LMFDB - Embedded newform 2016.2.s.q.865.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2016,2,Mod(289,2016)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2016.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2016, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2016 = 2^{5} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2016.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,2,0,-4,0,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.0978410475$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	2016.865
Dual form			2016.2.s.q.289.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.914214 - 1.58346i) q^{5} +(-1.00000 + 2.44949i) q^{7} +(-1.20711 + 2.09077i) q^{11} +2.82843 q^{13} +(-0.0857864 + 0.148586i) q^{17} +(-3.20711 - 5.55487i) q^{19} +(-2.62132 - 4.54026i) q^{23} +(0.828427 - 1.43488i) q^{25} +2.82843 q^{29} +(-2.79289 + 4.83743i) q^{31} +(4.79289 - 0.655892i) q^{35} +(-4.32843 - 7.49706i) q^{37} +6.82843 q^{41} +9.65685 q^{43} +(5.20711 + 9.01897i) q^{47} +(-5.00000 - 4.89898i) q^{49} +(-0.500000 + 0.866025i) q^{53} +4.41421 q^{55} +(5.44975 - 9.43924i) q^{59} +(-4.32843 - 7.49706i) q^{61} +(-2.58579 - 4.47871i) q^{65} +(1.37868 - 2.38794i) q^{67} -13.6569 q^{71} +(7.32843 - 12.6932i) q^{73} +(-3.91421 - 5.04757i) q^{77} +(-3.03553 - 5.25770i) q^{79} +7.31371 q^{83} +0.313708 q^{85} +(-4.50000 - 7.79423i) q^{89} +(-2.82843 + 6.92820i) q^{91} +(-5.86396 + 10.1567i) q^{95} -1.17157 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - 4 q^{7} - 2 q^{11} - 6 q^{17} - 10 q^{19} - 2 q^{23} - 8 q^{25} - 14 q^{31} + 22 q^{35} - 6 q^{37} + 16 q^{41} + 16 q^{43} + 18 q^{47} - 20 q^{49} - 2 q^{53} + 12 q^{55} + 2 q^{59} - 6 q^{61}+ \cdots - 16 q^{97}+O(q^{100}) $ 4 * q + 2 * q^5 - 4 * q^7 - 2 * q^11 - 6 * q^17 - 10 * q^19 - 2 * q^23 - 8 * q^25 - 14 * q^31 + 22 * q^35 - 6 * q^37 + 16 * q^41 + 16 * q^43 + 18 * q^47 - 20 * q^49 - 2 * q^53 + 12 * q^55 + 2 * q^59 - 6 * q^61 - 16 * q^65 + 14 * q^67 - 32 * q^71 + 18 * q^73 - 10 * q^77 + 2 * q^79 - 16 * q^83 - 44 * q^85 - 18 * q^89 + 2 * q^95 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$1765$	$1793$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.914214	−	1.58346i	−0.408849	−	0.708147i	0.585912	−	0.810374i	$-0.300736\pi$
$5$	−0.914214	−	1.58346i	−0.408849	−	0.708147i	−0.994761	+	0.102228i	$0.967403\pi$
$6$		0			0
$7$	−1.00000	+	2.44949i	−0.377964	+	0.925820i
$7$	−1.00000	+	2.44949i	−0.377964	+	0.925820i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.20711	+	2.09077i	−0.363956	+	0.630391i	−0.988608	−	0.150513i	$-0.951908\pi$
$11$	−1.20711	+	2.09077i	−0.363956	+	0.630391i	0.624652	+	0.780903i	$0.285241\pi$
$12$		0			0
$13$	2.82843			0.784465			0.392232	−	0.919866i	$-0.371703\pi$
$13$	2.82843			0.784465			0.392232	+	0.919866i	$0.371703\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.0857864	+	0.148586i	−0.0208063	+	0.0360375i	−0.876241	−	0.481873i	$-0.839957\pi$
$17$	−0.0857864	+	0.148586i	−0.0208063	+	0.0360375i	0.855435	+	0.517911i	$0.173290\pi$
$18$		0			0
$19$	−3.20711	−	5.55487i	−0.735761	−	1.27438i	−0.954389	−	0.298567i	$-0.903491\pi$
$19$	−3.20711	−	5.55487i	−0.735761	−	1.27438i	0.218628	−	0.975808i	$-0.429842\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.62132	−	4.54026i	−0.546583	−	0.946710i	−0.998505	−	0.0546524i	$-0.982595\pi$
$23$	−2.62132	−	4.54026i	−0.546583	−	0.946710i	0.451922	−	0.892057i	$-0.350738\pi$
$24$		0			0
$25$	0.828427	−	1.43488i	0.165685	−	0.286976i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.82843			0.525226			0.262613	−	0.964901i	$-0.415416\pi$
$29$	2.82843			0.525226			0.262613	+	0.964901i	$0.415416\pi$
$30$		0			0
$31$	−2.79289	+	4.83743i	−0.501618	+	0.868829i	0.498380	+	0.866959i	$0.333929\pi$
$31$	−2.79289	+	4.83743i	−0.501618	+	0.868829i	−0.999998	+	0.00186981i	$0.999405\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.79289	−	0.655892i	0.810147	−	0.110866i
$36$		0			0
$37$	−4.32843	−	7.49706i	−0.711589	−	1.23251i	−0.964260	−	0.264956i	$-0.914642\pi$
$37$	−4.32843	−	7.49706i	−0.711589	−	1.23251i	0.252671	−	0.967552i	$-0.418691\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.82843			1.06642			0.533211	−	0.845983i	$-0.320985\pi$
$41$	6.82843			1.06642			0.533211	+	0.845983i	$0.320985\pi$
$42$		0			0
$43$	9.65685			1.47266			0.736328	−	0.676625i	$-0.236558\pi$
$43$	9.65685			1.47266			0.736328	+	0.676625i	$0.236558\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.20711	+	9.01897i	0.759535	+	1.31555i	0.943088	+	0.332543i	$0.107907\pi$
$47$	5.20711	+	9.01897i	0.759535	+	1.31555i	−0.183554	+	0.983010i	$0.558760\pi$
$48$		0			0
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	−0.898321	−	0.439340i	$-0.855212\pi$
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	0.829640	+	0.558298i	$0.188546\pi$
$54$		0			0
$55$	4.41421			0.595212
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.44975	−	9.43924i	0.709497	−	1.22888i	−0.255547	−	0.966797i	$-0.582256\pi$
$59$	5.44975	−	9.43924i	0.709497	−	1.22888i	0.965044	−	0.262088i	$-0.0844110\pi$
$60$		0			0
$61$	−4.32843	−	7.49706i	−0.554198	−	0.959900i	−0.997965	−	0.0637575i	$-0.979692\pi$
$61$	−4.32843	−	7.49706i	−0.554198	−	0.959900i	0.443767	−	0.896142i	$-0.353642\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.58579	−	4.47871i	−0.320727	−	0.555516i
$66$		0			0
$67$	1.37868	−	2.38794i	0.168433	−	0.291734i	−0.769436	−	0.638723i	$-0.779463\pi$
$67$	1.37868	−	2.38794i	0.168433	−	0.291734i	0.937869	+	0.346990i	$0.112796\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−13.6569			−1.62077			−0.810385	−	0.585897i	$-0.800742\pi$
$71$	−13.6569			−1.62077			−0.810385	+	0.585897i	$0.800742\pi$
$72$		0			0
$73$	7.32843	−	12.6932i	0.857728	−	1.48563i	−0.0163639	−	0.999866i	$-0.505209\pi$
$73$	7.32843	−	12.6932i	0.857728	−	1.48563i	0.874091	−	0.485762i	$-0.161458\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.91421	−	5.04757i	−0.446066	−	0.575224i
$78$		0			0
$79$	−3.03553	−	5.25770i	−0.341524	−	0.591537i	0.643192	−	0.765705i	$-0.277610\pi$
$79$	−3.03553	−	5.25770i	−0.341524	−	0.591537i	−0.984716	+	0.174168i	$0.944276\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.31371			0.802784			0.401392	−	0.915906i	$-0.368527\pi$
$83$	7.31371			0.802784			0.401392	+	0.915906i	$0.368527\pi$
$84$		0			0
$85$	0.313708			0.0340265
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	0.522654	−	0.852545i	$-0.324942\pi$
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	−0.999653	+	0.0263586i	$0.991609\pi$
$90$		0			0
$91$	−2.82843	+	6.92820i	−0.296500	+	0.726273i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5.86396	+	10.1567i	−0.601630	+	1.04205i
$96$		0			0
$97$	−1.17157			−0.118955			−0.0594776	−	0.998230i	$-0.518943\pi$
$97$	−1.17157			−0.118955			−0.0594776	+	0.998230i	$0.518943\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.74264	−	11.6786i	0.670918	−	1.16206i	−0.306726	−	0.951798i	$-0.599234\pi$
$101$	6.74264	−	11.6786i	0.670918	−	1.16206i	0.977644	−	0.210266i	$-0.0674330\pi$
$102$		0			0
$103$	−4.20711	−	7.28692i	−0.414539	−	0.718002i	0.580841	−	0.814017i	$-0.302724\pi$
$103$	−4.20711	−	7.28692i	−0.414539	−	0.718002i	−0.995380	+	0.0960150i	$0.969390\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.44975	−	11.1713i	−0.623521	−	1.07997i	−0.988825	−	0.149081i	$-0.952368\pi$
$107$	−6.44975	−	11.1713i	−0.623521	−	1.07997i	0.365304	−	0.930888i	$-0.380965\pi$
$108$		0			0
$109$	4.08579	−	7.07679i	0.391347	−	0.677834i	−0.601280	−	0.799038i	$-0.705342\pi$
$109$	4.08579	−	7.07679i	0.391347	−	0.677834i	0.992628	+	0.121205i	$0.0386758\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−18.1421			−1.70667			−0.853334	−	0.521364i	$-0.825423\pi$
$113$	−18.1421			−1.70667			−0.853334	+	0.521364i	$0.825423\pi$
$114$		0			0
$115$	−4.79289	+	8.30153i	−0.446940	+	0.774122i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.278175	−	0.358719i	−0.0255002	−	0.0328838i
$120$		0			0
$121$	2.58579	+	4.47871i	0.235071	+	0.407156i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.1716			−1.08866
$126$		0			0
$127$	−5.65685			−0.501965			−0.250982	−	0.967992i	$-0.580754\pi$
$127$	−5.65685			−0.501965			−0.250982	+	0.967992i	$0.580754\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.86396	+	6.69258i	0.337596	+	0.584733i	0.983980	−	0.178279i	$-0.0570530\pi$
$131$	3.86396	+	6.69258i	0.337596	+	0.584733i	−0.646384	+	0.763012i	$0.723720\pi$
$132$		0			0
$133$	16.8137	−	2.30090i	1.45793	−	0.199514i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.57107	−	9.64937i	0.475968	−	0.824402i	−0.523653	−	0.851932i	$-0.675431\pi$
$137$	5.57107	−	9.64937i	0.475968	−	0.824402i	0.999621	+	0.0275304i	$0.00876431\pi$
$138$		0			0
$139$	15.3137			1.29889			0.649446	−	0.760408i	$-0.275001\pi$
$139$	15.3137			1.29889			0.649446	+	0.760408i	$0.275001\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.41421	+	5.91359i	−0.285511	+	0.494519i
$144$		0			0
$145$	−2.58579	−	4.47871i	−0.214738	−	0.371937i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.08579	+	5.34474i	0.252797	+	0.437858i	0.964295	−	0.264831i	$-0.0853160\pi$
$149$	3.08579	+	5.34474i	0.252797	+	0.437858i	−0.711497	+	0.702689i	$0.751983\pi$
$150$		0			0
$151$	−0.449747	+	0.778985i	−0.0365999	+	0.0633929i	−0.883745	−	0.467969i	$-0.844986\pi$
$151$	−0.449747	+	0.778985i	−0.0365999	+	0.0633929i	0.847145	+	0.531361i	$0.178319\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	10.2132			0.820344
$156$		0			0
$157$	−4.67157	+	8.09140i	−0.372832	+	0.645764i	−0.990000	−	0.141067i	$-0.954947\pi$
$157$	−4.67157	+	8.09140i	−0.372832	+	0.645764i	0.617168	+	0.786831i	$0.288280\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	13.7426	−	1.88064i	1.08307	−	0.148215i
$162$		0			0
$163$	−3.37868	−	5.85204i	−0.264639	−	0.458368i	0.702830	−	0.711358i	$-0.251919\pi$
$163$	−3.37868	−	5.85204i	−0.264639	−	0.458368i	−0.967469	+	0.252990i	$0.918586\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.00000			−0.154765			−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000			−0.154765			−0.0773823	+	0.997001i	$0.524656\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.50000	+	9.52628i	0.418157	+	0.724270i	0.995754	−	0.0920525i	$-0.0293428\pi$
$173$	5.50000	+	9.52628i	0.418157	+	0.724270i	−0.577597	+	0.816322i	$0.696009\pi$
$174$		0			0
$175$	2.68629	+	3.46410i	0.203065	+	0.261861i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	2.79289	−	4.83743i	0.208751	−	0.361567i	−0.742571	−	0.669768i	$-0.766394\pi$
$179$	2.79289	−	4.83743i	0.208751	−	0.361567i	0.951321	+	0.308201i	$0.0997270\pi$
$180$		0			0
$181$	−9.31371			−0.692283			−0.346141	−	0.938182i	$-0.612508\pi$
$181$	−9.31371			−0.692283			−0.346141	+	0.938182i	$0.612508\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−7.91421	+	13.7078i	−0.581865	+	1.00782i
$186$		0			0
$187$	−0.207107	−	0.358719i	−0.0151451	−	0.0262322i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.44975	−	7.70719i	−0.321972	−	0.557673i	0.658923	−	0.752211i	$-0.271013\pi$
$191$	−4.44975	−	7.70719i	−0.321972	−	0.557673i	−0.980895	+	0.194538i	$0.937679\pi$
$192$		0			0
$193$	4.57107	−	7.91732i	0.329033	−	0.569901i	−0.653288	−	0.757110i	$-0.726611\pi$
$193$	4.57107	−	7.91732i	0.329033	−	0.569901i	0.982320	+	0.187209i	$0.0599440\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.8284			1.34147			0.670735	−	0.741697i	$-0.265979\pi$
$197$	18.8284			1.34147			0.670735	+	0.741697i	$0.265979\pi$
$198$		0			0
$199$	−5.62132	+	9.73641i	−0.398485	+	0.690196i	−0.993539	−	0.113489i	$-0.963797\pi$
$199$	−5.62132	+	9.73641i	−0.398485	+	0.690196i	0.595054	+	0.803685i	$0.297131\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.82843	+	6.92820i	−0.198517	+	0.486265i
$204$		0			0
$205$	−6.24264	−	10.8126i	−0.436005	−	0.755183i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	15.4853			1.07114
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.82843	−	15.2913i	−0.602094	−	1.04286i
$216$		0			0
$217$	−9.05635	−	11.6786i	−0.614785	−	0.792795i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.242641	+	0.420266i	−0.0163218	+	0.0282702i
$222$		0			0
$223$	2.34315			0.156909			0.0784543	−	0.996918i	$-0.475002\pi$
$223$	2.34315			0.156909			0.0784543	+	0.996918i	$0.475002\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.03553	+	13.9180i	−0.533337	+	0.923767i	0.465905	+	0.884835i	$0.345729\pi$
$227$	−8.03553	+	13.9180i	−0.533337	+	0.923767i	−0.999242	+	0.0389321i	$0.987604\pi$
$228$		0			0
$229$	2.08579	+	3.61269i	0.137833	+	0.238733i	0.926676	−	0.375861i	$-0.122653\pi$
$229$	2.08579	+	3.61269i	0.137833	+	0.238733i	−0.788843	+	0.614594i	$0.789320\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.08579	+	1.88064i	0.0711322	+	0.123205i	0.899398	−	0.437131i	$-0.144005\pi$
$233$	1.08579	+	1.88064i	0.0711322	+	0.123205i	−0.828266	+	0.560336i	$0.810672\pi$
$234$		0			0
$235$	9.52082	−	16.4905i	0.621070	−	1.07572i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.31371			−0.0849767			−0.0424884	−	0.999097i	$-0.513529\pi$
$239$	−1.31371			−0.0849767			−0.0424884	+	0.999097i	$0.513529\pi$
$240$		0			0
$241$	−5.15685	+	8.93193i	−0.332182	+	0.575356i	−0.982939	−	0.183929i	$-0.941118\pi$
$241$	−5.15685	+	8.93193i	−0.332182	+	0.575356i	0.650757	+	0.759286i	$0.274452\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.18629	+	12.3960i	−0.203565	+	0.791954i
$246$		0			0
$247$	−9.07107	−	15.7116i	−0.577178	−	0.999702i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	30.9706			1.95484			0.977422	−	0.211295i	$-0.0677681\pi$
$251$	30.9706			1.95484			0.977422	+	0.211295i	$0.0677681\pi$
$252$		0			0
$253$	12.6569			0.795730
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.25736	+	3.90986i	0.140810	+	0.243890i	0.927802	−	0.373073i	$-0.121696\pi$
$257$	2.25736	+	3.90986i	0.140810	+	0.243890i	−0.786992	+	0.616964i	$0.788363\pi$
$258$		0			0
$259$	22.6924	−	3.10538i	1.41004	−	0.192959i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.44975	−	9.43924i	0.336046	−	0.582048i	−0.647639	−	0.761947i	$-0.724244\pi$
$263$	5.44975	−	9.43924i	0.336046	−	0.582048i	0.983685	+	0.179899i	$0.0575770\pi$
$264$		0			0
$265$	1.82843			0.112319
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6.32843	−	10.9612i	0.385851	−	0.668314i	−0.606036	−	0.795437i	$-0.707241\pi$
$269$	6.32843	−	10.9612i	0.385851	−	0.668314i	0.991887	+	0.127124i	$0.0405745\pi$
$270$		0			0
$271$	15.1066	+	26.1654i	0.917661	+	1.58943i	0.802958	+	0.596035i	$0.203258\pi$
$271$	15.1066	+	26.1654i	0.917661	+	1.58943i	0.114702	+	0.993400i	$0.463409\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$		0			0
$277$	−5.15685	+	8.93193i	−0.309845	+	0.536668i	−0.978328	−	0.207060i	$-0.933611\pi$
$277$	−5.15685	+	8.93193i	−0.309845	+	0.536668i	0.668483	+	0.743727i	$0.266944\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	12.4853			0.744809			0.372405	−	0.928070i	$-0.378533\pi$
$281$	12.4853			0.744809			0.372405	+	0.928070i	$0.378533\pi$
$282$		0			0
$283$	−2.79289	+	4.83743i	−0.166020	+	0.287556i	−0.937017	−	0.349283i	$-0.886425\pi$
$283$	−2.79289	+	4.83743i	−0.166020	+	0.287556i	0.770997	+	0.636839i	$0.219758\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.82843	+	16.7262i	−0.403069	+	0.987314i
$288$		0			0
$289$	8.48528	+	14.6969i	0.499134	+	0.864526i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−28.6274			−1.67243			−0.836216	−	0.548401i	$-0.815237\pi$
$293$	−28.6274			−1.67243			−0.836216	+	0.548401i	$0.815237\pi$
$294$		0			0
$295$	−19.9289			−1.16031
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.41421	−	12.8418i	−0.428775	−	0.742660i
$300$		0			0
$301$	−9.65685	+	23.6544i	−0.556612	+	1.36341i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.91421	+	13.7078i	−0.453167	+	0.784907i
$306$		0			0
$307$	14.3431			0.818607			0.409303	−	0.912398i	$-0.365772\pi$
$307$	14.3431			0.818607			0.409303	+	0.912398i	$0.365772\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.37868	+	16.2443i	−0.531816	+	0.921133i	0.467494	+	0.883996i	$0.345157\pi$
$311$	−9.37868	+	16.2443i	−0.531816	+	0.921133i	−0.999310	+	0.0371364i	$0.988176\pi$
$312$		0			0
$313$	14.6421	+	25.3609i	0.827622	+	1.43348i	0.899898	+	0.436099i	$0.143640\pi$
$313$	14.6421	+	25.3609i	0.827622	+	1.43348i	−0.0722760	+	0.997385i	$0.523026\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.84315	−	8.38857i	−0.272018	−	0.471149i	0.697360	−	0.716721i	$-0.254358\pi$
$317$	−4.84315	−	8.38857i	−0.272018	−	0.471149i	−0.969379	+	0.245571i	$0.921024\pi$
$318$		0			0
$319$	−3.41421	+	5.91359i	−0.191159	+	0.331098i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.10051			0.0612337
$324$		0			0
$325$	2.34315	−	4.05845i	0.129974	−	0.225122i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−27.2990	+	3.73578i	−1.50504	+	0.205960i
$330$		0			0
$331$	−14.2071	−	24.6074i	−0.780893	−	1.35255i	−0.931422	−	0.363941i	$-0.881431\pi$
$331$	−14.2071	−	24.6074i	−0.780893	−	1.35255i	0.150529	−	0.988606i	$-0.451902\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.04163			−0.275454
$336$		0			0
$337$	9.17157			0.499607			0.249804	−	0.968296i	$-0.419634\pi$
$337$	9.17157			0.499607			0.249804	+	0.968296i	$0.419634\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6.74264	−	11.6786i	−0.365134	−	0.632431i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	17.4497	−	30.2238i	0.936752	−	1.62250i	0.165271	−	0.986248i	$-0.447150\pi$
$347$	17.4497	−	30.2238i	0.936752	−	1.62250i	0.771480	−	0.636253i	$-0.219517\pi$
$348$		0			0
$349$	5.17157			0.276828			0.138414	−	0.990374i	$-0.455800\pi$
$349$	5.17157			0.276828			0.138414	+	0.990374i	$0.455800\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.08579	−	1.88064i	0.0577906	−	0.100096i	−0.835683	−	0.549212i	$-0.814928\pi$
$353$	1.08579	−	1.88064i	0.0577906	−	0.100096i	0.893473	+	0.449116i	$0.148261\pi$
$354$		0			0
$355$	12.4853	+	21.6251i	0.662650	+	1.14774i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.69239	+	9.85951i	0.300433	+	0.520365i	0.976234	−	0.216719i	$-0.0695356\pi$
$359$	5.69239	+	9.85951i	0.300433	+	0.520365i	−0.675801	+	0.737084i	$0.736202\pi$
$360$		0			0
$361$	−11.0711	+	19.1757i	−0.582688	+	1.00924i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−26.7990			−1.40272
$366$		0			0
$367$	−2.13604	+	3.69973i	−0.111500	+	0.193124i	−0.916375	−	0.400320i	$-0.868899\pi$
$367$	−2.13604	+	3.69973i	−0.111500	+	0.193124i	0.804875	+	0.593444i	$0.202232\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.62132	−	2.09077i	−0.0841748	−	0.108547i
$372$		0			0
$373$	4.15685	+	7.19988i	0.215234	+	0.372796i	0.953345	−	0.301883i	$-0.0976153\pi$
$373$	4.15685	+	7.19988i	0.215234	+	0.372796i	−0.738111	+	0.674679i	$0.764282\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8.00000			0.412021
$378$		0			0
$379$	−34.9706			−1.79632			−0.898159	−	0.439672i	$-0.855095\pi$
$379$	−34.9706			−1.79632			−0.898159	+	0.439672i	$0.855095\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−5.62132	−	9.73641i	−0.287236	−	0.497507i	0.685913	−	0.727684i	$-0.259403\pi$
$383$	−5.62132	−	9.73641i	−0.287236	−	0.497507i	−0.973149	+	0.230176i	$0.926070\pi$
$384$		0			0
$385$	−4.41421	+	10.8126i	−0.224969	+	0.551060i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	9.08579	−	15.7370i	0.460668	−	0.797900i	−0.538327	−	0.842736i	$-0.680943\pi$
$389$	9.08579	−	15.7370i	0.460668	−	0.797900i	0.998994	+	0.0448365i	$0.0142767\pi$
$390$		0			0
$391$	0.899495			0.0454894
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.55025	+	9.61332i	−0.279264	+	0.483699i
$396$		0			0
$397$	2.08579	+	3.61269i	0.104683	+	0.181316i	0.913608	−	0.406595i	$-0.133284\pi$
$397$	2.08579	+	3.61269i	0.104683	+	0.181316i	−0.808926	+	0.587911i	$0.799951\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.91421	+	6.77962i	0.195466	+	0.338558i	0.947053	−	0.321076i	$-0.104045\pi$
$401$	3.91421	+	6.77962i	0.195466	+	0.338558i	−0.751587	+	0.659634i	$0.770711\pi$
$402$		0			0
$403$	−7.89949	+	13.6823i	−0.393502	+	0.681565i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	20.8995			1.03595
$408$		0			0
$409$	−7.22792	+	12.5191i	−0.357398	+	0.619031i	−0.987525	−	0.157461i	$-0.949669\pi$
$409$	−7.22792	+	12.5191i	−0.357398	+	0.619031i	0.630128	+	0.776492i	$0.283003\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	17.6716	+	22.7883i	0.869561	+	1.12134i
$414$		0			0
$415$	−6.68629	−	11.5810i	−0.328217	−	0.568489i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−9.65685			−0.471768			−0.235884	−	0.971781i	$-0.575799\pi$
$419$	−9.65685			−0.471768			−0.235884	+	0.971781i	$0.575799\pi$
$420$		0			0
$421$	−16.4853			−0.803443			−0.401722	−	0.915762i	$-0.631588\pi$
$421$	−16.4853			−0.803443			−0.401722	+	0.915762i	$0.631588\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.142136	+	0.246186i	0.00689459	+	0.0119418i
$426$		0			0
$427$	22.6924	−	3.10538i	1.09816	−	0.150280i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6.37868	+	11.0482i	−0.307250	+	0.532173i	−0.977760	−	0.209728i	$-0.932742\pi$
$431$	−6.37868	+	11.0482i	−0.307250	+	0.532173i	0.670510	+	0.741901i	$0.266076\pi$
$432$		0			0
$433$	11.5147			0.553362			0.276681	−	0.960962i	$-0.410765\pi$
$433$	11.5147			0.553362			0.276681	+	0.960962i	$0.410765\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−16.8137	+	29.1222i	−0.804309	+	1.39310i
$438$		0			0
$439$	−11.3492	−	19.6575i	−0.541670	−	0.938200i	−0.998808	−	0.0488041i	$-0.984459\pi$
$439$	−11.3492	−	19.6575i	−0.541670	−	0.938200i	0.457139	−	0.889395i	$-0.348874\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.96447	−	10.3308i	−0.283380	−	0.490829i	0.688835	−	0.724918i	$-0.258123\pi$
$443$	−5.96447	−	10.3308i	−0.283380	−	0.490829i	−0.972215	+	0.234089i	$0.924789\pi$
$444$		0			0
$445$	−8.22792	+	14.2512i	−0.390041	+	0.675571i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.17157			−0.0552899			−0.0276450	−	0.999618i	$-0.508801\pi$
$449$	−1.17157			−0.0552899			−0.0276450	+	0.999618i	$0.508801\pi$
$450$		0			0
$451$	−8.24264	+	14.2767i	−0.388131	+	0.672262i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	13.5563	−	1.85514i	0.635531	−	0.0869705i
$456$		0			0
$457$	−9.64214	−	16.7007i	−0.451040	−	0.781224i	0.547411	−	0.836864i	$-0.315614\pi$
$457$	−9.64214	−	16.7007i	−0.451040	−	0.781224i	−0.998451	+	0.0556397i	$0.982280\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	25.4558			1.18560			0.592798	−	0.805351i	$-0.298023\pi$
$461$	25.4558			1.18560			0.592798	+	0.805351i	$0.298023\pi$
$462$		0			0
$463$	−11.3137			−0.525793			−0.262896	−	0.964824i	$-0.584678\pi$
$463$	−11.3137			−0.525793			−0.262896	+	0.964824i	$0.584678\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.27817	−	10.8741i	−0.290519	−	0.503194i	0.683413	−	0.730032i	$-0.260495\pi$
$467$	−6.27817	−	10.8741i	−0.290519	−	0.503194i	−0.973933	+	0.226837i	$0.927161\pi$
$468$		0			0
$469$	4.47056	+	5.76500i	0.206431	+	0.266203i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−11.6569	+	20.1903i	−0.535983	+	0.928349i
$474$		0			0
$475$	−10.6274			−0.487619
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−14.3492	+	24.8536i	−0.655634	+	1.13559i	0.326101	+	0.945335i	$0.394265\pi$
$479$	−14.3492	+	24.8536i	−0.655634	+	1.13559i	−0.981735	+	0.190256i	$0.939068\pi$
$480$		0			0
$481$	−12.2426	−	21.2049i	−0.558216	−	0.966859i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.07107	+	1.85514i	0.0486347	+	0.0842377i
$486$		0			0
$487$	5.86396	−	10.1567i	0.265721	−	0.460243i	−0.702031	−	0.712146i	$-0.747723\pi$
$487$	5.86396	−	10.1567i	0.265721	−	0.460243i	0.967752	+	0.251903i	$0.0810565\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.65685			−0.165032			−0.0825158	−	0.996590i	$-0.526295\pi$
$491$	−3.65685			−0.165032			−0.0825158	+	0.996590i	$0.526295\pi$
$492$		0			0
$493$	−0.242641	+	0.420266i	−0.0109280	+	0.0189278i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	13.6569	−	33.4523i	0.612594	−	1.50054i
$498$		0			0
$499$	2.27817	+	3.94591i	0.101985	+	0.176643i	0.912502	−	0.409071i	$-0.134147\pi$
$499$	2.27817	+	3.94591i	0.101985	+	0.176643i	−0.810517	+	0.585715i	$0.800814\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	10.3431			0.461178			0.230589	−	0.973051i	$-0.425935\pi$
$503$	10.3431			0.461178			0.230589	+	0.973051i	$0.425935\pi$
$504$		0			0
$505$	−24.6569			−1.09722
$506$		0			0
$507$		0			0
$508$		0			0
$509$	20.7426	+	35.9273i	0.919401	+	1.59245i	0.800326	+	0.599565i	$0.204660\pi$
$509$	20.7426	+	35.9273i	0.919401	+	1.59245i	0.119075	+	0.992885i	$0.462007\pi$
$510$		0			0
$511$	23.7635	+	30.6441i	1.05123	+	1.35562i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.69239	+	13.3236i	−0.338967	+	0.587108i
$516$		0			0
$517$	−25.1421			−1.10575
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.50000	−	6.06218i	0.153338	−	0.265589i	−0.779115	−	0.626881i	$-0.784331\pi$
$521$	3.50000	−	6.06218i	0.153338	−	0.265589i	0.932453	+	0.361293i	$0.117664\pi$
$522$		0			0
$523$	−8.86396	−	15.3528i	−0.387594	−	0.671332i	0.604531	−	0.796581i	$-0.293360\pi$
$523$	−8.86396	−	15.3528i	−0.387594	−	0.671332i	−0.992125	+	0.125249i	$0.960027\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.479185	−	0.829972i	−0.0208736	−	0.0361542i
$528$		0			0
$529$	−2.24264	+	3.88437i	−0.0975061	+	0.168886i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	19.3137			0.836570
$534$		0			0
$535$	−11.7929	+	20.4259i	−0.509851	+	0.883088i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	16.2782	−	4.54026i	0.701151	−	0.195563i
$540$		0			0
$541$	12.9142	+	22.3681i	0.555225	+	0.961679i	0.997886	+	0.0649894i	$0.0207013\pi$
$541$	12.9142	+	22.3681i	0.555225	+	0.961679i	−0.442661	+	0.896689i	$0.645965\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−14.9411			−0.640007
$546$		0			0
$547$	10.9706			0.469067			0.234534	−	0.972108i	$-0.424644\pi$
$547$	10.9706			0.469067			0.234534	+	0.972108i	$0.424644\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.07107	−	15.7116i	−0.386440	−	0.669335i
$552$		0			0
$553$	15.9142	−	2.17781i	0.676741	−	0.0926099i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.0857864	+	0.148586i	−0.00363489	+	0.00629581i	−0.867837	−	0.496849i	$-0.834490\pi$
$557$	−0.0857864	+	0.148586i	−0.00363489	+	0.00629581i	0.864202	+	0.503145i	$0.167824\pi$
$558$		0			0
$559$	27.3137			1.15525
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.03553	+	12.1859i	−0.296512	+	0.513575i	−0.975336	−	0.220727i	$-0.929157\pi$
$563$	−7.03553	+	12.1859i	−0.296512	+	0.513575i	0.678823	+	0.734302i	$0.262490\pi$
$564$		0			0
$565$	16.5858	+	28.7274i	0.697769	+	1.20857i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.3284	+	31.7458i	0.768368	+	1.33085i	0.938448	+	0.345422i	$0.112264\pi$
$569$	18.3284	+	31.7458i	0.768368	+	1.33085i	−0.170080	+	0.985430i	$0.554403\pi$
$570$		0			0
$571$	9.20711	−	15.9472i	0.385305	−	0.667369i	−0.606506	−	0.795079i	$-0.707429\pi$
$571$	9.20711	−	15.9472i	0.385305	−	0.667369i	0.991812	+	0.127710i	$0.0407628\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−8.68629			−0.362243
$576$		0			0
$577$	−19.5000	+	33.7750i	−0.811796	+	1.40607i	0.0998105	+	0.995006i	$0.468176\pi$
$577$	−19.5000	+	33.7750i	−0.811796	+	1.40607i	−0.911606	+	0.411065i	$0.865157\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.31371	+	17.9149i	−0.303424	+	0.743233i
$582$		0			0
$583$	−1.20711	−	2.09077i	−0.0499933	−	0.0865909i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−28.9706			−1.19574			−0.597872	−	0.801592i	$-0.703987\pi$
$587$	−28.9706			−1.19574			−0.597872	+	0.801592i	$0.703987\pi$
$588$		0			0
$589$	35.8284			1.47628
$590$		0			0
$591$		0			0
$592$		0			0
$593$	2.74264	+	4.75039i	0.112627	+	0.195075i	0.916829	−	0.399281i	$-0.130740\pi$
$593$	2.74264	+	4.75039i	0.112627	+	0.195075i	−0.804202	+	0.594356i	$0.797407\pi$
$594$		0			0
$595$	−0.313708	+	0.768426i	−0.0128608	+	0.0315024i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	17.9350	−	31.0644i	0.732805	−	1.26926i	−0.222874	−	0.974847i	$-0.571544\pi$
$599$	17.9350	−	31.0644i	0.732805	−	1.26926i	0.955680	−	0.294409i	$-0.0951228\pi$
$600$		0			0
$601$	26.1421			1.06636			0.533180	−	0.846002i	$-0.320997\pi$
$601$	26.1421			1.06636			0.533180	+	0.846002i	$0.320997\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.72792	−	8.18900i	0.192217	−	0.332930i
$606$		0			0
$607$	−17.6924	−	30.6441i	−0.718112	−	1.24381i	−0.961747	−	0.273939i	$-0.911673\pi$
$607$	−17.6924	−	30.6441i	−0.718112	−	1.24381i	0.243635	−	0.969867i	$-0.421660\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	14.7279	+	25.5095i	0.595828	+	1.03200i
$612$		0			0
$613$	−2.25736	+	3.90986i	−0.0911739	+	0.157918i	−0.908005	−	0.418959i	$-0.862395\pi$
$613$	−2.25736	+	3.90986i	−0.0911739	+	0.157918i	0.816831	+	0.576876i	$0.195729\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−19.1127			−0.769448			−0.384724	−	0.923032i	$-0.625703\pi$
$617$	−19.1127			−0.769448			−0.384724	+	0.923032i	$0.625703\pi$
$618$		0			0
$619$	−8.96447	+	15.5269i	−0.360312	+	0.624079i	−0.988012	−	0.154376i	$-0.950663\pi$
$619$	−8.96447	+	15.5269i	−0.360312	+	0.624079i	0.627700	+	0.778455i	$0.283997\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	23.5919	−	3.22848i	0.945189	−	0.129346i
$624$		0			0
$625$	6.98528	+	12.0989i	0.279411	+	0.483954i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.48528			0.0592220
$630$		0			0
$631$	29.6569			1.18062			0.590310	−	0.807176i	$-0.299005\pi$
$631$	29.6569			1.18062			0.590310	+	0.807176i	$0.299005\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.17157	+	8.95743i	0.205228	+	0.355465i
$636$		0			0
$637$	−14.1421	−	13.8564i	−0.560332	−	0.549011i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−8.50000	+	14.7224i	−0.335730	+	0.581501i	−0.983625	−	0.180229i	$-0.942316\pi$
$641$	−8.50000	+	14.7224i	−0.335730	+	0.581501i	0.647895	+	0.761730i	$0.275650\pi$
$642$		0			0
$643$	11.0294			0.434959			0.217479	−	0.976065i	$-0.430217\pi$
$643$	11.0294			0.434959			0.217479	+	0.976065i	$0.430217\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.9350	−	24.1362i	0.547843	−	0.948891i	−0.450580	−	0.892736i	$-0.648783\pi$
$647$	13.9350	−	24.1362i	0.547843	−	0.948891i	0.998422	−	0.0561548i	$-0.0178840\pi$
$648$		0			0
$649$	13.1569	+	22.7883i	0.516452	+	0.894521i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.4706	−	33.7240i	−0.761942	−	1.31972i	−0.941848	−	0.336038i	$-0.890913\pi$
$653$	−19.4706	−	33.7240i	−0.761942	−	1.31972i	0.179906	−	0.983684i	$-0.442421\pi$
$654$		0			0
$655$	7.06497	−	12.2369i	0.276051	−	0.478135i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−34.6274			−1.34889			−0.674446	−	0.738324i	$-0.735618\pi$
$659$	−34.6274			−1.34889			−0.674446	+	0.738324i	$0.735618\pi$
$660$		0			0
$661$	15.3284	−	26.5496i	0.596207	−	1.03266i	−0.397169	−	0.917746i	$-0.630007\pi$
$661$	15.3284	−	26.5496i	0.596207	−	1.03266i	0.993375	−	0.114915i	$-0.0366595\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−19.0147	−	24.5204i	−0.737359	−	0.950860i
$666$		0			0
$667$	−7.41421	−	12.8418i	−0.287079	−	0.497236i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	20.8995			0.806816
$672$		0			0
$673$	−2.14214			−0.0825733			−0.0412866	−	0.999147i	$-0.513146\pi$
$673$	−2.14214			−0.0825733			−0.0412866	+	0.999147i	$0.513146\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.39949	−	16.2804i	−0.361252	−	0.625707i	0.626915	−	0.779087i	$-0.284317\pi$
$677$	−9.39949	−	16.2804i	−0.361252	−	0.625707i	−0.988167	+	0.153381i	$0.950984\pi$
$678$		0			0
$679$	1.17157	−	2.86976i	0.0449608	−	0.110131i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.72183	+	15.1066i	−0.333731	+	0.578040i	−0.983240	−	0.182314i	$-0.941641\pi$
$683$	−8.72183	+	15.1066i	−0.333731	+	0.578040i	0.649509	+	0.760354i	$0.274975\pi$
$684$		0			0
$685$	−20.3726			−0.778396
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.41421	+	2.44949i	−0.0538772	+	0.0933181i
$690$		0			0
$691$	−13.5208	−	23.4187i	−0.514356	−	0.890891i	−0.999861	−	0.0166570i	$-0.994698\pi$
$691$	−13.5208	−	23.4187i	−0.514356	−	0.890891i	0.485505	−	0.874234i	$-0.338636\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−14.0000	−	24.2487i	−0.531050	−	0.919806i
$696$		0			0
$697$	−0.585786	+	1.01461i	−0.0221882	+	0.0384312i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−14.0000			−0.528773			−0.264386	−	0.964417i	$-0.585169\pi$
$701$	−14.0000			−0.528773			−0.264386	+	0.964417i	$0.585169\pi$
$702$		0			0
$703$	−27.7635	+	48.0877i	−1.04712	+	1.81366i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	21.8640	+	28.1946i	0.822279	+	1.06037i
$708$		0			0
$709$	18.2990	+	31.6948i	0.687233	+	1.19032i	0.972729	+	0.231943i	$0.0745082\pi$
$709$	18.2990	+	31.6948i	0.687233	+	1.19032i	−0.285496	+	0.958380i	$0.592158\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	29.2843			1.09670
$714$		0			0
$715$	12.4853			0.466923
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.5208	+	26.8828i	0.578829	+	1.00256i	0.995614	+	0.0935558i	$0.0298234\pi$
$719$	15.5208	+	26.8828i	0.578829	+	1.00256i	−0.416785	+	0.909005i	$0.636843\pi$
$720$		0			0
$721$	22.0563	−	3.01834i	0.821421	−	0.112409i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.34315	−	4.05845i	0.0870222	−	0.150727i
$726$		0			0
$727$	34.3431			1.27372			0.636858	−	0.770981i	$-0.280234\pi$
$727$	34.3431			1.27372			0.636858	+	0.770981i	$0.280234\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.828427	+	1.43488i	−0.0306405	+	0.0530709i
$732$		0			0
$733$	−11.8431	−	20.5129i	−0.437437	−	0.757662i	0.560054	−	0.828456i	$-0.310780\pi$
$733$	−11.8431	−	20.5129i	−0.437437	−	0.757662i	−0.997491	+	0.0707935i	$0.977447\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.32843	+	5.76500i	0.122604	+	0.212357i
$738$		0			0
$739$	3.34924	−	5.80106i	0.123204	−	0.213395i	−0.797826	−	0.602888i	$-0.794016\pi$
$739$	3.34924	−	5.80106i	0.123204	−	0.213395i	0.921029	+	0.389493i	$0.127350\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−26.3431			−0.966436			−0.483218	−	0.875500i	$-0.660532\pi$
$743$	−26.3431			−0.966436			−0.483218	+	0.875500i	$0.660532\pi$
$744$		0			0
$745$	5.64214	−	9.77247i	0.206712	−	0.358035i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	33.8137	−	4.62730i	1.23553	−	0.169078i
$750$		0			0
$751$	−10.8640	−	18.8169i	−0.396432	−	0.686640i	0.596851	−	0.802352i	$-0.296418\pi$
$751$	−10.8640	−	18.8169i	−0.396432	−	0.686640i	−0.993283	+	0.115712i	$0.963085\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.64466			0.0598553
$756$		0			0
$757$	−6.14214			−0.223240			−0.111620	−	0.993751i	$-0.535604\pi$
$757$	−6.14214			−0.223240			−0.111620	+	0.993751i	$0.535604\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−21.0563	−	36.4707i	−0.763292	−	1.32206i	−0.941145	−	0.338004i	$-0.890248\pi$
$761$	−21.0563	−	36.4707i	−0.763292	−	1.32206i	0.177853	−	0.984057i	$-0.443085\pi$
$762$		0			0
$763$	13.2487	+	17.0849i	0.479636	+	0.618514i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	15.4142	−	26.6982i	0.556575	−	0.964016i
$768$		0			0
$769$	13.8579			0.499727			0.249864	−	0.968281i	$-0.419614\pi$
$769$	13.8579			0.499727			0.249864	+	0.968281i	$0.419614\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.57107	+	7.91732i	−0.164410	+	0.284766i	−0.936446	−	0.350813i	$-0.885905\pi$
$773$	−4.57107	+	7.91732i	−0.164410	+	0.284766i	0.772036	+	0.635579i	$0.219239\pi$
$774$		0			0
$775$	4.62742	+	8.01492i	0.166222	+	0.287904i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−21.8995	−	37.9310i	−0.784631	−	1.35902i
$780$		0			0
$781$	16.4853	−	28.5533i	0.589890	−	1.02172i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	17.0833			0.609728
$786$		0			0
$787$	−23.1066	+	40.0218i	−0.823661	+	1.42662i	0.0792766	+	0.996853i	$0.474739\pi$
$787$	−23.1066	+	40.0218i	−0.823661	+	1.42662i	−0.902938	+	0.429771i	$0.858594\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	18.1421	−	44.4390i	0.645060	−	1.58007i
$792$		0			0
$793$	−12.2426	−	21.2049i	−0.434749	−	0.753007i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−47.1127			−1.66882			−0.834409	−	0.551146i	$-0.814191\pi$
$797$	−47.1127			−1.66882			−0.834409	+	0.551146i	$0.814191\pi$
$798$		0			0
$799$	−1.78680			−0.0632123
$800$		0			0
$801$		0			0
$802$		0			0
$803$	17.6924	+	30.6441i	0.624351	+	1.08141i
$804$		0			0
$805$	−15.5416	−	20.0417i	−0.547771	−	0.706376i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−8.98528	+	15.5630i	−0.315906	+	0.547165i	−0.979630	−	0.200813i	$-0.935642\pi$
$809$	−8.98528	+	15.5630i	−0.315906	+	0.547165i	0.663724	+	0.747978i	$0.268975\pi$
$810$		0			0
$811$	−17.6569			−0.620016			−0.310008	−	0.950734i	$-0.600332\pi$
$811$	−17.6569			−0.620016			−0.310008	+	0.950734i	$0.600332\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.17767	+	10.7000i	−0.216394	+	0.374806i
$816$		0			0
$817$	−30.9706	−	53.6426i	−1.08352	−	1.87672i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.57107	+	13.1135i	0.264232	+	0.457663i	0.967362	−	0.253398i	$-0.0815482\pi$
$821$	7.57107	+	13.1135i	0.264232	+	0.457663i	−0.703130	+	0.711061i	$0.748215\pi$
$822$		0			0
$823$	24.0061	−	41.5798i	0.836800	−	1.44938i	−0.0557566	−	0.998444i	$-0.517757\pi$
$823$	24.0061	−	41.5798i	0.836800	−	1.44938i	0.892556	−	0.450936i	$-0.148910\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−41.6569			−1.44855			−0.724275	−	0.689511i	$-0.757826\pi$
$827$	−41.6569			−1.44855			−0.724275	+	0.689511i	$0.757826\pi$
$828$		0			0
$829$	−0.600505	+	1.04011i	−0.0208564	+	0.0361243i	−0.876265	−	0.481829i	$-0.839973\pi$
$829$	−0.600505	+	1.04011i	−0.0208564	+	0.0361243i	0.855409	+	0.517953i	$0.173306\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.15685	−	0.322666i	0.0400826	−	0.0111797i
$834$		0			0
$835$	1.82843	+	3.16693i	0.0632753	+	0.109596i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	3.31371			0.114402			0.0572010	−	0.998363i	$-0.481782\pi$
$839$	3.31371			0.114402			0.0572010	+	0.998363i	$0.481782\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.57107	+	7.91732i	0.157250	+	0.272364i
$846$		0			0
$847$	−13.5563	+	1.85514i	−0.465802	+	0.0637435i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−22.6924	+	39.3044i	−0.777885	+	1.34734i
$852$		0			0
$853$	−40.4853			−1.38619			−0.693095	−	0.720846i	$-0.743753\pi$
$853$	−40.4853			−1.38619			−0.693095	+	0.720846i	$0.743753\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.6716	−	21.9478i	0.432853	−	0.749723i	−0.564265	−	0.825594i	$-0.690840\pi$
$857$	12.6716	−	21.9478i	0.432853	−	0.749723i	0.997118	+	0.0758709i	$0.0241737\pi$
$858$		0			0
$859$	−2.72183	−	4.71434i	−0.0928675	−	0.160851i	0.815849	−	0.578265i	$-0.196270\pi$
$859$	−2.72183	−	4.71434i	−0.0928675	−	0.160851i	−0.908717	+	0.417414i	$0.862937\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	16.6924	+	28.9121i	0.568216	+	0.984178i	0.996743	+	0.0806492i	$0.0256993\pi$
$863$	16.6924	+	28.9121i	0.568216	+	0.984178i	−0.428527	+	0.903529i	$0.640967\pi$
$864$		0			0
$865$	10.0563	−	17.4181i	0.341926	−	0.592233i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	14.6569			0.497200
$870$		0			0
$871$	3.89949	−	6.75412i	0.132129	−	0.228855i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	12.1716	−	29.8141i	0.411474	−	1.00790i
$876$		0			0
$877$	−25.7132	−	44.5366i	−0.868273	−	1.50389i	−0.863760	−	0.503903i	$-0.831897\pi$
$877$	−25.7132	−	44.5366i	−0.868273	−	1.50389i	−0.00451320	−	0.999990i	$-0.501437\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	26.0000			0.875962			0.437981	−	0.898984i	$-0.355694\pi$
$881$	26.0000			0.875962			0.437981	+	0.898984i	$0.355694\pi$
$882$		0			0
$883$	−41.2548			−1.38834			−0.694168	−	0.719813i	$-0.744227\pi$
$883$	−41.2548			−1.38834			−0.694168	+	0.719813i	$0.744227\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	15.5503	+	26.9338i	0.522126	+	0.904349i	0.999669	+	0.0257406i	$0.00819441\pi$
$887$	15.5503	+	26.9338i	0.522126	+	0.904349i	−0.477542	+	0.878609i	$0.658472\pi$
$888$		0			0
$889$	5.65685	−	13.8564i	0.189725	−	0.464729i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	33.3995	−	57.8496i	1.11767	−	1.93586i
$894$		0			0
$895$	−10.2132			−0.341390
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−7.89949	+	13.6823i	−0.263463	+	0.456331i
$900$		0			0
$901$	−0.0857864	−	0.148586i	−0.00285796	−	0.00495013i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	8.51472	+	14.7479i	0.283039	+	0.490238i
$906$		0			0
$907$	−12.7635	+	22.1070i	−0.423804	+	0.734049i	−0.996308	−	0.0858524i	$-0.972639\pi$
$907$	−12.7635	+	22.1070i	−0.423804	+	0.734049i	0.572504	+	0.819902i	$0.305972\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−8.00000			−0.265052			−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000			−0.265052			−0.132526	+	0.991180i	$0.542309\pi$
$912$		0			0
$913$	−8.82843	+	15.2913i	−0.292178	+	0.506068i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−20.2574	+	2.77216i	−0.668957	+	0.0915447i
$918$		0			0
$919$	3.27817	+	5.67796i	0.108137	+	0.187299i	0.915016	−	0.403419i	$-0.132178\pi$
$919$	3.27817	+	5.67796i	0.108137	+	0.187299i	−0.806879	+	0.590717i	$0.798845\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−38.6274			−1.27144
$924$		0			0
$925$	−14.3431			−0.471600
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−9.67157	−	16.7517i	−0.317314	−	0.549604i	0.662613	−	0.748962i	$-0.269448\pi$
$929$	−9.67157	−	16.7517i	−0.317314	−	0.549604i	−0.979927	+	0.199358i	$0.936114\pi$
$930$		0			0
$931$	−11.1777	+	43.4859i	−0.366333	+	1.42519i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.378680	+	0.655892i	−0.0123841	+	0.0214500i
$936$		0			0
$937$	16.6274			0.543194			0.271597	−	0.962411i	$-0.412448\pi$
$937$	16.6274			0.543194			0.271597	+	0.962411i	$0.412448\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−19.1274	+	33.1297i	−0.623536	+	1.08000i	0.365286	+	0.930895i	$0.380971\pi$
$941$	−19.1274	+	33.1297i	−0.623536	+	1.08000i	−0.988822	+	0.149101i	$0.952362\pi$
$942$		0			0
$943$	−17.8995	−	31.0028i	−0.582888	−	1.00959i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.10660	−	15.7731i	−0.295925	−	0.512557i	0.679275	−	0.733884i	$-0.262294\pi$
$947$	−9.10660	−	15.7731i	−0.295925	−	0.512557i	−0.975200	+	0.221327i	$0.928961\pi$
$948$		0			0
$949$	20.7279	−	35.9018i	0.672857	−	1.16542i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	27.1127			0.878266			0.439133	−	0.898422i	$-0.355286\pi$
$953$	27.1127			0.878266			0.439133	+	0.898422i	$0.355286\pi$
$954$		0			0
$955$	−8.13604	+	14.0920i	−0.263276	+	0.456007i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	18.0650	+	23.2956i	0.583348	+	0.752256i
$960$		0			0
$961$	−0.100505	−	0.174080i	−0.00324210	−	0.00561548i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−16.7157			−0.538098
$966$		0			0
$967$	−18.3431			−0.589876			−0.294938	−	0.955516i	$-0.595299\pi$
$967$	−18.3431			−0.589876			−0.294938	+	0.955516i	$0.595299\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−17.7929	−	30.8182i	−0.571001	−	0.989003i	−0.996463	−	0.0840268i	$-0.973222\pi$
$971$	−17.7929	−	30.8182i	−0.571001	−	0.989003i	0.425462	−	0.904976i	$-0.360111\pi$
$972$		0			0
$973$	−15.3137	+	37.5108i	−0.490935	+	1.20254i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−17.2574	+	29.8906i	−0.552112	+	0.956286i	0.446010	+	0.895028i	$0.352845\pi$
$977$	−17.2574	+	29.8906i	−0.552112	+	0.956286i	−0.998122	+	0.0612578i	$0.980489\pi$
$978$		0			0
$979$	21.7279			0.694427
$980$		0			0
$981$		0			0
$982$		0			0
$983$	13.4203	−	23.2447i	0.428041	−	0.741389i	−0.568658	−	0.822574i	$-0.692537\pi$
$983$	13.4203	−	23.2447i	0.428041	−	0.741389i	0.996699	+	0.0811848i	$0.0258704\pi$
$984$		0			0
$985$	−17.2132	−	29.8141i	−0.548458	−	0.949958i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−25.3137	−	43.8446i	−0.804929	−	1.39418i
$990$		0			0
$991$	22.3492	−	38.7100i	0.709947	−	1.22966i	−0.254929	−	0.966960i	$-0.582052\pi$
$991$	22.3492	−	38.7100i	0.709947	−	1.22966i	0.964876	−	0.262705i	$-0.0846145\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	20.5563			0.651680
$996$		0			0
$997$	22.6421	−	39.2173i	0.717084	−	1.24203i	−0.245067	−	0.969506i	$-0.578810\pi$
$997$	22.6421	−	39.2173i	0.717084	−	1.24203i	0.962150	−	0.272519i	$-0.0878568\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2016.2.s.q.865.1		4
3.2	odd	2		224.2.i.a.193.2	yes	4
4.3	odd	2		2016.2.s.s.865.1		4
7.2	even	3	inner	2016.2.s.q.289.1		4
12.11	even	2		224.2.i.d.193.1	yes	4
21.2	odd	6		224.2.i.a.65.2	✓	4
21.5	even	6		1568.2.i.x.961.1		4
21.11	odd	6		1568.2.a.w.1.1		2
21.17	even	6		1568.2.a.j.1.2		2
21.20	even	2		1568.2.i.x.1537.1		4
24.5	odd	2		448.2.i.j.193.1		4
24.11	even	2		448.2.i.g.193.2		4
28.23	odd	6		2016.2.s.s.289.1		4
84.11	even	6		1568.2.a.l.1.2		2
84.23	even	6		224.2.i.d.65.1	yes	4
84.47	odd	6		1568.2.i.o.961.2		4
84.59	odd	6		1568.2.a.u.1.1		2
84.83	odd	2		1568.2.i.o.1537.2		4
168.11	even	6		3136.2.a.bw.1.1		2
168.53	odd	6		3136.2.a.bd.1.2		2
168.59	odd	6		3136.2.a.be.1.2		2
168.101	even	6		3136.2.a.bx.1.1		2
168.107	even	6		448.2.i.g.65.2		4
168.149	odd	6		448.2.i.j.65.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.i.a.65.2	✓	4	21.2	odd	6
224.2.i.a.193.2	yes	4	3.2	odd	2
224.2.i.d.65.1	yes	4	84.23	even	6
224.2.i.d.193.1	yes	4	12.11	even	2
448.2.i.g.65.2		4	168.107	even	6
448.2.i.g.193.2		4	24.11	even	2
448.2.i.j.65.1		4	168.149	odd	6
448.2.i.j.193.1		4	24.5	odd	2
1568.2.a.j.1.2		2	21.17	even	6
1568.2.a.l.1.2		2	84.11	even	6
1568.2.a.u.1.1		2	84.59	odd	6
1568.2.a.w.1.1		2	21.11	odd	6
1568.2.i.o.961.2		4	84.47	odd	6
1568.2.i.o.1537.2		4	84.83	odd	2
1568.2.i.x.961.1		4	21.5	even	6
1568.2.i.x.1537.1		4	21.20	even	2
2016.2.s.q.289.1		4	7.2	even	3	inner
2016.2.s.q.865.1		4	1.1	even	1	trivial
2016.2.s.s.289.1		4	28.23	odd	6
2016.2.s.s.865.1		4	4.3	odd	2
3136.2.a.bd.1.2		2	168.53	odd	6
3136.2.a.be.1.2		2	168.59	odd	6
3136.2.a.bw.1.1		2	168.11	even	6
3136.2.a.bx.1.1		2	168.101	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.914214 - 1.58346i) q^{5} +(-1.00000 + 2.44949i) q^{7} +(-1.20711 + 2.09077i) q^{11} +2.82843 q^{13} +(-0.0857864 + 0.148586i) q^{17} +(-3.20711 - 5.55487i) q^{19} +(-2.62132 - 4.54026i) q^{23} +(0.828427 - 1.43488i) q^{25} +2.82843 q^{29} +(-2.79289 + 4.83743i) q^{31} +(4.79289 - 0.655892i) q^{35} +(-4.32843 - 7.49706i) q^{37} +6.82843 q^{41} +9.65685 q^{43} +(5.20711 + 9.01897i) q^{47} +(-5.00000 - 4.89898i) q^{49} +(-0.500000 + 0.866025i) q^{53} +4.41421 q^{55} +(5.44975 - 9.43924i) q^{59} +(-4.32843 - 7.49706i) q^{61} +(-2.58579 - 4.47871i) q^{65} +(1.37868 - 2.38794i) q^{67} -13.6569 q^{71} +(7.32843 - 12.6932i) q^{73} +(-3.91421 - 5.04757i) q^{77} +(-3.03553 - 5.25770i) q^{79} +7.31371 q^{83} +0.313708 q^{85} +(-4.50000 - 7.79423i) q^{89} +(-2.82843 + 6.92820i) q^{91} +(-5.86396 + 10.1567i) q^{95} -1.17157 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 4 q^{7} - 2 q^{11} - 6 q^{17} - 10 q^{19} - 2 q^{23} - 8 q^{25} - 14 q^{31} + 22 q^{35} - 6 q^{37} + 16 q^{41} + 16 q^{43} + 18 q^{47} - 20 q^{49} - 2 q^{53} + 12 q^{55} + 2 q^{59} - 6 q^{61}+ \cdots - 16 q^{97}+O(q^{100}) \) 4 * q + 2 * q^5 - 4 * q^7 - 2 * q^11 - 6 * q^17 - 10 * q^19 - 2 * q^23 - 8 * q^25 - 14 * q^31 + 22 * q^35 - 6 * q^37 + 16 * q^41 + 16 * q^43 + 18 * q^47 - 20 * q^49 - 2 * q^53 + 12 * q^55 + 2 * q^59 - 6 * q^61 - 16 * q^65 + 14 * q^67 - 32 * q^71 + 18 * q^73 - 10 * q^77 + 2 * q^79 - 16 * q^83 - 44 * q^85 - 18 * q^89 + 2 * q^95 - 16 * q^97

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