LMFDB - Embedded newform 975.1.bi.a.779.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,1,Mod(194,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9, 5]))

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

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

chi := DirichletCharacter("975.194");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	975.bi (of order $10$, 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:	$0.486588387317$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{20}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{20} - \cdots)$

Embedding invariants

Embedding label			779.3
Root			$0.987688 + 0.156434i$ of defining polynomial
Character	$\chi$	$=$	975.779
Dual form			975.1.bi.a.194.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.863541 + 0.280582i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.142040 - 0.103198i) q^{4} +(-0.987688 - 0.156434i) q^{5} +(0.734572 - 0.533698i) q^{6} +(-0.627399 - 0.863541i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.863541 + 0.280582i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.142040 - 0.103198i) q^{4} +(-0.987688 - 0.156434i) q^{5} +(0.734572 - 0.533698i) q^{6} +(-0.627399 - 0.863541i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.412215i) q^{10} +(0.0966818 - 0.297556i) q^{11} +(-0.166977 + 0.0542543i) q^{12} +(0.951057 - 0.309017i) q^{13} +(-0.707107 + 0.707107i) q^{15} +(-0.245237 - 0.754763i) q^{16} -0.907981i q^{18} +(0.124147 + 0.124147i) q^{20} +(0.166977 - 0.229825i) q^{22} -1.06740 q^{24} +(0.951057 + 0.309017i) q^{25} +0.907981 q^{26} +(-0.951057 - 0.309017i) q^{27} +(-0.809017 + 0.412215i) q^{30} +0.346818i q^{32} +(-0.183900 - 0.253116i) q^{33} +(-0.0542543 + 0.166977i) q^{36} +(0.309017 - 0.951057i) q^{39} +(0.484587 + 0.951057i) q^{40} +(0.550672 + 1.69480i) q^{41} +1.90211i q^{43} +(-0.0444398 + 0.0322874i) q^{44} +(0.156434 + 0.987688i) q^{45} +(1.04744 - 1.44168i) q^{47} +(-0.754763 - 0.245237i) q^{48} -1.00000 q^{49} +(0.734572 + 0.533698i) q^{50} +(-0.166977 - 0.0542543i) q^{52} +(-0.734572 - 0.533698i) q^{54} +(-0.142040 + 0.278768i) q^{55} +(0.610425 + 1.87869i) q^{59} +(0.173409 - 0.0274653i) q^{60} +(0.363271 - 1.11803i) q^{61} +(-0.342548 + 1.05425i) q^{64} +(-0.987688 + 0.156434i) q^{65} +(-0.0877853 - 0.270175i) q^{66} +(0.253116 + 0.183900i) q^{71} +(-0.627399 + 0.863541i) q^{72} +(0.809017 - 0.587785i) q^{75} +(0.533698 - 0.734572i) q^{78} +(0.124147 + 0.783834i) q^{80} +(-0.809017 + 0.587785i) q^{81} +1.61803i q^{82} +(-0.533698 - 0.734572i) q^{83} +(-0.533698 + 1.64255i) q^{86} +(-0.317610 + 0.103198i) q^{88} +(0.437016 - 1.34500i) q^{89} +(-0.142040 + 0.896802i) q^{90} +(1.30902 - 0.951057i) q^{94} +(0.280582 + 0.203854i) q^{96} +(-0.863541 - 0.280582i) q^{98} -0.312869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 4 * q^9	$ 16 q + 4 q^{4} + 4 q^{9} - 4 q^{10} - 16 q^{16} - 4 q^{30} - 4 q^{36} - 4 q^{39} - 20 q^{40} - 16 q^{49} + 4 q^{55} + 16 q^{64} + 8 q^{66} + 4 q^{75} - 4 q^{81} + 20 q^{88} + 4 q^{90} + 12 q^{94}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^9 - 4 * q^10 - 16 * q^16 - 4 * q^30 - 4 * q^36 - 4 * q^39 - 20 * q^40 - 16 * q^49 + 4 * q^55 + 16 * q^64 + 8 * q^66 + 4 * q^75 - 4 * q^81 + 20 * q^88 + 4 * q^90 + 12 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.863541	+	0.280582i	0.863541	+	0.280582i	0.707107	−	0.707107i	$-0.250000\pi$
$2$	0.863541	+	0.280582i	0.863541	+	0.280582i	0.156434	+	0.987688i	$0.450000\pi$
$3$	0.587785	−	0.809017i	0.587785	−	0.809017i
$3$	0.587785	−	0.809017i	0.587785	−	0.809017i
$4$	−0.142040	−	0.103198i	−0.142040	−	0.103198i
$5$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$5$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$6$	0.734572	−	0.533698i	0.734572	−	0.533698i
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$	−0.627399	−	0.863541i	−0.627399	−	0.863541i
$9$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$10$	−0.809017	−	0.412215i	−0.809017	−	0.412215i
$11$	0.0966818	−	0.297556i	0.0966818	−	0.297556i	−0.891007	−	0.453990i	$-0.850000\pi$
$11$	0.0966818	−	0.297556i	0.0966818	−	0.297556i	0.987688	+	0.156434i	$0.0500000\pi$
$12$	−0.166977	+	0.0542543i	−0.166977	+	0.0542543i
$13$	0.951057	−	0.309017i	0.951057	−	0.309017i
$13$	0.951057	−	0.309017i	0.951057	−	0.309017i
$14$		0			0
$15$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$16$	−0.245237	−	0.754763i	−0.245237	−	0.754763i
$17$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$17$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$18$		−	0.907981i		−	0.907981i
$19$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$19$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$20$	0.124147	+	0.124147i	0.124147	+	0.124147i
$21$		0			0
$22$	0.166977	−	0.229825i	0.166977	−	0.229825i
$23$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$23$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$24$	−1.06740			−1.06740
$25$	0.951057	+	0.309017i	0.951057	+	0.309017i
$26$	0.907981			0.907981
$27$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$28$		0			0
$29$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$29$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$30$	−0.809017	+	0.412215i	−0.809017	+	0.412215i
$31$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$31$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$32$			0.346818i			0.346818i
$33$	−0.183900	−	0.253116i	−0.183900	−	0.253116i
$34$		0			0
$35$		0			0
$36$	−0.0542543	+	0.166977i	−0.0542543	+	0.166977i
$37$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$37$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$38$		0			0
$39$	0.309017	−	0.951057i	0.309017	−	0.951057i
$40$	0.484587	+	0.951057i	0.484587	+	0.951057i
$41$	0.550672	+	1.69480i	0.550672	+	1.69480i	0.707107	+	0.707107i	$0.250000\pi$
$41$	0.550672	+	1.69480i	0.550672	+	1.69480i	−0.156434	+	0.987688i	$0.550000\pi$
$42$		0			0
$43$			1.90211i			1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$43$			1.90211i			1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$44$	−0.0444398	+	0.0322874i	−0.0444398	+	0.0322874i
$45$	0.156434	+	0.987688i	0.156434	+	0.987688i
$46$		0			0
$47$	1.04744	−	1.44168i	1.04744	−	1.44168i	0.156434	−	0.987688i	$-0.450000\pi$
$47$	1.04744	−	1.44168i	1.04744	−	1.44168i	0.891007	−	0.453990i	$-0.150000\pi$
$48$	−0.754763	−	0.245237i	−0.754763	−	0.245237i
$49$	−1.00000			−1.00000
$50$	0.734572	+	0.533698i	0.734572	+	0.533698i
$51$		0			0
$52$	−0.166977	−	0.0542543i	−0.166977	−	0.0542543i
$53$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$53$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$54$	−0.734572	−	0.533698i	−0.734572	−	0.533698i
$55$	−0.142040	+	0.278768i	−0.142040	+	0.278768i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.610425	+	1.87869i	0.610425	+	1.87869i	0.453990	+	0.891007i	$0.350000\pi$
$59$	0.610425	+	1.87869i	0.610425	+	1.87869i	0.156434	+	0.987688i	$0.450000\pi$
$60$	0.173409	−	0.0274653i	0.173409	−	0.0274653i
$61$	0.363271	−	1.11803i	0.363271	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$61$	0.363271	−	1.11803i	0.363271	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$62$		0			0
$63$		0			0
$64$	−0.342548	+	1.05425i	−0.342548	+	1.05425i
$65$	−0.987688	+	0.156434i	−0.987688	+	0.156434i
$66$	−0.0877853	−	0.270175i	−0.0877853	−	0.270175i
$67$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$67$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.253116	+	0.183900i	0.253116	+	0.183900i	0.707107	−	0.707107i	$-0.250000\pi$
$71$	0.253116	+	0.183900i	0.253116	+	0.183900i	−0.453990	+	0.891007i	$0.650000\pi$
$72$	−0.627399	+	0.863541i	−0.627399	+	0.863541i
$73$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$73$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$74$		0			0
$75$	0.809017	−	0.587785i	0.809017	−	0.587785i
$76$		0			0
$77$		0			0
$78$	0.533698	−	0.734572i	0.533698	−	0.734572i
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$	0.124147	+	0.783834i	0.124147	+	0.783834i
$81$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$82$			1.61803i			1.61803i
$83$	−0.533698	−	0.734572i	−0.533698	−	0.734572i	0.453990	−	0.891007i	$-0.350000\pi$
$83$	−0.533698	−	0.734572i	−0.533698	−	0.734572i	−0.987688	+	0.156434i	$0.950000\pi$
$84$		0			0
$85$		0			0
$86$	−0.533698	+	1.64255i	−0.533698	+	1.64255i
$87$		0			0
$88$	−0.317610	+	0.103198i	−0.317610	+	0.103198i
$89$	0.437016	−	1.34500i	0.437016	−	1.34500i	−0.453990	−	0.891007i	$-0.650000\pi$
$89$	0.437016	−	1.34500i	0.437016	−	1.34500i	0.891007	−	0.453990i	$-0.150000\pi$
$90$	−0.142040	+	0.896802i	−0.142040	+	0.896802i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	1.30902	−	0.951057i	1.30902	−	0.951057i
$95$		0			0
$96$	0.280582	+	0.203854i	0.280582	+	0.203854i
$97$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$97$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$98$	−0.863541	−	0.280582i	−0.863541	−	0.280582i
$99$	−0.312869			−0.312869
$100$	−0.103198	−	0.142040i	−0.103198	−	0.142040i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$		0			0
$103$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$103$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$104$	−0.863541	−	0.627399i	−0.863541	−	0.627399i
$105$		0			0
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	0.103198	+	0.142040i	0.103198	+	0.142040i
$109$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$109$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$110$	−0.200874	+	0.200874i	−0.200874	+	0.200874i
$111$		0			0
$112$		0			0
$113$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$113$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$118$			1.79360i			1.79360i
$119$		0			0
$120$	1.05425	+	0.166977i	1.05425	+	0.166977i
$121$	0.729825	+	0.530249i	0.729825	+	0.530249i
$122$	0.627399	−	0.863541i	0.627399	−	0.863541i
$123$	1.69480	+	0.550672i	1.69480	+	0.550672i
$124$		0			0
$125$	−0.891007	−	0.453990i	−0.891007	−	0.453990i
$126$		0			0
$127$	0.587785	+	0.190983i	0.587785	+	0.190983i	0.587785	−	0.809017i	$-0.300000\pi$
$127$	0.587785	+	0.190983i	0.587785	+	0.190983i			1.00000i	$0.5\pi$
$128$	−0.387754	+	0.533698i	−0.387754	+	0.533698i
$129$	1.53884	+	1.11803i	1.53884	+	1.11803i
$130$	−0.896802	−	0.142040i	−0.896802	−	0.142040i
$131$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$131$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$132$			0.0549306i			0.0549306i
$133$		0			0
$134$		0			0
$135$	0.891007	+	0.453990i	0.891007	+	0.453990i
$136$		0			0
$137$	1.34500	−	0.437016i	1.34500	−	0.437016i	0.453990	−	0.891007i	$-0.350000\pi$
$137$	1.34500	−	0.437016i	1.34500	−	0.437016i	0.891007	+	0.453990i	$0.150000\pi$
$138$		0			0
$139$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$139$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$140$		0			0
$141$	−0.550672	−	1.69480i	−0.550672	−	1.69480i
$142$	0.166977	+	0.229825i	0.166977	+	0.229825i
$143$		−	0.312869i		−	0.312869i
$144$	−0.642040	+	0.466469i	−0.642040	+	0.466469i
$145$		0			0
$146$		0			0
$147$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$148$		0			0
$149$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$149$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$150$	0.863541	−	0.280582i	0.863541	−	0.280582i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.142040	+	0.103198i	−0.142040	+	0.103198i
$157$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$157$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$158$		0			0
$159$		0			0
$160$	0.0542543	−	0.342548i	0.0542543	−	0.342548i
$161$		0			0
$162$	−0.863541	+	0.280582i	−0.863541	+	0.280582i
$163$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$163$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$164$	0.0966818	−	0.297556i	0.0966818	−	0.297556i
$165$	0.142040	+	0.278768i	0.142040	+	0.278768i
$166$	−0.254763	−	0.784079i	−0.254763	−	0.784079i
$167$	−1.16110	−	1.59811i	−1.16110	−	1.59811i	−0.707107	−	0.707107i	$-0.750000\pi$
$167$	−1.16110	−	1.59811i	−1.16110	−	1.59811i	−0.453990	−	0.891007i	$-0.650000\pi$
$168$		0			0
$169$	0.809017	−	0.587785i	0.809017	−	0.587785i
$170$		0			0
$171$		0			0
$172$	0.196294	−	0.270175i	0.196294	−	0.270175i
$173$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$173$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$174$		0			0
$175$		0			0
$176$	−0.248294			−0.248294
$177$	1.87869	+	0.610425i	1.87869	+	0.610425i
$178$	0.754763	−	1.03884i	0.754763	−	1.03884i
$179$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$179$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$180$	0.0797073	−	0.156434i	0.0797073	−	0.156434i
$181$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$181$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$182$		0			0
$183$	−0.690983	−	0.951057i	−0.690983	−	0.951057i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.297556	+	0.0966818i	−0.297556	+	0.0966818i
$189$		0			0
$190$		0			0
$191$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$191$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$192$	0.651565	+	0.896802i	0.651565	+	0.896802i
$193$		0			0			−	1.00000i	$-0.5\pi$
$193$		0			0				1.00000i	$0.5\pi$
$194$		0			0
$195$	−0.453990	+	0.891007i	−0.453990	+	0.891007i
$196$	0.142040	+	0.103198i	0.142040	+	0.103198i
$197$	0.831254	−	1.14412i	0.831254	−	1.14412i	−0.156434	−	0.987688i	$-0.550000\pi$
$197$	0.831254	−	1.14412i	0.831254	−	1.14412i	0.987688	−	0.156434i	$-0.0500000\pi$
$198$	−0.270175	−	0.0877853i	−0.270175	−	0.0877853i
$199$	−1.90211			−1.90211			−0.951057	−	0.309017i	$-0.900000\pi$
$199$	−1.90211			−1.90211			−0.951057	+	0.309017i	$0.900000\pi$
$200$	−0.329843	−	1.01515i	−0.329843	−	1.01515i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.278768	−	1.76007i	−0.278768	−	1.76007i
$206$		0			0
$207$		0			0
$208$	−0.466469	−	0.642040i	−0.466469	−	0.642040i
$209$		0			0
$210$		0			0
$211$	−0.587785	+	1.80902i	−0.587785	+	1.80902i			1.00000i	$0.5\pi$
$211$	−0.587785	+	1.80902i	−0.587785	+	1.80902i	−0.587785	+	0.809017i	$0.700000\pi$
$212$		0			0
$213$	0.297556	−	0.0966818i	0.297556	−	0.0966818i
$214$		0			0
$215$	0.297556	−	1.87869i	0.297556	−	1.87869i
$216$	0.329843	+	1.01515i	0.329843	+	1.01515i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	0.0489435	−	0.0249380i	0.0489435	−	0.0249380i
$221$		0			0
$222$		0			0
$223$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$223$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$224$		0			0
$225$		−	1.00000i		−	1.00000i
$226$		0			0
$227$	−1.34500	−	0.437016i	−1.34500	−	0.437016i	−0.453990	−	0.891007i	$-0.650000\pi$
$227$	−1.34500	−	0.437016i	−1.34500	−	0.437016i	−0.891007	+	0.453990i	$0.850000\pi$
$228$		0			0
$229$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$229$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$233$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$234$	−0.280582	−	0.863541i	−0.280582	−	0.863541i
$235$	−1.26007	+	1.26007i	−1.26007	+	1.26007i
$236$	0.107173	−	0.329843i	0.107173	−	0.329843i
$237$		0			0
$238$		0			0
$239$	−0.437016	+	1.34500i	−0.437016	+	1.34500i	0.453990	+	0.891007i	$0.350000\pi$
$239$	−0.437016	+	1.34500i	−0.437016	+	1.34500i	−0.891007	+	0.453990i	$0.850000\pi$
$240$	0.707107	+	0.360289i	0.707107	+	0.360289i
$241$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$241$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$242$	0.481456	+	0.662667i	0.481456	+	0.662667i
$243$			1.00000i			1.00000i
$244$	−0.166977	+	0.121316i	−0.166977	+	0.121316i
$245$	0.987688	+	0.156434i	0.987688	+	0.156434i
$246$	1.30902	+	0.951057i	1.30902	+	0.951057i
$247$		0			0
$248$		0			0
$249$	−0.907981			−0.907981
$250$	−0.642040	−	0.642040i	−0.642040	−	0.642040i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$		0			0
$254$	0.453990	+	0.329843i	0.453990	+	0.329843i
$255$		0			0
$256$	0.412215	−	0.299492i	0.412215	−	0.299492i
$257$		0			0			−	1.00000i	$-0.5\pi$
$257$		0			0				1.00000i	$0.5\pi$
$258$	1.01515	+	1.39724i	1.01515	+	1.39724i
$259$		0			0
$260$	0.156434	+	0.0797073i	0.156434	+	0.0797073i
$261$		0			0
$262$		0			0
$263$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$263$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$264$	−0.103198	+	0.317610i	−0.103198	+	0.317610i
$265$		0			0
$266$		0			0
$267$	−0.831254	−	1.14412i	−0.831254	−	1.14412i
$268$		0			0
$269$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$269$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$270$	0.642040	+	0.642040i	0.642040	+	0.642040i
$271$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$271$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$272$		0			0
$273$		0			0
$274$	1.28408			1.28408
$275$	0.183900	−	0.253116i	0.183900	−	0.253116i
$276$		0			0
$277$	1.80902	+	0.587785i	1.80902	+	0.587785i	1.00000			$0$
$277$	1.80902	+	0.587785i	1.80902	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$278$	−0.863541	+	1.18856i	−0.863541	+	1.18856i
$279$		0			0
$280$		0			0
$281$	−1.59811	+	1.16110i	−1.59811	+	1.16110i	−0.707107	+	0.707107i	$0.750000\pi$
$281$	−1.59811	+	1.16110i	−1.59811	+	1.16110i	−0.891007	+	0.453990i	$0.850000\pi$
$282$		−	1.61803i		−	1.61803i
$283$	−0.951057	−	1.30902i	−0.951057	−	1.30902i	−0.951057	−	0.309017i	$-0.900000\pi$
$283$	−0.951057	−	1.30902i	−0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$284$	−0.0169745	−	0.0522421i	−0.0169745	−	0.0522421i
$285$		0			0
$286$	0.0877853	−	0.270175i	0.0877853	−	0.270175i
$287$		0			0
$288$	0.329843	−	0.107173i	0.329843	−	0.107173i
$289$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			1.78201i			1.78201i	0.453990	+	0.891007i	$0.350000\pi$
$293$			1.78201i			1.78201i	−0.453990	+	0.891007i	$0.650000\pi$
$294$	−0.734572	+	0.533698i	−0.734572	+	0.533698i
$295$	−0.309017	−	1.95106i	−0.309017	−	1.95106i
$296$		0			0
$297$	−0.183900	+	0.253116i	−0.183900	+	0.253116i
$298$	−1.22123	−	0.396802i	−1.22123	−	0.396802i
$299$		0			0
$300$	−0.175571			−0.175571
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.533698	+	1.04744i	−0.533698	+	1.04744i
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$311$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$312$	−1.01515	+	0.329843i	−1.01515	+	0.329843i
$313$	0.587785	−	0.190983i	0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$313$	0.587785	−	0.190983i	0.587785	−	0.190983i	0.587785	+	0.809017i	$0.300000\pi$
$314$	0.329843	−	1.01515i	0.329843	−	1.01515i
$315$		0			0
$316$		0			0
$317$	0.533698	+	0.734572i	0.533698	+	0.734572i	0.987688	−	0.156434i	$-0.0500000\pi$
$317$	0.533698	+	0.734572i	0.533698	+	0.734572i	−0.453990	+	0.891007i	$0.650000\pi$
$318$		0			0
$319$		0			0
$320$	0.503252	−	0.987688i	0.503252	−	0.987688i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.175571			0.175571
$325$	1.00000			1.00000
$326$		0			0
$327$		0			0
$328$	1.11803	−	1.53884i	1.11803	−	1.53884i
$329$		0			0
$330$	0.0444398	+	0.280582i	0.0444398	+	0.280582i
$331$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$331$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$332$			0.159415i			0.159415i
$333$		0			0
$334$	−0.554254	−	1.70582i	−0.554254	−	1.70582i
$335$		0			0
$336$		0			0
$337$	0.587785	−	0.190983i	0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$337$	0.587785	−	0.190983i	0.587785	−	0.190983i	0.587785	+	0.809017i	$0.300000\pi$
$338$	0.863541	−	0.280582i	0.863541	−	0.280582i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	1.64255	−	1.19338i	1.64255	−	1.19338i
$345$		0			0
$346$		0			0
$347$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$347$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$	−1.00000			−1.00000
$352$	0.103198	+	0.0335310i	0.103198	+	0.0335310i
$353$	1.04744	−	1.44168i	1.04744	−	1.44168i	0.156434	−	0.987688i	$-0.450000\pi$
$353$	1.04744	−	1.44168i	1.04744	−	1.44168i	0.891007	−	0.453990i	$-0.150000\pi$
$354$	1.45106	+	1.05425i	1.45106	+	1.05425i
$355$	−0.221232	−	0.221232i	−0.221232	−	0.221232i
$356$	−0.200874	+	0.145944i	−0.200874	+	0.145944i
$357$		0			0
$358$		0			0
$359$	0.550672	+	1.69480i	0.550672	+	1.69480i	0.707107	+	0.707107i	$0.250000\pi$
$359$	0.550672	+	1.69480i	0.550672	+	1.69480i	−0.156434	+	0.987688i	$0.550000\pi$
$360$	0.754763	−	0.754763i	0.754763	−	0.754763i
$361$	0.309017	−	0.951057i	0.309017	−	0.951057i
$362$	−1.39724	+	0.453990i	−1.39724	+	0.453990i
$363$	0.857960	−	0.278768i	0.857960	−	0.278768i
$364$		0			0
$365$		0			0
$366$	−0.329843	−	1.01515i	−0.329843	−	1.01515i
$367$	−1.11803	−	1.53884i	−1.11803	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$367$	−1.11803	−	1.53884i	−1.11803	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$368$		0			0
$369$	1.44168	−	1.04744i	1.44168	−	1.04744i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$373$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$374$		0			0
$375$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$376$	−1.90211			−1.90211
$377$		0			0
$378$		0			0
$379$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$379$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$380$		0			0
$381$	0.500000	−	0.363271i	0.500000	−	0.363271i
$382$		0			0
$383$	0.831254	+	1.14412i	0.831254	+	1.14412i	0.987688	+	0.156434i	$0.0500000\pi$
$383$	0.831254	+	1.14412i	0.831254	+	1.14412i	−0.156434	+	0.987688i	$0.550000\pi$
$384$	0.203854	+	0.627399i	0.203854	+	0.627399i
$385$		0			0
$386$		0			0
$387$	1.80902	−	0.587785i	1.80902	−	0.587785i
$388$		0			0
$389$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$389$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$390$	−0.642040	+	0.642040i	−0.642040	+	0.642040i
$391$		0			0
$392$	0.627399	+	0.863541i	0.627399	+	0.863541i
$393$		0			0
$394$	1.03884	−	0.754763i	1.03884	−	0.754763i
$395$		0			0
$396$	0.0444398	+	0.0322874i	0.0444398	+	0.0322874i
$397$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$397$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$398$	−1.64255	−	0.533698i	−1.64255	−	0.533698i
$399$		0			0
$400$		−	0.793604i		−	0.793604i
$401$	−0.312869			−0.312869			−0.156434	−	0.987688i	$-0.550000\pi$
$401$	−0.312869			−0.312869			−0.156434	+	0.987688i	$0.550000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.891007	−	0.453990i	0.891007	−	0.453990i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$409$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$410$	0.253116	−	1.59811i	0.253116	−	1.59811i
$411$	0.437016	−	1.34500i	0.437016	−	1.34500i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	0.412215	+	0.809017i	0.412215	+	0.809017i
$416$	0.107173	+	0.329843i	0.107173	+	0.329843i
$417$	0.951057	+	1.30902i	0.951057	+	1.30902i
$418$		0			0
$419$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$419$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$420$		0			0
$421$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$421$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$422$	−1.01515	+	1.39724i	−1.01515	+	1.39724i
$423$	−1.69480	−	0.550672i	−1.69480	−	0.550672i
$424$		0			0
$425$		0			0
$426$	0.284079			0.284079
$427$		0			0
$428$		0			0
$429$	−0.253116	−	0.183900i	−0.253116	−	0.183900i
$430$	0.784079	−	1.53884i	0.784079	−	1.53884i
$431$	−0.734572	+	0.533698i	−0.734572	+	0.533698i	−0.891007	−	0.453990i	$-0.850000\pi$
$431$	−0.734572	+	0.533698i	−0.734572	+	0.533698i	0.156434	+	0.987688i	$0.450000\pi$
$432$			0.793604i			0.793604i
$433$	0.951057	+	1.30902i	0.951057	+	1.30902i	0.951057	+	0.309017i	$0.100000\pi$
$433$	0.951057	+	1.30902i	0.951057	+	1.30902i			1.00000i	$0.5\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$439$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$440$	0.329843	−	0.0522421i	0.329843	−	0.0522421i
$441$	0.309017	+	0.951057i	0.309017	+	0.951057i
$442$		0			0
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$	−0.642040	+	1.26007i	−0.642040	+	1.26007i
$446$		0			0
$447$	−0.831254	+	1.14412i	−0.831254	+	1.14412i
$448$		0			0
$449$	1.97538			1.97538			0.987688	−	0.156434i	$-0.0500000\pi$
$449$	1.97538			1.97538			0.987688	+	0.156434i	$0.0500000\pi$
$450$	0.280582	−	0.863541i	0.280582	−	0.863541i
$451$	0.557537			0.557537
$452$		0			0
$453$		0			0
$454$	−1.03884	−	0.754763i	−1.03884	−	0.754763i
$455$		0			0
$456$		0			0
$457$		0			0			−	1.00000i	$-0.5\pi$
$457$		0			0				1.00000i	$0.5\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.610425	−	1.87869i	0.610425	−	1.87869i	0.156434	−	0.987688i	$-0.450000\pi$
$461$	0.610425	−	1.87869i	0.610425	−	1.87869i	0.453990	−	0.891007i	$-0.350000\pi$
$462$		0			0
$463$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$463$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$467$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$468$			0.175571i			0.175571i
$469$		0			0
$470$	−1.44168	+	0.734572i	−1.44168	+	0.734572i
$471$	−0.951057	−	0.690983i	−0.951057	−	0.690983i
$472$	1.23935	−	1.70582i	1.23935	−	1.70582i
$473$	0.565985	+	0.183900i	0.565985	+	0.183900i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−0.754763	+	1.03884i	−0.754763	+	1.03884i
$479$	1.59811	+	1.16110i	1.59811	+	1.16110i	0.891007	+	0.453990i	$0.150000\pi$
$479$	1.59811	+	1.16110i	1.59811	+	1.16110i	0.707107	+	0.707107i	$0.250000\pi$
$480$	−0.245237	−	0.245237i	−0.245237	−	0.245237i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.0489435	−	0.150633i	−0.0489435	−	0.150633i
$485$		0			0
$486$	−0.280582	+	0.863541i	−0.280582	+	0.863541i
$487$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$487$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$488$	−1.19338	+	0.387754i	−1.19338	+	0.387754i
$489$		0			0
$490$	0.809017	+	0.412215i	0.809017	+	0.412215i
$491$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$491$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$492$	−0.183900	−	0.253116i	−0.183900	−	0.253116i
$493$		0			0
$494$		0			0
$495$	0.309017	+	0.0489435i	0.309017	+	0.0489435i
$496$		0			0
$497$		0			0
$498$	−0.784079	−	0.254763i	−0.784079	−	0.254763i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	0.0797073	+	0.156434i	0.0797073	+	0.156434i
$501$	−1.97538			−1.97538
$502$		0			0
$503$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$503$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	1.00000i		−	1.00000i
$508$	−0.0637797	−	0.0877853i	−0.0637797	−	0.0877853i
$509$	−0.280582	−	0.863541i	−0.280582	−	0.863541i	−0.987688	−	0.156434i	$-0.950000\pi$
$509$	−0.280582	−	0.863541i	−0.280582	−	0.863541i	0.707107	−	0.707107i	$-0.250000\pi$
$510$		0			0
$511$		0			0
$512$	1.06740	−	0.346818i	1.06740	−	0.346818i
$513$		0			0
$514$		0			0
$515$		0			0
$516$	−0.103198	−	0.317610i	−0.103198	−	0.317610i
$517$	−0.327712	−	0.451057i	−0.327712	−	0.451057i
$518$		0			0
$519$		0			0
$520$	0.754763	+	0.754763i	0.754763	+	0.754763i
$521$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$521$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$522$		0			0
$523$	−1.11803	−	0.363271i	−1.11803	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$523$	−1.11803	−	0.363271i	−1.11803	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.145944	+	0.200874i	−0.145944	+	0.200874i
$529$	0.809017	+	0.587785i	0.809017	+	0.587785i
$530$		0			0
$531$	1.59811	−	1.16110i	1.59811	−	1.16110i
$532$		0			0
$533$	1.04744	+	1.44168i	1.04744	+	1.44168i
$534$	−0.396802	−	1.22123i	−0.396802	−	1.22123i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.0966818	+	0.297556i	−0.0966818	+	0.297556i
$540$	−0.0797073	−	0.156434i	−0.0797073	−	0.156434i
$541$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$541$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$542$		0			0
$543$			1.61803i			1.61803i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.690983	+	0.951057i	−0.690983	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$547$	−0.690983	+	0.951057i	−0.690983	+	0.951057i	−1.00000			$1.00000\pi$
$548$	−0.236142	−	0.0767271i	−0.236142	−	0.0767271i
$549$	−1.17557			−1.17557
$550$	0.229825	−	0.166977i	0.229825	−	0.166977i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	1.39724	+	1.01515i	1.39724	+	1.01515i
$555$		0			0
$556$	0.229825	−	0.166977i	0.229825	−	0.166977i
$557$			1.97538i			1.97538i	0.156434	+	0.987688i	$0.450000\pi$
$557$			1.97538i			1.97538i	−0.156434	+	0.987688i	$0.550000\pi$
$558$		0			0
$559$	0.587785	+	1.80902i	0.587785	+	1.80902i
$560$		0			0
$561$		0			0
$562$	−1.70582	+	0.554254i	−1.70582	+	0.554254i
$563$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$563$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$564$	−0.0966818	+	0.297556i	−0.0966818	+	0.297556i
$565$		0			0
$566$	−0.453990	−	1.39724i	−0.453990	−	1.39724i
$567$		0			0
$568$		−	0.333955i		−	0.333955i
$569$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$569$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$570$		0			0
$571$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$571$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$572$	−0.0322874	+	0.0444398i	−0.0322874	+	0.0444398i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.10851			1.10851
$577$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$577$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$578$	−0.533698	+	0.734572i	−0.533698	+	0.734572i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	0.453990	+	0.891007i	0.453990	+	0.891007i
$586$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$587$	−1.87869	+	0.610425i	−1.87869	+	0.610425i	−0.891007	+	0.453990i	$0.850000\pi$
$587$	−1.87869	+	0.610425i	−1.87869	+	0.610425i	−0.987688	+	0.156434i	$0.950000\pi$
$588$	0.166977	−	0.0542543i	0.166977	−	0.0542543i
$589$		0			0
$590$	0.280582	−	1.77152i	0.280582	−	1.77152i
$591$	−0.437016	−	1.34500i	−0.437016	−	1.34500i
$592$		0			0
$593$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$593$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$594$	−0.229825	+	0.166977i	−0.229825	+	0.166977i
$595$		0			0
$596$	0.200874	+	0.145944i	0.200874	+	0.145944i
$597$	−1.11803	+	1.53884i	−1.11803	+	1.53884i
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−1.01515	−	0.329843i	−1.01515	−	0.329843i
$601$		0			0			−	1.00000i	$-0.5\pi$
$601$		0			0				1.00000i	$0.5\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.637890	−	0.637890i	−0.637890	−	0.637890i
$606$		0			0
$607$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$607$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$608$		0			0
$609$		0			0
$610$	−0.754763	+	0.754763i	−0.754763	+	0.754763i
$611$	0.550672	−	1.69480i	0.550672	−	1.69480i
$612$		0			0
$613$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$613$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$614$		0			0
$615$	−1.58779	−	0.809017i	−1.58779	−	0.809017i
$616$		0			0
$617$	−1.04744	−	1.44168i	−1.04744	−	1.44168i	−0.891007	−	0.453990i	$-0.850000\pi$
$617$	−1.04744	−	1.44168i	−1.04744	−	1.44168i	−0.156434	−	0.987688i	$-0.550000\pi$
$618$		0			0
$619$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$619$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−0.793604			−0.793604
$625$	0.809017	+	0.587785i	0.809017	+	0.587785i
$626$	0.561163			0.561163
$627$		0			0
$628$	−0.121316	+	0.166977i	−0.121316	+	0.166977i
$629$		0			0
$630$		0			0
$631$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$631$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$632$		0			0
$633$	1.11803	+	1.53884i	1.11803	+	1.53884i
$634$	0.254763	+	0.784079i	0.254763	+	0.784079i
$635$	−0.550672	−	0.280582i	−0.550672	−	0.280582i
$636$		0			0
$637$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$638$		0			0
$639$	0.0966818	−	0.297556i	0.0966818	−	0.297556i
$640$	0.466469	−	0.466469i	0.466469	−	0.466469i
$641$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$641$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$642$		0			0
$643$		0			0			−	1.00000i	$-0.5\pi$
$643$		0			0				1.00000i	$0.5\pi$
$644$		0			0
$645$	−1.34500	−	1.34500i	−1.34500	−	1.34500i
$646$		0			0
$647$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$647$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$648$	1.01515	+	0.329843i	1.01515	+	0.329843i
$649$	0.618034			0.618034
$650$	0.863541	+	0.280582i	0.863541	+	0.280582i
$651$		0			0
$652$		0			0
$653$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$653$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$654$		0			0
$655$		0			0
$656$	1.14412	−	0.831254i	1.14412	−	0.831254i
$657$		0			0
$658$		0			0
$659$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$659$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$660$	0.00859303	−	0.0542543i	0.00859303	−	0.0542543i
$661$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$661$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$662$		0			0
$663$		0			0
$664$	−0.299492	+	0.921740i	−0.299492	+	0.921740i
$665$		0			0
$666$		0			0
$667$		0			0
$668$			0.346818i			0.346818i
$669$		0			0
$670$		0			0
$671$	−0.297556	−	0.216187i	−0.297556	−	0.216187i
$672$		0			0
$673$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$673$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$674$	0.561163			0.561163
$675$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$676$	−0.175571			−0.175571
$677$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$677$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.14412	+	0.831254i	−1.14412	+	0.831254i
$682$		0			0
$683$	0.183900	+	0.253116i	0.183900	+	0.253116i	0.891007	−	0.453990i	$-0.150000\pi$
$683$	0.183900	+	0.253116i	0.183900	+	0.253116i	−0.707107	+	0.707107i	$0.750000\pi$
$684$		0			0
$685$	−1.39680	+	0.221232i	−1.39680	+	0.221232i
$686$		0			0
$687$		0			0
$688$	1.43564	−	0.466469i	1.43564	−	0.466469i
$689$		0			0
$690$		0			0
$691$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$691$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.734572	−	1.44168i	0.734572	−	1.44168i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−0.863541	−	0.280582i	−0.863541	−	0.280582i
$703$		0			0
$704$	0.280582	+	0.203854i	0.280582	+	0.203854i
$705$	0.278768	+	1.76007i	0.278768	+	1.76007i
$706$	1.30902	−	0.951057i	1.30902	−	0.951057i
$707$		0			0
$708$	−0.203854	−	0.280582i	−0.203854	−	0.280582i
$709$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$709$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$710$	−0.128969	−	0.253116i	−0.128969	−	0.253116i
$711$		0			0
$712$	−1.43564	+	0.466469i	−1.43564	+	0.466469i
$713$		0			0
$714$		0			0
$715$	−0.0489435	+	0.309017i	−0.0489435	+	0.309017i
$716$		0			0
$717$	0.831254	+	1.14412i	0.831254	+	1.14412i
$718$			1.61803i			1.61803i
$719$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$719$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$720$	0.707107	−	0.360289i	0.707107	−	0.360289i
$721$		0			0
$722$	0.533698	−	0.734572i	0.533698	−	0.734572i
$723$		0			0
$724$	0.284079			0.284079
$725$		0			0
$726$	0.819101			0.819101
$727$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$727$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$728$		0			0
$729$	0.809017	+	0.587785i	0.809017	+	0.587785i
$730$		0			0
$731$		0			0
$732$			0.206396i			0.206396i
$733$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$733$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$734$	−0.533698	−	1.64255i	−0.533698	−	1.64255i
$735$	0.707107	−	0.707107i	0.707107	−	0.707107i
$736$		0			0
$737$		0			0
$738$	1.53884	−	0.500000i	1.53884	−	0.500000i
$739$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$739$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			0.312869i			0.312869i	0.987688	+	0.156434i	$0.0500000\pi$
$743$			0.312869i			0.312869i	−0.987688	+	0.156434i	$0.950000\pi$
$744$		0			0
$745$	1.39680	+	0.221232i	1.39680	+	0.221232i
$746$	−1.18856	−	0.863541i	−1.18856	−	0.863541i
$747$	−0.533698	+	0.734572i	−0.533698	+	0.734572i
$748$		0			0
$749$		0			0
$750$	−0.896802	+	0.142040i	−0.896802	+	0.142040i
$751$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$751$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$752$	−1.34500	−	0.437016i	−1.34500	−	0.437016i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$757$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.550672	+	1.69480i	−0.550672	+	1.69480i	0.156434	+	0.987688i	$0.450000\pi$
$761$	−0.550672	+	1.69480i	−0.550672	+	1.69480i	−0.707107	+	0.707107i	$0.750000\pi$
$762$	0.533698	−	0.173409i	0.533698	−	0.173409i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	0.396802	+	1.22123i	0.396802	+	1.22123i
$767$	1.16110	+	1.59811i	1.16110	+	1.59811i
$768$		−	0.509525i		−	0.509525i
$769$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$769$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.87869	+	0.610425i	1.87869	+	0.610425i	0.987688	+	0.156434i	$0.0500000\pi$
$773$	1.87869	+	0.610425i	1.87869	+	0.610425i	0.891007	+	0.453990i	$0.150000\pi$
$774$	1.72708			1.72708
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	0.156434	−	0.0797073i	0.156434	−	0.0797073i
$781$	0.0791922	−	0.0575365i	0.0791922	−	0.0575365i
$782$		0			0
$783$		0			0
$784$	0.245237	+	0.754763i	0.245237	+	0.754763i
$785$	−0.183900	+	1.16110i	−0.183900	+	1.16110i
$786$		0			0
$787$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$787$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$788$	−0.236142	+	0.0767271i	−0.236142	+	0.0767271i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.196294	+	0.270175i	0.196294	+	0.270175i
$793$		−	1.17557i		−	1.17557i
$794$		0			0
$795$		0			0
$796$	0.270175	+	0.196294i	0.270175	+	0.196294i
$797$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$797$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$798$		0			0
$799$		0			0
$800$	−0.107173	+	0.329843i	−0.107173	+	0.329843i
$801$	−1.41421			−1.41421
$802$	−0.270175	−	0.0877853i	−0.270175	−	0.0877853i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$809$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$810$	0.896802	−	0.142040i	0.896802	−	0.142040i
$811$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$811$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−0.142040	+	0.278768i	−0.142040	+	0.278768i
$821$	−0.734572	−	0.533698i	−0.734572	−	0.533698i	0.156434	−	0.987688i	$-0.450000\pi$
$821$	−0.734572	−	0.533698i	−0.734572	−	0.533698i	−0.891007	+	0.453990i	$0.850000\pi$
$822$	0.754763	−	1.03884i	0.754763	−	1.03884i
$823$	−1.11803	−	0.363271i	−1.11803	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$823$	−1.11803	−	0.363271i	−1.11803	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$824$		0			0
$825$	−0.0966818	−	0.297556i	−0.0966818	−	0.297556i
$826$		0			0
$827$	−0.297556	−	0.0966818i	−0.297556	−	0.0966818i	0.156434	−	0.987688i	$-0.450000\pi$
$827$	−0.297556	−	0.0966818i	−0.297556	−	0.0966818i	−0.453990	+	0.891007i	$0.650000\pi$
$828$		0			0
$829$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$829$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$830$	0.128969	+	0.814279i	0.128969	+	0.814279i
$831$	1.53884	−	1.11803i	1.53884	−	1.11803i
$832$			1.10851i			1.10851i
$833$		0			0
$834$	0.453990	+	1.39724i	0.453990	+	1.39724i
$835$	0.896802	+	1.76007i	0.896802	+	1.76007i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.610425	+	1.87869i	−0.610425	+	1.87869i	−0.156434	+	0.987688i	$0.550000\pi$
$839$	−0.610425	+	1.87869i	−0.610425	+	1.87869i	−0.453990	+	0.891007i	$0.650000\pi$
$840$		0			0
$841$	0.309017	+	0.951057i	0.309017	+	0.951057i
$842$		0			0
$843$			1.97538i			1.97538i
$844$	0.270175	−	0.196294i	0.270175	−	0.196294i
$845$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$846$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$847$		0			0
$848$		0			0
$849$	−1.61803			−1.61803
$850$		0			0
$851$		0			0
$852$	−0.0522421	−	0.0169745i	−0.0522421	−	0.0169745i
$853$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$853$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$	−0.166977	−	0.229825i	−0.166977	−	0.229825i
$859$	−0.587785	−	1.80902i	−0.587785	−	1.80902i	−0.587785	−	0.809017i	$-0.700000\pi$
$859$	−0.587785	−	1.80902i	−0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$860$	−0.236142	+	0.236142i	−0.236142	+	0.236142i
$861$		0			0
$862$	−0.784079	+	0.254763i	−0.784079	+	0.254763i
$863$	−1.69480	+	0.550672i	−1.69480	+	0.550672i	−0.987688	−	0.156434i	$-0.950000\pi$
$863$	−1.69480	+	0.550672i	−1.69480	+	0.550672i	−0.707107	+	0.707107i	$0.750000\pi$
$864$	0.107173	−	0.329843i	0.107173	−	0.329843i
$865$		0			0
$866$	0.453990	+	1.39724i	0.453990	+	1.39724i
$867$	0.587785	+	0.809017i	0.587785	+	0.809017i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$877$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$878$	0.329843	−	0.453990i	0.329843	−	0.453990i
$879$	1.44168	+	1.04744i	1.44168	+	1.04744i
$880$	0.245237	+	0.0388418i	0.245237	+	0.0388418i
$881$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$881$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$882$			0.907981i			0.907981i
$883$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$883$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$884$		0			0
$885$	−1.76007	−	0.896802i	−1.76007	−	0.896802i
$886$		0			0
$887$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$887$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$888$		0			0
$889$		0			0
$890$	−0.907981	+	0.907981i	−0.907981	+	0.907981i
$891$	0.0966818	+	0.297556i	0.0966818	+	0.297556i
$892$		0			0
$893$		0			0
$894$	−1.03884	+	0.754763i	−1.03884	+	0.754763i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.70582	+	0.554254i	1.70582	+	0.554254i
$899$		0			0
$900$	−0.103198	+	0.142040i	−0.103198	+	0.142040i
$901$		0			0
$902$	0.481456	+	0.156434i	0.481456	+	0.156434i
$903$		0			0
$904$		0			0
$905$	1.44168	−	0.734572i	1.44168	−	0.734572i
$906$		0			0
$907$			0.618034i			0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$907$			0.618034i			0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$908$	0.145944	+	0.200874i	0.145944	+	0.200874i
$909$		0			0
$910$		0			0
$911$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$911$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$912$		0			0
$913$	−0.270175	+	0.0877853i	−0.270175	+	0.0877853i
$914$		0			0
$915$	0.533698	+	1.04744i	0.533698	+	1.04744i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.951057	−	0.690983i	0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$919$	0.951057	−	0.690983i	0.951057	−	0.690983i	0.951057	+	0.309017i	$0.100000\pi$
$920$		0			0
$921$		0			0
$922$	1.05425	−	1.45106i	1.05425	−	1.45106i
$923$	0.297556	+	0.0966818i	0.297556	+	0.0966818i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.44168	−	1.04744i	−1.44168	−	1.04744i	−0.987688	−	0.156434i	$-0.950000\pi$
$929$	−1.44168	−	1.04744i	−1.44168	−	1.04744i	−0.453990	−	0.891007i	$-0.650000\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.329843	+	1.01515i	−0.329843	+	1.01515i
$937$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$937$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$938$		0			0
$939$	0.190983	−	0.587785i	0.190983	−	0.587785i
$940$	0.309017	−	0.0489435i	0.309017	−	0.0489435i
$941$	−0.0966818	−	0.297556i	−0.0966818	−	0.297556i	0.891007	−	0.453990i	$-0.150000\pi$
$941$	−0.0966818	−	0.297556i	−0.0966818	−	0.297556i	−0.987688	+	0.156434i	$0.950000\pi$
$942$	−0.627399	−	0.863541i	−0.627399	−	0.863541i
$943$		0			0
$944$	1.26827	−	0.921452i	1.26827	−	0.921452i
$945$		0			0
$946$	0.437153	+	0.317610i	0.437153	+	0.317610i
$947$	−1.16110	+	1.59811i	−1.16110	+	1.59811i	−0.453990	+	0.891007i	$0.650000\pi$
$947$	−1.16110	+	1.59811i	−1.16110	+	1.59811i	−0.707107	+	0.707107i	$0.750000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	0.907981			0.907981
$952$		0			0
$953$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$953$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$954$		0			0
$955$		0			0
$956$	0.200874	−	0.145944i	0.200874	−	0.145944i
$957$		0			0
$958$	1.05425	+	1.45106i	1.05425	+	1.45106i
$959$		0			0
$960$	−0.503252	−	0.987688i	−0.503252	−	0.987688i
$961$	0.309017	−	0.951057i	0.309017	−	0.951057i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$967$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$968$		−	0.962912i		−	0.962912i
$969$		0			0
$970$		0			0
$971$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$971$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$972$	0.103198	−	0.142040i	0.103198	−	0.142040i
$973$		0			0
$974$		0			0
$975$	0.587785	−	0.809017i	0.587785	−	0.809017i
$976$	−0.932938			−0.932938
$977$	−1.87869	−	0.610425i	−1.87869	−	0.610425i	−0.987688	−	0.156434i	$-0.950000\pi$
$977$	−1.87869	−	0.610425i	−1.87869	−	0.610425i	−0.891007	−	0.453990i	$-0.850000\pi$
$978$		0			0
$979$	−0.357960	−	0.260074i	−0.357960	−	0.260074i
$980$	−0.124147	−	0.124147i	−0.124147	−	0.124147i
$981$		0			0
$982$		0			0
$983$	−1.04744	−	1.44168i	−1.04744	−	1.44168i	−0.891007	−	0.453990i	$-0.850000\pi$
$983$	−1.04744	−	1.44168i	−1.04744	−	1.44168i	−0.156434	−	0.987688i	$-0.550000\pi$
$984$	−0.587785	−	1.80902i	−0.587785	−	1.80902i
$985$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	0.253116	+	0.128969i	0.253116	+	0.128969i
$991$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$991$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.87869	+	0.297556i	1.87869	+	0.297556i
$996$	0.128969	+	0.0937016i	0.128969	+	0.0937016i
$997$	−1.11803	+	1.53884i	−1.11803	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$997$	−1.11803	+	1.53884i	−1.11803	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.1.bi.a.779.3	yes	16
3.2	odd	2	inner	975.1.bi.a.779.2	yes	16
13.12	even	2	inner	975.1.bi.a.779.2	yes	16
25.19	even	10	inner	975.1.bi.a.194.3	yes	16
39.38	odd	2	CM	975.1.bi.a.779.3	yes	16
75.44	odd	10	inner	975.1.bi.a.194.2	✓	16
325.194	even	10	inner	975.1.bi.a.194.2	✓	16
975.194	odd	10	inner	975.1.bi.a.194.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.1.bi.a.194.2	✓	16	75.44	odd	10	inner
975.1.bi.a.194.2	✓	16	325.194	even	10	inner
975.1.bi.a.194.3	yes	16	25.19	even	10	inner
975.1.bi.a.194.3	yes	16	975.194	odd	10	inner
975.1.bi.a.779.2	yes	16	3.2	odd	2	inner
975.1.bi.a.779.2	yes	16	13.12	even	2	inner
975.1.bi.a.779.3	yes	16	1.1	even	1	trivial
975.1.bi.a.779.3	yes	16	39.38	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	975.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.863541 + 0.280582i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.142040 - 0.103198i) q^{4} +(-0.987688 - 0.156434i) q^{5} +(0.734572 - 0.533698i) q^{6} +(-0.627399 - 0.863541i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.863541 + 0.280582i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.142040 - 0.103198i) q^{4} +(-0.987688 - 0.156434i) q^{5} +(0.734572 - 0.533698i) q^{6} +(-0.627399 - 0.863541i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.412215i) q^{10} +(0.0966818 - 0.297556i) q^{11} +(-0.166977 + 0.0542543i) q^{12} +(0.951057 - 0.309017i) q^{13} +(-0.707107 + 0.707107i) q^{15} +(-0.245237 - 0.754763i) q^{16} -0.907981i q^{18} +(0.124147 + 0.124147i) q^{20} +(0.166977 - 0.229825i) q^{22} -1.06740 q^{24} +(0.951057 + 0.309017i) q^{25} +0.907981 q^{26} +(-0.951057 - 0.309017i) q^{27} +(-0.809017 + 0.412215i) q^{30} +0.346818i q^{32} +(-0.183900 - 0.253116i) q^{33} +(-0.0542543 + 0.166977i) q^{36} +(0.309017 - 0.951057i) q^{39} +(0.484587 + 0.951057i) q^{40} +(0.550672 + 1.69480i) q^{41} +1.90211i q^{43} +(-0.0444398 + 0.0322874i) q^{44} +(0.156434 + 0.987688i) q^{45} +(1.04744 - 1.44168i) q^{47} +(-0.754763 - 0.245237i) q^{48} -1.00000 q^{49} +(0.734572 + 0.533698i) q^{50} +(-0.166977 - 0.0542543i) q^{52} +(-0.734572 - 0.533698i) q^{54} +(-0.142040 + 0.278768i) q^{55} +(0.610425 + 1.87869i) q^{59} +(0.173409 - 0.0274653i) q^{60} +(0.363271 - 1.11803i) q^{61} +(-0.342548 + 1.05425i) q^{64} +(-0.987688 + 0.156434i) q^{65} +(-0.0877853 - 0.270175i) q^{66} +(0.253116 + 0.183900i) q^{71} +(-0.627399 + 0.863541i) q^{72} +(0.809017 - 0.587785i) q^{75} +(0.533698 - 0.734572i) q^{78} +(0.124147 + 0.783834i) q^{80} +(-0.809017 + 0.587785i) q^{81} +1.61803i q^{82} +(-0.533698 - 0.734572i) q^{83} +(-0.533698 + 1.64255i) q^{86} +(-0.317610 + 0.103198i) q^{88} +(0.437016 - 1.34500i) q^{89} +(-0.142040 + 0.896802i) q^{90} +(1.30902 - 0.951057i) q^{94} +(0.280582 + 0.203854i) q^{96} +(-0.863541 - 0.280582i) q^{98} -0.312869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 4 * q^9	\( 16 q + 4 q^{4} + 4 q^{9} - 4 q^{10} - 16 q^{16} - 4 q^{30} - 4 q^{36} - 4 q^{39} - 20 q^{40} - 16 q^{49} + 4 q^{55} + 16 q^{64} + 8 q^{66} + 4 q^{75} - 4 q^{81} + 20 q^{88} + 4 q^{90} + 12 q^{94}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^9 - 4 * q^10 - 16 * q^16 - 4 * q^30 - 4 * q^36 - 4 * q^39 - 20 * q^40 - 16 * q^49 + 4 * q^55 + 16 * q^64 + 8 * q^66 + 4 * q^75 - 4 * q^81 + 20 * q^88 + 4 * q^90 + 12 * q^94

Introduction

L-functions

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