LMFDB - Embedded newform 572.2.bk.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(31,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 12, 15]))

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

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

chi := DirichletCharacter("572.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bk (of order $20$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$80$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	572.31
Dual form			572.2.bk.a.203.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41408 + 0.0192463i) q^{2} +(0.0675205 + 0.0929340i) q^{3} +(1.99926 - 0.0544317i) q^{4} +(3.09570 + 1.57734i) q^{5} +(-0.0972682 - 0.130117i) q^{6} +(0.303959 - 0.0481424i) q^{7} +(-2.82607 + 0.115449i) q^{8} +(0.922973 - 2.84062i) q^{9} +O(q^{10})$	\(q+(-1.41408 + 0.0192463i) q^{2} +(0.0675205 + 0.0929340i) q^{3} +(1.99926 - 0.0544317i) q^{4} +(3.09570 + 1.57734i) q^{5} +(-0.0972682 - 0.130117i) q^{6} +(0.303959 - 0.0481424i) q^{7} +(-2.82607 + 0.115449i) q^{8} +(0.922973 - 2.84062i) q^{9} +(-4.40794 - 2.17091i) q^{10} +(3.15364 - 1.02692i) q^{11} +(0.140049 + 0.182124i) q^{12} +(0.770209 - 3.52233i) q^{13} +(-0.428897 + 0.0739274i) q^{14} +(0.0624350 + 0.394199i) q^{15} +(3.99407 - 0.217646i) q^{16} +(3.97213 - 1.29062i) q^{17} +(-1.25049 + 4.03463i) q^{18} +(-6.05212 - 0.958561i) q^{19} +(6.27497 + 2.98501i) q^{20} +(0.0249975 + 0.0249975i) q^{21} +(-4.43974 + 1.51285i) q^{22} -1.50142 q^{23} +(-0.201547 - 0.254843i) q^{24} +(4.15646 + 5.72087i) q^{25} +(-1.02135 + 4.99568i) q^{26} +(0.654061 - 0.212517i) q^{27} +(0.605073 - 0.112794i) q^{28} +(-4.93277 - 3.58387i) q^{29} +(-0.0958750 - 0.556228i) q^{30} +(-3.33030 + 1.69687i) q^{31} +(-5.64376 + 0.384641i) q^{32} +(0.308371 + 0.223742i) q^{33} +(-5.59209 + 1.90150i) q^{34} +(1.01690 + 0.330412i) q^{35} +(1.69064 - 5.72937i) q^{36} +(1.41165 + 8.91282i) q^{37} +(8.57664 + 1.23900i) q^{38} +(0.379349 - 0.166250i) q^{39} +(-8.93078 - 4.10028i) q^{40} +(0.336546 - 2.12487i) q^{41} +(-0.0358297 - 0.0348675i) q^{42} +10.9305 q^{43} +(6.24904 - 2.22474i) q^{44} +(7.33788 - 7.33788i) q^{45} +(2.12313 - 0.0288967i) q^{46} +(0.332829 - 2.10140i) q^{47} +(0.289908 + 0.356490i) q^{48} +(-6.56732 + 2.13385i) q^{49} +(-5.98768 - 8.00979i) q^{50} +(0.388143 + 0.282003i) q^{51} +(1.34812 - 7.08397i) q^{52} +(-0.856495 + 2.63602i) q^{53} +(-0.920806 + 0.313105i) q^{54} +(11.3825 + 1.79532i) q^{55} +(-0.853452 + 0.171146i) q^{56} +(-0.319559 - 0.627170i) q^{57} +(7.04432 + 4.97295i) q^{58} +(3.74009 - 0.592372i) q^{59} +(0.146281 + 0.784707i) q^{60} +(1.67074 + 5.14201i) q^{61} +(4.67666 - 2.46362i) q^{62} +(0.143792 - 0.907867i) q^{63} +(7.97334 - 0.652535i) q^{64} +(7.94025 - 9.68920i) q^{65} +(-0.440368 - 0.310454i) q^{66} +(5.16018 + 5.16018i) q^{67} +(7.87108 - 2.79650i) q^{68} +(-0.101376 - 0.139533i) q^{69} +(-1.44435 - 0.447659i) q^{70} +(6.85281 - 13.4494i) q^{71} +(-2.28044 + 8.13435i) q^{72} +(1.67400 + 10.5692i) q^{73} +(-2.16773 - 12.5763i) q^{74} +(-0.251017 + 0.772552i) q^{75} +(-12.1519 - 1.58698i) q^{76} +(0.909139 - 0.463966i) q^{77} +(-0.533230 + 0.242393i) q^{78} +(-11.7864 - 3.82963i) q^{79} +(12.7078 + 5.62625i) q^{80} +(-7.18521 - 5.22036i) q^{81} +(-0.435008 + 3.01122i) q^{82} +(-6.89200 + 13.5263i) q^{83} +(0.0513372 + 0.0486159i) q^{84} +(14.3323 + 2.27001i) q^{85} +(-15.4566 + 0.210371i) q^{86} -0.700406i q^{87} +(-8.79384 + 3.26624i) q^{88} +(6.10473 + 6.10473i) q^{89} +(-10.2351 + 10.5176i) q^{90} +(0.0645390 - 1.10772i) q^{91} +(-3.00172 + 0.0817247i) q^{92} +(-0.382561 - 0.194924i) q^{93} +(-0.430203 + 2.97796i) q^{94} +(-17.2236 - 12.5137i) q^{95} +(-0.416816 - 0.498526i) q^{96} +(2.90319 + 5.69783i) q^{97} +(9.24567 - 3.14384i) q^{98} +(-0.00636881 - 9.90611i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9}+O(q^{10}) $ 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9	$ 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9} - 12 q^{13} + 4 q^{14} - 36 q^{16} - 10 q^{18} - 60 q^{20} - 56 q^{21} - 44 q^{22} - 14 q^{24} + 26 q^{26} - 14 q^{28} - 24 q^{29} - 16 q^{32} - 28 q^{33} + 12 q^{34} - 12 q^{37} + 4 q^{40} - 36 q^{41} - 8 q^{42} + 26 q^{44} - 16 q^{45} - 50 q^{46} + 48 q^{48} + 36 q^{50} - 52 q^{52} - 40 q^{53} + 116 q^{54} - 36 q^{57} - 70 q^{58} + 52 q^{60} - 8 q^{61} - 48 q^{65} - 228 q^{66} - 44 q^{68} - 68 q^{70} - 38 q^{72} - 12 q^{73} - 12 q^{74} + 108 q^{76} + 108 q^{78} + 62 q^{80} - 168 q^{81} - 36 q^{84} - 52 q^{85} - 62 q^{86} + 16 q^{89} - 80 q^{92} - 4 q^{93} - 124 q^{94} - 132 q^{96} - 4 q^{97} - 108 q^{98}+O(q^{100}) $ 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9 - 12 * q^13 + 4 * q^14 - 36 * q^16 - 10 * q^18 - 60 * q^20 - 56 * q^21 - 44 * q^22 - 14 * q^24 + 26 * q^26 - 14 * q^28 - 24 * q^29 - 16 * q^32 - 28 * q^33 + 12 * q^34 - 12 * q^37 + 4 * q^40 - 36 * q^41 - 8 * q^42 + 26 * q^44 - 16 * q^45 - 50 * q^46 + 48 * q^48 + 36 * q^50 - 52 * q^52 - 40 * q^53 + 116 * q^54 - 36 * q^57 - 70 * q^58 + 52 * q^60 - 8 * q^61 - 48 * q^65 - 228 * q^66 - 44 * q^68 - 68 * q^70 - 38 * q^72 - 12 * q^73 - 12 * q^74 + 108 * q^76 + 108 * q^78 + 62 * q^80 - 168 * q^81 - 36 * q^84 - 52 * q^85 - 62 * q^86 + 16 * q^89 - 80 * q^92 - 4 * q^93 - 124 * q^94 - 132 * q^96 - 4 * q^97 - 108 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.41408	+	0.0192463i	−0.999907	+	0.0136092i
$2$	−1.41408	+	0.0192463i	−0.999907	+	0.0136092i
$3$	0.0675205	+	0.0929340i	0.0389830	+	0.0536554i	0.828064	−	0.560634i	$-0.189443\pi$
$3$	0.0675205	+	0.0929340i	0.0389830	+	0.0536554i	−0.789081	+	0.614290i	$0.789443\pi$
$4$	1.99926	−	0.0544317i	0.999630	−	0.0272158i
$5$	3.09570	+	1.57734i	1.38444	+	0.705408i	0.978065	−	0.208298i	$-0.0667925\pi$
$5$	3.09570	+	1.57734i	1.38444	+	0.705408i	0.406376	+	0.913706i	$0.366792\pi$
$6$	−0.0972682	−	0.130117i	−0.0397096	−	0.0531199i
$7$	0.303959	−	0.0481424i	0.114886	−	0.0181961i	−0.0987268	−	0.995115i	$-0.531477\pi$
$7$	0.303959	−	0.0481424i	0.114886	−	0.0181961i	0.213613	+	0.976918i	$0.431477\pi$
$8$	−2.82607	+	0.115449i	−0.999167	+	0.0408175i
$9$	0.922973	−	2.84062i	0.307658	−	0.946873i
$10$	−4.40794	−	2.17091i	−1.39391	−	0.686501i
$11$	3.15364	−	1.02692i	0.950858	−	0.309628i
$11$	3.15364	−	1.02692i	0.950858	−	0.309628i
$12$	0.140049	+	0.182124i	0.0404288	+	0.0525746i
$13$	0.770209	−	3.52233i	0.213618	−	0.976917i
$13$	0.770209	−	3.52233i	0.213618	−	0.976917i
$14$	−0.428897	+	0.0739274i	−0.114628	+	0.0197579i
$15$	0.0624350	+	0.394199i	0.0161206	+	0.101782i
$16$	3.99407	−	0.217646i	0.998519	−	0.0544115i
$17$	3.97213	−	1.29062i	0.963384	−	0.313022i	0.215242	−	0.976561i	$-0.430946\pi$
$17$	3.97213	−	1.29062i	0.963384	−	0.313022i	0.748142	+	0.663538i	$0.230946\pi$
$18$	−1.25049	+	4.03463i	−0.294743	+	0.950973i
$19$	−6.05212	−	0.958561i	−1.38845	−	0.219909i	−0.582952	−	0.812507i	$-0.698102\pi$
$19$	−6.05212	−	0.958561i	−1.38845	−	0.219909i	−0.805499	+	0.592598i	$0.798102\pi$
$20$	6.27497	+	2.98501i	1.40313	+	0.667468i
$21$	0.0249975	+	0.0249975i	0.00545491	+	0.00545491i
$22$	−4.43974	+	1.51285i	−0.946556	+	0.322540i
$23$	−1.50142			−0.313067			−0.156534	−	0.987673i	$-0.550032\pi$
$23$	−1.50142			−0.313067			−0.156534	+	0.987673i	$0.550032\pi$
$24$	−0.201547	−	0.254843i	−0.0411406	−	0.0520195i
$25$	4.15646	+	5.72087i	0.831291	+	1.14417i
$26$	−1.02135	+	4.99568i	−0.200303	+	0.979734i
$27$	0.654061	−	0.212517i	0.125874	−	0.0408990i
$28$	0.605073	−	0.112794i	0.114348	−	0.0213161i
$29$	−4.93277	−	3.58387i	−0.915993	−	0.665508i	0.0265307	−	0.999648i	$-0.491554\pi$
$29$	−4.93277	−	3.58387i	−0.915993	−	0.665508i	−0.942523	+	0.334140i	$0.891554\pi$
$30$	−0.0958750	−	0.556228i	−0.0175043	−	0.101553i
$31$	−3.33030	+	1.69687i	−0.598140	+	0.304768i	−0.726722	−	0.686931i	$-0.758957\pi$
$31$	−3.33030	+	1.69687i	−0.598140	+	0.304768i	0.128582	+	0.991699i	$0.458957\pi$
$32$	−5.64376	+	0.384641i	−0.997686	+	0.0679955i
$33$	0.308371	+	0.223742i	0.0536805	+	0.0389485i
$34$	−5.59209	+	1.90150i	−0.959035	+	0.326104i
$35$	1.01690	+	0.330412i	0.171888	+	0.0558499i
$36$	1.69064	−	5.72937i	0.281774	−	0.954896i
$37$	1.41165	+	8.91282i	0.232074	+	1.46526i	0.778444	+	0.627714i	$0.216009\pi$
$37$	1.41165	+	8.91282i	0.232074	+	1.46526i	−0.546370	+	0.837544i	$0.683991\pi$
$38$	8.57664	+	1.23900i	1.39131	+	0.200993i
$39$	0.379349	−	0.166250i	0.0607444	−	0.0266214i
$40$	−8.93078	−	4.10028i	−1.41208	−	0.648311i
$41$	0.336546	−	2.12487i	0.0525597	−	0.331849i	−0.947372	−	0.320136i	$-0.896272\pi$
$41$	0.336546	−	2.12487i	0.0525597	−	0.331849i	0.999931	−	0.0117130i	$-0.00372846\pi$
$42$	−0.0358297	−	0.0348675i	−0.00552864	−	0.00538017i
$43$	10.9305			1.66688			0.833441	−	0.552608i	$-0.186367\pi$
$43$	10.9305			1.66688			0.833441	+	0.552608i	$0.186367\pi$
$44$	6.24904	−	2.22474i	0.942079	−	0.335392i
$45$	7.33788	−	7.33788i	1.09387	−	1.09387i
$46$	2.12313	−	0.0288967i	0.313038	−	0.00426059i
$47$	0.332829	−	2.10140i	0.0485481	−	0.306521i	−0.951451	−	0.307800i	$-0.900407\pi$
$47$	0.332829	−	2.10140i	0.0485481	−	0.306521i	0.999999	+	0.00127939i	$0.000407244\pi$
$48$	0.289908	+	0.356490i	0.0418447	+	0.0514548i
$49$	−6.56732	+	2.13385i	−0.938189	+	0.304836i
$50$	−5.98768	−	8.00979i	−0.846786	−	1.13276i
$51$	0.388143	+	0.282003i	0.0543509	+	0.0394883i
$52$	1.34812	−	7.08397i	0.186951	−	0.982369i
$53$	−0.856495	+	2.63602i	−0.117649	+	0.362085i	−0.992490	−	0.122324i	$-0.960965\pi$
$53$	−0.856495	+	2.63602i	−0.117649	+	0.362085i	0.874842	+	0.484409i	$0.160965\pi$
$54$	−0.920806	+	0.313105i	−0.125306	+	0.0426082i
$55$	11.3825	+	1.79532i	1.53482	+	0.242080i
$56$	−0.853452	+	0.171146i	−0.114047	+	0.0228703i
$57$	−0.319559	−	0.627170i	−0.0423266	−	0.0830706i
$58$	7.04432	+	4.97295i	0.924965	+	0.652980i
$59$	3.74009	−	0.592372i	0.486919	−	0.0771203i	0.0918517	−	0.995773i	$-0.470721\pi$
$59$	3.74009	−	0.592372i	0.486919	−	0.0771203i	0.395067	+	0.918652i	$0.370721\pi$
$60$	0.146281	+	0.784707i	0.0188847	+	0.101305i
$61$	1.67074	+	5.14201i	0.213917	+	0.658367i	0.999229	+	0.0392674i	$0.0125024\pi$
$61$	1.67074	+	5.14201i	0.213917	+	0.658367i	−0.785312	+	0.619100i	$0.787498\pi$
$62$	4.67666	−	2.46362i	0.593937	−	0.312879i
$63$	0.143792	−	0.907867i	0.0181161	−	0.114380i
$64$	7.97334	−	0.652535i	0.996668	−	0.0815669i
$65$	7.94025	−	9.68920i	0.984866	−	1.20180i
$66$	−0.440368	−	0.310454i	−0.0542056	−	0.0382143i
$67$	5.16018	+	5.16018i	0.630417	+	0.630417i	0.948173	−	0.317756i	$-0.102929\pi$
$67$	5.16018	+	5.16018i	0.630417	+	0.630417i	−0.317756	+	0.948173i	$0.602929\pi$
$68$	7.87108	−	2.79650i	0.954508	−	0.339126i
$69$	−0.101376	−	0.139533i	−0.0122043	−	0.0167978i
$70$	−1.44435	−	0.447659i	−0.172632	−	0.0535055i
$71$	6.85281	−	13.4494i	0.813279	−	1.59615i	0.0104452	−	0.999945i	$-0.496675\pi$
$71$	6.85281	−	13.4494i	0.813279	−	1.59615i	0.802833	−	0.596204i	$-0.203325\pi$
$72$	−2.28044	+	8.13435i	−0.268752	+	0.958642i
$73$	1.67400	+	10.5692i	0.195926	+	1.23703i	0.868007	+	0.496552i	$0.165401\pi$
$73$	1.67400	+	10.5692i	0.195926	+	1.23703i	−0.672081	+	0.740478i	$0.734599\pi$
$74$	−2.16773	−	12.5763i	−0.251994	−	1.46196i
$75$	−0.251017	+	0.772552i	−0.0289850	+	0.0892066i
$76$	−12.1519	−	1.58698i	−1.39392	−	0.182040i
$77$	0.909139	−	0.463966i	0.103606	−	0.0528738i
$78$	−0.533230	+	0.242393i	−0.0603765	+	0.0274456i
$79$	−11.7864	−	3.82963i	−1.32607	−	0.430867i	−0.441496	−	0.897263i	$-0.645552\pi$
$79$	−11.7864	−	3.82963i	−1.32607	−	0.430867i	−0.884576	+	0.466396i	$0.845552\pi$
$80$	12.7078	+	5.62625i	1.42077	+	0.629033i
$81$	−7.18521	−	5.22036i	−0.798357	−	0.580040i
$82$	−0.435008	+	3.01122i	−0.0480386	+	0.332533i
$83$	−6.89200	+	13.5263i	−0.756495	+	1.48471i	0.114505	+	0.993423i	$0.463472\pi$
$83$	−6.89200	+	13.5263i	−0.756495	+	1.48471i	−0.871000	+	0.491283i	$0.836528\pi$
$84$	0.0513372	+	0.0486159i	0.00560135	+	0.00530443i
$85$	14.3323	+	2.27001i	1.55456	+	0.246218i
$86$	−15.4566	+	0.210371i	−1.66673	+	0.0226849i
$87$		−	0.700406i		−	0.0750914i
$88$	−8.79384	+	3.26624i	−0.937427	+	0.348182i
$89$	6.10473	+	6.10473i	0.647100	+	0.647100i	0.952291	−	0.305191i	$-0.0987203\pi$
$89$	6.10473	+	6.10473i	0.647100	+	0.647100i	−0.305191	+	0.952291i	$0.598720\pi$
$90$	−10.2351	+	10.5176i	−1.07888	+	1.10865i
$91$	0.0645390	−	1.10772i	0.00676553	−	0.116121i
$92$	−3.00172	+	0.0817247i	−0.312951	+	0.00852039i
$93$	−0.382561	−	0.194924i	−0.0396697	−	0.0202127i
$94$	−0.430203	+	2.97796i	−0.0443721	+	0.307153i
$95$	−17.2236	−	12.5137i	−1.76710	−	1.28388i
$96$	−0.416816	−	0.498526i	−0.0425411	−	0.0508806i
$97$	2.90319	+	5.69783i	0.294774	+	0.578527i	0.990132	−	0.140137i	$-0.0447542\pi$
$97$	2.90319	+	5.69783i	0.294774	+	0.578527i	−0.695358	+	0.718664i	$0.744754\pi$
$98$	9.24567	−	3.14384i	0.933953	−	0.317576i
$99$	−0.00636881	−	9.90611i	−0.000640090	−	0.995601i
$100$	8.62123	+	11.2113i	0.862123	+	1.12113i
$101$	−2.35620	−	0.765577i	−0.234451	−	0.0761777i	0.189435	−	0.981893i	$-0.439334\pi$
$101$	−2.35620	−	0.765577i	−0.234451	−	0.0761777i	−0.423886	+	0.905715i	$0.639334\pi$
$102$	−0.554294	−	0.391305i	−0.0548833	−	0.0387449i
$103$	−6.34766	−	4.61185i	−0.625454	−	0.454419i	0.229368	−	0.973340i	$-0.426334\pi$
$103$	−6.34766	−	4.61185i	−0.625454	−	0.454419i	−0.854822	+	0.518921i	$0.826334\pi$
$104$	−1.77002	+	10.0433i	−0.173564	+	0.984823i
$105$	0.0379554	+	0.116815i	0.00370406	+	0.0113999i
$106$	1.16042	−	3.74404i	0.112710	−	0.363653i
$107$	0.806840	+	1.11052i	0.0780002	+	0.107358i	0.846234	−	0.532811i	$-0.178864\pi$
$107$	0.806840	+	1.11052i	0.0780002	+	0.107358i	−0.768234	+	0.640169i	$0.778864\pi$
$108$	1.29607	−	0.460479i	0.124714	−	0.0443096i
$109$	−10.7529	+	10.7529i	−1.02994	+	1.02994i	−0.0304016	+	0.999538i	$0.509679\pi$
$109$	−10.7529	+	10.7529i	−1.02994	+	1.02994i	−0.999538	+	0.0304016i	$0.990321\pi$
$110$	−16.1304	−	2.31965i	−1.53797	−	0.221170i
$111$	−0.732988	+	0.732988i	−0.0695722	+	0.0695722i
$112$	1.20356	−	0.258440i	0.113726	−	0.0244203i
$113$	−4.03671	+	2.93284i	−0.379742	+	0.275899i	−0.761239	−	0.648471i	$-0.775409\pi$
$113$	−4.03671	+	2.93284i	−0.379742	+	0.275899i	0.381497	+	0.924370i	$0.375409\pi$
$114$	0.463953	+	0.880719i	0.0434532	+	0.0824869i
$115$	−4.64794	−	2.36825i	−0.433423	−	0.220840i
$116$	−10.0570	−	6.89658i	−0.933766	−	0.640332i
$117$	−9.29470	−	5.43888i	−0.859296	−	0.502825i
$118$	−5.27740	+	0.909646i	−0.485824	+	0.0837397i
$119$	1.14523	−	0.583525i	0.104983	−	0.0534917i
$120$	−0.221955	−	1.10683i	−0.0202617	−	0.101039i
$121$	8.89087	−	6.47708i	0.808261	−	0.588825i
$122$	−2.46153	−	7.23908i	−0.222857	−	0.655395i
$123$	0.220196	−	0.112196i	0.0198544	−	0.0101163i
$124$	−6.56577	+	3.57376i	−0.589624	+	0.320934i
$125$	1.12583	+	7.10820i	0.100697	+	0.635776i
$126$	−0.185861	+	1.28657i	−0.0165578	+	0.114616i
$127$	2.45217	+	7.54699i	0.217595	+	0.669687i	0.998959	+	0.0456124i	$0.0145239\pi$
$127$	2.45217	+	7.54699i	0.217595	+	0.669687i	−0.781365	+	0.624075i	$0.785476\pi$
$128$	−11.2624	+	1.07620i	−0.995466	+	0.0951232i
$129$	0.738031	+	1.01581i	0.0649800	+	0.0894373i
$130$	−11.0417	+	13.8541i	−0.968420	+	1.21509i
$131$		−	3.23403i		−	0.282558i	−0.989970	−	0.141279i	$-0.954878\pi$
$131$		−	3.23403i		−	0.282558i	0.989970	−	0.141279i	$-0.0451215\pi$
$132$	0.628692	+	0.430533i	0.0547206	+	0.0374731i
$133$	−1.88574			−0.163515
$134$	−7.39624	−	7.19761i	−0.638938	−	0.621779i
$135$	2.35999	+	0.373786i	0.203116	+	0.0321704i
$136$	−11.0765	+	4.10598i	−0.949804	+	0.352085i
$137$	−2.67402	+	5.24806i	−0.228457	+	0.448372i	−0.976570	−	0.215199i	$-0.930960\pi$
$137$	−2.67402	+	5.24806i	−0.228457	+	0.448372i	0.748113	+	0.663571i	$0.230960\pi$
$138$	0.146040	+	0.195360i	0.0124318	+	0.0166301i
$139$	0.483698	−	0.665754i	0.0410268	−	0.0564685i	−0.788011	−	0.615661i	$-0.788889\pi$
$139$	0.483698	−	0.665754i	0.0410268	−	0.0564685i	0.829038	+	0.559193i	$0.188889\pi$
$140$	2.05104	+	0.605228i	0.173345	+	0.0511511i
$141$	0.217764	−	0.110956i	0.0183390	−	0.00934421i
$142$	−9.43158	+	19.1504i	−0.791481	+	1.60707i
$143$	−1.18819	−	11.8991i	−0.0993614	−	0.995051i
$144$	3.06817	−	11.5465i	0.255681	−	0.962211i
$145$	−9.61742	−	18.8753i	−0.798683	−	1.56750i
$146$	−2.57059	−	14.9135i	−0.212743	−	1.23425i
$147$	−0.641736	−	0.466249i	−0.0529295	−	0.0384555i
$148$	3.30740	+	17.7422i	0.271866	+	1.45840i
$149$	2.58593	+	1.31760i	0.211847	+	0.107942i	0.556695	−	0.830717i	$-0.312069\pi$
$149$	2.58593	+	1.31760i	0.211847	+	0.107942i	−0.344847	+	0.938659i	$0.612069\pi$
$150$	0.340090	−	1.09728i	0.0277683	−	0.0895928i
$151$	−3.14279	+	19.8428i	−0.255756	+	1.61478i	0.441023	+	0.897496i	$0.354616\pi$
$151$	−3.14279	+	19.8428i	−0.255756	+	1.61478i	−0.696779	+	0.717286i	$0.745384\pi$
$152$	17.2144	+	2.01025i	1.39627	+	0.163053i
$153$		−	12.4745i		−	1.00851i
$154$	−1.27667	+	0.673584i	−0.102877	+	0.0542789i
$155$	−12.9862			−1.04307
$156$	0.749367	−	0.353026i	0.0599974	−	0.0282647i
$157$	3.61196	−	2.62425i	0.288266	−	0.209438i	−0.434249	−	0.900793i	$-0.642986\pi$
$157$	3.61196	−	2.62425i	0.288266	−	0.209438i	0.722515	+	0.691355i	$0.242986\pi$
$158$	16.7406	+	5.18857i	1.33181	+	0.412780i
$159$	−0.302807	+	0.0983879i	−0.0240141	+	0.00780267i
$160$	−18.0781	−	7.71140i	−1.42920	−	0.609640i
$161$	−0.456370	+	0.0722819i	−0.0359670	+	0.00569661i
$162$	10.2610	+	7.24374i	0.806177	+	0.569122i
$163$	−1.90085	−	3.73062i	−0.148886	−	0.292205i	0.804503	−	0.593948i	$-0.202432\pi$
$163$	−1.90085	−	3.73062i	−0.148886	−	0.292205i	−0.953389	+	0.301743i	$0.902432\pi$
$164$	0.557183	−	4.26648i	0.0435086	−	0.333156i
$165$	0.601708	+	1.17904i	0.0468429	+	0.0917885i
$166$	9.48553	−	19.2600i	0.736220	−	1.49486i
$167$	6.71972	+	13.1882i	0.519988	+	1.02053i	0.990419	+	0.138097i	$0.0440985\pi$
$167$	6.71972	+	13.1882i	0.519988	+	1.02053i	−0.470431	+	0.882437i	$0.655901\pi$
$168$	−0.0735307	−	0.0677588i	−0.00567302	−	0.00522771i
$169$	−11.8136	−	5.42586i	−0.908735	−	0.417374i
$170$	−20.3108	−	2.93414i	−1.55776	−	0.225039i
$171$	−8.30885	+	16.3070i	−0.635394	+	1.24703i
$172$	21.8529	−	0.594964i	1.66626	−	0.0453656i
$173$	−5.75929	−	7.92699i	−0.437871	−	0.602678i	0.531866	−	0.846828i	$-0.321491\pi$
$173$	−5.75929	−	7.92699i	−0.437871	−	0.602678i	−0.969737	+	0.244151i	$0.921491\pi$
$174$	0.0134802	+	0.990432i	0.00102193	+	0.0750845i
$175$	1.53881	+	1.53881i	0.116323	+	0.116323i
$176$	12.3724	−	4.78798i	0.932602	−	0.360907i
$177$	0.307584	+	0.307584i	0.0231195	+	0.0231195i
$178$	−8.75009	−	8.51510i	−0.655847	−	0.638234i
$179$	18.0954	−	13.1471i	1.35251	−	0.982658i	0.353631	−	0.935385i	$-0.384947\pi$
$179$	18.0954	−	13.1471i	1.35251	−	0.982658i	0.998882	−	0.0472731i	$-0.0150531\pi$
$180$	14.2709	−	15.0697i	1.06369	−	1.12323i
$181$	−7.51113	+	2.44051i	−0.558298	+	0.181402i	−0.574555	−	0.818466i	$-0.694825\pi$
$181$	−7.51113	+	2.44051i	−0.558298	+	0.181402i	0.0162574	+	0.999868i	$0.494825\pi$
$182$	−0.0699439	+	1.56765i	−0.00518459	+	0.116202i
$183$	−0.365058	+	0.502460i	−0.0269859	+	0.0371429i
$184$	4.24311	−	0.173338i	0.312806	−	0.0127786i
$185$	−9.68849	+	29.8181i	−0.712312	+	2.19227i
$186$	0.544724	+	0.268276i	0.0399411	+	0.0196710i
$187$	11.2013	−	8.14923i	0.819121	−	0.595931i
$188$	0.551029	−	4.21936i	0.0401879	−	0.307728i
$189$	0.188577	−	0.0960847i	0.0137169	−	0.00698913i
$190$	24.5964	+	17.3639i	1.78441	+	1.25971i
$191$	−12.7500	+	17.5489i	−0.922558	+	1.26979i	0.0401342	+	0.999194i	$0.487221\pi$
$191$	−12.7500	+	17.5489i	−0.922558	+	1.26979i	−0.962692	+	0.270598i	$0.912779\pi$
$192$	0.599007	+	0.696935i	0.0432296	+	0.0502969i
$193$	−4.32796	+	8.49410i	−0.311533	+	0.611418i	−0.992686	−	0.120723i	$-0.961479\pi$
$193$	−4.32796	+	8.49410i	−0.311533	+	0.611418i	0.681153	+	0.732141i	$0.261479\pi$
$194$	−4.21501	−	8.00133i	−0.302620	−	0.574462i
$195$	1.43658	+	0.0836994i	0.102876	+	0.00599384i
$196$	−13.0136	+	4.62359i	−0.929545	+	0.330257i
$197$	0.765346	−	0.765346i	0.0545286	−	0.0545286i	−0.679317	−	0.733845i	$-0.737724\pi$
$197$	0.765346	−	0.765346i	0.0545286	−	0.0545286i	0.733845	+	0.679317i	$0.237724\pi$
$198$	0.199662	+	14.0079i	0.0141894	+	0.995500i
$199$	−19.4693			−1.38014			−0.690070	−	0.723742i	$-0.742420\pi$
$199$	−19.4693			−1.38014			−0.690070	+	0.723742i	$0.742420\pi$
$200$	−12.4069	−	15.6877i	−0.877301	−	1.10929i
$201$	−0.131138	+	0.827974i	−0.00924978	+	0.0584008i
$202$	3.34660	+	1.03724i	0.235466	+	0.0729800i
$203$	−1.67190	−	0.851874i	−0.117344	−	0.0597899i
$204$	0.791349	+	0.542669i	0.0554055	+	0.0379944i
$205$	4.39349	−	6.04711i	0.306854	−	0.422349i
$206$	9.06488	+	6.39936i	0.631580	+	0.445865i
$207$	−1.38577	+	4.26496i	−0.0963176	+	0.296435i
$208$	2.30965	−	14.2361i	0.160146	−	0.987093i
$209$	−20.0706	+	3.19209i	−1.38831	+	0.220802i
$210$	−0.0559203	−	0.164455i	−0.00385886	−	0.0113485i
$211$	−5.25709	−	1.70813i	−0.361913	−	0.117593i	0.122415	−	0.992479i	$-0.460936\pi$
$211$	−5.25709	−	1.70813i	−0.361913	−	0.117593i	−0.484328	+	0.874886i	$0.660936\pi$
$212$	−1.56887	+	5.31671i	−0.107751	+	0.365153i
$213$	1.71261	−	0.271251i	0.117346	−	0.0185858i
$214$	−1.16231	−	1.55484i	−0.0794540	−	0.106287i
$215$	33.8375	+	17.2411i	2.30770	+	1.17583i
$216$	−1.82389	+	0.676099i	−0.124100	+	0.0460027i
$217$	−0.930585	+	0.676109i	−0.0631722	+	0.0458973i
$218$	14.9985	−	15.4124i	1.01583	−	1.04386i
$219$	−0.869208	+	0.869208i	−0.0587356	+	0.0587356i
$220$	22.8544	+	2.96973i	1.54084	+	0.200219i
$221$	−1.48663	−	14.9852i	−0.100001	−	1.00801i
$222$	1.02240	−	1.05061i	0.0686189	−	0.0705125i
$223$	−14.6314	−	2.31739i	−0.979794	−	0.155184i	−0.354062	−	0.935222i	$-0.615200\pi$
$223$	−14.6314	−	2.31739i	−0.979794	−	0.155184i	−0.625732	+	0.780038i	$0.715200\pi$
$224$	−1.69696	+	0.388619i	−0.113383	+	0.0259657i
$225$	20.0871	−	6.52670i	1.33914	−	0.435113i
$226$	5.65179	−	4.22497i	0.375952	−	0.281041i
$227$	−3.71088	−	23.4296i	−0.246300	−	1.55508i	−0.732218	−	0.681071i	$-0.761515\pi$
$227$	−3.71088	−	23.4296i	−0.246300	−	1.55508i	0.485918	−	0.874004i	$-0.338485\pi$
$228$	−0.673019	−	1.23648i	−0.0445718	−	0.0818879i
$229$	9.16090	−	4.66771i	0.605369	−	0.308451i	−0.124307	−	0.992244i	$-0.539671\pi$
$229$	9.16090	−	4.66771i	0.605369	−	0.308451i	0.729676	+	0.683793i	$0.239671\pi$
$230$	6.61816	+	3.25944i	0.436388	+	0.214921i
$231$	0.104504	+	0.0531627i	0.00687584	+	0.00349785i
$232$	14.3541	+	9.55878i	0.942394	+	0.627564i
$233$	−15.4186	−	5.00980i	−1.01010	−	0.328203i	−0.243208	−	0.969974i	$-0.578200\pi$
$233$	−15.4186	−	5.00980i	−1.01010	−	0.328203i	−0.766896	+	0.641771i	$0.778200\pi$
$234$	13.2482	+	7.51214i	0.866059	+	0.491084i
$235$	4.34496	−	5.98033i	0.283434	−	0.390113i
$236$	7.44517	−	1.38789i	0.484639	−	0.0903437i
$237$	−0.439920	−	1.35393i	−0.0285759	−	0.0879475i
$238$	−1.60822	+	0.847195i	−0.104246	+	0.0549155i
$239$	15.5694	+	2.46595i	1.00710	+	0.159509i	0.638127	−	0.769931i	$-0.279709\pi$
$239$	15.5694	+	2.46595i	1.00710	+	0.159509i	0.368973	+	0.929440i	$0.379709\pi$
$240$	0.335166	+	1.56087i	0.0216349	+	0.100754i
$241$	6.29531	+	6.29531i	0.405517	+	0.405517i	0.880172	−	0.474655i	$-0.157427\pi$
$241$	6.29531	+	6.29531i	0.405517	+	0.405517i	−0.474655	+	0.880172i	$0.657427\pi$
$242$	−12.4478	+	9.33024i	−0.800172	+	0.599770i
$243$		−	3.08339i		−	0.197800i
$244$	3.62013	+	10.1893i	0.231755	+	0.652302i
$245$	−23.6963	−	3.75312i	−1.51390	−	0.239778i
$246$	−0.309216	+	0.162892i	−0.0197149	+	0.0103856i
$247$	−8.03776	+	20.5792i	−0.511430	+	1.30943i
$248$	9.21576	−	5.17996i	0.585202	−	0.328928i
$249$	−1.72240	+	0.272802i	−0.109153	+	0.0172881i
$250$	−1.72882	−	10.0299i	−0.109340	−	0.634347i
$251$	5.97435	−	18.3871i	0.377097	−	1.16059i	−0.564955	−	0.825121i	$-0.691107\pi$
$251$	5.97435	−	18.3871i	0.377097	−	1.16059i	0.942053	−	0.335465i	$-0.108893\pi$
$252$	0.238061	−	1.82289i	0.0149964	−	0.114831i
$253$	−4.73493	+	1.54184i	−0.297682	+	0.0969345i
$254$	−3.61282	−	10.6249i	−0.226688	−	0.666664i
$255$	0.756763	+	1.48523i	0.0473903	+	0.0930087i
$256$	15.9053	−	1.73859i	0.994079	−	0.108662i
$257$	−9.98315	+	13.7406i	−0.622732	+	0.857117i	−0.997548	−	0.0699823i	$-0.977706\pi$
$257$	−9.98315	+	13.7406i	−0.622732	+	0.857117i	0.374817	+	0.927099i	$0.377706\pi$
$258$	−1.06319	−	1.42224i	−0.0661912	−	0.0885447i
$259$	0.858169	+	2.64117i	0.0533240	+	0.164115i
$260$	15.3472	−	19.8034i	0.951794	−	1.22816i
$261$	−14.7332	+	10.7043i	−0.911964	+	0.662580i
$262$	0.0622430	+	4.57318i	0.00384539	+	0.282532i
$263$			14.0622i			0.867110i	0.901127	+	0.433555i	$0.142741\pi$
$263$			14.0622i			0.867110i	−0.901127	+	0.433555i	$0.857259\pi$
$264$	−0.897309	−	0.596709i	−0.0552255	−	0.0367249i
$265$	−6.80936	+	6.80936i	−0.418296	+	0.418296i
$266$	2.66660	−	0.0362936i	0.163500	−	0.00222530i
$267$	−0.155142	+	0.979531i	−0.00949457	+	0.0599463i
$268$	10.5974	+	10.0357i	0.647341	+	0.613026i
$269$	−3.18067	−	9.78910i	−0.193929	−	0.596852i	−0.999987	−	0.00501594i	$-0.998403\pi$
$269$	−3.18067	−	9.78910i	−0.193929	−	0.596852i	0.806059	−	0.591836i	$-0.201597\pi$
$270$	−3.34442	−	0.483143i	−0.203535	−	0.0294031i
$271$	7.94762	−	1.25878i	0.482784	−	0.0764654i	0.0897013	−	0.995969i	$-0.471409\pi$
$271$	7.94762	−	1.25878i	0.482784	−	0.0764654i	0.393082	+	0.919503i	$0.371409\pi$
$272$	15.5841	−	6.01937i	0.944925	−	0.364978i
$273$	0.107303	−	0.0687961i	0.00649426	−	0.00416373i
$274$	3.68028	−	7.47266i	0.222334	−	0.451440i
$275$	18.9828	+	13.7732i	1.14471	+	0.830555i
$276$	−0.210273	−	0.273444i	−0.0126569	−	0.0164594i
$277$	12.0219	+	3.90616i	0.722327	+	0.234698i	0.647032	−	0.762463i	$-0.276010\pi$
$277$	12.0219	+	3.90616i	0.722327	+	0.234698i	0.0752953	+	0.997161i	$0.476010\pi$
$278$	−0.671176	+	0.950740i	−0.0402545	+	0.0570216i
$279$	1.74639	+	11.0263i	0.104554	+	0.660127i
$280$	−2.91199	−	0.816368i	−0.174025	−	0.0487873i
$281$	13.0176	−	25.5485i	0.776566	−	1.52410i	−0.0734263	−	0.997301i	$-0.523393\pi$
$281$	13.0176	−	25.5485i	0.776566	−	1.52410i	0.849992	−	0.526796i	$-0.176607\pi$
$282$	−0.305801	+	0.161093i	−0.0182102	+	0.00959292i
$283$	1.55604	−	1.13053i	0.0924969	−	0.0672029i	−0.540576	−	0.841295i	$-0.681794\pi$
$283$	1.55604	−	1.13053i	0.0924969	−	0.0672029i	0.633072	+	0.774093i	$0.281794\pi$
$284$	12.9685	−	27.2618i	0.769537	−	1.61769i
$285$		−	2.44558i		−	0.144864i
$286$	1.90921	+	16.8034i	0.112894	+	0.993607i
$287$		−	0.662075i		−	0.0390811i
$288$	−4.11642	+	16.3868i	−0.242563	+	0.965601i
$289$	0.358852	−	0.260721i	0.0211089	−	0.0153365i
$290$	13.9631	+	26.5061i	0.819942	+	1.55649i
$291$	−0.333497	+	0.654525i	−0.0195499	+	0.0383689i
$292$	3.92205	+	21.0394i	0.229521	+	1.23124i
$293$	−2.78685	−	17.5955i	−0.162810	−	1.02794i	−0.924828	−	0.380385i	$-0.875792\pi$
$293$	−2.78685	−	17.5955i	−0.162810	−	1.02794i	0.762019	−	0.647555i	$-0.224208\pi$
$294$	0.916441	+	0.646963i	0.0534479	+	0.0377316i
$295$	12.5126	+	4.06559i	0.728511	+	0.236708i
$296$	−5.01841	−	25.0253i	−0.291689	−	1.45456i
$297$	1.84443	−	1.34187i	0.107025	−	0.0778633i
$298$	−3.68207	−	1.81342i	−0.213297	−	0.105049i
$299$	−1.15641	+	5.28848i	−0.0668767	+	0.305841i
$300$	−0.459797	+	1.55819i	−0.0265464	+	0.0899624i
$301$	3.32242	−	0.526220i	0.191501	−	0.0303308i
$302$	4.06226	−	28.1198i	0.233757	−	1.61811i
$303$	−0.0879439	−	0.270663i	−0.00505224	−	0.0155492i
$304$	−24.3812	−	2.51134i	−1.39836	−	0.144035i
$305$	−2.93858	+	18.5535i	−0.168263	+	1.06237i
$306$	0.240089	+	17.6400i	0.0137249	+	1.00841i
$307$	−16.4409	+	16.4409i	−0.938334	+	0.938334i	−0.998206	−	0.0598725i	$-0.980931\pi$
$307$	−16.4409	+	16.4409i	−0.938334	+	0.938334i	0.0598725	+	0.998206i	$0.480931\pi$
$308$	1.79235	−	0.977074i	0.102129	−	0.0556740i
$309$		−	0.901307i		−	0.0512736i
$310$	18.3635	−	0.249936i	1.04298	−	0.0141954i
$311$	10.2363	−	7.43711i	0.580447	−	0.421720i	−0.258438	−	0.966028i	$-0.583208\pi$
$311$	10.2363	−	7.43711i	0.580447	−	0.421720i	0.838885	+	0.544308i	$0.183208\pi$
$312$	−1.05287	+	0.513631i	−0.0596071	+	0.0290786i
$313$	−9.16914	−	28.2197i	−0.518270	−	1.59507i	−0.777252	−	0.629190i	$-0.783387\pi$
$313$	−9.16914	−	28.2197i	−0.518270	−	1.59507i	0.258981	−	0.965882i	$-0.416613\pi$
$314$	−5.05711	+	3.78042i	−0.285389	+	0.213341i
$315$	1.87715	−	2.58368i	0.105766	−	0.145574i
$316$	−23.7725	−	7.01487i	−1.33731	−	0.394617i
$317$	−5.65505	−	11.0987i	−0.317619	−	0.623363i	0.675904	−	0.736989i	$-0.263753\pi$
$317$	−5.65505	−	11.0987i	−0.317619	−	0.623363i	−0.993524	+	0.113627i	$0.963753\pi$
$318$	0.426300	−	0.144957i	0.0239057	−	0.00812876i
$319$	−19.2365	−	6.23666i	−1.07704	−	0.349186i
$320$	25.7124	+	10.5566i	1.43737	+	0.590133i
$321$	−0.0487268	+	0.149966i	−0.00271966	+	0.00837027i
$322$	0.643953	−	0.110996i	0.0358861	−	0.00618556i
$323$	−25.2770	+	4.00348i	−1.40645	+	0.222759i
$324$	−14.6493	−	10.0458i	−0.813848	−	0.558098i
$325$	23.3521	−	10.2341i	1.29534	−	0.567687i
$326$	2.75976	+	5.23883i	0.152849	+	0.290152i
$327$	−1.72535	−	0.273268i	−0.0954119	−	0.0151118i
$328$	−0.705788	+	6.04388i	−0.0389706	+	0.333717i
$329$		−	0.654763i		−	0.0360982i
$330$	−0.873557	−	1.65569i	−0.0480878	−	0.0911425i
$331$	−7.40531	−	7.40531i	−0.407033	−	0.407033i	0.473670	−	0.880702i	$-0.342929\pi$
$331$	−7.40531	−	7.40531i	−0.407033	−	0.407033i	−0.880702	+	0.473670i	$0.842929\pi$
$332$	−13.0426	+	27.4177i	−0.715808	+	1.50474i
$333$	26.6208	+	4.21633i	1.45881	+	0.231053i
$334$	−9.75607	−	18.5199i	−0.533828	−	1.01336i
$335$	7.83504	+	24.1138i	0.428074	+	1.31748i
$336$	0.105283	+	0.0944014i	0.00574364	+	0.00515002i
$337$	18.4966	−	25.4583i	1.00757	−	1.38680i	0.0870089	−	0.996208i	$-0.472269\pi$
$337$	18.4966	−	25.4583i	1.00757	−	1.38680i	0.920562	−	0.390595i	$-0.127731\pi$
$338$	16.8098	+	7.44524i	0.914331	+	0.404968i
$339$	−0.545121	−	0.177121i	−0.0296069	−	0.00961987i
$340$	28.7776	+	3.75822i	1.56068	+	0.203818i
$341$	−8.76001	+	8.77128i	−0.474381	+	0.474992i
$342$	11.4355	−	23.2194i	0.618364	−	1.25556i
$343$	−3.81291	+	1.94277i	−0.205878	+	0.104900i
$344$	−30.8903	+	1.26192i	−1.66549	+	0.0680379i
$345$	−0.0937409	−	0.591857i	−0.00504684	−	0.0318645i
$346$	8.29668	+	11.0986i	0.446032	+	0.596663i
$347$	22.7224	−	7.38295i	1.21980	−	0.396337i	0.372792	−	0.927915i	$-0.378401\pi$
$347$	22.7224	−	7.38295i	1.21980	−	0.396337i	0.847010	+	0.531578i	$0.178401\pi$
$348$	−0.0381243	−	1.40029i	−0.00204368	−	0.0750636i
$349$	−1.19318	−	0.188981i	−0.0638696	−	0.0101159i	0.124418	−	0.992230i	$-0.460294\pi$
$349$	−1.19318	−	0.188981i	−0.0638696	−	0.0101159i	−0.188287	+	0.982114i	$0.560294\pi$
$350$	−2.20562	−	2.14639i	−0.117895	−	0.114729i
$351$	−0.244791	−	2.46750i	−0.0130660	−	0.131705i
$352$	−17.4034	+	7.00872i	−0.927604	+	0.373566i
$353$	24.8891	−	24.8891i	1.32472	−	1.32472i	0.414805	−	0.909910i	$-0.363850\pi$
$353$	24.8891	−	24.8891i	1.32472	−	1.32472i	0.909910	−	0.414805i	$-0.136150\pi$
$354$	−0.440869	−	0.429030i	−0.0234319	−	0.0228027i
$355$	42.4285	−	30.8261i	2.25187	−	1.63608i
$356$	12.5372	+	11.8726i	0.664472	+	0.629249i
$357$	0.131556	+	0.0670311i	0.00696268	+	0.00354766i
$358$	−25.3353	+	18.9393i	−1.33901	+	1.00097i
$359$	18.8137	−	2.97980i	0.992950	−	0.157268i	0.361240	−	0.932473i	$-0.382353\pi$
$359$	18.8137	−	2.97980i	0.992950	−	0.157268i	0.631710	+	0.775205i	$0.282353\pi$
$360$	−19.8902	+	21.5845i	−1.04831	+	1.13760i
$361$	17.6392	+	5.73132i	0.928379	+	0.301649i
$362$	10.5744	−	3.59565i	0.555777	−	0.188983i
$363$	1.20226	+	0.388928i	0.0631021	+	0.0204134i
$364$	0.0687350	−	2.21814i	0.00360269	−	0.116262i
$365$	−11.4890	+	35.3595i	−0.601362	+	1.85080i
$366$	0.506552	−	0.717546i	0.0264779	−	0.0375067i
$367$	2.95275	−	4.06412i	0.154132	−	0.212145i	−0.724967	−	0.688784i	$-0.758145\pi$
$367$	2.95275	−	4.06412i	0.154132	−	0.212145i	0.879099	+	0.476639i	$0.158145\pi$
$368$	−5.99677	+	0.326778i	−0.312603	+	0.0170345i
$369$	−5.72532	−	2.91720i	−0.298048	−	0.151863i
$370$	13.1264	−	42.3517i	0.682411	−	2.20176i
$371$	−0.133435	+	0.842477i	−0.00692761	+	0.0437392i
$372$	−0.775448	−	0.368881i	−0.0402051	−	0.0191256i
$373$	12.8576			0.665741			0.332870	−	0.942973i	$-0.391983\pi$
$373$	12.8576			0.665741			0.332870	+	0.942973i	$0.391983\pi$
$374$	−15.6827	+	11.7393i	−0.810935	+	0.607023i
$375$	−0.584576	+	0.584576i	−0.0301874	+	0.0301874i
$376$	−0.697993	+	5.97713i	−0.0359962	+	0.308247i
$377$	−16.4228	+	14.6145i	−0.845818	+	0.752685i
$378$	−0.264814	+	0.139501i	−0.0136206	+	0.00717516i
$379$	−0.578959	+	1.13627i	−0.0297391	+	0.0583663i	−0.905398	−	0.424564i	$-0.860427\pi$
$379$	−0.578959	+	1.13627i	−0.0297391	+	0.0583663i	0.875659	+	0.482930i	$0.160427\pi$
$380$	−35.1155	−	24.0806i	−1.80139	−	1.23531i
$381$	−0.535800	+	0.737466i	−0.0274499	+	0.0377815i
$382$	17.6918	−	25.0610i	0.905192	−	1.28223i
$383$	−27.2988	+	13.9094i	−1.39490	+	0.710740i	−0.979976	−	0.199114i	$-0.936193\pi$
$383$	−27.2988	+	13.9094i	−1.39490	+	0.710740i	−0.414929	+	0.909854i	$0.636193\pi$
$384$	−0.860458	−	0.973995i	−0.0439101	−	0.0497040i
$385$	3.54626	−	0.00227995i	0.180734	−	0.000116197i
$386$	5.95661	−	12.0947i	0.303183	−	0.615601i
$387$	10.0885	−	31.0493i	0.512829	−	1.57833i
$388$	6.11437	+	11.2334i	0.310410	+	0.570290i
$389$	−15.9092	+	21.8972i	−0.806629	+	1.11023i	0.185205	+	0.982700i	$0.440705\pi$
$389$	−15.9092	+	21.8972i	−0.806629	+	1.11023i	−0.991835	+	0.127530i	$0.959295\pi$
$390$	−2.03306	−	0.0907089i	−0.102948	−	0.00459322i
$391$	−5.96383	+	1.93777i	−0.301604	+	0.0979971i
$392$	18.3134	−	6.78861i	0.924964	−	0.342876i
$393$	0.300551	−	0.218363i	0.0151608	−	0.0110150i
$394$	−1.06753	+	1.09699i	−0.0537815	+	0.0552657i
$395$	−30.4465	−	30.4465i	−1.53193	−	1.53193i
$396$	−0.551939	−	19.8045i	−0.0277360	−	0.995215i
$397$	−4.04693	−	4.04693i	−0.203110	−	0.203110i	0.598221	−	0.801331i	$-0.295874\pi$
$397$	−4.04693	−	4.04693i	−0.203110	−	0.203110i	−0.801331	+	0.598221i	$0.795874\pi$
$398$	27.5312	−	0.374712i	1.38001	−	0.0187826i
$399$	−0.127326	−	0.175250i	−0.00637429	−	0.00877346i
$400$	17.8463	+	21.9449i	0.892316	+	1.09725i
$401$	−9.69394	+	19.0254i	−0.484092	+	0.950085i	0.511762	+	0.859127i	$0.328993\pi$
$401$	−9.69394	+	19.0254i	−0.484092	+	0.950085i	−0.995855	+	0.0909577i	$0.971007\pi$
$402$	0.169505	−	1.17335i	0.00845414	−	0.0585213i
$403$	3.41191	+	13.0374i	0.169959	+	0.649437i
$404$	−4.75233	−	1.40233i	−0.236437	−	0.0697687i
$405$	−14.0090	−	27.4942i	−0.696113	−	1.36620i
$406$	2.38060	+	1.17244i	0.118147	+	0.0581874i
$407$	13.6046	+	26.6582i	0.674355	+	1.32140i
$408$	−1.12948	−	0.752148i	−0.0559174	−	0.0372369i
$409$	−10.7937	−	21.1839i	−0.533715	−	1.04748i	−0.987685	−	0.156458i	$-0.949992\pi$
$409$	−10.7937	−	21.1839i	−0.533715	−	1.04748i	0.453969	−	0.891017i	$-0.350008\pi$
$410$	−6.09637	+	8.63568i	−0.301078	+	0.426486i
$411$	−0.668275	+	0.105844i	−0.0329636	+	0.00522092i
$412$	−12.9417	−	8.87476i	−0.637590	−	0.437228i
$413$	1.10832	−	0.360114i	0.0545367	−	0.0177201i
$414$	1.87751	−	6.05767i	0.0922744	−	0.297718i
$415$	−42.6712	+	31.0024i	−2.09465	+	1.52185i
$416$	−2.99205	+	20.1754i	−0.146697	+	0.989181i
$417$	0.0945307			0.00462919
$418$	28.3200	−	4.90016i	1.38518	−	0.239675i
$419$		−	15.7621i		−	0.770029i	−0.922911	−	0.385015i	$-0.874196\pi$
$419$		−	15.7621i		−	0.770029i	0.922911	−	0.385015i	$-0.125804\pi$
$420$	0.0822410	+	0.231477i	0.00401295	+	0.0112949i
$421$	−0.00801259	+	0.0505895i	−0.000390510	+	0.00246558i	−0.987883	−	0.155202i	$-0.950397\pi$
$421$	−0.00801259	+	0.0505895i	−0.000390510	+	0.00246558i	0.987492	+	0.157667i	$0.0503973\pi$
$422$	7.46683	+	2.31426i	0.363480	+	0.112656i
$423$	−5.66208	−	2.88498i	−0.275300	−	0.140272i
$424$	2.11619	−	7.54846i	0.102771	−	0.366586i
$425$	23.8935	+	17.3596i	1.15901	+	0.842066i
$426$	−2.41655	+	0.416532i	−0.117082	+	0.0201811i
$427$	0.755386	+	1.48253i	0.0365557	+	0.0717446i
$428$	1.67353	+	2.17630i	0.0808931	+	0.105195i
$429$	1.02560	−	0.913855i	0.0495165	−	0.0441213i
$430$	−48.1809	−	23.7291i	−2.32349	−	1.14432i
$431$	−10.2479	+	5.22156i	−0.493624	+	0.251514i	−0.683037	−	0.730384i	$-0.739341\pi$
$431$	−10.2479	+	5.22156i	−0.493624	+	0.251514i	0.189414	+	0.981897i	$0.439341\pi$
$432$	2.56611	−	0.991164i	0.123462	−	0.0476874i
$433$	−1.00247	+	1.37979i	−0.0481759	+	0.0663084i	−0.832425	−	0.554137i	$-0.813048\pi$
$433$	−1.00247	+	1.37979i	−0.0481759	+	0.0663084i	0.784249	+	0.620446i	$0.213048\pi$
$434$	1.30291	−	0.973985i	0.0625417	−	0.0467528i
$435$	1.10478	−	2.16825i	0.0529701	−	0.103960i
$436$	−20.9125	+	22.0831i	−1.00153	+	1.05759i
$437$	9.08675	+	1.43920i	0.434678	+	0.0688463i
$438$	1.21240	−	1.24586i	0.0579308	−	0.0595295i
$439$	−40.3255			−1.92463			−0.962315	−	0.271937i	$-0.912336\pi$
$439$	−40.3255			−1.92463			−0.962315	+	0.271937i	$0.912336\pi$
$440$	−32.3751	−	3.75958i	−1.54342	−	0.179231i
$441$			20.6248i			0.982131i
$442$	2.39062	+	21.1617i	0.113710	+	1.00656i
$443$	11.8743	+	16.3435i	0.564163	+	0.776504i	0.991848	−	0.127424i	$-0.0406707\pi$
$443$	11.8743	+	16.3435i	0.564163	+	0.776504i	−0.427685	+	0.903928i	$0.640671\pi$
$444$	−1.42554	+	1.50533i	−0.0676529	+	0.0714398i
$445$	9.26920	+	28.5277i	0.439402	+	1.35234i
$446$	20.7347	+	2.99538i	0.981815	+	0.141836i
$447$	0.0521536	+	0.329285i	0.00246678	+	0.0155746i
$448$	2.39216	−	0.582200i	0.113019	−	0.0275064i
$449$	−2.32301	+	1.18363i	−0.109630	+	0.0558591i	−0.507945	−	0.861389i	$-0.669595\pi$
$449$	−2.32301	+	1.18363i	−0.109630	+	0.0558591i	0.398316	+	0.917248i	$0.369595\pi$
$450$	−28.2792	+	9.61590i	−1.33310	+	0.453298i
$451$	−1.12073	−	7.04667i	−0.0527730	−	0.331815i
$452$	−7.91079	+	6.08323i	−0.372092	+	0.286131i
$453$	−2.05627	+	1.04772i	−0.0966120	+	0.0492262i
$454$	5.69842	+	33.0599i	0.267440	+	1.55158i
$455$	1.94705	−	3.32738i	0.0912791	−	0.155990i
$456$	0.975502	+	1.73553i	0.0456821	+	0.0812737i
$457$	−22.0278	−	11.2237i	−1.03042	−	0.525024i	−0.144811	−	0.989459i	$-0.546257\pi$
$457$	−22.0278	−	11.2237i	−1.03042	−	0.525024i	−0.885607	+	0.464435i	$0.846257\pi$
$458$	−12.8644	+	6.77684i	−0.601115	+	0.316661i
$459$	2.32374	−	1.68829i	0.108463	−	0.0788028i
$460$	−9.42135	−	4.48174i	−0.439273	−	0.208962i
$461$	−20.8660	+	20.8660i	−0.971827	+	0.971827i	−0.999614	−	0.0277867i	$-0.991154\pi$
$461$	−20.8660	+	20.8660i	−0.971827	+	0.971827i	0.0277867	+	0.999614i	$0.491154\pi$
$462$	−0.148800	−	0.0731651i	−0.00692280	−	0.00340395i
$463$	−20.5416	+	20.5416i	−0.954647	+	0.954647i	−0.999015	−	0.0443682i	$-0.985873\pi$
$463$	−20.5416	+	20.5416i	−0.954647	+	0.954647i	0.0443682	+	0.999015i	$0.485873\pi$
$464$	−20.4819	−	13.2406i	−0.950847	−	0.614681i
$465$	−0.876833	−	1.20686i	−0.0406621	−	0.0559666i
$466$	21.8996	+	6.78752i	1.01448	+	0.314426i
$467$	0.695970	+	2.14198i	0.0322057	+	0.0991188i	0.965867	−	0.259038i	$-0.0834054\pi$
$467$	0.695970	+	2.14198i	0.0322057	+	0.0991188i	−0.933662	+	0.358157i	$0.883405\pi$
$468$	−18.8786	−	10.3678i	−0.872662	−	0.479252i
$469$	1.81691	+	1.32006i	0.0838971	+	0.0609548i
$470$	−6.02903	+	8.54030i	−0.278099	+	0.393935i
$471$	0.487763	+	0.158484i	0.0224749	+	0.00730255i
$472$	−10.5014	+	2.10588i	−0.483365	+	0.0969308i
$473$	34.4708	−	11.2247i	1.58497	−	0.516114i
$474$	0.648141	+	1.90611i	0.0297701	+	0.0875504i
$475$	−19.6716	−	38.6076i	−0.902593	−	1.77144i
$476$	2.25786	−	1.22896i	0.103489	−	0.0563291i
$477$	6.69741	+	4.86595i	0.306653	+	0.222797i
$478$	−22.0639	−	3.18740i	−1.00918	−	0.145788i
$479$	11.8379	+	6.03170i	0.540886	+	0.275595i	0.703016	−	0.711174i	$-0.251836\pi$
$479$	11.8379	+	6.03170i	0.540886	+	0.275595i	−0.162130	+	0.986769i	$0.551836\pi$
$480$	−0.503993	−	2.20075i	−0.0230040	−	0.100450i
$481$	32.4811	+	1.89244i	1.48101	+	0.0862878i
$482$	−9.02326	−	8.78093i	−0.410998	−	0.399961i
$483$	−0.0375317	−	0.0375317i	−0.00170775	−	0.00170775i
$484$	17.4226	−	13.4333i	0.791936	−	0.610604i
$485$			22.2181i			1.00887i
$486$	0.0593439	+	4.36017i	0.00269189	+	0.197781i
$487$	31.2169	+	4.94427i	1.41457	+	0.224046i	0.816476	−	0.577379i	$-0.195924\pi$
$487$	31.2169	+	4.94427i	1.41457	+	0.224046i	0.598095	+	0.801425i	$0.295924\pi$
$488$	−5.31527	−	14.3388i	−0.240611	−	0.649087i
$489$	0.218356	−	0.428547i	0.00987438	−	0.0193796i
$490$	33.5808	+	4.85116i	1.51702	+	0.219153i
$491$	4.59819	+	3.34078i	0.207513	+	0.150767i	0.686688	−	0.726952i	$-0.259064\pi$
$491$	4.59819	+	3.34078i	0.207513	+	0.150767i	−0.479175	+	0.877720i	$0.659064\pi$
$492$	0.434122	−	0.236294i	0.0195717	−	0.0106529i
$493$	−24.2191	−	7.86925i	−1.09077	−	0.354413i
$494$	10.9700	−	29.2554i	0.493563	−	1.31626i
$495$	15.6056	−	30.6764i	0.701419	−	1.37880i
$496$	−12.9322	+	7.50227i	−0.580671	+	0.336862i
$497$	1.43549	−	4.41798i	0.0643904	−	0.198173i
$498$	2.43037	−	0.418915i	0.108908	−	0.0187720i
$499$	−0.732841	−	4.62697i	−0.0328065	−	0.207132i	0.965840	−	0.259138i	$-0.0834384\pi$
$499$	−0.732841	−	4.62697i	−0.0328065	−	0.207132i	−0.998647	+	0.0520062i	$0.983438\pi$
$500$	2.63773	+	14.1498i	0.117963	+	0.632800i
$501$	−0.771913	+	1.51496i	−0.0344865	+	0.0676836i
$502$	−8.09433	+	26.1159i	−0.361268	+	1.16561i
$503$	8.00571	+	11.0189i	0.356957	+	0.491309i	0.949298	−	0.314378i	$-0.101796\pi$
$503$	8.00571	+	11.0189i	0.356957	+	0.491309i	−0.592341	+	0.805688i	$0.701796\pi$
$504$	−0.301554	+	2.58230i	−0.0134323	+	0.115025i
$505$	−6.08653	−	6.08653i	−0.270847	−	0.270847i
$506$	6.66590	−	2.27142i	0.296336	−	0.100977i
$507$	−0.293410	−	1.46424i	−0.0130308	−	0.0650290i
$508$	5.31331	+	14.9549i	0.235740	+	0.663517i
$509$	4.35092	−	27.4706i	0.192851	−	1.21761i	−0.681316	−	0.731989i	$-0.738592\pi$
$509$	4.35092	−	27.4706i	0.192851	−	1.21761i	0.874167	−	0.485625i	$-0.161408\pi$
$510$	−1.09871	−	2.08567i	−0.0486517	−	0.0923552i
$511$	1.01765	+	3.13201i	0.0450183	+	0.138552i
$512$	−22.4579	+	2.76463i	−0.992508	+	0.122180i
$513$	−4.16216	+	0.659222i	−0.183764	+	0.0291054i
$514$	13.8525	−	19.6225i	0.611009	−	0.865512i
$515$	−12.3760	−	24.2893i	−0.545353	−	1.07032i
$516$	1.53081	+	1.99070i	0.0673900	+	0.0876357i
$517$	−1.10835	−	6.96884i	−0.0487451	−	0.306489i
$518$	−1.26436	−	3.71832i	−0.0555526	−	0.163374i
$519$	0.347816	−	1.07047i	0.0152674	−	0.0469883i
$520$	−21.3211	+	28.2990i	−0.934991	+	1.24099i
$521$	8.48584	+	6.16532i	0.371771	+	0.270108i	0.757945	−	0.652318i	$-0.226203\pi$
$521$	8.48584	+	6.16532i	0.371771	+	0.270108i	−0.386174	+	0.922426i	$0.626203\pi$
$522$	20.6280	−	15.4203i	0.902862	−	0.674930i
$523$	19.4234	−	6.31104i	0.849325	−	0.275963i	0.148162	−	0.988963i	$-0.452664\pi$
$523$	19.4234	−	6.31104i	0.849325	−	0.275963i	0.701164	+	0.713001i	$0.252664\pi$
$524$	−0.176034	−	6.46566i	−0.00769006	−	0.282454i
$525$	−0.0391065	+	0.246909i	−0.00170675	+	0.0107760i
$526$	−0.270644	−	19.8851i	−0.0118007	−	0.867030i
$527$	−11.0384	+	11.0384i	−0.480839	+	0.480839i
$528$	1.28035	+	0.826526i	0.0557202	+	0.0359699i
$529$	−20.7457			−0.901989
$530$	9.49794	−	9.76005i	0.412564	−	0.423949i
$531$	1.76930	−	11.1709i	0.0767811	−	0.484777i
$532$	−3.77009	+	0.102644i	−0.163454	+	0.00445019i
$533$	−7.22527	−	2.82202i	−0.312961	−	0.122235i
$534$	0.200532	−	1.38812i	0.00867787	−	0.0600700i
$535$	0.746070	+	4.71050i	0.0322554	+	0.203653i
$536$	−15.1788	−	13.9873i	−0.655624	−	0.604159i
$537$	2.44362	+	0.793980i	0.105450	+	0.0342628i
$538$	4.68613	+	13.7814i	0.202034	+	0.594157i
$539$	−18.5197	+	13.4735i	−0.797698	+	0.580346i
$540$	4.73858	+	0.618836i	0.203916	+	0.0266305i
$541$	−9.88366	+	5.03598i	−0.424932	+	0.216514i	−0.653360	−	0.757047i	$-0.726641\pi$
$541$	−9.88366	+	5.03598i	−0.424932	+	0.216514i	0.228428	+	0.973561i	$0.426641\pi$
$542$	−11.2144	+	1.93298i	−0.481698	+	0.0830286i
$543$	−0.733961	−	0.533254i	−0.0314973	−	0.0228841i
$544$	−21.9214	+	8.81182i	−0.939870	+	0.377804i
$545$	−50.2487	+	16.3268i	−2.15242	+	0.699363i
$546$	−0.150411	+	0.0993486i	−0.00643699	+	0.00425173i
$547$	−12.2607	−	16.8754i	−0.524230	−	0.721541i	0.462007	−	0.886876i	$-0.347129\pi$
$547$	−12.2607	−	16.8754i	−0.524230	−	0.721541i	−0.986237	+	0.165335i	$0.947129\pi$
$548$	−5.06040	+	10.6378i	−0.216170	+	0.454424i
$549$	16.1486			0.689203
$550$	−27.1084	−	19.1111i	−1.15591	−	0.814900i
$551$	26.4183	+	26.4183i	1.12546	+	1.12546i
$552$	0.302606	+	0.382625i	0.0128798	+	0.0162856i
$553$	−3.76695	−	0.596626i	−0.160187	−	0.0253711i
$554$	−17.0752	−	5.29225i	−0.725454	−	0.224846i
$555$	−3.42529	+	1.11294i	−0.145395	+	0.0472418i
$556$	0.930800	−	1.35734i	0.0394747	−	0.0575642i
$557$	1.34841	+	8.51350i	0.0571338	+	0.360729i	0.999647	+	0.0265603i	$0.00845541\pi$
$557$	1.34841	+	8.51350i	0.0571338	+	0.360729i	−0.942513	+	0.334168i	$0.891545\pi$
$558$	−2.68176	−	15.5585i	−0.113528	−	0.658643i
$559$	8.41876	−	38.5007i	0.356075	−	1.62841i
$560$	4.13351	+	1.09837i	0.174673	+	0.0464145i
$561$	1.51366	+	0.490742i	0.0639067	+	0.0207191i
$562$	−17.9163	+	36.3782i	−0.755752	+	1.53452i
$563$	−2.40767	+	7.41003i	−0.101471	+	0.312296i	−0.988886	−	0.148676i	$-0.952499\pi$
$563$	−2.40767	+	7.41003i	−0.101471	+	0.312296i	0.887415	+	0.460971i	$0.152499\pi$
$564$	0.429327	−	0.233684i	0.0180779	−	0.00983986i
$565$	−17.1225	+	2.71195i	−0.720351	+	0.114092i
$566$	−2.17861	+	1.62861i	−0.0915737	+	0.0684555i
$567$	−2.43533	−	1.24086i	−0.102274	−	0.0521114i
$568$	−17.8138	+	38.8001i	−0.747450	+	1.62801i
$569$	−3.10378	−	4.27198i	−0.130117	−	0.179091i	0.738988	−	0.673719i	$-0.235304\pi$
$569$	−3.10378	−	4.27198i	−0.130117	−	0.179091i	−0.869105	+	0.494628i	$0.835304\pi$
$570$	0.0470684	+	3.45826i	0.00197148	+	0.144851i
$571$	36.0581			1.50898			0.754491	−	0.656310i	$-0.227884\pi$
$571$	36.0581			1.50898			0.754491	+	0.656310i	$0.227884\pi$
$572$	−3.02319	−	23.7247i	−0.126406	−	0.991979i
$573$	−2.49177			−0.104095
$574$	0.0127425	+	0.936229i	0.000531862	+	0.0390775i
$575$	−6.24058	−	8.58942i	−0.260250	−	0.358203i
$576$	5.50558	−	23.2515i	0.229399	−	0.968813i
$577$	25.5495	+	13.0181i	1.06364	+	0.541952i	0.896072	−	0.443909i	$-0.146409\pi$
$577$	25.5495	+	13.0181i	1.06364	+	0.541952i	0.167568	+	0.985860i	$0.446409\pi$
$578$	−0.502428	+	0.375588i	−0.0208983	+	0.0156224i
$579$	−1.08162	+	0.171311i	−0.0449504	+	0.00711945i
$580$	−20.2551	−	37.2130i	−0.841048	−	1.54519i
$581$	−1.44370	+	4.44325i	−0.0598947	+	0.184337i
$582$	0.458995	−	0.931971i	0.0190260	−	0.0386314i
$583$	0.00591009	+	9.19261i	0.000244771	+	0.380719i
$584$	−5.95103	−	29.6760i	−0.246255	−	1.22800i
$585$	−20.1947	−	31.4981i	−0.834947	−	1.30229i
$586$	4.27949	+	24.8278i	0.176784	+	1.02563i
$587$	0.867052	+	5.47435i	0.0357871	+	0.225951i	0.999099	−	0.0424324i	$-0.0135107\pi$
$587$	0.867052	+	5.47435i	0.0357871	+	0.225951i	−0.963312	+	0.268383i	$0.913511\pi$
$588$	−1.30838	−	0.897221i	−0.0539565	−	0.0370008i
$589$	21.7819	−	7.07738i	0.897509	−	0.291618i
$590$	−17.7721	−	5.50826i	−0.731665	−	0.226771i
$591$	0.122803	+	0.0194501i	0.00505145	+	0.000800070i
$592$	7.57808	+	35.2912i	0.311457	+	1.45046i
$593$	8.30100	+	8.30100i	0.340881	+	0.340881i	0.856699	−	0.515817i	$-0.172512\pi$
$593$	8.30100	+	8.30100i	0.340881	+	0.340881i	−0.515817	+	0.856699i	$0.672512\pi$
$594$	−2.58235	+	1.93302i	−0.105955	+	0.0793126i
$595$	4.46572			0.183077
$596$	5.24166	+	2.49346i	0.214707	+	0.102136i
$597$	−1.31458	−	1.80936i	−0.0538020	−	0.0740521i
$598$	1.53347	−	7.50061i	0.0627082	−	0.306723i
$599$	19.9629	−	6.48634i	0.815662	−	0.265025i	0.128668	−	0.991688i	$-0.458930\pi$
$599$	19.9629	−	6.48634i	0.815662	−	0.265025i	0.686994	+	0.726663i	$0.258930\pi$
$600$	0.620202	−	2.21227i	0.0253196	−	0.0903153i
$601$	30.8862	+	22.4401i	1.25987	+	0.915353i	0.998752	−	0.0499528i	$-0.0159071\pi$
$601$	30.8862	+	22.4401i	1.25987	+	0.915353i	0.261123	+	0.965305i	$0.415907\pi$
$602$	−4.68805	+	0.808062i	−0.191071	+	0.0329342i
$603$	19.4208	−	9.89541i	0.790877	−	0.402972i
$604$	−5.20317	+	39.8419i	−0.211714	+	1.62114i
$605$	37.7400	−	6.02719i	1.53435	−	0.245040i
$606$	0.129569	+	0.381048i	0.00526339	+	0.0154790i
$607$	−0.402453	−	0.130765i	−0.0163351	−	0.00530758i	0.300838	−	0.953675i	$-0.402734\pi$
$607$	−0.402453	−	0.130765i	−0.0163351	−	0.00530758i	−0.317173	+	0.948368i	$0.602734\pi$
$608$	34.5254	+	3.08200i	1.40019	+	0.124992i
$609$	−0.0337193	−	0.212895i	−0.00136637	−	0.00862694i
$610$	3.79831	−	26.2927i	0.153789	−	1.06456i
$611$	−7.14546	−	2.79085i	−0.289075	−	0.112906i
$612$	−0.679010	−	24.9398i	−0.0274474	−	1.00813i
$613$	6.25374	−	39.4846i	0.252586	−	1.59477i	−0.456551	−	0.889697i	$-0.650915\pi$
$613$	6.25374	−	39.4846i	0.252586	−	1.59477i	0.709137	−	0.705070i	$-0.249085\pi$
$614$	22.9324	−	23.5653i	0.925477	−	0.951017i
$615$	0.858633			0.0346234
$616$	−2.51573	+	1.41616i	−0.101361	+	0.0570587i
$617$	−19.4270	+	19.4270i	−0.782100	+	0.782100i	−0.980185	−	0.198085i	$-0.936528\pi$
$617$	−19.4270	+	19.4270i	−0.782100	+	0.782100i	0.198085	+	0.980185i	$0.436528\pi$
$618$	0.0173468	+	1.27452i	0.000697792	+	0.0512688i
$619$	5.39868	−	34.0860i	0.216991	−	1.37003i	−0.603040	−	0.797711i	$-0.706044\pi$
$619$	5.39868	−	34.0860i	0.216991	−	1.37003i	0.820031	−	0.572319i	$-0.193956\pi$
$620$	−25.9627	+	0.706860i	−1.04269	+	0.0283882i
$621$	−0.982019	+	0.319077i	−0.0394070	+	0.0128041i
$622$	−14.3318	+	10.7137i	−0.574654	+	0.429580i
$623$	2.14949	+	1.56169i	0.0861173	+	0.0625679i
$624$	1.47896	−	0.746581i	0.0592059	−	0.0298871i
$625$	3.19908	−	9.84575i	0.127963	−	0.393830i
$626$	13.5090	+	39.7285i	0.539930	+	1.58787i
$627$	−1.65183	−	1.64970i	−0.0659676	−	0.0658828i
$628$	7.07841	−	5.44315i	0.282459	−	0.217205i
$629$	17.1104	+	33.5810i	0.682235	+	1.33896i
$630$	−2.60472	+	3.68966i	−0.103775	+	0.147000i
$631$	−42.3653	+	6.71000i	−1.68654	+	0.267121i	−0.924713	−	0.380665i	$-0.875695\pi$
$631$	−42.3653	+	6.71000i	−1.68654	+	0.267121i	−0.761822	+	0.647786i	$0.775695\pi$
$632$	33.7513	+	9.46207i	1.34255	+	0.376381i
$633$	−0.196218	−	0.603896i	−0.00779895	−	0.0240027i
$634$	8.21031	+	15.5856i	0.326073	+	0.618982i
$635$	−4.31299	+	27.2311i	−0.171156	+	1.08064i
$636$	−0.600034	+	0.213185i	−0.0237929	+	0.00845334i
$637$	2.45791	+	24.7758i	0.0973859	+	0.981651i
$638$	27.3221	+	8.44891i	1.08169	+	0.334496i
$639$	−31.8796	−	31.8796i	−1.26114	−	1.26114i
$640$	−36.5626	−	14.4331i	−1.44526	−	0.570517i
$641$	17.5387	+	24.1400i	0.692738	+	0.953472i	0.999998	+	0.00184624i	$0.000587676\pi$
$641$	17.5387	+	24.1400i	0.692738	+	0.953472i	−0.307261	+	0.951625i	$0.599412\pi$
$642$	0.0660174	−	0.213002i	0.00260550	−	0.00840650i
$643$	−6.94744	+	13.6351i	−0.273980	+	0.537716i	−0.986465	−	0.163971i	$-0.947570\pi$
$643$	−6.94744	+	13.6351i	−0.273980	+	0.537716i	0.712485	+	0.701687i	$0.247570\pi$
$644$	−0.908467	+	0.169351i	−0.0357986	+	0.00667337i
$645$	0.682444	+	4.30878i	0.0268712	+	0.169658i
$646$	35.6667	−	6.14774i	1.40329	−	0.241879i
$647$	5.44978	−	16.7727i	0.214253	−	0.659403i	−0.784953	−	0.619556i	$-0.787313\pi$
$647$	5.44978	−	16.7727i	0.214253	−	0.659403i	0.999206	−	0.0398476i	$-0.0126872\pi$
$648$	20.9086	+	13.9236i	0.821368	+	0.546970i
$649$	11.1866	−	5.70891i	0.439112	−	0.224094i
$650$	−32.8248	+	14.9213i	−1.28750	+	0.585263i
$651$	−0.125667	−	0.0408317i	−0.00492528	−	0.00160032i
$652$	−4.00335	−	7.35502i	−0.156783	−	0.288045i
$653$	20.9581	+	15.2270i	0.820155	+	0.595878i	0.916757	−	0.399445i	$-0.130797\pi$
$653$	20.9581	+	15.2270i	0.820155	+	0.595878i	−0.0966016	+	0.995323i	$0.530797\pi$
$654$	2.44504	+	0.353217i	0.0956088	+	0.0138119i
$655$	5.10116	−	10.0116i	0.199319	−	0.391185i
$656$	0.881721	−	8.56013i	0.0344254	−	0.334217i
$657$	31.5681	+	4.99990i	1.23159	+	0.195065i
$658$	0.0126018	+	0.925889i	0.000491268	+	0.0360949i
$659$		−	25.9957i		−	1.01265i	−0.862343	−	0.506325i	$-0.831004\pi$
$659$		−	25.9957i		−	1.01265i	0.862343	−	0.506325i	$-0.168996\pi$
$660$	1.26715	+	2.32446i	0.0493237	+	0.0904796i
$661$	9.72873	+	9.72873i	0.378404	+	0.378404i	0.870526	−	0.492122i	$-0.163779\pi$
$661$	9.72873	+	9.72873i	0.378404	+	0.378404i	−0.492122	+	0.870526i	$0.663779\pi$
$662$	10.6142	+	10.3292i	0.412534	+	0.401456i
$663$	1.29226	−	1.14997i	0.0501871	−	0.0446610i
$664$	17.9157	−	39.0220i	0.695263	−	1.51435i
$665$	−5.83771	−	2.97446i	−0.226377	−	0.115345i
$666$	−37.7252	−	5.44988i	−1.46182	−	0.211179i
$667$	7.40615	+	5.38088i	0.286767	+	0.208349i
$668$	14.1523	+	26.0009i	0.547570	+	1.00600i
$669$	−0.772557	−	1.51623i	−0.0298688	−	0.0586208i
$670$	−11.5435	−	33.9481i	−0.445964	−	1.31153i
$671$	10.5494	+	14.5003i	0.407253	+	0.559779i
$672$	−0.150695	−	0.131465i	−0.00581319	−	0.00507138i
$673$	6.91277	+	2.24609i	0.266468	+	0.0865806i	0.439203	−	0.898388i	$-0.355261\pi$
$673$	6.91277	+	2.24609i	0.266468	+	0.0865806i	−0.172736	+	0.984968i	$0.555261\pi$
$674$	−25.6657	+	36.3562i	−0.988605	+	1.40039i
$675$	3.93436	+	2.85848i	0.151434	+	0.110023i
$676$	−23.9137	−	10.2047i	−0.919758	−	0.392487i
$677$	6.30150	+	19.3940i	0.242186	+	0.745373i	0.996086	+	0.0883838i	$0.0281702\pi$
$677$	6.30150	+	19.3940i	0.242186	+	0.745373i	−0.753900	+	0.656989i	$0.771830\pi$
$678$	0.774255	+	0.239972i	0.0297351	+	0.00921605i
$679$	1.15676	+	1.59214i	0.0443923	+	0.0611008i
$680$	−40.7662	−	4.76057i	−1.56331	−	0.182559i
$681$	1.92684	−	1.92684i	0.0738368	−	0.0738368i
$682$	12.2186	−	12.5719i	0.467873	−	0.481404i
$683$	15.9179	−	15.9179i	0.609081	−	0.609081i	−0.333625	−	0.942706i	$-0.608272\pi$
$683$	15.9179	−	15.9179i	0.609081	−	0.609081i	0.942706	+	0.333625i	$0.108272\pi$
$684$	−15.7239	+	33.0543i	−0.601219	+	1.26386i
$685$	−16.5560	+	12.0286i	−0.632571	+	0.459590i
$686$	5.35438	−	2.82063i	0.204431	−	0.107692i
$687$	1.05234	+	0.536192i	0.0401491	+	0.0204570i
$688$	43.6571	−	2.37898i	1.66441	−	0.0906976i
$689$	8.62524	+	5.04714i	0.328596	+	0.192281i
$690$	0.143948	+	0.835131i	0.00548003	+	0.0317929i
$691$	25.6770	−	13.0831i	0.976799	−	0.497704i	0.108689	−	0.994076i	$-0.465335\pi$
$691$	25.6770	−	13.0831i	0.976799	−	0.497704i	0.868110	+	0.496372i	$0.165335\pi$
$692$	−11.9458	−	15.5346i	−0.454111	−	0.590537i
$693$	−0.478840	−	3.01075i	−0.0181896	−	0.114369i
$694$	−31.9892	+	10.8774i	−1.21429	+	0.412901i
$695$	2.54751	−	1.29802i	0.0966325	−	0.0492367i
$696$	0.0808614	+	1.97940i	0.00306504	+	0.0750289i
$697$	−1.40560	−	8.87462i	−0.0532409	−	0.336150i
$698$	1.69089	+	0.244271i	0.0640013	+	0.00924579i
$699$	−0.575489	−	1.77117i	−0.0217670	−	0.0669919i
$700$	3.16024	+	2.99272i	0.119446	+	0.113114i
$701$	19.9875	+	27.5104i	0.754916	+	1.03905i	0.997620	+	0.0689522i	$0.0219656\pi$
$701$	19.9875	+	27.5104i	0.754916	+	1.03905i	−0.242704	+	0.970100i	$0.578034\pi$
$702$	0.393645	+	3.48453i	0.0148572	+	0.131515i
$703$		−	55.2946i		−	2.08547i
$704$	24.4749	−	10.2459i	0.922434	−	0.386155i
$705$	0.849149			0.0319808
$706$	−34.7163	+	35.6743i	−1.30656	+	1.34262i
$707$	−0.753047	−	0.119271i	−0.0283212	−	0.00448564i
$708$	0.631683	+	0.598198i	0.0237401	+	0.0224817i
$709$	16.2750	−	31.9415i	0.611221	−	1.19959i	−0.353283	−	0.935517i	$-0.614935\pi$
$709$	16.2750	−	31.9415i	0.611221	−	1.19959i	0.964503	−	0.264071i	$-0.0850654\pi$
$710$	−59.4041	+	44.4073i	−2.22940	+	1.66658i
$711$	−21.7570	+	29.9460i	−0.815953	+	1.12306i
$712$	−17.9572	−	16.5476i	−0.672974	−	0.620148i
$713$	5.00017	−	2.54772i	0.187258	−	0.0954127i
$714$	−0.187321	−	0.0922556i	−0.00701032	−	0.00345258i
$715$	15.0906	−	38.7102i	0.564357	−	1.44768i
$716$	35.4618	−	27.2694i	1.32527	−	1.01910i
$717$	0.822082	+	1.61343i	0.0307012	+	0.0602545i
$718$	−26.5468	+	4.57578i	−0.990718	+	0.170767i
$719$	−18.0150	−	13.0886i	−0.671845	−	0.488124i	0.198797	−	0.980041i	$-0.436296\pi$
$719$	−18.0150	−	13.0886i	−0.671845	−	0.488124i	−0.870642	+	0.491917i	$0.836296\pi$
$720$	27.7110	−	30.9051i	1.03273	−	1.15176i
$721$	−2.15146	−	1.09622i	−0.0801244	−	0.0408254i
$722$	−25.0536	−	7.76507i	−0.932398	−	0.288986i
$723$	−0.159986	+	1.01011i	−0.00594994	+	0.0375664i
$724$	−14.8838	+	5.28806i	−0.553154	+	0.196529i
$725$		−	43.1159i		−	1.60129i
$726$	−1.70757	−	0.526838i	−0.0633740	−	0.0195528i
$727$	−24.6186			−0.913053			−0.456526	−	0.889710i	$-0.650907\pi$
$727$	−24.6186			−0.913053			−0.456526	+	0.889710i	$0.650907\pi$
$728$	−0.0545060	+	3.13795i	−0.00202013	+	0.116300i
$729$	−21.2691	+	15.4529i	−0.787744	+	0.572330i
$730$	15.5659	−	50.2224i	0.576119	−	1.85882i
$731$	43.4173	−	14.1071i	1.60585	−	0.521772i
$732$	−0.702497	+	1.02442i	−0.0259650	+	0.0378636i
$733$	−0.629898	+	0.0997660i	−0.0232658	+	0.00368494i	−0.168057	−	0.985777i	$-0.553749\pi$
$733$	−0.629898	+	0.0997660i	−0.0232658	+	0.00368494i	0.144791	+	0.989462i	$0.453749\pi$
$734$	−4.09722	+	5.80383i	−0.151231	+	0.214223i
$735$	−1.25119	−	2.45560i	−0.0461509	−	0.0905763i
$736$	8.47364	−	0.577506i	0.312343	−	0.0212872i
$737$	21.5725	+	10.9743i	0.794632	+	0.404242i
$738$	8.15222	+	4.01496i	0.300087	+	0.147793i
$739$	9.66228	+	18.9633i	0.355433	+	0.697576i	0.997619	−	0.0689731i	$-0.0219723\pi$
$739$	9.66228	+	18.9633i	0.355433	+	0.697576i	−0.642186	+	0.766549i	$0.721972\pi$
$740$	−17.7468	+	60.1415i	−0.652384	+	2.21084i
$741$	−2.45522	+	0.642538i	−0.0901949	+	0.0236042i
$742$	0.172474	−	1.19390i	0.00633171	−	0.0438294i
$743$	−24.1566	+	47.4099i	−0.886219	+	1.73930i	−0.249203	+	0.968451i	$0.580169\pi$
$743$	−24.1566	+	47.4099i	−0.886219	+	1.73930i	−0.637016	+	0.770851i	$0.719831\pi$
$744$	1.10365	+	0.506704i	0.0404617	+	0.0185767i
$745$	5.92697	+	8.15777i	0.217147	+	0.298878i
$746$	−18.1817	+	0.247461i	−0.665679	+	0.00906019i
$747$	32.0620	+	32.0620i	1.17309	+	1.17309i
$748$	21.9507	−	16.9021i	0.802598	−	0.618003i
$749$	0.298710	+	0.298710i	0.0109146	+	0.0109146i
$750$	0.815388	−	0.837890i	0.0297738	−	0.0305954i
$751$	29.0572	−	21.1113i	1.06031	−	0.770361i	0.0861650	−	0.996281i	$-0.472539\pi$
$751$	29.0572	−	21.1113i	1.06031	−	0.770361i	0.974146	+	0.225920i	$0.0725388\pi$
$752$	0.871982	−	8.46558i	0.0317979	−	0.308708i
$753$	2.11218	−	0.686289i	0.0769722	−	0.0250098i
$754$	22.9419	−	20.9822i	0.835496	−	0.764126i
$755$	−41.0279	+	56.4701i	−1.49316	+	2.05516i
$756$	0.371784	−	0.202363i	0.0135216	−	0.00735986i
$757$	−0.924931	+	2.84665i	−0.0336172	+	0.103463i	−0.966457	−	0.256828i	$-0.917323\pi$
$757$	−0.924931	+	2.84665i	−0.0336172	+	0.103463i	0.932840	+	0.360291i	$0.117323\pi$
$758$	0.796827	−	1.61792i	0.0289420	−	0.0587656i
$759$	−0.462994	−	0.335930i	−0.0168056	−	0.0121935i
$760$	50.1197	+	33.3760i	1.81803	+	1.21068i
$761$	−7.46571	+	3.80397i	−0.270632	+	0.137894i	−0.584040	−	0.811725i	$-0.698529\pi$
$761$	−7.46571	+	3.80397i	−0.270632	+	0.137894i	0.313409	+	0.949618i	$0.398529\pi$
$762$	0.743472	−	1.05315i	0.0269332	−	0.0381516i
$763$	−2.75077	+	3.78611i	−0.0995845	+	0.137066i
$764$	−24.5354	+	35.7788i	−0.887658	+	1.29443i
$765$	19.6766	−	38.6175i	0.711408	−	1.39622i
$766$	38.3351	−	20.1945i	1.38510	−	0.729657i
$767$	0.794126	−	13.6301i	0.0286742	−	0.492153i
$768$	1.23550	+	1.36075i	0.0445824	+	0.0491018i
$769$	−22.2148	+	22.2148i	−0.801087	+	0.801087i	−0.983265	−	0.182179i	$-0.941685\pi$
$769$	−22.2148	+	22.2148i	−0.801087	+	0.801087i	0.182179	+	0.983265i	$0.441685\pi$
$770$	−5.01466	+	0.0714763i	−0.180716	+	0.00257583i
$771$	−1.95104			−0.0702649
$772$	−8.19036	+	17.2175i	−0.294778	+	0.619671i
$773$	8.03373	−	50.7230i	0.288953	−	1.82438i	−0.234256	−	0.972175i	$-0.575265\pi$
$773$	8.03373	−	50.7230i	0.288953	−	1.82438i	0.523209	−	0.852204i	$-0.324735\pi$
$774$	−13.6684	+	44.1005i	−0.491302	+	1.58516i
$775$	−23.5498	−	11.9992i	−0.845936	−	0.431026i
$776$	−8.86242	−	15.7673i	−0.318143	−	0.566013i
$777$	−0.187511	+	0.258086i	−0.00672691	+	0.00925880i
$778$	22.0755	−	31.2706i	0.791445	−	1.12110i
$779$	−4.07363	+	12.5373i	−0.145953	+	0.449197i
$780$	2.87666	+	0.0891410i	0.103001	+	0.00319176i
$781$	7.79981	−	49.4518i	0.279099	−	1.76952i
$782$	8.39606	−	2.85494i	0.300242	−	0.102093i
$783$	−3.98797	−	1.29577i	−0.142518	−	0.0463070i
$784$	−25.7659	+	9.95212i	−0.920212	+	0.355433i
$785$	15.3209	−	2.42659i	0.546826	−	0.0866088i
$786$	−0.420801	+	0.314568i	−0.0150095	+	0.0112203i
$787$	28.4098	+	14.4755i	1.01270	+	0.515996i	0.879906	−	0.475148i	$-0.157605\pi$
$787$	28.4098	+	14.4755i	1.01270	+	0.515996i	0.132793	+	0.991144i	$0.457605\pi$
$788$	1.48847	−	1.57178i	0.0530244	−	0.0559925i
$789$	−1.30685	+	0.949484i	−0.0465252	+	0.0338025i
$790$	43.6399	+	42.4679i	1.55264	+	1.51094i
$791$	−1.08580	+	1.08580i	−0.0386066	+	0.0386066i
$792$	1.16165	+	27.9946i	0.0412775	+	0.994745i
$793$	19.3987	−	1.92447i	0.688867	−	0.0683399i
$794$	5.80058	+	5.64481i	0.205855	+	0.200327i
$795$	−1.09259	−	0.173050i	−0.0387502	−	0.00613743i
$796$	−38.9241	+	1.05975i	−1.37963	+	0.0375617i
$797$	5.21250	−	1.69364i	0.184636	−	0.0599920i	−0.215240	−	0.976561i	$-0.569053\pi$
$797$	5.21250	−	1.69364i	0.184636	−	0.0599920i	0.399876	+	0.916569i	$0.369053\pi$
$798$	0.183423	+	0.245367i	0.00649310	+	0.00868590i
$799$	−1.39008	−	8.77660i	−0.0491774	−	0.310494i
$800$	−25.6585	−	30.6885i	−0.907166	−	1.08500i
$801$	22.9757	−	11.7067i	0.811807	−	0.413636i
$802$	13.3419	−	27.0901i	0.471118	−	0.956585i
$803$	16.1329	+	31.6123i	0.569318	+	1.11558i
$804$	−0.217111	+	1.66247i	−0.00765693	+	0.0586309i
$805$	−1.52680	−	0.496087i	−0.0538126	−	0.0174848i
$806$	−5.07565	−	18.3702i	−0.178782	−	0.647064i
$807$	0.694979	−	0.956557i	0.0244644	−	0.0336724i
$808$	6.74718	+	1.89155i	0.237365	+	0.0665446i
$809$	−10.2578	−	31.5704i	−0.360646	−	1.10995i	−0.952663	−	0.304029i	$-0.901668\pi$
$809$	−10.2578	−	31.5704i	−0.360646	−	1.10995i	0.592017	−	0.805926i	$-0.298332\pi$
$810$	20.3391	+	38.6095i	0.714642	+	1.35660i
$811$	−47.2055	−	7.47661i	−1.65761	−	0.262539i	−0.743716	−	0.668496i	$-0.766939\pi$
$811$	−47.2055	−	7.47661i	−1.65761	−	0.262539i	−0.913893	+	0.405956i	$0.866939\pi$
$812$	−3.38893	−	1.61211i	−0.118928	−	0.0565741i
$813$	0.653610	+	0.653610i	0.0229231	+	0.0229231i
$814$	−19.7511	−	37.4350i	−0.692276	−	1.31210i
$815$		−	14.5472i		−	0.509566i
$816$	1.61165	+	1.04186i	0.0564190	+	0.0364724i
$817$	−66.1525	−	10.4775i	−2.31438	−	0.366562i
$818$	15.6709	+	29.7480i	0.547921	+	1.04011i
$819$	−3.08705	−	1.20573i	−0.107870	−	0.0421316i
$820$	8.45456	−	12.3289i	0.295246	−	0.430544i
$821$	−16.0759	+	2.54617i	−0.561053	+	0.0888621i	−0.430519	−	0.902582i	$-0.641669\pi$
$821$	−16.0759	+	2.54617i	−0.561053	+	0.0888621i	−0.130535	+	0.991444i	$0.541669\pi$
$822$	0.942959	−	0.162534i	0.0328895	−	0.00566904i
$823$	−10.8725	+	33.4620i	−0.378991	+	1.16641i	0.561756	+	0.827303i	$0.310126\pi$
$823$	−10.8725	+	33.4620i	−0.378991	+	1.16641i	−0.940747	+	0.339110i	$0.889874\pi$
$824$	18.4714	+	12.3006i	0.643481	+	0.428511i
$825$	0.00173210	+	2.69412i	6.03040e−5	+	0.0937973i
$826$	−1.56032	+	0.530562i	−0.0542905	+	0.0184606i
$827$	−9.22924	−	18.1134i	−0.320932	−	0.629865i	0.673027	−	0.739618i	$-0.264994\pi$
$827$	−9.22924	−	18.1134i	−0.320932	−	0.629865i	−0.993959	+	0.109753i	$0.964994\pi$
$828$	−2.53836	+	8.60218i	−0.0882142	+	0.298947i
$829$	15.6231	−	21.5033i	0.542612	−	0.746841i	−0.446375	−	0.894846i	$-0.647285\pi$
$829$	15.6231	−	21.5033i	0.542612	−	0.746841i	0.988987	+	0.148005i	$0.0472852\pi$
$830$	59.7439	−	44.6613i	2.07374	−	1.55022i
$831$	0.448711	+	1.38099i	0.0155656	+	0.0479060i
$832$	3.84270	−	28.5873i	0.133222	−	0.991086i
$833$	−23.3323	+	16.9519i	−0.808416	+	0.587348i
$834$	−0.133674	+	0.00181937i	−0.00462876	+	6.29995e-5i
$835$			51.4261i			1.77967i
$836$	−39.9525	+	7.47429i	−1.38179	+	0.258504i
$837$	−1.81761	+	1.81761i	−0.0628256	+	0.0628256i
$838$	0.303362	+	22.2889i	0.0104795	+	0.769958i
$839$	−2.46098	+	15.5380i	−0.0849623	+	0.536431i	0.908092	+	0.418771i	$0.137539\pi$
$839$	−2.46098	+	15.5380i	−0.0849623	+	0.536431i	−0.993054	+	0.117660i	$0.962461\pi$
$840$	−0.120751	−	0.325744i	−0.00416629	−	0.0112392i
$841$	2.52663	+	7.77616i	0.0871251	+	0.268143i
$842$	0.0103568	−	0.0716919i	0.000356919	−	0.00247067i
$843$	3.25328	−	0.515269i	0.112049	−	0.0177468i
$844$	−10.6033	−	3.12885i	−0.364979	−	0.107699i
$845$	−28.0128	−	35.4308i	−0.963671	−	1.21886i
$846$	8.06218	+	3.97062i	0.277183	+	0.136513i
$847$	2.39064	−	2.39679i	0.0821433	−	0.0823548i
$848$	−2.84719	+	10.7149i	−0.0977728	+	0.367950i
$849$	0.210129	+	0.0682750i	0.00721161	+	0.00234319i
$850$	−34.1215	−	24.0881i	−1.17036	−	0.826215i
$851$	−2.11948	−	13.3819i	−0.0726548	−	0.458724i
$852$	3.40919	−	0.635521i	0.116797	−	0.0217726i
$853$	−7.80664	+	15.3214i	−0.267294	+	0.524594i	−0.985171	−	0.171576i	$-0.945114\pi$
$853$	−7.80664	+	15.3214i	−0.267294	+	0.524594i	0.717877	+	0.696170i	$0.245114\pi$
$854$	−1.09671	−	2.08188i	−0.0375287	−	0.0712405i
$855$	−51.4435	+	37.3759i	−1.75933	+	1.27823i
$856$	−2.40839	−	3.04526i	−0.0823172	−	0.104085i
$857$			13.8528i			0.473204i	0.971607	+	0.236602i	$0.0760337\pi$
$857$			13.8528i			0.473204i	−0.971607	+	0.236602i	$0.923966\pi$
$858$	−1.43270	+	1.31201i	−0.0489115	+	0.0447911i
$859$			28.4548i			0.970865i	0.874274	+	0.485432i	$0.161338\pi$
$859$			28.4548i			0.970865i	−0.874274	+	0.485432i	$0.838662\pi$
$860$	68.5884	+	32.6276i	2.33885	+	1.11259i
$861$	0.0615293	−	0.0447036i	0.00209691	−	0.00152350i
$862$	14.3909	−	7.58095i	0.490155	−	0.258208i
$863$	3.57201	−	7.01047i	0.121593	−	0.238639i	−0.822185	−	0.569221i	$-0.807245\pi$
$863$	3.57201	−	7.01047i	0.121593	−	0.238639i	0.943777	+	0.330582i	$0.107245\pi$
$864$	−3.60962	+	1.45098i	−0.122802	+	0.0493632i
$865$	−5.32551	−	33.6240i	−0.181073	−	1.14325i
$866$	1.39103	−	1.97043i	0.0472690	−	0.0669579i
$867$	0.0484597	+	0.0157455i	0.00164578	+	0.000534745i
$868$	−1.82368	+	1.40237i	−0.0618997	+	0.0475996i
$869$	−41.1027	+	0.0264257i	−1.39431	+	0.000896430i
$870$	−1.52052	+	3.08735i	−0.0515504	+	0.104671i
$871$	22.1503	−	14.2014i	0.750533	−	0.481197i
$872$	29.1470	−	31.6298i	0.987042	−	1.07112i
$873$	18.8649	−	2.98791i	0.638481	−	0.101125i
$874$	−12.8771	−	1.86026i	−0.435575	−	0.0629243i
$875$	0.684411	+	2.10640i	0.0231373	+	0.0712094i
$876$	−1.69046	+	1.78508i	−0.0571153	+	0.0603124i
$877$	3.26581	−	20.6195i	0.110279	−	0.696272i	−0.869160	−	0.494531i	$-0.835340\pi$
$877$	3.26581	−	20.6195i	0.110279	−	0.696272i	0.979439	−	0.201741i	$-0.0646600\pi$
$878$	57.0236	−	0.776116i	1.92445	−	0.0261926i
$879$	1.44705	−	1.44705i	0.0488078	−	0.0488078i
$880$	45.8534	+	4.69326i	1.54572	+	0.158210i
$881$		−	9.80802i		−	0.330441i	−0.986257	−	0.165220i	$-0.947166\pi$
$881$		−	9.80802i		−	0.330441i	0.986257	−	0.165220i	$-0.0528335\pi$
$882$	−0.396950	−	29.1651i	−0.0133660	−	0.982040i
$883$	−7.38961	+	5.36887i	−0.248680	+	0.180677i	−0.705142	−	0.709066i	$-0.749117\pi$
$883$	−7.38961	+	5.36887i	−0.248680	+	0.180677i	0.456462	+	0.889743i	$0.349117\pi$
$884$	−3.78782	−	29.8784i	−0.127398	−	1.00492i
$885$	0.467025	+	1.43736i	0.0156989	+	0.0483162i
$886$	−17.1057	−	22.8826i	−0.574679	−	0.768755i
$887$	3.95695	−	5.44627i	0.132861	−	0.182868i	−0.737403	−	0.675453i	$-0.763948\pi$
$887$	3.95695	−	5.44627i	0.132861	−	0.182868i	0.870264	+	0.492585i	$0.163948\pi$
$888$	1.98685	−	2.15610i	0.0666744	−	0.0723539i
$889$	1.10869	+	2.17592i	0.0371842	+	0.0729782i
$890$	−13.6565	−	40.1621i	−0.457766	−	1.34624i
$891$	−28.0205	−	9.08449i	−0.938721	−	0.304342i
$892$	−29.3782	−	3.83665i	−0.983654	−	0.128461i
$893$	−4.02864	+	12.3989i	−0.134813	+	0.414913i
$894$	−0.0800870	−	0.464632i	−0.00267851	−	0.0155396i
$895$	76.7554	−	12.1569i	2.56565	−	0.406359i
$896$	−3.37150	+	0.869319i	−0.112634	+	0.0290419i
$897$	−0.569561	+	0.249611i	−0.0190171	+	0.00833428i
$898$	3.26215	−	1.71846i	0.108859	−	0.0573458i
$899$	22.5090	+	3.56507i	0.750717	+	0.118902i
$900$	39.8041	−	14.1419i	1.32680	−	0.471398i
$901$			11.5760i			0.385654i
$902$	1.72042	+	9.94300i	0.0572838	+	0.331066i
$903$	0.273235	+	0.273235i	0.00909269	+	0.00909269i
$904$	11.0694	−	8.75445i	0.368164	−	0.291169i
$905$	−27.1017	−	4.29249i	−0.900892	−	0.142687i
$906$	2.88757	−	1.52114i	0.0959331	−	0.0505365i
$907$	11.9250	+	36.7015i	0.395965	+	1.21865i	0.928208	+	0.372062i	$0.121349\pi$
$907$	11.9250	+	36.7015i	0.395965	+	1.21865i	−0.532243	+	0.846591i	$0.678651\pi$
$908$	−8.69432	−	46.6398i	−0.288531	−	1.54780i
$909$	−4.34943	+	5.98647i	−0.144261	+	0.198559i
$910$	−2.68925	+	4.74267i	−0.0891478	+	0.157218i
$911$	56.9456	+	18.5028i	1.88669	+	0.613024i	0.982614	+	0.185658i	$0.0594417\pi$
$911$	56.9456	+	18.5028i	1.88669	+	0.613024i	0.904079	+	0.427366i	$0.140558\pi$
$912$	−1.41284	−	2.43541i	−0.0467839	−	0.0806445i
$913$	−7.84442	+	49.7346i	−0.259612	+	1.64598i
$914$	31.3652	+	15.4473i	1.03747	+	0.510953i
$915$	−1.92266	+	0.979646i	−0.0635613	+	0.0323861i
$916$	18.0609	−	9.83060i	0.596750	−	0.324812i
$917$	−0.155694	−	0.983012i	−0.00514147	−	0.0324619i
$918$	−3.25346	+	2.43211i	−0.107380	+	0.0802716i
$919$	13.4625	−	4.37423i	0.444087	−	0.144293i	−0.0784335	−	0.996919i	$-0.524992\pi$
$919$	13.4625	−	4.37423i	0.444087	−	0.144293i	0.522520	+	0.852627i	$0.324992\pi$
$920$	13.4088	+	6.15623i	0.442076	+	0.202965i
$921$	−2.63802	−	0.417821i	−0.0869257	−	0.0137677i
$922$	29.1047	−	29.9079i	0.958511	−	0.984963i
$923$	−42.0950	−	34.4967i	−1.38557	−	1.13547i
$924$	0.211824	+	0.100598i	0.00696849	+	0.00330942i
$925$	−45.1216	+	45.1216i	−1.48359	+	1.48359i
$926$	28.6521	−	29.4428i	0.941567	−	0.967551i
$927$	−18.9592	+	13.7747i	−0.622703	+	0.452420i
$928$	29.2179	+	18.3292i	0.959124	+	0.601684i
$929$	−26.9902	−	13.7522i	−0.885520	−	0.451195i	−0.0487887	−	0.998809i	$-0.515536\pi$
$929$	−26.9902	−	13.7522i	−0.885520	−	0.451195i	−0.836731	+	0.547614i	$0.815536\pi$
$930$	1.26314	+	1.68972i	0.0414200	+	0.0554081i
$931$	41.7916	−	6.61914i	1.36967	−	0.216934i
$932$	−31.0984	−	9.17663i	−1.01866	−	0.300590i
$933$	1.38232	+	0.449143i	0.0452551	+	0.0147043i
$934$	−1.02538	−	3.01554i	−0.0335516	−	0.0986714i
$935$	47.5300	−	7.55935i	1.55440	−	0.247217i
$936$	26.8954	+	14.2976i	0.879104	+	0.467332i
$937$	0.212966	−	0.655443i	0.00695731	−	0.0214124i	−0.947518	−	0.319704i	$-0.896417\pi$
$937$	0.212966	−	0.655443i	0.00695731	−	0.0214124i	0.954475	+	0.298291i	$0.0964167\pi$
$938$	−2.59467	−	1.83171i	−0.0847189	−	0.0598074i
$939$	2.00346	−	2.75753i	0.0653806	−	0.0899887i
$940$	8.36118	−	12.1927i	0.272712	−	0.397683i
$941$	39.2472	+	19.9974i	1.27942	+	0.651898i	0.955725	−	0.294263i	$-0.0950740\pi$
$941$	39.2472	+	19.9974i	1.27942	+	0.651898i	0.323697	+	0.946161i	$0.395074\pi$
$942$	−0.692787	−	0.214722i	−0.0225722	−	0.00699601i
$943$	−0.505296	+	3.19031i	−0.0164547	+	0.103891i
$944$	14.8093	−	3.18000i	0.482001	−	0.103500i
$945$	0.735336			0.0239205
$946$	−48.5285	+	16.5361i	−1.57780	+	0.537636i
$947$	−29.3565	+	29.3565i	−0.953958	+	0.953958i	−0.998986	−	0.0450281i	$-0.985662\pi$
$947$	−29.3565	+	29.3565i	−0.953958	+	0.953958i	0.0450281	+	0.998986i	$0.485662\pi$
$948$	−0.953211	−	2.68292i	−0.0309588	−	0.0871372i
$949$	38.5175	+	2.24413i	1.25033	+	0.0728476i
$950$	28.5603	+	54.2157i	0.926617	+	1.75899i
$951$	0.649611	−	1.27493i	0.0210651	−	0.0413425i
$952$	−3.16914	+	1.78130i	−0.102712	+	0.0577323i
$953$	6.80234	−	9.36261i	0.220349	−	0.303285i	−0.684503	−	0.729010i	$-0.739981\pi$
$953$	6.80234	−	9.36261i	0.220349	−	0.303285i	0.904853	+	0.425725i	$0.139981\pi$
$954$	−9.56434	−	6.75196i	−0.309657	−	0.218603i
$955$	−67.1508	+	34.2150i	−2.17295	+	1.10717i
$956$	31.2615	+	4.08260i	1.01107	+	0.132041i
$957$	−0.719262	−	2.20883i	−0.0232504	−	0.0714013i
$958$	−16.8558	−	8.30148i	−0.544587	−	0.268209i
$959$	−0.560139	+	1.72393i	−0.0180878	+	0.0556687i
$960$	0.755044	+	3.10234i	0.0243689	+	0.100128i
$961$	−10.0098	+	13.7773i	−0.322897	+	0.444430i
$962$	−45.9674	−	2.05092i	−1.48205	−	0.0661245i
$963$	3.89926	−	1.26695i	0.125652	−	0.0408267i
$964$	12.9286	+	12.2433i	0.416403	+	0.394330i
$965$	−26.7962	+	19.4685i	−0.862599	+	0.626715i
$966$	0.0537953	+	0.0523506i	0.00173084	+	0.00168435i
$967$	22.9915	+	22.9915i	0.739357	+	0.739357i	0.972454	−	0.233096i	$-0.0748858\pi$
$967$	22.9915	+	22.9915i	0.739357	+	0.739357i	−0.233096	+	0.972454i	$0.574886\pi$
$968$	−24.3784	+	19.3311i	−0.783553	+	0.621325i
$969$	−2.07877	−	2.07877i	−0.0667798	−	0.0667798i
$970$	−0.427616	−	31.4182i	−0.0137299	−	1.00878i
$971$	−27.3323	−	37.6196i	−0.877134	−	1.20727i	−0.977207	−	0.212291i	$-0.931908\pi$
$971$	−27.3323	−	37.6196i	−0.877134	−	1.20727i	0.100073	−	0.994980i	$-0.468092\pi$
$972$	−0.167834	−	6.16450i	−0.00538329	−	0.197726i
$973$	0.114974	−	0.225648i	0.00368589	−	0.00723396i
$974$	−44.2384	−	6.39079i	−1.41749	−	0.204774i
$975$	2.52784	+	1.47919i	0.0809558	+	0.0473720i
$976$	7.79220	+	20.1740i	0.249422	+	0.645753i
$977$	−13.2170	−	25.9398i	−0.422849	−	0.829888i	−0.999913	−	0.0131892i	$-0.995802\pi$
$977$	−13.2170	−	25.9398i	−0.422849	−	0.829888i	0.577064	−	0.816699i	$-0.304198\pi$
$978$	−0.300525	+	0.610203i	−0.00960972	+	0.0195121i
$979$	25.5212	+	12.9830i	0.815661	+	0.414940i
$980$	−47.5793	−	6.21364i	−1.51987	−	0.198487i
$981$	20.6202	+	40.4695i	0.658353	+	1.29209i
$982$	−6.56651	−	4.63564i	−0.209546	−	0.147929i
$983$	−35.5524	+	5.63094i	−1.13394	+	0.179599i	−0.695065	−	0.718947i	$-0.744624\pi$
$983$	−35.5524	+	5.63094i	−1.13394	+	0.179599i	−0.438879	+	0.898546i	$0.644624\pi$
$984$	−0.609337	+	0.342494i	−0.0194249	+	0.0109183i
$985$	3.57649	−	1.16207i	0.113957	−	0.0370267i
$986$	34.3992	+	10.6616i	1.09549	+	0.339536i
$987$	0.0608497	−	0.0442099i	0.00193687	−	0.00140722i
$988$	−14.9494	+	41.5807i	−0.475604	+	1.32286i
$989$	−16.4112			−0.521846
$990$	−21.4772	+	43.6793i	−0.682589	+	1.38822i
$991$			11.7638i			0.373688i	0.982390	+	0.186844i	$0.0598259\pi$
$991$			11.7638i			0.373688i	−0.982390	+	0.186844i	$0.940174\pi$
$992$	18.1427	−	10.8577i	0.576033	−	0.344733i
$993$	0.188195	−	1.18821i	0.00597218	−	0.0377069i
$994$	−1.94487	+	6.27501i	−0.0616875	+	0.199031i
$995$	−60.2711	−	30.7097i	−1.91072	−	0.973562i
$996$	−3.42868	+	0.639156i	−0.108642	+	0.0202524i
$997$	−16.8783	−	12.2628i	−0.534540	−	0.388366i	0.287513	−	0.957777i	$-0.407171\pi$
$997$	−16.8783	−	12.2628i	−0.534540	−	0.388366i	−0.822053	+	0.569411i	$0.807171\pi$
$998$	1.12535	+	6.52882i	0.0356223	+	0.206666i
$999$	2.81743	+	5.52953i	0.0891397	+	0.174946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bk.a.31.1	✓	640
4.3	odd	2	inner	572.2.bk.a.31.56	yes	640
11.5	even	5	inner	572.2.bk.a.291.65	yes	640
13.8	odd	4	inner	572.2.bk.a.515.40	yes	640
44.27	odd	10	inner	572.2.bk.a.291.40	yes	640
52.47	even	4	inner	572.2.bk.a.515.65	yes	640
143.60	odd	20	inner	572.2.bk.a.203.56	yes	640
572.203	even	20	inner	572.2.bk.a.203.1	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bk.a.31.1	✓	640	1.1	even	1	trivial
572.2.bk.a.31.56	yes	640	4.3	odd	2	inner
572.2.bk.a.203.1	yes	640	572.203	even	20	inner
572.2.bk.a.203.56	yes	640	143.60	odd	20	inner
572.2.bk.a.291.40	yes	640	44.27	odd	10	inner
572.2.bk.a.291.65	yes	640	11.5	even	5	inner
572.2.bk.a.515.40	yes	640	13.8	odd	4	inner
572.2.bk.a.515.65	yes	640	52.47	even	4	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.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41408 + 0.0192463i) q^{2} +(0.0675205 + 0.0929340i) q^{3} +(1.99926 - 0.0544317i) q^{4} +(3.09570 + 1.57734i) q^{5} +(-0.0972682 - 0.130117i) q^{6} +(0.303959 - 0.0481424i) q^{7} +(-2.82607 + 0.115449i) q^{8} +(0.922973 - 2.84062i) q^{9} +O(q^{10})\)	\(q+(-1.41408 + 0.0192463i) q^{2} +(0.0675205 + 0.0929340i) q^{3} +(1.99926 - 0.0544317i) q^{4} +(3.09570 + 1.57734i) q^{5} +(-0.0972682 - 0.130117i) q^{6} +(0.303959 - 0.0481424i) q^{7} +(-2.82607 + 0.115449i) q^{8} +(0.922973 - 2.84062i) q^{9} +(-4.40794 - 2.17091i) q^{10} +(3.15364 - 1.02692i) q^{11} +(0.140049 + 0.182124i) q^{12} +(0.770209 - 3.52233i) q^{13} +(-0.428897 + 0.0739274i) q^{14} +(0.0624350 + 0.394199i) q^{15} +(3.99407 - 0.217646i) q^{16} +(3.97213 - 1.29062i) q^{17} +(-1.25049 + 4.03463i) q^{18} +(-6.05212 - 0.958561i) q^{19} +(6.27497 + 2.98501i) q^{20} +(0.0249975 + 0.0249975i) q^{21} +(-4.43974 + 1.51285i) q^{22} -1.50142 q^{23} +(-0.201547 - 0.254843i) q^{24} +(4.15646 + 5.72087i) q^{25} +(-1.02135 + 4.99568i) q^{26} +(0.654061 - 0.212517i) q^{27} +(0.605073 - 0.112794i) q^{28} +(-4.93277 - 3.58387i) q^{29} +(-0.0958750 - 0.556228i) q^{30} +(-3.33030 + 1.69687i) q^{31} +(-5.64376 + 0.384641i) q^{32} +(0.308371 + 0.223742i) q^{33} +(-5.59209 + 1.90150i) q^{34} +(1.01690 + 0.330412i) q^{35} +(1.69064 - 5.72937i) q^{36} +(1.41165 + 8.91282i) q^{37} +(8.57664 + 1.23900i) q^{38} +(0.379349 - 0.166250i) q^{39} +(-8.93078 - 4.10028i) q^{40} +(0.336546 - 2.12487i) q^{41} +(-0.0358297 - 0.0348675i) q^{42} +10.9305 q^{43} +(6.24904 - 2.22474i) q^{44} +(7.33788 - 7.33788i) q^{45} +(2.12313 - 0.0288967i) q^{46} +(0.332829 - 2.10140i) q^{47} +(0.289908 + 0.356490i) q^{48} +(-6.56732 + 2.13385i) q^{49} +(-5.98768 - 8.00979i) q^{50} +(0.388143 + 0.282003i) q^{51} +(1.34812 - 7.08397i) q^{52} +(-0.856495 + 2.63602i) q^{53} +(-0.920806 + 0.313105i) q^{54} +(11.3825 + 1.79532i) q^{55} +(-0.853452 + 0.171146i) q^{56} +(-0.319559 - 0.627170i) q^{57} +(7.04432 + 4.97295i) q^{58} +(3.74009 - 0.592372i) q^{59} +(0.146281 + 0.784707i) q^{60} +(1.67074 + 5.14201i) q^{61} +(4.67666 - 2.46362i) q^{62} +(0.143792 - 0.907867i) q^{63} +(7.97334 - 0.652535i) q^{64} +(7.94025 - 9.68920i) q^{65} +(-0.440368 - 0.310454i) q^{66} +(5.16018 + 5.16018i) q^{67} +(7.87108 - 2.79650i) q^{68} +(-0.101376 - 0.139533i) q^{69} +(-1.44435 - 0.447659i) q^{70} +(6.85281 - 13.4494i) q^{71} +(-2.28044 + 8.13435i) q^{72} +(1.67400 + 10.5692i) q^{73} +(-2.16773 - 12.5763i) q^{74} +(-0.251017 + 0.772552i) q^{75} +(-12.1519 - 1.58698i) q^{76} +(0.909139 - 0.463966i) q^{77} +(-0.533230 + 0.242393i) q^{78} +(-11.7864 - 3.82963i) q^{79} +(12.7078 + 5.62625i) q^{80} +(-7.18521 - 5.22036i) q^{81} +(-0.435008 + 3.01122i) q^{82} +(-6.89200 + 13.5263i) q^{83} +(0.0513372 + 0.0486159i) q^{84} +(14.3323 + 2.27001i) q^{85} +(-15.4566 + 0.210371i) q^{86} -0.700406i q^{87} +(-8.79384 + 3.26624i) q^{88} +(6.10473 + 6.10473i) q^{89} +(-10.2351 + 10.5176i) q^{90} +(0.0645390 - 1.10772i) q^{91} +(-3.00172 + 0.0817247i) q^{92} +(-0.382561 - 0.194924i) q^{93} +(-0.430203 + 2.97796i) q^{94} +(-17.2236 - 12.5137i) q^{95} +(-0.416816 - 0.498526i) q^{96} +(2.90319 + 5.69783i) q^{97} +(9.24567 - 3.14384i) q^{98} +(-0.00636881 - 9.90611i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9}+O(q^{10}) \) 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9	\( 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9} - 12 q^{13} + 4 q^{14} - 36 q^{16} - 10 q^{18} - 60 q^{20} - 56 q^{21} - 44 q^{22} - 14 q^{24} + 26 q^{26} - 14 q^{28} - 24 q^{29} - 16 q^{32} - 28 q^{33} + 12 q^{34} - 12 q^{37} + 4 q^{40} - 36 q^{41} - 8 q^{42} + 26 q^{44} - 16 q^{45} - 50 q^{46} + 48 q^{48} + 36 q^{50} - 52 q^{52} - 40 q^{53} + 116 q^{54} - 36 q^{57} - 70 q^{58} + 52 q^{60} - 8 q^{61} - 48 q^{65} - 228 q^{66} - 44 q^{68} - 68 q^{70} - 38 q^{72} - 12 q^{73} - 12 q^{74} + 108 q^{76} + 108 q^{78} + 62 q^{80} - 168 q^{81} - 36 q^{84} - 52 q^{85} - 62 q^{86} + 16 q^{89} - 80 q^{92} - 4 q^{93} - 124 q^{94} - 132 q^{96} - 4 q^{97} - 108 q^{98}+O(q^{100}) \) 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9 - 12 * q^13 + 4 * q^14 - 36 * q^16 - 10 * q^18 - 60 * q^20 - 56 * q^21 - 44 * q^22 - 14 * q^24 + 26 * q^26 - 14 * q^28 - 24 * q^29 - 16 * q^32 - 28 * q^33 + 12 * q^34 - 12 * q^37 + 4 * q^40 - 36 * q^41 - 8 * q^42 + 26 * q^44 - 16 * q^45 - 50 * q^46 + 48 * q^48 + 36 * q^50 - 52 * q^52 - 40 * q^53 + 116 * q^54 - 36 * q^57 - 70 * q^58 + 52 * q^60 - 8 * q^61 - 48 * q^65 - 228 * q^66 - 44 * q^68 - 68 * q^70 - 38 * q^72 - 12 * q^73 - 12 * q^74 + 108 * q^76 + 108 * q^78 + 62 * q^80 - 168 * q^81 - 36 * q^84 - 52 * q^85 - 62 * q^86 + 16 * q^89 - 80 * q^92 - 4 * q^93 - 124 * q^94 - 132 * q^96 - 4 * q^97 - 108 * q^98

Introduction

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Modular forms

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