LMFDB - Embedded newform 3640.1.od.b.1403.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3640,1,Mod(467,3640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3640, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 3, 10, 6]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3640.467");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3640.od (of order $12$, degree $4$, 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:	$1.81659664598$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{72})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{12} + 1 $ x^24 - x^12 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{36}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{36} - \cdots)$

Embedding invariants

Embedding label			1403.4
Root			$-0.906308 + 0.422618i$ of defining polynomial
Character	$\chi$	$=$	3640.1403
Dual form			3640.1.od.b.467.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-0.515668 - 1.92450i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.0871557 + 0.996195i) q^{5} -1.99239i q^{6} +(-0.0871557 + 0.996195i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.57176 + 1.48481i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-0.515668 - 1.92450i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.0871557 + 0.996195i) q^{5} -1.99239i q^{6} +(-0.0871557 + 0.996195i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.57176 + 1.48481i) q^{9} +(-0.173648 + 0.984808i) q^{10} +(0.515668 - 1.92450i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(-0.342020 + 0.939693i) q^{14} +(1.87223 - 0.681437i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.58248 + 0.424024i) q^{17} +(-2.86843 + 0.768593i) q^{18} +(-0.422618 + 0.906308i) q^{20} +(1.96212 - 0.345975i) q^{21} +(0.996195 - 1.72546i) q^{24} +(-0.984808 + 0.173648i) q^{25} +(-0.866025 + 0.500000i) q^{26} +(2.77486 + 2.77486i) q^{27} +(-0.573576 + 0.819152i) q^{28} +(1.98481 - 0.173648i) q^{30} +(-0.448288 - 0.258819i) q^{31} +(0.258819 + 0.965926i) q^{32} -1.63830 q^{34} -1.00000 q^{35} -2.96962 q^{36} +(1.24177 + 0.332731i) q^{37} +(1.72546 + 0.996195i) q^{39} +(-0.642788 + 0.766044i) q^{40} +(1.98481 + 0.173648i) q^{42} +(0.597672 + 0.597672i) q^{43} +(-1.70330 - 2.43257i) q^{45} +(0.0898869 - 0.335463i) q^{47} +(1.40883 - 1.40883i) q^{48} +(-0.984808 - 0.173648i) q^{49} +(-0.996195 - 0.0871557i) q^{50} +(1.63207 + 2.82683i) q^{51} +(-0.965926 + 0.258819i) q^{52} +(1.96212 + 3.39849i) q^{54} +(-0.766044 + 0.642788i) q^{56} +(1.96212 + 0.345975i) q^{60} +(-0.366025 - 0.366025i) q^{62} +(-1.25501 - 2.69139i) q^{63} +1.00000i q^{64} +(-0.766044 - 0.642788i) q^{65} +(-1.58248 - 0.424024i) q^{68} +(-0.965926 - 0.258819i) q^{70} +1.14715 q^{71} +(-2.86843 - 0.768593i) q^{72} +(1.11334 + 0.642788i) q^{74} +(0.842020 + 1.80572i) q^{75} +(1.40883 + 1.40883i) q^{78} +(-0.819152 + 0.573576i) q^{80} +(2.42450 - 4.19936i) q^{81} +(1.87223 + 0.681437i) q^{84} +(-0.560333 - 1.53950i) q^{85} +(0.422618 + 0.731996i) q^{86} +(-1.01567 - 2.79053i) q^{90} +(-0.642788 - 0.766044i) q^{91} +(-0.266930 + 0.996195i) q^{93} +(0.173648 - 0.300767i) q^{94} +(1.72546 - 0.996195i) q^{96} +(-0.906308 - 0.422618i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 12 q^{16} + 12 q^{27} + 24 q^{30} - 24 q^{35} - 24 q^{36} + 24 q^{42} + 12 q^{62} + 12 q^{75} + 12 q^{81} - 12 q^{90}+O(q^{100}) $ 24 * q + 12 * q^16 + 12 * q^27 + 24 * q^30 - 24 * q^35 - 24 * q^36 + 24 * q^42 + 12 * q^62 + 12 * q^75 + 12 * q^81 - 12 * q^90

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3640\mathbb{Z}\right)^\times$.

$n$	$521$	$561$	$911$	$1457$	$1821$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.965926	+	0.258819i	0.965926	+	0.258819i
$2$	0.965926	+	0.258819i	0.965926	+	0.258819i
$3$	−0.515668	−	1.92450i	−0.515668	−	1.92450i	−0.342020	−	0.939693i	$-0.611111\pi$
$3$	−0.515668	−	1.92450i	−0.515668	−	1.92450i	−0.173648	−	0.984808i	$-0.555556\pi$
$4$	0.866025	+	0.500000i	0.866025	+	0.500000i
$5$	0.0871557	+	0.996195i	0.0871557	+	0.996195i
$5$	0.0871557	+	0.996195i	0.0871557	+	0.996195i
$6$		−	1.99239i		−	1.99239i
$7$	−0.0871557	+	0.996195i	−0.0871557	+	0.996195i
$7$	−0.0871557	+	0.996195i	−0.0871557	+	0.996195i
$8$	0.707107	+	0.707107i	0.707107	+	0.707107i
$9$	−2.57176	+	1.48481i	−2.57176	+	1.48481i
$10$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	0.515668	−	1.92450i	0.515668	−	1.92450i
$13$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$13$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$14$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$15$	1.87223	−	0.681437i	1.87223	−	0.681437i
$16$	0.500000	+	0.866025i	0.500000	+	0.866025i
$17$	−1.58248	+	0.424024i	−1.58248	+	0.424024i	−0.939693	−	0.342020i	$-0.888889\pi$
$17$	−1.58248	+	0.424024i	−1.58248	+	0.424024i	−0.642788	+	0.766044i	$0.722222\pi$
$18$	−2.86843	+	0.768593i	−2.86843	+	0.768593i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	−0.422618	+	0.906308i	−0.422618	+	0.906308i
$21$	1.96212	−	0.345975i	1.96212	−	0.345975i
$22$		0			0
$23$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$23$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$24$	0.996195	−	1.72546i	0.996195	−	1.72546i
$25$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$26$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$27$	2.77486	+	2.77486i	2.77486	+	2.77486i
$28$	−0.573576	+	0.819152i	−0.573576	+	0.819152i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	1.98481	−	0.173648i	1.98481	−	0.173648i
$31$	−0.448288	−	0.258819i	−0.448288	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$31$	−0.448288	−	0.258819i	−0.448288	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$32$	0.258819	+	0.965926i	0.258819	+	0.965926i
$33$		0			0
$34$	−1.63830			−1.63830
$35$	−1.00000			−1.00000
$36$	−2.96962			−2.96962
$37$	1.24177	+	0.332731i	1.24177	+	0.332731i	0.819152	−	0.573576i	$-0.194444\pi$
$37$	1.24177	+	0.332731i	1.24177	+	0.332731i	0.422618	+	0.906308i	$0.361111\pi$
$38$		0			0
$39$	1.72546	+	0.996195i	1.72546	+	0.996195i
$40$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	1.98481	+	0.173648i	1.98481	+	0.173648i
$43$	0.597672	+	0.597672i	0.597672	+	0.597672i	0.939693	−	0.342020i	$-0.111111\pi$
$43$	0.597672	+	0.597672i	0.597672	+	0.597672i	−0.342020	+	0.939693i	$0.611111\pi$
$44$		0			0
$45$	−1.70330	−	2.43257i	−1.70330	−	2.43257i
$46$		0			0
$47$	0.0898869	−	0.335463i	0.0898869	−	0.335463i	−0.906308	−	0.422618i	$-0.861111\pi$
$47$	0.0898869	−	0.335463i	0.0898869	−	0.335463i	0.996195	+	0.0871557i	$0.0277778\pi$
$48$	1.40883	−	1.40883i	1.40883	−	1.40883i
$49$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$50$	−0.996195	−	0.0871557i	−0.996195	−	0.0871557i
$51$	1.63207	+	2.82683i	1.63207	+	2.82683i
$52$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$53$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$53$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$54$	1.96212	+	3.39849i	1.96212	+	3.39849i
$55$		0			0
$56$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$57$		0			0
$58$		0			0
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$	1.96212	+	0.345975i	1.96212	+	0.345975i
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	−0.366025	−	0.366025i	−0.366025	−	0.366025i
$63$	−1.25501	−	2.69139i	−1.25501	−	2.69139i
$64$			1.00000i			1.00000i
$65$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$66$		0			0
$67$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$67$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$68$	−1.58248	−	0.424024i	−1.58248	−	0.424024i
$69$		0			0
$70$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$71$	1.14715			1.14715			0.573576	−	0.819152i	$-0.305556\pi$
$71$	1.14715			1.14715			0.573576	+	0.819152i	$0.305556\pi$
$72$	−2.86843	−	0.768593i	−2.86843	−	0.768593i
$73$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$73$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$74$	1.11334	+	0.642788i	1.11334	+	0.642788i
$75$	0.842020	+	1.80572i	0.842020	+	1.80572i
$76$		0			0
$77$		0			0
$78$	1.40883	+	1.40883i	1.40883	+	1.40883i
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−0.819152	+	0.573576i	−0.819152	+	0.573576i
$81$	2.42450	−	4.19936i	2.42450	−	4.19936i
$82$		0			0
$83$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$83$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$84$	1.87223	+	0.681437i	1.87223	+	0.681437i
$85$	−0.560333	−	1.53950i	−0.560333	−	1.53950i
$86$	0.422618	+	0.731996i	0.422618	+	0.731996i
$87$		0			0
$88$		0			0
$89$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$89$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$90$	−1.01567	−	2.79053i	−1.01567	−	2.79053i
$91$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$92$		0			0
$93$	−0.266930	+	0.996195i	−0.266930	+	0.996195i
$94$	0.173648	−	0.300767i	0.173648	−	0.300767i
$95$		0			0
$96$	1.72546	−	0.996195i	1.72546	−	0.996195i
$97$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$97$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$98$	−0.906308	−	0.422618i	−0.906308	−	0.422618i
$99$		0			0
$100$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	0.844822	+	3.15292i	0.844822	+	3.15292i
$103$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$103$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$104$	−1.00000			−1.00000
$105$	0.515668	+	1.92450i	0.515668	+	1.92450i
$106$		0			0
$107$	−1.86603	−	0.500000i	−1.86603	−	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$107$	−1.86603	−	0.500000i	−1.86603	−	0.500000i	−1.00000			$\pi$
$108$	1.01567	+	3.79053i	1.01567	+	3.79053i
$109$	1.56977	+	0.906308i	1.56977	+	0.906308i	0.996195	+	0.0871557i	$0.0277778\pi$
$109$	1.56977	+	0.906308i	1.56977	+	0.906308i	0.573576	+	0.819152i	$0.305556\pi$
$110$		0			0
$111$		−	2.56137i		−	2.56137i
$112$	−0.906308	+	0.422618i	−0.906308	+	0.422618i
$113$	−0.366025	−	0.366025i	−0.366025	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$113$	−0.366025	−	0.366025i	−0.366025	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.768593	−	2.86843i	0.768593	−	2.86843i
$118$		0			0
$119$	−0.284489	−	1.61341i	−0.284489	−	1.61341i
$120$	1.80572	+	0.842020i	1.80572	+	0.842020i
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$	−0.258819	−	0.448288i	−0.258819	−	0.448288i
$125$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$126$	−0.515668	−	2.92450i	−0.515668	−	2.92450i
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$129$	0.842020	−	1.45842i	0.842020	−	1.45842i
$130$	−0.573576	−	0.819152i	−0.573576	−	0.819152i
$131$	1.62760	−	0.939693i	1.62760	−	0.939693i	0.642788	−	0.766044i	$-0.277778\pi$
$131$	1.62760	−	0.939693i	1.62760	−	0.939693i	0.984808	−	0.173648i	$-0.0555556\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.52245	+	3.00614i	−2.52245	+	3.00614i
$136$	−1.41881	−	0.819152i	−1.41881	−	0.819152i
$137$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$137$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$138$		0			0
$139$	1.96962			1.96962			0.984808	−	0.173648i	$-0.0555556\pi$
$139$	1.96962			1.96962			0.984808	+	0.173648i	$0.0555556\pi$
$140$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$141$	−0.691950			−0.691950
$142$	1.10806	+	0.296905i	1.10806	+	0.296905i
$143$		0			0
$144$	−2.57176	−	1.48481i	−2.57176	−	1.48481i
$145$		0			0
$146$		0			0
$147$	0.173648	+	1.98481i	0.173648	+	1.98481i
$148$	0.909039	+	0.909039i	0.909039	+	0.909039i
$149$	1.67303	−	0.965926i	1.67303	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$149$	1.67303	−	0.965926i	1.67303	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$150$	0.345975	+	1.96212i	0.345975	+	1.96212i
$151$	−0.819152	+	1.41881i	−0.819152	+	1.41881i	0.0871557	+	0.996195i	$0.472222\pi$
$151$	−0.819152	+	1.41881i	−0.819152	+	1.41881i	−0.906308	+	0.422618i	$0.861111\pi$
$152$		0			0
$153$	3.44017	−	3.44017i	3.44017	−	3.44017i
$154$		0			0
$155$	0.218763	−	0.469139i	0.218763	−	0.469139i
$156$	0.996195	+	1.72546i	0.996195	+	1.72546i
$157$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$157$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$158$		0			0
$159$		0			0
$160$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$161$		0			0
$162$	3.42876	−	3.42876i	3.42876	−	3.42876i
$163$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$163$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$167$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$168$	1.63207	+	1.14279i	1.63207	+	1.14279i
$169$		−	1.00000i		−	1.00000i
$170$	−0.142788	−	1.63207i	−0.142788	−	1.63207i
$171$		0			0
$172$	0.218763	+	0.816436i	0.218763	+	0.816436i
$173$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$173$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$174$		0			0
$175$	−0.0871557	−	0.996195i	−0.0871557	−	0.996195i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.592396	+	0.342020i	0.592396	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$179$	0.592396	+	0.342020i	0.592396	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$180$	−0.258819	−	2.95832i	−0.258819	−	2.95832i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	−0.422618	−	0.906308i	−0.422618	−	0.906308i
$183$		0			0
$184$		0			0
$185$	−0.223238	+	1.26604i	−0.223238	+	1.26604i
$186$	−0.515668	+	0.893164i	−0.515668	+	0.893164i
$187$		0			0
$188$	0.245576	−	0.245576i	0.245576	−	0.245576i
$189$	−3.00614	+	2.52245i	−3.00614	+	2.52245i
$190$		0			0
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$	1.92450	−	0.515668i	1.92450	−	0.515668i
$193$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$193$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$194$		0			0
$195$	−0.842020	+	1.80572i	−0.842020	+	1.80572i
$196$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$197$	−1.32893	+	1.32893i	−1.32893	+	1.32893i	−0.422618	+	0.906308i	$0.638889\pi$
$197$	−1.32893	+	1.32893i	−1.32893	+	1.32893i	−0.906308	+	0.422618i	$0.861111\pi$
$198$		0			0
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	−0.819152	−	0.573576i	−0.819152	−	0.573576i
$201$		0			0
$202$		0			0
$203$		0			0
$204$			3.26414i			3.26414i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$209$		0			0
$210$			1.99239i			1.99239i
$211$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$211$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$212$		0			0
$213$	−0.591550	−	2.20770i	−0.591550	−	2.20770i
$214$	−1.67303	−	0.965926i	−1.67303	−	0.965926i
$215$	−0.543308	+	0.647489i	−0.543308	+	0.647489i
$216$			3.92424i			3.92424i
$217$	0.296905	−	0.424024i	0.296905	−	0.424024i
$218$	1.28171	+	1.28171i	1.28171	+	1.28171i
$219$		0			0
$220$		0			0
$221$	0.819152	−	1.41881i	0.819152	−	1.41881i
$222$	0.662930	−	2.47409i	0.662930	−	2.47409i
$223$	1.08335	−	1.08335i	1.08335	−	1.08335i	0.0871557	−	0.996195i	$-0.472222\pi$
$223$	1.08335	−	1.08335i	1.08335	−	1.08335i	0.996195	−	0.0871557i	$-0.0277778\pi$
$224$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$225$	2.27486	−	1.90883i	2.27486	−	1.90883i
$226$	−0.258819	−	0.448288i	−0.258819	−	0.448288i
$227$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$227$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$228$		0			0
$229$	0.0871557	+	0.150958i	0.0871557	+	0.150958i	0.906308	−	0.422618i	$-0.138889\pi$
$229$	0.0871557	+	0.150958i	0.0871557	+	0.150958i	−0.819152	+	0.573576i	$0.805556\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.0451151	+	0.168372i	−0.0451151	+	0.168372i	−0.984808	−	0.173648i	$-0.944444\pi$
$233$	−0.0451151	+	0.168372i	−0.0451151	+	0.168372i	0.939693	+	0.342020i	$0.111111\pi$
$234$	1.48481	−	2.57176i	1.48481	−	2.57176i
$235$	0.342020	+	0.0603074i	0.342020	+	0.0603074i
$236$		0			0
$237$		0			0
$238$	0.142788	−	1.63207i	0.142788	−	1.63207i
$239$		−	0.174311i		−	0.174311i	−0.996195	−	0.0871557i	$-0.972222\pi$
$239$		−	0.174311i		−	0.174311i	0.996195	−	0.0871557i	$-0.0277778\pi$
$240$	1.52626	+	1.28068i	1.52626	+	1.28068i
$241$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$241$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$242$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$243$	−5.54138	−	1.48481i	−5.54138	−	1.48481i
$244$		0			0
$245$	0.0871557	−	0.996195i	0.0871557	−	0.996195i
$246$		0			0
$247$		0			0
$248$	−0.133975	−	0.500000i	−0.133975	−	0.500000i
$249$		0			0
$250$		−	1.00000i		−	1.00000i
$251$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$251$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$252$	0.258819	−	2.95832i	0.258819	−	2.95832i
$253$		0			0
$254$		0			0
$255$	−2.67383	+	1.87223i	−2.67383	+	1.87223i
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$	−0.218763	+	0.816436i	−0.218763	+	0.816436i	0.766044	+	0.642788i	$0.222222\pi$
$257$	−0.218763	+	0.816436i	−0.218763	+	0.816436i	−0.984808	+	0.173648i	$0.944444\pi$
$258$	1.19080	−	1.19080i	1.19080	−	1.19080i
$259$	−0.439693	+	1.20805i	−0.439693	+	1.20805i
$260$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$261$		0			0
$262$	1.81535	−	0.486421i	1.81535	−	0.486421i
$263$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$263$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$269$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$270$	−3.21455	+	2.25085i	−3.21455	+	2.25085i
$271$	−1.56977	+	0.906308i	−1.56977	+	0.906308i	−0.573576	+	0.819152i	$0.694444\pi$
$271$	−1.56977	+	0.906308i	−1.56977	+	0.906308i	−0.996195	+	0.0871557i	$0.972222\pi$
$272$	−1.15846	−	1.15846i	−1.15846	−	1.15846i
$273$	−1.14279	+	1.63207i	−1.14279	+	1.63207i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$277$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$278$	1.90250	+	0.509774i	1.90250	+	0.509774i
$279$	1.53719			1.53719
$280$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−0.668372	−	0.179090i	−0.668372	−	0.179090i
$283$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$283$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$284$	0.993464	+	0.573576i	0.993464	+	0.573576i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.09984	−	2.09984i	−2.09984	−	2.09984i
$289$	1.45842	−	0.842020i	1.45842	−	0.842020i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.08335	+	1.08335i	−1.08335	+	1.08335i	−0.0871557	+	0.996195i	$0.527778\pi$
$293$	−1.08335	+	1.08335i	−1.08335	+	1.08335i	−0.996195	+	0.0871557i	$0.972222\pi$
$294$	−0.345975	+	1.96212i	−0.345975	+	1.96212i
$295$		0			0
$296$	0.642788	+	1.11334i	0.642788	+	1.11334i
$297$		0			0
$298$	1.86603	−	0.500000i	1.86603	−	0.500000i
$299$		0			0
$300$	−0.173648	+	1.98481i	−0.173648	+	1.98481i
$301$	−0.647489	+	0.543308i	−0.647489	+	0.543308i
$302$	−1.15846	+	1.15846i	−1.15846	+	1.15846i
$303$		0			0
$304$		0			0
$305$		0			0
$306$	4.21333	−	2.43257i	4.21333	−	2.43257i
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$		0			0
$309$		0			0
$310$	0.332731	−	0.396534i	0.332731	−	0.396534i
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$	0.515668	+	1.92450i	0.515668	+	1.92450i
$313$	−1.10806	−	0.296905i	−1.10806	−	0.296905i	−0.342020	−	0.939693i	$-0.611111\pi$
$313$	−1.10806	−	0.296905i	−1.10806	−	0.296905i	−0.766044	+	0.642788i	$0.777778\pi$
$314$		0			0
$315$	2.57176	−	1.48481i	2.57176	−	1.48481i
$316$		0			0
$317$	−1.67303	−	0.448288i	−1.67303	−	0.448288i	−0.707107	−	0.707107i	$-0.750000\pi$
$317$	−1.67303	−	0.448288i	−1.67303	−	0.448288i	−0.965926	+	0.258819i	$0.916667\pi$
$318$		0			0
$319$		0			0
$320$	−0.996195	+	0.0871557i	−0.996195	+	0.0871557i
$321$			3.84900i			3.84900i
$322$		0			0
$323$		0			0
$324$	4.19936	−	2.42450i	4.19936	−	2.42450i
$325$	0.573576	−	0.819152i	0.573576	−	0.819152i
$326$		0			0
$327$	0.934708	−	3.48838i	0.934708	−	3.48838i
$328$		0			0
$329$	0.326352	+	0.118782i	0.326352	+	0.118782i
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$		0			0
$333$	−3.68758	+	0.988084i	−3.68758	+	0.988084i
$334$	0.500000	+	0.866025i	0.500000	+	0.866025i
$335$		0			0
$336$	1.28068	+	1.52626i	1.28068	+	1.52626i
$337$	−1.28171	+	1.28171i	−1.28171	+	1.28171i	−0.342020	+	0.939693i	$0.611111\pi$
$337$	−1.28171	+	1.28171i	−1.28171	+	1.28171i	−0.939693	+	0.342020i	$0.888889\pi$
$338$	0.258819	−	0.965926i	0.258819	−	0.965926i
$339$	−0.515668	+	0.893164i	−0.515668	+	0.893164i
$340$	0.284489	−	1.61341i	0.284489	−	1.61341i
$341$		0			0
$342$		0			0
$343$	0.258819	−	0.965926i	0.258819	−	0.965926i
$344$			0.845237i			0.845237i
$345$		0			0
$346$		0			0
$347$	0.296905	+	1.10806i	0.296905	+	1.10806i	0.939693	+	0.342020i	$0.111111\pi$
$347$	0.296905	+	1.10806i	0.296905	+	1.10806i	−0.642788	+	0.766044i	$0.722222\pi$
$348$		0			0
$349$	1.14715			1.14715			0.573576	−	0.819152i	$-0.305556\pi$
$349$	1.14715			1.14715			0.573576	+	0.819152i	$0.305556\pi$
$350$	0.173648	−	0.984808i	0.173648	−	0.984808i
$351$	−3.92424			−3.92424
$352$		0			0
$353$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$353$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$354$		0			0
$355$	0.0999810	+	1.14279i	0.0999810	+	1.14279i
$356$		0			0
$357$	−2.95832	+	1.37949i	−2.95832	+	1.37949i
$358$	0.483690	+	0.483690i	0.483690	+	0.483690i
$359$	0.448288	−	0.258819i	0.448288	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$359$	0.448288	−	0.258819i	0.448288	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$360$	0.515668	−	2.92450i	0.515668	−	2.92450i
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$	−1.40883	+	1.40883i	−1.40883	+	1.40883i
$364$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$365$		0			0
$366$		0			0
$367$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$367$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$368$		0			0
$369$		0			0
$370$	−0.543308	+	1.16513i	−0.543308	+	1.16513i
$371$		0			0
$372$	−0.729265	+	0.729265i	−0.729265	+	0.729265i
$373$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$373$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$374$		0			0
$375$	−1.72546	+	0.996195i	−1.72546	+	0.996195i
$376$	0.300767	−	0.173648i	0.300767	−	0.173648i
$377$		0			0
$378$	−3.55657	+	1.65846i	−3.55657	+	1.65846i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.24177	+	0.332731i	1.24177	+	0.332731i	0.819152	−	0.573576i	$-0.194444\pi$
$383$	1.24177	+	0.332731i	1.24177	+	0.332731i	0.422618	+	0.906308i	$0.361111\pi$
$384$	1.99239			1.99239
$385$		0			0
$386$		0			0
$387$	−2.42450	−	0.649643i	−2.42450	−	0.649643i
$388$		0			0
$389$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$	−1.28068	+	1.52626i	−1.28068	+	1.52626i
$391$		0			0
$392$	−0.573576	−	0.819152i	−0.573576	−	0.819152i
$393$	−2.64774	−	2.64774i	−2.64774	−	2.64774i
$394$	−1.62760	+	0.939693i	−1.62760	+	0.939693i
$395$		0			0
$396$		0			0
$397$	−0.448288	+	1.67303i	−0.448288	+	1.67303i	0.258819	+	0.965926i	$0.416667\pi$
$397$	−0.448288	+	1.67303i	−0.448288	+	1.67303i	−0.707107	+	0.707107i	$0.750000\pi$
$398$		0			0
$399$		0			0
$400$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$	0.500000	−	0.133975i	0.500000	−	0.133975i
$404$		0			0
$405$	4.39469	+	2.04928i	4.39469	+	2.04928i
$406$		0			0
$407$		0			0
$408$	−0.844822	+	3.15292i	−0.844822	+	3.15292i
$409$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$409$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$417$	−1.01567	−	3.79053i	−1.01567	−	3.79053i
$418$		0			0
$419$	0.684040			0.684040			0.342020	−	0.939693i	$-0.388889\pi$
$419$	0.684040			0.684040			0.342020	+	0.939693i	$0.388889\pi$
$420$	−0.515668	+	1.92450i	−0.515668	+	1.92450i
$421$	0.845237			0.845237			0.422618	−	0.906308i	$-0.361111\pi$
$421$	0.845237			0.845237			0.422618	+	0.906308i	$0.361111\pi$
$422$	0.335463	+	0.0898869i	0.335463	+	0.0898869i
$423$	0.266930	+	0.996195i	0.266930	+	0.996195i
$424$		0			0
$425$	1.48481	−	0.692377i	1.48481	−	0.692377i
$426$		−	2.28558i		−	2.28558i
$427$		0			0
$428$	−1.36603	−	1.36603i	−1.36603	−	1.36603i
$429$		0			0
$430$	−0.692377	+	0.484808i	−0.692377	+	0.484808i
$431$	0.906308	−	1.56977i	0.906308	−	1.56977i	0.0871557	−	0.996195i	$-0.472222\pi$
$431$	0.906308	−	1.56977i	0.906308	−	1.56977i	0.819152	−	0.573576i	$-0.194444\pi$
$432$	−1.01567	+	3.79053i	−1.01567	+	3.79053i
$433$	−0.123257	+	0.123257i	−0.123257	+	0.123257i	−0.766044	−	0.642788i	$-0.777778\pi$
$433$	−0.123257	+	0.123257i	−0.123257	+	0.123257i	0.642788	+	0.766044i	$0.277778\pi$
$434$	0.396534	−	0.332731i	0.396534	−	0.332731i
$435$		0			0
$436$	0.906308	+	1.56977i	0.906308	+	1.56977i
$437$		0			0
$438$		0			0
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$	2.79053	−	1.01567i	2.79053	−	1.01567i
$442$	1.15846	−	1.15846i	1.15846	−	1.15846i
$443$	0.515668	−	1.92450i	0.515668	−	1.92450i	0.173648	−	0.984808i	$-0.444444\pi$
$443$	0.515668	−	1.92450i	0.515668	−	1.92450i	0.342020	−	0.939693i	$-0.388889\pi$
$444$	1.28068	−	2.21821i	1.28068	−	2.21821i
$445$		0			0
$446$	1.32683	−	0.766044i	1.32683	−	0.766044i
$447$	−2.72165	−	2.72165i	−2.72165	−	2.72165i
$448$	−0.996195	−	0.0871557i	−0.996195	−	0.0871557i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	2.69139	−	1.25501i	2.69139	−	1.25501i
$451$		0			0
$452$	−0.133975	−	0.500000i	−0.133975	−	0.500000i
$453$	3.15292	+	0.844822i	3.15292	+	0.844822i
$454$		0			0
$455$	0.707107	−	0.707107i	0.707107	−	0.707107i
$456$		0			0
$457$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$457$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$458$	0.0451151	+	0.168372i	0.0451151	+	0.168372i
$459$	−5.56776	−	3.21455i	−5.56776	−	3.21455i
$460$		0			0
$461$			1.14715i			1.14715i	0.819152	+	0.573576i	$0.194444\pi$
$461$			1.14715i			1.14715i	−0.819152	+	0.573576i	$0.805556\pi$
$462$		0			0
$463$	1.22474	+	1.22474i	1.22474	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$463$	1.22474	+	1.22474i	1.22474	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$464$		0			0
$465$	−1.01567	−	0.179090i	−1.01567	−	0.179090i
$466$	−0.0871557	+	0.150958i	−0.0871557	+	0.150958i
$467$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$467$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$468$	2.09984	−	2.09984i	2.09984	−	2.09984i
$469$		0			0
$470$	0.314757	+	0.146774i	0.314757	+	0.146774i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	0.560333	−	1.53950i	0.560333	−	1.53950i
$477$		0			0
$478$	0.0451151	−	0.168372i	0.0451151	−	0.168372i
$479$	0.0871557	−	0.150958i	0.0871557	−	0.150958i	−0.819152	−	0.573576i	$-0.805556\pi$
$479$	0.0871557	−	0.150958i	0.0871557	−	0.150958i	0.906308	+	0.422618i	$0.138889\pi$
$480$	1.14279	+	1.63207i	1.14279	+	1.63207i
$481$	−1.11334	+	0.642788i	−1.11334	+	0.642788i
$482$		0			0
$483$		0			0
$484$		−	1.00000i		−	1.00000i
$485$		0			0
$486$	−4.96826	−	2.86843i	−4.96826	−	2.86843i
$487$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$487$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$488$		0			0
$489$		0			0
$490$	0.342020	−	0.939693i	0.342020	−	0.939693i
$491$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$491$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		−	0.517638i		−	0.517638i
$497$	−0.0999810	+	1.14279i	−0.0999810	+	1.14279i
$498$		0			0
$499$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$499$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$500$	0.258819	−	0.965926i	0.258819	−	0.965926i
$501$	0.996195	−	1.72546i	0.996195	−	1.72546i
$502$	0.258819	−	0.965926i	0.258819	−	0.965926i
$503$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$503$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$504$	1.01567	−	2.79053i	1.01567	−	2.79053i
$505$		0			0
$506$		0			0
$507$	−1.92450	+	0.515668i	−1.92450	+	0.515668i
$508$		0			0
$509$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$509$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$510$	−3.06729	+	1.11640i	−3.06729	+	1.11640i
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$513$		0			0
$514$	−0.422618	+	0.731996i	−0.422618	+	0.731996i
$515$		0			0
$516$	1.45842	−	0.842020i	1.45842	−	0.842020i
$517$		0			0
$518$	−0.737376	+	1.05308i	−0.737376	+	1.05308i
$519$		0			0
$520$	−0.0871557	−	0.996195i	−0.0871557	−	0.996195i
$521$	−1.11334	−	0.642788i	−1.11334	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$521$	−1.11334	−	0.642788i	−1.11334	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$522$		0			0
$523$	0.500000	+	0.133975i	0.500000	+	0.133975i	0.500000	−	0.866025i	$-0.333333\pi$
$523$	0.500000	+	0.133975i	0.500000	+	0.133975i			1.00000i	$0.5\pi$
$524$	1.87939			1.87939
$525$	−1.87223	+	0.681437i	−1.87223	+	0.681437i
$526$		0			0
$527$	0.819152	+	0.219491i	0.819152	+	0.219491i
$528$		0			0
$529$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.335463	−	1.90250i	0.335463	−	1.90250i
$536$		0			0
$537$	0.352738	−	1.31644i	0.352738	−	1.31644i
$538$		0			0
$539$		0			0
$540$	−3.68758	+	1.34217i	−3.68758	+	1.34217i
$541$	−0.573576	−	0.993464i	−0.573576	−	0.993464i	−0.996195	−	0.0871557i	$-0.972222\pi$
$541$	−0.573576	−	0.993464i	−0.573576	−	0.993464i	0.422618	−	0.906308i	$-0.361111\pi$
$542$	−1.75085	+	0.469139i	−1.75085	+	0.469139i
$543$		0			0
$544$	−0.819152	−	1.41881i	−0.819152	−	1.41881i
$545$	−0.766044	+	1.64279i	−0.766044	+	1.64279i
$546$	−1.52626	+	1.28068i	−1.52626	+	1.28068i
$547$	1.40883	−	1.40883i	1.40883	−	1.40883i	0.642788	−	0.766044i	$-0.277778\pi$
$547$	1.40883	−	1.40883i	1.40883	−	1.40883i	0.766044	−	0.642788i	$-0.222222\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	2.55162	−	0.223238i	2.55162	−	0.223238i
$556$	1.70574	+	0.984808i	1.70574	+	0.984808i
$557$	−0.396534	−	1.47988i	−0.396534	−	1.47988i	−0.819152	−	0.573576i	$-0.805556\pi$
$557$	−0.396534	−	1.47988i	−0.396534	−	1.47988i	0.422618	−	0.906308i	$-0.361111\pi$
$558$	1.48481	+	0.397853i	1.48481	+	0.397853i
$559$	−0.845237			−0.845237
$560$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$561$		0			0
$562$		0			0
$563$	−0.469139	−	1.75085i	−0.469139	−	1.75085i	−0.642788	−	0.766044i	$-0.722222\pi$
$563$	−0.469139	−	1.75085i	−0.469139	−	1.75085i	0.173648	−	0.984808i	$-0.444444\pi$
$564$	−0.599246	−	0.345975i	−0.599246	−	0.345975i
$565$	0.332731	−	0.396534i	0.332731	−	0.396534i
$566$			1.41421i			1.41421i
$567$	3.97207	+	2.78127i	3.97207	+	2.78127i
$568$	0.811160	+	0.811160i	0.811160	+	0.811160i
$569$	0.300767	−	0.173648i	0.300767	−	0.173648i	−0.342020	−	0.939693i	$-0.611111\pi$
$569$	0.300767	−	0.173648i	0.300767	−	0.173648i	0.642788	+	0.766044i	$0.277778\pi$
$570$		0			0
$571$	−0.642788	+	1.11334i	−0.642788	+	1.11334i	0.342020	+	0.939693i	$0.388889\pi$
$571$	−0.642788	+	1.11334i	−0.642788	+	1.11334i	−0.984808	+	0.173648i	$0.944444\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−1.48481	−	2.57176i	−1.48481	−	2.57176i
$577$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$577$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$578$	1.62666	−	0.435862i	1.62666	−	0.435862i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	2.92450	+	0.515668i	2.92450	+	0.515668i
$586$	−1.32683	+	0.766044i	−1.32683	+	0.766044i
$587$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$587$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$588$	−0.842020	+	1.80572i	−0.842020	+	1.80572i
$589$		0			0
$590$		0			0
$591$	3.24280	+	1.87223i	3.24280	+	1.87223i
$592$	0.332731	+	1.24177i	0.332731	+	1.24177i
$593$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$593$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$594$		0			0
$595$	1.58248	−	0.424024i	1.58248	−	0.424024i
$596$	1.93185			1.93185
$597$		0			0
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$	−0.681437	+	1.87223i	−0.681437	+	1.87223i
$601$			1.53209i			1.53209i	0.642788	+	0.766044i	$0.277778\pi$
$601$			1.53209i			1.53209i	−0.642788	+	0.766044i	$0.722222\pi$
$602$	−0.766044	+	0.357212i	−0.766044	+	0.357212i
$603$		0			0
$604$	−1.41881	+	0.819152i	−1.41881	+	0.819152i
$605$	0.819152	−	0.573576i	0.819152	−	0.573576i
$606$		0			0
$607$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$607$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.173648	+	0.300767i	0.173648	+	0.300767i
$612$	4.69936	−	1.25919i	4.69936	−	1.25919i
$613$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$613$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$617$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$618$		0			0
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$	0.424024	−	0.296905i	0.424024	−	0.296905i
$621$		0			0
$622$		0			0
$623$		0			0
$624$			1.99239i			1.99239i
$625$	0.939693	−	0.342020i	0.939693	−	0.342020i
$626$	−0.993464	−	0.573576i	−0.993464	−	0.573576i
$627$		0			0
$628$		0			0
$629$	−2.10616			−2.10616
$630$	2.86843	−	0.768593i	2.86843	−	0.768593i
$631$	0.174311			0.174311			0.0871557	−	0.996195i	$-0.472222\pi$
$631$	0.174311			0.174311			0.0871557	+	0.996195i	$0.472222\pi$
$632$		0			0
$633$	−0.179090	−	0.668372i	−0.179090	−	0.668372i
$634$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$635$		0			0
$636$		0			0
$637$	0.819152	−	0.573576i	0.819152	−	0.573576i
$638$		0			0
$639$	−2.95020	+	1.70330i	−2.95020	+	1.70330i
$640$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$641$	−0.866025	+	1.50000i	−0.866025	+	1.50000i			1.00000i	$0.5\pi$
$641$	−0.866025	+	1.50000i	−0.866025	+	1.50000i	−0.866025	+	0.500000i	$0.833333\pi$
$642$	−0.996195	+	3.71785i	−0.996195	+	3.71785i
$643$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$643$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$644$		0			0
$645$	1.52626	+	0.711706i	1.52626	+	0.711706i
$646$		0			0
$647$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$647$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$648$	4.68378	−	1.25501i	4.68378	−	1.25501i
$649$		0			0
$650$	0.766044	−	0.642788i	0.766044	−	0.642788i
$651$	−0.969139	−	0.352738i	−0.969139	−	0.352738i
$652$		0			0
$653$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$653$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$654$	1.80572	−	3.12760i	1.80572	−	3.12760i
$655$	1.07797	+	1.53950i	1.07797	+	1.53950i
$656$		0			0
$657$		0			0
$658$	0.284489	+	0.199201i	0.284489	+	0.199201i
$659$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$659$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$660$		0			0
$661$	1.67303	+	0.965926i	1.67303	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$661$	1.67303	+	0.965926i	1.67303	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$662$		0			0
$663$	−3.15292	−	0.844822i	−3.15292	−	0.844822i
$664$		0			0
$665$		0			0
$666$	−3.81766			−3.81766
$667$		0			0
$668$	0.258819	+	0.965926i	0.258819	+	0.965926i
$669$	−2.64356	−	1.52626i	−2.64356	−	1.52626i
$670$		0			0
$671$		0			0
$672$	0.842020	+	1.80572i	0.842020	+	1.80572i
$673$	1.15846	+	1.15846i	1.15846	+	1.15846i	0.984808	+	0.173648i	$0.0555556\pi$
$673$	1.15846	+	1.15846i	1.15846	+	1.15846i	0.173648	+	0.984808i	$0.444444\pi$
$674$	−1.56977	+	0.906308i	−1.56977	+	0.906308i
$675$	−3.21455	−	2.25085i	−3.21455	−	2.25085i
$676$	0.500000	−	0.866025i	0.500000	−	0.866025i
$677$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$677$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$678$	−0.729265	+	0.729265i	−0.729265	+	0.729265i
$679$		0			0
$680$	0.692377	−	1.48481i	0.692377	−	1.48481i
$681$		0			0
$682$		0			0
$683$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$683$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$684$		0			0
$685$		0			0
$686$	0.500000	−	0.866025i	0.500000	−	0.866025i
$687$	0.245576	−	0.245576i	0.245576	−	0.245576i
$688$	−0.218763	+	0.816436i	−0.218763	+	0.816436i
$689$		0			0
$690$		0			0
$691$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$691$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$692$		0			0
$693$		0			0
$694$			1.14715i			1.14715i
$695$	0.171663	+	1.96212i	0.171663	+	1.96212i
$696$		0			0
$697$		0			0
$698$	1.10806	+	0.296905i	1.10806	+	0.296905i
$699$	0.347296			0.347296
$700$	0.422618	−	0.906308i	0.422618	−	0.906308i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−3.79053	−	1.01567i	−3.79053	−	1.01567i
$703$		0			0
$704$		0			0
$705$	−0.0603074	−	0.689316i	−0.0603074	−	0.689316i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$709$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$710$	−0.199201	+	1.12973i	−0.199201	+	1.12973i
$711$		0			0
$712$		0			0
$713$		0			0
$714$	−3.21455	+	0.566812i	−3.21455	+	0.566812i
$715$		0			0
$716$	0.342020	+	0.592396i	0.342020	+	0.592396i
$717$	−0.335463	+	0.0898869i	−0.335463	+	0.0898869i
$718$	0.500000	−	0.133975i	0.500000	−	0.133975i
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$	1.25501	−	2.69139i	1.25501	−	2.69139i
$721$		0			0
$722$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−1.72546	+	0.996195i	−1.72546	+	0.996195i
$727$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$727$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$728$	0.0871557	−	0.996195i	0.0871557	−	0.996195i
$729$			6.58105i			6.58105i
$730$		0			0
$731$	−1.19923	−	0.692377i	−1.19923	−	0.692377i
$732$		0			0
$733$	−0.335463	−	0.0898869i	−0.335463	−	0.0898869i	0.0871557	−	0.996195i	$-0.472222\pi$
$733$	−0.335463	−	0.0898869i	−0.335463	−	0.0898869i	−0.422618	+	0.906308i	$0.638889\pi$
$734$		0			0
$735$	−1.96212	+	0.345975i	−1.96212	+	0.345975i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$739$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$740$	−0.826352	+	0.984808i	−0.826352	+	0.984808i
$741$		0			0
$742$		0			0
$743$	−0.245576	−	0.245576i	−0.245576	−	0.245576i	0.573576	−	0.819152i	$-0.305556\pi$
$743$	−0.245576	−	0.245576i	−0.245576	−	0.245576i	−0.819152	+	0.573576i	$0.805556\pi$
$744$	−0.893164	+	0.515668i	−0.893164	+	0.515668i
$745$	1.10806	+	1.58248i	1.10806	+	1.58248i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.660732	−	1.81535i	0.660732	−	1.81535i
$750$	−1.92450	+	0.515668i	−1.92450	+	0.515668i
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	0.335463	−	0.0898869i	0.335463	−	0.0898869i
$753$	−1.92450	+	0.515668i	−1.92450	+	0.515668i
$754$		0			0
$755$	−1.48481	−	0.692377i	−1.48481	−	0.692377i
$756$	−3.86462	+	0.681437i	−3.86462	+	0.681437i
$757$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$757$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$		0			0
$763$	−1.03967	+	1.48481i	−1.03967	+	1.48481i
$764$		0			0
$765$	3.72691	+	3.12725i	3.72691	+	3.12725i
$766$	1.11334	+	0.642788i	1.11334	+	0.642788i
$767$		0			0
$768$	1.92450	+	0.515668i	1.92450	+	0.515668i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$	1.68404			1.68404
$772$		0			0
$773$	0.332731	+	1.24177i	0.332731	+	1.24177i	0.906308	+	0.422618i	$0.138889\pi$
$773$	0.332731	+	1.24177i	0.332731	+	1.24177i	−0.573576	+	0.819152i	$0.694444\pi$
$774$	−2.17375	−	1.25501i	−2.17375	−	1.25501i
$775$	0.486421	+	0.177043i	0.486421	+	0.177043i
$776$		0			0
$777$	2.55162	+	0.223238i	2.55162	+	0.223238i
$778$		0			0
$779$		0			0
$780$	−1.63207	+	1.14279i	−1.63207	+	1.14279i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$785$		0			0
$786$	−1.87223	−	3.24280i	−1.87223	−	3.24280i
$787$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$787$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$788$	−1.81535	+	0.486421i	−1.81535	+	0.486421i
$789$		0			0
$790$		0			0
$791$	0.396534	−	0.332731i	0.396534	−	0.332731i
$792$		0			0
$793$		0			0
$794$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$795$		0			0
$796$		0			0
$797$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$797$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$798$		0			0
$799$			0.568977i			0.568977i
$800$	−0.422618	−	0.906308i	−0.422618	−	0.906308i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	0.517638			0.517638
$807$		0			0
$808$		0			0
$809$	1.32683	+	0.766044i	1.32683	+	0.766044i	0.984808	−	0.173648i	$-0.0555556\pi$
$809$	1.32683	+	0.766044i	1.32683	+	0.766044i	0.342020	+	0.939693i	$0.388889\pi$
$810$	3.71455	+	3.11688i	3.71455	+	3.11688i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$	2.55367	+	2.55367i	2.55367	+	2.55367i
$814$		0			0
$815$		0			0
$816$	−1.63207	+	2.82683i	−1.63207	+	2.82683i
$817$		0			0
$818$		0			0
$819$	2.79053	+	1.01567i	2.79053	+	1.01567i
$820$		0			0
$821$	−0.996195	−	1.72546i	−0.996195	−	1.72546i	−0.573576	−	0.819152i	$-0.694444\pi$
$821$	−0.996195	−	1.72546i	−0.996195	−	1.72546i	−0.422618	−	0.906308i	$-0.638889\pi$
$822$		0			0
$823$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$823$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$827$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$828$		0			0
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$		0			0
$832$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$833$	1.63207	−	0.142788i	1.63207	−	0.142788i
$834$		−	3.92424i		−	3.92424i
$835$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$836$		0			0
$837$	−0.525749	−	1.96212i	−0.525749	−	1.96212i
$838$	0.660732	+	0.177043i	0.660732	+	0.177043i
$839$	−1.93185			−1.93185			−0.965926	−	0.258819i	$-0.916667\pi$
$839$	−1.93185			−1.93185			−0.965926	+	0.258819i	$0.916667\pi$
$840$	−0.996195	+	1.72546i	−0.996195	+	1.72546i
$841$	−1.00000			−1.00000
$842$	0.816436	+	0.218763i	0.816436	+	0.218763i
$843$		0			0
$844$	0.300767	+	0.173648i	0.300767	+	0.173648i
$845$	0.996195	−	0.0871557i	0.996195	−	0.0871557i
$846$			1.03134i			1.03134i
$847$	0.906308	−	0.422618i	0.906308	−	0.422618i
$848$		0			0
$849$	2.44017	−	1.40883i	2.44017	−	1.40883i
$850$	1.61341	−	0.284489i	1.61341	−	0.284489i
$851$		0			0
$852$	0.591550	−	2.20770i	0.591550	−	2.20770i
$853$	0.909039	−	0.909039i	0.909039	−	0.909039i	−0.0871557	−	0.996195i	$-0.527778\pi$
$853$	0.909039	−	0.909039i	0.909039	−	0.909039i	0.996195	+	0.0871557i	$0.0277778\pi$
$854$		0			0
$855$		0			0
$856$	−0.965926	−	1.67303i	−0.965926	−	1.67303i
$857$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$857$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$858$		0			0
$859$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$859$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$860$	−0.794263	+	0.289088i	−0.794263	+	0.289088i
$861$		0			0
$862$	1.28171	−	1.28171i	1.28171	−	1.28171i
$863$	0.332731	−	1.24177i	0.332731	−	1.24177i	−0.573576	−	0.819152i	$-0.694444\pi$
$863$	0.332731	−	1.24177i	0.332731	−	1.24177i	0.906308	−	0.422618i	$-0.138889\pi$
$864$	−1.96212	+	3.39849i	−1.96212	+	3.39849i
$865$		0			0
$866$	−0.150958	+	0.0871557i	−0.150958	+	0.0871557i
$867$	−2.37253	−	2.37253i	−2.37253	−	2.37253i
$868$	0.469139	−	0.218763i	0.469139	−	0.218763i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.469139	+	1.75085i	0.469139	+	1.75085i
$873$		0			0
$874$		0			0
$875$	0.984808	−	0.173648i	0.984808	−	0.173648i
$876$		0			0
$877$	1.81535	+	0.486421i	1.81535	+	0.486421i	0.996195	−	0.0871557i	$-0.0277778\pi$
$877$	1.81535	+	0.486421i	1.81535	+	0.486421i	0.819152	+	0.573576i	$0.194444\pi$
$878$		0			0
$879$	2.64356	+	1.52626i	2.64356	+	1.52626i
$880$		0			0
$881$		−	1.53209i		−	1.53209i	−0.642788	−	0.766044i	$-0.722222\pi$
$881$		−	1.53209i		−	1.53209i	0.642788	−	0.766044i	$-0.277778\pi$
$882$	2.95832	−	0.258819i	2.95832	−	0.258819i
$883$	0.123257	+	0.123257i	0.123257	+	0.123257i	0.766044	−	0.642788i	$-0.222222\pi$
$883$	0.123257	+	0.123257i	0.123257	+	0.123257i	−0.642788	+	0.766044i	$0.722222\pi$
$884$	1.41881	−	0.819152i	1.41881	−	0.819152i
$885$		0			0
$886$	0.996195	−	1.72546i	0.996195	−	1.72546i
$887$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$887$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$888$	1.81116	−	1.81116i	1.81116	−	1.81116i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	1.47988	−	0.396534i	1.47988	−	0.396534i
$893$		0			0
$894$	−1.92450	−	3.33333i	−1.92450	−	3.33333i
$895$	−0.289088	+	0.619951i	−0.289088	+	0.619951i
$896$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	2.92450	−	0.515668i	2.92450	−	0.515668i
$901$		0			0
$902$		0			0
$903$	1.37949	+	0.965926i	1.37949	+	0.965926i
$904$		−	0.517638i		−	0.517638i
$905$		0			0
$906$	2.82683	+	1.63207i	2.82683	+	1.63207i
$907$	−0.424024	−	1.58248i	−0.424024	−	1.58248i	−0.766044	−	0.642788i	$-0.777778\pi$
$907$	−0.424024	−	1.58248i	−0.424024	−	1.58248i	0.342020	−	0.939693i	$-0.388889\pi$
$908$		0			0
$909$		0			0
$910$	0.866025	−	0.500000i	0.866025	−	0.500000i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$			0.174311i			0.174311i
$917$	0.794263	+	1.70330i	0.794263	+	1.70330i
$918$	−4.54606	−	4.54606i	−4.54606	−	4.54606i
$919$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$919$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$920$		0			0
$921$		0			0
$922$	−0.296905	+	1.10806i	−0.296905	+	1.10806i
$923$	−0.811160	+	0.811160i	−0.811160	+	0.811160i
$924$		0			0
$925$	−1.28068	−	0.112045i	−1.28068	−	0.112045i
$926$	0.866025	+	1.50000i	0.866025	+	1.50000i
$927$		0			0
$928$		0			0
$929$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$929$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$930$	−0.934708	−	0.435862i	−0.934708	−	0.435862i
$931$		0			0
$932$	−0.123257	+	0.123257i	−0.123257	+	0.123257i
$933$		0			0
$934$	0.707107	−	1.22474i	0.707107	−	1.22474i
$935$		0			0
$936$	2.57176	−	1.48481i	2.57176	−	1.48481i
$937$	0.366025	+	0.366025i	0.366025	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$937$	0.366025	+	0.366025i	0.366025	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$938$		0			0
$939$			2.28558i			2.28558i
$940$	0.266044	+	0.223238i	0.266044	+	0.223238i
$941$	1.41881	+	0.819152i	1.41881	+	0.819152i	0.996195	−	0.0871557i	$-0.0277778\pi$
$941$	1.41881	+	0.819152i	1.41881	+	0.819152i	0.422618	+	0.906308i	$0.361111\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−2.77486	−	2.77486i	−2.77486	−	2.77486i
$946$		0			0
$947$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$947$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$			3.45092i			3.45092i
$952$	0.939693	−	1.34202i	0.939693	−	1.34202i
$953$	−1.15846	−	1.15846i	−1.15846	−	1.15846i	−0.984808	−	0.173648i	$-0.944444\pi$
$953$	−1.15846	−	1.15846i	−1.15846	−	1.15846i	−0.173648	−	0.984808i	$-0.555556\pi$
$954$		0			0
$955$		0			0
$956$	0.0871557	−	0.150958i	0.0871557	−	0.150958i
$957$		0			0
$958$	0.123257	−	0.123257i	0.123257	−	0.123257i
$959$		0			0
$960$	0.681437	+	1.87223i	0.681437	+	1.87223i
$961$	−0.366025	−	0.633975i	−0.366025	−	0.633975i
$962$	−1.24177	+	0.332731i	−1.24177	+	0.332731i
$963$	5.54138	−	1.48481i	5.54138	−	1.48481i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.483690	−	0.483690i	0.483690	−	0.483690i	−0.422618	−	0.906308i	$-0.638889\pi$
$967$	0.483690	−	0.483690i	0.483690	−	0.483690i	0.906308	+	0.422618i	$0.138889\pi$
$968$	0.258819	−	0.965926i	0.258819	−	0.965926i
$969$		0			0
$970$		0			0
$971$	1.70574	−	0.984808i	1.70574	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$971$	1.70574	−	0.984808i	1.70574	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$972$	−4.05657	−	4.05657i	−4.05657	−	4.05657i
$973$	−0.171663	+	1.96212i	−0.171663	+	1.96212i
$974$			1.00000i			1.00000i
$975$	−1.87223	−	0.681437i	−1.87223	−	0.681437i
$976$		0			0
$977$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$977$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$978$		0			0
$979$		0			0
$980$	0.573576	−	0.819152i	0.573576	−	0.819152i
$981$	−5.38277			−5.38277
$982$	−1.81535	−	0.486421i	−1.81535	−	0.486421i
$983$	−0.396534	−	1.47988i	−0.396534	−	1.47988i	−0.819152	−	0.573576i	$-0.805556\pi$
$983$	−0.396534	−	1.47988i	−0.396534	−	1.47988i	0.422618	−	0.906308i	$-0.361111\pi$
$984$		0			0
$985$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$986$		0			0
$987$	0.0603074	−	0.689316i	0.0603074	−	0.689316i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$	0.133975	−	0.500000i	0.133975	−	0.500000i
$993$		0			0
$994$	−0.392349	+	1.07797i	−0.392349	+	1.07797i
$995$		0			0
$996$		0			0
$997$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$997$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$998$		0			0
$999$	2.52245	+	4.36902i	2.52245	+	4.36902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3640.1.od.b.1403.4	yes	24
5.2	odd	4		3640.1.od.a.3587.1	yes	24
7.5	odd	6		3640.1.od.a.1923.1	✓	24
8.3	odd	2	inner	3640.1.od.b.1403.1	yes	24
13.12	even	2	inner	3640.1.od.b.1403.1	yes	24
35.12	even	12	inner	3640.1.od.b.467.4	yes	24
40.27	even	4		3640.1.od.a.3587.4	yes	24
56.19	even	6		3640.1.od.a.1923.4	yes	24
65.12	odd	4		3640.1.od.a.3587.4	yes	24
91.12	odd	6		3640.1.od.a.1923.4	yes	24
104.51	odd	2	CM	3640.1.od.b.1403.4	yes	24
280.187	odd	12	inner	3640.1.od.b.467.1	yes	24
455.12	even	12	inner	3640.1.od.b.467.1	yes	24
520.467	even	4		3640.1.od.a.3587.1	yes	24
728.467	even	6		3640.1.od.a.1923.1	✓	24
3640.467	odd	12	inner	3640.1.od.b.467.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3640.1.od.a.1923.1	✓	24	7.5	odd	6
3640.1.od.a.1923.1	✓	24	728.467	even	6
3640.1.od.a.1923.4	yes	24	56.19	even	6
3640.1.od.a.1923.4	yes	24	91.12	odd	6
3640.1.od.a.3587.1	yes	24	5.2	odd	4
3640.1.od.a.3587.1	yes	24	520.467	even	4
3640.1.od.a.3587.4	yes	24	40.27	even	4
3640.1.od.a.3587.4	yes	24	65.12	odd	4
3640.1.od.b.467.1	yes	24	280.187	odd	12	inner
3640.1.od.b.467.1	yes	24	455.12	even	12	inner
3640.1.od.b.467.4	yes	24	35.12	even	12	inner
3640.1.od.b.467.4	yes	24	3640.467	odd	12	inner
3640.1.od.b.1403.1	yes	24	8.3	odd	2	inner
3640.1.od.b.1403.1	yes	24	13.12	even	2	inner
3640.1.od.b.1403.4	yes	24	1.1	even	1	trivial
3640.1.od.b.1403.4	yes	24	104.51	odd	2	CM

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:	\( N \)	\(=\)	\( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3640.od (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.515668 - 1.92450i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.0871557 + 0.996195i) q^{5} -1.99239i q^{6} +(-0.0871557 + 0.996195i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.57176 + 1.48481i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.515668 - 1.92450i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.0871557 + 0.996195i) q^{5} -1.99239i q^{6} +(-0.0871557 + 0.996195i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.57176 + 1.48481i) q^{9} +(-0.173648 + 0.984808i) q^{10} +(0.515668 - 1.92450i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(-0.342020 + 0.939693i) q^{14} +(1.87223 - 0.681437i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.58248 + 0.424024i) q^{17} +(-2.86843 + 0.768593i) q^{18} +(-0.422618 + 0.906308i) q^{20} +(1.96212 - 0.345975i) q^{21} +(0.996195 - 1.72546i) q^{24} +(-0.984808 + 0.173648i) q^{25} +(-0.866025 + 0.500000i) q^{26} +(2.77486 + 2.77486i) q^{27} +(-0.573576 + 0.819152i) q^{28} +(1.98481 - 0.173648i) q^{30} +(-0.448288 - 0.258819i) q^{31} +(0.258819 + 0.965926i) q^{32} -1.63830 q^{34} -1.00000 q^{35} -2.96962 q^{36} +(1.24177 + 0.332731i) q^{37} +(1.72546 + 0.996195i) q^{39} +(-0.642788 + 0.766044i) q^{40} +(1.98481 + 0.173648i) q^{42} +(0.597672 + 0.597672i) q^{43} +(-1.70330 - 2.43257i) q^{45} +(0.0898869 - 0.335463i) q^{47} +(1.40883 - 1.40883i) q^{48} +(-0.984808 - 0.173648i) q^{49} +(-0.996195 - 0.0871557i) q^{50} +(1.63207 + 2.82683i) q^{51} +(-0.965926 + 0.258819i) q^{52} +(1.96212 + 3.39849i) q^{54} +(-0.766044 + 0.642788i) q^{56} +(1.96212 + 0.345975i) q^{60} +(-0.366025 - 0.366025i) q^{62} +(-1.25501 - 2.69139i) q^{63} +1.00000i q^{64} +(-0.766044 - 0.642788i) q^{65} +(-1.58248 - 0.424024i) q^{68} +(-0.965926 - 0.258819i) q^{70} +1.14715 q^{71} +(-2.86843 - 0.768593i) q^{72} +(1.11334 + 0.642788i) q^{74} +(0.842020 + 1.80572i) q^{75} +(1.40883 + 1.40883i) q^{78} +(-0.819152 + 0.573576i) q^{80} +(2.42450 - 4.19936i) q^{81} +(1.87223 + 0.681437i) q^{84} +(-0.560333 - 1.53950i) q^{85} +(0.422618 + 0.731996i) q^{86} +(-1.01567 - 2.79053i) q^{90} +(-0.642788 - 0.766044i) q^{91} +(-0.266930 + 0.996195i) q^{93} +(0.173648 - 0.300767i) q^{94} +(1.72546 - 0.996195i) q^{96} +(-0.906308 - 0.422618i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 12 q^{16} + 12 q^{27} + 24 q^{30} - 24 q^{35} - 24 q^{36} + 24 q^{42} + 12 q^{62} + 12 q^{75} + 12 q^{81} - 12 q^{90}+O(q^{100}) \) 24 * q + 12 * q^16 + 12 * q^27 + 24 * q^30 - 24 * q^35 - 24 * q^36 + 24 * q^42 + 12 * q^62 + 12 * q^75 + 12 * q^81 - 12 * q^90

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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