LMFDB - Embedded newform 429.2.bv.a.20.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(20,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 36, 55]))

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

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

chi := DirichletCharacter("429.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bv (of order $60$, degree $16$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$52$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			20.20
Character	$\chi$	$=$	429.20
Dual form			429.2.bv.a.236.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.719787 - 0.0377225i) q^{2} +(-0.704391 - 1.58235i) q^{3} +(-1.47237 - 0.154753i) q^{4} +(-2.50517 - 1.27645i) q^{5} +(0.447321 + 1.16553i) q^{6} +(-3.13449 - 3.87078i) q^{7} +(2.47776 + 0.392439i) q^{8} +(-2.00767 + 2.22919i) q^{9} +O(q^{10})$	\(q+(-0.719787 - 0.0377225i) q^{2} +(-0.704391 - 1.58235i) q^{3} +(-1.47237 - 0.154753i) q^{4} +(-2.50517 - 1.27645i) q^{5} +(0.447321 + 1.16553i) q^{6} +(-3.13449 - 3.87078i) q^{7} +(2.47776 + 0.392439i) q^{8} +(-2.00767 + 2.22919i) q^{9} +(1.75504 + 1.01327i) q^{10} +(3.08526 - 1.21703i) q^{11} +(0.792253 + 2.43882i) q^{12} +(1.05031 - 3.44918i) q^{13} +(2.11015 + 2.90438i) q^{14} +(-0.255169 + 4.86318i) q^{15} +(1.12761 + 0.239680i) q^{16} +(-5.00428 + 5.55781i) q^{17} +(1.52918 - 1.52881i) q^{18} +(0.933205 + 2.43108i) q^{19} +(3.49101 + 2.26709i) q^{20} +(-3.91702 + 7.68640i) q^{21} +(-2.26664 + 0.759616i) q^{22} +(0.755917 - 1.30929i) q^{23} +(-1.12434 - 4.19712i) q^{24} +(1.70763 + 2.35035i) q^{25} +(-0.886108 + 2.44306i) q^{26} +(4.94154 + 1.60661i) q^{27} +(4.01613 + 6.18430i) q^{28} +(-1.17130 - 2.63078i) q^{29} +(0.367119 - 3.49083i) q^{30} +(-0.267263 + 0.136177i) q^{31} +(-5.64893 - 1.51363i) q^{32} +(-4.09899 - 4.02471i) q^{33} +(3.81167 - 3.81167i) q^{34} +(2.91159 + 13.6980i) q^{35} +(3.30101 - 2.97150i) q^{36} +(2.26258 - 5.89422i) q^{37} +(-0.580003 - 1.78507i) q^{38} +(-6.19764 + 0.767622i) q^{39} +(-5.70628 - 4.14586i) q^{40} +(4.13209 + 3.34610i) q^{41} +(3.10937 - 5.38482i) q^{42} +(3.62019 - 2.09012i) q^{43} +(-4.73100 + 1.31446i) q^{44} +(7.87499 - 3.02181i) q^{45} +(-0.593489 + 0.913893i) q^{46} +(-3.28746 - 0.520682i) q^{47} +(-0.415017 - 1.95310i) q^{48} +(-3.70248 + 17.4188i) q^{49} +(-1.14047 - 1.75617i) q^{50} +(12.3194 + 4.00365i) q^{51} +(-2.08021 + 4.91595i) q^{52} +(-9.59151 - 3.11647i) q^{53} +(-3.49625 - 1.34283i) q^{54} +(-9.28258 - 0.889321i) q^{55} +(-6.24748 - 10.8209i) q^{56} +(3.18948 - 3.18909i) q^{57} +(0.743846 + 1.93778i) q^{58} +(2.03401 - 1.64711i) q^{59} +(1.12829 - 7.12092i) q^{60} +(3.15645 - 3.50560i) q^{61} +(0.197510 - 0.0879369i) q^{62} +(14.9217 + 0.783860i) q^{63} +(1.81618 + 0.590112i) q^{64} +(-7.03390 + 7.30013i) q^{65} +(2.79858 + 3.05156i) q^{66} +(-0.966352 + 0.258933i) q^{67} +(8.22825 - 7.40875i) q^{68} +(-2.60421 - 0.273876i) q^{69} +(-1.57901 - 9.96946i) q^{70} +(0.489763 + 9.34524i) q^{71} +(-5.84934 + 4.73550i) q^{72} +(-0.846837 + 0.134126i) q^{73} +(-1.85092 + 4.15724i) q^{74} +(2.51624 - 4.35764i) q^{75} +(-0.997809 - 3.72388i) q^{76} +(-14.3816 - 8.12760i) q^{77} +(4.48994 - 0.318734i) q^{78} +(-2.06127 + 6.34392i) q^{79} +(-2.51890 - 2.03977i) q^{80} +(-0.938546 - 8.95093i) q^{81} +(-2.84801 - 2.56436i) q^{82} +(2.14650 + 1.09369i) q^{83} +(6.95680 - 10.7111i) q^{84} +(19.6308 - 7.53557i) q^{85} +(-2.68461 + 1.36788i) q^{86} +(-3.33776 + 3.70650i) q^{87} +(8.12215 - 1.80472i) q^{88} +(-3.71426 + 0.995234i) q^{89} +(-5.78231 + 1.87800i) q^{90} +(-16.6432 + 6.74594i) q^{91} +(-1.31561 + 1.81078i) q^{92} +(0.403738 + 0.326982i) q^{93} +(2.34663 + 0.498791i) q^{94} +(0.765313 - 7.28146i) q^{95} +(1.58397 + 10.0048i) q^{96} +(-2.30155 - 1.49465i) q^{97} +(3.32208 - 12.3982i) q^{98} +(-3.48120 + 9.32101i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9}+O(q^{10}) $ 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9	$ 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9} - 96 q^{10} - 40 q^{13} + 12 q^{15} - 68 q^{16} - 20 q^{18} - 32 q^{19} - 84 q^{21} - 24 q^{22} - 72 q^{24} - 114 q^{30} - 8 q^{31} + 14 q^{33} - 24 q^{34} + 78 q^{36} - 24 q^{37} - 72 q^{39} - 112 q^{40} + 2 q^{42} - 96 q^{43} + 4 q^{45} - 16 q^{46} + 14 q^{48} - 36 q^{49} + 8 q^{52} + 32 q^{54} - 24 q^{55} - 12 q^{57} + 112 q^{58} - 120 q^{60} + 12 q^{61} + 28 q^{63} - 300 q^{66} - 32 q^{67} - 18 q^{69} - 140 q^{70} + 204 q^{72} - 24 q^{73} + 66 q^{75} + 176 q^{76} - 28 q^{78} - 224 q^{79} - 58 q^{81} - 264 q^{82} + 20 q^{84} - 168 q^{85} + 72 q^{87} - 120 q^{88} - 146 q^{93} - 4 q^{94} - 10 q^{96} - 88 q^{97} + 40 q^{99}+O(q^{100}) $ 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9 - 96 * q^10 - 40 * q^13 + 12 * q^15 - 68 * q^16 - 20 * q^18 - 32 * q^19 - 84 * q^21 - 24 * q^22 - 72 * q^24 - 114 * q^30 - 8 * q^31 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 24 * q^37 - 72 * q^39 - 112 * q^40 + 2 * q^42 - 96 * q^43 + 4 * q^45 - 16 * q^46 + 14 * q^48 - 36 * q^49 + 8 * q^52 + 32 * q^54 - 24 * q^55 - 12 * q^57 + 112 * q^58 - 120 * q^60 + 12 * q^61 + 28 * q^63 - 300 * q^66 - 32 * q^67 - 18 * q^69 - 140 * q^70 + 204 * q^72 - 24 * q^73 + 66 * q^75 + 176 * q^76 - 28 * q^78 - 224 * q^79 - 58 * q^81 - 264 * q^82 + 20 * q^84 - 168 * q^85 + 72 * q^87 - 120 * q^88 - 146 * q^93 - 4 * q^94 - 10 * q^96 - 88 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	−0.719787	−	0.0377225i	−0.508967	−	0.0266738i	−0.203875	−	0.978997i	$-0.565354\pi$
$2$	−0.719787	−	0.0377225i	−0.508967	−	0.0266738i	−0.305091	+	0.952323i	$0.598687\pi$
$3$	−0.704391	−	1.58235i	−0.406680	−	0.913571i
$3$	−0.704391	−	1.58235i	−0.406680	−	0.913571i
$4$	−1.47237	−	0.154753i	−0.736186	−	0.0773763i
$5$	−2.50517	−	1.27645i	−1.12035	−	0.570845i	−0.207127	−	0.978314i	$-0.566411\pi$
$5$	−2.50517	−	1.27645i	−1.12035	−	0.570845i	−0.913219	+	0.407469i	$0.866411\pi$
$6$	0.447321	+	1.16553i	0.182618	+	0.475825i
$7$	−3.13449	−	3.87078i	−1.18473	−	1.46302i	−0.854760	−	0.519023i	$-0.826296\pi$
$7$	−3.13449	−	3.87078i	−1.18473	−	1.46302i	−0.329966	−	0.943993i	$-0.607037\pi$
$8$	2.47776	+	0.392439i	0.876021	+	0.138748i
$9$	−2.00767	+	2.22919i	−0.669222	+	0.743062i
$10$	1.75504	+	1.01327i	0.554992	+	0.320425i
$11$	3.08526	−	1.21703i	0.930242	−	0.366947i
$11$	3.08526	−	1.21703i	0.930242	−	0.366947i
$12$	0.792253	+	2.43882i	0.228704	+	0.704026i
$13$	1.05031	−	3.44918i	0.291302	−	0.956631i
$13$	1.05031	−	3.44918i	0.291302	−	0.956631i
$14$	2.11015	+	2.90438i	0.563962	+	0.776227i
$15$	−0.255169	+	4.86318i	−0.0658844	+	1.25567i
$16$	1.12761	+	0.239680i	0.281901	+	0.0599200i
$17$	−5.00428	+	5.55781i	−1.21372	+	1.34797i	−0.293792	+	0.955869i	$0.594917\pi$
$17$	−5.00428	+	5.55781i	−1.21372	+	1.34797i	−0.919924	+	0.392098i	$0.871749\pi$
$18$	1.52918	−	1.52881i	0.360432	−	0.360343i
$19$	0.933205	+	2.43108i	0.214092	+	0.557729i	0.998005	−	0.0631427i	$-0.0201123\pi$
$19$	0.933205	+	2.43108i	0.214092	+	0.557729i	−0.783913	+	0.620871i	$0.786779\pi$
$20$	3.49101	+	2.26709i	0.780614	+	0.506937i
$21$	−3.91702	+	7.68640i	−0.854763	+	1.67731i
$22$	−2.26664	+	0.759616i	−0.483250	+	0.161951i
$23$	0.755917	−	1.30929i	0.157620	−	0.273005i	−0.776390	−	0.630253i	$-0.782951\pi$
$23$	0.755917	−	1.30929i	0.157620	−	0.273005i	0.934010	+	0.357247i	$0.116285\pi$
$24$	−1.12434	−	4.19712i	−0.229504	−	0.856733i
$25$	1.70763	+	2.35035i	0.341527	+	0.470071i
$26$	−0.886108	+	2.44306i	−0.173780	+	0.479123i
$27$	4.94154	+	1.60661i	0.950999	+	0.309193i
$28$	4.01613	+	6.18430i	0.758977	+	1.16872i
$29$	−1.17130	−	2.63078i	−0.217504	−	0.488523i	0.771533	−	0.636190i	$-0.219490\pi$
$29$	−1.17130	−	2.63078i	−0.217504	−	0.488523i	−0.989037	+	0.147667i	$0.952824\pi$
$30$	0.367119	−	3.49083i	0.0670264	−	0.637335i
$31$	−0.267263	+	0.136177i	−0.0480019	+	0.0244582i	−0.477827	−	0.878454i	$-0.658575\pi$
$31$	−0.267263	+	0.136177i	−0.0480019	+	0.0244582i	0.429825	+	0.902912i	$0.358575\pi$
$32$	−5.64893	−	1.51363i	−0.998599	−	0.267574i
$33$	−4.09899	−	4.02471i	−0.713543	−	0.700611i
$34$	3.81167	−	3.81167i	0.653696	−	0.653696i
$35$	2.91159	+	13.6980i	0.492149	+	2.31538i
$36$	3.30101	−	2.97150i	0.550168	−	0.495250i
$37$	2.26258	−	5.89422i	0.371966	−	0.969004i	−0.612034	−	0.790832i	$-0.709648\pi$
$37$	2.26258	−	5.89422i	0.371966	−	0.969004i	0.983999	−	0.178172i	$-0.0570184\pi$
$38$	−0.580003	−	1.78507i	−0.0940889	−	0.289576i
$39$	−6.19764	+	0.767622i	−0.992417	+	0.122918i
$40$	−5.70628	−	4.14586i	−0.902243	−	0.655518i
$41$	4.13209	+	3.34610i	0.645325	+	0.522574i	0.895177	−	0.445710i	$-0.147049\pi$
$41$	4.13209	+	3.34610i	0.645325	+	0.522574i	−0.249853	+	0.968284i	$0.580382\pi$
$42$	3.10937	−	5.38482i	0.479786	−	0.830895i
$43$	3.62019	−	2.09012i	0.552074	−	0.318740i	−0.197884	−	0.980225i	$-0.563407\pi$
$43$	3.62019	−	2.09012i	0.552074	−	0.318740i	0.749958	+	0.661485i	$0.230074\pi$
$44$	−4.73100	+	1.31446i	−0.713224	+	0.198163i
$45$	7.87499	−	3.02181i	1.17393	−	0.450465i
$46$	−0.593489	+	0.913893i	−0.0875052	+	0.134746i
$47$	−3.28746	−	0.520682i	−0.479525	−	0.0759492i	−0.0880070	−	0.996120i	$-0.528050\pi$
$47$	−3.28746	−	0.520682i	−0.479525	−	0.0759492i	−0.391518	+	0.920171i	$0.628050\pi$
$48$	−0.415017	−	1.95310i	−0.0599026	−	0.281905i
$49$	−3.70248	+	17.4188i	−0.528926	+	2.48840i
$50$	−1.14047	−	1.75617i	−0.161287	−	0.248360i
$51$	12.3194	+	4.00365i	1.72506	+	0.560623i
$52$	−2.08021	+	4.91595i	−0.288473	+	0.681719i
$53$	−9.59151	−	3.11647i	−1.31750	−	0.428080i	−0.435861	−	0.900014i	$-0.643556\pi$
$53$	−9.59151	−	3.11647i	−1.31750	−	0.428080i	−0.881634	+	0.471934i	$0.843556\pi$
$54$	−3.49625	−	1.34283i	−0.475779	−	0.182736i
$55$	−9.28258	−	0.889321i	−1.25166	−	0.119916i
$56$	−6.24748	−	10.8209i	−0.834854	−	1.44601i
$57$	3.18948	−	3.18909i	0.422457	−	0.422405i
$58$	0.743846	+	1.93778i	0.0976717	+	0.254444i
$59$	2.03401	−	1.64711i	0.264806	−	0.214436i	−0.487717	−	0.873002i	$-0.662170\pi$
$59$	2.03401	−	1.64711i	0.264806	−	0.214436i	0.752523	+	0.658566i	$0.228837\pi$
$60$	1.12829	−	7.12092i	0.145662	−	0.919307i
$61$	3.15645	−	3.50560i	0.404143	−	0.448846i	−0.506377	−	0.862312i	$-0.669015\pi$
$61$	3.15645	−	3.50560i	0.404143	−	0.448846i	0.910519	+	0.413467i	$0.135682\pi$
$62$	0.197510	−	0.0879369i	0.0250837	−	0.0111680i
$63$	14.9217	+	0.783860i	1.87996	+	0.0987571i
$64$	1.81618	+	0.590112i	0.227022	+	0.0737640i
$65$	−7.03390	+	7.30013i	−0.872447	+	0.905470i
$66$	2.79858	+	3.05156i	0.344482	+	0.375621i
$67$	−0.966352	+	0.258933i	−0.118059	+	0.0316337i	−0.317365	−	0.948304i	$-0.602798\pi$
$67$	−0.966352	+	0.258933i	−0.118059	+	0.0316337i	0.199306	+	0.979937i	$0.436131\pi$
$68$	8.22825	−	7.40875i	0.997821	−	0.898442i
$69$	−2.60421	−	0.273876i	−0.313510	−	0.0329708i
$70$	−1.57901	−	9.96946i	−0.188727	−	1.19158i
$71$	0.489763	+	9.34524i	0.0581242	+	1.10908i	0.859573	+	0.511013i	$0.170730\pi$
$71$	0.489763	+	9.34524i	0.0581242	+	1.10908i	−0.801449	+	0.598063i	$0.795937\pi$
$72$	−5.84934	+	4.73550i	−0.689351	+	0.558084i
$73$	−0.846837	+	0.134126i	−0.0991147	+	0.0156982i	−0.205795	−	0.978595i	$-0.565978\pi$
$73$	−0.846837	+	0.134126i	−0.0991147	+	0.0156982i	0.106680	+	0.994293i	$0.465978\pi$
$74$	−1.85092	+	4.15724i	−0.215165	+	0.483269i
$75$	2.51624	−	4.35764i	0.290551	−	0.503177i
$76$	−0.997809	−	3.72388i	−0.114457	−	0.427158i
$77$	−14.3816	−	8.12760i	−1.63893	−	0.926226i
$78$	4.48994	−	0.318734i	0.508386	−	0.0360895i
$79$	−2.06127	+	6.34392i	−0.231911	+	0.713747i	0.765606	+	0.643310i	$0.222439\pi$
$79$	−2.06127	+	6.34392i	−0.231911	+	0.713747i	−0.997516	+	0.0704371i	$0.977561\pi$
$80$	−2.51890	−	2.03977i	−0.281622	−	0.228053i
$81$	−0.938546	−	8.95093i	−0.104283	−	0.994548i
$82$	−2.84801	−	2.56436i	−0.314510	−	0.283186i
$83$	2.14650	+	1.09369i	0.235609	+	0.120049i	0.567809	−	0.823160i	$-0.307791\pi$
$83$	2.14650	+	1.09369i	0.235609	+	0.120049i	−0.332201	+	0.943209i	$0.607791\pi$
$84$	6.95680	−	10.7111i	0.759049	−	1.16868i
$85$	19.6308	−	7.53557i	2.12926	−	0.817347i
$86$	−2.68461	+	1.36788i	−0.289489	+	0.147502i
$87$	−3.33776	+	3.70650i	−0.357846	+	0.397378i
$88$	8.12215	−	1.80472i	0.865824	−	0.192384i
$89$	−3.71426	+	0.995234i	−0.393711	+	0.105495i	−0.450243	−	0.892906i	$-0.648663\pi$
$89$	−3.71426	+	0.995234i	−0.393711	+	0.105495i	0.0565315	+	0.998401i	$0.481996\pi$
$90$	−5.78231	+	1.87800i	−0.609509	+	0.197958i
$91$	−16.6432	+	6.74594i	−1.74468	+	0.707167i
$92$	−1.31561	+	1.81078i	−0.137162	+	0.188787i
$93$	0.403738	+	0.326982i	0.0418657	+	0.0339064i
$94$	2.34663	+	0.498791i	0.242036	+	0.0514464i
$95$	0.765313	−	7.28146i	0.0785194	−	0.747062i
$96$	1.58397	+	10.0048i	0.161663	+	1.02111i
$97$	−2.30155	−	1.49465i	−0.233687	−	0.151758i	0.422484	−	0.906371i	$-0.361158\pi$
$97$	−2.30155	−	1.49465i	−0.233687	−	0.151758i	−0.656171	+	0.754612i	$0.727825\pi$
$98$	3.32208	−	12.3982i	0.335580	−	1.25240i
$99$	−3.48120	+	9.32101i	−0.349874	+	0.936797i
$100$	−2.15055	−	3.72486i	−0.215055	−	0.372486i
$101$	−9.18208	−	10.1977i	−0.913651	−	1.01471i	−0.999830	−	0.0184324i	$-0.994132\pi$
$101$	−9.18208	−	10.1977i	−0.913651	−	1.01471i	0.0861793	−	0.996280i	$-0.472534\pi$
$102$	−8.71630	−	3.34649i	−0.863042	−	0.331352i
$103$	−5.64046	+	7.76342i	−0.555771	+	0.764953i	−0.990781	−	0.135473i	$-0.956745\pi$
$103$	−5.64046	+	7.76342i	−0.555771	+	0.764953i	0.435010	+	0.900425i	$0.356745\pi$
$104$	3.95600	−	8.13407i	0.387917	−	0.797611i
$105$	19.6241	−	14.2559i	1.91511	−	1.39123i
$106$	6.78629	+	2.60501i	0.659142	+	0.253021i
$107$	−15.7772	+	1.65825i	−1.52524	+	0.160309i	−0.829714	−	0.558189i	$-0.811496\pi$
$107$	−15.7772	+	1.65825i	−1.52524	+	0.160309i	−0.695528	+	0.718499i	$0.744830\pi$
$108$	−7.02716	−	3.13025i	−0.676189	−	0.301209i
$109$	6.40156	+	6.40156i	0.613158	+	0.613158i	0.943768	−	0.330610i	$-0.107254\pi$
$109$	6.40156	+	6.40156i	0.613158	+	0.613158i	−0.330610	+	0.943768i	$0.607254\pi$
$110$	6.64794	+	0.990284i	0.633856	+	0.0944199i
$111$	−10.9205	+	0.571641i	−1.03652	+	0.0542578i
$112$	−2.60672	−	5.11598i	−0.246312	−	0.483415i
$113$	1.79091	−	4.02246i	0.168475	−	0.378401i	−0.809501	−	0.587119i	$-0.800262\pi$
$113$	1.79091	−	4.02246i	0.168475	−	0.378401i	0.977976	+	0.208717i	$0.0669289\pi$
$114$	−2.41605	+	2.17515i	−0.226284	+	0.203722i
$115$	−3.56494	+	2.31510i	−0.332432	+	0.215884i
$116$	1.31747	+	4.05475i	0.122324	+	0.376474i
$117$	5.58021	+	9.26614i	0.515890	+	0.856655i
$118$	−1.52619	+	1.10884i	−0.140497	+	0.102077i
$119$	37.1989	+	1.94951i	3.41002	+	0.178711i
$120$	−2.54075	+	11.9496i	−0.231937	+	1.09085i
$121$	8.03770	−	7.50969i	0.730700	−	0.682699i
$122$	−2.40422	+	2.40422i	−0.217667	+	0.217667i
$123$	2.38410	−	8.89538i	0.214967	−	0.802070i
$124$	0.414585	−	0.159144i	0.0372308	−	0.0142916i
$125$	0.921365	+	5.81727i	0.0824094	+	0.520313i
$126$	−10.7109	−	1.12710i	−0.954201	−	0.100410i
$127$	3.74889	−	17.6372i	0.332660	−	1.56504i	−0.420553	−	0.907268i	$-0.638164\pi$
$127$	3.74889	−	17.6372i	0.332660	−	1.56504i	0.753213	−	0.657776i	$-0.228503\pi$
$128$	9.63453	+	3.69835i	0.851580	+	0.326891i
$129$	−5.85733	−	4.25615i	−0.515709	−	0.374733i
$130$	5.33829	−	4.98921i	0.468199	−	0.437582i
$131$			10.6554i			0.930968i	0.885056	+	0.465484i	$0.154120\pi$
$131$			10.6554i			0.930968i	−0.885056	+	0.465484i	$0.845880\pi$
$132$	5.41241	+	6.56020i	0.471090	+	0.570992i
$133$	6.48505	−	11.2324i	0.562325	−	0.973976i
$134$	0.705336	−	0.149924i	0.0609317	−	0.0129514i
$135$	−10.3286	−	10.3325i	−0.888947	−	0.889276i
$136$	−14.5805	+	11.8071i	−1.25027	+	1.01245i
$137$	2.56233	−	0.134286i	0.218914	−	0.0114728i	0.0574366	−	0.998349i	$-0.481707\pi$
$137$	2.56233	−	0.134286i	0.218914	−	0.0114728i	0.161478	+	0.986876i	$0.448374\pi$
$138$	1.86415	+	0.295370i	0.158687	+	0.0251436i
$139$	0.343568	−	3.26883i	0.0291411	−	0.277259i	−0.970242	−	0.242137i	$-0.922152\pi$
$139$	0.343568	−	3.26883i	0.0291411	−	0.277259i	0.999383	−	0.0351214i	$-0.0111818\pi$
$140$	−2.16715	−	20.6191i	−0.183158	−	1.74263i
$141$	1.49175	+	5.56867i	0.125628	+	0.468967i
$142$		−	6.74506i		−	0.566033i
$143$	−0.957276	−	11.9199i	−0.0800515	−	0.996791i
$144$	−2.79815	+	2.03245i	−0.233179	+	0.169370i
$145$	−0.423751	+	8.08565i	−0.0351906	+	0.671476i
$146$	0.614602	−	0.0645973i	0.0508648	−	0.00534611i
$147$	30.1706	−	6.41102i	2.48843	−	0.528772i
$148$	−4.24351	+	8.32835i	−0.348814	+	0.684586i
$149$	0.125521	+	2.39508i	0.0102831	+	0.196213i	0.998940	+	0.0460236i	$0.0146550\pi$
$149$	0.125521	+	2.39508i	0.0102831	+	0.196213i	−0.988657	+	0.150189i	$0.952012\pi$
$150$	−1.97554	+	3.04166i	−0.161302	+	0.248350i
$151$	0.577252	−	3.64463i	0.0469761	−	0.296595i	−0.953004	−	0.302959i	$-0.902026\pi$
$151$	0.577252	−	3.64463i	0.0469761	−	0.296595i	0.999980	+	0.00636336i	$0.00202553\pi$
$152$	1.35821	+	6.38986i	0.110165	+	0.518286i
$153$	−2.34248	−	22.3137i	−0.189378	−	1.80396i
$154$	10.0451	+	6.39265i	0.809455	+	0.515135i
$155$	0.843363			0.0677406
$156$	9.24403	−	0.171124i	0.740115	−	0.0137009i
$157$	−10.3993	+	7.55553i	−0.829954	+	0.602997i	−0.919546	−	0.392982i	$-0.871444\pi$
$157$	−10.3993	+	7.55553i	−0.829954	+	0.602997i	0.0895924	+	0.995979i	$0.471444\pi$
$158$	1.72298	−	4.48852i	0.137073	−	0.357087i
$159$	1.82482	+	17.3723i	0.144718	+	1.37772i
$160$	12.2195	+	11.0025i	0.966033	+	0.869820i
$161$	−7.43737	+	1.17796i	−0.586147	+	0.0928365i
$162$	0.337903	+	6.47817i	0.0265481	+	0.508973i
$163$	0.324404	−	0.499538i	0.0254093	−	0.0391268i	−0.825738	−	0.564054i	$-0.809241\pi$
$163$	0.324404	−	0.499538i	0.0254093	−	0.0391268i	0.851147	+	0.524927i	$0.175908\pi$
$164$	−5.56616	−	5.56616i	−0.434644	−	0.434644i
$165$	5.13135	+	15.3147i	0.399475	+	1.19225i
$166$	−1.50376	−	0.868199i	−0.116715	−	0.0673853i
$167$	−0.599003	+	11.4297i	−0.0463522	+	0.884453i	0.872199	+	0.489151i	$0.162693\pi$
$167$	−0.599003	+	11.4297i	−0.0463522	+	0.884453i	−0.918551	+	0.395302i	$0.870640\pi$
$168$	−12.7219	+	17.5079i	−0.981513	+	1.35076i
$169$	−10.7937	−	7.24539i	−0.830286	−	0.557337i
$170$	−14.4143	+	4.68348i	−1.10552	+	0.359207i
$171$	−7.29290	−	2.80052i	−0.557702	−	0.214161i
$172$	−5.65372	+	2.51720i	−0.431092	+	0.191935i
$173$	2.03511	+	0.906088i	0.154726	+	0.0688886i	0.482639	−	0.875820i	$-0.339678\pi$
$173$	2.03511	+	0.906088i	0.154726	+	0.0688886i	−0.327912	+	0.944708i	$0.606345\pi$
$174$	2.54230	−	2.54198i	0.192731	−	0.192707i
$175$	3.74513	−	13.9770i	0.283105	−	1.05656i
$176$	3.77066	−	0.632849i	0.284224	−	0.0477028i
$177$	−4.03905	−	2.05831i	−0.303594	−	0.154712i
$178$	2.71102	−	0.576246i	0.203200	−	0.0431914i
$179$	−0.205493	−	1.95513i	−0.0153593	−	0.146134i	0.984155	−	0.177313i	$-0.0567404\pi$
$179$	−0.205493	−	1.95513i	−0.0153593	−	0.146134i	−0.999514	+	0.0311792i	$0.990074\pi$
$180$	−12.0626	+	3.23056i	−0.899090	+	0.240791i
$181$	−10.2965	+	3.34554i	−0.765334	+	0.248672i	−0.665566	−	0.746339i	$-0.731810\pi$
$181$	−10.2965	+	3.34554i	−0.765334	+	0.248672i	−0.0997678	+	0.995011i	$0.531810\pi$
$182$	12.2340	−	4.22782i	0.906846	−	0.313387i
$183$	−7.77046	−	2.52531i	−0.574409	−	0.186676i
$184$	2.38680	−	2.94745i	0.175957	−	0.217289i
$185$	−13.1918	+	11.8780i	−0.969881	+	0.873285i
$186$	−0.278271	−	0.250587i	−0.0204038	−	0.0183740i
$187$	−8.67551	+	23.2376i	−0.634416	+	1.69930i
$188$	4.75978	+	1.27538i	0.347143	+	0.0930167i
$189$	−9.27036	−	24.1635i	−0.674320	−	1.75764i
$190$	−0.825537	+	5.21224i	−0.0598907	+	0.378135i
$191$	−6.57899	−	0.691480i	−0.476039	−	0.0500337i	−0.136529	−	0.990636i	$-0.543595\pi$
$191$	−6.57899	−	0.691480i	−0.476039	−	0.0500337i	−0.339510	+	0.940602i	$0.610261\pi$
$192$	−0.345535	−	3.28950i	−0.0249369	−	0.237399i
$193$	−3.04918	+	1.98016i	−0.219485	+	0.142535i	−0.649699	−	0.760192i	$-0.725105\pi$
$193$	−3.04918	+	1.98016i	−0.219485	+	0.142535i	0.430214	+	0.902727i	$0.358438\pi$
$194$	1.60025	+	1.16265i	0.114891	+	0.0834733i
$195$	16.5060	+	5.98794i	1.18202	+	0.428806i
$196$	8.14703	−	25.0740i	0.581931	−	1.79100i
$197$	4.05346	+	15.1277i	0.288797	+	1.07781i	0.946020	+	0.324109i	$0.105064\pi$
$197$	4.05346	+	15.1277i	0.288797	+	1.07781i	−0.657223	+	0.753696i	$0.728269\pi$
$198$	2.85734	−	6.57783i	0.203062	−	0.467466i
$199$	−21.4717	+	12.3967i	−1.52209	+	0.878777i	−0.522427	+	0.852684i	$0.674973\pi$
$199$	−21.4717	+	12.3967i	−1.52209	+	0.878777i	−0.999660	+	0.0260935i	$0.991693\pi$
$200$	3.30873	+	6.49376i	0.233963	+	0.459178i
$201$	1.09041	+	1.34672i	0.0769118	+	0.0949902i
$202$	6.22446	+	7.68657i	0.437951	+	0.540825i
$203$	−6.51172	+	12.7800i	−0.457033	+	0.896979i
$204$	−17.5191	−	7.80132i	−1.22658	−	0.546201i
$205$	−6.08047	−	13.6570i	−0.424678	−	0.953844i
$206$	4.35279	−	5.37524i	0.303273	−	0.374511i
$207$	1.40101	+	4.31369i	0.0973773	+	0.299822i
$208$	2.01103	−	3.63758i	0.139440	−	0.252221i
$209$	5.83787	+	6.36479i	0.403814	+	0.440262i
$210$	−14.6629	+	9.52094i	−1.01184	+	0.657007i
$211$	14.8684	+	16.5130i	1.02358	+	1.13680i	0.990523	+	0.137350i	$0.0438584\pi$
$211$	14.8684	+	16.5130i	1.02358	+	1.13680i	0.0330595	+	0.999453i	$0.489475\pi$
$212$	13.6400	+	6.07292i	0.936799	+	0.417090i
$213$	14.4425	−	7.35768i	0.989581	−	0.504140i
$214$	11.4188	−	0.598434i	0.780573	−	0.0409081i
$215$	−11.7371	+	0.615117i	−0.800465	+	0.0419506i
$216$	11.6134	+	5.92006i	0.790195	+	0.402809i
$217$	1.36485	+	0.607669i	0.0926518	+	0.0412512i
$218$	−4.36628	−	4.84924i	−0.295722	−	0.328432i
$219$	0.808738	+	1.24552i	0.0546494	+	0.0841641i
$220$	13.5298	+	2.74592i	0.912179	+	0.185130i
$221$	13.9139	+	23.0981i	0.935949	+	1.55374i
$222$	7.88198		0.000486542i	0.529004		3.26546e-5i
$223$	−0.794957	+	0.981690i	−0.0532343	+	0.0657388i	−0.803068	−	0.595888i	$-0.796800\pi$
$223$	−0.794957	+	0.981690i	−0.0532343	+	0.0657388i	0.749833	+	0.661627i	$0.230134\pi$
$224$	11.8476	+	26.6102i	0.791602	+	1.77797i
$225$	−8.66774	−	0.912098i	−0.577849	−	0.0608065i
$226$	−1.44081	+	2.82776i	−0.0958415	+	0.188100i
$227$	1.97885	+	2.44368i	0.131341	+	0.162193i	0.838574	−	0.544788i	$-0.183390\pi$
$227$	1.97885	+	2.44368i	0.131341	+	0.162193i	−0.707233	+	0.706981i	$0.750057\pi$
$228$	−5.18963	+	4.20195i	−0.343692	+	0.278281i
$229$	−0.761870	−	1.49525i	−0.0503458	−	0.0988091i	0.864463	−	0.502697i	$-0.167659\pi$
$229$	−0.761870	−	1.49525i	−0.0503458	−	0.0988091i	−0.914809	+	0.403888i	$0.867659\pi$
$230$	2.65333	−	1.53190i	0.174955	−	0.101010i
$231$	−2.73047	+	28.4817i	−0.179652	+	1.87396i
$232$	−1.86978	−	6.97810i	−0.122757	−	0.458135i
$233$	−1.47100	+	4.52727i	−0.0963683	+	0.296591i	−0.987608	−	0.156942i	$-0.949837\pi$
$233$	−1.47100	+	4.52727i	−0.0963683	+	0.296591i	0.891240	+	0.453533i	$0.149837\pi$
$234$	−3.66702	−	6.88015i	−0.239721	−	0.449769i
$235$	7.57101	+	5.50066i	0.493878	+	0.358824i
$236$	−3.24972	+	2.11039i	−0.211539	+	0.137375i
$237$	11.4902	−	1.20696i	0.746372	−	0.0784003i
$238$	−26.7018	−	2.80647i	−1.73082	−	0.181916i
$239$	4.15091	−	26.2078i	0.268500	−	1.69524i	−0.372766	−	0.927925i	$-0.621591\pi$
$239$	4.15091	−	26.2078i	0.268500	−	1.69524i	0.641266	−	0.767318i	$-0.278409\pi$
$240$	−1.45334	+	5.42258i	−0.0938124	+	0.350026i
$241$	−16.7623	−	4.49146i	−1.07976	−	0.289320i	−0.325261	−	0.945624i	$-0.605452\pi$
$241$	−16.7623	−	4.49146i	−1.07976	−	0.289320i	−0.754497	+	0.656304i	$0.772119\pi$
$242$	−6.06872	+	5.10218i	−0.390112	+	0.327980i
$243$	−13.5024	+	7.79006i	−0.866180	+	0.499733i
$244$	−5.18998	+	4.67308i	−0.332254	+	0.299163i
$245$	31.5095	−	38.9110i	2.01307	−	2.48593i
$246$	−2.05160	+	6.31285i	−0.130805	+	0.402493i
$247$	9.36540	−	0.665416i	0.595906	−	0.0423394i
$248$	−0.715655	+	0.232531i	−0.0454442	+	0.0147657i
$249$	0.218636	−	4.16690i	0.0138555	−	0.264066i
$250$	−0.443745	−	4.22195i	−0.0280649	−	0.267020i
$251$	−1.24413	+	0.264447i	−0.0785285	+	0.0166918i	−0.247008	−	0.969013i	$-0.579448\pi$
$251$	−1.24413	+	0.264447i	−0.0785285	+	0.0166918i	0.168480	+	0.985705i	$0.446114\pi$
$252$	−21.8490	−	3.46331i	−1.37636	−	0.218168i
$253$	0.738767	−	4.95946i	0.0464459	−	0.311799i
$254$	−3.36372	+	12.5536i	−0.211059	+	0.787682i
$255$	−25.7517	−	25.7549i	−1.61263	−	1.61283i
$256$	−10.2844	−	4.57891i	−0.642774	−	0.286182i
$257$	−2.85380	+	1.27059i	−0.178015	+	0.0792574i	−0.493809	−	0.869570i	$-0.664396\pi$
$257$	−2.85380	+	1.27059i	−0.178015	+	0.0792574i	0.315794	+	0.948828i	$0.397729\pi$
$258$	4.05548	+	3.28448i	0.252483	+	0.204483i
$259$	−29.9072	+	9.71745i	−1.85835	+	0.603813i
$260$	11.4862	−	9.66000i	0.712346	−	0.599088i
$261$	8.21607	+	2.67068i	0.508562	+	0.165311i
$262$	0.401948	−	7.66963i	0.0248325	−	0.473832i
$263$	8.27129	+	4.77543i	0.510030	+	0.294466i	0.732846	−	0.680395i	$-0.238192\pi$
$263$	8.27129	+	4.77543i	0.510030	+	0.294466i	−0.222816	+	0.974860i	$0.571525\pi$
$264$	−8.57687	−	11.5809i	−0.527870	−	0.712753i
$265$	20.0504	+	20.0504i	1.23168	+	1.23168i
$266$	−5.09157	+	7.84033i	−0.312184	+	0.480722i
$267$	4.19110	+	5.17623i	0.256491	+	0.316780i
$268$	1.46290	−	0.231701i	0.0893609	−	0.0141534i
$269$	−6.65515	−	5.99232i	−0.405772	−	0.365358i	0.440825	−	0.897593i	$-0.354686\pi$
$269$	−6.65515	−	5.99232i	−0.405772	−	0.365358i	−0.846597	+	0.532234i	$0.821352\pi$
$270$	7.04465	+	7.82679i	0.428724	+	0.476324i
$271$	2.69233	−	7.01375i	0.163547	−	0.426055i	−0.827177	−	0.561941i	$-0.810055\pi$
$271$	2.69233	−	7.01375i	0.163547	−	0.426055i	0.990724	+	0.135886i	$0.0433881\pi$
$272$	−6.97494	+	5.06759i	−0.422918	+	0.307268i
$273$	22.3977	+	21.5836i	1.35557	+	1.30630i
$274$	−1.84940			−0.111726
$275$	8.12894	+	5.17323i	0.490193	+	0.311957i
$276$	3.79199	+	0.806257i	0.228251	+	0.0485309i
$277$	3.77125	+	17.7423i	0.226592	+	1.06603i	0.933459	+	0.358685i	$0.116775\pi$
$277$	3.77125	+	17.7423i	0.226592	+	1.06603i	−0.706866	+	0.707347i	$0.749892\pi$
$278$	−0.370604	+	2.33990i	−0.0222274	+	0.140338i
$279$	0.233011	−	0.869178i	0.0139500	−	0.0520363i
$280$	1.83862	+	35.0829i	0.109878	+	2.09660i
$281$	9.13620	−	17.9308i	0.545020	−	1.06966i	−0.440125	−	0.897936i	$-0.645066\pi$
$281$	9.13620	−	17.9308i	0.545020	−	1.06966i	0.985145	−	0.171725i	$-0.0549341\pi$
$282$	−0.863681	−	4.06453i	−0.0514314	−	0.242039i
$283$	9.31128	−	0.978655i	0.553498	−	0.0581750i	0.176349	−	0.984328i	$-0.443571\pi$
$283$	9.31128	−	0.978655i	0.553498	−	0.0581750i	0.377149	+	0.926153i	$0.376905\pi$
$284$	0.725086	−	13.8355i	0.0430260	−	0.820984i
$285$	−12.0609	+	3.91800i	−0.714426	+	0.232082i
$286$	0.239388	+	8.61589i	0.0141553	+	0.509468i
$287$		−	26.4827i		−	1.56323i
$288$	14.7153	−	9.55366i	0.867108	−	0.562955i
$289$	−4.06951	−	38.7188i	−0.239383	−	2.27757i
$290$	0.610021	−	5.80396i	0.0358217	−	0.340820i
$291$	−0.743862	+	4.69468i	−0.0436059	+	0.275207i
$292$	1.26762	−	0.0664329i	0.0741816	−	0.00388769i
$293$	16.2414	−	13.1520i	0.948833	−	0.768350i	−0.0240346	−	0.999711i	$-0.507651\pi$
$293$	16.2414	−	13.1520i	0.948833	−	0.768350i	0.972868	+	0.231361i	$0.0743179\pi$
$294$	−21.9583	+	3.47646i	−1.28063	+	0.202751i
$295$	−7.19800	+	1.52998i	−0.419084	+	0.0890791i
$296$	7.91925	−	13.7165i	0.460297	−	0.797258i
$297$	17.2012	−	1.05715i	0.998117	−	0.0613420i
$298$		−	1.72869i		−	0.100140i
$299$	−3.72203	−	3.98245i	−0.215250	−	0.230311i
$300$	−4.37921	+	6.02668i	−0.252834	+	0.347950i
$301$	−19.4378	−	7.46149i	−1.12038	−	0.430073i
$302$	−0.552983	+	2.60158i	−0.0318206	+	0.149704i
$303$	−9.66861	+	21.7125i	−0.555447	+	1.24735i
$304$	0.469605	+	2.96497i	0.0269337	+	0.170053i
$305$	−12.3822	+	4.75307i	−0.709001	+	0.272160i
$306$	0.844359	+	16.1495i	0.0482688	+	0.923205i
$307$	16.1431	−	16.1431i	0.921338	−	0.921338i	−0.0757861	−	0.997124i	$-0.524147\pi$
$307$	16.1431	−	16.1431i	0.921338	−	0.921338i	0.997124	+	0.0757861i	$0.0241466\pi$
$308$	19.9173	+	14.1924i	1.13489	+	0.808690i
$309$	16.2575	+	3.45670i	0.924859	+	0.196645i
$310$	−0.607042	−	0.0318137i	−0.0344777	−	0.00180690i
$311$	−20.6507	+	15.0036i	−1.17100	+	0.850778i	−0.991128	−	0.132913i	$-0.957567\pi$
$311$	−20.6507	+	15.0036i	−1.17100	+	0.850778i	−0.179868	+	0.983691i	$0.557567\pi$
$312$	−15.6575	−	0.530212i	−0.886432	−	0.0300173i
$313$	−0.0217301	−	0.0668784i	−0.00122826	−	0.00378019i	0.950441	−	0.310906i	$-0.100633\pi$
$313$	−0.0217301	−	0.0668784i	−0.00122826	−	0.00378019i	−0.951669	+	0.307126i	$0.900633\pi$
$314$	7.77029	−	5.04609i	0.438503	−	0.284767i
$315$	−36.3808	−	21.0105i	−2.04983	−	1.18381i
$316$	4.01669	−	9.02163i	0.225957	−	0.507507i
$317$	−12.1817	−	23.9079i	−0.684191	−	1.34280i	−0.927855	−	0.372941i	$-0.878349\pi$
$317$	−12.1817	−	23.9079i	−0.684191	−	1.34280i	0.243664	−	0.969860i	$-0.421651\pi$
$318$	−0.658157	−	12.5732i	−0.0369076	−	0.705072i
$319$	−6.81548	−	6.69114i	−0.381594	−	0.374632i
$320$	−3.79659	−	3.79659i	−0.212236	−	0.212236i
$321$	13.7373	+	23.7970i	0.766740	+	1.32822i
$322$	5.39776	−	0.567328i	0.300805	−	0.0316159i
$323$	−18.1815	−	6.97923i	−1.01165	−	0.388335i
$324$	−0.00328997	+	13.3243i	−0.000182776	+	0.740242i
$325$	9.90034	−	3.42135i	0.549172	−	0.189782i
$326$	−0.252346	+	0.347324i	−0.0139761	+	0.0192365i
$327$	5.62031	−	14.6387i	0.310804	−	0.809522i
$328$	8.92520	+	9.91243i	0.492812	+	0.547323i
$329$	8.28906	+	14.3571i	0.456991	+	0.791531i
$330$	−3.11577	−	11.2169i	−0.171517	−	0.617471i
$331$	−6.50885	+	24.2913i	−0.357759	+	1.33517i	0.519219	+	0.854641i	$0.326223\pi$
$331$	−6.50885	+	24.2913i	−0.357759	+	1.33517i	−0.876977	+	0.480532i	$0.840444\pi$
$332$	−2.99119	−	1.94250i	−0.164163	−	0.106609i
$333$	8.59681	+	16.8773i	0.471102	+	0.924873i
$334$	0.862309	−	8.20433i	0.0471835	−	0.448921i
$335$	2.75139	+	0.584826i	0.150325	+	0.0319525i
$336$	−6.25912	+	7.72840i	−0.341463	+	0.421619i
$337$	18.3977	−	25.3223i	1.00219	−	1.37939i	0.0782165	−	0.996936i	$-0.475077\pi$
$337$	18.3977	−	25.3223i	1.00219	−	1.37939i	0.923973	−	0.382459i	$-0.124923\pi$
$338$	7.49587	+	5.62230i	0.407721	+	0.305813i
$339$	−7.62644		0.000470769i	−0.414211		2.55686e-5i
$340$	−30.0700	+	8.05724i	−1.63078	+	0.436965i
$341$	−0.658846	+	0.745409i	−0.0356785	+	0.0403662i
$342$	5.14370	+	2.29088i	0.278139	+	0.123877i
$343$	47.9644	−	24.4391i	2.58983	−	1.31959i
$344$	9.79021	−	3.75811i	0.527853	−	0.202624i
$345$	6.17441	+	4.01025i	0.332419	+	0.215904i
$346$	−1.43067	−	0.728960i	−0.0769130	−	0.0391891i
$347$	11.3882	+	10.2540i	0.611349	+	0.550461i	0.915579	−	0.402137i	$-0.131733\pi$
$347$	11.3882	+	10.2540i	0.611349	+	0.550461i	−0.304230	+	0.952599i	$0.598399\pi$
$348$	5.48802	−	4.94082i	0.294189	−	0.264856i
$349$	13.2089	+	10.6963i	0.707055	+	0.572562i	0.913963	−	0.405798i	$-0.133007\pi$
$349$	13.2089	+	10.6963i	0.707055	+	0.572562i	−0.206907	+	0.978361i	$0.566340\pi$
$350$	−3.22295	+	9.91921i	−0.172274	+	0.530204i
$351$	10.7316	−	15.3568i	0.572812	−	0.819687i
$352$	−19.2705	+	2.20496i	−1.02712	+	0.117525i
$353$	−6.84831	−	25.5582i	−0.364499	−	1.36033i	−0.868099	−	0.496391i	$-0.834658\pi$
$353$	−6.84831	−	25.5582i	−0.364499	−	1.36033i	0.503600	−	0.863937i	$-0.332008\pi$
$354$	2.82961	+	1.63391i	0.150392	+	0.0868414i
$355$	10.7018	−	24.0366i	0.567991	−	1.27573i
$356$	5.62280	−	0.890564i	0.298008	−	0.0471998i
$357$	−23.1178	−	60.2349i	−1.22352	−	3.18797i
$358$	0.0741587	+	1.41503i	0.00391941	+	0.0747868i
$359$	−2.61396	−	16.5039i	−0.137959	−	0.871042i	−0.955461	−	0.295116i	$-0.904642\pi$
$359$	−2.61396	−	16.5039i	−0.137959	−	0.871042i	0.817502	−	0.575926i	$-0.195358\pi$
$360$	20.6982	−	4.39687i	1.09089	−	0.231735i
$361$	9.08046	−	8.17609i	0.477919	−	0.430320i
$362$	7.53751	−	2.01967i	0.396163	−	0.106151i
$363$	−17.5446	−	7.42870i	−0.920855	−	0.389906i
$364$	25.5489	−	7.35696i	1.33913	−	0.385610i
$365$	2.29267	+	0.744935i	0.120004	+	0.0389917i
$366$	5.49782	+	2.11081i	0.287376	+	0.110334i
$367$	−11.9829	+	5.33514i	−0.625503	+	0.278492i	−0.694910	−	0.719096i	$-0.744556\pi$
$367$	−11.9829	+	5.33514i	−0.625503	+	0.278492i	0.0694071	+	0.997588i	$0.477889\pi$
$368$	1.16619	−	1.29518i	0.0607916	−	0.0675160i
$369$	−15.7550	+	2.49335i	−0.820170	+	0.129798i
$370$	9.94337	−	8.05198i	0.516931	−	0.418602i
$371$	18.0014	+	46.8951i	0.934584	+	2.43467i
$372$	−0.543852	−	0.543919i	−0.0281974	−	0.0282009i
$373$	−5.78814	−	10.0254i	−0.299699	−	0.519093i	0.676368	−	0.736564i	$-0.263553\pi$
$373$	−5.78814	−	10.0254i	−0.299699	−	0.519093i	−0.976067	+	0.217470i	$0.930219\pi$
$374$	7.12110	−	16.3989i	0.368223	−	0.847967i
$375$	8.55596	−	5.55556i	0.441828	−	0.286888i
$376$	−7.94119	−	2.58025i	−0.409536	−	0.133066i
$377$	−10.3043	+	1.27690i	−0.530696	+	0.0657637i
$378$	5.76118	+	17.7423i	0.296323	+	0.912565i
$379$	17.3944	+	26.7850i	0.893489	+	1.37585i	0.926459	+	0.376396i	$0.122837\pi$
$379$	17.3944	+	26.7850i	0.893489	+	1.37585i	−0.0329699	+	0.999456i	$0.510497\pi$
$380$	−2.25365	+	10.6026i	−0.115610	+	0.543902i
$381$	−30.5488	+	6.49139i	−1.56506	+	0.332564i
$382$	4.70939	+	0.745894i	0.240953	+	0.0381633i
$383$	−10.9808	+	16.9090i	−0.561093	+	0.864008i	−0.999394	−	0.0348206i	$-0.988914\pi$
$383$	−10.9808	+	16.9090i	−0.561093	+	0.864008i	0.438300	+	0.898829i	$0.355581\pi$
$384$	−0.934389	−	17.8503i	−0.0476828	−	0.910918i
$385$	25.6538	+	38.7183i	1.30744	+	1.97327i
$386$	2.26946	−	1.31027i	0.115513	−	0.0666912i
$387$	−2.60888	+	12.2663i	−0.132617	+	0.623533i
$388$	3.15745	+	2.55685i	0.160295	+	0.129804i
$389$	−16.5030	−	11.9901i	−0.836733	−	0.607922i	0.0847230	−	0.996405i	$-0.472999\pi$
$389$	−16.5030	−	11.9901i	−0.836733	−	0.607922i	−0.921456	+	0.388482i	$0.872999\pi$
$390$	−11.6549	−	4.93269i	−0.590169	−	0.249777i
$391$	3.49395	+	10.7533i	0.176697	+	0.543817i
$392$	−16.0097	+	41.7066i	−0.808610	+	2.10650i
$393$	16.8606	−	7.50558i	0.850505	−	0.378606i
$394$	−2.34697	−	11.0416i	−0.118239	−	0.556270i
$395$	13.2615	−	13.2615i	0.667259	−	0.667259i
$396$	6.56808	−	13.1853i	0.330058	−	0.662585i
$397$	−13.5998	−	3.64405i	−0.682554	−	0.182890i	−0.0991506	−	0.995072i	$-0.531613\pi$
$397$	−13.5998	−	3.64405i	−0.682554	−	0.182890i	−0.583403	+	0.812183i	$0.698279\pi$
$398$	15.9227	−	8.11301i	0.798132	−	0.406668i
$399$	−22.3417	−	2.34960i	−1.11848	−	0.117627i
$400$	1.36220	+	3.05956i	0.0681101	+	0.152978i
$401$	−18.9948	−	29.2494i	−0.948553	−	1.46064i	−0.886585	−	0.462565i	$-0.846929\pi$
$401$	−18.9948	−	29.2494i	−0.948553	−	1.46064i	−0.0619679	−	0.998078i	$-0.519738\pi$
$402$	−0.734064	−	1.01048i	−0.0366118	−	0.0503983i
$403$	0.188993	+	1.06487i	0.00941440	+	0.0530448i
$404$	11.9413	+	16.4358i	0.594103	+	0.817712i
$405$	−9.07418	+	23.6216i	−0.450900	+	1.17377i
$406$	5.16915	−	8.95323i	0.256541	−	0.444341i
$407$	−0.192765	−	20.9388i	−0.00955502	−	1.03790i
$408$	28.9533	+	14.7547i	1.43340	+	0.730465i
$409$	−5.66468	−	3.67869i	−0.280101	−	0.181899i	0.396941	−	0.917844i	$-0.370072\pi$
$409$	−5.66468	−	3.67869i	−0.280101	−	0.181899i	−0.677042	+	0.735945i	$0.736738\pi$
$410$	3.86147	+	10.0595i	0.190705	+	0.496802i
$411$	−2.01737	−	3.95991i	−0.0995094	−	0.195328i
$412$	9.50627	−	10.5578i	0.468340	−	0.520144i
$413$	−12.7512	−	2.71035i	−0.627446	−	0.133368i
$414$	−0.845710	−	3.15779i	−0.0415644	−	0.155197i
$415$	−3.98130	−	5.47978i	−0.195434	−	0.268992i
$416$	−11.1539	+	17.8944i	−0.546863	+	0.877346i
$417$	−5.41444	+	1.75889i	−0.265146	+	0.0861332i
$418$	−3.96193	−	4.80152i	−0.193784	−	0.234850i
$419$	−20.0467	−	11.5740i	−0.979347	−	0.565426i	−0.0772739	−	0.997010i	$-0.524622\pi$
$419$	−20.0467	−	11.5740i	−0.979347	−	0.565426i	−0.902073	+	0.431584i	$0.857955\pi$
$420$	−31.1001	+	17.9531i	−1.51753	+	0.876021i
$421$	−19.4894	−	3.08682i	−0.949856	−	0.150442i	−0.337765	−	0.941230i	$-0.609671\pi$
$421$	−19.4894	−	3.08682i	−0.949856	−	0.150442i	−0.612090	+	0.790788i	$0.709671\pi$
$422$	−10.0792	−	12.4467i	−0.490646	−	0.605898i
$423$	7.76081	−	6.28300i	0.377344	−	0.305490i
$424$	−22.5424	−	11.4859i	−1.09476	−	0.557807i
$425$	−21.6083	−	2.27112i	−1.04816	−	0.110166i
$426$	−10.6731	+	4.75116i	−0.517111	+	0.230194i
$427$	−23.4633	−	1.22966i	−1.13547	−	0.0595073i
$428$	23.4866			1.13527
$429$	−18.1871	+	9.91100i	−0.878083	+	0.478508i
$430$	8.47144			0.408529
$431$	19.4575	+	1.01973i	0.937236	+	0.0491184i	0.514834	−	0.857290i	$-0.327854\pi$
$431$	19.4575	+	1.01973i	0.937236	+	0.0491184i	0.422402	+	0.906409i	$0.361187\pi$
$432$	5.18703	+	2.99601i	0.249561	+	0.144146i
$433$	−0.626233	−	0.0658197i	−0.0300948	−	0.00316309i	0.0894691	−	0.995990i	$-0.471483\pi$
$433$	−0.626233	−	0.0658197i	−0.0300948	−	0.00316309i	−0.119564	+	0.992827i	$0.538150\pi$
$434$	−0.959476	−	0.488878i	−0.0460563	−	0.0234669i
$435$	13.0928	−	5.02493i	0.627752	−	0.240927i
$436$	−8.43482	−	10.4161i	−0.403955	−	0.498843i
$437$	3.88841	+	0.615864i	0.186008	+	0.0294607i
$438$	−0.535135	−	0.927014i	−0.0255698	−	0.0442944i
$439$	15.8593	+	9.15636i	0.756922	+	0.437009i	0.828190	−	0.560448i	$-0.189371\pi$
$439$	15.8593	+	9.15636i	0.756922	+	0.437009i	−0.0712675	+	0.997457i	$0.522704\pi$
$440$	−22.6510	−	5.84637i	−1.07984	−	0.278715i
$441$	−31.3964	−	43.2247i	−1.49507	−	2.05832i
$442$	−9.14373	−	17.1506i	−0.434923	−	0.815769i
$443$	−16.9386	−	23.3140i	−0.804777	−	1.10768i	−0.992108	−	0.125384i	$-0.959984\pi$
$443$	−16.9386	−	23.3140i	−0.804777	−	1.10768i	0.187331	−	0.982297i	$-0.440016\pi$
$444$	16.1675	+	0.848301i	0.767274	+	0.0402586i
$445$	10.5752	+	2.24783i	0.501314	+	0.106558i
$446$	0.609232	−	0.676621i	0.0288480	−	0.0320389i
$447$	3.70144	−	1.88569i	0.175072	−	0.0891902i
$448$	−3.40861	−	8.87972i	−0.161041	−	0.419527i
$449$	−2.62377	−	1.70390i	−0.123823	−	0.0804118i	0.481241	−	0.876588i	$-0.340186\pi$
$449$	−2.62377	−	1.70390i	−0.123823	−	0.0804118i	−0.605065	+	0.796176i	$0.706853\pi$
$450$	6.20452	+	0.983485i	0.292484	+	0.0463619i
$451$	16.8209	+	5.29475i	0.792065	+	0.249320i
$452$	−3.25938	+	5.64541i	−0.153308	+	0.265538i
$453$	−6.17369	+	1.65383i	−0.290065	+	0.0777035i
$454$	−1.33217	−	1.83358i	−0.0625219	−	0.0860540i
$455$	50.3048	+	4.34443i	2.35833	+	0.203670i
$456$	9.15430	−	6.65012i	0.428689	−	0.311421i
$457$	−15.7398	−	24.2372i	−0.736278	−	1.13377i	−0.986209	−	0.165505i	$-0.947074\pi$
$457$	−15.7398	−	24.2372i	−0.736278	−	1.13377i	0.249931	−	0.968264i	$-0.419592\pi$
$458$	0.491980	+	1.10500i	0.0229887	+	0.0516335i
$459$	−33.6581	+	19.4242i	−1.57102	+	0.906644i
$460$	5.60718	−	2.85700i	0.261436	−	0.133208i
$461$	−17.9349	−	4.80563i	−0.835310	−	0.223821i	−0.184281	−	0.982874i	$-0.558996\pi$
$461$	−17.9349	−	4.80563i	−0.835310	−	0.223821i	−0.651029	+	0.759053i	$0.725662\pi$
$462$	3.03976	−	20.3978i	0.141422	−	0.948990i
$463$	0.955255	−	0.955255i	0.0443945	−	0.0443945i	−0.684561	−	0.728956i	$-0.740006\pi$
$463$	0.955255	−	0.955255i	0.0443945	−	0.0443945i	0.728956	+	0.684561i	$0.240006\pi$
$464$	−0.690217	−	3.24722i	−0.0320425	−	0.150748i
$465$	−0.594057	−	1.33450i	−0.0275487	−	0.0618858i
$466$	1.22959	−	3.20318i	0.0569595	−	0.148384i
$467$	8.52634	+	26.2414i	0.394552	+	1.21431i	0.929310	+	0.369301i	$0.120403\pi$
$467$	8.52634	+	26.2414i	0.394552	+	1.21431i	−0.534758	+	0.845005i	$0.679597\pi$
$468$	−6.78219	−	14.5068i	−0.313507	−	0.670575i
$469$	4.03130	+	2.92891i	0.186148	+	0.135244i
$470$	−5.24202	−	4.24490i	−0.241796	−	0.195803i
$471$	19.2807	+	11.1333i	0.888406	+	0.512995i
$472$	5.68619	−	3.28292i	0.261728	−	0.151109i
$473$	8.62552	−	10.8544i	0.396602	−	0.499087i
$474$	−8.31606	+	0.435312i	−0.381970	+	0.0199945i
$475$	−4.12033	+	6.34476i	−0.189054	+	0.291117i
$476$	−54.4690	−	8.62704i	−2.49658	−	0.395420i
$477$	26.2038	−	15.1244i	1.19979	−	0.692500i
$478$	−3.97640	+	18.7075i	−0.181876	+	0.855660i
$479$	−10.9959	−	16.9322i	−0.502415	−	0.773651i	0.492926	−	0.870071i	$-0.335927\pi$
$479$	−10.9959	−	16.9322i	−0.502415	−	0.773651i	−0.995341	+	0.0964202i	$0.969261\pi$
$480$	8.80246	−	27.0855i	0.401775	−	1.23628i
$481$	−17.9538	−	13.9948i	−0.818625	−	0.638107i
$482$	11.8959	+	3.86521i	0.541843	+	0.176056i
$483$	7.10277	+	10.9388i	0.323187	+	0.497732i
$484$	−12.9966	+	9.81321i	−0.590756	+	0.446055i
$485$	3.85795	+	6.68216i	0.175180	+	0.303421i
$486$	10.0127	−	5.09784i	0.454186	−	0.231243i
$487$	9.90918	+	25.8143i	0.449028	+	1.16976i	0.952174	+	0.305556i	$0.0988423\pi$
$487$	9.90918	+	25.8143i	0.449028	+	1.16976i	−0.503146	+	0.864201i	$0.667824\pi$
$488$	9.19667	−	7.44732i	0.416314	−	0.337124i
$489$	−1.01895	−	0.161451i	−0.0460786	−	0.00730104i
$490$	−24.1480	+	26.8190i	−1.09089	+	1.21156i
$491$	−31.9461	+	14.2233i	−1.44171	+	0.641890i	−0.970712	−	0.240245i	$-0.922772\pi$
$491$	−31.9461	+	14.2233i	−1.44171	+	0.641890i	−0.470997	+	0.882135i	$0.656106\pi$
$492$	−4.88687	+	12.7284i	−0.220317	+	0.573840i
$493$	20.4829	+	6.65528i	0.922502	+	0.299739i
$494$	−6.76619	+	0.125673i	−0.304425	+	0.00565428i
$495$	20.6188	−	18.9071i	0.926746	−	0.849813i
$496$	−0.334006	+	0.0894967i	−0.0149973	+	0.00401852i
$497$	34.6382	−	31.1883i	1.55373	−	1.39899i
$498$	−0.314557	+	2.99103i	−0.0140956	+	0.134031i
$499$	−4.29533	−	27.1197i	−0.192285	−	1.21404i	−0.875279	−	0.483618i	$-0.839322\pi$
$499$	−4.29533	−	27.1197i	−0.192285	−	1.21404i	0.682994	−	0.730424i	$-0.260678\pi$
$500$	−0.456355	−	8.70778i	−0.0204088	−	0.389424i
$501$	18.5077	−	7.10311i	0.826861	−	0.317344i
$502$	0.905482	−	0.143414i	0.0404136	−	0.00640089i
$503$	4.54282	−	10.2033i	0.202554	−	0.454944i	−0.783495	−	0.621398i	$-0.786565\pi$
$503$	4.54282	−	10.2033i	0.202554	−	0.454944i	0.986049	+	0.166454i	$0.0532316\pi$
$504$	36.6648	+	7.79807i	1.63318	+	0.347354i
$505$	9.98580	+	37.2675i	0.444362	+	1.65838i
$506$	−0.718839	+	3.54189i	−0.0319563	+	0.157456i
$507$	−3.86175	+	22.1830i	−0.171506	+	0.985183i
$508$	−8.24916	+	25.3883i	−0.365997	+	1.12642i
$509$	8.78328	+	7.11256i	0.389312	+	0.315259i	0.803916	−	0.594743i	$-0.202746\pi$
$509$	8.78328	+	7.11256i	0.389312	+	0.315259i	−0.414603	+	0.910002i	$0.636080\pi$
$510$	17.5642	+	19.5094i	0.777756	+	0.863892i
$511$	3.17357	+	2.85750i	0.140391	+	0.126408i
$512$	−11.1605	−	5.68655i	−0.493228	−	0.251312i
$513$	0.705655	+	13.5126i	0.0311554	+	0.596595i
$514$	2.10206	−	0.806904i	0.0927178	−	0.0355910i
$515$	24.0399	−	12.2489i	1.05933	−	0.539753i
$516$	7.96552	+	7.17308i	0.350663	+	0.315777i
$517$	−10.7763	+	2.39448i	−0.473943	+	0.105309i
$518$	21.8934	−	5.86632i	0.961942	−	0.257751i
$519$	0.000238179	−	3.85849i	1.04549e−5	−	0.169369i
$520$	−20.2932	+	15.3276i	−0.889914	+	0.672160i
$521$	−14.4047	+	19.8264i	−0.631081	+	0.868609i	−0.998101	−	0.0616046i	$-0.980378\pi$
$521$	−14.4047	+	19.8264i	−0.631081	+	0.868609i	0.367020	+	0.930213i	$0.380378\pi$
$522$	−5.81308	−	2.23225i	−0.254432	−	0.0977031i
$523$	11.2329	+	2.38762i	0.491179	+	0.104403i	0.446841	−	0.894613i	$-0.352549\pi$
$523$	11.2329	+	2.38762i	0.491179	+	0.104403i	0.0443379	+	0.999017i	$0.485882\pi$
$524$	1.64895	−	15.6887i	0.0720349	−	0.685366i
$525$	−24.7546	+	3.91918i	−1.08038	+	0.171047i
$526$	−5.77343	−	3.74931i	−0.251733	−	0.163478i
$527$	0.580610	−	2.16687i	0.0252918	−	0.0943902i
$528$	−3.65740	−	5.52073i	−0.159168	−	0.240259i
$529$	10.3572	+	17.9392i	0.450312	+	0.779963i
$530$	−13.6756	−	15.1883i	−0.594032	−	0.659739i
$531$	−0.411903	+	7.84105i	−0.0178751	+	0.340273i
$532$	−11.2867	+	15.5348i	−0.489339	+	0.673517i
$533$	15.8813	−	10.7379i	0.687895	−	0.465111i
$534$	−2.82144	−	3.88389i	−0.122096	−	0.168072i
$535$	41.6413	+	15.9846i	1.80031	+	0.691075i
$536$	−2.49600	+	0.262341i	−0.107811	+	0.0113314i
$537$	−2.94896	+	1.70234i	−0.127257	+	0.0734614i
$538$	4.56425	+	4.56425i	0.196779	+	0.196779i
$539$	9.77600	+	58.2476i	0.421082	+	2.50890i
$540$	13.6086	+	16.8116i	0.585622	+	0.723457i
$541$	7.02802	+	13.7933i	0.302158	+	0.593019i	0.991302	−	0.131606i	$-0.0420133\pi$
$541$	7.02802	+	13.7933i	0.302158	+	0.593019i	−0.689144	+	0.724624i	$0.742013\pi$
$542$	−2.20248	+	4.94685i	−0.0946046	+	0.212485i
$543$	12.5466	+	13.9361i	0.538426	+	0.598057i
$544$	36.6812	−	23.8211i	1.57269	−	1.02132i
$545$	−7.86574	−	24.2082i	−0.336931	−	1.03697i
$546$	−15.3074	−	16.3805i	−0.655098	−	0.701020i
$547$	0.275118	−	0.199885i	0.0117632	−	0.00854646i	−0.581888	−	0.813269i	$-0.697686\pi$
$547$	0.275118	−	0.199885i	0.0117632	−	0.00854646i	0.593651	+	0.804722i	$0.297686\pi$
$548$	−3.79348	−	0.198808i	−0.162050	−	0.00849266i
$549$	1.47752	+	14.0744i	0.0630591	+	0.600681i
$550$	−5.65596	−	4.03027i	−0.241171	−	0.171851i
$551$	5.30258	−	5.30258i	0.225897	−	0.225897i
$552$	−6.34513	−	1.70059i	−0.270067	−	0.0723820i
$553$	31.0169	−	11.9063i	1.31897	−	0.506307i
$554$	−2.04521	−	12.9130i	−0.0868927	−	0.548619i
$555$	28.0873	+	12.5073i	1.19224	+	0.530907i
$556$	−1.01172	+	4.75977i	−0.0429065	+	0.201859i
$557$	27.8028	+	10.6725i	1.17804	+	0.452208i	0.867058	−	0.498207i	$-0.166008\pi$
$557$	27.8028	+	10.6725i	1.17804	+	0.452208i	0.310984	+	0.950415i	$0.399341\pi$
$558$	−0.200506	+	0.616834i	−0.00848808	+	0.0261127i
$559$	−3.40690	−	14.6820i	−0.144096	−	0.620981i
$560$			16.1438i			0.682198i
$561$	42.8810	−	2.64069i	1.81044	−	0.111490i
$562$	−7.25251	+	12.5617i	−0.305929	+	0.529884i
$563$	−3.23760	+	0.688174i	−0.136449	+	0.0290031i	−0.275630	−	0.961264i	$-0.588886\pi$
$563$	−3.23760	+	0.688174i	−0.136449	+	0.0290031i	0.139181	+	0.990267i	$0.455553\pi$
$564$	−1.33465	−	8.43001i	−0.0561989	−	0.354968i
$565$	−9.62100	+	7.79093i	−0.404759	+	0.327767i
$566$	−6.73906	+	0.353179i	−0.283264	+	0.0148452i
$567$	−31.7052	+	31.6895i	−1.33149	+	1.33083i
$568$	−2.45392	+	23.3475i	−0.102964	+	0.979638i
$569$	1.61019	+	15.3199i	0.0675026	+	0.642244i	0.975003	+	0.222193i	$0.0713214\pi$
$569$	1.61019	+	15.3199i	0.0675026	+	0.642244i	−0.907500	+	0.420052i	$0.862012\pi$
$570$	8.82908	−	2.36516i	0.369810	−	0.0990657i
$571$		−	26.2271i		−	1.09757i	−0.835964	−	0.548785i	$-0.815091\pi$
$571$		−	26.2271i		−	1.09757i	0.835964	−	0.548785i	$-0.184909\pi$
$572$	−0.435166	+	17.6987i	−0.0181952	+	0.740018i
$573$	3.54002	+	10.8973i	0.147886	+	0.455243i
$574$	−0.998994	+	19.0619i	−0.0416972	+	0.795630i
$575$	4.36812	−	0.459108i	0.182163	−	0.0191461i
$576$	−4.96175	+	2.86385i	−0.206740	+	0.119327i
$577$	−1.75830	+	3.45085i	−0.0731988	+	0.143661i	−0.924706	−	0.380682i	$-0.875689\pi$
$577$	−1.75830	+	3.45085i	−0.0731988	+	0.143661i	0.851507	+	0.524343i	$0.175689\pi$
$578$	1.46861	+	28.0228i	0.0610862	+	1.16559i
$579$	5.28113	+	3.43007i	0.219476	+	0.142549i
$580$	1.87519	−	11.8395i	0.0778632	−	0.491609i
$581$	−2.49473	−	11.7368i	−0.103499	−	0.486924i
$582$	0.712517	−	3.35111i	0.0295348	−	0.138908i
$583$	−33.3852	+	2.05798i	−1.38267	+	0.0852329i
$584$	−2.15089			−0.0890046
$585$	−2.15163	−	30.3361i	−0.0889590	−	1.25424i
$586$	−12.1865	+	8.85400i	−0.503419	+	0.365755i
$587$	−5.98652	+	15.5954i	−0.247090	+	0.643691i	−0.999894	−	0.0145532i	$-0.995367\pi$
$587$	−5.98652	+	15.5954i	−0.247090	+	0.643691i	0.752804	+	0.658245i	$0.228701\pi$
$588$	−45.4145	+	4.77043i	−1.87286	+	0.196729i
$589$	−0.580470	−	0.522657i	−0.0239178	−	0.0215357i
$590$	5.23875	−	0.829736i	0.215676	−	0.0341597i
$591$	21.0821	−	17.0698i	0.867203	−	0.702159i
$592$	3.96402	−	6.10406i	0.162920	−	0.250875i
$593$	−5.61765	−	5.61765i	−0.230689	−	0.230689i	0.582291	−	0.812980i	$-0.302156\pi$
$593$	−5.61765	−	5.61765i	−0.230689	−	0.230689i	−0.812980	+	0.582291i	$0.802156\pi$
$594$	−12.4211	+	0.112050i	−0.509644	+	0.00459746i
$595$	−90.7011	−	52.3663i	−3.71838	−	2.14681i
$596$	0.185832	−	3.54588i	0.00761196	−	0.145245i
$597$	34.7403	+	25.2436i	1.42183	+	1.03315i
$598$	2.52884	+	3.00692i	0.103412	+	0.122962i
$599$	32.5829	−	10.5868i	1.33130	−	0.432566i	0.444940	−	0.895560i	$-0.353225\pi$
$599$	32.5829	−	10.5868i	1.33130	−	0.432566i	0.886361	+	0.462995i	$0.153225\pi$
$600$	7.94476	−	9.80972i	0.324343	−	0.400480i
$601$	−32.6405	+	14.5325i	−1.33143	+	0.592793i	−0.944256	−	0.329212i	$-0.893217\pi$
$601$	−32.6405	+	14.5325i	−1.33143	+	0.592793i	−0.387178	+	0.922005i	$0.626550\pi$
$602$	13.7096	+	6.10393i	0.558763	+	0.248778i
$603$	1.36290	−	2.67403i	0.0555017	−	0.108895i
$604$	−1.41395	+	5.27692i	−0.0575326	+	0.214715i
$605$	−29.7215	+	8.55335i	−1.20835	+	0.347743i
$606$	7.77839	−	15.2636i	0.315976	−	0.620042i
$607$	−24.5647	+	5.22139i	−0.997050	+	0.211930i	−0.677407	−	0.735608i	$-0.736896\pi$
$607$	−24.5647	+	5.22139i	−0.997050	+	0.211930i	−0.319643	+	0.947538i	$0.603563\pi$
$608$	−1.59186	−	15.1455i	−0.0645584	−	0.614232i
$609$	24.8092	+	1.30173i	1.00532	+	0.0527488i
$610$	9.09183	−	2.95411i	0.368117	−	0.119609i
$611$	−5.24876	+	10.7922i	−0.212342	+	0.436604i
$612$	−0.00410082	+	33.2166i	−0.000165766	+	1.34270i
$613$	−13.9293	+	17.2013i	−0.562600	+	0.694754i	−0.976487	−	0.215575i	$-0.930838\pi$
$613$	−13.9293	+	17.2013i	−0.562600	+	0.694754i	0.413887	+	0.910328i	$0.364171\pi$
$614$	−12.2286	+	11.0107i	−0.493506	+	0.444355i
$615$	−17.3271	+	19.2413i	−0.698695	+	0.775883i
$616$	−32.4445	−	25.7821i	−1.30723	−	1.03879i
$617$	−12.5028	−	3.35012i	−0.503345	−	0.134871i	−0.00179309	−	0.999998i	$-0.500571\pi$
$617$	−12.5028	−	3.35012i	−0.503345	−	0.134871i	−0.501552	+	0.865127i	$0.667237\pi$
$618$	−11.5716	−	3.10136i	−0.465477	−	0.124755i
$619$	6.90901	−	43.6218i	0.277697	−	1.75331i	−0.316131	−	0.948716i	$-0.602384\pi$
$619$	6.90901	−	43.6218i	0.277697	−	1.75331i	0.593827	−	0.804592i	$-0.297616\pi$
$620$	−1.24175	−	0.130513i	−0.0498697	−	0.00524151i
$621$	5.83891	−	5.25542i	0.234307	−	0.210893i
$622$	15.4301	−	10.0204i	0.618691	−	0.401783i
$623$	15.4947	+	11.2575i	0.620780	+	0.451023i
$624$	−7.17248	−	0.619876i	−0.287129	−	0.0248149i
$625$	9.60604	−	29.5644i	0.384242	−	1.18257i
$626$	0.0131182	+	0.0489579i	0.000524310	+	0.00195675i
$627$	5.95919	−	13.7209i	0.237987	−	0.547959i
$628$	16.4809	−	9.51524i	0.657658	−	0.379699i
$629$	21.4364	+	42.0713i	0.854725	+	1.67749i
$630$	25.3939	+	16.4954i	1.01172	+	0.657194i
$631$	−0.399921	−	0.493862i	−0.0159206	−	0.0196603i	0.769123	−	0.639100i	$-0.220693\pi$
$631$	−0.399921	−	0.493862i	−0.0159206	−	0.0196603i	−0.785044	+	0.619440i	$0.787360\pi$
$632$	−7.59692	+	14.9098i	−0.302189	+	0.593080i
$633$	15.6562	−	35.1586i	0.622279	−	1.39743i
$634$	7.86636	+	17.6681i	0.312413	+	0.701691i
$635$	−31.9045	+	39.3988i	−1.26609	+	1.56349i
$636$	0.00159636	−	25.8610i	6.32997e−5	−	1.02545i
$637$	56.1919	+	31.0656i	2.22640	+	1.23086i
$638$	4.65329	+	5.07330i	0.184226	+	0.200854i
$639$	−21.8156	−	17.6704i	−0.863011	−	0.699029i
$640$	−19.4154	−	21.5630i	−0.767460	−	0.852351i
$641$	2.09292	+	0.931830i	0.0826655	+	0.0368051i	0.447653	−	0.894207i	$-0.352260\pi$
$641$	2.09292	+	0.931830i	0.0826655	+	0.0368051i	−0.364987	+	0.931012i	$0.618927\pi$
$642$	−8.99023	−	17.6470i	−0.354816	−	0.696472i
$643$	−36.4682	+	1.91122i	−1.43816	+	0.0753710i	−0.755398	−	0.655266i	$-0.772557\pi$
$643$	−36.4682	+	1.91122i	−1.43816	+	0.0753710i	−0.682766	+	0.730637i	$0.739223\pi$
$644$	11.1329	−	0.583449i	0.438697	−	0.0229911i
$645$	9.24085	+	18.1390i	0.363858	+	0.714221i
$646$	12.8235	+	5.70941i	0.504536	+	0.224634i
$647$	−26.2676	−	29.1731i	−1.03268	−	1.14691i	−0.989007	−	0.147866i	$-0.952759\pi$
$647$	−26.2676	−	29.1731i	−1.03268	−	1.14691i	−0.0436769	−	0.999046i	$-0.513907\pi$
$648$	1.18720	−	22.5466i	0.0466376	−	0.885713i
$649$	4.27089	−	7.55722i	0.167647	−	0.296647i
$650$	−7.25520	+	2.08918i	−0.284572	+	0.0819443i
$651$	0.000159735	−	2.58770i	6.26050e−6	−	0.101420i
$652$	−0.554948	+	0.685304i	−0.0217334	+	0.0268386i
$653$	−8.72186	−	19.5896i	−0.341313	−	0.766601i	−0.999901	−	0.0140973i	$-0.995513\pi$
$653$	−8.72186	−	19.5896i	−0.341313	−	0.766601i	0.658588	−	0.752504i	$-0.271154\pi$
$654$	−4.59764	+	10.3247i	−0.179782	+	0.403729i
$655$	13.6011	−	26.6936i	0.531438	−	1.04301i
$656$	3.85738	+	4.76346i	0.150605	+	0.185982i
$657$	1.40117	−	2.15704i	0.0546650	−	0.0841540i
$658$	−5.42478	−	10.6467i	−0.211480	−	0.415052i
$659$	−35.0999	+	20.2649i	−1.36730	+	0.789409i	−0.990582	−	0.136920i	$-0.956280\pi$
$659$	−35.0999	+	20.2649i	−1.36730	+	0.789409i	−0.376714	+	0.926329i	$0.622946\pi$
$660$	−5.18526	−	23.3431i	−0.201836	−	0.908628i
$661$	3.71634	+	13.8696i	0.144549	+	0.539464i	0.999775	+	0.0212087i	$0.00675145\pi$
$661$	3.71634	+	13.8696i	0.144549	+	0.539464i	−0.855226	+	0.518255i	$0.826582\pi$
$662$	5.60131	−	17.2391i	0.217701	−	0.670016i
$663$	26.7484	−	38.2867i	1.03882	−	1.48693i
$664$	4.88930	+	3.55228i	0.189741	+	0.137855i
$665$	−30.5838	+	19.8613i	−1.18599	+	0.770189i
$666$	−5.55122	−	12.4724i	−0.215105	−	0.483295i
$667$	−4.32985	−	0.455085i	−0.167652	−	0.0176210i
$668$	2.65072	−	16.7360i	0.102560	−	0.647536i
$669$	2.11334	+	0.566407i	0.0817064	+	0.0218986i
$670$	−1.95836	−	0.524740i	−0.0756579	−	0.0202725i
$671$	5.47209	−	14.6572i	0.211248	−	0.565834i
$672$	33.7613	−	37.4910i	1.30237	−	1.44625i
$673$	−17.7448	+	15.9775i	−0.684014	+	0.615889i	−0.936066	−	0.351825i	$-0.885561\pi$
$673$	−17.7448	+	15.9775i	−0.684014	+	0.615889i	0.252052	+	0.967714i	$0.418895\pi$
$674$	−14.1977	+	17.5327i	−0.546874	+	0.675334i
$675$	4.66222	+	14.3579i	0.179449	+	0.552635i
$676$	14.7711	+	12.3383i	0.568121	+	0.474549i
$677$	−9.84514	+	3.19888i	−0.378379	+	0.122943i	−0.492031	−	0.870578i	$-0.663745\pi$
$677$	−9.84514	+	3.19888i	−0.378379	+	0.122943i	0.113651	+	0.993521i	$0.463745\pi$
$678$	5.48940	+	0.288027i	0.210819	+	0.0110616i
$679$	1.42876	+	13.5938i	0.0548308	+	0.521681i
$680$	51.5977	−	10.9674i	1.97868	−	0.420582i
$681$	2.47287	−	4.85254i	0.0947606	−	0.185950i
$682$	0.502348	−	0.511683i	0.0192359	−	0.0195933i
$683$	1.45244	−	5.42058i	0.0555760	−	0.207413i	−0.932554	−	0.361029i	$-0.882425\pi$
$683$	1.45244	−	5.42058i	0.0555760	−	0.207413i	0.988131	+	0.153617i	$0.0490921\pi$
$684$	10.3045	+	5.25200i	0.394002	+	0.200815i
$685$	−6.59048	−	2.93427i	−0.251809	−	0.112113i
$686$	−35.4461	+	15.7816i	−1.35334	+	0.602545i
$687$	−1.82936	+	2.25879i	−0.0697945	+	0.0861781i
$688$	4.58311	−	1.48914i	0.174729	−	0.0567730i
$689$	−20.8233	+	29.8096i	−0.793304	+	1.13566i
$690$	−4.29298	−	3.11944i	−0.163431	−	0.118755i
$691$	2.52556	−	48.1906i	0.0960770	−	1.83326i	−0.348259	−	0.937398i	$-0.613227\pi$
$691$	2.52556	−	48.1906i	0.0960770	−	1.83326i	0.444336	−	0.895860i	$-0.353439\pi$
$692$	−2.85622	−	1.64904i	−0.108577	−	0.0626870i
$693$	46.9913	−	15.7417i	1.78505	−	0.597977i
$694$	−7.81026	−	7.81026i	−0.296473	−	0.296473i
$695$	−5.03319	+	7.75043i	−0.190920	+	0.293991i
$696$	−9.72474	+	7.87395i	−0.368615	+	0.298461i
$697$	−39.2751	+	6.22057i	−1.48765	+	0.235621i
$698$	−9.10409	−	8.19736i	−0.344595	−	0.310275i
$699$	8.19988	−	0.861331i	0.310148	−	0.0325785i
$700$	−7.67722	+	19.9998i	−0.290171	+	0.755922i
$701$	−14.8299	+	10.7746i	−0.560118	+	0.406949i	−0.831502	−	0.555522i	$-0.812519\pi$
$701$	−14.8299	+	10.7746i	−0.560118	+	0.406949i	0.271384	+	0.962471i	$0.412519\pi$
$702$	−8.30379	+	10.6488i	−0.313406	+	0.401914i
$703$	16.4408			0.620076
$704$	6.32157	−	0.389685i	0.238253	−	0.0146868i
$705$	3.37102	−	15.8546i	0.126960	−	0.597119i
$706$	3.96521	+	18.6548i	0.149233	+	0.702084i
$707$	−10.6920	+	67.5065i	−0.402113	+	2.53884i
$708$	5.62846	+	3.65566i	0.211530	+	0.137388i
$709$	−0.369330	−	7.04724i	−0.0138705	−	0.264665i	−0.996758	−	0.0804579i	$-0.974362\pi$
$709$	−0.369330	−	7.04724i	−0.0138705	−	0.264665i	0.982888	−	0.184207i	$-0.0589716\pi$
$710$	−8.60972	+	16.8975i	−0.323117	+	0.634153i
$711$	−10.0035	−	17.3314i	−0.375159	−	0.649979i
$712$	−9.59362	+	1.00833i	−0.359536	+	0.0377888i
$713$	−0.0237335	+	0.452863i	−0.000888828	+	0.0169598i
$714$	14.3677	+	44.2284i	0.537696	+	1.65521i
$715$	−12.8170	+	31.0833i	−0.479328	+	1.16245i
$716$			2.91049i			0.108770i
$717$	−44.3938	+	11.8924i	−1.65792	+	0.444128i
$718$	1.25893	+	11.9779i	0.0469827	+	0.447011i
$719$	−1.35847	+	12.9250i	−0.0506623	+	0.482020i	0.939546	+	0.342423i	$0.111247\pi$
$719$	−1.35847	+	12.9250i	−0.0506623	+	0.482020i	−0.990208	+	0.139597i	$0.955419\pi$
$720$	9.60415	−	1.51993i	0.357925	−	0.0566445i
$721$	47.7304	−	2.50145i	1.77757	−	0.0931587i
$722$	−6.84442	+	5.54251i	−0.254723	+	0.206271i
$723$	4.70018	+	29.6877i	0.174802	+	1.10410i
$724$	15.6780	−	3.33247i	0.582670	−	0.123850i
$725$	4.18311	−	7.24537i	0.155357	−	0.269086i
$726$	12.3482	+	6.00891i	0.458284	+	0.223012i
$727$			22.8743i			0.848360i	0.905578	+	0.424180i	$0.139438\pi$
$727$			22.8743i			0.848360i	−0.905578	+	0.424180i	$0.860562\pi$
$728$	−43.8852	+	10.1834i	−1.62649	+	0.377422i
$729$	21.8376	+	15.8783i	0.808799	+	0.588085i
$730$	−1.62214	−	0.622680i	−0.0600380	−	0.0230464i
$731$	−6.49995	+	30.5799i	−0.240409	+	1.13104i
$732$	11.0502	+	4.92069i	0.408428	+	0.181874i
$733$	2.68572	+	16.9570i	0.0991993	+	0.626320i	0.986328	+	0.164797i	$0.0526968\pi$
$733$	2.68572	+	16.9570i	0.0991993	+	0.626320i	−0.887128	+	0.461523i	$0.847303\pi$
$734$	8.82641	−	3.38814i	0.325789	−	0.125059i
$735$	−83.7659	−	22.4505i	−3.08975	−	0.828101i
$736$	−6.25189	+	6.25189i	−0.230448	+	0.230448i
$737$	−2.66632	+	1.97495i	−0.0982153	+	0.0727483i
$738$	11.4343	−	1.20036i	0.420901	−	0.0441860i
$739$	−19.9427	−	1.04515i	−0.733604	−	0.0384466i	−0.318124	−	0.948049i	$-0.603053\pi$
$739$	−19.9427	−	1.04515i	−0.733604	−	0.0384466i	−0.415480	+	0.909602i	$0.636386\pi$
$740$	21.2614	−	15.4473i	0.781585	−	0.567855i
$741$	−7.64982	−	14.3506i	−0.281023	−	0.527183i
$742$	−11.1881	−	34.4336i	−0.410730	−	1.26410i
$743$	35.2332	−	22.8807i	1.29258	−	0.839412i	0.299191	−	0.954193i	$-0.403283\pi$
$743$	35.2332	−	22.8807i	1.29258	−	0.839412i	0.993391	+	0.114781i	$0.0366167\pi$
$744$	0.872046	+	0.968625i	0.0319708	+	0.0355115i
$745$	2.74275	−	6.16031i	0.100486	−	0.225696i
$746$	3.78805	+	7.43447i	0.138690	+	0.272195i
$747$	−6.74750	+	2.58917i	−0.246878	+	0.0947327i
$748$	16.3697	−	32.8719i	0.598534	−	1.20192i
$749$	55.8723	+	55.8723i	2.04153	+	2.04153i
$750$	−6.36804	+	3.67607i	−0.232528	+	0.134231i
$751$	50.8497	−	5.34452i	1.85553	−	0.195024i	0.890116	−	0.455734i	$-0.150623\pi$
$751$	50.8497	−	5.34452i	1.85553	−	0.195024i	0.965417	+	0.260709i	$0.0839564\pi$
$752$	−3.58216	−	1.37506i	−0.130628	−	0.0501433i
$753$	1.29480	+	1.78237i	0.0471851	+	0.0649531i
$754$	7.46504	−	0.530395i	0.271861	−	0.0193158i
$755$	−6.09829	+	8.39358i	−0.221940	+	0.305474i
$756$	9.91007	+	37.0123i	0.360426	+	1.34612i
$757$	−7.67634	−	8.52544i	−0.279001	−	0.309862i	0.587315	−	0.809359i	$-0.300185\pi$
$757$	−7.67634	−	8.52544i	−0.279001	−	0.309862i	−0.866316	+	0.499496i	$0.833518\pi$
$758$	−11.5099	−	19.9357i	−0.418057	−	0.724096i
$759$	−8.36799	+	2.32441i	−0.303739	+	0.0843708i
$760$	4.75379	−	17.7414i	0.172438	−	0.643548i
$761$	−28.8142	−	18.7121i	−1.04451	−	0.678315i	−0.0961061	−	0.995371i	$-0.530639\pi$
$761$	−28.8142	−	18.7121i	−1.04451	−	0.678315i	−0.948407	+	0.317057i	$0.897305\pi$
$762$	22.2335	−	3.52004i	0.805436	−	0.127518i
$763$	4.71336	−	44.8446i	0.170635	−	1.62348i
$764$	9.57972	+	2.03623i	0.346582	+	0.0736683i
$765$	−22.6140	+	58.8897i	−0.817610	+	2.12916i
$766$	8.54170	−	11.7566i	0.308624	−	0.424785i
$767$	−3.54485	−	8.74566i	−0.127997	−	0.315787i
$768$	−0.00120363	+	19.4989i	−4.34324e−5	+	0.703604i
$769$	−33.8805	+	9.07826i	−1.22176	+	0.327370i	−0.811367	−	0.584537i	$-0.801276\pi$
$769$	−33.8805	+	9.07826i	−1.22176	+	0.327370i	−0.410396	+	0.911907i	$0.634610\pi$
$770$	−17.0047	−	28.8367i	−0.612808	−	1.03920i
$771$	4.02071	+	3.62071i	0.144802	+	0.130397i
$772$	4.79597	−	2.44367i	0.172611	−	0.0879496i
$773$	−45.0258	+	17.2838i	−1.61946	+	0.621654i	−0.988097	−	0.153830i	$-0.950839\pi$
$773$	−45.0258	+	17.2838i	−1.61946	+	0.621654i	−0.631367	+	0.775484i	$0.717506\pi$
$774$	2.34055	−	8.73075i	0.0841294	−	0.313820i
$775$	−0.776452	−	0.395622i	−0.0278910	−	0.0142112i
$776$	−5.11614	−	4.60660i	−0.183659	−	0.165367i
$777$	36.4428	+	40.4789i	1.30738	+	1.45217i
$778$	11.4263	+	9.25285i	0.409654	+	0.331731i
$779$	−4.27856	+	13.1681i	−0.153295	+	0.471795i
$780$	−23.3763	−	11.3708i	−0.837006	−	0.407141i
$781$	12.8844	+	28.2365i	0.461042	+	1.01038i
$782$	−2.10926	−	7.87187i	−0.0754271	−	0.281498i
$783$	−1.56137	−	14.8819i	−0.0557986	−	0.531836i
$784$	−8.34987	+	18.7541i	−0.298210	+	0.669790i
$785$	35.6962	−	5.65373i	1.27405	−	0.201790i
$786$	−12.4192	+	4.76640i	−0.442977	+	0.170012i
$787$	2.26236	+	43.1685i	0.0806446	+	1.53879i	0.676948	+	0.736031i	$0.263302\pi$
$787$	2.26236	+	43.1685i	0.0806446	+	1.53879i	−0.596303	+	0.802759i	$0.703364\pi$
$788$	−3.62715	−	22.9009i	−0.129212	−	0.815812i
$789$	1.73019	−	16.4519i	0.0615963	−	0.585701i
$790$	−10.0457	+	9.04521i	−0.357411	+	0.321814i
$791$	−21.1836	+	5.67614i	−0.753203	+	0.201820i
$792$	−12.2835	+	21.7291i	−0.436476	+	0.772109i
$793$	−8.77621	−	14.5691i	−0.311652	−	0.517365i
$794$	9.65149	+	3.13596i	0.342519	+	0.111291i
$795$	17.6034	−	45.8500i	0.624328	−	1.62613i
$796$	33.5327	−	14.9297i	1.18854	−	0.529170i
$797$	29.6964	−	32.9812i	1.05190	−	1.16826i	0.0665391	−	0.997784i	$-0.478804\pi$
$797$	29.6964	−	32.9812i	1.05190	−	1.16826i	0.985363	−	0.170471i	$-0.0545290\pi$
$798$	15.9926	+	2.53399i	0.566132	+	0.0897024i
$799$	19.3452	−	15.6654i	0.684383	−	0.554203i
$800$	−6.08873	−	15.8617i	−0.215269	−	0.560796i
$801$	5.23844	−	10.2779i	0.185091	−	0.363151i
$802$	12.5688	+	21.7699i	0.443821	+	0.768720i
$803$	−2.44948	+	1.44444i	−0.0864403	+	0.0509730i
$804$	−1.39709	−	2.15162i	−0.0492714	−	0.0758816i
$805$	20.1355	+	6.54242i	0.709683	+	0.230590i
$806$	−0.0958652	−	0.773607i	−0.00337671	−	0.0272492i
$807$	−4.79413	+	14.7517i	−0.168761	+	0.519285i
$808$	−18.7490	−	28.8709i	−0.659588	−	1.01568i
$809$	−4.92025	+	23.1479i	−0.172987	+	0.813838i	0.802995	+	0.595986i	$0.203239\pi$
$809$	−4.92025	+	23.1479i	−0.172987	+	0.813838i	−0.975982	+	0.217853i	$0.930095\pi$
$810$	7.42254	−	16.6602i	0.260802	−	0.585381i
$811$	25.4436	+	4.02988i	0.893447	+	0.141508i	0.586243	−	0.810135i	$-0.300606\pi$
$811$	25.4436	+	4.02988i	0.893447	+	0.141508i	0.307204	+	0.951644i	$0.400606\pi$
$812$	11.5654	−	17.8092i	0.405867	−	0.624980i
$813$	−12.9947	+	0.680217i	−0.455743	+	0.0238563i
$814$	−0.651114	+	15.0788i	−0.0228215	+	0.528511i
$815$	−1.45032	+	0.837343i	−0.0508025	+	0.0293309i
$816$	12.9318	+	7.46724i	0.452703	+	0.261406i
$817$	8.45963	+	6.85047i	0.295965	+	0.239668i
$818$	3.93860	+	2.86156i	0.137710	+	0.100052i
$819$	18.3760	−	50.6444i	0.642110	−	1.76966i
$820$	6.83927	+	21.0491i	0.238838	+	0.735067i
$821$	18.6743	−	48.6483i	0.651739	−	1.69784i	−0.0626006	−	0.998039i	$-0.519939\pi$
$821$	18.6743	−	48.6483i	0.651739	−	1.69784i	0.714340	−	0.699799i	$-0.246727\pi$
$822$	1.30270	+	2.92639i	0.0454368	+	0.102070i
$823$	9.07987	+	42.7174i	0.316504	+	1.48904i	0.792654	+	0.609672i	$0.208699\pi$
$823$	9.07987	+	42.7174i	0.316504	+	1.48904i	−0.476150	+	0.879364i	$0.657968\pi$
$824$	−17.0224	+	17.0224i	−0.593002	+	0.593002i
$825$	2.45991	−	16.5068i	0.0856432	−	0.574693i
$826$	9.07591	+	2.43188i	0.315791	+	0.0846160i
$827$	5.56462	−	2.83532i	0.193501	−	0.0985937i	−0.354556	−	0.935035i	$-0.615368\pi$
$827$	5.56462	−	2.83532i	0.193501	−	0.0985937i	0.548057	+	0.836441i	$0.315368\pi$
$828$	−1.39526	−	6.56817i	−0.0484887	−	0.228260i
$829$	3.96898	+	8.91447i	0.137848	+	0.309612i	0.969258	−	0.246048i	$-0.0791322\pi$
$829$	3.96898	+	8.91447i	0.137848	+	0.309612i	−0.831409	+	0.555660i	$0.812465\pi$
$830$	2.65898	+	4.09446i	0.0922944	+	0.142121i
$831$	25.4181	−	18.4650i	0.881745	−	0.640542i
$832$	3.94295	−	5.64453i	0.136697	−	0.195689i
$833$	−78.2821	−	107.746i	−2.71232	−	3.73318i
$834$	3.96360	−	1.06178i	0.137248	−	0.0367665i
$835$	16.0900	−	27.8686i	0.556816	−	0.964434i
$836$	−7.61056	−	10.2748i	−0.263217	−	0.355361i
$837$	−1.53948	+	0.243537i	−0.0532121	+	0.00841786i
$838$	13.9928	+	9.08702i	0.483373	+	0.313906i
$839$	8.92685	+	23.2552i	0.308189	+	0.802860i	0.996962	+	0.0778835i	$0.0248162\pi$
$839$	8.92685	+	23.2552i	0.308189	+	0.802860i	−0.688773	+	0.724977i	$0.741850\pi$
$840$	54.2183	−	27.6214i	1.87071	−	0.953029i
$841$	13.8557	−	15.3884i	0.477784	−	0.530633i
$842$	13.9118	+	2.95704i	0.479432	+	0.101906i
$843$	−34.8083	−	1.82638i	−1.19886	−	0.0629038i
$844$	−19.3364	−	26.6142i	−0.665586	−	0.916100i
$845$	17.7917	+	31.9286i	0.612055	+	1.09838i
$846$	−5.82314	+	4.22966i	−0.200204	+	0.145419i
$847$	−54.2624	−	7.57306i	−1.86448	−	0.260213i
$848$	−10.0685	−	5.81304i	−0.345753	−	0.199621i
$849$	−8.10736	−	14.0444i	−0.278244	−	0.482001i
$850$	15.4677	+	2.44984i	0.530538	+	0.0840289i
$851$	−6.00690	−	7.41791i	−0.205914	−	0.254283i
$852$	−22.4033	+	8.59824i	−0.767525	+	0.294571i
$853$	−11.2003	−	5.70681i	−0.383489	−	0.195398i	0.251609	−	0.967829i	$-0.419040\pi$
$853$	−11.2003	−	5.70681i	−0.383489	−	0.195398i	−0.635098	+	0.772431i	$0.719040\pi$
$854$	16.8422	+	1.77018i	0.576327	+	0.0605744i
$855$	14.6952	+	16.3248i	0.502567	+	0.558296i
$856$	−39.7429	−	2.08284i	−1.35839	−	0.0711900i
$857$	28.0774			0.959106			0.479553	−	0.877513i	$-0.340799\pi$
$857$	28.0774			0.959106			0.479553	+	0.877513i	$0.340799\pi$
$858$	13.4647	−	6.44775i	0.459679	−	0.220123i
$859$	−1.61314			−0.0550398			−0.0275199	−	0.999621i	$-0.508761\pi$
$859$	−1.61314			−0.0550398			−0.0275199	+	0.999621i	$0.508761\pi$
$860$	17.3766	+	0.910670i	0.592538	+	0.0310536i
$861$	−41.9050	+	18.6542i	−1.42812	+	0.635733i
$862$	−13.9668	−	1.46797i	−0.475711	−	0.0499993i
$863$	−39.9708	−	20.3661i	−1.36062	−	0.693271i	−0.387135	−	0.922023i	$-0.626535\pi$
$863$	−39.9708	−	20.3661i	−1.36062	−	0.693271i	−0.973485	+	0.228752i	$0.926535\pi$
$864$	−25.4826	−	16.5553i	−0.866935	−	0.563222i
$865$	−3.94172	−	4.86762i	−0.134022	−	0.165504i
$866$	0.448272	+	0.0709992i	0.0152329	+	0.00241265i
$867$	−58.4002	+	33.7125i	−1.98337	+	1.14494i
$868$	−1.91552	−	1.10593i	−0.0650171	−	0.0375377i
$869$	1.36117	+	22.0813i	0.0461746	+	0.749056i
$870$	−9.61359	+	3.12299i	−0.325931	+	0.105879i
$871$	−0.121856	+	3.60508i	−0.00412895	+	0.122154i
$872$	13.3493	+	18.3737i	0.452065	+	0.622213i
$873$	7.95260	−	2.12984i	0.269155	−	0.0720842i
$874$	−2.77560	−	0.589971i	−0.0938859	−	0.0199561i
$875$	19.6293	−	21.8006i	0.663593	−	0.736994i
$876$	−0.998017	−	1.95902i	−0.0337199	−	0.0661891i
$877$	−14.0433	−	36.5840i	−0.474209	−	1.23536i	−0.937138	−	0.348960i	$-0.886535\pi$
$877$	−14.0433	−	36.5840i	−0.474209	−	1.23536i	0.462929	−	0.886395i	$-0.346798\pi$
$878$	−11.0699	−	7.18888i	−0.373591	−	0.242613i
$879$	−32.2514	−	16.4354i	−1.08781	−	0.554353i
$880$	−10.2539	−	3.22765i	−0.345660	−	0.108804i
$881$	10.5060	−	18.1969i	0.353956	−	0.613070i	−0.632983	−	0.774166i	$-0.718170\pi$
$881$	10.5060	−	18.1969i	0.353956	−	0.613070i	0.986939	+	0.161096i	$0.0515029\pi$
$882$	20.9682	+	32.2969i	0.706036	+	1.08749i
$883$	20.6779	+	28.4607i	0.695867	+	0.957779i	0.999987	+	0.00514492i	$0.00163769\pi$
$883$	20.6779	+	28.4607i	0.695867	+	0.957779i	−0.304120	+	0.952634i	$0.598362\pi$
$884$	−16.9119	−	36.1622i	−0.568810	−	1.21627i
$885$	7.49118	+	10.3121i	0.251813	+	0.346636i
$886$	11.3127	+	17.4201i	0.380058	+	0.585239i
$887$	−3.85198	−	8.65169i	−0.129337	−	0.290495i	0.837256	−	0.546811i	$-0.184158\pi$
$887$	−3.85198	−	8.65169i	−0.129337	−	0.290495i	−0.966593	+	0.256315i	$0.917492\pi$
$888$	−27.2826	−	2.86922i	−0.915545	−	0.0962848i
$889$	−80.0203	+	40.7724i	−2.68380	+	1.36746i
$890$	−7.52712	−	2.01689i	−0.252310	−	0.0676062i
$891$	−13.7892	−	26.4737i	−0.461955	−	0.886904i
$892$	1.32239	−	1.32239i	0.0442770	−	0.0442770i
$893$	−1.80205	−	8.47798i	−0.0603033	−	0.283705i
$894$	−2.73539	+	1.21767i	−0.0914850	+	0.0407250i
$895$	−1.98083	+	5.16024i	−0.0662119	+	0.172488i
$896$	−15.8839	−	48.8855i	−0.530643	−	1.63315i
$897$	−3.67987	+	8.69475i	−0.122867	+	0.290309i
$898$	1.82428	+	1.32542i	0.0608770	+	0.0442298i
$899$	0.671297	+	0.543606i	0.0223890	+	0.0181303i
$900$	12.6210	+	2.68430i	0.420700	+	0.0894768i
$901$	65.3193	−	37.7121i	2.17610	−	1.25637i
$902$	−11.9077	−	4.44562i	−0.396484	−	0.148023i
$903$	1.88515	+	36.0133i	0.0627338	+	1.19845i
$904$	6.01602	−	9.26386i	0.200090	−	0.308111i
$905$	30.0649	+	4.76182i	0.999393	+	0.158288i
$906$	4.50613	−	0.957516i	0.149706	−	0.0318114i
$907$	8.78261	−	41.3189i	0.291622	−	1.37197i	−0.551466	−	0.834197i	$-0.685932\pi$
$907$	8.78261	−	41.3189i	0.291622	−	1.37197i	0.843088	−	0.537775i	$-0.180735\pi$
$908$	−2.53544	−	3.90424i	−0.0841416	−	0.129567i
$909$	41.1672	+	0.00508238i	1.36543	+	0.000168572i
$910$	−36.0449	−	5.02469i	−1.19488	−	0.166567i
$911$	−10.1055	−	3.28349i	−0.334812	−	0.108787i	0.136786	−	0.990601i	$-0.456323\pi$
$911$	−10.1055	−	3.28349i	−0.334812	−	0.108787i	−0.471598	+	0.881814i	$0.656323\pi$
$912$	4.36084	−	2.83158i	0.144402	−	0.0937630i
$913$	7.95356	+	0.761994i	0.263224	+	0.0252183i
$914$	10.4150	+	18.0394i	0.344499	+	0.596690i
$915$	16.2429	+	16.2449i	0.536974	+	0.537040i
$916$	0.890362	+	2.31947i	0.0294184	+	0.0766375i
$917$	41.2447	−	33.3993i	1.36202	−	1.10294i
$918$	24.9594	−	12.7116i	0.823782	−	0.419546i
$919$	−34.9892	+	38.8595i	−1.15419	+	1.28186i	−0.200962	+	0.979599i	$0.564407\pi$
$919$	−34.9892	+	38.8595i	−1.15419	+	1.28186i	−0.953227	+	0.302257i	$0.902260\pi$
$920$	−9.74159	+	4.33724i	−0.321171	+	0.142994i
$921$	−36.9152	−	14.1730i	−1.21640	−	0.467017i
$922$	12.7280	+	4.13558i	0.419175	+	0.136198i
$923$	32.7478	+	8.12607i	1.07791	+	0.267473i
$924$	8.42789	−	41.5131i	0.277257	−	1.36568i
$925$	17.7172	−	4.74730i	0.582537	−	0.156090i
$926$	−0.723615	+	0.651546i	−0.0237795	+	0.0214111i
$927$	−5.98196	−	28.1600i	−0.196473	−	0.924896i
$928$	2.63456	+	16.6340i	0.0864837	+	0.546037i
$929$	1.88504	+	35.9687i	0.0618461	+	1.18009i	0.836594	+	0.547824i	$0.184543\pi$
$929$	1.88504	+	35.9687i	0.0618461	+	1.18009i	−0.774748	+	0.632270i	$0.782123\pi$
$930$	0.377254	+	0.982963i	0.0123707	+	0.0322326i
$931$	−45.8017	+	7.25427i	−1.50109	+	0.237749i
$932$	2.86646	−	6.43819i	0.0938942	−	0.210890i
$933$	38.2872	+	22.1083i	1.25347	+	0.723793i
$934$	−5.14726	−	19.2098i	−0.168424	−	0.628565i
$935$	51.3953	−	47.1404i	1.68081	−	1.54166i
$936$	10.1900	+	25.1492i	0.333072	+	0.822026i
$937$	0.701825	−	2.16000i	0.0229276	−	0.0705640i	−0.938938	−	0.344086i	$-0.888189\pi$
$937$	0.701825	−	2.16000i	0.0229276	−	0.0705640i	0.961866	+	0.273522i	$0.0881887\pi$
$938$	−2.79119	−	2.26026i	−0.0911356	−	0.0738001i
$939$	−0.0905185	+	0.0814931i	−0.00295396	+	0.00265943i
$940$	−10.2961	−	9.27066i	−0.335822	−	0.302376i
$941$	12.8484	+	6.54659i	0.418846	+	0.213413i	0.650695	−	0.759339i	$-0.274478\pi$
$941$	12.8484	+	6.54659i	0.418846	+	0.213413i	−0.231849	+	0.972752i	$0.574478\pi$
$942$	−13.4580	−	8.74091i	−0.438485	−	0.284794i
$943$	7.50453	−	2.88072i	0.244381	−	0.0938091i
$944$	2.68834	−	1.36978i	0.0874982	−	0.0445825i
$945$	−7.61961	+	72.3668i	−0.247866	+	2.35409i
$946$	−6.61799	+	7.48751i	−0.215170	+	0.243440i
$947$	16.8210	−	4.50718i	0.546609	−	0.146464i	0.0250620	−	0.999686i	$-0.492022\pi$
$947$	16.8210	−	4.50718i	0.546609	−	0.146464i	0.521547	+	0.853222i	$0.325355\pi$
$948$	−17.1047	−	0.00105585i	−0.555535	−	3.42923e-5i
$949$	−0.426813	+	3.06177i	−0.0138549	+	0.0993892i
$950$	3.20510	−	4.41145i	0.103987	−	0.143126i
$951$	−29.2500	+	36.1162i	−0.948497	+	1.17115i
$952$	91.4049	+	19.4287i	2.96245	+	0.629688i
$953$	−3.55643	+	33.8372i	−0.115204	+	1.09609i	0.772288	+	0.635272i	$0.219112\pi$
$953$	−3.55643	+	33.8372i	−0.115204	+	1.09609i	−0.887492	+	0.460822i	$0.847555\pi$
$954$	−19.4317	+	9.89790i	−0.629123	+	0.320456i
$955$	15.5989	+	10.1300i	0.504767	+	0.327800i
$956$	−10.1674	+	37.9453i	−0.328838	+	1.22724i
$957$	−5.78697	+	15.4977i	−0.187066	+	0.500968i
$958$	7.27598	+	12.6024i	0.235076	+	0.407164i
$959$	−8.55138	−	9.49728i	−0.276139	−	0.306683i
$960$	−3.33325	+	8.68182i	−0.107580	+	0.280204i
$961$	−18.1685	+	25.0067i	−0.586079	+	0.806669i
$962$	12.3950	+	10.7505i	0.399632	+	0.346611i
$963$	27.9789	−	38.4996i	0.901606	−	1.24063i
$964$	23.9854	+	9.20712i	0.772517	+	0.296541i
$965$	10.1663	−	1.06852i	0.327265	−	0.0343969i
$966$	−4.69984	−	8.14153i	−0.151215	−	0.261949i
$967$	−23.5756	−	23.5756i	−0.758141	−	0.758141i	0.217843	−	0.975984i	$-0.430098\pi$
$967$	−23.5756	−	23.5756i	−0.758141	−	0.758141i	−0.975984	+	0.217843i	$0.930098\pi$
$968$	22.8626	−	15.4529i	0.734831	−	0.496675i
$969$	1.76330	+	33.6856i	0.0566455	+	1.08214i
$970$	−2.52483	−	4.95527i	−0.0810675	−	0.159104i
$971$	24.3319	−	54.6504i	0.780848	−	1.75381i	0.134300	−	0.990941i	$-0.457122\pi$
$971$	24.3319	−	54.6504i	0.780848	−	1.75381i	0.646548	−	0.762873i	$-0.276212\pi$
$972$	21.0861	−	9.38034i	0.676337	−	0.300875i
$973$	−13.7298	+	8.91625i	−0.440158	+	0.285842i
$974$	−6.15872	−	18.9546i	−0.197338	−	0.607345i
$975$	−12.3875	−	13.2558i	−0.396717	−	0.424527i
$976$	4.39946	−	3.19639i	0.140823	−	0.102314i
$977$	−28.4264	−	1.48976i	−0.909441	−	0.0476618i	−0.408125	−	0.912926i	$-0.633817\pi$
$977$	−28.4264	−	1.48976i	−0.909441	−	0.0476618i	−0.501316	+	0.865264i	$0.667151\pi$
$978$	0.727338	+	0.154647i	0.0232577	+	0.00494508i
$979$	−10.2483	+	7.59091i	−0.327536	+	0.242607i
$980$	−52.4154	+	52.4154i	−1.67435	+	1.67435i
$981$	−27.1225	+	1.41807i	−0.865954	+	0.0452755i
$982$	23.5310	−	9.03269i	0.750903	−	0.288245i
$983$	7.01990	+	44.3219i	0.223900	+	1.41365i	0.801824	+	0.597560i	$0.203863\pi$
$983$	7.01990	+	44.3219i	0.223900	+	1.41365i	−0.577924	+	0.816090i	$0.696137\pi$
$984$	9.39812	−	21.1050i	0.299601	−	0.672803i
$985$	9.15514	−	43.0715i	0.291707	−	1.37237i
$986$	−14.4923	−	5.56305i	−0.461527	−	0.177164i
$987$	16.8792	−	23.2292i	0.537270	−	0.739393i
$988$	−13.8923	−	0.469578i	−0.441974	−	0.0149393i
$989$		−	6.31983i		−	0.200959i
$990$	−15.5544	+	12.8313i	−0.494350	+	0.407806i
$991$	29.7567	−	51.5400i	0.945251	−	1.63722i	0.190004	−	0.981783i	$-0.439150\pi$
$991$	29.7567	−	51.5400i	0.945251	−	1.63722i	0.755247	−	0.655440i	$-0.227517\pi$
$992$	1.71587	−	0.364720i	0.0544790	−	0.0115799i
$993$	43.0222	−	6.81132i	1.36527	−	0.216151i
$994$	−26.1086	+	21.1423i	−0.828115	+	0.670594i
$995$	69.6139	−	3.64831i	2.20691	−	0.115659i
$996$	−0.966752	+	6.10139i	−0.0306327	+	0.193330i
$997$	1.81408	−	17.2598i	0.0574524	−	0.546623i	−0.927503	−	0.373815i	$-0.878049\pi$
$997$	1.81408	−	17.2598i	0.0574524	−	0.546623i	0.984956	−	0.172808i	$-0.0552839\pi$
$998$	2.06871	+	19.6824i	0.0654837	+	0.623036i
$999$	20.6504	−	25.4914i	0.653348	−	0.806513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bv.a.20.20	✓	832
3.2	odd	2	inner	429.2.bv.a.20.33	yes	832
11.5	even	5	inner	429.2.bv.a.137.33	yes	832
13.2	odd	12	inner	429.2.bv.a.119.20	yes	832
33.5	odd	10	inner	429.2.bv.a.137.20	yes	832
39.2	even	12	inner	429.2.bv.a.119.33	yes	832
143.93	odd	60	inner	429.2.bv.a.236.33	yes	832
429.236	even	60	inner	429.2.bv.a.236.20	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bv.a.20.20	✓	832	1.1	even	1	trivial
429.2.bv.a.20.33	yes	832	3.2	odd	2	inner
429.2.bv.a.119.20	yes	832	13.2	odd	12	inner
429.2.bv.a.119.33	yes	832	39.2	even	12	inner
429.2.bv.a.137.20	yes	832	33.5	odd	10	inner
429.2.bv.a.137.33	yes	832	11.5	even	5	inner
429.2.bv.a.236.20	yes	832	429.236	even	60	inner
429.2.bv.a.236.33	yes	832	143.93	odd	60	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.719787 - 0.0377225i) q^{2} +(-0.704391 - 1.58235i) q^{3} +(-1.47237 - 0.154753i) q^{4} +(-2.50517 - 1.27645i) q^{5} +(0.447321 + 1.16553i) q^{6} +(-3.13449 - 3.87078i) q^{7} +(2.47776 + 0.392439i) q^{8} +(-2.00767 + 2.22919i) q^{9} +O(q^{10})\)	\(q+(-0.719787 - 0.0377225i) q^{2} +(-0.704391 - 1.58235i) q^{3} +(-1.47237 - 0.154753i) q^{4} +(-2.50517 - 1.27645i) q^{5} +(0.447321 + 1.16553i) q^{6} +(-3.13449 - 3.87078i) q^{7} +(2.47776 + 0.392439i) q^{8} +(-2.00767 + 2.22919i) q^{9} +(1.75504 + 1.01327i) q^{10} +(3.08526 - 1.21703i) q^{11} +(0.792253 + 2.43882i) q^{12} +(1.05031 - 3.44918i) q^{13} +(2.11015 + 2.90438i) q^{14} +(-0.255169 + 4.86318i) q^{15} +(1.12761 + 0.239680i) q^{16} +(-5.00428 + 5.55781i) q^{17} +(1.52918 - 1.52881i) q^{18} +(0.933205 + 2.43108i) q^{19} +(3.49101 + 2.26709i) q^{20} +(-3.91702 + 7.68640i) q^{21} +(-2.26664 + 0.759616i) q^{22} +(0.755917 - 1.30929i) q^{23} +(-1.12434 - 4.19712i) q^{24} +(1.70763 + 2.35035i) q^{25} +(-0.886108 + 2.44306i) q^{26} +(4.94154 + 1.60661i) q^{27} +(4.01613 + 6.18430i) q^{28} +(-1.17130 - 2.63078i) q^{29} +(0.367119 - 3.49083i) q^{30} +(-0.267263 + 0.136177i) q^{31} +(-5.64893 - 1.51363i) q^{32} +(-4.09899 - 4.02471i) q^{33} +(3.81167 - 3.81167i) q^{34} +(2.91159 + 13.6980i) q^{35} +(3.30101 - 2.97150i) q^{36} +(2.26258 - 5.89422i) q^{37} +(-0.580003 - 1.78507i) q^{38} +(-6.19764 + 0.767622i) q^{39} +(-5.70628 - 4.14586i) q^{40} +(4.13209 + 3.34610i) q^{41} +(3.10937 - 5.38482i) q^{42} +(3.62019 - 2.09012i) q^{43} +(-4.73100 + 1.31446i) q^{44} +(7.87499 - 3.02181i) q^{45} +(-0.593489 + 0.913893i) q^{46} +(-3.28746 - 0.520682i) q^{47} +(-0.415017 - 1.95310i) q^{48} +(-3.70248 + 17.4188i) q^{49} +(-1.14047 - 1.75617i) q^{50} +(12.3194 + 4.00365i) q^{51} +(-2.08021 + 4.91595i) q^{52} +(-9.59151 - 3.11647i) q^{53} +(-3.49625 - 1.34283i) q^{54} +(-9.28258 - 0.889321i) q^{55} +(-6.24748 - 10.8209i) q^{56} +(3.18948 - 3.18909i) q^{57} +(0.743846 + 1.93778i) q^{58} +(2.03401 - 1.64711i) q^{59} +(1.12829 - 7.12092i) q^{60} +(3.15645 - 3.50560i) q^{61} +(0.197510 - 0.0879369i) q^{62} +(14.9217 + 0.783860i) q^{63} +(1.81618 + 0.590112i) q^{64} +(-7.03390 + 7.30013i) q^{65} +(2.79858 + 3.05156i) q^{66} +(-0.966352 + 0.258933i) q^{67} +(8.22825 - 7.40875i) q^{68} +(-2.60421 - 0.273876i) q^{69} +(-1.57901 - 9.96946i) q^{70} +(0.489763 + 9.34524i) q^{71} +(-5.84934 + 4.73550i) q^{72} +(-0.846837 + 0.134126i) q^{73} +(-1.85092 + 4.15724i) q^{74} +(2.51624 - 4.35764i) q^{75} +(-0.997809 - 3.72388i) q^{76} +(-14.3816 - 8.12760i) q^{77} +(4.48994 - 0.318734i) q^{78} +(-2.06127 + 6.34392i) q^{79} +(-2.51890 - 2.03977i) q^{80} +(-0.938546 - 8.95093i) q^{81} +(-2.84801 - 2.56436i) q^{82} +(2.14650 + 1.09369i) q^{83} +(6.95680 - 10.7111i) q^{84} +(19.6308 - 7.53557i) q^{85} +(-2.68461 + 1.36788i) q^{86} +(-3.33776 + 3.70650i) q^{87} +(8.12215 - 1.80472i) q^{88} +(-3.71426 + 0.995234i) q^{89} +(-5.78231 + 1.87800i) q^{90} +(-16.6432 + 6.74594i) q^{91} +(-1.31561 + 1.81078i) q^{92} +(0.403738 + 0.326982i) q^{93} +(2.34663 + 0.498791i) q^{94} +(0.765313 - 7.28146i) q^{95} +(1.58397 + 10.0048i) q^{96} +(-2.30155 - 1.49465i) q^{97} +(3.32208 - 12.3982i) q^{98} +(-3.48120 + 9.32101i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9}+O(q^{10}) \) 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9	\( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9} - 96 q^{10} - 40 q^{13} + 12 q^{15} - 68 q^{16} - 20 q^{18} - 32 q^{19} - 84 q^{21} - 24 q^{22} - 72 q^{24} - 114 q^{30} - 8 q^{31} + 14 q^{33} - 24 q^{34} + 78 q^{36} - 24 q^{37} - 72 q^{39} - 112 q^{40} + 2 q^{42} - 96 q^{43} + 4 q^{45} - 16 q^{46} + 14 q^{48} - 36 q^{49} + 8 q^{52} + 32 q^{54} - 24 q^{55} - 12 q^{57} + 112 q^{58} - 120 q^{60} + 12 q^{61} + 28 q^{63} - 300 q^{66} - 32 q^{67} - 18 q^{69} - 140 q^{70} + 204 q^{72} - 24 q^{73} + 66 q^{75} + 176 q^{76} - 28 q^{78} - 224 q^{79} - 58 q^{81} - 264 q^{82} + 20 q^{84} - 168 q^{85} + 72 q^{87} - 120 q^{88} - 146 q^{93} - 4 q^{94} - 10 q^{96} - 88 q^{97} + 40 q^{99}+O(q^{100}) \) 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9 - 96 * q^10 - 40 * q^13 + 12 * q^15 - 68 * q^16 - 20 * q^18 - 32 * q^19 - 84 * q^21 - 24 * q^22 - 72 * q^24 - 114 * q^30 - 8 * q^31 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 24 * q^37 - 72 * q^39 - 112 * q^40 + 2 * q^42 - 96 * q^43 + 4 * q^45 - 16 * q^46 + 14 * q^48 - 36 * q^49 + 8 * q^52 + 32 * q^54 - 24 * q^55 - 12 * q^57 + 112 * q^58 - 120 * q^60 + 12 * q^61 + 28 * q^63 - 300 * q^66 - 32 * q^67 - 18 * q^69 - 140 * q^70 + 204 * q^72 - 24 * q^73 + 66 * q^75 + 176 * q^76 - 28 * q^78 - 224 * q^79 - 58 * q^81 - 264 * q^82 + 20 * q^84 - 168 * q^85 + 72 * q^87 - 120 * q^88 - 146 * q^93 - 4 * q^94 - 10 * q^96 - 88 * q^97 + 40 * q^99

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