LMFDB - Embedded newform 570.2.f.b.341.2

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			341.2
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	570.341
Dual form			570.2.f.b.341.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(1.00000 - 1.41421i) q^{6} +0.585786 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(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} +0.585786 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +1.00000i q^{10} -5.41421i q^{11} +(1.00000 - 1.41421i) q^{12} +2.24264i q^{13} +0.585786 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} +(0.585786 - 0.828427i) q^{21} -5.41421i q^{22} +6.00000i q^{23} +(1.00000 - 1.41421i) q^{24} -1.00000 q^{25} +2.24264i q^{26} +(-5.00000 - 1.41421i) q^{27} +0.585786 q^{28} +5.07107 q^{29} +(1.41421 + 1.00000i) q^{30} +6.82843i q^{31} +1.00000 q^{32} +(-7.65685 - 5.41421i) q^{33} -2.82843i q^{34} +0.585786i q^{35} +(-1.00000 - 2.82843i) q^{36} +2.24264i q^{37} +(4.24264 + 1.00000i) q^{38} +(3.17157 + 2.24264i) q^{39} +1.00000i q^{40} -11.0711 q^{41} +(0.585786 - 0.828427i) q^{42} +6.58579 q^{43} -5.41421i q^{44} +(2.82843 - 1.00000i) q^{45} +6.00000i q^{46} -3.17157i q^{47} +(1.00000 - 1.41421i) q^{48} -6.65685 q^{49} -1.00000 q^{50} +(-4.00000 - 2.82843i) q^{51} +2.24264i q^{52} -3.17157 q^{53} +(-5.00000 - 1.41421i) q^{54} +5.41421 q^{55} +0.585786 q^{56} +(5.65685 - 5.00000i) q^{57} +5.07107 q^{58} -12.8284 q^{59} +(1.41421 + 1.00000i) q^{60} -4.48528 q^{61} +6.82843i q^{62} +(-0.585786 - 1.65685i) q^{63} +1.00000 q^{64} -2.24264 q^{65} +(-7.65685 - 5.41421i) q^{66} -2.82843i q^{68} +(8.48528 + 6.00000i) q^{69} +0.585786i q^{70} -2.82843 q^{71} +(-1.00000 - 2.82843i) q^{72} +2.48528 q^{73} +2.24264i q^{74} +(-1.00000 + 1.41421i) q^{75} +(4.24264 + 1.00000i) q^{76} -3.17157i q^{77} +(3.17157 + 2.24264i) q^{78} +13.3137i q^{79} +1.00000i q^{80} +(-7.00000 + 5.65685i) q^{81} -11.0711 q^{82} +12.8284i q^{83} +(0.585786 - 0.828427i) q^{84} +2.82843 q^{85} +6.58579 q^{86} +(5.07107 - 7.17157i) q^{87} -5.41421i q^{88} +10.5858 q^{89} +(2.82843 - 1.00000i) q^{90} +1.31371i q^{91} +6.00000i q^{92} +(9.65685 + 6.82843i) q^{93} -3.17157i q^{94} +(-1.00000 + 4.24264i) q^{95} +(1.00000 - 1.41421i) q^{96} +6.58579i q^{97} -6.65685 q^{98} +(-15.3137 + 5.41421i) 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
$7$	0.585786			0.221406			0.110703	−	0.993854i	$-0.464690\pi$
$7$	0.585786			0.221406			0.110703	+	0.993854i	$0.464690\pi$
$8$	1.00000			0.353553
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$			1.00000i			0.316228i
$11$		−	5.41421i		−	1.63245i	−0.577736	−	0.816223i	$-0.696064\pi$
$11$		−	5.41421i		−	1.63245i	0.577736	−	0.816223i	$-0.303936\pi$
$12$	1.00000	−	1.41421i	0.288675	−	0.408248i
$13$			2.24264i			0.621997i	0.950410	+	0.310998i	$0.100663\pi$
$13$			2.24264i			0.621997i	−0.950410	+	0.310998i	$0.899337\pi$
$14$	0.585786			0.156558
$15$	1.41421	+	1.00000i	0.365148	+	0.258199i
$16$	1.00000			0.250000
$17$		−	2.82843i		−	0.685994i	−0.939336	−	0.342997i	$-0.888558\pi$
$17$		−	2.82843i		−	0.685994i	0.939336	−	0.342997i	$-0.111442\pi$
$18$	−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
$21$	0.585786	−	0.828427i	0.127829	−	0.180778i
$22$		−	5.41421i		−	1.15431i
$23$			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
$26$			2.24264i			0.439818i
$27$	−5.00000	−	1.41421i	−0.962250	−	0.272166i
$28$	0.585786			0.110703
$29$	5.07107			0.941674			0.470837	−	0.882220i	$-0.343952\pi$
$29$	5.07107			0.941674			0.470837	+	0.882220i	$0.343952\pi$
$30$	1.41421	+	1.00000i	0.258199	+	0.182574i
$31$			6.82843i			1.22642i	0.789919	+	0.613211i	$0.210122\pi$
$31$			6.82843i			1.22642i	−0.789919	+	0.613211i	$0.789878\pi$
$32$	1.00000			0.176777
$33$	−7.65685	−	5.41421i	−1.33289	−	0.942494i
$34$		−	2.82843i		−	0.485071i
$35$			0.585786i			0.0990160i
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$			2.24264i			0.368688i	0.982862	+	0.184344i	$0.0590160\pi$
$37$			2.24264i			0.368688i	−0.982862	+	0.184344i	$0.940984\pi$
$38$	4.24264	+	1.00000i	0.688247	+	0.162221i
$39$	3.17157	+	2.24264i	0.507858	+	0.359110i
$40$			1.00000i			0.158114i
$41$	−11.0711			−1.72901			−0.864505	−	0.502624i	$-0.832368\pi$
$41$	−11.0711			−1.72901			−0.864505	+	0.502624i	$0.832368\pi$
$42$	0.585786	−	0.828427i	0.0903888	−	0.127829i
$43$	6.58579			1.00432			0.502162	−	0.864774i	$-0.332538\pi$
$43$	6.58579			1.00432			0.502162	+	0.864774i	$0.332538\pi$
$44$		−	5.41421i		−	0.816223i
$45$	2.82843	−	1.00000i	0.421637	−	0.149071i
$46$			6.00000i			0.884652i
$47$		−	3.17157i		−	0.462621i	−0.972880	−	0.231311i	$-0.925699\pi$
$47$		−	3.17157i		−	0.462621i	0.972880	−	0.231311i	$-0.0743014\pi$
$48$	1.00000	−	1.41421i	0.144338	−	0.204124i
$49$	−6.65685			−0.950979
$50$	−1.00000			−0.141421
$51$	−4.00000	−	2.82843i	−0.560112	−	0.396059i
$52$			2.24264i			0.310998i
$53$	−3.17157			−0.435649			−0.217825	−	0.975988i	$-0.569896\pi$
$53$	−3.17157			−0.435649			−0.217825	+	0.975988i	$0.569896\pi$
$54$	−5.00000	−	1.41421i	−0.680414	−	0.192450i
$55$	5.41421			0.730052
$56$	0.585786			0.0782790
$57$	5.65685	−	5.00000i	0.749269	−	0.662266i
$58$	5.07107			0.665864
$59$	−12.8284			−1.67012			−0.835059	−	0.550160i	$-0.814567\pi$
$59$	−12.8284			−1.67012			−0.835059	+	0.550160i	$0.814567\pi$
$60$	1.41421	+	1.00000i	0.182574	+	0.129099i
$61$	−4.48528			−0.574281			−0.287141	−	0.957888i	$-0.592705\pi$
$61$	−4.48528			−0.574281			−0.287141	+	0.957888i	$0.592705\pi$
$62$			6.82843i			0.867211i
$63$	−0.585786	−	1.65685i	−0.0738022	−	0.208744i
$64$	1.00000			0.125000
$65$	−2.24264			−0.278165
$66$	−7.65685	−	5.41421i	−0.942494	−	0.666444i
$67$		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
$70$			0.585786i			0.0700149i
$71$	−2.82843			−0.335673			−0.167836	−	0.985815i	$-0.553678\pi$
$71$	−2.82843			−0.335673			−0.167836	+	0.985815i	$0.553678\pi$
$72$	−1.00000	−	2.82843i	−0.117851	−	0.333333i
$73$	2.48528			0.290880			0.145440	−	0.989367i	$-0.453540\pi$
$73$	2.48528			0.290880			0.145440	+	0.989367i	$0.453540\pi$
$74$			2.24264i			0.260702i
$75$	−1.00000	+	1.41421i	−0.115470	+	0.163299i
$76$	4.24264	+	1.00000i	0.486664	+	0.114708i
$77$		−	3.17157i		−	0.361434i
$78$	3.17157	+	2.24264i	0.359110	+	0.253929i
$79$			13.3137i			1.49791i	0.662621	+	0.748955i	$0.269444\pi$
$79$			13.3137i			1.49791i	−0.662621	+	0.748955i	$0.730556\pi$
$80$			1.00000i			0.111803i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	−11.0711			−1.22259
$83$			12.8284i			1.40810i	0.710149	+	0.704051i	$0.248628\pi$
$83$			12.8284i			1.40810i	−0.710149	+	0.704051i	$0.751372\pi$
$84$	0.585786	−	0.828427i	0.0639145	−	0.0903888i
$85$	2.82843			0.306786
$86$	6.58579			0.710164
$87$	5.07107	−	7.17157i	0.543676	−	0.768873i
$88$		−	5.41421i		−	0.577157i
$89$	10.5858			1.12209			0.561046	−	0.827785i	$-0.310399\pi$
$89$	10.5858			1.12209			0.561046	+	0.827785i	$0.310399\pi$
$90$	2.82843	−	1.00000i	0.298142	−	0.105409i
$91$			1.31371i			0.137714i
$92$			6.00000i			0.625543i
$93$	9.65685	+	6.82843i	1.00137	+	0.708075i
$94$		−	3.17157i		−	0.327123i
$95$	−1.00000	+	4.24264i	−0.102598	+	0.435286i
$96$	1.00000	−	1.41421i	0.102062	−	0.144338i
$97$			6.58579i			0.668685i	0.942452	+	0.334343i	$0.108514\pi$
$97$			6.58579i			0.668685i	−0.942452	+	0.334343i	$0.891486\pi$
$98$	−6.65685			−0.672444
$99$	−15.3137	+	5.41421i	−1.53909	+	0.544149i
$100$	−1.00000			−0.100000
$101$		−	7.65685i		−	0.761885i	−0.924599	−	0.380943i	$-0.875599\pi$
$101$		−	7.65685i		−	0.761885i	0.924599	−	0.380943i	$-0.124401\pi$
$102$	−4.00000	−	2.82843i	−0.396059	−	0.280056i
$103$		−	4.34315i		−	0.427943i	−0.976840	−	0.213971i	$-0.931360\pi$
$103$		−	4.34315i		−	0.427943i	0.976840	−	0.213971i	$-0.0686399\pi$
$104$			2.24264i			0.219909i
$105$	0.828427	+	0.585786i	0.0808462	+	0.0571669i
$106$	−3.17157			−0.308050
$107$	3.65685			0.353521			0.176761	−	0.984254i	$-0.443438\pi$
$107$	3.65685			0.353521			0.176761	+	0.984254i	$0.443438\pi$
$108$	−5.00000	−	1.41421i	−0.481125	−	0.136083i
$109$			2.34315i			0.224433i	0.993684	+	0.112216i	$0.0357950\pi$
$109$			2.34315i			0.224433i	−0.993684	+	0.112216i	$0.964205\pi$
$110$	5.41421			0.516225
$111$	3.17157	+	2.24264i	0.301032	+	0.212862i
$112$	0.585786			0.0553516
$113$	12.8284			1.20680			0.603398	−	0.797440i	$-0.293813\pi$
$113$	12.8284			1.20680			0.603398	+	0.797440i	$0.293813\pi$
$114$	5.65685	−	5.00000i	0.529813	−	0.468293i
$115$	−6.00000			−0.559503
$116$	5.07107			0.470837
$117$	6.34315	−	2.24264i	0.586424	−	0.207332i
$118$	−12.8284			−1.18095
$119$		−	1.65685i		−	0.151884i
$120$	1.41421	+	1.00000i	0.129099	+	0.0912871i
$121$	−18.3137			−1.66488
$122$	−4.48528			−0.406078
$123$	−11.0711	+	15.6569i	−0.998245	+	1.41173i
$124$			6.82843i			0.613211i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.585786	−	1.65685i	−0.0521860	−	0.147604i
$127$			12.8284i			1.13834i	0.822220	+	0.569169i	$0.192735\pi$
$127$			12.8284i			1.13834i	−0.822220	+	0.569169i	$0.807265\pi$
$128$	1.00000			0.0883883
$129$	6.58579	−	9.31371i	0.579846	−	0.820026i
$130$	−2.24264			−0.196693
$131$		−	4.92893i		−	0.430643i	−0.976543	−	0.215321i	$-0.930920\pi$
$131$		−	4.92893i		−	0.430643i	0.976543	−	0.215321i	$-0.0690799\pi$
$132$	−7.65685	−	5.41421i	−0.666444	−	0.471247i
$133$	2.48528	+	0.585786i	0.215501	+	0.0507941i
$134$		0			0
$135$	1.41421	−	5.00000i	0.121716	−	0.430331i
$136$		−	2.82843i		−	0.242536i
$137$		−	14.4853i		−	1.23756i	−0.785564	−	0.618781i	$-0.787627\pi$
$137$		−	14.4853i		−	1.23756i	0.785564	−	0.618781i	$-0.212373\pi$
$138$	8.48528	+	6.00000i	0.722315	+	0.510754i
$139$	18.1421			1.53880			0.769398	−	0.638770i	$-0.220556\pi$
$139$	18.1421			1.53880			0.769398	+	0.638770i	$0.220556\pi$
$140$			0.585786i			0.0495080i
$141$	−4.48528	−	3.17157i	−0.377729	−	0.267095i
$142$	−2.82843			−0.237356
$143$	12.1421			1.01538
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$			5.07107i			0.421129i
$146$	2.48528			0.205683
$147$	−6.65685	+	9.41421i	−0.549048	+	0.776471i
$148$			2.24264i			0.184344i
$149$			14.4853i			1.18668i	0.804952	+	0.593340i	$0.202191\pi$
$149$			14.4853i			1.18668i	−0.804952	+	0.593340i	$0.797809\pi$
$150$	−1.00000	+	1.41421i	−0.0816497	+	0.115470i
$151$		−	20.4853i		−	1.66707i	−0.552468	−	0.833534i	$-0.686314\pi$
$151$		−	20.4853i		−	1.66707i	0.552468	−	0.833534i	$-0.313686\pi$
$152$	4.24264	+	1.00000i	0.344124	+	0.0811107i
$153$	−8.00000	+	2.82843i	−0.646762	+	0.228665i
$154$		−	3.17157i		−	0.255573i
$155$	−6.82843			−0.548472
$156$	3.17157	+	2.24264i	0.253929	+	0.179555i
$157$	−23.7990			−1.89937			−0.949683	−	0.313212i	$-0.898595\pi$
$157$	−23.7990			−1.89937			−0.949683	+	0.313212i	$0.898595\pi$
$158$			13.3137i			1.05918i
$159$	−3.17157	+	4.48528i	−0.251522	+	0.355706i
$160$			1.00000i			0.0790569i
$161$			3.51472i			0.276999i
$162$	−7.00000	+	5.65685i	−0.549972	+	0.444444i
$163$	12.7279			0.996928			0.498464	−	0.866910i	$-0.333898\pi$
$163$	12.7279			0.996928			0.498464	+	0.866910i	$0.333898\pi$
$164$	−11.0711			−0.864505
$165$	5.41421	−	7.65685i	0.421496	−	0.596085i
$166$			12.8284i			0.995679i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$	0.585786	−	0.828427i	0.0451944	−	0.0639145i
$169$	7.97056			0.613120
$170$	2.82843			0.216930
$171$	−1.41421	−	13.0000i	−0.108148	−	0.994135i
$172$	6.58579			0.502162
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$	5.07107	−	7.17157i	0.384437	−	0.543676i
$175$	−0.585786			−0.0442813
$176$		−	5.41421i		−	0.408112i
$177$	−12.8284	+	18.1421i	−0.964244	+	1.36365i
$178$	10.5858			0.793438
$179$	−21.7990			−1.62933			−0.814667	−	0.579930i	$-0.803080\pi$
$179$	−21.7990			−1.62933			−0.814667	+	0.579930i	$0.803080\pi$
$180$	2.82843	−	1.00000i	0.210819	−	0.0745356i
$181$		−	10.8284i		−	0.804871i	−0.915448	−	0.402435i	$-0.868164\pi$
$181$		−	10.8284i		−	0.804871i	0.915448	−	0.402435i	$-0.131836\pi$
$182$			1.31371i			0.0973786i
$183$	−4.48528	+	6.34315i	−0.331562	+	0.468899i
$184$			6.00000i			0.442326i
$185$	−2.24264			−0.164882
$186$	9.65685	+	6.82843i	0.708075	+	0.500685i
$187$	−15.3137			−1.11985
$188$		−	3.17157i		−	0.231311i
$189$	−2.92893	−	0.828427i	−0.213048	−	0.0602592i
$190$	−1.00000	+	4.24264i	−0.0725476	+	0.307794i
$191$		−	10.2426i		−	0.741131i	−0.928806	−	0.370566i	$-0.879164\pi$
$191$		−	10.2426i		−	0.741131i	0.928806	−	0.370566i	$-0.120836\pi$
$192$	1.00000	−	1.41421i	0.0721688	−	0.102062i
$193$		−	19.5563i		−	1.40770i	−0.710350	−	0.703848i	$-0.751463\pi$
$193$		−	19.5563i		−	1.40770i	0.710350	−	0.703848i	$-0.248537\pi$
$194$			6.58579i			0.472832i
$195$	−2.24264	+	3.17157i	−0.160599	+	0.227121i
$196$	−6.65685			−0.475490
$197$		−	18.1421i		−	1.29257i	−0.763095	−	0.646287i	$-0.776321\pi$
$197$		−	18.1421i		−	1.29257i	0.763095	−	0.646287i	$-0.223679\pi$
$198$	−15.3137	+	5.41421i	−1.08830	+	0.384771i
$199$	−16.9706			−1.20301			−0.601506	−	0.798869i	$-0.705432\pi$
$199$	−16.9706			−1.20301			−0.601506	+	0.798869i	$0.705432\pi$
$200$	−1.00000			−0.0707107
$201$		0			0
$202$		−	7.65685i		−	0.538734i
$203$	2.97056			0.208493
$204$	−4.00000	−	2.82843i	−0.280056	−	0.198030i
$205$		−	11.0711i		−	0.773237i
$206$		−	4.34315i		−	0.302601i
$207$	16.9706	−	6.00000i	1.17954	−	0.417029i
$208$			2.24264i			0.155499i
$209$	5.41421	−	22.9706i	0.374509	−	1.58891i
$210$	0.828427	+	0.585786i	0.0571669	+	0.0404231i
$211$			2.00000i			0.137686i	0.997628	+	0.0688428i	$0.0219307\pi$
$211$			2.00000i			0.137686i	−0.997628	+	0.0688428i	$0.978069\pi$
$212$	−3.17157			−0.217825
$213$	−2.82843	+	4.00000i	−0.193801	+	0.274075i
$214$	3.65685			0.249977
$215$			6.58579i			0.449147i
$216$	−5.00000	−	1.41421i	−0.340207	−	0.0962250i
$217$			4.00000i			0.271538i
$218$			2.34315i			0.158698i
$219$	2.48528	−	3.51472i	0.167940	−	0.237503i
$220$	5.41421			0.365026
$221$	6.34315			0.426686
$222$	3.17157	+	2.24264i	0.212862	+	0.150516i
$223$			18.0000i			1.20537i	0.797980	+	0.602685i	$0.205902\pi$
$223$			18.0000i			1.20537i	−0.797980	+	0.602685i	$0.794098\pi$
$224$	0.585786			0.0391395
$225$	1.00000	+	2.82843i	0.0666667	+	0.188562i
$226$	12.8284			0.853334
$227$	−2.34315			−0.155520			−0.0777600	−	0.996972i	$-0.524777\pi$
$227$	−2.34315			−0.155520			−0.0777600	+	0.996972i	$0.524777\pi$
$228$	5.65685	−	5.00000i	0.374634	−	0.331133i
$229$	8.48528			0.560723			0.280362	−	0.959894i	$-0.409546\pi$
$229$	8.48528			0.560723			0.280362	+	0.959894i	$0.409546\pi$
$230$	−6.00000			−0.395628
$231$	−4.48528	−	3.17157i	−0.295110	−	0.208674i
$232$	5.07107			0.332932
$233$		−	17.7990i		−	1.16605i	−0.812454	−	0.583025i	$-0.801869\pi$
$233$		−	17.7990i		−	1.16605i	0.812454	−	0.583025i	$-0.198131\pi$
$234$	6.34315	−	2.24264i	0.414664	−	0.146606i
$235$	3.17157			0.206891
$236$	−12.8284			−0.835059
$237$	18.8284	+	13.3137i	1.22304	+	0.864818i
$238$		−	1.65685i		−	0.107398i
$239$			0.100505i			0.00650113i	0.999995	+	0.00325057i	$0.00103469\pi$
$239$			0.100505i			0.00650113i	−0.999995	+	0.00325057i	$0.998965\pi$
$240$	1.41421	+	1.00000i	0.0912871	+	0.0645497i
$241$		−	8.48528i		−	0.546585i	−0.961931	−	0.273293i	$-0.911887\pi$
$241$		−	8.48528i		−	0.546585i	0.961931	−	0.273293i	$-0.0881127\pi$
$242$	−18.3137			−1.17725
$243$	1.00000	+	15.5563i	0.0641500	+	0.997940i
$244$	−4.48528			−0.287141
$245$		−	6.65685i		−	0.425291i
$246$	−11.0711	+	15.6569i	−0.705866	+	0.998245i
$247$	−2.24264	+	9.51472i	−0.142696	+	0.605407i
$248$			6.82843i			0.433606i
$249$	18.1421	+	12.8284i	1.14971	+	0.812969i
$250$		−	1.00000i		−	0.0632456i
$251$		−	4.92893i		−	0.311111i	−0.987827	−	0.155556i	$-0.950283\pi$
$251$		−	4.92893i		−	0.311111i	0.987827	−	0.155556i	$-0.0497168\pi$
$252$	−0.585786	−	1.65685i	−0.0369011	−	0.104372i
$253$	32.4853			2.04233
$254$			12.8284i			0.804927i
$255$	2.82843	−	4.00000i	0.177123	−	0.250490i
$256$	1.00000			0.0625000
$257$	28.1421			1.75546			0.877729	−	0.479157i	$-0.159058\pi$
$257$	28.1421			1.75546			0.877729	+	0.479157i	$0.159058\pi$
$258$	6.58579	−	9.31371i	0.410013	−	0.579846i
$259$			1.31371i			0.0816299i
$260$	−2.24264			−0.139083
$261$	−5.07107	−	14.3431i	−0.313891	−	0.887818i
$262$		−	4.92893i		−	0.304510i
$263$			11.1716i			0.688869i	0.938810	+	0.344434i	$0.111929\pi$
$263$			11.1716i			0.688869i	−0.938810	+	0.344434i	$0.888071\pi$
$264$	−7.65685	−	5.41421i	−0.471247	−	0.333222i
$265$		−	3.17157i		−	0.194828i
$266$	2.48528	+	0.585786i	0.152382	+	0.0359169i
$267$	10.5858	−	14.9706i	0.647840	−	0.916184i
$268$		0			0
$269$	−24.3848			−1.48677			−0.743383	−	0.668866i	$-0.766780\pi$
$269$	−24.3848			−1.48677			−0.743383	+	0.668866i	$0.766780\pi$
$270$	1.41421	−	5.00000i	0.0860663	−	0.304290i
$271$	−28.9706			−1.75984			−0.879918	−	0.475125i	$-0.842403\pi$
$271$	−28.9706			−1.75984			−0.879918	+	0.475125i	$0.842403\pi$
$272$		−	2.82843i		−	0.171499i
$273$	1.85786	+	1.31371i	0.112443	+	0.0795093i
$274$		−	14.4853i		−	0.875088i
$275$			5.41421i			0.326489i
$276$	8.48528	+	6.00000i	0.510754	+	0.361158i
$277$	24.9706			1.50034			0.750168	−	0.661247i	$-0.229973\pi$
$277$	24.9706			1.50034			0.750168	+	0.661247i	$0.229973\pi$
$278$	18.1421			1.08809
$279$	19.3137	−	6.82843i	1.15628	−	0.408807i
$280$			0.585786i			0.0350074i
$281$	−0.928932			−0.0554154			−0.0277077	−	0.999616i	$-0.508821\pi$
$281$	−0.928932			−0.0554154			−0.0277077	+	0.999616i	$0.508821\pi$
$282$	−4.48528	−	3.17157i	−0.267095	−	0.188864i
$283$	12.7279			0.756596			0.378298	−	0.925684i	$-0.376509\pi$
$283$	12.7279			0.756596			0.378298	+	0.925684i	$0.376509\pi$
$284$	−2.82843			−0.167836
$285$	5.00000	+	5.65685i	0.296174	+	0.335083i
$286$	12.1421			0.717980
$287$	−6.48528			−0.382814
$288$	−1.00000	−	2.82843i	−0.0589256	−	0.166667i
$289$	9.00000			0.529412
$290$			5.07107i			0.297783i
$291$	9.31371	+	6.58579i	0.545979	+	0.386066i
$292$	2.48528			0.145440
$293$	3.17157			0.185285			0.0926426	−	0.995699i	$-0.470469\pi$
$293$	3.17157			0.185285			0.0926426	+	0.995699i	$0.470469\pi$
$294$	−6.65685	+	9.41421i	−0.388236	+	0.549048i
$295$		−	12.8284i		−	0.746900i
$296$			2.24264i			0.130351i
$297$	−7.65685	+	27.0711i	−0.444296	+	1.57082i
$298$			14.4853i			0.839110i
$299$	−13.4558			−0.778172
$300$	−1.00000	+	1.41421i	−0.0577350	+	0.0816497i
$301$	3.85786			0.222364
$302$		−	20.4853i		−	1.17880i
$303$	−10.8284	−	7.65685i	−0.622077	−	0.439875i
$304$	4.24264	+	1.00000i	0.243332	+	0.0573539i
$305$		−	4.48528i		−	0.256826i
$306$	−8.00000	+	2.82843i	−0.457330	+	0.161690i
$307$			18.1421i			1.03543i	0.855554	+	0.517713i	$0.173217\pi$
$307$			18.1421i			1.03543i	−0.855554	+	0.517713i	$0.826783\pi$
$308$		−	3.17157i		−	0.180717i
$309$	−6.14214	−	4.34315i	−0.349414	−	0.247073i
$310$	−6.82843			−0.387829
$311$		−	5.07107i		−	0.287554i	−0.989610	−	0.143777i	$-0.954075\pi$
$311$		−	5.07107i		−	0.287554i	0.989610	−	0.143777i	$-0.0459248\pi$
$312$	3.17157	+	2.24264i	0.179555	+	0.126965i
$313$	−16.8284			−0.951199			−0.475599	−	0.879662i	$-0.657769\pi$
$313$	−16.8284			−0.951199			−0.475599	+	0.879662i	$0.657769\pi$
$314$	−23.7990			−1.34305
$315$	1.65685	−	0.585786i	0.0933532	−	0.0330053i
$316$			13.3137i			0.748955i
$317$	−0.343146			−0.0192730			−0.00963649	−	0.999954i	$-0.503067\pi$
$317$	−0.343146			−0.0192730			−0.00963649	+	0.999954i	$0.503067\pi$
$318$	−3.17157	+	4.48528i	−0.177853	+	0.251522i
$319$		−	27.4558i		−	1.53723i
$320$			1.00000i			0.0559017i
$321$	3.65685	−	5.17157i	0.204106	−	0.288649i
$322$			3.51472i			0.195868i
$323$	2.82843	−	12.0000i	0.157378	−	0.667698i
$324$	−7.00000	+	5.65685i	−0.388889	+	0.314270i
$325$		−	2.24264i		−	0.124399i
$326$	12.7279			0.704934
$327$	3.31371	+	2.34315i	0.183248	+	0.129576i
$328$	−11.0711			−0.611297
$329$		−	1.85786i		−	0.102427i
$330$	5.41421	−	7.65685i	0.298043	−	0.421496i
$331$		−	16.9706i		−	0.932786i	−0.884577	−	0.466393i	$-0.845553\pi$
$331$		−	16.9706i		−	0.932786i	0.884577	−	0.466393i	$-0.154447\pi$
$332$			12.8284i			0.704051i
$333$	6.34315	−	2.24264i	0.347602	−	0.122896i
$334$		0			0
$335$		0			0
$336$	0.585786	−	0.828427i	0.0319573	−	0.0451944i
$337$		−	29.2132i		−	1.59134i	−0.605727	−	0.795672i	$-0.707118\pi$
$337$		−	29.2132i		−	1.59134i	0.605727	−	0.795672i	$-0.292882\pi$
$338$	7.97056			0.433541
$339$	12.8284	−	18.1421i	0.696745	−	0.985346i
$340$	2.82843			0.153393
$341$	36.9706			2.00207
$342$	−1.41421	−	13.0000i	−0.0764719	−	0.702959i
$343$	−8.00000			−0.431959
$344$	6.58579			0.355082
$345$	−6.00000	+	8.48528i	−0.323029	+	0.456832i
$346$	6.00000			0.322562
$347$			30.2843i			1.62574i	0.582442	+	0.812872i	$0.302097\pi$
$347$			30.2843i			1.62574i	−0.582442	+	0.812872i	$0.697903\pi$
$348$	5.07107	−	7.17157i	0.271838	−	0.384437i
$349$	−10.9706			−0.587241			−0.293620	−	0.955922i	$-0.594860\pi$
$349$	−10.9706			−0.587241			−0.293620	+	0.955922i	$0.594860\pi$
$350$	−0.585786			−0.0313116
$351$	3.17157	−	11.2132i	0.169286	−	0.598517i
$352$		−	5.41421i		−	0.288579i
$353$		−	8.82843i		−	0.469890i	−0.972009	−	0.234945i	$-0.924509\pi$
$353$		−	8.82843i		−	0.469890i	0.972009	−	0.234945i	$-0.0754910\pi$
$354$	−12.8284	+	18.1421i	−0.681823	+	0.964244i
$355$		−	2.82843i		−	0.150117i
$356$	10.5858			0.561046
$357$	−2.34315	−	1.65685i	−0.124012	−	0.0876900i
$358$	−21.7990			−1.15211
$359$		−	19.4142i		−	1.02464i	−0.858794	−	0.512322i	$-0.828786\pi$
$359$		−	19.4142i		−	1.02464i	0.858794	−	0.512322i	$-0.171214\pi$
$360$	2.82843	−	1.00000i	0.149071	−	0.0527046i
$361$	17.0000	+	8.48528i	0.894737	+	0.446594i
$362$		−	10.8284i		−	0.569129i
$363$	−18.3137	+	25.8995i	−0.961220	+	1.35937i
$364$			1.31371i			0.0688570i
$365$			2.48528i			0.130086i
$366$	−4.48528	+	6.34315i	−0.234449	+	0.331562i
$367$	−14.2426			−0.743460			−0.371730	−	0.928341i	$-0.621235\pi$
$367$	−14.2426			−0.743460			−0.371730	+	0.928341i	$0.621235\pi$
$368$			6.00000i			0.312772i
$369$	11.0711	+	31.3137i	0.576337	+	1.63013i
$370$	−2.24264			−0.116589
$371$	−1.85786			−0.0964555
$372$	9.65685	+	6.82843i	0.500685	+	0.354037i
$373$		−	14.0416i		−	0.727048i	−0.931585	−	0.363524i	$-0.881573\pi$
$373$		−	14.0416i		−	0.727048i	0.931585	−	0.363524i	$-0.118427\pi$
$374$	−15.3137			−0.791853
$375$	−1.41421	−	1.00000i	−0.0730297	−	0.0516398i
$376$		−	3.17157i		−	0.163561i
$377$			11.3726i			0.585718i
$378$	−2.92893	−	0.828427i	−0.150648	−	0.0426097i
$379$		−	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
$381$	18.1421	+	12.8284i	0.929450	+	0.657220i
$382$		−	10.2426i		−	0.524059i
$383$	32.1421			1.64239			0.821193	−	0.570650i	$-0.193309\pi$
$383$	32.1421			1.64239			0.821193	+	0.570650i	$0.193309\pi$
$384$	1.00000	−	1.41421i	0.0510310	−	0.0721688i
$385$	3.17157			0.161638
$386$		−	19.5563i		−	0.995392i
$387$	−6.58579	−	18.6274i	−0.334774	−	0.946885i
$388$			6.58579i			0.334343i
$389$			20.3431i			1.03144i	0.856758	+	0.515719i	$0.172475\pi$
$389$			20.3431i			1.03144i	−0.856758	+	0.515719i	$0.827525\pi$
$390$	−2.24264	+	3.17157i	−0.113561	+	0.160599i
$391$	16.9706			0.858238
$392$	−6.65685			−0.336222
$393$	−6.97056	−	4.92893i	−0.351618	−	0.248632i
$394$		−	18.1421i		−	0.913988i
$395$	−13.3137			−0.669885
$396$	−15.3137	+	5.41421i	−0.769543	+	0.272074i
$397$	16.9706			0.851728			0.425864	−	0.904787i	$-0.359970\pi$
$397$	16.9706			0.851728			0.425864	+	0.904787i	$0.359970\pi$
$398$	−16.9706			−0.850657
$399$	3.31371	−	2.92893i	0.165893	−	0.146630i
$400$	−1.00000			−0.0500000
$401$	−18.3848			−0.918092			−0.459046	−	0.888413i	$-0.651809\pi$
$401$	−18.3848			−0.918092			−0.459046	+	0.888413i	$0.651809\pi$
$402$		0			0
$403$	−15.3137			−0.762830
$404$		−	7.65685i		−	0.380943i
$405$	−5.65685	−	7.00000i	−0.281091	−	0.347833i
$406$	2.97056			0.147427
$407$	12.1421			0.601863
$408$	−4.00000	−	2.82843i	−0.198030	−	0.140028i
$409$		−	4.48528i		−	0.221783i	−0.993833	−	0.110891i	$-0.964629\pi$
$409$		−	4.48528i		−	0.221783i	0.993833	−	0.110891i	$-0.0353706\pi$
$410$		−	11.0711i		−	0.546761i
$411$	−20.4853	−	14.4853i	−1.01046	−	0.714506i
$412$		−	4.34315i		−	0.213971i
$413$	−7.51472			−0.369775
$414$	16.9706	−	6.00000i	0.834058	−	0.294884i
$415$	−12.8284			−0.629723
$416$			2.24264i			0.109955i
$417$	18.1421	−	25.6569i	0.888424	−	1.25642i
$418$	5.41421	−	22.9706i	0.264818	−	1.12353i
$419$			6.38478i			0.311917i	0.987764	+	0.155958i	$0.0498466\pi$
$419$			6.38478i			0.311917i	−0.987764	+	0.155958i	$0.950153\pi$
$420$	0.828427	+	0.585786i	0.0404231	+	0.0285835i
$421$		−	24.2843i		−	1.18354i	−0.806106	−	0.591771i	$-0.798429\pi$
$421$		−	24.2843i		−	1.18354i	0.806106	−	0.591771i	$-0.201571\pi$
$422$			2.00000i			0.0973585i
$423$	−8.97056	+	3.17157i	−0.436164	+	0.154207i
$424$	−3.17157			−0.154025
$425$			2.82843i			0.137199i
$426$	−2.82843	+	4.00000i	−0.137038	+	0.193801i
$427$	−2.62742			−0.127150
$428$	3.65685			0.176761
$429$	12.1421	−	17.1716i	0.586228	−	0.829051i
$430$			6.58579i			0.317595i
$431$	−19.3137			−0.930309			−0.465154	−	0.885230i	$-0.654001\pi$
$431$	−19.3137			−0.930309			−0.465154	+	0.885230i	$0.654001\pi$
$432$	−5.00000	−	1.41421i	−0.240563	−	0.0680414i
$433$			14.3848i			0.691288i	0.938366	+	0.345644i	$0.112340\pi$
$433$			14.3848i			0.691288i	−0.938366	+	0.345644i	$0.887660\pi$
$434$			4.00000i			0.192006i
$435$	7.17157	+	5.07107i	0.343851	+	0.243139i
$436$			2.34315i			0.112216i
$437$	−6.00000	+	25.4558i	−0.287019	+	1.21772i
$438$	2.48528	−	3.51472i	0.118751	−	0.167940i
$439$		−	39.9411i		−	1.90629i	−0.302520	−	0.953143i	$-0.597828\pi$
$439$		−	39.9411i		−	1.90629i	0.302520	−	0.953143i	$-0.402172\pi$
$440$	5.41421			0.258113
$441$	6.65685	+	18.8284i	0.316993	+	0.896592i
$442$	6.34315			0.301713
$443$		−	18.0000i		−	0.855206i	−0.903967	−	0.427603i	$-0.859358\pi$
$443$		−	18.0000i		−	0.855206i	0.903967	−	0.427603i	$-0.140642\pi$
$444$	3.17157	+	2.24264i	0.150516	+	0.106431i
$445$			10.5858i			0.501814i
$446$			18.0000i			0.852325i
$447$	20.4853	+	14.4853i	0.968921	+	0.685130i
$448$	0.585786			0.0276758
$449$	−16.2426			−0.766538			−0.383269	−	0.923637i	$-0.625202\pi$
$449$	−16.2426			−0.766538			−0.383269	+	0.923637i	$0.625202\pi$
$450$	1.00000	+	2.82843i	0.0471405	+	0.133333i
$451$			59.9411i			2.82252i
$452$	12.8284			0.603398
$453$	−28.9706	−	20.4853i	−1.36116	−	0.962482i
$454$	−2.34315			−0.109969
$455$	−1.31371			−0.0615876
$456$	5.65685	−	5.00000i	0.264906	−	0.234146i
$457$	−0.828427			−0.0387522			−0.0193761	−	0.999812i	$-0.506168\pi$
$457$	−0.828427			−0.0387522			−0.0193761	+	0.999812i	$0.506168\pi$
$458$	8.48528			0.396491
$459$	−4.00000	+	14.1421i	−0.186704	+	0.660098i
$460$	−6.00000			−0.279751
$461$			28.1421i			1.31071i	0.755321	+	0.655355i	$0.227481\pi$
$461$			28.1421i			1.31071i	−0.755321	+	0.655355i	$0.772519\pi$
$462$	−4.48528	−	3.17157i	−0.208674	−	0.147555i
$463$	19.2132			0.892913			0.446457	−	0.894805i	$-0.352686\pi$
$463$	19.2132			0.892913			0.446457	+	0.894805i	$0.352686\pi$
$464$	5.07107			0.235418
$465$	−6.82843	+	9.65685i	−0.316661	+	0.447826i
$466$		−	17.7990i		−	0.824522i
$467$			25.7990i			1.19383i	0.802303	+	0.596917i	$0.203608\pi$
$467$			25.7990i			1.19383i	−0.802303	+	0.596917i	$0.796392\pi$
$468$	6.34315	−	2.24264i	0.293212	−	0.103666i
$469$		0			0
$470$	3.17157			0.146294
$471$	−23.7990	+	33.6569i	−1.09660	+	1.55083i
$472$	−12.8284			−0.590476
$473$		−	35.6569i		−	1.63950i
$474$	18.8284	+	13.3137i	0.864818	+	0.611519i
$475$	−4.24264	−	1.00000i	−0.194666	−	0.0458831i
$476$		−	1.65685i		−	0.0759418i
$477$	3.17157	+	8.97056i	0.145216	+	0.410734i
$478$			0.100505i			0.00459699i
$479$			3.41421i			0.155999i	0.996953	+	0.0779997i	$0.0248533\pi$
$479$			3.41421i			0.155999i	−0.996953	+	0.0779997i	$0.975147\pi$
$480$	1.41421	+	1.00000i	0.0645497	+	0.0456435i
$481$	−5.02944			−0.229323
$482$		−	8.48528i		−	0.386494i
$483$	4.97056	+	3.51472i	0.226168	+	0.159925i
$484$	−18.3137			−0.832441
$485$	−6.58579			−0.299045
$486$	1.00000	+	15.5563i	0.0453609	+	0.705650i
$487$		−	36.1421i		−	1.63776i	−0.573967	−	0.818878i	$-0.694596\pi$
$487$		−	36.1421i		−	1.63776i	0.573967	−	0.818878i	$-0.305404\pi$
$488$	−4.48528			−0.203039
$489$	12.7279	−	18.0000i	0.575577	−	0.813988i
$490$		−	6.65685i		−	0.300726i
$491$			43.5563i			1.96567i	0.184485	+	0.982835i	$0.440938\pi$
$491$			43.5563i			1.96567i	−0.184485	+	0.982835i	$0.559062\pi$
$492$	−11.0711	+	15.6569i	−0.499122	+	0.705866i
$493$		−	14.3431i		−	0.645983i
$494$	−2.24264	+	9.51472i	−0.100901	+	0.428087i
$495$	−5.41421	−	15.3137i	−0.243351	−	0.688300i
$496$			6.82843i			0.306605i
$497$	−1.65685			−0.0743201
$498$	18.1421	+	12.8284i	0.812969	+	0.574856i
$499$	−25.6569			−1.14856			−0.574279	−	0.818659i	$-0.694718\pi$
$499$	−25.6569			−1.14856			−0.574279	+	0.818659i	$0.694718\pi$
$500$		−	1.00000i		−	0.0447214i
$501$		0			0
$502$		−	4.92893i		−	0.219989i
$503$			14.2843i			0.636904i	0.947939	+	0.318452i	$0.103163\pi$
$503$			14.2843i			0.636904i	−0.947939	+	0.318452i	$0.896837\pi$
$504$	−0.585786	−	1.65685i	−0.0260930	−	0.0738022i
$505$	7.65685			0.340726
$506$	32.4853			1.44415
$507$	7.97056	−	11.2721i	0.353985	−	0.500611i
$508$			12.8284i			0.569169i
$509$	4.10051			0.181752			0.0908758	−	0.995862i	$-0.471033\pi$
$509$	4.10051			0.181752			0.0908758	+	0.995862i	$0.471033\pi$
$510$	2.82843	−	4.00000i	0.125245	−	0.177123i
$511$	1.45584			0.0644028
$512$	1.00000			0.0441942
$513$	−19.7990	−	11.0000i	−0.874147	−	0.485662i
$514$	28.1421			1.24130
$515$	4.34315			0.191382
$516$	6.58579	−	9.31371i	0.289923	−	0.410013i
$517$	−17.1716			−0.755205
$518$			1.31371i			0.0577210i
$519$	6.00000	−	8.48528i	0.263371	−	0.372463i
$520$	−2.24264			−0.0983463
$521$	14.3848			0.630208			0.315104	−	0.949057i	$-0.397961\pi$
$521$	14.3848			0.630208			0.315104	+	0.949057i	$0.397961\pi$
$522$	−5.07107	−	14.3431i	−0.221955	−	0.627782i
$523$			8.97056i			0.392255i	0.980578	+	0.196128i	$0.0628367\pi$
$523$			8.97056i			0.392255i	−0.980578	+	0.196128i	$0.937163\pi$
$524$		−	4.92893i		−	0.215321i
$525$	−0.585786	+	0.828427i	−0.0255658	+	0.0361555i
$526$			11.1716i			0.487104i
$527$	19.3137			0.841318
$528$	−7.65685	−	5.41421i	−0.333222	−	0.235623i
$529$	−13.0000			−0.565217
$530$		−	3.17157i		−	0.137764i
$531$	12.8284	+	36.2843i	0.556706	+	1.57460i
$532$	2.48528	+	0.585786i	0.107751	+	0.0253971i
$533$		−	24.8284i		−	1.07544i
$534$	10.5858	−	14.9706i	0.458092	−	0.647840i
$535$			3.65685i			0.158100i
$536$		0			0
$537$	−21.7990	+	30.8284i	−0.940696	+	1.33034i
$538$	−24.3848			−1.05130
$539$			36.0416i			1.55242i
$540$	1.41421	−	5.00000i	0.0608581	−	0.215166i
$541$	−42.9706			−1.84745			−0.923724	−	0.383058i	$-0.874871\pi$
$541$	−42.9706			−1.84745			−0.923724	+	0.383058i	$0.874871\pi$
$542$	−28.9706			−1.24439
$543$	−15.3137	−	10.8284i	−0.657174	−	0.464692i
$544$		−	2.82843i		−	0.121268i
$545$	−2.34315			−0.100369
$546$	1.85786	+	1.31371i	0.0795093	+	0.0562215i
$547$			13.1716i			0.563176i	0.959535	+	0.281588i	$0.0908611\pi$
$547$			13.1716i			0.563176i	−0.959535	+	0.281588i	$0.909139\pi$
$548$		−	14.4853i		−	0.618781i
$549$	4.48528	+	12.6863i	0.191427	+	0.541438i
$550$			5.41421i			0.230863i
$551$	21.5147	+	5.07107i	0.916558	+	0.216035i
$552$	8.48528	+	6.00000i	0.361158	+	0.255377i
$553$			7.79899i			0.331647i
$554$	24.9706			1.06090
$555$	−2.24264	+	3.17157i	−0.0951948	+	0.134626i
$556$	18.1421			0.769398
$557$		−	28.6274i		−	1.21298i	−0.795090	−	0.606491i	$-0.792576\pi$
$557$		−	28.6274i		−	1.21298i	0.795090	−	0.606491i	$-0.207424\pi$
$558$	19.3137	−	6.82843i	0.817614	−	0.289070i
$559$			14.7696i			0.624686i
$560$			0.585786i			0.0247540i
$561$	−15.3137	+	21.6569i	−0.646545	+	0.914353i
$562$	−0.928932			−0.0391846
$563$	−13.6569			−0.575568			−0.287784	−	0.957695i	$-0.592918\pi$
$563$	−13.6569			−0.575568			−0.287784	+	0.957695i	$0.592918\pi$
$564$	−4.48528	−	3.17157i	−0.188864	−	0.133547i
$565$			12.8284i			0.539696i
$566$	12.7279			0.534994
$567$	−4.10051	+	3.31371i	−0.172205	+	0.139163i
$568$	−2.82843			−0.118678
$569$	−28.9289			−1.21276			−0.606382	−	0.795174i	$-0.707380\pi$
$569$	−28.9289			−1.21276			−0.606382	+	0.795174i	$0.707380\pi$
$570$	5.00000	+	5.65685i	0.209427	+	0.236940i
$571$	−1.65685			−0.0693372			−0.0346686	−	0.999399i	$-0.511038\pi$
$571$	−1.65685			−0.0693372			−0.0346686	+	0.999399i	$0.511038\pi$
$572$	12.1421			0.507688
$573$	−14.4853	−	10.2426i	−0.605131	−	0.427892i
$574$	−6.48528			−0.270690
$575$		−	6.00000i		−	0.250217i
$576$	−1.00000	−	2.82843i	−0.0416667	−	0.117851i
$577$	−19.1716			−0.798123			−0.399062	−	0.916924i	$-0.630664\pi$
$577$	−19.1716			−0.798123			−0.399062	+	0.916924i	$0.630664\pi$
$578$	9.00000			0.374351
$579$	−27.6569	−	19.5563i	−1.14938	−	0.812734i
$580$			5.07107i			0.210565i
$581$			7.51472i			0.311763i
$582$	9.31371	+	6.58579i	0.386066	+	0.272990i
$583$			17.1716i			0.711174i
$584$	2.48528			0.102842
$585$	2.24264	+	6.34315i	0.0927218	+	0.262257i
$586$	3.17157			0.131016
$587$			3.17157i			0.130905i	0.997856	+	0.0654524i	$0.0208491\pi$
$587$			3.17157i			0.130905i	−0.997856	+	0.0654524i	$0.979151\pi$
$588$	−6.65685	+	9.41421i	−0.274524	+	0.388236i
$589$	−6.82843	+	28.9706i	−0.281360	+	1.19371i
$590$		−	12.8284i		−	0.528138i
$591$	−25.6569	−	18.1421i	−1.05538	−	0.746268i
$592$			2.24264i			0.0921720i
$593$			12.1421i			0.498618i	0.968424	+	0.249309i	$0.0802034\pi$
$593$			12.1421i			0.498618i	−0.968424	+	0.249309i	$0.919797\pi$
$594$	−7.65685	+	27.0711i	−0.314165	+	1.11074i
$595$	1.65685			0.0679244
$596$			14.4853i			0.593340i
$597$	−16.9706	+	24.0000i	−0.694559	+	0.982255i
$598$	−13.4558			−0.550250
$599$	21.1716			0.865047			0.432524	−	0.901623i	$-0.357623\pi$
$599$	21.1716			0.865047			0.432524	+	0.901623i	$0.357623\pi$
$600$	−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	$-0.0259972\pi$
$602$	3.85786			0.157235
$603$		0			0
$604$		−	20.4853i		−	0.833534i
$605$		−	18.3137i		−	0.744558i
$606$	−10.8284	−	7.65685i	−0.439875	−	0.311038i
$607$			1.51472i			0.0614805i	0.999527	+	0.0307403i	$0.00978647\pi$
$607$			1.51472i			0.0614805i	−0.999527	+	0.0307403i	$0.990214\pi$
$608$	4.24264	+	1.00000i	0.172062	+	0.0405554i
$609$	2.97056	−	4.20101i	0.120373	−	0.170234i
$610$		−	4.48528i		−	0.181604i
$611$	7.11270			0.287749
$612$	−8.00000	+	2.82843i	−0.323381	+	0.114332i
$613$	−23.1127			−0.933513			−0.466757	−	0.884386i	$-0.654578\pi$
$613$	−23.1127			−0.933513			−0.466757	+	0.884386i	$0.654578\pi$
$614$			18.1421i			0.732157i
$615$	−15.6569	−	11.0711i	−0.631345	−	0.446429i
$616$		−	3.17157i		−	0.127786i
$617$			18.8284i			0.758004i	0.925396	+	0.379002i	$0.123733\pi$
$617$			18.8284i			0.758004i	−0.925396	+	0.379002i	$0.876267\pi$
$618$	−6.14214	−	4.34315i	−0.247073	−	0.174707i
$619$	41.4558			1.66625			0.833126	−	0.553084i	$-0.186549\pi$
$619$	41.4558			1.66625			0.833126	+	0.553084i	$0.186549\pi$
$620$	−6.82843			−0.274236
$621$	8.48528	−	30.0000i	0.340503	−	1.20386i
$622$		−	5.07107i		−	0.203331i
$623$	6.20101			0.248438
$624$	3.17157	+	2.24264i	0.126965	+	0.0897775i
$625$	1.00000			0.0400000
$626$	−16.8284			−0.672599
$627$	−27.0711	−	30.6274i	−1.08111	−	1.22314i
$628$	−23.7990			−0.949683
$629$	6.34315			0.252918
$630$	1.65685	−	0.585786i	0.0660107	−	0.0233383i
$631$	23.5147			0.936106			0.468053	−	0.883700i	$-0.344956\pi$
$631$	23.5147			0.936106			0.468053	+	0.883700i	$0.344956\pi$
$632$			13.3137i			0.529591i
$633$	2.82843	+	2.00000i	0.112420	+	0.0794929i
$634$	−0.343146			−0.0136281
$635$	−12.8284			−0.509081
$636$	−3.17157	+	4.48528i	−0.125761	+	0.177853i
$637$		−	14.9289i		−	0.591506i
$638$		−	27.4558i		−	1.08699i
$639$	2.82843	+	8.00000i	0.111891	+	0.316475i
$640$			1.00000i			0.0395285i
$641$	−11.2721			−0.445220			−0.222610	−	0.974908i	$-0.571458\pi$
$641$	−11.2721			−0.445220			−0.222610	+	0.974908i	$0.571458\pi$
$642$	3.65685	−	5.17157i	0.144325	−	0.204106i
$643$	−20.7279			−0.817429			−0.408715	−	0.912662i	$-0.634023\pi$
$643$	−20.7279			−0.817429			−0.408715	+	0.912662i	$0.634023\pi$
$644$			3.51472i			0.138499i
$645$	9.31371	+	6.58579i	0.366727	+	0.259315i
$646$	2.82843	−	12.0000i	0.111283	−	0.472134i
$647$		−	2.68629i		−	0.105609i	−0.998605	−	0.0528045i	$-0.983184\pi$
$647$		−	2.68629i		−	0.105609i	0.998605	−	0.0528045i	$-0.0168160\pi$
$648$	−7.00000	+	5.65685i	−0.274986	+	0.222222i
$649$			69.4558i			2.72638i
$650$		−	2.24264i		−	0.0879636i
$651$	5.65685	+	4.00000i	0.221710	+	0.156772i
$652$	12.7279			0.498464
$653$			15.1127i			0.591406i	0.955280	+	0.295703i	$0.0955538\pi$
$653$			15.1127i			0.591406i	−0.955280	+	0.295703i	$0.904446\pi$
$654$	3.31371	+	2.34315i	0.129576	+	0.0916242i
$655$	4.92893			0.192589
$656$	−11.0711			−0.432253
$657$	−2.48528	−	7.02944i	−0.0969601	−	0.274244i
$658$		−	1.85786i		−	0.0724271i
$659$	−8.82843			−0.343907			−0.171953	−	0.985105i	$-0.555008\pi$
$659$	−8.82843			−0.343907			−0.171953	+	0.985105i	$0.555008\pi$
$660$	5.41421	−	7.65685i	0.210748	−	0.298043i
$661$		−	3.51472i		−	0.136707i	−0.997661	−	0.0683534i	$-0.978225\pi$
$661$		−	3.51472i		−	0.136707i	0.997661	−	0.0683534i	$-0.0217745\pi$
$662$		−	16.9706i		−	0.659580i
$663$	6.34315	−	8.97056i	0.246347	−	0.348388i
$664$			12.8284i			0.497840i
$665$	−0.585786	+	2.48528i	−0.0227158	+	0.0963751i
$666$	6.34315	−	2.24264i	0.245792	−	0.0869006i
$667$			30.4264i			1.17812i
$668$		0			0
$669$	25.4558	+	18.0000i	0.984180	+	0.695920i
$670$		0			0
$671$			24.2843i			0.937484i
$672$	0.585786	−	0.828427i	0.0225972	−	0.0319573i
$673$		−	37.6985i		−	1.45317i	−0.687077	−	0.726585i	$-0.741106\pi$
$673$		−	37.6985i		−	1.45317i	0.687077	−	0.726585i	$-0.258894\pi$
$674$		−	29.2132i		−	1.12525i
$675$	5.00000	+	1.41421i	0.192450	+	0.0544331i
$676$	7.97056			0.306560
$677$	−37.5980			−1.44501			−0.722504	−	0.691367i	$-0.757009\pi$
$677$	−37.5980			−1.44501			−0.722504	+	0.691367i	$0.757009\pi$
$678$	12.8284	−	18.1421i	0.492673	−	0.696745i
$679$			3.85786i			0.148051i
$680$	2.82843			0.108465
$681$	−2.34315	+	3.31371i	−0.0897895	+	0.126982i
$682$	36.9706			1.41568
$683$	39.2548			1.50204			0.751022	−	0.660277i	$-0.229561\pi$
$683$	39.2548			1.50204			0.751022	+	0.660277i	$0.229561\pi$
$684$	−1.41421	−	13.0000i	−0.0540738	−	0.497067i
$685$	14.4853			0.553454
$686$	−8.00000			−0.305441
$687$	8.48528	−	12.0000i	0.323734	−	0.457829i
$688$	6.58579			0.251081
$689$		−	7.11270i		−	0.270972i
$690$	−6.00000	+	8.48528i	−0.228416	+	0.323029i
$691$	36.9706			1.40643			0.703213	−	0.710979i	$-0.251748\pi$
$691$	36.9706			1.40643			0.703213	+	0.710979i	$0.251748\pi$
$692$	6.00000			0.228086
$693$	−8.97056	+	3.17157i	−0.340764	+	0.120478i
$694$			30.2843i			1.14958i
$695$			18.1421i			0.688170i
$696$	5.07107	−	7.17157i	0.192218	−	0.271838i
$697$			31.3137i			1.18609i
$698$	−10.9706			−0.415242
$699$	−25.1716	−	17.7990i	−0.952076	−	0.673220i
$700$	−0.585786			−0.0221406
$701$		−	2.48528i		−	0.0938678i	−0.998898	−	0.0469339i	$-0.985055\pi$
$701$		−	2.48528i		−	0.0938678i	0.998898	−	0.0469339i	$-0.0149450\pi$
$702$	3.17157	−	11.2132i	0.119703	−	0.423215i
$703$	−2.24264	+	9.51472i	−0.0845828	+	0.358854i
$704$		−	5.41421i		−	0.204056i
$705$	3.17157	−	4.48528i	0.119448	−	0.168925i
$706$		−	8.82843i		−	0.332262i
$707$		−	4.48528i		−	0.168686i
$708$	−12.8284	+	18.1421i	−0.482122	+	0.681823i
$709$	19.5147			0.732891			0.366445	−	0.930440i	$-0.380575\pi$
$709$	19.5147			0.732891			0.366445	+	0.930440i	$0.380575\pi$
$710$		−	2.82843i		−	0.106149i
$711$	37.6569	−	13.3137i	1.41224	−	0.499303i
$712$	10.5858			0.396719
$713$	−40.9706			−1.53436
$714$	−2.34315	−	1.65685i	−0.0876900	−	0.0620062i
$715$			12.1421i			0.454090i
$716$	−21.7990			−0.814667
$717$	0.142136	+	0.100505i	0.00530815	+	0.00375343i
$718$		−	19.4142i		−	0.724532i
$719$			30.7279i			1.14596i	0.819570	+	0.572979i	$0.194212\pi$
$719$			30.7279i			1.14596i	−0.819570	+	0.572979i	$0.805788\pi$
$720$	2.82843	−	1.00000i	0.105409	−	0.0372678i
$721$		−	2.54416i		−	0.0947493i
$722$	17.0000	+	8.48528i	0.632674	+	0.315789i
$723$	−12.0000	−	8.48528i	−0.446285	−	0.315571i
$724$		−	10.8284i		−	0.402435i
$725$	−5.07107			−0.188335
$726$	−18.3137	+	25.8995i	−0.679685	+	0.961220i
$727$	25.5563			0.947833			0.473916	−	0.880570i	$-0.342840\pi$
$727$	25.5563			0.947833			0.473916	+	0.880570i	$0.342840\pi$
$728$			1.31371i			0.0486893i
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$			2.48528i			0.0919844i
$731$		−	18.6274i		−	0.688960i
$732$	−4.48528	+	6.34315i	−0.165781	+	0.234449i
$733$	−15.5147			−0.573049			−0.286525	−	0.958073i	$-0.592500\pi$
$733$	−15.5147			−0.573049			−0.286525	+	0.958073i	$0.592500\pi$
$734$	−14.2426			−0.525705
$735$	−9.41421	−	6.65685i	−0.347248	−	0.245542i
$736$			6.00000i			0.221163i
$737$		0			0
$738$	11.0711	+	31.3137i	0.407532	+	1.15267i
$739$	−20.4853			−0.753563			−0.376782	−	0.926302i	$-0.622969\pi$
$739$	−20.4853			−0.753563			−0.376782	+	0.926302i	$0.622969\pi$
$740$	−2.24264			−0.0824411
$741$	11.2132	+	12.6863i	0.411927	+	0.466043i
$742$	−1.85786			−0.0682043
$743$	−43.1716			−1.58381			−0.791906	−	0.610643i	$-0.790911\pi$
$743$	−43.1716			−1.58381			−0.791906	+	0.610643i	$0.790911\pi$
$744$	9.65685	+	6.82843i	0.354037	+	0.250342i
$745$	−14.4853			−0.530700
$746$		−	14.0416i		−	0.514101i
$747$	36.2843	−	12.8284i	1.32757	−	0.469368i
$748$	−15.3137			−0.559925
$749$	2.14214			0.0782719
$750$	−1.41421	−	1.00000i	−0.0516398	−	0.0365148i
$751$		−	48.4853i		−	1.76925i	−0.466300	−	0.884627i	$-0.654413\pi$
$751$		−	48.4853i		−	1.76925i	0.466300	−	0.884627i	$-0.345587\pi$
$752$		−	3.17157i		−	0.115655i
$753$	−6.97056	−	4.92893i	−0.254021	−	0.179620i
$754$			11.3726i			0.414165i
$755$	20.4853			0.745536
$756$	−2.92893	−	0.828427i	−0.106524	−	0.0301296i
$757$	49.6569			1.80481			0.902405	−	0.430890i	$-0.141800\pi$
$757$	49.6569			1.80481			0.902405	+	0.430890i	$0.141800\pi$
$758$		−	8.00000i		−	0.290573i
$759$	32.4853	−	45.9411i	1.17914	−	1.66756i
$760$	−1.00000	+	4.24264i	−0.0362738	+	0.153897i
$761$			1.17157i			0.0424695i	0.999775	+	0.0212347i	$0.00675974\pi$
$761$			1.17157i			0.0424695i	−0.999775	+	0.0212347i	$0.993240\pi$
$762$	18.1421	+	12.8284i	0.657220	+	0.464725i
$763$			1.37258i			0.0496908i
$764$		−	10.2426i		−	0.370566i
$765$	−2.82843	−	8.00000i	−0.102262	−	0.289241i
$766$	32.1421			1.16134
$767$		−	28.7696i		−	1.03881i
$768$	1.00000	−	1.41421i	0.0360844	−	0.0510310i
$769$	−13.3137			−0.480105			−0.240052	−	0.970760i	$-0.577165\pi$
$769$	−13.3137			−0.480105			−0.240052	+	0.970760i	$0.577165\pi$
$770$	3.17157			0.114296
$771$	28.1421	−	39.7990i	1.01351	−	1.43333i
$772$		−	19.5563i		−	0.703848i
$773$	0.343146			0.0123421			0.00617105	−	0.999981i	$-0.498036\pi$
$773$	0.343146			0.0123421			0.00617105	+	0.999981i	$0.498036\pi$
$774$	−6.58579	−	18.6274i	−0.236721	−	0.669549i
$775$		−	6.82843i		−	0.245284i
$776$			6.58579i			0.236416i
$777$	1.85786	+	1.31371i	0.0666505	+	0.0471290i
$778$			20.3431i			0.729337i

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(1.00000 - 1.41421i) q^{6} +0.585786 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(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} +0.585786 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +1.00000i q^{10} -5.41421i q^{11} +(1.00000 - 1.41421i) q^{12} +2.24264i q^{13} +0.585786 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} +(0.585786 - 0.828427i) q^{21} -5.41421i q^{22} +6.00000i q^{23} +(1.00000 - 1.41421i) q^{24} -1.00000 q^{25} +2.24264i q^{26} +(-5.00000 - 1.41421i) q^{27} +0.585786 q^{28} +5.07107 q^{29} +(1.41421 + 1.00000i) q^{30} +6.82843i q^{31} +1.00000 q^{32} +(-7.65685 - 5.41421i) q^{33} -2.82843i q^{34} +0.585786i q^{35} +(-1.00000 - 2.82843i) q^{36} +2.24264i q^{37} +(4.24264 + 1.00000i) q^{38} +(3.17157 + 2.24264i) q^{39} +1.00000i q^{40} -11.0711 q^{41} +(0.585786 - 0.828427i) q^{42} +6.58579 q^{43} -5.41421i q^{44} +(2.82843 - 1.00000i) q^{45} +6.00000i q^{46} -3.17157i q^{47} +(1.00000 - 1.41421i) q^{48} -6.65685 q^{49} -1.00000 q^{50} +(-4.00000 - 2.82843i) q^{51} +2.24264i q^{52} -3.17157 q^{53} +(-5.00000 - 1.41421i) q^{54} +5.41421 q^{55} +0.585786 q^{56} +(5.65685 - 5.00000i) q^{57} +5.07107 q^{58} -12.8284 q^{59} +(1.41421 + 1.00000i) q^{60} -4.48528 q^{61} +6.82843i q^{62} +(-0.585786 - 1.65685i) q^{63} +1.00000 q^{64} -2.24264 q^{65} +(-7.65685 - 5.41421i) q^{66} -2.82843i q^{68} +(8.48528 + 6.00000i) q^{69} +0.585786i q^{70} -2.82843 q^{71} +(-1.00000 - 2.82843i) q^{72} +2.48528 q^{73} +2.24264i q^{74} +(-1.00000 + 1.41421i) q^{75} +(4.24264 + 1.00000i) q^{76} -3.17157i q^{77} +(3.17157 + 2.24264i) q^{78} +13.3137i q^{79} +1.00000i q^{80} +(-7.00000 + 5.65685i) q^{81} -11.0711 q^{82} +12.8284i q^{83} +(0.585786 - 0.828427i) q^{84} +2.82843 q^{85} +6.58579 q^{86} +(5.07107 - 7.17157i) q^{87} -5.41421i q^{88} +10.5858 q^{89} +(2.82843 - 1.00000i) q^{90} +1.31371i q^{91} +6.00000i q^{92} +(9.65685 + 6.82843i) q^{93} -3.17157i q^{94} +(-1.00000 + 4.24264i) q^{95} +(1.00000 - 1.41421i) q^{96} +6.58579i q^{97} -6.65685 q^{98} +(-15.3137 + 5.41421i) 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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