LMFDB - Embedded newform 147.2.i.b.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,2,Mod(22,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("147.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.i (of order $7$, degree $6$, 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:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			43.3
Character	$\chi$	$=$	147.43
Dual form			147.2.i.b.106.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.385632 + 0.483568i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(0.359916 + 1.57690i) q^{4} +(-3.63892 - 1.75241i) q^{5} +(0.557255 - 0.268360i) q^{6} +(-2.64500 - 0.0631583i) q^{7} +(-2.01584 - 0.970778i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})$	\(q+(-0.385632 + 0.483568i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(0.359916 + 1.57690i) q^{4} +(-3.63892 - 1.75241i) q^{5} +(0.557255 - 0.268360i) q^{6} +(-2.64500 - 0.0631583i) q^{7} +(-2.01584 - 0.970778i) q^{8} +(0.623490 + 0.781831i) q^{9} +(2.25069 - 1.08388i) q^{10} +(0.0332349 - 0.0416752i) q^{11} +(0.359916 - 1.57690i) q^{12} +(-0.237234 + 0.297483i) q^{13} +(1.05054 - 1.25468i) q^{14} +(2.51821 + 3.15773i) q^{15} +(-1.66773 + 0.803137i) q^{16} +(-0.172451 + 0.755556i) q^{17} -0.618506 q^{18} -4.32244 q^{19} +(1.45366 - 6.36892i) q^{20} +(2.35566 + 1.20453i) q^{21} +(0.00733635 + 0.0321427i) q^{22} +(-0.445501 - 1.95187i) q^{23} +(1.39501 + 1.74928i) q^{24} +(7.05333 + 8.84459i) q^{25} +(-0.0523677 - 0.229438i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(-0.852384 - 4.19362i) q^{28} +(-1.94604 + 8.52617i) q^{29} -2.49808 q^{30} +5.67978 q^{31} +(1.25050 - 5.47882i) q^{32} +(-0.0480258 + 0.0231280i) q^{33} +(-0.298860 - 0.374759i) q^{34} +(9.51425 + 4.86495i) q^{35} +(-1.00846 + 1.26457i) q^{36} +(2.39948 - 10.5128i) q^{37} +(1.66687 - 2.09020i) q^{38} +(0.342814 - 0.165090i) q^{39} +(5.63428 + 7.06516i) q^{40} +(-1.87432 - 0.902623i) q^{41} +(-1.49089 + 0.674616i) q^{42} +(-6.37201 + 3.06860i) q^{43} +(0.0776793 + 0.0374084i) q^{44} +(-0.898738 - 3.93763i) q^{45} +(1.11566 + 0.537273i) q^{46} +(-6.67934 + 8.37562i) q^{47} +1.85104 q^{48} +(6.99202 + 0.334107i) q^{49} -6.99695 q^{50} +(0.483196 - 0.605909i) q^{51} +(-0.554484 - 0.267025i) q^{52} +(-1.51990 - 6.65912i) q^{53} +(0.557255 + 0.268360i) q^{54} +(-0.193971 + 0.0934116i) q^{55} +(5.27058 + 2.69502i) q^{56} +(3.89439 + 1.87544i) q^{57} +(-3.37252 - 4.22901i) q^{58} +(-6.38163 + 3.07323i) q^{59} +(-4.07308 + 5.10748i) q^{60} +(1.24542 - 5.45654i) q^{61} +(-2.19031 + 2.74656i) q^{62} +(-1.59975 - 2.10732i) q^{63} +(-0.141068 - 0.176894i) q^{64} +(1.38459 - 0.666783i) q^{65} +(0.00733635 - 0.0321427i) q^{66} -10.4126 q^{67} -1.25350 q^{68} +(-0.445501 + 1.95187i) q^{69} +(-6.02153 + 2.72470i) q^{70} +(-2.39721 - 10.5029i) q^{71} +(-0.497872 - 2.18132i) q^{72} +(-1.54213 - 1.93377i) q^{73} +(4.15834 + 5.21440i) q^{74} +(-2.51730 - 11.0290i) q^{75} +(-1.55572 - 6.81605i) q^{76} +(-0.0905384 + 0.108132i) q^{77} +(-0.0523677 + 0.229438i) q^{78} -10.7607 q^{79} +7.47616 q^{80} +(-0.222521 + 0.974928i) q^{81} +(1.15928 - 0.558278i) q^{82} +(0.559861 + 0.702043i) q^{83} +(-1.05157 + 4.14816i) q^{84} +(1.95158 - 2.44720i) q^{85} +(0.973378 - 4.26465i) q^{86} +(5.45269 - 6.83746i) q^{87} +(-0.107454 + 0.0517470i) q^{88} +(7.55992 + 9.47984i) q^{89} +(2.25069 + 1.08388i) q^{90} +(0.646273 - 0.771857i) q^{91} +(2.91755 - 1.40502i) q^{92} +(-5.11731 - 2.46436i) q^{93} +(-1.47441 - 6.45983i) q^{94} +(15.7290 + 7.57469i) q^{95} +(-3.50383 + 4.39367i) q^{96} +9.99553 q^{97} +(-2.85791 + 3.25227i) q^{98} +0.0533046 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 6 q^{3} - 9 q^{4} - 4 q^{5} - q^{6} - 6 q^{7} - 15 q^{8} - 6 q^{9}+O(q^{10}) $ 36 * q - q^2 - 6 * q^3 - 9 * q^4 - 4 * q^5 - q^6 - 6 * q^7 - 15 * q^8 - 6 * q^9	\( 36 q - q^{2} - 6 q^{3} - 9 q^{4} - 4 q^{5} - q^{6} - 6 q^{7} - 15 q^{8} - 6 q^{9} + 10 q^{10} - 7 q^{11} - 9 q^{12} - 12 q^{13} - q^{14} + 3 q^{15} - 3 q^{16} - 3 q^{17} + 6 q^{18} + 6 q^{19} + 25 q^{20} + q^{21} - 21 q^{22} - 20 q^{23} + 6 q^{24} - 2 q^{25} + 6 q^{26} - 6 q^{27} - q^{28} - 22 q^{29} - 4 q^{30} + 16 q^{31} + 26 q^{32} + 6 q^{34} - 9 q^{35} - 9 q^{36} + 32 q^{37} + 17 q^{38} + 23 q^{39} - 21 q^{40} - 5 q^{41} - 8 q^{42} - 34 q^{43} + 2 q^{44} + 3 q^{45} - 32 q^{46} - 7 q^{47} + 74 q^{48} + 20 q^{49} + 236 q^{50} + 18 q^{51} + 20 q^{52} - 32 q^{53} - q^{54} - 17 q^{55} - 39 q^{56} - 8 q^{57} - 53 q^{58} - q^{59} - 17 q^{60} + 14 q^{61} - 60 q^{62} + 22 q^{63} - 21 q^{64} - 39 q^{65} - 21 q^{66} - 22 q^{67} - 110 q^{68} - 20 q^{69} - 40 q^{70} + 36 q^{71} + 6 q^{72} - 11 q^{73} - 46 q^{74} - 9 q^{75} - 101 q^{76} - 17 q^{77} + 6 q^{78} - 14 q^{79} - 112 q^{80} - 6 q^{81} + 2 q^{82} + 12 q^{83} - 22 q^{84} - 44 q^{85} + 184 q^{86} - q^{87} + 204 q^{88} + 12 q^{89} + 10 q^{90} - 16 q^{91} - 105 q^{92} - 19 q^{93} - 5 q^{94} + 18 q^{95} - 9 q^{96} + 172 q^{97} + q^{98}+O(q^{100}) \) 36 * q - q^2 - 6 * q^3 - 9 * q^4 - 4 * q^5 - q^6 - 6 * q^7 - 15 * q^8 - 6 * q^9 + 10 * q^10 - 7 * q^11 - 9 * q^12 - 12 * q^13 - q^14 + 3 * q^15 - 3 * q^16 - 3 * q^17 + 6 * q^18 + 6 * q^19 + 25 * q^20 + q^21 - 21 * q^22 - 20 * q^23 + 6 * q^24 - 2 * q^25 + 6 * q^26 - 6 * q^27 - q^28 - 22 * q^29 - 4 * q^30 + 16 * q^31 + 26 * q^32 + 6 * q^34 - 9 * q^35 - 9 * q^36 + 32 * q^37 + 17 * q^38 + 23 * q^39 - 21 * q^40 - 5 * q^41 - 8 * q^42 - 34 * q^43 + 2 * q^44 + 3 * q^45 - 32 * q^46 - 7 * q^47 + 74 * q^48 + 20 * q^49 + 236 * q^50 + 18 * q^51 + 20 * q^52 - 32 * q^53 - q^54 - 17 * q^55 - 39 * q^56 - 8 * q^57 - 53 * q^58 - q^59 - 17 * q^60 + 14 * q^61 - 60 * q^62 + 22 * q^63 - 21 * q^64 - 39 * q^65 - 21 * q^66 - 22 * q^67 - 110 * q^68 - 20 * q^69 - 40 * q^70 + 36 * q^71 + 6 * q^72 - 11 * q^73 - 46 * q^74 - 9 * q^75 - 101 * q^76 - 17 * q^77 + 6 * q^78 - 14 * q^79 - 112 * q^80 - 6 * q^81 + 2 * q^82 + 12 * q^83 - 22 * q^84 - 44 * q^85 + 184 * q^86 - q^87 + 204 * q^88 + 12 * q^89 + 10 * q^90 - 16 * q^91 - 105 * q^92 - 19 * q^93 - 5 * q^94 + 18 * q^95 - 9 * q^96 + 172 * q^97 + q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{7}\right)$

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 $

$2$	−0.385632	+	0.483568i	−0.272683	+	0.341934i	−0.899251	−	0.437433i	$-0.855888\pi$
$2$	−0.385632	+	0.483568i	−0.272683	+	0.341934i	0.626568	+	0.779367i	$0.284459\pi$
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$4$	0.359916	+	1.57690i	0.179958	+	0.788448i
$5$	−3.63892	−	1.75241i	−1.62737	−	0.783702i	−0.999988	−	0.00499272i	$-0.998411\pi$
$5$	−3.63892	−	1.75241i	−1.62737	−	0.783702i	−0.627385	−	0.778709i	$-0.715875\pi$
$6$	0.557255	−	0.268360i	0.227498	−	0.109557i
$7$	−2.64500	−	0.0631583i	−0.999715	−	0.0238716i
$7$	−2.64500	−	0.0631583i	−0.999715	−	0.0238716i
$8$	−2.01584	−	0.970778i	−0.712708	−	0.343222i
$9$	0.623490	+	0.781831i	0.207830	+	0.260610i
$10$	2.25069	−	1.08388i	0.711732	−	0.342752i
$11$	0.0332349	−	0.0416752i	0.0100207	−	0.0125656i	−0.776796	−	0.629752i	$-0.783156\pi$
$11$	0.0332349	−	0.0416752i	0.0100207	−	0.0125656i	0.786817	+	0.617187i	$0.211728\pi$
$12$	0.359916	−	1.57690i	0.103899	−	0.455211i
$13$	−0.237234	+	0.297483i	−0.0657970	+	0.0825068i	−0.813641	−	0.581368i	$-0.802518\pi$
$13$	−0.237234	+	0.297483i	−0.0657970	+	0.0825068i	0.747844	+	0.663875i	$0.231089\pi$
$14$	1.05054	−	1.25468i	0.280768	−	0.335327i
$15$	2.51821	+	3.15773i	0.650199	+	0.815323i
$16$	−1.66773	+	0.803137i	−0.416933	+	0.200784i
$17$	−0.172451	+	0.755556i	−0.0418254	+	0.183249i	−0.991526	−	0.129911i	$-0.958531\pi$
$17$	−0.172451	+	0.755556i	−0.0418254	+	0.183249i	0.949700	+	0.313161i	$0.101388\pi$
$18$	−0.618506			−0.145783
$19$	−4.32244			−0.991637			−0.495818	−	0.868426i	$-0.665132\pi$
$19$	−4.32244			−0.991637			−0.495818	+	0.868426i	$0.665132\pi$
$20$	1.45366	−	6.36892i	0.325049	−	1.42413i
$21$	2.35566	+	1.20453i	0.514046	+	0.262849i
$22$	0.00733635	+	0.0321427i	0.00156412	+	0.00685284i
$23$	−0.445501	−	1.95187i	−0.0928934	−	0.406992i	0.907007	−	0.421116i	$-0.138361\pi$
$23$	−0.445501	−	1.95187i	−0.0928934	−	0.406992i	−0.999900	+	0.0141234i	$0.995504\pi$
$24$	1.39501	+	1.74928i	0.284754	+	0.357071i
$25$	7.05333	+	8.84459i	1.41067	+	1.76892i
$26$	−0.0523677	−	0.229438i	−0.0102702	−	0.0449965i
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$	−0.852384	−	4.19362i	−0.161085	−	0.792520i
$29$	−1.94604	+	8.52617i	−0.361371	+	1.58327i	0.388347	+	0.921513i	$0.373046\pi$
$29$	−1.94604	+	8.52617i	−0.361371	+	1.58327i	−0.749718	+	0.661757i	$0.769811\pi$
$30$	−2.49808			−0.456085
$31$	5.67978			1.02012			0.510059	−	0.860139i	$-0.329623\pi$
$31$	5.67978			1.02012			0.510059	+	0.860139i	$0.329623\pi$
$32$	1.25050	−	5.47882i	0.221060	−	0.968527i
$33$	−0.0480258	+	0.0231280i	−0.00836022	+	0.00402607i
$34$	−0.298860	−	0.374759i	−0.0512541	−	0.0642706i
$35$	9.51425	+	4.86495i	1.60820	+	0.822326i
$36$	−1.00846	+	1.26457i	−0.168077	+	0.210762i
$37$	2.39948	−	10.5128i	0.394472	−	1.72830i	−0.254131	−	0.967170i	$-0.581789\pi$
$37$	2.39948	−	10.5128i	0.394472	−	1.72830i	0.648603	−	0.761127i	$-0.275353\pi$
$38$	1.66687	−	2.09020i	0.270403	−	0.339074i
$39$	0.342814	−	0.165090i	0.0548941	−	0.0264356i
$40$	5.63428	+	7.06516i	0.890858	+	1.11710i
$41$	−1.87432	−	0.902623i	−0.292719	−	0.140966i	0.281761	−	0.959485i	$-0.409081\pi$
$41$	−1.87432	−	0.902623i	−0.292719	−	0.140966i	−0.574480	+	0.818519i	$0.694796\pi$
$42$	−1.49089	+	0.674616i	−0.230049	+	0.104095i
$43$	−6.37201	+	3.06860i	−0.971722	+	0.467956i	−0.851250	−	0.524760i	$-0.824155\pi$
$43$	−6.37201	+	3.06860i	−0.971722	+	0.467956i	−0.120472	+	0.992717i	$0.538441\pi$
$44$	0.0776793	+	0.0374084i	0.0117106	+	0.00563953i
$45$	−0.898738	−	3.93763i	−0.133976	−	0.586987i
$46$	1.11566	+	0.537273i	0.164495	+	0.0792166i
$47$	−6.67934	+	8.37562i	−0.974282	+	1.22171i	0.000830966		1.00000i	$0.499735\pi$
$47$	−6.67934	+	8.37562i	−0.974282	+	1.22171i	−0.975112	+	0.221711i	$0.928836\pi$
$48$	1.85104			0.267175
$49$	6.99202	+	0.334107i	0.998860	+	0.0477296i
$50$	−6.99695			−0.989518
$51$	0.483196	−	0.605909i	0.0676610	−	0.0848442i
$52$	−0.554484	−	0.267025i	−0.0768931	−	0.0370298i
$53$	−1.51990	−	6.65912i	−0.208775	−	0.914701i	−0.965384	−	0.260834i	$-0.916003\pi$
$53$	−1.51990	−	6.65912i	−0.208775	−	0.914701i	0.756609	−	0.653867i	$-0.226855\pi$
$54$	0.557255	+	0.268360i	0.0758328	+	0.0365192i
$55$	−0.193971	+	0.0934116i	−0.0261551	+	0.0125956i
$56$	5.27058	+	2.69502i	0.704312	+	0.360138i
$57$	3.89439	+	1.87544i	0.515824	+	0.248408i
$58$	−3.37252	−	4.22901i	−0.442834	−	0.555297i
$59$	−6.38163	+	3.07323i	−0.830817	+	0.400101i	−0.800422	−	0.599437i	$-0.795391\pi$
$59$	−6.38163	+	3.07323i	−0.830817	+	0.400101i	−0.0303958	+	0.999538i	$0.509677\pi$
$60$	−4.07308	+	5.10748i	−0.525832	+	0.659372i
$61$	1.24542	−	5.45654i	0.159460	−	0.698638i	−0.830468	−	0.557066i	$-0.811927\pi$
$61$	1.24542	−	5.45654i	0.159460	−	0.698638i	0.989928	−	0.141572i	$-0.0452158\pi$
$62$	−2.19031	+	2.74656i	−0.278169	+	0.348813i
$63$	−1.59975	−	2.10732i	−0.201550	−	0.265497i
$64$	−0.141068	−	0.176894i	−0.0176336	−	0.0221118i
$65$	1.38459	−	0.666783i	0.171737	−	0.0827042i
$66$	0.00733635	−	0.0321427i	0.000903042	−	0.00395649i
$67$	−10.4126			−1.27210			−0.636049	−	0.771649i	$-0.719432\pi$
$67$	−10.4126			−1.27210			−0.636049	+	0.771649i	$0.719432\pi$
$68$	−1.25350			−0.152009
$69$	−0.445501	+	1.95187i	−0.0536320	+	0.234977i
$70$	−6.02153	+	2.72470i	−0.719711	+	0.325664i
$71$	−2.39721	−	10.5029i	−0.284496	−	1.24646i	−0.891961	−	0.452113i	$-0.850671\pi$
$71$	−2.39721	−	10.5029i	−0.284496	−	1.24646i	0.607465	−	0.794347i	$-0.292187\pi$
$72$	−0.497872	−	2.18132i	−0.0586748	−	0.257071i
$73$	−1.54213	−	1.93377i	−0.180493	−	0.226330i	0.683352	−	0.730089i	$-0.260522\pi$
$73$	−1.54213	−	1.93377i	−0.180493	−	0.226330i	−0.863844	+	0.503759i	$0.831950\pi$
$74$	4.15834	+	5.21440i	0.483397	+	0.606161i
$75$	−2.51730	−	11.0290i	−0.290673	−	1.27352i
$76$	−1.55572	−	6.81605i	−0.178453	−	0.781854i
$77$	−0.0905384	+	0.108132i	−0.0103178	+	0.0123228i
$78$	−0.0523677	+	0.229438i	−0.00592948	+	0.0259787i
$79$	−10.7607			−1.21067			−0.605337	−	0.795969i	$-0.706962\pi$
$79$	−10.7607			−1.21067			−0.605337	+	0.795969i	$0.706962\pi$
$80$	7.47616			0.835861
$81$	−0.222521	+	0.974928i	−0.0247245	+	0.108325i
$82$	1.15928	−	0.558278i	0.128021	−	0.0616515i
$83$	0.559861	+	0.702043i	0.0614527	+	0.0770593i	0.811608	−	0.584203i	$-0.198593\pi$
$83$	0.559861	+	0.702043i	0.0614527	+	0.0770593i	−0.750155	+	0.661262i	$0.770021\pi$
$84$	−1.05157	+	4.14816i	−0.114736	+	0.452601i
$85$	1.95158	−	2.44720i	0.211678	−	0.265436i
$86$	0.973378	−	4.26465i	0.104962	−	0.459869i
$87$	5.45269	−	6.83746i	0.584590	−	0.733052i
$88$	−0.107454	+	0.0517470i	−0.0114546	+	0.00551625i
$89$	7.55992	+	9.47984i	0.801350	+	1.00486i	0.999694	+	0.0247285i	$0.00787214\pi$
$89$	7.55992	+	9.47984i	0.801350	+	1.00486i	−0.198344	+	0.980132i	$0.563556\pi$
$90$	2.25069	+	1.08388i	0.237244	+	0.114251i
$91$	0.646273	−	0.771857i	0.0677478	−	0.0809126i
$92$	2.91755	−	1.40502i	0.304176	−	0.146483i
$93$	−5.11731	−	2.46436i	−0.530640	−	0.255543i
$94$	−1.47441	−	6.45983i	−0.152074	−	0.666280i
$95$	15.7290	+	7.57469i	1.61376	+	0.777147i
$96$	−3.50383	+	4.39367i	−0.357609	+	0.448427i
$97$	9.99553			1.01489			0.507446	−	0.861684i	$-0.330590\pi$
$97$	9.99553			1.01489			0.507446	+	0.861684i	$0.330590\pi$
$98$	−2.85791	+	3.25227i	−0.288693	+	0.328529i
$99$	0.0533046			0.00535732
$100$	−11.4084	+	14.3057i	−1.14084	+	1.43057i
$101$	−6.36439	−	3.06493i	−0.633280	−	0.304972i	0.0895657	−	0.995981i	$-0.471452\pi$
$101$	−6.36439	−	3.06493i	−0.633280	−	0.304972i	−0.722846	+	0.691009i	$0.757166\pi$
$102$	0.106662	+	0.467316i	0.0105611	+	0.0462712i
$103$	−16.6568	−	8.02148i	−1.64124	−	0.790380i	−0.999729	−	0.0232665i	$-0.992593\pi$
$103$	−16.6568	−	8.02148i	−1.64124	−	0.790380i	−0.641512	−	0.767113i	$-0.721692\pi$
$104$	0.767017	−	0.369376i	0.0752122	−	0.0362203i
$105$	−6.46122	−	8.51124i	−0.630550	−	0.830612i
$106$	3.80626	+	1.83300i	0.369697	+	0.178037i
$107$	7.11877	+	8.92665i	0.688197	+	0.862972i	0.996080	−	0.0884522i	$-0.0281921\pi$
$107$	7.11877	+	8.92665i	0.688197	+	0.862972i	−0.307883	+	0.951424i	$0.599621\pi$
$108$	1.45727	−	0.701785i	0.140226	−	0.0675293i
$109$	−3.11134	+	3.90149i	−0.298012	+	0.373695i	−0.908182	−	0.418575i	$-0.862530\pi$
$109$	−3.11134	+	3.90149i	−0.298012	+	0.373695i	0.610170	+	0.792270i	$0.291101\pi$
$110$	0.0296307	−	0.129821i	0.00282518	−	0.0123779i
$111$	−6.72320	+	8.43063i	−0.638138	+	0.800200i
$112$	4.46187	−	2.01897i	0.421607	−	0.190774i
$113$	7.46766	+	9.36415i	0.702499	+	0.880905i	0.997207	−	0.0746818i	$-0.0237941\pi$
$113$	7.46766	+	9.36415i	0.702499	+	0.880905i	−0.294709	+	0.955587i	$0.595223\pi$
$114$	−2.40870	+	1.15997i	−0.225596	+	0.108641i
$115$	−1.79933	+	7.88338i	−0.167788	+	0.735129i
$116$	−14.1453			−1.31336
$117$	−0.380495			−0.0351767
$118$	0.974848	−	4.27109i	0.0897420	−	0.393186i
$119$	0.503851	−	1.98755i	0.0461880	−	0.182199i
$120$	−2.01085	−	8.81012i	−0.183565	−	0.804250i
$121$	2.44710	+	10.7214i	0.222463	+	0.974676i
$122$	2.15833	+	2.70646i	0.195406	+	0.245032i
$123$	1.29707	+	1.62647i	0.116953	+	0.146654i
$124$	2.04425	+	8.95643i	0.183579	+	0.804311i
$125$	−5.67342	−	24.8569i	−0.507447	−	2.22327i
$126$	1.63595	+	0.0390638i	0.145742	+	0.00348008i
$127$	0.318999	−	1.39762i	0.0283065	−	0.124019i	−0.958801	−	0.284080i	$-0.908312\pi$
$127$	0.318999	−	1.39762i	0.0283065	−	0.124019i	0.987107	+	0.160061i	$0.0511690\pi$
$128$	11.3794			1.00580
$129$	7.07239			0.622689
$130$	−0.211508	+	0.926675i	−0.0185504	+	0.0812748i
$131$	−4.69568	+	2.26132i	−0.410263	+	0.197572i	−0.627620	−	0.778520i	$-0.715971\pi$
$131$	−4.69568	+	2.26132i	−0.410263	+	0.197572i	0.217357	+	0.976092i	$0.430257\pi$
$132$	−0.0537558	−	0.0674076i	−0.00467884	−	0.00586708i
$133$	11.4329	+	0.272998i	0.991354	+	0.0236720i
$134$	4.01543	−	5.03518i	0.346880	−	0.434974i
$135$	−0.898738	+	3.93763i	−0.0773511	+	0.338897i
$136$	1.08111	−	1.35567i	0.0927045	−	0.116248i
$137$	3.02721	−	1.45783i	0.258632	−	0.124551i	−0.300075	−	0.953916i	$-0.597012\pi$
$137$	3.02721	−	1.45783i	0.258632	−	0.124551i	0.558707	+	0.829365i	$0.311298\pi$
$138$	−0.772060	−	0.968133i	−0.0657221	−	0.0824130i
$139$	15.7861	+	7.60220i	1.33896	+	0.644810i	0.959843	−	0.280538i	$-0.0905129\pi$
$139$	15.7861	+	7.60220i	1.33896	+	0.644810i	0.379119	+	0.925348i	$0.376227\pi$
$140$	−4.24719	+	16.7540i	−0.358953	+	1.41597i
$141$	9.65192	−	4.64812i	0.812839	−	0.391442i
$142$	6.00328	+	2.89103i	0.503784	+	0.242610i
$143$	0.00451320	+	0.0197736i	0.000377413	+	0.00165355i
$144$	−1.66773	−	0.803137i	−0.138978	−	0.0669281i
$145$	22.0228	−	27.6158i	1.82890	−	2.29336i
$146$	1.52980			0.126607
$147$	−6.15463	−	3.33474i	−0.507625	−	0.275045i
$148$	17.4412			1.43366
$149$	10.1445	−	12.7208i	0.831071	−	1.04213i	−0.167347	−	0.985898i	$-0.553520\pi$
$149$	10.1445	−	12.7208i	0.831071	−	1.04213i	0.998418	−	0.0562321i	$-0.0179087\pi$
$150$	6.30403	+	3.03586i	0.514722	+	0.247877i
$151$	−1.07032	−	4.68939i	−0.0871017	−	0.381617i	0.912523	−	0.409026i	$-0.134132\pi$
$151$	−1.07032	−	4.68939i	−0.0871017	−	0.381617i	−0.999624	+	0.0274088i	$0.991274\pi$
$152$	8.71337	+	4.19614i	0.706747	+	0.340352i
$153$	−0.698239	+	0.336254i	−0.0564493	+	0.0271845i
$154$	−0.0173746	−	0.0854806i	−0.00140008	−	0.00688822i
$155$	−20.6682	−	9.95330i	−1.66011	−	0.799469i
$156$	0.383715	+	0.481163i	0.0307218	+	0.0385239i
$157$	−5.04259	+	2.42838i	−0.402442	+	0.193806i	−0.624145	−	0.781308i	$-0.714553\pi$
$157$	−5.04259	+	2.42838i	−0.402442	+	0.193806i	0.221703	+	0.975114i	$0.428838\pi$
$158$	4.14968	−	5.20353i	0.330131	−	0.413971i
$159$	−1.51990	+	6.65912i	−0.120536	+	0.528103i
$160$	−14.1516	+	17.7456i	−1.11878	+	1.40291i
$161$	1.05507	+	5.19082i	0.0831513	+	0.409094i
$162$	−0.385632	−	0.483568i	−0.0302981	−	0.0379927i
$163$	2.40582	−	1.15858i	0.188438	−	0.0907472i	−0.337286	−	0.941402i	$-0.609509\pi$
$163$	2.40582	−	1.15858i	0.188438	−	0.0907472i	0.525724	+	0.850655i	$0.323794\pi$
$164$	0.748746	−	3.28047i	0.0584672	−	0.256162i
$165$	0.215292			0.0167604
$166$	−0.555386			−0.0431063
$167$	−3.32240	+	14.5564i	−0.257095	+	1.12641i	0.667245	+	0.744839i	$0.267474\pi$
$167$	−3.32240	+	14.5564i	−0.257095	+	1.12641i	−0.924340	+	0.381570i	$0.875384\pi$
$168$	−3.57931	−	4.71495i	−0.276149	−	0.363767i
$169$	2.86056	+	12.5329i	0.220043	+	0.964071i
$170$	0.430796	+	1.88744i	0.0330405	+	0.144760i
$171$	−2.69500	−	3.37942i	−0.206092	−	0.258431i
$172$	−7.13225	−	8.94356i	−0.543829	−	0.681940i
$173$	0.900408	+	3.94494i	0.0684567	+	0.299929i	0.997553	−	0.0699084i	$-0.0222707\pi$
$173$	0.900408	+	3.94494i	0.0684567	+	0.299929i	−0.929097	+	0.369837i	$0.879414\pi$
$174$	1.20364	+	5.27349i	0.0912477	+	0.399782i
$175$	−18.0974	−	23.8394i	−1.36804	−	1.80209i
$176$	−0.0219560	+	0.0961953i	−0.00165499	+	0.00725100i
$177$	7.08307			0.532396
$178$	−7.49950			−0.562111
$179$	1.10290	−	4.83214i	0.0824350	−	0.361171i	−0.916840	−	0.399256i	$-0.869269\pi$
$179$	1.10290	−	4.83214i	0.0824350	−	0.361171i	0.999275	+	0.0380847i	$0.0121257\pi$
$180$	5.88576	−	2.83443i	0.438699	−	0.211266i
$181$	−8.04779	−	10.0916i	−0.598188	−	0.750104i	0.386906	−	0.922119i	$-0.373544\pi$
$181$	−8.04779	−	10.0916i	−0.598188	−	0.750104i	−0.985094	+	0.172015i	$0.944972\pi$
$182$	0.124022	+	0.610170i	0.00919309	+	0.0452288i
$183$	−3.48959	+	4.37581i	−0.257958	+	0.323469i
$184$	−0.996771	+	4.36714i	−0.0734829	+	0.321950i
$185$	−27.1543	+	34.0504i	−1.99642	+	2.50343i
$186$	3.16509	−	1.52423i	0.232075	−	0.111762i
$187$	0.0257566	+	0.0322977i	0.00188351	+	0.00236185i
$188$	−15.6115	−	7.51810i	−1.13859	−	0.548314i
$189$	0.526992	+	2.59274i	0.0383331	+	0.188594i
$190$	−9.72850	+	4.68500i	−0.705779	+	0.339885i
$191$	1.39236	+	0.670526i	0.100748	+	0.0485175i	0.483579	−	0.875301i	$-0.339337\pi$
$191$	1.39236	+	0.670526i	0.100748	+	0.0485175i	−0.382831	+	0.923818i	$0.625051\pi$
$192$	0.0503467	+	0.220584i	0.00363346	+	0.0159192i
$193$	−13.5003	−	6.50139i	−0.971771	−	0.467980i	−0.120504	−	0.992713i	$-0.538451\pi$
$193$	−13.5003	−	6.50139i	−0.971771	−	0.467980i	−0.851267	+	0.524732i	$0.824165\pi$
$194$	−3.85460	+	4.83351i	−0.276744	+	0.347026i
$195$	−1.53678			−0.110051
$196$	1.98969	+	11.1459i	0.142121	+	0.796139i
$197$	−8.90428			−0.634403			−0.317202	−	0.948358i	$-0.602743\pi$
$197$	−8.90428			−0.634403			−0.317202	+	0.948358i	$0.602743\pi$
$198$	−0.0205560	+	0.0257764i	−0.00146085	+	0.00183185i
$199$	12.6578	+	6.09570i	0.897291	+	0.432112i	0.824910	−	0.565265i	$-0.191226\pi$
$199$	12.6578	+	6.09570i	0.897291	+	0.432112i	0.0723811	+	0.997377i	$0.476940\pi$
$200$	−5.63225	−	24.6765i	−0.398260	−	1.74489i
$201$	9.38140	+	4.51785i	0.661713	+	0.318664i
$202$	3.93642	−	1.89568i	0.276965	−	0.133379i
$203$	5.68578	−	22.4288i	0.399063	−	1.57419i
$204$	1.12937	+	0.543874i	0.0790714	+	0.0380788i
$205$	5.23871	+	6.56914i	0.365888	+	0.458809i
$206$	10.3023	−	4.96134i	0.717797	−	0.345673i
$207$	1.24827	−	1.56528i	0.0867605	−	0.108794i
$208$	0.156724	−	0.686653i	0.0108669	−	0.0476108i
$209$	−0.143656	+	0.180139i	−0.00993689	+	0.0124605i
$210$	6.60742	+	0.157775i	0.455955	+	0.0108875i
$211$	−8.27635	−	10.3782i	−0.569767	−	0.714466i	0.410562	−	0.911832i	$-0.365332\pi$
$211$	−8.27635	−	10.3782i	−0.569767	−	0.714466i	−0.980330	+	0.197367i	$0.936761\pi$
$212$	9.95371	−	4.79346i	0.683624	−	0.329216i
$213$	−2.39721	+	10.5029i	−0.164254	+	0.719644i
$214$	−7.06187			−0.482739
$215$	28.5646			1.94809
$216$	−0.497872	+	2.18132i	−0.0338759	+	0.148420i
$217$	−15.0230	−	0.358726i	−1.01983	−	0.0243519i
$218$	−0.686804	−	3.00909i	−0.0465163	−	0.203801i
$219$	0.550379	+	2.41137i	0.0371912	+	0.162945i
$220$	−0.217114	−	0.272252i	−0.0146378	−	0.0183552i
$221$	−0.183854	−	0.230545i	−0.0123673	−	0.0155081i
$222$	−1.48410	−	6.50225i	−0.0996059	−	0.436402i
$223$	3.51294	+	15.3912i	0.235244	+	1.03067i	0.945217	+	0.326442i	$0.105850\pi$
$223$	3.51294	+	15.3912i	0.235244	+	1.03067i	−0.709973	+	0.704228i	$0.751293\pi$
$224$	−3.65361	+	14.4125i	−0.244117	+	0.962974i
$225$	−2.51730	+	11.0290i	−0.167820	+	0.735268i
$226$	−7.40798			−0.492771
$227$	−15.9623			−1.05946			−0.529729	−	0.848167i	$-0.677706\pi$
$227$	−15.9623			−1.05946			−0.529729	+	0.848167i	$0.677706\pi$
$228$	−1.55572	+	6.81605i	−0.103030	+	0.451404i
$229$	−7.76409	+	3.73899i	−0.513066	+	0.247079i	−0.672457	−	0.740136i	$-0.734761\pi$
$229$	−7.76409	+	3.73899i	−0.513066	+	0.247079i	0.159392	+	0.987215i	$0.449047\pi$
$230$	−3.11827	−	3.91019i	−0.205613	−	0.257830i
$231$	0.128489	−	0.0581403i	0.00845395	−	0.00382535i
$232$	12.1999	−	15.2982i	0.800965	−	1.00438i
$233$	1.22070	−	5.34823i	0.0799706	−	0.350374i	−0.919074	−	0.394086i	$-0.871061\pi$
$233$	1.22070	−	5.34823i	0.0799706	−	0.350374i	0.999044	+	0.0437119i	$0.0139184\pi$
$234$	0.146731	−	0.183995i	0.00959211	−	0.0120281i
$235$	38.9831	−	18.7733i	2.54298	−	1.22463i
$236$	−7.14302	−	8.95707i	−0.464971	−	0.583055i
$237$	9.69506	+	4.66889i	0.629762	+	0.303277i
$238$	0.766815	+	1.01011i	0.0497052	+	0.0654758i
$239$	−4.76555	+	2.29497i	−0.308258	+	0.148449i	−0.581617	−	0.813463i	$-0.697580\pi$
$239$	−4.76555	+	2.29497i	−0.308258	+	0.148449i	0.273359	+	0.961912i	$0.411865\pi$
$240$	−6.73579	−	3.24379i	−0.434793	−	0.209385i
$241$	−0.149391	−	0.654524i	−0.00962310	−	0.0421616i	0.969888	−	0.243550i	$-0.0783119\pi$
$241$	−0.149391	−	0.654524i	−0.00962310	−	0.0421616i	−0.979512	+	0.201388i	$0.935455\pi$
$242$	−6.12822	−	2.95120i	−0.393937	−	0.189710i
$243$	0.623490	−	0.781831i	0.0399969	−	0.0501545i
$244$	9.05265			0.579536
$245$	−24.8579	−	13.4687i	−1.58811	−	0.860482i
$246$	−1.28670			−0.0820370
$247$	1.02543	−	1.28585i	0.0652467	−	0.0818168i
$248$	−11.4495	−	5.51381i	−0.727047	−	0.350127i
$249$	−0.199812	−	0.875434i	−0.0126626	−	0.0554784i
$250$	14.2079	+	6.84214i	0.898584	+	0.432735i
$251$	−9.37828	+	4.51634i	−0.591952	+	0.285069i	−0.705780	−	0.708431i	$-0.749403\pi$
$251$	−9.37828	+	4.51634i	−0.591952	+	0.285069i	0.113828	+	0.993501i	$0.463689\pi$
$252$	2.74725	−	3.28110i	0.173061	−	0.206690i
$253$	−0.0961507	−	0.0463037i	−0.00604494	−	0.00291109i
$254$	0.552830	+	0.693227i	0.0346876	+	0.0434969i
$255$	−2.82011	+	1.35809i	−0.176602	+	0.0850471i
$256$	−4.10612	+	5.14891i	−0.256632	+	0.321807i
$257$	0.883387	−	3.87037i	0.0551041	−	0.241427i	−0.939874	−	0.341522i	$-0.889058\pi$
$257$	0.883387	−	3.87037i	0.0551041	−	0.241427i	0.994978	+	0.100095i	$0.0319147\pi$
$258$	−2.72734	+	3.41998i	−0.169797	+	0.212919i
$259$	−7.01060	+	27.6548i	−0.435617	+	1.71839i
$260$	1.54978	+	1.94337i	0.0961135	+	0.120522i
$261$	−7.87937	+	3.79450i	−0.487721	+	0.234874i
$262$	0.717305	−	3.14272i	0.0443152	−	0.194158i
$263$	6.59671			0.406771			0.203385	−	0.979099i	$-0.434806\pi$
$263$	6.59671			0.406771			0.203385	+	0.979099i	$0.434806\pi$
$264$	0.119265			0.00734023
$265$	−6.13872	+	26.8955i	−0.377098	+	1.65218i
$266$	−4.54089	+	5.42328i	−0.278420	+	0.332523i
$267$	−2.69810	−	11.8212i	−0.165121	−	0.723444i
$268$	−3.74766	−	16.4196i	−0.228924	−	1.00298i
$269$	−13.9706	−	17.5186i	−0.851804	−	1.06813i	−0.996898	−	0.0787100i	$-0.974920\pi$
$269$	−13.9706	−	17.5186i	−0.851804	−	1.06813i	0.145094	−	0.989418i	$-0.453652\pi$
$270$	−1.55753	−	1.95308i	−0.0947882	−	0.118861i
$271$	0.933332	+	4.08919i	0.0566959	+	0.248401i	0.995332	−	0.0965074i	$-0.0307672\pi$
$271$	0.933332	+	4.08919i	0.0566959	+	0.248401i	−0.938636	+	0.344908i	$0.887910\pi$
$272$	−0.319214	−	1.39857i	−0.0193552	−	0.0848006i
$273$	−0.917168	+	0.415012i	−0.0555096	+	0.0251177i
$274$	−0.462432	+	2.02605i	−0.0279365	+	0.122398i
$275$	0.603017			0.0363633
$276$	−3.23824			−0.194919
$277$	−4.48945	+	19.6696i	−0.269745	+	1.18183i	0.640566	+	0.767904i	$0.278700\pi$
$277$	−4.48945	+	19.6696i	−0.269745	+	1.18183i	−0.910310	+	0.413926i	$0.864157\pi$
$278$	−9.76382	+	4.70201i	−0.585595	+	0.282008i
$279$	3.54129	+	4.44063i	0.212011	+	0.265854i
$280$	−14.4564	−	19.0432i	−0.863937	−	1.13805i
$281$	10.7077	−	13.4270i	0.638767	−	0.800988i	−0.352081	−	0.935969i	$-0.614526\pi$
$281$	10.7077	−	13.4270i	0.638767	−	0.800988i	0.990848	+	0.134981i	$0.0430974\pi$
$282$	−1.47441	+	6.45983i	−0.0878000	+	0.384677i
$283$	6.91185	−	8.66719i	0.410867	−	0.515211i	−0.532740	−	0.846279i	$-0.678838\pi$
$283$	6.91185	−	8.66719i	0.410867	−	0.515211i	0.943607	+	0.331068i	$0.107409\pi$
$284$	15.6991	−	7.56030i	0.931572	−	0.448621i
$285$	−10.8848	−	13.6491i	−0.644761	−	0.808505i
$286$	−0.0113023	−	0.00544291i	−0.000668320	−	0.000321846i
$287$	4.90055	+	2.50581i	0.289270	+	0.147913i
$288$	5.06319	−	2.43830i	0.298351	−	0.143678i
$289$	14.7753	+	7.11543i	0.869138	+	0.418555i
$290$	4.86137	+	21.2991i	0.285470	+	1.25072i
$291$	−9.00566	−	4.33690i	−0.527921	−	0.254233i
$292$	2.49432	−	3.12777i	0.145969	−	0.183039i
$293$	32.7132			1.91112			0.955562	−	0.294791i	$-0.0952501\pi$
$293$	32.7132			1.91112			0.955562	+	0.294791i	$0.0952501\pi$
$294$	3.98600	−	1.69020i	0.232468	−	0.0985742i
$295$	28.6078			1.66561
$296$	−15.0426	+	18.8628i	−0.874333	+	1.09638i
$297$	−0.0480258	−	0.0231280i	−0.00278674	−	0.00134202i
$298$	2.23932	+	9.81112i	0.129721	+	0.568343i
$299$	0.686335	+	0.330521i	0.0396918	+	0.0191145i
$300$	16.4856	−	7.93905i	0.951797	−	0.458361i
$301$	17.0477	−	7.71398i	0.982616	−	0.444627i
$302$	2.68039	+	1.29081i	0.154239	+	0.0742777i
$303$	4.40429	+	5.52281i	0.253020	+	0.317277i
$304$	7.20868	−	3.47152i	0.413446	−	0.199105i
$305$	−14.0941	+	17.6734i	−0.807024	+	1.01198i
$306$	0.106662	−	0.467316i	0.00609745	−	0.0267147i
$307$	−3.38992	+	4.25082i	−0.193473	+	0.242607i	−0.869100	−	0.494636i	$-0.835301\pi$
$307$	−3.38992	+	4.25082i	−0.193473	+	0.242607i	0.675627	+	0.737243i	$0.263873\pi$
$308$	−0.203099	−	0.103851i	−0.0115726	−	0.00591747i
$309$	11.5268	+	14.4542i	0.655739	+	0.822271i
$310$	12.7834	−	6.15618i	0.726051	−	0.349648i
$311$	3.05055	−	13.3654i	0.172981	−	0.757880i	−0.811779	−	0.583964i	$-0.801501\pi$
$311$	3.05055	−	13.3654i	0.172981	−	0.757880i	0.984761	−	0.173916i	$-0.0556420\pi$
$312$	−0.851325			−0.0481968
$313$	−22.0195			−1.24462			−0.622309	−	0.782772i	$-0.713805\pi$
$313$	−22.0195			−1.24462			−0.622309	+	0.782772i	$0.713805\pi$
$314$	0.770298	−	3.37490i	0.0434704	−	0.190456i
$315$	2.12847	+	10.4718i	0.119925	+	0.590018i
$316$	−3.87295	−	16.9685i	−0.217871	−	0.954554i
$317$	2.21593	+	9.70861i	0.124459	+	0.545290i	0.998258	+	0.0590026i	$0.0187920\pi$
$317$	2.21593	+	9.70861i	0.124459	+	0.545290i	−0.873799	+	0.486287i	$0.838351\pi$
$318$	−2.63401	−	3.30295i	−0.147708	−	0.185220i
$319$	0.290654	+	0.364468i	0.0162735	+	0.0204063i
$320$	0.203345	+	0.890913i	0.0113673	+	0.0498036i
$321$	−2.54066	−	11.1314i	−0.141806	−	0.621291i
$322$	−2.91698	−	1.49155i	−0.162557	−	0.0831208i
$323$	0.745409	−	3.26585i	0.0414756	−	0.181717i
$324$	−1.61745			−0.0898583
$325$	−4.30440			−0.238765
$326$	−0.367510	+	1.61016i	−0.0203545	+	0.0891788i
$327$	4.49601	−	2.16517i	0.248630	−	0.119734i
$328$	2.90208	+	3.63909i	0.160240	+	0.200935i
$329$	18.1958	−	21.7316i	1.00317	−	1.19810i
$330$	−0.0830235	+	0.104108i	−0.00457029	+	0.00573096i
$331$	4.61336	−	20.2124i	0.253573	−	1.11098i	−0.674411	−	0.738356i	$-0.735602\pi$
$331$	4.61336	−	20.2124i	0.253573	−	1.11098i	0.927984	−	0.372620i	$-0.121540\pi$
$332$	−0.905547	+	1.13552i	−0.0496983	+	0.0623197i
$333$	9.71530	−	4.67864i	0.532395	−	0.256388i
$334$	−5.75778	−	7.22003i	−0.315052	−	0.395062i
$335$	37.8905	+	18.2471i	2.07018	+	0.996945i
$336$	−4.89600	−	0.116909i	−0.267099	−	0.00637790i
$337$	−19.6965	+	9.48533i	−1.07294	+	0.516699i	−0.885052	−	0.465492i	$-0.845877\pi$
$337$	−19.6965	+	9.48533i	−1.07294	+	0.516699i	−0.187885	+	0.982191i	$0.560163\pi$
$338$	−7.16364	−	3.44983i	−0.389651	−	0.187646i
$339$	−2.66518	−	11.6769i	−0.144753	−	0.634202i
$340$	4.56139	+	2.19665i	0.247376	+	0.119130i
$341$	0.188767	−	0.236706i	0.0102223	−	0.0128184i
$342$	2.67346			0.144564
$343$	−18.4728	−	1.32532i	−0.997436	−	0.0715604i
$344$	15.8239			0.853167
$345$	5.04161	−	6.32198i	0.271431	−	0.340364i
$346$	−2.25487	−	1.08589i	−0.121223	−	0.0583778i
$347$	−2.04869	−	8.97591i	−0.109980	−	0.481852i	−0.999680	−	0.0253068i	$-0.991944\pi$
$347$	−2.04869	−	8.97591i	−0.109980	−	0.481852i	0.889700	−	0.456545i	$-0.150913\pi$
$348$	12.7445	+	6.13742i	0.683176	+	0.329000i
$349$	−30.1787	+	14.5333i	−1.61543	+	0.777950i	−0.999948	−	0.0102001i	$-0.996753\pi$
$349$	−30.1787	+	14.5333i	−1.61543	+	0.777950i	−0.615483	+	0.788150i	$0.711039\pi$
$350$	18.5069	+	0.441916i	0.989236	+	0.0236214i
$351$	0.342814	+	0.165090i	0.0182980	+	0.00881187i
$352$	−0.186771	−	0.234203i	−0.00995491	−	0.0124831i
$353$	−4.69848	+	2.26267i	−0.250075	+	0.120430i	−0.554723	−	0.832035i	$-0.687176\pi$
$353$	−4.69848	+	2.26267i	−0.250075	+	0.120430i	0.304648	+	0.952465i	$0.401461\pi$
$354$	−2.73146	+	3.42515i	−0.145176	+	0.182045i
$355$	−9.68207	+	42.4199i	−0.513871	+	2.25141i
$356$	−12.2278	+	15.3332i	−0.648072	+	0.812656i
$357$	−1.31632	+	1.57211i	−0.0696671	+	0.0832048i
$358$	1.91135	+	2.39676i	0.101018	+	0.126673i
$359$	−14.7239	+	7.09065i	−0.777097	+	0.374230i	−0.780011	−	0.625766i	$-0.784787\pi$
$359$	−14.7239	+	7.09065i	−0.777097	+	0.374230i	0.00291421	+	0.999996i	$0.499072\pi$
$360$	−2.01085	+	8.81012i	−0.105981	+	0.464334i
$361$	−0.316475			−0.0166566
$362$	7.98347			0.419602
$363$	2.44710	−	10.7214i	0.128439	−	0.562729i
$364$	1.44974	+	0.741302i	0.0759872	+	0.0388548i
$365$	2.22292	+	9.73926i	0.116353	+	0.509776i
$366$	−0.770300	−	3.37491i	−0.0402642	−	0.176409i
$367$	−2.85353	−	3.57822i	−0.148953	−	0.186781i	0.701757	−	0.712416i	$-0.252399\pi$
$367$	−2.85353	−	3.57822i	−0.148953	−	0.186781i	−0.850710	+	0.525635i	$0.823828\pi$
$368$	2.31059	+	2.89739i	0.120448	+	0.151037i
$369$	−0.462918	−	2.02817i	−0.0240985	−	0.105583i
$370$	−5.99410	−	26.2619i	−0.311618	−	1.36529i
$371$	3.59956	+	17.7094i	0.186880	+	0.919424i
$372$	2.04425	−	8.95643i	0.105989	−	0.464369i
$373$	24.5427			1.27077			0.635387	−	0.772194i	$-0.280841\pi$
$373$	24.5427			1.27077			0.635387	+	0.772194i	$0.280841\pi$
$374$	−0.0255507			−0.00132120
$375$	−5.67342	+	24.8569i	−0.292974	+	1.28360i
$376$	21.5954	−	10.3998i	1.11370	−	0.536328i
$377$	−2.07472	−	2.60162i	−0.106853	−	0.133990i
$378$	−1.45699	−	0.745007i	−0.0749394	−	0.0383190i
$379$	−2.14950	+	2.69539i	−0.110412	+	0.138453i	−0.833967	−	0.551815i	$-0.813936\pi$
$379$	−2.14950	+	2.69539i	−0.110412	+	0.138453i	0.723555	+	0.690267i	$0.242507\pi$
$380$	−6.28338	+	27.5293i	−0.322331	+	1.41222i
$381$	−0.893814	+	1.12081i	−0.0457915	+	0.0574207i
$382$	−0.861184	+	0.414724i	−0.0440620	+	0.0212191i
$383$	−17.0160	−	21.3374i	−0.869476	−	1.09029i	−0.995165	−	0.0982187i	$-0.968686\pi$
$383$	−17.0160	−	21.3374i	−0.869476	−	1.09029i	0.125689	−	0.992070i	$-0.459886\pi$
$384$	−10.2525	−	4.93732i	−0.523194	−	0.251957i
$385$	0.518953	−	0.234822i	0.0264483	−	0.0119677i
$386$	8.35001	−	4.02115i	0.425004	−	0.204671i
$387$	−6.37201	−	3.06860i	−0.323907	−	0.155985i
$388$	3.59755	+	15.7619i	0.182638	+	0.800190i
$389$	−5.02221	−	2.41857i	−0.254636	−	0.122626i	0.302212	−	0.953241i	$-0.402275\pi$
$389$	−5.02221	−	2.41857i	−0.254636	−	0.122626i	−0.556848	+	0.830615i	$0.687989\pi$
$390$	0.592631	−	0.743136i	0.0300090	−	0.0376301i
$391$	1.55157			0.0784663
$392$	−13.7705	−	7.46121i	−0.695514	−	0.376848i
$393$	5.21181			0.262901
$394$	3.43378	−	4.30582i	0.172991	−	0.216924i
$395$	39.1573	+	18.8572i	1.97022	+	0.948807i
$396$	0.0191852	+	0.0840559i	0.000964093	+	0.00422397i
$397$	−1.96250	−	0.945088i	−0.0984948	−	0.0474326i	0.383988	−	0.923338i	$-0.374551\pi$
$397$	−1.96250	−	0.945088i	−0.0984948	−	0.0474326i	−0.482483	+	0.875906i	$0.660265\pi$
$398$	−7.82896	+	3.77023i	−0.392430	+	0.188984i
$399$	−10.1822	−	5.20649i	−0.509747	−	0.260651i
$400$	−18.8665	−	9.08562i	−0.943324	−	0.454281i
$401$	−0.819337	−	1.02742i	−0.0409157	−	0.0513067i	0.760953	−	0.648807i	$-0.224732\pi$
$401$	−0.819337	−	1.02742i	−0.0409157	−	0.0513067i	−0.801868	+	0.597501i	$0.796161\pi$
$402$	−5.80246	+	2.79432i	−0.289400	+	0.139368i
$403$	−1.34744	+	1.68964i	−0.0671208	+	0.0841668i
$404$	2.54243	−	11.1391i	0.126490	−	0.554191i
$405$	2.51821	−	3.15773i	0.125131	−	0.156909i
$406$	8.65322	+	11.3987i	0.429452	+	0.565709i
$407$	−0.358378	−	0.449391i	−0.0177641	−	0.0222755i
$408$	−1.56225	+	0.752340i	−0.0773429	+	0.0372464i
$409$	3.02377	−	13.2480i	0.149516	−	0.655071i	−0.843504	−	0.537123i	$-0.819511\pi$
$409$	3.02377	−	13.2480i	0.149516	−	0.655071i	0.993020	−	0.117948i	$-0.0376317\pi$
$410$	−5.19684			−0.256654
$411$	−3.35995			−0.165734
$412$	6.65400	−	29.1531i	0.327819	−	1.43627i
$413$	17.0735	−	7.72563i	0.840132	−	0.380154i
$414$	0.275545	+	1.20724i	0.0135423	+	0.0593327i
$415$	−0.807019	−	3.53578i	−0.0396150	−	0.173565i
$416$	1.33319	+	1.67177i	0.0653650	+	0.0819651i
$417$	−10.9243	−	13.6987i	−0.534967	−	0.670828i
$418$	−0.0317110	−	0.138935i	−0.00155103	−	0.00679552i
$419$	−4.25773	−	18.6544i	−0.208004	−	0.911325i	−0.965893	−	0.258941i	$-0.916626\pi$
$419$	−4.25773	−	18.6544i	−0.208004	−	0.911325i	0.757889	−	0.652383i	$-0.226231\pi$
$420$	11.0959	−	13.2520i	0.541422	−	0.646632i
$421$	1.32787	−	5.81777i	0.0647163	−	0.283541i	−0.932207	−	0.361926i	$-0.882119\pi$
$421$	1.32787	−	5.81777i	0.0647163	−	0.283541i	0.996923	+	0.0783853i	$0.0249764\pi$
$422$	8.21020			0.399666
$423$	−10.7128			−0.520875
$424$	−3.40065	+	14.8992i	−0.165150	+	0.723571i
$425$	−7.89893	+	3.80393i	−0.383155	+	0.184518i
$426$	−4.15440	−	5.20945i	−0.201281	−	0.252399i
$427$	−3.63876	+	14.3539i	−0.176092	+	0.694633i
$428$	−11.5142	+	14.4384i	−0.556562	+	0.697907i
$429$	0.00451320	−	0.0197736i	0.000217899	−	0.000954679i
$430$	−11.0155	+	13.8129i	−0.531212	+	0.666119i
$431$	−5.39828	+	2.59968i	−0.260026	+	0.125222i	−0.559356	−	0.828928i	$-0.688951\pi$
$431$	−5.39828	+	2.59968i	−0.260026	+	0.125222i	0.299329	+	0.954150i	$0.403237\pi$
$432$	1.15411	+	1.44720i	0.0555270	+	0.0696286i
$433$	−5.67798	−	2.73437i	−0.272866	−	0.131406i	0.292447	−	0.956282i	$-0.405530\pi$
$433$	−5.67798	−	2.73437i	−0.272866	−	0.131406i	−0.565313	+	0.824876i	$0.691245\pi$
$434$	5.96683	−	7.12631i	0.286417	−	0.342074i
$435$	−31.8239	+	15.3256i	−1.52584	+	0.734806i
$436$	−7.27208	−	3.50205i	−0.348269	−	0.167718i
$437$	1.92565	+	8.43684i	0.0921165	+	0.403589i
$438$	−1.37831	−	0.663757i	−0.0658580	−	0.0317155i
$439$	−1.98987	+	2.49521i	−0.0949711	+	0.119090i	−0.827046	−	0.562134i	$-0.809981\pi$
$439$	−1.98987	+	2.49521i	−0.0949711	+	0.119090i	0.732075	+	0.681224i	$0.238552\pi$
$440$	0.481697			0.0229640
$441$	4.09824	+	5.67490i	0.195154	+	0.270233i
$442$	0.182384			0.00867512
$443$	18.5532	−	23.2650i	0.881491	−	1.10535i	−0.112254	−	0.993680i	$-0.535807\pi$
$443$	18.5532	−	23.2650i	0.881491	−	1.10535i	0.993745	−	0.111675i	$-0.0356215\pi$
$444$	−15.7140	−	7.56747i	−0.745754	−	0.359136i
$445$	−10.8974	−	47.7444i	−0.516584	−	2.26330i
$446$	−8.79739	−	4.23660i	−0.416568	−	0.200609i
$447$	−14.6593	+	7.05952i	−0.693359	+	0.333904i
$448$	0.361953	+	0.476794i	0.0171007	+	0.0225264i
$449$	−27.0875	−	13.0446i	−1.27834	−	0.615614i	−0.333375	−	0.942794i	$-0.608187\pi$
$449$	−27.0875	−	13.0446i	−1.27834	−	0.615614i	−0.944962	+	0.327180i	$0.893902\pi$
$450$	−4.36253	−	5.47044i	−0.205652	−	0.257879i
$451$	−0.0999097	+	0.0481140i	−0.00470456	+	0.00226560i
$452$	−12.0786	+	15.1460i	−0.568128	+	0.712410i
$453$	−1.07032	+	4.68939i	−0.0502882	+	0.220327i
$454$	6.15560	−	7.71888i	0.288897	−	0.362265i
$455$	−3.70434	+	1.67619i	−0.173662	+	0.0785810i
$456$	−6.02984	−	7.56118i	−0.282373	−	0.354084i
$457$	−26.6941	+	12.8552i	−1.24870	+	0.601340i	−0.937162	−	0.348895i	$-0.886557\pi$
$457$	−26.6941	+	12.8552i	−1.24870	+	0.601340i	−0.311533	+	0.950235i	$0.600843\pi$
$458$	1.18603	−	5.19634i	0.0554196	−	0.242809i
$459$	0.774986			0.0361733
$460$	−13.0789			−0.609806
$461$	1.09106	−	4.78027i	0.0508159	−	0.222639i	−0.943144	−	0.332385i	$-0.892147\pi$
$461$	1.09106	−	4.78027i	0.0508159	−	0.222639i	0.993960	+	0.109746i	$0.0350037\pi$
$462$	−0.0214347	+	0.0845539i	−0.000997233	+	0.00393380i
$463$	3.59483	+	15.7500i	0.167066	+	0.731963i	0.987160	+	0.159734i	$0.0510638\pi$
$463$	3.59483	+	15.7500i	0.167066	+	0.731963i	−0.820094	+	0.572228i	$0.806079\pi$
$464$	−3.60221	−	15.7823i	−0.167228	−	0.732675i
$465$	14.3029	+	17.9352i	0.663280	+	0.831727i
$466$	2.11549	+	2.65274i	0.0979982	+	0.122886i
$467$	8.51045	+	37.2867i	0.393817	+	1.72542i	0.651014	+	0.759066i	$0.274344\pi$
$467$	8.51045	+	37.2867i	0.393817	+	1.72542i	−0.257197	+	0.966359i	$0.582799\pi$
$468$	−0.136946	−	0.600001i	−0.00633034	−	0.0277350i
$469$	27.5412	+	0.657641i	1.27174	+	0.0303670i
$470$	−5.95500	+	26.0905i	−0.274684	+	1.20347i
$471$	5.59685			0.257889
$472$	15.8478			0.729453
$473$	−0.0838885	+	0.367539i	−0.00385720	+	0.0168995i
$474$	−5.99646	+	2.88774i	−0.275426	+	0.132638i
$475$	−30.4876	−	38.2302i	−1.39887	−	1.75412i
$476$	3.31551	+	0.0791691i	0.151966	+	0.00362871i
$477$	4.25867	−	5.34020i	0.194991	−	0.244511i
$478$	0.727979	−	3.18948i	0.0332970	−	0.145884i
$479$	19.7900	−	24.8158i	0.904226	−	1.13386i	−0.0862630	−	0.996272i	$-0.527493\pi$
$479$	19.7900	−	24.8158i	0.904226	−	1.13386i	0.990489	−	0.137591i	$-0.0439361\pi$
$480$	20.4497	−	9.84804i	0.933396	−	0.449500i
$481$	2.55814	+	3.20781i	0.116641	+	0.146263i
$482$	0.374117	+	0.180165i	0.0170405	+	0.00820629i
$483$	1.30163	−	5.13455i	0.0592260	−	0.233630i
$484$	−16.0258	+	7.71764i	−0.728448	+	0.350802i
$485$	−36.3729	−	17.5163i	−1.65161	−	0.795372i
$486$	0.137631	+	0.602999i	0.00624305	+	0.0273526i
$487$	−8.30514	−	3.99954i	−0.376342	−	0.181237i	0.236144	−	0.971718i	$-0.424116\pi$
$487$	−8.30514	−	3.99954i	−0.376342	−	0.181237i	−0.612486	+	0.790481i	$0.709830\pi$
$488$	−7.80766	+	9.79050i	−0.353436	+	0.443195i
$489$	−2.67026			−0.120753
$490$	16.0990	−	6.82652i	0.727280	−	0.308391i
$491$	9.72710			0.438978			0.219489	−	0.975615i	$-0.429561\pi$
$491$	9.72710			0.438978			0.219489	+	0.975615i	$0.429561\pi$
$492$	−2.09794	+	2.63073i	−0.0945824	+	0.118603i
$493$	−6.10640	−	2.94069i	−0.275019	−	0.132442i
$494$	0.226357	+	0.991733i	0.0101843	+	0.0446202i
$495$	−0.193971	−	0.0934116i	−0.00871835	−	0.00419854i
$496$	−9.47235	+	4.56164i	−0.425321	+	0.204824i
$497$	5.67727	+	27.9314i	0.254660	+	1.25290i
$498$	0.500386	+	0.240973i	0.0224228	+	0.0107983i
$499$	−11.6707	−	14.6346i	−0.522453	−	0.655136i	0.448675	−	0.893695i	$-0.351896\pi$
$499$	−11.6707	−	14.6346i	−0.522453	−	0.655136i	−0.971128	+	0.238560i	$0.923325\pi$
$500$	37.1548	−	17.8928i	1.66161	−	0.800191i
$501$	9.30917	−	11.6733i	0.415903	−	0.521526i
$502$	1.43261	−	6.27669i	0.0639406	−	0.280142i
$503$	−11.4601	+	14.3705i	−0.510981	+	0.640749i	−0.968667	−	0.248364i	$-0.920107\pi$
$503$	−11.4601	+	14.3705i	−0.510981	+	0.640749i	0.457686	+	0.889114i	$0.348678\pi$
$504$	1.17910	+	5.80103i	0.0525214	+	0.258398i
$505$	17.7885	+	22.3060i	0.791576	+	0.992605i
$506$	0.0594698	−	0.0286392i	0.00264376	−	0.00127317i
$507$	2.86056	−	12.5329i	0.127042	−	0.556606i
$508$	2.31872			0.102877
$509$	11.0967			0.491855			0.245927	−	0.969288i	$-0.420908\pi$
$509$	11.0967			0.491855			0.245927	+	0.969288i	$0.420908\pi$
$510$	0.430796	−	1.88744i	0.0190760	−	0.0835773i
$511$	3.95679	+	5.21221i	0.175038	+	0.230575i
$512$	4.15790	+	18.2170i	0.183755	+	0.805083i
$513$	0.961834	+	4.21407i	0.0424660	+	0.186056i
$514$	1.53092	+	1.91972i	0.0675261	+	0.0846751i
$515$	46.5557	+	58.3790i	2.05149	+	2.57249i
$516$	2.54547	+	11.1524i	0.112058	+	0.490958i
$517$	0.127069	+	0.556726i	0.00558849	+	0.0244848i
$518$	−10.6695	−	14.0547i	−0.468790	−	0.617528i
$519$	0.900408	−	3.94494i	0.0395235	−	0.173164i
$520$	−3.43841			−0.150784
$521$	14.5769			0.638627			0.319313	−	0.947649i	$-0.396548\pi$
$521$	14.5769			0.638627			0.319313	+	0.947649i	$0.396548\pi$
$522$	1.20364	−	5.27349i	0.0526819	−	0.230814i
$523$	0.404037	−	0.194574i	0.0176673	−	0.00850813i	−0.425029	−	0.905180i	$-0.639736\pi$
$523$	0.404037	−	0.194574i	0.0176673	−	0.00850813i	0.442697	+	0.896671i	$0.354022\pi$
$524$	−5.25592	−	6.59072i	−0.229606	−	0.287917i
$525$	5.96168	+	29.3307i	0.260189	+	1.28010i
$526$	−2.54391	+	3.18996i	−0.110920	+	0.139089i
$527$	−0.979482	+	4.29139i	−0.0426669	+	0.186936i
$528$	0.0615192	−	0.0771427i	0.00267728	−	0.00335720i
$529$	17.1110	−	8.24021i	0.743955	−	0.358270i
$530$	−10.6385	−	13.3403i	−0.462107	−	0.579464i
$531$	−6.38163	−	3.07323i	−0.276939	−	0.133367i
$532$	3.68438	+	18.1267i	0.159738	+	0.785892i
$533$	0.713167	−	0.343443i	0.0308907	−	0.0148762i
$534$	6.75681	+	3.25391i	0.292396	+	0.140810i
$535$	−10.2614	−	44.9583i	−0.443641	−	1.94372i
$536$	20.9901	+	10.1083i	0.906634	+	0.436612i
$537$	−3.09027	+	3.87508i	−0.133355	+	0.167222i
$538$	13.8590			0.597502
$539$	0.246303	−	0.280290i	0.0106090	−	0.0120730i
$540$	−6.53271			−0.281123
$541$	−11.5661	+	14.5034i	−0.497266	+	0.623552i	−0.965610	−	0.259994i	$-0.916279\pi$
$541$	−11.5661	+	14.5034i	−0.497266	+	0.623552i	0.468344	+	0.883546i	$0.344851\pi$
$542$	−2.33733	−	1.12560i	−0.100397	−	0.0483485i
$543$	2.87222	+	12.5840i	0.123259	+	0.540033i
$544$	3.92390	+	1.88965i	0.168236	+	0.0810181i
$545$	18.1589	−	8.74487i	0.777843	−	0.374589i
$546$	0.153003	−	0.603555i	0.00654794	−	0.0258298i
$547$	6.21231	+	2.99169i	0.265619	+	0.127915i	0.561953	−	0.827169i	$-0.310050\pi$
$547$	6.21231	+	2.99169i	0.265619	+	0.127915i	−0.296334	+	0.955084i	$0.595764\pi$
$548$	3.38839	+	4.24890i	0.144745	+	0.181504i
$549$	5.04260	−	2.42839i	0.215213	−	0.103641i
$550$	−0.232543	+	0.291600i	−0.00991566	+	0.0124338i
$551$	8.41166	−	36.8539i	0.358349	−	1.57003i
$552$	2.79289	−	3.50217i	0.118873	−	0.149062i
$553$	28.4620	+	0.679628i	1.21033	+	0.0289007i
$554$	−7.78029	−	9.75618i	−0.330553	−	0.414500i
$555$	39.2391	−	18.8965i	1.66561	−	0.802114i
$556$	−6.30620	+	27.6292i	−0.267442	+	1.17174i
$557$	−40.3244			−1.70860			−0.854299	−	0.519781i	$-0.826013\pi$
$557$	−40.3244			−1.70860			−0.854299	+	0.519781i	$0.826013\pi$
$558$	−3.51298			−0.148716
$559$	0.598805	−	2.62354i	0.0253268	−	0.110964i
$560$	−19.7744	−	0.472182i	−0.835622	−	0.0199533i
$561$	−0.00919242	−	0.0402746i	−0.000388104	−	0.00170040i
$562$	2.36364	+	10.3558i	0.0997041	+	0.436832i
$563$	3.30611	+	4.14573i	0.139336	+	0.174722i	0.846603	−	0.532225i	$-0.178644\pi$
$563$	3.30611	+	4.14573i	0.139336	+	0.174722i	−0.707267	+	0.706946i	$0.750072\pi$
$564$	10.8035	+	13.5472i	0.454909	+	0.570438i
$565$	−10.7644	−	47.1618i	−0.452860	−	1.98411i
$566$	1.52574	+	6.68470i	0.0641316	+	0.280979i
$567$	0.650142	−	2.56463i	0.0273034	−	0.107704i
$568$	−5.36355	+	23.4993i	−0.225050	+	0.986007i
$569$	−42.7802			−1.79344			−0.896720	−	0.442598i	$-0.854057\pi$
$569$	−42.7802			−1.79344			−0.896720	+	0.442598i	$0.854057\pi$
$570$	10.7978			0.452271
$571$	−2.89677	+	12.6916i	−0.121226	+	0.531127i	0.877449	+	0.479670i	$0.159244\pi$
$571$	−2.89677	+	12.6916i	−0.121226	+	0.531127i	−0.998675	+	0.0514567i	$0.983614\pi$
$572$	−0.0295566	+	0.0142337i	−0.00123582	+	0.000595141i
$573$	−0.963543	−	1.20825i	−0.0402526	−	0.0504752i
$574$	−3.10154	+	1.40343i	−0.129456	+	0.0585779i
$575$	14.1212	−	17.7074i	0.588895	−	0.738451i
$576$	0.0503467	−	0.220584i	0.00209778	−	0.00919098i
$577$	13.5274	−	16.9629i	0.563154	−	0.706173i	−0.415983	−	0.909372i	$-0.636563\pi$
$577$	13.5274	−	16.9629i	0.563154	−	0.706173i	0.979137	+	0.203199i	$0.0651339\pi$
$578$	−9.13865	+	4.40094i	−0.380118	+	0.183055i
$579$	9.34248	+	11.7151i	0.388260	+	0.486863i
$580$	51.4736	+	24.7884i	2.13732	+	1.02928i
$581$	−1.43649	−	1.89226i	−0.0595957	−	0.0785043i
$582$	5.57006	−	2.68240i	0.230886	−	0.111189i
$583$	−0.328034	−	0.157973i	−0.0135858	−	0.00654257i
$584$	1.23143	+	5.39524i	0.0509568	+	0.223257i
$585$	1.38459	+	0.666783i	0.0572457	+	0.0275681i
$586$	−12.6153	+	15.8190i	−0.521132	+	0.653478i
$587$	−6.07713			−0.250830			−0.125415	−	0.992104i	$-0.540026\pi$
$587$	−6.07713			−0.250830			−0.125415	+	0.992104i	$0.540026\pi$
$588$	3.04340	−	10.9054i	0.125508	−	0.449733i
$589$	−24.5505			−1.01159
$590$	−11.0321	+	13.8338i	−0.454184	+	0.569529i
$591$	8.02248	+	3.86342i	0.330001	+	0.158920i
$592$	4.44154	+	19.4597i	0.182546	+	0.799788i
$593$	−21.0947	−	10.1587i	−0.866257	−	0.417167i	−0.0526709	−	0.998612i	$-0.516773\pi$
$593$	−21.0947	−	10.1587i	−0.866257	−	0.417167i	−0.813586	+	0.581445i	$0.802488\pi$
$594$	0.0297043	−	0.0143048i	0.00121878	−	0.000586934i
$595$	−5.31648	+	6.34958i	−0.217954	+	0.260307i
$596$	23.7106	+	11.4184i	0.971224	+	0.467717i
$597$	−8.75950	−	10.9841i	−0.358502	−	0.449548i
$598$	−0.424502	+	0.204430i	−0.0173592	+	0.00835975i
$599$	−1.68654	+	2.11485i	−0.0689102	+	0.0864106i	−0.815092	−	0.579332i	$-0.803314\pi$
$599$	−1.68654	+	2.11485i	−0.0689102	+	0.0864106i	0.746182	+	0.665742i	$0.231885\pi$
$600$	−5.63225	+	24.6765i	−0.229936	+	1.00741i
$601$	21.0204	−	26.3587i	0.857439	−	1.07519i	−0.138951	−	0.990299i	$-0.544373\pi$
$601$	21.0204	−	26.3587i	0.857439	−	1.07519i	0.996390	−	0.0848950i	$-0.0270555\pi$
$602$	−2.84393	+	11.2185i	−0.115910	+	0.457232i
$603$	−6.49213	−	8.14088i	−0.264380	−	0.331522i
$604$	7.00946	−	3.37558i	0.285211	−	0.137350i
$605$	9.88357	−	43.3027i	0.401824	−	1.76051i
$606$	−4.36909			−0.177482
$607$	17.5455			0.712148			0.356074	−	0.934458i	$-0.384115\pi$
$607$	17.5455			0.712148			0.356074	+	0.934458i	$0.384115\pi$
$608$	−5.40523	+	23.6819i	−0.219211	+	0.960427i
$609$	−14.8542	+	17.7407i	−0.601922	+	0.718888i
$610$	−3.11116	−	13.6309i	−0.125967	−	0.551898i
$611$	−0.907034	−	3.97397i	−0.0366947	−	0.160770i
$612$	−0.781545	−	0.980027i	−0.0315921	−	0.0396152i
$613$	13.9667	+	17.5137i	0.564110	+	0.707372i	0.979312	−	0.202358i	$-0.0648603\pi$
$613$	13.9667	+	17.5137i	0.564110	+	0.707372i	−0.415201	+	0.909730i	$0.636289\pi$
$614$	−0.748298	−	3.27851i	−0.0301989	−	0.132310i
$615$	−1.86967	−	8.19158i	−0.0753926	−	0.330316i
$616$	0.287483	−	0.130084i	0.0115830	−	0.00524124i
$617$	1.16088	−	5.08614i	0.0467352	−	0.204760i	−0.946170	−	0.323671i	$-0.895083\pi$
$617$	1.16088	−	5.08614i	0.0467352	−	0.204760i	0.992905	+	0.118910i	$0.0379401\pi$
$618$	−11.4347			−0.459972
$619$	4.76208			0.191404			0.0957020	−	0.995410i	$-0.469490\pi$
$619$	4.76208			0.191404			0.0957020	+	0.995410i	$0.469490\pi$
$620$	8.25649	−	36.1741i	0.331589	−	1.45278i
$621$	−1.80380	+	0.868662i	−0.0723838	+	0.0348582i
$622$	5.28666	+	6.62926i	0.211976	+	0.265809i
$623$	−19.3972	−	25.5516i	−0.777134	−	1.02370i
$624$	−0.439131	+	0.550653i	−0.0175793	+	0.0220438i
$625$	−10.3278	+	45.2492i	−0.413114	+	1.80997i
$626$	8.49145	−	10.6479i	0.339386	−	0.425577i
$627$	0.207589	−	0.0999696i	0.00829030	−	0.00399240i
$628$	−5.64422	−	7.07763i	−0.225229	−	0.282428i
$629$	7.52923	+	3.62589i	0.300210	+	0.144574i
$630$	−5.88462	−	3.00900i	−0.234449	−	0.119881i
$631$	11.6595	−	5.61490i	0.464155	−	0.223525i	−0.187165	−	0.982329i	$-0.559930\pi$
$631$	11.6595	−	5.61490i	0.464155	−	0.223525i	0.651320	+	0.758803i	$0.274216\pi$
$632$	21.6919	+	10.4463i	0.862857	+	0.415530i
$633$	2.95379	+	12.9414i	0.117403	+	0.514375i
$634$	−5.54931	−	2.67240i	−0.220391	−	0.106135i
$635$	−3.61002	+	4.52682i	−0.143259	+	0.179641i
$636$	−11.0478			−0.438073
$637$	−1.75814	+	2.00074i	−0.0696600	+	0.0792723i
$638$	−0.288331			−0.0114151
$639$	6.71683	−	8.42263i	0.265714	−	0.333194i
$640$	−41.4086	−	19.9413i	−1.63682	−	0.788250i
$641$	−0.803931	−	3.52225i	−0.0317534	−	0.139121i	0.956567	−	0.291514i	$-0.0941590\pi$
$641$	−0.803931	−	3.52225i	−0.0317534	−	0.139121i	−0.988320	+	0.152394i	$0.951302\pi$
$642$	6.36252	+	3.06403i	0.251109	+	0.120928i
$643$	27.2244	−	13.1106i	1.07363	−	0.517032i	0.188353	−	0.982101i	$-0.439685\pi$
$643$	27.2244	−	13.1106i	1.07363	−	0.517032i	0.885274	+	0.465070i	$0.153971\pi$
$644$	−7.80565	+	3.53200i	−0.307586	+	0.139180i
$645$	−25.7358	−	12.3937i	−1.01335	−	0.488003i
$646$	1.29181	+	1.61987i	0.0508254	+	0.0637330i
$647$	−1.40985	+	0.678946i	−0.0554268	+	0.0266921i	−0.461392	−	0.887196i	$-0.652650\pi$
$647$	−1.40985	+	0.678946i	−0.0554268	+	0.0266921i	0.405965	+	0.913889i	$0.366935\pi$
$648$	1.39501	−	1.74928i	0.0548010	−	0.0687183i
$649$	−0.0840152	+	0.368094i	−0.00329788	+	0.0144490i
$650$	1.65992	−	2.08147i	0.0651073	−	0.0816420i
$651$	13.3796	+	6.84144i	0.524388	+	0.268137i
$652$	2.69286	+	3.37674i	0.105461	+	0.132243i
$653$	−8.46598	+	4.07700i	−0.331299	+	0.159545i	−0.592137	−	0.805837i	$-0.701716\pi$
$653$	−8.46598	+	4.07700i	−0.331299	+	0.159545i	0.260838	+	0.965383i	$0.416001\pi$
$654$	−0.686804	+	3.00909i	−0.0268562	+	0.117665i
$655$	21.0499			0.822489
$656$	3.85079			0.150348
$657$	0.550379	−	2.41137i	0.0214723	−	0.0940765i
$658$	3.49183	+	17.1793i	0.136126	+	0.669721i
$659$	−5.36045	−	23.4857i	−0.208813	−	0.914871i	−0.965358	−	0.260929i	$-0.915971\pi$
$659$	−5.36045	−	23.4857i	−0.208813	−	0.914871i	0.756545	−	0.653942i	$-0.226886\pi$
$660$	0.0774870	+	0.339493i	0.00301618	+	0.0132147i
$661$	21.9239	+	27.4917i	0.852742	+	1.06930i	0.996816	+	0.0797377i	$0.0254083\pi$
$661$	21.9239	+	27.4917i	0.852742	+	1.06930i	−0.144074	+	0.989567i	$0.546020\pi$
$662$	7.99502	+	10.0254i	0.310735	+	0.389650i
$663$	0.0656166	+	0.287485i	0.00254834	+	0.0111650i
$664$	−0.447063	−	1.95871i	−0.0173494	−	0.0760127i
$665$	−41.1248	−	21.0285i	−1.59475	−	0.815449i
$666$	−1.48410	+	6.50225i	−0.0575075	+	0.251957i
$667$	17.5089			0.677948
$668$	−24.1497			−0.934381
$669$	3.51294	−	15.3912i	0.135818	−	0.595058i
$670$	−23.4355	+	11.2859i	−0.905393	+	0.436014i
$671$	−0.186011	−	0.233251i	−0.00718088	−	0.00900454i
$672$	9.54513	−	11.3999i	0.368211	−	0.439763i
$673$	−4.23581	+	5.31154i	−0.163278	+	0.204745i	−0.856739	−	0.515749i	$-0.827514\pi$
$673$	−4.23581	+	5.31154i	−0.163278	+	0.204745i	0.693461	+	0.720494i	$0.256085\pi$
$674$	3.00881	−	13.1824i	0.115895	−	0.507769i
$675$	7.05333	−	8.84459i	0.271483	−	0.340428i
$676$	−18.7336	+	9.02160i	−0.720521	+	0.346985i
$677$	8.78740	+	11.0190i	0.337727	+	0.423496i	0.921474	−	0.388439i	$-0.126986\pi$
$677$	8.78740	+	11.0190i	0.337727	+	0.423496i	−0.583747	+	0.811935i	$0.698414\pi$
$678$	6.67436	+	3.21420i	0.256327	+	0.123441i
$679$	−26.4381	−	0.631301i	−1.01460	−	0.0242271i
$680$	−6.30976	+	3.03862i	−0.241968	+	0.116526i
$681$	14.3816	+	6.92580i	0.551103	+	0.265397i
$682$	0.0416689	+	0.182563i	0.00159558	+	0.00699071i
$683$	30.7166	+	14.7924i	1.17534	+	0.566014i	0.916550	−	0.399920i	$-0.130962\pi$
$683$	30.7166	+	14.7924i	1.17534	+	0.566014i	0.258789	+	0.965934i	$0.416676\pi$
$684$	4.35903	−	5.46605i	0.166672	−	0.209000i
$685$	−13.5705			−0.518501
$686$	7.76458	−	8.42176i	0.296453	−	0.321544i
$687$	8.61749			0.328778
$688$	8.16229	−	10.2352i	0.311185	−	0.390213i
$689$	2.34155	+	1.12763i	0.0892058	+	0.0429593i
$690$	1.11290	+	4.87592i	0.0423673	+	0.185623i
$691$	10.9171	+	5.25738i	0.415305	+	0.200000i	0.629855	−	0.776713i	$-0.283114\pi$
$691$	10.9171	+	5.25738i	0.415305	+	0.200000i	−0.214550	+	0.976713i	$0.568829\pi$
$692$	−5.89670	+	2.83970i	−0.224159	+	0.107949i
$693$	−0.140991	−	0.00336663i	−0.00535579	−	0.000127888i
$694$	5.13050	+	2.47072i	0.194751	+	0.0937873i
$695$	−44.1222	−	55.3275i	−1.67365	−	2.09869i
$696$	−17.6294	+	8.48988i	−0.668242	+	0.321808i
$697$	1.00521	−	1.26049i	0.0380750	−	0.0477445i
$698$	4.61006	−	20.1980i	0.174493	−	0.764505i
$699$	−3.42032	+	4.28894i	−0.129368	+	0.162223i
$700$	31.0787	−	37.1180i	1.17466	−	1.40293i
$701$	25.7952	+	32.3461i	0.974270	+	1.22170i	0.975116	+	0.221696i	$0.0711594\pi$
$701$	25.7952	+	32.3461i	0.974270	+	1.22170i	−0.000845631		1.00000i	$0.500269\pi$
$702$	−0.212033	+	0.102109i	−0.00800265	+	0.00385387i
$703$	−10.3716	+	45.4411i	−0.391173	+	1.71384i
$704$	−0.0120605			−0.000454547
$705$	−43.2680			−1.62957
$706$	0.717733	−	3.14460i	0.0270122	−	0.118348i
$707$	16.6402	+	8.50869i	0.625820	+	0.320002i
$708$	2.54931	+	11.1693i	0.0958091	+	0.419767i
$709$	−2.85073	−	12.4899i	−0.107061	−	0.469067i	−0.999828	−	0.0185474i	$-0.994096\pi$
$709$	−2.85073	−	12.4899i	−0.107061	−	0.469067i	0.892766	−	0.450520i	$-0.148761\pi$
$710$	−16.7792	−	21.0404i	−0.629711	−	0.789633i
$711$	−6.70919	−	8.41306i	−0.251614	−	0.315514i
$712$	−6.03678	−	26.4489i	−0.226238	−	0.991213i
$713$	−2.53035	−	11.0862i	−0.0947622	−	0.415181i
$714$	−0.252605	−	1.24279i	−0.00945352	−	0.0465101i
$715$	0.0182283	−	0.0798635i	0.000681701	−	0.00298673i
$716$	8.01674			0.299600
$717$	5.28936			0.197535
$718$	2.24920	−	9.85438i	0.0839393	−	0.367762i
$719$	31.7889	−	15.3087i	1.18552	−	0.570918i	0.266008	−	0.963971i	$-0.414295\pi$
$719$	31.7889	−	15.3087i	1.18552	−	0.570918i	0.919516	+	0.393052i	$0.128581\pi$
$720$	4.66131	+	5.84510i	0.173717	+	0.217834i
$721$	43.5505	+	22.2688i	1.62191	+	0.829334i
$722$	0.122043	−	0.153037i	0.00454197	−	0.00569545i
$723$	−0.149391	+	0.654524i	−0.00555590	+	0.0243420i
$724$	13.0169	−	16.3227i	0.483769	−	0.606628i
$725$	−89.1366	+	42.9259i	−3.31045	+	1.59423i
$726$	4.24086	+	5.31787i	0.157393	+	0.197365i
$727$	−30.3425	−	14.6122i	−1.12534	−	0.541935i	−0.223802	−	0.974635i	$-0.571847\pi$
$727$	−30.3425	−	14.6122i	−1.12534	−	0.541935i	−0.901538	+	0.432699i	$0.857561\pi$
$728$	−2.05209	+	0.928555i	−0.0760554	+	0.0344145i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	−5.56683	−	2.68084i	−0.206038	−	0.0992224i
$731$	−1.21964	−	5.34359i	−0.0451100	−	0.197640i
$732$	−8.15615	−	3.92780i	−0.301460	−	0.145176i
$733$	−30.3410	+	38.0464i	−1.12067	+	1.40528i	−0.217466	+	0.976068i	$0.569779\pi$
$733$	−30.3410	+	38.0464i	−1.12067	+	1.40528i	−0.903205	+	0.429209i	$0.858792\pi$
$734$	2.83072			0.104484
$735$	16.5523	+	22.9203i	0.610543	+	0.845428i
$736$	−11.2510			−0.414718
$737$	−0.346061	+	0.433946i	−0.0127473	+	0.0159846i
$738$	1.15928	+	0.558278i	0.0426735	+	0.0205505i
$739$	−4.27327	−	18.7224i	−0.157195	−	0.688715i	−0.990684	−	0.136180i	$-0.956518\pi$
$739$	−4.27327	−	18.7224i	−0.157195	−	0.688715i	0.833489	−	0.552535i	$-0.186340\pi$
$740$	−63.4672	−	30.5642i	−2.33310	−	1.12356i
$741$	−1.48179	+	0.713594i	−0.0544350	+	0.0262145i
$742$	−9.95178	−	5.08867i	−0.365341	−	0.186811i
$743$	41.0343	+	19.7611i	1.50540	+	0.724963i	0.991159	−	0.132681i	$-0.0423585\pi$
$743$	41.0343	+	19.7611i	1.50540	+	0.724963i	0.514243	+	0.857644i	$0.328073\pi$
$744$	7.92333	+	9.93554i	0.290483	+	0.364255i
$745$	−59.2071	+	28.5127i	−2.16918	+	1.04462i
$746$	−9.46447	+	11.8681i	−0.346519	+	0.434521i
$747$	−0.199812	+	0.875434i	−0.00731074	+	0.0320304i
$748$	−0.0416600	+	0.0522400i	−0.00152324	+	0.00191008i
$749$	−18.2653	−	24.0606i	−0.667400	−	0.879154i
$750$	−9.83214	−	12.3291i	−0.359019	−	0.450196i
$751$	−25.5628	+	12.3104i	−0.932799	+	0.449212i	−0.837623	−	0.546248i	$-0.816056\pi$
$751$	−25.5628	+	12.3104i	−0.932799	+	0.449212i	−0.0951758	+	0.995460i	$0.530341\pi$
$752$	4.41257	−	19.3327i	0.160910	−	0.704992i
$753$	10.4091			0.379329
$754$	2.05814			0.0749529
$755$	−4.32292	+	18.9400i	−0.157327	+	0.689296i
$756$	−3.89880	+	1.76418i	−0.141798	+	0.0641626i
$757$	−7.68780	−	33.6824i	−0.279418	−	1.22421i	−0.898532	−	0.438908i	$-0.855365\pi$
$757$	−7.68780	−	33.6824i	−0.279418	−	1.22421i	0.619114	−	0.785301i	$-0.287492\pi$
$758$	−0.474485	−	2.07886i	−0.0172341	−	0.0755075i
$759$	0.0665383	+	0.0834364i	0.00241519	+	0.00302855i
$760$	−24.3539	−	30.5388i	−0.883407	−	1.10776i
$761$	6.67421	+	29.2416i	0.241940	+	1.06001i	0.939249	+	0.343238i	$0.111524\pi$
$761$	6.67421	+	29.2416i	0.241940	+	1.06001i	−0.697309	+	0.716771i	$0.745619\pi$
$762$	−0.197303	−	0.864439i	−0.00714752	−	0.0313153i
$763$	8.47589	−	10.1229i	0.306848	−	0.366475i
$764$	−0.556216	+	2.43694i	−0.0201232	+	0.0881655i
$765$	3.13009			0.113169
$766$	16.8800			0.609898
$767$	0.599710	−	2.62750i	0.0216543	−	0.0948735i
$768$	5.93351	−	2.85743i	0.214107	−	0.103109i
$769$	0.272327	+	0.341488i	0.00982038	+	0.0123144i	0.786717	−	0.617313i	$-0.211779\pi$
$769$	0.272327	+	0.341488i	0.00982038	+	0.0123144i	−0.776897	+	0.629628i	$0.783207\pi$
$770$	−0.0865725	+	0.341504i	−0.00311986	+	0.0123070i
$771$	−2.47519	+	3.10380i	−0.0891419	+	0.111780i
$772$	5.39305	−	23.6285i	0.194100	−	0.850408i
$773$	−25.7298	+	32.2642i	−0.925438	+	1.16046i	0.0612962	+	0.998120i	$0.480477\pi$
$773$	−25.7298	+	32.2642i	−0.925438	+	1.16046i	−0.986734	+	0.162343i	$0.948095\pi$
$774$	3.94113	−	1.89795i	0.141661	−	0.0682203i
$775$	40.0613	+	50.2353i	1.43905	+	1.80451i
$776$	−20.1494	−	9.70344i	−0.723321	−	0.348333i
$777$	18.3153	−	21.8744i	0.657058	−	0.784738i
$778$	3.10627	−	1.49590i	0.111365	−	0.0536306i
$779$	8.10162	+	3.90154i	0.290271	+	0.139787i
$780$	−0.553111	−	2.42334i	−0.0198046	−	0.0867694i
$781$	−0.517380	−	0.249157i	−0.0185133	−	0.00891554i
$782$	−0.598336	+	0.750290i	−0.0213965	+	0.0268303i
$783$	8.74544			0.312536
$784$	−11.9292	+	5.05835i	−0.426041	+	0.180655i
$785$	22.6051			0.806810
$786$	−2.00984	+	2.52026i	−0.0716887	+	0.0898948i
$787$	10.6071	+	5.10813i	0.378104	+	0.182085i	0.613276	−	0.789869i	$-0.289851\pi$
$787$	10.6071	+	5.10813i	0.378104	+	0.182085i	−0.235173	+	0.971954i	$0.575566\pi$
$788$	−3.20480	−	14.0411i	−0.114166	−	0.500194i
$789$	−5.94343	−	2.86221i	−0.211592	−	0.101897i
$790$	−24.2190	+	11.6633i	−0.861675	+	0.414961i
$791$	−19.1605	−	25.2398i	−0.681270	−	0.897424i
$792$	−0.107454	−	0.0517470i	−0.00381820	−	0.00183875i
$793$	1.32777	+	1.66497i	0.0471505	+	0.0591248i
$794$	1.21382	−	0.584543i	0.0430767	−	0.0207447i
$795$	17.2003	−	21.5685i	0.610032	−	0.764956i
$796$	−5.05652	+	22.1541i	−0.179224	+	0.785230i
$797$	0.111693	−	0.140059i	0.00395637	−	0.00496113i	−0.779849	−	0.625967i	$-0.784704\pi$
$797$	0.111693	−	0.140059i	0.00395637	−	0.00496113i	0.783806	+	0.621006i	$0.213276\pi$
$798$	6.44428	−	2.91599i	0.228125	−	0.103225i
$799$	−5.17640	−	6.49100i	−0.183128	−	0.229635i
$800$	57.2781	−	27.5837i	2.02509	−	0.975230i
$801$	−2.69810	+	11.8212i	−0.0953328	+	0.417680i
$802$	0.812788			0.0287005
$803$	−0.131843			−0.00465263
$804$	−3.74766	+	16.4196i	−0.132170	+	0.579073i
$805$	5.25713	−	20.7379i	0.185289	−	0.730914i
$806$	−0.297437	−	1.30316i	−0.0104768	−	0.0459018i
$807$	4.98606	+	21.8453i	0.175517	+	0.768992i
$808$	9.85424	+	12.3568i	0.346671	+	0.434711i
$809$	7.48548	+	9.38649i	0.263175	+	0.330011i	0.895809	−	0.444440i	$-0.146597\pi$
$809$	7.48548	+	9.38649i	0.263175	+	0.330011i	−0.632633	+	0.774452i	$0.718026\pi$
$810$	0.555875	+	2.43545i	0.0195315	+	0.0855730i
$811$	2.12740	+	9.32076i	0.0747032	+	0.327296i	0.998447	−	0.0557157i	$-0.0177440\pi$
$811$	2.12740	+	9.32076i	0.0747032	+	0.327296i	−0.923744	+	0.383012i	$0.874887\pi$
$812$	37.4143	+	0.893394i	1.31298	+	0.0313520i
$813$	0.933332	−	4.08919i	0.0327334	−	0.143414i
$814$	0.355513			0.0124607
$815$	−10.7849			−0.377778
$816$	−0.319214	+	1.39857i	−0.0111747	+	0.0489596i
$817$	27.5426	−	13.2638i	0.963595	−	0.464043i
$818$	5.24024	+	6.57105i	0.183221	+	0.229751i
$819$	1.00641	+	0.0240314i	0.0351667	+	0.000839725i
$820$	−8.47335	+	10.6253i	−0.295902	+	0.371050i
$821$	−9.56885	+	41.9239i	−0.333955	+	1.46315i	0.477444	+	0.878662i	$0.341563\pi$
$821$	−9.56885	+	41.9239i	−0.333955	+	1.46315i	−0.811400	+	0.584492i	$0.801294\pi$
$822$	1.29571	−	1.62476i	0.0451929	−	0.0566701i
$823$	5.41216	−	2.60636i	0.188656	−	0.0908519i	−0.337171	−	0.941443i	$-0.609470\pi$
$823$	5.41216	−	2.60636i	0.188656	−	0.0908519i	0.525827	+	0.850591i	$0.323756\pi$
$824$	25.7904	+	32.3401i	0.898449	+	1.12662i
$825$	−0.543300	−	0.261639i	−0.0189153	−	0.00910911i
$826$	−2.84823	+	11.2354i	−0.0991024	+	0.390931i
$827$	−28.3668	+	13.6607i	−0.986410	+	0.475030i	−0.856305	−	0.516470i	$-0.827246\pi$
$827$	−28.3668	+	13.6607i	−0.986410	+	0.475030i	−0.130105	+	0.991500i	$0.541531\pi$
$828$	2.91755	+	1.40502i	0.101392	+	0.0488277i
$829$	5.58609	+	24.4743i	0.194013	+	0.850026i	0.974416	+	0.224750i	$0.0721565\pi$
$829$	5.58609	+	24.4743i	0.194013	+	0.850026i	−0.780404	+	0.625276i	$0.784986\pi$
$830$	2.02100	+	0.973264i	0.0701501	+	0.0337825i
$831$	12.5792	−	15.7738i	0.436366	−	0.547186i
$832$	0.0860893			0.00298461
$833$	−1.45822	+	5.22525i	−0.0505242	+	0.181044i
$834$	10.8370			0.375255
$835$	37.5987	−	47.1473i	1.30116	−	1.63160i
$836$	−0.335765	−	0.161696i	−0.0116127	−	0.00559236i
$837$	−1.26387	−	5.53738i	−0.0436857	−	0.191400i
$838$	10.6626	+	5.13482i	0.368332	+	0.177379i
$839$	1.82613	−	0.879416i	0.0630449	−	0.0303608i	−0.402096	−	0.915598i	$-0.631718\pi$
$839$	1.82613	−	0.879416i	0.0630449	−	0.0303608i	0.465141	+	0.885237i	$0.346004\pi$
$840$	4.76226	+	23.4297i	0.164314	+	0.808403i
$841$	−42.7804	−	20.6020i	−1.47519	−	0.710412i
$842$	2.30122	+	2.88564i	0.0793052	+	0.0994456i
$843$	−15.4731	+	7.45143i	−0.532920	+	0.256641i
$844$	13.3866	−	16.7862i	0.460785	−	0.577806i
$845$	11.5535	−	50.6191i	0.397452	−	1.74135i
$846$	4.13121	−	5.18038i	0.142034	−	0.178105i
$847$	−5.79542	−	28.5127i	−0.199133	−	0.979709i
$848$	7.88298	+	9.88494i	0.270703	+	0.339450i
$849$	−9.98791	+	4.80993i	−0.342784	+	0.165076i
$850$	1.20663	−	5.28659i	0.0413870	−	0.181328i
$851$	−21.5886			−0.740047
$852$	−17.4247			−0.596961
$853$	−1.58776	+	6.95644i	−0.0543640	+	0.238184i	−0.994809	−	0.101762i	$-0.967552\pi$
$853$	−1.58776	+	6.95644i	−0.0543640	+	0.238184i	0.940445	+	0.339947i	$0.110409\pi$
$854$	−5.53785	−	7.29491i	−0.189501	−	0.249627i
$855$	3.88475	+	17.0202i	0.132856	+	0.582078i
$856$	−5.68451	−	24.9055i	−0.194293	−	0.851251i
$857$	22.6118	+	28.3544i	0.772406	+	0.968567i	0.999987	−	0.00519271i	$-0.00165290\pi$
$857$	22.6118	+	28.3544i	0.772406	+	0.968567i	−0.227580	+	0.973759i	$0.573081\pi$
$858$	0.00782145	+	0.00980778i	0.000267020	+	0.000334832i
$859$	0.00122908	+	0.00538497i	4.19358e−5	+	0.000183733i	0.974949	−	0.222429i	$-0.0713986\pi$
$859$	0.00122908	+	0.00538497i	4.19358e−5	+	0.000183733i	−0.974907	+	0.222613i	$0.928541\pi$
$860$	10.2809	+	45.0435i	0.350575	+	1.53597i
$861$	−3.32801	−	4.38393i	−0.113418	−	0.149404i
$862$	0.824634	−	3.61296i	0.0280871	−	0.123058i
$863$	2.81750			0.0959087			0.0479543	−	0.998850i	$-0.484730\pi$
$863$	2.81750			0.0959087			0.0479543	+	0.998850i	$0.484730\pi$
$864$	−5.61971			−0.191187
$865$	3.63665	−	15.9332i	0.123650	−	0.541745i
$866$	3.51187	−	1.69123i	0.119338	−	0.0574702i
$867$	−10.2249	−	12.8216i	−0.347254	−	0.435443i
$868$	−4.84135	−	23.8188i	−0.164326	−	0.808464i
$869$	−0.357631	+	0.448455i	−0.0121318	+	0.0152128i
$870$	4.86137	−	21.2991i	0.164816	−	0.722106i
$871$	2.47022	−	3.09756i	0.0837003	−	0.104957i
$872$	10.0595	−	4.84438i	0.340656	−	0.164051i
$873$	6.23211	+	7.81482i	0.210925	+	0.264491i
$874$	−4.82238	−	2.32233i	−0.163119	−	0.0785541i
$875$	13.4363	+	66.1048i	0.454229	+	2.23475i
$876$	−3.60439	+	1.73578i	−0.121781	+	0.0586467i
$877$	25.3716	+	12.2183i	0.856738	+	0.412583i	0.810074	−	0.586327i	$-0.199427\pi$
$877$	25.3716	+	12.2183i	0.856738	+	0.412583i	0.0466640	+	0.998911i	$0.485141\pi$
$878$	−0.439248	−	1.92447i	−0.0148239	−	0.0649477i
$879$	−29.4735	−	14.1937i	−0.994118	−	0.478742i
$880$	0.248470	−	0.311571i	0.00837591	−	0.0105031i
$881$	13.3084			0.448373			0.224186	−	0.974546i	$-0.428028\pi$
$881$	13.3084			0.448373			0.224186	+	0.974546i	$0.428028\pi$
$882$	−4.32461	−	0.206648i	−0.145617	−	0.00695819i
$883$	−46.3470			−1.55970			−0.779850	−	0.625966i	$-0.784705\pi$
$883$	−46.3470			−1.55970			−0.779850	+	0.625966i	$0.784705\pi$
$884$	0.297374	−	0.372895i	0.0100018	−	0.0125418i
$885$	−25.7747	−	12.4125i	−0.866408	−	0.417240i
$886$	4.09548	+	17.9435i	0.137591	+	0.602823i
$887$	3.36077	+	1.61846i	0.112844	+	0.0543426i	0.489454	−	0.872029i	$-0.337196\pi$
$887$	3.36077	+	1.61846i	0.112844	+	0.0543426i	−0.376610	+	0.926372i	$0.622910\pi$
$888$	21.7372	−	10.4681i	0.729452	−	0.351286i
$889$	−0.932022	+	3.67656i	−0.0312590	+	0.123308i
$890$	27.2900	+	13.1422i	0.914764	+	0.440527i
$891$	0.0332349	+	0.0416752i	0.00111341	+	0.00139617i
$892$	−23.0060	+	11.0791i	−0.770296	+	0.370955i
$893$	28.8711	−	36.2032i	0.966133	−	1.21149i
$894$	2.23932	−	9.81112i	0.0748942	−	0.328133i
$895$	−12.4813	+	15.6510i	−0.417203	+	0.523156i
$896$	−30.0984	−	0.718702i	−1.00552	−	0.0240102i
$897$	−0.474958	−	0.595579i	−0.0158584	−	0.0198858i
$898$	16.7538	−	8.06819i	0.559081	−	0.269239i
$899$	−11.0531	+	48.4268i	−0.368641	+	1.61512i
$900$	−18.2977			−0.609922
$901$	5.29345			0.176350
$902$	0.0152621	−	0.0668674i	0.000508171	−	0.00222644i
$903$	−18.7065	−	0.446681i	−0.622512	−	0.0148646i
$904$	−5.96311	−	26.1261i	−0.198330	−	0.868941i
$905$	11.6006	+	50.8256i	0.385617	+	1.68950i
$906$	−1.85489	−	2.32596i	−0.0616245	−	0.0772747i
$907$	8.37496	+	10.5019i	0.278086	+	0.348709i	0.901185	−	0.433434i	$-0.142698\pi$
$907$	8.37496	+	10.5019i	0.278086	+	0.348709i	−0.623099	+	0.782143i	$0.714127\pi$
$908$	−5.74511	−	25.1710i	−0.190658	−	0.835328i
$909$	−1.57187	−	6.88683i	−0.0521358	−	0.228422i
$910$	0.617964	−	2.43770i	0.0204853	−	0.0808088i
$911$	12.6197	−	55.2907i	0.418111	−	1.83186i	−0.124941	−	0.992164i	$-0.539874\pi$
$911$	12.6197	−	55.2907i	0.418111	−	1.83186i	0.543052	−	0.839699i	$-0.317269\pi$
$912$	−8.00103			−0.264941
$913$	0.0478647			0.00158409
$914$	4.07774	−	17.8658i	0.134880	−	0.590947i
$915$	20.3665	−	9.80800i	0.673297	−	0.324243i
$916$	−8.69043	−	10.8974i	−0.287140	−	0.360062i
$917$	12.5629	−	5.68461i	0.414863	−	0.187722i
$918$	−0.298860	+	0.374759i	−0.00986385	+	0.0123689i
$919$	−4.34213	+	19.0241i	−0.143234	+	0.627548i	0.851438	+	0.524455i	$0.175731\pi$
$919$	−4.34213	+	19.0241i	−0.143234	+	0.627548i	−0.994672	+	0.103093i	$0.967126\pi$
$920$	11.2802	−	14.1449i	0.371897	−	0.466344i
$921$	4.89857	−	2.35903i	0.161413	−	0.0777326i
$922$	1.89083	+	2.37103i	0.0622713	+	0.0780857i
$923$	3.69312	+	1.77851i	0.121560	+	0.0585404i
$924$	0.137927	+	0.181688i	0.00453745	+	0.00597710i
$925$	109.906	−	52.9279i	3.61368	−	1.74026i
$926$	−9.00246	−	4.33535i	−0.295839	−	0.142469i
$927$	−4.11388	−	18.0241i	−0.135118	−	0.591989i
$928$	44.2798	+	21.3240i	1.45356	+	0.699995i
$929$	11.3823	−	14.2729i	0.373440	−	0.468278i	−0.559229	−	0.829013i	$-0.688903\pi$
$929$	11.3823	−	14.2729i	0.373440	−	0.468278i	0.932668	+	0.360735i	$0.117474\pi$
$930$	−14.1886			−0.465261
$931$	−30.2226	−	1.44416i	−0.990507	−	0.0473304i
$932$	8.87295			0.290643
$933$	−8.54746	+	10.7182i	−0.279831	+	0.350897i
$934$	−21.3126	−	10.2636i	−0.697369	−	0.335835i
$935$	−0.0371272	−	0.162665i	−0.00121419	−	0.00531971i
$936$	0.767017	+	0.369376i	0.0250707	+	0.0120734i
$937$	15.0554	−	7.25031i	0.491839	−	0.236857i	−0.171489	−	0.985186i	$-0.554858\pi$
$937$	15.0554	−	7.25031i	0.491839	−	0.236857i	0.663328	+	0.748329i	$0.269143\pi$
$938$	−10.9388	+	13.0644i	−0.357165	+	0.426569i
$939$	19.8389	+	9.55392i	0.647418	+	0.311780i
$940$	43.6341	+	54.7155i	1.42319	+	1.78462i
$941$	24.8825	−	11.9828i	0.811145	−	0.390627i	0.0181350	−	0.999836i	$-0.494227\pi$
$941$	24.8825	−	11.9828i	0.811145	−	0.390627i	0.793010	+	0.609209i	$0.208513\pi$
$942$	−2.15833	+	2.70646i	−0.0703221	+	0.0881811i
$943$	−0.926790	+	4.06053i	−0.0301804	+	0.132229i
$944$	8.17462	−	10.2507i	0.266061	−	0.333630i
$945$	2.62585	−	10.3583i	0.0854190	−	0.336954i
$946$	−0.145380	−	0.182301i	−0.00472671	−	0.00592711i
$947$	−50.1247	+	24.1388i	−1.62883	+	0.784405i	−0.628858	+	0.777520i	$0.716477\pi$
$947$	−50.1247	+	24.1388i	−1.62883	+	0.784405i	−0.999976	+	0.00688524i	$0.997808\pi$
$948$	−3.87295	+	16.9685i	−0.125788	+	0.551112i
$949$	0.941109			0.0305497
$950$	30.2439			0.981243
$951$	2.21593	−	9.70861i	0.0718564	−	0.314823i
$952$	−2.94516	+	3.51746i	−0.0954531	+	0.114002i
$953$	8.39722	+	36.7906i	0.272013	+	1.19177i	0.907633	+	0.419764i	$0.137887\pi$
$953$	8.39722	+	36.7906i	0.272013	+	1.19177i	−0.635621	+	0.772002i	$0.719256\pi$
$954$	0.940069	+	4.11871i	0.0304359	+	0.133348i
$955$	−3.89165	−	4.87997i	−0.125931	−	0.157912i
$956$	−5.33413	−	6.68879i	−0.172518	−	0.216331i
$957$	−0.103733	−	0.454484i	−0.00335322	−	0.0146914i
$958$	4.36848	+	19.1396i	0.141139	+	0.618372i
$959$	−8.09904	+	3.66476i	−0.261532	+	0.118341i
$960$	0.203345	−	0.890913i	0.00656294	−	0.0287541i
$961$	1.25990			0.0406421
$962$	−2.53769			−0.0818186
$963$	−2.54066	+	11.1314i	−0.0818716	+	0.358703i
$964$	0.978348	−	0.471148i	0.0315105	−	0.0151746i
$965$	37.7333	+	47.3160i	1.21468	+	1.52316i
$966$	1.98095	+	2.60947i	0.0637361	+	0.0839584i
$967$	−13.4557	+	16.8729i	−0.432705	+	0.542595i	−0.949604	−	0.313451i	$-0.898515\pi$
$967$	−13.4557	+	16.8729i	−0.432705	+	0.542595i	0.516899	+	0.856046i	$0.327086\pi$
$968$	5.47518	−	23.9883i	0.175979	−	0.771014i
$969$	−2.08859	+	2.61901i	−0.0670951	+	0.0841346i
$970$	22.4969	−	10.8339i	0.722331	−	0.347856i
$971$	3.96219	+	4.96843i	0.127153	+	0.159444i	0.841333	−	0.540518i	$-0.181772\pi$
$971$	3.96219	+	4.96843i	0.127153	+	0.159444i	−0.714180	+	0.699962i	$0.753200\pi$
$972$	1.45727	+	0.701785i	0.0467420	+	0.0225098i
$973$	−41.2741	−	21.1048i	−1.32319	−	0.676589i
$974$	5.13678	−	2.47374i	0.164593	−	0.0792639i
$975$	3.87813	+	1.86761i	0.124200	+	0.0598114i
$976$	2.30533	+	10.1003i	0.0737917	+	0.323302i
$977$	5.95871	+	2.86956i	0.190636	+	0.0918055i	0.526767	−	0.850010i	$-0.323404\pi$
$977$	5.95871	+	2.86956i	0.190636	+	0.0918055i	−0.336131	+	0.941815i	$0.609118\pi$
$978$	1.02974	−	1.29125i	0.0329274	−	0.0412897i
$979$	0.646328			0.0206567
$980$	12.2920	−	44.0459i	0.392652	−	1.40700i
$981$	−4.99020			−0.159325
$982$	−3.75109	+	4.70371i	−0.119702	+	0.150102i
$983$	19.0045	+	9.15210i	0.606151	+	0.291907i	0.711674	−	0.702510i	$-0.247937\pi$
$983$	19.0045	+	9.15210i	0.606151	+	0.291907i	−0.105523	+	0.994417i	$0.533652\pi$
$984$	−1.03574	−	4.53787i	−0.0330182	−	0.144662i
$985$	32.4019	+	15.6039i	1.03241	+	0.497183i
$986$	3.77685	−	1.81883i	0.120279	−	0.0579235i
$987$	−25.8229	+	11.6847i	−0.821951	+	0.371927i
$988$	2.39673	+	1.15420i	0.0762500	+	0.0367201i
$989$	8.82822	+	11.0702i	0.280721	+	0.352013i
$990$	0.119972	−	0.0577757i	0.00381297	−	0.00183623i
$991$	0.0140925	−	0.0176715i	0.000447664	−	0.000561353i	−0.781608	−	0.623770i	$-0.785600\pi$
$991$	0.0140925	−	0.0176715i	0.000447664	−	0.000561353i	0.782055	+	0.623209i	$0.214171\pi$
$992$	7.10259	−	31.1185i	0.225507	−	0.988013i
$993$	−12.9263	+	16.2091i	−0.410205	+	0.514381i
$994$	−15.6961	−	8.02592i	−0.497849	−	0.254567i
$995$	−35.3787	−	44.3635i	−1.12158	−	1.40642i
$996$	1.30855	−	0.630166i	0.0414631	−	0.0199676i
$997$	13.5212	−	59.2405i	0.428222	−	1.87616i	−0.0513814	−	0.998679i	$-0.516362\pi$
$997$	13.5212	−	59.2405i	0.428222	−	1.87616i	0.479604	−	0.877485i	$-0.340780\pi$
$998$	11.5774			0.366478
$999$	−10.7832			−0.341165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.i.b.43.3	✓	36
3.2	odd	2		441.2.u.d.190.4		36
49.8	even	7	inner	147.2.i.b.106.3	yes	36
49.20	odd	14		7203.2.a.g.1.7		18
49.29	even	7		7203.2.a.h.1.7		18
147.8	odd	14		441.2.u.d.253.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.43.3	✓	36	1.1	even	1	trivial
147.2.i.b.106.3	yes	36	49.8	even	7	inner
441.2.u.d.190.4		36	3.2	odd	2
441.2.u.d.253.4		36	147.8	odd	14
7203.2.a.g.1.7		18	49.20	odd	14
7203.2.a.h.1.7		18	49.29	even	7

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.i (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.385632 + 0.483568i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(0.359916 + 1.57690i) q^{4} +(-3.63892 - 1.75241i) q^{5} +(0.557255 - 0.268360i) q^{6} +(-2.64500 - 0.0631583i) q^{7} +(-2.01584 - 0.970778i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})\)	\(q+(-0.385632 + 0.483568i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(0.359916 + 1.57690i) q^{4} +(-3.63892 - 1.75241i) q^{5} +(0.557255 - 0.268360i) q^{6} +(-2.64500 - 0.0631583i) q^{7} +(-2.01584 - 0.970778i) q^{8} +(0.623490 + 0.781831i) q^{9} +(2.25069 - 1.08388i) q^{10} +(0.0332349 - 0.0416752i) q^{11} +(0.359916 - 1.57690i) q^{12} +(-0.237234 + 0.297483i) q^{13} +(1.05054 - 1.25468i) q^{14} +(2.51821 + 3.15773i) q^{15} +(-1.66773 + 0.803137i) q^{16} +(-0.172451 + 0.755556i) q^{17} -0.618506 q^{18} -4.32244 q^{19} +(1.45366 - 6.36892i) q^{20} +(2.35566 + 1.20453i) q^{21} +(0.00733635 + 0.0321427i) q^{22} +(-0.445501 - 1.95187i) q^{23} +(1.39501 + 1.74928i) q^{24} +(7.05333 + 8.84459i) q^{25} +(-0.0523677 - 0.229438i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(-0.852384 - 4.19362i) q^{28} +(-1.94604 + 8.52617i) q^{29} -2.49808 q^{30} +5.67978 q^{31} +(1.25050 - 5.47882i) q^{32} +(-0.0480258 + 0.0231280i) q^{33} +(-0.298860 - 0.374759i) q^{34} +(9.51425 + 4.86495i) q^{35} +(-1.00846 + 1.26457i) q^{36} +(2.39948 - 10.5128i) q^{37} +(1.66687 - 2.09020i) q^{38} +(0.342814 - 0.165090i) q^{39} +(5.63428 + 7.06516i) q^{40} +(-1.87432 - 0.902623i) q^{41} +(-1.49089 + 0.674616i) q^{42} +(-6.37201 + 3.06860i) q^{43} +(0.0776793 + 0.0374084i) q^{44} +(-0.898738 - 3.93763i) q^{45} +(1.11566 + 0.537273i) q^{46} +(-6.67934 + 8.37562i) q^{47} +1.85104 q^{48} +(6.99202 + 0.334107i) q^{49} -6.99695 q^{50} +(0.483196 - 0.605909i) q^{51} +(-0.554484 - 0.267025i) q^{52} +(-1.51990 - 6.65912i) q^{53} +(0.557255 + 0.268360i) q^{54} +(-0.193971 + 0.0934116i) q^{55} +(5.27058 + 2.69502i) q^{56} +(3.89439 + 1.87544i) q^{57} +(-3.37252 - 4.22901i) q^{58} +(-6.38163 + 3.07323i) q^{59} +(-4.07308 + 5.10748i) q^{60} +(1.24542 - 5.45654i) q^{61} +(-2.19031 + 2.74656i) q^{62} +(-1.59975 - 2.10732i) q^{63} +(-0.141068 - 0.176894i) q^{64} +(1.38459 - 0.666783i) q^{65} +(0.00733635 - 0.0321427i) q^{66} -10.4126 q^{67} -1.25350 q^{68} +(-0.445501 + 1.95187i) q^{69} +(-6.02153 + 2.72470i) q^{70} +(-2.39721 - 10.5029i) q^{71} +(-0.497872 - 2.18132i) q^{72} +(-1.54213 - 1.93377i) q^{73} +(4.15834 + 5.21440i) q^{74} +(-2.51730 - 11.0290i) q^{75} +(-1.55572 - 6.81605i) q^{76} +(-0.0905384 + 0.108132i) q^{77} +(-0.0523677 + 0.229438i) q^{78} -10.7607 q^{79} +7.47616 q^{80} +(-0.222521 + 0.974928i) q^{81} +(1.15928 - 0.558278i) q^{82} +(0.559861 + 0.702043i) q^{83} +(-1.05157 + 4.14816i) q^{84} +(1.95158 - 2.44720i) q^{85} +(0.973378 - 4.26465i) q^{86} +(5.45269 - 6.83746i) q^{87} +(-0.107454 + 0.0517470i) q^{88} +(7.55992 + 9.47984i) q^{89} +(2.25069 + 1.08388i) q^{90} +(0.646273 - 0.771857i) q^{91} +(2.91755 - 1.40502i) q^{92} +(-5.11731 - 2.46436i) q^{93} +(-1.47441 - 6.45983i) q^{94} +(15.7290 + 7.57469i) q^{95} +(-3.50383 + 4.39367i) q^{96} +9.99553 q^{97} +(-2.85791 + 3.25227i) q^{98} +0.0533046 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 6 q^{3} - 9 q^{4} - 4 q^{5} - q^{6} - 6 q^{7} - 15 q^{8} - 6 q^{9}+O(q^{10}) \) 36 * q - q^2 - 6 * q^3 - 9 * q^4 - 4 * q^5 - q^6 - 6 * q^7 - 15 * q^8 - 6 * q^9	\( 36 q - q^{2} - 6 q^{3} - 9 q^{4} - 4 q^{5} - q^{6} - 6 q^{7} - 15 q^{8} - 6 q^{9} + 10 q^{10} - 7 q^{11} - 9 q^{12} - 12 q^{13} - q^{14} + 3 q^{15} - 3 q^{16} - 3 q^{17} + 6 q^{18} + 6 q^{19} + 25 q^{20} + q^{21} - 21 q^{22} - 20 q^{23} + 6 q^{24} - 2 q^{25} + 6 q^{26} - 6 q^{27} - q^{28} - 22 q^{29} - 4 q^{30} + 16 q^{31} + 26 q^{32} + 6 q^{34} - 9 q^{35} - 9 q^{36} + 32 q^{37} + 17 q^{38} + 23 q^{39} - 21 q^{40} - 5 q^{41} - 8 q^{42} - 34 q^{43} + 2 q^{44} + 3 q^{45} - 32 q^{46} - 7 q^{47} + 74 q^{48} + 20 q^{49} + 236 q^{50} + 18 q^{51} + 20 q^{52} - 32 q^{53} - q^{54} - 17 q^{55} - 39 q^{56} - 8 q^{57} - 53 q^{58} - q^{59} - 17 q^{60} + 14 q^{61} - 60 q^{62} + 22 q^{63} - 21 q^{64} - 39 q^{65} - 21 q^{66} - 22 q^{67} - 110 q^{68} - 20 q^{69} - 40 q^{70} + 36 q^{71} + 6 q^{72} - 11 q^{73} - 46 q^{74} - 9 q^{75} - 101 q^{76} - 17 q^{77} + 6 q^{78} - 14 q^{79} - 112 q^{80} - 6 q^{81} + 2 q^{82} + 12 q^{83} - 22 q^{84} - 44 q^{85} + 184 q^{86} - q^{87} + 204 q^{88} + 12 q^{89} + 10 q^{90} - 16 q^{91} - 105 q^{92} - 19 q^{93} - 5 q^{94} + 18 q^{95} - 9 q^{96} + 172 q^{97} + q^{98}+O(q^{100}) \) 36 * q - q^2 - 6 * q^3 - 9 * q^4 - 4 * q^5 - q^6 - 6 * q^7 - 15 * q^8 - 6 * q^9 + 10 * q^10 - 7 * q^11 - 9 * q^12 - 12 * q^13 - q^14 + 3 * q^15 - 3 * q^16 - 3 * q^17 + 6 * q^18 + 6 * q^19 + 25 * q^20 + q^21 - 21 * q^22 - 20 * q^23 + 6 * q^24 - 2 * q^25 + 6 * q^26 - 6 * q^27 - q^28 - 22 * q^29 - 4 * q^30 + 16 * q^31 + 26 * q^32 + 6 * q^34 - 9 * q^35 - 9 * q^36 + 32 * q^37 + 17 * q^38 + 23 * q^39 - 21 * q^40 - 5 * q^41 - 8 * q^42 - 34 * q^43 + 2 * q^44 + 3 * q^45 - 32 * q^46 - 7 * q^47 + 74 * q^48 + 20 * q^49 + 236 * q^50 + 18 * q^51 + 20 * q^52 - 32 * q^53 - q^54 - 17 * q^55 - 39 * q^56 - 8 * q^57 - 53 * q^58 - q^59 - 17 * q^60 + 14 * q^61 - 60 * q^62 + 22 * q^63 - 21 * q^64 - 39 * q^65 - 21 * q^66 - 22 * q^67 - 110 * q^68 - 20 * q^69 - 40 * q^70 + 36 * q^71 + 6 * q^72 - 11 * q^73 - 46 * q^74 - 9 * q^75 - 101 * q^76 - 17 * q^77 + 6 * q^78 - 14 * q^79 - 112 * q^80 - 6 * q^81 + 2 * q^82 + 12 * q^83 - 22 * q^84 - 44 * q^85 + 184 * q^86 - q^87 + 204 * q^88 + 12 * q^89 + 10 * q^90 - 16 * q^91 - 105 * q^92 - 19 * q^93 - 5 * q^94 + 18 * q^95 - 9 * q^96 + 172 * q^97 + q^98

Introduction

L-functions

Modular forms

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