LMFDB - Embedded newform 3879.1.g.c.430.5

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			430.5
Root			$0.980172 - 0.198146i$ of defining polynomial
Character	$\chi$	$=$	3879.430
Dual form			3879.1.g.c.1723.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.623490 + 1.07992i) q^{2} +(0.698237 - 0.715867i) q^{3} +(-0.277479 - 0.480608i) q^{4} +(0.661686 + 1.14607i) q^{5} +(0.337733 + 1.20037i) q^{6} -0.554958 q^{8} +(-0.0249307 - 0.999689i) q^{9} +O(q^{10})$	\(q+(-0.623490 + 1.07992i) q^{2} +(0.698237 - 0.715867i) q^{3} +(-0.277479 - 0.480608i) q^{4} +(0.661686 + 1.14607i) q^{5} +(0.337733 + 1.20037i) q^{6} -0.554958 q^{8} +(-0.0249307 - 0.999689i) q^{9} -1.65022 q^{10} +(0.939693 - 1.62760i) q^{11} +(-0.537797 - 0.136940i) q^{12} +(1.28245 + 0.326552i) q^{15} +(0.623490 - 1.07992i) q^{16} +(1.09512 + 0.596373i) q^{18} -0.822574 q^{19} +(0.367208 - 0.636023i) q^{20} +(1.17178 + 2.02958i) q^{22} +(0.797133 + 1.38067i) q^{23} +(-0.387492 + 0.397276i) q^{24} +(-0.375656 + 0.650656i) q^{25} +(-0.733052 - 0.680173i) q^{27} +(0.998757 - 1.72990i) q^{29} +(-1.15224 + 1.18134i) q^{30} +(0.500000 + 0.866025i) q^{32} +(-0.509014 - 1.80914i) q^{33} +(-0.473541 + 0.289375i) q^{36} +(0.512867 - 0.888311i) q^{38} +(-0.367208 - 0.636023i) q^{40} +(0.733052 + 1.26968i) q^{41} -1.04298 q^{44} +(1.12922 - 0.690053i) q^{45} -1.98802 q^{46} +(-0.337733 - 1.20037i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.468436 - 0.811354i) q^{50} +1.99006 q^{53} +(1.19158 - 0.367554i) q^{54} +2.48713 q^{55} +(-0.574352 + 0.588854i) q^{57} +(1.24543 + 2.15715i) q^{58} +(0.0249307 + 0.0431812i) q^{59} +(-0.198910 - 0.706967i) q^{60} +(-0.826239 + 1.43109i) q^{61} +(2.27109 + 0.578290i) q^{66} +(1.54497 + 0.393397i) q^{69} +(0.0138355 + 0.554786i) q^{72} +(0.203486 + 0.723232i) q^{75} +(0.228247 + 0.395336i) q^{76} +1.65022 q^{80} +(-0.998757 + 0.0498459i) q^{81} -1.82820 q^{82} +(-0.541008 - 1.92286i) q^{87} +(-0.521490 + 0.903247i) q^{88} +(0.0411411 + 1.64970i) q^{90} +(0.442375 - 0.766216i) q^{92} +(-0.544286 - 0.942730i) q^{95} +(0.969077 + 0.246757i) q^{96} +(-0.456211 + 0.790180i) q^{97} +1.24698 q^{98} +(-1.65052 - 0.898823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.623490	+	1.07992i	−0.623490	+	1.07992i	0.365341	+	0.930874i	$0.380952\pi$
$2$	−0.623490	+	1.07992i	−0.623490	+	1.07992i	−0.988831	+	0.149042i	$0.952381\pi$
$3$	0.698237	−	0.715867i	0.698237	−	0.715867i
$3$	0.698237	−	0.715867i	0.698237	−	0.715867i
$4$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$5$	0.661686	+	1.14607i	0.661686	+	1.14607i	0.980172	+	0.198146i	$0.0634921\pi$
$5$	0.661686	+	1.14607i	0.661686	+	1.14607i	−0.318487	+	0.947927i	$0.603175\pi$
$6$	0.337733	+	1.20037i	0.337733	+	1.20037i
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$	−0.554958			−0.554958
$9$	−0.0249307	−	0.999689i	−0.0249307	−	0.999689i
$10$	−1.65022			−1.65022
$11$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$11$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$12$	−0.537797	−	0.136940i	−0.537797	−	0.136940i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$		0			0
$15$	1.28245	+	0.326552i	1.28245	+	0.326552i
$16$	0.623490	−	1.07992i	0.623490	−	1.07992i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	1.09512	+	0.596373i	1.09512	+	0.596373i
$19$	−0.822574			−0.822574			−0.411287	−	0.911506i	$-0.634921\pi$
$19$	−0.822574			−0.822574			−0.411287	+	0.911506i	$0.634921\pi$
$20$	0.367208	−	0.636023i	0.367208	−	0.636023i
$21$		0			0
$22$	1.17178	+	2.02958i	1.17178	+	2.02958i
$23$	0.797133	+	1.38067i	0.797133	+	1.38067i	0.921476	+	0.388435i	$0.126984\pi$
$23$	0.797133	+	1.38067i	0.797133	+	1.38067i	−0.124344	+	0.992239i	$0.539683\pi$
$24$	−0.387492	+	0.397276i	−0.387492	+	0.397276i
$25$	−0.375656	+	0.650656i	−0.375656	+	0.650656i
$26$		0			0
$27$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$28$		0			0
$29$	0.998757	−	1.72990i	0.998757	−	1.72990i	0.456211	−	0.889872i	$-0.349206\pi$
$29$	0.998757	−	1.72990i	0.998757	−	1.72990i	0.542546	−	0.840026i	$-0.317460\pi$
$30$	−1.15224	+	1.18134i	−1.15224	+	1.18134i
$31$		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
$33$	−0.509014	−	1.80914i	−0.509014	−	1.80914i
$34$		0			0
$35$		0			0
$36$	−0.473541	+	0.289375i	−0.473541	+	0.289375i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	0.512867	−	0.888311i	0.512867	−	0.888311i
$39$		0			0
$40$	−0.367208	−	0.636023i	−0.367208	−	0.636023i
$41$	0.733052	+	1.26968i	0.733052	+	1.26968i	0.955573	+	0.294755i	$0.0952381\pi$
$41$	0.733052	+	1.26968i	0.733052	+	1.26968i	−0.222521	+	0.974928i	$0.571429\pi$
$42$		0			0
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$	−1.04298			−1.04298
$45$	1.12922	−	0.690053i	1.12922	−	0.690053i
$46$	−1.98802			−1.98802
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	−0.337733	−	1.20037i	−0.337733	−	1.20037i
$49$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$50$	−0.468436	−	0.811354i	−0.468436	−	0.811354i
$51$		0			0
$52$		0			0
$53$	1.99006			1.99006			0.995031	−	0.0995678i	$-0.0317460\pi$
$53$	1.99006			1.99006			0.995031	+	0.0995678i	$0.0317460\pi$
$54$	1.19158	−	0.367554i	1.19158	−	0.367554i
$55$	2.48713			2.48713
$56$		0			0
$57$	−0.574352	+	0.588854i	−0.574352	+	0.588854i
$58$	1.24543	+	2.15715i	1.24543	+	2.15715i
$59$	0.0249307	+	0.0431812i	0.0249307	+	0.0431812i	0.878222	−	0.478254i	$-0.158730\pi$
$59$	0.0249307	+	0.0431812i	0.0249307	+	0.0431812i	−0.853291	+	0.521435i	$0.825397\pi$
$60$	−0.198910	−	0.706967i	−0.198910	−	0.706967i
$61$	−0.826239	+	1.43109i	−0.826239	+	1.43109i	0.0747301	+	0.997204i	$0.476190\pi$
$61$	−0.826239	+	1.43109i	−0.826239	+	1.43109i	−0.900969	+	0.433884i	$0.857143\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$	2.27109	+	0.578290i	2.27109	+	0.578290i
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$	1.54497	+	0.393397i	1.54497	+	0.393397i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	0.0138355	+	0.554786i	0.0138355	+	0.554786i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	0.203486	+	0.723232i	0.203486	+	0.723232i
$76$	0.228247	+	0.395336i	0.228247	+	0.395336i
$77$		0			0
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	1.65022			1.65022
$81$	−0.998757	+	0.0498459i	−0.998757	+	0.0498459i
$82$	−1.82820			−1.82820
$83$		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
$87$	−0.541008	−	1.92286i	−0.541008	−	1.92286i
$88$	−0.521490	+	0.903247i	−0.521490	+	0.903247i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	0.0411411	+	1.64970i	0.0411411	+	1.64970i
$91$		0			0
$92$	0.442375	−	0.766216i	0.442375	−	0.766216i
$93$		0			0
$94$		0			0
$95$	−0.544286	−	0.942730i	−0.544286	−	0.942730i
$96$	0.969077	+	0.246757i	0.969077	+	0.246757i
$97$	−0.456211	+	0.790180i	−0.456211	+	0.790180i	−0.998757	−	0.0498459i	$-0.984127\pi$
$97$	−0.456211	+	0.790180i	−0.456211	+	0.790180i	0.542546	+	0.840026i	$0.317460\pi$
$98$	1.24698			1.24698
$99$	−1.65052	−	0.898823i	−1.65052	−	0.898823i
$100$	0.416947			0.416947
$101$		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
$106$	−1.24078	+	2.14910i	−1.24078	+	2.14910i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$109$	−1.97766			−1.97766			−0.988831	−	0.149042i	$-0.952381\pi$
$109$	−1.97766			−1.97766			−0.988831	+	0.149042i	$0.952381\pi$
$110$	−1.55070	+	2.68589i	−1.55070	+	2.68589i
$111$		0			0
$112$		0			0
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$	−0.277810	−	0.987396i	−0.277810	−	0.987396i
$115$	−1.05490	+	1.82714i	−1.05490	+	1.82714i
$116$	−1.10854			−1.10854
$117$		0			0
$118$	−0.0621761			−0.0621761
$119$		0			0
$120$	−0.711706	−	0.181223i	−0.711706	−	0.181223i
$121$	−1.26604	−	2.19285i	−1.26604	−	2.19285i
$122$	−1.03030	−	1.78454i	−1.03030	−	1.78454i
$123$	1.42077	+	0.361772i	1.42077	+	0.361772i
$124$		0			0
$125$	0.329106			0.329106
$126$		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	$0.333333\pi$
$132$	−0.728247	+	0.746635i	−0.728247	+	0.746635i
$133$		0			0
$134$		0			0
$135$	0.294478	−	1.29019i	0.294478	−	1.29019i
$136$		0			0
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$	−1.38811	+	1.42315i	−1.38811	+	1.42315i
$139$	−0.542546	−	0.939718i	−0.542546	−	0.939718i	−0.998757	−	0.0498459i	$-0.984127\pi$
$139$	−0.542546	−	0.939718i	−0.542546	−	0.939718i	0.456211	−	0.889872i	$-0.349206\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−1.09512	−	0.596373i	−1.09512	−	0.596373i
$145$	2.64345			2.64345
$146$		0			0
$147$	−0.969077	−	0.246757i	−0.969077	−	0.246757i
$148$		0			0
$149$	−0.270840	−	0.469109i	−0.270840	−	0.469109i	0.698237	−	0.715867i	$-0.253968\pi$
$149$	−0.270840	−	0.469109i	−0.270840	−	0.469109i	−0.969077	+	0.246757i	$0.920635\pi$
$150$	−0.907901	−	0.231180i	−0.907901	−	0.231180i
$151$	0.661686	−	1.14607i	0.661686	−	1.14607i	−0.318487	−	0.947927i	$-0.603175\pi$
$151$	0.661686	−	1.14607i	0.661686	−	1.14607i	0.980172	−	0.198146i	$-0.0634921\pi$
$152$	0.456494			0.456494
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$157$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$158$		0			0
$159$	1.38953	−	1.42462i	1.38953	−	1.42462i
$160$	−0.661686	+	1.14607i	−0.661686	+	1.14607i
$161$		0			0
$162$	0.568885	−	1.10965i	0.568885	−	1.10965i
$163$	−1.59427			−1.59427			−0.797133	−	0.603804i	$-0.793651\pi$
$163$	−1.59427			−1.59427			−0.797133	+	0.603804i	$0.793651\pi$
$164$	0.406813	−	0.704621i	0.406813	−	0.704621i
$165$	1.73660	−	1.78045i	1.73660	−	1.78045i
$166$		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
$171$	0.0205073	+	0.822319i	0.0205073	+	0.822319i
$172$		0			0
$173$	−0.921476	+	1.59604i	−0.921476	+	1.59604i	−0.124344	+	0.992239i	$0.539683\pi$
$173$	−0.921476	+	1.59604i	−0.921476	+	1.59604i	−0.797133	+	0.603804i	$0.793651\pi$
$174$	2.41383	+	0.614638i	2.41383	+	0.614638i
$175$		0			0
$176$	−1.17178	−	2.02958i	−1.17178	−	2.02958i
$177$	0.0483195	+	0.0123037i	0.0483195	+	0.0123037i
$178$		0			0
$179$	0.149460			0.149460			0.0747301	−	0.997204i	$-0.476190\pi$
$179$	0.149460			0.149460			0.0747301	+	0.997204i	$0.476190\pi$
$180$	−0.644980	−	0.351237i	−0.644980	−	0.351237i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	0.447558	+	1.59071i	0.447558	+	1.59071i
$184$	−0.442375	−	0.766216i	−0.442375	−	0.766216i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	1.35743			1.35743
$191$		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	$0.333333\pi$
$194$	−0.568885	−	0.985338i	−0.568885	−	0.985338i
$195$		0			0
$196$	−0.277479	+	0.480608i	−0.277479	+	0.480608i
$197$	−1.70658			−1.70658			−0.853291	−	0.521435i	$-0.825397\pi$
$197$	−1.70658			−1.70658			−0.853291	+	0.521435i	$0.825397\pi$
$198$	1.99973	−	1.22201i	1.99973	−	1.22201i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	0.208474	−	0.361087i	0.208474	−	0.361087i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.970100	+	1.68026i	−0.970100	+	1.68026i
$206$		0			0
$207$	1.36037	−	0.831306i	1.36037	−	0.831306i
$208$		0			0
$209$	−0.772967	+	1.33882i	−0.772967	+	1.33882i
$210$		0			0
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$	−0.552200	−	0.956439i	−0.552200	−	0.956439i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	0.406813	+	0.377467i	0.406813	+	0.377467i
$217$		0			0
$218$	1.23305	−	2.13571i	1.23305	−	2.13571i
$219$		0			0
$220$	−0.690125	−	1.19533i	−0.690125	−	1.19533i
$221$		0			0
$222$		0			0
$223$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$223$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$224$		0			0
$225$	0.659819	+	0.359318i	0.659819	+	0.359318i
$226$		0			0
$227$	−0.542546	+	0.939718i	−0.542546	+	0.939718i	0.456211	+	0.889872i	$0.349206\pi$
$227$	−0.542546	+	0.939718i	−0.542546	+	0.939718i	−0.998757	+	0.0498459i	$0.984127\pi$
$228$	0.442378	+	0.112643i	0.442378	+	0.112643i
$229$	0.969077	+	1.67849i	0.969077	+	1.67849i	0.698237	+	0.715867i	$0.253968\pi$
$229$	0.969077	+	1.67849i	0.969077	+	1.67849i	0.270840	+	0.962624i	$0.412698\pi$
$230$	−1.31544	−	2.27841i	−1.31544	−	2.27841i
$231$		0			0
$232$	−0.554268	+	0.960021i	−0.554268	+	0.960021i
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$		0			0
$236$	0.0138355	−	0.0239638i	0.0138355	−	0.0239638i
$237$		0			0
$238$		0			0
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$	1.15224	−	1.18134i	1.15224	−	1.18134i
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	3.15746			3.15746
$243$	−0.661686	+	0.749781i	−0.661686	+	0.749781i
$244$	0.917056			0.917056
$245$	0.661686	−	1.14607i	0.661686	−	1.14607i
$246$	−1.27652	+	1.30875i	−1.27652	+	1.30875i
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−0.205194	+	0.355407i	−0.205194	+	0.355407i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$	2.99624			2.99624
$254$		0			0
$255$		0			0
$256$	−0.623490	−	1.07992i	−0.623490	−	1.07992i
$257$		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
$261$	−1.75426	−	0.955319i	−1.75426	−	0.955319i
$262$		0			0
$263$	0.853291	−	1.47794i	0.853291	−	1.47794i	−0.0249307	−	0.999689i	$-0.507937\pi$
$263$	0.853291	−	1.47794i	0.853291	−	1.47794i	0.878222	−	0.478254i	$-0.158730\pi$
$264$	0.282481	+	1.00400i	0.282481	+	1.00400i
$265$	1.31680	+	2.28076i	1.31680	+	2.28076i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$	1.20970	+	1.12243i	1.20970	+	1.12243i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.706003	+	1.22283i	0.706003	+	1.22283i
$276$	−0.239626	−	0.851682i	−0.239626	−	0.851682i
$277$	−0.270840	+	0.469109i	−0.270840	+	0.469109i	−0.969077	−	0.246757i	$-0.920635\pi$
$277$	−0.270840	+	0.469109i	−0.270840	+	0.469109i	0.698237	+	0.715867i	$0.253968\pi$
$278$	1.35309			1.35309
$279$		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
$283$	0.0249307	+	0.0431812i	0.0249307	+	0.0431812i	0.878222	−	0.478254i	$-0.158730\pi$
$283$	0.0249307	+	0.0431812i	0.0249307	+	0.0431812i	−0.853291	+	0.521435i	$0.825397\pi$
$284$		0			0
$285$	−1.05491	−	0.268613i	−1.05491	−	0.268613i
$286$		0			0
$287$		0			0
$288$	0.853291	−	0.521435i	0.853291	−	0.521435i
$289$	1.00000			1.00000
$290$	−1.64817	+	2.85471i	−1.64817	+	2.85471i
$291$	0.247121	+	0.878319i	0.247121	+	0.878319i
$292$		0			0
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$	0.870687	−	0.892671i	0.870687	−	0.892671i
$295$	−0.0329926	+	0.0571448i	−0.0329926	+	0.0571448i
$296$		0			0
$297$	−1.79589	+	0.553959i	−1.79589	+	0.553959i
$298$	0.675465			0.675465
$299$		0			0
$300$	0.291128	−	0.298479i	0.291128	−	0.298479i
$301$		0			0
$302$	0.825109	+	1.42913i	0.825109	+	1.42913i
$303$		0			0
$304$	−0.512867	+	0.888311i	−0.512867	+	0.888311i
$305$	−2.18684			−2.18684
$306$		0			0
$307$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$307$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$308$		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	$0.666667\pi$
$314$	−2.34356			−2.34356
$315$		0			0
$316$		0			0
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$	0.672109	+	2.38882i	0.672109	+	2.38882i
$319$	−1.87705	−	3.25114i	−1.87705	−	3.25114i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.301090	+	0.466179i	0.301090	+	0.466179i
$325$		0			0
$326$	0.994008	−	1.72167i	0.994008	−	1.72167i
$327$	−1.38088	+	1.41574i	−1.38088	+	1.41574i
$328$	−0.406813	−	0.704621i	−0.406813	−	0.704621i
$329$		0			0
$330$	0.839983	+	2.98548i	0.839983	+	2.98548i
$331$		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
$337$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i	0.826239	−	0.563320i	$-0.190476\pi$
$337$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i	−0.900969	+	0.433884i	$0.857143\pi$
$338$	−0.623490	−	1.07992i	−0.623490	−	1.07992i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−0.900821	−	0.490561i	−0.900821	−	0.490561i
$343$		0			0
$344$		0			0
$345$	0.571421	+	2.03095i	0.571421	+	2.03095i
$346$	−1.14906	−	1.99023i	−1.14906	−	1.99023i
$347$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	−0.900969	−	0.433884i	$-0.857143\pi$
$347$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	0.0747301	−	0.997204i	$-0.476190\pi$
$348$	−0.774021	+	0.793565i	−0.774021	+	0.793565i
$349$		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
$352$	1.87939			1.87939
$353$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$353$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$354$	−0.0434137	+	0.0445098i	−0.0434137	+	0.0445098i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.0931869	+	0.161404i	−0.0931869	+	0.161404i
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	−0.626670	+	0.382950i	−0.626670	+	0.382950i
$361$	−0.323372			−0.323372
$362$		0			0
$363$	−2.45379	−	0.624812i	−2.45379	−	0.624812i
$364$		0			0
$365$		0			0
$366$	−1.99689	−	0.508470i	−1.99689	−	0.508470i
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$	1.98802			1.98802
$369$	1.25101	−	0.764478i	1.25101	−	0.764478i
$370$		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
$375$	0.229794	−	0.235596i	0.229794	−	0.235596i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.97766			−1.97766			−0.988831	−	0.149042i	$-0.952381\pi$
$379$	−1.97766			−1.97766			−0.988831	+	0.149042i	$0.952381\pi$
$380$	−0.302056	+	0.523176i	−0.302056	+	0.523176i
$381$		0			0
$382$		0			0
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$	0.270840	+	0.962624i	0.270840	+	0.962624i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	0.506356			0.506356
$389$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$389$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$390$		0			0
$391$		0			0
$392$	0.277479	+	0.480608i	0.277479	+	0.480608i
$393$		0			0
$394$	1.06404	−	1.84296i	1.06404	−	1.84296i
$395$		0			0
$396$	0.0260022	+	1.04266i	0.0260022	+	1.04266i
$397$	−1.70658			−1.70658			−0.853291	−	0.521435i	$-0.825397\pi$
$397$	−1.70658			−1.70658			−0.853291	+	0.521435i	$0.825397\pi$
$398$		0			0
$399$		0			0
$400$	0.468436	+	0.811354i	0.468436	+	0.811354i
$401$		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
$405$	−0.717990	−	1.11167i	−0.717990	−	1.11167i
$406$		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	$0.333333\pi$
$410$	−1.20970	−	2.09525i	−1.20970	−	2.09525i
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.0495626	+	1.98740i	0.0495626	+	1.98740i
$415$		0			0
$416$		0			0
$417$	−1.05154	−	0.267755i	−1.05154	−	0.267755i
$418$	−0.963874	−	1.66948i	−0.963874	−	1.66948i
$419$		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
$424$	−1.10440			−1.10440
$425$		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
$432$	−1.19158	+	0.367554i	−1.19158	+	0.367554i
$433$	1.96034			1.96034			0.980172	−	0.198146i	$-0.0634921\pi$
$433$	1.96034			1.96034			0.980172	+	0.198146i	$0.0634921\pi$
$434$		0			0
$435$	1.84576	−	1.89236i	1.84576	−	1.89236i
$436$	0.548760	+	0.950480i	0.548760	+	0.950480i
$437$	−0.655701	−	1.13571i	−0.655701	−	1.13571i
$438$		0			0
$439$	0.318487	−	0.551635i	0.318487	−	0.551635i	−0.661686	−	0.749781i	$-0.730159\pi$
$439$	0.318487	−	0.551635i	0.318487	−	0.551635i	0.980172	+	0.198146i	$0.0634921\pi$
$440$	−1.38025			−1.38025
$441$	−0.853291	+	0.521435i	−0.853291	+	0.521435i
$442$		0			0
$443$	0.583744	−	1.01107i	0.583744	−	1.01107i	−0.411287	−	0.911506i	$-0.634921\pi$
$443$	0.583744	−	1.01107i	0.583744	−	1.01107i	0.995031	−	0.0995678i	$-0.0317460\pi$
$444$		0			0
$445$		0			0
$446$	1.17178	+	2.02958i	1.17178	+	2.02958i
$447$	−0.524931	−	0.133664i	−0.524931	−	0.133664i
$448$		0			0
$449$	−0.822574			−0.822574			−0.411287	−	0.911506i	$-0.634921\pi$
$449$	−0.822574			−0.822574			−0.411287	+	0.911506i	$0.634921\pi$
$450$	−0.799424	+	0.488518i	−0.799424	+	0.488518i
$451$	2.75537			2.75537
$452$		0			0
$453$	−0.358423	−	1.27391i	−0.358423	−	1.27391i
$454$	−0.676544	−	1.17181i	−0.676544	−	1.17181i
$455$		0			0
$456$	0.318741	−	0.326789i	0.318741	−	0.326789i
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$	−2.41684			−2.41684
$459$		0			0
$460$	1.17085			1.17085
$461$	0.124344	−	0.215370i	0.124344	−	0.215370i	−0.797133	−	0.603804i	$-0.793651\pi$
$461$	0.124344	−	0.215370i	0.124344	−	0.215370i	0.921476	+	0.388435i	$0.126984\pi$
$462$		0			0
$463$	−0.456211	−	0.790180i	−0.456211	−	0.790180i	0.542546	−	0.840026i	$-0.317460\pi$
$463$	−0.456211	−	0.790180i	−0.456211	−	0.790180i	−0.998757	+	0.0498459i	$0.984127\pi$
$464$	−1.24543	−	2.15715i	−1.24543	−	2.15715i
$465$		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
$471$	1.82127	+	0.463752i	1.82127	+	0.463752i
$472$	−0.0138355	−	0.0239638i	−0.0138355	−	0.0239638i
$473$		0			0
$474$		0			0
$475$	0.309005	−	0.535213i	0.309005	−	0.535213i
$476$		0			0
$477$	−0.0496136	−	1.98944i	−0.0496136	−	1.98944i
$478$		0			0
$479$	−0.826239	+	1.43109i	−0.826239	+	1.43109i	0.0747301	+	0.997204i	$0.476190\pi$
$479$	−0.826239	+	1.43109i	−0.826239	+	1.43109i	−0.900969	+	0.433884i	$0.857143\pi$
$480$	0.358423	+	1.27391i	0.358423	+	1.27391i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.702602	+	1.21694i	−0.702602	+	1.21694i
$485$	−1.20747			−1.20747
$486$	−0.397146	−	1.18205i	−0.397146	−	1.18205i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$	0.458528	−	0.794194i	0.458528	−	0.794194i
$489$	−1.11317	+	1.14128i	−1.11317	+	1.14128i
$490$	0.825109	+	1.42913i	0.825109	+	1.42913i
$491$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.623490	+	0.781831i	$0.285714\pi$
$491$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.365341	+	0.930874i	$0.380952\pi$
$492$	−0.220363	−	0.783216i	−0.220363	−	0.783216i
$493$		0			0
$494$		0			0
$495$	−0.0620058	−	2.48635i	−0.0620058	−	2.48635i
$496$		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	$0.333333\pi$
$500$	−0.0913200	−	0.158171i	−0.0913200	−	0.158171i
$501$		0			0
$502$		0			0
$503$	1.75644			1.75644			0.878222	−	0.478254i	$-0.158730\pi$
$503$	1.75644			1.75644			0.878222	+	0.478254i	$0.158730\pi$
$504$		0			0
$505$		0			0
$506$	−1.86812	+	3.23569i	−1.86812	+	3.23569i
$507$	0.270840	+	0.962624i	0.270840	+	0.962624i
$508$		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
$512$	0.554958			0.554958
$513$	0.602990	+	0.559493i	0.602990	+	0.559493i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.499146	+	1.77407i	0.499146	+	1.77407i
$520$		0			0
$521$	−1.97766			−1.97766			−0.988831	−	0.149042i	$-0.952381\pi$
$521$	−1.97766			−1.97766			−0.988831	+	0.149042i	$0.952381\pi$
$522$	2.12543	−	1.29882i	2.12543	−	1.29882i
$523$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$523$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$524$		0			0
$525$		0			0
$526$	1.06404	+	1.84296i	1.06404	+	1.84296i
$527$		0			0
$528$	−2.27109	−	0.578290i	−2.27109	−	0.578290i
$529$	−0.770840	+	1.33513i	−0.770840	+	1.33513i
$530$	−3.28403			−3.28403
$531$	0.0425463	−	0.0259995i	0.0425463	−	0.0259995i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.104359	−	0.106994i	0.104359	−	0.106994i
$538$		0			0
$539$	−1.87939			−1.87939
$540$	−0.701788	+	0.216473i	−0.701788	+	0.216473i
$541$	−1.16749			−1.16749			−0.583744	−	0.811938i	$-0.698413\pi$
$541$	−1.16749			−1.16749			−0.583744	+	0.811938i	$0.698413\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.30859	−	2.26655i	−1.30859	−	2.26655i
$546$		0			0
$547$	0.318487	−	0.551635i	0.318487	−	0.551635i	−0.661686	−	0.749781i	$-0.730159\pi$
$547$	0.318487	−	0.551635i	0.318487	−	0.551635i	0.980172	+	0.198146i	$0.0634921\pi$
$548$		0			0
$549$	1.45124	+	0.790304i	1.45124	+	0.790304i
$550$	−1.76074			−1.76074
$551$	−0.821552	+	1.42297i	−0.821552	+	1.42297i
$552$	−0.857391	−	0.218319i	−0.857391	−	0.218319i
$553$		0			0
$554$	−0.337733	−	0.584970i	−0.337733	−	0.584970i
$555$		0			0
$556$	−0.301090	+	0.521504i	−0.301090	+	0.521504i
$557$		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
$563$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	0.623490	−	0.781831i	$-0.285714\pi$
$563$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	−0.988831	+	0.149042i	$0.952381\pi$
$564$		0			0
$565$		0			0
$566$	−0.0621761			−0.0621761
$567$		0			0
$568$		0			0
$569$	0.583744	−	1.01107i	0.583744	−	1.01107i	−0.411287	−	0.911506i	$-0.634921\pi$
$569$	0.583744	−	1.01107i	0.583744	−	1.01107i	0.995031	−	0.0995678i	$-0.0317460\pi$
$570$	0.947805	−	0.971737i	0.947805	−	0.971737i
$571$		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
$575$	−1.19779			−1.19779
$576$		0			0
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$579$		0			0
$580$	−0.733503	−	1.27046i	−0.733503	−	1.27046i
$581$		0			0
$582$	−1.10259	−	0.280753i	−1.10259	−	0.280753i
$583$	1.87005	−	3.23901i	1.87005	−	3.23901i
$584$		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	$0.666667\pi$
$588$	0.150305	+	0.534216i	0.150305	+	0.534216i
$589$		0			0
$590$	−0.0411411	−	0.0712584i	−0.0411411	−	0.0712584i
$591$	−1.19160	+	1.22169i	−1.19160	+	1.22169i
$592$		0			0
$593$	0.912421			0.912421			0.456211	−	0.889872i	$-0.349206\pi$
$593$	0.912421			0.912421			0.456211	+	0.889872i	$0.349206\pi$
$594$	0.521490	−	2.28480i	0.521490	−	2.28480i
$595$		0			0
$596$	−0.150305	+	0.260336i	−0.150305	+	0.260336i
$597$		0			0
$598$		0			0
$599$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$599$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$600$	−0.112926	−	0.401363i	−0.112926	−	0.401363i
$601$		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
$604$	−0.734416			−0.734416
$605$	1.67545	−	2.90196i	1.67545	−	2.90196i
$606$		0			0
$607$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	−0.900969	−	0.433884i	$-0.857143\pi$
$607$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	0.0747301	−	0.997204i	$-0.476190\pi$
$608$	−0.411287	−	0.712370i	−0.411287	−	0.712370i
$609$		0			0
$610$	1.36347	−	2.36161i	1.36347	−	2.36161i
$611$		0			0
$612$		0			0
$613$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$613$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$614$	−0.777479	+	1.34663i	−0.777479	+	1.34663i
$615$	0.525485	+	1.86768i	0.525485	+	1.86768i
$616$		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
$621$	0.354757	−	1.55429i	0.354757	−	1.55429i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.593421	+	1.02784i	0.593421	+	1.02784i
$626$		0			0
$627$	0.418701	+	1.48815i	0.418701	+	1.48815i
$628$	0.521490	−	0.903247i	0.521490	−	0.903247i
$629$		0			0
$630$		0			0
$631$	0.541681			0.541681			0.270840	−	0.962624i	$-0.412698\pi$
$631$	0.541681			0.541681			0.270840	+	0.962624i	$0.412698\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−1.07025	−	0.272519i	−1.07025	−	0.272519i
$637$		0			0
$638$	4.68128			4.68128
$639$		0			0
$640$	−1.32337			−1.32337
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$		0			0
$643$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.826239	+	0.563320i	$0.190476\pi$
$643$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.0747301	+	0.997204i	$0.476190\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.08509			1.08509			0.542546	−	0.840026i	$-0.317460\pi$
$647$	1.08509			1.08509			0.542546	+	0.840026i	$0.317460\pi$
$648$	0.554268	−	0.0276624i	0.554268	−	0.0276624i
$649$	0.0937087			0.0937087
$650$		0			0
$651$		0			0
$652$	0.442375	+	0.766216i	0.442375	+	0.766216i
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$	−0.667921	−	2.37393i	−0.667921	−	2.37393i
$655$		0			0
$656$	1.82820			1.82820
$657$		0			0
$658$		0			0
$659$	−0.995031	+	1.72344i	−0.995031	+	1.72344i	−0.411287	+	0.911506i	$0.634921\pi$
$659$	−0.995031	+	1.72344i	−0.995031	+	1.72344i	−0.583744	+	0.811938i	$0.698413\pi$
$660$	−1.33757	−	0.340587i	−1.33757	−	0.340587i
$661$	−0.878222	−	1.52112i	−0.878222	−	1.52112i	−0.853291	−	0.521435i	$-0.825397\pi$
$661$	−0.878222	−	1.52112i	−0.878222	−	1.52112i	−0.0249307	−	0.999689i	$-0.507937\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.18457			3.18457
$668$		0			0
$669$	−0.509014	−	1.80914i	−0.509014	−	1.80914i
$670$		0			0
$671$	1.55282	+	2.68956i	1.55282	+	2.68956i
$672$		0			0
$673$	−0.955573	+	1.65510i	−0.955573	+	1.65510i	−0.222521	+	0.974928i	$0.571429\pi$
$673$	−0.955573	+	1.65510i	−0.955573	+	1.65510i	−0.733052	+	0.680173i	$0.761905\pi$
$674$	0.186374			0.186374
$675$	0.717934	−	0.221453i	0.717934	−	0.221453i
$676$	0.554958			0.554958
$677$	−0.698237	+	1.20938i	−0.698237	+	1.20938i	0.270840	+	0.962624i	$0.412698\pi$
$677$	−0.698237	+	1.20938i	−0.698237	+	1.20938i	−0.969077	+	0.246757i	$0.920635\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.293887	+	1.04454i	0.293887	+	1.04454i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	0.389522	−	0.238032i	0.389522	−	0.238032i
$685$		0			0
$686$		0			0
$687$	1.87822	+	0.478254i	1.87822	+	0.478254i
$688$		0			0
$689$		0			0
$690$	−2.54953	−	0.649190i	−2.54953	−	0.649190i
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$	1.02276			1.02276
$693$		0			0
$694$	2.06061			2.06061
$695$	0.717990	−	1.24360i	0.717990	−	1.24360i
$696$	0.300237	+	1.06710i	0.300237	+	1.06710i
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.91115			1.91115			0.955573	−	0.294755i	$-0.0952381\pi$
$701$	1.91115			1.91115			0.955573	+	0.294755i	$0.0952381\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.216536	−	0.375051i	−0.216536	−	0.375051i
$707$		0			0
$708$	−0.00749442	−	0.0266368i	−0.00749442	−	0.0266368i
$709$	0.797133	−	1.38067i	0.797133	−	1.38067i	−0.124344	−	0.992239i	$-0.539683\pi$
$709$	0.797133	−	1.38067i	0.797133	−	1.38067i	0.921476	−	0.388435i	$-0.126984\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.0414721	−	0.0718317i	−0.0414721	−	0.0718317i
$717$		0			0
$718$		0			0
$719$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$719$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$720$	−0.0411411	−	1.64970i	−0.0411411	−	1.64970i
$721$		0			0
$722$	0.201619	−	0.349214i	0.201619	−	0.349214i
$723$		0			0
$724$		0			0
$725$	0.750379	+	1.29969i	0.750379	+	1.29969i
$726$	2.20466	−	2.26032i	2.20466	−	2.26032i
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$730$		0			0
$731$		0			0
$732$	0.640322	−	0.656490i	0.640322	−	0.656490i
$733$	−0.921476	−	1.59604i	−0.921476	−	1.59604i	−0.797133	−	0.603804i	$-0.793651\pi$
$733$	−0.921476	−	1.59604i	−0.921476	−	1.59604i	−0.124344	−	0.992239i	$-0.539683\pi$
$734$		0			0
$735$	−0.358423	−	1.27391i	−0.358423	−	1.27391i
$736$	−0.797133	+	1.38067i	−0.797133	+	1.38067i
$737$		0			0
$738$	0.0455783	+	1.82763i	0.0455783	+	1.82763i
$739$		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
$745$	0.358423	−	0.620806i	0.358423	−	0.620806i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$	0.111150	+	0.395050i	0.111150	+	0.395050i
$751$	−0.698237	−	1.20938i	−0.698237	−	1.20938i	−0.969077	−	0.246757i	$-0.920635\pi$
$751$	−0.698237	−	1.20938i	−0.698237	−	1.20938i	0.270840	−	0.962624i	$-0.412698\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.75131			1.75131
$756$		0			0
$757$	0.730682			0.730682			0.365341	−	0.930874i	$-0.380952\pi$
$757$	0.730682			0.730682			0.365341	+	0.930874i	$0.380952\pi$
$758$	1.23305	−	2.13571i	1.23305	−	2.13571i
$759$	2.09208	−	2.14491i	2.09208	−	2.14491i
$760$	0.302056	+	0.523176i	0.302056	+	0.523176i
$761$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	0.623490	−	0.781831i	$-0.285714\pi$
$761$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	−0.988831	+	0.149042i	$0.952381\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.20842	−	0.307701i	−1.20842	−	0.307701i
$769$	0.853291	+	1.47794i	0.853291	+	1.47794i	0.878222	+	0.478254i	$0.158730\pi$
$769$	0.853291	+	1.47794i	0.853291	+	1.47794i	−0.0249307	+	0.999689i	$0.507937\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$773$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$774$		0			0
$775$		0			0
$776$	0.253178	−	0.438517i	0.253178	−	0.438517i
$777$		0			0
$778$	−0.955242	−	1.65453i	−0.955242	−	1.65453i
$779$	−0.602990	−	1.04441i	−0.602990	−	1.04441i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.90877	+	0.588778i	−1.90877	+	0.588778i
$784$	−1.24698			−1.24698
$785$	−1.24356	+	2.15391i	−1.24356	+	2.15391i
$786$		0			0
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$	0.473541	+	0.820197i	0.473541	+	0.820197i
$789$	−0.462211	−	1.64280i	−0.462211	−	1.64280i
$790$		0			0
$791$		0			0
$792$	0.915968	+	0.498809i	0.915968	+	0.498809i
$793$		0			0
$794$	1.06404	−	1.84296i	1.06404	−	1.84296i
$795$	2.55215	+	0.649858i	2.55215	+	0.649858i
$796$		0			0
$797$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.733052	−	0.680173i	$-0.761905\pi$
$797$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.222521	−	0.974928i	$-0.571429\pi$
$798$		0			0
$799$		0			0
$800$	−0.751313			−0.751313
$801$		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			$\pi$
$810$	1.64817	−	0.0822566i	1.64817	−	0.0822566i
$811$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$811$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.05490	−	1.82714i	−1.05490	−	1.82714i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	1.07673			1.07673
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$		0			0
$823$	0.583744	+	1.01107i	0.583744	+	1.01107i	0.995031	+	0.0995678i	$0.0317460\pi$
$823$	0.583744	+	1.01107i	0.583744	+	1.01107i	−0.411287	+	0.911506i	$0.634921\pi$
$824$		0			0
$825$	1.36834	+	0.348423i	1.36834	+	0.348423i
$826$		0			0
$827$	1.96034			1.96034			0.980172	−	0.198146i	$-0.0634921\pi$
$827$	1.96034			1.96034			0.980172	+	0.198146i	$0.0634921\pi$
$828$	−0.777007	−	0.423135i	−0.777007	−	0.423135i
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$	0.146709	+	0.521435i	0.146709	+	0.521435i
$832$		0			0
$833$		0			0
$834$	0.944776	−	0.968631i	0.944776	−	0.968631i
$835$		0			0
$836$	0.857929			0.857929
$837$		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
$841$	−1.49503	−	2.58947i	−1.49503	−	2.58947i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.32337			−1.32337
$846$		0			0
$847$		0			0
$848$	1.24078	−	2.14910i	1.24078	−	2.14910i
$849$	0.0483195	+	0.0123037i	0.0483195	+	0.0123037i
$850$		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
$855$	−0.928868	+	0.567619i	−0.928868	+	0.567619i
$856$		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
$862$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$863$	−1.97766			−1.97766			−0.988831	−	0.149042i	$-0.952381\pi$
$863$	−1.97766			−1.97766			−0.988831	+	0.149042i	$0.952381\pi$
$864$	0.222521	−	0.974928i	0.222521	−	0.974928i
$865$	−2.43891			−2.43891
$866$	−1.22226	+	2.11701i	−1.22226	+	2.11701i
$867$	0.698237	−	0.715867i	0.698237	−	0.715867i
$868$		0			0
$869$		0			0
$870$	0.892780	+	3.17313i	0.892780	+	3.17313i
$871$		0			0
$872$	1.09752			1.09752
$873$	0.801308	+	0.436369i	0.801308	+	0.436369i
$874$	1.63529			1.63529
$875$		0			0
$876$		0			0
$877$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$877$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$878$	0.397146	+	0.687878i	0.397146	+	0.687878i
$879$		0			0
$880$	1.55070	−	2.68589i	1.55070	−	2.68589i
$881$	1.84295			1.84295			0.921476	−	0.388435i	$-0.126984\pi$
$881$	1.84295			1.84295			0.921476	+	0.388435i	$0.126984\pi$
$882$	−0.0310881	−	1.24659i	−0.0310881	−	1.24659i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$	0.0178714	+	0.0635189i	0.0178714	+	0.0635189i
$886$	0.727916	+	1.26079i	0.727916	+	1.26079i
$887$	−0.995031	−	1.72344i	−0.995031	−	1.72344i	−0.583744	−	0.811938i	$-0.698413\pi$
$887$	−0.995031	−	1.72344i	−0.995031	−	1.72344i	−0.411287	−	0.911506i	$-0.634921\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.857396	+	1.67241i	−0.857396	+	1.67241i
$892$	−1.04298			−1.04298
$893$		0			0
$894$	0.471635	−	0.483543i	0.471635	−	0.483543i
$895$	0.0988957	+	0.171292i	0.0988957	+	0.171292i
$896$		0			0
$897$		0			0
$898$	0.512867	−	0.888311i	0.512867	−	0.888311i
$899$		0			0
$900$	−0.0103948	−	0.416817i	−0.0103948	−	0.416817i
$901$		0			0
$902$	−1.71795	+	2.97557i	−1.71795	+	2.97557i
$903$		0			0
$904$		0			0
$905$		0			0
$906$	1.59919	+	0.407203i	1.59919	+	0.407203i
$907$	0.998757	−	1.72990i	0.998757	−	1.72990i	0.456211	−	0.889872i	$-0.349206\pi$
$907$	0.998757	−	1.72990i	0.998757	−	1.72990i	0.542546	−	0.840026i	$-0.317460\pi$
$908$	0.602181			0.602181
$909$		0			0
$910$		0			0
$911$	0.318487	−	0.551635i	0.318487	−	0.551635i	−0.661686	−	0.749781i	$-0.730159\pi$
$911$	0.318487	−	0.551635i	0.318487	−	0.551635i	0.980172	+	0.198146i	$0.0634921\pi$
$912$	0.277810	+	0.987396i	0.277810	+	0.987396i
$913$		0			0
$914$		0			0
$915$	−1.52693	+	1.56549i	−1.52693	+	1.56549i
$916$	0.537797	−	0.931492i	0.537797	−	0.931492i
$917$		0			0
$918$		0			0
$919$	−1.99751			−1.99751			−0.998757	−	0.0498459i	$-0.984127\pi$
$919$	−1.99751			−1.99751			−0.998757	+	0.0498459i	$0.984127\pi$
$920$	0.585427	−	1.01399i	0.585427	−	1.01399i
$921$	0.870687	−	0.892671i	0.870687	−	0.892671i
$922$	0.155054	+	0.268562i	0.155054	+	0.268562i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	1.13777			1.13777
$927$		0			0
$928$	1.99751			1.99751
$929$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$929$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$930$		0			0
$931$	0.411287	+	0.712370i	0.411287	+	0.712370i
$932$		0			0
$933$		0			0
$934$	0.623490	−	1.07992i	0.623490	−	1.07992i
$935$		0			0
$936$		0			0
$937$	1.99006			1.99006			0.995031	−	0.0995678i	$-0.0317460\pi$
$937$	1.99006			1.99006			0.995031	+	0.0995678i	$0.0317460\pi$
$938$		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	$0.333333\pi$
$942$	−1.63636	+	1.67767i	−1.63636	+	1.67767i
$943$	−1.16868	+	2.02421i	−1.16868	+	2.02421i
$944$	0.0621761			0.0621761
$945$		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
$950$	0.385323	+	0.667399i	0.385323	+	0.667399i
$951$		0			0
$952$		0			0
$953$	−0.0498614			−0.0498614			−0.0249307	−	0.999689i	$-0.507937\pi$
$953$	−0.0498614			−0.0498614			−0.0249307	+	0.999689i	$0.507937\pi$
$954$	2.17936	+	1.18682i	2.17936	+	1.18682i
$955$		0			0
$956$		0			0
$957$	−3.63801	−	0.926351i	−3.63801	−	0.926351i
$958$	−1.03030	−	1.78454i	−1.03030	−	1.78454i
$959$		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	$0.333333\pi$
$968$	0.702602	+	1.21694i	0.702602	+	1.21694i
$969$		0			0
$970$	0.752847	−	1.30397i	0.752847	−	1.30397i
$971$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$971$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$972$	0.543955	+	0.109963i	0.543955	+	0.109963i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	1.03030	+	1.78454i	1.03030	+	1.78454i
$977$	−0.270840	−	0.469109i	−0.270840	−	0.469109i	0.698237	−	0.715867i	$-0.253968\pi$
$977$	−0.270840	−	0.469109i	−0.270840	−	0.469109i	−0.969077	+	0.246757i	$0.920635\pi$
$978$	−0.538435	−	1.91371i	−0.538435	−	1.91371i
$979$		0			0
$980$	−0.734416			−0.734416
$981$	0.0493045	+	1.97705i	0.0493045	+	1.97705i
$982$	−2.46610			−2.46610
$983$	−0.270840	+	0.469109i	−0.270840	+	0.469109i	−0.969077	−	0.246757i	$-0.920635\pi$
$983$	−0.270840	+	0.469109i	−0.270840	+	0.469109i	0.698237	+	0.715867i	$0.253968\pi$
$984$	−0.788467	−	0.200768i	−0.788467	−	0.200768i
$985$	−1.12922	−	1.95587i	−1.12922	−	1.95587i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	2.72371	+	1.48325i	2.72371	+	1.48325i
$991$		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
$997$	−0.921476	+	1.59604i	−0.921476	+	1.59604i	−0.124344	+	0.992239i	$0.539683\pi$
$997$	−0.921476	+	1.59604i	−0.921476	+	1.59604i	−0.797133	+	0.603804i	$0.793651\pi$
$998$		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.430.5	✓	36
9.4	even	3	inner	3879.1.g.c.1723.5	yes	36
431.430	odd	2	CM	3879.1.g.c.430.5	✓	36
3879.1723	odd	6	inner	3879.1.g.c.1723.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3879.1.g.c.430.5	✓	36	1.1	even	1	trivial
3879.1.g.c.430.5	✓	36	431.430	odd	2	CM
3879.1.g.c.1723.5	yes	36	9.4	even	3	inner
3879.1.g.c.1723.5	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)

\(f(q)\)	\(=\)	\(q+(-0.623490 + 1.07992i) q^{2} +(0.698237 - 0.715867i) q^{3} +(-0.277479 - 0.480608i) q^{4} +(0.661686 + 1.14607i) q^{5} +(0.337733 + 1.20037i) q^{6} -0.554958 q^{8} +(-0.0249307 - 0.999689i) q^{9} +O(q^{10})\)	\(q+(-0.623490 + 1.07992i) q^{2} +(0.698237 - 0.715867i) q^{3} +(-0.277479 - 0.480608i) q^{4} +(0.661686 + 1.14607i) q^{5} +(0.337733 + 1.20037i) q^{6} -0.554958 q^{8} +(-0.0249307 - 0.999689i) q^{9} -1.65022 q^{10} +(0.939693 - 1.62760i) q^{11} +(-0.537797 - 0.136940i) q^{12} +(1.28245 + 0.326552i) q^{15} +(0.623490 - 1.07992i) q^{16} +(1.09512 + 0.596373i) q^{18} -0.822574 q^{19} +(0.367208 - 0.636023i) q^{20} +(1.17178 + 2.02958i) q^{22} +(0.797133 + 1.38067i) q^{23} +(-0.387492 + 0.397276i) q^{24} +(-0.375656 + 0.650656i) q^{25} +(-0.733052 - 0.680173i) q^{27} +(0.998757 - 1.72990i) q^{29} +(-1.15224 + 1.18134i) q^{30} +(0.500000 + 0.866025i) q^{32} +(-0.509014 - 1.80914i) q^{33} +(-0.473541 + 0.289375i) q^{36} +(0.512867 - 0.888311i) q^{38} +(-0.367208 - 0.636023i) q^{40} +(0.733052 + 1.26968i) q^{41} -1.04298 q^{44} +(1.12922 - 0.690053i) q^{45} -1.98802 q^{46} +(-0.337733 - 1.20037i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.468436 - 0.811354i) q^{50} +1.99006 q^{53} +(1.19158 - 0.367554i) q^{54} +2.48713 q^{55} +(-0.574352 + 0.588854i) q^{57} +(1.24543 + 2.15715i) q^{58} +(0.0249307 + 0.0431812i) q^{59} +(-0.198910 - 0.706967i) q^{60} +(-0.826239 + 1.43109i) q^{61} +(2.27109 + 0.578290i) q^{66} +(1.54497 + 0.393397i) q^{69} +(0.0138355 + 0.554786i) q^{72} +(0.203486 + 0.723232i) q^{75} +(0.228247 + 0.395336i) q^{76} +1.65022 q^{80} +(-0.998757 + 0.0498459i) q^{81} -1.82820 q^{82} +(-0.541008 - 1.92286i) q^{87} +(-0.521490 + 0.903247i) q^{88} +(0.0411411 + 1.64970i) q^{90} +(0.442375 - 0.766216i) q^{92} +(-0.544286 - 0.942730i) q^{95} +(0.969077 + 0.246757i) q^{96} +(-0.456211 + 0.790180i) q^{97} +1.24698 q^{98} +(-1.65052 - 0.898823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{2} - 12 q^{4} - 24 q^{8}+O(q^{10}) \) 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

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