LMFDB - Embedded newform 403.2.bk.a.9.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(9,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 2]))

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

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

chi := DirichletCharacter("403.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bk (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$35$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.19
Character	$\chi$	$=$	403.9
Dual form			403.2.bk.a.224.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.117605 + 0.130614i) q^{2} +(0.508986 - 0.565287i) q^{3} +(0.205828 - 1.95832i) q^{4} +(0.00796452 + 0.0137949i) q^{5} +0.133693 q^{6} +(3.75325 + 2.72689i) q^{7} +(0.564372 - 0.410040i) q^{8} +(0.253104 + 2.40812i) q^{9} +O(q^{10})$	\(q+(0.117605 + 0.130614i) q^{2} +(0.508986 - 0.565287i) q^{3} +(0.205828 - 1.95832i) q^{4} +(0.00796452 + 0.0137949i) q^{5} +0.133693 q^{6} +(3.75325 + 2.72689i) q^{7} +(0.564372 - 0.410040i) q^{8} +(0.253104 + 2.40812i) q^{9} +(-0.000865141 + 0.00266263i) q^{10} +(1.48452 + 1.07857i) q^{11} +(-1.00225 - 1.11311i) q^{12} +(-2.10621 - 2.92641i) q^{13} +(0.0852313 + 0.810921i) q^{14} +(0.0118519 + 0.00251921i) q^{15} +(-3.73223 - 0.793310i) q^{16} +(4.66547 - 3.38966i) q^{17} +(-0.284767 + 0.316266i) q^{18} +(-1.33923 + 4.12174i) q^{19} +(0.0286543 - 0.0127577i) q^{20} +(3.45183 - 0.733709i) q^{21} +(0.0337115 + 0.320743i) q^{22} +(-0.534373 - 5.08422i) q^{23} +(0.0554674 - 0.527737i) q^{24} +(2.49987 - 4.32991i) q^{25} +(0.134529 - 0.619260i) q^{26} +(3.33628 + 2.42395i) q^{27} +(6.11266 - 6.78880i) q^{28} +(-6.18267 - 6.86655i) q^{29} +(0.00106480 + 0.00184429i) q^{30} +(-5.20624 + 1.97360i) q^{31} +(-1.03291 - 1.78906i) q^{32} +(1.36530 - 0.290204i) q^{33} +(0.991419 + 0.210733i) q^{34} +(-0.00772456 + 0.0734942i) q^{35} +4.76797 q^{36} +(2.04605 + 3.54385i) q^{37} +(-0.695856 + 0.309815i) q^{38} +(-2.72629 - 0.298893i) q^{39} +(0.0101514 + 0.00451971i) q^{40} +(-3.20522 + 9.86464i) q^{41} +(0.501784 + 0.364568i) q^{42} +(-2.77048 + 8.52665i) q^{43} +(2.41774 - 2.68517i) q^{44} +(-0.0312040 + 0.0226711i) q^{45} +(0.601223 - 0.667726i) q^{46} +(-0.219280 - 0.674876i) q^{47} +(-2.34810 + 1.70600i) q^{48} +(4.48779 + 13.8120i) q^{49} +(0.859542 - 0.182701i) q^{50} +(0.458530 - 4.36262i) q^{51} +(-6.16437 + 3.52230i) q^{52} +(-2.78348 - 1.23928i) q^{53} +(0.0757626 + 0.720833i) q^{54} +(-0.00305529 + 0.0290691i) q^{55} +3.23636 q^{56} +(1.64831 + 2.85496i) q^{57} +(0.169752 - 1.61508i) q^{58} +(-3.04459 - 9.37028i) q^{59} +(0.00737288 - 0.0226914i) q^{60} +(0.462717 + 0.801450i) q^{61} +(-0.870059 - 0.447899i) q^{62} +(-5.61672 + 9.72845i) q^{63} +(-2.24598 + 6.91241i) q^{64} +(0.0235948 - 0.0523625i) q^{65} +(0.198471 + 0.144197i) q^{66} +3.18891 q^{67} +(-5.67777 - 9.83419i) q^{68} +(-3.14603 - 2.28572i) q^{69} +(-0.0105078 + 0.00763436i) q^{70} +(-0.227156 - 2.16125i) q^{71} +(1.13027 + 1.25529i) q^{72} +(0.616291 - 5.86362i) q^{73} +(-0.222250 + 0.684016i) q^{74} +(-1.17524 - 3.61701i) q^{75} +(7.79604 + 3.47102i) q^{76} +(2.63063 + 8.09626i) q^{77} +(-0.281586 - 0.391242i) q^{78} +(0.430006 + 4.09124i) q^{79} +(-0.0187817 - 0.0578042i) q^{80} +(-4.03706 + 0.858104i) q^{81} +(-1.66541 + 0.741486i) q^{82} +(-0.177337 + 0.0376942i) q^{83} +(-0.726355 - 6.91081i) q^{84} +(0.0839185 + 0.0373629i) q^{85} +(-1.43952 + 0.640915i) q^{86} -7.02847 q^{87} +1.28008 q^{88} +(5.78630 - 2.57622i) q^{89} +(-0.00663090 - 0.00140944i) q^{90} +(0.0748969 - 16.7270i) q^{91} -10.0665 q^{92} +(-1.53425 + 3.94755i) q^{93} +(0.0623594 - 0.108010i) q^{94} +(-0.0675255 + 0.0143530i) q^{95} +(-1.53707 - 0.326714i) q^{96} +(-1.50946 + 14.3615i) q^{97} +(-1.27625 + 2.21053i) q^{98} +(-2.22158 + 3.84789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9}+O(q^{10}) $ 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9} - 9 q^{10} - 6 q^{11} - 50 q^{12} - 6 q^{13} - 21 q^{15} + 23 q^{16} + 3 q^{17} - 15 q^{18} - 9 q^{19} + 60 q^{20} - 34 q^{21} + 41 q^{22} - 12 q^{23} - 89 q^{24} - 112 q^{25} + 39 q^{26} + 48 q^{27} + 66 q^{28} - 11 q^{29} + 24 q^{30} - 22 q^{31} + q^{32} - 37 q^{33} - 49 q^{34} + 41 q^{35} + 134 q^{36} + 17 q^{37} - 23 q^{38} + 10 q^{39} + 31 q^{40} + q^{41} - 71 q^{42} - 7 q^{43} - 42 q^{44} - 13 q^{45} + 21 q^{46} - 20 q^{47} - 3 q^{48} - 69 q^{49} - 42 q^{50} - 71 q^{51} - 140 q^{52} - 8 q^{53} - 149 q^{54} + 5 q^{55} - 126 q^{56} + 21 q^{57} + 79 q^{58} + 77 q^{59} + 2 q^{60} + 53 q^{61} + 72 q^{62} + 17 q^{63} - 91 q^{64} - 25 q^{65} - 62 q^{66} - 14 q^{67} + 83 q^{68} - 31 q^{69} + 134 q^{70} + 32 q^{71} - 70 q^{72} - 31 q^{73} + 51 q^{74} + 79 q^{75} + 98 q^{76} - 80 q^{77} - 141 q^{78} - 142 q^{79} + 6 q^{80} + 66 q^{81} - 48 q^{82} + 94 q^{83} + 130 q^{84} + 90 q^{85} - 34 q^{86} + 22 q^{87} - 122 q^{88} - 15 q^{89} + 43 q^{90} + 56 q^{91} - 294 q^{92} - 52 q^{93} - 57 q^{94} + 94 q^{95} + 24 q^{96} + 46 q^{97} + 73 q^{98} + 12 q^{99}+O(q^{100}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9 - 9 * q^10 - 6 * q^11 - 50 * q^12 - 6 * q^13 - 21 * q^15 + 23 * q^16 + 3 * q^17 - 15 * q^18 - 9 * q^19 + 60 * q^20 - 34 * q^21 + 41 * q^22 - 12 * q^23 - 89 * q^24 - 112 * q^25 + 39 * q^26 + 48 * q^27 + 66 * q^28 - 11 * q^29 + 24 * q^30 - 22 * q^31 + q^32 - 37 * q^33 - 49 * q^34 + 41 * q^35 + 134 * q^36 + 17 * q^37 - 23 * q^38 + 10 * q^39 + 31 * q^40 + q^41 - 71 * q^42 - 7 * q^43 - 42 * q^44 - 13 * q^45 + 21 * q^46 - 20 * q^47 - 3 * q^48 - 69 * q^49 - 42 * q^50 - 71 * q^51 - 140 * q^52 - 8 * q^53 - 149 * q^54 + 5 * q^55 - 126 * q^56 + 21 * q^57 + 79 * q^58 + 77 * q^59 + 2 * q^60 + 53 * q^61 + 72 * q^62 + 17 * q^63 - 91 * q^64 - 25 * q^65 - 62 * q^66 - 14 * q^67 + 83 * q^68 - 31 * q^69 + 134 * q^70 + 32 * q^71 - 70 * q^72 - 31 * q^73 + 51 * q^74 + 79 * q^75 + 98 * q^76 - 80 * q^77 - 141 * q^78 - 142 * q^79 + 6 * q^80 + 66 * q^81 - 48 * q^82 + 94 * q^83 + 130 * q^84 + 90 * q^85 - 34 * q^86 + 22 * q^87 - 122 * q^88 - 15 * q^89 + 43 * q^90 + 56 * q^91 - 294 * q^92 - 52 * q^93 - 57 * q^94 + 94 * q^95 + 24 * q^96 + 46 * q^97 + 73 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	0.117605	+	0.130614i	0.0831593	+	0.0923577i	0.783288	−	0.621659i	$-0.213541\pi$
$2$	0.117605	+	0.130614i	0.0831593	+	0.0923577i	−0.700129	+	0.714016i	$0.746874\pi$
$3$	0.508986	−	0.565287i	0.293863	−	0.326368i	−0.578075	−	0.815983i	$-0.696196\pi$
$3$	0.508986	−	0.565287i	0.293863	−	0.326368i	0.871939	+	0.489615i	$0.162863\pi$
$4$	0.205828	−	1.95832i	0.102914	−	0.979161i
$5$	0.00796452	+	0.0137949i	0.00356184	+	0.00616929i	0.867801	−	0.496912i	$-0.165533\pi$
$5$	0.00796452	+	0.0137949i	0.00356184	+	0.00616929i	−0.864239	+	0.503081i	$0.832200\pi$
$6$	0.133693			0.0545801
$7$	3.75325	+	2.72689i	1.41859	+	1.03067i	0.992002	+	0.126225i	$0.0402860\pi$
$7$	3.75325	+	2.72689i	1.41859	+	1.03067i	0.426592	+	0.904444i	$0.359714\pi$
$8$	0.564372	−	0.410040i	0.199536	−	0.144971i
$9$	0.253104	+	2.40812i	0.0843678	+	0.802706i
$10$	−0.000865141		0.00266263i	−0.000273581		0.000841997i
$11$	1.48452	+	1.07857i	0.447600	+	0.325200i	0.788647	−	0.614846i	$-0.210782\pi$
$11$	1.48452	+	1.07857i	0.447600	+	0.325200i	−0.341048	+	0.940046i	$0.610782\pi$
$12$	−1.00225	−	1.11311i	−0.289325	−	0.321328i
$13$	−2.10621	−	2.92641i	−0.584157	−	0.811641i
$13$	−2.10621	−	2.92641i	−0.584157	−	0.811641i
$14$	0.0852313	+	0.810921i	0.0227790	+	0.216728i
$15$	0.0118519	+	0.00251921i	0.00306016	+	0.000650456i
$16$	−3.73223	−	0.793310i	−0.933057	−	0.198327i
$17$	4.66547	−	3.38966i	1.13154	−	0.822114i	0.145625	−	0.989340i	$-0.453481\pi$
$17$	4.66547	−	3.38966i	1.13154	−	0.822114i	0.985919	+	0.167226i	$0.0534808\pi$
$18$	−0.284767	+	0.316266i	−0.0671202	+	0.0745445i
$19$	−1.33923	+	4.12174i	−0.307241	+	0.945592i	0.671590	+	0.740923i	$0.265612\pi$
$19$	−1.33923	+	4.12174i	−0.307241	+	0.945592i	−0.978831	+	0.204669i	$0.934388\pi$
$20$	0.0286543	−	0.0127577i	0.00640729	−	0.00285271i
$21$	3.45183	−	0.733709i	0.753251	−	0.160108i
$22$	0.0337115	+	0.320743i	0.00718731	+	0.0683827i
$23$	−0.534373	−	5.08422i	−0.111424	−	1.06013i	−0.897201	−	0.441622i	$-0.854403\pi$
$23$	−0.534373	−	5.08422i	−0.111424	−	1.06013i	0.785777	−	0.618510i	$-0.212263\pi$
$24$	0.0554674	−	0.527737i	0.0113222	−	0.107724i
$25$	2.49987	−	4.32991i	0.499975	−	0.865981i
$26$	0.134529	−	0.619260i	0.0263832	−	0.121447i
$27$	3.33628	+	2.42395i	0.642068	+	0.466490i
$28$	6.11266	−	6.78880i	1.15518	−	1.28296i
$29$	−6.18267	−	6.86655i	−1.14809	−	1.27509i	−0.955888	−	0.293732i	$-0.905103\pi$
$29$	−6.18267	−	6.86655i	−1.14809	−	1.27509i	−0.192206	−	0.981355i	$-0.561564\pi$
$30$	0.00106480	+	0.00184429i	0.000194406	+	0.000336721i
$31$	−5.20624	+	1.97360i	−0.935067	+	0.354470i
$31$	−5.20624	+	1.97360i	−0.935067	+	0.354470i
$32$	−1.03291	−	1.78906i	−0.182595	−	0.316264i
$33$	1.36530	−	0.290204i	0.237668	−	0.0505179i
$34$	0.991419	+	0.210733i	0.170027	+	0.0361403i
$35$	−0.00772456	+	0.0734942i	−0.00130569	+	0.0124228i
$36$	4.76797			0.794662
$37$	2.04605	+	3.54385i	0.336368	+	0.582606i	0.983747	−	0.179562i	$-0.0574681\pi$
$37$	2.04605	+	3.54385i	0.336368	+	0.582606i	−0.647379	+	0.762168i	$0.724135\pi$
$38$	−0.695856	+	0.309815i	−0.112883	+	0.0502586i
$39$	−2.72629	−	0.298893i	−0.436556	−	0.0478612i
$40$	0.0101514	+	0.00451971i	0.00160508	+	0.000714629i
$41$	−3.20522	+	9.86464i	−0.500571	+	1.54060i	0.307521	+	0.951541i	$0.400500\pi$
$41$	−3.20522	+	9.86464i	−0.500571	+	1.54060i	−0.808092	+	0.589057i	$0.799500\pi$
$42$	0.501784	+	0.364568i	0.0774270	+	0.0562540i
$43$	−2.77048	+	8.52665i	−0.422494	+	1.30030i	0.482880	+	0.875687i	$0.339591\pi$
$43$	−2.77048	+	8.52665i	−0.422494	+	1.30030i	−0.905374	+	0.424616i	$0.860409\pi$
$44$	2.41774	−	2.68517i	0.364488	−	0.404805i
$45$	−0.0312040	+	0.0226711i	−0.00465162	+	0.00337960i
$46$	0.601223	−	0.667726i	0.0886455	−	0.0984508i
$47$	−0.219280	−	0.674876i	−0.0319853	−	0.0984407i	0.933789	−	0.357823i	$-0.116481\pi$
$47$	−0.219280	−	0.674876i	−0.0319853	−	0.0984407i	−0.965775	+	0.259383i	$0.916481\pi$
$48$	−2.34810	+	1.70600i	−0.338919	+	0.246239i
$49$	4.48779	+	13.8120i	0.641113	+	1.97314i
$50$	0.859542	−	0.182701i	0.121558	−	0.0258379i
$51$	0.458530	−	4.36262i	0.0642071	−	0.610889i
$52$	−6.16437	+	3.52230i	−0.854845	+	0.488455i
$53$	−2.78348	−	1.23928i	−0.382340	−	0.170229i	0.206561	−	0.978434i	$-0.433773\pi$
$53$	−2.78348	−	1.23928i	−0.382340	−	0.170229i	−0.588901	+	0.808205i	$0.700439\pi$
$54$	0.0757626	+	0.720833i	0.0103100	+	0.0980929i
$55$	−0.00305529	+	0.0290691i	−0.000411975	+	0.00391968i
$56$	3.23636			0.432477
$57$	1.64831	+	2.85496i	0.218324	+	0.378149i
$58$	0.169752	−	1.61508i	0.0222895	−	0.212071i
$59$	−3.04459	−	9.37028i	−0.396371	−	1.21991i	−0.927888	−	0.372858i	$-0.878378\pi$
$59$	−3.04459	−	9.37028i	−0.396371	−	1.21991i	0.531517	−	0.847048i	$-0.321622\pi$
$60$	0.00737288	−	0.0226914i	0.000951834	−	0.00292944i
$61$	0.462717	+	0.801450i	0.0592449	+	0.102615i	0.894127	−	0.447814i	$-0.147797\pi$
$61$	0.462717	+	0.801450i	0.0592449	+	0.102615i	−0.834882	+	0.550429i	$0.814464\pi$
$62$	−0.870059	−	0.447899i	−0.110498	−	0.0568833i
$63$	−5.61672	+	9.72845i	−0.707641	+	1.22567i
$64$	−2.24598	+	6.91241i	−0.280747	+	0.864051i
$65$	0.0235948	−	0.0523625i	0.00292657	−	0.00649477i
$66$	0.198471	+	0.144197i	0.0244300	+	0.0177495i
$67$	3.18891			0.389588			0.194794	−	0.980844i	$-0.437596\pi$
$67$	3.18891			0.389588			0.194794	+	0.980844i	$0.437596\pi$
$68$	−5.67777	−	9.83419i	−0.688531	−	1.19257i
$69$	−3.14603	−	2.28572i	−0.378737	−	0.275169i
$70$	−0.0105078	+	0.00763436i	−0.00125592	+	0.000912480i
$71$	−0.227156	−	2.16125i	−0.0269585	−	0.256493i	−0.999698	−	0.0245907i	$-0.992172\pi$
$71$	−0.227156	−	2.16125i	−0.0269585	−	0.256493i	0.972739	−	0.231902i	$-0.0744949\pi$
$72$	1.13027	+	1.25529i	0.133204	+	0.147938i
$73$	0.616291	−	5.86362i	0.0721314	−	0.686285i	−0.897383	−	0.441252i	$-0.854535\pi$
$73$	0.616291	−	5.86362i	0.0721314	−	0.686285i	0.969515	−	0.245033i	$-0.0787988\pi$
$74$	−0.222250	+	0.684016i	−0.0258361	+	0.0795153i
$75$	−1.17524	−	3.61701i	−0.135705	−	0.417656i
$76$	7.79604	+	3.47102i	0.894267	+	0.398153i
$77$	2.63063	+	8.09626i	0.299788	+	0.922654i
$78$	−0.281586	−	0.391242i	−0.0318834	−	0.0442995i
$79$	0.430006	+	4.09124i	0.0483795	+	0.460300i	0.991715	+	0.128459i	$0.0410031\pi$
$79$	0.430006	+	4.09124i	0.0483795	+	0.460300i	−0.943335	+	0.331841i	$0.892330\pi$
$80$	−0.0187817	−	0.0578042i	−0.00209986	−	0.00646271i
$81$	−4.03706	+	0.858104i	−0.448562	+	0.0953449i
$82$	−1.66541	+	0.741486i	−0.183913	+	0.0818834i
$83$	−0.177337	+	0.0376942i	−0.0194653	+	0.00413747i	−0.217634	−	0.976030i	$-0.569834\pi$
$83$	−0.177337	+	0.0376942i	−0.0194653	+	0.00413747i	0.198169	+	0.980168i	$0.436501\pi$
$84$	−0.726355	−	6.91081i	−0.0792519	−	0.754031i
$85$	0.0839185	+	0.0373629i	0.00910224	+	0.00405258i
$86$	−1.43952	+	0.640915i	−0.155227	+	0.0691116i
$87$	−7.02847			−0.753531
$88$	1.28008			0.136457
$89$	5.78630	−	2.57622i	0.613346	−	0.273079i	−0.0764609	−	0.997073i	$-0.524362\pi$
$89$	5.78630	−	2.57622i	0.613346	−	0.273079i	0.689807	+	0.723993i	$0.257695\pi$
$90$	−0.00663090	−	0.00140944i	−0.000698958	−	0.000148568i
$91$	0.0748969	−	16.7270i	0.00785133	−	1.75346i
$92$	−10.0665			−1.04951
$93$	−1.53425	+	3.94755i	−0.159094	+	0.409342i
$94$	0.0623594	−	0.108010i	0.00643189	−	0.0111404i
$95$	−0.0675255	+	0.0143530i	−0.00692797	+	0.00147259i
$96$	−1.53707	−	0.326714i	−0.156877	−	0.0333452i
$97$	−1.50946	+	14.3615i	−0.153262	+	1.45819i	0.599752	+	0.800186i	$0.295266\pi$
$97$	−1.50946	+	14.3615i	−0.153262	+	1.45819i	−0.753014	+	0.658004i	$0.771401\pi$
$98$	−1.27625	+	2.21053i	−0.128921	+	0.223297i
$99$	−2.22158	+	3.84789i	−0.223277	+	0.386728i
$100$	−7.96481	−	5.78677i	−0.796481	−	0.578677i
$101$	0.0355312	+	0.338056i	0.00353548	+	0.0336379i	0.996147	−	0.0876946i	$-0.0279500\pi$
$101$	0.0355312	+	0.338056i	0.00353548	+	0.0336379i	−0.992612	+	0.121332i	$0.961283\pi$
$102$	0.623743	−	0.453176i	0.0617598	−	0.0448711i
$103$	−5.74181	+	1.22046i	−0.565757	+	0.120255i	−0.481906	−	0.876223i	$-0.660055\pi$
$103$	−5.74181	+	1.22046i	−0.565757	+	0.120255i	−0.0838513	+	0.996478i	$0.526722\pi$
$104$	−2.38863	−	0.787955i	−0.234225	−	0.0772654i
$105$	0.0376136	+	0.0417742i	0.00367071	+	0.00407674i
$106$	−0.165484	−	0.509306i	−0.0160732	−	0.0494682i
$107$	11.0329	+	4.91216i	1.06659	+	0.474876i	0.863534	−	0.504291i	$-0.168246\pi$
$107$	11.0329	+	4.91216i	1.06659	+	0.474876i	0.203056	+	0.979167i	$0.434913\pi$
$108$	5.43358	−	6.03460i	0.522847	−	0.580680i
$109$	−2.37741	−	7.31692i	−0.227715	−	0.700834i	−0.998005	−	0.0631403i	$-0.979888\pi$
$109$	−2.37741	−	7.31692i	−0.227715	−	0.700834i	0.770290	−	0.637694i	$-0.220112\pi$
$110$	−0.00415614	+	0.00301961i	−0.000396273	+	0.000287909i
$111$	3.04470	+	0.647172i	0.288990	+	0.0614268i
$112$	−11.8447	−	13.1549i	−1.11922	−	1.24302i
$113$	−12.9197	+	5.75224i	−1.21539	+	0.541125i	−0.911388	−	0.411548i	$-0.864988\pi$
$113$	−12.9197	+	5.75224i	−1.21539	+	0.541125i	−0.303998	+	0.952673i	$0.598322\pi$
$114$	−0.179047	+	0.551050i	−0.0167693	+	0.0516105i
$115$	0.0658805	−	0.0478650i	0.00614339	−	0.00446343i
$116$	−14.7195	+	10.6943i	−1.36667	+	0.992944i
$117$	6.51406	−	5.81268i	0.602225	−	0.537383i
$118$	0.865827	−	1.49966i	0.0797058	−	0.138054i
$119$	26.7539			2.45253
$120$	0.00772188	−	0.00343800i	0.000704908	−	0.000313845i
$121$	−2.35869	−	7.25931i	−0.214427	−	0.659938i
$122$	−0.0502624	+	0.154692i	−0.00455054	+	0.0140051i
$123$	3.94494	+	6.83283i	0.355703	+	0.616096i
$124$	2.79336	+	10.6017i	0.250851	+	0.952062i
$125$	0.159286			0.0142470
$126$	−1.93122	+	0.410494i	−0.172047	+	0.0365697i
$127$	−4.16129	+	4.62158i	−0.369254	+	0.410099i	−0.898923	−	0.438106i	$-0.855649\pi$
$127$	−4.16129	+	4.62158i	−0.369254	+	0.410099i	0.529669	+	0.848204i	$0.322316\pi$
$128$	−4.94145	+	2.20007i	−0.436766	+	0.194461i
$129$	3.40987	+	5.90606i	0.300222	+	0.520000i
$130$	0.00961412	−	0.00307629i	0.000843214	−	0.000269809i
$131$	−0.899799	+	0.400616i	−0.0786158	+	0.0350020i	−0.445668	−	0.895198i	$-0.647034\pi$
$131$	−0.899799	+	0.400616i	−0.0786158	+	0.0350020i	0.367052	+	0.930200i	$0.380367\pi$
$132$	−0.287295	−	2.73343i	−0.0250058	−	0.237915i
$133$	−16.2660	+	11.8180i	−1.41044	+	1.02475i
$134$	0.375032	+	0.416515i	0.0323978	+	0.0359815i
$135$	−0.00686641	+	0.0653295i	−0.000590966	+	0.00562267i
$136$	1.24316	−	3.82606i	0.106600	−	0.328082i
$137$	−20.0154	−	4.25441i	−1.71003	−	0.363479i	−0.754032	−	0.656838i	$-0.771894\pi$
$137$	−20.0154	−	4.25441i	−1.71003	−	0.363479i	−0.956002	+	0.293359i	$0.905227\pi$
$138$	−0.0714421	−	0.679726i	−0.00608156	−	0.0578622i
$139$	−4.51069	+	5.00963i	−0.382592	+	0.424911i	−0.903424	−	0.428748i	$-0.858955\pi$
$139$	−4.51069	+	5.00963i	−0.382592	+	0.424911i	0.520832	+	0.853659i	$0.325622\pi$
$140$	0.142335	+	0.0302543i	0.0120295	+	0.00255696i
$141$	−0.493109	−	0.219546i	−0.0415273	−	0.0184891i
$142$	0.255573	−	0.283843i	0.0214472	−	0.0238196i
$143$	0.0296240	−	6.61600i	0.00247728	−	0.553258i
$144$	0.965744	−	9.18844i	0.0804787	−	0.765703i
$145$	0.0454818	−	0.139978i	0.00377705	−	0.0116246i
$146$	0.838347	−	0.609095i	0.0693821	−	0.0504091i
$147$	10.0920	+	4.49324i	0.832372	+	0.370596i
$148$	7.36114	−	3.27739i	0.605082	−	0.269400i
$149$	9.88217			0.809579			0.404790	−	0.914410i	$-0.367345\pi$
$149$	9.88217			0.809579			0.404790	+	0.914410i	$0.367345\pi$
$150$	0.334217	−	0.578880i	0.0272887	−	0.0472654i
$151$	10.1273	+	7.35789i	0.824145	+	0.598776i	0.917897	−	0.396819i	$-0.129886\pi$
$151$	10.1273	+	7.35789i	0.824145	+	0.598776i	−0.0937518	+	0.995596i	$0.529886\pi$
$152$	0.934253	+	2.87533i	0.0757779	+	0.233220i
$153$	9.34356	+	10.3771i	0.755382	+	0.838937i
$154$	−0.748105	+	1.29576i	−0.0602840	+	0.104415i
$155$	−0.0686909	−	0.0561009i	−0.00551739	−	0.00450614i
$156$	−1.14648	+	5.27744i	−0.0917915	+	0.422533i
$157$	2.91571	−	8.97365i	0.232699	−	0.716175i	−0.764719	−	0.644364i	$-0.777122\pi$
$157$	2.91571	−	8.97365i	0.232699	−	0.716175i	0.997418	−	0.0718109i	$-0.0228778\pi$
$158$	−0.483800	+	0.537315i	−0.0384891	+	0.0427465i
$159$	−2.11730	+	0.942685i	−0.167913	+	0.0747597i
$160$	0.0164533	−	0.0284980i	0.00130075	−	0.00225296i
$161$	11.8585	−	20.5395i	0.934579	−	1.61874i
$162$	−0.586859	−	0.426378i	−0.0461080	−	0.0334994i
$163$	−16.6194	−	7.39943i	−1.30173	−	0.579568i	−0.365453	−	0.930830i	$-0.619086\pi$
$163$	−16.6194	−	7.39943i	−1.30173	−	0.579568i	−0.936277	+	0.351262i	$0.885753\pi$
$164$	18.6584	+	8.30726i	1.45698	+	0.648688i
$165$	0.0148773	+	0.0165229i	0.00115820	+	0.00128631i
$166$	−0.0257791	−	0.0187296i	−0.00200085	−	0.00145370i
$167$	24.6858	−	5.24713i	1.91025	−	0.406035i	0.910278	−	0.413997i	$-0.135868\pi$
$167$	24.6858	−	5.24713i	1.91025	−	0.406035i	0.999968	+	0.00796178i	$0.00253434\pi$
$168$	1.64727	−	1.82947i	0.127089	−	0.141147i
$169$	−4.12778	+	12.3273i	−0.317521	+	0.948251i
$170$	0.00498913	+	0.0153550i	0.000382649	+	0.00117767i
$171$	−10.2646	−	2.18181i	−0.784954	−	0.166847i
$172$	16.1277	+	7.18051i	1.22972	+	0.547509i
$173$	−22.6701	−	4.81867i	−1.72357	−	0.366357i	−0.763436	−	0.645883i	$-0.776489\pi$
$173$	−22.6701	−	4.81867i	−1.72357	−	0.366357i	−0.960138	+	0.279526i	$0.909823\pi$
$174$	−0.826583	−	0.918013i	−0.0626631	−	0.0695944i
$175$	21.1898	−	9.43432i	1.60180	−	0.713168i
$176$	−4.68493	−	5.20314i	−0.353140	−	0.392202i
$177$	−6.84655	−	3.04828i	−0.514618	−	0.229123i
$178$	1.01699	+	0.452792i	0.0762264	+	0.0339382i
$179$	−0.360437	+	3.42933i	−0.0269403	+	0.256320i	0.972759	+	0.231817i	$0.0744670\pi$
$179$	−0.360437	+	3.42933i	−0.0269403	+	0.256320i	−0.999700	+	0.0245032i	$0.992200\pi$
$180$	0.0379746	+	0.0657739i	0.00283046	+	0.00490250i
$181$	1.66753	+	2.88826i	0.123947	+	0.214682i	0.921321	−	0.388803i	$-0.127111\pi$
$181$	1.66753	+	2.88826i	0.123947	+	0.214682i	−0.797374	+	0.603486i	$0.793778\pi$
$182$	2.19358	−	1.95739i	0.162599	−	0.145091i
$183$	0.688566	+	0.146359i	0.0509002	+	0.0108192i
$184$	−2.38632	−	2.65028i	−0.175922	−	0.195381i
$185$	−0.0325915	+	0.0564502i	−0.00239618	+	0.00415030i
$186$	−0.696040	+	0.263858i	−0.0510361	+	0.0193470i
$187$	10.5820			0.773830
$188$	−1.36676	+	0.290513i	−0.0996811	+	0.0211879i
$189$	5.91204	+	18.1954i	0.430038	+	1.32352i
$190$	−0.00981604	−	0.00713177i	−0.000712130	−	0.000517393i
$191$	1.76965	−	3.06512i	0.128047	−	0.221785i	−0.794873	−	0.606776i	$-0.792462\pi$
$191$	1.76965	−	3.06512i	0.128047	−	0.221785i	0.922920	+	0.384992i	$0.125796\pi$
$192$	2.76432	+	4.78794i	0.199498	+	0.345540i
$193$	−0.410917	+	3.90961i	−0.0295784	+	0.281420i	0.969728	+	0.244187i	$0.0785210\pi$
$193$	−0.410917	+	3.90961i	−0.0295784	+	0.281420i	−0.999307	+	0.0372330i	$0.988146\pi$
$194$	−2.05333	+	1.49183i	−0.147420	+	0.107107i
$195$	−0.0175904	−	0.0399896i	−0.00125967	−	0.00286372i
$196$	27.9721	−	5.94565i	1.99801	−	0.424689i
$197$	−11.3084	−	8.21605i	−0.805691	−	0.585369i	0.106887	−	0.994271i	$-0.465912\pi$
$197$	−11.3084	−	8.21605i	−0.805691	−	0.585369i	−0.912578	+	0.408902i	$0.865912\pi$
$198$	−0.763856	+	0.162363i	−0.0542849	+	0.0115386i
$199$	19.3843	+	4.12027i	1.37412	+	0.292078i	0.835045	−	0.550181i	$-0.185441\pi$
$199$	19.3843	+	4.12027i	1.37412	+	0.292078i	0.539073	+	0.842259i	$0.318775\pi$
$200$	−0.364578	−	3.46873i	−0.0257796	−	0.245276i
$201$	1.62311	−	1.80265i	0.114486	−	0.127149i
$202$	−0.0399761	+	0.0443980i	−0.00281271	+	0.00312383i
$203$	−4.48074	−	42.6314i	−0.314486	−	2.99213i
$204$	−8.44904	−	1.79590i	−0.591551	−	0.125738i
$205$	−0.161610	+	0.0343513i	−0.0112873	+	0.00239920i
$206$	−0.834674	−	0.606426i	−0.0581545	−	0.0422517i
$207$	12.1081	−	2.57367i	0.841574	−	0.178882i
$208$	5.53930	+	12.5929i	0.384081	+	0.873162i
$209$	−6.43369	+	4.67435i	−0.445028	+	0.323332i
$210$	−0.00103272	+	0.00982570i	−7.12646e−5	+	0.000678038i
$211$	−9.44722	−	16.3631i	−0.650373	−	1.12648i	−0.983032	−	0.183433i	$-0.941279\pi$
$211$	−9.44722	−	16.3631i	−0.650373	−	1.12648i	0.332659	−	0.943047i	$-0.392054\pi$
$212$	−2.99984	+	5.19587i	−0.206030	+	0.356854i
$213$	−1.33734	−	0.971637i	−0.0916333	−	0.0665755i
$214$	0.655928	+	2.01874i	0.0448383	+	0.137998i
$215$	−0.139690	+	0.0296921i	−0.00952680	+	0.00202498i
$216$	2.87682			0.195743
$217$	−24.9221	−	6.78943i	−1.69182	−	0.460896i
$218$	0.676094	−	1.17103i	0.0457909	−	0.0793121i
$219$	−3.00094	−	3.33288i	−0.202785	−	0.225215i
$220$	0.0562979	+	0.0119665i	0.00379560	+	0.000806780i
$221$	−19.7460	−	6.51376i	−1.32826	−	0.438163i
$222$	0.273543	+	0.473790i	0.0183590	+	0.0317987i
$223$	4.83782	+	8.37935i	0.323964	+	0.561123i	0.981302	−	0.192473i	$-0.0616509\pi$
$223$	4.83782	+	8.37935i	0.323964	+	0.561123i	−0.657338	+	0.753596i	$0.728318\pi$
$224$	1.00179	−	9.53143i	0.0669351	−	0.636845i
$225$	11.0597	+	4.92408i	0.737311	+	0.328272i
$226$	−2.27074	−	1.01100i	−0.151048	−	0.0672508i
$227$	8.05318	+	8.94396i	0.534508	+	0.593631i	0.948550	−	0.316626i	$-0.102550\pi$
$227$	8.05318	+	8.94396i	0.534508	+	0.593631i	−0.414042	+	0.910258i	$0.635883\pi$
$228$	5.93020	−	2.64030i	0.392737	−	0.174858i
$229$	1.07457	+	1.19343i	0.0710093	+	0.0788639i	0.777603	−	0.628756i	$-0.216436\pi$
$229$	1.07457	+	1.19343i	0.0710093	+	0.0788639i	−0.706593	+	0.707620i	$0.749769\pi$
$230$	0.0139997	+	0.00297573i	0.000923112	+	0.000196214i
$231$	5.91566	+	2.63382i	0.389222	+	0.173293i
$232$	−6.30489	−	1.34015i	−0.413936	−	0.0879849i
$233$	5.66981	+	17.4499i	0.371442	+	1.14318i	0.945848	+	0.324609i	$0.105233\pi$
$233$	5.66981	+	17.4499i	0.371442	+	1.14318i	−0.574407	+	0.818570i	$0.694767\pi$
$234$	1.52530	+	0.167224i	0.0997121	+	0.0109318i
$235$	0.00756341	−	0.00840002i	0.000493383	−	0.000547957i
$236$	−18.9767	+	4.03362i	−1.23528	+	0.262566i
$237$	2.53159	+	1.83931i	0.164444	+	0.119476i
$238$	3.14639	+	3.49443i	0.203950	+	0.226510i
$239$	−11.0548	−	4.92191i	−0.715075	−	0.318372i	0.0167545	−	0.999860i	$-0.494667\pi$
$239$	−11.0548	−	4.92191i	−0.715075	−	0.318372i	−0.731830	+	0.681488i	$0.761333\pi$
$240$	−0.0422356	−	0.0188045i	−0.00272630	−	0.00121383i
$241$	10.7805	+	7.83247i	0.694431	+	0.504534i	0.878114	−	0.478452i	$-0.158802\pi$
$241$	10.7805	+	7.83247i	0.694431	+	0.504534i	−0.183683	+	0.982986i	$0.558802\pi$
$242$	0.670771	−	1.16181i	0.0431188	−	0.0746839i
$243$	−7.75555	+	13.4330i	−0.497519	+	0.861727i
$244$	1.66474	−	0.741189i	0.106574	−	0.0474497i
$245$	−0.154793	+	0.171915i	−0.00988935	+	0.0109832i
$246$	−0.428516	+	1.31884i	−0.0273212	+	0.0840860i
$247$	14.8826	−	4.76209i	0.946958	−	0.303004i
$248$	−2.12900	+	3.24861i	−0.135191	+	0.206287i
$249$	−0.0689541	+	0.119432i	−0.00436979	+	0.00756870i
$250$	0.0187329	+	0.0208050i	0.00118477	+	0.00131582i
$251$	−5.57821	−	17.1680i	−0.352093	−	1.08363i	−0.957676	−	0.287849i	$-0.907060\pi$
$251$	−5.57821	−	17.1680i	−0.352093	−	1.08363i	0.605582	−	0.795783i	$-0.292940\pi$
$252$	17.8954	+	13.0017i	1.12730	+	0.819033i
$253$	4.69038	−	8.12398i	0.294882	−	0.510750i
$254$	−1.09303			−0.0685827
$255$	0.0638341	−	0.0284208i	0.00399745	−	0.00177978i
$256$	12.4110	+	5.52575i	0.775690	+	0.345359i
$257$	−2.35413	+	1.71037i	−0.146846	+	0.106690i	−0.658783	−	0.752333i	$-0.728928\pi$
$257$	−2.35413	+	1.71037i	−0.146846	+	0.106690i	0.511936	+	0.859023i	$0.328928\pi$
$258$	−0.370395	+	1.13996i	−0.0230598	+	0.0709707i
$259$	−1.98440	+	18.8803i	−0.123305	+	1.17317i
$260$	−0.0976862	−	0.0569838i	−0.00605824	−	0.00353399i
$261$	14.9706	−	16.6266i	0.926658	−	1.02916i
$262$	−0.158147	−	0.0704115i	−0.00977034	−	0.00435004i
$263$	21.2417	+	4.51506i	1.30982	+	0.278411i	0.809341	−	0.587338i	$-0.199824\pi$
$263$	21.2417	+	4.51506i	1.30982	+	0.278411i	0.500478	+	0.865749i	$0.333158\pi$
$264$	0.651542	−	0.723611i	0.0400997	−	0.0445352i
$265$	−0.00507320	−	0.0482683i	−0.000311644	−	0.00296510i
$266$	−3.45655	−	0.734712i	−0.211935	−	0.0450481i
$267$	1.48884	−	4.58218i	0.0911155	−	0.280425i
$268$	0.656368	−	6.24492i	0.0400940	−	0.381469i
$269$	−11.6278	−	12.9140i	−0.708960	−	0.787380i	0.275816	−	0.961211i	$-0.411052\pi$
$269$	−11.6278	−	12.9140i	−0.708960	−	0.787380i	−0.984776	+	0.173831i	$0.944385\pi$
$270$	−0.00934044	+	0.00678623i	−0.000568441	+	0.000412997i
$271$	−0.864460	−	8.22478i	−0.0525122	−	0.499620i	−0.988892	−	0.148633i	$-0.952513\pi$
$271$	−0.864460	−	8.22478i	−0.0525122	−	0.499620i	0.936380	−	0.350987i	$-0.114154\pi$
$272$	−20.1017	+	8.94984i	−1.21884	+	0.542664i
$273$	−9.41740	−	8.55613i	−0.569967	−	0.517840i
$274$	−1.79823	−	3.11463i	−0.108635	−	0.188162i
$275$	8.38121	−	3.73155i	0.505406	−	0.225021i
$276$	−5.12372	+	5.69047i	−0.308412	+	0.342526i
$277$	15.7403	−	3.34570i	0.945741	−	0.201023i	0.290869	−	0.956763i	$-0.406056\pi$
$277$	15.7403	−	3.34570i	0.945741	−	0.201023i	0.654872	+	0.755740i	$0.272722\pi$
$278$	−1.18481			−0.0710599
$279$	−6.07039	−	12.0377i	−0.363425	−	0.720679i
$280$	0.0257761	+	0.0446455i	0.00154042	+	0.00266808i
$281$	9.74123	−	29.9804i	0.581113	−	1.78848i	−0.0332353	−	0.999448i	$-0.510581\pi$
$281$	9.74123	−	29.9804i	0.581113	−	1.78848i	0.614348	−	0.789035i	$-0.289419\pi$
$282$	−0.0293163	−	0.0902264i	−0.00174576	−	0.00537291i
$283$	24.2316	−	10.7886i	1.44042	−	0.641315i	0.469981	−	0.882676i	$-0.344261\pi$
$283$	24.2316	−	10.7886i	1.44042	−	0.641315i	0.970435	+	0.241362i	$0.0775940\pi$
$284$	−4.27917			−0.253922
$285$	−0.0262560	+	0.0454768i	−0.00155527	+	0.00269381i
$286$	0.867624	−	0.774206i	0.0513037	−	0.0457798i
$287$	−38.9298	+	28.2841i	−2.29795	+	1.66956i
$288$	4.04683	−	2.94020i	0.238462	−	0.173253i
$289$	5.02352	−	15.4608i	0.295501	−	0.909460i
$290$	0.0236320	−	0.0105216i	0.00138772	−	0.000617851i
$291$	7.35008	+	8.16309i	0.430869	+	0.478529i
$292$	−11.3560	−	2.41379i	−0.664560	−	0.141257i
$293$	−1.91797	+	1.39349i	−0.112049	+	0.0814083i	−0.642399	−	0.766371i	$-0.722061\pi$
$293$	−1.91797	+	1.39349i	−0.112049	+	0.0814083i	0.530350	+	0.847779i	$0.322061\pi$
$294$	0.599989	+	1.84658i	0.0349921	+	0.107694i
$295$	0.105014	−	0.116630i	0.00611414	−	0.00679044i
$296$	2.60785	+	1.16109i	0.151578	+	0.0674871i
$297$	2.33839	+	7.19681i	0.135687	+	0.417601i
$298$	1.16219	+	1.29075i	0.0673240	+	0.0747709i
$299$	−13.7530	+	12.2722i	−0.795357	+	0.709720i
$300$	−7.32517	+	1.55701i	−0.422919	+	0.0898941i
$301$	−33.6496	+	24.4478i	−1.93953	+	1.40915i
$302$	0.229977	+	2.18808i	0.0132337	+	0.125910i
$303$	0.209184	+	0.151981i	0.0120173	+	0.00873107i
$304$	8.26814	−	14.3208i	0.474211	−	0.821357i
$305$	−0.00737064	+	0.0127663i	−0.000422042	+	0.000730998i
$306$	−0.256538	+	2.44079i	−0.0146653	+	0.139531i
$307$	−9.98012	−	2.12134i	−0.569596	−	0.121071i	−0.0858940	−	0.996304i	$-0.527375\pi$
$307$	−9.98012	−	2.12134i	−0.569596	−	0.121071i	−0.483702	+	0.875233i	$0.660708\pi$
$308$	16.3965	−	3.48519i	0.934279	−	0.198587i
$309$	−2.23259	+	3.86697i	−0.127008	+	0.219984i
$310$	−0.000750849	−	0.0155697i	−4.26454e−5	−	0.000884301i
$311$	22.5608			1.27931			0.639653	−	0.768664i	$-0.279078\pi$
$311$	22.5608			1.27931			0.639653	+	0.768664i	$0.279078\pi$
$312$	−1.66120	+	0.949203i	−0.0940470	+	0.0537381i
$313$	13.4199	+	2.85250i	0.758540	+	0.161233i	0.570916	−	0.821008i	$-0.306588\pi$
$313$	13.4199	+	2.85250i	0.758540	+	0.161233i	0.187624	+	0.982241i	$0.439921\pi$
$314$	1.51498	−	0.674514i	0.0854954	−	0.0380650i
$315$	−0.178938			−0.0100820
$316$	8.10047			0.455687
$317$	−16.3271	+	7.26931i	−0.917023	+	0.408285i	−0.810308	−	0.586004i	$-0.800700\pi$
$317$	−16.3271	+	7.26931i	−0.917023	+	0.408285i	−0.106716	+	0.994290i	$0.534033\pi$
$318$	−0.372133	−	0.165684i	−0.0208682	−	0.00929111i
$319$	−1.77226	−	16.8620i	−0.0992277	−	0.944089i
$320$	−0.113244	+	0.0240708i	−0.00633055	+	0.00134560i
$321$	8.39237	−	3.73652i	0.468416	−	0.208552i
$322$	4.07735	−	0.866668i	0.227222	−	0.0482975i
$323$	7.72315	+	23.7694i	0.429728	+	1.32257i
$324$	0.849504	+	8.08249i	0.0471946	+	0.449027i
$325$	−17.9363	+	1.80402i	−0.994929	+	0.100069i
$326$	−0.988057	−	3.04093i	−0.0547234	−	0.168421i
$327$	−5.34623	−	2.38030i	−0.295647	−	0.131631i
$328$	2.23597	+	6.88160i	0.123461	+	0.379973i
$329$	1.01730	−	3.13093i	0.0560856	−	0.172614i
$330$	−0.000408472		0.00388635i	−2.24857e−5		0.000213937i
$331$	−12.8241	−	14.2426i	−0.704875	−	0.782843i	0.279269	−	0.960213i	$-0.409908\pi$
$331$	−12.8241	−	14.2426i	−0.704875	−	0.782843i	−0.984144	+	0.177369i	$0.943241\pi$
$332$	0.0373164	+	0.355042i	0.00204800	+	0.0194854i
$333$	−8.01616	+	5.82408i	−0.439283	+	0.319158i
$334$	3.58852	+	2.60721i	0.196355	+	0.142660i
$335$	0.0253982	+	0.0439909i	0.00138765	+	0.00240348i
$336$	−13.4651			−0.734580
$337$	10.0694	+	7.31587i	0.548517	+	0.398521i	0.827238	−	0.561851i	$-0.189911\pi$
$337$	10.0694	+	7.31587i	0.548517	+	0.398521i	−0.278722	+	0.960372i	$0.589911\pi$
$338$	−2.09556	+	0.910604i	−0.113983	+	0.0495303i
$339$	−3.32431	+	10.2312i	−0.180552	+	0.555680i
$340$	0.0904414	−	0.156649i	0.00490487	−	0.00849549i
$341$	−9.85743	−	2.68542i	−0.533810	−	0.145424i
$342$	−0.922195	−	1.59729i	−0.0498666	−	0.0863715i
$343$	−10.7848	+	33.1922i	−0.582324	+	1.79221i
$344$	1.93269	+	5.94821i	0.104204	+	0.320706i
$345$	0.00647484	−	0.0616040i	0.000348594	−	0.00331665i
$346$	−2.03673	−	3.52772i	−0.109495	−	0.189651i
$347$	−15.8464			−0.850677			−0.425338	−	0.905034i	$-0.639845\pi$
$347$	−15.8464			−0.850677			−0.425338	+	0.905034i	$0.639845\pi$
$348$	−1.44666	+	13.7640i	−0.0775489	+	0.737828i
$349$	3.73716	+	35.5567i	0.200045	+	1.90330i	0.388869	+	0.921293i	$0.372866\pi$
$349$	3.73716	+	35.5567i	0.200045	+	1.90330i	−0.188823	+	0.982011i	$0.560467\pi$
$350$	3.72428	+	1.65816i	0.199071	+	0.0886322i
$351$	0.0665763	−	14.8687i	0.00355358	−	0.793632i
$352$	0.396239	−	3.76996i	0.0211196	−	0.200940i
$353$	−4.03721	+	0.858135i	−0.214879	+	0.0456739i	−0.314093	−	0.949392i	$-0.601700\pi$
$353$	−4.03721	+	0.858135i	−0.214879	+	0.0456739i	0.0992143	+	0.995066i	$0.468367\pi$
$354$	−0.407041	−	1.25274i	−0.0216340	−	0.0665826i
$355$	0.0280051	−	0.0203469i	0.00148636	−	0.00107990i
$356$	−3.85410	−	11.8617i	−0.204267	−	0.628668i
$357$	13.6174	−	15.1236i	0.720708	−	0.800428i
$358$	−0.490306	+	0.356228i	−0.0259135	+	0.0188273i
$359$	12.1669	−	13.5127i	0.642146	−	0.713175i	−0.330931	−	0.943655i	$-0.607363\pi$
$359$	12.1669	−	13.5127i	0.642146	−	0.713175i	0.973077	+	0.230480i	$0.0740296\pi$
$360$	−0.00831464	+	0.0255898i	−0.000438220	+	0.00134870i
$361$	0.176138	+	0.127972i	0.00927041	+	0.00673535i
$362$	−0.181135	+	0.557476i	−0.00952024	+	0.0293003i
$363$	−5.30414	−	2.36155i	−0.278395	−	0.123949i
$364$	−32.7413	−	3.58955i	−1.71611	−	0.188143i
$365$	0.0857968	−	0.0381992i	0.00449081	−	0.00199944i
$366$	0.0618623	+	0.107149i	0.00323359	+	0.00560075i
$367$	−18.1082			−0.945238			−0.472619	−	0.881267i	$-0.656691\pi$
$367$	−18.1082			−0.945238			−0.472619	+	0.881267i	$0.656691\pi$
$368$	−2.03896	+	19.3994i	−0.106288	+	1.01126i
$369$	−24.5665	−	5.22177i	−1.27888	−	0.271834i
$370$	−0.0112061	+	0.00238193i	−0.000582577	+	0.000123831i
$371$	−7.06769	−	12.2416i	−0.366936	−	0.635552i
$372$	7.41479	+	3.81707i	0.384439	+	0.197906i
$373$	−7.30588	−	12.6542i	−0.378284	−	0.655207i	0.612529	−	0.790448i	$-0.290152\pi$
$373$	−7.30588	−	12.6542i	−0.378284	−	0.655207i	−0.990813	+	0.135241i	$0.956819\pi$
$374$	1.24449	+	1.38215i	0.0643512	+	0.0714692i
$375$	0.0810746	−	0.0900424i	0.00418667	−	0.00464977i
$376$	−0.400482	−	0.290967i	−0.0206533	−	0.0150055i
$377$	−7.07237	+	32.5554i	−0.364246	+	1.67669i
$378$	−1.68128	+	2.91206i	−0.0864757	+	0.149780i
$379$	1.83793	−	17.4868i	0.0944083	−	0.898235i	−0.840133	−	0.542381i	$-0.817523\pi$
$379$	1.83793	−	17.4868i	0.0944083	−	0.898235i	0.934541	−	0.355855i	$-0.115810\pi$
$380$	0.0142091	+	0.135191i	0.000728914	+	0.00693515i
$381$	0.494477	+	4.70464i	0.0253328	+	0.241026i
$382$	0.608466	−	0.129334i	0.0311318	−	0.00661728i
$383$	12.4075	−	5.52417i	0.633993	−	0.282272i	−0.0644682	−	0.997920i	$-0.520535\pi$
$383$	12.4075	−	5.52417i	0.633993	−	0.282272i	0.698461	+	0.715648i	$0.253868\pi$
$384$	−1.27146	+	3.91314i	−0.0648838	+	0.199692i
$385$	−0.0907357	+	0.100772i	−0.00462432	+	0.00513583i
$386$	−0.558974	+	0.406118i	−0.0284510	+	0.0206709i
$387$	−21.2344	−	4.51351i	−1.07941	−	0.229435i
$388$	27.8138	+	5.91200i	1.41203	+	0.300136i
$389$	−3.39460	−	32.2975i	−0.172113	−	1.63755i	−0.650577	−	0.759440i	$-0.725473\pi$
$389$	−3.39460	−	32.2975i	−0.172113	−	1.63755i	0.478464	−	0.878107i	$-0.341194\pi$
$390$	0.00315447	−	0.00700052i	0.000159733	−	0.000354485i
$391$	−19.7269	−	21.9089i	−0.997632	−	1.10798i
$392$	8.19627	+	5.95494i	0.413974	+	0.300770i
$393$	−0.231522	+	0.712553i	−0.0116788	+	0.0359435i
$394$	−0.256799	−	2.44328i	−0.0129374	−	0.123091i
$395$	−0.0530136	+	0.0385166i	−0.00266740	+	0.00193798i
$396$	7.07815	+	5.14257i	0.355690	+	0.258424i
$397$	15.1233			0.759015			0.379508	−	0.925189i	$-0.376093\pi$
$397$	15.1233			0.759015			0.379508	+	0.925189i	$0.376093\pi$
$398$	1.74153	+	3.01642i	0.0872950	+	0.151199i
$399$	−1.59865	+	15.2101i	−0.0800326	+	0.761460i
$400$	−12.7651	+	14.1770i	−0.638253	+	0.708852i
$401$	3.88892	+	4.31909i	0.194204	+	0.215685i	0.832380	−	0.554205i	$-0.186978\pi$
$401$	3.88892	+	4.31909i	0.194204	+	0.215685i	−0.638177	+	0.769890i	$0.720311\pi$
$402$	0.426337			0.0212638
$403$	16.7410	+	11.0788i	0.833928	+	0.551873i
$404$	0.669337			0.0333007
$405$	−0.0439907	−	0.0488567i	−0.00218592	−	0.00242771i
$406$	5.04128	−	5.59891i	0.250194	−	0.277869i
$407$	−0.784889	+	7.46772i	−0.0389055	+	0.370161i
$408$	−1.53007	−	2.65016i	−0.0757497	−	0.131202i
$409$	−4.62261			−0.228573			−0.114287	−	0.993448i	$-0.536458\pi$
$409$	−4.62261			−0.228573			−0.114287	+	0.993448i	$0.536458\pi$
$410$	−0.0234929	−	0.0170686i	−0.00116023	−	0.000842958i
$411$	−12.5925	+	9.14902i	−0.621145	+	0.451288i
$412$	1.20823	+	11.4955i	0.0595251	+	0.566344i
$413$	14.1247	−	43.4712i	0.695029	−	2.13908i
$414$	1.76013	+	1.27881i	0.0865059	+	0.0628502i
$415$	−0.00193239	−	0.00214614i	−9.48574e−5	−	0.000105350i
$416$	−3.05999	+	6.79086i	−0.150029	+	0.332949i
$417$	0.535997	+	5.09967i	0.0262479	+	0.249732i
$418$	−1.36717	−	0.290601i	−0.0668704	−	0.0142137i
$419$	26.5905	+	5.65199i	1.29903	+	0.276118i	0.804974	−	0.593311i	$-0.202179\pi$
$419$	26.5905	+	5.65199i	1.29903	+	0.276118i	0.494059	+	0.869428i	$0.335513\pi$
$420$	0.0895492	−	0.0650613i	0.00436955	−	0.00317467i
$421$	−9.68702	+	10.7585i	−0.472117	+	0.524339i	−0.931423	−	0.363940i	$-0.881431\pi$
$421$	−9.68702	+	10.7585i	−0.472117	+	0.524339i	0.459306	+	0.888278i	$0.348098\pi$
$422$	1.02620	−	3.15831i	0.0499546	−	0.153744i
$423$	1.56968	−	0.698867i	0.0763205	−	0.0339801i
$424$	−2.07907	+	0.441921i	−0.100969	+	0.0214616i
$425$	−3.01384	−	28.6748i	−0.146193	−	1.39093i
$426$	−0.0303693	−	0.288945i	−0.00147140	−	0.0139994i
$427$	−0.448776	+	4.26982i	−0.0217178	+	0.206631i
$428$	11.8905	−	20.5949i	0.574748	−	0.995492i
$429$	−3.72486	−	3.38420i	−0.179838	−	0.163391i
$430$	−0.0203065	−	0.0147535i	−0.000979264	−	0.000711477i
$431$	23.2209	−	25.7894i	1.11851	−	1.24223i	0.151236	−	0.988498i	$-0.451675\pi$
$431$	23.2209	−	25.7894i	1.11851	−	1.24223i	0.967274	−	0.253734i	$-0.0816586\pi$
$432$	−10.5288	−	11.6935i	−0.506569	−	0.562602i
$433$	−5.82884	−	10.0958i	−0.280116	−	0.485175i	0.691297	−	0.722571i	$-0.257040\pi$
$433$	−5.82884	−	10.0958i	−0.280116	−	0.485175i	−0.971413	+	0.237395i	$0.923706\pi$
$434$	−2.04417	−	4.05363i	−0.0981234	−	0.194581i
$435$	−0.0559784	−	0.0969574i	−0.00268396	−	0.00464875i
$436$	−14.8182	+	3.14971i	−0.709665	+	0.150844i
$437$	21.6715	+	4.60641i	1.03669	+	0.220355i
$438$	0.0823941	−	0.783927i	0.00393694	−	0.0374575i
$439$	−24.7053			−1.17912			−0.589560	−	0.807725i	$-0.700699\pi$
$439$	−24.7053			−1.17912			−0.589560	+	0.807725i	$0.700699\pi$
$440$	0.0101952	+	0.0176586i	0.000486037	+	0.000841841i
$441$	−32.1251	+	14.3030i	−1.52977	+	0.681096i
$442$	−1.47144	−	3.34515i	−0.0699895	−	0.159112i
$443$	10.0137	+	4.45839i	0.475766	+	0.211825i	0.630588	−	0.776118i	$-0.282814\pi$
$443$	10.0137	+	4.45839i	0.475766	+	0.211825i	−0.154822	+	0.987942i	$0.549480\pi$
$444$	1.89406	−	5.82930i	0.0898879	−	0.276647i
$445$	0.0816239	+	0.0593033i	0.00386935	+	0.00281124i
$446$	−0.525505	+	1.61734i	−0.0248834	+	0.0765832i
$447$	5.02989	−	5.58626i	0.237906	−	0.264221i
$448$	−27.2791	+	19.8194i	−1.28882	+	0.936380i
$449$	−12.3689	+	13.7371i	−0.583726	+	0.648294i	−0.960588	−	0.277976i	$-0.910337\pi$
$449$	−12.3689	+	13.7371i	−0.583726	+	0.648294i	0.376862	+	0.926270i	$0.377003\pi$
$450$	0.657520	+	2.02364i	0.0309958	+	0.0953952i
$451$	−15.3979	+	11.1872i	−0.725058	+	0.526785i
$452$	8.60549	+	26.4850i	0.404768	+	1.24575i
$453$	9.31395	−	1.97974i	0.437608	−	0.0930164i
$454$	−0.221109	+	2.10371i	−0.0103771	+	0.0987319i
$455$	0.231344	−	0.132189i	0.0108456	−	0.00619711i
$456$	2.10091	+	0.935386i	0.0983841	+	0.0438034i
$457$	1.41579	+	13.4704i	0.0662281	+	0.630118i	0.976412	+	0.215914i	$0.0692732\pi$
$457$	1.41579	+	13.4704i	0.0662281	+	0.630118i	−0.910184	+	0.414204i	$0.864060\pi$
$458$	−0.0295034	+	0.280706i	−0.00137860	+	0.0131165i
$459$	23.7817			1.11004
$460$	−0.0801750	−	0.138867i	−0.00373818	−	0.00647471i
$461$	−2.45839	+	23.3900i	−0.114499	+	1.08938i	0.774848	+	0.632148i	$0.217826\pi$
$461$	−2.45839	+	23.3900i	−0.114499	+	1.08938i	−0.889346	+	0.457234i	$0.848840\pi$
$462$	0.351698	+	1.08242i	0.0163625	+	0.0503586i
$463$	−2.92880	+	9.01393i	−0.136113	+	0.418913i	−0.995761	−	0.0919732i	$-0.970683\pi$
$463$	−2.92880	+	9.01393i	−0.136113	+	0.418913i	0.859648	+	0.510886i	$0.170683\pi$
$464$	17.6278	+	30.5323i	0.818352	+	1.41743i
$465$	−0.0666759	+	0.0102754i	−0.00309202	+	0.000476512i
$466$	−1.61239	+	2.79275i	−0.0746927	+	0.129371i
$467$	−1.35334	+	4.16515i	−0.0626251	+	0.192740i	−0.977474	−	0.211056i	$-0.932310\pi$
$467$	−1.35334	+	4.16515i	−0.0626251	+	0.192740i	0.914849	+	0.403797i	$0.132310\pi$
$468$	−10.0423	−	13.9530i	−0.464207	−	0.644980i
$469$	11.9688	+	8.69583i	0.552667	+	0.401536i
$470$	0.00198665			9.16374e−5
$471$	−3.58862	−	6.21568i	−0.165355	−	0.286403i
$472$	−5.56047	−	4.03992i	−0.255941	−	0.185952i
$473$	−13.3094	+	9.66984i	−0.611967	+	0.444620i
$474$	0.0574890	+	0.546972i	0.00264056	+	0.0251232i
$475$	14.4988	+	16.1026i	0.665252	+	0.738837i
$476$	5.50671	−	52.3928i	0.252399	−	2.40142i
$477$	2.27984	−	7.01662i	0.104387	−	0.321269i
$478$	−0.657230	−	2.02275i	−0.0300610	−	0.0925183i
$479$	−9.30044	−	4.14082i	−0.424948	−	0.189199i	0.183109	−	0.983093i	$-0.441384\pi$
$479$	−9.30044	−	4.14082i	−0.424948	−	0.189199i	−0.608057	+	0.793894i	$0.708051\pi$
$480$	−0.00773502	−	0.0238059i	−0.000353054	−	0.00108659i
$481$	6.06138	−	13.4517i	0.276375	−	0.613343i
$482$	0.244810	+	2.32921i	0.0111508	+	0.106093i
$483$	−5.57490	−	17.1578i	−0.253667	−	0.780705i
$484$	−14.7016	+	3.12491i	−0.668253	+	0.142041i
$485$	−0.210138	+	0.0935596i	−0.00954189	+	0.00424832i
$486$	−2.66662	+	0.566808i	−0.120960	+	0.0257109i
$487$	−3.08306	−	29.3333i	−0.139707	−	1.32922i	−0.809696	−	0.586850i	$-0.800368\pi$
$487$	−3.08306	−	29.3333i	−0.139707	−	1.32922i	0.669989	−	0.742371i	$-0.266299\pi$
$488$	0.589772	+	0.262583i	0.0266977	+	0.0118866i
$489$	−12.6418	+	5.62851i	−0.571684	+	0.254530i
$490$	−0.0406588			−0.00183678
$491$	−1.29070			−0.0582486			−0.0291243	−	0.999576i	$-0.509272\pi$
$491$	−1.29070			−0.0582486			−0.0291243	+	0.999576i	$0.509272\pi$
$492$	14.1929	−	6.31907i	0.639864	−	0.284886i
$493$	−52.1204	−	11.0785i	−2.34739	−	0.498952i
$494$	2.37226	+	1.38383i	0.106733	+	0.0622613i
$495$	−0.0707753			−0.00318111
$496$	20.9965	−	3.23578i	0.942773	−	0.145291i
$497$	5.04092	−	8.73112i	0.226116	−	0.391644i
$498$	−0.0237088	+	0.00503946i	−0.00106242	+	0.000225824i
$499$	−0.0618787	−	0.0131527i	−0.00277007	−	0.000588797i	0.206526	−	0.978441i	$-0.433784\pi$
$499$	−0.0618787	−	0.0131527i	−0.00277007	−	0.000588797i	−0.209297	+	0.977852i	$0.567117\pi$
$500$	0.0327856	−	0.311934i	0.00146622	−	0.0139501i
$501$	9.59861	−	16.6253i	0.428834	−	0.742763i
$502$	1.58634	−	2.74763i	0.0708020	−	0.122633i
$503$	30.0782	+	21.8531i	1.34112	+	0.974381i	0.999402	+	0.0345787i	$0.0110089\pi$
$503$	30.0782	+	21.8531i	1.34112	+	0.974381i	0.341719	+	0.939802i	$0.388991\pi$
$504$	0.819135	+	7.79355i	0.0364872	+	0.347152i
$505$	−0.00438048	+	0.00318261i	−0.000194929	+	0.000141624i
$506$	1.61271	−	0.342793i	0.0716939	−	0.0152390i
$507$	4.86746	+	8.60779i	0.216171	+	0.382285i
$508$	8.19402	+	9.10039i	0.363551	+	0.403764i
$509$	6.07855	+	18.7079i	0.269427	+	0.829211i	0.990640	+	0.136498i	$0.0435848\pi$
$509$	6.07855	+	18.7079i	0.269427	+	0.829211i	−0.721213	+	0.692713i	$0.756415\pi$
$510$	0.0112194	+	0.00499518i	0.000496801	+	0.000221190i
$511$	18.3026	−	20.3270i	0.809657	−	0.899216i
$512$	4.08086	+	12.5596i	0.180350	+	0.555061i
$513$	−14.4590	+	10.5051i	−0.638379	+	0.463809i
$514$	−0.500255	−	0.106332i	−0.0220653	−	0.00469012i
$515$	−0.0625669	−	0.0694876i	−0.00275703	−	0.00306199i
$516$	12.2678	−	5.46199i	0.540061	−	0.240451i
$517$	0.402372	−	1.23838i	0.0176963	−	0.0544637i
$518$	−2.69940	+	1.96123i	−0.118605	+	0.0861714i
$519$	−14.2627	+	10.3625i	−0.626063	+	0.454861i
$520$	−0.00815450	−	0.0392267i	−0.000357598	−	0.00172021i
$521$	−7.27801	+	12.6059i	−0.318855	+	0.552273i	−0.980249	−	0.197765i	$-0.936632\pi$
$521$	−7.27801	+	12.6059i	−0.318855	+	0.552273i	0.661394	+	0.750038i	$0.269965\pi$
$522$	3.93227			0.172111
$523$	4.43407	−	1.97418i	0.193889	−	0.0863247i	−0.307496	−	0.951549i	$-0.599491\pi$
$523$	4.43407	−	1.97418i	0.193889	−	0.0863247i	0.501384	+	0.865225i	$0.332824\pi$
$524$	0.599332	+	1.84455i	0.0261819	+	0.0805797i
$525$	5.45224	−	16.7803i	0.237955	−	0.732351i
$526$	1.90840	+	3.30545i	0.0832103	+	0.144124i
$527$	−17.5997	+	26.8552i	−0.766655	+	1.16983i
$528$	−5.32583			−0.231777
$529$	−3.06631	+	0.651764i	−0.133318	+	0.0283375i
$530$	0.00570786	−	0.00633922i	0.000247933	−	0.000275358i
$531$	21.7941	−	9.70338i	0.945785	−	0.421091i
$532$	19.7954	+	34.2866i	0.858238	+	1.48651i
$533$	35.6189	−	11.3972i	1.54282	−	0.493667i
$534$	0.773590	−	0.344424i	0.0334765	−	0.0149047i
$535$	0.0201087	+	0.191321i	0.000869373	+	0.00827153i
$536$	1.79973	−	1.30758i	0.0777367	−	0.0564790i
$537$	1.75510	+	1.94923i	0.0757380	+	0.0841156i
$538$	0.319254	−	3.03750i	0.0137640	−	0.130956i
$539$	−8.23496	+	25.3446i	−0.354705	+	1.09167i
$540$	0.126523	+	0.0268933i	0.00544468	+	0.00115730i
$541$	−0.550834	−	5.24083i	−0.0236822	−	0.225321i	−0.999961	−	0.00880486i	$-0.997197\pi$
$541$	−0.550834	−	5.24083i	−0.0236822	−	0.225321i	0.976279	−	0.216516i	$-0.0694694\pi$
$542$	0.972604	−	1.08019i	0.0417769	−	0.0463979i
$543$	2.48144	+	0.527447i	0.106489	+	0.0226349i
$544$	−10.8833	−	4.84558i	−0.466620	−	0.207752i
$545$	0.0820016	−	0.0910721i	0.00351256	−	0.00390110i
$546$	0.0100132	−	2.23628i	0.000428527	−	0.0957041i
$547$	2.07817	−	19.7725i	0.0888562	−	0.845410i	−0.855791	−	0.517322i	$-0.826929\pi$
$547$	2.07817	−	19.7725i	0.0888562	−	0.845410i	0.944647	−	0.328088i	$-0.106404\pi$
$548$	−12.4512	+	38.3210i	−0.531891	+	1.63699i
$549$	−1.81287	+	1.31713i	−0.0773715	+	0.0562137i
$550$	1.47306	+	0.655850i	0.0628116	+	0.0279655i
$551$	36.5822	−	16.2874i	1.55845	−	0.693868i
$552$	−2.71277			−0.115463
$553$	−9.54245	+	16.5280i	−0.405786	+	0.702842i
$554$	2.28813	+	1.66242i	0.0972132	+	0.0706295i
$555$	0.0153219	+	0.0471559i	0.000650378	+	0.00200166i
$556$	8.88205	+	9.86451i	0.376683	+	0.418348i
$557$	7.60737	−	13.1763i	0.322335	−	0.558300i	−0.658635	−	0.752463i	$-0.728866\pi$
$557$	7.60737	−	13.1763i	0.322335	−	0.558300i	0.980969	+	0.194163i	$0.0621991\pi$
$558$	0.858380	−	2.20857i	0.0363381	−	0.0934962i
$559$	30.7877	−	9.85134i	1.30218	−	0.416667i
$560$	0.0871335	−	0.268169i	0.00368206	−	0.0113322i
$561$	5.38608	−	5.98185i	0.227400	−	0.252554i
$562$	5.06147	−	2.25351i	0.213505	−	0.0950586i
$563$	−3.09733	+	5.36474i	−0.130537	+	0.226097i	−0.923884	−	0.382673i	$-0.875003\pi$
$563$	−3.09733	+	5.36474i	−0.130537	+	0.226097i	0.793347	+	0.608770i	$0.208337\pi$
$564$	−0.531438	+	0.920477i	−0.0223776	+	0.0387591i
$565$	−0.182251	−	0.132413i	−0.00766737	−	0.00557067i
$566$	4.25889	+	1.89618i	0.179014	+	0.0797023i
$567$	−17.4920	−	7.78796i	−0.734597	−	0.327064i
$568$	−1.01440	−	1.12660i	−0.0425632	−	0.0472713i
$569$	−25.8905	−	18.8106i	−1.08539	−	0.788579i	−0.106772	−	0.994284i	$-0.534052\pi$
$569$	−25.8905	−	18.8106i	−1.08539	−	0.788579i	−0.978614	+	0.205704i	$0.934052\pi$
$570$	−0.00902772	+	0.00191890i	−0.000378130	+	8.03739e-5i
$571$	19.3767	−	21.5200i	0.810890	−	0.900584i	−0.185742	−	0.982599i	$-0.559469\pi$
$571$	19.3767	−	21.5200i	0.810890	−	0.900584i	0.996631	+	0.0820146i	$0.0261354\pi$
$572$	−12.9502	−	1.41977i	−0.541474	−	0.0593636i
$573$	−0.831946	−	2.56047i	−0.0347550	−	0.106965i
$574$	−8.27263	−	1.75840i	−0.345293	−	0.0733943i
$575$	−23.3500	−	10.3961i	−0.973764	−	0.433548i
$576$	−17.2144	−	3.65903i	−0.717265	−	0.152459i
$577$	−2.44604	−	2.71660i	−0.101830	−	0.113093i	0.690075	−	0.723737i	$-0.257577\pi$
$577$	−2.44604	−	2.71660i	−0.101830	−	0.113093i	−0.791905	+	0.610644i	$0.790911\pi$
$578$	2.61018	−	1.16213i	0.108569	−	0.0483382i
$579$	2.00090	+	2.22222i	0.0831546	+	0.0923525i
$580$	−0.264761	−	0.117879i	−0.0109936	−	0.00489468i
$581$	−0.768378	−	0.342104i	−0.0318777	−	0.0141929i
$582$	−0.201804	+	1.92004i	−0.00836506	+	0.0795882i
$583$	−2.79548	−	4.84191i	−0.115777	−	0.200532i
$584$	−2.05650	−	3.56197i	−0.0850987	−	0.147395i
$585$	0.132067	+	0.0435659i	0.00546030	+	0.00180123i
$586$	−0.407571	−	0.0866319i	−0.0168366	−	0.00357873i
$587$	11.8735	+	13.1869i	0.490073	+	0.544281i	0.936559	−	0.350510i	$-0.113992\pi$
$587$	11.8735	+	13.1869i	0.490073	+	0.544281i	−0.446487	+	0.894790i	$0.647325\pi$
$588$	10.8764	−	18.8385i	0.448536	−	0.776887i
$589$	−1.16231	−	24.1019i	−0.0478922	−	0.993100i
$590$	0.0275836			0.00113560
$591$	−10.4003	+	2.21064i	−0.427809	+	0.0909337i
$592$	−4.82494	−	14.8496i	−0.198304	−	0.610316i
$593$	−1.03326	−	0.750709i	−0.0424310	−	0.0308279i	0.566368	−	0.824153i	$-0.308348\pi$
$593$	−1.03326	−	0.750709i	−0.0424310	−	0.0308279i	−0.608799	+	0.793325i	$0.708348\pi$
$594$	−0.664996	+	1.15181i	−0.0272851	+	0.0472592i
$595$	0.213082	+	0.369069i	0.00873551	+	0.0151304i
$596$	2.03403	−	19.3525i	0.0833170	−	0.792708i
$597$	12.1955	−	8.86054i	0.499128	−	0.362638i
$598$	−3.22034	−	0.353057i	−0.131690	−	0.0144376i
$599$	3.57189	−	0.759228i	0.145943	−	0.0310212i	−0.134361	−	0.990932i	$-0.542898\pi$
$599$	3.57189	−	0.759228i	0.145943	−	0.0310212i	0.280304	+	0.959911i	$0.409565\pi$
$600$	−2.14639	−	1.55944i	−0.0876260	−	0.0636640i
$601$	8.52538	−	1.81213i	0.347758	−	0.0739181i	−0.0307216	−	0.999528i	$-0.509781\pi$
$601$	8.52538	−	1.81213i	0.347758	−	0.0739181i	0.378479	+	0.925610i	$0.376447\pi$
$602$	−7.15057	−	1.51990i	−0.291436	−	0.0619466i
$603$	0.807125	+	7.67928i	0.0328687	+	0.312725i
$604$	16.4936	−	18.3180i	0.671115	−	0.745348i
$605$	0.0813560	−	0.0903550i	0.00330759	−	0.00367345i
$606$	0.00475028	+	0.0451959i	0.000192967	+	0.00183596i
$607$	−14.2307	−	3.02482i	−0.577605	−	0.122774i	−0.0901600	−	0.995927i	$-0.528738\pi$
$607$	−14.2307	−	3.02482i	−0.577605	−	0.122774i	−0.487445	+	0.873154i	$0.662071\pi$
$608$	8.75735	−	1.86143i	0.355157	−	0.0754911i
$609$	−26.3796	−	19.1659i	−1.06895	−	0.776641i
$610$	−0.00253428		0.000538678i	−0.000102610		2.18104e-5i
$611$	−1.51311	+	2.06313i	−0.0612140	+	0.0834654i
$612$	22.2448	−	16.1618i	0.899194	−	0.653303i
$613$	4.38624	−	41.7323i	0.177159	−	1.68555i	−0.439438	−	0.898273i	$-0.644823\pi$
$613$	4.38624	−	41.7323i	0.177159	−	1.68555i	0.616597	−	0.787279i	$-0.288511\pi$
$614$	−0.896636	−	1.55302i	−0.0361853	−	0.0626748i
$615$	−0.0628391	+	0.108840i	−0.00253392	+	0.00438887i
$616$	4.80445	+	3.49064i	0.193577	+	0.140642i
$617$	9.03039	+	27.7927i	0.363550	+	1.11889i	0.950884	+	0.309547i	$0.100177\pi$
$617$	9.03039	+	27.7927i	0.363550	+	1.11889i	−0.587334	+	0.809345i	$0.699823\pi$
$618$	−0.767643	+	0.163167i	−0.0308791	+	0.00656356i
$619$	19.2981			0.775657			0.387829	−	0.921731i	$-0.373225\pi$
$619$	19.2981			0.775657			0.387829	+	0.921731i	$0.373225\pi$
$620$	−0.124002	+	0.122972i	−0.00498005	+	0.00493867i
$621$	10.5411	−	18.2577i	0.422999	−	0.732656i
$622$	2.65326	+	2.94675i	0.106386	+	0.118154i
$623$	28.7425	+	6.10940i	1.15154	+	0.244768i
$624$	9.93803	+	3.27833i	0.397840	+	0.131238i
$625$	−12.4981	−	21.6473i	−0.499924	−	0.865894i
$626$	1.20568	+	2.08829i	0.0481886	+	0.0834650i
$627$	−0.632314	+	6.01606i	−0.0252522	+	0.240258i
$628$	−16.9732	−	7.55694i	−0.677303	−	0.301555i
$629$	21.5582	+	9.59835i	0.859584	+	0.382711i
$630$	−0.0210440	−	0.0233717i	−0.000838413	−	0.000931152i
$631$	9.12669	−	4.06346i	0.363328	−	0.161764i	−0.216950	−	0.976183i	$-0.569611\pi$
$631$	9.12669	−	4.06346i	0.363328	−	0.161764i	0.580277	+	0.814419i	$0.302944\pi$
$632$	1.92026	+	2.13266i	0.0763837	+	0.0848327i
$633$	−14.0583	−	2.98819i	−0.558768	−	0.118770i
$634$	−2.86962	−	1.27764i	−0.113967	−	0.0507415i
$635$	−0.0968970	−	0.0205961i	−0.00384524	−	0.000817331i
$636$	1.41028	+	4.34039i	0.0559212	+	0.172108i
$637$	30.9674	−	42.2241i	1.22697	−	1.67298i
$638$	1.99397	−	2.21453i	0.0789422	−	0.0876742i
$639$	5.14705	−	1.09404i	0.203614	−	0.0432795i
$640$	−0.0697062	−	0.0506445i	−0.00275538	−	0.00200190i
$641$	33.2513	+	36.9293i	1.31335	+	1.45862i	0.799403	+	0.600795i	$0.205149\pi$
$641$	33.2513	+	36.9293i	1.31335	+	1.45862i	0.513943	+	0.857824i	$0.328184\pi$
$642$	1.47503	+	0.656724i	0.0582146	+	0.0259188i
$643$	36.4229	+	16.2165i	1.43638	+	0.639516i	0.969564	−	0.244840i	$-0.0787353\pi$
$643$	36.4229	+	16.2165i	1.43638	+	0.639516i	0.466813	+	0.884356i	$0.345402\pi$
$644$	−37.7821	−	27.4503i	−1.48882	−	1.08169i
$645$	−0.0543159	+	0.0940779i	−0.00213869	+	0.00370431i
$646$	−2.19633	+	3.80415i	−0.0864133	+	0.149672i
$647$	21.6651	−	9.64591i	0.851742	−	0.379220i	0.0660336	−	0.997817i	$-0.478966\pi$
$647$	21.6651	−	9.64591i	0.851742	−	0.379220i	0.785708	+	0.618598i	$0.212299\pi$
$648$	−1.92655	+	2.13965i	−0.0756819	+	0.0840533i
$649$	5.58672	−	17.1942i	0.219298	−	0.674930i
$650$	−2.34503	−	2.13057i	−0.0919798	−	0.0835678i
$651$	−16.5230	+	10.6324i	−0.647587	+	0.416717i
$652$	−17.9112	+	31.0231i	−0.701457	+	1.21496i
$653$	25.2280	+	28.0185i	0.987246	+	1.09645i	0.995335	+	0.0964808i	$0.0307586\pi$
$653$	25.2280	+	28.0185i	0.987246	+	1.09645i	−0.00808854	+	0.999967i	$0.502575\pi$
$654$	−0.317845	−	0.978225i	−0.0124287	−	0.0382516i
$655$	−0.0126929	−	0.00922196i	−0.000495954	−	0.000360332i
$656$	19.7883	−	34.2744i	0.772604	−	1.33819i
$657$	14.2763			0.556971
$658$	0.528581	−	0.235340i	0.0206062	−	0.00917449i
$659$	−26.1155	−	11.6274i	−1.01732	−	0.452938i	−0.170802	−	0.985305i	$-0.554636\pi$
$659$	−26.1155	−	11.6274i	−1.01732	−	0.452938i	−0.846513	+	0.532367i	$0.821302\pi$
$660$	0.0354194	−	0.0257337i	0.00137870	−	0.00100168i
$661$	−3.94335	+	12.1364i	−0.153378	+	0.472050i	−0.997993	−	0.0633247i	$-0.979830\pi$
$661$	−3.94335	+	12.1364i	−0.153378	+	0.472050i	0.844615	+	0.535375i	$0.179830\pi$
$662$	0.352099	−	3.35000i	0.0136847	−	0.130201i
$663$	−13.7326	+	7.84674i	−0.533330	+	0.304742i
$664$	−0.0846280	+	0.0939889i	−0.00328420	+	0.00364748i
$665$	−0.292579	−	0.130265i	−0.0113457	−	0.00505144i
$666$	−1.70345	−	0.362078i	−0.0660072	−	0.0140303i
$667$	−31.6072	+	35.1033i	−1.22384	+	1.35921i
$668$	−5.19455	−	49.4228i	−0.200983	−	1.91223i
$669$	7.19912	+	1.53022i	0.278334	+	0.0591617i
$670$	−0.00275886	+	0.00849089i	−0.000106584	+	0.000328032i
$671$	−0.177504	+	1.68884i	−0.00685248	+	0.0651970i
$672$	−4.87809	−	5.41767i	−0.188176	−	0.208991i
$673$	23.1516	−	16.8206i	0.892428	−	0.648387i	−0.0440821	−	0.999028i	$-0.514036\pi$
$673$	23.1516	−	16.8206i	0.892428	−	0.648387i	0.936510	+	0.350641i	$0.114036\pi$
$674$	0.228663	+	2.17559i	0.00880778	+	0.0838005i
$675$	18.8358	−	8.38623i	0.724989	−	0.322786i
$676$	23.2911	+	10.6208i	0.895813	+	0.408493i
$677$	6.96178	+	12.0582i	0.267563	+	0.463433i	0.968232	−	0.250054i	$-0.0804483\pi$
$677$	6.96178	+	12.0582i	0.267563	+	0.463433i	−0.700669	+	0.713487i	$0.747115\pi$
$678$	−1.72728	+	0.769036i	−0.0663359	+	0.0295347i
$679$	−44.8277	+	49.7862i	−1.72033	+	1.91062i
$680$	0.0626816	−	0.0133234i	0.00240373	−	0.000510928i
$681$	9.15486			0.350815
$682$	−0.808530	−	1.60333i	−0.0309602	−	0.0613948i
$683$	−1.34231	−	2.32495i	−0.0513620	−	0.0889617i	0.839201	−	0.543821i	$-0.183023\pi$
$683$	−1.34231	−	2.32495i	−0.0513620	−	0.0889617i	−0.890563	+	0.454859i	$0.849690\pi$
$684$	−6.38543	+	19.6523i	−0.244153	+	0.751425i
$685$	−0.100724	−	0.309996i	−0.00384846	−	0.0118443i
$686$	−5.60369	+	2.49493i	−0.213950	+	0.0952567i
$687$	1.22157			0.0466057
$688$	17.1043	−	29.6256i	0.652097	−	1.12946i
$689$	2.23593	+	10.7558i	0.0851820	+	0.409763i
$690$	0.00880779	−	0.00639923i	0.000335307	−	0.000243615i
$691$	−7.34941	+	5.33966i	−0.279585	+	0.203130i	−0.718736	−	0.695283i	$-0.755279\pi$
$691$	−7.34941	+	5.33966i	−0.279585	+	0.203130i	0.439152	+	0.898413i	$0.355279\pi$
$692$	−14.1027	+	43.4035i	−0.536102	+	1.64995i
$693$	−18.8309	+	8.38407i	−0.715328	+	0.318484i
$694$	−1.86361	−	2.06975i	−0.0707417	−	0.0785666i
$695$	−0.105033	−	0.0223255i	−0.00398413	−	0.000846854i
$696$	−3.96667	+	2.88196i	−0.150356	+	0.109240i
$697$	18.4840	+	56.8878i	0.700130	+	2.15478i
$698$	−4.20467	+	4.66976i	−0.159149	+	0.176753i
$699$	12.7500	+	5.67668i	0.482251	+	0.214712i
$700$	−14.1140	−	43.4384i	−0.533458	−	1.64182i
$701$	−31.0517	−	34.4864i	−1.17281	−	1.30253i	−0.944335	−	0.328984i	$-0.893294\pi$
$701$	−31.0517	−	34.4864i	−1.17281	−	1.30253i	−0.228472	−	0.973550i	$-0.573373\pi$
$702$	1.94988	−	1.73994i	0.0735936	−	0.0656697i
$703$	−17.3470	+	3.68721i	−0.654254	+	0.139066i
$704$	−10.7897	+	7.83917i	−0.406652	+	0.295450i
$705$	−0.000898745	−	0.00855099i	−3.38487e−5	−	0.000322049i
$706$	−0.586880	−	0.426393i	−0.0220875	−	0.0160475i
$707$	−0.788487	+	1.36570i	−0.0296541	+	0.0513624i
$708$	−7.37872	+	12.7803i	−0.277309	+	0.480314i
$709$	−2.74878	+	26.1529i	−0.103233	+	0.982193i	0.813195	+	0.581992i	$0.197726\pi$
$709$	−2.74878	+	26.1529i	−0.103233	+	0.982193i	−0.916427	+	0.400201i	$0.868940\pi$
$710$	0.00595112	+	0.00126495i	0.000223342	+	4.74727e-5i
$711$	−9.74335	+	2.07101i	−0.365404	+	0.0776691i
$712$	2.20927	−	3.82656i	0.0827958	−	0.143407i
$713$	12.8163	+	25.4150i	0.479974	+	0.951799i
$714$	3.57682			0.133859
$715$	0.0915034	−	0.0522846i	0.00342203	−	0.00195533i
$716$	6.64154	+	1.41170i	0.248206	+	0.0527579i
$717$	−8.40903	+	3.74394i	−0.314041	+	0.139820i
$718$	3.19584			0.119268
$719$	30.7400			1.14641			0.573204	−	0.819413i	$-0.305700\pi$
$719$	30.7400			1.14641			0.573204	+	0.819413i	$0.305700\pi$
$720$	0.134446	−	0.0598591i	0.00501050	−	0.00223082i
$721$	−24.8785	−	11.0766i	−0.926524	−	0.412515i
$722$	0.00399986	+	0.0380561i	0.000148859	+	0.00141630i
$723$	9.91471	−	2.10744i	0.368732	−	0.0783764i
$724$	5.99936	−	2.67109i	0.222964	−	0.0992702i
$725$	−45.1874	+	9.60489i	−1.67822	+	0.356717i
$726$	−0.315342	−	0.970523i	−0.0117034	−	0.0360195i
$727$	3.55891	+	33.8608i	0.131993	+	1.25583i	0.837228	+	0.546853i	$0.184174\pi$
$727$	3.55891	+	33.8608i	0.131993	+	1.25583i	−0.705236	+	0.708973i	$0.749159\pi$
$728$	−6.81645	−	9.47094i	−0.252635	−	0.351016i
$729$	−0.180144	−	0.554426i	−0.00667200	−	0.0205343i
$730$	0.0150795	+	0.00671381i	0.000558116	+	0.000248489i
$731$	15.9769	+	49.1719i	0.590927	+	1.81869i
$732$	0.428344	−	1.31831i	0.0158321	−	0.0487261i
$733$	−1.29484	+	12.3195i	−0.0478259	+	0.455033i	0.944235	+	0.329273i	$0.106804\pi$
$733$	−1.29484	+	12.3195i	−0.0478259	+	0.455033i	−0.992061	+	0.125760i	$0.959863\pi$
$734$	−2.12961	−	2.36517i	−0.0786054	−	0.0873001i
$735$	0.0183937	+	0.175005i	0.000678463	+	0.00645514i
$736$	−8.54400	+	6.20758i	−0.314936	+	0.228815i
$737$	4.73401	+	3.43946i	0.174379	+	0.126694i
$738$	−2.20711	−	3.82282i	−0.0812447	−	0.140720i
$739$	32.1548			1.18283			0.591417	−	0.806366i	$-0.298569\pi$
$739$	32.1548			1.18283			0.591417	+	0.806366i	$0.298569\pi$
$740$	0.103839	+	0.0754437i	0.00381721	+	0.00277337i
$741$	4.88310	−	10.8368i	0.179385	−	0.398099i
$742$	0.767723	−	2.36281i	0.0281840	−	0.0867414i
$743$	11.7382	−	20.3312i	0.430633	−	0.745878i	−0.566295	−	0.824203i	$-0.691624\pi$
$743$	11.7382	−	20.3312i	0.430633	−	0.745878i	0.996928	+	0.0783247i	$0.0249571\pi$
$744$	0.752767	+	2.85699i	0.0275978	+	0.104742i
$745$	0.0787067	+	0.136324i	0.00288359	+	0.00499453i
$746$	0.793596	−	2.44244i	0.0290556	−	0.0894240i
$747$	−0.135657	−	0.417508i	−0.00496342	−	0.0152758i
$748$	2.17807	−	20.7229i	0.0796379	−	0.757704i
$749$	28.0142	+	48.5221i	1.02362	+	1.77296i
$750$	0.0212955			0.000777603
$751$	−2.55425	+	24.3020i	−0.0932058	+	0.886794i	0.843607	+	0.536962i	$0.180428\pi$
$751$	−2.55425	+	24.3020i	−0.0932058	+	0.886794i	−0.936812	+	0.349832i	$0.886239\pi$
$752$	0.283019	+	2.69275i	0.0103206	+	0.0981944i
$753$	−12.5441	−	5.58497i	−0.457131	−	0.203528i
$754$	−5.08393	+	2.90493i	−0.185146	+	0.105791i
$755$	−0.0208429	+	0.198307i	−0.000758551	+	0.00721713i
$756$	36.8493	−	7.83256i	1.34020	−	0.284867i
$757$	−13.1567	−	40.4922i	−0.478189	−	1.47171i	−0.841609	−	0.540088i	$-0.818391\pi$
$757$	−13.1567	−	40.4922i	−0.478189	−	1.47171i	0.363420	−	0.931625i	$-0.381609\pi$
$758$	2.50016	−	1.81647i	0.0908099	−	0.0659773i
$759$	−2.20504	−	6.78640i	−0.0800378	−	0.246331i
$760$	−0.0322242	+	0.0357886i	−0.00116890	+	0.00129819i
$761$	35.0820	−	25.4885i	1.27172	−	0.923959i	0.272451	−	0.962170i	$-0.412166\pi$
$761$	35.0820	−	25.4885i	1.27172	−	0.923959i	0.999270	+	0.0382108i	$0.0121658\pi$
$762$	−0.556337	+	0.617874i	−0.0201539	+	0.0223832i
$763$	11.0295	−	33.9452i	0.399293	−	1.22890i
$764$	−5.63826	−	4.09643i	−0.203985	−	0.148204i
$765$	−0.0687343	+	0.211542i	−0.00248509	+	0.00764833i
$766$	2.18071	+	0.970917i	0.0787924	+	0.0350806i
$767$	−21.0088	+	28.6455i	−0.758582	+	1.03433i
$768$	9.44068	−	4.20326i	0.340661	−	0.151672i
$769$	15.7274	+	27.2407i	0.567146	+	0.982325i	0.996847	+	0.0793539i	$0.0252857\pi$
$769$	15.7274	+	27.2407i	0.567146	+	0.982325i	−0.429701	+	0.902971i	$0.641381\pi$
$770$	−0.0238332			−0.000858889
$771$	−0.231367	+	2.20131i	−0.00833249	+	0.0792783i
$772$	7.57170	+	1.60941i	0.272511	+	0.0579241i
$773$	0.305474	−	0.0649304i	0.0109871	−	0.00233538i	−0.202415	−	0.979300i	$-0.564879\pi$
$773$	0.305474	−	0.0649304i	0.0109871	−	0.00233538i	0.213402	+	0.976964i	$0.431546\pi$
$774$	−1.90775	−	3.30431i	−0.0685725	−	0.118771i
$775$	−4.46941	+	27.4763i	−0.160546	+	0.986977i
$776$	5.03690	+	8.72417i	0.180814	+	0.313180i
$777$	9.66275	+	10.7316i	0.346649	+	0.384993i
$778$	3.81927	−	4.24173i	0.136927	−	0.152073i
$779$	−36.3669	−	26.4221i	−1.30298	−	0.946671i
$780$	−0.0819331	+	0.0262167i	−0.00293368	+	0.000938708i
$781$	1.99383	−	3.45342i	0.0713449	−	0.123573i
$782$	0.541623	−	5.15320i	0.0193684	−	0.184278i
$783$	−3.98295	−	37.8953i	−0.142339	−	1.35427i
$784$	−5.79227	−	55.1098i	−0.206867	−	1.96821i
$785$	0.147013	−	0.0312486i	0.00524713	−	0.00111531i
$786$	−0.120297	+	0.0535598i	−0.00429086	+	0.00191041i
$787$	−2.22638	+	6.85211i	−0.0793620	+	0.244251i	−0.982864	−	0.184333i	$-0.940987\pi$
$787$	−2.22638	+	6.85211i	−0.0793620	+	0.244251i	0.903502	+	0.428584i	$0.140987\pi$
$788$	−18.4173	+	20.4544i	−0.656088	+	0.728659i
$789$	13.3640	−	9.70955i	0.475773	−	0.345669i
$790$	−0.0112655	−	0.00239455i	−0.000400807	−	8.51942e-5i
$791$	−64.1767	−	13.6412i	−2.28186	−	0.485024i
$792$	0.323992	+	3.08258i	0.0115126	+	0.109535i
$793$	1.37079	−	3.04212i	0.0486783	−	0.108029i
$794$	1.77857	+	1.97530i	0.0631192	+	0.0701009i
$795$	−0.0298676	−	0.0217001i	−0.00105929	−	0.000769622i
$796$	12.0586	−	37.1127i	0.427407	−	1.31542i
$797$	−0.851701	−	8.10340i	−0.0301688	−	0.287037i	−0.999196	−	0.0400842i	$-0.987237\pi$
$797$	−0.851701	−	8.10340i	−0.0301688	−	0.287037i	0.969028	−	0.246953i	$-0.0794293\pi$
$798$	−2.17466	+	1.57998i	−0.0769821	+	0.0559308i
$799$	−3.31065	−	2.40533i	−0.117122	−	0.0850943i
$800$	−10.3286			−0.365172
$801$	7.66839	+	13.2820i	0.270949	+	0.469298i
$802$	−0.106775	+	1.01589i	−0.00377034	+	0.0358724i
$803$	7.23920	−	8.03995i	0.255466	−	0.283724i
$804$	−3.19609	−	3.54962i	−0.112717	−	0.125185i
$805$	0.377788			0.0133153
$806$	0.521786	+	3.48952i	0.0183791	+	0.122913i
$807$	−13.2185			−0.465313
$808$	0.158670	+	0.176220i	0.00558198	+	0.00619941i
$809$	−19.0555	+	21.1633i	−0.669956	+	0.744061i	−0.978295	−	0.207215i	$-0.933560\pi$
$809$	−19.0555	+	21.1633i	−0.669956	+	0.744061i	0.308339	+	0.951276i	$0.400227\pi$
$810$	0.00120781	−	0.0114916i	4.24382e−5	−	0.000403773i
$811$	11.9051	+	20.6203i	0.418046	+	0.724076i	0.995743	−	0.0921749i	$-0.0293819\pi$
$811$	11.9051	+	20.6203i	0.418046	+	0.724076i	−0.577697	+	0.816251i	$0.696049\pi$
$812$	−84.4082			−2.96215
$813$	−5.08936	−	3.69764i	−0.178492	−	0.129682i
$814$	−1.06769	+	0.775724i	−0.0374226	+	0.0271891i
$815$	−0.0302907	−	0.288196i	−0.00106104	−	0.0100951i
$816$	−5.17225	+	15.9186i	−0.181065	+	0.557261i
$817$	−31.4343	−	22.8384i	−1.09975	−	0.799013i
$818$	−0.543642	−	0.603775i	−0.0190080	−	0.0211105i
$819$	40.2994	−	4.05329i	1.40818	−	0.141633i
$820$	0.0340070	+	0.323555i	0.00118758	+	0.0112990i
$821$	−15.8856	−	3.37658i	−0.554410	−	0.117844i	−0.0778174	−	0.996968i	$-0.524795\pi$
$821$	−15.8856	−	3.37658i	−0.554410	−	0.117844i	−0.476593	+	0.879124i	$0.658128\pi$
$822$	−2.67593	−	0.568787i	−0.0933339	−	0.0198387i
$823$	−42.1158	+	30.5989i	−1.46806	+	1.06661i	−0.486894	+	0.873461i	$0.661870\pi$
$823$	−42.1158	+	30.5989i	−1.46806	+	1.06661i	−0.981169	+	0.193149i	$0.938130\pi$
$824$	−2.74008	+	3.04317i	−0.0954552	+	0.106014i
$825$	2.15652	−	6.63710i	0.0750805	−	0.231074i
$826$	7.33906	−	3.26756i	0.255359	−	0.113693i
$827$	−48.8080	+	10.3745i	−1.69722	+	0.360755i	−0.952008	−	0.306072i	$-0.900985\pi$
$827$	−48.8080	+	10.3745i	−1.69722	+	0.360755i	−0.745212	+	0.666828i	$0.767652\pi$
$828$	−2.54787	−	24.2414i	−0.0885447	−	0.842446i
$829$	−3.36469	−	32.0129i	−0.116861	−	1.11185i	−0.883063	−	0.469254i	$-0.844523\pi$
$829$	−3.36469	−	32.0129i	−0.116861	−	1.11185i	0.766202	−	0.642599i	$-0.222144\pi$
$830$	5.30559e−5	0	0.000504793i	1.84160e−6	0	1.75216e-5i
$831$	6.12030	−	10.6007i	0.212311	−	0.367733i
$832$	24.9590	−	7.98631i	0.865299	−	0.276875i
$833$	67.7558	+	49.2274i	2.34760	+	1.70563i
$834$	−0.603050	+	0.669755i	−0.0208819	+	0.0231917i
$835$	0.268995	+	0.298749i	0.00930894	+	0.0103386i
$836$	7.82965	+	13.5614i	0.270794	+	0.469029i
$837$	−22.1534	−	6.03516i	−0.765734	−	0.208606i
$838$	2.38895	+	4.13779i	0.0825250	+	0.142937i
$839$	25.8868	−	5.50242i	0.893713	−	0.189965i	0.261909	−	0.965093i	$-0.415648\pi$
$839$	25.8868	−	5.50242i	0.893713	−	0.189965i	0.631804	+	0.775128i	$0.282315\pi$
$840$	0.0383572	+	0.00815307i	0.00132345	+	0.000281308i
$841$	−5.89279	+	56.0662i	−0.203200	+	1.93332i
$842$	−2.54445			−0.0876876
$843$	−11.9894	−	20.7662i	−0.412936	−	0.715227i
$844$	−33.9887	+	15.1327i	−1.16994	+	0.520890i
$845$	−0.202930	+	0.0412382i	−0.00698100	+	0.00141864i
$846$	0.275884	+	0.122831i	0.00948508	+	0.00422303i
$847$	10.9426	−	33.6779i	0.375993	−	1.15719i
$848$	9.40544	+	6.83346i	0.322984	+	0.234662i
$849$	6.23489	−	19.1890i	0.213981	−	0.658565i
$850$	3.39087	−	3.76595i	0.116306	−	0.129171i
$851$	16.9244	−	12.2963i	0.580160	−	0.421511i
$852$	−2.17804	+	2.41896i	−0.0746184	+	0.0828722i
$853$	−6.10541	−	18.7905i	−0.209045	−	0.643375i	−0.999523	−	0.0308844i	$-0.990168\pi$
$853$	−6.10541	−	18.7905i	−0.209045	−	0.643375i	0.790478	−	0.612491i	$-0.209832\pi$
$854$	−0.610475	+	0.443536i	−0.0208900	+	0.0151775i
$855$	−0.0516547	−	0.158977i	−0.00176655	−	0.00543689i
$856$	8.24084	−	1.75164i	0.281666	−	0.0598700i
$857$	−3.28081	+	31.2148i	−0.112070	+	1.06628i	0.783510	+	0.621379i	$0.213427\pi$
$857$	−3.28081	+	31.2148i	−0.112070	+	1.06628i	−0.895581	+	0.444899i	$0.853239\pi$
$858$	0.00396053	−	0.884516i	0.000135210	−	0.0301969i
$859$	−22.0345	−	9.81038i	−0.751806	−	0.334726i	−0.00519526	−	0.999987i	$-0.501654\pi$
$859$	−22.0345	−	9.81038i	−0.751806	−	0.334726i	−0.746611	+	0.665261i	$0.768320\pi$
$860$	0.0293945	+	0.279670i	0.00100234	+	0.00953667i
$861$	−3.82608	+	36.4027i	−0.130392	+	1.24060i
$862$	6.09934			0.207744
$863$	−25.1362	−	43.5372i	−0.855646	−	1.48202i	−0.876045	−	0.482230i	$-0.839827\pi$
$863$	−25.1362	−	43.5372i	−0.855646	−	1.48202i	0.0203986	−	0.999792i	$-0.493506\pi$
$864$	0.890501	−	8.47255i	0.0302954	−	0.288242i
$865$	−0.114083	−	0.351111i	−0.00387893	−	0.0119381i
$866$	0.633154	−	1.94865i	0.0215154	−	0.0662177i
$867$	−6.18289	−	10.7091i	−0.209982	−	0.363699i
$868$	−18.4255	+	47.4080i	−0.625404	+	1.60913i
$869$	−3.77432	+	6.53732i	−0.128035	+	0.221763i
$870$	0.00608061	−	0.0187142i	0.000206152	−	0.000634471i
$871$	−6.71651	−	9.33208i	−0.227580	−	0.316205i
$872$	−4.34198	−	3.15463i	−0.147038	−	0.106829i
$873$	−34.9663			−1.18343
$874$	1.94701	+	3.37232i	0.0658587	+	0.114071i
$875$	0.597841	+	0.434357i	0.0202107	+	0.0146839i
$876$	−7.14454	+	5.19081i	−0.241392	+	0.175381i
$877$	3.16383	+	30.1019i	0.106835	+	1.01647i	0.908270	+	0.418385i	$0.137404\pi$
$877$	3.16383	+	30.1019i	0.106835	+	1.01647i	−0.801435	+	0.598082i	$0.795930\pi$
$878$	−2.90547	−	3.22685i	−0.0980548	−	0.108901i
$879$	−0.188501	+	1.79347i	−0.00635798	+	0.0604922i
$880$	0.0344639	−	0.106069i	0.00116178	−	0.00357558i
$881$	4.55801	+	14.0281i	0.153563	+	0.472619i	0.998012	−	0.0630165i	$-0.0200721\pi$
$881$	4.55801	+	14.0281i	0.153563	+	0.472619i	−0.844449	+	0.535636i	$0.820072\pi$
$882$	−5.64624	−	2.51387i	−0.190119	−	0.0846463i
$883$	−3.25284	−	10.0112i	−0.109467	−	0.336904i	0.881286	−	0.472583i	$-0.156678\pi$
$883$	−3.25284	−	10.0112i	−0.109467	−	0.336904i	−0.990753	+	0.135679i	$0.956678\pi$
$884$	−16.8203	+	37.3283i	−0.565729	+	1.25549i
$885$	−0.0124786	−	0.118726i	−0.000419463	−	0.00399092i
$886$	0.595336	+	1.83226i	0.0200007	+	0.0615558i
$887$	10.8581	−	2.30796i	0.364579	−	0.0774936i	−0.0219798	−	0.999758i	$-0.506997\pi$
$887$	10.8581	−	2.30796i	0.364579	−	0.0774936i	0.386559	+	0.922265i	$0.373664\pi$
$888$	1.98371	−	0.883206i	0.0665690	−	0.0296384i
$889$	−28.2209	+	5.99853i	−0.946498	+	0.201184i
$890$	0.00185357	+	0.0176356i	6.21319e−5	+	0.000591145i
$891$	−6.91862	−	3.08037i	−0.231783	−	0.103196i
$892$	17.4052	−	7.74930i	0.582770	−	0.259466i
$893$	3.07533			0.102912
$894$	1.32118			0.0441869
$895$	−0.0501781	+	0.0223407i	−0.00167727	+	0.000746769i
$896$	−24.5458	−	5.21738i	−0.820019	−	0.174300i
$897$	−0.0627797	+	14.0208i	−0.00209615	+	0.468140i
$898$	−3.24890			−0.108417
$899$	45.7403	+	23.5467i	1.52552	+	0.785328i
$900$	11.9193	−	20.6449i	0.397311	−	0.688162i
$901$	−17.1870	+	3.65321i	−0.572582	+	0.121706i
$902$	−3.27207	−	0.695500i	−0.108948	−	0.0231576i
$903$	−3.30713	+	31.4653i	−0.110054	+	1.04710i
$904$	−4.93289	+	8.54401i	−0.164065	+	0.284170i
$905$	−0.0265622	+	0.0460071i	−0.000882958	+	0.00152933i
$906$	1.35395	+	0.983701i	0.0449819	+	0.0326813i
$907$	1.13329	+	10.7826i	0.0376304	+	0.358030i	0.997093	+	0.0761937i	$0.0242767\pi$
$907$	1.13329	+	10.7826i	0.0376304	+	0.358030i	−0.959463	+	0.281836i	$0.909057\pi$
$908$	19.1727	−	13.9298i	0.636269	−	0.462277i
$909$	−0.805087	+	0.171127i	−0.0267031	+	0.00567591i
$910$	0.0444729	+	0.0146706i	0.00147426	+	0.000486325i
$911$	−20.0107	−	22.2241i	−0.662983	−	0.736317i	0.314050	−	0.949407i	$-0.398314\pi$
$911$	−20.0107	−	22.2241i	−0.662983	−	0.736317i	−0.977033	+	0.213089i	$0.931647\pi$
$912$	−3.88701	−	11.9630i	−0.128712	−	0.396134i
$913$	−0.303916	−	0.135312i	−0.0100582	−	0.00447818i
$914$	−1.59291	+	1.76911i	−0.0526888	+	0.0585168i
$915$	0.00346508	+	0.0106644i	0.000114552	+	0.000352554i
$916$	2.55829	−	1.85871i	0.0845283	−	0.0614134i
$917$	−4.46960	−	0.950044i	−0.147599	−	0.0313732i
$918$	2.79685	+	3.10622i	0.0923098	+	0.102520i
$919$	14.6417	−	6.51890i	0.482985	−	0.215039i	−0.150776	−	0.988568i	$-0.548177\pi$
$919$	14.6417	−	6.51890i	0.482985	−	0.215039i	0.633760	+	0.773529i	$0.281511\pi$
$920$	0.0175545	−	0.0540273i	0.000578756	−	0.00178123i
$921$	−6.27891	+	4.56190i	−0.206897	+	0.150320i
$922$	−3.34417	+	2.42968i	−0.110134	+	0.0800174i
$923$	−5.84626	+	5.21679i	−0.192432	+	0.171713i
$924$	6.37548	−	11.0427i	0.209738	−	0.363277i
$925$	20.4594			0.672701
$926$	−1.52178	+	0.677542i	−0.0500089	+	0.0222654i
$927$	−4.39229	−	13.5181i	−0.144262	−	0.443991i
$928$	−5.89850	+	18.1537i	−0.193628	+	0.595925i
$929$	7.52828	+	13.0394i	0.246995	+	0.427808i	0.962691	−	0.270605i	$-0.0872236\pi$
$929$	7.52828	+	13.0394i	0.246995	+	0.427808i	−0.715696	+	0.698412i	$0.753890\pi$
$930$	−0.00918353	−	0.00750033i	−0.000301140	−	0.000245945i
$931$	−62.9397			−2.06277
$932$	35.3395	−	7.51164i	1.15758	−	0.246052i
$933$	11.4831	−	12.7533i	0.375941	−	0.417525i
$934$	−0.703185	+	0.313078i	−0.0230089	+	0.0102442i
$935$	0.0842803	+	0.145978i	0.00275626	+	0.00477398i
$936$	1.29292	−	5.95155i	0.0422604	−	0.194532i
$937$	−39.4790	+	17.5772i	−1.28972	+	0.574221i	−0.932962	−	0.359975i	$-0.882785\pi$
$937$	−39.4790	+	17.5772i	−1.28972	+	0.574221i	−0.356760	+	0.934196i	$0.616118\pi$
$938$	0.271795	+	2.58596i	0.00887443	+	0.0844345i
$939$	8.44304	−	6.13423i	0.275528	−	0.200183i
$940$	−0.0148932	−	0.0165406i	−0.000485762	−	0.000539493i
$941$	−4.53995	+	43.1948i	−0.147998	+	1.40811i	0.628412	+	0.777881i	$0.283705\pi$
$941$	−4.53995	+	43.1948i	−0.147998	+	1.40811i	−0.776410	+	0.630228i	$0.782961\pi$
$942$	0.389812	−	1.19972i	0.0127008	−	0.0390889i
$943$	51.8667	+	11.0246i	1.68901	+	0.359011i
$944$	3.92957	+	37.3873i	0.127896	+	1.21685i
$945$	−0.203918	+	0.226474i	−0.00663345	+	0.00736719i
$946$	−2.82826	−	0.601166i	−0.0919548	−	0.0195456i
$947$	−14.9357	−	6.64981i	−0.485346	−	0.216090i	0.149451	−	0.988769i	$-0.452249\pi$
$947$	−14.9357	−	6.64981i	−0.485346	−	0.216090i	−0.634797	+	0.772679i	$0.718916\pi$
$948$	4.12303	−	4.57909i	0.133910	−	0.148722i
$949$	−18.4574	+	10.5465i	−0.599153	+	0.342353i
$950$	−0.398081	+	3.78749i	−0.0129155	+	0.122882i
$951$	−4.20105	+	12.9295i	−0.136228	+	0.419268i
$952$	15.0992	−	10.9702i	0.489367	−	0.355546i
$953$	−37.7283	−	16.7977i	−1.22214	−	0.544132i	−0.308721	−	0.951153i	$-0.599901\pi$
$953$	−37.7283	−	16.7977i	−1.22214	−	0.544132i	−0.913419	+	0.407021i	$0.866568\pi$
$954$	1.18459	−	0.527412i	0.0383524	−	0.0170756i
$955$	0.0563776			0.00182434
$956$	−11.9141	+	20.6358i	−0.385329	+	0.667409i
$957$	−10.4339	−	7.58067i	−0.337280	−	0.245048i
$958$	−0.552931	−	1.70175i	−0.0178644	−	0.0549809i
$959$	−63.5215	−	70.5478i	−2.05122	−	2.27811i
$960$	−0.0440329	+	0.0762673i	−0.00142116	+	0.00246152i
$961$	23.2098	−	20.5501i	0.748702	−	0.662906i
$962$	2.46982	−	0.790284i	0.0796302	−	0.0254798i
$963$	−9.03660	+	27.8118i	−0.291200	+	0.896223i
$964$	17.5574	−	19.4995i	0.565487	−	0.628037i
$965$	−0.0572056	+	0.0254696i	−0.00184151	+	0.000819895i
$966$	1.58540	−	2.74600i	0.0510095	−	0.0883510i
$967$	9.46705	−	16.3974i	0.304440	−	0.527305i	−0.672697	−	0.739918i	$-0.734864\pi$
$967$	9.46705	−	16.3974i	0.304440	−	0.527305i	0.977136	+	0.212613i	$0.0681974\pi$
$968$	−4.30779	−	3.12979i	−0.138458	−	0.100595i
$969$	17.3675	+	7.73252i	0.557925	+	0.248404i
$970$	−0.0369335	−	0.0164438i	−0.00118586	−	0.000527980i
$971$	25.5737	+	28.4024i	0.820698	+	0.911477i	0.997347	−	0.0727965i	$-0.0231924\pi$
$971$	25.5737	+	28.4024i	0.820698	+	0.911477i	−0.176649	+	0.984274i	$0.556526\pi$
$972$	24.7098	+	17.9527i	0.792568	+	0.575835i
$973$	−30.5905	+	6.50221i	−0.980686	+	0.208451i
$974$	3.46875	−	3.85244i	0.111146	−	0.123440i
$975$	−8.10957	+	11.0574i	−0.259714	+	0.354120i
$976$	−1.09117	−	3.35827i	−0.0349275	−	0.107496i
$977$	−8.78451	−	1.86721i	−0.281041	−	0.0597372i	0.0652343	−	0.997870i	$-0.479221\pi$
$977$	−8.78451	−	1.86721i	−0.281041	−	0.0597372i	−0.346276	+	0.938133i	$0.612554\pi$
$978$	−2.22190	−	0.989255i	−0.0710486	−	0.0316329i
$979$	11.3685	+	2.41645i	0.363339	+	0.0772301i
$980$	0.304804	+	0.338519i	0.00973661	+	0.0108136i
$981$	17.0183	−	7.57703i	0.543352	−	0.241916i
$982$	−0.151793	−	0.168583i	−0.00484391	−	0.00537971i
$983$	−7.27531	−	3.23918i	−0.232046	−	0.103314i	0.287420	−	0.957805i	$-0.407202\pi$
$983$	−7.27531	−	3.23918i	−0.232046	−	0.103314i	−0.519466	+	0.854491i	$0.673869\pi$
$984$	5.02815	+	2.23868i	0.160292	+	0.0713664i
$985$	0.0232738	−	0.221436i	0.000741567	−	0.00705553i
$986$	−4.68261	−	8.11052i	−0.149125	−	0.258292i
$987$	−1.25208	−	2.16867i	−0.0398541	−	0.0690294i
$988$	−6.26244	−	30.1251i	−0.199235	−	0.958408i
$989$	44.8318	+	9.52930i	1.42557	+	0.303014i
$990$	−0.00832353	−	0.00924421i	−0.000264539	−	0.000293800i
$991$	−2.86573	+	4.96359i	−0.0910330	+	0.157674i	−0.907946	−	0.419087i	$-0.862350\pi$
$991$	−2.86573	+	4.96359i	−0.0910330	+	0.157674i	0.816913	+	0.576761i	$0.195684\pi$
$992$	8.90849	+	7.27570i	0.282845	+	0.231004i
$993$	−14.5784			−0.462632
$994$	1.73324	−	0.368412i	0.0549750	−	0.0116853i
$995$	0.0975479	+	0.300222i	0.00309248	+	0.00951767i
$996$	0.219694	+	0.159617i	0.00696126	+	0.00505765i
$997$	29.1377	−	50.4680i	0.922800	−	1.59834i	0.127738	−	0.991808i	$-0.459228\pi$
$997$	29.1377	−	50.4680i	0.922800	−	1.59834i	0.795062	−	0.606528i	$-0.207438\pi$
$998$	−0.00555932	−	0.00962903i	−0.000175977	−	0.000304802i
$999$	−1.76395	+	16.7828i	−0.0558088	+	0.530985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bk.a.9.19	yes	280
13.3	even	3		403.2.bj.a.133.17	yes	280
31.7	even	15		403.2.bj.a.100.17	✓	280
403.224	even	15	inner	403.2.bk.a.224.19	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bj.a.100.17	✓	280	31.7	even	15
403.2.bj.a.133.17	yes	280	13.3	even	3
403.2.bk.a.9.19	yes	280	1.1	even	1	trivial
403.2.bk.a.224.19	yes	280	403.224	even	15	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bk (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.117605 + 0.130614i) q^{2} +(0.508986 - 0.565287i) q^{3} +(0.205828 - 1.95832i) q^{4} +(0.00796452 + 0.0137949i) q^{5} +0.133693 q^{6} +(3.75325 + 2.72689i) q^{7} +(0.564372 - 0.410040i) q^{8} +(0.253104 + 2.40812i) q^{9} +O(q^{10})\)	\(q+(0.117605 + 0.130614i) q^{2} +(0.508986 - 0.565287i) q^{3} +(0.205828 - 1.95832i) q^{4} +(0.00796452 + 0.0137949i) q^{5} +0.133693 q^{6} +(3.75325 + 2.72689i) q^{7} +(0.564372 - 0.410040i) q^{8} +(0.253104 + 2.40812i) q^{9} +(-0.000865141 + 0.00266263i) q^{10} +(1.48452 + 1.07857i) q^{11} +(-1.00225 - 1.11311i) q^{12} +(-2.10621 - 2.92641i) q^{13} +(0.0852313 + 0.810921i) q^{14} +(0.0118519 + 0.00251921i) q^{15} +(-3.73223 - 0.793310i) q^{16} +(4.66547 - 3.38966i) q^{17} +(-0.284767 + 0.316266i) q^{18} +(-1.33923 + 4.12174i) q^{19} +(0.0286543 - 0.0127577i) q^{20} +(3.45183 - 0.733709i) q^{21} +(0.0337115 + 0.320743i) q^{22} +(-0.534373 - 5.08422i) q^{23} +(0.0554674 - 0.527737i) q^{24} +(2.49987 - 4.32991i) q^{25} +(0.134529 - 0.619260i) q^{26} +(3.33628 + 2.42395i) q^{27} +(6.11266 - 6.78880i) q^{28} +(-6.18267 - 6.86655i) q^{29} +(0.00106480 + 0.00184429i) q^{30} +(-5.20624 + 1.97360i) q^{31} +(-1.03291 - 1.78906i) q^{32} +(1.36530 - 0.290204i) q^{33} +(0.991419 + 0.210733i) q^{34} +(-0.00772456 + 0.0734942i) q^{35} +4.76797 q^{36} +(2.04605 + 3.54385i) q^{37} +(-0.695856 + 0.309815i) q^{38} +(-2.72629 - 0.298893i) q^{39} +(0.0101514 + 0.00451971i) q^{40} +(-3.20522 + 9.86464i) q^{41} +(0.501784 + 0.364568i) q^{42} +(-2.77048 + 8.52665i) q^{43} +(2.41774 - 2.68517i) q^{44} +(-0.0312040 + 0.0226711i) q^{45} +(0.601223 - 0.667726i) q^{46} +(-0.219280 - 0.674876i) q^{47} +(-2.34810 + 1.70600i) q^{48} +(4.48779 + 13.8120i) q^{49} +(0.859542 - 0.182701i) q^{50} +(0.458530 - 4.36262i) q^{51} +(-6.16437 + 3.52230i) q^{52} +(-2.78348 - 1.23928i) q^{53} +(0.0757626 + 0.720833i) q^{54} +(-0.00305529 + 0.0290691i) q^{55} +3.23636 q^{56} +(1.64831 + 2.85496i) q^{57} +(0.169752 - 1.61508i) q^{58} +(-3.04459 - 9.37028i) q^{59} +(0.00737288 - 0.0226914i) q^{60} +(0.462717 + 0.801450i) q^{61} +(-0.870059 - 0.447899i) q^{62} +(-5.61672 + 9.72845i) q^{63} +(-2.24598 + 6.91241i) q^{64} +(0.0235948 - 0.0523625i) q^{65} +(0.198471 + 0.144197i) q^{66} +3.18891 q^{67} +(-5.67777 - 9.83419i) q^{68} +(-3.14603 - 2.28572i) q^{69} +(-0.0105078 + 0.00763436i) q^{70} +(-0.227156 - 2.16125i) q^{71} +(1.13027 + 1.25529i) q^{72} +(0.616291 - 5.86362i) q^{73} +(-0.222250 + 0.684016i) q^{74} +(-1.17524 - 3.61701i) q^{75} +(7.79604 + 3.47102i) q^{76} +(2.63063 + 8.09626i) q^{77} +(-0.281586 - 0.391242i) q^{78} +(0.430006 + 4.09124i) q^{79} +(-0.0187817 - 0.0578042i) q^{80} +(-4.03706 + 0.858104i) q^{81} +(-1.66541 + 0.741486i) q^{82} +(-0.177337 + 0.0376942i) q^{83} +(-0.726355 - 6.91081i) q^{84} +(0.0839185 + 0.0373629i) q^{85} +(-1.43952 + 0.640915i) q^{86} -7.02847 q^{87} +1.28008 q^{88} +(5.78630 - 2.57622i) q^{89} +(-0.00663090 - 0.00140944i) q^{90} +(0.0748969 - 16.7270i) q^{91} -10.0665 q^{92} +(-1.53425 + 3.94755i) q^{93} +(0.0623594 - 0.108010i) q^{94} +(-0.0675255 + 0.0143530i) q^{95} +(-1.53707 - 0.326714i) q^{96} +(-1.50946 + 14.3615i) q^{97} +(-1.27625 + 2.21053i) q^{98} +(-2.22158 + 3.84789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9}+O(q^{10}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9} - 9 q^{10} - 6 q^{11} - 50 q^{12} - 6 q^{13} - 21 q^{15} + 23 q^{16} + 3 q^{17} - 15 q^{18} - 9 q^{19} + 60 q^{20} - 34 q^{21} + 41 q^{22} - 12 q^{23} - 89 q^{24} - 112 q^{25} + 39 q^{26} + 48 q^{27} + 66 q^{28} - 11 q^{29} + 24 q^{30} - 22 q^{31} + q^{32} - 37 q^{33} - 49 q^{34} + 41 q^{35} + 134 q^{36} + 17 q^{37} - 23 q^{38} + 10 q^{39} + 31 q^{40} + q^{41} - 71 q^{42} - 7 q^{43} - 42 q^{44} - 13 q^{45} + 21 q^{46} - 20 q^{47} - 3 q^{48} - 69 q^{49} - 42 q^{50} - 71 q^{51} - 140 q^{52} - 8 q^{53} - 149 q^{54} + 5 q^{55} - 126 q^{56} + 21 q^{57} + 79 q^{58} + 77 q^{59} + 2 q^{60} + 53 q^{61} + 72 q^{62} + 17 q^{63} - 91 q^{64} - 25 q^{65} - 62 q^{66} - 14 q^{67} + 83 q^{68} - 31 q^{69} + 134 q^{70} + 32 q^{71} - 70 q^{72} - 31 q^{73} + 51 q^{74} + 79 q^{75} + 98 q^{76} - 80 q^{77} - 141 q^{78} - 142 q^{79} + 6 q^{80} + 66 q^{81} - 48 q^{82} + 94 q^{83} + 130 q^{84} + 90 q^{85} - 34 q^{86} + 22 q^{87} - 122 q^{88} - 15 q^{89} + 43 q^{90} + 56 q^{91} - 294 q^{92} - 52 q^{93} - 57 q^{94} + 94 q^{95} + 24 q^{96} + 46 q^{97} + 73 q^{98} + 12 q^{99}+O(q^{100}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9 - 9 * q^10 - 6 * q^11 - 50 * q^12 - 6 * q^13 - 21 * q^15 + 23 * q^16 + 3 * q^17 - 15 * q^18 - 9 * q^19 + 60 * q^20 - 34 * q^21 + 41 * q^22 - 12 * q^23 - 89 * q^24 - 112 * q^25 + 39 * q^26 + 48 * q^27 + 66 * q^28 - 11 * q^29 + 24 * q^30 - 22 * q^31 + q^32 - 37 * q^33 - 49 * q^34 + 41 * q^35 + 134 * q^36 + 17 * q^37 - 23 * q^38 + 10 * q^39 + 31 * q^40 + q^41 - 71 * q^42 - 7 * q^43 - 42 * q^44 - 13 * q^45 + 21 * q^46 - 20 * q^47 - 3 * q^48 - 69 * q^49 - 42 * q^50 - 71 * q^51 - 140 * q^52 - 8 * q^53 - 149 * q^54 + 5 * q^55 - 126 * q^56 + 21 * q^57 + 79 * q^58 + 77 * q^59 + 2 * q^60 + 53 * q^61 + 72 * q^62 + 17 * q^63 - 91 * q^64 - 25 * q^65 - 62 * q^66 - 14 * q^67 + 83 * q^68 - 31 * q^69 + 134 * q^70 + 32 * q^71 - 70 * q^72 - 31 * q^73 + 51 * q^74 + 79 * q^75 + 98 * q^76 - 80 * q^77 - 141 * q^78 - 142 * q^79 + 6 * q^80 + 66 * q^81 - 48 * q^82 + 94 * q^83 + 130 * q^84 + 90 * q^85 - 34 * q^86 + 22 * q^87 - 122 * q^88 - 15 * q^89 + 43 * q^90 + 56 * q^91 - 294 * q^92 - 52 * q^93 - 57 * q^94 + 94 * q^95 + 24 * q^96 + 46 * q^97 + 73 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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