LMFDB - Embedded newform 1734.2.f.g.829.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,2,Mod(829,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1734.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1734.f (of order $4$, degree $2$, not 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:	$13.8460597105$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 102)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1734.829
Dual form			1734.2.f.g.1483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.82843 + 2.82843i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.41421 - 1.41421i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.82843 + 2.82843i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.41421 - 1.41421i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-2.82843 + 2.82843i) q^{10} +(0.707107 + 0.707107i) q^{12} +6.00000 q^{13} +(1.41421 + 1.41421i) q^{14} -4.00000i q^{15} +1.00000 q^{16} -1.00000 q^{18} -4.00000i q^{19} +(-2.82843 - 2.82843i) q^{20} -2.00000 q^{21} +(4.24264 - 4.24264i) q^{23} +(-0.707107 + 0.707107i) q^{24} +11.0000i q^{25} +6.00000i q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.41421 + 1.41421i) q^{28} +(2.82843 + 2.82843i) q^{29} +4.00000 q^{30} +(-4.24264 - 4.24264i) q^{31} +1.00000i q^{32} +8.00000 q^{35} -1.00000i q^{36} +(-2.82843 - 2.82843i) q^{37} +4.00000 q^{38} +(-4.24264 - 4.24264i) q^{39} +(2.82843 - 2.82843i) q^{40} +(7.07107 - 7.07107i) q^{41} -2.00000i q^{42} -4.00000i q^{43} +(-2.82843 + 2.82843i) q^{45} +(4.24264 + 4.24264i) q^{46} -4.00000 q^{47} +(-0.707107 - 0.707107i) q^{48} +3.00000i q^{49} -11.0000 q^{50} -6.00000 q^{52} +2.00000i q^{53} +(0.707107 + 0.707107i) q^{54} +(-1.41421 - 1.41421i) q^{56} +(-2.82843 + 2.82843i) q^{57} +(-2.82843 + 2.82843i) q^{58} +12.0000i q^{59} +4.00000i q^{60} +(2.82843 - 2.82843i) q^{61} +(4.24264 - 4.24264i) q^{62} +(1.41421 + 1.41421i) q^{63} -1.00000 q^{64} +(16.9706 + 16.9706i) q^{65} -12.0000 q^{67} -6.00000 q^{69} +8.00000i q^{70} +(-4.24264 - 4.24264i) q^{71} +1.00000 q^{72} +(-1.41421 - 1.41421i) q^{73} +(2.82843 - 2.82843i) q^{74} +(7.77817 - 7.77817i) q^{75} +4.00000i q^{76} +(4.24264 - 4.24264i) q^{78} +(7.07107 - 7.07107i) q^{79} +(2.82843 + 2.82843i) q^{80} -1.00000 q^{81} +(7.07107 + 7.07107i) q^{82} +12.0000i q^{83} +2.00000 q^{84} +4.00000 q^{86} -4.00000i q^{87} +2.00000 q^{89} +(-2.82843 - 2.82843i) q^{90} +(8.48528 - 8.48528i) q^{91} +(-4.24264 + 4.24264i) q^{92} +6.00000i q^{93} -4.00000i q^{94} +(11.3137 - 11.3137i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-4.24264 - 4.24264i) q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4}+O(q^{10}) $ 4 * q - 4 * q^4	$ 4 q - 4 q^{4} + 24 q^{13} + 4 q^{16} - 4 q^{18} - 8 q^{21} + 16 q^{30} + 32 q^{35} + 16 q^{38} - 16 q^{47} - 44 q^{50} - 24 q^{52} - 4 q^{64} - 48 q^{67} - 24 q^{69} + 4 q^{72} - 4 q^{81} + 8 q^{84} + 16 q^{86} + 8 q^{89} - 12 q^{98}+O(q^{100}) $ 4 * q - 4 * q^4 + 24 * q^13 + 4 * q^16 - 4 * q^18 - 8 * q^21 + 16 * q^30 + 32 * q^35 + 16 * q^38 - 16 * q^47 - 44 * q^50 - 24 * q^52 - 4 * q^64 - 48 * q^67 - 24 * q^69 + 4 * q^72 - 4 * q^81 + 8 * q^84 + 16 * q^86 + 8 * q^89 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times$.

$n$	$1157$	$1159$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	2.82843	+	2.82843i	1.26491	+	1.26491i	0.948683	+	0.316228i	$0.102416\pi$
$5$	2.82843	+	2.82843i	1.26491	+	1.26491i	0.316228	+	0.948683i	$0.397584\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	1.41421	−	1.41421i	0.534522	−	0.534522i	−0.387392	−	0.921915i	$-0.626624\pi$
$7$	1.41421	−	1.41421i	0.534522	−	0.534522i	0.921915	+	0.387392i	$0.126624\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	−2.82843	+	2.82843i	−0.894427	+	0.894427i
$11$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$11$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	6.00000			1.66410			0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000			1.66410			0.832050	+	0.554700i	$0.187167\pi$
$14$	1.41421	+	1.41421i	0.377964	+	0.377964i
$15$		−	4.00000i		−	1.03280i
$16$	1.00000			0.250000
$17$		0			0
$17$		0			0
$18$	−1.00000			−0.235702
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	−2.82843	−	2.82843i	−0.632456	−	0.632456i
$21$	−2.00000			−0.436436
$22$		0			0
$23$	4.24264	−	4.24264i	0.884652	−	0.884652i	−0.109351	−	0.994003i	$-0.534877\pi$
$23$	4.24264	−	4.24264i	0.884652	−	0.884652i	0.994003	+	0.109351i	$0.0348774\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$			11.0000i			2.20000i
$26$			6.00000i			1.17670i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−1.41421	+	1.41421i	−0.267261	+	0.267261i
$29$	2.82843	+	2.82843i	0.525226	+	0.525226i	0.919145	−	0.393919i	$-0.128881\pi$
$29$	2.82843	+	2.82843i	0.525226	+	0.525226i	−0.393919	+	0.919145i	$0.628881\pi$
$30$	4.00000			0.730297
$31$	−4.24264	−	4.24264i	−0.762001	−	0.762001i	0.214683	−	0.976684i	$-0.431128\pi$
$31$	−4.24264	−	4.24264i	−0.762001	−	0.762001i	−0.976684	+	0.214683i	$0.931128\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$		0			0
$35$	8.00000			1.35225
$36$		−	1.00000i		−	0.166667i
$37$	−2.82843	−	2.82843i	−0.464991	−	0.464991i	0.435297	−	0.900287i	$-0.356644\pi$
$37$	−2.82843	−	2.82843i	−0.464991	−	0.464991i	−0.900287	+	0.435297i	$0.856644\pi$
$38$	4.00000			0.648886
$39$	−4.24264	−	4.24264i	−0.679366	−	0.679366i
$40$	2.82843	−	2.82843i	0.447214	−	0.447214i
$41$	7.07107	−	7.07107i	1.10432	−	1.10432i	0.110432	−	0.993884i	$-0.464777\pi$
$41$	7.07107	−	7.07107i	1.10432	−	1.10432i	0.993884	−	0.110432i	$-0.0352233\pi$
$42$		−	2.00000i		−	0.308607i
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$		0			0
$45$	−2.82843	+	2.82843i	−0.421637	+	0.421637i
$46$	4.24264	+	4.24264i	0.625543	+	0.625543i
$47$	−4.00000			−0.583460			−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000			−0.583460			−0.291730	+	0.956501i	$0.594231\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$			3.00000i			0.428571i
$50$	−11.0000			−1.55563
$51$		0			0
$52$	−6.00000			−0.832050
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$		0			0
$56$	−1.41421	−	1.41421i	−0.188982	−	0.188982i
$57$	−2.82843	+	2.82843i	−0.374634	+	0.374634i
$58$	−2.82843	+	2.82843i	−0.371391	+	0.371391i
$59$			12.0000i			1.56227i	0.624364	+	0.781133i	$0.285358\pi$
$59$			12.0000i			1.56227i	−0.624364	+	0.781133i	$0.714642\pi$
$60$			4.00000i			0.516398i
$61$	2.82843	−	2.82843i	0.362143	−	0.362143i	−0.502458	−	0.864601i	$-0.667571\pi$
$61$	2.82843	−	2.82843i	0.362143	−	0.362143i	0.864601	+	0.502458i	$0.167571\pi$
$62$	4.24264	−	4.24264i	0.538816	−	0.538816i
$63$	1.41421	+	1.41421i	0.178174	+	0.178174i
$64$	−1.00000			−0.125000
$65$	16.9706	+	16.9706i	2.10494	+	2.10494i
$66$		0			0
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$		0			0
$69$	−6.00000			−0.722315
$70$			8.00000i			0.956183i
$71$	−4.24264	−	4.24264i	−0.503509	−	0.503509i	0.409018	−	0.912526i	$-0.365871\pi$
$71$	−4.24264	−	4.24264i	−0.503509	−	0.503509i	−0.912526	+	0.409018i	$0.865871\pi$
$72$	1.00000			0.117851
$73$	−1.41421	−	1.41421i	−0.165521	−	0.165521i	0.619486	−	0.785007i	$-0.287341\pi$
$73$	−1.41421	−	1.41421i	−0.165521	−	0.165521i	−0.785007	+	0.619486i	$0.787341\pi$
$74$	2.82843	−	2.82843i	0.328798	−	0.328798i
$75$	7.77817	−	7.77817i	0.898146	−	0.898146i
$76$			4.00000i			0.458831i
$77$		0			0
$78$	4.24264	−	4.24264i	0.480384	−	0.480384i
$79$	7.07107	−	7.07107i	0.795557	−	0.795557i	−0.186834	−	0.982391i	$-0.559823\pi$
$79$	7.07107	−	7.07107i	0.795557	−	0.795557i	0.982391	+	0.186834i	$0.0598227\pi$
$80$	2.82843	+	2.82843i	0.316228	+	0.316228i
$81$	−1.00000			−0.111111
$82$	7.07107	+	7.07107i	0.780869	+	0.780869i
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$	2.00000			0.218218
$85$		0			0
$86$	4.00000			0.431331
$87$		−	4.00000i		−	0.428845i
$88$		0			0
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$	−2.82843	−	2.82843i	−0.298142	−	0.298142i
$91$	8.48528	−	8.48528i	0.889499	−	0.889499i
$92$	−4.24264	+	4.24264i	−0.442326	+	0.442326i
$93$			6.00000i			0.622171i
$94$		−	4.00000i		−	0.412568i
$95$	11.3137	−	11.3137i	1.16076	−	1.16076i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−4.24264	−	4.24264i	−0.430775	−	0.430775i	0.458117	−	0.888892i	$-0.348524\pi$
$97$	−4.24264	−	4.24264i	−0.430775	−	0.430775i	−0.888892	+	0.458117i	$0.848524\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$		−	11.0000i		−	1.10000i
$101$	14.0000			1.39305			0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000			1.39305			0.696526	+	0.717532i	$0.254728\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		−	6.00000i		−	0.588348i
$105$	−5.65685	−	5.65685i	−0.552052	−	0.552052i
$106$	−2.00000			−0.194257
$107$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$107$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	−11.3137	+	11.3137i	−1.08366	+	1.08366i	−0.0874915	+	0.996165i	$0.527885\pi$
$109$	−11.3137	+	11.3137i	−1.08366	+	1.08366i	−0.996165	+	0.0874915i	$0.972115\pi$
$110$		0			0
$111$			4.00000i			0.379663i
$112$	1.41421	−	1.41421i	0.133631	−	0.133631i
$113$	1.41421	−	1.41421i	0.133038	−	0.133038i	−0.637452	−	0.770490i	$-0.720012\pi$
$113$	1.41421	−	1.41421i	0.133038	−	0.133038i	0.770490	+	0.637452i	$0.220012\pi$
$114$	−2.82843	−	2.82843i	−0.264906	−	0.264906i
$115$	24.0000			2.23801
$116$	−2.82843	−	2.82843i	−0.262613	−	0.262613i
$117$			6.00000i			0.554700i
$118$	−12.0000			−1.10469
$119$		0			0
$120$	−4.00000			−0.365148
$121$			11.0000i			1.00000i
$122$	2.82843	+	2.82843i	0.256074	+	0.256074i
$123$	−10.0000			−0.901670
$124$	4.24264	+	4.24264i	0.381000	+	0.381000i
$125$	−16.9706	+	16.9706i	−1.51789	+	1.51789i
$126$	−1.41421	+	1.41421i	−0.125988	+	0.125988i
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−2.82843	+	2.82843i	−0.249029	+	0.249029i
$130$	−16.9706	+	16.9706i	−1.48842	+	1.48842i
$131$	11.3137	+	11.3137i	0.988483	+	0.988483i	0.999934	−	0.0114511i	$-0.00364509\pi$
$131$	11.3137	+	11.3137i	0.988483	+	0.988483i	−0.0114511	+	0.999934i	$0.503645\pi$
$132$		0			0
$133$	−5.65685	−	5.65685i	−0.490511	−	0.490511i
$134$		−	12.0000i		−	1.03664i
$135$	4.00000			0.344265
$136$		0			0
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$		−	6.00000i		−	0.510754i
$139$	5.65685	+	5.65685i	0.479808	+	0.479808i	0.905070	−	0.425262i	$-0.139818\pi$
$139$	5.65685	+	5.65685i	0.479808	+	0.479808i	−0.425262	+	0.905070i	$0.639818\pi$
$140$	−8.00000			−0.676123
$141$	2.82843	+	2.82843i	0.238197	+	0.238197i
$142$	4.24264	−	4.24264i	0.356034	−	0.356034i
$143$		0			0
$144$			1.00000i			0.0833333i
$145$			16.0000i			1.32873i
$146$	1.41421	−	1.41421i	0.117041	−	0.117041i
$147$	2.12132	−	2.12132i	0.174964	−	0.174964i
$148$	2.82843	+	2.82843i	0.232495	+	0.232495i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$	7.77817	+	7.77817i	0.635085	+	0.635085i
$151$			24.0000i			1.95309i	0.215308	+	0.976546i	$0.430924\pi$
$151$			24.0000i			1.95309i	−0.215308	+	0.976546i	$0.569076\pi$
$152$	−4.00000			−0.324443
$153$		0			0
$154$		0			0
$155$		−	24.0000i		−	1.92773i
$156$	4.24264	+	4.24264i	0.339683	+	0.339683i
$157$	−6.00000			−0.478852			−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000			−0.478852			−0.239426	+	0.970915i	$0.576959\pi$
$158$	7.07107	+	7.07107i	0.562544	+	0.562544i
$159$	1.41421	−	1.41421i	0.112154	−	0.112154i
$160$	−2.82843	+	2.82843i	−0.223607	+	0.223607i
$161$		−	12.0000i		−	0.945732i
$162$		−	1.00000i		−	0.0785674i
$163$	−8.48528	+	8.48528i	−0.664619	+	0.664619i	−0.956465	−	0.291847i	$-0.905730\pi$
$163$	−8.48528	+	8.48528i	−0.664619	+	0.664619i	0.291847	+	0.956465i	$0.405730\pi$
$164$	−7.07107	+	7.07107i	−0.552158	+	0.552158i
$165$		0			0
$166$	−12.0000			−0.931381
$167$	−1.41421	−	1.41421i	−0.109435	−	0.109435i	0.650269	−	0.759704i	$-0.274656\pi$
$167$	−1.41421	−	1.41421i	−0.109435	−	0.109435i	−0.759704	+	0.650269i	$0.774656\pi$
$168$			2.00000i			0.154303i
$169$	23.0000			1.76923
$170$		0			0
$171$	4.00000			0.305888
$172$			4.00000i			0.304997i
$173$	−2.82843	−	2.82843i	−0.215041	−	0.215041i	0.591364	−	0.806405i	$-0.298590\pi$
$173$	−2.82843	−	2.82843i	−0.215041	−	0.215041i	−0.806405	+	0.591364i	$0.798590\pi$
$174$	4.00000			0.303239
$175$	15.5563	+	15.5563i	1.17595	+	1.17595i
$176$		0			0
$177$	8.48528	−	8.48528i	0.637793	−	0.637793i
$178$			2.00000i			0.149906i
$179$		−	12.0000i		−	0.896922i	−0.893802	−	0.448461i	$-0.851972\pi$
$179$		−	12.0000i		−	0.896922i	0.893802	−	0.448461i	$-0.148028\pi$
$180$	2.82843	−	2.82843i	0.210819	−	0.210819i
$181$	−14.1421	+	14.1421i	−1.05118	+	1.05118i	−0.0525588	+	0.998618i	$0.516738\pi$
$181$	−14.1421	+	14.1421i	−1.05118	+	1.05118i	−0.998618	+	0.0525588i	$0.983262\pi$
$182$	8.48528	+	8.48528i	0.628971	+	0.628971i
$183$	−4.00000			−0.295689
$184$	−4.24264	−	4.24264i	−0.312772	−	0.312772i
$185$		−	16.0000i		−	1.17634i
$186$	−6.00000			−0.439941
$187$		0			0
$188$	4.00000			0.291730
$189$		−	2.00000i		−	0.145479i
$190$	11.3137	+	11.3137i	0.820783	+	0.820783i
$191$	4.00000			0.289430			0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000			0.289430			0.144715	+	0.989473i	$0.453773\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	4.24264	−	4.24264i	0.305392	−	0.305392i	−0.537727	−	0.843119i	$-0.680717\pi$
$193$	4.24264	−	4.24264i	0.305392	−	0.305392i	0.843119	+	0.537727i	$0.180717\pi$
$194$	4.24264	−	4.24264i	0.304604	−	0.304604i
$195$		−	24.0000i		−	1.71868i
$196$		−	3.00000i		−	0.214286i
$197$	−5.65685	+	5.65685i	−0.403034	+	0.403034i	−0.879301	−	0.476267i	$-0.841990\pi$
$197$	−5.65685	+	5.65685i	−0.403034	+	0.403034i	0.476267	+	0.879301i	$0.341990\pi$
$198$		0			0
$199$	−9.89949	−	9.89949i	−0.701757	−	0.701757i	0.263031	−	0.964787i	$-0.415278\pi$
$199$	−9.89949	−	9.89949i	−0.701757	−	0.701757i	−0.964787	+	0.263031i	$0.915278\pi$
$200$	11.0000			0.777817
$201$	8.48528	+	8.48528i	0.598506	+	0.598506i
$202$			14.0000i			0.985037i
$203$	8.00000			0.561490
$204$		0			0
$205$	40.0000			2.79372
$206$			4.00000i			0.278693i
$207$	4.24264	+	4.24264i	0.294884	+	0.294884i
$208$	6.00000			0.416025
$209$		0			0
$210$	5.65685	−	5.65685i	0.390360	−	0.390360i
$211$	−5.65685	+	5.65685i	−0.389434	+	0.389434i	−0.874486	−	0.485052i	$-0.838801\pi$
$211$	−5.65685	+	5.65685i	−0.389434	+	0.389434i	0.485052	+	0.874486i	$0.338801\pi$
$212$		−	2.00000i		−	0.137361i
$213$			6.00000i			0.411113i
$214$		0			0
$215$	11.3137	−	11.3137i	0.771589	−	0.771589i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−12.0000			−0.814613
$218$	−11.3137	−	11.3137i	−0.766261	−	0.766261i
$219$			2.00000i			0.135147i
$220$		0			0
$221$		0			0
$222$	−4.00000			−0.268462
$223$			4.00000i			0.267860i	0.990991	+	0.133930i	$0.0427597\pi$
$223$			4.00000i			0.267860i	−0.990991	+	0.133930i	$0.957240\pi$
$224$	1.41421	+	1.41421i	0.0944911	+	0.0944911i
$225$	−11.0000			−0.733333
$226$	1.41421	+	1.41421i	0.0940721	+	0.0940721i
$227$	2.82843	−	2.82843i	0.187729	−	0.187729i	−0.606984	−	0.794714i	$-0.707621\pi$
$227$	2.82843	−	2.82843i	0.187729	−	0.187729i	0.794714	+	0.606984i	$0.207621\pi$
$228$	2.82843	−	2.82843i	0.187317	−	0.187317i
$229$		−	2.00000i		−	0.132164i	−0.997814	−	0.0660819i	$-0.978950\pi$
$229$		−	2.00000i		−	0.132164i	0.997814	−	0.0660819i	$-0.0210498\pi$
$230$			24.0000i			1.58251i
$231$		0			0
$232$	2.82843	−	2.82843i	0.185695	−	0.185695i
$233$	4.24264	+	4.24264i	0.277945	+	0.277945i	0.832288	−	0.554343i	$-0.187031\pi$
$233$	4.24264	+	4.24264i	0.277945	+	0.277945i	−0.554343	+	0.832288i	$0.687031\pi$
$234$	−6.00000			−0.392232
$235$	−11.3137	−	11.3137i	−0.738025	−	0.738025i
$236$		−	12.0000i		−	0.781133i
$237$	−10.0000			−0.649570
$238$		0			0
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$		−	4.00000i		−	0.258199i
$241$	−12.7279	−	12.7279i	−0.819878	−	0.819878i	0.166212	−	0.986090i	$-0.446846\pi$
$241$	−12.7279	−	12.7279i	−0.819878	−	0.819878i	−0.986090	+	0.166212i	$0.946846\pi$
$242$	−11.0000			−0.707107
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−2.82843	+	2.82843i	−0.181071	+	0.181071i
$245$	−8.48528	+	8.48528i	−0.542105	+	0.542105i
$246$		−	10.0000i		−	0.637577i
$247$		−	24.0000i		−	1.52708i
$248$	−4.24264	+	4.24264i	−0.269408	+	0.269408i
$249$	8.48528	−	8.48528i	0.537733	−	0.537733i
$250$	−16.9706	−	16.9706i	−1.07331	−	1.07331i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$	−1.41421	−	1.41421i	−0.0890871	−	0.0890871i
$253$		0			0
$254$	−8.00000			−0.501965
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	18.0000i		−	1.12281i	−0.827541	−	0.561405i	$-0.810261\pi$
$257$		−	18.0000i		−	1.12281i	0.827541	−	0.561405i	$-0.189739\pi$
$258$	−2.82843	−	2.82843i	−0.176090	−	0.176090i
$259$	−8.00000			−0.497096
$260$	−16.9706	−	16.9706i	−1.05247	−	1.05247i
$261$	−2.82843	+	2.82843i	−0.175075	+	0.175075i
$262$	−11.3137	+	11.3137i	−0.698963	+	0.698963i
$263$		−	12.0000i		−	0.739952i	−0.929041	−	0.369976i	$-0.879366\pi$
$263$		−	12.0000i		−	0.739952i	0.929041	−	0.369976i	$-0.120634\pi$
$264$		0			0
$265$	−5.65685	+	5.65685i	−0.347498	+	0.347498i
$266$	5.65685	−	5.65685i	0.346844	−	0.346844i
$267$	−1.41421	−	1.41421i	−0.0865485	−	0.0865485i
$268$	12.0000			0.733017
$269$	−8.48528	−	8.48528i	−0.517357	−	0.517357i	0.399414	−	0.916771i	$-0.369214\pi$
$269$	−8.48528	−	8.48528i	−0.517357	−	0.517357i	−0.916771	+	0.399414i	$0.869214\pi$
$270$			4.00000i			0.243432i
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$		0			0
$273$	−12.0000			−0.726273
$274$		−	6.00000i		−	0.362473i
$275$		0			0
$276$	6.00000			0.361158
$277$	5.65685	+	5.65685i	0.339887	+	0.339887i	0.856325	−	0.516437i	$-0.172742\pi$
$277$	5.65685	+	5.65685i	0.339887	+	0.339887i	−0.516437	+	0.856325i	$0.672742\pi$
$278$	−5.65685	+	5.65685i	−0.339276	+	0.339276i
$279$	4.24264	−	4.24264i	0.254000	−	0.254000i
$280$		−	8.00000i		−	0.478091i
$281$		−	18.0000i		−	1.07379i	−0.843649	−	0.536895i	$-0.819597\pi$
$281$		−	18.0000i		−	1.07379i	0.843649	−	0.536895i	$-0.180403\pi$
$282$	−2.82843	+	2.82843i	−0.168430	+	0.168430i
$283$	22.6274	−	22.6274i	1.34506	−	1.34506i	0.454120	−	0.890941i	$-0.349954\pi$
$283$	22.6274	−	22.6274i	1.34506	−	1.34506i	0.890941	−	0.454120i	$-0.150046\pi$
$284$	4.24264	+	4.24264i	0.251754	+	0.251754i
$285$	−16.0000			−0.947758
$286$		0			0
$287$		−	20.0000i		−	1.18056i
$288$	−1.00000			−0.0589256
$289$		0			0
$290$	−16.0000			−0.939552
$291$			6.00000i			0.351726i
$292$	1.41421	+	1.41421i	0.0827606	+	0.0827606i
$293$	−2.00000			−0.116841			−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000			−0.116841			−0.0584206	+	0.998292i	$0.518606\pi$
$294$	2.12132	+	2.12132i	0.123718	+	0.123718i
$295$	−33.9411	+	33.9411i	−1.97613	+	1.97613i
$296$	−2.82843	+	2.82843i	−0.164399	+	0.164399i
$297$		0			0
$298$			6.00000i			0.347571i
$299$	25.4558	−	25.4558i	1.47215	−	1.47215i
$300$	−7.77817	+	7.77817i	−0.449073	+	0.449073i
$301$	−5.65685	−	5.65685i	−0.326056	−	0.326056i
$302$	−24.0000			−1.38104
$303$	−9.89949	−	9.89949i	−0.568711	−	0.568711i
$304$		−	4.00000i		−	0.229416i
$305$	16.0000			0.916157
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$	−2.82843	−	2.82843i	−0.160904	−	0.160904i
$310$	24.0000			1.36311
$311$	−21.2132	−	21.2132i	−1.20289	−	1.20289i	−0.973283	−	0.229607i	$-0.926256\pi$
$311$	−21.2132	−	21.2132i	−1.20289	−	1.20289i	−0.229607	−	0.973283i	$-0.573744\pi$
$312$	−4.24264	+	4.24264i	−0.240192	+	0.240192i
$313$	18.3848	−	18.3848i	1.03917	−	1.03917i	0.0399680	−	0.999201i	$-0.487274\pi$
$313$	18.3848	−	18.3848i	1.03917	−	1.03917i	0.999201	−	0.0399680i	$-0.0127256\pi$
$314$		−	6.00000i		−	0.338600i
$315$			8.00000i			0.450749i
$316$	−7.07107	+	7.07107i	−0.397779	+	0.397779i
$317$	−11.3137	+	11.3137i	−0.635441	+	0.635441i	−0.949428	−	0.313986i	$-0.898335\pi$
$317$	−11.3137	+	11.3137i	−0.635441	+	0.635441i	0.313986	+	0.949428i	$0.398335\pi$
$318$	1.41421	+	1.41421i	0.0793052	+	0.0793052i
$319$		0			0
$320$	−2.82843	−	2.82843i	−0.158114	−	0.158114i
$321$		0			0
$322$	12.0000			0.668734
$323$		0			0
$324$	1.00000			0.0555556
$325$			66.0000i			3.66102i
$326$	−8.48528	−	8.48528i	−0.469956	−	0.469956i
$327$	16.0000			0.884802
$328$	−7.07107	−	7.07107i	−0.390434	−	0.390434i
$329$	−5.65685	+	5.65685i	−0.311872	+	0.311872i
$330$		0			0
$331$			20.0000i			1.09930i	0.835395	+	0.549650i	$0.185239\pi$
$331$			20.0000i			1.09930i	−0.835395	+	0.549650i	$0.814761\pi$
$332$		−	12.0000i		−	0.658586i
$333$	2.82843	−	2.82843i	0.154997	−	0.154997i
$334$	1.41421	−	1.41421i	0.0773823	−	0.0773823i
$335$	−33.9411	−	33.9411i	−1.85440	−	1.85440i
$336$	−2.00000			−0.109109
$337$	−4.24264	−	4.24264i	−0.231111	−	0.231111i	0.582045	−	0.813156i	$-0.302253\pi$
$337$	−4.24264	−	4.24264i	−0.231111	−	0.231111i	−0.813156	+	0.582045i	$0.802253\pi$
$338$			23.0000i			1.25104i
$339$	−2.00000			−0.108625
$340$		0			0
$341$		0			0
$342$			4.00000i			0.216295i
$343$	14.1421	+	14.1421i	0.763604	+	0.763604i
$344$	−4.00000			−0.215666
$345$	−16.9706	−	16.9706i	−0.913664	−	0.913664i
$346$	2.82843	−	2.82843i	0.152057	−	0.152057i
$347$	2.82843	−	2.82843i	0.151838	−	0.151838i	−0.627100	−	0.778938i	$-0.715758\pi$
$347$	2.82843	−	2.82843i	0.151838	−	0.151838i	0.778938	+	0.627100i	$0.215758\pi$
$348$			4.00000i			0.214423i
$349$		−	30.0000i		−	1.60586i	−0.596071	−	0.802932i	$-0.703272\pi$
$349$		−	30.0000i		−	1.60586i	0.596071	−	0.802932i	$-0.296728\pi$
$350$	−15.5563	+	15.5563i	−0.831522	+	0.831522i
$351$	4.24264	−	4.24264i	0.226455	−	0.226455i
$352$		0			0
$353$	−14.0000			−0.745145			−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000			−0.745145			−0.372572	+	0.928003i	$0.621524\pi$
$354$	8.48528	+	8.48528i	0.450988	+	0.450988i
$355$		−	24.0000i		−	1.27379i
$356$	−2.00000			−0.106000
$357$		0			0
$358$	12.0000			0.634220
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	2.82843	+	2.82843i	0.149071	+	0.149071i
$361$	3.00000			0.157895
$362$	−14.1421	−	14.1421i	−0.743294	−	0.743294i
$363$	7.77817	−	7.77817i	0.408248	−	0.408248i
$364$	−8.48528	+	8.48528i	−0.444750	+	0.444750i
$365$		−	8.00000i		−	0.418739i
$366$		−	4.00000i		−	0.209083i
$367$	−7.07107	+	7.07107i	−0.369107	+	0.369107i	−0.867151	−	0.498045i	$-0.834052\pi$
$367$	−7.07107	+	7.07107i	−0.369107	+	0.369107i	0.498045	+	0.867151i	$0.334052\pi$
$368$	4.24264	−	4.24264i	0.221163	−	0.221163i
$369$	7.07107	+	7.07107i	0.368105	+	0.368105i
$370$	16.0000			0.831800
$371$	2.82843	+	2.82843i	0.146845	+	0.146845i
$372$		−	6.00000i		−	0.311086i
$373$	−14.0000			−0.724893			−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000			−0.724893			−0.362446	+	0.932005i	$0.618058\pi$
$374$		0			0
$375$	24.0000			1.23935
$376$			4.00000i			0.206284i
$377$	16.9706	+	16.9706i	0.874028	+	0.874028i
$378$	2.00000			0.102869
$379$	2.82843	+	2.82843i	0.145287	+	0.145287i	0.776009	−	0.630722i	$-0.217241\pi$
$379$	2.82843	+	2.82843i	0.145287	+	0.145287i	−0.630722	+	0.776009i	$0.717241\pi$
$380$	−11.3137	+	11.3137i	−0.580381	+	0.580381i
$381$	5.65685	−	5.65685i	0.289809	−	0.289809i
$382$			4.00000i			0.204658i
$383$			28.0000i			1.43073i	0.698749	+	0.715367i	$0.253740\pi$
$383$			28.0000i			1.43073i	−0.698749	+	0.715367i	$0.746260\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$		0			0
$386$	4.24264	+	4.24264i	0.215945	+	0.215945i
$387$	4.00000			0.203331
$388$	4.24264	+	4.24264i	0.215387	+	0.215387i
$389$			14.0000i			0.709828i	0.934899	+	0.354914i	$0.115490\pi$
$389$			14.0000i			0.709828i	−0.934899	+	0.354914i	$0.884510\pi$
$390$	24.0000			1.21529
$391$		0			0
$392$	3.00000			0.151523
$393$		−	16.0000i		−	0.807093i
$394$	−5.65685	−	5.65685i	−0.284988	−	0.284988i
$395$	40.0000			2.01262
$396$		0			0
$397$	14.1421	−	14.1421i	0.709773	−	0.709773i	−0.256714	−	0.966487i	$-0.582640\pi$
$397$	14.1421	−	14.1421i	0.709773	−	0.709773i	0.966487	+	0.256714i	$0.0826398\pi$
$398$	9.89949	−	9.89949i	0.496217	−	0.496217i
$399$			8.00000i			0.400501i
$400$			11.0000i			0.550000i
$401$	−21.2132	+	21.2132i	−1.05934	+	1.05934i	−0.0612120	+	0.998125i	$0.519497\pi$
$401$	−21.2132	+	21.2132i	−1.05934	+	1.05934i	−0.998125	+	0.0612120i	$0.980503\pi$
$402$	−8.48528	+	8.48528i	−0.423207	+	0.423207i
$403$	−25.4558	−	25.4558i	−1.26805	−	1.26805i
$404$	−14.0000			−0.696526
$405$	−2.82843	−	2.82843i	−0.140546	−	0.140546i
$406$			8.00000i			0.397033i
$407$		0			0
$408$		0			0
$409$	−26.0000			−1.28562			−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000			−1.28562			−0.642809	+	0.766027i	$0.722231\pi$
$410$			40.0000i			1.97546i
$411$	4.24264	+	4.24264i	0.209274	+	0.209274i
$412$	−4.00000			−0.197066
$413$	16.9706	+	16.9706i	0.835067	+	0.835067i
$414$	−4.24264	+	4.24264i	−0.208514	+	0.208514i
$415$	−33.9411	+	33.9411i	−1.66610	+	1.66610i
$416$			6.00000i			0.294174i
$417$		−	8.00000i		−	0.391762i
$418$		0			0
$419$	−8.48528	+	8.48528i	−0.414533	+	0.414533i	−0.883314	−	0.468781i	$-0.844693\pi$
$419$	−8.48528	+	8.48528i	−0.414533	+	0.414533i	0.468781	+	0.883314i	$0.344693\pi$
$420$	5.65685	+	5.65685i	0.276026	+	0.276026i
$421$	−34.0000			−1.65706			−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000			−1.65706			−0.828529	+	0.559946i	$0.810822\pi$
$422$	−5.65685	−	5.65685i	−0.275371	−	0.275371i
$423$		−	4.00000i		−	0.194487i
$424$	2.00000			0.0971286
$425$		0			0
$426$	−6.00000			−0.290701
$427$		−	8.00000i		−	0.387147i
$428$		0			0
$429$		0			0
$430$	11.3137	+	11.3137i	0.545595	+	0.545595i
$431$	9.89949	−	9.89949i	0.476842	−	0.476842i	−0.427278	−	0.904120i	$-0.640528\pi$
$431$	9.89949	−	9.89949i	0.476842	−	0.476842i	0.904120	+	0.427278i	$0.140528\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$		−	18.0000i		−	0.865025i	−0.901628	−	0.432512i	$-0.857627\pi$
$433$		−	18.0000i		−	0.865025i	0.901628	−	0.432512i	$-0.142373\pi$
$434$		−	12.0000i		−	0.576018i
$435$	11.3137	−	11.3137i	0.542451	−	0.542451i
$436$	11.3137	−	11.3137i	0.541828	−	0.541828i
$437$	−16.9706	−	16.9706i	−0.811812	−	0.811812i
$438$	−2.00000			−0.0955637
$439$	−7.07107	−	7.07107i	−0.337484	−	0.337484i	0.517936	−	0.855419i	$-0.326701\pi$
$439$	−7.07107	−	7.07107i	−0.337484	−	0.337484i	−0.855419	+	0.517936i	$0.826701\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$	12.0000			0.570137			0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000			0.570137			0.285069	+	0.958507i	$0.407984\pi$
$444$		−	4.00000i		−	0.189832i
$445$	5.65685	+	5.65685i	0.268161	+	0.268161i
$446$	−4.00000			−0.189405
$447$	−4.24264	−	4.24264i	−0.200670	−	0.200670i
$448$	−1.41421	+	1.41421i	−0.0668153	+	0.0668153i
$449$	18.3848	−	18.3848i	0.867631	−	0.867631i	−0.124579	−	0.992210i	$-0.539758\pi$
$449$	18.3848	−	18.3848i	0.867631	−	0.867631i	0.992210	+	0.124579i	$0.0397579\pi$
$450$		−	11.0000i		−	0.518545i
$451$		0			0
$452$	−1.41421	+	1.41421i	−0.0665190	+	0.0665190i
$453$	16.9706	−	16.9706i	0.797347	−	0.797347i
$454$	2.82843	+	2.82843i	0.132745	+	0.132745i
$455$	48.0000			2.25027
$456$	2.82843	+	2.82843i	0.132453	+	0.132453i
$457$		−	22.0000i		−	1.02912i	−0.857455	−	0.514558i	$-0.827956\pi$
$457$		−	22.0000i		−	1.02912i	0.857455	−	0.514558i	$-0.172044\pi$
$458$	2.00000			0.0934539
$459$		0			0
$460$	−24.0000			−1.11901
$461$			10.0000i			0.465746i	0.972507	+	0.232873i	$0.0748127\pi$
$461$			10.0000i			0.465746i	−0.972507	+	0.232873i	$0.925187\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	2.82843	+	2.82843i	0.131306	+	0.131306i
$465$	−16.9706	+	16.9706i	−0.786991	+	0.786991i
$466$	−4.24264	+	4.24264i	−0.196537	+	0.196537i
$467$		−	36.0000i		−	1.66588i	−0.553362	−	0.832941i	$-0.686655\pi$
$467$		−	36.0000i		−	1.66588i	0.553362	−	0.832941i	$-0.313345\pi$
$468$		−	6.00000i		−	0.277350i
$469$	−16.9706	+	16.9706i	−0.783628	+	0.783628i
$470$	11.3137	−	11.3137i	0.521862	−	0.521862i
$471$	4.24264	+	4.24264i	0.195491	+	0.195491i
$472$	12.0000			0.552345
$473$		0			0
$474$		−	10.0000i		−	0.459315i
$475$	44.0000			2.01886
$476$		0			0
$477$	−2.00000			−0.0915737
$478$		−	20.0000i		−	0.914779i
$479$	7.07107	+	7.07107i	0.323085	+	0.323085i	0.849949	−	0.526864i	$-0.176632\pi$
$479$	7.07107	+	7.07107i	0.323085	+	0.323085i	−0.526864	+	0.849949i	$0.676632\pi$
$480$	4.00000			0.182574
$481$	−16.9706	−	16.9706i	−0.773791	−	0.773791i
$482$	12.7279	−	12.7279i	0.579741	−	0.579741i
$483$	−8.48528	+	8.48528i	−0.386094	+	0.386094i
$484$		−	11.0000i		−	0.500000i
$485$		−	24.0000i		−	1.08978i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	−26.8701	+	26.8701i	−1.21760	+	1.21760i	−0.249128	+	0.968471i	$0.580144\pi$
$487$	−26.8701	+	26.8701i	−1.21760	+	1.21760i	−0.968471	+	0.249128i	$0.919856\pi$
$488$	−2.82843	−	2.82843i	−0.128037	−	0.128037i
$489$	12.0000			0.542659
$490$	−8.48528	−	8.48528i	−0.383326	−	0.383326i
$491$			20.0000i			0.902587i	0.892375	+	0.451294i	$0.149037\pi$
$491$			20.0000i			0.902587i	−0.892375	+	0.451294i	$0.850963\pi$
$492$	10.0000			0.450835
$493$		0			0
$494$	24.0000			1.07981
$495$		0			0
$496$	−4.24264	−	4.24264i	−0.190500	−	0.190500i
$497$	−12.0000			−0.538274
$498$	8.48528	+	8.48528i	0.380235	+	0.380235i
$499$	22.6274	−	22.6274i	1.01294	−	1.01294i	0.0130272	−	0.999915i	$-0.495853\pi$
$499$	22.6274	−	22.6274i	1.01294	−	1.01294i	0.999915	−	0.0130272i	$-0.00414679\pi$
$500$	16.9706	−	16.9706i	0.758947	−	0.758947i
$501$			2.00000i			0.0893534i
$502$		−	12.0000i		−	0.535586i
$503$	18.3848	−	18.3848i	0.819737	−	0.819737i	−0.166333	−	0.986070i	$-0.553193\pi$
$503$	18.3848	−	18.3848i	0.819737	−	0.819737i	0.986070	+	0.166333i	$0.0531927\pi$
$504$	1.41421	−	1.41421i	0.0629941	−	0.0629941i
$505$	39.5980	+	39.5980i	1.76209	+	1.76209i
$506$		0			0
$507$	−16.2635	−	16.2635i	−0.722285	−	0.722285i
$508$		−	8.00000i		−	0.354943i
$509$	26.0000			1.15243			0.576215	−	0.817298i	$-0.304529\pi$
$509$	26.0000			1.15243			0.576215	+	0.817298i	$0.304529\pi$
$510$		0			0
$511$	−4.00000			−0.176950
$512$			1.00000i			0.0441942i
$513$	−2.82843	−	2.82843i	−0.124878	−	0.124878i
$514$	18.0000			0.793946
$515$	11.3137	+	11.3137i	0.498542	+	0.498542i
$516$	2.82843	−	2.82843i	0.124515	−	0.124515i
$517$		0			0
$518$		−	8.00000i		−	0.351500i
$519$			4.00000i			0.175581i
$520$	16.9706	−	16.9706i	0.744208	−	0.744208i
$521$	−7.07107	+	7.07107i	−0.309789	+	0.309789i	−0.844828	−	0.535039i	$-0.820297\pi$
$521$	−7.07107	+	7.07107i	−0.309789	+	0.309789i	0.535039	+	0.844828i	$0.320297\pi$
$522$	−2.82843	−	2.82843i	−0.123797	−	0.123797i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	−11.3137	−	11.3137i	−0.494242	−	0.494242i
$525$		−	22.0000i		−	0.960159i
$526$	12.0000			0.523225
$527$		0			0
$528$		0			0
$529$		−	13.0000i		−	0.565217i
$530$	−5.65685	−	5.65685i	−0.245718	−	0.245718i
$531$	−12.0000			−0.520756
$532$	5.65685	+	5.65685i	0.245256	+	0.245256i
$533$	42.4264	−	42.4264i	1.83769	−	1.83769i
$534$	1.41421	−	1.41421i	0.0611990	−	0.0611990i
$535$		0			0
$536$			12.0000i			0.518321i
$537$	−8.48528	+	8.48528i	−0.366167	+	0.366167i
$538$	8.48528	−	8.48528i	0.365826	−	0.365826i
$539$		0			0
$540$	−4.00000			−0.172133
$541$	−8.48528	−	8.48528i	−0.364811	−	0.364811i	0.500770	−	0.865581i	$-0.333050\pi$
$541$	−8.48528	−	8.48528i	−0.364811	−	0.364811i	−0.865581	+	0.500770i	$0.833050\pi$
$542$		−	16.0000i		−	0.687259i
$543$	20.0000			0.858282
$544$		0			0
$545$	−64.0000			−2.74146
$546$		−	12.0000i		−	0.513553i
$547$	−5.65685	−	5.65685i	−0.241870	−	0.241870i	0.575754	−	0.817623i	$-0.304709\pi$
$547$	−5.65685	−	5.65685i	−0.241870	−	0.241870i	−0.817623	+	0.575754i	$0.804709\pi$
$548$	6.00000			0.256307
$549$	2.82843	+	2.82843i	0.120714	+	0.120714i
$550$		0			0
$551$	11.3137	−	11.3137i	0.481980	−	0.481980i
$552$			6.00000i			0.255377i
$553$		−	20.0000i		−	0.850487i
$554$	−5.65685	+	5.65685i	−0.240337	+	0.240337i
$555$	−11.3137	+	11.3137i	−0.480240	+	0.480240i
$556$	−5.65685	−	5.65685i	−0.239904	−	0.239904i
$557$	−14.0000			−0.593199			−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000			−0.593199			−0.296600	+	0.955002i	$0.595853\pi$
$558$	4.24264	+	4.24264i	0.179605	+	0.179605i
$559$		−	24.0000i		−	1.01509i
$560$	8.00000			0.338062
$561$		0			0
$562$	18.0000			0.759284
$563$			4.00000i			0.168580i	0.996441	+	0.0842900i	$0.0268622\pi$
$563$			4.00000i			0.168580i	−0.996441	+	0.0842900i	$0.973138\pi$
$564$	−2.82843	−	2.82843i	−0.119098	−	0.119098i
$565$	8.00000			0.336563
$566$	22.6274	+	22.6274i	0.951101	+	0.951101i
$567$	−1.41421	+	1.41421i	−0.0593914	+	0.0593914i
$568$	−4.24264	+	4.24264i	−0.178017	+	0.178017i
$569$		−	6.00000i		−	0.251533i	−0.992060	−	0.125767i	$-0.959861\pi$
$569$		−	6.00000i		−	0.251533i	0.992060	−	0.125767i	$-0.0401390\pi$
$570$		−	16.0000i		−	0.670166i
$571$	−31.1127	+	31.1127i	−1.30203	+	1.30203i	−0.375002	+	0.927024i	$0.622358\pi$
$571$	−31.1127	+	31.1127i	−1.30203	+	1.30203i	−0.927024	+	0.375002i	$0.877642\pi$
$572$		0			0
$573$	−2.82843	−	2.82843i	−0.118159	−	0.118159i
$574$	20.0000			0.834784
$575$	46.6690	+	46.6690i	1.94623	+	1.94623i
$576$		−	1.00000i		−	0.0416667i
$577$	−30.0000			−1.24892			−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000			−1.24892			−0.624458	+	0.781058i	$0.714680\pi$
$578$		0			0
$579$	−6.00000			−0.249351
$580$		−	16.0000i		−	0.664364i
$581$	16.9706	+	16.9706i	0.704058	+	0.704058i
$582$	−6.00000			−0.248708
$583$		0			0
$584$	−1.41421	+	1.41421i	−0.0585206	+	0.0585206i
$585$	−16.9706	+	16.9706i	−0.701646	+	0.701646i
$586$		−	2.00000i		−	0.0826192i
$587$			36.0000i			1.48588i	0.669359	+	0.742940i	$0.266569\pi$
$587$			36.0000i			1.48588i	−0.669359	+	0.742940i	$0.733431\pi$
$588$	−2.12132	+	2.12132i	−0.0874818	+	0.0874818i
$589$	−16.9706	+	16.9706i	−0.699260	+	0.699260i
$590$	−33.9411	−	33.9411i	−1.39733	−	1.39733i
$591$	8.00000			0.329076
$592$	−2.82843	−	2.82843i	−0.116248	−	0.116248i
$593$			30.0000i			1.23195i	0.787765	+	0.615976i	$0.211238\pi$
$593$			30.0000i			1.23195i	−0.787765	+	0.615976i	$0.788762\pi$
$594$		0			0
$595$		0			0
$596$	−6.00000			−0.245770
$597$			14.0000i			0.572982i
$598$	25.4558	+	25.4558i	1.04097	+	1.04097i
$599$	16.0000			0.653742			0.326871	−	0.945069i	$-0.394006\pi$
$599$	16.0000			0.653742			0.326871	+	0.945069i	$0.394006\pi$
$600$	−7.77817	−	7.77817i	−0.317543	−	0.317543i
$601$	−26.8701	+	26.8701i	−1.09605	+	1.09605i	−0.101185	+	0.994868i	$0.532263\pi$
$601$	−26.8701	+	26.8701i	−1.09605	+	1.09605i	−0.994868	+	0.101185i	$0.967737\pi$
$602$	5.65685	−	5.65685i	0.230556	−	0.230556i
$603$		−	12.0000i		−	0.488678i
$604$		−	24.0000i		−	0.976546i
$605$	−31.1127	+	31.1127i	−1.26491	+	1.26491i
$606$	9.89949	−	9.89949i	0.402139	−	0.402139i
$607$	26.8701	+	26.8701i	1.09062	+	1.09062i	0.995462	+	0.0951600i	$0.0303363\pi$
$607$	26.8701	+	26.8701i	1.09062	+	1.09062i	0.0951600	+	0.995462i	$0.469664\pi$
$608$	4.00000			0.162221
$609$	−5.65685	−	5.65685i	−0.229227	−	0.229227i
$610$			16.0000i			0.647821i
$611$	−24.0000			−0.970936
$612$		0			0
$613$	30.0000			1.21169			0.605844	−	0.795583i	$-0.292835\pi$
$613$	30.0000			1.21169			0.605844	+	0.795583i	$0.292835\pi$
$614$		−	12.0000i		−	0.484281i
$615$	−28.2843	−	28.2843i	−1.14053	−	1.14053i
$616$		0			0
$617$	4.24264	+	4.24264i	0.170802	+	0.170802i	0.787332	−	0.616530i	$-0.211462\pi$
$617$	4.24264	+	4.24264i	0.170802	+	0.170802i	−0.616530	+	0.787332i	$0.711462\pi$
$618$	2.82843	−	2.82843i	0.113776	−	0.113776i
$619$	14.1421	−	14.1421i	0.568420	−	0.568420i	−0.363265	−	0.931686i	$-0.618338\pi$
$619$	14.1421	−	14.1421i	0.568420	−	0.568420i	0.931686	+	0.363265i	$0.118338\pi$
$620$			24.0000i			0.963863i
$621$		−	6.00000i		−	0.240772i
$622$	21.2132	−	21.2132i	0.850572	−	0.850572i
$623$	2.82843	−	2.82843i	0.113319	−	0.113319i
$624$	−4.24264	−	4.24264i	−0.169842	−	0.169842i
$625$	−41.0000			−1.64000
$626$	18.3848	+	18.3848i	0.734803	+	0.734803i
$627$		0			0
$628$	6.00000			0.239426
$629$		0			0
$630$	−8.00000			−0.318728
$631$		−	20.0000i		−	0.796187i	−0.917345	−	0.398094i	$-0.869672\pi$
$631$		−	20.0000i		−	0.796187i	0.917345	−	0.398094i	$-0.130328\pi$
$632$	−7.07107	−	7.07107i	−0.281272	−	0.281272i
$633$	8.00000			0.317971
$634$	−11.3137	−	11.3137i	−0.449325	−	0.449325i
$635$	−22.6274	+	22.6274i	−0.897942	+	0.897942i
$636$	−1.41421	+	1.41421i	−0.0560772	+	0.0560772i
$637$			18.0000i			0.713186i
$638$		0			0
$639$	4.24264	−	4.24264i	0.167836	−	0.167836i
$640$	2.82843	−	2.82843i	0.111803	−	0.111803i
$641$	1.41421	+	1.41421i	0.0558581	+	0.0558581i	0.734484	−	0.678626i	$-0.237424\pi$
$641$	1.41421	+	1.41421i	0.0558581	+	0.0558581i	−0.678626	+	0.734484i	$0.737424\pi$
$642$		0			0
$643$	2.82843	+	2.82843i	0.111542	+	0.111542i	0.760675	−	0.649133i	$-0.224868\pi$
$643$	2.82843	+	2.82843i	0.111542	+	0.111542i	−0.649133	+	0.760675i	$0.724868\pi$
$644$			12.0000i			0.472866i
$645$	−16.0000			−0.629999
$646$		0			0
$647$	28.0000			1.10079			0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000			1.10079			0.550397	+	0.834903i	$0.314476\pi$
$648$			1.00000i			0.0392837i
$649$		0			0
$650$	−66.0000			−2.58873
$651$	8.48528	+	8.48528i	0.332564	+	0.332564i
$652$	8.48528	−	8.48528i	0.332309	−	0.332309i
$653$	−14.1421	+	14.1421i	−0.553425	+	0.553425i	−0.927428	−	0.374003i	$-0.877985\pi$
$653$	−14.1421	+	14.1421i	−0.553425	+	0.553425i	0.374003	+	0.927428i	$0.377985\pi$
$654$			16.0000i			0.625650i
$655$			64.0000i			2.50069i
$656$	7.07107	−	7.07107i	0.276079	−	0.276079i
$657$	1.41421	−	1.41421i	0.0551737	−	0.0551737i
$658$	−5.65685	−	5.65685i	−0.220527	−	0.220527i
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$			14.0000i			0.544537i	0.962221	+	0.272268i	$0.0877739\pi$
$661$			14.0000i			0.544537i	−0.962221	+	0.272268i	$0.912226\pi$
$662$	−20.0000			−0.777322
$663$		0			0
$664$	12.0000			0.465690
$665$		−	32.0000i		−	1.24091i
$666$	2.82843	+	2.82843i	0.109599	+	0.109599i
$667$	24.0000			0.929284
$668$	1.41421	+	1.41421i	0.0547176	+	0.0547176i
$669$	2.82843	−	2.82843i	0.109353	−	0.109353i
$670$	33.9411	−	33.9411i	1.31126	−	1.31126i
$671$		0			0
$672$		−	2.00000i		−	0.0771517i
$673$	18.3848	−	18.3848i	0.708681	−	0.708681i	−0.257577	−	0.966258i	$-0.582924\pi$
$673$	18.3848	−	18.3848i	0.708681	−	0.708681i	0.966258	+	0.257577i	$0.0829240\pi$
$674$	4.24264	−	4.24264i	0.163420	−	0.163420i
$675$	7.77817	+	7.77817i	0.299382	+	0.299382i
$676$	−23.0000			−0.884615
$677$	5.65685	+	5.65685i	0.217411	+	0.217411i	0.807406	−	0.589996i	$-0.200871\pi$
$677$	5.65685	+	5.65685i	0.217411	+	0.217411i	−0.589996	+	0.807406i	$0.700871\pi$
$678$		−	2.00000i		−	0.0768095i
$679$	−12.0000			−0.460518
$680$		0			0
$681$	−4.00000			−0.153280
$682$		0			0
$683$	8.48528	+	8.48528i	0.324680	+	0.324680i	0.850559	−	0.525879i	$-0.176264\pi$
$683$	8.48528	+	8.48528i	0.324680	+	0.324680i	−0.525879	+	0.850559i	$0.676264\pi$
$684$	−4.00000			−0.152944
$685$	−16.9706	−	16.9706i	−0.648412	−	0.648412i
$686$	−14.1421	+	14.1421i	−0.539949	+	0.539949i
$687$	−1.41421	+	1.41421i	−0.0539556	+	0.0539556i
$688$		−	4.00000i		−	0.152499i
$689$			12.0000i			0.457164i
$690$	16.9706	−	16.9706i	0.646058	−	0.646058i
$691$	11.3137	−	11.3137i	0.430394	−	0.430394i	−0.458368	−	0.888762i	$-0.651566\pi$
$691$	11.3137	−	11.3137i	0.430394	−	0.430394i	0.888762	+	0.458368i	$0.151566\pi$
$692$	2.82843	+	2.82843i	0.107521	+	0.107521i
$693$		0			0
$694$	2.82843	+	2.82843i	0.107366	+	0.107366i
$695$			32.0000i			1.21383i
$696$	−4.00000			−0.151620
$697$		0			0
$698$	30.0000			1.13552
$699$		−	6.00000i		−	0.226941i
$700$	−15.5563	−	15.5563i	−0.587975	−	0.587975i
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	4.24264	+	4.24264i	0.160128	+	0.160128i
$703$	−11.3137	+	11.3137i	−0.426705	+	0.426705i
$704$		0			0
$705$			16.0000i			0.602595i
$706$		−	14.0000i		−	0.526897i
$707$	19.7990	−	19.7990i	0.744618	−	0.744618i
$708$	−8.48528	+	8.48528i	−0.318896	+	0.318896i
$709$	11.3137	+	11.3137i	0.424895	+	0.424895i	0.886885	−	0.461990i	$-0.152864\pi$
$709$	11.3137	+	11.3137i	0.424895	+	0.424895i	−0.461990	+	0.886885i	$0.652864\pi$
$710$	24.0000			0.900704
$711$	7.07107	+	7.07107i	0.265186	+	0.265186i
$712$		−	2.00000i		−	0.0749532i
$713$	−36.0000			−1.34821
$714$		0			0
$715$		0			0
$716$			12.0000i			0.448461i
$717$	14.1421	+	14.1421i	0.528148	+	0.528148i
$718$		0			0
$719$	−29.6985	−	29.6985i	−1.10757	−	1.10757i	−0.993470	−	0.114097i	$-0.963603\pi$
$719$	−29.6985	−	29.6985i	−1.10757	−	1.10757i	−0.114097	−	0.993470i	$-0.536397\pi$
$720$	−2.82843	+	2.82843i	−0.105409	+	0.105409i
$721$	5.65685	−	5.65685i	0.210672	−	0.210672i
$722$			3.00000i			0.111648i
$723$			18.0000i			0.669427i
$724$	14.1421	−	14.1421i	0.525588	−	0.525588i
$725$	−31.1127	+	31.1127i	−1.15550	+	1.15550i
$726$	7.77817	+	7.77817i	0.288675	+	0.288675i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$	−8.48528	−	8.48528i	−0.314485	−	0.314485i
$729$		−	1.00000i		−	0.0370370i
$730$	8.00000			0.296093
$731$		0			0
$732$	4.00000			0.147844
$733$		−	18.0000i		−	0.664845i	−0.943131	−	0.332423i	$-0.892134\pi$
$733$		−	18.0000i		−	0.664845i	0.943131	−	0.332423i	$-0.107866\pi$
$734$	−7.07107	−	7.07107i	−0.260998	−	0.260998i
$735$	12.0000			0.442627
$736$	4.24264	+	4.24264i	0.156386	+	0.156386i
$737$		0			0
$738$	−7.07107	+	7.07107i	−0.260290	+	0.260290i
$739$		−	12.0000i		−	0.441427i	−0.975339	−	0.220714i	$-0.929161\pi$
$739$		−	12.0000i		−	0.441427i	0.975339	−	0.220714i	$-0.0708386\pi$
$740$			16.0000i			0.588172i
$741$	−16.9706	+	16.9706i	−0.623429	+	0.623429i
$742$	−2.82843	+	2.82843i	−0.103835	+	0.103835i
$743$	−26.8701	−	26.8701i	−0.985767	−	0.985767i	0.0141333	−	0.999900i	$-0.495501\pi$
$743$	−26.8701	−	26.8701i	−0.985767	−	0.985767i	−0.999900	+	0.0141333i	$0.995501\pi$
$744$	6.00000			0.219971
$745$	16.9706	+	16.9706i	0.621753	+	0.621753i
$746$		−	14.0000i		−	0.512576i
$747$	−12.0000			−0.439057
$748$		0			0
$749$		0			0
$750$			24.0000i			0.876356i
$751$	−24.0416	−	24.0416i	−0.877292	−	0.877292i	0.115962	−	0.993254i	$-0.463005\pi$
$751$	−24.0416	−	24.0416i	−0.877292	−	0.877292i	−0.993254	+	0.115962i	$0.963005\pi$
$752$	−4.00000			−0.145865
$753$	8.48528	+	8.48528i	0.309221	+	0.309221i
$754$	−16.9706	+	16.9706i	−0.618031	+	0.618031i
$755$	−67.8823	+	67.8823i	−2.47049	+	2.47049i
$756$			2.00000i			0.0727393i
$757$			14.0000i			0.508839i	0.967094	+	0.254419i	$0.0818843\pi$
$757$			14.0000i			0.508839i	−0.967094	+	0.254419i	$0.918116\pi$
$758$	−2.82843	+	2.82843i	−0.102733	+	0.102733i
$759$		0			0
$760$	−11.3137	−	11.3137i	−0.410391	−	0.410391i
$761$	−10.0000			−0.362500			−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000			−0.362500			−0.181250	+	0.983437i	$0.558014\pi$
$762$	5.65685	+	5.65685i	0.204926	+	0.204926i
$763$			32.0000i			1.15848i
$764$	−4.00000			−0.144715
$765$		0			0
$766$	−28.0000			−1.01168
$767$			72.0000i			2.59977i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−26.0000			−0.937584			−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000			−0.937584			−0.468792	+	0.883309i	$0.655311\pi$
$770$		0			0
$771$	−12.7279	+	12.7279i	−0.458385	+	0.458385i
$772$	−4.24264	+	4.24264i	−0.152696	+	0.152696i
$773$			42.0000i			1.51064i	0.655359	+	0.755318i	$0.272517\pi$
$773$			42.0000i			1.51064i	−0.655359	+	0.755318i	$0.727483\pi$
$774$			4.00000i			0.143777i
$775$	46.6690	−	46.6690i	1.67640	−	1.67640i
$776$	−4.24264	+	4.24264i	−0.152302	+	0.152302i
$777$	5.65685	+	5.65685i	0.202939	+	0.202939i
$778$	−14.0000			−0.501924
$779$	−28.2843	−	28.2843i

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:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1734.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.82843 + 2.82843i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.41421 - 1.41421i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.82843 + 2.82843i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.41421 - 1.41421i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-2.82843 + 2.82843i) q^{10} +(0.707107 + 0.707107i) q^{12} +6.00000 q^{13} +(1.41421 + 1.41421i) q^{14} -4.00000i q^{15} +1.00000 q^{16} -1.00000 q^{18} -4.00000i q^{19} +(-2.82843 - 2.82843i) q^{20} -2.00000 q^{21} +(4.24264 - 4.24264i) q^{23} +(-0.707107 + 0.707107i) q^{24} +11.0000i q^{25} +6.00000i q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.41421 + 1.41421i) q^{28} +(2.82843 + 2.82843i) q^{29} +4.00000 q^{30} +(-4.24264 - 4.24264i) q^{31} +1.00000i q^{32} +8.00000 q^{35} -1.00000i q^{36} +(-2.82843 - 2.82843i) q^{37} +4.00000 q^{38} +(-4.24264 - 4.24264i) q^{39} +(2.82843 - 2.82843i) q^{40} +(7.07107 - 7.07107i) q^{41} -2.00000i q^{42} -4.00000i q^{43} +(-2.82843 + 2.82843i) q^{45} +(4.24264 + 4.24264i) q^{46} -4.00000 q^{47} +(-0.707107 - 0.707107i) q^{48} +3.00000i q^{49} -11.0000 q^{50} -6.00000 q^{52} +2.00000i q^{53} +(0.707107 + 0.707107i) q^{54} +(-1.41421 - 1.41421i) q^{56} +(-2.82843 + 2.82843i) q^{57} +(-2.82843 + 2.82843i) q^{58} +12.0000i q^{59} +4.00000i q^{60} +(2.82843 - 2.82843i) q^{61} +(4.24264 - 4.24264i) q^{62} +(1.41421 + 1.41421i) q^{63} -1.00000 q^{64} +(16.9706 + 16.9706i) q^{65} -12.0000 q^{67} -6.00000 q^{69} +8.00000i q^{70} +(-4.24264 - 4.24264i) q^{71} +1.00000 q^{72} +(-1.41421 - 1.41421i) q^{73} +(2.82843 - 2.82843i) q^{74} +(7.77817 - 7.77817i) q^{75} +4.00000i q^{76} +(4.24264 - 4.24264i) q^{78} +(7.07107 - 7.07107i) q^{79} +(2.82843 + 2.82843i) q^{80} -1.00000 q^{81} +(7.07107 + 7.07107i) q^{82} +12.0000i q^{83} +2.00000 q^{84} +4.00000 q^{86} -4.00000i q^{87} +2.00000 q^{89} +(-2.82843 - 2.82843i) q^{90} +(8.48528 - 8.48528i) q^{91} +(-4.24264 + 4.24264i) q^{92} +6.00000i q^{93} -4.00000i q^{94} +(11.3137 - 11.3137i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-4.24264 - 4.24264i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4}+O(q^{10}) \) 4 * q - 4 * q^4	\( 4 q - 4 q^{4} + 24 q^{13} + 4 q^{16} - 4 q^{18} - 8 q^{21} + 16 q^{30} + 32 q^{35} + 16 q^{38} - 16 q^{47} - 44 q^{50} - 24 q^{52} - 4 q^{64} - 48 q^{67} - 24 q^{69} + 4 q^{72} - 4 q^{81} + 8 q^{84} + 16 q^{86} + 8 q^{89} - 12 q^{98}+O(q^{100}) \) 4 * q - 4 * q^4 + 24 * q^13 + 4 * q^16 - 4 * q^18 - 8 * q^21 + 16 * q^30 + 32 * q^35 + 16 * q^38 - 16 * q^47 - 44 * q^50 - 24 * q^52 - 4 * q^64 - 48 * q^67 - 24 * q^69 + 4 * q^72 - 4 * q^81 + 8 * q^84 + 16 * q^86 + 8 * q^89 - 12 * q^98

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