LMFDB - Embedded newform 2523.1.j.b.605.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2523,1,Mod(605,2523)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2523, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 8]))

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

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

chi := DirichletCharacter("2523.605");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2523 = 3 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2523.j (of order $14$, degree $6$, not 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:	$1.25914102687$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.87.1
Artin image:	$S_3\times C_{28}$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{84} - \cdots)$

Embedding invariants

Embedding label			605.1
Root			$0.781831 + 0.623490i$ of defining polynomial
Character	$\chi$	$=$	2523.605
Dual form			2523.1.j.b.2327.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.974928 - 0.222521i) q^{2} +(0.433884 + 0.900969i) q^{3} +(-0.222521 - 0.974928i) q^{6} +(0.900969 - 0.433884i) q^{7} +(0.781831 + 0.623490i) q^{8} +(-0.623490 + 0.781831i) q^{9} +O(q^{10})$	\(q+(-0.974928 - 0.222521i) q^{2} +(0.433884 + 0.900969i) q^{3} +(-0.222521 - 0.974928i) q^{6} +(0.900969 - 0.433884i) q^{7} +(0.781831 + 0.623490i) q^{8} +(-0.623490 + 0.781831i) q^{9} +(-0.781831 + 0.623490i) q^{11} +(0.623490 + 0.781831i) q^{13} +(-0.974928 + 0.222521i) q^{14} +(-0.623490 - 0.781831i) q^{16} +1.00000i q^{17} +(0.781831 - 0.623490i) q^{18} +(0.781831 + 0.623490i) q^{21} +(0.900969 - 0.433884i) q^{22} +(-0.222521 + 0.974928i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(-0.433884 - 0.900969i) q^{26} +(-0.974928 - 0.222521i) q^{27} +(-0.900969 - 0.433884i) q^{33} +(0.222521 - 0.974928i) q^{34} +(-0.433884 + 0.900969i) q^{39} +2.00000i q^{41} +(-0.623490 - 0.781831i) q^{42} +(0.781831 - 0.623490i) q^{47} +(0.433884 - 0.900969i) q^{48} +(0.781831 + 0.623490i) q^{50} +(-0.900969 + 0.433884i) q^{51} +(0.900969 + 0.433884i) q^{54} +(0.974928 + 0.222521i) q^{56} +(-0.222521 + 0.974928i) q^{63} +(0.222521 + 0.974928i) q^{64} +(0.781831 + 0.623490i) q^{66} +(0.623490 - 0.781831i) q^{67} +(-0.974928 + 0.222521i) q^{72} -1.00000i q^{75} +(-0.433884 + 0.900969i) q^{77} +(0.623490 - 0.781831i) q^{78} +(-0.222521 - 0.974928i) q^{81} +(0.445042 - 1.94986i) q^{82} -1.00000 q^{88} +(-0.974928 - 0.222521i) q^{89} +(0.900969 + 0.433884i) q^{91} +(-0.900969 + 0.433884i) q^{94} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 12 * q - 2 * q^6 + 2 * q^7 + 2 * q^9	$ 12 q - 2 q^{6} + 2 q^{7} + 2 q^{9} - 2 q^{13} + 2 q^{16} + 2 q^{22} - 2 q^{24} - 2 q^{25} - 2 q^{33} + 2 q^{34} + 2 q^{42} - 2 q^{51} + 2 q^{54} - 2 q^{63} + 2 q^{64} - 2 q^{67} - 2 q^{78} - 2 q^{81} + 4 q^{82} - 12 q^{88} + 2 q^{91} - 2 q^{94}+O(q^{100}) $ 12 * q - 2 * q^6 + 2 * q^7 + 2 * q^9 - 2 * q^13 + 2 * q^16 + 2 * q^22 - 2 * q^24 - 2 * q^25 - 2 * q^33 + 2 * q^34 + 2 * q^42 - 2 * q^51 + 2 * q^54 - 2 * q^63 + 2 * q^64 - 2 * q^67 - 2 * q^78 - 2 * q^81 + 4 * q^82 - 12 * q^88 + 2 * q^91 - 2 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2523\mathbb{Z}\right)^\times$.

$n$	$842$	$1684$
$\chi(n)$	$-1$	$e\left(\frac{4}{7}\right)$

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 $

$2$	−0.974928	−	0.222521i	−0.974928	−	0.222521i	−0.294755	−	0.955573i	$-0.595238\pi$
$2$	−0.974928	−	0.222521i	−0.974928	−	0.222521i	−0.680173	+	0.733052i	$0.738095\pi$
$3$	0.433884	+	0.900969i	0.433884	+	0.900969i
$3$	0.433884	+	0.900969i	0.433884	+	0.900969i
$4$		0			0
$5$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$5$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$6$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$7$	0.900969	−	0.433884i	0.900969	−	0.433884i	0.0747301	−	0.997204i	$-0.476190\pi$
$7$	0.900969	−	0.433884i	0.900969	−	0.433884i	0.826239	+	0.563320i	$0.190476\pi$
$8$	0.781831	+	0.623490i	0.781831	+	0.623490i
$9$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$10$		0			0
$11$	−0.781831	+	0.623490i	−0.781831	+	0.623490i	−0.930874	−	0.365341i	$-0.880952\pi$
$11$	−0.781831	+	0.623490i	−0.781831	+	0.623490i	0.149042	+	0.988831i	$0.452381\pi$
$12$		0			0
$13$	0.623490	+	0.781831i	0.623490	+	0.781831i	0.988831	−	0.149042i	$-0.0476190\pi$
$13$	0.623490	+	0.781831i	0.623490	+	0.781831i	−0.365341	+	0.930874i	$0.619048\pi$
$14$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$15$		0			0
$16$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$17$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$17$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$18$	0.781831	−	0.623490i	0.781831	−	0.623490i
$19$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$19$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$20$		0			0
$21$	0.781831	+	0.623490i	0.781831	+	0.623490i
$22$	0.900969	−	0.433884i	0.900969	−	0.433884i
$23$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$23$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$24$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$25$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$26$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$27$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$28$		0			0
$29$		0			0
$29$		0			0
$30$		0			0
$31$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$31$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$32$		0			0
$33$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$34$	0.222521	−	0.974928i	0.222521	−	0.974928i
$35$		0			0
$36$		0			0
$37$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$37$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$38$		0			0
$39$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$40$		0			0
$41$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$41$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$42$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$43$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$43$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.781831	−	0.623490i	0.781831	−	0.623490i	−0.149042	−	0.988831i	$-0.547619\pi$
$47$	0.781831	−	0.623490i	0.781831	−	0.623490i	0.930874	+	0.365341i	$0.119048\pi$
$48$	0.433884	−	0.900969i	0.433884	−	0.900969i
$49$		0			0
$50$	0.781831	+	0.623490i	0.781831	+	0.623490i
$51$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$52$		0			0
$53$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$53$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$54$	0.900969	+	0.433884i	0.900969	+	0.433884i
$55$		0			0
$56$	0.974928	+	0.222521i	0.974928	+	0.222521i
$57$		0			0
$58$		0			0
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$		0			0
$61$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$61$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$62$		0			0
$63$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$64$	0.222521	+	0.974928i	0.222521	+	0.974928i
$65$		0			0
$66$	0.781831	+	0.623490i	0.781831	+	0.623490i
$67$	0.623490	−	0.781831i	0.623490	−	0.781831i	−0.365341	−	0.930874i	$-0.619048\pi$
$67$	0.623490	−	0.781831i	0.623490	−	0.781831i	0.988831	+	0.149042i	$0.0476190\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$71$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$72$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$73$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$73$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$74$		0			0
$75$		−	1.00000i		−	1.00000i
$76$		0			0
$77$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$78$	0.623490	−	0.781831i	0.623490	−	0.781831i
$79$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$79$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$80$		0			0
$81$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$82$	0.445042	−	1.94986i	0.445042	−	1.94986i
$83$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$83$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−1.00000			−1.00000
$89$	−0.974928	−	0.222521i	−0.974928	−	0.222521i	−0.294755	−	0.955573i	$-0.595238\pi$
$89$	−0.974928	−	0.222521i	−0.974928	−	0.222521i	−0.680173	+	0.733052i	$0.738095\pi$
$90$		0			0
$91$	0.900969	+	0.433884i	0.900969	+	0.433884i
$92$		0			0
$93$		0			0
$94$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$95$		0			0
$96$		0			0
$97$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$97$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$98$		0			0
$99$		−	1.00000i		−	1.00000i
$100$		0			0
$101$	0.974928	−	0.222521i	0.974928	−	0.222521i	0.294755	−	0.955573i	$-0.404762\pi$
$101$	0.974928	−	0.222521i	0.974928	−	0.222521i	0.680173	+	0.733052i	$0.261905\pi$
$102$	0.974928	−	0.222521i	0.974928	−	0.222521i
$103$	1.24698	+	1.56366i	1.24698	+	1.56366i	0.623490	+	0.781831i	$0.285714\pi$
$103$	1.24698	+	1.56366i	1.24698	+	1.56366i	0.623490	+	0.781831i	$0.285714\pi$
$104$			1.00000i			1.00000i
$105$		0			0
$106$		0			0
$107$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$107$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$108$		0			0
$109$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.826239	−	0.563320i	$-0.809524\pi$
$109$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.0747301	+	0.997204i	$0.523810\pi$
$110$		0			0
$111$		0			0
$112$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$113$	0.433884	+	0.900969i	0.433884	+	0.900969i	0.997204	+	0.0747301i	$0.0238095\pi$
$113$	0.433884	+	0.900969i	0.433884	+	0.900969i	−0.563320	+	0.826239i	$0.690476\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.00000			−1.00000
$118$		0			0
$119$	0.433884	+	0.900969i	0.433884	+	0.900969i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−1.80194	+	0.867767i	−1.80194	+	0.867767i
$124$		0			0
$125$		0			0
$126$	0.433884	−	0.900969i	0.433884	−	0.900969i
$127$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$127$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$128$		−	1.00000i		−	1.00000i
$129$		0			0
$130$		0			0
$131$	−0.974928	+	0.222521i	−0.974928	+	0.222521i	−0.680173	−	0.733052i	$-0.738095\pi$
$131$	−0.974928	+	0.222521i	−0.974928	+	0.222521i	−0.294755	+	0.955573i	$0.595238\pi$
$132$		0			0
$133$		0			0
$134$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$135$		0			0
$136$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$137$	−1.56366	−	1.24698i	−1.56366	−	1.24698i	−0.781831	−	0.623490i	$-0.785714\pi$
$137$	−1.56366	−	1.24698i	−1.56366	−	1.24698i	−0.781831	−	0.623490i	$-0.785714\pi$
$138$		0			0
$139$	0.222521	+	0.974928i	0.222521	+	0.974928i	0.955573	+	0.294755i	$0.0952381\pi$
$139$	0.222521	+	0.974928i	0.222521	+	0.974928i	−0.733052	+	0.680173i	$0.761905\pi$
$140$		0			0
$141$	0.900969	+	0.433884i	0.900969	+	0.433884i
$142$		0			0
$143$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$144$	1.00000			1.00000
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$149$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$150$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$151$	0.445042	+	1.94986i	0.445042	+	1.94986i	0.222521	+	0.974928i	$0.428571\pi$
$151$	0.445042	+	1.94986i	0.445042	+	1.94986i	0.222521	+	0.974928i	$0.428571\pi$
$152$		0			0
$153$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$154$	0.623490	−	0.781831i	0.623490	−	0.781831i
$155$		0			0
$156$		0			0
$157$		0			0			−	1.00000i	$-0.5\pi$
$157$		0			0				1.00000i	$0.5\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$			1.00000i			1.00000i
$163$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$163$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$167$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$168$	0.222521	+	0.974928i	0.222521	+	0.974928i
$169$		0			0
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$		0			0
$175$	−1.00000			−1.00000
$176$	0.974928	+	0.222521i	0.974928	+	0.222521i
$177$		0			0
$178$	0.900969	+	0.433884i	0.900969	+	0.433884i
$179$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$179$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$180$		0			0
$181$	0.900969	−	0.433884i	0.900969	−	0.433884i	0.0747301	−	0.997204i	$-0.476190\pi$
$181$	0.900969	−	0.433884i	0.900969	−	0.433884i	0.826239	+	0.563320i	$0.190476\pi$
$182$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$188$		0			0
$189$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$190$		0			0
$191$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$191$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$192$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$193$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$193$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$197$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$198$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$199$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.826239	−	0.563320i	$-0.190476\pi$
$199$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.0747301	+	0.997204i	$0.476190\pi$
$200$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$201$	0.974928	+	0.222521i	0.974928	+	0.222521i
$202$	−1.00000			−1.00000
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.867767	−	1.80194i	−0.867767	−	1.80194i
$207$		0			0
$208$	0.222521	−	0.974928i	0.222521	−	0.974928i
$209$		0			0
$210$		0			0
$211$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$211$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$217$		0			0
$218$	0.974928	−	0.222521i	0.974928	−	0.222521i
$219$		0			0
$220$		0			0
$221$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$222$		0			0
$223$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	−0.988831	−	0.149042i	$-0.952381\pi$
$223$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	0.365341	+	0.930874i	$0.380952\pi$
$224$		0			0
$225$	0.900969	−	0.433884i	0.900969	−	0.433884i
$226$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$227$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$227$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$228$		0			0
$229$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$229$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$230$		0			0
$231$	−1.00000			−1.00000
$232$		0			0
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$	0.974928	+	0.222521i	0.974928	+	0.222521i
$235$		0			0
$236$		0			0
$237$		0			0
$238$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$239$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$239$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$240$		0			0
$241$	0.623490	−	0.781831i	0.623490	−	0.781831i	−0.365341	−	0.930874i	$-0.619048\pi$
$241$	0.623490	−	0.781831i	0.623490	−	0.781831i	0.988831	+	0.149042i	$0.0476190\pi$
$242$		0			0
$243$	0.781831	−	0.623490i	0.781831	−	0.623490i
$244$		0			0
$245$		0			0
$246$	1.94986	−	0.445042i	1.94986	−	0.445042i
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.433884	−	0.900969i	0.433884	−	0.900969i	−0.563320	−	0.826239i	$-0.690476\pi$
$251$	0.433884	−	0.900969i	0.433884	−	0.900969i	0.997204	−	0.0747301i	$-0.0238095\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$257$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.00000			1.00000
$263$	1.94986	+	0.445042i	1.94986	+	0.445042i	0.974928	+	0.222521i	$0.0714286\pi$
$263$	1.94986	+	0.445042i	1.94986	+	0.445042i	0.974928	+	0.222521i	$0.0714286\pi$
$264$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$265$		0			0
$266$		0			0
$267$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$268$		0			0
$269$	−0.781831	−	0.623490i	−0.781831	−	0.623490i	0.149042	−	0.988831i	$-0.452381\pi$
$269$	−0.781831	−	0.623490i	−0.781831	−	0.623490i	−0.930874	+	0.365341i	$0.880952\pi$
$270$		0			0
$271$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$271$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$272$	0.781831	−	0.623490i	0.781831	−	0.623490i
$273$			1.00000i			1.00000i
$274$	1.24698	+	1.56366i	1.24698	+	1.56366i
$275$	0.974928	−	0.222521i	0.974928	−	0.222521i
$276$		0			0
$277$	−0.623490	−	0.781831i	−0.623490	−	0.781831i	0.365341	−	0.930874i	$-0.380952\pi$
$277$	−0.623490	−	0.781831i	−0.623490	−	0.781831i	−0.988831	+	0.149042i	$0.952381\pi$
$278$		−	1.00000i		−	1.00000i
$279$		0			0
$280$		0			0
$281$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$281$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$282$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$283$	1.80194	−	0.867767i	1.80194	−	0.867767i	0.900969	−	0.433884i	$-0.142857\pi$
$283$	1.80194	−	0.867767i	1.80194	−	0.867767i	0.900969	−	0.433884i	$-0.142857\pi$
$284$		0			0
$285$		0			0
$286$	0.900969	+	0.433884i	0.900969	+	0.433884i
$287$	0.867767	+	1.80194i	0.867767	+	1.80194i
$288$		0			0
$289$		0			0
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.433884	−	0.900969i	−0.433884	−	0.900969i	−0.997204	−	0.0747301i	$-0.976190\pi$
$293$	−0.433884	−	0.900969i	−0.433884	−	0.900969i	0.563320	−	0.826239i	$-0.309524\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.900969	−	0.433884i	0.900969	−	0.433884i
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		−	2.00000i		−	2.00000i
$303$	0.623490	+	0.781831i	0.623490	+	0.781831i
$304$		0			0
$305$		0			0
$306$	0.623490	+	0.781831i	0.623490	+	0.781831i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$	−0.867767	+	1.80194i	−0.867767	+	1.80194i
$310$		0			0
$311$	0.781831	+	0.623490i	0.781831	+	0.623490i	0.930874	−	0.365341i	$-0.119048\pi$
$311$	0.781831	+	0.623490i	0.781831	+	0.623490i	−0.149042	+	0.988831i	$0.547619\pi$
$312$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$313$	0.222521	+	0.974928i	0.222521	+	0.974928i	0.955573	+	0.294755i	$0.0952381\pi$
$313$	0.222521	+	0.974928i	0.222521	+	0.974928i	−0.733052	+	0.680173i	$0.761905\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.974928	+	0.222521i	0.974928	+	0.222521i	0.680173	−	0.733052i	$-0.261905\pi$
$317$	0.974928	+	0.222521i	0.974928	+	0.222521i	0.294755	+	0.955573i	$0.404762\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$326$		0			0
$327$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$328$	−1.24698	+	1.56366i	−1.24698	+	1.56366i
$329$	0.433884	−	0.900969i	0.433884	−	0.900969i
$330$		0			0
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		−	1.00000i		−	1.00000i
$337$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$337$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$338$		0			0
$339$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		1.00000			$0$
$347$		0			0		−1.00000			$\pi$
$348$		0			0
$349$	2.00000			2.00000			1.00000			$0$
$349$	2.00000			2.00000			1.00000			$0$
$350$	0.974928	+	0.222521i	0.974928	+	0.222521i
$351$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$352$		0			0
$353$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$353$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$358$		0			0
$359$	1.56366	−	1.24698i	1.56366	−	1.24698i	0.781831	−	0.623490i	$-0.214286\pi$
$359$	1.56366	−	1.24698i	1.56366	−	1.24698i	0.781831	−	0.623490i	$-0.214286\pi$
$360$		0			0
$361$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$362$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$367$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$368$		0			0
$369$	−1.56366	−	1.24698i	−1.56366	−	1.24698i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.80194	−	0.867767i	−1.80194	−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$373$	−1.80194	−	0.867767i	−1.80194	−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$374$	0.433884	+	0.900969i	0.433884	+	0.900969i
$375$		0			0
$376$	1.00000			1.00000
$377$		0			0
$378$	1.00000			1.00000
$379$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$379$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$380$		0			0
$381$		0			0
$382$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$383$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$383$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$384$	0.900969	−	0.433884i	0.900969	−	0.433884i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$389$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$397$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$398$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$399$		0			0
$400$	0.222521	+	0.974928i	0.222521	+	0.974928i
$401$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$401$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$402$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$409$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$409$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$410$		0			0
$411$	0.445042	−	1.94986i	0.445042	−	1.94986i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$418$		0			0
$419$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$419$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$420$		0			0
$421$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$421$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$422$		0			0
$423$			1.00000i			1.00000i
$424$		0			0
$425$	0.433884	−	0.900969i	0.433884	−	0.900969i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$430$		0			0
$431$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$431$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$432$	0.433884	+	0.900969i	0.433884	+	0.900969i
$433$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$433$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−0.900969	−	0.433884i	−0.900969	−	0.433884i	−0.0747301	−	0.997204i	$-0.523810\pi$
$439$	−0.900969	−	0.433884i	−0.900969	−	0.433884i	−0.826239	+	0.563320i	$0.809524\pi$
$440$		0			0
$441$		0			0
$442$	0.900969	−	0.433884i	0.900969	−	0.433884i
$443$	−0.781831	−	0.623490i	−0.781831	−	0.623490i	0.149042	−	0.988831i	$-0.452381\pi$
$443$	−0.781831	−	0.623490i	−0.781831	−	0.623490i	−0.930874	+	0.365341i	$0.880952\pi$
$444$		0			0
$445$		0			0
$446$	0.781831	−	0.623490i	0.781831	−	0.623490i
$447$		0			0
$448$	0.623490	+	0.781831i	0.623490	+	0.781831i
$449$	0.974928	−	0.222521i	0.974928	−	0.222521i	0.294755	−	0.955573i	$-0.404762\pi$
$449$	0.974928	−	0.222521i	0.974928	−	0.222521i	0.680173	+	0.733052i	$0.261905\pi$
$450$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$451$	−1.24698	−	1.56366i	−1.24698	−	1.56366i
$452$		0			0
$453$	−1.56366	+	1.24698i	−1.56366	+	1.24698i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.826239	−	0.563320i	$-0.809524\pi$
$457$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.0747301	+	0.997204i	$0.523810\pi$
$458$		0			0
$459$	0.222521	−	0.974928i	0.222521	−	0.974928i
$460$		0			0
$461$	−0.867767	−	1.80194i	−0.867767	−	1.80194i	−0.433884	−	0.900969i	$-0.642857\pi$
$461$	−0.867767	−	1.80194i	−0.867767	−	1.80194i	−0.433884	−	0.900969i	$-0.642857\pi$
$462$	0.974928	+	0.222521i	0.974928	+	0.222521i
$463$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$463$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.867767	+	1.80194i	0.867767	+	1.80194i	0.433884	+	0.900969i	$0.357143\pi$
$467$	0.867767	+	1.80194i	0.867767	+	1.80194i	0.433884	+	0.900969i	$0.357143\pi$
$468$		0			0
$469$	0.222521	−	0.974928i	0.222521	−	0.974928i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.94986	−	0.445042i	1.94986	−	0.445042i	0.974928	−	0.222521i	$-0.0714286\pi$
$479$	1.94986	−	0.445042i	1.94986	−	0.445042i	0.974928	−	0.222521i	$-0.0714286\pi$
$480$		0			0
$481$		0			0
$482$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$483$		0			0
$484$		0			0
$485$		0			0
$486$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$487$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$487$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.94986	−	0.445042i	−1.94986	−	0.445042i	−0.974928	−	0.222521i	$-0.928571\pi$
$491$	−1.94986	−	0.445042i	−1.94986	−	0.445042i	−0.974928	−	0.222521i	$-0.928571\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−0.222521	−	0.974928i	−0.222521	−	0.974928i	−0.955573	−	0.294755i	$-0.904762\pi$
$499$	−0.222521	−	0.974928i	−0.222521	−	0.974928i	0.733052	−	0.680173i	$-0.238095\pi$
$500$		0			0
$501$		0			0
$502$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$503$	−0.433884	+	0.900969i	−0.433884	+	0.900969i	0.563320	+	0.826239i	$0.309524\pi$
$503$	−0.433884	+	0.900969i	−0.433884	+	0.900969i	−0.997204	+	0.0747301i	$0.976190\pi$
$504$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$509$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$510$		0			0
$511$		0			0
$512$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$523$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$524$		0			0
$525$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$526$	−1.80194	−	0.867767i	−1.80194	−	0.867767i
$527$		0			0
$528$	0.222521	+	0.974928i	0.222521	+	0.974928i
$529$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.56366	+	1.24698i	−1.56366	+	1.24698i
$534$			1.00000i			1.00000i
$535$		0			0
$536$	0.974928	−	0.222521i	0.974928	−	0.222521i
$537$		0			0
$538$	0.623490	+	0.781831i	0.623490	+	0.781831i
$539$		0			0
$540$		0			0
$541$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$541$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$542$		0			0
$543$	0.781831	+	0.623490i	0.781831	+	0.623490i
$544$		0			0
$545$		0			0
$546$	0.222521	−	0.974928i	0.222521	−	0.974928i
$547$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.826239	−	0.563320i	$-0.190476\pi$
$547$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.0747301	+	0.997204i	$0.476190\pi$
$548$		0			0
$549$		0			0
$550$	−1.00000			−1.00000
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.433884	+	0.900969i	0.433884	+	0.900969i
$555$		0			0
$556$		0			0
$557$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$557$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.433884	−	0.900969i	0.433884	−	0.900969i
$562$		0			0
$563$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$563$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$564$		0			0
$565$		0			0
$566$	−1.94986	+	0.445042i	−1.94986	+	0.445042i
$567$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$568$		0			0
$569$	0.781831	−	0.623490i	0.781831	−	0.623490i	−0.149042	−	0.988831i	$-0.547619\pi$
$569$	0.781831	−	0.623490i	0.781831	−	0.623490i	0.930874	+	0.365341i	$0.119048\pi$
$570$		0			0
$571$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$571$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$572$		0			0
$573$	1.80194	−	0.867767i	1.80194	−	0.867767i
$574$	−0.445042	−	1.94986i	−0.445042	−	1.94986i
$575$		0			0
$576$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$577$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$577$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	0.222521	+	0.974928i	0.222521	+	0.974928i
$587$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$587$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$593$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$594$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$595$		0			0
$596$		0			0
$597$			1.00000i			1.00000i
$598$		0			0
$599$	0.433884	−	0.900969i	0.433884	−	0.900969i	−0.563320	−	0.826239i	$-0.690476\pi$
$599$	0.433884	−	0.900969i	0.433884	−	0.900969i	0.997204	−	0.0747301i	$-0.0238095\pi$
$600$	0.623490	−	0.781831i	0.623490	−	0.781831i
$601$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$601$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$602$		0			0
$603$	0.222521	+	0.974928i	0.222521	+	0.974928i
$604$		0			0
$605$		0			0
$606$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$607$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$607$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.974928	+	0.222521i	0.974928	+	0.222521i
$612$		0			0
$613$	−0.900969	−	0.433884i	−0.900969	−	0.433884i	−0.0747301	−	0.997204i	$-0.523810\pi$
$613$	−0.900969	−	0.433884i	−0.900969	−	0.433884i	−0.826239	+	0.563320i	$0.809524\pi$
$614$		0			0
$615$		0			0
$616$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$617$	1.56366	+	1.24698i	1.56366	+	1.24698i	0.781831	+	0.623490i	$0.214286\pi$
$617$	1.56366	+	1.24698i	1.56366	+	1.24698i	0.781831	+	0.623490i	$0.214286\pi$
$618$	1.24698	−	1.56366i	1.24698	−	1.56366i
$619$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$619$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$620$		0			0
$621$		0			0
$622$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$623$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$624$	0.974928	−	0.222521i	0.974928	−	0.222521i
$625$	0.623490	+	0.781831i	0.623490	+	0.781831i
$626$		−	1.00000i		−	1.00000i
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.826239	−	0.563320i	$-0.809524\pi$
$631$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.0747301	+	0.997204i	$0.523810\pi$
$632$		0			0
$633$		0			0
$634$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.433884	−	0.900969i	−0.433884	−	0.900969i	−0.997204	−	0.0747301i	$-0.976190\pi$
$641$	−0.433884	−	0.900969i	−0.433884	−	0.900969i	0.563320	−	0.826239i	$-0.309524\pi$
$642$		0			0
$643$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	0.733052	+	0.680173i	$0.238095\pi$
$643$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	−0.955573	+	0.294755i	$0.904762\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$647$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$648$	0.433884	−	0.900969i	0.433884	−	0.900969i
$649$		0			0
$650$			1.00000i			1.00000i
$651$		0			0
$652$		0			0
$653$	−0.974928	+	0.222521i	−0.974928	+	0.222521i	−0.680173	−	0.733052i	$-0.738095\pi$
$653$	−0.974928	+	0.222521i	−0.974928	+	0.222521i	−0.294755	+	0.955573i	$0.595238\pi$
$654$	0.623490	+	0.781831i	0.623490	+	0.781831i
$655$		0			0
$656$	1.56366	−	1.24698i	1.56366	−	1.24698i
$657$		0			0
$658$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$659$	0.781831	+	0.623490i	0.781831	+	0.623490i	0.930874	−	0.365341i	$-0.119048\pi$
$659$	0.781831	+	0.623490i	0.781831	+	0.623490i	−0.149042	+	0.988831i	$0.547619\pi$
$660$		0			0
$661$	0.222521	+	0.974928i	0.222521	+	0.974928i	0.955573	+	0.294755i	$0.0952381\pi$
$661$	0.222521	+	0.974928i	0.222521	+	0.974928i	−0.733052	+	0.680173i	$0.761905\pi$
$662$		0			0
$663$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.222521	−	0.974928i	−0.222521	−	0.974928i	−0.955573	−	0.294755i	$-0.904762\pi$
$673$	−0.222521	−	0.974928i	−0.222521	−	0.974928i	0.733052	−	0.680173i	$-0.238095\pi$
$674$		0			0
$675$	0.781831	+	0.623490i	0.781831	+	0.623490i
$676$		0			0
$677$	−0.433884	+	0.900969i	−0.433884	+	0.900969i	0.563320	+	0.826239i	$0.309524\pi$
$677$	−0.433884	+	0.900969i	−0.433884	+	0.900969i	−0.997204	+	0.0747301i	$0.976190\pi$
$678$	0.781831	−	0.623490i	0.781831	−	0.623490i
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$683$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$684$		0			0
$685$		0			0
$686$	0.433884	−	0.900969i	0.433884	−	0.900969i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.222521	−	0.974928i	0.222521	−	0.974928i	−0.733052	−	0.680173i	$-0.761905\pi$
$691$	0.222521	−	0.974928i	0.222521	−	0.974928i	0.955573	−	0.294755i	$-0.0952381\pi$
$692$		0			0
$693$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.00000			−2.00000
$698$	−1.94986	−	0.445042i	−1.94986	−	0.445042i
$699$		0			0
$700$		0			0
$701$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$701$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$702$	0.222521	+	0.974928i	0.222521	+	0.974928i
$703$		0			0
$704$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$705$		0			0
$706$		0			0
$707$	0.781831	−	0.623490i	0.781831	−	0.623490i
$708$		0			0
$709$	−1.24698	−	1.56366i	−1.24698	−	1.56366i	−0.623490	−	0.781831i	$-0.714286\pi$
$709$	−1.24698	−	1.56366i	−1.24698	−	1.56366i	−0.623490	−	0.781831i	$-0.714286\pi$
$710$		0			0
$711$		0			0
$712$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$713$		0			0
$714$	0.781831	−	0.623490i	0.781831	−	0.623490i
$715$		0			0
$716$		0			0
$717$		0			0
$718$	−1.80194	+	0.867767i	−1.80194	+	0.867767i
$719$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$719$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$720$		0			0
$721$	1.80194	+	0.867767i	1.80194	+	0.867767i
$722$	0.433884	+	0.900969i	0.433884	+	0.900969i
$723$	0.974928	+	0.222521i	0.974928	+	0.222521i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$727$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$728$	0.433884	+	0.900969i	0.433884	+	0.900969i
$729$	0.900969	+	0.433884i	0.900969	+	0.433884i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$733$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			1.00000i			1.00000i
$738$	1.24698	+	1.56366i	1.24698	+	1.56366i
$739$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$739$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.781831	−	0.623490i	0.781831	−	0.623490i	−0.149042	−	0.988831i	$-0.547619\pi$
$743$	0.781831	−	0.623490i	0.781831	−	0.623490i	0.930874	+	0.365341i	$0.119048\pi$
$744$		0			0
$745$		0			0
$746$	1.56366	+	1.24698i	1.56366	+	1.24698i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$751$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$752$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$753$	1.00000			1.00000
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$757$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$761$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$762$		0			0
$763$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$769$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−0.867767	+	1.80194i	−0.867767	+	1.80194i	−0.433884	+	0.900969i	$0.642857\pi$
$773$	−0.867767	+	1.80194i	−0.867767	+	1.80194i	−0.433884	+	0.900969i	$0.642857\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$	0.433884	+	0.900969i	0.433884	+	0.900969i
$787$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$787$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$788$		0			0
$789$	0.445042	+	1.94986i	0.445042	+	1.94986i
$790$		0			0
$791$	0.781831	+	0.623490i	0.781831	+	0.623490i
$792$	0.623490	−	0.781831i	0.623490	−	0.781831i
$793$		0			0
$794$	−1.56366	+	1.24698i	−1.56366	+	1.24698i
$795$		0			0
$796$		0			0
$797$	−1.94986	+	0.445042i	−1.94986	+	0.445042i	−0.974928	+	0.222521i	$0.928571\pi$
$797$	−1.94986	+	0.445042i	−1.94986	+	0.445042i	−0.974928	+	0.222521i	$0.928571\pi$
$798$		0			0
$799$	0.623490	+	0.781831i	0.623490	+	0.781831i
$800$		0			0
$801$	0.781831	−	0.623490i	0.781831	−	0.623490i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.222521	−	0.974928i	0.222521	−	0.974928i
$808$	0.900969	+	0.433884i	0.900969	+	0.433884i
$809$	0.433884	+	0.900969i	0.433884	+	0.900969i	0.997204	+	0.0747301i	$0.0238095\pi$
$809$	0.433884	+	0.900969i	0.433884	+	0.900969i	−0.563320	+	0.826239i	$0.690476\pi$
$810$		0			0
$811$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$811$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.900969	+	0.433884i	0.900969	+	0.433884i
$817$		0			0
$818$		0			0
$819$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$820$		0			0
$821$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$821$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$822$	−0.867767	+	1.80194i	−0.867767	+	1.80194i
$823$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$823$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$824$			2.00000i			2.00000i
$825$	0.623490	+	0.781831i	0.623490	+	0.781831i
$826$		0			0
$827$	1.94986	−	0.445042i	1.94986	−	0.445042i	0.974928	−	0.222521i	$-0.0714286\pi$
$827$	1.94986	−	0.445042i	1.94986	−	0.445042i	0.974928	−	0.222521i	$-0.0714286\pi$
$828$		0			0
$829$		0			0			−	1.00000i	$-0.5\pi$
$829$		0			0				1.00000i	$0.5\pi$
$830$		0			0
$831$	0.433884	−	0.900969i	0.433884	−	0.900969i
$832$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$833$		0			0
$834$	0.900969	−	0.433884i	0.900969	−	0.433884i
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$	0.974928	+	0.222521i	0.974928	+	0.222521i	0.680173	−	0.733052i	$-0.261905\pi$
$839$	0.974928	+	0.222521i	0.974928	+	0.222521i	0.294755	+	0.955573i	$0.404762\pi$
$840$		0			0
$841$		0			0
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$	0.222521	−	0.974928i	0.222521	−	0.974928i
$847$		0			0
$848$		0			0
$849$	1.56366	+	1.24698i	1.56366	+	1.24698i
$850$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$851$		0			0
$852$		0			0
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$857$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$858$			1.00000i			1.00000i
$859$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$859$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$860$		0			0
$861$	−1.24698	+	1.56366i	−1.24698	+	1.56366i
$862$		0			0
$863$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$863$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	1.00000			1.00000
$872$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.80194	+	0.867767i	−1.80194	+	0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$877$	−1.80194	+	0.867767i	−1.80194	+	0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$878$	0.781831	+	0.623490i	0.781831	+	0.623490i
$879$	0.623490	−	0.781831i	0.623490	−	0.781831i
$880$		0			0
$881$	−0.781831	+	0.623490i	−0.781831	+	0.623490i	−0.930874	−	0.365341i	$-0.880952\pi$
$881$	−0.781831	+	0.623490i	−0.781831	+	0.623490i	0.149042	+	0.988831i	$0.452381\pi$
$882$		0			0
$883$	−1.24698	−	1.56366i	−1.24698	−	1.56366i	−0.623490	−	0.781831i	$-0.714286\pi$
$883$	−1.24698	−	1.56366i	−1.24698	−	1.56366i	−0.623490	−	0.781831i	$-0.714286\pi$
$884$		0			0
$885$		0			0
$886$	0.623490	+	0.781831i	0.623490	+	0.781831i
$887$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$887$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.781831	+	0.623490i	0.781831	+	0.623490i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$897$		0			0
$898$	−1.00000			−1.00000
$899$		0			0
$900$		0			0
$901$		0			0
$902$	0.867767	+	1.80194i	0.867767	+	1.80194i
$903$		0			0
$904$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$905$		0			0
$906$	1.80194	−	0.867767i	1.80194	−	0.867767i
$907$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$907$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$908$		0			0
$909$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$910$		0			0
$911$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$911$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$912$		0			0
$913$		0			0
$914$	0.974928	−	0.222521i	0.974928	−	0.222521i
$915$		0			0
$916$		0			0
$917$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$918$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$919$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	−0.988831	−	0.149042i	$-0.952381\pi$
$919$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	0.365341	+	0.930874i	$0.380952\pi$
$920$		0			0
$921$		0			0
$922$	0.445042	+	1.94986i	0.445042	+	1.94986i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$927$	−2.00000			−2.00000
$928$		0			0
$929$		0			0		1.00000			$0$
$929$		0			0		−1.00000			$\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$934$	−0.445042	−	1.94986i	−0.445042	−	1.94986i
$935$		0			0
$936$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$937$	0.623490	−	0.781831i	0.623490	−	0.781831i	−0.365341	−	0.930874i	$-0.619048\pi$
$937$	0.623490	−	0.781831i	0.623490	−	0.781831i	0.988831	+	0.149042i	$0.0476190\pi$
$938$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$939$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$940$		0			0
$941$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$941$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.433884	−	0.900969i	0.433884	−	0.900969i	−0.563320	−	0.826239i	$-0.690476\pi$
$947$	0.433884	−	0.900969i	0.433884	−	0.900969i	0.997204	−	0.0747301i	$-0.0238095\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	0.222521	+	0.974928i	0.222521	+	0.974928i
$952$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$953$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$953$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$	−2.00000			−2.00000
$959$	−1.94986	−	0.445042i	−1.94986	−	0.445042i
$960$		0			0
$961$	0.900969	+	0.433884i	0.900969	+	0.433884i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$967$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.94986	+	0.445042i	−1.94986	+	0.445042i	−0.974928	+	0.222521i	$0.928571\pi$
$971$	−1.94986	+	0.445042i	−1.94986	+	0.445042i	−0.974928	+	0.222521i	$0.928571\pi$
$972$		0			0
$973$	0.623490	+	0.781831i	0.623490	+	0.781831i
$974$			2.00000i			2.00000i
$975$	0.781831	−	0.623490i	0.781831	−	0.623490i
$976$		0			0
$977$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$977$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$978$		0			0
$979$	0.900969	−	0.433884i	0.900969	−	0.433884i
$980$		0			0
$981$	0.222521	−	0.974928i	0.222521	−	0.974928i
$982$	1.80194	+	0.867767i	1.80194	+	0.867767i
$983$	−0.867767	−	1.80194i	−0.867767	−	1.80194i	−0.433884	−	0.900969i	$-0.642857\pi$
$983$	−0.867767	−	1.80194i	−0.867767	−	1.80194i	−0.433884	−	0.900969i	$-0.642857\pi$
$984$	−1.94986	−	0.445042i	−1.94986	−	0.445042i
$985$		0			0
$986$		0			0
$987$	1.00000			1.00000
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	0.733052	+	0.680173i	$0.238095\pi$
$991$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	−0.955573	+	0.294755i	$0.904762\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$997$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$998$			1.00000i			1.00000i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2523.1.j.b.605.1		12
3.2	odd	2	inner	2523.1.j.b.605.2		12
29.2	odd	28		2523.1.h.a.2333.1		6
29.3	odd	28		2523.1.h.a.1037.1		6
29.4	even	14	inner	2523.1.j.b.1415.1		12
29.5	even	14	inner	2523.1.j.b.1031.1		12
29.6	even	14		2523.1.b.b.842.1		2
29.7	even	7	inner	2523.1.j.b.2327.2		12
29.8	odd	28		2523.1.h.b.1745.1		6
29.9	even	14	inner	2523.1.j.b.1619.2		12
29.10	odd	28		2523.1.h.b.1949.1		6
29.11	odd	28		2523.1.h.a.1952.1		6
29.12	odd	4		2523.1.h.b.236.1		6
29.13	even	14	inner	2523.1.j.b.1412.2		12
29.14	odd	28		87.1.d.b.86.1	yes	1
29.15	odd	28		87.1.d.a.86.1	✓	1
29.16	even	7	inner	2523.1.j.b.1412.1		12
29.17	odd	4		2523.1.h.a.236.1		6
29.18	odd	28		2523.1.h.b.1952.1		6
29.19	odd	28		2523.1.h.a.1949.1		6
29.20	even	7	inner	2523.1.j.b.1619.1		12
29.21	odd	28		2523.1.h.a.1745.1		6
29.22	even	14	inner	2523.1.j.b.2327.1		12
29.23	even	7		2523.1.b.b.842.2		2
29.24	even	7	inner	2523.1.j.b.1031.2		12
29.25	even	7	inner	2523.1.j.b.1415.2		12
29.26	odd	28		2523.1.h.b.1037.1		6
29.27	odd	28		2523.1.h.b.2333.1		6
29.28	even	2	inner	2523.1.j.b.605.2		12
87.2	even	28		2523.1.h.b.2333.1		6
87.5	odd	14	inner	2523.1.j.b.1031.2		12
87.8	even	28		2523.1.h.a.1745.1		6
87.11	even	28		2523.1.h.b.1952.1		6
87.14	even	28		87.1.d.a.86.1	✓	1
87.17	even	4		2523.1.h.b.236.1		6
87.20	odd	14	inner	2523.1.j.b.1619.2		12
87.23	odd	14		2523.1.b.b.842.1		2
87.26	even	28		2523.1.h.a.1037.1		6
87.32	even	28		2523.1.h.b.1037.1		6
87.35	odd	14		2523.1.b.b.842.2		2
87.38	odd	14	inner	2523.1.j.b.1619.1		12
87.41	even	4		2523.1.h.a.236.1		6
87.44	even	28		87.1.d.b.86.1	yes	1
87.47	even	28		2523.1.h.a.1952.1		6
87.50	even	28		2523.1.h.b.1745.1		6
87.53	odd	14	inner	2523.1.j.b.1031.1		12
87.56	even	28		2523.1.h.a.2333.1		6
87.62	odd	14	inner	2523.1.j.b.1415.2		12
87.65	odd	14	inner	2523.1.j.b.2327.1		12
87.68	even	28		2523.1.h.a.1949.1		6
87.71	odd	14	inner	2523.1.j.b.1412.1		12
87.74	odd	14	inner	2523.1.j.b.1412.2		12
87.77	even	28		2523.1.h.b.1949.1		6
87.80	odd	14	inner	2523.1.j.b.2327.2		12
87.83	odd	14	inner	2523.1.j.b.1415.1		12
87.86	odd	2	CM	2523.1.j.b.605.1		12
116.15	even	28		1392.1.i.a.1217.1		1
116.43	even	28		1392.1.i.b.1217.1		1
145.14	odd	28		2175.1.h.a.1826.1		1
145.43	even	28		2175.1.b.b.2174.1		2
145.44	odd	28		2175.1.h.b.1826.1		1
145.72	even	28		2175.1.b.b.2174.2		2
145.73	even	28		2175.1.b.a.2174.2		2
145.102	even	28		2175.1.b.a.2174.1		2
261.14	even	84		2349.1.h.b.1565.1		2
261.43	odd	84		2349.1.h.a.782.1		2
261.101	even	84		2349.1.h.b.782.1		2
261.130	odd	84		2349.1.h.a.1565.1		2
261.131	even	84		2349.1.h.a.1565.1		2
261.160	odd	84		2349.1.h.b.782.1		2
261.218	even	84		2349.1.h.a.782.1		2
261.247	odd	84		2349.1.h.b.1565.1		2
348.131	odd	28		1392.1.i.b.1217.1		1
348.275	odd	28		1392.1.i.a.1217.1		1
435.14	even	28		2175.1.h.b.1826.1		1
435.44	even	28		2175.1.h.a.1826.1		1
435.188	odd	28		2175.1.b.a.2174.2		2
435.218	odd	28		2175.1.b.b.2174.1		2
435.362	odd	28		2175.1.b.a.2174.1		2
435.392	odd	28		2175.1.b.b.2174.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.1.d.a.86.1	✓	1	29.15	odd	28
87.1.d.a.86.1	✓	1	87.14	even	28
87.1.d.b.86.1	yes	1	29.14	odd	28
87.1.d.b.86.1	yes	1	87.44	even	28
1392.1.i.a.1217.1		1	116.15	even	28
1392.1.i.a.1217.1		1	348.275	odd	28
1392.1.i.b.1217.1		1	116.43	even	28
1392.1.i.b.1217.1		1	348.131	odd	28
2175.1.b.a.2174.1		2	145.102	even	28
2175.1.b.a.2174.1		2	435.362	odd	28
2175.1.b.a.2174.2		2	145.73	even	28
2175.1.b.a.2174.2		2	435.188	odd	28
2175.1.b.b.2174.1		2	145.43	even	28
2175.1.b.b.2174.1		2	435.218	odd	28
2175.1.b.b.2174.2		2	145.72	even	28
2175.1.b.b.2174.2		2	435.392	odd	28
2175.1.h.a.1826.1		1	145.14	odd	28
2175.1.h.a.1826.1		1	435.44	even	28
2175.1.h.b.1826.1		1	145.44	odd	28
2175.1.h.b.1826.1		1	435.14	even	28
2349.1.h.a.782.1		2	261.43	odd	84
2349.1.h.a.782.1		2	261.218	even	84
2349.1.h.a.1565.1		2	261.130	odd	84
2349.1.h.a.1565.1		2	261.131	even	84
2349.1.h.b.782.1		2	261.101	even	84
2349.1.h.b.782.1		2	261.160	odd	84
2349.1.h.b.1565.1		2	261.14	even	84
2349.1.h.b.1565.1		2	261.247	odd	84
2523.1.b.b.842.1		2	29.6	even	14
2523.1.b.b.842.1		2	87.23	odd	14
2523.1.b.b.842.2		2	29.23	even	7
2523.1.b.b.842.2		2	87.35	odd	14
2523.1.h.a.236.1		6	29.17	odd	4
2523.1.h.a.236.1		6	87.41	even	4
2523.1.h.a.1037.1		6	29.3	odd	28
2523.1.h.a.1037.1		6	87.26	even	28
2523.1.h.a.1745.1		6	29.21	odd	28
2523.1.h.a.1745.1		6	87.8	even	28
2523.1.h.a.1949.1		6	29.19	odd	28
2523.1.h.a.1949.1		6	87.68	even	28
2523.1.h.a.1952.1		6	29.11	odd	28
2523.1.h.a.1952.1		6	87.47	even	28
2523.1.h.a.2333.1		6	29.2	odd	28
2523.1.h.a.2333.1		6	87.56	even	28
2523.1.h.b.236.1		6	29.12	odd	4
2523.1.h.b.236.1		6	87.17	even	4
2523.1.h.b.1037.1		6	29.26	odd	28
2523.1.h.b.1037.1		6	87.32	even	28
2523.1.h.b.1745.1		6	29.8	odd	28
2523.1.h.b.1745.1		6	87.50	even	28
2523.1.h.b.1949.1		6	29.10	odd	28
2523.1.h.b.1949.1		6	87.77	even	28
2523.1.h.b.1952.1		6	29.18	odd	28
2523.1.h.b.1952.1		6	87.11	even	28
2523.1.h.b.2333.1		6	29.27	odd	28
2523.1.h.b.2333.1		6	87.2	even	28
2523.1.j.b.605.1		12	1.1	even	1	trivial
2523.1.j.b.605.1		12	87.86	odd	2	CM
2523.1.j.b.605.2		12	3.2	odd	2	inner
2523.1.j.b.605.2		12	29.28	even	2	inner
2523.1.j.b.1031.1		12	29.5	even	14	inner
2523.1.j.b.1031.1		12	87.53	odd	14	inner
2523.1.j.b.1031.2		12	29.24	even	7	inner
2523.1.j.b.1031.2		12	87.5	odd	14	inner
2523.1.j.b.1412.1		12	29.16	even	7	inner
2523.1.j.b.1412.1		12	87.71	odd	14	inner
2523.1.j.b.1412.2		12	29.13	even	14	inner
2523.1.j.b.1412.2		12	87.74	odd	14	inner
2523.1.j.b.1415.1		12	29.4	even	14	inner
2523.1.j.b.1415.1		12	87.83	odd	14	inner
2523.1.j.b.1415.2		12	29.25	even	7	inner
2523.1.j.b.1415.2		12	87.62	odd	14	inner
2523.1.j.b.1619.1		12	29.20	even	7	inner
2523.1.j.b.1619.1		12	87.38	odd	14	inner
2523.1.j.b.1619.2		12	29.9	even	14	inner
2523.1.j.b.1619.2		12	87.20	odd	14	inner
2523.1.j.b.2327.1		12	29.22	even	14	inner
2523.1.j.b.2327.1		12	87.65	odd	14	inner
2523.1.j.b.2327.2		12	29.7	even	7	inner
2523.1.j.b.2327.2		12	87.80	odd	14	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:	\( N \)	\(=\)	\( 2523 = 3 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2523.j (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.974928 - 0.222521i) q^{2} +(0.433884 + 0.900969i) q^{3} +(-0.222521 - 0.974928i) q^{6} +(0.900969 - 0.433884i) q^{7} +(0.781831 + 0.623490i) q^{8} +(-0.623490 + 0.781831i) q^{9} +O(q^{10})\)	\(q+(-0.974928 - 0.222521i) q^{2} +(0.433884 + 0.900969i) q^{3} +(-0.222521 - 0.974928i) q^{6} +(0.900969 - 0.433884i) q^{7} +(0.781831 + 0.623490i) q^{8} +(-0.623490 + 0.781831i) q^{9} +(-0.781831 + 0.623490i) q^{11} +(0.623490 + 0.781831i) q^{13} +(-0.974928 + 0.222521i) q^{14} +(-0.623490 - 0.781831i) q^{16} +1.00000i q^{17} +(0.781831 - 0.623490i) q^{18} +(0.781831 + 0.623490i) q^{21} +(0.900969 - 0.433884i) q^{22} +(-0.222521 + 0.974928i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(-0.433884 - 0.900969i) q^{26} +(-0.974928 - 0.222521i) q^{27} +(-0.900969 - 0.433884i) q^{33} +(0.222521 - 0.974928i) q^{34} +(-0.433884 + 0.900969i) q^{39} +2.00000i q^{41} +(-0.623490 - 0.781831i) q^{42} +(0.781831 - 0.623490i) q^{47} +(0.433884 - 0.900969i) q^{48} +(0.781831 + 0.623490i) q^{50} +(-0.900969 + 0.433884i) q^{51} +(0.900969 + 0.433884i) q^{54} +(0.974928 + 0.222521i) q^{56} +(-0.222521 + 0.974928i) q^{63} +(0.222521 + 0.974928i) q^{64} +(0.781831 + 0.623490i) q^{66} +(0.623490 - 0.781831i) q^{67} +(-0.974928 + 0.222521i) q^{72} -1.00000i q^{75} +(-0.433884 + 0.900969i) q^{77} +(0.623490 - 0.781831i) q^{78} +(-0.222521 - 0.974928i) q^{81} +(0.445042 - 1.94986i) q^{82} -1.00000 q^{88} +(-0.974928 - 0.222521i) q^{89} +(0.900969 + 0.433884i) q^{91} +(-0.900969 + 0.433884i) q^{94} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 12 * q - 2 * q^6 + 2 * q^7 + 2 * q^9	\( 12 q - 2 q^{6} + 2 q^{7} + 2 q^{9} - 2 q^{13} + 2 q^{16} + 2 q^{22} - 2 q^{24} - 2 q^{25} - 2 q^{33} + 2 q^{34} + 2 q^{42} - 2 q^{51} + 2 q^{54} - 2 q^{63} + 2 q^{64} - 2 q^{67} - 2 q^{78} - 2 q^{81} + 4 q^{82} - 12 q^{88} + 2 q^{91} - 2 q^{94}+O(q^{100}) \) 12 * q - 2 * q^6 + 2 * q^7 + 2 * q^9 - 2 * q^13 + 2 * q^16 + 2 * q^22 - 2 * q^24 - 2 * q^25 - 2 * q^33 + 2 * q^34 + 2 * q^42 - 2 * q^51 + 2 * q^54 - 2 * q^63 + 2 * q^64 - 2 * q^67 - 2 * q^78 - 2 * q^81 + 4 * q^82 - 12 * q^88 + 2 * q^91 - 2 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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