LMFDB - Embedded newform 228.2.v.a.23.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(23,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 2]))

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

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

chi := DirichletCharacter("228.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.v (of order $18$, 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:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.5
Character	$\chi$	$=$	228.23
Dual form			228.2.v.a.119.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22517 - 0.706378i) q^{2} +(1.73132 + 0.0503667i) q^{3} +(1.00206 + 1.73086i) q^{4} +(0.942247 + 1.12293i) q^{5} +(-2.08557 - 1.28467i) q^{6} +(-0.536440 - 0.309714i) q^{7} +(-0.00504802 - 2.82842i) q^{8} +(2.99493 + 0.174402i) q^{9} +O(q^{10})$	\(q+(-1.22517 - 0.706378i) q^{2} +(1.73132 + 0.0503667i) q^{3} +(1.00206 + 1.73086i) q^{4} +(0.942247 + 1.12293i) q^{5} +(-2.08557 - 1.28467i) q^{6} +(-0.536440 - 0.309714i) q^{7} +(-0.00504802 - 2.82842i) q^{8} +(2.99493 + 0.174402i) q^{9} +(-0.361198 - 2.04135i) q^{10} +(0.904524 + 1.56668i) q^{11} +(1.64771 + 3.04714i) q^{12} +(-0.713547 + 4.04673i) q^{13} +(0.438453 + 0.758380i) q^{14} +(1.57477 + 1.99160i) q^{15} +(-1.99175 + 3.46885i) q^{16} +(1.11392 - 3.06048i) q^{17} +(-3.54609 - 2.32922i) q^{18} +(-2.89090 - 3.26232i) q^{19} +(-0.999439 + 2.75614i) q^{20} +(-0.913150 - 0.563232i) q^{21} +(-0.00152202 - 2.55838i) q^{22} +(5.20666 + 4.36891i) q^{23} +(0.133719 - 4.89715i) q^{24} +(0.495107 - 2.80789i) q^{25} +(3.73273 - 4.45388i) q^{26} +(5.17639 + 0.452789i) q^{27} +(-0.00147403 - 1.23885i) q^{28} +(-3.01423 - 8.28154i) q^{29} +(-0.522532 - 3.55242i) q^{30} +(1.40352 + 0.810320i) q^{31} +(4.89054 - 2.84299i) q^{32} +(1.48711 + 2.75798i) q^{33} +(-3.52660 + 2.96275i) q^{34} +(-0.157673 - 0.894209i) q^{35} +(2.69923 + 5.35856i) q^{36} -4.83914 q^{37} +(1.23740 + 6.03894i) q^{38} +(-1.43920 + 6.97024i) q^{39} +(3.17135 - 2.67074i) q^{40} +(-5.93228 + 1.04602i) q^{41} +(0.720904 + 1.33508i) q^{42} +(0.0815368 + 0.0971718i) q^{43} +(-1.80532 + 3.13551i) q^{44} +(2.62612 + 3.52741i) q^{45} +(-3.29292 - 9.03050i) q^{46} +(-0.234702 + 0.0854244i) q^{47} +(-3.62307 + 5.90537i) q^{48} +(-3.30815 - 5.72989i) q^{49} +(-2.59002 + 3.09040i) q^{50} +(2.08271 - 5.24257i) q^{51} +(-7.71934 + 2.82001i) q^{52} +(-2.93063 + 3.49259i) q^{53} +(-6.02209 - 4.21123i) q^{54} +(-0.906982 + 2.49191i) q^{55} +(-0.873294 + 1.51884i) q^{56} +(-4.84075 - 5.79371i) q^{57} +(-2.15696 + 12.2754i) q^{58} +(-10.0955 - 3.67447i) q^{59} +(-1.86916 + 4.72141i) q^{60} +(4.39992 + 3.69197i) q^{61} +(-1.14715 - 1.98419i) q^{62} +(-1.55258 - 1.02113i) q^{63} +(-7.99995 + 0.0285559i) q^{64} +(-5.21651 + 3.01175i) q^{65} +(0.126222 - 4.42945i) q^{66} +(-0.256563 - 0.704900i) q^{67} +(6.41349 - 1.13874i) q^{68} +(8.79434 + 7.82621i) q^{69} +(-0.438474 + 1.20693i) q^{70} +(-2.09293 + 1.75618i) q^{71} +(0.478163 - 8.47180i) q^{72} +(0.334207 + 1.89538i) q^{73} +(5.92875 + 3.41826i) q^{74} +(0.998613 - 4.83642i) q^{75} +(2.74976 - 8.27278i) q^{76} -1.12057i q^{77} +(6.68688 - 7.52307i) q^{78} +(-13.2403 + 2.33462i) q^{79} +(-5.77198 + 1.03192i) q^{80} +(8.93917 + 1.04464i) q^{81} +(8.00691 + 2.90888i) q^{82} +(-4.28803 + 7.42708i) q^{83} +(0.0598450 - 2.14493i) q^{84} +(4.48629 - 1.63288i) q^{85} +(-0.0312561 - 0.176647i) q^{86} +(-4.80149 - 14.4898i) q^{87} +(4.42667 - 2.56629i) q^{88} +(5.45617 + 0.962070i) q^{89} +(-0.725745 - 6.17669i) q^{90} +(1.63610 - 1.94983i) q^{91} +(-2.34458 + 13.3899i) q^{92} +(2.38912 + 1.47361i) q^{93} +(0.347890 + 0.0611290i) q^{94} +(0.939402 - 6.32017i) q^{95} +(8.61028 - 4.67579i) q^{96} +(7.61079 + 2.77010i) q^{97} +(0.00556655 + 9.35687i) q^{98} +(2.43575 + 4.84985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$	$-1$

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 $

$2$	−1.22517	−	0.706378i	−0.866323	−	0.499485i
$2$	−1.22517	−	0.706378i	−0.866323	−	0.499485i
$3$	1.73132	+	0.0503667i	0.999577	+	0.0290792i
$3$	1.73132	+	0.0503667i	0.999577	+	0.0290792i
$4$	1.00206	+	1.73086i	0.501030	+	0.865430i
$5$	0.942247	+	1.12293i	0.421385	+	0.502188i	0.934416	−	0.356182i	$-0.115922\pi$
$5$	0.942247	+	1.12293i	0.421385	+	0.502188i	−0.513031	+	0.858370i	$0.671477\pi$
$6$	−2.08557	−	1.28467i	−0.851432	−	0.524465i
$7$	−0.536440	−	0.309714i	−0.202755	−	0.117061i	0.395185	−	0.918602i	$-0.370681\pi$
$7$	−0.536440	−	0.309714i	−0.202755	−	0.117061i	−0.597940	+	0.801541i	$0.704014\pi$
$8$	−0.00504802	−	2.82842i	−0.00178475	−	0.999998i
$9$	2.99493	+	0.174402i	0.998309	+	0.0581339i
$10$	−0.361198	−	2.04135i	−0.114221	−	0.645532i
$11$	0.904524	+	1.56668i	0.272724	+	0.472372i	0.969558	−	0.244860i	$-0.0787420\pi$
$11$	0.904524	+	1.56668i	0.272724	+	0.472372i	−0.696834	+	0.717232i	$0.745409\pi$
$12$	1.64771	+	3.04714i	0.475652	+	0.879633i
$13$	−0.713547	+	4.04673i	−0.197902	+	1.12236i	0.710322	+	0.703877i	$0.248549\pi$
$13$	−0.713547	+	4.04673i	−0.197902	+	1.12236i	−0.908224	+	0.418484i	$0.862562\pi$
$14$	0.438453	+	0.758380i	0.117181	+	0.202686i
$15$	1.57477	+	1.99160i	0.406604	+	0.514229i
$16$	−1.99175	+	3.46885i	−0.497938	+	0.867213i
$17$	1.11392	−	3.06048i	0.270166	−	0.742276i	−0.728212	−	0.685352i	$-0.759648\pi$
$17$	1.11392	−	3.06048i	0.270166	−	0.742276i	0.998378	−	0.0569244i	$-0.0181294\pi$
$18$	−3.54609	−	2.32922i	−0.835821	−	0.549003i
$19$	−2.89090	−	3.26232i	−0.663217	−	0.748427i
$19$	−2.89090	−	3.26232i	−0.663217	−	0.748427i
$20$	−0.999439	+	2.75614i	−0.223481	+	0.616291i
$21$	−0.913150	−	0.563232i	−0.199266	−	0.122907i
$22$	−0.00152202	−	2.55838i	−0.000324496	−	0.545448i
$23$	5.20666	+	4.36891i	1.08566	+	0.910980i	0.996379	−	0.0850264i	$-0.0270975\pi$
$23$	5.20666	+	4.36891i	1.08566	+	0.910980i	0.0892847	+	0.996006i	$0.471542\pi$
$24$	0.133719	−	4.89715i	0.0272952	−	0.999627i
$25$	0.495107	−	2.80789i	0.0990215	−	0.561579i
$26$	3.73273	−	4.45388i	0.732049	−	0.873477i
$27$	5.17639	+	0.452789i	0.996196	+	0.0871394i
$28$	−0.00147403	−	1.23885i	−0.000278565	−	0.234122i
$29$	−3.01423	−	8.28154i	−0.559729	−	1.53784i	−0.820033	−	0.572317i	$-0.806045\pi$
$29$	−3.01423	−	8.28154i	−0.559729	−	1.53784i	0.260303	−	0.965527i	$-0.416177\pi$
$30$	−0.522532	−	3.55242i	−0.0954009	−	0.648581i
$31$	1.40352	+	0.810320i	0.252079	+	0.145538i	0.620716	−	0.784036i	$-0.286842\pi$
$31$	1.40352	+	0.810320i	0.252079	+	0.145538i	−0.368637	+	0.929573i	$0.620175\pi$
$32$	4.89054	−	2.84299i	0.864534	−	0.502574i
$33$	1.48711	+	2.75798i	0.258873	+	0.480103i
$34$	−3.52660	+	2.96275i	−0.604807	+	0.508107i
$35$	−0.157673	−	0.894209i	−0.0266516	−	0.151149i
$36$	2.69923	+	5.35856i	0.449872	+	0.893093i
$37$	−4.83914			−0.795550			−0.397775	−	0.917483i	$-0.630218\pi$
$37$	−4.83914			−0.795550			−0.397775	+	0.917483i	$0.630218\pi$
$38$	1.23740	+	6.03894i	0.200732	+	0.979646i
$39$	−1.43920	+	6.97024i	−0.230456	+	1.11613i
$40$	3.17135	−	2.67074i	0.501435	−	0.422281i
$41$	−5.93228	+	1.04602i	−0.926467	+	0.163361i	−0.616472	−	0.787377i	$-0.711439\pi$
$41$	−5.93228	+	1.04602i	−0.926467	+	0.163361i	−0.309995	+	0.950738i	$0.600327\pi$
$42$	0.720904	+	1.33508i	0.111238	+	0.206008i
$43$	0.0815368	+	0.0971718i	0.0124343	+	0.0148186i	0.772226	−	0.635348i	$-0.219143\pi$
$43$	0.0815368	+	0.0971718i	0.0124343	+	0.0148186i	−0.759791	+	0.650167i	$0.774699\pi$
$44$	−1.80532	+	3.13551i	−0.272162	+	0.472696i
$45$	2.62612	+	3.52741i	0.391479	+	0.525835i
$46$	−3.29292	−	9.03050i	−0.485514	−	1.33147i
$47$	−0.234702	+	0.0854244i	−0.0342347	+	0.0124604i	−0.359081	−	0.933306i	$-0.616910\pi$
$47$	−0.234702	+	0.0854244i	−0.0342347	+	0.0124604i	0.324846	+	0.945767i	$0.394688\pi$
$48$	−3.62307	+	5.90537i	−0.522945	+	0.852366i
$49$	−3.30815	−	5.72989i	−0.472594	−	0.818556i
$50$	−2.59002	+	3.09040i	−0.366284	+	0.437049i
$51$	2.08271	−	5.24257i	0.291637	−	0.734106i
$52$	−7.71934	+	2.82001i	−1.07048	+	0.391066i
$53$	−2.93063	+	3.49259i	−0.402553	+	0.479744i	−0.928797	−	0.370590i	$-0.879156\pi$
$53$	−2.93063	+	3.49259i	−0.402553	+	0.479744i	0.526243	+	0.850334i	$0.323600\pi$
$54$	−6.02209	−	4.21123i	−0.819503	−	0.573076i
$55$	−0.906982	+	2.49191i	−0.122297	+	0.336010i
$56$	−0.873294	+	1.51884i	−0.116699	+	0.202964i
$57$	−4.84075	−	5.79371i	−0.641173	−	0.767396i
$58$	−2.15696	+	12.2754i	−0.283223	+	1.61184i
$59$	−10.0955	−	3.67447i	−1.31433	−	0.478375i	−0.412690	−	0.910872i	$-0.635411\pi$
$59$	−10.0955	−	3.67447i	−1.31433	−	0.478375i	−0.901636	+	0.432496i	$0.857633\pi$
$60$	−1.86916	+	4.72141i	−0.241308	+	0.609531i
$61$	4.39992	+	3.69197i	0.563352	+	0.472709i	0.879432	−	0.476024i	$-0.157922\pi$
$61$	4.39992	+	3.69197i	0.563352	+	0.472709i	−0.316080	+	0.948733i	$0.602367\pi$
$62$	−1.14715	−	1.98419i	−0.145688	−	0.251992i
$63$	−1.55258	−	1.02113i	−0.195607	−	0.128650i
$64$	−7.99995	+	0.0285559i	−0.999994	+	0.00356949i
$65$	−5.21651	+	3.01175i	−0.647029	+	0.373562i
$66$	0.126222	−	4.42945i	0.0155369	−	0.545227i
$67$	−0.256563	−	0.704900i	−0.0313441	−	0.0861173i	0.923034	−	0.384720i	$-0.125702\pi$
$67$	−0.256563	−	0.704900i	−0.0313441	−	0.0861173i	−0.954378	+	0.298602i	$0.903480\pi$
$68$	6.41349	−	1.13874i	0.777750	−	0.138093i
$69$	8.79434	+	7.82621i	1.05871	+	0.942165i
$70$	−0.438474	+	1.20693i	−0.0524077	+	0.144256i
$71$	−2.09293	+	1.75618i	−0.248385	+	0.208420i	−0.758477	−	0.651700i	$-0.774056\pi$
$71$	−2.09293	+	1.75618i	−0.248385	+	0.208420i	0.510091	+	0.860120i	$0.329612\pi$
$72$	0.478163	−	8.47180i	0.0563521	−	0.998411i
$73$	0.334207	+	1.89538i	0.0391160	+	0.221838i	0.998099	−	0.0616245i	$-0.0196281\pi$
$73$	0.334207	+	1.89538i	0.0391160	+	0.221838i	−0.958983	+	0.283462i	$0.908517\pi$
$74$	5.92875	+	3.41826i	0.689203	+	0.397365i
$75$	0.998613	−	4.83642i	0.115310	−	0.558462i
$76$	2.74976	−	8.27278i	0.315419	−	0.948952i
$77$		−	1.12057i		−	0.127701i
$78$	6.68688	−	7.52307i	0.757140	−	0.851820i
$79$	−13.2403	+	2.33462i	−1.48965	+	0.262665i	−0.858427	−	0.512936i	$-0.828558\pi$
$79$	−13.2403	+	2.33462i	−1.48965	+	0.262665i	−0.631223	+	0.775602i	$0.717447\pi$
$80$	−5.77198	+	1.03192i	−0.645327	+	0.115373i
$81$	8.93917	+	1.04464i	0.993241	+	0.116071i
$82$	8.00691	+	2.90888i	0.884215	+	0.321233i
$83$	−4.28803	+	7.42708i	−0.470672	+	0.815228i	−0.999437	−	0.0335402i	$-0.989322\pi$
$83$	−4.28803	+	7.42708i	−0.470672	+	0.815228i	0.528765	+	0.848768i	$0.322655\pi$
$84$	0.0598450	−	2.14493i	0.00652963	−	0.234031i
$85$	4.48629	−	1.63288i	0.486606	−	0.177110i
$86$	−0.0312561	−	0.176647i	−0.00337043	−	0.0190484i
$87$	−4.80149	−	14.4898i	−0.514773	−	1.55347i
$88$	4.42667	−	2.56629i	0.471885	−	0.273567i
$89$	5.45617	+	0.962070i	0.578353	+	0.101979i	0.455170	−	0.890405i	$-0.349579\pi$
$89$	5.45617	+	0.962070i	0.578353	+	0.101979i	0.123183	+	0.992384i	$0.460690\pi$
$90$	−0.725745	−	6.17669i	−0.0765003	−	0.651081i
$91$	1.63610	−	1.94983i	0.171510	−	0.204398i
$92$	−2.34458	+	13.3899i	−0.244439	+	1.39599i
$93$	2.38912	+	1.47361i	0.247740	+	0.152807i
$94$	0.347890	+	0.0611290i	0.0358821	+	0.00630498i
$95$	0.939402	−	6.32017i	0.0963806	−	0.648436i
$96$	8.61028	−	4.67579i	0.878783	−	0.477221i
$97$	7.61079	+	2.77010i	0.772759	+	0.281261i	0.698150	−	0.715952i	$-0.254007\pi$
$97$	7.61079	+	2.77010i	0.772759	+	0.281261i	0.0746090	+	0.997213i	$0.476229\pi$
$98$	0.00556655	+	9.35687i	0.000562306	+	0.945187i
$99$	2.43575	+	4.84985i	0.244802	+	0.487428i
$100$	5.35620	−	1.95672i	0.535620	−	0.195672i
$101$	−16.6897	−	2.94285i	−1.66069	−	0.292824i	−0.736978	−	0.675917i	$-0.763748\pi$
$101$	−16.6897	−	2.94285i	−1.66069	−	0.292824i	−0.923710	+	0.383092i	$0.874859\pi$
$102$	−6.25489	+	4.95183i	−0.619327	+	0.490305i
$103$	9.43147	−	5.44526i	0.929311	−	0.536538i	0.0427171	−	0.999087i	$-0.486399\pi$
$103$	9.43147	−	5.44526i	0.929311	−	0.536538i	0.886593	+	0.462550i	$0.153065\pi$
$104$	11.4495	+	1.99779i	1.12271	+	0.195899i
$105$	−0.227944	−	1.55610i	−0.0222451	−	0.151860i
$106$	6.05760	−	2.20887i	0.588366	−	0.214544i
$107$	10.0177	−	17.3512i	0.968450	−	1.67740i	0.268405	−	0.963306i	$-0.413504\pi$
$107$	10.0177	−	17.3512i	0.968450	−	1.67740i	0.700045	−	0.714098i	$-0.253163\pi$
$108$	4.40334	+	9.41332i	0.423711	+	0.905797i
$109$	−6.96074	+	5.84075i	−0.666718	+	0.559443i	−0.912092	−	0.409986i	$-0.865534\pi$
$109$	−6.96074	+	5.84075i	−0.666718	+	0.559443i	0.245374	+	0.969428i	$0.421089\pi$
$110$	2.87144	−	2.41233i	0.273781	−	0.230007i
$111$	−8.37810	−	0.243732i	−0.795214	−	0.0231340i
$112$	2.14281	−	1.24396i	0.202476	−	0.117543i
$113$		−	12.2708i		−	1.15434i	−0.816625	−	0.577168i	$-0.804158\pi$
$113$		−	12.2708i		−	1.15434i	0.816625	−	0.577168i	$-0.195842\pi$
$114$	1.83817	+	10.5177i	0.172160	+	0.985069i
$115$			9.96328i			0.929080i
$116$	11.3137	−	13.5158i	1.05045	−	1.25491i
$117$	−2.84278	+	11.9952i	−0.262815	+	1.10896i
$118$	9.77312	+	11.6331i	0.899689	+	1.07091i
$119$	−1.54543	+	1.29677i	−0.141669	+	0.118875i
$120$	5.62514	−	4.46417i	0.513502	−	0.407521i
$121$	3.86367	−	6.69208i	0.351243	−	0.608371i
$122$	−2.78270	−	7.63129i	−0.251934	−	0.690904i
$123$	−10.3234	+	1.51221i	−0.930825	+	0.136351i
$124$	0.00385658	+	3.24128i	0.000346331	+	0.291075i
$125$	9.96699	−	5.75445i	0.891475	−	0.514693i
$126$	1.18087	+	2.34776i	0.105200	+	0.209155i
$127$	8.84109	+	1.55892i	0.784520	+	0.138332i	0.551539	−	0.834149i	$-0.314041\pi$
$127$	8.84109	+	1.55892i	0.784520	+	0.138332i	0.232981	+	0.972481i	$0.425152\pi$
$128$	9.82143	+	5.61600i	0.868100	+	0.496389i
$129$	0.136272	+	0.172342i	0.0119981	+	0.0151739i
$130$	8.51853	−	0.00506781i	0.747124	−	0.000444476i
$131$	−8.98207	−	3.26921i	−0.784767	−	0.285632i	−0.0816081	−	0.996664i	$-0.526006\pi$
$131$	−8.98207	−	3.26921i	−0.784767	−	0.285632i	−0.703159	+	0.711033i	$0.748228\pi$
$132$	−3.28351	+	5.33764i	−0.285793	+	0.464582i
$133$	0.540409	+	2.64539i	0.0468594	+	0.229384i
$134$	−0.183594	+	1.04485i	−0.0158601	+	0.0902613i
$135$	4.36898	+	6.23934i	0.376022	+	0.536997i
$136$	−8.66196	−	3.13520i	−0.742757	−	0.268841i
$137$	−6.65766	+	7.93429i	−0.568802	+	0.677872i	−0.971385	−	0.237511i	$-0.923668\pi$
$137$	−6.65766	+	7.93429i	−0.568802	+	0.677872i	0.402582	+	0.915384i	$0.368113\pi$
$138$	−5.24625	−	15.8005i	−0.446591	−	1.34503i
$139$	21.0816	+	3.71726i	1.78812	+	0.315294i	0.966869	−	0.255272i	$-0.0821650\pi$
$139$	21.0816	+	3.71726i	1.78812	+	0.315294i	0.821252	+	0.570566i	$0.193276\pi$
$140$	1.38975	−	1.16896i	0.117456	−	0.0987953i
$141$	−0.410646	+	0.136076i	−0.0345826	+	0.0114596i
$142$	3.80471	−	0.673208i	0.319285	−	0.0564944i
$143$	−6.98536	+	2.54246i	−0.584145	+	0.212611i
$144$	−6.57012	+	10.0416i	−0.547510	+	0.836799i
$145$	6.45940	−	11.1880i	0.536424	−	0.929114i
$146$	0.929397	−	2.55823i	0.0769174	−	0.211721i
$147$	−5.43887	−	10.0869i	−0.448591	−	0.831952i
$148$	−4.84911	−	8.37588i	−0.398595	−	0.688493i
$149$	14.3697	−	2.53376i	1.17721	−	0.207574i	0.449386	−	0.893338i	$-0.351643\pi$
$149$	14.3697	−	2.53376i	1.17721	−	0.207574i	0.727824	+	0.685764i	$0.240532\pi$
$150$	−4.63981	+	5.22002i	−0.378839	+	0.426213i
$151$		−	14.6754i		−	1.19427i	−0.802141	−	0.597135i	$-0.796306\pi$
$151$		−	14.6754i		−	1.19427i	0.802141	−	0.597135i	$-0.203694\pi$
$152$	−9.21262	+	8.19315i	−0.747242	+	0.664552i
$153$	3.86988	−	8.97165i	0.312861	−	0.725315i
$154$	−0.791550	+	1.37289i	−0.0637849	+	0.110631i
$155$	0.412528	+	2.33957i	0.0331351	+	0.187918i
$156$	−13.5067	+	4.49355i	−1.08140	+	0.359772i
$157$	−13.4848	+	11.3150i	−1.07620	+	0.903039i	−0.995600	−	0.0937073i	$-0.970128\pi$
$157$	−13.4848	+	11.3150i	−1.07620	+	0.903039i	−0.0806004	+	0.996746i	$0.525684\pi$
$158$	17.8707	+	6.49236i	1.42171	+	0.516504i
$159$	−5.24977	+	5.89918i	−0.416334	+	0.467835i
$160$	7.80056	+	2.81292i	0.616689	+	0.222381i
$161$	−1.43995	−	3.95623i	−0.113484	−	0.311795i
$162$	−10.2140	−	7.59429i	−0.802491	−	0.596664i
$163$	−15.4901	+	8.94322i	−1.21328	+	0.700487i	−0.963472	−	0.267809i	$-0.913700\pi$
$163$	−15.4901	+	8.94322i	−1.21328	+	0.700487i	−0.249807	+	0.968296i	$0.580367\pi$
$164$	−7.75502	−	9.21977i	−0.605565	−	0.719943i
$165$	−1.69578	+	4.26861i	−0.132017	+	0.332311i
$166$	10.4999	−	6.07043i	0.814948	−	0.471157i
$167$	0.0842477	+	0.0706922i	0.00651928	+	0.00547033i	0.646041	−	0.763302i	$-0.276423\pi$
$167$	0.0842477	+	0.0706922i	0.00651928	+	0.00547033i	−0.639522	+	0.768773i	$0.720868\pi$
$168$	−1.58845	+	2.58562i	−0.122551	+	0.199485i
$169$	−3.65086	−	1.32880i	−0.280835	−	0.102216i
$170$	−6.64987	−	1.16847i	−0.510022	−	0.0896178i
$171$	−8.08907	−	10.2746i	−0.618587	−	0.785717i
$172$	−0.0864860	+	0.238501i	−0.00659449	+	0.0181855i
$173$	−7.67084	+	21.0755i	−0.583203	+	1.60234i	0.199469	+	0.979904i	$0.436078\pi$
$173$	−7.67084	+	21.0755i	−0.583203	+	1.60234i	−0.782672	+	0.622434i	$0.786144\pi$
$174$	−4.35266	+	21.1441i	−0.329975	+	1.60293i
$175$	−1.13524	+	1.35293i	−0.0858160	+	0.102272i
$176$	−7.23617	+	0.0172197i	−0.545447	+	0.00129798i
$177$	−17.2935	−	6.87016i	−1.29986	−	0.516393i
$178$	−6.00513	−	5.03282i	−0.450103	−	0.377225i
$179$	3.04389	+	5.27218i	0.227511	+	0.394061i	0.957070	−	0.289857i	$-0.0936078\pi$
$179$	3.04389	+	5.27218i	0.227511	+	0.394061i	−0.729559	+	0.683918i	$0.760274\pi$
$180$	−3.47392	+	8.08012i	−0.258931	+	0.602257i
$181$	0.821449	−	0.298983i	0.0610578	−	0.0222232i	−0.311311	−	0.950308i	$-0.600768\pi$
$181$	0.821449	−	0.298983i	0.0610578	−	0.0222232i	0.372369	+	0.928085i	$0.378546\pi$
$182$	−3.38182	+	1.23316i	−0.250677	+	0.0914079i
$183$	7.43171	+	6.61359i	0.549368	+	0.488891i
$184$	12.3308	−	14.7487i	0.909041	−	1.08729i
$185$	−4.55967	−	5.43400i	−0.335233	−	0.399516i
$186$	−1.88614	−	3.49304i	−0.138298	−	0.256122i
$187$	5.80238	−	1.02312i	0.424312	−	0.0748176i
$188$	−0.383043	−	0.320635i	−0.0279363	−	0.0233847i
$189$	−2.63659	−	1.84609i	−0.191784	−	0.134284i
$190$	−5.61535	+	7.07968i	−0.407380	+	0.513614i
$191$	4.48705			0.324671			0.162336	−	0.986736i	$-0.448097\pi$
$191$	4.48705			0.324671			0.162336	+	0.986736i	$0.448097\pi$
$192$	−13.8519	−	0.353492i	−0.999675	−	0.0255111i
$193$	−1.02292	−	5.80126i	−0.0736313	−	0.417584i	−0.999236	−	0.0390913i	$-0.987554\pi$
$193$	−1.02292	−	5.80126i	−0.0736313	−	0.417584i	0.925604	−	0.378493i	$-0.123557\pi$
$194$	−7.36774	−	8.76993i	−0.528973	−	0.629644i
$195$	−9.18314	+	4.95157i	−0.657618	+	0.354589i
$196$	6.60267	−	11.4676i	0.471619	−	0.819118i
$197$	20.8978	+	12.0654i	1.48891	+	0.859621i	0.999920	−	0.0126690i	$-0.00403279\pi$
$197$	20.8978	+	12.0654i	1.48891	+	0.859621i	0.488988	+	0.872290i	$0.337366\pi$
$198$	0.441627	−	7.66243i	0.0313851	−	0.544545i
$199$	−2.62013	−	7.19876i	−0.185736	−	0.510306i	0.811521	−	0.584324i	$-0.198640\pi$
$199$	−2.62013	−	7.19876i	−0.185736	−	0.510306i	−0.997257	+	0.0740174i	$0.976418\pi$
$200$	−7.94441	−	1.38620i	−0.561754	−	0.0980190i
$201$	−0.408688	−	1.23333i	−0.0288266	−	0.0869923i
$202$	18.3689	+	15.3947i	1.29243	+	1.08317i
$203$	−0.947952	+	5.37610i	−0.0665332	+	0.377328i
$204$	11.1611	−	1.64850i	0.781436	−	0.115418i
$205$	−6.76428	−	5.67590i	−0.472437	−	0.396422i
$206$	−15.4015	+	0.00916261i	−1.07308	+	0.000638389i
$207$	14.8316	+	13.9926i	1.03087	+	0.972553i
$208$	−12.6163	−	10.5353i	−0.874782	−	0.730489i
$209$	2.49613	−	7.47996i	0.172661	−	0.517400i
$210$	−0.819927	+	2.06750i	−0.0565804	+	0.142671i
$211$	−5.43860	+	14.9424i	−0.374408	+	1.02868i	0.599229	+	0.800578i	$0.295474\pi$
$211$	−5.43860	+	14.9424i	−0.374408	+	1.02868i	−0.973638	+	0.228101i	$0.926748\pi$
$212$	−8.98185	−	1.57273i	−0.616876	−	0.108015i
$213$	−3.71199	+	2.93509i	−0.254341	+	0.201109i
$214$	−24.5299	+	14.1818i	−1.67683	+	0.969448i
$215$	−0.0322889	+	0.183120i	−0.00220209	+	0.0124887i
$216$	1.25455	−	14.6433i	0.0853613	−	0.996350i
$217$	−0.501935	−	0.869377i	−0.0340736	−	0.0590171i
$218$	12.6538	−	2.23897i	0.857026	−	0.151643i
$219$	0.483154	+	3.29834i	0.0326485	+	0.222881i
$220$	−5.22200	+	0.927188i	−0.352067	+	0.0625110i
$221$	11.5901	+	6.69155i	0.779635	+	0.450122i
$222$	10.0924	+	6.21672i	0.677357	+	0.417239i
$223$	4.29155	+	5.11447i	0.287383	+	0.342490i	0.890350	−	0.455276i	$-0.150459\pi$
$223$	4.29155	+	5.11447i	0.287383	+	0.342490i	−0.602967	+	0.797766i	$0.706015\pi$
$224$	−3.50400	+	0.0104229i	−0.234121	+	0.000696412i
$225$	1.97251	−	8.32309i	0.131501	−	0.554872i
$226$	−8.66780	+	15.0337i	−0.576574	+	1.00003i
$227$	25.8618			1.71650			0.858252	−	0.513228i	$-0.171550\pi$
$227$	25.8618			1.71650			0.858252	+	0.513228i	$0.171550\pi$
$228$	5.17738	−	14.1843i	0.342881	−	0.939379i
$229$	4.88524			0.322826			0.161413	−	0.986887i	$-0.448395\pi$
$229$	4.88524			0.322826			0.161413	+	0.986887i	$0.448395\pi$
$230$	7.03784	−	12.2067i	0.464061	−	0.804883i
$231$	0.0564397	−	1.94007i	0.00371346	−	0.127647i
$232$	−23.4085	+	8.56733i	−1.53684	+	0.562473i
$233$	12.7143	+	15.1523i	0.832943	+	0.992662i	0.999977	+	0.00671136i	$0.00213631\pi$
$233$	12.7143	+	15.1523i	0.832943	+	0.992662i	−0.167035	+	0.985951i	$0.553419\pi$
$234$	11.9560	−	12.6880i	0.781590	−	0.829443i
$235$	−0.317072	−	0.183062i	−0.0206835	−	0.0119416i
$236$	−3.75633	−	21.1560i	−0.244516	−	1.37714i
$237$	−23.0407	+	3.37510i	−1.49666	+	0.219236i
$238$	2.80941	−	0.497099i	0.182107	−	0.0322221i
$239$	5.67741	+	9.83356i	0.367241	+	0.636080i	0.989133	−	0.147023i	$-0.0469691\pi$
$239$	5.67741	+	9.83356i	0.367241	+	0.636080i	−0.621892	+	0.783103i	$0.713636\pi$
$240$	−10.0451	+	1.49587i	−0.648409	+	0.0965583i
$241$	4.45903	−	25.2884i	0.287231	−	1.62897i	−0.409974	−	0.912097i	$-0.634462\pi$
$241$	4.45903	−	25.2884i	0.287231	−	1.62897i	0.697205	−	0.716871i	$-0.254427\pi$
$242$	−9.46077	+	5.46969i	−0.608162	+	0.351605i
$243$	15.4239	+	2.25884i	0.989446	+	0.144905i
$244$	−1.98130	+	11.3152i	−0.126840	+	0.724383i
$245$	3.31715	−	9.11378i	0.211925	−	0.582258i
$246$	13.7160	+	5.43949i	0.874500	+	0.346809i
$247$	15.2645	−	9.37086i	0.971257	−	0.596253i
$248$	2.28484	−	3.97383i	0.145088	−	0.252338i
$249$	−7.79802	+	12.6427i	−0.494179	+	0.801196i
$250$	−16.2760	+	0.00968287i	−1.02939	+	0.000612398i
$251$	10.1717	+	8.53506i	0.642032	+	0.538728i	0.904641	−	0.426174i	$-0.140139\pi$
$251$	10.1717	+	8.53506i	0.642032	+	0.538728i	−0.262610	+	0.964902i	$0.584583\pi$
$252$	0.211644	−	3.71054i	0.0133323	−	0.233742i
$253$	−2.13514	+	12.1090i	−0.134235	+	0.761284i
$254$	−9.73061	−	8.15509i	−0.610553	−	0.511696i
$255$	7.84943	−	2.60107i	0.491551	−	0.162885i
$256$	−8.06586	−	13.8182i	−0.504116	−	0.863636i
$257$	−2.95094	−	8.10763i	−0.184074	−	0.505740i	0.812993	−	0.582274i	$-0.197837\pi$
$257$	−2.95094	−	8.10763i	−0.184074	−	0.505740i	−0.997067	+	0.0765339i	$0.975615\pi$
$258$	−0.0452171	−	0.307407i	−0.00281509	−	0.0191383i
$259$	2.59591	+	1.49875i	0.161302	+	0.0931278i
$260$	−10.4402	−	6.01109i	−0.647473	−	0.372792i
$261$	−7.58310	−	25.3283i	−0.469382	−	1.56778i
$262$	8.69523	+	10.3501i	0.537193	+	0.639429i
$263$	−0.492995	−	2.79591i	−0.0303994	−	0.172403i	0.965828	−	0.259183i	$-0.0834534\pi$
$263$	−0.492995	−	2.79591i	−0.0303994	−	0.172403i	−0.996228	+	0.0867800i	$0.972342\pi$
$264$	7.79323	−	4.22010i	0.479640	−	0.259729i
$265$	−6.68330			−0.410552
$266$	1.20656	−	3.62277i	0.0739786	−	0.222126i
$267$	9.39791	+	1.94046i	0.575143	+	0.118754i
$268$	0.962992	−	1.15043i	0.0588241	−	0.0702735i
$269$	16.0308	−	2.82666i	0.977415	−	0.172345i	0.337949	−	0.941164i	$-0.390267\pi$
$269$	16.0308	−	2.82666i	0.977415	−	0.172345i	0.639466	+	0.768820i	$0.279156\pi$
$270$	−0.945397	−	10.7304i	−0.0575350	−	0.653030i
$271$	−13.0506	−	15.5531i	−0.792767	−	0.944783i	0.206668	−	0.978411i	$-0.433738\pi$
$271$	−13.0506	−	15.5531i	−0.792767	−	0.944783i	−0.999434	+	0.0336285i	$0.989294\pi$
$272$	8.39770	+	9.95976i	0.509185	+	0.603899i
$273$	2.93082	−	3.29338i	0.177381	−	0.199324i
$274$	13.7613	−	5.01799i	0.831353	−	0.303148i
$275$	4.84691	−	1.76413i	0.292280	−	0.106381i
$276$	−4.73362	+	23.0641i	−0.284930	+	1.38830i
$277$	13.0094	+	22.5329i	0.781658	+	1.35387i	0.930975	+	0.365082i	$0.118959\pi$
$277$	13.0094	+	22.5329i	0.781658	+	1.35387i	−0.149317	+	0.988789i	$0.547707\pi$
$278$	−23.2027	−	19.4459i	−1.39161	−	1.16629i
$279$	4.06210	+	2.67162i	0.243192	+	0.159946i
$280$	−2.52841	+	0.450481i	−0.151101	+	0.0269214i
$281$	−3.93600	+	4.69074i	−0.234802	+	0.279826i	−0.870560	−	0.492062i	$-0.836243\pi$
$281$	−3.93600	+	4.69074i	−0.234802	+	0.279826i	0.635758	+	0.771888i	$0.280688\pi$
$282$	0.599230	+	0.123356i	0.0356836	+	0.00734574i
$283$	−3.97481	+	10.9207i	−0.236278	+	0.649168i	0.763716	+	0.645553i	$0.223373\pi$
$283$	−3.97481	+	10.9207i	−0.236278	+	0.649168i	−0.999993	+	0.00361523i	$0.998849\pi$
$284$	−5.13694	−	1.86278i	−0.304822	−	0.110535i
$285$	1.94473	−	10.8949i	0.115196	−	0.645359i
$286$	10.3542	+	1.81937i	0.612254	+	0.107581i
$287$	3.50628	+	1.27618i	0.206969	+	0.0753307i
$288$	15.1426	−	7.66162i	0.892289	−	0.451465i
$289$	4.89702	+	4.10909i	0.288060	+	0.241711i
$290$	−15.8168	+	9.14439i	−0.928795	+	0.536977i
$291$	13.0372	+	5.17926i	0.764253	+	0.303614i
$292$	−2.94574	+	2.47775i	−0.172387	+	0.144999i
$293$	−16.8204	+	9.71125i	−0.982657	+	0.567337i	−0.903071	−	0.429491i	$-0.858693\pi$
$293$	−16.8204	+	9.71125i	−0.982657	+	0.567337i	−0.0795856	+	0.996828i	$0.525360\pi$
$294$	−0.461638	+	16.2000i	−0.0269232	+	0.944803i
$295$	−5.38632	−	14.7988i	−0.313603	−	0.861618i
$296$	0.0244281	+	13.6871i	0.00141985	+	0.795549i
$297$	3.97279	+	8.51931i	0.230525	+	0.494341i
$298$	−19.3950	−	7.04615i	−1.12352	−	0.408173i
$299$	−21.3950	+	17.9525i	−1.23730	+	1.03822i
$300$	9.37183	−	3.11793i	0.541083	−	0.180013i
$301$	−0.0136442	−	0.0773800i	−0.000786437	−	0.00446011i
$302$	−10.3664	+	17.9798i	−0.596520	+	1.03462i
$303$	−28.7470	−	5.93561i	−1.65147	−	0.340992i
$304$	17.0744	−	3.53037i	0.979286	−	0.202481i
$305$			8.41954i			0.482101i
$306$	−11.0786	+	8.25816i	−0.633322	+	0.472088i
$307$	−24.1728	+	4.26231i	−1.37961	+	0.243263i	−0.813740	−	0.581229i	$-0.802572\pi$
$307$	−24.1728	+	4.26231i	−1.37961	+	0.243263i	−0.565873	+	0.824492i	$0.691461\pi$
$308$	1.93956	−	1.12288i	0.110517	−	0.0639822i
$309$	16.6031	−	8.95245i	0.944520	−	0.509287i
$310$	1.14720	−	3.15776i	0.0651567	−	0.179348i
$311$	7.76905	−	13.4564i	0.440542	−	0.763042i	−0.557187	−	0.830387i	$-0.688119\pi$
$311$	7.76905	−	13.4564i	0.440542	−	0.763042i	0.997730	+	0.0673450i	$0.0214528\pi$
$312$	19.7220	+	4.03547i	1.11654	+	0.228464i
$313$	−8.13431	+	2.96065i	−0.459778	+	0.167346i	−0.561516	−	0.827466i	$-0.689782\pi$
$313$	−8.13431	+	2.96065i	−0.459778	+	0.167346i	0.101738	+	0.994811i	$0.467560\pi$
$314$	24.5138	−	4.33747i	1.38339	−	0.244778i
$315$	−0.316268	−	2.70559i	−0.0178197	−	0.152443i
$316$	−17.3085	−	20.5777i	−0.973678	−	1.15758i
$317$	−14.8105	−	2.61149i	−0.831840	−	0.146676i	−0.258518	−	0.966006i	$-0.583234\pi$
$317$	−14.8105	−	2.61149i	−0.831840	−	0.146676i	−0.573321	+	0.819331i	$0.694345\pi$
$318$	10.5989	−	3.51915i	0.594356	−	0.197344i
$319$	10.2481	−	12.2132i	0.573783	−	0.683808i
$320$	−7.56999	−	8.95644i	−0.423175	−	0.500680i
$321$	18.2178	−	29.5359i	1.01682	−	1.64853i
$322$	−1.03042	+	5.86419i	−0.0574229	+	0.326798i
$323$	−13.2045	+	5.21357i	−0.734719	+	0.290091i
$324$	7.14946	+	16.5192i	0.397192	+	0.917735i
$325$	11.0095	+	4.00713i	0.610697	+	0.222276i
$326$	25.2952	−	0.0150485i	1.40097	−	0.000833461i
$327$	−12.3454	+	9.76161i	−0.682704	+	0.539818i
$328$	2.98854	+	16.7737i	0.165014	+	0.926174i
$329$	0.152360	+	0.0268653i	0.00839991	+	0.00148113i
$330$	5.09287	−	4.03189i	0.280353	−	0.221948i
$331$	0.851934	−	0.491864i	0.0468265	−	0.0270353i	−0.476404	−	0.879227i	$-0.658060\pi$
$331$	0.851934	−	0.491864i	0.0468265	−	0.0270353i	0.523230	+	0.852191i	$0.324727\pi$
$332$	−17.1521	+	0.0204081i	−0.941343	+	0.00112004i
$333$	−14.4929	−	0.843955i	−0.794205	−	0.0462484i
$334$	−0.0532819	−	0.146120i	−0.00291546	−	0.00799535i
$335$	0.549805	−	0.952291i	0.0300391	−	0.0520292i
$336$	3.77254	−	2.04576i	0.205809	−	0.111605i
$337$	6.07492	−	5.09747i	0.330922	−	0.277677i	−0.462153	−	0.886800i	$-0.652923\pi$
$337$	6.07492	−	5.09747i	0.330922	−	0.277677i	0.793075	+	0.609123i	$0.208479\pi$
$338$	3.53426	+	4.20689i	0.192239	+	0.228825i
$339$	0.618038	−	21.2446i	0.0335672	−	1.15385i
$340$	7.32181	+	6.12890i	0.397081	+	0.332386i
$341$			2.93182i			0.158767i
$342$	2.65271	+	18.3020i	0.143442	+	0.989659i
$343$			8.43432i			0.455411i
$344$	0.274431	−	0.231111i	0.0147964	−	0.0124607i
$345$	−0.501818	+	17.2496i	−0.0270169	+	0.928687i
$346$	24.2853	−	20.4024i	1.30559	−	1.09684i
$347$	15.7558	−	13.2207i	0.845818	−	0.709726i	−0.113046	−	0.993590i	$-0.536061\pi$
$347$	15.7558	−	13.2207i	0.845818	−	0.709726i	0.958865	+	0.283864i	$0.0916164\pi$
$348$	20.2684	−	22.8303i	1.08650	−	1.22384i
$349$	−7.92007	+	13.7180i	−0.423952	+	0.734306i	−0.996322	−	0.0856893i	$-0.972691\pi$
$349$	−7.92007	+	13.7180i	−0.423952	+	0.734306i	0.572370	+	0.819995i	$0.306024\pi$
$350$	2.34653	−	0.855649i	0.125427	−	0.0457364i
$351$	−5.52591	+	20.6243i	−0.294951	+	1.10085i
$352$	8.87767	+	5.09038i	0.473181	+	0.271318i
$353$	0.648535	−	0.374432i	0.0345180	−	0.0199290i	−0.482642	−	0.875818i	$-0.660323\pi$
$353$	0.648535	−	0.374432i	0.0345180	−	0.0199290i	0.517160	+	0.855889i	$0.326989\pi$
$354$	16.3345	+	20.6328i	0.868167	+	1.09662i
$355$	−3.94412	−	0.695454i	−0.209332	−	0.0369109i
$356$	3.80220	+	10.4079i	0.201516	+	0.551619i
$357$	−2.74094	+	2.16728i	−0.145066	+	0.114705i
$358$	−0.00512189	−	8.60943i	−0.000270700	−	0.455023i
$359$	−21.8200	−	7.94185i	−1.15162	−	0.419155i	−0.305522	−	0.952185i	$-0.598831\pi$
$359$	−21.8200	−	7.94185i	−1.15162	−	0.419155i	−0.846096	+	0.533030i	$0.821053\pi$
$360$	9.96375	−	7.44558i	0.525136	−	0.392417i
$361$	−2.28543	+	18.8620i	−0.120286	+	0.992739i
$362$	−1.21761	−	0.213950i	−0.0639960	−	0.0112450i
$363$	7.02630	−	11.3915i	0.368785	−	0.597899i
$364$	5.01436	+	0.878017i	0.262824	+	0.0460206i
$365$	−1.81347	+	2.16121i	−0.0949212	+	0.113123i
$366$	−4.43338	−	13.3523i	−0.231737	−	0.697938i
$367$	−8.59160	−	1.51493i	−0.448478	−	0.0790787i	−0.0551521	−	0.998478i	$-0.517564\pi$
$367$	−8.59160	−	1.51493i	−0.448478	−	0.0790787i	−0.393326	+	0.919399i	$0.628675\pi$
$368$	−25.5254	+	9.35935i	−1.33061	+	0.487890i
$369$	−17.9492	+	2.09816i	−0.934397	+	0.109226i
$370$	1.74789	+	9.87839i	0.0908684	+	0.513553i
$371$	2.65381	−	0.965909i	0.137779	−	0.0501475i
$372$	−0.156576	+	5.61188i	−0.00811807	+	0.290962i
$373$	13.8775	−	24.0365i	0.718548	−	1.24456i	−0.243028	−	0.970019i	$-0.578141\pi$
$373$	13.8775	−	24.0365i	0.718548	−	1.24456i	0.961575	−	0.274542i	$-0.0885261\pi$
$374$	−7.83158	−	2.84519i	−0.404961	−	0.147121i
$375$	17.5459	−	9.46078i	0.906065	−	0.488552i
$376$	0.242801	+	0.663404i	0.0125215	+	0.0342124i
$377$	35.6639	−	6.28852i	1.83679	−	0.323875i
$378$	1.92622	+	4.12420i	0.0990738	+	0.212126i
$379$			14.8014i			0.760295i	0.924926	+	0.380147i	$0.124127\pi$
$379$			14.8014i			0.760295i	−0.924926	+	0.380147i	$0.875873\pi$
$380$	11.8807	−	4.70722i	0.609465	−	0.241475i
$381$	15.2282	+	3.14429i	0.780166	+	0.161087i
$382$	−5.49738	−	3.16955i	−0.281270	−	0.162168i
$383$	1.97397	+	11.1950i	0.100865	+	0.572035i	0.992791	+	0.119854i	$0.0382428\pi$
$383$	1.97397	+	11.1950i	0.100865	+	0.572035i	−0.891926	+	0.452181i	$0.850646\pi$
$384$	16.7212	+	10.2178i	0.853298	+	0.521423i
$385$	1.25832	−	1.05586i	0.0641300	−	0.0538115i
$386$	−2.84464	+	7.83007i	−0.144788	+	0.398540i
$387$	0.227250	+	0.305243i	0.0115518	+	0.0155164i
$388$	2.83181	+	15.9490i	0.143764	+	0.809689i
$389$	−6.78254	−	18.6349i	−0.343888	−	0.944825i	−0.984255	−	0.176756i	$-0.943440\pi$
$389$	−6.78254	−	18.6349i	−0.343888	−	0.944825i	0.640366	−	0.768070i	$-0.278783\pi$
$390$	14.7485	+	0.420276i	0.746821	+	0.0212815i
$391$	19.1708	−	11.0683i	0.969508	−	0.559746i
$392$	−16.1899	+	9.38578i	−0.817711	+	0.474054i
$393$	−15.3862	−	6.11243i	−0.776129	−	0.308332i
$394$	−17.0806	−	29.5438i	−0.860507	−	1.48840i
$395$	−15.0972	−	12.6681i	−0.759624	−	0.637400i
$396$	−5.95364	+	9.07578i	−0.299181	+	0.456075i
$397$	−22.3254	−	8.12578i	−1.12048	−	0.407821i	−0.285652	−	0.958333i	$-0.592210\pi$
$397$	−22.3254	−	8.12578i	−1.12048	−	0.407821i	−0.834827	+	0.550512i	$0.814432\pi$
$398$	−1.87495	+	10.6705i	−0.0939826	+	0.534863i
$399$	0.802380	+	4.60723i	0.0401692	+	0.230650i
$400$	8.75403	+	7.31008i	0.437702	+	0.365504i
$401$	−12.9384	+	35.5480i	−0.646113	+	1.77518i	−0.0145039	+	0.999895i	$0.504617\pi$
$401$	−12.9384	+	35.5480i	−0.646113	+	1.77518i	−0.631609	+	0.775287i	$0.717605\pi$
$402$	−0.370486	+	1.79972i	−0.0184782	+	0.0897619i
$403$	−4.28062	+	5.10144i	−0.213233	+	0.254121i
$404$	−11.6304	−	31.8365i	−0.578636	−	1.58392i
$405$	7.24985	+	11.0223i	0.360248	+	0.547704i
$406$	4.95896	−	5.91700i	0.246109	−	0.293656i
$407$	−4.37712	−	7.58140i	−0.216966	−	0.375796i
$408$	−14.8387	−	5.86431i	−0.734625	−	0.290326i
$409$	−11.6847	+	4.25287i	−0.577770	+	0.210291i	−0.614342	−	0.789040i	$-0.710578\pi$
$409$	−11.6847	+	4.25287i	−0.577770	+	0.210291i	0.0365720	+	0.999331i	$0.488356\pi$
$410$	4.27802	+	11.7321i	0.211277	+	0.579405i
$411$	−11.9262	+	13.4015i	−0.588274	+	0.661045i
$412$	18.8759	+	10.8681i	0.929948	+	0.535432i
$413$	4.27761	+	5.09786i	0.210488	+	0.250849i
$414$	−8.28712	−	27.6200i	−0.407289	−	1.35745i
$415$	−12.3804	+	2.18301i	−0.607732	+	0.107160i
$416$	8.01516	+	21.8193i	0.392976	+	1.06978i
$417$	36.3118	+	7.49758i	1.77820	+	0.367158i
$418$	−8.34185	+	7.40098i	−0.408013	+	0.361994i
$419$	−21.9897			−1.07427			−0.537134	−	0.843497i	$-0.680493\pi$
$419$	−21.9897			−1.07427			−0.537134	+	0.843497i	$0.680493\pi$
$420$	2.46498	−	1.95385i	0.120279	−	0.0953380i
$421$	−3.19270	−	18.1067i	−0.155603	−	0.882466i	−0.958233	−	0.285989i	$-0.907678\pi$
$421$	−3.19270	−	18.1067i	−0.155603	−	0.882466i	0.802630	−	0.596477i	$-0.203433\pi$
$422$	17.2182	−	14.4652i	0.838168	−	0.704156i
$423$	−0.717812	+	0.214907i	−0.0349012	+	0.0104492i
$424$	9.89332	+	8.27143i	0.480462	+	0.401696i
$425$	−8.04200	−	4.64305i	−0.390094	−	0.225221i
$426$	6.62108	−	0.973906i	0.320792	−	0.0471859i
$427$	−1.21684	−	3.34324i	−0.0588870	−	0.161791i
$428$	40.0709	−	0.0476776i	1.93690	−	0.00230458i
$429$	−12.2219	+	4.04998i	−0.590080	+	0.195535i
$430$	0.168911	−	0.201544i	0.00814561	−	0.00971930i
$431$	1.39479	−	7.91025i	0.0671847	−	0.381023i	−0.932612	−	0.360880i	$-0.882477\pi$
$431$	1.39479	−	7.91025i	0.0671847	−	0.381023i	0.999797	−	0.0201436i	$-0.00641235\pi$
$432$	−11.8807	+	17.0543i	−0.571612	+	0.820524i
$433$	29.6588	+	24.8867i	1.42531	+	1.19598i	0.948419	+	0.317018i	$0.102682\pi$
$433$	29.6588	+	24.8867i	1.42531	+	1.19598i	0.476893	+	0.878961i	$0.341763\pi$
$434$	0.000844593		1.41969i	4.05418e−5		0.0681471i
$435$	11.7468	−	19.0447i	0.563215	−	0.913122i
$436$	−17.0846	−	6.19527i	−0.818204	−	0.296700i
$437$	−0.799160	−	29.6158i	−0.0382290	−	1.41672i
$438$	1.73793	−	4.38230i	0.0830416	−	0.209395i
$439$	0.0966412	−	0.265519i	0.00461243	−	0.0126726i	−0.937365	−	0.348349i	$-0.886743\pi$
$439$	0.0966412	−	0.265519i	0.00461243	−	0.0126726i	0.941977	+	0.335676i	$0.108965\pi$
$440$	7.05276	+	2.55275i	0.336227	+	0.121698i
$441$	−8.90838	−	17.7376i	−0.424208	−	0.844645i
$442$	−9.47303	−	16.3853i	−0.450586	−	0.779367i
$443$	6.06745	−	34.4102i	0.288273	−	1.63488i	−0.405081	−	0.914281i	$-0.632757\pi$
$443$	6.06745	−	34.4102i	0.288273	−	1.63488i	0.693354	−	0.720597i	$-0.256132\pi$
$444$	−7.97349	−	14.7455i	−0.378405	−	0.699793i
$445$	4.06073	+	7.03338i	0.192497	+	0.333414i
$446$	−1.64511	−	9.29753i	−0.0778982	−	0.440251i
$447$	25.0061	−	3.66300i	1.18275	−	0.173254i
$448$	4.30034	+	2.46238i	0.203172	+	0.116336i
$449$	27.6785	+	15.9802i	1.30623	+	0.754153i	0.981465	−	0.191641i	$-0.0613810\pi$
$449$	27.6785	+	15.9802i	1.30623	+	0.754153i	0.324766	+	0.945794i	$0.394714\pi$
$450$	−8.29590	+	8.80382i	−0.391072	+	0.415016i
$451$	−7.00467	−	8.34785i	−0.329837	−	0.393085i
$452$	21.2390	−	12.2960i	0.998998	−	0.578357i
$453$	0.739154	−	25.4079i	0.0347285	−	1.19377i
$454$	−31.6849	−	18.2682i	−1.48705	−	0.857368i
$455$	3.73113			0.174918
$456$	−16.3626	+	13.7209i	−0.766251	+	0.642542i
$457$	−21.9698			−1.02770			−0.513852	−	0.857879i	$-0.671782\pi$
$457$	−21.9698			−1.02770			−0.513852	+	0.857879i	$0.671782\pi$
$458$	−5.98523	−	3.45083i	−0.279671	−	0.161247i
$459$	7.15186	−	15.3379i	0.333820	−	0.715911i
$460$	−17.2450	+	9.98380i	−0.804054	+	0.465497i
$461$	10.0540	+	11.9818i	0.468259	+	0.558050i	0.947550	−	0.319606i	$-0.103551\pi$
$461$	10.0540	+	11.9818i	0.468259	+	0.558050i	−0.479291	+	0.877656i	$0.659106\pi$
$462$	−1.43957	+	2.33704i	−0.0669750	+	0.108729i
$463$	−18.4801	−	10.6695i	−0.858843	−	0.495853i	0.00478196	−	0.999989i	$-0.498478\pi$
$463$	−18.4801	−	10.6695i	−0.858843	−	0.495853i	−0.863625	+	0.504136i	$0.831811\pi$
$464$	34.7310	+	6.03884i	1.61235	+	0.280346i
$465$	0.596382	+	4.07131i	0.0276565	+	0.188802i
$466$	−4.87387	−	27.5452i	−0.225777	−	1.27601i
$467$	5.10473	+	8.84165i	0.236219	+	0.409143i	0.959626	−	0.281279i	$-0.0907585\pi$
$467$	5.10473	+	8.84165i	0.236219	+	0.409143i	−0.723408	+	0.690421i	$0.757425\pi$
$468$	−23.6107	+	7.09947i	−1.09140	+	0.328173i
$469$	−0.0806869	+	0.457598i	−0.00372577	+	0.0211299i
$470$	0.259155	+	0.448253i	0.0119539	+	0.0206764i
$471$	−23.9163	+	18.9108i	−1.10200	+	0.871362i
$472$	−10.3420	+	28.5730i	−0.476029	+	1.31518i
$473$	−0.0784853	+	0.215637i	−0.00360876	+	0.00991498i
$474$	30.6128	+	12.1404i	1.40609	+	0.557628i
$475$	−10.5915	+	6.50213i	−0.485973	+	0.298338i
$476$	−3.79314	−	1.37548i	−0.173858	−	0.0630450i
$477$	−9.38614	+	9.94894i	−0.429762	+	0.455531i
$478$	−0.00955323	−	16.0581i	−0.000436955	−	0.734482i
$479$	−26.2092	−	21.9921i	−1.19753	−	1.00485i	−0.999697	−	0.0246111i	$-0.992165\pi$
$479$	−26.2092	−	21.9921i	−1.19753	−	1.00485i	−0.197833	−	0.980236i	$-0.563390\pi$
$480$	13.3636	+	5.26295i	0.609961	+	0.240220i
$481$	3.45296	−	19.5827i	0.157441	−	0.892894i
$482$	−23.3262	+	27.8327i	−1.06248	+	1.26774i
$483$	−2.29375	−	6.92202i	−0.104369	−	0.314963i
$484$	15.4547	−	0.0183885i	0.702485	−	0.000835839i
$485$	4.06062	+	11.1565i	0.184383	+	0.506589i
$486$	−17.3013	−	13.6626i	−0.784802	−	0.619747i
$487$	2.98041	+	1.72074i	0.135055	+	0.0779742i	0.566005	−	0.824402i	$-0.308488\pi$
$487$	2.98041	+	1.72074i	0.135055	+	0.0779742i	−0.430950	+	0.902376i	$0.641821\pi$
$488$	10.4203	−	12.4635i	0.471703	−	0.564195i
$489$	−27.2687	+	14.7034i	−1.23314	+	0.664909i
$490$	−10.5018	+	8.82273i	−0.474424	+	0.398570i
$491$	3.64876	+	20.6932i	0.164666	+	0.933869i	0.949408	+	0.314046i	$0.101685\pi$
$491$	3.64876	+	20.6932i	0.164666	+	0.933869i	−0.784742	+	0.619823i	$0.787204\pi$
$492$	−12.9620	−	16.3530i	−0.584374	−	0.737248i
$493$	−28.7032			−1.29272
$494$	−25.3209	+	0.698340i	−1.13924	+	0.0314198i
$495$	−3.15094	+	7.30492i	−0.141624	+	0.328332i
$496$	−5.60633	+	3.25463i	−0.251732	+	0.146137i
$497$	1.66665	−	0.293875i	0.0747593	−	0.0131821i
$498$	18.4844	−	9.98101i	0.828304	−	0.447260i
$499$	12.2935	+	14.6508i	0.550332	+	0.655860i	0.967471	−	0.252983i	$-0.0814117\pi$
$499$	12.2935	+	14.6508i	0.550332	+	0.655860i	−0.417139	+	0.908843i	$0.636967\pi$
$500$	19.9477	+	11.4852i	0.892087	+	0.513632i
$501$	0.142299	+	0.126634i	0.00635745	+	0.00565759i
$502$	−6.43302	−	17.6419i	−0.287120	−	0.787398i
$503$	14.5343	−	5.29007i	0.648055	−	0.235873i	0.00298394	−	0.999996i	$-0.499050\pi$
$503$	14.5343	−	5.29007i	0.648055	−	0.235873i	0.645071	+	0.764123i	$0.276828\pi$
$504$	−2.88034	+	4.39652i	−0.128301	+	0.195837i
$505$	−12.4212	−	21.5142i	−0.552737	−	0.957369i
$506$	11.1694	−	13.3273i	0.496540	−	0.592469i
$507$	−6.25387	−	2.48446i	−0.277744	−	0.110339i
$508$	6.16103	+	16.8648i	0.273351	+	0.748255i
$509$	−14.8651	+	17.7155i	−0.658884	+	0.785228i	−0.987225	−	0.159332i	$-0.949066\pi$
$509$	−14.8651	+	17.7155i	−0.658884	+	0.785228i	0.328341	+	0.944559i	$0.393510\pi$
$510$	−11.4542	−	2.35793i	−0.507200	−	0.104411i
$511$	0.407744	−	1.12027i	0.0180375	−	0.0495577i
$512$	0.121152	+	22.6271i	0.00535421	+	0.999986i
$513$	−13.4873	−	18.1960i	−0.595477	−	0.803372i
$514$	−2.11167	+	12.0177i	−0.0931416	+	0.530076i
$515$	15.0014	+	5.46006i	0.661041	+	0.240599i
$516$	−0.161747	+	0.408565i	−0.00712053	+	0.0179861i
$517$	−0.346126	−	0.290434i	−0.0152226	−	0.0127733i
$518$	−2.12174	−	3.66991i	−0.0932238	−	0.161247i
$519$	−14.3422	+	36.1020i	−0.629551	+	1.58470i
$520$	8.54485	+	14.7393i	0.374716	+	0.646361i
$521$	−18.6733	+	10.7810i	−0.818091	+	0.472325i	−0.849758	−	0.527173i	$-0.823252\pi$
$521$	−18.6733	+	10.7810i	−0.818091	+	0.472325i	0.0316664	+	0.999498i	$0.489919\pi$
$522$	−8.60080	+	36.3879i	−0.376447	+	1.59265i
$523$	9.16006	+	25.1671i	0.400541	+	1.10048i	0.962018	+	0.272986i	$0.0880112\pi$
$523$	9.16006	+	25.1671i	0.400541	+	1.10048i	−0.561477	+	0.827493i	$0.689767\pi$
$524$	−3.34204	−	18.8226i	−0.145998	−	0.822271i
$525$	−2.03360	+	2.28517i	−0.0887537	+	0.0997328i
$526$	−1.37097	+	3.77370i	−0.0597772	+	0.164541i
$527$	4.04338	−	3.39280i	0.176133	−	0.147793i
$528$	−12.5290	−	0.334650i	−0.545254	−	0.0145638i
$529$	4.02805	+	22.8442i	0.175133	+	0.993227i
$530$	8.18814	+	4.72093i	0.355670	+	0.205064i
$531$	−29.5945	−	12.7654i	−1.28429	−	0.553973i
$532$	−4.03728	+	3.58621i	−0.175038	+	0.155482i
$533$		−	24.7527i		−	1.07216i
$534$	−10.1433	−	9.01586i	−0.438944	−	0.390155i
$535$	28.9233	−	5.09996i	1.25046	−	0.220490i
$536$	−1.99246	+	0.729226i	−0.0860612	+	0.0314978i
$537$	5.00441	+	9.28113i	0.215956	+	0.400510i
$538$	−21.6371	−	7.86067i	−0.932840	−	0.338898i
$539$	5.98461	−	10.3657i	0.257775	−	0.446480i
$540$	−6.42143	+	13.8143i	−0.276334	+	0.594472i
$541$	14.8581	−	5.40791i	0.638800	−	0.232504i	−0.00225703	−	0.999997i	$-0.500718\pi$
$541$	14.8581	−	5.40791i	0.638800	−	0.232504i	0.641057	+	0.767493i	$0.278496\pi$
$542$	5.00277	+	28.2738i	0.214887	+	1.21446i
$543$	1.43725	−	0.476261i	0.0616783	−	0.0204383i
$544$	−3.25322	−	18.1343i	−0.139480	−	0.777502i
$545$	−13.1175	−	2.31296i	−0.561890	−	0.0990764i
$546$	−5.91711	+	1.96466i	−0.253229	+	0.0840797i
$547$	−5.90814	+	7.04104i	−0.252614	+	0.301053i	−0.877417	−	0.479729i	$-0.840735\pi$
$547$	−5.90814	+	7.04104i	−0.252614	+	0.301053i	0.624803	+	0.780782i	$0.285179\pi$
$548$	−20.4045	−	3.57284i	−0.871638	−	0.152624i
$549$	12.5336	+	11.8245i	0.534919	+	0.504659i
$550$	−7.18441	−	1.26240i	−0.306344	−	0.0538289i
$551$	−18.3032	+	33.7745i	−0.779741	+	1.43884i
$552$	22.0914	−	24.9136i	0.940274	−	1.06039i
$553$	7.82569	+	2.84832i	0.332782	+	0.121123i
$554$	−0.0218906	−	36.7961i	−0.000930041	−	1.56332i
$555$	−7.62054	−	9.63764i	−0.323474	−	0.409095i
$556$	14.6910	+	40.2143i	0.623038	+	1.70547i
$557$	−17.8823	−	3.15314i	−0.757699	−	0.133603i	−0.218565	−	0.975822i	$-0.570137\pi$
$557$	−17.8823	−	3.15314i	−0.757699	−	0.133603i	−0.539135	+	0.842220i	$0.681249\pi$
$558$	−3.08957	−	6.14256i	−0.130792	−	0.260035i
$559$	−0.451408	+	0.260621i	−0.0190925	+	0.0110231i
$560$	3.41593	+	1.23410i	0.144349	+	0.0521501i
$561$	10.0973	−	1.47909i	0.426308	−	0.0624473i
$562$	8.13568	−	2.96663i	0.343183	−	0.125140i
$563$	0.334808	−	0.579905i	0.0141105	−	0.0244401i	−0.858884	−	0.512170i	$-0.828842\pi$
$563$	0.334808	−	0.579905i	0.0141105	−	0.0244401i	0.872994	+	0.487730i	$0.162175\pi$
$564$	−0.647019	−	0.574414i	−0.0272444	−	0.0241872i
$565$	13.7792	−	11.5621i	0.579694	−	0.486421i
$566$	12.5839	−	10.5719i	0.528942	−	0.444372i
$567$	−4.47179	−	3.32897i	−0.187798	−	0.139804i
$568$	4.97778	+	5.91083i	0.208863	+	0.248013i
$569$		−	26.5056i		−	1.11117i	−0.831459	−	0.555586i	$-0.812494\pi$
$569$		−	26.5056i		−	1.11117i	0.831459	−	0.555586i	$-0.187506\pi$
$570$	−10.0785	+	11.9744i	−0.422144	+	0.501550i
$571$		−	12.0086i		−	0.502545i	−0.967916	−	0.251273i	$-0.919151\pi$
$571$		−	12.0086i		−	0.502545i	0.967916	−	0.251273i	$-0.0808491\pi$
$572$	−11.4004	−	9.54297i	−0.476674	−	0.399012i
$573$	7.76851	+	0.225998i	0.324534	+	0.00944120i
$574$	−3.39431	−	4.04029i	−0.141676	−	0.168639i
$575$	14.8453	−	12.4567i	0.619091	−	0.519479i
$576$	−23.9642	−	1.30968i	−0.998510	−	0.0545701i
$577$	−3.95203	+	6.84512i	−0.164525	+	0.284966i	−0.936487	−	0.350703i	$-0.885943\pi$
$577$	−3.95203	+	6.84512i	−0.164525	+	0.284966i	0.771961	+	0.635669i	$0.219276\pi$
$578$	−3.09709	−	8.49347i	−0.128822	−	0.353282i
$579$	−1.47881	−	10.0953i	−0.0614571	−	0.419548i
$580$	25.8376	−	0.0307424i	1.07285	−	0.00127651i
$581$	4.60054	−	2.65612i	0.190863	−	0.110195i
$582$	−12.3142	−	15.5546i	−0.510440	−	0.644760i
$583$	−8.12260	−	1.43223i	−0.336404	−	0.0593171i
$584$	5.35925	−	0.954846i	0.221767	−	0.0395118i
$585$	−16.1483	+	8.11022i	−0.667651	+	0.335316i
$586$	27.4676	−	0.0163409i	1.13467	−	0.000675035i
$587$	−8.70163	−	3.16713i	−0.359155	−	0.130722i	0.156139	−	0.987735i	$-0.450095\pi$
$587$	−8.70163	−	3.16713i	−0.359155	−	0.130722i	−0.515294	+	0.857013i	$0.672317\pi$
$588$	12.0089	−	19.5216i	0.495239	−	0.805057i
$589$	−1.41390	−	6.92127i	−0.0582587	−	0.285186i
$590$	−3.85441	+	21.9357i	−0.158683	+	0.903080i
$591$	35.5731	+	21.9415i	1.46328	+	0.902554i
$592$	9.63837	−	16.7863i	0.396135	−	0.689911i
$593$	15.9731	−	19.0360i	0.655936	−	0.781714i	−0.330861	−	0.943680i	$-0.607339\pi$
$593$	15.9731	−	19.0360i	0.655936	−	0.781714i	0.986796	+	0.161966i	$0.0517834\pi$
$594$	1.15053	−	13.2439i	0.0472068	−	0.543402i
$595$	−2.91235	−	0.513526i	−0.119395	−	0.0210525i
$596$	18.7849	+	22.3329i	0.769458	+	0.914792i
$597$	−4.17371	−	12.5953i	−0.170818	−	0.515492i
$598$	38.8936	−	6.88186i	1.59048	−	0.281420i
$599$	−18.8121	+	6.84703i	−0.768640	+	0.279762i	−0.696428	−	0.717627i	$-0.745228\pi$
$599$	−18.8121	+	6.84703i	−0.768640	+	0.279762i	−0.0722126	+	0.997389i	$0.523006\pi$
$600$	−13.6845	−	2.80008i	−0.558667	−	0.114313i
$601$	−15.0096	+	25.9974i	−0.612255	+	1.06046i	0.378605	+	0.925559i	$0.376404\pi$
$601$	−15.0096	+	25.9974i	−0.612255	+	1.06046i	−0.990859	+	0.134898i	$0.956929\pi$
$602$	−0.0379431	+	0.104441i	−0.00154645	+	0.00425671i
$603$	−0.645451	−	2.15587i	−0.0262848	−	0.0877938i
$604$	25.4011	−	14.7057i	1.03356	−	0.598366i
$605$	11.1552	−	1.96697i	0.453525	−	0.0799687i
$606$	31.0270	+	27.5783i	1.26039	+	1.12029i
$607$			28.1791i			1.14375i	0.820340	+	0.571877i	$0.193784\pi$
$607$			28.1791i			1.14375i	−0.820340	+	0.571877i	$0.806216\pi$
$608$	−23.4128	−	7.73572i	−0.949514	−	0.313725i
$609$	−1.91198	+	9.26000i	−0.0774775	+	0.375234i
$610$	5.94738	−	10.3153i	0.240802	−	0.417655i
$611$	−0.178219	−	1.01073i	−0.00720995	−	0.0408897i
$612$	19.4065	−	2.29192i	0.784462	−	0.0926455i
$613$	21.1166	−	17.7189i	0.852890	−	0.715660i	−0.107534	−	0.994201i	$-0.534295\pi$
$613$	21.1166	−	17.7189i	0.852890	−	0.715660i	0.960424	+	0.278542i	$0.0898510\pi$
$614$	32.6264	+	11.8531i	1.31670	+	0.478351i
$615$	−11.4252	−	10.1675i	−0.460710	−	0.409993i
$616$	−3.16946	+	0.00565669i	−0.127701	+	0.000227914i
$617$	−8.95109	−	24.5929i	−0.360357	−	0.990074i	−0.978903	−	0.204325i	$-0.934500\pi$
$617$	−8.95109	−	24.5929i	−0.360357	−	0.990074i	0.618546	−	0.785749i	$-0.287722\pi$
$618$	−26.6654	−	0.759861i	−1.07264	−	0.0305661i
$619$	1.29877	−	0.749845i	0.0522020	−	0.0301388i	−0.473672	−	0.880701i	$-0.657072\pi$
$619$	1.29877	−	0.749845i	0.0522020	−	0.0301388i	0.525874	+	0.850563i	$0.323738\pi$
$620$	−3.63608	+	3.05841i	−0.146029	+	0.122829i
$621$	24.9735	+	24.9727i	1.00215	+	1.00212i
$622$	−19.0237	+	10.9984i	−0.762780	+	0.440996i
$623$	−2.62894	−	2.20595i	−0.105326	−	0.0883794i
$624$	−21.3122	−	18.8753i	−0.853170	−	0.755618i
$625$	2.45688	+	0.894231i	0.0982752	+	0.0357693i
$626$	12.0572	+	2.11862i	0.481903	+	0.0846769i
$627$	4.69833	−	12.8245i	0.187633	−	0.512160i
$628$	−33.0973	−	12.0019i	−1.32073	−	0.478926i
$629$	−5.39044	+	14.8101i	−0.214931	+	0.590518i
$630$	−1.52369	+	3.53820i	−0.0607052	+	0.140965i
$631$	9.24958	−	11.0232i	0.368220	−	0.438828i	−0.549839	−	0.835270i	$-0.685311\pi$
$631$	9.24958	−	11.0232i	0.368220	−	0.438828i	0.918059	+	0.396443i	$0.129755\pi$
$632$	6.67013	+	37.4374i	0.265324	+	1.48918i
$633$	−10.1685	+	25.5962i	−0.404163	+	1.01736i
$634$	16.3006	+	13.6613i	0.647379	+	0.542560i
$635$	6.57993	+	11.3968i	0.261117	+	0.452267i
$636$	−15.4712	−	3.17528i	−0.613474	−	0.125908i
$637$	25.5478	−	9.29865i	1.01224	−	0.368426i
$638$	−21.1827	+	7.72416i	−0.838633	+	0.305803i
$639$	−6.57446	+	4.89462i	−0.260082	+	0.193628i
$640$	2.94786	+	16.3204i	0.116524	+	0.645120i
$641$	−12.3500	−	14.7182i	−0.487798	−	0.581335i	0.464858	−	0.885385i	$-0.346105\pi$
$641$	−12.3500	−	14.7182i	−0.487798	−	0.581335i	−0.952656	+	0.304051i	$0.901661\pi$
$642$	−43.1833	+	23.3177i	−1.70431	+	0.920277i
$643$	23.6895	−	4.17710i	0.934224	−	0.164729i	0.314240	−	0.949344i	$-0.398250\pi$
$643$	23.6895	−	4.17710i	0.934224	−	0.164729i	0.619984	+	0.784615i	$0.287139\pi$
$644$	5.40476	−	6.45673i	0.212978	−	0.254431i
$645$	−0.0651256	+	0.315412i	−0.00256432	+	0.0124193i
$646$	19.8605	+	2.93989i	0.781399	+	0.115669i
$647$	29.8928			1.17521			0.587604	−	0.809149i	$-0.300071\pi$
$647$	29.8928			1.17521			0.587604	+	0.809149i	$0.300071\pi$
$648$	2.90956	−	25.2890i	0.114298	−	0.993446i
$649$	−3.37492	−	19.1401i	−0.132477	−	0.751316i
$650$	−10.6579	−	12.6863i	−0.418038	−	0.497596i
$651$	−0.825221	−	1.53045i	−0.0323430	−	0.0599830i
$652$	−31.0015	−	17.8496i	−1.21411	−	0.699043i
$653$	−10.6541	−	6.15114i	−0.416927	−	0.240713i	0.276835	−	0.960917i	$-0.410714\pi$
$653$	−10.6541	−	6.15114i	−0.416927	−	0.240713i	−0.693761	+	0.720205i	$0.744048\pi$
$654$	22.0206	−	3.23905i	0.861073	−	0.126657i
$655$	−4.79225	−	13.1666i	−0.187249	−	0.514461i
$656$	8.18713	−	22.6616i	0.319654	−	0.884787i
$657$	0.670367	+	5.73481i	0.0261535	+	0.223736i
$658$	−0.167690	−	0.140538i	−0.00653723	−	0.00547876i
$659$	−6.89230	+	39.0882i	−0.268486	+	1.52266i	0.490435	+	0.871478i	$0.336838\pi$
$659$	−6.89230	+	39.0882i	−0.268486	+	1.52266i	−0.758921	+	0.651182i	$0.774273\pi$
$660$	−9.08765	+	1.34224i	−0.353736	+	0.0522467i
$661$	0.569165	+	0.477586i	0.0221380	+	0.0185760i	0.653789	−	0.756676i	$-0.273178\pi$
$661$	0.569165	+	0.477586i	0.0221380	+	0.0185760i	−0.631652	+	0.775252i	$0.717623\pi$
$662$	−1.39120		0.000827647i	−0.0540706		3.21674e-5i
$663$	19.7291	+	12.1690i	0.766216	+	0.472603i
$664$	21.0286	+	12.0909i	0.816067	+	0.469216i
$665$	−2.46138	+	3.09945i	−0.0954481	+	0.120191i
$666$	17.1600	+	11.2714i	0.664937	+	0.436759i
$667$	20.4872	−	56.2881i	0.793267	−	2.17948i
$668$	−0.0379370	+	0.216659i	−0.00146783	+	0.00838278i
$669$	7.17244	+	9.07093i	0.277303	+	0.350702i
$670$	−1.34628	+	0.778343i	−0.0520113	+	0.0300700i
$671$	−1.80431	+	10.2328i	−0.0696547	+	0.395031i
$672$	−6.06706	−	0.158439i	−0.234042	−	0.00611193i
$673$	10.4287	+	18.0631i	0.401997	+	0.696279i	0.993967	−	0.109681i	$-0.0349828\pi$
$673$	10.4287	+	18.0631i	0.401997	+	0.696279i	−0.591970	+	0.805960i	$0.701650\pi$
$674$	−11.0435	+	1.95405i	−0.425381	+	0.0752670i
$675$	3.83425	−	14.3106i	0.147580	−	0.550814i
$676$	−1.35841	−	7.65066i	−0.0522464	−	0.294256i
$677$	−7.52995	−	4.34742i	−0.289400	−	0.167085i	0.348271	−	0.937394i	$-0.386769\pi$
$677$	−7.52995	−	4.34742i	−0.289400	−	0.167085i	−0.637671	+	0.770309i	$0.720102\pi$
$678$	−15.7639	+	25.5916i	−0.605410	+	0.982839i
$679$	−3.22480	−	3.84316i	−0.123756	−	0.147487i
$680$	−4.64111	−	12.6809i	−0.177978	−	0.486289i
$681$	44.7749	+	1.30257i	1.71578	+	0.0499146i
$682$	2.07097	−	3.59196i	0.0793016	−	0.137543i
$683$	6.42167			0.245718			0.122859	−	0.992424i	$-0.460794\pi$
$683$	6.42167			0.245718			0.122859	+	0.992424i	$0.460794\pi$
$684$	9.67812	−	24.2968i	0.370052	−	0.929011i
$685$	−15.1828			−0.580104
$686$	5.95782	−	10.3334i	0.227471	−	0.394533i
$687$	8.45791	+	0.246054i	0.322689	+	0.00938753i
$688$	−0.499476	+	0.0892971i	−0.0190423	+	0.00340442i
$689$	−12.0424	−	14.3516i	−0.458780	−	0.546752i
$690$	12.7996	−	20.7791i	0.487271	−	0.791048i
$691$	42.7193	+	24.6640i	1.62512	+	0.938262i	0.985521	+	0.169551i	$0.0542316\pi$
$691$	42.7193	+	24.6640i	1.62512	+	0.938262i	0.639596	+	0.768711i	$0.279102\pi$
$692$	−44.1653	+	7.84173i	−1.67891	+	0.298098i
$693$	0.195430	−	3.35604i	0.00742378	−	0.127485i
$694$	−28.6423	+	5.06799i	−1.08725	+	0.192378i
$695$	15.6899	+	27.1757i	0.595151	+	1.03083i
$696$	−40.9590	+	13.6538i	−1.55255	+	0.517545i
$697$	−3.40678	+	19.3208i	−0.129041	+	0.731829i
$698$	19.3935	−	11.2122i	0.734054	−	0.424389i
$699$	21.2494	+	26.8739i	0.803725	+	1.01646i
$700$	−3.47930	−	0.609227i	−0.131505	−	0.0230266i
$701$	8.04549	−	22.1048i	0.303874	−	0.834887i	−0.689944	−	0.723863i	$-0.742365\pi$
$701$	8.04549	−	22.1048i	0.303874	−	0.834887i	0.993818	−	0.111024i	$-0.0354131\pi$
$702$	21.3387	−	21.3648i	0.805379	−	0.806364i
$703$	13.9895	+	15.7868i	0.527623	+	0.595411i
$704$	−7.28089	−	12.5075i	−0.274409	−	0.471396i
$705$	−0.539732	−	0.332908i	−0.0203275	−	0.0125380i
$706$	−1.05905		0.000630047i	−0.0398580		2.37121e-5i
$707$	8.04159	+	6.74770i	0.302435	+	0.253773i
$708$	−5.43785	−	36.8169i	−0.204367	−	1.38366i
$709$	2.85180	−	16.1734i	0.107102	−	0.607404i	−0.883258	−	0.468887i	$-0.844655\pi$
$709$	2.85180	−	16.1734i	0.107102	−	0.607404i	0.990360	−	0.138517i	$-0.0442337\pi$
$710$	4.34094	+	3.63808i	0.162913	+	0.136535i
$711$	−40.0609	+	4.68289i	−1.50240	+	0.175622i
$712$	2.69360	−	15.4372i	0.100947	−	0.578534i
$713$	3.76741	+	10.3509i	0.141091	+	0.387644i
$714$	4.88903	−	0.719136i	0.182967	−	0.0269130i
$715$	−9.43692	−	5.44841i	−0.352921	−	0.203759i
$716$	−6.07524	+	10.5516i	−0.227042	+	0.394332i
$717$	9.33411	+	17.3110i	0.348589	+	0.646490i
$718$	21.1232	+	25.1433i	0.788311	+	0.938339i
$719$	6.43860	+	36.5151i	0.240119	+	1.36178i	0.831560	+	0.555435i	$0.187448\pi$
$719$	6.43860	+	36.5151i	0.240119	+	1.36178i	−0.591440	+	0.806349i	$0.701440\pi$
$720$	−17.4666	+	2.08390i	−0.650943	+	0.0776622i
$721$	−6.74590			−0.251230
$722$	16.1238	−	21.4948i	0.600064	−	0.799952i
$723$	8.99369	−	43.5577i	0.334479	−	1.61993i
$724$	1.34064	+	1.12221i	0.0498245	+	0.0417068i
$725$	−24.7461	+	4.36340i	−0.919045	+	0.162052i
$726$	−16.6551	+	8.99326i	−0.618129	+	0.333771i
$727$	12.4391	+	14.8243i	0.461339	+	0.549803i	0.945689	−	0.325072i	$-0.105388\pi$
$727$	12.4391	+	14.8243i	0.461339	+	0.549803i	−0.484350	+	0.874874i	$0.660944\pi$
$728$	−5.52321	−	4.61775i	−0.204704	−	0.171145i
$729$	26.5900	+	4.68763i	0.984813	+	0.173616i
$730$	3.74843	−	1.36684i	0.138735	−	0.0505891i
$731$	0.388219	−	0.141300i	0.0143588	−	0.00522617i
$732$	−4.00017	+	19.4905i	−0.147851	+	0.720389i
$733$	6.09258	+	10.5527i	0.225035	+	0.389772i	0.956330	−	0.292290i	$-0.0944171\pi$
$733$	6.09258	+	10.5527i	0.225035	+	0.389772i	−0.731295	+	0.682061i	$0.761084\pi$
$734$	9.45601	+	7.92495i	0.349028	+	0.292515i
$735$	6.20207	−	15.6118i	0.228767	−	0.575849i
$736$	37.8841	+	6.56386i	1.39643	+	0.241947i
$737$	0.872287	−	1.03955i	0.0321311	−	0.0382924i
$738$	23.4728	+	10.1083i	0.864046	+	0.372092i
$739$	−0.547843	+	1.50519i	−0.0201527	+	0.0553692i	−0.949361	−	0.314187i	$-0.898268\pi$
$739$	−0.547843	+	1.50519i	−0.0201527	+	0.0553692i	0.929208	+	0.369556i	$0.120490\pi$
$740$	4.83643	−	13.3373i	0.177791	−	0.490290i
$741$	26.8997	−	15.4551i	0.988185	−	0.567758i
$742$	−3.93366	−	0.691197i	−0.144409	−	0.0253746i
$743$	−6.69838	−	2.43801i	−0.245740	−	0.0894419i	0.216214	−	0.976346i	$-0.430629\pi$
$743$	−6.69838	−	2.43801i	−0.245740	−	0.0894419i	−0.461954	+	0.886904i	$0.652851\pi$
$744$	4.15594	−	6.76488i	0.152364	−	0.248012i
$745$	16.3850	+	13.7487i	0.600300	+	0.503712i
$746$	−33.9810	+	19.6459i	−1.24413	+	0.719288i
$747$	−14.1376	+	21.4957i	−0.517268	+	0.786487i
$748$	7.58520	+	9.01788i	0.277342	+	0.329726i
$749$	−10.7478	+	6.20526i	−0.392717	+	0.226735i
$750$	−28.1795	−	0.803006i	−1.02897	−	0.0293216i
$751$	−4.04011	−	11.1001i	−0.147426	−	0.405049i	0.843896	−	0.536507i	$-0.180256\pi$
$751$	−4.04011	−	11.1001i	−0.147426	−	0.405049i	−0.991322	+	0.131458i	$0.958034\pi$
$752$	0.171143	−	0.984289i	0.00624093	−	0.0358933i
$753$	17.1806	+	15.2892i	0.626094	+	0.557170i
$754$	−48.1363	−	17.4878i	−1.75302	−	0.636867i
$755$	16.4794	−	13.8279i	0.599748	−	0.503248i
$756$	0.553310	−	6.41346i	0.0201237	−	0.233255i
$757$	−4.90512	−	27.8183i	−0.178280	−	1.01107i	−0.934290	−	0.356514i	$-0.883965\pi$
$757$	−4.90512	−	27.8183i	−0.178280	−	1.01107i	0.756010	−	0.654560i	$-0.227146\pi$
$758$	10.4554	−	18.1341i	0.379756	−	0.658661i
$759$	−4.30649	+	20.8569i	−0.156316	+	0.757058i
$760$	−17.8809	−	2.62512i	−0.648607	−	0.0952231i
$761$			15.4901i			0.561516i	0.959779	+	0.280758i	$0.0905858\pi$
$761$			15.4901i			0.561516i	−0.959779	+	0.280758i	$0.909414\pi$
$762$	−16.4360	−	14.6092i	−0.595415	−	0.529234i
$763$	5.54298	−	0.977377i	0.200669	−	0.0353834i
$764$	4.49629	+	7.76645i	0.162670	+	0.280980i
$765$	13.7209	−	4.10792i	0.496079	−	0.148522i
$766$	5.48943	−	15.1100i	0.198341	−	0.545948i
$767$	22.0732	−	38.2319i	0.797018	−	1.38048i
$768$	−13.2686	−	24.3299i	−0.478789	−	0.877930i
$769$	30.2640	−	11.0152i	1.09135	−	0.397217i	0.267227	−	0.963634i	$-0.413893\pi$
$769$	30.2640	−	11.0152i	1.09135	−	0.397217i	0.824119	+	0.566416i	$0.191671\pi$
$770$	−2.28749	+	0.404749i	−0.0824353	+	0.0145861i
$771$	−4.70065	−	14.1855i	−0.169290	−	0.510879i
$772$	9.01614	−	7.58374i	0.324498	−	0.272945i
$773$	28.1699	+	4.96711i	1.01320	+	0.178654i	0.655510	−	0.755186i	$-0.272454\pi$
$773$	28.1699	+	4.96711i	1.01320	+	0.178654i	0.357689	+	0.933841i	$0.383565\pi$
$774$	−0.0628020	−	0.534497i	−0.00225737	−	0.0192121i
$775$	2.97018	−	3.53973i	0.106692	−	0.127151i
$776$	7.79660	−	21.5405i	0.279882	−	0.773260i
$777$	4.41886	+	2.72556i	0.158526	+	0.0977790i
$778$	−4.85353	+	27.6218i	−0.174008	+	0.990291i
$779$	20.5621	+	16.3290i	0.736713	+	0.585049i
$780$	−17.7725	−	10.9330i	−0.636358	−	0.391462i
$781$	−4.64448	−	1.69045i	−0.166193	−	0.0604892i
$782$	−31.3058	+	0.0186243i	−1.11949	+	0.000666003i
$783$	−11.8530	−	44.2333i	−0.423593	−	1.58077i
$784$	26.4652	−	0.0629783i	0.945184	−	0.00224922i
$785$	−25.4119	−	4.48081i	−0.906990	−	0.159927i
$786$	14.5329	+	18.3572i	0.518372	+	0.654779i
$787$	−27.5167	+	15.8868i	−0.980865	+	0.566303i	−0.902531	−	0.430624i	$-0.858293\pi$
$787$	−27.5167	+	15.8868i	−0.980865	+	0.566303i	−0.0783341	+	0.996927i	$0.524960\pi$
$788$	0.0574230	+	48.2614i	0.00204561	+	1.71924i
$789$	−0.712710	−	4.86545i	−0.0253732	−	0.173214i
$790$	9.54815	+	26.1848i	0.339708	+	0.931615i
$791$	−3.80043	+	6.58253i	−0.135128	+	0.234048i
$792$	13.7051	−	6.91382i	0.486990	−	0.245672i
$793$	−18.0800	+	15.1709i	−0.642038	+	0.538734i
$794$	21.6124	+	25.7256i	0.766996	+	0.912967i
$795$	−11.5709	−	0.336616i	−0.410378	−	0.0119385i
$796$	9.83451	−	11.7487i	0.348575	−	0.416421i
$797$			6.02310i			0.213349i	0.994294	+	0.106675i	$0.0340203\pi$
$797$			6.02310i			0.213349i	−0.994294	+	0.106675i	$0.965980\pi$
$798$	2.27140	−	6.21140i	0.0804066	−	0.219881i
$799$			0.813457i			0.0287780i
$800$	−5.56146	−	15.1397i	−0.196627	−	0.535270i
$801$	16.1730	+	3.83290i	0.571447	+	0.135429i
$802$	40.9620	−	34.4128i	1.44642	−	1.21516i
$803$	−2.66716	+	2.23801i	−0.0941221	+	0.0789778i
$804$	1.72519	−	1.94325i	0.0608427	−	0.0685332i
$805$	3.08577	−	5.34470i	0.108759	−	0.188376i
$806$	8.84802	−	3.22638i	0.311658	−	0.113644i
$807$	27.8968	−	4.08643i	0.982013	−	0.143849i
$808$	−8.23936	+	47.2204i	−0.289860	+	1.66121i
$809$	−0.495932	+	0.286327i	−0.0174361	+	0.0100667i	−0.508693	−	0.860948i	$-0.669871\pi$
$809$	−0.495932	+	0.286327i	−0.0174361	+	0.0100667i	0.491257	+	0.871015i	$0.336538\pi$
$810$	−1.09633	−	18.6253i	−0.0385211	−	0.654427i
$811$	−1.08049	−	0.190520i	−0.0379412	−	0.00669007i	0.154645	−	0.987970i	$-0.450577\pi$
$811$	−1.08049	−	0.190520i	−0.0379412	−	0.00669007i	−0.192587	+	0.981280i	$0.561688\pi$
$812$	−10.2552	+	3.74641i	−0.359886	+	0.131473i
$813$	−21.8114	−	27.5847i	−0.764958	−	0.967436i
$814$	0.00736527	+	12.3804i	0.000258153	+	0.433932i
$815$	−24.6381	−	8.96752i	−0.863034	−	0.314119i
$816$	14.0375	+	17.6665i	0.491409	+	0.618451i
$817$	0.0812907	−	0.546913i	0.00284400	−	0.0191341i
$818$	17.3198	+	3.04332i	0.605572	+	0.106407i
$819$	5.24006	−	5.55427i	0.183103	−	0.194082i
$820$	3.04598	−	17.3956i	0.106370	−	0.607481i
$821$	−18.0732	+	21.5387i	−0.630757	+	0.751708i	−0.982880	−	0.184246i	$-0.941016\pi$
$821$	−18.0732	+	21.5387i	−0.630757	+	0.751708i	0.352123	+	0.935954i	$0.385460\pi$
$822$	24.0780	−	7.99463i	0.839817	−	0.278845i
$823$	−44.7229	−	7.88585i	−1.55894	−	0.274883i	−0.673341	−	0.739332i	$-0.735141\pi$
$823$	−44.7229	−	7.88585i	−1.55894	−	0.274883i	−0.885600	+	0.464449i	$0.846252\pi$
$824$	−15.4491	−	26.6487i	−0.538195	−	0.928351i
$825$	8.48040	−	2.81015i	0.295250	−	0.0978369i
$826$	−1.63977	−	9.26733i	−0.0570547	−	0.322452i
$827$	−37.5949	+	13.6834i	−1.30730	+	0.475819i	−0.899368	−	0.437192i	$-0.855973\pi$
$827$	−37.5949	+	13.6834i	−1.30730	+	0.475819i	−0.407935	+	0.913011i	$0.633751\pi$
$828$	−9.35706	+	39.6929i	−0.325180	+	1.37942i
$829$	12.6714	−	21.9474i	0.440095	−	0.762266i	−0.557601	−	0.830109i	$-0.688278\pi$
$829$	12.6714	−	21.9474i	0.440095	−	0.762266i	0.997696	+	0.0678426i	$0.0216116\pi$
$830$	16.7101	+	6.07073i	0.580016	+	0.210718i
$831$	21.3885	+	39.6669i	0.741958	+	1.37603i
$832$	5.59278	−	32.3940i	0.193895	−	1.12306i
$833$	−21.2213	+	3.74188i	−0.735274	+	0.129649i
$834$	−39.1918	−	34.8356i	−1.35710	−	1.20626i
$835$			0.161213i			0.00557902i
$836$	15.4480	−	3.17493i	0.534281	−	0.109807i
$837$	6.89824	+	4.83003i	0.238438	+	0.166950i
$838$	26.9411	+	15.5331i	0.930663	+	0.536581i
$839$	−1.98945	−	11.2828i	−0.0686836	−	0.389524i	−0.999699	−	0.0245435i	$-0.992187\pi$
$839$	−1.98945	−	11.2828i	−0.0686836	−	0.389524i	0.931015	−	0.364980i	$-0.118924\pi$
$840$	−4.40017	+	0.652578i	−0.151820	+	0.0225161i
$841$	−37.2830	+	31.2842i	−1.28562	+	1.07876i
$842$	−8.87859	+	24.4389i	−0.305976	+	0.842222i
$843$	−7.05072	+	7.92292i	−0.242840	+	0.272880i
$844$	−31.3130	+	5.55976i	−1.07784	+	0.191375i
$845$	−1.94786	−	5.35170i	−0.0670084	−	0.184104i
$846$	1.03124	+	0.243750i	0.0354549	+	0.00838028i
$847$	−4.14526	+	2.39327i	−0.142433	+	0.0822336i
$848$	−6.27819	−	17.1223i	−0.215594	−	0.587982i
$849$	−7.43170	+	18.7070i	−0.255055	+	0.642023i
$850$	6.57303	+	11.3692i	0.225453	+	0.389960i
$851$	−25.1958	−	21.1418i	−0.863700	−	0.724730i
$852$	−8.79986	−	3.48379i	−0.301478	−	0.119353i
$853$	−22.1759	−	8.07137i	−0.759289	−	0.276359i	−0.0667799	−	0.997768i	$-0.521273\pi$
$853$	−22.1759	−	8.07137i	−0.759289	−	0.276359i	−0.692509	+	0.721409i	$0.743495\pi$
$854$	−0.870762	+	4.95557i	−0.0297968	+	0.169576i
$855$	3.91569	−	18.7646i	0.133914	−	0.641736i
$856$	−49.1271	−	28.2468i	−1.67913	−	0.965455i
$857$	7.98323	−	21.9338i	0.272702	−	0.749243i	−0.725438	−	0.688287i	$-0.758363\pi$
$857$	7.98323	−	21.9338i	0.272702	−	0.749243i	0.998140	−	0.0609556i	$-0.0194148\pi$
$858$	17.8347	+	3.67141i	0.608867	+	0.125340i
$859$	−11.7165	+	13.9632i	−0.399762	+	0.476417i	−0.927947	−	0.372712i	$-0.878428\pi$
$859$	−11.7165	+	13.9632i	−0.399762	+	0.476417i	0.528186	+	0.849129i	$0.322873\pi$
$860$	−0.349310	+	0.127609i	−0.0119114	+	0.00435144i
$861$	6.00621	+	2.38608i	0.204691	+	0.0813173i
$862$	−7.29647	+	8.70611i	−0.248519	+	0.296531i
$863$	−2.68946	−	4.65829i	−0.0915504	−	0.158570i	0.816613	−	0.577185i	$-0.195849\pi$
$863$	−2.68946	−	4.65829i	−0.0915504	−	0.158570i	−0.908164	+	0.418615i	$0.862516\pi$
$864$	26.6026	−	12.5020i	0.905040	−	0.425327i
$865$	−30.8940	+	11.2445i	−1.05043	+	0.382324i
$866$	−18.7575	−	51.4407i	−0.637407	−	1.74803i
$867$	8.27135	+	7.36079i	0.280910	+	0.249986i
$868$	1.00180	−	1.73995i	0.0340033	−	0.0590576i
$869$	−15.6338	−	18.6316i	−0.530339	−	0.632034i
$870$	−27.8445	+	15.0352i	−0.944017	+	0.509741i
$871$	3.03561	−	0.535260i	0.102858	−	0.0181366i
$872$	16.5553	+	19.6584i	0.560632	+	0.665718i
$873$	22.3107	+	9.62359i	0.755101	+	0.325709i
$874$	−19.9409	+	36.8488i	−0.674510	+	1.24643i
$875$	−7.12893			−0.241002
$876$	−5.22482	+	4.14141i	−0.176530	+	0.139925i
$877$	−3.19782	−	18.1358i	−0.107983	−	0.612401i	−0.989987	−	0.141159i	$-0.954917\pi$
$877$	−3.19782	−	18.1358i	−0.107983	−	0.612401i	0.882004	−	0.471242i	$-0.156194\pi$
$878$	−0.305959	+	0.257040i	−0.0103256	+	0.00867468i
$879$	−29.6105	+	15.9661i	−0.998739	+	0.538522i
$880$	−6.83759	−	8.10946i	−0.230495	−	0.273370i
$881$	7.79809	+	4.50223i	0.262724	+	0.151684i	0.625577	−	0.780163i	$-0.284864\pi$
$881$	7.79809	+	4.50223i	0.262724	+	0.151684i	−0.362852	+	0.931847i	$0.618197\pi$
$882$	−1.61518	+	28.0241i	−0.0543860	+	0.943621i
$883$	7.43385	+	20.4243i	0.250169	+	0.687334i	0.999679	+	0.0253406i	$0.00806702\pi$
$883$	7.43385	+	20.4243i	0.250169	+	0.687334i	−0.749510	+	0.661993i	$0.769711\pi$
$884$	0.0318473	+	26.7662i	0.00107114	+	0.900244i
$885$	−8.58006	−	25.8927i	−0.288416	−	0.870373i
$886$	−31.7402	+	37.8723i	−1.06633	+	1.27234i
$887$	−4.01824	+	22.7886i	−0.134919	+	0.765166i	0.839996	+	0.542592i	$0.182557\pi$
$887$	−4.01824	+	22.7886i	−0.134919	+	0.765166i	−0.974916	+	0.222574i	$0.928554\pi$
$888$	−0.647084	+	23.6980i	−0.0217147	+	0.795254i
$889$	−4.25990	−	3.57448i	−0.142872	−	0.119884i
$890$	−0.00683288	−	11.4855i	−0.000229039	−	0.384994i
$891$	6.44907	+	14.9497i	0.216052	+	0.500835i
$892$	−4.55204	+	12.5531i	−0.152414	+	0.420308i
$893$	0.957179	+	0.518718i	0.0320308	+	0.0173582i
$894$	−33.2241	−	13.1760i	−1.11118	−	0.440671i
$895$	−3.05217	+	8.38576i	−0.102023	+	0.280305i
$896$	−3.52926	−	6.05448i	−0.117904	−	0.202266i
$897$	−37.9457	+	30.0039i	−1.26697	+	1.00180i
$898$	−22.6227	−	39.1299i	−0.754930	−	1.30578i
$899$	2.48017	−	14.0658i	0.0827184	−	0.469120i
$900$	16.3827	−	4.92609i	0.546089	−	0.164203i
$901$	7.42451	+	12.8596i	0.247346	+	0.428416i
$902$	2.68515	+	15.1754i	0.0894057	+	0.505287i
$903$	−0.0197250	−	0.134657i	−0.000656408	−	0.00448109i
$904$	−34.7069	+	0.0619431i	−1.15434	+	0.00206020i
$905$	1.10974	+	0.640711i	0.0368891	+	0.0212979i
$906$	−18.8531	+	30.6067i	−0.626354	+	1.01684i
$907$	−6.09589	−	7.26480i	−0.202411	−	0.241224i	0.655284	−	0.755382i	$-0.272549\pi$
$907$	−6.09589	−	7.26480i	−0.202411	−	0.241224i	−0.857695	+	0.514158i	$0.828104\pi$
$908$	25.9150	+	44.7631i	0.860020	+	1.48551i
$909$	−49.4712	−	11.7243i	−1.64086	−	0.388871i
$910$	−4.57125	−	2.63559i	−0.151535	−	0.0873689i
$911$	2.00384			0.0663901			0.0331950	−	0.999449i	$-0.489432\pi$
$911$	2.00384			0.0663901			0.0331950	+	0.999449i	$0.489432\pi$
$912$	29.7391	−	5.25221i	0.984760	−	0.173918i
$913$	−15.5145			−0.513455
$914$	26.9167	+	15.5190i	0.890324	+	0.513323i
$915$	−0.424064	+	14.5769i	−0.0140191	+	0.481897i
$916$	4.89531	+	8.45567i	0.161746	+	0.279383i
$917$	3.80583	+	4.53561i	0.125679	+	0.149779i
$918$	−19.5965	+	13.7395i	−0.646782	+	0.453472i
$919$	−11.2439	−	6.49169i	−0.370903	−	0.214141i	0.302950	−	0.953007i	$-0.402029\pi$
$919$	−11.2439	−	6.49169i	−0.370903	−	0.214141i	−0.673853	+	0.738865i	$0.735362\pi$
$920$	28.1804	−	0.0502948i	0.929079	−	0.00165817i
$921$	−42.0654	+	6.16191i	−1.38610	+	0.203042i
$922$	−3.85405	−	21.7816i	−0.126926	−	0.717340i
$923$	−5.61337	−	9.72265i	−0.184766	−	0.320025i
$924$	3.41455	−	1.84638i	0.112330	−	0.0607414i
$925$	−2.39590	+	13.5878i	−0.0787766	+	0.446764i
$926$	15.1045	+	26.1258i	0.496364	+	0.858547i
$927$	29.1962	−	14.6633i	0.958930	−	0.481606i
$928$	−38.2856	−	31.9318i	−1.25679	−	1.04821i
$929$	−2.29216	+	6.29767i	−0.0752035	+	0.206620i	−0.971598	−	0.236637i	$-0.923955\pi$
$929$	−2.29216	+	6.29767i	−0.0752035	+	0.206620i	0.896395	+	0.443257i	$0.146177\pi$
$930$	2.14522	−	5.40930i	0.0703444	−	0.177378i
$931$	−9.12919	+	27.3568i	−0.299197	+	0.896582i
$932$	−13.4861	+	37.1902i	−0.441750	+	1.21821i
$933$	14.1285	−	22.9060i	0.462545	−	0.749908i
$934$	−0.00858960	−	14.4383i	−0.000281060	−	0.472437i
$935$	6.61615	+	5.55161i	0.216371	+	0.181557i
$936$	33.9419	+	7.98003i	1.10942	+	0.260835i
$937$	−2.72361	+	15.4464i	−0.0889766	+	0.504611i	0.907451	+	0.420158i	$0.138025\pi$
$937$	−2.72361	+	15.4464i	−0.0889766	+	0.504611i	−0.996427	+	0.0844532i	$0.973086\pi$
$938$	0.422092	−	0.503638i	0.0137818	−	0.0164444i
$939$	−14.2322	+	4.71612i	−0.464450	+	0.153905i
$940$	−0.000871249	−	0.732246i	−2.84170e−5	−	0.0238832i
$941$	−8.97740	−	24.6652i	−0.292655	−	0.804063i	−0.995676	−	0.0928937i	$-0.970388\pi$
$941$	−8.97740	−	24.6652i	−0.292655	−	0.804063i	0.703021	−	0.711169i	$-0.251834\pi$
$942$	42.6596	−	6.27487i	1.38992	−	0.204446i
$943$	−35.4573	−	20.4713i	−1.15465	−	0.666637i
$944$	32.8540	−	27.7012i	1.06931	−	0.901599i
$945$	−0.411289	−	4.70017i	−0.0133792	−	0.152896i
$946$	0.248478	−	0.208750i	0.00807873	−	0.00678705i
$947$	−9.88392	−	56.0545i	−0.321184	−	1.82153i	−0.535235	−	0.844703i	$-0.679777\pi$
$947$	−9.88392	−	56.0545i	−0.321184	−	1.82153i	0.214051	−	0.976823i	$-0.431334\pi$
$948$	−28.9300	−	36.4983i	−0.939604	−	1.18541i
$949$	−7.90857			−0.256723
$950$	17.5694	−	0.484555i	0.570025	−	0.0157211i
$951$	−25.5101	−	5.26727i	−0.827223	−	0.170803i
$952$	3.67561	+	4.36458i	0.119127	+	0.141457i
$953$	0.943737	−	0.166406i	0.0305706	−	0.00539043i	−0.158342	−	0.987384i	$-0.550615\pi$
$953$	0.943737	−	0.166406i	0.0305706	−	0.00539043i	0.188913	+	0.981994i	$0.439504\pi$
$954$	18.5273	−	5.55894i	0.599843	−	0.179977i
$955$	4.22791	+	5.03862i	0.136812	+	0.163046i
$956$	−11.3314	+	19.6806i	−0.366484	+	0.636516i
$957$	18.3578	−	20.6288i	0.593425	−	0.666834i
$958$	16.5759	+	45.4576i	0.535542	+	1.46867i
$959$	6.02880	−	2.19430i	0.194680	−	0.0708577i
$960$	−12.6550	−	15.8877i	−0.408437	−	0.512774i
$961$	−14.1868	−	24.5722i	−0.457638	−	0.792651i
$962$	−18.0632	+	21.5530i	−0.582382	+	0.694895i
$963$	33.0284	−	50.2185i	1.06433	−	1.61827i
$964$	48.2389	−	17.6225i	1.55367	−	0.567584i
$965$	5.55054	−	6.61488i	0.178678	−	0.212940i
$966$	−2.07934	+	10.1009i	−0.0669017	+	0.324990i
$967$	12.8925	−	35.4219i	0.414595	−	1.13909i	−0.540125	−	0.841585i	$-0.681623\pi$
$967$	12.8925	−	35.4219i	0.414595	−	1.13909i	0.954720	−	0.297506i	$-0.0961548\pi$
$968$	−18.9475	−	10.8943i	−0.608996	−	0.350157i
$969$	−23.1238	+	8.36128i	−0.742844	+	0.268603i
$970$	2.90575	−	16.5369i	0.0932981	−	0.530967i
$971$	−34.1815	−	12.4411i	−1.09694	−	0.399253i	−0.270751	−	0.962649i	$-0.587272\pi$
$971$	−34.1815	−	12.4411i	−1.09694	−	0.399253i	−0.826187	+	0.563397i	$0.809494\pi$
$972$	11.5460	+	28.9602i	0.370337	+	0.928897i
$973$	−10.1578	−	8.52337i	−0.325643	−	0.273247i
$974$	−2.43600	−	4.21349i	−0.0780545	−	0.135009i
$975$	18.8591	+	7.49213i	0.603975	+	0.239940i
$976$	−21.5705	+	7.90919i	−0.690454	+	0.253167i
$977$	41.5805	−	24.0065i	1.33028	−	0.768036i	0.344936	−	0.938626i	$-0.387901\pi$
$977$	41.5805	−	24.0065i	1.33028	−	0.768036i	0.985342	+	0.170590i	$0.0545674\pi$
$978$	43.7949	+	1.24798i	1.40041	+	0.0399061i
$979$	3.42798	+	9.41830i	0.109559	+	0.301010i
$980$	19.0987	−	3.39104i	0.610084	−	0.108323i
$981$	−21.8655	+	16.2787i	−0.698113	+	0.519738i
$982$	10.1469	−	27.9299i	0.323799	−	0.891280i
$983$	−10.7673	+	9.03483i	−0.343423	+	0.288166i	−0.798143	−	0.602468i	$-0.794184\pi$
$983$	−10.7673	+	9.03483i	−0.343423	+	0.288166i	0.454719	+	0.890635i	$0.349740\pi$
$984$	4.32927	+	29.1912i	0.138012	+	0.930580i
$985$	6.14239	+	34.8352i	0.195713	+	1.10994i
$986$	35.1661	+	20.2753i	1.11992	+	0.645696i
$987$	0.262431	+	0.0541862i	0.00835328	+	0.00172477i
$988$	31.5156	+	17.0306i	1.00264	+	0.541814i
$989$			0.862167i			0.0274153i
$990$	9.02046	−	6.72398i	0.286689	−	0.213702i
$991$	38.4196	−	6.77441i	1.22044	−	0.215196i	0.473924	−	0.880566i	$-0.342837\pi$
$991$	38.4196	−	6.77441i	1.22044	−	0.215196i	0.746514	+	0.665370i	$0.231726\pi$
$992$	9.16769	−	0.0272701i	0.291074	−	0.000865826i
$993$	1.49974	−	0.808664i	0.0475929	−	0.0256622i
$994$	−2.24950	−	0.817237i	−0.0713499	−	0.0259212i
$995$	5.61486	−	9.72522i	0.178003	−	0.308310i
$996$	−29.6968	−	0.828562i	−0.940978	−	0.0262540i
$997$	35.3566	−	12.8688i	1.11976	−	0.407558i	0.285192	−	0.958470i	$-0.407942\pi$
$997$	35.3566	−	12.8688i	1.11976	−	0.407558i	0.834563	+	0.550913i	$0.185720\pi$
$998$	−4.71254	−	26.6335i	−0.149173	−	0.843068i
$999$	−25.0493	−	2.19111i	−0.792524	−	0.0693237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.v.a.23.5	yes	216
3.2	odd	2	inner	228.2.v.a.23.32	yes	216
4.3	odd	2	inner	228.2.v.a.23.34	yes	216
12.11	even	2	inner	228.2.v.a.23.3	✓	216
19.5	even	9	inner	228.2.v.a.119.3	yes	216
57.5	odd	18	inner	228.2.v.a.119.34	yes	216
76.43	odd	18	inner	228.2.v.a.119.32	yes	216
228.119	even	18	inner	228.2.v.a.119.5	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.v.a.23.3	✓	216	12.11	even	2	inner
228.2.v.a.23.5	yes	216	1.1	even	1	trivial
228.2.v.a.23.32	yes	216	3.2	odd	2	inner
228.2.v.a.23.34	yes	216	4.3	odd	2	inner
228.2.v.a.119.3	yes	216	19.5	even	9	inner
228.2.v.a.119.5	yes	216	228.119	even	18	inner
228.2.v.a.119.32	yes	216	76.43	odd	18	inner
228.2.v.a.119.34	yes	216	57.5	odd	18	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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22517 - 0.706378i) q^{2} +(1.73132 + 0.0503667i) q^{3} +(1.00206 + 1.73086i) q^{4} +(0.942247 + 1.12293i) q^{5} +(-2.08557 - 1.28467i) q^{6} +(-0.536440 - 0.309714i) q^{7} +(-0.00504802 - 2.82842i) q^{8} +(2.99493 + 0.174402i) q^{9} +O(q^{10})\)	\(q+(-1.22517 - 0.706378i) q^{2} +(1.73132 + 0.0503667i) q^{3} +(1.00206 + 1.73086i) q^{4} +(0.942247 + 1.12293i) q^{5} +(-2.08557 - 1.28467i) q^{6} +(-0.536440 - 0.309714i) q^{7} +(-0.00504802 - 2.82842i) q^{8} +(2.99493 + 0.174402i) q^{9} +(-0.361198 - 2.04135i) q^{10} +(0.904524 + 1.56668i) q^{11} +(1.64771 + 3.04714i) q^{12} +(-0.713547 + 4.04673i) q^{13} +(0.438453 + 0.758380i) q^{14} +(1.57477 + 1.99160i) q^{15} +(-1.99175 + 3.46885i) q^{16} +(1.11392 - 3.06048i) q^{17} +(-3.54609 - 2.32922i) q^{18} +(-2.89090 - 3.26232i) q^{19} +(-0.999439 + 2.75614i) q^{20} +(-0.913150 - 0.563232i) q^{21} +(-0.00152202 - 2.55838i) q^{22} +(5.20666 + 4.36891i) q^{23} +(0.133719 - 4.89715i) q^{24} +(0.495107 - 2.80789i) q^{25} +(3.73273 - 4.45388i) q^{26} +(5.17639 + 0.452789i) q^{27} +(-0.00147403 - 1.23885i) q^{28} +(-3.01423 - 8.28154i) q^{29} +(-0.522532 - 3.55242i) q^{30} +(1.40352 + 0.810320i) q^{31} +(4.89054 - 2.84299i) q^{32} +(1.48711 + 2.75798i) q^{33} +(-3.52660 + 2.96275i) q^{34} +(-0.157673 - 0.894209i) q^{35} +(2.69923 + 5.35856i) q^{36} -4.83914 q^{37} +(1.23740 + 6.03894i) q^{38} +(-1.43920 + 6.97024i) q^{39} +(3.17135 - 2.67074i) q^{40} +(-5.93228 + 1.04602i) q^{41} +(0.720904 + 1.33508i) q^{42} +(0.0815368 + 0.0971718i) q^{43} +(-1.80532 + 3.13551i) q^{44} +(2.62612 + 3.52741i) q^{45} +(-3.29292 - 9.03050i) q^{46} +(-0.234702 + 0.0854244i) q^{47} +(-3.62307 + 5.90537i) q^{48} +(-3.30815 - 5.72989i) q^{49} +(-2.59002 + 3.09040i) q^{50} +(2.08271 - 5.24257i) q^{51} +(-7.71934 + 2.82001i) q^{52} +(-2.93063 + 3.49259i) q^{53} +(-6.02209 - 4.21123i) q^{54} +(-0.906982 + 2.49191i) q^{55} +(-0.873294 + 1.51884i) q^{56} +(-4.84075 - 5.79371i) q^{57} +(-2.15696 + 12.2754i) q^{58} +(-10.0955 - 3.67447i) q^{59} +(-1.86916 + 4.72141i) q^{60} +(4.39992 + 3.69197i) q^{61} +(-1.14715 - 1.98419i) q^{62} +(-1.55258 - 1.02113i) q^{63} +(-7.99995 + 0.0285559i) q^{64} +(-5.21651 + 3.01175i) q^{65} +(0.126222 - 4.42945i) q^{66} +(-0.256563 - 0.704900i) q^{67} +(6.41349 - 1.13874i) q^{68} +(8.79434 + 7.82621i) q^{69} +(-0.438474 + 1.20693i) q^{70} +(-2.09293 + 1.75618i) q^{71} +(0.478163 - 8.47180i) q^{72} +(0.334207 + 1.89538i) q^{73} +(5.92875 + 3.41826i) q^{74} +(0.998613 - 4.83642i) q^{75} +(2.74976 - 8.27278i) q^{76} -1.12057i q^{77} +(6.68688 - 7.52307i) q^{78} +(-13.2403 + 2.33462i) q^{79} +(-5.77198 + 1.03192i) q^{80} +(8.93917 + 1.04464i) q^{81} +(8.00691 + 2.90888i) q^{82} +(-4.28803 + 7.42708i) q^{83} +(0.0598450 - 2.14493i) q^{84} +(4.48629 - 1.63288i) q^{85} +(-0.0312561 - 0.176647i) q^{86} +(-4.80149 - 14.4898i) q^{87} +(4.42667 - 2.56629i) q^{88} +(5.45617 + 0.962070i) q^{89} +(-0.725745 - 6.17669i) q^{90} +(1.63610 - 1.94983i) q^{91} +(-2.34458 + 13.3899i) q^{92} +(2.38912 + 1.47361i) q^{93} +(0.347890 + 0.0611290i) q^{94} +(0.939402 - 6.32017i) q^{95} +(8.61028 - 4.67579i) q^{96} +(7.61079 + 2.77010i) q^{97} +(0.00556655 + 9.35687i) q^{98} +(2.43575 + 4.84985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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