LMFDB - Embedded newform 585.2.h.c.64.2

Newspace parameters

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.h (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	585.64
Dual form			585.2.h.c.64.1

$q$-expansion

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -3.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -3.00000 q^{8} +(1.00000 + 2.00000i) q^{10} +2.00000i q^{11} +(3.00000 + 2.00000i) q^{13} -1.00000 q^{16} +6.00000i q^{19} +(-1.00000 - 2.00000i) q^{20} +2.00000i q^{22} +6.00000i q^{23} +(-3.00000 + 4.00000i) q^{25} +(3.00000 + 2.00000i) q^{26} -6.00000 q^{29} -6.00000i q^{31} +5.00000 q^{32} +6.00000 q^{37} +6.00000i q^{38} +(-3.00000 - 6.00000i) q^{40} -8.00000i q^{41} +6.00000i q^{43} -2.00000i q^{44} +6.00000i q^{46} +8.00000 q^{47} -7.00000 q^{49} +(-3.00000 + 4.00000i) q^{50} +(-3.00000 - 2.00000i) q^{52} -12.0000i q^{53} +(-4.00000 + 2.00000i) q^{55} -6.00000 q^{58} +2.00000i q^{59} +6.00000 q^{61} -6.00000i q^{62} +7.00000 q^{64} +(-1.00000 + 8.00000i) q^{65} +12.0000 q^{67} -2.00000i q^{71} -6.00000 q^{73} +6.00000 q^{74} -6.00000i q^{76} +(-1.00000 - 2.00000i) q^{80} -8.00000i q^{82} +4.00000 q^{83} +6.00000i q^{86} -6.00000i q^{88} -8.00000i q^{89} -6.00000i q^{92} +8.00000 q^{94} +(-12.0000 + 6.00000i) q^{95} -6.00000 q^{97} -7.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 6 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 6 * q^8	$ 2 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 6 q^{8} + 2 q^{10} + 6 q^{13} - 2 q^{16} - 2 q^{20} - 6 q^{25} + 6 q^{26} - 12 q^{29} + 10 q^{32} + 12 q^{37} - 6 q^{40} + 16 q^{47} - 14 q^{49} - 6 q^{50} - 6 q^{52} - 8 q^{55} - 12 q^{58} + 12 q^{61} + 14 q^{64} - 2 q^{65} + 24 q^{67} - 12 q^{73} + 12 q^{74} - 2 q^{80} + 8 q^{83} + 16 q^{94} - 24 q^{95} - 12 q^{97} - 14 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 6 * q^8 + 2 * q^10 + 6 * q^13 - 2 * q^16 - 2 * q^20 - 6 * q^25 + 6 * q^26 - 12 * q^29 + 10 * q^32 + 12 * q^37 - 6 * q^40 + 16 * q^47 - 14 * q^49 - 6 * q^50 - 6 * q^52 - 8 * q^55 - 12 * q^58 + 12 * q^61 + 14 * q^64 - 2 * q^65 + 24 * q^67 - 12 * q^73 + 12 * q^74 - 2 * q^80 + 8 * q^83 + 16 * q^94 - 24 * q^95 - 12 * q^97 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.00000			0.707107			0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000			0.707107			0.353553	+	0.935414i	$0.384973\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$		0			0
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$	−3.00000			−1.06066
$9$		0			0
$10$	1.00000	+	2.00000i	0.316228	+	0.632456i
$11$			2.00000i			0.603023i	0.953463	+	0.301511i	$0.0974911\pi$
$11$			2.00000i			0.603023i	−0.953463	+	0.301511i	$0.902509\pi$
$12$		0			0
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$14$		0			0
$15$		0			0
$16$	−1.00000			−0.250000
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$		0			0
$19$			6.00000i			1.37649i	0.725476	+	0.688247i	$0.241620\pi$
$19$			6.00000i			1.37649i	−0.725476	+	0.688247i	$0.758380\pi$
$20$	−1.00000	−	2.00000i	−0.223607	−	0.447214i
$21$		0			0
$22$			2.00000i			0.426401i
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	3.00000	+	2.00000i	0.588348	+	0.392232i
$27$		0			0
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$		−	6.00000i		−	1.07763i	−0.842424	−	0.538816i	$-0.818872\pi$
$31$		−	6.00000i		−	1.07763i	0.842424	−	0.538816i	$-0.181128\pi$
$32$	5.00000			0.883883
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$			6.00000i			0.973329i
$39$		0			0
$40$	−3.00000	−	6.00000i	−0.474342	−	0.948683i
$41$		−	8.00000i		−	1.24939i	−0.780869	−	0.624695i	$-0.785223\pi$
$41$		−	8.00000i		−	1.24939i	0.780869	−	0.624695i	$-0.214777\pi$
$42$		0			0
$43$			6.00000i			0.914991i	0.889212	+	0.457496i	$0.151253\pi$
$43$			6.00000i			0.914991i	−0.889212	+	0.457496i	$0.848747\pi$
$44$		−	2.00000i		−	0.301511i
$45$		0			0
$46$			6.00000i			0.884652i
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$		0			0
$49$	−7.00000			−1.00000
$50$	−3.00000	+	4.00000i	−0.424264	+	0.565685i
$51$		0			0
$52$	−3.00000	−	2.00000i	−0.416025	−	0.277350i
$53$		−	12.0000i		−	1.64833i	−0.566352	−	0.824163i	$-0.691646\pi$
$53$		−	12.0000i		−	1.64833i	0.566352	−	0.824163i	$-0.308354\pi$
$54$		0			0
$55$	−4.00000	+	2.00000i	−0.539360	+	0.269680i
$56$		0			0
$57$		0			0
$58$	−6.00000			−0.787839
$59$			2.00000i			0.260378i	0.991489	+	0.130189i	$0.0415584\pi$
$59$			2.00000i			0.260378i	−0.991489	+	0.130189i	$0.958442\pi$
$60$		0			0
$61$	6.00000			0.768221			0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000			0.768221			0.384111	+	0.923287i	$0.374508\pi$
$62$		−	6.00000i		−	0.762001i
$63$		0			0
$64$	7.00000			0.875000
$65$	−1.00000	+	8.00000i	−0.124035	+	0.992278i
$66$		0			0
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	2.00000i		−	0.237356i	−0.992933	−	0.118678i	$-0.962134\pi$
$71$		−	2.00000i		−	0.237356i	0.992933	−	0.118678i	$-0.0378657\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	6.00000			0.697486
$75$		0			0
$76$		−	6.00000i		−	0.688247i
$77$		0			0
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	−1.00000	−	2.00000i	−0.111803	−	0.223607i
$81$		0			0
$82$		−	8.00000i		−	0.883452i
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$		0			0
$85$		0			0
$86$			6.00000i			0.646997i
$87$		0			0
$88$		−	6.00000i		−	0.639602i
$89$		−	8.00000i		−	0.847998i	−0.905663	−	0.423999i	$-0.860626\pi$
$89$		−	8.00000i		−	0.847998i	0.905663	−	0.423999i	$-0.139374\pi$
$90$		0			0
$91$		0			0
$92$		−	6.00000i		−	0.625543i
$93$		0			0
$94$	8.00000			0.825137
$95$	−12.0000	+	6.00000i	−1.23117	+	0.615587i
$96$		0			0
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$	−7.00000			−0.707107
$99$		0			0
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$		0			0
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$	−9.00000	−	6.00000i	−0.882523	−	0.588348i
$105$		0			0
$106$		−	12.0000i		−	1.16554i
$107$		−	6.00000i		−	0.580042i	−0.957020	−	0.290021i	$-0.906338\pi$
$107$		−	6.00000i		−	0.580042i	0.957020	−	0.290021i	$-0.0936623\pi$
$108$		0			0
$109$		−	12.0000i		−	1.14939i	−0.818367	−	0.574696i	$-0.805120\pi$
$109$		−	12.0000i		−	1.14939i	0.818367	−	0.574696i	$-0.194880\pi$
$110$	−4.00000	+	2.00000i	−0.381385	+	0.190693i
$111$		0			0
$112$		0			0
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$		0			0
$115$	−12.0000	+	6.00000i	−1.11901	+	0.559503i
$116$	6.00000			0.557086
$117$		0			0
$118$			2.00000i			0.184115i
$119$		0			0
$120$		0			0
$121$	7.00000			0.636364
$122$	6.00000			0.543214
$123$		0			0
$124$			6.00000i			0.538816i
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$	−3.00000			−0.265165
$129$		0			0
$130$	−1.00000	+	8.00000i	−0.0877058	+	0.701646i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$		0			0
$134$	12.0000			1.03664
$135$		0			0
$136$		0			0
$137$	−2.00000			−0.170872			−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000			−0.170872			−0.0854358	+	0.996344i	$0.527228\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$		0			0
$142$		−	2.00000i		−	0.167836i
$143$	−4.00000	+	6.00000i	−0.334497	+	0.501745i
$144$		0			0
$145$	−6.00000	−	12.0000i	−0.498273	−	0.996546i
$146$	−6.00000			−0.496564
$147$		0			0
$148$	−6.00000			−0.493197
$149$			20.0000i			1.63846i	0.573462	+	0.819232i	$0.305600\pi$
$149$			20.0000i			1.63846i	−0.573462	+	0.819232i	$0.694400\pi$
$150$		0			0
$151$			18.0000i			1.46482i	0.680864	+	0.732410i	$0.261604\pi$
$151$			18.0000i			1.46482i	−0.680864	+	0.732410i	$0.738396\pi$
$152$		−	18.0000i		−	1.45999i
$153$		0			0
$154$		0			0
$155$	12.0000	−	6.00000i	0.963863	−	0.481932i
$156$		0			0
$157$		−	12.0000i		−	0.957704i	−0.877896	−	0.478852i	$-0.841053\pi$
$157$		−	12.0000i		−	0.957704i	0.877896	−	0.478852i	$-0.158947\pi$
$158$		0			0
$159$		0			0
$160$	5.00000	+	10.0000i	0.395285	+	0.790569i
$161$		0			0
$162$		0			0
$163$	12.0000			0.939913			0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000			0.939913			0.469956	+	0.882690i	$0.344270\pi$
$164$			8.00000i			0.624695i
$165$		0			0
$166$	4.00000			0.310460
$167$	16.0000			1.23812			0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000			1.23812			0.619059	+	0.785345i	$0.287514\pi$
$168$		0			0
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$		0			0
$171$		0			0
$172$		−	6.00000i		−	0.457496i
$173$			12.0000i			0.912343i	0.889892	+	0.456172i	$0.150780\pi$
$173$			12.0000i			0.912343i	−0.889892	+	0.456172i	$0.849220\pi$
$174$		0			0
$175$		0			0
$176$		−	2.00000i		−	0.150756i
$177$		0			0
$178$		−	8.00000i		−	0.599625i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$		0			0
$184$		−	18.0000i		−	1.32698i
$185$	6.00000	+	12.0000i	0.441129	+	0.882258i
$186$		0			0
$187$		0			0
$188$	−8.00000			−0.583460
$189$		0			0
$190$	−12.0000	+	6.00000i	−0.870572	+	0.435286i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$	−6.00000			−0.431889			−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000			−0.431889			−0.215945	+	0.976406i	$0.569283\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	7.00000			0.500000
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	−24.0000			−1.70131			−0.850657	−	0.525720i	$-0.823796\pi$
$199$	−24.0000			−1.70131			−0.850657	+	0.525720i	$0.823796\pi$
$200$	9.00000	−	12.0000i	0.636396	−	0.848528i
$201$		0			0
$202$	−6.00000			−0.422159
$203$		0			0
$204$		0			0
$205$	16.0000	−	8.00000i	1.11749	−	0.558744i
$206$		−	6.00000i		−	0.418040i
$207$		0			0
$208$	−3.00000	−	2.00000i	−0.208013	−	0.138675i
$209$	−12.0000			−0.830057
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$			12.0000i			0.824163i
$213$		0			0
$214$		−	6.00000i		−	0.410152i
$215$	−12.0000	+	6.00000i	−0.818393	+	0.409197i
$216$		0			0
$217$		0			0
$218$		−	12.0000i		−	0.812743i
$219$		0			0
$220$	4.00000	−	2.00000i	0.269680	−	0.134840i
$221$		0			0
$222$		0			0
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.00000			0.265489			0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000			0.265489			0.132745	+	0.991150i	$0.457621\pi$
$228$		0			0
$229$			12.0000i			0.792982i	0.918039	+	0.396491i	$0.129772\pi$
$229$			12.0000i			0.792982i	−0.918039	+	0.396491i	$0.870228\pi$
$230$	−12.0000	+	6.00000i	−0.791257	+	0.395628i
$231$		0			0
$232$	18.0000			1.18176
$233$		−	24.0000i		−	1.57229i	−0.618041	−	0.786146i	$-0.712073\pi$
$233$		−	24.0000i		−	1.57229i	0.618041	−	0.786146i	$-0.287927\pi$
$234$		0			0
$235$	8.00000	+	16.0000i	0.521862	+	1.04372i
$236$		−	2.00000i		−	0.130189i
$237$		0			0
$238$		0			0
$239$		−	10.0000i		−	0.646846i	−0.946254	−	0.323423i	$-0.895166\pi$
$239$		−	10.0000i		−	0.646846i	0.946254	−	0.323423i	$-0.104834\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	7.00000			0.449977
$243$		0			0
$244$	−6.00000			−0.384111
$245$	−7.00000	−	14.0000i	−0.447214	−	0.894427i
$246$		0			0
$247$	−12.0000	+	18.0000i	−0.763542	+	1.14531i
$248$			18.0000i			1.14300i
$249$		0			0
$250$	−11.0000	−	2.00000i	−0.695701	−	0.126491i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$			2.00000i			0.125491i
$255$		0			0
$256$	−17.0000			−1.06250
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$		0			0
$259$		0			0
$260$	1.00000	−	8.00000i	0.0620174	−	0.496139i
$261$		0			0
$262$	12.0000			0.741362
$263$			6.00000i			0.369976i	0.982741	+	0.184988i	$0.0592246\pi$
$263$			6.00000i			0.369976i	−0.982741	+	0.184988i	$0.940775\pi$
$264$		0			0
$265$	24.0000	−	12.0000i	1.47431	−	0.737154i
$266$		0			0
$267$		0			0
$268$	−12.0000			−0.733017
$269$	18.0000			1.09748			0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$		0			0
$271$		−	6.00000i		−	0.364474i	−0.983255	−	0.182237i	$-0.941666\pi$
$271$		−	6.00000i		−	0.364474i	0.983255	−	0.182237i	$-0.0583338\pi$
$272$		0			0
$273$		0			0
$274$	−2.00000			−0.120824
$275$	−8.00000	−	6.00000i	−0.482418	−	0.361814i
$276$		0			0
$277$			12.0000i			0.721010i	0.932757	+	0.360505i	$0.117396\pi$
$277$			12.0000i			0.721010i	−0.932757	+	0.360505i	$0.882604\pi$
$278$	−4.00000			−0.239904
$279$		0			0
$280$		0			0
$281$			8.00000i			0.477240i	0.971113	+	0.238620i	$0.0766950\pi$
$281$			8.00000i			0.477240i	−0.971113	+	0.238620i	$0.923305\pi$
$282$		0			0
$283$			22.0000i			1.30776i	0.756596	+	0.653882i	$0.226861\pi$
$283$			22.0000i			1.30776i	−0.756596	+	0.653882i	$0.773139\pi$
$284$			2.00000i			0.118678i
$285$		0			0
$286$	−4.00000	+	6.00000i	−0.236525	+	0.354787i
$287$		0			0
$288$		0			0
$289$	17.0000			1.00000
$290$	−6.00000	−	12.0000i	−0.352332	−	0.704664i
$291$		0			0
$292$	6.00000			0.351123
$293$	26.0000			1.51894			0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000			1.51894			0.759468	+	0.650545i	$0.225459\pi$
$294$		0			0
$295$	−4.00000	+	2.00000i	−0.232889	+	0.116445i
$296$	−18.0000			−1.04623
$297$		0			0
$298$			20.0000i			1.15857i
$299$	−12.0000	+	18.0000i	−0.693978	+	1.04097i
$300$		0			0
$301$		0			0
$302$			18.0000i			1.03578i
$303$		0			0
$304$		−	6.00000i		−	0.344124i
$305$	6.00000	+	12.0000i	0.343559	+	0.687118i
$306$		0			0
$307$	12.0000			0.684876			0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000			0.684876			0.342438	+	0.939540i	$0.388747\pi$
$308$		0			0
$309$		0			0
$310$	12.0000	−	6.00000i	0.681554	−	0.340777i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$		−	8.00000i		−	0.452187i	−0.974106	−	0.226093i	$-0.927405\pi$
$313$		−	8.00000i		−	0.452187i	0.974106	−	0.226093i	$-0.0725954\pi$
$314$		−	12.0000i		−	0.677199i
$315$		0			0
$316$		0			0
$317$	2.00000			0.112331			0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000			0.112331			0.0561656	+	0.998421i	$0.482113\pi$
$318$		0			0
$319$		−	12.0000i		−	0.671871i
$320$	7.00000	+	14.0000i	0.391312	+	0.782624i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−17.0000	+	6.00000i	−0.942990	+	0.332820i
$326$	12.0000			0.664619
$327$		0			0
$328$			24.0000i			1.32518i
$329$		0			0
$330$		0			0
$331$			30.0000i			1.64895i	0.565899	+	0.824475i	$0.308529\pi$
$331$			30.0000i			1.64895i	−0.565899	+	0.824475i	$0.691471\pi$
$332$	−4.00000			−0.219529
$333$		0			0
$334$	16.0000			0.875481
$335$	12.0000	+	24.0000i	0.655630	+	1.31126i
$336$		0			0
$337$		−	32.0000i		−	1.74315i	−0.490261	−	0.871576i	$-0.663099\pi$
$337$		−	32.0000i		−	1.74315i	0.490261	−	0.871576i	$-0.336901\pi$
$338$	5.00000	+	12.0000i	0.271964	+	0.652714i
$339$		0			0
$340$		0			0
$341$	12.0000			0.649836
$342$		0			0
$343$		0			0
$344$		−	18.0000i		−	0.970495i
$345$		0			0
$346$			12.0000i			0.645124i
$347$		−	6.00000i		−	0.322097i	−0.986947	−	0.161048i	$-0.948512\pi$
$347$		−	6.00000i		−	0.322097i	0.986947	−	0.161048i	$-0.0514875\pi$
$348$		0			0
$349$		−	12.0000i		−	0.642345i	−0.947021	−	0.321173i	$-0.895923\pi$
$349$		−	12.0000i		−	0.642345i	0.947021	−	0.321173i	$-0.104077\pi$
$350$		0			0
$351$		0			0
$352$			10.0000i			0.533002i
$353$	14.0000			0.745145			0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000			0.745145			0.372572	+	0.928003i	$0.378476\pi$
$354$		0			0
$355$	4.00000	−	2.00000i	0.212298	−	0.106149i
$356$			8.00000i			0.423999i
$357$		0			0
$358$	12.0000			0.634220
$359$		−	2.00000i		−	0.105556i	−0.998606	−	0.0527780i	$-0.983192\pi$
$359$		−	2.00000i		−	0.105556i	0.998606	−	0.0527780i	$-0.0168076\pi$
$360$		0			0
$361$	−17.0000			−0.894737
$362$	−2.00000			−0.105118
$363$		0			0
$364$		0			0
$365$	−6.00000	−	12.0000i	−0.314054	−	0.628109i
$366$		0			0
$367$			18.0000i			0.939592i	0.882775	+	0.469796i	$0.155673\pi$
$367$			18.0000i			0.939592i	−0.882775	+	0.469796i	$0.844327\pi$
$368$		−	6.00000i		−	0.312772i
$369$		0			0
$370$	6.00000	+	12.0000i	0.311925	+	0.623850i
$371$		0			0
$372$		0			0
$373$		−	4.00000i		−	0.207112i	−0.994624	−	0.103556i	$-0.966978\pi$
$373$		−	4.00000i		−	0.207112i	0.994624	−	0.103556i	$-0.0330221\pi$
$374$		0			0
$375$		0			0
$376$	−24.0000			−1.23771
$377$	−18.0000	−	12.0000i	−0.927047	−	0.618031i
$378$		0			0
$379$		−	18.0000i		−	0.924598i	−0.886724	−	0.462299i	$-0.847025\pi$
$379$		−	18.0000i		−	0.924598i	0.886724	−	0.462299i	$-0.152975\pi$
$380$	12.0000	−	6.00000i	0.615587	−	0.307794i
$381$		0			0
$382$		0			0
$383$	−8.00000			−0.408781			−0.204390	−	0.978889i	$-0.565521\pi$
$383$	−8.00000			−0.408781			−0.204390	+	0.978889i	$0.565521\pi$
$384$		0			0
$385$		0			0
$386$	−6.00000			−0.305392
$387$		0			0
$388$	6.00000			0.304604
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$		0			0
$392$	21.0000			1.06066
$393$		0			0
$394$	2.00000			0.100759
$395$		0			0
$396$		0			0
$397$	−18.0000			−0.903394			−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000			−0.903394			−0.451697	+	0.892171i	$0.649181\pi$
$398$	−24.0000			−1.20301
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$			16.0000i			0.799002i	0.916733	+	0.399501i	$0.130817\pi$
$401$			16.0000i			0.799002i	−0.916733	+	0.399501i	$0.869183\pi$
$402$		0			0
$403$	12.0000	−	18.0000i	0.597763	−	0.896644i
$404$	6.00000			0.298511
$405$		0			0
$406$		0			0
$407$			12.0000i			0.594818i
$408$		0			0
$409$			24.0000i			1.18672i	0.804936	+	0.593362i	$0.202200\pi$
$409$			24.0000i			1.18672i	−0.804936	+	0.593362i	$0.797800\pi$
$410$	16.0000	−	8.00000i	0.790184	−	0.395092i
$411$		0			0
$412$			6.00000i			0.295599i
$413$		0			0
$414$		0			0
$415$	4.00000	+	8.00000i	0.196352	+	0.392705i
$416$	15.0000	+	10.0000i	0.735436	+	0.490290i
$417$		0			0
$418$	−12.0000			−0.586939
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$		−	36.0000i		−	1.75453i	−0.480004	−	0.877266i	$-0.659365\pi$
$421$		−	36.0000i		−	1.75453i	0.480004	−	0.877266i	$-0.340635\pi$
$422$	−12.0000			−0.584151
$423$		0			0
$424$			36.0000i			1.74831i
$425$		0			0
$426$		0			0
$427$		0			0
$428$			6.00000i			0.290021i
$429$		0			0
$430$	−12.0000	+	6.00000i	−0.578691	+	0.289346i
$431$		−	10.0000i		−	0.481683i	−0.970564	−	0.240842i	$-0.922577\pi$
$431$		−	10.0000i		−	0.481683i	0.970564	−	0.240842i	$-0.0774234\pi$
$432$		0			0
$433$		−	16.0000i		−	0.768911i	−0.923144	−	0.384455i	$-0.874389\pi$
$433$		−	16.0000i		−	0.768911i	0.923144	−	0.384455i	$-0.125611\pi$
$434$		0			0
$435$		0			0
$436$			12.0000i			0.574696i
$437$	−36.0000			−1.72211
$438$		0			0
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$	12.0000	−	6.00000i	0.572078	−	0.286039i
$441$		0			0
$442$		0			0
$443$		−	6.00000i		−	0.285069i	−0.989790	−	0.142534i	$-0.954475\pi$
$443$		−	6.00000i		−	0.285069i	0.989790	−	0.142534i	$-0.0455251\pi$
$444$		0			0
$445$	16.0000	−	8.00000i	0.758473	−	0.379236i
$446$	24.0000			1.13643
$447$		0			0
$448$		0			0
$449$		−	16.0000i		−	0.755087i	−0.925992	−	0.377543i	$-0.876769\pi$
$449$		−	16.0000i		−	0.755087i	0.925992	−	0.377543i	$-0.123231\pi$
$450$		0			0
$451$	16.0000			0.753411
$452$		0			0
$453$		0			0
$454$	4.00000			0.187729
$455$		0			0
$456$		0			0
$457$	−30.0000			−1.40334			−0.701670	−	0.712502i	$-0.747562\pi$
$457$	−30.0000			−1.40334			−0.701670	+	0.712502i	$0.747562\pi$
$458$			12.0000i			0.560723i
$459$		0			0
$460$	12.0000	−	6.00000i	0.559503	−	0.279751i
$461$		−	4.00000i		−	0.186299i	−0.995652	−	0.0931493i	$-0.970307\pi$
$461$		−	4.00000i		−	0.186299i	0.995652	−	0.0931493i	$-0.0296934\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$	6.00000			0.278543
$465$		0			0
$466$		−	24.0000i		−	1.11178i
$467$			18.0000i			0.832941i	0.909149	+	0.416470i	$0.136733\pi$
$467$			18.0000i			0.832941i	−0.909149	+	0.416470i	$0.863267\pi$
$468$		0			0
$469$		0			0
$470$	8.00000	+	16.0000i	0.369012	+	0.738025i
$471$		0			0
$472$		−	6.00000i		−	0.276172i
$473$	−12.0000			−0.551761
$474$		0			0
$475$	−24.0000	−	18.0000i	−1.10120	−	0.825897i
$476$		0			0
$477$		0			0
$478$		−	10.0000i		−	0.457389i
$479$			22.0000i			1.00521i	0.864517	+	0.502603i	$0.167624\pi$
$479$			22.0000i			1.00521i	−0.864517	+	0.502603i	$0.832376\pi$
$480$		0			0
$481$	18.0000	+	12.0000i	0.820729	+	0.547153i
$482$		0			0
$483$		0			0
$484$	−7.00000			−0.318182
$485$	−6.00000	−	12.0000i	−0.272446	−	0.544892i
$486$		0			0
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$	−18.0000			−0.814822
$489$		0			0
$490$	−7.00000	−	14.0000i	−0.316228	−	0.632456i
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$		0			0
$493$		0			0
$494$	−12.0000	+	18.0000i	−0.539906	+	0.809858i
$495$		0			0
$496$			6.00000i			0.269408i
$497$		0			0
$498$		0			0
$499$			6.00000i			0.268597i	0.990941	+	0.134298i	$0.0428781\pi$
$499$			6.00000i			0.268597i	−0.990941	+	0.134298i	$0.957122\pi$
$500$	11.0000	+	2.00000i	0.491935	+	0.0894427i
$501$		0			0
$502$	−12.0000			−0.535586
$503$			6.00000i			0.267527i	0.991013	+	0.133763i	$0.0427062\pi$
$503$			6.00000i			0.267527i	−0.991013	+	0.133763i	$0.957294\pi$
$504$		0			0
$505$	−6.00000	−	12.0000i	−0.266996	−	0.533993i
$506$	−12.0000			−0.533465
$507$		0			0
$508$		−	2.00000i		−	0.0887357i
$509$		−	20.0000i		−	0.886484i	−0.896402	−	0.443242i	$-0.853828\pi$
$509$		−	20.0000i		−	0.886484i	0.896402	−	0.443242i	$-0.146172\pi$
$510$		0			0
$511$		0			0
$512$	−11.0000			−0.486136
$513$		0			0
$514$		0			0
$515$	12.0000	−	6.00000i	0.528783	−	0.264392i
$516$		0			0
$517$			16.0000i			0.703679i
$518$		0			0
$519$		0			0
$520$	3.00000	−	24.0000i	0.131559	−	1.05247i
$521$	30.0000			1.31432			0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000			1.31432			0.657162	+	0.753749i	$0.271757\pi$
$522$		0			0
$523$		−	42.0000i		−	1.83653i	−0.395964	−	0.918266i	$-0.629590\pi$
$523$		−	42.0000i		−	1.83653i	0.395964	−	0.918266i	$-0.370410\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$			6.00000i			0.261612i
$527$		0			0
$528$		0			0
$529$	−13.0000			−0.565217
$530$	24.0000	−	12.0000i	1.04249	−	0.521247i
$531$		0			0
$532$		0			0
$533$	16.0000	−	24.0000i	0.693037	−	1.03956i
$534$		0			0
$535$	12.0000	−	6.00000i	0.518805	−	0.259403i
$536$	−36.0000			−1.55496
$537$		0			0
$538$	18.0000			0.776035
$539$		−	14.0000i		−	0.603023i
$540$		0			0
$541$		−	12.0000i		−	0.515920i	−0.966156	−	0.257960i	$-0.916950\pi$
$541$		−	12.0000i		−	0.515920i	0.966156	−	0.257960i	$-0.0830503\pi$
$542$		−	6.00000i		−	0.257722i
$543$		0			0
$544$		0			0
$545$	24.0000	−	12.0000i	1.02805	−	0.514024i
$546$		0			0
$547$		−	18.0000i		−	0.769624i	−0.922995	−	0.384812i	$-0.874266\pi$
$547$		−	18.0000i		−	0.769624i	0.922995	−	0.384812i	$-0.125734\pi$
$548$	2.00000			0.0854358
$549$		0			0
$550$	−8.00000	−	6.00000i	−0.341121	−	0.255841i
$551$		−	36.0000i		−	1.53365i
$552$		0			0
$553$		0			0
$554$			12.0000i			0.509831i
$555$		0			0
$556$	4.00000			0.169638
$557$	−14.0000			−0.593199			−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000			−0.593199			−0.296600	+	0.955002i	$0.595853\pi$
$558$		0			0
$559$	−12.0000	+	18.0000i	−0.507546	+	0.761319i
$560$		0			0
$561$		0			0
$562$			8.00000i			0.337460i
$563$		−	30.0000i		−	1.26435i	−0.774826	−	0.632175i	$-0.782163\pi$
$563$		−	30.0000i		−	1.26435i	0.774826	−	0.632175i	$-0.217837\pi$
$564$		0			0
$565$		0			0
$566$			22.0000i			0.924729i
$567$		0			0
$568$			6.00000i			0.251754i
$569$	−18.0000			−0.754599			−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000			−0.754599			−0.377300	+	0.926091i	$0.623147\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$	4.00000	−	6.00000i	0.167248	−	0.250873i
$573$		0			0
$574$		0			0
$575$	−24.0000	−	18.0000i	−1.00087	−	0.750652i
$576$		0			0
$577$	18.0000			0.749350			0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000			0.749350			0.374675	+	0.927156i	$0.377754\pi$
$578$	17.0000			0.707107
$579$		0			0
$580$	6.00000	+	12.0000i	0.249136	+	0.498273i
$581$		0			0
$582$		0			0
$583$	24.0000			0.993978
$584$	18.0000			0.744845
$585$		0			0
$586$	26.0000			1.07405
$587$	−20.0000			−0.825488			−0.412744	−	0.910847i	$-0.635430\pi$
$587$	−20.0000			−0.825488			−0.412744	+	0.910847i	$0.635430\pi$
$588$		0			0
$589$	36.0000			1.48335
$590$	−4.00000	+	2.00000i	−0.164677	+	0.0823387i
$591$		0			0
$592$	−6.00000			−0.246598
$593$	22.0000			0.903432			0.451716	−	0.892162i	$-0.350812\pi$
$593$	22.0000			0.903432			0.451716	+	0.892162i	$0.350812\pi$
$594$		0			0
$595$		0			0
$596$		−	20.0000i		−	0.819232i
$597$		0			0
$598$	−12.0000	+	18.0000i	−0.490716	+	0.736075i
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	−6.00000			−0.244745			−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000			−0.244745			−0.122373	+	0.992484i	$0.539050\pi$
$602$		0			0
$603$		0			0
$604$		−	18.0000i		−	0.732410i
$605$	7.00000	+	14.0000i	0.284590	+	0.569181i
$606$		0			0
$607$			18.0000i			0.730597i	0.930890	+	0.365299i	$0.119033\pi$
$607$			18.0000i			0.730597i	−0.930890	+	0.365299i	$0.880967\pi$
$608$			30.0000i			1.21666i
$609$		0			0
$610$	6.00000	+	12.0000i	0.242933	+	0.485866i
$611$	24.0000	+	16.0000i	0.970936	+	0.647291i
$612$		0			0
$613$	30.0000			1.21169			0.605844	−	0.795583i	$-0.292835\pi$
$613$	30.0000			1.21169			0.605844	+	0.795583i	$0.292835\pi$
$614$	12.0000			0.484281
$615$		0			0
$616$		0			0
$617$	−34.0000			−1.36879			−0.684394	−	0.729112i	$-0.739933\pi$
$617$	−34.0000			−1.36879			−0.684394	+	0.729112i	$0.739933\pi$
$618$		0			0
$619$		−	18.0000i		−	0.723481i	−0.932279	−	0.361741i	$-0.882183\pi$
$619$		−	18.0000i		−	0.723481i	0.932279	−	0.361741i	$-0.117817\pi$
$620$	−12.0000	+	6.00000i	−0.481932	+	0.240966i
$621$		0			0
$622$	−24.0000			−0.962312
$623$		0			0
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		−	8.00000i		−	0.319744i
$627$		0			0
$628$			12.0000i			0.478852i
$629$		0			0
$630$		0			0
$631$		−	30.0000i		−	1.19428i	−0.802137	−	0.597141i	$-0.796303\pi$
$631$		−	30.0000i		−	1.19428i	0.802137	−	0.597141i	$-0.203697\pi$
$632$		0			0
$633$		0			0
$634$	2.00000			0.0794301
$635$	−4.00000	+	2.00000i	−0.158735	+	0.0793676i
$636$		0			0
$637$	−21.0000	−	14.0000i	−0.832050	−	0.554700i
$638$		−	12.0000i		−	0.475085i
$639$		0			0
$640$	−3.00000	−	6.00000i	−0.118585	−	0.237171i
$641$	30.0000			1.18493			0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000			1.18493			0.592464	+	0.805597i	$0.298155\pi$
$642$		0			0
$643$	−36.0000			−1.41970			−0.709851	−	0.704352i	$-0.751238\pi$
$643$	−36.0000			−1.41970			−0.709851	+	0.704352i	$0.751238\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			6.00000i			0.235884i	0.993020	+	0.117942i	$0.0376297\pi$
$647$			6.00000i			0.235884i	−0.993020	+	0.117942i	$0.962370\pi$
$648$		0			0
$649$	−4.00000			−0.157014
$650$	−17.0000	+	6.00000i	−0.666795	+	0.235339i
$651$		0			0
$652$	−12.0000			−0.469956
$653$		−	36.0000i		−	1.40879i	−0.709809	−	0.704394i	$-0.751219\pi$
$653$		−	36.0000i		−	1.40879i	0.709809	−	0.704394i	$-0.248781\pi$
$654$		0			0
$655$	12.0000	+	24.0000i	0.468879	+	0.937758i
$656$			8.00000i			0.312348i
$657$		0			0
$658$		0			0
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$			12.0000i			0.466746i	0.972387	+	0.233373i	$0.0749763\pi$
$661$			12.0000i			0.466746i	−0.972387	+	0.233373i	$0.925024\pi$
$662$			30.0000i			1.16598i
$663$		0			0
$664$	−12.0000			−0.465690
$665$		0			0
$666$		0			0
$667$		−	36.0000i		−	1.39393i
$668$	−16.0000			−0.619059
$669$		0			0
$670$	12.0000	+	24.0000i	0.463600	+	0.927201i
$671$			12.0000i			0.463255i
$672$		0			0
$673$		−	48.0000i		−	1.85026i	−0.379646	−	0.925132i	$-0.623954\pi$
$673$		−	48.0000i		−	1.85026i	0.379646	−	0.925132i	$-0.376046\pi$
$674$		−	32.0000i		−	1.23259i
$675$		0			0
$676$	−5.00000	−	12.0000i	−0.192308	−	0.461538i
$677$			36.0000i			1.38359i	0.722093	+	0.691796i	$0.243180\pi$
$677$			36.0000i			1.38359i	−0.722093	+	0.691796i	$0.756820\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	12.0000			0.459504
$683$	44.0000			1.68361			0.841807	−	0.539779i	$-0.181492\pi$
$683$	44.0000			1.68361			0.841807	+	0.539779i	$0.181492\pi$
$684$		0			0
$685$	−2.00000	−	4.00000i	−0.0764161	−	0.152832i
$686$		0			0
$687$		0			0
$688$		−	6.00000i		−	0.228748i
$689$	24.0000	−	36.0000i	0.914327	−	1.37149i
$690$		0			0
$691$		−	42.0000i		−	1.59776i	−0.601494	−	0.798878i	$-0.705427\pi$
$691$		−	42.0000i		−	1.59776i	0.601494	−	0.798878i	$-0.294573\pi$
$692$		−	12.0000i		−	0.456172i
$693$		0			0
$694$		−	6.00000i		−	0.227757i
$695$	−4.00000	−	8.00000i	−0.151729	−	0.303457i
$696$		0			0
$697$		0			0
$698$		−	12.0000i		−	0.454207i
$699$		0			0
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$			36.0000i			1.35777i
$704$			14.0000i			0.527645i
$705$		0			0
$706$	14.0000			0.526897
$707$		0			0
$708$		0			0
$709$			12.0000i			0.450669i	0.974281	+	0.225335i	$0.0723476\pi$
$709$			12.0000i			0.450669i	−0.974281	+	0.225335i	$0.927652\pi$
$710$	4.00000	−	2.00000i	0.150117	−	0.0750587i
$711$		0			0
$712$			24.0000i			0.899438i
$713$	36.0000			1.34821
$714$		0			0
$715$	−16.0000	−	2.00000i	−0.598366	−	0.0747958i
$716$	−12.0000			−0.448461
$717$		0			0
$718$		−	2.00000i		−	0.0746393i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$		0			0
$722$	−17.0000			−0.632674
$723$		0			0
$724$	2.00000			0.0743294
$725$	18.0000	−	24.0000i	0.668503	−	0.891338i
$726$		0			0
$727$			26.0000i			0.964287i	0.876092	+	0.482143i	$0.160142\pi$
$727$			26.0000i			0.964287i	−0.876092	+	0.482143i	$0.839858\pi$
$728$		0			0
$729$		0			0
$730$	−6.00000	−	12.0000i	−0.222070	−	0.444140i
$731$		0			0
$732$		0			0
$733$	−42.0000			−1.55131			−0.775653	−	0.631160i	$-0.782579\pi$
$733$	−42.0000			−1.55131			−0.775653	+	0.631160i	$0.782579\pi$
$734$			18.0000i			0.664392i
$735$		0			0
$736$			30.0000i			1.10581i
$737$			24.0000i			0.884051i
$738$		0			0
$739$			6.00000i			0.220714i	0.993892	+	0.110357i	$0.0351994\pi$
$739$			6.00000i			0.220714i	−0.993892	+	0.110357i	$0.964801\pi$
$740$	−6.00000	−	12.0000i	−0.220564	−	0.441129i
$741$		0			0
$742$		0			0
$743$	16.0000			0.586983			0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000			0.586983			0.293492	+	0.955962i	$0.405183\pi$
$744$		0			0
$745$	−40.0000	+	20.0000i	−1.46549	+	0.732743i
$746$		−	4.00000i		−	0.146450i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$	−8.00000			−0.291730
$753$		0			0
$754$	−18.0000	−	12.0000i	−0.655521	−	0.437014i
$755$	−36.0000	+	18.0000i	−1.31017	+	0.655087i
$756$		0			0
$757$		−	20.0000i		−	0.726912i	−0.931611	−	0.363456i	$-0.881597\pi$
$757$		−	20.0000i		−	0.726912i	0.931611	−	0.363456i	$-0.118403\pi$
$758$		−	18.0000i		−	0.653789i
$759$		0			0
$760$	36.0000	−	18.0000i	1.30586	−	0.652929i
$761$		−	40.0000i		−	1.45000i	−0.688749	−	0.724999i	$-0.741840\pi$
$761$		−	40.0000i		−	1.45000i	0.688749	−	0.724999i	$-0.258160\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−8.00000			−0.289052
$767$	−4.00000	+	6.00000i	−0.144432	+	0.216647i
$768$		0			0
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$	6.00000			0.215945
$773$	−38.0000			−1.36677			−0.683383	−	0.730061i	$-0.739492\pi$
$773$	−38.0000			−1.36677			−0.683383	+	0.730061i	$0.739492\pi$
$774$		0			0
$775$	24.0000	+	18.0000i	0.862105	+	0.646579i
$776$	18.0000			0.646162
$777$		0			0
$778$	−6.00000			−0.215110
$779$	48.0000			1.71978
$780$		0			0
$781$	4.00000			0.143131
$782$		0			0
$783$		0			0
$784$	7.00000			0.250000
$785$	24.0000	−	12.0000i	0.856597	−	0.428298i
$786$		0			0
$787$	12.0000			0.427754			0.213877	−	0.976861i	$-0.431391\pi$
$787$	12.0000			0.427754			0.213877	+	0.976861i	$0.431391\pi$
$788$	−2.00000			−0.0712470
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	18.0000	+	12.0000i	0.639199	+	0.426132i
$794$	−18.0000			−0.638796
$795$		0			0
$796$	24.0000			0.850657
$797$			12.0000i			0.425062i	0.977154	+	0.212531i	$0.0681706\pi$
$797$			12.0000i			0.425062i	−0.977154	+	0.212531i	$0.931829\pi$
$798$

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -3.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -3.00000 q^{8} +(1.00000 + 2.00000i) q^{10} +2.00000i q^{11} +(3.00000 + 2.00000i) q^{13} -1.00000 q^{16} +6.00000i q^{19} +(-1.00000 - 2.00000i) q^{20} +2.00000i q^{22} +6.00000i q^{23} +(-3.00000 + 4.00000i) q^{25} +(3.00000 + 2.00000i) q^{26} -6.00000 q^{29} -6.00000i q^{31} +5.00000 q^{32} +6.00000 q^{37} +6.00000i q^{38} +(-3.00000 - 6.00000i) q^{40} -8.00000i q^{41} +6.00000i q^{43} -2.00000i q^{44} +6.00000i q^{46} +8.00000 q^{47} -7.00000 q^{49} +(-3.00000 + 4.00000i) q^{50} +(-3.00000 - 2.00000i) q^{52} -12.0000i q^{53} +(-4.00000 + 2.00000i) q^{55} -6.00000 q^{58} +2.00000i q^{59} +6.00000 q^{61} -6.00000i q^{62} +7.00000 q^{64} +(-1.00000 + 8.00000i) q^{65} +12.0000 q^{67} -2.00000i q^{71} -6.00000 q^{73} +6.00000 q^{74} -6.00000i q^{76} +(-1.00000 - 2.00000i) q^{80} -8.00000i q^{82} +4.00000 q^{83} +6.00000i q^{86} -6.00000i q^{88} -8.00000i q^{89} -6.00000i q^{92} +8.00000 q^{94} +(-12.0000 + 6.00000i) q^{95} -6.00000 q^{97} -7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 6 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 6 * q^8	\( 2 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 6 q^{8} + 2 q^{10} + 6 q^{13} - 2 q^{16} - 2 q^{20} - 6 q^{25} + 6 q^{26} - 12 q^{29} + 10 q^{32} + 12 q^{37} - 6 q^{40} + 16 q^{47} - 14 q^{49} - 6 q^{50} - 6 q^{52} - 8 q^{55} - 12 q^{58} + 12 q^{61} + 14 q^{64} - 2 q^{65} + 24 q^{67} - 12 q^{73} + 12 q^{74} - 2 q^{80} + 8 q^{83} + 16 q^{94} - 24 q^{95} - 12 q^{97} - 14 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 6 * q^8 + 2 * q^10 + 6 * q^13 - 2 * q^16 - 2 * q^20 - 6 * q^25 + 6 * q^26 - 12 * q^29 + 10 * q^32 + 12 * q^37 - 6 * q^40 + 16 * q^47 - 14 * q^49 - 6 * q^50 - 6 * q^52 - 8 * q^55 - 12 * q^58 + 12 * q^61 + 14 * q^64 - 2 * q^65 + 24 * q^67 - 12 * q^73 + 12 * q^74 - 2 * q^80 + 8 * q^83 + 16 * q^94 - 24 * q^95 - 12 * q^97 - 14 * q^98

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