LMFDB - Embedded newform 2303.1.j.b.1597.3

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			1597.3
Root			$-0.691063 - 0.722795i$ of defining polynomial
Character	$\chi$	$=$	2303.1597
Dual form			2303.1.j.b.610.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.45780 + 0.702039i) q^{2} +(-0.416664 - 1.82552i) q^{3} +(1.00883 + 1.26503i) q^{4} +(0.674176 - 2.95376i) q^{6} +(0.983930 + 0.178557i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-2.25796 + 1.08737i) q^{9} +(1.88900 - 2.36873i) q^{12} +(1.30902 + 0.951057i) q^{14} +(1.07047 - 1.34232i) q^{17} -4.05502 q^{18} +(-0.0840080 - 1.87058i) q^{21} +(1.68704 - 0.812434i) q^{24} +(-0.900969 + 0.433884i) q^{25} +(1.75837 + 2.20493i) q^{27} +(0.766736 + 1.42483i) q^{28} +(0.623490 - 0.781831i) q^{32} +(2.50289 - 1.20533i) q^{34} +(-3.65345 - 1.75941i) q^{36} +(-0.861741 + 1.08059i) q^{37} +(1.19076 - 2.78591i) q^{42} +(-0.900969 - 0.433884i) q^{47} +(0.936235 + 0.351375i) q^{49} -1.61803 q^{50} +(-2.89647 - 1.39487i) q^{51} +(-0.0559455 - 0.0701535i) q^{53} +(1.01541 + 4.44878i) q^{54} +(0.0448648 + 0.998993i) q^{56} +(-0.335148 + 1.46838i) q^{59} +(0.590905 - 0.740971i) q^{61} +(-2.41583 + 0.666726i) q^{63} +(1.45780 - 0.702039i) q^{64} +2.77800 q^{68} +(1.16747 + 1.46396i) q^{71} +(-1.56255 - 1.95938i) q^{72} +(-2.01486 + 0.970305i) q^{74} +(1.16747 + 1.46396i) q^{75} -1.99195 q^{79} +(1.72994 - 2.16928i) q^{81} +(-1.12349 + 0.541044i) q^{83} +(2.28160 - 1.99337i) q^{84} +(1.45780 - 0.702039i) q^{89} +(-1.00883 - 1.26503i) q^{94} +(-1.68704 - 0.812434i) q^{96} -1.61803 q^{97} +(1.11816 + 1.16951i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2303\mathbb{Z}\right)^\times$.

$n$	$99$	$2257$
$\chi(n)$	$-1$	$e\left(\frac{3}{7}\right)$

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 $

$2$	1.45780	+	0.702039i	1.45780	+	0.702039i	0.983930	−	0.178557i	$-0.0571429\pi$
$2$	1.45780	+	0.702039i	1.45780	+	0.702039i	0.473869	+	0.880596i	$0.342857\pi$
$3$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	−0.550897	−	0.834573i	$-0.685714\pi$
$3$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	0.134233	−	0.990950i	$-0.457143\pi$
$4$	1.00883	+	1.26503i	1.00883	+	1.26503i
$5$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$5$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$6$	0.674176	−	2.95376i	0.674176	−	2.95376i
$7$	0.983930	+	0.178557i	0.983930	+	0.178557i
$7$	0.983930	+	0.178557i	0.983930	+	0.178557i
$8$	0.222521	+	0.974928i	0.222521	+	0.974928i
$9$	−2.25796	+	1.08737i	−2.25796	+	1.08737i
$10$		0			0
$11$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$11$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$12$	1.88900	−	2.36873i	1.88900	−	2.36873i
$13$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$13$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$14$	1.30902	+	0.951057i	1.30902	+	0.951057i
$15$		0			0
$16$		0			0
$17$	1.07047	−	1.34232i	1.07047	−	1.34232i	0.134233	−	0.990950i	$-0.457143\pi$
$17$	1.07047	−	1.34232i	1.07047	−	1.34232i	0.936235	−	0.351375i	$-0.114286\pi$
$18$	−4.05502			−4.05502
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$	−0.0840080	−	1.87058i	−0.0840080	−	1.87058i
$22$		0			0
$23$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$23$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$24$	1.68704	−	0.812434i	1.68704	−	0.812434i
$25$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$26$		0			0
$27$	1.75837	+	2.20493i	1.75837	+	2.20493i
$28$	0.766736	+	1.42483i	0.766736	+	1.42483i
$29$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$29$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	0.623490	−	0.781831i	0.623490	−	0.781831i
$33$		0			0
$34$	2.50289	−	1.20533i	2.50289	−	1.20533i
$35$		0			0
$36$	−3.65345	−	1.75941i	−3.65345	−	1.75941i
$37$	−0.861741	+	1.08059i	−0.861741	+	1.08059i	0.134233	+	0.990950i	$0.457143\pi$
$37$	−0.861741	+	1.08059i	−0.861741	+	1.08059i	−0.995974	+	0.0896393i	$0.971429\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$41$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$42$	1.19076	−	2.78591i	1.19076	−	2.78591i
$43$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$43$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$47$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$48$		0			0
$49$	0.936235	+	0.351375i	0.936235	+	0.351375i
$50$	−1.61803			−1.61803
$51$	−2.89647	−	1.39487i	−2.89647	−	1.39487i
$52$		0			0
$53$	−0.0559455	−	0.0701535i	−0.0559455	−	0.0701535i	0.753071	−	0.657939i	$-0.228571\pi$
$53$	−0.0559455	−	0.0701535i	−0.0559455	−	0.0701535i	−0.809017	+	0.587785i	$0.800000\pi$
$54$	1.01541	+	4.44878i	1.01541	+	4.44878i
$55$		0			0
$56$	0.0448648	+	0.998993i	0.0448648	+	0.998993i
$57$		0			0
$58$		0			0
$59$	−0.335148	+	1.46838i	−0.335148	+	1.46838i	0.473869	+	0.880596i	$0.342857\pi$
$59$	−0.335148	+	1.46838i	−0.335148	+	1.46838i	−0.809017	+	0.587785i	$0.800000\pi$
$60$		0			0
$61$	0.590905	−	0.740971i	0.590905	−	0.740971i	−0.393025	−	0.919528i	$-0.628571\pi$
$61$	0.590905	−	0.740971i	0.590905	−	0.740971i	0.983930	+	0.178557i	$0.0571429\pi$
$62$		0			0
$63$	−2.41583	+	0.666726i	−2.41583	+	0.666726i
$64$	1.45780	−	0.702039i	1.45780	−	0.702039i
$65$		0			0
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	2.77800			2.77800
$69$		0			0
$70$		0			0
$71$	1.16747	+	1.46396i	1.16747	+	1.46396i	0.858449	+	0.512899i	$0.171429\pi$
$71$	1.16747	+	1.46396i	1.16747	+	1.46396i	0.309017	+	0.951057i	$0.400000\pi$
$72$	−1.56255	−	1.95938i	−1.56255	−	1.95938i
$73$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$73$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$74$	−2.01486	+	0.970305i	−2.01486	+	0.970305i
$75$	1.16747	+	1.46396i	1.16747	+	1.46396i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.99195			−1.99195			−0.995974	−	0.0896393i	$-0.971429\pi$
$79$	−1.99195			−1.99195			−0.995974	+	0.0896393i	$0.971429\pi$
$80$		0			0
$81$	1.72994	−	2.16928i	1.72994	−	2.16928i
$82$		0			0
$83$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$83$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$84$	2.28160	−	1.99337i	2.28160	−	1.99337i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.45780	−	0.702039i	1.45780	−	0.702039i	0.473869	−	0.880596i	$-0.342857\pi$
$89$	1.45780	−	0.702039i	1.45780	−	0.702039i	0.983930	+	0.178557i	$0.0571429\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−1.00883	−	1.26503i	−1.00883	−	1.26503i
$95$		0			0
$96$	−1.68704	−	0.812434i	−1.68704	−	0.812434i
$97$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$97$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$98$	1.11816	+	1.16951i	1.11816	+	1.16951i
$99$		0			0
$100$	−1.45780	−	0.702039i	−1.45780	−	0.702039i
$101$	−0.382046	−	1.67385i	−0.382046	−	1.67385i	−0.691063	−	0.722795i	$-0.742857\pi$
$101$	−0.382046	−	1.67385i	−0.382046	−	1.67385i	0.309017	−	0.951057i	$-0.400000\pi$
$102$	−3.24322	−	4.06687i	−3.24322	−	4.06687i
$103$	0.307552	+	1.34747i	0.307552	+	1.34747i	0.858449	+	0.512899i	$0.171429\pi$
$103$	0.307552	+	1.34747i	0.307552	+	1.34747i	−0.550897	+	0.834573i	$0.685714\pi$
$104$		0			0
$105$		0			0
$106$	−0.0323068	−	0.141546i	−0.0323068	−	0.141546i
$107$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$107$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$108$	−1.01541	+	4.44878i	−1.01541	+	4.44878i
$109$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$109$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$110$		0			0
$111$	2.33170	+	1.12289i	2.33170	+	1.12289i
$112$		0			0
$113$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$113$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.51944	+	1.90532i	−1.51944	+	1.90532i
$119$	1.29295	−	1.12961i	1.29295	−	1.12961i
$120$		0			0
$121$	0.623490	+	0.781831i	0.623490	+	0.781831i
$122$	1.38161	−	0.665348i	1.38161	−	0.665348i
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−3.98986	−	0.724053i	−3.98986	−	0.724053i
$127$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$127$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$128$	1.61803			1.61803
$129$		0			0
$130$		0			0
$131$	−0.210891	+	0.923976i	−0.210891	+	0.923976i	0.753071	+	0.657939i	$0.228571\pi$
$131$	−0.210891	+	0.923976i	−0.210891	+	0.923976i	−0.963963	+	0.266037i	$0.914286\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	1.54687	+	0.744934i	1.54687	+	0.744934i
$137$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$137$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$138$		0			0
$139$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$139$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$140$		0			0
$141$	−0.416664	+	1.82552i	−0.416664	+	1.82552i
$142$	0.674176	+	2.95376i	0.674176	+	2.95376i
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.251348	−	1.85552i	0.251348	−	1.85552i
$148$	−2.23633			−2.23633
$149$	0.992682	+	0.478050i	0.992682	+	0.478050i	0.858449	−	0.512899i	$-0.171429\pi$
$149$	0.992682	+	0.478050i	0.992682	+	0.478050i	0.134233	+	0.990950i	$0.457143\pi$
$150$	0.674176	+	2.95376i	0.674176	+	2.95376i
$151$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$151$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$152$		0			0
$153$	−0.957461	+	4.19491i	−0.957461	+	4.19491i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.437890	+	1.91852i	−0.437890	+	1.91852i	−0.0448648	+	0.998993i	$0.514286\pi$
$157$	−0.437890	+	1.91852i	−0.437890	+	1.91852i	−0.393025	+	0.919528i	$0.628571\pi$
$158$	−2.90386	−	1.39842i	−2.90386	−	1.39842i
$159$	−0.104756	+	0.131360i	−0.104756	+	0.131360i
$160$		0			0
$161$		0			0
$162$	4.04482	−	1.94788i	4.04482	−	1.94788i
$163$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$163$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$164$		0			0
$165$		0			0
$166$	−2.01766			−2.01766
$167$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$167$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$168$	1.80499	−	0.498146i	1.80499	−	0.498146i
$169$	0.623490	+	0.781831i	0.623490	+	0.781831i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.0559455	−	0.0701535i	−0.0559455	−	0.0701535i	0.753071	−	0.657939i	$-0.228571\pi$
$173$	−0.0559455	−	0.0701535i	−0.0559455	−	0.0701535i	−0.809017	+	0.587785i	$0.800000\pi$
$174$		0			0
$175$	−0.963963	+	0.266037i	−0.963963	+	0.266037i
$176$		0			0
$177$	2.82021			2.82021
$178$	2.61803			2.61803
$179$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$179$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$180$		0			0
$181$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$181$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$182$		0			0
$183$	−1.59887	−	0.769974i	−1.59887	−	0.769974i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.360046	−	1.57747i	−0.360046	−	1.57747i
$189$	1.33641	+	2.48346i	1.33641	+	2.48346i
$190$		0			0
$191$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$191$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$192$	−1.88900	−	2.36873i	−1.88900	−	2.36873i
$193$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$193$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$194$	−2.35877	−	1.13592i	−2.35877	−	1.13592i
$195$		0			0
$196$	0.500000	+	1.53884i	0.500000	+	1.53884i
$197$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$197$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$198$		0			0
$199$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$199$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$200$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$201$		0			0
$202$	0.618163	−	2.70835i	0.618163	−	2.70835i
$203$		0			0
$204$	−1.15749	−	5.07130i	−1.15749	−	5.07130i
$205$		0			0
$206$	−0.497629	+	2.18026i	−0.497629	+	2.18026i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$211$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$212$	0.0323068	−	0.141546i	0.0323068	−	0.141546i
$213$	2.18604	−	2.74121i	2.18604	−	2.74121i
$214$		0			0
$215$		0			0
$216$	−1.75837	+	2.20493i	−1.75837	+	2.20493i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$	2.61083	+	3.27388i	2.61083	+	3.27388i
$223$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$223$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$224$	0.753071	−	0.657939i	0.753071	−	0.657939i
$225$	1.56255	−	1.95938i	1.56255	−	1.95938i
$226$		0			0
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$		0			0
$229$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$229$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$233$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$234$		0			0
$235$		0			0
$236$	−2.19565	+	1.05737i	−2.19565	+	1.05737i
$237$	0.829973	+	3.63635i	0.829973	+	3.63635i
$238$	2.67789	−	0.739050i	2.67789	−	0.739050i
$239$	0.307552	−	1.34747i	0.307552	−	1.34747i	−0.550897	−	0.834573i	$-0.685714\pi$
$239$	0.307552	−	1.34747i	0.307552	−	1.34747i	0.858449	−	0.512899i	$-0.171429\pi$
$240$		0			0
$241$	0.167386	+	0.209896i	0.167386	+	0.209896i	0.858449	−	0.512899i	$-0.171429\pi$
$241$	0.167386	+	0.209896i	0.167386	+	0.209896i	−0.691063	+	0.722795i	$0.742857\pi$
$242$	0.360046	+	1.57747i	0.360046	+	1.57747i
$243$	−2.13995	−	1.03055i	−2.13995	−	1.03055i
$244$	1.53347			1.53347
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	1.45581	+	1.82552i	1.45581	+	1.82552i
$250$		0			0
$251$	0.443250	−	1.94201i	0.443250	−	1.94201i	0.134233	−	0.990950i	$-0.457143\pi$
$251$	0.443250	−	1.94201i	0.443250	−	1.94201i	0.309017	−	0.951057i	$-0.400000\pi$
$252$	−3.28058	−	2.38348i	−3.28058	−	2.38348i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.900969	+	0.433884i	0.900969	+	0.433884i
$257$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$257$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$258$		0			0
$259$	−1.04084	+	0.909354i	−1.04084	+	0.909354i
$260$		0			0
$261$		0			0
$262$	−0.956104	+	1.19892i	−0.956104	+	1.19892i
$263$	0.947737			0.947737			0.473869	−	0.880596i	$-0.342857\pi$
$263$	0.947737			0.947737			0.473869	+	0.880596i	$0.342857\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.88900	−	2.36873i	−1.88900	−	2.36873i
$268$		0			0
$269$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$269$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$270$		0			0
$271$	−0.861741	−	1.08059i	−0.861741	−	1.08059i	−0.995974	−	0.0896393i	$-0.971429\pi$
$271$	−0.861741	−	1.08059i	−0.861741	−	1.08059i	0.134233	−	0.990950i	$-0.457143\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.861741	+	1.08059i	−0.861741	+	1.08059i	0.134233	+	0.990950i	$0.457143\pi$
$277$	−0.861741	+	1.08059i	−0.861741	+	1.08059i	−0.995974	+	0.0896393i	$0.971429\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$281$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$282$	−1.88900	+	2.36873i	−1.88900	+	2.36873i
$283$	−1.77298	−	0.853822i	−1.77298	−	0.853822i	−0.963963	−	0.266037i	$-0.914286\pi$
$283$	−1.77298	−	0.853822i	−1.77298	−	0.853822i	−0.809017	−	0.587785i	$-0.800000\pi$
$284$	−0.674176	+	2.95376i	−0.674176	+	2.95376i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.557669	+	2.44331i	−0.557669	+	2.44331i
$289$	−0.433412	−	1.89890i	−0.433412	−	1.89890i
$290$		0			0
$291$	0.674176	+	2.95376i	0.674176	+	2.95376i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	1.66906	−	2.52852i	1.66906	−	2.52852i
$295$		0			0
$296$	−1.24525	−	0.599682i	−1.24525	−	0.599682i
$297$		0			0
$298$	1.11152	+	1.39380i	1.11152	+	1.39380i
$299$		0			0
$300$	−0.674176	+	2.95376i	−0.674176	+	2.95376i
$301$		0			0
$302$		0			0
$303$	−2.89647	+	1.39487i	−2.89647	+	1.39487i
$304$		0			0
$305$		0			0
$306$	−4.34077	+	5.44316i	−4.34077	+	5.44316i
$307$	−1.68704	−	0.812434i	−1.68704	−	0.812434i	−0.995974	−	0.0896393i	$-0.971429\pi$
$307$	−1.68704	−	0.812434i	−1.68704	−	0.812434i	−0.691063	−	0.722795i	$-0.742857\pi$
$308$		0			0
$309$	2.33170	−	1.12289i	2.33170	−	1.12289i
$310$		0			0
$311$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$311$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$312$		0			0
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	−1.98523	+	2.48940i	−1.98523	+	2.48940i
$315$		0			0
$316$	−2.00953	−	2.51987i	−2.00953	−	2.51987i
$317$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$317$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$318$	−0.244934	+	0.117954i	−0.244934	+	0.117954i
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	4.48941			4.48941
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$330$		0			0
$331$	−0.0559455	+	0.0701535i	−0.0559455	+	0.0701535i	−0.809017	−	0.587785i	$-0.800000\pi$
$331$	−0.0559455	+	0.0701535i	−0.0559455	+	0.0701535i	0.753071	+	0.657939i	$0.228571\pi$
$332$	−1.81784	−	0.875428i	−1.81784	−	0.875428i
$333$	0.770769	−	3.37696i	0.770769	−	3.37696i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.429004	−	1.87959i	0.429004	−	1.87959i	−0.0448648	−	0.998993i	$-0.514286\pi$
$337$	0.429004	−	1.87959i	0.429004	−	1.87959i	0.473869	−	0.880596i	$-0.342857\pi$
$338$	0.360046	+	1.57747i	0.360046	+	1.57747i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.858449	+	0.512899i	0.858449	+	0.512899i
$344$		0			0
$345$		0			0
$346$	−0.0323068	−	0.141546i	−0.0323068	−	0.141546i
$347$	−1.24196	−	1.55737i	−1.24196	−	1.55737i	−0.691063	−	0.722795i	$-0.742857\pi$
$347$	−1.24196	−	1.55737i	−1.24196	−	1.55737i	−0.550897	−	0.834573i	$-0.685714\pi$
$348$		0			0
$349$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$349$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$350$	−1.59203	−	0.288911i	−1.59203	−	0.288911i
$351$		0			0
$352$		0			0
$353$	0.360046	−	1.57747i	0.360046	−	1.57747i	−0.393025	−	0.919528i	$-0.628571\pi$
$353$	0.360046	−	1.57747i	0.360046	−	1.57747i	0.753071	−	0.657939i	$-0.228571\pi$
$354$	4.11129	+	1.97989i	4.11129	+	1.97989i
$355$		0			0
$356$	2.35877	+	1.13592i	2.35877	+	1.13592i
$357$	−2.60086	−	1.88963i	−2.60086	−	1.88963i
$358$		0			0
$359$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$359$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$360$		0			0
$361$	1.00000			1.00000
$362$		0			0
$363$	1.16747	−	1.46396i	1.16747	−	1.46396i
$364$		0			0
$365$		0			0
$366$	−1.79028	−	2.24493i	−1.79028	−	2.24493i
$367$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$367$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.0425201	−	0.0790155i	−0.0425201	−	0.0790155i
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$		0			0
$376$	0.222521	−	0.974928i	0.222521	−	0.974928i
$377$		0			0
$378$	0.204727	+	4.55860i	0.204727	+	4.55860i
$379$	−1.35699	−	0.653491i	−1.35699	−	0.653491i	−0.393025	−	0.919528i	$-0.628571\pi$
$379$	−1.35699	−	0.653491i	−1.35699	−	0.653491i	−0.963963	+	0.266037i	$0.914286\pi$
$380$		0			0
$381$		0			0
$382$	−0.648781	+	2.84250i	−0.648781	+	2.84250i
$383$	−1.68704	+	0.812434i	−1.68704	+	0.812434i	−0.691063	+	0.722795i	$0.742857\pi$
$383$	−1.68704	+	0.812434i	−1.68704	+	0.812434i	−0.995974	+	0.0896393i	$0.971429\pi$
$384$	−0.674176	−	2.95376i	−0.674176	−	2.95376i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−1.63232	−	2.04686i	−1.63232	−	2.04686i
$389$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$389$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$390$		0			0
$391$		0			0
$392$	−0.134233	+	0.990950i	−0.134233	+	0.990950i
$393$	1.77461			1.77461
$394$	−0.648781	−	0.312437i	−0.648781	−	0.312437i
$395$		0			0
$396$		0			0
$397$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	−0.550897	−	0.834573i	$-0.685714\pi$
$397$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	0.134233	−	0.990950i	$-0.457143\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.992682	−	0.478050i	0.992682	−	0.478050i	0.134233	−	0.990950i	$-0.457143\pi$
$401$	0.992682	−	0.478050i	0.992682	−	0.478050i	0.858449	+	0.512899i	$0.171429\pi$
$402$		0			0
$403$		0			0
$404$	1.73205	−	2.17193i	1.73205	−	2.17193i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.715369	−	3.13424i	0.715369	−	3.13424i
$409$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$409$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$410$		0			0
$411$		0			0
$412$	−1.39433	+	1.74843i	−1.39433	+	1.74843i
$413$	−0.591952	+	1.38494i	−0.591952	+	1.38494i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$419$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$420$		0			0
$421$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$421$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$422$		0			0
$423$	2.50614			2.50614
$424$	0.0559455	−	0.0701535i	0.0559455	−	0.0701535i
$425$	−0.382046	+	1.67385i	−0.382046	+	1.67385i
$426$	5.11125	−	2.46145i	5.11125	−	2.46145i
$427$	0.713714	−	0.623553i	0.713714	−	0.623553i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.429004	−	1.87959i	0.429004	−	1.87959i	−0.0448648	−	0.998993i	$-0.514286\pi$
$431$	0.429004	−	1.87959i	0.429004	−	1.87959i	0.473869	−	0.880596i	$-0.342857\pi$
$432$		0			0
$433$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$433$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$439$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$440$		0			0
$441$	−2.49605	+	0.224649i	−2.49605	+	0.224649i
$442$		0			0
$443$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$443$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$444$	0.931796	+	4.08246i	0.931796	+	4.08246i
$445$		0			0
$446$		0			0
$447$	0.459078	−	2.01135i	0.459078	−	2.01135i
$448$	1.55972	−	0.430457i	1.55972	−	0.430457i
$449$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$449$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$450$	3.65345	−	1.75941i	3.65345	−	1.75941i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.382046	+	1.67385i	−0.382046	+	1.67385i	0.309017	+	0.951057i	$0.400000\pi$
$457$	−0.382046	+	1.67385i	−0.382046	+	1.67385i	−0.691063	+	0.722795i	$0.742857\pi$
$458$		0			0
$459$	4.84201			4.84201
$460$		0			0
$461$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$461$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$462$		0			0
$463$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$463$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$467$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	3.68476			3.68476
$472$	−1.50614			−1.50614
$473$		0			0
$474$	−1.34292	+	5.88373i	−1.34292	+	5.88373i
$475$		0			0
$476$	2.73336	+	0.496031i	2.73336	+	0.496031i
$477$	0.202606	+	0.0975698i	0.202606	+	0.0975698i
$478$	1.39433	−	1.74843i	1.39433	−	1.74843i
$479$	1.73700	+	0.836496i	1.73700	+	0.836496i	0.983930	+	0.178557i	$0.0571429\pi$
$479$	1.73700	+	0.836496i	1.73700	+	0.836496i	0.753071	+	0.657939i	$0.228571\pi$
$480$		0			0
$481$		0			0
$482$	0.0966604	+	0.423497i	0.0966604	+	0.423497i
$483$		0			0
$484$	−0.360046	+	1.57747i	−0.360046	+	1.57747i
$485$		0			0
$486$	−2.39613	−	3.00466i	−2.39613	−	3.00466i
$487$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$487$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$488$	0.853882	+	0.411208i	0.853882	+	0.411208i
$489$		0			0
$490$		0			0
$491$	−0.786050			−0.786050			−0.393025	−	0.919528i	$-0.628571\pi$
$491$	−0.786050			−0.786050			−0.393025	+	0.919528i	$0.628571\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.887305	+	1.64889i	0.887305	+	1.64889i
$498$	0.840684	+	3.68328i	0.840684	+	3.68328i
$499$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$499$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$500$		0			0
$501$		0			0
$502$	2.00953	−	2.51987i	2.00953	−	2.51987i
$503$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$503$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$504$	−1.18758	−	2.20690i	−1.18758	−	2.20690i
$505$		0			0
$506$		0			0
$507$	1.16747	−	1.46396i	1.16747	−	1.46396i
$508$		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
$518$	−2.15573	+	0.594945i	−2.15573	+	0.594945i
$519$	−0.104756	+	0.131360i	−0.104756	+	0.131360i
$520$		0			0
$521$	1.96786			1.96786			0.983930	−	0.178557i	$-0.0571429\pi$
$521$	1.96786			1.96786			0.983930	+	0.178557i	$0.0571429\pi$
$522$		0			0
$523$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$523$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$524$	−1.38161	+	0.665348i	−1.38161	+	0.665348i
$525$	0.887305	+	1.64889i	0.887305	+	1.64889i
$526$	1.38161	+	0.665348i	1.38161	+	0.665348i
$527$		0			0
$528$		0			0
$529$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$530$		0			0
$531$	−0.839930	−	3.67997i	−0.839930	−	3.67997i
$532$		0			0
$533$		0			0
$534$	−1.09084	−	4.77928i	−1.09084	−	4.77928i
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.720093			0.720093
$539$		0			0
$540$		0			0
$541$	−1.77298	−	0.853822i	−1.77298	−	0.853822i	−0.963963	−	0.266037i	$-0.914286\pi$
$541$	−1.77298	−	0.853822i	−1.77298	−	0.853822i	−0.809017	−	0.587785i	$-0.800000\pi$
$542$	−0.497629	−	2.18026i	−0.497629	−	2.18026i
$543$		0			0
$544$	−0.382046	−	1.67385i	−0.382046	−	1.67385i
$545$		0			0
$546$		0			0
$547$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$547$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$548$		0			0
$549$	−0.528524	+	2.31561i	−0.528524	+	2.31561i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−1.95994	−	0.355676i	−1.95994	−	0.355676i
$554$	−2.01486	+	0.970305i	−2.01486	+	0.970305i
$555$		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		0.900969	−	0.433884i	$-0.142857\pi$
$563$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$564$	−2.72968	+	1.31455i	−2.72968	+	1.31455i
$565$		0			0
$566$	−1.98523	−	2.48940i	−1.98523	−	2.48940i
$567$	2.08948	−	1.82552i	2.08948	−	1.82552i
$568$	−1.16747	+	1.46396i	−1.16747	+	1.46396i
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$	0.167386	−	0.209896i	0.167386	−	0.209896i	−0.691063	−	0.722795i	$-0.742857\pi$
$571$	0.167386	−	0.209896i	0.167386	−	0.209896i	0.858449	+	0.512899i	$0.171429\pi$
$572$		0			0
$573$	3.03994	−	1.46396i	3.03994	−	1.46396i
$574$		0			0
$575$		0			0
$576$	−2.52827	+	3.17035i	−2.52827	+	3.17035i
$577$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$577$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$578$	0.701276	−	3.07249i	0.701276	−	3.07249i
$579$		0			0
$580$		0			0
$581$	−1.20204	+	0.331743i	−1.20204	+	0.331743i
$582$	−1.09084	+	4.77928i	−1.09084	+	4.77928i
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	2.60086	−	1.55394i	2.60086	−	1.55394i
$589$		0			0
$590$		0			0
$591$	0.185433	+	0.812434i	0.185433	+	0.812434i
$592$		0			0
$593$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$593$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$594$		0			0
$595$		0			0
$596$	0.396697	+	1.73804i	0.396697	+	1.73804i
$597$		0			0
$598$		0			0
$599$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$599$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$600$	−1.16747	+	1.46396i	−1.16747	+	1.46396i
$601$	−1.35699	−	0.653491i	−1.35699	−	0.653491i	−0.393025	−	0.919528i	$-0.628571\pi$
$601$	−1.35699	−	0.653491i	−1.35699	−	0.653491i	−0.963963	+	0.266037i	$0.914286\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	−5.20172			−5.20172
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−6.27260	+	3.02073i	−6.27260	+	3.02073i
$613$	1.73700	−	0.836496i	1.73700	−	0.836496i	0.753071	−	0.657939i	$-0.228571\pi$
$613$	1.73700	−	0.836496i	1.73700	−	0.836496i	0.983930	−	0.178557i	$-0.0571429\pi$
$614$	−1.88900	−	2.36873i	−1.88900	−	2.36873i
$615$		0			0
$616$		0			0
$617$	0.167386	−	0.209896i	0.167386	−	0.209896i	−0.691063	−	0.722795i	$-0.742857\pi$
$617$	0.167386	−	0.209896i	0.167386	−	0.209896i	0.858449	+	0.512899i	$0.171429\pi$
$618$	4.18745			4.18745
$619$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$619$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.55972	−	0.430457i	1.55972	−	0.430457i
$624$		0			0
$625$	0.623490	−	0.781831i	0.623490	−	0.781831i
$626$		0			0
$627$		0			0
$628$	−2.86874	+	1.38151i	−2.86874	+	1.38151i
$629$	0.528035	+	2.31347i	0.528035	+	2.31347i
$630$		0			0
$631$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$631$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$632$	−0.443250	−	1.94201i	−0.443250	−	1.94201i
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−0.271856			−0.271856
$637$		0			0
$638$		0			0
$639$	−4.22796	−	2.03608i	−4.22796	−	2.03608i
$640$		0			0
$641$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$641$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$642$		0			0
$643$	0.429004	−	1.87959i	0.429004	−	1.87959i	−0.0448648	−	0.998993i	$-0.514286\pi$
$643$	0.429004	−	1.87959i	0.429004	−	1.87959i	0.473869	−	0.880596i	$-0.342857\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.335148	+	1.46838i	−0.335148	+	1.46838i	0.473869	+	0.880596i	$0.342857\pi$
$647$	−0.335148	+	1.46838i	−0.335148	+	1.46838i	−0.809017	+	0.587785i	$0.800000\pi$
$648$	2.49984	+	1.20386i	2.49984	+	1.20386i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.245172	−	1.07417i	0.245172	−	1.07417i	−0.691063	−	0.722795i	$-0.742857\pi$
$653$	0.245172	−	1.07417i	0.245172	−	1.07417i	0.936235	−	0.351375i	$-0.114286\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	−0.766736	−	1.42483i	−0.766736	−	1.42483i
$659$	−0.861741	−	1.08059i	−0.861741	−	1.08059i	−0.995974	−	0.0896393i	$-0.971429\pi$
$659$	−0.861741	−	1.08059i	−0.861741	−	1.08059i	0.134233	−	0.990950i	$-0.457143\pi$
$660$		0			0
$661$	−0.241880	+	0.116483i	−0.241880	+	0.116483i	−0.550897	−	0.834573i	$-0.685714\pi$
$661$	−0.241880	+	0.116483i	−0.241880	+	0.116483i	0.309017	+	0.951057i	$0.400000\pi$
$662$	−0.130808	+	0.0629937i	−0.130808	+	0.0629937i
$663$		0			0
$664$	−0.777479	−	0.974928i	−0.777479	−	0.974928i
$665$		0			0
$666$	3.49438	−	4.38182i	3.49438	−	4.38182i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−1.51486	−	1.10061i	−1.51486	−	1.10061i
$673$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$673$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$674$	1.94494	−	2.43888i	1.94494	−	2.43888i
$675$	−2.54092	−	1.22364i	−2.54092	−	1.22364i
$676$	−0.360046	+	1.57747i	−0.360046	+	1.57747i
$677$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$677$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$678$		0			0
$679$	−1.59203	−	0.288911i	−1.59203	−	0.288911i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.360046	+	1.57747i	0.360046	+	1.57747i	0.753071	+	0.657939i	$0.228571\pi$
$683$	0.360046	+	1.57747i	0.360046	+	1.57747i	−0.393025	+	0.919528i	$0.628571\pi$
$684$		0			0
$685$		0			0
$686$	0.891370	+	1.35037i	0.891370	+	1.35037i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$691$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$692$	0.0323068	−	0.141546i	0.0323068	−	0.141546i
$693$		0			0
$694$	−0.717194	−	3.14223i	−0.717194	−	3.14223i
$695$		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		0.900969	−	0.433884i	$-0.142857\pi$
$701$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	1.63232	−	2.04686i	1.63232	−	2.04686i
$707$	−0.0770283	−	1.71517i	−0.0770283	−	1.71517i
$708$	2.84510	+	3.56765i	2.84510	+	3.56765i
$709$	0.939065	+	1.17755i	0.939065	+	1.17755i	0.983930	+	0.178557i	$0.0571429\pi$
$709$	0.939065	+	1.17755i	0.939065	+	1.17755i	−0.0448648	+	0.998993i	$0.514286\pi$
$710$		0			0
$711$	4.49773	−	2.16599i	4.49773	−	2.16599i
$712$	1.00883	+	1.26503i	1.00883	+	1.26503i
$713$		0			0
$714$	−2.46493	−	4.58061i	−2.46493	−	4.58061i
$715$		0			0
$716$		0			0
$717$	−2.58799			−2.58799
$718$		0			0
$719$	−0.437890	+	1.91852i	−0.437890	+	1.91852i	−0.0448648	+	0.998993i	$0.514286\pi$
$719$	−0.437890	+	1.91852i	−0.437890	+	1.91852i	−0.393025	+	0.919528i	$0.628571\pi$
$720$		0			0
$721$	0.0620088	+	1.38073i	0.0620088	+	1.38073i
$722$	1.45780	+	0.702039i	1.45780	+	0.702039i
$723$	0.313425	−	0.393023i	0.313425	−	0.393023i
$724$		0			0
$725$		0			0
$726$	2.72968	−	1.31455i	2.72968	−	1.31455i
$727$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$727$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$728$		0			0
$729$	−0.372236	+	1.63087i	−0.372236	+	1.63087i
$730$		0			0
$731$		0			0
$732$	−0.638942	−	2.79939i	−0.638942	−	2.79939i
$733$	0.992682	+	0.478050i	0.992682	+	0.478050i	0.858449	−	0.512899i	$-0.171429\pi$
$733$	0.992682	+	0.478050i	0.992682	+	0.478050i	0.134233	+	0.990950i	$0.457143\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	0.590905	+	0.740971i	0.590905	+	0.740971i	0.983930	−	0.178557i	$-0.0571429\pi$
$739$	0.590905	+	0.740971i	0.590905	+	0.740971i	−0.393025	+	0.919528i	$0.628571\pi$
$740$		0			0
$741$		0			0
$742$	−0.00651373	−	0.145039i	−0.00651373	−	0.145039i
$743$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$743$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.94847	−	2.44331i	1.94847	−	2.44331i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$751$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$752$		0			0
$753$	−3.72986			−3.72986
$754$		0			0
$755$		0			0
$756$	−1.79345	+	4.19598i	−1.79345	+	4.19598i
$757$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$757$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$758$	−1.51944	−	1.90532i	−1.51944	−	1.90532i
$759$		0			0
$760$		0			0
$761$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$761$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$762$		0			0
$763$		0			0
$764$	−1.81784	+	2.27951i	−1.81784	+	2.27951i
$765$		0			0
$766$	−3.02972			−3.02972
$767$		0			0
$768$	0.416664	−	1.82552i	0.416664	−	1.82552i
$769$	−1.54687	+	0.744934i	−1.54687	+	0.744934i	−0.995974	−	0.0896393i	$-0.971429\pi$
$769$	−1.54687	+	0.744934i	−1.54687	+	0.744934i	−0.550897	+	0.834573i	$0.685714\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.24525	+	0.599682i	1.24525	+	0.599682i	0.936235	−	0.351375i	$-0.114286\pi$
$773$	1.24525	+	0.599682i	1.24525	+	0.599682i	0.309017	+	0.951057i	$0.400000\pi$
$774$		0			0
$775$		0			0
$776$	−0.360046	−	1.57747i	−0.360046	−	1.57747i
$777$	2.09373	+	1.52118i	2.09373	+	1.52118i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$	2.58702	+	1.24584i	2.58702	+	1.24584i
$787$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$787$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$788$	−0.448971	−	0.562991i	−0.448971	−	0.562991i
$789$	−0.394888	−	1.73012i	−0.394888	−	1.73012i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	0.674176	−	2.95376i	0.674176	−	2.95376i
$795$		0			0
$796$		0			0
$797$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$797$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$798$		0			0
$799$	−1.54687	+	0.744934i	−1.54687	+	0.744934i
$800$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$801$	−2.52827	+	3.17035i	−2.52827	+	3.17035i
$802$	1.78274			1.78274
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.519571	−	0.651522i	−0.519571	−	0.651522i
$808$	1.54687	−	0.744934i	1.54687	−	0.744934i
$809$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$809$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$810$		0			0
$811$	0.385338	+	0.483198i	0.385338	+	0.483198i	0.936235	−	0.351375i	$-0.114286\pi$
$811$	0.385338	+	0.483198i	0.385338	+	0.483198i	−0.550897	+	0.834573i	$0.685714\pi$
$812$		0			0
$813$	−1.61358	+	2.02337i	−1.61358	+	2.02337i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$821$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$822$		0			0
$823$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$823$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$824$	−1.24525	+	0.599682i	−1.24525	+	0.599682i
$825$		0			0
$826$	−1.83523	+	1.60339i	−1.83523	+	1.60339i
$827$	0.174913	−	0.766342i	0.174913	−	0.766342i	−0.809017	−	0.587785i	$-0.800000\pi$
$827$	0.174913	−	0.766342i	0.174913	−	0.766342i	0.983930	−	0.178557i	$-0.0571429\pi$
$828$		0			0
$829$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$829$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$830$		0			0
$831$	2.33170	+	1.12289i	2.33170	+	1.12289i
$832$		0			0
$833$	1.47387	−	0.880596i	1.47387	−	0.880596i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$839$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$840$		0			0
$841$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$	3.65345	+	1.75941i	3.65345	+	1.75941i
$847$	0.473869	+	0.880596i	0.473869	+	0.880596i
$848$		0			0
$849$	−0.819936	+	3.59237i	−0.819936	+	3.59237i
$850$	−1.73205	+	2.17193i	−1.73205	+	2.17193i
$851$		0			0
$852$	5.67306			5.67306
$853$	0.385338	−	0.483198i	0.385338	−	0.483198i	−0.550897	−	0.834573i	$-0.685714\pi$
$853$	0.385338	−	0.483198i	0.385338	−	0.483198i	0.936235	+	0.351375i	$0.114286\pi$
$854$	1.47821	−	0.407960i	1.47821	−	0.407960i
$855$		0			0
$856$		0			0
$857$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$857$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$858$		0			0
$859$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$859$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$860$		0			0
$861$		0			0
$862$	1.94494	−	2.43888i	1.94494	−	2.43888i
$863$	1.87247			1.87247			0.936235	−	0.351375i	$-0.114286\pi$
$863$	1.87247			1.87247			0.936235	+	0.351375i	$0.114286\pi$
$864$	2.82021			2.82021
$865$		0			0
$866$		0			0
$867$	−3.28590	+	1.58241i	−3.28590	+	1.58241i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	3.65345	−	1.75941i	3.65345	−	1.75941i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$877$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$878$	0.448971	+	0.562991i	0.448971	+	0.562991i
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−3.79646	−	1.42483i	−3.79646	−	1.42483i
$883$	−0.786050			−0.786050			−0.393025	−	0.919528i	$-0.628571\pi$
$883$	−0.786050			−0.786050			−0.393025	+	0.919528i	$0.628571\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$887$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$888$	−0.575881	+	2.52310i	−0.575881	+	2.52310i
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$	2.08129	−	2.60985i	2.08129	−	2.60985i
$895$		0			0
$896$	1.59203	+	0.288911i	1.59203	+	0.288911i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	4.05502			4.05502
$901$	−0.154057			−0.154057
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−1.80194	+	0.867767i	−1.80194	+	0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$907$	−1.80194	+	0.867767i	−1.80194	+	0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$908$		0			0
$909$	2.68275	+	3.36406i	2.68275	+	3.36406i
$910$		0			0
$911$	0.590905	−	0.740971i	0.590905	−	0.740971i	−0.393025	−	0.919528i	$-0.628571\pi$
$911$	0.590905	−	0.740971i	0.590905	−	0.740971i	0.983930	+	0.178557i	$0.0571429\pi$
$912$		0			0
$913$		0			0
$914$	−1.73205	+	2.17193i	−1.73205	+	2.17193i
$915$		0			0
$916$		0			0
$917$	−0.372484	+	0.871471i	−0.372484	+	0.871471i
$918$	7.05867	+	3.39928i	7.05867	+	3.39928i
$919$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$919$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$920$		0			0
$921$	−0.780190	+	3.41824i	−0.780190	+	3.41824i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.307552	−	1.34747i	0.307552	−	1.34747i
$926$		0			0
$927$	−2.15965	−	2.70811i	−2.15965	−	2.70811i
$928$		0			0
$929$	0.992682	+	0.478050i	0.992682	+	0.478050i	0.858449	−	0.512899i	$-0.171429\pi$
$929$	0.992682	+	0.478050i	0.992682	+	0.478050i	0.134233	+	0.990950i	$0.457143\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$937$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.174913	−	0.766342i	0.174913	−	0.766342i	−0.809017	−	0.587785i	$-0.800000\pi$
$941$	0.174913	−	0.766342i	0.174913	−	0.766342i	0.983930	−	0.178557i	$-0.0571429\pi$
$942$	5.37163	+	2.58684i	5.37163	+	2.58684i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$947$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$948$	−3.76279	+	4.71839i	−3.76279	+	4.71839i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	1.38900	+	1.00917i	1.38900	+	1.00917i
$953$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$953$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$954$	0.226860	+	0.284474i	0.226860	+	0.284474i
$955$		0			0
$956$	2.01486	−	0.970305i	2.01486	−	0.970305i
$957$		0			0
$958$	1.94494	+	2.43888i	1.94494	+	2.43888i
$959$		0			0
$960$		0			0
$961$	1.00000			1.00000
$962$		0			0
$963$		0			0
$964$	−0.0966604	+	0.423497i	−0.0966604	+	0.423497i
$965$		0			0
$966$		0			0
$967$	0.708207	+	0.341054i	0.708207	+	0.341054i	0.753071	−	0.657939i	$-0.228571\pi$
$967$	0.708207	+	0.341054i	0.708207	+	0.341054i	−0.0448648	+	0.998993i	$0.514286\pi$
$968$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$969$		0			0
$970$		0			0
$971$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$971$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$972$	−0.855170	−	3.74674i	−0.855170	−	3.74674i
$973$		0			0
$974$	−0.648781	+	2.84250i	−0.648781	+	2.84250i
$975$		0			0
$976$		0			0
$977$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$977$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−1.14590	−	0.551838i	−1.14590	−	0.551838i
$983$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$983$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.735927	+	1.72179i	−0.735927	+	1.72179i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.0808436	+	0.0389322i	0.0808436	+	0.0389322i	0.473869	−	0.880596i	$-0.342857\pi$
$991$	0.0808436	+	0.0389322i	0.0808436	+	0.0389322i	−0.393025	+	0.919528i	$0.628571\pi$
$992$		0			0
$993$	0.151377	+	0.0728994i	0.151377	+	0.0728994i
$994$	0.135928	+	3.02667i	0.135928	+	3.02667i
$995$		0			0
$996$	−0.840684	+	3.68328i	−0.840684	+	3.68328i
$997$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$997$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$998$		0			0
$999$	−3.89788			−3.89788

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.1.j.b.1597.3	yes	24
47.46	odd	2	CM	2303.1.j.b.1597.3	yes	24
49.22	even	7	inner	2303.1.j.b.610.3	✓	24
2303.610	odd	14	inner	2303.1.j.b.610.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.1.j.b.610.3	✓	24	49.22	even	7	inner
2303.1.j.b.610.3	✓	24	2303.610	odd	14	inner
2303.1.j.b.1597.3	yes	24	1.1	even	1	trivial
2303.1.j.b.1597.3	yes	24	47.46	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(1.45780 + 0.702039i) q^{2} +(-0.416664 - 1.82552i) q^{3} +(1.00883 + 1.26503i) q^{4} +(0.674176 - 2.95376i) q^{6} +(0.983930 + 0.178557i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-2.25796 + 1.08737i) q^{9} +(1.88900 - 2.36873i) q^{12} +(1.30902 + 0.951057i) q^{14} +(1.07047 - 1.34232i) q^{17} -4.05502 q^{18} +(-0.0840080 - 1.87058i) q^{21} +(1.68704 - 0.812434i) q^{24} +(-0.900969 + 0.433884i) q^{25} +(1.75837 + 2.20493i) q^{27} +(0.766736 + 1.42483i) q^{28} +(0.623490 - 0.781831i) q^{32} +(2.50289 - 1.20533i) q^{34} +(-3.65345 - 1.75941i) q^{36} +(-0.861741 + 1.08059i) q^{37} +(1.19076 - 2.78591i) q^{42} +(-0.900969 - 0.433884i) q^{47} +(0.936235 + 0.351375i) q^{49} -1.61803 q^{50} +(-2.89647 - 1.39487i) q^{51} +(-0.0559455 - 0.0701535i) q^{53} +(1.01541 + 4.44878i) q^{54} +(0.0448648 + 0.998993i) q^{56} +(-0.335148 + 1.46838i) q^{59} +(0.590905 - 0.740971i) q^{61} +(-2.41583 + 0.666726i) q^{63} +(1.45780 - 0.702039i) q^{64} +2.77800 q^{68} +(1.16747 + 1.46396i) q^{71} +(-1.56255 - 1.95938i) q^{72} +(-2.01486 + 0.970305i) q^{74} +(1.16747 + 1.46396i) q^{75} -1.99195 q^{79} +(1.72994 - 2.16928i) q^{81} +(-1.12349 + 0.541044i) q^{83} +(2.28160 - 1.99337i) q^{84} +(1.45780 - 0.702039i) q^{89} +(-1.00883 - 1.26503i) q^{94} +(-1.68704 - 0.812434i) q^{96} -1.61803 q^{97} +(1.11816 + 1.16951i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} + q^{7} + 4 q^{8} - 2 q^{9} + 10 q^{12} + 18 q^{14} + 2 q^{17} - 18 q^{18} - 5 q^{21} - 2 q^{24} - 4 q^{25} - 3 q^{27} + 3 q^{28} - 4 q^{32} + 4 q^{34} + 4 q^{36}+ \cdots + 2 q^{98}+O(q^{100}) \) 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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