LMFDB - Embedded newform 720.2.t.a.541.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(181,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("720.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.t (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			541.2
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	720.541
Dual form			720.2.t.a.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +2.00000 q^{4} +(-0.707107 + 0.707107i) q^{5} +4.82843i q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+1.41421 q^{2} +2.00000 q^{4} +(-0.707107 + 0.707107i) q^{5} +4.82843i q^{7} +2.82843 q^{8} +(-1.00000 + 1.00000i) q^{10} +(-1.41421 + 1.41421i) q^{11} +(-0.585786 - 0.585786i) q^{13} +6.82843i q^{14} +4.00000 q^{16} -5.41421 q^{17} +(3.82843 + 3.82843i) q^{19} +(-1.41421 + 1.41421i) q^{20} +(-2.00000 + 2.00000i) q^{22} -5.41421i q^{23} -1.00000i q^{25} +(-0.828427 - 0.828427i) q^{26} +9.65685i q^{28} +(0.585786 + 0.585786i) q^{29} +3.65685 q^{31} +5.65685 q^{32} -7.65685 q^{34} +(-3.41421 - 3.41421i) q^{35} +(4.58579 - 4.58579i) q^{37} +(5.41421 + 5.41421i) q^{38} +(-2.00000 + 2.00000i) q^{40} +4.82843i q^{41} +(3.65685 - 3.65685i) q^{43} +(-2.82843 + 2.82843i) q^{44} -7.65685i q^{46} +7.07107 q^{47} -16.3137 q^{49} -1.41421i q^{50} +(-1.17157 - 1.17157i) q^{52} +(4.00000 - 4.00000i) q^{53} -2.00000i q^{55} +13.6569i q^{56} +(0.828427 + 0.828427i) q^{58} +(7.41421 - 7.41421i) q^{59} +(9.48528 + 9.48528i) q^{61} +5.17157 q^{62} +8.00000 q^{64} +0.828427 q^{65} +(-7.65685 - 7.65685i) q^{67} -10.8284 q^{68} +(-4.82843 - 4.82843i) q^{70} -8.00000i q^{71} -3.17157i q^{73} +(6.48528 - 6.48528i) q^{74} +(7.65685 + 7.65685i) q^{76} +(-6.82843 - 6.82843i) q^{77} -13.6569 q^{79} +(-2.82843 + 2.82843i) q^{80} +6.82843i q^{82} +(3.07107 + 3.07107i) q^{83} +(3.82843 - 3.82843i) q^{85} +(5.17157 - 5.17157i) q^{86} +(-4.00000 + 4.00000i) q^{88} +3.65685i q^{89} +(2.82843 - 2.82843i) q^{91} -10.8284i q^{92} +10.0000 q^{94} -5.41421 q^{95} -13.3137 q^{97} -23.0711 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4}+O(q^{10}) $ 4 * q + 8 * q^4	$ 4 q + 8 q^{4} - 4 q^{10} - 8 q^{13} + 16 q^{16} - 16 q^{17} + 4 q^{19} - 8 q^{22} + 8 q^{26} + 8 q^{29} - 8 q^{31} - 8 q^{34} - 8 q^{35} + 24 q^{37} + 16 q^{38} - 8 q^{40} - 8 q^{43} - 20 q^{49} - 16 q^{52} + 16 q^{53} - 8 q^{58} + 24 q^{59} + 4 q^{61} + 32 q^{62} + 32 q^{64} - 8 q^{65} - 8 q^{67} - 32 q^{68} - 8 q^{70} - 8 q^{74} + 8 q^{76} - 16 q^{77} - 32 q^{79} - 16 q^{83} + 4 q^{85} + 32 q^{86} - 16 q^{88} + 40 q^{94} - 16 q^{95} - 8 q^{97} - 64 q^{98}+O(q^{100}) $ 4 * q + 8 * q^4 - 4 * q^10 - 8 * q^13 + 16 * q^16 - 16 * q^17 + 4 * q^19 - 8 * q^22 + 8 * q^26 + 8 * q^29 - 8 * q^31 - 8 * q^34 - 8 * q^35 + 24 * q^37 + 16 * q^38 - 8 * q^40 - 8 * q^43 - 20 * q^49 - 16 * q^52 + 16 * q^53 - 8 * q^58 + 24 * q^59 + 4 * q^61 + 32 * q^62 + 32 * q^64 - 8 * q^65 - 8 * q^67 - 32 * q^68 - 8 * q^70 - 8 * q^74 + 8 * q^76 - 16 * q^77 - 32 * q^79 - 16 * q^83 + 4 * q^85 + 32 * q^86 - 16 * q^88 + 40 * q^94 - 16 * q^95 - 8 * q^97 - 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

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 $

$2$	1.41421			1.00000
$2$	1.41421			1.00000
$3$		0			0
$3$		0			0
$4$	2.00000			1.00000
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$		0			0
$7$			4.82843i			1.82497i	0.409106	+	0.912487i	$0.365841\pi$
$7$			4.82843i			1.82497i	−0.409106	+	0.912487i	$0.634159\pi$
$8$	2.82843			1.00000
$9$		0			0
$10$	−1.00000	+	1.00000i	−0.316228	+	0.316228i
$11$	−1.41421	+	1.41421i	−0.426401	+	0.426401i	−0.887401	−	0.460999i	$-0.847491\pi$
$11$	−1.41421	+	1.41421i	−0.426401	+	0.426401i	0.460999	+	0.887401i	$0.347491\pi$
$12$		0			0
$13$	−0.585786	−	0.585786i	−0.162468	−	0.162468i	0.621191	−	0.783659i	$-0.286649\pi$
$13$	−0.585786	−	0.585786i	−0.162468	−	0.162468i	−0.783659	+	0.621191i	$0.786649\pi$
$14$			6.82843i			1.82497i
$15$		0			0
$16$	4.00000			1.00000
$17$	−5.41421			−1.31314			−0.656570	−	0.754265i	$-0.727993\pi$
$17$	−5.41421			−1.31314			−0.656570	+	0.754265i	$0.727993\pi$
$18$		0			0
$19$	3.82843	+	3.82843i	0.878301	+	0.878301i	0.993359	−	0.115057i	$-0.0367052\pi$
$19$	3.82843	+	3.82843i	0.878301	+	0.878301i	−0.115057	+	0.993359i	$0.536705\pi$
$20$	−1.41421	+	1.41421i	−0.316228	+	0.316228i
$21$		0			0
$22$	−2.00000	+	2.00000i	−0.426401	+	0.426401i
$23$		−	5.41421i		−	1.12894i	−0.825453	−	0.564471i	$-0.809080\pi$
$23$		−	5.41421i		−	1.12894i	0.825453	−	0.564471i	$-0.190920\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	−0.828427	−	0.828427i	−0.162468	−	0.162468i
$27$		0			0
$28$			9.65685i			1.82497i
$29$	0.585786	+	0.585786i	0.108778	+	0.108778i	0.759401	−	0.650623i	$-0.225492\pi$
$29$	0.585786	+	0.585786i	0.108778	+	0.108778i	−0.650623	+	0.759401i	$0.725492\pi$
$30$		0			0
$31$	3.65685			0.656790			0.328395	−	0.944540i	$-0.393492\pi$
$31$	3.65685			0.656790			0.328395	+	0.944540i	$0.393492\pi$
$32$	5.65685			1.00000
$33$		0			0
$34$	−7.65685			−1.31314
$35$	−3.41421	−	3.41421i	−0.577107	−	0.577107i
$36$		0			0
$37$	4.58579	−	4.58579i	0.753899	−	0.753899i	−0.221306	−	0.975204i	$-0.571032\pi$
$37$	4.58579	−	4.58579i	0.753899	−	0.753899i	0.975204	+	0.221306i	$0.0710319\pi$
$38$	5.41421	+	5.41421i	0.878301	+	0.878301i
$39$		0			0
$40$	−2.00000	+	2.00000i	−0.316228	+	0.316228i
$41$			4.82843i			0.754074i	0.926198	+	0.377037i	$0.123057\pi$
$41$			4.82843i			0.754074i	−0.926198	+	0.377037i	$0.876943\pi$
$42$		0			0
$43$	3.65685	−	3.65685i	0.557665	−	0.557665i	−0.370977	−	0.928642i	$-0.620977\pi$
$43$	3.65685	−	3.65685i	0.557665	−	0.557665i	0.928642	+	0.370977i	$0.120977\pi$
$44$	−2.82843	+	2.82843i	−0.426401	+	0.426401i
$45$		0			0
$46$		−	7.65685i		−	1.12894i
$47$	7.07107			1.03142			0.515711	−	0.856763i	$-0.327528\pi$
$47$	7.07107			1.03142			0.515711	+	0.856763i	$0.327528\pi$
$48$		0			0
$49$	−16.3137			−2.33053
$50$		−	1.41421i		−	0.200000i
$51$		0			0
$52$	−1.17157	−	1.17157i	−0.162468	−	0.162468i
$53$	4.00000	−	4.00000i	0.549442	−	0.549442i	−0.376837	−	0.926279i	$-0.622988\pi$
$53$	4.00000	−	4.00000i	0.549442	−	0.549442i	0.926279	+	0.376837i	$0.122988\pi$
$54$		0			0
$55$		−	2.00000i		−	0.269680i
$56$			13.6569i			1.82497i
$57$		0			0
$58$	0.828427	+	0.828427i	0.108778	+	0.108778i
$59$	7.41421	−	7.41421i	0.965248	−	0.965248i	−0.0341677	−	0.999416i	$-0.510878\pi$
$59$	7.41421	−	7.41421i	0.965248	−	0.965248i	0.999416	+	0.0341677i	$0.0108780\pi$
$60$		0			0
$61$	9.48528	+	9.48528i	1.21447	+	1.21447i	0.969542	+	0.244923i	$0.0787628\pi$
$61$	9.48528	+	9.48528i	1.21447	+	1.21447i	0.244923	+	0.969542i	$0.421237\pi$
$62$	5.17157			0.656790
$63$		0			0
$64$	8.00000			1.00000
$65$	0.828427			0.102754
$66$		0			0
$67$	−7.65685	−	7.65685i	−0.935434	−	0.935434i	0.0626048	−	0.998038i	$-0.480059\pi$
$67$	−7.65685	−	7.65685i	−0.935434	−	0.935434i	−0.998038	+	0.0626048i	$0.980059\pi$
$68$	−10.8284			−1.31314
$69$		0			0
$70$	−4.82843	−	4.82843i	−0.577107	−	0.577107i
$71$		−	8.00000i		−	0.949425i	−0.880141	−	0.474713i	$-0.842552\pi$
$71$		−	8.00000i		−	0.949425i	0.880141	−	0.474713i	$-0.157448\pi$
$72$		0			0
$73$		−	3.17157i		−	0.371205i	−0.982625	−	0.185602i	$-0.940576\pi$
$73$		−	3.17157i		−	0.371205i	0.982625	−	0.185602i	$-0.0594236\pi$
$74$	6.48528	−	6.48528i	0.753899	−	0.753899i
$75$		0			0
$76$	7.65685	+	7.65685i	0.878301	+	0.878301i
$77$	−6.82843	−	6.82843i	−0.778171	−	0.778171i
$78$		0			0
$79$	−13.6569			−1.53652			−0.768258	−	0.640140i	$-0.778876\pi$
$79$	−13.6569			−1.53652			−0.768258	+	0.640140i	$0.778876\pi$
$80$	−2.82843	+	2.82843i	−0.316228	+	0.316228i
$81$		0			0
$82$			6.82843i			0.754074i
$83$	3.07107	+	3.07107i	0.337093	+	0.337093i	0.855272	−	0.518179i	$-0.173390\pi$
$83$	3.07107	+	3.07107i	0.337093	+	0.337093i	−0.518179	+	0.855272i	$0.673390\pi$
$84$		0			0
$85$	3.82843	−	3.82843i	0.415251	−	0.415251i
$86$	5.17157	−	5.17157i	0.557665	−	0.557665i
$87$		0			0
$88$	−4.00000	+	4.00000i	−0.426401	+	0.426401i
$89$			3.65685i			0.387626i	0.981039	+	0.193813i	$0.0620855\pi$
$89$			3.65685i			0.387626i	−0.981039	+	0.193813i	$0.937915\pi$
$90$		0			0
$91$	2.82843	−	2.82843i	0.296500	−	0.296500i
$92$		−	10.8284i		−	1.12894i
$93$		0			0
$94$	10.0000			1.03142
$95$	−5.41421			−0.555487
$96$		0			0
$97$	−13.3137			−1.35180			−0.675901	−	0.736992i	$-0.736245\pi$
$97$	−13.3137			−1.35180			−0.675901	+	0.736992i	$0.736245\pi$
$98$	−23.0711			−2.33053
$99$		0			0
$100$		−	2.00000i		−	0.200000i
$101$	0.585786	−	0.585786i	0.0582879	−	0.0582879i	−0.677362	−	0.735650i	$-0.736877\pi$
$101$	0.585786	−	0.585786i	0.0582879	−	0.0582879i	0.735650	+	0.677362i	$0.236877\pi$
$102$		0			0
$103$		−	10.0000i		−	0.985329i	−0.870219	−	0.492665i	$-0.836023\pi$
$103$		−	10.0000i		−	0.985329i	0.870219	−	0.492665i	$-0.163977\pi$
$104$	−1.65685	−	1.65685i	−0.162468	−	0.162468i
$105$		0			0
$106$	5.65685	−	5.65685i	0.549442	−	0.549442i
$107$	−12.2426	+	12.2426i	−1.18354	+	1.18354i	−0.204720	+	0.978821i	$0.565628\pi$
$107$	−12.2426	+	12.2426i	−1.18354	+	1.18354i	−0.978821	+	0.204720i	$0.934372\pi$
$108$		0			0
$109$	−5.48528	−	5.48528i	−0.525395	−	0.525395i	0.393801	−	0.919196i	$-0.371160\pi$
$109$	−5.48528	−	5.48528i	−0.525395	−	0.525395i	−0.919196	+	0.393801i	$0.871160\pi$
$110$		−	2.82843i		−	0.269680i
$111$		0			0
$112$			19.3137i			1.82497i
$113$	−17.4142			−1.63819			−0.819096	−	0.573657i	$-0.805524\pi$
$113$	−17.4142			−1.63819			−0.819096	+	0.573657i	$0.805524\pi$
$114$		0			0
$115$	3.82843	+	3.82843i	0.357003	+	0.357003i
$116$	1.17157	+	1.17157i	0.108778	+	0.108778i
$117$		0			0
$118$	10.4853	−	10.4853i	0.965248	−	0.965248i
$119$		−	26.1421i		−	2.39645i
$120$		0			0
$121$			7.00000i			0.636364i
$122$	13.4142	+	13.4142i	1.21447	+	1.21447i
$123$		0			0
$124$	7.31371			0.656790
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$	19.6569			1.74426			0.872132	−	0.489271i	$-0.162737\pi$
$127$	19.6569			1.74426			0.872132	+	0.489271i	$0.162737\pi$
$128$	11.3137			1.00000
$129$		0			0
$130$	1.17157			0.102754
$131$	13.4142	+	13.4142i	1.17201	+	1.17201i	0.981731	+	0.190274i	$0.0609377\pi$
$131$	13.4142	+	13.4142i	1.17201	+	1.17201i	0.190274	+	0.981731i	$0.439062\pi$
$132$		0			0
$133$	−18.4853	+	18.4853i	−1.60288	+	1.60288i
$134$	−10.8284	−	10.8284i	−0.935434	−	0.935434i
$135$		0			0
$136$	−15.3137			−1.31314
$137$		−	4.24264i		−	0.362473i	−0.983440	−	0.181237i	$-0.941990\pi$
$137$		−	4.24264i		−	0.362473i	0.983440	−	0.181237i	$-0.0580100\pi$
$138$		0			0
$139$	6.65685	−	6.65685i	0.564627	−	0.564627i	−0.365991	−	0.930618i	$-0.619270\pi$
$139$	6.65685	−	6.65685i	0.564627	−	0.564627i	0.930618	+	0.365991i	$0.119270\pi$
$140$	−6.82843	−	6.82843i	−0.577107	−	0.577107i
$141$		0			0
$142$		−	11.3137i		−	0.949425i
$143$	1.65685			0.138553
$144$		0			0
$145$	−0.828427			−0.0687971
$146$		−	4.48528i		−	0.371205i
$147$		0			0
$148$	9.17157	−	9.17157i	0.753899	−	0.753899i
$149$	−7.07107	+	7.07107i	−0.579284	+	0.579284i	−0.934706	−	0.355422i	$-0.884337\pi$
$149$	−7.07107	+	7.07107i	−0.579284	+	0.579284i	0.355422	+	0.934706i	$0.384337\pi$
$150$		0			0
$151$		−	3.65685i		−	0.297591i	−0.988868	−	0.148795i	$-0.952460\pi$
$151$		−	3.65685i		−	0.297591i	0.988868	−	0.148795i	$-0.0475395\pi$
$152$	10.8284	+	10.8284i	0.878301	+	0.878301i
$153$		0			0
$154$	−9.65685	−	9.65685i	−0.778171	−	0.778171i
$155$	−2.58579	+	2.58579i	−0.207695	+	0.207695i
$156$		0			0
$157$	−7.07107	−	7.07107i	−0.564333	−	0.564333i	0.366203	−	0.930535i	$-0.380658\pi$
$157$	−7.07107	−	7.07107i	−0.564333	−	0.564333i	−0.930535	+	0.366203i	$0.880658\pi$
$158$	−19.3137			−1.53652
$159$		0			0
$160$	−4.00000	+	4.00000i	−0.316228	+	0.316228i
$161$	26.1421			2.06029
$162$		0			0
$163$	2.34315	+	2.34315i	0.183529	+	0.183529i	0.792892	−	0.609362i	$-0.208575\pi$
$163$	2.34315	+	2.34315i	0.183529	+	0.183529i	−0.609362	+	0.792892i	$0.708575\pi$
$164$			9.65685i			0.754074i
$165$		0			0
$166$	4.34315	+	4.34315i	0.337093	+	0.337093i
$167$		−	3.07107i		−	0.237646i	−0.992915	−	0.118823i	$-0.962088\pi$
$167$		−	3.07107i		−	0.237646i	0.992915	−	0.118823i	$-0.0379122\pi$
$168$		0			0
$169$		−	12.3137i		−	0.947208i
$170$	5.41421	−	5.41421i	0.415251	−	0.415251i
$171$		0			0
$172$	7.31371	−	7.31371i	0.557665	−	0.557665i
$173$	−11.3137	−	11.3137i	−0.860165	−	0.860165i	0.131192	−	0.991357i	$-0.458120\pi$
$173$	−11.3137	−	11.3137i	−0.860165	−	0.860165i	−0.991357	+	0.131192i	$0.958120\pi$
$174$		0			0
$175$	4.82843			0.364995
$176$	−5.65685	+	5.65685i	−0.426401	+	0.426401i
$177$		0			0
$178$			5.17157i			0.387626i
$179$	10.5858	+	10.5858i	0.791219	+	0.791219i	0.981692	−	0.190474i	$-0.0610023\pi$
$179$	10.5858	+	10.5858i	0.791219	+	0.791219i	−0.190474	+	0.981692i	$0.561002\pi$
$180$		0			0
$181$	8.17157	−	8.17157i	0.607388	−	0.607388i	−0.334875	−	0.942263i	$-0.608694\pi$
$181$	8.17157	−	8.17157i	0.607388	−	0.607388i	0.942263	+	0.334875i	$0.108694\pi$
$182$	4.00000	−	4.00000i	0.296500	−	0.296500i
$183$		0			0
$184$		−	15.3137i		−	1.12894i
$185$			6.48528i			0.476807i
$186$		0			0
$187$	7.65685	−	7.65685i	0.559925	−	0.559925i
$188$	14.1421			1.03142
$189$		0			0
$190$	−7.65685			−0.555487
$191$	4.48528			0.324544			0.162272	−	0.986746i	$-0.448118\pi$
$191$	4.48528			0.324544			0.162272	+	0.986746i	$0.448118\pi$
$192$		0			0
$193$	0.828427			0.0596315			0.0298157	−	0.999555i	$-0.490508\pi$
$193$	0.828427			0.0596315			0.0298157	+	0.999555i	$0.490508\pi$
$194$	−18.8284			−1.35180
$195$		0			0
$196$	−32.6274			−2.33053
$197$	7.75736	−	7.75736i	0.552689	−	0.552689i	−0.374527	−	0.927216i	$-0.622195\pi$
$197$	7.75736	−	7.75736i	0.552689	−	0.552689i	0.927216	+	0.374527i	$0.122195\pi$
$198$		0			0
$199$		−	6.34315i		−	0.449654i	−0.974399	−	0.224827i	$-0.927818\pi$
$199$		−	6.34315i		−	0.449654i	0.974399	−	0.224827i	$-0.0721816\pi$
$200$		−	2.82843i		−	0.200000i
$201$		0			0
$202$	0.828427	−	0.828427i	0.0582879	−	0.0582879i
$203$	−2.82843	+	2.82843i	−0.198517	+	0.198517i
$204$		0			0
$205$	−3.41421	−	3.41421i	−0.238459	−	0.238459i
$206$		−	14.1421i		−	0.985329i
$207$		0			0
$208$	−2.34315	−	2.34315i	−0.162468	−	0.162468i
$209$	−10.8284			−0.749018
$210$		0			0
$211$	2.65685	+	2.65685i	0.182905	+	0.182905i	0.792621	−	0.609715i	$-0.208716\pi$
$211$	2.65685	+	2.65685i	0.182905	+	0.182905i	−0.609715	+	0.792621i	$0.708716\pi$
$212$	8.00000	−	8.00000i	0.549442	−	0.549442i
$213$		0			0
$214$	−17.3137	+	17.3137i	−1.18354	+	1.18354i
$215$			5.17157i			0.352698i
$216$		0			0
$217$			17.6569i			1.19863i
$218$	−7.75736	−	7.75736i	−0.525395	−	0.525395i
$219$		0			0
$220$		−	4.00000i		−	0.269680i
$221$	3.17157	+	3.17157i	0.213343	+	0.213343i
$222$		0			0
$223$	−15.1716			−1.01596			−0.507982	−	0.861368i	$-0.669608\pi$
$223$	−15.1716			−1.01596			−0.507982	+	0.861368i	$0.669608\pi$
$224$			27.3137i			1.82497i
$225$		0			0
$226$	−24.6274			−1.63819
$227$	14.5858	+	14.5858i	0.968093	+	0.968093i	0.999506	−	0.0314138i	$-0.0100010\pi$
$227$	14.5858	+	14.5858i	0.968093	+	0.968093i	−0.0314138	+	0.999506i	$0.510001\pi$
$228$		0			0
$229$	−13.0000	+	13.0000i	−0.859064	+	0.859064i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$	−13.0000	+	13.0000i	−0.859064	+	0.859064i	0.132164	+	0.991228i	$0.457808\pi$
$230$	5.41421	+	5.41421i	0.357003	+	0.357003i
$231$		0			0
$232$	1.65685	+	1.65685i	0.108778	+	0.108778i
$233$		−	3.55635i		−	0.232984i	−0.993192	−	0.116492i	$-0.962835\pi$
$233$		−	3.55635i		−	0.232984i	0.993192	−	0.116492i	$-0.0371650\pi$
$234$		0			0
$235$	−5.00000	+	5.00000i	−0.326164	+	0.326164i
$236$	14.8284	−	14.8284i	0.965248	−	0.965248i
$237$		0			0
$238$		−	36.9706i		−	2.39645i
$239$	−20.9706			−1.35647			−0.678236	−	0.734844i	$-0.737255\pi$
$239$	−20.9706			−1.35647			−0.678236	+	0.734844i	$0.737255\pi$
$240$		0			0
$241$	−10.3431			−0.666261			−0.333130	−	0.942881i	$-0.608105\pi$
$241$	−10.3431			−0.666261			−0.333130	+	0.942881i	$0.608105\pi$
$242$			9.89949i			0.636364i
$243$		0			0
$244$	18.9706	+	18.9706i	1.21447	+	1.21447i
$245$	11.5355	−	11.5355i	0.736978	−	0.736978i
$246$		0			0
$247$		−	4.48528i		−	0.285392i
$248$	10.3431			0.656790
$249$		0			0
$250$	1.00000	+	1.00000i	0.0632456	+	0.0632456i
$251$	3.89949	−	3.89949i	0.246134	−	0.246134i	−0.573248	−	0.819382i	$-0.694317\pi$
$251$	3.89949	−	3.89949i	0.246134	−	0.246134i	0.819382	+	0.573248i	$0.194317\pi$
$252$		0			0
$253$	7.65685	+	7.65685i	0.481382	+	0.481382i
$254$	27.7990			1.74426
$255$		0			0
$256$	16.0000			1.00000
$257$	−10.3848			−0.647785			−0.323892	−	0.946094i	$-0.604992\pi$
$257$	−10.3848			−0.647785			−0.323892	+	0.946094i	$0.604992\pi$
$258$		0			0
$259$	22.1421	+	22.1421i	1.37585	+	1.37585i
$260$	1.65685			0.102754
$261$		0			0
$262$	18.9706	+	18.9706i	1.17201	+	1.17201i
$263$			22.3848i			1.38030i	0.723664	+	0.690152i	$0.242456\pi$
$263$			22.3848i			1.38030i	−0.723664	+	0.690152i	$0.757544\pi$
$264$		0			0
$265$			5.65685i			0.347498i
$266$	−26.1421	+	26.1421i	−1.60288	+	1.60288i
$267$		0			0
$268$	−15.3137	−	15.3137i	−0.935434	−	0.935434i
$269$	18.7279	+	18.7279i	1.14186	+	1.14186i	0.988109	+	0.153752i	$0.0491357\pi$
$269$	18.7279	+	18.7279i	1.14186	+	1.14186i	0.153752	+	0.988109i	$0.450864\pi$
$270$		0			0
$271$	23.3137			1.41621			0.708103	−	0.706109i	$-0.249551\pi$
$271$	23.3137			1.41621			0.708103	+	0.706109i	$0.249551\pi$
$272$	−21.6569			−1.31314
$273$		0			0
$274$		−	6.00000i		−	0.362473i
$275$	1.41421	+	1.41421i	0.0852803	+	0.0852803i
$276$		0			0
$277$	16.5858	−	16.5858i	0.996543	−	0.996543i	−0.00345072	−	0.999994i	$-0.501098\pi$
$277$	16.5858	−	16.5858i	0.996543	−	0.996543i	0.999994	+	0.00345072i	$0.00109840\pi$
$278$	9.41421	−	9.41421i	0.564627	−	0.564627i
$279$		0			0
$280$	−9.65685	−	9.65685i	−0.577107	−	0.577107i
$281$		−	16.1421i		−	0.962959i	−0.876457	−	0.481480i	$-0.840100\pi$
$281$		−	16.1421i		−	0.962959i	0.876457	−	0.481480i	$-0.159900\pi$
$282$		0			0
$283$	−11.6569	+	11.6569i	−0.692928	+	0.692928i	−0.962875	−	0.269947i	$-0.912994\pi$
$283$	−11.6569	+	11.6569i	−0.692928	+	0.692928i	0.269947	+	0.962875i	$0.412994\pi$
$284$		−	16.0000i		−	0.949425i
$285$		0			0
$286$	2.34315			0.138553
$287$	−23.3137			−1.37616
$288$		0			0
$289$	12.3137			0.724336
$290$	−1.17157			−0.0687971
$291$		0			0
$292$		−	6.34315i		−	0.371205i
$293$	2.34315	−	2.34315i	0.136888	−	0.136888i	−0.635342	−	0.772231i	$-0.719141\pi$
$293$	2.34315	−	2.34315i	0.136888	−	0.136888i	0.772231	+	0.635342i	$0.219141\pi$
$294$		0			0
$295$			10.4853i			0.610477i
$296$	12.9706	−	12.9706i	0.753899	−	0.753899i
$297$		0			0
$298$	−10.0000	+	10.0000i	−0.579284	+	0.579284i
$299$	−3.17157	+	3.17157i	−0.183417	+	0.183417i
$300$		0			0
$301$	17.6569	+	17.6569i	1.01772	+	1.01772i
$302$		−	5.17157i		−	0.297591i
$303$		0			0
$304$	15.3137	+	15.3137i	0.878301	+	0.878301i
$305$	−13.4142			−0.768096
$306$		0			0
$307$	−3.65685	−	3.65685i	−0.208708	−	0.208708i	0.595010	−	0.803718i	$-0.297148\pi$
$307$	−3.65685	−	3.65685i	−0.208708	−	0.208708i	−0.803718	+	0.595010i	$0.797148\pi$
$308$	−13.6569	−	13.6569i	−0.778171	−	0.778171i
$309$		0			0
$310$	−3.65685	+	3.65685i	−0.207695	+	0.207695i
$311$			0.970563i			0.0550356i	0.999621	+	0.0275178i	$0.00876029\pi$
$311$			0.970563i			0.0550356i	−0.999621	+	0.0275178i	$0.991240\pi$
$312$		0			0
$313$			11.1716i			0.631455i	0.948850	+	0.315727i	$0.102248\pi$
$313$			11.1716i			0.631455i	−0.948850	+	0.315727i	$0.897752\pi$
$314$	−10.0000	−	10.0000i	−0.564333	−	0.564333i
$315$		0			0
$316$	−27.3137			−1.53652
$317$	6.58579	+	6.58579i	0.369895	+	0.369895i	0.867439	−	0.497544i	$-0.165765\pi$
$317$	6.58579	+	6.58579i	0.369895	+	0.369895i	−0.497544	+	0.867439i	$0.665765\pi$
$318$		0			0
$319$	−1.65685			−0.0927660
$320$	−5.65685	+	5.65685i	−0.316228	+	0.316228i
$321$		0			0
$322$	36.9706			2.06029
$323$	−20.7279	−	20.7279i	−1.15333	−	1.15333i
$324$		0			0
$325$	−0.585786	+	0.585786i	−0.0324936	+	0.0324936i
$326$	3.31371	+	3.31371i	0.183529	+	0.183529i
$327$		0			0
$328$			13.6569i			0.754074i
$329$			34.1421i			1.88232i
$330$		0			0
$331$	10.1716	−	10.1716i	0.559080	−	0.559080i	−0.369965	−	0.929046i	$-0.620630\pi$
$331$	10.1716	−	10.1716i	0.559080	−	0.559080i	0.929046	+	0.369965i	$0.120630\pi$
$332$	6.14214	+	6.14214i	0.337093	+	0.337093i
$333$		0			0
$334$		−	4.34315i		−	0.237646i
$335$	10.8284			0.591620
$336$		0			0
$337$	2.48528			0.135382			0.0676910	−	0.997706i	$-0.478437\pi$
$337$	2.48528			0.135382			0.0676910	+	0.997706i	$0.478437\pi$
$338$		−	17.4142i		−	0.947208i
$339$		0			0
$340$	7.65685	−	7.65685i	0.415251	−	0.415251i
$341$	−5.17157	+	5.17157i	−0.280056	+	0.280056i
$342$		0			0
$343$		−	44.9706i		−	2.42818i
$344$	10.3431	−	10.3431i	0.557665	−	0.557665i
$345$		0			0
$346$	−16.0000	−	16.0000i	−0.860165	−	0.860165i
$347$	−9.17157	+	9.17157i	−0.492356	+	0.492356i	−0.909048	−	0.416692i	$-0.863189\pi$
$347$	−9.17157	+	9.17157i	−0.492356	+	0.492356i	0.416692	+	0.909048i	$0.363189\pi$
$348$		0			0
$349$	−7.48528	−	7.48528i	−0.400678	−	0.400678i	0.477794	−	0.878472i	$-0.341437\pi$
$349$	−7.48528	−	7.48528i	−0.400678	−	0.400678i	−0.878472	+	0.477794i	$0.841437\pi$
$350$	6.82843			0.364995
$351$		0			0
$352$	−8.00000	+	8.00000i	−0.426401	+	0.426401i
$353$	−21.4142			−1.13976			−0.569882	−	0.821727i	$-0.693011\pi$
$353$	−21.4142			−1.13976			−0.569882	+	0.821727i	$0.693011\pi$
$354$		0			0
$355$	5.65685	+	5.65685i	0.300235	+	0.300235i
$356$			7.31371i			0.387626i
$357$		0			0
$358$	14.9706	+	14.9706i	0.791219	+	0.791219i
$359$		−	18.8284i		−	0.993726i	−0.867829	−	0.496863i	$-0.834485\pi$
$359$		−	18.8284i		−	0.993726i	0.867829	−	0.496863i	$-0.165515\pi$
$360$		0			0
$361$			10.3137i			0.542827i
$362$	11.5563	−	11.5563i	0.607388	−	0.607388i
$363$		0			0
$364$	5.65685	−	5.65685i	0.296500	−	0.296500i
$365$	2.24264	+	2.24264i	0.117385	+	0.117385i
$366$		0			0
$367$	−34.9706			−1.82545			−0.912724	−	0.408576i	$-0.866025\pi$
$367$	−34.9706			−1.82545			−0.912724	+	0.408576i	$0.866025\pi$
$368$		−	21.6569i		−	1.12894i
$369$		0			0
$370$			9.17157i			0.476807i
$371$	19.3137	+	19.3137i	1.00272	+	1.00272i
$372$		0			0
$373$	−11.0711	+	11.0711i	−0.573238	+	0.573238i	−0.933032	−	0.359794i	$-0.882847\pi$
$373$	−11.0711	+	11.0711i	−0.573238	+	0.573238i	0.359794	+	0.933032i	$0.382847\pi$
$374$	10.8284	−	10.8284i	0.559925	−	0.559925i
$375$		0			0
$376$	20.0000			1.03142
$377$		−	0.686292i		−	0.0353458i
$378$		0			0
$379$	5.34315	−	5.34315i	0.274459	−	0.274459i	−0.556433	−	0.830892i	$-0.687831\pi$
$379$	5.34315	−	5.34315i	0.274459	−	0.274459i	0.830892	+	0.556433i	$0.187831\pi$
$380$	−10.8284			−0.555487
$381$		0			0
$382$	6.34315			0.324544
$383$	23.0711			1.17888			0.589438	−	0.807813i	$-0.299349\pi$
$383$	23.0711			1.17888			0.589438	+	0.807813i	$0.299349\pi$
$384$		0			0
$385$	9.65685			0.492159
$386$	1.17157			0.0596315
$387$		0			0
$388$	−26.6274			−1.35180
$389$	10.3848	−	10.3848i	0.526529	−	0.526529i	−0.393007	−	0.919536i	$-0.628565\pi$
$389$	10.3848	−	10.3848i	0.526529	−	0.526529i	0.919536	+	0.393007i	$0.128565\pi$
$390$		0			0
$391$			29.3137i			1.48246i
$392$	−46.1421			−2.33053
$393$		0			0
$394$	10.9706	−	10.9706i	0.552689	−	0.552689i
$395$	9.65685	−	9.65685i	0.485889	−	0.485889i
$396$		0			0
$397$	−9.89949	−	9.89949i	−0.496841	−	0.496841i	0.413612	−	0.910453i	$-0.364267\pi$
$397$	−9.89949	−	9.89949i	−0.496841	−	0.496841i	−0.910453	+	0.413612i	$0.864267\pi$
$398$		−	8.97056i		−	0.449654i
$399$		0			0
$400$		−	4.00000i		−	0.200000i
$401$	−26.9706			−1.34685			−0.673423	−	0.739258i	$-0.735177\pi$
$401$	−26.9706			−1.34685			−0.673423	+	0.739258i	$0.735177\pi$
$402$		0			0
$403$	−2.14214	−	2.14214i	−0.106707	−	0.106707i
$404$	1.17157	−	1.17157i	0.0582879	−	0.0582879i
$405$		0			0
$406$	−4.00000	+	4.00000i	−0.198517	+	0.198517i
$407$			12.9706i			0.642927i
$408$		0			0
$409$			30.6274i			1.51443i	0.653167	+	0.757214i	$0.273440\pi$
$409$			30.6274i			1.51443i	−0.653167	+	0.757214i	$0.726560\pi$
$410$	−4.82843	−	4.82843i	−0.238459	−	0.238459i
$411$		0			0
$412$		−	20.0000i		−	0.985329i
$413$	35.7990	+	35.7990i	1.76155	+	1.76155i
$414$		0			0
$415$	−4.34315			−0.213197
$416$	−3.31371	−	3.31371i	−0.162468	−	0.162468i
$417$		0			0
$418$	−15.3137			−0.749018
$419$	−10.2426	−	10.2426i	−0.500386	−	0.500386i	0.411172	−	0.911558i	$-0.365120\pi$
$419$	−10.2426	−	10.2426i	−0.500386	−	0.500386i	−0.911558	+	0.411172i	$0.865120\pi$
$420$		0			0
$421$	3.00000	−	3.00000i	0.146211	−	0.146211i	−0.630212	−	0.776423i	$-0.717032\pi$
$421$	3.00000	−	3.00000i	0.146211	−	0.146211i	0.776423	+	0.630212i	$0.217032\pi$
$422$	3.75736	+	3.75736i	0.182905	+	0.182905i
$423$		0			0
$424$	11.3137	−	11.3137i	0.549442	−	0.549442i
$425$			5.41421i			0.262628i
$426$		0			0
$427$	−45.7990	+	45.7990i	−2.21637	+	2.21637i
$428$	−24.4853	+	24.4853i	−1.18354	+	1.18354i
$429$		0			0
$430$			7.31371i			0.352698i
$431$	12.4853			0.601395			0.300697	−	0.953720i	$-0.402781\pi$
$431$	12.4853			0.601395			0.300697	+	0.953720i	$0.402781\pi$
$432$		0			0
$433$	36.8284			1.76986			0.884931	−	0.465723i	$-0.154206\pi$
$433$	36.8284			1.76986			0.884931	+	0.465723i	$0.154206\pi$
$434$			24.9706i			1.19863i
$435$		0			0
$436$	−10.9706	−	10.9706i	−0.525395	−	0.525395i
$437$	20.7279	−	20.7279i	0.991551	−	0.991551i
$438$		0			0
$439$			6.34315i			0.302742i	0.988477	+	0.151371i	$0.0483688\pi$
$439$			6.34315i			0.302742i	−0.988477	+	0.151371i	$0.951631\pi$
$440$		−	5.65685i		−	0.269680i
$441$		0			0
$442$	4.48528	+	4.48528i	0.213343	+	0.213343i
$443$	10.5858	−	10.5858i	0.502946	−	0.502946i	−0.409406	−	0.912352i	$-0.634264\pi$
$443$	10.5858	−	10.5858i	0.502946	−	0.502946i	0.912352	+	0.409406i	$0.134264\pi$
$444$		0			0
$445$	−2.58579	−	2.58579i	−0.122578	−	0.122578i
$446$	−21.4558			−1.01596
$447$		0			0
$448$			38.6274i			1.82497i
$449$	−8.82843			−0.416639			−0.208320	−	0.978061i	$-0.566799\pi$
$449$	−8.82843			−0.416639			−0.208320	+	0.978061i	$0.566799\pi$
$450$		0			0
$451$	−6.82843	−	6.82843i	−0.321538	−	0.321538i
$452$	−34.8284			−1.63819
$453$		0			0
$454$	20.6274	+	20.6274i	0.968093	+	0.968093i
$455$			4.00000i			0.187523i
$456$		0			0
$457$		−	23.6569i		−	1.10662i	−0.832975	−	0.553310i	$-0.813364\pi$
$457$		−	23.6569i		−	1.10662i	0.832975	−	0.553310i	$-0.186636\pi$
$458$	−18.3848	+	18.3848i	−0.859064	+	0.859064i
$459$		0			0
$460$	7.65685	+	7.65685i	0.357003	+	0.357003i
$461$	8.72792	+	8.72792i	0.406500	+	0.406500i	0.880516	−	0.474016i	$-0.157196\pi$
$461$	8.72792	+	8.72792i	0.406500	+	0.406500i	−0.474016	+	0.880516i	$0.657196\pi$
$462$		0			0
$463$	11.6569			0.541740			0.270870	−	0.962616i	$-0.412689\pi$
$463$	11.6569			0.541740			0.270870	+	0.962616i	$0.412689\pi$
$464$	2.34315	+	2.34315i	0.108778	+	0.108778i
$465$		0			0
$466$		−	5.02944i		−	0.232984i
$467$	−7.31371	−	7.31371i	−0.338438	−	0.338438i	0.517341	−	0.855779i	$-0.326922\pi$
$467$	−7.31371	−	7.31371i	−0.338438	−	0.338438i	−0.855779	+	0.517341i	$0.826922\pi$
$468$		0			0
$469$	36.9706	−	36.9706i	1.70714	−	1.70714i
$470$	−7.07107	+	7.07107i	−0.326164	+	0.326164i
$471$		0			0
$472$	20.9706	−	20.9706i	0.965248	−	0.965248i
$473$			10.3431i			0.475578i
$474$		0			0
$475$	3.82843	−	3.82843i	0.175660	−	0.175660i
$476$		−	52.2843i		−	2.39645i
$477$		0			0
$478$	−29.6569			−1.35647
$479$	4.00000			0.182765			0.0913823	−	0.995816i	$-0.470871\pi$
$479$	4.00000			0.182765			0.0913823	+	0.995816i	$0.470871\pi$
$480$		0			0
$481$	−5.37258			−0.244969
$482$	−14.6274			−0.666261
$483$		0			0
$484$			14.0000i			0.636364i
$485$	9.41421	−	9.41421i	0.427477	−	0.427477i
$486$		0			0
$487$			26.0000i			1.17817i	0.808070	+	0.589086i	$0.200512\pi$
$487$			26.0000i			1.17817i	−0.808070	+	0.589086i	$0.799488\pi$
$488$	26.8284	+	26.8284i	1.21447	+	1.21447i
$489$		0			0
$490$	16.3137	−	16.3137i	0.736978	−	0.736978i
$491$	−2.24264	+	2.24264i	−0.101209	+	0.101209i	−0.755898	−	0.654689i	$-0.772800\pi$
$491$	−2.24264	+	2.24264i	−0.101209	+	0.101209i	0.654689	+	0.755898i	$0.272800\pi$
$492$		0			0
$493$	−3.17157	−	3.17157i	−0.142840	−	0.142840i
$494$		−	6.34315i		−	0.285392i
$495$		0			0
$496$	14.6274			0.656790
$497$	38.6274			1.73268
$498$		0			0
$499$	−4.51472	−	4.51472i	−0.202107	−	0.202107i	0.598795	−	0.800902i	$-0.295646\pi$
$499$	−4.51472	−	4.51472i	−0.202107	−	0.202107i	−0.800902	+	0.598795i	$0.795646\pi$
$500$	1.41421	+	1.41421i	0.0632456	+	0.0632456i
$501$		0			0
$502$	5.51472	−	5.51472i	0.246134	−	0.246134i
$503$			20.2426i			0.902575i	0.892379	+	0.451287i	$0.149035\pi$
$503$			20.2426i			0.902575i	−0.892379	+	0.451287i	$0.850965\pi$
$504$		0			0
$505$			0.828427i			0.0368645i
$506$	10.8284	+	10.8284i	0.481382	+	0.481382i
$507$		0			0
$508$	39.3137			1.74426
$509$	8.58579	+	8.58579i	0.380558	+	0.380558i	0.871303	−	0.490745i	$-0.163275\pi$
$509$	8.58579	+	8.58579i	0.380558	+	0.380558i	−0.490745	+	0.871303i	$0.663275\pi$
$510$		0			0
$511$	15.3137			0.677439
$512$	22.6274			1.00000
$513$		0			0
$514$	−14.6863			−0.647785
$515$	7.07107	+	7.07107i	0.311588	+	0.311588i
$516$		0			0
$517$	−10.0000	+	10.0000i	−0.439799	+	0.439799i
$518$	31.3137	+	31.3137i	1.37585	+	1.37585i
$519$		0			0
$520$	2.34315			0.102754
$521$			18.4853i			0.809855i	0.914349	+	0.404927i	$0.132703\pi$
$521$			18.4853i			0.809855i	−0.914349	+	0.404927i	$0.867297\pi$
$522$		0			0
$523$	−16.6274	+	16.6274i	−0.727066	+	0.727066i	−0.970034	−	0.242968i	$-0.921879\pi$
$523$	−16.6274	+	16.6274i	−0.727066	+	0.727066i	0.242968	+	0.970034i	$0.421879\pi$
$524$	26.8284	+	26.8284i	1.17201	+	1.17201i
$525$		0			0
$526$			31.6569i			1.38030i
$527$	−19.7990			−0.862458
$528$		0			0
$529$	−6.31371			−0.274509
$530$			8.00000i			0.347498i
$531$		0			0
$532$	−36.9706	+	36.9706i	−1.60288	+	1.60288i
$533$	2.82843	−	2.82843i	0.122513	−	0.122513i
$534$		0			0
$535$		−	17.3137i		−	0.748537i
$536$	−21.6569	−	21.6569i	−0.935434	−	0.935434i
$537$		0			0
$538$	26.4853	+	26.4853i	1.14186	+	1.14186i
$539$	23.0711	−	23.0711i	0.993741	−	0.993741i
$540$		0			0
$541$	−17.4853	−	17.4853i	−0.751751	−	0.751751i	0.223055	−	0.974806i	$-0.428397\pi$
$541$	−17.4853	−	17.4853i	−0.751751	−	0.751751i	−0.974806	+	0.223055i	$0.928397\pi$
$542$	32.9706			1.41621
$543$		0			0
$544$	−30.6274			−1.31314
$545$	7.75736			0.332289
$546$		0			0
$547$	−14.4853	−	14.4853i	−0.619346	−	0.619346i	0.326018	−	0.945364i	$-0.394293\pi$
$547$	−14.4853	−	14.4853i	−0.619346	−	0.619346i	−0.945364	+	0.326018i	$0.894293\pi$
$548$		−	8.48528i		−	0.362473i
$549$		0			0
$550$	2.00000	+	2.00000i	0.0852803	+	0.0852803i
$551$			4.48528i			0.191079i
$552$		0			0
$553$		−	65.9411i		−	2.80410i
$554$	23.4558	−	23.4558i	0.996543	−	0.996543i
$555$		0			0
$556$	13.3137	−	13.3137i	0.564627	−	0.564627i
$557$	−13.1716	−	13.1716i	−0.558097	−	0.558097i	0.370668	−	0.928765i	$-0.379129\pi$
$557$	−13.1716	−	13.1716i	−0.558097	−	0.558097i	−0.928765	+	0.370668i	$0.879129\pi$
$558$		0			0
$559$	−4.28427			−0.181205
$560$	−13.6569	−	13.6569i	−0.577107	−	0.577107i
$561$		0			0
$562$		−	22.8284i		−	0.962959i
$563$	−8.48528	−	8.48528i	−0.357612	−	0.357612i	0.505320	−	0.862932i	$-0.331374\pi$
$563$	−8.48528	−	8.48528i	−0.357612	−	0.357612i	−0.862932	+	0.505320i	$0.831374\pi$
$564$		0			0
$565$	12.3137	−	12.3137i	0.518042	−	0.518042i
$566$	−16.4853	+	16.4853i	−0.692928	+	0.692928i
$567$		0			0
$568$		−	22.6274i		−	0.949425i
$569$			10.6863i			0.447993i	0.974590	+	0.223996i	$0.0719104\pi$
$569$			10.6863i			0.447993i	−0.974590	+	0.223996i	$0.928090\pi$
$570$		0			0
$571$	−18.1716	+	18.1716i	−0.760457	+	0.760457i	−0.976405	−	0.215948i	$-0.930716\pi$
$571$	−18.1716	+	18.1716i	−0.760457	+	0.760457i	0.215948	+	0.976405i	$0.430716\pi$
$572$	3.31371			0.138553
$573$		0			0
$574$	−32.9706			−1.37616
$575$	−5.41421			−0.225788
$576$		0			0
$577$	−27.6569			−1.15137			−0.575685	−	0.817672i	$-0.695265\pi$
$577$	−27.6569			−1.15137			−0.575685	+	0.817672i	$0.695265\pi$
$578$	17.4142			0.724336
$579$		0			0
$580$	−1.65685			−0.0687971
$581$	−14.8284	+	14.8284i	−0.615187	+	0.615187i
$582$		0			0
$583$			11.3137i			0.468566i
$584$		−	8.97056i		−	0.371205i
$585$		0			0
$586$	3.31371	−	3.31371i	0.136888	−	0.136888i
$587$	3.07107	−	3.07107i	0.126757	−	0.126757i	−0.640882	−	0.767639i	$-0.721431\pi$
$587$	3.07107	−	3.07107i	0.126757	−	0.126757i	0.767639	+	0.640882i	$0.221431\pi$
$588$		0			0
$589$	14.0000	+	14.0000i	0.576860	+	0.576860i
$590$			14.8284i			0.610477i
$591$		0			0
$592$	18.3431	−	18.3431i	0.753899	−	0.753899i
$593$	−33.8995			−1.39209			−0.696043	−	0.718000i	$-0.745058\pi$
$593$	−33.8995			−1.39209			−0.696043	+	0.718000i	$0.745058\pi$
$594$		0			0
$595$	18.4853	+	18.4853i	0.757823	+	0.757823i
$596$	−14.1421	+	14.1421i	−0.579284	+	0.579284i
$597$		0			0
$598$	−4.48528	+	4.48528i	−0.183417	+	0.183417i
$599$		−	1.85786i		−	0.0759103i	−0.999279	−	0.0379551i	$-0.987916\pi$
$599$		−	1.85786i		−	0.0759103i	0.999279	−	0.0379551i	$-0.0120844\pi$
$600$		0			0
$601$		−	4.97056i		−	0.202753i	−0.994848	−	0.101377i	$-0.967675\pi$
$601$		−	4.97056i		−	0.202753i	0.994848	−	0.101377i	$-0.0323247\pi$
$602$	24.9706	+	24.9706i	1.01772	+	1.01772i
$603$		0			0
$604$		−	7.31371i		−	0.297591i
$605$	−4.94975	−	4.94975i	−0.201236	−	0.201236i
$606$		0			0
$607$	−18.4853			−0.750294			−0.375147	−	0.926965i	$-0.622408\pi$
$607$	−18.4853			−0.750294			−0.375147	+	0.926965i	$0.622408\pi$
$608$	21.6569	+	21.6569i	0.878301	+	0.878301i
$609$		0			0
$610$	−18.9706			−0.768096
$611$	−4.14214	−	4.14214i	−0.167573	−	0.167573i
$612$		0			0
$613$	−1.41421	+	1.41421i	−0.0571195	+	0.0571195i	−0.735090	−	0.677970i	$-0.762860\pi$
$613$	−1.41421	+	1.41421i	−0.0571195	+	0.0571195i	0.677970	+	0.735090i	$0.262860\pi$
$614$	−5.17157	−	5.17157i	−0.208708	−	0.208708i
$615$		0			0
$616$	−19.3137	−	19.3137i	−0.778171	−	0.778171i
$617$		−	40.7279i		−	1.63964i	−0.572618	−	0.819822i	$-0.694072\pi$
$617$		−	40.7279i		−	1.63964i	0.572618	−	0.819822i	$-0.305928\pi$
$618$		0			0
$619$	−16.3137	+	16.3137i	−0.655703	+	0.655703i	−0.954360	−	0.298657i	$-0.903461\pi$
$619$	−16.3137	+	16.3137i	−0.655703	+	0.655703i	0.298657	+	0.954360i	$0.403461\pi$
$620$	−5.17157	+	5.17157i	−0.207695	+	0.207695i
$621$		0			0
$622$			1.37258i			0.0550356i
$623$	−17.6569			−0.707407
$624$		0			0
$625$	−1.00000			−0.0400000
$626$			15.7990i			0.631455i
$627$		0			0
$628$	−14.1421	−	14.1421i	−0.564333	−	0.564333i
$629$	−24.8284	+	24.8284i	−0.989974	+	0.989974i
$630$		0			0
$631$			11.3137i			0.450392i	0.974314	+	0.225196i	$0.0723022\pi$
$631$			11.3137i			0.450392i	−0.974314	+	0.225196i	$0.927698\pi$
$632$	−38.6274			−1.53652
$633$		0			0
$634$	9.31371	+	9.31371i	0.369895	+	0.369895i
$635$	−13.8995	+	13.8995i	−0.551585	+	0.551585i
$636$		0			0
$637$	9.55635	+	9.55635i	0.378636	+	0.378636i
$638$	−2.34315			−0.0927660
$639$		0			0
$640$	−8.00000	+	8.00000i	−0.316228	+	0.316228i
$641$	−9.31371			−0.367869			−0.183935	−	0.982938i	$-0.558883\pi$
$641$	−9.31371			−0.367869			−0.183935	+	0.982938i	$0.558883\pi$
$642$		0			0
$643$	−0.970563	−	0.970563i	−0.0382753	−	0.0382753i	0.687710	−	0.725985i	$-0.258616\pi$
$643$	−0.970563	−	0.970563i	−0.0382753	−	0.0382753i	−0.725985	+	0.687710i	$0.758616\pi$
$644$	52.2843			2.06029
$645$		0			0
$646$	−29.3137	−	29.3137i	−1.15333	−	1.15333i
$647$		−	7.07107i		−	0.277992i	−0.990293	−	0.138996i	$-0.955612\pi$
$647$		−	7.07107i		−	0.277992i	0.990293	−	0.138996i	$-0.0443876\pi$
$648$		0			0
$649$			20.9706i			0.823167i
$650$	−0.828427	+	0.828427i	−0.0324936	+	0.0324936i
$651$		0			0
$652$	4.68629	+	4.68629i	0.183529	+	0.183529i
$653$	−9.65685	−	9.65685i	−0.377902	−	0.377902i	0.492443	−	0.870345i	$-0.336104\pi$
$653$	−9.65685	−	9.65685i	−0.377902	−	0.377902i	−0.870345	+	0.492443i	$0.836104\pi$
$654$		0			0
$655$	−18.9706			−0.741241
$656$			19.3137i			0.754074i
$657$		0			0
$658$			48.2843i			1.88232i
$659$	−9.27208	−	9.27208i	−0.361189	−	0.361189i	0.503062	−	0.864251i	$-0.332207\pi$
$659$	−9.27208	−	9.27208i	−0.361189	−	0.361189i	−0.864251	+	0.503062i	$0.832207\pi$
$660$		0			0
$661$	11.8284	−	11.8284i	0.460072	−	0.460072i	−0.438607	−	0.898679i	$-0.644528\pi$
$661$	11.8284	−	11.8284i	0.460072	−	0.460072i	0.898679	+	0.438607i	$0.144528\pi$
$662$	14.3848	−	14.3848i	0.559080	−	0.559080i
$663$		0			0
$664$	8.68629	+	8.68629i	0.337093	+	0.337093i
$665$		−	26.1421i		−	1.01375i
$666$		0			0
$667$	3.17157	−	3.17157i	0.122804	−	0.122804i
$668$		−	6.14214i		−	0.237646i
$669$		0			0
$670$	15.3137			0.591620
$671$	−26.8284			−1.03570
$672$		0			0
$673$	25.7990			0.994478			0.497239	−	0.867614i	$-0.334347\pi$
$673$	25.7990			0.994478			0.497239	+	0.867614i	$0.334347\pi$
$674$	3.51472			0.135382
$675$		0			0
$676$		−	24.6274i		−	0.947208i
$677$	20.0000	−	20.0000i	0.768662	−	0.768662i	−0.209209	−	0.977871i	$-0.567089\pi$
$677$	20.0000	−	20.0000i	0.768662	−	0.768662i	0.977871	+	0.209209i	$0.0670888\pi$
$678$		0			0
$679$		−	64.2843i		−	2.46700i
$680$	10.8284	−	10.8284i	0.415251	−	0.415251i
$681$		0			0
$682$	−7.31371	+	7.31371i	−0.280056	+	0.280056i
$683$	14.3431	−	14.3431i	0.548825	−	0.548825i	−0.377276	−	0.926101i	$-0.623139\pi$
$683$	14.3431	−	14.3431i	0.548825	−	0.548825i	0.926101	+	0.377276i	$0.123139\pi$
$684$		0			0
$685$	3.00000	+	3.00000i	0.114624	+	0.114624i
$686$		−	63.5980i		−	2.42818i
$687$		0			0
$688$	14.6274	−	14.6274i	0.557665	−	0.557665i
$689$	−4.68629			−0.178533
$690$		0			0
$691$	−4.17157	−	4.17157i	−0.158694	−	0.158694i	0.623294	−	0.781988i	$-0.285794\pi$
$691$	−4.17157	−	4.17157i	−0.158694	−	0.158694i	−0.781988	+	0.623294i	$0.785794\pi$
$692$	−22.6274	−	22.6274i	−0.860165	−	0.860165i
$693$		0			0
$694$	−12.9706	+	12.9706i	−0.492356	+	0.492356i
$695$			9.41421i			0.357101i
$696$		0			0
$697$		−	26.1421i		−	0.990204i
$698$	−10.5858	−	10.5858i	−0.400678	−	0.400678i
$699$		0			0
$700$	9.65685			0.364995
$701$	−29.0711	−	29.0711i	−1.09800	−	1.09800i	−0.994645	−	0.103354i	$-0.967042\pi$
$701$	−29.0711	−	29.0711i	−1.09800	−	1.09800i	−0.103354	−	0.994645i	$-0.532958\pi$
$702$		0			0
$703$	35.1127			1.32430
$704$	−11.3137	+	11.3137i	−0.426401	+	0.426401i
$705$		0			0
$706$	−30.2843			−1.13976
$707$	2.82843	+	2.82843i	0.106374	+	0.106374i
$708$		0			0
$709$	29.2843	−	29.2843i	1.09979	−	1.09979i	0.105360	−	0.994434i	$-0.466401\pi$
$709$	29.2843	−	29.2843i	1.09979	−	1.09979i	0.994434	−	0.105360i	$-0.0335994\pi$
$710$	8.00000	+	8.00000i	0.300235	+	0.300235i
$711$		0			0
$712$			10.3431i			0.387626i
$713$		−	19.7990i		−	0.741478i
$714$		0			0
$715$	−1.17157	+	1.17157i	−0.0438143	+	0.0438143i
$716$	21.1716	+	21.1716i	0.791219	+	0.791219i
$717$		0			0
$718$		−	26.6274i		−	0.993726i
$719$	−8.97056			−0.334546			−0.167273	−	0.985911i	$-0.553496\pi$
$719$	−8.97056			−0.334546			−0.167273	+	0.985911i	$0.553496\pi$
$720$		0			0
$721$	48.2843			1.79820
$722$			14.5858i			0.542827i
$723$		0			0
$724$	16.3431	−	16.3431i	0.607388	−	0.607388i
$725$	0.585786	−	0.585786i	0.0217556	−	0.0217556i
$726$		0			0
$727$		−	17.3137i		−	0.642130i	−0.947057	−	0.321065i	$-0.895959\pi$
$727$		−	17.3137i		−	0.642130i	0.947057	−	0.321065i	$-0.104041\pi$
$728$	8.00000	−	8.00000i	0.296500	−	0.296500i
$729$		0			0
$730$	3.17157	+	3.17157i	0.117385	+	0.117385i
$731$	−19.7990	+	19.7990i	−0.732292	+	0.732292i
$732$		0			0
$733$	−7.41421	−	7.41421i	−0.273850	−	0.273850i	0.556798	−	0.830648i	$-0.312030\pi$
$733$	−7.41421	−	7.41421i	−0.273850	−	0.273850i	−0.830648	+	0.556798i	$0.812030\pi$
$734$	−49.4558			−1.82545
$735$		0			0
$736$		−	30.6274i		−	1.12894i
$737$	21.6569			0.797740
$738$		0			0
$739$	−7.82843	−	7.82843i	−0.287973	−	0.287973i	0.548305	−	0.836278i	$-0.315273\pi$
$739$	−7.82843	−	7.82843i	−0.287973	−	0.287973i	−0.836278	+	0.548305i	$0.815273\pi$
$740$			12.9706i			0.476807i
$741$		0			0
$742$	27.3137	+	27.3137i	1.00272	+	1.00272i
$743$		−	46.1838i		−	1.69432i	−0.531339	−	0.847159i	$-0.678311\pi$
$743$		−	46.1838i		−	1.69432i	0.531339	−	0.847159i	$-0.321689\pi$
$744$		0			0
$745$		−	10.0000i		−	0.366372i
$746$	−15.6569	+	15.6569i	−0.573238	+	0.573238i
$747$		0			0
$748$	15.3137	−	15.3137i	0.559925	−	0.559925i
$749$	−59.1127	−	59.1127i	−2.15993	−	2.15993i
$750$		0			0
$751$	−11.6569			−0.425365			−0.212682	−	0.977121i	$-0.568220\pi$
$751$	−11.6569			−0.425365			−0.212682	+	0.977121i	$0.568220\pi$
$752$	28.2843			1.03142
$753$		0			0
$754$		−	0.970563i		−	0.0353458i
$755$	2.58579	+	2.58579i	0.0941064	+	0.0941064i
$756$		0			0
$757$	−4.58579	+	4.58579i	−0.166673	+	0.166673i	−0.785515	−	0.618842i	$-0.787602\pi$
$757$	−4.58579	+	4.58579i	−0.166673	+	0.166673i	0.618842	+	0.785515i	$0.287602\pi$
$758$	7.55635	−	7.55635i	0.274459	−	0.274459i
$759$		0			0
$760$	−15.3137			−0.555487
$761$		−	44.8284i		−	1.62503i	−0.582941	−	0.812515i	$-0.698098\pi$
$761$		−	44.8284i		−	1.62503i	0.582941	−	0.812515i	$-0.301902\pi$
$762$		0			0
$763$	26.4853	−	26.4853i	0.958832	−	0.958832i
$764$	8.97056			0.324544
$765$		0			0
$766$	32.6274			1.17888
$767$	−8.68629			−0.313644
$768$		0			0
$769$	−40.9706			−1.47744			−0.738718	−	0.674014i	$-0.764569\pi$
$769$	−40.9706			−1.47744			−0.738718	+	0.674014i	$0.764569\pi$
$770$	13.6569			0.492159
$771$		0			0
$772$	1.65685			0.0596315
$773$	3.27208	−	3.27208i	0.117688	−	0.117688i	−0.645810	−	0.763498i	$-0.723480\pi$
$773$	3.27208	−	3.27208i	0.117688	−	0.117688i	0.763498	+	0.645810i	$0.223480\pi$
$774$		0			0
$775$		−	3.65685i		−	0.131358i
$776$	−37.6569			−1.35180
$777$		0			0
$778$	14.6863	−	14.6863i	0.526529	−	0.526529i
$779$	−18.4853	+	18.4853i	−0.662304	+	0.662304i
$780$		0			0
$781$	11.3137	+	11.3137i	0.404836	+	0.404836i
$782$			41.4558i			1.48246i
$783$		0			0
$784$	−65.2548			−2.33053
$785$	10.0000			0.356915
$786$		0			0
$787$	16.1421	+	16.1421i	0.575405	+	0.575405i	0.933634	−	0.358229i	$-0.116619\pi$
$787$	16.1421	+	16.1421i	0.575405	+	0.575405i	−0.358229	+	0.933634i	$0.616619\pi$
$788$	15.5147	−	15.5147i	0.552689	−	0.552689i
$789$		0			0
$790$	13.6569	−	13.6569i	0.485889	−	0.485889i
$791$		−	84.0833i		−	2.98966i
$792$		0			0
$793$		−	11.1127i		−	0.394623i
$794$	−14.0000	−	14.0000i	−0.496841	−	0.496841i
$795$		0			0
$796$		−	12.6863i		−	0.449654i
$797$	9.89949	+	9.89949i	0.350658	+	0.350658i	0.860354	−	0.509696i	$-0.170242\pi$
$797$	9.89949	+	9.89949i	0.350658	+	0.350658i	−0.509696	+	0.860354i	$0.670242\pi$
$798$		0			0
$799$	−38.2843			−1.35440
$800$		−	5.65685i		−	0.200000i
$801$		0			0
$802$	−38.1421			−1.34685
$803$	4.48528	+	4.48528i	0.158282	+	0.158282i
$804$		0			0
$805$	−18.4853	+	18.4853i	−0.651521	+	0.651521i
$806$	−3.02944	−	3.02944i	−0.106707	−	0.106707i
$807$		0			0
$808$	1.65685	−	1.65685i	0.0582879	−	0.0582879i
$809$			22.9706i			0.807602i	0.914847	+	0.403801i	$0.132311\pi$
$809$			22.9706i			0.807602i	−0.914847	+	0.403801i	$0.867689\pi$
$810$		0			0
$811$	21.0000	−	21.0000i	0.737410	−	0.737410i	−0.234666	−	0.972076i	$-0.575400\pi$
$811$	21.0000	−	21.0000i	0.737410	−	0.737410i	0.972076	+	0.234666i	$0.0753997\pi$
$812$	−5.65685	+	5.65685i	−0.198517	+	0.198517i
$813$		0			0
$814$			18.3431i			0.642927i
$815$	−3.31371			−0.116074
$816$		0			0
$817$	28.0000			0.979596
$818$			43.3137i			1.51443i
$819$		0			0
$820$	−6.82843	−	6.82843i	−0.238459	−	0.238459i
$821$	−2.92893	+	2.92893i	−0.102220	+	0.102220i	−0.756367	−	0.654147i	$-0.773028\pi$
$821$	−2.92893	+	2.92893i	−0.102220	+	0.102220i	0.654147	+	0.756367i	$0.273028\pi$
$822$		0			0
$823$			54.0833i			1.88522i	0.333890	+	0.942612i	$0.391639\pi$
$823$			54.0833i			1.88522i	−0.333890	+	0.942612i	$0.608361\pi$
$824$		−	28.2843i		−	0.985329i
$825$		0			0
$826$	50.6274	+	50.6274i	1.76155	+	1.76155i
$827$	−26.1421	+	26.1421i	−0.909051	+	0.909051i	−0.996196	−	0.0871446i	$-0.972226\pi$
$827$	−26.1421	+	26.1421i	−0.909051	+	0.909051i	0.0871446	+	0.996196i	$0.472226\pi$
$828$		0			0
$829$	−12.5147	−	12.5147i	−0.434654	−	0.434654i	0.455554	−	0.890208i	$-0.349441\pi$
$829$	−12.5147	−	12.5147i	−0.434654	−	0.434654i	−0.890208	+	0.455554i	$0.849441\pi$
$830$	−6.14214			−0.213197
$831$		0			0
$832$	−4.68629	−	4.68629i	−0.162468	−	0.162468i
$833$	88.3259			3.06031
$834$		0			0
$835$	2.17157	+	2.17157i	0.0751504	+	0.0751504i
$836$	−21.6569			−0.749018
$837$		0			0
$838$	−14.4853	−	14.4853i	−0.500386	−	0.500386i
$839$			15.7990i			0.545442i	0.962093	+	0.272721i	$0.0879235\pi$
$839$			15.7990i			0.545442i	−0.962093	+	0.272721i	$0.912076\pi$
$840$		0			0
$841$		−	28.3137i		−	0.976335i
$842$	4.24264	−	4.24264i	0.146211	−	0.146211i
$843$		0			0
$844$	5.31371	+	5.31371i	0.182905	+	0.182905i
$845$	8.70711	+	8.70711i	0.299534	+	0.299534i
$846$		0			0
$847$	−33.7990			−1.16135
$848$	16.0000	−	16.0000i	0.549442	−	0.549442i
$849$		0			0
$850$			7.65685i			0.262628i
$851$	−24.8284	−	24.8284i	−0.851108	−	0.851108i
$852$		0			0
$853$	−40.0416	+	40.0416i	−1.37100	+	1.37100i	−0.512034	+	0.858965i	$0.671108\pi$
$853$	−40.0416	+	40.0416i	−1.37100	+	1.37100i	−0.858965	+	0.512034i	$0.828892\pi$
$854$	−64.7696	+	64.7696i	−2.21637	+	2.21637i
$855$		0			0
$856$	−34.6274	+	34.6274i	−1.18354	+	1.18354i
$857$		−	51.5563i		−	1.76113i	−0.473924	−	0.880566i	$-0.657163\pi$
$857$		−	51.5563i		−	1.76113i	0.473924	−	0.880566i	$-0.342837\pi$
$858$		0			0
$859$	29.2843	−	29.2843i	0.999166	−	0.999166i	−0.000833212	−	1.00000i	$-0.500265\pi$
$859$	29.2843	−	29.2843i	0.999166	−	0.999166i	1.00000		0.000833212i	$0.000265220\pi$
$860$			10.3431i			0.352698i
$861$		0			0
$862$	17.6569			0.601395
$863$	29.4142			1.00127			0.500636	−	0.865658i	$-0.333100\pi$
$863$	29.4142			1.00127			0.500636	+	0.865658i	$0.333100\pi$
$864$		0			0
$865$	16.0000			0.544016
$866$	52.0833			1.76986
$867$		0			0
$868$			35.3137i			1.19863i
$869$	19.3137	−	19.3137i	0.655173	−	0.655173i
$870$		0			0
$871$			8.97056i			0.303956i
$872$	−15.5147	−	15.5147i	−0.525395	−	0.525395i
$873$		0			0
$874$	29.3137	−	29.3137i	0.991551	−	0.991551i
$875$	−3.41421	+	3.41421i	−0.115421	+	0.115421i
$876$		0			0
$877$	19.0711	+	19.0711i	0.643984	+	0.643984i	0.951532	−	0.307548i	$-0.0995086\pi$
$877$	19.0711	+	19.0711i	0.643984	+	0.643984i	−0.307548	+	0.951532i	$0.599509\pi$
$878$			8.97056i			0.302742i
$879$		0			0
$880$		−	8.00000i		−	0.269680i
$881$	39.9411			1.34565			0.672825	−	0.739801i	$-0.265081\pi$
$881$	39.9411			1.34565			0.672825	+	0.739801i	$0.265081\pi$
$882$		0			0
$883$	−19.5147	−	19.5147i	−0.656723	−	0.656723i	0.297881	−	0.954603i	$-0.403720\pi$
$883$	−19.5147	−	19.5147i	−0.656723	−	0.656723i	−0.954603	+	0.297881i	$0.903720\pi$
$884$	6.34315	+	6.34315i	0.213343	+	0.213343i
$885$		0			0
$886$	14.9706	−	14.9706i	0.502946	−	0.502946i
$887$			14.7868i			0.496492i	0.968697	+	0.248246i	$0.0798541\pi$
$887$			14.7868i			0.496492i	−0.968697	+	0.248246i	$0.920146\pi$
$888$		0			0
$889$			94.9117i			3.18324i
$890$	−3.65685	−	3.65685i	−0.122578	−	0.122578i
$891$		0			0
$892$	−30.3431			−1.01596
$893$	27.0711	+	27.0711i	0.905899	+	0.905899i
$894$		0			0
$895$	−14.9706			−0.500411
$896$			54.6274i			1.82497i
$897$		0			0
$898$	−12.4853			−0.416639
$899$	2.14214	+	2.14214i	0.0714442	+	0.0714442i
$900$		0			0
$901$	−21.6569	+	21.6569i	−0.721494	+	0.721494i
$902$	−9.65685	−	9.65685i	−0.321538	−	0.321538i
$903$		0			0
$904$	−49.2548			−1.63819
$905$			11.5563i			0.384146i
$906$		0			0
$907$	25.1716	−	25.1716i	0.835808	−	0.835808i	−0.152496	−	0.988304i	$-0.548731\pi$
$907$	25.1716	−	25.1716i	0.835808	−	0.835808i	0.988304	+	0.152496i	$0.0487310\pi$
$908$	29.1716	+	29.1716i	0.968093	+	0.968093i
$909$		0			0
$910$			5.65685i			0.187523i
$911$	−6.82843			−0.226236			−0.113118	−	0.993582i	$-0.536084\pi$
$911$	−6.82843			−0.226236			−0.113118	+	0.993582i	$0.536084\pi$
$912$		0			0
$913$	−8.68629			−0.287474
$914$		−	33.4558i		−	1.10662i
$915$		0			0
$916$	−26.0000	+	26.0000i	−0.859064	+	0.859064i
$917$	−64.7696	+	64.7696i	−2.13888	+	2.13888i
$918$		0			0
$919$		−	16.6274i		−	0.548488i	−0.961660	−	0.274244i	$-0.911572\pi$
$919$		−	16.6274i		−	0.548488i	0.961660	−	0.274244i	$-0.0884276\pi$
$920$	10.8284	+	10.8284i	0.357003	+	0.357003i
$921$		0			0
$922$	12.3431	+	12.3431i	0.406500	+	0.406500i
$923$	−4.68629	+	4.68629i	−0.154251	+	0.154251i
$924$		0			0
$925$	−4.58579	−	4.58579i	−0.150780	−	0.150780i
$926$	16.4853			0.541740
$927$		0			0
$928$	3.31371	+	3.31371i	0.108778	+	0.108778i
$929$	−3.45584			−0.113383			−0.0566913	−	0.998392i	$-0.518055\pi$
$929$	−3.45584			−0.113383			−0.0566913	+	0.998392i	$0.518055\pi$
$930$		0			0
$931$	−62.4558	−	62.4558i	−2.04691	−	2.04691i
$932$		−	7.11270i		−	0.232984i
$933$		0			0
$934$	−10.3431	−	10.3431i	−0.338438	−	0.338438i
$935$			10.8284i			0.354127i
$936$		0			0
$937$		−	36.6274i		−	1.19657i	−0.801285	−	0.598283i	$-0.795850\pi$
$937$		−	36.6274i		−	1.19657i	0.801285	−	0.598283i	$-0.204150\pi$
$938$	52.2843	−	52.2843i	1.70714	−	1.70714i
$939$		0			0
$940$	−10.0000	+	10.0000i	−0.326164	+	0.326164i
$941$	21.2132	+	21.2132i	0.691531	+	0.691531i	0.962569	−	0.271038i	$-0.0873669\pi$
$941$	21.2132	+	21.2132i	0.691531	+	0.691531i	−0.271038	+	0.962569i	$0.587367\pi$
$942$		0			0
$943$	26.1421			0.851305
$944$	29.6569	−	29.6569i	0.965248	−	0.965248i
$945$		0			0
$946$			14.6274i			0.475578i
$947$	11.0711	+	11.0711i	0.359761	+	0.359761i	0.863725	−	0.503964i	$-0.168125\pi$
$947$	11.0711	+	11.0711i	0.359761	+	0.359761i	−0.503964	+	0.863725i	$0.668125\pi$
$948$		0			0
$949$	−1.85786	+	1.85786i	−0.0603088	+	0.0603088i
$950$	5.41421	−	5.41421i	0.175660	−	0.175660i
$951$		0			0
$952$		−	73.9411i		−	2.39645i
$953$			57.9828i			1.87825i	0.343582	+	0.939123i	$0.388360\pi$
$953$			57.9828i			1.87825i	−0.343582	+	0.939123i	$0.611640\pi$
$954$		0			0
$955$	−3.17157	+	3.17157i	−0.102630	+	0.102630i
$956$	−41.9411			−1.35647
$957$		0			0
$958$	5.65685			0.182765
$959$	20.4853			0.661504
$960$		0			0
$961$	−17.6274			−0.568626
$962$	−7.59798			−0.244969
$963$		0			0
$964$	−20.6863			−0.666261
$965$	−0.585786	+	0.585786i	−0.0188571	+	0.0188571i
$966$		0			0
$967$			19.4558i			0.625658i	0.949810	+	0.312829i	$0.101277\pi$
$967$			19.4558i			0.625658i	−0.949810	+	0.312829i	$0.898723\pi$
$968$			19.7990i			0.636364i
$969$		0			0
$970$	13.3137	−	13.3137i	0.427477	−	0.427477i
$971$	−22.2426	+	22.2426i	−0.713800	+	0.713800i	−0.967328	−	0.253528i	$-0.918409\pi$
$971$	−22.2426	+	22.2426i	−0.713800	+	0.713800i	0.253528	+	0.967328i	$0.418409\pi$
$972$		0			0
$973$	32.1421	+	32.1421i	1.03043	+	1.03043i
$974$			36.7696i			1.17817i
$975$		0			0
$976$	37.9411	+	37.9411i	1.21447	+	1.21447i
$977$	11.5563			0.369720			0.184860	−	0.982765i	$-0.440817\pi$
$977$	11.5563			0.369720			0.184860	+	0.982765i	$0.440817\pi$
$978$		0			0
$979$	−5.17157	−	5.17157i	−0.165284	−	0.165284i
$980$	23.0711	−	23.0711i	0.736978	−	0.736978i
$981$		0			0
$982$	−3.17157	+	3.17157i	−0.101209	+	0.101209i
$983$			20.7279i			0.661118i	0.943785	+	0.330559i	$0.107237\pi$
$983$			20.7279i			0.661118i	−0.943785	+	0.330559i	$0.892763\pi$
$984$		0			0
$985$			10.9706i			0.349551i
$986$	−4.48528	−	4.48528i	−0.142840	−	0.142840i
$987$		0			0
$988$		−	8.97056i		−	0.285392i
$989$	−19.7990	−	19.7990i	−0.629571	−	0.629571i
$990$		0			0
$991$	−4.00000			−0.127064			−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000			−0.127064			−0.0635321	+	0.997980i	$0.520237\pi$
$992$	20.6863			0.656790
$993$		0			0
$994$	54.6274			1.73268
$995$	4.48528	+	4.48528i	0.142193	+	0.142193i
$996$		0			0
$997$	9.75736	−	9.75736i	0.309019	−	0.309019i	−0.535510	−	0.844529i	$-0.679881\pi$
$997$	9.75736	−	9.75736i	0.309019	−	0.309019i	0.844529	+	0.535510i	$0.179881\pi$
$998$	−6.38478	−	6.38478i	−0.202107	−	0.202107i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.t.a.541.2		4
3.2	odd	2		240.2.s.a.61.1	✓	4
4.3	odd	2		2880.2.t.a.721.1		4
12.11	even	2		960.2.s.a.721.2		4
16.5	even	4	inner	720.2.t.a.181.2		4
16.11	odd	4		2880.2.t.a.2161.1		4
24.5	odd	2		1920.2.s.a.1441.2		4
24.11	even	2		1920.2.s.b.1441.1		4
48.5	odd	4		240.2.s.a.181.1	yes	4
48.11	even	4		960.2.s.a.241.2		4
48.29	odd	4		1920.2.s.a.481.2		4
48.35	even	4		1920.2.s.b.481.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.a.61.1	✓	4	3.2	odd	2
240.2.s.a.181.1	yes	4	48.5	odd	4
720.2.t.a.181.2		4	16.5	even	4	inner
720.2.t.a.541.2		4	1.1	even	1	trivial
960.2.s.a.241.2		4	48.11	even	4
960.2.s.a.721.2		4	12.11	even	2
1920.2.s.a.481.2		4	48.29	odd	4
1920.2.s.a.1441.2		4	24.5	odd	2
1920.2.s.b.481.1		4	48.35	even	4
1920.2.s.b.1441.1		4	24.11	even	2
2880.2.t.a.721.1		4	4.3	odd	2
2880.2.t.a.2161.1		4	16.11	odd	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +2.00000 q^{4} +(-0.707107 + 0.707107i) q^{5} +4.82843i q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+1.41421 q^{2} +2.00000 q^{4} +(-0.707107 + 0.707107i) q^{5} +4.82843i q^{7} +2.82843 q^{8} +(-1.00000 + 1.00000i) q^{10} +(-1.41421 + 1.41421i) q^{11} +(-0.585786 - 0.585786i) q^{13} +6.82843i q^{14} +4.00000 q^{16} -5.41421 q^{17} +(3.82843 + 3.82843i) q^{19} +(-1.41421 + 1.41421i) q^{20} +(-2.00000 + 2.00000i) q^{22} -5.41421i q^{23} -1.00000i q^{25} +(-0.828427 - 0.828427i) q^{26} +9.65685i q^{28} +(0.585786 + 0.585786i) q^{29} +3.65685 q^{31} +5.65685 q^{32} -7.65685 q^{34} +(-3.41421 - 3.41421i) q^{35} +(4.58579 - 4.58579i) q^{37} +(5.41421 + 5.41421i) q^{38} +(-2.00000 + 2.00000i) q^{40} +4.82843i q^{41} +(3.65685 - 3.65685i) q^{43} +(-2.82843 + 2.82843i) q^{44} -7.65685i q^{46} +7.07107 q^{47} -16.3137 q^{49} -1.41421i q^{50} +(-1.17157 - 1.17157i) q^{52} +(4.00000 - 4.00000i) q^{53} -2.00000i q^{55} +13.6569i q^{56} +(0.828427 + 0.828427i) q^{58} +(7.41421 - 7.41421i) q^{59} +(9.48528 + 9.48528i) q^{61} +5.17157 q^{62} +8.00000 q^{64} +0.828427 q^{65} +(-7.65685 - 7.65685i) q^{67} -10.8284 q^{68} +(-4.82843 - 4.82843i) q^{70} -8.00000i q^{71} -3.17157i q^{73} +(6.48528 - 6.48528i) q^{74} +(7.65685 + 7.65685i) q^{76} +(-6.82843 - 6.82843i) q^{77} -13.6569 q^{79} +(-2.82843 + 2.82843i) q^{80} +6.82843i q^{82} +(3.07107 + 3.07107i) q^{83} +(3.82843 - 3.82843i) q^{85} +(5.17157 - 5.17157i) q^{86} +(-4.00000 + 4.00000i) q^{88} +3.65685i q^{89} +(2.82843 - 2.82843i) q^{91} -10.8284i q^{92} +10.0000 q^{94} -5.41421 q^{95} -13.3137 q^{97} -23.0711 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4}+O(q^{10}) \) 4 * q + 8 * q^4	\( 4 q + 8 q^{4} - 4 q^{10} - 8 q^{13} + 16 q^{16} - 16 q^{17} + 4 q^{19} - 8 q^{22} + 8 q^{26} + 8 q^{29} - 8 q^{31} - 8 q^{34} - 8 q^{35} + 24 q^{37} + 16 q^{38} - 8 q^{40} - 8 q^{43} - 20 q^{49} - 16 q^{52} + 16 q^{53} - 8 q^{58} + 24 q^{59} + 4 q^{61} + 32 q^{62} + 32 q^{64} - 8 q^{65} - 8 q^{67} - 32 q^{68} - 8 q^{70} - 8 q^{74} + 8 q^{76} - 16 q^{77} - 32 q^{79} - 16 q^{83} + 4 q^{85} + 32 q^{86} - 16 q^{88} + 40 q^{94} - 16 q^{95} - 8 q^{97} - 64 q^{98}+O(q^{100}) \) 4 * q + 8 * q^4 - 4 * q^10 - 8 * q^13 + 16 * q^16 - 16 * q^17 + 4 * q^19 - 8 * q^22 + 8 * q^26 + 8 * q^29 - 8 * q^31 - 8 * q^34 - 8 * q^35 + 24 * q^37 + 16 * q^38 - 8 * q^40 - 8 * q^43 - 20 * q^49 - 16 * q^52 + 16 * q^53 - 8 * q^58 + 24 * q^59 + 4 * q^61 + 32 * q^62 + 32 * q^64 - 8 * q^65 - 8 * q^67 - 32 * q^68 - 8 * q^70 - 8 * q^74 + 8 * q^76 - 16 * q^77 - 32 * q^79 - 16 * q^83 + 4 * q^85 + 32 * q^86 - 16 * q^88 + 40 * q^94 - 16 * q^95 - 8 * q^97 - 64 * q^98

Introduction

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