LMFDB - Embedded newform 2303.1.j.b.281.3

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			281.3
Root			$0.858449 + 0.512899i$ of defining polynomial
Character	$\chi$	$=$	2303.281
Dual form			2303.1.j.b.1926.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.360046 + 1.57747i) q^{2} +(-0.861741 - 1.08059i) q^{3} +(-1.45780 + 0.702039i) q^{4} +(1.39433 - 1.74843i) q^{6} +(-0.393025 - 0.919528i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-0.202554 + 0.887448i) q^{9} +(2.01486 + 0.970305i) q^{12} +(1.30902 - 0.951057i) q^{14} +(-1.68704 - 0.812434i) q^{17} -1.47285 q^{18} +(-0.654946 + 1.21709i) q^{21} +(-0.307552 + 1.34747i) q^{24} +(-0.222521 + 0.974928i) q^{25} +(-0.111736 + 0.0538092i) q^{27} +(1.21850 + 1.06457i) q^{28} +(-0.900969 - 0.433884i) q^{32} +(0.674176 - 2.95376i) q^{34} +(-0.327740 - 1.43592i) q^{36} +(-1.54687 - 0.744934i) q^{37} +(-2.15573 - 0.594945i) q^{42} +(-0.222521 - 0.974928i) q^{47} +(-0.691063 + 0.722795i) q^{49} -1.61803 q^{50} +(0.575881 + 2.52310i) q^{51} +(-0.853882 + 0.411208i) q^{53} +(-0.125112 - 0.156886i) q^{54} +(-0.473869 + 0.880596i) q^{56} +(-0.0559455 + 0.0701535i) q^{59} +(-1.35699 - 0.653491i) q^{61} +(0.895642 - 0.162535i) q^{63} +(0.360046 - 1.57747i) q^{64} +3.02972 q^{68} +(1.24525 - 0.599682i) q^{71} +(0.820125 - 0.394951i) q^{72} +(0.618163 - 2.70835i) q^{74} +(1.24525 - 0.599682i) q^{75} -1.10179 q^{79} +(0.974558 + 0.469323i) q^{81} +(0.400969 - 1.75676i) q^{83} +(0.100332 - 2.23407i) q^{84} +(0.360046 - 1.57747i) q^{89} +(1.45780 - 0.702039i) q^{94} +(0.307552 + 1.34747i) q^{96} -1.61803 q^{97} +(-1.38900 - 0.829888i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2303\mathbb{Z}\right)^\times$.

$n$	$99$	$2257$
$\chi(n)$	$-1$	$e\left(\frac{2}{7}\right)$

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 $

$2$	0.360046	+	1.57747i	0.360046	+	1.57747i	0.753071	+	0.657939i	$0.228571\pi$
$2$	0.360046	+	1.57747i	0.360046	+	1.57747i	−0.393025	+	0.919528i	$0.628571\pi$
$3$	−0.861741	−	1.08059i	−0.861741	−	1.08059i	−0.995974	−	0.0896393i	$-0.971429\pi$
$3$	−0.861741	−	1.08059i	−0.861741	−	1.08059i	0.134233	−	0.990950i	$-0.457143\pi$
$4$	−1.45780	+	0.702039i	−1.45780	+	0.702039i
$5$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$5$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$6$	1.39433	−	1.74843i	1.39433	−	1.74843i
$7$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$7$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$8$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$9$	−0.202554	+	0.887448i	−0.202554	+	0.887448i
$10$		0			0
$11$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$11$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$12$	2.01486	+	0.970305i	2.01486	+	0.970305i
$13$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$13$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$14$	1.30902	−	0.951057i	1.30902	−	0.951057i
$15$		0			0
$16$		0			0
$17$	−1.68704	−	0.812434i	−1.68704	−	0.812434i	−0.995974	−	0.0896393i	$-0.971429\pi$
$17$	−1.68704	−	0.812434i	−1.68704	−	0.812434i	−0.691063	−	0.722795i	$-0.742857\pi$
$18$	−1.47285			−1.47285
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$	−0.654946	+	1.21709i	−0.654946	+	1.21709i
$22$		0			0
$23$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$23$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$24$	−0.307552	+	1.34747i	−0.307552	+	1.34747i
$25$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$26$		0			0
$27$	−0.111736	+	0.0538092i	−0.111736	+	0.0538092i
$28$	1.21850	+	1.06457i	1.21850	+	1.06457i
$29$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$29$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$33$		0			0
$34$	0.674176	−	2.95376i	0.674176	−	2.95376i
$35$		0			0
$36$	−0.327740	−	1.43592i	−0.327740	−	1.43592i
$37$	−1.54687	−	0.744934i	−1.54687	−	0.744934i	−0.550897	−	0.834573i	$-0.685714\pi$
$37$	−1.54687	−	0.744934i	−1.54687	−	0.744934i	−0.995974	+	0.0896393i	$0.971429\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$41$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$42$	−2.15573	−	0.594945i	−2.15573	−	0.594945i
$43$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$43$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$47$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$48$		0			0
$49$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$50$	−1.61803			−1.61803
$51$	0.575881	+	2.52310i	0.575881	+	2.52310i
$52$		0			0
$53$	−0.853882	+	0.411208i	−0.853882	+	0.411208i	−0.809017	−	0.587785i	$-0.800000\pi$
$53$	−0.853882	+	0.411208i	−0.853882	+	0.411208i	−0.0448648	+	0.998993i	$0.514286\pi$
$54$	−0.125112	−	0.156886i	−0.125112	−	0.156886i
$55$		0			0
$56$	−0.473869	+	0.880596i	−0.473869	+	0.880596i
$57$		0			0
$58$		0			0
$59$	−0.0559455	+	0.0701535i	−0.0559455	+	0.0701535i	−0.809017	−	0.587785i	$-0.800000\pi$
$59$	−0.0559455	+	0.0701535i	−0.0559455	+	0.0701535i	0.753071	+	0.657939i	$0.228571\pi$
$60$		0			0
$61$	−1.35699	−	0.653491i	−1.35699	−	0.653491i	−0.393025	−	0.919528i	$-0.628571\pi$
$61$	−1.35699	−	0.653491i	−1.35699	−	0.653491i	−0.963963	+	0.266037i	$0.914286\pi$
$62$		0			0
$63$	0.895642	−	0.162535i	0.895642	−	0.162535i
$64$	0.360046	−	1.57747i	0.360046	−	1.57747i
$65$		0			0
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	3.02972			3.02972
$69$		0			0
$70$		0			0
$71$	1.24525	−	0.599682i	1.24525	−	0.599682i	0.309017	−	0.951057i	$-0.400000\pi$
$71$	1.24525	−	0.599682i	1.24525	−	0.599682i	0.936235	+	0.351375i	$0.114286\pi$
$72$	0.820125	−	0.394951i	0.820125	−	0.394951i
$73$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$73$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$74$	0.618163	−	2.70835i	0.618163	−	2.70835i
$75$	1.24525	−	0.599682i	1.24525	−	0.599682i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.10179			−1.10179			−0.550897	−	0.834573i	$-0.685714\pi$
$79$	−1.10179			−1.10179			−0.550897	+	0.834573i	$0.685714\pi$
$80$		0			0
$81$	0.974558	+	0.469323i	0.974558	+	0.469323i
$82$		0			0
$83$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$83$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$84$	0.100332	−	2.23407i	0.100332	−	2.23407i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.360046	−	1.57747i	0.360046	−	1.57747i	−0.393025	−	0.919528i	$-0.628571\pi$
$89$	0.360046	−	1.57747i	0.360046	−	1.57747i	0.753071	−	0.657939i	$-0.228571\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	1.45780	−	0.702039i	1.45780	−	0.702039i
$95$		0			0
$96$	0.307552	+	1.34747i	0.307552	+	1.34747i
$97$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$97$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$98$	−1.38900	−	0.829888i	−1.38900	−	0.829888i
$99$		0			0
$100$	−0.360046	−	1.57747i	−0.360046	−	1.57747i
$101$	1.16747	+	1.46396i	1.16747	+	1.46396i	0.858449	+	0.512899i	$0.171429\pi$
$101$	1.16747	+	1.46396i	1.16747	+	1.46396i	0.309017	+	0.951057i	$0.400000\pi$
$102$	−3.77276	+	1.81687i	−3.77276	+	1.81687i
$103$	1.07047	+	1.34232i	1.07047	+	1.34232i	0.936235	+	0.351375i	$0.114286\pi$
$103$	1.07047	+	1.34232i	1.07047	+	1.34232i	0.134233	+	0.990950i	$0.457143\pi$
$104$		0			0
$105$		0			0
$106$	−0.956104	−	1.19892i	−0.956104	−	1.19892i
$107$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$107$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$108$	0.125112	−	0.156886i	0.125112	−	0.156886i
$109$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$109$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$110$		0			0
$111$	0.528035	+	2.31347i	0.528035	+	2.31347i
$112$		0			0
$113$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$113$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.130808	−	0.0629937i	−0.130808	−	0.0629937i
$119$	−0.0840080	+	1.87058i	−0.0840080	+	1.87058i
$120$		0			0
$121$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$122$	0.542281	−	2.37589i	0.542281	−	2.37589i
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.578866	+	1.35432i	0.578866	+	1.35432i
$127$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$127$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$128$	1.61803			1.61803
$129$		0			0
$130$		0			0
$131$	0.939065	−	1.17755i	0.939065	−	1.17755i	−0.0448648	−	0.998993i	$-0.514286\pi$
$131$	0.939065	−	1.17755i	0.939065	−	1.17755i	0.983930	−	0.178557i	$-0.0571429\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.416664	+	1.82552i	0.416664	+	1.82552i
$137$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$137$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$138$		0			0
$139$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$139$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$140$		0			0
$141$	−0.861741	+	1.08059i	−0.861741	+	1.08059i
$142$	1.39433	+	1.74843i	1.39433	+	1.74843i
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.37656	+	0.123893i	1.37656	+	0.123893i
$148$	2.77800			2.77800
$149$	−0.0597394	−	0.261736i	−0.0597394	−	0.261736i	0.936235	−	0.351375i	$-0.114286\pi$
$149$	−0.0597394	−	0.261736i	−0.0597394	−	0.261736i	−0.995974	+	0.0896393i	$0.971429\pi$
$150$	1.39433	+	1.74843i	1.39433	+	1.74843i
$151$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$151$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$152$		0			0
$153$	1.06271	−	1.33260i	1.06271	−	1.33260i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.490094	+	0.614559i	−0.490094	+	0.614559i	−0.963963	−	0.266037i	$-0.914286\pi$
$157$	−0.490094	+	0.614559i	−0.490094	+	0.614559i	0.473869	+	0.880596i	$0.342857\pi$
$158$	−0.396697	−	1.73804i	−0.396697	−	1.73804i
$159$	1.18017	+	0.568341i	1.18017	+	0.568341i
$160$		0			0
$161$		0			0
$162$	−0.389454	+	1.70631i	−0.389454	+	1.70631i
$163$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$163$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$164$		0			0
$165$		0			0
$166$	2.91560			2.91560
$167$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$167$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$168$	1.35991	−	0.246788i	1.35991	−	0.246788i
$169$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.853882	+	0.411208i	−0.853882	+	0.411208i	−0.809017	−	0.587785i	$-0.800000\pi$
$173$	−0.853882	+	0.411208i	−0.853882	+	0.411208i	−0.0448648	+	0.998993i	$0.514286\pi$
$174$		0			0
$175$	0.983930	−	0.178557i	0.983930	−	0.178557i
$176$		0			0
$177$	0.124018			0.124018
$178$	2.61803			2.61803
$179$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$179$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$180$		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
$183$	0.463217	+	2.02949i	0.463217	+	2.02949i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	1.00883	+	1.26503i	1.00883	+	1.26503i
$189$	0.0933941	+	0.0815960i	0.0933941	+	0.0815960i
$190$		0			0
$191$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$191$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$192$	−2.01486	+	0.970305i	−2.01486	+	0.970305i
$193$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$193$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$194$	−0.582567	−	2.55239i	−0.582567	−	2.55239i
$195$		0			0
$196$	0.500000	−	1.53884i	0.500000	−	1.53884i
$197$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$197$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$198$		0			0
$199$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$199$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$200$	0.900969	−	0.433884i	0.900969	−	0.433884i
$201$		0			0
$202$	−1.88900	+	2.36873i	−1.88900	+	2.36873i
$203$		0			0
$204$	−2.61083	−	3.27388i	−2.61083	−	3.27388i
$205$		0			0
$206$	−1.73205	+	2.17193i	−1.73205	+	2.17193i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$211$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$212$	0.956104	−	1.19892i	0.956104	−	1.19892i
$213$	−1.72109	−	0.828835i	−1.72109	−	0.828835i
$214$		0			0
$215$		0			0
$216$	0.111736	+	0.0538092i	0.111736	+	0.0538092i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$	−3.45931	+	1.66591i	−3.45931	+	1.66591i
$223$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$223$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$224$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$225$	−0.820125	−	0.394951i	−0.820125	−	0.394951i
$226$		0			0
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$		0			0
$229$		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			0		−0.900969	−	0.433884i	$-0.857143\pi$
$233$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$234$		0			0
$235$		0			0
$236$	0.0323068	−	0.141546i	0.0323068	−	0.141546i
$237$	0.949461	+	1.19059i	0.949461	+	1.19059i
$238$	−2.98103	+	0.540977i	−2.98103	+	0.540977i
$239$	1.07047	−	1.34232i	1.07047	−	1.34232i	0.134233	−	0.990950i	$-0.457143\pi$
$239$	1.07047	−	1.34232i	1.07047	−	1.34232i	0.936235	−	0.351375i	$-0.114286\pi$
$240$		0			0
$241$	1.79468	−	0.864274i	1.79468	−	0.864274i	0.858449	−	0.512899i	$-0.171429\pi$
$241$	1.79468	−	0.864274i	1.79468	−	0.864274i	0.936235	−	0.351375i	$-0.114286\pi$
$242$	−1.00883	−	1.26503i	−1.00883	−	1.26503i
$243$	−0.305076	−	1.33662i	−0.305076	−	1.33662i
$244$	2.43699			2.43699
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−2.24387	+	1.08059i	−2.24387	+	1.08059i
$250$		0			0
$251$	−0.686957	+	0.861417i	−0.686957	+	0.861417i	−0.995974	−	0.0896393i	$-0.971429\pi$
$251$	−0.686957	+	0.861417i	−0.686957	+	0.861417i	0.309017	+	0.951057i	$0.400000\pi$
$252$	−1.19156	+	0.865719i	−1.19156	+	0.865719i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.222521	+	0.974928i	0.222521	+	0.974928i
$257$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$257$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$258$		0			0
$259$	−0.0770283	+	1.71517i	−0.0770283	+	1.71517i
$260$		0			0
$261$		0			0
$262$	2.19565	+	1.05737i	2.19565	+	1.05737i
$263$	1.50614			1.50614			0.753071	−	0.657939i	$-0.228571\pi$
$263$	1.50614			1.50614			0.753071	+	0.657939i	$0.228571\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.01486	+	0.970305i	−2.01486	+	0.970305i
$268$		0			0
$269$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$269$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$270$		0			0
$271$	−1.54687	+	0.744934i	−1.54687	+	0.744934i	−0.995974	−	0.0896393i	$-0.971429\pi$
$271$	−1.54687	+	0.744934i	−1.54687	+	0.744934i	−0.550897	+	0.834573i	$0.685714\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.54687	−	0.744934i	−1.54687	−	0.744934i	−0.550897	−	0.834573i	$-0.685714\pi$
$277$	−1.54687	−	0.744934i	−1.54687	−	0.744934i	−0.995974	+	0.0896393i	$0.971429\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$281$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$282$	−2.01486	−	0.970305i	−2.01486	−	0.970305i
$283$	0.174913	+	0.766342i	0.174913	+	0.766342i	0.983930	+	0.178557i	$0.0571429\pi$
$283$	0.174913	+	0.766342i	0.174913	+	0.766342i	−0.809017	+	0.587785i	$0.800000\pi$
$284$	−1.39433	+	1.74843i	−1.39433	+	1.74843i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.567544	−	0.711678i	0.567544	−	0.711678i
$289$	1.56255	+	1.95938i	1.56255	+	1.95938i
$290$		0			0
$291$	1.39433	+	1.74843i	1.39433	+	1.74843i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	0.300189	+	2.21609i	0.300189	+	2.21609i
$295$		0			0
$296$	0.382046	+	1.67385i	0.382046	+	1.67385i
$297$		0			0
$298$	0.391370	−	0.188474i	0.391370	−	0.188474i
$299$		0			0
$300$	−1.39433	+	1.74843i	−1.39433	+	1.74843i
$301$		0			0
$302$		0			0
$303$	0.575881	−	2.52310i	0.575881	−	2.52310i
$304$		0			0
$305$		0			0
$306$	2.48475	+	1.19659i	2.48475	+	1.19659i
$307$	0.307552	+	1.34747i	0.307552	+	1.34747i	0.858449	+	0.512899i	$0.171429\pi$
$307$	0.307552	+	1.34747i	0.307552	+	1.34747i	−0.550897	+	0.834573i	$0.685714\pi$
$308$		0			0
$309$	0.528035	−	2.31347i	0.528035	−	2.31347i
$310$		0			0
$311$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$311$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$312$		0			0
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	−1.14590	−	0.551838i	−1.14590	−	0.551838i
$315$		0			0
$316$	1.60619	−	0.773502i	1.60619	−	0.773502i
$317$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$317$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$318$	−0.471622	+	2.06631i	−0.471622	+	2.06631i
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−1.75019			−1.75019
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$330$		0			0
$331$	−0.853882	−	0.411208i	−0.853882	−	0.411208i	−0.0448648	−	0.998993i	$-0.514286\pi$
$331$	−0.853882	−	0.411208i	−0.853882	−	0.411208i	−0.809017	+	0.587785i	$0.800000\pi$
$332$	0.648781	+	2.84250i	0.648781	+	2.84250i
$333$	0.974415	−	1.22188i	0.974415	−	1.22188i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.22694	−	1.53853i	1.22694	−	1.53853i	0.473869	−	0.880596i	$-0.342857\pi$
$337$	1.22694	−	1.53853i	1.22694	−	1.53853i	0.753071	−	0.657939i	$-0.228571\pi$
$338$	−1.00883	−	1.26503i	−1.00883	−	1.26503i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.936235	+	0.351375i	0.936235	+	0.351375i
$344$		0			0
$345$		0			0
$346$	−0.956104	−	1.19892i	−0.956104	−	1.19892i
$347$	0.992682	−	0.478050i	0.992682	−	0.478050i	0.134233	−	0.990950i	$-0.457143\pi$
$347$	0.992682	−	0.478050i	0.992682	−	0.478050i	0.858449	+	0.512899i	$0.171429\pi$
$348$		0			0
$349$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$349$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$350$	0.635928	+	1.48783i	0.635928	+	1.48783i
$351$		0			0
$352$		0			0
$353$	−1.00883	+	1.26503i	−1.00883	+	1.26503i	−0.0448648	+	0.998993i	$0.514286\pi$
$353$	−1.00883	+	1.26503i	−1.00883	+	1.26503i	−0.963963	+	0.266037i	$0.914286\pi$
$354$	0.0446521	+	0.195634i	0.0446521	+	0.195634i
$355$		0			0
$356$	0.582567	+	2.55239i	0.582567	+	2.55239i
$357$	2.09373	−	1.52118i	2.09373	−	1.52118i
$358$		0			0
$359$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$359$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$360$		0			0
$361$	1.00000			1.00000
$362$		0			0
$363$	1.24525	+	0.599682i	1.24525	+	0.599682i
$364$		0			0
$365$		0			0
$366$	−3.03467	+	1.46142i	−3.03467	+	1.46142i
$367$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$367$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.713714	+	0.623553i	0.713714	+	0.623553i
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$		0			0
$376$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$377$		0			0
$378$	−0.0950887	+	0.176704i	−0.0950887	+	0.176704i
$379$	0.0199667	+	0.0874800i	0.0199667	+	0.0874800i	0.983930	−	0.178557i	$-0.0571429\pi$
$379$	0.0199667	+	0.0874800i	0.0199667	+	0.0874800i	−0.963963	+	0.266037i	$0.914286\pi$
$380$		0			0
$381$		0			0
$382$	0.448971	−	0.562991i	0.448971	−	0.562991i
$383$	0.307552	−	1.34747i	0.307552	−	1.34747i	−0.550897	−	0.834573i	$-0.685714\pi$
$383$	0.307552	−	1.34747i	0.307552	−	1.34747i	0.858449	−	0.512899i	$-0.171429\pi$
$384$	−1.39433	−	1.74843i	−1.39433	−	1.74843i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	2.35877	−	1.13592i	2.35877	−	1.13592i
$389$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$389$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$390$		0			0
$391$		0			0
$392$	0.995974	+	0.0896393i	0.995974	+	0.0896393i
$393$	−2.08168			−2.08168
$394$	0.448971	+	1.96707i	0.448971	+	1.96707i
$395$		0			0
$396$		0			0
$397$	−0.861741	−	1.08059i	−0.861741	−	1.08059i	−0.995974	−	0.0896393i	$-0.971429\pi$
$397$	−0.861741	−	1.08059i	−0.861741	−	1.08059i	0.134233	−	0.990950i	$-0.457143\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.0597394	+	0.261736i	−0.0597394	+	0.261736i	−0.995974	−	0.0896393i	$-0.971429\pi$
$401$	−0.0597394	+	0.261736i	−0.0597394	+	0.261736i	0.936235	+	0.351375i	$0.114286\pi$
$402$		0			0
$403$		0			0
$404$	−2.72968	−	1.31455i	−2.72968	−	1.31455i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.61358	−	2.02337i	1.61358	−	2.02337i
$409$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$409$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$410$		0			0
$411$		0			0
$412$	−2.50289	−	1.20533i	−2.50289	−	1.20533i
$413$	0.0864961	+	0.0238714i	0.0864961	+	0.0238714i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$419$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$420$		0			0
$421$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$421$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$422$		0			0
$423$	0.910270			0.910270
$424$	0.853882	+	0.411208i	0.853882	+	0.411208i
$425$	1.16747	−	1.46396i	1.16747	−	1.46396i
$426$	0.687786	−	3.01339i	0.687786	−	3.01339i
$427$	−0.0675728	+	1.50463i	−0.0675728	+	1.50463i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.22694	−	1.53853i	1.22694	−	1.53853i	0.473869	−	0.880596i	$-0.342857\pi$
$431$	1.22694	−	1.53853i	1.22694	−	1.53853i	0.753071	−	0.657939i	$-0.228571\pi$
$432$		0			0
$433$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$433$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$439$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$440$		0			0
$441$	−0.501465	−	0.759687i	−0.501465	−	0.759687i
$442$		0			0
$443$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$443$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$444$	−2.39392	−	3.00187i	−2.39392	−	3.00187i
$445$		0			0
$446$		0			0
$447$	−0.231349	+	0.290102i	−0.231349	+	0.290102i
$448$	−1.59203	+	0.288911i	−1.59203	+	0.288911i
$449$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$449$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$450$	0.327740	−	1.43592i	0.327740	−	1.43592i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.16747	−	1.46396i	1.16747	−	1.46396i	0.309017	−	0.951057i	$-0.400000\pi$
$457$	1.16747	−	1.46396i	1.16747	−	1.46396i	0.858449	−	0.512899i	$-0.171429\pi$
$458$		0			0
$459$	0.232219			0.232219
$460$		0			0
$461$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$461$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$462$		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			0
$467$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$467$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.08642			1.08642
$472$	0.0897297			0.0897297
$473$		0			0
$474$	−1.53626	+	1.92641i	−1.53626	+	1.92641i
$475$		0			0
$476$	−1.19076	−	2.78591i	−1.19076	−	2.78591i
$477$	−0.191968	−	0.841068i	−0.191968	−	0.841068i
$478$	2.50289	+	1.20533i	2.50289	+	1.20533i
$479$	−0.437890	−	1.91852i	−0.437890	−	1.91852i	−0.393025	−	0.919528i	$-0.628571\pi$
$479$	−0.437890	−	1.91852i	−0.437890	−	1.91852i	−0.0448648	−	0.998993i	$-0.514286\pi$
$480$		0			0
$481$		0			0
$482$	2.00953	+	2.51987i	2.00953	+	2.51987i
$483$		0			0
$484$	1.00883	−	1.26503i	1.00883	−	1.26503i
$485$		0			0
$486$	1.99864	−	0.962493i	1.99864	−	0.962493i
$487$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$487$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$488$	0.335148	+	1.46838i	0.335148	+	1.46838i
$489$		0			0
$490$		0			0
$491$	−1.92793			−1.92793			−0.963963	−	0.266037i	$-0.914286\pi$
$491$	−1.92793			−1.92793			−0.963963	+	0.266037i	$0.914286\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.04084	−	0.909354i	−1.04084	−	0.909354i
$498$	−2.51249	−	3.15056i	−2.51249	−	3.15056i
$499$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$499$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$500$		0			0
$501$		0			0
$502$	−1.60619	−	0.773502i	−1.60619	−	0.773502i
$503$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$503$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$504$	−0.685499	−	0.598902i	−0.685499	−	0.598902i
$505$		0			0
$506$		0			0
$507$	1.24525	+	0.599682i	1.24525	+	0.599682i
$508$		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
$518$	−2.73336	+	0.496031i	−2.73336	+	0.496031i
$519$	1.18017	+	0.568341i	1.18017	+	0.568341i
$520$		0			0
$521$	−0.786050			−0.786050			−0.393025	−	0.919528i	$-0.628571\pi$
$521$	−0.786050			−0.786050			−0.393025	+	0.919528i	$0.628571\pi$
$522$		0			0
$523$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$523$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$524$	−0.542281	+	2.37589i	−0.542281	+	2.37589i
$525$	−1.04084	−	0.909354i	−1.04084	−	0.909354i
$526$	0.542281	+	2.37589i	0.542281	+	2.37589i
$527$		0			0
$528$		0			0
$529$	0.623490	−	0.781831i	0.623490	−	0.781831i
$530$		0			0
$531$	−0.0509256	−	0.0638586i	−0.0509256	−	0.0638586i
$532$		0			0
$533$		0			0
$534$	−2.25607	−	2.82902i	−2.25607	−	2.82902i
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−2.01766			−2.01766
$539$		0			0
$540$		0			0
$541$	0.174913	+	0.766342i	0.174913	+	0.766342i	0.983930	+	0.178557i	$0.0571429\pi$
$541$	0.174913	+	0.766342i	0.174913	+	0.766342i	−0.809017	+	0.587785i	$0.800000\pi$
$542$	−1.73205	−	2.17193i	−1.73205	−	2.17193i
$543$		0			0
$544$	1.16747	+	1.46396i	1.16747	+	1.46396i
$545$		0			0
$546$		0			0
$547$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$547$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$548$		0			0
$549$	0.854803	−	1.07189i	0.854803	−	1.07189i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	0.433033	+	1.01313i	0.433033	+	1.01313i
$554$	0.618163	−	2.70835i	0.618163	−	2.70835i
$555$		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		0.222521	−	0.974928i	$-0.428571\pi$
$563$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$564$	0.497629	−	2.18026i	0.497629	−	2.18026i
$565$		0			0
$566$	−1.14590	+	0.551838i	−1.14590	+	0.551838i
$567$	0.0485293	−	1.08059i	0.0485293	−	1.08059i
$568$	−1.24525	−	0.599682i	−1.24525	−	0.599682i
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$	1.79468	+	0.864274i	1.79468	+	0.864274i	0.936235	+	0.351375i	$0.114286\pi$
$571$	1.79468	+	0.864274i	1.79468	+	0.864274i	0.858449	+	0.512899i	$0.171429\pi$
$572$		0			0
$573$	−0.136873	+	0.599682i	−0.136873	+	0.599682i
$574$		0			0
$575$		0			0
$576$	1.32699	+	0.639045i	1.32699	+	0.639045i
$577$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$577$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$578$	−2.52827	+	3.17035i	−2.52827	+	3.17035i
$579$		0			0
$580$		0			0
$581$	−1.77298	+	0.321748i	−1.77298	+	0.321748i
$582$	−2.25607	+	2.82902i	−2.25607	+	2.82902i
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	−2.09373	+	0.785789i	−2.09373	+	0.785789i
$589$		0			0
$590$		0			0
$591$	−1.07457	−	1.34747i	−1.07457	−	1.34747i
$592$		0			0
$593$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$593$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$594$		0			0
$595$		0			0
$596$	0.270836	+	0.339618i	0.270836	+	0.339618i
$597$		0			0
$598$		0			0
$599$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$599$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$600$	−1.24525	−	0.599682i	−1.24525	−	0.599682i
$601$	0.0199667	+	0.0874800i	0.0199667	+	0.0874800i	0.983930	−	0.178557i	$-0.0571429\pi$
$601$	0.0199667	+	0.0874800i	0.0199667	+	0.0874800i	−0.963963	+	0.266037i	$0.914286\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	4.18745			4.18745
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.613682	+	2.68872i	−0.613682	+	2.68872i
$613$	−0.437890	+	1.91852i	−0.437890	+	1.91852i	−0.0448648	+	0.998993i	$0.514286\pi$
$613$	−0.437890	+	1.91852i	−0.437890	+	1.91852i	−0.393025	+	0.919528i	$0.628571\pi$
$614$	−2.01486	+	0.970305i	−2.01486	+	0.970305i
$615$		0			0
$616$		0			0
$617$	1.79468	+	0.864274i	1.79468	+	0.864274i	0.936235	+	0.351375i	$0.114286\pi$
$617$	1.79468	+	0.864274i	1.79468	+	0.864274i	0.858449	+	0.512899i	$0.171429\pi$
$618$	3.83954			3.83954
$619$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$619$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.59203	+	0.288911i	−1.59203	+	0.288911i
$624$		0			0
$625$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$626$		0			0
$627$		0			0
$628$	0.283015	−	1.23997i	0.283015	−	1.23997i
$629$	2.00442	+	2.51346i	2.00442	+	2.51346i
$630$		0			0
$631$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$631$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$632$	0.686957	+	0.861417i	0.686957	+	0.861417i
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−2.11945			−2.11945
$637$		0			0
$638$		0			0
$639$	0.279955	+	1.22656i	0.279955	+	1.22656i
$640$		0			0
$641$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$641$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$642$		0			0
$643$	1.22694	−	1.53853i	1.22694	−	1.53853i	0.473869	−	0.880596i	$-0.342857\pi$
$643$	1.22694	−	1.53853i	1.22694	−	1.53853i	0.753071	−	0.657939i	$-0.228571\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.0559455	+	0.0701535i	−0.0559455	+	0.0701535i	−0.809017	−	0.587785i	$-0.800000\pi$
$647$	−0.0559455	+	0.0701535i	−0.0559455	+	0.0701535i	0.753071	+	0.657939i	$0.228571\pi$
$648$	−0.240696	−	1.05456i	−0.240696	−	1.05456i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.167386	−	0.209896i	0.167386	−	0.209896i	−0.691063	−	0.722795i	$-0.742857\pi$
$653$	0.167386	−	0.209896i	0.167386	−	0.209896i	0.858449	+	0.512899i	$0.171429\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	−1.21850	−	1.06457i	−1.21850	−	1.06457i
$659$	−1.54687	+	0.744934i	−1.54687	+	0.744934i	−0.995974	−	0.0896393i	$-0.971429\pi$
$659$	−1.54687	+	0.744934i	−1.54687	+	0.744934i	−0.550897	+	0.834573i	$0.685714\pi$
$660$		0			0
$661$	0.443250	−	1.94201i	0.443250	−	1.94201i	0.134233	−	0.990950i	$-0.457143\pi$
$661$	0.443250	−	1.94201i	0.443250	−	1.94201i	0.309017	−	0.951057i	$-0.400000\pi$
$662$	0.341229	−	1.49502i	0.341229	−	1.49502i
$663$		0			0
$664$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$665$		0			0
$666$	2.27831	+	1.09717i	2.27831	+	1.09717i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	1.11816	−	0.812393i	1.11816	−	0.812393i
$673$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$673$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$674$	2.86874	+	1.38151i	2.86874	+	1.38151i
$675$	−0.0275965	−	0.120908i	−0.0275965	−	0.120908i
$676$	1.00883	−	1.26503i	1.00883	−	1.26503i
$677$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$677$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$678$		0			0
$679$	0.635928	+	1.48783i	0.635928	+	1.48783i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.00883	−	1.26503i	−1.00883	−	1.26503i	−0.963963	−	0.266037i	$-0.914286\pi$
$683$	−1.00883	−	1.26503i	−1.00883	−	1.26503i	−0.0448648	−	0.998993i	$-0.514286\pi$
$684$		0			0
$685$		0			0
$686$	−0.217194	+	1.60339i	−0.217194	+	1.60339i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$691$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$692$	0.956104	−	1.19892i	0.956104	−	1.19892i
$693$		0			0
$694$	1.11152	+	1.39380i	1.11152	+	1.39380i
$695$		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		0.222521	−	0.974928i	$-0.428571\pi$
$701$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−2.35877	−	1.13592i	−2.35877	−	1.13592i
$707$	0.887305	−	1.64889i	0.887305	−	1.64889i
$708$	−0.180793	+	0.0870652i	−0.180793	+	0.0870652i
$709$	0.0808436	−	0.0389322i	0.0808436	−	0.0389322i	−0.393025	−	0.919528i	$-0.628571\pi$
$709$	0.0808436	−	0.0389322i	0.0808436	−	0.0389322i	0.473869	+	0.880596i	$0.342857\pi$
$710$		0			0
$711$	0.223173	−	0.977785i	0.223173	−	0.977785i
$712$	−1.45780	+	0.702039i	−1.45780	+	0.702039i
$713$		0			0
$714$	3.15345	+	2.75509i	3.15345	+	2.75509i
$715$		0			0
$716$		0			0
$717$	−2.37297			−2.37297
$718$		0			0
$719$	−0.490094	+	0.614559i	−0.490094	+	0.614559i	−0.963963	−	0.266037i	$-0.914286\pi$
$719$	−0.490094	+	0.614559i	−0.490094	+	0.614559i	0.473869	+	0.880596i	$0.342857\pi$
$720$		0			0
$721$	0.813584	−	1.51189i	0.813584	−	1.51189i
$722$	0.360046	+	1.57747i	0.360046	+	1.57747i
$723$	−2.48048	−	1.19454i	−2.48048	−	1.19454i
$724$		0			0
$725$		0			0
$726$	−0.497629	+	2.18026i	−0.497629	+	2.18026i
$727$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$727$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$728$		0			0
$729$	−0.507029	+	0.635795i	−0.507029	+	0.635795i
$730$		0			0
$731$		0			0
$732$	−2.10005	−	2.63339i	−2.10005	−	2.63339i
$733$	−0.0597394	−	0.261736i	−0.0597394	−	0.261736i	0.936235	−	0.351375i	$-0.114286\pi$
$733$	−0.0597394	−	0.261736i	−0.0597394	−	0.261736i	−0.995974	+	0.0896393i	$0.971429\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−1.35699	+	0.653491i	−1.35699	+	0.653491i	−0.963963	−	0.266037i	$-0.914286\pi$
$739$	−1.35699	+	0.653491i	−1.35699	+	0.653491i	−0.393025	+	0.919528i	$0.628571\pi$
$740$		0			0
$741$		0			0
$742$	−0.726664	+	1.35037i	−0.726664	+	1.35037i
$743$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$743$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.47781	+	0.711678i	1.47781	+	0.711678i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$751$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$752$		0			0
$753$	1.52282			1.52282
$754$		0			0
$755$		0			0
$756$	−0.193433	−	0.0533842i	−0.193433	−	0.0533842i
$757$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$757$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$758$	−0.130808	+	0.0629937i	−0.130808	+	0.0629937i
$759$		0			0
$760$		0			0
$761$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$761$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$762$		0			0
$763$		0			0
$764$	0.648781	+	0.312437i	0.648781	+	0.312437i
$765$		0			0
$766$	2.23633			2.23633
$767$		0			0
$768$	0.861741	−	1.08059i	0.861741	−	1.08059i
$769$	−0.416664	+	1.82552i	−0.416664	+	1.82552i	0.134233	+	0.990950i	$0.457143\pi$
$769$	−0.416664	+	1.82552i	−0.416664	+	1.82552i	−0.550897	+	0.834573i	$0.685714\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−0.382046	−	1.67385i	−0.382046	−	1.67385i	−0.691063	−	0.722795i	$-0.742857\pi$
$773$	−0.382046	−	1.67385i	−0.382046	−	1.67385i	0.309017	−	0.951057i	$-0.400000\pi$
$774$		0			0
$775$		0			0
$776$	1.00883	+	1.26503i	1.00883	+	1.26503i
$777$	1.91977	−	1.39480i	1.91977	−	1.39480i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$	−0.749501	−	3.28378i	−0.749501	−	3.28378i
$787$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$787$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$788$	−1.81784	+	0.875428i	−1.81784	+	0.875428i
$789$	−1.29791	−	1.62752i	−1.29791	−	1.62752i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	1.39433	−	1.74843i	1.39433	−	1.74843i
$795$		0			0
$796$		0			0
$797$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$797$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$798$		0			0
$799$	−0.416664	+	1.82552i	−0.416664	+	1.82552i
$800$	0.623490	−	0.781831i	0.623490	−	0.781831i
$801$	1.32699	+	0.639045i	1.32699	+	0.639045i
$802$	−0.434388			−0.434388
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.55280	−	0.747791i	1.55280	−	0.747791i
$808$	0.416664	−	1.82552i	0.416664	−	1.82552i
$809$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$809$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$810$		0			0
$811$	−0.556829	+	0.268155i	−0.556829	+	0.268155i	−0.691063	−	0.722795i	$-0.742857\pi$
$811$	−0.556829	+	0.268155i	−0.556829	+	0.268155i	0.134233	+	0.990950i	$0.457143\pi$
$812$		0			0
$813$	2.13797	+	1.02959i	2.13797	+	1.02959i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$821$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$822$		0			0
$823$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$823$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$824$	0.382046	−	1.67385i	0.382046	−	1.67385i
$825$		0			0
$826$	−0.00651373	+	0.145039i	−0.00651373	+	0.145039i
$827$	−1.20204	+	1.50731i	−1.20204	+	1.50731i	−0.393025	+	0.919528i	$0.628571\pi$
$827$	−1.20204	+	1.50731i	−1.20204	+	1.50731i	−0.809017	+	0.587785i	$0.800000\pi$
$828$		0			0
$829$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$829$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$830$		0			0
$831$	0.528035	+	2.31347i	0.528035	+	2.31347i
$832$		0			0
$833$	1.75307	−	0.657939i	1.75307	−	0.657939i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$839$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$840$		0			0
$841$	0.623490	+	0.781831i	0.623490	+	0.781831i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$	0.327740	+	1.43592i	0.327740	+	1.43592i
$847$	0.753071	+	0.657939i	0.753071	+	0.657939i
$848$		0			0
$849$	0.677372	−	0.849397i	0.677372	−	0.849397i
$850$	2.72968	+	1.31455i	2.72968	+	1.31455i
$851$		0			0
$852$	3.09088			3.09088
$853$	−0.556829	−	0.268155i	−0.556829	−	0.268155i	0.134233	−	0.990950i	$-0.457143\pi$
$853$	−0.556829	−	0.268155i	−0.556829	−	0.268155i	−0.691063	+	0.722795i	$0.742857\pi$
$854$	−2.39783	+	0.435141i	−2.39783	+	0.435141i
$855$		0			0
$856$		0			0
$857$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$857$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$858$		0			0
$859$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$859$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$860$		0			0
$861$		0			0
$862$	2.86874	+	1.38151i	2.86874	+	1.38151i
$863$	−1.38213			−1.38213			−0.691063	−	0.722795i	$-0.742857\pi$
$863$	−1.38213			−1.38213			−0.691063	+	0.722795i	$0.742857\pi$
$864$	0.124018			0.124018
$865$		0			0
$866$		0			0
$867$	0.770769	−	3.37696i	0.770769	−	3.37696i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.327740	−	1.43592i	0.327740	−	1.43592i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$877$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$878$	1.81784	−	0.875428i	1.81784	−	0.875428i
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	1.01783	−	1.06457i	1.01783	−	1.06457i
$883$	−1.92793			−1.92793			−0.963963	−	0.266037i	$-0.914286\pi$
$883$	−1.92793			−1.92793			−0.963963	+	0.266037i	$0.914286\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$887$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$888$	1.47952	−	1.85526i	1.47952	−	1.85526i
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$	−0.540922	−	0.260495i	−0.540922	−	0.260495i
$895$		0			0
$896$	−0.635928	−	1.48783i	−0.635928	−	1.48783i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	1.47285			1.47285
$901$	1.77461			1.77461
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$907$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$908$		0			0
$909$	−1.53566	+	0.739535i	−1.53566	+	0.739535i
$910$		0			0
$911$	−1.35699	−	0.653491i	−1.35699	−	0.653491i	−0.393025	−	0.919528i	$-0.628571\pi$
$911$	−1.35699	−	0.653491i	−1.35699	−	0.653491i	−0.963963	+	0.266037i	$0.914286\pi$
$912$		0			0
$913$		0			0
$914$	2.72968	+	1.31455i	2.72968	+	1.31455i
$915$		0			0
$916$		0			0
$917$	−1.45187	−	0.400690i	−1.45187	−	0.400690i
$918$	0.0836097	+	0.366318i	0.0836097	+	0.366318i
$919$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$919$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$920$		0			0
$921$	1.19103	−	1.49351i	1.19103	−	1.49351i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	1.07047	−	1.34232i	1.07047	−	1.34232i
$926$		0			0
$927$	−1.40807	+	0.678091i	−1.40807	+	0.678091i
$928$		0			0
$929$	−0.0597394	−	0.261736i	−0.0597394	−	0.261736i	0.936235	−	0.351375i	$-0.114286\pi$
$929$	−0.0597394	−	0.261736i	−0.0597394	−	0.261736i	−0.995974	+	0.0896393i	$0.971429\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$937$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.20204	+	1.50731i	−1.20204	+	1.50731i	−0.393025	+	0.919528i	$0.628571\pi$
$941$	−1.20204	+	1.50731i	−1.20204	+	1.50731i	−0.809017	+	0.587785i	$0.800000\pi$
$942$	0.391162	+	1.71379i	0.391162	+	1.71379i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$947$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$948$	−2.21996	−	1.06908i	−2.21996	−	1.06908i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	1.51486	−	1.10061i	1.51486	−	1.10061i
$953$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$953$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$954$	1.25764	−	0.605647i	1.25764	−	0.605647i
$955$		0			0
$956$	−0.618163	+	2.70835i	−0.618163	+	2.70835i
$957$		0			0
$958$	2.86874	−	1.38151i	2.86874	−	1.38151i
$959$		0			0
$960$		0			0
$961$	1.00000			1.00000
$962$		0			0
$963$		0			0
$964$	−2.00953	+	2.51987i	−2.00953	+	2.51987i
$965$		0			0
$966$		0			0
$967$	0.429004	+	1.87959i	0.429004	+	1.87959i	0.473869	+	0.880596i	$0.342857\pi$
$967$	0.429004	+	1.87959i	0.429004	+	1.87959i	−0.0448648	+	0.998993i	$0.514286\pi$
$968$	0.900969	+	0.433884i	0.900969	+	0.433884i
$969$		0			0
$970$		0			0
$971$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$971$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$972$	1.38310	+	1.73435i	1.38310	+	1.73435i
$973$		0			0
$974$	0.448971	−	0.562991i	0.448971	−	0.562991i
$975$		0			0
$976$		0			0
$977$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$977$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−0.694143	−	3.04124i	−0.694143	−	3.04124i
$983$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$983$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	1.33232	+	0.367696i	1.33232	+	0.367696i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.210891	−	0.923976i	−0.210891	−	0.923976i	−0.963963	−	0.266037i	$-0.914286\pi$
$991$	−0.210891	−	0.923976i	−0.210891	−	0.923976i	0.753071	−	0.657939i	$-0.228571\pi$
$992$		0			0
$993$	0.291478	+	1.27705i	0.291478	+	1.27705i
$994$	1.05972	−	1.96930i	1.05972	−	1.96930i
$995$		0			0
$996$	2.51249	−	3.15056i	2.51249	−	3.15056i
$997$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$997$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$998$		0			0
$999$	0.212926			0.212926

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.1.j.b.281.3	✓	24
47.46	odd	2	CM	2303.1.j.b.281.3	✓	24
49.15	even	7	inner	2303.1.j.b.1926.3	yes	24
2303.1926	odd	14	inner	2303.1.j.b.1926.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.1.j.b.281.3	✓	24	1.1	even	1	trivial
2303.1.j.b.281.3	✓	24	47.46	odd	2	CM
2303.1.j.b.1926.3	yes	24	49.15	even	7	inner
2303.1.j.b.1926.3	yes	24	2303.1926	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)

\(f(q)\)	\(=\)	\(q+(0.360046 + 1.57747i) q^{2} +(-0.861741 - 1.08059i) q^{3} +(-1.45780 + 0.702039i) q^{4} +(1.39433 - 1.74843i) q^{6} +(-0.393025 - 0.919528i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-0.202554 + 0.887448i) q^{9} +(2.01486 + 0.970305i) q^{12} +(1.30902 - 0.951057i) q^{14} +(-1.68704 - 0.812434i) q^{17} -1.47285 q^{18} +(-0.654946 + 1.21709i) q^{21} +(-0.307552 + 1.34747i) q^{24} +(-0.222521 + 0.974928i) q^{25} +(-0.111736 + 0.0538092i) q^{27} +(1.21850 + 1.06457i) q^{28} +(-0.900969 - 0.433884i) q^{32} +(0.674176 - 2.95376i) q^{34} +(-0.327740 - 1.43592i) q^{36} +(-1.54687 - 0.744934i) q^{37} +(-2.15573 - 0.594945i) q^{42} +(-0.222521 - 0.974928i) q^{47} +(-0.691063 + 0.722795i) q^{49} -1.61803 q^{50} +(0.575881 + 2.52310i) q^{51} +(-0.853882 + 0.411208i) q^{53} +(-0.125112 - 0.156886i) q^{54} +(-0.473869 + 0.880596i) q^{56} +(-0.0559455 + 0.0701535i) q^{59} +(-1.35699 - 0.653491i) q^{61} +(0.895642 - 0.162535i) q^{63} +(0.360046 - 1.57747i) q^{64} +3.02972 q^{68} +(1.24525 - 0.599682i) q^{71} +(0.820125 - 0.394951i) q^{72} +(0.618163 - 2.70835i) q^{74} +(1.24525 - 0.599682i) q^{75} -1.10179 q^{79} +(0.974558 + 0.469323i) q^{81} +(0.400969 - 1.75676i) q^{83} +(0.100332 - 2.23407i) q^{84} +(0.360046 - 1.57747i) q^{89} +(1.45780 - 0.702039i) q^{94} +(0.307552 + 1.34747i) q^{96} -1.61803 q^{97} +(-1.38900 - 0.829888i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} + q^{7} + 4 q^{8} - 2 q^{9} + 10 q^{12} + 18 q^{14} + 2 q^{17} - 18 q^{18} - 5 q^{21} - 2 q^{24} - 4 q^{25} - 3 q^{27} + 3 q^{28} - 4 q^{32} + 4 q^{34} + 4 q^{36}+ \cdots + 2 q^{98}+O(q^{100}) \) 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

Introduction

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