LMFDB - Embedded newform 344.1.s.a.219.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [344,1,Mod(11,344)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("344.11"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(344, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 7, 10])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 344 = 2^{3} \cdot 43 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	344.s (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.171678364346$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{7}$
Projective field:	Galois closure of 7.1.3236537881088.1

Embedding invariants

Embedding label			219.1
Root			$0.900969 - 0.433884i$ of defining polynomial
Character	$\chi$	$=$	344.219
Dual form			344.1.s.a.11.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.623490 - 0.781831i) q^{2} +(-0.277479 - 0.347948i) q^{3} +(-0.222521 - 0.974928i) q^{4} -0.445042 q^{6} +(-0.900969 - 0.433884i) q^{8} +(0.178448 - 0.781831i) q^{9} +(-0.277479 + 1.21572i) q^{11} +(-0.277479 + 0.347948i) q^{12} +(-0.900969 + 0.433884i) q^{16} +(0.400969 - 0.193096i) q^{17} +(-0.500000 - 0.626980i) q^{18} +(0.0990311 + 0.433884i) q^{19} +(0.777479 + 0.974928i) q^{22} +(0.0990311 + 0.433884i) q^{24} +(0.623490 + 0.781831i) q^{25} +(-0.722521 + 0.347948i) q^{27} +(-0.222521 + 0.974928i) q^{32} +(0.500000 - 0.240787i) q^{33} +(0.0990311 - 0.433884i) q^{34} -0.801938 q^{36} +(0.400969 + 0.193096i) q^{38} +(-1.12349 + 1.40881i) q^{41} +(0.623490 - 0.781831i) q^{43} +1.24698 q^{44} +(0.400969 + 0.193096i) q^{48} +1.00000 q^{49} +1.00000 q^{50} +(-0.178448 - 0.0859360i) q^{51} +(-0.178448 + 0.781831i) q^{54} +(0.123490 - 0.154851i) q^{57} +(-1.12349 + 0.541044i) q^{59} +(0.623490 + 0.781831i) q^{64} +(0.123490 - 0.541044i) q^{66} +(-0.445042 - 1.94986i) q^{67} +(-0.277479 - 0.347948i) q^{68} +(-0.500000 + 0.626980i) q^{72} +(-1.80194 - 0.867767i) q^{73} +(0.0990311 - 0.433884i) q^{75} +(0.400969 - 0.193096i) q^{76} +(-0.400969 - 0.193096i) q^{81} +(0.400969 + 1.75676i) q^{82} +(0.777479 + 0.974928i) q^{83} +(-0.222521 - 0.974928i) q^{86} +(0.777479 - 0.974928i) q^{88} +(-1.12349 - 1.40881i) q^{89} +(0.400969 - 0.193096i) q^{96} +(-0.277479 + 1.21572i) q^{97} +(0.623490 - 0.781831i) q^{98} +(0.900969 + 0.433884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9} - 2 q^{11} - 2 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} + 5 q^{19} + 5 q^{22} + 5 q^{24} - q^{25} - 4 q^{27} - q^{32} + 3 q^{33} + 5 q^{34} + 4 q^{36}+ \cdots + q^{99}+O(q^{100}) $ 6 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9 - 2 * q^11 - 2 * q^12 - q^16 - 2 * q^17 - 3 * q^18 + 5 * q^19 + 5 * q^22 + 5 * q^24 - q^25 - 4 * q^27 - q^32 + 3 * q^33 + 5 * q^34 + 4 * q^36 - 2 * q^38 - 2 * q^41 - q^43 - 2 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 3 * q^51 + 3 * q^54 - 4 * q^57 - 2 * q^59 - q^64 - 4 * q^66 - 2 * q^67 - 2 * q^68 - 3 * q^72 - 2 * q^73 + 5 * q^75 - 2 * q^76 + 2 * q^81 - 2 * q^82 + 5 * q^83 - q^86 + 5 * q^88 - 2 * q^89 - 2 * q^96 - 2 * q^97 - q^98 + q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/344\mathbb{Z}\right)^\times$.

$n$	$87$	$89$	$173$
$\chi(n)$	$-1$	$e\left(\frac{2}{7}\right)$	$-1$

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	−	0.781831i	0.623490	−	0.781831i
$2$	0.623490	−	0.781831i	0.623490	−	0.781831i
$3$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$3$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$4$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$5$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$5$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$6$	−0.445042			−0.445042
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$9$	0.178448	−	0.781831i	0.178448	−	0.781831i
$10$		0			0
$11$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$11$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$12$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$13$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$13$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$14$		0			0
$15$		0			0
$16$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$17$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$17$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$18$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$19$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$19$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$20$		0			0
$21$		0			0
$22$	0.777479	+	0.974928i	0.777479	+	0.974928i
$23$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$23$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$24$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$25$	0.623490	+	0.781831i	0.623490	+	0.781831i
$26$		0			0
$27$	−0.722521	+	0.347948i	−0.722521	+	0.347948i
$28$		0			0
$29$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$29$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$30$		0			0
$31$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$31$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$32$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$33$	0.500000	−	0.240787i	0.500000	−	0.240787i
$34$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$35$		0			0
$36$	−0.801938			−0.801938
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	0.400969	+	0.193096i	0.400969	+	0.193096i
$39$		0			0
$40$		0			0
$41$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$41$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$42$		0			0
$43$	0.623490	−	0.781831i	0.623490	−	0.781831i
$43$	0.623490	−	0.781831i	0.623490	−	0.781831i
$44$	1.24698			1.24698
$45$		0			0
$46$		0			0
$47$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$47$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$48$	0.400969	+	0.193096i	0.400969	+	0.193096i
$49$	1.00000			1.00000
$50$	1.00000			1.00000
$51$	−0.178448	−	0.0859360i	−0.178448	−	0.0859360i
$52$		0			0
$53$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$53$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$54$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$55$		0			0
$56$		0			0
$57$	0.123490	−	0.154851i	0.123490	−	0.154851i
$58$		0			0
$59$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$59$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$60$		0			0
$61$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$61$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$62$		0			0
$63$		0			0
$64$	0.623490	+	0.781831i	0.623490	+	0.781831i
$65$		0			0
$66$	0.123490	−	0.541044i	0.123490	−	0.541044i
$67$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$67$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$68$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$69$		0			0
$70$		0			0
$71$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$71$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$72$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$73$	−1.80194	−	0.867767i	−1.80194	−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$73$	−1.80194	−	0.867767i	−1.80194	−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$74$		0			0
$75$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$76$	0.400969	−	0.193096i	0.400969	−	0.193096i
$77$		0			0
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$		0			0
$81$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$82$	0.400969	+	1.75676i	0.400969	+	1.75676i
$83$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$83$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$84$		0			0
$85$		0			0
$86$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$87$		0			0
$88$	0.777479	−	0.974928i	0.777479	−	0.974928i
$89$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$89$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.400969	−	0.193096i	0.400969	−	0.193096i
$97$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$97$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$98$	0.623490	−	0.781831i	0.623490	−	0.781831i
$99$	0.900969	+	0.433884i	0.900969	+	0.433884i
$100$	0.623490	−	0.781831i	0.623490	−	0.781831i
$101$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$101$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$102$	−0.178448	+	0.0859360i	−0.178448	+	0.0859360i
$103$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$103$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$107$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$108$	0.500000	+	0.626980i	0.500000	+	0.626980i
$109$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$109$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$113$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$114$	−0.0440730	−	0.193096i	−0.0440730	−	0.193096i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$119$		0			0
$120$		0			0
$121$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$122$		0			0
$123$	0.801938			0.801938
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$127$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$128$	1.00000			1.00000
$129$	−0.445042			−0.445042
$130$		0			0
$131$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$131$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$132$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$133$		0			0
$134$	−1.80194	−	0.867767i	−1.80194	−	0.867767i
$135$		0			0
$136$	−0.445042			−0.445042
$137$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$137$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$138$		0			0
$139$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$139$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.178448	+	0.781831i	0.178448	+	0.781831i
$145$		0			0
$146$	−1.80194	+	0.867767i	−1.80194	+	0.867767i
$147$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$148$		0			0
$149$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$149$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$150$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$151$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$151$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$152$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$153$	−0.0794168	−	0.347948i	−0.0794168	−	0.347948i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$157$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$163$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$163$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$164$	1.62349	+	0.781831i	1.62349	+	0.781831i
$165$		0			0
$166$	1.24698			1.24698
$167$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$167$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$168$		0			0
$169$	0.623490	+	0.781831i	0.623490	+	0.781831i
$170$		0			0
$171$	0.356896			0.356896
$172$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$		0			0
$175$		0			0
$176$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$177$	0.500000	+	0.240787i	0.500000	+	0.240787i
$178$	−1.80194			−1.80194
$179$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$179$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$180$		0			0
$181$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$181$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.123490	+	0.541044i	0.123490	+	0.541044i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$191$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$192$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$193$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$193$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$194$	0.777479	+	0.974928i	0.777479	+	0.974928i
$195$		0			0
$196$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$197$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$197$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$198$	0.900969	−	0.433884i	0.900969	−	0.433884i
$199$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$199$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$200$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$201$	−0.554958	+	0.695895i	−0.554958	+	0.695895i
$202$		0			0
$203$		0			0
$204$	−0.0440730	+	0.193096i	−0.0440730	+	0.193096i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.554958			−0.554958
$210$		0			0
$211$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$211$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$212$		0			0
$213$		0			0
$214$	−1.80194			−1.80194
$215$		0			0
$216$	0.801938			0.801938
$217$		0			0
$218$		0			0
$219$	0.198062	+	0.867767i	0.198062	+	0.867767i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$223$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$224$		0			0
$225$	0.722521	−	0.347948i	0.722521	−	0.347948i
$226$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$227$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$227$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$228$	−0.178448	−	0.0859360i	−0.178448	−	0.0859360i
$229$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$229$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$233$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$234$		0			0
$235$		0			0
$236$	0.777479	+	0.974928i	0.777479	+	0.974928i
$237$		0			0
$238$		0			0
$239$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$239$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$240$		0			0
$241$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$241$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$242$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$243$	0.222521	+	0.974928i	0.222521	+	0.974928i
$244$		0			0
$245$		0			0
$246$	0.500000	−	0.626980i	0.500000	−	0.626980i
$247$		0			0
$248$		0			0
$249$	0.123490	−	0.541044i	0.123490	−	0.541044i
$250$		0			0
$251$	2.00000			2.00000			1.00000			$0$
$251$	2.00000			2.00000			1.00000			$0$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.623490	−	0.781831i	0.623490	−	0.781831i
$257$	2.00000			2.00000			1.00000			$0$
$257$	2.00000			2.00000			1.00000			$0$
$258$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.400969	+	1.75676i	0.400969	+	1.75676i
$263$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$263$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$264$	−0.554958			−0.554958
$265$		0			0
$266$		0			0
$267$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$268$	−1.80194	+	0.867767i	−1.80194	+	0.867767i
$269$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$269$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$270$		0			0
$271$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$271$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$272$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$273$		0			0
$274$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$275$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$276$		0			0
$277$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$277$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$278$	0.400969	−	1.75676i	0.400969	−	1.75676i
$279$		0			0
$280$		0			0
$281$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$281$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$282$		0			0
$283$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$283$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.722521	+	0.347948i	0.722521	+	0.347948i
$289$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$290$		0			0
$291$	0.500000	−	0.240787i	0.500000	−	0.240787i
$292$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$293$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$293$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$294$	−0.445042			−0.445042
$295$		0			0
$296$		0			0
$297$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$298$		0			0
$299$		0			0
$300$	−0.445042			−0.445042
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$305$		0			0
$306$	−0.321552	−	0.154851i	−0.321552	−	0.154851i
$307$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$307$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$311$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$312$		0			0
$313$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$313$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$317$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$322$		0			0
$323$	0.123490	+	0.154851i	0.123490	+	0.154851i
$324$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$325$		0			0
$326$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$327$		0			0
$328$	1.62349	−	0.781831i	1.62349	−	0.781831i
$329$		0			0
$330$		0			0
$331$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$331$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$332$	0.777479	−	0.974928i	0.777479	−	0.974928i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$337$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$338$	1.00000			1.00000
$339$	−0.178448	−	0.0859360i	−0.178448	−	0.0859360i
$340$		0			0
$341$		0			0
$342$	0.222521	−	0.279032i	0.222521	−	0.279032i
$343$		0			0
$344$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$345$		0			0
$346$		0			0
$347$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$347$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$348$		0			0
$349$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$349$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$350$		0			0
$351$		0			0
$352$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$353$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$353$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$354$	0.500000	−	0.240787i	0.500000	−	0.240787i
$355$		0			0
$356$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$357$		0			0
$358$	0.777479	−	0.974928i	0.777479	−	0.974928i
$359$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$359$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$360$		0			0
$361$	0.722521	−	0.347948i	0.722521	−	0.347948i
$362$		0			0
$363$	0.0549581	+	0.240787i	0.0549581	+	0.240787i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$367$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$368$		0			0
$369$	0.900969	+	1.12978i	0.900969	+	1.12978i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$373$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$374$	0.500000	+	0.240787i	0.500000	+	0.240787i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$379$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$383$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$384$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$385$		0			0
$386$	1.24698			1.24698
$387$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$388$	1.24698			1.24698
$389$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$389$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$390$		0			0
$391$		0			0
$392$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$393$	0.801938			0.801938
$394$		0			0
$395$		0			0
$396$	0.222521	−	0.974928i	0.222521	−	0.974928i
$397$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$397$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$398$		0			0
$399$		0			0
$400$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$401$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$401$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$402$	0.198062	+	0.867767i	0.198062	+	0.867767i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.123490	+	0.154851i	0.123490	+	0.154851i
$409$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$409$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$410$		0			0
$411$	0.123490	+	0.541044i	0.123490	+	0.541044i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.722521	−	0.347948i	−0.722521	−	0.347948i
$418$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$419$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$419$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$420$		0			0
$421$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$421$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$422$	1.62349	+	0.781831i	1.62349	+	0.781831i
$423$		0			0
$424$		0			0
$425$	0.400969	+	0.193096i	0.400969	+	0.193096i
$426$		0			0
$427$		0			0
$428$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$429$		0			0
$430$		0			0
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	0.500000	−	0.626980i	0.500000	−	0.626980i
$433$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$433$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.801938	+	0.386193i	0.801938	+	0.386193i
$439$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$439$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$440$		0			0
$441$	0.178448	−	0.781831i	0.178448	−	0.781831i
$442$		0			0
$443$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$443$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$449$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$450$	0.178448	−	0.781831i	0.178448	−	0.781831i
$451$	−1.40097	−	1.75676i	−1.40097	−	1.75676i
$452$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$453$		0			0
$454$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$455$		0			0
$456$	−0.178448	+	0.0859360i	−0.178448	+	0.0859360i
$457$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$457$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$458$		0			0
$459$	−0.222521	+	0.279032i	−0.222521	+	0.279032i
$460$		0			0
$461$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$461$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$462$		0			0
$463$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$463$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$464$		0			0
$465$		0			0
$466$	−0.445042			−0.445042
$467$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$467$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.24698			1.24698
$473$	0.777479	+	0.974928i	0.777479	+	0.974928i
$474$		0			0
$475$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$		0			0
$481$		0			0
$482$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$483$		0			0
$484$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$485$		0			0
$486$	0.900969	+	0.433884i	0.900969	+	0.433884i
$487$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$487$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$488$		0			0
$489$	−0.722521	+	0.347948i	−0.722521	+	0.347948i
$490$		0			0
$491$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$491$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$492$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$499$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$499$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$500$		0			0
$501$		0			0
$502$	1.24698	−	1.56366i	1.24698	−	1.56366i
$503$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$503$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$508$		0			0
$509$		0			0		1.00000			$0$
$509$		0			0		−1.00000			$\pi$
$510$		0			0
$511$		0			0
$512$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$513$	−0.222521	−	0.279032i	−0.222521	−	0.279032i
$514$	1.24698	−	1.56366i	1.24698	−	1.56366i
$515$		0			0
$516$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$521$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$522$		0			0
$523$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$523$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$524$	1.62349	+	0.781831i	1.62349	+	0.781831i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$529$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$530$		0			0
$531$	0.222521	+	0.974928i	0.222521	+	0.974928i
$532$		0			0
$533$		0			0
$534$	0.500000	+	0.626980i	0.500000	+	0.626980i
$535$		0			0
$536$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$537$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$538$		0			0
$539$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$540$		0			0
$541$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$541$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$542$		0			0
$543$		0			0
$544$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$545$		0			0
$546$		0			0
$547$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$547$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$548$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$549$		0			0
$550$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$557$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$557$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.153989	−	0.193096i	0.153989	−	0.193096i
$562$	1.24698	+	1.56366i	1.24698	+	1.56366i
$563$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$563$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$564$		0			0
$565$		0			0
$566$	−0.445042			−0.445042
$567$		0			0
$568$		0			0
$569$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$569$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$570$		0			0
$571$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$571$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.722521	−	0.347948i	0.722521	−	0.347948i
$577$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$577$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$578$	0.178448	+	0.781831i	0.178448	+	0.781831i
$579$	0.123490	−	0.541044i	0.123490	−	0.541044i
$580$		0			0
$581$		0			0
$582$	0.123490	−	0.541044i	0.123490	−	0.541044i
$583$		0			0
$584$	1.24698	+	1.56366i	1.24698	+	1.56366i
$585$		0			0
$586$		0			0
$587$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$587$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$588$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$593$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$594$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$599$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$600$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$601$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$601$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$602$		0			0
$603$	−1.60388			−1.60388
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$607$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$608$	−0.445042			−0.445042
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.321552	+	0.154851i	−0.321552	+	0.154851i
$613$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$613$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$614$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$615$		0			0
$616$		0			0
$617$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$617$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$618$		0			0
$619$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$619$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$626$	0.400969	+	1.75676i	0.400969	+	1.75676i
$627$	0.153989	+	0.193096i	0.153989	+	0.193096i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$631$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$632$		0			0
$633$	0.500000	−	0.626980i	0.500000	−	0.626980i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$641$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$642$	0.500000	+	0.626980i	0.500000	+	0.626980i
$643$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$643$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$644$		0			0
$645$		0			0
$646$	0.198062			0.198062
$647$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$647$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$648$	0.277479	+	0.347948i	0.277479	+	0.347948i
$649$	−0.346011	−	1.51597i	−0.346011	−	1.51597i
$650$		0			0
$651$		0			0
$652$	−1.80194			−1.80194
$653$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$653$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$654$		0			0
$655$		0			0
$656$	0.400969	−	1.75676i	0.400969	−	1.75676i
$657$	−1.00000	+	1.25396i	−1.00000	+	1.25396i
$658$		0			0
$659$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$659$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$660$		0			0
$661$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$661$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$662$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$663$		0			0
$664$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$673$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$674$	0.777479	−	0.974928i	0.777479	−	0.974928i
$675$	−0.722521	−	0.347948i	−0.722521	−	0.347948i
$676$	0.623490	−	0.781831i	0.623490	−	0.781831i
$677$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$677$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$678$	−0.178448	+	0.0859360i	−0.178448	+	0.0859360i
$679$		0			0
$680$		0			0
$681$	−0.554958			−0.554958
$682$		0			0
$683$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$683$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$684$	−0.0794168	−	0.347948i	−0.0794168	−	0.347948i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$689$		0			0
$690$		0			0
$691$	1.24698	+	1.56366i	1.24698	+	1.56366i	0.623490	+	0.781831i	$0.285714\pi$
$691$	1.24698	+	1.56366i	1.24698	+	1.56366i	0.623490	+	0.781831i	$0.285714\pi$
$692$		0			0
$693$		0			0
$694$	−0.445042			−0.445042
$695$		0			0
$696$		0			0
$697$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$698$		0			0
$699$	−0.0440730	+	0.193096i	−0.0440730	+	0.193096i
$700$		0			0
$701$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$701$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$702$		0			0
$703$		0			0
$704$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$705$		0			0
$706$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$707$		0			0
$708$	0.123490	−	0.541044i	0.123490	−	0.541044i
$709$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$709$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$710$		0			0
$711$		0			0
$712$	0.400969	+	1.75676i	0.400969	+	1.75676i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$717$		0			0
$718$		0			0
$719$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$719$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$720$		0			0
$721$		0			0
$722$	0.178448	−	0.781831i	0.178448	−	0.781831i
$723$	0.500000	+	0.240787i	0.500000	+	0.240787i
$724$		0			0
$725$		0			0
$726$	0.222521	+	0.107160i	0.222521	+	0.107160i
$727$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$727$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$732$		0			0
$733$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$733$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.49396			2.49396
$738$	1.44504			1.44504
$739$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$739$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$743$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.900969	−	0.433884i	0.900969	−	0.433884i
$748$	0.500000	−	0.240787i	0.500000	−	0.240787i
$749$		0			0
$750$		0			0
$751$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$751$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$752$		0			0
$753$	−0.554958	−	0.695895i	−0.554958	−	0.695895i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$757$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$758$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$759$		0			0
$760$		0			0
$761$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$761$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.445042			−0.445042
$769$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$769$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$770$		0			0
$771$	−0.554958	−	0.695895i	−0.554958	−	0.695895i
$772$	0.777479	−	0.974928i	0.777479	−	0.974928i
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$	−0.801938			−0.801938
$775$		0			0
$776$	0.777479	−	0.974928i	0.777479	−	0.974928i
$777$		0			0
$778$		0			0
$779$	−0.722521	−	0.347948i	−0.722521	−	0.347948i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$785$		0			0
$786$	0.500000	−	0.626980i	0.500000	−	0.626980i
$787$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$787$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$797$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$798$		0			0
$799$		0			0
$800$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$801$	−1.30194	+	0.626980i	−1.30194	+	0.626980i
$802$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$803$	1.55496	−	1.94986i	1.55496	−	1.94986i
$804$	0.801938	+	0.386193i	0.801938	+	0.386193i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$809$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$810$		0			0
$811$	2.00000			2.00000			1.00000			$0$
$811$	2.00000			2.00000			1.00000			$0$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.198062			0.198062
$817$	0.400969	+	0.193096i	0.400969	+	0.193096i
$818$	−1.80194			−1.80194
$819$		0			0
$820$		0			0
$821$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$821$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$822$	0.500000	+	0.240787i	0.500000	+	0.240787i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	0.500000	+	0.240787i	0.500000	+	0.240787i
$826$		0			0
$827$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$827$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$828$		0			0
$829$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$829$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.400969	−	0.193096i	0.400969	−	0.193096i
$834$	−0.722521	+	0.347948i	−0.722521	+	0.347948i
$835$		0			0
$836$	0.123490	+	0.541044i	0.123490	+	0.541044i
$837$		0			0
$838$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$839$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$839$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$840$		0			0
$841$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$842$		0			0
$843$	0.801938	−	0.386193i	0.801938	−	0.386193i
$844$	1.62349	−	0.781831i	1.62349	−	0.781831i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.0440730	+	0.193096i	−0.0440730	+	0.193096i
$850$	0.400969	−	0.193096i	0.400969	−	0.193096i
$851$		0			0
$852$		0			0
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$		0			0
$855$		0			0
$856$	0.400969	+	1.75676i	0.400969	+	1.75676i
$857$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$857$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$858$		0			0
$859$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$859$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$863$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$864$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$865$		0			0
$866$	−1.80194			−1.80194
$867$	0.356896			0.356896
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.900969	+	0.433884i	0.900969	+	0.433884i
$874$		0			0
$875$		0			0
$876$	0.801938	−	0.386193i	0.801938	−	0.386193i
$877$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$877$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$881$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$882$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$883$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$883$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$884$		0			0
$885$		0			0
$886$	1.62349	−	0.781831i	1.62349	−	0.781831i
$887$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$887$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.346011	−	0.433884i	0.346011	−	0.433884i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$899$		0			0
$900$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$901$		0			0
$902$	−2.24698			−2.24698
$903$		0			0
$904$	−0.445042			−0.445042
$905$		0			0
$906$		0			0
$907$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$907$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$908$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$909$		0			0
$910$		0			0
$911$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$911$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$912$	−0.0440730	+	0.193096i	−0.0440730	+	0.193096i
$913$	−1.40097	+	0.674671i	−1.40097	+	0.674671i
$914$	0.400969	−	1.75676i	0.400969	−	1.75676i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.0794168	+	0.347948i	0.0794168	+	0.347948i
$919$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$919$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$920$		0			0
$921$	0.123490	+	0.154851i	0.123490	+	0.154851i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.80194	+	0.867767i	−1.80194	+	0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$929$	−1.80194	+	0.867767i	−1.80194	+	0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$930$		0			0
$931$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$932$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$933$		0			0
$934$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$935$		0			0
$936$		0			0
$937$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$937$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$938$		0			0
$939$	0.801938			0.801938
$940$		0			0
$941$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$941$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$942$		0			0
$943$		0			0
$944$	0.777479	−	0.974928i	0.777479	−	0.974928i
$945$		0			0
$946$	1.24698			1.24698
$947$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$947$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$948$		0			0
$949$		0			0
$950$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$951$		0			0
$952$		0			0
$953$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$953$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$962$		0			0
$963$	−1.30194	+	0.626980i	−1.30194	+	0.626980i
$964$	0.777479	+	0.974928i	0.777479	+	0.974928i
$965$		0			0
$966$		0			0
$967$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$967$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$968$	0.346011	+	0.433884i	0.346011	+	0.433884i
$969$	0.0196143	−	0.0859360i	0.0196143	−	0.0859360i
$970$		0			0
$971$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$971$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$972$	0.900969	−	0.433884i	0.900969	−	0.433884i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$977$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$978$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$979$	2.02446	−	0.974928i	2.02446	−	0.974928i
$980$		0			0
$981$		0			0
$982$	−0.445042			−0.445042
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$	−0.722521	−	0.347948i	−0.722521	−	0.347948i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$991$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$992$		0			0
$993$	0.123490	+	0.541044i	0.123490	+	0.541044i
$994$		0			0
$995$		0			0
$996$	−0.554958			−0.554958
$997$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$997$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$998$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	344.1.s.a.219.1	yes	6
3.2	odd	2		3096.1.dm.a.2971.1		6
4.3	odd	2		1376.1.be.a.47.1		6
8.3	odd	2	CM	344.1.s.a.219.1	yes	6
8.5	even	2		1376.1.be.a.47.1		6
24.11	even	2		3096.1.dm.a.2971.1		6
43.11	even	7	inner	344.1.s.a.11.1	✓	6
129.11	odd	14		3096.1.dm.a.1387.1		6
172.11	odd	14		1376.1.be.a.527.1		6
344.11	odd	14	inner	344.1.s.a.11.1	✓	6
344.269	even	14		1376.1.be.a.527.1		6
1032.11	even	14		3096.1.dm.a.1387.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
344.1.s.a.11.1	✓	6	43.11	even	7	inner
344.1.s.a.11.1	✓	6	344.11	odd	14	inner
344.1.s.a.219.1	yes	6	1.1	even	1	trivial
344.1.s.a.219.1	yes	6	8.3	odd	2	CM
1376.1.be.a.47.1		6	4.3	odd	2
1376.1.be.a.47.1		6	8.5	even	2
1376.1.be.a.527.1		6	172.11	odd	14
1376.1.be.a.527.1		6	344.269	even	14
3096.1.dm.a.1387.1		6	129.11	odd	14
3096.1.dm.a.1387.1		6	1032.11	even	14
3096.1.dm.a.2971.1		6	3.2	odd	2
3096.1.dm.a.2971.1		6	24.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 344 = 2^{3} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	344.s (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.623490 - 0.781831i) q^{2} +(-0.277479 - 0.347948i) q^{3} +(-0.222521 - 0.974928i) q^{4} -0.445042 q^{6} +(-0.900969 - 0.433884i) q^{8} +(0.178448 - 0.781831i) q^{9} +(-0.277479 + 1.21572i) q^{11} +(-0.277479 + 0.347948i) q^{12} +(-0.900969 + 0.433884i) q^{16} +(0.400969 - 0.193096i) q^{17} +(-0.500000 - 0.626980i) q^{18} +(0.0990311 + 0.433884i) q^{19} +(0.777479 + 0.974928i) q^{22} +(0.0990311 + 0.433884i) q^{24} +(0.623490 + 0.781831i) q^{25} +(-0.722521 + 0.347948i) q^{27} +(-0.222521 + 0.974928i) q^{32} +(0.500000 - 0.240787i) q^{33} +(0.0990311 - 0.433884i) q^{34} -0.801938 q^{36} +(0.400969 + 0.193096i) q^{38} +(-1.12349 + 1.40881i) q^{41} +(0.623490 - 0.781831i) q^{43} +1.24698 q^{44} +(0.400969 + 0.193096i) q^{48} +1.00000 q^{49} +1.00000 q^{50} +(-0.178448 - 0.0859360i) q^{51} +(-0.178448 + 0.781831i) q^{54} +(0.123490 - 0.154851i) q^{57} +(-1.12349 + 0.541044i) q^{59} +(0.623490 + 0.781831i) q^{64} +(0.123490 - 0.541044i) q^{66} +(-0.445042 - 1.94986i) q^{67} +(-0.277479 - 0.347948i) q^{68} +(-0.500000 + 0.626980i) q^{72} +(-1.80194 - 0.867767i) q^{73} +(0.0990311 - 0.433884i) q^{75} +(0.400969 - 0.193096i) q^{76} +(-0.400969 - 0.193096i) q^{81} +(0.400969 + 1.75676i) q^{82} +(0.777479 + 0.974928i) q^{83} +(-0.222521 - 0.974928i) q^{86} +(0.777479 - 0.974928i) q^{88} +(-1.12349 - 1.40881i) q^{89} +(0.400969 - 0.193096i) q^{96} +(-0.277479 + 1.21572i) q^{97} +(0.623490 - 0.781831i) q^{98} +(0.900969 + 0.433884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9} - 2 q^{11} - 2 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} + 5 q^{19} + 5 q^{22} + 5 q^{24} - q^{25} - 4 q^{27} - q^{32} + 3 q^{33} + 5 q^{34} + 4 q^{36}+ \cdots + q^{99}+O(q^{100}) \) 6 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9 - 2 * q^11 - 2 * q^12 - q^16 - 2 * q^17 - 3 * q^18 + 5 * q^19 + 5 * q^22 + 5 * q^24 - q^25 - 4 * q^27 - q^32 + 3 * q^33 + 5 * q^34 + 4 * q^36 - 2 * q^38 - 2 * q^41 - q^43 - 2 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 3 * q^51 + 3 * q^54 - 4 * q^57 - 2 * q^59 - q^64 - 4 * q^66 - 2 * q^67 - 2 * q^68 - 3 * q^72 - 2 * q^73 + 5 * q^75 - 2 * q^76 + 2 * q^81 - 2 * q^82 + 5 * q^83 - q^86 + 5 * q^88 - 2 * q^89 - 2 * q^96 - 2 * q^97 - q^98 + q^99

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