LMFDB - Embedded newform 441.3.n.b.410.1

Newspace parameters

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.n (of order $6$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
Defining polynomial:	$x^{2} - x + 1$
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			410.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	441.410
Dual form			441.3.n.b.128.1

$q$-expansion

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{2} +3.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(4.50000 + 2.59808i) q^{6} -8.66025i q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{2} +3.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(4.50000 + 2.59808i) q^{6} -8.66025i q^{8} +9.00000 q^{9} +(3.00000 - 5.19615i) q^{10} -1.73205i q^{11} +(-1.50000 - 2.59808i) q^{12} +(2.00000 - 3.46410i) q^{13} -10.3923i q^{15} +(5.50000 - 9.52628i) q^{16} +(-13.5000 - 7.79423i) q^{17} +(13.5000 + 7.79423i) q^{18} +(-5.50000 - 9.52628i) q^{19} +(-3.00000 + 1.73205i) q^{20} +(1.50000 - 2.59808i) q^{22} +27.7128i q^{23} -25.9808i q^{24} +13.0000 q^{25} +(6.00000 - 3.46410i) q^{26} +27.0000 q^{27} +(39.0000 - 22.5167i) q^{29} +(9.00000 - 15.5885i) q^{30} +(-16.0000 - 27.7128i) q^{31} +(-13.5000 + 7.79423i) q^{32} -5.19615i q^{33} +(-13.5000 - 23.3827i) q^{34} +(-4.50000 - 7.79423i) q^{36} +(17.0000 + 29.4449i) q^{37} -19.0526i q^{38} +(6.00000 - 10.3923i) q^{39} -30.0000 q^{40} +(-10.5000 - 6.06218i) q^{41} +(30.5000 + 52.8275i) q^{43} +(-1.50000 + 0.866025i) q^{44} -31.1769i q^{45} +(-24.0000 + 41.5692i) q^{46} +(42.0000 + 24.2487i) q^{47} +(16.5000 - 28.5788i) q^{48} +(19.5000 + 11.2583i) q^{50} +(-40.5000 - 23.3827i) q^{51} -4.00000 q^{52} +(40.5000 + 23.3827i) q^{54} -6.00000 q^{55} +(-16.5000 - 28.5788i) q^{57} +78.0000 q^{58} +(-43.5000 + 25.1147i) q^{59} +(-9.00000 + 5.19615i) q^{60} +(-28.0000 + 48.4974i) q^{61} -55.4256i q^{62} -71.0000 q^{64} +(-12.0000 - 6.92820i) q^{65} +(4.50000 - 7.79423i) q^{66} +(15.5000 + 26.8468i) q^{67} +15.5885i q^{68} +83.1384i q^{69} -31.1769i q^{71} -77.9423i q^{72} +(-32.5000 + 56.2917i) q^{73} +58.8897i q^{74} +39.0000 q^{75} +(-5.50000 + 9.52628i) q^{76} +(18.0000 - 10.3923i) q^{78} +(-19.0000 + 32.9090i) q^{79} +(-33.0000 - 19.0526i) q^{80} +81.0000 q^{81} +(-10.5000 - 18.1865i) q^{82} +(-42.0000 + 24.2487i) q^{83} +(-27.0000 + 46.7654i) q^{85} +105.655i q^{86} +(117.000 - 67.5500i) q^{87} -15.0000 q^{88} +(108.000 - 62.3538i) q^{89} +(27.0000 - 46.7654i) q^{90} +(24.0000 - 13.8564i) q^{92} +(-48.0000 - 83.1384i) q^{93} +(42.0000 + 72.7461i) q^{94} +(-33.0000 + 19.0526i) q^{95} +(-40.5000 + 23.3827i) q^{96} +(57.5000 + 99.5929i) q^{97} -15.5885i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2q + 3q^{2} + 6q^{3} - q^{4} + 9q^{6} + 18q^{9} + O(q^{10}) $	$ 2q + 3q^{2} + 6q^{3} - q^{4} + 9q^{6} + 18q^{9} + 6q^{10} - 3q^{12} + 4q^{13} + 11q^{16} - 27q^{17} + 27q^{18} - 11q^{19} - 6q^{20} + 3q^{22} + 26q^{25} + 12q^{26} + 54q^{27} + 78q^{29} + 18q^{30} - 32q^{31} - 27q^{32} - 27q^{34} - 9q^{36} + 34q^{37} + 12q^{39} - 60q^{40} - 21q^{41} + 61q^{43} - 3q^{44} - 48q^{46} + 84q^{47} + 33q^{48} + 39q^{50} - 81q^{51} - 8q^{52} + 81q^{54} - 12q^{55} - 33q^{57} + 156q^{58} - 87q^{59} - 18q^{60} - 56q^{61} - 142q^{64} - 24q^{65} + 9q^{66} + 31q^{67} - 65q^{73} + 78q^{75} - 11q^{76} + 36q^{78} - 38q^{79} - 66q^{80} + 162q^{81} - 21q^{82} - 84q^{83} - 54q^{85} + 234q^{87} - 30q^{88} + 216q^{89} + 54q^{90} + 48q^{92} - 96q^{93} + 84q^{94} - 66q^{95} - 81q^{96} + 115q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.50000	+	0.866025i	0.750000	+	0.433013i	0.825694	−	0.564118i	$-0.190784\pi$
$2$	1.50000	+	0.866025i	0.750000	+	0.433013i	−0.0756939	+	0.997131i	$0.524117\pi$
$3$	3.00000			1.00000
$3$	3.00000			1.00000
$4$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$5$		−	3.46410i		−	0.692820i	−0.938083	−	0.346410i	$-0.887401\pi$
$5$		−	3.46410i		−	0.692820i	0.938083	−	0.346410i	$-0.112599\pi$
$6$	4.50000	+	2.59808i	0.750000	+	0.433013i
$7$		0			0
$7$		0			0
$8$		−	8.66025i		−	1.08253i
$9$	9.00000			1.00000
$10$	3.00000	−	5.19615i	0.300000	−	0.519615i
$11$		−	1.73205i		−	0.157459i	−0.996896	−	0.0787296i	$-0.974914\pi$
$11$		−	1.73205i		−	0.157459i	0.996896	−	0.0787296i	$-0.0250864\pi$
$12$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$13$	2.00000	−	3.46410i	0.153846	−	0.266469i	−0.778792	−	0.627282i	$-0.784167\pi$
$13$	2.00000	−	3.46410i	0.153846	−	0.266469i	0.932638	+	0.360813i	$0.117501\pi$
$14$		0			0
$15$		−	10.3923i		−	0.692820i
$16$	5.50000	−	9.52628i	0.343750	−	0.595392i
$17$	−13.5000	−	7.79423i	−0.794118	−	0.458484i	0.0472925	−	0.998881i	$-0.484941\pi$
$17$	−13.5000	−	7.79423i	−0.794118	−	0.458484i	−0.841410	+	0.540397i	$0.818274\pi$
$18$	13.5000	+	7.79423i	0.750000	+	0.433013i
$19$	−5.50000	−	9.52628i	−0.289474	−	0.501383i	0.684211	−	0.729285i	$-0.260147\pi$
$19$	−5.50000	−	9.52628i	−0.289474	−	0.501383i	−0.973684	+	0.227901i	$0.926814\pi$
$20$	−3.00000	+	1.73205i	−0.150000	+	0.0866025i
$21$		0			0
$22$	1.50000	−	2.59808i	0.0681818	−	0.118094i
$23$			27.7128i			1.20490i	0.798155	+	0.602452i	$0.205810\pi$
$23$			27.7128i			1.20490i	−0.798155	+	0.602452i	$0.794190\pi$
$24$		−	25.9808i		−	1.08253i
$25$	13.0000			0.520000
$26$	6.00000	−	3.46410i	0.230769	−	0.133235i
$27$	27.0000			1.00000
$28$		0			0
$29$	39.0000	−	22.5167i	1.34483	−	0.776437i	0.357316	−	0.933984i	$-0.383692\pi$
$29$	39.0000	−	22.5167i	1.34483	−	0.776437i	0.987511	+	0.157547i	$0.0503586\pi$
$30$	9.00000	−	15.5885i	0.300000	−	0.519615i
$31$	−16.0000	−	27.7128i	−0.516129	−	0.893962i	−0.999825	−	0.0187254i	$-0.994039\pi$
$31$	−16.0000	−	27.7128i	−0.516129	−	0.893962i	0.483696	−	0.875236i	$-0.339294\pi$
$32$	−13.5000	+	7.79423i	−0.421875	+	0.243570i
$33$		−	5.19615i		−	0.157459i
$34$	−13.5000	−	23.3827i	−0.397059	−	0.687726i
$35$		0			0
$36$	−4.50000	−	7.79423i	−0.125000	−	0.216506i
$37$	17.0000	+	29.4449i	0.459459	+	0.795807i	0.998932	−	0.0461958i	$-0.0147098\pi$
$37$	17.0000	+	29.4449i	0.459459	+	0.795807i	−0.539473	+	0.842003i	$0.681376\pi$
$38$		−	19.0526i		−	0.501383i
$39$	6.00000	−	10.3923i	0.153846	−	0.266469i
$40$	−30.0000			−0.750000
$41$	−10.5000	−	6.06218i	−0.256098	−	0.147858i	0.366456	−	0.930436i	$-0.380571\pi$
$41$	−10.5000	−	6.06218i	−0.256098	−	0.147858i	−0.622553	+	0.782578i	$0.713905\pi$
$42$		0			0
$43$	30.5000	+	52.8275i	0.709302	+	1.22855i	0.965116	+	0.261822i	$0.0843232\pi$
$43$	30.5000	+	52.8275i	0.709302	+	1.22855i	−0.255814	+	0.966726i	$0.582343\pi$
$44$	−1.50000	+	0.866025i	−0.0340909	+	0.0196824i
$45$		−	31.1769i		−	0.692820i
$46$	−24.0000	+	41.5692i	−0.521739	+	0.903679i
$47$	42.0000	+	24.2487i	0.893617	+	0.515930i	0.875124	−	0.483899i	$-0.160780\pi$
$47$	42.0000	+	24.2487i	0.893617	+	0.515930i	0.0184931	+	0.999829i	$0.494113\pi$
$48$	16.5000	−	28.5788i	0.343750	−	0.595392i
$49$		0			0
$50$	19.5000	+	11.2583i	0.390000	+	0.225167i
$51$	−40.5000	−	23.3827i	−0.794118	−	0.458484i
$52$	−4.00000			−0.0769231
$53$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$53$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$54$	40.5000	+	23.3827i	0.750000	+	0.433013i
$55$	−6.00000			−0.109091
$56$		0			0
$57$	−16.5000	−	28.5788i	−0.289474	−	0.501383i
$58$	78.0000			1.34483
$59$	−43.5000	+	25.1147i	−0.737288	+	0.425674i	−0.821082	−	0.570810i	$-0.806629\pi$
$59$	−43.5000	+	25.1147i	−0.737288	+	0.425674i	0.0837943	+	0.996483i	$0.473296\pi$
$60$	−9.00000	+	5.19615i	−0.150000	+	0.0866025i
$61$	−28.0000	+	48.4974i	−0.459016	+	0.795040i	−0.998909	−	0.0466940i	$-0.985131\pi$
$61$	−28.0000	+	48.4974i	−0.459016	+	0.795040i	0.539893	+	0.841734i	$0.318465\pi$
$62$		−	55.4256i		−	0.893962i
$63$		0			0
$64$	−71.0000			−1.10938
$65$	−12.0000	−	6.92820i	−0.184615	−	0.106588i
$66$	4.50000	−	7.79423i	0.0681818	−	0.118094i
$67$	15.5000	+	26.8468i	0.231343	+	0.400698i	0.958204	−	0.286087i	$-0.0923546\pi$
$67$	15.5000	+	26.8468i	0.231343	+	0.400698i	−0.726860	+	0.686785i	$0.759021\pi$
$68$			15.5885i			0.229242i
$69$			83.1384i			1.20490i
$70$		0			0
$71$		−	31.1769i		−	0.439111i	−0.975600	−	0.219556i	$-0.929539\pi$
$71$		−	31.1769i		−	0.439111i	0.975600	−	0.219556i	$-0.0704608\pi$
$72$		−	77.9423i		−	1.08253i
$73$	−32.5000	+	56.2917i	−0.445205	+	0.771119i	−0.998067	−	0.0621550i	$-0.980203\pi$
$73$	−32.5000	+	56.2917i	−0.445205	+	0.771119i	0.552861	+	0.833273i	$0.313536\pi$
$74$			58.8897i			0.795807i
$75$	39.0000			0.520000
$76$	−5.50000	+	9.52628i	−0.0723684	+	0.125346i
$77$		0			0
$78$	18.0000	−	10.3923i	0.230769	−	0.133235i
$79$	−19.0000	+	32.9090i	−0.240506	+	0.416569i	−0.960859	−	0.277039i	$-0.910647\pi$
$79$	−19.0000	+	32.9090i	−0.240506	+	0.416569i	0.720352	+	0.693608i	$0.243980\pi$
$80$	−33.0000	−	19.0526i	−0.412500	−	0.238157i
$81$	81.0000			1.00000
$82$	−10.5000	−	18.1865i	−0.128049	−	0.221787i
$83$	−42.0000	+	24.2487i	−0.506024	+	0.292153i	−0.731198	−	0.682165i	$-0.761038\pi$
$83$	−42.0000	+	24.2487i	−0.506024	+	0.292153i	0.225174	+	0.974319i	$0.427705\pi$
$84$		0			0
$85$	−27.0000	+	46.7654i	−0.317647	+	0.550181i
$86$			105.655i			1.22855i
$87$	117.000	−	67.5500i	1.34483	−	0.776437i
$88$	−15.0000			−0.170455
$89$	108.000	−	62.3538i	1.21348	−	0.700605i	0.249967	−	0.968254i	$-0.419580\pi$
$89$	108.000	−	62.3538i	1.21348	−	0.700605i	0.963516	+	0.267650i	$0.0862469\pi$
$90$	27.0000	−	46.7654i	0.300000	−	0.519615i
$91$		0			0
$92$	24.0000	−	13.8564i	0.260870	−	0.150613i
$93$	−48.0000	−	83.1384i	−0.516129	−	0.893962i
$94$	42.0000	+	72.7461i	0.446809	+	0.773895i
$95$	−33.0000	+	19.0526i	−0.347368	+	0.200553i
$96$	−40.5000	+	23.3827i	−0.421875	+	0.243570i
$97$	57.5000	+	99.5929i	0.592784	+	1.02673i	0.993856	+	0.110685i	$0.0353044\pi$
$97$	57.5000	+	99.5929i	0.592784	+	1.02673i	−0.401072	+	0.916047i	$0.631362\pi$
$98$		0			0
$99$		−	15.5885i		−	0.157459i
$100$	−6.50000	−	11.2583i	−0.0650000	−	0.112583i
$101$			45.0333i			0.445874i	0.974833	+	0.222937i	$0.0715645\pi$
$101$			45.0333i			0.445874i	−0.974833	+	0.222937i	$0.928436\pi$
$102$	−40.5000	−	70.1481i	−0.397059	−	0.687726i
$103$	−40.0000			−0.388350			−0.194175	−	0.980967i	$-0.562203\pi$
$103$	−40.0000			−0.388350			−0.194175	+	0.980967i	$0.562203\pi$
$104$	−30.0000	−	17.3205i	−0.288462	−	0.166543i
$105$		0			0
$106$		0			0
$107$	−121.500	+	70.1481i	−1.13551	+	0.655589i	−0.945316	−	0.326156i	$-0.894246\pi$
$107$	−121.500	+	70.1481i	−1.13551	+	0.655589i	−0.190198	+	0.981746i	$0.560913\pi$
$108$	−13.5000	−	23.3827i	−0.125000	−	0.216506i
$109$	26.0000	−	45.0333i	0.238532	−	0.413150i	−0.721761	−	0.692142i	$-0.756667\pi$
$109$	26.0000	−	45.0333i	0.238532	−	0.413150i	0.960293	+	0.278992i	$0.0900004\pi$
$110$	−9.00000	−	5.19615i	−0.0818182	−	0.0472377i
$111$	51.0000	+	88.3346i	0.459459	+	0.795807i
$112$		0			0
$113$	−78.0000	−	45.0333i	−0.690265	−	0.398525i	0.113446	−	0.993544i	$-0.463811\pi$
$113$	−78.0000	−	45.0333i	−0.690265	−	0.398525i	−0.803711	+	0.595019i	$0.797144\pi$
$114$		−	57.1577i		−	0.501383i
$115$	96.0000			0.834783
$116$	−39.0000	−	22.5167i	−0.336207	−	0.194109i
$117$	18.0000	−	31.1769i	0.153846	−	0.266469i
$118$	−87.0000			−0.737288
$119$		0			0
$120$	−90.0000			−0.750000
$121$	118.000			0.975207
$122$	−84.0000	+	48.4974i	−0.688525	+	0.397520i
$123$	−31.5000	−	18.1865i	−0.256098	−	0.147858i
$124$	−16.0000	+	27.7128i	−0.129032	+	0.223490i
$125$		−	131.636i		−	1.05309i
$126$		0			0
$127$	−16.0000			−0.125984			−0.0629921	−	0.998014i	$-0.520064\pi$
$127$	−16.0000			−0.125984			−0.0629921	+	0.998014i	$0.520064\pi$
$128$	−52.5000	−	30.3109i	−0.410156	−	0.236804i
$129$	91.5000	+	158.483i	0.709302	+	1.22855i
$130$	−12.0000	−	20.7846i	−0.0923077	−	0.159882i
$131$		−	159.349i		−	1.21640i	−0.793783	−	0.608201i	$-0.791891\pi$
$131$		−	159.349i		−	1.21640i	0.793783	−	0.608201i	$-0.208109\pi$
$132$	−4.50000	+	2.59808i	−0.0340909	+	0.0196824i
$133$		0			0
$134$			53.6936i			0.400698i
$135$		−	93.5307i		−	0.692820i
$136$	−67.5000	+	116.913i	−0.496324	+	0.859658i
$137$		−	188.794i		−	1.37806i	−0.724735	−	0.689028i	$-0.758038\pi$
$137$		−	188.794i		−	1.37806i	0.724735	−	0.689028i	$-0.241962\pi$
$138$	−72.0000	+	124.708i	−0.521739	+	0.903679i
$139$	−2.50000	+	4.33013i	−0.0179856	+	0.0311520i	−0.874878	−	0.484343i	$-0.839059\pi$
$139$	−2.50000	+	4.33013i	−0.0179856	+	0.0311520i	0.856893	+	0.515495i	$0.172392\pi$
$140$		0			0
$141$	126.000	+	72.7461i	0.893617	+	0.515930i
$142$	27.0000	−	46.7654i	0.190141	−	0.329334i
$143$	−6.00000	−	3.46410i	−0.0419580	−	0.0242245i
$144$	49.5000	−	85.7365i	0.343750	−	0.595392i
$145$	−78.0000	−	135.100i	−0.537931	−	0.931724i
$146$	−97.5000	+	56.2917i	−0.667808	+	0.385559i
$147$		0			0
$148$	17.0000	−	29.4449i	0.114865	−	0.198952i
$149$			152.420i			1.02296i	0.859296	+	0.511478i	$0.170902\pi$
$149$			152.420i			1.02296i	−0.859296	+	0.511478i	$0.829098\pi$
$150$	58.5000	+	33.7750i	0.390000	+	0.225167i
$151$	20.0000			0.132450			0.0662252	−	0.997805i	$-0.478904\pi$
$151$	20.0000			0.132450			0.0662252	+	0.997805i	$0.478904\pi$
$152$	−82.5000	+	47.6314i	−0.542763	+	0.313364i
$153$	−121.500	−	70.1481i	−0.794118	−	0.458484i
$154$		0			0
$155$	−96.0000	+	55.4256i	−0.619355	+	0.357585i
$156$	−12.0000			−0.0769231
$157$	20.0000	+	34.6410i	0.127389	+	0.220643i	0.922664	−	0.385605i	$-0.126007\pi$
$157$	20.0000	+	34.6410i	0.127389	+	0.220643i	−0.795276	+	0.606248i	$0.792674\pi$
$158$	−57.0000	+	32.9090i	−0.360759	+	0.208285i
$159$		0			0
$160$	27.0000	+	46.7654i	0.168750	+	0.292284i
$161$		0			0
$162$	121.500	+	70.1481i	0.750000	+	0.433013i
$163$	53.0000	+	91.7987i	0.325153	+	0.563182i	0.981543	−	0.191240i	$-0.0612507\pi$
$163$	53.0000	+	91.7987i	0.325153	+	0.563182i	−0.656390	+	0.754422i	$0.727917\pi$
$164$			12.1244i			0.0739290i
$165$	−18.0000			−0.109091
$166$	−84.0000			−0.506024
$167$	165.000	+	95.2628i	0.988024	+	0.570436i	0.904683	−	0.426085i	$-0.140108\pi$
$167$	165.000	+	95.2628i	0.988024	+	0.570436i	0.0833409	+	0.996521i	$0.473441\pi$
$168$		0			0
$169$	76.5000	+	132.502i	0.452663	+	0.784035i
$170$	−81.0000	+	46.7654i	−0.476471	+	0.275090i
$171$	−49.5000	−	85.7365i	−0.289474	−	0.501383i
$172$	30.5000	−	52.8275i	0.177326	−	0.307137i
$173$	−201.000	−	116.047i	−1.16185	−	0.670794i	−0.210103	−	0.977679i	$-0.567380\pi$
$173$	−201.000	−	116.047i	−1.16185	−	0.670794i	−0.951747	+	0.306885i	$0.900713\pi$
$174$	234.000			1.34483
$175$		0			0
$176$	−16.5000	−	9.52628i	−0.0937500	−	0.0541266i
$177$	−130.500	+	75.3442i	−0.737288	+	0.425674i
$178$	216.000			1.21348
$179$	−54.0000	−	31.1769i	−0.301676	−	0.174173i	0.341520	−	0.939875i	$-0.389058\pi$
$179$	−54.0000	−	31.1769i	−0.301676	−	0.174173i	−0.643196	+	0.765702i	$0.722392\pi$
$180$	−27.0000	+	15.5885i	−0.150000	+	0.0866025i
$181$	−232.000			−1.28177			−0.640884	−	0.767638i	$-0.721432\pi$
$181$	−232.000			−1.28177			−0.640884	+	0.767638i	$0.721432\pi$
$182$		0			0
$183$	−84.0000	+	145.492i	−0.459016	+	0.795040i
$184$	240.000			1.30435
$185$	102.000	−	58.8897i	0.551351	−	0.318323i
$186$		−	166.277i		−	0.893962i
$187$	−13.5000	+	23.3827i	−0.0721925	+	0.125041i
$188$		−	48.4974i		−	0.257965i
$189$		0			0
$190$	−66.0000			−0.347368
$191$	−201.000	−	116.047i	−1.05236	−	0.607578i	−0.129048	−	0.991638i	$-0.541192\pi$
$191$	−201.000	−	116.047i	−1.05236	−	0.607578i	−0.923308	+	0.384060i	$0.874525\pi$
$192$	−213.000			−1.10938
$193$	132.500	+	229.497i	0.686528	+	1.18910i	0.972954	+	0.231000i	$0.0741996\pi$
$193$	132.500	+	229.497i	0.686528	+	1.18910i	−0.286425	+	0.958103i	$0.592467\pi$
$194$			199.186i			1.02673i
$195$	−36.0000	−	20.7846i	−0.184615	−	0.106588i
$196$		0			0
$197$			124.708i			0.633034i	0.948587	+	0.316517i	$0.102513\pi$
$197$			124.708i			0.633034i	−0.948587	+	0.316517i	$0.897487\pi$
$198$	13.5000	−	23.3827i	0.0681818	−	0.118094i
$199$	−145.000	+	251.147i	−0.728643	+	1.26205i	0.228814	+	0.973470i	$0.426515\pi$
$199$	−145.000	+	251.147i	−0.728643	+	1.26205i	−0.957457	+	0.288577i	$0.906818\pi$
$200$		−	112.583i		−	0.562917i
$201$	46.5000	+	80.5404i	0.231343	+	0.400698i
$202$	−39.0000	+	67.5500i	−0.193069	+	0.334406i
$203$		0			0
$204$			46.7654i			0.229242i
$205$	−21.0000	+	36.3731i	−0.102439	+	0.177430i
$206$	−60.0000	−	34.6410i	−0.291262	−	0.168160i
$207$			249.415i			1.20490i
$208$	−22.0000	−	38.1051i	−0.105769	−	0.183198i
$209$	−16.5000	+	9.52628i	−0.0789474	+	0.0455803i
$210$		0			0
$211$	47.0000	−	81.4064i	0.222749	−	0.385812i	−0.732893	−	0.680344i	$-0.761830\pi$
$211$	47.0000	−	81.4064i	0.222749	−	0.385812i	0.955642	+	0.294532i	$0.0951637\pi$
$212$		0			0
$213$		−	93.5307i		−	0.439111i
$214$	−243.000			−1.13551
$215$	183.000	−	105.655i	0.851163	−	0.491419i
$216$		−	233.827i		−	1.08253i
$217$		0			0
$218$	78.0000	−	45.0333i	0.357798	−	0.206575i
$219$	−97.5000	+	168.875i	−0.445205	+	0.771119i
$220$	3.00000	+	5.19615i	0.0136364	+	0.0236189i
$221$	−54.0000	+	31.1769i	−0.244344	+	0.141072i
$222$			176.669i			0.795807i
$223$	26.0000	+	45.0333i	0.116592	+	0.201943i	0.918415	−	0.395618i	$-0.129470\pi$
$223$	26.0000	+	45.0333i	0.116592	+	0.201943i	−0.801823	+	0.597562i	$0.796136\pi$
$224$		0			0
$225$	117.000			0.520000
$226$	−78.0000	−	135.100i	−0.345133	−	0.597787i
$227$		−	188.794i		−	0.831690i	−0.909436	−	0.415845i	$-0.863486\pi$
$227$		−	188.794i		−	0.831690i	0.909436	−	0.415845i	$-0.136514\pi$
$228$	−16.5000	+	28.5788i	−0.0723684	+	0.125346i
$229$	266.000			1.16157			0.580786	−	0.814056i	$-0.302745\pi$
$229$	266.000			1.16157			0.580786	+	0.814056i	$0.302745\pi$
$230$	144.000	+	83.1384i	0.626087	+	0.361471i
$231$		0			0
$232$	−195.000	−	337.750i	−0.840517	−	1.45582i
$233$	175.500	−	101.325i	0.753219	−	0.434871i	−0.0736369	−	0.997285i	$-0.523461\pi$
$233$	175.500	−	101.325i	0.753219	−	0.434871i	0.826856	+	0.562414i	$0.190127\pi$
$234$	54.0000	−	31.1769i	0.230769	−	0.133235i
$235$	84.0000	−	145.492i	0.357447	−	0.619116i
$236$	43.5000	+	25.1147i	0.184322	+	0.106418i
$237$	−57.0000	+	98.7269i	−0.240506	+	0.416569i
$238$		0			0
$239$	−348.000	−	200.918i	−1.45607	−	0.840661i	−0.457252	−	0.889337i	$-0.651166\pi$
$239$	−348.000	−	200.918i	−1.45607	−	0.840661i	−0.998815	+	0.0486764i	$0.984500\pi$
$240$	−99.0000	−	57.1577i	−0.412500	−	0.238157i
$241$	119.000			0.493776			0.246888	−	0.969044i	$-0.420592\pi$
$241$	119.000			0.493776			0.246888	+	0.969044i	$0.420592\pi$
$242$	177.000	+	102.191i	0.731405	+	0.422277i
$243$	243.000			1.00000
$244$	56.0000			0.229508
$245$		0			0
$246$	−31.5000	−	54.5596i	−0.128049	−	0.221787i
$247$	−44.0000			−0.178138
$248$	−240.000	+	138.564i	−0.967742	+	0.558726i
$249$	−126.000	+	72.7461i	−0.506024	+	0.292153i
$250$	114.000	−	197.454i	0.456000	−	0.789815i
$251$		−	389.711i		−	1.55264i	−0.630342	−	0.776318i	$-0.717085\pi$
$251$		−	389.711i		−	1.55264i	0.630342	−	0.776318i	$-0.282915\pi$
$252$		0			0
$253$	48.0000			0.189723
$254$	−24.0000	−	13.8564i	−0.0944882	−	0.0545528i
$255$	−81.0000	+	140.296i	−0.317647	+	0.550181i
$256$	89.5000	+	155.019i	0.349609	+	0.605541i
$257$		−	174.937i		−	0.680689i	−0.940301	−	0.340345i	$-0.889456\pi$
$257$		−	174.937i		−	0.680689i	0.940301	−	0.340345i	$-0.110544\pi$
$258$			316.965i			1.22855i
$259$		0			0
$260$			13.8564i			0.0532939i
$261$	351.000	−	202.650i	1.34483	−	0.776437i
$262$	138.000	−	239.023i	0.526718	−	0.912302i
$263$			45.0333i			0.171229i	0.996328	+	0.0856147i	$0.0272854\pi$
$263$			45.0333i			0.171229i	−0.996328	+	0.0856147i	$0.972715\pi$
$264$	−45.0000			−0.170455
$265$		0			0
$266$		0			0
$267$	324.000	−	187.061i	1.21348	−	0.700605i
$268$	15.5000	−	26.8468i	0.0578358	−	0.100175i
$269$	162.000	+	93.5307i	0.602230	+	0.347698i	0.769919	−	0.638142i	$-0.220297\pi$
$269$	162.000	+	93.5307i	0.602230	+	0.347698i	−0.167688	+	0.985840i	$0.553630\pi$
$270$	81.0000	−	140.296i	0.300000	−	0.519615i
$271$	134.000	+	232.095i	0.494465	+	0.856438i	0.999980	−	0.00637958i	$-0.00203070\pi$
$271$	134.000	+	232.095i	0.494465	+	0.856438i	−0.505515	+	0.862818i	$0.668697\pi$
$272$	−148.500	+	85.7365i	−0.545956	+	0.315208i
$273$		0			0
$274$	163.500	−	283.190i	0.596715	−	1.03354i
$275$		−	22.5167i		−	0.0818788i
$276$	72.0000	−	41.5692i	0.260870	−	0.150613i
$277$	56.0000			0.202166			0.101083	−	0.994878i	$-0.467769\pi$
$277$	56.0000			0.202166			0.101083	+	0.994878i	$0.467769\pi$
$278$	−7.50000	+	4.33013i	−0.0269784	+	0.0155760i
$279$	−144.000	−	249.415i	−0.516129	−	0.893962i
$280$		0			0
$281$	−42.0000	+	24.2487i	−0.149466	+	0.0862943i	−0.572868	−	0.819648i	$-0.694169\pi$
$281$	−42.0000	+	24.2487i	−0.149466	+	0.0862943i	0.423402	+	0.905942i	$0.360836\pi$
$282$	126.000	+	218.238i	0.446809	+	0.773895i
$283$	−187.000	−	323.894i	−0.660777	−	1.14450i	−0.980412	−	0.196959i	$-0.936893\pi$
$283$	−187.000	−	323.894i	−0.660777	−	1.14450i	0.319634	−	0.947541i	$-0.396440\pi$
$284$	−27.0000	+	15.5885i	−0.0950704	+	0.0548889i
$285$	−99.0000	+	57.1577i	−0.347368	+	0.200553i
$286$	−6.00000	−	10.3923i	−0.0209790	−	0.0363367i
$287$		0			0
$288$	−121.500	+	70.1481i	−0.421875	+	0.243570i
$289$	−23.0000	−	39.8372i	−0.0795848	−	0.137845i
$290$		−	270.200i		−	0.931724i
$291$	172.500	+	298.779i	0.592784	+	1.02673i
$292$	65.0000			0.222603
$293$	219.000	+	126.440i	0.747440	+	0.431535i	0.824768	−	0.565471i	$-0.191306\pi$
$293$	219.000	+	126.440i	0.747440	+	0.431535i	−0.0773280	+	0.997006i	$0.524639\pi$
$294$		0			0
$295$	87.0000	+	150.688i	0.294915	+	0.510808i
$296$	255.000	−	147.224i	0.861486	−	0.497379i
$297$		−	46.7654i		−	0.157459i
$298$	−132.000	+	228.631i	−0.442953	+	0.767217i
$299$	96.0000	+	55.4256i	0.321070	+	0.185370i
$300$	−19.5000	−	33.7750i	−0.0650000	−	0.112583i
$301$		0			0
$302$	30.0000	+	17.3205i	0.0993377	+	0.0573527i
$303$			135.100i			0.445874i
$304$	−121.000			−0.398026
$305$	168.000	+	96.9948i	0.550820	+	0.318016i
$306$	−121.500	−	210.444i	−0.397059	−	0.687726i
$307$	533.000			1.73616			0.868078	−	0.496428i	$-0.165355\pi$
$307$	533.000			1.73616			0.868078	+	0.496428i	$0.165355\pi$
$308$		0			0
$309$	−120.000			−0.388350
$310$	−192.000			−0.619355
$311$	213.000	−	122.976i	0.684887	−	0.395420i	−0.116806	−	0.993155i	$-0.537266\pi$
$311$	213.000	−	122.976i	0.684887	−	0.395420i	0.801694	+	0.597735i	$0.203932\pi$
$312$	−90.0000	−	51.9615i	−0.288462	−	0.166543i
$313$	−77.5000	+	134.234i	−0.247604	+	0.428862i	−0.962860	−	0.269999i	$-0.912976\pi$
$313$	−77.5000	+	134.234i	−0.247604	+	0.428862i	0.715257	+	0.698862i	$0.246310\pi$
$314$			69.2820i			0.220643i
$315$		0			0
$316$	38.0000			0.120253
$317$	42.0000	+	24.2487i	0.132492	+	0.0764944i	0.564781	−	0.825241i	$-0.308961\pi$
$317$	42.0000	+	24.2487i	0.132492	+	0.0764944i	−0.432289	+	0.901735i	$0.642294\pi$
$318$		0			0
$319$	−39.0000	−	67.5500i	−0.122257	−	0.211755i
$320$			245.951i			0.768598i
$321$	−364.500	+	210.444i	−1.13551	+	0.655589i
$322$		0			0
$323$			171.473i			0.530876i
$324$	−40.5000	−	70.1481i	−0.125000	−	0.216506i
$325$	26.0000	−	45.0333i	0.0800000	−	0.138564i
$326$			183.597i			0.563182i
$327$	78.0000	−	135.100i	0.238532	−	0.413150i
$328$	−52.5000	+	90.9327i	−0.160061	+	0.277234i
$329$		0			0
$330$	−27.0000	−	15.5885i	−0.0818182	−	0.0472377i
$331$	−1.00000	+	1.73205i	−0.00302115	+	0.00523278i	−0.867532	−	0.497381i	$-0.834295\pi$
$331$	−1.00000	+	1.73205i	−0.00302115	+	0.00523278i	0.864511	+	0.502614i	$0.167628\pi$
$332$	42.0000	+	24.2487i	0.126506	+	0.0730383i
$333$	153.000	+	265.004i	0.459459	+	0.795807i
$334$	165.000	+	285.788i	0.494012	+	0.855654i
$335$	93.0000	−	53.6936i	0.277612	−	0.160279i
$336$		0			0
$337$	−38.5000	+	66.6840i	−0.114243	+	0.197875i	−0.917477	−	0.397789i	$-0.869778\pi$
$337$	−38.5000	+	66.6840i	−0.114243	+	0.197875i	0.803234	+	0.595664i	$0.203111\pi$
$338$			265.004i			0.784035i
$339$	−234.000	−	135.100i	−0.690265	−	0.398525i
$340$	54.0000			0.158824
$341$	−48.0000	+	27.7128i	−0.140762	+	0.0812692i
$342$		−	171.473i		−	0.501383i
$343$		0			0
$344$	457.500	−	264.138i	1.32994	−	0.767842i
$345$	288.000			0.834783
$346$	−201.000	−	348.142i	−0.580925	−	1.00619i
$347$	−97.5000	+	56.2917i	−0.280980	+	0.162224i	−0.633867	−	0.773442i	$-0.718533\pi$
$347$	−97.5000	+	56.2917i	−0.280980	+	0.162224i	0.352887	+	0.935666i	$0.385200\pi$
$348$	−117.000	−	67.5500i	−0.336207	−	0.194109i
$349$	−208.000	−	360.267i	−0.595989	−	1.03228i	−0.993407	−	0.114645i	$-0.963427\pi$
$349$	−208.000	−	360.267i	−0.595989	−	1.03228i	0.397418	−	0.917638i	$-0.369906\pi$
$350$		0			0
$351$	54.0000	−	93.5307i	0.153846	−	0.266469i
$352$	13.5000	+	23.3827i	0.0383523	+	0.0664281i
$353$		−	1.73205i		−	0.00490666i	−0.999997	−	0.00245333i	$-0.999219\pi$
$353$		−	1.73205i		−	0.00490666i	0.999997	−	0.00245333i	$-0.000780920\pi$
$354$	−261.000			−0.737288
$355$	−108.000			−0.304225
$356$	−108.000	−	62.3538i	−0.303371	−	0.175151i
$357$		0			0
$358$	−54.0000	−	93.5307i	−0.150838	−	0.261259i
$359$	513.000	−	296.181i	1.42897	−	0.825016i	0.431930	−	0.901907i	$-0.357833\pi$
$359$	513.000	−	296.181i	1.42897	−	0.825016i	0.997039	+	0.0768913i	$0.0244995\pi$
$360$	−270.000			−0.750000
$361$	120.000	−	207.846i	0.332410	−	0.575751i
$362$	−348.000	−	200.918i	−0.961326	−	0.555022i
$363$	354.000			0.975207
$364$		0			0
$365$	195.000	+	112.583i	0.534247	+	0.308447i
$366$	−252.000	+	145.492i	−0.688525	+	0.397520i
$367$	−358.000			−0.975477			−0.487738	−	0.872990i	$-0.662178\pi$
$367$	−358.000			−0.975477			−0.487738	+	0.872990i	$0.662178\pi$
$368$	264.000	+	152.420i	0.717391	+	0.414186i
$369$	−94.5000	−	54.5596i	−0.256098	−	0.147858i
$370$	204.000			0.551351
$371$		0			0
$372$	−48.0000	+	83.1384i	−0.129032	+	0.223490i
$373$	−580.000			−1.55496			−0.777480	−	0.628908i	$-0.783502\pi$
$373$	−580.000			−1.55496			−0.777480	+	0.628908i	$0.783502\pi$
$374$	−40.5000	+	23.3827i	−0.108289	+	0.0625206i
$375$		−	394.908i		−	1.05309i
$376$	210.000	−	363.731i	0.558511	−	0.967369i
$377$		−	180.133i		−	0.477807i
$378$		0			0
$379$	83.0000			0.218997			0.109499	−	0.993987i	$-0.465075\pi$
$379$	83.0000			0.218997			0.109499	+	0.993987i	$0.465075\pi$
$380$	33.0000	+	19.0526i	0.0868421	+	0.0501383i
$381$	−48.0000			−0.125984
$382$	−201.000	−	348.142i	−0.526178	−	0.911367i
$383$			557.720i			1.45619i	0.685477	+	0.728094i	$0.259594\pi$
$383$			557.720i			1.45619i	−0.685477	+	0.728094i	$0.740406\pi$
$384$	−157.500	−	90.9327i	−0.410156	−	0.236804i
$385$		0			0
$386$			458.993i			1.18910i
$387$	274.500	+	475.448i	0.709302	+	1.22855i
$388$	57.5000	−	99.5929i	0.148196	−	0.256683i
$389$		−	516.151i		−	1.32687i	−0.748235	−	0.663433i	$-0.769099\pi$
$389$		−	516.151i		−	1.32687i	0.748235	−	0.663433i	$-0.230901\pi$
$390$	−36.0000	−	62.3538i	−0.0923077	−	0.159882i
$391$	216.000	−	374.123i	0.552430	−	0.956836i
$392$		0			0
$393$		−	478.046i		−	1.21640i
$394$	−108.000	+	187.061i	−0.274112	+	0.474775i
$395$	114.000	+	65.8179i	0.288608	+	0.166628i
$396$	−13.5000	+	7.79423i	−0.0340909	+	0.0196824i
$397$	−181.000	−	313.501i	−0.455919	−	0.789676i	0.542821	−	0.839848i	$-0.317356\pi$
$397$	−181.000	−	313.501i	−0.455919	−	0.789676i	−0.998741	+	0.0501728i	$0.984023\pi$
$398$	−435.000	+	251.147i	−1.09296	+	0.631024i
$399$		0			0
$400$	71.5000	−	123.842i	0.178750	−	0.309604i
$401$		−	393.176i		−	0.980488i	−0.871585	−	0.490244i	$-0.836908\pi$
$401$		−	393.176i		−	0.980488i	0.871585	−	0.490244i	$-0.163092\pi$
$402$			161.081i			0.400698i
$403$	−128.000			−0.317618
$404$	39.0000	−	22.5167i	0.0965347	−	0.0557343i
$405$		−	280.592i		−	0.692820i
$406$		0			0
$407$	51.0000	−	29.4449i	0.125307	−	0.0723461i
$408$	−202.500	+	350.740i	−0.496324	+	0.859658i
$409$	−110.500	−	191.392i	−0.270171	−	0.467950i	0.698734	−	0.715381i	$-0.253747\pi$
$409$	−110.500	−	191.392i	−0.270171	−	0.467950i	−0.968905	+	0.247431i	$0.920414\pi$
$410$	−63.0000	+	36.3731i	−0.153659	+	0.0887148i
$411$		−	566.381i		−	1.37806i
$412$	20.0000	+	34.6410i	0.0485437	+	0.0840801i
$413$		0			0
$414$	−216.000	+	374.123i	−0.521739	+	0.903679i
$415$	84.0000	+	145.492i	0.202410	+	0.350584i
$416$			62.3538i			0.149889i
$417$	−7.50000	+	12.9904i	−0.0179856	+	0.0311520i
$418$	−33.0000			−0.0789474
$419$	678.000	+	391.443i	1.61814	+	0.934233i	0.987401	+	0.158236i	$0.0505807\pi$
$419$	678.000	+	391.443i	1.61814	+	0.934233i	0.630737	+	0.775997i	$0.282753\pi$
$420$		0			0
$421$	341.000	+	590.629i	0.809976	+	1.40292i	0.912880	+	0.408229i	$0.133853\pi$
$421$	341.000	+	590.629i	0.809976	+	1.40292i	−0.102903	+	0.994691i	$0.532813\pi$
$422$	141.000	−	81.4064i	0.334123	−	0.192906i
$423$	378.000	+	218.238i	0.893617	+	0.515930i
$424$		0			0
$425$	−175.500	−	101.325i	−0.412941	−	0.238412i
$426$	81.0000	−	140.296i	0.190141	−	0.329334i
$427$		0			0
$428$	121.500	+	70.1481i	0.283879	+	0.163897i
$429$	−18.0000	−	10.3923i	−0.0419580	−	0.0242245i
$430$	366.000			0.851163
$431$	243.000	+	140.296i	0.563805	+	0.325513i	0.754671	−	0.656103i	$-0.227796\pi$
$431$	243.000	+	140.296i	0.563805	+	0.325513i	−0.190866	+	0.981616i	$0.561130\pi$
$432$	148.500	−	257.210i	0.343750	−	0.595392i
$433$	−295.000			−0.681293			−0.340647	−	0.940191i	$-0.610646\pi$
$433$	−295.000			−0.681293			−0.340647	+	0.940191i	$0.610646\pi$
$434$		0			0
$435$	−234.000	−	405.300i	−0.537931	−	0.931724i
$436$	−52.0000			−0.119266
$437$	264.000	−	152.420i	0.604119	−	0.348788i
$438$	−292.500	+	168.875i	−0.667808	+	0.385559i
$439$	−406.000	+	703.213i	−0.924829	+	1.60185i	−0.132993	+	0.991117i	$0.542459\pi$
$439$	−406.000	+	703.213i	−0.924829	+	1.60185i	−0.791836	+	0.610734i	$0.790874\pi$
$440$			51.9615i			0.118094i
$441$		0			0
$442$	−108.000			−0.244344
$443$	−79.5000	−	45.8993i	−0.179458	−	0.103610i	0.407580	−	0.913170i	$-0.366373\pi$
$443$	−79.5000	−	45.8993i	−0.179458	−	0.103610i	−0.587038	+	0.809559i	$0.699706\pi$
$444$	51.0000	−	88.3346i	0.114865	−	0.198952i
$445$	−216.000	−	374.123i	−0.485393	−	0.840726i
$446$			90.0666i			0.201943i
$447$			457.261i			1.02296i
$448$		0			0
$449$		−	639.127i		−	1.42344i	−0.702461	−	0.711722i	$-0.747915\pi$
$449$		−	639.127i		−	1.42344i	0.702461	−	0.711722i	$-0.252085\pi$
$450$	175.500	+	101.325i	0.390000	+	0.225167i
$451$	−10.5000	+	18.1865i	−0.0232816	+	0.0403249i
$452$			90.0666i			0.199262i
$453$	60.0000			0.132450
$454$	163.500	−	283.190i	0.360132	−	0.623767i
$455$		0			0
$456$	−247.500	+	142.894i	−0.542763	+	0.313364i
$457$	−32.5000	+	56.2917i	−0.0711160	+	0.123176i	−0.899391	−	0.437146i	$-0.855989\pi$
$457$	−32.5000	+	56.2917i	−0.0711160	+	0.123176i	0.828275	+	0.560322i	$0.189323\pi$
$458$	399.000	+	230.363i	0.871179	+	0.502975i
$459$	−364.500	−	210.444i	−0.794118	−	0.458484i
$460$	−48.0000	−	83.1384i	−0.104348	−	0.180736i
$461$	−690.000	+	398.372i	−1.49675	+	0.864147i	−0.999993	−	0.00374501i	$-0.998808\pi$
$461$	−690.000	+	398.372i	−1.49675	+	0.864147i	−0.496753	+	0.867892i	$0.665475\pi$
$462$		0			0
$463$	−367.000	+	635.663i	−0.792657	+	1.37292i	0.131660	+	0.991295i	$0.457969\pi$
$463$	−367.000	+	635.663i	−0.792657	+	1.37292i	−0.924317	+	0.381627i	$0.875364\pi$
$464$		−	495.367i		−	1.06760i
$465$	−288.000	+	166.277i	−0.619355	+	0.357585i
$466$	351.000			0.753219
$467$	−175.500	+	101.325i	−0.375803	+	0.216970i	−0.675991	−	0.736910i	$-0.736284\pi$
$467$	−175.500	+	101.325i	−0.375803	+	0.216970i	0.300188	+	0.953880i	$0.402951\pi$
$468$	−36.0000			−0.0769231
$469$		0			0
$470$	252.000	−	145.492i	0.536170	−	0.309558i
$471$	60.0000	+	103.923i	0.127389	+	0.220643i
$472$	217.500	+	376.721i	0.460805	+	0.798138i
$473$	91.5000	−	52.8275i	0.193446	−	0.111686i
$474$	−171.000	+	98.7269i	−0.360759	+	0.208285i
$475$	−71.5000	−	123.842i	−0.150526	−	0.260719i
$476$		0			0
$477$		0			0
$478$	−348.000	−	602.754i	−0.728033	−	1.26099i
$479$			606.218i			1.26559i	0.774319	+	0.632795i	$0.218092\pi$
$479$			606.218i			1.26559i	−0.774319	+	0.632795i	$0.781908\pi$
$480$	81.0000	+	140.296i	0.168750	+	0.292284i
$481$	136.000			0.282744
$482$	178.500	+	103.057i	0.370332	+	0.213811i
$483$		0			0
$484$	−59.0000	−	102.191i	−0.121901	−	0.211138i
$485$	345.000	−	199.186i	0.711340	−	0.410692i
$486$	364.500	+	210.444i	0.750000	+	0.433013i
$487$	53.0000	−	91.7987i	0.108830	−	0.188498i	−0.806467	−	0.591279i	$-0.798623\pi$
$487$	53.0000	−	91.7987i	0.108830	−	0.188498i	0.915296	+	0.402781i	$0.131956\pi$
$488$	420.000	+	242.487i	0.860656	+	0.496900i
$489$	159.000	+	275.396i	0.325153	+	0.563182i
$490$		0			0
$491$	−199.500	−	115.181i	−0.406314	−	0.234585i	0.282891	−	0.959152i	$-0.408707\pi$
$491$	−199.500	−	115.181i	−0.406314	−	0.234585i	−0.689205	+	0.724567i	$0.742040\pi$
$492$			36.3731i			0.0739290i
$493$	−702.000			−1.42394
$494$	−66.0000	−	38.1051i	−0.133603	−	0.0771359i
$495$	−54.0000			−0.109091
$496$	−352.000			−0.709677
$497$		0			0
$498$	−252.000			−0.506024
$499$	−787.000			−1.57715			−0.788577	−	0.614936i	$-0.789182\pi$
$499$	−787.000			−1.57715			−0.788577	+	0.614936i	$0.789182\pi$
$500$	−114.000	+	65.8179i	−0.228000	+	0.131636i
$501$	495.000	+	285.788i	0.988024	+	0.570436i
$502$	337.500	−	584.567i	0.672311	−	1.16448i
$503$			623.538i			1.23964i	0.784745	+	0.619819i	$0.212794\pi$
$503$			623.538i			1.23964i	−0.784745	+	0.619819i	$0.787206\pi$
$504$		0			0
$505$	156.000			0.308911
$506$	72.0000	+	41.5692i	0.142292	+	0.0821526i
$507$	229.500	+	397.506i	0.452663	+	0.784035i
$508$	8.00000	+	13.8564i	0.0157480	+	0.0272764i
$509$			214.774i			0.421953i	0.977491	+	0.210977i	$0.0676644\pi$
$509$			214.774i			0.421953i	−0.977491	+	0.210977i	$0.932336\pi$
$510$	−243.000	+	140.296i	−0.476471	+	0.275090i
$511$		0			0
$512$			552.524i			1.07915i
$513$	−148.500	−	257.210i	−0.289474	−	0.501383i
$514$	151.500	−	262.406i	0.294747	−	0.510517i
$515$			138.564i			0.269056i
$516$	91.5000	−	158.483i	0.177326	−	0.307137i
$517$	42.0000	−	72.7461i	0.0812379	−	0.140708i
$518$		0			0
$519$	−603.000	−	348.142i	−1.16185	−	0.670794i
$520$	−60.0000	+	103.923i	−0.115385	+	0.199852i
$521$	175.500	+	101.325i	0.336852	+	0.194482i	0.658879	−	0.752249i	$-0.271031\pi$
$521$	175.500	+	101.325i	0.336852	+	0.194482i	−0.322027	+	0.946730i	$0.604364\pi$
$522$	702.000			1.34483
$523$	125.000	+	216.506i	0.239006	+	0.413970i	0.960429	−	0.278524i	$-0.0898452\pi$
$523$	125.000	+	216.506i	0.239006	+	0.413970i	−0.721424	+	0.692494i	$0.756512\pi$
$524$	−138.000	+	79.6743i	−0.263359	+	0.152050i
$525$		0			0
$526$	−39.0000	+	67.5500i	−0.0741445	+	0.128422i
$527$			498.831i			0.946548i
$528$	−49.5000	−	28.5788i	−0.0937500	−	0.0541266i
$529$	−239.000			−0.451796
$530$		0			0
$531$	−391.500	+	226.033i	−0.737288	+	0.425674i
$532$		0			0
$533$	−42.0000	+	24.2487i	−0.0787992	+	0.0454948i
$534$	648.000			1.21348
$535$	243.000	+	420.888i	0.454206	+	0.786707i
$536$	232.500	−	134.234i	0.433769	−	0.250436i
$537$	−162.000	−	93.5307i	−0.301676	−	0.174173i
$538$	162.000	+	280.592i	0.301115	+	0.521547i
$539$		0			0
$540$	−81.0000	+	46.7654i	−0.150000	+	0.0866025i
$541$	−325.000	−	562.917i	−0.600739	−	1.04051i	−0.992709	−	0.120533i	$-0.961540\pi$
$541$	−325.000	−	562.917i	−0.600739	−	1.04051i	0.391970	−	0.919978i	$-0.371794\pi$
$542$			464.190i			0.856438i
$543$	−696.000			−1.28177
$544$	243.000			0.446691
$545$	−156.000	−	90.0666i	−0.286239	−	0.165260i
$546$		0			0
$547$	−311.500	−	539.534i	−0.569470	−	0.986351i	−0.996618	−	0.0821692i	$-0.973815\pi$
$547$	−311.500	−	539.534i	−0.569470	−	0.986351i	0.427149	−	0.904181i	$-0.359518\pi$
$548$	−163.500	+	94.3968i	−0.298358	+	0.172257i
$549$	−252.000	+	436.477i	−0.459016	+	0.795040i
$550$	19.5000	−	33.7750i	0.0354545	−	0.0614091i
$551$	−429.000	−	247.683i	−0.778584	−	0.449516i
$552$	720.000			1.30435
$553$		0			0
$554$	84.0000	+	48.4974i	0.151625	+	0.0875405i
$555$	306.000	−	176.669i	0.551351	−	0.318323i
$556$	5.00000			0.00899281
$557$	−459.000	−	265.004i	−0.824057	−	0.475770i	0.0277562	−	0.999615i	$-0.491164\pi$
$557$	−459.000	−	265.004i	−0.824057	−	0.475770i	−0.851814	+	0.523845i	$0.824497\pi$
$558$		−	498.831i		−	0.893962i
$559$	244.000			0.436494
$560$		0			0
$561$	−40.5000	+	70.1481i	−0.0721925	+	0.125041i
$562$	−84.0000			−0.149466
$563$	−97.5000	+	56.2917i	−0.173179	+	0.0999852i	−0.584084	−	0.811693i	$-0.698546\pi$
$563$	−97.5000	+	56.2917i	−0.173179	+	0.0999852i	0.410905	+	0.911678i	$0.365213\pi$
$564$		−	145.492i		−	0.257965i
$565$	−156.000	+	270.200i	−0.276106	+	0.478230i
$566$		−	647.787i		−	1.14450i
$567$		0			0
$568$	−270.000			−0.475352
$569$	−565.500	−	326.492i	−0.993849	−	0.573799i	−0.0874263	−	0.996171i	$-0.527864\pi$
$569$	−565.500	−	326.492i	−0.993849	−	0.573799i	−0.906423	+	0.422372i	$0.861198\pi$
$570$	−198.000			−0.347368
$571$	−272.500	−	471.984i	−0.477233	−	0.826592i	0.522427	−	0.852684i	$-0.325027\pi$
$571$	−272.500	−	471.984i	−0.477233	−	0.826592i	−0.999660	+	0.0260926i	$0.991694\pi$
$572$			6.92820i			0.0121122i
$573$	−603.000	−	348.142i	−1.05236	−	0.607578i
$574$		0			0
$575$			360.267i			0.626551i
$576$	−639.000			−1.10938
$577$	435.500	−	754.308i	0.754766	−	1.30729i	−0.190725	−	0.981644i	$-0.561084\pi$
$577$	435.500	−	754.308i	0.754766	−	1.30729i	0.945491	−	0.325650i	$-0.105583\pi$
$578$		−	79.6743i		−	0.137845i
$579$	397.500	+	688.490i	0.686528	+	1.18910i
$580$	−78.0000	+	135.100i	−0.134483	+	0.232931i
$581$		0			0
$582$			597.558i			1.02673i
$583$		0			0
$584$	487.500	+	281.458i	0.834760	+	0.481949i
$585$	−108.000	−	62.3538i	−0.184615	−	0.106588i
$586$	219.000	+	379.319i	0.373720	+	0.647302i
$587$	−1.50000	+	0.866025i	−0.00255537	+	0.00147534i	−0.501277	−	0.865287i	$-0.667136\pi$
$587$	−1.50000	+	0.866025i	−0.00255537	+	0.00147534i	0.498722	+	0.866762i	$0.333803\pi$
$588$		0			0
$589$	−176.000	+	304.841i	−0.298812	+	0.517557i
$590$			301.377i			0.510808i
$591$			374.123i			0.633034i
$592$	374.000			0.631757
$593$	162.000	−	93.5307i	0.273187	−	0.157725i	−0.357148	−	0.934048i	$-0.616251\pi$
$593$	162.000	−	93.5307i	0.273187	−	0.157725i	0.630335	+	0.776323i	$0.282917\pi$
$594$	40.5000	−	70.1481i	0.0681818	−	0.118094i
$595$		0			0
$596$	132.000	−	76.2102i	0.221477	−	0.127870i
$597$	−435.000	+	753.442i	−0.728643	+	1.26205i
$598$	96.0000	+	166.277i	0.160535	+	0.278055i
$599$	−489.000	+	282.324i	−0.816361	+	0.471326i	−0.849160	−	0.528136i	$-0.822891\pi$
$599$	−489.000	+	282.324i	−0.816361	+	0.471326i	0.0327992	+	0.999462i	$0.489558\pi$
$600$		−	337.750i		−	0.562917i
$601$	−230.500	−	399.238i	−0.383527	−	0.664289i	0.608036	−	0.793909i	$-0.291958\pi$
$601$	−230.500	−	399.238i	−0.383527	−	0.664289i	−0.991564	+	0.129620i	$0.958624\pi$
$602$		0			0
$603$	139.500	+	241.621i	0.231343	+	0.400698i
$604$	−10.0000	−	17.3205i	−0.0165563	−	0.0286763i
$605$		−	408.764i		−	0.675643i
$606$	−117.000	+	202.650i	−0.193069	+	0.334406i
$607$	−112.000			−0.184514			−0.0922570	−	0.995735i	$-0.529408\pi$
$607$	−112.000			−0.184514			−0.0922570	+	0.995735i	$0.529408\pi$
$608$	148.500	+	85.7365i	0.244243	+	0.141014i
$609$		0			0
$610$	168.000	+	290.985i	0.275410	+	0.477024i
$611$	168.000	−	96.9948i	0.274959	−	0.158748i
$612$			140.296i			0.229242i
$613$	−451.000	+	781.155i	−0.735726	+	1.27431i	0.218678	+	0.975797i	$0.429826\pi$
$613$	−451.000	+	781.155i	−0.735726	+	1.27431i	−0.954404	+	0.298518i	$0.903508\pi$
$614$	799.500	+	461.592i	1.30212	+	0.751778i
$615$	−63.0000	+	109.119i	−0.102439	+	0.177430i
$616$		0			0
$617$	−307.500	−	177.535i	−0.498379	−	0.287739i	0.229665	−	0.973270i	$-0.426237\pi$
$617$	−307.500	−	177.535i	−0.498379	−	0.287739i	−0.728044	+	0.685530i	$0.759570\pi$
$618$	−180.000	−	103.923i	−0.291262	−	0.168160i
$619$	−799.000			−1.29079			−0.645396	−	0.763848i	$-0.723308\pi$
$619$	−799.000			−1.29079			−0.645396	+	0.763848i	$0.723308\pi$
$620$	96.0000	+	55.4256i	0.154839	+	0.0893962i
$621$			748.246i			1.20490i
$622$	426.000			0.684887
$623$		0			0
$624$	−66.0000	−	114.315i	−0.105769	−	0.183198i
$625$	−131.000			−0.209600
$626$	−232.500	+	134.234i	−0.371406	+	0.214431i
$627$	−49.5000	+	28.5788i	−0.0789474	+	0.0455803i
$628$	20.0000	−	34.6410i	0.0318471	−	0.0551609i
$629$		−	530.008i		−	0.842619i
$630$		0			0
$631$	830.000			1.31537			0.657686	−	0.753292i	$-0.271535\pi$
$631$	830.000			1.31537			0.657686	+	0.753292i	$0.271535\pi$
$632$	285.000	+	164.545i	0.450949	+	0.260356i
$633$	141.000	−	244.219i	0.222749	−	0.385812i
$634$	42.0000	+	72.7461i	0.0662461	+	0.114742i
$635$			55.4256i			0.0872845i
$636$		0			0
$637$		0			0
$638$		−	135.100i		−	0.211755i
$639$		−	280.592i		−	0.439111i
$640$	−105.000	+	181.865i	−0.164062	+	0.284165i
$641$		−	375.855i		−	0.586357i	−0.956058	−	0.293179i	$-0.905287\pi$
$641$		−	375.855i		−	0.586357i	0.956058	−	0.293179i	$-0.0947131\pi$
$642$	−729.000			−1.13551
$643$	6.50000	−	11.2583i	0.0101089	−	0.0175091i	−0.860927	−	0.508729i	$-0.830116\pi$
$643$	6.50000	−	11.2583i	0.0101089	−	0.0175091i	0.871036	+	0.491220i	$0.163449\pi$
$644$		0			0
$645$	549.000	−	316.965i	0.851163	−	0.491419i
$646$	−148.500	+	257.210i	−0.229876	+	0.398157i
$647$	−405.000	−	233.827i	−0.625966	−	0.361402i	0.153222	−	0.988192i	$-0.451035\pi$
$647$	−405.000	−	233.827i	−0.625966	−	0.361402i	−0.779188	+	0.626790i	$0.784368\pi$
$648$		−	701.481i		−	1.08253i
$649$	43.5000	+	75.3442i	0.0670262	+	0.116093i
$650$	78.0000	−	45.0333i	0.120000	−	0.0692820i
$651$		0			0
$652$	53.0000	−	91.7987i	0.0812883	−	0.140796i
$653$		−	377.587i		−	0.578234i	−0.957294	−	0.289117i	$-0.906638\pi$
$653$		−	377.587i		−	0.578234i	0.957294	−	0.289117i	$-0.0933617\pi$
$654$	234.000	−	135.100i	0.357798	−	0.206575i
$655$	−552.000			−0.842748
$656$	−115.500	+	66.6840i	−0.176067	+	0.101652i
$657$	−292.500	+	506.625i	−0.445205	+	0.771119i
$658$		0			0
$659$	−852.000	+	491.902i	−1.29287	+	0.746438i	−0.979162	−	0.203082i	$-0.934904\pi$
$659$	−852.000	+	491.902i	−1.29287	+	0.746438i	−0.313706	+	0.949520i	$0.601571\pi$
$660$	9.00000	+	15.5885i	0.0136364	+	0.0236189i
$661$	191.000	+	330.822i	0.288956	+	0.500487i	0.973561	−	0.228428i	$-0.0733585\pi$
$661$	191.000	+	330.822i	0.288956	+	0.500487i	−0.684605	+	0.728915i	$0.740025\pi$
$662$	−3.00000	+	1.73205i	−0.00453172	+	0.00261639i
$663$	−162.000	+	93.5307i	−0.244344	+	0.141072i
$664$	210.000	+	363.731i	0.316265	+	0.547787i
$665$		0			0
$666$			530.008i			0.795807i
$667$	624.000	+	1080.80i	0.935532	+	1.62039i
$668$		−	190.526i		−	0.285218i
$669$	78.0000	+	135.100i	0.116592	+	0.201943i
$670$	186.000			0.277612
$671$	84.0000	+	48.4974i	0.125186	+	0.0722763i
$672$		0			0
$673$	−289.000	−	500.563i	−0.429421	−	0.743778i	0.567401	−	0.823441i	$-0.307949\pi$
$673$	−289.000	−	500.563i	−0.429421	−	0.743778i	−0.996822	+	0.0796633i	$0.974615\pi$
$674$	−115.500	+	66.6840i	−0.171365	+	0.0989376i
$675$	351.000			0.520000
$676$	76.5000	−	132.502i	0.113166	−	0.196009i
$677$	−606.000	−	349.874i	−0.895126	−	0.516801i	−0.0195100	−	0.999810i	$-0.506211\pi$
$677$	−606.000	−	349.874i	−0.895126	−	0.516801i	−0.875616	+	0.483009i	$0.839544\pi$
$678$	−234.000	−	405.300i	−0.345133	−	0.597787i
$679$		0			0
$680$	405.000	+	233.827i	0.595588	+	0.343863i
$681$		−	566.381i		−	0.831690i
$682$	−96.0000			−0.140762
$683$	904.500	+	522.213i	1.32430	+	0.764588i	0.984412	−	0.175877i	$-0.0562760\pi$
$683$	904.500	+	522.213i	1.32430	+	0.764588i	0.339892	+	0.940464i	$0.389609\pi$
$684$	−49.5000	+	85.7365i	−0.0723684	+	0.125346i
$685$	−654.000			−0.954745
$686$		0			0
$687$	798.000			1.16157
$688$	671.000			0.975291
$689$		0			0
$690$	432.000	+	249.415i	0.626087	+	0.361471i
$691$	−91.0000	+	157.617i	−0.131693	+	0.228099i	−0.924329	−	0.381596i	$-0.875375\pi$
$691$	−91.0000	+	157.617i	−0.131693	+	0.228099i	0.792636	+	0.609695i	$0.208708\pi$
$692$			232.095i			0.335397i
$693$		0			0
$694$	−195.000			−0.280980
$695$	15.0000	+	8.66025i	0.0215827	+	0.0124608i
$696$	−585.000	−	1013.25i	−0.840517	−	1.45582i
$697$	94.5000	+	163.679i	0.135581	+	0.234833i
$698$		−	720.533i		−	1.03228i
$699$	526.500	−	303.975i	0.753219	−	0.434871i
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	162.000	−	93.5307i	0.230769	−	0.133235i
$703$	187.000	−	323.894i	0.266003	−	0.460730i
$704$			122.976i			0.174681i
$705$	252.000	−	436.477i	0.357447	−	0.619116i
$706$	1.50000	−	2.59808i	0.00212465	−	0.00367999i
$707$		0			0
$708$	130.500	+	75.3442i	0.184322	+	0.106418i
$709$	350.000	−	606.218i	0.493653	−	0.855032i	−0.506320	−	0.862346i	$-0.668995\pi$
$709$	350.000	−	606.218i	0.493653	−	0.855032i	0.999973	+	0.00731341i	$0.00232795\pi$
$710$	−162.000	−	93.5307i	−0.228169	−	0.131733i
$711$	−171.000	+	296.181i	−0.240506	+	0.416569i
$712$	−540.000	−	935.307i	−0.758427	−	1.31363i
$713$	768.000	−	443.405i	1.07714	−	0.621886i
$714$		0			0
$715$	−12.0000	+	20.7846i	−0.0167832	+	0.0290694i
$716$			62.3538i			0.0870864i
$717$	−1044.00	−	602.754i	−1.45607	−	0.840661i
$718$	1026.00			1.42897
$719$	−513.000	+	296.181i	−0.713491	+	0.411934i	−0.812352	−	0.583167i	$-0.801813\pi$
$719$	−513.000	+	296.181i	−0.713491	+	0.411934i	0.0988613	+	0.995101i	$0.468480\pi$
$720$	−297.000	−	171.473i	−0.412500	−	0.238157i
$721$		0			0
$722$	360.000	−	207.846i	0.498615	−	0.287875i
$723$	357.000			0.493776
$724$	116.000	+	200.918i	0.160221	+	0.277511i
$725$	507.000	−	292.717i	0.699310	−	0.403747i
$726$	531.000	+	306.573i	0.731405	+	0.422277i
$727$	332.000	+	575.041i	0.456671	+	0.790978i	0.998783	−	0.0493289i	$-0.0157082\pi$
$727$	332.000	+	575.041i	0.456671	+	0.790978i	−0.542111	+	0.840307i	$0.682375\pi$
$728$		0			0
$729$	729.000			1.00000
$730$	195.000	+	337.750i	0.267123	+	0.462671i
$731$		−	950.896i		−	1.30082i
$732$	168.000			0.229508
$733$	−670.000			−0.914052			−0.457026	−	0.889453i	$-0.651085\pi$
$733$	−670.000			−0.914052			−0.457026	+	0.889453i	$0.651085\pi$
$734$	−537.000	−	310.037i	−0.731608	−	0.422394i
$735$		0			0
$736$	−216.000	−	374.123i	−0.293478	−	0.508319i
$737$	46.5000	−	26.8468i	0.0630936	−	0.0364271i
$738$	−94.5000	−	163.679i	−0.128049	−	0.221787i
$739$	−158.500	+	274.530i	−0.214479	+	0.371489i	−0.953111	−	0.302620i	$-0.902139\pi$
$739$	−158.500	+	274.530i	−0.214479	+	0.371489i	0.738632	+	0.674109i	$0.235472\pi$
$740$	−102.000	−	58.8897i	−0.137838	−	0.0795807i
$741$	−132.000			−0.178138
$742$		0			0
$743$	−537.000	−	310.037i	−0.722746	−	0.417277i	0.0930168	−	0.995665i	$-0.470349\pi$
$743$	−537.000	−	310.037i	−0.722746	−	0.417277i	−0.815762	+	0.578387i	$0.803682\pi$
$744$	−720.000	+	415.692i	−0.967742	+	0.558726i
$745$	528.000			0.708725
$746$	−870.000	−	502.295i	−1.16622	−	0.673317i
$747$	−378.000	+	218.238i	−0.506024	+	0.292153i
$748$	27.0000			0.0360963
$749$		0			0
$750$	342.000	−	592.361i	0.456000	−	0.789815i
$751$	1310.00			1.74434			0.872170	−	0.489202i	$-0.162712\pi$
$751$	1310.00			1.74434			0.872170	+	0.489202i	$0.162712\pi$
$752$	462.000	−	266.736i	0.614362	−	0.354702i
$753$		−	1169.13i		−	1.55264i
$754$	156.000	−	270.200i	0.206897	−	0.358355i
$755$		−	69.2820i		−	0.0917643i
$756$		0			0
$757$	218.000			0.287979			0.143989	−	0.989579i	$-0.454007\pi$
$757$	218.000			0.287979			0.143989	+	0.989579i	$0.454007\pi$
$758$	124.500	+	71.8801i	0.164248	+	0.0948286i
$759$	144.000			0.189723
$760$	165.000	+	285.788i	0.217105	+	0.376037i
$761$		−	658.179i		−	0.864887i	−0.901661	−	0.432444i	$-0.857651\pi$
$761$		−	658.179i		−	0.864887i	0.901661	−	0.432444i	$-0.142349\pi$
$762$	−72.0000	−	41.5692i	−0.0944882	−	0.0545528i
$763$		0			0
$764$			232.095i			0.303789i
$765$	−243.000	+	420.888i	−0.317647	+	0.550181i
$766$	−483.000	+	836.581i	−0.630548	+	1.09214i
$767$			200.918i			0.261953i
$768$	268.500	+	465.056i	0.349609	+	0.605541i
$769$	−511.000	+	885.078i	−0.664499	+	1.15095i	0.314921	+	0.949118i	$0.398022\pi$
$769$	−511.000	+	885.078i	−0.664499	+	1.15095i	−0.979421	+	0.201829i	$0.935312\pi$
$770$		0			0
$771$		−	524.811i		−	0.680689i
$772$	132.500	−	229.497i	0.171632	−	0.297276i
$773$	−1026.00	−	592.361i	−1.32730	−	0.766315i	−0.342416	−	0.939549i	$-0.611245\pi$
$773$	−1026.00	−	592.361i	−1.32730	−	0.766315i	−0.984881	+	0.173234i	$0.944578\pi$
$774$			950.896i			1.22855i
$775$	−208.000	−	360.267i	−0.268387	−	0.464860i
$776$	862.500	−	497.965i	1.11147	−	0.641707i
$777$		0			0
$778$	447.000	−	774.227i	0.574550	−	0.995150i
$779$			133.368i			0.171204i
$780$			41.5692i

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.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{2} +3.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(4.50000 + 2.59808i) q^{6} -8.66025i q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{2} +3.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(4.50000 + 2.59808i) q^{6} -8.66025i q^{8} +9.00000 q^{9} +(3.00000 - 5.19615i) q^{10} -1.73205i q^{11} +(-1.50000 - 2.59808i) q^{12} +(2.00000 - 3.46410i) q^{13} -10.3923i q^{15} +(5.50000 - 9.52628i) q^{16} +(-13.5000 - 7.79423i) q^{17} +(13.5000 + 7.79423i) q^{18} +(-5.50000 - 9.52628i) q^{19} +(-3.00000 + 1.73205i) q^{20} +(1.50000 - 2.59808i) q^{22} +27.7128i q^{23} -25.9808i q^{24} +13.0000 q^{25} +(6.00000 - 3.46410i) q^{26} +27.0000 q^{27} +(39.0000 - 22.5167i) q^{29} +(9.00000 - 15.5885i) q^{30} +(-16.0000 - 27.7128i) q^{31} +(-13.5000 + 7.79423i) q^{32} -5.19615i q^{33} +(-13.5000 - 23.3827i) q^{34} +(-4.50000 - 7.79423i) q^{36} +(17.0000 + 29.4449i) q^{37} -19.0526i q^{38} +(6.00000 - 10.3923i) q^{39} -30.0000 q^{40} +(-10.5000 - 6.06218i) q^{41} +(30.5000 + 52.8275i) q^{43} +(-1.50000 + 0.866025i) q^{44} -31.1769i q^{45} +(-24.0000 + 41.5692i) q^{46} +(42.0000 + 24.2487i) q^{47} +(16.5000 - 28.5788i) q^{48} +(19.5000 + 11.2583i) q^{50} +(-40.5000 - 23.3827i) q^{51} -4.00000 q^{52} +(40.5000 + 23.3827i) q^{54} -6.00000 q^{55} +(-16.5000 - 28.5788i) q^{57} +78.0000 q^{58} +(-43.5000 + 25.1147i) q^{59} +(-9.00000 + 5.19615i) q^{60} +(-28.0000 + 48.4974i) q^{61} -55.4256i q^{62} -71.0000 q^{64} +(-12.0000 - 6.92820i) q^{65} +(4.50000 - 7.79423i) q^{66} +(15.5000 + 26.8468i) q^{67} +15.5885i q^{68} +83.1384i q^{69} -31.1769i q^{71} -77.9423i q^{72} +(-32.5000 + 56.2917i) q^{73} +58.8897i q^{74} +39.0000 q^{75} +(-5.50000 + 9.52628i) q^{76} +(18.0000 - 10.3923i) q^{78} +(-19.0000 + 32.9090i) q^{79} +(-33.0000 - 19.0526i) q^{80} +81.0000 q^{81} +(-10.5000 - 18.1865i) q^{82} +(-42.0000 + 24.2487i) q^{83} +(-27.0000 + 46.7654i) q^{85} +105.655i q^{86} +(117.000 - 67.5500i) q^{87} -15.0000 q^{88} +(108.000 - 62.3538i) q^{89} +(27.0000 - 46.7654i) q^{90} +(24.0000 - 13.8564i) q^{92} +(-48.0000 - 83.1384i) q^{93} +(42.0000 + 72.7461i) q^{94} +(-33.0000 + 19.0526i) q^{95} +(-40.5000 + 23.3827i) q^{96} +(57.5000 + 99.5929i) q^{97} -15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2q + 3q^{2} + 6q^{3} - q^{4} + 9q^{6} + 18q^{9} + O(q^{10}) \)	\( 2q + 3q^{2} + 6q^{3} - q^{4} + 9q^{6} + 18q^{9} + 6q^{10} - 3q^{12} + 4q^{13} + 11q^{16} - 27q^{17} + 27q^{18} - 11q^{19} - 6q^{20} + 3q^{22} + 26q^{25} + 12q^{26} + 54q^{27} + 78q^{29} + 18q^{30} - 32q^{31} - 27q^{32} - 27q^{34} - 9q^{36} + 34q^{37} + 12q^{39} - 60q^{40} - 21q^{41} + 61q^{43} - 3q^{44} - 48q^{46} + 84q^{47} + 33q^{48} + 39q^{50} - 81q^{51} - 8q^{52} + 81q^{54} - 12q^{55} - 33q^{57} + 156q^{58} - 87q^{59} - 18q^{60} - 56q^{61} - 142q^{64} - 24q^{65} + 9q^{66} + 31q^{67} - 65q^{73} + 78q^{75} - 11q^{76} + 36q^{78} - 38q^{79} - 66q^{80} + 162q^{81} - 21q^{82} - 84q^{83} - 54q^{85} + 234q^{87} - 30q^{88} + 216q^{89} + 54q^{90} + 48q^{92} - 96q^{93} + 84q^{94} - 66q^{95} - 81q^{96} + 115q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more