LMFDB - Embedded newform 153.2.s.a.113.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,2,Mod(5,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([40, 15])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			113.10
Character	$\chi$	$=$	153.113
Dual form			153.2.s.a.65.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.320101 - 0.0421420i) q^{2} +(-1.38752 - 1.03672i) q^{3} +(-1.83116 + 0.490659i) q^{4} +(-0.356267 - 0.722438i) q^{5} +(-0.487834 - 0.273383i) q^{6} +(-2.50374 - 1.23471i) q^{7} +(-1.16205 + 0.481337i) q^{8} +(0.850404 + 2.87694i) q^{9} +(-0.144486 - 0.216239i) q^{10} +(-4.03644 + 1.37019i) q^{11} +(3.04945 + 1.21761i) q^{12} +(-1.31045 - 4.89065i) q^{13} +(-0.853480 - 0.289717i) q^{14} +(-0.254643 + 1.37175i) q^{15} +(2.93186 - 1.69271i) q^{16} +(0.361775 - 4.10720i) q^{17} +(0.393455 + 0.885074i) q^{18} +(5.27449 + 2.18477i) q^{19} +(1.00685 + 1.14810i) q^{20} +(2.19392 + 4.30886i) q^{21} +(-1.23432 + 0.608702i) q^{22} +(-5.12541 + 5.84441i) q^{23} +(2.11138 + 0.536864i) q^{24} +(2.64882 - 3.45201i) q^{25} +(-0.625576 - 1.51027i) q^{26} +(1.80265 - 4.87344i) q^{27} +(5.19057 + 1.03247i) q^{28} +(0.0416189 - 0.634981i) q^{29} +(-0.0237032 + 0.449827i) q^{30} +(-0.702337 + 2.06902i) q^{31} +(2.86291 - 2.19679i) q^{32} +(7.02114 + 2.28352i) q^{33} +(-0.0572816 - 1.32996i) q^{34} +2.24868i q^{35} +(-2.96883 - 4.85090i) q^{36} +(-0.897790 - 4.51350i) q^{37} +(1.78044 + 0.477067i) q^{38} +(-3.25199 + 8.14443i) q^{39} +(0.761737 + 0.668025i) q^{40} +(-4.17643 + 0.273738i) q^{41} +(0.883860 + 1.28681i) q^{42} +(-6.50611 - 4.99232i) q^{43} +(6.71909 - 4.48955i) q^{44} +(1.77544 - 1.63932i) q^{45} +(-1.39435 + 2.08679i) q^{46} +(-0.793260 + 2.96048i) q^{47} +(-5.82289 - 0.690869i) q^{48} +(0.482862 + 0.629278i) q^{49} +(0.702413 - 1.21662i) q^{50} +(-4.76001 + 5.32375i) q^{51} +(4.79928 + 8.31260i) q^{52} +(-3.67083 + 8.86216i) q^{53} +(0.371652 - 1.63596i) q^{54} +(2.42793 + 2.42793i) q^{55} +(3.50378 + 0.229650i) q^{56} +(-5.05345 - 8.49960i) q^{57} +(-0.0134372 - 0.205012i) q^{58} +(1.28296 - 9.74504i) q^{59} +(-0.206766 - 2.63683i) q^{60} +(-0.138416 + 0.280680i) q^{61} +(-0.137626 + 0.691891i) q^{62} +(1.42299 - 8.25311i) q^{63} +(-3.96387 + 3.96387i) q^{64} +(-3.06632 + 2.68909i) q^{65} +(2.34370 + 0.435071i) q^{66} +(2.17017 + 1.25295i) q^{67} +(1.35277 + 7.69847i) q^{68} +(13.1706 - 2.79558i) q^{69} +(0.0947639 + 0.719803i) q^{70} +(1.92783 - 0.383470i) q^{71} +(-2.37299 - 2.93383i) q^{72} +(-4.62155 - 3.08802i) q^{73} +(-0.477591 - 1.40694i) q^{74} +(-7.25406 + 2.04362i) q^{75} +(-10.7304 - 1.41269i) q^{76} +(11.7980 + 1.55323i) q^{77} +(-0.697742 + 2.74408i) q^{78} +(-1.95640 - 5.76336i) q^{79} +(-2.26741 - 1.51503i) q^{80} +(-7.55363 + 4.89313i) q^{81} +(-1.32534 + 0.263627i) q^{82} +(-1.40476 - 10.6702i) q^{83} +(-6.13161 - 6.81375i) q^{84} +(-3.09609 + 1.20190i) q^{85} +(-2.29300 - 1.32386i) q^{86} +(-0.716048 + 0.837900i) q^{87} +(4.03103 - 3.53512i) q^{88} +(-9.50851 + 9.50851i) q^{89} +(0.499236 - 0.599569i) q^{90} +(-2.75750 + 13.8629i) q^{91} +(6.51785 - 13.2169i) q^{92} +(3.11950 - 2.14267i) q^{93} +(-0.129162 + 0.981082i) q^{94} +(-0.300769 - 4.58885i) q^{95} +(-6.24980 + 0.0800307i) q^{96} +(11.4948 + 0.753408i) q^{97} +(0.181083 + 0.181083i) q^{98} +(-7.37456 - 10.4474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22}+ \cdots + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.320101	−	0.0421420i	0.226345	−	0.0297989i	−0.0165004	−	0.999864i	$-0.505252\pi$
$2$	0.320101	−	0.0421420i	0.226345	−	0.0297989i	0.242846	+	0.970065i	$0.421919\pi$
$3$	−1.38752	−	1.03672i	−0.801083	−	0.598553i
$3$	−1.38752	−	1.03672i	−0.801083	−	0.598553i
$4$	−1.83116	+	0.490659i	−0.915582	+	0.245329i
$5$	−0.356267	−	0.722438i	−0.159327	−	0.323084i	0.802541	−	0.596597i	$-0.203481\pi$
$5$	−0.356267	−	0.722438i	−0.159327	−	0.323084i	−0.961868	+	0.273513i	$0.911814\pi$
$6$	−0.487834	−	0.273383i	−0.199158	−	0.111608i
$7$	−2.50374	−	1.23471i	−0.946323	−	0.466675i	−0.0974316	−	0.995242i	$-0.531063\pi$
$7$	−2.50374	−	1.23471i	−0.946323	−	0.466675i	−0.848891	+	0.528567i	$0.822729\pi$
$8$	−1.16205	+	0.481337i	−0.410847	+	0.170178i
$9$	0.850404	+	2.87694i	0.283468	+	0.958982i
$10$	−0.144486	−	0.216239i	−0.0456906	−	0.0683807i
$11$	−4.03644	+	1.37019i	−1.21703	+	0.413127i	−0.854799	−	0.518960i	$-0.826319\pi$
$11$	−4.03644	+	1.37019i	−1.21703	+	0.413127i	−0.362234	+	0.932087i	$0.617986\pi$
$12$	3.04945	+	1.21761i	0.880300	+	0.351495i
$13$	−1.31045	−	4.89065i	−0.363452	−	1.35642i	−0.869507	−	0.493921i	$-0.835563\pi$
$13$	−1.31045	−	4.89065i	−0.363452	−	1.35642i	0.506055	−	0.862501i	$-0.331103\pi$
$14$	−0.853480	−	0.289717i	−0.228102	−	0.0774302i
$15$	−0.254643	+	1.37175i	−0.0657485	+	0.354183i
$16$	2.93186	−	1.69271i	0.732966	−	0.423178i
$17$	0.361775	−	4.10720i	0.0877433	−	0.996143i
$17$	0.361775	−	4.10720i	0.0877433	−	0.996143i
$18$	0.393455	+	0.885074i	0.0927383	+	0.208614i
$19$	5.27449	+	2.18477i	1.21005	+	0.501220i	0.894234	−	0.447600i	$-0.147721\pi$
$19$	5.27449	+	2.18477i	1.21005	+	0.501220i	0.315818	+	0.948820i	$0.397721\pi$
$20$	1.00685	+	1.14810i	0.225139	+	0.256722i
$21$	2.19392	+	4.30886i	0.478754	+	0.940270i
$22$	−1.23432	+	0.608702i	−0.263159	+	0.129776i
$23$	−5.12541	+	5.84441i	−1.06872	+	1.21864i	−0.0939185	+	0.995580i	$0.529939\pi$
$23$	−5.12541	+	5.84441i	−1.06872	+	1.21864i	−0.974804	+	0.223064i	$0.928394\pi$
$24$	2.11138	+	0.536864i	0.430984	+	0.109587i
$25$	2.64882	−	3.45201i	0.529763	−	0.690401i
$26$	−0.625576	−	1.51027i	−0.122686	−	0.296189i
$27$	1.80265	−	4.87344i	0.346920	−	0.937895i
$28$	5.19057	+	1.03247i	0.980925	+	0.195118i
$29$	0.0416189	−	0.634981i	0.00772843	−	0.117913i	−0.992252	−	0.124245i	$-0.960349\pi$
$29$	0.0416189	−	0.634981i	0.00772843	−	0.117913i	0.999980	+	0.00633233i	$0.00201566\pi$
$30$	−0.0237032	+	0.449827i	−0.00432759	+	0.0821269i
$31$	−0.702337	+	2.06902i	−0.126143	+	0.371606i	−0.991594	−	0.129388i	$-0.958699\pi$
$31$	−0.702337	+	2.06902i	−0.126143	+	0.371606i	0.865451	+	0.500994i	$0.167032\pi$
$32$	2.86291	−	2.19679i	0.506096	−	0.388341i
$33$	7.02114	+	2.28352i	1.22222	+	0.397510i
$34$	−0.0572816	−	1.32996i	−0.00982372	−	0.228087i
$35$			2.24868i			0.380096i
$36$	−2.96883	−	4.85090i	−0.494805	−	0.808483i
$37$	−0.897790	−	4.51350i	−0.147596	−	0.742014i	−0.981704	−	0.190413i	$-0.939017\pi$
$37$	−0.897790	−	4.51350i	−0.147596	−	0.742014i	0.834108	−	0.551601i	$-0.185983\pi$
$38$	1.78044	+	0.477067i	0.288825	+	0.0773905i
$39$	−3.25199	+	8.14443i	−0.520735	+	1.30415i
$40$	0.761737	+	0.668025i	0.120441	+	0.105624i
$41$	−4.17643	+	0.273738i	−0.652249	+	0.0427507i	−0.387936	−	0.921686i	$-0.626812\pi$
$41$	−4.17643	+	0.273738i	−0.652249	+	0.0427507i	−0.264313	+	0.964437i	$0.585145\pi$
$42$	0.883860	+	1.28681i	0.136383	+	0.198559i
$43$	−6.50611	−	4.99232i	−0.992173	−	0.761321i	−0.0210200	−	0.999779i	$-0.506691\pi$
$43$	−6.50611	−	4.99232i	−0.992173	−	0.761321i	−0.971153	+	0.238458i	$0.923358\pi$
$44$	6.71909	−	4.48955i	1.01294	−	0.676825i
$45$	1.77544	−	1.63932i	0.264667	−	0.244376i
$46$	−1.39435	+	2.08679i	−0.205586	+	0.307681i
$47$	−0.793260	+	2.96048i	−0.115709	+	0.431831i	−0.999339	−	0.0363545i	$-0.988425\pi$
$47$	−0.793260	+	2.96048i	−0.115709	+	0.431831i	0.883630	+	0.468186i	$0.155092\pi$
$48$	−5.82289	−	0.690869i	−0.840461	−	0.0997183i
$49$	0.482862	+	0.629278i	0.0689803	+	0.0898969i
$50$	0.702413	−	1.21662i	0.0993362	−	0.172055i
$51$	−4.76001	+	5.32375i	−0.666534	+	0.745474i
$52$	4.79928	+	8.31260i	0.665540	+	1.15275i
$53$	−3.67083	+	8.86216i	−0.504227	+	1.21731i	0.442935	+	0.896554i	$0.353937\pi$
$53$	−3.67083	+	8.86216i	−0.504227	+	1.21731i	−0.947162	+	0.320757i	$0.896063\pi$
$54$	0.371652	−	1.63596i	0.0505755	−	0.222626i
$55$	2.42793	+	2.42793i	0.327381	+	0.327381i
$56$	3.50378	+	0.229650i	0.468212	+	0.0306882i
$57$	−5.05345	−	8.49960i	−0.669345	−	1.12580i
$58$	−0.0134372	−	0.205012i	−0.00176439	−	0.0269194i
$59$	1.28296	−	9.74504i	0.167027	−	1.26870i	−0.678435	−	0.734661i	$-0.737341\pi$
$59$	1.28296	−	9.74504i	0.167027	−	1.26870i	0.845462	−	0.534036i	$-0.179325\pi$
$60$	−0.206766	−	2.63683i	−0.0266934	−	0.340414i
$61$	−0.138416	+	0.280680i	−0.0177224	+	0.0359374i	−0.905554	−	0.424231i	$-0.860544\pi$
$61$	−0.138416	+	0.280680i	−0.0177224	+	0.0359374i	0.887832	+	0.460169i	$0.152211\pi$
$62$	−0.137626	+	0.691891i	−0.0174785	+	0.0878703i
$63$	1.42299	−	8.25311i	0.179280	−	1.03979i
$64$	−3.96387	+	3.96387i	−0.495484	+	0.495484i
$65$	−3.06632	+	2.68909i	−0.380330	+	0.333541i
$66$	2.34370	+	0.435071i	0.288490	+	0.0535536i
$67$	2.17017	+	1.25295i	0.265128	+	0.153072i	0.626672	−	0.779283i	$-0.284417\pi$
$67$	2.17017	+	1.25295i	0.265128	+	0.153072i	−0.361543	+	0.932355i	$0.617750\pi$
$68$	1.35277	+	7.69847i	0.164047	+	0.933576i
$69$	13.1706	−	2.79558i	1.58556	−	0.336548i
$70$	0.0947639	+	0.719803i	0.0113264	+	0.0860329i
$71$	1.92783	−	0.383470i	0.228792	−	0.0455095i	−0.0793629	−	0.996846i	$-0.525289\pi$
$71$	1.92783	−	0.383470i	0.228792	−	0.0455095i	0.308155	+	0.951336i	$0.400289\pi$
$72$	−2.37299	−	2.93383i	−0.279660	−	0.345755i
$73$	−4.62155	−	3.08802i	−0.540912	−	0.361426i	0.254902	−	0.966967i	$-0.417957\pi$
$73$	−4.62155	−	3.08802i	−0.540912	−	0.361426i	−0.795814	+	0.605541i	$0.792957\pi$
$74$	−0.477591	−	1.40694i	−0.0555188	−	0.163553i
$75$	−7.25406	+	2.04362i	−0.837626	+	0.235977i
$76$	−10.7304	−	1.41269i	−1.23087	−	0.162046i
$77$	11.7980	+	1.55323i	1.34450	+	0.177007i
$78$	−0.697742	+	2.74408i	−0.0790037	+	0.310706i
$79$	−1.95640	−	5.76336i	−0.220112	−	0.648429i	−0.999753	−	0.0222028i	$-0.992932\pi$
$79$	−1.95640	−	5.76336i	−0.220112	−	0.648429i	0.779642	−	0.626226i	$-0.215401\pi$
$80$	−2.26741	−	1.51503i	−0.253504	−	0.169386i
$81$	−7.55363	+	4.89313i	−0.839292	+	0.543681i
$82$	−1.32534	+	0.263627i	−0.146360	+	0.0291127i
$83$	−1.40476	−	10.6702i	−0.154192	−	1.17121i	−0.877116	−	0.480278i	$-0.840536\pi$
$83$	−1.40476	−	10.6702i	−0.154192	−	1.17121i	0.722924	−	0.690927i	$-0.242798\pi$
$84$	−6.13161	−	6.81375i	−0.669014	−	0.743442i
$85$	−3.09609	+	1.20190i	−0.335818	+	0.130364i
$86$	−2.29300	−	1.32386i	−0.247260	−	0.142756i
$87$	−0.716048	+	0.837900i	−0.0767684	+	0.0898323i
$88$	4.03103	−	3.53512i	0.429709	−	0.376845i
$89$	−9.50851	+	9.50851i	−1.00790	+	1.00790i	−0.00793097	+	0.999969i	$0.502525\pi$
$89$	−9.50851	+	9.50851i	−1.00790	+	1.00790i	−0.999969	+	0.00793097i	$0.997475\pi$
$90$	0.499236	−	0.599569i	0.0526241	−	0.0632002i
$91$	−2.75750	+	13.8629i	−0.289065	+	1.45323i
$92$	6.51785	−	13.2169i	0.679533	−	1.37796i
$93$	3.11950	−	2.14267i	0.323478	−	0.222184i
$94$	−0.129162	+	0.981082i	−0.0133220	+	0.101191i
$95$	−0.300769	−	4.58885i	−0.0308583	−	0.470806i
$96$	−6.24980	+	0.0800307i	−0.637867	+	0.00816809i
$97$	11.4948	+	0.753408i	1.16712	+	0.0764969i	0.636612	−	0.771184i	$-0.280335\pi$
$97$	11.4948	+	0.753408i	1.16712	+	0.0764969i	0.530506	+	0.847681i	$0.322002\pi$
$98$	0.181083	+	0.181083i	0.0182922	+	0.0182922i
$99$	−7.37456	−	10.4474i	−0.741171	−	1.05000i
$100$	−3.15666	+	7.62085i	−0.315666	+	0.762085i
$101$	0.533410	+	0.923893i	0.0530762	+	0.0919307i	0.891343	−	0.453330i	$-0.149764\pi$
$101$	0.533410	+	0.923893i	0.0530762	+	0.0919307i	−0.838267	+	0.545261i	$0.816431\pi$
$102$	−1.29933	+	1.90473i	−0.128653	+	0.188597i
$103$	−6.64266	+	11.5054i	−0.654521	+	1.13366i	0.327493	+	0.944854i	$0.393796\pi$
$103$	−6.64266	+	11.5054i	−0.654521	+	1.13366i	−0.982014	+	0.188810i	$0.939537\pi$
$104$	3.87686	+	5.05242i	0.380157	+	0.495431i
$105$	2.33126	−	3.12008i	0.227508	−	0.304488i
$106$	−0.801564	+	2.99148i	−0.0778548	+	0.290558i
$107$	9.57936	−	14.3365i	0.926072	−	1.38596i	0.00356116	−	0.999994i	$-0.498866\pi$
$107$	9.57936	−	14.3365i	0.926072	−	1.38596i	0.922511	−	0.385971i	$-0.126134\pi$
$108$	−0.909748	+	9.80856i	−0.0875405	+	0.943829i
$109$	4.45912	−	2.97949i	0.427106	−	0.285383i	−0.323380	−	0.946269i	$-0.604819\pi$
$109$	4.45912	−	2.97949i	0.427106	−	0.285383i	0.750487	+	0.660886i	$0.229819\pi$
$110$	0.879498	+	0.674863i	0.0838569	+	0.0643456i
$111$	−3.43355	+	7.19331i	−0.325898	+	0.682759i
$112$	−9.43061	+	0.618115i	−0.891109	+	0.0584064i
$113$	5.67323	+	4.97529i	0.533692	+	0.468035i	0.883265	−	0.468874i	$-0.155340\pi$
$113$	5.67323	+	4.97529i	0.533692	+	0.468035i	−0.349573	+	0.936909i	$0.613673\pi$
$114$	−1.97580	−	2.50776i	−0.185051	−	0.234874i
$115$	6.04824	+	1.62062i	0.564001	+	0.151124i
$116$	0.235348	+	1.18318i	0.0218515	+	0.109855i
$117$	12.9557	−	7.92911i	1.19776	−	0.733046i
$118$		−	3.17346i		−	0.292141i
$119$	−5.97697	+	9.83666i	−0.547908	+	0.901726i
$120$	−0.364364	−	1.71661i	−0.0332618	−	0.156704i
$121$	5.68856	−	4.36499i	0.517142	−	0.396817i
$122$	−0.0324787	+	0.0956790i	−0.00294048	+	0.00866237i
$123$	6.07866	+	3.95000i	0.548094	+	0.356159i
$124$	0.270912	−	4.13332i	0.0243286	−	0.371183i
$125$	−7.38770	−	1.46950i	−0.660776	−	0.131436i
$126$	0.107698	−	2.70179i	0.00959450	−	0.240695i
$127$	−1.70901	−	4.12592i	−0.151650	−	0.366116i	0.829737	−	0.558154i	$-0.188490\pi$
$127$	−1.70901	−	4.12592i	−0.151650	−	0.366116i	−0.981387	+	0.192038i	$0.938490\pi$
$128$	−5.49537	+	7.16170i	−0.485726	+	0.633011i
$129$	3.85168	+	13.6720i	0.339122	+	1.20375i
$130$	−0.868208	+	0.990001i	−0.0761468	+	0.0868288i
$131$	4.30765	−	2.12430i	0.376361	−	0.185601i	−0.244263	−	0.969709i	$-0.578546\pi$
$131$	4.30765	−	2.12430i	0.376361	−	0.185601i	0.620624	+	0.784108i	$0.286879\pi$
$132$	−13.9773	−	0.736517i	−1.21657	−	0.0641056i
$133$	−10.5084	−	11.9825i	−0.911193	−	1.03902i
$134$	0.747474	+	0.309614i	0.0645720	+	0.0267466i
$135$	−4.16298	+	0.433945i	−0.358293	+	0.0373480i
$136$	1.55655	+	4.94692i	0.133473	+	0.424195i
$137$	11.1827	−	6.45634i	0.955403	−	0.551602i	0.0606478	−	0.998159i	$-0.480683\pi$
$137$	11.1827	−	6.45634i	0.955403	−	0.551602i	0.894755	+	0.446557i	$0.147350\pi$
$138$	4.09812	−	1.44990i	0.348855	−	0.123424i
$139$	11.5966	+	3.93652i	0.983613	+	0.333892i	0.766492	−	0.642253i	$-0.222000\pi$
$139$	11.5966	+	3.93652i	0.983613	+	0.333892i	0.217120	+	0.976145i	$0.430334\pi$
$140$	−1.10333	−	4.11770i	−0.0932487	−	0.348009i
$141$	4.16987	−	3.28533i	0.351166	−	0.276675i
$142$	0.600940	−	0.203992i	0.0504298	−	0.0171186i
$143$	11.9906	+	17.9453i	1.00271	+	1.50066i
$144$	7.36311	+	6.99532i	0.613592	+	0.582943i
$145$	−0.473562	+	0.196156i	−0.0393272	+	0.0162899i
$146$	−1.60950	−	0.793716i	−0.133203	−	0.0656884i
$147$	−0.0175910	−	1.37373i	−0.00145088	−	0.113303i
$148$	3.85859	+	7.82444i	0.317174	+	0.643165i
$149$	6.93257	−	1.85758i	0.567939	−	0.152179i	0.0365876	−	0.999330i	$-0.488351\pi$
$149$	6.93257	−	1.85758i	0.567939	−	0.152179i	0.531351	+	0.847152i	$0.321685\pi$
$150$	−2.23590	+	0.959865i	−0.182561	+	0.0783726i
$151$	−5.26475	+	0.693117i	−0.428439	+	0.0564051i	−0.341662	−	0.939823i	$-0.610990\pi$
$151$	−5.26475	+	0.693117i	−0.428439	+	0.0564051i	−0.0867766	+	0.996228i	$0.527657\pi$
$152$	−7.18084			−0.582443
$153$	12.1239	−	2.45198i	0.980155	−	0.198231i
$154$	3.84199			0.309596
$155$	1.74496	−	0.229728i	0.140158	−	0.0184522i
$156$	1.95879	−	16.5094i	0.156829	−	1.32181i
$157$	16.3128	−	4.37101i	1.30190	−	0.348844i	0.459735	−	0.888056i	$-0.347945\pi$
$157$	16.3128	−	4.37101i	1.30190	−	0.348844i	0.842170	+	0.539212i	$0.181278\pi$
$158$	−0.869124	−	1.76241i	−0.0691438	−	0.140210i
$159$	14.2809	−	8.49075i	1.13255	−	0.673361i
$160$	−2.60700	−	1.28563i	−0.206102	−	0.101638i
$161$	20.0488	−	8.30449i	1.58007	−	0.654485i
$162$	−2.21171	+	1.88462i	−0.173769	+	0.148070i
$163$	−5.10782	−	7.64440i	−0.400076	−	0.598755i	0.575665	−	0.817686i	$-0.304743\pi$
$163$	−5.10782	−	7.64440i	−0.400076	−	0.598755i	−0.975740	+	0.218930i	$0.929743\pi$
$164$	7.51342	−	2.55046i	0.586700	−	0.199158i
$165$	−0.851697	−	5.88588i	−0.0663045	−	0.458215i
$166$	−0.899327	−	3.35633i	−0.0698013	−	0.260502i
$167$	−12.9628	−	4.40028i	−1.00309	−	0.340504i	−0.228897	−	0.973451i	$-0.573512\pi$
$167$	−12.9628	−	4.40028i	−1.00309	−	0.340504i	−0.774195	+	0.632947i	$0.781845\pi$
$168$	−4.62347	−	3.95110i	−0.356708	−	0.304834i
$169$	−10.9429	+	6.31786i	−0.841758	+	0.485989i
$170$	−0.940409	+	0.515205i	−0.0721261	+	0.0395144i
$171$	−1.80000	+	17.0324i	−0.137650	+	1.30250i
$172$	14.3633	+	5.94946i	1.09519	+	0.453642i
$173$	0.529731	+	0.604042i	0.0402747	+	0.0459245i	0.771626	−	0.636076i	$-0.219444\pi$
$173$	0.529731	+	0.604042i	0.0402747	+	0.0459245i	−0.731352	+	0.682000i	$0.761110\pi$
$174$	−0.193896	+	0.298388i	−0.0146993	+	0.0226207i
$175$	−10.8941	+	5.37240i	−0.823520	+	0.406115i
$176$	−9.51496	+	10.8497i	−0.717217	+	0.817830i
$177$	−11.8830	+	12.1913i	−0.893185	+	0.916356i
$178$	−2.64297	+	3.44439i	−0.198099	+	0.258168i
$179$	−2.75669	−	6.65524i	−0.206045	−	0.497436i	0.786749	−	0.617273i	$-0.211763\pi$
$179$	−2.75669	−	6.65524i	−0.206045	−	0.497436i	−0.992794	+	0.119837i	$0.961763\pi$
$180$	−2.44678	+	3.87301i	−0.182372	+	0.288677i
$181$	−3.34914	−	0.666185i	−0.248939	−	0.0495171i	0.0690433	−	0.997614i	$-0.478005\pi$
$181$	−3.34914	−	0.666185i	−0.248939	−	0.0495171i	−0.317983	+	0.948097i	$0.603005\pi$
$182$	−0.298467	+	4.55373i	−0.0221239	+	0.337545i
$183$	0.483043	−	0.245949i	0.0357076	−	0.0181811i
$184$	3.14286	−	9.25856i	0.231695	−	0.682550i
$185$	−2.94087	+	2.25661i	−0.216217	+	0.165909i
$186$	0.908259	−	0.817331i	0.0665968	−	0.0599296i
$187$	4.16736	+	17.0742i	0.304747	+	1.24859i
$188$		−	5.81035i		−	0.423763i
$189$	−10.5306	+	9.97607i	−0.765990	+	0.725652i
$190$	−0.289660	−	1.45622i	−0.0210142	−	0.105645i
$191$	8.09867	+	2.17003i	0.585999	+	0.157018i	0.539624	−	0.841906i	$-0.318566\pi$
$191$	8.09867	+	2.17003i	0.585999	+	0.157018i	0.0463750	+	0.998924i	$0.485233\pi$
$192$	9.60938	−	1.39049i	0.693497	−	0.100350i
$193$	7.90835	+	6.93543i	0.569255	+	0.499223i	0.894899	−	0.446269i	$-0.147248\pi$
$193$	7.90835	+	6.93543i	0.569255	+	0.499223i	−0.325644	+	0.945493i	$0.605581\pi$
$194$	3.71123	−	0.243247i	0.266451	−	0.0174641i
$195$	7.04242	−	0.552229i	0.504318	−	0.0395459i
$196$	−1.19296	−	0.915390i	−0.0852114	−	0.0653850i
$197$	−12.4640	+	8.32821i	−0.888027	+	0.593360i	−0.913736	−	0.406309i	$-0.866816\pi$
$197$	−12.4640	+	8.32821i	−0.888027	+	0.593360i	0.0257092	+	0.999669i	$0.491816\pi$
$198$	−2.80088	−	3.03344i	−0.199050	−	0.215577i
$199$	5.21079	−	7.79850i	0.369383	−	0.552821i	−0.599489	−	0.800383i	$-0.704629\pi$
$199$	5.21079	−	7.79850i	0.369383	−	0.552821i	0.968872	+	0.247562i	$0.0796295\pi$
$200$	−1.41648	+	5.28638i	−0.100160	+	0.373804i
$201$	−1.71218	−	3.98836i	−0.120768	−	0.281317i
$202$	0.209679	+	0.273260i	0.0147530	+	0.0192265i
$203$	−0.888218	+	1.53844i	−0.0623407	+	0.107977i
$204$	6.10420	−	12.0842i	0.427380	−	0.846063i
$205$	1.68568	+	2.91969i	0.117733	+	0.203920i
$206$	−1.64146	+	3.96283i	−0.114366	+	0.276103i
$207$	−21.1727	−	9.77541i	−1.47161	−	0.679438i
$208$	−12.1205	−	12.1205i	−0.840406	−	0.840406i
$209$	−24.2837	−	1.59164i	−1.67974	−	0.110096i
$210$	0.614751	−	1.09698i	0.0424218	−	0.0756990i
$211$	−0.545030	−	8.31554i	−0.0375214	−	0.572466i	−0.974686	−	0.223578i	$-0.928226\pi$
$211$	−0.545030	−	8.31554i	−0.0375214	−	0.572466i	0.937165	−	0.348887i	$-0.113440\pi$
$212$	2.37359	−	18.0292i	0.163019	−	1.23825i
$213$	−3.07245	−	1.46656i	−0.210521	−	0.100487i
$214$	2.46219	−	4.99283i	0.168312	−	0.341302i
$215$	−1.28873	+	6.47886i	−0.0878903	+	0.441854i
$216$	0.251000	+	6.53087i	0.0170784	+	0.444370i
$217$	4.31309	−	4.31309i	0.292792	−	0.292792i
$218$	1.30181	−	1.14165i	0.0881694	−	0.0773225i
$219$	3.21105	+	9.07596i	0.216983	+	0.613296i
$220$	−5.63721	−	3.25465i	−0.380061	−	0.219428i
$221$	−20.5610	+	3.61295i	−1.38308	+	0.243034i
$222$	−0.795942	+	2.44728i	−0.0534201	+	0.164251i
$223$	−0.998189	−	7.58200i	−0.0668437	−	0.507728i	−0.991814	−	0.127689i	$-0.959244\pi$
$223$	−0.998189	−	7.58200i	−0.0668437	−	0.507728i	0.924970	−	0.380039i	$-0.124089\pi$
$224$	−9.88035	+	1.96532i	−0.660159	+	0.131314i
$225$	12.1838	+	4.68490i	0.812253	+	0.312327i
$226$	2.02567	+	1.35351i	0.134746	+	0.0900342i
$227$	−0.711868	−	2.09710i	−0.0472484	−	0.139189i	0.920745	−	0.390165i	$-0.127582\pi$
$227$	−0.711868	−	2.09710i	−0.0472484	−	0.139189i	−0.967993	+	0.250976i	$0.919249\pi$
$228$	13.4241	+	13.0846i	0.889032	+	0.866551i
$229$	−19.4061	−	2.55486i	−1.28239	−	0.168830i	−0.541641	−	0.840610i	$-0.682197\pi$
$229$	−19.4061	−	2.55486i	−1.28239	−	0.168830i	−0.740751	+	0.671780i	$0.765530\pi$
$230$	2.00434	+	0.263876i	0.132162	+	0.0173995i
$231$	−14.7596	−	14.3864i	−0.971110	−	0.946554i
$232$	0.257277	+	0.757914i	0.0168911	+	0.0497595i
$233$	−15.2210	−	10.1704i	−0.997161	−	0.666282i	−0.0539737	−	0.998542i	$-0.517189\pi$
$233$	−15.2210	−	10.1704i	−0.997161	−	0.666282i	−0.943188	+	0.332260i	$0.892189\pi$
$234$	3.81298	−	3.08409i	0.249263	−	0.201613i
$235$	2.42138	−	0.481642i	0.157953	−	0.0314189i
$236$	2.43218	+	18.4743i	0.158322	+	1.20257i
$237$	−3.26048	+	10.0250i	−0.211791	+	0.651194i
$238$	−1.49870	+	3.40060i	−0.0971460	+	0.220428i
$239$	−18.9106	−	10.9180i	−1.22323	−	0.706229i	−0.257621	−	0.966246i	$-0.582939\pi$
$239$	−18.9106	−	10.9180i	−1.22323	−	0.706229i	−0.965604	+	0.260017i	$0.916272\pi$
$240$	1.57539	+	4.45281i	0.101691	+	0.287427i
$241$	6.23041	−	5.46392i	0.401336	−	0.351962i	−0.434759	−	0.900547i	$-0.643166\pi$
$241$	6.23041	−	5.46392i	0.401336	−	0.351962i	0.836095	+	0.548585i	$0.184833\pi$
$242$	1.63696	−	1.63696i	0.105228	−	0.105228i
$243$	15.5536	+	1.04173i	0.997765	+	0.0668267i
$244$	0.115744	−	0.581886i	0.00740978	−	0.0372515i
$245$	0.282586	−	0.573029i	0.0180538	−	0.0366095i
$246$	2.11224	+	1.00823i	0.134672	+	0.0642823i
$247$	3.77299	−	28.6587i	0.240070	−	1.82351i
$248$	−0.179744	−	2.74236i	−0.0114138	−	0.174140i
$249$	−9.11292	+	16.2614i	−0.577508	+	1.03053i
$250$	−2.42673	−	0.159056i	−0.153480	−	0.0100596i
$251$	−5.47029	−	5.47029i	−0.345282	−	0.345282i	0.513067	−	0.858349i	$-0.328509\pi$
$251$	−5.47029	−	5.47029i	−0.345282	−	0.345282i	−0.858349	+	0.513067i	$0.828509\pi$
$252$	1.44373	+	15.8110i	0.0909463	+	0.995999i
$253$	12.6805	−	30.6134i	0.797215	−	1.92465i
$254$	−0.720930	−	1.24869i	−0.0452351	−	0.0783496i
$255$	5.54191	+	1.54213i	0.347048	+	0.0965721i
$256$	4.14850	−	7.18541i	0.259281	−	0.449088i
$257$	17.1196	+	22.3107i	1.06789	+	1.39170i	0.914997	+	0.403461i	$0.132193\pi$
$257$	17.1196	+	22.3107i	1.06789	+	1.39170i	0.152895	+	0.988242i	$0.451140\pi$
$258$	1.80909	+	4.21409i	0.112629	+	0.262358i
$259$	−3.32501	+	12.4091i	−0.206606	+	0.771064i
$260$	4.29551	−	6.42868i	0.266396	−	0.398690i
$261$	1.86220	−	0.420256i	0.115267	−	0.0260132i
$262$	1.28936	−	0.861522i	0.0796569	−	0.0532250i
$263$	−12.3492	−	9.47588i	−0.761485	−	0.584308i	0.153333	−	0.988175i	$-0.450999\pi$
$263$	−12.3492	−	9.47588i	−0.761485	−	0.584308i	−0.914818	+	0.403867i	$0.867666\pi$
$264$	−9.25807	+	0.725968i	−0.569795	+	0.0446802i
$265$	7.71015	−	0.505350i	0.473631	−	0.0310434i
$266$	−3.86871	−	3.39277i	−0.237206	−	0.208024i
$267$	23.0509	−	3.33551i	1.41069	−	0.204130i
$268$	−4.58871	−	1.22954i	−0.280300	−	0.0751061i
$269$	−0.513314	−	2.58060i	−0.0312973	−	0.157342i	0.961976	−	0.273133i	$-0.0880598\pi$
$269$	−0.513314	−	2.58060i	−0.0312973	−	0.157342i	−0.993274	+	0.115791i	$0.963060\pi$
$270$	−1.31429	+	0.314343i	−0.0799849	+	0.0191303i
$271$			9.04660i			0.549542i	0.961510	+	0.274771i	$0.0886020\pi$
$271$			9.04660i			0.549542i	−0.961510	+	0.274771i	$0.911398\pi$
$272$	−5.89164	−	12.6541i	−0.357233	−	0.767270i
$273$	18.1981	−	16.3762i	1.10140	−	0.991135i
$274$	3.30751	−	2.53794i	0.199814	−	0.153323i
$275$	−5.96190	+	17.5632i	−0.359516	+	1.05910i
$276$	−22.7459	+	11.5814i	−1.36914	+	0.697121i
$277$	−1.28518	+	19.6081i	−0.0772190	+	1.17813i	0.766823	+	0.641858i	$0.221836\pi$
$277$	−1.28518	+	19.6081i	−0.0772190	+	1.17813i	−0.844042	+	0.536276i	$0.819830\pi$
$278$	3.87798	+	0.771378i	0.232586	+	0.0462642i
$279$	−6.54972	−	0.261083i	−0.392121	−	0.0156306i
$280$	−1.08237	−	2.61308i	−0.0646841	−	0.156161i
$281$	−6.99661	+	9.11816i	−0.417383	+	0.543944i	−0.953970	−	0.299901i	$-0.903046\pi$
$281$	−6.99661	+	9.11816i	−0.417383	+	0.543944i	0.536588	+	0.843845i	$0.319713\pi$
$282$	1.19633	−	1.22736i	0.0712402	−	0.0730884i
$283$	18.2768	−	20.8407i	1.08644	−	1.23885i	0.117108	−	0.993119i	$-0.462638\pi$
$283$	18.2768	−	20.8407i	1.08644	−	1.23885i	0.969337	−	0.245734i	$-0.0790289\pi$
$284$	−3.34203	+	1.64810i	−0.198313	+	0.0977970i
$285$	−4.34006	+	6.67893i	−0.257083	+	0.395625i
$286$	4.59446	+	5.23898i	0.271676	+	0.309787i
$287$	10.7947	+	4.47130i	0.637189	+	0.263932i
$288$	8.75467	+	6.36827i	0.515874	+	0.375254i
$289$	−16.7382	−	2.97176i	−0.984602	−	0.174810i
$290$	−0.143321	+	0.0827464i	−0.00841610	+	0.00485904i
$291$	−15.1681	−	12.9623i	−0.889171	−	0.759863i
$292$	9.97798	+	3.38707i	0.583917	+	0.198213i
$293$	−1.96402	−	7.32982i	−0.114739	−	0.428213i	0.884528	−	0.466487i	$-0.154481\pi$
$293$	−1.96402	−	7.32982i	−0.114739	−	0.428213i	−0.999267	+	0.0382743i	$0.987814\pi$
$294$	−0.0635226	−	0.438990i	−0.00370471	−	0.0256024i
$295$	−7.49726	+	2.54498i	−0.436507	+	0.148174i
$296$	3.21579	+	4.81277i	0.186914	+	0.279737i
$297$	−0.598759	+	22.1413i	−0.0347435	+	1.28477i
$298$	2.14084	−	0.886764i	0.124015	−	0.0513689i
$299$	35.2995	+	17.4078i	2.04143	+	1.00672i
$300$	12.2806	−	7.30147i	0.709023	−	0.421551i
$301$	10.1255	+	20.5326i	0.583627	+	1.18348i
$302$	−1.65604	+	0.443734i	−0.0952943	+	0.0255340i
$303$	0.217707	−	1.83492i	0.0125070	−	0.105413i
$304$	19.1623	−	2.52276i	1.09903	−	0.144690i
$305$	0.252087			0.0144345
$306$	3.77752	−	1.29580i	0.215946	−	0.0740761i
$307$	−17.0157			−0.971135			−0.485568	−	0.874199i	$-0.661387\pi$
$307$	−17.0157			−0.971135			−0.485568	+	0.874199i	$0.661387\pi$
$308$	−22.3661	+	2.94455i	−1.27443	+	0.167781i
$309$	21.1448	−	9.07736i	1.20288	−	0.516393i
$310$	0.548880	−	0.147072i	0.0311743	−	0.00835312i
$311$	1.14874	+	2.32942i	0.0651392	+	0.132089i	0.927007	−	0.375043i	$-0.122372\pi$
$311$	1.14874	+	2.32942i	0.0651392	+	0.132089i	−0.861868	+	0.507132i	$0.830705\pi$
$312$	−0.141237	−	11.0296i	−0.00799597	−	0.624425i
$313$	−4.96783	−	2.44986i	−0.280798	−	0.138474i	0.296437	−	0.955053i	$-0.404202\pi$
$313$	−4.96783	−	2.44986i	−0.280798	−	0.138474i	−0.577235	+	0.816578i	$0.695868\pi$
$314$	5.03754	−	2.08662i	0.284285	−	0.117755i
$315$	−6.46932	+	1.91229i	−0.364505	+	0.107745i
$316$	6.41033	+	9.59373i	0.360609	+	0.539690i
$317$	4.93594	−	1.67552i	0.277230	−	0.0941068i	−0.179362	−	0.983783i	$-0.557403\pi$
$317$	4.93594	−	1.67552i	0.277230	−	0.0941068i	0.456592	+	0.889676i	$0.349070\pi$
$318$	4.21352	−	3.31972i	0.236283	−	0.186161i
$319$	0.702051	+	2.62009i	0.0393073	+	0.146697i
$320$	4.27585	+	1.45145i	0.239027	+	0.0811388i
$321$	−28.1546	+	9.96101i	−1.57143	+	0.555969i
$322$	6.06766	−	3.50317i	0.338138	−	0.195224i
$323$	10.8815	−	20.8730i	0.605461	−	1.16141i
$324$	11.4311	−	12.6664i	0.635059	−	0.703688i
$325$	−20.3537	−	8.43077i	−1.12902	−	0.467655i
$326$	−1.95717	−	2.23172i	−0.108397	−	0.123604i
$327$	−9.27602	−	0.488790i	−0.512965	−	0.0270301i
$328$	4.72147	−	2.32837i	0.260700	−	0.128563i
$329$	5.64144	−	6.43283i	0.311023	−	0.354653i
$330$	−0.520671	−	1.84818i	−0.0286620	−	0.101739i
$331$	−16.2968	+	21.2384i	−0.895752	+	1.16737i	0.0894539	+	0.995991i	$0.471488\pi$
$331$	−16.2968	+	21.2384i	−0.895752	+	1.16737i	−0.985206	+	0.171376i	$0.945179\pi$
$332$	7.80776	+	18.8496i	0.428507	+	1.03451i
$333$	12.2216	−	6.42119i	0.669739	−	0.351879i
$334$	−4.33484	−	0.862253i	−0.237192	−	0.0471804i
$335$	0.132017	−	2.01420i	0.00721288	−	0.110047i
$336$	13.7259	+	8.91930i	0.748812	+	0.486588i
$337$	−3.99585	+	11.7714i	−0.217668	+	0.641229i	0.782167	+	0.623068i	$0.214114\pi$
$337$	−3.99585	+	11.7714i	−0.217668	+	0.641229i	−0.999835	+	0.0181602i	$0.994219\pi$
$338$	−3.23657	+	2.48351i	−0.176046	+	0.135085i
$339$	−2.71369	−	12.7849i	−0.147388	−	0.694378i
$340$	5.07972	−	3.72000i	0.275486	−	0.201745i
$341$		−	9.31380i		−	0.504371i
$342$	0.141597	+	5.52792i	0.00765668	+	0.298916i
$343$	3.38035	+	16.9942i	0.182522	+	0.917599i
$344$	9.96343	+	2.66969i	0.537192	+	0.143940i
$345$	−6.71189	−	8.51900i	−0.361356	−	0.458647i
$346$	0.195023	+	0.171030i	0.0104845	+	0.00919465i
$347$	5.45262	−	0.357383i	0.292712	−	0.0191853i	0.0816601	−	0.996660i	$-0.473978\pi$
$347$	5.45262	−	0.357383i	0.292712	−	0.0191853i	0.211052	+	0.977475i	$0.432311\pi$
$348$	0.900077	−	1.88567i	0.0482492	−	0.101082i
$349$	0.573008	+	0.439684i	0.0306724	+	0.0235358i	0.623984	−	0.781437i	$-0.285513\pi$
$349$	0.573008	+	0.439684i	0.0306724	+	0.0235358i	−0.593311	+	0.804973i	$0.702180\pi$
$350$	−3.26082	+	2.17881i	−0.174298	+	0.116462i
$351$	−26.1966	−	2.42974i	−1.39827	−	0.129690i
$352$	−8.54596	+	12.7899i	−0.455501	+	0.681705i
$353$	1.31318	−	4.90084i	0.0698934	−	0.260846i	−0.922134	−	0.386872i	$-0.873556\pi$
$353$	1.31318	−	4.90084i	0.0698934	−	0.260846i	0.992027	+	0.126026i	$0.0402223\pi$
$354$	−3.29000	+	4.40323i	−0.174862	+	0.234029i
$355$	−0.963857	−	1.25612i	−0.0511562	−	0.0666680i
$356$	12.7462	−	22.0771i	0.675547	−	1.17008i
$357$	18.4911	−	7.45206i	0.978651	−	0.394405i
$358$	−1.16288	−	2.01417i	−0.0614603	−	0.106452i
$359$	8.31165	−	20.0661i	0.438672	−	1.05905i	−0.537736	−	0.843113i	$-0.680720\pi$
$359$	8.31165	−	20.0661i	0.438672	−	1.05905i	0.976408	−	0.215934i	$-0.0692798\pi$
$360$	−1.27409	+	2.75957i	−0.0671503	+	0.145442i
$361$	9.61205	+	9.61205i	0.505897	+	0.505897i
$362$	−1.10013	−	0.0721066i	−0.0578218	−	0.00378984i
$363$	−12.4183	+	0.159020i	−0.651790	+	0.00834638i
$364$	−1.75252	−	26.7382i	−0.0918568	−	1.40146i
$365$	−0.584398	+	4.43894i	−0.0305888	+	0.232345i
$366$	0.144257	−	0.0990848i	0.00754046	−	0.00517925i
$367$	−13.7512	+	27.8847i	−0.717807	+	1.45557i	0.165224	+	0.986256i	$0.447165\pi$
$367$	−13.7512	+	27.8847i	−0.717807	+	1.45557i	−0.883032	+	0.469313i	$0.844502\pi$
$368$	−5.13410	+	25.8109i	−0.267633	+	1.34548i
$369$	−4.33919	−	11.7826i	−0.225889	−	0.613377i
$370$	−0.846275	+	0.846275i	−0.0439958	+	0.0439958i
$371$	20.1329	−	17.6561i	1.04525	−	0.916659i
$372$	−4.66100	+	5.45418i	−0.241662	+	0.282786i
$373$	13.1878	+	7.61399i	0.682839	+	0.394237i	0.800924	−	0.598766i	$-0.204342\pi$
$373$	13.1878	+	7.61399i	0.682839	+	0.394237i	−0.118085	+	0.993004i	$0.537675\pi$
$374$	2.05351	+	5.28984i	0.106185	+	0.273531i
$375$	8.72708	+	9.69797i	0.450664	+	0.500801i
$376$	−0.503184	−	3.82206i	−0.0259497	−	0.197108i
$377$	−3.16001	+	0.628565i	−0.162749	+	0.0323728i
$378$	−2.95045	+	3.63713i	−0.151755	+	0.187074i
$379$	−4.09074	−	2.73335i	−0.210127	−	0.140403i	0.446053	−	0.895006i	$-0.352829\pi$
$379$	−4.09074	−	2.73335i	−0.210127	−	0.140403i	−0.656181	+	0.754604i	$0.727829\pi$
$380$	2.80232	+	8.25537i	0.143756	+	0.423491i
$381$	−1.90616	+	7.49655i	−0.0976554	+	0.384060i
$382$	2.68384	+	0.353334i	0.137317	+	0.0180781i
$383$	37.9150	+	4.99161i	1.93737	+	0.255059i	0.996492	−	0.0836937i	$-0.0266717\pi$
$383$	37.9150	+	4.99161i	1.93737	+	0.255059i	0.940875	+	0.338753i	$0.110005\pi$
$384$	15.0496	−	4.23980i	0.767998	−	0.216361i
$385$	−3.08111	−	9.07666i	−0.157028	−	0.462589i
$386$	2.82374	+	1.88676i	0.143725	+	0.0960337i
$387$	8.82979	−	22.9632i	0.448844	−	1.16729i
$388$	−21.4185	+	4.26040i	−1.08736	+	0.216289i
$389$	−1.70185	−	12.9268i	−0.0862871	−	0.655415i	−0.978863	−	0.204518i	$-0.934437\pi$
$389$	−1.70185	−	12.9268i	−0.0862871	−	0.655415i	0.892576	−	0.450898i	$-0.148896\pi$
$390$	2.23101	−	0.473551i	0.112972	−	0.0239792i
$391$	22.1499	+	23.1655i	1.12017	+	1.17153i
$392$	−0.864006	−	0.498834i	−0.0436389	−	0.0251949i
$393$	−8.17925	−	1.51835i	−0.412588	−	0.0765905i
$394$	−3.63878	+	3.19112i	−0.183319	+	0.160767i
$395$	−3.46667	+	3.46667i	−0.174427	+	0.174427i
$396$	18.6301	+	15.5125i	0.936200	+	0.779533i
$397$	5.01160	−	25.1950i	0.251525	−	1.26450i	−0.624036	−	0.781395i	$-0.714508\pi$
$397$	5.01160	−	25.1950i	0.251525	−	1.26450i	0.875561	−	0.483107i	$-0.160492\pi$
$398$	1.33933	−	2.71590i	0.0671347	−	0.136136i
$399$	2.15799	+	27.5203i	0.108035	+	1.37774i
$400$	1.92272	−	14.6045i	0.0961359	−	0.730225i
$401$	−2.54401	−	38.8141i	−0.127042	−	1.93828i	−0.301187	−	0.953565i	$-0.597383\pi$
$401$	−2.54401	−	38.8141i	−0.127042	−	1.93828i	0.174145	−	0.984720i	$-0.444284\pi$
$402$	−0.716149	−	1.20452i	−0.0357182	−	0.0600760i
$403$	11.0392	+	0.723548i	0.549902	+	0.0360425i
$404$	−1.43008	−	1.43008i	−0.0711489	−	0.0711489i
$405$	6.22609	+	3.71376i	0.309377	+	0.184538i
$406$	−0.219486	+	0.529886i	−0.0108929	+	0.0262978i
$407$	9.80821	+	16.9883i	0.486175	+	0.842080i
$408$	2.96885	−	8.47764i	0.146980	−	0.419706i
$409$	−15.8253	+	27.4102i	−0.782509	+	1.35535i	0.147967	+	0.988992i	$0.452727\pi$
$409$	−15.8253	+	27.4102i	−0.782509	+	1.35535i	−0.930476	+	0.366353i	$0.880606\pi$
$410$	0.662630	+	0.863556i	0.0327250	+	0.0426480i
$411$	−22.2096	−	2.63511i	−1.09552	−	0.129980i
$412$	6.51856	−	24.3276i	0.321146	−	1.19853i
$413$	−15.2444	+	22.8149i	−0.750130	+	1.12265i
$414$	−7.18936	−	2.23685i	−0.353338	−	0.109935i
$415$	−7.20808	+	4.81629i	−0.353831	+	0.236422i
$416$	−14.4954	−	11.1227i	−0.710696	−	0.545336i
$417$	−12.0094	−	17.4845i	−0.588104	−	0.856219i
$418$	−7.84031	+	0.513881i	−0.383482	+	0.0251347i
$419$	10.0828	+	8.84238i	0.492577	+	0.431979i	0.869254	−	0.494366i	$-0.164600\pi$
$419$	10.0828	+	8.84238i	0.492577	+	0.431979i	−0.376676	+	0.926345i	$0.622933\pi$
$420$	−2.73802	+	6.85722i	−0.133602	+	0.334598i
$421$	−13.8990	−	3.72424i	−0.677398	−	0.181508i	−0.0963130	−	0.995351i	$-0.530705\pi$
$421$	−13.8990	−	3.72424i	−0.677398	−	0.181508i	−0.581085	+	0.813843i	$0.697372\pi$
$422$	−0.524898	−	2.63884i	−0.0255516	−	0.128457i
$423$	−9.19174	+	0.235445i	−0.446918	+	0.0114477i
$424$		−	12.0652i		−	0.585937i
$425$	−13.2198	−	12.1281i	−0.641255	−	0.588298i
$426$	−1.04530	−	0.339968i	−0.0506449	−	0.0164715i
$427$	0.693115	−	0.531846i	0.0335422	−	0.0257378i
$428$	−10.5070	+	30.9527i	−0.507877	+	1.49616i
$429$	1.96708	−	37.3304i	0.0949716	−	1.80233i
$430$	−0.139489	+	2.12820i	−0.00672677	+	0.102631i
$431$	−19.9425	−	3.96681i	−0.960596	−	0.191074i	−0.310201	−	0.950671i	$-0.600396\pi$
$431$	−19.9425	−	3.96681i	−0.960596	−	0.191074i	−0.650395	+	0.759597i	$0.725396\pi$
$432$	−2.96422	−	17.3396i	−0.142616	−	0.834254i
$433$	−4.60087	−	11.1075i	−0.221104	−	0.533792i	0.773937	−	0.633263i	$-0.218285\pi$
$433$	−4.60087	−	11.1075i	−0.221104	−	0.533792i	−0.995040	+	0.0994712i	$0.968285\pi$
$434$	1.19886	−	1.56239i	0.0575471	−	0.0749969i
$435$	0.860435	+	0.218784i	0.0412547	+	0.0104899i
$436$	−6.70347	+	7.64384i	−0.321038	+	0.366074i
$437$	−39.8026	+	19.6285i	−1.90402	+	0.938958i
$438$	1.41034	+	2.76990i	0.0673886	+	0.132351i
$439$	26.6831	+	30.4262i	1.27351	+	1.45216i	0.831867	+	0.554975i	$0.187272\pi$
$439$	26.6831	+	30.4262i	1.27351	+	1.45216i	0.441647	+	0.897189i	$0.354394\pi$
$440$	−3.99003	−	1.65272i	−0.190217	−	0.0787905i
$441$	−1.39977	+	1.92431i	−0.0666557	+	0.0916337i
$442$	−6.42932	+	2.02299i	−0.305812	+	0.0962238i
$443$	−19.5513	+	11.2880i	−0.928912	+	0.536308i	−0.886467	−	0.462791i	$-0.846848\pi$
$443$	−19.5513	+	11.2880i	−0.928912	+	0.536308i	−0.0424450	+	0.999099i	$0.513515\pi$
$444$	2.75794	−	14.8568i	0.130886	−	0.705074i
$445$	10.2569	+	3.48174i	0.486222	+	0.165050i
$446$	−0.639042	−	2.38494i	−0.0302595	−	0.112930i
$447$	−11.5449	−	4.60975i	−0.546053	−	0.218034i
$448$	14.8187	−	5.03027i	0.700118	−	0.237658i
$449$	16.1218	+	24.1280i	0.760836	+	1.13867i	0.986387	+	0.164440i	$0.0525817\pi$
$449$	16.1218	+	24.1280i	0.760836	+	1.13867i	−0.225551	+	0.974231i	$0.572418\pi$
$450$	4.09747	+	0.986189i	0.193157	+	0.0464894i
$451$	16.4829	−	6.82742i	0.776148	−	0.321491i
$452$	−12.8298	−	6.32694i	−0.603462	−	0.297594i
$453$	8.02350	+	4.49638i	0.376977	+	0.211258i
$454$	−0.316245	−	0.641282i	−0.0148421	−	0.0300969i
$455$	10.9975	−	2.94677i	0.515571	−	0.138147i
$456$	9.96354	+	7.44456i	0.466585	+	0.348623i
$457$	−33.7118	+	4.43824i	−1.57697	+	0.207612i	−0.867614	−	0.497238i	$-0.834347\pi$
$457$	−33.7118	+	4.43824i	−1.57697	+	0.207612i	−0.709356	+	0.704850i	$0.751014\pi$
$458$	−6.31957			−0.295294
$459$	−19.3641	−	9.16694i	−0.903837	−	0.427876i
$460$	−11.8705			−0.553464
$461$	27.0179	−	3.55698i	1.25835	−	0.165665i	0.528300	−	0.849058i	$-0.322830\pi$
$461$	27.0179	−	3.55698i	1.25835	−	0.165665i	0.730051	+	0.683393i	$0.239496\pi$
$462$	−5.33082	−	3.98308i	−0.248012	−	0.185310i
$463$	−24.9892	+	6.69584i	−1.16135	+	0.311182i	−0.787504	−	0.616310i	$-0.788627\pi$
$463$	−24.9892	+	6.69584i	−1.16135	+	0.311182i	−0.373843	+	0.927492i	$0.621960\pi$
$464$	−0.952820	−	1.93213i	−0.0442335	−	0.0896968i
$465$	−2.65932	−	1.49029i	−0.123323	−	0.0691104i
$466$	−5.30085	−	2.61409i	−0.245557	−	0.121095i
$467$	28.3180	−	11.7297i	1.31040	−	0.542787i	0.385401	−	0.922749i	$-0.374063\pi$
$467$	28.3180	−	11.7297i	1.31040	−	0.542787i	0.925002	+	0.379962i	$0.124063\pi$
$468$	−19.8336	+	20.8763i	−0.916806	+	0.965009i
$469$	−3.88651	−	5.81657i	−0.179462	−	0.268584i
$470$	0.754787	−	0.256216i	0.0348157	−	0.0118183i
$471$	−27.1658	−	10.8471i	−1.25174	−	0.499806i
$472$	3.19979	+	11.9418i	0.147282	+	0.549665i
$473$	33.1020	+	11.2366i	1.52203	+	0.516659i
$474$	−0.621209	+	3.34641i	−0.0285331	+	0.153706i
$475$	21.5130	−	12.4205i	0.987084	−	0.569893i
$476$	6.11837	−	20.9452i	0.280435	−	0.960021i
$477$	−28.6176	−	3.02435i	−1.31031	−	0.138475i
$478$	−6.51340	−	2.69794i	−0.297916	−	0.123401i
$479$	−18.4393	−	21.0259i	−0.842511	−	0.960700i	0.157128	−	0.987578i	$-0.449777\pi$
$479$	−18.4393	−	21.0259i	−0.842511	−	0.960700i	−0.999639	+	0.0268785i	$0.991443\pi$
$480$	2.28441	+	4.48658i	0.104269	+	0.204783i
$481$	−20.8974	+	10.3055i	−0.952841	+	0.469889i
$482$	1.76410	−	2.01157i	0.0803524	−	0.0916244i
$483$	−36.4275	−	9.26247i	−1.65751	−	0.421457i
$484$	−8.27497	+	10.7841i	−0.376135	+	0.490189i
$485$	−3.55092	−	8.57268i	−0.161239	−	0.389265i
$486$	5.02262	−	0.322004i	0.227831	−	0.0146064i
$487$	10.4183	+	2.07233i	0.472098	+	0.0939062i	0.425405	−	0.905003i	$-0.360132\pi$
$487$	10.4183	+	2.07233i	0.472098	+	0.0939062i	0.0466932	+	0.998909i	$0.485132\pi$
$488$	0.0257448	−	0.392790i	0.00116541	−	0.0177808i
$489$	−0.837946	+	15.9021i	−0.0378932	+	0.719119i
$490$	0.0663075	−	0.195336i	0.00299547	−	0.00882436i
$491$	22.6045	−	17.3450i	1.02012	−	0.782769i	0.0437913	−	0.999041i	$-0.486056\pi$
$491$	22.6045	−	17.3450i	1.02012	−	0.782769i	0.976333	+	0.216272i	$0.0693897\pi$
$492$	−13.0691	−	4.25054i	−0.589201	−	0.191629i
$493$	−2.59294	−	0.400657i	−0.116780	−	0.0180447i
$494$		−	9.33267i		−	0.419897i
$495$	−4.92029	+	9.04973i	−0.221151	+	0.406755i
$496$	1.44309	+	7.25493i	0.0647969	+	0.325756i
$497$	−5.30026	−	1.42020i	−0.237749	−	0.0637047i
$498$	−2.23176	+	5.58932i	−0.100008	+	0.250464i
$499$	10.6758	+	9.36242i	0.477914	+	0.419120i	0.864114	−	0.503295i	$-0.167879\pi$
$499$	10.6758	+	9.36242i	0.477914	+	0.419120i	−0.386200	+	0.922415i	$0.626213\pi$
$500$	14.2491	−	0.933935i	0.637239	−	0.0417669i
$501$	13.4242	+	19.5443i	0.599751	+	0.873176i
$502$	−1.98157	−	1.52051i	−0.0884419	−	0.0678638i
$503$	−16.9393	+	11.3185i	−0.755288	+	0.504667i	−0.872605	−	0.488427i	$-0.837571\pi$
$503$	−16.9393	+	11.3185i	−0.755288	+	0.504667i	0.117317	+	0.993095i	$0.462571\pi$
$504$	2.31894	+	10.2755i	0.103294	+	0.457706i
$505$	0.477419	−	0.714508i	0.0212449	−	0.0317952i
$506$	2.76892	−	10.3337i	0.123093	−	0.459391i
$507$	21.7333	+	2.57859i	0.965209	+	0.114519i
$508$	5.15389	+	6.71668i	0.228667	+	0.298005i
$509$	−6.50648	+	11.2696i	−0.288395	+	0.499514i	−0.973427	−	0.228999i	$-0.926455\pi$
$509$	−6.50648	+	11.2696i	−0.288395	+	0.499514i	0.685032	+	0.728513i	$0.259788\pi$
$510$	1.83896	+	0.260090i	0.0814304	+	0.0115170i
$511$	7.75834	+	13.4378i	0.343209	+	0.594455i
$512$	7.93419	−	19.1548i	0.350645	−	0.846532i
$513$	20.1554	−	21.7666i	0.889883	−	0.961018i
$514$	6.42021	+	6.42021i	0.283183	+	0.283183i
$515$	10.6785	+	0.699907i	0.470552	+	0.0308416i
$516$	−13.7613	−	23.1457i	−0.605809	−	1.01893i
$517$	−0.854473	−	13.0367i	−0.0375797	−	0.573355i
$518$	−0.541392	+	4.11228i	−0.0237874	+	0.180683i
$519$	−0.108785	−	1.38730i	−0.00477513	−	0.0608959i
$520$	2.26886	−	4.60080i	0.0994962	−	0.201758i
$521$	1.11715	−	5.61631i	0.0489434	−	0.246055i	−0.948567	−	0.316577i	$-0.897466\pi$
$521$	1.11715	−	5.61631i	0.0489434	−	0.246055i	0.997510	+	0.0705218i	$0.0224664\pi$
$522$	0.578381	−	0.213001i	0.0253150	−	0.00932280i
$523$	−3.38005	+	3.38005i	−0.147799	+	0.147799i	−0.777134	−	0.629335i	$-0.783327\pi$
$523$	−3.38005	+	3.38005i	−0.147799	+	0.147799i	0.629335	+	0.777134i	$0.283327\pi$
$524$	−6.84571	+	6.00352i	−0.299056	+	0.262265i
$525$	20.6855	+	3.83994i	0.902789	+	0.167589i
$526$	−4.35232	−	2.51281i	−0.189770	−	0.109564i
$527$	8.24379	+	3.63316i	0.359105	+	0.158263i
$528$	24.4504	−	5.18979i	1.06407	−	0.225857i
$529$	−4.88520	−	37.1068i	−0.212400	−	1.61334i
$530$	2.44673	−	0.486684i	0.106279	−	0.0211402i
$531$	29.1270	−	4.59622i	1.26400	−	0.199459i
$532$	25.1219	+	16.7859i	1.08917	+	0.727762i
$533$	6.81175	+	20.0668i	0.295049	+	0.869188i
$534$	7.23804	−	2.03911i	0.313221	−	0.0882409i
$535$	−13.7701	−	1.81286i	−0.595332	−	0.0783769i
$536$	−3.12494	−	0.411406i	−0.134977	−	0.0177700i
$537$	−3.07470	+	12.0922i	−0.132683	+	0.521817i
$538$	−0.273064	−	0.804421i	−0.0117726	−	0.0346810i
$539$	−2.81127	−	1.87843i	−0.121090	−	0.0809098i
$540$	7.41019	−	2.83723i	0.318884	−	0.122095i
$541$	36.6083	−	7.28184i	1.57391	−	0.313071i	0.670522	−	0.741890i	$-0.266070\pi$
$541$	36.6083	−	7.28184i	1.57391	−	0.313071i	0.903390	+	0.428819i	$0.141070\pi$
$542$	0.381242	+	2.89582i	0.0163757	+	0.124386i
$543$	3.95633	+	4.39647i	0.169782	+	0.188671i
$544$	−7.98692	−	12.5533i	−0.342437	−	0.538218i
$545$	−3.74113	−	2.15995i	−0.160253	−	0.0925219i
$546$	5.13509	−	6.00895i	0.219762	−	0.257159i
$547$	1.56544	−	1.37285i	0.0669332	−	0.0586988i	−0.625226	−	0.780444i	$-0.714993\pi$
$547$	1.56544	−	1.37285i	0.0669332	−	0.0586988i	0.692159	+	0.721745i	$0.256660\pi$
$548$	−17.3095	+	17.3095i	−0.739425	+	0.739425i
$549$	−0.925211	−	0.159524i	−0.0394871	−	0.00680832i
$550$	−1.16826	+	5.87323i	−0.0498147	+	0.250436i
$551$	1.60680	−	3.25828i	0.0684522	−	0.138807i
$552$	−13.9593	+	9.58813i	−0.594149	+	0.408098i
$553$	−2.21775	+	16.8455i	−0.0943085	+	0.716344i
$554$	0.414937	+	6.33071i	0.0176290	+	0.268966i
$555$	6.41998	−	0.0822099i	0.272513	−	0.00348962i
$556$	−23.1668	−	1.51843i	−0.982491	−	0.0643959i
$557$	10.6020	+	10.6020i	0.449223	+	0.449223i	0.895096	−	0.445873i	$-0.147107\pi$
$557$	10.6020	+	10.6020i	0.449223	+	0.449223i	−0.445873	+	0.895096i	$0.647107\pi$
$558$	−2.10757	+	0.192446i	−0.0892206	+	0.00814687i
$559$	−15.8898	+	38.3613i	−0.672065	+	1.62251i
$560$	3.80636	+	6.59282i	0.160848	+	0.278597i
$561$	11.9190	−	28.0111i	0.503219	−	1.18263i
$562$	−1.85536	+	3.21358i	−0.0782637	+	0.135557i
$563$	−9.75205	−	12.7091i	−0.411000	−	0.535625i	0.541284	−	0.840840i	$-0.317938\pi$
$563$	−9.75205	−	12.7091i	−0.411000	−	0.535625i	−0.952284	+	0.305215i	$0.901272\pi$
$564$	−6.02373	+	8.06196i	−0.253645	+	0.339470i
$565$	1.57315	−	5.87108i	0.0661830	−	0.246998i
$566$	4.97215	−	7.44135i	0.208995	−	0.312783i
$567$	24.9539	−	2.92461i	1.04796	−	0.122822i
$568$	−2.05566	+	1.37355i	−0.0862537	+	0.0576329i
$569$	32.8414	+	25.2001i	1.37678	+	1.05644i	0.991001	+	0.133854i	$0.0427353\pi$
$569$	32.8414	+	25.2001i	1.37678	+	1.05644i	0.385783	+	0.922590i	$0.373931\pi$
$570$	−1.10779	+	2.32083i	−0.0464002	+	0.0972087i
$571$	17.7180	−	1.16130i	0.741474	−	0.0485988i	0.310016	−	0.950731i	$-0.399666\pi$
$571$	17.7180	−	1.16130i	0.741474	−	0.0485988i	0.431459	+	0.902133i	$0.357999\pi$
$572$	−30.7618	−	26.9774i	−1.28622	−	1.12798i
$573$	−8.98731	−	11.4070i	−0.375450	−	0.476536i
$574$	3.64381	+	0.976356i	0.152090	+	0.0407523i
$575$	6.59866	+	33.1737i	0.275183	+	1.38344i
$576$	−14.7747	−	8.03295i	−0.615614	−	0.334706i
$577$			2.00687i			0.0835470i	0.999127	+	0.0417735i	$0.0133008\pi$
$577$			2.00687i			0.0835470i	−0.999127	+	0.0417735i	$0.986699\pi$
$578$	−5.48316	−	0.245880i	−0.228069	−	0.0102273i
$579$	−3.78283	−	17.8218i	−0.157209	−	0.740649i
$580$	0.770924	−	0.591551i	0.0320109	−	0.0245628i
$581$	−9.65740	+	28.4498i	−0.400657	+	1.18030i
$582$	−5.40158	−	3.51002i	−0.223903	−	0.145495i
$583$	2.67426	−	40.8013i	0.110756	−	1.68982i
$584$	6.85686	+	1.36391i	0.283739	+	0.0564392i
$585$	−10.3440	−	6.53482i	−0.427671	−	0.270182i
$586$	−0.937577	−	2.26351i	−0.0387310	−	0.0935048i
$587$	−9.45552	+	12.3227i	−0.390271	+	0.508611i	−0.946626	−	0.322334i	$-0.895533\pi$
$587$	−9.45552	+	12.3227i	−0.390271	+	0.508611i	0.556355	+	0.830945i	$0.312199\pi$
$588$	0.706244	+	2.50689i	0.0291250	+	0.103382i
$589$	−8.22479	+	9.37857i	−0.338897	+	0.386437i
$590$	−2.29263	+	1.13060i	−0.0943860	+	0.0465460i
$591$	25.9281	+	1.36625i	1.06654	+	0.0562002i
$592$	−10.2722	−	11.7133i	−0.422187	−	0.481412i
$593$	0.256906	+	0.106414i	0.0105499	+	0.00436989i	0.387952	−	0.921680i	$-0.373183\pi$
$593$	0.256906	+	0.106414i	0.0105499	+	0.00436989i	−0.377402	+	0.926049i	$0.623183\pi$
$594$	0.741418	+	7.11269i	0.0304208	+	0.291837i
$595$	9.23578	+	0.813515i	0.378630	+	0.0333509i
$596$	−11.7832	+	6.80306i	−0.482660	+	0.278664i
$597$	−15.3150	+	5.41839i	−0.626799	+	0.221760i
$598$	12.0330	+	4.08465i	0.492066	+	0.167034i
$599$	−10.3597	−	38.6629i	−0.423286	−	1.57972i	−0.767638	−	0.640884i	$-0.778568\pi$
$599$	−10.3597	−	38.6629i	−0.423286	−	1.57972i	0.344352	−	0.938841i	$-0.388099\pi$
$600$	7.44591	−	5.86644i	0.303978	−	0.239496i
$601$	34.4601	−	11.6976i	1.40566	−	0.477156i	0.487413	−	0.873171i	$-0.337940\pi$
$601$	34.4601	−	11.6976i	1.40566	−	0.477156i	0.918244	+	0.396015i	$0.129607\pi$
$602$	4.10648	+	6.14578i	0.167367	+	0.250483i
$603$	−1.75914	+	7.30897i	−0.0716378	+	0.297644i
$604$	9.30053	−	3.85240i	0.378433	−	0.156752i
$605$	−5.18008	−	2.55453i	−0.210600	−	0.103857i
$606$	−0.00763878	−	0.596532i	−0.000310304	−	0.0242325i
$607$	−8.60587	−	17.4510i	−0.349301	−	0.708313i	0.649336	−	0.760502i	$-0.275047\pi$
$607$	−8.60587	−	17.4510i	−0.349301	−	0.708313i	−0.998637	+	0.0521887i	$0.983380\pi$
$608$	19.8999	−	5.33215i	0.807046	−	0.216247i
$609$	2.82735	−	1.21377i	0.114570	−	0.0491845i
$610$	0.0806932	−	0.0106235i	0.00326717	−	0.000430132i
$611$	15.5182			0.627800
$612$	−20.9977	+	10.4386i	−0.848780	+	0.421957i
$613$	−8.57112			−0.346184			−0.173092	−	0.984906i	$-0.555376\pi$
$613$	−8.57112			−0.346184			−0.173092	+	0.984906i	$0.555376\pi$
$614$	−5.44672	+	0.717075i	−0.219812	+	0.0289388i
$615$	0.688000	−	5.79871i	0.0277428	−	0.233826i
$616$	−14.4575	+	3.87387i	−0.582508	+	0.156082i
$617$	−12.8123	−	25.9808i	−0.515804	−	1.04595i	−0.986517	−	0.163661i	$-0.947670\pi$
$617$	−12.8123	−	25.9808i	−0.515804	−	1.04595i	0.470712	−	0.882287i	$-0.343997\pi$
$618$	6.38591	−	3.79675i	0.256879	−	0.152728i
$619$	21.7591	+	10.7304i	0.874573	+	0.431292i	0.823442	−	0.567400i	$-0.192051\pi$
$619$	21.7591	+	10.7304i	0.874573	+	0.431292i	0.0511308	+	0.998692i	$0.483717\pi$
$620$	−3.08258	+	1.27685i	−0.123799	+	0.0512794i
$621$	19.2431	+	35.5138i	0.772199	+	1.42512i
$622$	0.465880	+	0.697238i	0.0186801	+	0.0279567i
$623$	35.5470	−	12.0666i	1.42416	−	0.483437i
$624$	4.25178	+	29.3830i	0.170207	+	1.17626i
$625$	−4.06045	−	15.1538i	−0.162418	−	0.606152i
$626$	−1.69345	−	0.574848i	−0.0676838	−	0.0229755i
$627$	32.0440	+	27.3840i	1.27971	+	1.09361i
$628$	−27.7268	+	16.0081i	−1.10642	+	0.638791i
$629$	−18.8626	+	2.05454i	−0.752103	+	0.0819198i
$630$	−1.99025	+	0.884754i	−0.0792933	+	0.0352494i
$631$	10.5557	+	4.37233i	0.420217	+	0.174060i	0.582764	−	0.812641i	$-0.301971\pi$
$631$	10.5557	+	4.37233i	0.420217	+	0.174060i	−0.162547	+	0.986701i	$0.551971\pi$
$632$	5.04756	+	5.75564i	0.200781	+	0.228947i
$633$	−7.86469	+	12.1030i	−0.312593	+	0.481051i
$634$	1.50939	−	0.744347i	0.0599454	−	0.0295618i
$635$	−2.37185	+	2.70458i	−0.0941241	+	0.107328i
$636$	−21.9847	+	22.5550i	−0.871749	+	0.894365i
$637$	2.44481	−	3.18614i	0.0968671	−	0.126240i
$638$	0.335143	+	0.809107i	0.0132684	+	0.0320328i
$639$	2.74266	+	5.22017i	0.108498	+	0.206507i
$640$	7.13170	+	1.41858i	0.281905	+	0.0560744i
$641$	0.0808990	−	1.23428i	0.00319532	−	0.0487511i	−0.995963	−	0.0897592i	$-0.971390\pi$
$641$	0.0808990	−	1.23428i	0.00319532	−	0.0487511i	0.999159	+	0.0410080i	$0.0130569\pi$
$642$	−8.59251	+	4.37502i	−0.339119	+	0.172668i
$643$	11.6385	−	34.2859i	0.458977	−	1.35210i	−0.433559	−	0.901125i	$-0.642742\pi$
$643$	11.6385	−	34.2859i	0.458977	−	1.35210i	0.892535	−	0.450977i	$-0.148924\pi$
$644$	−32.6380	+	25.0440i	−1.28612	+	0.986871i
$645$	8.50492	−	7.65347i	0.334881	−	0.301355i
$646$	2.60353	−	7.14003i	0.102434	−	0.280921i
$647$		−	42.3860i		−	1.66637i	−0.552997	−	0.833183i	$-0.686516\pi$
$647$		−	42.3860i		−	1.66637i	0.552997	−	0.833183i	$-0.313484\pi$
$648$	6.42245	−	9.32191i	0.252298	−	0.366199i
$649$	8.17394	+	41.0932i	0.320855	+	1.61305i
$650$	−6.87051	−	1.84095i	−0.269484	−	0.0722079i
$651$	−10.4560	+	1.51300i	−0.409802	+	0.0592991i
$652$	13.1040	+	11.4919i	0.513194	+	0.450059i
$653$	−47.5967	+	3.11965i	−1.86260	+	0.122082i	−0.954788	−	0.297287i	$-0.903918\pi$
$653$	−47.5967	+	3.11965i	−1.86260	+	0.122082i	−0.907816	+	0.419369i	$0.862251\pi$
$654$	−2.98986	+	0.234448i	−0.116913	+	0.00916766i
$655$	−3.06935	−	2.35519i	−0.119929	−	0.0920250i
$656$	−11.7814	+	7.87206i	−0.459985	+	0.307352i
$657$	4.95388	−	15.9220i	0.193269	−	0.621177i
$658$	1.53474	−	2.29689i	0.0598302	−	0.0895422i
$659$	3.31593	−	12.3752i	0.129170	−	0.482070i	−0.870784	−	0.491666i	$-0.836388\pi$
$659$	3.31593	−	12.3752i	0.129170	−	0.482070i	0.999954	+	0.00959616i	$0.00305460\pi$
$660$	4.44755	+	10.3601i	0.173121	+	0.403267i
$661$	−22.3621	−	29.1429i	−0.869786	−	1.13353i	−0.990040	−	0.140784i	$-0.955038\pi$
$661$	−22.3621	−	29.1429i	−0.869786	−	1.13353i	0.120254	−	0.992743i	$-0.461629\pi$
$662$	−4.32158	+	7.48519i	−0.167963	+	0.290920i
$663$	32.2743	+	16.3030i	1.25343	+	0.633158i
$664$	6.76836	+	11.7231i	0.262663	+	0.454946i
$665$	−4.91284	+	11.8606i	−0.190512	+	0.459936i
$666$	3.64154	−	2.57047i	0.141107	−	0.0996037i
$667$	3.49778	+	3.49778i	0.135435	+	0.135435i
$668$	25.8961	+	1.69732i	1.00195	+	0.0656712i
$669$	−6.47544	+	11.5550i	−0.250355	+	0.446742i
$670$	−0.0426235	−	0.650309i	−0.00164669	−	0.0251236i
$671$	0.174124	−	1.32261i	0.00672200	−	0.0510586i
$672$	15.7467	+	7.51628i	0.607440	+	0.289947i
$673$	3.85867	−	7.82462i	0.148741	−	0.301617i	−0.809732	−	0.586800i	$-0.800388\pi$
$673$	3.85867	−	7.82462i	0.148741	−	0.301617i	0.958473	+	0.285183i	$0.0920543\pi$
$674$	−0.783003	+	3.93642i	−0.0301602	+	0.151625i
$675$	−12.0483	−	19.1316i	−0.463738	−	0.736376i
$676$	16.9382	−	16.9382i	0.651471	−	0.651471i
$677$	−14.5855	+	12.7911i	−0.560566	+	0.491603i	−0.892099	−	0.451841i	$-0.850768\pi$
$677$	−14.5855	+	12.7911i	−0.560566	+	0.491603i	0.331533	+	0.943444i	$0.392434\pi$
$678$	−1.40743	−	3.97808i	−0.0540522	−	0.152777i
$679$	−27.8496	−	16.0790i	−1.06877	−	0.617055i
$680$	3.01929	−	2.88693i	0.115785	−	0.110709i
$681$	−1.18638	+	3.64777i	−0.0454623	+	0.139783i
$682$	−0.392502	−	2.98135i	−0.0150297	−	0.114162i
$683$	−21.7757	+	4.33145i	−0.833223	+	0.165738i	−0.593227	−	0.805036i	$-0.702146\pi$
$683$	−21.7757	+	4.33145i	−0.833223	+	0.165738i	−0.239996	+	0.970774i	$0.577146\pi$
$684$	−5.06098	−	32.0722i	−0.193511	−	1.22631i
$685$	−8.64833	−	5.77863i	−0.330436	−	0.220790i
$686$	1.79822	+	5.29739i	0.0686564	+	0.202255i
$687$	24.2776	+	23.6637i	0.926248	+	0.902826i
$688$	−27.5256	−	3.62381i	−1.04940	−	0.138157i
$689$	48.1521	+	6.33935i	1.83445	+	0.241510i
$690$	−2.50749	−	2.44408i	−0.0954585	−	0.0930446i
$691$	1.14925	+	3.38558i	0.0437195	+	0.128793i	0.966598	−	0.256299i	$-0.0825030\pi$
$691$	1.14925	+	3.38558i	0.0437195	+	0.128793i	−0.922878	+	0.385092i	$0.874170\pi$
$692$	−1.26640	−	0.846183i	−0.0481414	−	0.0321671i
$693$	5.56448	+	35.2630i	0.211377	+	1.33953i
$694$	1.73032	−	0.344183i	0.0656822	−	0.0130650i
$695$	−1.28760	−	9.78029i	−0.0488414	−	0.370988i
$696$	0.428772	−	1.31834i	0.0162525	−	0.0499717i
$697$	−0.386631	+	17.2525i	−0.0146447	+	0.653485i
$698$	0.201949	+	0.116596i	0.00764390	+	0.00441321i
$699$	10.5755	+	29.8915i	0.400004	+	1.13060i
$700$	17.3129	−	15.1830i	0.654368	−	0.573865i
$701$	21.3393	−	21.3393i	0.805976	−	0.805976i	−0.178046	−	0.984022i	$-0.556978\pi$
$701$	21.3393	−	21.3393i	0.805976	−	0.805976i	0.984022	+	0.178046i	$0.0569776\pi$
$702$	−8.48793	+	0.326215i	−0.320356	+	0.0123122i
$703$	5.12555	−	25.7679i	0.193314	−	0.971854i
$704$	10.5687	−	21.4312i	0.398322	−	0.807718i
$705$	−3.85903	−	1.84202i	−0.145340	−	0.0693743i
$706$	0.213817	−	1.62410i	0.00804711	−	0.0611239i
$707$	−0.194781	−	2.97179i	−0.00732550	−	0.111766i
$708$	15.7780	−	28.1548i	0.592974	−	1.05812i
$709$	1.45605	+	0.0954348i	0.0546832	+	0.00358413i	0.0927202	−	0.995692i	$-0.470444\pi$
$709$	1.45605	+	0.0954348i	0.0546832	+	0.00358413i	−0.0380370	+	0.999276i	$0.512110\pi$
$710$	−0.361467	−	0.361467i	−0.0135656	−	0.0135656i
$711$	14.9171	−	10.5296i	0.559437	−	0.394892i
$712$	6.47257	−	15.6262i	0.242570	−	0.585616i
$713$	−8.49242	−	14.7093i	−0.318044	−	0.550868i
$714$	5.60495	−	3.16466i	0.209760	−	0.118434i
$715$	8.69247	−	15.0558i	0.325080	−	0.563055i
$716$	8.31341	+	10.8342i	0.310687	+	0.404895i
$717$	14.9198	+	34.7540i	0.557189	+	1.29791i
$718$	1.81494	−	6.77344i	0.0677328	−	0.252782i
$719$	2.37660	−	3.55683i	0.0886321	−	0.132647i	−0.784504	−	0.620124i	$-0.787082\pi$
$719$	2.37660	−	3.55683i	0.0886321	−	0.132647i	0.873136	+	0.487476i	$0.162082\pi$
$720$	2.43045	−	7.81159i	0.0905776	−	0.291121i
$721$	30.8373	−	20.6048i	1.14844	−	0.767363i
$722$	3.48189	+	2.67175i	0.129583	+	0.0994323i
$723$	−14.3094	+	1.12206i	−0.532172	+	0.0417300i
$724$	6.45968	−	0.423390i	0.240072	−	0.0157352i
$725$	−2.08172	−	1.82562i	−0.0773131	−	0.0678017i
$726$	−3.96839	+	0.574233i	−0.147281	+	0.0213118i
$727$	9.12275	+	2.44443i	0.338344	+	0.0906591i	0.423991	−	0.905667i	$-0.360629\pi$
$727$	9.12275	+	2.44443i	0.338344	+	0.0906591i	−0.0856465	+	0.996326i	$0.527296\pi$
$728$	−3.46838	−	17.4367i	−0.128547	−	0.646247i
$729$	−20.5009	−	17.5702i	−0.759293	−	0.650749i
$730$			1.44554i			0.0535017i
$731$	−22.8582	+	24.9158i	−0.845441	+	0.921545i
$732$	−0.763853	+	0.687382i	−0.0282328	+	0.0254064i
$733$	0.200113	−	0.153552i	0.00739133	−	0.00567157i	−0.605059	−	0.796181i	$-0.706851\pi$
$733$	0.200113	−	0.153552i	0.00739133	−	0.00567157i	0.612450	+	0.790509i	$0.290184\pi$
$734$	−3.22665	+	9.50541i	−0.119098	+	0.350851i
$735$	−0.986166	+	0.502122i	−0.0363753	+	0.0185211i
$736$	−1.83466	+	27.9915i	−0.0676264	+	1.03178i
$737$	−10.4765	−	2.08391i	−0.385908	−	0.0767619i
$738$	−1.88552	−	3.58875i	−0.0694069	−	0.132104i
$739$	5.65622	+	13.6553i	0.208067	+	0.502319i	0.993119	−	0.117111i	$-0.0373635\pi$
$739$	5.65622	+	13.6553i	0.208067	+	0.502319i	−0.785051	+	0.619431i	$0.787363\pi$
$740$	4.27798	−	5.57518i	0.157262	−	0.204948i
$741$	−34.9463	+	35.8529i	−1.28378	+	1.31709i
$742$	5.70050	−	6.50017i	0.209272	−	0.238629i
$743$	−7.95251	+	3.92174i	−0.291749	+	0.143875i	−0.582274	−	0.812993i	$-0.697837\pi$
$743$	−7.95251	+	3.92174i	−0.291749	+	0.143875i	0.290525	+	0.956868i	$0.406170\pi$
$744$	−2.59368	+	3.99142i	−0.0950889	+	0.146333i
$745$	−3.81183	−	4.34656i	−0.139655	−	0.159246i
$746$	4.54230	+	1.88148i	0.166305	+	0.0688859i
$747$	29.5029	−	13.1154i	1.07946	−	0.479867i
$748$	−16.0087	−	29.2209i	−0.585336	−	1.06842i
$749$	−41.6856	+	24.0672i	−1.52316	+	0.879396i
$750$	3.20223	+	2.73655i	0.116929	+	0.0999246i
$751$	−43.5355	−	14.7783i	−1.58863	−	0.539268i	−0.619328	−	0.785132i	$-0.712595\pi$
$751$	−43.5355	−	14.7783i	−1.58863	−	0.539268i	−0.969304	+	0.245864i	$0.920928\pi$
$752$	2.68552	+	10.0225i	0.0979308	+	0.365483i
$753$	1.91893	+	13.2613i	0.0699298	+	0.483269i
$754$	−0.985032	+	0.334373i	−0.0358728	+	0.0121772i
$755$	2.37639	+	3.55652i	0.0864857	+	0.129435i
$756$	14.3884	−	23.4348i	0.523303	−	0.852314i
$757$	−31.0055	+	12.8429i	−1.12691	+	0.466782i	−0.866730	−	0.498777i	$-0.833783\pi$
$757$	−31.0055	+	12.8429i	−1.12691	+	0.466782i	−0.260182	+	0.965560i	$0.583783\pi$
$758$	−1.42464	−	0.702554i	−0.0517452	−	0.0255179i
$759$	−49.3321	+	29.3304i	−1.79064	+	1.06463i
$760$	2.55830	+	5.18771i	0.0927992	+	0.188178i
$761$	−34.9400	+	9.36216i	−1.26658	+	0.339378i	−0.828718	−	0.559666i	$-0.810929\pi$
$761$	−34.9400	+	9.36216i	−1.26658	+	0.339378i	−0.437858	+	0.899044i	$0.644263\pi$
$762$	−0.294242	+	2.47998i	−0.0106593	+	0.0898402i
$763$	−14.8433	+	1.95415i	−0.537362	+	0.0707450i
$764$	−15.8947			−0.575051
$765$	−6.09073	−	7.88517i	−0.220211	−	0.285089i
$766$	12.3470			0.446114
$767$	−49.3408	+	6.49584i	−1.78159	+	0.234551i
$768$	−13.2054	+	5.66903i	−0.476509	+	0.204563i
$769$	21.9369	−	5.87798i	0.791065	−	0.211965i	0.159408	−	0.987213i	$-0.449042\pi$
$769$	21.9369	−	5.87798i	0.791065	−	0.211965i	0.631657	+	0.775248i	$0.282375\pi$
$770$	−1.36877	−	2.77560i	−0.0493272	−	0.100026i
$771$	−0.623680	−	48.7048i	−0.0224613	−	1.75406i
$772$	−17.8844	−	8.81961i	−0.643674	−	0.317425i
$773$	−38.1699	+	15.8105i	−1.37288	+	0.568664i	−0.942567	−	0.334017i	$-0.891596\pi$
$773$	−38.1699	+	15.8105i	−1.37288	+	0.568664i	−0.430310	+	0.902681i	$0.641596\pi$
$774$	1.85870	−	7.72264i	0.0668097	−	0.277585i
$775$	5.28190	+	7.90492i	0.189731	+	0.283953i
$776$	−13.7202	+	4.65737i	−0.492525	+	0.167190i
$777$	17.4783	−	13.7707i	0.627032	−	0.494022i
$778$	−1.08952	−	4.06616i	−0.0390613	−	0.145779i
$779$	−22.6266	−	7.68070i	−0.810683	−	0.275190i
$780$	−12.6249	+	4.46665i	−0.452043	+	0.159932i
$781$	−7.25616	+	4.18935i	−0.259646	+	0.149907i
$782$	8.06645	+	6.48184i	0.288456	+	0.231790i
$783$	−3.01952	−	1.34748i	−0.107909	−	0.0481549i
$784$	2.48087	+	1.02761i	0.0886026	+	0.0367004i
$785$	−8.96950	−	10.2278i	−0.320135	−	0.365044i
$786$	−2.68217	−	0.141334i	−0.0956698	−	0.00504121i
$787$	5.68131	−	2.80171i	0.202517	−	0.0998702i	−0.338202	−	0.941073i	$-0.609819\pi$
$787$	5.68131	−	2.80171i	0.202517	−	0.0998702i	0.540719	+	0.841203i	$0.318152\pi$
$788$	18.7374	−	21.3659i	0.667492	−	0.761129i
$789$	7.31085	+	25.9507i	0.260273	+	0.923868i
$790$	−0.963591	+	1.25578i	−0.0342830	+	0.0446785i
$791$	−8.06124	−	19.4616i	−0.286625	−	0.691973i
$792$	13.5983	+	8.59077i	0.483196	+	0.305260i
$793$	1.55410	+	0.309129i	0.0551876	+	0.0109775i
$794$	0.542447	−	8.27614i	0.0192507	−	0.293709i
$795$	−11.2219	−	7.29212i	−0.397999	−	0.258625i
$796$	−5.71541	+	16.8370i	−0.202577	+	0.596773i
$797$	−0.364434	+	0.279640i	−0.0129089	+	0.00990536i	−0.615196	−	0.788374i	$-0.710923\pi$
$797$	−0.364434	+	0.279640i	−0.0129089	+	0.00990536i	0.602287	+	0.798280i	$0.294256\pi$
$798$	1.85053	+	8.71831i	0.0655082	+	0.308625i
$799$	11.8723	+	4.32911i	0.420013	+	0.153153i
$800$		−	15.7017i		−	0.555138i
$801$	−35.4415	−	19.2694i	−1.25226	−	0.680850i
$802$	−2.45005	−	12.3172i	−0.0865141	−	0.434936i
$803$	22.8858	+	6.13223i	0.807622	+	0.216402i
$804$	5.09221	+	6.46323i	0.179588	+	0.227941i
$805$	−13.1422	−	11.5254i	−0.463202	−	0.406217i
$806$	3.56415	−	0.233607i	0.125542	−	0.00822844i
$807$	−1.96314	+	4.11280i	−0.0691059	+	0.144777i
$808$	−1.06455	−	0.816861i	−0.0374509	−	0.0287371i
$809$	10.9710	−	7.33062i	0.385721	−	0.257731i	−0.347558	−	0.937659i	$-0.612989\pi$
$809$	10.9710	−	7.33062i	0.385721	−	0.257731i	0.733279	+	0.679928i	$0.237989\pi$
$810$	2.14948	+	0.926397i	0.0755250	+	0.0325503i
$811$	−6.77215	+	10.1352i	−0.237802	+	0.355897i	−0.931106	−	0.364749i	$-0.881155\pi$
$811$	−6.77215	+	10.1352i	−0.237802	+	0.355897i	0.693303	+	0.720646i	$0.256155\pi$
$812$	0.871623	−	3.25294i	0.0305880	−	0.114156i
$813$	9.37883	−	12.5523i	0.328930	−	0.440228i
$814$	3.85554	+	5.02463i	0.135137	+	0.176113i
$815$	−3.70285	+	6.41353i	−0.129705	+	0.224656i
$816$	−4.94411	+	23.6658i	−0.173079	+	0.828470i
$817$	−23.4094	−	40.5463i	−0.818991	−	1.41853i
$818$	−3.91056	+	9.44092i	−0.136729	+	0.330094i
$819$	−42.2278	+	3.85589i	−1.47556	+	0.134736i
$820$	−4.51933	−	4.51933i	−0.157822	−	0.157822i
$821$	18.8669	+	1.23660i	0.658460	+	0.0431578i	0.390971	−	0.920403i	$-0.372139\pi$
$821$	18.8669	+	1.23660i	0.658460	+	0.0431578i	0.267489	+	0.963561i	$0.413806\pi$
$822$	−7.22036	+	0.0924591i	−0.251839	+	0.00322488i
$823$	2.41286	+	36.8132i	0.0841071	+	1.28323i	0.806289	+	0.591522i	$0.201473\pi$
$823$	2.41286	+	36.8132i	0.0841071	+	1.28323i	−0.722181	+	0.691704i	$0.756860\pi$
$824$	2.18112	−	16.5673i	0.0759830	−	0.577148i
$825$	26.4804	−	18.1884i	0.921930	−	0.633238i
$826$	−3.91829	+	7.94550i	−0.136335	+	0.276459i
$827$	−3.07795	+	15.4739i	−0.107031	+	0.538079i	0.889648	+	0.456647i	$0.150950\pi$
$827$	−3.07795	+	15.4739i	−0.107031	+	0.538079i	−0.996679	+	0.0814328i	$0.974050\pi$
$828$	43.5671	+	7.51180i	1.51406	+	0.261053i
$829$	−11.0403	+	11.0403i	−0.383447	+	0.383447i	−0.872342	−	0.488896i	$-0.837400\pi$
$829$	−11.0403	+	11.0403i	−0.383447	+	0.383447i	0.488896	+	0.872342i	$0.337400\pi$
$830$	−2.10434	+	1.84546i	−0.0730428	+	0.0640568i
$831$	22.1114	−	25.8741i	0.767035	−	0.897564i
$832$	24.5803	+	14.1915i	0.852170	+	0.492001i
$833$	2.75926	−	1.75556i	0.0956027	−	0.0608264i
$834$	−4.58105	−	5.09069i	−0.158629	−	0.176276i
$835$	1.43929	+	10.9325i	0.0498087	+	0.378335i
$836$	45.2484	−	9.00047i	1.56495	−	0.311288i
$837$	8.81717	+	7.15251i	0.304766	+	0.247227i
$838$	3.60015	+	2.40554i	0.124365	+	0.0830981i
$839$	−8.05826	−	23.7389i	−0.278202	−	0.819556i	−0.992774	−	0.119995i	$-0.961712\pi$
$839$	−8.05826	−	23.7389i	−0.278202	−	0.819556i	0.714573	−	0.699561i	$-0.246621\pi$
$840$	−1.20723	+	4.74781i	−0.0416535	+	0.163815i
$841$	28.3504	+	3.73241i	0.977601	+	0.128704i
$842$	−4.60604	−	0.606397i	−0.158735	−	0.0208978i
$843$	19.1609	−	5.39804i	0.659938	−	0.185918i
$844$	5.07813	+	14.9597i	0.174797	+	0.514934i
$845$	8.46284	+	5.65469i	0.291131	+	0.194527i
$846$	−2.93236	+	0.462725i	−0.100817	+	0.0159088i
$847$	−19.6321	+	3.90507i	−0.674568	+	0.134180i
$848$	4.23872	+	32.1963i	0.145558	+	1.10562i
$849$	−46.9655	+	9.96882i	−1.61185	+	0.342129i
$850$	−4.74277	−	3.32509i	−0.162676	−	0.114050i
$851$	30.9803	+	17.8865i	1.06199	+	0.613140i
$852$	6.34575	+	1.17799i	0.217402	+	0.0403572i
$853$	−0.102906	+	0.0902462i	−0.00352344	+	0.00308997i	−0.661106	−	0.750293i	$-0.729913\pi$
$853$	−0.102906	+	0.0902462i	−0.00352344	+	0.00308997i	0.657582	+	0.753383i	$0.271579\pi$
$854$	0.199453	−	0.199453i	0.00682515	−	0.00682515i
$855$	12.9461	−	4.76768i	0.442747	−	0.163051i
$856$	−4.23100	+	21.2707i	−0.144613	+	0.727017i
$857$	17.9159	−	36.3299i	0.611997	−	1.24101i	−0.341579	−	0.939853i	$-0.610962\pi$
$857$	17.9159	−	36.3299i	0.611997	−	1.24101i	0.953576	−	0.301154i	$-0.0973717\pi$
$858$	−0.943513	−	12.0324i	−0.0322110	−	0.410778i
$859$	5.10460	−	38.7733i	0.174167	−	1.32293i	−0.651448	−	0.758693i	$-0.725838\pi$
$859$	5.10460	−	38.7733i	0.174167	−	1.32293i	0.825615	−	0.564234i	$-0.190829\pi$
$860$	−0.819042	−	12.4962i	−0.0279291	−	0.426116i
$861$	−10.3423	−	17.3951i	−0.352464	−	0.592823i
$862$	−6.55077	−	0.429360i	−0.223120	−	0.0146241i
$863$	30.7086	+	30.7086i	1.04533	+	1.04533i	0.998922	+	0.0464096i	$0.0147779\pi$
$863$	30.7086	+	30.7086i	1.04533	+	1.04533i	0.0464096	+	0.998922i	$0.485222\pi$
$864$	−5.54510	−	17.9123i	−0.188648	−	0.609388i
$865$	0.247657	−	0.597898i	0.00842061	−	0.0203291i
$866$	−1.94083	−	3.36162i	−0.0659522	−	0.114233i
$867$	20.1437	+	21.4763i	0.684115	+	0.729374i
$868$	−5.78172	+	10.0142i	−0.196244	+	0.339905i
$869$	15.7938	+	20.5828i	0.535767	+	0.698225i
$870$	0.284646	+	0.0337724i	0.00965039	+	0.00114499i
$871$	3.28384	−	12.2555i	0.111269	−	0.415261i
$872$	−3.74759	+	5.60866i	−0.126909	+	0.189933i
$873$	7.60770	+	33.7105i	0.257482	+	1.14093i
$874$	−11.9137	+	7.96045i	−0.402986	+	0.269266i
$875$	16.6824	+	12.8009i	0.563969	+	0.432749i
$876$	−10.3332	−	15.0440i	−0.349125	−	0.508291i
$877$	−43.5406	+	2.85380i	−1.47026	+	0.0963660i	−0.779357	−	0.626581i	$-0.784454\pi$
$877$	−43.5406	+	2.85380i	−1.47026	+	0.0963660i	−0.690904	+	0.722947i	$0.742787\pi$
$878$	9.82349	+	8.61497i	0.331527	+	0.290741i
$879$	−4.87390	+	12.2064i	−0.164392	+	0.411712i
$880$	11.2281	+	3.00857i	0.378500	+	0.101419i
$881$	−0.892792	−	4.48837i	−0.0300789	−	0.151217i	0.962827	−	0.270118i	$-0.0870628\pi$
$881$	−0.892792	−	4.48837i	−0.0300789	−	0.151217i	−0.992906	+	0.118901i	$0.962063\pi$
$882$	−0.366973	+	0.674961i	−0.0123566	+	0.0227271i
$883$			12.1431i			0.408647i	0.978903	+	0.204324i	$0.0654995\pi$
$883$			12.1431i			0.408647i	−0.978903	+	0.204324i	$0.934500\pi$
$884$	35.8778	−	16.7043i	1.20670	−	0.561827i
$885$	13.0410	+	4.24140i	0.438369	+	0.142573i
$886$	−5.78270	+	4.43722i	−0.194274	+	0.149071i
$887$	1.52852	−	4.50288i	0.0513227	−	0.151192i	−0.918246	−	0.396009i	$-0.870395\pi$
$887$	1.52852	−	4.50288i	0.0513227	−	0.151192i	0.969569	+	0.244818i	$0.0787281\pi$
$888$	0.527555	−	10.0117i	0.0177036	−	0.335971i
$889$	−0.815382	+	12.4403i	−0.0273470	+	0.417235i
$890$	3.42996	+	0.682261i	0.114972	+	0.0228694i
$891$	23.7853	−	30.1007i	0.796836	−	1.00841i
$892$	5.54802	+	13.3941i	0.185762	+	0.448468i
$893$	−10.6520	+	13.8820i	−0.356456	+	0.464542i
$894$	−3.88978	−	0.989060i	−0.130094	−	0.0330791i
$895$	−3.82588	+	4.36258i	−0.127885	+	0.145825i
$896$	22.6015	−	11.1458i	0.755064	−	0.372356i
$897$	−30.9316	−	60.7495i	−1.03278	−	2.02837i
$898$	6.17741	+	7.04398i	0.206143	+	0.235061i
$899$	1.28456	+	0.532081i	0.0428424	+	0.0177459i
$900$	−24.6092	−	2.60073i	−0.820307	−	0.0866911i
$901$	35.0707	+	18.2829i	1.16837	+	0.609093i
$902$	4.98845	−	2.88008i	0.166097	−	0.0958963i
$903$	7.23726	−	38.9867i	0.240841	−	1.29740i
$904$	−8.98737	−	3.05080i	−0.298916	−	0.101468i
$905$	0.711909	+	2.65688i	0.0236647	+	0.0883177i
$906$	2.75781	+	1.10117i	0.0916222	+	0.0365838i
$907$	−0.993157	+	0.337131i	−0.0329772	+	0.0111943i	−0.337879	−	0.941189i	$-0.609710\pi$
$907$	−0.993157	+	0.337131i	−0.0329772	+	0.0111943i	0.304902	+	0.952384i	$0.401376\pi$
$908$	2.33251	+	3.49084i	0.0774069	+	0.115848i
$909$	−2.20437	+	2.32027i	−0.0731145	+	0.0769586i
$910$	3.39612	−	1.40672i	0.112580	−	0.0466323i
$911$	26.2447	+	12.9424i	0.869525	+	0.428802i	0.821611	−	0.570049i	$-0.193076\pi$
$911$	26.2447	+	12.9424i	0.869525	+	0.428802i	0.0479145	+	0.998851i	$0.484742\pi$
$912$	−29.2034	−	16.3656i	−0.967021	−	0.541920i
$913$	20.2904	+	41.1448i	0.671514	+	1.36169i
$914$	−10.6041	+	2.84137i	−0.350753	+	0.0939840i
$915$	−0.349775	−	0.261345i	−0.0115632	−	0.00863980i
$916$	36.7893	−	4.84340i	1.21555	−	0.160031i
$917$	−13.4081			−0.442774
$918$	−6.58476	−	2.11830i	−0.217330	−	0.0699143i
$919$	1.45071			0.0478547			0.0239273	−	0.999714i	$-0.492383\pi$
$919$	1.45071			0.0478547			0.0239273	+	0.999714i	$0.492383\pi$
$920$	−7.80843	+	1.02800i	−0.257436	+	0.0338921i
$921$	23.6095	+	17.6406i	0.777960	+	0.581276i
$922$	8.49856	−	2.27718i	0.279885	−	0.0749950i
$923$	−4.40174	−	8.92584i	−0.144885	−	0.293798i
$924$	34.0860	+	19.1019i	1.12135	+	0.628405i
$925$	−17.9587	−	8.85625i	−0.590478	−	0.291192i
$926$	−7.71688	+	3.19644i	−0.253593	+	0.105041i
$927$	−38.7494	−	9.32631i	−1.27270	−	0.306316i
$928$	−1.27577	−	1.90932i	−0.0418791	−	0.0626766i
$929$	−22.5459	+	7.65331i	−0.739708	+	0.251097i	−0.665761	−	0.746165i	$-0.731893\pi$
$929$	−22.5459	+	7.65331i	−0.739708	+	0.251097i	−0.0739472	+	0.997262i	$0.523560\pi$
$930$	−0.914053	−	0.364973i	−0.0299730	−	0.0119679i
$931$	1.17203	+	4.37406i	0.0384116	+	0.143354i
$932$	32.8623	+	11.1553i	1.07644	+	0.365403i
$933$	0.821067	−	4.42304i	0.0268805	−	0.144804i
$934$	8.57031	−	4.94807i	0.280429	−	0.161906i
$935$	10.8503	−	9.09362i	0.354844	−	0.297393i
$936$	−11.2386	+	15.4501i	−0.367346	+	0.505003i
$937$	25.8156	+	10.6932i	0.843357	+	0.349330i	0.762176	−	0.647369i	$-0.224131\pi$
$937$	25.8156	+	10.6932i	0.843357	+	0.349330i	0.0811809	+	0.996699i	$0.474131\pi$
$938$	−1.48920	−	1.69810i	−0.0486240	−	0.0554450i
$939$	4.35311	+	8.54950i	0.142059	+	0.279002i
$940$	−4.19762	+	2.07004i	−0.136911	+	0.0675171i
$941$	24.6539	−	28.1124i	0.803694	−	0.916438i	−0.194222	−	0.980958i	$-0.562218\pi$
$941$	24.6539	−	28.1124i	0.803694	−	0.916438i	0.997916	+	0.0645199i	$0.0205516\pi$
$942$	−9.15291	−	2.32732i	−0.298218	−	0.0758283i
$943$	19.8061	−	25.8118i	0.644976	−	0.840548i
$944$	−12.7341	−	30.7428i	−0.414459	−	1.00059i
$945$	10.9588	+	4.05358i	0.356490	+	0.131863i
$946$	11.0695	+	2.20186i	0.359900	+	0.0715886i
$947$	−2.89959	+	44.2392i	−0.0942240	+	1.43758i	0.645032	+	0.764155i	$0.276844\pi$
$947$	−2.89959	+	44.2392i	−0.0942240	+	1.43758i	−0.739256	+	0.673424i	$0.764823\pi$
$948$	1.05162	−	19.9572i	0.0341551	−	0.648180i
$949$	−9.04614	+	26.6491i	−0.293650	+	0.865066i
$950$	6.36289	−	4.88242i	0.206440	−	0.158407i
$951$	−8.58575	−	2.79239i	−0.278412	−	0.0905494i
$952$	2.21080	−	14.3077i	0.0716523	−	0.463714i
$953$		−	26.1473i		−	0.846993i	−0.905898	−	0.423496i	$-0.860803\pi$
$953$		−	26.1473i		−	0.846993i	0.905898	−	0.423496i	$-0.139197\pi$
$954$	−9.28797	+	0.237910i	−0.300709	+	0.00770262i
$955$	−1.31757	−	6.62389i	−0.0426357	−	0.214344i
$956$	39.9854	+	10.7141i	1.29322	+	0.346518i
$957$	1.74221	−	4.36325i	0.0563175	−	0.141044i
$958$	−6.78849	−	5.95335i	−0.219326	−	0.192344i
$959$	−35.9702	+	2.35761i	−1.16154	+	0.0761313i
$960$	−4.42805	−	6.44679i	−0.142915	−	0.208069i
$961$	20.8064	+	15.9653i	0.671174	+	0.515010i
$962$	−6.25498	+	4.17945i	−0.201669	+	0.134751i
$963$	49.3917	+	15.3675i	1.59163	+	0.495209i
$964$	−8.72798	+	13.0623i	−0.281109	+	0.420710i
$965$	2.19294	−	8.18415i	0.0705932	−	0.263457i
$966$	−12.0508	−	1.42979i	−0.387728	−	0.0460029i
$967$	15.5940	+	20.3225i	0.501470	+	0.653528i	0.973670	−	0.227963i	$-0.0732066\pi$
$967$	15.5940	+	20.3225i	0.501470	+	0.653528i	−0.472200	+	0.881491i	$0.656540\pi$
$968$	−4.50937	+	7.81046i	−0.144937	+	0.251038i
$969$	−36.7378	+	17.6806i	−1.18019	+	0.567982i
$970$	−1.49792	−	2.59448i	−0.0480953	−	0.0833036i
$971$	−2.58935	+	6.25124i	−0.0830962	+	0.200612i	−0.959966	−	0.280115i	$-0.909627\pi$
$971$	−2.58935	+	6.25124i	−0.0830962	+	0.200612i	0.876870	+	0.480727i	$0.159627\pi$
$972$	−28.9923	+	5.72394i	−0.929929	+	0.183596i
$973$	−24.1744	−	24.1744i	−0.774997	−	0.774997i
$974$	3.42223	+	0.224305i	0.109655	+	0.00718720i
$975$	19.5007	+	32.7990i	0.624522	+	1.05041i
$976$	0.0692935	+	1.05721i	0.00221803	+	0.0338406i
$977$	1.78434	−	13.5534i	0.0570861	−	0.433612i	−0.938906	−	0.344173i	$-0.888159\pi$
$977$	1.78434	−	13.5534i	0.0570861	−	0.433612i	0.995992	−	0.0894390i	$-0.0285074\pi$
$978$	0.401921	+	5.12559i	0.0128520	+	0.163898i
$979$	25.3521	−	51.4090i	0.810256	−	1.64304i
$980$	−0.236300	+	1.18796i	−0.00754834	+	0.0379481i
$981$	12.3639	+	10.2949i	0.394749	+	0.328690i
$982$	6.50474	−	6.50474i	0.207575	−	0.207575i
$983$	7.37127	−	6.46443i	0.235107	−	0.206183i	−0.533683	−	0.845685i	$-0.679192\pi$
$983$	7.37127	−	6.46443i	0.235107	−	0.206183i	0.768790	+	0.639501i	$0.220859\pi$
$984$	−8.96500	−	1.66421i	−0.285794	−	0.0530531i
$985$	10.4571	+	6.03743i	0.333192	+	0.192369i
$986$	−0.846886	−	0.0189788i	−0.0269704	−	0.000604409i
$987$	−14.4967	+	3.07704i	−0.461434	+	0.0979432i
$988$	7.15269	+	54.3300i	0.227557	+	1.72847i
$989$	62.5237	−	12.4367i	1.98814	−	0.395465i
$990$	−1.19361	+	3.10417i	−0.0379355	+	0.0986571i
$991$	−25.8145	−	17.2487i	−0.820024	−	0.547922i	0.0733136	−	0.997309i	$-0.476643\pi$
$991$	−25.8145	−	17.2487i	−0.820024	−	0.547922i	−0.893337	+	0.449387i	$0.851643\pi$
$992$	2.53446	+	7.46629i	0.0804693	+	0.237055i
$993$	44.6304	−	12.5733i	1.41630	−	0.399002i
$994$	−1.75647	−	0.231243i	−0.0557117	−	0.00733458i
$995$	−7.49036	−	0.986125i	−0.237460	−	0.0312623i
$996$	8.70845	−	34.2486i	0.275938	−	1.08521i
$997$	−8.79884	−	25.9205i	−0.278662	−	0.820912i	−0.992679	−	0.120783i	$-0.961459\pi$
$997$	−8.79884	−	25.9205i	−0.278662	−	0.820912i	0.714017	−	0.700129i	$-0.246874\pi$
$998$	3.81188	+	2.54702i	0.120663	+	0.0806244i
$999$	−23.6147	−	3.76092i	−0.747135	−	0.118990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.113.10	yes	256
3.2	odd	2		459.2.y.a.368.7		256
9.2	odd	6	inner	153.2.s.a.11.10	✓	256
9.7	even	3		459.2.y.a.62.7		256
17.14	odd	16	inner	153.2.s.a.14.10	yes	256
51.14	even	16		459.2.y.a.422.7		256
153.65	even	48	inner	153.2.s.a.65.10	yes	256
153.133	odd	48		459.2.y.a.116.7		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.10	✓	256	9.2	odd	6	inner
153.2.s.a.14.10	yes	256	17.14	odd	16	inner
153.2.s.a.65.10	yes	256	153.65	even	48	inner
153.2.s.a.113.10	yes	256	1.1	even	1	trivial
459.2.y.a.62.7		256	9.7	even	3
459.2.y.a.116.7		256	153.133	odd	48
459.2.y.a.368.7		256	3.2	odd	2
459.2.y.a.422.7		256	51.14	even	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.320101 - 0.0421420i) q^{2} +(-1.38752 - 1.03672i) q^{3} +(-1.83116 + 0.490659i) q^{4} +(-0.356267 - 0.722438i) q^{5} +(-0.487834 - 0.273383i) q^{6} +(-2.50374 - 1.23471i) q^{7} +(-1.16205 + 0.481337i) q^{8} +(0.850404 + 2.87694i) q^{9} +(-0.144486 - 0.216239i) q^{10} +(-4.03644 + 1.37019i) q^{11} +(3.04945 + 1.21761i) q^{12} +(-1.31045 - 4.89065i) q^{13} +(-0.853480 - 0.289717i) q^{14} +(-0.254643 + 1.37175i) q^{15} +(2.93186 - 1.69271i) q^{16} +(0.361775 - 4.10720i) q^{17} +(0.393455 + 0.885074i) q^{18} +(5.27449 + 2.18477i) q^{19} +(1.00685 + 1.14810i) q^{20} +(2.19392 + 4.30886i) q^{21} +(-1.23432 + 0.608702i) q^{22} +(-5.12541 + 5.84441i) q^{23} +(2.11138 + 0.536864i) q^{24} +(2.64882 - 3.45201i) q^{25} +(-0.625576 - 1.51027i) q^{26} +(1.80265 - 4.87344i) q^{27} +(5.19057 + 1.03247i) q^{28} +(0.0416189 - 0.634981i) q^{29} +(-0.0237032 + 0.449827i) q^{30} +(-0.702337 + 2.06902i) q^{31} +(2.86291 - 2.19679i) q^{32} +(7.02114 + 2.28352i) q^{33} +(-0.0572816 - 1.32996i) q^{34} +2.24868i q^{35} +(-2.96883 - 4.85090i) q^{36} +(-0.897790 - 4.51350i) q^{37} +(1.78044 + 0.477067i) q^{38} +(-3.25199 + 8.14443i) q^{39} +(0.761737 + 0.668025i) q^{40} +(-4.17643 + 0.273738i) q^{41} +(0.883860 + 1.28681i) q^{42} +(-6.50611 - 4.99232i) q^{43} +(6.71909 - 4.48955i) q^{44} +(1.77544 - 1.63932i) q^{45} +(-1.39435 + 2.08679i) q^{46} +(-0.793260 + 2.96048i) q^{47} +(-5.82289 - 0.690869i) q^{48} +(0.482862 + 0.629278i) q^{49} +(0.702413 - 1.21662i) q^{50} +(-4.76001 + 5.32375i) q^{51} +(4.79928 + 8.31260i) q^{52} +(-3.67083 + 8.86216i) q^{53} +(0.371652 - 1.63596i) q^{54} +(2.42793 + 2.42793i) q^{55} +(3.50378 + 0.229650i) q^{56} +(-5.05345 - 8.49960i) q^{57} +(-0.0134372 - 0.205012i) q^{58} +(1.28296 - 9.74504i) q^{59} +(-0.206766 - 2.63683i) q^{60} +(-0.138416 + 0.280680i) q^{61} +(-0.137626 + 0.691891i) q^{62} +(1.42299 - 8.25311i) q^{63} +(-3.96387 + 3.96387i) q^{64} +(-3.06632 + 2.68909i) q^{65} +(2.34370 + 0.435071i) q^{66} +(2.17017 + 1.25295i) q^{67} +(1.35277 + 7.69847i) q^{68} +(13.1706 - 2.79558i) q^{69} +(0.0947639 + 0.719803i) q^{70} +(1.92783 - 0.383470i) q^{71} +(-2.37299 - 2.93383i) q^{72} +(-4.62155 - 3.08802i) q^{73} +(-0.477591 - 1.40694i) q^{74} +(-7.25406 + 2.04362i) q^{75} +(-10.7304 - 1.41269i) q^{76} +(11.7980 + 1.55323i) q^{77} +(-0.697742 + 2.74408i) q^{78} +(-1.95640 - 5.76336i) q^{79} +(-2.26741 - 1.51503i) q^{80} +(-7.55363 + 4.89313i) q^{81} +(-1.32534 + 0.263627i) q^{82} +(-1.40476 - 10.6702i) q^{83} +(-6.13161 - 6.81375i) q^{84} +(-3.09609 + 1.20190i) q^{85} +(-2.29300 - 1.32386i) q^{86} +(-0.716048 + 0.837900i) q^{87} +(4.03103 - 3.53512i) q^{88} +(-9.50851 + 9.50851i) q^{89} +(0.499236 - 0.599569i) q^{90} +(-2.75750 + 13.8629i) q^{91} +(6.51785 - 13.2169i) q^{92} +(3.11950 - 2.14267i) q^{93} +(-0.129162 + 0.981082i) q^{94} +(-0.300769 - 4.58885i) q^{95} +(-6.24980 + 0.0800307i) q^{96} +(11.4948 + 0.753408i) q^{97} +(0.181083 + 0.181083i) q^{98} +(-7.37456 - 10.4474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22}+ \cdots + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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