LMFDB - Embedded newform 3879.1.g.c.430.14

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			430.14
Root			$-0.583744 + 0.811938i$ of defining polynomial
Character	$\chi$	$=$	3879.430
Dual form			3879.1.g.c.1723.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 - 1.56052i) q^{2} +(-0.797133 + 0.603804i) q^{3} +(-1.12349 - 1.94594i) q^{4} +(-0.995031 - 1.72344i) q^{5} +(0.224060 + 1.78795i) q^{6} -2.24698 q^{8} +(0.270840 - 0.962624i) q^{9} +O(q^{10})$	\(q+(0.900969 - 1.56052i) q^{2} +(-0.797133 + 0.603804i) q^{3} +(-1.12349 - 1.94594i) q^{4} +(-0.995031 - 1.72344i) q^{5} +(0.224060 + 1.78795i) q^{6} -2.24698 q^{8} +(0.270840 - 0.962624i) q^{9} -3.58597 q^{10} +(-0.766044 + 1.32683i) q^{11} +(2.07054 + 0.872805i) q^{12} +(1.83379 + 0.773009i) q^{15} +(-0.900969 + 1.56052i) q^{16} +(-1.25818 - 1.28995i) q^{18} -1.99751 q^{19} +(-2.23581 + 3.87254i) q^{20} +(1.38036 + 2.39086i) q^{22} +(0.661686 + 1.14607i) q^{23} +(1.79114 - 1.35674i) q^{24} +(-1.48017 + 2.56373i) q^{25} +(0.365341 + 0.930874i) q^{27} +(0.853291 - 1.47794i) q^{29} +(2.85849 - 2.16522i) q^{30} +(0.500000 + 0.866025i) q^{32} +(-0.190506 - 1.52020i) q^{33} +(-2.17750 + 0.554459i) q^{36} +(-1.79970 + 3.11717i) q^{38} +(2.23581 + 3.87254i) q^{40} +(-0.365341 - 0.632789i) q^{41} +3.44257 q^{44} +(-1.92852 + 0.491062i) q^{45} +2.38463 q^{46} +(-0.224060 - 1.78795i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(2.66718 + 4.61969i) q^{50} +0.912421 q^{53} +(1.78181 + 0.268565i) q^{54} +3.04895 q^{55} +(1.59228 - 1.20611i) q^{57} +(-1.53758 - 2.66316i) q^{58} +(-0.270840 - 0.469109i) q^{59} +(-0.556019 - 4.43692i) q^{60} +(-0.955573 + 1.65510i) q^{61} +(-2.54395 - 1.07236i) q^{66} +(-1.21946 - 0.514044i) q^{69} +(-0.608573 + 2.16300i) q^{72} +(-0.368100 - 2.93737i) q^{75} +(2.24419 + 3.88704i) q^{76} +3.58597 q^{80} +(-0.853291 - 0.521435i) q^{81} -1.31664 q^{82} +(0.212203 + 1.69334i) q^{87} +(1.72129 - 2.98136i) q^{88} +(-0.971225 + 3.45194i) q^{90} +(1.48679 - 2.57520i) q^{92} +(1.98759 + 3.44260i) q^{95} +(-0.921476 - 0.388435i) q^{96} +(-0.878222 + 1.52112i) q^{97} -1.80194 q^{98} +(1.06976 + 1.09677i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.0747301	−	0.997204i	$-0.476190\pi$
$2$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.826239	−	0.563320i	$-0.190476\pi$
$3$	−0.797133	+	0.603804i	−0.797133	+	0.603804i
$3$	−0.797133	+	0.603804i	−0.797133	+	0.603804i
$4$	−1.12349	−	1.94594i	−1.12349	−	1.94594i
$5$	−0.995031	−	1.72344i	−0.995031	−	1.72344i	−0.583744	−	0.811938i	$-0.698413\pi$
$5$	−0.995031	−	1.72344i	−0.995031	−	1.72344i	−0.411287	−	0.911506i	$-0.634921\pi$
$6$	0.224060	+	1.78795i	0.224060	+	1.78795i
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$	−2.24698			−2.24698
$9$	0.270840	−	0.962624i	0.270840	−	0.962624i
$10$	−3.58597			−3.58597
$11$	−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	$0.888889\pi$
$12$	2.07054	+	0.872805i	2.07054	+	0.872805i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$		0			0
$15$	1.83379	+	0.773009i	1.83379	+	0.773009i
$16$	−0.900969	+	1.56052i	−0.900969	+	1.56052i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	−1.25818	−	1.28995i	−1.25818	−	1.28995i
$19$	−1.99751			−1.99751			−0.998757	−	0.0498459i	$-0.984127\pi$
$19$	−1.99751			−1.99751			−0.998757	+	0.0498459i	$0.984127\pi$
$20$	−2.23581	+	3.87254i	−2.23581	+	3.87254i
$21$		0			0
$22$	1.38036	+	2.39086i	1.38036	+	2.39086i
$23$	0.661686	+	1.14607i	0.661686	+	1.14607i	0.980172	+	0.198146i	$0.0634921\pi$
$23$	0.661686	+	1.14607i	0.661686	+	1.14607i	−0.318487	+	0.947927i	$0.603175\pi$
$24$	1.79114	−	1.35674i	1.79114	−	1.35674i
$25$	−1.48017	+	2.56373i	−1.48017	+	2.56373i
$26$		0			0
$27$	0.365341	+	0.930874i	0.365341	+	0.930874i
$28$		0			0
$29$	0.853291	−	1.47794i	0.853291	−	1.47794i	−0.0249307	−	0.999689i	$-0.507937\pi$
$29$	0.853291	−	1.47794i	0.853291	−	1.47794i	0.878222	−	0.478254i	$-0.158730\pi$
$30$	2.85849	−	2.16522i	2.85849	−	2.16522i
$31$		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
$33$	−0.190506	−	1.52020i	−0.190506	−	1.52020i
$34$		0			0
$35$		0			0
$36$	−2.17750	+	0.554459i	−2.17750	+	0.554459i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−1.79970	+	3.11717i	−1.79970	+	3.11717i
$39$		0			0
$40$	2.23581	+	3.87254i	2.23581	+	3.87254i
$41$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	0.623490	−	0.781831i	$-0.285714\pi$
$41$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	−0.988831	+	0.149042i	$0.952381\pi$
$42$		0			0
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$	3.44257			3.44257
$45$	−1.92852	+	0.491062i	−1.92852	+	0.491062i
$46$	2.38463			2.38463
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	−0.224060	−	1.78795i	−0.224060	−	1.78795i
$49$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$50$	2.66718	+	4.61969i	2.66718	+	4.61969i
$51$		0			0
$52$		0			0
$53$	0.912421			0.912421			0.456211	−	0.889872i	$-0.349206\pi$
$53$	0.912421			0.912421			0.456211	+	0.889872i	$0.349206\pi$
$54$	1.78181	+	0.268565i	1.78181	+	0.268565i
$55$	3.04895			3.04895
$56$		0			0
$57$	1.59228	−	1.20611i	1.59228	−	1.20611i
$58$	−1.53758	−	2.66316i	−1.53758	−	2.66316i
$59$	−0.270840	−	0.469109i	−0.270840	−	0.469109i	0.698237	−	0.715867i	$-0.253968\pi$
$59$	−0.270840	−	0.469109i	−0.270840	−	0.469109i	−0.969077	+	0.246757i	$0.920635\pi$
$60$	−0.556019	−	4.43692i	−0.556019	−	4.43692i
$61$	−0.955573	+	1.65510i	−0.955573	+	1.65510i	−0.222521	+	0.974928i	$0.571429\pi$
$61$	−0.955573	+	1.65510i	−0.955573	+	1.65510i	−0.733052	+	0.680173i	$0.761905\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$	−2.54395	−	1.07236i	−2.54395	−	1.07236i
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$	−1.21946	−	0.514044i	−1.21946	−	0.514044i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−0.608573	+	2.16300i	−0.608573	+	2.16300i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	−0.368100	−	2.93737i	−0.368100	−	2.93737i
$76$	2.24419	+	3.88704i	2.24419	+	3.88704i
$77$		0			0
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	3.58597			3.58597
$81$	−0.853291	−	0.521435i	−0.853291	−	0.521435i
$82$	−1.31664			−1.31664
$83$		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
$87$	0.212203	+	1.69334i	0.212203	+	1.69334i
$88$	1.72129	−	2.98136i	1.72129	−	2.98136i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	−0.971225	+	3.45194i	−0.971225	+	3.45194i
$91$		0			0
$92$	1.48679	−	2.57520i	1.48679	−	2.57520i
$93$		0			0
$94$		0			0
$95$	1.98759	+	3.44260i	1.98759	+	3.44260i
$96$	−0.921476	−	0.388435i	−0.921476	−	0.388435i
$97$	−0.878222	+	1.52112i	−0.878222	+	1.52112i	−0.0249307	+	0.999689i	$0.507937\pi$
$97$	−0.878222	+	1.52112i	−0.878222	+	1.52112i	−0.853291	+	0.521435i	$0.825397\pi$
$98$	−1.80194			−1.80194
$99$	1.06976	+	1.09677i	1.06976	+	1.09677i
$100$	6.65183			6.65183
$101$		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
$106$	0.822063	−	1.42386i	0.822063	−	1.42386i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	1.40097	−	1.75676i	1.40097	−	1.75676i
$109$	0.149460			0.149460			0.0747301	−	0.997204i	$-0.476190\pi$
$109$	0.149460			0.149460			0.0747301	+	0.997204i	$0.476190\pi$
$110$	2.74701	−	4.75796i	2.74701	−	4.75796i
$111$		0			0
$112$		0			0
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$	−0.447562	−	3.57146i	−0.447562	−	3.57146i
$115$	1.31680	−	2.28076i	1.31680	−	2.28076i
$116$	−3.83465			−3.83465
$117$		0			0
$118$	−0.976075			−0.976075
$119$		0			0
$120$	−4.12050	−	1.73694i	−4.12050	−	1.73694i
$121$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$122$	1.72188	+	2.98239i	1.72188	+	2.98239i
$123$	0.673306	+	0.283822i	0.673306	+	0.283822i
$124$		0			0
$125$	3.90121			3.90121
$126$		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	$0.333333\pi$
$132$	−2.74419	+	2.07864i	−2.74419	+	2.07864i
$133$		0			0
$134$		0			0
$135$	1.24078	−	1.55589i	1.24078	−	1.55589i
$136$		0			0
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$	−1.90087	+	1.43985i	−1.90087	+	1.43985i
$139$	0.0249307	+	0.0431812i	0.0249307	+	0.0431812i	0.878222	−	0.478254i	$-0.158730\pi$
$139$	0.0249307	+	0.0431812i	0.0249307	+	0.0431812i	−0.853291	+	0.521435i	$0.825397\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	1.25818	+	1.28995i	1.25818	+	1.28995i
$145$	−3.39620			−3.39620
$146$		0			0
$147$	0.921476	+	0.388435i	0.921476	+	0.388435i
$148$		0			0
$149$	0.124344	+	0.215370i	0.124344	+	0.215370i	0.921476	−	0.388435i	$-0.126984\pi$
$149$	0.124344	+	0.215370i	0.124344	+	0.215370i	−0.797133	+	0.603804i	$0.793651\pi$
$150$	−4.91548	−	2.07205i	−4.91548	−	2.07205i
$151$	−0.995031	+	1.72344i	−0.995031	+	1.72344i	−0.411287	+	0.911506i	$0.634921\pi$
$151$	−0.995031	+	1.72344i	−0.995031	+	1.72344i	−0.583744	+	0.811938i	$0.698413\pi$
$152$	4.48837			4.48837
$153$		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
$159$	−0.727321	+	0.550924i	−0.727321	+	0.550924i
$160$	0.995031	−	1.72344i	0.995031	−	1.72344i
$161$		0			0
$162$	−1.58250	+	0.861784i	−1.58250	+	0.861784i
$163$	−1.32337			−1.32337			−0.661686	−	0.749781i	$-0.730159\pi$
$163$	−1.32337			−1.32337			−0.661686	+	0.749781i	$0.730159\pi$
$164$	−0.820914	+	1.42186i	−0.820914	+	1.42186i
$165$	−2.43042	+	1.84097i	−2.43042	+	1.84097i
$166$		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
$171$	−0.541008	+	1.92286i	−0.541008	+	1.92286i
$172$		0			0
$173$	0.318487	−	0.551635i	0.318487	−	0.551635i	−0.661686	−	0.749781i	$-0.730159\pi$
$173$	0.318487	−	0.551635i	0.318487	−	0.551635i	0.980172	+	0.198146i	$0.0634921\pi$
$174$	2.83368	+	1.19450i	2.83368	+	1.19450i
$175$		0			0
$176$	−1.38036	−	2.39086i	−1.38036	−	2.39086i
$177$	0.499146	+	0.210408i	0.499146	+	0.210408i
$178$		0			0
$179$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$179$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$180$	3.12226	+	3.20109i	3.12226	+	3.20109i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	−0.237639	−	1.89631i	−0.237639	−	1.89631i
$184$	−1.48679	−	2.57520i	−1.48679	−	2.57520i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	7.16302			7.16302
$191$		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	$0.333333\pi$
$194$	1.58250	+	2.74097i	1.58250	+	2.74097i
$195$		0			0
$196$	−1.12349	+	1.94594i	−1.12349	+	1.94594i
$197$	−1.93815			−1.93815			−0.969077	−	0.246757i	$-0.920635\pi$
$197$	−1.93815			−1.93815			−0.969077	+	0.246757i	$0.920635\pi$
$198$	2.67536	−	0.681230i	2.67536	−	0.681230i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	3.32592	−	5.76066i	3.32592	−	5.76066i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.727051	+	1.25929i	−0.727051	+	1.25929i
$206$		0			0
$207$	1.28245	−	0.326552i	1.28245	−	0.326552i
$208$		0			0
$209$	1.53018	−	2.65036i	1.53018	−	2.65036i
$210$		0			0
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$	−1.02510	−	1.77552i	−1.02510	−	1.77552i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	−0.820914	−	2.09165i	−0.820914	−	2.09165i
$217$		0			0
$218$	0.134659	−	0.233236i	0.134659	−	0.233236i
$219$		0			0
$220$	−3.42547	−	5.93308i	−3.42547	−	5.93308i
$221$		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
$225$	2.06702	+	2.11921i	2.06702	+	2.11921i
$226$		0			0
$227$	0.0249307	−	0.0431812i	0.0249307	−	0.0431812i	−0.853291	−	0.521435i	$-0.825397\pi$
$227$	0.0249307	−	0.0431812i	0.0249307	−	0.0431812i	0.878222	+	0.478254i	$0.158730\pi$
$228$	−4.13593	−	1.74344i	−4.13593	−	1.74344i
$229$	−0.921476	−	1.59604i	−0.921476	−	1.59604i	−0.797133	−	0.603804i	$-0.793651\pi$
$229$	−0.921476	−	1.59604i	−0.921476	−	1.59604i	−0.124344	−	0.992239i	$-0.539683\pi$
$230$	−2.37278	−	4.10978i	−2.37278	−	4.10978i
$231$		0			0
$232$	−1.91733	+	3.32091i	−1.91733	+	3.32091i
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$		0			0
$236$	−0.608573	+	1.05408i	−0.608573	+	1.05408i
$237$		0			0
$238$		0			0
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$	−2.85849	+	2.16522i	−2.85849	+	2.16522i
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	−2.42774			−2.42774
$243$	0.995031	−	0.0995678i	0.995031	−	0.0995678i
$244$	4.29431			4.29431
$245$	−0.995031	+	1.72344i	−0.995031	+	1.72344i
$246$	1.04954	−	0.794995i	1.04954	−	0.794995i
$247$		0			0
$248$		0			0
$249$		0			0
$250$	3.51487	−	6.08793i	3.51487	−	6.08793i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$	−2.02752			−2.02752
$254$		0			0
$255$		0			0
$256$	0.900969	+	1.56052i	0.900969	+	1.56052i
$257$		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
$261$	−1.19160	−	1.22169i	−1.19160	−	1.22169i
$262$		0			0
$263$	0.969077	−	1.67849i	0.969077	−	1.67849i	0.270840	−	0.962624i	$-0.412698\pi$
$263$	0.969077	−	1.67849i	0.969077	−	1.67849i	0.698237	−	0.715867i	$-0.253968\pi$
$264$	0.428062	+	3.41586i	0.428062	+	3.41586i
$265$	−0.907887	−	1.57251i	−0.907887	−	1.57251i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$	−1.31010	−	3.33808i	−1.31010	−	3.33808i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.26776	−	3.92787i	−2.26776	−	3.92787i
$276$	0.369747	+	2.95051i	0.369747	+	2.95051i
$277$	0.124344	−	0.215370i	0.124344	−	0.215370i	−0.797133	−	0.603804i	$-0.793651\pi$
$277$	0.124344	−	0.215370i	0.124344	−	0.215370i	0.921476	+	0.388435i	$0.126984\pi$
$278$	0.0898471			0.0898471
$279$		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
$283$	−0.270840	−	0.469109i	−0.270840	−	0.469109i	0.698237	−	0.715867i	$-0.253968\pi$
$283$	−0.270840	−	0.469109i	−0.270840	−	0.469109i	−0.969077	+	0.246757i	$0.920635\pi$
$284$		0			0
$285$	−3.66303	−	1.54410i	−3.66303	−	1.54410i
$286$		0			0
$287$		0			0
$288$	0.969077	−	0.246757i	0.969077	−	0.246757i
$289$	1.00000			1.00000
$290$	−3.05987	+	5.29986i	−3.05987	+	5.29986i
$291$	−0.218403	−	1.74281i	−0.218403	−	1.74281i
$292$		0			0
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$	1.43638	−	1.08802i	1.43638	−	1.08802i
$295$	−0.538989	+	0.933557i	−0.538989	+	0.933557i
$296$		0			0
$297$	−1.51498	−	0.228346i	−1.51498	−	0.228346i
$298$	0.448119			0.448119
$299$		0			0
$300$	−5.30239	+	4.01641i	−5.30239	+	4.01641i
$301$		0			0
$302$	1.79298	+	3.10554i	1.79298	+	3.10554i
$303$		0			0
$304$	1.79970	−	3.11717i	1.79970	−	3.11717i
$305$	3.80330			3.80330
$306$		0			0
$307$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$307$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$308$		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	$0.666667\pi$
$314$	−2.76073			−2.76073
$315$		0			0
$316$		0			0
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$	0.204437	+	1.63137i	0.204437	+	1.63137i
$319$	1.30732	+	2.26434i	1.30732	+	2.26434i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.0560188	+	2.24628i	−0.0560188	+	2.24628i
$325$		0			0
$326$	−1.19232	+	2.06515i	−1.19232	+	2.06515i
$327$	−0.119140	+	0.0902447i	−0.119140	+	0.0902447i
$328$	0.820914	+	1.42186i	0.820914	+	1.42186i
$329$		0			0
$330$	0.683147	+	5.45138i	0.683147	+	5.45138i
$331$		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
$337$	0.733052	+	1.26968i	0.733052	+	1.26968i	0.955573	+	0.294755i	$0.0952381\pi$
$337$	0.733052	+	1.26968i	0.733052	+	1.26968i	−0.222521	+	0.974928i	$0.571429\pi$
$338$	0.900969	+	1.56052i	0.900969	+	1.56052i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	2.51323	+	2.57669i	2.51323	+	2.57669i
$343$		0			0
$344$		0			0
$345$	0.327470	+	2.61315i	0.327470	+	2.61315i
$346$	−0.573893	−	0.994012i	−0.573893	−	0.994012i
$347$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.733052	−	0.680173i	$-0.761905\pi$
$347$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.222521	−	0.974928i	$-0.571429\pi$
$348$	3.05673	−	2.31538i	3.05673	−	2.31538i
$349$		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	$-0.222222\pi$
$354$	0.778061	−	0.589359i	0.778061	−	0.589359i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.32091	+	2.28789i	−1.32091	+	2.28789i
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	4.33335	−	1.10341i	4.33335	−	1.10341i
$361$	2.99006			2.99006
$362$		0			0
$363$	1.24150	+	0.523337i	1.24150	+	0.523337i
$364$		0			0
$365$		0			0
$366$	−3.17335	−	1.33768i	−3.17335	−	1.33768i
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$	−2.38463			−2.38463
$369$	−0.708087	+	0.180301i	−0.708087	+	0.180301i
$370$		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
$375$	−3.10978	+	2.35557i	−3.10978	+	2.35557i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.149460			0.149460			0.0747301	−	0.997204i	$-0.476190\pi$
$379$	0.149460			0.149460			0.0747301	+	0.997204i	$0.476190\pi$
$380$	4.46607	−	7.73546i	4.46607	−	7.73546i
$381$		0			0
$382$		0			0
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$	−0.124344	−	0.992239i	−0.124344	−	0.992239i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	3.94669			3.94669
$389$	−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
$392$	1.12349	+	1.94594i	1.12349	+	1.94594i
$393$		0			0
$394$	−1.74622	+	3.02454i	−1.74622	+	3.02454i
$395$		0			0
$396$	0.932388	−	3.31390i	0.932388	−	3.31390i
$397$	−1.93815			−1.93815			−0.969077	−	0.246757i	$-0.920635\pi$
$397$	−1.93815			−1.93815			−0.969077	+	0.246757i	$0.920635\pi$
$398$		0			0
$399$		0			0
$400$	−2.66718	−	4.61969i	−2.66718	−	4.61969i
$401$		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
$405$	−0.0496136	+	1.98944i	−0.0496136	+	1.98944i
$406$		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	$0.333333\pi$
$410$	1.31010	+	2.26916i	1.31010	+	2.26916i
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.645855	−	2.29551i	0.645855	−	2.29551i
$415$		0			0
$416$		0			0
$417$	−0.0459461	−	0.0193679i	−0.0459461	−	0.0193679i
$418$	−2.75730	−	4.77578i	−2.75730	−	4.77578i
$419$		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
$424$	−2.05019			−2.05019
$425$		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
$432$	−1.78181	−	0.268565i	−1.78181	−	0.268565i
$433$	−1.16749			−1.16749			−0.583744	−	0.811938i	$-0.698413\pi$
$433$	−1.16749			−1.16749			−0.583744	+	0.811938i	$0.698413\pi$
$434$		0			0
$435$	2.70722	−	2.05064i	2.70722	−	2.05064i
$436$	−0.167917	−	0.290841i	−0.167917	−	0.290841i
$437$	−1.32173	−	2.28930i	−1.32173	−	2.28930i
$438$		0			0
$439$	0.411287	−	0.712370i	0.411287	−	0.712370i	−0.583744	−	0.811938i	$-0.698413\pi$
$439$	0.411287	−	0.712370i	0.411287	−	0.712370i	0.995031	+	0.0995678i	$0.0317460\pi$
$440$	−6.85093			−6.85093
$441$	−0.969077	+	0.246757i	−0.969077	+	0.246757i
$442$		0			0
$443$	−0.542546	+	0.939718i	−0.542546	+	0.939718i	0.456211	+	0.889872i	$0.349206\pi$
$443$	−0.542546	+	0.939718i	−0.542546	+	0.939718i	−0.998757	+	0.0498459i	$0.984127\pi$
$444$		0			0
$445$		0			0
$446$	1.38036	+	2.39086i	1.38036	+	2.39086i
$447$	−0.229160	−	0.0965988i	−0.229160	−	0.0965988i
$448$		0			0
$449$	−1.99751			−1.99751			−0.998757	−	0.0498459i	$-0.984127\pi$
$449$	−1.99751			−1.99751			−0.998757	+	0.0498459i	$0.984127\pi$
$450$	5.16940	−	1.31629i	5.16940	−	1.31629i
$451$	1.11947			1.11947
$452$		0			0
$453$	−0.247452	−	1.97462i	−0.247452	−	1.97462i
$454$	−0.0449236	−	0.0778099i	−0.0449236	−	0.0778099i
$455$		0			0
$456$	−3.57783	+	2.71010i	−3.57783	+	2.71010i
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$	−3.32089			−3.32089
$459$		0			0
$460$	−5.91763			−5.91763
$461$	−0.980172	+	1.69771i	−0.980172	+	1.69771i	−0.318487	+	0.947927i	$0.603175\pi$
$461$	−0.980172	+	1.69771i	−0.980172	+	1.69771i	−0.661686	+	0.749781i	$0.730159\pi$
$462$		0			0
$463$	−0.878222	−	1.52112i	−0.878222	−	1.52112i	−0.853291	−	0.521435i	$-0.825397\pi$
$463$	−0.878222	−	1.52112i	−0.878222	−	1.52112i	−0.0249307	−	0.999689i	$-0.507937\pi$
$464$	1.53758	+	2.66316i	1.53758	+	2.66316i
$465$		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
$471$	1.41178	+	0.595117i	1.41178	+	0.595117i
$472$	0.608573	+	1.05408i	0.608573	+	1.05408i
$473$		0			0
$474$		0			0
$475$	2.95667	−	5.12109i	2.95667	−	5.12109i
$476$		0			0
$477$	0.247121	−	0.878319i	0.247121	−	0.878319i
$478$		0			0
$479$	−0.955573	+	1.65510i	−0.955573	+	1.65510i	−0.222521	+	0.974928i	$0.571429\pi$
$479$	−0.955573	+	1.65510i	−0.955573	+	1.65510i	−0.733052	+	0.680173i	$0.761905\pi$
$480$	0.247452	+	1.97462i	0.247452	+	1.97462i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.51367	+	2.62176i	−1.51367	+	2.62176i
$485$	3.49543			3.49543
$486$	0.741114	−	1.64248i	0.741114	−	1.64248i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$	2.14715	−	3.71898i	2.14715	−	3.71898i
$489$	1.05490	−	0.799058i	1.05490	−	0.799058i
$490$	1.79298	+	3.10554i	1.79298	+	3.10554i
$491$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i	0.826239	−	0.563320i	$-0.190476\pi$
$491$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i	−0.900969	+	0.433884i	$0.857143\pi$
$492$	−0.204151	−	1.62909i	−0.204151	−	1.62909i
$493$		0			0
$494$		0			0
$495$	0.825779	−	2.93499i	0.825779	−	2.93499i
$496$		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	$0.333333\pi$
$500$	−4.38297	−	7.59152i	−4.38297	−	7.59152i
$501$		0			0
$502$		0			0
$503$	1.39647			1.39647			0.698237	−	0.715867i	$-0.253968\pi$
$503$	1.39647			1.39647			0.698237	+	0.715867i	$0.253968\pi$
$504$		0			0
$505$		0			0
$506$	−1.82674	+	3.16400i	−1.82674	+	3.16400i
$507$	−0.124344	−	0.992239i	−0.124344	−	0.992239i
$508$		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
$512$	2.24698			2.24698
$513$	−0.729774	−	1.85943i	−0.729774	−	1.85943i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.0792036	+	0.632030i	0.0792036	+	0.632030i
$520$		0			0
$521$	0.149460			0.149460			0.0747301	−	0.997204i	$-0.476190\pi$
$521$	0.149460			0.149460			0.0747301	+	0.997204i	$0.476190\pi$
$522$	−2.98006	+	0.758817i	−2.98006	+	0.758817i
$523$	0.730682			0.730682			0.365341	−	0.930874i	$-0.380952\pi$
$523$	0.730682			0.730682			0.365341	+	0.930874i	$0.380952\pi$
$524$		0			0
$525$		0			0
$526$	−1.74622	−	3.02454i	−1.74622	−	3.02454i
$527$		0			0
$528$	2.54395	+	1.07236i	2.54395	+	1.07236i
$529$	−0.375656	+	0.650656i	−0.375656	+	0.650656i
$530$	−3.27191			−3.27191
$531$	−0.524931	+	0.133664i	−0.524931	+	0.133664i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	1.16868	−	0.885240i	1.16868	−	0.885240i
$538$		0			0
$539$	1.53209			1.53209
$540$	−4.42168	−	0.666462i	−4.42168	−	0.666462i
$541$	1.08509			1.08509			0.542546	−	0.840026i	$-0.317460\pi$
$541$	1.08509			1.08509			0.542546	+	0.840026i	$0.317460\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.148717	−	0.257586i	−0.148717	−	0.257586i
$546$		0			0
$547$	0.411287	−	0.712370i	0.411287	−	0.712370i	−0.583744	−	0.811938i	$-0.698413\pi$
$547$	0.411287	−	0.712370i	0.411287	−	0.712370i	0.995031	+	0.0995678i	$0.0317460\pi$
$548$		0			0
$549$	1.33443	+	1.36813i	1.33443	+	1.36813i
$550$	−8.17271			−8.17271
$551$	−1.70446	+	2.95221i	−1.70446	+	2.95221i
$552$	2.74009	+	1.15505i	2.74009	+	1.15505i
$553$		0			0
$554$	−0.224060	−	0.388083i	−0.224060	−	0.388083i
$555$		0			0
$556$	0.0560188	−	0.0970273i	0.0560188	−	0.0970273i
$557$		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
$563$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	−0.900969	−	0.433884i	$-0.857143\pi$
$563$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	0.0747301	−	0.997204i	$-0.476190\pi$
$564$		0			0
$565$		0			0
$566$	−0.976075			−0.976075
$567$		0			0
$568$		0			0
$569$	−0.542546	+	0.939718i	−0.542546	+	0.939718i	0.456211	+	0.889872i	$0.349206\pi$
$569$	−0.542546	+	0.939718i	−0.542546	+	0.939718i	−0.998757	+	0.0498459i	$0.984127\pi$
$570$	−5.70988	+	4.32506i	−5.70988	+	4.32506i
$571$		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
$575$	−3.91764			−3.91764
$576$		0			0
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	0.900969	−	1.56052i	0.900969	−	1.56052i
$579$		0			0
$580$	3.81560	+	6.60881i	3.81560	+	6.60881i
$581$		0			0
$582$	−2.91647	−	1.22940i	−2.91647	−	1.22940i
$583$	−0.698955	+	1.21063i	−0.698955	+	1.21063i
$584$		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	$0.666667\pi$
$588$	−0.279398	−	2.22954i	−0.279398	−	2.22954i
$589$		0			0
$590$	0.971225	+	1.68221i	0.971225	+	1.68221i
$591$	1.54497	−	1.17027i	1.54497	−	1.17027i
$592$		0			0
$593$	1.75644			1.75644			0.878222	−	0.478254i	$-0.158730\pi$
$593$	1.75644			1.75644			0.878222	+	0.478254i	$0.158730\pi$
$594$	−1.72129	+	2.15842i	−1.72129	+	2.15842i
$595$		0			0
$596$	0.279398	−	0.483931i	0.279398	−	0.483931i
$597$		0			0
$598$		0			0
$599$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$599$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$600$	0.827114	+	6.60021i	0.827114	+	6.60021i
$601$		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
$604$	4.47163			4.47163
$605$	−1.34060	+	2.32199i	−1.34060	+	2.32199i
$606$		0			0
$607$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.733052	−	0.680173i	$-0.761905\pi$
$607$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.222521	−	0.974928i	$-0.571429\pi$
$608$	−0.998757	−	1.72990i	−0.998757	−	1.72990i
$609$		0			0
$610$	3.42665	−	5.93514i	3.42665	−	5.93514i
$611$		0			0
$612$		0			0
$613$	0.730682			0.730682			0.365341	−	0.930874i	$-0.380952\pi$
$613$	0.730682			0.730682			0.365341	+	0.930874i	$0.380952\pi$
$614$	−1.62349	+	2.81197i	−1.62349	+	2.81197i
$615$	−0.180808	−	1.44282i	−0.180808	−	1.44282i
$616$		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
$621$	−0.825109	+	1.03465i	−0.825109	+	1.03465i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−2.40165	−	4.15978i	−2.40165	−	4.15978i
$626$		0			0
$627$	0.380538	+	3.03662i	0.380538	+	3.03662i
$628$	−1.72129	+	2.98136i	−1.72129	+	2.98136i
$629$		0			0
$630$		0			0
$631$	−0.248687			−0.248687			−0.124344	−	0.992239i	$-0.539683\pi$
$631$	−0.248687			−0.248687			−0.124344	+	0.992239i	$0.539683\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	1.88920	+	0.796366i	1.88920	+	0.796366i
$637$		0			0
$638$	4.71141			4.71141
$639$		0			0
$640$	1.99006			1.99006
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$		0			0
$643$	0.222521	+	0.385418i	0.222521	+	0.385418i	0.955573	−	0.294755i	$-0.0952381\pi$
$643$	0.222521	+	0.385418i	0.222521	+	0.385418i	−0.733052	+	0.680173i	$0.761905\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.0498614			−0.0498614			−0.0249307	−	0.999689i	$-0.507937\pi$
$647$	−0.0498614			−0.0498614			−0.0249307	+	0.999689i	$0.507937\pi$
$648$	1.91733	+	1.17165i	1.91733	+	1.17165i
$649$	0.829903			0.829903
$650$		0			0
$651$		0			0
$652$	1.48679	+	2.57520i	1.48679	+	2.57520i
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$	0.0334880	+	0.267228i	0.0334880	+	0.267228i
$655$		0			0
$656$	1.31664			1.31664
$657$		0			0
$658$		0			0
$659$	−0.456211	+	0.790180i	−0.456211	+	0.790180i	−0.998757	−	0.0498459i	$-0.984127\pi$
$659$	−0.456211	+	0.790180i	−0.456211	+	0.790180i	0.542546	+	0.840026i	$0.317460\pi$
$660$	6.31297	+	2.66114i	6.31297	+	2.66114i
$661$	−0.698237	−	1.20938i	−0.698237	−	1.20938i	−0.969077	−	0.246757i	$-0.920635\pi$
$661$	−0.698237	−	1.20938i	−0.698237	−	1.20938i	0.270840	−	0.962624i	$-0.412698\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.25844			2.25844
$668$		0			0
$669$	−0.190506	−	1.52020i	−0.190506	−	1.52020i
$670$		0			0
$671$	−1.46402	−	2.53576i	−1.46402	−	2.53576i
$672$		0			0
$673$	0.988831	−	1.71271i	0.988831	−	1.71271i	0.365341	−	0.930874i	$-0.380952\pi$
$673$	0.988831	−	1.71271i	0.988831	−	1.71271i	0.623490	−	0.781831i	$-0.285714\pi$
$674$	2.64183			2.64183
$675$	−2.92728	−	0.441217i	−2.92728	−	0.441217i
$676$	2.24698			2.24698
$677$	0.797133	−	1.38067i	0.797133	−	1.38067i	−0.124344	−	0.992239i	$-0.539683\pi$
$677$	0.797133	−	1.38067i	0.797133	−	1.38067i	0.921476	−	0.388435i	$-0.126984\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.00619995	+	0.0494744i	0.00619995	+	0.0494744i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	4.34958	−	1.10754i	4.34958	−	1.10754i
$685$		0			0
$686$		0			0
$687$	1.69824	+	0.715867i	1.69824	+	0.715867i
$688$		0			0
$689$		0			0
$690$	4.37293	+	1.84334i	4.37293	+	1.84334i
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$	−1.43127			−1.43127
$693$		0			0
$694$	−3.44377			−3.44377
$695$	0.0496136	−	0.0859333i	0.0496136	−	0.0859333i
$696$	−0.476815	−	3.80489i	−0.476815	−	3.80489i
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−1.97766			−1.97766			−0.988831	−	0.149042i	$-0.952381\pi$
$701$	−1.97766			−1.97766			−0.988831	+	0.149042i	$0.952381\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−1.69327	−	2.93283i	−1.69327	−	2.93283i
$707$		0			0
$708$	−0.151344	−	1.20770i	−0.151344	−	1.20770i
$709$	0.661686	−	1.14607i	0.661686	−	1.14607i	−0.318487	−	0.947927i	$-0.603175\pi$
$709$	0.661686	−	1.14607i	0.661686	−	1.14607i	0.980172	−	0.198146i	$-0.0634921\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.64715	+	2.85295i	1.64715	+	2.85295i
$717$		0			0
$718$		0			0
$719$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$719$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$720$	0.971225	−	3.45194i	0.971225	−	3.45194i
$721$		0			0
$722$	2.69395	−	4.66606i	2.69395	−	4.66606i
$723$		0			0
$724$		0			0
$725$	2.52604	+	4.37522i	2.52604	+	4.37522i
$726$	1.93523	−	1.46588i	1.93523	−	1.46588i
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$730$		0			0
$731$		0			0
$732$	−3.42313	+	2.59292i	−3.42313	+	2.59292i
$733$	0.318487	+	0.551635i	0.318487	+	0.551635i	0.980172	−	0.198146i	$-0.0634921\pi$
$733$	0.318487	+	0.551635i	0.318487	+	0.551635i	−0.661686	+	0.749781i	$0.730159\pi$
$734$		0			0
$735$	−0.247452	−	1.97462i	−0.247452	−	1.97462i
$736$	−0.661686	+	1.14607i	−0.661686	+	1.14607i
$737$		0			0
$738$	−0.356600	+	1.26743i	−0.356600	+	1.26743i
$739$		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
$745$	0.247452	−	0.428599i	0.247452	−	0.428599i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$	0.874103	+	6.97518i	0.874103	+	6.97518i
$751$	0.797133	+	1.38067i	0.797133	+	1.38067i	0.921476	+	0.388435i	$0.126984\pi$
$751$	0.797133	+	1.38067i	0.797133	+	1.38067i	−0.124344	+	0.992239i	$0.539683\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.96034			3.96034
$756$		0			0
$757$	1.65248			1.65248			0.826239	−	0.563320i	$-0.190476\pi$
$757$	1.65248			1.65248			0.826239	+	0.563320i	$0.190476\pi$
$758$	0.134659	−	0.233236i	0.134659	−	0.233236i
$759$	1.61620	−	1.22423i	1.61620	−	1.22423i
$760$	−4.46607	−	7.73546i	−4.46607	−	7.73546i
$761$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	−0.900969	−	0.433884i	$-0.857143\pi$
$761$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	0.0747301	−	0.997204i	$-0.476190\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.66044	−	0.699935i	−1.66044	−	0.699935i
$769$	0.969077	+	1.67849i	0.969077	+	1.67849i	0.698237	+	0.715867i	$0.253968\pi$
$769$	0.969077	+	1.67849i	0.969077	+	1.67849i	0.270840	+	0.962624i	$0.412698\pi$
$770$		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
$776$	1.97335	−	3.41794i	1.97335	−	3.41794i
$777$		0			0
$778$	0.312903	+	0.541964i	0.312903	+	0.541964i
$779$	0.729774	+	1.26401i	0.729774	+	1.26401i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	1.68752	+	0.254353i	1.68752	+	0.254353i
$784$	1.80194			1.80194
$785$	−1.52448	+	2.64047i	−1.52448	+	2.64047i
$786$		0			0
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$	2.17750	+	3.77154i	2.17750	+	3.77154i
$789$	0.240997	+	1.92311i	0.240997	+	1.92311i
$790$		0			0
$791$		0			0
$792$	−2.40373	−	2.46442i	−2.40373	−	2.46442i
$793$		0			0
$794$	−1.74622	+	3.02454i	−1.74622	+	3.02454i
$795$	1.67319	+	0.705310i	1.67319	+	0.705310i
$796$		0			0
$797$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.623490	+	0.781831i	$0.285714\pi$
$797$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.365341	+	0.930874i	$0.380952\pi$
$798$		0			0
$799$		0			0
$800$	−2.96034			−2.96034
$801$		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			$\pi$
$810$	3.05987	+	1.86985i	3.05987	+	1.86985i
$811$	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
$815$	1.31680	+	2.28076i	1.31680	+	2.28076i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	3.26734			3.26734
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$		0			0
$823$	−0.542546	−	0.939718i	−0.542546	−	0.939718i	−0.998757	−	0.0498459i	$-0.984127\pi$
$823$	−0.542546	−	0.939718i	−0.542546	−	0.939718i	0.456211	−	0.889872i	$-0.349206\pi$
$824$		0			0
$825$	4.17937	+	1.76175i	4.17937	+	1.76175i
$826$		0			0
$827$	−1.16749			−1.16749			−0.583744	−	0.811938i	$-0.698413\pi$
$827$	−1.16749			−1.16749			−0.583744	+	0.811938i	$0.698413\pi$
$828$	−2.07627	−	2.12869i	−2.07627	−	2.12869i
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$	0.0309227	+	0.246757i	0.0309227	+	0.246757i
$832$		0			0
$833$		0			0
$834$	−0.0716201	+	0.0542501i	−0.0716201	+	0.0542501i
$835$		0			0
$836$	−6.87659			−6.87659
$837$		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
$841$	−0.956211	−	1.65621i	−0.956211	−	1.65621i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.99006			1.99006
$846$		0			0
$847$		0			0
$848$	−0.822063	+	1.42386i	−0.822063	+	1.42386i
$849$	0.499146	+	0.210408i	0.499146	+	0.210408i
$850$		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
$855$	3.85225	−	0.980904i	3.85225	−	0.980904i
$856$		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
$862$	0.900969	−	1.56052i	0.900969	−	1.56052i
$863$	0.149460			0.149460			0.0747301	−	0.997204i	$-0.476190\pi$
$863$	0.149460			0.149460			0.0747301	+	0.997204i	$0.476190\pi$
$864$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$865$	−1.26762			−1.26762
$866$	−1.05187	+	1.82189i	−1.05187	+	1.82189i
$867$	−0.797133	+	0.603804i	−0.797133	+	0.603804i
$868$		0			0
$869$		0			0
$870$	−0.760952	−	6.07225i	−0.760952	−	6.07225i
$871$		0			0
$872$	−0.335834			−0.335834
$873$	1.22641	+	1.25738i	1.22641	+	1.25738i
$874$	−4.76334			−4.76334
$875$		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	$0.444444\pi$
$878$	−0.741114	−	1.28365i	−0.741114	−	1.28365i
$879$		0			0
$880$	−2.74701	+	4.75796i	−2.74701	+	4.75796i
$881$	−0.636973			−0.636973			−0.318487	−	0.947927i	$-0.603175\pi$
$881$	−0.636973			−0.636973			−0.318487	+	0.947927i	$0.603175\pi$
$882$	−0.488038	+	1.73459i	−0.488038	+	1.73459i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$	−0.134040	−	1.06961i	−0.134040	−	1.06961i
$886$	0.977635	+	1.69331i	0.977635	+	1.69331i
$887$	−0.456211	−	0.790180i	−0.456211	−	0.790180i	0.542546	−	0.840026i	$-0.317460\pi$
$887$	−0.456211	−	0.790180i	−0.456211	−	0.790180i	−0.998757	+	0.0498459i	$0.984127\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.34551	−	0.732728i	1.34551	−	0.732728i
$892$	3.44257			3.44257
$893$		0			0
$894$	−0.357210	+	0.270576i	−0.357210	+	0.270576i
$895$	1.45882	+	2.52675i	1.45882	+	2.52675i
$896$		0			0
$897$		0			0
$898$	−1.79970	+	3.11717i	−1.79970	+	3.11717i
$899$		0			0
$900$	1.80159	−	6.40322i	1.80159	−	6.40322i
$901$		0			0
$902$	1.00861	−	1.74696i	1.00861	−	1.74696i
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−3.30438	−	1.39291i	−3.30438	−	1.39291i
$907$	0.853291	−	1.47794i	0.853291	−	1.47794i	−0.0249307	−	0.999689i	$-0.507937\pi$
$907$	0.853291	−	1.47794i	0.853291	−	1.47794i	0.878222	−	0.478254i	$-0.158730\pi$
$908$	−0.112038			−0.112038
$909$		0			0
$910$		0			0
$911$	0.411287	−	0.712370i	0.411287	−	0.712370i	−0.583744	−	0.811938i	$-0.698413\pi$
$911$	0.411287	−	0.712370i	0.411287	−	0.712370i	0.995031	+	0.0995678i	$0.0317460\pi$
$912$	0.447562	+	3.57146i	0.447562	+	3.57146i
$913$		0			0
$914$		0			0
$915$	−3.03173	+	2.29645i	−3.03173	+	2.29645i
$916$	−2.07054	+	3.58628i	−2.07054	+	3.58628i
$917$		0			0
$918$		0			0
$919$	−1.70658			−1.70658			−0.853291	−	0.521435i	$-0.825397\pi$
$919$	−1.70658			−1.70658			−0.853291	+	0.521435i	$0.825397\pi$
$920$	−2.95881	+	5.12481i	−2.95881	+	5.12481i
$921$	1.43638	−	1.08802i	1.43638	−	1.08802i
$922$	1.76621	+	3.05917i	1.76621	+	3.05917i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−3.16500			−3.16500
$927$		0			0
$928$	1.70658			1.70658
$929$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$929$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$930$		0			0
$931$	0.998757	+	1.72990i	0.998757	+	1.72990i
$932$		0			0
$933$		0			0
$934$	−0.900969	+	1.56052i	−0.900969	+	1.56052i
$935$		0			0
$936$		0			0
$937$	0.912421			0.912421			0.456211	−	0.889872i	$-0.349206\pi$
$937$	0.912421			0.912421			0.456211	+	0.889872i	$0.349206\pi$
$938$		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	$0.333333\pi$
$942$	2.20067	−	1.66694i	2.20067	−	1.66694i
$943$	0.483482	−	0.837415i	0.483482	−	0.837415i
$944$	0.976075			0.976075
$945$		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
$950$	−5.32773	−	9.22789i	−5.32773	−	9.22789i
$951$		0			0
$952$		0			0
$953$	0.541681			0.541681			0.270840	−	0.962624i	$-0.412698\pi$
$953$	0.541681			0.541681			0.270840	+	0.962624i	$0.412698\pi$
$954$	−1.14799	−	1.17698i	−1.14799	−	1.17698i
$955$		0			0
$956$		0			0
$957$	−2.40932	−	1.01562i	−2.40932	−	1.01562i
$958$	1.72188	+	2.98239i	1.72188	+	2.98239i
$959$		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	$0.333333\pi$
$968$	1.51367	+	2.62176i	1.51367	+	2.62176i
$969$		0			0
$970$	3.14927	−	5.45470i	3.14927	−	5.45470i
$971$	0.730682			0.730682			0.365341	−	0.930874i	$-0.380952\pi$
$971$	0.730682			0.730682			0.365341	+	0.930874i	$0.380952\pi$
$972$	−1.31166	−	1.82441i	−1.31166	−	1.82441i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−1.72188	−	2.98239i	−1.72188	−	2.98239i
$977$	0.124344	+	0.215370i	0.124344	+	0.215370i	0.921476	−	0.388435i	$-0.126984\pi$
$977$	0.124344	+	0.215370i	0.124344	+	0.215370i	−0.797133	+	0.603804i	$0.793651\pi$
$978$	−0.296514	−	2.36613i	−0.296514	−	2.36613i
$979$		0			0
$980$	4.47163			4.47163
$981$	0.0404799	−	0.143874i	0.0404799	−	0.143874i
$982$	−0.269318			−0.269318
$983$	0.124344	−	0.215370i	0.124344	−	0.215370i	−0.797133	−	0.603804i	$-0.793651\pi$
$983$	0.124344	−	0.215370i	0.124344	−	0.215370i	0.921476	+	0.388435i	$0.126984\pi$
$984$	−1.51291	−	0.637743i	−1.51291	−	0.637743i
$985$	1.92852	+	3.34030i	1.92852	+	3.34030i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−3.83613	−	3.93299i	−3.83613	−	3.93299i
$991$		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
$997$	0.318487	−	0.551635i	0.318487	−	0.551635i	−0.661686	−	0.749781i	$-0.730159\pi$
$997$	0.318487	−	0.551635i	0.318487	−	0.551635i	0.980172	+	0.198146i	$0.0634921\pi$
$998$		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.430.14	✓	36
9.4	even	3	inner	3879.1.g.c.1723.14	yes	36
431.430	odd	2	CM	3879.1.g.c.430.14	✓	36
3879.1723	odd	6	inner	3879.1.g.c.1723.14	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3879.1.g.c.430.14	✓	36	1.1	even	1	trivial
3879.1.g.c.430.14	✓	36	431.430	odd	2	CM
3879.1.g.c.1723.14	yes	36	9.4	even	3	inner
3879.1.g.c.1723.14	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)

\(f(q)\)	\(=\)	\(q+(0.900969 - 1.56052i) q^{2} +(-0.797133 + 0.603804i) q^{3} +(-1.12349 - 1.94594i) q^{4} +(-0.995031 - 1.72344i) q^{5} +(0.224060 + 1.78795i) q^{6} -2.24698 q^{8} +(0.270840 - 0.962624i) q^{9} +O(q^{10})\)	\(q+(0.900969 - 1.56052i) q^{2} +(-0.797133 + 0.603804i) q^{3} +(-1.12349 - 1.94594i) q^{4} +(-0.995031 - 1.72344i) q^{5} +(0.224060 + 1.78795i) q^{6} -2.24698 q^{8} +(0.270840 - 0.962624i) q^{9} -3.58597 q^{10} +(-0.766044 + 1.32683i) q^{11} +(2.07054 + 0.872805i) q^{12} +(1.83379 + 0.773009i) q^{15} +(-0.900969 + 1.56052i) q^{16} +(-1.25818 - 1.28995i) q^{18} -1.99751 q^{19} +(-2.23581 + 3.87254i) q^{20} +(1.38036 + 2.39086i) q^{22} +(0.661686 + 1.14607i) q^{23} +(1.79114 - 1.35674i) q^{24} +(-1.48017 + 2.56373i) q^{25} +(0.365341 + 0.930874i) q^{27} +(0.853291 - 1.47794i) q^{29} +(2.85849 - 2.16522i) q^{30} +(0.500000 + 0.866025i) q^{32} +(-0.190506 - 1.52020i) q^{33} +(-2.17750 + 0.554459i) q^{36} +(-1.79970 + 3.11717i) q^{38} +(2.23581 + 3.87254i) q^{40} +(-0.365341 - 0.632789i) q^{41} +3.44257 q^{44} +(-1.92852 + 0.491062i) q^{45} +2.38463 q^{46} +(-0.224060 - 1.78795i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(2.66718 + 4.61969i) q^{50} +0.912421 q^{53} +(1.78181 + 0.268565i) q^{54} +3.04895 q^{55} +(1.59228 - 1.20611i) q^{57} +(-1.53758 - 2.66316i) q^{58} +(-0.270840 - 0.469109i) q^{59} +(-0.556019 - 4.43692i) q^{60} +(-0.955573 + 1.65510i) q^{61} +(-2.54395 - 1.07236i) q^{66} +(-1.21946 - 0.514044i) q^{69} +(-0.608573 + 2.16300i) q^{72} +(-0.368100 - 2.93737i) q^{75} +(2.24419 + 3.88704i) q^{76} +3.58597 q^{80} +(-0.853291 - 0.521435i) q^{81} -1.31664 q^{82} +(0.212203 + 1.69334i) q^{87} +(1.72129 - 2.98136i) q^{88} +(-0.971225 + 3.45194i) q^{90} +(1.48679 - 2.57520i) q^{92} +(1.98759 + 3.44260i) q^{95} +(-0.921476 - 0.388435i) q^{96} +(-0.878222 + 1.52112i) q^{97} -1.80194 q^{98} +(1.06976 + 1.09677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{2} - 12 q^{4} - 24 q^{8}+O(q^{10}) \) 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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