1.92842i	0.0471535	−	0.0657203i
$862$	−10.3058	+	10.8084i	−0.351017	+	0.368136i
$863$	−1.77515	−	6.04562i	−0.0604269	−	0.205795i	0.923746	−	0.383005i	$-0.125111\pi$
$863$	−1.77515	−	6.04562i	−0.0604269	−	0.205795i	−0.984173	+	0.177210i	$0.943293\pi$
$864$	5.19262	−	0.191687i	0.176656	−	0.00652132i
$865$	−11.7074	+	1.68327i	−0.398064	+	0.0572330i
$866$	8.54063	−	24.6765i	0.290222	−	0.838543i
$867$	−6.77349	−	28.3619i	−0.230040	−	0.963221i
$868$	−1.06822	+	0.0508855i	−0.0362577	+	0.00172717i
$869$	2.24734	−	2.85773i	0.0762359	−	0.0969418i
$870$	−1.24882	+	5.06872i	−0.0423389	+	0.171846i
$871$	1.72750	−	8.96313i	0.0585342	−	0.303704i
$872$	−11.8918	−	3.49176i	−0.402708	−	0.118246i
$873$	−32.8879	+	4.48932i	−1.11309	+	0.151941i
$874$	3.83522	−	3.07255i	0.129728	−	0.103931i
$875$	−1.26547	+	0.730622i	−0.0427809	+	0.0246995i
$876$	4.56559	−	2.91117i	0.154257	−	0.0983593i
$877$	−4.72553	−	13.6535i	−0.159570	−	0.461047i	0.836668	−	0.547711i	$-0.184501\pi$
$877$	−4.72553	−	13.6535i	−0.159570	−	0.461047i	−0.996238	+	0.0866640i	$0.972379\pi$
$878$	−6.03801	−	11.7121i	−0.203773	−	0.395264i
$879$	−2.83557	−	3.29611i	−0.0956414	−	0.111175i
$880$	−3.36917	−	1.73693i	−0.113575	−	0.0585518i
$881$	−6.20970	−	13.5973i	−0.209210	−	0.458106i	0.775716	−	0.631082i	$-0.217389\pi$
$881$	−6.20970	−	13.5973i	−0.209210	−	0.458106i	−0.984926	+	0.172976i	$0.944662\pi$
$882$	−19.7061	+	6.66330i	−0.663539	+	0.224365i
$883$	7.90650	+	54.9909i	0.266075	+	1.85059i	0.484570	+	0.874753i	$0.338976\pi$
$883$	7.90650	+	54.9909i	0.266075	+	1.85059i	−0.218495	+	0.975838i	$0.570115\pi$
$884$	−1.60427	+	0.153189i	−0.0539573	+	0.00515230i
$885$	−6.89248	+	4.87115i	−0.231688	+	0.163742i
$886$	−2.83488	+	11.6855i	−0.0952396	+	0.392583i
$887$	12.7553	−	9.08298i	0.428280	−	0.304976i	−0.345515	−	0.938413i	$-0.612296\pi$
$887$	12.7553	−	9.08298i	0.428280	−	0.304976i	0.773794	+	0.633437i	$0.218356\pi$
$888$	−0.179977	+	3.51438i	−0.00603964	+	0.117935i
$889$	3.25828	+	1.12770i	0.109279	+	0.0378218i
$890$	9.18373	−	4.19407i	0.307839	−	0.140586i
$891$	−18.1458	−	54.9534i	−0.607906	−	1.84101i
$892$	−2.09966	+	14.6034i	−0.0703018	+	0.488959i
$893$	0.603706	−	12.6734i	0.0202023	−	0.424098i
$894$	23.2205	+	29.7450i	0.776610	+	0.994823i
$895$	−1.62832	−	1.70774i	−0.0544288	−	0.0570833i
$896$	0.128403	−	0.222401i	0.00428965	−	0.00742989i
$897$	−21.7344	−	24.8073i	−0.725690	−	0.828292i
$898$	10.0033	+	17.3263i	0.333816	+	0.578186i
$899$	5.99847	−	20.4289i	0.200060	−	0.681343i
$900$	−12.4512	+	6.30703i	−0.415041	+	0.210234i
$901$	3.70762	+	2.38274i	0.123519	+	0.0793807i
$902$	−31.8533	+	12.7522i	−1.06060	+	0.424600i
$903$	−0.446211	+	3.02678i	−0.0148490	+	0.100725i
$904$	−0.965170	+	10.1077i	−0.0321011	+	0.336178i
$905$	1.60071	+	8.30528i	0.0532094	+	0.276077i
$906$	−3.93061	+	6.06844i	−0.130586	+	0.201610i
$907$	−0.229983	−	2.40849i	−0.00763647	−	0.0799727i	0.990850	−	0.134966i	$-0.0430924\pi$
$907$	−0.229983	−	2.40849i	−0.00763647	−	0.0799727i	−0.998487	+	0.0549930i	$0.982486\pi$
$908$	−17.6769	+	5.19039i	−0.586627	+	0.172249i
$909$	30.0194	−	13.4514i	0.995680	−	0.446155i
$910$	0.249697	−	0.546759i	0.00827736	−	0.0181249i
$911$	−23.7486	+	18.6761i	−0.786827	+	0.618768i	−0.928579	−	0.371135i	$-0.878969\pi$
$911$	−23.7486	+	18.6761i	−0.786827	+	0.618768i	0.141752	+	0.989902i	$0.454726\pi$
$912$	1.53385	+	0.892880i	0.0507909	+	0.0295662i
$913$	20.1936	+	1.92826i	0.668311	+	0.0638160i
$914$	−1.65708	−	34.7864i	−0.0548114	−	1.15063i
$915$	−0.603654	−	0.211341i	−0.0199562	−	0.00698671i
$916$	−17.0710	−	0.813191i	−0.564041	−	0.0268686i
$917$	−1.34154	+	1.54822i	−0.0443016	+	0.0511268i
$918$	−1.98554	−	0.711083i	−0.0655324	−	0.0234692i
$919$		−	34.5273i		−	1.13895i	−0.822008	−	0.569475i	$-0.807146\pi$
$919$		−	34.5273i		−	1.13895i	0.822008	−	0.569475i	$-0.192854\pi$
$920$	−2.46102	−	1.39137i	−0.0811373	−	0.0458720i
$921$	−23.7441	−	4.66421i	−0.782395	−	0.153691i
$922$	9.03223	−	8.61222i	0.297461	−	0.283628i
$923$	4.28408	−	1.48273i	0.141012	−	0.0488048i
$924$	−2.77711	−	0.684219i	−0.0913604	−	0.0225092i
$925$	−3.51311	−	8.77532i	−0.115510	−	0.288531i
$926$	−6.50153	−	10.1166i	−0.213654	−	0.332451i
$927$	−21.4485	+	40.8855i	−0.704463	+	1.34286i
$928$	3.34816	+	3.86398i	0.109909	+	0.126841i
$929$	−3.67365	−	4.67142i	−0.120528	−	0.153264i	0.722045	−	0.691847i	$-0.243203\pi$
$929$	−3.67365	−	4.67142i	−0.120528	−	0.153264i	−0.842573	+	0.538582i	$0.818960\pi$
$930$	−3.87395	+	1.75250i	−0.127032	+	0.0574668i
$931$	−6.90493	−	1.67512i	−0.226300	−	0.0548998i
$932$	−2.64704	−	0.642166i	−0.0867068	−	0.0210348i
$933$	53.1416	−	24.0402i	1.73978	−	0.787041i
$934$	−11.0444	−	14.0440i	−0.361383	−	0.459535i
$935$	1.00751	+	1.16273i	0.0329492	+	0.0380254i
$936$	5.53359	−	10.5482i	0.180871	−	0.344779i
$937$	−24.6266	−	38.3197i	−0.804515	−	1.25185i	−0.964330	−	0.264702i	$-0.914726\pi$
$937$	−24.6266	−	38.3197i	−0.804515	−	1.25185i	0.159816	−	0.987147i	$-0.448910\pi$
$938$	−0.219425	−	0.548098i	−0.00716449	−	0.0178960i
$939$	−40.4128	−	9.95681i	−1.31882	−	0.324928i
$940$	−6.89768	+	2.38731i	−0.224977	+	0.0778655i
$941$	−6.09970	+	5.81605i	−0.198844	+	0.189598i	−0.782959	−	0.622074i	$-0.786290\pi$
$941$	−6.09970	+	5.81605i	−0.198844	+	0.189598i	0.584114	+	0.811671i	$0.301442\pi$
$942$	4.16214	+	0.817595i	0.135610	+	0.0266387i
$943$	−24.1062	+	8.58796i	−0.785005	+	0.279662i
$944$			8.26622i			0.269043i
$945$	0.599966	−	0.508735i	0.0195169	−	0.0165492i
$946$	28.9639	−	33.4261i	0.941697	−	1.08678i
$947$	−26.5246	−	1.26352i	−0.861934	−	0.0410590i	−0.388042	−	0.921642i	$-0.626848\pi$
$947$	−26.5246	−	1.26352i	−0.861934	−	0.0410590i	−0.473892	+	0.880583i	$0.657151\pi$
$948$	0.924269	+	0.323589i	0.0300189	+	0.0105097i
$949$	−0.590619	−	12.3986i	−0.0191723	−	0.402476i
$950$	−4.74576	−	0.453165i	−0.153973	−	0.0147026i
$951$	37.3565	+	21.7458i	1.21137	+	0.705156i
$952$	−0.0819328	+	0.0644326i	−0.00265546	+	0.00208827i
$953$	10.9221	−	23.9161i	0.353802	−	0.774719i	−0.646132	−	0.763226i	$-0.723614\pi$
$953$	10.9221	−	23.9161i	0.353802	−	0.774719i	0.999934	−	0.0114929i	$-0.00365837\pi$
$954$	−29.7274	+	13.3206i	−0.962460	+	0.431269i
$955$	−0.886212	+	0.260215i	−0.0286771	+	0.00842037i
$956$	−1.41519	−	14.8206i	−0.0457706	−	0.479331i
$957$	30.9565	−	47.7935i	1.00068	−	1.54495i
$958$	0.535866	+	2.78034i	0.0173130	+	0.0898286i
$959$	0.150269	−	1.57369i	0.00485244	−	0.0508171i
$960$	0.148912	−	1.01011i	0.00480610	−	0.0326012i
$961$	−12.6799	+	5.07625i	−0.409028	+	0.163750i
$962$	6.78627	+	4.36127i	0.218798	+	0.140613i
$963$	29.5863	−	14.9866i	0.953404	−	0.482936i
$964$	2.44991	−	8.34362i	0.0789062	−	0.268730i
$965$	−4.94078	−	8.55768i	−0.159049	−	0.275481i
$966$	−2.05004	−	0.589785i	−0.0659590	−	0.0189760i
$967$	16.0628	−	27.8215i	0.516543	−	0.894680i	−0.483272	−	0.875470i	$-0.660552\pi$
$967$	16.0628	−	27.8215i	0.516543	−	0.894680i	0.999815	−	0.0192093i	$-0.00611488\pi$
$968$	20.9421	+	21.9635i	0.673105	+	0.705932i
$969$	−0.443276	−	0.567828i	−0.0142401	−	0.0182413i
$970$	−0.310344	+	6.51492i	−0.00996453	+	0.209181i
$971$	−6.69832	+	46.5878i	−0.214959	+	1.49508i	0.541315	+	0.840820i	$0.317927\pi$
$971$	−6.69832	+	46.5878i	−0.214959	+	1.49508i	−0.756274	+	0.654255i	$0.772982\pi$
$972$	12.4233	−	9.41608i	0.398476	−	0.302021i
$973$	1.74909	−	0.798781i	0.0560731	−	0.0256077i
$974$	0.473514	+	0.163885i	0.0151724	+	0.00525121i
$975$	−1.63642	+	31.9540i	−0.0524074	+	1.02335i
$976$	−0.510257	+	0.363352i	−0.0163329	+	0.0116306i
$977$	8.99377	−	37.0728i	0.287736	−	1.18607i	−0.626021	−	0.779806i	$-0.715318\pi$
$977$	8.99377	−	37.0728i	0.287736	−	1.18607i	0.913758	−	0.406259i	$-0.133167\pi$
$978$	−22.3942	+	15.8268i	−0.716089	+	0.506085i
$979$	−109.630	+	10.4684i	−3.50379	+	0.334571i
$980$	0.581721	+	4.04596i	0.0185824	+	0.129243i
$981$	−35.2225	+	11.9099i	−1.12457	+	0.380255i
$982$	17.0181	+	37.2644i	0.543068	+	1.18915i
$983$	−1.97956	−	1.02053i	−0.0631382	−	0.0325500i	0.426368	−	0.904550i	$-0.359793\pi$
$983$	−1.97956	−	1.02053i	−0.0631382	−	0.0325500i	−0.489506	+	0.872000i	$0.662823\pi$
$984$	−6.02734	−	7.00627i	−0.192145	−	0.223352i
$985$	−0.697905	−	1.35375i	−0.0222371	−	0.0431340i
$986$	−0.678727	−	1.96105i	−0.0216151	−	0.0624526i
$987$	−4.64385	+	2.96107i	−0.147815	+	0.0942519i
$988$	3.52345	−	2.03427i	0.112096	−	0.0647186i
$989$	22.5472	−	24.0788i	0.716959	−	0.765662i
$990$	−11.2671	+	1.53801i	−0.358093	+	0.0488811i
$991$	17.6086	+	5.17036i	0.559357	+	0.164242i	0.549177	−	0.835706i	$-0.314941\pi$
$991$	17.6086	+	5.17036i	0.559357	+	0.164242i	0.0101799	+	0.999948i	$0.496760\pi$
$992$	−0.788107	+	4.08909i	−0.0250224	+	0.129829i
$993$	1.77288	−	7.19578i	0.0562607	−	0.228351i
$994$	0.181252	−	0.230481i	0.00574898	−	0.00731042i
$995$	−1.95136	+	0.0929546i	−0.0618622	+	0.00294686i
$996$	1.26927	+	5.31467i	0.0402183	+	0.168402i
$997$	9.89658	−	28.5943i	0.313428	−	0.905590i	−0.672746	−	0.739874i	$-0.734885\pi$
$997$	9.89658	−	28.5943i	0.313428	−	0.905590i	0.986173	−	0.165717i	$-0.0529937\pi$
$998$	−1.50241	+	0.216015i	−0.0475581	+	0.00683782i
$999$	5.61215	+	8.94164i	0.177561	+	0.282901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.p.a.5.15	✓	480
9.2	odd	6	inner	414.2.p.a.281.16	yes	480
23.14	odd	22	inner	414.2.p.a.221.16	yes	480
207.83	even	66	inner	414.2.p.a.83.15	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.p.a.5.15	✓	480	1.1	even	1	trivial
414.2.p.a.83.15	yes	480	207.83	even	66	inner
414.2.p.a.221.16	yes	480	23.14	odd	22	inner
414.2.p.a.281.16	yes	480	9.2	odd	6	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.971812 - 0.235759i) q^{2} +(-1.36529 + 1.06582i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-0.463371 - 0.364399i) q^{5} +(-1.07553 + 1.35766i) q^{6} +(0.209188 + 0.148962i) q^{7} +(0.755750 - 0.654861i) q^{8} +(0.728058 - 2.91031i) q^{9} +O(q^{10})\)	\(q+(0.971812 - 0.235759i) q^{2} +(-1.36529 + 1.06582i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-0.463371 - 0.364399i) q^{5} +(-1.07553 + 1.35766i) q^{6} +(0.209188 + 0.148962i) q^{7} +(0.755750 - 0.654861i) q^{8} +(0.728058 - 2.91031i) q^{9} +(-0.536220 - 0.244883i) q^{10} +(4.65375 + 4.43734i) q^{11} +(-0.725135 + 1.57295i) q^{12} +(2.30313 + 3.23429i) q^{13} +(0.238411 + 0.0954453i) q^{14} +(1.02102 + 0.00364213i) q^{15} +(0.580057 - 0.814576i) q^{16} +(-0.341450 + 0.219437i) q^{17} +(0.0214025 - 2.99992i) q^{18} +(0.553986 - 0.862020i) q^{19} +(-0.578838 - 0.111562i) q^{20} +(-0.444370 + 0.0195795i) q^{21} +(5.56871 + 3.21510i) q^{22} +(4.05778 + 2.55626i) q^{23} +(-0.333857 + 1.69957i) q^{24} +(-1.09687 - 4.52135i) q^{25} +(3.00072 + 2.60014i) q^{26} +(2.10786 + 4.74941i) q^{27} +(0.254192 + 0.0365474i) q^{28} +(-2.34281 + 4.54442i) q^{29} +(0.993100 - 0.237176i) q^{30} +(-4.08909 + 0.788107i) q^{31} +(0.371662 - 0.928368i) q^{32} +(-11.0831 - 1.09822i) q^{33} +(-0.280091 + 0.293751i) q^{34} +(-0.0426501 - 0.145253i) q^{35} +(-0.686460 - 2.92041i) q^{36} +(2.01101 - 0.289139i) q^{37} +(0.335142 - 0.968328i) q^{38} +(-6.59162 - 1.96104i) q^{39} +(-0.588823 + 0.0280491i) q^{40} +(-3.29846 + 4.19433i) q^{41} +(-0.427228 + 0.123792i) q^{42} +(1.30173 - 6.75404i) q^{43} +(6.16973 + 1.81160i) q^{44} +(-1.39788 + 1.08325i) q^{45} +(4.54606 + 1.52754i) q^{46} +(10.7232 - 6.19104i) q^{47} +(0.0762423 + 1.73037i) q^{48} +(-2.26791 - 6.55268i) q^{49} +(-2.13190 - 4.13531i) q^{50} +(0.232300 - 0.663519i) q^{51} +(3.52914 + 1.81940i) q^{52} +(-4.51077 - 9.87720i) q^{53} +(3.16816 + 4.11859i) q^{54} +(-0.539451 - 3.75196i) q^{55} +(0.255643 - 0.0244110i) q^{56} +(0.162403 + 1.76736i) q^{57} +(-1.20538 + 4.96866i) q^{58} +(-6.73346 + 4.79488i) q^{59} +(0.909190 - 0.464622i) q^{60} +(-0.591956 - 0.204878i) q^{61} +(-3.78802 + 1.72993i) q^{62} +(0.585828 - 0.500350i) q^{63} +(0.142315 - 0.989821i) q^{64} +(0.111370 - 2.33794i) q^{65} +(-11.0296 + 1.54569i) q^{66} +(-1.58647 - 1.66384i) q^{67} +(-0.202941 + 0.351504i) q^{68} +(-8.26457 + 0.834817i) q^{69} +(-0.0756925 - 0.131103i) q^{70} +(0.321673 - 1.09552i) q^{71} +(-1.35562 - 2.67625i) q^{72} +(-2.62993 - 1.69016i) q^{73} +(1.88615 - 0.755101i) q^{74} +(6.31649 + 5.00392i) q^{75} +(0.0974025 - 1.02004i) q^{76} +(0.312513 + 1.62147i) q^{77} +(-6.86814 - 0.351729i) q^{78} +(-0.0537433 - 0.562826i) q^{79} +(-0.565613 + 0.166079i) q^{80} +(-7.93986 - 4.23776i) q^{81} +(-2.21663 + 4.85374i) q^{82} +(2.47978 - 1.95012i) q^{83} +(-0.386000 + 0.221025i) q^{84} +(0.238181 + 0.0227435i) q^{85} +(-0.327285 - 6.87055i) q^{86} +(-1.64490 - 8.70148i) q^{87} +(6.42291 + 0.305961i) q^{88} +(-11.2157 + 12.9436i) q^{89} +(-1.10309 + 1.38228i) q^{90} +1.01965i q^{91} +(4.77804 + 0.412709i) q^{92} +(4.74283 - 5.43423i) q^{93} +(8.96133 - 8.54461i) q^{94} +(-0.570821 + 0.197563i) q^{95} +(0.482044 + 1.66362i) q^{96} +(-4.11218 - 10.2717i) q^{97} +(-3.74883 - 5.83329i) q^{98} +(16.3023 - 10.3132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more