LMFDB - Embedded newform 539.2.r.a.23.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(23,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([38, 0]))

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

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

chi := DirichletCharacter("539.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.r (of order $21$, degree $12$, 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$276$
Relative dimension:	$23$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			23.5
Character	$\chi$	$=$	539.23
Dual form			539.2.r.a.375.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.141924 + 1.89385i) q^{2} +(-1.56085 + 0.481458i) q^{3} +(-1.58885 - 0.239481i) q^{4} +(0.329056 + 0.305319i) q^{5} +(-0.690286 - 3.02434i) q^{6} +(-2.09779 + 1.61223i) q^{7} +(-0.166167 + 0.728025i) q^{8} +(-0.274269 + 0.186993i) q^{9} +O(q^{10})$	\(q+(-0.141924 + 1.89385i) q^{2} +(-1.56085 + 0.481458i) q^{3} +(-1.58885 - 0.239481i) q^{4} +(0.329056 + 0.305319i) q^{5} +(-0.690286 - 3.02434i) q^{6} +(-2.09779 + 1.61223i) q^{7} +(-0.166167 + 0.728025i) q^{8} +(-0.274269 + 0.186993i) q^{9} +(-0.624929 + 0.579849i) q^{10} +(-0.826239 - 0.563320i) q^{11} +(2.59526 - 0.391173i) q^{12} +(2.69216 - 1.29647i) q^{13} +(-2.75559 - 4.20171i) q^{14} +(-0.660605 - 0.318131i) q^{15} +(-4.42602 - 1.36524i) q^{16} +(0.215980 - 0.550308i) q^{17} +(-0.315212 - 0.545963i) q^{18} +(-3.29969 + 5.71523i) q^{19} +(-0.449704 - 0.563910i) q^{20} +(2.49811 - 3.52644i) q^{21} +(1.18411 - 1.48482i) q^{22} +(-1.42792 - 3.63828i) q^{23} +(-0.0911521 - 1.21634i) q^{24} +(-0.358593 - 4.78508i) q^{25} +(2.07324 + 5.28253i) q^{26} +(3.39332 - 4.25509i) q^{27} +(3.71918 - 2.05922i) q^{28} +(-3.49978 - 4.38858i) q^{29} +(0.696247 - 1.20593i) q^{30} +(-0.195523 - 0.338655i) q^{31} +(2.66809 - 6.79818i) q^{32} +(1.56085 + 0.481458i) q^{33} +(1.01155 + 0.487136i) q^{34} +(-1.18253 - 0.109981i) q^{35} +(0.480555 - 0.231423i) q^{36} +(1.89601 - 0.285777i) q^{37} +(-10.3555 - 7.06024i) q^{38} +(-3.57785 + 3.31976i) q^{39} +(-0.276958 + 0.188827i) q^{40} +(-1.57410 + 6.89660i) q^{41} +(6.32401 + 5.23153i) q^{42} +(-0.172237 - 0.754620i) q^{43} +(1.17787 + 1.09290i) q^{44} +(-0.147343 - 0.0222083i) q^{45} +(7.09299 - 2.18790i) q^{46} +(-0.628919 + 8.39234i) q^{47} +7.56565 q^{48} +(1.80143 - 6.76423i) q^{49} +9.11311 q^{50} +(-0.0721619 + 0.962934i) q^{51} +(-4.58792 + 1.41519i) q^{52} +(-2.11167 - 0.318284i) q^{53} +(7.57689 + 7.03033i) q^{54} +(-0.0998863 - 0.437630i) q^{55} +(-0.825161 - 1.79514i) q^{56} +(2.39867 - 10.5093i) q^{57} +(8.80801 - 6.00520i) q^{58} +(-2.91202 + 2.70196i) q^{59} +(0.973419 + 0.663665i) q^{60} +(2.69464 - 0.406152i) q^{61} +(0.669110 - 0.322227i) q^{62} +(0.273882 - 0.834457i) q^{63} +(4.14985 + 1.99846i) q^{64} +(1.28171 + 0.395355i) q^{65} +(-1.13333 + 2.88768i) q^{66} +(1.43644 + 2.48799i) q^{67} +(-0.474950 + 0.822637i) q^{68} +(3.98044 + 4.99132i) q^{69} +(0.376118 - 2.22393i) q^{70} +(-4.50183 + 5.64512i) q^{71} +(-0.0905615 - 0.230747i) q^{72} +(0.0174074 + 0.232286i) q^{73} +(0.272129 + 3.63131i) q^{74} +(2.86353 + 7.29615i) q^{75} +(6.61142 - 8.29045i) q^{76} +(2.64148 - 0.150361i) q^{77} +(-5.77933 - 7.24706i) q^{78} +(-3.66280 + 6.34416i) q^{79} +(-1.03957 - 1.80059i) q^{80} +(-2.88399 + 7.34828i) q^{81} +(-12.8377 - 3.95991i) q^{82} +(-10.4293 - 5.02249i) q^{83} +(-4.81365 + 5.00475i) q^{84} +(0.239089 - 0.115139i) q^{85} +(1.45358 - 0.219092i) q^{86} +(7.57555 + 5.16492i) q^{87} +(0.547405 - 0.507917i) q^{88} +(-3.99001 + 2.72034i) q^{89} +(0.0629706 - 0.275892i) q^{90} +(-3.55736 + 7.06010i) q^{91} +(1.39745 + 6.12265i) q^{92} +(0.468229 + 0.434453i) q^{93} +(-15.8045 - 2.38215i) q^{94} +(-2.83075 + 0.873171i) q^{95} +(-0.891445 + 11.8955i) q^{96} +0.620107 q^{97} +(12.5548 + 4.37164i) q^{98} +0.331949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 276 q - q^{3} + 24 q^{4} - 2 q^{5} - 12 q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 276 * q - q^3 + 24 * q^4 - 2 * q^5 - 12 * q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9	\( 276 q - q^{3} + 24 q^{4} - 2 q^{5} - 12 q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9} - 9 q^{10} - 23 q^{11} - 44 q^{12} + 43 q^{13} - 47 q^{14} + 6 q^{15} - 34 q^{16} - 3 q^{17} + 10 q^{18} + 59 q^{19} - 28 q^{20} + 25 q^{21} + 6 q^{23} + 2 q^{24} + 53 q^{25} + q^{26} - 4 q^{27} - 13 q^{28} - 28 q^{29} - 6 q^{30} - 3 q^{31} - 253 q^{32} + q^{33} - 50 q^{34} - 9 q^{35} - 76 q^{36} - 17 q^{37} + 8 q^{38} + 10 q^{39} - 59 q^{40} + 73 q^{41} - 12 q^{42} - 38 q^{44} - 9 q^{45} + 74 q^{46} - 87 q^{47} - 160 q^{48} - 60 q^{49} + 30 q^{50} + 128 q^{51} + 49 q^{52} + 21 q^{53} + 76 q^{54} - 4 q^{55} + 102 q^{56} - 41 q^{57} + 17 q^{58} + 36 q^{59} + 10 q^{60} + 11 q^{61} + 72 q^{62} - 201 q^{63} - 42 q^{64} - 215 q^{65} - 34 q^{66} - 8 q^{67} + 75 q^{68} + 6 q^{69} + 97 q^{70} + q^{71} - 95 q^{72} - 20 q^{73} + 154 q^{74} - 101 q^{75} - 27 q^{76} + 2 q^{77} - 87 q^{78} - 14 q^{79} - 124 q^{80} - 203 q^{81} - 15 q^{82} + 29 q^{83} - 96 q^{84} - 74 q^{85} + 63 q^{86} + 65 q^{87} + 3 q^{88} + 141 q^{89} + 491 q^{90} + 71 q^{91} + 41 q^{92} + 121 q^{93} + 116 q^{94} - 7 q^{95} - 141 q^{96} - 298 q^{97} - 102 q^{98} - 268 q^{99}+O(q^{100}) \) 276 * q - q^3 + 24 * q^4 - 2 * q^5 - 12 * q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9 - 9 * q^10 - 23 * q^11 - 44 * q^12 + 43 * q^13 - 47 * q^14 + 6 * q^15 - 34 * q^16 - 3 * q^17 + 10 * q^18 + 59 * q^19 - 28 * q^20 + 25 * q^21 + 6 * q^23 + 2 * q^24 + 53 * q^25 + q^26 - 4 * q^27 - 13 * q^28 - 28 * q^29 - 6 * q^30 - 3 * q^31 - 253 * q^32 + q^33 - 50 * q^34 - 9 * q^35 - 76 * q^36 - 17 * q^37 + 8 * q^38 + 10 * q^39 - 59 * q^40 + 73 * q^41 - 12 * q^42 - 38 * q^44 - 9 * q^45 + 74 * q^46 - 87 * q^47 - 160 * q^48 - 60 * q^49 + 30 * q^50 + 128 * q^51 + 49 * q^52 + 21 * q^53 + 76 * q^54 - 4 * q^55 + 102 * q^56 - 41 * q^57 + 17 * q^58 + 36 * q^59 + 10 * q^60 + 11 * q^61 + 72 * q^62 - 201 * q^63 - 42 * q^64 - 215 * q^65 - 34 * q^66 - 8 * q^67 + 75 * q^68 + 6 * q^69 + 97 * q^70 + q^71 - 95 * q^72 - 20 * q^73 + 154 * q^74 - 101 * q^75 - 27 * q^76 + 2 * q^77 - 87 * q^78 - 14 * q^79 - 124 * q^80 - 203 * q^81 - 15 * q^82 + 29 * q^83 - 96 * q^84 - 74 * q^85 + 63 * q^86 + 65 * q^87 + 3 * q^88 + 141 * q^89 + 491 * q^90 + 71 * q^91 + 41 * q^92 + 121 * q^93 + 116 * q^94 - 7 * q^95 - 141 * q^96 - 298 * q^97 - 102 * q^98 - 268 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{19}{21}\right)$	$1$

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 $

$2$	−0.141924	+	1.89385i	−0.100356	+	1.33915i	0.688797	+	0.724955i	$0.258139\pi$
$2$	−0.141924	+	1.89385i	−0.100356	+	1.33915i	−0.789152	+	0.614198i	$0.789480\pi$
$3$	−1.56085	+	0.481458i	−0.901157	+	0.277970i	−0.710509	−	0.703689i	$-0.751535\pi$
$3$	−1.56085	+	0.481458i	−0.901157	+	0.277970i	−0.190648	+	0.981658i	$0.561059\pi$
$4$	−1.58885	−	0.239481i	−0.794427	−	0.119741i
$5$	0.329056	+	0.305319i	0.147158	+	0.136543i	0.750317	−	0.661078i	$-0.229901\pi$
$5$	0.329056	+	0.305319i	0.147158	+	0.136543i	−0.603159	+	0.797621i	$0.706091\pi$
$6$	−0.690286	−	3.02434i	−0.281808	−	1.23468i
$7$	−2.09779	+	1.61223i	−0.792889	+	0.609366i
$7$	−2.09779	+	1.61223i	−0.792889	+	0.609366i
$8$	−0.166167	+	0.728025i	−0.0587489	+	0.257396i
$9$	−0.274269	+	0.186993i	−0.0914230	+	0.0623312i
$10$	−0.624929	+	0.579849i	−0.197620	+	0.183364i
$11$	−0.826239	−	0.563320i	−0.249120	−	0.169847i
$11$	−0.826239	−	0.563320i	−0.249120	−	0.169847i
$12$	2.59526	−	0.391173i	0.749187	−	0.112922i
$13$	2.69216	−	1.29647i	0.746670	−	0.359577i	−0.0215464	−	0.999768i	$-0.506859\pi$
$13$	2.69216	−	1.29647i	0.746670	−	0.359577i	0.768216	+	0.640191i	$0.221145\pi$
$14$	−2.75559	−	4.20171i	−0.736462	−	1.12295i
$15$	−0.660605	−	0.318131i	−0.170567	−	0.0821410i
$16$	−4.42602	−	1.36524i	−1.10650	−	0.341311i
$17$	0.215980	−	0.550308i	0.0523829	−	0.133469i	−0.902287	−	0.431136i	$-0.858113\pi$
$17$	0.215980	−	0.550308i	0.0523829	−	0.133469i	0.954670	+	0.297666i	$0.0962083\pi$
$18$	−0.315212	−	0.545963i	−0.0742961	−	0.128685i
$19$	−3.29969	+	5.71523i	−0.757001	+	1.31116i	0.187373	+	0.982289i	$0.440003\pi$
$19$	−3.29969	+	5.71523i	−0.757001	+	1.31116i	−0.944374	+	0.328875i	$0.893331\pi$
$20$	−0.449704	−	0.563910i	−0.100557	−	0.126094i
$21$	2.49811	−	3.52644i	0.545132	−	0.769533i
$22$	1.18411	−	1.48482i	0.252452	−	0.316565i
$23$	−1.42792	−	3.63828i	−0.297741	−	0.758633i	−0.998956	−	0.0456825i	$-0.985454\pi$
$23$	−1.42792	−	3.63828i	−0.297741	−	0.758633i	0.701215	−	0.712950i	$-0.252641\pi$
$24$	−0.0911521	−	1.21634i	−0.0186063	−	0.248284i
$25$	−0.358593	−	4.78508i	−0.0717185	−	0.957017i
$26$	2.07324	+	5.28253i	0.406596	+	1.03599i
$27$	3.39332	−	4.25509i	0.653045	−	0.818892i
$28$	3.71918	−	2.05922i	0.702859	−	0.389155i
$29$	−3.49978	−	4.38858i	−0.649893	−	0.814940i	0.342308	−	0.939588i	$-0.388791\pi$
$29$	−3.49978	−	4.38858i	−0.649893	−	0.814940i	−0.992201	+	0.124648i	$0.960220\pi$
$30$	0.696247	−	1.20593i	0.127117	−	0.220173i
$31$	−0.195523	−	0.338655i	−0.0351169	−	0.0608242i	0.847933	−	0.530104i	$-0.177847\pi$
$31$	−0.195523	−	0.338655i	−0.0351169	−	0.0608242i	−0.883050	+	0.469279i	$0.844514\pi$
$32$	2.66809	−	6.79818i	0.471656	−	1.20176i
$33$	1.56085	+	0.481458i	0.271709	+	0.0838111i
$34$	1.01155	+	0.487136i	0.173479	+	0.0835431i
$35$	−1.18253	−	0.109981i	−0.199885	−	0.0185902i
$36$	0.480555	−	0.231423i	0.0800925	−	0.0385705i
$37$	1.89601	−	0.285777i	0.311702	−	0.0469815i	0.00867161	−	0.999962i	$-0.497240\pi$
$37$	1.89601	−	0.285777i	0.311702	−	0.0469815i	0.303030	+	0.952981i	$0.402002\pi$
$38$	−10.3555	−	7.06024i	−1.67988	−	1.14532i
$39$	−3.57785	+	3.31976i	−0.572914	+	0.531587i
$40$	−0.276958	+	0.188827i	−0.0437910	+	0.0298562i
$41$	−1.57410	+	6.89660i	−0.245834	+	1.07707i	0.689773	+	0.724025i	$0.257710\pi$
$41$	−1.57410	+	6.89660i	−0.245834	+	1.07707i	−0.935607	+	0.353043i	$0.885147\pi$
$42$	6.32401	+	5.23153i	0.975815	+	0.807242i
$43$	−0.172237	−	0.754620i	−0.0262659	−	0.115078i	0.960096	−	0.279672i	$-0.0902258\pi$
$43$	−0.172237	−	0.754620i	−0.0262659	−	0.115078i	−0.986361	+	0.164594i	$0.947369\pi$
$44$	1.17787	+	1.09290i	0.177570	+	0.164761i
$45$	−0.147343	−	0.0222083i	−0.0219645	−	0.00331062i
$46$	7.09299	−	2.18790i	1.04580	−	0.322588i
$47$	−0.628919	+	8.39234i	−0.0917372	+	1.22415i	0.741393	+	0.671071i	$0.234166\pi$
$47$	−0.628919	+	8.39234i	−0.0917372	+	1.22415i	−0.833130	+	0.553077i	$0.813454\pi$
$48$	7.56565			1.09201
$49$	1.80143	−	6.76423i	0.257347	−	0.966319i
$50$	9.11311			1.28879
$51$	−0.0721619	+	0.962934i	−0.0101047	+	0.134838i
$52$	−4.58792	+	1.41519i	−0.636230	+	0.196251i
$53$	−2.11167	−	0.318284i	−0.290061	−	0.0437196i	0.00240006	−	0.999997i	$-0.499236\pi$
$53$	−2.11167	−	0.318284i	−0.290061	−	0.0437196i	−0.292461	+	0.956277i	$0.594474\pi$
$54$	7.57689	+	7.03033i	1.03108	+	0.956707i
$55$	−0.0998863	−	0.437630i	−0.0134687	−	0.0590101i
$56$	−0.825161	−	1.79514i	−0.110267	−	0.239886i
$57$	2.39867	−	10.5093i	0.317712	−	1.39199i
$58$	8.80801	−	6.00520i	1.15655	−	0.788522i
$59$	−2.91202	+	2.70196i	−0.379113	+	0.351766i	−0.846596	−	0.532237i	$-0.821352\pi$
$59$	−2.91202	+	2.70196i	−0.379113	+	0.351766i	0.467482	+	0.884002i	$0.345161\pi$
$60$	0.973419	+	0.663665i	0.125668	+	0.0856788i
$61$	2.69464	−	0.406152i	0.345014	−	0.0520024i	0.0257501	−	0.999668i	$-0.491803\pi$
$61$	2.69464	−	0.406152i	0.345014	−	0.0520024i	0.319264	+	0.947666i	$0.396564\pi$
$62$	0.669110	−	0.322227i	0.0849771	−	0.0409228i
$63$	0.273882	−	0.834457i	0.0345059	−	0.105132i
$64$	4.14985	+	1.99846i	0.518731	+	0.249808i
$65$	1.28171	+	0.395355i	0.158976	+	0.0490377i
$66$	−1.13333	+	2.88768i	−0.139503	+	0.355449i
$67$	1.43644	+	2.48799i	0.175489	+	0.303956i	0.940331	−	0.340262i	$-0.110516\pi$
$67$	1.43644	+	2.48799i	0.175489	+	0.303956i	−0.764841	+	0.644219i	$0.777183\pi$
$68$	−0.474950	+	0.822637i	−0.0575961	+	0.0997593i
$69$	3.98044	+	4.99132i	0.479189	+	0.600884i
$70$	0.376118	−	2.22393i	0.0449547	−	0.265811i
$71$	−4.50183	+	5.64512i	−0.534269	+	0.669952i	−0.973570	−	0.228388i	$-0.926655\pi$
$71$	−4.50183	+	5.64512i	−0.534269	+	0.669952i	0.439301	+	0.898340i	$0.355226\pi$
$72$	−0.0905615	−	0.230747i	−0.0106728	−	0.0271938i
$73$	0.0174074	+	0.232286i	0.00203738	+	0.0271870i	0.998130	−	0.0611297i	$-0.0194703\pi$
$73$	0.0174074	+	0.232286i	0.00203738	+	0.0271870i	−0.996092	+	0.0883166i	$0.971851\pi$
$74$	0.272129	+	3.63131i	0.0316344	+	0.422131i
$75$	2.86353	+	7.29615i	0.330652	+	0.842486i
$76$	6.61142	−	8.29045i	0.758381	−	0.950980i
$77$	2.64148	−	0.150361i	0.301024	−	0.0171352i
$78$	−5.77933	−	7.24706i	−0.654381	−	0.820568i
$79$	−3.66280	+	6.34416i	−0.412098	+	0.713774i	−0.995119	−	0.0986828i	$-0.968537\pi$
$79$	−3.66280	+	6.34416i	−0.412098	+	0.713774i	0.583021	+	0.812457i	$0.301870\pi$
$80$	−1.03957	−	1.80059i	−0.116228	−	0.201312i
$81$	−2.88399	+	7.34828i	−0.320443	+	0.816476i
$82$	−12.8377	−	3.95991i	−1.41769	−	0.437299i
$83$	−10.4293	−	5.02249i	−1.14476	−	0.551290i	−0.237308	−	0.971435i	$-0.576265\pi$
$83$	−10.4293	−	5.02249i	−1.14476	−	0.551290i	−0.907457	+	0.420145i	$0.861979\pi$
$84$	−4.81365	+	5.00475i	−0.525212	+	0.546064i
$85$	0.239089	−	0.115139i	0.0259329	−	0.0124886i
$86$	1.45358	−	0.219092i	0.156743	−	0.0236253i
$87$	7.57555	+	5.16492i	0.812184	+	0.553738i
$88$	0.547405	−	0.507917i	0.0583535	−	0.0541442i
$89$	−3.99001	+	2.72034i	−0.422940	+	0.288356i	−0.756027	−	0.654541i	$-0.772862\pi$
$89$	−3.99001	+	2.72034i	−0.422940	+	0.288356i	0.333087	+	0.942896i	$0.391910\pi$
$90$	0.0629706	−	0.275892i	0.00663769	−	0.0290816i
$91$	−3.55736	+	7.06010i	−0.372912	+	0.740100i
$92$	1.39745	+	6.12265i	0.145695	+	0.638330i
$93$	0.468229	+	0.434453i	0.0485531	+	0.0450507i
$94$	−15.8045	−	2.38215i	−1.63011	−	0.245700i
$95$	−2.83075	+	0.873171i	−0.290429	+	0.0895855i
$96$	−0.891445	+	11.8955i	−0.0909827	+	1.21408i
$97$	0.620107			0.0629624			0.0314812	−	0.999504i	$-0.489978\pi$
$97$	0.620107			0.0629624			0.0314812	+	0.999504i	$0.489978\pi$
$98$	12.5548	+	4.37164i	1.26822	+	0.441603i
$99$	0.331949			0.0333621
$100$	−0.576187	+	7.68868i	−0.0576187	+	0.768868i
$101$	−16.5685	+	5.11071i	−1.64863	+	0.508534i	−0.973407	−	0.229081i	$-0.926428\pi$
$101$	−16.5685	+	5.11071i	−1.64863	+	0.508534i	−0.675221	+	0.737616i	$0.735952\pi$
$102$	−1.81341	−	0.273327i	−0.179554	−	0.0270634i
$103$	0.242671	+	0.225165i	0.0239111	+	0.0221862i	0.692038	−	0.721861i	$-0.256713\pi$
$103$	0.242671	+	0.225165i	0.0239111	+	0.0221862i	−0.668127	+	0.744047i	$0.732904\pi$
$104$	0.496518	+	2.17539i	0.0486876	+	0.213314i
$105$	1.89871	−	0.397676i	0.185295	−	0.0388092i
$106$	0.902479	−	3.95402i	0.0876565	−	0.384048i
$107$	−10.2006	+	6.95465i	−0.986129	+	0.672331i	−0.945085	−	0.326826i	$-0.894021\pi$
$107$	−10.2006	+	6.95465i	−0.986129	+	0.672331i	−0.0410444	+	0.999157i	$0.513069\pi$
$108$	−6.41050	+	5.94808i	−0.616851	+	0.572354i
$109$	10.2741	+	7.00478i	0.984083	+	0.670937i	0.944579	−	0.328283i	$-0.106470\pi$
$109$	10.2741	+	7.00478i	0.984083	+	0.670937i	0.0395038	+	0.999219i	$0.487422\pi$
$110$	0.842981	−	0.127059i	0.0803751	−	0.0121146i
$111$	−2.82179	+	1.35890i	−0.267833	+	0.128982i
$112$	11.4859	−	4.27176i	1.08532	−	0.403643i
$113$	−18.0225	−	8.67920i	−1.69542	−	0.816470i	−0.994676	−	0.103055i	$-0.967138\pi$
$113$	−18.0225	−	8.67920i	−1.69542	−	0.816470i	−0.700742	−	0.713415i	$-0.747148\pi$
$114$	19.5625	+	6.03424i	1.83220	+	0.565158i
$115$	0.640971	−	1.63317i	0.0597708	−	0.152294i
$116$	4.50966	+	7.81095i	0.418711	+	0.725229i
$117$	−0.495943	+	0.858998i	−0.0458499	+	0.0794144i
$118$	−4.70382	−	5.89840i	−0.433022	−	0.542992i
$119$	0.434143	+	1.50264i	0.0397978	+	0.137747i
$120$	0.341378	−	0.428074i	0.0311634	−	0.0390777i
$121$	0.365341	+	0.930874i	0.0332128	+	0.0846249i
$122$	0.386755	+	5.16089i	0.0350151	+	0.467245i
$123$	−0.863486	−	11.5224i	−0.0778579	−	1.03894i
$124$	0.229555	+	0.584897i	0.0206147	+	0.0525253i
$125$	2.74236	−	3.43881i	0.245284	−	0.307576i
$126$	1.54146	+	0.637120i	0.137325	+	0.0567592i
$127$	−7.78442	−	9.76136i	−0.690756	−	0.866181i	0.305539	−	0.952179i	$-0.401163\pi$
$127$	−7.78442	−	9.76136i	−0.690756	−	0.866181i	−0.996295	+	0.0859989i	$0.972592\pi$
$128$	2.92926	−	5.07364i	0.258913	−	0.448450i
$129$	0.632154	+	1.09492i	0.0556580	+	0.0964025i
$130$	−0.930647	+	2.37125i	−0.0816231	+	0.207972i
$131$	11.9536	+	3.68719i	1.04439	+	0.322151i	0.769045	−	0.639195i	$-0.220732\pi$
$131$	11.9536	+	3.68719i	1.04439	+	0.322151i	0.275344	+	0.961346i	$0.411208\pi$
$132$	−2.36466	−	1.13876i	−0.205817	−	0.0991164i
$133$	−2.29221	−	17.3092i	−0.198760	−	1.50090i
$134$	−4.91574	+	2.36730i	−0.424655	+	0.204503i
$135$	2.41575	−	0.364116i	0.207915	−	0.0313381i
$136$	0.364750	+	0.248682i	0.0312770	+	0.0213243i
$137$	−8.50635	+	7.89274i	−0.726747	+	0.674322i	−0.954099	−	0.299490i	$-0.903183\pi$
$137$	−8.50635	+	7.89274i	−0.726747	+	0.674322i	0.227353	+	0.973812i	$0.426993\pi$
$138$	−10.0177	+	6.82996i	−0.852764	+	0.581405i
$139$	−3.28935	+	14.4116i	−0.278999	+	1.22237i	0.620063	+	0.784552i	$0.287107\pi$
$139$	−3.28935	+	14.4116i	−0.278999	+	1.22237i	−0.899062	+	0.437822i	$0.855750\pi$
$140$	1.85254	+	0.457939i	0.156568	+	0.0387029i
$141$	−3.05891	−	13.4020i	−0.257607	−	1.12865i
$142$	−10.0521	−	9.32696i	−0.843551	−	0.782701i
$143$	−2.95469	−	0.445348i	−0.247084	−	0.0372419i
$144$	1.46921	−	0.453192i	0.122434	−	0.0377660i
$145$	0.188296	−	2.51264i	0.0156372	−	0.208663i
$146$	−0.442384			−0.0366120
$147$	0.444935	+	11.4253i	0.0366976	+	0.942339i
$148$	−3.08092			−0.253250
$149$	−0.413205	+	5.51384i	−0.0338511	+	0.451711i	0.954365	+	0.298644i	$0.0965342\pi$
$149$	−0.413205	+	5.51384i	−0.0338511	+	0.451711i	−0.988216	+	0.153067i	$0.951085\pi$
$150$	−14.2242	+	4.38758i	−1.16140	+	0.358245i
$151$	17.4496	+	2.63010i	1.42003	+	0.214035i	0.813748	−	0.581218i	$-0.197423\pi$
$151$	17.4496	+	2.63010i	1.42003	+	0.214035i	0.606279	+	0.795252i	$0.292662\pi$
$152$	−3.61253	−	3.35194i	−0.293015	−	0.271878i
$153$	0.0436674	+	0.191319i	0.00353030	+	0.0154673i
$154$	−0.0901293	+	5.02389i	−0.00726283	+	0.404837i
$155$	0.0390600	−	0.171133i	0.00313738	−	0.0137458i
$156$	6.47970	−	4.41779i	0.518791	−	0.353706i
$157$	5.97270	−	5.54185i	0.476673	−	0.442288i	−0.404882	−	0.914369i	$-0.632687\pi$
$157$	5.97270	−	5.54185i	0.476673	−	0.442288i	0.881555	+	0.472081i	$0.156497\pi$
$158$	−11.4950	−	7.83718i	−0.914496	−	0.623493i
$159$	3.44925	−	0.519890i	0.273543	−	0.0412300i
$160$	2.95357	−	1.42236i	0.233500	−	0.112448i
$161$	8.86120	+	5.33020i	0.698361	+	0.420079i
$162$	−13.5072	−	6.50473i	−1.06123	−	0.511060i
$163$	−16.9306	−	5.22239i	−1.32611	−	0.409049i	−0.450802	−	0.892624i	$-0.648862\pi$
$163$	−16.9306	−	5.22239i	−1.32611	−	0.409049i	−0.875303	+	0.483575i	$0.839338\pi$
$164$	4.15263	−	10.5807i	0.324266	−	0.826216i
$165$	0.366608	+	0.634984i	0.0285404	+	0.0494334i
$166$	10.9920	−	19.0387i	0.853145	−	1.47769i
$167$	5.98510	+	7.50508i	0.463141	+	0.580761i	0.957477	−	0.288510i	$-0.0931600\pi$
$167$	5.98510	+	7.50508i	0.463141	+	0.580761i	−0.494335	+	0.869271i	$0.664589\pi$
$168$	2.15224	+	2.40466i	0.166049	+	0.185524i
$169$	−2.53851	+	3.18319i	−0.195270	+	0.244861i
$170$	0.184124	+	0.469140i	0.0141217	+	0.0359814i
$171$	−0.163708	−	2.18453i	−0.0125191	−	0.167055i
$172$	0.0929422	+	1.24023i	0.00708678	+	0.0945665i
$173$	7.85138	+	20.0050i	0.596930	+	1.52095i	0.835309	+	0.549780i	$0.185289\pi$
$173$	7.85138	+	20.0050i	0.596930	+	1.52095i	−0.238380	+	0.971172i	$0.576616\pi$
$174$	−10.8567	+	13.6139i	−0.823046	+	1.03207i
$175$	8.46691	+	9.45996i	0.640038	+	0.715106i
$176$	2.88788	+	3.62128i	0.217682	+	0.272964i
$177$	3.24435	−	5.61937i	0.243860	−	0.422378i
$178$	−4.58563	−	7.94255i	−0.343708	−	0.595319i
$179$	1.24836	−	3.18076i	0.0933065	−	0.237741i	−0.876600	−	0.481221i	$-0.840194\pi$
$179$	1.24836	−	3.18076i	0.0933065	−	0.237741i	0.969906	+	0.243479i	$0.0782889\pi$
$180$	0.228787	+	0.0705715i	0.0170528	+	0.00526009i
$181$	−0.968986	−	0.466639i	−0.0720242	−	0.0346850i	0.397525	−	0.917591i	$-0.369869\pi$
$181$	−0.968986	−	0.466639i	−0.0720242	−	0.0346850i	−0.469549	+	0.882906i	$0.655584\pi$
$182$	−12.8659	−	7.73909i	−0.953682	−	0.573660i
$183$	−4.01039	+	1.93130i	−0.296456	+	0.142766i
$184$	2.88603	−	0.434999i	0.212761	−	0.0320685i
$185$	0.711146	+	0.484851i	0.0522845	+	0.0356470i
$186$	−0.889242	+	0.825096i	−0.0652024	+	0.0604989i
$187$	−0.488451	+	0.333020i	−0.0357191	+	0.0243529i
$188$	3.00907	−	13.1836i	0.219459	−	0.961512i
$189$	−0.258286	+	14.3971i	−0.0187875	+	1.04723i
$190$	−1.25190	−	5.48494i	−0.0908224	−	0.397919i
$191$	2.56888	+	2.38357i	0.185877	+	0.172469i	0.767623	−	0.640902i	$-0.221439\pi$
$191$	2.56888	+	2.38357i	0.185877	+	0.172469i	−0.581745	+	0.813371i	$0.697630\pi$
$192$	−7.43946	−	1.12132i	−0.536897	−	0.0809242i
$193$	19.8283	−	6.11623i	1.42727	−	0.440256i	0.517616	−	0.855613i	$-0.326820\pi$
$193$	19.8283	−	6.11623i	1.42727	−	0.440256i	0.909658	+	0.415357i	$0.136343\pi$
$194$	−0.0880083	+	1.17439i	−0.00631863	+	0.0843162i
$195$	−2.19090			−0.156894
$196$	−4.48212	+	10.3160i	−0.320151	+	0.736855i
$197$	27.5156			1.96040			0.980201	−	0.198004i	$-0.0634460\pi$
$197$	27.5156			1.96040			0.980201	+	0.198004i	$0.0634460\pi$
$198$	−0.0471116	+	0.628661i	−0.00334808	+	0.0446770i
$199$	−14.2303	+	4.38946i	−1.00876	+	0.311161i	−0.754729	−	0.656036i	$-0.772232\pi$
$199$	−14.2303	+	4.38946i	−1.00876	+	0.311161i	−0.254028	+	0.967197i	$0.581756\pi$
$200$	3.54325	+	0.534059i	0.250545	+	0.0377637i
$201$	−3.43993	−	3.19179i	−0.242634	−	0.225132i
$202$	−7.32743	−	32.1036i	−0.515556	−	2.25880i
$203$	14.4172	+	3.56387i	1.01189	+	0.250135i
$204$	0.345259	−	1.51268i	0.0241730	−	0.105909i
$205$	−2.62363	+	1.78876i	−0.183242	+	0.124933i
$206$	−0.460870	+	0.427625i	−0.0321103	+	0.0297940i
$207$	1.07197	+	0.730855i	0.0745069	+	0.0507979i
$208$	−13.6855	+	2.06276i	−0.948920	+	0.143027i
$209$	5.94584	−	2.86336i	0.411282	−	0.198063i
$210$	0.483666	+	3.65230i	0.0333761	+	0.252033i
$211$	−12.6265	−	6.08061i	−0.869245	−	0.418606i	−0.0545604	−	0.998510i	$-0.517376\pi$
$211$	−12.6265	−	6.08061i	−0.869245	−	0.418606i	−0.814685	+	0.579904i	$0.803090\pi$
$212$	3.27892	+	1.01141i	0.225197	+	0.0694641i
$213$	4.30879	−	10.9786i	0.295233	−	0.752242i
$214$	−11.7233	−	20.3054i	−0.801391	−	1.38805i
$215$	0.173724	−	0.300899i	0.0118479	−	0.0205212i
$216$	2.53395	+	3.17748i	0.172414	+	0.216200i
$217$	0.956155	+	0.395199i	0.0649080	+	0.0268279i
$218$	−14.7241	+	18.4635i	−0.997245	+	1.25051i
$219$	−0.139006	−	0.354182i	−0.00939316	−	0.0239334i
$220$	0.0539005	+	0.719252i	0.00363397	+	0.0484919i
$221$	−0.132008	−	1.76153i	−0.00887984	−	0.118493i
$222$	−2.17308	−	5.53691i	−0.145847	−	0.371613i
$223$	7.12763	−	8.93776i	0.477301	−	0.598517i	−0.483641	−	0.875267i	$-0.660686\pi$
$223$	7.12763	−	8.93776i	0.477301	−	0.598517i	0.960942	+	0.276750i	$0.0892573\pi$
$224$	5.36314	+	18.5627i	0.358340	+	1.24027i
$225$	0.993130	+	1.24535i	0.0662087	+	0.0830231i
$226$	18.9949	−	32.9001i	1.26352	−	2.18849i
$227$	13.8564	+	23.9999i	0.919680	+	1.59293i	0.799902	+	0.600131i	$0.204885\pi$
$227$	13.8564	+	23.9999i	0.919680	+	1.59293i	0.119778	+	0.992801i	$0.461782\pi$
$228$	−6.32791	+	16.1233i	−0.419076	+	1.06779i
$229$	−24.1969	−	7.46375i	−1.59897	−	0.493218i	−0.638042	−	0.770001i	$-0.720255\pi$
$229$	−24.1969	−	7.46375i	−1.59897	−	0.493218i	−0.960932	+	0.276783i	$0.910732\pi$
$230$	3.00200	+	1.44569i	0.197946	+	0.0953258i
$231$	−4.05055	+	1.50645i	−0.266507	+	0.0991171i
$232$	3.77655	−	1.81869i	0.247943	−	0.119403i
$233$	−15.6507	+	2.35896i	−1.02531	+	0.154540i	−0.640102	−	0.768290i	$-0.721108\pi$
$233$	−15.6507	+	2.35896i	−1.02531	+	0.154540i	−0.385207	+	0.922830i	$0.625870\pi$
$234$	−1.55642	−	1.06115i	−0.101747	−	0.0693697i
$235$	−2.76929	+	2.56953i	−0.180649	+	0.167617i
$236$	5.27385	−	3.59565i	0.343298	−	0.234057i
$237$	2.66264	−	11.6658i	0.172957	−	0.757773i
$238$	−2.90739	+	0.608940i	−0.188458	+	0.0394717i
$239$	−1.97431	−	8.65002i	−0.127708	−	0.559523i	−0.997780	−	0.0665992i	$-0.978785\pi$
$239$	−1.97431	−	8.65002i	−0.127708	−	0.559523i	0.870072	−	0.492924i	$-0.164072\pi$
$240$	2.48952	+	2.30994i	0.160698	+	0.149106i
$241$	27.8954	+	4.20455i	1.79690	+	0.270839i	0.960700	−	0.277588i	$-0.0895351\pi$
$241$	27.8954	+	4.20455i	1.79690	+	0.270839i	0.836198	+	0.548427i	$0.184773\pi$
$242$	−1.81478	+	0.559787i	−0.116659	+	0.0359844i
$243$	−0.256567	+	3.42365i	−0.0164588	+	0.219627i
$244$	−4.37866			−0.280315
$245$	2.65802	−	1.67580i	0.169815	−	0.107063i
$246$	21.9443			1.39911
$247$	−1.47363	+	19.6642i	−0.0937649	+	1.25121i
$248$	0.279039	−	0.0860721i	0.0177190	−	0.00546558i
$249$	18.6967	+	2.81807i	1.18485	+	0.178588i
$250$	6.12337	+	5.68166i	0.387276	+	0.359339i
$251$	1.96180	+	8.59522i	0.123828	+	0.542525i	0.998344	+	0.0575286i	$0.0183220\pi$
$251$	1.96180	+	8.59522i	0.123828	+	0.542525i	−0.874516	+	0.484997i	$0.838821\pi$
$252$	−0.634995	+	1.26024i	−0.0400009	+	0.0793877i
$253$	−0.869712	+	3.81046i	−0.0546783	+	0.239561i
$254$	19.5913	−	13.3571i	1.22927	−	0.838101i
$255$	−0.317748	+	0.294827i	−0.0198981	+	0.0184628i
$256$	16.8042	+	11.4569i	1.05027	+	0.716059i
$257$	11.7542	−	1.77166i	0.733208	−	0.110513i	0.228184	−	0.973618i	$-0.426721\pi$
$257$	11.7542	−	1.77166i	0.733208	−	0.110513i	0.505025	+	0.863105i	$0.331483\pi$
$258$	−2.16333	+	1.04181i	−0.134683	+	0.0648600i
$259$	−3.51669	+	3.65630i	−0.218516	+	0.227192i
$260$	−1.94177	−	0.935106i	−0.120423	−	0.0579928i
$261$	1.78052	+	0.549217i	0.110211	+	0.0339957i
$262$	−8.67948	+	22.1149i	−0.536220	+	1.36627i
$263$	−9.21364	−	15.9585i	−0.568137	−	0.984043i	−0.996750	−	0.0805543i	$-0.974331\pi$
$263$	−9.21364	−	15.9585i	−0.568137	−	0.984043i	0.428613	−	0.903488i	$-0.359002\pi$
$264$	−0.609875	+	1.05633i	−0.0375352	+	0.0650129i
$265$	−0.597681	−	0.749468i	−0.0367152	−	0.0460395i
$266$	33.1063	−	1.88451i	2.02988	−	0.115547i
$267$	4.91807	−	6.16706i	0.300981	−	0.377418i
$268$	−1.68647	−	4.29706i	−0.103018	−	0.262484i
$269$	1.35020	+	18.0172i	0.0823234	+	1.09853i	0.873462	+	0.486892i	$0.161870\pi$
$269$	1.35020	+	18.0172i	0.0823234	+	1.09853i	−0.791139	+	0.611637i	$0.790511\pi$
$270$	0.346726	+	4.62674i	0.0211011	+	0.281575i
$271$	0.0197535	+	0.0503311i	0.00119994	+	0.00305740i	0.931472	−	0.363812i	$-0.118525\pi$
$271$	0.0197535	+	0.0503311i	0.00119994	+	0.00305740i	−0.930273	+	0.366869i	$0.880430\pi$
$272$	−1.70724	+	2.14081i	−0.103516	+	0.129806i
$273$	2.15336	−	12.7325i	0.130327	−	0.770604i
$274$	−13.7404	−	17.2299i	−0.830087	−	1.04090i
$275$	−2.39925	+	4.15562i	−0.144680	+	0.250594i
$276$	−5.12901	−	8.88371i	−0.308730	−	0.534737i
$277$	11.6981	−	29.8063i	0.702870	−	1.79088i	0.0970551	−	0.995279i	$-0.469058\pi$
$277$	11.6981	−	29.8063i	0.702870	−	1.79088i	0.605815	−	0.795605i	$-0.292847\pi$
$278$	−26.8265	−	8.27487i	−1.60895	−	0.496294i
$279$	0.116952	+	0.0563211i	0.00700174	+	0.00337186i
$280$	0.276567	−	0.842639i	0.0165281	−	0.0503573i
$281$	−8.11216	+	3.90661i	−0.483931	+	0.233049i	−0.659909	−	0.751345i	$-0.729405\pi$
$281$	−8.11216	+	3.90661i	−0.483931	+	0.233049i	0.175979	+	0.984394i	$0.443691\pi$
$282$	25.8154	−	3.89105i	1.53729	−	0.231709i
$283$	9.08599	+	6.19473i	0.540106	+	0.368238i	0.802434	−	0.596741i	$-0.203538\pi$
$283$	9.08599	+	6.19473i	0.540106	+	0.368238i	−0.262328	+	0.964979i	$0.584490\pi$
$284$	8.50465	−	7.89116i	0.504658	−	0.468254i
$285$	3.99798	−	2.72578i	0.236820	−	0.161461i
$286$	1.26276	−	5.53253i	0.0746688	−	0.327145i
$287$	−7.81677	−	17.0054i	−0.461409	−	1.00380i
$288$	0.539441	+	2.36345i	0.0317869	+	0.139267i
$289$	12.2057	+	11.3252i	0.717982	+	0.666190i
$290$	4.73183	+	0.713209i	0.277863	+	0.0418811i
$291$	−0.967894	+	0.298556i	−0.0567390	+	0.0175016i
$292$	0.0279702	−	0.373237i	0.00163683	−	0.0218420i
$293$	−18.7388			−1.09473			−0.547366	−	0.836893i	$-0.684370\pi$
$293$	−18.7388			−1.09473			−0.547366	+	0.836893i	$0.684370\pi$
$294$	−21.7008	−	0.778883i	−1.26562	−	0.0454254i
$295$	−1.78318			−0.103821
$296$	−0.107001	+	1.42783i	−0.00621931	+	0.0829909i
$297$	−5.20067	+	1.60419i	−0.301773	+	0.0930848i
$298$	−10.3837	−	1.56509i	−0.601513	−	0.0906635i
$299$	−8.56110	−	7.94354i	−0.495101	−	0.459387i
$300$	−2.80244	−	12.2783i	−0.161799	−	0.708886i
$301$	1.57794	+	1.30535i	0.0909508	+	0.0752389i
$302$	−7.45753	+	32.6736i	−0.429133	+	1.88015i
$303$	23.4003	−	15.9541i	1.34431	−	0.916538i
$304$	22.4072	−	20.7908i	1.28514	−	1.19243i
$305$	1.01069	+	0.689080i	0.0578722	+	0.0394566i
$306$	−0.368527	+	0.0555466i	−0.0210673	+	0.00317539i
$307$	5.40667	−	2.60371i	0.308575	−	0.148602i	−0.273187	−	0.961961i	$-0.588078\pi$
$307$	5.40667	−	2.60371i	0.308575	−	0.148602i	0.581762	+	0.813359i	$0.302364\pi$
$308$	−4.23293	−	0.393683i	−0.241193	−	0.0224321i
$309$	−0.487180	−	0.234614i	−0.0277147	−	0.0133467i
$310$	0.318557	+	0.0982617i	0.0180928	+	0.00558089i
$311$	−1.54374	+	3.93339i	−0.0875376	+	0.223042i	−0.967938	−	0.251189i	$-0.919179\pi$
$311$	−1.54374	+	3.93339i	−0.0875376	+	0.223042i	0.880401	+	0.474231i	$0.157274\pi$
$312$	−1.82235	−	3.15640i	−0.103170	−	0.178696i
$313$	7.30319	−	12.6495i	0.412800	−	0.714991i	−0.582394	−	0.812906i	$-0.697884\pi$
$313$	7.30319	−	12.6495i	0.412800	−	0.714991i	0.995195	+	0.0979151i	$0.0312174\pi$
$314$	9.64776	+	12.0979i	0.544454	+	0.682724i
$315$	0.344898	−	0.190962i	0.0194328	−	0.0107595i
$316$	7.33897	−	9.20278i	0.412849	−	0.517697i
$317$	−3.97804	−	10.1359i	−0.223429	−	0.569288i	0.774572	−	0.632486i	$-0.217965\pi$
$317$	−3.97804	−	10.1359i	−0.223429	−	0.569288i	−0.998001	+	0.0631977i	$0.979870\pi$
$318$	0.495061	+	6.60613i	0.0277616	+	0.370453i
$319$	0.419476	+	5.59752i	0.0234861	+	0.313401i
$320$	0.755363	+	1.92463i	0.0422261	+	0.107590i
$321$	12.5732	−	15.7663i	0.701769	−	0.879990i
$322$	−11.3522	+	16.0253i	−0.632634	+	0.893054i
$323$	2.43247	+	3.05022i	0.135346	+	0.169719i
$324$	6.34201	−	10.9847i	0.352334	−	0.610260i
$325$	−7.16912	−	12.4173i	−0.397671	−	0.688787i
$326$	12.2933	−	31.3227i	0.680861	−	1.73481i
$327$	−19.4089	−	5.98685i	−1.07331	−	0.331073i
$328$	−4.75933	−	2.29197i	−0.262790	−	0.126553i
$329$	−12.2110	−	18.6193i	−0.673216	−	1.02652i
$330$	−1.25459	+	0.604180i	−0.0690631	+	0.0332590i
$331$	−14.2182	+	2.14305i	−0.781504	+	0.117793i	−0.527664	−	0.849453i	$-0.676932\pi$
$331$	−14.2182	+	2.14305i	−0.781504	+	0.117793i	−0.253840	+	0.967246i	$0.581694\pi$
$332$	15.3679	+	10.4776i	0.843420	+	0.575034i
$333$	−0.466578	+	0.432921i	−0.0255683	+	0.0237239i
$334$	−15.0629	+	10.2697i	−0.824206	+	0.561934i
$335$	−0.286962	+	1.25726i	−0.0156784	+	0.0686915i
$336$	−15.8711	+	12.1976i	−0.865841	+	0.665432i
$337$	−1.78236	−	7.80903i	−0.0970914	−	0.425385i	0.902899	−	0.429854i	$-0.141435\pi$
$337$	−1.78236	−	7.80903i	−0.0970914	−	0.425385i	−0.999990	+	0.00446837i	$0.998578\pi$
$338$	−5.66820	−	5.25932i	−0.308310	−	0.286070i
$339$	32.3091	+	4.86982i	1.75479	+	0.264492i
$340$	−0.407452	+	0.125682i	−0.0220972	+	0.00681608i
$341$	−0.0292228	+	0.389952i	−0.00158251	+	0.0211171i
$342$	4.16040			0.224969
$343$	7.12648	+	17.0942i	0.384794	+	0.923003i
$344$	0.578002			0.0311638
$345$	−0.214157	+	2.85773i	−0.0115298	+	0.153855i
$346$	−39.0007	+	12.0301i	−2.09669	+	0.646744i
$347$	−1.25073	−	0.188517i	−0.0671426	−	0.0101201i	0.115385	−	0.993321i	$-0.463190\pi$
$347$	−1.25073	−	0.188517i	−0.0671426	−	0.0101201i	−0.182528	+	0.983201i	$0.558428\pi$
$348$	−10.7995	−	10.0205i	−0.578916	−	0.537155i
$349$	−6.56144	−	28.7475i	−0.351226	−	1.53882i	−0.774355	−	0.632751i	$-0.781926\pi$
$349$	−6.56144	−	28.7475i	−0.351226	−	1.53882i	0.423129	−	0.906069i	$-0.360932\pi$
$350$	−19.1174	+	14.6924i	−1.02187	+	0.785344i
$351$	3.61873	−	15.8547i	0.193154	−	0.846262i
$352$	−6.03403	+	4.11393i	−0.321615	+	0.219273i
$353$	16.2598	−	15.0869i	0.865423	−	0.802995i	−0.116319	−	0.993212i	$-0.537109\pi$
$353$	16.2598	−	15.0869i	0.865423	−	0.802995i	0.981742	+	0.190216i	$0.0609190\pi$
$354$	10.1818	+	6.94182i	0.541156	+	0.368954i
$355$	−3.20492	+	0.483063i	−0.170099	+	0.0256383i
$356$	6.99101	−	3.36669i	0.370523	−	0.178434i
$357$	−1.40109	−	2.13637i	−0.0741536	−	0.113069i
$358$	5.84670	+	2.81562i	0.309008	+	0.148810i
$359$	−19.4291	−	5.99309i	−1.02543	−	0.316303i	−0.263980	−	0.964528i	$-0.585035\pi$
$359$	−19.4291	−	5.99309i	−1.02543	−	0.316303i	−0.761449	+	0.648225i	$0.775512\pi$
$360$	0.0406517	−	0.103579i	0.00214253	−	0.00545908i
$361$	−12.2759	−	21.2625i	−0.646100	−	1.11908i
$362$	1.02127	−	1.76888i	0.0536765	−	0.0929705i
$363$	−1.01842	−	1.27706i	−0.0534531	−	0.0670281i
$364$	7.34288	−	10.3655i	0.384872	−	0.543302i
$365$	−0.0651933	+	0.0817498i	−0.00341237	+	0.00427898i
$366$	−3.08842	−	7.86916i	−0.161434	−	0.411327i
$367$	−0.189602	−	2.53006i	−0.00989714	−	0.132068i	0.990066	−	0.140600i	$-0.0449032\pi$
$367$	−0.189602	−	2.53006i	−0.00989714	−	0.132068i	−0.999964	+	0.00853202i	$0.997284\pi$
$368$	1.35285	+	18.0525i	0.0705221	+	0.941053i
$369$	−0.857891	−	2.18587i	−0.0446600	−	0.113792i
$370$	−1.01916	+	1.27799i	−0.0529838	+	0.0664396i
$371$	4.94299	−	2.73681i	0.256627	−	0.142088i
$372$	−0.639905	−	0.802415i	−0.0331775	−	0.0416033i
$373$	−16.4602	+	28.5099i	−0.852275	+	1.47618i	0.0268744	+	0.999639i	$0.491445\pi$
$373$	−16.4602	+	28.5099i	−0.852275	+	1.47618i	−0.879150	+	0.476545i	$0.841889\pi$
$374$	−0.561367	−	0.972315i	−0.0290276	−	0.0502772i
$375$	−2.62476	+	6.68779i	−0.135542	+	0.345356i
$376$	−6.00533	−	1.85240i	−0.309701	−	0.0955301i
$377$	−15.1116	−	7.27738i	−0.778289	−	0.374804i
$378$	−27.2292	−	2.53245i	−1.40052	−	0.130255i
$379$	−9.46834	+	4.55971i	−0.486356	+	0.234217i	−0.660959	−	0.750422i	$-0.729850\pi$
$379$	−9.46834	+	4.55971i	−0.486356	+	0.234217i	0.174603	+	0.984639i	$0.444136\pi$
$380$	4.70676	−	0.709430i	0.241452	−	0.0363930i
$381$	16.8500	+	11.4881i	0.863251	+	0.588555i
$382$	−4.87870	+	4.52677i	−0.249616	+	0.231610i
$383$	11.4853	−	7.83054i	0.586871	−	0.400122i	−0.233162	−	0.972438i	$-0.574907\pi$
$383$	11.4853	−	7.83054i	0.586871	−	0.400122i	0.820033	+	0.572316i	$0.193955\pi$
$384$	−2.12940	+	9.32950i	−0.108665	+	0.476094i
$385$	0.915101	+	0.757016i	0.0466379	+	0.0385811i
$386$	8.76908	+	38.4199i	0.446335	+	1.95552i
$387$	0.188348	+	0.174762i	0.00957428	+	0.00888363i
$388$	−0.985260	−	0.148504i	−0.0500190	−	0.00753915i
$389$	−31.5828	+	9.74200i	−1.60131	+	0.493939i	−0.961549	−	0.274634i	$-0.911443\pi$
$389$	−31.5828	+	9.74200i	−1.60131	+	0.493939i	−0.639762	+	0.768573i	$0.720967\pi$
$390$	0.310942	−	4.14923i	0.0157451	−	0.210104i
$391$	−2.31058			−0.116851
$392$	4.62519	+	2.43548i	0.233608	+	0.123010i
$393$	−20.4330			−1.03071
$394$	−3.90512	+	52.1103i	−0.196737	+	2.62528i
$395$	−3.14226	+	0.969260i	−0.158104	+	0.0487687i
$396$	−0.527418	−	0.0794955i	−0.0265038	−	0.00399480i
$397$	9.13729	+	8.47817i	0.458587	+	0.425507i	0.875336	−	0.483515i	$-0.160640\pi$
$397$	9.13729	+	8.47817i	0.458587	+	0.425507i	−0.416749	+	0.909022i	$0.636831\pi$
$398$	−6.29334	−	27.5729i	−0.315457	−	1.38211i
$399$	11.9115	+	25.9134i	0.596319	+	1.29729i
$400$	−4.94568	+	21.6684i	−0.247284	+	1.08342i
$401$	−2.57017	+	1.75231i	−0.128348	+	0.0875063i	−0.625792	−	0.779990i	$-0.715224\pi$
$401$	−2.57017	+	1.75231i	−0.128348	+	0.0875063i	0.497444	+	0.867496i	$0.334272\pi$
$402$	6.53297	−	6.06171i	0.325835	−	0.302331i
$403$	−0.965435	−	0.658222i	−0.0480917	−	0.0327884i
$404$	27.5489	−	4.15232i	1.37061	−	0.206586i
$405$	−3.19257	+	1.53746i	−0.158640	+	0.0763969i
$406$	−8.79558	+	26.7982i	−0.436517	+	1.32997i
$407$	−1.72754	−	0.831940i	−0.0856310	−	0.0412377i
$408$	−0.689049	−	0.212543i	−0.0341130	−	0.0105225i
$409$	−5.55967	+	14.1658i	−0.274908	+	0.700454i	0.725023	+	0.688724i	$0.241829\pi$
$409$	−5.55967	+	14.1658i	−0.274908	+	0.700454i	−0.999931	+	0.0117294i	$0.996266\pi$
$410$	−3.01529	−	5.22263i	−0.148914	−	0.257927i
$411$	9.47711	−	16.4148i	0.467471	−	0.809684i
$412$	−0.331645	−	0.415870i	−0.0163390	−	0.0204885i
$413$	1.75262	−	10.3630i	0.0862410	−	0.509930i
$414$	−1.53627	+	1.92642i	−0.0755034	+	0.0946782i
$415$	−1.89836	−	4.83695i	−0.0931869	−	0.237436i
$416$	−1.63075	−	21.7609i	−0.0799542	−	1.06691i
$417$	−1.80439	−	24.0780i	−0.0883616	−	1.17910i
$418$	4.57892	+	11.6669i	0.223962	+	0.570646i
$419$	−3.52296	+	4.41765i	−0.172108	+	0.215816i	−0.860403	−	0.509615i	$-0.829788\pi$
$419$	−3.52296	+	4.41765i	−0.172108	+	0.215816i	0.688295	+	0.725431i	$0.258359\pi$
$420$	−3.11201	+	0.177145i	−0.151850	+	0.00864378i
$421$	0.351217	+	0.440412i	0.0171173	+	0.0214644i	0.790316	−	0.612699i	$-0.209916\pi$
$421$	0.351217	+	0.440412i	0.0171173	+	0.0214644i	−0.773199	+	0.634163i	$0.781345\pi$
$422$	13.3078	−	23.0497i	0.647811	−	1.12204i
$423$	−1.39682	−	2.41936i	−0.0679157	−	0.117633i
$424$	0.582609	−	1.48446i	0.0282940	−	0.0720919i
$425$	−2.71072	−	0.836147i	−0.131489	−	0.0405591i
$426$	20.1803	+	9.71832i	0.977739	+	0.470854i
$427$	−4.99798	+	5.19641i	−0.241869	+	0.251472i
$428$	17.8728	−	8.60707i	0.863913	−	0.416039i
$429$	4.82625	−	0.727439i	0.233013	−	0.0351211i
$430$	0.545202	+	0.371712i	0.0262920	+	0.0179256i
$431$	2.37818	−	2.20662i	0.114553	−	0.106289i	−0.620817	−	0.783956i	$-0.713199\pi$
$431$	2.37818	−	2.20662i	0.114553	−	0.106289i	0.735370	+	0.677666i	$0.237009\pi$
$432$	−20.8281	+	14.2004i	−1.00209	+	0.683216i
$433$	2.06698	−	9.05605i	0.0993329	−	0.435206i	−0.900667	−	0.434510i	$-0.856921\pi$
$433$	2.06698	−	9.05605i	0.0993329	−	0.435206i	1.00000		0.000695577i	$-0.000221409\pi$
$434$	−0.884149	+	1.75472i	−0.0424405	+	0.0842294i
$435$	0.915829	+	4.01251i	0.0439106	+	0.192385i
$436$	−14.6466	−	13.5900i	−0.701444	−	0.650845i
$437$	25.5053	+	3.84430i	1.22008	+	0.183898i
$438$	0.690495	−	0.212989i	0.0329931	−	0.0101770i
$439$	1.51072	−	20.1591i	0.0721026	−	0.962142i	−0.837439	−	0.546530i	$-0.815948\pi$
$439$	1.51072	−	20.1591i	0.0721026	−	0.962142i	0.909542	−	0.415612i	$-0.136433\pi$
$440$	0.335204			0.0159802
$441$	0.770791	+	2.19208i	0.0367043	+	0.104385i
$442$	3.35480			0.159572
$443$	0.0623374	−	0.831835i	0.00296174	−	0.0395217i	−0.995527	−	0.0944763i	$-0.969882\pi$
$443$	0.0623374	−	0.831835i	0.00296174	−	0.0395217i	0.998489	+	0.0549546i	$0.0175014\pi$
$444$	4.80885	−	1.48333i	0.228218	−	0.0703959i
$445$	−2.14351	−	0.323082i	−0.101612	−	0.0153155i
$446$	15.9152	+	14.7671i	0.753605	+	0.699243i
$447$	−2.00973	−	8.80521i	−0.0950570	−	0.416472i
$448$	−11.9275	+	2.49816i	−0.563521	+	0.118027i
$449$	−2.98166	+	13.0635i	−0.140713	+	0.616505i	0.854557	+	0.519358i	$0.173829\pi$
$449$	−2.98166	+	13.0635i	−0.140713	+	0.616505i	−0.995270	+	0.0971469i	$0.969028\pi$
$450$	−2.49944	+	1.70409i	−0.117825	+	0.0803317i
$451$	5.18558	−	4.81151i	0.244179	−	0.226565i
$452$	26.5567	+	18.1060i	1.24912	+	0.851636i
$453$	−28.5024	+	4.29605i	−1.33916	+	0.201846i
$454$	−47.4188	+	22.8357i	−2.22547	+	1.07173i
$455$	−3.32615	+	1.23704i	−0.155933	+	0.0579932i
$456$	7.25243	+	3.49259i	0.339626	+	0.163555i
$457$	31.4473	+	9.70019i	1.47104	+	0.453756i	0.923688	−	0.383146i	$-0.125159\pi$
$457$	31.4473	+	9.70019i	1.47104	+	0.453756i	0.547353	+	0.836902i	$0.315636\pi$
$458$	17.5693	−	44.7659i	0.820961	−	2.09177i
$459$	−1.60872	−	2.78639i	−0.0750887	−	0.130057i
$460$	−1.40952	+	2.44136i	−0.0657193	+	0.113829i
$461$	7.00449	+	8.78335i	0.326232	+	0.409082i	0.917717	−	0.397234i	$-0.130030\pi$
$461$	7.00449	+	8.78335i	0.326232	+	0.409082i	−0.591486	+	0.806315i	$0.701458\pi$
$462$	−2.27811	−	7.88493i	−0.105987	−	0.366840i
$463$	−16.9191	+	21.2159i	−0.786299	+	0.985987i	0.213660	+	0.976908i	$0.431461\pi$
$463$	−16.9191	+	21.2159i	−0.786299	+	0.985987i	−0.999959	+	0.00907929i	$0.997110\pi$
$464$	9.49859	+	24.2020i	0.440961	+	1.12355i
$465$	0.0214267	+	0.285919i	0.000993638	+	0.0132592i
$466$	−2.24630	−	29.9748i	−0.104058	−	1.38855i
$467$	−10.8084	−	27.5393i	−0.500153	−	1.27437i	−0.928694	−	0.370846i	$-0.879068\pi$
$467$	−10.8084	−	27.5393i	−0.500153	−	1.27437i	0.428542	−	0.903522i	$-0.359028\pi$
$468$	0.993695	−	1.24605i	0.0459335	−	0.0575988i
$469$	−7.02456	−	2.90340i	−0.324364	−	0.134067i
$470$	−4.47326	−	5.60929i	−0.206336	−	0.258737i
$471$	−6.65431	+	11.5256i	−0.306614	+	0.531072i
$472$	−1.48322	−	2.56900i	−0.0682705	−	0.118248i
$473$	−0.282783	+	0.720520i	−0.0130024	+	0.0331296i
$474$	21.7153	+	6.69828i	0.997416	+	0.307662i
$475$	28.5311	+	13.7399i	1.30910	+	0.630428i
$476$	−0.329936	−	2.49145i	−0.0151226	−	0.114195i
$477$	0.638684	−	0.307574i	0.0292433	−	0.0140828i
$478$	16.6620	−	2.51140i	0.762103	−	0.114869i
$479$	−12.5618	−	8.56451i	−0.573965	−	0.391322i	0.241266	−	0.970459i	$-0.422437\pi$
$479$	−12.5618	−	8.56451i	−0.573965	−	0.391322i	−0.815231	+	0.579137i	$0.803390\pi$
$480$	−3.92526	+	3.64211i	−0.179163	+	0.166239i
$481$	4.73385	−	3.22748i	0.215845	−	0.147161i
$482$	−11.9218	+	52.2328i	−0.543023	+	2.37914i
$483$	−16.3973	−	4.05334i	−0.746102	−	0.184433i
$484$	−0.357547	−	1.56651i	−0.0162521	−	0.0712052i
$485$	0.204050	+	0.189331i	0.00926543	+	0.00859707i
$486$	−6.44746	−	0.971798i	−0.292463	−	0.0440817i
$487$	24.7253	−	7.62674i	1.12041	−	0.345601i	0.321415	−	0.946938i	$-0.395842\pi$
$487$	24.7253	−	7.62674i	1.12041	−	0.345601i	0.798995	+	0.601338i	$0.205365\pi$
$488$	−0.152072	+	2.02926i	−0.00688397	+	0.0918602i
$489$	28.9404			1.30873
$490$	2.79647	+	5.27172i	0.126332	+	0.238152i
$491$	16.8847			0.761995			0.380997	−	0.924576i	$-0.375581\pi$
$491$	16.8847			0.761995			0.380997	+	0.924576i	$0.375581\pi$
$492$	−1.38745	+	18.5142i	−0.0625511	+	0.834686i
$493$	−3.17096	+	0.978111i	−0.142813	+	0.0440519i
$494$	−37.0319	−	5.58167i	−1.66615	−	0.251131i
$495$	0.109230	+	0.101350i	0.00490951	+	0.00455536i
$496$	0.403039	+	1.76583i	0.0180970	+	0.0792880i
$497$	0.342661	−	19.1002i	0.0153704	−	0.856763i
$498$	−7.99051	+	35.0087i	−0.358063	+	1.56878i
$499$	−8.07224	+	5.50356i	−0.361363	+	0.246373i	−0.730367	−	0.683054i	$-0.760651\pi$
$499$	−8.07224	+	5.50356i	−0.361363	+	0.246373i	0.369004	+	0.929428i	$0.379699\pi$
$500$	−5.18073	+	4.80702i	−0.231690	+	0.214976i
$501$	−12.9552	−	8.83272i	−0.578797	−	0.394617i
$502$	−16.5565	+	2.49548i	−0.738951	+	0.111379i
$503$	2.97647	−	1.43339i	0.132714	−	0.0639119i	−0.366348	−	0.930478i	$-0.619392\pi$
$503$	2.97647	−	1.43339i	0.132714	−	0.0639119i	0.499063	+	0.866566i	$0.333678\pi$
$504$	0.561996	+	0.338052i	0.0250333	+	0.0150580i
$505$	−7.01236	−	3.37698i	−0.312046	−	0.150273i
$506$	−7.09299	−	2.18790i	−0.315322	−	0.0972640i
$507$	2.42966	−	6.19067i	0.107905	−	0.274937i
$508$	10.0307	+	17.3736i	0.445038	+	0.770829i
$509$	−10.1385	+	17.5603i	−0.449379	+	0.778348i	−0.998346	−	0.0574967i	$-0.981688\pi$
$509$	−10.1385	+	17.5603i	−0.449379	+	0.778348i	0.548966	+	0.835844i	$0.315021\pi$
$510$	−0.513261	−	0.643608i	−0.0227276	−	0.0284995i
$511$	−0.411015	−	0.459221i	−0.0181822	−	0.0203148i
$512$	−16.7772	+	21.0379i	−0.741453	+	0.929752i
$513$	13.1219	+	33.4341i	0.579346	+	1.47615i
$514$	1.68705	+	22.5122i	0.0744127	+	0.992969i
$515$	0.0111049	+	0.148184i	0.000489339	+	0.00652977i
$516$	−0.742186	−	1.89106i	−0.0326729	−	0.0832493i
$517$	5.24721	−	6.57979i	0.230772	−	0.289379i
$518$	−6.42538	−	7.17899i	−0.282315	−	0.315427i
$519$	−21.8864	−	27.4447i	−0.960706	−	1.20469i
$520$	−0.500806	+	0.867421i	−0.0219618	+	0.0380389i
$521$	−18.8031	−	32.5679i	−0.823779	−	1.42683i	−0.902849	−	0.429958i	$-0.858528\pi$
$521$	−18.8031	−	32.5679i	−0.823779	−	1.42683i	0.0790694	−	0.996869i	$-0.474805\pi$
$522$	−1.29283	+	3.29408i	−0.0565857	+	0.144178i
$523$	39.5510	+	12.1999i	1.72944	+	0.533462i	0.990161	−	0.139934i	$-0.0446889\pi$
$523$	39.5510	+	12.1999i	1.72944	+	0.533462i	0.739282	+	0.673396i	$0.235165\pi$
$524$	−18.1095	−	8.72106i	−0.791116	−	0.380981i
$525$	−17.7701	−	10.6891i	−0.775552	−	0.466511i
$526$	31.5306	−	15.1843i	1.37480	−	0.662068i
$527$	−0.228594	+	0.0344550i	−0.00995770	+	0.00150088i
$528$	−6.25103	−	4.26188i	−0.272041	−	0.185475i
$529$	5.66210	−	5.25366i	0.246178	−	0.228420i
$530$	1.50420	−	1.02555i	0.0653384	−	0.0445470i
$531$	0.293429	−	1.28559i	0.0127337	−	0.0557900i
$532$	−0.503234	+	28.0507i	−0.0218180	+	1.21615i
$533$	4.70353	+	20.6075i	0.203732	+	0.892610i
$534$	10.9815	+	10.1893i	0.475215	+	0.440935i
$535$	−5.47996	−	0.825970i	−0.236919	−	0.0357098i
$536$	−2.05001	+	0.632344i	−0.0885469	+	0.0273131i
$537$	−0.417093	+	5.56571i	−0.0179989	+	0.240178i
$538$	−34.3135			−1.47936
$539$	−5.29884	+	4.57409i	−0.228237	+	0.197020i
$540$	−3.92548			−0.168926
$541$	−3.05464	+	40.7614i	−0.131329	+	1.75247i	0.410392	+	0.911909i	$0.365392\pi$
$541$	−3.05464	+	40.7614i	−0.131329	+	1.75247i	−0.541721	+	0.840558i	$0.682227\pi$
$542$	−0.0981229	+	0.0302669i	−0.00421474	+	0.00130008i
$543$	1.73711	+	0.261827i	0.0745464	+	0.0112361i
$544$	−3.16484	−	2.93654i	−0.135691	−	0.125903i
$545$	1.24207	+	5.44186i	0.0532043	+	0.233103i
$546$	23.8077	+	5.88517i	1.01888	+	0.251862i
$547$	−2.95134	+	12.9307i	−0.126190	+	0.552875i	0.871820	+	0.489826i	$0.162940\pi$
$547$	−2.95134	+	12.9307i	−0.126190	+	0.552875i	−0.998010	+	0.0630490i	$0.979918\pi$
$548$	15.4055	−	10.5033i	0.658091	−	0.448679i
$549$	−0.663109	+	0.615276i	−0.0283008	+	0.0262593i
$550$	−7.52961	−	5.13360i	−0.321064	−	0.218897i
$551$	36.6300	−	5.52108i	1.56049	−	0.235206i
$552$	−4.29522	+	2.06847i	−0.182817	+	0.0880399i
$553$	−2.54446	−	19.2140i	−0.108202	−	0.817062i
$554$	54.7883	+	26.3846i	2.32773	+	1.12098i
$555$	−1.34343	−	0.414393i	−0.0570253	−	0.0175900i
$556$	8.67759	−	22.1101i	0.368012	−	0.937679i
$557$	−4.93088	−	8.54053i	−0.208928	−	0.361874i	0.742449	−	0.669902i	$-0.233664\pi$
$557$	−4.93088	−	8.54053i	−0.208928	−	0.361874i	−0.951377	+	0.308029i	$0.900331\pi$
$558$	−0.123262	+	0.213496i	−0.00521810	+	0.00903801i
$559$	−1.44203	−	1.80825i	−0.0609915	−	0.0764809i
$560$	5.08376	+	2.10123i	0.214828	+	0.0887931i
$561$	0.602063	−	0.754963i	0.0254191	−	0.0318746i
$562$	−6.24721	−	15.9176i	−0.263523	−	0.671445i
$563$	1.02472	+	13.6740i	0.0431869	+	0.576289i	0.976260	+	0.216602i	$0.0694975\pi$
$563$	1.02472	+	13.6740i	0.0431869	+	0.576289i	−0.933073	+	0.359687i	$0.882883\pi$
$564$	1.65064	+	22.0263i	0.0695047	+	0.927475i
$565$	−3.28050	−	8.35857i	−0.138012	−	0.351648i
$566$	−13.0214	+	16.3283i	−0.547330	+	0.686330i
$567$	−5.79712	−	20.0648i	−0.243456	−	0.842642i
$568$	−3.36173	−	4.21548i	−0.141055	−	0.176877i
$569$	15.9084	−	27.5542i	0.666915	−	1.15513i	−0.311847	−	0.950132i	$-0.600948\pi$
$569$	15.9084	−	27.5542i	0.666915	−	1.15513i	0.978762	−	0.204999i	$-0.0657190\pi$
$570$	4.59480	+	7.95842i	0.192455	+	0.333342i
$571$	3.14230	−	8.00646i	0.131501	−	0.335060i	−0.849924	−	0.526906i	$-0.823352\pi$
$571$	3.14230	−	8.00646i	0.131501	−	0.335060i	0.981425	+	0.191846i	$0.0614474\pi$
$572$	4.58792	+	1.41519i	0.191831	+	0.0591719i
$573$	−5.15722	−	2.48358i	−0.215446	−	0.103753i
$574$	33.3151	−	12.3903i	1.39054	−	0.517161i
$575$	−16.8974	+	8.13737i	−0.704671	+	0.339352i
$576$	−1.51187	+	0.227878i	−0.0629948	+	0.00949493i
$577$	17.2593	+	11.7672i	0.718513	+	0.489874i	0.866539	−	0.499110i	$-0.166340\pi$
$577$	17.2593	+	11.7672i	0.718513	+	0.489874i	−0.148026	+	0.988983i	$0.547292\pi$
$578$	−23.1805	+	21.5084i	−0.964183	+	0.894631i
$579$	−28.0043	+	19.0930i	−1.16382	+	0.793479i
$580$	−0.900905	+	3.94712i	−0.0374081	+	0.163895i
$581$	29.9759	−	6.27832i	1.24361	−	0.260469i
$582$	−0.428051	−	1.87542i	−0.0177433	−	0.0777385i
$583$	1.56545	+	1.45253i	0.0648344	+	0.0601575i
$584$	−0.172002	−	0.0259252i	−0.00711751	−	0.00107279i
$585$	−0.425462	+	0.131237i	−0.0175907	+	0.00542600i
$586$	2.65949	−	35.4884i	0.109863	−	1.46601i
$587$	−31.7735			−1.31143			−0.655716	−	0.755008i	$-0.727633\pi$
$587$	−31.7735			−1.31143			−0.655716	+	0.755008i	$0.727633\pi$
$588$	2.02920	−	18.2596i	0.0836827	−	0.753014i
$589$	2.58066			0.106334
$590$	0.253077	−	3.37707i	0.0104190	−	0.139032i
$591$	−42.9476	+	13.2476i	−1.76663	+	0.544933i
$592$	−8.78192	−	1.32366i	−0.360935	−	0.0544022i
$593$	−5.20566	−	4.83014i	−0.213771	−	0.198350i	0.566018	−	0.824393i	$-0.308483\pi$
$593$	−5.20566	−	4.83014i	−0.213771	−	0.198350i	−0.779789	+	0.626043i	$0.784674\pi$
$594$	−2.30000	−	10.0769i	−0.0943700	−	0.413462i
$595$	−0.315928	+	0.627005i	−0.0129518	+	0.0257047i
$596$	1.97698	−	8.66173i	0.0809804	−	0.354798i
$597$	20.0980	−	13.7026i	0.822555	−	0.560809i
$598$	16.2589	−	15.0860i	0.664875	−	0.616914i
$599$	23.3989	+	15.9531i	0.956053	+	0.651826i	0.937494	−	0.348002i	$-0.113140\pi$
$599$	23.3989	+	15.9531i	0.956053	+	0.651826i	0.0185588	+	0.999828i	$0.494092\pi$
$600$	−5.78760	+	0.872341i	−0.236278	+	0.0356132i
$601$	−12.1328	+	5.84285i	−0.494908	+	0.238335i	−0.664652	−	0.747153i	$-0.731420\pi$
$601$	−12.1328	+	5.84285i	−0.494908	+	0.238335i	0.169744	+	0.985488i	$0.445706\pi$
$602$	−2.69607	+	2.80311i	−0.109884	+	0.114246i
$603$	−0.859210	−	0.413774i	−0.0349897	−	0.0168502i
$604$	−27.0950	−	8.35769i	−1.10248	−	0.340070i
$605$	−0.163996	+	0.417855i	−0.00666739	+	0.0169882i
$606$	26.8935	+	46.5810i	1.09247	+	1.89222i
$607$	8.43191	−	14.6045i	0.342241	−	0.592778i	−0.642608	−	0.766195i	$-0.722147\pi$
$607$	8.43191	−	14.6045i	0.342241	−	0.592778i	0.984849	+	0.173417i	$0.0554808\pi$
$608$	30.0493	+	37.6806i	1.21866	+	1.52815i
$609$	−24.2189	+	1.37861i	−0.981401	+	0.0558642i
$610$	−1.44845	+	1.81630i	−0.0586462	+	0.0735400i
$611$	9.18730	+	23.4089i	0.371678	+	0.947021i
$612$	−0.0235637	−	0.314436i	−0.000952508	−	0.0127103i
$613$	2.16769	+	28.9259i	0.0875524	+	1.16831i	0.851972	+	0.523587i	$0.175406\pi$
$613$	2.16769	+	28.9259i	0.0875524	+	1.16831i	−0.764420	+	0.644719i	$0.776975\pi$
$614$	4.16370	+	10.6089i	0.168033	+	0.428142i
$615$	3.23388	−	4.05516i	0.130403	−	0.163520i
$616$	−0.329460	+	1.94805i	−0.0132743	+	0.0784890i
$617$	−3.24953	−	4.07478i	−0.130821	−	0.164045i	0.712107	−	0.702071i	$-0.247741\pi$
$617$	−3.24953	−	4.07478i	−0.130821	−	0.164045i	−0.842928	+	0.538027i	$0.819170\pi$
$618$	0.513465	−	0.889347i	0.0206546	−	0.0357748i
$619$	−0.689434	−	1.19413i	−0.0277107	−	0.0479963i	0.851837	−	0.523806i	$-0.175488\pi$
$619$	−0.689434	−	1.19413i	−0.0277107	−	0.0479963i	−0.879548	+	0.475810i	$0.842155\pi$
$620$	−0.103044	+	0.262552i	−0.00413834	+	0.0105443i
$621$	−20.3266	−	6.26991i	−0.815677	−	0.251603i
$622$	−7.23015	−	3.48186i	−0.289903	−	0.139610i
$623$	3.98437	−	12.1395i	0.159631	−	0.486359i
$624$	20.3679	−	9.80867i	0.815369	−	0.392661i
$625$	−21.7722	+	3.28163i	−0.870889	+	0.131265i
$626$	22.9197	+	15.6264i	0.916055	+	0.624556i
$627$	−7.90196	+	7.33195i	−0.315574	+	0.292810i
$628$	−10.8169	+	7.37485i	−0.431642	+	0.294289i
$629$	0.252235	−	1.10511i	0.0100573	−	0.0440637i
$630$	0.312703	+	0.680287i	0.0124584	+	0.0271033i
$631$	2.14380	+	9.39261i	0.0853434	+	0.373914i	0.999506	−	0.0314342i	$-0.0100075\pi$
$631$	2.14380	+	9.39261i	0.0853434	+	0.373914i	−0.914162	+	0.405348i	$0.867150\pi$
$632$	−4.01007	−	3.72080i	−0.159512	−	0.148006i
$633$	22.6356	+	3.41177i	0.899686	+	0.135606i
$634$	19.7604	−	6.09528i	0.784786	−	0.242074i
$635$	0.418820	−	5.58877i	0.0166204	−	0.221783i
$636$	−5.60485			−0.222247
$637$	−3.91992	−	20.5459i	−0.155313	−	0.814057i
$638$	−10.6604			−0.422048
$639$	0.179113	−	2.39009i	0.00708559	−	0.0945506i
$640$	2.51297	−	0.775149i	0.0993339	−	0.0306404i
$641$	27.0942	+	4.08379i	1.07015	+	0.161300i	0.660414	−	0.750902i	$-0.270381\pi$
$641$	27.0942	+	4.08379i	1.07015	+	0.161300i	0.409741	+	0.912202i	$0.365619\pi$
$642$	28.0746	+	26.0494i	1.10801	+	1.02809i
$643$	5.77164	+	25.2872i	0.227611	+	0.997231i	0.951581	+	0.307399i	$0.0994585\pi$
$643$	5.77164	+	25.2872i	0.227611	+	0.997231i	−0.723970	+	0.689832i	$0.757684\pi$
$644$	−12.8027	−	10.5910i	−0.504496	−	0.417344i
$645$	−0.126287	+	0.553299i	−0.00497254	+	0.0217861i
$646$	−6.12189	+	4.17383i	−0.240862	+	0.164217i
$647$	15.8524	−	14.7089i	0.623222	−	0.578266i	−0.304049	−	0.952656i	$-0.598339\pi$
$647$	15.8524	−	14.7089i	0.623222	−	0.578266i	0.927271	+	0.374391i	$0.122148\pi$
$648$	−4.87051	−	3.32066i	−0.191332	−	0.130448i
$649$	3.92810	−	0.592065i	0.154191	−	0.0232406i
$650$	24.5339	−	11.8149i	0.962299	−	0.463419i
$651$	−1.68268	−	0.156498i	−0.0659496	−	0.00613363i
$652$	25.6496	+	12.3522i	1.00451	+	0.483748i
$653$	9.96963	+	3.07522i	0.390142	+	0.120343i	0.483619	−	0.875279i	$-0.339322\pi$
$653$	9.96963	+	3.07522i	0.390142	+	0.120343i	−0.0934773	+	0.995621i	$0.529798\pi$
$654$	14.0928	−	35.9078i	0.551071	−	1.40410i
$655$	2.80762	+	4.86295i	0.109703	+	0.190011i
$656$	16.3826	−	28.3754i	0.639631	−	1.10787i
$657$	−0.0482102	−	0.0604537i	−0.00188086	−	0.00235852i
$658$	36.9952	−	20.4833i	1.44222	−	0.798523i
$659$	4.90914	−	6.15587i	0.191233	−	0.239799i	−0.676967	−	0.736014i	$-0.736706\pi$
$659$	4.90914	−	6.15587i	0.191233	−	0.239799i	0.868200	+	0.496215i	$0.165277\pi$
$660$	−0.430420	−	1.09669i	−0.0167541	−	0.0426887i
$661$	1.91155	+	25.5079i	0.0743507	+	0.992141i	0.902236	+	0.431243i	$0.141925\pi$
$661$	1.91155	+	25.5079i	0.0743507	+	0.992141i	−0.827885	+	0.560898i	$0.810456\pi$
$662$	−2.04070	−	27.2313i	−0.0793142	−	1.05837i
$663$	1.05415	+	2.68592i	0.0409397	+	0.104313i
$664$	5.38950	−	6.75822i	0.209153	−	0.262270i
$665$	4.53057	−	6.39555i	0.175688	−	0.248009i
$666$	−0.753668	−	0.945070i	−0.0292040	−	0.0366207i
$667$	−10.9695	+	18.9997i	−0.424740	+	0.735671i
$668$	−7.71213	−	13.3578i	−0.298391	−	0.516829i
$669$	−6.82199	+	17.3821i	−0.263753	+	0.672033i
$670$	−2.34033	−	0.721898i	−0.0904150	−	0.0278893i
$671$	−2.45521	−	1.18237i	−0.0947824	−	0.0456448i
$672$	−17.3082	−	26.3915i	−0.667679	−	1.01807i
$673$	27.5730	−	13.2784i	1.06286	−	0.511846i	0.181061	−	0.983472i	$-0.442047\pi$
$673$	27.5730	−	13.2784i	1.06286	−	0.511846i	0.881799	+	0.471626i	$0.156333\pi$
$674$	15.0421	−	2.26723i	0.579399	−	0.0873304i
$675$	−21.5778	−	14.7115i	−0.830529	−	0.566245i
$676$	4.79564	−	4.44970i	0.184448	−	0.171142i
$677$	5.67868	−	3.87166i	0.218249	−	0.148800i	−0.449261	−	0.893401i	$-0.648313\pi$
$677$	5.67868	−	3.87166i	0.218249	−	0.148800i	0.667510	+	0.744601i	$0.267360\pi$
$678$	−13.8081	+	60.4974i	−0.530298	+	2.32339i
$679$	−1.30085	+	0.999756i	−0.0499222	+	0.0383671i
$680$	0.0440956	+	0.193195i	0.00169099	+	0.00740871i
$681$	−33.1827	−	30.7890i	−1.27156	−	1.17984i
$682$	−0.734362	−	0.110687i	−0.0281202	−	0.00423843i
$683$	−42.7819	+	13.1965i	−1.63700	+	0.504949i	−0.970611	−	0.240653i	$-0.922639\pi$
$683$	−42.7819	+	13.1965i	−1.63700	+	0.504949i	−0.666392	+	0.745601i	$0.732162\pi$
$684$	−0.263046	+	3.51011i	−0.0100578	+	0.134212i
$685$	−5.20887			−0.199021
$686$	−33.3853	+	11.0704i	−1.27466	+	0.422669i
$687$	41.3611			1.57803
$688$	−0.267917	+	3.57510i	−0.0102142	+	0.136300i
$689$	−6.09760	+	1.88086i	−0.232300	+	0.0716551i
$690$	−5.38170	−	0.811161i	−0.204878	−	0.0308804i
$691$	−26.9182	−	24.9764i	−1.02402	−	0.950147i	−0.0252430	−	0.999681i	$-0.508036\pi$
$691$	−26.9182	−	24.9764i	−1.02402	−	0.950147i	−0.998772	+	0.0495338i	$0.984226\pi$
$692$	−7.68388	−	33.6653i	−0.292097	−	1.27976i
$693$	−0.696358	+	0.535178i	−0.0264525	+	0.0203297i
$694$	0.534531	−	2.34193i	0.0202905	−	0.0888985i
$695$	−5.48251	+	3.73791i	−0.207963	+	0.141787i
$696$	−5.01900	+	4.65695i	−0.190245	+	0.176521i
$697$	3.45528	+	2.35577i	0.130878	+	0.0892312i
$698$	55.3747	−	8.34639i	2.09596	−	0.315916i
$699$	23.2926	−	11.2171i	0.881006	−	0.424270i
$700$	−11.1872	−	17.0582i	−0.422836	−	0.644738i
$701$	−13.7824	−	6.63724i	−0.520553	−	0.250685i	0.155108	−	0.987898i	$-0.450427\pi$
$701$	−13.7824	−	6.63724i	−0.520553	−	0.250685i	−0.675661	+	0.737212i	$0.736142\pi$
$702$	29.5128	+	9.10350i	1.11389	+	0.343589i
$703$	−4.62296	+	11.7791i	−0.174358	+	0.444257i
$704$	−2.30299	−	3.98890i	−0.0867973	−	0.150337i
$705$	3.08533	−	5.34394i	0.116200	−	0.201264i
$706$	26.2647	+	32.9348i	0.988483	+	1.23952i
$707$	26.5176	−	37.4334i	0.997296	−	1.40783i
$708$	−6.50053	+	8.15141i	−0.244305	+	0.306349i
$709$	10.1734	+	25.9215i	0.382071	+	0.973501i	0.984509	+	0.175335i	$0.0561010\pi$
$709$	10.1734	+	25.9215i	0.382071	+	0.973501i	−0.602438	+	0.798166i	$0.705804\pi$
$710$	−0.459993	−	6.13818i	−0.0172632	−	0.230362i
$711$	−0.181723	−	2.42493i	−0.00681515	−	0.0909419i
$712$	−1.31747	−	3.35686i	−0.0493742	−	0.125804i
$713$	−0.952930	+	1.19494i	−0.0356875	+	0.0447507i
$714$	4.24481	−	2.35025i	0.158858	−	0.0879558i
$715$	−0.836286	−	1.04867i	−0.0312753	−	0.0392180i
$716$	−2.74519	+	4.75480i	−0.102592	+	0.177695i
$717$	7.24622	+	12.5508i	0.270615	+	0.468719i
$718$	14.1075	−	35.9452i	0.526485	−	1.34146i
$719$	17.0827	+	5.26931i	0.637077	+	0.196512i	0.596435	−	0.802662i	$-0.296583\pi$
$719$	17.0827	+	5.26931i	0.637077	+	0.196512i	0.0406421	+	0.999174i	$0.487060\pi$
$720$	0.621821	+	0.299453i	0.0231739	+	0.0111600i
$721$	−0.872090	−	0.0811086i	−0.0324783	−	0.00302064i
$722$	42.0102	−	20.2310i	1.56346	−	0.752921i
$723$	−45.5648	+	6.86778i	−1.69457	+	0.255416i
$724$	1.42783	+	0.973475i	0.0530647	+	0.0361789i
$725$	−19.7448	+	18.3205i	−0.733302	+	0.680405i
$726$	2.56309	−	1.74748i	0.0951252	−	0.0648552i
$727$	−7.35258	+	32.2137i	−0.272692	+	1.19474i	0.634130	+	0.773227i	$0.281359\pi$
$727$	−7.35258	+	32.2137i	−0.272692	+	1.19474i	−0.906822	+	0.421515i	$0.861499\pi$
$728$	−4.54881	−	3.76300i	−0.168590	−	0.139466i
$729$	−6.51760	−	28.5555i	−0.241393	−	1.05761i
$730$	−0.145569	−	0.135068i	−0.00538775	−	0.00499911i
$731$	−0.452473	−	0.0681994i	−0.0167353	−	0.00252245i
$732$	6.83443	−	2.10814i	0.252608	−	0.0779192i
$733$	−2.00454	+	26.7487i	−0.0740393	+	0.987986i	0.829229	+	0.558909i	$0.188780\pi$
$733$	−2.00454	+	26.7487i	−0.0740393	+	0.987986i	−0.903268	+	0.429077i	$0.858839\pi$
$734$	4.81846			0.177853
$735$	−3.34194	+	3.89540i	−0.123269	+	0.143684i
$736$	−28.5435			−1.05213
$737$	0.214691	−	2.86485i	0.00790824	−	0.105528i
$738$	4.26146	−	1.31449i	0.156867	−	0.0483869i
$739$	41.5279	+	6.25932i	1.52763	+	0.230253i	0.858469	−	0.512866i	$-0.171416\pi$
$739$	41.5279	+	6.25932i	1.52763	+	0.230253i	0.669159	+	0.743119i	$0.266654\pi$
$740$	−1.01380	−	0.940664i	−0.0372678	−	0.0345795i
$741$	−7.16740	−	31.4024i	−0.263301	−	1.15360i
$742$	4.48158	+	9.74969i	0.164524	+	0.357923i
$743$	−8.05006	+	35.2696i	−0.295328	+	1.29392i	0.581671	+	0.813424i	$0.302399\pi$
$743$	−8.05006	+	35.2696i	−0.295328	+	1.29392i	−0.876999	+	0.480492i	$0.840458\pi$
$744$	−0.394097	+	0.268691i	−0.0144483	+	0.00985069i
$745$	−1.81945	+	1.68820i	−0.0666594	+	0.0618509i
$746$	−51.6572	−	35.2193i	−1.89131	−	1.28947i
$747$	3.79961	−	0.572699i	0.139020	−	0.0209540i
$748$	0.855829	−	0.412146i	0.0312922	−	0.0150695i
$749$	10.1862	−	31.0351i	0.372196	−	1.13400i
$750$	−12.2931	−	5.92006i	−0.448882	−	0.216170i
$751$	−3.67345	−	1.13311i	−0.134046	−	0.0413478i	0.227006	−	0.973893i	$-0.427106\pi$
$751$	−3.67345	−	1.13311i	−0.134046	−	0.0413478i	−0.361052	+	0.932546i	$0.617582\pi$
$752$	14.2412	−	36.2860i	0.519323	−	1.32321i
$753$	−7.20031	−	12.4713i	−0.262394	−	0.454480i
$754$	15.9270	−	27.5863i	0.580025	−	1.00463i
$755$	4.93887	+	6.19314i	0.179744	+	0.225392i
$756$	3.85821	−	22.8130i	0.140322	−	0.829701i
$757$	−9.91166	+	12.4288i	−0.360245	+	0.451733i	−0.928618	−	0.371038i	$-0.879002\pi$
$757$	−9.91166	+	12.4288i	−0.360245	+	0.451733i	0.568372	+	0.822771i	$0.307573\pi$
$758$	−7.29162	−	18.5787i	−0.264843	−	0.674810i
$759$	−0.477087	−	6.36628i	−0.0173172	−	0.231081i
$760$	−0.165313	−	2.20595i	−0.00599654	−	0.0800183i
$761$	−5.75416	−	14.6614i	−0.208588	−	0.531474i	0.787844	−	0.615875i	$-0.211198\pi$
$761$	−5.75416	−	14.6614i	−0.208588	−	0.531474i	−0.996432	+	0.0844011i	$0.973102\pi$
$762$	−24.1482	+	30.2809i	−0.874797	+	1.09696i
$763$	−32.8463	+	1.86971i	−1.18911	+	0.0676879i
$764$	−3.51075	−	4.40234i	−0.127014	−	0.159271i
$765$	−0.0440445	+	0.0762873i	−0.00159243	+	0.00275817i
$766$	13.1998	+	22.8627i	0.476928	+	0.826064i
$767$	−4.33660	+	11.0495i	−0.156585	+	0.398973i
$768$	−31.7449	−	9.79201i	−1.14550	−	0.353339i
$769$	−24.2186	−	11.6631i	−0.873347	−	0.420582i	−0.0571568	−	0.998365i	$-0.518203\pi$
$769$	−24.2186	−	11.6631i	−0.873347	−	0.420582i	−0.816190	+	0.577784i	$0.803918\pi$
$770$	−1.56355	+	1.62562i	−0.0563464	+	0.0585834i
$771$	−17.4936	+	8.42447i	−0.630016	+	0.303400i
$772$	−32.9690	+	4.96928i	−1.18658	+	0.178848i
$773$	−13.6654	−	9.31691i	−0.491510	−	0.335106i	0.292070	−	0.956397i	$-0.405656\pi$
$773$	−13.6654	−	9.31691i	−0.491510	−	0.335106i	−0.783580	+	0.621291i	$0.786608\pi$
$774$	−0.357703	+	0.331900i	−0.0128574	+	0.0119299i
$775$	−1.55038	+	1.05703i	−0.0556913	+	0.0379697i
$776$	−0.103041	+	0.451454i	−0.00369897	+	0.0162062i
$777$	3.72866	−	7.40008i	0.133765	−	0.265476i
$778$	−13.9675	−	61.1956i	−0.500759	−	2.19397i
$779$	−34.2216	−	31.7530i	−1.22612	−	1.13767i
$780$	3.48102	+	0.524679i	0.124640	+	0.0187865i
$781$	6.89959	−	2.12824i	0.246887	−	0.0761545i
$782$	0.327927	−	4.37588i	0.0117266	−	0.156481i
$783$	−30.5497			−1.09176
$784$	−17.2080	+	27.4792i	−0.614571	+	0.981400i
$785$	3.65739			0.130538
$786$	2.89993	−	38.6969i	0.103437	−	1.38027i
$787$	−43.4502	+	13.4026i	−1.54883	+	0.477751i	−0.947098	−	0.320946i	$-0.895999\pi$
$787$	−43.4502	+	13.4026i	−1.54883	+	0.477751i	−0.601734	+	0.798697i	$0.705523\pi$
$788$	−43.7182	−	6.58946i	−1.55740	−	0.234740i
$789$	22.0644	+	20.4728i	0.785515	+	0.728851i
$790$	−1.38967	−	6.08853i	−0.0494421	−	0.216620i
$791$	51.8003	−	10.8494i	1.84181	−	0.385759i
$792$	−0.0551589	+	0.241667i	−0.00195999	+	0.00858727i
$793$	6.72783	−	4.58696i	0.238912	−	0.162888i
$794$	−17.3532	+	16.1014i	−0.615841	+	0.571416i
$795$	1.29373	+	0.882048i	0.0458838	+	0.0312830i
$796$	23.6610	−	3.56633i	0.838643	−	0.126405i
$797$	20.6642	−	9.95135i	0.731963	−	0.352495i	−0.0304929	−	0.999535i	$-0.509708\pi$
$797$	20.6642	−	9.95135i	0.731963	−	0.352495i	0.762456	+	0.647040i	$0.223993\pi$
$798$	−50.7666	+	18.8807i	−1.79712	+	0.668371i
$799$	4.48254	+	2.15868i	0.158581	+	0.0763685i
$800$	−33.4866	−	10.3293i	−1.18393	−	0.365194i
$801$	0.585649	−	1.49221i	0.0206929	−	0.0527247i
$802$	−2.95384	−	5.11620i	−0.104304	−	0.180659i
$803$	0.116468	−	0.201729i	0.00411008	−	0.00711887i
$804$	4.70118	+	5.89509i	0.165798	+	0.207904i
$805$	1.28842	+	4.45943i	0.0454108	+	0.157174i
$806$	1.38359	−	1.73497i	0.0487349	−	0.0611116i
$807$	−10.7820	−	27.4721i	−0.379544	−	0.967063i
$808$	−0.967585	−	12.9115i	−0.0340395	−	0.454226i
$809$	3.44435	+	45.9617i	0.121097	+	1.61593i	0.645022	+	0.764164i	$0.276848\pi$
$809$	3.44435	+	45.9617i	0.121097	+	1.61593i	−0.523925	+	0.851764i	$0.675533\pi$
$810$	−2.45861	−	6.26444i	−0.0863867	−	0.220110i
$811$	6.50173	−	8.15292i	0.228307	−	0.286288i	−0.654462	−	0.756095i	$-0.727105\pi$
$811$	6.50173	−	8.15292i	0.228307	−	0.286288i	0.882769	+	0.469807i	$0.155676\pi$
$812$	−22.0534	−	9.11512i	−0.773921	−	0.319878i
$813$	−0.0550646	−	0.0690488i	−0.00193120	−	0.00242165i
$814$	1.82075	−	3.15363i	0.0638171	−	0.110535i
$815$	−3.97661	−	6.88769i	−0.139295	−	0.241265i
$816$	1.63403	−	4.16344i	0.0572025	−	0.145750i
$817$	4.88115	+	1.50564i	0.170770	+	0.0526755i
$818$	−26.0388	−	12.5396i	−0.910426	−	0.438438i
$819$	−0.344519	−	2.60157i	−0.0120385	−	0.0909062i
$820$	4.59695	−	2.21377i	0.160532	−	0.0773083i
$821$	−33.1142	+	4.99116i	−1.15569	+	0.174193i	−0.698792	−	0.715325i	$-0.746279\pi$
$821$	−33.1142	+	4.99116i	−1.15569	+	0.174193i	−0.456901	+	0.889518i	$0.651040\pi$
$822$	29.7422	+	20.2779i	1.03738	+	0.707271i
$823$	12.7361	−	11.8174i	0.443953	−	0.411928i	−0.426262	−	0.904600i	$-0.640170\pi$
$823$	12.7361	−	11.8174i	0.443953	−	0.411928i	0.870215	+	0.492671i	$0.163980\pi$
$824$	−0.204250	+	0.139255i	−0.00711539	+	0.00485119i
$825$	1.74411	−	7.64144i	0.0607221	−	0.266041i
$826$	19.3772	+	4.78996i	0.674219	+	0.166664i
$827$	−11.9158	−	52.2065i	−0.414352	−	1.81540i	−0.562940	−	0.826498i	$-0.690330\pi$
$827$	−11.9158	−	52.2065i	−0.414352	−	1.81540i	0.148588	−	0.988899i	$-0.452527\pi$
$828$	−1.52817	−	1.41794i	−0.0531077	−	0.0492767i
$829$	−19.3590	−	2.91790i	−0.672366	−	0.101343i	−0.196019	−	0.980600i	$-0.562801\pi$
$829$	−19.3590	−	2.91790i	−0.672366	−	0.101343i	−0.476347	+	0.879257i	$0.658039\pi$
$830$	9.42986	−	2.90873i	0.327315	−	0.100963i
$831$	−3.90849	+	52.1552i	−0.135584	+	1.80924i
$832$	13.7630			0.477146
$833$	−3.33334	−	2.45228i	−0.115493	−	0.0849666i
$834$	45.8561			1.58787
$835$	−0.322013	+	4.29696i	−0.0111437	+	0.148702i
$836$	−10.1328	+	3.12555i	−0.350450	+	0.108099i
$837$	−2.10448	−	0.317199i	−0.0727414	−	0.0109640i
$838$	−7.86636	−	7.29891i	−0.271739	−	0.252137i
$839$	−2.18354	−	9.56670i	−0.0753841	−	0.330279i	0.923148	−	0.384445i	$-0.125607\pi$
$839$	−2.18354	−	9.56670i	−0.0753841	−	0.330279i	−0.998532	+	0.0541659i	$0.982750\pi$
$840$	−0.0259843	+	1.44839i	−0.000896543	+	0.0499741i
$841$	−0.558112	+	2.44525i	−0.0192453	+	0.0843190i
$842$	−0.883919	+	0.602646i	−0.0304619	+	0.0207685i
$843$	10.7810	−	10.0033i	0.371317	−	0.344532i
$844$	18.6055	+	12.6850i	0.640428	+	0.436636i
$845$	−1.80720	+	0.272392i	−0.0621696	+	0.00937056i
$846$	4.78014	−	2.30200i	0.164345	−	0.0791443i
$847$	−2.26719	−	1.36376i	−0.0779016	−	0.0468594i
$848$	8.91177	+	4.29168i	0.306031	+	0.147377i
$849$	−17.1644	−	5.29451i	−0.589080	−	0.181707i
$850$	1.96825	−	5.01502i	0.0675105	−	0.172014i
$851$	−3.74708	−	6.49014i	−0.128448	−	0.222479i
$852$	−9.47521	+	16.4115i	−0.324615	+	0.562250i
$853$	7.79775	+	9.77807i	0.266990	+	0.334795i	0.897196	−	0.441634i	$-0.145601\pi$
$853$	7.79775	+	9.77807i	0.266990	+	0.334795i	−0.630206	+	0.776428i	$0.717029\pi$
$854$	−9.13186	−	10.2029i	−0.312486	−	0.349136i
$855$	0.613110	−	0.768816i	0.0209679	−	0.0262930i
$856$	−3.36816	−	8.58192i	−0.115121	−	0.293324i
$857$	3.23650	+	43.1881i	0.110557	+	1.47528i	0.726326	+	0.687351i	$0.241226\pi$
$857$	3.23650	+	43.1881i	0.110557	+	1.47528i	−0.615769	+	0.787927i	$0.711154\pi$
$858$	0.692698	+	9.24341i	0.0236483	+	0.315565i
$859$	−14.0424	−	35.7794i	−0.479120	−	1.22078i	−0.942377	−	0.334554i	$-0.891414\pi$
$859$	−14.0424	−	35.7794i	−0.479120	−	1.22078i	0.463256	−	0.886224i	$-0.346681\pi$
$860$	−0.348082	+	0.436481i	−0.0118695	+	0.0148839i
$861$	20.3882	+	22.7795i	0.694828	+	0.776322i
$862$	3.84149	+	4.81708i	0.130842	+	0.164070i
$863$	9.18047	−	15.9010i	0.312507	−	0.541278i	−0.666398	−	0.745597i	$-0.732165\pi$
$863$	9.18047	−	15.9010i	0.312507	−	0.541278i	0.978904	+	0.204319i	$0.0654980\pi$
$864$	−19.8732	−	34.4214i	−0.676099	−	1.17104i
$865$	−3.52437	+	8.97994i	−0.119832	+	0.305327i
$866$	16.8574	+	5.19983i	0.572838	+	0.176697i
$867$	−24.5039	−	11.8004i	−0.832195	−	0.400764i
$868$	−1.42455	−	0.856895i	−0.0483523	−	0.0290849i
$869$	6.60015	−	3.17846i	0.223895	−	0.107822i
$870$	−7.72906	+	1.16497i	−0.262040	+	0.0394961i
$871$	7.09274	+	4.83575i	0.240328	+	0.163853i
$872$	−6.80688	+	6.31586i	−0.230510	+	0.213882i
$873$	−0.170076	+	0.115956i	−0.00575621	+	0.00392452i
$874$	−10.9003	+	47.7575i	−0.368709	+	1.61542i
$875$	−0.208737	+	11.6352i	−0.00705660	+	0.393342i
$876$	0.136041	+	0.596033i	0.00459638	+	0.0201381i
$877$	−30.3616	−	28.1715i	−1.02524	−	0.951283i	−0.0264099	−	0.999651i	$-0.508408\pi$
$877$	−30.3616	−	28.1715i	−1.02524	−	0.951283i	−0.998830	+	0.0483680i	$0.984598\pi$
$878$	37.9639	+	5.72213i	1.28122	+	0.193113i
$879$	29.2484	−	9.02195i	0.986526	−	0.304303i
$880$	−0.155374	+	2.07333i	−0.00523767	+	0.0698919i
$881$	53.0572			1.78754			0.893772	−	0.448522i	$-0.148049\pi$
$881$	53.0572			1.78754			0.893772	+	0.448522i	$0.148049\pi$
$882$	−4.26085	+	1.14865i	−0.143470	+	0.0386771i
$883$	47.3639			1.59392			0.796961	−	0.604030i	$-0.206439\pi$
$883$	47.3639			1.59392			0.796961	+	0.604030i	$0.206439\pi$
$884$	−0.212111	+	2.83043i	−0.00713407	+	0.0951975i
$885$	2.78327	−	0.858527i	0.0935588	−	0.0288591i
$886$	1.56652	+	0.236115i	0.0526283	+	0.00793245i
$887$	−13.1295	−	12.1824i	−0.440845	−	0.409044i	0.428273	−	0.903649i	$-0.359122\pi$
$887$	−13.1295	−	12.1824i	−0.440845	−	0.409044i	−0.869118	+	0.494605i	$0.835313\pi$
$888$	−0.520428	−	2.28014i	−0.0174644	−	0.0765166i
$889$	32.0676	+	7.92698i	1.07551	+	0.265862i
$890$	0.916083	−	4.01362i	0.0307072	−	0.134537i
$891$	6.52230	−	4.44683i	0.218505	−	0.148974i
$892$	−13.4652	+	12.4939i	−0.450848	+	0.418325i
$893$	−45.8889	−	31.2865i	−1.53561	−	1.04696i
$894$	16.9610	−	2.55645i	0.567259	−	0.0855006i
$895$	1.38193	−	0.665500i	0.0461927	−	0.0222452i
$896$	2.03489	+	15.3661i	0.0679809	+	0.513344i
$897$	17.1871	+	8.27686i	0.573860	+	0.276356i
$898$	−24.3171	−	7.50083i	−0.811472	−	0.250306i
$899$	−0.801930	+	2.04329i	−0.0267459	+	0.0681474i
$900$	−1.27970	−	2.21651i	−0.0426567	−	0.0738836i
$901$	−0.631234	+	1.09333i	−0.0210295	+	0.0364241i
$902$	8.37632	+	10.5036i	0.278901	+	0.349731i
$903$	−3.09139	−	1.27774i	−0.102875	−	0.0425205i
$904$	9.31342	−	11.6787i	0.309760	−	0.388427i
$905$	−0.176377	−	0.449400i	−0.00586296	−	0.0149386i
$906$	−4.09088	−	54.5890i	−0.135910	−	1.81360i
$907$	2.06376	+	27.5389i	0.0685259	+	0.914415i	0.920478	+	0.390795i	$0.127800\pi$
$907$	2.06376	+	27.5389i	0.0685259	+	0.914415i	−0.851952	+	0.523620i	$0.824581\pi$
$908$	−16.2682	−	41.4507i	−0.539880	−	1.37559i
$909$	3.58856	−	4.49991i	0.119025	−	0.149253i
$910$	−1.87070	−	6.47479i	−0.0620131	−	0.214637i
$911$	1.50960	+	1.89298i	0.0500154	+	0.0627173i	0.806210	−	0.591629i	$-0.201515\pi$
$911$	1.50960	+	1.89298i	0.0500154	+	0.0627173i	−0.756195	+	0.654347i	$0.772944\pi$
$912$	−24.9643	+	43.2394i	−0.826650	+	1.43180i
$913$	5.78783	+	10.0248i	0.191549	+	0.331773i
$914$	−22.8338	+	58.1796i	−0.755275	+	1.92441i
$915$	−1.90930	−	0.588942i	−0.0631196	−	0.0194698i
$916$	36.6579	+	17.6535i	1.21121	+	0.583288i
$917$	−31.0207	+	11.5370i	−1.02439	+	0.380984i
$918$	5.50531	−	2.65122i	0.181702	−	0.0875032i
$919$	29.1179	−	4.38882i	0.960512	−	0.144774i	0.349973	−	0.936760i	$-0.386191\pi$
$919$	29.1179	−	4.38882i	0.960512	−	0.144774i	0.610539	+	0.791986i	$0.290953\pi$
$920$	1.08248	+	0.738021i	0.0356883	+	0.0243318i
$921$	−7.18541	+	6.66709i	−0.236767	+	0.219688i
$922$	−17.6284	+	12.0189i	−0.580562	+	0.395820i
$923$	−4.80088	+	21.0340i	−0.158023	+	0.692344i
$924$	6.79650	−	1.42350i	0.223588	−	0.0468296i
$925$	−2.04736	−	8.97009i	−0.0673169	−	0.294935i
$926$	−37.7785	−	35.0533i	−1.24148	−	1.15192i
$927$	−0.108662	−	0.0163781i	−0.00356891	−	0.000537927i
$928$	−39.1721	+	12.0830i	−1.28589	+	0.396644i
$929$	1.28975	−	17.2106i	0.0423155	−	0.564661i	−0.935244	−	0.354003i	$-0.884820\pi$
$929$	1.28975	−	17.2106i	0.0423155	−	0.564661i	0.977560	−	0.210658i	$-0.0675606\pi$
$930$	−0.544528			−0.0178558
$931$	32.7150	+	32.6155i	1.07219	+	1.06893i
$932$	25.4315			0.833038
$933$	0.515785	−	6.88268i	0.0168861	−	0.225329i
$934$	53.6893	−	16.5609i	1.75677	−	0.541891i
$935$	−0.262405	−	0.0395512i	−0.00858157	−	0.00129346i
$936$	−0.542963	−	0.503796i	−0.0177473	−	0.0164671i
$937$	8.41923	+	36.8870i	0.275044	+	1.20505i	0.903975	+	0.427586i	$0.140636\pi$
$937$	8.41923	+	36.8870i	0.275044	+	1.20505i	−0.628931	+	0.777461i	$0.716507\pi$
$938$	6.49556	−	12.8914i	0.212087	−	0.420919i
$939$	−5.30897	+	23.2601i	−0.173252	+	0.759065i
$940$	5.01535	−	3.41941i	0.163583	−	0.111529i
$941$	−23.0530	+	21.3901i	−0.751507	+	0.697296i	−0.959773	−	0.280776i	$-0.909408\pi$
$941$	−23.0530	+	21.3901i	−0.751507	+	0.697296i	0.208267	+	0.978072i	$0.433218\pi$
$942$	−20.8833	−	14.2380i	−0.680415	−	0.463899i
$943$	27.3394	−	4.12076i	0.890294	−	0.134190i
$944$	16.5775	−	7.98331i	0.539552	−	0.259834i
$945$	−4.48070	+	4.65859i	−0.145757	+	0.151544i
$946$	−1.32442	−	0.637808i	−0.0430607	−	0.0207369i
$947$	−37.8761	−	11.6832i	−1.23081	−	0.379654i	−0.389914	−	0.920851i	$-0.627495\pi$
$947$	−37.8761	−	11.6832i	−1.23081	−	0.379654i	−0.840896	+	0.541197i	$0.817971\pi$
$948$	−7.02427	+	17.8975i	−0.228138	+	0.581285i
$949$	0.348016	+	0.602781i	0.0112971	+	0.0195671i
$950$	−30.0704	+	52.0835i	−0.975614	+	1.68981i
$951$	11.0891	+	13.9053i	0.359590	+	0.450911i
$952$	−1.16610	+	0.0663779i	−0.0377935	+	0.00215132i
$953$	−12.3590	+	15.4977i	−0.400349	+	0.502021i	−0.940616	−	0.339472i	$-0.889752\pi$
$953$	−12.3590	+	15.4977i	−0.400349	+	0.502021i	0.540268	+	0.841493i	$0.318323\pi$
$954$	0.491853	+	1.25322i	0.0159243	+	0.0405746i
$955$	0.117554	+	1.56865i	0.00380397	+	0.0507605i
$956$	1.06537	+	14.2164i	0.0344567	+	0.459792i
$957$	−3.34971	−	8.53492i	−0.108281	−	0.275895i
$958$	18.0027	−	22.5747i	0.581641	−	0.729355i
$959$	5.11961	−	30.2715i	0.165321	−	0.977518i
$960$	−2.10564	−	2.64039i	−0.0679592	−	0.0852181i
$961$	15.4235	−	26.7144i	0.497534	−	0.861753i
$962$	5.44051	+	9.42325i	0.175409	+	0.303818i
$963$	1.49723	−	3.81489i	0.0482477	−	0.122933i
$964$	−43.3148	−	13.3608i	−1.39507	−	0.430323i
$965$	8.39203	+	4.04139i	0.270149	+	0.130097i
$966$	10.0036	−	30.4787i	0.321860	−	0.980635i
$967$	30.4287	−	14.6537i	0.978521	−	0.471231i	0.124925	−	0.992166i	$-0.460131\pi$
$967$	30.4287	−	14.6537i	0.978521	−	0.471231i	0.853596	+	0.520936i	$0.174417\pi$
$968$	−0.738407	+	0.111297i	−0.0237333	+	0.00357722i
$969$	−5.26528	−	3.58980i	−0.169145	−	0.115321i
$970$	−0.387523	+	0.359569i	−0.0124426	+	0.0115451i
$971$	26.0781	−	17.7798i	0.836887	−	0.570580i	−0.0672921	−	0.997733i	$-0.521436\pi$
$971$	26.0781	−	17.7798i	0.836887	−	0.570580i	0.904179	+	0.427153i	$0.140484\pi$
$972$	1.22755	−	5.37824i	0.0393736	−	0.172507i
$973$	−16.3344	−	35.5356i	−0.523657	−	1.13922i
$974$	10.9348	+	47.9084i	0.350373	+	1.53508i
$975$	17.1683	+	15.9299i	0.549826	+	0.510164i
$976$	−12.4810	−	1.88121i	−0.399508	−	0.0602161i
$977$	54.3364	−	16.7606i	1.73838	−	0.536218i	0.746720	−	0.665138i	$-0.231627\pi$
$977$	54.3364	−	16.7606i	1.73838	−	0.536218i	0.991655	+	0.128920i	$0.0411511\pi$
$978$	−4.10735	+	54.8088i	−0.131339	+	1.75259i
$979$	4.82912			0.154339
$980$	−4.62453	+	2.02605i	−0.147725	+	0.0647199i
$981$	−4.12772			−0.131788
$982$	−2.39634	+	31.9770i	−0.0764704	+	1.02043i
$983$	8.47890	−	2.61540i	0.270435	−	0.0834181i	−0.156572	−	0.987667i	$-0.550044\pi$
$983$	8.47890	−	2.61540i	0.270435	−	0.0834181i	0.427007	+	0.904248i	$0.359568\pi$
$984$	8.53209	+	1.28601i	0.271993	+	0.0409964i
$985$	9.05416	+	8.40103i	0.288489	+	0.267679i
$986$	−1.40236	−	6.14413i	−0.0446602	−	0.195669i
$987$	28.0240	+	23.1828i	0.892014	+	0.737917i
$988$	7.05060	−	30.8907i	0.224310	−	0.982764i
$989$	−2.49957	+	1.70418i	−0.0794818	+	0.0541898i
$990$	−0.207445	+	0.192480i	−0.00659302	+	0.00611743i
$991$	21.0972	+	14.3838i	0.670173	+	0.456916i	0.850000	−	0.526782i	$-0.176602\pi$
$991$	21.0972	+	14.3838i	0.670173	+	0.456916i	−0.179827	+	0.983698i	$0.557554\pi$
$992$	−2.82391	+	0.425636i	−0.0896592	+	0.0135140i
$993$	21.1607	−	10.1905i	0.671515	−	0.323384i
$994$	36.1243	+	3.35973i	1.14579	+	0.106564i
$995$	−6.02274	−	2.90040i	−0.190934	−	0.0919489i
$996$	−29.0314	−	8.95501i	−0.919896	−	0.283750i
$997$	−12.5949	+	32.0912i	−0.398884	+	1.01634i	0.580487	+	0.814270i	$0.302862\pi$
$997$	−12.5949	+	32.0912i	−0.398884	+	1.01634i	−0.979371	+	0.202070i	$0.935233\pi$
$998$	−9.27726	−	16.0687i	−0.293666	−	0.508645i
$999$	5.21776	−	9.03742i	0.165083	−	0.285931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.r.a.23.5	✓	276
49.32	even	21	inner	539.2.r.a.375.5	yes	276

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
539.2.r.a.23.5	✓	276	1.1	even	1	trivial
539.2.r.a.375.5	yes	276	49.32	even	21	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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.r (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.141924 + 1.89385i) q^{2} +(-1.56085 + 0.481458i) q^{3} +(-1.58885 - 0.239481i) q^{4} +(0.329056 + 0.305319i) q^{5} +(-0.690286 - 3.02434i) q^{6} +(-2.09779 + 1.61223i) q^{7} +(-0.166167 + 0.728025i) q^{8} +(-0.274269 + 0.186993i) q^{9} +O(q^{10})\)	\(q+(-0.141924 + 1.89385i) q^{2} +(-1.56085 + 0.481458i) q^{3} +(-1.58885 - 0.239481i) q^{4} +(0.329056 + 0.305319i) q^{5} +(-0.690286 - 3.02434i) q^{6} +(-2.09779 + 1.61223i) q^{7} +(-0.166167 + 0.728025i) q^{8} +(-0.274269 + 0.186993i) q^{9} +(-0.624929 + 0.579849i) q^{10} +(-0.826239 - 0.563320i) q^{11} +(2.59526 - 0.391173i) q^{12} +(2.69216 - 1.29647i) q^{13} +(-2.75559 - 4.20171i) q^{14} +(-0.660605 - 0.318131i) q^{15} +(-4.42602 - 1.36524i) q^{16} +(0.215980 - 0.550308i) q^{17} +(-0.315212 - 0.545963i) q^{18} +(-3.29969 + 5.71523i) q^{19} +(-0.449704 - 0.563910i) q^{20} +(2.49811 - 3.52644i) q^{21} +(1.18411 - 1.48482i) q^{22} +(-1.42792 - 3.63828i) q^{23} +(-0.0911521 - 1.21634i) q^{24} +(-0.358593 - 4.78508i) q^{25} +(2.07324 + 5.28253i) q^{26} +(3.39332 - 4.25509i) q^{27} +(3.71918 - 2.05922i) q^{28} +(-3.49978 - 4.38858i) q^{29} +(0.696247 - 1.20593i) q^{30} +(-0.195523 - 0.338655i) q^{31} +(2.66809 - 6.79818i) q^{32} +(1.56085 + 0.481458i) q^{33} +(1.01155 + 0.487136i) q^{34} +(-1.18253 - 0.109981i) q^{35} +(0.480555 - 0.231423i) q^{36} +(1.89601 - 0.285777i) q^{37} +(-10.3555 - 7.06024i) q^{38} +(-3.57785 + 3.31976i) q^{39} +(-0.276958 + 0.188827i) q^{40} +(-1.57410 + 6.89660i) q^{41} +(6.32401 + 5.23153i) q^{42} +(-0.172237 - 0.754620i) q^{43} +(1.17787 + 1.09290i) q^{44} +(-0.147343 - 0.0222083i) q^{45} +(7.09299 - 2.18790i) q^{46} +(-0.628919 + 8.39234i) q^{47} +7.56565 q^{48} +(1.80143 - 6.76423i) q^{49} +9.11311 q^{50} +(-0.0721619 + 0.962934i) q^{51} +(-4.58792 + 1.41519i) q^{52} +(-2.11167 - 0.318284i) q^{53} +(7.57689 + 7.03033i) q^{54} +(-0.0998863 - 0.437630i) q^{55} +(-0.825161 - 1.79514i) q^{56} +(2.39867 - 10.5093i) q^{57} +(8.80801 - 6.00520i) q^{58} +(-2.91202 + 2.70196i) q^{59} +(0.973419 + 0.663665i) q^{60} +(2.69464 - 0.406152i) q^{61} +(0.669110 - 0.322227i) q^{62} +(0.273882 - 0.834457i) q^{63} +(4.14985 + 1.99846i) q^{64} +(1.28171 + 0.395355i) q^{65} +(-1.13333 + 2.88768i) q^{66} +(1.43644 + 2.48799i) q^{67} +(-0.474950 + 0.822637i) q^{68} +(3.98044 + 4.99132i) q^{69} +(0.376118 - 2.22393i) q^{70} +(-4.50183 + 5.64512i) q^{71} +(-0.0905615 - 0.230747i) q^{72} +(0.0174074 + 0.232286i) q^{73} +(0.272129 + 3.63131i) q^{74} +(2.86353 + 7.29615i) q^{75} +(6.61142 - 8.29045i) q^{76} +(2.64148 - 0.150361i) q^{77} +(-5.77933 - 7.24706i) q^{78} +(-3.66280 + 6.34416i) q^{79} +(-1.03957 - 1.80059i) q^{80} +(-2.88399 + 7.34828i) q^{81} +(-12.8377 - 3.95991i) q^{82} +(-10.4293 - 5.02249i) q^{83} +(-4.81365 + 5.00475i) q^{84} +(0.239089 - 0.115139i) q^{85} +(1.45358 - 0.219092i) q^{86} +(7.57555 + 5.16492i) q^{87} +(0.547405 - 0.507917i) q^{88} +(-3.99001 + 2.72034i) q^{89} +(0.0629706 - 0.275892i) q^{90} +(-3.55736 + 7.06010i) q^{91} +(1.39745 + 6.12265i) q^{92} +(0.468229 + 0.434453i) q^{93} +(-15.8045 - 2.38215i) q^{94} +(-2.83075 + 0.873171i) q^{95} +(-0.891445 + 11.8955i) q^{96} +0.620107 q^{97} +(12.5548 + 4.37164i) q^{98} +0.331949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 276 q - q^{3} + 24 q^{4} - 2 q^{5} - 12 q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 276 * q - q^3 + 24 * q^4 - 2 * q^5 - 12 * q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9	\( 276 q - q^{3} + 24 q^{4} - 2 q^{5} - 12 q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9} - 9 q^{10} - 23 q^{11} - 44 q^{12} + 43 q^{13} - 47 q^{14} + 6 q^{15} - 34 q^{16} - 3 q^{17} + 10 q^{18} + 59 q^{19} - 28 q^{20} + 25 q^{21} + 6 q^{23} + 2 q^{24} + 53 q^{25} + q^{26} - 4 q^{27} - 13 q^{28} - 28 q^{29} - 6 q^{30} - 3 q^{31} - 253 q^{32} + q^{33} - 50 q^{34} - 9 q^{35} - 76 q^{36} - 17 q^{37} + 8 q^{38} + 10 q^{39} - 59 q^{40} + 73 q^{41} - 12 q^{42} - 38 q^{44} - 9 q^{45} + 74 q^{46} - 87 q^{47} - 160 q^{48} - 60 q^{49} + 30 q^{50} + 128 q^{51} + 49 q^{52} + 21 q^{53} + 76 q^{54} - 4 q^{55} + 102 q^{56} - 41 q^{57} + 17 q^{58} + 36 q^{59} + 10 q^{60} + 11 q^{61} + 72 q^{62} - 201 q^{63} - 42 q^{64} - 215 q^{65} - 34 q^{66} - 8 q^{67} + 75 q^{68} + 6 q^{69} + 97 q^{70} + q^{71} - 95 q^{72} - 20 q^{73} + 154 q^{74} - 101 q^{75} - 27 q^{76} + 2 q^{77} - 87 q^{78} - 14 q^{79} - 124 q^{80} - 203 q^{81} - 15 q^{82} + 29 q^{83} - 96 q^{84} - 74 q^{85} + 63 q^{86} + 65 q^{87} + 3 q^{88} + 141 q^{89} + 491 q^{90} + 71 q^{91} + 41 q^{92} + 121 q^{93} + 116 q^{94} - 7 q^{95} - 141 q^{96} - 298 q^{97} - 102 q^{98} - 268 q^{99}+O(q^{100}) \) 276 * q - q^3 + 24 * q^4 - 2 * q^5 - 12 * q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9 - 9 * q^10 - 23 * q^11 - 44 * q^12 + 43 * q^13 - 47 * q^14 + 6 * q^15 - 34 * q^16 - 3 * q^17 + 10 * q^18 + 59 * q^19 - 28 * q^20 + 25 * q^21 + 6 * q^23 + 2 * q^24 + 53 * q^25 + q^26 - 4 * q^27 - 13 * q^28 - 28 * q^29 - 6 * q^30 - 3 * q^31 - 253 * q^32 + q^33 - 50 * q^34 - 9 * q^35 - 76 * q^36 - 17 * q^37 + 8 * q^38 + 10 * q^39 - 59 * q^40 + 73 * q^41 - 12 * q^42 - 38 * q^44 - 9 * q^45 + 74 * q^46 - 87 * q^47 - 160 * q^48 - 60 * q^49 + 30 * q^50 + 128 * q^51 + 49 * q^52 + 21 * q^53 + 76 * q^54 - 4 * q^55 + 102 * q^56 - 41 * q^57 + 17 * q^58 + 36 * q^59 + 10 * q^60 + 11 * q^61 + 72 * q^62 - 201 * q^63 - 42 * q^64 - 215 * q^65 - 34 * q^66 - 8 * q^67 + 75 * q^68 + 6 * q^69 + 97 * q^70 + q^71 - 95 * q^72 - 20 * q^73 + 154 * q^74 - 101 * q^75 - 27 * q^76 + 2 * q^77 - 87 * q^78 - 14 * q^79 - 124 * q^80 - 203 * q^81 - 15 * q^82 + 29 * q^83 - 96 * q^84 - 74 * q^85 + 63 * q^86 + 65 * q^87 + 3 * q^88 + 141 * q^89 + 491 * q^90 + 71 * q^91 + 41 * q^92 + 121 * q^93 + 116 * q^94 - 7 * q^95 - 141 * q^96 - 298 * q^97 - 102 * q^98 - 268 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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