LMFDB - Embedded newform 441.3.bf.a.305.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(44,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("441.44");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.bf (of order $42$, degree $12$, 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:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$456$
Relative dimension:	$38$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			305.23
Character	$\chi$	$=$	441.305
Dual form			441.3.bf.a.107.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.735818 + 0.793024i) q^{2} +(0.211463 - 2.82177i) q^{4} +(-2.21024 - 0.867457i) q^{5} +(-1.00290 + 6.92778i) q^{7} +(5.77651 - 4.60661i) q^{8} +O(q^{10})$	\(q+(0.735818 + 0.793024i) q^{2} +(0.211463 - 2.82177i) q^{4} +(-2.21024 - 0.867457i) q^{5} +(-1.00290 + 6.92778i) q^{7} +(5.77651 - 4.60661i) q^{8} +(-0.938425 - 2.39107i) q^{10} +(2.23029 - 7.23043i) q^{11} +(-3.79013 - 16.6056i) q^{13} +(-6.23185 + 4.30226i) q^{14} +(-3.28871 - 0.495693i) q^{16} +(12.7341 + 18.6776i) q^{17} +(-13.1038 - 22.6965i) q^{19} +(-2.91515 + 6.05337i) q^{20} +(7.37499 - 3.55161i) q^{22} +(10.3961 - 15.2482i) q^{23} +(-14.1936 - 13.1697i) q^{25} +(10.3798 - 15.2244i) q^{26} +(19.3365 + 4.29494i) q^{28} +(8.98905 - 18.6660i) q^{29} +(-1.98041 + 3.43018i) q^{31} +(-18.6750 - 27.3912i) q^{32} +(-5.44173 + 23.8418i) q^{34} +(8.22622 - 14.4421i) q^{35} +(-4.62668 - 61.7388i) q^{37} +(8.35682 - 27.0921i) q^{38} +(-16.7635 + 5.17086i) q^{40} +(-6.35132 + 5.06501i) q^{41} +(-19.2920 + 24.1914i) q^{43} +(-19.9310 - 7.82234i) q^{44} +(19.7418 - 2.97560i) q^{46} +(-26.3811 - 28.4320i) q^{47} +(-46.9884 - 13.8958i) q^{49} -20.9464i q^{50} +(-47.6588 + 7.18340i) q^{52} +(65.1077 + 4.87915i) q^{53} +(-11.2016 + 14.0463i) q^{55} +(26.1203 + 44.6384i) q^{56} +(21.4169 - 6.60622i) q^{58} +(58.1336 - 22.8158i) q^{59} +(4.11452 + 54.9045i) q^{61} +(-4.17744 + 0.953473i) q^{62} +(5.02017 - 21.9948i) q^{64} +(-6.02756 + 39.9903i) q^{65} +(28.2203 - 48.8791i) q^{67} +(55.3966 - 31.9832i) q^{68} +(17.5059 - 4.10319i) q^{70} +(56.8247 + 117.998i) q^{71} +(49.7508 + 46.1620i) q^{73} +(45.5559 - 49.0976i) q^{74} +(-66.8153 + 32.1766i) q^{76} +(47.8541 + 22.7024i) q^{77} +(14.2376 + 24.6603i) q^{79} +(6.83885 + 3.94841i) q^{80} +(-8.69009 - 1.30982i) q^{82} +(-102.045 - 23.2911i) q^{83} +(-11.9436 - 52.3283i) q^{85} +(-33.3797 + 2.50147i) q^{86} +(-20.4245 - 52.0407i) q^{88} +(-9.78256 - 31.7143i) q^{89} +(118.841 - 9.60330i) q^{91} +(-40.8286 - 32.5597i) q^{92} +(3.13560 - 41.8417i) q^{94} +(9.27443 + 61.5318i) q^{95} +102.066 q^{97} +(-23.5552 - 47.4877i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 456 q - 80 q^{4} + 2 q^{7}+O(q^{10}) $ 456 * q - 80 * q^4 + 2 * q^7	$ 456 q - 80 q^{4} + 2 q^{7} + 16 q^{10} + 52 q^{13} + 176 q^{16} - 26 q^{19} - 184 q^{22} - 234 q^{25} - 504 q^{28} - 22 q^{31} - 32 q^{34} + 684 q^{37} + 1828 q^{40} - 76 q^{43} - 100 q^{46} - 226 q^{49} - 1148 q^{52} - 464 q^{55} - 1088 q^{58} - 1362 q^{61} + 472 q^{64} + 110 q^{67} - 472 q^{70} + 482 q^{73} + 84 q^{76} - 106 q^{79} + 2032 q^{82} - 768 q^{85} + 24 q^{88} + 338 q^{91} + 788 q^{94} - 568 q^{97}+O(q^{100}) $ 456 * q - 80 * q^4 + 2 * q^7 + 16 * q^10 + 52 * q^13 + 176 * q^16 - 26 * q^19 - 184 * q^22 - 234 * q^25 - 504 * q^28 - 22 * q^31 - 32 * q^34 + 684 * q^37 + 1828 * q^40 - 76 * q^43 - 100 * q^46 - 226 * q^49 - 1148 * q^52 - 464 * q^55 - 1088 * q^58 - 1362 * q^61 + 472 * q^64 + 110 * q^67 - 472 * q^70 + 482 * q^73 + 84 * q^76 - 106 * q^79 + 2032 * q^82 - 768 * q^85 + 24 * q^88 + 338 * q^91 + 788 * q^94 - 568 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{20}{21}\right)$	$-1$

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 $

$2$	0.735818	+	0.793024i	0.367909	+	0.396512i	0.889688	−	0.456569i	$-0.150922\pi$
$2$	0.735818	+	0.793024i	0.367909	+	0.396512i	−0.521779	+	0.853081i	$0.674731\pi$
$3$		0			0
$3$		0			0
$4$	0.211463	−	2.82177i	0.0528656	−	0.705443i
$5$	−2.21024	−	0.867457i	−0.442049	−	0.173491i	0.133869	−	0.990999i	$-0.457260\pi$
$5$	−2.21024	−	0.867457i	−0.442049	−	0.173491i	−0.575918	+	0.817508i	$0.695355\pi$
$6$		0			0
$7$	−1.00290	+	6.92778i	−0.143272	+	0.989683i
$7$	−1.00290	+	6.92778i	−0.143272	+	0.989683i
$8$	5.77651	−	4.60661i	0.722063	−	0.575826i
$9$		0			0
$10$	−0.938425	−	2.39107i	−0.0938425	−	0.239107i
$11$	2.23029	−	7.23043i	0.202754	−	0.657312i	−0.795899	−	0.605429i	$-0.793002\pi$
$11$	2.23029	−	7.23043i	0.202754	−	0.657312i	0.998653	−	0.0518827i	$-0.0165222\pi$
$12$		0			0
$13$	−3.79013	−	16.6056i	−0.291548	−	1.27736i	−0.882371	−	0.470554i	$-0.844054\pi$
$13$	−3.79013	−	16.6056i	−0.291548	−	1.27736i	0.590823	−	0.806801i	$-0.298803\pi$
$14$	−6.23185	+	4.30226i	−0.445132	+	0.307305i
$15$		0			0
$16$	−3.28871	−	0.495693i	−0.205544	−	0.0309808i
$17$	12.7341	+	18.6776i	0.749067	+	1.09868i	0.991702	+	0.128562i	$0.0410360\pi$
$17$	12.7341	+	18.6776i	0.749067	+	1.09868i	−0.242635	+	0.970118i	$0.578012\pi$
$18$		0			0
$19$	−13.1038	−	22.6965i	−0.689675	−	1.19455i	−0.971943	−	0.235217i	$-0.924420\pi$
$19$	−13.1038	−	22.6965i	−0.689675	−	1.19455i	0.282268	−	0.959336i	$-0.408913\pi$
$20$	−2.91515	+	6.05337i	−0.145757	+	0.302669i
$21$		0			0
$22$	7.37499	−	3.55161i	0.335227	−	0.161437i
$23$	10.3961	−	15.2482i	0.452003	−	0.662966i	−0.530827	−	0.847480i	$-0.678119\pi$
$23$	10.3961	−	15.2482i	0.452003	−	0.662966i	0.982830	+	0.184514i	$0.0590711\pi$
$24$		0			0
$25$	−14.1936	−	13.1697i	−0.567744	−	0.526789i
$26$	10.3798	−	15.2244i	0.399223	−	0.585553i
$27$		0			0
$28$	19.3365	+	4.29494i	0.690591	+	0.153391i
$29$	8.98905	−	18.6660i	0.309967	−	0.643654i	−0.686546	−	0.727086i	$-0.740874\pi$
$29$	8.98905	−	18.6660i	0.309967	−	0.643654i	0.996513	+	0.0834326i	$0.0265883\pi$
$30$		0			0
$31$	−1.98041	+	3.43018i	−0.0638843	+	0.110651i	−0.896199	−	0.443653i	$-0.853682\pi$
$31$	−1.98041	+	3.43018i	−0.0638843	+	0.110651i	0.832314	+	0.554304i	$0.187016\pi$
$32$	−18.6750	−	27.3912i	−0.583594	−	0.855975i
$33$		0			0
$34$	−5.44173	+	23.8418i	−0.160051	+	0.701228i
$35$	8.22622	−	14.4421i	0.235035	−	0.412632i
$36$		0			0
$37$	−4.62668	−	61.7388i	−0.125045	−	1.66862i	−0.608734	−	0.793375i	$-0.708322\pi$
$37$	−4.62668	−	61.7388i	−0.125045	−	1.66862i	0.483688	−	0.875240i	$-0.339297\pi$
$38$	8.35682	−	27.0921i	0.219916	−	0.712951i
$39$		0			0
$40$	−16.7635	+	5.17086i	−0.419088	+	0.129272i
$41$	−6.35132	+	5.06501i	−0.154910	+	0.123537i	−0.697878	−	0.716217i	$-0.745872\pi$
$41$	−6.35132	+	5.06501i	−0.154910	+	0.123537i	0.542967	+	0.839754i	$0.317301\pi$
$42$		0			0
$43$	−19.2920	+	24.1914i	−0.448651	+	0.562590i	−0.953800	−	0.300442i	$-0.902866\pi$
$43$	−19.2920	+	24.1914i	−0.448651	+	0.562590i	0.505149	+	0.863032i	$0.331437\pi$
$44$	−19.9310	−	7.82234i	−0.452977	−	0.177780i
$45$		0			0
$46$	19.7418	−	2.97560i	0.429170	−	0.0646869i
$47$	−26.3811	−	28.4320i	−0.561300	−	0.604937i	0.387091	−	0.922042i	$-0.373480\pi$
$47$	−26.3811	−	28.4320i	−0.561300	−	0.604937i	−0.948391	+	0.317104i	$0.897289\pi$
$48$		0			0
$49$	−46.9884	−	13.8958i	−0.958946	−	0.283588i
$50$		−	20.9464i		−	0.418928i
$51$		0			0
$52$	−47.6588	+	7.18340i	−0.916515	+	0.138142i
$53$	65.1077	+	4.87915i	1.22845	+	0.0920594i	0.673095	−	0.739556i	$-0.264965\pi$
$53$	65.1077	+	4.87915i	1.22845	+	0.0920594i	0.555352	+	0.831616i	$0.312584\pi$
$54$		0			0
$55$	−11.2016	+	14.0463i	−0.203665	+	0.255388i
$56$	26.1203	+	44.6384i	0.466434	+	0.797114i
$57$		0			0
$58$	21.4169	−	6.60622i	0.369256	−	0.113900i
$59$	58.1336	−	22.8158i	0.985316	−	0.386708i	0.182677	−	0.983173i	$-0.441524\pi$
$59$	58.1336	−	22.8158i	0.985316	−	0.386708i	0.802639	+	0.596465i	$0.203429\pi$
$60$		0			0
$61$	4.11452	+	54.9045i	0.0674512	+	0.900074i	0.923603	+	0.383350i	$0.125230\pi$
$61$	4.11452	+	54.9045i	0.0674512	+	0.900074i	−0.856152	+	0.516724i	$0.827151\pi$
$62$	−4.17744	+	0.953473i	−0.0673780	+	0.0153786i
$63$		0			0
$64$	5.02017	−	21.9948i	0.0784401	−	0.343669i
$65$	−6.02756	+	39.9903i	−0.0927317	+	0.615235i
$66$		0			0
$67$	28.2203	−	48.8791i	0.421199	−	0.729538i	−0.574858	−	0.818253i	$-0.694943\pi$
$67$	28.2203	−	48.8791i	0.421199	−	0.729538i	0.996057	+	0.0887148i	$0.0282760\pi$
$68$	55.3966	−	31.9832i	0.814656	−	0.470342i
$69$		0			0
$70$	17.5059	−	4.10319i	0.250085	−	0.0586170i
$71$	56.8247	+	117.998i	0.800347	+	1.66194i	0.748362	+	0.663290i	$0.230841\pi$
$71$	56.8247	+	117.998i	0.800347	+	1.66194i	0.0519850	+	0.998648i	$0.483445\pi$
$72$		0			0
$73$	49.7508	+	46.1620i	0.681518	+	0.632356i	0.942977	−	0.332858i	$-0.108013\pi$
$73$	49.7508	+	46.1620i	0.681518	+	0.632356i	−0.261459	+	0.965215i	$0.584204\pi$
$74$	45.5559	−	49.0976i	0.615620	−	0.663481i
$75$		0			0
$76$	−66.8153	+	32.1766i	−0.879149	+	0.423376i
$77$	47.8541	+	22.7024i	0.621481	+	0.294836i
$78$		0			0
$79$	14.2376	+	24.6603i	0.180223	+	0.312156i	0.941957	−	0.335735i	$-0.108985\pi$
$79$	14.2376	+	24.6603i	0.180223	+	0.312156i	−0.761733	+	0.647891i	$0.775651\pi$
$80$	6.83885	+	3.94841i	0.0854856	+	0.0493552i
$81$		0			0
$82$	−8.69009	−	1.30982i	−0.105977	−	0.0159734i
$83$	−102.045	−	23.2911i	−1.22945	−	0.280615i	−0.442016	−	0.897007i	$-0.645736\pi$
$83$	−102.045	−	23.2911i	−1.22945	−	0.280615i	−0.787439	+	0.616392i	$0.788594\pi$
$84$		0			0
$85$	−11.9436	−	52.3283i	−0.140513	−	0.615627i
$86$	−33.3797	+	2.50147i	−0.388137	+	0.0290868i
$87$		0			0
$88$	−20.4245	−	52.0407i	−0.232096	−	0.591372i
$89$	−9.78256	−	31.7143i	−0.109916	−	0.356340i	0.883857	−	0.467756i	$-0.154938\pi$
$89$	−9.78256	−	31.7143i	−0.109916	−	0.356340i	−0.993774	+	0.111416i	$0.964461\pi$
$90$		0			0
$91$	118.841	−	9.60330i	1.30595	−	0.105531i
$92$	−40.8286	−	32.5597i	−0.443789	−	0.353910i
$93$		0			0
$94$	3.13560	−	41.8417i	0.0333574	−	0.445124i
$95$	9.27443	+	61.5318i	0.0976256	+	0.647703i
$96$		0			0
$97$	102.066			1.05222			0.526112	−	0.850415i	$-0.323649\pi$
$97$	102.066			1.05222			0.526112	+	0.850415i	$0.323649\pi$
$98$	−23.5552	−	47.4877i	−0.240359	−	0.484568i
$99$		0			0
$100$	−40.1634	+	37.2662i	−0.401634	+	0.372662i
$101$	27.3702	+	181.590i	0.270993	+	1.79792i	0.547393	+	0.836876i	$0.315620\pi$
$101$	27.3702	+	181.590i	0.270993	+	1.79792i	−0.276401	+	0.961043i	$0.589142\pi$
$102$		0			0
$103$	−53.3260	+	135.872i	−0.517728	+	1.31915i	0.398013	+	0.917380i	$0.369700\pi$
$103$	−53.3260	+	135.872i	−0.517728	+	1.31915i	−0.915741	+	0.401769i	$0.868395\pi$
$104$	−98.3893	−	78.4629i	−0.946051	−	0.754451i
$105$		0			0
$106$	44.0382	+	55.2221i	0.415454	+	0.520963i
$107$	−39.7693	−	128.929i	−0.371675	−	1.20494i	−0.927557	−	0.373681i	$-0.878096\pi$
$107$	−39.7693	−	128.929i	−0.371675	−	1.20494i	0.555882	−	0.831261i	$-0.312381\pi$
$108$		0			0
$109$	−94.5642	−	29.1692i	−0.867561	−	0.267607i	−0.171146	−	0.985246i	$-0.554747\pi$
$109$	−94.5642	−	29.1692i	−0.867561	−	0.267607i	−0.696416	+	0.717638i	$0.745223\pi$
$110$	−19.3814	+	1.45243i	−0.176195	+	0.0132040i
$111$		0			0
$112$	6.73231	−	22.2863i	0.0601099	−	0.198985i
$113$	65.2867	+	14.9013i	0.577758	+	0.131870i	0.501407	−	0.865211i	$-0.332816\pi$
$113$	65.2867	+	14.9013i	0.577758	+	0.131870i	0.0763511	+	0.997081i	$0.475673\pi$
$114$		0			0
$115$	−36.2050	+	24.6842i	−0.314826	+	0.214645i
$116$	−50.7702	−	29.3122i	−0.437674	−	0.252691i
$117$		0			0
$118$	60.8692	+	29.3131i	0.515841	+	0.248416i
$119$	−142.165	+	69.4875i	−1.19467	+	0.583929i
$120$		0			0
$121$	52.6700	+	35.9098i	0.435289	+	0.296775i
$122$	−40.5130	+	43.6627i	−0.332074	+	0.357891i
$123$		0			0
$124$	9.26040	+	6.31363i	0.0746806	+	0.0509164i
$125$	45.7022	+	94.9016i	0.365618	+	0.759213i
$126$		0			0
$127$	−93.9150	−	45.2271i	−0.739488	−	0.356119i	0.0259201	−	0.999664i	$-0.491748\pi$
$127$	−93.9150	−	45.2271i	−0.739488	−	0.356119i	−0.765408	+	0.643545i	$0.777463\pi$
$128$	−93.7044	+	54.1003i	−0.732066	+	0.422658i
$129$		0			0
$130$	−36.1484	+	24.6456i	−0.278065	+	0.189581i
$131$	−0.541791	+	3.59455i	−0.00413581	+	0.0274393i	−0.990804	−	0.135308i	$-0.956798\pi$
$131$	−0.541791	+	3.59455i	−0.00413581	+	0.0274393i	0.986668	+	0.162748i	$0.0520356\pi$
$132$		0			0
$133$	170.378	−	68.0181i	1.28104	−	0.511414i
$134$	59.5273	−	13.5867i	0.444234	−	0.101393i
$135$		0			0
$136$	159.599	+	49.2298i	1.17352	+	0.361984i
$137$	−82.0847	+	32.2159i	−0.599158	+	0.235152i	−0.645484	−	0.763774i	$-0.723344\pi$
$137$	−82.0847	+	32.2159i	−0.599158	+	0.235152i	0.0463254	+	0.998926i	$0.485249\pi$
$138$		0			0
$139$	−24.9031	−	31.2275i	−0.179159	−	0.224658i	0.684141	−	0.729350i	$-0.260177\pi$
$139$	−24.9031	−	31.2275i	−0.179159	−	0.224658i	−0.863299	+	0.504692i	$0.831606\pi$
$140$	−39.0128	−	26.2665i	−0.278663	−	0.187618i
$141$		0			0
$142$	−51.7623	+	131.888i	−0.364523	+	0.928790i
$143$	−128.519	−	9.63116i	−0.898733	−	0.0673507i
$144$		0			0
$145$	−36.0599	+	33.4587i	−0.248689	+	0.230750i
$146$			73.4205i			0.502880i
$147$		0			0
$148$	−175.191			−1.18372
$149$	21.6900	+	23.3763i	0.145571	+	0.156888i	0.801628	−	0.597823i	$-0.203968\pi$
$149$	21.6900	+	23.3763i	0.145571	+	0.156888i	−0.656057	+	0.754711i	$0.727777\pi$
$150$		0			0
$151$	15.8783	−	211.882i	0.105155	−	1.40319i	−0.656069	−	0.754701i	$-0.727782\pi$
$151$	15.8783	−	211.882i	0.105155	−	1.40319i	0.761224	−	0.648489i	$-0.224599\pi$
$152$	−180.248	−	70.7422i	−1.18584	−	0.465409i
$153$		0			0
$154$	17.2084	+	54.6543i	0.111743	+	0.354898i
$155$	7.35273	−	5.86361i	0.0474370	−	0.0378297i
$156$		0			0
$157$	41.6486	+	106.119i	0.265278	+	0.675916i	0.999997	−	0.00245499i	$-0.000781448\pi$
$157$	41.6486	+	106.119i	0.265278	+	0.675916i	−0.734719	+	0.678371i	$0.762686\pi$
$158$	−9.07990	+	29.4363i	−0.0574677	+	0.186306i
$159$		0			0
$160$	17.5156	+	76.7410i	0.109473	+	0.479631i
$161$	95.2101	+	87.3142i	0.591367	+	0.542324i
$162$		0			0
$163$	142.095	+	21.4174i	0.871750	+	0.131395i	0.569656	−	0.821883i	$-0.307076\pi$
$163$	142.095	+	21.4174i	0.871750	+	0.131395i	0.302094	+	0.953278i	$0.402314\pi$
$164$	12.9492	+	18.9930i	0.0789588	+	0.115811i
$165$		0			0
$166$	−56.6161	−	98.0619i	−0.341061	−	0.590734i
$167$	−112.641	+	233.902i	−0.674498	+	1.40061i	0.229600	+	0.973285i	$0.426258\pi$
$167$	−112.641	+	233.902i	−0.674498	+	1.40061i	−0.904098	+	0.427325i	$0.859456\pi$
$168$		0			0
$169$	−109.118	+	52.5484i	−0.645668	+	0.310937i
$170$	32.7092	−	47.9757i	0.192407	−	0.282210i
$171$		0			0
$172$	64.1830	+	59.5532i	0.373157	+	0.346239i
$173$	166.841	−	244.711i	0.964399	−	1.41451i	0.0550479	−	0.998484i	$-0.482469\pi$
$173$	166.841	−	244.711i	0.964399	−	1.41451i	0.909351	−	0.416030i	$-0.136579\pi$
$174$		0			0
$175$	105.472	−	85.1222i	0.602697	−	0.486412i
$176$	−10.9188	+	22.6732i	−0.0620389	+	0.128825i
$177$		0			0
$178$	17.9520	−	31.0937i	0.100854	−	0.174684i
$179$	168.028	+	246.452i	0.938706	+	1.37683i	0.926251	+	0.376906i	$0.123012\pi$
$179$	168.028	+	246.452i	0.938706	+	1.37683i	0.0124543	+	0.999922i	$0.496036\pi$
$180$		0			0
$181$	18.9155	−	82.8743i	0.104506	−	0.457869i	−0.895415	−	0.445233i	$-0.853121\pi$
$181$	18.9155	−	82.8743i	0.104506	−	0.457869i	0.999920	−	0.0126357i	$-0.00402217\pi$
$182$	95.0613	+	87.1777i	0.522315	+	0.478998i
$183$		0			0
$184$	−10.1897	−	135.972i	−0.0553788	−	0.738978i
$185$	−43.3296	+	140.471i	−0.234214	+	0.759304i
$186$		0			0
$187$	163.448	−	50.4169i	0.874051	−	0.269609i
$188$	−85.8074	+	68.4291i	−0.456422	+	0.363985i
$189$		0			0
$190$	−41.9719	+	52.6311i	−0.220905	+	0.277006i
$191$	−210.904	−	82.7735i	−1.10421	−	0.433369i	−0.257958	−	0.966156i	$-0.583049\pi$
$191$	−210.904	−	82.7735i	−1.10421	−	0.433369i	−0.846249	+	0.532787i	$0.821145\pi$
$192$		0			0
$193$	50.6037	−	7.62728i	0.262195	−	0.0395196i	−0.0166289	−	0.999862i	$-0.505293\pi$
$193$	50.6037	−	7.62728i	0.262195	−	0.0395196i	0.278824	+	0.960342i	$0.410055\pi$
$194$	75.1019	+	80.9406i	0.387123	+	0.417219i
$195$		0			0
$196$	−49.1471	+	129.652i	−0.250751	+	0.661490i
$197$		−	270.383i		−	1.37250i	−0.727364	−	0.686252i	$-0.759255\pi$
$197$		−	270.383i		−	1.37250i	0.727364	−	0.686252i	$-0.240745\pi$
$198$		0			0
$199$	223.604	−	33.7029i	1.12364	−	0.169361i	0.439170	−	0.898404i	$-0.355273\pi$
$199$	223.604	−	33.7029i	1.12364	−	0.169361i	0.684468	+	0.729043i	$0.260035\pi$
$200$	−142.657	−	10.6907i	−0.713286	−	0.0534534i
$201$		0			0
$202$	−123.865	+	155.322i	−0.613195	+	0.768922i
$203$	120.299	+	80.9944i	0.592604	+	0.398987i
$204$		0			0
$205$	18.4317	−	5.68541i	0.0899105	−	0.0277337i
$206$	−146.988	+	57.6886i	−0.713535	+	0.280042i
$207$		0			0
$208$	4.23332	+	56.4897i	0.0203525	+	0.271585i
$209$	−193.331	+	44.1265i	−0.925027	+	0.211131i
$210$		0			0
$211$	30.0467	−	131.643i	0.142401	−	0.623901i	−0.852472	−	0.522773i	$-0.824898\pi$
$211$	30.0467	−	131.643i	0.142401	−	0.623901i	0.994873	−	0.101128i	$-0.0322452\pi$
$212$	27.5357	−	182.687i	0.129885	−	0.861732i
$213$		0			0
$214$	72.9806	−	126.406i	0.341031	−	0.590683i
$215$	63.6250	−	36.7339i	0.295930	−	0.170855i
$216$		0			0
$217$	−21.7774	−	17.1600i	−0.100357	−	0.0790784i
$218$	−46.4502	−	96.4549i	−0.213074	−	0.442454i
$219$		0			0
$220$	37.2668	+	34.5786i	0.169395	+	0.157175i
$221$	261.888	−	282.249i	1.18502	−	1.27714i
$222$		0			0
$223$	−144.791	+	69.7275i	−0.649285	+	0.312679i	−0.729381	−	0.684108i	$-0.760192\pi$
$223$	−144.791	+	69.7275i	−0.649285	+	0.312679i	0.0800957	+	0.996787i	$0.474477\pi$
$224$	208.489	−	101.906i	0.930757	−	0.454936i
$225$		0			0
$226$	36.2221	+	62.7385i	0.160275	+	0.277604i
$227$	119.697	+	69.1073i	0.527301	+	0.304437i	0.739917	−	0.672698i	$-0.234865\pi$
$227$	119.697	+	69.1073i	0.527301	+	0.304437i	−0.212616	+	0.977136i	$0.568198\pi$
$228$		0			0
$229$	−286.624	−	43.2017i	−1.25164	−	0.188654i	−0.510422	−	0.859924i	$-0.670511\pi$
$229$	−286.624	−	43.2017i	−1.25164	−	0.188654i	−0.741213	+	0.671270i	$0.765749\pi$
$230$	−46.2154	−	10.5484i	−0.200937	−	0.0458625i
$231$		0			0
$232$	−34.0615	−	149.233i	−0.146817	−	0.643246i
$233$	−238.820	+	17.8971i	−1.02498	+	0.0768114i	−0.576595	−	0.817030i	$-0.695619\pi$
$233$	−238.820	+	17.8971i	−1.02498	+	0.0768114i	−0.448382	+	0.893842i	$0.648000\pi$
$234$		0			0
$235$	33.6451	+	85.7262i	0.143170	+	0.364792i
$236$	−52.0878	−	168.865i	−0.220711	−	0.715528i
$237$		0			0
$238$	−159.713	−	61.6101i	−0.671063	−	0.258866i
$239$	−64.3258	−	51.2981i	−0.269145	−	0.214636i	0.479612	−	0.877481i	$-0.340778\pi$
$239$	−64.3258	−	51.2981i	−0.269145	−	0.214636i	−0.748757	+	0.662845i	$0.769349\pi$
$240$		0			0
$241$	−8.12450	+	108.414i	−0.0337116	+	0.449850i	0.954650	+	0.297729i	$0.0962293\pi$
$241$	−8.12450	+	108.414i	−0.0337116	+	0.449850i	−0.988362	+	0.152121i	$0.951390\pi$
$242$	10.2782	+	68.1917i	0.0424721	+	0.281784i
$243$		0			0
$244$	155.798			0.638517
$245$	91.8017	+	71.4735i	0.374701	+	0.291729i
$246$		0			0
$247$	−327.224	+	303.620i	−1.32479	+	1.22923i
$248$	4.36162	+	28.9374i	0.0175872	+	0.116683i
$249$		0			0
$250$	−41.6307	+	106.073i	−0.166523	+	0.424293i
$251$	235.950	+	188.164i	0.940041	+	0.749658i	0.968260	−	0.249944i	$-0.0804123\pi$
$251$	235.950	+	188.164i	0.940041	+	0.749658i	−0.0282193	+	0.999602i	$0.508984\pi$
$252$		0			0
$253$	−87.0649	−	109.176i	−0.344130	−	0.431525i
$254$	−33.2382	−	107.756i	−0.130859	−	0.424235i
$255$		0			0
$256$	−198.085	−	61.1011i	−0.773769	−	0.238676i
$257$	16.3462	−	1.22498i	0.0636039	−	0.00476645i	−0.0428901	−	0.999080i	$-0.513657\pi$
$257$	16.3462	−	1.22498i	0.0636039	−	0.00476645i	0.106494	+	0.994313i	$0.466037\pi$
$258$		0			0
$259$	432.353	+	29.8655i	1.66932	+	0.115311i
$260$	111.569	+	25.4648i	0.429111	+	0.0979417i
$261$		0			0
$262$	−3.24922	+	2.21528i	−0.0124016	+	0.00845527i
$263$	350.486	+	202.353i	1.33264	+	0.769403i	0.985704	−	0.168484i	$-0.0538873\pi$
$263$	350.486	+	202.353i	1.33264	+	0.769403i	0.346940	+	0.937887i	$0.387221\pi$
$264$		0			0
$265$	−139.671	−	67.2622i	−0.527062	−	0.253820i
$266$	179.307	+	85.0651i	0.674088	+	0.319794i
$267$		0			0
$268$	−131.958	−	89.9675i	−0.492381	−	0.335700i
$269$	−89.9226	+	96.9135i	−0.334285	+	0.360273i	−0.877717	−	0.479180i	$-0.840934\pi$
$269$	−89.9226	+	96.9135i	−0.334285	+	0.360273i	0.543432	+	0.839453i	$0.317125\pi$
$270$		0			0
$271$	223.869	+	152.632i	0.826086	+	0.563216i	0.900923	−	0.433980i	$-0.142891\pi$
$271$	223.869	+	152.632i	0.826086	+	0.563216i	−0.0748362	+	0.997196i	$0.523843\pi$
$272$	−32.6205	−	67.7372i	−0.119928	−	0.249034i
$273$		0			0
$274$	−85.9473	−	41.3901i	−0.313676	−	0.151059i
$275$	−126.879	+	73.2534i	−0.461377	+	0.266376i
$276$		0			0
$277$	363.778	−	248.020i	1.31328	−	0.895378i	0.314726	−	0.949182i	$-0.398087\pi$
$277$	363.778	−	248.020i	1.31328	−	0.895378i	0.998551	+	0.0538047i	$0.0171348\pi$
$278$	6.43998	−	42.7265i	0.0231654	−	0.153692i
$279$		0			0
$280$	−19.0104	−	121.320i	−0.0678943	−	0.433286i
$281$	407.780	−	93.0732i	1.45118	−	0.331221i	0.576965	−	0.816769i	$-0.304237\pi$
$281$	407.780	−	93.0732i	1.45118	−	0.331221i	0.874210	+	0.485547i	$0.161380\pi$
$282$		0			0
$283$	−272.914	−	84.1829i	−0.964361	−	0.297466i	−0.227702	−	0.973731i	$-0.573121\pi$
$283$	−272.914	−	84.1829i	−0.964361	−	0.297466i	−0.736659	+	0.676265i	$0.763598\pi$
$284$	344.979	−	135.394i	1.21471	−	0.476740i
$285$		0			0
$286$	−86.9288	−	109.005i	−0.303947	−	0.381137i
$287$	−28.7195	−	49.0803i	−0.100068	−	0.171012i
$288$		0			0
$289$	−81.1091	+	206.663i	−0.280654	+	0.715095i
$290$	−53.0671	−	3.97683i	−0.182990	−	0.0137132i
$291$		0			0
$292$	140.779	−	130.624i	0.482120	−	0.447342i
$293$		−	453.668i		−	1.54836i	−0.632968	−	0.774178i	$-0.718164\pi$
$293$		−	453.668i		−	1.54836i	0.632968	−	0.774178i	$-0.281836\pi$
$294$		0			0
$295$	−148.281			−0.502648
$296$	−311.132	−	335.321i	−1.05112	−	1.13284i
$297$		0			0
$298$	−2.57803	+	34.4014i	−0.00865110	+	0.115441i
$299$	−292.609	−	114.840i	−0.978624	−	0.384082i
$300$		0			0
$301$	−148.245	−	157.912i	−0.492507	−	0.524626i
$302$	179.711	−	143.315i	0.595069	−	0.474551i
$303$		0			0
$304$	31.8441	+	81.1376i	0.104750	+	0.266900i
$305$	38.5332	−	124.922i	0.126338	−	0.409579i
$306$		0			0
$307$	68.9625	+	302.144i	0.224634	+	0.984184i	0.953940	+	0.299997i	$0.0969857\pi$
$307$	68.9625	+	302.144i	0.224634	+	0.984184i	−0.729307	+	0.684187i	$0.760157\pi$
$308$	74.1804	−	130.233i	0.240845	−	0.422833i
$309$		0			0
$310$	10.0603	+	1.51634i	0.0324524	+	0.00489142i
$311$	75.9644	+	111.419i	0.244258	+	0.358261i	0.928716	−	0.370791i	$-0.120913\pi$
$311$	75.9644	+	111.419i	0.244258	+	0.358261i	−0.684458	+	0.729052i	$0.739961\pi$
$312$		0			0
$313$	−119.733	−	207.383i	−0.382533	−	0.662567i	0.608890	−	0.793254i	$-0.291615\pi$
$313$	−119.733	−	207.383i	−0.382533	−	0.662567i	−0.991424	+	0.130687i	$0.958282\pi$
$314$	−53.5090	+	111.112i	−0.170411	+	0.353861i
$315$		0			0
$316$	72.5965	−	34.9606i	0.229736	−	0.110635i
$317$	32.9709	−	48.3595i	0.104009	−	0.152554i	−0.770706	−	0.637191i	$-0.780096\pi$
$317$	32.9709	−	48.3595i	0.104009	−	0.152554i	0.874715	+	0.484638i	$0.161049\pi$
$318$		0			0
$319$	−114.915	−	106.625i	−0.360234	−	0.334248i
$320$	−30.1753	+	44.2591i	−0.0942979	+	0.138310i
$321$		0			0
$322$	0.815147	+	139.751i	0.00253151	+	0.434010i
$323$	257.049	−	533.768i	0.795817	−	1.65253i
$324$		0			0
$325$	−164.896	+	285.608i	−0.507373	+	0.878795i
$326$	87.5718	+	128.444i	0.268625	+	0.394001i
$327$		0			0
$328$	−13.3559	+	58.5161i	−0.0407193	+	0.178403i
$329$	223.429	−	154.248i	0.679115	−	0.468838i
$330$		0			0
$331$	24.5371	+	327.425i	0.0741302	+	0.989199i	0.902967	+	0.429709i	$0.141384\pi$
$331$	24.5371	+	327.425i	0.0741302	+	0.989199i	−0.828837	+	0.559490i	$0.810997\pi$
$332$	−87.3007	+	283.022i	−0.262954	+	0.852476i
$333$		0			0
$334$	−268.373	+	82.7822i	−0.803513	+	0.247851i
$335$	−104.774	+	83.5548i	−0.312759	+	0.249417i
$336$		0			0
$337$	241.418	−	302.729i	0.716374	−	0.898304i	−0.281753	−	0.959487i	$-0.590916\pi$
$337$	241.418	−	302.729i	0.716374	−	0.898304i	0.998127	+	0.0611826i	$0.0194872\pi$
$338$	−121.963	−	47.8670i	−0.360838	−	0.141618i
$339$		0			0
$340$	−150.184	+	22.6366i	−0.441718	+	0.0665783i
$341$	20.3848	+	21.9695i	0.0597793	+	0.0644268i
$342$		0			0
$343$	143.392	−	311.589i	0.418053	−	0.908423i
$344$			228.612i			0.664571i
$345$		0			0
$346$	316.826	−	47.7539i	0.915683	−	0.138017i
$347$	−121.948	−	9.13872i	−0.351434	−	0.0263364i	−0.102156	−	0.994768i	$-0.532574\pi$
$347$	−121.948	−	9.13872i	−0.351434	−	0.0263364i	−0.249278	+	0.968432i	$0.580193\pi$
$348$		0			0
$349$	275.738	−	345.765i	0.790080	−	0.990729i	−0.209835	−	0.977737i	$-0.567293\pi$
$349$	275.738	−	345.765i	0.790080	−	0.990729i	0.999916	−	0.0129926i	$-0.00413579\pi$
$350$	145.112	+	21.0072i	0.414606	+	0.0600207i
$351$		0			0
$352$	−239.701	+	73.9379i	−0.680968	+	0.210051i
$353$	241.204	−	94.6654i	0.683296	−	0.268174i	0.00180304	−	0.999998i	$-0.499426\pi$
$353$	241.204	−	94.6654i	0.683296	−	0.268174i	0.681493	+	0.731824i	$0.261331\pi$
$354$		0			0
$355$	−23.2385	−	310.096i	−0.0654606	−	0.873511i
$356$	−91.5591	+	20.8978i	−0.257188	+	0.0587016i
$357$		0			0
$358$	−71.8042	+	314.595i	−0.200570	+	0.878756i
$359$	−13.4910	+	89.5069i	−0.0375794	+	0.249323i	−0.999731	−	0.0231916i	$-0.992617\pi$
$359$	−13.4910	+	89.5069i	−0.0375794	+	0.249323i	0.962152	+	0.272515i	$0.0878553\pi$
$360$		0			0
$361$	−162.921	+	282.187i	−0.451304	+	0.781681i
$362$	79.6397	−	45.9800i	0.219999	−	0.127017i
$363$		0			0
$364$	−1.96785	−	337.374i	−0.00540617	−	0.926851i
$365$	−69.9179	−	145.186i	−0.191556	−	0.397770i
$366$		0			0
$367$	91.0671	+	84.4979i	0.248139	+	0.230239i	0.794429	−	0.607356i	$-0.207770\pi$
$367$	91.0671	+	84.4979i	0.248139	+	0.230239i	−0.546290	+	0.837596i	$0.683960\pi$
$368$	−41.7480	+	44.9936i	−0.113446	+	0.122265i
$369$		0			0
$370$	−143.280	+	68.9999i	−0.387243	+	0.186486i
$371$	−99.0985	+	446.159i	−0.267112	+	1.20258i
$372$		0			0
$373$	−348.059	−	602.857i	−0.933135	−	1.61624i	−0.777926	−	0.628356i	$-0.783728\pi$
$373$	−348.059	−	602.857i	−0.933135	−	1.61624i	−0.155209	−	0.987882i	$-0.549605\pi$
$374$	160.249	+	92.5201i	0.428475	+	0.247380i
$375$		0			0
$376$	−283.366	−	42.7105i	−0.753633	−	0.113592i
$377$	−344.029	−	78.5225i	−0.912545	−	0.208282i
$378$		0			0
$379$	−39.5386	−	173.230i	−0.104323	−	0.457071i	−0.999925	−	0.0122145i	$-0.996112\pi$
$379$	−39.5386	−	173.230i	−0.104323	−	0.457071i	0.895602	−	0.444856i	$-0.146745\pi$
$380$	175.590	−	13.1586i	0.462079	−	0.0346280i
$381$		0			0
$382$	−89.5453	−	228.158i	−0.234412	−	0.597272i
$383$	−147.160	−	477.081i	−0.384230	−	1.24564i	−0.916831	−	0.399276i	$-0.869261\pi$
$383$	−147.160	−	477.081i	−0.384230	−	1.24564i	0.532601	−	0.846367i	$-0.321215\pi$
$384$		0			0
$385$	−86.0758	−	91.6892i	−0.223574	−	0.238154i
$386$	43.2838	+	34.5177i	0.112134	+	0.0894240i
$387$		0			0
$388$	21.5831	−	288.006i	0.0556265	−	0.742284i
$389$	1.70896	+	11.3382i	0.00439320	+	0.0291470i	0.990920	−	0.134453i	$-0.0429276\pi$
$389$	1.70896	+	11.3382i	0.00439320	+	0.0291470i	−0.986527	+	0.163600i	$0.947689\pi$
$390$		0			0
$391$	417.184			1.06697
$392$	−335.441	+	136.188i	−0.855717	+	0.347418i
$393$		0			0
$394$	214.420	−	198.953i	0.544214	−	0.504957i
$395$	−10.0769	−	66.8559i	−0.0255111	−	0.169255i
$396$		0			0
$397$	−58.1476	+	148.158i	−0.146468	+	0.373193i	−0.985214	−	0.171329i	$-0.945194\pi$
$397$	−58.1476	+	148.158i	−0.146468	+	0.373193i	0.838746	+	0.544522i	$0.183289\pi$
$398$	191.259	+	152.524i	0.480550	+	0.383226i
$399$		0			0
$400$	40.1504	+	50.3470i	0.100376	+	0.125868i
$401$	143.735	+	465.978i	0.358442	+	1.16204i	0.937861	+	0.347010i	$0.112803\pi$
$401$	143.735	+	465.978i	0.358442	+	1.16204i	−0.579420	+	0.815029i	$0.696721\pi$
$402$		0			0
$403$	64.4663	+	19.8852i	0.159966	+	0.0493429i
$404$	518.193	−	38.8332i	1.28266	−	0.0961217i
$405$		0			0
$406$	24.2874	+	154.997i	0.0598212	+	0.381765i
$407$	−456.716	−	104.243i	−1.12215	−	0.256124i
$408$		0			0
$409$	304.120	−	207.346i	0.743570	−	0.506957i	−0.131284	−	0.991345i	$-0.541910\pi$
$409$	304.120	−	207.346i	0.743570	−	0.506957i	0.874854	+	0.484388i	$0.160958\pi$
$410$	18.0710	+	10.4333i	0.0440757	+	0.0254471i
$411$		0			0
$412$	372.124	+	179.206i	0.903214	+	0.434965i
$413$	99.7602	+	425.619i	0.241550	+	1.03056i
$414$		0			0
$415$	205.340	+	139.998i	0.494795	+	0.337345i
$416$	−384.067	+	413.926i	−0.923238	+	0.995014i
$417$		0			0
$418$	−177.250	−	120.847i	−0.424042	−	0.289107i
$419$	−22.8154	−	47.3766i	−0.0544520	−	0.113071i	0.871967	−	0.489564i	$-0.162844\pi$
$419$	−22.8154	−	47.3766i	−0.0544520	−	0.113071i	−0.926419	+	0.376493i	$0.877130\pi$
$420$		0			0
$421$	−364.426	−	175.498i	−0.865619	−	0.416860i	−0.0522681	−	0.998633i	$-0.516645\pi$
$421$	−364.426	−	175.498i	−0.865619	−	0.416860i	−0.813351	+	0.581773i	$0.802359\pi$
$422$	126.505	−	73.0377i	0.299775	−	0.173075i
$423$		0			0
$424$	398.571	−	271.741i	0.940026	−	0.640899i
$425$	65.2351	−	432.807i	0.153494	−	1.01837i
$426$		0			0
$427$	−384.493	−	26.5595i	−0.900452	−	0.0622002i
$428$	−372.217	+	84.9562i	−0.869666	+	0.198496i
$429$		0			0
$430$	75.9473	+	23.4266i	0.176622	+	0.0544806i
$431$	168.065	−	65.9606i	0.389942	−	0.153041i	−0.162267	−	0.986747i	$-0.551881\pi$
$431$	168.065	−	65.9606i	0.389942	−	0.153041i	0.552208	+	0.833706i	$0.313785\pi$
$432$		0			0
$433$	287.198	+	360.135i	0.663275	+	0.831720i	0.993695	−	0.112113i	$-0.0357620\pi$
$433$	287.198	+	360.135i	0.663275	+	0.831720i	−0.330420	+	0.943834i	$0.607191\pi$
$434$	−2.41588	−	29.8966i	−0.00556655	−	0.0688862i
$435$		0			0
$436$	−102.306	+	260.670i	−0.234646	+	0.597868i
$437$	−482.309	−	36.1441i	−1.10368	−	0.0827096i
$438$		0			0
$439$	−246.704	+	228.908i	−0.561969	+	0.521431i	−0.909206	−	0.416346i	$-0.863310\pi$
$439$	−246.704	+	228.908i	−0.561969	+	0.521431i	0.347237	+	0.937777i	$0.387120\pi$
$440$			132.740i			0.301682i
$441$		0			0
$442$	416.532			0.942380
$443$	13.7741	+	14.8449i	0.0310927	+	0.0335100i	0.748407	−	0.663240i	$-0.230819\pi$
$443$	13.7741	+	14.8449i	0.0310927	+	0.0335100i	−0.717314	+	0.696750i	$0.754629\pi$
$444$		0			0
$445$	−5.88892	+	78.5822i	−0.0132335	+	0.176589i
$446$	−161.835	−	63.5156i	−0.362859	−	0.142412i
$447$		0			0
$448$	147.340	+	56.8373i	0.328885	+	0.126869i
$449$	486.015	−	387.584i	1.08244	−	0.863217i	0.0912713	−	0.995826i	$-0.470907\pi$
$449$	486.015	−	387.584i	1.08244	−	0.863217i	0.991168	+	0.132609i	$0.0423355\pi$
$450$		0			0
$451$	22.4569	+	57.2192i	0.0497935	+	0.126872i
$452$	55.8537	−	181.073i	0.123570	−	0.400604i
$453$		0			0
$454$	33.2718	+	145.773i	0.0732859	+	0.321087i
$455$	−270.999	−	81.8641i	−0.595602	−	0.179921i
$456$		0			0
$457$	657.392	+	99.0858i	1.43849	+	0.216818i	0.821526	−	0.570171i	$-0.193123\pi$
$457$	657.392	+	99.0858i	1.43849	+	0.216818i	0.616967	+	0.786989i	$0.288361\pi$
$458$	−176.644	−	259.089i	−0.385685	−	0.565696i
$459$		0			0
$460$	61.9971	+	107.382i	0.134776	+	0.233439i
$461$	200.524	−	416.392i	0.434975	−	0.903236i	−0.562119	−	0.827057i	$-0.690014\pi$
$461$	200.524	−	416.392i	0.434975	−	0.903236i	0.997094	−	0.0761792i	$-0.0242721\pi$
$462$		0			0
$463$	−577.975	+	278.338i	−1.24833	+	0.601162i	−0.937062	−	0.349162i	$-0.886466\pi$
$463$	−577.975	+	278.338i	−1.24833	+	0.601162i	−0.311263	+	0.950324i	$0.600752\pi$
$464$	−38.8149	+	56.9310i	−0.0836528	+	0.122696i
$465$		0			0
$466$	−189.921	−	176.221i	−0.407555	−	0.378156i
$467$	−311.415	+	456.762i	−0.666841	+	0.978077i	0.332546	+	0.943087i	$0.392092\pi$
$467$	−311.415	+	456.762i	−0.666841	+	0.978077i	−0.999388	+	0.0349897i	$0.988860\pi$
$468$		0			0
$469$	310.321	+	244.526i	0.661666	+	0.521376i
$470$	−43.2263	+	89.7603i	−0.0919708	+	0.190979i
$471$		0			0
$472$	230.706	−	399.594i	0.488784	−	0.846598i
$473$	131.887	+	193.443i	0.278831	+	0.408971i
$474$		0			0
$475$	−112.916	+	494.719i	−0.237719	+	1.04151i
$476$	166.015	+	415.852i	0.348772	+	0.873638i
$477$		0			0
$478$	−6.65149	−	88.7579i	−0.0139152	−	0.185686i
$479$	20.6076	−	66.8080i	0.0430220	−	0.139474i	−0.931514	−	0.363706i	$-0.881511\pi$
$479$	20.6076	−	66.8080i	0.0430220	−	0.139474i	0.974536	+	0.224232i	$0.0719874\pi$
$480$		0			0
$481$	−1007.67	+	310.827i	−2.09496	+	0.646209i
$482$	−91.9530	+	73.3300i	−0.190774	+	0.152137i
$483$		0			0
$484$	112.467	−	141.029i	0.232370	−	0.291383i
$485$	−225.590	−	88.5376i	−0.465134	−	0.182552i
$486$		0			0
$487$	321.337	−	48.4337i	0.659829	−	0.0994533i	0.189413	−	0.981898i	$-0.439342\pi$
$487$	321.337	−	48.4337i	0.659829	−	0.0994533i	0.470417	+	0.882444i	$0.344104\pi$
$488$	276.691	+	298.202i	0.566990	+	0.611070i
$489$		0			0
$490$	10.8692	+	125.393i	0.0221821	+	0.255903i
$491$			357.873i			0.728866i	0.931230	+	0.364433i	$0.118737\pi$
$491$			357.873i			0.728866i	−0.931230	+	0.364433i	$0.881263\pi$
$492$		0			0
$493$	463.102	−	69.8014i	0.939355	−	0.141585i
$494$	−481.555	−	36.0876i	−0.974809	−	0.0730518i
$495$		0			0
$496$	8.21331	−	10.2992i	0.0165591	−	0.0207645i
$497$	−874.452	+	275.328i	−1.75946	+	0.553981i
$498$		0			0
$499$	−373.418	+	115.184i	−0.748332	+	0.230830i	−0.645385	−	0.763857i	$-0.723303\pi$
$499$	−373.418	+	115.184i	−0.748332	+	0.230830i	−0.102946	+	0.994687i	$0.532827\pi$
$500$	277.455	−	108.893i	0.554910	−	0.217786i
$501$		0			0
$502$	24.3980	+	325.569i	0.0486016	+	0.648543i
$503$	−730.585	+	166.751i	−1.45245	+	0.331513i	−0.874687	−	0.484688i	$-0.838933\pi$
$503$	−730.585	+	166.751i	−1.45245	+	0.331513i	−0.577768	+	0.816201i	$0.696076\pi$
$504$		0			0
$505$	97.0263	−	425.100i	0.192131	−	0.841783i
$506$	22.5151	−	149.378i	0.0444963	−	0.295214i
$507$		0			0
$508$	−147.480	+	255.443i	−0.290315	+	0.502840i
$509$	−434.163	+	250.664i	−0.852972	+	0.492464i	−0.861653	−	0.507498i	$-0.830570\pi$
$509$	−434.163	+	250.664i	−0.852972	+	0.492464i	0.00868021	+	0.999962i	$0.497237\pi$
$510$		0			0
$511$	−369.696	+	298.367i	−0.723475	+	0.583888i
$512$	90.4859	+	187.896i	0.176730	+	0.366984i
$513$		0			0
$514$	12.9993	+	12.0616i	0.0252904	+	0.0234661i
$515$	235.727	−	254.053i	0.457722	−	0.493307i
$516$		0			0
$517$	−264.413	+	127.335i	−0.511438	+	0.246295i
$518$	294.449	+	364.842i	0.568435	+	0.704328i
$519$		0			0
$520$	149.401	+	258.771i	0.287310	+	0.497636i
$521$	−37.7967	−	21.8219i	−0.0725464	−	0.0418847i	0.463288	−	0.886208i	$-0.346670\pi$
$521$	−37.7967	−	21.8219i	−0.0725464	−	0.0418847i	−0.535834	+	0.844323i	$0.680003\pi$
$522$		0			0
$523$	612.732	+	92.3545i	1.17157	+	0.176586i	0.705861	−	0.708350i	$-0.250560\pi$
$523$	612.732	+	92.3545i	1.17157	+	0.176586i	0.465712	+	0.884937i	$0.345798\pi$
$524$	10.0284	+	2.28892i	0.0191382	+	0.00436817i
$525$		0			0
$526$	97.4231	+	426.838i	0.185215	+	0.811480i
$527$	−89.2862	+	6.69107i	−0.169424	+	0.0126965i
$528$		0			0
$529$	68.8353	+	175.389i	0.130123	+	0.331549i
$530$	−49.4323	−	160.256i	−0.0932685	−	0.302369i
$531$		0			0
$532$	−155.903	−	495.152i	−0.293050	−	0.930737i
$533$	108.180	+	86.2706i	0.202964	+	0.161859i
$534$		0			0
$535$	−23.9404	+	319.462i	−0.0447484	+	0.597126i
$536$	−62.1518	−	412.350i	−0.115955	−	0.769311i
$537$		0			0
$538$	−143.021			−0.265839
$539$	−205.270	+	308.754i	−0.380836	+	0.572828i
$540$		0			0
$541$	−581.065	+	539.150i	−1.07406	+	0.996580i	−1.00000		0.000673711i	$-0.999786\pi$
$541$	−581.065	+	539.150i	−1.07406	+	0.996580i	−0.0740582	+	0.997254i	$0.523595\pi$
$542$	43.6868	+	289.843i	0.0806029	+	0.534766i
$543$		0			0
$544$	273.790	−	697.606i	0.503291	−	1.28236i
$545$	183.707	+	146.501i	0.337077	+	0.268810i
$546$		0			0
$547$	359.109	+	450.308i	0.656506	+	0.823233i	0.992958	−	0.118468i	$-0.0377984\pi$
$547$	359.109	+	450.308i	0.656506	+	0.823233i	−0.336452	+	0.941701i	$0.609227\pi$
$548$	73.5480	+	238.437i	0.134212	+	0.435103i
$549$		0			0
$550$	−151.451	−	46.7166i	−0.275366	−	0.0849392i
$551$	−541.443	+	40.5755i	−0.982655	+	0.0736398i
$552$		0			0
$553$	−185.120	+	73.9033i	−0.334757	+	0.133641i
$554$	464.360	+	105.987i	0.838195	+	0.191313i
$555$		0			0
$556$	−93.3829	+	63.6674i	−0.167955	+	0.114510i
$557$	378.504	+	218.529i	0.679540	+	0.392333i	0.799682	−	0.600424i	$-0.205001\pi$
$557$	378.504	+	218.529i	0.679540	+	0.392333i	−0.120141	+	0.992757i	$0.538335\pi$
$558$		0			0
$559$	474.832	+	228.667i	0.849431	+	0.409065i
$560$	−34.2125	+	43.4182i	−0.0610937	+	0.0775325i
$561$		0			0
$562$	373.862	+	254.895i	0.665234	+	0.453549i
$563$	16.3931	−	17.6676i	0.0291174	−	0.0313811i	−0.718325	−	0.695707i	$-0.755091\pi$
$563$	16.3931	−	17.6676i	0.0291174	−	0.0313811i	0.747443	+	0.664326i	$0.231281\pi$
$564$		0			0
$565$	−131.373	−	89.5688i	−0.232519	−	0.158529i
$566$	−134.056	−	278.371i	−0.236849	−	0.491821i
$567$		0			0
$568$	871.817	+	419.845i	1.53489	+	0.739164i
$569$	508.873	−	293.798i	0.894329	−	0.516341i	0.0189731	−	0.999820i	$-0.493960\pi$
$569$	508.873	−	293.798i	0.894329	−	0.516341i	0.875356	+	0.483479i	$0.160627\pi$
$570$		0			0
$571$	−233.207	+	158.998i	−0.408418	+	0.278455i	−0.750053	−	0.661378i	$-0.769972\pi$
$571$	−233.207	+	158.998i	−0.408418	+	0.278455i	0.341634	+	0.939833i	$0.389020\pi$
$572$	−54.3539	+	360.614i	−0.0950242	+	0.630444i
$573$		0			0
$574$	17.7895	−	58.8895i	0.0309921	−	0.102595i
$575$	−348.372	+	79.5137i	−0.605865	+	0.138285i
$576$		0			0
$577$	−450.506	−	138.963i	−0.780773	−	0.240836i	−0.121351	−	0.992610i	$-0.538723\pi$
$577$	−450.506	−	138.963i	−0.780773	−	0.240836i	−0.659422	+	0.751773i	$0.729199\pi$
$578$	−223.570	+	87.7447i	−0.386799	+	0.151807i
$579$		0			0
$580$	86.7875	+	108.828i	0.149634	+	0.187635i
$581$	263.697	−	683.585i	0.453867	−	1.17657i
$582$		0			0
$583$	180.487	−	459.874i	0.309584	−	0.788807i
$584$	500.036	+	37.4725i	0.856227	+	0.0641653i
$585$		0			0
$586$	359.770	−	333.817i	0.613941	−	0.569654i
$587$		−	188.225i		−	0.320655i	−0.987064	−	0.160328i	$-0.948745\pi$
$587$		−	188.225i		−	0.320655i	0.987064	−	0.160328i	$-0.0512551\pi$
$588$		0			0
$589$	103.804			0.176238
$590$	−109.108	−	117.591i	−0.184929	−	0.199306i
$591$		0			0
$592$	−15.3877	+	205.334i	−0.0259927	+	0.346848i
$593$	−140.214	−	55.0299i	−0.236448	−	0.0927991i	0.244158	−	0.969735i	$-0.421488\pi$
$593$	−140.214	−	55.0299i	−0.236448	−	0.0927991i	−0.480607	+	0.876936i	$0.659584\pi$
$594$		0			0
$595$	374.497	−	30.2623i	0.629407	−	0.0508610i
$596$	70.5491	−	56.2611i	0.118371	−	0.0943977i
$597$		0			0
$598$	−124.236	−	316.547i	−0.207752	−	0.529343i
$599$	−19.3289	+	62.6627i	−0.0322686	+	0.104612i	−0.970274	−	0.242007i	$-0.922194\pi$
$599$	−19.3289	+	62.6627i	−0.0322686	+	0.104612i	0.938006	+	0.346619i	$0.112670\pi$
$600$		0			0
$601$	−189.756	−	831.375i	−0.315734	−	1.38332i	−0.844956	−	0.534836i	$-0.820373\pi$
$601$	−189.756	−	831.375i	−0.315734	−	1.38332i	0.529222	−	0.848483i	$-0.322484\pi$
$602$	16.1471	−	233.756i	0.0268224	−	0.388300i
$603$		0			0
$604$	−594.524	−	89.6101i	−0.984311	−	0.148361i
$605$	−85.2634	−	125.058i	−0.140931	−	0.206708i
$606$		0			0
$607$	223.185	+	386.567i	0.367685	+	0.636849i	0.989203	−	0.146551i	$-0.0468172\pi$
$607$	223.185	+	386.567i	0.367685	+	0.636849i	−0.621518	+	0.783400i	$0.713484\pi$
$608$	−376.970	+	782.786i	−0.620017	+	1.28748i
$609$		0			0
$610$	127.419	−	61.3619i	0.208884	−	0.100593i
$611$	−372.144	+	545.835i	−0.609074	+	0.893348i
$612$		0			0
$613$	−141.472	−	131.267i	−0.230786	−	0.214138i	0.556300	−	0.830982i	$-0.312221\pi$
$613$	−141.472	−	131.267i	−0.230786	−	0.214138i	−0.787086	+	0.616844i	$0.788411\pi$
$614$	−188.864	+	277.012i	−0.307596	+	0.451160i
$615$		0			0
$616$	381.010	−	89.3044i	0.618523	−	0.144975i
$617$	−277.891	+	577.046i	−0.450390	+	0.935245i	0.544918	+	0.838489i	$0.316561\pi$
$617$	−277.891	+	577.046i	−0.450390	+	0.935245i	−0.995308	+	0.0967555i	$0.969154\pi$
$618$		0			0
$619$	83.8846	−	145.292i	0.135516	−	0.234721i	−0.790278	−	0.612748i	$-0.790064\pi$
$619$	83.8846	−	145.292i	0.135516	−	0.234721i	0.925795	+	0.378027i	$0.123397\pi$
$620$	−14.9909	−	21.9877i	−0.0241789	−	0.0354640i
$621$		0			0
$622$	−32.4621	+	142.226i	−0.0521899	+	0.228659i
$623$	229.521	−	35.9650i	0.368412	−	0.0577288i
$624$		0			0
$625$	17.4837	+	233.304i	0.0279740	+	0.373287i
$626$	76.3583	−	247.548i	0.121978	−	0.395443i
$627$		0			0
$628$	308.250	−	95.0826i	0.490844	−	0.151405i
$629$	1094.21	−	872.605i	1.73961	−	1.38729i
$630$		0			0
$631$	325.914	−	408.683i	0.516504	−	0.647676i	−0.453358	−	0.891328i	$-0.649774\pi$
$631$	325.914	−	408.683i	0.516504	−	0.647676i	0.969863	+	0.243653i	$0.0783457\pi$
$632$	195.844	+	76.8632i	0.309880	+	0.121619i
$633$		0			0
$634$	62.6108	−	9.43706i	0.0987552	−	0.0148850i
$635$	168.342	+	181.430i	0.265106	+	0.285717i
$636$		0			0
$637$	−52.6569	+	832.938i	−0.0826639	+	1.30759i
$638$		−	169.587i		−	0.265810i
$639$		0			0
$640$	254.039	−	38.2903i	0.396936	−	0.0598285i
$641$	900.766	+	67.5031i	1.40525	+	0.105309i	0.755654	−	0.654970i	$-0.227319\pi$
$641$	900.766	+	67.5031i	1.40525	+	0.105309i	0.649596	+	0.760279i	$0.274938\pi$
$642$		0			0
$643$	93.9879	−	117.857i	0.146171	−	0.183292i	−0.703356	−	0.710838i	$-0.748316\pi$
$643$	93.9879	−	117.857i	0.146171	−	0.183292i	0.849527	+	0.527545i	$0.176887\pi$
$644$	266.514	−	250.197i	0.413842	−	0.388505i
$645$		0			0
$646$	612.432	−	188.910i	0.948037	−	0.292431i
$647$	−234.338	+	91.9708i	−0.362191	+	0.142150i	−0.539456	−	0.842014i	$-0.681370\pi$
$647$	−234.338	+	91.9708i	−0.362191	+	0.142150i	0.177265	+	0.984163i	$0.443275\pi$
$648$		0			0
$649$	−35.3128	−	471.217i	−0.0544111	−	0.726066i
$650$	−347.828	+	79.3895i	−0.535120	+	0.122138i
$651$		0			0
$652$	90.4829	−	396.432i	0.138777	−	0.608024i
$653$	−155.672	+	1032.82i	−0.238395	+	1.58165i	0.474420	+	0.880298i	$0.342658\pi$
$653$	−155.672	+	1032.82i	−0.238395	+	1.58165i	−0.712816	+	0.701351i	$0.752580\pi$
$654$		0			0
$655$	4.31560	−	7.47484i	0.00658871	−	0.0114120i
$656$	23.3983	−	13.5090i	0.0356682	−	0.0205930i
$657$		0			0
$658$	286.725	+	63.6859i	0.435753	+	0.0967872i
$659$	−62.2654	−	129.295i	−0.0944847	−	0.196199i	0.848370	−	0.529404i	$-0.177584\pi$
$659$	−62.2654	−	129.295i	−0.0944847	−	0.196199i	−0.942855	+	0.333204i	$0.891870\pi$
$660$		0			0
$661$	−558.420	−	518.138i	−0.844812	−	0.783871i	0.133491	−	0.991050i	$-0.457381\pi$
$661$	−558.420	−	518.138i	−0.844812	−	0.783871i	−0.978303	+	0.207179i	$0.933572\pi$
$662$	−241.601	+	260.384i	−0.364956	+	0.393329i
$663$		0			0
$664$	−696.755	+	335.540i	−1.04933	+	0.505331i
$665$	−435.580	+	2.54067i	−0.655008	+	0.00382056i
$666$		0			0
$667$	−191.172	−	331.119i	−0.286614	−	0.496431i
$668$	636.198	+	367.309i	0.952393	+	0.549864i
$669$		0			0
$670$	−143.356	−	21.6074i	−0.213964	−	0.0322499i
$671$	406.160	+	92.7033i	0.605305	+	0.138157i
$672$		0			0
$673$	−62.9828	−	275.946i	−0.0935852	−	0.410023i	0.906336	−	0.422557i	$-0.138867\pi$
$673$	−62.9828	−	275.946i	−0.0935852	−	0.410023i	−0.999921	+	0.0125337i	$0.996010\pi$
$674$	417.711	−	31.3031i	0.619749	−	0.0464438i
$675$		0			0
$676$	125.205	+	319.018i	0.185215	+	0.471920i
$677$	−319.199	−	1034.82i	−0.471490	−	1.52853i	−0.809344	−	0.587335i	$-0.800177\pi$
$677$	−319.199	−	1034.82i	−0.471490	−	1.52853i	0.337854	−	0.941199i	$-0.390299\pi$
$678$		0			0
$679$	−102.362	+	707.089i	−0.150754	+	1.04137i
$680$	−310.048	−	247.255i	−0.455953	−	0.363611i
$681$		0			0
$682$	−2.42289	+	32.3312i	−0.00355262	+	0.0474064i
$683$	100.995	+	670.059i	0.147870	+	0.981053i	0.932521	+	0.361115i	$0.117604\pi$
$683$	100.995	+	670.059i	0.147870	+	0.981053i	−0.784651	+	0.619938i	$0.787158\pi$
$684$		0			0
$685$	209.373			0.305654
$686$	352.608	−	115.560i	0.514006	−	0.168454i
$687$		0			0
$688$	75.4371	−	69.9954i	0.109647	−	0.101738i
$689$	−165.745	−	1099.65i	−0.240559	−	1.59600i
$690$		0			0
$691$	−306.526	+	781.015i	−0.443597	+	1.13027i	0.517897	+	0.855443i	$0.326715\pi$
$691$	−306.526	+	781.015i	−0.443597	+	1.13027i	−0.961494	+	0.274825i	$0.911380\pi$
$692$	−655.238	−	522.535i	−0.946875	−	0.755108i
$693$		0			0
$694$	−82.4842	−	103.432i	−0.118853	−	0.149037i
$695$	27.9534	+	90.6227i	0.0402207	+	0.130392i
$696$		0			0
$697$	−175.481	−	54.1286i	−0.251766	−	0.0776594i
$698$	477.093	−	35.7531i	0.683514	−	0.0512223i
$699$		0			0
$700$	−217.892	−	315.618i	−0.311274	−	0.450883i
$701$	−617.760	−	141.000i	−0.881255	−	0.201141i	−0.242130	−	0.970244i	$-0.577846\pi$
$701$	−617.760	−	141.000i	−0.881255	−	0.201141i	−0.639125	+	0.769103i	$0.720703\pi$
$702$		0			0
$703$	−1340.63	+	914.024i	−1.90701	+	1.30018i
$704$	−147.835	−	85.3528i	−0.209993	−	0.121240i
$705$		0			0
$706$	252.554	+	121.624i	0.357725	+	0.172271i
$707$	−1285.46	+	7.49791i	−1.81820	+	0.0106052i
$708$		0			0
$709$	−431.763	−	294.371i	−0.608974	−	0.415192i	0.219186	−	0.975683i	$-0.429660\pi$
$709$	−431.763	−	294.371i	−0.608974	−	0.415192i	−0.828160	+	0.560491i	$0.810612\pi$
$710$	228.815	−	246.603i	0.322274	−	0.347329i
$711$		0			0
$712$	−202.604	−	138.133i	−0.284557	−	0.194007i
$713$	31.7156	+	65.8581i	0.0444819	+	0.0923676i
$714$		0			0
$715$	275.703	+	132.772i	0.385599	+	0.185695i
$716$	730.964	−	422.022i	1.02090	−	0.589417i
$717$		0			0
$718$	−80.9081	+	55.1622i	−0.112685	+	0.0768275i
$719$	37.4757	−	248.635i	0.0521220	−	0.345807i	−0.947536	−	0.319650i	$-0.896435\pi$
$719$	37.4757	−	248.635i	0.0521220	−	0.345807i	0.999658	−	0.0261574i	$-0.00832711\pi$
$720$		0			0
$721$	−887.813	−	505.698i	−1.23136	−	0.701384i
$722$	−343.661	+	78.4384i	−0.475985	+	0.108640i
$723$		0			0
$724$	−229.853	−	70.9001i	−0.317476	−	0.0979283i
$725$	−373.413	+	146.554i	−0.515052	+	0.202143i
$726$		0			0
$727$	−684.100	−	857.835i	−0.940991	−	1.17997i	−0.983507	−	0.180870i	$-0.942109\pi$
$727$	−684.100	−	857.835i	−0.940991	−	1.17997i	0.0425160	−	0.999096i	$-0.486463\pi$
$728$	642.249	−	602.929i	0.882210	−	0.828199i
$729$		0			0
$730$	63.6891	−	162.277i	0.0872453	−	0.222297i
$731$	−697.503	−	52.2706i	−0.954176	−	0.0715056i
$732$		0			0
$733$	703.778	−	653.011i	0.960134	−	0.890874i	−0.0339569	−	0.999423i	$-0.510811\pi$
$733$	703.778	−	653.011i	0.960134	−	0.890874i	0.994091	+	0.108549i	$0.0346204\pi$
$734$			134.393i			0.183097i
$735$		0			0
$736$	−611.813			−0.831268
$737$	−290.477	−	313.060i	−0.394134	−	0.424776i
$738$		0			0
$739$	−70.0167	+	934.307i	−0.0947451	+	1.26429i	0.723867	+	0.689939i	$0.242363\pi$
$739$	−70.0167	+	934.307i	−0.0947451	+	1.26429i	−0.818612	+	0.574347i	$0.805256\pi$
$740$	387.215	+	151.971i	0.523264	+	0.205366i
$741$		0			0
$742$	−426.733	+	249.704i	−0.575112	+	0.336529i
$743$	244.487	−	194.972i	0.329053	−	0.262411i	−0.445002	−	0.895530i	$-0.646797\pi$
$743$	244.487	−	194.972i	0.329053	−	0.262411i	0.774055	+	0.633119i	$0.218225\pi$
$744$		0			0
$745$	−27.6623	−	70.4824i	−0.0371306	−	0.0946073i
$746$	221.971	−	719.612i	0.297548	−	0.964628i
$747$		0			0
$748$	−107.702	−	471.873i	−0.143987	−	0.630846i
$749$	933.075	−	146.209i	1.24576	−	0.195206i
$750$		0			0
$751$	−231.334	−	34.8680i	−0.308035	−	0.0464288i	−0.00679423	−	0.999977i	$-0.502163\pi$
$751$	−231.334	−	34.8680i	−0.308035	−	0.0464288i	−0.301241	+	0.953548i	$0.597401\pi$
$752$	72.6661	+	106.582i	0.0966304	+	0.141731i
$753$		0			0
$754$	−190.873	−	330.602i	−0.253147	−	0.438464i
$755$	−218.893	+	454.536i	−0.289925	+	0.602035i
$756$		0			0
$757$	−907.699	+	437.125i	−1.19907	+	0.577443i	−0.923412	−	0.383811i	$-0.874611\pi$
$757$	−907.699	+	437.125i	−1.19907	+	0.577443i	−0.275662	+	0.961255i	$0.588897\pi$
$758$	108.282	−	158.821i	0.142852	−	0.209526i
$759$		0			0
$760$	337.027	+	312.715i	0.443456	+	0.411467i
$761$	−64.8934	+	95.1811i	−0.0852738	+	0.125074i	−0.866506	−	0.499167i	$-0.833639\pi$
$761$	−64.8934	+	95.1811i	−0.0852738	+	0.125074i	0.781232	+	0.624241i	$0.214592\pi$
$762$		0			0
$763$	296.917	−	625.866i	0.389144	−	0.820270i
$764$	−278.166	+	577.618i	−0.364092	+	0.756045i
$765$		0			0
$766$	270.054	−	467.747i	0.352550	−	0.610635i
$767$	−599.204	−	878.871i	−0.781231	−	1.14585i
$768$		0			0
$769$	−24.9600	+	109.357i	−0.0324577	+	0.142207i	−0.988560	−	0.150825i	$-0.951807\pi$
$769$	−24.9600	+	109.357i	−0.0324577	+	0.142207i	0.956103	+	0.293032i	$0.0946641\pi$
$770$	9.37554	−	135.727i	0.0121760	−	0.176269i
$771$		0			0
$772$	−10.8217	−	144.405i	−0.0140177	−	0.187053i
$773$	99.4881	−	322.532i	0.128704	−	0.417248i	−0.868169	−	0.496268i	$-0.834703\pi$
$773$	99.4881	−	322.532i	0.128704	−	0.417248i	0.996873	+	0.0790208i	$0.0251794\pi$
$774$		0			0
$775$	73.2837	−	22.6050i	0.0945597	−	0.0291678i
$776$	589.583	−	470.177i	0.759772	−	0.605898i
$777$		0			0
$778$	−7.73397	+	9.69809i	−0.00994083	+	0.0124654i
$779$	198.185	+	77.7817i	0.254409	+	0.0998482i
$780$		0			0
$781$	979.909	−	147.697i	1.25468	−	0.189113i
$782$	306.972	+	330.837i	0.392547	+	0.423065i
$783$		0			0
$784$	147.643	+	68.9910i	0.188320	+	0.0879988i
$785$		−	270.677i		−	0.344811i
$786$		0			0
$787$	−68.3835	+	10.3072i	−0.0868914	+	0.0130968i	−0.192344	−	0.981328i	$-0.561609\pi$
$787$	−68.3835	+	10.3072i	−0.0868914	+	0.0130968i	0.105453	+	0.994424i	$0.466371\pi$
$788$	−762.960	−	57.1760i	−0.968224	−	0.0725583i
$789$		0			0
$790$	45.6035	−	57.1850i	0.0577260	−	0.0723861i
$791$	−168.709	+	437.347i	−0.213286	+	0.552905i
$792$		0			0
$793$	896.129	−	276.419i	1.13005	−	0.348574i
$794$	−160.279	+	62.9047i	−0.201862	+	0.0792251i
$795$		0			0
$796$	−47.8179	−	638.086i	−0.0600728	−	0.801616i
$797$	1133.43	−	258.699i	1.42212	−	0.324590i	0.558826	−	0.829285i	$-0.311252\pi$
$797$	1133.43	−	258.699i	1.42212	−	0.324590i	0.863298	+	0.504695i	$0.168395\pi$
$798$		0			0
$799$	195.101	−	854.792i	0.244181	−	1.06983i
$800$	−95.6693	+	634.724i	−0.119587	+	0.793405i
$801$		0			0
$802$	−263.768	+	456.860i	−0.328888	+	0.569651i
$803$	444.730	−	256.765i	0.553836	−	0.319757i
$804$		0			0
$805$	−134.696	−	275.576i	−0.167325	−	0.342331i
$806$	31.6660	+	65.7552i	0.0392879	+	0.0815821i
$807$		0			0
$808$	994.618	+	922.870i	1.23096	+	1.14217i
$809$	364.776	−	393.135i	0.450897	−	0.485952i	−0.466164	−	0.884698i	$-0.654364\pi$
$809$	364.776	−	393.135i	0.450897	−	0.485952i	0.917061	+	0.398747i	$0.130555\pi$
$810$		0			0
$811$	653.744	−	314.826i	0.806096	−	0.388195i	0.0150000	−	0.999887i	$-0.495225\pi$
$811$	653.744	−	314.826i	0.806096	−	0.388195i	0.791096	+	0.611692i	$0.209511\pi$
$812$	253.986	−	322.328i	0.312791	−	0.396955i
$813$		0			0
$814$	−253.394	−	438.891i	−0.311294	−	0.539178i
$815$	−295.487	−	170.599i	−0.362560	−	0.209324i
$816$		0			0
$817$	801.859	+	120.861i	0.981467	+	0.147932i
$818$	388.207	+	88.6057i	0.474581	+	0.108320i
$819$		0			0
$820$	−12.1453	−	53.2122i	−0.0148114	−	0.0648929i
$821$	859.466	−	64.4081i	1.04685	−	0.0784508i	0.459819	−	0.888013i	$-0.347914\pi$
$821$	859.466	−	64.4081i	1.04685	−	0.0784508i	0.587034	+	0.809562i	$0.300295\pi$
$822$		0			0
$823$	−83.5373	−	212.850i	−0.101503	−	0.258626i	0.871096	−	0.491112i	$-0.163409\pi$
$823$	−83.5373	−	212.850i	−0.101503	−	0.258626i	−0.972600	+	0.232486i	$0.925314\pi$
$824$	317.873	+	1030.52i	0.385768	+	1.25063i
$825$		0			0
$826$	−264.121	+	392.291i	−0.319759	+	0.474928i
$827$	69.2320	+	55.2107i	0.0837147	+	0.0667602i	0.664453	−	0.747330i	$-0.268665\pi$
$827$	69.2320	+	55.2107i	0.0837147	+	0.0667602i	−0.580738	+	0.814090i	$0.697236\pi$
$828$		0			0
$829$	89.3328	−	1192.06i	0.107760	−	1.43795i	−0.637125	−	0.770760i	$-0.719877\pi$
$829$	89.3328	−	1192.06i	0.107760	−	1.43795i	0.744885	−	0.667193i	$-0.232504\pi$
$830$	40.0709	+	265.853i	0.0482781	+	0.320305i
$831$		0			0
$832$	−384.264			−0.461856
$833$	−338.817	−	1054.58i	−0.406743	−	1.26600i
$834$		0			0
$835$	451.864	−	419.269i	0.541155	−	0.502118i
$836$	83.6326	+	554.866i	0.100039	+	0.663716i
$837$		0			0
$838$	20.7828	−	52.9537i	0.0248005	−	0.0631906i
$839$	1269.94	+	1012.75i	1.51364	+	1.20709i	0.913262	+	0.407373i	$0.133555\pi$
$839$	1269.94	+	1012.75i	1.51364	+	1.20709i	0.600379	+	0.799715i	$0.295016\pi$
$840$		0			0
$841$	256.740	+	321.942i	0.305280	+	0.382808i
$842$	−128.977	−	418.133i	−0.153179	−	0.496595i
$843$		0			0
$844$	−365.113	−	112.622i	−0.432598	−	0.133439i
$845$	286.761	−	21.4898i	0.339362	−	0.0254317i
$846$		0			0
$847$	−301.598	+	328.872i	−0.356078	+	0.388279i
$848$	−211.701	−	48.3195i	−0.249648	−	0.0569805i
$849$		0			0
$850$	391.227	−	266.734i	0.460267	−	0.313805i
$851$	−989.505	−	571.291i	−1.16276	−	0.671317i
$852$		0			0
$853$	−1355.00	−	652.532i	−1.58851	−	0.764985i	−0.589425	−	0.807823i	$-0.700646\pi$
$853$	−1355.00	−	652.532i	−1.58851	−	0.764985i	−0.999082	+	0.0428379i	$0.986360\pi$
$854$	−261.855	−	324.455i	−0.306622	−	0.379924i
$855$		0			0
$856$	−823.652	−	561.556i	−0.962210	−	0.656024i
$857$	524.670	−	565.460i	0.612218	−	0.659814i	−0.348511	−	0.937305i	$-0.613312\pi$
$857$	524.670	−	565.460i	0.612218	−	0.659814i	0.960728	+	0.277491i	$0.0895029\pi$
$858$		0			0
$859$	317.852	+	216.708i	0.370025	+	0.252279i	0.734028	−	0.679119i	$-0.237638\pi$
$859$	317.852	+	216.708i	0.370025	+	0.252279i	−0.364003	+	0.931398i	$0.618590\pi$
$860$	−90.2004	−	187.303i	−0.104884	−	0.217794i
$861$		0			0
$862$	175.974	+	84.7444i	0.204146	+	0.0983114i
$863$	1415.51	−	817.245i	1.64022	−	0.946981i	0.659466	−	0.751735i	$-0.270783\pi$
$863$	1415.51	−	817.245i	1.64022	−	0.946981i	0.980754	−	0.195246i	$-0.0625507\pi$
$864$		0			0
$865$	−581.036	+	396.143i	−0.671717	+	0.457969i
$866$	−74.2699	+	492.749i	−0.0857621	+	0.568994i
$867$		0			0
$868$	−53.0268	+	57.8220i	−0.0610907	+	0.0666153i
$869$	210.059	−	47.9445i	0.241725	−	0.0551721i
$870$		0			0
$871$	−918.626	−	283.359i	−1.05468	−	0.325326i
$872$	−680.622	+	267.124i	−0.780530	+	0.306335i
$873$		0			0
$874$	−326.229	−	409.078i	−0.373260	−	0.468053i
$875$	−703.293	+	221.438i	−0.803763	+	0.253072i
$876$		0			0
$877$	−258.831	+	659.490i	−0.295132	+	0.751984i	0.703995	+	0.710205i	$0.251398\pi$
$877$	−258.831	+	659.490i	−0.295132	+	0.751984i	−0.999127	+	0.0417788i	$0.986698\pi$
$878$	−363.059	−	27.2075i	−0.413507	−	0.0309881i
$879$		0			0
$880$	43.8013	−	40.6417i	0.0497742	−	0.0461838i
$881$			273.551i			0.310501i	0.987875	+	0.155251i	$0.0496185\pi$
$881$			273.551i			0.310501i	−0.987875	+	0.155251i	$0.950382\pi$
$882$		0			0
$883$	−796.850			−0.902434			−0.451217	−	0.892414i	$-0.649010\pi$
$883$	−796.850			−0.902434			−0.451217	+	0.892414i	$0.649010\pi$
$884$	−741.062	−	798.674i	−0.838305	−	0.903478i
$885$		0			0
$886$	−1.63716	+	21.8463i	−0.00184781	+	0.0246572i
$887$	−568.623	−	223.168i	−0.641063	−	0.251599i	0.0224679	−	0.999748i	$-0.492848\pi$
$887$	−568.623	−	223.168i	−0.641063	−	0.251599i	−0.663531	+	0.748149i	$0.730943\pi$
$888$		0			0
$889$	407.511	−	605.264i	0.458393	−	0.680837i
$890$	−66.6508	+	53.1522i	−0.0748885	+	0.0597216i
$891$		0			0
$892$	166.137	+	423.311i	0.186252	+	0.474564i
$893$	−299.615	+	971.327i	−0.335515	+	1.08771i
$894$		0			0
$895$	−157.597	−	690.477i	−0.176086	−	0.771483i
$896$	−280.818	−	703.421i	−0.313413	−	0.785068i
$897$		0			0
$898$	664.983	+	100.230i	0.740515	+	0.111615i
$899$	46.2255	+	67.8004i	0.0514188	+	0.0754175i
$900$		0			0
$901$	737.960	+	1278.18i	0.819045	+	1.41863i
$902$	−28.8520	+	59.9118i	−0.0319867	+	0.0664211i
$903$		0			0
$904$	445.773	−	214.673i	0.493112	−	0.237470i
$905$	−113.698	+	166.764i	−0.125633	+	0.184270i
$906$		0			0
$907$	80.0053	+	74.2340i	0.0882087	+	0.0818457i	0.723045	−	0.690801i	$-0.242742\pi$
$907$	80.0053	+	74.2340i	0.0882087	+	0.0818457i	−0.634836	+	0.772647i	$0.718932\pi$
$908$	220.317	−	323.145i	0.242639	−	0.355887i
$909$		0			0
$910$	−134.486	−	275.146i	−0.147787	−	0.302358i
$911$	375.990	−	780.751i	0.412722	−	0.857026i	−0.586180	−	0.810181i	$-0.699369\pi$
$911$	375.990	−	780.751i	0.412722	−	0.857026i	0.998902	−	0.0468456i	$-0.0149169\pi$
$912$		0			0
$913$	−395.994	+	685.881i	−0.433728	+	0.751239i
$914$	405.144	+	594.236i	0.443264	+	0.650149i
$915$		0			0
$916$	−182.516	+	799.653i	−0.199253	+	0.872984i
$917$	−24.3589	−	7.35839i	−0.0265637	−	0.00802442i
$918$		0			0
$919$	−80.3649	−	1072.40i	−0.0874482	−	1.16692i	−0.852422	−	0.522854i	$-0.824867\pi$
$919$	−80.3649	−	1072.40i	−0.0874482	−	1.16692i	0.764974	−	0.644061i	$-0.222752\pi$
$920$	−95.4282	+	309.371i	−0.103726	+	0.336272i
$921$		0			0
$922$	477.757	−	147.369i	0.518175	−	0.159836i
$923$	1744.05	−	1390.83i	1.88955	−	1.50686i
$924$		0			0
$925$	−747.414	+	937.227i	−0.808015	+	1.01322i
$926$	−646.013	−	253.541i	−0.697638	−	0.273803i
$927$		0			0
$928$	−679.153	+	102.366i	−0.731846	+	0.110308i
$929$	1147.42	+	1236.62i	1.23511	+	1.33113i	0.924781	+	0.380500i	$0.124248\pi$
$929$	1147.42	+	1236.62i	1.23511	+	1.33113i	0.310327	+	0.950630i	$0.399561\pi$
$930$		0			0
$931$	300.341	+	1248.56i	0.322601	+	1.34110i
$932$			677.679i			0.727123i
$933$		0			0
$934$	−591.368	+	89.1344i	−0.633156	+	0.0954329i
$935$	−404.993	−	30.3501i	−0.433148	−	0.0324600i
$936$		0			0
$937$	976.978	−	1225.09i	1.04267	−	1.30746i	0.0925019	−	0.995713i	$-0.470514\pi$
$937$	976.978	−	1225.09i	1.04267	−	1.30746i	0.950164	−	0.311750i	$-0.100915\pi$
$938$	34.4256	+	426.019i	0.0367011	+	0.454178i
$939$		0			0
$940$	249.015	−	76.8108i	0.264909	−	0.0817136i
$941$	1267.33	−	497.391i	1.34679	−	0.528577i	0.421154	−	0.906989i	$-0.361625\pi$
$941$	1267.33	−	497.391i	1.34679	−	0.528577i	0.925637	+	0.378413i	$0.123530\pi$
$942$		0			0
$943$	11.2037	+	149.502i	0.0118809	+	0.158539i
$944$	−202.494	+	46.2179i	−0.214506	+	0.0489597i
$945$		0			0
$946$	−56.3599	+	246.929i	−0.0595770	+	0.261024i
$947$	−257.966	+	1711.49i	−0.272403	+	1.80728i	0.265324	+	0.964159i	$0.414521\pi$
$947$	−257.966	+	1711.49i	−0.272403	+	1.80728i	−0.537728	+	0.843119i	$0.680717\pi$
$948$		0			0
$949$	577.987	−	1001.10i	0.609049	−	1.05490i
$950$	−475.410	+	274.478i	−0.500431	+	0.288924i
$951$		0			0
$952$	−501.116	+	1056.29i	−0.526382	+	1.10955i
$953$	639.976	+	1328.92i	0.671539	+	1.39446i	0.906394	+	0.422434i	$0.138824\pi$
$953$	639.976	+	1328.92i	0.671539	+	1.39446i	−0.234855	+	0.972030i	$0.575462\pi$
$954$		0			0
$955$	394.346	+	365.899i	0.412928	+	0.383141i
$956$	−158.354	+	170.665i	−0.165642	+	0.178520i
$957$		0			0
$958$	68.1438	−	32.8163i	0.0711313	−	0.0342550i
$959$	−140.861	−	600.974i	−0.146884	−	0.626668i
$960$		0			0
$961$	472.656	+	818.664i	0.491838	+	0.851888i
$962$	−987.959	−	570.398i	−1.02698	−	0.592930i
$963$		0			0
$964$	304.201	+	45.8510i	0.315562	+	0.0475632i
$965$	−118.463	−	27.0384i	−0.122759	−	0.0280191i
$966$		0			0
$967$	305.616	+	1338.99i	0.316046	+	1.38469i	0.844423	+	0.535678i	$0.179944\pi$
$967$	305.616	+	1338.99i	0.316046	+	1.38469i	−0.528377	+	0.849010i	$0.677199\pi$
$968$	469.671	−	35.1970i	0.485198	−	0.0363605i
$969$		0			0
$970$	−95.7810	−	244.046i	−0.0987433	−	0.251594i
$971$	250.780	+	813.008i	0.258270	+	0.837290i	0.988120	+	0.153683i	$0.0491134\pi$
$971$	250.780	+	813.008i	0.258270	+	0.837290i	−0.729851	+	0.683607i	$0.760410\pi$
$972$		0			0
$973$	241.313	−	141.205i	0.248009	−	0.145123i
$974$	274.855	+	219.189i	0.282192	+	0.225040i
$975$		0			0
$976$	13.6843	−	182.604i	0.0140208	−	0.187095i
$977$	9.37457	+	62.1962i	0.00959526	+	0.0636604i	0.993116	−	0.117135i	$-0.0373710\pi$
$977$	9.37457	+	62.1962i	0.00959526	+	0.0636604i	−0.983521	+	0.180795i	$0.942133\pi$
$978$		0			0
$979$	−251.126			−0.256512
$980$	221.095	−	243.930i	0.225607	−	0.248908i
$981$		0			0
$982$	−283.802	+	263.330i	−0.289004	+	0.268157i
$983$	−218.944	−	1452.60i	−0.222731	−	1.47772i	−0.768534	−	0.639809i	$-0.779013\pi$
$983$	−218.944	−	1452.60i	−0.222731	−	1.47772i	0.545803	−	0.837913i	$-0.316225\pi$
$984$		0			0
$985$	−234.546	+	597.613i	−0.238118	+	0.606714i
$986$	396.113	+	315.890i	0.401738	+	0.320375i
$987$		0			0
$988$	787.550	+	987.557i	0.797116	+	0.999551i
$989$	168.315	+	545.663i	0.170187	+	0.551732i
$990$		0			0
$991$	61.5502	+	18.9857i	0.0621092	+	0.0191581i	0.325654	−	0.945489i	$-0.394416\pi$
$991$	61.5502	+	18.9857i	0.0621092	+	0.0191581i	−0.263545	+	0.964647i	$0.584892\pi$
$992$	130.941	−	9.81266i	0.131997	−	0.00989180i
$993$		0			0
$994$	−861.780	−	490.869i	−0.866982	−	0.493832i
$995$	−523.455	−	119.475i	−0.526085	−	0.120076i
$996$		0			0
$997$	−355.679	+	242.498i	−0.356749	+	0.243227i	−0.728410	−	0.685141i	$-0.759741\pi$
$997$	−355.679	+	242.498i	−0.356749	+	0.243227i	0.371662	+	0.928368i	$0.378788\pi$
$998$	−366.111	−	211.374i	−0.366845	−	0.211798i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.bf.a.305.23	yes	456
3.2	odd	2	inner	441.3.bf.a.305.16	yes	456
49.9	even	21	inner	441.3.bf.a.107.16	✓	456
147.107	odd	42	inner	441.3.bf.a.107.23	yes	456

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.3.bf.a.107.16	✓	456	49.9	even	21	inner
441.3.bf.a.107.23	yes	456	147.107	odd	42	inner
441.3.bf.a.305.16	yes	456	3.2	odd	2	inner
441.3.bf.a.305.23	yes	456	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.bf (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.735818 + 0.793024i) q^{2} +(0.211463 - 2.82177i) q^{4} +(-2.21024 - 0.867457i) q^{5} +(-1.00290 + 6.92778i) q^{7} +(5.77651 - 4.60661i) q^{8} +O(q^{10})\)	\(q+(0.735818 + 0.793024i) q^{2} +(0.211463 - 2.82177i) q^{4} +(-2.21024 - 0.867457i) q^{5} +(-1.00290 + 6.92778i) q^{7} +(5.77651 - 4.60661i) q^{8} +(-0.938425 - 2.39107i) q^{10} +(2.23029 - 7.23043i) q^{11} +(-3.79013 - 16.6056i) q^{13} +(-6.23185 + 4.30226i) q^{14} +(-3.28871 - 0.495693i) q^{16} +(12.7341 + 18.6776i) q^{17} +(-13.1038 - 22.6965i) q^{19} +(-2.91515 + 6.05337i) q^{20} +(7.37499 - 3.55161i) q^{22} +(10.3961 - 15.2482i) q^{23} +(-14.1936 - 13.1697i) q^{25} +(10.3798 - 15.2244i) q^{26} +(19.3365 + 4.29494i) q^{28} +(8.98905 - 18.6660i) q^{29} +(-1.98041 + 3.43018i) q^{31} +(-18.6750 - 27.3912i) q^{32} +(-5.44173 + 23.8418i) q^{34} +(8.22622 - 14.4421i) q^{35} +(-4.62668 - 61.7388i) q^{37} +(8.35682 - 27.0921i) q^{38} +(-16.7635 + 5.17086i) q^{40} +(-6.35132 + 5.06501i) q^{41} +(-19.2920 + 24.1914i) q^{43} +(-19.9310 - 7.82234i) q^{44} +(19.7418 - 2.97560i) q^{46} +(-26.3811 - 28.4320i) q^{47} +(-46.9884 - 13.8958i) q^{49} -20.9464i q^{50} +(-47.6588 + 7.18340i) q^{52} +(65.1077 + 4.87915i) q^{53} +(-11.2016 + 14.0463i) q^{55} +(26.1203 + 44.6384i) q^{56} +(21.4169 - 6.60622i) q^{58} +(58.1336 - 22.8158i) q^{59} +(4.11452 + 54.9045i) q^{61} +(-4.17744 + 0.953473i) q^{62} +(5.02017 - 21.9948i) q^{64} +(-6.02756 + 39.9903i) q^{65} +(28.2203 - 48.8791i) q^{67} +(55.3966 - 31.9832i) q^{68} +(17.5059 - 4.10319i) q^{70} +(56.8247 + 117.998i) q^{71} +(49.7508 + 46.1620i) q^{73} +(45.5559 - 49.0976i) q^{74} +(-66.8153 + 32.1766i) q^{76} +(47.8541 + 22.7024i) q^{77} +(14.2376 + 24.6603i) q^{79} +(6.83885 + 3.94841i) q^{80} +(-8.69009 - 1.30982i) q^{82} +(-102.045 - 23.2911i) q^{83} +(-11.9436 - 52.3283i) q^{85} +(-33.3797 + 2.50147i) q^{86} +(-20.4245 - 52.0407i) q^{88} +(-9.78256 - 31.7143i) q^{89} +(118.841 - 9.60330i) q^{91} +(-40.8286 - 32.5597i) q^{92} +(3.13560 - 41.8417i) q^{94} +(9.27443 + 61.5318i) q^{95} +102.066 q^{97} +(-23.5552 - 47.4877i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 456 q - 80 q^{4} + 2 q^{7}+O(q^{10}) \) 456 * q - 80 * q^4 + 2 * q^7	\( 456 q - 80 q^{4} + 2 q^{7} + 16 q^{10} + 52 q^{13} + 176 q^{16} - 26 q^{19} - 184 q^{22} - 234 q^{25} - 504 q^{28} - 22 q^{31} - 32 q^{34} + 684 q^{37} + 1828 q^{40} - 76 q^{43} - 100 q^{46} - 226 q^{49} - 1148 q^{52} - 464 q^{55} - 1088 q^{58} - 1362 q^{61} + 472 q^{64} + 110 q^{67} - 472 q^{70} + 482 q^{73} + 84 q^{76} - 106 q^{79} + 2032 q^{82} - 768 q^{85} + 24 q^{88} + 338 q^{91} + 788 q^{94} - 568 q^{97}+O(q^{100}) \) 456 * q - 80 * q^4 + 2 * q^7 + 16 * q^10 + 52 * q^13 + 176 * q^16 - 26 * q^19 - 184 * q^22 - 234 * q^25 - 504 * q^28 - 22 * q^31 - 32 * q^34 + 684 * q^37 + 1828 * q^40 - 76 * q^43 - 100 * q^46 - 226 * q^49 - 1148 * q^52 - 464 * q^55 - 1088 * q^58 - 1362 * q^61 + 472 * q^64 + 110 * q^67 - 472 * q^70 + 482 * q^73 + 84 * q^76 - 106 * q^79 + 2032 * q^82 - 768 * q^85 + 24 * q^88 + 338 * q^91 + 788 * q^94 - 568 * q^97

Introduction

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