LMFDB - Embedded newform 572.2.bs.a.15.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(15,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 12, 5]))

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

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

chi := DirichletCharacter("572.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bs (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$80$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			15.9
Character	$\chi$	$=$	572.15
Dual form			572.2.bs.a.267.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36092 - 0.384566i) q^{2} +(-0.238841 - 1.12366i) q^{3} +(1.70422 + 1.04673i) q^{4} +(0.255413 - 1.61261i) q^{5} +(-0.107076 + 1.62106i) q^{6} +(3.96409 - 2.57431i) q^{7} +(-1.91677 - 2.07990i) q^{8} +(1.53508 - 0.683460i) q^{9} +O(q^{10})$	\(q+(-1.36092 - 0.384566i) q^{2} +(-0.238841 - 1.12366i) q^{3} +(1.70422 + 1.04673i) q^{4} +(0.255413 - 1.61261i) q^{5} +(-0.107076 + 1.62106i) q^{6} +(3.96409 - 2.57431i) q^{7} +(-1.91677 - 2.07990i) q^{8} +(1.53508 - 0.683460i) q^{9} +(-0.967752 + 2.09642i) q^{10} +(-3.30819 + 0.236435i) q^{11} +(0.769127 - 2.16496i) q^{12} +(2.08886 - 2.93882i) q^{13} +(-6.38481 + 1.97898i) q^{14} +(-1.87303 + 0.0981611i) q^{15} +(1.80872 + 3.56771i) q^{16} +(3.69119 - 0.387960i) q^{17} +(-2.35196 + 0.339798i) q^{18} +(-0.406177 + 7.75031i) q^{19} +(2.12325 - 2.48090i) q^{20} +(-3.83942 - 3.83942i) q^{21} +(4.59311 + 0.950445i) q^{22} +(1.15063 + 1.99294i) q^{23} +(-1.87929 + 2.65056i) q^{24} +(2.22000 + 0.721321i) q^{25} +(-3.97294 + 3.19621i) q^{26} +(-3.16029 - 4.34976i) q^{27} +(9.45027 - 0.237862i) q^{28} +(1.90358 - 2.11414i) q^{29} +(2.58679 + 0.586712i) q^{30} +(-0.612295 - 3.86588i) q^{31} +(-1.08951 - 5.55094i) q^{32} +(1.05580 + 3.66080i) q^{33} +(-5.17262 - 0.891523i) q^{34} +(-3.13888 - 7.05005i) q^{35} +(3.33150 + 0.442043i) q^{36} +(-1.88384 + 0.0987277i) q^{37} +(3.53328 - 10.3914i) q^{38} +(-3.80113 - 1.64525i) q^{39} +(-3.84364 + 2.55978i) q^{40} +(-4.41708 + 6.80170i) q^{41} +(3.74865 + 6.70167i) q^{42} +(-4.74603 + 8.22037i) q^{43} +(-5.88536 - 3.05983i) q^{44} +(-0.710078 - 2.65005i) q^{45} +(-0.799496 - 3.15473i) q^{46} +(-2.83647 - 5.56689i) q^{47} +(3.57688 - 2.88449i) q^{48} +(6.23977 - 14.0148i) q^{49} +(-2.74385 - 1.83540i) q^{50} +(-1.31754 - 4.05497i) q^{51} +(6.63601 - 2.82193i) q^{52} +(-1.95148 - 1.41783i) q^{53} +(2.62813 + 7.13502i) q^{54} +(-0.463675 + 5.39521i) q^{55} +(-12.9526 - 3.31054i) q^{56} +(8.80570 - 1.39469i) q^{57} +(-3.40365 + 2.14513i) q^{58} +(-6.34846 + 4.12274i) q^{59} +(-3.29479 - 1.79326i) q^{60} +(-0.427787 - 4.07012i) q^{61} +(-0.653399 + 5.49663i) q^{62} +(4.32574 - 6.66106i) q^{63} +(-0.651964 + 7.97339i) q^{64} +(-4.20566 - 4.11913i) q^{65} +(-0.0290466 - 5.38808i) q^{66} +(3.06990 - 11.4570i) q^{67} +(6.69669 + 3.20251i) q^{68} +(1.96457 - 1.76891i) q^{69} +(1.56057 + 10.8017i) q^{70} +(-1.90598 + 2.35368i) q^{71} +(-4.36392 - 1.88277i) q^{72} +(-4.87700 + 9.57165i) q^{73} +(2.60172 + 0.590098i) q^{74} +(0.280292 - 2.66680i) q^{75} +(-8.80468 + 12.7831i) q^{76} +(-12.5053 + 9.45354i) q^{77} +(4.54034 + 3.70084i) q^{78} +(-1.72898 + 2.37974i) q^{79} +(6.21530 - 2.00553i) q^{80} +(-0.759711 + 0.843745i) q^{81} +(8.62700 - 7.55793i) q^{82} +(7.43983 + 1.17835i) q^{83} +(-2.52438 - 10.5621i) q^{84} +(0.317149 - 6.05155i) q^{85} +(9.62026 - 9.36213i) q^{86} +(-2.83022 - 1.63403i) q^{87} +(6.83280 + 6.42750i) q^{88} +(0.926842 - 3.45902i) q^{89} +(-0.0527565 + 3.87958i) q^{90} +(0.714968 - 17.0271i) q^{91} +(-0.125151 + 4.60081i) q^{92} +(-4.19768 + 1.61134i) q^{93} +(1.71938 + 8.66691i) q^{94} +(12.3945 + 2.63453i) q^{95} +(-5.97714 + 2.55003i) q^{96} +(2.53938 - 6.61531i) q^{97} +(-13.8814 + 16.6734i) q^{98} +(-4.91673 + 2.62396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.36092	−	0.384566i	−0.962317	−	0.271929i
$2$	−1.36092	−	0.384566i	−0.962317	−	0.271929i
$3$	−0.238841	−	1.12366i	−0.137895	−	0.648744i	−0.991745	−	0.128225i	$-0.959072\pi$
$3$	−0.238841	−	1.12366i	−0.137895	−	0.648744i	0.853850	−	0.520518i	$-0.174261\pi$
$4$	1.70422	+	1.04673i	0.852109	+	0.523364i
$5$	0.255413	−	1.61261i	0.114224	−	0.721182i	−0.862400	−	0.506228i	$-0.831040\pi$
$5$	0.255413	−	1.61261i	0.114224	−	0.721182i	0.976624	−	0.214955i	$-0.0689604\pi$
$6$	−0.107076	+	1.62106i	−0.0437138	+	0.661795i
$7$	3.96409	−	2.57431i	1.49828	−	0.972997i	0.504294	−	0.863532i	$-0.331753\pi$
$7$	3.96409	−	2.57431i	1.49828	−	0.972997i	0.993991	−	0.109465i	$-0.0349137\pi$
$8$	−1.91677	−	2.07990i	−0.677682	−	0.735356i
$9$	1.53508	−	0.683460i	0.511692	−	0.227820i
$10$	−0.967752	+	2.09642i	−0.306030	+	0.662945i
$11$	−3.30819	+	0.236435i	−0.997456	+	0.0712879i
$11$	−3.30819	+	0.236435i	−0.997456	+	0.0712879i
$12$	0.769127	−	2.16496i	0.222028	−	0.624969i
$13$	2.08886	−	2.93882i	0.579344	−	0.815083i
$13$	2.08886	−	2.93882i	0.579344	−	0.815083i
$14$	−6.38481	+	1.97898i	−1.70641	+	0.528905i
$15$	−1.87303	+	0.0981611i	−0.483613	+	0.0253451i
$16$	1.80872	+	3.56771i	0.452180	+	0.891927i
$17$	3.69119	−	0.387960i	0.895246	−	0.0940941i	0.354281	−	0.935139i	$-0.384726\pi$
$17$	3.69119	−	0.387960i	0.895246	−	0.0940941i	0.540965	+	0.841045i	$0.318059\pi$
$18$	−2.35196	+	0.339798i	−0.554361	+	0.0800912i
$19$	−0.406177	+	7.75031i	−0.0931833	+	1.77804i	0.408272	+	0.912860i	$0.366131\pi$
$19$	−0.406177	+	7.75031i	−0.0931833	+	1.77804i	−0.501456	+	0.865183i	$0.667202\pi$
$20$	2.12325	−	2.48090i	0.474772	−	0.554745i
$21$	−3.83942	−	3.83942i	−0.837831	−	0.837831i
$22$	4.59311	+	0.950445i	0.979254	+	0.202636i
$23$	1.15063	+	1.99294i	0.239922	+	0.415558i	0.960692	−	0.277617i	$-0.0895447\pi$
$23$	1.15063	+	1.99294i	0.239922	+	0.415558i	−0.720769	+	0.693175i	$0.756211\pi$
$24$	−1.87929	+	2.65056i	−0.383608	+	0.541043i
$25$	2.22000	+	0.721321i	0.444000	+	0.144264i
$26$	−3.97294	+	3.19621i	−0.779158	+	0.626828i
$27$	−3.16029	−	4.34976i	−0.608197	−	0.837112i
$28$	9.45027	−	0.237862i	1.78593	−	0.0449517i
$29$	1.90358	−	2.11414i	0.353485	−	0.392585i	−0.540009	−	0.841659i	$-0.681579\pi$
$29$	1.90358	−	2.11414i	0.353485	−	0.392585i	0.893495	+	0.449074i	$0.148246\pi$
$30$	2.58679	+	0.586712i	0.472281	+	0.107118i
$31$	−0.612295	−	3.86588i	−0.109972	−	0.694333i	−0.979650	−	0.200714i	$-0.935674\pi$
$31$	−0.612295	−	3.86588i	−0.109972	−	0.694333i	0.869678	−	0.493619i	$-0.164326\pi$
$32$	−1.08951	−	5.55094i	−0.192600	−	0.981277i
$33$	1.05580	+	3.66080i	0.183791	+	0.637263i
$34$	−5.17262	−	0.891523i	−0.887097	−	0.152895i
$35$	−3.13888	−	7.05005i	−0.530568	−	1.19168i
$36$	3.33150	+	0.442043i	0.555250	+	0.0736738i
$37$	−1.88384	+	0.0987277i	−0.309701	+	0.0162307i	−0.206553	−	0.978435i	$-0.566225\pi$
$37$	−1.88384	+	0.0987277i	−0.309701	+	0.0162307i	−0.103147	+	0.994666i	$0.532891\pi$
$38$	3.53328	−	10.3914i	0.573174	−	1.68570i
$39$	−3.80113	−	1.64525i	−0.608668	−	0.263450i
$40$	−3.84364	+	2.55978i	−0.607733	+	0.404737i
$41$	−4.41708	+	6.80170i	−0.689831	+	1.06225i	0.304142	+	0.952627i	$0.401630\pi$
$41$	−4.41708	+	6.80170i	−0.689831	+	1.06225i	−0.993974	+	0.109620i	$0.965036\pi$
$42$	3.74865	+	6.70167i	0.578429	+	1.03409i
$43$	−4.74603	+	8.22037i	−0.723764	+	1.25360i	0.235717	+	0.971822i	$0.424256\pi$
$43$	−4.74603	+	8.22037i	−0.723764	+	1.25360i	−0.959481	+	0.281774i	$0.909077\pi$
$44$	−5.88536	−	3.05983i	−0.887251	−	0.461287i
$45$	−0.710078	−	2.65005i	−0.105852	−	0.395046i
$46$	−0.799496	−	3.15473i	−0.117879	−	0.465140i
$47$	−2.83647	−	5.56689i	−0.413742	−	0.812014i	−0.999998	−	0.00188872i	$-0.999399\pi$
$47$	−2.83647	−	5.56689i	−0.413742	−	0.812014i	0.586256	−	0.810126i	$-0.300601\pi$
$48$	3.57688	−	2.88449i	0.516278	−	0.416341i
$49$	6.23977	−	14.0148i	0.891396	−	2.00211i
$50$	−2.74385	−	1.83540i	−0.388039	−	0.259564i
$51$	−1.31754	−	4.05497i	−0.184493	−	0.567810i
$52$	6.63601	−	2.82193i	0.920250	−	0.391332i
$53$	−1.95148	−	1.41783i	−0.268056	−	0.194754i	0.445635	−	0.895215i	$-0.352978\pi$
$53$	−1.95148	−	1.41783i	−0.268056	−	0.194754i	−0.713691	+	0.700461i	$0.752978\pi$
$54$	2.62813	+	7.13502i	0.357644	+	0.970954i
$55$	−0.463675	+	5.39521i	−0.0625219	+	0.727490i
$56$	−12.9526	−	3.31054i	−1.73086	−	0.442389i
$57$	8.80570	−	1.39469i	1.16634	−	0.184731i
$58$	−3.40365	+	2.14513i	−0.446921	+	0.281669i
$59$	−6.34846	+	4.12274i	−0.826499	+	0.536735i	−0.887181	−	0.461422i	$-0.847339\pi$
$59$	−6.34846	+	4.12274i	−0.826499	+	0.536735i	0.0606814	+	0.998157i	$0.480673\pi$
$60$	−3.29479	−	1.79326i	−0.425356	−	0.231509i
$61$	−0.427787	−	4.07012i	−0.0547726	−	0.521126i	−0.987168	−	0.159686i	$-0.948952\pi$
$61$	−0.427787	−	4.07012i	−0.0547726	−	0.521126i	0.932395	−	0.361440i	$-0.117715\pi$
$62$	−0.653399	+	5.49663i	−0.0829818	+	0.698073i
$63$	4.32574	−	6.66106i	0.544992	−	0.839214i
$64$	−0.651964	+	7.97339i	−0.0814955	+	0.996674i
$65$	−4.20566	−	4.11913i	−0.521648	−	0.510915i
$66$	−0.0290466	−	5.38808i	−0.00357539	−	0.663227i
$67$	3.06990	−	11.4570i	0.375048	−	1.39970i	−0.478226	−	0.878237i	$-0.658720\pi$
$67$	3.06990	−	11.4570i	0.375048	−	1.39970i	0.853274	−	0.521462i	$-0.174613\pi$
$68$	6.69669	+	3.20251i	0.812093	+	0.388361i
$69$	1.96457	−	1.76891i	0.236506	−	0.212951i
$70$	1.56057	+	10.8017i	0.186524	+	1.29105i
$71$	−1.90598	+	2.35368i	−0.226198	+	0.279331i	−0.877592	−	0.479409i	$-0.840851\pi$
$71$	−1.90598	+	2.35368i	−0.226198	+	0.279331i	0.651394	+	0.758740i	$0.274185\pi$
$72$	−4.36392	−	1.88277i	−0.514293	−	0.221886i
$73$	−4.87700	+	9.57165i	−0.570810	+	1.12028i	0.407514	+	0.913199i	$0.366396\pi$
$73$	−4.87700	+	9.57165i	−0.570810	+	1.12028i	−0.978324	+	0.207079i	$0.933604\pi$
$74$	2.60172	+	0.590098i	0.302444	+	0.0685975i
$75$	0.280292	−	2.66680i	0.0323653	−	0.307935i
$76$	−8.80468	+	12.7831i	−1.00997	+	1.46632i
$77$	−12.5053	+	9.45354i	−1.42511	+	1.07733i
$78$	4.54034	+	3.70084i	0.514092	+	0.419037i
$79$	−1.72898	+	2.37974i	−0.194525	+	0.267741i	−0.895127	−	0.445812i	$-0.852915\pi$
$79$	−1.72898	+	2.37974i	−0.194525	+	0.267741i	0.700601	+	0.713553i	$0.252915\pi$
$80$	6.21530	−	2.00553i	0.694892	−	0.224225i
$81$	−0.759711	+	0.843745i	−0.0844123	+	0.0937494i
$82$	8.62700	−	7.55793i	0.952693	−	0.834634i
$83$	7.43983	+	1.17835i	0.816628	+	0.129341i	0.550755	−	0.834667i	$-0.314340\pi$
$83$	7.43983	+	1.17835i	0.816628	+	0.129341i	0.265873	+	0.964008i	$0.414340\pi$
$84$	−2.52438	−	10.5621i	−0.275433	−	1.15241i
$85$	0.317149	−	6.05155i	0.0343996	−	0.656383i
$86$	9.62026	−	9.36213i	1.03738	−	1.00954i
$87$	−2.83022	−	1.63403i	−0.303431	−	0.175186i
$88$	6.83280	+	6.42750i	0.728379	+	0.685174i
$89$	0.926842	−	3.45902i	0.0982451	−	0.366656i	−0.899246	−	0.437442i	$-0.855884\pi$
$89$	0.926842	−	3.45902i	0.0982451	−	0.366656i	0.997491	+	0.0707869i	$0.0225510\pi$
$90$	−0.0527565	+	3.87958i	−0.00556102	+	0.408944i
$91$	0.714968	−	17.0271i	0.0749490	−	1.78493i
$92$	−0.125151	+	4.60081i	−0.0130479	+	0.479667i
$93$	−4.19768	+	1.61134i	−0.435279	+	0.167088i
$94$	1.71938	+	8.66691i	0.177341	+	0.893924i
$95$	12.3945	+	2.63453i	1.27165	+	0.270297i
$96$	−5.97714	+	2.55003i	−0.610039	+	0.260261i
$97$	2.53938	−	6.61531i	0.257835	−	0.671683i	−0.742164	−	0.670218i	$-0.766201\pi$
$97$	2.53938	−	6.61531i	0.257835	−	0.671683i	0.999999	−	0.00146441i	$-0.000466136\pi$
$98$	−13.8814	+	16.6734i	−1.40224	+	1.68427i
$99$	−4.91673	+	2.62396i	−0.494150	+	0.263718i
$100$	3.02834	+	3.55302i	0.302834	+	0.355302i
$101$	0.253416	+	0.0266351i	0.0252159	+	0.00265029i	0.117128	−	0.993117i	$-0.462631\pi$
$101$	0.253416	+	0.0266351i	0.0252159	+	0.00265029i	−0.0919121	+	0.995767i	$0.529298\pi$
$102$	0.233667	+	6.02518i	0.0231364	+	0.596582i
$103$	−1.82239	−	5.60874i	−0.179565	−	0.552645i	0.820247	−	0.572009i	$-0.193836\pi$
$103$	−1.82239	−	5.60874i	−0.179565	−	0.552645i	−0.999812	+	0.0193641i	$0.993836\pi$
$104$	−10.1163	+	1.28845i	−0.991987	+	0.126343i
$105$	−7.17214	+	5.21087i	−0.699929	+	0.508528i
$106$	2.11056	+	2.68003i	0.204996	+	0.260307i
$107$	3.09527	+	14.5621i	0.299231	+	1.40777i	0.828819	+	0.559517i	$0.189013\pi$
$107$	3.09527	+	14.5621i	0.299231	+	1.40777i	−0.529587	+	0.848255i	$0.677653\pi$
$108$	−0.832801	−	10.7209i	−0.0801363	−	1.03162i
$109$	−5.73804	+	5.73804i	−0.549604	+	0.549604i	−0.926326	−	0.376722i	$-0.877051\pi$
$109$	−5.73804	+	5.73804i	−0.549604	+	0.549604i	0.376722	+	0.926326i	$0.377051\pi$
$110$	2.70584	−	7.16415i	0.257992	−	0.683075i
$111$	0.560873	+	2.09320i	0.0532357	+	0.198678i
$112$	16.3543	+	9.48650i	1.54534	+	0.896390i
$113$	5.91438	+	6.56859i	0.556378	+	0.617921i	0.954065	−	0.299601i	$-0.0968535\pi$
$113$	5.91438	+	6.56859i	0.556378	+	0.617921i	−0.397686	+	0.917521i	$0.630187\pi$
$114$	−12.5202	−	1.48831i	−1.17263	−	0.139393i
$115$	3.50773	−	1.34649i	0.327098	−	0.125561i
$116$	5.45704	−	1.61042i	0.506673	−	0.149524i
$117$	1.19798	−	5.93897i	0.110754	−	0.549058i
$118$	10.2252	−	3.16933i	0.941308	−	0.291760i
$119$	13.6335	−	11.0402i	1.24978	−	1.01205i
$120$	3.79433	+	3.70755i	0.346373	+	0.338452i
$121$	10.8882	−	1.56434i	0.989836	−	0.142213i
$122$	−0.983045	+	5.70364i	−0.0890007	+	0.516383i
$123$	8.69775	+	3.33876i	0.784250	+	0.301045i
$124$	3.00304	−	7.22921i	0.269681	−	0.649202i
$125$	5.43641	−	10.6696i	0.486247	−	0.954314i
$126$	−8.44861	+	7.40165i	−0.752662	+	0.659391i
$127$	6.58189	+	2.93045i	0.584048	+	0.260035i	0.677420	−	0.735596i	$-0.263098\pi$
$127$	6.58189	+	2.93045i	0.584048	+	0.260035i	−0.0933719	+	0.995631i	$0.529765\pi$
$128$	3.95357	−	10.6004i	0.349449	−	0.936955i
$129$	10.3704	+	3.36956i	0.913065	+	0.296673i
$130$	4.13950	+	7.22317i	0.363059	+	0.633514i
$131$		−	7.00943i		−	0.612416i	−0.951965	−	0.306208i	$-0.900940\pi$
$131$		−	7.00943i		−	0.612416i	0.951965	−	0.306208i	$-0.0990604\pi$
$132$	−2.03254	+	7.34393i	−0.176910	+	0.639207i
$133$	18.3416	+	31.7685i	1.59042	+	2.75468i
$134$	−8.58388	+	14.4115i	−0.741534	+	1.24497i
$135$	−7.82166	+	3.98533i	−0.673181	+	0.343003i
$136$	−7.88210	−	6.93368i	−0.675884	−	0.594558i
$137$	−11.2231	+	13.8594i	−0.958858	+	1.18409i	0.0239968	+	0.999712i	$0.492361\pi$
$137$	−11.2231	+	13.8594i	−0.958858	+	1.18409i	−0.982855	+	0.184379i	$0.940972\pi$
$138$	−3.35389	+	1.65184i	−0.285502	+	0.140614i
$139$	−1.96049	+	9.22336i	−0.166286	+	0.782315i	0.813388	+	0.581721i	$0.197621\pi$
$139$	−1.96049	+	9.22336i	−0.166286	+	0.782315i	−0.979674	+	0.200594i	$0.935713\pi$
$140$	2.03014	−	15.3004i	0.171578	−	1.29312i
$141$	−5.57781	+	4.51682i	−0.469736	+	0.380385i
$142$	3.49903	−	2.47021i	0.293632	−	0.207295i
$143$	−6.21548	+	10.2161i	−0.519765	+	0.854309i
$144$	5.21491	+	4.24051i	0.434576	+	0.353376i
$145$	−2.92309	−	3.60971i	−0.242749	−	0.299770i
$146$	10.3181	−	11.1507i	0.853936	−	0.922843i
$147$	−17.2381	−	3.66407i	−1.42177	−	0.302207i
$148$	−3.31381	−	1.80361i	−0.272393	−	0.148256i
$149$	4.90887	+	3.97512i	0.402150	+	0.325655i	0.808966	−	0.587856i	$-0.200028\pi$
$149$	4.90887	+	3.97512i	0.402150	+	0.325655i	−0.406816	+	0.913510i	$0.633361\pi$
$150$	−1.40701	+	3.52151i	−0.114882	+	0.287530i
$151$	0.677750	+	1.33016i	0.0551545	+	0.108247i	0.916938	−	0.399029i	$-0.130653\pi$
$151$	0.677750	+	1.33016i	0.0551545	+	0.108247i	−0.861784	+	0.507276i	$0.830653\pi$
$152$	16.8984	−	14.0108i	1.37064	−	1.13642i
$153$	5.40111	−	3.11833i	0.436654	−	0.252102i
$154$	20.6542	−	8.05643i	1.66437	−	0.649206i
$155$	−6.39056			−0.513302
$156$	−4.75583	−	6.78261i	−0.380771	−	0.543043i
$157$	−7.09649	+	21.8408i	−0.566362	+	1.74308i	0.0975083	+	0.995235i	$0.468913\pi$
$157$	−7.09649	+	21.8408i	−0.566362	+	1.74308i	−0.663870	+	0.747848i	$0.731087\pi$
$158$	3.26817	−	2.57373i	0.260002	−	0.204755i
$159$	−1.12706	+	2.53143i	−0.0893820	+	0.200755i
$160$	−9.22980	+	0.339176i	−0.729679	+	0.0268142i
$161$	9.69164	+	4.93814i	0.763808	+	0.389180i
$162$	1.35838	−	0.856112i	0.106725	−	0.0672625i
$163$	−1.87465	+	4.88362i	−0.146834	+	0.382515i	−0.987196	−	0.159510i	$-0.949009\pi$
$163$	−1.87465	+	4.88362i	−0.146834	+	0.382515i	0.840363	+	0.542024i	$0.182342\pi$
$164$	−14.6472	+	6.96811i	−1.14375	+	0.544118i
$165$	6.17311	−	0.767585i	0.480576	−	0.0597564i
$166$	−9.67188	−	4.46475i	−0.750684	−	0.346532i
$167$	2.20204	+	2.71929i	0.170399	+	0.210425i	0.855191	−	0.518314i	$-0.173440\pi$
$167$	2.20204	+	2.71929i	0.170399	+	0.210425i	−0.684791	+	0.728739i	$0.740107\pi$
$168$	−0.626313	+	15.3449i	−0.0483211	+	1.18389i
$169$	−4.27337	−	12.2776i	−0.328720	−	0.944427i
$170$	−2.75883	+	8.11373i	−0.211593	+	0.622295i
$171$	4.67352	+	12.1749i	0.357393	+	0.931040i
$172$	−16.6928	+	9.04150i	−1.27281	+	0.689408i
$173$	−6.15967	+	5.54619i	−0.468311	+	0.421669i	−0.869202	−	0.494456i	$-0.835367\pi$
$173$	−6.15967	+	5.54619i	−0.468311	+	0.421669i	0.400891	+	0.916126i	$0.368700\pi$
$174$	3.22331	+	3.31219i	0.244359	+	0.251096i
$175$	10.6572	−	2.85558i	0.805607	−	0.215862i
$176$	−6.82712	−	11.3750i	−0.514613	−	0.857422i
$177$	6.14881	+	6.14881i	0.462173	+	0.462173i
$178$	−2.59158	+	4.35103i	−0.194247	+	0.326123i
$179$	−4.30271	+	0.914569i	−0.321599	+	0.0683581i	−0.365883	−	0.930661i	$-0.619233\pi$
$179$	−4.30271	+	0.914569i	−0.321599	+	0.0683581i	0.0442834	+	0.999019i	$0.485900\pi$
$180$	1.56375	−	5.25952i	0.116555	−	0.392021i
$181$	11.7806	+	16.2146i	0.875647	+	1.20523i	0.977608	+	0.210437i	$0.0674885\pi$
$181$	11.7806	+	16.2146i	0.875647	+	1.20523i	−0.101960	+	0.994788i	$0.532511\pi$
$182$	−7.52106	+	22.8976i	−0.557498	+	1.69728i
$183$	−4.47125	+	1.45280i	−0.330524	+	0.107394i
$184$	1.93963	−	6.21321i	0.142992	−	0.458044i
$185$	−0.321946	+	3.06311i	−0.0236700	+	0.225205i
$186$	6.33239	−	0.578623i	0.464313	−	0.0424267i
$187$	−12.1194	+	2.15617i	−0.886260	+	0.157675i
$188$	0.993052	−	12.4562i	0.0724258	−	0.908463i
$189$	−23.7253	−	9.10728i	−1.72576	−	0.662457i
$190$	−15.8548	−	8.35190i	−1.15023	−	0.605910i
$191$	−1.15333	+	5.42601i	−0.0834523	+	0.392612i	−0.999973	−	0.00737540i	$-0.997652\pi$
$191$	−1.15333	+	5.42601i	−0.0834523	+	0.392612i	0.916520	+	0.399988i	$0.130986\pi$
$192$	9.11507	−	1.17179i	0.657823	−	0.0845663i
$193$	−4.16116	−	10.8402i	−0.299527	−	0.780293i	−0.997913	−	0.0645726i	$-0.979432\pi$
$193$	−4.16116	−	10.8402i	−0.299527	−	0.780293i	0.698386	−	0.715721i	$-0.253902\pi$
$194$	−5.99992	+	8.02636i	−0.430769	+	0.576259i
$195$	−3.62400	+	5.70954i	−0.259520	+	0.408868i
$196$	25.3036	−	17.3529i	1.80740	−	1.23949i
$197$	2.52942	+	0.677755i	0.180213	+	0.0482880i	0.347797	−	0.937570i	$-0.386930\pi$
$197$	2.52942	+	0.677755i	0.180213	+	0.0482880i	−0.167584	+	0.985858i	$0.553596\pi$
$198$	7.70037	−	1.68020i	0.547241	−	0.119407i
$199$	2.01873	−	3.49655i	0.143104	−	0.247864i	−0.785560	−	0.618786i	$-0.787625\pi$
$199$	2.01873	−	3.49655i	0.143104	−	0.247864i	0.928664	+	0.370922i	$0.120958\pi$
$200$	−2.75496	−	5.99998i	−0.194805	−	0.424263i
$201$	−13.6070	−	0.713112i	−0.959763	−	0.0502990i
$202$	−0.334637	−	0.133704i	−0.0235450	−	0.00940735i
$203$	2.10351	−	13.2810i	0.147637	−	0.932145i
$204$	1.99908	−	8.28967i	0.139963	−	0.580393i
$205$	9.84033	+	8.86027i	0.687278	+	0.618828i
$206$	0.323202	+	8.33388i	0.0225185	+	0.580649i
$207$	3.12840	+	2.27291i	0.217439	+	0.157978i
$208$	14.2630	+	2.13691i	0.988962	+	0.148168i
$209$	−0.488738	−	25.7355i	−0.0338067	−	1.78016i
$210$	11.7646	−	4.33342i	0.811838	−	0.299035i
$211$	6.99595	+	0.735304i	0.481621	+	0.0506204i	0.342228	−	0.939617i	$-0.388818\pi$
$211$	6.99595	+	0.735304i	0.481621	+	0.0506204i	0.139393	+	0.990237i	$0.455485\pi$
$212$	−1.84166	−	4.45896i	−0.126486	−	0.306243i
$213$	3.09996	+	1.57951i	0.212406	+	0.108226i
$214$	1.38766	−	21.0082i	0.0948588	−	1.43609i
$215$	12.0441	+	9.75310i	0.821399	+	0.665156i
$216$	−2.98951	+	14.9106i	−0.203411	+	1.01454i
$217$	−12.3792	−	13.7485i	−0.840352	−	0.933306i
$218$	10.0157	−	5.60237i	0.678347	−	0.379440i
$219$	11.9201	+	3.19398i	0.805484	+	0.215829i
$220$	−6.43752	+	8.70928i	−0.434018	+	0.587179i
$221$	6.57022	−	11.6582i	0.441961	−	0.784212i
$222$	0.0416710	−	3.06438i	0.00279677	−	0.205668i
$223$	−5.80831	−	3.77196i	−0.388954	−	0.252589i	0.335317	−	0.942105i	$-0.391157\pi$
$223$	−5.80831	−	3.77196i	−0.388954	−	0.252589i	−0.724270	+	0.689516i	$0.757823\pi$
$224$	−18.6088	−	19.1997i	−1.24335	−	1.28283i
$225$	3.90086	−	0.409997i	0.260058	−	0.0273331i
$226$	−5.52296	−	11.2138i	−0.367382	−	0.745931i
$227$	−2.52762	−	3.89220i	−0.167764	−	0.258334i	0.744782	−	0.667308i	$-0.232553\pi$
$227$	−2.52762	−	3.89220i	−0.167764	−	0.258334i	−0.912546	+	0.408974i	$0.865887\pi$
$228$	16.4667	+	6.84033i	1.09053	+	0.453012i
$229$	−3.20942	−	20.2635i	−0.212084	−	1.33905i	−0.832173	−	0.554516i	$-0.812903\pi$
$229$	−3.20942	−	20.2635i	−0.212084	−	1.33905i	0.620089	−	0.784532i	$-0.287097\pi$
$230$	−5.29157	+	0.483517i	−0.348915	+	0.0318822i
$231$	13.6093	+	11.7938i	0.895427	+	0.775972i
$232$	−8.04592	+	0.0930703i	−0.528240	+	0.00611037i
$233$	−7.05702	+	9.71315i	−0.462321	+	0.636330i	−0.974988	−	0.222258i	$-0.928657\pi$
$233$	−7.05702	+	9.71315i	−0.462321	+	0.636330i	0.512667	+	0.858587i	$0.328657\pi$
$234$	−3.91429	+	7.62177i	−0.255885	+	0.498251i
$235$	−9.70171	+	3.15228i	−0.632870	+	0.205632i
$236$	−15.1346	+	0.380935i	−0.985175	+	0.0247967i
$237$	3.08696	+	1.37440i	0.200519	+	0.0892770i
$238$	−22.7998	+	9.78185i	−1.47789	+	0.634063i
$239$	23.3479	−	11.8964i	1.51025	−	0.769512i	0.514148	−	0.857701i	$-0.328108\pi$
$239$	23.3479	−	11.8964i	1.51025	−	0.769512i	0.996104	+	0.0881893i	$0.0281080\pi$
$240$	−3.73799	−	6.50486i	−0.241286	−	0.419887i
$241$	−6.83905	+	1.83252i	−0.440542	+	0.118043i	−0.472271	−	0.881454i	$-0.656565\pi$
$241$	−6.83905	+	1.83252i	−0.440542	+	0.118043i	0.0317285	+	0.999497i	$0.489899\pi$
$242$	−15.4196	−	2.05828i	−0.991208	−	0.132311i
$243$	−12.8393	−	7.41276i	−0.823641	−	0.475529i
$244$	3.53127	−	7.38416i	0.226066	−	0.472722i
$245$	−21.0066	−	13.6419i	−1.34207	−	0.871548i
$246$	−10.5530	−	7.88864i	−0.672834	−	0.502962i
$247$	21.9284	+	17.3830i	1.39527	+	1.10605i
$248$	−6.86701	+	8.68353i	−0.436056	+	0.551405i
$249$	−0.452869	−	8.64126i	−0.0286994	−	0.547618i
$250$	−11.5017	+	12.4298i	−0.727430	+	0.786128i
$251$	26.7976	−	11.9311i	1.69145	−	0.753083i	0.691936	−	0.721959i	$-0.256758\pi$
$251$	26.7976	−	11.9311i	1.69145	−	0.753083i	0.999516	−	0.0311237i	$-0.00990858\pi$
$252$	14.3443	−	6.82402i	0.903607	−	0.429873i
$253$	−4.27769	−	6.32098i	−0.268936	−	0.397397i
$254$	−7.83049	−	6.51928i	−0.491329	−	0.409056i
$255$	−6.87562	+	1.08899i	−0.430568	+	0.0681953i
$256$	−9.45706	+	12.9060i	−0.591066	+	0.806623i
$257$	−2.35273	−	2.11841i	−0.146759	−	0.132143i	0.592481	−	0.805584i	$-0.298149\pi$
$257$	−2.35273	−	2.11841i	−0.146759	−	0.132143i	−0.739240	+	0.673442i	$0.764815\pi$
$258$	−12.8175	−	8.57381i	−0.797984	−	0.533782i
$259$	−7.21354	+	5.24094i	−0.448227	+	0.325656i
$260$	−2.85576	−	11.4221i	−0.177107	−	0.708367i
$261$	1.47721	−	4.54638i	0.0914369	−	0.281414i
$262$	−2.69559	+	9.53928i	−0.166534	+	0.589339i
$263$	13.5651	−	7.83183i	0.836462	−	0.482931i	−0.0195983	−	0.999808i	$-0.506239\pi$
$263$	13.5651	−	7.83183i	0.836462	−	0.482931i	0.856060	+	0.516877i	$0.172905\pi$
$264$	5.59036	−	9.21287i	0.344063	−	0.567013i
$265$	−2.78484	+	2.78484i	−0.171072	+	0.171072i
$266$	−12.7444	−	50.2881i	−0.781407	−	3.08336i
$267$	−4.10812	−	0.215297i	−0.251413	−	0.0131760i
$268$	17.2242	−	16.3119i	1.05213	−	0.996410i
$269$	−1.56019	−	14.8442i	−0.0951264	−	0.905067i	−0.933163	−	0.359453i	$-0.882963\pi$
$269$	−1.56019	−	14.8442i	−0.0951264	−	0.905067i	0.838037	−	0.545614i	$-0.183703\pi$
$270$	12.1773	−	2.41579i	0.741086	−	0.147020i
$271$	0.403841	+	7.70574i	0.0245316	+	0.468090i	0.983082	+	0.183167i	$0.0586348\pi$
$271$	0.403841	+	7.70574i	0.0245316	+	0.468090i	−0.958550	+	0.284923i	$0.908032\pi$
$272$	8.06046	+	12.4674i	0.488737	+	0.755946i
$273$	−19.3034	+	3.26339i	−1.16829	+	0.197509i
$274$	20.6037	−	14.5456i	1.24471	−	0.878730i
$275$	−7.51472	−	1.86138i	−0.453154	−	0.112245i
$276$	5.19962	−	0.958232i	0.312980	−	0.0576788i
$277$	11.5384	+	25.9157i	0.693277	+	1.55712i	0.824557	+	0.565779i	$0.191425\pi$
$277$	11.5384	+	25.9157i	0.693277	+	1.55712i	−0.131280	+	0.991345i	$0.541909\pi$
$278$	6.21506	−	11.7983i	0.372754	−	0.707617i
$279$	−3.58210	−	5.51594i	−0.214454	−	0.330231i
$280$	−8.64687	+	20.0419i	−0.516749	+	1.19773i
$281$	−25.3703	−	4.01826i	−1.51347	−	0.239709i	−0.656202	−	0.754586i	$-0.727838\pi$
$281$	−25.3703	−	4.01826i	−1.51347	−	0.239709i	−0.857265	+	0.514876i	$0.827838\pi$
$282$	9.32798	−	4.00201i	0.555473	−	0.238316i
$283$	−13.6210	+	2.89522i	−0.809682	+	0.172103i	−0.594109	−	0.804385i	$-0.702495\pi$
$283$	−13.6210	+	2.89522i	−0.809682	+	0.172103i	−0.215573	+	0.976488i	$0.569162\pi$
$284$	−5.71187	+	2.01615i	−0.338937	+	0.119637i
$285$		−	14.5564i		−	0.862247i
$286$	12.3875	−	11.5130i	0.732490	−	0.680778i
$287$			38.3335i			2.26275i
$288$	−5.46633	−	7.77649i	−0.322107	−	0.458234i
$289$	−3.15412	+	0.670428i	−0.185536	+	0.0394369i
$290$	2.58992	+	6.03665i	0.152085	+	0.354485i
$291$	−8.03984	−	1.27339i	−0.471304	−	0.0746472i
$292$	−18.3304	+	11.2073i	−1.07271	+	0.655857i
$293$	−13.1581	−	20.2617i	−0.768704	−	1.18370i	−0.978559	−	0.205968i	$-0.933966\pi$
$293$	−13.1581	−	20.2617i	−0.768704	−	1.18370i	0.209855	−	0.977733i	$-0.432701\pi$
$294$	22.0506	+	11.6157i	1.28602	+	0.677441i
$295$	5.02690	+	11.2906i	0.292678	+	0.657365i
$296$	3.81623	+	3.72895i	0.221814	+	0.216741i
$297$	11.4833	+	13.6426i	0.666326	+	0.791625i
$298$	−5.15189	−	7.29761i	−0.298441	−	0.422739i
$299$	8.26041	+	0.781483i	0.477712	+	0.0451944i
$300$	3.26909	−	4.25142i	0.188741	−	0.245456i
$301$	2.34808	+	44.8040i	0.135341	+	2.58246i
$302$	−0.410831	−	2.07088i	−0.0236407	−	0.119166i
$303$	−0.0305974	−	0.291115i	−0.00175777	−	0.0167241i
$304$	−28.3855	+	12.5690i	−1.62802	+	0.720883i
$305$	−6.67280	−	0.349706i	−0.382083	−	0.0200241i
$306$	−8.54969	+	2.16673i	−0.488753	+	0.123863i
$307$	15.0268	−	15.0268i	0.857624	−	0.857624i	−0.133434	−	0.991058i	$-0.542600\pi$
$307$	15.0268	−	15.0268i	0.857624	−	0.857624i	0.991058	+	0.133434i	$0.0426003\pi$
$308$	−31.2070	+	3.02127i	−1.77819	+	0.172153i
$309$	−5.86703	+	3.38733i	−0.333764	+	0.192699i
$310$	8.69705	+	2.45759i	0.493959	+	0.139582i
$311$	−1.76971	+	5.44662i	−0.100351	+	0.308849i	−0.988611	−	0.150492i	$-0.951914\pi$
$311$	−1.76971	+	5.44662i	−0.100351	+	0.308849i	0.888260	+	0.459341i	$0.151914\pi$
$312$	3.86396	+	11.0595i	0.218754	+	0.626123i
$313$	7.14509	−	5.19121i	0.403864	−	0.293425i	−0.367249	−	0.930123i	$-0.619700\pi$
$313$	7.14509	−	5.19121i	0.403864	−	0.293425i	0.771113	+	0.636698i	$0.219700\pi$
$314$	18.0570	−	26.9945i	1.01901	−	1.52339i
$315$	−9.63685	−	8.67706i	−0.542975	−	0.488897i
$316$	−5.43749	+	2.24582i	−0.305883	+	0.126337i
$317$	32.1137	−	5.08631i	1.80368	−	0.285675i	0.838052	−	0.545590i	$-0.183694\pi$
$317$	32.1137	−	5.08631i	1.80368	−	0.285675i	0.965632	+	0.259914i	$0.0836944\pi$
$318$	2.50735	−	3.01164i	0.140605	−	0.168885i
$319$	−5.79753	+	7.44403i	−0.324600	+	0.416786i
$320$	12.6915	+	3.08787i	0.709475	+	0.172617i
$321$	15.6235	−	6.95605i	0.872021	−	0.388249i
$322$	−11.2905	−	10.4475i	−0.629197	−	0.582216i
$323$	1.50753	+	28.7655i	0.0838815	+	1.60055i
$324$	−2.17788	+	0.642714i	−0.120994	+	0.0357063i
$325$	6.75709	−	5.01745i	0.374816	−	0.278318i
$326$	4.42932	−	5.92530i	0.245317	−	0.328172i
$327$	7.81806	+	5.07711i	0.432340	+	0.280765i
$328$	22.6134	−	3.85024i	1.24862	−	0.212594i
$329$	−25.5749	−	14.7657i	−1.40999	−	0.814059i
$330$	−8.69631	−	1.32934i	−0.478716	−	0.0731780i
$331$	−15.8060	+	4.23522i	−0.868779	+	0.232789i	−0.665560	−	0.746345i	$-0.731807\pi$
$331$	−15.8060	+	4.23522i	−0.868779	+	0.232789i	−0.203219	+	0.979133i	$0.565140\pi$
$332$	11.4457	+	9.79566i	0.628164	+	0.537606i
$333$	−2.82436	+	1.43908i	−0.154774	+	0.0788612i
$334$	−1.95106	−	4.54758i	−0.106757	−	0.248832i
$335$	−17.6917	−	7.87683i	−0.966598	−	0.430357i
$336$	6.75349	−	20.6424i	0.368433	−	1.12613i
$337$	25.1837	−	8.18269i	1.37184	−	0.445739i	0.471865	−	0.881671i	$-0.343581\pi$
$337$	25.1837	−	8.18269i	1.37184	−	0.445739i	0.899980	+	0.435932i	$0.143581\pi$
$338$	1.09419	+	18.3522i	0.0595161	+	0.998227i
$339$	5.96824	−	8.21458i	0.324150	−	0.446155i
$340$	6.87482	−	9.98120i	0.372840	−	0.541307i
$341$	2.93962	+	12.6443i	0.159189	+	0.684727i
$342$	−1.67823	−	18.3664i	−0.0907484	−	0.993141i
$343$	−6.16745	−	38.9397i	−0.333011	−	2.10255i
$344$	26.1946	−	5.88531i	1.41232	−	0.317315i
$345$	−2.35078	−	3.61989i	−0.126562	−	0.194888i
$346$	10.5157	−	5.17914i	0.565328	−	0.278432i
$347$	1.42298	−	0.149561i	0.0763894	−	0.00802885i	−0.0662566	−	0.997803i	$-0.521106\pi$
$347$	1.42298	−	0.149561i	0.0763894	−	0.00802885i	0.142646	+	0.989774i	$0.454439\pi$
$348$	−3.11293	−	5.74720i	−0.166870	−	0.308082i
$349$	27.9860	+	18.1743i	1.49806	+	0.972849i	0.994024	+	0.109165i	$0.0348177\pi$
$349$	27.9860	+	18.1743i	1.49806	+	0.972849i	0.504033	+	0.863684i	$0.331849\pi$
$350$	−15.6017	−	0.212160i	−0.833948	−	0.0113404i
$351$	−19.3846	+	0.201501i	−1.03467	+	0.0107553i
$352$	4.91674	+	18.1060i	0.262063	+	0.965051i
$353$	17.7616	+	4.75921i	0.945354	+	0.253307i	0.698390	−	0.715718i	$-0.253900\pi$
$353$	17.7616	+	4.75921i	0.945354	+	0.253307i	0.246965	+	0.969025i	$0.420567\pi$
$354$	−6.00343	−	10.7327i	−0.319079	−	0.570436i
$355$	3.30877	+	3.67476i	0.175611	+	0.195036i
$356$	5.20020	−	4.92478i	0.275610	−	0.261013i
$357$	−15.6616	−	12.6825i	−0.828900	−	0.671230i
$358$	6.20736	+	0.410017i	0.328069	+	0.0216701i
$359$	15.6911	+	7.99501i	0.828144	+	0.421961i	0.816061	−	0.577966i	$-0.196154\pi$
$359$	15.6911	+	7.99501i	0.828144	+	0.421961i	0.0120838	+	0.999927i	$0.496154\pi$
$360$	−4.15078	+	6.55643i	−0.218765	+	0.345554i
$361$	−41.0064	−	4.30995i	−2.15823	−	0.226840i
$362$	−9.79692	−	26.5973i	−0.514915	−	1.39792i
$363$	−4.35833	−	11.8610i	−0.228753	−	0.622539i
$364$	19.0412	−	28.2695i	0.998031	−	1.48173i
$365$	14.1897	+	10.3094i	0.742724	+	0.539621i
$366$	6.64372	−	0.257654i	0.347273	−	0.0134678i
$367$	−12.6812	−	11.4182i	−0.661954	−	0.596026i	0.268126	−	0.963384i	$-0.413596\pi$
$367$	−12.6812	−	11.4182i	−0.661954	−	0.596026i	−0.930080	+	0.367358i	$0.880262\pi$
$368$	−5.02908	+	7.70978i	−0.262159	+	0.401900i
$369$	−2.13186	+	13.4600i	−0.110980	+	0.700701i
$370$	1.61611	−	4.04485i	0.0840177	−	0.210282i
$371$	−11.3858	−	0.596702i	−0.591119	−	0.0309792i
$372$	−8.84040	−	1.64776i	−0.458354	−	0.0854323i
$373$	8.80909	−	15.2578i	0.456117	−	0.790018i	−0.542635	−	0.839969i	$-0.682573\pi$
$373$	8.80909	−	15.2578i	0.456117	−	0.790018i	0.998752	+	0.0499508i	$0.0159065\pi$
$374$	17.3228	+	1.72633i	0.895740	+	0.0892666i
$375$	−13.2874	−	3.56034i	−0.686156	−	0.183855i
$376$	−6.14170	+	16.5700i	−0.316734	+	0.854535i
$377$	−2.23678	−	10.0104i	−0.115200	−	0.515562i
$378$	28.7859	+	21.5182i	1.48059	+	1.10678i
$379$	−4.42029	−	11.5152i	−0.227055	−	0.591498i	0.771970	−	0.635659i	$-0.219272\pi$
$379$	−4.42029	−	11.5152i	−0.227055	−	0.591498i	−0.999024	+	0.0441614i	$0.985938\pi$
$380$	18.3653	+	17.4635i	0.942120	+	0.895859i
$381$	1.72079	−	8.09570i	0.0881589	−	0.414755i
$382$	3.65626	−	6.94085i	0.187070	−	0.355125i
$383$	33.8178	+	12.9814i	1.72801	+	0.663320i	0.999758	−	0.0219913i	$-0.00700061\pi$
$383$	33.8178	+	12.9814i	1.72801	+	0.663320i	0.728250	+	0.685312i	$0.240334\pi$
$384$	−12.8555	−	1.91063i	−0.656031	−	0.0975017i
$385$	12.0509	+	22.5807i	0.614170	+	1.15082i
$386$	1.49425	+	16.3529i	0.0760552	+	0.832340i
$387$	−1.66723	+	15.8626i	−0.0847500	+	0.806343i
$388$	11.2521	−	8.61589i	0.571238	−	0.437405i
$389$	−17.2097	+	5.59176i	−0.872565	+	0.283514i	−0.710867	−	0.703327i	$-0.751697\pi$
$389$	−17.2097	+	5.59176i	−0.872565	+	0.283514i	−0.161698	+	0.986840i	$0.551697\pi$
$390$	7.12768	−	6.37657i	0.360924	−	0.322890i
$391$	5.02037	+	6.90995i	0.253891	+	0.349451i
$392$	−41.1095	+	13.8850i	−2.07634	+	0.701298i
$393$	−7.87619	+	1.67414i	−0.397301	+	0.0844490i
$394$	−3.18170	−	1.89510i	−0.160292	−	0.0954737i
$395$	3.39599	+	3.39599i	0.170871	+	0.170871i
$396$	−11.1257	−	0.674675i	−0.559090	−	0.0339037i
$397$	−20.7887	+	5.57031i	−1.04335	+	0.279566i	−0.739502	−	0.673154i	$-0.764939\pi$
$397$	−20.7887	+	5.57031i	−1.04335	+	0.279566i	−0.303851	+	0.952720i	$0.598272\pi$
$398$	−4.09199	+	3.98219i	−0.205113	+	0.199609i
$399$	31.3162	−	28.1973i	1.56777	−	1.41163i
$400$	1.44189	+	9.22497i	0.0720947	+	0.461249i
$401$	7.92830	+	20.6539i	0.395920	+	1.03141i	0.976177	+	0.216974i	$0.0696187\pi$
$401$	7.92830	+	20.6539i	0.395920	+	1.03141i	−0.580257	+	0.814433i	$0.697048\pi$
$402$	18.2438	+	6.20327i	0.909919	+	0.309391i
$403$	−12.6401	−	6.27584i	−0.629650	−	0.312622i
$404$	0.403997	+	0.310650i	0.0200996	+	0.0154554i
$405$	1.16659	+	1.44062i	0.0579685	+	0.0715851i
$406$	−7.97013	+	17.2655i	−0.395551	+	0.856872i
$407$	6.20874	−	0.772015i	0.307756	−	0.0382673i
$408$	−5.90851	+	10.5128i	−0.292515	+	0.520462i
$409$	−4.27365	+	11.1332i	−0.211318	+	0.550503i	−0.997740	−	0.0671865i	$-0.978598\pi$
$409$	−4.27365	+	11.1332i	−0.211318	+	0.550503i	0.786422	+	0.617689i	$0.211931\pi$
$410$	−9.98457	−	15.8424i	−0.493103	−	0.782400i
$411$	18.2538	+	9.30077i	0.900393	+	0.458773i
$412$	2.76507	−	11.4661i	0.136225	−	0.564892i
$413$	−14.5527	+	32.6858i	−0.716089	+	1.60836i
$414$	−3.38342	−	4.29634i	−0.166286	−	0.211153i
$415$	3.80046	−	11.6966i	0.186557	−	0.574164i
$416$	−18.5891	−	8.39324i	−0.911404	−	0.411512i
$417$	10.8321			0.530452
$418$	−9.23186	+	35.2120i	−0.451545	+	1.72227i
$419$	9.19399	−	5.30815i	0.449156	−	0.259320i	−0.258318	−	0.966060i	$-0.583168\pi$
$419$	9.19399	−	5.30815i	0.449156	−	0.259320i	0.707474	+	0.706740i	$0.249835\pi$
$420$	−17.6773	+	1.37317i	−0.862562	+	0.0670039i
$421$	−6.01860	−	11.8122i	−0.293329	−	0.575690i	0.696566	−	0.717492i	$-0.254710\pi$
$421$	−6.01860	−	11.8122i	−0.293329	−	0.575690i	−0.989895	+	0.141803i	$0.954710\pi$
$422$	−9.23817	−	3.69109i	−0.449707	−	0.179680i
$423$	−8.15895	−	6.60699i	−0.396702	−	0.321243i
$424$	0.791592	+	6.77654i	0.0384431	+	0.329098i
$425$	8.47429	+	1.80127i	0.411063	+	0.0873742i
$426$	−3.61138	−	3.34172i	−0.174972	−	0.161907i
$427$	−12.1735	−	15.0331i	−0.589119	−	0.727501i
$428$	−9.96755	+	28.0569i	−0.481800	+	1.35618i
$429$	12.9638	+	4.54406i	0.625901	+	0.219389i
$430$	−12.6403	−	17.9050i	−0.609572	−	0.863454i
$431$	−25.1452	+	20.3621i	−1.21120	+	0.980810i	−0.211205	+	0.977442i	$0.567739\pi$
$431$	−25.1452	+	20.3621i	−1.21120	+	0.980810i	−0.999994	+	0.00336847i	$0.998928\pi$
$432$	9.80259	−	19.1425i	0.471628	−	0.920993i
$433$	−0.439422	+	2.06732i	−0.0211173	+	0.0993489i	−0.987444	−	0.157969i	$-0.949505\pi$
$433$	−0.439422	+	2.06732i	−0.0211173	+	0.0993489i	0.966327	+	0.257318i	$0.0828387\pi$
$434$	11.5599	+	23.4712i	0.554893	+	1.12665i
$435$	−3.35792	+	4.14669i	−0.161000	+	0.198819i
$436$	−15.7850	+	3.77270i	−0.755966	+	0.180680i
$437$	−15.9133	+	8.10823i	−0.761236	+	0.387869i
$438$	−14.9940	−	8.93081i	−0.716441	−	0.426730i
$439$	−6.34317	−	10.9867i	−0.302743	−	0.524366i	0.674013	−	0.738719i	$-0.264569\pi$
$439$	−6.34317	−	10.9867i	−0.302743	−	0.524366i	−0.976756	+	0.214353i	$0.931236\pi$
$440$	12.1103	−	9.37700i	0.577334	−	0.447031i
$441$		−	25.7784i		−	1.22754i
$442$	−13.4249	+	13.3392i	−0.638557	+	0.634479i
$443$	−19.3588	−	6.29006i	−0.919764	−	0.298850i	−0.189394	−	0.981901i	$-0.560652\pi$
$443$	−19.3588	−	6.29006i	−0.919764	−	0.298850i	−0.730370	+	0.683052i	$0.760652\pi$
$444$	−1.23517	+	4.15436i	−0.0586184	+	0.197157i
$445$	−5.34133	−	2.37812i	−0.253204	−	0.112733i
$446$	6.45410	+	7.36703i	0.305610	+	0.348839i
$447$	3.29424	−	6.46530i	0.155812	−	0.305798i
$448$	17.9415	+	33.2856i	0.847657	+	1.57260i
$449$	−0.216261	−	0.0830150i	−0.0102060	−	0.00391772i	0.353260	−	0.935525i	$-0.385073\pi$
$449$	−0.216261	−	0.0830150i	−0.0102060	−	0.00391772i	−0.363466	+	0.931608i	$0.618407\pi$
$450$	−5.46644	−	0.942164i	−0.257691	−	0.0444140i
$451$	13.0044	−	23.5456i	0.612351	−	1.10872i
$452$	3.20387	+	17.3851i	0.150698	+	0.817724i
$453$	1.33277	−	1.07925i	0.0626189	−	0.0507078i
$454$	1.94309	+	6.26902i	0.0911938	+	0.294219i
$455$	−27.2755	−	5.50191i	−1.27870	−	0.257933i
$456$	−19.7793	−	15.6417i	−0.926252	−	0.732489i
$457$	22.9946	−	8.82679i	1.07564	−	0.412900i	0.244894	−	0.969550i	$-0.421247\pi$
$457$	22.9946	−	8.82679i	1.07564	−	0.412900i	0.830747	+	0.556650i	$0.187914\pi$
$458$	−3.42487	+	28.8112i	−0.160034	+	1.34626i
$459$	−13.3528	−	14.8297i	−0.623253	−	0.692193i
$460$	7.38735	+	1.37693i	0.344437	+	0.0641995i
$461$	8.39149	+	31.3175i	0.390831	+	1.45860i	0.828767	+	0.559594i	$0.189043\pi$
$461$	8.39149	+	31.3175i	0.390831	+	1.45860i	−0.437936	+	0.899006i	$0.644290\pi$
$462$	−13.9857	−	21.2841i	−0.650675	−	0.990224i
$463$	−17.9141	+	17.9141i	−0.832540	+	0.832540i	−0.987864	−	0.155324i	$-0.950358\pi$
$463$	−17.9141	+	17.9141i	−0.832540	+	0.832540i	0.155324	+	0.987864i	$0.450358\pi$
$464$	10.9857	+	2.96752i	0.509996	+	0.137764i
$465$	1.52632	+	7.18079i	0.0707816	+	0.333001i
$466$	13.3394	−	10.5050i	0.617936	−	0.486633i
$467$	9.52857	−	6.92291i	0.440929	−	0.320354i	−0.345075	−	0.938575i	$-0.612146\pi$
$467$	9.52857	−	6.92291i	0.440929	−	0.320354i	0.786004	+	0.618221i	$0.212146\pi$
$468$	8.25811	−	8.86734i	0.381731	−	0.409893i
$469$	−17.3246	−	53.3195i	−0.799974	−	2.46207i
$470$	14.4155	−	0.559058i	0.664939	−	0.0257874i
$471$	26.2365	+	2.75756i	1.20891	+	0.127062i
$472$	20.7434	+	5.30181i	0.954794	+	0.244035i
$473$	13.7572	−	28.3167i	0.632556	−	1.30200i
$474$	−3.67256	−	3.05759i	−0.168686	−	0.140440i
$475$	−6.49218	+	16.9127i	−0.297882	+	0.776008i
$476$	34.7905	−	4.54432i	1.59462	−	0.208289i
$477$	−3.96470	−	0.842723i	−0.181531	−	0.0385856i
$478$	−36.3497	+	7.21121i	−1.66259	+	0.329833i
$479$	−20.3108	+	7.79660i	−0.928026	+	0.356236i	−0.774982	−	0.631984i	$-0.782241\pi$
$479$	−20.3108	+	7.79660i	−0.928026	+	0.356236i	−0.153044	+	0.988219i	$0.548908\pi$
$480$	2.58557	+	10.2901i	0.118014	+	0.469677i
$481$	−3.64492	+	5.74249i	−0.166194	+	0.261835i
$482$	10.0121	+	0.136150i	0.456041	+	0.00620147i
$483$	3.23401	−	12.0695i	0.147153	−	0.549182i
$484$	20.1933	+	8.73100i	0.917878	+	0.396864i
$485$	−10.0193	−	5.78467i	−0.454955	−	0.262668i
$486$	14.6226	+	15.0257i	0.663293	+	0.681582i
$487$	−1.61630	+	30.8408i	−0.0732415	+	1.39753i	0.676813	+	0.736155i	$0.263360\pi$
$487$	−1.61630	+	30.8408i	−0.0732415	+	1.39753i	−0.750055	+	0.661376i	$0.769973\pi$
$488$	−7.64548	+	8.69126i	−0.346095	+	0.393435i
$489$	5.93526	+	0.940052i	0.268402	+	0.0425106i
$490$	23.3422	+	26.6440i	1.05449	+	1.20365i
$491$	−10.7877	+	11.9810i	−0.486844	+	0.540695i	−0.935648	−	0.352935i	$-0.885184\pi$
$491$	−10.7877	+	11.9810i	−0.486844	+	0.540695i	0.448804	+	0.893630i	$0.351850\pi$
$492$	11.3281	+	14.7942i	0.510710	+	0.666972i
$493$	6.20627	−	8.54220i	0.279516	−	0.384721i
$494$	−23.1579	−	32.0898i	−1.04192	−	1.44379i
$495$	2.97564	+	8.59897i	0.133745	+	0.386495i
$496$	12.6849	−	9.17679i	0.569567	−	0.412050i
$497$	−1.49635	+	14.2368i	−0.0671203	+	0.638607i
$498$	−2.70681	+	11.9342i	−0.121295	+	0.534786i
$499$	13.8594	−	27.2006i	0.620431	−	1.21766i	−0.340335	−	0.940304i	$-0.610541\pi$
$499$	13.8594	−	27.2006i	0.620431	−	1.21766i	0.960766	−	0.277360i	$-0.0894595\pi$
$500$	20.4330	−	12.4928i	0.913790	−	0.558696i
$501$	2.52962	−	3.12382i	0.113015	−	0.139562i
$502$	−41.0578	+	5.93181i	−1.83250	+	0.264750i
$503$	22.9711	−	20.6833i	1.02423	−	0.922221i	0.0272310	−	0.999629i	$-0.491331\pi$
$503$	22.9711	−	20.6833i	1.02423	−	0.922221i	0.997000	+	0.0774079i	$0.0246644\pi$
$504$	−22.1458	+	3.77063i	−0.986452	+	0.167957i
$505$	0.107678	−	0.401859i	0.00479160	−	0.0178825i
$506$	3.39077	+	10.2474i	0.150738	+	0.455553i
$507$	−12.7751	+	7.73418i	−0.567362	+	0.343487i
$508$	8.14960	+	11.8836i	0.361580	+	0.527248i
$509$	2.02438	−	3.11728i	0.0897293	−	0.138171i	−0.790956	−	0.611874i	$-0.790416\pi$
$509$	2.02438	−	3.11728i	0.0897293	−	0.138171i	0.880685	+	0.473703i	$0.157083\pi$
$510$	9.77597	+	1.16210i	0.432887	+	0.0514584i
$511$	5.30753	+	50.4978i	0.234791	+	2.23389i
$512$	17.8335	−	13.9272i	0.788138	−	0.615499i
$513$	34.9956	−	22.7264i	1.54510	−	1.00340i
$514$	2.38722	+	3.78777i	0.105296	+	0.167071i
$515$	−9.51018	+	1.50626i	−0.419069	+	0.0663739i
$516$	14.1465	+	16.5975i	0.622763	+	0.730663i
$517$	10.6998	+	17.7457i	0.470576	+	0.780454i
$518$	11.8325	−	4.35843i	0.519892	−	0.191499i
$519$	7.70320	+	5.59670i	0.338133	+	0.245668i
$520$	−0.506071	+	16.6428i	−0.0221927	+	0.729835i
$521$	3.01375	+	9.27536i	0.132035	+	0.406361i	0.995117	−	0.0987023i	$-0.0314692\pi$
$521$	3.01375	+	9.27536i	0.132035	+	0.406361i	−0.863082	+	0.505063i	$0.831469\pi$
$522$	−3.75875	+	5.61919i	−0.164516	+	0.245945i
$523$	7.88136	−	17.7018i	0.344628	−	0.774047i	−0.655199	−	0.755456i	$-0.727415\pi$
$523$	7.88136	−	17.7018i	0.344628	−	0.774047i	0.999827	−	0.0185908i	$-0.00591796\pi$
$524$	7.33696	−	11.9456i	0.320517	−	0.521846i
$525$	−5.75406	−	11.2930i	−0.251128	−	0.492866i
$526$	−21.4729	+	5.44183i	−0.936265	+	0.237275i
$527$	−3.75991	−	14.0322i	−0.163784	−	0.611251i
$528$	−11.1510	+	10.3881i	−0.485285	+	0.452086i
$529$	8.85211	−	15.3323i	0.384875	−	0.666622i
$530$	4.86091	−	2.71900i	0.211145	−	0.118106i
$531$	−6.92765	+	10.6676i	−0.300634	+	0.462936i
$532$	−1.99498	+	73.3392i	−0.0864931	+	3.17966i
$533$	10.7624	+	27.1888i	0.466170	+	1.17768i
$534$	5.50804	+	1.87285i	0.238356	+	0.0810460i
$535$	24.2736	−	1.27213i	1.04944	−	0.0549988i
$536$	−29.7138	+	15.5754i	−1.28344	+	0.672756i
$537$	2.05532	+	4.61633i	0.0886937	+	0.199209i
$538$	−3.58528	+	20.8018i	−0.154572	+	0.896830i
$539$	−17.3287	+	47.8387i	−0.746402	+	2.06056i
$540$	−17.5014	−	1.39527i	−0.753139	−	0.0600429i
$541$	−3.65769	−	23.0938i	−0.157257	−	0.992879i	−0.932488	−	0.361201i	$-0.882367\pi$
$541$	−3.65769	−	23.0938i	−0.157257	−	0.992879i	0.775231	−	0.631677i	$-0.217633\pi$
$542$	2.41377	−	10.6422i	0.103680	−	0.457122i
$543$	15.4060	−	17.1101i	0.661135	−	0.734265i
$544$	−6.17514	−	20.0669i	−0.264757	−	0.860362i
$545$	7.78766	+	10.7188i	0.333587	+	0.459143i
$546$	27.5254	+	2.98221i	1.17798	+	0.127627i
$547$	−43.2631	−	14.0570i	−1.84979	−	0.601035i	−0.996875	−	0.0789925i	$-0.974830\pi$
$547$	−43.2631	−	14.0570i	−1.84979	−	0.601035i	−0.852920	−	0.522042i	$-0.825170\pi$
$548$	−33.6338	+	11.8719i	−1.43676	+	0.507143i
$549$	−3.43845	−	5.95558i	−0.146750	−	0.254178i
$550$	9.51112	+	5.42310i	0.405556	+	0.231242i
$551$	15.6120	+	15.6120i	0.665095	+	0.665095i
$552$	−7.44478	−	0.695516i	−0.316871	−	0.0296031i
$553$	−0.727651	+	13.8844i	−0.0309429	+	0.590425i
$554$	−5.73660	−	39.7066i	−0.243725	−	1.68697i
$555$	3.51878	−	0.369839i	0.149364	−	0.0156988i
$556$	−12.9954	+	13.6665i	−0.551130	+	0.579590i
$557$	−19.1557	+	1.00391i	−0.811652	+	0.0425369i	−0.453646	−	0.891182i	$-0.649877\pi$
$557$	−19.1557	+	1.00391i	−0.811652	+	0.0425369i	−0.358007	+	0.933719i	$0.616543\pi$
$558$	2.75371	+	8.88432i	0.116574	+	0.376103i
$559$	14.2444	+	31.1189i	0.602476	+	1.31619i
$560$	19.4751	−	23.9502i	0.822975	−	1.01208i
$561$	5.31741	+	13.1031i	0.224501	+	0.553213i
$562$	32.9817	+	15.2251i	1.39125	+	0.642232i
$563$	42.2497	−	18.8108i	1.78061	−	0.792780i	0.799149	−	0.601133i	$-0.205284\pi$
$563$	42.2497	−	18.8108i	1.78061	−	0.792780i	0.981464	−	0.191647i	$-0.0613830\pi$
$564$	−14.2337	+	1.85920i	−0.599346	+	0.0782864i
$565$	12.1032	−	7.85990i	0.509185	−	0.330669i
$566$	19.6505	+	1.29798i	0.825970	+	0.0545581i
$567$	−0.839502	+	5.30041i	−0.0352558	+	0.222596i
$568$	8.54875	−	0.547240i	0.358698	−	0.0229617i
$569$	−0.401034	−	1.88672i	−0.0168122	−	0.0790954i	0.968942	−	0.247289i	$-0.0795398\pi$
$569$	−0.401034	−	1.88672i	−0.0168122	−	0.0790954i	−0.985754	+	0.168194i	$0.946206\pi$
$570$	−5.59790	+	19.8101i	−0.234470	+	0.829755i
$571$	7.91526			0.331243			0.165622	−	0.986189i	$-0.447037\pi$
$571$	7.91526			0.331243			0.165622	+	0.986189i	$0.447037\pi$
$572$	−21.2860	+	10.9045i	−0.890011	+	0.455939i
$573$	6.37244			0.266212
$574$	14.7417	−	52.1688i	0.615308	−	2.17749i
$575$	1.11684	+	5.25431i	0.0465753	+	0.219120i
$576$	4.44868	+	12.6854i	0.185362	+	0.528556i
$577$	−5.35129	+	33.7867i	−0.222777	+	1.40656i	0.582100	+	0.813118i	$0.302231\pi$
$577$	−5.35129	+	33.7867i	−0.222777	+	1.40656i	−0.804877	+	0.593442i	$0.797769\pi$
$578$	4.55033	+	0.300565i	0.189269	+	0.0125018i
$579$	−11.1868	+	7.26479i	−0.464907	+	0.301914i
$580$	−1.20319	−	9.21141i	−0.0499598	−	0.382483i
$581$	32.5256	−	14.4813i	1.34939	−	0.600787i
$582$	10.4519	+	4.82483i	0.433245	+	0.199995i
$583$	6.79108	+	4.22905i	0.281258	+	0.175149i
$584$	29.2562	−	8.20301i	1.21063	−	0.339443i
$585$	−9.27127	−	3.44877i	−0.383320	−	0.142589i
$586$	10.1152	+	32.6347i	0.417855	+	1.34813i
$587$	44.6221	−	2.33854i	1.84175	−	0.0965220i	0.900629	−	0.434590i	$-0.143107\pi$
$587$	44.6221	−	2.33854i	1.84175	−	0.0965220i	0.941122	+	0.338068i	$0.109773\pi$
$588$	−25.5422	−	24.2880i	−1.05334	−	1.00162i
$589$	30.2105	−	3.17525i	1.24480	−	0.130834i
$590$	−2.49924	−	17.2988i	−0.102892	−	0.712181i
$591$	0.157437	−	3.00407i	0.00647608	−	0.123571i
$592$	−3.75956	−	6.54240i	−0.154517	−	0.268891i
$593$	−0.861283	−	0.861283i	−0.0353687	−	0.0353687i	0.689201	−	0.724570i	$-0.257962\pi$
$593$	−0.861283	−	0.861283i	−0.0353687	−	0.0353687i	−0.724570	+	0.689201i	$0.757962\pi$
$594$	−10.3813	−	22.9826i	−0.425951	−	0.942988i
$595$	−14.3214	−	24.8053i	−0.587119	−	1.01692i
$596$	4.20491	+	11.9127i	0.172240	+	0.487964i
$597$	−4.41108	−	1.43325i	−0.180533	−	0.0586588i
$598$	−10.9412	−	4.24021i	−0.447420	−	0.173395i
$599$	−1.85719	−	2.55620i	−0.0758825	−	0.104443i	0.769389	−	0.638781i	$-0.220561\pi$
$599$	−1.85719	−	2.55620i	−0.0758825	−	0.104443i	−0.845271	+	0.534338i	$0.820561\pi$
$600$	−6.08393	+	4.52867i	−0.248375	+	0.184882i
$601$	−8.02487	+	8.91252i	−0.327341	+	0.363549i	−0.884241	−	0.467030i	$-0.845324\pi$
$601$	−8.02487	+	8.91252i	−0.327341	+	0.363549i	0.556900	+	0.830580i	$0.311991\pi$
$602$	14.0345	−	61.8778i	0.572005	−	2.52195i
$603$	−3.11789	−	19.6856i	−0.126970	−	0.801658i
$604$	−0.237281	+	2.97630i	−0.00965483	+	0.121104i
$605$	0.258305	−	17.9580i	0.0105016	−	0.730096i
$606$	−0.0703120	+	0.407951i	−0.00285623	+	0.0165719i
$607$	−15.2797	−	34.3188i	−0.620185	−	1.39296i	−0.901263	−	0.433273i	$-0.857359\pi$
$607$	−15.2797	−	34.3188i	−0.620185	−	1.39296i	0.281078	−	0.959685i	$-0.409308\pi$
$608$	43.4641	−	6.18938i	1.76270	−	0.251013i
$609$	−15.4257	+	0.808427i	−0.625081	+	0.0327591i
$610$	8.94667	+	3.04205i	0.362240	+	0.123169i
$611$	−22.2851	−	3.29254i	−0.901558	−	0.133202i
$612$	12.4687	+	0.339174i	0.504018	+	0.0137103i
$613$	−13.7299	+	21.1421i	−0.554544	+	0.853923i	−0.999125	−	0.0418157i	$-0.986686\pi$
$613$	−13.7299	+	21.1421i	−0.554544	+	0.853923i	0.444581	+	0.895738i	$0.353352\pi$
$614$	−26.2291	+	14.6715i	−1.05852	+	0.592094i
$615$	7.60564	−	13.1733i	0.306689	−	0.531201i
$616$	43.6322	+	7.88944i	1.75799	+	0.317875i
$617$	9.12927	+	34.0709i	0.367531	+	1.37164i	0.863958	+	0.503564i	$0.167978\pi$
$617$	9.12927	+	34.0709i	0.367531	+	1.37164i	−0.496427	+	0.868078i	$0.665355\pi$
$618$	9.28723	−	2.35364i	0.373587	−	0.0946772i
$619$	−19.1751	−	37.6332i	−0.770711	−	1.51261i	−0.856417	−	0.516285i	$-0.827315\pi$
$619$	−19.1751	−	37.6332i	−0.770711	−	1.51261i	0.0857061	−	0.996320i	$-0.472685\pi$
$620$	−10.8909	−	6.68918i	−0.437389	−	0.268644i
$621$	5.03252	−	11.3032i	0.201948	−	0.453583i
$622$	4.50303	−	6.73185i	0.180555	−	0.269923i
$623$	−5.23051	−	16.0978i	−0.209556	−	0.644946i
$624$	−1.00543	−	16.5371i	−0.0402494	−	0.662014i
$625$	−6.37511	−	4.63179i	−0.255005	−	0.185272i
$626$	−11.7203	+	4.31708i	−0.468436	+	0.172545i
$627$	−28.8012	+	6.69586i	−1.15021	+	0.267407i
$628$	−34.9553	+	29.7933i	−1.39487	+	1.18888i
$629$	−6.91530	+	1.09528i	−0.275731	+	0.0436715i
$630$	9.77811	+	15.5148i	0.389569	+	0.618125i
$631$	8.30014	−	5.39017i	0.330423	−	0.214579i	−0.368755	−	0.929527i	$-0.620216\pi$
$631$	8.30014	−	5.39017i	0.330423	−	0.214579i	0.699179	+	0.714947i	$0.253549\pi$
$632$	8.26367	−	0.965310i	0.328711	−	0.0383980i
$633$	−0.844688	−	8.03667i	−0.0335733	−	0.319429i
$634$	−45.6602	−	5.42775i	−1.81340	−	0.215564i
$635$	6.40677	−	9.86557i	0.254245	−	0.391503i
$636$	−4.57048	+	3.13437i	−0.181231	+	0.124286i
$637$	−28.1529	−	47.6124i	−1.11546	−	1.88647i
$638$	10.7527	−	7.90122i	0.425704	−	0.312812i
$639$	−1.31717	+	4.91575i	−0.0521064	+	0.194464i
$640$	−16.0846	−	9.08306i	−0.635800	−	0.359039i
$641$	−35.9298	+	32.3513i	−1.41914	+	1.27780i	−0.510717	+	0.859749i	$0.670620\pi$
$641$	−35.9298	+	32.3513i	−1.41914	+	1.27780i	−0.908424	+	0.418051i	$0.862713\pi$
$642$	−23.9375	+	3.45836i	−0.944737	+	0.136491i
$643$	16.8469	−	20.8042i	0.664376	−	0.820437i	−0.327870	−	0.944723i	$-0.606331\pi$
$643$	16.8469	−	20.8042i	0.664376	−	0.820437i	0.992246	+	0.124286i	$0.0396641\pi$
$644$	11.3478	+	18.5602i	0.447165	+	0.731373i
$645$	8.08253	−	15.8629i	0.318249	−	0.624599i
$646$	9.01058	−	39.7273i	0.354517	−	1.56305i
$647$	3.69545	−	35.1599i	0.145283	−	1.38228i	−0.642481	−	0.766302i	$-0.722095\pi$
$647$	3.69545	−	35.1599i	0.145283	−	1.38228i	0.787764	−	0.615977i	$-0.211238\pi$
$648$	3.21110	−	0.0371440i	0.126144	−	0.00145916i
$649$	20.0271	−	15.1398i	0.786134	−	0.594289i
$650$	−11.1254	+	4.22981i	−0.436375	+	0.165907i
$651$	−12.4919	+	17.1936i	−0.489596	+	0.673871i
$652$	−8.30663	+	6.36051i	−0.325313	+	0.249097i
$653$	10.1272	−	11.2474i	0.396307	−	0.440143i	−0.511658	−	0.859189i	$-0.670969\pi$
$653$	10.1272	−	11.2474i	0.396307	−	0.440143i	0.907965	+	0.419046i	$0.137635\pi$
$654$	−8.68729	−	9.91611i	−0.339700	−	0.387750i
$655$	−11.3035	−	1.79030i	−0.441664	−	0.0699527i
$656$	−32.2557	−	3.45646i	−1.25937	−	0.134952i
$657$	−0.944727	+	18.0265i	−0.0368573	+	0.703279i
$658$	29.1271	+	29.9302i	1.13549	+	1.16680i
$659$	−33.9193	−	19.5833i	−1.32131	−	0.762858i	−0.337372	−	0.941371i	$-0.609538\pi$
$659$	−33.9193	−	19.5833i	−1.32131	−	0.762858i	−0.983938	+	0.178513i	$0.942871\pi$
$660$	11.3238	+	5.15344i	0.440778	+	0.200597i
$661$	8.07194	−	30.1249i	0.313962	−	1.17172i	−0.610990	−	0.791638i	$-0.709228\pi$
$661$	8.07194	−	30.1249i	0.313962	−	1.17172i	0.924952	−	0.380084i	$-0.124105\pi$
$662$	23.1395	+	0.314663i	0.899343	+	0.0122297i
$663$	−14.6690	−	4.59823i	−0.569697	−	0.178581i
$664$	−11.8096	−	17.7327i	−0.458302	−	0.688164i
$665$	55.9150	−	21.4638i	2.16829	−	0.832329i
$666$	4.39715	−	0.872327i	0.170386	−	0.0338020i
$667$	6.40367	+	1.36114i	0.247951	+	0.0527036i
$668$	0.906397	+	6.93921i	0.0350696	+	0.268486i
$669$	−2.85113	+	7.42745i	−0.110231	+	0.287162i
$670$	21.0478	+	17.5234i	0.813148	+	0.676987i
$671$	2.37752	+	13.3636i	0.0917832	+	0.515896i
$672$	−17.1293	+	25.4955i	−0.660778	+	0.983511i
$673$	−4.19733	−	0.441157i	−0.161795	−	0.0170054i	0.0232844	−	0.999729i	$-0.492588\pi$
$673$	−4.19733	−	0.441157i	−0.161795	−	0.0170054i	−0.185080	+	0.982724i	$0.559254\pi$
$674$	−37.4199	+	1.45120i	−1.44136	+	0.0558983i
$675$	−3.87826	−	11.9360i	−0.149274	−	0.459419i
$676$	5.56851	−	25.3967i	0.214174	−	0.976796i
$677$	−6.94294	+	5.04434i	−0.266839	+	0.193870i	−0.713157	−	0.701005i	$-0.752735\pi$
$677$	−6.94294	+	5.04434i	−0.266839	+	0.193870i	0.446318	+	0.894875i	$0.352735\pi$
$678$	−11.2814	+	8.88422i	−0.433258	+	0.341196i
$679$	−6.96352	−	32.7608i	−0.267235	−	1.25724i
$680$	−13.1945	+	10.9398i	−0.505987	+	0.419523i
$681$	−3.76980	+	3.76980i	−0.144459	+	0.144459i
$682$	0.861969	−	18.3384i	0.0330065	−	0.702212i
$683$	−0.248623	−	0.927875i	−0.00951330	−	0.0355041i	0.961006	−	0.276527i	$-0.0891837\pi$
$683$	−0.248623	−	0.927875i	−0.00951330	−	0.0355041i	−0.970519	+	0.241023i	$0.922517\pi$
$684$	−4.77915	+	25.6406i	−0.182735	+	0.980394i
$685$	19.4834	+	21.6385i	0.744421	+	0.826763i
$686$	−6.58147	+	55.3657i	−0.251282	+	2.11387i
$687$	−22.0027	+	8.44603i	−0.839453	+	0.322236i
$688$	−37.9121	−	2.06410i	−1.44539	−	0.0786931i
$689$	−8.24311	+	2.77340i	−0.314037	+	0.105658i
$690$	1.80715	+	5.83042i	0.0687970	+	0.221960i
$691$	−24.0873	+	19.5055i	−0.916323	+	0.742023i	−0.966486	−	0.256718i	$-0.917359\pi$
$691$	−24.0873	+	19.5055i	−0.916323	+	0.742023i	0.0501638	+	0.998741i	$0.484026\pi$
$692$	−16.3028	+	3.00442i	−0.619739	+	0.114211i
$693$	−12.7355	+	23.0588i	−0.483780	+	0.875930i
$694$	−1.99408	−	0.343688i	−0.0756941	−	0.0130462i
$695$	14.3730	+	5.51727i	0.545198	+	0.209282i
$696$	2.02627	+	9.01862i	0.0768056	+	0.341850i
$697$	−13.6655	+	26.8200i	−0.517617	+	1.01588i
$698$	−31.0976	−	35.4963i	−1.17706	−	1.34355i
$699$	12.5997	+	5.60977i	0.476566	+	0.212181i
$700$	21.1512	+	6.28863i	0.799439	+	0.237688i
$701$	−21.3821	−	6.94747i	−0.807591	−	0.262402i	−0.124014	−	0.992280i	$-0.539577\pi$
$701$	−21.3821	−	6.94747i	−0.807591	−	0.262402i	−0.683577	+	0.729878i	$0.739577\pi$
$702$	26.4584	+	7.18041i	0.998607	+	0.271007i
$703$		−	14.6404i		−	0.552174i
$704$	0.271629	−	26.5316i	0.0102374	−	0.999948i
$705$	5.85924	+	10.1485i	0.220672	+	0.382215i
$706$	−22.3419	−	13.3074i	−0.840849	−	0.500831i
$707$	1.07313	−	0.546788i	0.0403593	−	0.0205641i
$708$	4.04279	+	16.9151i	0.151937	+	0.635707i
$709$	11.4650	−	14.1582i	0.430579	−	0.531721i	−0.514967	−	0.857210i	$-0.672196\pi$
$709$	11.4650	−	14.1582i	0.430579	−	0.531721i	0.945546	+	0.325489i	$0.105529\pi$
$710$	−3.08979	−	6.27351i	−0.115958	−	0.235440i
$711$	−1.02766	+	4.83477i	−0.0385403	+	0.181318i
$712$	−8.97096	+	4.70242i	−0.336201	+	0.176231i
$713$	6.99996	−	5.66846i	0.262151	−	0.212285i
$714$	16.4370	+	23.2828i	0.615138	+	0.871338i
$715$	14.8870	+	12.6325i	0.556743	+	0.472428i
$716$	−8.29006	−	2.94514i	−0.309814	−	0.110065i
$717$	−18.9439	−	23.3937i	−0.707472	−	0.873655i
$718$	−18.2798	−	16.9149i	−0.682194	−	0.631257i
$719$	10.3822	+	2.20680i	0.387191	+	0.0822999i	0.397394	−	0.917648i	$-0.369915\pi$
$719$	10.3822	+	2.20680i	0.387191	+	0.0822999i	−0.0102034	+	0.999948i	$0.503248\pi$
$720$	8.17026	−	7.32655i	0.304488	−	0.273044i
$721$	−21.6627	−	17.5421i	−0.806762	−	0.653303i
$722$	54.1491	+	21.6352i	2.01522	+	0.805178i
$723$	3.69257	+	7.24707i	0.137328	+	0.269521i
$724$	3.10444	+	39.9644i	0.115376	+	1.48527i
$725$	5.75091	−	3.32029i	0.213584	−	0.123312i
$726$	1.37002	+	17.8179i	0.0508464	+	0.661285i
$727$	7.29792			0.270665			0.135332	−	0.990800i	$-0.456790\pi$
$727$	7.29792			0.270665			0.135332	+	0.990800i	$0.456790\pi$
$728$	−36.7851	+	31.1500i	−1.36335	+	1.15450i
$729$	−6.31541	+	19.4368i	−0.233904	+	0.719882i
$730$	−15.3465	−	19.4872i	−0.567998	−	0.721254i
$731$	−14.3294	+	32.1843i	−0.529990	+	1.19038i
$732$	−9.14067	−	2.20430i	−0.337849	−	0.0814733i
$733$	−11.8249	−	6.02509i	−0.436763	−	0.222542i	0.221762	−	0.975101i	$-0.428819\pi$
$733$	−11.8249	−	6.02509i	−0.436763	−	0.222542i	−0.658525	+	0.752559i	$0.728819\pi$
$734$	12.8671	+	20.4161i	0.474933	+	0.753571i
$735$	−10.3115	+	26.8625i	−0.380347	+	0.990838i
$736$	9.80910	−	8.55840i	0.361568	−	0.315467i
$737$	−7.44696	+	38.6278i	−0.274312	+	1.42287i
$738$	8.07756	−	17.4982i	0.297339	−	0.644118i
$739$	6.13706	+	7.57864i	0.225756	+	0.278785i	0.877421	−	0.479722i	$-0.159262\pi$
$739$	6.13706	+	7.57864i	0.225756	+	0.278785i	−0.651665	+	0.758507i	$0.725929\pi$
$740$	−3.75491	+	4.88322i	−0.138033	+	0.179511i
$741$	14.2951	−	28.7917i	0.525144	−	1.05769i
$742$	15.2657	+	5.19064i	0.560420	+	0.190554i
$743$	2.87089	+	7.47892i	0.105323	+	0.274375i	0.976107	−	0.217290i	$-0.0697218\pi$
$743$	2.87089	+	7.47892i	0.105323	+	0.274375i	−0.870784	+	0.491665i	$0.836388\pi$
$744$	11.3974	+	5.64219i	0.417850	+	0.206853i
$745$	7.66412	−	6.90080i	0.280792	−	0.252826i
$746$	−17.8561	+	17.3770i	−0.653758	+	0.636217i
$747$	12.2261	−	3.27597i	0.447329	−	0.119861i
$748$	−22.9111	−	9.01116i	−0.837712	−	0.329481i
$749$	49.7573	+	49.7573i	1.81809	+	1.81809i
$750$	16.7139	+	9.95520i	0.610304	+	0.363513i
$751$	25.2406	−	5.36505i	0.921041	−	0.195773i	0.277094	−	0.960843i	$-0.410629\pi$
$751$	25.2406	−	5.36505i	0.921041	−	0.195773i	0.643948	+	0.765070i	$0.277295\pi$
$752$	14.7306	−	20.1887i	0.537171	−	0.736204i
$753$	−19.8068	−	27.2617i	−0.721800	−	0.993472i
$754$	−0.805579	+	14.4836i	−0.0293375	+	0.527460i
$755$	2.31814	−	0.753208i	0.0843656	−	0.0274121i
$756$	−30.9002	−	40.3547i	−1.12383	−	1.46769i
$757$	3.35569	−	31.9273i	0.121965	−	1.16042i	−0.746750	−	0.665104i	$-0.768387\pi$
$757$	3.35569	−	31.9273i	0.121965	−	1.16042i	0.868715	−	0.495312i	$-0.164946\pi$
$758$	1.58730	+	17.3712i	0.0576533	+	0.630952i
$759$	−6.08093	+	6.31636i	−0.220724	+	0.229269i
$760$	−18.2779	−	30.8291i	−0.663009	−	1.11829i
$761$	26.0696	+	10.0072i	0.945021	+	0.362760i	0.781588	−	0.623795i	$-0.214410\pi$
$761$	26.0696	+	10.0072i	0.945021	+	0.362760i	0.163433	+	0.986554i	$0.447743\pi$
$762$	−5.45519	+	10.3559i	−0.197621	+	0.375153i
$763$	−7.97460	+	37.5176i	−0.288700	+	1.35823i
$764$	−7.64509	+	8.03988i	−0.276590	+	0.290873i
$765$	−3.64915	−	9.50636i	−0.131935	−	0.343703i
$766$	−41.0312	−	30.6719i	−1.48252	−	1.10822i
$767$	−1.14502	+	27.2688i	−0.0413441	+	0.984620i
$768$	16.7606	+	7.54402i	0.604796	+	0.272221i
$769$	−7.02764	−	1.88305i	−0.253423	−	0.0679045i	0.129871	−	0.991531i	$-0.458544\pi$
$769$	−7.02764	−	1.88305i	−0.253423	−	0.0679045i	−0.383294	+	0.923626i	$0.625210\pi$
$770$	−7.71655	−	35.3650i	−0.278085	−	1.27447i
$771$	−1.81844	+	3.14963i	−0.0654894	+	0.113431i
$772$	4.25521	−	22.8296i	0.153148	−	0.821657i
$773$	−24.0258	−	1.25914i	−0.864148	−	0.0452881i	−0.384890	−	0.922962i	$-0.625761\pi$
$773$	−24.0258	−	1.25914i	−0.864148	−	0.0452881i	−0.479258	+	0.877674i	$0.659094\pi$
$774$	8.36919	−	20.9466i	0.300824	−	0.752912i
$775$	1.42925	−	9.02391i	0.0513401	−	0.324149i
$776$	−18.6266	+	7.39839i	−0.668655	+	0.265587i
$777$	7.61190	+	6.85379i	0.273076	+	0.245878i
$778$	25.5714	−	0.991702i	0.916780	−	0.0355542i
$779$	−50.9212	−	36.9964i	−1.82444	−	1.32553i
$780$	−12.1524	+	5.93695i	−0.435127	+	0.212577i
$781$	5.74883	−	8.23707i	0.205709	−	0.294745i
$782$	−4.17500	−	11.3346i	−0.149298	−	0.405323i
$783$	−15.2118	−	1.59883i	−0.543627	−	0.0571375i
$784$	61.2865	−	3.08710i	2.18880	−	0.110254i
$785$	33.4082	+	17.0223i	1.19239	+	0.607552i
$786$	11.3627	+	0.750544i	0.405294	+	0.0267710i
$787$	−2.63980	−	2.13767i	−0.0940987	−	0.0761996i	0.581117	−	0.813820i	$-0.302616\pi$
$787$	−2.63980	−	2.13767i	−0.0940987	−	0.0761996i	−0.675215	+	0.737621i	$0.735949\pi$
$788$	3.60125	+	3.80265i	0.128289	+	0.135464i
$789$	−12.0402	−	13.3720i	−0.428642	−	0.476055i
$790$	−3.31570	−	5.92766i	−0.117967	−	0.210897i
$791$	40.3547	+	10.8130i	1.43485	+	0.384466i
$792$	14.8818	+	5.19676i	0.528802	+	0.184659i
$793$	−12.8550	−	7.24471i	−0.456493	−	0.257267i
$794$	30.4339	+	0.413856i	1.08006	+	0.0146872i
$795$	3.79434	+	2.46408i	0.134571	+	0.0873917i
$796$	7.10030	−	3.84582i	0.251663	−	0.136311i
$797$	1.09639	−	0.115235i	0.0388360	−	0.00408182i	−0.0850906	−	0.996373i	$-0.527118\pi$
$797$	1.09639	−	0.115235i	0.0388360	−	0.00408182i	0.123927	+	0.992291i	$0.460451\pi$
$798$	−53.4626	+	26.3311i	−1.89256	+	0.932112i
$799$	−12.6297	−	19.4480i	−0.446807	−	0.688022i
$800$	1.58530	−	13.1090i	0.0560489	−	0.463472i
$801$	−0.941330	−	5.94332i	−0.0332603	−	0.209997i
$802$	−2.84700	−	31.1573i	−0.100531	−	1.10020i
$803$	13.8710	−	32.8179i	0.489495	−	1.15812i
$804$	−22.4428	−	15.4581i	−0.791498	−	0.545166i
$805$	10.4387	−	14.3676i	0.367915	−	0.506391i
$806$	14.7888	+	13.4019i	0.520912	+	0.472062i
$807$	−16.3072	+	5.29852i	−0.574039	+	0.186517i
$808$	−0.430343	−	0.578134i	−0.0151394	−	0.0203387i
$809$	−37.7078	−	16.7886i	−1.32574	−	0.590256i	−0.382986	−	0.923754i	$-0.625104\pi$
$809$	−37.7078	−	16.7886i	−1.32574	−	0.590256i	−0.942751	+	0.333498i	$0.891771\pi$
$810$	−1.03363	−	2.40921i	−0.0363180	−	0.0846509i
$811$	−2.13207	+	1.08634i	−0.0748669	+	0.0381466i	−0.491023	−	0.871147i	$-0.663377\pi$
$811$	−2.13207	+	1.08634i	−0.0748669	+	0.0381466i	0.416156	+	0.909293i	$0.363377\pi$
$812$	17.4865	−	20.4320i	0.613654	−	0.717021i
$813$	8.56215	−	2.29422i	0.300288	−	0.0804619i
$814$	−8.74650	−	1.33702i	−0.306565	−	0.0468624i
$815$	7.39658	+	4.27042i	0.259091	+	0.149586i
$816$	12.0839	−	12.0349i	0.423021	−	0.421306i
$817$	−61.7827	−	40.1222i	−2.16150	−	1.40370i
$818$	10.0976	−	13.5080i	0.353053	−	0.472295i
$819$	−10.5398	−	26.6266i	−0.368291	−	0.930408i
$820$	7.49577	+	25.4000i	0.261764	+	0.887006i
$821$	2.30648	+	44.0103i	0.0804968	+	1.53597i	0.678574	+	0.734532i	$0.262598\pi$
$821$	2.30648	+	44.0103i	0.0804968	+	1.53597i	−0.598077	+	0.801438i	$0.704068\pi$
$822$	−21.2652	−	19.6774i	−0.741710	−	0.686328i
$823$	−39.4571	+	17.5674i	−1.37539	+	0.612362i	−0.955440	−	0.295187i	$-0.904618\pi$
$823$	−39.4571	+	17.5674i	−1.37539	+	0.612362i	−0.419947	+	0.907549i	$0.637951\pi$
$824$	−8.17250	+	14.5411i	−0.284703	+	0.506562i
$825$	−0.296733	+	8.88854i	−0.0103309	+	0.309459i
$826$	32.3749	−	38.8864i	1.12647	−	1.35303i
$827$	−33.8313	+	5.35836i	−1.17643	+	0.186328i	−0.713883	−	0.700265i	$-0.753065\pi$
$827$	−33.8313	+	5.35836i	−1.17643	+	0.186328i	−0.462549	+	0.886594i	$0.653065\pi$
$828$	2.95235	+	7.14813i	0.102601	+	0.248415i
$829$	−6.54267	−	5.89104i	−0.227236	−	0.204604i	0.547646	−	0.836710i	$-0.315524\pi$
$829$	−6.54267	−	5.89104i	−0.227236	−	0.204604i	−0.774882	+	0.632106i	$0.782191\pi$
$830$	−9.67024	+	14.4566i	−0.335659	+	0.501797i
$831$	26.3645	−	19.1550i	0.914575	−	0.664478i
$832$	22.0705	+	18.5713i	0.765158	+	0.643843i
$833$	17.5950	−	54.1519i	0.609632	−	1.87625i
$834$	−14.7417	−	4.16567i	−0.510463	−	0.144245i
$835$	4.94760	−	2.85650i	0.171219	−	0.0988531i
$836$	26.1052	−	44.3705i	0.902866	−	1.53459i
$837$	−14.8806	+	14.8806i	−0.514350	+	0.514350i
$838$	−14.5536	+	3.68829i	−0.502747	+	0.127410i
$839$	31.3387	+	1.64239i	1.08193	+	0.0567016i	0.584958	−	0.811064i	$-0.301111\pi$
$839$	31.3387	+	1.64239i	1.08193	+	0.0567016i	0.496974	+	0.867766i	$0.334445\pi$
$840$	24.5854	+	4.92929i	0.848278	+	0.170077i
$841$	2.18536	+	20.7923i	0.0753572	+	0.716975i
$842$	3.64829	+	18.3900i	0.125728	+	0.633761i
$843$	1.54431	+	29.4673i	0.0531890	+	1.01491i
$844$	11.1530	+	8.57598i	0.383901	+	0.295197i
$845$	−20.8904	+	3.75544i	−0.718652	+	0.129191i
$846$	8.56288	+	12.1292i	0.294398	+	0.417012i
$847$	39.1347	−	34.2308i	1.34468	−	1.17618i
$848$	1.52873	−	9.52676i	0.0524968	−	0.327150i
$849$	6.50647	+	14.6138i	0.223302	+	0.501544i
$850$	−10.8401	−	5.71030i	−0.371814	−	0.195862i
$851$	−2.36435	−	3.64078i	−0.0810489	−	0.124804i
$852$	3.62969	+	5.93664i	0.124351	+	0.203386i
$853$	7.73404	+	1.22495i	0.264808	+	0.0419415i	0.287427	−	0.957803i	$-0.407200\pi$
$853$	7.73404	+	1.22495i	0.264808	+	0.0419415i	−0.0226183	+	0.999744i	$0.507200\pi$
$854$	10.7860	+	25.1404i	0.369091	+	0.860286i
$855$	20.8271	−	4.42694i	0.712272	−	0.151398i
$856$	24.3548	−	34.3501i	0.832430	−	1.17406i
$857$			33.8234i			1.15539i	0.816254	+	0.577693i	$0.196047\pi$
$857$			33.8234i			1.15539i	−0.816254	+	0.577693i	$0.803953\pi$
$858$	−15.8953	−	11.1696i	−0.542657	−	0.381323i
$859$			30.0672i			1.02588i	0.858424	+	0.512940i	$0.171444\pi$
$859$			30.0672i			1.02588i	−0.858424	+	0.512940i	$0.828556\pi$
$860$	10.3169	+	29.2283i	0.351803	+	0.996677i
$861$	43.0736	−	9.15559i	1.46795	−	0.312022i
$862$	42.0512	−	18.0413i	1.43227	−	0.614490i
$863$	−26.5393	−	4.20341i	−0.903407	−	0.143086i	−0.312587	−	0.949889i	$-0.601196\pi$
$863$	−26.5393	−	4.20341i	−0.903407	−	0.143086i	−0.590820	+	0.806804i	$0.701196\pi$
$864$	−20.7021	+	22.2817i	−0.704300	+	0.758038i
$865$	7.37060	+	11.3497i	0.250608	+	0.385902i
$866$	1.39304	−	2.64447i	0.0473374	−	0.0898628i
$867$	1.50666	+	3.38402i	0.0511689	+	0.114927i
$868$	−6.70590	−	36.3880i	−0.227613	−	1.23509i
$869$	5.15713	−	8.28140i	0.174944	−	0.280927i
$870$	6.16455	−	4.35198i	0.208998	−	0.147546i
$871$	−27.2576	−	32.9540i	−0.923589	−	1.11660i
$872$	22.9331	+	0.936027i	0.776611	+	0.0316979i
$873$	−0.623158	−	11.8906i	−0.0210907	−	0.402435i
$874$	24.7749	−	4.91496i	0.838024	−	0.166251i
$875$	−5.91632	−	56.2901i	−0.200008	−	1.90295i
$876$	16.9712	+	17.9203i	0.573404	+	0.605471i
$877$	−25.1895	−	1.32013i	−0.850589	−	0.0445775i	−0.377942	−	0.925829i	$-0.623368\pi$
$877$	−25.1895	−	1.32013i	−0.850589	−	0.0445775i	−0.472647	+	0.881252i	$0.656701\pi$
$878$	4.40745	+	17.3914i	0.148744	+	0.586931i
$879$	−19.6245	+	19.6245i	−0.661918	+	0.661918i
$880$	−20.0872	+	8.10417i	−0.677139	+	0.273192i
$881$	−11.7958	+	6.81029i	−0.397410	+	0.229445i	−0.685366	−	0.728199i	$-0.740358\pi$
$881$	−11.7958	+	6.81029i	−0.397410	+	0.229445i	0.287956	+	0.957644i	$0.407024\pi$
$882$	−9.91347	+	35.0823i	−0.333804	+	1.18128i
$883$	−3.14663	+	9.68434i	−0.105893	+	0.325904i	−0.989939	−	0.141495i	$-0.954809\pi$
$883$	−3.14663	+	9.68434i	−0.105893	+	0.325904i	0.884046	+	0.467399i	$0.154809\pi$
$884$	23.4000	−	12.9908i	0.787028	−	0.436928i
$885$	11.4861	−	8.34517i	0.386102	−	0.280520i
$886$	23.9269	+	16.0050i	0.803839	+	0.537699i
$887$	23.0377	+	20.7433i	0.773531	+	0.696491i	0.958133	−	0.286323i	$-0.0924329\pi$
$887$	23.0377	+	20.7433i	0.773531	+	0.696491i	−0.184602	+	0.982813i	$0.559100\pi$
$888$	3.27859	−	5.17876i	0.110022	−	0.173788i
$889$	33.6351	−	5.32727i	1.12808	−	0.178671i
$890$	6.35460	+	5.29052i	0.213007	+	0.177339i
$891$	2.31378	−	2.97089i	0.0775144	−	0.0995285i
$892$	−5.95042	−	12.5080i	−0.199235	−	0.418798i
$893$	44.2972	−	19.7224i	1.48235	−	0.659985i
$894$	−6.96953	+	7.53192i	−0.233096	+	0.251905i
$895$	0.375879	+	7.17219i	0.0125642	+	0.239740i
$896$	−11.6165	−	52.1988i	−0.388081	−	1.74384i
$897$	−1.09480	−	9.46851i	−0.0365544	−	0.316144i
$898$	0.262390	+	0.196144i	0.00875608	+	0.00654540i
$899$	−9.33855	−	6.06453i	−0.311458	−	0.202263i
$900$	7.07708	+	3.38442i	0.235903	+	0.112814i
$901$	−7.75334	−	4.47639i	−0.258301	−	0.149130i
$902$	−26.7528	+	27.0428i	−0.890769	+	0.900426i
$903$	49.7835	−	13.3395i	1.65669	−	0.443909i
$904$	2.32547	−	24.8918i	0.0773441	−	0.827889i
$905$	29.1569	−	14.8562i	0.969207	−	0.493836i
$906$	−2.22884	+	0.956244i	−0.0740482	+	0.0317691i
$907$	23.7475	+	10.5731i	0.788522	+	0.351073i	0.761169	−	0.648553i	$-0.224626\pi$
$907$	23.7475	+	10.5731i	0.788522	+	0.351073i	0.0273529	+	0.999626i	$0.491292\pi$
$908$	−0.233548	−	9.27889i	−0.00775057	−	0.307931i
$909$	0.407218	−	0.132313i	0.0135066	−	0.00438855i
$910$	35.0040	+	17.9769i	1.16037	+	0.595928i
$911$	−5.99271	+	8.24826i	−0.198547	+	0.273277i	−0.896668	−	0.442703i	$-0.854020\pi$
$911$	−5.99271	+	8.24826i	−0.198547	+	0.273277i	0.698121	+	0.715980i	$0.254020\pi$
$912$	20.9029	+	28.8936i	0.692164	+	0.956762i
$913$	−24.8910	−	2.13918i	−0.823771	−	0.0707964i
$914$	−34.6883	+	3.16965i	−1.14739	+	0.104843i
$915$	1.20078	+	7.58146i	0.0396967	+	0.250635i
$916$	15.7408	−	37.8928i	0.520091	−	1.25201i
$917$	−18.0444	−	27.7860i	−0.595879	−	0.917574i
$918$	12.4691	+	25.3171i	0.411540	+	0.835590i
$919$	−58.9011	+	6.19075i	−1.94297	+	0.204214i	−0.993852	−	0.110715i	$-0.964686\pi$
$919$	−58.9011	+	6.19075i	−1.94297	+	0.204214i	−0.949115	+	0.314929i	$0.898019\pi$
$920$	−9.52409	−	4.71481i	−0.314000	−	0.155443i
$921$	−20.4740	−	13.2959i	−0.674640	−	0.438116i
$922$	0.623460	−	45.8477i	0.0205326	−	1.50991i
$923$	2.93575	+	10.5178i	0.0966315	+	0.346199i
$924$	10.8484	+	34.3444i	0.356885	+	1.12985i
$925$	−4.25333	−	1.13968i	−0.139849	−	0.0374723i
$926$	31.2689	−	17.4906i	1.02756	−	0.574776i
$927$	−6.63085	−	7.36431i	−0.217786	−	0.241876i
$928$	−13.8094	−	8.26328i	−0.453316	−	0.271255i
$929$	−3.80615	−	3.08216i	−0.124876	−	0.101122i	0.564848	−	0.825195i	$-0.308935\pi$
$929$	−3.80615	−	3.08216i	−0.124876	−	0.101122i	−0.689724	+	0.724073i	$0.742268\pi$
$930$	0.684278	−	10.3595i	0.0224384	−	0.339700i
$931$	106.084	+	54.0526i	3.47677	+	1.77150i
$932$	−22.1937	+	9.16655i	−0.726980	+	0.300260i
$933$	6.54281	+	0.687677i	0.214202	+	0.0225135i
$934$	−15.6299	+	5.75718i	−0.511428	+	0.188381i
$935$	0.381614	+	20.0947i	0.0124801	+	0.657165i
$936$	−14.6487	+	8.89197i	−0.478808	+	0.290643i
$937$	−43.1040	−	31.3169i	−1.40815	−	1.02308i	−0.993589	−	0.113056i	$-0.963936\pi$
$937$	−43.1040	−	31.3169i	−1.40815	−	1.02308i	−0.414559	−	0.910023i	$-0.636064\pi$
$938$	3.07252	+	79.2262i	0.100321	+	2.58683i
$939$	−7.53968	−	6.78876i	−0.246048	−	0.221543i
$940$	−19.8334	−	4.78288i	−0.646894	−	0.156000i
$941$	1.64073	−	10.3592i	0.0534863	−	0.337699i	−0.946405	−	0.322981i	$-0.895315\pi$
$941$	1.64073	−	10.3592i	0.0534863	−	0.337699i	0.999892	−	0.0147181i	$-0.00468510\pi$
$942$	−34.6453	−	13.8425i	−1.12881	−	0.451012i
$943$	−18.6378	−	0.976767i	−0.606931	−	0.0318079i
$944$	−26.1913	−	15.1926i	−0.852455	−	0.494476i
$945$	−20.7463	+	35.9336i	−0.674876	+	1.16892i
$946$	−29.6121	+	33.2462i	−0.962772	+	1.08093i
$947$	26.6555	+	7.14232i	0.866187	+	0.232094i	0.664438	−	0.747343i	$-0.268671\pi$
$947$	26.6555	+	7.14232i	0.866187	+	0.232094i	0.201749	+	0.979437i	$0.435337\pi$
$948$	3.82222	+	5.57349i	0.124140	+	0.181018i
$949$	17.9420	+	34.3264i	0.582424	+	1.11428i
$950$	15.3394	−	20.5202i	0.497676	−	0.665763i
$951$	−13.3853	−	34.8699i	−0.434049	−	1.13074i
$952$	−49.0948	−	7.19476i	−1.59117	−	0.233184i
$953$	9.93859	−	46.7574i	0.321943	−	1.51462i	−0.458103	−	0.888899i	$-0.651471\pi$
$953$	9.93859	−	46.7574i	0.321943	−	1.51462i	0.780046	−	0.625722i	$-0.215196\pi$
$954$	5.07156	+	2.67157i	0.164198	+	0.0864952i
$955$	8.45548	+	3.24575i	0.273613	+	0.105030i
$956$	52.2422	+	4.16493i	1.68963	+	0.134704i
$957$	9.74922	+	4.73650i	0.315148	+	0.153109i
$958$	30.6398	−	2.79971i	0.989926	−	0.0904546i
$959$	−8.81108	+	83.8319i	−0.284525	+	2.70707i
$960$	0.438469	−	14.9984i	0.0141515	−	0.484070i
$961$	14.9126	−	4.84540i	0.481052	−	0.156303i
$962$	7.16881	−	6.41337i	0.231132	−	0.206775i
$963$	14.7041	+	20.2385i	0.473833	+	0.652175i
$964$	−13.5734	−	4.03562i	−0.437169	−	0.129978i
$965$	−18.5438	+	3.94161i	−0.596947	+	0.126885i
$966$	−9.04276	+	15.1820i	−0.290946	+	0.488472i
$967$	3.44714	+	3.44714i	0.110853	+	0.110853i	0.760357	−	0.649505i	$-0.225024\pi$
$967$	3.44714	+	3.44714i	0.110853	+	0.110853i	−0.649505	+	0.760357i	$0.725024\pi$
$968$	−24.1239	−	19.6479i	−0.775371	−	0.631506i
$969$	31.9625	−	8.56432i	1.02678	−	0.275125i
$970$	11.4110	+	11.7256i	0.366384	+	0.376486i
$971$	−10.0847	+	9.08033i	−0.323634	+	0.291402i	−0.814892	−	0.579612i	$-0.803204\pi$
$971$	−10.0847	+	9.08033i	−0.323634	+	0.291402i	0.491258	+	0.871014i	$0.336537\pi$
$972$	−14.1218	−	26.0722i	−0.452957	−	0.836267i
$973$	15.9722	+	41.6091i	0.512046	+	1.33393i
$974$	14.0600	−	41.3504i	0.450511	−	1.32495i
$975$	−7.25176	−	6.39428i	−0.232242	−	0.204781i
$976$	13.7473	−	8.88794i	0.440039	−	0.284496i
$977$	−19.7415	−	24.3788i	−0.631588	−	0.779946i	0.356424	−	0.934324i	$-0.383996\pi$
$977$	−19.7415	−	24.3788i	−0.631588	−	0.779946i	−0.988012	+	0.154378i	$0.950663\pi$
$978$	−7.71591	−	3.56183i	−0.246728	−	0.113895i
$979$	−2.24833	+	11.6622i	−0.0718570	+	0.372726i
$980$	−21.5206	−	45.2370i	−0.687450	−	1.44504i
$981$	−4.88661	+	12.7300i	−0.156017	+	0.406439i
$982$	19.2888	−	12.1566i	0.615529	−	0.387933i
$983$	−23.8595	−	12.1570i	−0.761000	−	0.387749i	0.0300123	−	0.999550i	$-0.490445\pi$
$983$	−23.8595	−	12.1570i	−0.761000	−	0.387749i	−0.791012	+	0.611801i	$0.790445\pi$
$984$	−9.72734	−	24.4901i	−0.310096	−	0.780716i
$985$	1.73900	−	3.90586i	0.0554092	−	0.124451i
$986$	−11.7313	+	9.23855i	−0.373600	+	0.294215i
$987$	−10.4832	+	32.2641i	−0.333685	+	1.02698i
$988$	19.1755	+	52.5774i	0.610053	+	1.67271i
$989$	−21.8437			−0.694588
$990$	−0.742741	−	12.8469i	−0.0236059	−	0.408300i
$991$	−15.2149	+	8.78432i	−0.483317	+	0.279043i	−0.721798	−	0.692104i	$-0.756684\pi$
$991$	−15.2149	+	8.78432i	−0.483317	+	0.279043i	0.238481	+	0.971147i	$0.423351\pi$
$992$	−20.7922	+	7.61073i	−0.660153	+	0.241641i
$993$	8.53406	+	16.7490i	0.270820	+	0.531514i
$994$	7.51139	−	18.7997i	0.238247	−	0.596291i
$995$	−5.12297	−	4.14850i	−0.162409	−	0.131516i
$996$	8.27326	−	15.2006i	0.262148	−	0.481650i
$997$	33.9047	+	7.20667i	1.07377	+	0.228237i	0.710680	−	0.703515i	$-0.248387\pi$
$997$	33.9047	+	7.20667i	1.07377	+	0.228237i	0.363093	+	0.931753i	$0.381721\pi$
$998$	−29.3219	+	31.6880i	−0.928170	+	1.00307i
$999$	6.38290	+	7.88223i	0.201946	+	0.249383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bs.a.15.9	✓	1280
4.3	odd	2	inner	572.2.bs.a.15.41	yes	1280
11.3	even	5	inner	572.2.bs.a.223.27	yes	1280
13.7	odd	12	inner	572.2.bs.a.59.8	yes	1280
44.3	odd	10	inner	572.2.bs.a.223.8	yes	1280
52.7	even	12	inner	572.2.bs.a.59.27	yes	1280
143.124	odd	60	inner	572.2.bs.a.267.41	yes	1280
572.267	even	60	inner	572.2.bs.a.267.9	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bs.a.15.9	✓	1280	1.1	even	1	trivial
572.2.bs.a.15.41	yes	1280	4.3	odd	2	inner
572.2.bs.a.59.8	yes	1280	13.7	odd	12	inner
572.2.bs.a.59.27	yes	1280	52.7	even	12	inner
572.2.bs.a.223.8	yes	1280	44.3	odd	10	inner
572.2.bs.a.223.27	yes	1280	11.3	even	5	inner
572.2.bs.a.267.9	yes	1280	572.267	even	60	inner
572.2.bs.a.267.41	yes	1280	143.124	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36092 - 0.384566i) q^{2} +(-0.238841 - 1.12366i) q^{3} +(1.70422 + 1.04673i) q^{4} +(0.255413 - 1.61261i) q^{5} +(-0.107076 + 1.62106i) q^{6} +(3.96409 - 2.57431i) q^{7} +(-1.91677 - 2.07990i) q^{8} +(1.53508 - 0.683460i) q^{9} +O(q^{10})\)	\(q+(-1.36092 - 0.384566i) q^{2} +(-0.238841 - 1.12366i) q^{3} +(1.70422 + 1.04673i) q^{4} +(0.255413 - 1.61261i) q^{5} +(-0.107076 + 1.62106i) q^{6} +(3.96409 - 2.57431i) q^{7} +(-1.91677 - 2.07990i) q^{8} +(1.53508 - 0.683460i) q^{9} +(-0.967752 + 2.09642i) q^{10} +(-3.30819 + 0.236435i) q^{11} +(0.769127 - 2.16496i) q^{12} +(2.08886 - 2.93882i) q^{13} +(-6.38481 + 1.97898i) q^{14} +(-1.87303 + 0.0981611i) q^{15} +(1.80872 + 3.56771i) q^{16} +(3.69119 - 0.387960i) q^{17} +(-2.35196 + 0.339798i) q^{18} +(-0.406177 + 7.75031i) q^{19} +(2.12325 - 2.48090i) q^{20} +(-3.83942 - 3.83942i) q^{21} +(4.59311 + 0.950445i) q^{22} +(1.15063 + 1.99294i) q^{23} +(-1.87929 + 2.65056i) q^{24} +(2.22000 + 0.721321i) q^{25} +(-3.97294 + 3.19621i) q^{26} +(-3.16029 - 4.34976i) q^{27} +(9.45027 - 0.237862i) q^{28} +(1.90358 - 2.11414i) q^{29} +(2.58679 + 0.586712i) q^{30} +(-0.612295 - 3.86588i) q^{31} +(-1.08951 - 5.55094i) q^{32} +(1.05580 + 3.66080i) q^{33} +(-5.17262 - 0.891523i) q^{34} +(-3.13888 - 7.05005i) q^{35} +(3.33150 + 0.442043i) q^{36} +(-1.88384 + 0.0987277i) q^{37} +(3.53328 - 10.3914i) q^{38} +(-3.80113 - 1.64525i) q^{39} +(-3.84364 + 2.55978i) q^{40} +(-4.41708 + 6.80170i) q^{41} +(3.74865 + 6.70167i) q^{42} +(-4.74603 + 8.22037i) q^{43} +(-5.88536 - 3.05983i) q^{44} +(-0.710078 - 2.65005i) q^{45} +(-0.799496 - 3.15473i) q^{46} +(-2.83647 - 5.56689i) q^{47} +(3.57688 - 2.88449i) q^{48} +(6.23977 - 14.0148i) q^{49} +(-2.74385 - 1.83540i) q^{50} +(-1.31754 - 4.05497i) q^{51} +(6.63601 - 2.82193i) q^{52} +(-1.95148 - 1.41783i) q^{53} +(2.62813 + 7.13502i) q^{54} +(-0.463675 + 5.39521i) q^{55} +(-12.9526 - 3.31054i) q^{56} +(8.80570 - 1.39469i) q^{57} +(-3.40365 + 2.14513i) q^{58} +(-6.34846 + 4.12274i) q^{59} +(-3.29479 - 1.79326i) q^{60} +(-0.427787 - 4.07012i) q^{61} +(-0.653399 + 5.49663i) q^{62} +(4.32574 - 6.66106i) q^{63} +(-0.651964 + 7.97339i) q^{64} +(-4.20566 - 4.11913i) q^{65} +(-0.0290466 - 5.38808i) q^{66} +(3.06990 - 11.4570i) q^{67} +(6.69669 + 3.20251i) q^{68} +(1.96457 - 1.76891i) q^{69} +(1.56057 + 10.8017i) q^{70} +(-1.90598 + 2.35368i) q^{71} +(-4.36392 - 1.88277i) q^{72} +(-4.87700 + 9.57165i) q^{73} +(2.60172 + 0.590098i) q^{74} +(0.280292 - 2.66680i) q^{75} +(-8.80468 + 12.7831i) q^{76} +(-12.5053 + 9.45354i) q^{77} +(4.54034 + 3.70084i) q^{78} +(-1.72898 + 2.37974i) q^{79} +(6.21530 - 2.00553i) q^{80} +(-0.759711 + 0.843745i) q^{81} +(8.62700 - 7.55793i) q^{82} +(7.43983 + 1.17835i) q^{83} +(-2.52438 - 10.5621i) q^{84} +(0.317149 - 6.05155i) q^{85} +(9.62026 - 9.36213i) q^{86} +(-2.83022 - 1.63403i) q^{87} +(6.83280 + 6.42750i) q^{88} +(0.926842 - 3.45902i) q^{89} +(-0.0527565 + 3.87958i) q^{90} +(0.714968 - 17.0271i) q^{91} +(-0.125151 + 4.60081i) q^{92} +(-4.19768 + 1.61134i) q^{93} +(1.71938 + 8.66691i) q^{94} +(12.3945 + 2.63453i) q^{95} +(-5.97714 + 2.55003i) q^{96} +(2.53938 - 6.61531i) q^{97} +(-13.8814 + 16.6734i) q^{98} +(-4.91673 + 2.62396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Introduction

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