LMFDB - Embedded newform 2523.1.h.c.1037.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2523,1,Mod(236,2523)]

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, 1]))

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

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

chi := DirichletCharacter("2523.236");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2523 = 3 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2523.h (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:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Coefficient field:	24.0.326829122755018756096000000000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - 3 x^{22} + 8 x^{20} - 21 x^{18} + 55 x^{16} - 144 x^{14} + 377 x^{12} - 144 x^{10} + 55 x^{8} + \cdots + 1 $ x^24 - 3x^22 + 8x^20 - 21x^18 + 55x^16 - 144x^14 + 377x^12 - 144x^10 + 55x^8 - 21x^6 + 8x^4 - 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{5}$
Projective field:	Galois closure of 5.1.6365529.1

Embedding invariants

Embedding label			1037.2
Root			$-0.268155 + 0.556829i$ of defining polynomial
Character	$\chi$	$=$	2523.1037
Dual form			2523.1.h.c.236.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.433884 + 0.900969i) q^{3} +(0.900969 - 0.433884i) q^{4} +(1.45780 + 0.702039i) q^{7} +(-0.623490 - 0.781831i) q^{9} +O(q^{10})$	$q+(-0.433884 + 0.900969i) q^{3} +(0.900969 - 0.433884i) q^{4} +(1.45780 + 0.702039i) q^{7} +(-0.623490 - 0.781831i) q^{9} +1.00000i q^{12} +(-0.385338 + 0.483198i) q^{13} +(0.623490 - 0.781831i) q^{16} +(0.268155 + 0.556829i) q^{19} +(-1.26503 + 1.00883i) q^{21} +(-0.900969 + 0.433884i) q^{25} +(0.974928 - 0.222521i) q^{27} +1.61803 q^{28} +(1.57747 - 0.360046i) q^{31} +(-0.900969 - 0.433884i) q^{36} +(-0.483198 + 0.385338i) q^{37} +(-0.268155 - 0.556829i) q^{39} +(-1.57747 - 0.360046i) q^{43} +(0.433884 + 0.900969i) q^{48} +(1.00883 + 1.26503i) q^{49} +(-0.137526 + 0.602539i) q^{52} -0.618034 q^{57} +(0.702039 - 1.45780i) q^{61} +(-0.360046 - 1.57747i) q^{63} +(0.222521 - 0.974928i) q^{64} +(-0.385338 - 0.483198i) q^{67} +(-0.602539 - 0.137526i) q^{73} -1.00000i q^{75} +(0.483198 + 0.385338i) q^{76} +(0.483198 - 0.385338i) q^{79} +(-0.222521 + 0.974928i) q^{81} +(-0.702039 + 1.45780i) q^{84} +(-0.900969 + 0.433884i) q^{91} +(-0.360046 + 1.57747i) q^{93} +(0.702039 + 1.45780i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} + 2 q^{7} + 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^4 + 2 * q^7 + 4 * q^9	$ 24 q + 4 q^{4} + 2 q^{7} + 4 q^{9} - 2 q^{13} - 4 q^{16} - 4 q^{25} + 12 q^{28} - 4 q^{36} - 2 q^{49} + 2 q^{52} + 12 q^{57} - 2 q^{63} + 4 q^{64} - 2 q^{67} - 4 q^{81} - 4 q^{91} - 2 q^{93}+O(q^{100}) $ 24 * q + 4 * q^4 + 2 * q^7 + 4 * q^9 - 2 * q^13 - 4 * q^16 - 4 * q^25 + 12 * q^28 - 4 * q^36 - 2 * q^49 + 2 * q^52 + 12 * q^57 - 2 * q^63 + 4 * q^64 - 2 * q^67 - 4 * q^81 - 4 * q^91 - 2 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$842$	$1684$
$\chi(n)$	$-1$	$e\left(\frac{13}{14}\right)$

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			0		0.974928	−	0.222521i	$-0.0714286\pi$
$2$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$3$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$3$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$4$	0.900969	−	0.433884i	0.900969	−	0.433884i
$5$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$5$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$6$		0			0
$7$	1.45780	+	0.702039i	1.45780	+	0.702039i	0.983930	−	0.178557i	$-0.0571429\pi$
$7$	1.45780	+	0.702039i	1.45780	+	0.702039i	0.473869	+	0.880596i	$0.342857\pi$
$8$		0			0
$9$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$10$		0			0
$11$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$11$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$12$			1.00000i			1.00000i
$13$	−0.385338	+	0.483198i	−0.385338	+	0.483198i	−0.936235	−	0.351375i	$-0.885714\pi$
$13$	−0.385338	+	0.483198i	−0.385338	+	0.483198i	0.550897	+	0.834573i	$0.314286\pi$
$14$		0			0
$15$		0			0
$16$	0.623490	−	0.781831i	0.623490	−	0.781831i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$	0.268155	+	0.556829i	0.268155	+	0.556829i	0.990950	−	0.134233i	$-0.0428571\pi$
$19$	0.268155	+	0.556829i	0.268155	+	0.556829i	−0.722795	+	0.691063i	$0.757143\pi$
$20$		0			0
$21$	−1.26503	+	1.00883i	−1.26503	+	1.00883i
$22$		0			0
$23$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$23$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$24$		0			0
$25$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$26$		0			0
$27$	0.974928	−	0.222521i	0.974928	−	0.222521i
$28$	1.61803			1.61803
$29$		0			0
$29$		0			0
$30$		0			0
$31$	1.57747	−	0.360046i	1.57747	−	0.360046i	0.657939	−	0.753071i	$-0.271429\pi$
$31$	1.57747	−	0.360046i	1.57747	−	0.360046i	0.919528	+	0.393025i	$0.128571\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$37$	−0.483198	+	0.385338i	−0.483198	+	0.385338i	−0.834573	−	0.550897i	$-0.814286\pi$
$37$	−0.483198	+	0.385338i	−0.483198	+	0.385338i	0.351375	+	0.936235i	$0.385714\pi$
$38$		0			0
$39$	−0.268155	−	0.556829i	−0.268155	−	0.556829i
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	−1.57747	−	0.360046i	−1.57747	−	0.360046i	−0.657939	−	0.753071i	$-0.728571\pi$
$43$	−1.57747	−	0.360046i	−1.57747	−	0.360046i	−0.919528	+	0.393025i	$0.871429\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$47$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$48$	0.433884	+	0.900969i	0.433884	+	0.900969i
$49$	1.00883	+	1.26503i	1.00883	+	1.26503i
$50$		0			0
$51$		0			0
$52$	−0.137526	+	0.602539i	−0.137526	+	0.602539i
$53$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$53$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.618034			−0.618034
$58$		0			0
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$		0			0
$61$	0.702039	−	1.45780i	0.702039	−	1.45780i	−0.178557	−	0.983930i	$-0.557143\pi$
$61$	0.702039	−	1.45780i	0.702039	−	1.45780i	0.880596	−	0.473869i	$-0.157143\pi$
$62$		0			0
$63$	−0.360046	−	1.57747i	−0.360046	−	1.57747i
$64$	0.222521	−	0.974928i	0.222521	−	0.974928i
$65$		0			0
$66$		0			0
$67$	−0.385338	−	0.483198i	−0.385338	−	0.483198i	0.550897	−	0.834573i	$-0.314286\pi$
$67$	−0.385338	−	0.483198i	−0.385338	−	0.483198i	−0.936235	+	0.351375i	$0.885714\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$71$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$72$		0			0
$73$	−0.602539	−	0.137526i	−0.602539	−	0.137526i	−0.0896393	−	0.995974i	$-0.528571\pi$
$73$	−0.602539	−	0.137526i	−0.602539	−	0.137526i	−0.512899	+	0.858449i	$0.671429\pi$
$74$		0			0
$75$		−	1.00000i		−	1.00000i
$76$	0.483198	+	0.385338i	0.483198	+	0.385338i
$77$		0			0
$78$		0			0
$79$	0.483198	−	0.385338i	0.483198	−	0.385338i	−0.351375	−	0.936235i	$-0.614286\pi$
$79$	0.483198	−	0.385338i	0.483198	−	0.385338i	0.834573	+	0.550897i	$0.185714\pi$
$80$		0			0
$81$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$82$		0			0
$83$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$83$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$84$	−0.702039	+	1.45780i	−0.702039	+	1.45780i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$89$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$90$		0			0
$91$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$92$		0			0
$93$	−0.360046	+	1.57747i	−0.360046	+	1.57747i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.702039	+	1.45780i	0.702039	+	1.45780i	0.880596	+	0.473869i	$0.157143\pi$
$97$	0.702039	+	1.45780i	0.702039	+	1.45780i	−0.178557	+	0.983930i	$0.557143\pi$
$98$		0			0
$99$		0			0
$100$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$101$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$101$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$102$		0			0
$103$	−1.00883	+	1.26503i	−1.00883	+	1.26503i	−0.0448648	+	0.998993i	$0.514286\pi$
$103$	−1.00883	+	1.26503i	−1.00883	+	1.26503i	−0.963963	+	0.266037i	$0.914286\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$107$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$108$	0.781831	−	0.623490i	0.781831	−	0.623490i
$109$	−1.45780	−	0.702039i	−1.45780	−	0.702039i	−0.473869	−	0.880596i	$-0.657143\pi$
$109$	−1.45780	−	0.702039i	−1.45780	−	0.702039i	−0.983930	+	0.178557i	$0.942857\pi$
$110$		0			0
$111$	−0.137526	−	0.602539i	−0.137526	−	0.602539i
$112$	1.45780	−	0.702039i	1.45780	−	0.702039i
$113$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$113$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.618034			0.618034
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.222521	+	0.974928i	0.222521	+	0.974928i
$122$		0			0
$123$		0			0
$124$	1.26503	−	1.00883i	1.26503	−	1.00883i
$125$		0			0
$126$		0			0
$127$	1.26503	+	1.00883i	1.26503	+	1.00883i	0.998993	+	0.0448648i	$0.0142857\pi$
$127$	1.26503	+	1.00883i	1.26503	+	1.00883i	0.266037	+	0.963963i	$0.414286\pi$
$128$		0			0
$129$	1.00883	−	1.26503i	1.00883	−	1.26503i
$130$		0			0
$131$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$131$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$132$		0			0
$133$			1.00000i			1.00000i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$137$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$138$		0			0
$139$	0.360046	−	1.57747i	0.360046	−	1.57747i	−0.393025	−	0.919528i	$-0.628571\pi$
$139$	0.360046	−	1.57747i	0.360046	−	1.57747i	0.753071	−	0.657939i	$-0.228571\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−1.00000			−1.00000
$145$		0			0
$146$		0			0
$147$	−1.57747	+	0.360046i	−1.57747	+	0.360046i
$148$	−0.268155	+	0.556829i	−0.268155	+	0.556829i
$149$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$149$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$150$		0			0
$151$	0.137526	−	0.602539i	0.137526	−	0.602539i	−0.858449	−	0.512899i	$-0.828571\pi$
$151$	0.137526	−	0.602539i	0.137526	−	0.602539i	0.995974	−	0.0896393i	$-0.0285714\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.483198	−	0.385338i	−0.483198	−	0.385338i
$157$			0.618034i			0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$157$			0.618034i			0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.26503	−	1.00883i	−1.26503	−	1.00883i	−0.998993	−	0.0448648i	$-0.985714\pi$
$163$	−1.26503	−	1.00883i	−1.26503	−	1.00883i	−0.266037	−	0.963963i	$-0.585714\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$167$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$168$		0			0
$169$	0.137526	+	0.602539i	0.137526	+	0.602539i
$170$		0			0
$171$	0.268155	−	0.556829i	0.268155	−	0.556829i
$172$	−1.57747	+	0.360046i	−1.57747	+	0.360046i
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$		0			0
$175$	−1.61803			−1.61803
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$179$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$180$		0			0
$181$	−0.556829	−	0.268155i	−0.556829	−	0.268155i	0.134233	−	0.990950i	$-0.457143\pi$
$181$	−0.556829	−	0.268155i	−0.556829	−	0.268155i	−0.691063	+	0.722795i	$0.742857\pi$
$182$		0			0
$183$	1.00883	+	1.26503i	1.00883	+	1.26503i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	1.57747	+	0.360046i	1.57747	+	0.360046i
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	0.781831	+	0.623490i	0.781831	+	0.623490i
$193$	−0.702039	−	1.45780i	−0.702039	−	1.45780i	−0.880596	−	0.473869i	$-0.842857\pi$
$193$	−0.702039	−	1.45780i	−0.702039	−	1.45780i	0.178557	−	0.983930i	$-0.442857\pi$
$194$		0			0
$195$		0			0
$196$	1.45780	+	0.702039i	1.45780	+	0.702039i
$197$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$197$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$198$		0			0
$199$	−0.556829	+	0.268155i	−0.556829	+	0.268155i	−0.691063	−	0.722795i	$-0.742857\pi$
$199$	−0.556829	+	0.268155i	−0.556829	+	0.268155i	0.134233	+	0.990950i	$0.457143\pi$
$200$		0			0
$201$	0.602539	−	0.137526i	0.602539	−	0.137526i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	0.137526	+	0.602539i	0.137526	+	0.602539i
$209$		0			0
$210$		0			0
$211$	−1.56366	+	1.24698i	−1.56366	+	1.24698i	−0.781831	+	0.623490i	$0.785714\pi$
$211$	−1.56366	+	1.24698i	−1.56366	+	1.24698i	−0.781831	+	0.623490i	$0.785714\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	2.55239	+	0.582567i	2.55239	+	0.582567i
$218$		0			0
$219$	0.385338	−	0.483198i	0.385338	−	0.483198i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−1.00883	−	1.26503i	−1.00883	−	1.26503i	−0.963963	−	0.266037i	$-0.914286\pi$
$223$	−1.00883	−	1.26503i	−1.00883	−	1.26503i	−0.0448648	−	0.998993i	$-0.514286\pi$
$224$		0			0
$225$	0.900969	+	0.433884i	0.900969	+	0.433884i
$226$		0			0
$227$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$227$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$228$	−0.556829	+	0.268155i	−0.556829	+	0.268155i
$229$	0.867767	−	1.80194i	0.867767	−	1.80194i	0.433884	−	0.900969i	$-0.357143\pi$
$229$	0.867767	−	1.80194i	0.867767	−	1.80194i	0.433884	−	0.900969i	$-0.357143\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.137526	+	0.602539i	0.137526	+	0.602539i
$238$		0			0
$239$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$239$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$240$		0			0
$241$	1.00883	+	1.26503i	1.00883	+	1.26503i	0.963963	+	0.266037i	$0.0857143\pi$
$241$	1.00883	+	1.26503i	1.00883	+	1.26503i	0.0448648	+	0.998993i	$0.485714\pi$
$242$		0			0
$243$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$244$		−	1.61803i		−	1.61803i
$245$		0			0
$246$		0			0
$247$	−0.372389	−	0.0849954i	−0.372389	−	0.0849954i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$251$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$252$	−1.00883	−	1.26503i	−1.00883	−	1.26503i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$257$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$257$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$258$		0			0
$259$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$263$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.556829	−	0.268155i	−0.556829	−	0.268155i
$269$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$269$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$270$		0			0
$271$	−0.867767	−	1.80194i	−0.867767	−	1.80194i	−0.433884	−	0.900969i	$-0.642857\pi$
$271$	−0.867767	−	1.80194i	−0.867767	−	1.80194i	−0.433884	−	0.900969i	$-0.642857\pi$
$272$		0			0
$273$		−	1.00000i		−	1.00000i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	0.385338	−	0.483198i	0.385338	−	0.483198i	−0.550897	−	0.834573i	$-0.685714\pi$
$277$	0.385338	−	0.483198i	0.385338	−	0.483198i	0.936235	+	0.351375i	$0.114286\pi$
$278$		0			0
$279$	−1.26503	−	1.00883i	−1.26503	−	1.00883i
$280$		0			0
$281$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$281$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$282$		0			0
$283$	0.556829	+	0.268155i	0.556829	+	0.268155i	0.691063	−	0.722795i	$-0.257143\pi$
$283$	0.556829	+	0.268155i	0.556829	+	0.268155i	−0.134233	+	0.990950i	$0.542857\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1.00000			−1.00000
$290$		0			0
$291$	−1.61803			−1.61803
$292$	−0.602539	+	0.137526i	−0.602539	+	0.137526i
$293$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$293$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$301$	−2.04686	−	1.63232i	−2.04686	−	1.63232i
$302$		0			0
$303$		0			0
$304$	0.602539	+	0.137526i	0.602539	+	0.137526i
$305$		0			0
$306$		0			0
$307$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$307$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$308$		0			0
$309$	−0.702039	−	1.45780i	−0.702039	−	1.45780i
$310$		0			0
$311$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$311$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$312$		0			0
$313$	0.360046	−	1.57747i	0.360046	−	1.57747i	−0.393025	−	0.919528i	$-0.628571\pi$
$313$	0.360046	−	1.57747i	0.360046	−	1.57747i	0.753071	−	0.657939i	$-0.228571\pi$
$314$		0			0
$315$		0			0
$316$	0.268155	−	0.556829i	0.268155	−	0.556829i
$317$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$317$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.222521	+	0.974928i	0.222521	+	0.974928i
$325$	0.137526	−	0.602539i	0.137526	−	0.602539i
$326$		0			0
$327$	1.26503	−	1.00883i	1.26503	−	1.00883i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		−	1.61803i		−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$331$		−	1.61803i		−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$332$		0			0
$333$	0.602539	+	0.137526i	0.602539	+	0.137526i
$334$		0			0
$335$		0			0
$336$			1.61803i			1.61803i
$337$	1.56366	+	1.24698i	1.56366	+	1.24698i	0.781831	+	0.623490i	$0.214286\pi$
$337$	1.56366	+	1.24698i	1.56366	+	1.24698i	0.781831	+	0.623490i	$0.214286\pi$
$338$		0			0
$339$		0			0
$340$		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
$349$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$349$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$350$		0			0
$351$	−0.268155	+	0.556829i	−0.268155	+	0.556829i
$352$		0			0
$353$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$353$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$359$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$360$		0			0
$361$	0.385338	−	0.483198i	0.385338	−	0.483198i
$362$		0			0
$363$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$364$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$365$		0			0
$366$		0			0
$367$	−0.702039	−	1.45780i	−0.702039	−	1.45780i	−0.880596	−	0.473869i	$-0.842857\pi$
$367$	−0.702039	−	1.45780i	−0.702039	−	1.45780i	0.178557	−	0.983930i	$-0.442857\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.360046	+	1.57747i	0.360046	+	1.57747i
$373$	1.45780	−	0.702039i	1.45780	−	0.702039i	0.473869	−	0.880596i	$-0.342857\pi$
$373$	1.45780	−	0.702039i	1.45780	−	0.702039i	0.983930	+	0.178557i	$0.0571429\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.94986	+	0.445042i	−1.94986	+	0.445042i	−0.974928	+	0.222521i	$0.928571\pi$
$379$	−1.94986	+	0.445042i	−1.94986	+	0.445042i	−0.974928	+	0.222521i	$0.928571\pi$
$380$		0			0
$381$	−1.45780	+	0.702039i	−1.45780	+	0.702039i
$382$		0			0
$383$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$383$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.702039	+	1.45780i	0.702039	+	1.45780i
$388$	1.26503	+	1.00883i	1.26503	+	1.00883i
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−1.00883	−	1.26503i	−1.00883	−	1.26503i	−0.963963	−	0.266037i	$-0.914286\pi$
$397$	−1.00883	−	1.26503i	−1.00883	−	1.26503i	−0.0448648	−	0.998993i	$-0.514286\pi$
$398$		0			0
$399$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$400$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$401$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$401$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$402$		0			0
$403$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.268155	+	0.556829i	−0.268155	+	0.556829i	−0.990950	−	0.134233i	$-0.957143\pi$
$409$	−0.268155	+	0.556829i	−0.268155	+	0.556829i	0.722795	+	0.691063i	$0.242857\pi$
$410$		0			0
$411$		0			0
$412$	−0.360046	+	1.57747i	−0.360046	+	1.57747i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.26503	+	1.00883i	1.26503	+	1.00883i
$418$		0			0
$419$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$419$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$420$		0			0
$421$	−0.602539	−	0.137526i	−0.602539	−	0.137526i	−0.0896393	−	0.995974i	$-0.528571\pi$
$421$	−0.602539	−	0.137526i	−0.602539	−	0.137526i	−0.512899	+	0.858449i	$0.671429\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	2.04686	−	1.63232i	2.04686	−	1.63232i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$431$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$432$	0.433884	−	0.900969i	0.433884	−	0.900969i
$433$	0.602539	−	0.137526i	0.602539	−	0.137526i	0.0896393	−	0.995974i	$-0.471429\pi$
$433$	0.602539	−	0.137526i	0.602539	−	0.137526i	0.512899	+	0.858449i	$0.328571\pi$
$434$		0			0
$435$		0			0
$436$	−1.61803			−1.61803
$437$		0			0
$438$		0			0
$439$	0.556829	−	0.268155i	0.556829	−	0.268155i	−0.134233	−	0.990950i	$-0.542857\pi$
$439$	0.556829	−	0.268155i	0.556829	−	0.268155i	0.691063	+	0.722795i	$0.257143\pi$
$440$		0			0
$441$	0.360046	−	1.57747i	0.360046	−	1.57747i
$442$		0			0
$443$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$443$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$444$	−0.385338	−	0.483198i	−0.385338	−	0.483198i
$445$		0			0
$446$		0			0
$447$		0			0
$448$	1.00883	−	1.26503i	1.00883	−	1.26503i
$449$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$449$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	0.483198	+	0.385338i	0.483198	+	0.385338i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.45780	−	0.702039i	−1.45780	−	0.702039i	−0.473869	−	0.880596i	$-0.657143\pi$
$457$	−1.45780	−	0.702039i	−1.45780	−	0.702039i	−0.983930	+	0.178557i	$0.942857\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$461$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$462$		0			0
$463$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$463$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$467$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$468$	0.556829	−	0.268155i	0.556829	−	0.268155i
$469$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$470$		0			0
$471$	−0.556829	−	0.268155i	−0.556829	−	0.268155i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.483198	−	0.385338i	−0.483198	−	0.385338i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$479$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$480$		0			0
$481$		−	0.381966i		−	0.381966i
$482$		0			0
$483$		0			0
$484$	0.623490	+	0.781831i	0.623490	+	0.781831i
$485$		0			0
$486$		0			0
$487$	−0.137526	+	0.602539i	−0.137526	+	0.602539i	0.858449	+	0.512899i	$0.171429\pi$
$487$	−0.137526	+	0.602539i	−0.137526	+	0.602539i	−0.995974	+	0.0896393i	$0.971429\pi$
$488$		0			0
$489$	1.45780	−	0.702039i	1.45780	−	0.702039i
$490$		0			0
$491$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$491$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.702039	−	1.45780i	0.702039	−	1.45780i
$497$		0			0
$498$		0			0
$499$	−0.360046	+	1.57747i	−0.360046	+	1.57747i	0.393025	+	0.919528i	$0.371429\pi$
$499$	−0.360046	+	1.57747i	−0.360046	+	1.57747i	−0.753071	+	0.657939i	$0.771429\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$503$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.602539	−	0.137526i	−0.602539	−	0.137526i
$508$	1.57747	+	0.360046i	1.57747	+	0.360046i
$509$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$509$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$510$		0			0
$511$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$512$		0			0
$513$	0.385338	+	0.483198i	0.385338	+	0.483198i
$514$		0			0
$515$		0			0
$516$	0.360046	−	1.57747i	0.360046	−	1.57747i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$523$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$524$		0			0
$525$	0.702039	−	1.45780i	0.702039	−	1.45780i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$530$		0			0
$531$		0			0
$532$	0.433884	+	0.900969i	0.433884	+	0.900969i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	0.867767	+	1.80194i	0.867767	+	1.80194i	0.433884	+	0.900969i	$0.357143\pi$
$541$	0.867767	+	1.80194i	0.867767	+	1.80194i	0.433884	+	0.900969i	$0.357143\pi$
$542$		0			0
$543$	0.483198	−	0.385338i	0.483198	−	0.385338i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.556829	+	0.268155i	−0.556829	+	0.268155i	−0.691063	−	0.722795i	$-0.742857\pi$
$547$	−0.556829	+	0.268155i	−0.556829	+	0.268155i	0.134233	+	0.990950i	$0.457143\pi$
$548$		0			0
$549$	−1.57747	+	0.360046i	−1.57747	+	0.360046i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	0.974928	−	0.222521i	0.974928	−	0.222521i
$554$		0			0
$555$		0			0
$556$	−0.360046	−	1.57747i	−0.360046	−	1.57747i
$557$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$557$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$558$		0			0
$559$	0.781831	−	0.623490i	0.781831	−	0.623490i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0			−	1.00000i	$-0.5\pi$
$563$		0			0				1.00000i	$0.5\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.00883	+	1.26503i	−1.00883	+	1.26503i
$568$		0			0
$569$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$569$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$570$		0			0
$571$	0.385338	+	0.483198i	0.385338	+	0.483198i	0.936235	−	0.351375i	$-0.114286\pi$
$571$	0.385338	+	0.483198i	0.385338	+	0.483198i	−0.550897	+	0.834573i	$0.685714\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$577$	−0.702039	+	1.45780i	−0.702039	+	1.45780i	0.178557	+	0.983930i	$0.442857\pi$
$577$	−0.702039	+	1.45780i	−0.702039	+	1.45780i	−0.880596	+	0.473869i	$0.842857\pi$
$578$		0			0
$579$	1.61803			1.61803
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$587$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$588$	−1.26503	+	1.00883i	−1.26503	+	1.00883i
$589$	0.623490	+	0.781831i	0.623490	+	0.781831i
$590$		0			0
$591$		0			0
$592$			0.618034i			0.618034i
$593$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$593$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	0.618034i		−	0.618034i
$598$		0			0
$599$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$599$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$600$		0			0
$601$	−1.26503	+	1.00883i	−1.26503	+	1.00883i	−0.266037	+	0.963963i	$0.585714\pi$
$601$	−1.26503	+	1.00883i	−1.26503	+	1.00883i	−0.998993	+	0.0448648i	$0.985714\pi$
$602$		0			0
$603$	−0.137526	+	0.602539i	−0.137526	+	0.602539i
$604$	−0.137526	−	0.602539i	−0.137526	−	0.602539i
$605$		0			0
$606$		0			0
$607$	1.94986	−	0.445042i	1.94986	−	0.445042i	0.974928	−	0.222521i	$-0.0714286\pi$
$607$	1.94986	−	0.445042i	1.94986	−	0.445042i	0.974928	−	0.222521i	$-0.0714286\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.45780	+	0.702039i	−1.45780	+	0.702039i	−0.983930	−	0.178557i	$-0.942857\pi$
$613$	−1.45780	+	0.702039i	−1.45780	+	0.702039i	−0.473869	+	0.880596i	$0.657143\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$617$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$618$		0			0
$619$	−0.268155	−	0.556829i	−0.268155	−	0.556829i	0.722795	−	0.691063i	$-0.242857\pi$
$619$	−0.268155	−	0.556829i	−0.268155	−	0.556829i	−0.990950	+	0.134233i	$0.957143\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−0.602539	−	0.137526i	−0.602539	−	0.137526i
$625$	0.623490	−	0.781831i	0.623490	−	0.781831i
$626$		0			0
$627$		0			0
$628$	0.268155	+	0.556829i	0.268155	+	0.556829i
$629$		0			0
$630$		0			0
$631$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$631$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$632$		0			0
$633$	−0.445042	−	1.94986i	−0.445042	−	1.94986i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.00000			−1.00000
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$641$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$642$		0			0
$643$	0.445042	+	1.94986i	0.445042	+	1.94986i	0.222521	+	0.974928i	$0.428571\pi$
$643$	0.445042	+	1.94986i	0.445042	+	1.94986i	0.222521	+	0.974928i	$0.428571\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$647$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−1.63232	+	2.04686i	−1.63232	+	2.04686i
$652$	−1.57747	−	0.360046i	−1.57747	−	0.360046i
$653$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$653$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	0.268155	+	0.556829i	0.268155	+	0.556829i
$658$		0			0
$659$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$659$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$660$		0			0
$661$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$661$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	1.57747	−	0.360046i	1.57747	−	0.360046i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.445042	−	1.94986i	0.445042	−	1.94986i	0.222521	−	0.974928i	$-0.428571\pi$
$673$	0.445042	−	1.94986i	0.445042	−	1.94986i	0.222521	−	0.974928i	$-0.428571\pi$
$674$		0			0
$675$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$676$	0.385338	+	0.483198i	0.385338	+	0.483198i
$677$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$677$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$678$		0			0
$679$			2.61803i			2.61803i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$683$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$684$		−	0.618034i		−	0.618034i
$685$		0			0
$686$		0			0
$687$	1.24698	+	1.56366i	1.24698	+	1.56366i
$688$	−1.26503	+	1.00883i	−1.26503	+	1.00883i
$689$		0			0
$690$		0			0
$691$	−0.137526	−	0.602539i	−0.137526	−	0.602539i	−0.995974	−	0.0896393i	$-0.971429\pi$
$691$	−0.137526	−	0.602539i	−0.137526	−	0.602539i	0.858449	−	0.512899i	$-0.171429\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−1.45780	+	0.702039i	−1.45780	+	0.702039i
$701$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$701$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$702$		0			0
$703$	−0.344139	−	0.165729i	−0.344139	−	0.165729i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.385338	+	0.483198i	−0.385338	+	0.483198i	−0.936235	−	0.351375i	$-0.885714\pi$
$709$	−0.385338	+	0.483198i	−0.385338	+	0.483198i	0.550897	+	0.834573i	$0.314286\pi$
$710$		0			0
$711$	−0.602539	−	0.137526i	−0.602539	−	0.137526i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$719$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$720$		0			0
$721$	−2.35877	+	1.13592i	−2.35877	+	1.13592i
$722$		0			0
$723$	−1.57747	+	0.360046i	−1.57747	+	0.360046i
$724$	−0.618034			−0.618034
$725$		0			0
$726$		0			0
$727$	−0.602539	+	0.137526i	−0.602539	+	0.137526i	−0.512899	−	0.858449i	$-0.671429\pi$
$727$	−0.602539	+	0.137526i	−0.602539	+	0.137526i	−0.0896393	+	0.995974i	$0.528571\pi$
$728$		0			0
$729$	0.900969	−	0.433884i	0.900969	−	0.433884i
$730$		0			0
$731$		0			0
$732$	1.45780	+	0.702039i	1.45780	+	0.702039i
$733$	1.26503	−	1.00883i	1.26503	−	1.00883i	0.266037	−	0.963963i	$-0.414286\pi$
$733$	1.26503	−	1.00883i	1.26503	−	1.00883i	0.998993	−	0.0448648i	$-0.0142857\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−1.57747	−	0.360046i	−1.57747	−	0.360046i	−0.657939	−	0.753071i	$-0.728571\pi$
$739$	−1.57747	−	0.360046i	−1.57747	−	0.360046i	−0.919528	+	0.393025i	$0.871429\pi$
$740$		0			0
$741$	0.238152	−	0.298633i	0.238152	−	0.298633i
$742$		0			0
$743$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$743$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−0.702039	+	1.45780i	−0.702039	+	1.45780i	0.178557	+	0.983930i	$0.442857\pi$
$751$	−0.702039	+	1.45780i	−0.702039	+	1.45780i	−0.880596	+	0.473869i	$0.842857\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	1.57747	−	0.360046i	1.57747	−	0.360046i
$757$	−0.867767	+	1.80194i	−0.867767	+	1.80194i	−0.433884	+	0.900969i	$0.642857\pi$
$757$	−0.867767	+	1.80194i	−0.867767	+	1.80194i	−0.433884	+	0.900969i	$0.642857\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$761$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$762$		0			0
$763$	−1.63232	−	2.04686i	−1.63232	−	2.04686i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.974928	+	0.222521i	0.974928	+	0.222521i
$769$	1.57747	+	0.360046i	1.57747	+	0.360046i	0.919528	−	0.393025i	$-0.128571\pi$
$769$	1.57747	+	0.360046i	1.57747	+	0.360046i	0.657939	+	0.753071i	$0.271429\pi$
$770$		0			0
$771$		0			0
$772$	−1.26503	−	1.00883i	−1.26503	−	1.00883i
$773$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$773$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$774$		0			0
$775$	−1.26503	+	1.00883i	−1.26503	+	1.00883i
$776$		0			0
$777$	0.222521	−	0.974928i	0.222521	−	0.974928i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	1.61803			1.61803
$785$		0			0
$786$		0			0
$787$	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			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.433884	+	0.900969i	0.433884	+	0.900969i
$794$		0			0
$795$		0			0
$796$	−0.385338	+	0.483198i	−0.385338	+	0.483198i
$797$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$797$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$798$		0			0

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.h (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.433884 + 0.900969i) q^{3} +(0.900969 - 0.433884i) q^{4} +(1.45780 + 0.702039i) q^{7} +(-0.623490 - 0.781831i) q^{9} +O(q^{10})\)	\(q+(-0.433884 + 0.900969i) q^{3} +(0.900969 - 0.433884i) q^{4} +(1.45780 + 0.702039i) q^{7} +(-0.623490 - 0.781831i) q^{9} +1.00000i q^{12} +(-0.385338 + 0.483198i) q^{13} +(0.623490 - 0.781831i) q^{16} +(0.268155 + 0.556829i) q^{19} +(-1.26503 + 1.00883i) q^{21} +(-0.900969 + 0.433884i) q^{25} +(0.974928 - 0.222521i) q^{27} +1.61803 q^{28} +(1.57747 - 0.360046i) q^{31} +(-0.900969 - 0.433884i) q^{36} +(-0.483198 + 0.385338i) q^{37} +(-0.268155 - 0.556829i) q^{39} +(-1.57747 - 0.360046i) q^{43} +(0.433884 + 0.900969i) q^{48} +(1.00883 + 1.26503i) q^{49} +(-0.137526 + 0.602539i) q^{52} -0.618034 q^{57} +(0.702039 - 1.45780i) q^{61} +(-0.360046 - 1.57747i) q^{63} +(0.222521 - 0.974928i) q^{64} +(-0.385338 - 0.483198i) q^{67} +(-0.602539 - 0.137526i) q^{73} -1.00000i q^{75} +(0.483198 + 0.385338i) q^{76} +(0.483198 - 0.385338i) q^{79} +(-0.222521 + 0.974928i) q^{81} +(-0.702039 + 1.45780i) q^{84} +(-0.900969 + 0.433884i) q^{91} +(-0.360046 + 1.57747i) q^{93} +(0.702039 + 1.45780i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^4 + 2 * q^7 + 4 * q^9	\( 24 q + 4 q^{4} + 2 q^{7} + 4 q^{9} - 2 q^{13} - 4 q^{16} - 4 q^{25} + 12 q^{28} - 4 q^{36} - 2 q^{49} + 2 q^{52} + 12 q^{57} - 2 q^{63} + 4 q^{64} - 2 q^{67} - 4 q^{81} - 4 q^{91} - 2 q^{93}+O(q^{100}) \) 24 * q + 4 * q^4 + 2 * q^7 + 4 * q^9 - 2 * q^13 - 4 * q^16 - 4 * q^25 + 12 * q^28 - 4 * q^36 - 2 * q^49 + 2 * q^52 + 12 * q^57 - 2 * q^63 + 4 * q^64 - 2 * q^67 - 4 * q^81 - 4 * q^91 - 2 * q^93

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