LMFDB - Embedded newform 216.3.p.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(19,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("216.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.p (of order $6$, degree $2$, not 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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	216.19
Dual form			216.3.p.b.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99426 + 0.151428i) q^{2} +(3.95414 - 0.603974i) q^{4} +(1.70411 - 0.983869i) q^{5} +(-8.69613 - 5.02071i) q^{7} +(-7.79412 + 1.80325i) q^{8} +O(q^{10})$	\(q+(-1.99426 + 0.151428i) q^{2} +(3.95414 - 0.603974i) q^{4} +(1.70411 - 0.983869i) q^{5} +(-8.69613 - 5.02071i) q^{7} +(-7.79412 + 1.80325i) q^{8} +(-3.24945 + 2.22014i) q^{10} +(-6.08627 + 10.5417i) q^{11} +(4.28857 - 2.47601i) q^{13} +(18.1026 + 8.69576i) q^{14} +(15.2704 - 4.77640i) q^{16} -4.71370 q^{17} -20.5288 q^{19} +(6.14406 - 4.91959i) q^{20} +(10.5413 - 21.9446i) q^{22} +(3.33400 - 1.92488i) q^{23} +(-10.5640 + 18.2974i) q^{25} +(-8.17758 + 5.58721i) q^{26} +(-37.4181 - 14.6004i) q^{28} +(-40.7608 - 23.5333i) q^{29} +(-49.9323 + 28.8285i) q^{31} +(-29.7299 + 11.8377i) q^{32} +(9.40035 - 0.713788i) q^{34} -19.7589 q^{35} -7.93672i q^{37} +(40.9398 - 3.10864i) q^{38} +(-11.5079 + 10.7413i) q^{40} +(11.3426 + 19.6460i) q^{41} +(30.7806 - 53.3136i) q^{43} +(-17.6990 + 45.3594i) q^{44} +(-6.35737 + 4.34358i) q^{46} +(-44.7133 - 25.8152i) q^{47} +(25.9151 + 44.8862i) q^{49} +(18.2966 - 38.0894i) q^{50} +(15.4622 - 12.3807i) q^{52} -51.0133i q^{53} +23.9524i q^{55} +(76.8322 + 23.4507i) q^{56} +(84.8513 + 40.7591i) q^{58} +(-16.7094 - 28.9415i) q^{59} +(39.7329 + 22.9398i) q^{61} +(95.2126 - 65.0526i) q^{62} +(57.4966 - 28.1095i) q^{64} +(4.87213 - 8.43878i) q^{65} +(26.9209 + 46.6284i) q^{67} +(-18.6386 + 2.84696i) q^{68} +(39.4043 - 2.99205i) q^{70} +132.571i q^{71} +24.6995 q^{73} +(1.20184 + 15.8279i) q^{74} +(-81.1738 + 12.3989i) q^{76} +(105.854 - 61.1148i) q^{77} +(-84.3214 - 48.6830i) q^{79} +(21.3232 - 23.1636i) q^{80} +(-25.5951 - 37.4616i) q^{82} +(-0.187458 + 0.324687i) q^{83} +(-8.03267 + 4.63767i) q^{85} +(-53.3113 + 110.982i) q^{86} +(28.4278 - 93.1386i) q^{88} +134.821 q^{89} -49.7252 q^{91} +(12.0205 - 9.62490i) q^{92} +(93.0790 + 44.7114i) q^{94} +(-34.9834 + 20.1977i) q^{95} +(10.8826 - 18.8492i) q^{97} +(-58.4784 - 85.5905i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.99426	+	0.151428i	−0.997130	+	0.0757141i
$2$	−1.99426	+	0.151428i	−0.997130	+	0.0757141i
$3$		0			0
$3$		0			0
$4$	3.95414	−	0.603974i	0.988535	−	0.150994i
$5$	1.70411	−	0.983869i	0.340822	−	0.196774i	−0.319813	−	0.947481i	$-0.603620\pi$
$5$	1.70411	−	0.983869i	0.340822	−	0.196774i	0.660636	+	0.750707i	$0.270287\pi$
$6$		0			0
$7$	−8.69613	−	5.02071i	−1.24230	−	0.717244i	−0.272741	−	0.962087i	$-0.587930\pi$
$7$	−8.69613	−	5.02071i	−1.24230	−	0.717244i	−0.969563	+	0.244843i	$0.921264\pi$
$8$	−7.79412	+	1.80325i	−0.974265	+	0.225406i
$9$		0			0
$10$	−3.24945	+	2.22014i	−0.324945	+	0.222014i
$11$	−6.08627	+	10.5417i	−0.553298	+	0.958339i	0.444736	+	0.895662i	$0.353297\pi$
$11$	−6.08627	+	10.5417i	−0.553298	+	0.958339i	−0.998034	+	0.0626779i	$0.980036\pi$
$12$		0			0
$13$	4.28857	−	2.47601i	0.329890	−	0.190462i	−0.325902	−	0.945403i	$-0.605668\pi$
$13$	4.28857	−	2.47601i	0.329890	−	0.190462i	0.655792	+	0.754941i	$0.272335\pi$
$14$	18.1026	+	8.69576i	1.29304	+	0.621126i
$15$		0			0
$16$	15.2704	−	4.77640i	0.954402	−	0.298525i
$17$	−4.71370			−0.277277			−0.138638	−	0.990343i	$-0.544273\pi$
$17$	−4.71370			−0.277277			−0.138638	+	0.990343i	$0.544273\pi$
$18$		0			0
$19$	−20.5288			−1.08046			−0.540232	−	0.841516i	$-0.681663\pi$
$19$	−20.5288			−1.08046			−0.540232	+	0.841516i	$0.681663\pi$
$20$	6.14406	−	4.91959i	0.307203	−	0.245980i
$21$		0			0
$22$	10.5413	−	21.9446i	0.479149	−	0.997481i
$23$	3.33400	−	1.92488i	0.144956	−	0.0836906i	−0.425768	−	0.904832i	$-0.639996\pi$
$23$	3.33400	−	1.92488i	0.144956	−	0.0836906i	0.570724	+	0.821142i	$0.306663\pi$
$24$		0			0
$25$	−10.5640	+	18.2974i	−0.422560	+	0.731896i
$26$	−8.17758	+	5.58721i	−0.314522	+	0.214893i
$27$		0			0
$28$	−37.4181	−	14.6004i	−1.33636	−	0.521441i
$29$	−40.7608	−	23.5333i	−1.40555	−	0.811492i	−0.410592	−	0.911819i	$-0.634678\pi$
$29$	−40.7608	−	23.5333i	−1.40555	−	0.811492i	−0.994955	+	0.100327i	$0.968011\pi$
$30$		0			0
$31$	−49.9323	+	28.8285i	−1.61072	+	0.929950i	−0.621517	+	0.783400i	$0.713483\pi$
$31$	−49.9323	+	28.8285i	−1.61072	+	0.929950i	−0.989203	+	0.146550i	$0.953183\pi$
$32$	−29.7299	+	11.8377i	−0.929060	+	0.369930i
$33$		0			0
$34$	9.40035	−	0.713788i	0.276481	−	0.0209938i
$35$	−19.7589			−0.564540
$36$		0			0
$37$		−	7.93672i		−	0.214506i	−0.994232	−	0.107253i	$-0.965795\pi$
$37$		−	7.93672i		−	0.214506i	0.994232	−	0.107253i	$-0.0342055\pi$
$38$	40.9398	−	3.10864i	1.07736	−	0.0818063i
$39$		0			0
$40$	−11.5079	+	10.7413i	−0.287697	+	0.268533i
$41$	11.3426	+	19.6460i	0.276649	+	0.479171i	0.970550	−	0.240900i	$-0.0774426\pi$
$41$	11.3426	+	19.6460i	0.276649	+	0.479171i	−0.693901	+	0.720071i	$0.744109\pi$
$42$		0			0
$43$	30.7806	−	53.3136i	0.715828	−	1.23985i	−0.246811	−	0.969064i	$-0.579383\pi$
$43$	30.7806	−	53.3136i	0.715828	−	1.23985i	0.962639	−	0.270787i	$-0.0872840\pi$
$44$	−17.6990	+	45.3594i	−0.402251	+	1.03090i
$45$		0			0
$46$	−6.35737	+	4.34358i	−0.138204	+	0.0944256i
$47$	−44.7133	−	25.8152i	−0.951346	−	0.549260i	−0.0578471	−	0.998325i	$-0.518424\pi$
$47$	−44.7133	−	25.8152i	−0.951346	−	0.549260i	−0.893499	+	0.449066i	$0.851757\pi$
$48$		0			0
$49$	25.9151	+	44.8862i	0.528879	+	0.916045i
$50$	18.2966	−	38.0894i	0.365932	−	0.761789i
$51$		0			0
$52$	15.4622	−	12.3807i	0.297349	−	0.238090i
$53$		−	51.0133i		−	0.962515i	−0.876579	−	0.481258i	$-0.840180\pi$
$53$		−	51.0133i		−	0.962515i	0.876579	−	0.481258i	$-0.159820\pi$
$54$		0			0
$55$			23.9524i			0.435498i
$56$	76.8322	+	23.4507i	1.37200	+	0.418763i
$57$		0			0
$58$	84.8513	+	40.7591i	1.46295	+	0.702743i
$59$	−16.7094	−	28.9415i	−0.283209	−	0.490533i	0.688964	−	0.724796i	$-0.258066\pi$
$59$	−16.7094	−	28.9415i	−0.283209	−	0.490533i	−0.972173	+	0.234262i	$0.924732\pi$
$60$		0			0
$61$	39.7329	+	22.9398i	0.651359	+	0.376062i	0.788977	−	0.614423i	$-0.210611\pi$
$61$	39.7329	+	22.9398i	0.651359	+	0.376062i	−0.137618	+	0.990485i	$0.543945\pi$
$62$	95.2126	−	65.0526i	1.53569	−	1.04923i
$63$		0			0
$64$	57.4966	−	28.1095i	0.898384	−	0.439211i
$65$	4.87213	−	8.43878i	0.0749559	−	0.129827i
$66$		0			0
$67$	26.9209	+	46.6284i	0.401805	+	0.695946i	0.993944	−	0.109889i	$-0.0350497\pi$
$67$	26.9209	+	46.6284i	0.401805	+	0.695946i	−0.592139	+	0.805836i	$0.701716\pi$
$68$	−18.6386	+	2.84696i	−0.274098	+	0.0418670i
$69$		0			0
$70$	39.4043	−	2.99205i	0.562919	−	0.0427436i
$71$			132.571i			1.86720i	0.358313	+	0.933601i	$0.383352\pi$
$71$			132.571i			1.86720i	−0.358313	+	0.933601i	$0.616648\pi$
$72$		0			0
$73$	24.6995			0.338349			0.169175	−	0.985586i	$-0.445890\pi$
$73$	24.6995			0.338349			0.169175	+	0.985586i	$0.445890\pi$
$74$	1.20184	+	15.8279i	0.0162411	+	0.213890i
$75$		0			0
$76$	−81.1738	+	12.3989i	−1.06808	+	0.163143i
$77$	105.854	−	61.1148i	1.37473	−	0.793699i
$78$		0			0
$79$	−84.3214	−	48.6830i	−1.06736	−	0.616241i	−0.139901	−	0.990166i	$-0.544678\pi$
$79$	−84.3214	−	48.6830i	−1.06736	−	0.616241i	−0.927459	+	0.373925i	$0.878012\pi$
$80$	21.3232	−	23.1636i	0.266539	−	0.289545i
$81$		0			0
$82$	−25.5951	−	37.4616i	−0.312135	−	0.456849i
$83$	−0.187458	+	0.324687i	−0.00225853	+	0.00391189i	−0.867152	−	0.498043i	$-0.834052\pi$
$83$	−0.187458	+	0.324687i	−0.00225853	+	0.00391189i	0.864894	+	0.501955i	$0.167386\pi$
$84$		0			0
$85$	−8.03267	+	4.63767i	−0.0945021	+	0.0545608i
$86$	−53.3113	+	110.982i	−0.619899	+	1.29049i
$87$		0			0
$88$	28.4278	−	93.1386i	0.323043	−	1.05839i
$89$	134.821			1.51485			0.757423	−	0.652925i	$-0.226458\pi$
$89$	134.821			1.51485			0.757423	+	0.652925i	$0.226458\pi$
$90$		0			0
$91$	−49.7252			−0.546431
$92$	12.0205	−	9.62490i	0.130658	−	0.104618i
$93$		0			0
$94$	93.0790	+	44.7114i	0.990202	+	0.475653i
$95$	−34.9834	+	20.1977i	−0.368246	+	0.212607i
$96$		0			0
$97$	10.8826	−	18.8492i	0.112192	−	0.194322i	−0.804462	−	0.594004i	$-0.797546\pi$
$97$	10.8826	−	18.8492i	0.112192	−	0.194322i	0.916654	+	0.399682i	$0.130880\pi$
$98$	−58.4784	−	85.5905i	−0.596719	−	0.873372i
$99$		0			0
$100$	−30.7204	+	78.7308i	−0.307204	+	0.787308i
$101$	40.3177	+	23.2774i	0.399185	+	0.230470i	0.686132	−	0.727477i	$-0.259307\pi$
$101$	40.3177	+	23.2774i	0.399185	+	0.230470i	−0.286947	+	0.957946i	$0.592640\pi$
$102$		0			0
$103$	87.3356	−	50.4232i	0.847918	−	0.489546i	−0.0120298	−	0.999928i	$-0.503829\pi$
$103$	87.3356	−	50.4232i	0.847918	−	0.489546i	0.859948	+	0.510382i	$0.170496\pi$
$104$	−28.9608	+	27.0316i	−0.278469	+	0.259920i
$105$		0			0
$106$	7.72485	+	101.734i	0.0728760	+	0.959752i
$107$	12.9467			0.120997			0.0604986	−	0.998168i	$-0.480731\pi$
$107$	12.9467			0.120997			0.0604986	+	0.998168i	$0.480731\pi$
$108$		0			0
$109$		−	117.693i		−	1.07975i	−0.841745	−	0.539875i	$-0.818471\pi$
$109$		−	117.693i		−	1.07975i	0.841745	−	0.539875i	$-0.181529\pi$
$110$	−3.62707	−	47.7672i	−0.0329733	−	0.434248i
$111$		0			0
$112$	−156.774	−	35.1323i	−1.39977	−	0.313681i
$113$	−14.6904	−	25.4446i	−0.130004	−	0.225173i	0.793674	−	0.608343i	$-0.208166\pi$
$113$	−14.6904	−	25.4446i	−0.130004	−	0.225173i	−0.923678	+	0.383170i	$0.874832\pi$
$114$		0			0
$115$	3.78766	−	6.56043i	0.0329362	−	0.0570472i
$116$	−175.388	−	68.4354i	−1.51196	−	0.589960i
$117$		0			0
$118$	37.7053	+	55.1865i	0.319537	+	0.467682i
$119$	40.9910	+	23.6661i	0.344462	+	0.198875i
$120$		0			0
$121$	−13.5854	−	23.5307i	−0.112276	−	0.194468i
$122$	−82.7114	−	39.7312i	−0.677962	−	0.325666i
$123$		0			0
$124$	−180.028	+	144.150i	−1.45184	+	1.16250i
$125$			90.7678i			0.726143i
$126$		0			0
$127$			112.463i			0.885532i	0.896637	+	0.442766i	$0.146003\pi$
$127$			112.463i			0.885532i	−0.896637	+	0.442766i	$0.853997\pi$
$128$	−110.407	+	64.7642i	−0.862551	+	0.505970i
$129$		0			0
$130$	−8.43842	+	17.5669i	−0.0649109	+	0.135130i
$131$	−89.1863	−	154.475i	−0.680812	−	1.17920i	−0.974733	−	0.223371i	$-0.928294\pi$
$131$	−89.1863	−	154.475i	−0.680812	−	1.17920i	0.293922	−	0.955829i	$-0.405039\pi$
$132$		0			0
$133$	178.521	+	103.069i	1.34226	+	0.774956i
$134$	−60.7482	−	88.9125i	−0.453344	−	0.663526i
$135$		0			0
$136$	36.7392	−	8.49999i	0.270141	−	0.0624999i
$137$	−64.0732	+	110.978i	−0.467688	+	0.810059i	−0.999318	−	0.0369173i	$-0.988246\pi$
$137$	−64.0732	+	110.978i	−0.467688	+	0.810059i	0.531631	+	0.846976i	$0.321580\pi$
$138$		0			0
$139$	−96.3171	−	166.826i	−0.692929	−	1.20019i	−0.970874	−	0.239591i	$-0.922987\pi$
$139$	−96.3171	−	166.826i	−0.692929	−	1.20019i	0.277945	−	0.960597i	$-0.410347\pi$
$140$	−78.1294	+	11.9339i	−0.558067	+	0.0852418i
$141$		0			0
$142$	−20.0751	−	264.382i	−0.141374	−	1.86184i
$143$			60.2786i			0.421529i
$144$		0			0
$145$	−92.6146			−0.638722
$146$	−49.2572	+	3.74020i	−0.337378	+	0.0256178i
$147$		0			0
$148$	−4.79357	−	31.3829i	−0.0323890	−	0.212046i
$149$	31.9061	−	18.4210i	0.214135	−	0.123631i	−0.389097	−	0.921197i	$-0.627213\pi$
$149$	31.9061	−	18.4210i	0.214135	−	0.123631i	0.603231	+	0.797566i	$0.293880\pi$
$150$		0			0
$151$	−1.53781	−	0.887854i	−0.0101842	−	0.00587983i	0.494899	−	0.868950i	$-0.335205\pi$
$151$	−1.53781	−	0.887854i	−0.0101842	−	0.00587983i	−0.505083	+	0.863071i	$0.668538\pi$
$152$	160.004	−	37.0186i	1.05266	−	0.243543i
$153$		0			0
$154$	−201.846	+	137.908i	−1.31069	+	0.895507i
$155$	−56.7268	+	98.2538i	−0.365980	+	0.633895i
$156$		0			0
$157$	28.4676	−	16.4358i	0.181322	−	0.104686i	−0.406592	−	0.913610i	$-0.633283\pi$
$157$	28.4676	−	16.4358i	0.181322	−	0.104686i	0.587914	+	0.808924i	$0.299949\pi$
$158$	175.531	+	84.3179i	1.11095	+	0.533657i
$159$		0			0
$160$	−39.0163	+	49.4232i	−0.243852	+	0.308895i
$161$	−38.6571			−0.240106
$162$		0			0
$163$	26.1023			0.160137			0.0800686	−	0.996789i	$-0.474486\pi$
$163$	26.1023			0.160137			0.0800686	+	0.996789i	$0.474486\pi$
$164$	56.7160	+	70.8324i	0.345829	+	0.431905i
$165$		0			0
$166$	0.324673	−	0.675896i	0.00195586	−	0.00407166i
$167$	113.333	−	65.4331i	0.678643	−	0.391815i	−0.120700	−	0.992689i	$-0.538514\pi$
$167$	113.333	−	65.4331i	0.678643	−	0.391815i	0.799344	+	0.600874i	$0.205181\pi$
$168$		0			0
$169$	−72.2388	+	125.121i	−0.427448	+	0.740362i
$170$	15.3170	−	10.4651i	0.0900998	−	0.0615593i
$171$		0			0
$172$	89.5108	−	229.400i	0.520412	−	1.33372i
$173$	−159.107	−	91.8606i	−0.919695	−	0.530986i	−0.0361571	−	0.999346i	$-0.511512\pi$
$173$	−159.107	−	91.8606i	−0.919695	−	0.530986i	−0.883538	+	0.468360i	$0.844845\pi$
$174$		0			0
$175$	183.732	−	106.078i	1.04990	−	0.606158i
$176$	−42.5885	+	190.047i	−0.241980	+	1.07981i
$177$		0			0
$178$	−268.869	+	20.4157i	−1.51050	+	0.114695i
$179$	24.4312			0.136487			0.0682435	−	0.997669i	$-0.478261\pi$
$179$	24.4312			0.136487			0.0682435	+	0.997669i	$0.478261\pi$
$180$		0			0
$181$		−	101.654i		−	0.561622i	−0.959763	−	0.280811i	$-0.909397\pi$
$181$		−	101.654i		−	0.561622i	0.959763	−	0.280811i	$-0.0906034\pi$
$182$	99.1650	−	7.52981i	0.544863	−	0.0413726i
$183$		0			0
$184$	−22.5145	+	21.0148i	−0.122361	+	0.114211i
$185$	−7.80869	−	13.5250i	−0.0422091	−	0.0731084i
$186$		0			0
$187$	28.6889	−	49.6906i	0.153417	−	0.265725i
$188$	−192.394	−	75.0713i	−1.02337	−	0.399315i
$189$		0			0
$190$	66.7074	−	45.5768i	0.351092	−	0.239878i
$191$	25.0116	+	14.4405i	0.130951	+	0.0756046i	0.564044	−	0.825744i	$-0.309245\pi$
$191$	25.0116	+	14.4405i	0.130951	+	0.0756046i	−0.433093	+	0.901349i	$0.642578\pi$
$192$		0			0
$193$	−142.662	−	247.098i	−0.739181	−	1.28030i	−0.952864	−	0.303396i	$-0.901879\pi$
$193$	−142.662	−	247.098i	−0.739181	−	1.28030i	0.213683	−	0.976903i	$-0.431454\pi$
$194$	−18.8484	+	39.2382i	−0.0971569	+	0.202259i
$195$		0			0
$196$	129.582	+	161.834i	0.661132	+	0.825685i
$197$			191.958i			0.974405i	0.873289	+	0.487202i	$0.161983\pi$
$197$			191.958i			0.974405i	−0.873289	+	0.487202i	$0.838017\pi$
$198$		0			0
$199$			33.7936i			0.169817i	0.996389	+	0.0849085i	$0.0270598\pi$
$199$			33.7936i			0.169817i	−0.996389	+	0.0849085i	$0.972940\pi$
$200$	49.3423	−	161.662i	0.246712	−	0.808308i
$201$		0			0
$202$	−83.9288	−	40.3160i	−0.415489	−	0.199584i
$203$	236.308	+	409.297i	1.16408	+	2.01624i
$204$		0			0
$205$	38.6582	+	22.3193i	0.188576	+	0.108875i
$206$	−166.534	+	113.782i	−0.808419	+	0.552340i
$207$		0			0
$208$	53.6619	−	58.2936i	0.257990	−	0.280258i
$209$	124.944	−	216.409i	0.597818	−	1.03545i
$210$		0			0
$211$	129.688	+	224.627i	0.614636	+	1.06458i	0.990448	+	0.137885i	$0.0440306\pi$
$211$	129.688	+	224.627i	0.614636	+	1.06458i	−0.375812	+	0.926696i	$0.622636\pi$
$212$	−30.8107	−	201.714i	−0.145334	−	0.951480i
$213$		0			0
$214$	−25.8191	+	1.96050i	−0.120650	+	0.00916120i
$215$		−	121.136i		−	0.563425i
$216$		0			0
$217$	578.957			2.66801
$218$	17.8220	+	234.710i	0.0817524	+	1.07665i
$219$		0			0
$220$	14.4666	+	94.7110i	0.0657574	+	0.430505i
$221$	−20.2150	+	11.6712i	−0.0914708	+	0.0528107i
$222$		0			0
$223$	−107.192	−	61.8873i	−0.480681	−	0.277521i	0.240019	−	0.970768i	$-0.422846\pi$
$223$	−107.192	−	61.8873i	−0.480681	−	0.277521i	−0.720700	+	0.693247i	$0.756180\pi$
$224$	317.969	+	46.3228i	1.41950	+	0.206798i
$225$		0			0
$226$	33.1495	+	48.5185i	0.146679	+	0.214684i
$227$	127.486	−	220.813i	0.561614	−	0.972745i	−0.435741	−	0.900072i	$-0.643514\pi$
$227$	127.486	−	220.813i	0.561614	−	0.972745i	0.997356	−	0.0726729i	$-0.0231529\pi$
$228$		0			0
$229$	−216.736	+	125.132i	−0.946444	+	0.546430i	−0.891975	−	0.452085i	$-0.850680\pi$
$229$	−216.736	+	125.132i	−0.946444	+	0.546430i	−0.0544698	+	0.998515i	$0.517347\pi$
$230$	−6.56015	+	13.6568i	−0.0285224	+	0.0593772i
$231$		0			0
$232$	360.131	+	109.919i	1.55229	+	0.473790i
$233$	−231.979			−0.995619			−0.497810	−	0.867286i	$-0.665862\pi$
$233$	−231.979			−0.995619			−0.497810	+	0.867286i	$0.665862\pi$
$234$		0			0
$235$	−101.595			−0.432320
$236$	−83.5510	−	104.347i	−0.354030	−	0.442146i
$237$		0			0
$238$	−85.3303	−	40.9892i	−0.358531	−	0.172224i
$239$	209.313	−	120.847i	0.875786	−	0.505635i	0.00651903	−	0.999979i	$-0.497925\pi$
$239$	209.313	−	120.847i	0.875786	−	0.505635i	0.869267	+	0.494344i	$0.164592\pi$
$240$		0			0
$241$	−115.503	+	200.057i	−0.479266	+	0.830113i	−0.999717	−	0.0237786i	$-0.992430\pi$
$241$	−115.503	+	200.057i	−0.479266	+	0.830113i	0.520451	+	0.853891i	$0.325764\pi$
$242$	30.6561	+	44.8690i	0.126678	+	0.185409i
$243$		0			0
$244$	170.964	+	66.7095i	0.700674	+	0.273400i
$245$	88.3243	+	50.9941i	0.360507	+	0.208139i
$246$		0			0
$247$	−88.0392	+	50.8294i	−0.356434	+	0.205787i
$248$	337.194	−	314.733i	1.35965	−	1.26908i
$249$		0			0
$250$	−13.7448	−	181.015i	−0.0549792	−	0.724058i
$251$	78.5229			0.312840			0.156420	−	0.987691i	$-0.450005\pi$
$251$	78.5229			0.312840			0.156420	+	0.987691i	$0.450005\pi$
$252$		0			0
$253$			46.8615i			0.185223i
$254$	−17.0300	−	224.280i	−0.0670473	−	0.882991i
$255$		0			0
$256$	210.372	−	145.875i	0.821766	−	0.569825i
$257$	−130.836	−	226.615i	−0.509090	−	0.881770i	−0.999945	−	0.0105283i	$-0.996649\pi$
$257$	−130.836	−	226.615i	−0.509090	−	0.881770i	0.490855	−	0.871242i	$-0.336685\pi$
$258$		0			0
$259$	−39.8480	+	69.0187i	−0.153853	+	0.266481i
$260$	14.1683	−	36.3107i	0.0544934	−	0.139657i
$261$		0			0
$262$	201.253	+	294.558i	0.768140	+	1.12427i
$263$	−275.353	−	158.975i	−1.04697	−	0.604469i	−0.125171	−	0.992135i	$-0.539948\pi$
$263$	−275.353	−	158.975i	−1.04697	−	0.604469i	−0.921800	+	0.387667i	$0.873281\pi$
$264$		0			0
$265$	−50.1904	−	86.9323i	−0.189398	−	0.328046i
$266$	−371.625	−	178.514i	−1.39709	−	0.671104i
$267$		0			0
$268$	134.611	+	168.116i	0.502281	+	0.627297i
$269$			135.043i			0.502020i	0.967985	+	0.251010i	$0.0807627\pi$
$269$			135.043i			0.502020i	−0.967985	+	0.251010i	$0.919237\pi$
$270$		0			0
$271$			161.415i			0.595628i	0.954624	+	0.297814i	$0.0962575\pi$
$271$			161.415i			0.595628i	−0.954624	+	0.297814i	$0.903742\pi$
$272$	−71.9803	+	22.5145i	−0.264633	+	0.0827740i
$273$		0			0
$274$	110.973	−	231.022i	0.405012	−	0.843144i
$275$	−128.591	−	222.726i	−0.467603	−	0.809912i
$276$		0			0
$277$	−367.934	−	212.427i	−1.32828	−	0.766884i	−0.343248	−	0.939245i	$-0.611527\pi$
$277$	−367.934	−	212.427i	−1.32828	−	0.766884i	−0.985034	+	0.172361i	$0.944860\pi$
$278$	217.344	+	318.109i	0.781811	+	1.14428i
$279$		0			0
$280$	154.003	−	35.6302i	0.550011	−	0.127251i
$281$	−80.5450	+	139.508i	−0.286637	+	0.496470i	−0.973005	−	0.230785i	$-0.925871\pi$
$281$	−80.5450	+	139.508i	−0.286637	+	0.496470i	0.686368	+	0.727255i	$0.259204\pi$
$282$		0			0
$283$	182.383	+	315.897i	0.644464	+	1.11625i	0.984425	+	0.175805i	$0.0562530\pi$
$283$	182.383	+	315.897i	0.644464	+	1.11625i	−0.339960	+	0.940440i	$0.610414\pi$
$284$	80.0697	+	524.206i	0.281936	+	1.84580i
$285$		0			0
$286$	−9.12788	−	120.211i	−0.0319157	−	0.420319i
$287$		−	227.792i		−	0.793701i
$288$		0			0
$289$	−266.781			−0.923118
$290$	184.698	−	14.0245i	0.636888	−	0.0483602i
$291$		0			0
$292$	97.6653	−	14.9179i	0.334470	−	0.0510886i
$293$	−437.041	+	252.326i	−1.49161	+	0.861180i	−0.999954	−	0.00961009i	$-0.996941\pi$
$293$	−437.041	+	252.326i	−1.49161	+	0.861180i	−0.491654	+	0.870790i	$0.663608\pi$
$294$		0			0
$295$	−56.9492	−	32.8796i	−0.193048	−	0.111456i
$296$	14.3119	+	61.8597i	0.0483510	+	0.208986i
$297$		0			0
$298$	−60.8395	+	41.5677i	−0.204159	+	0.139489i
$299$	9.53204	−	16.5100i	0.0318797	−	0.0552173i
$300$		0			0
$301$	−535.344	+	309.081i	−1.77855	+	1.02685i
$302$	3.20124	+	1.53774i	0.0106001	+	0.00509187i
$303$		0			0
$304$	−313.484	+	98.0537i	−1.03120	+	0.322545i
$305$	90.2790			0.295997
$306$		0			0
$307$	42.6361			0.138880			0.0694400	−	0.997586i	$-0.477879\pi$
$307$	42.6361			0.138880			0.0694400	+	0.997586i	$0.477879\pi$
$308$	381.650	−	305.590i	1.23912	−	0.992174i
$309$		0			0
$310$	98.2496	−	204.533i	0.316934	−	0.659785i
$311$	−170.776	+	98.5973i	−0.549117	+	0.317033i	−0.748766	−	0.662834i	$-0.769353\pi$
$311$	−170.776	+	98.5973i	−0.549117	+	0.317033i	0.199649	+	0.979868i	$0.436020\pi$
$312$		0			0
$313$	73.0920	−	126.599i	0.233521	−	0.404470i	−0.725321	−	0.688411i	$-0.758309\pi$
$313$	73.0920	−	126.599i	0.233521	−	0.404470i	0.958842	+	0.283941i	$0.0916420\pi$
$314$	−54.2829	+	37.0880i	−0.172876	+	0.118115i
$315$		0			0
$316$	−362.822	−	141.571i	−1.14817	−	0.448011i
$317$	61.0328	+	35.2373i	0.192533	+	0.111159i	0.593168	−	0.805079i	$-0.297877\pi$
$317$	61.0328	+	35.2373i	0.192533	+	0.111159i	−0.400635	+	0.916238i	$0.631210\pi$
$318$		0			0
$319$	496.163	−	286.460i	1.55537	−	0.897993i
$320$	70.3245	−	104.471i	0.219764	−	0.326471i
$321$		0			0
$322$	77.0923	−	5.85378i	0.239417	−	0.0181794i
$323$	96.7667			0.299587
$324$		0			0
$325$			104.626i			0.321927i
$326$	−52.0548	+	3.95263i	−0.159677	+	0.0121246i
$327$		0			0
$328$	−123.832	−	132.670i	−0.377538	−	0.404481i
$329$	259.221	+	448.985i	0.787907	+	1.36470i
$330$		0			0
$331$	54.0633	−	93.6405i	0.163333	−	0.282902i	−0.772729	−	0.634736i	$-0.781109\pi$
$331$	54.0633	−	93.6405i	0.163333	−	0.282902i	0.936062	+	0.351835i	$0.114442\pi$
$332$	−0.545133	+	1.39708i	−0.00164197	+	0.00420806i
$333$		0			0
$334$	−216.108	+	147.652i	−0.647029	+	0.442073i
$335$	91.7525	+	52.9733i	0.273888	+	0.158129i
$336$		0			0
$337$	−168.695	−	292.189i	−0.500580	−	0.867030i	−1.00000		0.000669822i	$-0.999787\pi$
$337$	−168.695	−	292.189i	−0.500580	−	0.867030i	0.499420	−	0.866360i	$-0.333547\pi$
$338$	125.116	−	260.463i	0.370166	−	0.770601i
$339$		0			0
$340$	−28.9613	+	23.1895i	−0.0851802	+	0.0682044i
$341$		−	701.831i		−	2.05816i
$342$		0			0
$343$		−	28.4187i		−	0.0828534i
$344$	−143.770	+	471.038i	−0.417936	+	1.36930i
$345$		0			0
$346$	331.211	+	159.100i	0.957258	+	0.459828i
$347$	−12.3560	−	21.4012i	−0.0356081	−	0.0616750i	0.847672	−	0.530520i	$-0.178003\pi$
$347$	−12.3560	−	21.4012i	−0.0356081	−	0.0616750i	−0.883280	+	0.468845i	$0.844670\pi$
$348$		0			0
$349$	−12.1159	−	6.99512i	−0.0347160	−	0.0200433i	0.482542	−	0.875873i	$-0.339714\pi$
$349$	−12.1159	−	6.99512i	−0.0347160	−	0.0200433i	−0.517258	+	0.855830i	$0.673047\pi$
$350$	−350.346	+	239.368i	−1.00099	+	0.683910i
$351$		0			0
$352$	56.1540	−	385.453i	0.159528	−	1.09504i
$353$	−157.831	+	273.371i	−0.447113	+	0.774422i	−0.998197	−	0.0600276i	$-0.980881\pi$
$353$	−157.831	+	273.371i	−0.447113	+	0.774422i	0.551084	+	0.834450i	$0.314214\pi$
$354$		0			0
$355$	130.433	+	225.916i	0.367417	+	0.636384i
$356$	533.102	−	81.4286i	1.49748	−	0.228732i
$357$		0			0
$358$	−48.7221	+	3.69957i	−0.136095	+	0.0103340i
$359$		−	629.848i		−	1.75445i	−0.480078	−	0.877226i	$-0.659392\pi$
$359$		−	629.848i		−	1.75445i	0.480078	−	0.877226i	$-0.340608\pi$
$360$		0			0
$361$	60.4319			0.167401
$362$	15.3932	+	202.724i	0.0425227	+	0.560010i
$363$		0			0
$364$	−196.621	+	30.0328i	−0.540166	+	0.0825076i
$365$	42.0907	−	24.3011i	0.115317	−	0.0665783i
$366$		0			0
$367$	224.072	+	129.368i	0.610550	+	0.352501i	0.773181	−	0.634186i	$-0.218665\pi$
$367$	224.072	+	129.368i	0.610550	+	0.352501i	−0.162631	+	0.986687i	$0.551998\pi$
$368$	41.7175	−	45.3183i	0.113363	−	0.123147i
$369$		0			0
$370$	17.6206	+	25.7900i	0.0476233	+	0.0697027i
$371$	−256.123	+	443.618i	−0.690359	+	1.19574i
$372$		0			0
$373$	−107.907	+	62.3003i	−0.289296	+	0.167025i	−0.637624	−	0.770348i	$-0.720083\pi$
$373$	−107.907	+	62.3003i	−0.289296	+	0.167025i	0.348329	+	0.937373i	$0.386749\pi$
$374$	−49.6885	+	103.440i	−0.132857	+	0.276578i
$375$		0			0
$376$	395.052	+	120.578i	1.05067	+	0.320685i
$377$	−233.074			−0.618234
$378$		0			0
$379$	−154.148			−0.406724			−0.203362	−	0.979104i	$-0.565187\pi$
$379$	−154.148			−0.406724			−0.203362	+	0.979104i	$0.565187\pi$
$380$	−126.130	+	100.993i	−0.331922	+	0.265772i
$381$		0			0
$382$	−52.0664	−	25.0106i	−0.136299	−	0.0654727i
$383$	−344.678	+	199.000i	−0.899944	+	0.519583i	−0.877182	−	0.480158i	$-0.840579\pi$
$383$	−344.678	+	199.000i	−0.899944	+	0.519583i	−0.0227617	+	0.999741i	$0.507246\pi$
$384$		0			0
$385$	120.258	−	208.293i	0.312358	−	0.541020i
$386$	321.922	+	471.174i	0.833996	+	1.22066i
$387$		0			0
$388$	31.6469	−	81.1053i	0.0815642	−	0.209034i
$389$	279.310	+	161.260i	0.718020	+	0.414549i	0.814024	−	0.580832i	$-0.197273\pi$
$389$	279.310	+	161.260i	0.718020	+	0.414549i	−0.0960032	+	0.995381i	$0.530606\pi$
$390$		0			0
$391$	−15.7155	+	9.07333i	−0.0401930	+	0.0232054i
$392$	−282.926	−	303.117i	−0.721751	−	0.773258i
$393$		0			0
$394$	−29.0678	−	382.813i	−0.0737762	−	0.971608i
$395$	−191.591			−0.485040
$396$		0			0
$397$		−	286.878i		−	0.722615i	−0.932447	−	0.361308i	$-0.882330\pi$
$397$		−	286.878i		−	0.722615i	0.932447	−	0.361308i	$-0.117670\pi$
$398$	−5.11730	−	67.3931i	−0.0128575	−	0.169329i
$399$		0			0
$400$	−73.9213	+	329.867i	−0.184803	+	0.824667i
$401$	−296.251	−	513.122i	−0.738781	−	1.27961i	−0.953044	−	0.302831i	$-0.902068\pi$
$401$	−296.251	−	513.122i	−0.738781	−	1.27961i	0.214263	−	0.976776i	$-0.431265\pi$
$402$		0			0
$403$	−142.759	+	247.266i	−0.354240	+	0.613562i
$404$	173.481	+	67.6913i	0.429408	+	0.167553i
$405$		0			0
$406$	−533.238	−	780.460i	−1.31339	−	1.92232i
$407$	83.6668	+	48.3050i	0.205569	+	0.118686i
$408$		0			0
$409$	258.131	+	447.095i	0.631126	+	1.09314i	0.987322	+	0.158731i	$0.0507403\pi$
$409$	258.131	+	447.095i	0.631126	+	1.09314i	−0.356196	+	0.934411i	$0.615926\pi$
$410$	−80.4742	−	38.6566i	−0.196279	−	0.0942843i
$411$		0			0
$412$	314.883	−	252.129i	0.764278	−	0.611963i
$413$			335.571i			0.812522i
$414$		0			0
$415$			0.737736i			0.00177768i
$416$	−98.1884	+	124.378i	−0.236030	+	0.298987i
$417$		0			0
$418$	−216.400	+	450.496i	−0.517704	+	1.07774i
$419$	155.891	+	270.011i	0.372054	+	0.644417i	0.989881	−	0.141897i	$-0.0453202\pi$
$419$	155.891	+	270.011i	0.372054	+	0.644417i	−0.617827	+	0.786314i	$0.711987\pi$
$420$		0			0
$421$	567.466	+	327.627i	1.34790	+	0.778211i	0.987952	−	0.154761i	$-0.0494608\pi$
$421$	567.466	+	327.627i	1.34790	+	0.778211i	0.359949	+	0.932972i	$0.382794\pi$
$422$	−292.647	−	428.325i	−0.693476	−	1.01499i
$423$		0			0
$424$	91.9897	+	397.604i	0.216957	+	0.937745i
$425$	49.7956	−	86.2485i	0.117166	−	0.202938i
$426$		0			0
$427$	−230.348	−	398.975i	−0.539457	−	0.934367i
$428$	51.1931	−	7.81948i	0.119610	−	0.0182698i
$429$		0			0
$430$	18.3435	+	241.577i	0.0426592	+	0.561808i
$431$			204.753i			0.475064i	0.971380	+	0.237532i	$0.0763384\pi$
$431$			204.753i			0.475064i	−0.971380	+	0.237532i	$0.923662\pi$
$432$		0			0
$433$	−561.451			−1.29665			−0.648327	−	0.761362i	$-0.724531\pi$
$433$	−561.451			−1.29665			−0.648327	+	0.761362i	$0.724531\pi$
$434$	−1154.59	+	87.6705i	−2.66035	+	0.202006i
$435$		0			0
$436$	−71.0835	−	465.374i	−0.163035	−	1.06737i
$437$	−68.4429	+	39.5155i	−0.156620	+	0.0904246i
$438$		0			0
$439$	−261.544	−	151.002i	−0.595771	−	0.343969i	0.171605	−	0.985166i	$-0.445105\pi$
$439$	−261.544	−	151.002i	−0.595771	−	0.343969i	−0.767376	+	0.641197i	$0.778438\pi$
$440$	−43.1921	−	186.688i	−0.0981639	−	0.424290i
$441$		0			0
$442$	38.5467	−	26.3364i	0.0872097	−	0.0595847i
$443$	228.326	−	395.472i	0.515408	−	0.892713i	−0.484432	−	0.874829i	$-0.660974\pi$
$443$	228.326	−	395.472i	0.515408	−	0.892713i	0.999840	−	0.0178842i	$-0.00569301\pi$
$444$		0			0
$445$	229.750	−	132.646i	0.516293	−	0.298082i
$446$	223.140	+	107.187i	0.500314	+	0.240330i
$447$		0			0
$448$	−641.127	−	44.2301i	−1.43109	−	0.0987279i
$449$	−418.640			−0.932384			−0.466192	−	0.884684i	$-0.654374\pi$
$449$	−418.640			−0.932384			−0.466192	+	0.884684i	$0.654374\pi$
$450$		0			0
$451$	−276.137			−0.612278
$452$	−73.4558	−	91.7387i	−0.162513	−	0.202962i
$453$		0			0
$454$	−220.804	+	459.664i	−0.486352	+	1.01247i
$455$	−84.7373	+	48.9231i	−0.186236	+	0.107523i
$456$		0			0
$457$	117.305	−	203.178i	0.256684	−	0.444590i	−0.708668	−	0.705543i	$-0.750703\pi$
$457$	117.305	−	203.178i	0.256684	−	0.444590i	0.965352	+	0.260953i	$0.0840367\pi$
$458$	413.279	−	282.366i	0.902355	−	0.616521i
$459$		0			0
$460$	11.0146	−	28.2285i	0.0239448	−	0.0613663i
$461$	104.947	+	60.5913i	0.227651	+	0.131435i	0.609488	−	0.792795i	$-0.291375\pi$
$461$	104.947	+	60.5913i	0.227651	+	0.131435i	−0.381837	+	0.924230i	$0.624708\pi$
$462$		0			0
$463$	−213.979	+	123.541i	−0.462157	+	0.266827i	−0.712951	−	0.701214i	$-0.752642\pi$
$463$	−213.979	+	123.541i	−0.462157	+	0.266827i	0.250794	+	0.968041i	$0.419308\pi$
$464$	−734.840	−	164.673i	−1.58371	−	0.354900i
$465$		0			0
$466$	462.627	−	35.1282i	0.992761	−	0.0753824i
$467$	276.509			0.592097			0.296049	−	0.955173i	$-0.404331\pi$
$467$	276.509			0.592097			0.296049	+	0.955173i	$0.404331\pi$
$468$		0			0
$469$		−	540.649i		−	1.15277i
$470$	202.607	−	15.3844i	0.431079	−	0.0327327i
$471$		0			0
$472$	182.423	+	195.442i	0.386490	+	0.414072i
$473$	374.678	+	648.962i	0.792132	+	1.37201i
$474$		0			0
$475$	216.866	−	375.624i	0.456561	−	0.790787i
$476$	176.378	+	68.8217i	0.370541	+	0.144583i
$477$		0			0
$478$	−399.124	+	272.696i	−0.834988	+	0.570493i
$479$	613.932	+	354.454i	1.28169	+	0.739987i	0.977158	−	0.212514i	$-0.0681652\pi$
$479$	613.932	+	354.454i	1.28169	+	0.739987i	0.304536	+	0.952501i	$0.401499\pi$
$480$		0			0
$481$	−19.6514	−	34.0372i	−0.0408552	−	0.0707633i
$482$	200.049	−	416.456i	0.415039	−	0.864017i
$483$		0			0
$484$	−67.9306	−	84.8382i	−0.140352	−	0.175286i
$485$		−	42.8283i		−	0.0883057i
$486$		0			0
$487$			204.394i			0.419699i	0.977734	+	0.209850i	$0.0672975\pi$
$487$			204.394i			0.419699i	−0.977734	+	0.209850i	$0.932703\pi$
$488$	−351.049	−	107.147i	−0.719363	−	0.219564i
$489$		0			0
$490$	−183.864	−	88.3206i	−0.375232	−	0.180246i
$491$	−113.951	−	197.369i	−0.232080	−	0.401974i	0.726340	−	0.687335i	$-0.241220\pi$
$491$	−113.951	−	197.369i	−0.232080	−	0.401974i	−0.958420	+	0.285361i	$0.907886\pi$
$492$		0			0
$493$	192.135	+	110.929i	0.389725	+	0.225008i
$494$	167.876	−	114.699i	0.339830	−	0.232184i
$495$		0			0
$496$	−624.792	+	678.720i	−1.25966	+	1.36839i
$497$	665.603	−	1152.86i	1.33924	−	2.31963i
$498$		0			0
$499$	−190.463	−	329.891i	−0.381689	−	0.661105i	0.609615	−	0.792698i	$-0.291324\pi$
$499$	−190.463	−	329.891i	−0.381689	−	0.661105i	−0.991304	+	0.131593i	$0.957991\pi$
$500$	54.8214	+	358.909i	0.109643	+	0.717817i
$501$		0			0
$502$	−156.595	+	11.8906i	−0.311942	+	0.0236864i
$503$			697.917i			1.38751i	0.720212	+	0.693754i	$0.244045\pi$
$503$			697.917i			1.38751i	−0.720212	+	0.693754i	$0.755955\pi$
$504$		0			0
$505$	91.6077			0.181401
$506$	−7.09615	−	93.4539i	−0.0140240	−	0.184691i
$507$		0			0
$508$	67.9245	+	444.693i	0.133710	+	0.875380i
$509$	64.0084	−	36.9552i	0.125753	−	0.0726036i	−0.435804	−	0.900042i	$-0.643536\pi$
$509$	64.0084	−	36.9552i	0.125753	−	0.0726036i	0.561557	+	0.827438i	$0.310203\pi$
$510$		0			0
$511$	−214.790	−	124.009i	−0.420333	−	0.242679i
$512$	−397.447	+	322.769i	−0.776263	+	0.630409i
$513$		0			0
$514$	295.237	+	432.116i	0.574391	+	0.840693i
$515$	99.2196	−	171.853i	0.192659	−	0.333696i
$516$		0			0
$517$	544.274	−	314.237i	1.05275	−	0.607808i
$518$	69.0158	−	143.675i	0.133235	−	0.277365i
$519$		0			0
$520$	−22.7567	+	74.5585i	−0.0437630	+	0.143382i
$521$	994.276			1.90840			0.954200	−	0.299171i	$-0.0967100\pi$
$521$	994.276			1.90840			0.954200	+	0.299171i	$0.0967100\pi$
$522$		0			0
$523$	342.943			0.655722			0.327861	−	0.944726i	$-0.393672\pi$
$523$	342.943			0.655722			0.327861	+	0.944726i	$0.393672\pi$
$524$	−445.954	−	556.950i	−0.851058	−	1.06288i
$525$		0			0
$526$	573.199	+	275.342i	1.08973	+	0.523463i
$527$	235.366	−	135.889i	0.446615	−	0.257854i
$528$		0			0
$529$	−257.090	+	445.292i	−0.485992	+	0.841762i
$530$	113.257	+	165.765i	0.213692	+	0.312765i
$531$		0			0
$532$	768.148	+	299.728i	1.44389	+	0.563398i
$533$	97.2872	+	56.1688i	0.182528	+	0.105382i
$534$		0			0
$535$	22.0626	−	12.7379i	0.0412385	−	0.0238091i
$536$	−293.908	−	314.882i	−0.548335	−	0.587467i
$537$		0			0
$538$	−20.4494	−	269.311i	−0.0380100	−	0.500579i
$539$	−630.905			−1.17051
$540$		0			0
$541$			571.225i			1.05587i	0.849285	+	0.527934i	$0.177033\pi$
$541$			571.225i			1.05587i	−0.849285	+	0.527934i	$0.822967\pi$
$542$	−24.4428	−	321.904i	−0.0450974	−	0.593918i
$543$		0			0
$544$	140.138	−	55.7996i	0.257607	−	0.102573i
$545$	−115.794	−	200.562i	−0.212467	−	0.368003i
$546$		0			0
$547$	390.615	−	676.565i	0.714104	−	1.23686i	−0.249200	−	0.968452i	$-0.580168\pi$
$547$	390.615	−	676.565i	0.714104	−	1.23686i	0.963304	−	0.268413i	$-0.0864990\pi$
$548$	−186.327	+	477.521i	−0.340012	+	0.871389i
$549$		0			0
$550$	290.170	+	424.701i	0.527583	+	0.772183i
$551$	836.771	+	483.110i	1.51864	+	0.876788i
$552$		0			0
$553$	488.847	+	846.707i	0.883990	+	1.53112i
$554$	765.923	+	367.918i	1.38253	+	0.664113i
$555$		0			0
$556$	−481.610	−	601.481i	−0.866205	−	1.08180i
$557$		−	439.321i		−	0.788727i	−0.918954	−	0.394364i	$-0.870965\pi$
$557$		−	439.321i		−	0.788727i	0.918954	−	0.394364i	$-0.129035\pi$
$558$		0			0
$559$		−	304.852i		−	0.545352i
$560$	−301.727	+	94.3763i	−0.538798	+	0.168529i
$561$		0			0
$562$	139.502	−	290.412i	0.248224	−	0.516747i
$563$	−16.1013	−	27.8883i	−0.0285992	−	0.0495352i	0.851372	−	0.524563i	$-0.175771\pi$
$563$	−16.1013	−	27.8883i	−0.0285992	−	0.0495352i	−0.879971	+	0.475028i	$0.842438\pi$
$564$		0			0
$565$	−50.0682	−	28.9069i	−0.0886163	−	0.0511626i
$566$	−411.556	−	602.363i	−0.727130	−	1.06425i
$567$		0			0
$568$	−239.059	−	1033.28i	−0.420879	−	1.81915i
$569$	−402.885	+	697.818i	−0.708058	+	1.22639i	0.257518	+	0.966274i	$0.417095\pi$
$569$	−402.885	+	697.818i	−0.708058	+	1.22639i	−0.965576	+	0.260120i	$0.916238\pi$
$570$		0			0
$571$	250.021	+	433.050i	0.437866	+	0.758406i	0.997525	−	0.0703173i	$-0.0224012\pi$
$571$	250.021	+	433.050i	0.437866	+	0.758406i	−0.559659	+	0.828723i	$0.689068\pi$
$572$	36.4067	+	238.350i	0.0636481	+	0.416696i
$573$		0			0
$574$	34.4942	+	454.277i	0.0600944	+	0.791423i
$575$			81.3379i			0.141457i
$576$		0			0
$577$	408.301			0.707628			0.353814	−	0.935316i	$-0.384885\pi$
$577$	408.301			0.707628			0.353814	+	0.935316i	$0.384885\pi$
$578$	532.030	−	40.3982i	0.920468	−	0.0698930i
$579$		0			0
$580$	−366.211	+	55.9369i	−0.631399	+	0.0964429i
$581$	3.26032	−	1.88235i	0.00561156	−	0.00323984i
$582$		0			0
$583$	537.769	+	310.481i	0.922416	+	0.532557i
$584$	−192.511	+	44.5394i	−0.329642	+	0.0762660i
$585$		0			0
$586$	833.364	−	569.384i	1.42212	−	0.971644i
$587$	231.965	−	401.775i	0.395171	−	0.684456i	−0.597952	−	0.801532i	$-0.704019\pi$
$587$	231.965	−	401.775i	0.395171	−	0.684456i	0.993123	+	0.117076i	$0.0373521\pi$
$588$		0			0
$589$	1025.05	−	591.814i	1.74032	−	1.00478i
$590$	118.550	+	56.9468i	0.200933	+	0.0965200i
$591$		0			0
$592$	−37.9089	−	121.197i	−0.0640353	−	0.204725i
$593$	80.8523			0.136344			0.0681722	−	0.997674i	$-0.478283\pi$
$593$	80.8523			0.136344			0.0681722	+	0.997674i	$0.478283\pi$
$594$		0			0
$595$	93.1375			0.156534
$596$	115.035	−	92.1095i	0.193012	−	0.154546i
$597$		0			0
$598$	−16.5093	+	34.3686i	−0.0276075	+	0.0574726i
$599$	−153.902	+	88.8554i	−0.256932	+	0.148339i	−0.622934	−	0.782274i	$-0.714059\pi$
$599$	−153.902	+	88.8554i	−0.256932	+	0.148339i	0.366002	+	0.930614i	$0.380726\pi$
$600$		0			0
$601$	99.6250	−	172.555i	0.165765	−	0.287114i	−0.771161	−	0.636640i	$-0.780324\pi$
$601$	99.6250	−	172.555i	0.165765	−	0.287114i	0.936927	+	0.349526i	$0.113657\pi$
$602$	1020.81	−	697.454i	1.69570	−	1.15856i
$603$		0			0
$604$	−6.61695	−	2.58190i	−0.0109552	−	0.00427467i
$605$	−46.3022	−	26.7326i	−0.0765325	−	0.0441861i
$606$		0			0
$607$	−967.595	+	558.641i	−1.59406	+	0.920332i	−0.601461	+	0.798902i	$0.705415\pi$
$607$	−967.595	+	558.641i	−1.59406	+	0.920332i	−0.992600	+	0.121430i	$0.961252\pi$
$608$	610.320	−	243.015i	1.00382	−	0.399695i
$609$		0			0
$610$	−180.040	+	13.6708i	−0.295147	+	0.0224111i
$611$	−255.674			−0.418453
$612$		0			0
$613$			131.929i			0.215218i	0.994193	+	0.107609i	$0.0343194\pi$
$613$			131.929i			0.215218i	−0.994193	+	0.107609i	$0.965681\pi$
$614$	−85.0275	+	6.45631i	−0.138481	+	0.0105152i
$615$		0			0
$616$	−714.833	+	667.217i	−1.16044	+	1.08315i
$617$	57.7694	+	100.060i	0.0936295	+	0.162171i	0.909036	−	0.416718i	$-0.136820\pi$
$617$	57.7694	+	100.060i	0.0936295	+	0.162171i	−0.815406	+	0.578889i	$0.803486\pi$
$618$		0			0
$619$	−337.518	+	584.599i	−0.545264	+	0.944424i	0.453327	+	0.891344i	$0.350237\pi$
$619$	−337.518	+	584.599i	−0.545264	+	0.944424i	−0.998590	+	0.0530799i	$0.983096\pi$
$620$	−164.963	+	422.771i	−0.266069	+	0.681888i
$621$		0			0
$622$	325.640	−	222.489i	0.523537	−	0.357699i
$623$	−1172.42	−	676.899i	−1.88190	−	1.08651i
$624$		0			0
$625$	−174.796	−	302.756i	−0.279674	−	0.484410i
$626$	−126.594	+	263.540i	−0.202226	+	0.420990i
$627$		0			0
$628$	102.638	−	82.1830i	0.163436	−	0.130865i
$629$			37.4113i			0.0594775i
$630$		0			0
$631$		−	214.708i		−	0.340267i	−0.985421	−	0.170133i	$-0.945580\pi$
$631$		−	214.708i		−	0.340267i	0.985421	−	0.170133i	$-0.0544199\pi$
$632$	744.999	+	227.389i	1.17880	+	0.359792i
$633$		0			0
$634$	−127.051	−	61.0303i	−0.200396	−	0.0962622i
$635$	110.648	+	191.649i	0.174250	+	0.301809i
$636$		0			0
$637$	222.277	+	128.332i	0.348944	+	0.201463i
$638$	−946.100	+	646.408i	−1.48291	+	1.01318i
$639$		0			0
$640$	−124.425	+	218.991i	−0.194415	+	0.342173i
$641$	−90.7182	+	157.129i	−0.141526	+	0.245130i	−0.928072	−	0.372402i	$-0.878534\pi$
$641$	−90.7182	+	157.129i	−0.141526	+	0.245130i	0.786545	+	0.617532i	$0.211868\pi$
$642$		0			0
$643$	−544.280	−	942.721i	−0.846470	−	1.46613i	−0.884338	−	0.466847i	$-0.845390\pi$
$643$	−544.280	−	942.721i	−0.846470	−	1.46613i	0.0378680	−	0.999283i	$-0.487943\pi$
$644$	−152.856	+	23.3479i	−0.237353	+	0.0362545i
$645$		0			0
$646$	−192.978	+	14.6532i	−0.298727	+	0.0226830i
$647$			162.166i			0.250643i	0.992116	+	0.125321i	$0.0399962\pi$
$647$			162.166i			0.250643i	−0.992116	+	0.125321i	$0.960004\pi$
$648$		0			0
$649$	406.791			0.626796
$650$	−15.8434	−	208.652i	−0.0243744	−	0.321003i
$651$		0			0
$652$	103.212	−	15.7651i	0.158301	−	0.0241797i
$653$	441.606	−	254.961i	0.676272	−	0.390446i	−0.122177	−	0.992508i	$-0.538987\pi$
$653$	441.606	−	254.961i	0.676272	−	0.390446i	0.798449	+	0.602062i	$0.205654\pi$
$654$		0			0
$655$	−303.967	−	175.495i	−0.464071	−	0.267932i
$656$	267.044	+	245.826i	0.407079	+	0.374735i
$657$		0			0
$658$	−584.944	−	856.138i	−0.888972	−	1.30112i
$659$	−392.592	+	679.989i	−0.595739	+	1.03185i	0.397703	+	0.917514i	$0.369807\pi$
$659$	−392.592	+	679.989i	−0.595739	+	1.03185i	−0.993442	+	0.114336i	$0.963526\pi$
$660$		0			0
$661$	219.088	−	126.491i	0.331450	−	0.191363i	−0.325035	−	0.945702i	$-0.605376\pi$
$661$	219.088	−	126.491i	0.331450	−	0.191363i	0.656485	+	0.754339i	$0.272043\pi$
$662$	−93.6365	+	194.930i	−0.141445	+	0.294456i
$663$		0			0
$664$	0.875579	−	2.86868i	0.00131864	−	0.00432030i
$665$	405.626			0.609964
$666$		0			0
$667$	−181.195			−0.271657
$668$	408.616	−	327.182i	0.611701	−	0.489793i
$669$		0			0
$670$	−191.000	−	91.7486i	−0.285074	−	0.136938i
$671$	−483.650	+	279.236i	−0.720790	+	0.416149i
$672$		0			0
$673$	−54.8126	+	94.9383i	−0.0814452	+	0.141067i	−0.903871	−	0.427805i	$-0.859287\pi$
$673$	−54.8126	+	94.9383i	−0.0814452	+	0.141067i	0.822426	+	0.568873i	$0.192620\pi$
$674$	380.668	+	557.156i	0.564789	+	0.826640i
$675$		0			0
$676$	−210.072	+	538.377i	−0.310758	+	0.796416i
$677$	−415.870	−	240.103i	−0.614284	−	0.354657i	0.160356	−	0.987059i	$-0.448736\pi$
$677$	−415.870	−	240.103i	−0.614284	−	0.354657i	−0.774640	+	0.632402i	$0.782069\pi$
$678$		0			0
$679$	−189.273	+	109.277i	−0.278753	+	0.160938i
$680$	54.2448	−	50.6314i	0.0797717	−	0.0744580i
$681$		0			0
$682$	106.277	+	1399.63i	0.155831	+	2.05225i
$683$	27.4345			0.0401677			0.0200838	−	0.999798i	$-0.493607\pi$
$683$	27.4345			0.0401677			0.0200838	+	0.999798i	$0.493607\pi$
$684$		0			0
$685$			252.159i			0.368115i
$686$	4.30339	+	56.6743i	0.00627317	+	0.0826155i
$687$		0			0
$688$	215.386	−	961.142i	0.313062	−	1.39701i
$689$	−126.309	−	218.774i	−0.183323	−	0.317524i
$690$		0			0
$691$	4.69502	−	8.13201i	0.00679452	−	0.0117685i	−0.862608	−	0.505873i	$-0.831171\pi$
$691$	4.69502	−	8.13201i	0.00679452	−	0.0117685i	0.869403	+	0.494104i	$0.164504\pi$
$692$	−684.613	−	267.133i	−0.989326	−	0.386030i
$693$		0			0
$694$	27.8818	+	40.8085i	0.0401755	+	0.0588019i
$695$	−328.270	−	189.527i	−0.472331	−	0.272701i
$696$		0			0
$697$	−53.4658	−	92.6055i	−0.0767084	−	0.132863i
$698$	25.2215	+	12.1154i	0.0361339	+	0.0173573i
$699$		0			0
$700$	662.433	−	530.415i	0.946333	−	0.757736i
$701$		−	821.246i		−	1.17153i	−0.810479	−	0.585767i	$-0.800793\pi$
$701$		−	821.246i		−	1.17153i	0.810479	−	0.585767i	$-0.199207\pi$
$702$		0			0
$703$			162.931i			0.231766i
$704$	−53.6172	+	777.196i	−0.0761608	+	1.10397i
$705$		0			0
$706$	273.360	−	569.073i	0.387195	−	0.806052i
$707$	−233.738	−	404.847i	−0.330606	−	0.572626i
$708$		0			0
$709$	−719.455	−	415.378i	−1.01475	−	0.585864i	−0.102168	−	0.994767i	$-0.532578\pi$
$709$	−719.455	−	415.378i	−1.01475	−	0.585864i	−0.912578	+	0.408903i	$0.865911\pi$
$710$	−294.327	−	430.785i	−0.414545	−	0.606739i
$711$		0			0
$712$	−1050.81	+	243.116i	−1.47586	+	0.341456i
$713$	−110.983	+	192.228i	−0.155656	+	0.269604i
$714$		0			0
$715$	59.3062	+	102.721i	0.0829458	+	0.143666i
$716$	96.6042	−	14.7558i	0.134922	−	0.0206087i
$717$		0			0
$718$	95.3768	+	1256.08i	0.132837	+	1.74942i
$719$			195.460i			0.271850i	0.990719	+	0.135925i	$0.0434006\pi$
$719$			195.460i			0.271850i	−0.990719	+	0.135925i	$0.956599\pi$
$720$		0			0
$721$	−1012.64			−1.40450
$722$	−120.517	+	9.15110i	−0.166921	+	0.0126746i
$723$		0			0
$724$	−61.3961	−	401.952i	−0.0848013	−	0.555183i
$725$	861.195	−	497.211i	1.18786	−	0.685809i
$726$		0			0
$727$	208.982	+	120.656i	0.287457	+	0.165964i	0.636795	−	0.771033i	$-0.280260\pi$
$727$	208.982	+	120.656i	0.287457	+	0.165964i	−0.349337	+	0.936997i	$0.613593\pi$
$728$	387.564	−	89.6670i	0.532369	−	0.123169i
$729$		0			0
$730$	−80.2599	+	54.8363i	−0.109945	+	0.0751183i
$731$	−145.091	+	251.304i	−0.198482	+	0.343782i
$732$		0			0
$733$	−907.973	+	524.218i	−1.23871	+	0.715168i	−0.968830	−	0.247726i	$-0.920317\pi$
$733$	−907.973	+	524.218i	−1.23871	+	0.715168i	−0.269878	+	0.962895i	$0.586983\pi$
$734$	−466.447	−	224.062i	−0.635487	−	0.305262i
$735$		0			0
$736$	−76.3331	+	96.6936i	−0.103713	+	0.131377i
$737$	−655.392			−0.889271
$738$		0			0
$739$	−166.542			−0.225362			−0.112681	−	0.993631i	$-0.535944\pi$
$739$	−166.542			−0.225362			−0.112681	+	0.993631i	$0.535944\pi$
$740$	−39.0454	−	48.7637i	−0.0527641	−	0.0658968i
$741$		0			0
$742$	443.599	−	923.474i	0.597843	−	1.24457i
$743$	−242.538	+	140.029i	−0.326430	+	0.188465i	−0.654255	−	0.756274i	$-0.727018\pi$
$743$	−242.538	+	140.029i	−0.326430	+	0.188465i	0.327825	+	0.944739i	$0.393684\pi$
$744$		0			0
$745$	36.2476	−	62.7828i	0.0486545	−	0.0842722i
$746$	205.761	−	140.583i	0.275819	−	0.188449i
$747$		0			0
$748$	83.4280	−	213.811i	0.111535	−	0.285844i
$749$	−112.586	−	65.0017i	−0.150315	−	0.0867846i
$750$		0			0
$751$	−189.292	+	109.288i	−0.252053	+	0.145523i	−0.620704	−	0.784045i	$-0.713153\pi$
$751$	−189.292	+	109.288i	−0.252053	+	0.145523i	0.368651	+	0.929568i	$0.379820\pi$
$752$	−806.094	−	180.641i	−1.07193	−	0.240214i
$753$		0			0
$754$	464.810	−	35.2940i	0.616459	−	0.0468090i
$755$	−3.49413			−0.00462799
$756$		0			0
$757$			1241.72i			1.64031i	0.572138	+	0.820157i	$0.306114\pi$
$757$			1241.72i			1.64031i	−0.572138	+	0.820157i	$0.693886\pi$
$758$	307.412	−	23.3424i	0.405556	−	0.0307947i
$759$		0			0
$760$	236.243	−	220.507i	0.310846	−	0.290140i
$761$	353.625	+	612.496i	0.464684	+	0.804857i	0.999187	−	0.0403097i	$-0.0128345\pi$
$761$	353.625	+	612.496i	0.464684	+	0.804857i	−0.534503	+	0.845167i	$0.679501\pi$
$762$		0			0
$763$	−590.902	+	1023.47i	−0.774445	+	1.34138i
$764$	107.621	+	41.9933i	0.140865	+	0.0549650i
$765$		0			0
$766$	657.244	−	449.052i	0.858021	−	0.586230i
$767$	−143.318	−	82.7449i	−0.186856	−	0.107881i
$768$		0			0
$769$	−469.232	−	812.734i	−0.610185	−	1.05687i	−0.991209	−	0.132307i	$-0.957762\pi$
$769$	−469.232	−	812.734i	−0.610185	−	1.05687i	0.381024	−	0.924565i	$-0.375572\pi$
$770$	−208.284	+	433.600i	−0.270499	+	0.563117i
$771$		0			0
$772$	−713.346	−	890.895i	−0.924023	−	1.15401i
$773$			419.774i			0.543045i	0.962432	+	0.271522i	$0.0875271\pi$
$773$			419.774i			0.543045i	−0.962432	+	0.271522i	$0.912473\pi$
$774$		0			0
$775$		−	1218.18i		−	1.57184i
$776$	−50.8305	+	166.537i	−0.0655032	+	0.214610i
$777$		0			0
$778$	−581.436	−	279.298i	−0.747347	−	0.358995i
$779$	−232.851	−	403.309i	−0.298910	−	0.517727i
$780$		0			0
$781$	−1397.53	−	806.866i	−1.78941	−	1.03312i
$782$	29.9668	−	20.4743i	0.0383207	−	0.0261820i
$783$		0			0
$784$	610.129	+	561.651i	0.778225	+	0.716392i
$785$	32.3413	−	56.0168i	0.0411991	−	0.0713589i
$786$		0			0
$787$	43.1357	+	74.7132i	0.0548103	+	0.0949341i	0.892129	−	0.451781i	$-0.149211\pi$
$787$	43.1357	+	74.7132i	0.0548103	+	0.0949341i	−0.837318	+	0.546715i	$0.815878\pi$
$788$	115.938	+	759.027i	0.147129	+	0.963233i
$789$		0			0
$790$	382.082	−	29.0123i	0.483648	−	0.0367244i
$791$			295.025i			0.372978i
$792$		0			0
$793$	227.196			0.286502
$794$	43.4415	+	572.110i	0.0547122	+	0.720541i
$795$		0			0
$796$	20.4104	+	133.624i	0.0256413	+	0.167870i
$797$	−865.089	+	499.459i	−1.08543	+	0.626674i	−0.932356	−	0.361540i	$-0.882251\pi$
$797$	−865.089	+	499.459i	−1.08543	+	0.626674i	−0.153075	+	0.988215i	$0.548918\pi$
$798$		0			0
$799$	210.765	+	121.685i	0.263786	+	0.152297i
$800$	97.4670	−	669.034i	0.121834	−	0.836292i
$801$		0			0
$802$	668.503	+	978.438i	0.833545	+	1.22000i
$803$	−150.328	+	260.376i	−0.187208	+	0.324253i
$804$		0			0
$805$	−65.8760	+	38.0335i	−0.0818336	+	0.0472466i
$806$	247.255	−	514.729i	0.306768	−	0.638622i
$807$		0			0
$808$	−356.216	−	108.724i	−0.440861	−	0.134560i
$809$	−526.876			−0.651268			−0.325634	−	0.945496i	$-0.605578\pi$
$809$	−526.876			−0.651268			−0.325634	+	0.945496i	$0.605578\pi$
$810$		0			0
$811$	980.131			1.20855			0.604273	−	0.796777i	$-0.293464\pi$
$811$	980.131			1.20855			0.604273	+	0.796777i	$0.293464\pi$
$812$	1181.60	+	1475.69i	1.45517	+	1.81736i
$813$		0			0
$814$	−174.168	−	83.6632i	−0.213966	−	0.102780i
$815$	44.4813	−	25.6813i	0.0545783	−	0.0315108i
$816$		0			0
$817$	−631.889	+	1094.46i	−0.773426	+	1.33961i
$818$	−582.482	−	852.536i	−0.712081	−	1.04222i
$819$		0			0
$820$	166.340	+	64.9051i	0.202854	+	0.0791526i
$821$	−1151.54	−	664.844i	−1.40261	−	0.809798i	−0.407951	−	0.913004i	$-0.633757\pi$
$821$	−1151.54	−	664.844i	−1.40261	−	0.809798i	−0.994660	+	0.103205i	$0.967090\pi$
$822$		0			0
$823$	−354.999	+	204.959i	−0.431347	+	0.249038i	−0.699920	−	0.714221i	$-0.746781\pi$
$823$	−354.999	+	204.959i	−0.431347	+	0.249038i	0.268573	+	0.963259i	$0.413448\pi$
$824$	−589.778	+	550.492i	−0.715750	+	0.668073i
$825$		0			0
$826$	−50.8150	−	669.216i	−0.0615194	−	0.810189i
$827$	−756.431			−0.914668			−0.457334	−	0.889295i	$-0.651196\pi$
$827$	−756.431			−0.914668			−0.457334	+	0.889295i	$0.651196\pi$
$828$		0			0
$829$		−	1028.26i		−	1.24036i	−0.784460	−	0.620179i	$-0.787060\pi$
$829$		−	1028.26i		−	1.24036i	0.784460	−	0.620179i	$-0.212940\pi$
$830$	−0.111714	−	1.47124i	−0.000134595	−	0.00177258i
$831$		0			0
$832$	176.979	−	262.911i	0.212715	−	0.315999i
$833$	−122.156	−	211.580i	−0.146646	−	0.253998i
$834$		0			0
$835$	128.755	−	223.010i	0.154198	−	0.267078i
$836$	363.340	−	931.175i	0.434617	−	1.11385i
$837$		0			0
$838$	−351.774	−	514.865i	−0.419778	−	0.614398i
$839$	−140.269	−	80.9842i	−0.167186	−	0.0965247i	0.414072	−	0.910244i	$-0.364106\pi$
$839$	−140.269	−	80.9842i	−0.167186	−	0.0965247i	−0.581258	+	0.813719i	$0.697439\pi$
$840$		0			0
$841$	687.130	+	1190.14i	0.817040	+	1.41515i
$842$	−1181.29	−	567.442i	−1.40295	−	0.673922i
$843$		0			0
$844$	648.474	+	809.877i	0.768334	+	0.959570i
$845$			284.294i			0.336443i
$846$		0			0
$847$			272.834i			0.322118i
$848$	−243.660	−	778.995i	−0.287335	−	0.918626i
$849$		0			0
$850$	−86.2449	+	179.542i	−0.101465	+	0.211226i
$851$	−15.2773	−	26.4610i	−0.0179521	−	0.0310940i
$852$		0			0
$853$	64.6457	+	37.3232i	0.0757863	+	0.0437552i	0.537414	−	0.843318i	$-0.319401\pi$
$853$	64.6457	+	37.3232i	0.0757863	+	0.0437552i	−0.461628	+	0.887074i	$0.652734\pi$
$854$	519.790	+	760.778i	0.608653	+	0.890840i
$855$		0			0
$856$	−100.908	+	23.3461i	−0.117883	+	0.0272735i
$857$	−619.475	+	1072.96i	−0.722841	+	1.25200i	0.237015	+	0.971506i	$0.423831\pi$
$857$	−619.475	+	1072.96i	−0.722841	+	1.25200i	−0.959856	+	0.280492i	$0.909502\pi$
$858$		0			0
$859$	−59.7685	−	103.522i	−0.0695792	−	0.120515i	0.829137	−	0.559046i	$-0.188832\pi$
$859$	−59.7685	−	103.522i	−0.0695792	−	0.120515i	−0.898716	+	0.438531i	$0.855499\pi$
$860$	−73.1632	−	478.990i	−0.0850735	−	0.556965i
$861$		0			0
$862$	−31.0053	−	408.330i	−0.0359690	−	0.473700i
$863$		−	1262.84i		−	1.46332i	−0.681672	−	0.731658i	$-0.738747\pi$
$863$		−	1262.84i		−	1.46332i	0.681672	−	0.731658i	$-0.261253\pi$
$864$		0			0
$865$	−361.515			−0.417936
$866$	1119.68	−	85.0195i	1.29293	−	0.0981749i
$867$		0			0
$868$	2289.28	−	349.675i	2.63742	−	0.402852i
$869$	1026.41	−	592.596i	1.18114	−	0.681929i
$870$		0			0
$871$	230.904	+	133.313i	0.265103	+	0.153057i
$872$	212.230	+	917.312i	0.243383	+	1.05196i
$873$		0			0
$874$	130.509	−	89.1684i	0.149324	−	0.102023i
$875$	455.719	−	789.328i	0.520822	−	0.902090i
$876$		0			0
$877$	329.652	−	190.325i	0.375886	−	0.217018i	−0.300141	−	0.953895i	$-0.597034\pi$
$877$	329.652	−	190.325i	0.375886	−	0.217018i	0.676027	+	0.736877i	$0.263700\pi$
$878$	544.452	+	261.533i	0.620104	+	0.297873i
$879$		0			0
$880$	114.406	+	365.763i	0.130007	+	0.415640i
$881$	1191.72			1.35268			0.676342	−	0.736587i	$-0.263564\pi$
$881$	1191.72			1.35268			0.676342	+	0.736587i	$0.263564\pi$
$882$		0			0
$883$	1390.74			1.57502			0.787509	−	0.616303i	$-0.211370\pi$
$883$	1390.74			1.57502			0.787509	+	0.616303i	$0.211370\pi$
$884$	−72.8840	+	58.3588i	−0.0824480	+	0.0660167i
$885$		0			0
$886$	−395.455	+	823.248i	−0.446338	+	0.929174i
$887$	1389.31	−	802.119i	1.56630	−	0.904306i	0.569709	−	0.821847i	$-0.307056\pi$
$887$	1389.31	−	802.119i	1.56630	−	0.904306i	0.996594	−	0.0824589i	$-0.0262773\pi$
$888$		0			0
$889$	564.642	−	977.989i	0.635143	−	1.10010i
$890$	−438.095	+	299.322i	−0.492242	+	0.336317i
$891$		0			0
$892$	−461.230	−	179.970i	−0.517074	−	0.201760i
$893$	917.910	+	529.955i	1.02789	+	0.593455i
$894$		0			0
$895$	41.6334	−	24.0371i	0.0465178	−	0.0268570i
$896$	1285.27	−	8.87848i	1.43445	−	0.00990902i
$897$		0			0
$898$	834.877	−	63.3940i	0.929708	−	0.0705946i
$899$	2713.71			3.01859
$900$		0			0
$901$			240.462i			0.266883i
$902$	550.689	−	41.8150i	0.610520	−	0.0463581i
$903$		0			0
$904$	160.382	+	171.827i	0.177413	+	0.190075i
$905$	−100.014	−	173.229i	−0.110512	−	0.191413i
$906$		0			0
$907$	−321.020	+	556.023i	−0.353936	+	0.613035i	−0.986935	−	0.161117i	$-0.948490\pi$
$907$	−321.020	+	556.023i	−0.353936	+	0.613035i	0.632999	+	0.774152i	$0.281824\pi$
$908$	370.734	−	950.124i	0.408297	−	1.04639i
$909$		0			0
$910$	161.580	−	110.397i	0.177560	−	0.121315i
$911$	−23.6696	−	13.6656i	−0.0259820	−	0.0150007i	0.486953	−	0.873428i	$-0.338108\pi$
$911$	−23.6696	−	13.6656i	−0.0259820	−	0.0150007i	−0.512935	+	0.858428i	$0.671442\pi$
$912$		0			0
$913$	−2.28184	−	3.95227i	−0.00249928	−	0.00432888i
$914$	−203.169	+	422.952i	−0.222286	+	0.462748i
$915$		0			0
$916$	−781.427	+	625.694i	−0.853086	+	0.683072i
$917$			1791.12i			1.95323i
$918$		0			0
$919$			678.306i			0.738091i	0.929411	+	0.369046i	$0.120315\pi$
$919$			678.306i			0.738091i	−0.929411	+	0.369046i	$0.879685\pi$
$920$	−17.6914	+	57.9629i	−0.0192298	+	0.0630031i
$921$		0			0
$922$	−218.467	−	104.943i	−0.236949	−	0.113821i
$923$	328.248	+	568.542i	0.355631	+	0.615971i
$924$		0			0
$925$	145.221	+	83.8435i	0.156996	+	0.0906416i
$926$	408.022	−	278.775i	0.440628	−	0.301053i
$927$		0			0
$928$	1490.40	+	217.126i	1.60603	+	0.233972i
$929$	635.493	−	1100.71i	0.684062	−	1.18483i	−0.289669	−	0.957127i	$-0.593545\pi$
$929$	635.493	−	1100.71i	0.684062	−	1.18483i	0.973731	−	0.227703i	$-0.0731215\pi$
$930$		0			0
$931$	−532.006	−	921.461i	−0.571435	−	0.989754i
$932$	−917.278	+	140.110i	−0.984204	+	0.150332i
$933$		0			0
$934$	−551.431	+	41.8713i	−0.590398	+	0.0448301i
$935$		−	112.904i		−	0.120753i
$936$		0			0
$937$	1049.34			1.11990			0.559948	−	0.828528i	$-0.310821\pi$
$937$	1049.34			1.11990			0.559948	+	0.828528i	$0.310821\pi$
$938$	81.8695	+	1078.19i	0.0872809	+	1.14946i
$939$		0			0
$940$	−401.721	+	61.3608i	−0.427363	+	0.0652775i
$941$	−1206.53	+	696.589i	−1.28218	+	0.740265i	−0.977246	−	0.212109i	$-0.931967\pi$
$941$	−1206.53	+	696.589i	−1.28218	+	0.740265i	−0.304931	+	0.952374i	$0.598633\pi$
$942$		0			0
$943$	75.6325	+	43.6665i	0.0802042	+	0.0463059i
$944$	−393.395	−	362.138i	−0.416732	−	0.383621i
$945$		0			0
$946$	−845.477	−	1237.46i	−0.893739	−	1.30810i
$947$	−751.624	+	1301.85i	−0.793690	+	1.37471i	0.129978	+	0.991517i	$0.458509\pi$
$947$	−751.624	+	1301.85i	−0.793690	+	1.37471i	−0.923668	+	0.383194i	$0.874824\pi$
$948$		0			0
$949$	105.925	−	61.1561i	0.111618	−	0.0644427i
$950$	−375.608	+	781.931i	−0.395377	+	0.823085i
$951$		0			0
$952$	−362.164	−	110.540i	−0.380425	−	0.116113i
$953$	−788.992			−0.827903			−0.413951	−	0.910299i	$-0.635852\pi$
$953$	−788.992			−0.827903			−0.413951	+	0.910299i	$0.635852\pi$
$954$		0			0
$955$	56.8301			0.0595080
$956$	754.663	−	604.264i	0.789397	−	0.632076i
$957$		0			0
$958$	−1278.01	−	613.906i	−1.33404	−	0.640820i
$959$	1114.38	−	643.386i	1.16202	−	0.670893i
$960$		0			0
$961$	1181.66	−	2046.69i	1.22961	−	2.12975i
$962$	44.3441	+	64.9031i	0.0460957	+	0.0674669i
$963$		0			0
$964$	−335.886	+	860.815i	−0.348429	+	0.892961i
$965$	−486.224	−	280.721i	−0.503859	−	0.290903i
$966$		0			0
$967$	396.835	−	229.113i	0.410377	−	0.236931i	−0.280575	−	0.959832i	$-0.590525\pi$
$967$	396.835	−	229.113i	0.410377	−	0.236931i	0.690952	+	0.722901i	$0.257192\pi$
$968$	148.318	+	158.903i	0.153221	+	0.164156i
$969$		0			0
$970$	6.48541	+	85.4106i	0.00668599	+	0.0880522i
$971$	25.2266			0.0259800			0.0129900	−	0.999916i	$-0.495865\pi$
$971$	25.2266			0.0259800			0.0129900	+	0.999916i	$0.495865\pi$
$972$		0			0
$973$			1934.32i			1.98800i
$974$	−30.9510	−	407.614i	−0.0317772	−	0.418495i
$975$		0			0
$976$	716.308	+	160.520i	0.733922	+	0.164468i
$977$	−736.113	−	1274.98i	−0.753442	−	1.30500i	−0.946145	−	0.323743i	$-0.895059\pi$
$977$	−736.113	−	1274.98i	−0.753442	−	1.30500i	0.192703	−	0.981257i	$-0.438274\pi$
$978$		0			0
$979$	−820.559	+	1421.25i	−0.838160	+	1.45174i
$980$	380.046	+	148.292i	0.387802	+	0.151318i
$981$		0			0
$982$	257.136	+	376.350i	0.261849	+	0.383249i
$983$	−909.975	−	525.374i	−0.925712	−	0.534460i	−0.0402592	−	0.999189i	$-0.512818\pi$
$983$	−909.975	−	525.374i	−0.925712	−	0.534460i	−0.885453	+	0.464729i	$0.846152\pi$
$984$		0			0
$985$	188.861	+	327.117i	0.191737	+	0.332099i
$986$	−399.964	−	192.126i	−0.405643	−	0.194854i
$987$		0			0
$988$	−317.420	+	254.160i	−0.321275	+	0.257247i
$989$		−	236.996i		−	0.239632i
$990$		0			0
$991$		−	1021.63i		−	1.03091i	−0.856917	−	0.515454i	$-0.827623\pi$
$991$		−	1021.63i		−	1.03091i	0.856917	−	0.515454i	$-0.172377\pi$
$992$	1143.22	−	1448.15i	1.15244	−	1.45983i
$993$		0			0
$994$	−1152.81	+	2399.89i	−1.15977	+	2.41437i
$995$	33.2484	+	57.5880i	0.0334155	+	0.0578774i
$996$		0			0
$997$	−331.758	−	191.540i	−0.332756	−	0.192117i	0.324308	−	0.945952i	$-0.394869\pi$
$997$	−331.758	−	191.540i	−0.332756	−	0.192117i	−0.657064	+	0.753835i	$0.728202\pi$
$998$	429.787	+	629.047i	0.430648	+	0.630308i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.p.b.19.1		40
3.2	odd	2		72.3.p.b.43.20	yes	40
4.3	odd	2		864.3.t.b.559.13		40
8.3	odd	2	inner	216.3.p.b.19.13		40
8.5	even	2		864.3.t.b.559.8		40
9.2	odd	6		648.3.b.f.163.5		20
9.4	even	3	inner	216.3.p.b.91.13		40
9.5	odd	6		72.3.p.b.67.8	yes	40
9.7	even	3		648.3.b.e.163.16		20
12.11	even	2		288.3.t.b.79.5		40
24.5	odd	2		288.3.t.b.79.6		40
24.11	even	2		72.3.p.b.43.8	✓	40
36.7	odd	6		2592.3.b.f.1135.13		20
36.11	even	6		2592.3.b.e.1135.8		20
36.23	even	6		288.3.t.b.175.6		40
36.31	odd	6		864.3.t.b.847.8		40
72.5	odd	6		288.3.t.b.175.5		40
72.11	even	6		648.3.b.f.163.6		20
72.13	even	6		864.3.t.b.847.13		40
72.29	odd	6		2592.3.b.e.1135.13		20
72.43	odd	6		648.3.b.e.163.15		20
72.59	even	6		72.3.p.b.67.20	yes	40
72.61	even	6		2592.3.b.f.1135.8		20
72.67	odd	6	inner	216.3.p.b.91.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.p.b.43.8	✓	40	24.11	even	2
72.3.p.b.43.20	yes	40	3.2	odd	2
72.3.p.b.67.8	yes	40	9.5	odd	6
72.3.p.b.67.20	yes	40	72.59	even	6
216.3.p.b.19.1		40	1.1	even	1	trivial
216.3.p.b.19.13		40	8.3	odd	2	inner
216.3.p.b.91.1		40	72.67	odd	6	inner
216.3.p.b.91.13		40	9.4	even	3	inner
288.3.t.b.79.5		40	12.11	even	2
288.3.t.b.79.6		40	24.5	odd	2
288.3.t.b.175.5		40	72.5	odd	6
288.3.t.b.175.6		40	36.23	even	6
648.3.b.e.163.15		20	72.43	odd	6
648.3.b.e.163.16		20	9.7	even	3
648.3.b.f.163.5		20	9.2	odd	6
648.3.b.f.163.6		20	72.11	even	6
864.3.t.b.559.8		40	8.5	even	2
864.3.t.b.559.13		40	4.3	odd	2
864.3.t.b.847.8		40	36.31	odd	6
864.3.t.b.847.13		40	72.13	even	6
2592.3.b.e.1135.8		20	36.11	even	6
2592.3.b.e.1135.13		20	72.29	odd	6
2592.3.b.f.1135.8		20	72.61	even	6
2592.3.b.f.1135.13		20	36.7	odd	6

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.99426 + 0.151428i) q^{2} +(3.95414 - 0.603974i) q^{4} +(1.70411 - 0.983869i) q^{5} +(-8.69613 - 5.02071i) q^{7} +(-7.79412 + 1.80325i) q^{8} +O(q^{10})\)	\(q+(-1.99426 + 0.151428i) q^{2} +(3.95414 - 0.603974i) q^{4} +(1.70411 - 0.983869i) q^{5} +(-8.69613 - 5.02071i) q^{7} +(-7.79412 + 1.80325i) q^{8} +(-3.24945 + 2.22014i) q^{10} +(-6.08627 + 10.5417i) q^{11} +(4.28857 - 2.47601i) q^{13} +(18.1026 + 8.69576i) q^{14} +(15.2704 - 4.77640i) q^{16} -4.71370 q^{17} -20.5288 q^{19} +(6.14406 - 4.91959i) q^{20} +(10.5413 - 21.9446i) q^{22} +(3.33400 - 1.92488i) q^{23} +(-10.5640 + 18.2974i) q^{25} +(-8.17758 + 5.58721i) q^{26} +(-37.4181 - 14.6004i) q^{28} +(-40.7608 - 23.5333i) q^{29} +(-49.9323 + 28.8285i) q^{31} +(-29.7299 + 11.8377i) q^{32} +(9.40035 - 0.713788i) q^{34} -19.7589 q^{35} -7.93672i q^{37} +(40.9398 - 3.10864i) q^{38} +(-11.5079 + 10.7413i) q^{40} +(11.3426 + 19.6460i) q^{41} +(30.7806 - 53.3136i) q^{43} +(-17.6990 + 45.3594i) q^{44} +(-6.35737 + 4.34358i) q^{46} +(-44.7133 - 25.8152i) q^{47} +(25.9151 + 44.8862i) q^{49} +(18.2966 - 38.0894i) q^{50} +(15.4622 - 12.3807i) q^{52} -51.0133i q^{53} +23.9524i q^{55} +(76.8322 + 23.4507i) q^{56} +(84.8513 + 40.7591i) q^{58} +(-16.7094 - 28.9415i) q^{59} +(39.7329 + 22.9398i) q^{61} +(95.2126 - 65.0526i) q^{62} +(57.4966 - 28.1095i) q^{64} +(4.87213 - 8.43878i) q^{65} +(26.9209 + 46.6284i) q^{67} +(-18.6386 + 2.84696i) q^{68} +(39.4043 - 2.99205i) q^{70} +132.571i q^{71} +24.6995 q^{73} +(1.20184 + 15.8279i) q^{74} +(-81.1738 + 12.3989i) q^{76} +(105.854 - 61.1148i) q^{77} +(-84.3214 - 48.6830i) q^{79} +(21.3232 - 23.1636i) q^{80} +(-25.5951 - 37.4616i) q^{82} +(-0.187458 + 0.324687i) q^{83} +(-8.03267 + 4.63767i) q^{85} +(-53.3113 + 110.982i) q^{86} +(28.4278 - 93.1386i) q^{88} +134.821 q^{89} -49.7252 q^{91} +(12.0205 - 9.62490i) q^{92} +(93.0790 + 44.7114i) q^{94} +(-34.9834 + 20.1977i) q^{95} +(10.8826 - 18.8492i) q^{97} +(-58.4784 - 85.5905i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

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