LMFDB - Embedded newform 3311.1.gb.a.545.1

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			545.1
Root			$0.599822 + 0.800134i$ of defining polynomial
Character	$\chi$	$=$	3311.545
Dual form			3311.1.gb.a.1938.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.267104 - 0.279369i) q^{2} +(0.0381624 - 0.849752i) q^{4} +(-0.104528 - 0.994522i) q^{7} +(-0.538659 + 0.470612i) q^{8} +(0.447313 + 0.894377i) q^{9} +O(q^{10})$	\(q+(-0.267104 - 0.279369i) q^{2} +(0.0381624 - 0.849752i) q^{4} +(-0.104528 - 0.994522i) q^{7} +(-0.538659 + 0.470612i) q^{8} +(0.447313 + 0.894377i) q^{9} +(0.995974 + 0.0896393i) q^{11} +(-0.249918 + 0.294843i) q^{14} +(-0.571832 - 0.0514658i) q^{16} +(0.130382 - 0.363857i) q^{18} +(-0.240986 - 0.302187i) q^{22} +(0.438279 - 1.11672i) q^{23} +(0.999552 + 0.0299155i) q^{25} +(-0.849086 + 0.0508699i) q^{28} +(0.172233 + 0.278713i) q^{29} +(0.584332 + 0.732729i) q^{32} +(0.777070 - 0.345974i) q^{36} +(0.748011 - 1.68006i) q^{37} +(-0.998210 + 0.0598042i) q^{43} +(0.114180 - 0.842910i) q^{44} +(-0.429042 + 0.175838i) q^{46} +(-0.978148 + 0.207912i) q^{49} +(-0.258627 - 0.287234i) q^{50} +(1.73978 + 0.970057i) q^{53} +(0.524339 + 0.486515i) q^{56} +(0.0318597 - 0.122562i) q^{58} +(0.842721 - 0.538351i) q^{63} +(-0.0284449 + 0.209989i) q^{64} +(-1.56447 - 0.235806i) q^{67} +(-0.0888863 - 1.48363i) q^{71} +(-0.661854 - 0.271253i) q^{72} +(-0.669153 + 0.239780i) q^{74} +(-0.0149594 - 0.999888i) q^{77} +(-0.0248680 + 0.116995i) q^{79} +(-0.599822 + 0.800134i) q^{81} +(0.283333 + 0.262895i) q^{86} +(-0.578675 + 0.420432i) q^{88} +(-0.932207 - 0.415045i) q^{92} +(0.319351 + 0.217730i) q^{98} +(0.365341 + 0.930874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3311\mathbb{Z}\right)^\times$.

$n$	$904$	$1893$	$2927$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{41}{42}\right)$

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 $

$2$	−0.267104	−	0.279369i	−0.267104	−	0.279369i	0.575617	−	0.817719i	$-0.304762\pi$
$2$	−0.267104	−	0.279369i	−0.267104	−	0.279369i	−0.842721	+	0.538351i	$0.819048\pi$
$3$		0			0		−0.850680	−	0.525684i	$-0.823810\pi$
$3$		0			0		0.850680	+	0.525684i	$0.176190\pi$
$4$	0.0381624	−	0.849752i	0.0381624	−	0.849752i
$5$		0			0		−0.999888	−	0.0149594i	$-0.995238\pi$
$5$		0			0		0.999888	+	0.0149594i	$0.00476190\pi$
$6$		0			0
$7$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$7$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$8$	−0.538659	+	0.470612i	−0.538659	+	0.470612i
$9$	0.447313	+	0.894377i	0.447313	+	0.894377i
$10$		0			0
$11$	0.995974	+	0.0896393i	0.995974	+	0.0896393i
$11$	0.995974	+	0.0896393i	0.995974	+	0.0896393i
$12$		0			0
$13$		0			0		−0.907359	−	0.420357i	$-0.861905\pi$
$13$		0			0		0.907359	+	0.420357i	$0.138095\pi$
$14$	−0.249918	+	0.294843i	−0.249918	+	0.294843i
$15$		0			0
$16$	−0.571832	−	0.0514658i	−0.571832	−	0.0514658i
$17$		0			0		−0.817719	−	0.575617i	$-0.804762\pi$
$17$		0			0		0.817719	+	0.575617i	$0.195238\pi$
$18$	0.130382	−	0.363857i	0.130382	−	0.363857i
$19$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$19$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$20$		0			0
$21$		0			0
$22$	−0.240986	−	0.302187i	−0.240986	−	0.302187i
$23$	0.438279	−	1.11672i	0.438279	−	1.11672i	−0.525684	−	0.850680i	$-0.676190\pi$
$23$	0.438279	−	1.11672i	0.438279	−	1.11672i	0.963963	−	0.266037i	$-0.0857143\pi$
$24$		0			0
$25$	0.999552	+	0.0299155i	0.999552	+	0.0299155i
$26$		0			0
$27$		0			0
$28$	−0.849086	+	0.0508699i	−0.849086	+	0.0508699i
$29$	0.172233	+	0.278713i	0.172233	+	0.278713i	0.925304	−	0.379225i	$-0.123810\pi$
$29$	0.172233	+	0.278713i	0.172233	+	0.278713i	−0.753071	+	0.657939i	$0.771429\pi$
$30$		0			0
$31$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$31$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$32$	0.584332	+	0.732729i	0.584332	+	0.732729i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.777070	−	0.345974i	0.777070	−	0.345974i
$37$	0.748011	−	1.68006i	0.748011	−	1.68006i	0.0149594	−	0.999888i	$-0.495238\pi$
$37$	0.748011	−	1.68006i	0.748011	−	1.68006i	0.733052	−	0.680173i	$-0.238095\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.178557	−	0.983930i	$-0.442857\pi$
$41$		0			0		−0.178557	+	0.983930i	$0.557143\pi$
$42$		0			0
$43$	−0.998210	+	0.0598042i	−0.998210	+	0.0598042i
$43$	−0.998210	+	0.0598042i	−0.998210	+	0.0598042i
$44$	0.114180	−	0.842910i	0.114180	−	0.842910i
$45$		0			0
$46$	−0.429042	+	0.175838i	−0.429042	+	0.175838i
$47$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$47$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$48$		0			0
$49$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$50$	−0.258627	−	0.287234i	−0.258627	−	0.287234i
$51$		0			0
$52$		0			0
$53$	1.73978	+	0.970057i	1.73978	+	0.970057i	0.913545	+	0.406737i	$0.133333\pi$
$53$	1.73978	+	0.970057i	1.73978	+	0.970057i	0.826239	+	0.563320i	$0.190476\pi$
$54$		0			0
$55$		0			0
$56$	0.524339	+	0.486515i	0.524339	+	0.486515i
$57$		0			0
$58$	0.0318597	−	0.122562i	0.0318597	−	0.122562i
$59$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$59$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$60$		0			0
$61$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$61$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$62$		0			0
$63$	0.842721	−	0.538351i	0.842721	−	0.538351i
$64$	−0.0284449	+	0.209989i	−0.0284449	+	0.209989i
$65$		0			0
$66$		0			0
$67$	−1.56447	−	0.235806i	−1.56447	−	0.235806i	−0.691063	−	0.722795i	$-0.742857\pi$
$67$	−1.56447	−	0.235806i	−1.56447	−	0.235806i	−0.873408	+	0.486989i	$0.838095\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.0888863	−	1.48363i	−0.0888863	−	1.48363i	−0.712376	−	0.701798i	$-0.752381\pi$
$71$	−0.0888863	−	1.48363i	−0.0888863	−	1.48363i	0.623490	−	0.781831i	$-0.285714\pi$
$72$	−0.661854	−	0.271253i	−0.661854	−	0.271253i
$73$		0			0		−0.992847	−	0.119394i	$-0.961905\pi$
$73$		0			0		0.992847	+	0.119394i	$0.0380952\pi$
$74$	−0.669153	+	0.239780i	−0.669153	+	0.239780i
$75$		0			0
$76$		0			0
$77$	−0.0149594	−	0.999888i	−0.0149594	−	0.999888i
$78$		0			0
$79$	−0.0248680	+	0.116995i	−0.0248680	+	0.116995i	−0.988831	−	0.149042i	$-0.952381\pi$
$79$	−0.0248680	+	0.116995i	−0.0248680	+	0.116995i	0.963963	+	0.266037i	$0.0857143\pi$
$80$		0			0
$81$	−0.599822	+	0.800134i	−0.599822	+	0.800134i
$82$		0			0
$83$		0			0		0.237080	−	0.971490i	$-0.423810\pi$
$83$		0			0		−0.237080	+	0.971490i	$0.576190\pi$
$84$		0			0
$85$		0			0
$86$	0.283333	+	0.262895i	0.283333	+	0.262895i
$87$		0			0
$88$	−0.578675	+	0.420432i	−0.578675	+	0.420432i
$89$		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
$92$	−0.932207	−	0.415045i	−0.932207	−	0.415045i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$97$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$98$	0.319351	+	0.217730i	0.319351	+	0.217730i
$99$	0.365341	+	0.930874i	0.365341	+	0.930874i
$100$	0.0635661	−	0.848230i	0.0635661	−	0.848230i
$101$		0			0		−0.635116	−	0.772417i	$-0.719048\pi$
$101$		0			0		0.635116	+	0.772417i	$0.280952\pi$
$102$		0			0
$103$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$103$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$104$		0			0
$105$		0			0
$106$	−0.193700	−	0.745147i	−0.193700	−	0.745147i
$107$	0.468542	−	0.252133i	0.468542	−	0.252133i	−0.222521	−	0.974928i	$-0.571429\pi$
$107$	0.468542	−	0.252133i	0.468542	−	0.252133i	0.691063	+	0.722795i	$0.257143\pi$
$108$		0			0
$109$	−0.757241	−	0.297195i	−0.757241	−	0.297195i	−0.0448648	−	0.998993i	$-0.514286\pi$
$109$	−0.757241	−	0.297195i	−0.757241	−	0.297195i	−0.712376	+	0.701798i	$0.752381\pi$
$110$		0			0
$111$		0			0
$112$	0.00858885	+	0.574079i	0.00858885	+	0.574079i
$113$	−1.76526	−	0.754510i	−1.76526	−	0.754510i	−0.992847	−	0.119394i	$-0.961905\pi$
$113$	−1.76526	−	0.754510i	−1.76526	−	0.754510i	−0.772417	−	0.635116i	$-0.780952\pi$
$114$		0			0
$115$		0			0
$116$	0.243410	−	0.135719i	0.243410	−	0.135719i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.983930	+	0.178557i	0.983930	+	0.178557i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.375492	−	0.0916344i	−0.375492	−	0.0916344i
$127$	−1.97104	+	0.266996i	−1.97104	+	0.266996i	−0.971490	+	0.237080i	$0.923810\pi$
$127$	−1.97104	+	0.266996i	−1.97104	+	0.266996i	−0.999552	+	0.0299155i	$0.990476\pi$
$128$	0.824469	−	0.599012i	0.824469	−	0.599012i
$129$		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
$134$	0.351999	+	0.500049i	0.351999	+	0.500049i
$135$		0			0
$136$		0			0
$137$	0.782509	−	1.30970i	0.782509	−	1.30970i	−0.163818	−	0.986491i	$-0.552381\pi$
$137$	0.782509	−	1.30970i	0.782509	−	1.30970i	0.946327	−	0.323210i	$-0.104762\pi$
$138$		0			0
$139$		0			0		−0.981148	−	0.193256i	$-0.938095\pi$
$139$		0			0		0.981148	+	0.193256i	$0.0619048\pi$
$140$		0			0
$141$		0			0
$142$	−0.390738	+	0.421115i	−0.390738	+	0.421115i
$143$		0			0
$144$	−0.209758	−	0.534455i	−0.209758	−	0.534455i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−1.39909	−	0.699739i	−1.39909	−	0.699739i
$149$	0.564391	+	0.464068i	0.564391	+	0.464068i	0.873408	−	0.486989i	$-0.161905\pi$
$149$	0.564391	+	0.464068i	0.564391	+	0.464068i	−0.309017	+	0.951057i	$0.600000\pi$
$150$		0			0
$151$	−0.612807	−	1.13879i	−0.612807	−	1.13879i	−0.978148	−	0.207912i	$-0.933333\pi$
$151$	−0.612807	−	1.13879i	−0.612807	−	1.13879i	0.365341	−	0.930874i	$-0.380952\pi$
$152$		0			0
$153$		0			0
$154$	−0.275342	+	0.271253i	−0.275342	+	0.271253i
$155$		0			0
$156$		0			0
$157$		0			0		−0.967835	−	0.251587i	$-0.919048\pi$
$157$		0			0		0.967835	+	0.251587i	$0.0809524\pi$
$158$	0.0393270	−	0.0243024i	0.0393270	−	0.0243024i
$159$		0			0
$160$		0			0
$161$	−1.15641	−	0.319149i	−1.15641	−	0.319149i
$162$	0.383747	−	0.0461473i	0.383747	−	0.0461473i
$163$	0.0535114	−	0.0267632i	0.0535114	−	0.0267632i	−0.420357	−	0.907359i	$-0.638095\pi$
$163$	0.0535114	−	0.0267632i	0.0535114	−	0.0267632i	0.473869	+	0.880596i	$0.342857\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.817719	−	0.575617i	$-0.195238\pi$
$167$		0			0		−0.817719	+	0.575617i	$0.804762\pi$
$168$		0			0
$169$	0.646600	+	0.762830i	0.646600	+	0.762830i
$170$		0			0
$171$		0			0
$172$	0.0127246	+	0.850513i	0.0127246	+	0.850513i
$173$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$173$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$174$		0			0
$175$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$176$	−0.564917	−	0.102517i	−0.564917	−	0.102517i
$177$		0			0
$178$		0			0
$179$	0.262922	+	0.590533i	0.262922	+	0.590533i	0.995974	−	0.0896393i	$-0.0285714\pi$
$179$	0.262922	+	0.590533i	0.262922	+	0.590533i	−0.733052	+	0.680173i	$0.761905\pi$
$180$		0			0
$181$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$181$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$182$		0			0
$183$		0			0
$184$	0.289457	+	0.807788i	0.289457	+	0.807788i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.665900	+	1.28308i	0.665900	+	1.28308i	0.946327	+	0.323210i	$0.104762\pi$
$191$	0.665900	+	1.28308i	0.665900	+	1.28308i	−0.280427	+	0.959875i	$0.590476\pi$
$192$		0			0
$193$	0.918117	+	0.877810i	0.918117	+	0.877810i	0.992847	−	0.119394i	$-0.0380952\pi$
$193$	0.918117	+	0.877810i	0.918117	+	0.877810i	−0.0747301	+	0.997204i	$0.523810\pi$
$194$		0			0
$195$		0			0
$196$	0.139345	+	0.839117i	0.139345	+	0.839117i
$197$	1.06060	+	1.55562i	1.06060	+	1.55562i	0.809017	+	0.587785i	$0.200000\pi$
$197$	1.06060	+	1.55562i	1.06060	+	1.55562i	0.251587	+	0.967835i	$0.419048\pi$
$198$	0.162473	−	0.350705i	0.162473	−	0.350705i
$199$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$199$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$200$	−0.552496	+	0.454287i	−0.552496	+	0.454287i
$201$		0			0
$202$		0			0
$203$	0.259183	−	0.200423i	0.259183	−	0.200423i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.19481	−	0.107535i	1.19481	−	0.107535i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.57797	+	0.592222i	1.57797	+	0.592222i	0.978148	−	0.207912i	$-0.0666667\pi$
$211$	1.57797	+	0.592222i	1.57797	+	0.592222i	0.599822	+	0.800134i	$0.295238\pi$
$212$	0.890702	−	1.44137i	0.890702	−	1.44137i
$213$		0			0
$214$	−0.195587	−	0.0635502i	−0.195587	−	0.0635502i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.119235	+	0.290931i	0.119235	+	0.290931i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.657939	−	0.753071i	$-0.728571\pi$
$223$		0			0		0.657939	+	0.753071i	$0.271429\pi$
$224$	0.667636	−	0.657722i	0.667636	−	0.657722i
$225$	0.420357	+	0.907359i	0.420357	+	0.907359i
$226$	0.260722	+	0.694692i	0.260722	+	0.694692i
$227$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$227$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$228$		0			0
$229$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$229$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$230$		0			0
$231$		0			0
$232$	−0.223940	−	0.0690765i	−0.223940	−	0.0690765i
$233$	−0.791071	−	0.611724i	−0.791071	−	0.611724i	0.134233	−	0.990950i	$-0.457143\pi$
$233$	−0.791071	−	0.611724i	−0.791071	−	0.611724i	−0.925304	+	0.379225i	$0.876190\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.27356	+	1.29276i	−1.27356	+	1.29276i	−0.337330	+	0.941386i	$0.609524\pi$
$239$	−1.27356	+	1.29276i	−1.27356	+	1.29276i	−0.936235	+	0.351375i	$0.885714\pi$
$240$		0			0
$241$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$241$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$242$	−0.212928	−	0.322572i	−0.212928	−	0.322572i
$243$		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		−0.978148	−	0.207912i	$-0.933333\pi$
$251$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$252$	−0.425304	−	0.736649i	−0.425304	−	0.736649i
$253$	0.536616	−	1.07293i	0.536616	−	1.07293i
$254$	0.601063	+	0.479332i	0.601063	+	0.479332i
$255$		0			0
$256$	−0.179063	−	0.0324952i	−0.179063	−	0.0324952i
$257$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$257$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$258$		0			0
$259$	−1.74905	−	0.568299i	−1.74905	−	0.568299i
$260$		0			0
$261$	−0.172233	+	0.278713i	−0.172233	+	0.278713i
$262$		0			0
$263$	1.47620	−	0.455348i	1.47620	−	0.455348i	0.550897	−	0.834573i	$-0.314286\pi$
$263$	1.47620	−	0.455348i	1.47620	−	0.455348i	0.925304	+	0.379225i	$0.123810\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.260081	+	1.32041i	−0.260081	+	1.32041i
$269$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$269$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$270$		0			0
$271$		0			0		0.119394	−	0.992847i	$-0.461905\pi$
$271$		0			0		−0.119394	+	0.992847i	$0.538095\pi$
$272$		0			0
$273$		0			0
$274$	−0.574901	+	0.131217i	−0.574901	+	0.131217i
$275$	0.992847	+	0.119394i	0.992847	+	0.119394i
$276$		0			0
$277$	−0.299310	−	1.80241i	−0.299310	−	1.80241i	−0.550897	−	0.834573i	$-0.685714\pi$
$277$	−0.299310	−	1.80241i	−0.299310	−	1.80241i	0.251587	−	0.967835i	$-0.419048\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.13607	+	1.38166i	−1.13607	+	1.38166i	−0.222521	+	0.974928i	$0.571429\pi$
$281$	−1.13607	+	1.38166i	−1.13607	+	1.38166i	−0.913545	+	0.406737i	$0.866667\pi$
$282$		0			0
$283$		0			0		0.0299155	−	0.999552i	$-0.490476\pi$
$283$		0			0		−0.0299155	+	0.999552i	$0.509524\pi$
$284$	−1.26411	+	0.0189124i	−1.26411	+	0.0189124i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.393957	+	0.850372i	−0.393957	+	0.850372i
$289$	0.337330	+	0.941386i	0.337330	+	0.941386i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.919528	−	0.393025i	$-0.128571\pi$
$293$		0			0		−0.919528	+	0.393025i	$0.871429\pi$
$294$		0			0
$295$		0			0
$296$	0.387734	+	1.25700i	0.387734	+	1.25700i
$297$		0			0
$298$	−0.0211051	−	0.281628i	−0.0211051	−	0.281628i
$299$		0			0
$300$		0			0
$301$	0.163818	+	0.986491i	0.163818	+	0.986491i
$302$	−0.154458	+	0.475373i	−0.154458	+	0.475373i
$303$		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	$0.833333\pi$
$308$	−0.850228	−	0.0254464i	−0.850228	−	0.0254464i
$309$		0			0
$310$		0			0
$311$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$311$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$312$		0			0
$313$		0			0		−0.611724	−	0.791071i	$-0.709524\pi$
$313$		0			0		0.611724	+	0.791071i	$0.290476\pi$
$314$		0			0
$315$		0			0
$316$	0.0984674	+	0.0255964i	0.0984674	+	0.0255964i
$317$	1.71382	−	1.02396i	1.71382	−	1.02396i	0.826239	−	0.563320i	$-0.190476\pi$
$317$	1.71382	−	1.02396i	1.71382	−	1.02396i	0.887586	−	0.460642i	$-0.152381\pi$
$318$		0			0
$319$	0.146556	+	0.293030i	0.146556	+	0.293030i
$320$		0			0
$321$		0			0
$322$	0.219722	+	0.408311i	0.219722	+	0.408311i
$323$		0			0
$324$	0.657025	+	0.540235i	0.657025	+	0.540235i
$325$		0			0
$326$	−0.0217699	−	0.00780088i	−0.0217699	−	0.00780088i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.242899	−	0.261783i	0.242899	−	0.261783i	−0.599822	−	0.800134i	$-0.704762\pi$
$331$	0.242899	−	0.261783i	0.242899	−	0.261783i	0.842721	+	0.538351i	$0.180952\pi$
$332$		0			0
$333$	1.83720	−	0.0825089i	1.83720	−	0.0825089i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.95155	+	0.205116i	−1.95155	+	0.205116i	−0.995974	−	0.0896393i	$-0.971429\pi$
$337$	−1.95155	+	0.205116i	−1.95155	+	0.205116i	−0.955573	+	0.294755i	$0.904762\pi$
$338$	0.0404015	−	0.384394i	0.0404015	−	0.384394i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.309017	+	0.951057i	0.309017	+	0.951057i
$344$	0.509550	−	0.501983i	0.509550	−	0.501983i
$345$		0			0
$346$		0			0
$347$	−1.88759	−	0.460642i	−1.88759	−	0.460642i	−0.887586	−	0.460642i	$-0.847619\pi$
$347$	−1.88759	−	0.460642i	−1.88759	−	0.460642i	−1.00000			$\pi$
$348$		0			0
$349$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$349$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$350$	−0.258627	+	0.287234i	−0.258627	+	0.287234i
$351$		0			0
$352$	0.516298	+	0.782158i	0.516298	+	0.782158i
$353$		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
$358$	0.0947490	−	0.231186i	0.0947490	−	0.231186i
$359$	0.708403	−	1.10892i	0.708403	−	1.10892i	−0.280427	−	0.959875i	$-0.590476\pi$
$359$	0.708403	−	1.10892i	0.708403	−	1.10892i	0.988831	−	0.149042i	$-0.0476190\pi$
$360$		0			0
$361$	0.0149594	+	0.999888i	0.0149594	+	0.999888i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.251587	−	0.967835i	$-0.580952\pi$
$367$		0			0		0.251587	+	0.967835i	$0.419048\pi$
$368$	−0.308095	+	0.616018i	−0.308095	+	0.616018i
$369$		0			0
$370$		0			0
$371$	0.782886	−	1.83165i	0.782886	−	1.83165i
$372$		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
$379$	−1.70462	−	1.01846i	−1.70462	−	1.01846i	−0.913545	−	0.406737i	$-0.866667\pi$
$379$	−1.70462	−	1.01846i	−1.70462	−	1.01846i	−0.791071	−	0.611724i	$-0.790476\pi$
$380$		0			0
$381$		0			0
$382$	0.180589	−	0.528749i	0.180589	−	0.528749i
$383$		0			0		0.351375	−	0.936235i	$-0.385714\pi$
$383$		0			0		−0.351375	+	0.936235i	$0.614286\pi$
$384$		0			0
$385$		0			0
$386$		−	0.490960i		−	0.490960i
$387$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$388$		0			0
$389$	1.49821	+	0.806221i	1.49821	+	0.806221i	0.998210	−	0.0598042i	$-0.0190476\pi$
$389$	1.49821	+	0.806221i	1.49821	+	0.806221i	0.500000	+	0.866025i	$0.333333\pi$
$390$		0			0
$391$		0			0
$392$	0.429042	−	0.572321i	0.429042	−	0.572321i
$393$		0			0
$394$	0.151300	−	0.711812i	0.151300	−	0.711812i
$395$		0			0
$396$	0.804954	−	0.274925i	0.804954	−	0.274925i
$397$		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
$400$	−0.570037	−	0.0685494i	−0.570037	−	0.0685494i
$401$	0.624266	+	0.255848i	0.624266	+	0.255848i	0.669131	−	0.743145i	$-0.266667\pi$
$401$	0.624266	+	0.255848i	0.624266	+	0.255848i	−0.0448648	+	0.998993i	$0.514286\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.125221	−	0.0188740i	−0.125221	−	0.0188740i
$407$	0.895599	−	1.60625i	0.895599	−	1.60625i
$408$		0			0
$409$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$409$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.349182	−	0.305071i	−0.349182	−	0.305071i
$415$		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
$421$	−0.920357	+	1.77338i	−0.920357	+	1.77338i	−0.420357	+	0.907359i	$0.638095\pi$
$421$	−0.920357	+	1.77338i	−0.920357	+	1.77338i	−0.500000	+	0.866025i	$0.666667\pi$
$422$	−0.256034	−	0.599020i	−0.256034	−	0.599020i
$423$		0			0
$424$	−1.39367	+	0.296234i	−1.39367	+	0.296234i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.196370	−	0.407766i	−0.196370	−	0.407766i
$429$		0			0
$430$		0			0
$431$	1.33490	−	0.433735i	1.33490	−	0.433735i	0.447313	−	0.894377i	$-0.352381\pi$
$431$	1.33490	−	0.433735i	1.33490	−	0.433735i	0.887586	+	0.460642i	$0.152381\pi$
$432$		0			0
$433$		0			0		0.762830	−	0.646600i	$-0.223810\pi$
$433$		0			0		−0.762830	+	0.646600i	$0.776190\pi$
$434$		0			0
$435$		0			0
$436$	−0.281440	+	0.632125i	−0.281440	+	0.632125i
$437$		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
$443$	0.378066	+	1.91942i	0.378066	+	1.91942i	0.393025	+	0.919528i	$0.371429\pi$
$443$	0.378066	+	1.91942i	0.378066	+	1.91942i	−0.0149594	+	0.999888i	$0.504762\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.211812	+	0.00633928i	0.211812	+	0.00633928i
$449$	−1.06216	+	0.176383i	−1.06216	+	0.176383i	−0.669131	−	0.743145i	$-0.733333\pi$
$449$	−1.06216	+	0.176383i	−1.06216	+	0.176383i	−0.393025	+	0.919528i	$0.628571\pi$
$450$	0.141209	−	0.359794i	0.141209	−	0.359794i
$451$		0			0
$452$	−0.708513	+	1.47124i	−0.708513	+	1.47124i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.92016	−	0.172818i	−1.92016	−	0.172818i	−0.936235	−	0.351375i	$-0.885714\pi$
$457$	−1.92016	−	0.172818i	−1.92016	−	0.172818i	−0.983930	+	0.178557i	$0.942857\pi$
$458$		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
$463$	1.34197	+	1.44630i	1.34197	+	1.44630i	0.791071	+	0.611724i	$0.209524\pi$
$463$	1.34197	+	1.44630i	1.34197	+	1.44630i	0.550897	+	0.834573i	$0.314286\pi$
$464$	−0.0841441	−	0.168241i	−0.0841441	−	0.168241i
$465$		0			0
$466$	0.0404015	+	0.384394i	0.0404015	+	0.384394i
$467$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$467$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$468$		0			0
$469$	−0.0709825	+	1.58055i	−0.0709825	+	1.58055i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.999552	−	0.0299155i	−0.999552	−	0.0299155i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.0893684	+	1.98994i	−0.0893684	+	1.98994i
$478$	0.701331	+	0.0104927i	0.701331	+	0.0104927i
$479$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$479$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.189278	−	0.829282i	0.189278	−	0.829282i
$485$		0			0
$486$		0			0
$487$	0.578465	−	0.682447i	0.578465	−	0.682447i	−0.393025	−	0.919528i	$-0.628571\pi$
$487$	0.578465	−	0.682447i	0.578465	−	0.682447i	0.971490	+	0.237080i	$0.0761905\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.667125	+	1.86174i	−0.667125	+	1.86174i	−0.193256	+	0.981148i	$0.561905\pi$
$491$	−0.667125	+	1.86174i	−0.667125	+	1.86174i	−0.473869	+	0.880596i	$0.657143\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.46621	+	0.243481i	−1.46621	+	0.243481i
$498$		0			0
$499$	0.539484	+	1.57956i	0.539484	+	1.57956i	0.791071	+	0.611724i	$0.209524\pi$
$499$	0.539484	+	1.57956i	0.539484	+	1.57956i	−0.251587	+	0.967835i	$0.580952\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$503$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$504$	−0.200585	+	0.686582i	−0.200585	+	0.686582i
$505$		0			0
$506$	−0.443077	+	0.136671i	−0.443077	+	0.136671i
$507$		0			0
$508$	0.151661	+	1.68509i	0.151661	+	1.68509i
$509$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$509$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$510$		0			0
$511$		0			0
$512$	−0.522669	−	0.791809i	−0.522669	−	0.791809i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.308412	+	0.640424i	0.308412	+	0.640424i
$519$		0			0
$520$		0			0
$521$		0			0		−0.800134	−	0.599822i	$-0.795238\pi$
$521$		0			0		0.800134	+	0.599822i	$0.204762\pi$
$522$	0.123868	−	0.0263289i	0.123868	−	0.0263289i
$523$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$523$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$524$		0			0
$525$		0			0
$526$	−0.521509	−	0.290779i	−0.521509	−	0.290779i
$527$		0			0
$528$		0			0
$529$	−0.321916	−	0.298695i	−0.321916	−	0.298695i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.953689	−	0.609240i	0.953689	−	0.609240i
$537$		0			0
$538$		0			0
$539$	−0.992847	+	0.119394i	−0.992847	+	0.119394i
$540$		0			0
$541$	−1.22222	+	1.58055i	−1.22222	+	1.58055i	−0.575617	+	0.817719i	$0.695238\pi$
$541$	−1.22222	+	1.58055i	−1.22222	+	1.58055i	−0.646600	+	0.762830i	$0.723810\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.28061	−	0.458885i	1.28061	−	0.458885i	0.393025	−	0.919528i	$-0.371429\pi$
$547$	1.28061	−	0.458885i	1.28061	−	0.458885i	0.887586	+	0.460642i	$0.152381\pi$
$548$	−1.08306	−	0.714920i	−1.08306	−	0.714920i
$549$		0			0
$550$	−0.231838	−	0.309261i	−0.231838	−	0.309261i
$551$		0			0
$552$		0			0
$553$	0.118953	+	0.0125025i	0.118953	+	0.0125025i
$554$	−0.423590	+	0.565048i	−0.423590	+	0.565048i
$555$		0			0
$556$		0			0
$557$	0.618838	+	0.333011i	0.618838	+	0.333011i	0.753071	−	0.657939i	$-0.228571\pi$
$557$	0.618838	+	0.333011i	0.618838	+	0.333011i	−0.134233	+	0.990950i	$0.542857\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.689442	−	0.0516665i	0.689442	−	0.0516665i
$563$		0			0		0.351375	−	0.936235i	$-0.385714\pi$
$563$		0			0		−0.351375	+	0.936235i	$0.614286\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.858449	+	0.512899i	0.858449	+	0.512899i
$568$	0.746093	+	0.757339i	0.746093	+	0.757339i
$569$	−0.0703841	−	0.585294i	−0.0703841	−	0.585294i	−0.983930	−	0.178557i	$-0.942857\pi$
$569$	−0.0703841	−	0.585294i	−0.0703841	−	0.585294i	0.913545	−	0.406737i	$-0.133333\pi$
$570$		0			0
$571$	0.0741381	+	0.0505465i	0.0741381	+	0.0505465i	0.599822	−	0.800134i	$-0.295238\pi$
$571$	0.0741381	+	0.0505465i	0.0741381	+	0.0505465i	−0.525684	+	0.850680i	$0.676190\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.471490	−	1.10311i	0.471490	−	1.10311i
$576$	−0.200533	+	0.0684902i	−0.200533	+	0.0684902i
$577$		0			0		0.959875	−	0.280427i	$-0.0904762\pi$
$577$		0			0		−0.959875	+	0.280427i	$0.909524\pi$
$578$	0.172892	−	0.345687i	0.172892	−	0.345687i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.64583	+	1.12210i	1.64583	+	1.12210i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.538351	−	0.842721i	$-0.319048\pi$
$587$		0			0		−0.538351	+	0.842721i	$0.680952\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.514203	+	0.922216i	−0.514203	+	0.922216i
$593$		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
$596$	0.415881	−	0.461883i	0.415881	−	0.461883i
$597$		0			0
$598$		0			0
$599$	0.0871715	+	0.0212731i	0.0871715	+	0.0212731i	0.280427	−	0.959875i	$-0.409524\pi$
$599$	0.0871715	+	0.0212731i	0.0871715	+	0.0212731i	−0.193256	+	0.981148i	$0.561905\pi$
$600$		0			0
$601$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$601$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$602$	0.231838	−	0.309261i	0.231838	−	0.309261i
$603$	−0.488909	−	1.50471i	−0.488909	−	1.50471i
$604$	−0.991071	+	0.477275i	−0.991071	+	0.477275i
$605$		0			0
$606$		0			0
$607$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$607$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.99776	−	0.0897196i	1.99776	−	0.0897196i	0.998210	−	0.0598042i	$-0.0190476\pi$
$613$	1.99776	−	0.0897196i	1.99776	−	0.0897196i	0.999552	−	0.0299155i	$-0.00952381\pi$
$614$		0			0
$615$		0			0
$616$	0.478617	+	0.531558i	0.478617	+	0.531558i
$617$	0.307147	+	0.782599i	0.307147	+	0.782599i	0.998210	+	0.0598042i	$0.0190476\pi$
$617$	0.307147	+	0.782599i	0.307147	+	0.782599i	−0.691063	+	0.722795i	$0.742857\pi$
$618$		0			0
$619$		0			0		−0.599822	−	0.800134i	$-0.704762\pi$
$619$		0			0		0.599822	+	0.800134i	$0.295238\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.998210	+	0.0598042i	0.998210	+	0.0598042i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.11939	+	0.691735i	−1.11939	+	0.691735i	−0.955573	−	0.294755i	$-0.904762\pi$
$631$	−1.11939	+	0.691735i	−1.11939	+	0.691735i	−0.163818	+	0.986491i	$0.552381\pi$
$632$	−0.0416637	−	0.0747233i	−0.0416637	−	0.0747233i
$633$		0			0
$634$	−0.743832	−	0.205285i	−0.743832	−	0.205285i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.0427178	−	0.119213i	0.0427178	−	0.119213i
$639$	1.28716	−	0.743145i	1.28716	−	0.743145i
$640$		0			0
$641$	−0.186957	−	0.677425i	−0.186957	−	0.677425i	−0.995974	−	0.0896393i	$-0.971429\pi$
$641$	−0.186957	−	0.677425i	−0.186957	−	0.677425i	0.809017	−	0.587785i	$-0.200000\pi$
$642$		0			0
$643$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$643$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$644$	−0.315329	+	0.970484i	−0.315329	+	0.970484i
$645$		0			0
$646$		0			0
$647$		0			0		0.722795	−	0.691063i	$-0.242857\pi$
$647$		0			0		−0.722795	+	0.691063i	$0.757143\pi$
$648$	−0.0534531	−	0.713282i	−0.0534531	−	0.713282i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.0206999	−	0.0464928i	−0.0206999	−	0.0464928i
$653$	−1.47149	+	0.628945i	−1.47149	+	0.628945i	−0.971490	−	0.237080i	$-0.923810\pi$
$653$	−1.47149	+	0.628945i	−1.47149	+	0.628945i	−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	$0.428571\pi$
$662$	−0.138013	+	0.00206483i	−0.138013	+	0.00206483i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.513775	−	0.491219i	−0.513775	−	0.491219i
$667$	0.386730	−	0.0701811i	0.386730	−	0.0701811i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.207368	+	0.170507i	−0.207368	+	0.170507i	−0.733052	−	0.680173i	$-0.761905\pi$
$673$	−0.207368	+	0.170507i	−0.207368	+	0.170507i	0.525684	+	0.850680i	$0.323810\pi$
$674$	0.578569	+	0.490414i	0.578569	+	0.490414i
$675$		0			0
$676$	0.672892	−	0.520338i	0.672892	−	0.520338i
$677$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$677$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.199769	+	0.0616206i	−0.199769	+	0.0616206i	−0.393025	−	0.919528i	$-0.628571\pi$
$683$	−0.199769	+	0.0616206i	−0.199769	+	0.0616206i	0.193256	+	0.981148i	$0.438095\pi$
$684$		0			0
$685$		0			0
$686$	0.183156	−	0.340361i	0.183156	−	0.340361i
$687$		0			0
$688$	0.573887	+	0.0171758i	0.573887	+	0.0171758i
$689$		0			0
$690$		0			0
$691$		0			0		−0.379225	−	0.925304i	$-0.623810\pi$
$691$		0			0		0.379225	+	0.925304i	$0.376190\pi$
$692$		0			0
$693$	0.887586	−	0.460642i	0.887586	−	0.460642i
$694$	0.375492	+	0.650372i	0.375492	+	0.650372i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.850228	+	0.0254464i	−0.850228	+	0.0254464i
$701$	−1.89918	+	0.374080i	−1.89918	+	0.374080i	−0.998210	−	0.0598042i	$-0.980952\pi$
$701$	−1.89918	+	0.374080i	−1.89918	+	0.374080i	−0.900969	+	0.433884i	$0.857143\pi$
$702$		0			0
$703$		0			0
$704$	−0.0471536	+	0.206594i	−0.0471536	+	0.206594i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.795575	−	0.832106i	0.795575	−	0.832106i	−0.193256	−	0.981148i	$-0.561905\pi$
$709$	0.795575	−	0.832106i	0.795575	−	0.832106i	0.988831	+	0.149042i	$0.0476190\pi$
$710$		0			0
$711$	−0.115761	+	0.0300919i	−0.115761	+	0.0300919i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.511841	−	0.200883i	0.511841	−	0.200883i
$717$		0			0
$718$	−0.499014	+	0.0982904i	−0.499014	+	0.0982904i
$719$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$719$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$720$		0			0
$721$		0			0
$722$	0.275342	−	0.271253i	0.275342	−	0.271253i
$723$		0			0
$724$		0			0
$725$	0.163818	+	0.283741i	0.163818	+	0.283741i
$726$		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
$729$	−0.983930	−	0.178557i	−0.983930	−	0.178557i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$733$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$734$		0			0
$735$		0			0
$736$	1.07435	−	0.331393i	1.07435	−	0.331393i
$737$	−1.53704	−	0.375095i	−1.53704	−	0.375095i
$738$		0			0
$739$	−1.70999	+	0.153902i	−1.70999	+	0.153902i	−0.900969	−	0.433884i	$-0.857143\pi$
$739$	−1.70999	+	0.153902i	−1.70999	+	0.153902i	−0.809017	+	0.587785i	$0.800000\pi$
$740$		0			0
$741$		0			0
$742$	−0.720818	+	0.270528i	−0.720818	+	0.270528i
$743$	0.0236679	−	0.0183021i	0.0236679	−	0.0183021i	−0.599822	−	0.800134i	$-0.704762\pi$
$743$	0.0236679	−	0.0183021i	0.0236679	−	0.0183021i	0.623490	+	0.781831i	$0.285714\pi$
$744$		0			0
$745$		0			0
$746$	0.570569	−	0.469148i	0.570569	−	0.469148i
$747$		0			0
$748$		0			0
$749$	−0.299728	−	0.439620i	−0.299728	−	0.439620i
$750$		0			0
$751$	−0.495974	−	0.776386i	−0.495974	−	0.776386i	0.500000	−	0.866025i	$-0.333333\pi$
$751$	−0.495974	−	0.776386i	−0.495974	−	0.776386i	−0.995974	+	0.0896393i	$0.971429\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.415777	−	0.00622047i	0.415777	−	0.00622047i	0.193256	−	0.981148i	$-0.438095\pi$
$757$	0.415777	−	0.00622047i	0.415777	−	0.00622047i	0.222521	+	0.974928i	$0.428571\pi$
$758$	0.170784	+	0.748251i	0.170784	+	0.748251i
$759$		0			0
$760$		0			0
$761$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$761$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$762$		0			0
$763$	−0.216414	+	0.784158i	−0.216414	+	0.784158i
$764$	1.11572	−	0.516884i	1.11572	−	0.516884i
$765$		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
$772$	0.780958	−	0.746672i	0.780958	−	0.746672i
$773$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$773$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$774$	−0.108389	+	0.371003i	−0.108389	+	0.371003i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.174945	−	0.633898i	−0.174945	−	0.633898i
$779$		0			0
$780$		0			0
$781$	0.0444630	−	1.48562i	0.0444630	−	1.48562i
$782$		0			0
$783$		0			0
$784$	0.570037	−	0.0685494i	0.570037	−	0.0685494i
$785$		0			0
$786$		0			0
$787$		0			0		−0.486989	−	0.873408i	$-0.661905\pi$
$787$		0			0		0.486989	+	0.873408i	$0.338095\pi$
$788$	1.36237	−	0.841884i	1.36237	−	0.841884i
$789$		0			0
$790$		0			0
$791$	−0.565856	+	1.83446i	−0.565856	+	1.83446i
$792$	−0.634874	−	0.329489i	−0.634874	−	0.329489i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$797$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$798$		0			0
$799$		0			0
$800$	0.562150	+	0.749881i	0.562150	+	0.749881i
$801$		0			0
$802$	−0.0952678	−	0.242738i	−0.0952678	−	0.242738i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.872626	+	1.46053i	−0.872626	+	1.46053i	0.0149594	+	0.999888i	$0.495238\pi$
$809$	−0.872626	+	1.46053i	−0.872626	+	1.46053i	−0.887586	+	0.460642i	$0.847619\pi$
$810$		0			0
$811$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$811$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$812$	−0.160419	−	0.227890i	−0.160419	−	0.227890i
$813$		0			0
$814$	−0.687953	+	0.178832i	−0.687953	+	0.178832i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.297784	+	0.0133735i	0.297784	+	0.0133735i	0.193256	−	0.981148i	$-0.438095\pi$
$821$	0.297784	+	0.0133735i	0.297784	+	0.0133735i	0.104528	+	0.994522i	$0.466667\pi$
$822$		0			0
$823$	−1.30011	+	1.44392i	−1.30011	+	1.44392i	−0.473869	+	0.880596i	$0.657143\pi$
$823$	−1.30011	+	1.44392i	−1.30011	+	1.44392i	−0.826239	+	0.563320i	$0.809524\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.971254	−	1.74193i	0.971254	−	1.74193i	0.420357	−	0.907359i	$-0.361905\pi$
$827$	0.971254	−	1.74193i	0.971254	−	1.74193i	0.550897	−	0.834573i	$-0.314286\pi$
$828$	−0.0457813	−	1.01940i	−0.0457813	−	1.01940i
$829$		0			0		−0.0299155	−	0.999552i	$-0.509524\pi$
$829$		0			0		0.0299155	+	0.999552i	$0.490476\pi$
$830$		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		0.880596	−	0.473869i	$-0.157143\pi$
$839$		0			0		−0.880596	+	0.473869i	$0.842857\pi$
$840$		0			0
$841$	0.399296	−	0.798370i	0.399296	−	0.798370i
$842$	0.741259	−	0.216559i	0.741259	−	0.216559i
$843$		0			0
$844$	0.563461	−	1.31828i	0.563461	−	1.31828i
$845$		0			0
$846$		0			0
$847$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$848$	−0.944940	−	0.644249i	−0.944940	−	0.644249i
$849$		0			0
$850$		0			0
$851$	−1.54831	−	1.57165i	−1.54831	−	1.57165i
$852$		0			0
$853$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$853$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$854$		0			0
$855$		0			0
$856$	−0.133727	+	0.356315i	−0.133727	+	0.356315i
$857$		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
$862$	−0.477729	−	0.257077i	−0.477729	−	0.257077i
$863$	0.441384	−	1.80867i	0.441384	−	1.80867i	−0.134233	−	0.990950i	$-0.542857\pi$
$863$	0.441384	−	1.80867i	0.441384	−	1.80867i	0.575617	−	0.817719i	$-0.304762\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.0352552	+	0.114294i	−0.0352552	+	0.114294i
$870$		0			0
$871$		0			0
$872$	0.547758	−	0.196280i	0.547758	−	0.196280i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.606862	+	0.454935i	−0.606862	+	0.454935i	−0.858449	−	0.512899i	$-0.828571\pi$
$877$	−0.606862	+	0.454935i	−0.606862	+	0.454935i	0.251587	+	0.967835i	$0.419048\pi$
$878$		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	$0.142857\pi$
$882$	−0.0518827	+	0.383014i	−0.0518827	+	0.383014i
$883$	0.375046	−	0.239589i	0.375046	−	0.239589i	−0.337330	−	0.941386i	$-0.609524\pi$
$883$	0.375046	−	0.239589i	0.375046	−	0.239589i	0.712376	+	0.701798i	$0.247619\pi$
$884$		0			0
$885$		0			0
$886$	0.435242	−	0.618303i	0.435242	−	0.618303i
$887$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$887$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$888$		0			0
$889$	0.471563	+	1.93234i	0.471563	+	1.93234i
$890$		0			0
$891$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.681911	−	0.757339i	−0.681911	−	0.757339i
$897$		0			0
$898$	0.332982	+	0.249621i	0.332982	+	0.249621i
$899$		0			0
$900$	0.787072	−	0.322572i	0.787072	−	0.322572i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	1.30596	−	0.424331i	1.30596	−	0.424331i
$905$		0			0
$906$		0			0
$907$	−0.851044	−	1.28928i	−0.851044	−	1.28928i	−0.955573	−	0.294755i	$-0.904762\pi$
$907$	−0.851044	−	1.28928i	−0.851044	−	1.28928i	0.104528	−	0.994522i	$-0.466667\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.100991	−	1.12210i	−0.100991	−	1.12210i	−0.873408	−	0.486989i	$-0.838095\pi$
$911$	−0.100991	−	1.12210i	−0.100991	−	1.12210i	0.772417	−	0.635116i	$-0.219048\pi$
$912$		0			0
$913$		0			0
$914$	0.464603	+	0.582594i	0.464603	+	0.582594i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.109669	+	1.21852i	−0.109669	+	1.21852i	0.733052	+	0.680173i	$0.238095\pi$
$919$	−0.109669	+	1.21852i	−0.109669	+	1.21852i	−0.842721	+	0.538351i	$0.819048\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.797936	−	1.65693i	0.797936	−	1.65693i
$926$	0.0456055	−	0.761216i	0.0456055	−	0.761216i
$927$		0			0
$928$	−0.103580	+	0.289061i	−0.103580	+	0.289061i
$929$		0			0		−0.817719	−	0.575617i	$-0.804762\pi$
$929$		0			0		0.817719	+	0.575617i	$0.195238\pi$
$930$		0			0
$931$		0			0
$932$	−0.550003	+	0.648869i	−0.550003	+	0.648869i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.447313	−	0.894377i	$-0.647619\pi$
$937$		0			0		0.447313	+	0.894377i	$0.352381\pi$
$938$	0.460516	−	0.402340i	0.460516	−	0.402340i
$939$		0			0
$940$		0			0
$941$		0			0		−0.999888	−	0.0149594i	$-0.995238\pi$
$941$		0			0		0.999888	+	0.0149594i	$0.00476190\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	0.258627	+	0.287234i	0.258627	+	0.287234i
$947$	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
$953$	0.205697	+	1.95708i	0.205697	+	1.95708i	0.280427	+	0.959875i	$0.409524\pi$
$953$	0.205697	+	1.95708i	0.205697	+	1.95708i	−0.0747301	+	0.997204i	$0.523810\pi$
$954$	0.579799	−	0.506555i	0.579799	−	0.506555i
$955$		0			0
$956$	1.04992	+	1.13155i	1.04992	+	1.13155i
$957$		0			0
$958$		0			0
$959$	−1.38432	−	0.641322i	−1.38432	−	0.641322i
$960$		0			0
$961$	−0.842721	−	0.538351i	−0.842721	−	0.538351i
$962$		0			0
$963$	0.435087	+	0.306271i	0.435087	+	0.306271i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.103606	+	0.215141i	−0.103606	+	0.215141i	−0.946327	−	0.323210i	$-0.895238\pi$
$967$	−0.103606	+	0.215141i	−0.103606	+	0.215141i	0.842721	+	0.538351i	$0.180952\pi$
$968$	−0.614033	+	0.366868i	−0.614033	+	0.366868i
$969$		0			0
$970$		0			0
$971$		0			0		−0.999552	−	0.0299155i	$-0.990476\pi$
$971$		0			0		0.999552	+	0.0299155i	$0.00952381\pi$
$972$		0			0
$973$		0			0
$974$	−0.345165	+	0.0206793i	−0.345165	+	0.0206793i
$975$		0			0
$976$		0			0
$977$	−0.422364	+	1.44571i	−0.422364	+	1.44571i	0.420357	+	0.907359i	$0.361905\pi$
$977$	−0.422364	+	1.44571i	−0.422364	+	1.44571i	−0.842721	+	0.538351i	$0.819048\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.0729192	−	0.810198i	−0.0729192	−	0.810198i
$982$	0.698305	−	0.310905i	0.698305	−	0.310905i
$983$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$983$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.370710	+	1.14093i	−0.370710	+	1.14093i
$990$		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
$994$	0.459652	+	0.344579i	0.459652	+	0.344579i
$995$		0			0
$996$		0			0
$997$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$997$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$998$	0.297181	−	0.572621i	0.297181	−	0.572621i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3311.1.gb.a.545.1	✓	48
7.6	odd	2	CM	3311.1.gb.a.545.1	✓	48
11.2	odd	10		3311.1.gb.b.244.1	yes	48
43.3	odd	42		3311.1.gb.b.2239.1	yes	48
77.13	even	10		3311.1.gb.b.244.1	yes	48
301.132	even	42		3311.1.gb.b.2239.1	yes	48
473.46	even	210	inner	3311.1.gb.a.1938.1	yes	48
3311.1938	odd	210	inner	3311.1.gb.a.1938.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3311.1.gb.a.545.1	✓	48	1.1	even	1	trivial
3311.1.gb.a.545.1	✓	48	7.6	odd	2	CM
3311.1.gb.a.1938.1	yes	48	473.46	even	210	inner
3311.1.gb.a.1938.1	yes	48	3311.1938	odd	210	inner
3311.1.gb.b.244.1	yes	48	11.2	odd	10
3311.1.gb.b.244.1	yes	48	77.13	even	10
3311.1.gb.b.2239.1	yes	48	43.3	odd	42
3311.1.gb.b.2239.1	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)

\(f(q)\)	\(=\)	\(q+(-0.267104 - 0.279369i) q^{2} +(0.0381624 - 0.849752i) q^{4} +(-0.104528 - 0.994522i) q^{7} +(-0.538659 + 0.470612i) q^{8} +(0.447313 + 0.894377i) q^{9} +O(q^{10})\)	\(q+(-0.267104 - 0.279369i) q^{2} +(0.0381624 - 0.849752i) q^{4} +(-0.104528 - 0.994522i) q^{7} +(-0.538659 + 0.470612i) q^{8} +(0.447313 + 0.894377i) q^{9} +(0.995974 + 0.0896393i) q^{11} +(-0.249918 + 0.294843i) q^{14} +(-0.571832 - 0.0514658i) q^{16} +(0.130382 - 0.363857i) q^{18} +(-0.240986 - 0.302187i) q^{22} +(0.438279 - 1.11672i) q^{23} +(0.999552 + 0.0299155i) q^{25} +(-0.849086 + 0.0508699i) q^{28} +(0.172233 + 0.278713i) q^{29} +(0.584332 + 0.732729i) q^{32} +(0.777070 - 0.345974i) q^{36} +(0.748011 - 1.68006i) q^{37} +(-0.998210 + 0.0598042i) q^{43} +(0.114180 - 0.842910i) q^{44} +(-0.429042 + 0.175838i) q^{46} +(-0.978148 + 0.207912i) q^{49} +(-0.258627 - 0.287234i) q^{50} +(1.73978 + 0.970057i) q^{53} +(0.524339 + 0.486515i) q^{56} +(0.0318597 - 0.122562i) q^{58} +(0.842721 - 0.538351i) q^{63} +(-0.0284449 + 0.209989i) q^{64} +(-1.56447 - 0.235806i) q^{67} +(-0.0888863 - 1.48363i) q^{71} +(-0.661854 - 0.271253i) q^{72} +(-0.669153 + 0.239780i) q^{74} +(-0.0149594 - 0.999888i) q^{77} +(-0.0248680 + 0.116995i) q^{79} +(-0.599822 + 0.800134i) q^{81} +(0.283333 + 0.262895i) q^{86} +(-0.578675 + 0.420432i) q^{88} +(-0.932207 - 0.415045i) q^{92} +(0.319351 + 0.217730i) q^{98} +(0.365341 + 0.930874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{2} + 6 q^{7} - 21 q^{8} + q^{9}+O(q^{10}) \) 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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