LMFDB - Embedded newform 3311.1.gb.a.1525.1

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			1525.1
Root			$-0.971490 - 0.237080i$ of defining polynomial
Character	$\chi$	$=$	3311.1525
Dual form			3311.1.gb.a.888.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0709825 - 1.58055i) q^{2} +(-1.49712 + 0.134743i) q^{4} +(0.669131 - 0.743145i) q^{7} +(0.106862 + 0.788887i) q^{8} +(-0.992847 + 0.119394i) q^{9} +O(q^{10})$	\(q+(-0.0709825 - 1.58055i) q^{2} +(-1.49712 + 0.134743i) q^{4} +(0.669131 - 0.743145i) q^{7} +(0.106862 + 0.788887i) q^{8} +(-0.992847 + 0.119394i) q^{9} +(-0.983930 + 0.178557i) q^{11} +(-1.22207 - 1.00484i) q^{14} +(-0.239727 + 0.0435041i) q^{16} +(0.259183 + 1.56077i) q^{18} +(0.352060 + 1.54247i) q^{22} +(-1.85666 - 0.572703i) q^{23} +(0.447313 - 0.894377i) q^{25} +(-0.901636 + 1.20274i) q^{28} +(-0.385820 - 0.0231150i) q^{29} +(0.262924 + 1.15195i) q^{32} +(1.47033 - 0.312527i) q^{36} +(-0.300555 + 1.41400i) q^{37} +(0.599822 - 0.800134i) q^{43} +(1.44900 - 0.399900i) q^{44} +(-0.773395 + 2.97519i) q^{46} +(-0.104528 - 0.994522i) q^{49} +(-1.44536 - 0.643515i) q^{50} +(-1.96698 - 0.0588694i) q^{53} +(0.657762 + 0.448455i) q^{56} +(-0.00914793 + 0.611448i) q^{58} +(-0.575617 + 0.817719i) q^{63} +(1.56718 - 0.432514i) q^{64} +(-1.04442 - 0.969078i) q^{67} +(0.650887 + 0.487939i) q^{71} +(-0.200286 - 0.770486i) q^{72} +(2.25623 + 0.374673i) q^{74} +(-0.525684 + 0.850680i) q^{77} +(-1.59150 - 0.167273i) q^{79} +(0.971490 - 0.237080i) q^{81} +(-1.30723 - 0.891252i) q^{86} +(-0.246006 - 0.757128i) q^{88} +(2.85681 + 0.607234i) q^{92} +(-1.56447 + 0.235806i) q^{98} +(0.955573 - 0.294755i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3311\mathbb{Z}\right)^\times$.

$n$	$904$	$1893$	$2927$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{37}{42}\right)$

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 $

$2$	−0.0709825	−	1.58055i	−0.0709825	−	1.58055i	−0.646600	−	0.762830i	$-0.723810\pi$
$2$	−0.0709825	−	1.58055i	−0.0709825	−	1.58055i	0.575617	−	0.817719i	$-0.304762\pi$
$3$		0			0		−0.0598042	−	0.998210i	$-0.519048\pi$
$3$		0			0		0.0598042	+	0.998210i	$0.480952\pi$
$4$	−1.49712	+	0.134743i	−1.49712	+	0.134743i
$5$		0			0		0.850680	−	0.525684i	$-0.176190\pi$
$5$		0			0		−0.850680	+	0.525684i	$0.823810\pi$
$6$		0			0
$7$	0.669131	−	0.743145i	0.669131	−	0.743145i
$7$	0.669131	−	0.743145i	0.669131	−	0.743145i
$8$	0.106862	+	0.788887i	0.106862	+	0.788887i
$9$	−0.992847	+	0.119394i	−0.992847	+	0.119394i
$10$		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		0.941386	−	0.337330i	$-0.109524\pi$
$13$		0			0		−0.941386	+	0.337330i	$0.890476\pi$
$14$	−1.22207	−	1.00484i	−1.22207	−	1.00484i
$15$		0			0
$16$	−0.239727	+	0.0435041i	−0.239727	+	0.0435041i
$17$		0			0		0.762830	−	0.646600i	$-0.223810\pi$
$17$		0			0		−0.762830	+	0.646600i	$0.776190\pi$
$18$	0.259183	+	1.56077i	0.259183	+	1.56077i
$19$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$19$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$20$		0			0
$21$		0			0
$22$	0.352060	+	1.54247i	0.352060	+	1.54247i
$23$	−1.85666	−	0.572703i	−1.85666	−	0.572703i	−0.998210	−	0.0598042i	$-0.980952\pi$
$23$	−1.85666	−	0.572703i	−1.85666	−	0.572703i	−0.858449	−	0.512899i	$-0.828571\pi$
$24$		0			0
$25$	0.447313	−	0.894377i	0.447313	−	0.894377i
$26$		0			0
$27$		0			0
$28$	−0.901636	+	1.20274i	−0.901636	+	1.20274i
$29$	−0.385820	−	0.0231150i	−0.385820	−	0.0231150i	−0.134233	−	0.990950i	$-0.542857\pi$
$29$	−0.385820	−	0.0231150i	−0.385820	−	0.0231150i	−0.251587	+	0.967835i	$0.580952\pi$
$30$		0			0
$31$		0			0		−0.887586	−	0.460642i	$-0.847619\pi$
$31$		0			0		0.887586	+	0.460642i	$0.152381\pi$
$32$	0.262924	+	1.15195i	0.262924	+	1.15195i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	1.47033	−	0.312527i	1.47033	−	0.312527i
$37$	−0.300555	+	1.41400i	−0.300555	+	1.41400i	0.525684	+	0.850680i	$0.323810\pi$
$37$	−0.300555	+	1.41400i	−0.300555	+	1.41400i	−0.826239	+	0.563320i	$0.809524\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.351375	−	0.936235i	$-0.614286\pi$
$41$		0			0		0.351375	+	0.936235i	$0.385714\pi$
$42$		0			0
$43$	0.599822	−	0.800134i	0.599822	−	0.800134i
$43$	0.599822	−	0.800134i	0.599822	−	0.800134i
$44$	1.44900	−	0.399900i	1.44900	−	0.399900i
$45$		0			0
$46$	−0.773395	+	2.97519i	−0.773395	+	2.97519i
$47$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$47$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$48$		0			0
$49$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$50$	−1.44536	−	0.643515i	−1.44536	−	0.643515i
$51$		0			0
$52$		0			0
$53$	−1.96698	−	0.0588694i	−1.96698	−	0.0588694i	−0.978148	−	0.207912i	$-0.933333\pi$
$53$	−1.96698	−	0.0588694i	−1.96698	−	0.0588694i	−0.988831	+	0.149042i	$0.952381\pi$
$54$		0			0
$55$		0			0
$56$	0.657762	+	0.448455i	0.657762	+	0.448455i
$57$		0			0
$58$	−0.00914793	+	0.611448i	−0.00914793	+	0.611448i
$59$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$59$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$60$		0			0
$61$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$61$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$62$		0			0
$63$	−0.575617	+	0.817719i	−0.575617	+	0.817719i
$64$	1.56718	−	0.432514i	1.56718	−	0.432514i
$65$		0			0
$66$		0			0
$67$	−1.04442	−	0.969078i	−1.04442	−	0.969078i	−0.0448648	−	0.998993i	$-0.514286\pi$
$67$	−1.04442	−	0.969078i	−1.04442	−	0.969078i	−0.999552	+	0.0299155i	$0.990476\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.650887	+	0.487939i	0.650887	+	0.487939i	0.873408	−	0.486989i	$-0.161905\pi$
$71$	0.650887	+	0.487939i	0.650887	+	0.487939i	−0.222521	+	0.974928i	$0.571429\pi$
$72$	−0.200286	−	0.770486i	−0.200286	−	0.770486i
$73$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$73$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$74$	2.25623	+	0.374673i	2.25623	+	0.374673i
$75$		0			0
$76$		0			0
$77$	−0.525684	+	0.850680i	−0.525684	+	0.850680i
$78$		0			0
$79$	−1.59150	−	0.167273i	−1.59150	−	0.167273i	−0.733052	−	0.680173i	$-0.761905\pi$
$79$	−1.59150	−	0.167273i	−1.59150	−	0.167273i	−0.858449	+	0.512899i	$0.828571\pi$
$80$		0			0
$81$	0.971490	−	0.237080i	0.971490	−	0.237080i
$82$		0			0
$83$		0			0		0.538351	−	0.842721i	$-0.319048\pi$
$83$		0			0		−0.538351	+	0.842721i	$0.680952\pi$
$84$		0			0
$85$		0			0
$86$	−1.30723	−	0.891252i	−1.30723	−	0.891252i
$87$		0			0
$88$	−0.246006	−	0.757128i	−0.246006	−	0.757128i
$89$		0			0		0.930874	−	0.365341i	$-0.119048\pi$
$89$		0			0		−0.930874	+	0.365341i	$0.880952\pi$
$90$		0			0
$91$		0			0
$92$	2.85681	+	0.607234i	2.85681	+	0.607234i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$97$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$98$	−1.56447	+	0.235806i	−1.56447	+	0.235806i
$99$	0.955573	−	0.294755i	0.955573	−	0.294755i
$100$	−0.549171	+	1.39926i	−0.549171	+	1.39926i
$101$		0			0		0.323210	−	0.946327i	$-0.395238\pi$
$101$		0			0		−0.323210	+	0.946327i	$0.604762\pi$
$102$		0			0
$103$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$103$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$104$		0			0
$105$		0			0
$106$	0.0465751	+	3.11308i	0.0465751	+	3.11308i
$107$	−0.856104	+	0.565109i	−0.856104	+	0.565109i	−0.900969	−	0.433884i	$-0.857143\pi$
$107$	−0.856104	+	0.565109i	−0.856104	+	0.565109i	0.0448648	+	0.998993i	$0.485714\pi$
$108$		0			0
$109$	−0.122566	+	0.397350i	−0.122566	+	0.397350i	−0.995974	−	0.0896393i	$-0.971429\pi$
$109$	−0.122566	+	0.397350i	−0.122566	+	0.397350i	0.873408	+	0.486989i	$0.161905\pi$
$110$		0			0
$111$		0			0
$112$	−0.128079	+	0.207262i	−0.128079	+	0.207262i
$113$	−0.665900	−	0.636666i	−0.665900	−	0.636666i	0.280427	−	0.959875i	$-0.409524\pi$
$113$	−0.665900	−	0.636666i	−0.665900	−	0.636666i	−0.946327	+	0.323210i	$0.895238\pi$
$114$		0			0
$115$		0			0
$116$	0.580734	−	0.0173807i	0.580734	−	0.0173807i
$117$		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
$126$	1.33330	+	0.851747i	1.33330	+	0.851747i
$127$	0.395408	−	1.43273i	0.395408	−	1.43273i	−0.447313	−	0.894377i	$-0.647619\pi$
$127$	0.395408	−	1.43273i	0.395408	−	1.43273i	0.842721	−	0.538351i	$-0.180952\pi$
$128$	−0.429727	−	1.32256i	−0.429727	−	1.32256i
$129$		0			0
$130$		0			0
$131$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$131$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$132$		0			0
$133$		0			0
$134$	−1.45754	+	1.71954i	−1.45754	+	1.71954i
$135$		0			0
$136$		0			0
$137$	1.11856	+	0.601923i	1.11856	+	0.601923i	0.925304	−	0.379225i	$-0.123810\pi$
$137$	1.11856	+	0.601923i	1.11856	+	0.601923i	0.193256	+	0.981148i	$0.438095\pi$
$138$		0			0
$139$		0			0		0.611724	−	0.791071i	$-0.290476\pi$
$139$		0			0		−0.611724	+	0.791071i	$0.709524\pi$
$140$		0			0
$141$		0			0
$142$	0.725010	−	1.06339i	0.725010	−	1.06339i
$143$		0			0
$144$	0.232819	−	0.0718150i	0.232819	−	0.0718150i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	0.259440	−	2.15743i	0.259440	−	2.15743i
$149$	1.80857	−	0.617701i	1.80857	−	0.617701i	0.809017	−	0.587785i	$-0.200000\pi$
$149$	1.80857	−	0.617701i	1.80857	−	0.617701i	0.999552	−	0.0299155i	$-0.00952381\pi$
$150$		0			0
$151$	0.851044	+	1.28928i	0.851044	+	1.28928i	0.955573	+	0.294755i	$0.0952381\pi$
$151$	0.851044	+	1.28928i	0.851044	+	1.28928i	−0.104528	+	0.994522i	$0.533333\pi$
$152$		0			0
$153$		0			0
$154$	1.38186	+	0.770486i	1.38186	+	0.770486i
$155$		0			0
$156$		0			0
$157$		0			0		−0.999888	−	0.0149594i	$-0.995238\pi$
$157$		0			0		0.999888	+	0.0149594i	$0.00476190\pi$
$158$	−0.151415	+	2.52732i	−0.151415	+	2.52732i
$159$		0			0
$160$		0			0
$161$	−1.66795	+	0.996553i	−1.66795	+	0.996553i
$162$	−0.443676	−	1.51866i	−0.443676	−	1.51866i
$163$	−0.213567	−	1.77596i	−0.213567	−	1.77596i	−0.550897	−	0.834573i	$-0.685714\pi$
$163$	−0.213567	−	1.77596i	−0.213567	−	1.77596i	0.337330	−	0.941386i	$-0.390476\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.762830	−	0.646600i	$-0.776190\pi$
$167$		0			0		0.762830	+	0.646600i	$0.223810\pi$
$168$		0			0
$169$	0.772417	−	0.635116i	0.772417	−	0.635116i
$170$		0			0
$171$		0			0
$172$	−0.790194	+	1.27872i	−0.790194	+	1.27872i
$173$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$173$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$174$		0			0
$175$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$176$	0.228107	−	0.0856100i	0.228107	−	0.0856100i
$177$		0			0
$178$		0			0
$179$	−0.157691	−	0.741877i	−0.157691	−	0.741877i	−0.983930	−	0.178557i	$-0.942857\pi$
$179$	−0.157691	−	0.741877i	−0.157691	−	0.741877i	0.826239	−	0.563320i	$-0.190476\pi$
$180$		0			0
$181$		0			0		0.193256	−	0.981148i	$-0.438095\pi$
$181$		0			0		−0.193256	+	0.981148i	$0.561905\pi$
$182$		0			0
$183$		0			0
$184$	0.253392	−	1.52589i	0.253392	−	1.52589i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.81289	+	0.839868i	1.81289	+	0.839868i	0.925304	+	0.379225i	$0.123810\pi$
$191$	1.81289	+	0.839868i	1.81289	+	0.839868i	0.887586	+	0.460642i	$0.152381\pi$
$192$		0			0
$193$	−0.645768	−	0.0290015i	−0.645768	−	0.0290015i	−0.280427	−	0.959875i	$-0.590476\pi$
$193$	−0.645768	−	0.0290015i	−0.645768	−	0.0290015i	−0.365341	+	0.930874i	$0.619048\pi$
$194$		0			0
$195$		0			0
$196$	0.290497	+	1.47484i	0.290497	+	1.47484i
$197$	−0.294058	+	1.95094i	−0.294058	+	1.95094i	0.0149594	+	0.999888i	$0.495238\pi$
$197$	−0.294058	+	1.95094i	−0.294058	+	1.95094i	−0.309017	+	0.951057i	$0.600000\pi$
$198$	−0.533704	−	1.48941i	−0.533704	−	1.48941i
$199$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$199$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$200$	0.753364	+	0.257305i	0.753364	+	0.257305i
$201$		0			0
$202$		0			0
$203$	−0.275342	+	0.271253i	−0.275342	+	0.271253i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.91176	+	0.346932i	1.91176	+	0.346932i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.866962	+	0.757442i	−0.866962	+	0.757442i	−0.971490	−	0.237080i	$-0.923810\pi$
$211$	−0.866962	+	0.757442i	−0.866962	+	0.757442i	0.104528	+	0.994522i	$0.466667\pi$
$212$	2.95274	−	0.176903i	2.95274	−	0.176903i
$213$		0			0
$214$	0.953951	+	1.31300i	0.953951	+	1.31300i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.636730	+	0.165517i	0.636730	+	0.165517i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.990950	−	0.134233i	$-0.0428571\pi$
$223$		0			0		−0.990950	+	0.134233i	$0.957143\pi$
$224$	1.03199	+	0.575411i	1.03199	+	0.575411i
$225$	−0.337330	+	0.941386i	−0.337330	+	0.941386i
$226$	−0.959014	+	1.09768i	−0.959014	+	1.09768i
$227$		0			0		−0.447313	−	0.894377i	$-0.647619\pi$
$227$		0			0		0.447313	+	0.894377i	$0.352381\pi$
$228$		0			0
$229$		0			0		0.842721	−	0.538351i	$-0.180952\pi$
$229$		0			0		−0.842721	+	0.538351i	$0.819048\pi$
$230$		0			0
$231$		0			0
$232$	−0.0229944	−	0.306839i	−0.0229944	−	0.306839i
$233$	−0.712376	−	0.701798i	−0.712376	−	0.701798i	0.251587	−	0.967835i	$-0.419048\pi$
$233$	−0.712376	−	0.701798i	−0.712376	−	0.701798i	−0.963963	+	0.266037i	$0.914286\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.916889	−	1.64443i	−0.916889	−	1.64443i	−0.753071	−	0.657939i	$-0.771429\pi$
$239$	−0.916889	−	1.64443i	−0.916889	−	1.64443i	−0.163818	−	0.986491i	$-0.552381\pi$
$240$		0			0
$241$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$241$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$242$	−0.621821	−	1.45482i	−0.621821	−	1.45482i
$243$		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		0.104528	−	0.994522i	$-0.466667\pi$
$251$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$252$	0.751587	−	1.30179i	0.751587	−	1.30179i
$253$	1.92908	+	0.231981i	1.92908	+	0.231981i
$254$	−2.29256	−	0.523263i	−2.29256	−	0.523263i
$255$		0			0
$256$	−0.537774	+	0.201830i	−0.537774	+	0.201830i
$257$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$257$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$258$		0			0
$259$	0.849696	+	1.16951i	0.849696	+	1.16951i
$260$		0			0
$261$	0.385820	−	0.0231150i	0.385820	−	0.0231150i
$262$		0			0
$263$	0.141438	−	1.88736i	0.141438	−	1.88736i	−0.251587	−	0.967835i	$-0.580952\pi$
$263$	0.141438	−	1.88736i	0.141438	−	1.88736i	0.393025	−	0.919528i	$-0.371429\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	1.69420	+	1.31010i	1.69420	+	1.31010i
$269$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$269$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$270$		0			0
$271$		0			0		−0.959875	−	0.280427i	$-0.909524\pi$
$271$		0			0		0.959875	+	0.280427i	$0.0904762\pi$
$272$		0			0
$273$		0			0
$274$	0.871970	−	1.81067i	0.871970	−	1.81067i
$275$	−0.280427	+	0.959875i	−0.280427	+	0.959875i
$276$		0			0
$277$	−0.378066	−	1.91942i	−0.378066	−	1.91942i	−0.393025	−	0.919528i	$-0.628571\pi$
$277$	−0.378066	−	1.91942i	−0.378066	−	1.91942i	0.0149594	−	0.999888i	$-0.495238\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.0771787	+	0.225972i	0.0771787	+	0.225972i	0.978148	−	0.207912i	$-0.0666667\pi$
$281$	0.0771787	+	0.225972i	0.0771787	+	0.225972i	−0.900969	+	0.433884i	$0.857143\pi$
$282$		0			0
$283$		0			0		−0.894377	−	0.447313i	$-0.852381\pi$
$283$		0			0		0.894377	+	0.447313i	$0.147619\pi$
$284$	−1.04020	−	0.642802i	−1.04020	−	0.642802i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.398579	−	1.11231i	−0.398579	−	1.11231i
$289$	0.163818	−	0.986491i	0.163818	−	0.986491i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.722795	−	0.691063i	$-0.242857\pi$
$293$		0			0		−0.722795	+	0.691063i	$0.757143\pi$
$294$		0			0
$295$		0			0
$296$	−1.14760	−	0.0860011i	−1.14760	−	0.0860011i
$297$		0			0
$298$	−1.10468	−	2.81469i	−1.10468	−	2.81469i
$299$		0			0
$300$		0			0
$301$	−0.193256	−	0.981148i	−0.193256	−	0.981148i
$302$	1.97736	−	1.43663i	1.97736	−	1.43663i
$303$		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	$0.166667\pi$
$308$	0.672389	−	1.34440i	0.672389	−	1.34440i
$309$		0			0
$310$		0			0
$311$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$311$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$312$		0			0
$313$		0			0		−0.701798	−	0.712376i	$-0.747619\pi$
$313$		0			0		0.701798	+	0.712376i	$0.252381\pi$
$314$		0			0
$315$		0			0
$316$	2.40521	+	0.0359845i	2.40521	+	0.0359845i
$317$	−0.568474	−	1.05640i	−0.568474	−	1.05640i	−0.988831	−	0.149042i	$-0.952381\pi$
$317$	−0.568474	−	1.05640i	−0.568474	−	1.05640i	0.420357	−	0.907359i	$-0.361905\pi$
$318$		0			0
$319$	0.383747	−	0.0461473i	0.383747	−	0.0461473i
$320$		0			0
$321$		0			0
$322$	1.69350	+	2.56554i	1.69350	+	2.56554i
$323$		0			0
$324$	−1.42249	+	0.485840i	−1.42249	+	0.485840i
$325$		0			0
$326$	−2.79183	+	0.463615i	−2.79183	+	0.463615i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.395873	−	0.580639i	0.395873	−	0.580639i	−0.575617	−	0.817719i	$-0.695238\pi$
$331$	0.395873	−	0.580639i	0.395873	−	0.580639i	0.971490	+	0.237080i	$0.0761905\pi$
$332$		0			0
$333$	0.129582	−	1.43977i	0.129582	−	1.43977i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.909199	+	0.818647i	0.909199	+	0.818647i	0.983930	−	0.178557i	$-0.0571429\pi$
$337$	0.909199	+	0.818647i	0.909199	+	0.818647i	−0.0747301	+	0.997204i	$0.523810\pi$
$338$	−1.05866	−	1.17576i	−1.05866	−	1.17576i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$344$	0.695313	+	0.387688i	0.695313	+	0.387688i
$345$		0			0
$346$		0			0
$347$	−1.42036	−	0.907359i	−1.42036	−	0.907359i	−0.420357	−	0.907359i	$-0.638095\pi$
$347$	−1.42036	−	0.907359i	−1.42036	−	0.907359i	−1.00000			$\pi$
$348$		0			0
$349$		0			0		−0.925304	−	0.379225i	$-0.876190\pi$
$349$		0			0		0.925304	+	0.379225i	$0.123810\pi$
$350$	−1.44536	+	0.643515i	−1.44536	+	0.643515i
$351$		0			0
$352$	−0.464386	−	1.08649i	−0.464386	−	1.08649i
$353$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$353$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.16138	+	0.301898i	−1.16138	+	0.301898i
$359$	1.62064	−	1.14082i	1.62064	−	1.14082i	0.733052	−	0.680173i	$-0.238095\pi$
$359$	1.62064	−	1.14082i	1.62064	−	1.14082i	0.887586	−	0.460642i	$-0.152381\pi$
$360$		0			0
$361$	0.525684	−	0.850680i	0.525684	−	0.850680i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$367$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$368$	0.470007	+	0.0565204i	0.470007	+	0.0565204i
$369$		0			0
$370$		0			0
$371$	−1.35991	+	1.42236i	−1.35991	+	1.42236i
$372$		0			0
$373$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i	−0.955573	−	0.294755i	$-0.904762\pi$
$373$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i	0.900969	+	0.433884i	$0.142857\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.265772	−	0.493886i	0.265772	−	0.493886i	−0.712376	−	0.701798i	$-0.752381\pi$
$379$	0.265772	−	0.493886i	0.265772	−	0.493886i	0.978148	+	0.207912i	$0.0666667\pi$
$380$		0			0
$381$		0			0
$382$	1.19877	−	2.92498i	1.19877	−	2.92498i
$383$		0			0		−0.657939	−	0.753071i	$-0.728571\pi$
$383$		0			0		0.657939	+	0.753071i	$0.271429\pi$
$384$		0			0
$385$		0			0
$386$			1.02273i			1.02273i
$387$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$388$		0			0
$389$	−0.0998219	−	0.0658919i	−0.0998219	−	0.0658919i	0.500000	−	0.866025i	$-0.333333\pi$
$389$	−0.0998219	−	0.0658919i	−0.0998219	−	0.0658919i	−0.599822	+	0.800134i	$0.704762\pi$
$390$		0			0
$391$		0			0
$392$	0.773395	−	0.188738i	0.773395	−	0.188738i
$393$		0			0
$394$	3.10444	+	0.326289i	3.10444	+	0.326289i
$395$		0			0
$396$	−1.39089	+	0.570042i	−1.39089	+	0.570042i
$397$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$397$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$398$		0			0
$399$		0			0
$400$	−0.0683241	+	0.233867i	−0.0683241	+	0.233867i
$401$	−0.0824288	−	0.317097i	−0.0824288	−	0.317097i	0.913545	−	0.406737i	$-0.133333\pi$
$401$	−0.0824288	−	0.317097i	−0.0824288	−	0.317097i	−0.995974	+	0.0896393i	$0.971429\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.448273	+	0.415937i	0.448273	+	0.415937i
$407$	0.0432455	−	1.44494i	0.0432455	−	1.44494i
$408$		0			0
$409$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$409$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.412643	−	3.04625i	0.412643	−	3.04625i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$419$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$420$		0			0
$421$	−0.162670	+	0.0753611i	−0.162670	+	0.0753611i	−0.500000	−	0.866025i	$-0.666667\pi$
$421$	−0.162670	+	0.0753611i	−0.162670	+	0.0753611i	0.337330	+	0.941386i	$0.390476\pi$
$422$	1.25871	+	1.31651i	1.25871	+	1.31651i
$423$		0			0
$424$	−0.163754	−	1.55801i	−0.163754	−	1.55801i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	1.20555	−	0.961392i	1.20555	−	0.961392i
$429$		0			0
$430$		0			0
$431$	−0.572490	+	0.787964i	−0.572490	+	0.787964i	−0.992847	−	0.119394i	$-0.961905\pi$
$431$	−0.572490	+	0.787964i	−0.572490	+	0.787964i	0.420357	+	0.907359i	$0.361905\pi$
$432$		0			0
$433$		0			0		−0.635116	−	0.772417i	$-0.719048\pi$
$433$		0			0		0.635116	+	0.772417i	$0.280952\pi$
$434$		0			0
$435$		0			0
$436$	0.129956	−	0.611396i	0.129956	−	0.611396i
$437$		0			0
$438$		0			0
$439$		0			0		−0.680173	−	0.733052i	$-0.738095\pi$
$439$		0			0		0.680173	+	0.733052i	$0.261905\pi$
$440$		0			0
$441$	0.222521	+	0.974928i	0.222521	+	0.974928i
$442$		0			0
$443$	0.165379	−	0.127885i	0.165379	−	0.127885i	−0.525684	−	0.850680i	$-0.676190\pi$
$443$	0.165379	−	0.127885i	0.165379	−	0.127885i	0.691063	+	0.722795i	$0.257143\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.727227	−	1.45405i	0.727227	−	1.45405i
$449$	−1.60461	+	0.316058i	−1.60461	+	0.316058i	−0.913545	−	0.406737i	$-0.866667\pi$
$449$	−1.60461	+	0.316058i	−1.60461	+	0.316058i	−0.691063	+	0.722795i	$0.742857\pi$
$450$	1.51185	+	0.466345i	1.51185	+	0.466345i
$451$		0			0
$452$	1.08272	+	0.863441i	1.08272	+	0.863441i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.68931	+	0.306564i	−1.68931	+	0.306564i	−0.936235	−	0.351375i	$-0.885714\pi$
$457$	−1.68931	+	0.306564i	−1.68931	+	0.306564i	−0.753071	+	0.657939i	$0.771429\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.149042	−	0.988831i	$-0.547619\pi$
$461$		0			0		0.149042	+	0.988831i	$0.452381\pi$
$462$		0			0
$463$	1.10540	+	1.62133i	1.10540	+	1.62133i	0.712376	+	0.701798i	$0.247619\pi$
$463$	1.10540	+	1.62133i	1.10540	+	1.62133i	0.393025	+	0.919528i	$0.371429\pi$
$464$	0.0934972	−	0.0112435i	0.0934972	−	0.0112435i
$465$		0			0
$466$	−1.05866	+	1.17576i	−1.05866	+	1.17576i
$467$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$467$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$468$		0			0
$469$	−1.41902	+	0.127714i	−1.41902	+	0.127714i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.447313	+	0.894377i	−0.447313	+	0.894377i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.95994	−	0.176398i	1.95994	−	0.176398i
$478$	−2.53402	+	1.56591i	−2.53402	+	1.56591i
$479$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$479$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.35431	+	0.652203i	−1.35431	+	0.652203i
$485$		0			0
$486$		0			0
$487$	−1.53378	−	1.26115i	−1.53378	−	1.26115i	−0.842721	−	0.538351i	$-0.819048\pi$
$487$	−1.53378	−	1.26115i	−1.53378	−	1.26115i	−0.691063	−	0.722795i	$-0.742857\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.240174	−	1.44630i	−0.240174	−	1.44630i	−0.791071	−	0.611724i	$-0.790476\pi$
$491$	−0.240174	−	1.44630i	−0.240174	−	1.44630i	0.550897	−	0.834573i	$-0.314286\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.798138	−	0.157209i	0.798138	−	0.157209i
$498$		0			0
$499$	0.697417	+	1.70169i	0.697417	+	1.70169i	0.712376	+	0.701798i	$0.247619\pi$
$499$	0.697417	+	1.70169i	0.697417	+	1.70169i	−0.0149594	+	0.999888i	$0.504762\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.791071	−	0.611724i	$-0.209524\pi$
$503$		0			0		−0.791071	+	0.611724i	$0.790476\pi$
$504$	−0.706600	−	0.366714i	−0.706600	−	0.366714i
$505$		0			0
$506$	0.229726	−	3.06547i	0.229726	−	3.06547i
$507$		0			0
$508$	−0.398923	+	2.19825i	−0.398923	+	2.19825i
$509$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$509$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$510$		0			0
$511$		0			0
$512$	−0.189376	−	0.443068i	−0.189376	−	0.443068i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	1.78815	−	1.42600i	1.78815	−	1.42600i
$519$		0			0
$520$		0			0
$521$		0			0		−0.237080	−	0.971490i	$-0.576190\pi$
$521$		0			0		0.237080	+	0.971490i	$0.423810\pi$
$522$	−0.0639209	−	0.608167i	−0.0639209	−	0.608167i
$523$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$523$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$524$		0			0
$525$		0			0
$526$	−2.99311	−	0.0895803i	−2.99311	−	0.0895803i
$527$		0			0
$528$		0			0
$529$	2.29295	+	1.56331i	2.29295	+	1.56331i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.652884	−	0.927485i	0.652884	−	0.927485i
$537$		0			0
$538$		0			0
$539$	0.280427	+	0.959875i	0.280427	+	0.959875i
$540$		0			0
$541$	−0.125817	+	0.127714i	−0.125817	+	0.127714i	−0.772417	−	0.635116i	$-0.780952\pi$
$541$	−0.125817	+	0.127714i	−0.125817	+	0.127714i	0.646600	+	0.762830i	$0.276190\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.11142	+	0.184564i	1.11142	+	0.184564i	0.691063	−	0.722795i	$-0.257143\pi$
$547$	1.11142	+	0.184564i	1.11142	+	0.184564i	0.420357	+	0.907359i	$0.361905\pi$
$548$	−1.75573	−	0.750434i	−1.75573	−	0.750434i
$549$		0			0
$550$	1.53704	+	0.375095i	1.53704	+	0.375095i
$551$		0			0
$552$		0			0
$553$	−1.18923	+	1.07079i	−1.18923	+	1.07079i
$554$	−3.00689	+	0.733796i	−3.00689	+	0.733796i
$555$		0			0
$556$		0			0
$557$	1.09820	+	0.724913i	1.09820	+	0.724913i	0.963963	−	0.266037i	$-0.0857143\pi$
$557$	1.09820	+	0.724913i	1.09820	+	0.724913i	0.134233	+	0.990950i	$0.457143\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.351682	−	0.138025i	0.351682	−	0.138025i
$563$		0			0		−0.657939	−	0.753071i	$-0.728571\pi$
$563$		0			0		0.657939	+	0.753071i	$0.271429\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.473869	−	0.880596i	0.473869	−	0.880596i
$568$	−0.315374	+	0.565619i	−0.315374	+	0.565619i
$569$	−1.91438	+	0.559287i	−1.91438	+	0.559287i	−0.936235	+	0.351375i	$0.885714\pi$
$569$	−1.91438	+	0.559287i	−1.91438	+	0.559287i	−0.978148	+	0.207912i	$0.933333\pi$
$570$		0			0
$571$	−1.96970	+	0.296885i	−1.96970	+	0.296885i	−0.971490	+	0.237080i	$0.923810\pi$
$571$	−1.96970	+	0.296885i	−1.96970	+	0.296885i	−0.998210	+	0.0598042i	$0.980952\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.34272	+	1.40438i	−1.34272	+	1.40438i
$576$	−1.50433	+	0.616533i	−1.50433	+	0.616533i
$577$		0			0		−0.460642	−	0.887586i	$-0.652381\pi$
$577$		0			0		0.460642	+	0.887586i	$0.347619\pi$
$578$	−1.57082	−	0.188899i	−1.57082	−	0.188899i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.94588	−	0.293294i	1.94588	−	0.293294i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.817719	−	0.575617i	$-0.195238\pi$
$587$		0			0		−0.817719	+	0.575617i	$0.804762\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.0105365	−	0.352050i	0.0105365	−	0.352050i
$593$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$593$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$594$		0			0
$595$		0			0
$596$	−2.62442	+	1.16847i	−2.62442	+	1.16847i
$597$		0			0
$598$		0			0
$599$	−1.67866	−	1.07237i	−1.67866	−	1.07237i	−0.887586	−	0.460642i	$-0.847619\pi$
$599$	−1.67866	−	1.07237i	−1.67866	−	1.07237i	−0.791071	−	0.611724i	$-0.790476\pi$
$600$		0			0
$601$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$601$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$602$	−1.53704	+	0.375095i	−1.53704	+	0.375095i
$603$	1.15265	+	0.837448i	1.15265	+	0.837448i
$604$	−1.44784	−	1.81553i	−1.44784	−	1.81553i
$605$		0			0
$606$		0			0
$607$		0			0		0.646600	−	0.762830i	$-0.276190\pi$
$607$		0			0		−0.646600	+	0.762830i	$0.723810\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.152509	+	1.69451i	−0.152509	+	1.69451i	0.447313	+	0.894377i	$0.352381\pi$
$613$	−0.152509	+	1.69451i	−0.152509	+	1.69451i	−0.599822	+	0.800134i	$0.704762\pi$
$614$		0			0
$615$		0			0
$616$	−0.727266	−	0.323800i	−0.727266	−	0.323800i
$617$	−0.644687	+	0.198860i	−0.644687	+	0.198860i	−0.599822	−	0.800134i	$-0.704762\pi$
$617$	−0.644687	+	0.198860i	−0.644687	+	0.198860i	−0.0448648	+	0.998993i	$0.514286\pi$
$618$		0			0
$619$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$619$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.599822	−	0.800134i	−0.599822	−	0.800134i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.118526	−	1.97835i	0.118526	−	1.97835i	−0.0747301	−	0.997204i	$-0.523810\pi$
$631$	0.118526	−	1.97835i	0.118526	−	1.97835i	0.193256	−	0.981148i	$-0.438095\pi$
$632$	−0.0381111	−	1.27339i	−0.0381111	−	1.27339i
$633$		0			0
$634$	−1.62934	+	0.973486i	−1.62934	+	0.973486i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.100177	−	0.603255i	−0.100177	−	0.603255i
$639$	−0.704489	−	0.406737i	−0.704489	−	0.406737i
$640$		0			0
$641$	0.674913	−	1.12961i	0.674913	−	1.12961i	−0.309017	−	0.951057i	$-0.600000\pi$
$641$	0.674913	−	1.12961i	0.674913	−	1.12961i	0.983930	−	0.178557i	$-0.0571429\pi$
$642$		0			0
$643$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$643$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$644$	2.36284	−	1.71671i	2.36284	−	1.71671i
$645$		0			0
$646$		0			0
$647$		0			0		0.998993	−	0.0448648i	$-0.0142857\pi$
$647$		0			0		−0.998993	+	0.0448648i	$0.985714\pi$
$648$	0.290845	+	0.741061i	0.290845	+	0.741061i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.559035	+	2.63005i	0.559035	+	2.63005i
$653$	0.342721	−	0.327675i	0.342721	−	0.327675i	−0.500000	−	0.866025i	$-0.666667\pi$
$653$	0.342721	−	0.327675i	0.342721	−	0.327675i	0.842721	+	0.538351i	$0.180952\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.548760	−	0.215372i	−0.548760	−	0.215372i	0.0747301	−	0.997204i	$-0.476190\pi$
$659$	−0.548760	−	0.215372i	−0.548760	−	0.215372i	−0.623490	+	0.781831i	$0.714286\pi$
$660$		0			0
$661$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$661$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$662$	−0.945828	−	0.584481i	−0.945828	−	0.584481i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−2.28483	−	0.102612i	−2.28483	−	0.102612i
$667$	0.703098	+	0.263877i	0.703098	+	0.263877i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.82445	+	0.623124i	1.82445	+	0.623124i	0.998210	+	0.0598042i	$0.0190476\pi$
$673$	1.82445	+	0.623124i	1.82445	+	0.623124i	0.826239	+	0.563320i	$0.190476\pi$
$674$	1.22937	−	1.49514i	1.22937	−	1.49514i
$675$		0			0
$676$	−1.07082	+	1.05492i	−1.07082	+	1.05492i
$677$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$677$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.100008	−	1.33452i	0.100008	−	1.33452i	−0.691063	−	0.722795i	$-0.742857\pi$
$683$	0.100008	−	1.33452i	0.100008	−	1.33452i	0.791071	−	0.611724i	$-0.209524\pi$
$684$		0			0
$685$		0			0
$686$	−0.871597	+	1.32041i	−0.871597	+	1.32041i
$687$		0			0
$688$	−0.108985	+	0.217909i	−0.108985	+	0.217909i
$689$		0			0
$690$		0			0
$691$		0			0		−0.967835	−	0.251587i	$-0.919048\pi$
$691$		0			0		0.967835	+	0.251587i	$0.0809524\pi$
$692$		0			0
$693$	0.420357	−	0.907359i	0.420357	−	0.907359i
$694$	−1.33330	+	2.30935i	−1.33330	+	2.30935i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.672389	+	1.34440i	0.672389	+	1.34440i
$701$	1.22331	+	1.58197i	1.22331	+	1.58197i	0.623490	+	0.781831i	$0.285714\pi$
$701$	1.22331	+	1.58197i	1.22331	+	1.58197i	0.599822	+	0.800134i	$0.295238\pi$
$702$		0			0
$703$		0			0
$704$	−1.46477	+	0.705394i	−1.46477	+	0.705394i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.0580192	+	1.29190i	−0.0580192	+	1.29190i	0.733052	+	0.680173i	$0.238095\pi$
$709$	−0.0580192	+	1.29190i	−0.0580192	+	1.29190i	−0.791071	+	0.611724i	$0.790476\pi$
$710$		0			0
$711$	1.60009	−	0.0239390i	1.60009	−	0.0239390i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.336045	+	1.08943i	0.336045	+	1.08943i
$717$		0			0
$718$	−1.91815	−	2.48052i	−1.91815	−	2.48052i
$719$		0			0		−0.447313	−	0.894377i	$-0.647619\pi$
$719$		0			0		0.447313	+	0.894377i	$0.352381\pi$
$720$		0			0
$721$		0			0
$722$	−1.38186	−	0.770486i	−1.38186	−	0.770486i
$723$		0			0
$724$		0			0
$725$	−0.193256	+	0.334729i	−0.193256	+	0.334729i
$726$		0			0
$727$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$727$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$728$		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	$-0.314286\pi$
$733$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$734$		0			0
$735$		0			0
$736$	0.171563	−	2.28935i	0.171563	−	2.28935i
$737$	1.20067	+	0.767016i	1.20067	+	0.767016i
$738$		0			0
$739$	0.932507	+	0.169225i	0.932507	+	0.169225i	0.623490	−	0.781831i	$-0.285714\pi$
$739$	0.932507	+	0.169225i	0.932507	+	0.169225i	0.309017	+	0.951057i	$0.400000\pi$
$740$		0			0
$741$		0			0
$742$	2.34464	+	2.04845i	2.34464	+	2.04845i
$743$	0.748969	−	0.737848i	0.748969	−	0.737848i	−0.222521	−	0.974928i	$-0.571429\pi$
$743$	0.748969	−	0.737848i	0.748969	−	0.737848i	0.971490	+	0.237080i	$0.0761905\pi$
$744$		0			0
$745$		0			0
$746$	0.223775	+	0.0764285i	0.223775	+	0.0764285i
$747$		0			0
$748$		0			0
$749$	−0.152887	+	1.01434i	−0.152887	+	1.01434i
$750$		0			0
$751$	1.48393	+	1.04458i	1.48393	+	1.04458i	0.983930	+	0.178557i	$0.0571429\pi$
$751$	1.48393	+	1.04458i	1.48393	+	1.04458i	0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.69204	+	1.04561i	1.69204	+	1.04561i	0.900969	+	0.433884i	$0.142857\pi$
$757$	1.69204	+	1.04561i	1.69204	+	1.04561i	0.791071	+	0.611724i	$0.209524\pi$
$758$	−0.799476	−	0.385008i	−0.799476	−	0.385008i
$759$		0			0
$760$		0			0
$761$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$761$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$762$		0			0
$763$	0.213276	+	0.356963i	0.213276	+	0.356963i
$764$	−2.82728	−	1.01311i	−2.82728	−	1.01311i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.997204	−	0.0747301i	$-0.976190\pi$
$769$		0			0		0.997204	+	0.0747301i	$0.0238095\pi$
$770$		0			0
$771$		0			0
$772$	0.970702	−	0.0435943i	0.970702	−	0.0435943i
$773$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$773$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$774$	1.40429	+	0.728802i	1.40429	+	0.728802i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.0970597	+	0.162451i	−0.0970597	+	0.162451i
$779$		0			0
$780$		0			0
$781$	−0.727552	−	0.363877i	−0.727552	−	0.363877i
$782$		0			0
$783$		0			0
$784$	0.0683241	+	0.233867i	0.0683241	+	0.233867i
$785$		0			0
$786$		0			0
$787$		0			0		−0.0299155	−	0.999552i	$-0.509524\pi$
$787$		0			0		0.0299155	+	0.999552i	$0.490476\pi$
$788$	0.177363	−	2.96042i	0.177363	−	2.96042i
$789$		0			0
$790$		0			0
$791$	−0.918709	+	0.0688477i	−0.918709	+	0.0688477i
$792$	0.334643	+	0.722341i	0.334643	+	0.722341i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$797$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$798$		0			0
$799$		0			0
$800$	1.14788	+	0.280127i	1.14788	+	0.280127i
$801$		0			0
$802$	−0.495337	+	0.152791i	−0.495337	+	0.152791i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.105327	+	0.0566786i	0.105327	+	0.0566786i	0.525684	−	0.850680i	$-0.323810\pi$
$809$	0.105327	+	0.0566786i	0.105327	+	0.0566786i	−0.420357	+	0.907359i	$0.638095\pi$
$810$		0			0
$811$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$811$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$812$	0.375671	−	0.443200i	0.375671	−	0.443200i
$813$		0			0
$814$	−2.28687	+	0.0342141i	−2.28687	+	0.0342141i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.121940	+	1.35487i	0.121940	+	1.35487i	0.791071	+	0.611724i	$0.209524\pi$
$821$	0.121940	+	1.35487i	0.121940	+	1.35487i	−0.669131	+	0.743145i	$0.733333\pi$
$822$		0			0
$823$	1.53973	−	0.685531i	1.53973	−	0.685531i	0.550897	−	0.834573i	$-0.314286\pi$
$823$	1.53973	−	0.685531i	1.53973	−	0.685531i	0.988831	+	0.149042i	$0.0476190\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.0556950	−	1.86091i	0.0556950	−	1.86091i	−0.337330	−	0.941386i	$-0.609524\pi$
$827$	0.0556950	−	1.86091i	0.0556950	−	1.86091i	0.393025	−	0.919528i	$-0.371429\pi$
$828$	−2.90888	−	0.261804i	−2.90888	−	0.261804i
$829$		0			0		0.894377	−	0.447313i	$-0.147619\pi$
$829$		0			0		−0.894377	+	0.447313i	$0.852381\pi$
$830$		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	$-0.185714\pi$
$839$		0			0		−0.834573	+	0.550897i	$0.814286\pi$
$840$		0			0
$841$	−0.844524	−	0.101558i	−0.844524	−	0.101558i
$842$	0.130659	+	0.251759i	0.130659	+	0.251759i
$843$		0			0
$844$	1.19589	−	1.25080i	1.19589	−	1.25080i
$845$		0			0
$846$		0			0
$847$	0.365341	−	0.930874i	0.365341	−	0.930874i
$848$	0.474100	−	0.0714590i	0.474100	−	0.0714590i
$849$		0			0
$850$		0			0
$851$	1.36783	−	2.45319i	1.36783	−	2.45319i
$852$		0			0
$853$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$853$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$854$		0			0
$855$		0			0
$856$	−0.537293	−	0.614981i	−0.537293	−	0.614981i
$857$		0			0		0.930874	−	0.365341i	$-0.119048\pi$
$857$		0			0		−0.930874	+	0.365341i	$0.880952\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$	1.28605	+	0.848916i	1.28605	+	0.848916i
$863$	0.317363	−	0.496793i	0.317363	−	0.496793i	−0.646600	−	0.762830i	$-0.723810\pi$
$863$	0.317363	−	0.496793i	0.317363	−	0.496793i	0.963963	+	0.266037i	$0.0857143\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.59579	−	0.119588i	1.59579	−	0.119588i
$870$		0			0
$871$		0			0
$872$	−0.326562	−	0.0542292i	−0.326562	−	0.0542292i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.458909	+	1.88048i	−0.458909	+	1.88048i	0.0149594	+	0.999888i	$0.495238\pi$
$877$	−0.458909	+	1.88048i	−0.458909	+	1.88048i	−0.473869	+	0.880596i	$0.657143\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$881$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$882$	1.52513	−	0.420908i	1.52513	−	0.420908i
$883$	−1.03723	+	1.47348i	−1.03723	+	1.47348i	−0.163818	+	0.986491i	$0.552381\pi$
$883$	−1.03723	+	1.47348i	−1.03723	+	1.47348i	−0.873408	+	0.486989i	$0.838095\pi$
$884$		0			0
$885$		0			0
$886$	−0.213868	−	0.252312i	−0.213868	−	0.252312i
$887$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$887$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$888$		0			0
$889$	−0.800145	−	1.25253i	−0.800145	−	1.25253i
$890$		0			0
$891$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−1.27040	−	0.565619i	−1.27040	−	0.565619i
$897$		0			0
$898$	0.613445	+	2.51373i	0.613445	+	2.51373i
$899$		0			0
$900$	0.378179	−	1.45482i	0.378179	−	1.45482i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.431098	−	0.593355i	0.431098	−	0.593355i
$905$		0			0
$906$		0			0
$907$	−0.743861	−	1.74035i	−0.743861	−	1.74035i	−0.669131	−	0.743145i	$-0.733333\pi$
$907$	−0.743861	−	1.74035i	−0.743861	−	1.74035i	−0.0747301	−	0.997204i	$-0.523810\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.0532250	+	0.293294i	−0.0532250	+	0.293294i	−0.999552	−	0.0299155i	$-0.990476\pi$
$911$	−0.0532250	+	0.293294i	−0.0532250	+	0.293294i	0.946327	+	0.323210i	$0.104762\pi$
$912$		0			0
$913$		0			0
$914$	0.604451	+	2.64827i	0.604451	+	2.64827i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.250622	−	1.38104i	−0.250622	−	1.38104i	−0.826239	−	0.563320i	$-0.809524\pi$
$919$	−0.250622	−	1.38104i	−0.250622	−	1.38104i	0.575617	−	0.817719i	$-0.304762\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	1.13021	+	0.901310i	1.13021	+	0.901310i
$926$	2.48412	−	1.86223i	2.48412	−	1.86223i
$927$		0			0
$928$	−0.0748141	−	0.450521i	−0.0748141	−	0.450521i
$929$		0			0		0.762830	−	0.646600i	$-0.223810\pi$
$929$		0			0		−0.762830	+	0.646600i	$0.776190\pi$
$930$		0			0
$931$		0			0
$932$	1.16108	+	0.954689i	1.16108	+	0.954689i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$937$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$938$	0.302583	+	2.23376i	0.302583	+	2.23376i
$939$		0			0
$940$		0			0
$941$		0			0		0.850680	−	0.525684i	$-0.176190\pi$
$941$		0			0		−0.850680	+	0.525684i	$0.823810\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	1.44536	+	0.643515i	1.44536	+	0.643515i
$947$	0.730682			0.730682			0.365341	−	0.930874i	$-0.380952\pi$
$947$	0.730682			0.730682			0.365341	+	0.930874i	$0.380952\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.25293	+	1.39152i	−1.25293	+	1.39152i	−0.365341	+	0.930874i	$0.619048\pi$
$953$	−1.25293	+	1.39152i	−1.25293	+	1.39152i	−0.887586	+	0.460642i	$0.847619\pi$
$954$	−0.417926	−	3.08526i	−0.417926	−	3.08526i
$955$		0			0
$956$	1.59427	+	2.33837i	1.59427	+	2.33837i
$957$		0			0
$958$		0			0
$959$	1.19578	−	0.428487i	1.19578	−	0.428487i
$960$		0			0
$961$	0.575617	+	0.817719i	0.575617	+	0.817719i
$962$		0			0
$963$	0.782509	−	0.663281i	0.782509	−	0.663281i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.50092	−	1.19694i	−1.50092	−	1.19694i	−0.925304	−	0.379225i	$-0.876190\pi$
$967$	−1.50092	−	1.19694i	−1.50092	−	1.19694i	−0.575617	−	0.817719i	$-0.695238\pi$
$968$	0.377243	+	0.701035i	0.377243	+	0.701035i
$969$		0			0
$970$		0			0
$971$		0			0		0.447313	−	0.894377i	$-0.352381\pi$
$971$		0			0		−0.447313	+	0.894377i	$0.647619\pi$
$972$		0			0
$973$		0			0
$974$	−1.88443	+	2.51374i	−1.88443	+	2.51374i
$975$		0			0
$976$		0			0
$977$	0.238287	+	0.123667i	0.238287	+	0.123667i	0.575617	−	0.817719i	$-0.304762\pi$
$977$	0.238287	+	0.123667i	0.238287	+	0.123667i	−0.337330	+	0.941386i	$0.609524\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.0742481	−	0.409141i	0.0742481	−	0.409141i
$982$	−2.26890	+	0.482269i	−2.26890	+	0.482269i
$983$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$983$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.57190	+	1.14206i	−1.57190	+	1.14206i
$990$		0			0
$991$	1.52446	−	1.21572i	1.52446	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$991$	1.52446	−	1.21572i	1.52446	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$992$		0			0
$993$		0			0
$994$	−0.305130	−	1.25034i	−0.305130	−	1.25034i
$995$		0			0
$996$		0			0
$997$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$997$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$998$	2.64009	−	1.22309i	2.64009	−	1.22309i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3311.1.gb.a.1525.1	yes	48
7.6	odd	2	CM	3311.1.gb.a.1525.1	yes	48
11.8	odd	10		3311.1.gb.b.2428.1	yes	48
43.28	odd	42		3311.1.gb.b.3296.1	yes	48
77.41	even	10		3311.1.gb.b.2428.1	yes	48
301.286	even	42		3311.1.gb.b.3296.1	yes	48
473.415	even	210	inner	3311.1.gb.a.888.1	✓	48
3311.888	odd	210	inner	3311.1.gb.a.888.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3311.1.gb.a.888.1	✓	48	473.415	even	210	inner
3311.1.gb.a.888.1	✓	48	3311.888	odd	210	inner
3311.1.gb.a.1525.1	yes	48	1.1	even	1	trivial
3311.1.gb.a.1525.1	yes	48	7.6	odd	2	CM
3311.1.gb.b.2428.1	yes	48	11.8	odd	10
3311.1.gb.b.2428.1	yes	48	77.41	even	10
3311.1.gb.b.3296.1	yes	48	43.28	odd	42
3311.1.gb.b.3296.1	yes	48	301.286	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)

\(f(q)\)	\(=\)	\(q+(-0.0709825 - 1.58055i) q^{2} +(-1.49712 + 0.134743i) q^{4} +(0.669131 - 0.743145i) q^{7} +(0.106862 + 0.788887i) q^{8} +(-0.992847 + 0.119394i) q^{9} +O(q^{10})\)	\(q+(-0.0709825 - 1.58055i) q^{2} +(-1.49712 + 0.134743i) q^{4} +(0.669131 - 0.743145i) q^{7} +(0.106862 + 0.788887i) q^{8} +(-0.992847 + 0.119394i) q^{9} +(-0.983930 + 0.178557i) q^{11} +(-1.22207 - 1.00484i) q^{14} +(-0.239727 + 0.0435041i) q^{16} +(0.259183 + 1.56077i) q^{18} +(0.352060 + 1.54247i) q^{22} +(-1.85666 - 0.572703i) q^{23} +(0.447313 - 0.894377i) q^{25} +(-0.901636 + 1.20274i) q^{28} +(-0.385820 - 0.0231150i) q^{29} +(0.262924 + 1.15195i) q^{32} +(1.47033 - 0.312527i) q^{36} +(-0.300555 + 1.41400i) q^{37} +(0.599822 - 0.800134i) q^{43} +(1.44900 - 0.399900i) q^{44} +(-0.773395 + 2.97519i) q^{46} +(-0.104528 - 0.994522i) q^{49} +(-1.44536 - 0.643515i) q^{50} +(-1.96698 - 0.0588694i) q^{53} +(0.657762 + 0.448455i) q^{56} +(-0.00914793 + 0.611448i) q^{58} +(-0.575617 + 0.817719i) q^{63} +(1.56718 - 0.432514i) q^{64} +(-1.04442 - 0.969078i) q^{67} +(0.650887 + 0.487939i) q^{71} +(-0.200286 - 0.770486i) q^{72} +(2.25623 + 0.374673i) q^{74} +(-0.525684 + 0.850680i) q^{77} +(-1.59150 - 0.167273i) q^{79} +(0.971490 - 0.237080i) q^{81} +(-1.30723 - 0.891252i) q^{86} +(-0.246006 - 0.757128i) q^{88} +(2.85681 + 0.607234i) q^{92} +(-1.56447 + 0.235806i) q^{98} +(0.955573 - 0.294755i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{2} + 6 q^{7} - 21 q^{8} + q^{9}+O(q^{10}) \) 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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