LMFDB - Embedded newform 3311.1.gb.a.965.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3311,1,Mod(62,3311)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3311, base_ring=CyclotomicField(210))

chi = DirichletCharacter(H, H._module([105, 147, 95]))

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

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

chi := DirichletCharacter("3311.62");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3311 = 7 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3311.gb (of order $210$, degree $48$, 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:	$1.65240425683$
Analytic rank:	$0$
Dimension:	$48$
Coefficient field:	$\Q(\zeta_{210})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{48} - x^{47} + x^{46} + x^{43} - x^{42} + 2 x^{41} - x^{40} + x^{39} + x^{36} - x^{35} + x^{34} + \cdots + 1 $ x^48 - x^47 + x^46 + x^43 - x^42 + 2x^41 - x^40 + x^39 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 - x^28 - x^26 - x^24 - x^22 - x^20 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 + x^9 - x^8 + 2x^7 - x^6 + x^5 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{210}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{210} - \cdots)$

Embedding invariants

Embedding label			965.1
Root			$0.280427 - 0.959875i$ of defining polynomial
Character	$\chi$	$=$	3311.965
Dual form			3311.1.gb.a.2141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0830272 - 1.84875i) q^{2} +(-2.41499 - 0.217353i) q^{4} +(-0.978148 + 0.207912i) q^{7} +(-0.353927 + 2.61280i) q^{8} +(0.599822 - 0.800134i) q^{9} +O(q^{10})$	\(q+(0.0830272 - 1.84875i) q^{2} +(-2.41499 - 0.217353i) q^{4} +(-0.978148 + 0.207912i) q^{7} +(-0.353927 + 2.61280i) q^{8} +(0.599822 - 0.800134i) q^{9} +(-0.983930 - 0.178557i) q^{11} +(0.303163 + 1.82561i) q^{14} +(2.41522 + 0.438298i) q^{16} +(-1.42944 - 1.17535i) q^{18} +(-0.411799 + 1.80421i) q^{22} +(-0.411136 - 0.381478i) q^{23} +(-0.998210 - 0.0598042i) q^{25} +(2.40741 - 0.289501i) q^{28} +(-0.846609 + 1.69275i) q^{29} +(0.424120 - 1.85819i) q^{32} +(-1.62248 + 1.80194i) q^{36} +(-1.07428 + 0.967288i) q^{37} +(-0.992847 + 0.119394i) q^{43} +(2.33737 + 0.645073i) q^{44} +(-0.739391 + 0.728412i) q^{46} +(0.913545 - 0.406737i) q^{49} +(-0.193441 + 1.84047i) q^{50} +(1.03447 + 1.67402i) q^{53} +(-0.197038 - 2.62929i) q^{56} +(3.05917 + 1.70571i) q^{58} +(-0.420357 + 0.907359i) q^{63} +(-1.03389 - 0.285337i) q^{64} +(0.480819 + 0.148313i) q^{67} +(-0.237480 - 1.97482i) q^{71} +(1.87829 + 1.85040i) q^{72} +(1.69907 + 2.06639i) q^{74} +(0.999552 - 0.0299155i) q^{77} +(0.0971240 - 0.218144i) q^{79} +(-0.280427 - 0.959875i) q^{81} +(0.138296 + 1.84543i) q^{86} +(0.814772 - 2.50761i) q^{88} +(0.909973 + 1.01063i) q^{92} +(-0.676103 - 1.72268i) q^{98} +(-0.733052 + 0.680173i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{2} + 6 q^{7} - 21 q^{8} + q^{9}+O(q^{10}) $ 48 * q - 2 * q^2 + 6 * q^7 - 21 * q^8 + q^9	$ 48 q - 2 q^{2} + 6 q^{7} - 21 q^{8} + q^{9} - 2 q^{11} - 9 q^{14} + 3 q^{16} - 6 q^{18} + 2 q^{22} - q^{23} + q^{25} - 10 q^{28} - q^{29} - 4 q^{32} - 7 q^{36} - 5 q^{37} + q^{43} + 23 q^{44} + 4 q^{46} + 6 q^{49} - q^{50} + 10 q^{53} - 15 q^{56} + 4 q^{58} + q^{63} - 21 q^{64} + q^{67} - 7 q^{71} - 4 q^{72} - 14 q^{74} + q^{77} + 2 q^{79} - q^{81} + 13 q^{86} - 7 q^{88} + 20 q^{92} + q^{98} + 4 q^{99}+O(q^{100}) $ 48 * q - 2 * q^2 + 6 * q^7 - 21 * q^8 + q^9 - 2 * q^11 - 9 * q^14 + 3 * q^16 - 6 * q^18 + 2 * q^22 - q^23 + q^25 - 10 * q^28 - q^29 - 4 * q^32 - 7 * q^36 - 5 * q^37 + q^43 + 23 * q^44 + 4 * q^46 + 6 * q^49 - q^50 + 10 * q^53 - 15 * q^56 + 4 * q^58 + q^63 - 21 * q^64 + q^67 - 7 * q^71 - 4 * q^72 - 14 * q^74 + q^77 + 2 * q^79 - q^81 + 13 * q^86 - 7 * q^88 + 20 * q^92 + q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3311\mathbb{Z}\right)^\times$.

$n$	$904$	$1893$	$2927$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{19}{42}\right)$

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 $

$2$	0.0830272	−	1.84875i	0.0830272	−	1.84875i	−0.337330	−	0.941386i	$-0.609524\pi$
$2$	0.0830272	−	1.84875i	0.0830272	−	1.84875i	0.420357	−	0.907359i	$-0.361905\pi$
$3$		0			0		0.894377	−	0.447313i	$-0.147619\pi$
$3$		0			0		−0.894377	+	0.447313i	$0.852381\pi$
$4$	−2.41499	−	0.217353i	−2.41499	−	0.217353i
$5$		0			0		0.0299155	−	0.999552i	$-0.490476\pi$
$5$		0			0		−0.0299155	+	0.999552i	$0.509524\pi$
$6$		0			0
$7$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$7$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$8$	−0.353927	+	2.61280i	−0.353927	+	2.61280i
$9$	0.599822	−	0.800134i	0.599822	−	0.800134i
$10$		0			0
$11$	−0.983930	−	0.178557i	−0.983930	−	0.178557i
$11$	−0.983930	−	0.178557i	−0.983930	−	0.178557i
$12$		0			0
$13$		0			0		0.762830	−	0.646600i	$-0.223810\pi$
$13$		0			0		−0.762830	+	0.646600i	$0.776190\pi$
$14$	0.303163	+	1.82561i	0.303163	+	1.82561i
$15$		0			0
$16$	2.41522	+	0.438298i	2.41522	+	0.438298i
$17$		0			0		0.941386	−	0.337330i	$-0.109524\pi$
$17$		0			0		−0.941386	+	0.337330i	$0.890476\pi$
$18$	−1.42944	−	1.17535i	−1.42944	−	1.17535i
$19$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$19$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$20$		0			0
$21$		0			0
$22$	−0.411799	+	1.80421i	−0.411799	+	1.80421i
$23$	−0.411136	−	0.381478i	−0.411136	−	0.381478i	0.447313	−	0.894377i	$-0.352381\pi$
$23$	−0.411136	−	0.381478i	−0.411136	−	0.381478i	−0.858449	+	0.512899i	$0.828571\pi$
$24$		0			0
$25$	−0.998210	−	0.0598042i	−0.998210	−	0.0598042i
$26$		0			0
$27$		0			0
$28$	2.40741	−	0.289501i	2.40741	−	0.289501i
$29$	−0.846609	+	1.69275i	−0.846609	+	1.69275i	−0.134233	+	0.990950i	$0.542857\pi$
$29$	−0.846609	+	1.69275i	−0.846609	+	1.69275i	−0.712376	+	0.701798i	$0.752381\pi$
$30$		0			0
$31$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$31$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$32$	0.424120	−	1.85819i	0.424120	−	1.85819i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−1.62248	+	1.80194i	−1.62248	+	1.80194i
$37$	−1.07428	+	0.967288i	−1.07428	+	0.967288i	−0.999552	−	0.0299155i	$-0.990476\pi$
$37$	−1.07428	+	0.967288i	−1.07428	+	0.967288i	−0.0747301	+	0.997204i	$0.523810\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.351375	−	0.936235i	$-0.385714\pi$
$41$		0			0		−0.351375	+	0.936235i	$0.614286\pi$
$42$		0			0
$43$	−0.992847	+	0.119394i	−0.992847	+	0.119394i
$43$	−0.992847	+	0.119394i	−0.992847	+	0.119394i
$44$	2.33737	+	0.645073i	2.33737	+	0.645073i
$45$		0			0
$46$	−0.739391	+	0.728412i	−0.739391	+	0.728412i
$47$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$47$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$48$		0			0
$49$	0.913545	−	0.406737i	0.913545	−	0.406737i
$50$	−0.193441	+	1.84047i	−0.193441	+	1.84047i
$51$		0			0
$52$		0			0
$53$	1.03447	+	1.67402i	1.03447	+	1.67402i	0.669131	+	0.743145i	$0.266667\pi$
$53$	1.03447	+	1.67402i	1.03447	+	1.67402i	0.365341	+	0.930874i	$0.380952\pi$
$54$		0			0
$55$		0			0
$56$	−0.197038	−	2.62929i	−0.197038	−	2.62929i
$57$		0			0
$58$	3.05917	+	1.70571i	3.05917	+	1.70571i
$59$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$59$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$60$		0			0
$61$		0			0		0.842721	−	0.538351i	$-0.180952\pi$
$61$		0			0		−0.842721	+	0.538351i	$0.819048\pi$
$62$		0			0
$63$	−0.420357	+	0.907359i	−0.420357	+	0.907359i
$64$	−1.03389	−	0.285337i	−1.03389	−	0.285337i
$65$		0			0
$66$		0			0
$67$	0.480819	+	0.148313i	0.480819	+	0.148313i	0.525684	−	0.850680i	$-0.323810\pi$
$67$	0.480819	+	0.148313i	0.480819	+	0.148313i	−0.0448648	+	0.998993i	$0.514286\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.237480	−	1.97482i	−0.237480	−	1.97482i	−0.222521	−	0.974928i	$-0.571429\pi$
$71$	−0.237480	−	1.97482i	−0.237480	−	1.97482i	−0.0149594	−	0.999888i	$-0.504762\pi$
$72$	1.87829	+	1.85040i	1.87829	+	1.85040i
$73$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$73$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$74$	1.69907	+	2.06639i	1.69907	+	2.06639i
$75$		0			0
$76$		0			0
$77$	0.999552	−	0.0299155i	0.999552	−	0.0299155i
$78$		0			0
$79$	0.0971240	−	0.218144i	0.0971240	−	0.218144i	−0.858449	−	0.512899i	$-0.828571\pi$
$79$	0.0971240	−	0.218144i	0.0971240	−	0.218144i	0.955573	+	0.294755i	$0.0952381\pi$
$80$		0			0
$81$	−0.280427	−	0.959875i	−0.280427	−	0.959875i
$82$		0			0
$83$		0			0		0.460642	−	0.887586i	$-0.347619\pi$
$83$		0			0		−0.460642	+	0.887586i	$0.652381\pi$
$84$		0			0
$85$		0			0
$86$	0.138296	+	1.84543i	0.138296	+	1.84543i
$87$		0			0
$88$	0.814772	−	2.50761i	0.814772	−	2.50761i
$89$		0			0		−0.149042	−	0.988831i	$-0.547619\pi$
$89$		0			0		0.149042	+	0.988831i	$0.452381\pi$
$90$		0			0
$91$		0			0
$92$	0.909973	+	1.01063i	0.909973	+	1.01063i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$97$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$98$	−0.676103	−	1.72268i	−0.676103	−	1.72268i
$99$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$100$	2.39767	+	0.361391i	2.39767	+	0.361391i
$101$		0			0		−0.981148	−	0.193256i	$-0.938095\pi$
$101$		0			0		0.981148	+	0.193256i	$0.0619048\pi$
$102$		0			0
$103$		0			0		0.791071	−	0.611724i	$-0.209524\pi$
$103$		0			0		−0.791071	+	0.611724i	$0.790476\pi$
$104$		0			0
$105$		0			0
$106$	3.18072	−	1.77349i	3.18072	−	1.77349i
$107$	−0.856104	−	0.565109i	−0.856104	−	0.565109i	0.0448648	−	0.998993i	$-0.485714\pi$
$107$	−0.856104	−	0.565109i	−0.856104	−	0.565109i	−0.900969	+	0.433884i	$0.857143\pi$
$108$		0			0
$109$	−1.01093	+	1.08953i	−1.01093	+	1.08953i	−0.0149594	+	0.999888i	$0.504762\pi$
$109$	−1.01093	+	1.08953i	−1.01093	+	1.08953i	−0.995974	+	0.0896393i	$0.971429\pi$
$110$		0			0
$111$		0			0
$112$	−2.45357	+	0.0734326i	−2.45357	+	0.0734326i
$113$	−0.778234	+	0.744068i	−0.778234	+	0.744068i	−0.971490	−	0.237080i	$-0.923810\pi$
$113$	−0.778234	+	0.744068i	−0.778234	+	0.744068i	0.193256	+	0.981148i	$0.438095\pi$
$114$		0			0
$115$		0			0
$116$	2.41248	−	3.90396i	2.41248	−	3.90396i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.936235	+	0.351375i	0.936235	+	0.351375i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	1.64257	+	0.852469i	1.64257	+	0.852469i
$127$	0.110624	+	0.400838i	0.110624	+	0.400838i	0.998210	−	0.0598042i	$-0.0190476\pi$
$127$	0.110624	+	0.400838i	0.110624	+	0.400838i	−0.887586	+	0.460642i	$0.847619\pi$
$128$	−0.0243770	+	0.0750248i	−0.0243770	+	0.0750248i
$129$		0			0
$130$		0			0
$131$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$131$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$132$		0			0
$133$		0			0
$134$	0.314114	−	0.876598i	0.314114	−	0.876598i
$135$		0			0
$136$		0			0
$137$	−1.73740	+	0.934934i	−1.73740	+	0.934934i	−0.791071	+	0.611724i	$0.790476\pi$
$137$	−1.73740	+	0.934934i	−1.73740	+	0.934934i	−0.946327	+	0.323210i	$0.895238\pi$
$138$		0			0
$139$		0			0		0.379225	−	0.925304i	$-0.376190\pi$
$139$		0			0		−0.379225	+	0.925304i	$0.623810\pi$
$140$		0			0
$141$		0			0
$142$	−3.67065	+	0.275077i	−3.67065	+	0.275077i
$143$		0			0
$144$	1.79940	−	1.66960i	1.79940	−	1.66960i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	2.80463	−	2.10249i	2.80463	−	2.10249i
$149$	0.283333	+	1.43847i	0.283333	+	1.43847i	0.809017	+	0.587785i	$0.200000\pi$
$149$	0.283333	+	1.43847i	0.283333	+	1.43847i	−0.525684	+	0.850680i	$0.676190\pi$
$150$		0			0
$151$	0.180494	−	0.273436i	0.180494	−	0.273436i	−0.733052	−	0.680173i	$-0.761905\pi$
$151$	0.180494	−	0.273436i	0.180494	−	0.273436i	0.913545	+	0.406737i	$0.133333\pi$
$152$		0			0
$153$		0			0
$154$	0.0276840	−	1.85040i	0.0276840	−	1.85040i
$155$		0			0
$156$		0			0
$157$		0			0		0.486989	−	0.873408i	$-0.338095\pi$
$157$		0			0		−0.486989	+	0.873408i	$0.661905\pi$
$158$	−0.395229	−	0.197669i	−0.395229	−	0.197669i
$159$		0			0
$160$		0			0
$161$	0.481465	+	0.287662i	0.481465	+	0.287662i
$162$	−1.79785	+	0.438743i	−1.79785	+	0.438743i
$163$	0.0957026	+	0.0717437i	0.0957026	+	0.0717437i	0.646600	−	0.762830i	$-0.276190\pi$
$163$	0.0957026	+	0.0717437i	0.0957026	+	0.0717437i	−0.550897	+	0.834573i	$0.685714\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.941386	−	0.337330i	$-0.890476\pi$
$167$		0			0		0.941386	+	0.337330i	$0.109524\pi$
$168$		0			0
$169$	0.163818	−	0.986491i	0.163818	−	0.986491i
$170$		0			0
$171$		0			0
$172$	2.42367	−	0.0725376i	2.42367	−	0.0725376i
$173$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$173$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$174$		0			0
$175$	0.988831	−	0.149042i	0.988831	−	0.149042i
$176$	−2.29815	−	0.862510i	−2.29815	−	0.862510i
$177$		0			0
$178$		0			0
$179$	−0.909199	−	0.818647i	−0.909199	−	0.818647i	0.0747301	−	0.997204i	$-0.476190\pi$
$179$	−0.909199	−	0.818647i	−0.909199	−	0.818647i	−0.983930	+	0.178557i	$0.942857\pi$
$180$		0			0
$181$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$181$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$182$		0			0
$183$		0			0
$184$	1.14224	−	0.939198i	1.14224	−	0.939198i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.63379	−	1.15007i	−1.63379	−	1.15007i	−0.842721	−	0.538351i	$-0.819048\pi$
$191$	−1.63379	−	1.15007i	−1.63379	−	1.15007i	−0.791071	−	0.611724i	$-0.790476\pi$
$192$		0			0
$193$	1.96032	−	0.0880381i	1.96032	−	0.0880381i	0.971490	−	0.237080i	$-0.0761905\pi$
$193$	1.96032	−	0.0880381i	1.96032	−	0.0880381i	0.988831	+	0.149042i	$0.0476190\pi$
$194$		0			0
$195$		0			0
$196$	−2.29461	+	0.783703i	−2.29461	+	0.783703i
$197$	−1.18243	−	0.464068i	−1.18243	−	0.464068i	−0.309017	−	0.951057i	$-0.600000\pi$
$197$	−1.18243	−	0.464068i	−1.18243	−	0.464068i	−0.873408	+	0.486989i	$0.838095\pi$
$198$	1.19660	+	1.41170i	1.19660	+	1.41170i
$199$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$199$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$200$	0.509550	−	2.58695i	0.509550	−	2.58695i
$201$		0			0
$202$		0			0
$203$	0.476167	−	1.83178i	0.476167	−	1.83178i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.551842	+	0.100144i	−0.551842	+	0.100144i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.633118	−	0.553139i	−0.633118	−	0.553139i	0.280427	−	0.959875i	$-0.409524\pi$
$211$	−0.633118	−	0.553139i	−0.633118	−	0.553139i	−0.913545	+	0.406737i	$0.866667\pi$
$212$	−2.13439	−	4.26759i	−2.13439	−	4.26759i
$213$		0			0
$214$	−1.11582	+	1.53580i	−1.11582	+	1.53580i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.93032	+	1.95942i	1.93032	+	1.95942i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.990950	−	0.134233i	$-0.957143\pi$
$223$		0			0		0.990950	+	0.134233i	$0.0428571\pi$
$224$	−0.0285123	+	1.90576i	−0.0285123	+	1.90576i
$225$	−0.646600	+	0.762830i	−0.646600	+	0.762830i
$226$	1.31098	+	1.50053i	1.31098	+	1.50053i
$227$		0			0		0.998210	−	0.0598042i	$-0.0190476\pi$
$227$		0			0		−0.998210	+	0.0598042i	$0.980952\pi$
$228$		0			0
$229$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$229$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$230$		0			0
$231$		0			0
$232$	−4.12317	−	2.81113i	−4.12317	−	2.81113i
$233$	−0.251587	−	0.967835i	−0.251587	−	0.967835i	−0.963963	−	0.266037i	$-0.914286\pi$
$233$	−0.251587	−	0.967835i	−0.251587	−	0.967835i	0.712376	−	0.701798i	$-0.247619\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.52549	+	0.0228230i	−1.52549	+	0.0228230i	−0.772417	−	0.635116i	$-0.780952\pi$
$239$	−1.52549	+	0.0228230i	−1.52549	+	0.0228230i	−0.753071	+	0.657939i	$0.771429\pi$
$240$		0			0
$241$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$241$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$242$	0.727336	−	1.70169i	0.727336	−	1.70169i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$251$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$252$	1.21238	−	2.09990i	1.21238	−	2.09990i
$253$	0.336413	+	0.448759i	0.336413	+	0.448759i
$254$	0.750233	−	0.171236i	0.750233	−	0.171236i
$255$		0			0
$256$	−0.867477	−	0.325570i	−0.867477	−	0.325570i
$257$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$257$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$258$		0			0
$259$	0.849696	−	1.16951i	0.849696	−	1.16951i
$260$		0			0
$261$	0.846609	+	1.69275i	0.846609	+	1.69275i
$262$		0			0
$263$	−0.319351	+	0.217730i	−0.319351	+	0.217730i	−0.712376	−	0.701798i	$-0.752381\pi$
$263$	−0.319351	+	0.217730i	−0.319351	+	0.217730i	0.393025	+	0.919528i	$0.371429\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−1.12894	−	0.462682i	−1.12894	−	0.462682i
$269$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$269$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$270$		0			0
$271$		0			0		0.237080	−	0.971490i	$-0.423810\pi$
$271$		0			0		−0.237080	+	0.971490i	$0.576190\pi$
$272$		0			0
$273$		0			0
$274$	1.58420	+	3.28963i	1.58420	+	3.28963i
$275$	0.971490	+	0.237080i	0.971490	+	0.237080i
$276$		0			0
$277$	−1.26643	+	0.432539i	−1.26643	+	0.432539i	−0.873408	−	0.486989i	$-0.838095\pi$
$277$	−1.26643	+	0.432539i	−1.26643	+	0.432539i	−0.393025	+	0.919528i	$0.628571\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.57010	+	0.309261i	−1.57010	+	0.309261i	−0.900969	−	0.433884i	$-0.857143\pi$
$281$	−1.57010	+	0.309261i	−1.57010	+	0.309261i	−0.669131	+	0.743145i	$0.733333\pi$
$282$		0			0
$283$		0			0		0.0598042	−	0.998210i	$-0.480952\pi$
$283$		0			0		−0.0598042	+	0.998210i	$0.519048\pi$
$284$	0.144280	+	4.82078i	0.144280	+	4.82078i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.23240	−	1.45394i	−1.23240	−	1.45394i
$289$	0.772417	−	0.635116i	0.772417	−	0.635116i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.722795	−	0.691063i	$-0.757143\pi$
$293$		0			0		0.722795	+	0.691063i	$0.242857\pi$
$294$		0			0
$295$		0			0
$296$	−2.14711	−	3.14923i	−2.14711	−	3.14923i
$297$		0			0
$298$	2.68288	−	0.404379i	2.68288	−	0.404379i
$299$		0			0
$300$		0			0
$301$	0.946327	−	0.323210i	0.946327	−	0.323210i
$302$	−0.490528	−	0.356389i	−0.490528	−	0.356389i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$307$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$308$	−2.42041	−	0.145010i	−2.42041	−	0.145010i
$309$		0			0
$310$		0			0
$311$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$311$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$312$		0			0
$313$		0			0		−0.967835	−	0.251587i	$-0.919048\pi$
$313$		0			0		0.967835	+	0.251587i	$0.0809524\pi$
$314$		0			0
$315$		0			0
$316$	−0.281968	+	0.505706i	−0.281968	+	0.505706i
$317$	0.940958	−	1.74859i	0.940958	−	1.74859i	0.365341	−	0.930874i	$-0.380952\pi$
$317$	0.940958	−	1.74859i	0.940958	−	1.74859i	0.575617	−	0.817719i	$-0.304762\pi$
$318$		0			0
$319$	1.13526	−	1.51438i	1.13526	−	1.51438i
$320$		0			0
$321$		0			0
$322$	0.571788	−	0.866223i	0.571788	−	0.866223i
$323$		0			0
$324$	0.468598	+	2.37904i	0.468598	+	2.37904i
$325$		0			0
$326$	0.140582	−	0.170973i	0.140582	−	0.170973i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.700785	+	0.0525165i	−0.700785	+	0.0525165i	−0.420357	−	0.907359i	$-0.638095\pi$
$331$	−0.700785	+	0.0525165i	−0.700785	+	0.0525165i	−0.280427	+	0.959875i	$0.590476\pi$
$332$		0			0
$333$	0.129582	+	1.43977i	0.129582	+	1.43977i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.157691	+	0.741877i	0.157691	+	0.741877i	0.983930	+	0.178557i	$0.0571429\pi$
$337$	0.157691	+	0.741877i	0.157691	+	0.741877i	−0.826239	+	0.563320i	$0.809524\pi$
$338$	−1.81017	−	0.384763i	−1.81017	−	0.384763i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$344$	0.0394429	−	2.63636i	0.0394429	−	2.63636i
$345$		0			0
$346$		0			0
$347$	−1.57562	−	0.817719i	−1.57562	−	0.817719i	−0.575617	−	0.817719i	$-0.695238\pi$
$347$	−1.57562	−	0.817719i	−1.57562	−	0.817719i	−1.00000			$\pi$
$348$		0			0
$349$		0			0		−0.791071	−	0.611724i	$-0.790476\pi$
$349$		0			0		0.791071	+	0.611724i	$0.209524\pi$
$350$	−0.193441	−	1.84047i	−0.193441	−	1.84047i
$351$		0			0
$352$	−0.749097	+	1.75260i	−0.749097	+	1.75260i
$353$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$353$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.58896	+	1.61291i	−1.58896	+	1.61291i
$359$	−1.79829	+	0.833106i	−1.79829	+	0.833106i	−0.842721	+	0.538351i	$0.819048\pi$
$359$	−1.79829	+	0.833106i	−1.79829	+	0.833106i	−0.955573	+	0.294755i	$0.904762\pi$
$360$		0			0
$361$	−0.999552	+	0.0299155i	−0.999552	+	0.0299155i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$367$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$368$	−0.825783	−	1.10156i	−0.825783	−	1.10156i
$369$		0			0
$370$		0			0
$371$	−1.35991	−	1.42236i	−1.35991	−	1.42236i
$372$		0			0
$373$	1.63402	+	0.246289i	1.63402	+	0.246289i	0.900969	−	0.433884i	$-0.142857\pi$
$373$	1.63402	+	0.246289i	1.63402	+	0.246289i	0.733052	+	0.680173i	$0.238095\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.920717	−	1.71098i	−0.920717	−	1.71098i	−0.669131	−	0.743145i	$-0.733333\pi$
$379$	−0.920717	−	1.71098i	−0.920717	−	1.71098i	−0.251587	−	0.967835i	$-0.580952\pi$
$380$		0			0
$381$		0			0
$382$	−2.26184	+	2.92498i	−2.26184	+	2.92498i
$383$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$383$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$384$		0			0
$385$		0			0
$386$		−	3.63144i		−	3.63144i
$387$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$388$		0			0
$389$	1.49285	−	0.985420i	1.49285	−	0.985420i	0.500000	−	0.866025i	$-0.333333\pi$
$389$	1.49285	−	0.985420i	1.49285	−	0.985420i	0.992847	−	0.119394i	$-0.0380952\pi$
$390$		0			0
$391$		0			0
$392$	0.739391	+	2.53086i	0.739391	+	2.53086i
$393$		0			0
$394$	−0.956116	+	2.14747i	−0.956116	+	2.14747i
$395$		0			0
$396$	1.91815	−	1.48328i	1.91815	−	1.48328i
$397$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$397$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$398$		0			0
$399$		0			0
$400$	−2.38469	−	0.581954i	−2.38469	−	0.581954i
$401$	−1.10050	−	1.08416i	−1.10050	−	1.08416i	−0.995974	−	0.0896393i	$-0.971429\pi$
$401$	−1.10050	−	1.08416i	−1.10050	−	1.08416i	−0.104528	−	0.994522i	$-0.533333\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−3.34695	−	1.03240i	−3.34695	−	1.03240i
$407$	1.22973	−	0.759923i	1.22973	−	0.759923i
$408$		0			0
$409$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$409$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.139324	+	1.02853i	0.139324	+	1.02853i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$419$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$420$		0			0
$421$	0.146600	−	0.103196i	0.146600	−	0.103196i	−0.500000	−	0.866025i	$-0.666667\pi$
$421$	0.146600	−	0.103196i	0.146600	−	0.103196i	0.646600	+	0.762830i	$0.276190\pi$
$422$	−1.07518	+	1.12455i	−1.07518	+	1.12455i
$423$		0			0
$424$	−4.74000	+	2.11038i	−4.74000	+	2.11038i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	1.94466	+	1.55081i	1.94466	+	1.55081i
$429$		0			0
$430$		0			0
$431$	1.17544	+	1.61785i	1.17544	+	1.61785i	0.599822	+	0.800134i	$0.295238\pi$
$431$	1.17544	+	1.61785i	1.17544	+	1.61785i	0.575617	+	0.817719i	$0.304762\pi$
$432$		0			0
$433$		0			0		−0.986491	−	0.163818i	$-0.947619\pi$
$433$		0			0		0.986491	+	0.163818i	$0.0523810\pi$
$434$		0			0
$435$		0			0
$436$	2.67821	−	2.41147i	2.67821	−	2.41147i
$437$		0			0
$438$		0			0
$439$		0			0		−0.294755	−	0.955573i	$-0.595238\pi$
$439$		0			0		0.294755	+	0.955573i	$0.404762\pi$
$440$		0			0
$441$	0.222521	−	0.974928i	0.222521	−	0.974928i
$442$		0			0
$443$	1.69062	−	0.692879i	1.69062	−	0.692879i	0.691063	−	0.722795i	$-0.257143\pi$
$443$	1.69062	−	0.692879i	1.69062	−	0.692879i	0.999552	+	0.0299155i	$0.00952381\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	1.07063	+	0.0641427i	1.07063	+	0.0641427i
$449$	−0.586534	−	1.71732i	−0.586534	−	1.71732i	−0.691063	−	0.722795i	$-0.742857\pi$
$449$	−0.586534	−	1.71732i	−0.586534	−	1.71732i	0.104528	−	0.994522i	$-0.466667\pi$
$450$	1.35659	+	1.25873i	1.35659	+	1.25873i
$451$		0			0
$452$	2.04115	−	1.62777i	2.04115	−	1.62777i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.68931	−	0.306564i	−1.68931	−	0.306564i	−0.753071	−	0.657939i	$-0.771429\pi$
$457$	−1.68931	−	0.306564i	−1.68931	−	0.306564i	−0.936235	+	0.351375i	$0.885714\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.930874	−	0.365341i	$-0.119048\pi$
$461$		0			0		−0.930874	+	0.365341i	$0.880952\pi$
$462$		0			0
$463$	0.644612	+	0.0483070i	0.644612	+	0.0483070i	0.393025	−	0.919528i	$-0.371429\pi$
$463$	0.644612	+	0.0483070i	0.644612	+	0.0483070i	0.251587	+	0.967835i	$0.419048\pi$
$464$	−2.78668	+	3.71730i	−2.78668	+	3.71730i
$465$		0			0
$466$	−1.81017	+	0.384763i	−1.81017	+	0.384763i
$467$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$467$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$468$		0			0
$469$	−0.501148	−	0.0451041i	−0.501148	−	0.0451041i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.998210	+	0.0598042i	0.998210	+	0.0598042i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.95994	+	0.176398i	1.95994	+	0.176398i
$478$	−0.0844633	+	2.82213i	−0.0844633	+	2.82213i
$479$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$479$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−2.18463	−	1.05206i	−2.18463	−	1.05206i
$485$		0			0
$486$		0			0
$487$	0.196523	+	1.18344i	0.196523	+	1.18344i	0.887586	+	0.460642i	$0.152381\pi$
$487$	0.196523	+	1.18344i	0.196523	+	1.18344i	−0.691063	+	0.722795i	$0.742857\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.47620	+	1.21380i	1.47620	+	1.21380i	0.925304	+	0.379225i	$0.123810\pi$
$491$	1.47620	+	1.21380i	1.47620	+	1.21380i	0.550897	+	0.834573i	$0.314286\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.642878	+	1.88229i	0.642878	+	1.88229i
$498$		0			0
$499$	1.12499	+	1.45482i	1.12499	+	1.45482i	0.873408	+	0.486989i	$0.161905\pi$
$499$	1.12499	+	1.45482i	1.12499	+	1.45482i	0.251587	+	0.967835i	$0.419048\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$503$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$504$	−2.22197	−	1.41945i	−2.22197	−	1.41945i
$505$		0			0
$506$	0.857572	−	0.584683i	0.857572	−	0.584683i
$507$		0			0
$508$	−0.180033	−	0.992065i	−0.180033	−	0.992065i
$509$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$509$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$510$		0			0
$511$		0			0
$512$	−0.704923	+	1.64925i	−0.704923	+	1.64925i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−2.09157	−	1.66797i	−2.09157	−	1.66797i
$519$		0			0
$520$		0			0
$521$		0			0		0.959875	−	0.280427i	$-0.0904762\pi$
$521$		0			0		−0.959875	+	0.280427i	$0.909524\pi$
$522$	3.19975	−	1.42462i	3.19975	−	1.42462i
$523$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$523$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$524$		0			0
$525$		0			0
$526$	0.376012	+	0.608476i	0.376012	+	0.608476i
$527$		0			0
$528$		0			0
$529$	−0.0512231	−	0.683525i	−0.0512231	−	0.683525i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.557687	+	1.20379i	−0.557687	+	1.20379i
$537$		0			0
$538$		0			0
$539$	−0.971490	+	0.237080i	−0.971490	+	0.237080i
$540$		0			0
$541$	0.173512	−	0.0451041i	0.173512	−	0.0451041i	−0.163818	−	0.986491i	$-0.552381\pi$
$541$	0.173512	−	0.0451041i	0.173512	−	0.0451041i	0.337330	+	0.941386i	$0.390476\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.26668	+	1.54051i	1.26668	+	1.54051i	0.691063	+	0.722795i	$0.257143\pi$
$547$	1.26668	+	1.54051i	1.26668	+	1.54051i	0.575617	+	0.817719i	$0.304762\pi$
$548$	4.39901	−	1.88023i	4.39901	−	1.88023i
$549$		0			0
$550$	0.518961	−	1.77635i	0.518961	−	1.77635i
$551$		0			0
$552$		0			0
$553$	−0.0496469	+	0.233570i	−0.0496469	+	0.233570i
$554$	0.694506	+	2.37722i	0.694506	+	2.37722i
$555$		0			0
$556$		0			0
$557$	1.09820	−	0.724913i	1.09820	−	0.724913i	0.134233	−	0.990950i	$-0.457143\pi$
$557$	1.09820	−	0.724913i	1.09820	−	0.724913i	0.963963	+	0.266037i	$0.0857143\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.441384	+	2.92839i	0.441384	+	2.92839i
$563$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$563$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.473869	+	0.880596i	0.473869	+	0.880596i
$568$	5.24384	+	0.0784536i	5.24384	+	0.0784536i
$569$	−0.267104	−	1.09452i	−0.267104	−	1.09452i	−0.936235	−	0.351375i	$-0.885714\pi$
$569$	−0.267104	−	1.09452i	−0.267104	−	1.09452i	0.669131	−	0.743145i	$-0.266667\pi$
$570$		0			0
$571$	0.727741	+	1.85425i	0.727741	+	1.85425i	0.447313	+	0.894377i	$0.352381\pi$
$571$	0.727741	+	1.85425i	0.727741	+	1.85425i	0.280427	+	0.959875i	$0.409524\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.387586	+	0.405383i	0.387586	+	0.405383i
$576$	−0.848460	+	0.656102i	−0.848460	+	0.656102i
$577$		0			0		−0.538351	−	0.842721i	$-0.680952\pi$
$577$		0			0		0.538351	+	0.842721i	$0.319048\pi$
$578$	−1.11004	−	1.48073i	−1.11004	−	1.48073i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.718940	−	1.83183i	−0.718940	−	1.83183i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.907359	−	0.420357i	$-0.138095\pi$
$587$		0			0		−0.907359	+	0.420357i	$0.861905\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−3.01859	+	1.86536i	−3.01859	+	1.86536i
$593$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$593$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$594$		0			0
$595$		0			0
$596$	−0.371592	−	3.53546i	−0.371592	−	3.53546i
$597$		0			0
$598$		0			0
$599$	1.76803	+	0.917576i	1.76803	+	0.917576i	0.925304	+	0.379225i	$0.123810\pi$
$599$	1.76803	+	0.917576i	1.76803	+	0.917576i	0.842721	+	0.538351i	$0.180952\pi$
$600$		0			0
$601$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$601$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$602$	−0.518961	−	1.77635i	−0.518961	−	1.77635i
$603$	0.407076	−	0.295758i	0.407076	−	0.295758i
$604$	−0.495323	+	0.621115i	−0.495323	+	0.621115i
$605$		0			0
$606$		0			0
$607$		0			0		0.337330	−	0.941386i	$-0.390476\pi$
$607$		0			0		−0.337330	+	0.941386i	$0.609524\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.00536320	−	0.0595901i	−0.00536320	−	0.0595901i	0.992847	−	0.119394i	$-0.0380952\pi$
$613$	−0.00536320	−	0.0595901i	−0.00536320	−	0.0595901i	−0.998210	+	0.0598042i	$0.980952\pi$
$614$		0			0
$615$		0			0
$616$	−0.275606	+	2.62221i	−0.275606	+	2.62221i
$617$	0.947982	−	0.879599i	0.947982	−	0.879599i	−0.0448648	−	0.998993i	$-0.514286\pi$
$617$	0.947982	−	0.879599i	0.947982	−	0.879599i	0.992847	+	0.119394i	$0.0380952\pi$
$618$		0			0
$619$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$619$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.992847	+	0.119394i	0.992847	+	0.119394i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.77257	−	0.886530i	−1.77257	−	0.886530i	−0.946327	−	0.323210i	$-0.895238\pi$
$631$	−1.77257	−	0.886530i	−1.77257	−	0.886530i	−0.826239	−	0.563320i	$-0.809524\pi$
$632$	0.535591	+	0.330972i	0.535591	+	0.330972i
$633$		0			0
$634$	−3.15458	−	1.88477i	−3.15458	−	1.88477i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−2.70544	−	2.22453i	−2.70544	−	2.22453i
$639$	−1.72256	−	0.994522i	−1.72256	−	0.994522i
$640$		0			0
$641$	0.674913	+	1.12961i	0.674913	+	1.12961i	0.983930	+	0.178557i	$0.0571429\pi$
$641$	0.674913	+	1.12961i	0.674913	+	1.12961i	−0.309017	+	0.951057i	$0.600000\pi$
$642$		0			0
$643$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$643$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$644$	−1.10021	−	0.799349i	−1.10021	−	0.799349i
$645$		0			0
$646$		0			0
$647$		0			0		−0.998993	−	0.0448648i	$-0.985714\pi$
$647$		0			0		0.998993	+	0.0448648i	$0.0142857\pi$
$648$	2.60721	−	0.392974i	2.60721	−	0.392974i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.215527	−	0.194062i	−0.215527	−	0.194062i
$653$	−1.38759	−	1.32667i	−1.38759	−	1.32667i	−0.887586	−	0.460642i	$-0.847619\pi$
$653$	−1.38759	−	1.32667i	−1.38759	−	1.32667i	−0.500000	−	0.866025i	$-0.666667\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.202749	−	1.34515i	0.202749	−	1.34515i	−0.623490	−	0.781831i	$-0.714286\pi$
$659$	0.202749	−	1.34515i	0.202749	−	1.34515i	0.826239	−	0.563320i	$-0.190476\pi$
$660$		0			0
$661$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$661$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$662$	0.0389055	+	1.29993i	0.0389055	+	1.29993i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	2.67253	−	0.120023i	2.67253	−	0.120023i
$667$	0.993818	−	0.372986i	0.993818	−	0.372986i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.372583	+	1.89158i	−0.372583	+	1.89158i	0.0747301	+	0.997204i	$0.476190\pi$
$673$	−0.372583	+	1.89158i	−0.372583	+	1.89158i	−0.447313	+	0.894377i	$0.647619\pi$
$674$	1.38463	−	0.229934i	1.38463	−	0.229934i
$675$		0			0
$676$	−0.610036	+	2.34676i	−0.610036	+	2.34676i
$677$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$677$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.61637	+	1.10202i	−1.61637	+	1.10202i	−0.691063	+	0.722795i	$0.742857\pi$
$683$	−1.61637	+	1.10202i	−1.61637	+	1.10202i	−0.925304	+	0.379225i	$0.876190\pi$
$684$		0			0
$685$		0			0
$686$	1.01949	+	1.54447i	1.01949	+	1.54447i
$687$		0			0
$688$	−2.45028	−	0.146800i	−2.45028	−	0.146800i
$689$		0			0
$690$		0			0
$691$		0			0		−0.701798	−	0.712376i	$-0.747619\pi$
$691$		0			0		0.701798	+	0.712376i	$0.252381\pi$
$692$		0			0
$693$	0.575617	−	0.817719i	0.575617	−	0.817719i
$694$	−1.64257	+	2.84502i	−1.64257	+	2.84502i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−2.42041	+	0.145010i	−2.42041	+	0.145010i
$701$	−0.369357	−	0.901226i	−0.369357	−	0.901226i	−0.992847	−	0.119394i	$-0.961905\pi$
$701$	−0.369357	−	0.901226i	−0.369357	−	0.901226i	0.623490	−	0.781831i	$-0.285714\pi$
$702$		0			0
$703$		0			0
$704$	0.966330	+	0.465360i	0.966330	+	0.465360i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.0302685	−	0.673981i	−0.0302685	−	0.673981i	−0.955573	−	0.294755i	$-0.904762\pi$
$709$	−0.0302685	−	0.673981i	−0.0302685	−	0.673981i	0.925304	−	0.379225i	$-0.123810\pi$
$710$		0			0
$711$	−0.116287	−	0.208560i	−0.116287	−	0.208560i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	2.01777	+	2.17464i	2.01777	+	2.17464i
$717$		0			0
$718$	1.39089	+	3.39376i	1.39089	+	3.39376i
$719$		0			0		0.998210	−	0.0598042i	$-0.0190476\pi$
$719$		0			0		−0.998210	+	0.0598042i	$0.980952\pi$
$720$		0			0
$721$		0			0
$722$	−0.0276840	+	1.85040i	−0.0276840	+	1.85040i
$723$		0			0
$724$		0			0
$725$	0.946327	−	1.63909i	0.946327	−	1.63909i
$726$		0			0
$727$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$727$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$728$		0			0
$729$	−0.936235	−	0.351375i	−0.936235	−	0.351375i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$733$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$734$		0			0
$735$		0			0
$736$	−0.883229	+	0.602176i	−0.883229	+	0.602176i
$737$	−0.446610	−	0.231783i	−0.446610	−	0.231783i
$738$		0			0
$739$	0.932507	−	0.169225i	0.932507	−	0.169225i	0.309017	−	0.951057i	$-0.400000\pi$
$739$	0.932507	−	0.169225i	0.932507	−	0.169225i	0.623490	+	0.781831i	$0.285714\pi$
$740$		0			0
$741$		0			0
$742$	−2.74249	+	2.39604i	−2.74249	+	2.39604i
$743$	−0.502948	+	1.93480i	−0.502948	+	1.93480i	−0.222521	+	0.974928i	$0.571429\pi$
$743$	−0.502948	+	1.93480i	−0.502948	+	1.93480i	−0.280427	+	0.959875i	$0.590476\pi$
$744$		0			0
$745$		0			0
$746$	0.590994	−	3.00044i	0.590994	−	3.00044i
$747$		0			0
$748$		0			0
$749$	0.954889	+	0.374766i	0.954889	+	0.374766i
$750$		0			0
$751$	1.48393	+	0.687469i	1.48393	+	0.687469i	0.983930	−	0.178557i	$-0.0571429\pi$
$751$	1.48393	+	0.687469i	1.48393	+	0.687469i	0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.0243354	−	0.813109i	−0.0243354	−	0.813109i	−0.925304	−	0.379225i	$-0.876190\pi$
$757$	−0.0243354	−	0.813109i	−0.0243354	−	0.813109i	0.900969	−	0.433884i	$-0.142857\pi$
$758$	−3.23961	+	1.56011i	−3.23961	+	1.56011i
$759$		0			0
$760$		0			0
$761$		0			0		−0.646600	−	0.762830i	$-0.723810\pi$
$761$		0			0		0.646600	+	0.762830i	$0.276190\pi$
$762$		0			0
$763$	0.762317	−	1.27590i	0.762317	−	1.27590i
$764$	3.69562	+	3.13253i	3.69562	+	3.13253i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.563320	−	0.826239i	$-0.690476\pi$
$769$		0			0		0.563320	+	0.826239i	$0.309524\pi$
$770$		0			0
$771$		0			0
$772$	−4.75329	−	0.213471i	−4.75329	−	0.213471i
$773$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$773$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$774$	1.55955	+	0.996276i	1.55955	+	0.996276i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.69784	−	2.84171i	−1.69784	−	2.84171i
$779$		0			0
$780$		0			0
$781$	−0.118953	+	1.98548i	−0.118953	+	1.98548i
$782$		0			0
$783$		0			0
$784$	2.38469	−	0.581954i	2.38469	−	0.581954i
$785$		0			0
$786$		0			0
$787$		0			0		−0.850680	−	0.525684i	$-0.823810\pi$
$787$		0			0		0.850680	+	0.525684i	$0.176190\pi$
$788$	2.75468	+	1.37772i	2.75468	+	1.37772i
$789$		0			0
$790$		0			0
$791$	0.606527	−	0.889612i	0.606527	−	0.889612i
$792$	−1.51771	−	2.15605i	−1.51771	−	2.15605i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$797$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$798$		0			0
$799$		0			0
$800$	−0.534488	+	1.82950i	−0.534488	+	1.82950i
$801$		0			0
$802$	−2.09571	+	1.94453i	−2.09571	+	1.94453i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.57517	+	0.847635i	−1.57517	+	0.847635i	−0.575617	+	0.817719i	$0.695238\pi$
$809$	−1.57517	+	0.847635i	−1.57517	+	0.847635i	−0.999552	+	0.0299155i	$0.990476\pi$
$810$		0			0
$811$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$811$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$812$	−1.54808	+	4.32023i	−1.54808	+	4.32023i
$813$		0			0
$814$	−1.30280	−	2.33656i	−1.30280	−	2.33656i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.0528433	−	0.587137i	0.0528433	−	0.587137i	−0.925304	−	0.379225i	$-0.876190\pi$
$821$	0.0528433	−	0.587137i	0.0528433	−	0.587137i	0.978148	−	0.207912i	$-0.0666667\pi$
$822$		0			0
$823$	0.185556	+	1.76545i	0.185556	+	1.76545i	0.550897	+	0.834573i	$0.314286\pi$
$823$	0.185556	+	1.76545i	0.185556	+	1.76545i	−0.365341	+	0.930874i	$0.619048\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.253575	+	0.156698i	−0.253575	+	0.156698i	−0.646600	−	0.762830i	$-0.723810\pi$
$827$	−0.253575	+	0.156698i	−0.253575	+	0.156698i	0.393025	+	0.919528i	$0.371429\pi$
$828$	1.35446	−	0.121904i	1.35446	−	0.121904i
$829$		0			0		−0.0598042	−	0.998210i	$-0.519048\pi$
$829$		0			0		0.0598042	+	0.998210i	$0.480952\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.834573	−	0.550897i	$-0.814286\pi$
$839$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$840$		0			0
$841$	−1.54883	−	2.06606i	−1.54883	−	2.06606i
$842$	−0.178611	−	0.279593i	−0.178611	−	0.279593i
$843$		0			0
$844$	1.40875	+	1.47343i	1.40875	+	1.47343i
$845$		0			0
$846$		0			0
$847$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$848$	1.76476	+	4.49654i	1.76476	+	4.49654i
$849$		0			0
$850$		0			0
$851$	0.810675	+	0.0121286i	0.810675	+	0.0121286i
$852$		0			0
$853$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$853$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$854$		0			0
$855$		0			0
$856$	1.77951	−	2.03682i	1.77951	−	2.03682i
$857$		0			0		−0.149042	−	0.988831i	$-0.547619\pi$
$857$		0			0		0.149042	+	0.988831i	$0.452381\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$	3.08859	−	2.03876i	3.08859	−	2.03876i
$863$	0.626633	−	1.20742i	0.626633	−	1.20742i	−0.337330	−	0.941386i	$-0.609524\pi$
$863$	0.626633	−	1.20742i	0.626633	−	1.20742i	0.963963	−	0.266037i	$-0.0857143\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.134514	+	0.197296i	−0.134514	+	0.197296i
$870$		0			0
$871$		0			0
$872$	−2.48892	−	3.02698i	−2.48892	−	3.02698i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.34728	−	0.393607i	−1.34728	−	0.393607i	−0.473869	−	0.880596i	$-0.657143\pi$
$877$	−1.34728	−	0.393607i	−1.34728	−	0.393607i	−0.873408	+	0.486989i	$0.838095\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$881$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$882$	−1.78392	−	0.492330i	−1.78392	−	0.492330i
$883$	−0.757458	+	1.63500i	−0.757458	+	1.63500i	0.0149594	+	0.999888i	$0.495238\pi$
$883$	−0.757458	+	1.63500i	−0.757458	+	1.63500i	−0.772417	+	0.635116i	$0.780952\pi$
$884$		0			0
$885$		0			0
$886$	−1.14059	−	3.18304i	−1.14059	−	3.18304i
$887$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$887$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$888$		0			0
$889$	−0.191546	−	0.369079i	−0.191546	−	0.369079i
$890$		0			0
$891$	0.104528	+	0.994522i	0.104528	+	0.994522i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.00824580	−	0.0784536i	0.00824580	−	0.0784536i
$897$		0			0
$898$	−3.22358	+	0.941768i	−3.22358	+	0.941768i
$899$		0			0
$900$	1.72734	−	1.70169i	1.72734	−	1.70169i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−1.66866	−	2.29671i	−1.66866	−	2.29671i
$905$		0			0
$906$		0			0
$907$	0.151909	−	0.355408i	0.151909	−	0.355408i	−0.826239	−	0.563320i	$-0.809524\pi$
$907$	0.151909	−	0.355408i	0.151909	−	0.355408i	0.978148	+	0.207912i	$0.0666667\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.332428	+	1.83183i	0.332428	+	1.83183i	0.525684	+	0.850680i	$0.323810\pi$
$911$	0.332428	+	1.83183i	0.332428	+	1.83183i	−0.193256	+	0.981148i	$0.561905\pi$
$912$		0			0
$913$		0			0
$914$	−0.707017	+	3.09764i	−0.707017	+	3.09764i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.345627	−	1.90456i	0.345627	−	1.90456i	−0.0747301	−	0.997204i	$-0.523810\pi$
$919$	0.345627	−	1.90456i	0.345627	−	1.90456i	0.420357	−	0.907359i	$-0.361905\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	1.13021	−	0.901310i	1.13021	−	0.901310i
$926$	0.142828	−	1.18771i	0.142828	−	1.18771i
$927$		0			0
$928$	2.78638	+	2.29109i	2.78638	+	2.29109i
$929$		0			0		0.941386	−	0.337330i	$-0.109524\pi$
$929$		0			0		−0.941386	+	0.337330i	$0.890476\pi$
$930$		0			0
$931$		0			0
$932$	0.397218	+	2.39200i	0.397218	+	2.39200i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.599822	−	0.800134i	$-0.295238\pi$
$937$		0			0		−0.599822	+	0.800134i	$0.704762\pi$
$938$	−0.124995	+	0.922750i	−0.124995	+	0.922750i
$939$		0			0
$940$		0			0
$941$		0			0		0.0299155	−	0.999552i	$-0.490476\pi$
$941$		0			0		−0.0299155	+	0.999552i	$0.509524\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	0.193441	−	1.84047i	0.193441	−	1.84047i
$947$	−1.97766			−1.97766			−0.988831	−	0.149042i	$-0.952381\pi$
$947$	−1.97766			−1.97766			−0.988831	+	0.149042i	$0.952381\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.83155	−	0.389308i	1.83155	−	0.389308i	0.842721	−	0.538351i	$-0.180952\pi$
$953$	1.83155	−	0.389308i	1.83155	−	0.389308i	0.988831	+	0.149042i	$0.0476190\pi$
$954$	0.488842	−	3.60878i	0.488842	−	3.60878i
$955$		0			0
$956$	3.68900	+	0.276452i	3.68900	+	0.276452i
$957$		0			0
$958$		0			0
$959$	1.50505	−	1.27573i	1.50505	−	1.27573i
$960$		0			0
$961$	0.420357	+	0.907359i	0.420357	+	0.907359i
$962$		0			0
$963$	−0.965673	+	0.346033i	−0.965673	+	0.346033i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.370714	−	0.295634i	0.370714	−	0.295634i	−0.420357	−	0.907359i	$-0.638095\pi$
$967$	0.370714	−	0.295634i	0.370714	−	0.295634i	0.791071	+	0.611724i	$0.209524\pi$
$968$	−1.24943	+	2.32183i	−1.24943	+	2.32183i
$969$		0			0
$970$		0			0
$971$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$971$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$972$		0			0
$973$		0			0
$974$	2.20419	−	0.265064i	2.20419	−	0.265064i
$975$		0			0
$976$		0			0
$977$	−0.226242	−	0.144529i	−0.226242	−	0.144529i	0.420357	−	0.907359i	$-0.361905\pi$
$977$	−0.226242	−	0.144529i	−0.226242	−	0.144529i	−0.646600	+	0.762830i	$0.723810\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.265387	+	1.46240i	0.265387	+	1.46240i
$982$	2.36657	−	2.62834i	2.36657	−	2.62834i
$983$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$983$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.453741	+	0.329662i	0.453741	+	0.329662i
$990$		0			0
$991$	1.52446	+	1.21572i	1.52446	+	1.21572i	0.900969	+	0.433884i	$0.142857\pi$
$991$	1.52446	+	1.21572i	1.52446	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$992$		0			0
$993$		0			0
$994$	3.53324	−	1.03224i	3.53324	−	1.03224i
$995$		0			0
$996$		0			0
$997$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$997$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$998$	2.78300	−	1.95904i	2.78300	−	1.95904i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3311.1.gb.a.965.1	✓	48
7.6	odd	2	CM	3311.1.gb.a.965.1	✓	48
11.7	odd	10		3311.1.gb.b.62.1	yes	48
43.34	odd	42		3311.1.gb.b.3044.1	yes	48
77.62	even	10		3311.1.gb.b.62.1	yes	48
301.34	even	42		3311.1.gb.b.3044.1	yes	48
473.249	even	210	inner	3311.1.gb.a.2141.1	yes	48
3311.2141	odd	210	inner	3311.1.gb.a.2141.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3311.1.gb.a.965.1	✓	48	1.1	even	1	trivial
3311.1.gb.a.965.1	✓	48	7.6	odd	2	CM
3311.1.gb.a.2141.1	yes	48	473.249	even	210	inner
3311.1.gb.a.2141.1	yes	48	3311.2141	odd	210	inner
3311.1.gb.b.62.1	yes	48	11.7	odd	10
3311.1.gb.b.62.1	yes	48	77.62	even	10
3311.1.gb.b.3044.1	yes	48	43.34	odd	42
3311.1.gb.b.3044.1	yes	48	301.34	even	42

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:	\( N \)	\(=\)	\( 3311 = 7 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3311.gb (of order \(210\), degree \(48\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0830272 - 1.84875i) q^{2} +(-2.41499 - 0.217353i) q^{4} +(-0.978148 + 0.207912i) q^{7} +(-0.353927 + 2.61280i) q^{8} +(0.599822 - 0.800134i) q^{9} +O(q^{10})\)	\(q+(0.0830272 - 1.84875i) q^{2} +(-2.41499 - 0.217353i) q^{4} +(-0.978148 + 0.207912i) q^{7} +(-0.353927 + 2.61280i) q^{8} +(0.599822 - 0.800134i) q^{9} +(-0.983930 - 0.178557i) q^{11} +(0.303163 + 1.82561i) q^{14} +(2.41522 + 0.438298i) q^{16} +(-1.42944 - 1.17535i) q^{18} +(-0.411799 + 1.80421i) q^{22} +(-0.411136 - 0.381478i) q^{23} +(-0.998210 - 0.0598042i) q^{25} +(2.40741 - 0.289501i) q^{28} +(-0.846609 + 1.69275i) q^{29} +(0.424120 - 1.85819i) q^{32} +(-1.62248 + 1.80194i) q^{36} +(-1.07428 + 0.967288i) q^{37} +(-0.992847 + 0.119394i) q^{43} +(2.33737 + 0.645073i) q^{44} +(-0.739391 + 0.728412i) q^{46} +(0.913545 - 0.406737i) q^{49} +(-0.193441 + 1.84047i) q^{50} +(1.03447 + 1.67402i) q^{53} +(-0.197038 - 2.62929i) q^{56} +(3.05917 + 1.70571i) q^{58} +(-0.420357 + 0.907359i) q^{63} +(-1.03389 - 0.285337i) q^{64} +(0.480819 + 0.148313i) q^{67} +(-0.237480 - 1.97482i) q^{71} +(1.87829 + 1.85040i) q^{72} +(1.69907 + 2.06639i) q^{74} +(0.999552 - 0.0299155i) q^{77} +(0.0971240 - 0.218144i) q^{79} +(-0.280427 - 0.959875i) q^{81} +(0.138296 + 1.84543i) q^{86} +(0.814772 - 2.50761i) q^{88} +(0.909973 + 1.01063i) q^{92} +(-0.676103 - 1.72268i) q^{98} +(-0.733052 + 0.680173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{2} + 6 q^{7} - 21 q^{8} + q^{9}+O(q^{10}) \) 48 * q - 2 * q^2 + 6 * q^7 - 21 * q^8 + q^9	\( 48 q - 2 q^{2} + 6 q^{7} - 21 q^{8} + q^{9} - 2 q^{11} - 9 q^{14} + 3 q^{16} - 6 q^{18} + 2 q^{22} - q^{23} + q^{25} - 10 q^{28} - q^{29} - 4 q^{32} - 7 q^{36} - 5 q^{37} + q^{43} + 23 q^{44} + 4 q^{46} + 6 q^{49} - q^{50} + 10 q^{53} - 15 q^{56} + 4 q^{58} + q^{63} - 21 q^{64} + q^{67} - 7 q^{71} - 4 q^{72} - 14 q^{74} + q^{77} + 2 q^{79} - q^{81} + 13 q^{86} - 7 q^{88} + 20 q^{92} + q^{98} + 4 q^{99}+O(q^{100}) \) 48 * q - 2 * q^2 + 6 * q^7 - 21 * q^8 + q^9 - 2 * q^11 - 9 * q^14 + 3 * q^16 - 6 * q^18 + 2 * q^22 - q^23 + q^25 - 10 * q^28 - q^29 - 4 * q^32 - 7 * q^36 - 5 * q^37 + q^43 + 23 * q^44 + 4 * q^46 + 6 * q^49 - q^50 + 10 * q^53 - 15 * q^56 + 4 * q^58 + q^63 - 21 * q^64 + q^67 - 7 * q^71 - 4 * q^72 - 14 * q^74 + q^77 + 2 * q^79 - q^81 + 13 * q^86 - 7 * q^88 + 20 * q^92 + q^98 + 4 * q^99

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