LMFDB - Embedded newform 3311.1.gb.a.1448.1

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			1448.1
Root			$-0.575617 + 0.817719i$ of defining polynomial
Character	$\chi$	$=$	3311.1448
Dual form			3311.1.gb.a.734.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71874 - 0.311906i) q^{2} +(1.92056 + 0.720799i) q^{4} +(-0.978148 - 0.207912i) q^{7} +(-1.57658 - 0.941963i) q^{8} +(-0.887586 - 0.460642i) q^{9} +O(q^{10})$	\(q+(-1.71874 - 0.311906i) q^{2} +(1.92056 + 0.720799i) q^{4} +(-0.978148 - 0.207912i) q^{7} +(-1.57658 - 0.941963i) q^{8} +(-0.887586 - 0.460642i) q^{9} +(-0.753071 - 0.657939i) q^{11} +(1.61634 + 0.662437i) q^{14} +(0.871109 + 0.761065i) q^{16} +(1.38186 + 1.06857i) q^{18} +(1.08912 + 1.36572i) q^{22} +(-0.420593 + 1.07165i) q^{23} +(0.280427 + 0.959875i) q^{25} +(-1.72873 - 1.10435i) q^{28} +(-1.38413 + 0.337781i) q^{29} +(-0.114765 - 0.143911i) q^{32} +(-1.37263 - 1.52446i) q^{36} +(0.133230 + 0.119961i) q^{37} +(0.842721 + 0.538351i) q^{43} +(-0.972079 - 1.80643i) q^{44} +(1.05715 - 1.71071i) q^{46} +(0.913545 + 0.406737i) q^{49} +(-0.182592 - 1.73725i) q^{50} +(1.49537 - 0.179825i) q^{53} +(1.34628 + 1.24917i) q^{56} +(2.48433 - 0.148839i) q^{58} +(0.772417 + 0.635116i) q^{63} +(-0.395779 - 0.735480i) q^{64} +(1.97678 + 0.297951i) q^{67} +(1.07080 - 1.67621i) q^{71} +(0.965442 + 1.56231i) q^{72} +(-0.191572 - 0.247737i) q^{74} +(0.599822 + 0.800134i) q^{77} +(-0.437934 - 0.983616i) q^{79} +(0.575617 + 0.817719i) q^{81} +(-1.28051 - 1.18814i) q^{86} +(0.567524 + 1.74666i) q^{88} +(-1.58022 + 1.75501i) q^{92} +(-1.44329 - 0.984017i) q^{98} +(0.365341 + 0.930874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3311\mathbb{Z}\right)^\times$.

$n$	$904$	$1893$	$2927$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{41}{42}\right)$

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 $

$2$	−1.71874	−	0.311906i	−1.71874	−	0.311906i	−0.772417	−	0.635116i	$-0.780952\pi$
$2$	−1.71874	−	0.311906i	−1.71874	−	0.311906i	−0.946327	+	0.323210i	$0.895238\pi$
$3$		0			0		0.237080	−	0.971490i	$-0.423810\pi$
$3$		0			0		−0.237080	+	0.971490i	$0.576190\pi$
$4$	1.92056	+	0.720799i	1.92056	+	0.720799i
$5$		0			0		−0.800134	−	0.599822i	$-0.795238\pi$
$5$		0			0		0.800134	+	0.599822i	$0.204762\pi$
$6$		0			0
$7$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$7$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$8$	−1.57658	−	0.941963i	−1.57658	−	0.941963i
$9$	−0.887586	−	0.460642i	−0.887586	−	0.460642i
$10$		0			0
$11$	−0.753071	−	0.657939i	−0.753071	−	0.657939i
$11$	−0.753071	−	0.657939i	−0.753071	−	0.657939i
$12$		0			0
$13$		0			0		0.981148	−	0.193256i	$-0.0619048\pi$
$13$		0			0		−0.981148	+	0.193256i	$0.938095\pi$
$14$	1.61634	+	0.662437i	1.61634	+	0.662437i
$15$		0			0
$16$	0.871109	+	0.761065i	0.871109	+	0.761065i
$17$		0			0		−0.323210	−	0.946327i	$-0.604762\pi$
$17$		0			0		0.323210	+	0.946327i	$0.395238\pi$
$18$	1.38186	+	1.06857i	1.38186	+	1.06857i
$19$		0			0		0.447313	−	0.894377i	$-0.352381\pi$
$19$		0			0		−0.447313	+	0.894377i	$0.647619\pi$
$20$		0			0
$21$		0			0
$22$	1.08912	+	1.36572i	1.08912	+	1.36572i
$23$	−0.420593	+	1.07165i	−0.420593	+	1.07165i	0.550897	+	0.834573i	$0.314286\pi$
$23$	−0.420593	+	1.07165i	−0.420593	+	1.07165i	−0.971490	+	0.237080i	$0.923810\pi$
$24$		0			0
$25$	0.280427	+	0.959875i	0.280427	+	0.959875i
$26$		0			0
$27$		0			0
$28$	−1.72873	−	1.10435i	−1.72873	−	1.10435i
$29$	−1.38413	+	0.337781i	−1.38413	+	0.337781i	−0.858449	−	0.512899i	$-0.828571\pi$
$29$	−1.38413	+	0.337781i	−1.38413	+	0.337781i	−0.525684	+	0.850680i	$0.676190\pi$
$30$		0			0
$31$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$31$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$32$	−0.114765	−	0.143911i	−0.114765	−	0.143911i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−1.37263	−	1.52446i	−1.37263	−	1.52446i
$37$	0.133230	+	0.119961i	0.133230	+	0.119961i	0.733052	−	0.680173i	$-0.238095\pi$
$37$	0.133230	+	0.119961i	0.133230	+	0.119961i	−0.599822	+	0.800134i	$0.704762\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.990950	−	0.134233i	$-0.0428571\pi$
$41$		0			0		−0.990950	+	0.134233i	$0.957143\pi$
$42$		0			0
$43$	0.842721	+	0.538351i	0.842721	+	0.538351i
$43$	0.842721	+	0.538351i	0.842721	+	0.538351i
$44$	−0.972079	−	1.80643i	−0.972079	−	1.80643i
$45$		0			0
$46$	1.05715	−	1.71071i	1.05715	−	1.71071i
$47$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$47$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$48$		0			0
$49$	0.913545	+	0.406737i	0.913545	+	0.406737i
$50$	−0.182592	−	1.73725i	−0.182592	−	1.73725i
$51$		0			0
$52$		0			0
$53$	1.49537	−	0.179825i	1.49537	−	0.179825i	0.669131	−	0.743145i	$-0.266667\pi$
$53$	1.49537	−	0.179825i	1.49537	−	0.179825i	0.826239	+	0.563320i	$0.190476\pi$
$54$		0			0
$55$		0			0
$56$	1.34628	+	1.24917i	1.34628	+	1.24917i
$57$		0			0
$58$	2.48433	−	0.148839i	2.48433	−	0.148839i
$59$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$59$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$60$		0			0
$61$		0			0		0.337330	−	0.941386i	$-0.390476\pi$
$61$		0			0		−0.337330	+	0.941386i	$0.609524\pi$
$62$		0			0
$63$	0.772417	+	0.635116i	0.772417	+	0.635116i
$64$	−0.395779	−	0.735480i	−0.395779	−	0.735480i
$65$		0			0
$66$		0			0
$67$	1.97678	+	0.297951i	1.97678	+	0.297951i	0.992847	+	0.119394i	$0.0380952\pi$
$67$	1.97678	+	0.297951i	1.97678	+	0.297951i	0.983930	+	0.178557i	$0.0571429\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.07080	−	1.67621i	1.07080	−	1.67621i	0.447313	−	0.894377i	$-0.352381\pi$
$71$	1.07080	−	1.67621i	1.07080	−	1.67621i	0.623490	−	0.781831i	$-0.285714\pi$
$72$	0.965442	+	1.56231i	0.965442	+	1.56231i
$73$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$73$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$74$	−0.191572	−	0.247737i	−0.191572	−	0.247737i
$75$		0			0
$76$		0			0
$77$	0.599822	+	0.800134i	0.599822	+	0.800134i
$78$		0			0
$79$	−0.437934	−	0.983616i	−0.437934	−	0.983616i	−0.988831	−	0.149042i	$-0.952381\pi$
$79$	−0.437934	−	0.983616i	−0.437934	−	0.983616i	0.550897	−	0.834573i	$-0.314286\pi$
$80$		0			0
$81$	0.575617	+	0.817719i	0.575617	+	0.817719i
$82$		0			0
$83$		0			0		0.762830	−	0.646600i	$-0.223810\pi$
$83$		0			0		−0.762830	+	0.646600i	$0.776190\pi$
$84$		0			0
$85$		0			0
$86$	−1.28051	−	1.18814i	−1.28051	−	1.18814i
$87$		0			0
$88$	0.567524	+	1.74666i	0.567524	+	1.74666i
$89$		0			0		0.997204	−	0.0747301i	$-0.0238095\pi$
$89$		0			0		−0.997204	+	0.0747301i	$0.976190\pi$
$90$		0			0
$91$		0			0
$92$	−1.58022	+	1.75501i	−1.58022	+	1.75501i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$97$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$98$	−1.44329	−	0.984017i	−1.44329	−	0.984017i
$99$	0.365341	+	0.930874i	0.365341	+	0.930874i
$100$	−0.153299	+	2.04563i	−0.153299	+	2.04563i
$101$		0			0		−0.967835	−	0.251587i	$-0.919048\pi$
$101$		0			0		0.967835	+	0.251587i	$0.0809524\pi$
$102$		0			0
$103$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$103$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$104$		0			0
$105$		0			0
$106$	−2.62625	−	0.157342i	−2.62625	−	0.157342i
$107$	−1.20645	−	1.15348i	−1.20645	−	1.15348i	−0.983930	−	0.178557i	$-0.942857\pi$
$107$	−1.20645	−	1.15348i	−1.20645	−	1.15348i	−0.222521	−	0.974928i	$-0.571429\pi$
$108$		0			0
$109$	1.38355	+	0.543003i	1.38355	+	0.543003i	0.936235	−	0.351375i	$-0.114286\pi$
$109$	1.38355	+	0.543003i	1.38355	+	0.543003i	0.447313	+	0.894377i	$0.352381\pi$
$110$		0			0
$111$		0			0
$112$	−0.693839	−	0.925547i	−0.693839	−	0.925547i
$113$	−0.168770	+	1.87519i	−0.168770	+	1.87519i	0.251587	+	0.967835i	$0.419048\pi$
$113$	−0.168770	+	1.87519i	−0.168770	+	1.87519i	−0.420357	+	0.907359i	$0.638095\pi$
$114$		0			0
$115$		0			0
$116$	−2.90178	−	0.348952i	−2.90178	−	0.348952i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.134233	+	0.990950i	0.134233	+	0.990950i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.12949	−	1.33252i	−1.12949	−	1.33252i
$127$	0.366172	+	0.197046i	0.366172	+	0.197046i	0.646600	−	0.762830i	$-0.276190\pi$
$127$	0.366172	+	0.197046i	0.366172	+	0.197046i	−0.280427	+	0.959875i	$0.590476\pi$
$128$	0.507722	+	1.56261i	0.507722	+	1.56261i
$129$		0			0
$130$		0			0
$131$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$131$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$132$		0			0
$133$		0			0
$134$	−3.30464	−	1.12867i	−3.30464	−	1.12867i
$135$		0			0
$136$		0			0
$137$	0.697417	−	0.298090i	0.697417	−	0.298090i	−0.0149594	−	0.999888i	$-0.504762\pi$
$137$	0.697417	−	0.298090i	0.697417	−	0.298090i	0.712376	+	0.701798i	$0.247619\pi$
$138$		0			0
$139$		0			0		0.486989	−	0.873408i	$-0.338095\pi$
$139$		0			0		−0.486989	+	0.873408i	$0.661905\pi$
$140$		0			0
$141$		0			0
$142$	−2.36326	+	2.54698i	−2.36326	+	2.54698i
$143$		0			0
$144$	−0.422605	−	1.07678i	−0.422605	−	1.07678i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	0.169409	+	0.326424i	0.169409	+	0.326424i
$149$	−0.183830	−	0.707179i	−0.183830	−	0.707179i	−0.992847	−	0.119394i	$-0.961905\pi$
$149$	−0.183830	−	0.707179i	−0.183830	−	0.707179i	0.809017	−	0.587785i	$-0.200000\pi$
$150$		0			0
$151$	1.27889	−	1.33761i	1.27889	−	1.33761i	0.365341	−	0.930874i	$-0.380952\pi$
$151$	1.27889	−	1.33761i	1.27889	−	1.33761i	0.913545	−	0.406737i	$-0.133333\pi$
$152$		0			0
$153$		0			0
$154$	−0.781374	−	1.56231i	−0.781374	−	1.56231i
$155$		0			0
$156$		0			0
$157$		0			0		−0.0598042	−	0.998210i	$-0.519048\pi$
$157$		0			0		0.0598042	+	0.998210i	$0.480952\pi$
$158$	0.445901	+	1.82718i	0.445901	+	1.82718i
$159$		0			0
$160$		0			0
$161$	0.634211	−	0.960789i	0.634211	−	0.960789i
$162$	−0.734287	−	1.58499i	−0.734287	−	1.58499i
$163$	−0.884319	+	1.70394i	−0.884319	+	1.70394i	−0.193256	+	0.981148i	$0.561905\pi$
$163$	−0.884319	+	1.70394i	−0.884319	+	1.70394i	−0.691063	+	0.722795i	$0.742857\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.323210	−	0.946327i	$-0.395238\pi$
$167$		0			0		−0.323210	+	0.946327i	$0.604762\pi$
$168$		0			0
$169$	0.925304	−	0.379225i	0.925304	−	0.379225i
$170$		0			0
$171$		0			0
$172$	1.23046	+	1.64137i	1.23046	+	1.64137i
$173$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$173$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$174$		0			0
$175$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$176$	−0.155273	−	1.14627i	−0.155273	−	1.14627i
$177$		0			0
$178$		0			0
$179$	−1.48612	+	1.33811i	−1.48612	+	1.33811i	−0.733052	+	0.680173i	$0.761905\pi$
$179$	−1.48612	+	1.33811i	−1.48612	+	1.33811i	−0.753071	+	0.657939i	$0.771429\pi$
$180$		0			0
$181$		0			0		0.712376	−	0.701798i	$-0.247619\pi$
$181$		0			0		−0.712376	+	0.701798i	$0.752381\pi$
$182$		0			0
$183$		0			0
$184$	1.67256	−	1.29337i	1.67256	−	1.29337i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.352289	+	0.0585016i	−0.352289	+	0.0585016i	−0.337330	−	0.941386i	$-0.609524\pi$
$191$	−0.352289	+	0.0585016i	−0.352289	+	0.0585016i	−0.0149594	+	0.999888i	$0.504762\pi$
$192$		0			0
$193$	0.345627	+	1.90456i	0.345627	+	1.90456i	0.420357	+	0.907359i	$0.361905\pi$
$193$	0.345627	+	1.90456i	0.345627	+	1.90456i	−0.0747301	+	0.997204i	$0.523810\pi$
$194$		0			0
$195$		0			0
$196$	1.46135	+	1.43965i	1.46135	+	1.43965i
$197$	0.689193	+	1.01086i	0.689193	+	1.01086i	0.998210	+	0.0598042i	$0.0190476\pi$
$197$	0.689193	+	1.01086i	0.689193	+	1.01086i	−0.309017	+	0.951057i	$0.600000\pi$
$198$	−0.337583	−	1.71389i	−0.337583	−	1.71389i
$199$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$199$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$200$	0.462051	−	1.77747i	0.462051	−	1.77747i
$201$		0			0
$202$		0			0
$203$	1.42411	−	0.0426221i	1.42411	−	0.0426221i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.866962	−	0.757442i	0.866962	−	0.757442i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.48916	+	0.410983i	−1.48916	+	0.410983i	−0.913545	−	0.406737i	$-0.866667\pi$
$211$	−1.48916	+	0.410983i	−1.48916	+	0.410983i	−0.575617	+	0.817719i	$0.695238\pi$
$212$	3.00157	+	0.732496i	3.00157	+	0.732496i
$213$		0			0
$214$	1.71380	+	2.35884i	1.71380	+	2.35884i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−2.20860	−	1.36482i	−2.20860	−	1.36482i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.512899	−	0.858449i	$-0.328571\pi$
$223$		0			0		−0.512899	+	0.858449i	$0.671429\pi$
$224$	0.0823363	+	0.164627i	0.0823363	+	0.164627i
$225$	0.193256	−	0.981148i	0.193256	−	0.981148i
$226$	0.874958	−	3.17034i	0.874958	−	3.17034i
$227$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$227$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$228$		0			0
$229$		0			0		0.646600	−	0.762830i	$-0.276190\pi$
$229$		0			0		−0.646600	+	0.762830i	$0.723810\pi$
$230$		0			0
$231$		0			0
$232$	2.50037	+	0.771263i	2.50037	+	0.771263i
$233$	0.999552	+	0.0299155i	0.999552	+	0.0299155i	0.525684	−	0.850680i	$-0.323810\pi$
$233$	0.999552	+	0.0299155i	0.999552	+	0.0299155i	0.473869	+	0.880596i	$0.342857\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.75503	+	0.877761i	1.75503	+	0.877761i	0.963963	+	0.266037i	$0.0857143\pi$
$239$	1.75503	+	0.877761i	1.75503	+	0.877761i	0.791071	+	0.611724i	$0.209524\pi$
$240$		0			0
$241$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$241$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$242$	0.0783706	−	1.74506i	0.0783706	−	1.74506i
$243$		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	$-0.133333\pi$
$251$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$252$	1.02568	+	1.77654i	1.02568	+	1.77654i
$253$	1.02182	−	0.530307i	1.02182	−	0.530307i
$254$	−0.567897	−	0.452882i	−0.567897	−	0.452882i
$255$		0			0
$256$	−0.273145	−	2.01644i	−0.273145	−	2.01644i
$257$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$257$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$258$		0			0
$259$	−0.105377	−	0.145039i	−0.105377	−	0.145039i
$260$		0			0
$261$	1.38413	+	0.337781i	1.38413	+	0.337781i
$262$		0			0
$263$	−0.480819	+	0.148313i	−0.480819	+	0.148313i	−0.525684	−	0.850680i	$-0.676190\pi$
$263$	−0.480819	+	0.148313i	−0.480819	+	0.148313i	0.0448648	+	0.998993i	$0.485714\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	3.58176	+	1.99709i	3.58176	+	1.99709i
$269$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$269$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$270$		0			0
$271$		0			0		−0.907359	−	0.420357i	$-0.861905\pi$
$271$		0			0		0.907359	+	0.420357i	$0.138095\pi$
$272$		0			0
$273$		0			0
$274$	−1.29166	+	0.294812i	−1.29166	+	0.294812i
$275$	0.420357	−	0.907359i	0.420357	−	0.907359i
$276$		0			0
$277$	0.953345	+	0.939189i	0.953345	+	0.939189i	0.998210	−	0.0598042i	$-0.0190476\pi$
$277$	0.953345	+	0.939189i	0.953345	+	0.939189i	−0.0448648	+	0.998993i	$0.514286\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.891652	+	0.231783i	−0.891652	+	0.231783i	−0.669131	−	0.743145i	$-0.733333\pi$
$281$	−0.891652	+	0.231783i	−0.891652	+	0.231783i	−0.222521	+	0.974928i	$0.571429\pi$
$282$		0			0
$283$		0			0		0.959875	−	0.280427i	$-0.0904762\pi$
$283$		0			0		−0.959875	+	0.280427i	$0.909524\pi$
$284$	3.26475	−	2.44743i	3.26475	−	2.44743i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.0355723	+	0.180599i	0.0355723	+	0.180599i
$289$	−0.791071	+	0.611724i	−0.791071	+	0.611724i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.0896393	−	0.995974i	$-0.528571\pi$
$293$		0			0		0.0896393	+	0.995974i	$0.471429\pi$
$294$		0			0
$295$		0			0
$296$	−0.0970492	−	0.314626i	−0.0970492	−	0.314626i
$297$		0			0
$298$	0.0953831	+	1.27280i	0.0953831	+	1.27280i
$299$		0			0
$300$		0			0
$301$	−0.712376	−	0.701798i	−0.712376	−	0.701798i
$302$	−2.61529	+	1.90012i	−2.61529	+	1.90012i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$307$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$308$	0.575260	+	1.96906i	0.575260	+	1.96906i
$309$		0			0
$310$		0			0
$311$		0			0		−0.420357	−	0.907359i	$-0.638095\pi$
$311$		0			0		0.420357	+	0.907359i	$0.361905\pi$
$312$		0			0
$313$		0			0		−0.0299155	−	0.999552i	$-0.509524\pi$
$313$		0			0		0.0299155	+	0.999552i	$0.490476\pi$
$314$		0			0
$315$		0			0
$316$	−0.132090	−	2.20476i	−0.132090	−	2.20476i
$317$	0.662421	−	1.54981i	0.662421	−	1.54981i	−0.163818	−	0.986491i	$-0.552381\pi$
$317$	0.662421	−	1.54981i	0.662421	−	1.54981i	0.826239	−	0.563320i	$-0.190476\pi$
$318$		0			0
$319$	1.26459	+	0.656301i	1.26459	+	0.656301i
$320$		0			0
$321$		0			0
$322$	−1.38972	+	1.45354i	−1.38972	+	1.45354i
$323$		0			0
$324$	0.516097	+	1.98538i	0.516097	+	1.98538i
$325$		0			0
$326$	2.05139	−	2.65282i	2.05139	−	2.65282i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.34803	−	1.45284i	1.34803	−	1.45284i	0.575617	−	0.817719i	$-0.304762\pi$
$331$	1.34803	−	1.45284i	1.34803	−	1.45284i	0.772417	−	0.635116i	$-0.219048\pi$
$332$		0			0
$333$	−0.0629940	−	0.167847i	−0.0629940	−	0.167847i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.202501	+	0.952694i	−0.202501	+	0.952694i	0.753071	+	0.657939i	$0.228571\pi$
$337$	−0.202501	+	0.952694i	−0.202501	+	0.952694i	−0.955573	+	0.294755i	$0.904762\pi$
$338$	−1.70864	+	0.363184i	−1.70864	+	0.363184i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$344$	−0.821511	−	1.64257i	−0.821511	−	1.64257i
$345$		0			0
$346$		0			0
$347$	−0.836182	−	0.986491i	−0.836182	−	0.986491i	0.163818	−	0.986491i	$-0.447619\pi$
$347$	−0.836182	−	0.986491i	−0.836182	−	0.986491i	−1.00000			$\pi$
$348$		0			0
$349$		0			0		0.0149594	−	0.999888i	$-0.495238\pi$
$349$		0			0		−0.0149594	+	0.999888i	$0.504762\pi$
$350$	−0.182592	+	1.73725i	−0.182592	+	1.73725i
$351$		0			0
$352$	−0.00825820	+	0.183883i	−0.00825820	+	0.183883i
$353$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$353$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	2.97163	−	1.83634i	2.97163	−	1.83634i
$359$	0.651501	+	0.792344i	0.651501	+	0.792344i	0.988831	−	0.149042i	$-0.0476190\pi$
$359$	0.651501	+	0.792344i	0.651501	+	0.792344i	−0.337330	+	0.941386i	$0.609524\pi$
$360$		0			0
$361$	−0.599822	−	0.800134i	−0.599822	−	0.800134i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$367$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$368$	−1.18198	+	0.613428i	−1.18198	+	0.613428i
$369$		0			0
$370$		0			0
$371$	−1.50008	−	0.135010i	−1.50008	−	0.135010i
$372$		0			0
$373$	−0.142820	+	1.90580i	−0.142820	+	1.90580i	0.222521	+	0.974928i	$0.428571\pi$
$373$	−0.142820	+	1.90580i	−0.142820	+	1.90580i	−0.365341	+	0.930874i	$0.619048\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.330422	+	0.773060i	0.330422	+	0.773060i	0.999552	+	0.0299155i	$0.00952381\pi$
$379$	0.330422	+	0.773060i	0.330422	+	0.773060i	−0.669131	+	0.743145i	$0.733333\pi$
$380$		0			0
$381$		0			0
$382$	0.623742	+	0.00933186i	0.623742	+	0.00933186i
$383$		0			0		−0.266037	−	0.963963i	$-0.585714\pi$
$383$		0			0		0.266037	+	0.963963i	$0.414286\pi$
$384$		0			0
$385$		0			0
$386$		−	3.38126i		−	3.38126i
$387$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$388$		0			0
$389$	−0.342721	+	0.327675i	−0.342721	+	0.327675i	−0.842721	−	0.538351i	$-0.819048\pi$
$389$	−0.342721	+	0.327675i	−0.342721	+	0.327675i	0.500000	+	0.866025i	$0.333333\pi$
$390$		0			0
$391$		0			0
$392$	−1.05715	−	1.50178i	−1.05715	−	1.50178i
$393$		0			0
$394$	−0.869253	−	1.95237i	−0.869253	−	1.95237i
$395$		0			0
$396$	0.0306872	+	2.05114i	0.0306872	+	2.05114i
$397$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$397$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$398$		0			0
$399$		0			0
$400$	−0.486245	+	1.04958i	−0.486245	+	1.04958i
$401$	0.831706	+	1.34590i	0.831706	+	1.34590i	0.936235	+	0.351375i	$0.114286\pi$
$401$	0.831706	+	1.34590i	0.831706	+	1.34590i	−0.104528	+	0.994522i	$0.533333\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−2.46098	−	0.370933i	−2.46098	−	0.370933i
$407$	−0.0214048	−	0.177996i	−0.0214048	−	0.177996i
$408$		0			0
$409$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$409$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−1.72634	+	1.03144i	−1.72634	+	1.03144i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$419$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$420$		0			0
$421$	−0.693256	−	0.115123i	−0.693256	−	0.115123i	−0.193256	−	0.981148i	$-0.561905\pi$
$421$	−0.693256	−	0.115123i	−0.693256	−	0.115123i	−0.500000	+	0.866025i	$0.666667\pi$
$422$	2.68768	−	0.241895i	2.68768	−	0.241895i
$423$		0			0
$424$	−2.52696	−	1.12507i	−2.52696	−	1.12507i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−1.48563	−	3.08495i	−1.48563	−	3.08495i
$429$		0			0
$430$		0			0
$431$	−1.05140	+	1.44713i	−1.05140	+	1.44713i	−0.163818	+	0.986491i	$0.552381\pi$
$431$	−1.05140	+	1.44713i	−1.05140	+	1.44713i	−0.887586	+	0.460642i	$0.847619\pi$
$432$		0			0
$433$		0			0		−0.379225	−	0.925304i	$-0.623810\pi$
$433$		0			0		0.379225	+	0.925304i	$0.376190\pi$
$434$		0			0
$435$		0			0
$436$	2.26579	+	2.04013i	2.26579	+	2.04013i
$437$		0			0
$438$		0			0
$439$		0			0		−0.149042	−	0.988831i	$-0.547619\pi$
$439$		0			0		0.149042	+	0.988831i	$0.452381\pi$
$440$		0			0
$441$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$442$		0			0
$443$	1.59580	−	0.889773i	1.59580	−	0.889773i	0.599822	−	0.800134i	$-0.295238\pi$
$443$	1.59580	−	0.889773i	1.59580	−	0.889773i	0.995974	−	0.0896393i	$-0.0285714\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.234215	+	0.801695i	0.234215	+	0.801695i
$449$	−0.891446	+	0.904883i	−0.891446	+	0.904883i	−0.995974	−	0.0896393i	$-0.971429\pi$
$449$	−0.891446	+	0.904883i	−0.891446	+	0.904883i	0.104528	+	0.994522i	$0.466667\pi$
$450$	−0.638184	+	1.62607i	−0.638184	+	1.62607i
$451$		0			0
$452$	−1.67577	+	3.47978i	−1.67577	+	3.47978i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.829730	+	0.724913i	0.829730	+	0.724913i	0.963963	−	0.266037i	$-0.0857143\pi$
$457$	0.829730	+	0.724913i	0.829730	+	0.724913i	−0.134233	+	0.990950i	$0.542857\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.563320	−	0.826239i	$-0.309524\pi$
$461$		0			0		−0.563320	+	0.826239i	$0.690476\pi$
$462$		0			0
$463$	−0.954688	−	1.02891i	−0.954688	−	1.02891i	−0.999552	−	0.0299155i	$-0.990476\pi$
$463$	−0.954688	−	1.02891i	−0.954688	−	1.02891i	0.0448648	−	0.998993i	$-0.485714\pi$
$464$	−1.46280	−	0.759171i	−1.46280	−	0.759171i
$465$		0			0
$466$	−1.70864	−	0.363184i	−1.70864	−	0.363184i
$467$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$467$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$468$		0			0
$469$	−1.87163	−	0.702435i	−1.87163	−	0.702435i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.280427	−	0.959875i	−0.280427	−	0.959875i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.41010	−	0.529221i	−1.41010	−	0.529221i
$478$	−2.74268	−	2.05605i	−2.74268	−	2.05605i
$479$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$479$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.456472	+	1.99994i	−0.456472	+	1.99994i
$485$		0			0
$486$		0			0
$487$	−1.64257	−	0.673190i	−1.64257	−	0.673190i	−0.646600	−	0.762830i	$-0.723810\pi$
$487$	−1.64257	−	0.673190i	−1.64257	−	0.673190i	−0.995974	+	0.0896393i	$0.971429\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.56447	+	1.20978i	1.56447	+	1.20978i	0.873408	+	0.486989i	$0.161905\pi$
$491$	1.56447	+	1.20978i	1.56447	+	1.20978i	0.691063	+	0.722795i	$0.257143\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.39591	+	1.41695i	−1.39591	+	1.41695i
$498$		0			0
$499$	−1.99776	+	0.0298887i	−1.99776	+	0.0298887i	−0.999552	−	0.0299155i	$-0.990476\pi$
$499$	−1.99776	+	0.0298887i	−1.99776	+	0.0298887i	−0.998210	+	0.0598042i	$0.980952\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$503$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$504$	−0.619522	−	1.72890i	−0.619522	−	1.72890i
$505$		0			0
$506$	−1.92165	+	0.592751i	−1.92165	+	0.592751i
$507$		0			0
$508$	0.561226	+	0.642375i	0.561226	+	0.642375i
$509$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$509$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$510$		0			0
$511$		0			0
$512$	−0.0857586	+	1.90956i	−0.0857586	+	1.90956i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.135878	+	0.282154i	0.135878	+	0.282154i
$519$		0			0
$520$		0			0
$521$		0			0		0.817719	−	0.575617i	$-0.195238\pi$
$521$		0			0		−0.817719	+	0.575617i	$0.804762\pi$
$522$	−2.27361	−	1.01228i	−2.27361	−	1.01228i
$523$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$523$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$524$		0			0
$525$		0			0
$526$	0.872665	−	0.104942i	0.872665	−	0.104942i
$527$		0			0
$528$		0			0
$529$	−0.238491	−	0.221287i	−0.238491	−	0.221287i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−2.83589	−	2.33179i	−2.83589	−	2.33179i
$537$		0			0
$538$		0			0
$539$	−0.420357	−	0.907359i	−0.420357	−	0.907359i
$540$		0			0
$541$	0.0210231	−	0.702435i	0.0210231	−	0.702435i	−0.925304	−	0.379225i	$-0.876190\pi$
$541$	0.0210231	−	0.702435i	0.0210231	−	0.702435i	0.946327	−	0.323210i	$-0.104762\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.832156	+	1.07613i	0.832156	+	1.07613i	0.995974	+	0.0896393i	$0.0285714\pi$
$547$	0.832156	+	1.07613i	0.832156	+	1.07613i	−0.163818	+	0.986491i	$0.552381\pi$
$548$	1.55429	−	0.0698035i	1.55429	−	0.0698035i
$549$		0			0
$550$	−1.00550	+	1.42841i	−1.00550	+	1.42841i
$551$		0			0
$552$		0			0
$553$	0.223859	+	1.05317i	0.223859	+	1.05317i
$554$	−1.34562	−	1.91158i	−1.34562	−	1.91158i
$555$		0			0
$556$		0			0
$557$	0.384580	−	0.367696i	0.384580	−	0.367696i	−0.473869	−	0.880596i	$-0.657143\pi$
$557$	0.384580	−	0.367696i	0.384580	−	0.367696i	0.858449	+	0.512899i	$0.171429\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.60482	−	0.120264i	1.60482	−	0.120264i
$563$		0			0		−0.266037	−	0.963963i	$-0.585714\pi$
$563$		0			0		0.266037	+	0.963963i	$0.414286\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$568$	−3.26713	+	1.63402i	−3.26713	+	1.63402i
$569$	0.534897	−	0.247805i	0.534897	−	0.247805i	−0.134233	−	0.990950i	$-0.542857\pi$
$569$	0.534897	−	0.247805i	0.534897	−	0.247805i	0.669131	+	0.743145i	$0.266667\pi$
$570$		0			0
$571$	−1.54711	−	1.05480i	−1.54711	−	1.05480i	−0.971490	−	0.237080i	$-0.923810\pi$
$571$	−1.54711	−	1.05480i	−1.54711	−	1.05480i	−0.575617	−	0.817719i	$-0.695238\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.14660	−	0.103196i	−1.14660	−	0.103196i
$576$	0.0124942	+	0.835114i	0.0124942	+	0.835114i
$577$		0			0		−0.941386	−	0.337330i	$-0.890476\pi$
$577$		0			0		0.941386	+	0.337330i	$0.109524\pi$
$578$	1.55045	−	0.804658i	1.55045	−	0.804658i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.24443	−	0.848441i	−1.24443	−	0.848441i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.635116	−	0.772417i	$-0.719048\pi$
$587$		0			0		0.635116	+	0.772417i	$0.280952\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.0247599	+	0.205896i	0.0247599	+	0.205896i
$593$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$593$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$594$		0			0
$595$		0			0
$596$	0.156677	−	1.49069i	0.156677	−	1.49069i
$597$		0			0
$598$		0			0
$599$	1.21074	+	1.42838i	1.21074	+	1.42838i	0.873408	+	0.486989i	$0.161905\pi$
$599$	1.21074	+	1.42838i	1.21074	+	1.42838i	0.337330	+	0.941386i	$0.390476\pi$
$600$		0			0
$601$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$601$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$602$	1.00550	+	1.42841i	1.00550	+	1.42841i
$603$	−1.61731	−	1.17504i	−1.61731	−	1.17504i
$604$	3.42033	−	1.64714i	3.42033	−	1.64714i
$605$		0			0
$606$		0			0
$607$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$607$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.562294	−	1.49823i	−0.562294	−	1.49823i	−0.842721	−	0.538351i	$-0.819048\pi$
$613$	−0.562294	−	1.49823i	−0.562294	−	1.49823i	0.280427	−	0.959875i	$-0.409524\pi$
$614$		0			0
$615$		0			0
$616$	−0.191971	−	1.82649i	−0.191971	−	1.82649i
$617$	0.141209	+	0.359794i	0.141209	+	0.359794i	0.983930	−	0.178557i	$-0.0571429\pi$
$617$	0.141209	+	0.359794i	0.141209	+	0.359794i	−0.842721	+	0.538351i	$0.819048\pi$
$618$		0			0
$619$		0			0		0.575617	−	0.817719i	$-0.304762\pi$
$619$		0			0		−0.575617	+	0.817719i	$0.695238\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.842721	+	0.538351i	−0.842721	+	0.538351i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.243197	−	0.996553i	−0.243197	−	0.996553i	−0.955573	−	0.294755i	$-0.904762\pi$
$631$	−0.243197	−	0.996553i	−0.243197	−	0.996553i	0.712376	−	0.701798i	$-0.247619\pi$
$632$	−0.236092	+	1.96327i	−0.236092	+	1.96327i
$633$		0			0
$634$	−1.62193	+	2.45712i	−1.62193	+	2.45712i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−1.96880	−	1.52245i	−1.96880	−	1.52245i
$639$	−1.72256	+	0.994522i	−1.72256	+	0.994522i
$640$		0			0
$641$	0.444054	−	0.293118i	0.444054	−	0.293118i	−0.309017	−	0.951057i	$-0.600000\pi$
$641$	0.444054	−	0.293118i	0.444054	−	0.293118i	0.753071	+	0.657939i	$0.228571\pi$
$642$		0			0
$643$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$643$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$644$	1.91058	−	1.38812i	1.91058	−	1.38812i
$645$		0			0
$646$		0			0
$647$		0			0		0.178557	−	0.983930i	$-0.442857\pi$
$647$		0			0		−0.178557	+	0.983930i	$0.557143\pi$
$648$	−0.137245	−	1.83141i	−0.137245	−	1.83141i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−2.92659	+	2.63511i	−2.92659	+	2.63511i
$653$	0.146600	+	1.62885i	0.146600	+	1.62885i	0.646600	+	0.762830i	$0.276190\pi$
$653$	0.146600	+	1.62885i	0.146600	+	1.62885i	−0.500000	+	0.866025i	$0.666667\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.85654	+	0.139129i	1.85654	+	0.139129i	0.955573	−	0.294755i	$-0.0952381\pi$
$659$	1.85654	+	0.139129i	1.85654	+	0.139129i	0.900969	+	0.433884i	$0.142857\pi$
$660$		0			0
$661$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$661$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$662$	−2.77007	+	2.07659i	−2.77007	+	2.07659i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.0559181	+	0.308134i	0.0559181	+	0.308134i
$667$	0.220173	−	1.62538i	0.220173	−	1.62538i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.238438	−	0.917253i	0.238438	−	0.917253i	−0.733052	−	0.680173i	$-0.761905\pi$
$673$	0.238438	−	0.917253i	0.238438	−	0.917253i	0.971490	−	0.237080i	$-0.0761905\pi$
$674$	0.645199	−	1.57428i	0.645199	−	1.57428i
$675$		0			0
$676$	2.05045	−	0.0613676i	2.05045	−	0.0613676i
$677$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$677$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.86938	+	0.576628i	−1.86938	+	0.576628i	−0.873408	+	0.486989i	$0.838095\pi$
$683$	−1.86938	+	0.576628i	−1.86938	+	0.576628i	−0.995974	+	0.0896393i	$0.971429\pi$
$684$		0			0
$685$		0			0
$686$	1.20716	+	1.26259i	1.20716	+	1.26259i
$687$		0			0
$688$	0.324382	+	1.11033i	0.324382	+	1.11033i
$689$		0			0
$690$		0			0
$691$		0			0		−0.850680	−	0.525684i	$-0.823810\pi$
$691$		0			0		0.850680	+	0.525684i	$0.176190\pi$
$692$		0			0
$693$	−0.163818	−	0.986491i	−0.163818	−	0.986491i
$694$	1.12949	+	1.95634i	1.12949	+	1.95634i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.575260	−	1.96906i	0.575260	−	1.96906i
$701$	−0.0582479	−	0.104467i	−0.0582479	−	0.104467i	0.842721	−	0.538351i	$-0.180952\pi$
$701$	−0.0582479	−	0.104467i	−0.0582479	−	0.104467i	−0.900969	+	0.433884i	$0.857143\pi$
$702$		0			0
$703$		0			0
$704$	−0.185851	+	0.814267i	−0.185851	+	0.814267i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.86224	−	0.337947i	1.86224	−	0.337947i	0.873408	−	0.486989i	$-0.161905\pi$
$709$	1.86224	−	0.337947i	1.86224	−	0.337947i	0.988831	+	0.149042i	$0.0476190\pi$
$710$		0			0
$711$	−0.0643912	+	1.07477i	−0.0643912	+	1.07477i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−3.81870	+	1.49873i	−3.81870	+	1.49873i
$717$		0			0
$718$	−0.872626	−	1.56504i	−0.872626	−	1.56504i
$719$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$719$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$720$		0			0
$721$		0			0
$722$	0.781374	+	1.56231i	0.781374	+	1.56231i
$723$		0			0
$724$		0			0
$725$	−0.712376	−	1.23387i	−0.712376	−	1.23387i
$726$		0			0
$727$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$727$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$728$		0			0
$729$	−0.134233	−	0.990950i	−0.134233	−	0.990950i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$733$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$734$		0			0
$735$		0			0
$736$	0.202492	−	0.0624604i	0.202492	−	0.0624604i
$737$	−1.29262	−	1.52498i	−1.29262	−	1.52498i
$738$		0			0
$739$	−0.591952	+	0.517173i	−0.591952	+	0.517173i	−0.900969	−	0.433884i	$-0.857143\pi$
$739$	−0.591952	+	0.517173i	−0.591952	+	0.517173i	0.309017	+	0.951057i	$0.400000\pi$
$740$		0			0
$741$		0			0
$742$	2.53614	+	0.699931i	2.53614	+	0.699931i
$743$	1.19911	−	0.0358879i	1.19911	−	0.0358879i	0.575617	−	0.817719i	$-0.304762\pi$
$743$	1.19911	−	0.0358879i	1.19911	−	0.0358879i	0.623490	+	0.781831i	$0.285714\pi$
$744$		0			0
$745$		0			0
$746$	0.839902	−	3.23104i	0.839902	−	3.23104i
$747$		0			0
$748$		0			0
$749$	0.940264	+	1.37911i	0.940264	+	1.37911i
$750$		0			0
$751$	1.25307	−	1.52396i	1.25307	−	1.52396i	0.500000	−	0.866025i	$-0.333333\pi$
$751$	1.25307	−	1.52396i	1.25307	−	1.52396i	0.753071	−	0.657939i	$-0.228571\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.650887	+	0.487939i	−0.650887	+	0.487939i	−0.873408	−	0.486989i	$-0.838095\pi$
$757$	−0.650887	+	0.487939i	−0.650887	+	0.487939i	0.222521	+	0.974928i	$0.428571\pi$
$758$	−0.326788	−	1.43175i	−0.326788	−	1.43175i
$759$		0			0
$760$		0			0
$761$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$761$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$762$		0			0
$763$	−1.24042	−	0.818792i	−1.24042	−	0.818792i
$764$	−0.718761	−	0.141574i	−0.718761	−	0.141574i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.294755	−	0.955573i	$-0.595238\pi$
$769$		0			0		0.294755	+	0.955573i	$0.404762\pi$
$770$		0			0
$771$		0			0
$772$	−0.709008	+	3.90696i	−0.709008	+	3.90696i
$773$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$773$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$774$	0.589254	+	1.64443i	0.589254	+	1.64443i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.691253	−	0.456292i	0.691253	−	0.456292i
$779$		0			0
$780$		0			0
$781$	−1.90923	+	0.557782i	−1.90923	+	0.557782i
$782$		0			0
$783$		0			0
$784$	0.486245	+	1.04958i	0.486245	+	1.04958i
$785$		0			0
$786$		0			0
$787$		0			0		0.119394	−	0.992847i	$-0.461905\pi$
$787$		0			0		−0.119394	+	0.992847i	$0.538095\pi$
$788$	0.595011	+	2.43819i	0.595011	+	2.43819i
$789$		0			0
$790$		0			0
$791$	0.554957	−	1.79913i	0.554957	−	1.79913i
$792$	0.300859	−	1.81174i	0.300859	−	1.81174i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.251587	−	0.967835i	$-0.580952\pi$
$797$		0			0		0.251587	+	0.967835i	$0.419048\pi$
$798$		0			0
$799$		0			0
$800$	0.105953	−	0.150516i	0.105953	−	0.150516i
$801$		0			0
$802$	−1.00970	−	2.57267i	−1.00970	−	2.57267i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.436004	+	0.186357i	−0.436004	+	0.186357i	−0.599822	−	0.800134i	$-0.704762\pi$
$809$	−0.436004	+	0.186357i	−0.436004	+	0.186357i	0.163818	+	0.986491i	$0.447619\pi$
$810$		0			0
$811$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$811$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$812$	2.76582	+	0.944642i	2.76582	+	0.944642i
$813$		0			0
$814$	−0.0187287	+	0.312606i	−0.0187287	+	0.312606i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.104739	−	0.279077i	0.104739	−	0.279077i	−0.873408	−	0.486989i	$-0.838095\pi$
$821$	0.104739	−	0.279077i	0.104739	−	0.279077i	0.978148	+	0.207912i	$0.0666667\pi$
$822$		0			0
$823$	−0.135176	+	1.28611i	−0.135176	+	1.28611i	0.691063	+	0.722795i	$0.257143\pi$
$823$	−0.135176	+	1.28611i	−0.135176	+	1.28611i	−0.826239	+	0.563320i	$0.809524\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.238121	+	1.98014i	0.238121	+	1.98014i	0.193256	+	0.981148i	$0.438095\pi$
$827$	0.238121	+	1.98014i	0.238121	+	1.98014i	0.0448648	+	0.998993i	$0.485714\pi$
$828$	2.21102	−	0.829808i	2.21102	−	0.829808i
$829$		0			0		−0.959875	−	0.280427i	$-0.909524\pi$
$829$		0			0		0.959875	+	0.280427i	$0.0904762\pi$
$830$		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		−0.722795	−	0.691063i	$-0.757143\pi$
$839$		0			0		0.722795	+	0.691063i	$0.242857\pi$
$840$		0			0
$841$	0.914141	−	0.474424i	0.914141	−	0.474424i
$842$	1.15562	+	0.414098i	1.15562	+	0.414098i
$843$		0			0
$844$	−3.15626	−	0.284069i	−3.15626	−	0.284069i
$845$		0			0
$846$		0			0
$847$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$848$	1.43949	+	0.981426i	1.43949	+	0.981426i
$849$		0			0
$850$		0			0
$851$	−0.184592	+	0.0923217i	−0.184592	+	0.0923217i
$852$		0			0
$853$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$853$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$854$		0			0
$855$		0			0
$856$	0.815526	+	2.95499i	0.815526	+	2.95499i
$857$		0			0		0.997204	−	0.0747301i	$-0.0238095\pi$
$857$		0			0		−0.997204	+	0.0747301i	$0.976190\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$	2.25846	−	2.15931i	2.25846	−	2.15931i
$863$	−1.42020	+	1.20381i	−1.42020	+	1.20381i	−0.473869	+	0.880596i	$0.657143\pi$
$863$	−1.42020	+	1.20381i	−1.42020	+	1.20381i	−0.946327	+	0.323210i	$0.895238\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.317363	+	1.02887i	−0.317363	+	1.02887i
$870$		0			0
$871$		0			0
$872$	−1.66979	−	2.15934i	−1.66979	−	2.15934i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.39124	+	0.979332i	1.39124	+	0.979332i	0.998210	+	0.0598042i	$0.0190476\pi$
$877$	1.39124	+	0.979332i	1.39124	+	0.979332i	0.393025	+	0.919528i	$0.371429\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$881$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$882$	0.827762	+	1.53824i	0.827762	+	1.53824i
$883$	0.343758	+	0.282653i	0.343758	+	0.282653i	0.791071	−	0.611724i	$-0.209524\pi$
$883$	0.343758	+	0.282653i	0.343758	+	0.282653i	−0.447313	+	0.894377i	$0.647619\pi$
$884$		0			0
$885$		0			0
$886$	−3.02029	+	1.03155i	−3.02029	+	1.03155i
$887$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$887$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$888$		0			0
$889$	−0.317202	−	0.268871i	−0.317202	−	0.268871i
$890$		0			0
$891$	0.104528	−	0.994522i	0.104528	−	0.994522i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.171743	−	1.63402i	−0.171743	−	1.63402i
$897$		0			0
$898$	1.81441	−	1.27721i	1.81441	−	1.27721i
$899$		0			0
$900$	1.07837	−	1.74506i	1.07837	−	1.74506i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	2.03244	−	2.79742i	2.03244	−	2.79742i
$905$		0			0
$906$		0			0
$907$	0.0225748	−	0.502667i	0.0225748	−	0.502667i	−0.955573	−	0.294755i	$-0.904762\pi$
$907$	0.0225748	−	0.502667i	0.0225748	−	0.502667i	0.978148	−	0.207912i	$-0.0666667\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.741260	+	0.848441i	0.741260	+	0.848441i	0.992847	−	0.119394i	$-0.0380952\pi$
$911$	0.741260	+	0.848441i	0.741260	+	0.848441i	−0.251587	+	0.967835i	$0.580952\pi$
$912$		0			0
$913$		0			0
$914$	−1.19999	−	1.50474i	−1.19999	−	1.50474i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.0393651	+	0.0450570i	−0.0393651	+	0.0450570i	−0.772417	−	0.635116i	$-0.780952\pi$
$919$	−0.0393651	+	0.0450570i	−0.0393651	+	0.0450570i	0.733052	+	0.680173i	$0.238095\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.0777861	+	0.161524i	−0.0777861	+	0.161524i
$926$	1.31994	+	2.06620i	1.31994	+	2.06620i
$927$		0			0
$928$	0.207460	+	0.160426i	0.207460	+	0.160426i
$929$		0			0		−0.323210	−	0.946327i	$-0.604762\pi$
$929$		0			0		0.323210	+	0.946327i	$0.395238\pi$
$930$		0			0
$931$		0			0
$932$	1.89814	+	0.777931i	1.89814	+	0.777931i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.887586	−	0.460642i	$-0.847619\pi$
$937$		0			0		0.887586	+	0.460642i	$0.152381\pi$
$938$	2.99776	+	1.79108i	2.99776	+	1.79108i
$939$		0			0
$940$		0			0
$941$		0			0		−0.800134	−	0.599822i	$-0.795238\pi$
$941$		0			0		0.800134	+	0.599822i	$0.204762\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	0.182592	+	1.73725i	0.182592	+	1.73725i
$947$	0.149460			0.149460			0.0747301	−	0.997204i	$-0.476190\pi$
$947$	0.149460			0.149460			0.0747301	+	0.997204i	$0.476190\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.262600	+	0.0558173i	0.262600	+	0.0558173i	0.337330	−	0.941386i	$-0.390476\pi$
$953$	0.262600	+	0.0558173i	0.262600	+	0.0558173i	−0.0747301	+	0.997204i	$0.523810\pi$
$954$	2.25854	+	1.34942i	2.25854	+	1.34942i
$955$		0			0
$956$	2.73796	+	2.95082i	2.73796	+	2.95082i
$957$		0			0
$958$		0			0
$959$	−0.744153	+	0.146575i	−0.744153	+	0.146575i
$960$		0			0
$961$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$962$		0			0
$963$	0.539484	+	1.57956i	0.539484	+	1.57956i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.787376	−	1.63500i	0.787376	−	1.63500i	0.0149594	−	0.999888i	$-0.495238\pi$
$967$	0.787376	−	1.63500i	0.787376	−	1.63500i	0.772417	−	0.635116i	$-0.219048\pi$
$968$	0.721809	−	1.68876i	0.721809	−	1.68876i
$969$		0			0
$970$		0			0
$971$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$971$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$972$		0			0
$973$		0			0
$974$	2.61319	+	1.66937i	2.61319	+	1.66937i
$975$		0			0
$976$		0			0
$977$	−0.579161	−	1.61626i	−0.579161	−	1.61626i	−0.772417	−	0.635116i	$-0.780952\pi$
$977$	−0.579161	−	1.61626i	−0.579161	−	1.61626i	0.193256	−	0.981148i	$-0.438095\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.977888	−	1.11928i	−0.977888	−	1.11928i
$982$	−2.31159	−	2.56728i	−2.31159	−	2.56728i
$983$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$983$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.931368	+	0.676678i	−0.931368	+	0.676678i
$990$		0			0
$991$	−0.678448	−	1.40881i	−0.678448	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$991$	−0.678448	−	1.40881i	−0.678448	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$992$		0			0
$993$		0			0
$994$	2.84116	−	1.99998i	2.84116	−	1.99998i
$995$		0			0
$996$		0			0
$997$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$997$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$998$	3.44297	+	0.571743i	3.44297	+	0.571743i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3311.1.gb.a.1448.1	yes	48
7.6	odd	2	CM	3311.1.gb.a.1448.1	yes	48
11.8	odd	10		3311.1.gb.b.2351.1	yes	48
43.3	odd	42		3311.1.gb.b.3142.1	yes	48
77.41	even	10		3311.1.gb.b.2351.1	yes	48
301.132	even	42		3311.1.gb.b.3142.1	yes	48
473.261	even	210	inner	3311.1.gb.a.734.1	✓	48
3311.734	odd	210	inner	3311.1.gb.a.734.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3311.1.gb.a.734.1	✓	48	473.261	even	210	inner
3311.1.gb.a.734.1	✓	48	3311.734	odd	210	inner
3311.1.gb.a.1448.1	yes	48	1.1	even	1	trivial
3311.1.gb.a.1448.1	yes	48	7.6	odd	2	CM
3311.1.gb.b.2351.1	yes	48	11.8	odd	10
3311.1.gb.b.2351.1	yes	48	77.41	even	10
3311.1.gb.b.3142.1	yes	48	43.3	odd	42
3311.1.gb.b.3142.1	yes	48	301.132	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)

\(f(q)\)	\(=\)	\(q+(-1.71874 - 0.311906i) q^{2} +(1.92056 + 0.720799i) q^{4} +(-0.978148 - 0.207912i) q^{7} +(-1.57658 - 0.941963i) q^{8} +(-0.887586 - 0.460642i) q^{9} +O(q^{10})\)	\(q+(-1.71874 - 0.311906i) q^{2} +(1.92056 + 0.720799i) q^{4} +(-0.978148 - 0.207912i) q^{7} +(-1.57658 - 0.941963i) q^{8} +(-0.887586 - 0.460642i) q^{9} +(-0.753071 - 0.657939i) q^{11} +(1.61634 + 0.662437i) q^{14} +(0.871109 + 0.761065i) q^{16} +(1.38186 + 1.06857i) q^{18} +(1.08912 + 1.36572i) q^{22} +(-0.420593 + 1.07165i) q^{23} +(0.280427 + 0.959875i) q^{25} +(-1.72873 - 1.10435i) q^{28} +(-1.38413 + 0.337781i) q^{29} +(-0.114765 - 0.143911i) q^{32} +(-1.37263 - 1.52446i) q^{36} +(0.133230 + 0.119961i) q^{37} +(0.842721 + 0.538351i) q^{43} +(-0.972079 - 1.80643i) q^{44} +(1.05715 - 1.71071i) q^{46} +(0.913545 + 0.406737i) q^{49} +(-0.182592 - 1.73725i) q^{50} +(1.49537 - 0.179825i) q^{53} +(1.34628 + 1.24917i) q^{56} +(2.48433 - 0.148839i) q^{58} +(0.772417 + 0.635116i) q^{63} +(-0.395779 - 0.735480i) q^{64} +(1.97678 + 0.297951i) q^{67} +(1.07080 - 1.67621i) q^{71} +(0.965442 + 1.56231i) q^{72} +(-0.191572 - 0.247737i) q^{74} +(0.599822 + 0.800134i) q^{77} +(-0.437934 - 0.983616i) q^{79} +(0.575617 + 0.817719i) q^{81} +(-1.28051 - 1.18814i) q^{86} +(0.567524 + 1.74666i) q^{88} +(-1.58022 + 1.75501i) q^{92} +(-1.44329 - 0.984017i) q^{98} +(0.365341 + 0.930874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{2} + 6 q^{7} - 21 q^{8} + q^{9}+O(q^{10}) \) 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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