LMFDB - Embedded newform 429.2.f.a.131.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(131,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("429.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.f (of order $2$, degree $1$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.19
Character	$\chi$	$=$	429.131
Dual form			429.2.f.a.131.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.791616 q^{2} +(-0.917209 - 1.46926i) q^{3} -1.37334 q^{4} +1.17632i q^{5} +(0.726077 + 1.16309i) q^{6} -0.422249i q^{7} +2.67039 q^{8} +(-1.31745 + 2.69524i) q^{9} +O(q^{10})$	\(q-0.791616 q^{2} +(-0.917209 - 1.46926i) q^{3} -1.37334 q^{4} +1.17632i q^{5} +(0.726077 + 1.16309i) q^{6} -0.422249i q^{7} +2.67039 q^{8} +(-1.31745 + 2.69524i) q^{9} -0.931196i q^{10} +(1.23267 + 3.07905i) q^{11} +(1.25964 + 2.01780i) q^{12} -1.00000i q^{13} +0.334259i q^{14} +(1.72833 - 1.07894i) q^{15} +0.632764 q^{16} +0.541327 q^{17} +(1.04292 - 2.13359i) q^{18} -6.79972i q^{19} -1.61550i q^{20} +(-0.620394 + 0.387291i) q^{21} +(-0.975803 - 2.43742i) q^{22} -1.90837i q^{23} +(-2.44931 - 3.92350i) q^{24} +3.61626 q^{25} +0.791616i q^{26} +(5.16839 - 0.536417i) q^{27} +0.579894i q^{28} +10.1937 q^{29} +(-1.36817 + 0.854102i) q^{30} -1.41929 q^{31} -5.84169 q^{32} +(3.39330 - 4.63525i) q^{33} -0.428523 q^{34} +0.496702 q^{35} +(1.80932 - 3.70149i) q^{36} -6.19734 q^{37} +5.38276i q^{38} +(-1.46926 + 0.917209i) q^{39} +3.14125i q^{40} +10.8583 q^{41} +(0.491114 - 0.306586i) q^{42} -9.30752i q^{43} +(-1.69288 - 4.22859i) q^{44} +(-3.17047 - 1.54975i) q^{45} +1.51070i q^{46} +1.34691i q^{47} +(-0.580377 - 0.929696i) q^{48} +6.82171 q^{49} -2.86269 q^{50} +(-0.496511 - 0.795351i) q^{51} +1.37334i q^{52} -4.75439i q^{53} +(-4.09138 + 0.424636i) q^{54} +(-3.62195 + 1.45002i) q^{55} -1.12757i q^{56} +(-9.99056 + 6.23676i) q^{57} -8.06948 q^{58} +7.23149i q^{59} +(-2.37359 + 1.48175i) q^{60} +12.4925i q^{61} +1.12353 q^{62} +(1.13806 + 0.556294i) q^{63} +3.35885 q^{64} +1.17632 q^{65} +(-2.68619 + 3.66933i) q^{66} +9.42183 q^{67} -0.743429 q^{68} +(-2.80390 + 1.75038i) q^{69} -0.393197 q^{70} -6.54436i q^{71} +(-3.51812 + 7.19735i) q^{72} +4.36845i q^{73} +4.90591 q^{74} +(-3.31687 - 5.31323i) q^{75} +9.33835i q^{76} +(1.30012 - 0.520495i) q^{77} +(1.16309 - 0.726077i) q^{78} +4.73363i q^{79} +0.744336i q^{80} +(-5.52863 - 7.10171i) q^{81} -8.59559 q^{82} +10.7329 q^{83} +(0.852015 - 0.531884i) q^{84} +0.636776i q^{85} +7.36798i q^{86} +(-9.34974 - 14.9772i) q^{87} +(3.29172 + 8.22226i) q^{88} +12.0717i q^{89} +(2.50980 + 1.22681i) q^{90} -0.422249 q^{91} +2.62085i q^{92} +(1.30179 + 2.08531i) q^{93} -1.06624i q^{94} +7.99867 q^{95} +(5.35805 + 8.58297i) q^{96} -15.2047 q^{97} -5.40017 q^{98} +(-9.92275 - 0.734152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.791616			−0.559757			−0.279878	−	0.960035i	$-0.590294\pi$
$2$	−0.791616			−0.559757			−0.279878	+	0.960035i	$0.590294\pi$
$3$	−0.917209	−	1.46926i	−0.529551	−	0.848278i
$3$	−0.917209	−	1.46926i	−0.529551	−	0.848278i
$4$	−1.37334			−0.686672
$5$			1.17632i			0.526068i	0.964787	+	0.263034i	$0.0847231\pi$
$5$			1.17632i			0.526068i	−0.964787	+	0.263034i	$0.915277\pi$
$6$	0.726077	+	1.16309i	0.296420	+	0.474829i
$7$		−	0.422249i		−	0.159595i	−0.996811	−	0.0797976i	$-0.974573\pi$
$7$		−	0.422249i		−	0.159595i	0.996811	−	0.0797976i	$-0.0254274\pi$
$8$	2.67039			0.944126
$9$	−1.31745	+	2.69524i	−0.439151	+	0.898413i
$10$		−	0.931196i		−	0.294470i
$11$	1.23267	+	3.07905i	0.371665	+	0.928367i
$11$	1.23267	+	3.07905i	0.371665	+	0.928367i
$12$	1.25964	+	2.01780i	0.363628	+	0.582489i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$			0.334259i			0.0893345i
$15$	1.72833	−	1.07894i	0.446252	−	0.278580i
$16$	0.632764			0.158191
$17$	0.541327			0.131291			0.0656456	−	0.997843i	$-0.479089\pi$
$17$	0.541327			0.131291			0.0656456	+	0.997843i	$0.479089\pi$
$18$	1.04292	−	2.13359i	0.245818	−	0.502893i
$19$		−	6.79972i		−	1.55996i	−0.625803	−	0.779981i	$-0.715229\pi$
$19$		−	6.79972i		−	1.55996i	0.625803	−	0.779981i	$-0.284771\pi$
$20$		−	1.61550i		−	0.361236i
$21$	−0.620394	+	0.387291i	−0.135381	+	0.0845138i
$22$	−0.975803	−	2.43742i	−0.208042	−	0.519660i
$23$		−	1.90837i		−	0.397923i	−0.980007	−	0.198962i	$-0.936243\pi$
$23$		−	1.90837i		−	0.397923i	0.980007	−	0.198962i	$-0.0637569\pi$
$24$	−2.44931	−	3.92350i	−0.499963	−	0.800882i
$25$	3.61626			0.723252
$26$			0.791616i			0.155249i
$27$	5.16839	−	0.536417i	0.994657	−	0.103233i
$28$			0.579894i			0.109590i
$29$	10.1937			1.89292			0.946460	−	0.322822i	$-0.104632\pi$
$29$	10.1937			1.89292			0.946460	+	0.322822i	$0.104632\pi$
$30$	−1.36817	+	0.854102i	−0.249793	+	0.155937i
$31$	−1.41929			−0.254912			−0.127456	−	0.991844i	$-0.540681\pi$
$31$	−1.41929			−0.254912			−0.127456	+	0.991844i	$0.540681\pi$
$32$	−5.84169			−1.03267
$33$	3.39330	−	4.63525i	0.590698	−	0.806893i
$34$	−0.428523			−0.0734911
$35$	0.496702			0.0839579
$36$	1.80932	−	3.70149i	0.301553	−	0.616915i
$37$	−6.19734			−1.01884			−0.509418	−	0.860519i	$-0.670139\pi$
$37$	−6.19734			−1.01884			−0.509418	+	0.860519i	$0.670139\pi$
$38$			5.38276i			0.873199i
$39$	−1.46926	+	0.917209i	−0.235270	+	0.146871i
$40$			3.14125i			0.496675i
$41$	10.8583			1.69578			0.847890	−	0.530173i	$-0.177873\pi$
$41$	10.8583			1.69578			0.847890	+	0.530173i	$0.177873\pi$
$42$	0.491114	−	0.306586i	0.0757805	−	0.0473072i
$43$		−	9.30752i		−	1.41938i	−0.704512	−	0.709692i	$-0.748834\pi$
$43$		−	9.30752i		−	1.41938i	0.704512	−	0.709692i	$-0.251166\pi$
$44$	−1.69288	−	4.22859i	−0.255212	−	0.637484i
$45$	−3.17047	−	1.54975i	−0.472626	−	0.231023i
$46$			1.51070i			0.222740i
$47$			1.34691i			0.196467i	0.995163	+	0.0982335i	$0.0313192\pi$
$47$			1.34691i			0.196467i	−0.995163	+	0.0982335i	$0.968681\pi$
$48$	−0.580377	−	0.929696i	−0.0837703	−	0.134190i
$49$	6.82171			0.974529
$50$	−2.86269			−0.404846
$51$	−0.496511	−	0.795351i	−0.0695254	−	0.111371i
$52$			1.37334i			0.190449i
$53$		−	4.75439i		−	0.653066i	−0.945186	−	0.326533i	$-0.894120\pi$
$53$		−	4.75439i		−	0.653066i	0.945186	−	0.326533i	$-0.105880\pi$
$54$	−4.09138	+	0.424636i	−0.556766	+	0.0577856i
$55$	−3.62195	+	1.45002i	−0.488384	+	0.195521i
$56$		−	1.12757i		−	0.150678i
$57$	−9.99056	+	6.23676i	−1.32328	+	0.826080i
$58$	−8.06948			−1.05957
$59$			7.23149i			0.941460i	0.882277	+	0.470730i	$0.156009\pi$
$59$			7.23149i			0.941460i	−0.882277	+	0.470730i	$0.843991\pi$
$60$	−2.37359	+	1.48175i	−0.306429	+	0.191293i
$61$			12.4925i			1.59951i	0.600330	+	0.799753i	$0.295036\pi$
$61$			12.4925i			1.59951i	−0.600330	+	0.799753i	$0.704964\pi$
$62$	1.12353			0.142689
$63$	1.13806	+	0.556294i	0.143382	+	0.0700864i
$64$	3.35885			0.419856
$65$	1.17632			0.145905
$66$	−2.68619	+	3.66933i	−0.330647	+	0.451664i
$67$	9.42183			1.15106			0.575530	−	0.817781i	$-0.304796\pi$
$67$	9.42183			1.15106			0.575530	+	0.817781i	$0.304796\pi$
$68$	−0.743429			−0.0901540
$69$	−2.80390	+	1.75038i	−0.337549	+	0.210721i
$70$	−0.393197			−0.0469960
$71$		−	6.54436i		−	0.776673i	−0.921518	−	0.388336i	$-0.873050\pi$
$71$		−	6.54436i		−	0.776673i	0.921518	−	0.388336i	$-0.126950\pi$
$72$	−3.51812	+	7.19735i	−0.414614	+	0.848216i
$73$			4.36845i			0.511288i	0.966771	+	0.255644i	$0.0822876\pi$
$73$			4.36845i			0.511288i	−0.966771	+	0.255644i	$0.917712\pi$
$74$	4.90591			0.570300
$75$	−3.31687	−	5.31323i	−0.382999	−	0.613519i
$76$			9.33835i			1.07118i
$77$	1.30012	−	0.520495i	0.148163	−	0.0593159i
$78$	1.16309	−	0.726077i	0.131694	−	0.0822121i
$79$			4.73363i			0.532574i	0.963894	+	0.266287i	$0.0857970\pi$
$79$			4.73363i			0.532574i	−0.963894	+	0.266287i	$0.914203\pi$
$80$			0.744336i			0.0832192i
$81$	−5.52863	−	7.10171i	−0.614293	−	0.789078i
$82$	−8.59559			−0.949224
$83$	10.7329			1.17808			0.589042	−	0.808102i	$-0.299505\pi$
$83$	10.7329			1.17808			0.589042	+	0.808102i	$0.299505\pi$
$84$	0.852015	−	0.531884i	0.0929624	−	0.0580333i
$85$			0.636776i			0.0690681i
$86$			7.36798i			0.794510i
$87$	−9.34974	−	14.9772i	−1.00240	−	1.60572i
$88$	3.29172	+	8.22226i	0.350898	+	0.876496i
$89$			12.0717i			1.27960i	0.768543	+	0.639799i	$0.220982\pi$
$89$			12.0717i			1.27960i	−0.768543	+	0.639799i	$0.779018\pi$
$90$	2.50980	+	1.22681i	0.264556	+	0.129317i
$91$	−0.422249			−0.0442637
$92$			2.62085i			0.273243i
$93$	1.30179	+	2.08531i	0.134989	+	0.216237i
$94$		−	1.06624i		−	0.109974i
$95$	7.99867			0.820646
$96$	5.35805	+	8.58297i	0.546854	+	0.875995i
$97$	−15.2047			−1.54381			−0.771904	−	0.635740i	$-0.780695\pi$
$97$	−15.2047			−1.54381			−0.771904	+	0.635740i	$0.780695\pi$
$98$	−5.40017			−0.545500
$99$	−9.92275	−	0.734152i	−0.997274	−	0.0737851i
$100$	−4.96637			−0.496637
$101$	−8.07804			−0.803795			−0.401898	−	0.915685i	$-0.631649\pi$
$101$	−8.07804			−0.803795			−0.401898	+	0.915685i	$0.631649\pi$
$102$	0.393046	+	0.629612i	0.0389173	+	0.0623409i
$103$	19.6417			1.93535			0.967677	−	0.252193i	$-0.0811518\pi$
$103$	19.6417			1.93535			0.967677	+	0.252193i	$0.0811518\pi$
$104$		−	2.67039i		−	0.261854i
$105$	−0.455580	−	0.729784i	−0.0444600	−	0.0712197i
$106$			3.76365i			0.365558i
$107$	−8.50876			−0.822573			−0.411287	−	0.911506i	$-0.634920\pi$
$107$	−8.50876			−0.822573			−0.411287	+	0.911506i	$0.634920\pi$
$108$	−7.09798	+	0.736685i	−0.683003	+	0.0708875i
$109$		−	12.8446i		−	1.23029i	−0.788415	−	0.615144i	$-0.789098\pi$
$109$		−	12.8446i		−	1.23029i	0.788415	−	0.615144i	$-0.210902\pi$
$110$	2.86720	−	1.14786i	0.273376	−	0.109444i
$111$	5.68426	+	9.10550i	0.539526	+	0.864256i
$112$		−	0.267184i		−	0.0252465i
$113$		−	8.30598i		−	0.781361i	−0.920526	−	0.390680i	$-0.872240\pi$
$113$		−	8.30598i		−	0.781361i	0.920526	−	0.390680i	$-0.127760\pi$
$114$	7.90868	−	4.93712i	0.740716	−	0.462404i
$115$	2.24486			0.209335
$116$	−13.9994			−1.29982
$117$	2.69524	+	1.31745i	0.249175	+	0.121799i
$118$		−	5.72456i		−	0.526989i
$119$		−	0.228575i		−	0.0209534i
$120$	4.61531	−	2.88118i	0.421318	−	0.263015i
$121$	−7.96104	+	7.59091i	−0.723731	+	0.690082i
$122$		−	9.88929i		−	0.895334i
$123$	−9.95932	−	15.9536i	−0.898002	−	1.43849i
$124$	1.94918			0.175041
$125$			10.1355i			0.906548i
$126$	−0.900908	−	0.440371i	−0.0802593	−	0.0392314i
$127$		−	12.2654i		−	1.08838i	−0.838962	−	0.544189i	$-0.816837\pi$
$127$		−	12.2654i		−	1.08838i	0.838962	−	0.544189i	$-0.183163\pi$
$128$	9.02447			0.797658
$129$	−13.6752	+	8.53695i	−1.20403	+	0.751636i
$130$	−0.931196			−0.0816713
$131$	−6.42870			−0.561679			−0.280839	−	0.959755i	$-0.590613\pi$
$131$	−6.42870			−0.561679			−0.280839	+	0.959755i	$0.590613\pi$
$132$	−4.66017	+	6.36579i	−0.405616	+	0.554071i
$133$	−2.87117			−0.248962
$134$	−7.45847			−0.644314
$135$	0.631000	+	6.07970i	0.0543078	+	0.523257i
$136$	1.44556			0.123955
$137$			10.8763i			0.929224i	0.885514	+	0.464612i	$0.153806\pi$
$137$			10.8763i			0.929224i	−0.885514	+	0.464612i	$0.846194\pi$
$138$	2.21961	−	1.38563i	0.188946	−	0.117952i
$139$		−	3.19422i		−	0.270930i	−0.990782	−	0.135465i	$-0.956747\pi$
$139$		−	3.19422i		−	0.270930i	0.990782	−	0.135465i	$-0.0432529\pi$
$140$	−0.682143			−0.0576516
$141$	1.97896	−	1.23540i	0.166659	−	0.104039i
$142$			5.18062i			0.434748i
$143$	3.07905	−	1.23267i	0.257483	−	0.103081i
$144$	−0.833637	+	1.70545i	−0.0694698	+	0.142121i
$145$			11.9911i			0.995804i
$146$		−	3.45813i		−	0.286197i
$147$	−6.25693	−	10.0229i	−0.516063	−	0.826672i
$148$	8.51108			0.699606
$149$	−0.226481			−0.0185540			−0.00927702	−	0.999957i	$-0.502953\pi$
$149$	−0.226481			−0.0185540			−0.00927702	+	0.999957i	$0.502953\pi$
$150$	2.62569	+	4.20604i	0.214386	+	0.343422i
$151$		−	15.0745i		−	1.22674i	−0.789795	−	0.613371i	$-0.789813\pi$
$151$		−	15.0745i		−	1.22674i	0.789795	−	0.613371i	$-0.210187\pi$
$152$		−	18.1579i		−	1.47280i
$153$	−0.713174	+	1.45901i	−0.0576567	+	0.117954i
$154$	−1.02920	+	0.412032i	−0.0829352	+	0.0332025i
$155$		−	1.66955i		−	0.134101i
$156$	2.01780	−	1.25964i	0.161553	−	0.100852i
$157$	9.13891			0.729365			0.364682	−	0.931132i	$-0.381178\pi$
$157$	9.13891			0.729365			0.364682	+	0.931132i	$0.381178\pi$
$158$		−	3.74721i		−	0.298112i
$159$	−6.98544	+	4.36077i	−0.553981	+	0.345832i
$160$		−	6.87172i		−	0.543257i
$161$	−0.805808			−0.0635066
$162$	4.37655	+	5.62182i	0.343854	+	0.441692i
$163$	13.8258			1.08292			0.541461	−	0.840726i	$-0.317871\pi$
$163$	13.8258			1.08292			0.541461	+	0.840726i	$0.317871\pi$
$164$	−14.9122			−1.16444
$165$	5.45255	+	3.99162i	0.424480	+	0.310747i
$166$	−8.49630			−0.659441
$167$	0.223671			0.0173082			0.00865410	−	0.999963i	$-0.497245\pi$
$167$	0.223671			0.0173082			0.00865410	+	0.999963i	$0.497245\pi$
$168$	−1.65670	+	1.03422i	−0.127817	+	0.0797917i
$169$	−1.00000			−0.0769231
$170$		−	0.504082i		−	0.0386613i
$171$	18.3269	+	8.95831i	1.40149	+	0.685059i
$172$			12.7824i			0.974651i
$173$	3.40843			0.259138			0.129569	−	0.991570i	$-0.458641\pi$
$173$	3.40843			0.259138			0.129569	+	0.991570i	$0.458641\pi$
$174$	7.40140	+	11.8562i	0.561099	+	0.898814i
$175$		−	1.52696i		−	0.115428i
$176$	0.779991	+	1.94831i	0.0587940	+	0.146859i
$177$	10.6249	−	6.63279i	0.798620	−	0.498551i
$178$		−	9.55615i		−	0.716263i
$179$			15.5363i			1.16124i	0.814176	+	0.580618i	$0.197189\pi$
$179$			15.5363i			1.16124i	−0.814176	+	0.580618i	$0.802811\pi$
$180$	4.35415	+	2.12834i	0.324539	+	0.158637i
$181$	8.58522			0.638134			0.319067	−	0.947732i	$-0.396630\pi$
$181$	8.58522			0.638134			0.319067	+	0.947732i	$0.396630\pi$
$182$	0.334259			0.0247769
$183$	18.3548	−	11.4583i	1.35683	−	0.847020i
$184$		−	5.09610i		−	0.375690i
$185$		−	7.29007i		−	0.535977i
$186$	−1.03052	−	1.65076i	−0.0755611	−	0.121040i
$187$	0.667279	+	1.66677i	0.0487963	+	0.121886i
$188$		−	1.84977i		−	0.134908i
$189$	−0.226502	−	2.18235i	−0.0164756	−	0.158743i
$190$	−6.33187			−0.459362
$191$			0.793049i			0.0573830i	0.999588	+	0.0286915i	$0.00913405\pi$
$191$			0.793049i			0.0573830i	−0.999588	+	0.0286915i	$0.990866\pi$
$192$	−3.08077	−	4.93502i	−0.222335	−	0.356154i
$193$		−	1.61649i		−	0.116357i	−0.998306	−	0.0581786i	$-0.981471\pi$
$193$		−	1.61649i		−	0.116357i	0.998306	−	0.0581786i	$-0.0185293\pi$
$194$	12.0363			0.864157
$195$	−1.07894	−	1.72833i	−0.0772642	−	0.123768i
$196$	−9.36855			−0.669182
$197$	−13.5082			−0.962418			−0.481209	−	0.876606i	$-0.659802\pi$
$197$	−13.5082			−0.962418			−0.481209	+	0.876606i	$0.659802\pi$
$198$	7.85501	+	0.581166i	0.558231	+	0.0413017i
$199$	−9.07824			−0.643539			−0.321770	−	0.946818i	$-0.604278\pi$
$199$	−9.07824			−0.643539			−0.321770	+	0.946818i	$0.604278\pi$
$200$	9.65684			0.682842
$201$	−8.64179	−	13.8431i	−0.609545	−	0.976419i
$202$	6.39470			0.449930
$203$		−	4.30427i		−	0.302101i
$204$	0.681880	+	1.09229i	0.0477412	+	0.0764757i
$205$			12.7729i			0.892095i
$206$	−15.5487			−1.08333
$207$	5.14352	+	2.51419i	0.357499	+	0.174748i
$208$		−	0.632764i		−	0.0438743i
$209$	20.9366	−	8.38182i	1.44822	−	0.579783i
$210$	0.360644	+	0.577709i	0.0248868	+	0.0398657i
$211$		−	12.7812i		−	0.879895i	−0.898024	−	0.439947i	$-0.854997\pi$
$211$		−	12.7812i		−	0.879895i	0.898024	−	0.439947i	$-0.145003\pi$
$212$			6.52942i			0.448442i
$213$	−9.61537	+	6.00255i	−0.658835	+	0.411288i
$214$	6.73567			0.460441
$215$	10.9487			0.746692
$216$	13.8016	−	1.43244i	0.939082	−	0.0974654i
$217$			0.599295i			0.0406828i
$218$			10.1680i			0.688662i
$219$	6.41839	−	4.00678i	0.433715	−	0.270753i
$220$	4.97419	−	1.99138i	0.335360	−	0.134259i
$221$		−	0.541327i		−	0.0364136i
$222$	−4.49975	−	7.20806i	−0.302003	−	0.483773i
$223$	0.105455			0.00706177			0.00353089	−	0.999994i	$-0.498876\pi$
$223$	0.105455			0.00706177			0.00353089	+	0.999994i	$0.498876\pi$
$224$			2.46665i			0.164810i
$225$	−4.76426	+	9.74669i	−0.317617	+	0.649780i
$226$			6.57514i			0.437372i
$227$	10.5968			0.703336			0.351668	−	0.936125i	$-0.385615\pi$
$227$	10.5968			0.703336			0.351668	+	0.936125i	$0.385615\pi$
$228$	13.7205	−	8.56523i	0.908661	−	0.567246i
$229$	2.63421			0.174074			0.0870368	−	0.996205i	$-0.472260\pi$
$229$	2.63421			0.174074			0.0870368	+	0.996205i	$0.472260\pi$
$230$	−1.77707			−0.117176
$231$	−1.95723	−	1.43282i	−0.128776	−	0.0942725i
$232$	27.2211			1.78715
$233$	−13.5027			−0.884594			−0.442297	−	0.896869i	$-0.645836\pi$
$233$	−13.5027			−0.884594			−0.442297	+	0.896869i	$0.645836\pi$
$234$	−2.13359	−	1.04292i	−0.139477	−	0.0681776i
$235$	−1.58440			−0.103355
$236$		−	9.93133i		−	0.646474i
$237$	6.95493	−	4.34173i	0.451771	−	0.282025i
$238$			0.180944i			0.0117288i
$239$	−19.0742			−1.23381			−0.616903	−	0.787039i	$-0.711613\pi$
$239$	−19.0742			−1.23381			−0.616903	+	0.787039i	$0.711613\pi$
$240$	1.09362	−	0.682712i	0.0705931	−	0.0440688i
$241$			12.4200i			0.800041i	0.916506	+	0.400020i	$0.130997\pi$
$241$			12.4200i			0.800041i	−0.916506	+	0.400020i	$0.869003\pi$
$242$	6.30208	−	6.00908i	0.405113	−	0.386278i
$243$	−5.36334	+	14.6368i	−0.344059	+	0.938948i
$244$		−	17.1566i		−	1.09834i
$245$			8.02453i			0.512669i
$246$	7.88396	+	12.6292i	0.502663	+	0.805206i
$247$	−6.79972			−0.432656
$248$	−3.79007			−0.240670
$249$	−9.84428	−	15.7694i	−0.623856	−	0.999343i
$250$		−	8.02343i		−	0.507446i
$251$		−	22.0224i		−	1.39004i	−0.718990	−	0.695020i	$-0.755395\pi$
$251$		−	22.0224i		−	1.39004i	0.718990	−	0.695020i	$-0.244605\pi$
$252$	−1.56295	−	0.763983i	−0.0984567	−	0.0481264i
$253$	5.87596	−	2.35240i	0.369419	−	0.147894i
$254$			9.70949i			0.609227i
$255$	0.935590	−	0.584057i	0.0585889	−	0.0365751i
$256$	−13.8616			−0.866350
$257$			1.30241i			0.0812423i	0.999175	+	0.0406211i	$0.0129337\pi$
$257$			1.30241i			0.0812423i	−0.999175	+	0.0406211i	$0.987066\pi$
$258$	10.8255	−	6.75798i	0.673965	−	0.420734i
$259$			2.61682i			0.162601i
$260$	−1.61550			−0.100189
$261$	−13.4297	+	27.4744i	−0.831278	+	1.70062i
$262$	5.08906			0.314403
$263$	5.40110			0.333046			0.166523	−	0.986038i	$-0.446746\pi$
$263$	5.40110			0.333046			0.166523	+	0.986038i	$0.446746\pi$
$264$	9.06145	−	12.3779i	0.557693	−	0.761809i
$265$	5.59270			0.343557
$266$	2.27287			0.139358
$267$	17.7365	−	11.0723i	1.08545	−	0.677612i
$268$	−12.9394			−0.790401
$269$		−	22.0497i		−	1.34439i	−0.740373	−	0.672197i	$-0.765351\pi$
$269$		−	22.0497i		−	1.34439i	0.740373	−	0.672197i	$-0.234649\pi$
$270$	−0.499509	−	4.81279i	−0.0303992	−	0.292897i
$271$			22.6385i			1.37519i	0.726093	+	0.687596i	$0.241334\pi$
$271$			22.6385i			1.37519i	−0.726093	+	0.687596i	$0.758666\pi$
$272$	0.342533			0.0207691
$273$	0.387291	+	0.620394i	0.0234399	+	0.0375480i
$274$		−	8.60984i		−	0.520140i
$275$	4.45767	+	11.1346i	0.268807	+	0.671444i
$276$	3.85071	−	2.40387i	0.231786	−	0.144696i
$277$		−	19.5316i		−	1.17354i	−0.809754	−	0.586770i	$-0.800399\pi$
$277$		−	19.5316i		−	1.17354i	0.809754	−	0.586770i	$-0.199601\pi$
$278$			2.52860i			0.151655i
$279$	1.86985	−	3.82533i	0.111945	−	0.229017i
$280$	1.32639			0.0792669
$281$	13.0649			0.779385			0.389693	−	0.920945i	$-0.372581\pi$
$281$	13.0649			0.779385			0.389693	+	0.920945i	$0.372581\pi$
$282$	−1.56658	+	0.977961i	−0.0932883	+	0.0582367i
$283$		−	25.9250i		−	1.54108i	−0.637392	−	0.770540i	$-0.719987\pi$
$283$		−	25.9250i		−	1.54108i	0.637392	−	0.770540i	$-0.280013\pi$
$284$			8.98766i			0.533320i
$285$	−7.33645	−	11.7521i	−0.434574	−	0.696136i
$286$	−2.43742	+	0.975803i	−0.144128	+	0.0577004i
$287$		−	4.58490i		−	0.270638i
$288$	7.69616	−	15.7448i	0.453500	−	0.927769i
$289$	−16.7070			−0.982763
$290$		−	9.49232i		−	0.557408i
$291$	13.9459	+	22.3397i	0.817525	+	1.30958i
$292$		−	5.99939i		−	0.351088i
$293$	−20.8778			−1.21969			−0.609847	−	0.792519i	$-0.708769\pi$
$293$	−20.8778			−1.21969			−0.609847	+	0.792519i	$0.708769\pi$
$294$	4.95309	+	7.93426i	0.288870	+	0.462735i
$295$	−8.50657			−0.495272
$296$	−16.5493			−0.961910
$297$	8.02258	+	15.2525i	0.465517	+	0.885039i
$298$	0.179286			0.0103857
$299$	−1.90837			−0.110364
$300$	4.55521	+	7.29690i	0.262995	+	0.421287i
$301$	−3.93009			−0.226527
$302$			11.9332i			0.686677i
$303$	7.40925	+	11.8687i	0.425651	+	0.681842i
$304$		−	4.30262i		−	0.246772i
$305$	−14.6953			−0.841449
$306$	0.564559	−	1.15497i	0.0322737	−	0.0660254i
$307$			15.9078i			0.907908i	0.891025	+	0.453954i	$0.149987\pi$
$307$			15.9078i			0.907908i	−0.891025	+	0.453954i	$0.850013\pi$
$308$	−1.78552	+	0.714819i	−0.101739	+	0.0407306i
$309$	−18.0156	−	28.8588i	−1.02487	−	1.64172i
$310$			1.32164i			0.0750641i
$311$			12.7429i			0.722582i	0.932453	+	0.361291i	$0.117664\pi$
$311$			12.7429i			0.722582i	−0.932453	+	0.361291i	$0.882336\pi$
$312$	−3.92350	+	2.44931i	−0.222125	+	0.138665i
$313$	−10.5689			−0.597391			−0.298696	−	0.954348i	$-0.596552\pi$
$313$	−10.5689			−0.597391			−0.298696	+	0.954348i	$0.596552\pi$
$314$	−7.23451			−0.408267
$315$	−0.654381	+	1.33873i	−0.0368702	+	0.0754289i
$316$		−	6.50090i		−	0.365704i
$317$			20.9384i			1.17602i	0.808855	+	0.588008i	$0.200088\pi$
$317$			20.9384i			1.17602i	−0.808855	+	0.588008i	$0.799912\pi$
$318$	5.52978	−	3.45206i	0.310095	−	0.193582i
$319$	12.5655	+	31.3868i	0.703531	+	1.75732i
$320$			3.95109i			0.220873i
$321$	7.80432	+	12.5016i	0.435594	+	0.697771i
$322$	0.637891			0.0355483
$323$		−	3.68087i		−	0.204809i
$324$	7.59272	+	9.75309i	0.421818	+	0.541838i
$325$		−	3.61626i		−	0.200594i
$326$	−10.9447			−0.606173
$327$	−18.8720	+	11.7812i	−1.04363	+	0.651500i
$328$	28.9959			1.60103
$329$	0.568732			0.0313552
$330$	−4.31632	−	3.15983i	−0.237606	−	0.173943i
$331$	−20.5719			−1.13073			−0.565367	−	0.824840i	$-0.691265\pi$
$331$	−20.5719			−1.13073			−0.565367	+	0.824840i	$0.691265\pi$
$332$	−14.7399			−0.808958
$333$	8.16470	−	16.7033i	0.447423	−	0.915336i
$334$	−0.177062			−0.00968839
$335$			11.0831i			0.605536i
$336$	−0.392563	+	0.245064i	−0.0214161	+	0.0133693i
$337$			15.3510i			0.836223i	0.908396	+	0.418112i	$0.137308\pi$
$337$			15.3510i			0.836223i	−0.908396	+	0.418112i	$0.862692\pi$
$338$	0.791616			0.0430582
$339$	−12.2036	+	7.61832i	−0.662811	+	0.413770i
$340$		−	0.874513i		−	0.0474271i
$341$	−1.74952	−	4.37007i	−0.0947419	−	0.236652i
$342$	−14.5078	−	7.09154i	−0.784494	−	0.383467i
$343$		−	5.83620i		−	0.315125i
$344$		−	24.8547i		−	1.34008i
$345$	−2.05901	−	3.29829i	−0.110853	−	0.177574i
$346$	−2.69817			−0.145055
$347$	21.9603			1.17889			0.589446	−	0.807808i	$-0.299346\pi$
$347$	21.9603			1.17889			0.589446	+	0.807808i	$0.299346\pi$
$348$	12.8404	+	20.5688i	0.688319	+	1.10260i
$349$		−	0.253359i		−	0.0135620i	−0.999977	−	0.00678100i	$-0.997842\pi$
$349$		−	0.253359i		−	0.0135620i	0.999977	−	0.00678100i	$-0.00215848\pi$
$350$			1.20877i			0.0646114i
$351$	−0.536417	−	5.16839i	−0.0286318	−	0.275868i
$352$	−7.20089	−	17.9868i	−0.383809	−	0.958701i
$353$			7.85980i			0.418335i	0.977880	+	0.209167i	$0.0670754\pi$
$353$			7.85980i			0.418335i	−0.977880	+	0.209167i	$0.932925\pi$
$354$	−8.41087	+	5.25062i	−0.447033	+	0.279067i
$355$	7.69829			0.408583
$356$		−	16.5786i		−	0.878664i
$357$	−0.335836	+	0.209651i	−0.0177743	+	0.0110959i
$358$		−	12.2988i		−	0.650010i
$359$	−11.6282			−0.613713			−0.306856	−	0.951756i	$-0.599277\pi$
$359$	−11.6282			−0.613713			−0.306856	+	0.951756i	$0.599277\pi$
$360$	−8.46641	−	4.13845i	−0.446219	−	0.218115i
$361$	−27.2361			−1.43348
$362$	−6.79619			−0.357200
$363$	18.4550	+	4.73439i	0.968634	+	0.248491i
$364$	0.579894			0.0303947
$365$	−5.13871			−0.268972
$366$	−14.5299	+	9.07055i	−0.759492	+	0.474125i
$367$	−37.8638			−1.97647			−0.988237	−	0.152930i	$-0.951129\pi$
$367$	−37.8638			−1.97647			−0.988237	+	0.152930i	$0.951129\pi$
$368$		−	1.20755i		−	0.0629479i
$369$	−14.3053	+	29.2657i	−0.744703	+	1.52351i
$370$			5.77094i			0.300017i
$371$	−2.00754			−0.104226
$372$	−1.78780	−	2.86385i	−0.0926933	−	0.148484i
$373$		−	8.38711i		−	0.434268i	−0.976142	−	0.217134i	$-0.930329\pi$
$373$		−	8.38711i		−	0.434268i	0.976142	−	0.217134i	$-0.0696709\pi$
$374$	−0.528229	−	1.31944i	−0.0273141	−	0.0682267i
$375$	14.8917	−	9.29639i	0.769005	−	0.480063i
$376$			3.59678i			0.185490i
$377$		−	10.1937i		−	0.525001i
$378$	0.179302	+	1.72758i	0.00922231	+	0.0888572i
$379$	−5.28430			−0.271436			−0.135718	−	0.990747i	$-0.543334\pi$
$379$	−5.28430			−0.271436			−0.135718	+	0.990747i	$0.543334\pi$
$380$	−10.9849			−0.563515
$381$	−18.0211	+	11.2499i	−0.923248	+	0.576352i
$382$		−	0.627790i		−	0.0321206i
$383$			0.100678i			0.00514442i	0.999997	+	0.00257221i	$0.000818760\pi$
$383$			0.100678i			0.00514442i	−0.999997	+	0.00257221i	$0.999181\pi$
$384$	−8.27733	−	13.2593i	−0.422401	−	0.676636i
$385$	0.612270	+	1.52937i	0.0312042	+	0.0779438i
$386$			1.27964i			0.0651318i
$387$	25.0860	+	12.2622i	1.27519	+	0.623324i
$388$	20.8813			1.06009
$389$		−	2.95150i		−	0.149647i	−0.997197	−	0.0748234i	$-0.976161\pi$
$389$		−	2.95150i		−	0.149647i	0.997197	−	0.0748234i	$-0.0238393\pi$
$390$	0.854102	+	1.36817i	0.0432491	+	0.0692800i
$391$		−	1.03305i		−	0.0522438i
$392$	18.2166			0.920079
$393$	5.89647	+	9.44544i	0.297438	+	0.476460i
$394$	10.6933			0.538720
$395$	−5.56828			−0.280170
$396$	13.6274	+	1.00824i	0.684801	+	0.0506662i
$397$	3.61071			0.181217			0.0906083	−	0.995887i	$-0.471119\pi$
$397$	3.61071			0.181217			0.0906083	+	0.995887i	$0.471119\pi$
$398$	7.18647			0.360225
$399$	2.63347	+	4.21850i	0.131838	+	0.211189i
$400$	2.28824			0.114412
$401$		−	19.4088i		−	0.969229i	−0.874728	−	0.484614i	$-0.838960\pi$
$401$		−	19.4088i		−	0.969229i	0.874728	−	0.484614i	$-0.161040\pi$
$402$	6.84098	+	10.9584i	0.341197	+	0.546557i
$403$			1.41929i			0.0707000i
$404$	11.0939			0.551944
$405$	8.35390	−	6.50346i	0.415109	−	0.323160i
$406$			3.40733i			0.169103i
$407$	−7.63928	−	19.0819i	−0.378665	−	0.945854i
$408$	−1.32588	−	2.12390i	−0.0656408	−	0.105149i
$409$			36.3038i			1.79511i	0.440904	+	0.897554i	$0.354658\pi$
$409$			36.3038i			1.79511i	−0.440904	+	0.897554i	$0.645342\pi$
$410$		−	10.1112i		−	0.499356i
$411$	15.9801	−	9.97583i	0.788240	−	0.492072i
$412$	−26.9748			−1.32895
$413$	3.05349			0.150252
$414$	−4.07169	−	1.99027i	−0.200113	−	0.0978166i
$415$			12.6253i			0.619753i
$416$			5.84169i			0.286412i
$417$	−4.69314	+	2.92977i	−0.229824	+	0.143471i
$418$	−16.5738	+	6.63518i	−0.810650	+	0.324537i
$419$			16.9815i			0.829601i	0.909912	+	0.414800i	$0.136149\pi$
$419$			16.9815i			0.829601i	−0.909912	+	0.414800i	$0.863851\pi$
$420$	0.625668	+	1.00225i	0.0305295	+	0.0489046i
$421$	29.4877			1.43714			0.718571	−	0.695454i	$-0.244797\pi$
$421$	29.4877			1.43714			0.718571	+	0.695454i	$0.244797\pi$
$422$			10.1178i			0.492527i
$423$	−3.63024	−	1.77449i	−0.176509	−	0.0862787i
$424$		−	12.6961i		−	0.616577i
$425$	1.95758			0.0949567
$426$	7.61168	−	4.75171i	0.368787	−	0.230221i
$427$	5.27496			0.255273
$428$	11.6855			0.564838
$429$	−4.63525	−	3.39330i	−0.223792	−	0.163830i
$430$	−8.66713			−0.417966
$431$	−20.6901			−0.996608			−0.498304	−	0.867002i	$-0.666044\pi$
$431$	−20.6901			−0.996608			−0.498304	+	0.867002i	$0.666044\pi$
$432$	3.27037	−	0.339425i	0.157346	−	0.0163306i
$433$	11.5038			0.552839			0.276419	−	0.961037i	$-0.410852\pi$
$433$	11.5038			0.552839			0.276419	+	0.961037i	$0.410852\pi$
$434$		−	0.474411i		−	0.0227725i
$435$	17.6180	−	10.9983i	0.844719	−	0.527329i
$436$			17.6400i			0.844804i
$437$	−12.9764			−0.620745
$438$	−5.08090	+	3.17183i	−0.242775	+	0.151556i
$439$			20.8711i			0.996122i	0.867142	+	0.498061i	$0.165954\pi$
$439$			20.8711i			0.996122i	−0.867142	+	0.498061i	$0.834046\pi$
$440$	−9.67204	+	3.87213i	−0.461096	+	0.184596i
$441$	−8.98728	+	18.3861i	−0.427966	+	0.875530i
$442$			0.428523i			0.0203828i
$443$		−	1.76046i		−	0.0836418i	−0.999125	−	0.0418209i	$-0.986684\pi$
$443$		−	1.76046i		−	0.0836418i	0.999125	−	0.0418209i	$-0.0133159\pi$
$444$	−7.80644	−	12.5050i	−0.370477	−	0.593461i
$445$	−14.2002			−0.673155
$446$	−0.0834797			−0.00395288
$447$	0.207730	+	0.332759i	0.00982531	+	0.0157390i
$448$		−	1.41827i		−	0.0670070i
$449$			13.7401i			0.648435i	0.945983	+	0.324217i	$0.105101\pi$
$449$			13.7401i			0.648435i	−0.945983	+	0.324217i	$0.894899\pi$
$450$	3.77146	−	7.71564i	0.177788	−	0.363719i
$451$	13.3847	+	33.4331i	0.630261	+	1.57431i
$452$			11.4070i			0.536539i
$453$	−22.1483	+	13.8264i	−1.04062	+	0.649622i
$454$	−8.38861			−0.393697
$455$		−	0.496702i		−	0.0232857i
$456$	−26.6787	+	16.6546i	−1.24934	+	0.779924i
$457$		−	9.95393i		−	0.465625i	−0.972522	−	0.232813i	$-0.925207\pi$
$457$		−	9.95393i		−	0.465625i	0.972522	−	0.232813i	$-0.0747929\pi$
$458$	−2.08528			−0.0974389
$459$	2.79779	−	0.290377i	0.130590	−	0.0135536i
$460$	−3.08297			−0.143744
$461$	−3.21744			−0.149851			−0.0749257	−	0.997189i	$-0.523872\pi$
$461$	−3.21744			−0.149851			−0.0749257	+	0.997189i	$0.523872\pi$
$462$	1.54937	+	1.13424i	0.0720834	+	0.0527697i
$463$	11.4070			0.530130			0.265065	−	0.964231i	$-0.414607\pi$
$463$	11.4070			0.530130			0.265065	+	0.964231i	$0.414607\pi$
$464$	6.45020			0.299443
$465$	−2.45300	+	1.53132i	−0.113755	+	0.0710135i
$466$	10.6890			0.495157
$467$		−	35.6119i		−	1.64792i	−0.566647	−	0.823961i	$-0.691760\pi$
$467$		−	35.6119i		−	1.64792i	0.566647	−	0.823961i	$-0.308240\pi$
$468$	−3.70149	−	1.80932i	−0.171102	−	0.0836357i
$469$		−	3.97836i		−	0.183704i
$470$	1.25424			0.0578537
$471$	−8.38230	−	13.4274i	−0.386236	−	0.618704i
$472$			19.3109i			0.888857i
$473$	28.6583	−	11.4731i	1.31771	−	0.527535i
$474$	−5.50563	+	3.43698i	−0.252882	+	0.157866i
$475$		−	24.5896i		−	1.12825i
$476$			0.313912i			0.0143881i
$477$	12.8142	+	6.26369i	0.586723	+	0.286795i
$478$	15.0994			0.690631
$479$	10.5084			0.480140			0.240070	−	0.970756i	$-0.422830\pi$
$479$	10.5084			0.480140			0.240070	+	0.970756i	$0.422830\pi$
$480$	−10.0963	+	6.30281i	−0.460833	+	0.287682i
$481$			6.19734i			0.282574i
$482$		−	9.83184i		−	0.447828i
$483$	0.739095	+	1.18394i	0.0336300	+	0.0538713i
$484$	10.9332	−	10.4249i	0.496966	−	0.473860i
$485$		−	17.8857i		−	0.812147i
$486$	4.24571	−	11.5867i	0.192589	−	0.525583i
$487$	−17.2377			−0.781113			−0.390557	−	0.920579i	$-0.627717\pi$
$487$	−17.2377			−0.781113			−0.390557	+	0.920579i	$0.627717\pi$
$488$			33.3600i			1.51014i
$489$	−12.6812	−	20.3137i	−0.573463	−	0.918619i
$490$		−	6.35235i		−	0.286970i
$491$	−29.3071			−1.32261			−0.661306	−	0.750116i	$-0.729998\pi$
$491$	−29.3071			−1.32261			−0.661306	+	0.750116i	$0.729998\pi$
$492$	13.6776	+	21.9099i	0.616633	+	0.987773i
$493$	5.51812			0.248524
$494$	5.38276			0.242182
$495$	0.863601	−	11.6724i	0.0388160	−	0.524634i
$496$	−0.898078			−0.0403249
$497$	−2.76335			−0.123953
$498$	7.79289	+	12.4833i	0.349208	+	0.559389i
$499$	−9.01669			−0.403643			−0.201821	−	0.979422i	$-0.564686\pi$
$499$	−9.01669			−0.403643			−0.201821	+	0.979422i	$0.564686\pi$
$500$		−	13.9196i		−	0.622501i
$501$	−0.205153	−	0.328631i	−0.00916558	−	0.0146822i
$502$			17.4333i			0.778084i
$503$	−28.0113			−1.24896			−0.624481	−	0.781040i	$-0.714690\pi$
$503$	−28.0113			−1.24896			−0.624481	+	0.781040i	$0.714690\pi$
$504$	3.03907	+	1.48552i	0.135371	+	0.0661704i
$505$		−	9.50239i		−	0.422851i
$506$	−4.65150	+	1.86219i	−0.206785	+	0.0827846i
$507$	0.917209	+	1.46926i	0.0407347	+	0.0652522i
$508$			16.8446i			0.747359i
$509$			34.8187i			1.54331i	0.636039	+	0.771657i	$0.280572\pi$
$509$			34.8187i			1.54331i	−0.636039	+	0.771657i	$0.719428\pi$
$510$	−0.740628	+	0.462349i	−0.0327956	+	0.0204732i
$511$	1.84457			0.0815992
$512$	−7.07587			−0.312712
$513$	−3.64748	−	35.1436i	−0.161040	−	1.55163i
$514$		−	1.03101i		−	0.0454759i
$515$			23.1050i			1.01813i
$516$	18.7807	−	11.7242i	0.826775	−	0.516128i
$517$	−4.14720	+	1.66030i	−0.182393	+	0.0730198i
$518$		−	2.07152i		−	0.0910172i
$519$	−3.12625	−	5.00788i	−0.137227	−	0.219821i
$520$	3.14125			0.137753
$521$			1.34449i			0.0589031i	0.999566	+	0.0294516i	$0.00937608\pi$
$521$			1.34449i			0.0589031i	−0.999566	+	0.0294516i	$0.990624\pi$
$522$	10.6312	−	21.7492i	0.465313	−	0.951936i
$523$		−	19.6953i		−	0.861215i	−0.902539	−	0.430608i	$-0.858299\pi$
$523$		−	19.6953i		−	0.861215i	0.902539	−	0.430608i	$-0.141701\pi$
$524$	8.82883			0.385689
$525$	−2.24351	+	1.40055i	−0.0979147	+	0.0611248i
$526$	−4.27559			−0.186425
$527$	−0.768302			−0.0334678
$528$	2.14716	−	2.93302i	0.0934431	−	0.127643i
$529$	19.3581			0.841657
$530$	−4.42727			−0.192308
$531$	−19.4906	−	9.52715i	−0.845820	−	0.413443i
$532$	3.94311			0.170956
$533$		−	10.8583i		−	0.470324i
$534$	−14.0405	+	8.76499i	−0.607590	+	0.379298i
$535$		−	10.0091i		−	0.432729i
$536$	25.1600			1.08675
$537$	22.8268	−	14.2500i	0.985051	−	0.614934i
$538$			17.4549i			0.752533i
$539$	8.40893	+	21.0043i	0.362198	+	0.904721i
$540$	−0.866580	−	8.34952i	−0.0372917	−	0.359306i
$541$			9.95304i			0.427915i	0.976843	+	0.213957i	$0.0686354\pi$
$541$			9.95304i			0.427915i	−0.976843	+	0.213957i	$0.931365\pi$
$542$		−	17.9210i		−	0.769773i
$543$	−7.87444	−	12.6139i	−0.337925	−	0.541315i
$544$	−3.16227			−0.135581
$545$	15.1094			0.647215
$546$	−0.306586	−	0.491114i	−0.0131207	−	0.0210177i
$547$		−	19.4132i		−	0.830049i	−0.909810	−	0.415024i	$-0.863773\pi$
$547$		−	19.4132i		−	0.830049i	0.909810	−	0.415024i	$-0.136227\pi$
$548$		−	14.9369i		−	0.638072i
$549$	−33.6704	−	16.4583i	−1.43702	−	0.702425i
$550$	−3.52876	−	8.81435i	−0.150467	−	0.375845i
$551$		−	69.3141i		−	2.95288i
$552$	−7.48750	+	4.67419i	−0.318689	+	0.198947i
$553$	1.99877			0.0849963
$554$			15.4615i			0.656897i
$555$	−10.7110	+	6.68653i	−0.454657	+	0.283827i
$556$			4.38677i			0.186040i
$557$	5.43523			0.230298			0.115149	−	0.993348i	$-0.463265\pi$
$557$	5.43523			0.230298			0.115149	+	0.993348i	$0.463265\pi$
$558$	−1.48020	+	3.02819i	−0.0626620	+	0.128194i
$559$	−9.30752			−0.393666
$560$	0.314295			0.0132814
$561$	1.83689	−	2.50919i	0.0775534	−	0.105938i
$562$	−10.3424			−0.436266
$563$	28.2108			1.18894			0.594472	−	0.804116i	$-0.297361\pi$
$563$	28.2108			1.18894			0.594472	+	0.804116i	$0.297361\pi$
$564$	−2.71780	+	1.69663i	−0.114440	+	0.0714409i
$565$	9.77052			0.411049
$566$			20.5226i			0.862630i
$567$	−2.99869	+	2.33446i	−0.125933	+	0.0980381i
$568$		−	17.4760i		−	0.733277i
$569$	30.8157			1.29186			0.645930	−	0.763397i	$-0.276470\pi$
$569$	30.8157			1.29186			0.645930	+	0.763397i	$0.276470\pi$
$570$	5.80765	+	9.30317i	0.243256	+	0.389667i
$571$		−	25.0705i		−	1.04917i	−0.851359	−	0.524584i	$-0.824221\pi$
$571$		−	25.0705i		−	1.04917i	0.851359	−	0.524584i	$-0.175779\pi$
$572$	−4.22859	+	1.69288i	−0.176806	+	0.0707830i
$573$	1.16520	−	0.727392i	0.0486768	−	0.0303873i
$574$			3.62948i			0.151492i
$575$		−	6.90117i		−	0.287799i
$576$	−4.42512	+	9.05290i	−0.184380	+	0.377204i
$577$	11.7783			0.490338			0.245169	−	0.969480i	$-0.421157\pi$
$577$	11.7783			0.490338			0.245169	+	0.969480i	$0.421157\pi$
$578$	13.2255			0.550108
$579$	−2.37504	+	1.48266i	−0.0987033	+	0.0616171i
$580$		−	16.4679i		−	0.683791i
$581$		−	4.53194i		−	0.188017i
$582$	−11.0398	−	17.6845i	−0.457615	−	0.733045i
$583$	14.6390	−	5.86061i	0.606285	−	0.242721i
$584$			11.6655i			0.482721i
$585$	−1.54975	+	3.17047i	−0.0640744	+	0.131083i
$586$	16.5272			0.682733
$587$			15.2718i			0.630333i	0.949036	+	0.315167i	$0.102060\pi$
$587$			15.2718i			0.630333i	−0.949036	+	0.315167i	$0.897940\pi$
$588$	8.59292	+	13.7648i	0.354366	+	0.567653i
$589$			9.65079i			0.397654i
$590$	6.73394			0.277232
$591$	12.3898	+	19.8470i	0.509650	+	0.816398i
$592$	−3.92145			−0.161171
$593$	−8.12540			−0.333670			−0.166835	−	0.985985i	$-0.553355\pi$
$593$	−8.12540			−0.333670			−0.166835	+	0.985985i	$0.553355\pi$
$594$	−6.35080	−	12.0741i	−0.260577	−	0.495406i
$595$	0.268878			0.0110229
$596$	0.311036			0.0127405
$597$	8.32664	+	13.3383i	0.340787	+	0.545900i
$598$	1.51070			0.0617770
$599$			19.6292i			0.802025i	0.916072	+	0.401013i	$0.131342\pi$
$599$			19.6292i			0.802025i	−0.916072	+	0.401013i	$0.868658\pi$
$600$	−8.85735	−	14.1884i	−0.361600	−	0.579240i
$601$		−	6.88725i		−	0.280937i	−0.990085	−	0.140468i	$-0.955139\pi$
$601$		−	6.88725i		−	0.280937i	0.990085	−	0.140468i	$-0.0448608\pi$
$602$	3.11112			0.126800
$603$	−12.4128	+	25.3941i	−0.505489	+	1.03413i
$604$			20.7024i			0.842369i
$605$	−8.92936	−	9.36476i	−0.363030	−	0.380732i
$606$	−5.86528	−	9.39549i	−0.238261	−	0.381666i
$607$		−	5.66395i		−	0.229893i	−0.993372	−	0.114946i	$-0.963330\pi$
$607$		−	5.66395i		−	0.229893i	0.993372	−	0.114946i	$-0.0366696\pi$
$608$			39.7218i			1.61093i
$609$	−6.32410	+	3.94792i	−0.256265	+	0.159978i
$610$	11.6330			0.471007
$611$	1.34691			0.0544901
$612$	0.979433	−	2.00372i	0.0395912	−	0.0809955i
$613$		−	42.1982i		−	1.70437i	−0.523240	−	0.852185i	$-0.675277\pi$
$613$		−	42.1982i		−	1.70437i	0.523240	−	0.852185i	$-0.324723\pi$
$614$		−	12.5929i		−	0.508208i
$615$	18.7667	−	11.7154i	0.756745	−	0.472410i
$616$	3.47184	−	1.38993i	0.139885	−	0.0560017i
$617$			31.3719i			1.26298i	0.775383	+	0.631492i	$0.217557\pi$
$617$			31.3719i			1.26298i	−0.775383	+	0.631492i	$0.782443\pi$
$618$	14.2614	+	22.8451i	0.573677	+	0.918963i
$619$	32.2357			1.29566			0.647832	−	0.761783i	$-0.275676\pi$
$619$	32.2357			1.29566			0.647832	+	0.761783i	$0.275676\pi$
$620$			2.29286i			0.0920836i
$621$	−1.02368	−	9.86321i	−0.0410790	−	0.395797i
$622$		−	10.0875i		−	0.404470i
$623$	5.09726			0.204218
$624$	−0.929696	+	0.580377i	−0.0372176	+	0.0232337i
$625$	6.15867			0.246347
$626$	8.36653			0.334394
$627$	−31.5184	−	23.0735i	−1.25872	−	0.921466i
$628$	−12.5509			−0.500834
$629$	−3.35479			−0.133764
$630$	0.518019	−	1.05976i	0.0206384	−	0.0422218i
$631$	8.14185			0.324122			0.162061	−	0.986781i	$-0.448186\pi$
$631$	8.14185			0.324122			0.162061	+	0.986781i	$0.448186\pi$
$632$			12.6406i			0.502818i
$633$	−18.7789	+	11.7230i	−0.746395	+	0.465949i
$634$		−	16.5751i		−	0.658283i
$635$	14.4281			0.572561
$636$	9.59341	−	5.98884i	0.380404	−	0.237473i
$637$		−	6.82171i		−	0.270286i
$638$	−9.94702	−	24.8463i	−0.393806	−	0.983674i
$639$	17.6386	+	8.62189i	0.697773	+	0.341077i
$640$			10.6157i			0.419622i
$641$			47.5292i			1.87729i	0.344886	+	0.938644i	$0.387917\pi$
$641$			47.5292i			1.87729i	−0.344886	+	0.938644i	$0.612083\pi$
$642$	−6.17802	−	9.89645i	−0.243827	−	0.390582i
$643$	−10.9378			−0.431343			−0.215671	−	0.976466i	$-0.569194\pi$
$643$	−10.9378			−0.431343			−0.215671	+	0.976466i	$0.569194\pi$
$644$	1.10665			0.0436082
$645$	−10.0422	−	16.0864i	−0.395412	−	0.633403i
$646$			2.91384i			0.114643i
$647$			29.9198i			1.17627i	0.808763	+	0.588134i	$0.200137\pi$
$647$			29.9198i			1.17627i	−0.808763	+	0.588134i	$0.799863\pi$
$648$	−14.7636	−	18.9643i	−0.579970	−	0.744990i
$649$	−22.2661	+	8.91406i	−0.874020	+	0.349907i
$650$			2.86269i			0.112284i
$651$	0.880521	−	0.549679i	0.0345103	−	0.0215436i
$652$	−18.9876			−0.743613
$653$		−	39.1984i		−	1.53395i	−0.641675	−	0.766976i	$-0.721760\pi$
$653$		−	39.1984i		−	1.53395i	0.641675	−	0.766976i	$-0.278240\pi$
$654$	14.9394	−	9.32616i	0.584177	−	0.364682i
$655$		−	7.56224i		−	0.295481i
$656$	6.87073			0.268257
$657$	−11.7740	−	5.75523i	−0.459348	−	0.224533i
$658$	−0.450217			−0.0175513
$659$	43.4608			1.69299			0.846496	−	0.532396i	$-0.178708\pi$
$659$	43.4608			1.69299			0.846496	+	0.532396i	$0.178708\pi$
$660$	−7.48823	−	5.48187i	−0.291479	−	0.213382i
$661$	−23.7769			−0.924813			−0.462407	−	0.886668i	$-0.653014\pi$
$661$	−23.7769			−0.924813			−0.462407	+	0.886668i	$0.653014\pi$
$662$	16.2850			0.632936
$663$	−0.795351	+	0.496511i	−0.0308889	+	0.0192829i
$664$	28.6610			1.11226
$665$		−	3.37743i		−	0.130971i
$666$	−6.46331	+	13.2226i	−0.250448	+	0.512365i
$667$		−	19.4533i		−	0.753236i
$668$	−0.307178			−0.0118851
$669$	−0.0967241	−	0.154941i	−0.00373957	−	0.00599035i
$670$		−	8.77358i		−	0.338953i
$671$	−38.4651	+	15.3992i	−1.48493	+	0.594480i
$672$	3.62415	−	2.26243i	0.139805	−	0.0872753i
$673$		−	24.4544i		−	0.942648i	−0.881960	−	0.471324i	$-0.843776\pi$
$673$		−	24.4544i		−	0.942648i	0.881960	−	0.471324i	$-0.156224\pi$
$674$		−	12.1521i		−	0.468082i
$675$	18.6903	−	1.93982i	0.719388	−	0.0746639i
$676$	1.37334			0.0528209
$677$	31.1795			1.19832			0.599162	−	0.800628i	$-0.295501\pi$
$677$	31.1795			1.19832			0.599162	+	0.800628i	$0.295501\pi$
$678$	9.66060	−	6.03078i	0.371013	−	0.231611i
$679$			6.42019i			0.246384i
$680$			1.70044i			0.0652090i
$681$	−9.71950	−	15.5695i	−0.372452	−	0.596624i
$682$	1.38495	+	3.45941i	0.0530325	+	0.132468i
$683$			35.0644i			1.34170i	0.741592	+	0.670851i	$0.234071\pi$
$683$			35.0644i			1.34170i	−0.741592	+	0.670851i	$0.765929\pi$
$684$	−25.1691	−	12.3028i	−0.962365	−	0.470411i
$685$	−12.7940			−0.488835
$686$			4.62003i			0.176394i
$687$	−2.41612	−	3.87034i	−0.0921809	−	0.147663i
$688$		−	5.88947i		−	0.224534i
$689$	−4.75439			−0.181128
$690$	1.62994	+	2.61098i	0.0620509	+	0.0993982i
$691$	35.7462			1.35985			0.679924	−	0.733282i	$-0.262013\pi$
$691$	35.7462			1.35985			0.679924	+	0.733282i	$0.262013\pi$
$692$	−4.68095			−0.177943
$693$	−0.309995	+	4.18987i	−0.0117757	+	0.159160i
$694$	−17.3841			−0.659892
$695$	3.75744			0.142528
$696$	−24.9675	−	39.9949i	−0.946390	−	1.51600i
$697$	5.87789			0.222641
$698$			0.200563i			0.00759142i
$699$	12.3848	+	19.8390i	0.468438	+	0.750381i
$700$			2.09705i			0.0792609i
$701$	29.8148			1.12609			0.563044	−	0.826427i	$-0.309630\pi$
$701$	29.8148			1.12609			0.563044	+	0.826427i	$0.309630\pi$
$702$	0.424636	+	4.09138i	0.0160269	+	0.154419i
$703$			42.1401i			1.58935i
$704$	4.14036	+	10.3420i	0.156046	+	0.389780i
$705$	1.45323	+	2.32790i	0.0547318	+	0.0876738i
$706$		−	6.22194i		−	0.234166i
$707$			3.41095i			0.128282i
$708$	−14.5917	+	9.10911i	−0.548390	+	0.342341i
$709$	−43.4189			−1.63063			−0.815315	−	0.579018i	$-0.803436\pi$
$709$	−43.4189			−1.63063			−0.815315	+	0.579018i	$0.803436\pi$
$710$	−6.09409			−0.228707
$711$	−12.7583	−	6.23633i	−0.478472	−	0.233881i
$712$			32.2362i			1.20810i
$713$			2.70854i			0.101436i
$714$	0.265853	−	0.165963i	0.00994931	−	0.00621102i
$715$	1.45002	+	3.62195i	0.0542277	+	0.135453i
$716$		−	21.3367i		−	0.797389i
$717$	17.4950	+	28.0249i	0.653363	+	1.04661i
$718$	9.20506			0.343530
$719$		−	21.0525i		−	0.785124i	−0.919725	−	0.392562i	$-0.871589\pi$
$719$		−	21.0525i		−	0.785124i	0.919725	−	0.392562i	$-0.128411\pi$
$720$	−2.00616	−	0.980627i	−0.0747653	−	0.0365458i
$721$		−	8.29369i		−	0.308873i
$722$	21.5606			0.802401
$723$	18.2482	−	11.3917i	0.678657	−	0.423662i
$724$	−11.7905			−0.438189
$725$	36.8630			1.36906
$726$	−14.6092	−	3.74782i	−0.542200	−	0.139095i
$727$	−12.2570			−0.454586			−0.227293	−	0.973826i	$-0.572988\pi$
$727$	−12.2570			−0.454586			−0.227293	+	0.973826i	$0.572988\pi$
$728$	−1.12757			−0.0417906
$729$	26.4245	−	5.54482i	0.978686	−	0.205364i
$730$	4.06789			0.150559
$731$		−	5.03842i		−	0.186353i
$732$	−25.2075	+	15.7362i	−0.931694	+	0.581625i
$733$		−	16.8459i		−	0.622216i	−0.950375	−	0.311108i	$-0.899300\pi$
$733$		−	16.8459i		−	0.622216i	0.950375	−	0.311108i	$-0.100700\pi$
$734$	29.9736			1.10634
$735$	11.7901	−	7.36018i	0.434886	−	0.271484i
$736$			11.1481i			0.410925i
$737$	11.6140	+	29.0102i	0.427808	+	1.06861i
$738$	11.3243	−	23.1672i	0.416853	−	0.852795i
$739$		−	22.0444i		−	0.810915i	−0.914114	−	0.405458i	$-0.867112\pi$
$739$		−	22.0444i		−	0.810915i	0.914114	−	0.405458i	$-0.132888\pi$
$740$			10.0118i			0.368040i
$741$	6.23676	+	9.99056i	0.229113	+	0.367012i
$742$	1.58920			0.0583413
$743$	−10.9486			−0.401664			−0.200832	−	0.979626i	$-0.564364\pi$
$743$	−10.9486			−0.401664			−0.200832	+	0.979626i	$0.564364\pi$
$744$	3.47629	+	5.56860i	0.127447	+	0.204155i
$745$		−	0.266415i		−	0.00976068i
$746$			6.63937i			0.243085i
$747$	−14.1400	+	28.9276i	−0.517357	+	1.05841i
$748$	−0.916404	−	2.28905i	−0.0335071	−	0.0836960i
$749$			3.59282i			0.131279i
$750$	−11.7885	+	7.35917i	−0.430456	+	0.268719i
$751$	10.8100			0.394461			0.197230	−	0.980357i	$-0.436805\pi$
$751$	10.8100			0.394461			0.197230	+	0.980357i	$0.436805\pi$
$752$			0.852276i			0.0310793i
$753$	−32.3566	+	20.1991i	−1.17914	+	0.736097i
$754$			8.06948i			0.293873i
$755$	17.7324			0.645349
$756$	0.311065	+	2.99712i	0.0113133	+	0.109004i
$757$	24.5936			0.893869			0.446934	−	0.894567i	$-0.352516\pi$
$757$	24.5936			0.893869			0.446934	+	0.894567i	$0.352516\pi$
$758$	4.18313			0.151938
$759$	−8.84577	−	6.47568i	−0.321081	−	0.235052i
$760$	21.3596			0.774794
$761$	28.5614			1.03535			0.517675	−	0.855577i	$-0.326798\pi$
$761$	28.5614			1.03535			0.517675	+	0.855577i	$0.326798\pi$
$762$	14.2658	−	8.90563i	0.516794	−	0.322617i
$763$	−5.42361			−0.196348
$764$		−	1.08913i		−	0.0394033i
$765$	−1.71626	−	0.838923i	−0.0620517	−	0.0303313i
$766$		−	0.0796985i		−	0.00287962i
$767$	7.23149			0.261114
$768$	12.7140	+	20.3663i	0.458777	+	0.734906i
$769$			50.7381i			1.82966i	0.403837	+	0.914831i	$0.367676\pi$
$769$			50.7381i			1.82966i	−0.403837	+	0.914831i	$0.632324\pi$
$770$	−0.484683	−	1.21067i	−0.0174668	−	0.0436296i
$771$	1.91358	−	1.19459i	0.0689160	−	0.0430219i
$772$			2.21999i			0.0798993i
$773$		−	25.9915i		−	0.934850i	−0.884033	−	0.467425i	$-0.845182\pi$
$773$		−	25.9915i		−	0.934850i	0.884033	−	0.467425i	$-0.154818\pi$
$774$	−19.8585	−	9.70697i	−0.713798	−	0.348910i
$775$	−5.13253			−0.184366
$776$	−40.6026			−1.45755
$777$	3.84479	−	2.40017i	0.137931	−	0.0861057i
$778$			2.33645i			0.0837658i
$779$		−	73.8333i		−	2.64535i
$780$	1.48175	+	2.37359i	0.0530552	+	0.0849881i
$781$	20.1504	−	8.06705i	0.721038	−	0.288662i
$782$			0.817782i			0.0292438i
$783$	52.6849	−	5.46806i	1.88281	−	0.195413i
$784$	4.31653			0.154162
$785$			10.7503i			0.383695i
$786$	−4.66774	−	7.47716i	−0.166493	−	0.266702i
$787$			28.5816i			1.01882i	0.860523	+	0.509411i	$0.170137\pi$
$787$			28.5816i			1.01882i	−0.860523	+	0.509411i	$0.829863\pi$
$788$	18.5514			0.660866
$789$	−4.95394	−	7.93562i	−0.176365	−	0.282516i
$790$	4.40793			0.156827
$791$	−3.50719			−0.124701
$792$	−26.4976	−	1.96047i	−0.941553	−	0.0696624i
$793$	12.4925			0.443623
$794$	−2.85830			−0.101437
$795$	−5.12968	−	8.21714i	−0.181931	−	0.291432i
$796$	12.4675			0.441900
$797$			24.1772i			0.856402i	0.903684	+	0.428201i	$0.140852\pi$
$797$			24.1772i			0.856402i	−0.903684	+	0.428201i	$0.859148\pi$
$798$	−2.08470	−	3.33943i	−0.0737974	−	0.118215i
$799$			0.729119i			0.0257944i
$800$	−21.1251			−0.746885
$801$	−32.5361	−	15.9039i	−1.14961	−	0.561937i
$802$			15.3643i			0.542532i
$803$	−13.4507	+	5.38487i	−0.474663	+	0.190028i
$804$	11.8682	+	19.0114i	0.418558	+	0.670480i
$805$		−	0.947892i		−	0.0334088i
$806$		−	1.12353i		−	0.0395748i
$807$	−32.3967	+	20.2242i	−1.14042	+	0.711925i
$808$	−21.5715			−0.758884
$809$	−4.86200			−0.170939			−0.0854694	−	0.996341i	$-0.527239\pi$
$809$	−4.86200			−0.170939			−0.0854694	+	0.996341i	$0.527239\pi$
$810$	−6.61308	+	5.14824i	−0.232360	+	0.180891i
$811$		−	21.7622i		−	0.764175i	−0.924126	−	0.382088i	$-0.875205\pi$
$811$		−	21.7622i		−	0.764175i	0.924126	−	0.382088i	$-0.124795\pi$
$812$			5.91125i			0.207444i
$813$	33.2619	−	20.7643i	1.16655	−	0.728235i
$814$	6.04738	+	15.1055i	0.211960	+	0.529448i
$815$			16.2637i			0.569691i
$816$	−0.314174	−	0.503270i	−0.0109983	−	0.0176180i
$817$	−63.2885			−2.21418
$818$		−	28.7387i		−	1.00482i
$819$	0.556294	−	1.13806i	0.0194385	−	0.0397671i
$820$		−	17.5415i		−	0.612577i
$821$	−49.4231			−1.72488			−0.862439	−	0.506161i	$-0.831064\pi$
$821$	−49.4231			−1.72488			−0.862439	+	0.506161i	$0.831064\pi$
$822$	−12.6501	+	7.89703i	−0.441223	+	0.275440i
$823$	−2.99642			−0.104449			−0.0522244	−	0.998635i	$-0.516631\pi$
$823$	−2.99642			−0.104449			−0.0522244	+	0.998635i	$0.516631\pi$
$824$	52.4510			1.82722
$825$	12.2711	−	16.7623i	0.427224	−	0.583587i
$826$	−2.41719			−0.0841049
$827$	−2.61482			−0.0909263			−0.0454632	−	0.998966i	$-0.514476\pi$
$827$	−2.61482			−0.0909263			−0.0454632	+	0.998966i	$0.514476\pi$
$828$	−7.06382	−	3.45285i	−0.245485	−	0.119995i
$829$	−5.87331			−0.203989			−0.101994	−	0.994785i	$-0.532522\pi$
$829$	−5.87331			−0.203989			−0.101994	+	0.994785i	$0.532522\pi$
$830$		−	9.99440i		−	0.346911i
$831$	−28.6970	+	17.9146i	−0.995488	+	0.621449i
$832$		−	3.35885i		−	0.116447i
$833$	3.69278			0.127947
$834$	3.71517	−	2.31925i	0.128646	−	0.0803091i
$835$			0.263110i			0.00910529i
$836$	−28.7532	+	11.5111i	−0.994451	+	0.398121i
$837$	−7.33546	+	0.761332i	−0.253551	+	0.0263155i
$838$		−	13.4428i		−	0.464375i
$839$		−	26.6273i		−	0.919275i	−0.888107	−	0.459638i	$-0.847979\pi$
$839$		−	26.6273i		−	0.919275i	0.888107	−	0.459638i	$-0.152021\pi$
$840$	−1.21658	−	1.94881i	−0.0419759	−	0.0672404i
$841$	74.9111			2.58314
$842$	−23.3429			−0.804450
$843$	−11.9832	−	19.1957i	−0.412724	−	0.661135i
$844$			17.5530i			0.604199i
$845$		−	1.17632i		−	0.0404668i
$846$	2.87376	+	1.40472i	0.0988019	+	0.0482951i
$847$	3.20525	+	3.36154i	0.110134	+	0.115504i
$848$		−	3.00841i		−	0.103309i
$849$	−38.0905	+	23.7786i	−1.30726	+	0.816081i
$850$	−1.54965			−0.0531526
$851$			11.8268i			0.405418i
$852$	13.2052	−	8.24357i	0.452403	−	0.282420i
$853$		−	10.3225i		−	0.353435i	−0.984262	−	0.176717i	$-0.943452\pi$
$853$		−	10.3225i		−	0.353435i	0.984262	−	0.176717i	$-0.0565479\pi$
$854$	−4.17574			−0.142891
$855$	−10.5379	+	21.5583i	−0.360388	+	0.737279i
$856$	−22.7217			−0.776613
$857$	−11.2266			−0.383492			−0.191746	−	0.981445i	$-0.561415\pi$
$857$	−11.2266			−0.383492			−0.191746	+	0.981445i	$0.561415\pi$
$858$	3.66933	+	2.68619i	0.125269	+	0.0917050i
$859$	3.85761			0.131620			0.0658099	−	0.997832i	$-0.479037\pi$
$859$	3.85761			0.131620			0.0658099	+	0.997832i	$0.479037\pi$
$860$	−15.0363			−0.512733
$861$	−6.73642	+	4.20532i	−0.229576	+	0.143317i
$862$	16.3786			0.557858
$863$			24.3417i			0.828600i	0.910140	+	0.414300i	$0.135974\pi$
$863$			24.3417i			0.828600i	−0.910140	+	0.414300i	$0.864026\pi$
$864$	−30.1921	+	3.13358i	−1.02716	+	0.106607i
$865$			4.00942i			0.136324i
$866$	−9.10661			−0.309455
$867$	15.3238	+	24.5469i	0.520423	+	0.833656i
$868$		−	0.823039i		−	0.0279358i
$869$	−14.5750	+	5.83501i	−0.494425	+	0.197939i
$870$	−13.9467	+	8.70645i	−0.472837	+	0.295176i
$871$		−	9.42183i		−	0.319247i
$872$		−	34.3001i		−	1.16155i
$873$	20.0315	−	40.9804i	0.677965	−	1.38698i
$874$	10.2723			0.347466
$875$	4.27971			0.144681
$876$	−8.81466	+	5.50269i	−0.297820	+	0.185919i
$877$		−	27.8512i		−	0.940469i	−0.882542	−	0.470234i	$-0.844169\pi$
$877$		−	27.8512i		−	0.940469i	0.882542	−	0.470234i	$-0.155831\pi$
$878$		−	16.5219i		−	0.557586i
$879$	19.1493	+	30.6749i	0.645891	+	1.03464i
$880$	−2.29184	+	0.917522i	−0.0772580	+	0.0309297i
$881$		−	38.5115i		−	1.29749i	−0.761008	−	0.648743i	$-0.775295\pi$
$881$		−	38.5115i		−	1.29749i	0.761008	−	0.648743i	$-0.224705\pi$
$882$	7.11447	−	14.5548i	0.239557	−	0.490084i
$883$	−19.2648			−0.648312			−0.324156	−	0.946004i	$-0.605080\pi$
$883$	−19.2648			−0.648312			−0.324156	+	0.946004i	$0.605080\pi$
$884$			0.743429i			0.0250042i
$885$	7.80231	+	12.4984i	0.262272	+	0.420128i
$886$			1.39360i			0.0468191i
$887$	−31.9919			−1.07418			−0.537091	−	0.843524i	$-0.680477\pi$
$887$	−31.9919			−1.07418			−0.537091	+	0.843524i	$0.680477\pi$
$888$	15.1792	+	24.3153i	0.509380	+	0.815967i
$889$	−5.17906			−0.173700
$890$	11.2411			0.376803
$891$	15.0515	−	25.7770i	0.504244	−	0.863561i
$892$	−0.144826			−0.00484912
$893$	9.15861			0.306481
$894$	−0.164443	−	0.263418i	−0.00549978	−	0.00881000i
$895$	−18.2757			−0.610889
$896$		−	3.81057i		−	0.127302i
$897$	1.75038	+	2.80390i	0.0584434	+	0.0936193i
$898$		−	10.8769i		−	0.362966i
$899$	−14.4678			−0.482529
$900$	6.54297	−	13.3856i	0.218099	−	0.446186i
$901$		−	2.57368i		−	0.0857418i
$902$	−10.5955	−	26.4662i	−0.352793	−	0.881228i
$903$	3.60472	+	5.77433i	0.119958	+	0.192158i
$904$		−	22.1802i		−	0.737703i
$905$			10.0990i			0.335702i
$906$	17.5329	−	10.9452i	0.582493	−	0.363631i
$907$	34.1655			1.13445			0.567223	−	0.823564i	$-0.308018\pi$
$907$	34.1655			1.13445			0.567223	+	0.823564i	$0.308018\pi$
$908$	−14.5531			−0.482961
$909$	10.6424	−	21.7723i	0.352988	−	0.722140i
$910$			0.393197i			0.0130344i
$911$			40.1272i			1.32947i	0.747077	+	0.664737i	$0.231456\pi$
$911$			40.1272i			1.32947i	−0.747077	+	0.664737i	$0.768544\pi$
$912$	−6.32167	+	3.94640i	−0.209331	+	0.130678i
$913$	13.2301	+	33.0470i	0.437852	+	1.09370i
$914$			7.87969i			0.260637i
$915$	13.4786	+	21.5912i	0.445590	+	0.713782i
$916$	−3.61768			−0.119531
$917$			2.71452i			0.0896412i
$918$	−2.21478	+	0.229867i	−0.0730985	+	0.00758674i
$919$			25.1316i			0.829016i	0.910046	+	0.414508i	$0.136046\pi$
$919$			25.1316i			0.829016i	−0.910046	+	0.414508i	$0.863954\pi$
$920$	5.99467			0.197638
$921$	23.3727	−	14.5908i	0.770158	−	0.480784i
$922$	2.54698			0.0838803
$923$	−6.54436			−0.215410
$924$	2.68795	+	1.96775i	0.0884271	+	0.0647343i
$925$	−22.4112			−0.736876
$926$	−9.02999			−0.296744
$927$	−25.8770	+	52.9391i	−0.849913	+	1.73875i
$928$	−59.5483			−1.95477
$929$			6.58674i			0.216104i	0.994145	+	0.108052i	$0.0344613\pi$
$929$			6.58674i			0.216104i	−0.994145	+	0.108052i	$0.965539\pi$
$930$	1.94183	−	1.21222i	0.0636752	−	0.0397503i
$931$		−	46.3857i		−	1.52023i
$932$	18.5439			0.607426
$933$	18.7226	−	11.6879i	0.612950	−	0.382644i
$934$			28.1909i			0.922435i
$935$	−1.96066	+	0.784936i	−0.0641205	+	0.0256702i
$936$	7.19735	+	3.51812i	0.235253	+	0.114993i
$937$			24.1549i			0.789107i	0.918873	+	0.394554i	$0.129101\pi$
$937$			24.1549i			0.789107i	−0.918873	+	0.394554i	$0.870899\pi$
$938$			3.14933i			0.102829i
$939$	9.69392	+	15.5285i	0.316349	+	0.506754i
$940$	2.17593			0.0709710
$941$	−26.9975			−0.880094			−0.440047	−	0.897975i	$-0.645038\pi$
$941$	−26.9975			−0.880094			−0.440047	+	0.897975i	$0.645038\pi$
$942$	6.63556	+	10.6294i	0.216198	+	0.346324i
$943$		−	20.7216i		−	0.674790i
$944$			4.57583i			0.148931i
$945$	2.56715	−	0.266439i	0.0835093	−	0.00866727i
$946$	−22.6863	+	9.08230i	−0.737597	+	0.295291i
$947$		−	21.8752i		−	0.710849i	−0.934705	−	0.355424i	$-0.884336\pi$
$947$		−	21.8752i		−	0.710849i	0.934705	−	0.355424i	$-0.115664\pi$
$948$	−9.55151	+	5.96269i	−0.310219	+	0.193659i
$949$	4.36845			0.141806
$950$			19.4655i			0.631544i
$951$	30.7639	−	19.2049i	0.997589	−	0.622761i
$952$		−	0.610385i		−	0.0197827i
$953$	−6.95238			−0.225210			−0.112605	−	0.993640i	$-0.535919\pi$
$953$	−6.95238			−0.225210			−0.112605	+	0.993640i	$0.535919\pi$
$954$	−10.1439	−	4.95843i	−0.328422	−	0.160535i
$955$	−0.932883			−0.0301874
$956$	26.1954			0.847220
$957$	34.5902	−	47.2502i	1.11814	−	1.52738i
$958$	−8.31860			−0.268762
$959$	4.59250			0.148300
$960$	5.80518	−	3.62398i	0.187361	−	0.116963i
$961$	−28.9856			−0.935020
$962$		−	4.90591i		−	0.158173i
$963$	11.2099	−	22.9332i	0.361234	−	0.739010i
$964$		−	17.0569i		−	0.549366i
$965$	1.90151			0.0612118
$966$	−0.585079	−	0.937228i	−0.0188246	−	0.0301548i
$967$			1.81373i			0.0583255i	0.999575	+	0.0291628i	$0.00928411\pi$
$967$			1.81373i			0.0583255i	−0.999575	+	0.0291628i	$0.990716\pi$
$968$	−21.2591	+	20.2707i	−0.683293	+	0.651525i
$969$	−5.40816	+	3.37613i	−0.173735	+	0.108457i
$970$			14.1586i			0.454605i
$971$		−	31.7380i		−	1.01852i	−0.860612	−	0.509261i	$-0.829919\pi$
$971$		−	31.7380i		−	1.01852i	0.860612	−	0.509261i	$-0.170081\pi$
$972$	7.36572	−	20.1013i	0.236255	−	0.644750i
$973$	−1.34876			−0.0432392
$974$	13.6456			0.437234
$975$	−5.31323	+	3.31687i	−0.170160	+	0.106225i
$976$			7.90483i			0.253027i
$977$		−	35.4339i		−	1.13363i	−0.823845	−	0.566815i	$-0.808175\pi$
$977$		−	35.4339i		−	1.13363i	0.823845	−	0.566815i	$-0.191825\pi$
$978$	10.0386	+	16.0807i	0.321000	+	0.514204i
$979$	−37.1693	+	14.8804i	−1.18794	+	0.475581i
$980$		−	11.0205i		−	0.352035i
$981$	34.6192	+	16.9221i	1.10531	+	0.540282i
$982$	23.2000			0.740342
$983$			39.1279i			1.24799i	0.781430	+	0.623993i	$0.214491\pi$
$983$			39.1279i			1.24799i	−0.781430	+	0.623993i	$0.785509\pi$
$984$	−26.5953	−	42.6025i	−0.847827	−	1.35812i
$985$		−	15.8900i		−	0.506297i
$986$	−4.36823			−0.139113
$987$	−0.521646	−	0.835615i	−0.0166042	−	0.0265979i
$988$	9.33835			0.297093
$989$	−17.7622			−0.564806
$990$	−0.683640	+	9.24003i	−0.0217275	+	0.293667i
$991$	−16.9838			−0.539508			−0.269754	−	0.962929i	$-0.586942\pi$
$991$	−16.9838			−0.539508			−0.269754	+	0.962929i	$0.586942\pi$
$992$	8.29107			0.263242
$993$	18.8687	+	30.2255i	0.598781	+	0.959176i
$994$	2.18751			0.0693837
$995$		−	10.6789i		−	0.338545i
$996$	13.5196	+	21.6568i	0.428385	+	0.686221i
$997$			53.9445i			1.70844i	0.519913	+	0.854219i	$0.325964\pi$
$997$			53.9445i			1.70844i	−0.519913	+	0.854219i	$0.674036\pi$
$998$	7.13776			0.225942
$999$	−32.0303	+	3.32436i	−1.01339	+	0.105178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.f.a.131.19	✓	48
3.2	odd	2	inner	429.2.f.a.131.30	yes	48
11.10	odd	2	inner	429.2.f.a.131.29	yes	48
33.32	even	2	inner	429.2.f.a.131.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.f.a.131.19	✓	48	1.1	even	1	trivial
429.2.f.a.131.20	yes	48	33.32	even	2	inner
429.2.f.a.131.29	yes	48	11.10	odd	2	inner
429.2.f.a.131.30	yes	48	3.2	odd	2	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.791616 q^{2} +(-0.917209 - 1.46926i) q^{3} -1.37334 q^{4} +1.17632i q^{5} +(0.726077 + 1.16309i) q^{6} -0.422249i q^{7} +2.67039 q^{8} +(-1.31745 + 2.69524i) q^{9} +O(q^{10})\)	\(q-0.791616 q^{2} +(-0.917209 - 1.46926i) q^{3} -1.37334 q^{4} +1.17632i q^{5} +(0.726077 + 1.16309i) q^{6} -0.422249i q^{7} +2.67039 q^{8} +(-1.31745 + 2.69524i) q^{9} -0.931196i q^{10} +(1.23267 + 3.07905i) q^{11} +(1.25964 + 2.01780i) q^{12} -1.00000i q^{13} +0.334259i q^{14} +(1.72833 - 1.07894i) q^{15} +0.632764 q^{16} +0.541327 q^{17} +(1.04292 - 2.13359i) q^{18} -6.79972i q^{19} -1.61550i q^{20} +(-0.620394 + 0.387291i) q^{21} +(-0.975803 - 2.43742i) q^{22} -1.90837i q^{23} +(-2.44931 - 3.92350i) q^{24} +3.61626 q^{25} +0.791616i q^{26} +(5.16839 - 0.536417i) q^{27} +0.579894i q^{28} +10.1937 q^{29} +(-1.36817 + 0.854102i) q^{30} -1.41929 q^{31} -5.84169 q^{32} +(3.39330 - 4.63525i) q^{33} -0.428523 q^{34} +0.496702 q^{35} +(1.80932 - 3.70149i) q^{36} -6.19734 q^{37} +5.38276i q^{38} +(-1.46926 + 0.917209i) q^{39} +3.14125i q^{40} +10.8583 q^{41} +(0.491114 - 0.306586i) q^{42} -9.30752i q^{43} +(-1.69288 - 4.22859i) q^{44} +(-3.17047 - 1.54975i) q^{45} +1.51070i q^{46} +1.34691i q^{47} +(-0.580377 - 0.929696i) q^{48} +6.82171 q^{49} -2.86269 q^{50} +(-0.496511 - 0.795351i) q^{51} +1.37334i q^{52} -4.75439i q^{53} +(-4.09138 + 0.424636i) q^{54} +(-3.62195 + 1.45002i) q^{55} -1.12757i q^{56} +(-9.99056 + 6.23676i) q^{57} -8.06948 q^{58} +7.23149i q^{59} +(-2.37359 + 1.48175i) q^{60} +12.4925i q^{61} +1.12353 q^{62} +(1.13806 + 0.556294i) q^{63} +3.35885 q^{64} +1.17632 q^{65} +(-2.68619 + 3.66933i) q^{66} +9.42183 q^{67} -0.743429 q^{68} +(-2.80390 + 1.75038i) q^{69} -0.393197 q^{70} -6.54436i q^{71} +(-3.51812 + 7.19735i) q^{72} +4.36845i q^{73} +4.90591 q^{74} +(-3.31687 - 5.31323i) q^{75} +9.33835i q^{76} +(1.30012 - 0.520495i) q^{77} +(1.16309 - 0.726077i) q^{78} +4.73363i q^{79} +0.744336i q^{80} +(-5.52863 - 7.10171i) q^{81} -8.59559 q^{82} +10.7329 q^{83} +(0.852015 - 0.531884i) q^{84} +0.636776i q^{85} +7.36798i q^{86} +(-9.34974 - 14.9772i) q^{87} +(3.29172 + 8.22226i) q^{88} +12.0717i q^{89} +(2.50980 + 1.22681i) q^{90} -0.422249 q^{91} +2.62085i q^{92} +(1.30179 + 2.08531i) q^{93} -1.06624i q^{94} +7.99867 q^{95} +(5.35805 + 8.58297i) q^{96} -15.2047 q^{97} -5.40017 q^{98} +(-9.92275 - 0.734152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

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