LMFDB - Embedded newform 3879.1.g.c.430.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3879,1,Mod(430,3879)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3879, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("3879.430");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3879 = 3^{2} \cdot 431 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3879.g (of order $6$, degree $2$, 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:	$1.93587318400$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{63})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{36} - x^{33} + x^{27} - x^{24} + x^{18} - x^{12} + x^{9} - x^{3} + 1 $ x^36 - x^33 + x^27 - x^24 + x^18 - x^12 + x^9 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{63}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{63} - \cdots)$

Embedding invariants

Embedding label			430.12
Root			$-0.998757 + 0.0498459i$ of defining polynomial
Character	$\chi$	$=$	3879.430
Dual form			3879.1.g.c.1723.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.222521 - 0.385418i) q^{2} +(0.980172 - 0.198146i) q^{3} +(0.400969 + 0.694498i) q^{4} +(-0.542546 - 0.939718i) q^{5} +(0.141740 - 0.421867i) q^{6} +0.801938 q^{8} +(0.921476 - 0.388435i) q^{9} +O(q^{10})$	\(q+(0.222521 - 0.385418i) q^{2} +(0.980172 - 0.198146i) q^{3} +(0.400969 + 0.694498i) q^{4} +(-0.542546 - 0.939718i) q^{5} +(0.141740 - 0.421867i) q^{6} +0.801938 q^{8} +(0.921476 - 0.388435i) q^{9} -0.482912 q^{10} +(-0.766044 + 1.32683i) q^{11} +(0.530631 + 0.601278i) q^{12} +(-0.717990 - 0.813582i) q^{15} +(-0.222521 + 0.385418i) q^{16} +(0.0553382 - 0.441588i) q^{18} +1.75644 q^{19} +(0.435088 - 0.753595i) q^{20} +(0.340922 + 0.590494i) q^{22} +(0.583744 + 1.01107i) q^{23} +(0.786037 - 0.158901i) q^{24} +(-0.0887129 + 0.153655i) q^{25} +(0.826239 - 0.563320i) q^{27} +(-0.698237 + 1.20938i) q^{29} +(-0.473337 + 0.0956871i) q^{30} +(0.500000 + 0.866025i) q^{32} +(-0.487950 + 1.45231i) q^{33} +(0.639251 + 0.484214i) q^{36} +(0.390845 - 0.676964i) q^{38} +(-0.435088 - 0.753595i) q^{40} +(-0.826239 - 1.43109i) q^{41} -1.22864 q^{44} +(-0.864963 - 0.655184i) q^{45} +0.519581 q^{46} +(-0.141740 + 0.421867i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.0394810 + 0.0683830i) q^{50} -0.0498614 q^{53} +(-0.0332580 - 0.443797i) q^{54} +1.66246 q^{55} +(1.72162 - 0.348032i) q^{57} +(0.310745 + 0.538225i) q^{58} +(-0.921476 - 1.59604i) q^{59} +(0.277140 - 0.824864i) q^{60} +(0.988831 - 1.71271i) q^{61} +(0.451166 + 0.511234i) q^{66} +(0.772510 + 0.875360i) q^{69} +(0.738967 - 0.311501i) q^{72} +(-0.0565077 + 0.168187i) q^{75} +(0.704279 + 1.21985i) q^{76} +0.482912 q^{80} +(0.698237 - 0.715867i) q^{81} -0.735422 q^{82} +(-0.444758 + 1.32376i) q^{87} +(-0.614320 + 1.06403i) q^{88} +(-0.444992 + 0.187580i) q^{90} +(-0.468126 + 0.810818i) q^{92} +(-0.952952 - 1.65056i) q^{95} +(0.661686 + 0.749781i) q^{96} +(-0.270840 + 0.469109i) q^{97} -0.445042 q^{98} +(-0.190506 + 1.52020i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{2} - 12 q^{4} - 24 q^{8}+O(q^{10}) $ 36 * q + 6 * q^2 - 12 * q^4 - 24 * q^8	$ 36 q + 6 q^{2} - 12 q^{4} - 24 q^{8} + 3 q^{15} - 6 q^{16} - 18 q^{25} + 3 q^{27} + 6 q^{30} + 18 q^{32} + 3 q^{33} - 3 q^{41} + 3 q^{45} - 18 q^{49} + 6 q^{50} + 6 q^{54} + 6 q^{55} + 3 q^{57} - 18 q^{60} - 3 q^{61} + 6 q^{66} - 6 q^{69} + 3 q^{75} + 12 q^{82} - 6 q^{87} + 6 q^{90} - 3 q^{95} - 12 q^{98} + 3 q^{99}+O(q^{100}) $ 36 * q + 6 * q^2 - 12 * q^4 - 24 * q^8 + 3 * q^15 - 6 * q^16 - 18 * q^25 + 3 * q^27 + 6 * q^30 + 18 * q^32 + 3 * q^33 - 3 * q^41 + 3 * q^45 - 18 * q^49 + 6 * q^50 + 6 * q^54 + 6 * q^55 + 3 * q^57 - 18 * q^60 - 3 * q^61 + 6 * q^66 - 6 * q^69 + 3 * q^75 + 12 * q^82 - 6 * q^87 + 6 * q^90 - 3 * q^95 - 12 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3879\mathbb{Z}\right)^\times$.

$n$	$2593$	$3449$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.222521	−	0.385418i	0.222521	−	0.385418i	−0.733052	−	0.680173i	$-0.761905\pi$
$2$	0.222521	−	0.385418i	0.222521	−	0.385418i	0.955573	+	0.294755i	$0.0952381\pi$
$3$	0.980172	−	0.198146i	0.980172	−	0.198146i
$3$	0.980172	−	0.198146i	0.980172	−	0.198146i
$4$	0.400969	+	0.694498i	0.400969	+	0.694498i
$5$	−0.542546	−	0.939718i	−0.542546	−	0.939718i	−0.998757	−	0.0498459i	$-0.984127\pi$
$5$	−0.542546	−	0.939718i	−0.542546	−	0.939718i	0.456211	−	0.889872i	$-0.349206\pi$
$6$	0.141740	−	0.421867i	0.141740	−	0.421867i
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$	0.801938			0.801938
$9$	0.921476	−	0.388435i	0.921476	−	0.388435i
$10$	−0.482912			−0.482912
$11$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$11$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$12$	0.530631	+	0.601278i	0.530631	+	0.601278i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$		0			0
$15$	−0.717990	−	0.813582i	−0.717990	−	0.813582i
$16$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	0.0553382	−	0.441588i	0.0553382	−	0.441588i
$19$	1.75644			1.75644			0.878222	−	0.478254i	$-0.158730\pi$
$19$	1.75644			1.75644			0.878222	+	0.478254i	$0.158730\pi$
$20$	0.435088	−	0.753595i	0.435088	−	0.753595i
$21$		0			0
$22$	0.340922	+	0.590494i	0.340922	+	0.590494i
$23$	0.583744	+	1.01107i	0.583744	+	1.01107i	0.995031	+	0.0995678i	$0.0317460\pi$
$23$	0.583744	+	1.01107i	0.583744	+	1.01107i	−0.411287	+	0.911506i	$0.634921\pi$
$24$	0.786037	−	0.158901i	0.786037	−	0.158901i
$25$	−0.0887129	+	0.153655i	−0.0887129	+	0.153655i
$26$		0			0
$27$	0.826239	−	0.563320i	0.826239	−	0.563320i
$28$		0			0
$29$	−0.698237	+	1.20938i	−0.698237	+	1.20938i	0.270840	+	0.962624i	$0.412698\pi$
$29$	−0.698237	+	1.20938i	−0.698237	+	1.20938i	−0.969077	+	0.246757i	$0.920635\pi$
$30$	−0.473337	+	0.0956871i	−0.473337	+	0.0956871i
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	0.500000	+	0.866025i	0.500000	+	0.866025i
$33$	−0.487950	+	1.45231i	−0.487950	+	1.45231i
$34$		0			0
$35$		0			0
$36$	0.639251	+	0.484214i	0.639251	+	0.484214i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	0.390845	−	0.676964i	0.390845	−	0.676964i
$39$		0			0
$40$	−0.435088	−	0.753595i	−0.435088	−	0.753595i
$41$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	−0.900969	−	0.433884i	$-0.857143\pi$
$41$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	0.0747301	−	0.997204i	$-0.476190\pi$
$42$		0			0
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$	−1.22864			−1.22864
$45$	−0.864963	−	0.655184i	−0.864963	−	0.655184i
$46$	0.519581			0.519581
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	−0.141740	+	0.421867i	−0.141740	+	0.421867i
$49$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$50$	0.0394810	+	0.0683830i	0.0394810	+	0.0683830i
$51$		0			0
$52$		0			0
$53$	−0.0498614			−0.0498614			−0.0249307	−	0.999689i	$-0.507937\pi$
$53$	−0.0498614			−0.0498614			−0.0249307	+	0.999689i	$0.507937\pi$
$54$	−0.0332580	−	0.443797i	−0.0332580	−	0.443797i
$55$	1.66246			1.66246
$56$		0			0
$57$	1.72162	−	0.348032i	1.72162	−	0.348032i
$58$	0.310745	+	0.538225i	0.310745	+	0.538225i
$59$	−0.921476	−	1.59604i	−0.921476	−	1.59604i	−0.797133	−	0.603804i	$-0.793651\pi$
$59$	−0.921476	−	1.59604i	−0.921476	−	1.59604i	−0.124344	−	0.992239i	$-0.539683\pi$
$60$	0.277140	−	0.824864i	0.277140	−	0.824864i
$61$	0.988831	−	1.71271i	0.988831	−	1.71271i	0.365341	−	0.930874i	$-0.380952\pi$
$61$	0.988831	−	1.71271i	0.988831	−	1.71271i	0.623490	−	0.781831i	$-0.285714\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$	0.451166	+	0.511234i	0.451166	+	0.511234i
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$	0.772510	+	0.875360i	0.772510	+	0.875360i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	0.738967	−	0.311501i	0.738967	−	0.311501i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	−0.0565077	+	0.168187i	−0.0565077	+	0.168187i
$76$	0.704279	+	1.21985i	0.704279	+	1.21985i
$77$		0			0
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	0.482912			0.482912
$81$	0.698237	−	0.715867i	0.698237	−	0.715867i
$82$	−0.735422			−0.735422
$83$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$83$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.444758	+	1.32376i	−0.444758	+	1.32376i
$88$	−0.614320	+	1.06403i	−0.614320	+	1.06403i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	−0.444992	+	0.187580i	−0.444992	+	0.187580i
$91$		0			0
$92$	−0.468126	+	0.810818i	−0.468126	+	0.810818i
$93$		0			0
$94$		0			0
$95$	−0.952952	−	1.65056i	−0.952952	−	1.65056i
$96$	0.661686	+	0.749781i	0.661686	+	0.749781i
$97$	−0.270840	+	0.469109i	−0.270840	+	0.469109i	−0.969077	−	0.246757i	$-0.920635\pi$
$97$	−0.270840	+	0.469109i	−0.270840	+	0.469109i	0.698237	+	0.715867i	$0.253968\pi$
$98$	−0.445042			−0.445042
$99$	−0.190506	+	1.52020i	−0.190506	+	1.52020i
$100$	−0.142284			−0.142284
$101$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$101$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		0			0
$105$		0			0
$106$	−0.0110952	+	0.0192175i	−0.0110952	+	0.0192175i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	0.722521	+	0.347948i	0.722521	+	0.347948i
$109$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$109$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$110$	0.369932	−	0.640741i	0.369932	−	0.640741i
$111$		0			0
$112$		0			0
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$	0.248958	−	0.740986i	0.248958	−	0.740986i
$115$	0.633416	−	1.09711i	0.633416	−	1.09711i
$116$	−1.11988			−1.11988
$117$		0			0
$118$	−0.820191			−0.820191
$119$		0			0
$120$	−0.575784	−	0.652442i	−0.575784	−	0.652442i
$121$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$122$	−0.440071	−	0.762226i	−0.440071	−	0.762226i
$123$	−1.09342	−	1.23900i	−1.09342	−	1.23900i
$124$		0			0
$125$	−0.892569			−0.892569
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$129$		0			0
$130$		0			0
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$	−1.20428	+	0.243450i	−1.20428	+	0.243450i
$133$		0			0
$134$		0			0
$135$	−0.977635	−	0.470804i	−0.977635	−	0.470804i
$136$		0			0
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$	0.509279	−	0.102953i	0.509279	−	0.102953i
$139$	0.969077	+	1.67849i	0.969077	+	1.67849i	0.698237	+	0.715867i	$0.253968\pi$
$139$	0.969077	+	1.67849i	0.969077	+	1.67849i	0.270840	+	0.962624i	$0.412698\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.0553382	+	0.441588i	−0.0553382	+	0.441588i
$145$	1.51530			1.51530
$146$		0			0
$147$	−0.661686	−	0.749781i	−0.661686	−	0.749781i
$148$		0			0
$149$	0.318487	+	0.551635i	0.318487	+	0.551635i	0.980172	−	0.198146i	$-0.0634921\pi$
$149$	0.318487	+	0.551635i	0.318487	+	0.551635i	−0.661686	+	0.749781i	$0.730159\pi$
$150$	0.0522480	+	0.0592042i	0.0522480	+	0.0592042i
$151$	−0.542546	+	0.939718i	−0.542546	+	0.939718i	0.456211	+	0.889872i	$0.349206\pi$
$151$	−0.542546	+	0.939718i	−0.542546	+	0.939718i	−0.998757	+	0.0498459i	$0.984127\pi$
$152$	1.40856			1.40856
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$157$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$158$		0			0
$159$	−0.0488728	+	0.00987984i	−0.0488728	+	0.00987984i
$160$	0.542546	−	0.939718i	0.542546	−	0.939718i
$161$		0			0
$162$	−0.120535	−	0.428408i	−0.120535	−	0.428408i
$163$	−1.16749			−1.16749			−0.583744	−	0.811938i	$-0.698413\pi$
$163$	−1.16749			−1.16749			−0.583744	+	0.811938i	$0.698413\pi$
$164$	0.662592	−	1.14764i	0.662592	−	1.14764i
$165$	1.62950	−	0.329410i	1.62950	−	0.329410i
$166$		0			0
$167$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$167$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$170$		0			0
$171$	1.61852	−	0.682264i	1.61852	−	0.682264i
$172$		0			0
$173$	−0.995031	+	1.72344i	−0.995031	+	1.72344i	−0.411287	+	0.911506i	$0.634921\pi$
$173$	−0.995031	+	1.72344i	−0.995031	+	1.72344i	−0.583744	+	0.811938i	$0.698413\pi$
$174$	0.411231	+	0.465981i	0.411231	+	0.465981i
$175$		0			0
$176$	−0.340922	−	0.590494i	−0.340922	−	0.590494i
$177$	−1.21946	−	1.38181i	−1.21946	−	1.38181i
$178$		0			0
$179$	0.730682			0.730682			0.365341	−	0.930874i	$-0.380952\pi$
$179$	0.730682			0.730682			0.365341	+	0.930874i	$0.380952\pi$
$180$	0.108201	−	0.863423i	0.108201	−	0.863423i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	0.629859	−	1.87468i	0.629859	−	1.87468i
$184$	0.468126	+	0.810818i	0.468126	+	0.810818i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−0.848207			−0.848207
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$		0			0
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$	0.120535	+	0.208773i	0.120535	+	0.208773i
$195$		0			0
$196$	0.400969	−	0.694498i	0.400969	−	0.694498i
$197$	−1.59427			−1.59427			−0.797133	−	0.603804i	$-0.793651\pi$
$197$	−1.59427			−1.59427			−0.797133	+	0.603804i	$0.793651\pi$
$198$	0.543520	+	0.411700i	0.543520	+	0.411700i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−0.0711422	+	0.123222i	−0.0711422	+	0.123222i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.896546	+	1.55286i	−0.896546	+	1.55286i
$206$		0			0
$207$	0.930642	+	0.704934i	0.930642	+	0.704934i
$208$		0			0
$209$	−1.34551	+	2.33050i	−1.34551	+	2.33050i
$210$		0			0
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$	−0.0199929	−	0.0346287i	−0.0199929	−	0.0346287i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	0.662592	−	0.451748i	0.662592	−	0.451748i
$217$		0			0
$218$	−0.326239	+	0.565062i	−0.326239	+	0.565062i
$219$		0			0
$220$	0.666594	+	1.15457i	0.666594	+	1.15457i
$221$		0			0
$222$		0			0
$223$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$223$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$224$		0			0
$225$	−0.0220618	+	0.176049i	−0.0220618	+	0.176049i
$226$		0			0
$227$	0.969077	−	1.67849i	0.969077	−	1.67849i	0.270840	−	0.962624i	$-0.412698\pi$
$227$	0.969077	−	1.67849i	0.969077	−	1.67849i	0.698237	−	0.715867i	$-0.253968\pi$
$228$	0.932023	+	1.05611i	0.932023	+	1.05611i
$229$	0.661686	+	1.14607i	0.661686	+	1.14607i	0.980172	+	0.198146i	$0.0634921\pi$
$229$	0.661686	+	1.14607i	0.661686	+	1.14607i	−0.318487	+	0.947927i	$0.603175\pi$
$230$	−0.281897	−	0.488259i	−0.281897	−	0.488259i
$231$		0			0
$232$	−0.559942	+	0.969849i	−0.559942	+	0.969849i
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$		0			0
$236$	0.738967	−	1.27993i	0.738967	−	1.27993i
$237$		0			0
$238$		0			0
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$	0.473337	−	0.0956871i	0.473337	−	0.0956871i
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	−0.599603			−0.599603
$243$	0.542546	−	0.840026i	0.542546	−	0.840026i
$244$	1.58596			1.58596
$245$	−0.542546	+	0.939718i	−0.542546	+	0.939718i
$246$	−0.720840	+	0.145721i	−0.720840	+	0.145721i
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−0.198615	+	0.344012i	−0.198615	+	0.344012i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$	−1.78869			−1.78869
$254$		0			0
$255$		0			0
$256$	0.222521	+	0.385418i	0.222521	+	0.385418i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.173643	+	1.38564i	−0.173643	+	1.38564i
$262$		0			0
$263$	0.797133	−	1.38067i	0.797133	−	1.38067i	−0.124344	−	0.992239i	$-0.539683\pi$
$263$	0.797133	−	1.38067i	0.797133	−	1.38067i	0.921476	−	0.388435i	$-0.126984\pi$
$264$	−0.391305	+	1.16466i	−0.391305	+	1.16466i
$265$	0.0270521	+	0.0468556i	0.0270521	+	0.0468556i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$	−0.399000	+	0.272034i	−0.399000	+	0.272034i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.135916	−	0.235413i	−0.135916	−	0.235413i
$276$	−0.298184	+	0.887499i	−0.298184	+	0.887499i
$277$	0.318487	−	0.551635i	0.318487	−	0.551635i	−0.661686	−	0.749781i	$-0.730159\pi$
$277$	0.318487	−	0.551635i	0.318487	−	0.551635i	0.980172	+	0.198146i	$0.0634921\pi$
$278$	0.862560			0.862560
$279$		0			0
$280$		0			0
$281$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$281$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$282$		0			0
$283$	−0.921476	−	1.59604i	−0.921476	−	1.59604i	−0.797133	−	0.603804i	$-0.793651\pi$
$283$	−0.921476	−	1.59604i	−0.921476	−	1.59604i	−0.124344	−	0.992239i	$-0.539683\pi$
$284$		0			0
$285$	−1.26111	−	1.42901i	−1.26111	−	1.42901i
$286$		0			0
$287$		0			0
$288$	0.797133	+	0.603804i	0.797133	+	0.603804i
$289$	1.00000			1.00000
$290$	0.337187	−	0.584024i	0.337187	−	0.584024i
$291$	−0.172518	+	0.513474i	−0.172518	+	0.513474i
$292$		0			0
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$	−0.436218	+	0.0881833i	−0.436218	+	0.0881833i
$295$	−0.999887	+	1.73186i	−0.999887	+	1.73186i
$296$		0			0
$297$	0.114493	+	1.52780i	0.114493	+	1.52780i
$298$	0.283480			0.283480
$299$		0			0
$300$	−0.139463	+	0.0281931i	−0.139463	+	0.0281931i
$301$		0			0
$302$	0.241456	+	0.418214i	0.241456	+	0.418214i
$303$		0			0
$304$	−0.390845	+	0.676964i	−0.390845	+	0.676964i
$305$	−2.14595			−2.14595
$306$		0			0
$307$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$307$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$311$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$	−0.681844			−0.681844
$315$		0			0
$316$		0			0
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$	−0.00706735	+	0.0210349i	−0.00706735	+	0.0210349i
$319$	−1.06976	−	1.85288i	−1.06976	−	1.85288i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.777140	+	0.197884i	0.777140	+	0.197884i
$325$		0			0
$326$	−0.259790	+	0.449970i	−0.259790	+	0.449970i
$327$	−1.43703	+	0.290503i	−1.43703	+	0.290503i
$328$	−0.662592	−	1.14764i	−0.662592	−	1.14764i
$329$		0			0
$330$	0.235637	−	0.701337i	0.235637	−	0.701337i
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	0.623490	−	0.781831i	$-0.285714\pi$
$337$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	−0.988831	+	0.149042i	$0.952381\pi$
$338$	0.222521	+	0.385418i	0.222521	+	0.385418i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	0.0971983	−	0.775624i	0.0971983	−	0.775624i
$343$		0			0
$344$		0			0
$345$	0.403469	−	1.20086i	0.403469	−	1.20086i
$346$	0.442830	+	0.767005i	0.442830	+	0.767005i
$347$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.623490	+	0.781831i	$0.285714\pi$
$347$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.365341	+	0.930874i	$0.380952\pi$
$348$	−1.09768	+	0.221901i	−1.09768	+	0.221901i
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$		0			0
$351$		0			0
$352$	−1.53209			−1.53209
$353$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$353$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$354$	−0.803929	+	0.162518i	−0.803929	+	0.162518i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.162592	−	0.281618i	0.162592	−	0.281618i
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	−0.693646	−	0.525416i	−0.693646	−	0.525416i
$361$	2.08509			2.08509
$362$		0			0
$363$	−0.891487	−	1.01018i	−0.891487	−	1.01018i
$364$		0			0
$365$		0			0
$366$	−0.582378	−	0.659914i	−0.582378	−	0.659914i
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$	−0.519581			−0.519581
$369$	−1.31724	−	0.997773i	−1.31724	−	0.997773i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	−0.874872	+	0.176859i	−0.874872	+	0.176859i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$379$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$380$	0.764208	−	1.32365i	0.764208	−	1.32365i
$381$		0			0
$382$		0			0
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$	−0.318487	+	0.947927i	−0.318487	+	0.947927i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−0.434394			−0.434394
$389$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$389$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$390$		0			0
$391$		0			0
$392$	−0.400969	−	0.694498i	−0.400969	−	0.694498i
$393$		0			0
$394$	−0.354757	+	0.614458i	−0.354757	+	0.614458i
$395$		0			0
$396$	−1.13216	+	0.477246i	−1.13216	+	0.477246i
$397$	−1.59427			−1.59427			−0.797133	−	0.603804i	$-0.793651\pi$
$397$	−1.59427			−1.59427			−0.797133	+	0.603804i	$0.793651\pi$
$398$		0			0
$399$		0			0
$400$	−0.0394810	−	0.0683830i	−0.0394810	−	0.0683830i
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−1.05154	−	0.267755i	−1.05154	−	0.267755i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$409$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$410$	0.399000	+	0.691089i	0.399000	+	0.691089i
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.478781	−	0.201823i	0.478781	−	0.201823i
$415$		0			0
$416$		0			0
$417$	1.28245	+	1.45319i	1.28245	+	1.45319i
$418$	0.598810	+	1.03717i	0.598810	+	1.03717i
$419$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$419$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$420$		0			0
$421$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$421$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$422$		0			0
$423$		0			0
$424$	−0.0399857			−0.0399857
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.00000			1.00000
$431$	1.00000			1.00000
$432$	0.0332580	+	0.443797i	0.0332580	+	0.443797i
$433$	−1.99751			−1.99751			−0.998757	−	0.0498459i	$-0.984127\pi$
$433$	−1.99751			−1.99751			−0.998757	+	0.0498459i	$0.984127\pi$
$434$		0			0
$435$	1.48526	−	0.300251i	1.48526	−	0.300251i
$436$	−0.587862	−	1.01821i	−0.587862	−	1.01821i
$437$	1.02531	+	1.77589i	1.02531	+	1.77589i
$438$		0			0
$439$	−0.456211	+	0.790180i	−0.456211	+	0.790180i	−0.998757	−	0.0498459i	$-0.984127\pi$
$439$	−0.456211	+	0.790180i	−0.456211	+	0.790180i	0.542546	+	0.840026i	$0.317460\pi$
$440$	1.33319			1.33319
$441$	−0.797133	−	0.603804i	−0.797133	−	0.603804i
$442$		0			0
$443$	0.853291	−	1.47794i	0.853291	−	1.47794i	−0.0249307	−	0.999689i	$-0.507937\pi$
$443$	0.853291	−	1.47794i	0.853291	−	1.47794i	0.878222	−	0.478254i	$-0.158730\pi$
$444$		0			0
$445$		0			0
$446$	0.340922	+	0.590494i	0.340922	+	0.590494i
$447$	0.421476	+	0.477591i	0.421476	+	0.477591i
$448$		0			0
$449$	1.75644			1.75644			0.878222	−	0.478254i	$-0.158730\pi$
$449$	1.75644			1.75644			0.878222	+	0.478254i	$0.158730\pi$
$450$	0.0629431	+	0.0476775i	0.0629431	+	0.0476775i
$451$	2.53174			2.53174
$452$		0			0
$453$	−0.345587	+	1.02859i	−0.345587	+	1.02859i
$454$	−0.431280	−	0.746999i	−0.431280	−	0.746999i
$455$		0			0
$456$	1.38063	−	0.279100i	1.38063	−	0.279100i
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$	0.588956			0.588956
$459$		0			0
$460$	1.01592			1.01592
$461$	0.411287	−	0.712370i	0.411287	−	0.712370i	−0.583744	−	0.811938i	$-0.698413\pi$
$461$	0.411287	−	0.712370i	0.411287	−	0.712370i	0.995031	+	0.0995678i	$0.0317460\pi$
$462$		0			0
$463$	−0.270840	−	0.469109i	−0.270840	−	0.469109i	0.698237	−	0.715867i	$-0.253968\pi$
$463$	−0.270840	−	0.469109i	−0.270840	−	0.469109i	−0.969077	+	0.246757i	$0.920635\pi$
$464$	−0.310745	−	0.538225i	−0.310745	−	0.538225i
$465$		0			0
$466$		0			0
$467$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$467$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.01376	−	1.14873i	−1.01376	−	1.14873i
$472$	−0.738967	−	1.27993i	−0.738967	−	1.27993i
$473$		0			0
$474$		0			0
$475$	−0.155819	+	0.269887i	−0.155819	+	0.269887i
$476$		0			0
$477$	−0.0459461	+	0.0193679i	−0.0459461	+	0.0193679i
$478$		0			0
$479$	0.988831	−	1.71271i	0.988831	−	1.71271i	0.365341	−	0.930874i	$-0.380952\pi$
$479$	0.988831	−	1.71271i	0.988831	−	1.71271i	0.623490	−	0.781831i	$-0.285714\pi$
$480$	0.345587	−	1.02859i	0.345587	−	1.02859i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.540224	−	0.935695i	0.540224	−	0.935695i
$485$	0.587774			0.587774
$486$	−0.203033	−	0.396030i	−0.203033	−	0.396030i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$	0.792981	−	1.37348i	0.792981	−	1.37348i
$489$	−1.14434	+	0.231333i	−1.14434	+	0.231333i
$490$	0.241456	+	0.418214i	0.241456	+	0.418214i
$491$	0.733052	+	1.26968i	0.733052	+	1.26968i	0.955573	+	0.294755i	$0.0952381\pi$
$491$	0.733052	+	1.26968i	0.733052	+	1.26968i	−0.222521	+	0.974928i	$0.571429\pi$
$492$	0.422053	−	1.25618i	0.422053	−	1.25618i
$493$		0			0
$494$		0			0
$495$	1.53192	−	0.645757i	1.53192	−	0.645757i
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	−0.357892	−	0.619888i	−0.357892	−	0.619888i
$501$		0			0
$502$		0			0
$503$	−0.248687			−0.248687			−0.124344	−	0.992239i	$-0.539683\pi$
$503$	−0.248687			−0.248687			−0.124344	+	0.992239i	$0.539683\pi$
$504$		0			0
$505$		0			0
$506$	−0.398022	+	0.689394i	−0.398022	+	0.689394i
$507$	−0.318487	+	0.947927i	−0.318487	+	0.947927i
$508$		0			0
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$		0			0
$511$		0			0
$512$	−0.801938			−0.801938
$513$	1.45124	−	0.989440i	1.45124	−	0.989440i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.633808	+	1.88643i	−0.633808	+	1.88643i
$520$		0			0
$521$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$521$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$522$	0.495409	+	0.375258i	0.495409	+	0.375258i
$523$	1.65248			1.65248			0.826239	−	0.563320i	$-0.190476\pi$
$523$	1.65248			1.65248			0.826239	+	0.563320i	$0.190476\pi$
$524$		0			0
$525$		0			0
$526$	−0.354757	−	0.614458i	−0.354757	−	0.614458i
$527$		0			0
$528$	−0.451166	−	0.511234i	−0.451166	−	0.511234i
$529$	−0.181513	+	0.314390i	−0.181513	+	0.314390i
$530$	0.0240786			0.0240786
$531$	−1.46908	−	1.11278i	−1.46908	−	1.11278i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.716194	−	0.144782i	0.716194	−	0.144782i
$538$		0			0
$539$	1.53209			1.53209
$540$	−0.0650284	−	0.867743i	−0.0650284	−	0.867743i
$541$	−1.70658			−1.70658			−0.853291	−	0.521435i	$-0.825397\pi$
$541$	−1.70658			−1.70658			−0.853291	+	0.521435i	$0.825397\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.795429	+	1.37772i	0.795429	+	1.37772i
$546$		0			0
$547$	−0.456211	+	0.790180i	−0.456211	+	0.790180i	−0.998757	−	0.0498459i	$-0.984127\pi$
$547$	−0.456211	+	0.790180i	−0.456211	+	0.790180i	0.542546	+	0.840026i	$0.317460\pi$
$548$		0			0
$549$	0.245910	−	1.96231i	0.245910	−	1.96231i
$550$	−0.120977			−0.120977
$551$	−1.22641	+	2.12421i	−1.22641	+	2.12421i
$552$	0.619505	+	0.701984i	0.619505	+	0.701984i
$553$		0			0
$554$	−0.141740	−	0.245501i	−0.141740	−	0.245501i
$555$		0			0
$556$	−0.777140	+	1.34605i	−0.777140	+	1.34605i
$557$		0			0		1.00000			$0$
$557$		0			0		−1.00000			$\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.733052	−	0.680173i	$-0.761905\pi$
$563$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.222521	−	0.974928i	$-0.571429\pi$
$564$		0			0
$565$		0			0
$566$	−0.820191			−0.820191
$567$		0			0
$568$		0			0
$569$	0.853291	−	1.47794i	0.853291	−	1.47794i	−0.0249307	−	0.999689i	$-0.507937\pi$
$569$	0.853291	−	1.47794i	0.853291	−	1.47794i	0.878222	−	0.478254i	$-0.158730\pi$
$570$	−0.831389	+	0.168069i	−0.831389	+	0.168069i
$571$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$571$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.207142			−0.207142
$576$		0			0
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	0.222521	−	0.385418i	0.222521	−	0.385418i
$579$		0			0
$580$	0.607589	+	1.05238i	0.607589	+	1.05238i
$581$		0			0
$582$	0.159513	+	0.180750i	0.159513	+	0.180750i
$583$	0.0381960	−	0.0661575i	0.0381960	−	0.0661575i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$	0.255406	−	0.760179i	0.255406	−	0.760179i
$589$		0			0
$590$	0.444992	+	0.770748i	0.444992	+	0.770748i
$591$	−1.56265	+	0.315897i	−1.56265	+	0.315897i
$592$		0			0
$593$	0.541681			0.541681			0.270840	−	0.962624i	$-0.412698\pi$
$593$	0.541681			0.541681			0.270840	+	0.962624i	$0.412698\pi$
$594$	0.614320	+	0.295841i	0.614320	+	0.295841i
$595$		0			0
$596$	−0.255406	+	0.442377i	−0.255406	+	0.442377i
$597$		0			0
$598$		0			0
$599$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$599$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$600$	−0.0453157	+	0.134875i	−0.0453157	+	0.134875i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$	−0.870177			−0.870177
$605$	−0.730971	+	1.26608i	−0.730971	+	1.26608i
$606$		0			0
$607$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.623490	+	0.781831i	$0.285714\pi$
$607$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.365341	+	0.930874i	$0.380952\pi$
$608$	0.878222	+	1.52112i	0.878222	+	1.52112i
$609$		0			0
$610$	−0.477518	+	0.827085i	−0.477518	+	0.827085i
$611$		0			0
$612$		0			0
$613$	1.65248			1.65248			0.826239	−	0.563320i	$-0.190476\pi$
$613$	1.65248			1.65248			0.826239	+	0.563320i	$0.190476\pi$
$614$	−0.0990311	+	0.171527i	−0.0990311	+	0.171527i
$615$	−0.571076	+	1.69972i	−0.571076	+	1.69972i
$616$		0			0
$617$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$617$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$618$		0			0
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	1.05187	+	0.506554i	1.05187	+	0.506554i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.572973	+	0.992418i	0.572973	+	0.992418i
$626$		0			0
$627$	−0.857056	+	2.55090i	−0.857056	+	2.55090i
$628$	0.614320	−	1.06403i	0.614320	−	1.06403i
$629$		0			0
$630$		0			0
$631$	−0.636973			−0.636973			−0.318487	−	0.947927i	$-0.603175\pi$
$631$	−0.636973			−0.636973			−0.318487	+	0.947927i	$0.603175\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−0.0264580	−	0.0299805i	−0.0264580	−	0.0299805i
$637$		0			0
$638$	−0.952177			−0.952177
$639$		0			0
$640$	1.08509			1.08509
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$		0			0
$643$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$643$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.93815			−1.93815			−0.969077	−	0.246757i	$-0.920635\pi$
$647$	−1.93815			−1.93815			−0.969077	+	0.246757i	$0.920635\pi$
$648$	0.559942	−	0.574081i	0.559942	−	0.574081i
$649$	2.82357			2.82357
$650$		0			0
$651$		0			0
$652$	−0.468126	−	0.810818i	−0.468126	−	0.810818i
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$	−0.207805	+	0.618501i	−0.207805	+	0.618501i
$655$		0			0
$656$	0.735422			0.735422
$657$		0			0
$658$		0			0
$659$	0.0249307	−	0.0431812i	0.0249307	−	0.0431812i	−0.853291	−	0.521435i	$-0.825397\pi$
$659$	0.0249307	−	0.0431812i	0.0249307	−	0.0431812i	0.878222	+	0.478254i	$0.158730\pi$
$660$	0.882152	+	0.999599i	0.882152	+	0.999599i
$661$	0.124344	+	0.215370i	0.124344	+	0.215370i	0.921476	−	0.388435i	$-0.126984\pi$
$661$	0.124344	+	0.215370i	0.124344	+	0.215370i	−0.797133	+	0.603804i	$0.793651\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.63037			−1.63037
$668$		0			0
$669$	−0.487950	+	1.45231i	−0.487950	+	1.45231i
$670$		0			0
$671$	1.51498	+	2.62402i	1.51498	+	2.62402i
$672$		0			0
$673$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i	−0.900969	−	0.433884i	$-0.857143\pi$
$673$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i	0.826239	+	0.563320i	$0.190476\pi$
$674$	−0.325184			−0.325184
$675$	0.0132590	+	0.176930i	0.0132590	+	0.176930i
$676$	−0.801938			−0.801938
$677$	−0.980172	+	1.69771i	−0.980172	+	1.69771i	−0.318487	+	0.947927i	$0.603175\pi$
$677$	−0.980172	+	1.69771i	−0.980172	+	1.69771i	−0.661686	+	0.749781i	$0.730159\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.617276	−	1.83723i	0.617276	−	1.83723i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	1.12281	+	0.850494i	1.12281	+	0.850494i
$685$		0			0
$686$		0			0
$687$	0.875656	+	0.992239i	0.875656	+	0.992239i
$688$		0			0
$689$		0			0
$690$	−0.373054	−	0.422722i	−0.373054	−	0.422722i
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$	−1.59591			−1.59591
$693$		0			0
$694$	0.880142			0.880142
$695$	1.05154	−	1.82132i	1.05154	−	1.82132i
$696$	−0.356668	+	1.06157i	−0.356668	+	1.06157i
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	0.149460			0.149460			0.0747301	−	0.997204i	$-0.476190\pi$
$701$	0.149460			0.149460			0.0747301	+	0.997204i	$0.476190\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.418203	−	0.724348i	−0.418203	−	0.724348i
$707$		0			0
$708$	0.470702	−	1.40097i	0.470702	−	1.40097i
$709$	0.583744	−	1.01107i	0.583744	−	1.01107i	−0.411287	−	0.911506i	$-0.634921\pi$
$709$	0.583744	−	1.01107i	0.583744	−	1.01107i	0.995031	−	0.0995678i	$-0.0317460\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.292981	+	0.507458i	0.292981	+	0.507458i
$717$		0			0
$718$		0			0
$719$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$719$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$720$	0.444992	−	0.187580i	0.444992	−	0.187580i
$721$		0			0
$722$	0.463977	−	0.803631i	0.463977	−	0.803631i
$723$		0			0
$724$		0			0
$725$	−0.123885	−	0.214575i	−0.123885	−	0.214575i
$726$	−0.587715	+	0.118809i	−0.587715	+	0.118809i
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$	0.365341	−	0.930874i	0.365341	−	0.930874i
$730$		0			0
$731$		0			0
$732$	1.55452	−	0.314252i	1.55452	−	0.314252i
$733$	−0.995031	−	1.72344i	−0.995031	−	1.72344i	−0.583744	−	0.811938i	$-0.698413\pi$
$733$	−0.995031	−	1.72344i	−0.995031	−	1.72344i	−0.411287	−	0.911506i	$-0.634921\pi$
$734$		0			0
$735$	−0.345587	+	1.02859i	−0.345587	+	1.02859i
$736$	−0.583744	+	1.01107i	−0.583744	+	1.01107i
$737$		0			0
$738$	−0.677674	+	0.285663i	−0.677674	+	0.285663i
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$743$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$744$		0			0
$745$	0.345587	−	0.598575i	0.345587	−	0.598575i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$	−0.126513	+	0.376546i	−0.126513	+	0.376546i
$751$	−0.980172	−	1.69771i	−0.980172	−	1.69771i	−0.661686	−	0.749781i	$-0.730159\pi$
$751$	−0.980172	−	1.69771i	−0.980172	−	1.69771i	−0.318487	−	0.947927i	$-0.603175\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.17743			1.17743
$756$		0			0
$757$	1.91115			1.91115			0.955573	−	0.294755i	$-0.0952381\pi$
$757$	1.91115			1.91115			0.955573	+	0.294755i	$0.0952381\pi$
$758$	−0.326239	+	0.565062i	−0.326239	+	0.565062i
$759$	−1.75323	+	0.354423i	−1.75323	+	0.354423i
$760$	−0.764208	−	1.32365i	−0.764208	−	1.32365i
$761$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.733052	−	0.680173i	$-0.761905\pi$
$761$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.222521	−	0.974928i	$-0.571429\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.294478	+	0.333684i	0.294478	+	0.333684i
$769$	0.797133	+	1.38067i	0.797133	+	1.38067i	0.921476	+	0.388435i	$0.126984\pi$
$769$	0.797133	+	1.38067i	0.797133	+	1.38067i	−0.124344	+	0.992239i	$0.539683\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$773$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$774$		0			0
$775$		0			0
$776$	−0.217197	+	0.376197i	−0.217197	+	0.376197i
$777$		0			0
$778$	0.0772807	+	0.133854i	0.0772807	+	0.133854i
$779$	−1.45124	−	2.51362i	−1.45124	−	2.51362i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.104359	+	1.39257i	0.104359	+	1.39257i
$784$	0.445042			0.445042
$785$	−0.831229	+	1.43973i	−0.831229	+	1.43973i
$786$		0			0
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$	−0.639251	−	1.10721i	−0.639251	−	1.10721i
$789$	0.507752	−	1.51125i	0.507752	−	1.51125i
$790$		0			0
$791$		0			0
$792$	−0.152774	+	1.21910i	−0.152774	+	1.21910i
$793$		0			0
$794$	−0.354757	+	0.614458i	−0.354757	+	0.614458i
$795$	0.0358000	+	0.0405663i	0.0358000	+	0.0405663i
$796$		0			0
$797$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i	0.826239	−	0.563320i	$-0.190476\pi$
$797$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i	−0.900969	+	0.433884i	$0.857143\pi$
$798$		0			0
$799$		0			0
$800$	−0.177426			−0.177426
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$	−0.337187	+	0.345700i	−0.337187	+	0.345700i
$811$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$811$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.633416	+	1.09711i	0.633416	+	1.09711i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−1.43795			−1.43795
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$		0			0
$823$	0.853291	+	1.47794i	0.853291	+	1.47794i	0.878222	+	0.478254i	$0.158730\pi$
$823$	0.853291	+	1.47794i	0.853291	+	1.47794i	−0.0249307	+	0.999689i	$0.507937\pi$
$824$		0			0
$825$	−0.179867	−	0.203815i	−0.179867	−	0.203815i
$826$		0			0
$827$	−1.99751			−1.99751			−0.998757	−	0.0498459i	$-0.984127\pi$
$827$	−1.99751			−1.99751			−0.998757	+	0.0498459i	$0.984127\pi$
$828$	−0.116417	+	0.928986i	−0.116417	+	0.928986i
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$	0.202867	−	0.603804i	0.202867	−	0.603804i
$832$		0			0
$833$		0			0
$834$	0.845458	−	0.170913i	0.845458	−	0.170913i
$835$		0			0
$836$	−2.15804			−2.15804
$837$		0			0
$838$		0			0
$839$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$839$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$840$		0			0
$841$	−0.475069	−	0.822844i	−0.475069	−	0.822844i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.08509			1.08509
$846$		0			0
$847$		0			0
$848$	0.0110952	−	0.0192175i	0.0110952	−	0.0192175i
$849$	−1.21946	−	1.38181i	−1.21946	−	1.38181i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$853$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$854$		0			0
$855$	−1.51926	−	1.15079i	−1.51926	−	1.15079i
$856$		0			0
$857$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$857$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$859$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$860$		0			0
$861$		0			0
$862$	0.222521	−	0.385418i	0.222521	−	0.385418i
$863$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$863$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$864$	0.900969	+	0.433884i	0.900969	+	0.433884i
$865$	2.15940			2.15940
$866$	−0.444489	+	0.769877i	−0.444489	+	0.769877i
$867$	0.980172	−	0.198146i	0.980172	−	0.198146i
$868$		0			0
$869$		0			0
$870$	0.214779	−	0.639257i	0.214779	−	0.639257i
$871$		0			0
$872$	−1.17572			−1.17572
$873$	−0.0673546	+	0.537477i	−0.0673546	+	0.537477i
$874$	0.912614			0.912614
$875$		0			0
$876$		0			0
$877$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$877$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$878$	0.203033	+	0.351663i	0.203033	+	0.351663i
$879$		0			0
$880$	−0.369932	+	0.640741i	−0.369932	+	0.640741i
$881$	1.99006			1.99006			0.995031	−	0.0995678i	$-0.0317460\pi$
$881$	1.99006			1.99006			0.995031	+	0.0995678i	$0.0317460\pi$
$882$	−0.410095	+	0.172870i	−0.410095	+	0.172870i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$	−0.636901	+	1.89564i	−0.636901	+	1.89564i
$886$	−0.379750	−	0.657747i	−0.379750	−	0.657747i
$887$	0.0249307	+	0.0431812i	0.0249307	+	0.0431812i	0.878222	−	0.478254i	$-0.158730\pi$
$887$	0.0249307	+	0.0431812i	0.0249307	+	0.0431812i	−0.853291	+	0.521435i	$0.825397\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.414952	+	1.47483i	0.414952	+	1.47483i
$892$	−1.22864			−1.22864
$893$		0			0
$894$	0.277859	−	0.0561704i	0.277859	−	0.0561704i
$895$	−0.396429	−	0.686635i	−0.396429	−	0.686635i
$896$		0			0
$897$		0			0
$898$	0.390845	−	0.676964i	0.390845	−	0.676964i
$899$		0			0
$900$	−0.131112	+	0.0552682i	−0.131112	+	0.0552682i
$901$		0			0
$902$	0.563366	−	0.975778i	0.563366	−	0.975778i
$903$		0			0
$904$		0			0
$905$		0			0
$906$	0.319536	+	0.362078i	0.319536	+	0.362078i
$907$	−0.698237	+	1.20938i	−0.698237	+	1.20938i	0.270840	+	0.962624i	$0.412698\pi$
$907$	−0.698237	+	1.20938i	−0.698237	+	1.20938i	−0.969077	+	0.246757i	$0.920635\pi$
$908$	1.55428			1.55428
$909$		0			0
$910$		0			0
$911$	−0.456211	+	0.790180i	−0.456211	+	0.790180i	−0.998757	−	0.0498459i	$-0.984127\pi$
$911$	−0.456211	+	0.790180i	−0.456211	+	0.790180i	0.542546	+	0.840026i	$0.317460\pi$
$912$	−0.248958	+	0.740986i	−0.248958	+	0.740986i
$913$		0			0
$914$		0			0
$915$	−2.10340	+	0.425211i	−2.10340	+	0.425211i
$916$	−0.530631	+	0.919080i	−0.530631	+	0.919080i
$917$		0			0
$918$		0			0
$919$	1.39647			1.39647			0.698237	−	0.715867i	$-0.253968\pi$
$919$	1.39647			1.39647			0.698237	+	0.715867i	$0.253968\pi$
$920$	0.507960	−	0.879813i	0.507960	−	0.879813i
$921$	−0.436218	+	0.0881833i	−0.436218	+	0.0881833i
$922$	−0.183040	−	0.317035i	−0.183040	−	0.317035i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.241071			−0.241071
$927$		0			0
$928$	−1.39647			−1.39647
$929$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$929$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$930$		0			0
$931$	−0.878222	−	1.52112i	−0.878222	−	1.52112i
$932$		0			0
$933$		0			0
$934$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$935$		0			0
$936$		0			0
$937$	−0.0498614			−0.0498614			−0.0249307	−	0.999689i	$-0.507937\pi$
$937$	−0.0498614			−0.0498614			−0.0249307	+	0.999689i	$0.507937\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$941$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$942$	−0.668324	+	0.135105i	−0.668324	+	0.135105i
$943$	0.964623	−	1.67078i	0.964623	−	1.67078i
$944$	0.820191			0.820191
$945$		0			0
$946$		0			0
$947$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$947$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$948$		0			0
$949$		0			0
$950$	0.0693460	+	0.120111i	0.0693460	+	0.120111i
$951$		0			0
$952$		0			0
$953$	1.84295			1.84295			0.921476	−	0.388435i	$-0.126984\pi$
$953$	1.84295			1.84295			0.921476	+	0.388435i	$0.126984\pi$
$954$	−0.00275924	+	0.0220182i	−0.00275924	+	0.0220182i
$955$		0			0
$956$		0			0
$957$	−1.41569	−	1.60417i	−1.41569	−	1.60417i
$958$	−0.440071	−	0.762226i	−0.440071	−	0.762226i
$959$		0			0
$960$		0			0
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$967$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$968$	−0.540224	−	0.935695i	−0.540224	−	0.935695i
$969$		0			0
$970$	0.130792	−	0.226538i	0.130792	−	0.226538i
$971$	1.65248			1.65248			0.826239	−	0.563320i	$-0.190476\pi$
$971$	1.65248			1.65248			0.826239	+	0.563320i	$0.190476\pi$
$972$	0.800941	+	0.0399733i	0.800941	+	0.0399733i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.440071	+	0.762226i	0.440071	+	0.762226i
$977$	0.318487	+	0.551635i	0.318487	+	0.551635i	0.980172	−	0.198146i	$-0.0634921\pi$
$977$	0.318487	+	0.551635i	0.318487	+	0.551635i	−0.661686	+	0.749781i	$0.730159\pi$
$978$	−0.165480	+	0.492525i	−0.165480	+	0.492525i
$979$		0			0
$980$	−0.870177			−0.870177
$981$	−1.35098	+	0.569486i	−1.35098	+	0.569486i
$982$	0.652478			0.652478
$983$	0.318487	−	0.551635i	0.318487	−	0.551635i	−0.661686	−	0.749781i	$-0.730159\pi$
$983$	0.318487	−	0.551635i	0.318487	−	0.551635i	0.980172	+	0.198146i	$0.0634921\pi$
$984$	−0.876856	−	0.993598i	−0.876856	−	0.993598i
$985$	0.864963	+	1.49816i	0.864963	+	1.49816i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	0.0919974	−	0.734122i	0.0919974	−	0.734122i
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.995031	+	1.72344i	−0.995031	+	1.72344i	−0.411287	+	0.911506i	$0.634921\pi$
$997$	−0.995031	+	1.72344i	−0.995031	+	1.72344i	−0.583744	+	0.811938i	$0.698413\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3879.1.g.c.430.12	✓	36
9.4	even	3	inner	3879.1.g.c.1723.12	yes	36
431.430	odd	2	CM	3879.1.g.c.430.12	✓	36
3879.1723	odd	6	inner	3879.1.g.c.1723.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3879.1.g.c.430.12	✓	36	1.1	even	1	trivial
3879.1.g.c.430.12	✓	36	431.430	odd	2	CM
3879.1.g.c.1723.12	yes	36	9.4	even	3	inner
3879.1.g.c.1723.12	yes	36	3879.1723	odd	6	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:	\( N \)	\(=\)	\( 3879 = 3^{2} \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3879.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 - 0.385418i) q^{2} +(0.980172 - 0.198146i) q^{3} +(0.400969 + 0.694498i) q^{4} +(-0.542546 - 0.939718i) q^{5} +(0.141740 - 0.421867i) q^{6} +0.801938 q^{8} +(0.921476 - 0.388435i) q^{9} +O(q^{10})\)	\(q+(0.222521 - 0.385418i) q^{2} +(0.980172 - 0.198146i) q^{3} +(0.400969 + 0.694498i) q^{4} +(-0.542546 - 0.939718i) q^{5} +(0.141740 - 0.421867i) q^{6} +0.801938 q^{8} +(0.921476 - 0.388435i) q^{9} -0.482912 q^{10} +(-0.766044 + 1.32683i) q^{11} +(0.530631 + 0.601278i) q^{12} +(-0.717990 - 0.813582i) q^{15} +(-0.222521 + 0.385418i) q^{16} +(0.0553382 - 0.441588i) q^{18} +1.75644 q^{19} +(0.435088 - 0.753595i) q^{20} +(0.340922 + 0.590494i) q^{22} +(0.583744 + 1.01107i) q^{23} +(0.786037 - 0.158901i) q^{24} +(-0.0887129 + 0.153655i) q^{25} +(0.826239 - 0.563320i) q^{27} +(-0.698237 + 1.20938i) q^{29} +(-0.473337 + 0.0956871i) q^{30} +(0.500000 + 0.866025i) q^{32} +(-0.487950 + 1.45231i) q^{33} +(0.639251 + 0.484214i) q^{36} +(0.390845 - 0.676964i) q^{38} +(-0.435088 - 0.753595i) q^{40} +(-0.826239 - 1.43109i) q^{41} -1.22864 q^{44} +(-0.864963 - 0.655184i) q^{45} +0.519581 q^{46} +(-0.141740 + 0.421867i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.0394810 + 0.0683830i) q^{50} -0.0498614 q^{53} +(-0.0332580 - 0.443797i) q^{54} +1.66246 q^{55} +(1.72162 - 0.348032i) q^{57} +(0.310745 + 0.538225i) q^{58} +(-0.921476 - 1.59604i) q^{59} +(0.277140 - 0.824864i) q^{60} +(0.988831 - 1.71271i) q^{61} +(0.451166 + 0.511234i) q^{66} +(0.772510 + 0.875360i) q^{69} +(0.738967 - 0.311501i) q^{72} +(-0.0565077 + 0.168187i) q^{75} +(0.704279 + 1.21985i) q^{76} +0.482912 q^{80} +(0.698237 - 0.715867i) q^{81} -0.735422 q^{82} +(-0.444758 + 1.32376i) q^{87} +(-0.614320 + 1.06403i) q^{88} +(-0.444992 + 0.187580i) q^{90} +(-0.468126 + 0.810818i) q^{92} +(-0.952952 - 1.65056i) q^{95} +(0.661686 + 0.749781i) q^{96} +(-0.270840 + 0.469109i) q^{97} -0.445042 q^{98} +(-0.190506 + 1.52020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{2} - 12 q^{4} - 24 q^{8}+O(q^{10}) \) 36 * q + 6 * q^2 - 12 * q^4 - 24 * q^8	\( 36 q + 6 q^{2} - 12 q^{4} - 24 q^{8} + 3 q^{15} - 6 q^{16} - 18 q^{25} + 3 q^{27} + 6 q^{30} + 18 q^{32} + 3 q^{33} - 3 q^{41} + 3 q^{45} - 18 q^{49} + 6 q^{50} + 6 q^{54} + 6 q^{55} + 3 q^{57} - 18 q^{60} - 3 q^{61} + 6 q^{66} - 6 q^{69} + 3 q^{75} + 12 q^{82} - 6 q^{87} + 6 q^{90} - 3 q^{95} - 12 q^{98} + 3 q^{99}+O(q^{100}) \) 36 * q + 6 * q^2 - 12 * q^4 - 24 * q^8 + 3 * q^15 - 6 * q^16 - 18 * q^25 + 3 * q^27 + 6 * q^30 + 18 * q^32 + 3 * q^33 - 3 * q^41 + 3 * q^45 - 18 * q^49 + 6 * q^50 + 6 * q^54 + 6 * q^55 + 3 * q^57 - 18 * q^60 - 3 * q^61 + 6 * q^66 - 6 * q^69 + 3 * q^75 + 12 * q^82 - 6 * q^87 + 6 * q^90 - 3 * q^95 - 12 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

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