LMFDB - Embedded newform 441.3.bf.a.107.23

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			107.23
Character	$\chi$	$=$	441.107
Dual form			441.3.bf.a.305.23

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

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	−0.521779	−	0.853081i	$-0.674731\pi$
$2$	0.735818	−	0.793024i	0.367909	−	0.396512i	0.889688	+	0.456569i	$0.150922\pi$
$3$		0			0
$3$		0			0
$4$	0.211463	+	2.82177i	0.0528656	+	0.705443i
$5$	−2.21024	+	0.867457i	−0.442049	+	0.173491i	−0.575918	−	0.817508i	$-0.695355\pi$
$5$	−2.21024	+	0.867457i	−0.442049	+	0.173491i	0.133869	+	0.990999i	$0.457260\pi$
$6$		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	0.998653	+	0.0518827i	$0.0165222\pi$
$11$	2.23029	+	7.23043i	0.202754	+	0.657312i	−0.795899	+	0.605429i	$0.793002\pi$
$12$		0			0
$13$	−3.79013	+	16.6056i	−0.291548	+	1.27736i	0.590823	+	0.806801i	$0.298803\pi$
$13$	−3.79013	+	16.6056i	−0.291548	+	1.27736i	−0.882371	+	0.470554i	$0.844054\pi$
$14$	−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	−0.242635	−	0.970118i	$-0.578012\pi$
$17$	12.7341	−	18.6776i	0.749067	−	1.09868i	0.991702	−	0.128562i	$-0.0410360\pi$
$18$		0			0
$19$	−13.1038	+	22.6965i	−0.689675	+	1.19455i	0.282268	+	0.959336i	$0.408913\pi$
$19$	−13.1038	+	22.6965i	−0.689675	+	1.19455i	−0.971943	+	0.235217i	$0.924420\pi$
$20$	−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	0.982830	−	0.184514i	$-0.0590711\pi$
$23$	10.3961	+	15.2482i	0.452003	+	0.662966i	−0.530827	+	0.847480i	$0.678119\pi$
$24$		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	0.996513	−	0.0834326i	$-0.0265883\pi$
$29$	8.98905	+	18.6660i	0.309967	+	0.643654i	−0.686546	+	0.727086i	$0.740874\pi$
$30$		0			0
$31$	−1.98041	−	3.43018i	−0.0638843	−	0.110651i	0.832314	−	0.554304i	$-0.187016\pi$
$31$	−1.98041	−	3.43018i	−0.0638843	−	0.110651i	−0.896199	+	0.443653i	$0.853682\pi$
$32$	−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	0.483688	+	0.875240i	$0.339297\pi$
$37$	−4.62668	+	61.7388i	−0.125045	+	1.66862i	−0.608734	+	0.793375i	$0.708322\pi$
$38$	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	0.542967	−	0.839754i	$-0.317301\pi$
$41$	−6.35132	−	5.06501i	−0.154910	−	0.123537i	−0.697878	+	0.716217i	$0.745872\pi$
$42$		0			0
$43$	−19.2920	−	24.1914i	−0.448651	−	0.562590i	0.505149	−	0.863032i	$-0.331437\pi$
$43$	−19.2920	−	24.1914i	−0.448651	−	0.562590i	−0.953800	+	0.300442i	$0.902866\pi$
$44$	−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	−0.948391	−	0.317104i	$-0.897289\pi$
$47$	−26.3811	+	28.4320i	−0.561300	+	0.604937i	0.387091	+	0.922042i	$0.373480\pi$
$48$		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	0.555352	−	0.831616i	$-0.312584\pi$
$53$	65.1077	−	4.87915i	1.22845	−	0.0920594i	0.673095	+	0.739556i	$0.264965\pi$
$54$		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	0.802639	−	0.596465i	$-0.203429\pi$
$59$	58.1336	+	22.8158i	0.985316	+	0.386708i	0.182677	+	0.983173i	$0.441524\pi$
$60$		0			0
$61$	4.11452	−	54.9045i	0.0674512	−	0.900074i	−0.856152	−	0.516724i	$-0.827151\pi$
$61$	4.11452	−	54.9045i	0.0674512	−	0.900074i	0.923603	−	0.383350i	$-0.125230\pi$
$62$	−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	0.996057	−	0.0887148i	$-0.0282760\pi$
$67$	28.2203	+	48.8791i	0.421199	+	0.729538i	−0.574858	+	0.818253i	$0.694943\pi$
$68$	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	0.0519850	−	0.998648i	$-0.483445\pi$
$71$	56.8247	−	117.998i	0.800347	−	1.66194i	0.748362	−	0.663290i	$-0.230841\pi$
$72$		0			0
$73$	49.7508	−	46.1620i	0.681518	−	0.632356i	−0.261459	−	0.965215i	$-0.584204\pi$
$73$	49.7508	−	46.1620i	0.681518	−	0.632356i	0.942977	+	0.332858i	$0.108013\pi$
$74$	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	−0.761733	−	0.647891i	$-0.775651\pi$
$79$	14.2376	−	24.6603i	0.180223	−	0.312156i	0.941957	+	0.335735i	$0.108985\pi$
$80$	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	−0.787439	−	0.616392i	$-0.788594\pi$
$83$	−102.045	+	23.2911i	−1.22945	+	0.280615i	−0.442016	+	0.897007i	$0.645736\pi$
$84$		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	−0.993774	−	0.111416i	$-0.964461\pi$
$89$	−9.78256	+	31.7143i	−0.109916	+	0.356340i	0.883857	+	0.467756i	$0.154938\pi$
$90$		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	−0.276401	−	0.961043i	$-0.589142\pi$
$101$	27.3702	−	181.590i	0.270993	−	1.79792i	0.547393	−	0.836876i	$-0.315620\pi$
$102$		0			0
$103$	−53.3260	−	135.872i	−0.517728	−	1.31915i	−0.915741	−	0.401769i	$-0.868395\pi$
$103$	−53.3260	−	135.872i	−0.517728	−	1.31915i	0.398013	−	0.917380i	$-0.369700\pi$
$104$	−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	0.555882	+	0.831261i	$0.312381\pi$
$107$	−39.7693	+	128.929i	−0.371675	+	1.20494i	−0.927557	+	0.373681i	$0.878096\pi$
$108$		0			0
$109$	−94.5642	+	29.1692i	−0.867561	+	0.267607i	−0.696416	−	0.717638i	$-0.745223\pi$
$109$	−94.5642	+	29.1692i	−0.867561	+	0.267607i	−0.171146	+	0.985246i	$0.554747\pi$
$110$	−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	0.0763511	−	0.997081i	$-0.475673\pi$
$113$	65.2867	−	14.9013i	0.577758	−	0.131870i	0.501407	+	0.865211i	$0.332816\pi$
$114$		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	−0.765408	−	0.643545i	$-0.777463\pi$
$127$	−93.9150	+	45.2271i	−0.739488	+	0.356119i	0.0259201	+	0.999664i	$0.491748\pi$
$128$	−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	0.986668	−	0.162748i	$-0.0520356\pi$
$131$	−0.541791	−	3.59455i	−0.00413581	−	0.0274393i	−0.990804	+	0.135308i	$0.956798\pi$
$132$		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	0.0463254	−	0.998926i	$-0.485249\pi$
$137$	−82.0847	−	32.2159i	−0.599158	−	0.235152i	−0.645484	+	0.763774i	$0.723344\pi$
$138$		0			0
$139$	−24.9031	+	31.2275i	−0.179159	+	0.224658i	−0.863299	−	0.504692i	$-0.831606\pi$
$139$	−24.9031	+	31.2275i	−0.179159	+	0.224658i	0.684141	+	0.729350i	$0.260177\pi$
$140$	−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	−0.656057	−	0.754711i	$-0.727777\pi$
$149$	21.6900	−	23.3763i	0.145571	−	0.156888i	0.801628	+	0.597823i	$0.203968\pi$
$150$		0			0
$151$	15.8783	+	211.882i	0.105155	+	1.40319i	0.761224	+	0.648489i	$0.224599\pi$
$151$	15.8783	+	211.882i	0.105155	+	1.40319i	−0.656069	+	0.754701i	$0.727782\pi$
$152$	−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	−0.734719	−	0.678371i	$-0.762686\pi$
$157$	41.6486	−	106.119i	0.265278	−	0.675916i	0.999997	+	0.00245499i	$0.000781448\pi$
$158$	−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	0.302094	−	0.953278i	$-0.402314\pi$
$163$	142.095	−	21.4174i	0.871750	−	0.131395i	0.569656	+	0.821883i	$0.307076\pi$
$164$	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	−0.904098	−	0.427325i	$-0.859456\pi$
$167$	−112.641	−	233.902i	−0.674498	−	1.40061i	0.229600	−	0.973285i	$-0.426258\pi$
$168$		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	0.909351	+	0.416030i	$0.136579\pi$
$173$	166.841	+	244.711i	0.964399	+	1.41451i	0.0550479	+	0.998484i	$0.482469\pi$
$174$		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	0.0124543	−	0.999922i	$-0.496036\pi$
$179$	168.028	−	246.452i	0.938706	−	1.37683i	0.926251	−	0.376906i	$-0.123012\pi$
$180$		0			0
$181$	18.9155	+	82.8743i	0.104506	+	0.457869i	0.999920	+	0.0126357i	$0.00402217\pi$
$181$	18.9155	+	82.8743i	0.104506	+	0.457869i	−0.895415	+	0.445233i	$0.853121\pi$
$182$	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	−0.846249	−	0.532787i	$-0.821145\pi$
$191$	−210.904	+	82.7735i	−1.10421	+	0.433369i	−0.257958	+	0.966156i	$0.583049\pi$
$192$		0			0
$193$	50.6037	+	7.62728i	0.262195	+	0.0395196i	0.278824	−	0.960342i	$-0.410055\pi$
$193$	50.6037	+	7.62728i	0.262195	+	0.0395196i	−0.0166289	+	0.999862i	$0.505293\pi$
$194$	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	$0.240745\pi$
$197$			270.383i			1.37250i	−0.727364	+	0.686252i	$0.759255\pi$
$198$		0			0
$199$	223.604	+	33.7029i	1.12364	+	0.169361i	0.684468	−	0.729043i	$-0.260035\pi$
$199$	223.604	+	33.7029i	1.12364	+	0.169361i	0.439170	+	0.898404i	$0.355273\pi$
$200$	−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	0.994873	+	0.101128i	$0.0322452\pi$
$211$	30.0467	+	131.643i	0.142401	+	0.623901i	−0.852472	+	0.522773i	$0.824898\pi$
$212$	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	0.0800957	−	0.996787i	$-0.474477\pi$
$223$	−144.791	−	69.7275i	−0.649285	−	0.312679i	−0.729381	+	0.684108i	$0.760192\pi$
$224$	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	−0.212616	−	0.977136i	$-0.568198\pi$
$227$	119.697	−	69.1073i	0.527301	−	0.304437i	0.739917	+	0.672698i	$0.234865\pi$
$228$		0			0
$229$	−286.624	+	43.2017i	−1.25164	+	0.188654i	−0.741213	−	0.671270i	$-0.765749\pi$
$229$	−286.624	+	43.2017i	−1.25164	+	0.188654i	−0.510422	+	0.859924i	$0.670511\pi$
$230$	−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	−0.448382	−	0.893842i	$-0.648000\pi$
$233$	−238.820	−	17.8971i	−1.02498	−	0.0768114i	−0.576595	+	0.817030i	$0.695619\pi$
$234$		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	−0.748757	−	0.662845i	$-0.769349\pi$
$239$	−64.3258	+	51.2981i	−0.269145	+	0.214636i	0.479612	+	0.877481i	$0.340778\pi$
$240$		0			0
$241$	−8.12450	−	108.414i	−0.0337116	−	0.449850i	−0.988362	−	0.152121i	$-0.951390\pi$
$241$	−8.12450	−	108.414i	−0.0337116	−	0.449850i	0.954650	−	0.297729i	$-0.0962293\pi$
$242$	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	−0.0282193	−	0.999602i	$-0.508984\pi$
$251$	235.950	−	188.164i	0.940041	−	0.749658i	0.968260	+	0.249944i	$0.0804123\pi$
$252$		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	0.106494	−	0.994313i	$-0.466037\pi$
$257$	16.3462	+	1.22498i	0.0636039	+	0.00476645i	−0.0428901	+	0.999080i	$0.513657\pi$
$258$		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	0.346940	−	0.937887i	$-0.387221\pi$
$263$	350.486	−	202.353i	1.33264	−	0.769403i	0.985704	+	0.168484i	$0.0538873\pi$
$264$		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	0.543432	−	0.839453i	$-0.317125\pi$
$269$	−89.9226	−	96.9135i	−0.334285	−	0.360273i	−0.877717	+	0.479180i	$0.840934\pi$
$270$		0			0
$271$	223.869	−	152.632i	0.826086	−	0.563216i	−0.0748362	−	0.997196i	$-0.523843\pi$
$271$	223.869	−	152.632i	0.826086	−	0.563216i	0.900923	+	0.433980i	$0.142891\pi$
$272$	−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	0.998551	−	0.0538047i	$-0.0171348\pi$
$277$	363.778	+	248.020i	1.31328	+	0.895378i	0.314726	+	0.949182i	$0.398087\pi$
$278$	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	0.874210	−	0.485547i	$-0.161380\pi$
$281$	407.780	+	93.0732i	1.45118	+	0.331221i	0.576965	+	0.816769i	$0.304237\pi$
$282$		0			0
$283$	−272.914	+	84.1829i	−0.964361	+	0.297466i	−0.736659	−	0.676265i	$-0.763598\pi$
$283$	−272.914	+	84.1829i	−0.964361	+	0.297466i	−0.227702	+	0.973731i	$0.573121\pi$
$284$	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	$0.281836\pi$
$293$			453.668i			1.54836i	−0.632968	+	0.774178i	$0.718164\pi$
$294$		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	−0.729307	−	0.684187i	$-0.760157\pi$
$307$	68.9625	−	302.144i	0.224634	−	0.984184i	0.953940	−	0.299997i	$-0.0969857\pi$
$308$	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	−0.684458	−	0.729052i	$-0.739961\pi$
$311$	75.9644	−	111.419i	0.244258	−	0.358261i	0.928716	+	0.370791i	$0.120913\pi$
$312$		0			0
$313$	−119.733	+	207.383i	−0.382533	+	0.662567i	−0.991424	−	0.130687i	$-0.958282\pi$
$313$	−119.733	+	207.383i	−0.382533	+	0.662567i	0.608890	+	0.793254i	$0.291615\pi$
$314$	−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	0.874715	−	0.484638i	$-0.161049\pi$
$317$	32.9709	+	48.3595i	0.104009	+	0.152554i	−0.770706	+	0.637191i	$0.780096\pi$
$318$		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	−0.828837	−	0.559490i	$-0.810997\pi$
$331$	24.5371	−	327.425i	0.0741302	−	0.989199i	0.902967	−	0.429709i	$-0.141384\pi$
$332$	−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	0.998127	−	0.0611826i	$-0.0194872\pi$
$337$	241.418	+	302.729i	0.716374	+	0.898304i	−0.281753	+	0.959487i	$0.590916\pi$
$338$	−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	−0.249278	−	0.968432i	$-0.580193\pi$
$347$	−121.948	+	9.13872i	−0.351434	+	0.0263364i	−0.102156	+	0.994768i	$0.532574\pi$
$348$		0			0
$349$	275.738	+	345.765i	0.790080	+	0.990729i	0.999916	+	0.0129926i	$0.00413579\pi$
$349$	275.738	+	345.765i	0.790080	+	0.990729i	−0.209835	+	0.977737i	$0.567293\pi$
$350$	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	0.681493	−	0.731824i	$-0.261331\pi$
$353$	241.204	+	94.6654i	0.683296	+	0.268174i	0.00180304	+	0.999998i	$0.499426\pi$
$354$		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	0.962152	−	0.272515i	$-0.0878553\pi$
$359$	−13.4910	−	89.5069i	−0.0375794	−	0.249323i	−0.999731	+	0.0231916i	$0.992617\pi$
$360$		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	−0.546290	−	0.837596i	$-0.683960\pi$
$367$	91.0671	−	84.4979i	0.248139	−	0.230239i	0.794429	+	0.607356i	$0.207770\pi$
$368$	−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	−0.155209	+	0.987882i	$0.549605\pi$
$373$	−348.059	+	602.857i	−0.933135	+	1.61624i	−0.777926	+	0.628356i	$0.783728\pi$
$374$	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	0.895602	+	0.444856i	$0.146745\pi$
$379$	−39.5386	+	173.230i	−0.104323	+	0.457071i	−0.999925	+	0.0122145i	$0.996112\pi$
$380$	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	0.532601	+	0.846367i	$0.321215\pi$
$383$	−147.160	+	477.081i	−0.384230	+	1.24564i	−0.916831	+	0.399276i	$0.869261\pi$
$384$		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	−0.986527	−	0.163600i	$-0.947689\pi$
$389$	1.70896	−	11.3382i	0.00439320	−	0.0291470i	0.990920	+	0.134453i	$0.0429276\pi$
$390$		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	0.838746	−	0.544522i	$-0.183289\pi$
$397$	−58.1476	−	148.158i	−0.146468	−	0.373193i	−0.985214	+	0.171329i	$0.945194\pi$
$398$	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	−0.579420	−	0.815029i	$-0.696721\pi$
$401$	143.735	−	465.978i	0.358442	−	1.16204i	0.937861	−	0.347010i	$-0.112803\pi$
$402$		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	0.874854	−	0.484388i	$-0.160958\pi$
$409$	304.120	+	207.346i	0.743570	+	0.506957i	−0.131284	+	0.991345i	$0.541910\pi$
$410$	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	−0.926419	−	0.376493i	$-0.877130\pi$
$419$	−22.8154	+	47.3766i	−0.0544520	+	0.113071i	0.871967	+	0.489564i	$0.162844\pi$
$420$		0			0
$421$	−364.426	+	175.498i	−0.865619	+	0.416860i	−0.813351	−	0.581773i	$-0.802359\pi$
$421$	−364.426	+	175.498i	−0.865619	+	0.416860i	−0.0522681	+	0.998633i	$0.516645\pi$
$422$	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	0.552208	−	0.833706i	$-0.313785\pi$
$431$	168.065	+	65.9606i	0.389942	+	0.153041i	−0.162267	+	0.986747i	$0.551881\pi$
$432$		0			0
$433$	287.198	−	360.135i	0.663275	−	0.831720i	−0.330420	−	0.943834i	$-0.607191\pi$
$433$	287.198	−	360.135i	0.663275	−	0.831720i	0.993695	+	0.112113i	$0.0357620\pi$
$434$	−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	0.347237	−	0.937777i	$-0.387120\pi$
$439$	−246.704	−	228.908i	−0.561969	−	0.521431i	−0.909206	+	0.416346i	$0.863310\pi$
$440$		−	132.740i		−	0.301682i
$441$		0			0
$442$	416.532			0.942380
$443$	13.7741	−	14.8449i	0.0310927	−	0.0335100i	−0.717314	−	0.696750i	$-0.754629\pi$
$443$	13.7741	−	14.8449i	0.0310927	−	0.0335100i	0.748407	+	0.663240i	$0.230819\pi$
$444$		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	0.991168	−	0.132609i	$-0.0423355\pi$
$449$	486.015	+	387.584i	1.08244	+	0.863217i	0.0912713	+	0.995826i	$0.470907\pi$
$450$		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	0.616967	−	0.786989i	$-0.288361\pi$
$457$	657.392	−	99.0858i	1.43849	−	0.216818i	0.821526	+	0.570171i	$0.193123\pi$
$458$	−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	0.997094	+	0.0761792i	$0.0242721\pi$
$461$	200.524	+	416.392i	0.434975	+	0.903236i	−0.562119	+	0.827057i	$0.690014\pi$
$462$		0			0
$463$	−577.975	−	278.338i	−1.24833	−	0.601162i	−0.311263	−	0.950324i	$-0.600752\pi$
$463$	−577.975	−	278.338i	−1.24833	−	0.601162i	−0.937062	+	0.349162i	$0.886466\pi$
$464$	−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	−0.999388	−	0.0349897i	$-0.988860\pi$
$467$	−311.415	−	456.762i	−0.666841	−	0.978077i	0.332546	−	0.943087i	$-0.392092\pi$
$468$		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	0.974536	−	0.224232i	$-0.0719874\pi$
$479$	20.6076	+	66.8080i	0.0430220	+	0.139474i	−0.931514	+	0.363706i	$0.881511\pi$
$480$		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	0.470417	−	0.882444i	$-0.344104\pi$
$487$	321.337	+	48.4337i	0.659829	+	0.0994533i	0.189413	+	0.981898i	$0.439342\pi$
$488$	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	$-0.881263\pi$
$491$		−	357.873i		−	0.728866i	0.931230	−	0.364433i	$-0.118737\pi$
$492$		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	−0.102946	−	0.994687i	$-0.532827\pi$
$499$	−373.418	−	115.184i	−0.748332	−	0.230830i	−0.645385	+	0.763857i	$0.723303\pi$
$500$	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	−0.577768	−	0.816201i	$-0.696076\pi$
$503$	−730.585	−	166.751i	−1.45245	−	0.331513i	−0.874687	+	0.484688i	$0.838933\pi$
$504$		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	0.00868021	−	0.999962i	$-0.497237\pi$
$509$	−434.163	−	250.664i	−0.852972	−	0.492464i	−0.861653	+	0.507498i	$0.830570\pi$
$510$		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	−0.535834	−	0.844323i	$-0.680003\pi$
$521$	−37.7967	+	21.8219i	−0.0725464	+	0.0418847i	0.463288	+	0.886208i	$0.346670\pi$
$522$		0			0
$523$	612.732	−	92.3545i	1.17157	−	0.176586i	0.465712	−	0.884937i	$-0.345798\pi$
$523$	612.732	−	92.3545i	1.17157	−	0.176586i	0.705861	+	0.708350i	$0.250560\pi$
$524$	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	−0.0740582	−	0.997254i	$-0.523595\pi$
$541$	−581.065	−	539.150i	−1.07406	−	0.996580i	−1.00000		0.000673711i	$0.999786\pi$
$542$	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	−0.336452	−	0.941701i	$-0.609227\pi$
$547$	359.109	−	450.308i	0.656506	−	0.823233i	0.992958	+	0.118468i	$0.0377984\pi$
$548$	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	−0.120141	−	0.992757i	$-0.538335\pi$
$557$	378.504	−	218.529i	0.679540	−	0.392333i	0.799682	+	0.600424i	$0.205001\pi$
$558$		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	0.747443	−	0.664326i	$-0.231281\pi$
$563$	16.3931	+	17.6676i	0.0291174	+	0.0313811i	−0.718325	+	0.695707i	$0.755091\pi$
$564$		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	0.875356	−	0.483479i	$-0.160627\pi$
$569$	508.873	+	293.798i	0.894329	+	0.516341i	0.0189731	+	0.999820i	$0.493960\pi$
$570$		0			0
$571$	−233.207	−	158.998i	−0.408418	−	0.278455i	0.341634	−	0.939833i	$-0.389020\pi$
$571$	−233.207	−	158.998i	−0.408418	−	0.278455i	−0.750053	+	0.661378i	$0.769972\pi$
$572$	−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	−0.659422	−	0.751773i	$-0.729199\pi$
$577$	−450.506	+	138.963i	−0.780773	+	0.240836i	−0.121351	+	0.992610i	$0.538723\pi$
$578$	−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	$0.0512551\pi$
$587$			188.225i			0.320655i	−0.987064	+	0.160328i	$0.948745\pi$
$588$		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	−0.480607	−	0.876936i	$-0.659584\pi$
$593$	−140.214	+	55.0299i	−0.236448	+	0.0927991i	0.244158	+	0.969735i	$0.421488\pi$
$594$		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	0.938006	−	0.346619i	$-0.112670\pi$
$599$	−19.3289	−	62.6627i	−0.0322686	−	0.104612i	−0.970274	+	0.242007i	$0.922194\pi$
$600$		0			0
$601$	−189.756	+	831.375i	−0.315734	+	1.38332i	0.529222	+	0.848483i	$0.322484\pi$
$601$	−189.756	+	831.375i	−0.315734	+	1.38332i	−0.844956	+	0.534836i	$0.820373\pi$
$602$	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	−0.621518	−	0.783400i	$-0.713484\pi$
$607$	223.185	−	386.567i	0.367685	−	0.636849i	0.989203	+	0.146551i	$0.0468172\pi$
$608$	−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	−0.787086	−	0.616844i	$-0.788411\pi$
$613$	−141.472	+	131.267i	−0.230786	+	0.214138i	0.556300	+	0.830982i	$0.312221\pi$
$614$	−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	−0.995308	−	0.0967555i	$-0.969154\pi$
$617$	−277.891	−	577.046i	−0.450390	−	0.935245i	0.544918	−	0.838489i	$-0.316561\pi$
$618$		0			0
$619$	83.8846	+	145.292i	0.135516	+	0.234721i	0.925795	−	0.378027i	$-0.123397\pi$
$619$	83.8846	+	145.292i	0.135516	+	0.234721i	−0.790278	+	0.612748i	$0.790064\pi$
$620$	−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	0.969863	−	0.243653i	$-0.0783457\pi$
$631$	325.914	+	408.683i	0.516504	+	0.647676i	−0.453358	+	0.891328i	$0.649774\pi$
$632$	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	0.649596	−	0.760279i	$-0.274938\pi$
$641$	900.766	−	67.5031i	1.40525	−	0.105309i	0.755654	+	0.654970i	$0.227319\pi$
$642$		0			0
$643$	93.9879	+	117.857i	0.146171	+	0.183292i	0.849527	−	0.527545i	$-0.176887\pi$
$643$	93.9879	+	117.857i	0.146171	+	0.183292i	−0.703356	+	0.710838i	$0.748316\pi$
$644$	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	0.177265	−	0.984163i	$-0.443275\pi$
$647$	−234.338	−	91.9708i	−0.362191	−	0.142150i	−0.539456	+	0.842014i	$0.681370\pi$
$648$		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	−0.712816	−	0.701351i	$-0.752580\pi$
$653$	−155.672	−	1032.82i	−0.238395	−	1.58165i	0.474420	−	0.880298i	$-0.342658\pi$
$654$		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	−0.942855	−	0.333204i	$-0.891870\pi$
$659$	−62.2654	+	129.295i	−0.0944847	+	0.196199i	0.848370	+	0.529404i	$0.177584\pi$
$660$		0			0
$661$	−558.420	+	518.138i	−0.844812	+	0.783871i	−0.978303	−	0.207179i	$-0.933572\pi$
$661$	−558.420	+	518.138i	−0.844812	+	0.783871i	0.133491	+	0.991050i	$0.457381\pi$
$662$	−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	−0.999921	−	0.0125337i	$-0.996010\pi$
$673$	−62.9828	+	275.946i	−0.0935852	+	0.410023i	0.906336	+	0.422557i	$0.138867\pi$
$674$	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	0.337854	+	0.941199i	$0.390299\pi$
$677$	−319.199	+	1034.82i	−0.471490	+	1.52853i	−0.809344	+	0.587335i	$0.800177\pi$
$678$		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	−0.784651	−	0.619938i	$-0.787158\pi$
$683$	100.995	−	670.059i	0.147870	−	0.981053i	0.932521	−	0.361115i	$-0.117604\pi$
$684$		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	−0.961494	−	0.274825i	$-0.911380\pi$
$691$	−306.526	−	781.015i	−0.443597	−	1.13027i	0.517897	−	0.855443i	$-0.326715\pi$
$692$	−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	−0.639125	−	0.769103i	$-0.720703\pi$
$701$	−617.760	+	141.000i	−0.881255	+	0.201141i	−0.242130	+	0.970244i	$0.577846\pi$
$702$		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	−0.828160	−	0.560491i	$-0.810612\pi$
$709$	−431.763	+	294.371i	−0.608974	+	0.415192i	0.219186	+	0.975683i	$0.429660\pi$
$710$	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	0.999658	+	0.0261574i	$0.00832711\pi$
$719$	37.4757	+	248.635i	0.0521220	+	0.345807i	−0.947536	+	0.319650i	$0.896435\pi$
$720$		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	0.0425160	+	0.999096i	$0.486463\pi$
$727$	−684.100	+	857.835i	−0.940991	+	1.17997i	−0.983507	+	0.180870i	$0.942109\pi$
$728$	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	0.994091	−	0.108549i	$-0.0346204\pi$
$733$	703.778	+	653.011i	0.960134	+	0.890874i	−0.0339569	+	0.999423i	$0.510811\pi$
$734$		−	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	−0.818612	−	0.574347i	$-0.805256\pi$
$739$	−70.0167	−	934.307i	−0.0947451	−	1.26429i	0.723867	−	0.689939i	$-0.242363\pi$
$740$	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	0.774055	−	0.633119i	$-0.218225\pi$
$743$	244.487	+	194.972i	0.329053	+	0.262411i	−0.445002	+	0.895530i	$0.646797\pi$
$744$		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	−0.301241	−	0.953548i	$-0.597401\pi$
$751$	−231.334	+	34.8680i	−0.308035	+	0.0464288i	−0.00679423	+	0.999977i	$0.502163\pi$
$752$	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	−0.275662	−	0.961255i	$-0.588897\pi$
$757$	−907.699	−	437.125i	−1.19907	−	0.577443i	−0.923412	+	0.383811i	$0.874611\pi$
$758$	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	0.781232	−	0.624241i	$-0.214592\pi$
$761$	−64.8934	−	95.1811i	−0.0852738	−	0.125074i	−0.866506	+	0.499167i	$0.833639\pi$
$762$		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	0.956103	−	0.293032i	$-0.0946641\pi$
$769$	−24.9600	−	109.357i	−0.0324577	−	0.142207i	−0.988560	+	0.150825i	$0.951807\pi$
$770$	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	0.996873	−	0.0790208i	$-0.0251794\pi$
$773$	99.4881	+	322.532i	0.128704	+	0.417248i	−0.868169	+	0.496268i	$0.834703\pi$
$774$		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	0.105453	−	0.994424i	$-0.466371\pi$
$787$	−68.3835	−	10.3072i	−0.0868914	−	0.0130968i	−0.192344	+	0.981328i	$0.561609\pi$
$788$	−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	0.863298	−	0.504695i	$-0.168395\pi$
$797$	1133.43	+	258.699i	1.42212	+	0.324590i	0.558826	+	0.829285i	$0.311252\pi$
$798$		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	0.917061	−	0.398747i	$-0.130555\pi$
$809$	364.776	+	393.135i	0.450897	+	0.485952i	−0.466164	+	0.884698i	$0.654364\pi$
$810$		0			0
$811$	653.744	+	314.826i	0.806096	+	0.388195i	0.791096	−	0.611692i	$-0.209511\pi$
$811$	653.744	+	314.826i	0.806096	+	0.388195i	0.0150000	+	0.999887i	$0.495225\pi$
$812$	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	0.587034	−	0.809562i	$-0.300295\pi$
$821$	859.466	+	64.4081i	1.04685	+	0.0784508i	0.459819	+	0.888013i	$0.347914\pi$
$822$		0			0
$823$	−83.5373	+	212.850i	−0.101503	+	0.258626i	−0.972600	−	0.232486i	$-0.925314\pi$
$823$	−83.5373	+	212.850i	−0.101503	+	0.258626i	0.871096	+	0.491112i	$0.163409\pi$
$824$	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	−0.580738	−	0.814090i	$-0.697236\pi$
$827$	69.2320	−	55.2107i	0.0837147	−	0.0667602i	0.664453	+	0.747330i	$0.268665\pi$
$828$		0			0
$829$	89.3328	+	1192.06i	0.107760	+	1.43795i	0.744885	+	0.667193i	$0.232504\pi$
$829$	89.3328	+	1192.06i	0.107760	+	1.43795i	−0.637125	+	0.770760i	$0.719877\pi$
$830$	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	0.600379	−	0.799715i	$-0.295016\pi$
$839$	1269.94	−	1012.75i	1.51364	−	1.20709i	0.913262	−	0.407373i	$-0.133555\pi$
$840$		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	−0.999082	−	0.0428379i	$-0.986360\pi$
$853$	−1355.00	+	652.532i	−1.58851	+	0.764985i	−0.589425	+	0.807823i	$0.700646\pi$
$854$	−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	0.960728	−	0.277491i	$-0.0895029\pi$
$857$	524.670	+	565.460i	0.612218	+	0.659814i	−0.348511	+	0.937305i	$0.613312\pi$
$858$		0			0
$859$	317.852	−	216.708i	0.370025	−	0.252279i	−0.364003	−	0.931398i	$-0.618590\pi$
$859$	317.852	−	216.708i	0.370025	−	0.252279i	0.734028	+	0.679119i	$0.237638\pi$
$860$	−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	0.980754	+	0.195246i	$0.0625507\pi$
$863$	1415.51	+	817.245i	1.64022	+	0.946981i	0.659466	+	0.751735i	$0.270783\pi$
$864$		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	−0.999127	−	0.0417788i	$-0.986698\pi$
$877$	−258.831	−	659.490i	−0.295132	−	0.751984i	0.703995	−	0.710205i	$-0.251398\pi$
$878$	−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	$-0.950382\pi$
$881$		−	273.551i		−	0.310501i	0.987875	−	0.155251i	$-0.0496185\pi$
$882$		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	−0.663531	−	0.748149i	$-0.730943\pi$
$887$	−568.623	+	223.168i	−0.641063	+	0.251599i	0.0224679	+	0.999748i	$0.492848\pi$
$888$		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	−0.634836	−	0.772647i	$-0.718932\pi$
$907$	80.0053	−	74.2340i	0.0882087	−	0.0818457i	0.723045	+	0.690801i	$0.242742\pi$
$908$	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	0.998902	+	0.0468456i	$0.0149169\pi$
$911$	375.990	+	780.751i	0.412722	+	0.857026i	−0.586180	+	0.810181i	$0.699369\pi$
$912$		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	0.764974	+	0.644061i	$0.222752\pi$
$919$	−80.3649	+	1072.40i	−0.0874482	+	1.16692i	−0.852422	+	0.522854i	$0.824867\pi$
$920$	−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	0.310327	−	0.950630i	$-0.399561\pi$
$929$	1147.42	−	1236.62i	1.23511	−	1.33113i	0.924781	−	0.380500i	$-0.124248\pi$
$930$		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	0.950164	+	0.311750i	$0.100915\pi$
$937$	976.978	+	1225.09i	1.04267	+	1.30746i	0.0925019	+	0.995713i	$0.470514\pi$
$938$	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	0.925637	−	0.378413i	$-0.123530\pi$
$941$	1267.33	+	497.391i	1.34679	+	0.528577i	0.421154	+	0.906989i	$0.361625\pi$
$942$		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	−0.537728	−	0.843119i	$-0.680717\pi$
$947$	−257.966	−	1711.49i	−0.272403	−	1.80728i	0.265324	−	0.964159i	$-0.414521\pi$
$948$		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	−0.234855	−	0.972030i	$-0.575462\pi$
$953$	639.976	−	1328.92i	0.671539	−	1.39446i	0.906394	−	0.422434i	$-0.138824\pi$
$954$		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	−0.528377	−	0.849010i	$-0.677199\pi$
$967$	305.616	−	1338.99i	0.316046	−	1.38469i	0.844423	−	0.535678i	$-0.179944\pi$
$968$	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	−0.729851	−	0.683607i	$-0.760410\pi$
$971$	250.780	−	813.008i	0.258270	−	0.837290i	0.988120	−	0.153683i	$-0.0491134\pi$
$972$		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	−0.983521	−	0.180795i	$-0.942133\pi$
$977$	9.37457	−	62.1962i	0.00959526	−	0.0636604i	0.993116	+	0.117135i	$0.0373710\pi$
$978$		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	0.545803	+	0.837913i	$0.316225\pi$
$983$	−218.944	+	1452.60i	−0.222731	+	1.47772i	−0.768534	+	0.639809i	$0.779013\pi$
$984$		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	−0.263545	−	0.964647i	$-0.584892\pi$
$991$	61.5502	−	18.9857i	0.0621092	−	0.0191581i	0.325654	+	0.945489i	$0.394416\pi$
$992$	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	0.371662	−	0.928368i	$-0.378788\pi$
$997$	−355.679	−	242.498i	−0.356749	−	0.243227i	−0.728410	+	0.685141i	$0.759741\pi$
$998$	−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.107.23	yes	456
3.2	odd	2	inner	441.3.bf.a.107.16	✓	456
49.11	even	21	inner	441.3.bf.a.305.16	yes	456
147.11	odd	42	inner	441.3.bf.a.305.23	yes	456

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.3.bf.a.107.16	✓	456	3.2	odd	2	inner
441.3.bf.a.107.23	yes	456	1.1	even	1	trivial
441.3.bf.a.305.16	yes	456	49.11	even	21	inner
441.3.bf.a.305.23	yes	456	147.11	odd	42	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
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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