LMFDB - Embedded newform 3640.1.od.a.1403.3

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			1403.3
Root			$-0.573576 - 0.819152i$ of defining polynomial
Character	$\chi$	$=$	3640.1403
Dual form			3640.1.od.a.467.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.424024 + 1.58248i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.422618 - 0.906308i) q^{5} -1.63830i q^{6} +(0.819152 + 0.573576i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.45842 + 0.842020i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.424024 + 1.58248i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.422618 - 0.906308i) q^{5} -1.63830i q^{6} +(0.819152 + 0.573576i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.45842 + 0.842020i) q^{9} +(0.173648 + 0.984808i) q^{10} +(-0.424024 + 1.58248i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(-0.642788 - 0.766044i) q^{14} +(1.25501 - 1.05308i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.816436 + 0.218763i) q^{17} +(1.62666 - 0.435862i) q^{18} +(0.0871557 - 0.996195i) q^{20} +(-0.560333 + 1.53950i) q^{21} +(0.819152 - 1.41881i) q^{24} +(-0.642788 + 0.766044i) q^{25} +(0.866025 - 0.500000i) q^{26} +(-0.792431 - 0.792431i) q^{27} +(0.422618 + 0.906308i) q^{28} +(-1.48481 + 0.692377i) q^{30} +(1.67303 + 0.965926i) q^{31} +(-0.258819 - 0.965926i) q^{32} +0.845237 q^{34} +(0.173648 - 0.984808i) q^{35} -1.68404 q^{36} +(-1.90250 - 0.509774i) q^{37} +(-1.41881 - 0.819152i) q^{39} +(-0.342020 + 0.939693i) q^{40} +(0.939693 - 1.34202i) q^{42} +(-0.123257 - 0.123257i) q^{43} +(1.37949 + 0.965926i) q^{45} +(-0.486421 + 1.81535i) q^{47} +(-1.15846 + 1.15846i) q^{48} +(0.342020 + 0.939693i) q^{49} +(0.819152 - 0.573576i) q^{50} +(-0.692377 - 1.19923i) q^{51} +(-0.965926 + 0.258819i) q^{52} +(0.560333 + 0.970525i) q^{54} +(-0.173648 - 0.984808i) q^{56} +(1.61341 - 0.284489i) q^{60} +(-1.36603 - 1.36603i) q^{62} +(-1.67763 - 0.146774i) q^{63} +1.00000i q^{64} +(0.939693 + 0.342020i) q^{65} +(-0.816436 - 0.218763i) q^{68} +(-0.422618 + 0.906308i) q^{70} -1.81262 q^{71} +(1.62666 + 0.435862i) q^{72} +(1.70574 + 0.984808i) q^{74} +(-1.48481 - 0.692377i) q^{75} +(1.15846 + 1.15846i) q^{78} +(0.573576 - 0.819152i) q^{80} +(0.0759757 - 0.131594i) q^{81} +(-1.25501 + 1.05308i) q^{84} +(0.543308 + 0.647489i) q^{85} +(0.0871557 + 0.150958i) q^{86} +(-1.08248 - 1.29005i) q^{90} +(-0.984808 + 0.173648i) q^{91} +(-0.819152 + 3.05712i) q^{93} +(0.939693 - 1.62760i) q^{94} +(1.41881 - 0.819152i) q^{96} +(-0.0871557 - 0.996195i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 12 q^{16} - 12 q^{27} - 12 q^{30} - 24 q^{36} - 12 q^{62} - 12 q^{75} + 12 q^{81} + 12 q^{90}+O(q^{100}) $ 24 * q + 12 * q^16 - 12 * q^27 - 12 * q^30 - 24 * q^36 - 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
$3$	0.424024	+	1.58248i	0.424024	+	1.58248i	0.766044	+	0.642788i	$0.222222\pi$
$3$	0.424024	+	1.58248i	0.424024	+	1.58248i	−0.342020	+	0.939693i	$0.611111\pi$
$4$	0.866025	+	0.500000i	0.866025	+	0.500000i
$5$	−0.422618	−	0.906308i	−0.422618	−	0.906308i
$5$	−0.422618	−	0.906308i	−0.422618	−	0.906308i
$6$		−	1.63830i		−	1.63830i
$7$	0.819152	+	0.573576i	0.819152	+	0.573576i
$7$	0.819152	+	0.573576i	0.819152	+	0.573576i
$8$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$9$	−1.45842	+	0.842020i	−1.45842	+	0.842020i
$10$	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	$0.666667\pi$
$12$	−0.424024	+	1.58248i	−0.424024	+	1.58248i
$13$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$13$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$14$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$15$	1.25501	−	1.05308i	1.25501	−	1.05308i
$16$	0.500000	+	0.866025i	0.500000	+	0.866025i
$17$	−0.816436	+	0.218763i	−0.816436	+	0.218763i	−0.642788	−	0.766044i	$-0.722222\pi$
$17$	−0.816436	+	0.218763i	−0.816436	+	0.218763i	−0.173648	+	0.984808i	$0.555556\pi$
$18$	1.62666	−	0.435862i	1.62666	−	0.435862i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	0.0871557	−	0.996195i	0.0871557	−	0.996195i
$21$	−0.560333	+	1.53950i	−0.560333	+	1.53950i
$22$		0			0
$23$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$23$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$24$	0.819152	−	1.41881i	0.819152	−	1.41881i
$25$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$26$	0.866025	−	0.500000i	0.866025	−	0.500000i
$27$	−0.792431	−	0.792431i	−0.792431	−	0.792431i
$28$	0.422618	+	0.906308i	0.422618	+	0.906308i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	−1.48481	+	0.692377i	−1.48481	+	0.692377i
$31$	1.67303	+	0.965926i	1.67303	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$31$	1.67303	+	0.965926i	1.67303	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$32$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$33$		0			0
$34$	0.845237			0.845237
$35$	0.173648	−	0.984808i	0.173648	−	0.984808i
$36$	−1.68404			−1.68404
$37$	−1.90250	−	0.509774i	−1.90250	−	0.509774i	−0.996195	−	0.0871557i	$-0.972222\pi$
$37$	−1.90250	−	0.509774i	−1.90250	−	0.509774i	−0.906308	−	0.422618i	$-0.861111\pi$
$38$		0			0
$39$	−1.41881	−	0.819152i	−1.41881	−	0.819152i
$40$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	0.939693	−	1.34202i	0.939693	−	1.34202i
$43$	−0.123257	−	0.123257i	−0.123257	−	0.123257i	0.642788	−	0.766044i	$-0.277778\pi$
$43$	−0.123257	−	0.123257i	−0.123257	−	0.123257i	−0.766044	+	0.642788i	$0.777778\pi$
$44$		0			0
$45$	1.37949	+	0.965926i	1.37949	+	0.965926i
$46$		0			0
$47$	−0.486421	+	1.81535i	−0.486421	+	1.81535i	0.0871557	+	0.996195i	$0.472222\pi$
$47$	−0.486421	+	1.81535i	−0.486421	+	1.81535i	−0.573576	+	0.819152i	$0.694444\pi$
$48$	−1.15846	+	1.15846i	−1.15846	+	1.15846i
$49$	0.342020	+	0.939693i	0.342020	+	0.939693i
$50$	0.819152	−	0.573576i	0.819152	−	0.573576i
$51$	−0.692377	−	1.19923i	−0.692377	−	1.19923i
$52$	−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	$0.916667\pi$
$54$	0.560333	+	0.970525i	0.560333	+	0.970525i
$55$		0			0
$56$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$57$		0			0
$58$		0			0
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$	1.61341	−	0.284489i	1.61341	−	0.284489i
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	−1.36603	−	1.36603i	−1.36603	−	1.36603i
$63$	−1.67763	−	0.146774i	−1.67763	−	0.146774i
$64$			1.00000i			1.00000i
$65$	0.939693	+	0.342020i	0.939693	+	0.342020i
$66$		0			0
$67$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$67$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$68$	−0.816436	−	0.218763i	−0.816436	−	0.218763i
$69$		0			0
$70$	−0.422618	+	0.906308i	−0.422618	+	0.906308i
$71$	−1.81262			−1.81262			−0.906308	−	0.422618i	$-0.861111\pi$
$71$	−1.81262			−1.81262			−0.906308	+	0.422618i	$0.861111\pi$
$72$	1.62666	+	0.435862i	1.62666	+	0.435862i
$73$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$73$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$74$	1.70574	+	0.984808i	1.70574	+	0.984808i
$75$	−1.48481	−	0.692377i	−1.48481	−	0.692377i
$76$		0			0
$77$		0			0
$78$	1.15846	+	1.15846i	1.15846	+	1.15846i
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	0.573576	−	0.819152i	0.573576	−	0.819152i
$81$	0.0759757	−	0.131594i	0.0759757	−	0.131594i
$82$		0			0
$83$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$83$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$84$	−1.25501	+	1.05308i	−1.25501	+	1.05308i
$85$	0.543308	+	0.647489i	0.543308	+	0.647489i
$86$	0.0871557	+	0.150958i	0.0871557	+	0.150958i
$87$		0			0
$88$		0			0
$89$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$89$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$90$	−1.08248	−	1.29005i	−1.08248	−	1.29005i
$91$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$92$		0			0
$93$	−0.819152	+	3.05712i	−0.819152	+	3.05712i
$94$	0.939693	−	1.62760i	0.939693	−	1.62760i
$95$		0			0
$96$	1.41881	−	0.819152i	1.41881	−	0.819152i
$97$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$97$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$98$	−0.0871557	−	0.996195i	−0.0871557	−	0.996195i
$99$		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	$0.166667\pi$
$102$	0.358401	+	1.33757i	0.358401	+	1.33757i
$103$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$103$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$104$	1.00000			1.00000
$105$	1.63207	−	0.142788i	1.63207	−	0.142788i
$106$		0			0
$107$	0.500000	+	0.133975i	0.500000	+	0.133975i	0.500000	−	0.866025i	$-0.333333\pi$
$107$	0.500000	+	0.133975i	0.500000	+	0.133975i			1.00000i	$0.5\pi$
$108$	−0.290050	−	1.08248i	−0.290050	−	1.08248i
$109$	1.72546	+	0.996195i	1.72546	+	0.996195i	0.906308	+	0.422618i	$0.138889\pi$
$109$	1.72546	+	0.996195i	1.72546	+	0.996195i	0.819152	+	0.573576i	$0.194444\pi$
$110$		0			0
$111$		−	3.22683i		−	3.22683i
$112$	−0.0871557	+	0.996195i	−0.0871557	+	0.996195i
$113$	1.36603	+	1.36603i	1.36603	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$113$	1.36603	+	1.36603i	1.36603	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.435862	−	1.62666i	0.435862	−	1.62666i
$118$		0			0
$119$	−0.794263	−	0.289088i	−0.794263	−	0.289088i
$120$	−1.63207	−	0.142788i	−1.63207	−	0.142788i
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$	0.965926	+	1.67303i	0.965926	+	1.67303i
$125$	0.965926	+	0.258819i	0.965926	+	0.258819i
$126$	1.58248	+	0.575976i	1.58248	+	0.575976i
$127$		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
$129$	0.142788	−	0.247315i	0.142788	−	0.247315i
$130$	−0.819152	−	0.573576i	−0.819152	−	0.573576i
$131$	1.32683	−	0.766044i	1.32683	−	0.766044i	0.342020	−	0.939693i	$-0.388889\pi$
$131$	1.32683	−	0.766044i	1.32683	−	0.766044i	0.984808	+	0.173648i	$0.0555556\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.383290	+	1.05308i	−0.383290	+	1.05308i
$136$	0.731996	+	0.422618i	0.731996	+	0.422618i
$137$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$137$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$138$		0			0
$139$	−0.684040			−0.684040			−0.342020	−	0.939693i	$-0.611111\pi$
$139$	−0.684040			−0.684040			−0.342020	+	0.939693i	$0.611111\pi$
$140$	0.642788	−	0.766044i	0.642788	−	0.766044i
$141$	−3.07900			−3.07900
$142$	1.75085	+	0.469139i	1.75085	+	0.469139i
$143$		0			0
$144$	−1.45842	−	0.842020i	−1.45842	−	0.842020i
$145$		0			0
$146$		0			0
$147$	−1.34202	+	0.939693i	−1.34202	+	0.939693i
$148$	−1.39273	−	1.39273i	−1.39273	−	1.39273i
$149$	0.448288	−	0.258819i	0.448288	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$149$	0.448288	−	0.258819i	0.448288	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$150$	1.25501	+	1.05308i	1.25501	+	1.05308i
$151$	−0.422618	+	0.731996i	−0.422618	+	0.731996i	−0.996195	−	0.0871557i	$-0.972222\pi$
$151$	−0.422618	+	0.731996i	−0.422618	+	0.731996i	0.573576	+	0.819152i	$0.305556\pi$
$152$		0			0
$153$	1.00650	−	1.00650i	1.00650	−	1.00650i
$154$		0			0
$155$	0.168372	−	1.92450i	0.168372	−	1.92450i
$156$	−0.819152	−	1.41881i	−0.819152	−	1.41881i
$157$		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
$160$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$161$		0			0
$162$	−0.107446	+	0.107446i	−0.107446	+	0.107446i
$163$		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	$0.583333\pi$
$168$	1.48481	−	0.692377i	1.48481	−	0.692377i
$169$		−	1.00000i		−	1.00000i
$170$	−0.357212	−	0.766044i	−0.357212	−	0.766044i
$171$		0			0
$172$	−0.0451151	−	0.168372i	−0.0451151	−	0.168372i
$173$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$173$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$174$		0			0
$175$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.11334	−	0.642788i	−1.11334	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$179$	−1.11334	−	0.642788i	−1.11334	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$180$	0.711706	+	1.52626i	0.711706	+	1.52626i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	0.996195	+	0.0871557i	0.996195	+	0.0871557i
$183$		0			0
$184$		0			0
$185$	0.342020	+	1.93969i	0.342020	+	1.93969i
$186$	1.58248	−	2.74094i	1.58248	−	2.74094i
$187$		0			0
$188$	−1.32893	+	1.32893i	−1.32893	+	1.32893i
$189$	−0.194602	−	1.10364i	−0.194602	−	1.10364i
$190$		0			0
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$	−1.58248	+	0.424024i	−1.58248	+	0.424024i
$193$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$193$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$194$		0			0
$195$	−0.142788	+	1.63207i	−0.142788	+	1.63207i
$196$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$197$	−1.08335	+	1.08335i	−1.08335	+	1.08335i	−0.0871557	+	0.996195i	$0.527778\pi$
$197$	−1.08335	+	1.08335i	−1.08335	+	1.08335i	−0.996195	+	0.0871557i	$0.972222\pi$
$198$		0			0
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	0.996195	−	0.0871557i	0.996195	−	0.0871557i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		−	1.38475i		−	1.38475i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$209$		0			0
$210$	−1.61341	−	0.284489i	−1.61341	−	0.284489i
$211$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$211$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$212$		0			0
$213$	−0.768593	−	2.86843i	−0.768593	−	2.86843i
$214$	−0.448288	−	0.258819i	−0.448288	−	0.258819i
$215$	−0.0596180	+	0.163799i	−0.0596180	+	0.163799i
$216$			1.12067i			1.12067i
$217$	0.816436	+	1.75085i	0.816436	+	1.75085i
$218$	−1.40883	−	1.40883i	−1.40883	−	1.40883i
$219$		0			0
$220$		0			0
$221$	0.422618	−	0.731996i	0.422618	−	0.731996i
$222$	−0.835165	+	3.11688i	−0.835165	+	3.11688i
$223$	0.245576	−	0.245576i	0.245576	−	0.245576i	−0.573576	−	0.819152i	$-0.694444\pi$
$223$	0.245576	−	0.245576i	0.245576	−	0.245576i	0.819152	+	0.573576i	$0.194444\pi$
$224$	0.342020	−	0.939693i	0.342020	−	0.939693i
$225$	0.292431	−	1.65846i	0.292431	−	1.65846i
$226$	−0.965926	−	1.67303i	−0.965926	−	1.67303i
$227$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$227$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$228$		0			0
$229$	−0.573576	−	0.993464i	−0.573576	−	0.993464i	−0.996195	−	0.0871557i	$-0.972222\pi$
$229$	−0.573576	−	0.993464i	−0.573576	−	0.993464i	0.422618	−	0.906308i	$-0.361111\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.296905	−	1.10806i	0.296905	−	1.10806i	−0.642788	−	0.766044i	$-0.722222\pi$
$233$	0.296905	−	1.10806i	0.296905	−	1.10806i	0.939693	−	0.342020i	$-0.111111\pi$
$234$	−0.842020	+	1.45842i	−0.842020	+	1.45842i
$235$	1.85083	−	0.326352i	1.85083	−	0.326352i
$236$		0			0
$237$		0			0
$238$	0.692377	+	0.484808i	0.692377	+	0.484808i
$239$		−	1.14715i		−	1.14715i	−0.819152	−	0.573576i	$-0.805556\pi$
$239$		−	1.14715i		−	1.14715i	0.819152	−	0.573576i	$-0.194444\pi$
$240$	1.53950	+	0.560333i	1.53950	+	0.560333i
$241$		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
$243$	−0.842020	−	0.225619i	−0.842020	−	0.225619i
$244$		0			0
$245$	0.707107	−	0.707107i	0.707107	−	0.707107i
$246$		0			0
$247$		0			0
$248$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$249$		0			0
$250$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$251$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$251$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$252$	−1.37949	−	0.965926i	−1.37949	−	0.965926i
$253$		0			0
$254$		0			0
$255$	−0.794263	+	1.13432i	−0.794263	+	1.13432i
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$	−0.0451151	+	0.168372i	−0.0451151	+	0.168372i	−0.984808	−	0.173648i	$-0.944444\pi$
$257$	−0.0451151	+	0.168372i	−0.0451151	+	0.168372i	0.939693	+	0.342020i	$0.111111\pi$
$258$	−0.201932	+	0.201932i	−0.201932	+	0.201932i
$259$	−1.26604	−	1.50881i	−1.26604	−	1.50881i
$260$	0.642788	+	0.766044i	0.642788	+	0.766044i
$261$		0			0
$262$	−1.47988	+	0.396534i	−1.47988	+	0.396534i
$263$		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	$0.666667\pi$
$270$	0.642788	−	0.917996i	0.642788	−	0.917996i
$271$	1.72546	−	0.996195i	1.72546	−	0.996195i	0.819152	−	0.573576i	$-0.194444\pi$
$271$	1.72546	−	0.996195i	1.72546	−	0.996195i	0.906308	−	0.422618i	$-0.138889\pi$
$272$	−0.597672	−	0.597672i	−0.597672	−	0.597672i
$273$	−0.692377	−	1.48481i	−0.692377	−	1.48481i
$274$		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	$0.416667\pi$
$278$	0.660732	+	0.177043i	0.660732	+	0.177043i
$279$	−3.25332			−3.25332
$280$	−0.819152	+	0.573576i	−0.819152	+	0.573576i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	2.97409	+	0.796905i	2.97409	+	0.796905i
$283$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$283$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$284$	−1.56977	−	0.906308i	−1.56977	−	0.906308i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.19080	+	1.19080i	1.19080	+	1.19080i
$289$	−0.247315	+	0.142788i	−0.247315	+	0.142788i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.245576	+	0.245576i	−0.245576	+	0.245576i	−0.819152	−	0.573576i	$-0.805556\pi$
$293$	−0.245576	+	0.245576i	−0.245576	+	0.245576i	0.573576	+	0.819152i	$0.305556\pi$
$294$	1.53950	−	0.560333i	1.53950	−	0.560333i
$295$		0			0
$296$	0.984808	+	1.70574i	0.984808	+	1.70574i
$297$		0			0
$298$	−0.500000	+	0.133975i	−0.500000	+	0.133975i
$299$		0			0
$300$	−0.939693	−	1.34202i	−0.939693	−	1.34202i
$301$	−0.0302689	−	0.171663i	−0.0302689	−	0.171663i
$302$	0.597672	−	0.597672i	0.597672	−	0.597672i
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−1.23271	+	0.711706i	−1.23271	+	0.711706i
$307$		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
$310$	−0.660732	+	1.81535i	−0.660732	+	1.81535i
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$	0.424024	+	1.58248i	0.424024	+	1.58248i
$313$	1.75085	+	0.469139i	1.75085	+	0.469139i	0.984808	−	0.173648i	$-0.0555556\pi$
$313$	1.75085	+	0.469139i	1.75085	+	0.469139i	0.766044	+	0.642788i	$0.222222\pi$
$314$		0			0
$315$	0.575976	+	1.58248i	0.575976	+	1.58248i
$316$		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
$320$	0.906308	−	0.422618i	0.906308	−	0.422618i
$321$			0.848049i			0.848049i
$322$		0			0
$323$		0			0
$324$	0.131594	−	0.0759757i	0.131594	−	0.0759757i
$325$	−0.0871557	−	0.996195i	−0.0871557	−	0.996195i
$326$		0			0
$327$	−0.844822	+	3.15292i	−0.844822	+	3.15292i
$328$		0			0
$329$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$330$		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
$333$	3.20389	−	0.858480i	3.20389	−	0.858480i
$334$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$335$		0			0
$336$	−1.61341	+	0.284489i	−1.61341	+	0.284489i
$337$	1.40883	−	1.40883i	1.40883	−	1.40883i	0.642788	−	0.766044i	$-0.277778\pi$
$337$	1.40883	−	1.40883i	1.40883	−	1.40883i	0.766044	−	0.642788i	$-0.222222\pi$
$338$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$339$	−1.58248	+	2.74094i	−1.58248	+	2.74094i
$340$	0.146774	+	0.832395i	0.146774	+	0.832395i
$341$		0			0
$342$		0			0
$343$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$344$			0.174311i			0.174311i
$345$		0			0
$346$		0			0
$347$	0.469139	+	1.75085i	0.469139	+	1.75085i	0.642788	+	0.766044i	$0.277778\pi$
$347$	0.469139	+	1.75085i	0.469139	+	1.75085i	−0.173648	+	0.984808i	$0.555556\pi$
$348$		0			0
$349$	1.81262			1.81262			0.906308	−	0.422618i	$-0.138889\pi$
$349$	1.81262			1.81262			0.906308	+	0.422618i	$0.138889\pi$
$350$	1.00000			1.00000
$351$	1.12067			1.12067
$352$		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
$355$	0.766044	+	1.64279i	0.766044	+	1.64279i
$356$		0			0
$357$	0.120689	−	1.37949i	0.120689	−	1.37949i
$358$	0.909039	+	0.909039i	0.909039	+	0.909039i
$359$	1.67303	−	0.965926i	1.67303	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$359$	1.67303	−	0.965926i	1.67303	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$360$	−0.292431	−	1.65846i	−0.292431	−	1.65846i
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$	1.15846	−	1.15846i	1.15846	−	1.15846i
$364$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$365$		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
$370$	0.171663	−	1.96212i	0.171663	−	1.96212i
$371$		0			0
$372$	−2.23797	+	2.23797i	−2.23797	+	2.23797i
$373$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$373$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$374$		0			0
$375$			1.63830i			1.63830i
$376$	1.62760	−	0.939693i	1.62760	−	0.939693i
$377$		0			0
$378$	−0.0976725	+	1.11640i	−0.0976725	+	1.11640i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.90250	+	0.509774i	1.90250	+	0.509774i	0.996195	+	0.0871557i	$0.0277778\pi$
$383$	1.90250	+	0.509774i	1.90250	+	0.509774i	0.906308	+	0.422618i	$0.138889\pi$
$384$	1.63830			1.63830
$385$		0			0
$386$		0			0
$387$	0.283545	+	0.0759757i	0.283545	+	0.0759757i
$388$		0			0
$389$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$	0.560333	−	1.53950i	0.560333	−	1.53950i
$391$		0			0
$392$	0.422618	−	0.906308i	0.422618	−	0.906308i
$393$	1.77486	+	1.77486i	1.77486	+	1.77486i
$394$	1.32683	−	0.766044i	1.32683	−	0.766044i
$395$		0			0
$396$		0			0
$397$	0.448288	−	1.67303i	0.448288	−	1.67303i	−0.258819	−	0.965926i	$-0.583333\pi$
$397$	0.448288	−	1.67303i	0.448288	−	1.67303i	0.707107	−	0.707107i	$-0.250000\pi$
$398$		0			0
$399$		0			0
$400$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$	−1.86603	+	0.500000i	−1.86603	+	0.500000i
$404$		0			0
$405$	−0.151373	−	0.0132434i	−0.151373	−	0.0132434i
$406$		0			0
$407$		0			0
$408$	−0.358401	+	1.33757i	−0.358401	+	1.33757i
$409$		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
$417$	−0.290050	−	1.08248i	−0.290050	−	1.08248i
$418$		0			0
$419$	1.28558			1.28558			0.642788	−	0.766044i	$-0.277778\pi$
$419$	1.28558			1.28558			0.642788	+	0.766044i	$0.277778\pi$
$420$	1.48481	+	0.692377i	1.48481	+	0.692377i
$421$	0.174311			0.174311			0.0871557	−	0.996195i	$-0.472222\pi$
$421$	0.174311			0.174311			0.0871557	+	0.996195i	$0.472222\pi$
$422$	1.81535	+	0.486421i	1.81535	+	0.486421i
$423$	−0.819152	−	3.05712i	−0.819152	−	3.05712i
$424$		0			0
$425$	0.357212	−	0.766044i	0.357212	−	0.766044i
$426$			2.96962i			2.96962i
$427$		0			0
$428$	0.366025	+	0.366025i	0.366025	+	0.366025i
$429$		0			0
$430$	0.0999810	−	0.142788i	0.0999810	−	0.142788i
$431$	0.996195	−	1.72546i	0.996195	−	1.72546i	0.422618	−	0.906308i	$-0.361111\pi$
$431$	0.996195	−	1.72546i	0.996195	−	1.72546i	0.573576	−	0.819152i	$-0.305556\pi$
$432$	0.290050	−	1.08248i	0.290050	−	1.08248i
$433$	−0.811160	+	0.811160i	−0.811160	+	0.811160i	−0.984808	−	0.173648i	$-0.944444\pi$
$433$	−0.811160	+	0.811160i	−0.811160	+	0.811160i	0.173648	+	0.984808i	$0.444444\pi$
$434$	−0.335463	−	1.90250i	−0.335463	−	1.90250i
$435$		0			0
$436$	0.996195	+	1.72546i	0.996195	+	1.72546i
$437$		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
$441$	−1.29005	−	1.08248i	−1.29005	−	1.08248i
$442$	−0.597672	+	0.597672i	−0.597672	+	0.597672i
$443$	0.424024	−	1.58248i	0.424024	−	1.58248i	−0.342020	−	0.939693i	$-0.611111\pi$
$443$	0.424024	−	1.58248i	0.424024	−	1.58248i	0.766044	−	0.642788i	$-0.222222\pi$
$444$	1.61341	−	2.79452i	1.61341	−	2.79452i
$445$		0			0
$446$	−0.300767	+	0.173648i	−0.300767	+	0.173648i
$447$	0.599661	+	0.599661i	0.599661	+	0.599661i
$448$	−0.573576	+	0.819152i	−0.573576	+	0.819152i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	−0.711706	+	1.52626i	−0.711706	+	1.52626i
$451$		0			0
$452$	0.500000	+	1.86603i	0.500000	+	1.86603i
$453$	−1.33757	−	0.358401i	−1.33757	−	0.358401i
$454$		0			0
$455$	0.573576	+	0.819152i	0.573576	+	0.819152i
$456$		0			0
$457$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$457$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$458$	0.296905	+	1.10806i	0.296905	+	1.10806i
$459$	0.820323	+	0.473614i	0.820323	+	0.473614i
$460$		0			0
$461$			1.81262i			1.81262i	0.422618	+	0.906308i	$0.361111\pi$
$461$			1.81262i			1.81262i	−0.422618	+	0.906308i	$0.638889\pi$
$462$		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
$465$	3.11688	−	0.549590i	3.11688	−	0.549590i
$466$	−0.573576	+	0.993464i	−0.573576	+	0.993464i
$467$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$467$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$468$	1.19080	−	1.19080i	1.19080	−	1.19080i
$469$		0			0
$470$	−1.87223	−	0.163799i	−1.87223	−	0.163799i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	−0.543308	−	0.647489i	−0.543308	−	0.647489i
$477$		0			0
$478$	−0.296905	+	1.10806i	−0.296905	+	1.10806i
$479$	−0.573576	+	0.993464i	−0.573576	+	0.993464i	0.422618	+	0.906308i	$0.361111\pi$
$479$	−0.573576	+	0.993464i	−0.573576	+	0.993464i	−0.996195	+	0.0871557i	$0.972222\pi$
$480$	−1.34202	−	0.939693i	−1.34202	−	0.939693i
$481$	1.70574	−	0.984808i	1.70574	−	0.984808i
$482$		0			0
$483$		0			0
$484$		−	1.00000i		−	1.00000i
$485$		0			0
$486$	0.754935	+	0.435862i	0.754935	+	0.435862i
$487$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$487$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$488$		0			0
$489$		0			0
$490$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$491$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$491$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$			1.93185i			1.93185i
$497$	−1.48481	−	1.03967i	−1.48481	−	1.03967i
$498$		0			0
$499$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$499$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$500$	0.707107	+	0.707107i	0.707107	+	0.707107i
$501$	−0.819152	+	1.41881i	−0.819152	+	1.41881i
$502$	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	$0.750000\pi$
$504$	1.08248	+	1.29005i	1.08248	+	1.29005i
$505$		0			0
$506$		0			0
$507$	1.58248	−	0.424024i	1.58248	−	0.424024i
$508$		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	$0.583333\pi$
$510$	1.06078	−	0.890103i	1.06078	−	0.890103i
$511$		0			0
$512$	0.707107	−	0.707107i	0.707107	−	0.707107i
$513$		0			0
$514$	0.0871557	−	0.150958i	0.0871557	−	0.150958i
$515$		0			0
$516$	0.247315	−	0.142788i	0.247315	−	0.142788i
$517$		0			0
$518$	0.832395	+	1.78508i	0.832395	+	1.78508i
$519$		0			0
$520$	−0.422618	−	0.906308i	−0.422618	−	0.906308i
$521$	1.70574	+	0.984808i	1.70574	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$521$	1.70574	+	0.984808i	1.70574	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$522$		0			0
$523$	1.86603	+	0.500000i	1.86603	+	0.500000i	1.00000			$0$
$523$	1.86603	+	0.500000i	1.86603	+	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$524$	1.53209			1.53209
$525$	−0.819152	−	1.41881i	−0.819152	−	1.41881i
$526$		0			0
$527$	−1.57723	−	0.422618i	−1.57723	−	0.422618i
$528$		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
$535$	−0.0898869	−	0.509774i	−0.0898869	−	0.509774i
$536$		0			0
$537$	0.545115	−	2.03440i	0.545115	−	2.03440i
$538$		0			0
$539$		0			0
$540$	−0.858480	+	0.720350i	−0.858480	+	0.720350i
$541$	0.906308	+	1.56977i	0.906308	+	1.56977i	0.819152	+	0.573576i	$0.194444\pi$
$541$	0.906308	+	1.56977i	0.906308	+	1.56977i	0.0871557	+	0.996195i	$0.472222\pi$
$542$	−1.92450	+	0.515668i	−1.92450	+	0.515668i
$543$		0			0
$544$	0.422618	+	0.731996i	0.422618	+	0.731996i
$545$	0.173648	−	1.98481i	0.173648	−	1.98481i
$546$	0.284489	+	1.61341i	0.284489	+	1.61341i
$547$	1.15846	−	1.15846i	1.15846	−	1.15846i	0.173648	−	0.984808i	$-0.444444\pi$
$547$	1.15846	−	1.15846i	1.15846	−	1.15846i	0.984808	−	0.173648i	$-0.0555556\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−2.92450	+	1.36372i	−2.92450	+	1.36372i
$556$	−0.592396	−	0.342020i	−0.592396	−	0.342020i
$557$	0.0898869	+	0.335463i	0.0898869	+	0.335463i	0.996195	−	0.0871557i	$-0.0277778\pi$
$557$	0.0898869	+	0.335463i	0.0898869	+	0.335463i	−0.906308	+	0.422618i	$0.861111\pi$
$558$	3.14246	+	0.842020i	3.14246	+	0.842020i
$559$	0.174311			0.174311
$560$	0.939693	−	0.342020i	0.939693	−	0.342020i
$561$		0			0
$562$		0			0
$563$	−0.515668	−	1.92450i	−0.515668	−	1.92450i	−0.342020	−	0.939693i	$-0.611111\pi$
$563$	−0.515668	−	1.92450i	−0.515668	−	1.92450i	−0.173648	−	0.984808i	$-0.555556\pi$
$564$	−2.66650	−	1.53950i	−2.66650	−	1.53950i
$565$	0.660732	−	1.81535i	0.660732	−	1.81535i
$566$			1.41421i			1.41421i
$567$	0.137715	−	0.0642174i	0.137715	−	0.0642174i
$568$	1.28171	+	1.28171i	1.28171	+	1.28171i
$569$	−1.62760	+	0.939693i	−1.62760	+	0.939693i	−0.642788	+	0.766044i	$0.722222\pi$
$569$	−1.62760	+	0.939693i	−1.62760	+	0.939693i	−0.984808	+	0.173648i	$0.944444\pi$
$570$		0			0
$571$	−0.984808	+	1.70574i	−0.984808	+	1.70574i	−0.342020	+	0.939693i	$0.611111\pi$
$571$	−0.984808	+	1.70574i	−0.984808	+	1.70574i	−0.642788	+	0.766044i	$0.722222\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.842020	−	1.45842i	−0.842020	−	1.45842i
$577$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$577$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$578$	0.275844	−	0.0739123i	0.275844	−	0.0739123i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−1.65846	+	0.292431i	−1.65846	+	0.292431i
$586$	0.300767	−	0.173648i	0.300767	−	0.173648i
$587$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$587$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$588$	−1.63207	+	0.142788i	−1.63207	+	0.142788i
$589$		0			0
$590$		0			0
$591$	−2.17375	−	1.25501i	−2.17375	−	1.25501i
$592$	−0.509774	−	1.90250i	−0.509774	−	1.90250i
$593$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$593$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$594$		0			0
$595$	0.0736672	+	0.842020i	0.0736672	+	0.842020i
$596$	0.517638			0.517638
$597$		0			0
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$	0.560333	+	1.53950i	0.560333	+	1.53950i
$601$		−	0.347296i		−	0.347296i	−0.984808	−	0.173648i	$-0.944444\pi$
$601$		−	0.347296i		−	0.347296i	0.984808	−	0.173648i	$-0.0555556\pi$
$602$	−0.0151922	+	0.173648i	−0.0151922	+	0.173648i
$603$		0			0
$604$	−0.731996	+	0.422618i	−0.731996	+	0.422618i
$605$	−0.573576	+	0.819152i	−0.573576	+	0.819152i
$606$		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
$611$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$612$	1.37491	−	0.368406i	1.37491	−	0.368406i
$613$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$613$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$614$		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	$0.666667\pi$
$620$	1.10806	−	1.58248i	1.10806	−	1.58248i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		−	1.63830i		−	1.63830i
$625$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$626$	−1.56977	−	0.906308i	−1.56977	−	0.906308i
$627$		0			0
$628$		0			0
$629$	1.66479			1.66479
$630$	−0.146774	−	1.67763i	−0.146774	−	1.67763i
$631$	1.14715			1.14715			0.573576	−	0.819152i	$-0.305556\pi$
$631$	1.14715			1.14715			0.573576	+	0.819152i	$0.305556\pi$
$632$		0			0
$633$	−0.796905	−	2.97409i	−0.796905	−	2.97409i
$634$	1.50000	+	0.866025i	1.50000	+	0.866025i
$635$		0			0
$636$		0			0
$637$	−0.906308	−	0.422618i	−0.906308	−	0.422618i
$638$		0			0
$639$	2.64356	−	1.52626i	2.64356	−	1.52626i
$640$	−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	$-0.166667\pi$
$642$	0.219491	−	0.819152i	0.219491	−	0.819152i
$643$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$643$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$644$		0			0
$645$	−0.284489	−	0.0248895i	−0.284489	−	0.0248895i
$646$		0			0
$647$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$647$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$648$	−0.146774	+	0.0393279i	−0.146774	+	0.0393279i
$649$		0			0
$650$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$651$	−2.42450	+	2.03440i	−2.42450	+	2.03440i
$652$		0			0
$653$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$653$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$654$	1.63207	−	2.82683i	1.63207	−	2.82683i
$655$	−1.25501	−	0.878770i	−1.25501	−	0.878770i
$656$		0			0
$657$		0			0
$658$	1.70330	−	0.794263i	1.70330	−	0.794263i
$659$		−	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
$661$	−0.448288	−	0.258819i	−0.448288	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$661$	−0.448288	−	0.258819i	−0.448288	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$662$		0			0
$663$	1.33757	+	0.358401i	1.33757	+	0.358401i
$664$		0			0
$665$		0			0
$666$	−3.31691			−3.31691
$667$		0			0
$668$	0.258819	+	0.965926i	0.258819	+	0.965926i
$669$	0.492749	+	0.284489i	0.492749	+	0.284489i
$670$		0			0
$671$		0			0
$672$	1.63207	+	0.142788i	1.63207	+	0.142788i
$673$	−0.597672	−	0.597672i	−0.597672	−	0.597672i	0.342020	−	0.939693i	$-0.388889\pi$
$673$	−0.597672	−	0.597672i	−0.597672	−	0.597672i	−0.939693	+	0.342020i	$0.888889\pi$
$674$	−1.72546	+	0.996195i	−1.72546	+	0.996195i
$675$	1.11640	−	0.0976725i	1.11640	−	0.0976725i
$676$	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	$0.583333\pi$
$678$	2.23797	−	2.23797i	2.23797	−	2.23797i
$679$		0			0
$680$	0.0736672	−	0.842020i	0.0736672	−	0.842020i
$681$		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
$687$	1.32893	−	1.32893i	1.32893	−	1.32893i
$688$	0.0451151	−	0.168372i	0.0451151	−	0.168372i
$689$		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
$694$		−	1.81262i		−	1.81262i
$695$	0.289088	+	0.619951i	0.289088	+	0.619951i
$696$		0			0
$697$		0			0
$698$	−1.75085	−	0.469139i	−1.75085	−	0.469139i
$699$	1.87939			1.87939
$700$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−1.08248	−	0.290050i	−1.08248	−	0.290050i
$703$		0			0
$704$		0			0
$705$	1.30124	+	2.79053i	1.30124	+	2.79053i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$709$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$710$	−0.314757	−	1.78508i	−0.314757	−	1.78508i
$711$		0			0
$712$		0			0
$713$		0			0
$714$	−0.473614	+	1.30124i	−0.473614	+	1.30124i
$715$		0			0
$716$	−0.642788	−	1.11334i	−0.642788	−	1.11334i
$717$	1.81535	−	0.486421i	1.81535	−	0.486421i
$718$	−1.86603	+	0.500000i	−1.86603	+	0.500000i
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$	−0.146774	+	1.67763i	−0.146774	+	1.67763i
$721$		0			0
$722$	0.707107	−	0.707107i	0.707107	−	0.707107i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−1.41881	+	0.819152i	−1.41881	+	0.819152i
$727$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$727$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$728$	0.819152	+	0.573576i	0.819152	+	0.573576i
$729$		−	1.58010i		−	1.58010i
$730$		0			0
$731$	0.127595	+	0.0736672i	0.127595	+	0.0736672i
$732$		0			0
$733$	1.81535	+	0.486421i	1.81535	+	0.486421i	0.996195	−	0.0871557i	$-0.0277778\pi$
$733$	1.81535	+	0.486421i	1.81535	+	0.486421i	0.819152	+	0.573576i	$0.194444\pi$
$734$		0			0
$735$	1.41881	+	0.819152i	1.41881	+	0.819152i
$736$		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	$0.166667\pi$
$740$	−0.673648	+	1.85083i	−0.673648	+	1.85083i
$741$		0			0
$742$		0			0
$743$	−1.32893	−	1.32893i	−1.32893	−	1.32893i	−0.906308	−	0.422618i	$-0.861111\pi$
$743$	−1.32893	−	1.32893i	−1.32893	−	1.32893i	−0.422618	−	0.906308i	$-0.638889\pi$
$744$	2.74094	−	1.58248i	2.74094	−	1.58248i
$745$	−0.424024	−	0.296905i	−0.424024	−	0.296905i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.332731	+	0.396534i	0.332731	+	0.396534i
$750$	0.424024	−	1.58248i	0.424024	−	1.58248i
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	−1.81535	+	0.486421i	−1.81535	+	0.486421i
$753$	−1.58248	+	0.424024i	−1.58248	+	0.424024i
$754$		0			0
$755$	0.842020	+	0.0736672i	0.842020	+	0.0736672i
$756$	0.383290	−	1.05308i	0.383290	−	1.05308i
$757$		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
$763$	0.842020	+	1.80572i	0.842020	+	1.80572i
$764$		0			0
$765$	−1.33757	−	0.486836i	−1.33757	−	0.486836i
$766$	−1.70574	−	0.984808i	−1.70574	−	0.984808i
$767$		0			0
$768$	−1.58248	−	0.424024i	−1.58248	−	0.424024i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$	−0.285575			−0.285575
$772$		0			0
$773$	0.509774	+	1.90250i	0.509774	+	1.90250i	0.422618	+	0.906308i	$0.361111\pi$
$773$	0.509774	+	1.90250i	0.509774	+	1.90250i	0.0871557	+	0.996195i	$0.472222\pi$
$774$	−0.254220	−	0.146774i	−0.254220	−	0.146774i
$775$	−1.81535	+	0.660732i	−1.81535	+	0.660732i
$776$		0			0
$777$	1.85083	−	2.64326i	1.85083	−	2.64326i
$778$		0			0
$779$		0			0
$780$	−0.939693	+	1.34202i	−0.939693	+	1.34202i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$785$		0			0
$786$	−1.25501	−	2.17375i	−1.25501	−	2.17375i
$787$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$787$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$788$	−1.47988	+	0.396534i	−1.47988	+	0.396534i
$789$		0			0
$790$		0			0
$791$	0.335463	+	1.90250i	0.335463	+	1.90250i
$792$		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
$799$		−	1.58853i		−	1.58853i
$800$	0.906308	+	0.422618i	0.906308	+	0.422618i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	1.93185			1.93185
$807$		0			0
$808$		0			0
$809$	0.300767	+	0.173648i	0.300767	+	0.173648i	0.642788	−	0.766044i	$-0.277778\pi$
$809$	0.300767	+	0.173648i	0.300767	+	0.173648i	−0.342020	+	0.939693i	$0.611111\pi$
$810$	0.142788	+	0.0519704i	0.142788	+	0.0519704i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$	2.30810	+	2.30810i	2.30810	+	2.30810i
$814$		0			0
$815$		0			0
$816$	0.692377	−	1.19923i	0.692377	−	1.19923i
$817$		0			0
$818$		0			0
$819$	1.29005	−	1.08248i	1.29005	−	1.08248i
$820$		0			0
$821$	0.819152	+	1.41881i	0.819152	+	1.41881i	0.906308	+	0.422618i	$0.138889\pi$
$821$	0.819152	+	1.41881i	0.819152	+	1.41881i	−0.0871557	+	0.996195i	$0.527778\pi$
$822$		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
$833$	−0.484808	−	0.692377i	−0.484808	−	0.692377i
$834$			1.12067i			1.12067i
$835$	0.342020	−	0.939693i	0.342020	−	0.939693i
$836$		0			0
$837$	−0.560333	−	2.09119i	−0.560333	−	2.09119i
$838$	−1.24177	−	0.332731i	−1.24177	−	0.332731i
$839$	0.517638			0.517638			0.258819	−	0.965926i	$-0.416667\pi$
$839$	0.517638			0.517638			0.258819	+	0.965926i	$0.416667\pi$
$840$	−1.25501	−	1.05308i	−1.25501	−	1.05308i
$841$	−1.00000			−1.00000
$842$	−0.168372	−	0.0451151i	−0.168372	−	0.0451151i
$843$		0			0
$844$	−1.62760	−	0.939693i	−1.62760	−	0.939693i
$845$	−0.906308	+	0.422618i	−0.906308	+	0.422618i
$846$			3.16496i			3.16496i
$847$	0.0871557	−	0.996195i	0.0871557	−	0.996195i
$848$		0			0
$849$	2.00650	−	1.15846i	2.00650	−	1.15846i
$850$	−0.543308	+	0.647489i	−0.543308	+	0.647489i
$851$		0			0
$852$	0.768593	−	2.86843i	0.768593	−	2.86843i
$853$	1.39273	−	1.39273i	1.39273	−	1.39273i	0.573576	−	0.819152i	$-0.305556\pi$
$853$	1.39273	−	1.39273i	1.39273	−	1.39273i	0.819152	−	0.573576i	$-0.194444\pi$
$854$		0			0
$855$		0			0
$856$	−0.258819	−	0.448288i	−0.258819	−	0.448288i
$857$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$857$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$859$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$860$	−0.133530	+	0.112045i	−0.133530	+	0.112045i
$861$		0			0
$862$	−1.40883	+	1.40883i	−1.40883	+	1.40883i
$863$	−0.509774	+	1.90250i	−0.509774	+	1.90250i	−0.0871557	+	0.996195i	$0.527778\pi$
$863$	−0.509774	+	1.90250i	−0.509774	+	1.90250i	−0.422618	+	0.906308i	$0.638889\pi$
$864$	−0.560333	+	0.970525i	−0.560333	+	0.970525i
$865$		0			0
$866$	0.993464	−	0.573576i	0.993464	−	0.573576i
$867$	−0.330826	−	0.330826i	−0.330826	−	0.330826i
$868$	−0.168372	+	1.92450i	−0.168372	+	1.92450i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.515668	−	1.92450i	−0.515668	−	1.92450i
$873$		0			0
$874$		0			0
$875$	0.642788	+	0.766044i	0.642788	+	0.766044i
$876$		0			0
$877$	1.47988	+	0.396534i	1.47988	+	0.396534i	0.906308	−	0.422618i	$-0.138889\pi$
$877$	1.47988	+	0.396534i	1.47988	+	0.396534i	0.573576	+	0.819152i	$0.305556\pi$
$878$		0			0
$879$	−0.492749	−	0.284489i	−0.492749	−	0.284489i
$880$		0			0
$881$			0.347296i			0.347296i	0.984808	+	0.173648i	$0.0555556\pi$
$881$			0.347296i			0.347296i	−0.984808	+	0.173648i	$0.944444\pi$
$882$	0.965926	+	1.37949i	0.965926	+	1.37949i
$883$	−0.811160	−	0.811160i	−0.811160	−	0.811160i	0.173648	−	0.984808i	$-0.444444\pi$
$883$	−0.811160	−	0.811160i	−0.811160	−	0.811160i	−0.984808	+	0.173648i	$0.944444\pi$
$884$	0.731996	−	0.422618i	0.731996	−	0.422618i
$885$		0			0
$886$	−0.819152	+	1.41881i	−0.819152	+	1.41881i
$887$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$887$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$888$	−2.28171	+	2.28171i	−2.28171	+	2.28171i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	0.335463	−	0.0898869i	0.335463	−	0.0898869i
$893$		0			0
$894$	−0.424024	−	0.734432i	−0.424024	−	0.734432i
$895$	−0.112045	+	1.28068i	−0.112045	+	1.28068i
$896$	0.766044	−	0.642788i	0.766044	−	0.642788i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	1.08248	−	1.29005i	1.08248	−	1.29005i
$901$		0			0
$902$		0			0
$903$	0.258819	−	0.120689i	0.258819	−	0.120689i
$904$		−	1.93185i		−	1.93185i
$905$		0			0
$906$	1.19923	+	0.692377i	1.19923	+	0.692377i
$907$	0.218763	+	0.816436i	0.218763	+	0.816436i	0.984808	+	0.173648i	$0.0555556\pi$
$907$	0.218763	+	0.816436i	0.218763	+	0.816436i	−0.766044	+	0.642788i	$0.777778\pi$
$908$		0			0
$909$		0			0
$910$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		−	1.14715i		−	1.14715i
$917$	1.52626	+	0.133530i	1.52626	+	0.133530i
$918$	−0.669791	−	0.669791i	−0.669791	−	0.669791i
$919$		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
$922$	0.469139	−	1.75085i	0.469139	−	1.75085i
$923$	1.28171	−	1.28171i	1.28171	−	1.28171i
$924$		0			0
$925$	1.61341	−	1.12973i	1.61341	−	1.12973i
$926$	−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	$0.333333\pi$
$930$	−3.15292	−	0.275844i	−3.15292	−	0.275844i
$931$		0			0
$932$	0.811160	−	0.811160i	0.811160	−	0.811160i
$933$		0			0
$934$	0.707107	−	1.22474i	0.707107	−	1.22474i
$935$		0			0
$936$	−1.45842	+	0.842020i	−1.45842	+	0.842020i
$937$	1.36603	+	1.36603i	1.36603	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$937$	1.36603	+	1.36603i	1.36603	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$938$		0			0
$939$			2.96962i			2.96962i
$940$	1.76604	+	0.642788i	1.76604	+	0.642788i
$941$	−0.731996	−	0.422618i	−0.731996	−	0.422618i	0.0871557	−	0.996195i	$-0.472222\pi$
$941$	−0.731996	−	0.422618i	−0.731996	−	0.422618i	−0.819152	+	0.573576i	$0.805556\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−0.917996	+	0.642788i	−0.917996	+	0.642788i
$946$		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
$951$		−	2.83763i		−	2.83763i
$952$	0.357212	+	0.766044i	0.357212	+	0.766044i
$953$	0.597672	+	0.597672i	0.597672	+	0.597672i	0.939693	−	0.342020i	$-0.111111\pi$
$953$	0.597672	+	0.597672i	0.597672	+	0.597672i	−0.342020	+	0.939693i	$0.611111\pi$
$954$		0			0
$955$		0			0
$956$	0.573576	−	0.993464i	0.573576	−	0.993464i
$957$		0			0
$958$	0.811160	−	0.811160i	0.811160	−	0.811160i
$959$		0			0
$960$	1.05308	+	1.25501i	1.05308	+	1.25501i
$961$	1.36603	+	2.36603i	1.36603	+	2.36603i
$962$	−1.90250	+	0.509774i	−1.90250	+	0.509774i
$963$	−0.842020	+	0.225619i	−0.842020	+	0.225619i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.909039	−	0.909039i	0.909039	−	0.909039i	−0.0871557	−	0.996195i	$-0.527778\pi$
$967$	0.909039	−	0.909039i	0.909039	−	0.909039i	0.996195	+	0.0871557i	$0.0277778\pi$
$968$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$969$		0			0
$970$		0			0
$971$	−0.592396	+	0.342020i	−0.592396	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$971$	−0.592396	+	0.342020i	−0.592396	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$972$	−0.616402	−	0.616402i	−0.616402	−	0.616402i
$973$	−0.560333	−	0.392349i	−0.560333	−	0.392349i
$974$			1.00000i			1.00000i
$975$	1.53950	−	0.560333i	1.53950	−	0.560333i
$976$		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
$980$	0.965926	−	0.258819i	0.965926	−	0.258819i
$981$	−3.35526			−3.35526
$982$	−1.47988	−	0.396534i	−1.47988	−	0.396534i
$983$	−0.0898869	−	0.335463i	−0.0898869	−	0.335463i	0.906308	−	0.422618i	$-0.138889\pi$
$983$	−0.0898869	−	0.335463i	−0.0898869	−	0.335463i	−0.996195	+	0.0871557i	$0.972222\pi$
$984$		0			0
$985$	1.43969	+	0.524005i	1.43969	+	0.524005i
$986$		0			0
$987$	−2.52217	−	1.76604i	−2.52217	−	1.76604i
$988$		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	$0.666667\pi$
$992$	0.500000	−	1.86603i	0.500000	−	1.86603i
$993$		0			0
$994$	1.16513	+	1.38854i	1.16513	+	1.38854i
$995$		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
$999$	1.10364	+	1.91156i	1.10364	+	1.91156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3640.1.od.a.1403.3	yes	24
5.2	odd	4		3640.1.od.b.3587.6	yes	24
7.5	odd	6		3640.1.od.b.1923.6	yes	24
8.3	odd	2	inner	3640.1.od.a.1403.6	yes	24
13.12	even	2	inner	3640.1.od.a.1403.6	yes	24
35.12	even	12	inner	3640.1.od.a.467.3	✓	24
40.27	even	4		3640.1.od.b.3587.3	yes	24
56.19	even	6		3640.1.od.b.1923.3	yes	24
65.12	odd	4		3640.1.od.b.3587.3	yes	24
91.12	odd	6		3640.1.od.b.1923.3	yes	24
104.51	odd	2	CM	3640.1.od.a.1403.3	yes	24
280.187	odd	12	inner	3640.1.od.a.467.6	yes	24
455.12	even	12	inner	3640.1.od.a.467.6	yes	24
520.467	even	4		3640.1.od.b.3587.6	yes	24
728.467	even	6		3640.1.od.b.1923.6	yes	24
3640.467	odd	12	inner	3640.1.od.a.467.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3640.1.od.a.467.3	✓	24	35.12	even	12	inner
3640.1.od.a.467.3	✓	24	3640.467	odd	12	inner
3640.1.od.a.467.6	yes	24	280.187	odd	12	inner
3640.1.od.a.467.6	yes	24	455.12	even	12	inner
3640.1.od.a.1403.3	yes	24	1.1	even	1	trivial
3640.1.od.a.1403.3	yes	24	104.51	odd	2	CM
3640.1.od.a.1403.6	yes	24	8.3	odd	2	inner
3640.1.od.a.1403.6	yes	24	13.12	even	2	inner
3640.1.od.b.1923.3	yes	24	56.19	even	6
3640.1.od.b.1923.3	yes	24	91.12	odd	6
3640.1.od.b.1923.6	yes	24	7.5	odd	6
3640.1.od.b.1923.6	yes	24	728.467	even	6
3640.1.od.b.3587.3	yes	24	40.27	even	4
3640.1.od.b.3587.3	yes	24	65.12	odd	4
3640.1.od.b.3587.6	yes	24	5.2	odd	4
3640.1.od.b.3587.6	yes	24	520.467	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.424024 + 1.58248i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.422618 - 0.906308i) q^{5} -1.63830i q^{6} +(0.819152 + 0.573576i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.45842 + 0.842020i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.424024 + 1.58248i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.422618 - 0.906308i) q^{5} -1.63830i q^{6} +(0.819152 + 0.573576i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.45842 + 0.842020i) q^{9} +(0.173648 + 0.984808i) q^{10} +(-0.424024 + 1.58248i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(-0.642788 - 0.766044i) q^{14} +(1.25501 - 1.05308i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.816436 + 0.218763i) q^{17} +(1.62666 - 0.435862i) q^{18} +(0.0871557 - 0.996195i) q^{20} +(-0.560333 + 1.53950i) q^{21} +(0.819152 - 1.41881i) q^{24} +(-0.642788 + 0.766044i) q^{25} +(0.866025 - 0.500000i) q^{26} +(-0.792431 - 0.792431i) q^{27} +(0.422618 + 0.906308i) q^{28} +(-1.48481 + 0.692377i) q^{30} +(1.67303 + 0.965926i) q^{31} +(-0.258819 - 0.965926i) q^{32} +0.845237 q^{34} +(0.173648 - 0.984808i) q^{35} -1.68404 q^{36} +(-1.90250 - 0.509774i) q^{37} +(-1.41881 - 0.819152i) q^{39} +(-0.342020 + 0.939693i) q^{40} +(0.939693 - 1.34202i) q^{42} +(-0.123257 - 0.123257i) q^{43} +(1.37949 + 0.965926i) q^{45} +(-0.486421 + 1.81535i) q^{47} +(-1.15846 + 1.15846i) q^{48} +(0.342020 + 0.939693i) q^{49} +(0.819152 - 0.573576i) q^{50} +(-0.692377 - 1.19923i) q^{51} +(-0.965926 + 0.258819i) q^{52} +(0.560333 + 0.970525i) q^{54} +(-0.173648 - 0.984808i) q^{56} +(1.61341 - 0.284489i) q^{60} +(-1.36603 - 1.36603i) q^{62} +(-1.67763 - 0.146774i) q^{63} +1.00000i q^{64} +(0.939693 + 0.342020i) q^{65} +(-0.816436 - 0.218763i) q^{68} +(-0.422618 + 0.906308i) q^{70} -1.81262 q^{71} +(1.62666 + 0.435862i) q^{72} +(1.70574 + 0.984808i) q^{74} +(-1.48481 - 0.692377i) q^{75} +(1.15846 + 1.15846i) q^{78} +(0.573576 - 0.819152i) q^{80} +(0.0759757 - 0.131594i) q^{81} +(-1.25501 + 1.05308i) q^{84} +(0.543308 + 0.647489i) q^{85} +(0.0871557 + 0.150958i) q^{86} +(-1.08248 - 1.29005i) q^{90} +(-0.984808 + 0.173648i) q^{91} +(-0.819152 + 3.05712i) q^{93} +(0.939693 - 1.62760i) q^{94} +(1.41881 - 0.819152i) q^{96} +(-0.0871557 - 0.996195i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 12 q^{16} - 12 q^{27} - 12 q^{30} - 24 q^{36} - 12 q^{62} - 12 q^{75} + 12 q^{81} + 12 q^{90}+O(q^{100}) \) 24 * q + 12 * q^16 - 12 * q^27 - 12 * q^30 - 24 * q^36 - 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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