LMFDB - Embedded newform 1925.1.cb.a.174.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,1,Mod(174,1925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 6]))

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

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

chi := DirichletCharacter("1925.174");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1925.cb (of order $10$, degree $4$, 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:	$0.960700149319$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Projective image:	$D_{5}$
Projective field:	Galois closure of 5.1.717409.1

Embedding invariants

Embedding label			174.1
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	1925.174
Dual form			1925.1.cb.a.874.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53884 - 0.500000i) q^{2} +(1.30902 + 0.951057i) q^{4} +(0.587785 - 0.809017i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	$q+(-1.53884 - 0.500000i) q^{2} +(1.30902 + 0.951057i) q^{4} +(0.587785 - 0.809017i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(0.309017 + 0.951057i) q^{11} +(-1.30902 + 0.951057i) q^{14} +(0.951057 - 1.30902i) q^{18} -1.61803i q^{22} +1.61803i q^{23} +(1.53884 - 0.500000i) q^{28} +(0.500000 + 0.363271i) q^{29} +1.00000i q^{32} +(-1.30902 + 0.951057i) q^{36} +(-0.951057 + 1.30902i) q^{37} -0.618034i q^{43} +(-0.500000 + 1.53884i) q^{44} +(0.809017 - 2.48990i) q^{46} +(-0.309017 - 0.951057i) q^{49} +(-0.587785 - 0.190983i) q^{53} -1.00000 q^{56} +(-0.587785 - 0.809017i) q^{58} +(0.587785 + 0.809017i) q^{63} +(0.500000 - 1.53884i) q^{64} +0.618034i q^{67} +(0.190983 + 0.587785i) q^{71} +(0.951057 - 0.309017i) q^{72} +(2.11803 - 1.53884i) q^{74} +(0.951057 + 0.309017i) q^{77} +(-0.190983 + 0.587785i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-0.309017 + 0.951057i) q^{86} +(0.587785 - 0.809017i) q^{88} +(-1.53884 + 2.11803i) q^{92} +1.61803i q^{98} -1.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{4} + 2 q^{9}+O(q^{10}) $ 8 * q + 6 * q^4 + 2 * q^9	$ 8 q + 6 q^{4} + 2 q^{9} - 2 q^{11} - 6 q^{14} + 4 q^{29} - 6 q^{36} - 4 q^{44} + 2 q^{46} + 2 q^{49} - 8 q^{56} + 4 q^{64} + 6 q^{71} + 8 q^{74} - 6 q^{79} - 2 q^{81} + 2 q^{86} - 8 q^{99}+O(q^{100}) $ 8 * q + 6 * q^4 + 2 * q^9 - 2 * q^11 - 6 * q^14 + 4 * q^29 - 6 * q^36 - 4 * q^44 + 2 * q^46 + 2 * q^49 - 8 * q^56 + 4 * q^64 + 6 * q^71 + 8 * q^74 - 6 * q^79 - 2 * q^81 + 2 * q^86 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1925\mathbb{Z}\right)^\times$.

$n$	$276$	$1002$	$1751$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$2$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$3$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$3$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$4$	1.30902	+	0.951057i	1.30902	+	0.951057i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.587785	−	0.809017i	0.587785	−	0.809017i
$7$	0.587785	−	0.809017i	0.587785	−	0.809017i
$8$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$9$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$10$		0			0
$11$	0.309017	+	0.951057i	0.309017	+	0.951057i
$11$	0.309017	+	0.951057i	0.309017	+	0.951057i
$12$		0			0
$13$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$13$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$14$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$15$		0			0
$16$		0			0
$17$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$17$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$18$	0.951057	−	1.30902i	0.951057	−	1.30902i
$19$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$19$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$20$		0			0
$21$		0			0
$22$		−	1.61803i		−	1.61803i
$23$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$23$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		0			0
$28$	1.53884	−	0.500000i	1.53884	−	0.500000i
$29$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$29$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$30$		0			0
$31$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$31$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$32$			1.00000i			1.00000i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$37$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$37$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$41$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$42$		0			0
$43$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$43$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$44$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$45$		0			0
$46$	0.809017	−	2.48990i	0.809017	−	2.48990i
$47$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$47$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.587785	−	0.190983i	−0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$53$	−0.587785	−	0.190983i	−0.587785	−	0.190983i	−0.587785	+	0.809017i	$0.700000\pi$
$54$		0			0
$55$		0			0
$56$	−1.00000			−1.00000
$57$		0			0
$58$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$59$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$59$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$60$		0			0
$61$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$61$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$62$		0			0
$63$	0.587785	+	0.809017i	0.587785	+	0.809017i
$64$	0.500000	−	1.53884i	0.500000	−	1.53884i
$65$		0			0
$66$		0			0
$67$			0.618034i			0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$67$			0.618034i			0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$71$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$72$	0.951057	−	0.309017i	0.951057	−	0.309017i
$73$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$73$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$74$	2.11803	−	1.53884i	2.11803	−	1.53884i
$75$		0			0
$76$		0			0
$77$	0.951057	+	0.309017i	0.951057	+	0.309017i
$78$		0			0
$79$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$79$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$82$		0			0
$83$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$83$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$84$		0			0
$85$		0			0
$86$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$87$		0			0
$88$	0.587785	−	0.809017i	0.587785	−	0.809017i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$		0			0
$92$	−1.53884	+	2.11803i	−1.53884	+	2.11803i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$97$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$98$			1.61803i			1.61803i
$99$	−1.00000			−1.00000
$100$		0			0
$101$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$101$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$102$		0			0
$103$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$103$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$104$		0			0
$105$		0			0
$106$	0.809017	+	0.587785i	0.809017	+	0.587785i
$107$	0.951057	+	1.30902i	0.951057	+	1.30902i	0.951057	+	0.309017i	$0.100000\pi$
$107$	0.951057	+	1.30902i	0.951057	+	1.30902i			1.00000i	$0.5\pi$
$108$		0			0
$109$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$109$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$113$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$114$		0			0
$115$		0			0
$116$	0.309017	+	0.951057i	0.309017	+	0.951057i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$127$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$127$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$128$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$129$		0			0
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$	0.309017	−	0.951057i	0.309017	−	0.951057i
$135$		0			0
$136$		0			0
$137$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$137$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$138$		0			0
$139$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$139$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$140$		0			0
$141$		0			0
$142$		−	1.00000i		−	1.00000i
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$149$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$149$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$150$		0			0
$151$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$151$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$152$		0			0
$153$		0			0
$154$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$155$		0			0
$156$		0			0
$157$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$157$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$158$	0.587785	−	0.809017i	0.587785	−	0.809017i
$159$		0			0
$160$		0			0
$161$	1.30902	+	0.951057i	1.30902	+	0.951057i
$162$	0.951057	+	1.30902i	0.951057	+	1.30902i
$163$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$163$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$167$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$168$		0			0
$169$	0.809017	+	0.587785i	0.809017	+	0.587785i
$170$		0			0
$171$		0			0
$172$	0.587785	−	0.809017i	0.587785	−	0.809017i
$173$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$173$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$179$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$180$		0			0
$181$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$181$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$182$		0			0
$183$		0			0
$184$	1.30902	−	0.951057i	1.30902	−	0.951057i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$191$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$192$		0			0
$193$	0.587785	−	0.190983i	0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$193$	0.587785	−	0.190983i	0.587785	−	0.190983i	0.587785	+	0.809017i	$0.300000\pi$
$194$		0			0
$195$		0			0
$196$	0.500000	−	1.53884i	0.500000	−	1.53884i
$197$		−	1.61803i		−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$197$		−	1.61803i		−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$198$	1.53884	+	0.500000i	1.53884	+	0.500000i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.587785	−	0.190983i	0.587785	−	0.190983i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$211$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$212$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$213$		0			0
$214$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−2.48990	−	0.809017i	−2.48990	−	0.809017i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$223$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$224$	0.809017	+	0.587785i	0.809017	+	0.587785i
$225$		0			0
$226$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$227$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$227$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$228$		0			0
$229$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$229$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$230$		0			0
$231$		0			0
$232$		−	0.618034i		−	0.618034i
$233$	−1.90211	−	0.618034i	−1.90211	−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$233$	−1.90211	−	0.618034i	−1.90211	−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$239$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	1.53884	−	0.500000i	1.53884	−	0.500000i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$251$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$252$			1.61803i			1.61803i
$253$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$254$	−2.61803			−2.61803
$255$		0			0
$256$	0.809017	−	0.587785i	0.809017	−	0.587785i
$257$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$257$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$258$		0			0
$259$	0.500000	+	1.53884i	0.500000	+	1.53884i
$260$		0			0
$261$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$262$		0			0
$263$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$263$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$269$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$269$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$270$		0			0
$271$		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
$274$	−2.61803			−2.61803
$275$		0			0
$276$		0			0
$277$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$277$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$281$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$282$		0			0
$283$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$283$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$284$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$289$	0.809017	−	0.587785i	0.809017	−	0.587785i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$293$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$294$		0			0
$295$		0			0
$296$	1.61803			1.61803
$297$		0			0
$298$			3.23607i			3.23607i
$299$		0			0
$300$		0			0
$301$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$302$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	0.951057	+	1.30902i	0.951057	+	1.30902i
$309$		0			0
$310$		0			0
$311$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$311$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$312$		0			0
$313$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$313$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$314$		0			0
$315$		0			0
$316$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$317$	0.587785	+	0.190983i	0.587785	+	0.190983i	0.587785	−	0.809017i	$-0.300000\pi$
$317$	0.587785	+	0.190983i	0.587785	+	0.190983i			1.00000i	$0.5\pi$
$318$		0			0
$319$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$320$		0			0
$321$		0			0
$322$	−1.53884	−	2.11803i	−1.53884	−	2.11803i
$323$		0			0
$324$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$325$		0			0
$326$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$331$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$332$		0			0
$333$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$337$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$338$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$344$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$345$		0			0
$346$		0			0
$347$	−0.587785	+	0.190983i	−0.587785	+	0.190983i	−0.587785	−	0.809017i	$-0.700000\pi$
$347$	−0.587785	+	0.190983i	−0.587785	+	0.190983i			1.00000i	$0.5\pi$
$348$		0			0
$349$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$349$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$350$		0			0
$351$		0			0
$352$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$353$		0			0			−	1.00000i	$-0.5\pi$
$353$		0			0				1.00000i	$0.5\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	2.48990	−	0.809017i	2.48990	−	0.809017i
$359$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$359$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$360$		0			0
$361$	0.309017	−	0.951057i	0.309017	−	0.951057i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$367$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$372$		0			0
$373$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$373$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$379$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$380$		0			0
$381$		0			0
$382$	0.587785	+	0.809017i	0.587785	+	0.809017i
$383$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$383$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$384$		0			0
$385$		0			0
$386$	−1.00000			−1.00000
$387$	0.587785	+	0.190983i	0.587785	+	0.190983i
$388$		0			0
$389$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$389$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$393$		0			0
$394$	−0.809017	+	2.48990i	−0.809017	+	2.48990i
$395$		0			0
$396$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$397$		0			0			−	1.00000i	$-0.5\pi$
$397$		0			0				1.00000i	$0.5\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$401$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−1.00000			−1.00000
$407$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$408$		0			0
$409$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$409$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	2.11803	+	1.53884i	2.11803	+	1.53884i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$421$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$422$	1.53884	−	2.11803i	1.53884	−	2.11803i
$423$		0			0
$424$	0.190983	+	0.587785i	0.190983	+	0.587785i
$425$		0			0
$426$		0			0
$427$		0			0
$428$			2.61803i			2.61803i
$429$		0			0
$430$		0			0
$431$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$431$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$432$		0			0
$433$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$433$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$434$		0			0
$435$		0			0
$436$	2.11803	+	1.53884i	2.11803	+	1.53884i
$437$		0			0
$438$		0			0
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$	1.00000			1.00000
$442$		0			0
$443$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$443$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$449$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$449$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$450$		0			0
$451$		0			0
$452$			1.00000i			1.00000i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$457$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$463$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$464$		0			0
$465$		0			0
$466$	2.61803	+	1.90211i	2.61803	+	1.90211i
$467$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$467$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$468$		0			0
$469$	0.500000	+	0.363271i	0.500000	+	0.363271i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.587785	−	0.190983i	0.587785	−	0.190983i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.363271	−	0.500000i	0.363271	−	0.500000i
$478$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$479$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$479$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.61803			−1.61803
$485$		0			0
$486$		0			0
$487$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$487$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$491$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.587785	+	0.190983i	0.587785	+	0.190983i
$498$		0			0
$499$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$499$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$503$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$504$	0.309017	−	0.951057i	0.309017	−	0.951057i
$505$		0			0
$506$	2.61803			2.61803
$507$		0			0
$508$	2.48990	+	0.809017i	2.48990	+	0.809017i
$509$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$509$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		−	2.61803i		−	2.61803i
$519$		0			0
$520$		0			0
$521$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$521$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$522$	0.951057	−	0.309017i	0.951057	−	0.309017i
$523$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$523$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$524$		0			0
$525$		0			0
$526$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$527$		0			0
$528$		0			0
$529$	−1.61803			−1.61803
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.500000	−	0.363271i	0.500000	−	0.363271i
$537$		0			0
$538$		0			0
$539$	0.809017	−	0.587785i	0.809017	−	0.587785i
$540$		0			0
$541$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$541$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.17557	−	1.61803i	−1.17557	−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$547$	−1.17557	−	1.61803i	−1.17557	−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$548$	2.48990	+	0.809017i	2.48990	+	0.809017i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	0.363271	+	0.500000i	0.363271	+	0.500000i
$554$	2.11803	+	1.53884i	2.11803	+	1.53884i
$555$		0			0
$556$		0			0
$557$	0.363271	−	0.500000i	0.363271	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$557$	0.363271	−	0.500000i	0.363271	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		−	1.00000i		−	1.00000i
$563$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$563$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$568$	0.363271	−	0.500000i	0.363271	−	0.500000i
$569$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$569$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$570$		0			0
$571$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$571$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.30902	+	0.951057i	1.30902	+	0.951057i
$577$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$577$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$578$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		−	0.618034i		−	0.618034i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$587$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$	1.00000	−	3.07768i	1.00000	−	3.07768i
$597$		0			0
$598$		0			0
$599$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$599$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$600$		0			0
$601$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$601$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$602$	0.587785	+	0.809017i	0.587785	+	0.809017i
$603$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$604$	2.61803			2.61803
$605$		0			0
$606$		0			0
$607$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$607$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$613$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$614$		0			0
$615$		0			0
$616$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$617$			0.618034i			0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$617$			0.618034i			0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$618$		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			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$631$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$632$	0.587785	−	0.190983i	0.587785	−	0.190983i
$633$		0			0
$634$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.587785	−	0.809017i	0.587785	−	0.809017i
$639$	−0.618034			−0.618034
$640$		0			0
$641$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$641$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$642$		0			0
$643$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$643$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$644$	0.809017	+	2.48990i	0.809017	+	2.48990i
$645$		0			0
$646$		0			0
$647$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$647$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$648$			1.00000i			1.00000i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.53884	+	2.11803i	1.53884	+	2.11803i
$653$	0.951057	−	1.30902i	0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$653$	0.951057	−	1.30902i	0.951057	−	1.30902i	0.951057	−	0.309017i	$-0.100000\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.00000			−2.00000			−1.00000			$\pi$
$659$	−2.00000			−2.00000			−1.00000			$\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$	2.48990	+	0.809017i	2.48990	+	0.809017i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.809017	+	2.48990i	0.809017	+	2.48990i
$667$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.587785	−	0.190983i	−0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$673$	−0.587785	−	0.190983i	−0.587785	−	0.190983i	−0.587785	+	0.809017i	$0.700000\pi$
$674$	2.11803	−	1.53884i	2.11803	−	1.53884i
$675$		0			0
$676$	0.500000	+	1.53884i	0.500000	+	1.53884i
$677$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$677$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$683$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$684$		0			0
$685$		0			0
$686$	1.30902	+	0.951057i	1.30902	+	0.951057i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$691$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$692$		0			0
$693$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$694$	1.00000			1.00000
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$701$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$702$		0			0
$703$		0			0
$704$	1.61803			1.61803
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$709$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$710$		0			0
$711$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−2.61803			−2.61803
$717$		0			0
$718$	1.53884	+	2.11803i	1.53884	+	2.11803i
$719$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$719$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$720$		0			0
$721$		0			0
$722$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	0.809017	−	0.587785i	0.809017	−	0.587785i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$733$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$734$		0			0
$735$		0			0
$736$	−1.61803			−1.61803
$737$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$738$		0			0
$739$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$739$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$	0.951057	−	0.309017i	0.951057	−	0.309017i
$743$	0.587785	−	0.190983i	0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$743$	0.587785	−	0.190983i	0.587785	−	0.190983i	0.587785	+	0.809017i	$0.300000\pi$
$744$		0			0
$745$		0			0
$746$	−1.00000	+	3.07768i	−1.00000	+	3.07768i
$747$		0			0
$748$		0			0
$749$	1.61803			1.61803
$750$		0			0
$751$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$751$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.587785	+	0.190983i	0.587785	+	0.190983i	0.587785	−	0.809017i	$-0.300000\pi$
$757$	0.587785	+	0.190983i	0.587785	+	0.190983i			1.00000i	$0.5\pi$
$758$		−	2.61803i		−	2.61803i
$759$		0			0
$760$		0			0
$761$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$761$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$762$		0			0
$763$	0.951057	−	1.30902i	0.951057	−	1.30902i
$764$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$	0.951057	+	0.309017i	0.951057	+	0.309017i
$773$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$773$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$774$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	1.53884	+	2.11803i	1.53884	+	2.11803i
$779$		0			0
$780$		0			0
$781$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$787$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$788$	1.53884	−	2.11803i	1.53884	−	2.11803i
$789$		0			0
$790$		0			0
$791$	0.618034			0.618034
$792$	0.587785	+	0.809017i	0.587785	+	0.809017i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$797$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$			2.61803i			2.61803i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$809$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$810$		0			0
$811$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$811$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$812$	0.951057	+	0.309017i	0.951057	+	0.309017i
$813$		0			0
$814$	2.11803	+	1.53884i	2.11803	+	1.53884i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$821$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$822$		0			0
$823$	−0.587785	−	0.190983i	−0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$823$	−0.587785	−	0.190983i	−0.587785	−	0.190983i	−0.587785	+	0.809017i	$0.700000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.90211	+	0.618034i	1.90211	+	0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$827$	1.90211	+	0.618034i	1.90211	+	0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$828$	−1.53884	−	2.11803i	−1.53884	−	2.11803i
$829$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$829$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$839$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$840$		0			0
$841$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$842$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$843$		0			0
$844$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$845$		0			0
$846$		0			0
$847$			1.00000i			1.00000i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$852$		0			0
$853$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$853$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$854$		0			0
$855$		0			0
$856$	0.500000	−	1.53884i	0.500000	−	1.53884i
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$	1.53884	−	2.11803i	1.53884	−	2.11803i
$863$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$863$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.618034			−0.618034
$870$		0			0
$871$		0			0
$872$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$877$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$883$	1.17557	+	1.61803i	1.17557	+	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$883$	1.17557	+	1.61803i	1.17557	+	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$884$		0			0
$885$		0			0
$886$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$887$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$887$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$888$		0			0
$889$	0.500000	−	1.53884i	0.500000	−	1.53884i
$890$		0			0
$891$	0.309017	−	0.951057i	0.309017	−	0.951057i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.500000	+	1.53884i	0.500000	+	1.53884i
$897$		0			0
$898$	−1.53884	+	2.11803i	−1.53884	+	2.11803i
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.190983	−	0.587785i	0.190983	−	0.587785i
$905$		0			0
$906$		0			0
$907$	−0.587785	+	0.190983i	−0.587785	+	0.190983i	−0.587785	−	0.809017i	$-0.700000\pi$
$907$	−0.587785	+	0.190983i	−0.587785	+	0.190983i			1.00000i	$0.5\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$911$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$912$		0			0
$913$		0			0
$914$	−2.61803			−2.61803
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$919$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$927$		0			0
$928$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$929$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$929$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$930$		0			0
$931$		0			0
$932$	−1.90211	−	2.61803i	−1.90211	−	2.61803i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$937$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$938$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$939$		0			0
$940$		0			0
$941$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$941$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−1.00000			−1.00000
$947$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$947$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.951057	−	1.30902i	0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$953$	0.951057	−	1.30902i	0.951057	−	1.30902i	0.951057	−	0.309017i	$-0.100000\pi$
$954$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$955$		0			0
$956$	1.00000			1.00000
$957$		0			0
$958$		0			0
$959$	0.500000	−	1.53884i	0.500000	−	1.53884i
$960$		0			0
$961$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$962$		0			0
$963$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	1.61803i		−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$967$		−	1.61803i		−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$968$	0.951057	+	0.309017i	0.951057	+	0.309017i
$969$		0			0
$970$		0			0
$971$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$971$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$972$		0			0
$973$		0			0
$974$	0.309017	+	0.951057i	0.309017	+	0.951057i
$975$		0			0
$976$		0			0
$977$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$977$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$982$	1.90211	+	2.61803i	1.90211	+	2.61803i
$983$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$983$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.00000			1.00000
$990$		0			0
$991$	2.00000			2.00000			1.00000			$0$
$991$	2.00000			2.00000			1.00000			$0$
$992$		0			0
$993$		0			0
$994$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$995$		0			0
$996$		0			0
$997$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$997$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$998$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.1.cb.a.174.1		8
5.2	odd	4		1925.1.bn.a.251.1		4
5.3	odd	4		77.1.j.a.20.1	✓	4
5.4	even	2	inner	1925.1.cb.a.174.2		8
7.6	odd	2	CM	1925.1.cb.a.174.1		8
11.5	even	5	inner	1925.1.cb.a.874.2		8
15.8	even	4		693.1.br.a.559.1		4
20.3	even	4		1232.1.cd.a.97.1		4
35.3	even	12		539.1.u.a.460.1		8
35.13	even	4		77.1.j.a.20.1	✓	4
35.18	odd	12		539.1.u.a.460.1		8
35.23	odd	12		539.1.u.a.31.1		8
35.27	even	4		1925.1.bn.a.251.1		4
35.33	even	12		539.1.u.a.31.1		8
35.34	odd	2	inner	1925.1.cb.a.174.2		8
55.3	odd	20		847.1.j.c.202.1		4
55.8	even	20		847.1.j.a.202.1		4
55.13	even	20		847.1.j.a.608.1		4
55.18	even	20		847.1.d.b.727.2		2
55.27	odd	20		1925.1.bn.a.951.1		4
55.28	even	20		847.1.j.b.27.1		4
55.38	odd	20		77.1.j.a.27.1	yes	4
55.43	even	4		847.1.j.b.251.1		4
55.48	odd	20		847.1.d.a.727.1		2
55.49	even	10	inner	1925.1.cb.a.874.1		8
55.53	odd	20		847.1.j.c.608.1		4
77.27	odd	10	inner	1925.1.cb.a.874.2		8
105.83	odd	4		693.1.br.a.559.1		4
140.83	odd	4		1232.1.cd.a.97.1		4
165.38	even	20		693.1.br.a.181.1		4
220.203	even	20		1232.1.cd.a.1105.1		4
385.13	odd	20		847.1.j.a.608.1		4
385.27	even	20		1925.1.bn.a.951.1		4
385.38	even	60		539.1.u.a.313.1		8
385.48	even	20		847.1.d.a.727.1		2
385.83	odd	20		847.1.j.b.27.1		4
385.93	odd	60		539.1.u.a.423.1		8
385.104	odd	10	inner	1925.1.cb.a.874.1		8
385.118	odd	20		847.1.j.a.202.1		4
385.153	odd	4		847.1.j.b.251.1		4
385.223	even	20		847.1.j.c.202.1		4
385.258	even	20		77.1.j.a.27.1	yes	4
385.293	odd	20		847.1.d.b.727.2		2
385.313	even	60		539.1.u.a.423.1		8
385.328	even	20		847.1.j.c.608.1		4
385.368	odd	60		539.1.u.a.313.1		8
1155.1028	odd	20		693.1.br.a.181.1		4
1540.643	odd	20		1232.1.cd.a.1105.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.1.j.a.20.1	✓	4	5.3	odd	4
77.1.j.a.20.1	✓	4	35.13	even	4
77.1.j.a.27.1	yes	4	55.38	odd	20
77.1.j.a.27.1	yes	4	385.258	even	20
539.1.u.a.31.1		8	35.23	odd	12
539.1.u.a.31.1		8	35.33	even	12
539.1.u.a.313.1		8	385.38	even	60
539.1.u.a.313.1		8	385.368	odd	60
539.1.u.a.423.1		8	385.93	odd	60
539.1.u.a.423.1		8	385.313	even	60
539.1.u.a.460.1		8	35.3	even	12
539.1.u.a.460.1		8	35.18	odd	12
693.1.br.a.181.1		4	165.38	even	20
693.1.br.a.181.1		4	1155.1028	odd	20
693.1.br.a.559.1		4	15.8	even	4
693.1.br.a.559.1		4	105.83	odd	4
847.1.d.a.727.1		2	55.48	odd	20
847.1.d.a.727.1		2	385.48	even	20
847.1.d.b.727.2		2	55.18	even	20
847.1.d.b.727.2		2	385.293	odd	20
847.1.j.a.202.1		4	55.8	even	20
847.1.j.a.202.1		4	385.118	odd	20
847.1.j.a.608.1		4	55.13	even	20
847.1.j.a.608.1		4	385.13	odd	20
847.1.j.b.27.1		4	55.28	even	20
847.1.j.b.27.1		4	385.83	odd	20
847.1.j.b.251.1		4	55.43	even	4
847.1.j.b.251.1		4	385.153	odd	4
847.1.j.c.202.1		4	55.3	odd	20
847.1.j.c.202.1		4	385.223	even	20
847.1.j.c.608.1		4	55.53	odd	20
847.1.j.c.608.1		4	385.328	even	20
1232.1.cd.a.97.1		4	20.3	even	4
1232.1.cd.a.97.1		4	140.83	odd	4
1232.1.cd.a.1105.1		4	220.203	even	20
1232.1.cd.a.1105.1		4	1540.643	odd	20
1925.1.bn.a.251.1		4	5.2	odd	4
1925.1.bn.a.251.1		4	35.27	even	4
1925.1.bn.a.951.1		4	55.27	odd	20
1925.1.bn.a.951.1		4	385.27	even	20
1925.1.cb.a.174.1		8	1.1	even	1	trivial
1925.1.cb.a.174.1		8	7.6	odd	2	CM
1925.1.cb.a.174.2		8	5.4	even	2	inner
1925.1.cb.a.174.2		8	35.34	odd	2	inner
1925.1.cb.a.874.1		8	55.49	even	10	inner
1925.1.cb.a.874.1		8	385.104	odd	10	inner
1925.1.cb.a.874.2		8	11.5	even	5	inner
1925.1.cb.a.874.2		8	77.27	odd	10	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:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1925.cb (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.53884 - 0.500000i) q^{2} +(1.30902 + 0.951057i) q^{4} +(0.587785 - 0.809017i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-1.53884 - 0.500000i) q^{2} +(1.30902 + 0.951057i) q^{4} +(0.587785 - 0.809017i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(0.309017 + 0.951057i) q^{11} +(-1.30902 + 0.951057i) q^{14} +(0.951057 - 1.30902i) q^{18} -1.61803i q^{22} +1.61803i q^{23} +(1.53884 - 0.500000i) q^{28} +(0.500000 + 0.363271i) q^{29} +1.00000i q^{32} +(-1.30902 + 0.951057i) q^{36} +(-0.951057 + 1.30902i) q^{37} -0.618034i q^{43} +(-0.500000 + 1.53884i) q^{44} +(0.809017 - 2.48990i) q^{46} +(-0.309017 - 0.951057i) q^{49} +(-0.587785 - 0.190983i) q^{53} -1.00000 q^{56} +(-0.587785 - 0.809017i) q^{58} +(0.587785 + 0.809017i) q^{63} +(0.500000 - 1.53884i) q^{64} +0.618034i q^{67} +(0.190983 + 0.587785i) q^{71} +(0.951057 - 0.309017i) q^{72} +(2.11803 - 1.53884i) q^{74} +(0.951057 + 0.309017i) q^{77} +(-0.190983 + 0.587785i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-0.309017 + 0.951057i) q^{86} +(0.587785 - 0.809017i) q^{88} +(-1.53884 + 2.11803i) q^{92} +1.61803i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{4} + 2 q^{9}+O(q^{10}) \) 8 * q + 6 * q^4 + 2 * q^9	\( 8 q + 6 q^{4} + 2 q^{9} - 2 q^{11} - 6 q^{14} + 4 q^{29} - 6 q^{36} - 4 q^{44} + 2 q^{46} + 2 q^{49} - 8 q^{56} + 4 q^{64} + 6 q^{71} + 8 q^{74} - 6 q^{79} - 2 q^{81} + 2 q^{86} - 8 q^{99}+O(q^{100}) \) 8 * q + 6 * q^4 + 2 * q^9 - 2 * q^11 - 6 * q^14 + 4 * q^29 - 6 * q^36 - 4 * q^44 + 2 * q^46 + 2 * q^49 - 8 * q^56 + 4 * q^64 + 6 * q^71 + 8 * q^74 - 6 * q^79 - 2 * q^81 + 2 * q^86 - 8 * q^99

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