LMFDB - Embedded newform 462.2.bc.a.95.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (of order $30$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			95.12
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.a.107.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 - 0.994522i) q^{2} +(0.891795 + 1.48482i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.333330 + 0.748672i) q^{5} +(1.56991 - 0.731703i) q^{6} +(-2.01015 + 1.72026i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-1.40940 + 2.64832i) q^{9} +O(q^{10})$	\(q+(0.104528 - 0.994522i) q^{2} +(0.891795 + 1.48482i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.333330 + 0.748672i) q^{5} +(1.56991 - 0.731703i) q^{6} +(-2.01015 + 1.72026i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-1.40940 + 2.64832i) q^{9} +(0.709728 + 0.409762i) q^{10} +(-3.26863 + 0.562216i) q^{11} +(-0.563595 - 1.63779i) q^{12} +(-3.17222 + 4.36618i) q^{13} +(1.50072 + 2.17895i) q^{14} +(-1.40891 + 0.172725i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.578545 - 5.50449i) q^{17} +(2.48649 + 1.67851i) q^{18} +(-0.283650 - 1.33447i) q^{19} +(0.481704 - 0.663008i) q^{20} +(-4.34693 - 1.45060i) q^{21} +(0.217472 + 3.30949i) q^{22} +(1.94955 - 1.12557i) q^{23} +(-1.68773 + 0.389312i) q^{24} +(2.89625 + 3.21661i) q^{25} +(4.01068 + 3.61123i) q^{26} +(-5.18918 + 0.269041i) q^{27} +(2.32388 - 1.26474i) q^{28} +(1.93527 + 5.95615i) q^{29} +(0.0245081 + 1.41924i) q^{30} +(5.27750 - 2.34969i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.74974 - 4.35195i) q^{33} -5.53481 q^{34} +(-0.617869 - 2.07836i) q^{35} +(1.92922 - 2.29741i) q^{36} +(4.14442 - 4.60285i) q^{37} +(-1.35681 + 0.142606i) q^{38} +(-9.31198 - 0.816444i) q^{39} +(-0.609025 - 0.548368i) q^{40} +(-3.35806 + 10.3350i) q^{41} +(-1.89703 + 4.17149i) q^{42} +7.89449i q^{43} +(3.31409 + 0.129655i) q^{44} +(-1.51292 - 1.93794i) q^{45} +(-0.915622 - 2.05652i) q^{46} +(-0.101280 - 0.476484i) q^{47} +(0.210763 + 1.71918i) q^{48} +(1.08140 - 6.91597i) q^{49} +(3.50173 - 2.54416i) q^{50} +(7.65725 - 5.76791i) q^{51} +(4.01068 - 3.61123i) q^{52} +(5.29538 + 11.8936i) q^{53} +(-0.274851 + 5.18888i) q^{54} +(0.668616 - 2.63453i) q^{55} +(-1.01490 - 2.44336i) q^{56} +(1.72849 - 1.61124i) q^{57} +(6.12582 - 1.30208i) q^{58} +(0.606629 - 2.85396i) q^{59} +(1.41403 + 0.123978i) q^{60} +(-1.10861 + 2.48998i) q^{61} +(-1.78517 - 5.49419i) q^{62} +(-1.72269 - 7.74805i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-2.21144 - 3.83033i) q^{65} +(-4.72007 + 3.27429i) q^{66} +(2.35441 - 4.07795i) q^{67} +(-0.578545 + 5.50449i) q^{68} +(3.40987 + 1.89095i) q^{69} +(-2.13156 + 0.397236i) q^{70} +(-2.12867 - 2.92987i) q^{71} +(-2.08317 - 2.15880i) q^{72} +(0.719776 - 3.38628i) q^{73} +(-4.14442 - 4.60285i) q^{74} +(-2.19324 + 7.16899i) q^{75} +1.36428i q^{76} +(5.60327 - 6.75303i) q^{77} +(-1.78534 + 9.17563i) q^{78} +(10.1418 + 1.06594i) q^{79} +(-0.609025 + 0.548368i) q^{80} +(-5.02717 - 7.46509i) q^{81} +(9.92741 + 4.41997i) q^{82} +(7.40963 - 5.38341i) q^{83} +(3.95034 + 2.32267i) q^{84} +(4.31390 + 1.40167i) q^{85} +(7.85124 + 0.825199i) q^{86} +(-7.11797 + 8.18521i) q^{87} +(0.475362 - 3.28238i) q^{88} +(-5.82848 + 3.36507i) q^{89} +(-2.08547 + 1.30207i) q^{90} +(-1.13435 - 14.2337i) q^{91} +(-2.14096 + 0.695641i) q^{92} +(8.19532 + 5.74071i) q^{93} +(-0.484461 + 0.0509189i) q^{94} +(1.09363 + 0.232458i) q^{95} +(1.73179 - 0.0299053i) q^{96} +(4.17913 + 3.03631i) q^{97} +(-6.76504 - 1.79839i) q^{98} +(3.11789 - 9.44875i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$3$	0.891795	+	1.48482i	0.514878	+	0.857263i
$3$	0.891795	+	1.48482i	0.514878	+	0.857263i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	−0.333330	+	0.748672i	−0.149070	+	0.334816i	−0.972611	−	0.232441i	$-0.925329\pi$
$5$	−0.333330	+	0.748672i	−0.149070	+	0.334816i	0.823541	+	0.567257i	$0.191995\pi$
$6$	1.56991	−	0.731703i	0.640912	−	0.298717i
$7$	−2.01015	+	1.72026i	−0.759765	+	0.650198i
$7$	−2.01015	+	1.72026i	−0.759765	+	0.650198i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−1.40940	+	2.64832i	−0.469801	+	0.882772i
$10$	0.709728	+	0.409762i	0.224436	+	0.129578i
$11$	−3.26863	+	0.562216i	−0.985528	+	0.169514i
$11$	−3.26863	+	0.562216i	−0.985528	+	0.169514i
$12$	−0.563595	−	1.63779i	−0.162696	−	0.472790i
$13$	−3.17222	+	4.36618i	−0.879815	+	1.21096i	0.0966573	+	0.995318i	$0.469185\pi$
$13$	−3.17222	+	4.36618i	−0.879815	+	1.21096i	−0.976472	+	0.215644i	$0.930815\pi$
$14$	1.50072	+	2.17895i	0.401084	+	0.582350i
$15$	−1.40891	+	0.172725i	−0.363778	+	0.0445975i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−0.578545	−	5.50449i	−0.140318	−	1.33503i	−0.807380	−	0.590032i	$-0.799115\pi$
$17$	−0.578545	−	5.50449i	−0.140318	−	1.33503i	0.667062	−	0.745002i	$-0.267552\pi$
$18$	2.48649	+	1.67851i	0.586070	+	0.395628i
$19$	−0.283650	−	1.33447i	−0.0650738	−	0.306148i	0.933559	−	0.358424i	$-0.116686\pi$
$19$	−0.283650	−	1.33447i	−0.0650738	−	0.306148i	−0.998633	+	0.0522760i	$0.983352\pi$
$20$	0.481704	−	0.663008i	0.107712	−	0.148253i
$21$	−4.34693	−	1.45060i	−0.948577	−	0.316546i
$22$	0.217472	+	3.30949i	0.0463651	+	0.705585i
$23$	1.94955	−	1.12557i	0.406508	−	0.234698i	−0.282780	−	0.959185i	$-0.591257\pi$
$23$	1.94955	−	1.12557i	0.406508	−	0.234698i	0.689288	+	0.724487i	$0.257923\pi$
$24$	−1.68773	+	0.389312i	−0.344507	+	0.0794679i
$25$	2.89625	+	3.21661i	0.579250	+	0.643323i
$26$	4.01068	+	3.61123i	0.786559	+	0.708221i
$27$	−5.18918	+	0.269041i	−0.998659	+	0.0517769i
$28$	2.32388	−	1.26474i	0.439173	−	0.239013i
$29$	1.93527	+	5.95615i	0.359371	+	1.10603i	0.953432	+	0.301610i	$0.0975239\pi$
$29$	1.93527	+	5.95615i	0.359371	+	1.10603i	−0.594061	+	0.804420i	$0.702476\pi$
$30$	0.0245081	+	1.41924i	0.00447454	+	0.259117i
$31$	5.27750	−	2.34969i	0.947866	−	0.422017i	0.126212	−	0.992003i	$-0.459718\pi$
$31$	5.27750	−	2.34969i	0.947866	−	0.422017i	0.821654	+	0.569986i	$0.193051\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−3.74974	−	4.35195i	−0.652745	−	0.757578i
$34$	−5.53481			−0.949212
$35$	−0.617869	−	2.07836i	−0.104439	−	0.351306i
$36$	1.92922	−	2.29741i	0.321537	−	0.382902i
$37$	4.14442	−	4.60285i	0.681338	−	0.756703i	−0.298951	−	0.954268i	$-0.596637\pi$
$37$	4.14442	−	4.60285i	0.681338	−	0.756703i	0.980290	+	0.197565i	$0.0633035\pi$
$38$	−1.35681	+	0.142606i	−0.220103	+	0.0231338i
$39$	−9.31198	−	0.816444i	−1.49111	−	0.130736i
$40$	−0.609025	−	0.548368i	−0.0962952	−	0.0867046i
$41$	−3.35806	+	10.3350i	−0.524440	+	1.61406i	0.240979	+	0.970530i	$0.422531\pi$
$41$	−3.35806	+	10.3350i	−0.524440	+	1.61406i	−0.765420	+	0.643531i	$0.777469\pi$
$42$	−1.89703	+	4.17149i	−0.292718	+	0.643674i
$43$			7.89449i			1.20390i	0.798534	+	0.601949i	$0.205609\pi$
$43$			7.89449i			1.20390i	−0.798534	+	0.601949i	$0.794391\pi$
$44$	3.31409	+	0.129655i	0.499618	+	0.0195463i
$45$	−1.51292	−	1.93794i	−0.225533	−	0.288892i
$46$	−0.915622	−	2.05652i	−0.135001	−	0.303217i
$47$	−0.101280	−	0.476484i	−0.0147732	−	0.0695024i	0.970144	−	0.242532i	$-0.0779778\pi$
$47$	−0.101280	−	0.476484i	−0.0147732	−	0.0695024i	−0.984917	+	0.173029i	$0.944644\pi$
$48$	0.210763	+	1.71918i	0.0304210	+	0.248142i
$49$	1.08140	−	6.91597i	0.154485	−	0.987995i
$50$	3.50173	−	2.54416i	0.495220	−	0.359798i
$51$	7.65725	−	5.76791i	1.07223	−	0.807670i
$52$	4.01068	−	3.61123i	0.556181	−	0.500788i
$53$	5.29538	+	11.8936i	0.727377	+	1.63371i	0.772723	+	0.634743i	$0.218894\pi$
$53$	5.29538	+	11.8936i	0.727377	+	1.63371i	−0.0453466	+	0.998971i	$0.514439\pi$
$54$	−0.274851	+	5.18888i	−0.0374024	+	0.706117i
$55$	0.668616	−	2.63453i	0.0901562	−	0.355240i
$56$	−1.01490	−	2.44336i	−0.135621	−	0.326507i
$57$	1.72849	−	1.61124i	0.228944	−	0.213414i
$58$	6.12582	−	1.30208i	0.804359	−	0.170972i
$59$	0.606629	−	2.85396i	0.0789764	−	0.371555i	−0.920855	−	0.389905i	$-0.872508\pi$
$59$	0.606629	−	2.85396i	0.0789764	−	0.371555i	0.999832	+	0.0183500i	$0.00584132\pi$
$60$	1.41403	+	0.123978i	0.182551	+	0.0160054i
$61$	−1.10861	+	2.48998i	−0.141943	+	0.318809i	−0.970502	−	0.241092i	$-0.922494\pi$
$61$	−1.10861	+	2.48998i	−0.141943	+	0.318809i	0.828559	+	0.559901i	$0.189161\pi$
$62$	−1.78517	−	5.49419i	−0.226717	−	0.697763i
$63$	−1.72269	−	7.74805i	−0.217038	−	0.976163i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−2.21144	−	3.83033i	−0.274296	−	0.475094i
$66$	−4.72007	+	3.27429i	−0.581000	+	0.403037i
$67$	2.35441	−	4.07795i	0.287636	−	0.498201i	−0.685609	−	0.727970i	$-0.740464\pi$
$67$	2.35441	−	4.07795i	0.287636	−	0.498201i	0.973245	+	0.229769i	$0.0737972\pi$
$68$	−0.578545	+	5.50449i	−0.0701589	+	0.667517i
$69$	3.40987	+	1.89095i	0.410500	+	0.227644i
$70$	−2.13156	+	0.397236i	−0.254770	+	0.0474788i
$71$	−2.12867	−	2.92987i	−0.252627	−	0.347711i	0.663802	−	0.747908i	$-0.268942\pi$
$71$	−2.12867	−	2.92987i	−0.252627	−	0.347711i	−0.916429	+	0.400197i	$0.868942\pi$
$72$	−2.08317	−	2.15880i	−0.245504	−	0.254417i
$73$	0.719776	−	3.38628i	0.0842435	−	0.396334i	−0.915742	−	0.401767i	$-0.868396\pi$
$73$	0.719776	−	3.38628i	0.0842435	−	0.396334i	0.999985	+	0.00543304i	$0.00172940\pi$
$74$	−4.14442	−	4.60285i	−0.481779	−	0.535070i
$75$	−2.19324	+	7.16899i	−0.253254	+	0.827803i
$76$			1.36428i			0.156494i
$77$	5.60327	−	6.75303i	0.638551	−	0.769579i
$78$	−1.78534	+	9.17563i	−0.202150	+	1.03894i
$79$	10.1418	+	1.06594i	1.14104	+	0.119928i	0.656137	−	0.754642i	$-0.272189\pi$
$79$	10.1418	+	1.06594i	1.14104	+	0.119928i	0.484900	+	0.874570i	$0.338856\pi$
$80$	−0.609025	+	0.548368i	−0.0680910	+	0.0613094i
$81$	−5.02717	−	7.46509i	−0.558574	−	0.829455i
$82$	9.92741	+	4.41997i	1.09630	+	0.488104i
$83$	7.40963	−	5.38341i	0.813312	−	0.590906i	−0.101477	−	0.994838i	$-0.532357\pi$
$83$	7.40963	−	5.38341i	0.813312	−	0.590906i	0.914789	+	0.403932i	$0.132357\pi$
$84$	3.95034	+	2.32267i	0.431017	+	0.253424i
$85$	4.31390	+	1.40167i	0.467908	+	0.152033i
$86$	7.85124	+	0.825199i	0.846621	+	0.0889835i
$87$	−7.11797	+	8.18521i	−0.763127	+	0.877546i
$88$	0.475362	−	3.28238i	0.0506737	−	0.349903i
$89$	−5.82848	+	3.36507i	−0.617818	+	0.356697i	−0.776019	−	0.630710i	$-0.782764\pi$
$89$	−5.82848	+	3.36507i	−0.617818	+	0.356697i	0.158201	+	0.987407i	$0.449431\pi$
$90$	−2.08547	+	1.30207i	−0.219828	+	0.137250i
$91$	−1.13435	−	14.2337i	−0.118912	−	1.49210i
$92$	−2.14096	+	0.695641i	−0.223211	+	0.0725256i
$93$	8.19532	+	5.74071i	0.849815	+	0.595284i
$94$	−0.484461	+	0.0509189i	−0.0499683	+	0.00525188i
$95$	1.09363	+	0.232458i	0.112204	+	0.0238497i
$96$	1.73179	−	0.0299053i	0.176750	−	0.00305220i
$97$	4.17913	+	3.03631i	0.424326	+	0.308291i	0.779376	−	0.626556i	$-0.215536\pi$
$97$	4.17913	+	3.03631i	0.424326	+	0.308291i	−0.355050	+	0.934847i	$0.615536\pi$
$98$	−6.76504	−	1.79839i	−0.683372	−	0.181665i
$99$	3.11789	−	9.44875i	0.313359	−	0.949635i
$100$	−2.16419	−	3.74849i	−0.216419	−	0.374849i
$101$	−13.9380	+	6.20560i	−1.38688	+	0.617480i	−0.958232	−	0.285991i	$-0.907677\pi$
$101$	−13.9380	+	6.20560i	−1.38688	+	0.617480i	−0.428650	+	0.903471i	$0.641011\pi$
$102$	−4.93592	−	8.21822i	−0.488728	−	0.813725i
$103$	−1.48077	+	1.64456i	−0.145905	+	0.162044i	−0.811667	−	0.584120i	$-0.801440\pi$
$103$	−1.48077	+	1.64456i	−0.145905	+	0.162044i	0.665763	+	0.746164i	$0.268106\pi$
$104$	−3.17222	−	4.36618i	−0.311062	−	0.428139i
$105$	2.53498	−	2.77089i	0.247389	−	0.270412i
$106$	12.3820	−	4.02315i	1.20264	−	0.390763i
$107$	−11.5667	+	2.45858i	−1.11820	+	0.237680i	−0.729699	−	0.683769i	$-0.760340\pi$
$107$	−11.5667	+	2.45858i	−1.11820	+	0.237680i	−0.388499	+	0.921449i	$0.627006\pi$
$108$	5.13172	+	0.815730i	0.493800	+	0.0784937i
$109$	−6.24870	−	3.60769i	−0.598517	−	0.345554i	0.169941	−	0.985454i	$-0.445642\pi$
$109$	−6.24870	−	3.60769i	−0.598517	−	0.345554i	−0.768458	+	0.639900i	$0.778976\pi$
$110$	−2.55021	−	0.940337i	−0.243153	−	0.0896576i
$111$	10.5304	+	2.04894i	0.999500	+	0.194477i
$112$	−2.53606	+	0.753936i	−0.239635	+	0.0712403i
$113$	11.7571	+	3.82011i	1.10601	+	0.359365i	0.804414	−	0.594069i	$-0.202480\pi$
$113$	11.7571	+	3.82011i	1.10601	+	0.359365i	0.301599	+	0.953435i	$0.402480\pi$
$114$	−1.42174	−	1.88744i	−0.133158	−	0.176775i
$115$	0.192841	+	1.83476i	0.0179825	+	0.171092i
$116$	−0.654627	−	6.22836i	−0.0607806	−	0.578289i
$117$	−7.09210	−	14.5548i	−0.655665	−	1.34559i
$118$	−2.77492	−	0.901626i	−0.255452	−	0.0830014i
$119$	10.6321	+	10.0696i	0.974645	+	0.923078i
$120$	0.271105	−	1.39333i	0.0247484	−	0.127193i
$121$	10.3678	−	3.67535i	0.942530	−	0.334122i
$122$	2.36046	+	1.36281i	0.213706	+	0.123383i
$123$	−18.3404	+	4.23061i	−1.65370	+	0.381461i
$124$	−5.65070	+	1.20109i	−0.507448	+	0.107861i
$125$	−7.27066	+	2.36238i	−0.650308	+	0.211298i
$126$	−7.88568	+	0.903360i	−0.702512	+	0.0804777i
$127$	−3.83348	−	5.27633i	−0.340166	−	0.468198i	0.604324	−	0.796739i	$-0.293443\pi$
$127$	−3.83348	−	5.27633i	−0.340166	−	0.468198i	−0.944490	+	0.328540i	$0.893443\pi$
$128$	−0.669131	+	0.743145i	−0.0591433	+	0.0656853i
$129$	−11.7219	+	7.04027i	−1.03206	+	0.619861i
$130$	−4.04051	+	1.79895i	−0.354376	+	0.157778i
$131$	−10.9098	−	18.8963i	−0.953193	−	1.65098i	−0.738450	−	0.674308i	$-0.764442\pi$
$131$	−10.9098	−	18.8963i	−0.953193	−	1.65098i	−0.214743	−	0.976671i	$-0.568891\pi$
$132$	2.76297	+	5.03646i	0.240486	+	0.438368i
$133$	2.86581	+	2.19453i	0.248498	+	0.190290i
$134$	−3.80951	−	2.76777i	−0.329091	−	0.239099i
$135$	1.52829	−	3.97467i	0.131534	−	0.342086i
$136$	5.41386	+	1.15075i	0.464235	+	0.0986761i
$137$	−7.20162	+	0.756920i	−0.615276	+	0.0646681i	−0.407040	−	0.913411i	$-0.633439\pi$
$137$	−7.20162	+	0.756920i	−0.615276	+	0.0646681i	−0.208236	+	0.978079i	$0.566772\pi$
$138$	2.23702	−	3.19353i	0.190428	−	0.271851i
$139$	−20.5836	+	6.68803i	−1.74588	+	0.567271i	−0.995588	−	0.0938343i	$-0.970088\pi$
$139$	−20.5836	+	6.68803i	−1.74588	+	0.567271i	−0.750293	+	0.661105i	$0.770088\pi$
$140$	0.172252	+	2.16140i	0.0145579	+	0.182672i
$141$	0.617174	−	0.575309i	0.0519754	−	0.0484498i
$142$	−3.13632	+	1.81076i	−0.263195	+	0.151955i
$143$	7.91405	−	16.0549i	0.661806	−	1.34258i
$144$	−2.36472	+	1.84610i	−0.197060	+	0.153842i
$145$	−5.10429	−	0.536482i	−0.423888	−	0.0445524i
$146$	−3.29249	−	1.06980i	−0.272489	−	0.0885370i
$147$	11.2334	−	4.56194i	0.926513	−	0.376263i
$148$	−5.01084	+	3.64059i	−0.411889	+	0.299255i
$149$	6.03743	+	2.68804i	0.494606	+	0.220213i	0.638853	−	0.769329i	$-0.279409\pi$
$149$	6.03743	+	2.68804i	0.494606	+	0.220213i	−0.144247	+	0.989542i	$0.546076\pi$
$150$	6.90046	+	2.93059i	0.563420	+	0.239282i
$151$	13.4063	−	12.0711i	1.09099	−	0.982330i	0.0910788	−	0.995844i	$-0.470968\pi$
$151$	13.4063	−	12.0711i	1.09099	−	0.982330i	0.999909	+	0.0135142i	$0.00430182\pi$
$152$	1.35681	+	0.142606i	0.110052	+	0.0115669i
$153$	15.3930	+	6.22587i	1.24445	+	0.503332i
$154$	−6.13034	−	6.27845i	−0.493997	−	0.505932i
$155$			4.73434i			0.380271i
$156$	8.93874	+	2.73467i	0.715672	+	0.218949i
$157$	9.03791	+	10.0376i	0.721304	+	0.801089i	0.986614	−	0.163074i	$-0.0521409\pi$
$157$	9.03791	+	10.0376i	0.721304	+	0.801089i	−0.265310	+	0.964163i	$0.585474\pi$
$158$	2.12020	−	9.97477i	0.168674	−	0.793550i
$159$	−12.9375	+	18.4694i	−1.02601	+	1.46472i
$160$	0.481704	+	0.663008i	0.0380820	+	0.0524154i
$161$	−1.98260	+	5.61629i	−0.156251	+	0.442626i
$162$	−7.94968	+	4.21931i	−0.624586	+	0.331500i
$163$	0.747732	−	7.11419i	0.0585669	−	0.557227i	−0.925415	−	0.378956i	$-0.876283\pi$
$163$	0.747732	−	7.11419i	0.0585669	−	0.557227i	0.983982	−	0.178270i	$-0.0570502\pi$
$164$	5.43345	−	9.41101i	0.424281	−	0.734877i
$165$	4.50808	−	1.35668i	0.350954	−	0.105618i
$166$	−4.57940	−	7.93176i	−0.355431	−	0.615624i
$167$	−0.591761	−	0.429939i	−0.0457918	−	0.0332697i	0.564654	−	0.825328i	$-0.309010\pi$
$167$	−0.591761	−	0.429939i	−0.0457918	−	0.0332697i	−0.610446	+	0.792058i	$0.709010\pi$
$168$	2.72287	−	3.68591i	0.210074	−	0.284374i
$169$	−4.98337	−	15.3372i	−0.383336	−	1.17979i
$170$	1.84492	−	4.14376i	0.141499	−	0.317812i
$171$	3.93387	+	1.12961i	0.300831	+	0.0863833i
$172$	1.64136	−	7.72198i	0.125152	−	0.588795i
$173$	16.0384	−	3.40908i	1.21938	−	0.259187i	0.447109	−	0.894480i	$-0.352454\pi$
$173$	16.0384	−	3.40908i	1.21938	−	0.259187i	0.772272	+	0.635292i	$0.219120\pi$
$174$	7.39633	+	7.93457i	0.560715	+	0.601518i
$175$	−11.3553	−	1.48356i	−0.858381	−	0.112147i
$176$	−3.21471	−	0.815860i	−0.242318	−	0.0614978i
$177$	4.77862	−	1.64441i	0.359183	−	0.123602i
$178$	2.73740	+	6.14830i	0.205177	+	0.460834i
$179$	−18.7330	+	16.8672i	−1.40017	+	1.26072i	−0.475618	+	0.879652i	$0.657776\pi$
$179$	−18.7330	+	16.8672i	−1.40017	+	1.26072i	−0.924549	+	0.381064i	$0.875558\pi$
$180$	1.07694	+	2.21015i	0.0802705	+	0.164735i
$181$	6.22315	−	4.52139i	0.462563	−	0.336072i	−0.331973	−	0.943289i	$-0.607714\pi$
$181$	6.22315	−	4.52139i	0.462563	−	0.336072i	0.794536	+	0.607217i	$0.207714\pi$
$182$	−14.2743	−	0.359694i	−1.05808	−	0.0266623i
$183$	−4.68583	+	0.574460i	−0.346387	+	0.0424653i
$184$	0.468039	+	2.20195i	0.0345043	+	0.162330i
$185$	2.06456	+	4.63708i	0.151789	+	0.340925i
$186$	6.56590	−	7.55036i	0.481435	−	0.553619i
$187$	4.98576	+	17.6668i	0.364595	+	1.29193i
$188$			0.487129i			0.0355275i
$189$	9.96821	−	9.46757i	0.725081	−	0.688664i
$190$	0.345500	−	1.06334i	0.0250652	−	0.0771427i
$191$	6.46030	+	5.81688i	0.467451	+	0.420895i	0.868901	−	0.494986i	$-0.164827\pi$
$191$	6.46030	+	5.81688i	0.467451	+	0.420895i	−0.401450	+	0.915881i	$0.631494\pi$
$192$	0.151280	−	1.72543i	0.0109177	−	0.124522i
$193$	2.61720	−	0.275079i	0.188390	−	0.0198006i	−0.00986337	−	0.999951i	$-0.503140\pi$
$193$	2.61720	−	0.275079i	0.188390	−	0.0198006i	0.198254	+	0.980151i	$0.436473\pi$
$194$	3.45652	−	3.83885i	0.248163	−	0.275613i
$195$	3.71521	−	6.69947i	0.266052	−	0.479759i
$196$	−2.49568	+	6.54000i	−0.178263	+	0.467143i
$197$	14.5091			1.03373			0.516866	−	0.856066i	$-0.327099\pi$
$197$	14.5091			1.03373			0.516866	+	0.856066i	$0.327099\pi$
$198$	−9.07108	−	4.08847i	−0.644653	−	0.290555i
$199$	−5.00511	+	8.66910i	−0.354803	+	0.614536i	−0.987084	−	0.160202i	$-0.948785\pi$
$199$	−5.00511	+	8.66910i	−0.354803	+	0.614536i	0.632281	+	0.774739i	$0.282119\pi$
$200$	−3.95417	+	1.76051i	−0.279602	+	0.124487i
$201$	8.15469	−	0.140818i	0.575187	−	0.00993256i
$202$	4.71468	+	14.5103i	0.331724	+	1.02094i
$203$	−14.1363	−	8.64358i	−0.992176	−	0.606660i
$204$	−8.68914	+	4.04984i	−0.608362	+	0.283545i
$205$	−6.61821	−	5.95906i	−0.462236	−	0.416199i
$206$	1.48077	+	1.64456i	0.103170	+	0.114582i
$207$	0.233172	+	6.74940i	0.0162066	+	0.469116i
$208$	−4.67385	+	2.69845i	−0.324073	+	0.187104i
$209$	1.67740	+	4.20240i	0.116029	+	0.290686i
$210$	−2.49074	−	2.81073i	−0.171877	−	0.193959i
$211$	−14.1618	+	19.4920i	−0.974938	+	1.34189i	−0.0354260	+	0.999372i	$0.511279\pi$
$211$	−14.1618	+	19.4920i	−0.974938	+	1.34189i	−0.939512	+	0.342515i	$0.888721\pi$
$212$	−2.70684	−	12.7347i	−0.185907	−	0.874622i
$213$	2.45200	−	5.77355i	0.168008	−	0.395597i
$214$	1.23606	+	11.7604i	0.0844956	+	0.803922i
$215$	−5.91038	−	2.63147i	−0.403085	−	0.179465i
$216$	1.34767	−	5.01834i	0.0916975	−	0.341455i
$217$	−6.56646	+	13.8019i	−0.445761	+	0.936934i
$218$	−4.24109	+	5.83736i	−0.287243	+	0.395356i
$219$	5.66992	−	1.95113i	0.383138	−	0.131845i
$220$	−1.20176	+	2.43795i	−0.0810223	+	0.164366i
$221$	25.8689	+	14.9354i	1.74013	+	1.00466i
$222$	3.13844	−	10.2585i	0.210638	−	0.688507i
$223$	−5.39133	+	16.5928i	−0.361030	+	1.11114i	0.591400	+	0.806378i	$0.298575\pi$
$223$	−5.39133	+	16.5928i	−0.361030	+	1.11114i	−0.952430	+	0.304758i	$0.901425\pi$
$224$	0.484716	+	2.60097i	0.0323865	+	0.173785i
$225$	−12.6006	+	3.13669i	−0.840040	+	0.209113i
$226$	5.02813	−	11.2934i	0.334466	−	0.751223i
$227$	13.5237	+	2.87456i	0.897601	+	0.190791i	0.633535	−	0.773714i	$-0.281603\pi$
$227$	13.5237	+	2.87456i	0.897601	+	0.190791i	0.264065	+	0.964505i	$0.414936\pi$
$228$	−2.02572	+	1.21666i	−0.134156	+	0.0805752i
$229$	−1.22865	+	11.6898i	−0.0811915	+	0.772486i	0.875860	+	0.482566i	$0.160295\pi$
$229$	−1.22865	+	11.6898i	−0.0811915	+	0.772486i	−0.957051	+	0.289920i	$0.906371\pi$
$230$	1.84486			0.121647
$231$	15.0240	+	2.29754i	0.988508	+	0.151167i
$232$	−6.26267			−0.411164
$233$	−2.01977	+	19.2169i	−0.132320	+	1.25894i	0.703802	+	0.710396i	$0.251484\pi$
$233$	−2.01977	+	19.2169i	−0.132320	+	1.25894i	−0.836122	+	0.548543i	$0.815183\pi$
$234$	−15.2163	+	5.53187i	−0.994724	+	0.361629i
$235$	0.390490	+	0.0830012i	0.0254728	+	0.00541440i
$236$	−1.18675	+	2.66547i	−0.0772505	+	0.173508i
$237$	7.46163	+	16.0093i	0.484685	+	1.03992i
$238$	11.1258	−	9.52132i	0.721178	−	0.617176i
$239$	3.70446	−	11.4011i	0.239621	−	0.737479i	−0.756853	−	0.653585i	$-0.773264\pi$
$239$	3.70446	−	11.4011i	0.239621	−	0.737479i	0.996475	−	0.0838939i	$-0.0267357\pi$
$240$	−1.35736	−	0.415262i	−0.0876169	−	0.0268051i
$241$	9.19652	+	5.30961i	0.592400	+	0.342022i	0.766046	−	0.642786i	$-0.222222\pi$
$241$	9.19652	+	5.30961i	0.592400	+	0.342022i	−0.173646	+	0.984808i	$0.555555\pi$
$242$	−2.57148	−	10.6952i	−0.165301	−	0.687514i
$243$	6.60115	−	14.1218i	0.423464	−	0.905913i
$244$	1.60208	−	2.20507i	0.102563	−	0.141165i
$245$	4.81733	+	3.11491i	0.307768	+	0.199004i
$246$	2.29034	+	18.6822i	0.146027	+	1.19113i
$247$	6.72633	+	2.99476i	0.427986	+	0.190552i
$248$	0.603854	+	5.74529i	0.0383448	+	0.364826i
$249$	14.6013	+	6.20109i	0.925319	+	0.392978i
$250$	1.58945	+	7.47777i	0.100526	+	0.472936i
$251$	−0.290555	+	0.399915i	−0.0183397	+	0.0252424i	−0.818088	−	0.575093i	$-0.804966\pi$
$251$	−0.290555	+	0.399915i	−0.0183397	+	0.0252424i	0.799749	+	0.600335i	$0.204966\pi$
$252$	0.0741332	+	7.93691i	0.00466995	+	0.499978i
$253$	−5.73952	+	4.77514i	−0.360841	+	0.300210i
$254$	−5.64813	+	3.26095i	−0.354395	+	0.204610i
$255$	1.76588	+	7.65539i	0.110584	+	0.479399i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	4.50621	+	4.05741i	0.281090	+	0.253095i	0.797600	−	0.603186i	$-0.206103\pi$
$257$	4.50621	+	4.05741i	0.281090	+	0.253095i	−0.516510	+	0.856281i	$0.672769\pi$
$258$	5.77643	+	12.3936i	0.359625	+	0.771593i
$259$	−0.412802	+	16.3819i	−0.0256502	+	1.01792i
$260$	1.36675	+	4.20641i	0.0847620	+	0.260871i
$261$	−18.5014	−	3.26941i	−1.14521	−	0.202371i
$262$	−19.9332	+	8.87483i	−1.23148	+	0.548289i
$263$	7.85828	−	13.6109i	0.484562	−	0.839287i	−0.515280	−	0.857022i	$-0.672312\pi$
$263$	7.85828	−	13.6109i	0.484562	−	0.839287i	0.999843	+	0.0177350i	$0.00564551\pi$
$264$	5.29768	−	2.22138i	0.326050	−	0.136717i
$265$	−10.6695			−0.655424
$266$	2.48206	−	2.62072i	0.152185	−	0.160687i
$267$	−10.1944	−	5.65331i	−0.623884	−	0.345977i
$268$	−3.15081	+	3.49933i	−0.192466	+	0.213756i
$269$	19.3123	−	2.02980i	1.17749	−	0.123759i	0.504501	−	0.863411i	$-0.331677\pi$
$269$	19.3123	−	2.02980i	1.17749	−	0.123759i	0.672989	+	0.739652i	$0.265010\pi$
$270$	−3.79315	−	1.93538i	−0.230844	−	0.117784i
$271$	0.997419	+	0.898080i	0.0605889	+	0.0545545i	0.698869	−	0.715250i	$-0.253687\pi$
$271$	0.997419	+	0.898080i	0.0605889	+	0.0545545i	−0.638280	+	0.769804i	$0.720354\pi$
$272$	1.71035	−	5.26392i	0.103705	−	0.319172i
$273$	20.1230	−	14.3779i	1.21790	−	0.870188i
$274$			7.24129i			0.437462i
$275$	−11.2752	−	8.88559i	−0.679920	−	0.535821i
$276$	−2.94220	−	2.55858i	−0.177100	−	0.154009i
$277$	−4.26795	−	9.58596i	−0.256436	−	0.575965i	0.738749	−	0.673981i	$-0.235417\pi$
$277$	−4.26795	−	9.58596i	−0.256436	−	0.575965i	−0.995185	+	0.0980161i	$0.968750\pi$
$278$	4.49981	+	21.1700i	0.269881	+	1.26969i
$279$	−1.21539	+	17.2881i	−0.0727634	+	1.03501i
$280$	2.16757	+	0.0546198i	0.129537	+	0.00326416i
$281$	2.46866	−	1.79359i	0.147268	−	0.106997i	−0.511712	−	0.859157i	$-0.670988\pi$
$281$	2.46866	−	1.79359i	0.147268	−	0.106997i	0.658980	+	0.752161i	$0.270988\pi$
$282$	−0.507645	−	0.673929i	−0.0302298	−	0.0401319i
$283$	−1.18492	+	1.06691i	−0.0704363	+	0.0634211i	−0.703597	−	0.710599i	$-0.748424\pi$
$283$	−1.18492	+	1.06691i	−0.0704363	+	0.0634211i	0.633161	+	0.774020i	$0.281757\pi$
$284$	1.47300	+	3.30842i	0.0874067	+	0.196319i
$285$	0.630133	+	1.83115i	0.0373259	+	0.108468i
$286$	−15.1397	−	9.54889i	−0.895229	−	0.564638i
$287$	−11.0288	−	26.5517i	−0.651008	−	1.56730i
$288$	1.58881	+	2.54474i	0.0936214	+	0.149950i
$289$	−13.3362	+	2.83469i	−0.784481	+	0.166747i
$290$	−1.06709	+	5.02025i	−0.0626615	+	0.294799i
$291$	−0.781465	+	8.91303i	−0.0458103	+	0.522491i
$292$	−1.40810	+	3.16263i	−0.0824025	+	0.185079i
$293$	4.76787	+	14.6740i	0.278542	+	0.857264i	0.988260	+	0.152779i	$0.0488222\pi$
$293$	4.76787	+	14.6740i	0.278542	+	0.857264i	−0.709718	+	0.704486i	$0.751178\pi$
$294$	−3.36274	−	11.6487i	−0.196119	−	0.679365i
$295$	1.93448	+	1.40548i	0.112630	+	0.0818301i
$296$	3.09687	+	5.36394i	0.180002	+	0.311772i
$297$	16.8102	−	3.79683i	0.975429	−	0.220315i
$298$	3.30440	−	5.72338i	0.191418	−	0.331547i
$299$	−1.26994	+	12.0826i	−0.0734423	+	0.698757i
$300$	3.63583	−	6.55632i	0.209915	−	0.378530i
$301$	−13.5806	−	15.8691i	−0.782772	−	0.914680i
$302$	−10.6036	−	14.5946i	−0.610169	−	0.839825i
$303$	−21.6441	−	15.1613i	−1.24342	−	0.870997i
$304$	0.283650	−	1.33447i	0.0162684	−	0.0765370i
$305$	−1.49464	−	1.65997i	−0.0855831	−	0.0950496i
$306$	7.80078	−	14.6579i	0.445941	−	0.837938i
$307$		−	22.7875i		−	1.30055i	−0.759699	−	0.650275i	$-0.774654\pi$
$307$		−	22.7875i		−	1.30055i	0.759699	−	0.650275i	$-0.225346\pi$
$308$	−6.88485	+	5.44048i	−0.392301	+	0.310000i
$309$	−3.76243	−	0.732071i	−0.214037	−	0.0416461i
$310$	4.70840	+	0.494873i	0.267419	+	0.0281069i
$311$	7.79971	−	7.02289i	0.442281	−	0.398231i	−0.417678	−	0.908595i	$-0.637156\pi$
$311$	7.79971	−	7.02289i	0.442281	−	0.398231i	0.859959	+	0.510364i	$0.170489\pi$
$312$	3.65404	−	8.60392i	0.206870	−	0.487101i
$313$	−20.1622	−	8.97678i	−1.13963	−	0.507398i	−0.251899	−	0.967753i	$-0.581055\pi$
$313$	−20.1622	−	8.97678i	−1.13963	−	0.507398i	−0.887735	+	0.460356i	$0.847722\pi$
$314$	10.9274	−	7.93919i	0.616666	−	0.448034i
$315$	6.37497	+	1.29293i	0.359189	+	0.0728484i
$316$	−9.69851	−	3.15124i	−0.545584	−	0.177271i
$317$	23.8951	+	2.51147i	1.34208	+	0.141058i	0.748189	−	0.663486i	$-0.230924\pi$
$317$	23.8951	+	2.51147i	1.34208	+	0.141058i	0.593893	+	0.804544i	$0.297590\pi$
$318$	17.0159	+	14.7972i	0.954202	+	0.829788i
$319$	−9.67432	−	18.3804i	−0.541658	−	1.02910i
$320$	0.709728	−	0.409762i	0.0396750	−	0.0229064i
$321$	−13.9657	−	14.9820i	−0.779490	−	0.836214i
$322$	5.37829	+	2.55880i	0.299720	+	0.142596i
$323$	−7.18146	+	2.33340i	−0.399587	+	0.129834i
$324$	3.36523	+	8.34717i	0.186957	+	0.463732i
$325$	−23.2319	+	2.44177i	−1.28867	+	0.135445i
$326$	−6.99706	−	1.48727i	−0.387531	−	0.0823723i
$327$	−0.215778	−	12.4955i	−0.0119325	−	0.691005i
$328$	−8.79151	−	6.38740i	−0.485430	−	0.352685i
$329$	1.02327	+	0.783576i	0.0564144	+	0.0432000i
$330$	−0.878030	−	4.62520i	−0.0483339	−	0.254609i
$331$	−1.32492	−	2.29483i	−0.0728242	−	0.126135i	0.827314	−	0.561740i	$-0.189868\pi$
$331$	−1.32492	−	2.29483i	−0.0728242	−	0.126135i	−0.900138	+	0.435605i	$0.856535\pi$
$332$	−8.36698	+	3.72522i	−0.459198	+	0.204448i
$333$	6.34863	+	17.4630i	0.347903	+	0.956967i
$334$	−0.489440	+	0.543578i	−0.0267810	+	0.0297433i
$335$	2.26825	+	3.12198i	0.123928	+	0.170572i
$336$	−3.38110	−	3.09324i	−0.184454	−	0.168750i
$337$	11.2086	−	3.64189i	0.610570	−	0.198386i	0.0126209	−	0.999920i	$-0.495983\pi$
$337$	11.2086	−	3.64189i	0.610570	−	0.198386i	0.597949	+	0.801534i	$0.295983\pi$
$338$	−15.7741	+	3.35289i	−0.857999	+	0.182373i
$339$	4.81272	+	20.8639i	0.261391	+	1.13317i
$340$	−3.92821	−	2.26795i	−0.213037	−	0.122997i
$341$	−15.9291	+	10.6474i	−0.862610	+	0.576587i
$342$	1.53462	−	3.79425i	0.0829829	−	0.205169i
$343$	9.72351	+	15.7624i	0.525020	+	0.851090i
$344$	−7.50811	−	2.43953i	−0.404810	−	0.131531i
$345$	−2.55232	+	1.92256i	−0.137412	+	0.103507i
$346$	−1.71393	−	16.3069i	−0.0921413	−	0.876666i
$347$	1.08634	+	10.3358i	0.0583177	+	0.554856i	0.984202	+	0.177049i	$0.0566550\pi$
$347$	1.08634	+	10.3358i	0.0583177	+	0.554856i	−0.925884	+	0.377807i	$0.876678\pi$
$348$	8.66423	−	6.52643i	0.464451	−	0.349853i
$349$	5.57527	+	1.81152i	0.298438	+	0.0969682i	0.454409	−	0.890793i	$-0.349851\pi$
$349$	5.57527	+	1.81152i	0.298438	+	0.0969682i	−0.155971	+	0.987762i	$0.549851\pi$
$350$	−2.66239	+	11.1380i	−0.142311	+	0.595353i
$351$	15.2865	−	23.5104i	0.815935	−	1.25489i
$352$	−1.14742	+	3.11182i	−0.0611577	+	0.165861i
$353$	−24.6487	−	14.2309i	−1.31192	−	0.757436i	−0.329503	−	0.944154i	$-0.606881\pi$
$353$	−24.6487	−	14.2309i	−1.31192	−	0.757436i	−0.982413	+	0.186719i	$0.940215\pi$
$354$	−1.13590	−	4.92433i	−0.0603726	−	0.261725i
$355$	2.90306	−	0.617065i	0.154078	−	0.0327504i
$356$	6.40075	−	2.07973i	0.339239	−	0.110226i
$357$	−5.46989	+	24.7668i	−0.289497	+	1.31080i
$358$	14.8167	+	20.3934i	0.783087	+	1.07783i
$359$	−2.01803	+	2.24125i	−0.106508	+	0.118289i	−0.794041	−	0.607864i	$-0.792027\pi$
$359$	−2.01803	+	2.24125i	−0.106508	+	0.118289i	0.687534	+	0.726153i	$0.258693\pi$
$360$	2.31061	−	0.840018i	0.121780	−	0.0442728i
$361$	15.6570	−	6.97095i	0.824053	−	0.366892i
$362$	−3.84612	−	6.66168i	−0.202148	−	0.350130i
$363$	14.7032	+	12.1167i	0.771719	+	0.635964i
$364$	−1.84980	+	14.1585i	−0.0969557	+	0.742108i
$365$	2.29529	+	1.66763i	0.120141	+	0.0872875i
$366$	0.0815105	+	4.72021i	0.00426062	+	0.246729i
$367$	−10.2044	−	2.16902i	−0.532666	−	0.113222i	−0.0662769	−	0.997801i	$-0.521112\pi$
$367$	−10.2044	−	2.16902i	−0.532666	−	0.113222i	−0.466389	+	0.884580i	$0.654445\pi$
$368$	2.23881	−	0.235308i	0.116706	−	0.0122663i
$369$	−22.6376	−	23.4594i	−1.17847	−	1.22125i
$370$	4.82748	−	1.56854i	0.250969	−	0.0815447i
$371$	−31.1047	−	14.7985i	−1.61487	−	0.768300i
$372$	−6.82268	−	7.31916i	−0.353739	−	0.379481i
$373$	28.1083	−	16.2283i	1.45539	−	0.840271i	0.456613	−	0.889666i	$-0.349063\pi$
$373$	28.1083	−	16.2283i	1.45539	−	0.840271i	0.998779	+	0.0493948i	$0.0157293\pi$
$374$	18.0912	−	3.11176i	0.935475	−	0.160905i
$375$	−9.99166	−	8.68889i	−0.515967	−	0.448692i
$376$	0.484461	+	0.0509189i	0.0249841	+	0.00262594i
$377$	−32.1448	−	10.4445i	−1.65554	−	0.537917i
$378$	−8.37374	−	10.9032i	−0.430699	−	0.560802i
$379$	21.4569	−	15.5894i	1.10217	−	0.800773i	0.120757	−	0.992682i	$-0.461468\pi$
$379$	21.4569	−	15.5894i	1.10217	−	0.800773i	0.981413	+	0.191909i	$0.0614680\pi$
$380$	−1.02140	−	0.454756i	−0.0523967	−	0.0233285i
$381$	4.41574	−	10.3974i	0.226225	−	0.532677i
$382$	6.46030	−	5.81688i	0.330538	−	0.297618i
$383$	−4.21706	−	0.443231i	−0.215482	−	0.0226481i	−0.00382765	−	0.999993i	$-0.501218\pi$
$383$	−4.21706	−	0.443231i	−0.215482	−	0.0226481i	−0.211654	+	0.977345i	$0.567885\pi$
$384$	−1.70017	−	0.330808i	−0.0867613	−	0.0168815i
$385$	3.18807	+	6.44600i	0.162479	+	0.328518i
$386$		−	2.63162i		−	0.133946i
$387$	−20.9071	−	11.1265i	−1.06277	−	0.565593i
$388$	−3.45652	−	3.83885i	−0.175478	−	0.194888i
$389$	−3.92933	+	18.4860i	−0.199225	+	0.937280i	0.758962	+	0.651135i	$0.225707\pi$
$389$	−3.92933	+	18.4860i	−0.199225	+	0.937280i	−0.958187	+	0.286144i	$0.907626\pi$
$390$	−6.27443	−	4.39515i	−0.317718	−	0.222557i
$391$	−7.32359	−	10.0801i	−0.370370	−	0.509771i
$392$	6.24330	+	3.16562i	0.315334	+	0.159888i
$393$	18.3284	−	33.0508i	0.924545	−	1.66719i
$394$	1.51662	−	14.4296i	0.0764060	−	0.726954i
$395$	−4.17859	+	7.23754i	−0.210248	+	0.364160i
$396$	−5.01426	+	8.59402i	−0.251976	+	0.431866i
$397$	3.08815	+	5.34884i	0.154990	+	0.268451i	0.933055	−	0.359733i	$-0.117132\pi$
$397$	3.08815	+	5.34884i	0.154990	+	0.268451i	−0.778065	+	0.628183i	$0.783799\pi$
$398$	8.09844	+	5.88386i	0.405938	+	0.294931i
$399$	−0.702768	+	6.21230i	−0.0351824	+	0.311004i
$400$	1.33754	+	4.11654i	0.0668772	+	0.205827i
$401$	−3.72705	+	8.37109i	−0.186120	+	0.418032i	−0.982373	−	0.186931i	$-0.940146\pi$
$401$	−3.72705	+	8.37109i	−0.186120	+	0.418032i	0.796253	+	0.604964i	$0.206812\pi$
$402$	0.712350	−	8.12473i	0.0355288	−	0.405225i
$403$	−6.48218	+	30.4962i	−0.322900	+	1.51913i
$404$	14.9236	−	3.17212i	0.742478	−	0.157819i
$405$	7.26461	−	1.27536i	0.360981	−	0.0633730i
$406$	−10.0739	+	13.1554i	−0.499958	+	0.652891i
$407$	−10.9588	+	17.3750i	−0.543206	+	0.861249i
$408$	3.11939	+	9.06486i	0.154433	+	0.448778i
$409$	−2.43028	−	5.45851i	−0.120170	−	0.269906i	0.843438	−	0.537227i	$-0.180528\pi$
$409$	−2.43028	−	5.45851i	−0.120170	−	0.269906i	−0.963607	+	0.267321i	$0.913862\pi$
$410$	−6.61821	+	5.95906i	−0.326850	+	0.294297i
$411$	−7.54626	−	10.0181i	−0.372230	−	0.494157i
$412$	1.79034	−	1.30076i	0.0882035	−	0.0640836i
$413$	3.69015	+	6.78045i	0.181581	+	0.333644i
$414$	6.73680	+	0.473609i	0.331096	+	0.0232766i
$415$	1.56056	+	7.34183i	0.0766046	+	0.360396i
$416$	2.19512	+	4.93031i	0.107624	+	0.241728i
$417$	−28.2869	−	24.5987i	−1.38522	−	1.20460i
$418$	4.35472	−	1.22895i	0.212996	−	0.0601097i
$419$			3.24937i			0.158742i	0.996845	+	0.0793710i	$0.0252912\pi$
$419$			3.24937i			0.158742i	−0.996845	+	0.0793710i	$0.974709\pi$
$420$	−3.05569	+	2.18329i	−0.149102	+	0.106534i
$421$	−8.63563	+	26.5777i	−0.420875	+	1.29532i	0.486015	+	0.873951i	$0.338450\pi$
$421$	−8.63563	+	26.5777i	−0.420875	+	1.29532i	−0.906889	+	0.421369i	$0.861550\pi$
$422$	17.9050	+	16.1217i	0.871599	+	0.784792i
$423$	1.40463	+	0.403337i	0.0682952	+	0.0196109i
$424$	−12.9479	+	1.36088i	−0.628804	+	0.0660900i
$425$	16.0302	−	17.8033i	0.777579	−	0.863589i
$426$	−5.48562	−	3.04206i	−0.265779	−	0.147389i
$427$	−2.05495	−	6.91233i	−0.0994458	−	0.334511i
$428$	11.8251			0.571590
$429$	30.8964	−	2.56670i	1.49169	−	0.123921i
$430$	−3.23486	+	5.60294i	−0.155999	+	0.270198i
$431$	16.5278	−	7.35864i	0.796115	−	0.354453i	0.0319625	−	0.999489i	$-0.489824\pi$
$431$	16.5278	−	7.35864i	0.796115	−	0.354453i	0.764152	+	0.645036i	$0.223158\pi$
$432$	−4.84998	−	1.86485i	−0.233345	−	0.0897226i
$433$	−9.64182	−	29.6745i	−0.463356	−	1.42606i	−0.861038	−	0.508541i	$-0.830185\pi$
$433$	−9.64182	−	29.6745i	−0.463356	−	1.42606i	0.397682	−	0.917523i	$-0.369815\pi$
$434$	13.0399	+	7.97318i	0.625936	+	0.382725i
$435$	−3.75540	−	8.05740i	−0.180058	−	0.386323i
$436$	5.36207	+	4.82803i	0.256797	+	0.231221i
$437$	−2.05503	−	2.28234i	−0.0983053	−	0.109179i
$438$	−1.34777	−	5.84281i	−0.0643990	−	0.279180i
$439$	−12.9943	+	7.50224i	−0.620182	+	0.358062i	−0.776940	−	0.629575i	$-0.783229\pi$
$439$	−12.9943	+	7.50224i	−0.620182	+	0.358062i	0.156758	+	0.987637i	$0.449896\pi$
$440$	2.29897	+	1.45001i	0.109599	+	0.0691264i
$441$	16.7915	+	12.6113i	0.799597	+	0.600536i
$442$	17.5576	−	24.1660i	0.835131	−	1.14946i
$443$	−1.55941	−	7.33643i	−0.0740897	−	0.348564i	0.925451	−	0.378867i	$-0.123686\pi$
$443$	−1.55941	−	7.33643i	−0.0740897	−	0.348564i	−0.999541	+	0.0303026i	$0.990353\pi$
$444$	−9.87427	−	4.19356i	−0.468612	−	0.199017i
$445$	−0.576528	−	5.48530i	−0.0273301	−	0.260028i
$446$	15.9384	+	7.09621i	0.754703	+	0.336015i
$447$	1.39289	+	11.3617i	0.0658814	+	0.537390i
$448$	2.63739	−	0.210185i	0.124605	−	0.00993033i
$449$	16.1391	−	22.2136i	0.761653	−	1.04833i	−0.235421	−	0.971893i	$-0.575647\pi$
$449$	16.1391	−	22.2136i	0.761653	−	1.04833i	0.997075	−	0.0764326i	$-0.0243530\pi$
$450$	1.80238	+	12.8594i	0.0849652	+	0.606200i
$451$	5.16571	−	35.6693i	0.243244	−	1.67960i
$452$	−10.7059	−	6.18106i	−0.503564	−	0.290733i
$453$	29.8791	+	9.14104i	1.40384	+	0.429484i
$454$	4.27242	−	13.1492i	0.200515	−	0.617121i
$455$	11.0345	+	3.89527i	0.517305	+	0.182613i
$456$	0.998249	+	2.14180i	0.0467473	+	0.100299i
$457$	−5.73200	+	12.8743i	−0.268132	+	0.602234i	−0.996559	−	0.0828897i	$-0.973585\pi$
$457$	−5.73200	+	12.8743i	−0.268132	+	0.602234i	0.728427	+	0.685123i	$0.240252\pi$
$458$	11.4974	+	2.44384i	0.537236	+	0.114193i
$459$	4.48311	+	28.4081i	0.209254	+	1.32598i
$460$	0.192841	−	1.83476i	0.00899125	−	0.0855460i
$461$	−33.9622			−1.58178			−0.790890	−	0.611959i	$-0.790382\pi$
$461$	−33.9622			−1.58178			−0.790890	+	0.611959i	$0.790382\pi$
$462$	3.85539	−	14.7016i	0.179369	−	0.683979i
$463$	39.7696			1.84825			0.924124	−	0.382093i	$-0.124797\pi$
$463$	39.7696			1.84825			0.924124	+	0.382093i	$0.124797\pi$
$464$	−0.654627	+	6.22836i	−0.0303903	+	0.289144i
$465$	−7.02965	+	4.22206i	−0.325992	+	0.195793i
$466$	18.9005	+	4.01742i	0.875548	+	0.186103i
$467$	6.24968	−	14.0370i	0.289201	−	0.649556i	−0.709264	−	0.704943i	$-0.750973\pi$
$467$	6.24968	−	14.0370i	0.289201	−	0.649556i	0.998465	+	0.0553871i	$0.0176393\pi$
$468$	3.91102	+	15.7112i	0.180787	+	0.726252i
$469$	2.28244	+	12.2475i	0.105393	+	0.565536i
$470$	0.123364	−	0.379675i	0.00569035	−	0.0175131i
$471$	−6.84413	+	22.3712i	−0.315361	+	1.03081i
$472$	2.52682	+	1.45886i	0.116306	+	0.0671496i
$473$	−4.43841	−	25.8041i	−0.204078	−	1.18648i
$474$	16.7016	−	5.74733i	0.767129	−	0.263983i
$475$	3.47095	−	4.77735i	0.159258	−	0.219200i
$476$	−8.30620	−	12.0601i	−0.380714	−	0.552773i
$477$	−38.9614	−	2.73906i	−1.78392	−	0.125413i
$478$	−10.9515	−	4.87591i	−0.500908	−	0.223019i
$479$	−0.168090	−	1.59927i	−0.00768025	−	0.0730727i	0.990010	−	0.140994i	$-0.0450299\pi$
$479$	−0.168090	−	1.59927i	−0.00768025	−	0.0730727i	−0.997691	+	0.0679216i	$0.978363\pi$
$480$	−0.554870	+	1.30651i	−0.0253262	+	0.0596339i
$481$	6.94986	+	32.6965i	0.316886	+	1.49083i
$482$	6.24182	−	8.59113i	0.284307	−	0.391315i
$483$	−10.1073	+	2.06477i	−0.459897	+	0.0939504i
$484$	−10.9054	+	1.43944i	−0.495701	+	0.0654291i
$485$	−3.66623	+	2.11670i	−0.166475	+	0.0961144i
$486$	−13.3544	−	8.04111i	−0.605769	−	0.364752i
$487$	−0.980414	−	1.08886i	−0.0444268	−	0.0493410i	0.720522	−	0.693432i	$-0.243902\pi$
$487$	−0.980414	−	1.08886i	−0.0444268	−	0.0493410i	−0.764949	+	0.644091i	$0.777236\pi$
$488$	−2.02553	−	1.82380i	−0.0916915	−	0.0825594i
$489$	11.2301	−	5.23415i	0.507845	−	0.236697i
$490$	3.60140	−	4.46534i	0.162694	−	0.201724i
$491$	3.58459	+	11.0322i	0.161770	+	0.497878i	0.998784	−	0.0493045i	$-0.0157005\pi$
$491$	3.58459	+	11.0322i	0.161770	+	0.497878i	−0.837014	+	0.547182i	$0.815700\pi$
$492$	18.8192	−	0.324978i	0.848436	−	0.0146511i
$493$	31.6659	−	14.0986i	1.42616	−	0.634968i
$494$	3.68144	−	6.37645i	0.165636	−	0.286890i
$495$	6.03472	+	5.48383i	0.271241	+	0.246480i
$496$	5.77694			0.259392
$497$	9.31909	+	2.22759i	0.418018	+	0.0999212i
$498$	7.69337	−	13.8731i	0.344748	−	0.621669i
$499$	−20.6887	+	22.9772i	−0.926155	+	1.02860i	0.0733553	+	0.997306i	$0.476629\pi$
$499$	−20.6887	+	22.9772i	−0.926155	+	1.02860i	−0.999510	+	0.0312934i	$0.990037\pi$
$500$	7.60295	−	0.799102i	0.340014	−	0.0357369i
$501$	0.110655	−	1.26208i	0.00494369	−	0.0563855i
$502$	0.367353	+	0.330766i	0.0163958	+	0.0147628i
$503$	−2.45888	+	7.56765i	−0.109636	+	0.337425i	−0.990791	−	0.135403i	$-0.956767\pi$
$503$	−2.45888	+	7.56765i	−0.109636	+	0.337425i	0.881155	+	0.472828i	$0.156767\pi$
$504$	7.90118	+	0.755906i	0.351946	+	0.0336707i
$505$		−	12.5035i		−	0.556398i
$506$	4.14903	+	6.20722i	0.184447	+	0.275944i
$507$	18.3289	−	21.0771i	0.814017	−	0.936066i
$508$	2.65270	+	5.95805i	0.117694	+	0.264346i
$509$	0.0146057	+	0.0687144i	0.000647386	+	0.00304571i	0.978470	−	0.206389i	$-0.0661711\pi$
$509$	0.0146057	+	0.0687144i	0.000647386	+	0.00304571i	−0.977823	+	0.209434i	$0.932838\pi$
$510$	7.79804	−	0.956002i	0.345303	−	0.0423325i
$511$	4.37843	+	8.04513i	0.193691	+	0.355896i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	1.83094	+	6.84849i	0.0808379	+	0.302368i
$514$	4.50621	−	4.05741i	0.198761	−	0.178965i
$515$	−0.737652	−	1.65679i	−0.0325048	−	0.0730071i
$516$	12.9295	−	4.44930i	0.569191	−	0.195869i
$517$	0.598933	+	1.50051i	0.0263410	+	0.0659922i
$518$	16.2490	+	2.12291i	0.713940	+	0.0932755i
$519$	19.3649	+	20.7741i	0.850024	+	0.911880i
$520$	4.32623	−	0.919570i	0.189718	−	0.0403258i
$521$	1.08172	−	5.08908i	0.0473909	−	0.222957i	−0.948079	−	0.318035i	$-0.896977\pi$
$521$	1.08172	−	5.08908i	0.0473909	−	0.222957i	0.995470	+	0.0950787i	$0.0303103\pi$
$522$	−5.18542	+	18.0583i	−0.226960	+	0.790389i
$523$	11.1632	−	25.0729i	0.488132	−	1.09636i	−0.486731	−	0.873552i	$-0.661811\pi$
$523$	11.1632	−	25.0729i	0.488132	−	1.09636i	0.974862	−	0.222809i	$-0.0715227\pi$
$524$	6.74262	+	20.7517i	0.294553	+	0.906540i
$525$	−7.92379	−	18.1837i	−0.345823	−	0.793601i
$526$	−12.7150	−	9.23796i	−0.554399	−	0.402794i
$527$	−15.9871	−	27.6905i	−0.696410	−	1.20622i
$528$	−1.65546	−	5.50086i	−0.0720445	−	0.239394i
$529$	−8.96618	+	15.5299i	−0.389834	+	0.675212i
$530$	−1.11527	+	10.6111i	−0.0484442	+	0.460916i
$531$	6.70322	+	5.62893i	0.290895	+	0.244275i
$532$	−2.34692	−	2.74241i	−0.101752	−	0.118898i
$533$	−34.4722	−	47.4469i	−1.49316	−	2.05515i
$534$	−6.68794	+	9.54758i	−0.289415	+	0.413164i
$535$	2.01487	−	9.47921i	0.0871103	−	0.409822i
$536$	3.15081	+	3.49933i	0.136094	+	0.151148i
$537$	−41.7508	−	12.7730i	−1.80168	−	0.551197i
$538$		−	19.4186i		−	0.837197i
$539$	0.353586	+	23.2137i	0.0152300	+	0.999884i
$540$	−2.32127	+	3.57007i	−0.0998917	+	0.153631i
$541$	−11.7909	−	1.23927i	−0.506930	−	0.0532805i	−0.152388	−	0.988321i	$-0.548696\pi$
$541$	−11.7909	−	1.23927i	−0.506930	−	0.0532805i	−0.354542	+	0.935040i	$0.615363\pi$
$542$	0.997419	−	0.898080i	0.0428428	−	0.0385758i
$543$	12.2632	+	5.20814i	0.526266	+	0.223503i
$544$	−5.05630	−	2.25121i	−0.216787	−	0.0965198i
$545$	4.78386	−	3.47568i	0.204918	−	0.148882i
$546$	−12.1957	−	21.5156i	−0.521927	−	0.920784i
$547$	−14.9485	−	4.85707i	−0.639153	−	0.207673i	−0.0285276	−	0.999593i	$-0.509082\pi$
$547$	−14.9485	−	4.85707i	−0.639153	−	0.207673i	−0.610625	+	0.791920i	$0.709082\pi$
$548$	7.20162	+	0.756920i	0.307638	+	0.0323340i
$549$	−5.03178	−	6.44534i	−0.214751	−	0.275080i
$550$	−10.0155	+	10.2846i	−0.427062	+	0.438538i
$551$	7.39936	−	4.27202i	0.315223	−	0.181994i
$552$	−2.85211	+	2.65864i	−0.121394	+	0.113159i
$553$	−22.2201	+	15.3038i	−0.944896	+	0.650783i
$554$	−9.97957	+	3.24256i	−0.423991	+	0.137763i
$555$	−5.04408	+	7.20083i	−0.214109	+	0.305658i
$556$	21.5243	−	2.26230i	0.912836	−	0.0959429i
$557$	17.4054	+	3.69964i	0.737492	+	0.156759i	0.561318	−	0.827600i	$-0.310295\pi$
$557$	17.4054	+	3.69964i	0.737492	+	0.156759i	0.176174	+	0.984359i	$0.443628\pi$
$558$	17.0664	+	3.01583i	0.722478	+	0.127670i
$559$	−34.4688	−	25.0430i	−1.45787	−	1.05921i
$560$	0.280893	−	2.14998i	0.0118699	−	0.0908534i
$561$	−21.7859	+	23.1582i	−0.919801	+	0.977739i
$562$	−1.52572	−	2.64262i	−0.0643585	−	0.111472i
$563$	−16.6751	+	7.42424i	−0.702773	+	0.312895i	−0.726831	−	0.686816i	$-0.759008\pi$
$563$	−16.6751	+	7.42424i	−0.702773	+	0.312895i	0.0240586	+	0.999711i	$0.492341\pi$
$564$	−0.723301	+	0.434419i	−0.0304565	+	0.0182924i
$565$	−6.77900	+	7.52884i	−0.285195	+	0.316741i
$566$	0.937205	+	1.28995i	0.0393937	+	0.0542207i
$567$	22.9473	+	6.35791i	0.963695	+	0.267007i
$568$	3.44427	−	1.11911i	0.144518	−	0.0469568i
$569$	−15.0281	+	3.19431i	−0.630009	+	0.133913i	−0.511840	−	0.859081i	$-0.671036\pi$
$569$	−15.0281	+	3.19431i	−0.630009	+	0.133913i	−0.118169	+	0.992993i	$0.537702\pi$
$570$	1.88699	−	0.435274i	0.0790371	−	0.0182316i
$571$	33.4687	+	19.3232i	1.40062	+	0.808649i	0.994456	−	0.105150i	$-0.0335323\pi$
$571$	33.4687	+	19.3232i	1.40062	+	0.808649i	0.406165	+	0.913800i	$0.366866\pi$
$572$	−11.0791	+	14.0586i	−0.463241	+	0.587821i
$573$	−2.87578	+	14.7799i	−0.120137	+	0.617438i
$574$	−27.5591	+	8.19295i	−1.15029	+	0.341967i
$575$	9.26690	+	3.01100i	0.386457	+	0.125567i
$576$	2.69687	−	1.31411i	0.112370	−	0.0547545i
$577$	−0.243104	−	2.31298i	−0.0101206	−	0.0962907i	0.988296	−	0.152551i	$-0.0487489\pi$
$577$	−0.243104	−	2.31298i	−0.0101206	−	0.0962907i	−0.998416	+	0.0562606i	$0.982082\pi$
$578$	1.42515	+	13.5594i	0.0592786	+	0.563998i
$579$	2.74245	+	3.64077i	0.113972	+	0.151305i
$580$	4.88121	+	1.58600i	0.202681	+	0.0658551i
$581$	−5.63358	+	23.5680i	−0.233720	+	0.977764i
$582$	8.78252	+	1.70885i	0.364047	+	0.0708341i
$583$	−23.9954	−	35.8986i	−0.993788	−	1.48677i
$584$	2.99812	+	1.73097i	0.124063	+	0.0716279i
$585$	13.2607	−	0.458120i	0.548264	−	0.0189409i
$586$	15.0920	−	3.20790i	0.623444	−	0.132517i
$587$	40.4542	−	13.1444i	1.66972	−	0.542526i	0.686850	−	0.726800i	$-0.258993\pi$
$587$	40.4542	−	13.1444i	1.66972	−	0.542526i	0.982875	+	0.184273i	$0.0589931\pi$
$588$	−11.9364	+	2.12670i	−0.492248	+	0.0877037i
$589$	−4.63255	−	6.37616i	−0.190881	−	0.262725i
$590$	1.59999	−	1.77697i	0.0658704	−	0.0731565i
$591$	12.9392	+	21.5435i	0.532246	+	0.886180i
$592$	5.65826	−	2.51922i	0.232553	−	0.103539i
$593$	−17.3843	−	30.1104i	−0.713886	−	1.23649i	−0.963388	−	0.268112i	$-0.913600\pi$
$593$	−17.3843	−	30.1104i	−0.713886	−	1.23649i	0.249502	−	0.968374i	$-0.419733\pi$
$594$	−2.01889	−	17.1150i	−0.0828359	−	0.702238i
$595$	−11.0828	+	4.60347i	−0.454352	+	0.188724i
$596$	−5.34662	−	3.88455i	−0.219006	−	0.159117i
$597$	−17.3356	+	0.299358i	−0.709500	+	0.0122519i
$598$	11.8837	+	2.52596i	0.485960	+	0.103294i
$599$	−12.0970	+	1.27144i	−0.494270	+	0.0519498i	−0.348384	−	0.937352i	$-0.613270\pi$
$599$	−12.0970	+	1.27144i	−0.494270	+	0.0519498i	−0.145885	+	0.989302i	$0.546603\pi$
$600$	−6.14036	−	4.30123i	−0.250679	−	0.175597i
$601$	−22.3148	+	7.25051i	−0.910239	+	0.295755i	−0.726457	−	0.687212i	$-0.758834\pi$
$601$	−22.3148	+	7.25051i	−0.910239	+	0.295755i	−0.183783	+	0.982967i	$0.558834\pi$
$602$	−17.2017	+	11.8474i	−0.701090	+	0.482865i
$603$	7.48140	+	11.9827i	0.304666	+	0.487973i
$604$	−15.6230	+	9.01996i	−0.635692	+	0.367017i
$605$	−0.704281	+	8.98720i	−0.0286331	+	0.365382i
$606$	−17.3407	+	19.9407i	−0.704418	+	0.810035i
$607$	20.8756	+	2.19411i	0.847314	+	0.0890563i	0.518227	−	0.855243i	$-0.326592\pi$
$607$	20.8756	+	2.19411i	0.847314	+	0.0890563i	0.329087	+	0.944299i	$0.393259\pi$
$608$	−1.29751	−	0.421586i	−0.0526209	−	0.0170976i
$609$	0.227486	−	28.6983i	0.00921818	−	1.16291i
$610$	−1.80711	+	1.31294i	−0.0731677	+	0.0531595i
$611$	2.40170	+	1.06931i	0.0971623	+	0.0432595i
$612$	−13.7622	−	9.29022i	−0.556305	−	0.375535i
$613$	25.4857	−	22.9475i	1.02936	−	0.926839i	0.0320013	−	0.999488i	$-0.489812\pi$
$613$	25.4857	−	22.9475i	1.02936	−	0.926839i	0.997358	+	0.0726490i	$0.0231453\pi$
$614$	−22.6627	−	2.38194i	−0.914590	−	0.0961273i
$615$	2.94607	−	15.1411i	0.118797	−	0.610550i
$616$	4.69101	+	7.41582i	0.189006	+	0.298792i
$617$			30.7003i			1.23595i	0.786199	+	0.617973i	$0.212046\pi$
$617$			30.7003i			1.23595i	−0.786199	+	0.617973i	$0.787954\pi$
$618$	−1.12134	+	3.66530i	−0.0451070	+	0.147440i
$619$	9.60052	+	10.6625i	0.385877	+	0.428560i	0.904520	−	0.426431i	$-0.140229\pi$
$619$	9.60052	+	10.6625i	0.385877	+	0.428560i	−0.518643	+	0.854991i	$0.673563\pi$
$620$	0.984324	−	4.63088i	0.0395314	−	0.185981i
$621$	−9.81373	+	6.36530i	−0.393811	+	0.255431i
$622$	−6.16912	−	8.49107i	−0.247359	−	0.340461i
$623$	5.92730	−	16.7908i	0.237472	−	0.672710i
$624$	−8.17484	−	4.53338i	−0.327255	−	0.181481i
$625$	−1.60731	+	15.2926i	−0.0642925	+	0.611702i
$626$	−11.0351	+	19.1134i	−0.441052	+	0.763925i
$627$	−4.74393	+	6.23833i	−0.189454	+	0.249135i
$628$	−6.75347	−	11.6974i	−0.269493	−	0.466776i
$629$	−27.7340	−	20.1500i	−1.10583	−	0.803432i
$630$	1.95222	−	6.20490i	0.0777781	−	0.247209i
$631$	−0.104217	−	0.320748i	−0.00414882	−	0.0127688i	0.948961	−	0.315394i	$-0.102137\pi$
$631$	−0.104217	−	0.320748i	−0.00414882	−	0.0127688i	−0.953109	+	0.302626i	$0.902137\pi$
$632$	−4.14774	+	9.31599i	−0.164988	+	0.370570i
$633$	−41.5717	−	3.64487i	−1.65233	−	0.144870i
$634$	4.99543	−	23.5017i	0.198394	−	0.933370i
$635$	5.22805	−	1.11126i	0.207469	−	0.0440989i
$636$	16.4948	−	15.3759i	0.654062	−	0.609695i
$637$	26.7659	+	26.6605i	1.06051	+	1.05633i
$638$	−19.2909	+	7.70005i	−0.763736	+	0.304848i
$639$	10.7594	−	1.50804i	0.425634	−	0.0596570i
$640$	−0.333330	−	0.748672i	−0.0131760	−	0.0295939i
$641$	18.8990	−	17.0167i	0.746465	−	0.672120i	−0.205386	−	0.978681i	$-0.565845\pi$
$641$	18.8990	−	17.0167i	0.746465	−	0.672120i	0.951851	+	0.306561i	$0.0991782\pi$
$642$	−16.3597	+	12.3232i	−0.645668	+	0.486357i
$643$	−3.27731	+	2.38111i	−0.129244	+	0.0939016i	−0.650529	−	0.759481i	$-0.725453\pi$
$643$	−3.27731	+	2.38111i	−0.129244	+	0.0939016i	0.521285	+	0.853383i	$0.325453\pi$
$644$	3.10697	−	5.08136i	0.122432	−	0.200234i
$645$	−1.36358	−	11.1226i	−0.0536908	−	0.437952i
$646$	1.56995	+	7.38603i	0.0617688	+	0.290599i
$647$	−14.9973	−	33.6845i	−0.589606	−	1.32428i	−0.924198	−	0.381913i	$-0.875265\pi$
$647$	−14.9973	−	33.6845i	−0.589606	−	1.32428i	0.334593	−	0.942363i	$-0.391401\pi$
$648$	8.65320	−	2.47428i	0.339930	−	0.0971988i
$649$	−0.378298	+	9.66960i	−0.0148495	+	0.379565i
$650$			23.3598i			0.916248i
$651$	−26.3493	+	2.55843i	−1.03271	+	0.100273i
$652$	−2.21052	+	6.80327i	−0.0865705	+	0.266437i
$653$	12.2670	+	11.0453i	0.480045	+	0.432235i	0.873291	−	0.487199i	$-0.161981\pi$
$653$	12.2670	+	11.0453i	0.480045	+	0.432235i	−0.393246	+	0.919433i	$0.628648\pi$
$654$	−12.4496	−	1.09154i	−0.486820	−	0.0426827i
$655$	17.7837	−	1.86914i	0.694867	−	0.0730334i
$656$	−7.27138	+	8.07568i	−0.283900	+	0.315302i
$657$	7.95349	+	6.67883i	0.310295	+	0.260566i
$658$	0.886244	−	0.935754i	0.0345494	−	0.0364795i
$659$	36.2251			1.41113			0.705565	−	0.708646i	$-0.250693\pi$
$659$	36.2251			1.41113			0.705565	+	0.708646i	$0.250693\pi$
$660$	−4.69164	+	0.389755i	−0.182622	+	0.0151712i
$661$	−6.22054	+	10.7743i	−0.241951	+	0.419071i	−0.961270	−	0.275609i	$-0.911121\pi$
$661$	−6.22054	+	10.7743i	−0.241951	+	0.419071i	0.719319	+	0.694680i	$0.244454\pi$
$662$	−2.42075	+	1.07779i	−0.0940851	+	0.0418894i
$663$	0.893295	+	51.7300i	0.0346927	+	2.00903i
$664$	2.83023	+	8.71054i	0.109834	+	0.338035i
$665$	−2.59824	+	1.41405i	−0.100756	+	0.0548346i
$666$	18.0310	−	4.48847i	0.698685	−	0.173925i
$667$	10.4770	+	9.43351i	0.405670	+	0.365267i
$668$	0.489440	+	0.543578i	0.0189370	+	0.0210317i
$669$	−29.4453	+	6.79221i	−1.13842	+	0.262602i
$670$	3.34198	−	1.92949i	0.129112	−	0.0745427i
$671$	2.22373	−	8.76209i	0.0858460	−	0.338257i
$672$	−3.42972	+	3.03925i	−0.132304	+	0.117242i
$673$	10.2158	−	14.0609i	0.393792	−	0.542008i	−0.565381	−	0.824830i	$-0.691271\pi$
$673$	10.2158	−	14.0609i	0.393792	−	0.542008i	0.959172	+	0.282822i	$0.0912707\pi$
$674$	−2.45032	−	11.5279i	−0.0943828	−	0.444036i
$675$	−15.8946	−	15.9124i	−0.611783	−	0.612468i
$676$	1.68568	+	16.0382i	0.0648339	+	0.616853i
$677$	40.3007	+	17.9430i	1.54888	+	0.689607i	0.990185	−	0.139764i	$-0.0446344\pi$
$677$	40.3007	+	17.9430i	1.54888	+	0.689607i	0.558698	+	0.829371i	$0.311301\pi$
$678$	21.2527	−	2.60548i	0.816206	−	0.100063i
$679$	−13.6239	+	1.08575i	−0.522838	+	0.0416673i
$680$	−2.66614	+	3.66963i	−0.102242	+	0.140724i
$681$	7.79218	+	22.6439i	0.298597	+	0.867714i
$682$	8.92398	+	16.9548i	0.341717	+	0.649233i
$683$	−1.82174	−	1.05178i	−0.0697069	−	0.0402453i	0.464741	−	0.885446i	$-0.346147\pi$
$683$	−1.82174	−	1.05178i	−0.0697069	−	0.0402453i	−0.534448	+	0.845201i	$0.679481\pi$
$684$	−3.61305	−	1.92282i	−0.138148	−	0.0735209i
$685$	1.83383	−	5.64395i	0.0700671	−	0.215644i
$686$	16.6924	−	8.02262i	0.637320	−	0.306305i
$687$	−18.4530	+	8.60060i	−0.704027	+	0.328133i
$688$	−3.21098	+	7.21198i	−0.122417	+	0.274954i
$689$	−68.7278	−	14.6086i	−2.61832	−	0.556541i
$690$	1.64524	+	2.73930i	0.0626332	+	0.104283i
$691$	0.477462	−	4.54275i	0.0181635	−	0.172814i	−0.981679	−	0.190540i	$-0.938976\pi$
$691$	0.477462	−	4.54275i	0.0181635	−	0.172814i	0.999843	+	0.0177261i	$0.00564268\pi$
$692$	−16.3968			−0.623311
$693$	9.98691	+	24.3570i	0.379371	+	0.925245i
$694$	10.3928			0.394503
$695$	1.85401	−	17.6397i	0.0703265	−	0.669112i
$696$	−5.58502	−	9.29896i	−0.211700	−	0.352476i
$697$	58.8319	+	12.5051i	2.22842	+	0.473665i
$698$	2.38437	−	5.35538i	0.0902496	−	0.202704i
$699$	−30.3349	+	14.1385i	−1.14737	+	0.534767i
$700$	10.7987	+	3.81204i	0.408154	+	0.144082i
$701$	−6.74430	+	20.7568i	−0.254729	+	0.783974i	0.739154	+	0.673536i	$0.235225\pi$
$701$	−6.74430	+	20.7568i	−0.254729	+	0.783974i	−0.993883	+	0.110438i	$0.964775\pi$
$702$	−21.7837	−	17.6603i	−0.822173	−	0.666545i
$703$	−7.31792	−	4.22500i	−0.276000	−	0.159349i
$704$	2.97484	+	1.46641i	0.112118	+	0.0552673i
$705$	0.224995	+	0.653829i	0.00847380	+	0.0246246i
$706$	−16.7295	+	23.0261i	−0.629621	+	0.866599i
$707$	17.3422	−	36.4512i	0.652220	−	1.37089i
$708$	−5.01609	+	0.614948i	−0.188516	+	0.0231112i
$709$	−9.01963	−	4.01580i	−0.338739	−	0.150817i	0.230316	−	0.973116i	$-0.426024\pi$
$709$	−9.01963	−	4.01580i	−0.338739	−	0.150817i	−0.569055	+	0.822299i	$0.692691\pi$
$710$	−0.310232	−	2.95166i	−0.0116428	−	0.110774i
$711$	−17.1168	+	25.3562i	−0.641929	+	0.950933i
$712$	−1.39928	−	6.58308i	−0.0524401	−	0.246711i
$713$	7.64397	−	10.5210i	0.286269	−	0.394016i
$714$	24.0594	+	8.02877i	0.900401	+	0.300469i
$715$	9.38185	+	11.2766i	0.350861	+	0.421721i
$716$	21.8305	−	12.6038i	0.815844	−	0.471028i
$717$	20.2323	−	4.66702i	0.755589	−	0.174293i
$718$	2.01803	+	2.24125i	0.0753123	+	0.0836428i
$719$	−12.8719	−	11.5899i	−0.480042	−	0.432232i	0.393248	−	0.919432i	$-0.371351\pi$
$719$	−12.8719	−	11.5899i	−0.480042	−	0.432232i	−0.873290	+	0.487201i	$0.838018\pi$
$720$	−0.593892	−	2.38576i	−0.0221330	−	0.0889121i
$721$	0.147491	−	5.85313i	0.00549285	−	0.217982i
$722$	−5.29616	−	16.2999i	−0.197103	−	0.606620i
$723$	0.317571	+	18.3903i	0.0118106	+	0.683942i
$724$	−7.02721	+	3.12872i	−0.261164	+	0.116278i
$725$	−13.5536	+	23.4755i	−0.503369	+	0.871860i
$726$	13.5873	−	13.3561i	0.504271	−	0.495692i
$727$	32.9051			1.22038			0.610192	−	0.792254i	$-0.291092\pi$
$727$	32.9051			1.22038			0.610192	+	0.792254i	$0.291092\pi$
$728$	13.8876	+	3.31963i	0.514709	+	0.123034i
$729$	26.8552	−	2.79220i	0.994638	−	0.103415i
$730$	1.89841	−	2.10840i	0.0702635	−	0.0780355i
$731$	43.4551	−	4.56732i	1.60725	−	0.168928i
$732$	4.70287	+	0.412332i	0.173823	+	0.0152402i
$733$	−14.3093	−	12.8841i	−0.528526	−	0.475887i	0.361132	−	0.932515i	$-0.382390\pi$
$733$	−14.3093	−	12.8841i	−0.528526	−	0.475887i	−0.889658	+	0.456628i	$0.849057\pi$
$734$	−3.22378	+	9.92179i	−0.118992	+	0.366220i
$735$	−0.329026	+	9.93074i	−0.0121363	+	0.366301i
$736$		−	2.25114i		−	0.0829782i
$737$	−5.40298	+	14.6530i	−0.199021	+	0.539749i
$738$	−25.6972	+	20.0614i	−0.945927	+	0.738471i
$739$	−0.433453	−	0.973551i	−0.0159448	−	0.0358126i	0.905398	−	0.424565i	$-0.139573\pi$
$739$	−0.433453	−	0.973551i	−0.0159448	−	0.0358126i	−0.921342	+	0.388752i	$0.872906\pi$
$740$	−1.05534	−	4.96499i	−0.0387951	−	0.182517i
$741$	1.55182	+	12.6581i	0.0570077	+	0.465008i
$742$	−17.9688	+	29.3874i	−0.659654	+	1.07885i
$743$	11.4625	−	8.32797i	0.420517	−	0.305524i	−0.357329	−	0.933979i	$-0.616312\pi$
$743$	11.4625	−	8.32797i	0.420517	−	0.305524i	0.777846	+	0.628455i	$0.216312\pi$
$744$	−7.99223	+	6.02024i	−0.293009	+	0.220713i
$745$	−4.02492	+	3.62405i	−0.147462	+	0.132775i
$746$	−13.2013	−	29.6506i	−0.483334	−	1.08559i
$747$	3.81382	+	27.2104i	0.139540	+	0.995578i
$748$	−1.20366	−	18.3174i	−0.0440103	−	0.669750i
$749$	19.0214	−	24.8399i	0.695028	−	0.907631i
$750$	−9.68571	+	9.02869i	−0.353672	+	0.329681i
$751$	−44.5286	+	9.46484i	−1.62487	+	0.345377i	−0.928219	−	0.372033i	$-0.878661\pi$
$751$	−44.5286	+	9.46484i	−1.62487	+	0.345377i	−0.696651	+	0.717410i	$0.745327\pi$
$752$	0.101280	−	0.476484i	0.00369330	−	0.0173756i
$753$	−0.852919	−	0.0747811i	−0.0310821	−	0.00272518i
$754$	−13.7473	+	30.8769i	−0.500647	+	1.12447i
$755$	4.56855	+	14.0606i	0.166267	+	0.511716i
$756$	−11.7188	+	7.18817i	−0.426209	+	0.261431i
$757$	6.54374	+	4.75430i	0.237836	+	0.172798i	0.700319	−	0.713830i	$-0.253041\pi$
$757$	6.54374	+	4.75430i	0.237836	+	0.172798i	−0.462483	+	0.886628i	$0.653041\pi$
$758$	−13.2611	−	22.9689i	−0.481666	−	0.834269i
$759$	−12.2087	−	4.26374i	−0.443148	−	0.154764i
$760$	−0.559030	+	0.968269i	−0.0202782	+	0.0351228i
$761$	1.81333	−	17.2527i	0.0657333	−	0.625411i	−0.911214	−	0.411932i	$-0.864854\pi$
$761$	1.81333	−	17.2527i	0.0657333	−	0.625411i	0.976948	−	0.213478i	$-0.0684793\pi$
$762$	−9.87891	−	5.47838i	−0.357875	−	0.198461i
$763$	18.7670	−	3.49741i	0.679411	−	0.126615i
$764$	−5.10973	−	7.03294i	−0.184864	−	0.254443i
$765$	−9.79210	+	9.44906i	−0.354034	+	0.341632i
$766$	−0.881606	+	4.14763i	−0.0318537	+	0.149860i
$767$	10.5366	+	11.7020i	0.380454	+	0.422537i
$768$	−0.506712	+	1.65627i	−0.0182844	+	0.0597656i
$769$			19.5906i			0.706455i	0.935537	+	0.353228i	$0.114916\pi$
$769$			19.5906i			0.706455i	−0.935537	+	0.353228i	$0.885084\pi$
$770$	6.74393	−	2.49681i	0.243034	−	0.0899789i
$771$	−2.00592	+	10.3093i	−0.0722416	+	0.371281i
$772$	−2.61720	−	0.275079i	−0.0941952	−	0.00990031i
$773$	−20.3417	+	18.3157i	−0.731640	+	0.658772i	−0.948264	−	0.317484i	$-0.897162\pi$
$773$	−20.3417	+	18.3157i	−0.731640	+	0.658772i	0.216624	+	0.976255i	$0.430495\pi$
$774$	−13.2510	+	19.6295i	−0.476296	+	0.705569i
$775$	22.8430	+	10.1704i	0.820545	+	0.365330i
$776$	−4.17913	+	3.03631i	−0.150022	+	0.108997i
$777$	−24.6924	+	13.9964i	−0.885833	+	0.502116i
$778$	17.9740	+	5.84012i	0.644401	+	0.209379i
$779$	14.7443	+	1.54969i	0.528269	+	0.0555233i
$780$	−5.02693	+	5.78064i	−0.179993	+	0.206980i
$781$	8.60506	+	8.37987i	0.307913	+	0.299855i
$782$	−10.7904	+	6.22982i	−0.385863	+	0.222778i
$783$	−11.6449	−	30.3869i	−0.416156	−	1.08594i
$784$	3.80088	−	5.87821i	0.135746	−	0.209936i
$785$	−10.5275	+	3.42059i	−0.375742	+	0.122086i
$786$	−30.9539	−	21.6827i	−1.10409	−	0.773398i
$787$	37.0752	−	3.89676i	1.32159	−	0.138904i	0.582675	−	0.812706i	$-0.302006\pi$
$787$	37.0752	−	3.89676i	1.32159	−	0.138904i	0.738913	+	0.673801i	$0.235340\pi$
$788$	−14.1921	−	3.01661i	−0.505571	−	0.107462i
$789$	27.2178	−	0.470008i	0.968980	−	0.0167327i
$790$	6.76111	+	4.91223i	0.240549	+	0.174769i
$791$	−30.2051	+	12.5463i	−1.07397	+	0.446094i
$792$	8.02281	+	5.88511i	0.285078	+	0.209118i
$793$	−7.35495	−	12.7392i	−0.261182	−	0.452381i
$794$	5.64234	−	2.51213i	0.200239	−	0.0891522i
$795$	−9.51503	−	15.8424i	−0.337463	−	0.561871i
$796$	6.69814	−	7.43904i	0.237409	−	0.263670i
$797$	0.329589	+	0.453640i	0.0116746	+	0.0160688i	0.814814	−	0.579722i	$-0.196839\pi$
$797$	0.329589	+	0.453640i	0.0116746	+	0.0160688i	−0.803140	+	0.595791i	$0.796839\pi$
$798$	6.10481	+	1.34828i	0.216108	+	0.0477286i
$799$	−2.56421	+	0.833161i	−0.0907151	+	0.0294751i
$800$	4.23380	−	0.899921i	0.149687	−	0.0318170i
$801$	−0.697106	−	20.1784i	−0.0246310	−	0.712969i
$802$	7.93565	+	4.58165i	0.280218	+	0.161784i
$803$	−0.448858	+	11.4732i	−0.0158398	+	0.404879i
$804$	−8.00576	−	1.55771i	−0.282342	−	0.0549363i
$805$	−3.54390	−	3.35640i	−0.124906	−	0.118297i
$806$	29.6516	+	9.63439i	1.04443	+	0.339357i
$807$	20.2365	+	26.8652i	0.712358	+	0.945698i
$808$	−1.59479	−	15.1735i	−0.0561047	−	0.533800i
$809$	−0.000811612	−	0.00772197i	−2.85348e−5	−	0.000271490i	0.994508	−	0.104664i	$-0.0333768\pi$
$809$	−0.000811612	−	0.00772197i	−2.85348e−5	−	0.000271490i	−0.994536	+	0.104393i	$0.966710\pi$
$810$	−0.509011	−	7.35813i	−0.0178848	−	0.258538i
$811$	17.5754	+	5.71058i	0.617155	+	0.200526i	0.600877	−	0.799342i	$-0.294818\pi$
$811$	17.5754	+	5.71058i	0.617155	+	0.200526i	0.0162781	+	0.999868i	$0.494818\pi$
$812$	12.0303	+	11.3938i	0.422181	+	0.399844i
$813$	−0.443997	+	2.28190i	−0.0155717	+	0.0800296i
$814$	16.1344	+	12.7149i	0.565509	+	0.445658i
$815$	5.07695	+	2.93118i	0.177838	+	0.102675i
$816$	9.34127	−	2.15477i	0.327010	−	0.0754319i
$817$	10.5349	−	2.23927i	0.368571	−	0.0783422i
$818$	−5.68264	+	1.84640i	−0.198689	+	0.0645579i
$819$	39.2942	+	17.0569i	1.37305	+	0.596018i
$820$	5.23463	+	7.20485i	0.182801	+	0.251604i
$821$	−21.7746	+	24.1831i	−0.759939	+	0.843998i	−0.991673	−	0.128782i	$-0.958893\pi$
$821$	−21.7746	+	24.1831i	−0.759939	+	0.843998i	0.231734	+	0.972779i	$0.425560\pi$
$822$	−10.7520	+	6.45774i	−0.375020	+	0.225240i
$823$	−0.709226	+	0.315768i	−0.0247221	+	0.0110070i	−0.419060	−	0.907958i	$-0.637640\pi$
$823$	−0.709226	+	0.315768i	−0.0247221	+	0.0110070i	0.394338	+	0.918965i	$0.370974\pi$
$824$	−1.10649	−	1.91649i	−0.0385464	−	0.0667642i
$825$	3.13837	−	24.6658i	0.109264	−	0.858753i
$826$	7.12904	−	2.96119i	0.248051	−	0.103033i
$827$	33.5218	+	24.3550i	1.16567	+	0.846907i	0.990484	−	0.137629i	$-0.0439480\pi$
$827$	33.5218	+	24.3550i	1.16567	+	0.846907i	0.175184	+	0.984536i	$0.443948\pi$
$828$	1.17520	−	6.65039i	0.0408411	−	0.231117i
$829$	−45.2020	−	9.60798i	−1.56993	−	0.333699i	−0.660915	−	0.750461i	$-0.729832\pi$
$829$	−45.2020	−	9.60798i	−1.56993	−	0.333699i	−0.909016	+	0.416762i	$0.863165\pi$
$830$	7.46474	−	0.784575i	0.259105	−	0.0272330i
$831$	10.4273	−	14.8859i	0.361720	−	0.516385i
$832$	5.13276	−	1.66773i	0.177946	−	0.0578183i
$833$	−38.6945	−	1.95134i	−1.34068	−	0.0676098i
$834$	−27.4208	+	25.5607i	−0.949503	+	0.885095i
$835$	0.519135	−	0.299723i	0.0179654	−	0.0103723i
$836$	−0.767021	−	4.45932i	−0.0265280	−	0.154229i
$837$	−26.7537	+	13.6128i	−0.924744	+	0.470529i
$838$	3.23157	+	0.339651i	0.111633	+	0.0117331i
$839$	27.5617	+	8.95535i	0.951537	+	0.309173i	0.743340	−	0.668914i	$-0.233240\pi$
$839$	27.5617	+	8.95535i	0.951537	+	0.309173i	0.208197	+	0.978087i	$0.433240\pi$
$840$	1.85192	+	3.26716i	0.0638975	+	0.112728i
$841$	−8.26899	+	6.00777i	−0.285138	+	0.207165i
$842$	25.5295	+	11.3665i	0.879803	+	0.391714i
$843$	4.86471	+	2.06602i	0.167549	+	0.0711574i
$844$	17.9050	−	16.1217i	0.616314	−	0.554931i
$845$	13.1437	+	1.38145i	0.452156	+	0.0475235i
$846$	0.547951	−	1.35477i	0.0188389	−	0.0465780i
$847$	−14.5183	+	25.2234i	−0.498855	+	0.866685i
$848$			13.0192i			0.447081i
$849$	−2.64088	−	0.807936i	−0.0906347	−	0.0277283i
$850$	−16.0302	−	17.8033i	−0.549832	−	0.610650i
$851$	2.89891	−	13.6383i	0.0993733	−	0.467515i
$852$	−3.59880	+	5.13758i	−0.123293	+	0.176011i
$853$	−17.4590	−	24.0303i	−0.597785	−	0.822781i	0.397718	−	0.917508i	$-0.369802\pi$
$853$	−17.4590	−	24.0303i	−0.597785	−	0.822781i	−0.995503	+	0.0947268i	$0.969802\pi$
$854$	−7.08926	+	1.32115i	−0.242590	+	0.0452089i
$855$	−2.15698	+	2.56865i	−0.0737673	+	0.0878459i
$856$	1.23606	−	11.7604i	0.0422478	−	0.401961i
$857$	−20.0507	+	34.7289i	−0.684920	+	1.18632i	0.288542	+	0.957467i	$0.406830\pi$
$857$	−20.0507	+	34.7289i	−0.684920	+	1.18632i	−0.973462	+	0.228849i	$0.926504\pi$
$858$	0.676918	−	30.9954i	0.0231096	−	1.05817i
$859$	−17.3091	−	29.9802i	−0.590578	−	1.02291i	−0.994155	−	0.107966i	$-0.965566\pi$
$859$	−17.3091	−	29.9802i	−0.590578	−	1.02291i	0.403576	−	0.914946i	$-0.367767\pi$
$860$	5.23411	+	3.80281i	0.178482	+	0.129675i
$861$	29.5892	−	40.0545i	1.00840	−	1.36505i
$862$	−5.59070	−	17.2064i	−0.190420	−	0.586053i
$863$	19.7117	−	44.2733i	0.670995	−	1.50708i	−0.180973	−	0.983488i	$-0.557925\pi$
$863$	19.7117	−	44.2733i	0.670995	−	1.50708i	0.851969	−	0.523592i	$-0.175409\pi$
$864$	−2.36160	+	4.62848i	−0.0803431	+	0.157464i
$865$	−2.79382	+	13.1439i	−0.0949927	+	0.446905i
$866$	−30.5198	+	6.48717i	−1.03710	+	0.220443i
$867$	−16.1022	−	17.2739i	−0.546858	−	0.586653i
$868$	9.29255	−	12.1351i	0.315410	−	0.411891i
$869$	−33.7489	+	2.21769i	−1.14485	+	0.0752301i
$870$	−8.40581	+	2.89260i	−0.284984	+	0.0980682i
$871$	10.3364	+	23.2159i	0.350235	+	0.786641i
$872$	5.36207	−	4.82803i	0.181583	−	0.163498i
$873$	−13.9312	+	6.78826i	−0.471499	+	0.229748i
$874$	−2.48464	+	1.80520i	−0.0840444	+	0.0610618i
$875$	10.5512	−	17.2562i	0.356696	−	0.583365i
$876$	−5.95169	+	0.729648i	−0.201089	+	0.0246525i
$877$	−6.38077	−	30.0192i	−0.215463	−	1.01368i	−0.944325	−	0.329014i	$-0.893284\pi$
$877$	−6.38077	−	30.0192i	−0.215463	−	1.01368i	0.728862	−	0.684661i	$-0.240050\pi$
$878$	6.10287	+	13.7073i	0.205962	+	0.462598i
$879$	−17.5363	+	20.1657i	−0.591486	+	0.680171i
$880$	1.68237	−	2.13481i	0.0567127	−	0.0719646i
$881$		−	26.7883i		−	0.902519i	−0.892393	−	0.451260i	$-0.850975\pi$
$881$		−	26.7883i		−	0.902519i	0.892393	−	0.451260i	$-0.149025\pi$
$882$	14.2974	−	15.3813i	0.481418	−	0.517916i
$883$	3.00148	−	9.23762i	0.101008	−	0.310871i	−0.887765	−	0.460297i	$-0.847743\pi$
$883$	3.00148	−	9.23762i	0.101008	−	0.310871i	0.988773	+	0.149427i	$0.0477428\pi$
$884$	−22.1983	−	19.9875i	−0.746611	−	0.672251i
$885$	−0.361733	+	4.12575i	−0.0121595	+	0.138686i
$886$	−7.45925	+	0.783998i	−0.250598	+	0.0263389i
$887$	−19.6086	+	21.7775i	−0.658391	+	0.731217i	−0.976184	−	0.216943i	$-0.930392\pi$
$887$	−19.6086	+	21.7775i	−0.658391	+	0.731217i	0.317793	+	0.948160i	$0.397058\pi$
$888$	−5.20273	+	9.38184i	−0.174592	+	0.314834i
$889$	16.7825	+	4.01162i	0.562868	+	0.134545i
$890$	−5.51552			−0.184880
$891$	20.6289	+	21.5742i	0.691095	+	0.722764i
$892$	8.72335	−	15.1093i	0.292079	−	0.505896i
$893$	−0.607125	+	0.270309i	−0.0203167	+	0.00904556i
$894$	11.4451	−	0.197638i	0.382780	−	0.00661000i
$895$	−6.38376	−	19.6472i	−0.213386	−	0.656733i
$896$	0.0666482	−	2.64491i	0.00222656	−	0.0883603i
$897$	−19.0731	+	8.88960i	−0.636832	+	0.296815i
$898$	−20.4049	−	18.3727i	−0.680922	−	0.613105i
$899$	24.2085	+	26.8863i	0.807399	+	0.896708i
$900$	12.9774	−	0.448332i	0.432580	−	0.0149444i
$901$	62.4047	−	36.0294i	2.07900	−	1.20031i
$902$	−34.9340	−	8.86587i	−1.16317	−	0.295201i
$903$	11.4517	−	34.3168i	0.381089	−	1.14199i
$904$	−7.26628	+	10.0012i	−0.241673	+	0.332634i
$905$	1.31067	+	6.16622i	0.0435681	+	0.204972i
$906$	12.2142	−	28.7599i	0.405789	−	0.955483i
$907$	−1.86772	−	17.7701i	−0.0620165	−	0.590047i	−0.980763	−	0.195200i	$-0.937464\pi$
$907$	−1.86772	−	17.7701i	−0.0620165	−	0.590047i	0.918747	−	0.394847i	$-0.129202\pi$
$908$	−12.6305	−	5.62348i	−0.419159	−	0.186622i
$909$	3.20987	−	45.6584i	0.106465	−	1.51439i
$910$	5.02736	−	10.5669i	0.166655	−	0.350289i
$911$	−18.8753	+	25.9796i	−0.625367	+	0.860744i	−0.997730	−	0.0673435i	$-0.978548\pi$
$911$	−18.8753	+	25.9796i	−0.625367	+	0.860744i	0.372363	+	0.928087i	$0.378548\pi$
$912$	2.23441	−	0.768902i	0.0739886	−	0.0254609i
$913$	−21.1927	+	21.7622i	−0.701375	+	0.720223i
$914$	12.2046	+	7.04633i	0.403692	+	0.233072i
$915$	1.13185	−	3.69964i	0.0374177	−	0.122306i
$916$	3.63225	−	11.1789i	0.120013	−	0.369362i
$917$	54.4369	+	19.2167i	1.79767	+	0.634591i
$918$	28.7211	−	1.48909i	0.947939	−	0.0491472i
$919$	11.8116	−	26.5293i	0.389628	−	0.875119i	−0.607125	−	0.794606i	$-0.707677\pi$
$919$	11.8116	−	26.5293i	0.389628	−	0.875119i	0.996754	−	0.0805132i	$-0.0256559\pi$
$920$	−1.80455	−	0.383569i	−0.0594942	−	0.0126459i
$921$	33.8354	−	20.3218i	1.11491	−	0.669625i
$922$	−3.55002	+	33.7762i	−0.116914	+	1.11236i
$923$	19.5450			0.643330
$924$	−14.2180	−	5.37101i	−0.467739	−	0.176693i
$925$	26.8089			0.881470
$926$	4.15705	−	39.5517i	0.136609	−	1.29975i
$927$	−2.26832	−	6.23940i	−0.0745014	−	0.204929i
$928$	6.12582	+	1.30208i	0.201090	+	0.0427429i
$929$	16.0860	−	36.1298i	0.527765	−	1.18538i	−0.431304	−	0.902206i	$-0.641947\pi$
$929$	16.0860	−	36.1298i	0.527765	−	1.18538i	0.959069	−	0.283172i	$-0.0913868\pi$
$930$	3.46413	+	7.43247i	0.113593	+	0.243720i
$931$	−9.53587	+	0.518624i	−0.312526	+	0.0169972i
$932$	5.97105	−	18.3770i	0.195588	−	0.601959i
$933$	17.3835	+	5.31821i	0.569110	+	0.174110i
$934$	−13.3069	−	7.68272i	−0.435414	−	0.251386i
$935$	−14.8886	−	2.15620i	−0.486909	−	0.0705151i
$936$	16.0340	−	2.24733i	0.524087	−	0.0734561i
$937$	24.5557	−	33.7980i	0.802200	−	1.10413i	−0.190280	−	0.981730i	$-0.560940\pi$
$937$	24.5557	−	33.7980i	0.802200	−	1.10413i	0.992480	−	0.122404i	$-0.0390603\pi$
$938$	12.4190	−	0.989724i	0.405494	−	0.0323156i
$939$	−4.65159	−	37.9427i	−0.151799	−	1.23821i
$940$	−0.364700	−	0.162375i	−0.0118952	−	0.00529608i
$941$	2.01602	+	19.1812i	0.0657205	+	0.625289i	0.976962	+	0.213415i	$0.0684588\pi$
$941$	2.01602	+	19.1812i	0.0657205	+	0.625289i	−0.911241	+	0.411874i	$0.864875\pi$
$942$	21.5332	+	9.14506i	0.701591	+	0.297962i
$943$	5.08613	+	23.9284i	0.165627	+	0.779215i
$944$	1.71500	−	2.36049i	0.0558183	−	0.0768273i
$945$	3.76540	+	10.6187i	0.122488	+	0.345428i
$946$	−26.1267	+	1.71683i	−0.849453	+	0.0558189i
$947$	−20.0706	+	11.5878i	−0.652208	+	0.376552i	−0.789301	−	0.614006i	$-0.789557\pi$
$947$	−20.0706	+	11.5878i	−0.652208	+	0.376552i	0.137094	+	0.990558i	$0.456224\pi$
$948$	−3.97005	−	17.2108i	−0.128941	−	0.558982i
$949$	12.5018	+	13.8847i	0.405827	+	0.450716i
$950$	−4.38837	−	3.95130i	−0.142377	−	0.128197i
$951$	17.5804	+	37.7197i	0.570084	+	1.22315i
$952$	−12.8623	+	7.00008i	−0.416868	+	0.226874i
$953$	0.450278	+	1.38581i	0.0145859	+	0.0448908i	0.958085	−	0.286486i	$-0.0924870\pi$
$953$	0.450278	+	1.38581i	0.0145859	+	0.0448908i	−0.943499	+	0.331376i	$0.892487\pi$
$954$	−6.79663	+	38.4617i	−0.220049	+	1.24524i
$955$	−6.50835	+	2.89770i	−0.210605	+	0.0937675i
$956$	−5.99394	+	10.3818i	−0.193858	+	0.335771i
$957$	18.6641	−	30.7562i	0.603326	−	0.994207i
$958$	−1.60808			−0.0519548
$959$	13.1742	−	13.9102i	0.425418	−	0.449184i
$960$	1.24136	+	0.688398i	0.0400646	+	0.0222179i
$961$	1.58785	−	1.76349i	0.0512211	−	0.0568868i
$962$	33.2439	−	3.49407i	1.07183	−	0.112653i
$963$	9.79108	−	34.0975i	0.315513	−	1.09878i
$964$	−7.89162	−	7.10565i	−0.254172	−	0.228858i
$965$	−0.666449	+	2.05112i	−0.0214537	+	0.0660278i
$966$	0.996962	+	10.2677i	0.0320767	+	0.330359i
$967$			7.66929i			0.246628i	0.992368	+	0.123314i	$0.0393522\pi$
$967$			7.66929i			0.246628i	−0.992368	+	0.123314i	$0.960648\pi$
$968$	0.291628	+	10.9961i	0.00937329	+	0.353429i
$969$	−9.86908	−	8.58229i	−0.317040	−	0.275703i
$970$	1.72188	+	3.86740i	0.0552862	+	0.124175i
$971$	9.83285	+	46.2599i	0.315551	+	1.48455i	0.794799	+	0.606873i	$0.207576\pi$
$971$	9.83285	+	46.2599i	0.315551	+	1.48455i	−0.479248	+	0.877680i	$0.659091\pi$
$972$	−9.39298	+	12.4407i	−0.301280	+	0.399037i
$973$	29.8710	−	48.8532i	0.957620	−	1.56616i
$974$	−1.18538	+	0.861227i	−0.0379819	+	0.0275955i
$975$	−24.3437	−	32.3177i	−0.779621	−	1.03499i
$976$	−2.02553	+	1.82380i	−0.0648357	+	0.0583783i
$977$	−18.6128	−	41.8050i	−0.595475	−	1.33746i	−0.920125	−	0.391625i	$-0.871913\pi$
$977$	−18.6128	−	41.8050i	−0.595475	−	1.33746i	0.324650	−	0.945834i	$-0.394754\pi$
$978$	−4.03161	−	11.7157i	−0.128917	−	0.374628i
$979$	17.1592	−	14.2760i	0.548411	−	0.456264i
$980$	−4.06443	−	4.04842i	−0.129833	−	0.129322i
$981$	18.3612	−	11.4639i	0.586229	−	0.366013i
$982$	11.3465	−	2.41177i	0.362081	−	0.0769627i
$983$	−2.13306	+	10.0352i	−0.0680339	+	0.320074i	−0.998984	−	0.0450728i	$-0.985648\pi$
$983$	−2.13306	+	10.0352i	−0.0680339	+	0.320074i	0.930950	+	0.365147i	$0.118981\pi$
$984$	1.64395	−	18.7501i	0.0524071	−	0.597731i
$985$	−4.83633	+	10.8626i	−0.154098	+	0.346110i
$986$	−10.7114	−	32.9662i	−0.341119	−	1.04986i
$987$	−0.250930	+	2.21816i	−0.00798718	+	0.0706047i
$988$	−5.95670	−	4.32780i	−0.189508	−	0.137686i
$989$	8.88581	+	15.3907i	0.282552	+	0.489395i
$990$	6.08458	−	5.42845i	0.193381	−	0.172527i
$991$	4.08317	−	7.07226i	0.129706	−	0.224658i	−0.793857	−	0.608105i	$-0.791930\pi$
$991$	4.08317	−	7.07226i	0.129706	−	0.224658i	0.923563	+	0.383447i	$0.125263\pi$
$992$	0.603854	−	5.74529i	0.0191724	−	0.182413i
$993$	2.22586	−	4.01379i	0.0706355	−	0.127374i
$994$	3.18950	−	9.03519i	0.101165	−	0.286579i
$995$	−4.82196	−	6.63686i	−0.152866	−	0.210403i
$996$	−12.9929	−	9.10136i	−0.411697	−	0.288388i
$997$	0.773610	−	3.63955i	0.0245005	−	0.115266i	−0.964198	−	0.265183i	$-0.914568\pi$
$997$	0.773610	−	3.63955i	0.0245005	−	0.115266i	0.988698	+	0.149918i	$0.0479009\pi$
$998$	20.6887	+	22.9772i	0.654890	+	0.727330i
$999$	−20.2678	+	25.0000i	−0.641245	+	0.790966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.a.95.12	✓	128
3.2	odd	2		462.2.bc.b.95.13	yes	128
7.2	even	3	inner	462.2.bc.a.359.1	yes	128
11.8	odd	10		462.2.bc.b.305.3	yes	128
21.2	odd	6		462.2.bc.b.359.3	yes	128
33.8	even	10	inner	462.2.bc.a.305.1	yes	128
77.30	odd	30		462.2.bc.b.107.13	yes	128
231.107	even	30	inner	462.2.bc.a.107.12	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.12	✓	128	1.1	even	1	trivial
462.2.bc.a.107.12	yes	128	231.107	even	30	inner
462.2.bc.a.305.1	yes	128	33.8	even	10	inner
462.2.bc.a.359.1	yes	128	7.2	even	3	inner
462.2.bc.b.95.13	yes	128	3.2	odd	2
462.2.bc.b.107.13	yes	128	77.30	odd	30
462.2.bc.b.305.3	yes	128	11.8	odd	10
462.2.bc.b.359.3	yes	128	21.2	odd	6

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 - 0.994522i) q^{2} +(0.891795 + 1.48482i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.333330 + 0.748672i) q^{5} +(1.56991 - 0.731703i) q^{6} +(-2.01015 + 1.72026i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-1.40940 + 2.64832i) q^{9} +O(q^{10})\)	\(q+(0.104528 - 0.994522i) q^{2} +(0.891795 + 1.48482i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.333330 + 0.748672i) q^{5} +(1.56991 - 0.731703i) q^{6} +(-2.01015 + 1.72026i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-1.40940 + 2.64832i) q^{9} +(0.709728 + 0.409762i) q^{10} +(-3.26863 + 0.562216i) q^{11} +(-0.563595 - 1.63779i) q^{12} +(-3.17222 + 4.36618i) q^{13} +(1.50072 + 2.17895i) q^{14} +(-1.40891 + 0.172725i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.578545 - 5.50449i) q^{17} +(2.48649 + 1.67851i) q^{18} +(-0.283650 - 1.33447i) q^{19} +(0.481704 - 0.663008i) q^{20} +(-4.34693 - 1.45060i) q^{21} +(0.217472 + 3.30949i) q^{22} +(1.94955 - 1.12557i) q^{23} +(-1.68773 + 0.389312i) q^{24} +(2.89625 + 3.21661i) q^{25} +(4.01068 + 3.61123i) q^{26} +(-5.18918 + 0.269041i) q^{27} +(2.32388 - 1.26474i) q^{28} +(1.93527 + 5.95615i) q^{29} +(0.0245081 + 1.41924i) q^{30} +(5.27750 - 2.34969i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.74974 - 4.35195i) q^{33} -5.53481 q^{34} +(-0.617869 - 2.07836i) q^{35} +(1.92922 - 2.29741i) q^{36} +(4.14442 - 4.60285i) q^{37} +(-1.35681 + 0.142606i) q^{38} +(-9.31198 - 0.816444i) q^{39} +(-0.609025 - 0.548368i) q^{40} +(-3.35806 + 10.3350i) q^{41} +(-1.89703 + 4.17149i) q^{42} +7.89449i q^{43} +(3.31409 + 0.129655i) q^{44} +(-1.51292 - 1.93794i) q^{45} +(-0.915622 - 2.05652i) q^{46} +(-0.101280 - 0.476484i) q^{47} +(0.210763 + 1.71918i) q^{48} +(1.08140 - 6.91597i) q^{49} +(3.50173 - 2.54416i) q^{50} +(7.65725 - 5.76791i) q^{51} +(4.01068 - 3.61123i) q^{52} +(5.29538 + 11.8936i) q^{53} +(-0.274851 + 5.18888i) q^{54} +(0.668616 - 2.63453i) q^{55} +(-1.01490 - 2.44336i) q^{56} +(1.72849 - 1.61124i) q^{57} +(6.12582 - 1.30208i) q^{58} +(0.606629 - 2.85396i) q^{59} +(1.41403 + 0.123978i) q^{60} +(-1.10861 + 2.48998i) q^{61} +(-1.78517 - 5.49419i) q^{62} +(-1.72269 - 7.74805i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-2.21144 - 3.83033i) q^{65} +(-4.72007 + 3.27429i) q^{66} +(2.35441 - 4.07795i) q^{67} +(-0.578545 + 5.50449i) q^{68} +(3.40987 + 1.89095i) q^{69} +(-2.13156 + 0.397236i) q^{70} +(-2.12867 - 2.92987i) q^{71} +(-2.08317 - 2.15880i) q^{72} +(0.719776 - 3.38628i) q^{73} +(-4.14442 - 4.60285i) q^{74} +(-2.19324 + 7.16899i) q^{75} +1.36428i q^{76} +(5.60327 - 6.75303i) q^{77} +(-1.78534 + 9.17563i) q^{78} +(10.1418 + 1.06594i) q^{79} +(-0.609025 + 0.548368i) q^{80} +(-5.02717 - 7.46509i) q^{81} +(9.92741 + 4.41997i) q^{82} +(7.40963 - 5.38341i) q^{83} +(3.95034 + 2.32267i) q^{84} +(4.31390 + 1.40167i) q^{85} +(7.85124 + 0.825199i) q^{86} +(-7.11797 + 8.18521i) q^{87} +(0.475362 - 3.28238i) q^{88} +(-5.82848 + 3.36507i) q^{89} +(-2.08547 + 1.30207i) q^{90} +(-1.13435 - 14.2337i) q^{91} +(-2.14096 + 0.695641i) q^{92} +(8.19532 + 5.74071i) q^{93} +(-0.484461 + 0.0509189i) q^{94} +(1.09363 + 0.232458i) q^{95} +(1.73179 - 0.0299053i) q^{96} +(4.17913 + 3.03631i) q^{97} +(-6.76504 - 1.79839i) q^{98} +(3.11789 - 9.44875i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

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