LMFDB - Embedded newform 1386.2.ba.b.1187.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(989,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("1386.989");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.ba (of order $6$, degree $2$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1187.4
Character	$\chi$	$=$	1386.1187
Dual form			1386.2.ba.b.989.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.87061 + 1.08000i) q^{5} +(-2.63666 - 0.219149i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.87061 + 1.08000i) q^{5} +(-2.63666 - 0.219149i) q^{7} -1.00000 q^{8} +(-1.87061 - 1.08000i) q^{10} +(-3.25136 - 0.654737i) q^{11} +3.53956i q^{13} +(-1.12854 - 2.39299i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.82953 - 6.63294i) q^{17} +(-1.66946 + 0.963864i) q^{19} -2.15999i q^{20} +(-1.05866 - 3.14313i) q^{22} +(7.21952 - 4.16819i) q^{23} +(-0.167211 + 0.289618i) q^{25} +(-3.06535 + 1.76978i) q^{26} +(1.50812 - 2.17384i) q^{28} +4.79594 q^{29} +(2.97154 - 5.14685i) q^{31} +(0.500000 - 0.866025i) q^{32} +7.65906 q^{34} +(5.16884 - 2.43764i) q^{35} +(-1.55673 - 2.69634i) q^{37} +(-1.66946 - 0.963864i) q^{38} +(1.87061 - 1.08000i) q^{40} -9.00600 q^{41} -2.48924i q^{43} +(2.19270 - 2.48839i) q^{44} +(7.21952 + 4.16819i) q^{46} +(7.34212 - 4.23898i) q^{47} +(6.90395 + 1.15564i) q^{49} -0.334422 q^{50} +(-3.06535 - 1.76978i) q^{52} +(-4.83344 - 2.79059i) q^{53} +(6.78914 - 2.28670i) q^{55} +(2.63666 + 0.219149i) q^{56} +(2.39797 + 4.15341i) q^{58} +(-3.95479 - 2.28330i) q^{59} +(-9.71354 + 5.60811i) q^{61} +5.94307 q^{62} +1.00000 q^{64} +(-3.82272 - 6.62114i) q^{65} +(1.46173 - 2.53179i) q^{67} +(3.82953 + 6.63294i) q^{68} +(4.69548 + 3.25753i) q^{70} -14.9539i q^{71} +(-0.486281 - 0.280755i) q^{73} +(1.55673 - 2.69634i) q^{74} -1.92773i q^{76} +(8.42924 + 2.43885i) q^{77} +(-6.63288 + 3.82950i) q^{79} +(1.87061 + 1.08000i) q^{80} +(-4.50300 - 7.79943i) q^{82} -8.45117 q^{83} +16.5435i q^{85} +(2.15574 - 1.24462i) q^{86} +(3.25136 + 0.654737i) q^{88} +(-0.609275 + 0.351765i) q^{89} +(0.775692 - 9.33262i) q^{91} +8.33638i q^{92} +(7.34212 + 4.23898i) q^{94} +(2.08194 - 3.60603i) q^{95} -1.23783 q^{97} +(2.45116 + 6.55682i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8}+O(q^{10}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 2 q^{11} - 16 q^{16} + 4 q^{17} + 4 q^{22} + 4 q^{25} + 16 q^{29} + 4 q^{31} + 16 q^{32} + 8 q^{34} + 16 q^{35} + 4 q^{37} - 32 q^{41} + 2 q^{44} + 20 q^{49} + 8 q^{50} - 12 q^{55} + 8 q^{58} + 8 q^{62} + 32 q^{64} - 8 q^{67} + 4 q^{68} - 4 q^{70} - 4 q^{74} + 14 q^{77} - 16 q^{82} + 88 q^{83} - 2 q^{88} - 24 q^{95} - 32 q^{97} - 8 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 2 * q^11 - 16 * q^16 + 4 * q^17 + 4 * q^22 + 4 * q^25 + 16 * q^29 + 4 * q^31 + 16 * q^32 + 8 * q^34 + 16 * q^35 + 4 * q^37 - 32 * q^41 + 2 * q^44 + 20 * q^49 + 8 * q^50 - 12 * q^55 + 8 * q^58 + 8 * q^62 + 32 * q^64 - 8 * q^67 + 4 * q^68 - 4 * q^70 - 4 * q^74 + 14 * q^77 - 16 * q^82 + 88 * q^83 - 2 * q^88 - 24 * q^95 - 32 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.87061	+	1.08000i	−0.836562	+	0.482990i	−0.856094	−	0.516820i	$-0.827116\pi$
$5$	−1.87061	+	1.08000i	−0.836562	+	0.482990i	0.0195319	+	0.999809i	$0.493782\pi$
$6$		0			0
$7$	−2.63666	−	0.219149i	−0.996564	−	0.0828306i
$7$	−2.63666	−	0.219149i	−0.996564	−	0.0828306i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.87061	−	1.08000i	−0.591539	−	0.341525i
$11$	−3.25136	−	0.654737i	−0.980321	−	0.197411i
$11$	−3.25136	−	0.654737i	−0.980321	−	0.197411i
$12$		0			0
$13$			3.53956i			0.981698i	0.871245	+	0.490849i	$0.163313\pi$
$13$			3.53956i			0.981698i	−0.871245	+	0.490849i	$0.836687\pi$
$14$	−1.12854	−	2.39299i	−0.301615	−	0.639553i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.82953	−	6.63294i	0.928798	−	1.60873i	0.143461	−	0.989656i	$-0.454177\pi$
$17$	3.82953	−	6.63294i	0.928798	−	1.60873i	0.785336	−	0.619069i	$-0.212490\pi$
$18$		0			0
$19$	−1.66946	+	0.963864i	−0.383001	+	0.221126i	−0.679123	−	0.734024i	$-0.737640\pi$
$19$	−1.66946	+	0.963864i	−0.383001	+	0.221126i	0.296122	+	0.955150i	$0.404306\pi$
$20$		−	2.15999i		−	0.482990i
$21$		0			0
$22$	−1.05866	−	3.14313i	−0.225707	−	0.670117i
$23$	7.21952	−	4.16819i	1.50537	−	0.869128i	0.505394	−	0.862889i	$-0.331347\pi$
$23$	7.21952	−	4.16819i	1.50537	−	0.869128i	0.999981	−	0.00623916i	$-0.00198600\pi$
$24$		0			0
$25$	−0.167211	+	0.289618i	−0.0334422	+	0.0579236i
$26$	−3.06535	+	1.76978i	−0.601165	+	0.347083i
$27$		0			0
$28$	1.50812	−	2.17384i	0.285008	−	0.410817i
$29$	4.79594			0.890584			0.445292	−	0.895385i	$-0.353100\pi$
$29$	4.79594			0.890584			0.445292	+	0.895385i	$0.353100\pi$
$30$		0			0
$31$	2.97154	−	5.14685i	0.533704	−	0.924402i	−0.465521	−	0.885037i	$-0.654133\pi$
$31$	2.97154	−	5.14685i	0.533704	−	0.924402i	0.999225	−	0.0393651i	$-0.0125335\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	7.65906			1.31352
$35$	5.16884	−	2.43764i	0.873694	−	0.412037i
$36$		0			0
$37$	−1.55673	−	2.69634i	−0.255926	−	0.443276i	0.709221	−	0.704986i	$-0.249047\pi$
$37$	−1.55673	−	2.69634i	−0.255926	−	0.443276i	−0.965147	+	0.261710i	$0.915714\pi$
$38$	−1.66946	−	0.963864i	−0.270822	−	0.156359i
$39$		0			0
$40$	1.87061	−	1.08000i	0.295769	−	0.170763i
$41$	−9.00600			−1.40650			−0.703251	−	0.710942i	$-0.748269\pi$
$41$	−9.00600			−1.40650			−0.703251	+	0.710942i	$0.748269\pi$
$42$		0			0
$43$		−	2.48924i		−	0.379605i	−0.981822	−	0.189803i	$-0.939215\pi$
$43$		−	2.48924i		−	0.379605i	0.981822	−	0.189803i	$-0.0607848\pi$
$44$	2.19270	−	2.48839i	0.330562	−	0.375139i
$45$		0			0
$46$	7.21952	+	4.16819i	1.06446	+	0.614566i
$47$	7.34212	−	4.23898i	1.07096	−	0.618318i	0.142515	−	0.989793i	$-0.454481\pi$
$47$	7.34212	−	4.23898i	1.07096	−	0.618318i	0.928443	+	0.371474i	$0.121148\pi$
$48$		0			0
$49$	6.90395	+	1.15564i	0.986278	+	0.165092i
$50$	−0.334422			−0.0472945
$51$		0			0
$52$	−3.06535	−	1.76978i	−0.425088	−	0.245424i
$53$	−4.83344	−	2.79059i	−0.663923	−	0.383316i	0.129847	−	0.991534i	$-0.458551\pi$
$53$	−4.83344	−	2.79059i	−0.663923	−	0.383316i	−0.793770	+	0.608218i	$0.791885\pi$
$54$		0			0
$55$	6.78914	−	2.28670i	0.915447	−	0.308338i
$56$	2.63666	+	0.219149i	0.352338	+	0.0292850i
$57$		0			0
$58$	2.39797	+	4.15341i	0.314869	+	0.545369i
$59$	−3.95479	−	2.28330i	−0.514870	−	0.297260i	0.219963	−	0.975508i	$-0.429406\pi$
$59$	−3.95479	−	2.28330i	−0.514870	−	0.297260i	−0.734833	+	0.678248i	$0.762740\pi$
$60$		0			0
$61$	−9.71354	+	5.60811i	−1.24369	+	0.718045i	−0.969844	−	0.243728i	$-0.921630\pi$
$61$	−9.71354	+	5.60811i	−1.24369	+	0.718045i	−0.273847	+	0.961773i	$0.588296\pi$
$62$	5.94307			0.754771
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.82272	−	6.62114i	−0.474150	−	0.821252i
$66$		0			0
$67$	1.46173	−	2.53179i	0.178578	−	0.309307i	−0.762815	−	0.646616i	$-0.776183\pi$
$67$	1.46173	−	2.53179i	0.178578	−	0.309307i	0.941394	+	0.337309i	$0.109517\pi$
$68$	3.82953	+	6.63294i	0.464399	+	0.804363i
$69$		0			0
$70$	4.69548	+	3.25753i	0.561217	+	0.389349i
$71$		−	14.9539i		−	1.77470i	−0.461093	−	0.887352i	$-0.652542\pi$
$71$		−	14.9539i		−	1.77470i	0.461093	−	0.887352i	$-0.347458\pi$
$72$		0			0
$73$	−0.486281	−	0.280755i	−0.0569149	−	0.0328598i	0.471273	−	0.881988i	$-0.343795\pi$
$73$	−0.486281	−	0.280755i	−0.0569149	−	0.0328598i	−0.528187	+	0.849128i	$0.677128\pi$
$74$	1.55673	−	2.69634i	0.180967	−	0.313444i
$75$		0			0
$76$		−	1.92773i		−	0.221126i
$77$	8.42924	+	2.43885i	0.960600	+	0.277933i
$78$		0			0
$79$	−6.63288	+	3.82950i	−0.746258	+	0.430852i	−0.824340	−	0.566095i	$-0.808454\pi$
$79$	−6.63288	+	3.82950i	−0.746258	+	0.430852i	0.0780826	+	0.996947i	$0.475120\pi$
$80$	1.87061	+	1.08000i	0.209141	+	0.120747i
$81$		0			0
$82$	−4.50300	−	7.79943i	−0.497273	−	0.861303i
$83$	−8.45117			−0.927637			−0.463818	−	0.885930i	$-0.653521\pi$
$83$	−8.45117			−0.927637			−0.463818	+	0.885930i	$0.653521\pi$
$84$		0			0
$85$			16.5435i			1.79440i
$86$	2.15574	−	1.24462i	0.232460	−	0.134211i
$87$		0			0
$88$	3.25136	+	0.654737i	0.346596	+	0.0697952i
$89$	−0.609275	+	0.351765i	−0.0645830	+	0.0372870i	−0.531944	−	0.846780i	$-0.678538\pi$
$89$	−0.609275	+	0.351765i	−0.0645830	+	0.0372870i	0.467361	+	0.884067i	$0.345205\pi$
$90$		0			0
$91$	0.775692	−	9.33262i	0.0813146	−	0.978324i
$92$			8.33638i			0.869128i
$93$		0			0
$94$	7.34212	+	4.23898i	0.757282	+	0.437217i
$95$	2.08194	−	3.60603i	0.213603	−	0.369971i
$96$		0			0
$97$	−1.23783			−0.125682			−0.0628412	−	0.998024i	$-0.520016\pi$
$97$	−1.23783			−0.125682			−0.0628412	+	0.998024i	$0.520016\pi$
$98$	2.45116	+	6.55682i	0.247604	+	0.662338i
$99$		0			0
$100$	−0.167211	−	0.289618i	−0.0167211	−	0.0289618i
$101$	−1.57357	+	2.72549i	−0.156576	+	0.271197i	−0.933632	−	0.358235i	$-0.883379\pi$
$101$	−1.57357	+	2.72549i	−0.156576	+	0.271197i	0.777056	+	0.629431i	$0.216712\pi$
$102$		0			0
$103$	−0.118651	−	0.205510i	−0.0116911	−	0.0202495i	0.860121	−	0.510091i	$-0.170388\pi$
$103$	−0.118651	−	0.205510i	−0.0116911	−	0.0202495i	−0.871812	+	0.489841i	$0.837055\pi$
$104$		−	3.53956i		−	0.347083i
$105$		0			0
$106$		−	5.58117i		−	0.542091i
$107$	5.40857	+	9.36792i	0.522866	+	0.905631i	0.999646	+	0.0266081i	$0.00847061\pi$
$107$	5.40857	+	9.36792i	0.522866	+	0.905631i	−0.476780	+	0.879023i	$0.658196\pi$
$108$		0			0
$109$	3.77972	+	2.18222i	0.362032	+	0.209019i	0.669972	−	0.742387i	$-0.266306\pi$
$109$	3.77972	+	2.18222i	0.362032	+	0.209019i	−0.307940	+	0.951406i	$0.599640\pi$
$110$	5.37491	+	4.73621i	0.512477	+	0.451580i
$111$		0			0
$112$	1.12854	+	2.39299i	0.106637	+	0.226116i
$113$		−	17.7468i		−	1.66948i	−0.550648	−	0.834738i	$-0.685619\pi$
$113$		−	17.7468i		−	1.66948i	0.550648	−	0.834738i	$-0.314381\pi$
$114$		0			0
$115$	−9.00327	+	15.5941i	−0.839560	+	1.45416i
$116$	−2.39797	+	4.15341i	−0.222646	+	0.385634i
$117$		0			0
$118$		−	4.56660i		−	0.420389i
$119$	−11.5508	+	16.6496i	−1.05886	+	1.52626i
$120$		0			0
$121$	10.1426	+	4.25757i	0.922058	+	0.387052i
$122$	−9.71354	−	5.60811i	−0.879422	−	0.507735i
$123$		0			0
$124$	2.97154	+	5.14685i	0.266852	+	0.462201i
$125$		−	11.5223i		−	1.03059i
$126$		0			0
$127$		−	12.6515i		−	1.12264i	−0.827598	−	0.561322i	$-0.810293\pi$
$127$		−	12.6515i		−	1.12264i	0.827598	−	0.561322i	$-0.189707\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	3.82272	−	6.62114i	0.335275	−	0.580713i
$131$	1.52954	+	2.64924i	0.133637	+	0.231466i	0.925076	−	0.379782i	$-0.124001\pi$
$131$	1.52954	+	2.64924i	0.133637	+	0.231466i	−0.791439	+	0.611248i	$0.790668\pi$
$132$		0			0
$133$	4.61303	−	2.17552i	0.400001	−	0.188642i
$134$	2.92346			0.252548
$135$		0			0
$136$	−3.82953	+	6.63294i	−0.328380	+	0.568770i
$137$	6.20778	+	3.58406i	0.530366	+	0.306207i	0.741166	−	0.671322i	$-0.234273\pi$
$137$	6.20778	+	3.58406i	0.530366	+	0.306207i	−0.210799	+	0.977529i	$0.567607\pi$
$138$		0			0
$139$		−	2.77438i		−	0.235320i	−0.993054	−	0.117660i	$-0.962461\pi$
$139$		−	2.77438i		−	0.235320i	0.993054	−	0.117660i	$-0.0375393\pi$
$140$	−0.473361	+	5.69517i	−0.0400063	+	0.481330i
$141$		0			0
$142$	12.9505	−	7.47696i	1.08678	−	0.627453i
$143$	2.31748	−	11.5084i	0.193798	−	0.962379i
$144$		0			0
$145$	−8.97134	+	5.17960i	−0.745029	+	0.430143i
$146$		−	0.561509i		−	0.0464708i
$147$		0			0
$148$	3.11347			0.255926
$149$	−11.7155	−	20.2918i	−0.959770	−	1.66237i	−0.723054	−	0.690792i	$-0.757262\pi$
$149$	−11.7155	−	20.2918i	−0.959770	−	1.66237i	−0.236716	−	0.971579i	$-0.576071\pi$
$150$		0			0
$151$	7.98285	+	4.60890i	0.649635	+	0.375067i	0.788317	−	0.615270i	$-0.210953\pi$
$151$	7.98285	+	4.60890i	0.649635	+	0.375067i	−0.138681	+	0.990337i	$0.544286\pi$
$152$	1.66946	−	0.963864i	0.135411	−	0.0781797i
$153$		0			0
$154$	2.10251	+	8.51936i	0.169425	+	0.686509i
$155$			12.8370i			1.03109i
$156$		0			0
$157$	−11.5804	+	20.0579i	−0.924218	+	1.60079i	−0.131403	+	0.991329i	$0.541948\pi$
$157$	−11.5804	+	20.0579i	−0.924218	+	1.60079i	−0.792814	+	0.609463i	$0.791385\pi$
$158$	−6.63288	−	3.82950i	−0.527684	−	0.304658i
$159$		0			0
$160$			2.15999i			0.170763i
$161$	−19.9489	+	9.40795i	−1.57219	+	0.741450i
$162$		0			0
$163$	−9.30376	−	16.1146i	−0.728727	−	1.26219i	−0.957422	−	0.288693i	$-0.906779\pi$
$163$	−9.30376	−	16.1146i	−0.728727	−	1.26219i	0.228695	−	0.973498i	$-0.426554\pi$
$164$	4.50300	−	7.79943i	0.351625	−	0.609033i
$165$		0			0
$166$	−4.22559	−	7.31893i	−0.327969	−	0.568059i
$167$	−21.3908			−1.65527			−0.827636	−	0.561265i	$-0.810315\pi$
$167$	−21.3908			−1.65527			−0.827636	+	0.561265i	$0.810315\pi$
$168$		0			0
$169$	0.471500			0.0362692
$170$	−14.3271	+	8.27177i	−1.09884	+	0.634416i
$171$		0			0
$172$	2.15574	+	1.24462i	0.164374	+	0.0949013i
$173$	−0.430083	−	0.744926i	−0.0326986	−	0.0566356i	0.849213	−	0.528050i	$-0.177077\pi$
$173$	−0.430083	−	0.744926i	−0.0326986	−	0.0566356i	−0.881912	+	0.471415i	$0.843743\pi$
$174$		0			0
$175$	0.504349	−	0.726981i	0.0381252	−	0.0549546i
$176$	1.05866	+	3.14313i	0.0797994	+	0.236922i
$177$		0			0
$178$	−0.609275	−	0.351765i	−0.0456671	−	0.0263659i
$179$	9.01762	+	5.20633i	0.674009	+	0.389139i	0.797594	−	0.603195i	$-0.206106\pi$
$179$	9.01762	+	5.20633i	0.674009	+	0.389139i	−0.123585	+	0.992334i	$0.539439\pi$
$180$		0			0
$181$	−7.02598			−0.522237			−0.261118	−	0.965307i	$-0.584091\pi$
$181$	−7.02598			−0.522237			−0.261118	+	0.965307i	$0.584091\pi$
$182$	8.47013	−	3.99454i	0.627848	−	0.296095i
$183$		0			0
$184$	−7.21952	+	4.16819i	−0.532230	+	0.307283i
$185$	5.82409	+	3.36254i	0.428196	+	0.247219i
$186$		0			0
$187$	−16.7940	+	19.0587i	−1.22810	+	1.39371i
$188$			8.47795i			0.618318i
$189$		0			0
$190$	4.16388			0.302080
$191$	−4.03039	+	2.32695i	−0.291629	+	0.168372i	−0.638676	−	0.769476i	$-0.720518\pi$
$191$	−4.03039	+	2.32695i	−0.291629	+	0.168372i	0.347047	+	0.937848i	$0.387184\pi$
$192$		0			0
$193$	13.5837	+	7.84257i	0.977778	+	0.564521i	0.901599	−	0.432574i	$-0.142394\pi$
$193$	13.5837	+	7.84257i	0.977778	+	0.564521i	0.0761796	+	0.997094i	$0.475728\pi$
$194$	−0.618915	−	1.07199i	−0.0444355	−	0.0769645i
$195$		0			0
$196$	−4.45279	+	5.40117i	−0.318056	+	0.385798i
$197$	6.39141			0.455369			0.227684	−	0.973735i	$-0.426885\pi$
$197$	6.39141			0.455369			0.227684	+	0.973735i	$0.426885\pi$
$198$		0			0
$199$	12.8469	−	22.2515i	0.910694	−	1.57737i	0.0976086	−	0.995225i	$-0.468881\pi$
$199$	12.8469	−	22.2515i	0.910694	−	1.57737i	0.813086	−	0.582144i	$-0.197786\pi$
$200$	0.167211	−	0.289618i	0.0118236	−	0.0204791i
$201$		0			0
$202$	−3.14713			−0.221431
$203$	−12.6453	−	1.05103i	−0.887524	−	0.0737676i
$204$		0			0
$205$	16.8467	−	9.72646i	1.17663	−	0.679326i
$206$	0.118651	−	0.205510i	0.00826683	−	0.0143186i
$207$		0			0
$208$	3.06535	−	1.76978i	0.212544	−	0.122712i
$209$	6.05909	−	2.04081i	0.419116	−	0.141166i
$210$		0			0
$211$		−	16.6604i		−	1.14695i	−0.819224	−	0.573474i	$-0.805595\pi$
$211$		−	16.6604i		−	1.14695i	0.819224	−	0.573474i	$-0.194405\pi$
$212$	4.83344	−	2.79059i	0.331962	−	0.191658i
$213$		0			0
$214$	−5.40857	+	9.36792i	−0.369722	+	0.640378i
$215$	2.68837	+	4.65639i	0.183345	+	0.317563i
$216$		0			0
$217$	−8.96286	+	12.9193i	−0.608438	+	0.877018i
$218$			4.36445i			0.295598i
$219$		0			0
$220$	−1.41423	+	7.02291i	−0.0953473	+	0.473485i
$221$	23.4777	+	13.5549i	1.57928	+	0.911799i
$222$		0			0
$223$	9.81557			0.657299			0.328650	−	0.944452i	$-0.393406\pi$
$223$	9.81557			0.657299			0.328650	+	0.944452i	$0.393406\pi$
$224$	−1.50812	+	2.17384i	−0.100765	+	0.145246i
$225$		0			0
$226$	15.3691	−	8.87338i	1.02234	−	0.590249i
$227$	−5.08719	+	8.81128i	−0.337649	+	0.584825i	−0.983990	−	0.178224i	$-0.942965\pi$
$227$	−5.08719	+	8.81128i	−0.337649	+	0.584825i	0.646341	+	0.763049i	$0.276298\pi$
$228$		0			0
$229$	−13.3669	−	23.1522i	−0.883310	−	1.52994i	−0.847639	−	0.530574i	$-0.821976\pi$
$229$	−13.3669	−	23.1522i	−0.883310	−	1.52994i	−0.0356712	−	0.999364i	$-0.511357\pi$
$230$	−18.0065			−1.18732
$231$		0			0
$232$	−4.79594			−0.314869
$233$	2.09943	+	3.63631i	0.137538	+	0.238223i	0.926564	−	0.376137i	$-0.122748\pi$
$233$	2.09943	+	3.63631i	0.137538	+	0.238223i	−0.789026	+	0.614360i	$0.789414\pi$
$234$		0			0
$235$	−9.15617	+	15.8589i	−0.597283	+	1.03452i
$236$	3.95479	−	2.28330i	0.257435	−	0.148630i
$237$		0			0
$238$	−20.1943	−	1.67848i	−1.30900	−	0.108800i
$239$	19.4583			1.25865			0.629326	−	0.777141i	$-0.283331\pi$
$239$	19.4583			1.25865			0.629326	+	0.777141i	$0.283331\pi$
$240$		0			0
$241$	4.53621	+	2.61898i	0.292203	+	0.168704i	0.638935	−	0.769261i	$-0.279375\pi$
$241$	4.53621	+	2.61898i	0.292203	+	0.168704i	−0.346732	+	0.937964i	$0.612709\pi$
$242$	1.38416	+	10.9126i	0.0889770	+	0.701486i
$243$		0			0
$244$		−	11.2162i		−	0.718045i
$245$	−14.1627	+	5.29449i	−0.904821	+	0.338252i
$246$		0			0
$247$	−3.41166	−	5.90916i	−0.217079	−	0.375991i
$248$	−2.97154	+	5.14685i	−0.188693	+	0.326825i
$249$		0			0
$250$	9.97863	−	5.76116i	0.631104	−	0.364368i
$251$			17.2995i			1.09193i	0.837807	+	0.545967i	$0.183838\pi$
$251$			17.2995i			1.09193i	−0.837807	+	0.545967i	$0.816162\pi$
$252$		0			0
$253$	−26.2023	+	8.82539i	−1.64732	+	0.554848i
$254$	10.9566	−	6.32577i	0.687476	−	0.396914i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−22.9253	+	13.2359i	−1.43004	+	0.825635i	−0.997123	−	0.0757980i	$-0.975850\pi$
$257$	−22.9253	+	13.2359i	−1.43004	+	0.825635i	−0.432919	+	0.901433i	$0.642516\pi$
$258$		0			0
$259$	3.51368	+	7.45050i	0.218329	+	0.462951i
$260$	7.64544			0.474150
$261$		0			0
$262$	−1.52954	+	2.64924i	−0.0944954	+	0.163671i
$263$	6.30039	−	10.9126i	0.388499	−	0.672900i	−0.603749	−	0.797175i	$-0.706327\pi$
$263$	6.30039	−	10.9126i	0.388499	−	0.672900i	0.992248	+	0.124275i	$0.0396604\pi$
$264$		0			0
$265$	12.0553			0.740551
$266$	4.19057	+	2.90724i	0.256940	+	0.178254i
$267$		0			0
$268$	1.46173	+	2.53179i	0.0892892	+	0.154653i
$269$	16.2413	+	9.37693i	0.990251	+	0.571722i	0.905349	−	0.424668i	$-0.139609\pi$
$269$	16.2413	+	9.37693i	0.990251	+	0.571722i	0.0849016	+	0.996389i	$0.472942\pi$
$270$		0			0
$271$	3.87768	−	2.23878i	0.235552	−	0.135996i	−0.377579	−	0.925978i	$-0.623243\pi$
$271$	3.87768	−	2.23878i	0.235552	−	0.135996i	0.613131	+	0.789981i	$0.289910\pi$
$272$	−7.65906			−0.464399
$273$		0			0
$274$			7.16812i			0.433042i
$275$	0.733287	−	0.832173i	0.0442189	−	0.0501819i
$276$		0			0
$277$	−8.09768	−	4.67520i	−0.486543	−	0.280905i	0.236596	−	0.971608i	$-0.423968\pi$
$277$	−8.09768	−	4.67520i	−0.486543	−	0.280905i	−0.723139	+	0.690703i	$0.757301\pi$
$278$	2.40268	−	1.38719i	0.144103	−	0.0831981i
$279$		0			0
$280$	−5.16884	+	2.43764i	−0.308897	+	0.145677i
$281$	−23.8976			−1.42561			−0.712807	−	0.701361i	$-0.752576\pi$
$281$	−23.8976			−1.42561			−0.712807	+	0.701361i	$0.752576\pi$
$282$		0			0
$283$	−15.6461	−	9.03326i	−0.930063	−	0.536972i	−0.0432312	−	0.999065i	$-0.513765\pi$
$283$	−15.6461	−	9.03326i	−0.930063	−	0.536972i	−0.886831	+	0.462093i	$0.847099\pi$
$284$	12.9505	+	7.47696i	0.768469	+	0.443676i
$285$		0			0
$286$	11.1253	−	3.74719i	0.657852	−	0.221576i
$287$	23.7458	+	1.97366i	1.40167	+	0.116501i
$288$		0			0
$289$	−20.8306	−	36.0797i	−1.22533	−	2.12234i
$290$	−8.97134	−	5.17960i	−0.526815	−	0.304157i
$291$		0			0
$292$	0.486281	−	0.280755i	0.0284574	−	0.0164299i
$293$	−16.3262			−0.953785			−0.476893	−	0.878962i	$-0.658237\pi$
$293$	−16.3262			−0.953785			−0.476893	+	0.878962i	$0.658237\pi$
$294$		0			0
$295$	9.86383			0.574294
$296$	1.55673	+	2.69634i	0.0904834	+	0.156722i
$297$		0			0
$298$	11.7155	−	20.2918i	0.678660	−	1.17547i
$299$	14.7536	+	25.5539i	0.853221	+	1.47782i
$300$		0			0
$301$	−0.545514	+	6.56327i	−0.0314429	+	0.378301i
$302$			9.21781i			0.530425i
$303$		0			0
$304$	1.66946	+	0.963864i	0.0957502	+	0.0552814i
$305$	12.1135	−	20.9812i	0.693617	−	1.20138i
$306$		0			0
$307$		−	6.91177i		−	0.394476i	−0.980356	−	0.197238i	$-0.936803\pi$
$307$		−	6.91177i		−	0.394476i	0.980356	−	0.197238i	$-0.0631971\pi$
$308$	−6.32672	+	6.08051i	−0.360499	+	0.346469i
$309$		0			0
$310$	−11.1172	+	6.41850i	−0.631413	+	0.364546i
$311$	0.717875	+	0.414465i	0.0407069	+	0.0235022i	0.520215	−	0.854035i	$-0.325852\pi$
$311$	0.717875	+	0.414465i	0.0407069	+	0.0235022i	−0.479508	+	0.877537i	$0.659185\pi$
$312$		0			0
$313$	8.66175	+	15.0026i	0.489591	+	0.847996i	0.999928	−	0.0119780i	$-0.00381282\pi$
$313$	8.66175	+	15.0026i	0.489591	+	0.847996i	−0.510337	+	0.859974i	$0.670479\pi$
$314$	−23.1608			−1.30704
$315$		0			0
$316$		−	7.65899i		−	0.430852i
$317$	24.1286	−	13.9306i	1.35520	−	0.782423i	0.366224	−	0.930527i	$-0.380650\pi$
$317$	24.1286	−	13.9306i	1.35520	−	0.782423i	0.988972	+	0.148104i	$0.0473170\pi$
$318$		0			0
$319$	−15.5933	−	3.14008i	−0.873058	−	0.175811i
$320$	−1.87061	+	1.08000i	−0.104570	+	0.0603737i
$321$		0			0
$322$	−18.1220	−	12.5723i	−1.00990	−	0.700624i
$323$			14.7646i			0.821524i
$324$		0			0
$325$	−1.02512	−	0.591854i	−0.0568635	−	0.0328302i
$326$	9.30376	−	16.1146i	0.515288	−	0.892504i
$327$		0			0
$328$	9.00600			0.497273
$329$	−20.2876	+	9.56772i	−1.11849	+	0.527485i
$330$		0			0
$331$	2.76388	+	4.78718i	0.151916	+	0.263127i	0.931932	−	0.362633i	$-0.118122\pi$
$331$	2.76388	+	4.78718i	0.151916	+	0.263127i	−0.780015	+	0.625760i	$0.784789\pi$
$332$	4.22559	−	7.31893i	0.231909	−	0.401679i
$333$		0			0
$334$	−10.6954	−	18.5250i	−0.585227	−	1.01364i
$335$			6.31465i			0.345006i
$336$		0			0
$337$			23.7409i			1.29325i	0.762809	+	0.646624i	$0.223820\pi$
$337$			23.7409i			1.29325i	−0.762809	+	0.646624i	$0.776180\pi$
$338$	0.235750	+	0.408331i	0.0128231	+	0.0222103i
$339$		0			0
$340$	−14.3271	−	8.27177i	−0.776997	−	0.448600i
$341$	−13.0314	+	14.7887i	−0.705688	+	0.800852i
$342$		0			0
$343$	−17.9501	−	4.56003i	−0.969214	−	0.246219i
$344$			2.48924i			0.134211i
$345$		0			0
$346$	0.430083	−	0.744926i	0.0231214	−	0.0400475i
$347$	10.1900	−	17.6496i	0.547027	−	0.947478i	−0.451450	−	0.892297i	$-0.649093\pi$
$347$	10.1900	−	17.6496i	0.547027	−	0.947478i	0.998476	−	0.0551813i	$-0.0175737\pi$
$348$		0			0
$349$		−	11.3460i		−	0.607338i	−0.952778	−	0.303669i	$-0.901788\pi$
$349$		−	11.3460i		−	0.607338i	0.952778	−	0.303669i	$-0.0982118\pi$
$350$	0.881758	+	0.0732884i	0.0471319	+	0.00391743i
$351$		0			0
$352$	−2.19270	+	2.48839i	−0.116871	+	0.132632i
$353$	8.88905	+	5.13209i	0.473116	+	0.273154i	0.717543	−	0.696514i	$-0.245267\pi$
$353$	8.88905	+	5.13209i	0.473116	+	0.273154i	−0.244427	+	0.969668i	$0.578600\pi$
$354$		0			0
$355$	16.1502	+	27.9730i	0.857163	+	1.48465i
$356$		−	0.703530i		−	0.0372870i
$357$		0			0
$358$			10.4127i			0.550326i
$359$	−8.12523	−	14.0733i	−0.428833	−	0.742761i	0.567937	−	0.823072i	$-0.307742\pi$
$359$	−8.12523	−	14.0733i	−0.428833	−	0.742761i	−0.996770	+	0.0803116i	$0.974408\pi$
$360$		0			0
$361$	−7.64193	+	13.2362i	−0.402207	+	0.696643i
$362$	−3.51299	−	6.08468i	−0.184639	−	0.319803i
$363$		0			0
$364$	7.69444	+	5.33808i	0.403298	+	0.279791i
$365$	1.21286			0.0634838
$366$		0			0
$367$	−18.3681	+	31.8145i	−0.958808	+	1.66070i	−0.233407	+	0.972379i	$0.574987\pi$
$367$	−18.3681	+	31.8145i	−0.958808	+	1.66070i	−0.725402	+	0.688326i	$0.758346\pi$
$368$	−7.21952	−	4.16819i	−0.376344	−	0.217282i
$369$		0			0
$370$			6.72508i			0.349620i
$371$	12.1326	+	8.41707i	0.629892	+	0.436992i
$372$		0			0
$373$	0.721045	−	0.416295i	0.0373343	−	0.0215550i	−0.481217	−	0.876602i	$-0.659805\pi$
$373$	0.721045	−	0.416295i	0.0373343	−	0.0215550i	0.518551	+	0.855047i	$0.326472\pi$
$374$	−24.9023	−	5.01467i	−1.28767	−	0.259303i
$375$		0			0
$376$	−7.34212	+	4.23898i	−0.378641	+	0.218609i
$377$			16.9755i			0.874284i
$378$		0			0
$379$	−35.9823			−1.84829			−0.924143	−	0.382047i	$-0.875219\pi$
$379$	−35.9823			−1.84829			−0.924143	+	0.382047i	$0.875219\pi$
$380$	2.08194	+	3.60603i	0.106801	+	0.184985i
$381$		0			0
$382$	−4.03039	−	2.32695i	−0.206213	−	0.119057i
$383$	1.51172	−	0.872794i	0.0772454	−	0.0445977i	−0.460880	−	0.887463i	$-0.652466\pi$
$383$	1.51172	−	0.872794i	0.0772454	−	0.0445977i	0.538125	+	0.842865i	$0.319133\pi$
$384$		0			0
$385$	−18.4018	+	4.54141i	−0.937841	+	0.231452i
$386$			15.6851i			0.798353i
$387$		0			0
$388$	0.618915	−	1.07199i	0.0314206	−	0.0544221i
$389$	−19.9922	−	11.5425i	−1.01364	−	0.585228i	−0.101388	−	0.994847i	$-0.532328\pi$
$389$	−19.9922	−	11.5425i	−1.01364	−	0.585228i	−0.912257	+	0.409619i	$0.865662\pi$
$390$		0			0
$391$		−	63.8489i		−	3.22898i
$392$	−6.90395	−	1.15564i	−0.348702	−	0.0583688i
$393$		0			0
$394$	3.19570	+	5.53512i	0.160997	+	0.278855i
$395$	8.27169	−	14.3270i	0.416194	−	0.720869i
$396$		0			0
$397$	−3.99083	−	6.91231i	−0.200294	−	0.346919i	0.748329	−	0.663327i	$-0.230856\pi$
$397$	−3.99083	−	6.91231i	−0.200294	−	0.346919i	−0.948623	+	0.316408i	$0.897523\pi$
$398$	25.6938			1.28792
$399$		0			0
$400$	0.334422			0.0167211
$401$	−8.88905	+	5.13209i	−0.443898	+	0.256285i	−0.705250	−	0.708959i	$-0.749165\pi$
$401$	−8.88905	+	5.13209i	−0.443898	+	0.256285i	0.261352	+	0.965244i	$0.415832\pi$
$402$		0			0
$403$	18.2176	+	10.5179i	0.907483	+	0.523936i
$404$	−1.57357	−	2.72549i	−0.0782878	−	0.135598i
$405$		0			0
$406$	−5.41242	−	11.4766i	−0.268614	−	0.569576i
$407$	3.29610	+	9.78603i	0.163382	+	0.485075i
$408$		0			0
$409$	6.14427	+	3.54740i	0.303815	+	0.175407i	0.644155	−	0.764895i	$-0.277209\pi$
$409$	6.14427	+	3.54740i	0.303815	+	0.175407i	−0.340341	+	0.940302i	$0.610542\pi$
$410$	16.8467	+	9.72646i	0.832001	+	0.480356i
$411$		0			0
$412$	0.237303			0.0116911
$413$	9.92705	+	6.88697i	0.488478	+	0.338886i
$414$		0			0
$415$	15.8089	−	9.12725i	0.776026	−	0.448039i
$416$	3.06535	+	1.76978i	0.150291	+	0.0867707i
$417$		0			0
$418$	4.79694	+	4.22692i	0.234626	+	0.206746i
$419$		−	20.6094i		−	1.00684i	−0.864043	−	0.503418i	$-0.832076\pi$
$419$		−	20.6094i		−	1.00684i	0.864043	−	0.503418i	$-0.167924\pi$
$420$		0			0
$421$	0.107995			0.00526337			0.00263169	−	0.999997i	$-0.499162\pi$
$421$	0.107995			0.00526337			0.00263169	+	0.999997i	$0.499162\pi$
$422$	14.4283	−	8.33019i	0.702359	−	0.405507i
$423$		0			0
$424$	4.83344	+	2.79059i	0.234732	+	0.135523i
$425$	1.28068	+	2.21820i	0.0621221	+	0.107599i
$426$		0			0
$427$	26.8403	−	12.6580i	1.29889	−	0.612562i
$428$	−10.8171			−0.522866
$429$		0			0
$430$	−2.68837	+	4.65639i	−0.129645	+	0.224551i
$431$	20.2561	−	35.0846i	0.975702	−	1.68997i	0.298105	−	0.954533i	$-0.403646\pi$
$431$	20.2561	−	35.0846i	0.975702	−	1.68997i	0.677598	−	0.735433i	$-0.263021\pi$
$432$		0			0
$433$	−3.27124			−0.157206			−0.0786028	−	0.996906i	$-0.525046\pi$
$433$	−3.27124			−0.157206			−0.0786028	+	0.996906i	$0.525046\pi$
$434$	−15.6699	−	1.30242i	−0.752177	−	0.0625181i
$435$		0			0
$436$	−3.77972	+	2.18222i	−0.181016	+	0.104510i
$437$	−8.03514	+	13.9173i	−0.384373	+	0.665753i
$438$		0			0
$439$	5.95716	−	3.43937i	0.284320	−	0.164152i	−0.351058	−	0.936354i	$-0.614178\pi$
$439$	5.95716	−	3.43937i	0.284320	−	0.164152i	0.635377	+	0.772202i	$0.280845\pi$
$440$	−6.78914	+	2.28670i	−0.323659	+	0.109014i
$441$		0			0
$442$			27.1097i			1.28948i
$443$	−5.64003	+	3.25627i	−0.267966	+	0.154710i	−0.627963	−	0.778243i	$-0.716111\pi$
$443$	−5.64003	+	3.25627i	−0.267966	+	0.154710i	0.359997	+	0.932953i	$0.382778\pi$
$444$		0			0
$445$	0.759811	−	1.31603i	0.0360185	−	0.0623858i
$446$	4.90779	+	8.50054i	0.232390	+	0.402512i
$447$		0			0
$448$	−2.63666	−	0.219149i	−0.124570	−	0.0103538i
$449$		−	13.3141i		−	0.628331i	−0.949368	−	0.314165i	$-0.898275\pi$
$449$		−	13.3141i		−	0.628331i	0.949368	−	0.314165i	$-0.101725\pi$
$450$		0			0
$451$	29.2817	+	5.89657i	1.37882	+	0.277658i
$452$	15.3691	+	8.87338i	0.722904	+	0.417369i
$453$		0			0
$454$	−10.1744			−0.477508
$455$	8.62819	+	18.2954i	0.404496	+	0.857704i
$456$		0			0
$457$	−22.5222	+	13.0032i	−1.05354	+	0.608263i	−0.923639	−	0.383264i	$-0.874800\pi$
$457$	−22.5222	+	13.0032i	−1.05354	+	0.608263i	−0.129904	+	0.991527i	$0.541467\pi$
$458$	13.3669	−	23.1522i	0.624594	−	1.08183i
$459$		0			0
$460$	−9.00327	−	15.5941i	−0.419780	−	0.727080i
$461$	−15.8542			−0.738404			−0.369202	−	0.929349i	$-0.620369\pi$
$461$	−15.8542			−0.738404			−0.369202	+	0.929349i	$0.620369\pi$
$462$		0			0
$463$	−27.6377			−1.28443			−0.642216	−	0.766524i	$-0.721985\pi$
$463$	−27.6377			−1.28443			−0.642216	+	0.766524i	$0.721985\pi$
$464$	−2.39797	−	4.15341i	−0.111323	−	0.192817i
$465$		0			0
$466$	−2.09943	+	3.63631i	−0.0972540	+	0.168449i
$467$	3.49877	−	2.02001i	0.161904	−	0.0934751i	−0.416859	−	0.908971i	$-0.636869\pi$
$467$	3.49877	−	2.02001i	0.161904	−	0.0934751i	0.578763	+	0.815496i	$0.303536\pi$
$468$		0			0
$469$	−4.40892	+	6.35512i	−0.203585	+	0.293452i
$470$	−18.3123			−0.844685
$471$		0			0
$472$	3.95479	+	2.28330i	0.182034	+	0.105097i
$473$	−1.62980	+	8.09340i	−0.0749381	+	0.372135i
$474$		0			0
$475$		−	0.644675i		−	0.0295797i
$476$	−8.64357	−	18.3281i	−0.396177	−	0.840065i
$477$		0			0
$478$	9.72914	+	16.8514i	0.445001	+	0.770764i
$479$	3.06163	−	5.30290i	0.139890	−	0.242296i	−0.787565	−	0.616231i	$-0.788659\pi$
$479$	3.06163	−	5.30290i	0.139890	−	0.242296i	0.927455	+	0.373936i	$0.121992\pi$
$480$		0			0
$481$	9.54388	−	5.51016i	0.435163	−	0.251242i
$482$			5.23797i			0.238583i
$483$		0			0
$484$	−8.75848	+	6.65500i	−0.398113	+	0.302500i
$485$	2.31550	−	1.33685i	0.105141	−	0.0607033i
$486$		0			0
$487$	3.06196	−	5.30347i	0.138751	−	0.240323i	−0.788273	−	0.615325i	$-0.789025\pi$
$487$	3.06196	−	5.30347i	0.138751	−	0.240323i	0.927024	+	0.375002i	$0.122358\pi$
$488$	9.71354	−	5.60811i	0.439711	−	0.253867i
$489$		0			0
$490$	−11.6665	−	9.61800i	−0.527039	−	0.434497i
$491$	20.9024			0.943311			0.471656	−	0.881783i	$-0.343657\pi$
$491$	20.9024			0.943311			0.471656	+	0.881783i	$0.343657\pi$
$492$		0			0
$493$	18.3662	−	31.8112i	0.827173	−	1.43270i
$494$	3.41166	−	5.90916i	0.153498	−	0.265866i
$495$		0			0
$496$	−5.94307			−0.266852
$497$	−3.27714	+	39.4284i	−0.147000	+	1.76861i
$498$		0			0
$499$	13.3081	+	23.0503i	0.595753	+	1.03188i	0.993440	+	0.114354i	$0.0364798\pi$
$499$	13.3081	+	23.0503i	0.595753	+	1.03188i	−0.397687	+	0.917521i	$0.630187\pi$
$500$	9.97863	+	5.76116i	0.446258	+	0.257647i
$501$		0			0
$502$	−14.9818	+	8.64975i	−0.668670	+	0.386057i
$503$	−15.2781			−0.681215			−0.340607	−	0.940206i	$-0.610633\pi$
$503$	−15.2781			−0.681215			−0.340607	+	0.940206i	$0.610633\pi$
$504$		0			0
$505$		−	6.79779i		−	0.302497i
$506$	−20.7442	−	18.2792i	−0.922191	−	0.812608i
$507$		0			0
$508$	10.9566	+	6.32577i	0.486119	+	0.280661i
$509$	−13.3048	+	7.68152i	−0.589724	+	0.340478i	−0.764989	−	0.644044i	$-0.777255\pi$
$509$	−13.3048	+	7.68152i	−0.589724	+	0.340478i	0.175264	+	0.984521i	$0.443922\pi$
$510$		0			0
$511$	1.22063	+	0.846822i	0.0539975	+	0.0374612i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−22.9253	−	13.2359i	−1.01119	−	0.583812i
$515$	0.443901	+	0.256286i	0.0195606	+	0.0112933i
$516$		0			0
$517$	−26.6473	+	8.97526i	−1.17195	+	0.394732i
$518$	−4.69548	+	6.76818i	−0.206308	+	0.297377i
$519$		0			0
$520$	3.82272	+	6.62114i	0.167637	+	0.290356i
$521$	−15.9036	−	9.18197i	−0.696751	−	0.402269i	0.109385	−	0.993999i	$-0.465112\pi$
$521$	−15.9036	−	9.18197i	−0.696751	−	0.402269i	−0.806136	+	0.591730i	$0.798445\pi$
$522$		0			0
$523$	33.5412	−	19.3650i	1.46666	−	0.846774i	0.467352	−	0.884071i	$-0.345208\pi$
$523$	33.5412	−	19.3650i	1.46666	−	0.846774i	0.999304	+	0.0372968i	$0.0118747\pi$
$524$	−3.05908			−0.133637
$525$		0			0
$526$	12.6008			0.549420
$527$	−22.7592	−	39.4201i	−0.991406	−	1.71716i
$528$		0			0
$529$	23.2477	−	40.2661i	1.01077	−	1.75070i
$530$	6.02765	+	10.4402i	0.261824	+	0.453493i
$531$		0			0
$532$	−0.422460	+	5.08276i	−0.0183160	+	0.220366i
$533$		−	31.8773i		−	1.38076i
$534$		0			0
$535$	−20.2347	−	11.6825i	−0.874820	−	0.505078i
$536$	−1.46173	+	2.53179i	−0.0631370	+	0.109357i
$537$		0			0
$538$			18.7539i			0.808536i
$539$	−21.6906	−	8.27768i	−0.934278	−	0.356545i
$540$		0			0
$541$	25.5849	−	14.7714i	1.09998	−	0.635073i	0.163763	−	0.986500i	$-0.447637\pi$
$541$	25.5849	−	14.7714i	1.09998	−	0.635073i	0.936215	+	0.351426i	$0.114303\pi$
$542$	3.87768	+	2.23878i	0.166561	+	0.0961638i
$543$		0			0
$544$	−3.82953	−	6.63294i	−0.164190	−	0.284385i
$545$	−9.42718			−0.403816
$546$		0			0
$547$		−	8.96112i		−	0.383150i	−0.981478	−	0.191575i	$-0.938640\pi$
$547$		−	8.96112i		−	0.383150i	0.981478	−	0.191575i	$-0.0613595\pi$
$548$	−6.20778	+	3.58406i	−0.265183	+	0.153104i
$549$		0			0
$550$	1.08733	+	0.218959i	0.0463637	+	0.00933643i
$551$	−8.00664	+	4.62264i	−0.341094	+	0.196931i
$552$		0			0
$553$	18.3279	−	8.64349i	0.779381	−	0.367558i
$554$		−	9.35040i		−	0.397260i
$555$		0			0
$556$	2.40268	+	1.38719i	0.101896	+	0.0588299i
$557$	−11.1860	+	19.3748i	−0.473968	+	0.820936i	−0.999556	−	0.0298032i	$-0.990512\pi$
$557$	−11.1860	+	19.3748i	−0.473968	+	0.820936i	0.525588	+	0.850739i	$0.323845\pi$
$558$		0			0
$559$	8.81081			0.372658
$560$	−4.69548	−	3.25753i	−0.198420	−	0.137656i
$561$		0			0
$562$	−11.9488	−	20.6960i	−0.504030	−	0.873006i
$563$	−12.3032	+	21.3098i	−0.518518	+	0.898100i	0.481250	+	0.876583i	$0.340183\pi$
$563$	−12.3032	+	21.3098i	−0.518518	+	0.898100i	−0.999768	+	0.0215165i	$0.993151\pi$
$564$		0			0
$565$	19.1665	+	33.1973i	0.806339	+	1.39662i
$566$		−	18.0665i		−	0.759393i
$567$		0			0
$568$			14.9539i			0.627453i
$569$	20.0433	+	34.7160i	0.840258	+	1.45537i	0.889677	+	0.456591i	$0.150930\pi$
$569$	20.0433	+	34.7160i	0.840258	+	1.45537i	−0.0494186	+	0.998778i	$0.515737\pi$
$570$		0			0
$571$	10.6799	+	6.16602i	0.446938	+	0.258040i	0.706536	−	0.707677i	$-0.250257\pi$
$571$	10.6799	+	6.16602i	0.446938	+	0.258040i	−0.259598	+	0.965717i	$0.583590\pi$
$572$	8.80781	+	7.76119i	0.368273	+	0.324512i
$573$		0			0
$574$	10.1636	+	21.5513i	0.424222	+	0.899533i
$575$			2.78787i			0.116262i
$576$		0			0
$577$	−8.58087	+	14.8625i	−0.357226	+	0.618734i	−0.987496	−	0.157642i	$-0.949611\pi$
$577$	−8.58087	+	14.8625i	−0.357226	+	0.618734i	0.630270	+	0.776376i	$0.282944\pi$
$578$	20.8306	−	36.0797i	0.866440	−	1.50072i
$579$		0			0
$580$		−	10.3592i		−	0.430143i
$581$	22.2829	+	1.85207i	0.924449	+	0.0768367i
$582$		0			0
$583$	13.8881	+	12.2378i	0.575187	+	0.506839i
$584$	0.486281	+	0.280755i	0.0201225	+	0.0116177i
$585$		0			0
$586$	−8.16309	−	14.1389i	−0.337214	−	0.584072i
$587$		−	27.7349i		−	1.14474i	−0.819995	−	0.572371i	$-0.806024\pi$
$587$		−	27.7349i		−	1.14474i	0.819995	−	0.572371i	$-0.193976\pi$
$588$		0			0
$589$			11.4566i			0.472062i
$590$	4.93191	+	8.54232i	0.203044	+	0.351682i
$591$		0			0
$592$	−1.55673	+	2.69634i	−0.0639814	+	0.110819i
$593$	10.2740	+	17.7950i	0.421901	+	0.730753i	0.996125	−	0.0879443i	$-0.0280298\pi$
$593$	10.2740	+	17.7950i	0.421901	+	0.730753i	−0.574225	+	0.818698i	$0.694696\pi$
$594$		0			0
$595$	3.62550	−	43.6197i	0.148631	−	1.78823i
$596$	23.4310			0.959770
$597$		0			0
$598$	−14.7536	+	25.5539i	−0.603319	+	1.04498i
$599$	−26.0773	−	15.0557i	−1.06549	−	0.615161i	−0.138544	−	0.990356i	$-0.544242\pi$
$599$	−26.0773	−	15.0557i	−1.06549	−	0.615161i	−0.926946	+	0.375195i	$0.877576\pi$
$600$		0			0
$601$		−	17.8081i		−	0.726406i	−0.931710	−	0.363203i	$-0.881683\pi$
$601$		−	17.8081i		−	0.726406i	0.931710	−	0.363203i	$-0.118317\pi$
$602$	−5.95672	+	2.80921i	−0.242778	+	0.114495i
$603$		0			0
$604$	−7.98285	+	4.60890i	−0.324818	+	0.187534i
$605$	−23.5711	+	2.98977i	−0.958301	+	0.121552i
$606$		0			0
$607$	−4.13802	+	2.38909i	−0.167957	+	0.0969700i	−0.581622	−	0.813459i	$-0.697582\pi$
$607$	−4.13802	+	2.38909i	−0.167957	+	0.0969700i	0.413665	+	0.910429i	$0.364248\pi$
$608$			1.92773i			0.0781797i
$609$		0			0
$610$	24.2270			0.980922
$611$	15.0041	+	25.9879i	0.607002	+	1.05136i
$612$		0			0
$613$	31.0386	+	17.9202i	1.25364	+	0.723788i	0.971830	−	0.235683i	$-0.0757325\pi$
$613$	31.0386	+	17.9202i	1.25364	+	0.723788i	0.281808	+	0.959471i	$0.409066\pi$
$614$	5.98577	−	3.45589i	0.241566	−	0.139468i
$615$		0			0
$616$	−8.42924	−	2.43885i	−0.339624	−	0.0982641i
$617$			26.4982i			1.06678i	0.845871	+	0.533388i	$0.179081\pi$
$617$			26.4982i			1.06678i	−0.845871	+	0.533388i	$0.820919\pi$
$618$		0			0
$619$	10.4961	−	18.1798i	0.421874	−	0.730707i	−0.574249	−	0.818681i	$-0.694706\pi$
$619$	10.4961	−	18.1798i	0.421874	−	0.730707i	0.996123	+	0.0879736i	$0.0280391\pi$
$620$	−11.1172	−	6.41850i	−0.446476	−	0.257773i
$621$		0			0
$622$			0.828930i			0.0332371i
$623$	1.68354	−	0.793963i	0.0674496	−	0.0318094i
$624$		0			0
$625$	11.6080	+	20.1057i	0.464321	+	0.804228i
$626$	−8.66175	+	15.0026i	−0.346193	+	0.599624i
$627$		0			0
$628$	−11.5804	−	20.0579i	−0.462109	−	0.800396i
$629$	−23.8463			−0.950813
$630$		0			0
$631$	−3.84169			−0.152935			−0.0764676	−	0.997072i	$-0.524364\pi$
$631$	−3.84169			−0.152935			−0.0764676	+	0.997072i	$0.524364\pi$
$632$	6.63288	−	3.82950i	0.263842	−	0.152329i
$633$		0			0
$634$	24.1286	+	13.9306i	0.958268	+	0.553256i
$635$	13.6636	+	23.6661i	0.542225	+	0.939161i
$636$		0			0
$637$	−4.09047	+	24.4370i	−0.162070	+	0.968227i
$638$	−5.07727	−	15.0742i	−0.201011	−	0.596795i
$639$		0			0
$640$	−1.87061	−	1.08000i	−0.0739424	−	0.0426906i
$641$	22.0788	+	12.7472i	0.872061	+	0.503485i	0.868033	−	0.496507i	$-0.165384\pi$
$641$	22.0788	+	12.7472i	0.872061	+	0.503485i	0.00402867	+	0.999992i	$0.498718\pi$
$642$		0			0
$643$	47.8391			1.88659			0.943296	−	0.331953i	$-0.107708\pi$
$643$	47.8391			1.88659			0.943296	+	0.331953i	$0.107708\pi$
$644$	1.82691	−	21.9802i	0.0719904	−	0.866141i
$645$		0			0
$646$	−12.7865	+	7.38230i	−0.503079	+	0.290453i
$647$	40.1193	+	23.1629i	1.57725	+	0.910628i	0.995241	+	0.0974487i	$0.0310682\pi$
$647$	40.1193	+	23.1629i	1.57725	+	0.910628i	0.582013	+	0.813179i	$0.302265\pi$
$648$		0			0
$649$	11.3635	+	10.0132i	0.446055	+	0.393051i
$650$		−	1.18371i		−	0.0464289i
$651$		0			0
$652$	18.6075			0.728727
$653$	19.4171	−	11.2105i	0.759850	−	0.438699i	−0.0693921	−	0.997589i	$-0.522106\pi$
$653$	19.4171	−	11.2105i	0.759850	−	0.438699i	0.829242	+	0.558890i	$0.188773\pi$
$654$		0			0
$655$	−5.72235	−	3.30380i	−0.223591	−	0.129090i
$656$	4.50300	+	7.79943i	0.175813	+	0.304517i
$657$		0			0
$658$	−18.4297	−	12.7858i	−0.718465	−	0.498441i
$659$	34.8470			1.35745			0.678724	−	0.734394i	$-0.262533\pi$
$659$	34.8470			1.35745			0.678724	+	0.734394i	$0.262533\pi$
$660$		0			0
$661$	14.7306	−	25.5141i	0.572953	−	0.992383i	−0.423308	−	0.905986i	$-0.639131\pi$
$661$	14.7306	−	25.5141i	0.572953	−	0.992383i	0.996261	−	0.0863973i	$-0.0275354\pi$
$662$	−2.76388	+	4.78718i	−0.107421	+	0.186059i
$663$		0			0
$664$	8.45117			0.327969
$665$	−6.27963	+	9.05161i	−0.243514	+	0.351007i
$666$		0			0
$667$	34.6244	−	19.9904i	1.34066	−	0.774032i
$668$	10.6954	−	18.5250i	0.413818	−	0.716754i
$669$		0			0
$670$	−5.46865	+	3.15732i	−0.211272	+	0.121978i
$671$	35.2540	−	11.8742i	1.36097	−	0.458397i
$672$		0			0
$673$			18.7674i			0.723430i	0.932289	+	0.361715i	$0.117809\pi$
$673$			18.7674i			0.723430i	−0.932289	+	0.361715i	$0.882191\pi$
$674$	−20.5602	+	11.8704i	−0.791949	+	0.457232i
$675$		0			0
$676$	−0.235750	+	0.408331i	−0.00906730	+	0.0157050i
$677$	−19.4967	−	33.7692i	−0.749317	−	1.29786i	−0.948150	−	0.317822i	$-0.897049\pi$
$677$	−19.4967	−	33.7692i	−0.749317	−	1.29786i	0.198833	−	0.980033i	$-0.436285\pi$
$678$		0			0
$679$	3.26373	+	0.271269i	0.125251	+	0.0104104i
$680$		−	16.5435i		−	0.634416i
$681$		0			0
$682$	−19.3230	−	3.89115i	−0.739918	−	0.149000i
$683$	−9.14108	−	5.27760i	−0.349774	−	0.201942i	0.314812	−	0.949154i	$-0.398059\pi$
$683$	−9.14108	−	5.27760i	−0.349774	−	0.201942i	−0.664586	+	0.747212i	$0.731392\pi$
$684$		0			0
$685$	−15.4831			−0.591579
$686$	−5.02595	−	17.8253i	−0.191891	−	0.680572i
$687$		0			0
$688$	−2.15574	+	1.24462i	−0.0821869	+	0.0474506i
$689$	9.87745	−	17.1082i	0.376301	−	0.651772i
$690$		0			0
$691$	−5.97059	−	10.3414i	−0.227132	−	0.393404i	0.729825	−	0.683634i	$-0.239602\pi$
$691$	−5.97059	−	10.3414i	−0.227132	−	0.393404i	−0.956957	+	0.290230i	$0.906268\pi$
$692$	0.860166			0.0326986
$693$		0			0
$694$	20.3800			0.773612
$695$	2.99632	+	5.18978i	0.113657	+	0.196860i
$696$		0			0
$697$	−34.4888	+	59.7363i	−1.30636	+	2.26267i
$698$	9.82594	−	5.67301i	0.371917	−	0.214727i
$699$		0			0
$700$	0.377409	+	0.800269i	0.0142647	+	0.0302473i
$701$	42.9751			1.62315			0.811573	−	0.584251i	$-0.198612\pi$
$701$	42.9751			1.62315			0.811573	+	0.584251i	$0.198612\pi$
$702$		0			0
$703$	5.19782	+	3.00096i	0.196039	+	0.113183i
$704$	−3.25136	−	0.654737i	−0.122540	−	0.0246763i
$705$		0			0
$706$			10.2642i			0.386298i
$707$	4.74625	−	6.84136i	0.178501	−	0.257296i
$708$		0			0
$709$	12.1613	+	21.0640i	0.456726	+	0.791073i	0.998786	−	0.0492669i	$-0.0156885\pi$
$709$	12.1613	+	21.0640i	0.456726	+	0.791073i	−0.542059	+	0.840340i	$0.682355\pi$
$710$	−16.1502	+	27.9730i	−0.606106	+	1.04981i
$711$		0			0
$712$	0.609275	−	0.351765i	0.0228335	−	0.0131830i
$713$		−	49.5437i		−	1.85543i
$714$		0			0
$715$	8.09391	+	24.0306i	0.302695	+	0.898692i
$716$	−9.01762	+	5.20633i	−0.337004	+	0.194570i
$717$		0			0
$718$	8.12523	−	14.0733i	0.303231	−	0.525211i
$719$	−9.25091	+	5.34101i	−0.345001	+	0.199186i	−0.662481	−	0.749079i	$-0.730497\pi$
$719$	−9.25091	+	5.34101i	−0.345001	+	0.199186i	0.317480	+	0.948265i	$0.397163\pi$
$720$		0			0
$721$	0.267806	+	0.567862i	0.00997360	+	0.0211483i
$722$	−15.2839			−0.568807
$723$		0			0
$724$	3.51299	−	6.08468i	0.130559	−	0.226135i
$725$	−0.801935	+	1.38899i	−0.0297831	+	0.0515859i
$726$		0			0
$727$	31.0522			1.15166			0.575832	−	0.817568i	$-0.304678\pi$
$727$	31.0522			1.15166			0.575832	+	0.817568i	$0.304678\pi$
$728$	−0.775692	+	9.33262i	−0.0287491	+	0.345890i
$729$		0			0
$730$	0.606428	+	1.05036i	0.0224449	+	0.0388757i
$731$	−16.5110	−	9.53261i	−0.610680	−	0.352576i
$732$		0			0
$733$	−23.6044	+	13.6280i	−0.871848	+	0.503362i	−0.867962	−	0.496631i	$-0.834570\pi$
$733$	−23.6044	+	13.6280i	−0.871848	+	0.503362i	−0.00388629	+	0.999992i	$0.501237\pi$
$734$	−36.7363			−1.35596
$735$		0			0
$736$		−	8.33638i		−	0.307283i
$737$	−6.41025	+	7.27469i	−0.236125	+	0.267967i
$738$		0			0
$739$	−30.9864	−	17.8900i	−1.13985	−	0.658095i	−0.193460	−	0.981108i	$-0.561971\pi$
$739$	−30.9864	−	17.8900i	−1.13985	−	0.658095i	−0.946394	+	0.323013i	$0.895304\pi$
$740$	−5.82409	+	3.36254i	−0.214098	+	0.123609i
$741$		0			0
$742$	−1.22311	+	14.7156i	−0.0449017	+	0.540228i
$743$	13.7096			0.502957			0.251478	−	0.967863i	$-0.419083\pi$
$743$	13.7096			0.502957			0.251478	+	0.967863i	$0.419083\pi$
$744$		0			0
$745$	43.8302	+	25.3054i	1.60582	+	0.927118i
$746$	0.721045	+	0.416295i	0.0263993	+	0.0152417i
$747$		0			0
$748$	−8.10834	−	24.0734i	−0.296470	−	0.880211i
$749$	−12.2076	−	25.8853i	−0.446056	−	0.945828i
$750$		0			0
$751$	2.74195	+	4.74920i	0.100055	+	0.173301i	0.911707	−	0.410840i	$-0.134765\pi$
$751$	2.74195	+	4.74920i	0.100055	+	0.173301i	−0.811652	+	0.584141i	$0.801431\pi$
$752$	−7.34212	−	4.23898i	−0.267740	−	0.154580i
$753$		0			0
$754$	−14.7012	+	8.48777i	−0.535388	+	0.309106i
$755$	−19.9104			−0.724614
$756$		0			0
$757$	39.5786			1.43851			0.719254	−	0.694747i	$-0.244484\pi$
$757$	39.5786			1.43851			0.719254	+	0.694747i	$0.244484\pi$
$758$	−17.9911	−	31.1616i	−0.653468	−	1.13184i
$759$		0			0
$760$	−2.08194	+	3.60603i	−0.0755200	+	0.130804i
$761$	−12.9323	−	22.3994i	−0.468794	−	0.811976i	0.530569	−	0.847642i	$-0.321978\pi$
$761$	−12.9323	−	22.3994i	−0.468794	−	0.811976i	−0.999364	+	0.0356657i	$0.988645\pi$
$762$		0			0
$763$	−9.48761	−	6.58210i	−0.343474	−	0.238288i
$764$		−	4.65390i		−	0.168372i
$765$		0			0
$766$	1.51172	+	0.872794i	0.0546208	+	0.0315353i
$767$	8.08188	−	13.9982i	0.291820	−	0.505447i
$768$		0			0
$769$			30.4651i			1.09860i	0.835626	+	0.549299i	$0.185105\pi$
$769$			30.4651i			1.09860i	−0.835626	+	0.549299i	$0.814895\pi$
$770$	−13.1339	−	13.6657i	−0.473312	−	0.492477i
$771$		0			0
$772$	−13.5837	+	7.84257i	−0.488889	+	0.282260i
$773$	−34.2466	−	19.7723i	−1.23177	−	0.711160i	−0.264367	−	0.964422i	$-0.585163\pi$
$773$	−34.2466	−	19.7723i	−1.23177	−	0.711160i	−0.967398	+	0.253262i	$0.918497\pi$
$774$		0			0
$775$	0.993748	+	1.72122i	0.0356965	+	0.0618281i
$776$	1.23783			0.0444355
$777$		0			0
$778$		−	23.0850i		−	0.827637i
$779$	15.0352	−	8.68057i	0.538691	−	0.311014i
$780$		0			0
$781$	−9.79089	+	48.6205i	−0.350346	+	1.73978i
$782$	55.2948	−	31.9244i	1.97734	−	1.14162i
$783$		0			0
$784$	−2.45116	−	6.55682i	−0.0875413	−	0.234172i
$785$		−	50.0273i		−	1.78555i
$786$		0			0
$787$	26.6490	+	15.3858i	0.949933	+	0.548444i	0.893060	−	0.449937i	$-0.148554\pi$
$787$	26.6490	+	15.3858i	0.949933	+	0.548444i	0.0568731	+	0.998381i	$0.481887\pi$
$788$	−3.19570	+	5.53512i	−0.113842	+	0.197181i
$789$		0			0
$790$	16.5434			0.588587
$791$	−3.88919	+	46.7922i	−0.138284	+	1.66374i
$792$		0			0
$793$	−19.8503	−	34.3817i	−0.704904	−	1.22093i
$794$	3.99083	−	6.91231i	0.141629	−	0.245309i
$795$		0			0
$796$	12.8469	+	22.2515i	0.455347	+	0.788684i
$797$		−	8.28034i		−	0.293305i	−0.989188	−	0.146652i	$-0.953150\pi$
$797$		−	8.28034i		−	0.293305i	0.989188	−	0.146652i	$-0.0468498\pi$
$798$		0			0
$799$		−	64.9332i		−	2.29717i
$800$	0.167211	+	0.289618i	0.00591181	+	0.0102396i
$801$		0			0
$802$	−8.88905	−	5.13209i	−0.313883	−	0.181221i
$803$	1.39725	+	1.23122i	0.0493080	+	0.0434488i
$804$		0			0
$805$	27.1560	−	39.1433i	0.957123	−	1.37962i
$806$			21.0359i			0.740957i
$807$		0			0
$808$	1.57357	−	2.72549i	0.0553578	−	0.0958826i
$809$	13.0401	−	22.5861i	0.458466	−	0.794086i	−0.540414	−	0.841399i	$-0.681733\pi$
$809$	13.0401	−	22.5861i	0.458466	−	0.794086i	0.998880	+	0.0473131i	$0.0150658\pi$
$810$		0			0
$811$			27.0252i			0.948983i	0.880260	+	0.474492i	$0.157368\pi$
$811$			27.0252i			0.948983i	−0.880260	+	0.474492i	$0.842632\pi$
$812$	7.23285	−	10.4256i	0.253823	−	0.365867i
$813$		0			0
$814$	−6.82690	+	7.74752i	−0.239283	+	0.271551i
$815$	34.8074	+	20.0961i	1.21925	+	0.703935i
$816$		0			0
$817$	2.39929	+	4.15569i	0.0839404	+	0.145389i
$818$			7.09479i			0.248064i
$819$		0			0
$820$			19.4529i			0.679326i
$821$	1.47291	+	2.55116i	0.0514050	+	0.0890360i	0.890583	−	0.454821i	$-0.150297\pi$
$821$	1.47291	+	2.55116i	0.0514050	+	0.0890360i	−0.839178	+	0.543857i	$0.816963\pi$
$822$		0			0
$823$	8.76000	−	15.1728i	0.305354	−	0.528889i	−0.671986	−	0.740564i	$-0.734558\pi$
$823$	8.76000	−	15.1728i	0.305354	−	0.528889i	0.977340	+	0.211675i	$0.0678917\pi$
$824$	0.118651	+	0.205510i	0.00413341	+	0.00715928i
$825$		0			0
$826$	−1.00077	+	12.0406i	−0.0348211	+	0.418945i
$827$	−34.7309			−1.20771			−0.603856	−	0.797093i	$-0.706370\pi$
$827$	−34.7309			−1.20771			−0.603856	+	0.797093i	$0.706370\pi$
$828$		0			0
$829$	14.0532	−	24.3409i	0.488088	−	0.845394i	−0.511818	−	0.859094i	$-0.671028\pi$
$829$	14.0532	−	24.3409i	0.488088	−	0.845394i	0.999906	+	0.0137004i	$0.00436110\pi$
$830$	15.8089	+	9.12725i	0.548733	+	0.316811i
$831$		0			0
$832$			3.53956i			0.122712i
$833$	34.1042	−	41.3679i	1.18164	−	1.43331i
$834$		0			0
$835$	40.0139	−	23.1020i	1.38474	−	0.799479i
$836$	−1.26216	+	6.26773i	−0.0436526	+	0.216774i
$837$		0			0
$838$	17.8483	−	10.3047i	0.616558	−	0.355970i
$839$			5.84466i			0.201780i	0.994898	+	0.100890i	$0.0321690\pi$
$839$			5.84466i			0.201780i	−0.994898	+	0.100890i	$0.967831\pi$
$840$		0			0
$841$	−5.99894			−0.206860
$842$	0.0539977	+	0.0935268i	0.00186088	+	0.00322315i
$843$		0			0
$844$	14.4283	+	8.33019i	0.496643	+	0.286737i
$845$	−0.881992	+	0.509218i	−0.0303414	+	0.0175176i
$846$		0			0
$847$	−25.8096	−	13.4485i	−0.886830	−	0.462096i
$848$			5.58117i			0.191658i
$849$		0			0
$850$	−1.28068	+	2.21820i	−0.0439270	+	0.0760838i
$851$	−22.4778	−	12.9775i	−0.770528	−	0.444864i
$852$		0			0
$853$		−	33.5879i		−	1.15003i	−0.818143	−	0.575014i	$-0.804996\pi$
$853$		−	33.5879i		−	1.15003i	0.818143	−	0.575014i	$-0.195004\pi$
$854$	24.3823	+	16.9154i	0.834344	+	0.578833i
$855$		0			0
$856$	−5.40857	−	9.36792i	−0.184861	−	0.320189i
$857$	6.10111	−	10.5674i	0.208410	−	0.360977i	−0.742804	−	0.669509i	$-0.766505\pi$
$857$	6.10111	−	10.5674i	0.208410	−	0.360977i	0.951214	+	0.308532i	$0.0998378\pi$
$858$		0			0
$859$	13.1737	+	22.8176i	0.449482	+	0.778525i	0.998352	−	0.0573821i	$-0.0182753\pi$
$859$	13.1737	+	22.8176i	0.449482	+	0.778525i	−0.548870	+	0.835907i	$0.684942\pi$
$860$	−5.37674			−0.183345
$861$		0			0
$862$	40.5122			1.37985
$863$	−9.29024	+	5.36372i	−0.316244	+	0.182583i	−0.649717	−	0.760176i	$-0.725113\pi$
$863$	−9.29024	+	5.36372i	−0.316244	+	0.182583i	0.333473	+	0.942760i	$0.391779\pi$
$864$		0			0
$865$	1.60904	+	0.928977i	0.0547089	+	0.0315862i
$866$	−1.63562	−	2.83297i	−0.0555806	−	0.0962683i
$867$		0			0
$868$	−6.70700	−	14.2217i	−0.227650	−	0.482716i
$869$	24.0732	−	8.10826i	0.816627	−	0.275054i
$870$		0			0
$871$	8.96142	+	5.17388i	0.303646	+	0.175310i
$872$	−3.77972	−	2.18222i	−0.127998	−	0.0738994i
$873$		0			0
$874$	−16.0703			−0.543585
$875$	−2.52511	+	30.3804i	−0.0853642	+	1.02705i
$876$		0			0
$877$	−31.2834	+	18.0615i	−1.05637	+	0.609893i	−0.924425	−	0.381365i	$-0.875454\pi$
$877$	−31.2834	+	18.0615i	−1.05637	+	0.609893i	−0.131941	+	0.991258i	$0.542121\pi$
$878$	5.95716	+	3.43937i	0.201044	+	0.116073i
$879$		0			0
$880$	−5.37491	−	4.73621i	−0.181188	−	0.159658i
$881$		−	2.25462i		−	0.0759602i	−0.999278	−	0.0379801i	$-0.987908\pi$
$881$		−	2.25462i		−	0.0759602i	0.999278	−	0.0379801i	$-0.0120923\pi$
$882$		0			0
$883$	−18.2202			−0.613160			−0.306580	−	0.951845i	$-0.599185\pi$
$883$	−18.2202			−0.613160			−0.306580	+	0.951845i	$0.599185\pi$
$884$	−23.4777	+	13.5549i	−0.789641	+	0.455899i
$885$		0			0
$886$	−5.64003	−	3.25627i	−0.189481	−	0.109397i
$887$	2.23053	+	3.86340i	0.0748940	+	0.129720i	0.901040	−	0.433736i	$-0.142805\pi$
$887$	2.23053	+	3.86340i	0.0748940	+	0.129720i	−0.826146	+	0.563456i	$0.809472\pi$
$888$		0			0
$889$	−2.77258	+	33.3578i	−0.0929892	+	1.11879i
$890$	1.51962			0.0509378
$891$		0			0
$892$	−4.90779	+	8.50054i	−0.164325	+	0.284619i
$893$	−8.17160	+	14.1536i	−0.273452	+	0.473633i
$894$		0			0
$895$	−22.4913			−0.751801
$896$	−1.12854	−	2.39299i	−0.0377019	−	0.0799441i
$897$		0			0
$898$	11.5303	−	6.65704i	0.384772	−	0.222148i
$899$	14.2513	−	24.6840i	0.475308	−	0.823258i
$900$		0			0
$901$	−37.0196	+	21.3733i	−1.23330	+	0.712047i
$902$	9.53429	+	28.3070i	0.317457	+	0.942520i
$903$		0			0
$904$			17.7468i			0.590249i
$905$	13.1429	−	7.58804i	0.436884	−	0.252235i
$906$		0			0
$907$	−4.56876	+	7.91332i	−0.151703	+	0.262758i	−0.931854	−	0.362834i	$-0.881809\pi$
$907$	−4.56876	+	7.91332i	−0.151703	+	0.262758i	0.780151	+	0.625592i	$0.215142\pi$
$908$	−5.08719	−	8.81128i	−0.168824	−	0.292413i
$909$		0			0
$910$	−11.5302	+	16.6200i	−0.382223	+	0.550946i
$911$		−	24.0642i		−	0.797283i	−0.917107	−	0.398641i	$-0.869482\pi$
$911$		−	24.0642i		−	0.797283i	0.917107	−	0.398641i	$-0.130518\pi$
$912$		0			0
$913$	27.4778	+	5.53330i	0.909382	+	0.183125i
$914$	−22.5222	−	13.0032i	−0.744967	−	0.430107i
$915$		0			0
$916$	26.7338			0.883310
$917$	−3.45230	−	7.32035i	−0.114005	−	0.241739i
$918$		0			0
$919$	−35.4309	+	20.4560i	−1.16876	+	0.674783i	−0.953387	−	0.301750i	$-0.902429\pi$
$919$	−35.4309	+	20.4560i	−1.16876	+	0.674783i	−0.215371	+	0.976532i	$0.569096\pi$
$920$	9.00327	−	15.5941i	0.296829	−	0.514123i
$921$		0			0
$922$	−7.92710	−	13.7301i	−0.261065	−	0.452178i
$923$	52.9303			1.74222
$924$		0			0
$925$	1.04121			0.0342349
$926$	−13.8188	−	23.9349i	−0.454115	−	0.786551i
$927$		0			0
$928$	2.39797	−	4.15341i	0.0787173	−	0.136342i
$929$	−49.2202	+	28.4173i	−1.61486	+	0.932341i	−0.626642	+	0.779307i	$0.715571\pi$
$929$	−49.2202	+	28.4173i	−1.61486	+	0.932341i	−0.988221	+	0.153034i	$0.951096\pi$
$930$		0			0
$931$	−12.6398	+	4.72516i	−0.414251	+	0.154861i
$932$	−4.19885			−0.137538
$933$		0			0
$934$	3.49877	+	2.02001i	0.114483	+	0.0660969i
$935$	10.8317	−	53.7889i	0.354233	−	1.75909i
$936$		0			0
$937$		−	21.7330i		−	0.709987i	−0.934869	−	0.354994i	$-0.884483\pi$
$937$		−	21.7330i		−	0.709987i	0.934869	−	0.354994i	$-0.115517\pi$
$938$	−7.70816	−	0.640673i	−0.251680	−	0.0209187i
$939$		0			0
$940$	−9.15617	−	15.8589i	−0.298641	−	0.517262i
$941$	−19.5613	+	33.8811i	−0.637679	+	1.10449i	0.348262	+	0.937397i	$0.386772\pi$
$941$	−19.5613	+	33.8811i	−0.637679	+	1.10449i	−0.985941	+	0.167095i	$0.946561\pi$
$942$		0			0
$943$	−65.0190	+	37.5388i	−2.11731	+	1.22243i
$944$			4.56660i			0.148630i
$945$		0			0
$946$	−7.82399	+	2.63525i	−0.254380	+	0.0856795i
$947$	4.84961	−	2.79992i	0.157591	−	0.0909853i	−0.419131	−	0.907926i	$-0.637665\pi$
$947$	4.84961	−	2.79992i	0.157591	−	0.0909853i	0.576722	+	0.816941i	$0.304332\pi$
$948$		0			0
$949$	0.993748	−	1.72122i	0.0322584	−	0.0558732i
$950$	0.558305	−	0.322338i	0.0181138	−	0.0104580i
$951$		0			0
$952$	11.5508	−	16.6496i	0.374363	−	0.539616i
$953$	−37.2517			−1.20670			−0.603350	−	0.797477i	$-0.706168\pi$
$953$	−37.2517			−1.20670			−0.603350	+	0.797477i	$0.706168\pi$
$954$		0			0
$955$	5.02620	−	8.70563i	0.162644	−	0.281708i
$956$	−9.72914	+	16.8514i	−0.314663	+	0.545012i
$957$		0			0
$958$	6.12326			0.197834
$959$	−15.5824	−	10.8104i	−0.503180	−	0.349085i
$960$		0			0
$961$	−2.16005	−	3.74132i	−0.0696792	−	0.120688i
$962$	9.54388	+	5.51016i	0.307707	+	0.177655i
$963$		0			0
$964$	−4.53621	+	2.61898i	−0.146102	+	0.0843518i
$965$	−33.8798			−1.09063
$966$		0			0
$967$			12.7892i			0.411272i	0.978629	+	0.205636i	$0.0659263\pi$
$967$			12.7892i			0.411272i	−0.978629	+	0.205636i	$0.934074\pi$
$968$	−10.1426	−	4.25757i	−0.325997	−	0.136843i
$969$		0			0
$970$	2.31550	+	1.33685i	0.0743461	+	0.0429237i
$971$	33.1789	−	19.1559i	1.06476	−	0.614740i	0.138016	−	0.990430i	$-0.455927\pi$
$971$	33.1789	−	19.1559i	1.06476	−	0.614740i	0.926746	+	0.375689i	$0.122594\pi$
$972$		0			0
$973$	−0.608003	+	7.31509i	−0.0194917	+	0.234511i
$974$	6.12392			0.196223
$975$		0			0
$976$	9.71354	+	5.60811i	0.310923	+	0.179511i
$977$	21.7513	+	12.5581i	0.695885	+	0.401770i	0.805813	−	0.592170i	$-0.201729\pi$
$977$	21.7513	+	12.5581i	0.695885	+	0.401770i	−0.109928	+	0.993940i	$0.535062\pi$
$978$		0			0
$979$	2.21128	−	0.744799i	0.0706729	−	0.0238039i
$980$	2.49618	−	14.9125i	0.0797377	−	0.476362i
$981$		0			0
$982$	10.4512	+	18.1020i	0.333511	+	0.577658i
$983$	2.11529	+	1.22127i	0.0674674	+	0.0389523i	0.533354	−	0.845892i	$-0.320931\pi$
$983$	2.11529	+	1.22127i	0.0674674	+	0.0389523i	−0.465887	+	0.884844i	$0.654265\pi$
$984$		0			0
$985$	−11.9558	+	6.90270i	−0.380944	+	0.219938i
$986$	36.7324			1.16980
$987$		0			0
$988$	6.82331			0.217079
$989$	−10.3756	−	17.9711i	−0.329925	−	0.571448i
$990$		0			0
$991$	−2.56512	+	4.44291i	−0.0814836	+	0.141134i	−0.903887	−	0.427770i	$-0.859299\pi$
$991$	−2.56512	+	4.44291i	−0.0814836	+	0.141134i	0.822404	+	0.568904i	$0.192632\pi$
$992$	−2.97154	−	5.14685i	−0.0943464	−	0.163413i
$993$		0			0
$994$	−35.7846	+	16.8761i	−1.13502	+	0.535278i
$995$			55.4986i			1.75942i
$996$		0			0
$997$	−39.8987	−	23.0355i	−1.26361	−	0.729543i	−0.289835	−	0.957077i	$-0.593600\pi$
$997$	−39.8987	−	23.0355i	−1.26361	−	0.729543i	−0.973770	+	0.227534i	$0.926934\pi$
$998$	−13.3081	+	23.0503i	−0.421261	+	0.729646i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.ba.b.1187.4	yes	32
3.2	odd	2		1386.2.ba.a.1187.13	yes	32
7.2	even	3	inner	1386.2.ba.b.989.13	yes	32
11.10	odd	2		1386.2.ba.a.1187.4	yes	32
21.2	odd	6		1386.2.ba.a.989.4	✓	32
33.32	even	2	inner	1386.2.ba.b.1187.13	yes	32
77.65	odd	6		1386.2.ba.a.989.13	yes	32
231.65	even	6	inner	1386.2.ba.b.989.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.ba.a.989.4	✓	32	21.2	odd	6
1386.2.ba.a.989.13	yes	32	77.65	odd	6
1386.2.ba.a.1187.4	yes	32	11.10	odd	2
1386.2.ba.a.1187.13	yes	32	3.2	odd	2
1386.2.ba.b.989.4	yes	32	231.65	even	6	inner
1386.2.ba.b.989.13	yes	32	7.2	even	3	inner
1386.2.ba.b.1187.4	yes	32	1.1	even	1	trivial
1386.2.ba.b.1187.13	yes	32	33.32	even	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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.87061 + 1.08000i) q^{5} +(-2.63666 - 0.219149i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.87061 + 1.08000i) q^{5} +(-2.63666 - 0.219149i) q^{7} -1.00000 q^{8} +(-1.87061 - 1.08000i) q^{10} +(-3.25136 - 0.654737i) q^{11} +3.53956i q^{13} +(-1.12854 - 2.39299i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.82953 - 6.63294i) q^{17} +(-1.66946 + 0.963864i) q^{19} -2.15999i q^{20} +(-1.05866 - 3.14313i) q^{22} +(7.21952 - 4.16819i) q^{23} +(-0.167211 + 0.289618i) q^{25} +(-3.06535 + 1.76978i) q^{26} +(1.50812 - 2.17384i) q^{28} +4.79594 q^{29} +(2.97154 - 5.14685i) q^{31} +(0.500000 - 0.866025i) q^{32} +7.65906 q^{34} +(5.16884 - 2.43764i) q^{35} +(-1.55673 - 2.69634i) q^{37} +(-1.66946 - 0.963864i) q^{38} +(1.87061 - 1.08000i) q^{40} -9.00600 q^{41} -2.48924i q^{43} +(2.19270 - 2.48839i) q^{44} +(7.21952 + 4.16819i) q^{46} +(7.34212 - 4.23898i) q^{47} +(6.90395 + 1.15564i) q^{49} -0.334422 q^{50} +(-3.06535 - 1.76978i) q^{52} +(-4.83344 - 2.79059i) q^{53} +(6.78914 - 2.28670i) q^{55} +(2.63666 + 0.219149i) q^{56} +(2.39797 + 4.15341i) q^{58} +(-3.95479 - 2.28330i) q^{59} +(-9.71354 + 5.60811i) q^{61} +5.94307 q^{62} +1.00000 q^{64} +(-3.82272 - 6.62114i) q^{65} +(1.46173 - 2.53179i) q^{67} +(3.82953 + 6.63294i) q^{68} +(4.69548 + 3.25753i) q^{70} -14.9539i q^{71} +(-0.486281 - 0.280755i) q^{73} +(1.55673 - 2.69634i) q^{74} -1.92773i q^{76} +(8.42924 + 2.43885i) q^{77} +(-6.63288 + 3.82950i) q^{79} +(1.87061 + 1.08000i) q^{80} +(-4.50300 - 7.79943i) q^{82} -8.45117 q^{83} +16.5435i q^{85} +(2.15574 - 1.24462i) q^{86} +(3.25136 + 0.654737i) q^{88} +(-0.609275 + 0.351765i) q^{89} +(0.775692 - 9.33262i) q^{91} +8.33638i q^{92} +(7.34212 + 4.23898i) q^{94} +(2.08194 - 3.60603i) q^{95} -1.23783 q^{97} +(2.45116 + 6.55682i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8}+O(q^{10}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 2 q^{11} - 16 q^{16} + 4 q^{17} + 4 q^{22} + 4 q^{25} + 16 q^{29} + 4 q^{31} + 16 q^{32} + 8 q^{34} + 16 q^{35} + 4 q^{37} - 32 q^{41} + 2 q^{44} + 20 q^{49} + 8 q^{50} - 12 q^{55} + 8 q^{58} + 8 q^{62} + 32 q^{64} - 8 q^{67} + 4 q^{68} - 4 q^{70} - 4 q^{74} + 14 q^{77} - 16 q^{82} + 88 q^{83} - 2 q^{88} - 24 q^{95} - 32 q^{97} - 8 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 2 * q^11 - 16 * q^16 + 4 * q^17 + 4 * q^22 + 4 * q^25 + 16 * q^29 + 4 * q^31 + 16 * q^32 + 8 * q^34 + 16 * q^35 + 4 * q^37 - 32 * q^41 + 2 * q^44 + 20 * q^49 + 8 * q^50 - 12 * q^55 + 8 * q^58 + 8 * q^62 + 32 * q^64 - 8 * q^67 + 4 * q^68 - 4 * q^70 - 4 * q^74 + 14 * q^77 - 16 * q^82 + 88 * q^83 - 2 * q^88 - 24 * q^95 - 32 * q^97 - 8 * q^98

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