LMFDB - Embedded newform 2601.1.x.a.2470.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2601,1,Mod(40,2601)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2601, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([16, 45]))

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

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

chi := DirichletCharacter("2601.40");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2601 = 3^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2601.x (of order $48$, degree $16$, 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:	$1.29806809786$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$2$ over $\Q(\zeta_{48})$
Coefficient field:	$\Q(\zeta_{96})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{32} - x^{16} + 1 $ x^32 - x^16 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.23409.1

Embedding invariants

Embedding label			2470.1
Root			$0.659346 - 0.751840i$ of defining polynomial
Character	$\chi$	$=$	2601.2470
Dual form			2601.1.x.a.1231.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.608761 - 0.793353i) q^{2} +(-0.555570 - 0.831470i) q^{3} +(-0.751840 - 0.659346i) q^{5} +(-0.997859 - 0.0654031i) q^{6} +(-0.751840 + 0.659346i) q^{7} +(0.923880 + 0.382683i) q^{8} +(-0.382683 + 0.923880i) q^{9} +O(q^{10})$	\(q+(0.608761 - 0.793353i) q^{2} +(-0.555570 - 0.831470i) q^{3} +(-0.751840 - 0.659346i) q^{5} +(-0.997859 - 0.0654031i) q^{6} +(-0.751840 + 0.659346i) q^{7} +(0.923880 + 0.382683i) q^{8} +(-0.382683 + 0.923880i) q^{9} +(-0.980785 + 0.195090i) q^{10} +(-0.0654031 + 0.997859i) q^{11} +(-0.965926 + 0.258819i) q^{13} +(0.0654031 + 0.997859i) q^{14} +(-0.130526 + 0.991445i) q^{15} +(0.866025 - 0.500000i) q^{16} +(0.500000 + 0.866025i) q^{18} +(0.965926 + 0.258819i) q^{21} +(0.751840 + 0.659346i) q^{22} +(0.442289 + 0.896873i) q^{23} +(-0.195090 - 0.980785i) q^{24} +(-0.382683 + 0.923880i) q^{26} +(0.980785 - 0.195090i) q^{27} +(0.321439 + 0.946930i) q^{29} +(0.707107 + 0.707107i) q^{30} +(-0.0654031 - 0.997859i) q^{31} +(0.866025 - 0.500000i) q^{33} +1.00000 q^{35} +(1.11114 + 1.66294i) q^{37} +(0.751840 + 0.659346i) q^{39} +(-0.442289 - 0.896873i) q^{40} +(0.946930 + 0.321439i) q^{41} +(0.793353 - 0.608761i) q^{42} +(-0.991445 + 0.130526i) q^{43} +(0.896873 - 0.442289i) q^{45} +(0.980785 + 0.195090i) q^{46} +(-0.258819 + 0.965926i) q^{47} +(-0.896873 - 0.442289i) q^{48} +(0.442289 - 0.896873i) q^{54} +(0.707107 - 0.707107i) q^{55} +(-0.946930 + 0.321439i) q^{56} +(0.946930 + 0.321439i) q^{58} +(-0.793353 + 0.608761i) q^{59} +(-0.659346 - 0.751840i) q^{61} +(-0.831470 - 0.555570i) q^{62} +(-0.321439 - 0.946930i) q^{63} +(0.707107 + 0.707107i) q^{64} +(0.896873 + 0.442289i) q^{65} +(0.130526 - 0.991445i) q^{66} +(-0.866025 - 0.500000i) q^{67} +(0.500000 - 0.866025i) q^{69} +(0.608761 - 0.793353i) q^{70} +(-0.707107 + 0.707107i) q^{72} +(1.99572 + 0.130806i) q^{74} +(-0.608761 - 0.793353i) q^{77} +(0.980785 - 0.195090i) q^{78} +(0.0654031 - 0.997859i) q^{79} +(-0.980785 - 0.195090i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(0.831470 - 0.555570i) q^{82} +(0.793353 + 0.608761i) q^{83} +(-0.500000 + 0.866025i) q^{86} +(0.608761 - 0.793353i) q^{87} +(-0.442289 + 0.896873i) q^{88} +(0.195090 - 0.980785i) q^{90} +(0.555570 - 0.831470i) q^{91} +(-0.793353 + 0.608761i) q^{93} +(0.608761 + 0.793353i) q^{94} +(-0.321439 - 0.946930i) q^{97} +(-0.896873 - 0.442289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{18} + 32 q^{35} + 16 q^{69} - 16 q^{86}+O(q^{100}) $ 32 * q + 16 * q^18 + 32 * q^35 + 16 * q^69 - 16 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2601\mathbb{Z}\right)^\times$.

$n$	$290$	$2026$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{16}\right)$

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 $

$2$	0.608761	−	0.793353i	0.608761	−	0.793353i	−0.382683	−	0.923880i	$-0.625000\pi$
$2$	0.608761	−	0.793353i	0.608761	−	0.793353i	0.991445	+	0.130526i	$0.0416667\pi$
$3$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$3$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$4$		0			0
$5$	−0.751840	−	0.659346i	−0.751840	−	0.659346i	0.195090	−	0.980785i	$-0.437500\pi$
$5$	−0.751840	−	0.659346i	−0.751840	−	0.659346i	−0.946930	+	0.321439i	$0.895833\pi$
$6$	−0.997859	−	0.0654031i	−0.997859	−	0.0654031i
$7$	−0.751840	+	0.659346i	−0.751840	+	0.659346i	−0.946930	−	0.321439i	$-0.895833\pi$
$7$	−0.751840	+	0.659346i	−0.751840	+	0.659346i	0.195090	+	0.980785i	$0.437500\pi$
$8$	0.923880	+	0.382683i	0.923880	+	0.382683i
$9$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$10$	−0.980785	+	0.195090i	−0.980785	+	0.195090i
$11$	−0.0654031	+	0.997859i	−0.0654031	+	0.997859i	0.831470	+	0.555570i	$0.187500\pi$
$11$	−0.0654031	+	0.997859i	−0.0654031	+	0.997859i	−0.896873	+	0.442289i	$0.854167\pi$
$12$		0			0
$13$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$13$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$14$	0.0654031	+	0.997859i	0.0654031	+	0.997859i
$15$	−0.130526	+	0.991445i	−0.130526	+	0.991445i
$16$	0.866025	−	0.500000i	0.866025	−	0.500000i
$17$		0			0
$17$		0			0
$18$	0.500000	+	0.866025i	0.500000	+	0.866025i
$19$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$19$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$20$		0			0
$21$	0.965926	+	0.258819i	0.965926	+	0.258819i
$22$	0.751840	+	0.659346i	0.751840	+	0.659346i
$23$	0.442289	+	0.896873i	0.442289	+	0.896873i	0.997859	+	0.0654031i	$0.0208333\pi$
$23$	0.442289	+	0.896873i	0.442289	+	0.896873i	−0.555570	+	0.831470i	$0.687500\pi$
$24$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$25$		0			0
$26$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$27$	0.980785	−	0.195090i	0.980785	−	0.195090i
$28$		0			0
$29$	0.321439	+	0.946930i	0.321439	+	0.946930i	0.980785	+	0.195090i	$0.0625000\pi$
$29$	0.321439	+	0.946930i	0.321439	+	0.946930i	−0.659346	+	0.751840i	$0.729167\pi$
$30$	0.707107	+	0.707107i	0.707107	+	0.707107i
$31$	−0.0654031	−	0.997859i	−0.0654031	−	0.997859i	−0.896873	−	0.442289i	$-0.854167\pi$
$31$	−0.0654031	−	0.997859i	−0.0654031	−	0.997859i	0.831470	−	0.555570i	$-0.187500\pi$
$32$		0			0
$33$	0.866025	−	0.500000i	0.866025	−	0.500000i
$34$		0			0
$35$	1.00000			1.00000
$36$		0			0
$37$	1.11114	+	1.66294i	1.11114	+	1.66294i	0.555570	+	0.831470i	$0.312500\pi$
$37$	1.11114	+	1.66294i	1.11114	+	1.66294i	0.555570	+	0.831470i	$0.312500\pi$
$38$		0			0
$39$	0.751840	+	0.659346i	0.751840	+	0.659346i
$40$	−0.442289	−	0.896873i	−0.442289	−	0.896873i
$41$	0.946930	+	0.321439i	0.946930	+	0.321439i	0.751840	−	0.659346i	$-0.229167\pi$
$41$	0.946930	+	0.321439i	0.946930	+	0.321439i	0.195090	+	0.980785i	$0.437500\pi$
$42$	0.793353	−	0.608761i	0.793353	−	0.608761i
$43$	−0.991445	+	0.130526i	−0.991445	+	0.130526i	−0.608761	−	0.793353i	$-0.708333\pi$
$43$	−0.991445	+	0.130526i	−0.991445	+	0.130526i	−0.382683	+	0.923880i	$0.625000\pi$
$44$		0			0
$45$	0.896873	−	0.442289i	0.896873	−	0.442289i
$46$	0.980785	+	0.195090i	0.980785	+	0.195090i
$47$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$47$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$48$	−0.896873	−	0.442289i	−0.896873	−	0.442289i
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$53$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$54$	0.442289	−	0.896873i	0.442289	−	0.896873i
$55$	0.707107	−	0.707107i	0.707107	−	0.707107i
$56$	−0.946930	+	0.321439i	−0.946930	+	0.321439i
$57$		0			0
$58$	0.946930	+	0.321439i	0.946930	+	0.321439i
$59$	−0.793353	+	0.608761i	−0.793353	+	0.608761i	−0.923880	−	0.382683i	$-0.875000\pi$
$59$	−0.793353	+	0.608761i	−0.793353	+	0.608761i	0.130526	+	0.991445i	$0.458333\pi$
$60$		0			0
$61$	−0.659346	−	0.751840i	−0.659346	−	0.751840i	0.321439	−	0.946930i	$-0.395833\pi$
$61$	−0.659346	−	0.751840i	−0.659346	−	0.751840i	−0.980785	+	0.195090i	$0.937500\pi$
$62$	−0.831470	−	0.555570i	−0.831470	−	0.555570i
$63$	−0.321439	−	0.946930i	−0.321439	−	0.946930i
$64$	0.707107	+	0.707107i	0.707107	+	0.707107i
$65$	0.896873	+	0.442289i	0.896873	+	0.442289i
$66$	0.130526	−	0.991445i	0.130526	−	0.991445i
$67$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$67$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$68$		0			0
$69$	0.500000	−	0.866025i	0.500000	−	0.866025i
$70$	0.608761	−	0.793353i	0.608761	−	0.793353i
$71$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$71$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$72$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$73$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$73$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$74$	1.99572	+	0.130806i	1.99572	+	0.130806i
$75$		0			0
$76$		0			0
$77$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$78$	0.980785	−	0.195090i	0.980785	−	0.195090i
$79$	0.0654031	−	0.997859i	0.0654031	−	0.997859i	−0.831470	−	0.555570i	$-0.812500\pi$
$79$	0.0654031	−	0.997859i	0.0654031	−	0.997859i	0.896873	−	0.442289i	$-0.145833\pi$
$80$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$81$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$82$	0.831470	−	0.555570i	0.831470	−	0.555570i
$83$	0.793353	+	0.608761i	0.793353	+	0.608761i	0.923880	−	0.382683i	$-0.125000\pi$
$83$	0.793353	+	0.608761i	0.793353	+	0.608761i	−0.130526	+	0.991445i	$0.541667\pi$
$84$		0			0
$85$		0			0
$86$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$87$	0.608761	−	0.793353i	0.608761	−	0.793353i
$88$	−0.442289	+	0.896873i	−0.442289	+	0.896873i
$89$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$89$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$90$	0.195090	−	0.980785i	0.195090	−	0.980785i
$91$	0.555570	−	0.831470i	0.555570	−	0.831470i
$92$		0			0
$93$	−0.793353	+	0.608761i	−0.793353	+	0.608761i
$94$	0.608761	+	0.793353i	0.608761	+	0.793353i
$95$		0			0
$96$		0			0
$97$	−0.321439	−	0.946930i	−0.321439	−	0.946930i	−0.980785	−	0.195090i	$-0.937500\pi$
$97$	−0.321439	−	0.946930i	−0.321439	−	0.946930i	0.659346	−	0.751840i	$-0.270833\pi$
$98$		0			0
$99$	−0.896873	−	0.442289i	−0.896873	−	0.442289i
$100$		0			0
$101$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$101$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$103$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$104$	−0.991445	−	0.130526i	−0.991445	−	0.130526i
$105$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$106$		0			0
$107$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$107$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$108$		0			0
$109$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$109$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$110$	−0.130526	−	0.991445i	−0.130526	−	0.991445i
$111$	0.765367	−	1.84776i	0.765367	−	1.84776i
$112$	−0.321439	+	0.946930i	−0.321439	+	0.946930i
$113$	−0.896873	+	0.442289i	−0.896873	+	0.442289i	−0.831470	−	0.555570i	$-0.812500\pi$
$113$	−0.896873	+	0.442289i	−0.896873	+	0.442289i	−0.0654031	+	0.997859i	$0.520833\pi$
$114$		0			0
$115$	0.258819	−	0.965926i	0.258819	−	0.965926i
$116$		0			0
$117$	0.130526	−	0.991445i	0.130526	−	0.991445i
$118$			1.00000i			1.00000i
$119$		0			0
$120$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$121$		0			0
$122$	−0.997859	+	0.0654031i	−0.997859	+	0.0654031i
$123$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$124$		0			0
$125$	−0.555570	+	0.831470i	−0.555570	+	0.831470i
$126$	−0.946930	−	0.321439i	−0.946930	−	0.321439i
$127$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$127$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$128$	0.991445	−	0.130526i	0.991445	−	0.130526i
$129$	0.659346	+	0.751840i	0.659346	+	0.751840i
$130$	0.896873	−	0.442289i	0.896873	−	0.442289i
$131$	−0.659346	+	0.751840i	−0.659346	+	0.751840i	−0.980785	−	0.195090i	$-0.937500\pi$
$131$	−0.659346	+	0.751840i	−0.659346	+	0.751840i	0.321439	+	0.946930i	$0.395833\pi$
$132$		0			0
$133$		0			0
$134$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$135$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$136$		0			0
$137$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$137$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$138$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$139$	0.997859	−	0.0654031i	0.997859	−	0.0654031i	0.442289	−	0.896873i	$-0.354167\pi$
$139$	0.997859	−	0.0654031i	0.997859	−	0.0654031i	0.555570	+	0.831470i	$0.312500\pi$
$140$		0			0
$141$	0.946930	−	0.321439i	0.946930	−	0.321439i
$142$		0			0
$143$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$144$	0.130526	+	0.991445i	0.130526	+	0.991445i
$145$	0.382683	−	0.923880i	0.382683	−	0.923880i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$149$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$150$		0			0
$151$	0.793353	+	0.608761i	0.793353	+	0.608761i	0.923880	−	0.382683i	$-0.125000\pi$
$151$	0.793353	+	0.608761i	0.793353	+	0.608761i	−0.130526	+	0.991445i	$0.541667\pi$
$152$		0			0
$153$		0			0
$154$	−1.00000			−1.00000
$155$	−0.608761	+	0.793353i	−0.608761	+	0.793353i
$156$		0			0
$157$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$157$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$158$	−0.751840	−	0.659346i	−0.751840	−	0.659346i
$159$		0			0
$160$		0			0
$161$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$162$	−0.991445	+	0.130526i	−0.991445	+	0.130526i
$163$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$163$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$164$		0			0
$165$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$166$	0.965926	−	0.258819i	0.965926	−	0.258819i
$167$	0.0654031	+	0.997859i	0.0654031	+	0.997859i	0.896873	+	0.442289i	$0.145833\pi$
$167$	0.0654031	+	0.997859i	0.0654031	+	0.997859i	−0.831470	+	0.555570i	$0.812500\pi$
$168$	0.793353	+	0.608761i	0.793353	+	0.608761i
$169$		0			0
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.442289	+	0.896873i	−0.442289	+	0.896873i	0.555570	+	0.831470i	$0.312500\pi$
$173$	−0.442289	+	0.896873i	−0.442289	+	0.896873i	−0.997859	+	0.0654031i	$0.979167\pi$
$174$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$175$		0			0
$176$	0.442289	+	0.896873i	0.442289	+	0.896873i
$177$	0.946930	+	0.321439i	0.946930	+	0.321439i
$178$		0			0
$179$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$179$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$180$		0			0
$181$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$181$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$182$	−0.321439	−	0.946930i	−0.321439	−	0.946930i
$183$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$184$	0.0654031	+	0.997859i	0.0654031	+	0.997859i
$185$	0.261052	−	1.98289i	0.261052	−	1.98289i
$186$			1.00000i			1.00000i
$187$		0			0
$188$		0			0
$189$	−0.608761	+	0.793353i	−0.608761	+	0.793353i
$190$		0			0
$191$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$191$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$192$	0.195090	−	0.980785i	0.195090	−	0.980785i
$193$	−0.442289	−	0.896873i	−0.442289	−	0.896873i	−0.997859	−	0.0654031i	$-0.979167\pi$
$193$	−0.442289	−	0.896873i	−0.442289	−	0.896873i	0.555570	−	0.831470i	$-0.312500\pi$
$194$	−0.946930	−	0.321439i	−0.946930	−	0.321439i
$195$	−0.130526	−	0.991445i	−0.130526	−	0.991445i
$196$		0			0
$197$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$197$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$198$	−0.896873	+	0.442289i	−0.896873	+	0.442289i
$199$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$199$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$200$		0			0
$201$	0.0654031	+	0.997859i	0.0654031	+	0.997859i
$202$	0.130526	−	0.991445i	0.130526	−	0.991445i
$203$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$204$		0			0
$205$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$206$	0.382683	+	0.923880i	0.382683	+	0.923880i
$207$	−0.997859	+	0.0654031i	−0.997859	+	0.0654031i
$208$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$209$		0			0
$210$	−0.997859	−	0.0654031i	−0.997859	−	0.0654031i
$211$	−0.946930	−	0.321439i	−0.946930	−	0.321439i	−0.195090	−	0.980785i	$-0.562500\pi$
$211$	−0.946930	−	0.321439i	−0.946930	−	0.321439i	−0.751840	+	0.659346i	$0.770833\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.831470	+	0.555570i	0.831470	+	0.555570i
$216$	0.980785	+	0.195090i	0.980785	+	0.195090i
$217$	0.707107	+	0.707107i	0.707107	+	0.707107i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$223$	−0.608761	+	0.793353i	−0.608761	+	0.793353i	−0.991445	−	0.130526i	$-0.958333\pi$
$223$	−0.608761	+	0.793353i	−0.608761	+	0.793353i	0.382683	+	0.923880i	$0.375000\pi$
$224$		0			0
$225$		0			0
$226$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$227$	−0.997859	−	0.0654031i	−0.997859	−	0.0654031i	−0.442289	−	0.896873i	$-0.645833\pi$
$227$	−0.997859	−	0.0654031i	−0.997859	−	0.0654031i	−0.555570	+	0.831470i	$0.687500\pi$
$228$		0			0
$229$	−0.793353	+	0.608761i	−0.793353	+	0.608761i	−0.923880	−	0.382683i	$-0.875000\pi$
$229$	−0.793353	+	0.608761i	−0.793353	+	0.608761i	0.130526	+	0.991445i	$0.458333\pi$
$230$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$231$	−0.321439	+	0.946930i	−0.321439	+	0.946930i
$232$	−0.0654031	+	0.997859i	−0.0654031	+	0.997859i
$233$	1.96157	+	0.390181i	1.96157	+	0.390181i	0.980785	+	0.195090i	$0.0625000\pi$
$233$	1.96157	+	0.390181i	1.96157	+	0.390181i	0.980785	+	0.195090i	$0.0625000\pi$
$234$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$235$	0.831470	−	0.555570i	0.831470	−	0.555570i
$236$		0			0
$237$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$238$		0			0
$239$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$239$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$240$	0.382683	+	0.923880i	0.382683	+	0.923880i
$241$	0.442289	−	0.896873i	0.442289	−	0.896873i	−0.555570	−	0.831470i	$-0.687500\pi$
$241$	0.442289	−	0.896873i	0.442289	−	0.896873i	0.997859	−	0.0654031i	$-0.0208333\pi$
$242$		0			0
$243$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$244$		0			0
$245$		0			0
$246$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$247$		0			0
$248$	0.321439	−	0.946930i	0.321439	−	0.946930i
$249$	0.0654031	−	0.997859i	0.0654031	−	0.997859i
$250$	0.321439	+	0.946930i	0.321439	+	0.946930i
$251$	−1.41421	−	1.41421i	−1.41421	−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$251$	−1.41421	−	1.41421i	−1.41421	−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$252$		0			0
$253$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.991445	+	0.130526i	0.991445	+	0.130526i	0.608761	−	0.793353i	$-0.291667\pi$
$257$	0.991445	+	0.130526i	0.991445	+	0.130526i	0.382683	+	0.923880i	$0.375000\pi$
$258$	0.997859	−	0.0654031i	0.997859	−	0.0654031i
$259$	−1.93185	−	0.517638i	−1.93185	−	0.517638i
$260$		0			0
$261$	−0.997859	−	0.0654031i	−0.997859	−	0.0654031i
$262$	0.195090	+	0.980785i	0.195090	+	0.980785i
$263$	−0.130526	−	0.991445i	−0.130526	−	0.991445i	−0.923880	−	0.382683i	$-0.875000\pi$
$263$	−0.130526	−	0.991445i	−0.130526	−	0.991445i	0.793353	−	0.608761i	$-0.208333\pi$
$264$	0.991445	−	0.130526i	0.991445	−	0.130526i
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$269$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$270$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	−1.00000			−1.00000
$274$	−0.991445	−	0.130526i	−0.991445	−	0.130526i
$275$		0			0
$276$		0			0
$277$	−0.946930	+	0.321439i	−0.946930	+	0.321439i	−0.751840	−	0.659346i	$-0.770833\pi$
$277$	−0.946930	+	0.321439i	−0.946930	+	0.321439i	−0.195090	+	0.980785i	$0.562500\pi$
$278$	0.555570	−	0.831470i	0.555570	−	0.831470i
$279$	0.946930	+	0.321439i	0.946930	+	0.321439i
$280$	0.923880	+	0.382683i	0.923880	+	0.382683i
$281$	0.991445	−	0.130526i	0.991445	−	0.130526i	0.382683	−	0.923880i	$-0.375000\pi$
$281$	0.991445	−	0.130526i	0.991445	−	0.130526i	0.608761	+	0.793353i	$0.291667\pi$
$282$	0.321439	−	0.946930i	0.321439	−	0.946930i
$283$	−0.896873	+	0.442289i	−0.896873	+	0.442289i	−0.831470	−	0.555570i	$-0.812500\pi$
$283$	−0.896873	+	0.442289i	−0.896873	+	0.442289i	−0.0654031	+	0.997859i	$0.520833\pi$
$284$		0			0
$285$		0			0
$286$	−0.896873	−	0.442289i	−0.896873	−	0.442289i
$287$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$288$		0			0
$289$		0			0
$290$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$291$	−0.608761	+	0.793353i	−0.608761	+	0.793353i
$292$		0			0
$293$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$293$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$294$		0			0
$295$	0.997859	+	0.0654031i	0.997859	+	0.0654031i
$296$	0.390181	+	1.96157i	0.390181	+	1.96157i
$297$	0.130526	+	0.991445i	0.130526	+	0.991445i
$298$	0.382683	−	0.923880i	0.382683	−	0.923880i
$299$	−0.659346	−	0.751840i	−0.659346	−	0.751840i
$300$		0			0
$301$	0.659346	−	0.751840i	0.659346	−	0.751840i
$302$	0.965926	−	0.258819i	0.965926	−	0.258819i
$303$	−0.896873	−	0.442289i	−0.896873	−	0.442289i
$304$		0			0
$305$			1.00000i			1.00000i
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$	0.997859	−	0.0654031i	0.997859	−	0.0654031i
$310$	0.258819	+	0.965926i	0.258819	+	0.965926i
$311$	0.751840	+	0.659346i	0.751840	+	0.659346i	0.946930	−	0.321439i	$-0.104167\pi$
$311$	0.751840	+	0.659346i	0.751840	+	0.659346i	−0.195090	+	0.980785i	$0.562500\pi$
$312$	0.442289	+	0.896873i	0.442289	+	0.896873i
$313$	0.751840	−	0.659346i	0.751840	−	0.659346i	−0.195090	−	0.980785i	$-0.562500\pi$
$313$	0.751840	−	0.659346i	0.751840	−	0.659346i	0.946930	+	0.321439i	$0.104167\pi$
$314$	0.923880	+	0.382683i	0.923880	+	0.382683i
$315$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$316$		0			0
$317$	0.0654031	−	0.997859i	0.0654031	−	0.997859i	−0.831470	−	0.555570i	$-0.812500\pi$
$317$	0.0654031	−	0.997859i	0.0654031	−	0.997859i	0.896873	−	0.442289i	$-0.145833\pi$
$318$		0			0
$319$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$320$	−0.0654031	−	0.997859i	−0.0654031	−	0.997859i
$321$		0			0
$322$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$		0			0
$328$	0.751840	+	0.659346i	0.751840	+	0.659346i
$329$	−0.442289	−	0.896873i	−0.442289	−	0.896873i
$330$	−0.751840	+	0.659346i	−0.751840	+	0.659346i
$331$	−0.130526	−	0.991445i	−0.130526	−	0.991445i	−0.923880	−	0.382683i	$-0.875000\pi$
$331$	−0.130526	−	0.991445i	−0.130526	−	0.991445i	0.793353	−	0.608761i	$-0.208333\pi$
$332$		0			0
$333$	−1.96157	+	0.390181i	−1.96157	+	0.390181i
$334$	0.831470	+	0.555570i	0.831470	+	0.555570i
$335$	0.321439	+	0.946930i	0.321439	+	0.946930i
$336$	0.965926	−	0.258819i	0.965926	−	0.258819i
$337$	−0.0654031	−	0.997859i	−0.0654031	−	0.997859i	−0.896873	−	0.442289i	$-0.854167\pi$
$337$	−0.0654031	−	0.997859i	−0.0654031	−	0.997859i	0.831470	−	0.555570i	$-0.187500\pi$
$338$		0			0
$339$	0.866025	+	0.500000i	0.866025	+	0.500000i
$340$		0			0
$341$	1.00000			1.00000
$342$		0			0
$343$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$344$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$345$	−0.946930	+	0.321439i	−0.946930	+	0.321439i
$346$	0.442289	+	0.896873i	0.442289	+	0.896873i
$347$	−0.946930	−	0.321439i	−0.946930	−	0.321439i	−0.195090	−	0.980785i	$-0.562500\pi$
$347$	−0.946930	−	0.321439i	−0.946930	−	0.321439i	−0.751840	+	0.659346i	$0.770833\pi$
$348$		0			0
$349$	0.991445	−	0.130526i	0.991445	−	0.130526i	0.382683	−	0.923880i	$-0.375000\pi$
$349$	0.991445	−	0.130526i	0.991445	−	0.130526i	0.608761	+	0.793353i	$0.291667\pi$
$350$		0			0
$351$	−0.896873	+	0.442289i	−0.896873	+	0.442289i
$352$		0			0
$353$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$353$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$354$	0.831470	−	0.555570i	0.831470	−	0.555570i
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$359$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$360$	0.997859	−	0.0654031i	0.997859	−	0.0654031i
$361$	0.707107	−	0.707107i	0.707107	−	0.707107i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$	0.608761	+	0.793353i	0.608761	+	0.793353i
$367$	0.659346	+	0.751840i	0.659346	+	0.751840i	0.980785	−	0.195090i	$-0.0625000\pi$
$367$	0.659346	+	0.751840i	0.659346	+	0.751840i	−0.321439	+	0.946930i	$0.604167\pi$
$368$	0.831470	+	0.555570i	0.831470	+	0.555570i
$369$	−0.659346	+	0.751840i	−0.659346	+	0.751840i
$370$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$371$		0			0
$372$		0			0
$373$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$373$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$374$		0			0
$375$	1.00000			1.00000
$376$	−0.608761	+	0.793353i	−0.608761	+	0.793353i
$377$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$378$	0.258819	+	0.965926i	0.258819	+	0.965926i
$379$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$379$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$380$		0			0
$381$		0			0
$382$	0.793353	−	0.608761i	0.793353	−	0.608761i
$383$	0.608761	+	0.793353i	0.608761	+	0.793353i	0.991445	−	0.130526i	$-0.0416667\pi$
$383$	0.608761	+	0.793353i	0.608761	+	0.793353i	−0.382683	+	0.923880i	$0.625000\pi$
$384$	−0.659346	−	0.751840i	−0.659346	−	0.751840i
$385$	−0.0654031	+	0.997859i	−0.0654031	+	0.997859i
$386$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$387$	0.258819	−	0.965926i	0.258819	−	0.965926i
$388$		0			0
$389$	0.793353	+	0.608761i	0.793353	+	0.608761i	0.923880	−	0.382683i	$-0.125000\pi$
$389$	0.793353	+	0.608761i	0.793353	+	0.608761i	−0.130526	+	0.991445i	$0.541667\pi$
$390$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$391$		0			0
$392$		0			0
$393$	0.991445	+	0.130526i	0.991445	+	0.130526i
$394$		0			0
$395$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$396$		0			0
$397$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$397$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.321439	−	0.946930i	0.321439	−	0.946930i	−0.659346	−	0.751840i	$-0.729167\pi$
$401$	0.321439	−	0.946930i	0.321439	−	0.946930i	0.980785	−	0.195090i	$-0.0625000\pi$
$402$	0.831470	+	0.555570i	0.831470	+	0.555570i
$403$	0.321439	+	0.946930i	0.321439	+	0.946930i
$404$		0			0
$405$	0.0654031	+	0.997859i	0.0654031	+	0.997859i
$406$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$407$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$408$		0			0
$409$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$409$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$410$	−0.991445	−	0.130526i	−0.991445	−	0.130526i
$411$	−0.442289	+	0.896873i	−0.442289	+	0.896873i
$412$		0			0
$413$	0.195090	−	0.980785i	0.195090	−	0.980785i
$414$	−0.555570	+	0.831470i	−0.555570	+	0.831470i
$415$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$416$		0			0
$417$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$418$		0			0
$419$	0.896873	−	0.442289i	0.896873	−	0.442289i	0.0654031	−	0.997859i	$-0.479167\pi$
$419$	0.896873	−	0.442289i	0.896873	−	0.442289i	0.831470	+	0.555570i	$0.187500\pi$
$420$		0			0
$421$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$421$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$422$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$423$	−0.793353	−	0.608761i	−0.793353	−	0.608761i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.991445	+	0.130526i	0.991445	+	0.130526i
$428$		0			0
$429$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$430$	0.946930	−	0.321439i	0.946930	−	0.321439i
$431$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$431$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$432$	0.751840	−	0.659346i	0.751840	−	0.659346i
$433$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$433$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$434$	0.991445	−	0.130526i	0.991445	−	0.130526i
$435$	−0.980785	+	0.195090i	−0.980785	+	0.195090i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.896873	+	0.442289i	0.896873	+	0.442289i	0.831470	−	0.555570i	$-0.187500\pi$
$439$	0.896873	+	0.442289i	0.896873	+	0.442289i	0.0654031	+	0.997859i	$0.479167\pi$
$440$	0.923880	−	0.382683i	0.923880	−	0.382683i
$441$		0			0
$442$		0			0
$443$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$443$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$444$		0			0
$445$		0			0
$446$	0.258819	+	0.965926i	0.258819	+	0.965926i
$447$	−0.751840	−	0.659346i	−0.751840	−	0.659346i
$448$	−0.997859	−	0.0654031i	−0.997859	−	0.0654031i
$449$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$449$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$450$		0			0
$451$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$452$		0			0
$453$	0.0654031	−	0.997859i	0.0654031	−	0.997859i
$454$	−0.659346	+	0.751840i	−0.659346	+	0.751840i
$455$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$456$		0			0
$457$	−0.793353	−	0.608761i	−0.793353	−	0.608761i	0.130526	−	0.991445i	$-0.458333\pi$
$457$	−0.793353	−	0.608761i	−0.793353	−	0.608761i	−0.923880	+	0.382683i	$0.875000\pi$
$458$			1.00000i			1.00000i
$459$		0			0
$460$		0			0
$461$	0.608761	−	0.793353i	0.608761	−	0.793353i	−0.382683	−	0.923880i	$-0.625000\pi$
$461$	0.608761	−	0.793353i	0.608761	−	0.793353i	0.991445	+	0.130526i	$0.0416667\pi$
$462$	0.555570	+	0.831470i	0.555570	+	0.831470i
$463$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$463$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$464$	0.751840	+	0.659346i	0.751840	+	0.659346i
$465$	0.997859	+	0.0654031i	0.997859	+	0.0654031i
$466$	1.50368	−	1.31869i	1.50368	−	1.31869i
$467$	1.84776	+	0.765367i	1.84776	+	0.765367i	0.923880	+	0.382683i	$0.125000\pi$
$467$	1.84776	+	0.765367i	1.84776	+	0.765367i	0.923880	+	0.382683i	$0.125000\pi$
$468$		0			0
$469$	0.980785	−	0.195090i	0.980785	−	0.195090i
$470$	0.0654031	−	0.997859i	0.0654031	−	0.997859i
$471$	0.659346	−	0.751840i	0.659346	−	0.751840i
$472$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$473$	−0.0654031	−	0.997859i	−0.0654031	−	0.997859i
$474$	−0.130526	+	0.991445i	−0.130526	+	0.991445i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	0.382683	+	0.923880i	0.382683	+	0.923880i
$479$	−0.442289	+	0.896873i	−0.442289	+	0.896873i	0.555570	+	0.831470i	$0.312500\pi$
$479$	−0.442289	+	0.896873i	−0.442289	+	0.896873i	−0.997859	+	0.0654031i	$0.979167\pi$
$480$		0			0
$481$	−1.50368	−	1.31869i	−1.50368	−	1.31869i
$482$	−0.442289	−	0.896873i	−0.442289	−	0.896873i
$483$	0.195090	+	0.980785i	0.195090	+	0.980785i
$484$		0			0
$485$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$486$	0.659346	+	0.751840i	0.659346	+	0.751840i
$487$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$487$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$488$	−0.321439	−	0.946930i	−0.321439	−	0.946930i
$489$		0			0
$490$		0			0
$491$	−0.130526	+	0.991445i	−0.130526	+	0.991445i	0.793353	+	0.608761i	$0.208333\pi$
$491$	−0.130526	+	0.991445i	−0.130526	+	0.991445i	−0.923880	+	0.382683i	$0.875000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	0.382683	+	0.923880i	0.382683	+	0.923880i
$496$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$497$		0			0
$498$	−0.751840	−	0.659346i	−0.751840	−	0.659346i
$499$	0.442289	+	0.896873i	0.442289	+	0.896873i	0.997859	+	0.0654031i	$0.0208333\pi$
$499$	0.442289	+	0.896873i	0.442289	+	0.896873i	−0.555570	+	0.831470i	$0.687500\pi$
$500$		0			0
$501$	0.793353	−	0.608761i	0.793353	−	0.608761i
$502$	−1.98289	+	0.261052i	−1.98289	+	0.261052i
$503$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$503$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$504$	0.0654031	−	0.997859i	0.0654031	−	0.997859i
$505$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$506$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$507$		0			0
$508$		0			0
$509$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$509$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$510$		0			0
$511$		0			0
$512$	0.382683	+	0.923880i	0.382683	+	0.923880i
$513$		0			0
$514$	0.707107	−	0.707107i	0.707107	−	0.707107i
$515$	0.946930	−	0.321439i	0.946930	−	0.321439i
$516$		0			0
$517$	−0.946930	−	0.321439i	−0.946930	−	0.321439i
$518$	−1.58671	+	1.21752i	−1.58671	+	1.21752i
$519$	0.991445	−	0.130526i	0.991445	−	0.130526i
$520$	0.659346	+	0.751840i	0.659346	+	0.751840i
$521$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$521$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$522$	−0.659346	+	0.751840i	−0.659346	+	0.751840i
$523$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$523$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$524$		0			0
$525$		0			0
$526$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$527$		0			0
$528$	0.500000	−	0.866025i	0.500000	−	0.866025i
$529$		0			0
$530$		0			0
$531$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$532$		0			0
$533$	−0.997859	−	0.0654031i	−0.997859	−	0.0654031i
$534$		0			0
$535$		0			0
$536$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−1.66294	+	1.11114i	−1.66294	+	1.11114i	−0.831470	+	0.555570i	$0.812500\pi$
$541$	−1.66294	+	1.11114i	−1.66294	+	1.11114i	−0.831470	+	0.555570i	$0.812500\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$	−0.608761	+	0.793353i	−0.608761	+	0.793353i
$547$	0.442289	−	0.896873i	0.442289	−	0.896873i	−0.555570	−	0.831470i	$-0.687500\pi$
$547$	0.442289	−	0.896873i	0.442289	−	0.896873i	0.997859	−	0.0654031i	$-0.0208333\pi$
$548$		0			0
$549$	0.946930	−	0.321439i	0.946930	−	0.321439i
$550$		0			0
$551$		0			0
$552$	0.793353	−	0.608761i	0.793353	−	0.608761i
$553$	0.608761	+	0.793353i	0.608761	+	0.793353i
$554$	−0.321439	+	0.946930i	−0.321439	+	0.946930i
$555$	−1.79375	+	0.884577i	−1.79375	+	0.884577i
$556$		0			0
$557$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$557$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$558$	0.831470	−	0.555570i	0.831470	−	0.555570i
$559$	0.923880	−	0.382683i	0.923880	−	0.382683i
$560$	0.866025	−	0.500000i	0.866025	−	0.500000i
$561$		0			0
$562$	0.500000	−	0.866025i	0.500000	−	0.866025i
$563$	−0.991445	−	0.130526i	−0.991445	−	0.130526i	−0.382683	−	0.923880i	$-0.625000\pi$
$563$	−0.991445	−	0.130526i	−0.991445	−	0.130526i	−0.608761	+	0.793353i	$0.708333\pi$
$564$		0			0
$565$	0.965926	+	0.258819i	0.965926	+	0.258819i
$566$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$567$	0.997859	+	0.0654031i	0.997859	+	0.0654031i
$568$		0			0
$569$	0.130526	+	0.991445i	0.130526	+	0.991445i	0.923880	+	0.382683i	$0.125000\pi$
$569$	0.130526	+	0.991445i	0.130526	+	0.991445i	−0.793353	+	0.608761i	$0.791667\pi$
$570$		0			0
$571$	0.321439	−	0.946930i	0.321439	−	0.946930i	−0.659346	−	0.751840i	$-0.729167\pi$
$571$	0.321439	−	0.946930i	0.321439	−	0.946930i	0.980785	−	0.195090i	$-0.0625000\pi$
$572$		0			0
$573$	−0.321439	−	0.946930i	−0.321439	−	0.946930i
$574$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$575$		0			0
$576$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$		0			0
$579$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$580$		0			0
$581$	−0.997859	+	0.0654031i	−0.997859	+	0.0654031i
$582$	0.258819	+	0.965926i	0.258819	+	0.965926i
$583$		0			0
$584$		0			0
$585$	−0.751840	+	0.659346i	−0.751840	+	0.659346i
$586$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$587$	−0.991445	+	0.130526i	−0.991445	+	0.130526i	−0.608761	−	0.793353i	$-0.708333\pi$
$587$	−0.991445	+	0.130526i	−0.991445	+	0.130526i	−0.382683	+	0.923880i	$0.625000\pi$
$588$		0			0
$589$		0			0
$590$	0.659346	−	0.751840i	0.659346	−	0.751840i
$591$		0			0
$592$	1.79375	+	0.884577i	1.79375	+	0.884577i
$593$	−1.84776	+	0.765367i	−1.84776	+	0.765367i	−0.923880	+	0.382683i	$0.875000\pi$
$593$	−1.84776	+	0.765367i	−1.84776	+	0.765367i	−0.923880	+	0.382683i	$0.875000\pi$
$594$	0.866025	+	0.500000i	0.866025	+	0.500000i
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−0.997859	+	0.0654031i	−0.997859	+	0.0654031i
$599$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$599$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$600$		0			0
$601$	0.997859	+	0.0654031i	0.997859	+	0.0654031i	0.555570	−	0.831470i	$-0.312500\pi$
$601$	0.997859	+	0.0654031i	0.997859	+	0.0654031i	0.442289	+	0.896873i	$0.354167\pi$
$602$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$603$	0.793353	−	0.608761i	0.793353	−	0.608761i
$604$		0			0
$605$		0			0
$606$	−0.896873	+	0.442289i	−0.896873	+	0.442289i
$607$	0.659346	−	0.751840i	0.659346	−	0.751840i	−0.321439	−	0.946930i	$-0.604167\pi$
$607$	0.659346	−	0.751840i	0.659346	−	0.751840i	0.980785	+	0.195090i	$0.0625000\pi$
$608$		0			0
$609$	0.0654031	+	0.997859i	0.0654031	+	0.997859i
$610$	0.793353	+	0.608761i	0.793353	+	0.608761i
$611$		−	1.00000i		−	1.00000i
$612$		0			0
$613$		0			0			−	1.00000i	$-0.5\pi$
$613$		0			0				1.00000i	$0.5\pi$
$614$		0			0
$615$	−0.442289	+	0.896873i	−0.442289	+	0.896873i
$616$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$617$	0.751840	+	0.659346i	0.751840	+	0.659346i	0.946930	−	0.321439i	$-0.104167\pi$
$617$	0.751840	+	0.659346i	0.751840	+	0.659346i	−0.195090	+	0.980785i	$0.562500\pi$
$618$	0.555570	−	0.831470i	0.555570	−	0.831470i
$619$	−0.751840	+	0.659346i	−0.751840	+	0.659346i	−0.946930	−	0.321439i	$-0.895833\pi$
$619$	−0.751840	+	0.659346i	−0.751840	+	0.659346i	0.195090	+	0.980785i	$0.437500\pi$
$620$		0			0
$621$	0.608761	+	0.793353i	0.608761	+	0.793353i
$622$	0.980785	−	0.195090i	0.980785	−	0.195090i
$623$		0			0
$624$	0.980785	+	0.195090i	0.980785	+	0.195090i
$625$	0.965926	−	0.258819i	0.965926	−	0.258819i
$626$	−0.0654031	−	0.997859i	−0.0654031	−	0.997859i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.500000	+	0.866025i	0.500000	+	0.866025i
$631$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$631$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$632$	0.442289	−	0.896873i	0.442289	−	0.896873i
$633$	0.258819	+	0.965926i	0.258819	+	0.965926i
$634$	−0.751840	−	0.659346i	−0.751840	−	0.659346i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$639$		0			0
$640$	−0.831470	−	0.555570i	−0.831470	−	0.555570i
$641$	−0.321439	−	0.946930i	−0.321439	−	0.946930i	−0.980785	−	0.195090i	$-0.937500\pi$
$641$	−0.321439	−	0.946930i	−0.321439	−	0.946930i	0.659346	−	0.751840i	$-0.270833\pi$
$642$		0			0
$643$	0.0654031	+	0.997859i	0.0654031	+	0.997859i	0.896873	+	0.442289i	$0.145833\pi$
$643$	0.0654031	+	0.997859i	0.0654031	+	0.997859i	−0.831470	+	0.555570i	$0.812500\pi$
$644$		0			0
$645$		−	1.00000i		−	1.00000i
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$649$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$650$		0			0
$651$	0.195090	−	0.980785i	0.195090	−	0.980785i
$652$		0			0
$653$	−0.946930	−	0.321439i	−0.946930	−	0.321439i	−0.195090	−	0.980785i	$-0.562500\pi$
$653$	−0.946930	−	0.321439i	−0.946930	−	0.321439i	−0.751840	+	0.659346i	$0.770833\pi$
$654$		0			0
$655$	0.991445	−	0.130526i	0.991445	−	0.130526i
$656$	0.980785	−	0.195090i	0.980785	−	0.195090i
$657$		0			0
$658$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$659$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$659$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$660$		0			0
$661$	0.130526	−	0.991445i	0.130526	−	0.991445i	−0.793353	−	0.608761i	$-0.791667\pi$
$661$	0.130526	−	0.991445i	0.130526	−	0.991445i	0.923880	−	0.382683i	$-0.125000\pi$
$662$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$663$		0			0
$664$	0.500000	+	0.866025i	0.500000	+	0.866025i
$665$		0			0
$666$	−0.884577	+	1.79375i	−0.884577	+	1.79375i
$667$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$668$		0			0
$669$	0.997859	+	0.0654031i	0.997859	+	0.0654031i
$670$	0.946930	+	0.321439i	0.946930	+	0.321439i
$671$	0.793353	−	0.608761i	0.793353	−	0.608761i
$672$		0			0
$673$	0.659346	+	0.751840i	0.659346	+	0.751840i	0.980785	−	0.195090i	$-0.0625000\pi$
$673$	0.659346	+	0.751840i	0.659346	+	0.751840i	−0.321439	+	0.946930i	$0.604167\pi$
$674$	−0.831470	−	0.555570i	−0.831470	−	0.555570i
$675$		0			0
$676$		0			0
$677$	−0.896873	−	0.442289i	−0.896873	−	0.442289i	−0.0654031	−	0.997859i	$-0.520833\pi$
$677$	−0.896873	−	0.442289i	−0.896873	−	0.442289i	−0.831470	+	0.555570i	$0.812500\pi$
$678$	0.923880	−	0.382683i	0.923880	−	0.382683i
$679$	0.866025	+	0.500000i	0.866025	+	0.500000i
$680$		0			0
$681$	0.500000	+	0.866025i	0.500000	+	0.866025i
$682$	0.608761	−	0.793353i	0.608761	−	0.793353i
$683$	1.11114	+	1.66294i	1.11114	+	1.66294i	0.555570	+	0.831470i	$0.312500\pi$
$683$	1.11114	+	1.66294i	1.11114	+	1.66294i	0.555570	+	0.831470i	$0.312500\pi$
$684$		0			0
$685$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$686$	−0.997859	−	0.0654031i	−0.997859	−	0.0654031i
$687$	0.946930	+	0.321439i	0.946930	+	0.321439i
$688$	−0.793353	+	0.608761i	−0.793353	+	0.608761i
$689$		0			0
$690$	−0.321439	+	0.946930i	−0.321439	+	0.946930i
$691$	0.0654031	−	0.997859i	0.0654031	−	0.997859i	−0.831470	−	0.555570i	$-0.812500\pi$
$691$	0.0654031	−	0.997859i	0.0654031	−	0.997859i	0.896873	−	0.442289i	$-0.145833\pi$
$692$		0			0
$693$	0.965926	−	0.258819i	0.965926	−	0.258819i
$694$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$695$	−0.793353	−	0.608761i	−0.793353	−	0.608761i
$696$	0.866025	−	0.500000i	0.866025	−	0.500000i
$697$		0			0
$698$	0.500000	−	0.866025i	0.500000	−	0.866025i
$699$	−0.765367	−	1.84776i	−0.765367	−	1.84776i
$700$		0			0
$701$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$701$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$702$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$703$		0			0
$704$	−0.751840	+	0.659346i	−0.751840	+	0.659346i
$705$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$706$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$707$	−0.321439	+	0.946930i	−0.321439	+	0.946930i
$708$		0			0
$709$	−0.321439	−	0.946930i	−0.321439	−	0.946930i	−0.980785	−	0.195090i	$-0.937500\pi$
$709$	−0.321439	−	0.946930i	−0.321439	−	0.946930i	0.659346	−	0.751840i	$-0.270833\pi$
$710$		0			0
$711$	0.896873	+	0.442289i	0.896873	+	0.442289i
$712$		0			0
$713$	0.866025	−	0.500000i	0.866025	−	0.500000i
$714$		0			0
$715$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$716$		0			0
$717$	0.997859	−	0.0654031i	0.997859	−	0.0654031i
$718$		0			0
$719$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$719$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$720$	0.555570	−	0.831470i	0.555570	−	0.831470i
$721$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$722$	−0.130526	−	0.991445i	−0.130526	−	0.991445i
$723$	−0.991445	+	0.130526i	−0.991445	+	0.130526i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$727$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$728$	0.831470	−	0.555570i	0.831470	−	0.555570i
$729$	0.923880	−	0.382683i	0.923880	−	0.382683i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	0.991445	+	0.130526i	0.991445	+	0.130526i	0.608761	−	0.793353i	$-0.291667\pi$
$733$	0.991445	+	0.130526i	0.991445	+	0.130526i	0.382683	+	0.923880i	$0.375000\pi$
$734$	0.997859	−	0.0654031i	0.997859	−	0.0654031i
$735$		0			0
$736$		0			0
$737$	0.555570	−	0.831470i	0.555570	−	0.831470i
$738$	0.195090	+	0.980785i	0.195090	+	0.980785i
$739$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$739$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.659346	−	0.751840i	0.659346	−	0.751840i	−0.321439	−	0.946930i	$-0.604167\pi$
$743$	0.659346	−	0.751840i	0.659346	−	0.751840i	0.980785	+	0.195090i	$0.0625000\pi$
$744$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$745$	−0.896873	−	0.442289i	−0.896873	−	0.442289i
$746$	0.923880	−	0.382683i	0.923880	−	0.382683i
$747$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$748$		0			0
$749$		0			0
$750$	0.608761	−	0.793353i	0.608761	−	0.793353i
$751$	0.997859	−	0.0654031i	0.997859	−	0.0654031i	0.442289	−	0.896873i	$-0.354167\pi$
$751$	0.997859	−	0.0654031i	0.997859	−	0.0654031i	0.555570	+	0.831470i	$0.312500\pi$
$752$	0.258819	+	0.965926i	0.258819	+	0.965926i
$753$	−0.390181	+	1.96157i	−0.390181	+	1.96157i
$754$	−0.997859	−	0.0654031i	−0.997859	−	0.0654031i
$755$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$756$		0			0
$757$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$757$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$758$		0			0
$759$	0.831470	+	0.555570i	0.831470	+	0.555570i
$760$		0			0
$761$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$761$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	1.00000			1.00000
$767$	0.608761	−	0.793353i	0.608761	−	0.793353i
$768$		0			0
$769$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$769$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$770$	0.751840	+	0.659346i	0.751840	+	0.659346i
$771$	−0.442289	−	0.896873i	−0.442289	−	0.896873i
$772$		0			0
$773$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$773$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$774$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$775$		0			0
$776$	0.0654031	−	0.997859i	0.0654031	−	0.997859i
$777$	0.642879	+	1.89386i	0.642879	+	1.89386i
$778$	0.965926	−	0.258819i	0.965926	−	0.258819i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.500000	+	0.866025i	0.500000	+	0.866025i
$784$		0			0
$785$	0.442289	−	0.896873i	0.442289	−	0.896873i
$786$	0.707107	−	0.707107i	0.707107	−	0.707107i
$787$	−0.751840	−	0.659346i	−0.751840	−	0.659346i	0.195090	−	0.980785i	$-0.437500\pi$
$787$	−0.751840	−	0.659346i	−0.751840	−	0.659346i	−0.946930	+	0.321439i	$0.895833\pi$
$788$		0			0
$789$	−0.751840	+	0.659346i	−0.751840	+	0.659346i
$790$	0.130526	+	0.991445i	0.130526	+	0.991445i
$791$	0.382683	−	0.923880i	0.382683	−	0.923880i
$792$	−0.659346	−	0.751840i	−0.659346	−	0.751840i
$793$	0.831470	+	0.555570i	0.831470	+	0.555570i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.130526	−	0.991445i	0.130526	−	0.991445i	−0.793353	−	0.608761i	$-0.791667\pi$
$797$	0.130526	−	0.991445i	0.130526	−	0.991445i	0.923880	−	0.382683i	$-0.125000\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$803$		0			0
$804$		0			0
$805$	0.442289	+	0.896873i	0.442289	+	0.896873i
$806$	0.946930	+	0.321439i	0.946930	+	0.321439i
$807$		0			0
$808$	0.991445	−	0.130526i	0.991445	−	0.130526i
$809$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$809$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$810$	0.831470	+	0.555570i	0.831470	+	0.555570i
$811$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$811$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$812$		0			0
$813$		0			0
$814$	−0.261052	+	1.98289i	−0.261052	+	1.98289i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$819$	0.555570	+	0.831470i	0.555570	+	0.831470i
$820$		0			0
$821$	0.946930	−	0.321439i	0.946930	−	0.321439i	0.195090	−	0.980785i	$-0.437500\pi$
$821$	0.946930	−	0.321439i	0.946930	−	0.321439i	0.751840	+	0.659346i	$0.229167\pi$
$822$	0.442289	+	0.896873i	0.442289	+	0.896873i
$823$	0.946930	+	0.321439i	0.946930	+	0.321439i	0.751840	−	0.659346i	$-0.229167\pi$
$823$	0.946930	+	0.321439i	0.946930	+	0.321439i	0.195090	+	0.980785i	$0.437500\pi$
$824$	−0.793353	+	0.608761i	−0.793353	+	0.608761i
$825$		0			0
$826$	−0.659346	−	0.751840i	−0.659346	−	0.751840i
$827$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$827$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$828$		0			0
$829$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$829$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$830$	−0.896873	−	0.442289i	−0.896873	−	0.442289i
$831$	0.793353	+	0.608761i	0.793353	+	0.608761i
$832$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$833$		0			0
$834$	−1.00000			−1.00000
$835$	0.608761	−	0.793353i	0.608761	−	0.793353i
$836$		0			0
$837$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$838$	0.195090	−	0.980785i	0.195090	−	0.980785i
$839$	−0.997859	−	0.0654031i	−0.997859	−	0.0654031i	−0.442289	−	0.896873i	$-0.645833\pi$
$839$	−0.997859	−	0.0654031i	−0.997859	−	0.0654031i	−0.555570	+	0.831470i	$0.687500\pi$
$840$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$841$		0			0
$842$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$843$	−0.659346	−	0.751840i	−0.659346	−	0.751840i
$844$		0			0
$845$		0			0
$846$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$847$		0			0
$848$		0			0
$849$	0.866025	+	0.500000i	0.866025	+	0.500000i
$850$		0			0
$851$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$852$		0			0
$853$	−0.442289	+	0.896873i	−0.442289	+	0.896873i	0.555570	+	0.831470i	$0.312500\pi$
$853$	−0.442289	+	0.896873i	−0.442289	+	0.896873i	−0.997859	+	0.0654031i	$0.979167\pi$
$854$	0.707107	−	0.707107i	0.707107	−	0.707107i
$855$		0			0
$856$		0			0
$857$	0.751840	−	0.659346i	0.751840	−	0.659346i	−0.195090	−	0.980785i	$-0.562500\pi$
$857$	0.751840	−	0.659346i	0.751840	−	0.659346i	0.946930	+	0.321439i	$0.104167\pi$
$858$	0.130526	+	0.991445i	0.130526	+	0.991445i
$859$	−0.608761	−	0.793353i	−0.608761	−	0.793353i	0.382683	−	0.923880i	$-0.375000\pi$
$859$	−0.608761	−	0.793353i	−0.608761	−	0.793353i	−0.991445	+	0.130526i	$0.958333\pi$
$860$		0			0
$861$	0.831470	+	0.555570i	0.831470	+	0.555570i
$862$		0			0
$863$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$863$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$864$		0			0
$865$	0.923880	−	0.382683i	0.923880	−	0.382683i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.991445	+	0.130526i	0.991445	+	0.130526i
$870$	−0.442289	+	0.896873i	−0.442289	+	0.896873i
$871$	0.965926	+	0.258819i	0.965926	+	0.258819i
$872$		0			0
$873$	0.997859	+	0.0654031i	0.997859	+	0.0654031i
$874$		0			0
$875$	−0.130526	−	0.991445i	−0.130526	−	0.991445i
$876$		0			0
$877$	0.321439	−	0.946930i	0.321439	−	0.946930i	−0.659346	−	0.751840i	$-0.729167\pi$
$877$	0.321439	−	0.946930i	0.321439	−	0.946930i	0.980785	−	0.195090i	$-0.0625000\pi$
$878$	0.896873	−	0.442289i	0.896873	−	0.442289i
$879$	−0.659346	+	0.751840i	−0.659346	+	0.751840i
$880$	0.258819	−	0.965926i	0.258819	−	0.965926i
$881$	1.66294	−	1.11114i	1.66294	−	1.11114i	0.831470	−	0.555570i	$-0.187500\pi$
$881$	1.66294	−	1.11114i	1.66294	−	1.11114i	0.831470	−	0.555570i	$-0.187500\pi$
$882$		0			0
$883$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$883$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$884$		0			0
$885$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$886$	−0.991445	−	0.130526i	−0.991445	−	0.130526i
$887$	0.997859	−	0.0654031i	0.997859	−	0.0654031i	0.442289	−	0.896873i	$-0.354167\pi$
$887$	0.997859	−	0.0654031i	0.997859	−	0.0654031i	0.555570	+	0.831470i	$0.312500\pi$
$888$	1.41421	−	1.41421i	1.41421	−	1.41421i
$889$		0			0
$890$		0			0
$891$	0.751840	−	0.659346i	0.751840	−	0.659346i
$892$		0			0
$893$		0			0
$894$	−0.980785	+	0.195090i	−0.980785	+	0.195090i
$895$		0			0
$896$	−0.659346	+	0.751840i	−0.659346	+	0.751840i
$897$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$898$		0			0
$899$	0.923880	−	0.382683i	0.923880	−	0.382683i
$900$		0			0
$901$		0			0
$902$	0.500000	+	0.866025i	0.500000	+	0.866025i
$903$	−0.991445	−	0.130526i	−0.991445	−	0.130526i
$904$	−0.997859	+	0.0654031i	−0.997859	+	0.0654031i
$905$		0			0
$906$	−0.751840	−	0.659346i	−0.751840	−	0.659346i
$907$	−0.997859	−	0.0654031i	−0.997859	−	0.0654031i	−0.442289	−	0.896873i	$-0.645833\pi$
$907$	−0.997859	−	0.0654031i	−0.997859	−	0.0654031i	−0.555570	+	0.831470i	$0.687500\pi$
$908$		0			0
$909$	0.130526	+	0.991445i	0.130526	+	0.991445i
$910$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$911$	0.659346	+	0.751840i	0.659346	+	0.751840i	0.980785	−	0.195090i	$-0.0625000\pi$
$911$	0.659346	+	0.751840i	0.659346	+	0.751840i	−0.321439	+	0.946930i	$0.604167\pi$
$912$		0			0
$913$	−0.659346	+	0.751840i	−0.659346	+	0.751840i
$914$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$915$	0.831470	−	0.555570i	0.831470	−	0.555570i
$916$		0			0
$917$		−	1.00000i		−	1.00000i
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	0.608761	−	0.793353i	0.608761	−	0.793353i
$921$		0			0
$922$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$927$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$928$		0			0
$929$	−0.0654031	+	0.997859i	−0.0654031	+	0.997859i	0.831470	+	0.555570i	$0.187500\pi$
$929$	−0.0654031	+	0.997859i	−0.0654031	+	0.997859i	−0.896873	+	0.442289i	$0.854167\pi$
$930$	0.659346	−	0.751840i	0.659346	−	0.751840i
$931$		0			0
$932$		0			0
$933$	0.130526	−	0.991445i	0.130526	−	0.991445i
$934$	1.73205	−	1.00000i	1.73205	−	1.00000i
$935$		0			0
$936$	0.500000	−	0.866025i	0.500000	−	0.866025i
$937$	−0.765367	−	1.84776i	−0.765367	−	1.84776i	−0.382683	−	0.923880i	$-0.625000\pi$
$937$	−0.765367	−	1.84776i	−0.765367	−	1.84776i	−0.382683	−	0.923880i	$-0.625000\pi$
$938$	0.442289	−	0.896873i	0.442289	−	0.896873i
$939$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$940$		0			0
$941$	−0.442289	−	0.896873i	−0.442289	−	0.896873i	−0.997859	−	0.0654031i	$-0.979167\pi$
$941$	−0.442289	−	0.896873i	−0.442289	−	0.896873i	0.555570	−	0.831470i	$-0.312500\pi$
$942$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$943$	0.130526	+	0.991445i	0.130526	+	0.991445i
$944$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$945$	0.980785	−	0.195090i	0.980785	−	0.195090i
$946$	−0.831470	−	0.555570i	−0.831470	−	0.555570i
$947$	0.321439	+	0.946930i	0.321439	+	0.946930i	0.980785	+	0.195090i	$0.0625000\pi$
$947$	0.321439	+	0.946930i	0.321439	+	0.946930i	−0.659346	+	0.751840i	$0.729167\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$952$		0			0
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$956$		0			0
$957$	0.751840	+	0.659346i	0.751840	+	0.659346i
$958$	0.442289	+	0.896873i	0.442289	+	0.896873i
$959$	0.946930	+	0.321439i	0.946930	+	0.321439i
$960$	−0.793353	+	0.608761i	−0.793353	+	0.608761i
$961$		0			0
$962$	−1.96157	+	0.390181i	−1.96157	+	0.390181i
$963$		0			0
$964$		0			0
$965$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$966$	0.896873	+	0.442289i	0.896873	+	0.442289i
$967$	−0.130526	+	0.991445i	−0.130526	+	0.991445i	0.793353	+	0.608761i	$0.208333\pi$
$967$	−0.130526	+	0.991445i	−0.130526	+	0.991445i	−0.923880	+	0.382683i	$0.875000\pi$
$968$		0			0
$969$		0			0
$970$	0.500000	+	0.866025i	0.500000	+	0.866025i
$971$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$971$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$972$		0			0
$973$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$974$		0			0
$975$		0			0
$976$	−0.946930	−	0.321439i	−0.946930	−	0.321439i
$977$	0.793353	−	0.608761i	0.793353	−	0.608761i	−0.130526	−	0.991445i	$-0.541667\pi$
$977$	0.793353	−	0.608761i	0.793353	−	0.608761i	0.923880	+	0.382683i	$0.125000\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	0.707107	+	0.707107i	0.707107	+	0.707107i
$983$	−0.896873	−	0.442289i	−0.896873	−	0.442289i	−0.0654031	−	0.997859i	$-0.520833\pi$
$983$	−0.896873	−	0.442289i	−0.896873	−	0.442289i	−0.831470	+	0.555570i	$0.812500\pi$
$984$	0.130526	−	0.991445i	0.130526	−	0.991445i
$985$		0			0
$986$		0			0
$987$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$988$		0			0
$989$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$990$	0.965926	+	0.258819i	0.965926	+	0.258819i
$991$	0.390181	−	1.96157i	0.390181	−	1.96157i	0.195090	−	0.980785i	$-0.437500\pi$
$991$	0.390181	−	1.96157i	0.390181	−	1.96157i	0.195090	−	0.980785i	$-0.437500\pi$
$992$		0			0
$993$	−0.751840	+	0.659346i	−0.751840	+	0.659346i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.0654031	+	0.997859i	−0.0654031	+	0.997859i	0.831470	+	0.555570i	$0.187500\pi$
$997$	−0.0654031	+	0.997859i	−0.0654031	+	0.997859i	−0.896873	+	0.442289i	$0.854167\pi$
$998$	0.980785	+	0.195090i	0.980785	+	0.195090i
$999$	1.41421	+	1.41421i	1.41421	+	1.41421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.1.x.a.2470.1	yes	32
9.7	even	3	inner	2601.1.x.a.736.1	yes	32
17.2	even	8	inner	2601.1.x.a.1669.1	yes	32
17.3	odd	16	inner	2601.1.x.a.2272.1	yes	32
17.4	even	4	inner	2601.1.x.a.2443.1	yes	32
17.5	odd	16	inner	2601.1.x.a.40.2	yes	32
17.6	odd	16	inner	2601.1.x.a.1948.1	yes	32
17.7	odd	16	inner	2601.1.x.a.364.1	yes	32
17.8	even	8	inner	2601.1.x.a.643.1	yes	32
17.9	even	8	inner	2601.1.x.a.643.2	yes	32
17.10	odd	16	inner	2601.1.x.a.364.2	yes	32
17.11	odd	16	inner	2601.1.x.a.1948.2	yes	32
17.12	odd	16	inner	2601.1.x.a.40.1	✓	32
17.13	even	4	inner	2601.1.x.a.2443.2	yes	32
17.14	odd	16	inner	2601.1.x.a.2272.2	yes	32
17.15	even	8	inner	2601.1.x.a.1669.2	yes	32
17.16	even	2	inner	2601.1.x.a.2470.2	yes	32
153.7	odd	48	inner	2601.1.x.a.1231.1	yes	32
153.16	even	6	inner	2601.1.x.a.736.2	yes	32
153.25	even	24	inner	2601.1.x.a.1510.1	yes	32
153.43	even	24	inner	2601.1.x.a.1510.2	yes	32
153.61	odd	48	inner	2601.1.x.a.1231.2	yes	32
153.70	even	24	inner	2601.1.x.a.2536.1	yes	32
153.79	odd	48	inner	2601.1.x.a.214.2	yes	32
153.88	odd	48	inner	2601.1.x.a.538.1	yes	32
153.97	odd	48	inner	2601.1.x.a.907.1	yes	32
153.106	even	12	inner	2601.1.x.a.709.1	yes	32
153.115	even	12	inner	2601.1.x.a.709.2	yes	32
153.124	odd	48	inner	2601.1.x.a.907.2	yes	32
153.133	odd	48	inner	2601.1.x.a.538.2	yes	32
153.142	odd	48	inner	2601.1.x.a.214.1	yes	32
153.151	even	24	inner	2601.1.x.a.2536.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2601.1.x.a.40.1	✓	32	17.12	odd	16	inner
2601.1.x.a.40.2	yes	32	17.5	odd	16	inner
2601.1.x.a.214.1	yes	32	153.142	odd	48	inner
2601.1.x.a.214.2	yes	32	153.79	odd	48	inner
2601.1.x.a.364.1	yes	32	17.7	odd	16	inner
2601.1.x.a.364.2	yes	32	17.10	odd	16	inner
2601.1.x.a.538.1	yes	32	153.88	odd	48	inner
2601.1.x.a.538.2	yes	32	153.133	odd	48	inner
2601.1.x.a.643.1	yes	32	17.8	even	8	inner
2601.1.x.a.643.2	yes	32	17.9	even	8	inner
2601.1.x.a.709.1	yes	32	153.106	even	12	inner
2601.1.x.a.709.2	yes	32	153.115	even	12	inner
2601.1.x.a.736.1	yes	32	9.7	even	3	inner
2601.1.x.a.736.2	yes	32	153.16	even	6	inner
2601.1.x.a.907.1	yes	32	153.97	odd	48	inner
2601.1.x.a.907.2	yes	32	153.124	odd	48	inner
2601.1.x.a.1231.1	yes	32	153.7	odd	48	inner
2601.1.x.a.1231.2	yes	32	153.61	odd	48	inner
2601.1.x.a.1510.1	yes	32	153.25	even	24	inner
2601.1.x.a.1510.2	yes	32	153.43	even	24	inner
2601.1.x.a.1669.1	yes	32	17.2	even	8	inner
2601.1.x.a.1669.2	yes	32	17.15	even	8	inner
2601.1.x.a.1948.1	yes	32	17.6	odd	16	inner
2601.1.x.a.1948.2	yes	32	17.11	odd	16	inner
2601.1.x.a.2272.1	yes	32	17.3	odd	16	inner
2601.1.x.a.2272.2	yes	32	17.14	odd	16	inner
2601.1.x.a.2443.1	yes	32	17.4	even	4	inner
2601.1.x.a.2443.2	yes	32	17.13	even	4	inner
2601.1.x.a.2470.1	yes	32	1.1	even	1	trivial
2601.1.x.a.2470.2	yes	32	17.16	even	2	inner
2601.1.x.a.2536.1	yes	32	153.70	even	24	inner
2601.1.x.a.2536.2	yes	32	153.151	even	24	inner

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:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2601.x (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.608761 - 0.793353i) q^{2} +(-0.555570 - 0.831470i) q^{3} +(-0.751840 - 0.659346i) q^{5} +(-0.997859 - 0.0654031i) q^{6} +(-0.751840 + 0.659346i) q^{7} +(0.923880 + 0.382683i) q^{8} +(-0.382683 + 0.923880i) q^{9} +O(q^{10})\)	\(q+(0.608761 - 0.793353i) q^{2} +(-0.555570 - 0.831470i) q^{3} +(-0.751840 - 0.659346i) q^{5} +(-0.997859 - 0.0654031i) q^{6} +(-0.751840 + 0.659346i) q^{7} +(0.923880 + 0.382683i) q^{8} +(-0.382683 + 0.923880i) q^{9} +(-0.980785 + 0.195090i) q^{10} +(-0.0654031 + 0.997859i) q^{11} +(-0.965926 + 0.258819i) q^{13} +(0.0654031 + 0.997859i) q^{14} +(-0.130526 + 0.991445i) q^{15} +(0.866025 - 0.500000i) q^{16} +(0.500000 + 0.866025i) q^{18} +(0.965926 + 0.258819i) q^{21} +(0.751840 + 0.659346i) q^{22} +(0.442289 + 0.896873i) q^{23} +(-0.195090 - 0.980785i) q^{24} +(-0.382683 + 0.923880i) q^{26} +(0.980785 - 0.195090i) q^{27} +(0.321439 + 0.946930i) q^{29} +(0.707107 + 0.707107i) q^{30} +(-0.0654031 - 0.997859i) q^{31} +(0.866025 - 0.500000i) q^{33} +1.00000 q^{35} +(1.11114 + 1.66294i) q^{37} +(0.751840 + 0.659346i) q^{39} +(-0.442289 - 0.896873i) q^{40} +(0.946930 + 0.321439i) q^{41} +(0.793353 - 0.608761i) q^{42} +(-0.991445 + 0.130526i) q^{43} +(0.896873 - 0.442289i) q^{45} +(0.980785 + 0.195090i) q^{46} +(-0.258819 + 0.965926i) q^{47} +(-0.896873 - 0.442289i) q^{48} +(0.442289 - 0.896873i) q^{54} +(0.707107 - 0.707107i) q^{55} +(-0.946930 + 0.321439i) q^{56} +(0.946930 + 0.321439i) q^{58} +(-0.793353 + 0.608761i) q^{59} +(-0.659346 - 0.751840i) q^{61} +(-0.831470 - 0.555570i) q^{62} +(-0.321439 - 0.946930i) q^{63} +(0.707107 + 0.707107i) q^{64} +(0.896873 + 0.442289i) q^{65} +(0.130526 - 0.991445i) q^{66} +(-0.866025 - 0.500000i) q^{67} +(0.500000 - 0.866025i) q^{69} +(0.608761 - 0.793353i) q^{70} +(-0.707107 + 0.707107i) q^{72} +(1.99572 + 0.130806i) q^{74} +(-0.608761 - 0.793353i) q^{77} +(0.980785 - 0.195090i) q^{78} +(0.0654031 - 0.997859i) q^{79} +(-0.980785 - 0.195090i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(0.831470 - 0.555570i) q^{82} +(0.793353 + 0.608761i) q^{83} +(-0.500000 + 0.866025i) q^{86} +(0.608761 - 0.793353i) q^{87} +(-0.442289 + 0.896873i) q^{88} +(0.195090 - 0.980785i) q^{90} +(0.555570 - 0.831470i) q^{91} +(-0.793353 + 0.608761i) q^{93} +(0.608761 + 0.793353i) q^{94} +(-0.321439 - 0.946930i) q^{97} +(-0.896873 - 0.442289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{18} + 32 q^{35} + 16 q^{69} - 16 q^{86}+O(q^{100}) \) 32 * q + 16 * q^18 + 32 * q^35 + 16 * q^69 - 16 * q^86

Introduction

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