LMFDB - Embedded newform 65.2.d.b.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(64,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("65.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.d (of order $2$, degree $1$, 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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	65.64
Dual form			65.2.d.b.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +2.00000i q^{6} -3.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +2.00000i q^{6} -3.00000 q^{8} -1.00000 q^{9} +(1.00000 - 2.00000i) q^{10} -2.00000i q^{11} -2.00000i q^{12} +(-3.00000 - 2.00000i) q^{13} +(4.00000 + 2.00000i) q^{15} -1.00000 q^{16} -1.00000 q^{18} +6.00000i q^{19} +(-1.00000 + 2.00000i) q^{20} -2.00000i q^{22} +6.00000i q^{23} -6.00000i q^{24} +(-3.00000 - 4.00000i) q^{25} +(-3.00000 - 2.00000i) q^{26} +4.00000i q^{27} +6.00000 q^{29} +(4.00000 + 2.00000i) q^{30} -6.00000i q^{31} +5.00000 q^{32} +4.00000 q^{33} +1.00000 q^{36} -6.00000 q^{37} +6.00000i q^{38} +(4.00000 - 6.00000i) q^{39} +(-3.00000 + 6.00000i) q^{40} +8.00000i q^{41} -6.00000i q^{43} +2.00000i q^{44} +(-1.00000 + 2.00000i) q^{45} +6.00000i q^{46} +8.00000 q^{47} -2.00000i q^{48} -7.00000 q^{49} +(-3.00000 - 4.00000i) q^{50} +(3.00000 + 2.00000i) q^{52} -12.0000i q^{53} +4.00000i q^{54} +(-4.00000 - 2.00000i) q^{55} -12.0000 q^{57} +6.00000 q^{58} -2.00000i q^{59} +(-4.00000 - 2.00000i) q^{60} +6.00000 q^{61} -6.00000i q^{62} +7.00000 q^{64} +(-7.00000 + 4.00000i) q^{65} +4.00000 q^{66} -12.0000 q^{67} -12.0000 q^{69} +2.00000i q^{71} +3.00000 q^{72} +6.00000 q^{73} -6.00000 q^{74} +(8.00000 - 6.00000i) q^{75} -6.00000i q^{76} +(4.00000 - 6.00000i) q^{78} +(-1.00000 + 2.00000i) q^{80} -11.0000 q^{81} +8.00000i q^{82} +4.00000 q^{83} -6.00000i q^{86} +12.0000i q^{87} +6.00000i q^{88} +8.00000i q^{89} +(-1.00000 + 2.00000i) q^{90} -6.00000i q^{92} +12.0000 q^{93} +8.00000 q^{94} +(12.0000 + 6.00000i) q^{95} +10.0000i q^{96} +6.00000 q^{97} -7.00000 q^{98} +2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 6 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 6 * q^8 - 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 6 q^{8} - 2 q^{9} + 2 q^{10} - 6 q^{13} + 8 q^{15} - 2 q^{16} - 2 q^{18} - 2 q^{20} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 8 q^{30} + 10 q^{32} + 8 q^{33} + 2 q^{36} - 12 q^{37} + 8 q^{39} - 6 q^{40} - 2 q^{45} + 16 q^{47} - 14 q^{49} - 6 q^{50} + 6 q^{52} - 8 q^{55} - 24 q^{57} + 12 q^{58} - 8 q^{60} + 12 q^{61} + 14 q^{64} - 14 q^{65} + 8 q^{66} - 24 q^{67} - 24 q^{69} + 6 q^{72} + 12 q^{73} - 12 q^{74} + 16 q^{75} + 8 q^{78} - 2 q^{80} - 22 q^{81} + 8 q^{83} - 2 q^{90} + 24 q^{93} + 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^9 + 2 * q^10 - 6 * q^13 + 8 * q^15 - 2 * q^16 - 2 * q^18 - 2 * q^20 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 8 * q^30 + 10 * q^32 + 8 * q^33 + 2 * q^36 - 12 * q^37 + 8 * q^39 - 6 * q^40 - 2 * q^45 + 16 * q^47 - 14 * q^49 - 6 * q^50 + 6 * q^52 - 8 * q^55 - 24 * q^57 + 12 * q^58 - 8 * q^60 + 12 * q^61 + 14 * q^64 - 14 * q^65 + 8 * q^66 - 24 * q^67 - 24 * q^69 + 6 * q^72 + 12 * q^73 - 12 * q^74 + 16 * q^75 + 8 * q^78 - 2 * q^80 - 22 * q^81 + 8 * q^83 - 2 * q^90 + 24 * q^93 + 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 $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$-1$

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	$0.384973\pi$
$3$			2.00000i			1.15470i	0.816497	+	0.577350i	$0.195913\pi$
$3$			2.00000i			1.15470i	−0.816497	+	0.577350i	$0.804087\pi$
$4$	−1.00000			−0.500000
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$			2.00000i			0.816497i
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$	−3.00000			−1.06066
$9$	−1.00000			−0.333333
$10$	1.00000	−	2.00000i	0.316228	−	0.632456i
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$		−	2.00000i		−	0.577350i
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$14$		0			0
$15$	4.00000	+	2.00000i	1.03280	+	0.516398i
$16$	−1.00000			−0.250000
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	−1.00000			−0.235702
$19$			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	$0.784877\pi$
$24$		−	6.00000i		−	1.22474i
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	−3.00000	−	2.00000i	−0.588348	−	0.392232i
$27$			4.00000i			0.769800i
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	4.00000	+	2.00000i	0.730297	+	0.365148i
$31$		−	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
$33$	4.00000			0.696311
$34$		0			0
$35$		0			0
$36$	1.00000			0.166667
$37$	−6.00000			−0.986394			−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000			−0.986394			−0.493197	+	0.869918i	$0.664172\pi$
$38$			6.00000i			0.973329i
$39$	4.00000	−	6.00000i	0.640513	−	0.960769i
$40$	−3.00000	+	6.00000i	−0.474342	+	0.948683i
$41$			8.00000i			1.24939i	0.780869	+	0.624695i	$0.214777\pi$
$41$			8.00000i			1.24939i	−0.780869	+	0.624695i	$0.785223\pi$
$42$		0			0
$43$		−	6.00000i		−	0.914991i	−0.889212	−	0.457496i	$-0.848747\pi$
$43$		−	6.00000i		−	0.914991i	0.889212	−	0.457496i	$-0.151253\pi$
$44$			2.00000i			0.301511i
$45$	−1.00000	+	2.00000i	−0.149071	+	0.298142i
$46$			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	$0.301699\pi$
$48$		−	2.00000i		−	0.288675i
$49$	−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	$-0.308354\pi$
$54$			4.00000i			0.544331i
$55$	−4.00000	−	2.00000i	−0.539360	−	0.269680i
$56$		0			0
$57$	−12.0000			−1.58944
$58$	6.00000			0.787839
$59$		−	2.00000i		−	0.260378i	−0.991489	−	0.130189i	$-0.958442\pi$
$59$		−	2.00000i		−	0.260378i	0.991489	−	0.130189i	$-0.0415584\pi$
$60$	−4.00000	−	2.00000i	−0.516398	−	0.258199i
$61$	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
$65$	−7.00000	+	4.00000i	−0.868243	+	0.496139i
$66$	4.00000			0.492366
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$		0			0
$69$	−12.0000			−1.44463
$70$		0			0
$71$			2.00000i			0.237356i	0.992933	+	0.118678i	$0.0378657\pi$
$71$			2.00000i			0.237356i	−0.992933	+	0.118678i	$0.962134\pi$
$72$	3.00000			0.353553
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	−6.00000			−0.697486
$75$	8.00000	−	6.00000i	0.923760	−	0.692820i
$76$		−	6.00000i		−	0.688247i
$77$		0			0
$78$	4.00000	−	6.00000i	0.452911	−	0.679366i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	−1.00000	+	2.00000i	−0.111803	+	0.223607i
$81$	−11.0000			−1.22222
$82$			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
$87$			12.0000i			1.28654i
$88$			6.00000i			0.639602i
$89$			8.00000i			0.847998i	0.905663	+	0.423999i	$0.139374\pi$
$89$			8.00000i			0.847998i	−0.905663	+	0.423999i	$0.860626\pi$
$90$	−1.00000	+	2.00000i	−0.105409	+	0.210819i
$91$		0			0
$92$		−	6.00000i		−	0.625543i
$93$	12.0000			1.24434
$94$	8.00000			0.825137
$95$	12.0000	+	6.00000i	1.23117	+	0.615587i
$96$			10.0000i			1.02062i
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$	−7.00000			−0.707107
$99$			2.00000i			0.201008i
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$		0			0
$103$			6.00000i			0.591198i	0.955312	+	0.295599i	$0.0955191\pi$
$103$			6.00000i			0.591198i	−0.955312	+	0.295599i	$0.904481\pi$
$104$	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	$-0.0936623\pi$
$108$		−	4.00000i		−	0.384900i
$109$		−	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
$111$		−	12.0000i		−	1.13899i
$112$		0			0
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$	−12.0000			−1.12390
$115$	12.0000	+	6.00000i	1.11901	+	0.559503i
$116$	−6.00000			−0.557086
$117$	3.00000	+	2.00000i	0.277350	+	0.184900i
$118$		−	2.00000i		−	0.184115i
$119$		0			0
$120$	−12.0000	−	6.00000i	−1.09545	−	0.547723i
$121$	7.00000			0.636364
$122$	6.00000			0.543214
$123$	−16.0000			−1.44267
$124$			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	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$	−3.00000			−0.265165
$129$	12.0000			1.05654
$130$	−7.00000	+	4.00000i	−0.613941	+	0.350823i
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	−4.00000			−0.348155
$133$		0			0
$134$	−12.0000			−1.03664
$135$	8.00000	+	4.00000i	0.688530	+	0.344265i
$136$		0			0
$137$	−2.00000			−0.170872			−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000			−0.170872			−0.0854358	+	0.996344i	$0.527228\pi$
$138$	−12.0000			−1.02151
$139$	−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
$141$			16.0000i			1.34744i
$142$			2.00000i			0.167836i
$143$	−4.00000	+	6.00000i	−0.334497	+	0.501745i
$144$	1.00000			0.0833333
$145$	6.00000	−	12.0000i	0.498273	−	0.996546i
$146$	6.00000			0.496564
$147$		−	14.0000i		−	1.15470i
$148$	6.00000			0.493197
$149$		−	20.0000i		−	1.63846i	−0.573462	−	0.819232i	$-0.694400\pi$
$149$		−	20.0000i		−	1.63846i	0.573462	−	0.819232i	$-0.305600\pi$
$150$	8.00000	−	6.00000i	0.653197	−	0.489898i
$151$			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
$156$	−4.00000	+	6.00000i	−0.320256	+	0.480384i
$157$			12.0000i			0.957704i	0.877896	+	0.478852i	$0.158947\pi$
$157$			12.0000i			0.957704i	−0.877896	+	0.478852i	$0.841053\pi$
$158$		0			0
$159$	24.0000			1.90332
$160$	5.00000	−	10.0000i	0.395285	−	0.790569i
$161$		0			0
$162$	−11.0000			−0.864242
$163$	−12.0000			−0.939913			−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000			−0.939913			−0.469956	+	0.882690i	$0.655730\pi$
$164$		−	8.00000i		−	0.624695i
$165$	4.00000	−	8.00000i	0.311400	−	0.622799i
$166$	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
$171$		−	6.00000i		−	0.458831i
$172$			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	$0.849220\pi$
$174$			12.0000i			0.909718i
$175$		0			0
$176$			2.00000i			0.150756i
$177$	4.00000			0.300658
$178$			8.00000i			0.599625i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	1.00000	−	2.00000i	0.0745356	−	0.149071i
$181$	−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
$183$			12.0000i			0.887066i
$184$		−	18.0000i		−	1.32698i
$185$	−6.00000	+	12.0000i	−0.441129	+	0.882258i
$186$	12.0000			0.879883
$187$		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	$0.5\pi$
$192$			14.0000i			1.01036i
$193$	6.00000			0.431889			0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000			0.431889			0.215945	+	0.976406i	$0.430717\pi$
$194$	6.00000			0.430775
$195$	−8.00000	−	14.0000i	−0.572892	−	1.00256i
$196$	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	$0.477302\pi$
$198$			2.00000i			0.142134i
$199$	−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
$201$		−	24.0000i		−	1.69283i
$202$	6.00000			0.422159
$203$		0			0
$204$		0			0
$205$	16.0000	+	8.00000i	1.11749	+	0.558744i
$206$			6.00000i			0.418040i
$207$		−	6.00000i		−	0.417029i
$208$	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
$213$	−4.00000			−0.274075
$214$		−	6.00000i		−	0.410152i
$215$	−12.0000	−	6.00000i	−0.818393	−	0.409197i
$216$		−	12.0000i		−	0.816497i
$217$		0			0
$218$		−	12.0000i		−	0.812743i
$219$			12.0000i			0.810885i
$220$	4.00000	+	2.00000i	0.269680	+	0.134840i
$221$		0			0
$222$		−	12.0000i		−	0.805387i
$223$	−24.0000			−1.60716			−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000			−1.60716			−0.803579	+	0.595198i	$0.797074\pi$
$224$		0			0
$225$	3.00000	+	4.00000i	0.200000	+	0.266667i
$226$		0			0
$227$	4.00000			0.265489			0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000			0.265489			0.132745	+	0.991150i	$0.457621\pi$
$228$	12.0000			0.794719
$229$			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	$-0.287927\pi$
$234$	3.00000	+	2.00000i	0.196116	+	0.130744i
$235$	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	$0.104834\pi$
$239$			10.0000i			0.646846i	−0.946254	+	0.323423i	$0.895166\pi$
$240$	−4.00000	−	2.00000i	−0.258199	−	0.129099i
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	7.00000			0.449977
$243$		−	10.0000i		−	0.641500i
$244$	−6.00000			−0.384111
$245$	−7.00000	+	14.0000i	−0.447214	+	0.894427i
$246$	−16.0000			−1.02012
$247$	12.0000	−	18.0000i	0.763542	−	1.14531i
$248$			18.0000i			1.14300i
$249$			8.00000i			0.506979i
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		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			$\pi$
$258$	12.0000			0.747087
$259$		0			0
$260$	7.00000	−	4.00000i	0.434122	−	0.248069i
$261$	−6.00000			−0.371391
$262$	−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	$0.940775\pi$
$264$	−12.0000			−0.738549
$265$	−24.0000	−	12.0000i	−1.47431	−	0.737154i
$266$		0			0
$267$	−16.0000			−0.979184
$268$	12.0000			0.733017
$269$	−18.0000			−1.09748			−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000			−1.09748			−0.548740	+	0.835993i	$0.684892\pi$
$270$	8.00000	+	4.00000i	0.486864	+	0.243432i
$271$		−	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
$276$	12.0000			0.722315
$277$		−	12.0000i		−	0.721010i	−0.932757	−	0.360505i	$-0.882604\pi$
$277$		−	12.0000i		−	0.721010i	0.932757	−	0.360505i	$-0.117396\pi$
$278$	−4.00000			−0.239904
$279$			6.00000i			0.359211i
$280$		0			0
$281$		−	8.00000i		−	0.477240i	−0.971113	−	0.238620i	$-0.923305\pi$
$281$		−	8.00000i		−	0.477240i	0.971113	−	0.238620i	$-0.0766950\pi$
$282$			16.0000i			0.952786i
$283$		−	22.0000i		−	1.30776i	−0.756596	−	0.653882i	$-0.773139\pi$
$283$		−	22.0000i		−	1.30776i	0.756596	−	0.653882i	$-0.226861\pi$
$284$		−	2.00000i		−	0.118678i
$285$	−12.0000	+	24.0000i	−0.710819	+	1.42164i
$286$	−4.00000	+	6.00000i	−0.236525	+	0.354787i
$287$		0			0
$288$	−5.00000			−0.294628
$289$	17.0000			1.00000
$290$	6.00000	−	12.0000i	0.352332	−	0.704664i
$291$			12.0000i			0.703452i
$292$	−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	$0.225459\pi$
$294$		−	14.0000i		−	0.816497i
$295$	−4.00000	−	2.00000i	−0.232889	−	0.116445i
$296$	18.0000			1.04623
$297$	8.00000			0.464207
$298$		−	20.0000i		−	1.15857i
$299$	12.0000	−	18.0000i	0.693978	−	1.04097i
$300$	−8.00000	+	6.00000i	−0.461880	+	0.346410i
$301$		0			0
$302$			18.0000i			1.03578i
$303$			12.0000i			0.689382i
$304$		−	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	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$	−12.0000			−0.682656
$310$	−12.0000	−	6.00000i	−0.681554	−	0.340777i
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$	−12.0000	+	18.0000i	−0.679366	+	1.01905i
$313$			8.00000i			0.452187i	0.974106	+	0.226093i	$0.0725954\pi$
$313$			8.00000i			0.452187i	−0.974106	+	0.226093i	$0.927405\pi$
$314$			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	$0.482113\pi$
$318$	24.0000			1.34585
$319$		−	12.0000i		−	0.671871i
$320$	7.00000	−	14.0000i	0.391312	−	0.782624i
$321$	12.0000			0.669775
$322$		0			0
$323$		0			0
$324$	11.0000			0.611111
$325$	1.00000	+	18.0000i	0.0554700	+	0.998460i
$326$	−12.0000			−0.664619
$327$	24.0000			1.32720
$328$		−	24.0000i		−	1.32518i
$329$		0			0
$330$	4.00000	−	8.00000i	0.220193	−	0.440386i
$331$			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
$333$	6.00000			0.328798
$334$	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	$0.336901\pi$
$337$			32.0000i			1.74315i	−0.490261	+	0.871576i	$0.663099\pi$
$338$	5.00000	+	12.0000i	0.271964	+	0.652714i
$339$		0			0
$340$		0			0
$341$	−12.0000			−0.649836
$342$		−	6.00000i		−	0.324443i
$343$		0			0
$344$			18.0000i			0.970495i
$345$	−12.0000	+	24.0000i	−0.646058	+	1.29212i
$346$			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	$-0.0514875\pi$
$348$		−	12.0000i		−	0.643268i
$349$		−	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
$351$	8.00000	−	12.0000i	0.427008	−	0.640513i
$352$		−	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	$0.378476\pi$
$354$	4.00000			0.212598
$355$	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	$0.0168076\pi$
$359$			2.00000i			0.105556i	−0.998606	+	0.0527780i	$0.983192\pi$
$360$	3.00000	−	6.00000i	0.158114	−	0.316228i
$361$	−17.0000			−0.894737
$362$	−2.00000			−0.105118
$363$			14.0000i			0.734809i
$364$		0			0
$365$	6.00000	−	12.0000i	0.314054	−	0.628109i
$366$			12.0000i			0.627250i
$367$		−	18.0000i		−	0.939592i	−0.882775	−	0.469796i	$-0.844327\pi$
$367$		−	18.0000i		−	0.939592i	0.882775	−	0.469796i	$-0.155673\pi$
$368$		−	6.00000i		−	0.312772i
$369$		−	8.00000i		−	0.416463i
$370$	−6.00000	+	12.0000i	−0.311925	+	0.623850i
$371$		0			0
$372$	−12.0000			−0.622171
$373$			4.00000i			0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$			4.00000i			0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$		0			0
$375$	−4.00000	−	22.0000i	−0.206559	−	1.13608i
$376$	−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
$381$	4.00000			0.204926
$382$		0			0
$383$	−8.00000			−0.408781			−0.204390	−	0.978889i	$-0.565521\pi$
$383$	−8.00000			−0.408781			−0.204390	+	0.978889i	$0.565521\pi$
$384$		−	6.00000i		−	0.306186i
$385$		0			0
$386$	6.00000			0.305392
$387$			6.00000i			0.304997i
$388$	−6.00000			−0.304604
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$	−8.00000	−	14.0000i	−0.405096	−	0.708918i
$391$		0			0
$392$	21.0000			1.06066
$393$		−	24.0000i		−	1.21064i
$394$	2.00000			0.100759
$395$		0			0
$396$		−	2.00000i		−	0.100504i
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$	−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	$-0.869183\pi$
$401$		−	16.0000i		−	0.799002i	0.916733	−	0.399501i	$-0.130817\pi$
$402$		−	24.0000i		−	1.19701i
$403$	−12.0000	+	18.0000i	−0.597763	+	0.896644i
$404$	−6.00000			−0.298511
$405$	−11.0000	+	22.0000i	−0.546594	+	1.09319i
$406$		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
$411$		−	4.00000i		−	0.197305i
$412$		−	6.00000i		−	0.295599i
$413$		0			0
$414$		−	6.00000i		−	0.294884i
$415$	4.00000	−	8.00000i	0.196352	−	0.392705i
$416$	−15.0000	−	10.0000i	−0.735436	−	0.490290i
$417$		−	8.00000i		−	0.391762i
$418$	12.0000			0.586939
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		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
$423$	−8.00000			−0.388973
$424$			36.0000i			1.74831i
$425$		0			0
$426$	−4.00000			−0.193801
$427$		0			0
$428$			6.00000i			0.290021i
$429$	−12.0000	−	8.00000i	−0.579365	−	0.386244i
$430$	−12.0000	−	6.00000i	−0.578691	−	0.289346i
$431$			10.0000i			0.481683i	0.970564	+	0.240842i	$0.0774234\pi$
$431$			10.0000i			0.481683i	−0.970564	+	0.240842i	$0.922577\pi$
$432$		−	4.00000i		−	0.192450i
$433$			16.0000i			0.768911i	0.923144	+	0.384455i	$0.125611\pi$
$433$			16.0000i			0.768911i	−0.923144	+	0.384455i	$0.874389\pi$
$434$		0			0
$435$	24.0000	+	12.0000i	1.15071	+	0.575356i
$436$			12.0000i			0.574696i
$437$	−36.0000			−1.72211
$438$			12.0000i			0.573382i
$439$	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
$441$	7.00000			0.333333
$442$		0			0
$443$		−	6.00000i		−	0.285069i	−0.989790	−	0.142534i	$-0.954475\pi$
$443$		−	6.00000i		−	0.285069i	0.989790	−	0.142534i	$-0.0455251\pi$
$444$			12.0000i			0.569495i
$445$	16.0000	+	8.00000i	0.758473	+	0.379236i
$446$	−24.0000			−1.13643
$447$	40.0000			1.89194
$448$		0			0
$449$			16.0000i			0.755087i	0.925992	+	0.377543i	$0.123231\pi$
$449$			16.0000i			0.755087i	−0.925992	+	0.377543i	$0.876769\pi$
$450$	3.00000	+	4.00000i	0.141421	+	0.188562i
$451$	16.0000			0.753411
$452$		0			0
$453$	−36.0000			−1.69143
$454$	4.00000			0.187729
$455$		0			0
$456$	36.0000			1.68585
$457$	30.0000			1.40334			0.701670	−	0.712502i	$-0.252438\pi$
$457$	30.0000			1.40334			0.701670	+	0.712502i	$0.252438\pi$
$458$			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	$0.0296934\pi$
$461$			4.00000i			0.186299i	−0.995652	+	0.0931493i	$0.970307\pi$
$462$		0			0
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$	−6.00000			−0.278543
$465$	12.0000	−	24.0000i	0.556487	−	1.11297i
$466$		−	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	$0.863267\pi$
$468$	−3.00000	−	2.00000i	−0.138675	−	0.0924500i
$469$		0			0
$470$	8.00000	−	16.0000i	0.369012	−	0.738025i
$471$	−24.0000			−1.10586
$472$			6.00000i			0.276172i
$473$	−12.0000			−0.551761
$474$		0			0
$475$	24.0000	−	18.0000i	1.10120	−	0.825897i
$476$		0			0
$477$			12.0000i			0.549442i
$478$			10.0000i			0.457389i
$479$		−	22.0000i		−	1.00521i	−0.864517	−	0.502603i	$-0.832376\pi$
$479$		−	22.0000i		−	1.00521i	0.864517	−	0.502603i	$-0.167624\pi$
$480$	20.0000	+	10.0000i	0.912871	+	0.456435i
$481$	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
$486$		−	10.0000i		−	0.453609i
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$	−18.0000			−0.814822
$489$		−	24.0000i		−	1.08532i
$490$	−7.00000	+	14.0000i	−0.316228	+	0.632456i
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$	16.0000			0.721336
$493$		0			0
$494$	12.0000	−	18.0000i	0.539906	−	0.809858i
$495$	4.00000	+	2.00000i	0.179787	+	0.0898933i
$496$			6.00000i			0.269408i
$497$		0			0
$498$			8.00000i			0.358489i
$499$			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
$501$			32.0000i			1.42965i
$502$	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
$507$	−24.0000	+	10.0000i	−1.06588	+	0.444116i
$508$			2.00000i			0.0887357i
$509$			20.0000i			0.886484i	0.896402	+	0.443242i	$0.146172\pi$
$509$			20.0000i			0.886484i	−0.896402	+	0.443242i	$0.853828\pi$
$510$		0			0
$511$		0			0
$512$	−11.0000			−0.486136
$513$	−24.0000			−1.05963
$514$		0			0
$515$	12.0000	+	6.00000i	0.528783	+	0.264392i
$516$	−12.0000			−0.528271
$517$		−	16.0000i		−	0.703679i
$518$		0			0
$519$	−24.0000			−1.05348
$520$	21.0000	−	12.0000i	0.920911	−	0.526235i
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$	−6.00000			−0.262613
$523$			42.0000i			1.83653i	0.395964	+	0.918266i	$0.370410\pi$
$523$			42.0000i			1.83653i	−0.395964	+	0.918266i	$0.629590\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$			6.00000i			0.261612i
$527$		0			0
$528$	−4.00000			−0.174078
$529$	−13.0000			−0.565217
$530$	−24.0000	−	12.0000i	−1.04249	−	0.521247i
$531$			2.00000i			0.0867926i
$532$		0			0
$533$	16.0000	−	24.0000i	0.693037	−	1.03956i
$534$	−16.0000			−0.692388
$535$	−12.0000	−	6.00000i	−0.518805	−	0.259403i
$536$	36.0000			1.55496
$537$		−	24.0000i		−	1.03568i
$538$	−18.0000			−0.776035
$539$			14.0000i			0.603023i
$540$	−8.00000	−	4.00000i	−0.344265	−	0.172133i
$541$		−	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
$543$		−	4.00000i		−	0.171656i
$544$		0			0
$545$	−24.0000	−	12.0000i	−1.02805	−	0.514024i
$546$		0			0
$547$			18.0000i			0.769624i	0.922995	+	0.384812i	$0.125734\pi$
$547$			18.0000i			0.769624i	−0.922995	+	0.384812i	$0.874266\pi$
$548$	2.00000			0.0854358
$549$	−6.00000			−0.256074
$550$	−8.00000	+	6.00000i	−0.341121	+	0.255841i
$551$			36.0000i			1.53365i
$552$	36.0000			1.53226
$553$		0			0
$554$		−	12.0000i		−	0.509831i
$555$	−24.0000	−	12.0000i	−1.01874	−	0.509372i
$556$	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	$0.595853\pi$
$558$			6.00000i			0.254000i
$559$	−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	$-0.217837\pi$
$564$		−	16.0000i		−	0.673722i
$565$		0			0
$566$		−	22.0000i		−	0.924729i
$567$		0			0
$568$		−	6.00000i		−	0.251754i
$569$	18.0000			0.754599			0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000			0.754599			0.377300	+	0.926091i	$0.376853\pi$
$570$	−12.0000	+	24.0000i	−0.502625	+	1.00525i
$571$	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
$576$	−7.00000			−0.291667
$577$	−18.0000			−0.749350			−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000			−0.749350			−0.374675	+	0.927156i	$0.622246\pi$
$578$	17.0000			0.707107
$579$			12.0000i			0.498703i
$580$	−6.00000	+	12.0000i	−0.249136	+	0.498273i
$581$		0			0
$582$			12.0000i			0.497416i
$583$	−24.0000			−0.993978
$584$	−18.0000			−0.744845
$585$	7.00000	−	4.00000i	0.289414	−	0.165380i
$586$	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	$0.635430\pi$
$588$			14.0000i			0.577350i
$589$	36.0000			1.48335
$590$	−4.00000	−	2.00000i	−0.164677	−	0.0823387i
$591$			4.00000i			0.164538i
$592$	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	$0.350812\pi$
$594$	8.00000			0.328244
$595$		0			0
$596$			20.0000i			0.819232i
$597$		−	48.0000i		−	1.96451i
$598$	12.0000	−	18.0000i	0.490716	−	0.736075i
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$	−24.0000	+	18.0000i	−0.979796	+	0.734847i
$601$	−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
$603$	12.0000			0.488678
$604$		−	18.0000i		−	0.732410i
$605$	7.00000	−	14.0000i	0.284590	−	0.569181i
$606$			12.0000i			0.487467i
$607$		−	18.0000i		−	0.730597i	−0.930890	−	0.365299i	$-0.880967\pi$
$607$		−	18.0000i		−	0.730597i	0.930890	−	0.365299i	$-0.119033\pi$
$608$			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	$-0.707165\pi$
$613$	−30.0000			−1.21169			−0.605844	+	0.795583i	$0.707165\pi$
$614$	−12.0000			−0.484281
$615$	−16.0000	+	32.0000i	−0.645182	+	1.29036i
$616$		0			0
$617$	−34.0000			−1.36879			−0.684394	−	0.729112i	$-0.739933\pi$
$617$	−34.0000			−1.36879			−0.684394	+	0.729112i	$0.739933\pi$
$618$	−12.0000			−0.482711
$619$		−	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
$621$	−24.0000			−0.963087
$622$	24.0000			0.962312
$623$		0			0
$624$	−4.00000	+	6.00000i	−0.160128	+	0.240192i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$			8.00000i			0.319744i
$627$			24.0000i			0.958468i
$628$		−	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
$633$		−	24.0000i		−	0.953914i
$634$	2.00000			0.0794301
$635$	−4.00000	−	2.00000i	−0.158735	−	0.0793676i
$636$	−24.0000			−0.951662
$637$	21.0000	+	14.0000i	0.832050	+	0.554700i
$638$		−	12.0000i		−	0.475085i
$639$		−	2.00000i		−	0.0791188i
$640$	−3.00000	+	6.00000i	−0.118585	+	0.237171i
$641$	−30.0000			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$642$	12.0000			0.473602
$643$	36.0000			1.41970			0.709851	−	0.704352i	$-0.248762\pi$
$643$	36.0000			1.41970			0.709851	+	0.704352i	$0.248762\pi$
$644$		0			0
$645$	12.0000	−	24.0000i	0.472500	−	0.944999i
$646$		0			0
$647$			6.00000i			0.235884i	0.993020	+	0.117942i	$0.0376297\pi$
$647$			6.00000i			0.235884i	−0.993020	+	0.117942i	$0.962370\pi$
$648$	33.0000			1.29636
$649$	−4.00000			−0.157014
$650$	1.00000	+	18.0000i	0.0392232	+	0.706018i
$651$		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	$-0.248781\pi$
$654$	24.0000			0.938474
$655$	−12.0000	+	24.0000i	−0.468879	+	0.937758i
$656$		−	8.00000i		−	0.312348i
$657$	−6.00000			−0.234082
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$	−4.00000	+	8.00000i	−0.155700	+	0.311400i
$661$			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
$666$	6.00000			0.232495
$667$			36.0000i			1.39393i
$668$	−16.0000			−0.619059
$669$		−	48.0000i		−	1.85579i
$670$	−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	$0.376046\pi$
$673$			48.0000i			1.85026i	−0.379646	+	0.925132i	$0.623954\pi$
$674$			32.0000i			1.23259i
$675$	16.0000	−	12.0000i	0.615840	−	0.461880i
$676$	−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
$681$			8.00000i			0.306561i
$682$	−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	$0.181492\pi$
$684$			6.00000i			0.229416i
$685$	−2.00000	+	4.00000i	−0.0764161	+	0.152832i
$686$		0			0
$687$	−24.0000			−0.915657
$688$			6.00000i			0.228748i
$689$	−24.0000	+	36.0000i	−0.914327	+	1.37149i
$690$	−12.0000	+	24.0000i	−0.456832	+	0.913664i
$691$		−	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
$696$		−	36.0000i		−	1.36458i
$697$		0			0
$698$		−	12.0000i		−	0.454207i
$699$	48.0000			1.81553
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	8.00000	−	12.0000i	0.301941	−	0.452911i
$703$		−	36.0000i		−	1.35777i
$704$		−	14.0000i		−	0.527645i
$705$	32.0000	+	16.0000i	1.20519	+	0.602595i
$706$	14.0000			0.526897
$707$		0			0
$708$	−4.00000			−0.150329
$709$			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
$715$	8.00000	+	14.0000i	0.299183	+	0.523570i
$716$	12.0000			0.448461
$717$	−20.0000			−0.746914
$718$			2.00000i			0.0746393i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	1.00000	−	2.00000i	0.0372678	−	0.0745356i
$721$		0			0
$722$	−17.0000			−0.632674
$723$		0			0
$724$	2.00000			0.0743294
$725$	−18.0000	−	24.0000i	−0.668503	−	0.891338i
$726$			14.0000i			0.519589i
$727$		−	26.0000i		−	0.964287i	−0.876092	−	0.482143i	$-0.839858\pi$
$727$		−	26.0000i		−	0.964287i	0.876092	−	0.482143i	$-0.160142\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$	6.00000	−	12.0000i	0.222070	−	0.444140i
$731$		0			0
$732$		−	12.0000i		−	0.443533i
$733$	42.0000			1.55131			0.775653	−	0.631160i	$-0.217421\pi$
$733$	42.0000			1.55131			0.775653	+	0.631160i	$0.217421\pi$
$734$		−	18.0000i		−	0.664392i
$735$	−28.0000	−	14.0000i	−1.03280	−	0.516398i
$736$			30.0000i			1.10581i
$737$			24.0000i			0.884051i
$738$		−	8.00000i		−	0.294484i
$739$			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
$741$	36.0000	+	24.0000i	1.32249	+	0.881662i
$742$		0			0
$743$	16.0000			0.586983			0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000			0.586983			0.293492	+	0.955962i	$0.405183\pi$
$744$	−36.0000			−1.31982
$745$	−40.0000	−	20.0000i	−1.46549	−	0.732743i
$746$			4.00000i			0.146450i
$747$	−4.00000			−0.146352
$748$		0			0
$749$		0			0
$750$	−4.00000	−	22.0000i	−0.146059	−	0.803326i
$751$	−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
$753$			24.0000i			0.874609i
$754$	−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	$0.118403\pi$
$757$			20.0000i			0.726912i	−0.931611	+	0.363456i	$0.881597\pi$
$758$		−	18.0000i		−	0.653789i
$759$			24.0000i			0.871145i
$760$	−36.0000	−	18.0000i	−1.30586	−	0.652929i
$761$			40.0000i			1.45000i	0.688749	+	0.724999i	$0.258160\pi$
$761$			40.0000i			1.45000i	−0.688749	+	0.724999i	$0.741840\pi$
$762$	4.00000			0.144905
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−8.00000			−0.289052
$767$	−4.00000	+	6.00000i	−0.144432	+	0.216647i
$768$		−	34.0000i		−	1.22687i
$769$		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	$0.739492\pi$
$774$			6.00000i			0.215666i
$775$	−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
$780$	8.00000	+	14.0000i	0.286446	+	0.501280i
$781$	4.00000			0.143131
$782$		0			0
$783$			24.0000i			0.857690i
$784$	7.00000			0.250000
$785$	24.0000	+	12.0000i	0.856597	+	0.428298i
$786$		−	24.0000i		−	0.856052i
$787$	−12.0000			−0.427754			−0.213877	−	0.976861i	$-0.568609\pi$
$787$	−12.0000			−0.427754			−0.213877	+	0.976861i	$0.568609\pi$
$788$	−2.00000			−0.0712470
$789$	−12.0000			−0.427211
$790$		0			0
$791$		0			0
$792$		−	6.00000i		−	0.213201i
$793$	−18.0000	−	12.0000i	−0.639199	−	0.426132i
$794$	18.0000			0.638796
$795$	24.0000	−	48.0000i	0.851192	−	1.70238i
$796$	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	$0.931829\pi$
$798$		0			0
$799$		0			0
$800$	−15.0000	−	20.0000i	−0.530330	−	0.707107i
$801$		−	8.00000i		−	0.282666i
$802$		−	16.0000i		−	0.564980i
$803$		−	12.0000i		−	0.423471i
$804$			24.0000i			0.846415i
$805$		0			0
$806$	−12.0000	+	18.0000i	−0.422682	+	0.634023i
$807$		−	36.0000i		−	1.26726i
$808$	−18.0000			−0.633238
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$	−11.0000	+	22.0000i	−0.386501	+	0.773001i
$811$			30.0000i			1.05344i	0.850038	+	0.526721i	$0.176579\pi$
$811$			30.0000i			1.05344i	−0.850038	+	0.526721i	$0.823421\pi$
$812$		0			0
$813$	12.0000			0.420858
$814$			12.0000i			0.420600i
$815$	−12.0000	+	24.0000i	−0.420342	+	0.840683i
$816$		0			0
$817$	36.0000			1.25948
$818$			24.0000i			0.839140i
$819$		0			0
$820$	−16.0000	−	8.00000i	−0.558744	−	0.279372i
$821$		−	20.0000i		−	0.698005i	−0.937122	−	0.349002i	$-0.886521\pi$
$821$		−	20.0000i		−	0.698005i	0.937122	−	0.349002i	$-0.113479\pi$
$822$		−	4.00000i		−	0.139516i
$823$		−	42.0000i		−	1.46403i	−0.681290	−	0.732014i	$-0.738581\pi$
$823$		−	42.0000i		−	1.46403i	0.681290	−	0.732014i	$-0.261419\pi$
$824$		−	18.0000i		−	0.627060i
$825$	−12.0000	−	16.0000i	−0.417786	−	0.557048i
$826$		0			0
$827$	−4.00000			−0.139094			−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000			−0.139094			−0.0695468	+	0.997579i	$0.522155\pi$
$828$			6.00000i			0.208514i
$829$	6.00000			0.208389			0.104194	−	0.994557i	$-0.466774\pi$
$829$	6.00000			0.208389			0.104194	+	0.994557i	$0.466774\pi$
$830$	4.00000	−	8.00000i	0.138842	−	0.277684i
$831$	24.0000			0.832551
$832$	−21.0000	−	14.0000i	−0.728044	−	0.485363i
$833$		0			0
$834$		−	8.00000i		−	0.277017i
$835$	16.0000	−	32.0000i	0.553703	−	1.10741i
$836$	−12.0000			−0.415029
$837$	24.0000			0.829561
$838$	−12.0000			−0.414533
$839$		−	46.0000i		−	1.58810i	−0.607855	−	0.794048i	$-0.707970\pi$
$839$		−	46.0000i		−	1.58810i	0.607855	−	0.794048i	$-0.292030\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		−	36.0000i		−	1.24064i
$843$	16.0000			0.551069
$844$	12.0000			0.413057
$845$	29.0000	+	2.00000i	0.997630	+	0.0688021i
$846$	−8.00000			−0.275046
$847$		0			0
$848$			12.0000i			0.412082i
$849$	44.0000			1.51008
$850$		0			0
$851$		−	36.0000i		−	1.23406i
$852$	4.00000			0.137038
$853$	−54.0000			−1.84892			−0.924462	−	0.381273i	$-0.875486\pi$
$853$	−54.0000			−1.84892			−0.924462	+	0.381273i	$0.875486\pi$
$854$		0			0
$855$	−12.0000	−	6.00000i	−0.410391	−	0.205196i
$856$			18.0000i			0.615227i
$857$			24.0000i			0.819824i	0.912125	+	0.409912i	$0.134441\pi$
$857$			24.0000i			0.819824i	−0.912125	+	0.409912i	$0.865559\pi$
$858$	−12.0000	−	8.00000i	−0.409673	−	0.273115i
$859$	−36.0000			−1.22830			−0.614152	−	0.789188i	$-0.710502\pi$
$859$	−36.0000			−1.22830			−0.614152	+	0.789188i	$0.710502\pi$
$860$	12.0000	+	6.00000i	0.409197	+	0.204598i
$861$		0			0
$862$			10.0000i			0.340601i
$863$	8.00000			0.272323			0.136162	−	0.990687i	$-0.456523\pi$
$863$	8.00000			0.272323			0.136162	+	0.990687i	$0.456523\pi$
$864$			20.0000i			0.680414i
$865$	24.0000	+	12.0000i	0.816024	+	0.408012i
$866$			16.0000i			0.543702i
$867$			34.0000i			1.15470i
$868$		0			0
$869$		0			0
$870$	24.0000	+	12.0000i	0.813676	+	0.406838i
$871$	36.0000	+	24.0000i	1.21981	+	0.813209i
$872$			36.0000i			1.21911i
$873$	−6.00000			−0.203069
$874$	−36.0000			−1.21772
$875$		0			0
$876$		−	12.0000i		−	0.405442i
$877$	−6.00000			−0.202606			−0.101303	−	0.994856i	$-0.532301\pi$
$877$	−6.00000			−0.202606			−0.101303	+	0.994856i	$0.532301\pi$
$878$	8.00000			0.269987
$879$			52.0000i			1.75392i
$880$	4.00000	+	2.00000i	0.134840	+	0.0674200i
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$	7.00000			0.235702
$883$			2.00000i			0.0673054i	0.999434	+	0.0336527i	$0.0107140\pi$
$883$			2.00000i			0.0673054i	−0.999434	+	0.0336527i	$0.989286\pi$
$884$		0			0
$885$	4.00000	−	8.00000i	0.134459	−	0.268917i
$886$		−	6.00000i		−	0.201574i
$887$		−	42.0000i		−	1.41022i	−0.709097	−	0.705111i	$-0.750897\pi$
$887$		−	42.0000i		−	1.41022i	0.709097	−	0.705111i	$-0.249103\pi$
$888$			36.0000i			1.20808i
$889$		0			0
$890$	16.0000	+	8.00000i	0.536321	+	0.268161i
$891$			22.0000i			0.737028i
$892$	24.0000			0.803579
$893$			48.0000i			1.60626i
$894$	40.0000			1.33780
$895$	−12.0000	+	24.0000i	−0.401116	+	0.802232i
$896$		0			0
$897$	36.0000	+	24.0000i	1.20201	+	0.801337i
$898$			16.0000i			0.533927i
$899$		−	36.0000i		−	1.20067i
$900$	−3.00000	−	4.00000i	−0.100000	−	0.133333i
$901$		0			0
$902$	16.0000			0.532742
$903$		0			0
$904$		0			0
$905$	−2.00000	+	4.00000i	−0.0664822	+	0.132964i
$906$	−36.0000			−1.19602
$907$			10.0000i			0.332045i	0.986122	+	0.166022i	$0.0530924\pi$
$907$			10.0000i			0.332045i	−0.986122	+	0.166022i	$0.946908\pi$
$908$	−4.00000			−0.132745
$909$	−6.00000			−0.199007
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$	12.0000			0.397360
$913$		−	8.00000i		−	0.264761i
$914$	30.0000			0.992312
$915$	24.0000	+	12.0000i	0.793416	+	0.396708i
$916$		−	12.0000i		−	0.396491i
$917$		0			0
$918$		0			0
$919$	24.0000			0.791687			0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000			0.791687			0.395843	+	0.918318i	$0.370452\pi$
$920$	−36.0000	−	18.0000i	−1.18688	−	0.593442i
$921$		−	24.0000i		−	0.790827i
$922$			4.00000i			0.131733i
$923$	4.00000	−	6.00000i	0.131662	−	0.197492i
$924$		0			0
$925$	18.0000	+	24.0000i	0.591836	+	0.789115i
$926$	24.0000			0.788689
$927$		−	6.00000i		−	0.197066i
$928$	30.0000			0.984798
$929$		−	16.0000i		−	0.524943i	−0.964940	−	0.262471i	$-0.915462\pi$
$929$		−	16.0000i		−	0.524943i	0.964940	−	0.262471i	$-0.0845376\pi$
$930$	12.0000	−	24.0000i	0.393496	−	0.786991i
$931$		−	42.0000i		−	1.37649i
$932$			24.0000i			0.786146i
$933$			48.0000i			1.57145i
$934$			18.0000i			0.588978i
$935$		0			0
$936$	−9.00000	−	6.00000i	−0.294174	−	0.196116i
$937$		−	56.0000i		−	1.82944i	−0.404088	−	0.914720i	$-0.632411\pi$
$937$		−	56.0000i		−	1.82944i	0.404088	−	0.914720i	$-0.367589\pi$
$938$		0			0
$939$	−16.0000			−0.522140
$940$	−8.00000	+	16.0000i	−0.260931	+	0.521862i
$941$		−	28.0000i		−	0.912774i	−0.889781	−	0.456387i	$-0.849143\pi$
$941$		−	28.0000i		−	0.912774i	0.889781	−	0.456387i	$-0.150857\pi$
$942$	−24.0000			−0.781962
$943$	−48.0000			−1.56310
$944$			2.00000i			0.0650945i
$945$		0			0
$946$	−12.0000			−0.390154
$947$	−28.0000			−0.909878			−0.454939	−	0.890523i	$-0.650339\pi$
$947$	−28.0000			−0.909878			−0.454939	+	0.890523i	$0.650339\pi$
$948$		0			0
$949$	−18.0000	−	12.0000i	−0.584305	−	0.389536i
$950$	24.0000	−	18.0000i	0.778663	−	0.583997i
$951$			4.00000i			0.129709i
$952$		0			0
$953$			24.0000i			0.777436i	0.921357	+	0.388718i	$0.127082\pi$
$953$			24.0000i			0.777436i	−0.921357	+	0.388718i	$0.872918\pi$
$954$			12.0000i			0.388514i
$955$		0			0
$956$		−	10.0000i		−	0.323423i
$957$	24.0000			0.775810
$958$		−	22.0000i		−	0.710788i
$959$		0			0
$960$	28.0000	+	14.0000i	0.903696	+	0.451848i
$961$	−5.00000			−0.161290
$962$	18.0000	+	12.0000i	0.580343	+	0.386896i
$963$			6.00000i			0.193347i
$964$		0			0
$965$	6.00000	−	12.0000i	0.193147	−	0.386294i
$966$		0			0
$967$	−48.0000			−1.54358			−0.771788	−	0.635880i	$-0.780637\pi$
$967$	−48.0000			−1.54358			−0.771788	+	0.635880i	$0.780637\pi$
$968$	−21.0000			−0.674966
$969$		0			0
$970$	6.00000	−	12.0000i	0.192648	−	0.385297i
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$			10.0000i			0.320750i
$973$		0			0
$974$		0			0
$975$	−36.0000	+	2.00000i	−1.15292	+	0.0640513i
$976$	−6.00000			−0.192055
$977$	−34.0000			−1.08776			−0.543878	−	0.839164i	$-0.683045\pi$
$977$	−34.0000			−1.08776			−0.543878	+	0.839164i	$0.683045\pi$
$978$		−	24.0000i		−	0.767435i
$979$	16.0000			0.511362
$980$	7.00000	−	14.0000i	0.223607	−	0.447214i
$981$			12.0000i			0.383131i
$982$	12.0000			0.382935
$983$	−16.0000			−0.510321			−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000			−0.510321			−0.255160	+	0.966899i	$0.582128\pi$
$984$	48.0000			1.53018
$985$	2.00000	−	4.00000i	0.0637253	−	0.127451i
$986$		0			0
$987$		0			0
$988$	−12.0000	+	18.0000i	−0.381771	+	0.572656i
$989$	36.0000			1.14473
$990$	4.00000	+	2.00000i	0.127128	+	0.0635642i
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		−	30.0000i		−	0.952501i
$993$	−60.0000			−1.90404
$994$		0			0
$995$	−24.0000	+	48.0000i	−0.760851	+	1.52170i
$996$		−	8.00000i		−	0.253490i
$997$		−	60.0000i		−	1.90022i	−0.311916	−	0.950110i	$-0.600971\pi$
$997$		−	60.0000i		−	1.90022i	0.311916	−	0.950110i	$-0.399029\pi$
$998$			6.00000i			0.189927i
$999$		−	24.0000i		−	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.d.b.64.2	yes	2
3.2	odd	2		585.2.h.b.64.2		2
4.3	odd	2		1040.2.f.b.129.1		2
5.2	odd	4		325.2.c.e.51.2		2
5.3	odd	4		325.2.c.b.51.1		2
5.4	even	2		65.2.d.a.64.1	✓	2
13.2	odd	12		845.2.n.a.529.2		4
13.3	even	3		845.2.l.a.654.1		4
13.4	even	6		845.2.l.b.699.2		4
13.5	odd	4		845.2.b.a.339.1		2
13.6	odd	12		845.2.n.a.484.1		4
13.7	odd	12		845.2.n.b.484.2		4
13.8	odd	4		845.2.b.b.339.2		2
13.9	even	3		845.2.l.a.699.2		4
13.10	even	6		845.2.l.b.654.1		4
13.11	odd	12		845.2.n.b.529.1		4
13.12	even	2		65.2.d.a.64.2	yes	2
15.14	odd	2		585.2.h.c.64.2		2
20.19	odd	2		1040.2.f.a.129.2		2
39.38	odd	2		585.2.h.c.64.1		2
52.51	odd	2		1040.2.f.a.129.1		2
65.4	even	6		845.2.l.a.699.1		4
65.8	even	4		4225.2.a.k.1.1		1
65.9	even	6		845.2.l.b.699.1		4
65.12	odd	4		325.2.c.e.51.1		2
65.18	even	4		4225.2.a.e.1.1		1
65.19	odd	12		845.2.n.a.484.2		4
65.24	odd	12		845.2.n.b.529.2		4
65.29	even	6		845.2.l.b.654.2		4
65.34	odd	4		845.2.b.b.339.1		2
65.38	odd	4		325.2.c.b.51.2		2
65.44	odd	4		845.2.b.a.339.2		2
65.47	even	4		4225.2.a.h.1.1		1
65.49	even	6		845.2.l.a.654.2		4
65.54	odd	12		845.2.n.a.529.1		4
65.57	even	4		4225.2.a.m.1.1		1
65.59	odd	12		845.2.n.b.484.1		4
65.64	even	2	inner	65.2.d.b.64.1	yes	2
195.194	odd	2		585.2.h.b.64.1		2
260.259	odd	2		1040.2.f.b.129.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.d.a.64.1	✓	2	5.4	even	2
65.2.d.a.64.2	yes	2	13.12	even	2
65.2.d.b.64.1	yes	2	65.64	even	2	inner
65.2.d.b.64.2	yes	2	1.1	even	1	trivial
325.2.c.b.51.1		2	5.3	odd	4
325.2.c.b.51.2		2	65.38	odd	4
325.2.c.e.51.1		2	65.12	odd	4
325.2.c.e.51.2		2	5.2	odd	4
585.2.h.b.64.1		2	195.194	odd	2
585.2.h.b.64.2		2	3.2	odd	2
585.2.h.c.64.1		2	39.38	odd	2
585.2.h.c.64.2		2	15.14	odd	2
845.2.b.a.339.1		2	13.5	odd	4
845.2.b.a.339.2		2	65.44	odd	4
845.2.b.b.339.1		2	65.34	odd	4
845.2.b.b.339.2		2	13.8	odd	4
845.2.l.a.654.1		4	13.3	even	3
845.2.l.a.654.2		4	65.49	even	6
845.2.l.a.699.1		4	65.4	even	6
845.2.l.a.699.2		4	13.9	even	3
845.2.l.b.654.1		4	13.10	even	6
845.2.l.b.654.2		4	65.29	even	6
845.2.l.b.699.1		4	65.9	even	6
845.2.l.b.699.2		4	13.4	even	6
845.2.n.a.484.1		4	13.6	odd	12
845.2.n.a.484.2		4	65.19	odd	12
845.2.n.a.529.1		4	65.54	odd	12
845.2.n.a.529.2		4	13.2	odd	12
845.2.n.b.484.1		4	65.59	odd	12
845.2.n.b.484.2		4	13.7	odd	12
845.2.n.b.529.1		4	13.11	odd	12
845.2.n.b.529.2		4	65.24	odd	12
1040.2.f.a.129.1		2	52.51	odd	2
1040.2.f.a.129.2		2	20.19	odd	2
1040.2.f.b.129.1		2	4.3	odd	2
1040.2.f.b.129.2		2	260.259	odd	2
4225.2.a.e.1.1		1	65.18	even	4
4225.2.a.h.1.1		1	65.47	even	4
4225.2.a.k.1.1		1	65.8	even	4
4225.2.a.m.1.1		1	65.57	even	4

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +2.00000i q^{6} -3.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +2.00000i q^{6} -3.00000 q^{8} -1.00000 q^{9} +(1.00000 - 2.00000i) q^{10} -2.00000i q^{11} -2.00000i q^{12} +(-3.00000 - 2.00000i) q^{13} +(4.00000 + 2.00000i) q^{15} -1.00000 q^{16} -1.00000 q^{18} +6.00000i q^{19} +(-1.00000 + 2.00000i) q^{20} -2.00000i q^{22} +6.00000i q^{23} -6.00000i q^{24} +(-3.00000 - 4.00000i) q^{25} +(-3.00000 - 2.00000i) q^{26} +4.00000i q^{27} +6.00000 q^{29} +(4.00000 + 2.00000i) q^{30} -6.00000i q^{31} +5.00000 q^{32} +4.00000 q^{33} +1.00000 q^{36} -6.00000 q^{37} +6.00000i q^{38} +(4.00000 - 6.00000i) q^{39} +(-3.00000 + 6.00000i) q^{40} +8.00000i q^{41} -6.00000i q^{43} +2.00000i q^{44} +(-1.00000 + 2.00000i) q^{45} +6.00000i q^{46} +8.00000 q^{47} -2.00000i q^{48} -7.00000 q^{49} +(-3.00000 - 4.00000i) q^{50} +(3.00000 + 2.00000i) q^{52} -12.0000i q^{53} +4.00000i q^{54} +(-4.00000 - 2.00000i) q^{55} -12.0000 q^{57} +6.00000 q^{58} -2.00000i q^{59} +(-4.00000 - 2.00000i) q^{60} +6.00000 q^{61} -6.00000i q^{62} +7.00000 q^{64} +(-7.00000 + 4.00000i) q^{65} +4.00000 q^{66} -12.0000 q^{67} -12.0000 q^{69} +2.00000i q^{71} +3.00000 q^{72} +6.00000 q^{73} -6.00000 q^{74} +(8.00000 - 6.00000i) q^{75} -6.00000i q^{76} +(4.00000 - 6.00000i) q^{78} +(-1.00000 + 2.00000i) q^{80} -11.0000 q^{81} +8.00000i q^{82} +4.00000 q^{83} -6.00000i q^{86} +12.0000i q^{87} +6.00000i q^{88} +8.00000i q^{89} +(-1.00000 + 2.00000i) q^{90} -6.00000i q^{92} +12.0000 q^{93} +8.00000 q^{94} +(12.0000 + 6.00000i) q^{95} +10.0000i q^{96} +6.00000 q^{97} -7.00000 q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 6 * q^8 - 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 6 q^{8} - 2 q^{9} + 2 q^{10} - 6 q^{13} + 8 q^{15} - 2 q^{16} - 2 q^{18} - 2 q^{20} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 8 q^{30} + 10 q^{32} + 8 q^{33} + 2 q^{36} - 12 q^{37} + 8 q^{39} - 6 q^{40} - 2 q^{45} + 16 q^{47} - 14 q^{49} - 6 q^{50} + 6 q^{52} - 8 q^{55} - 24 q^{57} + 12 q^{58} - 8 q^{60} + 12 q^{61} + 14 q^{64} - 14 q^{65} + 8 q^{66} - 24 q^{67} - 24 q^{69} + 6 q^{72} + 12 q^{73} - 12 q^{74} + 16 q^{75} + 8 q^{78} - 2 q^{80} - 22 q^{81} + 8 q^{83} - 2 q^{90} + 24 q^{93} + 16 q^{94} + 24 q^{95} + 12 q^{97} - 14 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 6 * q^8 - 2 * q^9 + 2 * q^10 - 6 * q^13 + 8 * q^15 - 2 * q^16 - 2 * q^18 - 2 * q^20 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 8 * q^30 + 10 * q^32 + 8 * q^33 + 2 * q^36 - 12 * q^37 + 8 * q^39 - 6 * q^40 - 2 * q^45 + 16 * q^47 - 14 * q^49 - 6 * q^50 + 6 * q^52 - 8 * q^55 - 24 * q^57 + 12 * q^58 - 8 * q^60 + 12 * q^61 + 14 * q^64 - 14 * q^65 + 8 * q^66 - 24 * q^67 - 24 * q^69 + 6 * q^72 + 12 * q^73 - 12 * q^74 + 16 * q^75 + 8 * q^78 - 2 * q^80 - 22 * q^81 + 8 * q^83 - 2 * q^90 + 24 * q^93 + 16 * q^94 + 24 * q^95 + 12 * q^97 - 14 * q^98

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