LMFDB - Embedded newform 378.2.u.e.85.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			85.6
Character	$\chi$	$=$	378.85
Dual form			378.2.u.e.169.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(1.32079 - 1.12050i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.359180 - 2.03701i) q^{5} +(1.62437 - 0.601188i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.488967 - 2.95988i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(1.32079 - 1.12050i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.359180 - 2.03701i) q^{5} +(1.62437 - 0.601188i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.488967 - 2.95988i) q^{9} +(1.03422 - 1.79132i) q^{10} +(0.153289 + 0.869347i) q^{11} +(1.73203 - 0.00936481i) q^{12} +(-6.62538 + 2.41144i) q^{13} +(0.939693 - 0.342020i) q^{14} +(-1.80807 - 3.09292i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-0.458052 + 0.793370i) q^{17} +(1.47182 - 2.61414i) q^{18} +(0.0604165 + 0.104644i) q^{19} +(1.58451 - 1.32956i) q^{20} +(0.291541 - 1.70734i) q^{21} +(-0.153289 + 0.869347i) q^{22} +(4.30709 + 3.61408i) q^{23} +(1.63077 + 0.583588i) q^{24} +(0.678066 + 0.246796i) q^{25} -7.05058 q^{26} +(-2.67072 - 4.45727i) q^{27} +1.00000 q^{28} +(6.98432 + 2.54209i) q^{29} +(-0.641185 - 3.52479i) q^{30} +(1.33637 + 1.12135i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(1.17657 + 0.976464i) q^{33} +(-0.701777 + 0.588861i) q^{34} +(-1.03422 - 1.79132i) q^{35} +(2.27715 - 1.95310i) q^{36} +(-3.42905 + 5.93929i) q^{37} +(0.0209824 + 0.118997i) q^{38} +(-6.04871 + 10.6087i) q^{39} +(1.94369 - 0.707446i) q^{40} +(-2.97981 + 1.08456i) q^{41} +(0.857903 - 1.50466i) q^{42} +(-1.63188 - 9.25486i) q^{43} +(-0.441379 + 0.764491i) q^{44} +(-5.85368 - 2.05916i) q^{45} +(2.81125 + 4.86923i) q^{46} +(-4.61848 + 3.87537i) q^{47} +(1.33283 + 1.10615i) q^{48} +(0.173648 - 0.984808i) q^{49} +(0.552765 + 0.463825i) q^{50} +(0.283979 + 1.56112i) q^{51} +(-6.62538 - 2.41144i) q^{52} +7.30416 q^{53} +(-0.985183 - 5.10190i) q^{54} +1.82593 q^{55} +(0.939693 + 0.342020i) q^{56} +(0.197051 + 0.0705166i) q^{57} +(5.69367 + 4.77756i) q^{58} +(-0.366714 + 2.07974i) q^{59} +(0.603032 - 3.53152i) q^{60} +(3.69091 - 3.09705i) q^{61} +(0.872256 + 1.51079i) q^{62} +(-1.52801 - 2.58170i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.53242 + 14.3621i) q^{65} +(0.771639 + 1.31998i) q^{66} +(-13.2026 + 4.80535i) q^{67} +(-0.860857 + 0.313326i) q^{68} +(9.73833 - 0.0526537i) q^{69} +(-0.359180 - 2.03701i) q^{70} +(0.0193766 - 0.0335613i) q^{71} +(2.80782 - 1.05648i) q^{72} +(-6.28891 - 10.8927i) q^{73} +(-5.25361 + 4.40830i) q^{74} +(1.17212 - 0.433807i) q^{75} +(-0.0209824 + 0.118997i) q^{76} +(0.676232 + 0.567426i) q^{77} +(-9.31232 + 7.90016i) q^{78} +(-7.01001 - 2.55143i) q^{79} +2.06843 q^{80} +(-8.52182 - 2.89457i) q^{81} -3.17104 q^{82} +(0.691629 + 0.251732i) q^{83} +(1.32079 - 1.12050i) q^{84} +(1.45158 + 1.21802i) q^{85} +(1.63188 - 9.25486i) q^{86} +(12.0732 - 4.46836i) q^{87} +(-0.676232 + 0.567426i) q^{88} +(0.567520 + 0.982974i) q^{89} +(-4.79639 - 3.93706i) q^{90} +(-3.52529 + 6.10598i) q^{91} +(0.976338 + 5.53709i) q^{92} +(3.02154 - 0.0163370i) q^{93} +(-5.66541 + 2.06204i) q^{94} +(0.234862 - 0.0854828i) q^{95} +(0.874123 + 1.49530i) q^{96} +(0.809402 + 4.59034i) q^{97} +(0.500000 - 0.866025i) q^{98} +(2.64812 - 0.0286368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	1.32079	−	1.12050i	0.762558	−	0.646920i
$3$	1.32079	−	1.12050i	0.762558	−	0.646920i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.359180	−	2.03701i	0.160630	−	0.910978i	−0.792826	−	0.609448i	$-0.791391\pi$
$5$	0.359180	−	2.03701i	0.160630	−	0.910978i	0.953456	−	0.301531i	$-0.0974976\pi$
$6$	1.62437	−	0.601188i	0.663146	−	0.245434i
$7$	0.766044	−	0.642788i	0.289538	−	0.242951i
$7$	0.766044	−	0.642788i	0.289538	−	0.242951i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.488967	−	2.95988i	0.162989	−	0.986628i
$10$	1.03422	−	1.79132i	0.327048	−	0.566464i
$11$	0.153289	+	0.869347i	0.0462185	+	0.262118i	0.999157	−	0.0410446i	$-0.0130686\pi$
$11$	0.153289	+	0.869347i	0.0462185	+	0.262118i	−0.952939	+	0.303163i	$0.901957\pi$
$12$	1.73203	−	0.00936481i	0.499993	−	0.00270339i
$13$	−6.62538	+	2.41144i	−1.83755	+	0.668813i	−0.847010	+	0.531577i	$0.821600\pi$
$13$	−6.62538	+	2.41144i	−1.83755	+	0.668813i	−0.990538	+	0.137236i	$0.956178\pi$
$14$	0.939693	−	0.342020i	0.251143	−	0.0914087i
$15$	−1.80807	−	3.09292i	−0.466840	−	0.798588i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−0.458052	+	0.793370i	−0.111094	+	0.192421i	−0.916212	−	0.400695i	$-0.868769\pi$
$17$	−0.458052	+	0.793370i	−0.111094	+	0.192421i	0.805118	+	0.593115i	$0.202102\pi$
$18$	1.47182	−	2.61414i	0.346911	−	0.616160i
$19$	0.0604165	+	0.104644i	0.0138605	+	0.0240071i	0.872872	−	0.487948i	$-0.162255\pi$
$19$	0.0604165	+	0.104644i	0.0138605	+	0.0240071i	−0.859012	+	0.511956i	$0.828921\pi$
$20$	1.58451	−	1.32956i	0.354308	−	0.297299i
$21$	0.291541	−	1.70734i	0.0636194	−	0.372572i
$22$	−0.153289	+	0.869347i	−0.0326814	+	0.185345i
$23$	4.30709	+	3.61408i	0.898090	+	0.753587i	0.969816	−	0.243837i	$-0.0784062\pi$
$23$	4.30709	+	3.61408i	0.898090	+	0.753587i	−0.0717258	+	0.997424i	$0.522851\pi$
$24$	1.63077	+	0.583588i	0.332880	+	0.119124i
$25$	0.678066	+	0.246796i	0.135613	+	0.0493592i
$26$	−7.05058			−1.38273
$27$	−2.67072	−	4.45727i	−0.513981	−	0.857802i
$28$	1.00000			0.188982
$29$	6.98432	+	2.54209i	1.29696	+	0.472053i	0.896004	−	0.444046i	$-0.146457\pi$
$29$	6.98432	+	2.54209i	1.29696	+	0.472053i	0.400952	+	0.916099i	$0.368679\pi$
$30$	−0.641185	−	3.52479i	−0.117064	−	0.643535i
$31$	1.33637	+	1.12135i	0.240020	+	0.201400i	0.754861	−	0.655885i	$-0.227705\pi$
$31$	1.33637	+	1.12135i	0.240020	+	0.201400i	−0.514841	+	0.857286i	$0.672149\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	1.17657	+	0.976464i	0.204814	+	0.169981i
$34$	−0.701777	+	0.588861i	−0.120354	+	0.100989i
$35$	−1.03422	−	1.79132i	−0.174815	−	0.302788i
$36$	2.27715	−	1.95310i	0.379524	−	0.325517i
$37$	−3.42905	+	5.93929i	−0.563732	+	0.976413i	0.433434	+	0.901185i	$0.357302\pi$
$37$	−3.42905	+	5.93929i	−0.563732	+	0.976413i	−0.997166	+	0.0752279i	$0.976032\pi$
$38$	0.0209824	+	0.118997i	0.00340380	+	0.0193039i
$39$	−6.04871	+	10.6087i	−0.968569	+	1.69876i
$40$	1.94369	−	0.707446i	0.307325	−	0.111857i
$41$	−2.97981	+	1.08456i	−0.465368	+	0.169380i	−0.564053	−	0.825739i	$-0.690759\pi$
$41$	−2.97981	+	1.08456i	−0.465368	+	0.169380i	0.0986851	+	0.995119i	$0.468536\pi$
$42$	0.857903	−	1.50466i	0.132377	−	0.232174i
$43$	−1.63188	−	9.25486i	−0.248860	−	1.41135i	−0.811356	−	0.584553i	$-0.801270\pi$
$43$	−1.63188	−	9.25486i	−0.248860	−	1.41135i	0.562496	−	0.826800i	$-0.309841\pi$
$44$	−0.441379	+	0.764491i	−0.0665404	+	0.115251i
$45$	−5.85368	−	2.05916i	−0.872616	−	0.306961i
$46$	2.81125	+	4.86923i	0.414497	+	0.717929i
$47$	−4.61848	+	3.87537i	−0.673675	+	0.565280i	−0.914150	−	0.405375i	$-0.867141\pi$
$47$	−4.61848	+	3.87537i	−0.673675	+	0.565280i	0.240476	+	0.970655i	$0.422697\pi$
$48$	1.33283	+	1.10615i	0.192377	+	0.159659i
$49$	0.173648	−	0.984808i	0.0248069	−	0.140687i
$50$	0.552765	+	0.463825i	0.0781727	+	0.0655947i
$51$	0.283979	+	1.56112i	0.0397651	+	0.218601i
$52$	−6.62538	−	2.41144i	−0.918774	−	0.334406i
$53$	7.30416			1.00330			0.501652	−	0.865070i	$-0.332726\pi$
$53$	7.30416			1.00330			0.501652	+	0.865070i	$0.332726\pi$
$54$	−0.985183	−	5.10190i	−0.134066	−	0.694281i
$55$	1.82593			0.246208
$56$	0.939693	+	0.342020i	0.125572	+	0.0457044i
$57$	0.197051	+	0.0705166i	0.0261001	+	0.00934015i
$58$	5.69367	+	4.77756i	0.747616	+	0.627324i
$59$	−0.366714	+	2.07974i	−0.0477421	+	0.270759i	−0.999329	−	0.0366203i	$-0.988341\pi$
$59$	−0.366714	+	2.07974i	−0.0477421	+	0.270759i	0.951587	+	0.307379i	$0.0994519\pi$
$60$	0.603032	−	3.53152i	0.0778511	−	0.455917i
$61$	3.69091	−	3.09705i	0.472573	−	0.396536i	−0.375159	−	0.926960i	$-0.622412\pi$
$61$	3.69091	−	3.09705i	0.472573	−	0.396536i	0.847732	+	0.530424i	$0.177967\pi$
$62$	0.872256	+	1.51079i	0.110777	+	0.191871i
$63$	−1.52801	−	2.58170i	−0.192511	−	0.325264i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.53242	+	14.3621i	0.314109	+	1.78140i
$66$	0.771639	+	1.31998i	0.0949822	+	0.162479i
$67$	−13.2026	+	4.80535i	−1.61295	+	0.587067i	−0.982021	−	0.188771i	$-0.939550\pi$
$67$	−13.2026	+	4.80535i	−1.61295	+	0.587067i	−0.630932	+	0.775838i	$0.717327\pi$
$68$	−0.860857	+	0.313326i	−0.104394	+	0.0379964i
$69$	9.73833	−	0.0526537i	1.17236	−	0.00633876i
$70$	−0.359180	−	2.03701i	−0.0429302	−	0.243469i
$71$	0.0193766	−	0.0335613i	0.00229958	−	0.00398299i	−0.864873	−	0.501990i	$-0.832601\pi$
$71$	0.0193766	−	0.0335613i	0.00229958	−	0.00398299i	0.867173	+	0.498007i	$0.165935\pi$
$72$	2.80782	−	1.05648i	0.330905	−	0.124508i
$73$	−6.28891	−	10.8927i	−0.736062	−	1.27490i	−0.954256	−	0.298991i	$-0.903350\pi$
$73$	−6.28891	−	10.8927i	−0.736062	−	1.27490i	0.218194	−	0.975905i	$-0.429983\pi$
$74$	−5.25361	+	4.40830i	−0.610720	+	0.512455i
$75$	1.17212	−	0.433807i	0.135344	−	0.0500917i
$76$	−0.0209824	+	0.118997i	−0.00240685	+	0.0136499i
$77$	0.676232	+	0.567426i	0.0770638	+	0.0646642i
$78$	−9.31232	+	7.90016i	−1.05441	+	0.894517i
$79$	−7.01001	−	2.55143i	−0.788687	−	0.287059i	−0.0838970	−	0.996474i	$-0.526737\pi$
$79$	−7.01001	−	2.55143i	−0.788687	−	0.287059i	−0.704790	+	0.709416i	$0.748959\pi$
$80$	2.06843			0.231258
$81$	−8.52182	−	2.89457i	−0.946869	−	0.321619i
$82$	−3.17104			−0.350183
$83$	0.691629	+	0.251732i	0.0759161	+	0.0276312i	0.379699	−	0.925110i	$-0.376028\pi$
$83$	0.691629	+	0.251732i	0.0759161	+	0.0276312i	−0.303783	+	0.952741i	$0.598250\pi$
$84$	1.32079	−	1.12050i	0.144110	−	0.122256i
$85$	1.45158	+	1.21802i	0.157446	+	0.132113i
$86$	1.63188	−	9.25486i	0.175970	−	0.997977i
$87$	12.0732	−	4.46836i	1.29438	−	0.479059i
$88$	−0.676232	+	0.567426i	−0.0720866	+	0.0604878i
$89$	0.567520	+	0.982974i	0.0601570	+	0.104195i	0.894535	−	0.446997i	$-0.147507\pi$
$89$	0.567520	+	0.982974i	0.0601570	+	0.104195i	−0.834378	+	0.551192i	$0.814173\pi$
$90$	−4.79639	−	3.93706i	−0.505584	−	0.415002i
$91$	−3.52529	+	6.10598i	−0.369551	+	0.640081i
$92$	0.976338	+	5.53709i	0.101790	+	0.577281i
$93$	3.02154	−	0.0163370i	0.313319	−	0.00169407i
$94$	−5.66541	+	2.06204i	−0.584342	+	0.212683i
$95$	0.234862	−	0.0854828i	0.0240963	−	0.00877035i
$96$	0.874123	+	1.49530i	0.0892148	+	0.152613i
$97$	0.809402	+	4.59034i	0.0821823	+	0.466079i	0.997929	+	0.0643231i	$0.0204888\pi$
$97$	0.809402	+	4.59034i	0.0821823	+	0.466079i	−0.915747	+	0.401756i	$0.868400\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	2.64812	−	0.0286368i	0.266146	−	0.00287811i
$100$	0.360792	+	0.624909i	0.0360792	+	0.0624909i
$101$	11.1333	−	9.34197i	1.10781	−	0.929560i	0.109882	−	0.993945i	$-0.464953\pi$
$101$	11.1333	−	9.34197i	1.10781	−	0.929560i	0.997925	+	0.0643844i	$0.0205084\pi$
$102$	−0.267082	+	1.56410i	−0.0264450	+	0.154869i
$103$	−1.31566	+	7.46150i	−0.129636	+	0.735203i	0.848810	+	0.528699i	$0.177320\pi$
$103$	−1.31566	+	7.46150i	−0.129636	+	0.735203i	−0.978446	+	0.206504i	$0.933791\pi$
$104$	−5.40106	−	4.53202i	−0.529617	−	0.444401i
$105$	−3.37315	−	1.20711i	−0.329186	−	0.117802i
$106$	6.86366	+	2.49817i	0.666658	+	0.242644i
$107$	−13.2357			−1.27955			−0.639774	−	0.768563i	$-0.720972\pi$
$107$	−13.2357			−1.27955			−0.639774	+	0.768563i	$0.720972\pi$
$108$	0.819184	−	5.13117i	0.0788260	−	0.493747i
$109$	−18.8127			−1.80193			−0.900967	−	0.433887i	$-0.857142\pi$
$109$	−18.8127			−1.80193			−0.900967	+	0.433887i	$0.857142\pi$
$110$	1.71581	+	0.624504i	0.163596	+	0.0595441i
$111$	2.12591	+	11.6868i	0.201783	+	1.10926i
$112$	0.766044	+	0.642788i	0.0723844	+	0.0607377i
$113$	1.80084	−	10.2131i	0.169409	−	0.960767i	−0.774992	−	0.631971i	$-0.782246\pi$
$113$	1.80084	−	10.2131i	0.169409	−	0.960767i	0.944401	−	0.328796i	$-0.106643\pi$
$114$	0.161050	+	0.133659i	0.0150837	+	0.0125184i
$115$	8.90893	−	7.47548i	0.830762	−	0.697092i
$116$	3.71628	+	6.43679i	0.345048	+	0.597641i
$117$	3.89799	+	20.7895i	0.360369	+	1.92199i
$118$	−1.05591	+	1.82889i	−0.0972044	+	0.168363i
$119$	0.159080	+	0.902187i	0.0145828	+	0.0827034i
$120$	1.77451	−	3.11229i	0.161990	−	0.284112i
$121$	9.60435	−	3.49570i	0.873123	−	0.317791i
$122$	4.52758	−	1.64790i	0.409908	−	0.149194i
$123$	−2.72045	+	4.77134i	−0.245294	+	0.430218i
$124$	0.302931	+	1.71801i	0.0272040	+	0.154282i
$125$	5.91736	−	10.2492i	0.529264	−	0.916713i
$126$	−0.552861	−	2.94862i	−0.0492528	−	0.262684i
$127$	−4.14561	−	7.18040i	−0.367863	−	0.637158i	0.621368	−	0.783519i	$-0.286577\pi$
$127$	−4.14561	−	7.18040i	−0.367863	−	0.637158i	−0.989231	+	0.146361i	$0.953244\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−12.5254	−	10.3952i	−1.10280	−	0.915246i
$130$	−2.53242	+	14.3621i	−0.222108	+	1.25964i
$131$	−6.90894	−	5.79729i	−0.603636	−	0.506511i	0.288976	−	0.957336i	$-0.406685\pi$
$131$	−6.90894	−	5.79729i	−0.603636	−	0.506511i	−0.892612	+	0.450825i	$0.851130\pi$
$132$	0.273642	+	1.50430i	0.0238175	+	0.130932i
$133$	0.113546	+	0.0413273i	0.00984567	+	0.00358353i
$134$	−14.0499			−1.21373
$135$	−10.0388	+	3.83933i	−0.863999	+	0.330437i
$136$	−0.916105			−0.0785553
$137$	18.5227	+	6.74171i	1.58250	+	0.575983i	0.975746	−	0.218906i	$-0.0702486\pi$
$137$	18.5227	+	6.74171i	1.58250	+	0.575983i	0.606755	+	0.794889i	$0.292471\pi$
$138$	9.16904	+	3.28123i	0.780521	+	0.279316i
$139$	−9.30457	−	7.80746i	−0.789203	−	0.662220i	0.156345	−	0.987703i	$-0.450029\pi$
$139$	−9.30457	−	7.80746i	−0.789203	−	0.662220i	−0.945548	+	0.325482i	$0.894473\pi$
$140$	0.359180	−	2.03701i	0.0303562	−	0.172159i
$141$	−1.75770	+	10.2935i	−0.148025	+	0.866872i
$142$	0.0296867	−	0.0249101i	0.00249125	−	0.00209041i
$143$	−3.11198	−	5.39010i	−0.260237	−	0.450743i
$144$	2.99982	−	0.0324402i	0.249985	−	0.00270335i
$145$	7.68688	−	13.3141i	0.638360	−	1.10567i
$146$	−2.18412	−	12.3867i	−0.180759	−	1.02513i
$147$	−0.874123	−	1.49530i	−0.0720964	−	0.123330i
$148$	−6.44451	+	2.34561i	−0.529735	+	0.192808i
$149$	−10.4945	+	3.81967i	−0.859740	+	0.312920i	−0.734005	−	0.679144i	$-0.762351\pi$
$149$	−10.4945	+	3.81967i	−0.859740	+	0.312920i	−0.125735	+	0.992064i	$0.540129\pi$
$150$	1.24980	−	0.00675749i	0.102046	−	0.000551746i
$151$	2.20189	+	12.4875i	0.179187	+	1.01622i	0.933199	+	0.359360i	$0.117005\pi$
$151$	2.20189	+	12.4875i	0.179187	+	1.01622i	−0.754012	+	0.656861i	$0.771884\pi$
$152$	−0.0604165	+	0.104644i	−0.00490042	+	0.00848778i
$153$	2.12431	+	1.74371i	0.171740	+	0.140971i
$154$	0.441379	+	0.764491i	0.0355673	+	0.0616045i
$155$	2.76420	−	2.31944i	0.222026	−	0.186302i
$156$	−11.4527	+	4.23872i	−0.916953	+	0.339369i
$157$	−1.15279	+	6.53778i	−0.0920024	+	0.521772i	0.903622	+	0.428330i	$0.140898\pi$
$157$	−1.15279	+	6.53778i	−0.0920024	+	0.521772i	−0.995625	+	0.0934416i	$0.970213\pi$
$158$	−5.71461	−	4.79513i	−0.454630	−	0.381480i
$159$	9.64725	−	8.18430i	0.765077	−	0.649057i
$160$	1.94369	+	0.707446i	0.153662	+	0.0559285i
$161$	5.62251			0.443116
$162$	−7.01789	−	5.63464i	−0.551378	−	0.442699i
$163$	−3.66259			−0.286877			−0.143438	−	0.989659i	$-0.545816\pi$
$163$	−3.66259			−0.286877			−0.143438	+	0.989659i	$0.545816\pi$
$164$	−2.97981	−	1.08456i	−0.232684	−	0.0846900i
$165$	2.41166	−	2.04595i	0.187748	−	0.159277i
$166$	0.563821	+	0.473102i	0.0437610	+	0.0367198i
$167$	4.13837	−	23.4698i	0.320236	−	1.81615i	−0.220992	−	0.975276i	$-0.570930\pi$
$167$	4.13837	−	23.4698i	0.320236	−	1.81615i	0.541229	−	0.840875i	$-0.317959\pi$
$168$	1.62437	−	0.601188i	0.125323	−	0.0463826i
$169$	28.1220	−	23.5971i	2.16323	−	1.81517i
$170$	0.947451	+	1.64103i	0.0726662	+	0.125862i
$171$	0.339277	−	0.127658i	0.0259451	−	0.00976226i
$172$	4.69882	−	8.13859i	0.358281	−	0.620562i
$173$	4.22350	+	23.9527i	0.321107	+	1.82109i	0.535730	+	0.844389i	$0.320037\pi$
$173$	4.22350	+	23.9527i	0.321107	+	1.82109i	−0.214623	+	0.976697i	$0.568852\pi$
$174$	12.8734	−	0.0696045i	0.975929	−	0.00527670i
$175$	0.678066	−	0.246796i	0.0512570	−	0.0186560i
$176$	−0.829522	+	0.301921i	−0.0625275	+	0.0227582i
$177$	1.84599	+	3.15780i	0.138753	+	0.237354i
$178$	0.197098	+	1.11780i	0.0147731	+	0.0837824i
$179$	4.54296	−	7.86863i	0.339556	−	0.588129i	−0.644793	−	0.764357i	$-0.723056\pi$
$179$	4.54296	−	7.86863i	0.339556	−	0.588129i	0.984349	+	0.176228i	$0.0563897\pi$
$180$	−3.16058	−	5.34008i	−0.235576	−	0.398026i
$181$	−4.67849	−	8.10339i	−0.347750	−	0.602320i	0.638100	−	0.769954i	$-0.279721\pi$
$181$	−4.67849	−	8.10339i	−0.347750	−	0.602320i	−0.985849	+	0.167634i	$0.946387\pi$
$182$	−5.40106	+	4.53202i	−0.400353	+	0.335936i
$183$	1.40469	−	8.22621i	0.103837	−	0.608099i
$184$	−0.976338	+	5.53709i	−0.0719766	+	0.408200i
$185$	10.8667	+	9.11828i	0.798939	+	0.670389i
$186$	2.84490	+	1.01807i	0.208598	+	0.0746489i
$187$	−0.759929	−	0.276591i	−0.0555715	−	0.0202264i
$188$	−6.02900			−0.439710
$189$	−4.91097	−	1.69776i	−0.357220	−	0.123494i
$190$	0.249935			0.0181322
$191$	16.9984	+	6.18692i	1.22996	+	0.447670i	0.873585	−	0.486672i	$-0.161789\pi$
$191$	16.9984	+	6.18692i	1.22996	+	0.447670i	0.356378	+	0.934342i	$0.384012\pi$
$192$	0.309986	+	1.70409i	0.0223713	+	0.122982i
$193$	11.6854	+	9.80523i	0.841135	+	0.705796i	0.957819	−	0.287373i	$-0.0927821\pi$
$193$	11.6854	+	9.80523i	0.841135	+	0.705796i	−0.116684	+	0.993169i	$0.537227\pi$
$194$	−0.809402	+	4.59034i	−0.0581116	+	0.329568i
$195$	19.4375	+	16.1317i	1.39195	+	1.15522i
$196$	0.766044	−	0.642788i	0.0547175	−	0.0459134i
$197$	8.98077	+	15.5552i	0.639854	+	1.10826i	0.985465	+	0.169881i	$0.0543383\pi$
$197$	8.98077	+	15.5552i	0.639854	+	1.10826i	−0.345611	+	0.938378i	$0.612328\pi$
$198$	2.49821	+	0.878801i	0.177540	+	0.0624536i
$199$	−5.46073	+	9.45826i	−0.387101	+	0.670478i	−0.992058	−	0.125780i	$-0.959857\pi$
$199$	−5.46073	+	9.45826i	−0.387101	+	0.670478i	0.604957	+	0.796258i	$0.293190\pi$
$200$	0.125302	+	0.710621i	0.00886016	+	0.0502485i
$201$	−12.0534	+	21.1403i	−0.850185	+	1.49112i
$202$	13.6570	−	4.97076i	0.960906	−	0.349741i
$203$	6.98432	−	2.54209i	0.490203	−	0.178419i
$204$	−0.785929	+	1.37843i	−0.0550260	+	0.0965092i
$205$	1.13897	+	6.45945i	0.0795494	+	0.451147i
$206$	−3.78830	+	6.56153i	−0.263943	+	0.457163i
$207$	12.8033	−	10.9813i	0.889889	−	0.763255i
$208$	−3.52529	−	6.10598i	−0.244435	−	0.423373i
$209$	−0.0817111	+	0.0685638i	−0.00565208	+	0.00474265i
$210$	−2.75687	−	2.28800i	−0.190242	−	0.157887i
$211$	1.77245	−	10.0521i	0.122021	−	0.692014i	−0.861012	−	0.508584i	$-0.830169\pi$
$211$	1.77245	−	10.0521i	0.122021	−	0.692014i	0.983033	−	0.183430i	$-0.0587199\pi$
$212$	5.59531	+	4.69502i	0.384287	+	0.322455i
$213$	−0.0120130	−	0.0660389i	−0.000823114	−	0.00452491i
$214$	−12.4375	−	4.52689i	−0.850212	−	0.309452i
$215$	−19.4384			−1.32569
$216$	2.52475	−	4.54155i	0.171787	−	0.309013i
$217$	1.74451			0.118425
$218$	−17.6782	−	6.43434i	−1.19732	−	0.435788i
$219$	−20.5116	−	7.34026i	−1.38605	−	0.496009i
$220$	1.39874	+	1.17368i	0.0943031	+	0.0791297i
$221$	1.12161	−	6.36094i	0.0754473	−	0.427883i
$222$	−1.99941	+	11.7091i	−0.134192	+	0.785863i
$223$	16.4427	−	13.7970i	1.10108	−	0.923917i	0.103585	−	0.994621i	$-0.466969\pi$
$223$	16.4427	−	13.7970i	1.10108	−	0.923917i	0.997497	+	0.0707032i	$0.0225243\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	1.06204	−	1.88632i	0.0708026	−	0.125755i
$226$	5.18532	−	8.98124i	0.344922	−	0.597423i
$227$	−3.14312	−	17.8255i	−0.208616	−	1.18312i	−0.891647	−	0.452731i	$-0.850450\pi$
$227$	−3.14312	−	17.8255i	−0.208616	−	1.18312i	0.683031	−	0.730389i	$-0.260661\pi$
$228$	0.105623	+	0.180681i	0.00699504	+	0.0119659i
$229$	21.4409	−	7.80383i	1.41685	−	0.515692i	0.483719	−	0.875224i	$-0.339286\pi$
$229$	21.4409	−	7.80383i	1.41685	−	0.515692i	0.933133	+	0.359532i	$0.117064\pi$
$230$	10.9284	−	3.97762i	0.720599	−	0.262276i
$231$	1.52896	−	0.00826686i	0.100598	−	0.000543920i
$232$	1.29065	+	7.31964i	0.0847354	+	0.480558i
$233$	3.53155	−	6.11683i	0.231360	−	0.400727i	−0.726849	−	0.686798i	$-0.759016\pi$
$233$	3.53155	−	6.11683i	0.231360	−	0.400727i	0.958209	+	0.286071i	$0.0923492\pi$
$234$	−3.44750	+	20.8689i	−0.225370	+	1.36424i
$235$	6.23529	+	10.7998i	0.406746	+	0.704504i
$236$	−1.61775	+	1.35745i	−0.105306	+	0.0883626i
$237$	−12.1176	+	4.48480i	−0.787124	+	0.291319i
$238$	−0.159080	+	0.902187i	−0.0103116	+	0.0584801i
$239$	−21.0313	−	17.6474i	−1.36040	−	1.14151i	−0.975858	−	0.218407i	$-0.929914\pi$
$239$	−21.0313	−	17.6474i	−1.36040	−	1.14151i	−0.384545	−	0.923106i	$-0.625642\pi$
$240$	2.73196	−	2.31768i	0.176348	−	0.149605i
$241$	16.7233	+	6.08678i	1.07724	+	0.392084i	0.818881	−	0.573964i	$-0.194595\pi$
$241$	16.7233	+	6.08678i	1.07724	+	0.392084i	0.258362	+	0.966048i	$0.416817\pi$
$242$	10.2207			0.657014
$243$	−14.4989	+	5.72557i	−0.930104	+	0.367296i
$244$	4.81815			0.308450
$245$	−1.94369	−	0.707446i	−0.124178	−	0.0451971i
$246$	−4.18828	+	3.55315i	−0.267035	+	0.226541i
$247$	−0.652625	−	0.547618i	−0.0415256	−	0.0348441i
$248$	−0.302931	+	1.71801i	−0.0192361	+	0.109094i
$249$	1.19556	−	0.442484i	0.0757656	−	0.0280413i
$250$	9.06592	−	7.60721i	0.573379	−	0.481122i
$251$	−3.16200	−	5.47674i	−0.199583	−	0.345689i	0.748810	−	0.662785i	$-0.230626\pi$
$251$	−3.16200	−	5.47674i	−0.199583	−	0.345689i	−0.948393	+	0.317096i	$0.897292\pi$
$252$	0.488967	−	2.95988i	0.0308020	−	0.186455i
$253$	−2.48166	+	4.29836i	−0.156020	+	0.270235i
$254$	−1.43975	−	8.16526i	−0.0903382	−	0.512334i
$255$	3.28202	−	0.0177454i	0.205528	−	0.00111126i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−16.9549	+	6.17106i	−1.05761	+	0.384940i	−0.811532	−	0.584309i	$-0.801366\pi$
$257$	−16.9549	+	6.17106i	−1.05761	+	0.384940i	−0.246083	+	0.969249i	$0.579144\pi$
$258$	−8.21469	−	14.0522i	−0.511424	−	0.874854i
$259$	1.19090	+	6.75391i	0.0739987	+	0.419668i
$260$	−7.29182	+	12.6298i	−0.452220	+	0.783268i
$261$	10.9394	−	19.4298i	0.677131	−	1.20267i
$262$	−4.50949	−	7.81066i	−0.278597	−	0.482544i
$263$	−5.94163	+	4.98562i	−0.366377	+	0.307426i	−0.807326	−	0.590105i	$-0.799086\pi$
$263$	−5.94163	+	4.98562i	−0.366377	+	0.307426i	0.440950	+	0.897532i	$0.354642\pi$
$264$	−0.257360	+	1.50717i	−0.0158394	+	0.0927597i
$265$	2.62351	−	14.8786i	0.161161	−	0.913987i
$266$	0.0925634	+	0.0776699i	0.00567543	+	0.00476225i
$267$	1.85099	+	0.662395i	0.113279	+	0.0405379i
$268$	−13.2026	−	4.80535i	−0.806477	−	0.293533i
$269$	−19.3852			−1.18193			−0.590967	−	0.806695i	$-0.701254\pi$
$269$	−19.3852			−1.18193			−0.590967	+	0.806695i	$0.701254\pi$
$270$	−10.7465	+	0.174328i	−0.654010	+	0.0106092i
$271$	11.4852			0.697673			0.348837	−	0.937184i	$-0.386577\pi$
$271$	11.4852			0.697673			0.348837	+	0.937184i	$0.386577\pi$
$272$	−0.860857	−	0.313326i	−0.0521971	−	0.0189982i
$273$	2.18558	+	12.0148i	0.132277	+	0.727168i
$274$	15.0998	+	12.6703i	0.912215	+	0.765439i
$275$	−0.110611	+	0.627306i	−0.00667010	+	0.0378280i
$276$	7.49384	+	6.21934i	0.451076	+	0.374360i
$277$	2.16203	−	1.81416i	0.129904	−	0.109002i	−0.575521	−	0.817787i	$-0.695201\pi$
$277$	2.16203	−	1.81416i	0.129904	−	0.109002i	0.705425	+	0.708785i	$0.250756\pi$
$278$	−6.07313	−	10.5190i	−0.364242	−	0.630886i
$279$	3.97251	−	3.40721i	0.237828	−	0.203984i
$280$	1.03422	−	1.79132i	0.0618063	−	0.107052i
$281$	−3.19165	−	18.1007i	−0.190398	−	1.07980i	−0.918822	−	0.394673i	$-0.870858\pi$
$281$	−3.19165	−	18.1007i	−0.190398	−	1.07980i	0.728424	−	0.685127i	$-0.240253\pi$
$282$	−5.17229	+	9.07160i	−0.308006	+	0.540206i
$283$	6.67862	−	2.43082i	0.397003	−	0.144497i	−0.135801	−	0.990736i	$-0.543361\pi$
$283$	6.67862	−	2.43082i	0.397003	−	0.144497i	0.532804	+	0.846239i	$0.321138\pi$
$284$	0.0364162	−	0.0132544i	0.00216090	−	0.000786504i
$285$	0.214420	−	0.376067i	0.0127011	−	0.0222763i
$286$	−1.08078	−	6.12940i	−0.0639078	−	0.362439i
$287$	−1.58552	+	2.74620i	−0.0935904	+	0.162103i
$288$	2.83001	+	0.995517i	0.166760	+	0.0586614i
$289$	8.08038	+	13.9956i	0.475316	+	0.823272i
$290$	11.7770	−	9.88206i	0.691568	−	0.580295i
$291$	6.21252	+	5.15594i	0.364184	+	0.302247i
$292$	2.18412	−	12.3867i	0.127816	−	0.724879i
$293$	8.24830	+	6.92114i	0.481871	+	0.404338i	0.851102	−	0.525000i	$-0.175935\pi$
$293$	8.24830	+	6.92114i	0.481871	+	0.404338i	−0.369232	+	0.929337i	$0.620379\pi$
$294$	−0.309986	−	1.70409i	−0.0180787	−	0.0993843i
$295$	4.10473	+	1.49400i	0.238986	+	0.0869839i
$296$	−6.85810			−0.398619
$297$	3.46552	−	3.00504i	0.201090	−	0.174370i
$298$	−11.1680			−0.646943
$299$	−37.2512	−	13.5583i	−2.15429	−	0.784099i
$300$	1.17674	+	0.421107i	0.0679391	+	0.0243126i
$301$	−7.19900	−	6.04068i	−0.414944	−	0.348179i
$302$	−2.20189	+	12.4875i	−0.126704	+	0.718576i
$303$	4.23711	−	24.8136i	0.243416	−	1.42551i
$304$	−0.0925634	+	0.0776699i	−0.00530887	+	0.00445467i
$305$	−4.98301	−	8.63082i	−0.285326	−	0.494200i
$306$	1.39981	+	2.36511i	0.0800220	+	0.135204i
$307$	−14.1490	+	24.5068i	−0.807527	+	1.39868i	0.107045	+	0.994254i	$0.465861\pi$
$307$	−14.1490	+	24.5068i	−0.807527	+	1.39868i	−0.914572	+	0.404424i	$0.867472\pi$
$308$	0.153289	+	0.869347i	0.00873447	+	0.0495357i
$309$	6.62288	+	11.3293i	0.376763	+	0.644499i
$310$	3.39079	−	1.23415i	0.192584	−	0.0700948i
$311$	−1.30133	+	0.473646i	−0.0737917	+	0.0268580i	−0.378652	−	0.925539i	$-0.623612\pi$
$311$	−1.30133	+	0.473646i	−0.0737917	+	0.0268580i	0.304861	+	0.952397i	$0.401390\pi$
$312$	−12.2118	+	0.0660273i	−0.691356	+	0.00373806i
$313$	−0.593729	−	3.36720i	−0.0335595	−	0.190326i	0.963419	−	0.267998i	$-0.0863622\pi$
$313$	−0.593729	−	3.36720i	−0.0335595	−	0.190326i	−0.996979	+	0.0776727i	$0.975251\pi$
$314$	−3.31932	+	5.74923i	−0.187320	+	0.324448i
$315$	−5.80778	+	2.18527i	−0.327232	+	0.123126i
$316$	−3.72995	−	6.46046i	−0.209826	−	0.363429i
$317$	4.32633	−	3.63022i	0.242991	−	0.203894i	−0.513156	−	0.858295i	$-0.671524\pi$
$317$	4.32633	−	3.63022i	0.242991	−	0.203894i	0.756147	+	0.654402i	$0.227079\pi$
$318$	11.8646	−	4.39117i	0.665336	−	0.246245i
$319$	−1.13933	+	6.46148i	−0.0637904	+	0.361773i
$320$	1.58451	+	1.32956i	0.0885769	+	0.0743249i
$321$	−17.4816	+	14.8306i	−0.975729	+	0.827765i
$322$	5.28343	+	1.92301i	0.294434	+	0.107165i
$323$	−0.110696			−0.00615927
$324$	−4.66750	−	7.69509i	−0.259306	−	0.427505i
$325$	−5.08758			−0.282208
$326$	−3.44171	−	1.25268i	−0.190619	−	0.0693796i
$327$	−24.8477	+	21.0797i	−1.37408	+	1.16571i
$328$	−2.42916	−	2.03831i	−0.134128	−	0.112547i
$329$	−1.04692	+	5.93740i	−0.0577188	+	0.327340i
$330$	2.96598	−	1.09772i	0.163272	−	0.0604278i
$331$	−7.65668	+	6.42471i	−0.420849	+	0.353134i	−0.828486	−	0.560010i	$-0.810797\pi$
$331$	−7.65668	+	6.42471i	−0.420849	+	0.353134i	0.407637	+	0.913144i	$0.366353\pi$
$332$	0.368008	+	0.637409i	0.0201971	+	0.0349823i
$333$	15.9029	+	13.0537i	0.871474	+	0.715339i
$334$	11.9160	−	20.6390i	0.652012	−	1.12932i
$335$	5.04644	+	28.6198i	0.275716	+	1.56367i
$336$	1.73203	−	0.00936481i	0.0944897	−	0.000510892i
$337$	−22.3456	+	8.13315i	−1.21724	+	0.443041i	−0.869211	−	0.494442i	$-0.835373\pi$
$337$	−22.3456	+	8.13315i	−1.21724	+	0.443041i	−0.348033	+	0.937482i	$0.613150\pi$
$338$	34.4967	−	12.5558i	1.87637	−	0.682944i
$339$	−9.06522	−	15.5072i	−0.492355	−	0.842234i
$340$	0.329046	+	1.86611i	0.0178450	+	0.101204i
$341$	−0.769991	+	1.33366i	−0.0416973	+	0.0722219i
$342$	0.362478	−	0.00391984i	0.0196005	−	0.000211961i
$343$	−0.500000	−	0.866025i	−0.0269975	−	0.0467610i
$344$	7.19900	−	6.04068i	0.388144	−	0.325692i
$345$	3.39055	−	19.8560i	0.182541	−	1.06901i
$346$	−4.22350	+	23.9527i	−0.227057	+	1.28770i
$347$	−6.99913	−	5.87297i	−0.375733	−	0.315278i	0.435291	−	0.900290i	$-0.356645\pi$
$347$	−6.99913	−	5.87297i	−0.375733	−	0.315278i	−0.811025	+	0.585012i	$0.801090\pi$
$348$	12.1208	+	4.33755i	0.649745	+	0.232517i
$349$	−23.0506	−	8.38972i	−1.23387	−	0.449092i	−0.358948	−	0.933358i	$-0.616864\pi$
$349$	−23.0506	−	8.38972i	−1.23387	−	0.449092i	−0.874921	+	0.484266i	$0.839087\pi$
$350$	0.721583			0.0385702
$351$	28.4430	+	23.0908i	1.51817	+	1.23250i
$352$	−0.882758			−0.0470512
$353$	12.2327	+	4.45233i	0.651080	+	0.236974i	0.646380	−	0.763015i	$-0.276282\pi$
$353$	12.2327	+	4.45233i	0.651080	+	0.236974i	0.00469940	+	0.999989i	$0.498504\pi$
$354$	0.654634	+	3.59872i	0.0347934	+	0.191270i
$355$	−0.0614050	−	0.0515249i	−0.00325904	−	0.00273466i
$356$	−0.197098	+	1.11780i	−0.0104462	+	0.0592431i
$357$	1.22101	+	1.01335i	0.0646227	+	0.0536322i
$358$	6.96021	−	5.84031i	0.367859	−	0.308670i
$359$	10.4650	+	18.1259i	0.552321	+	0.956648i	0.998107	+	0.0615079i	$0.0195909\pi$
$359$	10.4650	+	18.1259i	0.552321	+	0.956648i	−0.445786	+	0.895140i	$0.647076\pi$
$360$	−1.14356	−	6.09902i	−0.0602707	−	0.321447i
$361$	9.49270	−	16.4418i	0.499616	−	0.865360i
$362$	−1.62482	−	9.21484i	−0.0853989	−	0.484321i
$363$	8.76840	−	15.3787i	0.460222	−	0.807175i
$364$	−6.62538	+	2.41144i	−0.347264	+	0.126394i
$365$	−24.4474	+	8.89813i	−1.27964	+	0.465750i
$366$	4.13350	−	7.24968i	0.216062	−	0.378947i
$367$	5.62360	+	31.8930i	0.293549	+	1.66480i	0.673041	+	0.739605i	$0.264988\pi$
$367$	5.62360	+	31.8930i	0.293549	+	1.66480i	−0.379491	+	0.925195i	$0.623901\pi$
$368$	−2.81125	+	4.86923i	−0.146547	+	0.253826i
$369$	1.75315	+	9.35020i	0.0912652	+	0.486752i
$370$	7.09276	+	12.2850i	0.368735	+	0.638668i
$371$	5.59531	−	4.69502i	0.290494	−	0.243753i
$372$	2.32513	+	1.92969i	0.120553	+	0.100050i
$373$	−0.663390	+	3.76227i	−0.0343491	+	0.194803i	−0.997154	−	0.0753952i	$-0.975978\pi$
$373$	−0.663390	+	3.76227i	−0.0343491	+	0.194803i	0.962805	+	0.270198i	$0.0870893\pi$
$374$	−0.619500	−	0.519822i	−0.0320336	−	0.0268793i
$375$	−3.66859	−	20.1674i	−0.189445	−	1.04144i
$376$	−5.66541	−	2.06204i	−0.292171	−	0.106342i
$377$	−52.4038			−2.69894
$378$	−4.03413	−	3.27502i	−0.207493	−	0.168449i
$379$	7.45865			0.383125			0.191563	−	0.981480i	$-0.438645\pi$
$379$	7.45865			0.383125			0.191563	+	0.981480i	$0.438645\pi$
$380$	0.234862	+	0.0854828i	0.0120482	+	0.00438517i
$381$	−13.5211	−	4.83865i	−0.692707	−	0.247892i
$382$	13.8572	+	11.6276i	0.708998	+	0.594920i
$383$	−1.21848	+	6.91036i	−0.0622616	+	0.353103i	0.937722	+	0.347386i	$0.112931\pi$
$383$	−1.21848	+	6.91036i	−0.0622616	+	0.353103i	−0.999984	+	0.00571657i	$0.998180\pi$
$384$	−0.291541	+	1.70734i	−0.0148776	+	0.0871272i
$385$	1.39874	−	1.17368i	0.0712865	−	0.0598164i
$386$	7.62711	+	13.2105i	0.388210	+	0.672399i
$387$	−28.1912	+	0.304861i	−1.43304	+	0.0154969i
$388$	−2.33058	+	4.03668i	−0.118317	+	0.204931i
$389$	0.711614	+	4.03576i	0.0360802	+	0.204621i	0.997519	−	0.0703979i	$-0.0224269\pi$
$389$	0.711614	+	4.03576i	0.0360802	+	0.204621i	−0.961439	+	0.275019i	$0.911316\pi$
$390$	12.7479	+	21.8069i	0.645515	+	1.10423i
$391$	−4.84017	+	1.76168i	−0.244778	+	0.0890920i
$392$	0.939693	−	0.342020i	0.0474616	−	0.0172746i
$393$	−15.6211	+	0.0844610i	−0.787980	+	0.00426049i
$394$	3.11899	+	17.6887i	0.157132	+	0.891142i
$395$	−7.71515	+	13.3630i	−0.388191	+	0.672367i
$396$	2.04699	+	1.68024i	0.102865	+	0.0844353i
$397$	1.37006	+	2.37301i	0.0687613	+	0.119098i	0.898356	−	0.439268i	$-0.144762\pi$
$397$	1.37006	+	2.37301i	0.0687613	+	0.119098i	−0.829595	+	0.558366i	$0.811429\pi$
$398$	−8.36632	+	7.02018i	−0.419366	+	0.351890i
$399$	0.196277	−	0.0726433i	0.00982615	−	0.00363671i
$400$	−0.125302	+	0.710621i	−0.00626508	+	0.0355310i
$401$	−7.05067	−	5.91621i	−0.352094	−	0.295442i	0.449537	−	0.893262i	$-0.351589\pi$
$401$	−7.05067	−	5.91621i	−0.352094	−	0.295442i	−0.801630	+	0.597820i	$0.796034\pi$
$402$	−18.5570	+	15.7429i	−0.925537	+	0.785184i
$403$	−11.5580	−	4.20678i	−0.575747	−	0.209555i
$404$	14.5335			0.723070
$405$	−8.95713	+	16.3194i	−0.445083	+	0.810916i
$406$	7.43256			0.368872
$407$	−5.68894	−	2.07061i	−0.281990	−	0.102636i
$408$	−1.20998	+	1.02649i	−0.0599030	+	0.0508190i
$409$	10.2568	+	8.60645i	0.507164	+	0.425561i	0.860130	−	0.510075i	$-0.170382\pi$
$409$	10.2568	+	8.60645i	0.507164	+	0.425561i	−0.352966	+	0.935636i	$0.614827\pi$
$410$	−1.13897	+	6.45945i	−0.0562499	+	0.319009i
$411$	32.0187	−	11.8503i	1.57936	−	0.584531i
$412$	−5.80401	+	4.87015i	−0.285943	+	0.239935i
$413$	1.05591	+	1.82889i	0.0519579	+	0.0899938i
$414$	15.7870	−	5.94009i	0.775888	−	0.291940i
$415$	0.761200	−	1.31844i	0.0373658	−	0.0647195i
$416$	−1.22432	−	6.94346i	−0.0600272	−	0.340431i
$417$	−21.0376	+	0.113747i	−1.03022	+	0.00557023i
$418$	−0.100234	+	0.0364820i	−0.00490258	+	0.00178439i
$419$	29.9050	−	10.8845i	1.46096	−	0.531745i	0.515328	−	0.856993i	$-0.327670\pi$
$419$	29.9050	−	10.8845i	1.46096	−	0.531745i	0.945629	+	0.325248i	$0.105448\pi$
$420$	−1.80807	−	3.09292i	−0.0882245	−	0.150919i
$421$	3.51287	+	19.9225i	0.171207	+	0.970961i	0.942432	+	0.334399i	$0.108533\pi$
$421$	3.51287	+	19.9225i	0.171207	+	0.970961i	−0.771225	+	0.636563i	$0.780356\pi$
$422$	5.10358	−	8.83965i	0.248438	−	0.430308i
$423$	9.21235	+	15.5651i	0.447920	+	0.756801i
$424$	3.65208	+	6.32559i	0.177361	+	0.307198i
$425$	−0.506390	+	0.424912i	−0.0245635	+	0.0206113i
$426$	0.0112981	−	0.0661649i	0.000547397	−	0.00320570i
$427$	0.836662	−	4.74495i	0.0404889	−	0.229624i
$428$	−10.1392	−	8.50777i	−0.490095	−	0.411239i
$429$	−10.1499	−	3.63222i	−0.490040	−	0.175365i
$430$	−18.2661	−	6.64832i	−0.880870	−	0.320610i
$431$	17.7556			0.855257			0.427629	−	0.903954i	$-0.359349\pi$
$431$	17.7556			0.855257			0.427629	+	0.903954i	$0.359349\pi$
$432$	3.92579	−	3.40415i	0.188879	−	0.163782i
$433$	−12.6379			−0.607339			−0.303669	−	0.952777i	$-0.598212\pi$
$433$	−12.6379			−0.607339			−0.303669	+	0.952777i	$0.598212\pi$
$434$	1.63930	+	0.596658i	0.0786891	+	0.0286405i
$435$	−4.76564	−	26.1982i	−0.228495	−	1.25611i
$436$	−14.4114	−	12.0926i	−0.690181	−	0.579131i
$437$	−0.117974	+	0.669063i	−0.00564345	+	0.0320056i
$438$	−16.7641	−	13.9130i	−0.801019	−	0.664788i
$439$	−8.10334	+	6.79951i	−0.386751	+	0.324523i	−0.815346	−	0.578974i	$-0.803453\pi$
$439$	−8.10334	+	6.79951i	−0.386751	+	0.324523i	0.428595	+	0.903497i	$0.359009\pi$
$440$	0.912963	+	1.58130i	0.0435238	+	0.0753855i
$441$	−2.83001	−	0.995517i	−0.134762	−	0.0474056i
$442$	3.22953	−	5.59372i	0.153613	−	0.266066i
$443$	−2.08942	−	11.8497i	−0.0992712	−	0.562995i	−0.993355	−	0.115094i	$-0.963283\pi$
$443$	−2.08942	−	11.8497i	−0.0992712	−	0.562995i	0.894083	−	0.447900i	$-0.147828\pi$
$444$	−5.88358	+	10.3191i	−0.279222	+	0.489723i
$445$	2.20617	−	0.802980i	0.104582	−	0.0380649i
$446$	20.1699	−	7.34125i	0.955073	−	0.347618i
$447$	−9.58103	+	16.8040i	−0.453167	+	0.794802i
$448$	0.173648	+	0.984808i	0.00820411	+	0.0465278i
$449$	2.29376	−	3.97291i	0.108249	−	0.187493i	−0.806812	−	0.590808i	$-0.798809\pi$
$449$	2.29376	−	3.97291i	0.108249	−	0.187493i	0.915061	+	0.403315i	$0.132142\pi$
$450$	1.64315	−	1.40932i	0.0774589	−	0.0664362i
$451$	−1.39963	−	2.42424i	−0.0659061	−	0.114153i
$452$	7.94437	−	6.66612i	0.373672	−	0.313548i
$453$	16.9005	+	14.0262i	0.794054	+	0.659007i
$454$	3.14312	−	17.8255i	0.147514	−	0.836592i
$455$	11.1717	+	9.37419i	0.523738	+	0.439469i
$456$	0.0374565	+	0.205910i	0.00175406	+	0.00964260i
$457$	−5.17979	−	1.88529i	−0.242301	−	0.0881902i	0.218015	−	0.975945i	$-0.430042\pi$
$457$	−5.17979	−	1.88529i	−0.242301	−	0.0881902i	−0.460316	+	0.887755i	$0.652264\pi$
$458$	22.8169			1.06616
$459$	4.75959	−	0.0772093i	0.222159	−	0.00360382i
$460$	11.6298			0.542241
$461$	−10.1488	−	3.69386i	−0.472677	−	0.172040i	0.0946878	−	0.995507i	$-0.469815\pi$
$461$	−10.1488	−	3.69386i	−0.472677	−	0.172040i	−0.567364	+	0.823467i	$0.692037\pi$
$462$	1.43958	+	0.515167i	0.0669753	+	0.0239677i
$463$	−1.67358	−	1.40430i	−0.0777779	−	0.0652634i	0.603070	−	0.797688i	$-0.293944\pi$
$463$	−1.67358	−	1.40430i	−0.0777779	−	0.0652634i	−0.680848	+	0.732425i	$0.738388\pi$
$464$	−1.29065	+	7.31964i	−0.0599169	+	0.339806i
$465$	1.05200	−	6.16077i	0.0487852	−	0.285699i
$466$	5.41065	−	4.54008i	0.250644	−	0.210315i
$467$	−16.1979	−	28.0557i	−0.749551	−	1.29826i	−0.948038	−	0.318157i	$-0.896936\pi$
$467$	−16.1979	−	28.0557i	−0.749551	−	1.29826i	0.198487	−	0.980104i	$-0.436397\pi$
$468$	−10.3772	+	18.4312i	−0.479685	+	0.851984i
$469$	−7.02495	+	12.1676i	−0.324382	+	0.561846i
$470$	2.16549	+	12.2811i	0.0998868	+	0.566486i
$471$	5.80298	+	9.92672i	0.267387	+	0.457399i
$472$	−1.98446	+	0.722285i	−0.0913422	+	0.0332459i
$473$	7.79554	−	2.83734i	0.358439	−	0.130461i
$474$	−12.9207	+	0.0698604i	−0.593469	+	0.00320880i
$475$	0.0151406	+	0.0858664i	0.000694696	+	0.00393982i
$476$	−0.458052	+	0.793370i	−0.0209948	+	0.0363641i
$477$	3.57149	−	21.6195i	0.163527	−	0.989887i
$478$	−13.7272	−	23.7762i	−0.627868	−	1.08750i
$479$	−22.8104	+	19.1402i	−1.04223	+	0.874538i	−0.992256	−	0.124212i	$-0.960360\pi$
$479$	−22.8104	+	19.1402i	−1.04223	+	0.874538i	−0.0499784	+	0.998750i	$0.515915\pi$
$480$	3.35990	−	1.24352i	0.153358	−	0.0567585i
$481$	8.39651	−	47.6190i	0.382848	−	2.17124i
$482$	13.6330	+	11.4394i	0.620964	+	0.521051i
$483$	7.42615	−	6.30001i	0.337901	−	0.286660i
$484$	9.60435	+	3.49570i	0.436561	+	0.158895i
$485$	9.64129			0.437789
$486$	−15.5828	+	0.421367i	−0.706848	+	0.0191136i
$487$	−31.0180			−1.40556			−0.702781	−	0.711407i	$-0.748058\pi$
$487$	−31.0180			−1.40556			−0.702781	+	0.711407i	$0.748058\pi$
$488$	4.52758	+	1.64790i	0.204954	+	0.0745971i
$489$	−4.83751	+	4.10393i	−0.218760	+	0.185586i
$490$	−1.58451	−	1.32956i	−0.0715810	−	0.0600636i
$491$	−4.08518	+	23.1682i	−0.184361	+	1.04557i	0.742412	+	0.669944i	$0.233682\pi$
$491$	−4.08518	+	23.1682i	−0.184361	+	1.04557i	−0.926773	+	0.375622i	$0.877429\pi$
$492$	−5.15094	+	1.90639i	−0.232223	+	0.0859468i
$493$	−5.21600	+	4.37674i	−0.234917	+	0.197119i
$494$	−0.425971	−	0.737803i	−0.0191653	−	0.0331953i
$495$	0.892818	−	5.40453i	0.0401292	−	0.242916i
$496$	−0.872256	+	1.51079i	−0.0391654	+	0.0678365i
$497$	−0.00672943	−	0.0381645i	−0.000301856	−	0.00171191i
$498$	1.27480	−	0.00689265i	0.0571251	−	0.000308867i
$499$	1.37937	−	0.502049i	0.0617490	−	0.0224748i	−0.310961	−	0.950423i	$-0.600651\pi$
$499$	1.37937	−	0.502049i	0.0617490	−	0.0224748i	0.372710	+	0.927948i	$0.378429\pi$
$500$	11.1210	−	4.04771i	0.497346	−	0.181019i
$501$	−20.8320	−	35.6357i	−0.930706	−	1.59209i
$502$	−1.09815	−	6.22792i	−0.0490128	−	0.277965i
$503$	3.12372	−	5.41044i	0.139280	−	0.241239i	−0.787945	−	0.615746i	$-0.788855\pi$
$503$	3.12372	−	5.41044i	0.139280	−	0.241239i	0.927224	+	0.374507i	$0.122188\pi$
$504$	1.47182	−	2.61414i	0.0655600	−	0.116443i
$505$	−15.0308	−	26.0341i	−0.668862	−	1.15850i
$506$	−3.80212	+	3.19036i	−0.169025	+	0.141829i
$507$	10.7026	−	62.6775i	0.475321	−	2.78360i
$508$	1.43975	−	8.16526i	0.0638788	−	0.362275i
$509$	16.3209	+	13.6949i	0.723413	+	0.607016i	0.928327	−	0.371764i	$-0.121247\pi$
$509$	16.3209	+	13.6949i	0.723413	+	0.607016i	−0.204914	+	0.978780i	$0.565691\pi$
$510$	3.09016	+	1.10584i	0.136834	+	0.0489675i
$511$	−11.8193	−	4.30187i	−0.522855	−	0.190304i
$512$	−1.00000			−0.0441942
$513$	0.305072	−	0.548769i	0.0134693	−	0.0242287i
$514$	−18.0430			−0.795842
$515$	14.7266	+	5.36004i	0.648931	+	0.236191i
$516$	−2.91313	−	16.0144i	−0.128243	−	0.704993i
$517$	−4.07700	−	3.42101i	−0.179306	−	0.150456i
$518$	−1.19090	+	6.75391i	−0.0523250	+	0.296750i
$519$	32.4173	+	26.9040i	1.42296	+	1.18095i
$520$	−11.1717	+	9.37419i	−0.489913	+	0.411085i
$521$	10.3091	+	17.8559i	0.451649	+	0.782280i	0.998489	−	0.0549579i	$-0.0175025\pi$
$521$	10.3091	+	17.8559i	0.451649	+	0.782280i	−0.546839	+	0.837238i	$0.684169\pi$
$522$	16.9250	−	14.5165i	0.740788	−	0.635372i
$523$	−4.09556	+	7.09371i	−0.179086	+	0.310186i	−0.941568	−	0.336823i	$-0.890647\pi$
$523$	−4.09556	+	7.09371i	−0.179086	+	0.310186i	0.762482	+	0.647010i	$0.223981\pi$
$524$	−1.56613	−	8.88196i	−0.0684166	−	0.388010i
$525$	0.619048	−	1.08574i	0.0270175	−	0.0473855i
$526$	−7.28849	+	2.65279i	−0.317793	+	0.115667i
$527$	−1.50177	+	0.546601i	−0.0654183	+	0.0238103i
$528$	−0.757321	+	1.32825i	−0.0329582	+	0.0578047i
$529$	1.49556	+	8.48174i	0.0650244	+	0.368771i
$530$	7.55408	−	13.0841i	0.328128	−	0.568335i
$531$	5.97647	+	2.10235i	0.259357	+	0.0912343i
$532$	0.0604165	+	0.104644i	0.00261939	+	0.00453691i
$533$	17.1270	−	14.3712i	0.741852	−	0.622488i
$534$	1.51281	+	1.25553i	0.0654658	+	0.0543319i
$535$	−4.75401	+	26.9613i	−0.205534	+	1.16564i
$536$	−10.7628	−	9.03110i	−0.464884	−	0.390084i
$537$	−2.81650	−	15.4832i	−0.121541	−	0.668148i
$538$	−18.2161	−	6.63012i	−0.785352	−	0.285845i
$539$	0.882758			0.0380231
$540$	−10.1580	−	3.51170i	−0.437131	−	0.151119i
$541$	39.5661			1.70108			0.850541	−	0.525909i	$-0.176275\pi$
$541$	39.5661			1.70108			0.850541	+	0.525909i	$0.176275\pi$
$542$	10.7925	+	3.92815i	0.463578	+	0.168729i
$543$	−15.2591	−	5.46062i	−0.654832	−	0.234338i
$544$	−0.701777	−	0.588861i	−0.0300884	−	0.0252472i
$545$	−6.75716	+	38.3217i	−0.289445	+	1.64152i
$546$	−2.05553	+	12.0377i	−0.0879685	+	0.515167i
$547$	17.4536	−	14.6453i	0.746260	−	0.626187i	−0.188251	−	0.982121i	$-0.560282\pi$
$547$	17.4536	−	14.6453i	0.746260	−	0.626187i	0.934511	+	0.355934i	$0.115837\pi$
$548$	9.85572	+	17.0706i	0.421016	+	0.729220i
$549$	−7.36216	−	12.4390i	−0.314209	−	0.530885i
$550$	−0.318492	+	0.551644i	−0.0135805	+	0.0235222i
$551$	0.155953	+	0.884454i	0.00664382	+	0.0376790i
$552$	4.91476	+	8.40731i	0.209186	+	0.357839i
$553$	−7.01001	+	2.55143i	−0.298096	+	0.108498i
$554$	2.65213	−	0.965296i	0.112678	−	0.0410115i
$555$	24.5697	−	0.132845i	1.04293	−	0.00563894i
$556$	−2.10917	−	11.9617i	−0.0894489	−	0.507290i
$557$	15.0245	−	26.0233i	0.636610	−	1.10264i	−0.349561	−	0.936914i	$-0.613669\pi$
$557$	15.0245	−	26.0233i	0.636610	−	1.10264i	0.986171	−	0.165728i	$-0.0529974\pi$
$558$	4.89827	−	1.84305i	0.207360	−	0.0780225i
$559$	33.1294	+	57.3817i	1.40122	+	2.42699i
$560$	1.58451	−	1.32956i	0.0669579	−	0.0561843i
$561$	−1.31363	+	0.486180i	−0.0554613	+	0.0205265i
$562$	3.19165	−	18.1007i	0.134632	−	0.763534i
$563$	15.4251	+	12.9432i	0.650090	+	0.545490i	0.907098	−	0.420919i	$-0.138292\pi$
$563$	15.4251	+	12.9432i	0.650090	+	0.545490i	−0.257008	+	0.966409i	$0.582737\pi$
$564$	−7.96303	+	6.75548i	−0.335304	+	0.284457i
$565$	−20.1573	−	7.33667i	−0.848025	−	0.308656i
$566$	7.10724			0.298740
$567$	−8.38869	+	3.26035i	−0.352292	+	0.136922i
$568$	0.0387533			0.00162605
$569$	9.26716	+	3.37297i	0.388499	+	0.141402i	0.528883	−	0.848695i	$-0.322611\pi$
$569$	9.26716	+	3.37297i	0.388499	+	0.141402i	−0.140383	+	0.990097i	$0.544833\pi$
$570$	0.330111	−	0.280052i	0.0138268	−	0.0117301i
$571$	−16.1161	−	13.5230i	−0.674437	−	0.565920i	0.239938	−	0.970788i	$-0.422873\pi$
$571$	−16.1161	−	13.5230i	−0.674437	−	0.565920i	−0.914375	+	0.404868i	$0.867317\pi$
$572$	1.08078	−	6.12940i	0.0451896	−	0.256283i
$573$	29.3838	−	10.8751i	1.22752	−	0.454313i
$574$	−2.42916	+	2.03831i	−0.101391	+	0.0850773i
$575$	2.02855	+	3.51356i	0.0845965	+	0.146525i
$576$	2.31885	+	1.90340i	0.0966188	+	0.0793083i
$577$	−4.95487	+	8.58208i	−0.206274	+	0.357277i	−0.950538	−	0.310609i	$-0.899467\pi$
$577$	−4.95487	+	8.58208i	−0.206274	+	0.357277i	0.744264	+	0.667886i	$0.232800\pi$
$578$	2.80629	+	15.9152i	0.116726	+	0.661986i
$579$	26.4207	−	0.142853i	1.09801	−	0.00593676i
$580$	14.4466	−	5.25813i	0.599863	−	0.218332i
$581$	0.691629	−	0.251732i	0.0286936	−	0.0104436i
$582$	4.07442	+	6.96981i	0.168890	+	0.288908i
$583$	1.11965	+	6.34985i	0.0463712	+	0.262984i
$584$	6.28891	−	10.8927i	0.260237	−	0.450744i
$585$	43.7484	−	0.473096i	1.80877	−	0.0195601i
$586$	5.38369	+	9.32483i	0.222398	+	0.385205i
$587$	−16.4908	+	13.8374i	−0.680647	+	0.571131i	−0.916195	−	0.400732i	$-0.868756\pi$
$587$	−16.4908	+	13.8374i	−0.680647	+	0.571131i	0.235548	+	0.971863i	$0.424311\pi$
$588$	0.291541	−	1.70734i	0.0120229	−	0.0704094i
$589$	−0.0366041	+	0.207592i	−0.00150824	+	0.00855368i
$590$	3.34620	+	2.80780i	0.137761	+	0.115595i
$591$	29.2912	+	10.4821i	1.20488	+	0.431177i
$592$	−6.44451	−	2.34561i	−0.264868	−	0.0964039i
$593$	32.6714			1.34165			0.670827	−	0.741614i	$-0.265939\pi$
$593$	32.6714			1.34165			0.670827	+	0.741614i	$0.265939\pi$
$594$	4.28431	−	1.63853i	0.175787	−	0.0672299i
$595$	1.89490			0.0776834
$596$	−10.4945	−	3.81967i	−0.429870	−	0.156460i
$597$	3.38549	+	18.6111i	0.138559	+	0.761702i
$598$	−30.3675	−	25.4813i	−1.24182	−	1.04201i
$599$	4.97901	−	28.2374i	0.203437	−	1.15375i	−0.696444	−	0.717611i	$-0.745236\pi$
$599$	4.97901	−	28.2374i	0.203437	−	1.15375i	0.899881	−	0.436136i	$-0.143653\pi$
$600$	0.961746	+	0.798180i	0.0392631	+	0.0325855i
$601$	−1.12974	+	0.947960i	−0.0460829	+	0.0386681i	−0.665538	−	0.746364i	$-0.731798\pi$
$601$	−1.12974	+	0.947960i	−0.0460829	+	0.0386681i	0.619455	+	0.785032i	$0.287353\pi$
$602$	−4.69882	−	8.13859i	−0.191509	−	0.331704i
$603$	7.76765	+	41.4278i	0.316323	+	1.68707i
$604$	−6.34008	+	10.9813i	−0.257974	+	0.446825i
$605$	−3.67108	−	20.8197i	−0.149251	−	0.846443i
$606$	12.4683	−	21.8680i	0.506492	−	0.888327i
$607$	33.7917	−	12.2992i	1.37156	−	0.499208i	0.451953	−	0.892042i	$-0.350727\pi$
$607$	33.7917	−	12.2992i	1.37156	−	0.499208i	0.919610	+	0.392834i	$0.128505\pi$
$608$	−0.113546	+	0.0413273i	−0.00460489	+	0.00167604i
$609$	6.37641	−	11.1835i	0.258385	−	0.453177i
$610$	−1.73058	−	9.81461i	−0.0700692	−	0.397382i
$611$	21.2540	−	36.8129i	0.859843	−	1.48929i
$612$	0.506479	+	2.70124i	0.0204732	+	0.109191i
$613$	−21.7284	−	37.6347i	−0.877602	−	1.52005i	−0.853965	−	0.520330i	$-0.825809\pi$
$613$	−21.7284	−	37.6347i	−0.877602	−	1.52005i	−0.0236366	−	0.999721i	$-0.507524\pi$
$614$	−21.6776	+	18.1896i	−0.874835	+	0.734074i
$615$	8.74214	+	7.25535i	0.352517	+	0.292564i
$616$	−0.153289	+	0.869347i	−0.00617621	+	0.0350270i
$617$	2.26327	+	1.89911i	0.0911160	+	0.0764554i	0.687208	−	0.726461i	$-0.258836\pi$
$617$	2.26327	+	1.89911i	0.0911160	+	0.0764554i	−0.596092	+	0.802916i	$0.703281\pi$
$618$	2.34864	+	12.9112i	0.0944761	+	0.519364i
$619$	16.2650	+	5.91996i	0.653744	+	0.237943i	0.647533	−	0.762037i	$-0.275801\pi$
$619$	16.2650	+	5.91996i	0.653744	+	0.237943i	0.00621073	+	0.999981i	$0.498023\pi$
$620$	3.60840			0.144917
$621$	4.60587	−	28.8501i	0.184827	−	1.15771i
$622$	−1.38485			−0.0555273
$623$	1.06659	+	0.388207i	0.0427320	+	0.0155532i
$624$	−11.4979	−	4.11463i	−0.460284	−	0.164717i
$625$	−15.9884	−	13.4159i	−0.639537	−	0.536635i
$626$	0.593729	−	3.36720i	0.0237302	−	0.134581i
$627$	−0.0310975	+	0.182115i	−0.00124192	+	0.00727299i
$628$	−5.08549	+	4.26723i	−0.202933	+	0.170281i
$629$	−3.14137	−	5.44101i	−0.125255	−	0.216947i
$630$	−6.20494	+	0.0671003i	−0.247211	+	0.00267334i
$631$	−10.1757	+	17.6249i	−0.405090	+	0.701637i	−0.994332	−	0.106320i	$-0.966093\pi$
$631$	−10.1757	+	17.6249i	−0.405090	+	0.701637i	0.589242	+	0.807957i	$0.299427\pi$
$632$	−1.29540	−	7.34656i	−0.0515281	−	0.292230i
$633$	−8.92231	−	15.2627i	−0.354630	−	0.606638i
$634$	5.30703	−	1.93160i	0.210769	−	0.0767137i
$635$	−16.1156	+	5.86559i	−0.639527	+	0.232769i
$636$	12.6510	−	0.0684020i	0.501644	−	0.00271232i
$637$	1.22432	+	6.94346i	0.0485093	+	0.275110i
$638$	−3.28058	+	5.68213i	−0.129879	+	0.224958i
$639$	−0.0898630	−	0.0737629i	−0.00355493	−	0.00291802i
$640$	1.03422	+	1.79132i	0.0408810	+	0.0708080i
$641$	7.96917	−	6.68693i	0.314763	−	0.264118i	−0.471694	−	0.881762i	$-0.656357\pi$
$641$	7.96917	−	6.68693i	0.314763	−	0.264118i	0.786458	+	0.617644i	$0.211913\pi$
$642$	−21.4997	+	7.95716i	−0.848526	+	0.314044i
$643$	−0.100845	+	0.571918i	−0.00397692	+	0.0225542i	−0.986732	−	0.162360i	$-0.948090\pi$
$643$	−0.100845	+	0.571918i	−0.00397692	+	0.0225542i	0.982755	+	0.184914i	$0.0592006\pi$
$644$	4.30709	+	3.61408i	0.169723	+	0.142415i
$645$	−25.6740	+	21.7807i	−1.01091	+	0.857613i
$646$	−0.104020	−	0.0378601i	−0.00409261	−	0.00148959i
$647$	37.4488			1.47226			0.736132	−	0.676838i	$-0.236650\pi$
$647$	37.4488			1.47226			0.736132	+	0.676838i	$0.236650\pi$
$648$	−1.75414	−	8.82740i	−0.0689092	−	0.346773i
$649$	−1.86423			−0.0731773
$650$	−4.78076	−	1.74005i	−0.187517	−	0.0682505i
$651$	2.30413	−	1.95472i	0.0903060	−	0.0766116i
$652$	−2.80571	−	2.35427i	−0.109880	−	0.0922003i
$653$	0.438088	−	2.48452i	0.0171437	−	0.0972267i	−0.975035	−	0.222050i	$-0.928725\pi$
$653$	0.438088	−	2.48452i	0.0171437	−	0.0972267i	0.992179	+	0.124823i	$0.0398363\pi$
$654$	−30.5588	+	11.3100i	−1.19495	+	0.442256i
$655$	−14.2907	+	11.9913i	−0.558383	+	0.468539i
$656$	−1.58552	−	2.74620i	−0.0619042	−	0.107221i
$657$	−35.3163	+	13.2883i	−1.37782	+	0.518425i
$658$	−3.01450	+	5.22127i	−0.117517	+	0.203546i
$659$	−7.47918	−	42.4166i	−0.291348	−	1.65231i	−0.681687	−	0.731644i	$-0.738754\pi$
$659$	−7.47918	−	42.4166i	−0.291348	−	1.65231i	0.390340	−	0.920671i	$-0.372358\pi$
$660$	3.16255	−	0.0170995i	0.123102	−	0.000665595i
$661$	8.95137	−	3.25803i	0.348168	−	0.126723i	−0.162016	−	0.986788i	$-0.551800\pi$
$661$	8.95137	−	3.25803i	0.348168	−	0.126723i	0.510184	+	0.860065i	$0.329577\pi$
$662$	−9.39230	+	3.41852i	−0.365042	+	0.132865i
$663$	−5.64602	−	9.65822i	−0.219273	−	0.375094i
$664$	0.127808	+	0.724834i	0.00495991	+	0.0281290i
$665$	0.124967	−	0.216450i	0.00484603	−	0.00839357i
$666$	10.4792	+	17.7056i	0.406062	+	0.686078i
$667$	20.8948	+	36.1909i	0.809050	+	1.40132i
$668$	18.2563	−	15.3189i	0.706357	−	0.592704i
$669$	6.25773	−	36.6469i	0.241938	−	1.41685i
$670$	−5.04644	+	28.6198i	−0.194961	+	1.10568i
$671$	3.25819	+	2.73394i	0.125781	+	0.105543i
$672$	1.63077	+	0.583588i	0.0629085	+	0.0225124i
$673$	−5.28408	−	1.92325i	−0.203686	−	0.0741357i	0.238162	−	0.971225i	$-0.423455\pi$
$673$	−5.28408	−	1.92325i	−0.203686	−	0.0741357i	−0.441849	+	0.897090i	$0.645677\pi$
$674$	−23.7797			−0.915961
$675$	−0.710892	−	3.68145i	−0.0273622	−	0.141699i
$676$	36.7106			1.41195
$677$	−24.1148	−	8.77708i	−0.926808	−	0.337331i	−0.165865	−	0.986149i	$-0.553042\pi$
$677$	−24.1148	−	8.77708i	−0.926808	−	0.337331i	−0.760944	+	0.648818i	$0.775264\pi$
$678$	−3.21475	−	17.6725i	−0.123462	−	0.678707i
$679$	3.57065	+	2.99613i	0.137029	+	0.114981i
$680$	−0.329046	+	1.86611i	−0.0126183	+	0.0715622i
$681$	−24.1248	−	20.0219i	−0.924466	−	0.767240i
$682$	−1.17969	+	0.989881i	−0.0451728	+	0.0379045i
$683$	18.4301	+	31.9219i	0.705210	+	1.22146i	0.966616	+	0.256230i	$0.0824805\pi$
$683$	18.4301	+	31.9219i	0.705210	+	1.22146i	−0.261406	+	0.965229i	$0.584186\pi$
$684$	0.341958	+	0.120291i	0.0130751	+	0.00459945i
$685$	20.3859	−	35.3094i	0.778906	−	1.34910i
$686$	−0.173648	−	0.984808i	−0.00662992	−	0.0376001i
$687$	19.5747	−	34.3317i	0.746820	−	1.30983i
$688$	8.83089	−	3.21418i	0.336674	−	0.122539i
$689$	−48.3928	+	17.6135i	−1.84362	+	0.671022i
$690$	9.97722	−	17.4989i	0.379826	−	0.666171i
$691$	4.07772	+	23.1259i	0.155124	+	0.879750i	0.958673	+	0.284511i	$0.0918313\pi$
$691$	4.07772	+	23.1259i	0.155124	+	0.879750i	−0.803549	+	0.595238i	$0.797058\pi$
$692$	−12.1611	+	21.0636i	−0.462295	+	0.800718i
$693$	2.01017	−	1.72412i	0.0763601	−	0.0654938i
$694$	−4.56836	−	7.91263i	−0.173413	−	0.300359i
$695$	−19.2459	+	16.1492i	−0.730038	+	0.612575i
$696$	9.90632	+	8.22153i	0.375498	+	0.311636i
$697$	0.504450	−	2.86088i	0.0191074	−	0.108363i
$698$	−18.7910	−	15.7675i	−0.711250	−	0.596809i
$699$	−2.18946	−	12.0361i	−0.0828130	−	0.455249i
$700$	0.678066	+	0.246796i	0.0256285	+	0.00932801i
$701$	40.0892			1.51415			0.757075	−	0.653328i	$-0.226628\pi$
$701$	40.0892			1.51415			0.757075	+	0.653328i	$0.226628\pi$
$702$	18.8301	+	31.4263i	0.710698	+	1.18611i
$703$	−0.828684			−0.0312544
$704$	−0.829522	−	0.301921i	−0.0312638	−	0.0113791i
$705$	20.3367	+	7.27768i	0.765925	+	0.274093i
$706$	9.97217	+	8.36765i	0.375308	+	0.314921i
$707$	2.52372	−	14.3127i	0.0949142	−	0.538285i
$708$	−0.615681	+	3.60559i	−0.0231387	+	0.135506i
$709$	−3.45771	+	2.90137i	−0.129857	+	0.108963i	−0.705403	−	0.708806i	$-0.749234\pi$
$709$	−3.45771	+	2.90137i	−0.129857	+	0.108963i	0.575546	+	0.817769i	$0.304790\pi$
$710$	−0.0400793	−	0.0694193i	−0.00150415	−	0.00260526i
$711$	−10.9796	+	19.5012i	−0.411767	+	0.731354i
$712$	−0.567520	+	0.982974i	−0.0212687	+	0.0368385i
$713$	1.70323	+	9.65951i	0.0637866	+	0.361752i
$714$	0.800788	+	1.36985i	0.0299687	+	0.0512653i
$715$	−12.0975	+	4.40311i	−0.452419	+	0.164667i
$716$	8.53796	−	3.10757i	0.319079	−	0.116135i
$717$	−47.5518	+	0.257105i	−1.77585	+	0.00960178i
$718$	3.63445	+	20.6120i	0.135636	+	0.769233i
$719$	−8.05616	+	13.9537i	−0.300444	+	0.520385i	−0.976237	−	0.216707i	$-0.930468\pi$
$719$	−8.05616	+	13.9537i	−0.300444	+	0.520385i	0.675792	+	0.737092i	$0.263802\pi$
$720$	1.01140	−	6.12232i	0.0376925	−	0.228165i
$721$	3.78830	+	6.56153i	0.141084	+	0.244364i
$722$	14.5437	−	12.2036i	0.541259	−	0.454170i
$723$	28.9082	−	10.6991i	1.07511	−	0.397903i
$724$	1.62482	−	9.21484i	0.0603861	−	0.342467i
$725$	4.10846	+	3.44741i	0.152584	+	0.128033i
$726$	13.4994	−	11.4523i	0.501011	−	0.425035i
$727$	9.00703	+	3.27829i	0.334052	+	0.121585i	0.503600	−	0.863937i	$-0.332009\pi$
$727$	9.00703	+	3.27829i	0.334052	+	0.121585i	−0.169548	+	0.985522i	$0.554231\pi$
$728$	−7.05058			−0.261312
$729$	−12.7345	+	23.8083i	−0.471647	+	0.881787i
$730$	−26.0164			−0.962910
$731$	8.09002	+	2.94453i	0.299220	+	0.108907i
$732$	6.36376	−	5.39873i	0.235211	−	0.199543i
$733$	−28.5495	−	23.9559i	−1.05450	−	0.884830i	−0.0609398	−	0.998141i	$-0.519410\pi$
$733$	−28.5495	−	23.9559i	−1.05450	−	0.884830i	−0.993560	+	0.113311i	$0.963854\pi$
$734$	−5.62360	+	31.8930i	−0.207571	+	1.17719i
$735$	−3.35990	+	1.24352i	−0.123932	+	0.0458678i
$736$	−4.30709	+	3.61408i	−0.158761	+	0.133217i
$737$	−6.20133	−	10.7410i	−0.228429	−	0.395651i
$738$	−1.55054	+	9.38592i	−0.0570760	+	0.345501i
$739$	14.8314	−	25.6888i	0.545583	−	0.944977i	−0.452987	−	0.891517i	$-0.649642\pi$
$739$	14.8314	−	25.6888i	0.545583	−	0.944977i	0.998570	−	0.0534598i	$-0.0170249\pi$
$740$	2.46329	+	13.9700i	0.0905524	+	0.513548i
$741$	−1.47559	+	0.00797827i	−0.0542070	+	0.000293089i
$742$	6.86366	−	2.49817i	0.251973	−	0.0917107i
$743$	−33.0791	+	12.0398i	−1.21355	+	0.441698i	−0.867935	−	0.496677i	$-0.834553\pi$
$743$	−33.0791	+	12.0398i	−1.21355	+	0.441698i	−0.345619	+	0.938375i	$0.612331\pi$
$744$	1.52492	+	2.60856i	0.0559062	+	0.0956344i
$745$	4.01131	+	22.7493i	0.146963	+	0.833468i
$746$	−1.91016	+	3.30849i	−0.0699358	+	0.121132i
$747$	1.08328	−	1.92405i	0.0396352	−	0.0703974i
$748$	−0.404350	−	0.700354i	−0.0147845	−	0.0256075i
$749$	−10.1392	+	8.50777i	−0.370477	+	0.310867i
$750$	3.45030	−	20.2059i	0.125987	−	0.737814i
$751$	−7.33575	+	41.6031i	−0.267685	+	1.51812i	0.493593	+	0.869693i	$0.335683\pi$
$751$	−7.33575	+	41.6031i	−0.267685	+	1.51812i	−0.761278	+	0.648425i	$0.775428\pi$
$752$	−4.61848	−	3.87537i	−0.168419	−	0.141320i
$753$	−10.3130	−	3.69060i	−0.375827	−	0.134493i
$754$	−49.2435	−	17.9232i	−1.79334	−	0.652723i
$755$	26.2281			0.954537
$756$	−2.67072	−	4.45727i	−0.0971333	−	0.162109i
$757$	−47.5821			−1.72940			−0.864700	−	0.502289i	$-0.832492\pi$
$757$	−47.5821			−1.72940			−0.864700	+	0.502289i	$0.832492\pi$
$758$	7.00884	+	2.55101i	0.254573	+	0.0926568i
$759$	1.53856	+	8.45792i	0.0558461	+	0.307003i
$760$	0.191461	+	0.160655i	0.00694503	+	0.00582757i
$761$	2.33835	−	13.2615i	0.0847652	−	0.480727i	−0.912642	−	0.408760i	$-0.865961\pi$
$761$	2.33835	−	13.2615i	0.0847652	−	0.480727i	0.997407	−	0.0719671i	$-0.0229277\pi$
$762$	−11.0508	−	9.17134i	−0.400327	−	0.332242i
$763$	−14.4114	+	12.0926i	−0.521728	+	0.437782i
$764$	9.04467	+	15.6658i	0.327225	+	0.566770i
$765$	4.31497	−	3.70093i	0.156008	−	0.133808i
$766$	−3.50848	+	6.07687i	−0.126767	+	0.219566i
$767$	−2.58554	−	14.6633i	−0.0933585	−	0.529463i
$768$	−0.857903	+	1.50466i	−0.0309569	+	0.0542948i
$769$	0.542616	−	0.197496i	0.0195672	−	0.00712189i	−0.332218	−	0.943203i	$-0.607797\pi$
$769$	0.542616	−	0.197496i	0.0195672	−	0.00712189i	0.351785	+	0.936081i	$0.385575\pi$
$770$	1.71581	−	0.624504i	0.0618335	−	0.0225056i
$771$	−15.4791	+	27.1486i	−0.557467	+	0.977731i
$772$	2.64887	+	15.0225i	0.0953349	+	0.540671i
$773$	−25.6433	+	44.4155i	−0.922325	+	1.59751i	−0.126518	+	0.991964i	$0.540380\pi$
$773$	−25.6433	+	44.4155i	−0.922325	+	1.59751i	−0.795807	+	0.605550i	$0.792953\pi$
$774$	−26.5954	−	9.35550i	−0.955951	−	0.336276i
$775$	0.629405	+	1.09016i	0.0226089	+	0.0391597i
$776$	−3.57065	+	2.99613i	−0.128179	+	0.107555i
$777$	9.14067	+	7.58609i	0.327920	+	0.272150i
$778$	−0.711614	+	4.03576i	−0.0255126	+	0.144689i
$779$	−0.293523	−	0.246295i	−0.0105165	−	0.00882442i
$780$	4.52072	+	24.8518i	0.161868	+	0.889837i
$781$	0.0321467	+	0.0117004i	0.00115030	+	0.000418674i
$782$	−5.15081			−0.184192
$783$	−7.32243	−	37.9202i	−0.261682	−	1.35516i
$784$	1.00000			0.0357143
$785$	12.9035	+	4.69648i	0.460544	+	0.167624i
$786$	−14.7079	−	5.26336i	−0.524614	−	0.187738i
$787$	−41.5632	−	34.8756i	−1.48157	−	1.24318i	−0.904492	−	0.426490i	$-0.859750\pi$
$787$	−41.5632	−	34.8756i	−1.48157	−	1.24318i	−0.577074	−	0.816692i	$-0.695806\pi$
$788$	−3.11899	+	17.6887i	−0.111109	+	0.630133i
$789$	−2.26126	+	13.2425i	−0.0805030	+	0.471447i
$790$	−11.8203	+	9.91840i	−0.420547	+	0.352881i
$791$	−5.18532	−	8.98124i	−0.184369	−	0.319336i
$792$	1.34886	+	2.27902i	0.0479297	+	0.0809815i
$793$	−16.9854	+	29.4195i	−0.603168	+	1.04472i
$794$	0.475816	+	2.69849i	0.0168861	+	0.0957658i
$795$	−13.2064	−	22.5912i	−0.468382	−	0.801226i
$796$	−10.2628	+	3.73536i	−0.363756	+	0.132396i
$797$	−11.9708	+	4.35702i	−0.424028	+	0.154334i	−0.545215	−	0.838296i	$-0.683552\pi$
$797$	−11.9708	+	4.35702i	−0.424028	+	0.154334i	0.121187	+	0.992630i	$0.461330\pi$
$798$	0.209286	−	0.00113158i	0.00740863	−	4.00574e-5i
$799$	−0.959093	−	5.43928i	−0.0339303	−	0.192428i
$800$	−0.360792	+	0.624909i	−0.0127559	+	0.0220939i
$801$	3.18699	−	1.19915i	0.112607	−	0.0423700i
$802$	−4.60200	−	7.97089i	−0.162502	−	0.281462i
$803$	8.50553	−	7.13699i	0.300154	−	0.251859i
$804$	−22.8222	+	8.44663i	−0.804878	+	0.297890i
$805$	2.01949	−	11.4531i	0.0711777	−	0.403669i
$806$	−9.42220	−	7.90617i	−0.331883	−	0.278483i
$807$	−25.6037	+	21.7211i	−0.901294	+	0.764617i
$808$	13.6570	+	4.97076i	0.480453	+	0.174871i
$809$	36.0103			1.26605			0.633027	−	0.774129i	$-0.281812\pi$
$809$	36.0103			1.26605			0.633027	+	0.774129i	$0.281812\pi$
$810$	−13.9985	+	12.2717i	−0.491857	+	0.431182i
$811$	42.7028			1.49950			0.749750	−	0.661722i	$-0.230174\pi$
$811$	42.7028			1.49950			0.749750	+	0.661722i	$0.230174\pi$
$812$	6.98432	+	2.54209i	0.245102	+	0.0892097i
$813$	15.1695	−	12.8691i	0.532016	−	0.451339i
$814$	−4.63767	−	3.89147i	−0.162550	−	0.136396i
$815$	−1.31553	+	7.46074i	−0.0460810	+	0.261338i
$816$	−1.48809	+	0.550751i	−0.0520936	+	0.0192801i
$817$	0.869877	−	0.729913i	0.0304331	−	0.0255364i
$818$	6.69463	+	11.5954i	0.234072	+	0.405425i
$819$	16.3492	+	13.4201i	0.571289	+	0.468935i
$820$	−3.27955	+	5.68034i	−0.114527	+	0.198366i
$821$	8.43552	+	47.8402i	0.294402	+	1.66964i	0.669624	+	0.742700i	$0.266455\pi$
$821$	8.43552	+	47.8402i	0.294402	+	1.66964i	−0.375222	+	0.926935i	$0.622434\pi$
$822$	34.1407	−	0.184594i	1.19079	−	0.00643845i
$823$	−19.2676	+	7.01282i	−0.671625	+	0.244452i	−0.655247	−	0.755414i	$-0.727436\pi$
$823$	−19.2676	+	7.01282i	−0.671625	+	0.244452i	−0.0163776	+	0.999866i	$0.505213\pi$
$824$	−7.11968	+	2.59135i	−0.248026	+	0.0902740i
$825$	0.556802	+	0.952479i	0.0193854	+	0.0331611i
$826$	0.366714	+	2.07974i	0.0127596	+	0.0723633i
$827$	−22.6321	+	39.2000i	−0.786996	+	1.36312i	0.140804	+	0.990037i	$0.455031\pi$
$827$	−22.6321	+	39.2000i	−0.786996	+	1.36312i	−0.927800	+	0.373079i	$0.878302\pi$
$828$	16.8665	−	0.182395i	0.586153	−	0.00633867i
$829$	20.5465	+	35.5875i	0.713609	+	1.23601i	0.963494	+	0.267731i	$0.0862739\pi$
$829$	20.5465	+	35.5875i	0.713609	+	1.23601i	−0.249885	+	0.968276i	$0.580393\pi$
$830$	1.16623	−	0.978580i	0.0404803	−	0.0339670i
$831$	0.822825	−	4.81868i	0.0285435	−	0.167158i
$832$	1.22432	−	6.94346i	0.0424457	−	0.240721i
$833$	0.701777	+	0.588861i	0.0243151	+	0.0204028i
$834$	−19.8078	−	7.08840i	−0.685888	−	0.245451i
$835$	−46.3219	−	16.8598i	−1.60303	−	0.583457i
$836$	−0.106666			−0.00368913
$837$	1.42908	−	8.95139i	0.0493961	−	0.309405i
$838$	31.8243			1.09935
$839$	−22.7877	−	8.29405i	−0.786719	−	0.286342i	−0.0827475	−	0.996571i	$-0.526369\pi$
$839$	−22.7877	−	8.29405i	−0.786719	−	0.286342i	−0.703971	+	0.710228i	$0.748592\pi$
$840$	−0.641185	−	3.52479i	−0.0221230	−	0.121617i
$841$	20.1033	+	16.8686i	0.693216	+	0.581677i
$842$	−3.51287	+	19.9225i	−0.121061	+	0.686573i
$843$	−24.4973	−	20.3310i	−0.843733	−	0.700237i
$844$	7.81913	−	6.56103i	0.269146	−	0.225840i
$845$	−37.9668	−	65.7604i	−1.30610	−	2.26222i
$846$	3.33320	+	17.7772i	0.114598	+	0.611193i
$847$	5.11037	−	8.85142i	0.175594	−	0.304138i
$848$	1.26835	+	7.19319i	0.0435554	+	0.247015i
$849$	6.09732	−	10.6940i	0.209260	−	0.367017i
$850$	−0.621180	+	0.226091i	−0.0213063	+	0.00775486i
$851$	−36.2343	+	13.1882i	−1.24210	+	0.452086i
$852$	0.0332465	−	0.0583105i	0.00113901	−	0.00199768i
$853$	7.95520	+	45.1162i	0.272381	+	1.54475i	0.747161	+	0.664644i	$0.231417\pi$
$853$	7.95520	+	45.1162i	0.272381	+	1.54475i	−0.474780	+	0.880105i	$0.657472\pi$
$854$	2.40907	−	4.17264i	0.0824368	−	0.142785i
$855$	−0.138179	−	0.736962i	−0.00472563	−	0.0252036i
$856$	−6.61787	−	11.4625i	−0.226194	−	0.391780i
$857$	−15.6229	+	13.1092i	−0.533668	+	0.447801i	−0.869366	−	0.494169i	$-0.835472\pi$
$857$	−15.6229	+	13.1092i	−0.533668	+	0.447801i	0.335698	+	0.941970i	$0.391028\pi$
$858$	−8.29546	−	6.88463i	−0.283202	−	0.235038i
$859$	−1.95235	+	11.0723i	−0.0666135	+	0.377784i	0.933216	+	0.359316i	$0.116990\pi$
$859$	−1.95235	+	11.0723i	−0.0666135	+	0.377784i	−0.999829	+	0.0184678i	$0.994121\pi$
$860$	−14.8907	−	12.4947i	−0.507767	−	0.426067i
$861$	0.982978	+	5.40373i	0.0334998	+	0.184159i
$862$	16.6848	+	6.07277i	0.568287	+	0.206840i
$863$	1.49208			0.0507909			0.0253954	−	0.999677i	$-0.491916\pi$
$863$	1.49208			0.0507909			0.0253954	+	0.999677i	$0.491916\pi$
$864$	4.85332	−	1.85615i	0.165113	−	0.0631476i
$865$	50.3088			1.71055
$866$	−11.8757	−	4.32242i	−0.403554	−	0.146882i
$867$	26.3545	+	9.43121i	0.895047	+	0.320301i
$868$	1.33637	+	1.12135i	0.0453595	+	0.0380611i
$869$	1.14352	−	6.48524i	0.0387913	−	0.219997i
$870$	4.48207	−	26.2482i	0.151957	−	0.889897i
$871$	75.8843	−	63.6745i	2.57124	−	2.15753i
$872$	−9.40637	−	16.2923i	−0.318540	−	0.551727i
$873$	13.9827	−	0.151209i	0.473241	−	0.00511764i
$874$	−0.339692	+	0.588364i	−0.0114903	+	0.0199017i
$875$	−2.05508	−	11.6549i	−0.0694743	−	0.394008i
$876$	−10.9946	−	18.8076i	−0.371472	−	0.635449i
$877$	−1.85517	+	0.675227i	−0.0626447	+	0.0228008i	−0.373152	−	0.927770i	$-0.621723\pi$
$877$	−1.85517	+	0.675227i	−0.0626447	+	0.0228008i	0.310508	+	0.950571i	$0.399501\pi$
$878$	−9.94022	+	3.61794i	−0.335466	+	0.122100i
$879$	18.6494	−	0.100834i	0.629028	−	0.00340106i
$880$	0.317069	+	1.79819i	0.0106884	+	0.0606169i
$881$	19.4343	−	33.6612i	0.654759	−	1.13408i	−0.327196	−	0.944957i	$-0.606104\pi$
$881$	19.4343	−	33.6612i	0.654759	−	1.13408i	0.981954	−	0.189119i	$-0.0605630\pi$
$882$	−2.31885	−	1.90340i	−0.0780798	−	0.0640908i
$883$	−2.78726	−	4.82767i	−0.0937987	−	0.162464i	0.815308	−	0.579028i	$-0.196568\pi$
$883$	−2.78726	−	4.82767i	−0.0937987	−	0.162464i	−0.909107	+	0.416564i	$0.863234\pi$
$884$	4.94793	−	4.15181i	0.166417	−	0.139640i
$885$	7.09550	−	2.62608i	0.238513	−	0.0882748i
$886$	2.08942	−	11.8497i	0.0701953	−	0.398097i
$887$	26.3280	+	22.0918i	0.884006	+	0.741769i	0.966999	−	0.254781i	$-0.0820033\pi$
$887$	26.3280	+	22.0918i	0.884006	+	0.741769i	−0.0829926	+	0.996550i	$0.526448\pi$
$888$	−9.05810	+	7.68449i	−0.303970	+	0.257875i
$889$	−7.79120	−	2.83576i	−0.261308	−	0.0951084i
$890$	2.34776			0.0786969
$891$	1.21008	−	7.85213i	0.0405392	−	0.263056i
$892$	21.4644			0.718680
$893$	−0.684567	−	0.249162i	−0.0229082	−	0.00833789i
$894$	−14.7505	+	12.5137i	−0.493332	+	0.418521i
$895$	−14.3967	−	12.0803i	−0.481230	−	0.403800i
$896$	−0.173648	+	0.984808i	−0.00580118	+	0.0329001i
$897$	−64.3931	+	23.8322i	−2.15002	+	0.795735i
$898$	3.51424	−	2.94880i	0.117272	−	0.0984028i
$899$	6.48309	+	11.2290i	0.216223	+	0.374510i
$900$	2.02607	−	0.762341i	0.0675358	−	0.0254114i
$901$	−3.34569	+	5.79490i	−0.111461	+	0.193056i
$902$	−0.486087	−	2.75674i	−0.0161849	−	0.0917894i
$903$	−16.2769	+	0.0880070i	−0.541663	+	0.00292869i
$904$	9.74522	−	3.54697i	0.324121	−	0.117970i
$905$	−18.1871	+	6.61956i	−0.604560	+	0.220042i
$906$	11.0840	+	18.9606i	0.368242	+	0.629924i
$907$	−8.19980	−	46.5034i	−0.272270	−	1.54412i	−0.747502	−	0.664259i	$-0.768747\pi$
$907$	−8.19980	−	46.5034i	−0.272270	−	1.54412i	0.475233	−	0.879860i	$-0.342364\pi$
$908$	9.05025	−	15.6755i	0.300343	−	0.520209i
$909$	−22.2073	−	37.5212i	−0.736570	−	1.24450i
$910$	7.29182	+	12.6298i	0.241722	+	0.418674i
$911$	35.4526	−	29.7483i	1.17460	−	0.985605i	0.174599	−	0.984640i	$-0.444137\pi$
$911$	35.4526	−	29.7483i	1.17460	−	0.985605i	1.00000		0.000965450i	$-0.000307312\pi$
$912$	−0.0352277	+	0.206303i	−0.00116651	+	0.00683136i
$913$	−0.112823	+	0.639854i	−0.00373391	+	0.0211761i
$914$	−4.22261	−	3.54319i	−0.139671	−	0.117198i
$915$	−16.2523	−	5.81604i	−0.537285	−	0.192272i
$916$	21.4409	+	7.80383i	0.708426	+	0.257846i
$917$	−9.01897			−0.297833
$918$	4.49896	+	1.55532i	0.148488	+	0.0513333i
$919$	28.4419			0.938211			0.469106	−	0.883142i	$-0.344576\pi$
$919$	28.4419			0.938211			0.469106	+	0.883142i	$0.344576\pi$
$920$	10.9284	+	3.97762i	0.360299	+	0.131138i
$921$	8.77198	+	48.2223i	0.289047	+	1.58898i
$922$	−8.27338	−	6.94219i	−0.272469	−	0.228629i
$923$	−0.0474464	+	0.269082i	−0.00156172	+	0.00885694i
$924$	1.17657	+	0.976464i	0.0387062	+	0.0321233i
$925$	−3.79092	+	3.18096i	−0.124645	+	0.104589i
$926$	−1.09235	−	1.89201i	−0.0358969	−	0.0621753i
$927$	21.4418	+	7.54263i	0.704243	+	0.247733i
$928$	−3.71628	+	6.43679i	−0.121993	+	0.211298i
$929$	7.00943	+	39.7525i	0.229972	+	1.30424i	0.852948	+	0.521996i	$0.174812\pi$
$929$	7.00943	+	39.7525i	0.229972	+	1.30424i	−0.622976	+	0.782241i	$0.714077\pi$
$930$	3.09566	−	5.42942i	0.101511	−	0.178038i
$931$	0.113546	−	0.0413273i	0.00372131	−	0.00135445i
$932$	6.63715	−	2.41572i	0.217407	−	0.0791297i
$933$	−1.18806	+	2.08372i	−0.0388955	+	0.0682181i
$934$	−5.62549	−	31.9037i	−0.184072	−	1.04392i
$935$	−0.836370	+	1.44864i	−0.0273522	+	0.0473755i
$936$	−16.0552	+	13.7705i	−0.524781	+	0.450102i
$937$	0.424543	+	0.735331i	0.0138692	+	0.0240222i	0.872877	−	0.487941i	$-0.162252\pi$
$937$	0.424543	+	0.735331i	0.0138692	+	0.0240222i	−0.859007	+	0.511963i	$0.828918\pi$
$938$	−10.7628	+	9.03110i	−0.351420	+	0.294876i
$939$	−4.55714	−	3.78209i	−0.148717	−	0.123424i
$940$	−2.16549	+	12.2811i	−0.0706306	+	0.400566i
$941$	−25.6295	−	21.5057i	−0.835496	−	0.701065i	0.121050	−	0.992646i	$-0.461374\pi$
$941$	−25.6295	−	21.5057i	−0.835496	−	0.701065i	−0.956546	+	0.291582i	$0.905818\pi$
$942$	2.05788	+	11.3128i	0.0670494	+	0.368591i
$943$	−16.7540	−	6.09795i	−0.545585	−	0.198577i
$944$	−2.11182			−0.0687339
$945$	−5.22227	+	9.39389i	−0.169880	+	0.305583i
$946$	8.29584			0.269721
$947$	−28.1961	−	10.2625i	−0.916250	−	0.333488i	−0.159504	−	0.987197i	$-0.550990\pi$
$947$	−28.1961	−	10.2625i	−0.916250	−	0.333488i	−0.756746	+	0.653710i	$0.773212\pi$
$948$	−12.1654	−	4.35350i	−0.395114	−	0.141395i
$949$	67.9336	+	57.0030i	2.20522	+	1.85040i
$950$	−0.0151406	+	0.0858664i	−0.000491225	+	0.00278587i
$951$	1.64651	−	9.64240i	0.0533918	−	0.312676i
$952$	−0.701777	+	0.588861i	−0.0227447	+	0.0190851i
$953$	10.2806	+	17.8065i	0.333020	+	0.576808i	0.983102	−	0.183056i	$-0.0585990\pi$
$953$	10.2806	+	17.8065i	0.333020	+	0.576808i	−0.650082	+	0.759864i	$0.725266\pi$
$954$	10.7504	−	19.0941i	0.348057	−	0.618195i
$955$	18.7083	−	32.4037i	0.605386	−	1.04856i
$956$	−4.76741	−	27.0373i	−0.154189	−	0.874450i
$957$	5.73526	+	9.81087i	0.185394	+	0.317140i
$958$	−27.9811	+	10.1843i	−0.904028	+	0.329039i
$959$	18.5227	−	6.74171i	0.598129	−	0.217701i
$960$	3.58258	−	0.0193705i	0.115627	−	0.000625179i
$961$	−4.85463	−	27.5320i	−0.156601	−	0.888128i
$962$	24.1768	−	41.8754i	0.779491	−	1.35012i
$963$	−6.47184	+	39.1762i	−0.208552	+	1.26244i
$964$	8.89828	+	15.4123i	0.286594	+	0.496396i
$965$	24.1705	−	20.2815i	0.778076	−	0.652883i
$966$	9.13302	−	3.38018i	0.293850	−	0.108756i
$967$	−3.41061	+	19.3425i	−0.109678	+	0.622014i	0.879571	+	0.475768i	$0.157830\pi$
$967$	−3.41061	+	19.3425i	−0.109678	+	0.622014i	−0.989248	+	0.146245i	$0.953281\pi$
$968$	7.82954	+	6.56976i	0.251651	+	0.211160i
$969$	−0.146206	+	0.124034i	−0.00469680	+	0.00398455i
$970$	9.05985	+	3.29752i	0.290894	+	0.105877i
$971$	−7.78911			−0.249964			−0.124982	−	0.992159i	$-0.539887\pi$
$971$	−7.78911			−0.249964			−0.124982	+	0.992159i	$0.539887\pi$
$972$	−14.7871	−	4.93366i	−0.474297	−	0.158247i
$973$	−12.1463			−0.389391
$974$	−29.1474	−	10.6088i	−0.933943	−	0.339928i
$975$	−6.71962	+	5.70062i	−0.215200	+	0.182566i
$976$	3.69091	+	3.09705i	0.118143	+	0.0991340i
$977$	−6.66092	+	37.7759i	−0.213102	+	1.20856i	0.671069	+	0.741395i	$0.265835\pi$
$977$	−6.66092	+	37.7759i	−0.213102	+	1.20856i	−0.884171	+	0.467164i	$0.845276\pi$
$978$	−5.94940	+	2.20191i	−0.190241	+	0.0704092i
$979$	−0.767551	+	0.644051i	−0.0245310	+	0.0205840i
$980$	−1.03422	−	1.79132i	−0.0330368	−	0.0572215i
$981$	−9.19881	+	55.6835i	−0.293695	+	1.77784i
$982$	−11.7628	+	20.3738i	−0.375366	+	0.650153i
$983$	−5.94370	−	33.7084i	−0.189574	−	1.07513i	−0.919936	−	0.392069i	$-0.871759\pi$
$983$	−5.94370	−	33.7084i	−0.189574	−	1.07513i	0.730361	−	0.683061i	$-0.239352\pi$
$984$	−5.49233	+	0.0296962i	−0.175089	+	0.000946681i
$985$	34.9117	−	12.7068i	1.11238	−	0.404873i
$986$	−6.39837	+	2.32882i	−0.203766	+	0.0741646i
$987$	5.27009	+	9.01513i	0.167749	+	0.286955i
$988$	−0.147938	−	0.838999i	−0.00470654	−	0.0266921i
$989$	26.4191	−	45.7593i	0.840079	−	1.45506i
$990$	2.68743	−	4.77324i	0.0854122	−	0.151703i
$991$	−11.9231	−	20.6514i	−0.378749	−	0.656013i	0.612131	−	0.790756i	$-0.290312\pi$
$991$	−11.9231	−	20.6514i	−0.378749	−	0.656013i	−0.990881	+	0.134743i	$0.956979\pi$
$992$	−1.33637	+	1.12135i	−0.0424299	+	0.0356029i
$993$	−2.91397	+	17.0650i	−0.0924721	+	0.541541i
$994$	0.00672943	−	0.0381645i	0.000213445	−	0.00121050i
$995$	17.3052	+	14.5208i	0.548611	+	0.460339i
$996$	1.20028	+	0.429530i	0.0380322	+	0.0136102i
$997$	−18.4575	−	6.71798i	−0.584555	−	0.212761i	0.0327779	−	0.999463i	$-0.489565\pi$
$997$	−18.4575	−	6.71798i	−0.584555	−	0.212761i	−0.617333	+	0.786702i	$0.711787\pi$
$998$	1.46789			0.0464653
$999$	35.6311	−	0.578001i	1.12732	−	0.0182871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.e.85.6	✓	36
27.7	even	9	inner	378.2.u.e.169.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.e.85.6	✓	36	1.1	even	1	trivial
378.2.u.e.169.6	yes	36	27.7	even	9	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(1.32079 - 1.12050i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.359180 - 2.03701i) q^{5} +(1.62437 - 0.601188i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.488967 - 2.95988i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(1.32079 - 1.12050i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.359180 - 2.03701i) q^{5} +(1.62437 - 0.601188i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.488967 - 2.95988i) q^{9} +(1.03422 - 1.79132i) q^{10} +(0.153289 + 0.869347i) q^{11} +(1.73203 - 0.00936481i) q^{12} +(-6.62538 + 2.41144i) q^{13} +(0.939693 - 0.342020i) q^{14} +(-1.80807 - 3.09292i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-0.458052 + 0.793370i) q^{17} +(1.47182 - 2.61414i) q^{18} +(0.0604165 + 0.104644i) q^{19} +(1.58451 - 1.32956i) q^{20} +(0.291541 - 1.70734i) q^{21} +(-0.153289 + 0.869347i) q^{22} +(4.30709 + 3.61408i) q^{23} +(1.63077 + 0.583588i) q^{24} +(0.678066 + 0.246796i) q^{25} -7.05058 q^{26} +(-2.67072 - 4.45727i) q^{27} +1.00000 q^{28} +(6.98432 + 2.54209i) q^{29} +(-0.641185 - 3.52479i) q^{30} +(1.33637 + 1.12135i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(1.17657 + 0.976464i) q^{33} +(-0.701777 + 0.588861i) q^{34} +(-1.03422 - 1.79132i) q^{35} +(2.27715 - 1.95310i) q^{36} +(-3.42905 + 5.93929i) q^{37} +(0.0209824 + 0.118997i) q^{38} +(-6.04871 + 10.6087i) q^{39} +(1.94369 - 0.707446i) q^{40} +(-2.97981 + 1.08456i) q^{41} +(0.857903 - 1.50466i) q^{42} +(-1.63188 - 9.25486i) q^{43} +(-0.441379 + 0.764491i) q^{44} +(-5.85368 - 2.05916i) q^{45} +(2.81125 + 4.86923i) q^{46} +(-4.61848 + 3.87537i) q^{47} +(1.33283 + 1.10615i) q^{48} +(0.173648 - 0.984808i) q^{49} +(0.552765 + 0.463825i) q^{50} +(0.283979 + 1.56112i) q^{51} +(-6.62538 - 2.41144i) q^{52} +7.30416 q^{53} +(-0.985183 - 5.10190i) q^{54} +1.82593 q^{55} +(0.939693 + 0.342020i) q^{56} +(0.197051 + 0.0705166i) q^{57} +(5.69367 + 4.77756i) q^{58} +(-0.366714 + 2.07974i) q^{59} +(0.603032 - 3.53152i) q^{60} +(3.69091 - 3.09705i) q^{61} +(0.872256 + 1.51079i) q^{62} +(-1.52801 - 2.58170i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.53242 + 14.3621i) q^{65} +(0.771639 + 1.31998i) q^{66} +(-13.2026 + 4.80535i) q^{67} +(-0.860857 + 0.313326i) q^{68} +(9.73833 - 0.0526537i) q^{69} +(-0.359180 - 2.03701i) q^{70} +(0.0193766 - 0.0335613i) q^{71} +(2.80782 - 1.05648i) q^{72} +(-6.28891 - 10.8927i) q^{73} +(-5.25361 + 4.40830i) q^{74} +(1.17212 - 0.433807i) q^{75} +(-0.0209824 + 0.118997i) q^{76} +(0.676232 + 0.567426i) q^{77} +(-9.31232 + 7.90016i) q^{78} +(-7.01001 - 2.55143i) q^{79} +2.06843 q^{80} +(-8.52182 - 2.89457i) q^{81} -3.17104 q^{82} +(0.691629 + 0.251732i) q^{83} +(1.32079 - 1.12050i) q^{84} +(1.45158 + 1.21802i) q^{85} +(1.63188 - 9.25486i) q^{86} +(12.0732 - 4.46836i) q^{87} +(-0.676232 + 0.567426i) q^{88} +(0.567520 + 0.982974i) q^{89} +(-4.79639 - 3.93706i) q^{90} +(-3.52529 + 6.10598i) q^{91} +(0.976338 + 5.53709i) q^{92} +(3.02154 - 0.0163370i) q^{93} +(-5.66541 + 2.06204i) q^{94} +(0.234862 - 0.0854828i) q^{95} +(0.874123 + 1.49530i) q^{96} +(0.809402 + 4.59034i) q^{97} +(0.500000 - 0.866025i) q^{98} +(2.64812 - 0.0286368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Introduction

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