LMFDB - Embedded newform 2303.1.j.b.939.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2303,1,Mod(281,2303)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2303, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([4, 7]))

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

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

chi := DirichletCharacter("2303.281");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2303 = 7^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2303.j (of order $14$, degree $6$, 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:	$1.14934672409$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{35})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{23} + x^{19} - x^{18} + x^{17} - x^{16} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} + \cdots + 1 $ x^24 - x^23 + x^19 - x^18 + x^17 - x^16 + x^14 - x^13 + x^12 - x^11 + x^10 - x^8 + x^7 - x^6 + x^5 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{35}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{35} - \cdots)$

Embedding invariants

Embedding label			939.1
Root			$0.936235 + 0.351375i$ of defining polynomial
Character	$\chi$	$=$	2303.939
Dual form			2303.1.j.b.1268.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00883 - 1.26503i) q^{2} +(-1.54687 + 0.744934i) q^{3} +(-0.360046 + 1.57747i) q^{4} +(2.50289 + 1.20533i) q^{6} +(-0.963963 + 0.266037i) q^{7} +(0.900969 - 0.433884i) q^{8} +(1.21439 - 1.52280i) q^{9} +(-0.618163 - 2.70835i) q^{12} +(1.30902 + 0.951057i) q^{14} +(0.307552 + 1.34747i) q^{17} -3.15151 q^{18} +(1.29295 - 1.12961i) q^{21} +(-1.07047 + 1.34232i) q^{24} +(0.623490 - 0.781831i) q^{25} +(-0.362079 + 1.58637i) q^{27} +(-0.0725928 - 1.61640i) q^{28} +(-0.222521 - 0.974928i) q^{32} +(1.39433 - 1.74843i) q^{34} +(1.96493 + 2.46395i) q^{36} +(-0.416664 - 1.82552i) q^{37} +(-2.73336 - 0.496031i) q^{42} +(0.623490 + 0.781831i) q^{47} +(0.858449 - 0.512899i) q^{49} -1.61803 q^{50} +(-1.47952 - 1.85526i) q^{51} +(-0.335148 + 1.46838i) q^{53} +(2.37208 - 1.14233i) q^{54} +(-0.753071 + 0.657939i) q^{56} +(-0.853882 - 0.411208i) q^{59} +(0.0199667 + 0.0874800i) q^{61} +(-0.765510 + 1.79100i) q^{63} +(-1.00883 + 1.26503i) q^{64} -2.23633 q^{68} +(-0.382046 + 1.67385i) q^{71} +(0.433412 - 1.89890i) q^{72} +(-1.88900 + 2.36873i) q^{74} +(-0.382046 + 1.67385i) q^{75} +0.268467 q^{79} +(-0.188240 - 0.824734i) q^{81} +(-0.277479 + 0.347948i) q^{83} +(1.31641 + 2.44629i) q^{84} +(-1.00883 + 1.26503i) q^{89} +(0.360046 - 1.57747i) q^{94} +(1.07047 + 1.34232i) q^{96} -1.61803 q^{97} +(-1.51486 - 0.568536i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} + q^{7} + 4 q^{8} - 2 q^{9} + 10 q^{12} + 18 q^{14} + 2 q^{17} - 18 q^{18} - 5 q^{21} - 2 q^{24} - 4 q^{25} - 3 q^{27} + 3 q^{28} - 4 q^{32} + 4 q^{34} + 4 q^{36}+ \cdots + 2 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 + q^7 + 4 * q^8 - 2 * q^9 + 10 * q^12 + 18 * q^14 + 2 * q^17 - 18 * q^18 - 5 * q^21 - 2 * q^24 - 4 * q^25 - 3 * q^27 + 3 * q^28 - 4 * q^32 + 4 * q^34 + 4 * q^36 + 2 * q^37 - q^42 - 4 * q^47 + q^49 - 12 * q^50 - 13 * q^51 - 5 * q^53 - 2 * q^54 - q^56 - 5 * q^59 + 2 * q^61 - 2 * q^63 + 2 * q^64 - 4 * q^68 - 5 * q^71 + 2 * q^72 - 10 * q^74 - 5 * q^75 + 2 * q^79 - 8 * q^83 + q^84 + 2 * q^89 + 2 * q^94 + 2 * q^96 - 12 * q^97 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2303\mathbb{Z}\right)^\times$.

$n$	$99$	$2257$
$\chi(n)$	$-1$	$e\left(\frac{6}{7}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00883	−	1.26503i	−1.00883	−	1.26503i	−0.963963	−	0.266037i	$-0.914286\pi$
$2$	−1.00883	−	1.26503i	−1.00883	−	1.26503i	−0.0448648	−	0.998993i	$-0.514286\pi$
$3$	−1.54687	+	0.744934i	−1.54687	+	0.744934i	−0.995974	−	0.0896393i	$-0.971429\pi$
$3$	−1.54687	+	0.744934i	−1.54687	+	0.744934i	−0.550897	+	0.834573i	$0.685714\pi$
$4$	−0.360046	+	1.57747i	−0.360046	+	1.57747i
$5$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$5$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$6$	2.50289	+	1.20533i	2.50289	+	1.20533i
$7$	−0.963963	+	0.266037i	−0.963963	+	0.266037i
$7$	−0.963963	+	0.266037i	−0.963963	+	0.266037i
$8$	0.900969	−	0.433884i	0.900969	−	0.433884i
$9$	1.21439	−	1.52280i	1.21439	−	1.52280i
$10$		0			0
$11$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$11$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$12$	−0.618163	−	2.70835i	−0.618163	−	2.70835i
$13$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$13$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$14$	1.30902	+	0.951057i	1.30902	+	0.951057i
$15$		0			0
$16$		0			0
$17$	0.307552	+	1.34747i	0.307552	+	1.34747i	0.858449	+	0.512899i	$0.171429\pi$
$17$	0.307552	+	1.34747i	0.307552	+	1.34747i	−0.550897	+	0.834573i	$0.685714\pi$
$18$	−3.15151			−3.15151
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$	1.29295	−	1.12961i	1.29295	−	1.12961i
$22$		0			0
$23$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$23$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$24$	−1.07047	+	1.34232i	−1.07047	+	1.34232i
$25$	0.623490	−	0.781831i	0.623490	−	0.781831i
$26$		0			0
$27$	−0.362079	+	1.58637i	−0.362079	+	1.58637i
$28$	−0.0725928	−	1.61640i	−0.0725928	−	1.61640i
$29$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$29$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$33$		0			0
$34$	1.39433	−	1.74843i	1.39433	−	1.74843i
$35$		0			0
$36$	1.96493	+	2.46395i	1.96493	+	2.46395i
$37$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	−0.550897	−	0.834573i	$-0.685714\pi$
$37$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	0.134233	−	0.990950i	$-0.457143\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$41$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$42$	−2.73336	−	0.496031i	−2.73336	−	0.496031i
$43$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$43$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.623490	+	0.781831i	0.623490	+	0.781831i
$47$	0.623490	+	0.781831i	0.623490	+	0.781831i
$48$		0			0
$49$	0.858449	−	0.512899i	0.858449	−	0.512899i
$50$	−1.61803			−1.61803
$51$	−1.47952	−	1.85526i	−1.47952	−	1.85526i
$52$		0			0
$53$	−0.335148	+	1.46838i	−0.335148	+	1.46838i	0.473869	+	0.880596i	$0.342857\pi$
$53$	−0.335148	+	1.46838i	−0.335148	+	1.46838i	−0.809017	+	0.587785i	$0.800000\pi$
$54$	2.37208	−	1.14233i	2.37208	−	1.14233i
$55$		0			0
$56$	−0.753071	+	0.657939i	−0.753071	+	0.657939i
$57$		0			0
$58$		0			0
$59$	−0.853882	−	0.411208i	−0.853882	−	0.411208i	−0.0448648	−	0.998993i	$-0.514286\pi$
$59$	−0.853882	−	0.411208i	−0.853882	−	0.411208i	−0.809017	+	0.587785i	$0.800000\pi$
$60$		0			0
$61$	0.0199667	+	0.0874800i	0.0199667	+	0.0874800i	0.983930	−	0.178557i	$-0.0571429\pi$
$61$	0.0199667	+	0.0874800i	0.0199667	+	0.0874800i	−0.963963	+	0.266037i	$0.914286\pi$
$62$		0			0
$63$	−0.765510	+	1.79100i	−0.765510	+	1.79100i
$64$	−1.00883	+	1.26503i	−1.00883	+	1.26503i
$65$		0			0
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	−2.23633			−2.23633
$69$		0			0
$70$		0			0
$71$	−0.382046	+	1.67385i	−0.382046	+	1.67385i	0.309017	+	0.951057i	$0.400000\pi$
$71$	−0.382046	+	1.67385i	−0.382046	+	1.67385i	−0.691063	+	0.722795i	$0.742857\pi$
$72$	0.433412	−	1.89890i	0.433412	−	1.89890i
$73$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$73$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$74$	−1.88900	+	2.36873i	−1.88900	+	2.36873i
$75$	−0.382046	+	1.67385i	−0.382046	+	1.67385i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.268467			0.268467			0.134233	−	0.990950i	$-0.457143\pi$
$79$	0.268467			0.268467			0.134233	+	0.990950i	$0.457143\pi$
$80$		0			0
$81$	−0.188240	−	0.824734i	−0.188240	−	0.824734i
$82$		0			0
$83$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$83$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$84$	1.31641	+	2.44629i	1.31641	+	2.44629i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.00883	+	1.26503i	−1.00883	+	1.26503i	−0.0448648	+	0.998993i	$0.514286\pi$
$89$	−1.00883	+	1.26503i	−1.00883	+	1.26503i	−0.963963	+	0.266037i	$0.914286\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	0.360046	−	1.57747i	0.360046	−	1.57747i
$95$		0			0
$96$	1.07047	+	1.34232i	1.07047	+	1.34232i
$97$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$97$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$98$	−1.51486	−	0.568536i	−1.51486	−	0.568536i
$99$		0			0
$100$	1.00883	+	1.26503i	1.00883	+	1.26503i
$101$	1.24525	−	0.599682i	1.24525	−	0.599682i	0.309017	−	0.951057i	$-0.400000\pi$
$101$	1.24525	−	0.599682i	1.24525	−	0.599682i	0.936235	+	0.351375i	$0.114286\pi$
$102$	−0.854379	+	3.74328i	−0.854379	+	3.74328i
$103$	−1.68704	+	0.812434i	−1.68704	+	0.812434i	−0.691063	+	0.722795i	$0.742857\pi$
$103$	−1.68704	+	0.812434i	−1.68704	+	0.812434i	−0.995974	+	0.0896393i	$0.971429\pi$
$104$		0			0
$105$		0			0
$106$	2.19565	−	1.05737i	2.19565	−	1.05737i
$107$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$107$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$108$	−2.37208	−	1.14233i	−2.37208	−	1.14233i
$109$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$109$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$110$		0			0
$111$	2.00442	+	2.51346i	2.00442	+	2.51346i
$112$		0			0
$113$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$113$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.341229	+	1.49502i	0.341229	+	1.49502i
$119$	−0.654946	−	1.21709i	−0.654946	−	1.21709i
$120$		0			0
$121$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$122$	0.0905218	−	0.113511i	0.0905218	−	0.113511i
$123$		0			0
$124$		0			0
$125$		0			0
$126$	3.03793	−	0.838417i	3.03793	−	0.838417i
$127$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$127$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$128$	1.61803			1.61803
$129$		0			0
$130$		0			0
$131$	0.0808436	+	0.0389322i	0.0808436	+	0.0389322i	0.473869	−	0.880596i	$-0.342857\pi$
$131$	0.0808436	+	0.0389322i	0.0808436	+	0.0389322i	−0.393025	+	0.919528i	$0.628571\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.861741	+	1.08059i	0.861741	+	1.08059i
$137$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$137$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$138$		0			0
$139$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$139$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$140$		0			0
$141$	−1.54687	−	0.744934i	−1.54687	−	0.744934i
$142$	2.50289	−	1.20533i	2.50289	−	1.20533i
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.945834	+	1.43288i	−0.945834	+	1.43288i
$148$	3.02972			3.02972
$149$	−1.24196	−	1.55737i	−1.24196	−	1.55737i	−0.691063	−	0.722795i	$-0.742857\pi$
$149$	−1.24196	−	1.55737i	−1.24196	−	1.55737i	−0.550897	−	0.834573i	$-0.685714\pi$
$150$	2.50289	−	1.20533i	2.50289	−	1.20533i
$151$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$151$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$152$		0			0
$153$	2.42542	+	1.16802i	2.42542	+	1.16802i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.73700	+	0.836496i	1.73700	+	0.836496i	0.983930	+	0.178557i	$0.0571429\pi$
$157$	1.73700	+	0.836496i	1.73700	+	0.836496i	0.753071	+	0.657939i	$0.228571\pi$
$158$	−0.270836	−	0.339618i	−0.270836	−	0.339618i
$159$	−0.575415	−	2.52106i	−0.575415	−	2.52106i
$160$		0			0
$161$		0			0
$162$	−0.853411	+	1.07014i	−0.853411	+	1.07014i
$163$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$163$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$164$		0			0
$165$		0			0
$166$	0.720093			0.720093
$167$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$167$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$168$	0.674784	−	1.57874i	0.674784	−	1.57874i
$169$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.335148	+	1.46838i	−0.335148	+	1.46838i	0.473869	+	0.880596i	$0.342857\pi$
$173$	−0.335148	+	1.46838i	−0.335148	+	1.46838i	−0.809017	+	0.587785i	$0.800000\pi$
$174$		0			0
$175$	−0.393025	+	0.919528i	−0.393025	+	0.919528i
$176$		0			0
$177$	1.62717			1.62717
$178$	2.61803			2.61803
$179$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$179$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$180$		0			0
$181$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$181$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$182$		0			0
$183$	−0.0960527	−	0.120446i	−0.0960527	−	0.120446i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−1.45780	+	0.702039i	−1.45780	+	0.702039i
$189$	−0.0730026	−	1.62553i	−0.0730026	−	1.62553i
$190$		0			0
$191$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$191$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$192$	0.618163	−	2.70835i	0.618163	−	2.70835i
$193$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$193$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$194$	1.63232	+	2.04686i	1.63232	+	2.04686i
$195$		0			0
$196$	0.500000	+	1.53884i	0.500000	+	1.53884i
$197$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$197$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$198$		0			0
$199$		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			0
$202$	−2.01486	−	0.970305i	−2.01486	−	0.970305i
$203$		0			0
$204$	3.45931	−	1.66591i	3.45931	−	1.66591i
$205$		0			0
$206$	2.72968	+	1.31455i	2.72968	+	1.31455i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$211$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$212$	−2.19565	−	1.05737i	−2.19565	−	1.05737i
$213$	−0.655933	−	2.87383i	−0.655933	−	2.87383i
$214$		0			0
$215$		0			0
$216$	0.362079	+	1.58637i	0.362079	+	1.58637i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$	1.15749	−	5.07130i	1.15749	−	5.07130i
$223$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$223$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$224$	0.473869	+	0.880596i	0.473869	+	0.880596i
$225$	−0.433412	−	1.89890i	−0.433412	−	1.89890i
$226$		0			0
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$		0			0
$229$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$229$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$233$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$234$		0			0
$235$		0			0
$236$	0.956104	−	1.19892i	0.956104	−	1.19892i
$237$	−0.415283	+	0.199990i	−0.415283	+	0.199990i
$238$	−0.878932	+	2.05636i	−0.878932	+	2.05636i
$239$	−1.68704	−	0.812434i	−1.68704	−	0.812434i	−0.995974	−	0.0896393i	$-0.971429\pi$
$239$	−1.68704	−	0.812434i	−1.68704	−	0.812434i	−0.691063	−	0.722795i	$-0.742857\pi$
$240$		0			0
$241$	0.245172	−	1.07417i	0.245172	−	1.07417i	−0.691063	−	0.722795i	$-0.742857\pi$
$241$	0.245172	−	1.07417i	0.245172	−	1.07417i	0.936235	−	0.351375i	$-0.114286\pi$
$242$	1.45780	−	0.702039i	1.45780	−	0.702039i
$243$	−0.108967	−	0.136641i	−0.108967	−	0.136641i
$244$	−0.145186			−0.145186
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	0.170026	−	0.744934i	0.170026	−	0.744934i
$250$		0			0
$251$	−0.241880	−	0.116483i	−0.241880	−	0.116483i	0.309017	−	0.951057i	$-0.400000\pi$
$251$	−0.241880	−	0.116483i	−0.241880	−	0.116483i	−0.550897	+	0.834573i	$0.685714\pi$
$252$	−2.54962	−	1.85241i	−2.54962	−	1.85241i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$257$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$257$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$258$		0			0
$259$	0.887305	+	1.64889i	0.887305	+	1.64889i
$260$		0			0
$261$		0			0
$262$	−0.0323068	−	0.141546i	−0.0323068	−	0.141546i
$263$	−0.0897297			−0.0897297			−0.0448648	−	0.998993i	$-0.514286\pi$
$263$	−0.0897297			−0.0897297			−0.0448648	+	0.998993i	$0.514286\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.618163	−	2.70835i	0.618163	−	2.70835i
$268$		0			0
$269$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$269$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$270$		0			0
$271$	−0.416664	+	1.82552i	−0.416664	+	1.82552i	0.134233	+	0.990950i	$0.457143\pi$
$271$	−0.416664	+	1.82552i	−0.416664	+	1.82552i	−0.550897	+	0.834573i	$0.685714\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	−0.550897	−	0.834573i	$-0.685714\pi$
$277$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	0.134233	−	0.990950i	$-0.457143\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$281$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$282$	0.618163	+	2.70835i	0.618163	+	2.70835i
$283$	−1.20204	−	1.50731i	−1.20204	−	1.50731i	−0.809017	−	0.587785i	$-0.800000\pi$
$283$	−1.20204	−	1.50731i	−1.20204	−	1.50731i	−0.393025	−	0.919528i	$-0.628571\pi$
$284$	−2.50289	−	1.20533i	−2.50289	−	1.20533i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.75485	−	0.845092i	−1.75485	−	0.845092i
$289$	−0.820125	+	0.394951i	−0.820125	+	0.394951i
$290$		0			0
$291$	2.50289	−	1.20533i	2.50289	−	1.20533i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	2.76682	−	0.249018i	2.76682	−	0.249018i
$295$		0			0
$296$	−1.16747	−	1.46396i	−1.16747	−	1.46396i
$297$		0			0
$298$	−0.717194	+	3.14223i	−0.717194	+	3.14223i
$299$		0			0
$300$	−2.50289	−	1.20533i	−2.50289	−	1.20533i
$301$		0			0
$302$		0			0
$303$	−1.47952	+	1.85526i	−1.47952	+	1.85526i
$304$		0			0
$305$		0			0
$306$	−0.969251	−	4.24657i	−0.969251	−	4.24657i
$307$	1.07047	+	1.34232i	1.07047	+	1.34232i	0.936235	+	0.351375i	$0.114286\pi$
$307$	1.07047	+	1.34232i	1.07047	+	1.34232i	0.134233	+	0.990950i	$0.457143\pi$
$308$		0			0
$309$	2.00442	−	2.51346i	2.00442	−	2.51346i
$310$		0			0
$311$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$311$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$312$		0			0
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	−0.694143	−	3.04124i	−0.694143	−	3.04124i
$315$		0			0
$316$	−0.0966604	+	0.423497i	−0.0966604	+	0.423497i
$317$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$317$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$318$	−2.60872	+	3.27123i	−2.60872	+	3.27123i
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	1.36877			1.36877
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$330$		0			0
$331$	−0.335148	−	1.46838i	−0.335148	−	1.46838i	−0.809017	−	0.587785i	$-0.800000\pi$
$331$	−0.335148	−	1.46838i	−0.335148	−	1.46838i	0.473869	−	0.880596i	$-0.342857\pi$
$332$	−0.448971	−	0.562991i	−0.448971	−	0.562991i
$333$	−3.28590	−	1.58241i	−3.28590	−	1.58241i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.708207	+	0.341054i	0.708207	+	0.341054i	0.753071	−	0.657939i	$-0.228571\pi$
$337$	0.708207	+	0.341054i	0.708207	+	0.341054i	−0.0448648	+	0.998993i	$0.514286\pi$
$338$	1.45780	−	0.702039i	1.45780	−	0.702039i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$344$		0			0
$345$		0			0
$346$	2.19565	−	1.05737i	2.19565	−	1.05737i
$347$	−0.0597394	+	0.261736i	−0.0597394	+	0.261736i	−0.995974	−	0.0896393i	$-0.971429\pi$
$347$	−0.0597394	+	0.261736i	−0.0597394	+	0.261736i	0.936235	+	0.351375i	$0.114286\pi$
$348$		0			0
$349$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$349$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$350$	1.55972	−	0.430457i	1.55972	−	0.430457i
$351$		0			0
$352$		0			0
$353$	1.45780	+	0.702039i	1.45780	+	0.702039i	0.983930	−	0.178557i	$-0.0571429\pi$
$353$	1.45780	+	0.702039i	1.45780	+	0.702039i	0.473869	+	0.880596i	$0.342857\pi$
$354$	−1.64153	−	2.05842i	−1.64153	−	2.05842i
$355$		0			0
$356$	−1.63232	−	2.04686i	−1.63232	−	2.04686i
$357$	1.91977	+	1.39480i	1.91977	+	1.39480i
$358$		0			0
$359$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$359$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$360$		0			0
$361$	1.00000			1.00000
$362$		0			0
$363$	−0.382046	−	1.67385i	−0.382046	−	1.67385i
$364$		0			0
$365$		0			0
$366$	−0.0554675	+	0.243019i	−0.0554675	+	0.243019i
$367$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$367$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.0675728	−	1.50463i	−0.0675728	−	1.50463i
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$		0			0
$376$	0.900969	+	0.433884i	0.900969	+	0.433884i
$377$		0			0
$378$	−1.98270	+	1.73223i	−1.98270	+	1.73223i
$379$	0.590905	+	0.740971i	0.590905	+	0.740971i	0.983930	−	0.178557i	$-0.0571429\pi$
$379$	0.590905	+	0.740971i	0.590905	+	0.740971i	−0.393025	+	0.919528i	$0.628571\pi$
$380$		0			0
$381$		0			0
$382$	1.81784	+	0.875428i	1.81784	+	0.875428i
$383$	1.07047	−	1.34232i	1.07047	−	1.34232i	0.134233	−	0.990950i	$-0.457143\pi$
$383$	1.07047	−	1.34232i	1.07047	−	1.34232i	0.936235	−	0.351375i	$-0.114286\pi$
$384$	−2.50289	+	1.20533i	−2.50289	+	1.20533i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	0.582567	−	2.55239i	0.582567	−	2.55239i
$389$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$389$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$390$		0			0
$391$		0			0
$392$	0.550897	−	0.834573i	0.550897	−	0.834573i
$393$	−0.154057			−0.154057
$394$	1.81784	+	2.27951i	1.81784	+	2.27951i
$395$		0			0
$396$		0			0
$397$	−1.54687	+	0.744934i	−1.54687	+	0.744934i	−0.995974	−	0.0896393i	$-0.971429\pi$
$397$	−1.54687	+	0.744934i	−1.54687	+	0.744934i	−0.550897	+	0.834573i	$0.685714\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.24196	+	1.55737i	−1.24196	+	1.55737i	−0.550897	+	0.834573i	$0.685714\pi$
$401$	−1.24196	+	1.55737i	−1.24196	+	1.55737i	−0.691063	+	0.722795i	$0.742857\pi$
$402$		0			0
$403$		0			0
$404$	0.497629	+	2.18026i	0.497629	+	2.18026i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−2.13797	−	1.02959i	−2.13797	−	1.02959i
$409$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$409$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$410$		0			0
$411$		0			0
$412$	−0.674176	−	2.95376i	−0.674176	−	2.95376i
$413$	0.932507	+	0.169225i	0.932507	+	0.169225i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$419$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$420$		0			0
$421$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$421$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$422$		0			0
$423$	1.94774			1.94774
$424$	0.335148	+	1.46838i	0.335148	+	1.46838i
$425$	1.24525	+	0.599682i	1.24525	+	0.599682i
$426$	−2.97376	+	3.72898i	−2.97376	+	3.72898i
$427$	−0.0425201	−	0.0790155i	−0.0425201	−	0.0790155i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.708207	+	0.341054i	0.708207	+	0.341054i	0.753071	−	0.657939i	$-0.228571\pi$
$431$	0.708207	+	0.341054i	0.708207	+	0.341054i	−0.0448648	+	0.998993i	$0.514286\pi$
$432$		0			0
$433$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$433$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$439$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$440$		0			0
$441$	0.261451	−	1.93011i	0.261451	−	1.93011i
$442$		0			0
$443$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$443$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$444$	−4.68659	+	2.25694i	−4.68659	+	2.25694i
$445$		0			0
$446$		0			0
$447$	3.08129	+	1.48387i	3.08129	+	1.48387i
$448$	0.635928	−	1.48783i	0.635928	−	1.48783i
$449$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$449$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$450$	−1.96493	+	2.46395i	−1.96493	+	2.46395i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.24525	+	0.599682i	1.24525	+	0.599682i	0.936235	−	0.351375i	$-0.114286\pi$
$457$	1.24525	+	0.599682i	1.24525	+	0.599682i	0.309017	+	0.951057i	$0.400000\pi$
$458$		0			0
$459$	−2.24895			−2.24895
$460$		0			0
$461$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$461$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$462$		0			0
$463$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$463$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$467$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−3.31005			−3.31005
$472$	−0.947737			−0.947737
$473$		0			0
$474$	0.671942	+	0.323590i	0.671942	+	0.323590i
$475$		0			0
$476$	2.15573	−	0.594945i	2.15573	−	0.594945i
$477$	1.82905	+	2.29356i	1.82905	+	2.29356i
$478$	0.674176	+	2.95376i	0.674176	+	2.95376i
$479$	−0.490094	−	0.614559i	−0.490094	−	0.614559i	0.473869	−	0.880596i	$-0.342857\pi$
$479$	−0.490094	−	0.614559i	−0.490094	−	0.614559i	−0.963963	+	0.266037i	$0.914286\pi$
$480$		0			0
$481$		0			0
$482$	−1.60619	+	0.773502i	−1.60619	+	0.773502i
$483$		0			0
$484$	−1.45780	−	0.702039i	−1.45780	−	0.702039i
$485$		0			0
$486$	−0.0629252	+	0.275694i	−0.0629252	+	0.275694i
$487$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$487$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$488$	0.0559455	+	0.0701535i	0.0559455	+	0.0701535i
$489$		0			0
$490$		0			0
$491$	1.96786			1.96786			0.983930	−	0.178557i	$-0.0571429\pi$
$491$	1.96786			1.96786			0.983930	+	0.178557i	$0.0571429\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.0770283	−	1.71517i	−0.0770283	−	1.71517i
$498$	−1.11389	+	0.536422i	−1.11389	+	0.536422i
$499$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$499$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$500$		0			0
$501$		0			0
$502$	0.0966604	+	0.423497i	0.0966604	+	0.423497i
$503$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$503$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$504$	0.0873849	+	1.94578i	0.0873849	+	1.94578i
$505$		0			0
$506$		0			0
$507$	−0.382046	−	1.67385i	−0.382046	−	1.67385i
$508$		0			0
$509$		0			0		1.00000			$0$
$509$		0			0		−1.00000			$\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	1.19076	−	2.78591i	1.19076	−	2.78591i
$519$	−0.575415	−	2.52106i	−0.575415	−	2.52106i
$520$		0			0
$521$	−1.92793			−1.92793			−0.963963	−	0.266037i	$-0.914286\pi$
$521$	−1.92793			−1.92793			−0.963963	+	0.266037i	$0.914286\pi$
$522$		0			0
$523$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$523$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$524$	−0.0905218	+	0.113511i	−0.0905218	+	0.113511i
$525$	−0.0770283	−	1.71517i	−0.0770283	−	1.71517i
$526$	0.0905218	+	0.113511i	0.0905218	+	0.113511i
$527$		0			0
$528$		0			0
$529$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$530$		0			0
$531$	−1.66314	+	0.800925i	−1.66314	+	0.800925i
$532$		0			0
$533$		0			0
$534$	−4.04976	+	1.95026i	−4.04976	+	1.95026i
$535$		0			0
$536$		0			0
$537$		0			0
$538$	2.91560			2.91560
$539$		0			0
$540$		0			0
$541$	−1.20204	−	1.50731i	−1.20204	−	1.50731i	−0.809017	−	0.587785i	$-0.800000\pi$
$541$	−1.20204	−	1.50731i	−1.20204	−	1.50731i	−0.393025	−	0.919528i	$-0.628571\pi$
$542$	2.72968	−	1.31455i	2.72968	−	1.31455i
$543$		0			0
$544$	1.24525	−	0.599682i	1.24525	−	0.599682i
$545$		0			0
$546$		0			0
$547$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$547$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$548$		0			0
$549$	0.157462	+	0.0758298i	0.157462	+	0.0758298i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−0.258792	+	0.0714220i	−0.258792	+	0.0714220i
$554$	−1.88900	+	2.36873i	−1.88900	+	2.36873i
$555$		0			0
$556$		0			0
$557$		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			0		0.623490	−	0.781831i	$-0.285714\pi$
$563$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$564$	1.73205	−	2.17193i	1.73205	−	2.17193i
$565$		0			0
$566$	−0.694143	+	3.04124i	−0.694143	+	3.04124i
$567$	0.400866	+	0.744934i	0.400866	+	0.744934i
$568$	0.382046	+	1.67385i	0.382046	+	1.67385i
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$	0.245172	+	1.07417i	0.245172	+	1.07417i	0.936235	+	0.351375i	$0.114286\pi$
$571$	0.245172	+	1.07417i	0.245172	+	1.07417i	−0.691063	+	0.722795i	$0.742857\pi$
$572$		0			0
$573$	1.33485	−	1.67385i	1.33485	−	1.67385i
$574$		0			0
$575$		0			0
$576$	0.701276	+	3.07249i	0.701276	+	3.07249i
$577$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$577$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$578$	1.32699	+	0.639045i	1.32699	+	0.639045i
$579$		0			0
$580$		0			0
$581$	0.174913	−	0.409228i	0.174913	−	0.409228i
$582$	−4.04976	−	1.95026i	−4.04976	−	1.95026i
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	−1.91977	−	2.00792i	−1.91977	−	2.00792i
$589$		0			0
$590$		0			0
$591$	2.78737	−	1.34232i	2.78737	−	1.34232i
$592$		0			0
$593$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$593$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$594$		0			0
$595$		0			0
$596$	2.90386	−	1.39842i	2.90386	−	1.39842i
$597$		0			0
$598$		0			0
$599$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$599$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$600$	0.382046	+	1.67385i	0.382046	+	1.67385i
$601$	0.590905	+	0.740971i	0.590905	+	0.740971i	0.983930	−	0.178557i	$-0.0571429\pi$
$601$	0.590905	+	0.740971i	0.590905	+	0.740971i	−0.393025	+	0.919528i	$0.628571\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	3.83954			3.83954
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−2.71578	+	3.40548i	−2.71578	+	3.40548i
$613$	−0.490094	+	0.614559i	−0.490094	+	0.614559i	−0.963963	−	0.266037i	$-0.914286\pi$
$613$	−0.490094	+	0.614559i	−0.490094	+	0.614559i	0.473869	+	0.880596i	$0.342857\pi$
$614$	0.618163	−	2.70835i	0.618163	−	2.70835i
$615$		0			0
$616$		0			0
$617$	0.245172	+	1.07417i	0.245172	+	1.07417i	0.936235	+	0.351375i	$0.114286\pi$
$617$	0.245172	+	1.07417i	0.245172	+	1.07417i	−0.691063	+	0.722795i	$0.742857\pi$
$618$	−5.20172			−5.20172
$619$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$619$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.635928	−	1.48783i	0.635928	−	1.48783i
$624$		0			0
$625$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$626$		0			0
$627$		0			0
$628$	−1.94494	+	2.43888i	−1.94494	+	2.43888i
$629$	2.33170	−	1.12289i	2.33170	−	1.12289i
$630$		0			0
$631$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$631$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$632$	0.241880	−	0.116483i	0.241880	−	0.116483i
$633$		0			0
$634$		0			0
$635$		0			0
$636$	4.18406			4.18406
$637$		0			0
$638$		0			0
$639$	2.08499	+	2.61450i	2.08499	+	2.61450i
$640$		0			0
$641$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$641$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$642$		0			0
$643$	0.708207	+	0.341054i	0.708207	+	0.341054i	0.753071	−	0.657939i	$-0.228571\pi$
$643$	0.708207	+	0.341054i	0.708207	+	0.341054i	−0.0448648	+	0.998993i	$0.514286\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.853882	−	0.411208i	−0.853882	−	0.411208i	−0.0448648	−	0.998993i	$-0.514286\pi$
$647$	−0.853882	−	0.411208i	−0.853882	−	0.411208i	−0.809017	+	0.587785i	$0.800000\pi$
$648$	−0.527437	−	0.661385i	−0.527437	−	0.661385i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.79468	+	0.864274i	1.79468	+	0.864274i	0.936235	+	0.351375i	$0.114286\pi$
$653$	1.79468	+	0.864274i	1.79468	+	0.864274i	0.858449	+	0.512899i	$0.171429\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	0.0725928	+	1.61640i	0.0725928	+	1.61640i
$659$	−0.416664	+	1.82552i	−0.416664	+	1.82552i	0.134233	+	0.990950i	$0.457143\pi$
$659$	−0.416664	+	1.82552i	−0.416664	+	1.82552i	−0.550897	+	0.834573i	$0.685714\pi$
$660$		0			0
$661$	−0.686957	+	0.861417i	−0.686957	+	0.861417i	−0.995974	−	0.0896393i	$-0.971429\pi$
$661$	−0.686957	+	0.861417i	−0.686957	+	0.861417i	0.309017	+	0.951057i	$0.400000\pi$
$662$	−1.51944	+	1.90532i	−1.51944	+	1.90532i
$663$		0			0
$664$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$665$		0			0
$666$	1.31312	+	5.75315i	1.31312	+	5.75315i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−1.38900	−	1.00917i	−1.38900	−	1.00917i
$673$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$673$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$674$	−0.283015	−	1.23997i	−0.283015	−	1.23997i
$675$	1.01452	+	1.27217i	1.01452	+	1.27217i
$676$	−1.45780	−	0.702039i	−1.45780	−	0.702039i
$677$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$677$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$678$		0			0
$679$	1.55972	−	0.430457i	1.55972	−	0.430457i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.45780	−	0.702039i	1.45780	−	0.702039i	0.473869	−	0.880596i	$-0.342857\pi$
$683$	1.45780	−	0.702039i	1.45780	−	0.702039i	0.983930	+	0.178557i	$0.0571429\pi$
$684$		0			0
$685$		0			0
$686$	1.61152	+	0.145039i	1.61152	+	0.145039i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$691$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$692$	−2.19565	−	1.05737i	−2.19565	−	1.05737i
$693$		0			0
$694$	0.391370	−	0.188474i	0.391370	−	0.188474i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$701$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$701$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.582567	−	2.55239i	−0.582567	−	2.55239i
$707$	−1.04084	+	0.909354i	−1.04084	+	0.909354i
$708$	−0.585856	+	2.56680i	−0.585856	+	2.56680i
$709$	−0.210891	+	0.923976i	−0.210891	+	0.923976i	0.753071	+	0.657939i	$0.228571\pi$
$709$	−0.210891	+	0.923976i	−0.210891	+	0.923976i	−0.963963	+	0.266037i	$0.914286\pi$
$710$		0			0
$711$	0.326024	−	0.408821i	0.326024	−	0.408821i
$712$	−0.360046	+	1.57747i	−0.360046	+	1.57747i
$713$		0			0
$714$	−0.172260	−	3.83568i	−0.172260	−	3.83568i
$715$		0			0
$716$		0			0
$717$	3.21484			3.21484
$718$		0			0
$719$	1.73700	+	0.836496i	1.73700	+	0.836496i	0.983930	+	0.178557i	$0.0571429\pi$
$719$	1.73700	+	0.836496i	1.73700	+	0.836496i	0.753071	+	0.657939i	$0.228571\pi$
$720$		0			0
$721$	1.41010	−	1.23197i	1.41010	−	1.23197i
$722$	−1.00883	−	1.26503i	−1.00883	−	1.26503i
$723$	0.420936	+	1.84424i	0.420936	+	1.84424i
$724$		0			0
$725$		0			0
$726$	−1.73205	+	2.17193i	−1.73205	+	2.17193i
$727$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$727$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$728$		0			0
$729$	1.03252	+	0.497233i	1.03252	+	0.497233i
$730$		0			0
$731$		0			0
$732$	0.224583	−	0.108154i	0.224583	−	0.108154i
$733$	−1.24196	−	1.55737i	−1.24196	−	1.55737i	−0.691063	−	0.722795i	$-0.742857\pi$
$733$	−1.24196	−	1.55737i	−1.24196	−	1.55737i	−0.550897	−	0.834573i	$-0.685714\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	0.0199667	−	0.0874800i	0.0199667	−	0.0874800i	−0.963963	−	0.266037i	$-0.914286\pi$
$739$	0.0199667	−	0.0874800i	0.0199667	−	0.0874800i	0.983930	+	0.178557i	$0.0571429\pi$
$740$		0			0
$741$		0			0
$742$	−1.83523	+	1.60339i	−1.83523	+	1.60339i
$743$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$743$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.192887	+	0.845092i	0.192887	+	0.845092i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$751$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$752$		0			0
$753$	0.460930			0.460930
$754$		0			0
$755$		0			0
$756$	2.59050	+	0.470107i	2.59050	+	0.470107i
$757$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$757$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$758$	0.341229	−	1.49502i	0.341229	−	1.49502i
$759$		0			0
$760$		0			0
$761$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$761$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$762$		0			0
$763$		0			0
$764$	−0.448971	−	1.96707i	−0.448971	−	1.96707i
$765$		0			0
$766$	−2.77800			−2.77800
$767$		0			0
$768$	1.54687	+	0.744934i	1.54687	+	0.744934i
$769$	−0.861741	+	1.08059i	−0.861741	+	1.08059i	0.134233	+	0.990950i	$0.457143\pi$
$769$	−0.861741	+	1.08059i	−0.861741	+	1.08059i	−0.995974	+	0.0896393i	$0.971429\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.16747	+	1.46396i	1.16747	+	1.46396i	0.858449	+	0.512899i	$0.171429\pi$
$773$	1.16747	+	1.46396i	1.16747	+	1.46396i	0.309017	+	0.951057i	$0.400000\pi$
$774$		0			0
$775$		0			0
$776$	−1.45780	+	0.702039i	−1.45780	+	0.702039i
$777$	−2.60086	−	1.88963i	−2.60086	−	1.88963i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$	0.155417	+	0.194886i	0.155417	+	0.194886i
$787$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$787$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$788$	0.648781	−	2.84250i	0.648781	−	2.84250i
$789$	0.138800	−	0.0668427i	0.138800	−	0.0668427i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	2.50289	+	1.20533i	2.50289	+	1.20533i
$795$		0			0
$796$		0			0
$797$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$797$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$798$		0			0
$799$	−0.861741	+	1.08059i	−0.861741	+	1.08059i
$800$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$801$	0.701276	+	3.07249i	0.701276	+	3.07249i
$802$	3.22304			3.22304
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.688422	−	3.01618i	0.688422	−	3.01618i
$808$	0.861741	−	1.08059i	0.861741	−	1.08059i
$809$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$809$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$810$		0			0
$811$	−0.137526	+	0.602539i	−0.137526	+	0.602539i	0.858449	+	0.512899i	$0.171429\pi$
$811$	−0.137526	+	0.602539i	−0.137526	+	0.602539i	−0.995974	+	0.0896393i	$0.971429\pi$
$812$		0			0
$813$	−0.715369	−	3.13424i	−0.715369	−	3.13424i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		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			0
$823$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$823$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$824$	−1.16747	+	1.46396i	−1.16747	+	1.46396i
$825$		0			0
$826$	−0.726664	−	1.35037i	−0.726664	−	1.35037i
$827$	−1.77298	−	0.853822i	−1.77298	−	0.853822i	−0.963963	−	0.266037i	$-0.914286\pi$
$827$	−1.77298	−	0.853822i	−1.77298	−	0.853822i	−0.809017	−	0.587785i	$-0.800000\pi$
$828$		0			0
$829$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$829$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$830$		0			0
$831$	2.00442	+	2.51346i	2.00442	+	2.51346i
$832$		0			0
$833$	0.955135	+	0.998993i	0.955135	+	0.998993i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$839$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$840$		0			0
$841$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$	−1.96493	−	2.46395i	−1.96493	−	2.46395i
$847$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$848$		0			0
$849$	2.98225	+	1.43618i	2.98225	+	1.43618i
$850$	−0.497629	−	2.18026i	−0.497629	−	2.18026i
$851$		0			0
$852$	4.76954			4.76954
$853$	−0.137526	−	0.602539i	−0.137526	−	0.602539i	−0.995974	−	0.0896393i	$-0.971429\pi$
$853$	−0.137526	−	0.602539i	−0.137526	−	0.602539i	0.858449	−	0.512899i	$-0.171429\pi$
$854$	−0.0570616	+	0.133502i	−0.0570616	+	0.133502i
$855$		0			0
$856$		0			0
$857$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$857$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$858$		0			0
$859$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$859$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$860$		0			0
$861$		0			0
$862$	−0.283015	−	1.23997i	−0.283015	−	1.23997i
$863$	1.71690			1.71690			0.858449	−	0.512899i	$-0.171429\pi$
$863$	1.71690			1.71690			0.858449	+	0.512899i	$0.171429\pi$
$864$	1.62717			1.62717
$865$		0			0
$866$		0			0
$867$	0.974415	−	1.22188i	0.974415	−	1.22188i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−1.96493	+	2.46395i	−1.96493	+	2.46395i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$877$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$878$	−0.648781	+	2.84250i	−0.648781	+	2.84250i
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−2.70541	+	1.61640i	−2.70541	+	1.61640i
$883$	1.96786			1.96786			0.983930	−	0.178557i	$-0.0571429\pi$
$883$	1.96786			1.96786			0.983930	+	0.178557i	$0.0571429\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$887$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$888$	2.89647	+	1.39487i	2.89647	+	1.39487i
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$	−1.23135	−	5.39489i	−1.23135	−	5.39489i
$895$		0			0
$896$	−1.55972	+	0.430457i	−1.55972	+	0.430457i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	3.15151			3.15151
$901$	−2.08168			−2.08168
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$907$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$908$		0			0
$909$	0.599030	−	2.62452i	0.599030	−	2.62452i
$910$		0			0
$911$	0.0199667	+	0.0874800i	0.0199667	+	0.0874800i	0.983930	−	0.178557i	$-0.0571429\pi$
$911$	0.0199667	+	0.0874800i	0.0199667	+	0.0874800i	−0.963963	+	0.266037i	$0.914286\pi$
$912$		0			0
$913$		0			0
$914$	−0.497629	−	2.18026i	−0.497629	−	2.18026i
$915$		0			0
$916$		0			0
$917$	−0.0882877	−	0.0160218i	−0.0882877	−	0.0160218i
$918$	2.26880	+	2.84499i	2.26880	+	2.84499i
$919$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$919$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$920$		0			0
$921$	−2.65582	−	1.27898i	−2.65582	−	1.27898i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.68704	−	0.812434i	−1.68704	−	0.812434i
$926$		0			0
$927$	−0.811551	+	3.55564i	−0.811551	+	3.55564i
$928$		0			0
$929$	−1.24196	−	1.55737i	−1.24196	−	1.55737i	−0.691063	−	0.722795i	$-0.742857\pi$
$929$	−1.24196	−	1.55737i	−1.24196	−	1.55737i	−0.550897	−	0.834573i	$-0.685714\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$937$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.77298	−	0.853822i	−1.77298	−	0.853822i	−0.963963	−	0.266037i	$-0.914286\pi$
$941$	−1.77298	−	0.853822i	−1.77298	−	0.853822i	−0.809017	−	0.587785i	$-0.800000\pi$
$942$	3.33927	+	4.18731i	3.33927	+	4.18731i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$947$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$948$	−0.165956	−	0.727101i	−0.165956	−	0.727101i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	−1.11816	−	0.812393i	−1.11816	−	0.812393i
$953$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$953$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$954$	1.05622	−	4.62761i	1.05622	−	4.62761i
$955$		0			0
$956$	1.88900	−	2.36873i	1.88900	−	2.36873i
$957$		0			0
$958$	−0.283015	+	1.23997i	−0.283015	+	1.23997i
$959$		0			0
$960$		0			0
$961$	1.00000			1.00000
$962$		0			0
$963$		0			0
$964$	1.60619	+	0.773502i	1.60619	+	0.773502i
$965$		0			0
$966$		0			0
$967$	1.22694	+	1.53853i	1.22694	+	1.53853i	0.753071	+	0.657939i	$0.228571\pi$
$967$	1.22694	+	1.53853i	1.22694	+	1.53853i	0.473869	+	0.880596i	$0.342857\pi$
$968$	0.222521	+	0.974928i	0.222521	+	0.974928i
$969$		0			0
$970$		0			0
$971$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$971$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$972$	0.254779	−	0.122695i	0.254779	−	0.122695i
$973$		0			0
$974$	1.81784	+	0.875428i	1.81784	+	0.875428i
$975$		0			0
$976$		0			0
$977$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$977$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−1.98523	−	2.48940i	−1.98523	−	2.48940i
$983$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$983$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	1.68931	+	0.306564i	1.68931	+	0.306564i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.939065	+	1.17755i	0.939065	+	1.17755i	0.983930	+	0.178557i	$0.0571429\pi$
$991$	0.939065	+	1.17755i	0.939065	+	1.17755i	−0.0448648	+	0.998993i	$0.514286\pi$
$992$		0			0
$993$	1.61228	+	2.02173i	1.61228	+	2.02173i
$994$	−2.09203	+	1.82775i	−2.09203	+	1.82775i
$995$		0			0
$996$	1.11389	+	0.536422i	1.11389	+	0.536422i
$997$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$997$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$998$		0			0
$999$	3.04682			3.04682

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.1.j.b.939.1	✓	24
47.46	odd	2	CM	2303.1.j.b.939.1	✓	24
49.43	even	7	inner	2303.1.j.b.1268.1	yes	24
2303.1268	odd	14	inner	2303.1.j.b.1268.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.1.j.b.939.1	✓	24	1.1	even	1	trivial
2303.1.j.b.939.1	✓	24	47.46	odd	2	CM
2303.1.j.b.1268.1	yes	24	49.43	even	7	inner
2303.1.j.b.1268.1	yes	24	2303.1268	odd	14	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:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2303.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00883 - 1.26503i) q^{2} +(-1.54687 + 0.744934i) q^{3} +(-0.360046 + 1.57747i) q^{4} +(2.50289 + 1.20533i) q^{6} +(-0.963963 + 0.266037i) q^{7} +(0.900969 - 0.433884i) q^{8} +(1.21439 - 1.52280i) q^{9} +(-0.618163 - 2.70835i) q^{12} +(1.30902 + 0.951057i) q^{14} +(0.307552 + 1.34747i) q^{17} -3.15151 q^{18} +(1.29295 - 1.12961i) q^{21} +(-1.07047 + 1.34232i) q^{24} +(0.623490 - 0.781831i) q^{25} +(-0.362079 + 1.58637i) q^{27} +(-0.0725928 - 1.61640i) q^{28} +(-0.222521 - 0.974928i) q^{32} +(1.39433 - 1.74843i) q^{34} +(1.96493 + 2.46395i) q^{36} +(-0.416664 - 1.82552i) q^{37} +(-2.73336 - 0.496031i) q^{42} +(0.623490 + 0.781831i) q^{47} +(0.858449 - 0.512899i) q^{49} -1.61803 q^{50} +(-1.47952 - 1.85526i) q^{51} +(-0.335148 + 1.46838i) q^{53} +(2.37208 - 1.14233i) q^{54} +(-0.753071 + 0.657939i) q^{56} +(-0.853882 - 0.411208i) q^{59} +(0.0199667 + 0.0874800i) q^{61} +(-0.765510 + 1.79100i) q^{63} +(-1.00883 + 1.26503i) q^{64} -2.23633 q^{68} +(-0.382046 + 1.67385i) q^{71} +(0.433412 - 1.89890i) q^{72} +(-1.88900 + 2.36873i) q^{74} +(-0.382046 + 1.67385i) q^{75} +0.268467 q^{79} +(-0.188240 - 0.824734i) q^{81} +(-0.277479 + 0.347948i) q^{83} +(1.31641 + 2.44629i) q^{84} +(-1.00883 + 1.26503i) q^{89} +(0.360046 - 1.57747i) q^{94} +(1.07047 + 1.34232i) q^{96} -1.61803 q^{97} +(-1.51486 - 0.568536i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} + q^{7} + 4 q^{8} - 2 q^{9} + 10 q^{12} + 18 q^{14} + 2 q^{17} - 18 q^{18} - 5 q^{21} - 2 q^{24} - 4 q^{25} - 3 q^{27} + 3 q^{28} - 4 q^{32} + 4 q^{34} + 4 q^{36}+ \cdots + 2 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 + q^7 + 4 * q^8 - 2 * q^9 + 10 * q^12 + 18 * q^14 + 2 * q^17 - 18 * q^18 - 5 * q^21 - 2 * q^24 - 4 * q^25 - 3 * q^27 + 3 * q^28 - 4 * q^32 + 4 * q^34 + 4 * q^36 + 2 * q^37 - q^42 - 4 * q^47 + q^49 - 12 * q^50 - 13 * q^51 - 5 * q^53 - 2 * q^54 - q^56 - 5 * q^59 + 2 * q^61 - 2 * q^63 + 2 * q^64 - 4 * q^68 - 5 * q^71 + 2 * q^72 - 10 * q^74 - 5 * q^75 + 2 * q^79 - 8 * q^83 + q^84 + 2 * q^89 + 2 * q^94 + 2 * q^96 - 12 * q^97 + 2 * q^98

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