LMFDB - Embedded newform 1710.2.d.d.1369.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1369,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1710.1369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.d (of order $2$, degree $1$, 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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.5161984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 4x^{3} + 25x^{2} - 20x + 8 $ x^6 - 4x^3 + 25x^2 - 20*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1369.6
Root			$0.432320 - 0.432320i$ of defining polynomial
Character	$\chi$	$=$	1710.1369
Dual form			1710.2.d.d.1369.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(2.19388 - 0.432320i) q^{5} +0.761557i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.19388 - 0.432320i) q^{5} +0.761557i q^{7} -1.00000i q^{8} +(0.432320 + 2.19388i) q^{10} +0.864641 q^{11} +5.62620i q^{13} -0.761557 q^{14} +1.00000 q^{16} -3.62620i q^{17} -1.00000 q^{19} +(-2.19388 + 0.432320i) q^{20} +0.864641i q^{22} +8.01395i q^{23} +(4.62620 - 1.89692i) q^{25} -5.62620 q^{26} -0.761557i q^{28} -7.35548 q^{29} +8.11704 q^{31} +1.00000i q^{32} +3.62620 q^{34} +(0.329237 + 1.67076i) q^{35} -0.476886i q^{37} -1.00000i q^{38} +(-0.432320 - 2.19388i) q^{40} +2.65847 q^{41} +6.86464i q^{43} -0.864641 q^{44} -8.01395 q^{46} +1.25240i q^{47} +6.42003 q^{49} +(1.89692 + 4.62620i) q^{50} -5.62620i q^{52} -2.37380i q^{53} +(1.89692 - 0.373802i) q^{55} +0.761557 q^{56} -7.35548i q^{58} +4.49084 q^{59} -10.8646 q^{61} +8.11704i q^{62} -1.00000 q^{64} +(2.43232 + 12.3432i) q^{65} -1.03228i q^{67} +3.62620i q^{68} +(-1.67076 + 0.329237i) q^{70} +10.1816 q^{71} +16.4017i q^{73} +0.476886 q^{74} +1.00000 q^{76} +0.658473i q^{77} +12.5693 q^{79} +(2.19388 - 0.432320i) q^{80} +2.65847i q^{82} +0.270718i q^{83} +(-1.56768 - 7.95543i) q^{85} -6.86464 q^{86} -0.864641i q^{88} +0.387755 q^{89} -4.28467 q^{91} -8.01395i q^{92} -1.25240 q^{94} +(-2.19388 + 0.432320i) q^{95} +8.50479i q^{97} +6.42003i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 2 q^{5}+O(q^{10}) $ 6 * q - 6 * q^4 - 2 * q^5	$ 6 q - 6 q^{4} - 2 q^{5} + 8 q^{14} + 6 q^{16} - 6 q^{19} + 2 q^{20} + 10 q^{25} - 16 q^{26} - 16 q^{29} + 8 q^{31} + 4 q^{34} - 8 q^{35} - 4 q^{41} + 6 q^{49} + 4 q^{50} + 4 q^{55} - 8 q^{56} + 4 q^{59} - 60 q^{61} - 6 q^{64} + 12 q^{65} - 20 q^{70} + 16 q^{71} + 28 q^{74} + 6 q^{76} - 2 q^{80} - 12 q^{85} - 36 q^{86} - 28 q^{89} + 12 q^{91} + 28 q^{94} + 2 q^{95}+O(q^{100}) $ 6 * q - 6 * q^4 - 2 * q^5 + 8 * q^14 + 6 * q^16 - 6 * q^19 + 2 * q^20 + 10 * q^25 - 16 * q^26 - 16 * q^29 + 8 * q^31 + 4 * q^34 - 8 * q^35 - 4 * q^41 + 6 * q^49 + 4 * q^50 + 4 * q^55 - 8 * q^56 + 4 * q^59 - 60 * q^61 - 6 * q^64 + 12 * q^65 - 20 * q^70 + 16 * q^71 + 28 * q^74 + 6 * q^76 - 2 * q^80 - 12 * q^85 - 36 * q^86 - 28 * q^89 + 12 * q^91 + 28 * q^94 + 2 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	2.19388	−	0.432320i	0.981132	−	0.193340i
$5$	2.19388	−	0.432320i	0.981132	−	0.193340i
$6$		0			0
$7$			0.761557i			0.287842i	0.989589	+	0.143921i	$0.0459710\pi$
$7$			0.761557i			0.287842i	−0.989589	+	0.143921i	$0.954029\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.432320	+	2.19388i	0.136712	+	0.693765i
$11$	0.864641			0.260699			0.130350	−	0.991468i	$-0.458390\pi$
$11$	0.864641			0.260699			0.130350	+	0.991468i	$0.458390\pi$
$12$		0			0
$13$			5.62620i			1.56043i	0.625514	+	0.780213i	$0.284889\pi$
$13$			5.62620i			1.56043i	−0.625514	+	0.780213i	$0.715111\pi$
$14$	−0.761557			−0.203535
$15$		0			0
$16$	1.00000			0.250000
$17$		−	3.62620i		−	0.879482i	−0.898125	−	0.439741i	$-0.855070\pi$
$17$		−	3.62620i		−	0.879482i	0.898125	−	0.439741i	$-0.144930\pi$
$18$		0			0
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−2.19388	+	0.432320i	−0.490566	+	0.0966698i
$21$		0			0
$22$			0.864641i			0.184342i
$23$			8.01395i			1.67102i	0.549472	+	0.835512i	$0.314829\pi$
$23$			8.01395i			1.67102i	−0.549472	+	0.835512i	$0.685171\pi$
$24$		0			0
$25$	4.62620	−	1.89692i	0.925240	−	0.379383i
$26$	−5.62620			−1.10339
$27$		0			0
$28$		−	0.761557i		−	0.143921i
$29$	−7.35548			−1.36588			−0.682939	−	0.730475i	$-0.739299\pi$
$29$	−7.35548			−1.36588			−0.682939	+	0.730475i	$0.739299\pi$
$30$		0			0
$31$	8.11704			1.45786			0.728931	−	0.684587i	$-0.240017\pi$
$31$	8.11704			1.45786			0.728931	+	0.684587i	$0.240017\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	3.62620			0.621888
$35$	0.329237	+	1.67076i	0.0556512	+	0.282411i
$36$		0			0
$37$		−	0.476886i		−	0.0783995i	−0.999231	−	0.0391998i	$-0.987519\pi$
$37$		−	0.476886i		−	0.0783995i	0.999231	−	0.0391998i	$-0.0124809\pi$
$38$		−	1.00000i		−	0.162221i
$39$		0			0
$40$	−0.432320	−	2.19388i	−0.0683559	−	0.346883i
$41$	2.65847			0.415184			0.207592	−	0.978216i	$-0.433437\pi$
$41$	2.65847			0.415184			0.207592	+	0.978216i	$0.433437\pi$
$42$		0			0
$43$			6.86464i			1.04685i	0.852072	+	0.523424i	$0.175346\pi$
$43$			6.86464i			1.04685i	−0.852072	+	0.523424i	$0.824654\pi$
$44$	−0.864641			−0.130350
$45$		0			0
$46$	−8.01395			−1.18159
$47$			1.25240i			0.182681i	0.995820	+	0.0913404i	$0.0291151\pi$
$47$			1.25240i			0.182681i	−0.995820	+	0.0913404i	$0.970885\pi$
$48$		0			0
$49$	6.42003			0.917147
$50$	1.89692	+	4.62620i	0.268264	+	0.654243i
$51$		0			0
$52$		−	5.62620i		−	0.780213i
$53$		−	2.37380i		−	0.326067i	−0.986621	−	0.163033i	$-0.947872\pi$
$53$		−	2.37380i		−	0.326067i	0.986621	−	0.163033i	$-0.0521278\pi$
$54$		0			0
$55$	1.89692	−	0.373802i	0.255780	−	0.0504034i
$56$	0.761557			0.101767
$57$		0			0
$58$		−	7.35548i		−	0.965822i
$59$	4.49084			0.584657			0.292329	−	0.956318i	$-0.405570\pi$
$59$	4.49084			0.584657			0.292329	+	0.956318i	$0.405570\pi$
$60$		0			0
$61$	−10.8646			−1.39107			−0.695537	−	0.718490i	$-0.744834\pi$
$61$	−10.8646			−1.39107			−0.695537	+	0.718490i	$0.744834\pi$
$62$			8.11704i			1.03086i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.43232	+	12.3432i	0.301692	+	1.53098i
$66$		0			0
$67$		−	1.03228i		−	0.126113i	−0.998010	−	0.0630563i	$-0.979915\pi$
$67$		−	1.03228i		−	0.126113i	0.998010	−	0.0630563i	$-0.0200848\pi$
$68$			3.62620i			0.439741i
$69$		0			0
$70$	−1.67076	+	0.329237i	−0.199694	+	0.0393513i
$71$	10.1816			1.20833			0.604166	−	0.796858i	$-0.293506\pi$
$71$	10.1816			1.20833			0.604166	+	0.796858i	$0.293506\pi$
$72$		0			0
$73$			16.4017i			1.91967i	0.280557	+	0.959837i	$0.409481\pi$
$73$			16.4017i			1.91967i	−0.280557	+	0.959837i	$0.590519\pi$
$74$	0.476886			0.0554368
$75$		0			0
$76$	1.00000			0.114708
$77$			0.658473i			0.0750400i
$78$		0			0
$79$	12.5693			1.41416			0.707081	−	0.707133i	$-0.250012\pi$
$79$	12.5693			1.41416			0.707081	+	0.707133i	$0.250012\pi$
$80$	2.19388	−	0.432320i	0.245283	−	0.0483349i
$81$		0			0
$82$			2.65847i			0.293579i
$83$			0.270718i			0.0297152i	0.999890	+	0.0148576i	$0.00472949\pi$
$83$			0.270718i			0.0297152i	−0.999890	+	0.0148576i	$0.995271\pi$
$84$		0			0
$85$	−1.56768	−	7.95543i	−0.170039	−	0.862888i
$86$	−6.86464			−0.740233
$87$		0			0
$88$		−	0.864641i		−	0.0921710i
$89$	0.387755			0.0411020			0.0205510	−	0.999789i	$-0.493458\pi$
$89$	0.387755			0.0411020			0.0205510	+	0.999789i	$0.493458\pi$
$90$		0			0
$91$	−4.28467			−0.449156
$92$		−	8.01395i		−	0.835512i
$93$		0			0
$94$	−1.25240			−0.129175
$95$	−2.19388	+	0.432320i	−0.225087	+	0.0443551i
$96$		0			0
$97$			8.50479i			0.863531i	0.901986	+	0.431765i	$0.142109\pi$
$97$			8.50479i			0.863531i	−0.901986	+	0.431765i	$0.857891\pi$
$98$			6.42003i			0.648521i
$99$		0			0
$100$	−4.62620	+	1.89692i	−0.462620	+	0.189692i
$101$	−16.4157			−1.63342			−0.816710	−	0.577049i	$-0.804204\pi$
$101$	−16.4157			−1.63342			−0.816710	+	0.577049i	$0.804204\pi$
$102$		0			0
$103$		−	9.64015i		−	0.949872i	−0.880020	−	0.474936i	$-0.842471\pi$
$103$		−	9.64015i		−	0.949872i	0.880020	−	0.474936i	$-0.157529\pi$
$104$	5.62620			0.551694
$105$		0			0
$106$	2.37380			0.230564
$107$			4.28467i			0.414215i	0.978318	+	0.207107i	$0.0664050\pi$
$107$			4.28467i			0.414215i	−0.978318	+	0.207107i	$0.933595\pi$
$108$		0			0
$109$	13.4200			1.28541			0.642703	−	0.766116i	$-0.277813\pi$
$109$	13.4200			1.28541			0.642703	+	0.766116i	$0.277813\pi$
$110$	0.373802	+	1.89692i	0.0356406	+	0.180864i
$111$		0			0
$112$			0.761557i			0.0719604i
$113$			10.3232i			0.971125i	0.874202	+	0.485563i	$0.161385\pi$
$113$			10.3232i			0.971125i	−0.874202	+	0.485563i	$0.838615\pi$
$114$		0			0
$115$	3.46460	+	17.5816i	0.323075	+	1.63950i
$116$	7.35548			0.682939
$117$		0			0
$118$			4.49084i			0.413415i
$119$	2.76156			0.253152
$120$		0			0
$121$	−10.2524			−0.932036
$122$		−	10.8646i		−	0.983638i
$123$		0			0
$124$	−8.11704			−0.728931
$125$	9.32924	−	6.16160i	0.834432	−	0.551110i
$126$		0			0
$127$		−	16.9817i		−	1.50688i	−0.657517	−	0.753440i	$-0.728393\pi$
$127$		−	16.9817i		−	1.50688i	0.657517	−	0.753440i	$-0.271607\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−12.3432	+	2.43232i	−1.08257	+	0.213329i
$131$	−0.541436			−0.0473055			−0.0236528	−	0.999720i	$-0.507530\pi$
$131$	−0.541436			−0.0473055			−0.0236528	+	0.999720i	$0.507530\pi$
$132$		0			0
$133$		−	0.761557i		−	0.0660354i
$134$	1.03228			0.0891750
$135$		0			0
$136$	−3.62620			−0.310944
$137$			2.87859i			0.245935i	0.992411	+	0.122967i	$0.0392411\pi$
$137$			2.87859i			0.245935i	−0.992411	+	0.122967i	$0.960759\pi$
$138$		0			0
$139$	−3.58767			−0.304302			−0.152151	−	0.988357i	$-0.548620\pi$
$139$	−3.58767			−0.304302			−0.152151	+	0.988357i	$0.548620\pi$
$140$	−0.329237	−	1.67076i	−0.0278256	−	0.141205i
$141$		0			0
$142$			10.1816i			0.854420i
$143$			4.86464i			0.406802i
$144$		0			0
$145$	−16.1370	+	3.17992i	−1.34011	+	0.264078i
$146$	−16.4017			−1.35742
$147$		0			0
$148$			0.476886i			0.0391998i
$149$	−16.8401			−1.37959			−0.689796	−	0.724004i	$-0.742300\pi$
$149$	−16.8401			−1.37959			−0.689796	+	0.724004i	$0.742300\pi$
$150$		0			0
$151$	−16.9817			−1.38195			−0.690975	−	0.722879i	$-0.742818\pi$
$151$	−16.9817			−1.38195			−0.690975	+	0.722879i	$0.742818\pi$
$152$			1.00000i			0.0811107i
$153$		0			0
$154$	−0.658473			−0.0530613
$155$	17.8078	−	3.50916i	1.43036	−	0.281863i
$156$		0			0
$157$		−	14.8401i		−	1.18437i	−0.805804	−	0.592183i	$-0.798266\pi$
$157$		−	14.8401i		−	1.18437i	0.805804	−	0.592183i	$-0.201734\pi$
$158$			12.5693i			0.999963i
$159$		0			0
$160$	0.432320	+	2.19388i	0.0341779	+	0.173441i
$161$	−6.10308			−0.480990
$162$		0			0
$163$			13.3694i			1.04717i	0.851972	+	0.523587i	$0.175407\pi$
$163$			13.3694i			1.04717i	−0.851972	+	0.523587i	$0.824593\pi$
$164$	−2.65847			−0.207592
$165$		0			0
$166$	−0.270718			−0.0210118
$167$			9.84632i			0.761931i	0.924589	+	0.380966i	$0.124408\pi$
$167$			9.84632i			0.761931i	−0.924589	+	0.380966i	$0.875592\pi$
$168$		0			0
$169$	−18.6541			−1.43493
$170$	7.95543	−	1.56768i	0.610154	−	0.120236i
$171$		0			0
$172$		−	6.86464i		−	0.523424i
$173$		−	2.98168i		−	0.226693i	−0.993556	−	0.113346i	$-0.963843\pi$
$173$		−	2.98168i		−	0.226693i	0.993556	−	0.113346i	$-0.0361570\pi$
$174$		0			0
$175$	1.44461	+	3.52311i	0.109202	+	0.266322i
$176$	0.864641			0.0651748
$177$		0			0
$178$			0.387755i			0.0290635i
$179$	11.7938			0.881512			0.440756	−	0.897627i	$-0.354710\pi$
$179$	11.7938			0.881512			0.440756	+	0.897627i	$0.354710\pi$
$180$		0			0
$181$	14.5693			1.08293			0.541465	−	0.840723i	$-0.317870\pi$
$181$	14.5693			1.08293			0.541465	+	0.840723i	$0.317870\pi$
$182$		−	4.28467i		−	0.317601i
$183$		0			0
$184$	8.01395			0.590796
$185$	−0.206167	−	1.04623i	−0.0151577	−	0.0769203i
$186$		0			0
$187$		−	3.13536i		−	0.229280i
$188$		−	1.25240i		−	0.0913404i
$189$		0			0
$190$	−0.432320	−	2.19388i	−0.0313638	−	0.159161i
$191$	−13.2384			−0.957900			−0.478950	−	0.877842i	$-0.658983\pi$
$191$	−13.2384			−0.957900			−0.478950	+	0.877842i	$0.658983\pi$
$192$		0			0
$193$			2.54144i			0.182937i	0.995808	+	0.0914683i	$0.0291560\pi$
$193$			2.54144i			0.182937i	−0.995808	+	0.0914683i	$0.970844\pi$
$194$	−8.50479			−0.610609
$195$		0			0
$196$	−6.42003			−0.458574
$197$		−	19.9109i		−	1.41859i	−0.704911	−	0.709295i	$-0.749013\pi$
$197$		−	19.9109i		−	1.41859i	0.704911	−	0.709295i	$-0.250987\pi$
$198$		0			0
$199$	20.3126			1.43992			0.719960	−	0.694015i	$-0.244160\pi$
$199$	20.3126			1.43992			0.719960	+	0.694015i	$0.244160\pi$
$200$	−1.89692	−	4.62620i	−0.134132	−	0.327122i
$201$		0			0
$202$		−	16.4157i		−	1.15500i
$203$		−	5.60162i		−	0.393157i
$204$		0			0
$205$	5.83237	−	1.14931i	0.407350	−	0.0802715i
$206$	9.64015			0.671661
$207$		0			0
$208$			5.62620i			0.390107i
$209$	−0.864641			−0.0598085
$210$		0			0
$211$	18.0419			1.24205			0.621026	−	0.783790i	$-0.286716\pi$
$211$	18.0419			1.24205			0.621026	+	0.783790i	$0.286716\pi$
$212$			2.37380i			0.163033i
$213$		0			0
$214$	−4.28467			−0.292894
$215$	2.96772	+	15.0602i	0.202397	+	1.02710i
$216$		0			0
$217$			6.18159i			0.419634i
$218$			13.4200i			0.908919i
$219$		0			0
$220$	−1.89692	+	0.373802i	−0.127890	+	0.0252017i
$221$	20.4017			1.37237
$222$		0			0
$223$		−	13.5231i		−	0.905575i	−0.891619	−	0.452787i	$-0.850430\pi$
$223$		−	13.5231i		−	0.905575i	0.891619	−	0.452787i	$-0.149570\pi$
$224$	−0.761557			−0.0508837
$225$		0			0
$226$	−10.3232			−0.686689
$227$			13.6016i			0.902771i	0.892329	+	0.451386i	$0.149070\pi$
$227$			13.6016i			0.902771i	−0.892329	+	0.451386i	$0.850930\pi$
$228$		0			0
$229$	−13.5877			−0.897898			−0.448949	−	0.893557i	$-0.648202\pi$
$229$	−13.5877			−0.897898			−0.448949	+	0.893557i	$0.648202\pi$
$230$	−17.5816	+	3.46460i	−1.15930	+	0.228449i
$231$		0			0
$232$			7.35548i			0.482911i
$233$		−	25.5510i		−	1.67390i	−0.547277	−	0.836952i	$-0.684336\pi$
$233$		−	25.5510i		−	1.67390i	0.547277	−	0.836952i	$-0.315664\pi$
$234$		0			0
$235$	0.541436	+	2.74760i	0.0353194	+	0.179234i
$236$	−4.49084			−0.292329
$237$		0			0
$238$			2.76156i			0.179005i
$239$	−11.3309			−0.732935			−0.366468	−	0.930431i	$-0.619433\pi$
$239$	−11.3309			−0.732935			−0.366468	+	0.930431i	$0.619433\pi$
$240$		0			0
$241$	−1.25240			−0.0806739			−0.0403370	−	0.999186i	$-0.512843\pi$
$241$	−1.25240			−0.0806739			−0.0403370	+	0.999186i	$0.512843\pi$
$242$		−	10.2524i		−	0.659049i
$243$		0			0
$244$	10.8646			0.695537
$245$	14.0848	−	2.77551i	0.899842	−	0.177321i
$246$		0			0
$247$		−	5.62620i		−	0.357986i
$248$		−	8.11704i		−	0.515432i
$249$		0			0
$250$	6.16160	+	9.32924i	0.389694	+	0.590033i
$251$	−10.5939			−0.668682			−0.334341	−	0.942452i	$-0.608514\pi$
$251$	−10.5939			−0.668682			−0.334341	+	0.942452i	$0.608514\pi$
$252$		0			0
$253$			6.92919i			0.435635i
$254$	16.9817			1.06553
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	0.153681i		−	0.00958637i	−0.999989	−	0.00479319i	$-0.998474\pi$
$257$		−	0.153681i		−	0.00958637i	0.999989	−	0.00479319i	$-0.00152572\pi$
$258$		0			0
$259$	0.363176			0.0225666
$260$	−2.43232	−	12.3432i	−0.150846	−	0.765492i
$261$		0			0
$262$		−	0.541436i		−	0.0334501i
$263$		−	0.504792i		−	0.0311268i	−0.999879	−	0.0155634i	$-0.995046\pi$
$263$		−	0.504792i		−	0.0311268i	0.999879	−	0.0155634i	$-0.00495419\pi$
$264$		0			0
$265$	−1.02624	−	5.20783i	−0.0630416	−	0.319915i
$266$	0.761557			0.0466941
$267$		0			0
$268$			1.03228i			0.0630563i
$269$	−3.49521			−0.213107			−0.106553	−	0.994307i	$-0.533981\pi$
$269$	−3.49521			−0.213107			−0.106553	+	0.994307i	$0.533981\pi$
$270$		0			0
$271$	5.47252			0.332432			0.166216	−	0.986089i	$-0.446845\pi$
$271$	5.47252			0.332432			0.166216	+	0.986089i	$0.446845\pi$
$272$		−	3.62620i		−	0.219871i
$273$		0			0
$274$	−2.87859			−0.173902
$275$	4.00000	−	1.64015i	0.241209	−	0.0989049i
$276$		0			0
$277$		−	12.9538i		−	0.778317i	−0.921171	−	0.389158i	$-0.872766\pi$
$277$		−	12.9538i		−	0.778317i	0.921171	−	0.389158i	$-0.127234\pi$
$278$		−	3.58767i		−	0.215174i
$279$		0			0
$280$	1.67076	−	0.329237i	0.0998472	−	0.0196757i
$281$	−0.153681			−0.00916785			−0.00458393	−	0.999989i	$-0.501459\pi$
$281$	−0.153681			−0.00916785			−0.00458393	+	0.999989i	$0.501459\pi$
$282$		0			0
$283$		−	18.2341i		−	1.08390i	−0.840410	−	0.541952i	$-0.817686\pi$
$283$		−	18.2341i		−	1.08390i	0.840410	−	0.541952i	$-0.182314\pi$
$284$	−10.1816			−0.604166
$285$		0			0
$286$	−4.86464			−0.287652
$287$			2.02458i			0.119507i
$288$		0			0
$289$	3.85069			0.226511
$290$	−3.17992	−	16.1370i	−0.186732	−	0.947599i
$291$		0			0
$292$		−	16.4017i		−	0.959837i
$293$		−	2.03853i		−	0.119092i	−0.998226	−	0.0595462i	$-0.981035\pi$
$293$		−	2.03853i		−	0.119092i	0.998226	−	0.0595462i	$-0.0189654\pi$
$294$		0			0
$295$	9.85235	−	1.94148i	0.573626	−	0.113037i
$296$	−0.476886			−0.0277184
$297$		0			0
$298$		−	16.8401i		−	0.975519i
$299$	−45.0881			−2.60751
$300$		0			0
$301$	−5.22782			−0.301326
$302$		−	16.9817i		−	0.977186i
$303$		0			0
$304$	−1.00000			−0.0573539
$305$	−23.8357	+	4.69701i	−1.36483	+	0.268950i
$306$		0			0
$307$		−	16.5414i		−	0.944070i	−0.881580	−	0.472035i	$-0.843520\pi$
$307$		−	16.5414i		−	0.944070i	0.881580	−	0.472035i	$-0.156480\pi$
$308$		−	0.658473i		−	0.0375200i
$309$		0			0
$310$	3.50916	+	17.8078i	0.199307	+	1.01141i
$311$	21.4725			1.21759			0.608797	−	0.793326i	$-0.291652\pi$
$311$	21.4725			1.21759			0.608797	+	0.793326i	$0.291652\pi$
$312$		0			0
$313$		−	1.12141i		−	0.0633856i	−0.999498	−	0.0316928i	$-0.989910\pi$
$313$		−	1.12141i		−	0.0633856i	0.999498	−	0.0316928i	$-0.0100898\pi$
$314$	14.8401			0.837473
$315$		0			0
$316$	−12.5693			−0.707081
$317$		−	29.8882i		−	1.67869i	−0.543601	−	0.839344i	$-0.682940\pi$
$317$		−	29.8882i		−	1.67869i	0.543601	−	0.839344i	$-0.317060\pi$
$318$		0			0
$319$	−6.35985			−0.356083
$320$	−2.19388	+	0.432320i	−0.122641	+	0.0241674i
$321$		0			0
$322$		−	6.10308i		−	0.340112i
$323$			3.62620i			0.201767i
$324$		0			0
$325$	10.6724	+	26.0279i	0.592000	+	1.44377i
$326$	−13.3694			−0.740464
$327$		0			0
$328$		−	2.65847i		−	0.146790i
$329$	−0.953771			−0.0525831
$330$		0			0
$331$	32.3126			1.77606			0.888030	−	0.459786i	$-0.152074\pi$
$331$	32.3126			1.77606			0.888030	+	0.459786i	$0.152074\pi$
$332$		−	0.270718i		−	0.0148576i
$333$		0			0
$334$	−9.84632			−0.538767
$335$	−0.446274	−	2.26469i	−0.0243825	−	0.123733i
$336$		0			0
$337$		−	26.3511i		−	1.43544i	−0.696334	−	0.717718i	$-0.745187\pi$
$337$		−	26.3511i		−	1.43544i	0.696334	−	0.717718i	$-0.254813\pi$
$338$		−	18.6541i		−	1.01465i
$339$		0			0
$340$	1.56768	+	7.95543i	0.0850194	+	0.431444i
$341$	7.01832			0.380063
$342$		0			0
$343$			10.2201i			0.551835i
$344$	6.86464			0.370117
$345$		0			0
$346$	2.98168			0.160296
$347$		−	2.77551i		−	0.148997i	−0.997221	−	0.0744986i	$-0.976264\pi$
$347$		−	2.77551i		−	0.148997i	0.997221	−	0.0744986i	$-0.0237356\pi$
$348$		0			0
$349$	−11.5510			−0.618312			−0.309156	−	0.951011i	$-0.600047\pi$
$349$	−11.5510			−0.618312			−0.309156	+	0.951011i	$0.600047\pi$
$350$	−3.52311	+	1.44461i	−0.188318	+	0.0772177i
$351$		0			0
$352$			0.864641i			0.0460855i
$353$			8.40171i			0.447178i	0.974684	+	0.223589i	$0.0717773\pi$
$353$			8.40171i			0.447178i	−0.974684	+	0.223589i	$0.928223\pi$
$354$		0			0
$355$	22.3372	−	4.40171i	1.18553	−	0.233618i
$356$	−0.387755			−0.0205510
$357$		0			0
$358$			11.7938i			0.623323i
$359$	22.7895			1.20278			0.601391	−	0.798955i	$-0.294613\pi$
$359$	22.7895			1.20278			0.601391	+	0.798955i	$0.294613\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$			14.5693i			0.765748i
$363$		0			0
$364$	4.28467			0.224578
$365$	7.09079	+	35.9833i	0.371149	+	1.88345i
$366$		0			0
$367$		−	4.06455i		−	0.212168i	−0.994357	−	0.106084i	$-0.966169\pi$
$367$		−	4.06455i		−	0.212168i	0.994357	−	0.106084i	$-0.0338312\pi$
$368$			8.01395i			0.417756i
$369$		0			0
$370$	1.04623	−	0.206167i	0.0543908	−	0.0107181i
$371$	1.80779			0.0938556
$372$		0			0
$373$		−	18.4017i		−	0.952804i	−0.879227	−	0.476402i	$-0.841941\pi$
$373$		−	18.4017i		−	0.952804i	0.879227	−	0.476402i	$-0.158059\pi$
$374$	3.13536			0.162126
$375$		0			0
$376$	1.25240			0.0645874
$377$		−	41.3834i		−	2.13135i
$378$		0			0
$379$	−1.23844			−0.0636145			−0.0318073	−	0.999494i	$-0.510126\pi$
$379$	−1.23844			−0.0636145			−0.0318073	+	0.999494i	$0.510126\pi$
$380$	2.19388	−	0.432320i	0.112544	−	0.0221776i
$381$		0			0
$382$		−	13.2384i		−	0.677338i
$383$		−	16.8646i		−	0.861743i	−0.902413	−	0.430871i	$-0.858206\pi$
$383$		−	16.8646i		−	0.861743i	0.902413	−	0.430871i	$-0.141794\pi$
$384$		0			0
$385$	0.284672	+	1.44461i	0.0145082	+	0.0736242i
$386$	−2.54144			−0.129356
$387$		0			0
$388$		−	8.50479i		−	0.431765i
$389$	8.59392			0.435729			0.217865	−	0.975979i	$-0.430091\pi$
$389$	8.59392			0.435729			0.217865	+	0.975979i	$0.430091\pi$
$390$		0			0
$391$	29.0602			1.46964
$392$		−	6.42003i		−	0.324261i
$393$		0			0
$394$	19.9109			1.00310
$395$	27.5756	−	5.43398i	1.38748	−	0.273413i
$396$		0			0
$397$		−	16.0558i		−	0.805818i	−0.915240	−	0.402909i	$-0.867999\pi$
$397$		−	16.0558i		−	0.805818i	0.915240	−	0.402909i	$-0.132001\pi$
$398$			20.3126i			1.01818i
$399$		0			0
$400$	4.62620	−	1.89692i	0.231310	−	0.0948458i
$401$	14.8925			0.743698			0.371849	−	0.928293i	$-0.378724\pi$
$401$	14.8925			0.743698			0.371849	+	0.928293i	$0.378724\pi$
$402$		0			0
$403$			45.6681i			2.27489i
$404$	16.4157			0.816710
$405$		0			0
$406$	5.60162			0.278004
$407$		−	0.412335i		−	0.0204387i
$408$		0			0
$409$	18.3511			0.907404			0.453702	−	0.891153i	$-0.350103\pi$
$409$	18.3511			0.907404			0.453702	+	0.891153i	$0.350103\pi$
$410$	1.14931	+	5.83237i	0.0567605	+	0.288040i
$411$		0			0
$412$			9.64015i			0.474936i
$413$			3.42003i			0.168289i
$414$		0			0
$415$	0.117037	+	0.593923i	0.00574512	+	0.0291545i
$416$	−5.62620			−0.275847
$417$		0			0
$418$		−	0.864641i		−	0.0422910i
$419$	34.7509			1.69769			0.848847	−	0.528639i	$-0.177297\pi$
$419$	34.7509			1.69769			0.848847	+	0.528639i	$0.177297\pi$
$420$		0			0
$421$	−40.1589			−1.95722			−0.978612	−	0.205713i	$-0.934049\pi$
$421$	−40.1589			−1.95722			−0.978612	+	0.205713i	$0.934049\pi$
$422$			18.0419i			0.878264i
$423$		0			0
$424$	−2.37380			−0.115282
$425$	−6.87859	−	16.7755i	−0.333661	−	0.813732i
$426$		0			0
$427$		−	8.27405i		−	0.400409i
$428$		−	4.28467i		−	0.207107i
$429$		0			0
$430$	−15.0602	+	2.96772i	−0.726266	+	0.143116i
$431$	−34.9571			−1.68382			−0.841912	−	0.539615i	$-0.818570\pi$
$431$	−34.9571			−1.68382			−0.841912	+	0.539615i	$0.818570\pi$
$432$		0			0
$433$			1.13536i			0.0545619i	0.999628	+	0.0272809i	$0.00868487\pi$
$433$			1.13536i			0.0545619i	−0.999628	+	0.0272809i	$0.991315\pi$
$434$	−6.18159			−0.296726
$435$		0			0
$436$	−13.4200			−0.642703
$437$		−	8.01395i		−	0.383359i
$438$		0			0
$439$	6.80009			0.324551			0.162275	−	0.986746i	$-0.448117\pi$
$439$	6.80009			0.324551			0.162275	+	0.986746i	$0.448117\pi$
$440$	−0.373802	−	1.89692i	−0.0178203	−	0.0904319i
$441$		0			0
$442$			20.4017i			0.970410i
$443$		−	38.0679i		−	1.80866i	−0.426835	−	0.904330i	$-0.640371\pi$
$443$		−	38.0679i		−	1.80866i	0.426835	−	0.904330i	$-0.359629\pi$
$444$		0			0
$445$	0.850688	−	0.167635i	0.0403265	−	0.00794664i
$446$	13.5231			0.640338
$447$		0			0
$448$		−	0.761557i		−	0.0359802i
$449$	−18.5414			−0.875024			−0.437512	−	0.899212i	$-0.644140\pi$
$449$	−18.5414			−0.875024			−0.437512	+	0.899212i	$0.644140\pi$
$450$		0			0
$451$	2.29862			0.108238
$452$		−	10.3232i		−	0.485563i
$453$		0			0
$454$	−13.6016			−0.638356
$455$	−9.40005	+	1.85235i	−0.440681	+	0.0868396i
$456$		0			0
$457$		−	16.3738i		−	0.765934i	−0.923762	−	0.382967i	$-0.874902\pi$
$457$		−	16.3738i		−	0.765934i	0.923762	−	0.382967i	$-0.125098\pi$
$458$		−	13.5877i		−	0.634910i
$459$		0			0
$460$	−3.46460	−	17.5816i	−0.161538	−	0.819748i
$461$	−1.70470			−0.0793959			−0.0396979	−	0.999212i	$-0.512640\pi$
$461$	−1.70470			−0.0793959			−0.0396979	+	0.999212i	$0.512640\pi$
$462$		0			0
$463$		−	10.0279i		−	0.466036i	−0.972472	−	0.233018i	$-0.925140\pi$
$463$		−	10.0279i		−	0.466036i	0.972472	−	0.233018i	$-0.0748602\pi$
$464$	−7.35548			−0.341470
$465$		0			0
$466$	25.5510			1.18363
$467$			32.7509i			1.51553i	0.652526	+	0.757766i	$0.273709\pi$
$467$			32.7509i			1.51553i	−0.652526	+	0.757766i	$0.726291\pi$
$468$		0			0
$469$	0.786137			0.0363004
$470$	−2.74760	+	0.541436i	−0.126738	+	0.0249746i
$471$		0			0
$472$		−	4.49084i		−	0.206708i
$473$			5.93545i			0.272912i
$474$		0			0
$475$	−4.62620	+	1.89692i	−0.212265	+	0.0870365i
$476$	−2.76156			−0.126576
$477$		0			0
$478$		−	11.3309i		−	0.518263i
$479$	27.2803			1.24647			0.623234	−	0.782035i	$-0.285818\pi$
$479$	27.2803			1.24647			0.623234	+	0.782035i	$0.285818\pi$
$480$		0			0
$481$	2.68305			0.122337
$482$		−	1.25240i		−	0.0570451i
$483$		0			0
$484$	10.2524			0.466018
$485$	3.67680	+	18.6585i	0.166955	+	0.847238i
$486$		0			0
$487$			11.0741i			0.501817i	0.968011	+	0.250908i	$0.0807293\pi$
$487$			11.0741i			0.501817i	−0.968011	+	0.250908i	$0.919271\pi$
$488$			10.8646i			0.491819i
$489$		0			0
$490$	2.77551	+	14.0848i	0.125385	+	0.636285i
$491$	−8.11704			−0.366317			−0.183158	−	0.983083i	$-0.558632\pi$
$491$	−8.11704			−0.366317			−0.183158	+	0.983083i	$0.558632\pi$
$492$		0			0
$493$			26.6724i			1.20127i
$494$	5.62620			0.253135
$495$		0			0
$496$	8.11704			0.364466
$497$			7.75386i			0.347808i
$498$		0			0
$499$	−0.295298			−0.0132193			−0.00660967	−	0.999978i	$-0.502104\pi$
$499$	−0.295298			−0.0132193			−0.00660967	+	0.999978i	$0.502104\pi$
$500$	−9.32924	+	6.16160i	−0.417216	+	0.275555i
$501$		0			0
$502$		−	10.5939i		−	0.472830i
$503$		−	19.6016i		−	0.873993i	−0.899463	−	0.436996i	$-0.856042\pi$
$503$		−	19.6016i		−	0.873993i	0.899463	−	0.436996i	$-0.143958\pi$
$504$		0			0
$505$	−36.0140	+	7.09683i	−1.60260	+	0.315805i
$506$	−6.92919			−0.308040
$507$		0			0
$508$			16.9817i			0.753440i
$509$	−1.79383			−0.0795102			−0.0397551	−	0.999209i	$-0.512658\pi$
$509$	−1.79383			−0.0795102			−0.0397551	+	0.999209i	$0.512658\pi$
$510$		0			0
$511$	−12.4908			−0.552562
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	0.153681			0.00677859
$515$	−4.16763	−	21.1493i	−0.183648	−	0.931950i
$516$		0			0
$517$			1.08287i			0.0476247i
$518$			0.363176i			0.0159570i
$519$		0			0
$520$	12.3432	−	2.43232i	0.541285	−	0.106664i
$521$	2.61850			0.114719			0.0573593	−	0.998354i	$-0.481732\pi$
$521$	2.61850			0.114719			0.0573593	+	0.998354i	$0.481732\pi$
$522$		0			0
$523$			14.9956i			0.655713i	0.944728	+	0.327857i	$0.106326\pi$
$523$			14.9956i			0.655713i	−0.944728	+	0.327857i	$0.893674\pi$
$524$	0.541436			0.0236528
$525$		0			0
$526$	0.504792			0.0220100
$527$		−	29.4340i		−	1.28216i
$528$		0			0
$529$	−41.2234			−1.79232
$530$	5.20783	−	1.02624i	0.226214	−	0.0445772i
$531$		0			0
$532$			0.761557i			0.0330177i
$533$			14.9571i			0.647864i
$534$		0			0
$535$	1.85235	+	9.40005i	0.0800841	+	0.406399i
$536$	−1.03228			−0.0445875
$537$		0			0
$538$		−	3.49521i		−	0.150689i
$539$	5.55102			0.239099
$540$		0			0
$541$	3.40608			0.146439			0.0732194	−	0.997316i	$-0.476673\pi$
$541$	3.40608			0.146439			0.0732194	+	0.997316i	$0.476673\pi$
$542$			5.47252i			0.235065i
$543$		0			0
$544$	3.62620			0.155472
$545$	29.4419	−	5.80175i	1.26115	−	0.248520i
$546$		0			0
$547$		−	4.74760i		−	0.202993i	−0.994836	−	0.101496i	$-0.967637\pi$
$547$		−	4.74760i		−	0.202993i	0.994836	−	0.101496i	$-0.0323630\pi$
$548$		−	2.87859i		−	0.122967i
$549$		0			0
$550$	1.64015	+	4.00000i	0.0699363	+	0.170561i
$551$	7.35548			0.313354
$552$		0			0
$553$			9.57227i			0.407054i
$554$	12.9538			0.550353
$555$		0			0
$556$	3.58767			0.152151
$557$			43.0462i			1.82393i	0.410271	+	0.911964i	$0.365434\pi$
$557$			43.0462i			1.82393i	−0.410271	+	0.911964i	$0.634566\pi$
$558$		0			0
$559$	−38.6218			−1.63353
$560$	0.329237	+	1.67076i	0.0139128	+	0.0706026i
$561$		0			0
$562$		−	0.153681i		−	0.00648265i
$563$		−	17.0096i		−	0.716869i	−0.933555	−	0.358434i	$-0.883311\pi$
$563$		−	17.0096i		−	0.716869i	0.933555	−	0.358434i	$-0.116689\pi$
$564$		0			0
$565$	4.46293	+	22.6478i	0.187757	+	0.952802i
$566$	18.2341			0.766435
$567$		0			0
$568$		−	10.1816i		−	0.427210i
$569$	−19.7572			−0.828264			−0.414132	−	0.910217i	$-0.635915\pi$
$569$	−19.7572			−0.828264			−0.414132	+	0.910217i	$0.635915\pi$
$570$		0			0
$571$	−11.3973			−0.476964			−0.238482	−	0.971147i	$-0.576650\pi$
$571$	−11.3973			−0.476964			−0.238482	+	0.971147i	$0.576650\pi$
$572$		−	4.86464i		−	0.203401i
$573$		0			0
$574$	−2.02458			−0.0845043
$575$	15.2018	+	37.0741i	0.633959	+	1.54610i
$576$		0			0
$577$			18.3372i			0.763386i	0.924289	+	0.381693i	$0.124659\pi$
$577$			18.3372i			0.763386i	−0.924289	+	0.381693i	$0.875341\pi$
$578$			3.85069i			0.160167i
$579$		0			0
$580$	16.1370	−	3.17992i	0.670053	−	0.132039i
$581$	−0.206167			−0.00855327
$582$		0			0
$583$		−	2.05249i		−	0.0850053i
$584$	16.4017			0.678708
$585$		0			0
$586$	2.03853			0.0842110
$587$		−	11.9475i		−	0.493127i	−0.969127	−	0.246563i	$-0.920699\pi$
$587$		−	11.9475i		−	0.493127i	0.969127	−	0.246563i	$-0.0793013\pi$
$588$		0			0
$589$	−8.11704			−0.334457
$590$	1.94148	+	9.85235i	0.0799295	+	0.405615i
$591$		0			0
$592$		−	0.476886i		−	0.0195999i
$593$			24.3911i			1.00162i	0.865557	+	0.500811i	$0.166965\pi$
$593$			24.3911i			1.00162i	−0.865557	+	0.500811i	$0.833035\pi$
$594$		0			0
$595$	6.05852	−	1.19388i	0.248375	−	0.0489442i
$596$	16.8401			0.689796
$597$		0			0
$598$		−	45.0881i		−	1.84379i
$599$	−21.0708			−0.860930			−0.430465	−	0.902607i	$-0.641650\pi$
$599$	−21.0708			−0.860930			−0.430465	+	0.902607i	$0.641650\pi$
$600$		0			0
$601$	32.3878			1.32112			0.660562	−	0.750771i	$-0.270318\pi$
$601$	32.3878			1.32112			0.660562	+	0.750771i	$0.270318\pi$
$602$		−	5.22782i		−	0.213070i
$603$		0			0
$604$	16.9817			0.690975
$605$	−22.4925	+	4.43232i	−0.914450	+	0.180199i
$606$		0			0
$607$		−	19.0183i		−	0.771930i	−0.922513	−	0.385965i	$-0.873869\pi$
$607$		−	19.0183i		−	0.771930i	0.922513	−	0.385965i	$-0.126131\pi$
$608$		−	1.00000i		−	0.0405554i
$609$		0			0
$610$	−4.69701	−	23.8357i	−0.190176	−	0.965079i
$611$	−7.04623			−0.285060
$612$		0			0
$613$		−	23.5756i		−	0.952210i	−0.879389	−	0.476105i	$-0.842048\pi$
$613$		−	23.5756i		−	0.952210i	0.879389	−	0.476105i	$-0.157952\pi$
$614$	16.5414			0.667558
$615$		0			0
$616$	0.658473			0.0265307
$617$		−	26.2707i		−	1.05762i	−0.848740	−	0.528810i	$-0.822639\pi$
$617$		−	26.2707i		−	1.05762i	0.848740	−	0.528810i	$-0.177361\pi$
$618$		0			0
$619$	−11.4985			−0.462165			−0.231083	−	0.972934i	$-0.574227\pi$
$619$	−11.4985			−0.462165			−0.231083	+	0.972934i	$0.574227\pi$
$620$	−17.8078	+	3.50916i	−0.715178	+	0.140931i
$621$		0			0
$622$			21.4725i			0.860969i
$623$			0.295298i			0.0118309i
$624$		0			0
$625$	17.8034	−	17.5510i	0.712137	−	0.702041i
$626$	1.12141			0.0448204
$627$		0			0
$628$			14.8401i			0.592183i
$629$	−1.72928			−0.0689510
$630$		0			0
$631$	−45.8130			−1.82379			−0.911893	−	0.410427i	$-0.865380\pi$
$631$	−45.8130			−1.82379			−0.911893	+	0.410427i	$0.865380\pi$
$632$		−	12.5693i		−	0.499982i
$633$		0			0
$634$	29.8882			1.18701
$635$	−7.34153	−	37.2557i	−0.291340	−	1.47845i
$636$		0			0
$637$			36.1204i			1.43114i
$638$		−	6.35985i		−	0.251789i
$639$		0			0
$640$	−0.432320	−	2.19388i	−0.0170890	−	0.0867206i
$641$	−1.36943			−0.0540894			−0.0270447	−	0.999634i	$-0.508610\pi$
$641$	−1.36943			−0.0540894			−0.0270447	+	0.999634i	$0.508610\pi$
$642$		0			0
$643$		−	24.7389i		−	0.975606i	−0.872954	−	0.487803i	$-0.837799\pi$
$643$		−	24.7389i		−	0.975606i	0.872954	−	0.487803i	$-0.162201\pi$
$644$	6.10308			0.240495
$645$		0			0
$646$	−3.62620			−0.142671
$647$		−	6.82611i		−	0.268362i	−0.990957	−	0.134181i	$-0.957160\pi$
$647$		−	6.82611i		−	0.268362i	0.990957	−	0.134181i	$-0.0428404\pi$
$648$		0			0
$649$	3.88296			0.152420
$650$	−26.0279	+	10.6724i	−1.02090	+	0.418607i
$651$		0			0
$652$		−	13.3694i		−	0.523587i
$653$		−	6.91713i		−	0.270688i	−0.990799	−	0.135344i	$-0.956786\pi$
$653$		−	6.91713i		−	0.270688i	0.990799	−	0.135344i	$-0.0432140\pi$
$654$		0			0
$655$	−1.18785	+	0.234074i	−0.0464130	+	0.00914603i
$656$	2.65847			0.103796
$657$		0			0
$658$		−	0.953771i		−	0.0371819i
$659$	9.44461			0.367910			0.183955	−	0.982935i	$-0.441110\pi$
$659$	9.44461			0.367910			0.183955	+	0.982935i	$0.441110\pi$
$660$		0			0
$661$	−22.1955			−0.863306			−0.431653	−	0.902040i	$-0.642070\pi$
$661$	−22.1955			−0.863306			−0.431653	+	0.902040i	$0.642070\pi$
$662$			32.3126i			1.25586i
$663$		0			0
$664$	0.270718			0.0105059
$665$	−0.329237	−	1.67076i	−0.0127673	−	0.0647894i
$666$		0			0
$667$		−	58.9465i		−	2.28242i
$668$		−	9.84632i		−	0.380966i
$669$		0			0
$670$	2.26469	−	0.446274i	0.0874925	−	0.0172411i
$671$	−9.39401			−0.362652
$672$		0			0
$673$			12.2986i			0.474077i	0.971500	+	0.237039i	$0.0761768\pi$
$673$			12.2986i			0.474077i	−0.971500	+	0.237039i	$0.923823\pi$
$674$	26.3511			1.01501
$675$		0			0
$676$	18.6541			0.717466
$677$		−	35.9527i		−	1.38178i	−0.722962	−	0.690888i	$-0.757220\pi$
$677$		−	35.9527i		−	1.38178i	0.722962	−	0.690888i	$-0.242780\pi$
$678$		0			0
$679$	−6.47689			−0.248560
$680$	−7.95543	+	1.56768i	−0.305077	+	0.0601178i
$681$		0			0
$682$			7.01832i			0.268745i
$683$			9.00958i			0.344742i	0.985032	+	0.172371i	$0.0551428\pi$
$683$			9.00958i			0.344742i	−0.985032	+	0.172371i	$0.944857\pi$
$684$		0			0
$685$	1.24448	+	6.31528i	0.0475490	+	0.241295i
$686$	−10.2201			−0.390206
$687$		0			0
$688$			6.86464i			0.261712i
$689$	13.3555			0.508803
$690$		0			0
$691$	−9.11078			−0.346590			−0.173295	−	0.984870i	$-0.555441\pi$
$691$	−9.11078			−0.346590			−0.173295	+	0.984870i	$0.555441\pi$
$692$			2.98168i			0.113346i
$693$		0			0
$694$	2.77551			0.105357
$695$	−7.87090	+	1.55102i	−0.298560	+	0.0588336i
$696$		0			0
$697$		−	9.64015i		−	0.365147i
$698$		−	11.5510i		−	0.437213i
$699$		0			0
$700$	−1.44461	−	3.52311i	−0.0546011	−	0.133161i
$701$	14.7476			0.557009			0.278505	−	0.960435i	$-0.410161\pi$
$701$	14.7476			0.557009			0.278505	+	0.960435i	$0.410161\pi$
$702$		0			0
$703$			0.476886i			0.0179861i
$704$	−0.864641			−0.0325874
$705$		0			0
$706$	−8.40171			−0.316202
$707$		−	12.5015i		−	0.470166i
$708$		0			0
$709$	8.63389			0.324253			0.162126	−	0.986770i	$-0.448165\pi$
$709$	8.63389			0.324253			0.162126	+	0.986770i	$0.448165\pi$
$710$	4.40171	+	22.3372i	0.165193	+	0.838299i
$711$		0			0
$712$		−	0.387755i		−	0.0145317i
$713$			65.0496i			2.43613i
$714$		0			0
$715$	2.10308	+	10.6724i	0.0786509	+	0.399126i
$716$	−11.7938			−0.440756
$717$		0			0
$718$			22.7895i			0.850495i
$719$	−38.2759			−1.42745			−0.713726	−	0.700425i	$-0.752994\pi$
$719$	−38.2759			−1.42745			−0.713726	+	0.700425i	$0.752994\pi$
$720$		0			0
$721$	7.34153			0.273413
$722$			1.00000i			0.0372161i
$723$		0			0
$724$	−14.5693			−0.541465
$725$	−34.0279	+	13.9527i	−1.26376	+	0.518191i
$726$		0			0
$727$			31.1893i			1.15675i	0.815772	+	0.578373i	$0.196312\pi$
$727$			31.1893i			1.15675i	−0.815772	+	0.578373i	$0.803688\pi$
$728$			4.28467i			0.158800i
$729$		0			0
$730$	−35.9833	+	7.09079i	−1.33180	+	0.262442i
$731$	24.8925			0.920684
$732$		0			0
$733$		−	13.9634i		−	0.515748i	−0.966179	−	0.257874i	$-0.916978\pi$
$733$		−	13.9634i		−	0.515748i	0.966179	−	0.257874i	$-0.0830220\pi$
$734$	4.06455			0.150025
$735$		0			0
$736$	−8.01395			−0.295398
$737$		−	0.892548i		−	0.0328774i
$738$		0			0
$739$	−9.02165			−0.331867			−0.165933	−	0.986137i	$-0.553064\pi$
$739$	−9.02165			−0.331867			−0.165933	+	0.986137i	$0.553064\pi$
$740$	0.206167	+	1.04623i	0.00757886	+	0.0384601i
$741$		0			0
$742$			1.80779i			0.0663659i
$743$			15.0342i			0.551550i	0.961222	+	0.275775i	$0.0889345\pi$
$743$			15.0342i			0.551550i	−0.961222	+	0.275775i	$0.911066\pi$
$744$		0			0
$745$	−36.9450	+	7.28030i	−1.35356	+	0.266730i
$746$	18.4017			0.673734
$747$		0			0
$748$			3.13536i			0.114640i
$749$	−3.26302			−0.119228
$750$		0			0
$751$	29.6681			1.08260			0.541301	−	0.840829i	$-0.317932\pi$
$751$	29.6681			1.08260			0.541301	+	0.840829i	$0.317932\pi$
$752$			1.25240i			0.0456702i
$753$		0			0
$754$	41.3834			1.50709
$755$	−37.2557	+	7.34153i	−1.35587	+	0.267186i
$756$		0			0
$757$		−	10.5819i		−	0.384604i	−0.981336	−	0.192302i	$-0.938405\pi$
$757$		−	10.5819i		−	0.384604i	0.981336	−	0.192302i	$-0.0615953\pi$
$758$		−	1.23844i		−	0.0449823i
$759$		0			0
$760$	0.432320	+	2.19388i	0.0156819	+	0.0795803i
$761$	0.979789			0.0355173			0.0177587	−	0.999842i	$-0.494347\pi$
$761$	0.979789			0.0355173			0.0177587	+	0.999842i	$0.494347\pi$
$762$		0			0
$763$			10.2201i			0.369993i
$764$	13.2384			0.478950
$765$		0			0
$766$	16.8646			0.609344
$767$			25.2663i			0.912315i
$768$		0			0
$769$	−43.1772			−1.55701			−0.778505	−	0.627638i	$-0.784022\pi$
$769$	−43.1772			−1.55701			−0.778505	+	0.627638i	$0.784022\pi$
$770$	−1.44461	+	0.284672i	−0.0520601	+	0.0102589i
$771$		0			0
$772$		−	2.54144i		−	0.0914683i
$773$		−	37.5250i		−	1.34968i	−0.737964	−	0.674840i	$-0.764213\pi$
$773$		−	37.5250i		−	1.34968i	0.737964	−	0.674840i	$-0.235787\pi$
$774$		0			0
$775$	37.5510	−	15.3973i	1.34887	−	0.553089i
$776$	8.50479			0.305304
$777$		0			0
$778$			8.59392i			0.308107i
$779$	−2.65847			−0.0952497
$780$		0			0
$781$	8.80342			0.315011
$782$			29.0602i			1.03919i
$783$		0			0
$784$	6.42003			0.229287
$785$	−6.41566	−	32.5573i	−0.228985	−	1.16202i
$786$		0			0
$787$		−	22.5833i		−	0.805008i	−0.915418	−	0.402504i	$-0.868140\pi$
$787$		−	22.5833i		−	0.805008i	0.915418	−	0.402504i	$-0.131860\pi$
$788$			19.9109i			0.709295i
$789$		0			0
$790$	5.43398	+	27.5756i	0.193332	+	0.981096i
$791$	−7.86171			−0.279530
$792$		0			0
$793$		−	61.1266i		−	2.17067i
$794$	16.0558			0.569799
$795$		0			0
$796$	−20.3126			−0.719960
$797$			35.9806i			1.27450i	0.770657	+	0.637250i	$0.219928\pi$
$797$			35.9806i			1.27450i	−0.770657	+	0.637250i	$0.780072\pi$
$798$		0			0
$799$	4.54144			0.160664
$800$	1.89692	+	4.62620i	0.0670661	+	0.163561i
$801$		0			0
$802$			14.8925i			0.525874i
$803$			14.1816i			0.500457i
$804$		0			0
$805$	−13.3894	+	2.63849i	−0.471915	+	0.0929945i
$806$	−45.6681			−1.60859
$807$		0			0
$808$			16.4157i			0.577501i
$809$	−0.955660			−0.0335992			−0.0167996	−	0.999859i	$-0.505348\pi$
$809$	−0.955660			−0.0335992			−0.0167996	+	0.999859i	$0.505348\pi$
$810$		0			0
$811$	−7.53707			−0.264662			−0.132331	−	0.991206i	$-0.542246\pi$
$811$	−7.53707			−0.264662			−0.132331	+	0.991206i	$0.542246\pi$
$812$			5.60162i			0.196578i
$813$		0			0
$814$	0.412335			0.0144523
$815$	5.77988	+	29.3309i	0.202460	+	1.02742i
$816$		0			0
$817$		−	6.86464i		−	0.240163i
$818$			18.3511i			0.641632i
$819$		0			0
$820$	−5.83237	+	1.14931i	−0.203675	+	0.0401357i
$821$	−13.3082			−0.464460			−0.232230	−	0.972661i	$-0.574602\pi$
$821$	−13.3082			−0.464460			−0.232230	+	0.972661i	$0.574602\pi$
$822$		0			0
$823$			24.4050i			0.850706i	0.905028	+	0.425353i	$0.139850\pi$
$823$			24.4050i			0.850706i	−0.905028	+	0.425353i	$0.860150\pi$
$824$	−9.64015			−0.335831
$825$		0			0
$826$	−3.42003			−0.118998
$827$		−	11.6874i		−	0.406411i	−0.979136	−	0.203206i	$-0.934864\pi$
$827$		−	11.6874i		−	0.406411i	0.979136	−	0.203206i	$-0.0651360\pi$
$828$		0			0
$829$	−25.6541			−0.891004			−0.445502	−	0.895281i	$-0.646975\pi$
$829$	−25.6541			−0.891004			−0.445502	+	0.895281i	$0.646975\pi$
$830$	−0.593923	+	0.117037i	−0.0206154	+	0.00406241i
$831$		0			0
$832$		−	5.62620i		−	0.195053i
$833$		−	23.2803i		−	0.806615i
$834$		0			0
$835$	4.25676	+	21.6016i	0.147311	+	0.747555i
$836$	0.864641			0.0299042
$837$		0			0
$838$			34.7509i			1.20045i
$839$	−2.91713			−0.100710			−0.0503552	−	0.998731i	$-0.516035\pi$
$839$	−2.91713			−0.100710			−0.0503552	+	0.998731i	$0.516035\pi$
$840$		0			0
$841$	25.1031			0.865624
$842$		−	40.1589i		−	1.38397i
$843$		0			0
$844$	−18.0419			−0.621026
$845$	−40.9248	+	8.06455i	−1.40786	+	0.277429i
$846$		0			0
$847$		−	7.80779i		−	0.268279i
$848$		−	2.37380i		−	0.0815167i
$849$		0			0
$850$	16.7755	−	6.87859i	0.575395	−	0.235934i
$851$	3.82174			0.131008
$852$		0			0
$853$		−	6.24281i		−	0.213750i	−0.994272	−	0.106875i	$-0.965916\pi$
$853$		−	6.24281i		−	0.213750i	0.994272	−	0.106875i	$-0.0340844\pi$
$854$	8.27405			0.283132
$855$		0			0
$856$	4.28467			0.146447
$857$		−	23.2158i		−	0.793035i	−0.918027	−	0.396517i	$-0.870219\pi$
$857$		−	23.2158i		−	0.793035i	0.918027	−	0.396517i	$-0.129781\pi$
$858$		0			0
$859$	7.13536			0.243455			0.121728	−	0.992564i	$-0.461157\pi$
$859$	7.13536			0.243455			0.121728	+	0.992564i	$0.461157\pi$
$860$	−2.96772	−	15.0602i	−0.101199	−	0.513548i
$861$		0			0
$862$		−	34.9571i		−	1.19064i
$863$			7.31362i			0.248959i	0.992222	+	0.124479i	$0.0397260\pi$
$863$			7.31362i			0.248959i	−0.992222	+	0.124479i	$0.960274\pi$
$864$		0			0
$865$	−1.28904	−	6.54144i	−0.0438287	−	0.222416i
$866$	−1.13536			−0.0385811
$867$		0			0
$868$		−	6.18159i		−	0.209817i
$869$	10.8680			0.368671
$870$		0			0
$871$	5.80779			0.196789
$872$		−	13.4200i		−	0.454460i
$873$		0			0
$874$	8.01395			0.271076
$875$	4.69241	+	7.10475i	0.158632	+	0.240184i
$876$		0			0
$877$			22.0173i			0.743471i	0.928339	+	0.371735i	$0.121237\pi$
$877$			22.0173i			0.743471i	−0.928339	+	0.371735i	$0.878763\pi$
$878$			6.80009i			0.229492i
$879$		0			0
$880$	1.89692	−	0.373802i	0.0639450	−	0.0126009i
$881$	−11.7572			−0.396110			−0.198055	−	0.980191i	$-0.563462\pi$
$881$	−11.7572			−0.396110			−0.198055	+	0.980191i	$0.563462\pi$
$882$		0			0
$883$			55.6560i			1.87297i	0.350703	+	0.936487i	$0.385943\pi$
$883$			55.6560i			1.87297i	−0.350703	+	0.936487i	$0.614057\pi$
$884$	−20.4017			−0.686184
$885$		0			0
$886$	38.0679			1.27892
$887$		−	6.41566i		−	0.215417i	−0.994183	−	0.107708i	$-0.965649\pi$
$887$		−	6.41566i		−	0.215417i	0.994183	−	0.107708i	$-0.0343513\pi$
$888$		0			0
$889$	12.9325			0.433743
$890$	0.167635	+	0.850688i	0.00561912	+	0.0285151i
$891$		0			0
$892$			13.5231i			0.452787i
$893$		−	1.25240i		−	0.0419098i
$894$		0			0
$895$	25.8742	−	5.09871i	0.864880	−	0.170431i
$896$	0.761557			0.0254418
$897$		0			0
$898$		−	18.5414i		−	0.618736i
$899$	−59.7047			−1.99126
$900$		0			0
$901$	−8.60788			−0.286770
$902$			2.29862i			0.0765358i
$903$		0			0
$904$	10.3232			0.343345
$905$	31.9634	−	6.29862i	1.06250	−	0.209373i
$906$		0			0
$907$			57.1160i			1.89651i	0.317516	+	0.948253i	$0.397151\pi$
$907$			57.1160i			1.89651i	−0.317516	+	0.948253i	$0.602849\pi$
$908$		−	13.6016i		−	0.451386i
$909$		0			0
$910$	−1.85235	−	9.40005i	−0.0614048	−	0.311608i
$911$	26.6339			0.882420			0.441210	−	0.897404i	$-0.354549\pi$
$911$	26.6339			0.882420			0.441210	+	0.897404i	$0.354549\pi$
$912$		0			0
$913$			0.234074i			0.00774672i
$914$	16.3738			0.541597
$915$		0			0
$916$	13.5877			0.448949
$917$		−	0.412335i		−	0.0136165i
$918$		0			0
$919$	−6.63246			−0.218785			−0.109392	−	0.993999i	$-0.534890\pi$
$919$	−6.63246			−0.218785			−0.109392	+	0.993999i	$0.534890\pi$
$920$	17.5816	−	3.46460i	0.579649	−	0.114224i
$921$		0			0
$922$		−	1.70470i		−	0.0561414i
$923$			57.2836i			1.88551i
$924$		0			0
$925$	−0.904612	−	2.20617i	−0.0297435	−	0.0725383i
$926$	10.0279			0.329537
$927$		0			0
$928$		−	7.35548i		−	0.241455i
$929$	−50.0173			−1.64101			−0.820507	−	0.571637i	$-0.806309\pi$
$929$	−50.0173			−1.64101			−0.820507	+	0.571637i	$0.806309\pi$
$930$		0			0
$931$	−6.42003			−0.210408
$932$			25.5510i			0.836952i
$933$		0			0
$934$	−32.7509			−1.07164
$935$	−1.35548	−	6.87859i	−0.0443289	−	0.224954i
$936$		0			0
$937$			39.8882i			1.30309i	0.758610	+	0.651545i	$0.225879\pi$
$937$			39.8882i			1.30309i	−0.758610	+	0.651545i	$0.774121\pi$
$938$			0.786137i			0.0256683i
$939$		0			0
$940$	−0.541436	−	2.74760i	−0.0176597	−	0.0896170i
$941$	5.59829			0.182499			0.0912495	−	0.995828i	$-0.470914\pi$
$941$	5.59829			0.182499			0.0912495	+	0.995828i	$0.470914\pi$
$942$		0			0
$943$			21.3049i			0.693782i
$944$	4.49084			0.146164
$945$		0			0
$946$	−5.93545			−0.192978
$947$			12.7110i			0.413051i	0.978441	+	0.206525i	$0.0662156\pi$
$947$			12.7110i			0.413051i	−0.978441	+	0.206525i	$0.933784\pi$
$948$		0			0
$949$	−92.2793			−2.99551
$950$	−1.89692	−	4.62620i	−0.0615441	−	0.150094i
$951$		0			0
$952$		−	2.76156i		−	0.0895026i
$953$			57.0129i			1.84683i	0.383804	+	0.923415i	$0.374614\pi$
$953$			57.0129i			1.84683i	−0.383804	+	0.923415i	$0.625386\pi$
$954$		0			0
$955$	−29.0435	+	5.72325i	−0.939826	+	0.185200i
$956$	11.3309			0.366468
$957$		0			0
$958$			27.2803i			0.881387i
$959$	−2.19221			−0.0707903
$960$		0			0
$961$	34.8863			1.12536
$962$			2.68305i			0.0865051i
$963$		0			0
$964$	1.25240			0.0403370
$965$	1.09871	+	5.57560i	0.0353689	+	0.179485i
$966$		0			0
$967$			33.0183i			1.06180i	0.847435	+	0.530899i	$0.178146\pi$
$967$			33.0183i			1.06180i	−0.847435	+	0.530899i	$0.821854\pi$
$968$			10.2524i			0.329524i
$969$		0			0
$970$	−18.6585	+	3.67680i	−0.599087	+	0.118055i
$971$	3.04623			0.0977581			0.0488791	−	0.998805i	$-0.484435\pi$
$971$	3.04623			0.0977581			0.0488791	+	0.998805i	$0.484435\pi$
$972$		0			0
$973$		−	2.73221i		−	0.0875907i
$974$	−11.0741			−0.354838
$975$		0			0
$976$	−10.8646			−0.347769
$977$			13.4465i			0.430192i	0.976593	+	0.215096i	$0.0690064\pi$
$977$			13.4465i			0.430192i	−0.976593	+	0.215096i	$0.930994\pi$
$978$		0			0
$979$	0.335269			0.0107152
$980$	−14.0848	+	2.77551i	−0.449921	+	0.0886604i
$981$		0			0
$982$		−	8.11704i		−	0.259025i
$983$			22.0646i			0.703750i	0.936047	+	0.351875i	$0.114456\pi$
$983$			22.0646i			0.703750i	−0.936047	+	0.351875i	$0.885544\pi$
$984$		0			0
$985$	−8.60788	−	43.6820i	−0.274270	−	1.39182i
$986$	−26.6724			−0.849423
$987$		0			0
$988$			5.62620i			0.178993i
$989$	−55.0129			−1.74931
$990$		0			0
$991$	51.9946			1.65166			0.825831	−	0.563917i	$-0.190706\pi$
$991$	51.9946			1.65166			0.825831	+	0.563917i	$0.190706\pi$
$992$			8.11704i			0.257716i
$993$		0			0
$994$	−7.75386			−0.245938
$995$	44.5633	−	8.78154i	1.41275	−	0.278394i
$996$		0			0
$997$			37.7693i			1.19616i	0.801435	+	0.598082i	$0.204070\pi$
$997$			37.7693i			1.19616i	−0.801435	+	0.598082i	$0.795930\pi$
$998$		−	0.295298i		−	0.00934749i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.d.d.1369.6		6
3.2	odd	2		190.2.b.b.39.3	✓	6
5.2	odd	4		8550.2.a.ck.1.1		3
5.3	odd	4		8550.2.a.cl.1.3		3
5.4	even	2	inner	1710.2.d.d.1369.3		6
12.11	even	2		1520.2.d.j.609.1		6
15.2	even	4		950.2.a.n.1.3		3
15.8	even	4		950.2.a.i.1.1		3
15.14	odd	2		190.2.b.b.39.4	yes	6
60.23	odd	4		7600.2.a.cd.1.3		3
60.47	odd	4		7600.2.a.bi.1.1		3
60.59	even	2		1520.2.d.j.609.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.b.b.39.3	✓	6	3.2	odd	2
190.2.b.b.39.4	yes	6	15.14	odd	2
950.2.a.i.1.1		3	15.8	even	4
950.2.a.n.1.3		3	15.2	even	4
1520.2.d.j.609.1		6	12.11	even	2
1520.2.d.j.609.6		6	60.59	even	2
1710.2.d.d.1369.3		6	5.4	even	2	inner
1710.2.d.d.1369.6		6	1.1	even	1	trivial
7600.2.a.bi.1.1		3	60.47	odd	4
7600.2.a.cd.1.3		3	60.23	odd	4
8550.2.a.ck.1.1		3	5.2	odd	4
8550.2.a.cl.1.3		3	5.3	odd	4

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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.19388 - 0.432320i) q^{5} +0.761557i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.19388 - 0.432320i) q^{5} +0.761557i q^{7} -1.00000i q^{8} +(0.432320 + 2.19388i) q^{10} +0.864641 q^{11} +5.62620i q^{13} -0.761557 q^{14} +1.00000 q^{16} -3.62620i q^{17} -1.00000 q^{19} +(-2.19388 + 0.432320i) q^{20} +0.864641i q^{22} +8.01395i q^{23} +(4.62620 - 1.89692i) q^{25} -5.62620 q^{26} -0.761557i q^{28} -7.35548 q^{29} +8.11704 q^{31} +1.00000i q^{32} +3.62620 q^{34} +(0.329237 + 1.67076i) q^{35} -0.476886i q^{37} -1.00000i q^{38} +(-0.432320 - 2.19388i) q^{40} +2.65847 q^{41} +6.86464i q^{43} -0.864641 q^{44} -8.01395 q^{46} +1.25240i q^{47} +6.42003 q^{49} +(1.89692 + 4.62620i) q^{50} -5.62620i q^{52} -2.37380i q^{53} +(1.89692 - 0.373802i) q^{55} +0.761557 q^{56} -7.35548i q^{58} +4.49084 q^{59} -10.8646 q^{61} +8.11704i q^{62} -1.00000 q^{64} +(2.43232 + 12.3432i) q^{65} -1.03228i q^{67} +3.62620i q^{68} +(-1.67076 + 0.329237i) q^{70} +10.1816 q^{71} +16.4017i q^{73} +0.476886 q^{74} +1.00000 q^{76} +0.658473i q^{77} +12.5693 q^{79} +(2.19388 - 0.432320i) q^{80} +2.65847i q^{82} +0.270718i q^{83} +(-1.56768 - 7.95543i) q^{85} -6.86464 q^{86} -0.864641i q^{88} +0.387755 q^{89} -4.28467 q^{91} -8.01395i q^{92} -1.25240 q^{94} +(-2.19388 + 0.432320i) q^{95} +8.50479i q^{97} +6.42003i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 2 q^{5}+O(q^{10}) \) 6 * q - 6 * q^4 - 2 * q^5	\( 6 q - 6 q^{4} - 2 q^{5} + 8 q^{14} + 6 q^{16} - 6 q^{19} + 2 q^{20} + 10 q^{25} - 16 q^{26} - 16 q^{29} + 8 q^{31} + 4 q^{34} - 8 q^{35} - 4 q^{41} + 6 q^{49} + 4 q^{50} + 4 q^{55} - 8 q^{56} + 4 q^{59} - 60 q^{61} - 6 q^{64} + 12 q^{65} - 20 q^{70} + 16 q^{71} + 28 q^{74} + 6 q^{76} - 2 q^{80} - 12 q^{85} - 36 q^{86} - 28 q^{89} + 12 q^{91} + 28 q^{94} + 2 q^{95}+O(q^{100}) \) 6 * q - 6 * q^4 - 2 * q^5 + 8 * q^14 + 6 * q^16 - 6 * q^19 + 2 * q^20 + 10 * q^25 - 16 * q^26 - 16 * q^29 + 8 * q^31 + 4 * q^34 - 8 * q^35 - 4 * q^41 + 6 * q^49 + 4 * q^50 + 4 * q^55 - 8 * q^56 + 4 * q^59 - 60 * q^61 - 6 * q^64 + 12 * q^65 - 20 * q^70 + 16 * q^71 + 28 * q^74 + 6 * q^76 - 2 * q^80 - 12 * q^85 - 36 * q^86 - 28 * q^89 + 12 * q^91 + 28 * q^94 + 2 * q^95

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