LMFDB - Embedded newform 570.2.f.b.341.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(341,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("570.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.f (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			341.4
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	570.341
Dual form			570.2.f.b.341.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(1.00000 + 1.41421i) q^{6} +3.41421 q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(1.00000 + 1.41421i) q^{6} +3.41421 q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +1.00000i q^{10} -2.58579i q^{11} +(1.00000 + 1.41421i) q^{12} -6.24264i q^{13} +3.41421 q^{14} +(-1.41421 + 1.00000i) q^{15} +1.00000 q^{16} +2.82843i q^{17} +(-1.00000 + 2.82843i) q^{18} +(-4.24264 + 1.00000i) q^{19} +1.00000i q^{20} +(3.41421 + 4.82843i) q^{21} -2.58579i q^{22} +6.00000i q^{23} +(1.00000 + 1.41421i) q^{24} -1.00000 q^{25} -6.24264i q^{26} +(-5.00000 + 1.41421i) q^{27} +3.41421 q^{28} -9.07107 q^{29} +(-1.41421 + 1.00000i) q^{30} +1.17157i q^{31} +1.00000 q^{32} +(3.65685 - 2.58579i) q^{33} +2.82843i q^{34} +3.41421i q^{35} +(-1.00000 + 2.82843i) q^{36} -6.24264i q^{37} +(-4.24264 + 1.00000i) q^{38} +(8.82843 - 6.24264i) q^{39} +1.00000i q^{40} +3.07107 q^{41} +(3.41421 + 4.82843i) q^{42} +9.41421 q^{43} -2.58579i q^{44} +(-2.82843 - 1.00000i) q^{45} +6.00000i q^{46} -8.82843i q^{47} +(1.00000 + 1.41421i) q^{48} +4.65685 q^{49} -1.00000 q^{50} +(-4.00000 + 2.82843i) q^{51} -6.24264i q^{52} -8.82843 q^{53} +(-5.00000 + 1.41421i) q^{54} +2.58579 q^{55} +3.41421 q^{56} +(-5.65685 - 5.00000i) q^{57} -9.07107 q^{58} -7.17157 q^{59} +(-1.41421 + 1.00000i) q^{60} +12.4853 q^{61} +1.17157i q^{62} +(-3.41421 + 9.65685i) q^{63} +1.00000 q^{64} +6.24264 q^{65} +(3.65685 - 2.58579i) q^{66} +2.82843i q^{68} +(-8.48528 + 6.00000i) q^{69} +3.41421i q^{70} +2.82843 q^{71} +(-1.00000 + 2.82843i) q^{72} -14.4853 q^{73} -6.24264i q^{74} +(-1.00000 - 1.41421i) q^{75} +(-4.24264 + 1.00000i) q^{76} -8.82843i q^{77} +(8.82843 - 6.24264i) q^{78} -9.31371i q^{79} +1.00000i q^{80} +(-7.00000 - 5.65685i) q^{81} +3.07107 q^{82} +7.17157i q^{83} +(3.41421 + 4.82843i) q^{84} -2.82843 q^{85} +9.41421 q^{86} +(-9.07107 - 12.8284i) q^{87} -2.58579i q^{88} +13.4142 q^{89} +(-2.82843 - 1.00000i) q^{90} -21.3137i q^{91} +6.00000i q^{92} +(-1.65685 + 1.17157i) q^{93} -8.82843i q^{94} +(-1.00000 - 4.24264i) q^{95} +(1.00000 + 1.41421i) q^{96} +9.41421i q^{97} +4.65685 q^{98} +(7.31371 + 2.58579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^6 + 8 * q^7 + 4 * q^8 - 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9} + 4 q^{12} + 8 q^{14} + 4 q^{16} - 4 q^{18} + 8 q^{21} + 4 q^{24} - 4 q^{25} - 20 q^{27} + 8 q^{28} - 8 q^{29} + 4 q^{32} - 8 q^{33} - 4 q^{36} + 24 q^{39} - 16 q^{41} + 8 q^{42} + 32 q^{43} + 4 q^{48} - 4 q^{49} - 4 q^{50} - 16 q^{51} - 24 q^{53} - 20 q^{54} + 16 q^{55} + 8 q^{56} - 8 q^{58} - 40 q^{59} + 16 q^{61} - 8 q^{63} + 4 q^{64} + 8 q^{65} - 8 q^{66} - 4 q^{72} - 24 q^{73} - 4 q^{75} + 24 q^{78} - 28 q^{81} - 16 q^{82} + 8 q^{84} + 32 q^{86} - 8 q^{87} + 48 q^{89} + 16 q^{93} - 4 q^{95} + 4 q^{96} - 4 q^{98} - 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^6 + 8 * q^7 + 4 * q^8 - 4 * q^9 + 4 * q^12 + 8 * q^14 + 4 * q^16 - 4 * q^18 + 8 * q^21 + 4 * q^24 - 4 * q^25 - 20 * q^27 + 8 * q^28 - 8 * q^29 + 4 * q^32 - 8 * q^33 - 4 * q^36 + 24 * q^39 - 16 * q^41 + 8 * q^42 + 32 * q^43 + 4 * q^48 - 4 * q^49 - 4 * q^50 - 16 * q^51 - 24 * q^53 - 20 * q^54 + 16 * q^55 + 8 * q^56 - 8 * q^58 - 40 * q^59 + 16 * q^61 - 8 * q^63 + 4 * q^64 + 8 * q^65 - 8 * q^66 - 4 * q^72 - 24 * q^73 - 4 * q^75 + 24 * q^78 - 28 * q^81 - 16 * q^82 + 8 * q^84 + 32 * q^86 - 8 * q^87 + 48 * q^89 + 16 * q^93 - 4 * q^95 + 4 * q^96 - 4 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$4$	1.00000			0.500000
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	1.00000	+	1.41421i	0.408248	+	0.577350i
$7$	3.41421			1.29045			0.645226	−	0.763992i	$-0.276763\pi$
$7$	3.41421			1.29045			0.645226	+	0.763992i	$0.276763\pi$
$8$	1.00000			0.353553
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$			1.00000i			0.316228i
$11$		−	2.58579i		−	0.779644i	−0.920890	−	0.389822i	$-0.872537\pi$
$11$		−	2.58579i		−	0.779644i	0.920890	−	0.389822i	$-0.127463\pi$
$12$	1.00000	+	1.41421i	0.288675	+	0.408248i
$13$		−	6.24264i		−	1.73140i	−0.500566	−	0.865699i	$-0.666875\pi$
$13$		−	6.24264i		−	1.73140i	0.500566	−	0.865699i	$-0.333125\pi$
$14$	3.41421			0.912487
$15$	−1.41421	+	1.00000i	−0.365148	+	0.258199i
$16$	1.00000			0.250000
$17$			2.82843i			0.685994i	0.939336	+	0.342997i	$0.111442\pi$
$17$			2.82843i			0.685994i	−0.939336	+	0.342997i	$0.888558\pi$
$18$	−1.00000	+	2.82843i	−0.235702	+	0.666667i
$19$	−4.24264	+	1.00000i	−0.973329	+	0.229416i
$19$	−4.24264	+	1.00000i	−0.973329	+	0.229416i
$20$			1.00000i			0.223607i
$21$	3.41421	+	4.82843i	0.745042	+	1.05365i
$22$		−	2.58579i		−	0.551292i
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	1.00000	+	1.41421i	0.204124	+	0.288675i
$25$	−1.00000			−0.200000
$26$		−	6.24264i		−	1.22428i
$27$	−5.00000	+	1.41421i	−0.962250	+	0.272166i
$28$	3.41421			0.645226
$29$	−9.07107			−1.68446			−0.842228	−	0.539122i	$-0.818756\pi$
$29$	−9.07107			−1.68446			−0.842228	+	0.539122i	$0.818756\pi$
$30$	−1.41421	+	1.00000i	−0.258199	+	0.182574i
$31$			1.17157i			0.210421i	0.994450	+	0.105210i	$0.0335516\pi$
$31$			1.17157i			0.210421i	−0.994450	+	0.105210i	$0.966448\pi$
$32$	1.00000			0.176777
$33$	3.65685	−	2.58579i	0.636577	−	0.450128i
$34$			2.82843i			0.485071i
$35$			3.41421i			0.577107i
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$		−	6.24264i		−	1.02628i	−0.858304	−	0.513142i	$-0.828481\pi$
$37$		−	6.24264i		−	1.02628i	0.858304	−	0.513142i	$-0.171519\pi$
$38$	−4.24264	+	1.00000i	−0.688247	+	0.162221i
$39$	8.82843	−	6.24264i	1.41368	−	0.999623i
$40$			1.00000i			0.158114i
$41$	3.07107			0.479620			0.239810	−	0.970820i	$-0.422915\pi$
$41$	3.07107			0.479620			0.239810	+	0.970820i	$0.422915\pi$
$42$	3.41421	+	4.82843i	0.526825	+	0.745042i
$43$	9.41421			1.43565			0.717827	−	0.696221i	$-0.245137\pi$
$43$	9.41421			1.43565			0.717827	+	0.696221i	$0.245137\pi$
$44$		−	2.58579i		−	0.389822i
$45$	−2.82843	−	1.00000i	−0.421637	−	0.149071i
$46$			6.00000i			0.884652i
$47$		−	8.82843i		−	1.28776i	−0.765127	−	0.643879i	$-0.777324\pi$
$47$		−	8.82843i		−	1.28776i	0.765127	−	0.643879i	$-0.222676\pi$
$48$	1.00000	+	1.41421i	0.144338	+	0.204124i
$49$	4.65685			0.665265
$50$	−1.00000			−0.141421
$51$	−4.00000	+	2.82843i	−0.560112	+	0.396059i
$52$		−	6.24264i		−	0.865699i
$53$	−8.82843			−1.21268			−0.606339	−	0.795206i	$-0.707362\pi$
$53$	−8.82843			−1.21268			−0.606339	+	0.795206i	$0.707362\pi$
$54$	−5.00000	+	1.41421i	−0.680414	+	0.192450i
$55$	2.58579			0.348667
$56$	3.41421			0.456243
$57$	−5.65685	−	5.00000i	−0.749269	−	0.662266i
$58$	−9.07107			−1.19109
$59$	−7.17157			−0.933659			−0.466830	−	0.884347i	$-0.654604\pi$
$59$	−7.17157			−0.933659			−0.466830	+	0.884347i	$0.654604\pi$
$60$	−1.41421	+	1.00000i	−0.182574	+	0.129099i
$61$	12.4853			1.59858			0.799288	−	0.600948i	$-0.205210\pi$
$61$	12.4853			1.59858			0.799288	+	0.600948i	$0.205210\pi$
$62$			1.17157i			0.148790i
$63$	−3.41421	+	9.65685i	−0.430150	+	1.21665i
$64$	1.00000			0.125000
$65$	6.24264			0.774304
$66$	3.65685	−	2.58579i	0.450128	−	0.318288i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$			2.82843i			0.342997i
$69$	−8.48528	+	6.00000i	−1.02151	+	0.722315i
$70$			3.41421i			0.408077i
$71$	2.82843			0.335673			0.167836	−	0.985815i	$-0.446322\pi$
$71$	2.82843			0.335673			0.167836	+	0.985815i	$0.446322\pi$
$72$	−1.00000	+	2.82843i	−0.117851	+	0.333333i
$73$	−14.4853			−1.69537			−0.847687	−	0.530497i	$-0.822005\pi$
$73$	−14.4853			−1.69537			−0.847687	+	0.530497i	$0.822005\pi$
$74$		−	6.24264i		−	0.725692i
$75$	−1.00000	−	1.41421i	−0.115470	−	0.163299i
$76$	−4.24264	+	1.00000i	−0.486664	+	0.114708i
$77$		−	8.82843i		−	1.00609i
$78$	8.82843	−	6.24264i	0.999623	−	0.706840i
$79$		−	9.31371i		−	1.04787i	−0.851757	−	0.523937i	$-0.824463\pi$
$79$		−	9.31371i		−	1.04787i	0.851757	−	0.523937i	$-0.175537\pi$
$80$			1.00000i			0.111803i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$	3.07107			0.339143
$83$			7.17157i			0.787182i	0.919286	+	0.393591i	$0.128767\pi$
$83$			7.17157i			0.787182i	−0.919286	+	0.393591i	$0.871233\pi$
$84$	3.41421	+	4.82843i	0.372521	+	0.526825i
$85$	−2.82843			−0.306786
$86$	9.41421			1.01516
$87$	−9.07107	−	12.8284i	−0.972521	−	1.37535i
$88$		−	2.58579i		−	0.275646i
$89$	13.4142			1.42190			0.710952	−	0.703241i	$-0.248264\pi$
$89$	13.4142			1.42190			0.710952	+	0.703241i	$0.248264\pi$
$90$	−2.82843	−	1.00000i	−0.298142	−	0.105409i
$91$		−	21.3137i		−	2.23428i
$92$			6.00000i			0.625543i
$93$	−1.65685	+	1.17157i	−0.171808	+	0.121486i
$94$		−	8.82843i		−	0.910583i
$95$	−1.00000	−	4.24264i	−0.102598	−	0.435286i
$96$	1.00000	+	1.41421i	0.102062	+	0.144338i
$97$			9.41421i			0.955869i	0.878396	+	0.477934i	$0.158614\pi$
$97$			9.41421i			0.955869i	−0.878396	+	0.477934i	$0.841386\pi$
$98$	4.65685			0.470413
$99$	7.31371	+	2.58579i	0.735055	+	0.259881i
$100$	−1.00000			−0.100000
$101$			3.65685i			0.363871i	0.983311	+	0.181935i	$0.0582361\pi$
$101$			3.65685i			0.363871i	−0.983311	+	0.181935i	$0.941764\pi$
$102$	−4.00000	+	2.82843i	−0.396059	+	0.280056i
$103$		−	15.6569i		−	1.54272i	−0.636402	−	0.771358i	$-0.719578\pi$
$103$		−	15.6569i		−	1.54272i	0.636402	−	0.771358i	$-0.280422\pi$
$104$		−	6.24264i		−	0.612141i
$105$	−4.82843	+	3.41421i	−0.471206	+	0.333193i
$106$	−8.82843			−0.857493
$107$	−7.65685			−0.740216			−0.370108	−	0.928989i	$-0.620679\pi$
$107$	−7.65685			−0.740216			−0.370108	+	0.928989i	$0.620679\pi$
$108$	−5.00000	+	1.41421i	−0.481125	+	0.136083i
$109$			13.6569i			1.30809i	0.756456	+	0.654045i	$0.226929\pi$
$109$			13.6569i			1.30809i	−0.756456	+	0.654045i	$0.773071\pi$
$110$	2.58579			0.246545
$111$	8.82843	−	6.24264i	0.837957	−	0.592525i
$112$	3.41421			0.322613
$113$	7.17157			0.674645			0.337322	−	0.941389i	$-0.390479\pi$
$113$	7.17157			0.674645			0.337322	+	0.941389i	$0.390479\pi$
$114$	−5.65685	−	5.00000i	−0.529813	−	0.468293i
$115$	−6.00000			−0.559503
$116$	−9.07107			−0.842228
$117$	17.6569	+	6.24264i	1.63238	+	0.577132i
$118$	−7.17157			−0.660197
$119$			9.65685i			0.885242i
$120$	−1.41421	+	1.00000i	−0.129099	+	0.0912871i
$121$	4.31371			0.392155
$122$	12.4853			1.13036
$123$	3.07107	+	4.34315i	0.276909	+	0.391608i
$124$			1.17157i			0.105210i
$125$		−	1.00000i		−	0.0894427i
$126$	−3.41421	+	9.65685i	−0.304162	+	0.860301i
$127$			7.17157i			0.636374i	0.948028	+	0.318187i	$0.103074\pi$
$127$			7.17157i			0.636374i	−0.948028	+	0.318187i	$0.896926\pi$
$128$	1.00000			0.0883883
$129$	9.41421	+	13.3137i	0.828875	+	1.17221i
$130$	6.24264			0.547516
$131$		−	19.0711i		−	1.66625i	−0.553087	−	0.833123i	$-0.686550\pi$
$131$		−	19.0711i		−	1.66625i	0.553087	−	0.833123i	$-0.313450\pi$
$132$	3.65685	−	2.58579i	0.318288	−	0.225064i
$133$	−14.4853	+	3.41421i	−1.25603	+	0.296050i
$134$		0			0
$135$	−1.41421	−	5.00000i	−0.121716	−	0.430331i
$136$			2.82843i			0.242536i
$137$			2.48528i			0.212332i	0.994348	+	0.106166i	$0.0338575\pi$
$137$			2.48528i			0.212332i	−0.994348	+	0.106166i	$0.966143\pi$
$138$	−8.48528	+	6.00000i	−0.722315	+	0.510754i
$139$	−10.1421			−0.860245			−0.430122	−	0.902771i	$-0.641530\pi$
$139$	−10.1421			−0.860245			−0.430122	+	0.902771i	$0.641530\pi$
$140$			3.41421i			0.288554i
$141$	12.4853	−	8.82843i	1.05145	−	0.743488i
$142$	2.82843			0.237356
$143$	−16.1421			−1.34987
$144$	−1.00000	+	2.82843i	−0.0833333	+	0.235702i
$145$		−	9.07107i		−	0.753311i
$146$	−14.4853			−1.19881
$147$	4.65685	+	6.58579i	0.384091	+	0.543187i
$148$		−	6.24264i		−	0.513142i
$149$		−	2.48528i		−	0.203602i	−0.994805	−	0.101801i	$-0.967539\pi$
$149$		−	2.48528i		−	0.203602i	0.994805	−	0.101801i	$-0.0324605\pi$
$150$	−1.00000	−	1.41421i	−0.0816497	−	0.115470i
$151$		−	3.51472i		−	0.286024i	−0.989721	−	0.143012i	$-0.954321\pi$
$151$		−	3.51472i		−	0.286024i	0.989721	−	0.143012i	$-0.0456787\pi$
$152$	−4.24264	+	1.00000i	−0.344124	+	0.0811107i
$153$	−8.00000	−	2.82843i	−0.646762	−	0.228665i
$154$		−	8.82843i		−	0.711415i
$155$	−1.17157			−0.0941030
$156$	8.82843	−	6.24264i	0.706840	−	0.499811i
$157$	15.7990			1.26090			0.630448	−	0.776231i	$-0.282871\pi$
$157$	15.7990			1.26090			0.630448	+	0.776231i	$0.282871\pi$
$158$		−	9.31371i		−	0.740959i
$159$	−8.82843	−	12.4853i	−0.700140	−	0.990147i
$160$			1.00000i			0.0790569i
$161$			20.4853i			1.61447i
$162$	−7.00000	−	5.65685i	−0.549972	−	0.444444i
$163$	−12.7279			−0.996928			−0.498464	−	0.866910i	$-0.666102\pi$
$163$	−12.7279			−0.996928			−0.498464	+	0.866910i	$0.666102\pi$
$164$	3.07107			0.239810
$165$	2.58579	+	3.65685i	0.201303	+	0.284686i
$166$			7.17157i			0.556622i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$	3.41421	+	4.82843i	0.263412	+	0.372521i
$169$	−25.9706			−1.99774
$170$	−2.82843			−0.216930
$171$	1.41421	−	13.0000i	0.108148	−	0.994135i
$172$	9.41421			0.717827
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$	−9.07107	−	12.8284i	−0.687676	−	0.972521i
$175$	−3.41421			−0.258090
$176$		−	2.58579i		−	0.194911i
$177$	−7.17157	−	10.1421i	−0.539048	−	0.762330i
$178$	13.4142			1.00544
$179$	17.7990			1.33036			0.665179	−	0.746684i	$-0.268355\pi$
$179$	17.7990			1.33036			0.665179	+	0.746684i	$0.268355\pi$
$180$	−2.82843	−	1.00000i	−0.210819	−	0.0745356i
$181$		−	5.17157i		−	0.384400i	−0.981356	−	0.192200i	$-0.938438\pi$
$181$		−	5.17157i		−	0.384400i	0.981356	−	0.192200i	$-0.0615622\pi$
$182$		−	21.3137i		−	1.57988i
$183$	12.4853	+	17.6569i	0.922939	+	1.30523i
$184$			6.00000i			0.442326i
$185$	6.24264			0.458968
$186$	−1.65685	+	1.17157i	−0.121486	+	0.0859039i
$187$	7.31371			0.534831
$188$		−	8.82843i		−	0.643879i
$189$	−17.0711	+	4.82843i	−1.24174	+	0.351216i
$190$	−1.00000	−	4.24264i	−0.0725476	−	0.307794i
$191$		−	1.75736i		−	0.127158i	−0.997977	−	0.0635790i	$-0.979749\pi$
$191$		−	1.75736i		−	0.127158i	0.997977	−	0.0635790i	$-0.0202515\pi$
$192$	1.00000	+	1.41421i	0.0721688	+	0.102062i
$193$			11.5563i			0.831844i	0.909400	+	0.415922i	$0.136541\pi$
$193$			11.5563i			0.831844i	−0.909400	+	0.415922i	$0.863459\pi$
$194$			9.41421i			0.675901i
$195$	6.24264	+	8.82843i	0.447045	+	0.632217i
$196$	4.65685			0.332632
$197$			10.1421i			0.722597i	0.932450	+	0.361299i	$0.117667\pi$
$197$			10.1421i			0.722597i	−0.932450	+	0.361299i	$0.882333\pi$
$198$	7.31371	+	2.58579i	0.519763	+	0.183764i
$199$	16.9706			1.20301			0.601506	−	0.798869i	$-0.294568\pi$
$199$	16.9706			1.20301			0.601506	+	0.798869i	$0.294568\pi$
$200$	−1.00000			−0.0707107
$201$		0			0
$202$			3.65685i			0.257295i
$203$	−30.9706			−2.17371
$204$	−4.00000	+	2.82843i	−0.280056	+	0.198030i
$205$			3.07107i			0.214493i
$206$		−	15.6569i		−	1.09086i
$207$	−16.9706	−	6.00000i	−1.17954	−	0.417029i
$208$		−	6.24264i		−	0.432849i
$209$	2.58579	+	10.9706i	0.178863	+	0.758850i
$210$	−4.82843	+	3.41421i	−0.333193	+	0.235603i
$211$			2.00000i			0.137686i	0.997628	+	0.0688428i	$0.0219307\pi$
$211$			2.00000i			0.137686i	−0.997628	+	0.0688428i	$0.978069\pi$
$212$	−8.82843			−0.606339
$213$	2.82843	+	4.00000i	0.193801	+	0.274075i
$214$	−7.65685			−0.523412
$215$			9.41421i			0.642044i
$216$	−5.00000	+	1.41421i	−0.340207	+	0.0962250i
$217$			4.00000i			0.271538i
$218$			13.6569i			0.924959i
$219$	−14.4853	−	20.4853i	−0.978825	−	1.38427i
$220$	2.58579			0.174334
$221$	17.6569			1.18773
$222$	8.82843	−	6.24264i	0.592525	−	0.418979i
$223$			18.0000i			1.20537i	0.797980	+	0.602685i	$0.205902\pi$
$223$			18.0000i			1.20537i	−0.797980	+	0.602685i	$0.794098\pi$
$224$	3.41421			0.228122
$225$	1.00000	−	2.82843i	0.0666667	−	0.188562i
$226$	7.17157			0.477046
$227$	−13.6569			−0.906437			−0.453219	−	0.891399i	$-0.649724\pi$
$227$	−13.6569			−0.906437			−0.453219	+	0.891399i	$0.649724\pi$
$228$	−5.65685	−	5.00000i	−0.374634	−	0.331133i
$229$	−8.48528			−0.560723			−0.280362	−	0.959894i	$-0.590454\pi$
$229$	−8.48528			−0.560723			−0.280362	+	0.959894i	$0.590454\pi$
$230$	−6.00000			−0.395628
$231$	12.4853	−	8.82843i	0.821471	−	0.580868i
$232$	−9.07107			−0.595545
$233$			21.7990i			1.42810i	0.700095	+	0.714050i	$0.253141\pi$
$233$			21.7990i			1.42810i	−0.700095	+	0.714050i	$0.746859\pi$
$234$	17.6569	+	6.24264i	1.15426	+	0.408094i
$235$	8.82843			0.575903
$236$	−7.17157			−0.466830
$237$	13.1716	−	9.31371i	0.855586	−	0.604990i
$238$			9.65685i			0.625961i
$239$			19.8995i			1.28719i	0.765366	+	0.643596i	$0.222558\pi$
$239$			19.8995i			1.28719i	−0.765366	+	0.643596i	$0.777442\pi$
$240$	−1.41421	+	1.00000i	−0.0912871	+	0.0645497i
$241$			8.48528i			0.546585i	0.961931	+	0.273293i	$0.0881127\pi$
$241$			8.48528i			0.546585i	−0.961931	+	0.273293i	$0.911887\pi$
$242$	4.31371			0.277296
$243$	1.00000	−	15.5563i	0.0641500	−	0.997940i
$244$	12.4853			0.799288
$245$			4.65685i			0.297516i
$246$	3.07107	+	4.34315i	0.195804	+	0.276909i
$247$	6.24264	+	26.4853i	0.397210	+	1.68522i
$248$			1.17157i			0.0743950i
$249$	−10.1421	+	7.17157i	−0.642732	+	0.454480i
$250$		−	1.00000i		−	0.0632456i
$251$		−	19.0711i		−	1.20376i	−0.798588	−	0.601878i	$-0.794420\pi$
$251$		−	19.0711i		−	1.20376i	0.798588	−	0.601878i	$-0.205580\pi$
$252$	−3.41421	+	9.65685i	−0.215075	+	0.608325i
$253$	15.5147			0.975402
$254$			7.17157i			0.449985i
$255$	−2.82843	−	4.00000i	−0.177123	−	0.250490i
$256$	1.00000			0.0625000
$257$	−0.142136			−0.00886618			−0.00443309	−	0.999990i	$-0.501411\pi$
$257$	−0.142136			−0.00886618			−0.00443309	+	0.999990i	$0.501411\pi$
$258$	9.41421	+	13.3137i	0.586103	+	0.828875i
$259$		−	21.3137i		−	1.32437i
$260$	6.24264			0.387152
$261$	9.07107	−	25.6569i	0.561485	−	1.58812i
$262$		−	19.0711i		−	1.17821i
$263$			16.8284i			1.03769i	0.854870	+	0.518843i	$0.173637\pi$
$263$			16.8284i			1.03769i	−0.854870	+	0.518843i	$0.826363\pi$
$264$	3.65685	−	2.58579i	0.225064	−	0.159144i
$265$		−	8.82843i		−	0.542326i
$266$	−14.4853	+	3.41421i	−0.888150	+	0.209339i
$267$	13.4142	+	18.9706i	0.820937	+	1.16098i
$268$		0			0
$269$	12.3848			0.755113			0.377557	−	0.925987i	$-0.376764\pi$
$269$	12.3848			0.755113			0.377557	+	0.925987i	$0.376764\pi$
$270$	−1.41421	−	5.00000i	−0.0860663	−	0.304290i
$271$	4.97056			0.301940			0.150970	−	0.988538i	$-0.451760\pi$
$271$	4.97056			0.301940			0.150970	+	0.988538i	$0.451760\pi$
$272$			2.82843i			0.171499i
$273$	30.1421	−	21.3137i	1.82429	−	1.28996i
$274$			2.48528i			0.150141i
$275$			2.58579i			0.155929i
$276$	−8.48528	+	6.00000i	−0.510754	+	0.361158i
$277$	−8.97056			−0.538989			−0.269494	−	0.963002i	$-0.586857\pi$
$277$	−8.97056			−0.538989			−0.269494	+	0.963002i	$0.586857\pi$
$278$	−10.1421			−0.608285
$279$	−3.31371	−	1.17157i	−0.198387	−	0.0701402i
$280$			3.41421i			0.204038i
$281$	−15.0711			−0.899065			−0.449532	−	0.893264i	$-0.648409\pi$
$281$	−15.0711			−0.899065			−0.449532	+	0.893264i	$0.648409\pi$
$282$	12.4853	−	8.82843i	0.743488	−	0.525725i
$283$	−12.7279			−0.756596			−0.378298	−	0.925684i	$-0.623491\pi$
$283$	−12.7279			−0.756596			−0.378298	+	0.925684i	$0.623491\pi$
$284$	2.82843			0.167836
$285$	5.00000	−	5.65685i	0.296174	−	0.335083i
$286$	−16.1421			−0.954504
$287$	10.4853			0.618927
$288$	−1.00000	+	2.82843i	−0.0589256	+	0.166667i
$289$	9.00000			0.529412
$290$		−	9.07107i		−	0.532671i
$291$	−13.3137	+	9.41421i	−0.780463	+	0.551871i
$292$	−14.4853			−0.847687
$293$	8.82843			0.515762			0.257881	−	0.966177i	$-0.416976\pi$
$293$	8.82843			0.515762			0.257881	+	0.966177i	$0.416976\pi$
$294$	4.65685	+	6.58579i	0.271593	+	0.384091i
$295$		−	7.17157i		−	0.417545i
$296$		−	6.24264i		−	0.362846i
$297$	3.65685	+	12.9289i	0.212192	+	0.750213i
$298$		−	2.48528i		−	0.143968i
$299$	37.4558			2.16613
$300$	−1.00000	−	1.41421i	−0.0577350	−	0.0816497i
$301$	32.1421			1.85264
$302$		−	3.51472i		−	0.202249i
$303$	−5.17157	+	3.65685i	−0.297099	+	0.210081i
$304$	−4.24264	+	1.00000i	−0.243332	+	0.0573539i
$305$			12.4853i			0.714905i
$306$	−8.00000	−	2.82843i	−0.457330	−	0.161690i
$307$		−	10.1421i		−	0.578842i	−0.957202	−	0.289421i	$-0.906537\pi$
$307$		−	10.1421i		−	0.578842i	0.957202	−	0.289421i	$-0.0934628\pi$
$308$		−	8.82843i		−	0.503046i
$309$	22.1421	−	15.6569i	1.25962	−	0.890687i
$310$	−1.17157			−0.0665409
$311$			9.07107i			0.514373i	0.966362	+	0.257187i	$0.0827955\pi$
$311$			9.07107i			0.514373i	−0.966362	+	0.257187i	$0.917205\pi$
$312$	8.82843	−	6.24264i	0.499811	−	0.353420i
$313$	−11.1716			−0.631455			−0.315727	−	0.948850i	$-0.602248\pi$
$313$	−11.1716			−0.631455			−0.315727	+	0.948850i	$0.602248\pi$
$314$	15.7990			0.891589
$315$	−9.65685	−	3.41421i	−0.544102	−	0.192369i
$316$		−	9.31371i		−	0.523937i
$317$	−11.6569			−0.654714			−0.327357	−	0.944901i	$-0.606158\pi$
$317$	−11.6569			−0.654714			−0.327357	+	0.944901i	$0.606158\pi$
$318$	−8.82843	−	12.4853i	−0.495074	−	0.700140i
$319$			23.4558i			1.31328i
$320$			1.00000i			0.0559017i
$321$	−7.65685	−	10.8284i	−0.427364	−	0.604384i
$322$			20.4853i			1.14160i
$323$	−2.82843	−	12.0000i	−0.157378	−	0.667698i
$324$	−7.00000	−	5.65685i	−0.388889	−	0.314270i
$325$			6.24264i			0.346279i
$326$	−12.7279			−0.704934
$327$	−19.3137	+	13.6569i	−1.06805	+	0.755226i
$328$	3.07107			0.169571
$329$		−	30.1421i		−	1.66179i
$330$	2.58579	+	3.65685i	0.142343	+	0.201303i
$331$			16.9706i			0.932786i	0.884577	+	0.466393i	$0.154447\pi$
$331$			16.9706i			0.932786i	−0.884577	+	0.466393i	$0.845553\pi$
$332$			7.17157i			0.393591i
$333$	17.6569	+	6.24264i	0.967590	+	0.342095i
$334$		0			0
$335$		0			0
$336$	3.41421	+	4.82843i	0.186261	+	0.263412i
$337$			13.2132i			0.719769i	0.932997	+	0.359885i	$0.117184\pi$
$337$			13.2132i			0.719769i	−0.932997	+	0.359885i	$0.882816\pi$
$338$	−25.9706			−1.41261
$339$	7.17157	+	10.1421i	0.389506	+	0.550845i
$340$	−2.82843			−0.153393
$341$	3.02944			0.164053
$342$	1.41421	−	13.0000i	0.0764719	−	0.702959i
$343$	−8.00000			−0.431959
$344$	9.41421			0.507580
$345$	−6.00000	−	8.48528i	−0.323029	−	0.456832i
$346$	6.00000			0.322562
$347$		−	26.2843i		−	1.41101i	−0.708703	−	0.705507i	$-0.750719\pi$
$347$		−	26.2843i		−	1.41101i	0.708703	−	0.705507i	$-0.249281\pi$
$348$	−9.07107	−	12.8284i	−0.486260	−	0.687676i
$349$	22.9706			1.22959			0.614793	−	0.788688i	$-0.289240\pi$
$349$	22.9706			1.22959			0.614793	+	0.788688i	$0.289240\pi$
$350$	−3.41421			−0.182497
$351$	8.82843	+	31.2132i	0.471227	+	1.66604i
$352$		−	2.58579i		−	0.137823i
$353$		−	3.17157i		−	0.168806i	−0.996432	−	0.0844029i	$-0.973102\pi$
$353$		−	3.17157i		−	0.168806i	0.996432	−	0.0844029i	$-0.0268983\pi$
$354$	−7.17157	−	10.1421i	−0.381165	−	0.539048i
$355$			2.82843i			0.150117i
$356$	13.4142			0.710952
$357$	−13.6569	+	9.65685i	−0.722797	+	0.511095i
$358$	17.7990			0.940706
$359$		−	16.5858i		−	0.875364i	−0.899130	−	0.437682i	$-0.855800\pi$
$359$		−	16.5858i		−	0.875364i	0.899130	−	0.437682i	$-0.144200\pi$
$360$	−2.82843	−	1.00000i	−0.149071	−	0.0527046i
$361$	17.0000	−	8.48528i	0.894737	−	0.446594i
$362$		−	5.17157i		−	0.271812i
$363$	4.31371	+	6.10051i	0.226411	+	0.320193i
$364$		−	21.3137i		−	1.11714i
$365$		−	14.4853i		−	0.758194i
$366$	12.4853	+	17.6569i	0.652616	+	0.922939i
$367$	−5.75736			−0.300532			−0.150266	−	0.988646i	$-0.548013\pi$
$367$	−5.75736			−0.300532			−0.150266	+	0.988646i	$0.548013\pi$
$368$			6.00000i			0.312772i
$369$	−3.07107	+	8.68629i	−0.159873	+	0.452190i
$370$	6.24264			0.324539
$371$	−30.1421			−1.56490
$372$	−1.65685	+	1.17157i	−0.0859039	+	0.0607432i
$373$			34.0416i			1.76261i	0.472549	+	0.881304i	$0.343334\pi$
$373$			34.0416i			1.76261i	−0.472549	+	0.881304i	$0.656666\pi$
$374$	7.31371			0.378183
$375$	1.41421	−	1.00000i	0.0730297	−	0.0516398i
$376$		−	8.82843i		−	0.455291i
$377$			56.6274i			2.91646i
$378$	−17.0711	+	4.82843i	−0.878041	+	0.248347i
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$	−1.00000	−	4.24264i	−0.0512989	−	0.217643i
$381$	−10.1421	+	7.17157i	−0.519597	+	0.367411i
$382$		−	1.75736i		−	0.0899143i
$383$	3.85786			0.197128			0.0985638	−	0.995131i	$-0.468575\pi$
$383$	3.85786			0.197128			0.0985638	+	0.995131i	$0.468575\pi$
$384$	1.00000	+	1.41421i	0.0510310	+	0.0721688i
$385$	8.82843			0.449938
$386$			11.5563i			0.588203i
$387$	−9.41421	+	26.6274i	−0.478551	+	1.35355i
$388$			9.41421i			0.477934i
$389$			31.6569i			1.60507i	0.596608	+	0.802533i	$0.296515\pi$
$389$			31.6569i			1.60507i	−0.596608	+	0.802533i	$0.703485\pi$
$390$	6.24264	+	8.82843i	0.316108	+	0.447045i
$391$	−16.9706			−0.858238
$392$	4.65685			0.235207
$393$	26.9706	−	19.0711i	1.36048	−	0.962008i
$394$			10.1421i			0.510953i
$395$	9.31371			0.468624
$396$	7.31371	+	2.58579i	0.367528	+	0.129941i
$397$	−16.9706			−0.851728			−0.425864	−	0.904787i	$-0.640030\pi$
$397$	−16.9706			−0.851728			−0.425864	+	0.904787i	$0.640030\pi$
$398$	16.9706			0.850657
$399$	−19.3137	−	17.0711i	−0.966895	−	0.854622i
$400$	−1.00000			−0.0500000
$401$	18.3848			0.918092			0.459046	−	0.888413i	$-0.348191\pi$
$401$	18.3848			0.918092			0.459046	+	0.888413i	$0.348191\pi$
$402$		0			0
$403$	7.31371			0.364322
$404$			3.65685i			0.181935i
$405$	5.65685	−	7.00000i	0.281091	−	0.347833i
$406$	−30.9706			−1.53704
$407$	−16.1421			−0.800136
$408$	−4.00000	+	2.82843i	−0.198030	+	0.140028i
$409$			12.4853i			0.617357i	0.951166	+	0.308679i	$0.0998868\pi$
$409$			12.4853i			0.617357i	−0.951166	+	0.308679i	$0.900113\pi$
$410$			3.07107i			0.151669i
$411$	−3.51472	+	2.48528i	−0.173368	+	0.122590i
$412$		−	15.6569i		−	0.771358i
$413$	−24.4853			−1.20484
$414$	−16.9706	−	6.00000i	−0.834058	−	0.294884i
$415$	−7.17157			−0.352039
$416$		−	6.24264i		−	0.306071i
$417$	−10.1421	−	14.3431i	−0.496663	−	0.702387i
$418$	2.58579	+	10.9706i	0.126475	+	0.536588i
$419$		−	30.3848i		−	1.48439i	−0.670182	−	0.742197i	$-0.733784\pi$
$419$		−	30.3848i		−	1.48439i	0.670182	−	0.742197i	$-0.266216\pi$
$420$	−4.82843	+	3.41421i	−0.235603	+	0.166597i
$421$			32.2843i			1.57344i	0.617311	+	0.786720i	$0.288222\pi$
$421$			32.2843i			1.57344i	−0.617311	+	0.786720i	$0.711778\pi$
$422$			2.00000i			0.0973585i
$423$	24.9706	+	8.82843i	1.21411	+	0.429253i
$424$	−8.82843			−0.428746
$425$		−	2.82843i		−	0.137199i
$426$	2.82843	+	4.00000i	0.137038	+	0.193801i
$427$	42.6274			2.06289
$428$	−7.65685			−0.370108
$429$	−16.1421	−	22.8284i	−0.779350	−	1.10217i
$430$			9.41421i			0.453994i
$431$	3.31371			0.159616			0.0798079	−	0.996810i	$-0.474569\pi$
$431$	3.31371			0.159616			0.0798079	+	0.996810i	$0.474569\pi$
$432$	−5.00000	+	1.41421i	−0.240563	+	0.0680414i
$433$		−	22.3848i		−	1.07574i	−0.843027	−	0.537872i	$-0.819228\pi$
$433$		−	22.3848i		−	1.07574i	0.843027	−	0.537872i	$-0.180772\pi$
$434$			4.00000i			0.192006i
$435$	12.8284	−	9.07107i	0.615076	−	0.434924i
$436$			13.6569i			0.654045i
$437$	−6.00000	−	25.4558i	−0.287019	−	1.21772i
$438$	−14.4853	−	20.4853i	−0.692134	−	0.978825i
$439$			27.9411i			1.33356i	0.745256	+	0.666779i	$0.232327\pi$
$439$			27.9411i			1.33356i	−0.745256	+	0.666779i	$0.767673\pi$
$440$	2.58579			0.123273
$441$	−4.65685	+	13.1716i	−0.221755	+	0.627218i
$442$	17.6569			0.839851
$443$		−	18.0000i		−	0.855206i	−0.903967	−	0.427603i	$-0.859358\pi$
$443$		−	18.0000i		−	0.855206i	0.903967	−	0.427603i	$-0.140642\pi$
$444$	8.82843	−	6.24264i	0.418979	−	0.296263i
$445$			13.4142i			0.635895i
$446$			18.0000i			0.852325i
$447$	3.51472	−	2.48528i	0.166240	−	0.117550i
$448$	3.41421			0.161306
$449$	−7.75736			−0.366092			−0.183046	−	0.983104i	$-0.558596\pi$
$449$	−7.75736			−0.366092			−0.183046	+	0.983104i	$0.558596\pi$
$450$	1.00000	−	2.82843i	0.0471405	−	0.133333i
$451$		−	7.94113i		−	0.373933i
$452$	7.17157			0.337322
$453$	4.97056	−	3.51472i	0.233537	−	0.165136i
$454$	−13.6569			−0.640948
$455$	21.3137			0.999202
$456$	−5.65685	−	5.00000i	−0.264906	−	0.234146i
$457$	4.82843			0.225864			0.112932	−	0.993603i	$-0.463976\pi$
$457$	4.82843			0.225864			0.112932	+	0.993603i	$0.463976\pi$
$458$	−8.48528			−0.396491
$459$	−4.00000	−	14.1421i	−0.186704	−	0.660098i
$460$	−6.00000			−0.279751
$461$		−	0.142136i		−	0.00661992i	−0.999995	−	0.00330996i	$-0.998946\pi$
$461$		−	0.142136i		−	0.00661992i	0.999995	−	0.00330996i	$-0.00105359\pi$
$462$	12.4853	−	8.82843i	0.580868	−	0.410736i
$463$	−23.2132			−1.07881			−0.539405	−	0.842047i	$-0.681351\pi$
$463$	−23.2132			−1.07881			−0.539405	+	0.842047i	$0.681351\pi$
$464$	−9.07107			−0.421114
$465$	−1.17157	−	1.65685i	−0.0543304	−	0.0768348i
$466$			21.7990i			1.00982i
$467$		−	13.7990i		−	0.638541i	−0.947664	−	0.319271i	$-0.896562\pi$
$467$		−	13.7990i		−	0.638541i	0.947664	−	0.319271i	$-0.103438\pi$
$468$	17.6569	+	6.24264i	0.816188	+	0.288566i
$469$		0			0
$470$	8.82843			0.407225
$471$	15.7990	+	22.3431i	0.727979	+	1.02952i
$472$	−7.17157			−0.330098
$473$		−	24.3431i		−	1.11930i
$474$	13.1716	−	9.31371i	0.604990	−	0.427793i
$475$	4.24264	−	1.00000i	0.194666	−	0.0458831i
$476$			9.65685i			0.442621i
$477$	8.82843	−	24.9706i	0.404226	−	1.14332i
$478$			19.8995i			0.910182i
$479$			0.585786i			0.0267653i	0.999910	+	0.0133826i	$0.00425995\pi$
$479$			0.585786i			0.0267653i	−0.999910	+	0.0133826i	$0.995740\pi$
$480$	−1.41421	+	1.00000i	−0.0645497	+	0.0456435i
$481$	−38.9706			−1.77690
$482$			8.48528i			0.386494i
$483$	−28.9706	+	20.4853i	−1.31821	+	0.932113i
$484$	4.31371			0.196078
$485$	−9.41421			−0.427477
$486$	1.00000	−	15.5563i	0.0453609	−	0.705650i
$487$		−	7.85786i		−	0.356074i	−0.984024	−	0.178037i	$-0.943025\pi$
$487$		−	7.85786i		−	0.356074i	0.984024	−	0.178037i	$-0.0569746\pi$
$488$	12.4853			0.565182
$489$	−12.7279	−	18.0000i	−0.575577	−	0.813988i
$490$			4.65685i			0.210375i
$491$			12.4437i			0.561574i	0.959770	+	0.280787i	$0.0905955\pi$
$491$			12.4437i			0.561574i	−0.959770	+	0.280787i	$0.909405\pi$
$492$	3.07107	+	4.34315i	0.138454	+	0.195804i
$493$		−	25.6569i		−	1.15553i
$494$	6.24264	+	26.4853i	0.280870	+	1.19163i
$495$	−2.58579	+	7.31371i	−0.116222	+	0.328727i
$496$			1.17157i			0.0526052i
$497$	9.65685			0.433169
$498$	−10.1421	+	7.17157i	−0.454480	+	0.321366i
$499$	−14.3431			−0.642087			−0.321044	−	0.947064i	$-0.604034\pi$
$499$	−14.3431			−0.642087			−0.321044	+	0.947064i	$0.604034\pi$
$500$		−	1.00000i		−	0.0447214i
$501$		0			0
$502$		−	19.0711i		−	0.851183i
$503$		−	42.2843i		−	1.88536i	−0.333695	−	0.942681i	$-0.608295\pi$
$503$		−	42.2843i		−	1.88536i	0.333695	−	0.942681i	$-0.391705\pi$
$504$	−3.41421	+	9.65685i	−0.152081	+	0.430150i
$505$	−3.65685			−0.162728
$506$	15.5147			0.689713
$507$	−25.9706	−	36.7279i	−1.15339	−	1.63114i
$508$			7.17157i			0.318187i
$509$	23.8995			1.05933			0.529663	−	0.848208i	$-0.322318\pi$
$509$	23.8995			1.05933			0.529663	+	0.848208i	$0.322318\pi$
$510$	−2.82843	−	4.00000i	−0.125245	−	0.177123i
$511$	−49.4558			−2.18780
$512$	1.00000			0.0441942
$513$	19.7990	−	11.0000i	0.874147	−	0.485662i
$514$	−0.142136			−0.00626933
$515$	15.6569			0.689923
$516$	9.41421	+	13.3137i	0.414438	+	0.586103i
$517$	−22.8284			−1.00399
$518$		−	21.3137i		−	0.936471i
$519$	6.00000	+	8.48528i	0.263371	+	0.372463i
$520$	6.24264			0.273758
$521$	−22.3848			−0.980695			−0.490347	−	0.871527i	$-0.663130\pi$
$521$	−22.3848			−0.980695			−0.490347	+	0.871527i	$0.663130\pi$
$522$	9.07107	−	25.6569i	0.397030	−	1.12297i
$523$		−	24.9706i		−	1.09189i	−0.837822	−	0.545943i	$-0.816171\pi$
$523$		−	24.9706i		−	1.09189i	0.837822	−	0.545943i	$-0.183829\pi$
$524$		−	19.0711i		−	0.833123i
$525$	−3.41421	−	4.82843i	−0.149008	−	0.210730i
$526$			16.8284i			0.733754i
$527$	−3.31371			−0.144347
$528$	3.65685	−	2.58579i	0.159144	−	0.112532i
$529$	−13.0000			−0.565217
$530$		−	8.82843i		−	0.383482i
$531$	7.17157	−	20.2843i	0.311220	−	0.880262i
$532$	−14.4853	+	3.41421i	−0.628017	+	0.148025i
$533$		−	19.1716i		−	0.830413i
$534$	13.4142	+	18.9706i	0.580490	+	0.820937i
$535$		−	7.65685i		−	0.331035i
$536$		0			0
$537$	17.7990	+	25.1716i	0.768083	+	1.08623i
$538$	12.3848			0.533946
$539$		−	12.0416i		−	0.518670i
$540$	−1.41421	−	5.00000i	−0.0608581	−	0.215166i
$541$	−9.02944			−0.388206			−0.194103	−	0.980981i	$-0.562180\pi$
$541$	−9.02944			−0.388206			−0.194103	+	0.980981i	$0.562180\pi$
$542$	4.97056			0.213504
$543$	7.31371	−	5.17157i	0.313861	−	0.221933i
$544$			2.82843i			0.121268i
$545$	−13.6569			−0.584995
$546$	30.1421	−	21.3137i	1.28996	−	0.912143i
$547$			18.8284i			0.805045i	0.915410	+	0.402523i	$0.131867\pi$
$547$			18.8284i			0.805045i	−0.915410	+	0.402523i	$0.868133\pi$
$548$			2.48528i			0.106166i
$549$	−12.4853	+	35.3137i	−0.532859	+	1.50715i
$550$			2.58579i			0.110258i
$551$	38.4853	−	9.07107i	1.63953	−	0.386440i
$552$	−8.48528	+	6.00000i	−0.361158	+	0.255377i
$553$		−	31.7990i		−	1.35223i
$554$	−8.97056			−0.381123
$555$	6.24264	+	8.82843i	0.264985	+	0.374746i
$556$	−10.1421			−0.430122
$557$			16.6274i			0.704526i	0.935901	+	0.352263i	$0.114588\pi$
$557$			16.6274i			0.704526i	−0.935901	+	0.352263i	$0.885412\pi$
$558$	−3.31371	−	1.17157i	−0.140280	−	0.0495966i
$559$		−	58.7696i		−	2.48569i
$560$			3.41421i			0.144277i
$561$	7.31371	+	10.3431i	0.308785	+	0.436688i
$562$	−15.0711			−0.635735
$563$	−2.34315			−0.0987518			−0.0493759	−	0.998780i	$-0.515723\pi$
$563$	−2.34315			−0.0987518			−0.0493759	+	0.998780i	$0.515723\pi$
$564$	12.4853	−	8.82843i	0.525725	−	0.371744i
$565$			7.17157i			0.301710i
$566$	−12.7279			−0.534994
$567$	−23.8995	−	19.3137i	−1.00368	−	0.811100i
$568$	2.82843			0.118678
$569$	−43.0711			−1.80563			−0.902817	−	0.430026i	$-0.858504\pi$
$569$	−43.0711			−1.80563			−0.902817	+	0.430026i	$0.858504\pi$
$570$	5.00000	−	5.65685i	0.209427	−	0.236940i
$571$	9.65685			0.404127			0.202063	−	0.979372i	$-0.435235\pi$
$571$	9.65685			0.404127			0.202063	+	0.979372i	$0.435235\pi$
$572$	−16.1421			−0.674937
$573$	2.48528	−	1.75736i	0.103824	−	0.0734147i
$574$	10.4853			0.437647
$575$		−	6.00000i		−	0.250217i
$576$	−1.00000	+	2.82843i	−0.0416667	+	0.117851i
$577$	−24.8284			−1.03362			−0.516810	−	0.856100i	$-0.672881\pi$
$577$	−24.8284			−1.03362			−0.516810	+	0.856100i	$0.672881\pi$
$578$	9.00000			0.374351
$579$	−16.3431	+	11.5563i	−0.679198	+	0.480265i
$580$		−	9.07107i		−	0.376656i
$581$			24.4853i			1.01582i
$582$	−13.3137	+	9.41421i	−0.551871	+	0.390232i
$583$			22.8284i			0.945457i
$584$	−14.4853			−0.599405
$585$	−6.24264	+	17.6569i	−0.258101	+	0.730021i
$586$	8.82843			0.364699
$587$			8.82843i			0.364388i	0.983263	+	0.182194i	$0.0583199\pi$
$587$			8.82843i			0.364388i	−0.983263	+	0.182194i	$0.941680\pi$
$588$	4.65685	+	6.58579i	0.192045	+	0.271593i
$589$	−1.17157	−	4.97056i	−0.0482738	−	0.204808i
$590$		−	7.17157i		−	0.295249i
$591$	−14.3431	+	10.1421i	−0.589998	+	0.417192i
$592$		−	6.24264i		−	0.256571i
$593$		−	16.1421i		−	0.662878i	−0.943477	−	0.331439i	$-0.892466\pi$
$593$		−	16.1421i		−	0.662878i	0.943477	−	0.331439i	$-0.107534\pi$
$594$	3.65685	+	12.9289i	0.150043	+	0.530481i
$595$	−9.65685			−0.395892
$596$		−	2.48528i		−	0.101801i
$597$	16.9706	+	24.0000i	0.694559	+	0.982255i
$598$	37.4558			1.53168
$599$	26.8284			1.09618			0.548090	−	0.836419i	$-0.315355\pi$
$599$	26.8284			1.09618			0.548090	+	0.836419i	$0.315355\pi$
$600$	−1.00000	−	1.41421i	−0.0408248	−	0.0577350i
$601$		−	4.00000i		−	0.163163i	−0.996667	−	0.0815817i	$-0.974003\pi$
$601$		−	4.00000i		−	0.163163i	0.996667	−	0.0815817i	$-0.0259972\pi$
$602$	32.1421			1.31002
$603$		0			0
$604$		−	3.51472i		−	0.143012i
$605$			4.31371i			0.175377i
$606$	−5.17157	+	3.65685i	−0.210081	+	0.148550i
$607$			18.4853i			0.750294i	0.926965	+	0.375147i	$0.122408\pi$
$607$			18.4853i			0.750294i	−0.926965	+	0.375147i	$0.877592\pi$
$608$	−4.24264	+	1.00000i	−0.172062	+	0.0405554i
$609$	−30.9706	−	43.7990i	−1.25499	−	1.77482i
$610$			12.4853i			0.505514i
$611$	−55.1127			−2.22962
$612$	−8.00000	−	2.82843i	−0.323381	−	0.114332i
$613$	39.1127			1.57975			0.789874	−	0.613270i	$-0.210146\pi$
$613$	39.1127			1.57975			0.789874	+	0.613270i	$0.210146\pi$
$614$		−	10.1421i		−	0.409303i
$615$	−4.34315	+	3.07107i	−0.175133	+	0.123837i
$616$		−	8.82843i		−	0.355707i
$617$			13.1716i			0.530268i	0.964212	+	0.265134i	$0.0854161\pi$
$617$			13.1716i			0.530268i	−0.964212	+	0.265134i	$0.914584\pi$
$618$	22.1421	−	15.6569i	0.890687	−	0.629811i
$619$	−9.45584			−0.380062			−0.190031	−	0.981778i	$-0.560859\pi$
$619$	−9.45584			−0.380062			−0.190031	+	0.981778i	$0.560859\pi$
$620$	−1.17157			−0.0470515
$621$	−8.48528	−	30.0000i	−0.340503	−	1.20386i
$622$			9.07107i			0.363717i
$623$	45.7990			1.83490
$624$	8.82843	−	6.24264i	0.353420	−	0.249906i
$625$	1.00000			0.0400000
$626$	−11.1716			−0.446506
$627$	−12.9289	+	14.6274i	−0.516332	+	0.584163i
$628$	15.7990			0.630448
$629$	17.6569			0.704025
$630$	−9.65685	−	3.41421i	−0.384738	−	0.136026i
$631$	40.4853			1.61169			0.805847	−	0.592124i	$-0.201710\pi$
$631$	40.4853			1.61169			0.805847	+	0.592124i	$0.201710\pi$
$632$		−	9.31371i		−	0.370479i
$633$	−2.82843	+	2.00000i	−0.112420	+	0.0794929i
$634$	−11.6569			−0.462953
$635$	−7.17157			−0.284595
$636$	−8.82843	−	12.4853i	−0.350070	−	0.495074i
$637$		−	29.0711i		−	1.15184i
$638$			23.4558i			0.928626i
$639$	−2.82843	+	8.00000i	−0.111891	+	0.316475i
$640$			1.00000i			0.0395285i
$641$	−36.7279			−1.45067			−0.725333	−	0.688398i	$-0.758314\pi$
$641$	−36.7279			−1.45067			−0.725333	+	0.688398i	$0.758314\pi$
$642$	−7.65685	−	10.8284i	−0.302192	−	0.427364i
$643$	4.72792			0.186451			0.0932255	−	0.995645i	$-0.470282\pi$
$643$	4.72792			0.186451			0.0932255	+	0.995645i	$0.470282\pi$
$644$			20.4853i			0.807233i
$645$	−13.3137	+	9.41421i	−0.524227	+	0.370684i
$646$	−2.82843	−	12.0000i	−0.111283	−	0.472134i
$647$		−	25.3137i		−	0.995185i	−0.867411	−	0.497592i	$-0.834218\pi$
$647$		−	25.3137i		−	0.995185i	0.867411	−	0.497592i	$-0.165782\pi$
$648$	−7.00000	−	5.65685i	−0.274986	−	0.222222i
$649$			18.5442i			0.727922i
$650$			6.24264i			0.244857i
$651$	−5.65685	+	4.00000i	−0.221710	+	0.156772i
$652$	−12.7279			−0.498464
$653$		−	47.1127i		−	1.84366i	−0.387592	−	0.921831i	$-0.626693\pi$
$653$		−	47.1127i		−	1.84366i	0.387592	−	0.921831i	$-0.373307\pi$
$654$	−19.3137	+	13.6569i	−0.755226	+	0.534025i
$655$	19.0711			0.745168
$656$	3.07107			0.119905
$657$	14.4853	−	40.9706i	0.565125	−	1.59841i
$658$		−	30.1421i		−	1.17506i
$659$	−3.17157			−0.123547			−0.0617735	−	0.998090i	$-0.519676\pi$
$659$	−3.17157			−0.123547			−0.0617735	+	0.998090i	$0.519676\pi$
$660$	2.58579	+	3.65685i	0.100652	+	0.142343i
$661$		−	20.4853i		−	0.796785i	−0.917215	−	0.398393i	$-0.869568\pi$
$661$		−	20.4853i		−	0.796785i	0.917215	−	0.398393i	$-0.130432\pi$
$662$			16.9706i			0.659580i
$663$	17.6569	+	24.9706i	0.685735	+	0.969776i
$664$			7.17157i			0.278311i
$665$	−3.41421	−	14.4853i	−0.132398	−	0.561715i
$666$	17.6569	+	6.24264i	0.684189	+	0.241897i
$667$		−	54.4264i		−	2.10740i
$668$		0			0
$669$	−25.4558	+	18.0000i	−0.984180	+	0.695920i
$670$		0			0
$671$		−	32.2843i		−	1.24632i
$672$	3.41421	+	4.82843i	0.131706	+	0.186261i
$673$			21.6985i			0.836415i	0.908351	+	0.418208i	$0.137342\pi$
$673$			21.6985i			0.836415i	−0.908351	+	0.418208i	$0.862658\pi$
$674$			13.2132i			0.508954i
$675$	5.00000	−	1.41421i	0.192450	−	0.0544331i
$676$	−25.9706			−0.998868
$677$	41.5980			1.59874			0.799370	−	0.600839i	$-0.205167\pi$
$677$	41.5980			1.59874			0.799370	+	0.600839i	$0.205167\pi$
$678$	7.17157	+	10.1421i	0.275423	+	0.389506i
$679$			32.1421i			1.23350i
$680$	−2.82843			−0.108465
$681$	−13.6569	−	19.3137i	−0.523332	−	0.740103i
$682$	3.02944			0.116003
$683$	−51.2548			−1.96121			−0.980606	−	0.195990i	$-0.937208\pi$
$683$	−51.2548			−1.96121			−0.980606	+	0.195990i	$0.937208\pi$
$684$	1.41421	−	13.0000i	0.0540738	−	0.497067i
$685$	−2.48528			−0.0949577
$686$	−8.00000			−0.305441
$687$	−8.48528	−	12.0000i	−0.323734	−	0.457829i
$688$	9.41421			0.358914
$689$			55.1127i			2.09963i
$690$	−6.00000	−	8.48528i	−0.228416	−	0.323029i
$691$	3.02944			0.115245			0.0576226	−	0.998338i	$-0.481648\pi$
$691$	3.02944			0.115245			0.0576226	+	0.998338i	$0.481648\pi$
$692$	6.00000			0.228086
$693$	24.9706	+	8.82843i	0.948553	+	0.335364i
$694$		−	26.2843i		−	0.997737i
$695$		−	10.1421i		−	0.384713i
$696$	−9.07107	−	12.8284i	−0.343838	−	0.486260i
$697$			8.68629i			0.329017i
$698$	22.9706			0.869449
$699$	−30.8284	+	21.7990i	−1.16604	+	0.824514i
$700$	−3.41421			−0.129045
$701$			14.4853i			0.547102i	0.961858	+	0.273551i	$0.0881982\pi$
$701$			14.4853i			0.547102i	−0.961858	+	0.273551i	$0.911802\pi$
$702$	8.82843	+	31.2132i	0.333208	+	1.17807i
$703$	6.24264	+	26.4853i	0.235446	+	0.998911i
$704$		−	2.58579i		−	0.0974555i
$705$	8.82843	+	12.4853i	0.332498	+	0.470223i
$706$		−	3.17157i		−	0.119364i
$707$			12.4853i			0.469557i
$708$	−7.17157	−	10.1421i	−0.269524	−	0.381165i
$709$	36.4853			1.37023			0.685117	−	0.728433i	$-0.259751\pi$
$709$	36.4853			1.37023			0.685117	+	0.728433i	$0.259751\pi$
$710$			2.82843i			0.106149i
$711$	26.3431	+	9.31371i	0.987945	+	0.349291i
$712$	13.4142			0.502719
$713$	−7.02944			−0.263254
$714$	−13.6569	+	9.65685i	−0.511095	+	0.361399i
$715$		−	16.1421i		−	0.603682i
$716$	17.7990			0.665179
$717$	−28.1421	+	19.8995i	−1.05099	+	0.743160i
$718$		−	16.5858i		−	0.618976i
$719$			5.27208i			0.196615i	0.995156	+	0.0983077i	$0.0313429\pi$
$719$			5.27208i			0.196615i	−0.995156	+	0.0983077i	$0.968657\pi$
$720$	−2.82843	−	1.00000i	−0.105409	−	0.0372678i
$721$		−	53.4558i		−	1.99080i
$722$	17.0000	−	8.48528i	0.632674	−	0.315789i
$723$	−12.0000	+	8.48528i	−0.446285	+	0.315571i
$724$		−	5.17157i		−	0.192200i
$725$	9.07107			0.336891
$726$	4.31371	+	6.10051i	0.160097	+	0.226411i
$727$	−5.55635			−0.206074			−0.103037	−	0.994678i	$-0.532856\pi$
$727$	−5.55635			−0.206074			−0.103037	+	0.994678i	$0.532856\pi$
$728$		−	21.3137i		−	0.789939i
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$		−	14.4853i		−	0.536124i
$731$			26.6274i			0.984851i
$732$	12.4853	+	17.6569i	0.461469	+	0.652616i
$733$	−32.4853			−1.19987			−0.599936	−	0.800048i	$-0.704807\pi$
$733$	−32.4853			−1.19987			−0.599936	+	0.800048i	$0.704807\pi$
$734$	−5.75736			−0.212508
$735$	−6.58579	+	4.65685i	−0.242920	+	0.171771i
$736$			6.00000i			0.221163i
$737$		0			0
$738$	−3.07107	+	8.68629i	−0.113048	+	0.319747i
$739$	−3.51472			−0.129291			−0.0646455	−	0.997908i	$-0.520592\pi$
$739$	−3.51472			−0.129291			−0.0646455	+	0.997908i	$0.520592\pi$
$740$	6.24264			0.229484
$741$	−31.2132	+	35.3137i	−1.14665	+	1.29728i
$742$	−30.1421			−1.10655
$743$	−48.8284			−1.79134			−0.895671	−	0.444718i	$-0.853304\pi$
$743$	−48.8284			−1.79134			−0.895671	+	0.444718i	$0.853304\pi$
$744$	−1.65685	+	1.17157i	−0.0607432	+	0.0429519i
$745$	2.48528			0.0910537
$746$			34.0416i			1.24635i
$747$	−20.2843	−	7.17157i	−0.742163	−	0.262394i
$748$	7.31371			0.267416
$749$	−26.1421			−0.955213
$750$	1.41421	−	1.00000i	0.0516398	−	0.0365148i
$751$		−	31.5147i		−	1.14999i	−0.818157	−	0.574994i	$-0.805004\pi$
$751$		−	31.5147i		−	1.14999i	0.818157	−	0.574994i	$-0.194996\pi$
$752$		−	8.82843i		−	0.321940i
$753$	26.9706	−	19.0711i	0.982862	−	0.694988i
$754$			56.6274i			2.06225i
$755$	3.51472			0.127914
$756$	−17.0711	+	4.82843i	−0.620869	+	0.175608i
$757$	38.3431			1.39361			0.696803	−	0.717263i	$-0.254605\pi$
$757$	38.3431			1.39361			0.696803	+	0.717263i	$0.254605\pi$
$758$		−	8.00000i		−	0.290573i
$759$	15.5147	+	21.9411i	0.563149	+	0.796412i
$760$	−1.00000	−	4.24264i	−0.0362738	−	0.153897i
$761$			6.82843i			0.247530i	0.992312	+	0.123765i	$0.0394969\pi$
$761$			6.82843i			0.247530i	−0.992312	+	0.123765i	$0.960503\pi$
$762$	−10.1421	+	7.17157i	−0.367411	+	0.259799i
$763$			46.6274i			1.68803i
$764$		−	1.75736i		−	0.0635790i
$765$	2.82843	−	8.00000i	0.102262	−	0.289241i
$766$	3.85786			0.139390
$767$			44.7696i			1.61653i
$768$	1.00000	+	1.41421i	0.0360844	+	0.0510310i
$769$	9.31371			0.335861			0.167930	−	0.985799i	$-0.446292\pi$
$769$	9.31371			0.335861			0.167930	+	0.985799i	$0.446292\pi$
$770$	8.82843			0.318154
$771$	−0.142136	−	0.201010i	−0.00511889	−	0.00723920i
$772$			11.5563i			0.415922i
$773$	11.6569			0.419268			0.209634	−	0.977780i	$-0.432773\pi$
$773$	11.6569			0.419268			0.209634	+	0.977780i	$0.432773\pi$
$774$	−9.41421	+	26.6274i	−0.338387	+	0.957103i
$775$		−	1.17157i		−	0.0420841i
$776$			9.41421i			0.337951i
$777$	30.1421	−	21.3137i	1.08134	−	0.764625i
$778$			31.6569i			1.13495i
$779$	−13.0294	+ <

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(1.00000 + 1.41421i) q^{6} +3.41421 q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(1.00000 + 1.41421i) q^{6} +3.41421 q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +1.00000i q^{10} -2.58579i q^{11} +(1.00000 + 1.41421i) q^{12} -6.24264i q^{13} +3.41421 q^{14} +(-1.41421 + 1.00000i) q^{15} +1.00000 q^{16} +2.82843i q^{17} +(-1.00000 + 2.82843i) q^{18} +(-4.24264 + 1.00000i) q^{19} +1.00000i q^{20} +(3.41421 + 4.82843i) q^{21} -2.58579i q^{22} +6.00000i q^{23} +(1.00000 + 1.41421i) q^{24} -1.00000 q^{25} -6.24264i q^{26} +(-5.00000 + 1.41421i) q^{27} +3.41421 q^{28} -9.07107 q^{29} +(-1.41421 + 1.00000i) q^{30} +1.17157i q^{31} +1.00000 q^{32} +(3.65685 - 2.58579i) q^{33} +2.82843i q^{34} +3.41421i q^{35} +(-1.00000 + 2.82843i) q^{36} -6.24264i q^{37} +(-4.24264 + 1.00000i) q^{38} +(8.82843 - 6.24264i) q^{39} +1.00000i q^{40} +3.07107 q^{41} +(3.41421 + 4.82843i) q^{42} +9.41421 q^{43} -2.58579i q^{44} +(-2.82843 - 1.00000i) q^{45} +6.00000i q^{46} -8.82843i q^{47} +(1.00000 + 1.41421i) q^{48} +4.65685 q^{49} -1.00000 q^{50} +(-4.00000 + 2.82843i) q^{51} -6.24264i q^{52} -8.82843 q^{53} +(-5.00000 + 1.41421i) q^{54} +2.58579 q^{55} +3.41421 q^{56} +(-5.65685 - 5.00000i) q^{57} -9.07107 q^{58} -7.17157 q^{59} +(-1.41421 + 1.00000i) q^{60} +12.4853 q^{61} +1.17157i q^{62} +(-3.41421 + 9.65685i) q^{63} +1.00000 q^{64} +6.24264 q^{65} +(3.65685 - 2.58579i) q^{66} +2.82843i q^{68} +(-8.48528 + 6.00000i) q^{69} +3.41421i q^{70} +2.82843 q^{71} +(-1.00000 + 2.82843i) q^{72} -14.4853 q^{73} -6.24264i q^{74} +(-1.00000 - 1.41421i) q^{75} +(-4.24264 + 1.00000i) q^{76} -8.82843i q^{77} +(8.82843 - 6.24264i) q^{78} -9.31371i q^{79} +1.00000i q^{80} +(-7.00000 - 5.65685i) q^{81} +3.07107 q^{82} +7.17157i q^{83} +(3.41421 + 4.82843i) q^{84} -2.82843 q^{85} +9.41421 q^{86} +(-9.07107 - 12.8284i) q^{87} -2.58579i q^{88} +13.4142 q^{89} +(-2.82843 - 1.00000i) q^{90} -21.3137i q^{91} +6.00000i q^{92} +(-1.65685 + 1.17157i) q^{93} -8.82843i q^{94} +(-1.00000 - 4.24264i) q^{95} +(1.00000 + 1.41421i) q^{96} +9.41421i q^{97} +4.65685 q^{98} +(7.31371 + 2.58579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^6 + 8 * q^7 + 4 * q^8 - 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9} + 4 q^{12} + 8 q^{14} + 4 q^{16} - 4 q^{18} + 8 q^{21} + 4 q^{24} - 4 q^{25} - 20 q^{27} + 8 q^{28} - 8 q^{29} + 4 q^{32} - 8 q^{33} - 4 q^{36} + 24 q^{39} - 16 q^{41} + 8 q^{42} + 32 q^{43} + 4 q^{48} - 4 q^{49} - 4 q^{50} - 16 q^{51} - 24 q^{53} - 20 q^{54} + 16 q^{55} + 8 q^{56} - 8 q^{58} - 40 q^{59} + 16 q^{61} - 8 q^{63} + 4 q^{64} + 8 q^{65} - 8 q^{66} - 4 q^{72} - 24 q^{73} - 4 q^{75} + 24 q^{78} - 28 q^{81} - 16 q^{82} + 8 q^{84} + 32 q^{86} - 8 q^{87} + 48 q^{89} + 16 q^{93} - 4 q^{95} + 4 q^{96} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^6 + 8 * q^7 + 4 * q^8 - 4 * q^9 + 4 * q^12 + 8 * q^14 + 4 * q^16 - 4 * q^18 + 8 * q^21 + 4 * q^24 - 4 * q^25 - 20 * q^27 + 8 * q^28 - 8 * q^29 + 4 * q^32 - 8 * q^33 - 4 * q^36 + 24 * q^39 - 16 * q^41 + 8 * q^42 + 32 * q^43 + 4 * q^48 - 4 * q^49 - 4 * q^50 - 16 * q^51 - 24 * q^53 - 20 * q^54 + 16 * q^55 + 8 * q^56 - 8 * q^58 - 40 * q^59 + 16 * q^61 - 8 * q^63 + 4 * q^64 + 8 * q^65 - 8 * q^66 - 4 * q^72 - 24 * q^73 - 4 * q^75 + 24 * q^78 - 28 * q^81 - 16 * q^82 + 8 * q^84 + 32 * q^86 - 8 * q^87 + 48 * q^89 + 16 * q^93 - 4 * q^95 + 4 * q^96 - 4 * q^98 - 16 * q^99

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