LMFDB - Embedded newform 104.2.e.b.77.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [104,2,Mod(77,104)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(104, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("104.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.e (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:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			77.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	104.77
Dual form			104.2.e.b.77.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +1.00000i q^{3} +2.00000i q^{4} -1.00000 q^{5} +(-1.00000 + 1.00000i) q^{6} -3.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +2.00000 q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +1.00000i q^{3} +2.00000i q^{4} -1.00000 q^{5} +(-1.00000 + 1.00000i) q^{6} -3.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +2.00000 q^{9} +(-1.00000 - 1.00000i) q^{10} -2.00000 q^{11} -2.00000 q^{12} +(3.00000 - 2.00000i) q^{13} +(3.00000 - 3.00000i) q^{14} -1.00000i q^{15} -4.00000 q^{16} +3.00000 q^{17} +(2.00000 + 2.00000i) q^{18} -2.00000i q^{20} +3.00000 q^{21} +(-2.00000 - 2.00000i) q^{22} -6.00000 q^{23} +(-2.00000 - 2.00000i) q^{24} -4.00000 q^{25} +(5.00000 + 1.00000i) q^{26} +5.00000i q^{27} +6.00000 q^{28} -6.00000i q^{29} +(1.00000 - 1.00000i) q^{30} +(-4.00000 - 4.00000i) q^{32} -2.00000i q^{33} +(3.00000 + 3.00000i) q^{34} +3.00000i q^{35} +4.00000i q^{36} -3.00000 q^{37} +(2.00000 + 3.00000i) q^{39} +(2.00000 - 2.00000i) q^{40} +10.0000i q^{41} +(3.00000 + 3.00000i) q^{42} -9.00000i q^{43} -4.00000i q^{44} -2.00000 q^{45} +(-6.00000 - 6.00000i) q^{46} +7.00000i q^{47} -4.00000i q^{48} -2.00000 q^{49} +(-4.00000 - 4.00000i) q^{50} +3.00000i q^{51} +(4.00000 + 6.00000i) q^{52} +6.00000i q^{53} +(-5.00000 + 5.00000i) q^{54} +2.00000 q^{55} +(6.00000 + 6.00000i) q^{56} +(6.00000 - 6.00000i) q^{58} -10.0000 q^{59} +2.00000 q^{60} +10.0000i q^{61} -6.00000i q^{63} -8.00000i q^{64} +(-3.00000 + 2.00000i) q^{65} +(2.00000 - 2.00000i) q^{66} +12.0000 q^{67} +6.00000i q^{68} -6.00000i q^{69} +(-3.00000 + 3.00000i) q^{70} +5.00000i q^{71} +(-4.00000 + 4.00000i) q^{72} -6.00000i q^{73} +(-3.00000 - 3.00000i) q^{74} -4.00000i q^{75} +6.00000i q^{77} +(-1.00000 + 5.00000i) q^{78} +4.00000 q^{80} +1.00000 q^{81} +(-10.0000 + 10.0000i) q^{82} +16.0000 q^{83} +6.00000i q^{84} -3.00000 q^{85} +(9.00000 - 9.00000i) q^{86} +6.00000 q^{87} +(4.00000 - 4.00000i) q^{88} -4.00000i q^{89} +(-2.00000 - 2.00000i) q^{90} +(-6.00000 - 9.00000i) q^{91} -12.0000i q^{92} +(-7.00000 + 7.00000i) q^{94} +(4.00000 - 4.00000i) q^{96} -18.0000i q^{97} +(-2.00000 - 2.00000i) q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{5} - 2 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^5 - 2 * q^6 - 4 * q^8 + 4 * q^9	$ 2 q + 2 q^{2} - 2 q^{5} - 2 q^{6} - 4 q^{8} + 4 q^{9} - 2 q^{10} - 4 q^{11} - 4 q^{12} + 6 q^{13} + 6 q^{14} - 8 q^{16} + 6 q^{17} + 4 q^{18} + 6 q^{21} - 4 q^{22} - 12 q^{23} - 4 q^{24} - 8 q^{25} + 10 q^{26} + 12 q^{28} + 2 q^{30} - 8 q^{32} + 6 q^{34} - 6 q^{37} + 4 q^{39} + 4 q^{40} + 6 q^{42} - 4 q^{45} - 12 q^{46} - 4 q^{49} - 8 q^{50} + 8 q^{52} - 10 q^{54} + 4 q^{55} + 12 q^{56} + 12 q^{58} - 20 q^{59} + 4 q^{60} - 6 q^{65} + 4 q^{66} + 24 q^{67} - 6 q^{70} - 8 q^{72} - 6 q^{74} - 2 q^{78} + 8 q^{80} + 2 q^{81} - 20 q^{82} + 32 q^{83} - 6 q^{85} + 18 q^{86} + 12 q^{87} + 8 q^{88} - 4 q^{90} - 12 q^{91} - 14 q^{94} + 8 q^{96} - 4 q^{98} - 8 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^5 - 2 * q^6 - 4 * q^8 + 4 * q^9 - 2 * q^10 - 4 * q^11 - 4 * q^12 + 6 * q^13 + 6 * q^14 - 8 * q^16 + 6 * q^17 + 4 * q^18 + 6 * q^21 - 4 * q^22 - 12 * q^23 - 4 * q^24 - 8 * q^25 + 10 * q^26 + 12 * q^28 + 2 * q^30 - 8 * q^32 + 6 * q^34 - 6 * q^37 + 4 * q^39 + 4 * q^40 + 6 * q^42 - 4 * q^45 - 12 * q^46 - 4 * q^49 - 8 * q^50 + 8 * q^52 - 10 * q^54 + 4 * q^55 + 12 * q^56 + 12 * q^58 - 20 * q^59 + 4 * q^60 - 6 * q^65 + 4 * q^66 + 24 * q^67 - 6 * q^70 - 8 * q^72 - 6 * q^74 - 2 * q^78 + 8 * q^80 + 2 * q^81 - 20 * q^82 + 32 * q^83 - 6 * q^85 + 18 * q^86 + 12 * q^87 + 8 * q^88 - 4 * q^90 - 12 * q^91 - 14 * q^94 + 8 * q^96 - 4 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$-1$	$-1$	$1$

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	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$			1.00000i			0.577350i	0.957427	+	0.288675i	$0.0932147\pi$
$3$			1.00000i			0.577350i	−0.957427	+	0.288675i	$0.906785\pi$
$4$			2.00000i			1.00000i
$5$	−1.00000			−0.447214			−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000			−0.447214			−0.223607	+	0.974679i	$0.571783\pi$
$6$	−1.00000	+	1.00000i	−0.408248	+	0.408248i
$7$		−	3.00000i		−	1.13389i	−0.823754	−	0.566947i	$-0.808125\pi$
$7$		−	3.00000i		−	1.13389i	0.823754	−	0.566947i	$-0.191875\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	2.00000			0.666667
$10$	−1.00000	−	1.00000i	−0.316228	−	0.316228i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$	−2.00000			−0.577350
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$14$	3.00000	−	3.00000i	0.801784	−	0.801784i
$15$		−	1.00000i		−	0.258199i
$16$	−4.00000			−1.00000
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$	2.00000	+	2.00000i	0.471405	+	0.471405i
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$		−	2.00000i		−	0.447214i
$21$	3.00000			0.654654
$22$	−2.00000	−	2.00000i	−0.426401	−	0.426401i
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$	−2.00000	−	2.00000i	−0.408248	−	0.408248i
$25$	−4.00000			−0.800000
$26$	5.00000	+	1.00000i	0.980581	+	0.196116i
$27$			5.00000i			0.962250i
$28$	6.00000			1.13389
$29$		−	6.00000i		−	1.11417i	−0.830455	−	0.557086i	$-0.811919\pi$
$29$		−	6.00000i		−	1.11417i	0.830455	−	0.557086i	$-0.188081\pi$
$30$	1.00000	−	1.00000i	0.182574	−	0.182574i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$		−	2.00000i		−	0.348155i
$34$	3.00000	+	3.00000i	0.514496	+	0.514496i
$35$			3.00000i			0.507093i
$36$			4.00000i			0.666667i
$37$	−3.00000			−0.493197			−0.246598	−	0.969118i	$-0.579313\pi$
$37$	−3.00000			−0.493197			−0.246598	+	0.969118i	$0.579313\pi$
$38$		0			0
$39$	2.00000	+	3.00000i	0.320256	+	0.480384i
$40$	2.00000	−	2.00000i	0.316228	−	0.316228i
$41$			10.0000i			1.56174i	0.624695	+	0.780869i	$0.285223\pi$
$41$			10.0000i			1.56174i	−0.624695	+	0.780869i	$0.714777\pi$
$42$	3.00000	+	3.00000i	0.462910	+	0.462910i
$43$		−	9.00000i		−	1.37249i	−0.727372	−	0.686244i	$-0.759258\pi$
$43$		−	9.00000i		−	1.37249i	0.727372	−	0.686244i	$-0.240742\pi$
$44$		−	4.00000i		−	0.603023i
$45$	−2.00000			−0.298142
$46$	−6.00000	−	6.00000i	−0.884652	−	0.884652i
$47$			7.00000i			1.02105i	0.859861	+	0.510527i	$0.170550\pi$
$47$			7.00000i			1.02105i	−0.859861	+	0.510527i	$0.829450\pi$
$48$		−	4.00000i		−	0.577350i
$49$	−2.00000			−0.285714
$50$	−4.00000	−	4.00000i	−0.565685	−	0.565685i
$51$			3.00000i			0.420084i
$52$	4.00000	+	6.00000i	0.554700	+	0.832050i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$	−5.00000	+	5.00000i	−0.680414	+	0.680414i
$55$	2.00000			0.269680
$56$	6.00000	+	6.00000i	0.801784	+	0.801784i
$57$		0			0
$58$	6.00000	−	6.00000i	0.787839	−	0.787839i
$59$	−10.0000			−1.30189			−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000			−1.30189			−0.650945	+	0.759125i	$0.725627\pi$
$60$	2.00000			0.258199
$61$			10.0000i			1.28037i	0.768221	+	0.640184i	$0.221142\pi$
$61$			10.0000i			1.28037i	−0.768221	+	0.640184i	$0.778858\pi$
$62$		0			0
$63$		−	6.00000i		−	0.755929i
$64$		−	8.00000i		−	1.00000i
$65$	−3.00000	+	2.00000i	−0.372104	+	0.248069i
$66$	2.00000	−	2.00000i	0.246183	−	0.246183i
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$			6.00000i			0.727607i
$69$		−	6.00000i		−	0.722315i
$70$	−3.00000	+	3.00000i	−0.358569	+	0.358569i
$71$			5.00000i			0.593391i	0.954972	+	0.296695i	$0.0958846\pi$
$71$			5.00000i			0.593391i	−0.954972	+	0.296695i	$0.904115\pi$
$72$	−4.00000	+	4.00000i	−0.471405	+	0.471405i
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$	−3.00000	−	3.00000i	−0.348743	−	0.348743i
$75$		−	4.00000i		−	0.461880i
$76$		0			0
$77$			6.00000i			0.683763i
$78$	−1.00000	+	5.00000i	−0.113228	+	0.566139i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	4.00000			0.447214
$81$	1.00000			0.111111
$82$	−10.0000	+	10.0000i	−1.10432	+	1.10432i
$83$	16.0000			1.75623			0.878114	−	0.478451i	$-0.158802\pi$
$83$	16.0000			1.75623			0.878114	+	0.478451i	$0.158802\pi$
$84$			6.00000i			0.654654i
$85$	−3.00000			−0.325396
$86$	9.00000	−	9.00000i	0.970495	−	0.970495i
$87$	6.00000			0.643268
$88$	4.00000	−	4.00000i	0.426401	−	0.426401i
$89$		−	4.00000i		−	0.423999i	−0.977270	−	0.212000i	$-0.932002\pi$
$89$		−	4.00000i		−	0.423999i	0.977270	−	0.212000i	$-0.0679975\pi$
$90$	−2.00000	−	2.00000i	−0.210819	−	0.210819i
$91$	−6.00000	−	9.00000i	−0.628971	−	0.943456i
$92$		−	12.0000i		−	1.25109i
$93$		0			0
$94$	−7.00000	+	7.00000i	−0.721995	+	0.721995i
$95$		0			0
$96$	4.00000	−	4.00000i	0.408248	−	0.408248i
$97$		−	18.0000i		−	1.82762i	−0.406138	−	0.913812i	$-0.633125\pi$
$97$		−	18.0000i		−	1.82762i	0.406138	−	0.913812i	$-0.366875\pi$
$98$	−2.00000	−	2.00000i	−0.202031	−	0.202031i
$99$	−4.00000			−0.402015
$100$		−	8.00000i		−	0.800000i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$	−3.00000	+	3.00000i	−0.297044	+	0.297044i
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$	−2.00000	+	10.0000i	−0.196116	+	0.980581i
$105$	−3.00000			−0.292770
$106$	−6.00000	+	6.00000i	−0.582772	+	0.582772i
$107$		−	12.0000i		−	1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$		−	12.0000i		−	1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$	−10.0000			−0.962250
$109$	−15.0000			−1.43674			−0.718370	−	0.695662i	$-0.755111\pi$
$109$	−15.0000			−1.43674			−0.718370	+	0.695662i	$0.755111\pi$
$110$	2.00000	+	2.00000i	0.190693	+	0.190693i
$111$		−	3.00000i		−	0.284747i
$112$			12.0000i			1.13389i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	6.00000			0.559503
$116$	12.0000			1.11417
$117$	6.00000	−	4.00000i	0.554700	−	0.369800i
$118$	−10.0000	−	10.0000i	−0.920575	−	0.920575i
$119$		−	9.00000i		−	0.825029i
$120$	2.00000	+	2.00000i	0.182574	+	0.182574i
$121$	−7.00000			−0.636364
$122$	−10.0000	+	10.0000i	−0.905357	+	0.905357i
$123$	−10.0000			−0.901670
$124$		0			0
$125$	9.00000			0.804984
$126$	6.00000	−	6.00000i	0.534522	−	0.534522i
$127$	18.0000			1.59724			0.798621	−	0.601834i	$-0.205563\pi$
$127$	18.0000			1.59724			0.798621	+	0.601834i	$0.205563\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$	9.00000			0.792406
$130$	−5.00000	−	1.00000i	−0.438529	−	0.0877058i
$131$			15.0000i			1.31056i	0.755388	+	0.655278i	$0.227449\pi$
$131$			15.0000i			1.31056i	−0.755388	+	0.655278i	$0.772551\pi$
$132$	4.00000			0.348155
$133$		0			0
$134$	12.0000	+	12.0000i	1.03664	+	1.03664i
$135$		−	5.00000i		−	0.430331i
$136$	−6.00000	+	6.00000i	−0.514496	+	0.514496i
$137$			2.00000i			0.170872i	0.996344	+	0.0854358i	$0.0272282\pi$
$137$			2.00000i			0.170872i	−0.996344	+	0.0854358i	$0.972772\pi$
$138$	6.00000	−	6.00000i	0.510754	−	0.510754i
$139$			9.00000i			0.763370i	0.924292	+	0.381685i	$0.124656\pi$
$139$			9.00000i			0.763370i	−0.924292	+	0.381685i	$0.875344\pi$
$140$	−6.00000			−0.507093
$141$	−7.00000			−0.589506
$142$	−5.00000	+	5.00000i	−0.419591	+	0.419591i
$143$	−6.00000	+	4.00000i	−0.501745	+	0.334497i
$144$	−8.00000			−0.666667
$145$			6.00000i			0.498273i
$146$	6.00000	−	6.00000i	0.496564	−	0.496564i
$147$		−	2.00000i		−	0.164957i
$148$		−	6.00000i		−	0.493197i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$	4.00000	−	4.00000i	0.326599	−	0.326599i
$151$			15.0000i			1.22068i	0.792139	+	0.610341i	$0.208968\pi$
$151$			15.0000i			1.22068i	−0.792139	+	0.610341i	$0.791032\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$	−6.00000	+	6.00000i	−0.483494	+	0.483494i
$155$		0			0
$156$	−6.00000	+	4.00000i	−0.480384	+	0.320256i
$157$			18.0000i			1.43656i	0.695756	+	0.718278i	$0.255069\pi$
$157$			18.0000i			1.43656i	−0.695756	+	0.718278i	$0.744931\pi$
$158$		0			0
$159$	−6.00000			−0.475831
$160$	4.00000	+	4.00000i	0.316228	+	0.316228i
$161$			18.0000i			1.41860i
$162$	1.00000	+	1.00000i	0.0785674	+	0.0785674i
$163$	6.00000			0.469956			0.234978	−	0.972001i	$-0.424498\pi$
$163$	6.00000			0.469956			0.234978	+	0.972001i	$0.424498\pi$
$164$	−20.0000			−1.56174
$165$			2.00000i			0.155700i
$166$	16.0000	+	16.0000i	1.24184	+	1.24184i
$167$		−	8.00000i		−	0.619059i	−0.950890	−	0.309529i	$-0.899829\pi$
$167$		−	8.00000i		−	0.619059i	0.950890	−	0.309529i	$-0.100171\pi$
$168$	−6.00000	+	6.00000i	−0.462910	+	0.462910i
$169$	5.00000	−	12.0000i	0.384615	−	0.923077i
$170$	−3.00000	−	3.00000i	−0.230089	−	0.230089i
$171$		0			0
$172$	18.0000			1.37249
$173$		−	24.0000i		−	1.82469i	−0.409426	−	0.912343i	$-0.634271\pi$
$173$		−	24.0000i		−	1.82469i	0.409426	−	0.912343i	$-0.365729\pi$
$174$	6.00000	+	6.00000i	0.454859	+	0.454859i
$175$			12.0000i			0.907115i
$176$	8.00000			0.603023
$177$		−	10.0000i		−	0.751646i
$178$	4.00000	−	4.00000i	0.299813	−	0.299813i
$179$			9.00000i			0.672692i	0.941739	+	0.336346i	$0.109191\pi$
$179$			9.00000i			0.672692i	−0.941739	+	0.336346i	$0.890809\pi$
$180$		−	4.00000i		−	0.298142i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	3.00000	−	15.0000i	0.222375	−	1.11187i
$183$	−10.0000			−0.739221
$184$	12.0000	−	12.0000i	0.884652	−	0.884652i
$185$	3.00000			0.220564
$186$		0			0
$187$	−6.00000			−0.438763
$188$	−14.0000			−1.02105
$189$	15.0000			1.09109
$190$		0			0
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$	8.00000			0.577350
$193$			24.0000i			1.72756i	0.503871	+	0.863779i	$0.331909\pi$
$193$			24.0000i			1.72756i	−0.503871	+	0.863779i	$0.668091\pi$
$194$	18.0000	−	18.0000i	1.29232	−	1.29232i
$195$	−2.00000	−	3.00000i	−0.143223	−	0.214834i
$196$		−	4.00000i		−	0.285714i
$197$	−23.0000			−1.63868			−0.819341	−	0.573306i	$-0.805660\pi$
$197$	−23.0000			−1.63868			−0.819341	+	0.573306i	$0.805660\pi$
$198$	−4.00000	−	4.00000i	−0.284268	−	0.284268i
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	8.00000	−	8.00000i	0.565685	−	0.565685i
$201$			12.0000i			0.846415i
$202$		0			0
$203$	−18.0000			−1.26335
$204$	−6.00000			−0.420084
$205$		−	10.0000i		−	0.698430i
$206$	4.00000	+	4.00000i	0.278693	+	0.278693i
$207$	−12.0000			−0.834058
$208$	−12.0000	+	8.00000i	−0.832050	+	0.554700i
$209$		0			0
$210$	−3.00000	−	3.00000i	−0.207020	−	0.207020i
$211$		−	5.00000i		−	0.344214i	−0.985078	−	0.172107i	$-0.944942\pi$
$211$		−	5.00000i		−	0.344214i	0.985078	−	0.172107i	$-0.0550575\pi$
$212$	−12.0000			−0.824163
$213$	−5.00000			−0.342594
$214$	12.0000	−	12.0000i	0.820303	−	0.820303i
$215$			9.00000i			0.613795i
$216$	−10.0000	−	10.0000i	−0.680414	−	0.680414i
$217$		0			0
$218$	−15.0000	−	15.0000i	−1.01593	−	1.01593i
$219$	6.00000			0.405442
$220$			4.00000i			0.269680i
$221$	9.00000	−	6.00000i	0.605406	−	0.403604i
$222$	3.00000	−	3.00000i	0.201347	−	0.201347i
$223$		−	21.0000i		−	1.40626i	−0.711059	−	0.703132i	$-0.751784\pi$
$223$		−	21.0000i		−	1.40626i	0.711059	−	0.703132i	$-0.248216\pi$
$224$	−12.0000	+	12.0000i	−0.801784	+	0.801784i
$225$	−8.00000			−0.533333
$226$	−6.00000	−	6.00000i	−0.399114	−	0.399114i
$227$	2.00000			0.132745			0.0663723	−	0.997795i	$-0.478857\pi$
$227$	2.00000			0.132745			0.0663723	+	0.997795i	$0.478857\pi$
$228$		0			0
$229$	15.0000			0.991228			0.495614	−	0.868543i	$-0.334943\pi$
$229$	15.0000			0.991228			0.495614	+	0.868543i	$0.334943\pi$
$230$	6.00000	+	6.00000i	0.395628	+	0.395628i
$231$	−6.00000			−0.394771
$232$	12.0000	+	12.0000i	0.787839	+	0.787839i
$233$	9.00000			0.589610			0.294805	−	0.955557i	$-0.404745\pi$
$233$	9.00000			0.589610			0.294805	+	0.955557i	$0.404745\pi$
$234$	10.0000	+	2.00000i	0.653720	+	0.130744i
$235$		−	7.00000i		−	0.456630i
$236$		−	20.0000i		−	1.30189i
$237$		0			0
$238$	9.00000	−	9.00000i	0.583383	−	0.583383i
$239$		−	19.0000i		−	1.22901i	−0.788914	−	0.614504i	$-0.789356\pi$
$239$		−	19.0000i		−	1.22901i	0.788914	−	0.614504i	$-0.210644\pi$
$240$			4.00000i			0.258199i
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−7.00000	−	7.00000i	−0.449977	−	0.449977i
$243$			16.0000i			1.02640i
$244$	−20.0000			−1.28037
$245$	2.00000			0.127775
$246$	−10.0000	−	10.0000i	−0.637577	−	0.637577i
$247$		0			0
$248$		0			0
$249$			16.0000i			1.01396i
$250$	9.00000	+	9.00000i	0.569210	+	0.569210i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$	12.0000			0.755929
$253$	12.0000			0.754434
$254$	18.0000	+	18.0000i	1.12942	+	1.12942i
$255$		−	3.00000i		−	0.187867i
$256$	16.0000			1.00000
$257$	3.00000			0.187135			0.0935674	−	0.995613i	$-0.470173\pi$
$257$	3.00000			0.187135			0.0935674	+	0.995613i	$0.470173\pi$
$258$	9.00000	+	9.00000i	0.560316	+	0.560316i
$259$			9.00000i			0.559233i
$260$	−4.00000	−	6.00000i	−0.248069	−	0.372104i
$261$		−	12.0000i		−	0.742781i
$262$	−15.0000	+	15.0000i	−0.926703	+	0.926703i
$263$	−6.00000			−0.369976			−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000			−0.369976			−0.184988	+	0.982741i	$0.559225\pi$
$264$	4.00000	+	4.00000i	0.246183	+	0.246183i
$265$		−	6.00000i		−	0.368577i
$266$		0			0
$267$	4.00000			0.244796
$268$			24.0000i			1.46603i
$269$		−	6.00000i		−	0.365826i	−0.983129	−	0.182913i	$-0.941447\pi$
$269$		−	6.00000i		−	0.365826i	0.983129	−	0.182913i	$-0.0585527\pi$
$270$	5.00000	−	5.00000i	0.304290	−	0.304290i
$271$			15.0000i			0.911185i	0.890188	+	0.455593i	$0.150573\pi$
$271$			15.0000i			0.911185i	−0.890188	+	0.455593i	$0.849427\pi$
$272$	−12.0000			−0.727607
$273$	9.00000	−	6.00000i	0.544705	−	0.363137i
$274$	−2.00000	+	2.00000i	−0.120824	+	0.120824i
$275$	8.00000			0.482418
$276$	12.0000			0.722315
$277$			18.0000i			1.08152i	0.841178	+	0.540758i	$0.181862\pi$
$277$			18.0000i			1.08152i	−0.841178	+	0.540758i	$0.818138\pi$
$278$	−9.00000	+	9.00000i	−0.539784	+	0.539784i
$279$		0			0
$280$	−6.00000	−	6.00000i	−0.358569	−	0.358569i
$281$		−	20.0000i		−	1.19310i	−0.802576	−	0.596550i	$-0.796538\pi$
$281$		−	20.0000i		−	1.19310i	0.802576	−	0.596550i	$-0.203462\pi$
$282$	−7.00000	−	7.00000i	−0.416844	−	0.416844i
$283$		−	4.00000i		−	0.237775i	−0.992908	−	0.118888i	$-0.962067\pi$
$283$		−	4.00000i		−	0.237775i	0.992908	−	0.118888i	$-0.0379328\pi$
$284$	−10.0000			−0.593391
$285$		0			0
$286$	−10.0000	−	2.00000i	−0.591312	−	0.118262i
$287$	30.0000			1.77084
$288$	−8.00000	−	8.00000i	−0.471405	−	0.471405i
$289$	−8.00000			−0.470588
$290$	−6.00000	+	6.00000i	−0.352332	+	0.352332i
$291$	18.0000			1.05518
$292$	12.0000			0.702247
$293$	1.00000			0.0584206			0.0292103	−	0.999573i	$-0.490701\pi$
$293$	1.00000			0.0584206			0.0292103	+	0.999573i	$0.490701\pi$
$294$	2.00000	−	2.00000i	0.116642	−	0.116642i
$295$	10.0000			0.582223
$296$	6.00000	−	6.00000i	0.348743	−	0.348743i
$297$		−	10.0000i		−	0.580259i
$298$	10.0000	+	10.0000i	0.579284	+	0.579284i
$299$	−18.0000	+	12.0000i	−1.04097	+	0.693978i
$300$	8.00000			0.461880
$301$	−27.0000			−1.55625
$302$	−15.0000	+	15.0000i	−0.863153	+	0.863153i
$303$		0			0
$304$		0			0
$305$		−	10.0000i		−	0.572598i
$306$	6.00000	+	6.00000i	0.342997	+	0.342997i
$307$	−18.0000			−1.02731			−0.513657	−	0.857996i	$-0.671710\pi$
$307$	−18.0000			−1.02731			−0.513657	+	0.857996i	$0.671710\pi$
$308$	−12.0000			−0.683763
$309$			4.00000i			0.227552i
$310$		0			0
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$	−10.0000	−	2.00000i	−0.566139	−	0.113228i
$313$	9.00000			0.508710			0.254355	−	0.967111i	$-0.418137\pi$
$313$	9.00000			0.508710			0.254355	+	0.967111i	$0.418137\pi$
$314$	−18.0000	+	18.0000i	−1.01580	+	1.01580i
$315$			6.00000i			0.338062i
$316$		0			0
$317$	2.00000			0.112331			0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000			0.112331			0.0561656	+	0.998421i	$0.482113\pi$
$318$	−6.00000	−	6.00000i	−0.336463	−	0.336463i
$319$			12.0000i			0.671871i
$320$			8.00000i			0.447214i
$321$	12.0000			0.669775
$322$	−18.0000	+	18.0000i	−1.00310	+	1.00310i
$323$		0			0
$324$			2.00000i			0.111111i
$325$	−12.0000	+	8.00000i	−0.665640	+	0.443760i
$326$	6.00000	+	6.00000i	0.332309	+	0.332309i
$327$		−	15.0000i		−	0.829502i
$328$	−20.0000	−	20.0000i	−1.10432	−	1.10432i
$329$	21.0000			1.15777
$330$	−2.00000	+	2.00000i	−0.110096	+	0.110096i
$331$	−12.0000			−0.659580			−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000			−0.659580			−0.329790	+	0.944054i	$0.606978\pi$
$332$			32.0000i			1.75623i
$333$	−6.00000			−0.328798
$334$	8.00000	−	8.00000i	0.437741	−	0.437741i
$335$	−12.0000			−0.655630
$336$	−12.0000			−0.654654
$337$	−27.0000			−1.47078			−0.735392	−	0.677642i	$-0.763002\pi$
$337$	−27.0000			−1.47078			−0.735392	+	0.677642i	$0.763002\pi$
$338$	17.0000	−	7.00000i	0.924678	−	0.380750i
$339$		−	6.00000i		−	0.325875i
$340$		−	6.00000i		−	0.325396i
$341$		0			0
$342$		0			0
$343$		−	15.0000i		−	0.809924i
$344$	18.0000	+	18.0000i	0.970495	+	0.970495i
$345$			6.00000i			0.323029i
$346$	24.0000	−	24.0000i	1.29025	−	1.29025i
$347$		−	27.0000i		−	1.44944i	−0.689046	−	0.724718i	$-0.741970\pi$
$347$		−	27.0000i		−	1.44944i	0.689046	−	0.724718i	$-0.258030\pi$
$348$			12.0000i			0.643268i
$349$	15.0000			0.802932			0.401466	−	0.915874i	$-0.368501\pi$
$349$	15.0000			0.802932			0.401466	+	0.915874i	$0.368501\pi$
$350$	−12.0000	+	12.0000i	−0.641427	+	0.641427i
$351$	10.0000	+	15.0000i	0.533761	+	0.800641i
$352$	8.00000	+	8.00000i	0.426401	+	0.426401i
$353$		−	16.0000i		−	0.851594i	−0.904819	−	0.425797i	$-0.859994\pi$
$353$		−	16.0000i		−	0.851594i	0.904819	−	0.425797i	$-0.140006\pi$
$354$	10.0000	−	10.0000i	0.531494	−	0.531494i
$355$		−	5.00000i		−	0.265372i
$356$	8.00000			0.423999
$357$	9.00000			0.476331
$358$	−9.00000	+	9.00000i	−0.475665	+	0.475665i
$359$		−	4.00000i		−	0.211112i	−0.994413	−	0.105556i	$-0.966338\pi$
$359$		−	4.00000i		−	0.211112i	0.994413	−	0.105556i	$-0.0336622\pi$
$360$	4.00000	−	4.00000i	0.210819	−	0.210819i
$361$	−19.0000			−1.00000
$362$		0			0
$363$		−	7.00000i		−	0.367405i
$364$	18.0000	−	12.0000i	0.943456	−	0.628971i
$365$			6.00000i			0.314054i
$366$	−10.0000	−	10.0000i	−0.522708	−	0.522708i
$367$	28.0000			1.46159			0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000			1.46159			0.730794	+	0.682598i	$0.239150\pi$
$368$	24.0000			1.25109
$369$			20.0000i			1.04116i
$370$	3.00000	+	3.00000i	0.155963	+	0.155963i
$371$	18.0000			0.934513
$372$		0			0
$373$		−	4.00000i		−	0.207112i	−0.994624	−	0.103556i	$-0.966978\pi$
$373$		−	4.00000i		−	0.207112i	0.994624	−	0.103556i	$-0.0330221\pi$
$374$	−6.00000	−	6.00000i	−0.310253	−	0.310253i
$375$			9.00000i			0.464758i
$376$	−14.0000	−	14.0000i	−0.721995	−	0.721995i
$377$	−12.0000	−	18.0000i	−0.618031	−	0.927047i
$378$	15.0000	+	15.0000i	0.771517	+	0.771517i
$379$	30.0000			1.54100			0.770498	−	0.637442i	$-0.220007\pi$
$379$	30.0000			1.54100			0.770498	+	0.637442i	$0.220007\pi$
$380$		0			0
$381$			18.0000i			0.922168i
$382$	−18.0000	−	18.0000i	−0.920960	−	0.920960i
$383$		−	1.00000i		−	0.0510976i	−0.999674	−	0.0255488i	$-0.991867\pi$
$383$		−	1.00000i		−	0.0510976i	0.999674	−	0.0255488i	$-0.00813332\pi$
$384$	8.00000	+	8.00000i	0.408248	+	0.408248i
$385$		−	6.00000i		−	0.305788i
$386$	−24.0000	+	24.0000i	−1.22157	+	1.22157i
$387$		−	18.0000i		−	0.914991i
$388$	36.0000			1.82762
$389$		−	6.00000i		−	0.304212i	−0.988364	−	0.152106i	$-0.951394\pi$
$389$		−	6.00000i		−	0.304212i	0.988364	−	0.152106i	$-0.0486055\pi$
$390$	1.00000	−	5.00000i	0.0506370	−	0.253185i
$391$	−18.0000			−0.910299
$392$	4.00000	−	4.00000i	0.202031	−	0.202031i
$393$	−15.0000			−0.756650
$394$	−23.0000	−	23.0000i	−1.15872	−	1.15872i
$395$		0			0
$396$		−	8.00000i		−	0.402015i
$397$	−18.0000			−0.903394			−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000			−0.903394			−0.451697	+	0.892171i	$0.649181\pi$
$398$		0			0
$399$		0			0
$400$	16.0000			0.800000
$401$			10.0000i			0.499376i	0.968326	+	0.249688i	$0.0803281\pi$
$401$			10.0000i			0.499376i	−0.968326	+	0.249688i	$0.919672\pi$
$402$	−12.0000	+	12.0000i	−0.598506	+	0.598506i
$403$		0			0
$404$		0			0
$405$	−1.00000			−0.0496904
$406$	−18.0000	−	18.0000i	−0.893325	−	0.893325i
$407$	6.00000			0.297409
$408$	−6.00000	−	6.00000i	−0.297044	−	0.297044i
$409$			6.00000i			0.296681i	0.988936	+	0.148340i	$0.0473931\pi$
$409$			6.00000i			0.296681i	−0.988936	+	0.148340i	$0.952607\pi$
$410$	10.0000	−	10.0000i	0.493865	−	0.493865i
$411$	−2.00000			−0.0986527
$412$			8.00000i			0.394132i
$413$			30.0000i			1.47620i
$414$	−12.0000	−	12.0000i	−0.589768	−	0.589768i
$415$	−16.0000			−0.785409
$416$	−20.0000	−	4.00000i	−0.980581	−	0.196116i
$417$	−9.00000			−0.440732
$418$		0			0
$419$			9.00000i			0.439679i	0.975536	+	0.219839i	$0.0705533\pi$
$419$			9.00000i			0.439679i	−0.975536	+	0.219839i	$0.929447\pi$
$420$		−	6.00000i		−	0.292770i
$421$	3.00000			0.146211			0.0731055	−	0.997324i	$-0.476709\pi$
$421$	3.00000			0.146211			0.0731055	+	0.997324i	$0.476709\pi$
$422$	5.00000	−	5.00000i	0.243396	−	0.243396i
$423$			14.0000i			0.680703i
$424$	−12.0000	−	12.0000i	−0.582772	−	0.582772i
$425$	−12.0000			−0.582086
$426$	−5.00000	−	5.00000i	−0.242251	−	0.242251i
$427$	30.0000			1.45180
$428$	24.0000			1.16008
$429$	−4.00000	−	6.00000i	−0.193122	−	0.289683i
$430$	−9.00000	+	9.00000i	−0.434019	+	0.434019i
$431$			5.00000i			0.240842i	0.992723	+	0.120421i	$0.0384244\pi$
$431$			5.00000i			0.240842i	−0.992723	+	0.120421i	$0.961576\pi$
$432$		−	20.0000i		−	0.962250i
$433$	9.00000			0.432512			0.216256	−	0.976337i	$-0.430615\pi$
$433$	9.00000			0.432512			0.216256	+	0.976337i	$0.430615\pi$
$434$		0			0
$435$	−6.00000			−0.287678
$436$		−	30.0000i		−	1.43674i
$437$		0			0
$438$	6.00000	+	6.00000i	0.286691	+	0.286691i
$439$	−10.0000			−0.477274			−0.238637	−	0.971109i	$-0.576701\pi$
$439$	−10.0000			−0.477274			−0.238637	+	0.971109i	$0.576701\pi$
$440$	−4.00000	+	4.00000i	−0.190693	+	0.190693i
$441$	−4.00000			−0.190476
$442$	15.0000	+	3.00000i	0.713477	+	0.142695i
$443$		−	9.00000i		−	0.427603i	−0.976877	−	0.213801i	$-0.931415\pi$
$443$		−	9.00000i		−	0.427603i	0.976877	−	0.213801i	$-0.0685846\pi$
$444$	6.00000			0.284747
$445$			4.00000i			0.189618i
$446$	21.0000	−	21.0000i	0.994379	−	0.994379i
$447$			10.0000i			0.472984i
$448$	−24.0000			−1.13389
$449$		−	14.0000i		−	0.660701i	−0.943858	−	0.330350i	$-0.892833\pi$
$449$		−	14.0000i		−	0.660701i	0.943858	−	0.330350i	$-0.107167\pi$
$450$	−8.00000	−	8.00000i	−0.377124	−	0.377124i
$451$		−	20.0000i		−	0.941763i
$452$		−	12.0000i		−	0.564433i
$453$	−15.0000			−0.704761
$454$	2.00000	+	2.00000i	0.0938647	+	0.0938647i
$455$	6.00000	+	9.00000i	0.281284	+	0.421927i
$456$		0			0
$457$			12.0000i			0.561336i	0.959805	+	0.280668i	$0.0905560\pi$
$457$			12.0000i			0.561336i	−0.959805	+	0.280668i	$0.909444\pi$
$458$	15.0000	+	15.0000i	0.700904	+	0.700904i
$459$			15.0000i			0.700140i
$460$			12.0000i			0.559503i
$461$	−7.00000			−0.326023			−0.163011	−	0.986624i	$-0.552121\pi$
$461$	−7.00000			−0.326023			−0.163011	+	0.986624i	$0.552121\pi$
$462$	−6.00000	−	6.00000i	−0.279145	−	0.279145i
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$			24.0000i			1.11417i
$465$		0			0
$466$	9.00000	+	9.00000i	0.416917	+	0.416917i
$467$		−	12.0000i		−	0.555294i	−0.960683	−	0.277647i	$-0.910445\pi$
$467$		−	12.0000i		−	0.555294i	0.960683	−	0.277647i	$-0.0895545\pi$
$468$	8.00000	+	12.0000i	0.369800	+	0.554700i
$469$		−	36.0000i		−	1.66233i
$470$	7.00000	−	7.00000i	0.322886	−	0.322886i
$471$	−18.0000			−0.829396
$472$	20.0000	−	20.0000i	0.920575	−	0.920575i
$473$			18.0000i			0.827641i
$474$		0			0
$475$		0			0
$476$	18.0000			0.825029
$477$			12.0000i			0.549442i
$478$	19.0000	−	19.0000i	0.869040	−	0.869040i
$479$		−	29.0000i		−	1.32504i	−0.749043	−	0.662522i	$-0.769486\pi$
$479$		−	29.0000i		−	1.32504i	0.749043	−	0.662522i	$-0.230514\pi$
$480$	−4.00000	+	4.00000i	−0.182574	+	0.182574i
$481$	−9.00000	+	6.00000i	−0.410365	+	0.273576i
$482$		0			0
$483$	−18.0000			−0.819028
$484$		−	14.0000i		−	0.636364i
$485$			18.0000i			0.817338i
$486$	−16.0000	+	16.0000i	−0.725775	+	0.725775i
$487$			12.0000i			0.543772i	0.962329	+	0.271886i	$0.0876473\pi$
$487$			12.0000i			0.543772i	−0.962329	+	0.271886i	$0.912353\pi$
$488$	−20.0000	−	20.0000i	−0.905357	−	0.905357i
$489$			6.00000i			0.271329i
$490$	2.00000	+	2.00000i	0.0903508	+	0.0903508i
$491$			15.0000i			0.676941i	0.940977	+	0.338470i	$0.109909\pi$
$491$			15.0000i			0.676941i	−0.940977	+	0.338470i	$0.890091\pi$
$492$		−	20.0000i		−	0.901670i
$493$		−	18.0000i		−	0.810679i
$494$		0			0
$495$	4.00000			0.179787
$496$		0			0
$497$	15.0000			0.672842
$498$	−16.0000	+	16.0000i	−0.716977	+	0.716977i
$499$	−30.0000			−1.34298			−0.671492	−	0.741012i	$-0.734346\pi$
$499$	−30.0000			−1.34298			−0.671492	+	0.741012i	$0.734346\pi$
$500$			18.0000i			0.804984i
$501$	8.00000			0.357414
$502$		0			0
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$	12.0000	+	12.0000i	0.534522	+	0.534522i
$505$		0			0
$506$	12.0000	+	12.0000i	0.533465	+	0.533465i
$507$	12.0000	+	5.00000i	0.532939	+	0.222058i
$508$			36.0000i			1.59724i
$509$	10.0000			0.443242			0.221621	−	0.975133i	$-0.428865\pi$
$509$	10.0000			0.443242			0.221621	+	0.975133i	$0.428865\pi$
$510$	3.00000	−	3.00000i	0.132842	−	0.132842i
$511$	−18.0000			−0.796273
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		0			0
$514$	3.00000	+	3.00000i	0.132324	+	0.132324i
$515$	−4.00000			−0.176261
$516$			18.0000i			0.792406i
$517$		−	14.0000i		−	0.615719i
$518$	−9.00000	+	9.00000i	−0.395437	+	0.395437i
$519$	24.0000			1.05348
$520$	2.00000	−	10.0000i	0.0877058	−	0.438529i
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$	12.0000	−	12.0000i	0.525226	−	0.525226i
$523$			36.0000i			1.57417i	0.616844	+	0.787085i	$0.288411\pi$
$523$			36.0000i			1.57417i	−0.616844	+	0.787085i	$0.711589\pi$
$524$	−30.0000			−1.31056
$525$	−12.0000			−0.523723
$526$	−6.00000	−	6.00000i	−0.261612	−	0.261612i
$527$		0			0
$528$			8.00000i			0.348155i
$529$	13.0000			0.565217
$530$	6.00000	−	6.00000i	0.260623	−	0.260623i
$531$	−20.0000			−0.867926
$532$		0			0
$533$	20.0000	+	30.0000i	0.866296	+	1.29944i
$534$	4.00000	+	4.00000i	0.173097	+	0.173097i
$535$			12.0000i			0.518805i
$536$	−24.0000	+	24.0000i	−1.03664	+	1.03664i
$537$	−9.00000			−0.388379
$538$	6.00000	−	6.00000i	0.258678	−	0.258678i
$539$	4.00000			0.172292
$540$	10.0000			0.430331
$541$	33.0000			1.41878			0.709390	−	0.704816i	$-0.248970\pi$
$541$	33.0000			1.41878			0.709390	+	0.704816i	$0.248970\pi$
$542$	−15.0000	+	15.0000i	−0.644305	+	0.644305i
$543$		0			0
$544$	−12.0000	−	12.0000i	−0.514496	−	0.514496i
$545$	15.0000			0.642529
$546$	15.0000	+	3.00000i	0.641941	+	0.128388i
$547$		−	27.0000i		−	1.15444i	−0.816590	−	0.577218i	$-0.804138\pi$
$547$		−	27.0000i		−	1.15444i	0.816590	−	0.577218i	$-0.195862\pi$
$548$	−4.00000			−0.170872
$549$			20.0000i			0.853579i
$550$	8.00000	+	8.00000i	0.341121	+	0.341121i
$551$		0			0
$552$	12.0000	+	12.0000i	0.510754	+	0.510754i
$553$		0			0
$554$	−18.0000	+	18.0000i	−0.764747	+	0.764747i
$555$			3.00000i			0.127343i
$556$	−18.0000			−0.763370
$557$	−23.0000			−0.974541			−0.487271	−	0.873251i	$-0.662007\pi$
$557$	−23.0000			−0.974541			−0.487271	+	0.873251i	$0.662007\pi$
$558$		0			0
$559$	−18.0000	−	27.0000i	−0.761319	−	1.14198i
$560$		−	12.0000i		−	0.507093i
$561$		−	6.00000i		−	0.253320i
$562$	20.0000	−	20.0000i	0.843649	−	0.843649i
$563$			21.0000i			0.885044i	0.896758	+	0.442522i	$0.145916\pi$
$563$			21.0000i			0.885044i	−0.896758	+	0.442522i	$0.854084\pi$
$564$		−	14.0000i		−	0.589506i
$565$	6.00000			0.252422
$566$	4.00000	−	4.00000i	0.168133	−	0.168133i
$567$		−	3.00000i		−	0.125988i
$568$	−10.0000	−	10.0000i	−0.419591	−	0.419591i
$569$	15.0000			0.628833			0.314416	−	0.949285i	$-0.398191\pi$
$569$	15.0000			0.628833			0.314416	+	0.949285i	$0.398191\pi$
$570$		0			0
$571$			5.00000i			0.209243i	0.994512	+	0.104622i	$0.0333632\pi$
$571$			5.00000i			0.209243i	−0.994512	+	0.104622i	$0.966637\pi$
$572$	−8.00000	−	12.0000i	−0.334497	−	0.501745i
$573$		−	18.0000i		−	0.751961i
$574$	30.0000	+	30.0000i	1.25218	+	1.25218i
$575$	24.0000			1.00087
$576$		−	16.0000i		−	0.666667i
$577$		−	18.0000i		−	0.749350i	−0.927156	−	0.374675i	$-0.877754\pi$
$577$		−	18.0000i		−	0.749350i	0.927156	−	0.374675i	$-0.122246\pi$
$578$	−8.00000	−	8.00000i	−0.332756	−	0.332756i
$579$	−24.0000			−0.997406
$580$	−12.0000			−0.498273
$581$		−	48.0000i		−	1.99138i
$582$	18.0000	+	18.0000i	0.746124	+	0.746124i
$583$		−	12.0000i		−	0.496989i
$584$	12.0000	+	12.0000i	0.496564	+	0.496564i
$585$	−6.00000	+	4.00000i	−0.248069	+	0.165380i
$586$	1.00000	+	1.00000i	0.0413096	+	0.0413096i
$587$	2.00000			0.0825488			0.0412744	−	0.999148i	$-0.486858\pi$
$587$	2.00000			0.0825488			0.0412744	+	0.999148i	$0.486858\pi$
$588$	4.00000			0.164957
$589$		0			0
$590$	10.0000	+	10.0000i	0.411693	+	0.411693i
$591$		−	23.0000i		−	0.946094i
$592$	12.0000			0.493197
$593$			14.0000i			0.574911i	0.957794	+	0.287456i	$0.0928094\pi$
$593$			14.0000i			0.574911i	−0.957794	+	0.287456i	$0.907191\pi$
$594$	10.0000	−	10.0000i	0.410305	−	0.410305i
$595$			9.00000i			0.368964i
$596$			20.0000i			0.819232i
$597$		0			0
$598$	−30.0000	−	6.00000i	−1.22679	−	0.245358i
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$	8.00000	+	8.00000i	0.326599	+	0.326599i
$601$	27.0000			1.10135			0.550676	−	0.834719i	$-0.314370\pi$
$601$	27.0000			1.10135			0.550676	+	0.834719i	$0.314370\pi$
$602$	−27.0000	−	27.0000i	−1.10044	−	1.10044i
$603$	24.0000			0.977356
$604$	−30.0000			−1.22068
$605$	7.00000			0.284590
$606$		0			0
$607$	−22.0000			−0.892952			−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000			−0.892952			−0.446476	+	0.894795i	$0.647321\pi$
$608$		0			0
$609$		−	18.0000i		−	0.729397i
$610$	10.0000	−	10.0000i	0.404888	−	0.404888i
$611$	14.0000	+	21.0000i	0.566379	+	0.849569i
$612$			12.0000i			0.485071i
$613$	6.00000			0.242338			0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000			0.242338			0.121169	+	0.992632i	$0.461336\pi$
$614$	−18.0000	−	18.0000i	−0.726421	−	0.726421i
$615$	10.0000			0.403239
$616$	−12.0000	−	12.0000i	−0.483494	−	0.483494i
$617$		−	8.00000i		−	0.322068i	−0.986949	−	0.161034i	$-0.948517\pi$
$617$		−	8.00000i		−	0.322068i	0.986949	−	0.161034i	$-0.0514829\pi$
$618$	−4.00000	+	4.00000i	−0.160904	+	0.160904i
$619$	30.0000			1.20580			0.602901	−	0.797816i	$-0.294011\pi$
$619$	30.0000			1.20580			0.602901	+	0.797816i	$0.294011\pi$
$620$		0			0
$621$		−	30.0000i		−	1.20386i
$622$	12.0000	+	12.0000i	0.481156	+	0.481156i
$623$	−12.0000			−0.480770
$624$	−8.00000	−	12.0000i	−0.320256	−	0.480384i
$625$	11.0000			0.440000
$626$	9.00000	+	9.00000i	0.359712	+	0.359712i
$627$		0			0
$628$	−36.0000			−1.43656
$629$	−9.00000			−0.358854
$630$	−6.00000	+	6.00000i	−0.239046	+	0.239046i
$631$		−	45.0000i		−	1.79142i	−0.444637	−	0.895711i	$-0.646667\pi$
$631$		−	45.0000i		−	1.79142i	0.444637	−	0.895711i	$-0.353333\pi$
$632$		0			0
$633$	5.00000			0.198732
$634$	2.00000	+	2.00000i	0.0794301	+	0.0794301i
$635$	−18.0000			−0.714308
$636$		−	12.0000i		−	0.475831i
$637$	−6.00000	+	4.00000i	−0.237729	+	0.158486i
$638$	−12.0000	+	12.0000i	−0.475085	+	0.475085i
$639$			10.0000i			0.395594i
$640$	−8.00000	+	8.00000i	−0.316228	+	0.316228i
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$	12.0000	+	12.0000i	0.473602	+	0.473602i
$643$	−24.0000			−0.946468			−0.473234	−	0.880937i	$-0.656913\pi$
$643$	−24.0000			−0.946468			−0.473234	+	0.880937i	$0.656913\pi$
$644$	−36.0000			−1.41860
$645$	−9.00000			−0.354375
$646$		0			0
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$	−2.00000	+	2.00000i	−0.0785674	+	0.0785674i
$649$	20.0000			0.785069
$650$	−20.0000	−	4.00000i	−0.784465	−	0.156893i
$651$		0			0
$652$			12.0000i			0.469956i
$653$		−	24.0000i		−	0.939193i	−0.882881	−	0.469596i	$-0.844399\pi$
$653$		−	24.0000i		−	0.939193i	0.882881	−	0.469596i	$-0.155601\pi$
$654$	15.0000	−	15.0000i	0.586546	−	0.586546i
$655$		−	15.0000i		−	0.586098i
$656$		−	40.0000i		−	1.56174i
$657$		−	12.0000i		−	0.468165i
$658$	21.0000	+	21.0000i	0.818665	+	0.818665i
$659$		−	36.0000i		−	1.40236i	−0.712984	−	0.701180i	$-0.752657\pi$
$659$		−	36.0000i		−	1.40236i	0.712984	−	0.701180i	$-0.247343\pi$
$660$	−4.00000			−0.155700
$661$	18.0000			0.700119			0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000			0.700119			0.350059	+	0.936727i	$0.386161\pi$
$662$	−12.0000	−	12.0000i	−0.466393	−	0.466393i
$663$	6.00000	+	9.00000i	0.233021	+	0.349531i
$664$	−32.0000	+	32.0000i	−1.24184	+	1.24184i
$665$		0			0
$666$	−6.00000	−	6.00000i	−0.232495	−	0.232495i
$667$			36.0000i			1.39393i
$668$	16.0000			0.619059
$669$	21.0000			0.811907
$670$	−12.0000	−	12.0000i	−0.463600	−	0.463600i
$671$		−	20.0000i		−	0.772091i
$672$	−12.0000	−	12.0000i	−0.462910	−	0.462910i
$673$	19.0000			0.732396			0.366198	−	0.930537i	$-0.380659\pi$
$673$	19.0000			0.732396			0.366198	+	0.930537i	$0.380659\pi$
$674$	−27.0000	−	27.0000i	−1.04000	−	1.04000i
$675$		−	20.0000i		−	0.769800i
$676$	24.0000	+	10.0000i	0.923077	+	0.384615i
$677$		−	12.0000i		−	0.461197i	−0.973049	−	0.230599i	$-0.925932\pi$
$677$		−	12.0000i		−	0.461197i	0.973049	−	0.230599i	$-0.0740685\pi$
$678$	6.00000	−	6.00000i	0.230429	−	0.230429i
$679$	−54.0000			−2.07233
$680$	6.00000	−	6.00000i	0.230089	−	0.230089i
$681$			2.00000i			0.0766402i
$682$		0			0
$683$	−4.00000			−0.153056			−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000			−0.153056			−0.0765279	+	0.997067i	$0.524383\pi$
$684$		0			0
$685$		−	2.00000i		−	0.0764161i
$686$	15.0000	−	15.0000i	0.572703	−	0.572703i
$687$			15.0000i			0.572286i
$688$			36.0000i			1.37249i
$689$	12.0000	+	18.0000i	0.457164	+	0.685745i
$690$	−6.00000	+	6.00000i	−0.228416	+	0.228416i
$691$	−12.0000			−0.456502			−0.228251	−	0.973602i	$-0.573301\pi$
$691$	−12.0000			−0.456502			−0.228251	+	0.973602i	$0.573301\pi$
$692$	48.0000			1.82469
$693$			12.0000i			0.455842i
$694$	27.0000	−	27.0000i	1.02491	−	1.02491i
$695$		−	9.00000i		−	0.341389i
$696$	−12.0000	+	12.0000i	−0.454859	+	0.454859i
$697$			30.0000i			1.13633i
$698$	15.0000	+	15.0000i	0.567758	+	0.567758i
$699$			9.00000i			0.340411i
$700$	−24.0000			−0.907115
$701$			30.0000i			1.13308i	0.824033	+	0.566542i	$0.191719\pi$
$701$			30.0000i			1.13308i	−0.824033	+	0.566542i	$0.808281\pi$
$702$	−5.00000	+	25.0000i	−0.188713	+	0.943564i
$703$		0			0
$704$			16.0000i			0.603023i
$705$	7.00000			0.263635
$706$	16.0000	−	16.0000i	0.602168	−	0.602168i
$707$		0			0
$708$	20.0000			0.751646
$709$	−30.0000			−1.12667			−0.563337	−	0.826227i	$-0.690483\pi$
$709$	−30.0000			−1.12667			−0.563337	+	0.826227i	$0.690483\pi$
$710$	5.00000	−	5.00000i	0.187647	−	0.187647i
$711$		0			0
$712$	8.00000	+	8.00000i	0.299813	+	0.299813i
$713$		0			0
$714$	9.00000	+	9.00000i	0.336817	+	0.336817i
$715$	6.00000	−	4.00000i	0.224387	−	0.149592i
$716$	−18.0000			−0.672692
$717$	19.0000			0.709568
$718$	4.00000	−	4.00000i	0.149279	−	0.149279i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	8.00000			0.298142
$721$		−	12.0000i		−	0.446903i
$722$	−19.0000	−	19.0000i	−0.707107	−	0.707107i
$723$		0			0
$724$		0			0
$725$			24.0000i			0.891338i
$726$	7.00000	−	7.00000i	0.259794	−	0.259794i
$727$	18.0000			0.667583			0.333792	−	0.942647i	$-0.391672\pi$
$727$	18.0000			0.667583			0.333792	+	0.942647i	$0.391672\pi$
$728$	30.0000	+	6.00000i	1.11187	+	0.222375i
$729$	−13.0000			−0.481481
$730$	−6.00000	+	6.00000i	−0.222070	+	0.222070i
$731$		−	27.0000i		−	0.998631i
$732$		−	20.0000i		−	0.739221i
$733$	51.0000			1.88373			0.941864	−	0.335994i	$-0.109072\pi$
$733$	51.0000			1.88373			0.941864	+	0.335994i	$0.109072\pi$
$734$	28.0000	+	28.0000i	1.03350	+	1.03350i
$735$			2.00000i			0.0737711i
$736$	24.0000	+	24.0000i	0.884652	+	0.884652i
$737$	−24.0000			−0.884051
$738$	−20.0000	+	20.0000i	−0.736210	+	0.736210i
$739$	−30.0000			−1.10357			−0.551784	−	0.833987i	$-0.686053\pi$
$739$	−30.0000			−1.10357			−0.551784	+	0.833987i	$0.686053\pi$
$740$			6.00000i			0.220564i
$741$		0			0
$742$	18.0000	+	18.0000i	0.660801	+	0.660801i
$743$			19.0000i			0.697042i	0.937301	+	0.348521i	$0.113316\pi$
$743$			19.0000i			0.697042i	−0.937301	+	0.348521i	$0.886684\pi$
$744$		0			0
$745$	−10.0000			−0.366372
$746$	4.00000	−	4.00000i	0.146450	−	0.146450i
$747$	32.0000			1.17082
$748$		−	12.0000i		−	0.438763i
$749$	−36.0000			−1.31541
$750$	−9.00000	+	9.00000i	−0.328634	+	0.328634i
$751$	22.0000			0.802791			0.401396	−	0.915905i	$-0.368525\pi$
$751$	22.0000			0.802791			0.401396	+	0.915905i	$0.368525\pi$
$752$		−	28.0000i		−	1.02105i
$753$		0			0
$754$	6.00000	−	30.0000i	0.218507	−	1.09254i
$755$		−	15.0000i		−	0.545906i
$756$			30.0000i			1.09109i
$757$			38.0000i			1.38113i	0.723269	+	0.690567i	$0.242639\pi$
$757$			38.0000i			1.38113i	−0.723269	+	0.690567i	$0.757361\pi$
$758$	30.0000	+	30.0000i	1.08965	+	1.08965i
$759$			12.0000i			0.435572i
$760$		0			0
$761$		−	10.0000i		−	0.362500i	−0.983437	−	0.181250i	$-0.941986\pi$
$761$		−	10.0000i		−	0.362500i	0.983437	−	0.181250i	$-0.0580143\pi$
$762$	−18.0000	+	18.0000i	−0.652071	+	0.652071i
$763$			45.0000i			1.62911i
$764$		−	36.0000i		−	1.30243i
$765$	−6.00000			−0.216930
$766$	1.00000	−	1.00000i	0.0361315	−	0.0361315i
$767$	−30.0000	+	20.0000i	−1.08324	+	0.722158i
$768$			16.0000i			0.577350i
$769$			36.0000i			1.29819i	0.760706	+	0.649097i	$0.224853\pi$
$769$			36.0000i			1.29819i	−0.760706	+	0.649097i	$0.775147\pi$
$770$	6.00000	−	6.00000i	0.216225	−	0.216225i
$771$			3.00000i			0.108042i
$772$	−48.0000			−1.72756
$773$	−49.0000			−1.76241			−0.881204	−	0.472737i	$-0.843266\pi$
$773$	−49.0000			−1.76241			−0.881204	+	0.472737i	$0.843266\pi$
$774$	18.0000	−	18.0000i	0.646997	−	0.646997i
$775$		0			0
$776$	36.0000	+	36.0000i	1.29232	+	1.29232i
$777$	−9.00000			−0.322873
$778$	6.00000	−	6.00000i	0.215110	−	0.215110i
$779$		0			0
$780$	6.00000

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:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +1.00000i q^{3} +2.00000i q^{4} -1.00000 q^{5} +(-1.00000 + 1.00000i) q^{6} -3.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +1.00000i q^{3} +2.00000i q^{4} -1.00000 q^{5} +(-1.00000 + 1.00000i) q^{6} -3.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +2.00000 q^{9} +(-1.00000 - 1.00000i) q^{10} -2.00000 q^{11} -2.00000 q^{12} +(3.00000 - 2.00000i) q^{13} +(3.00000 - 3.00000i) q^{14} -1.00000i q^{15} -4.00000 q^{16} +3.00000 q^{17} +(2.00000 + 2.00000i) q^{18} -2.00000i q^{20} +3.00000 q^{21} +(-2.00000 - 2.00000i) q^{22} -6.00000 q^{23} +(-2.00000 - 2.00000i) q^{24} -4.00000 q^{25} +(5.00000 + 1.00000i) q^{26} +5.00000i q^{27} +6.00000 q^{28} -6.00000i q^{29} +(1.00000 - 1.00000i) q^{30} +(-4.00000 - 4.00000i) q^{32} -2.00000i q^{33} +(3.00000 + 3.00000i) q^{34} +3.00000i q^{35} +4.00000i q^{36} -3.00000 q^{37} +(2.00000 + 3.00000i) q^{39} +(2.00000 - 2.00000i) q^{40} +10.0000i q^{41} +(3.00000 + 3.00000i) q^{42} -9.00000i q^{43} -4.00000i q^{44} -2.00000 q^{45} +(-6.00000 - 6.00000i) q^{46} +7.00000i q^{47} -4.00000i q^{48} -2.00000 q^{49} +(-4.00000 - 4.00000i) q^{50} +3.00000i q^{51} +(4.00000 + 6.00000i) q^{52} +6.00000i q^{53} +(-5.00000 + 5.00000i) q^{54} +2.00000 q^{55} +(6.00000 + 6.00000i) q^{56} +(6.00000 - 6.00000i) q^{58} -10.0000 q^{59} +2.00000 q^{60} +10.0000i q^{61} -6.00000i q^{63} -8.00000i q^{64} +(-3.00000 + 2.00000i) q^{65} +(2.00000 - 2.00000i) q^{66} +12.0000 q^{67} +6.00000i q^{68} -6.00000i q^{69} +(-3.00000 + 3.00000i) q^{70} +5.00000i q^{71} +(-4.00000 + 4.00000i) q^{72} -6.00000i q^{73} +(-3.00000 - 3.00000i) q^{74} -4.00000i q^{75} +6.00000i q^{77} +(-1.00000 + 5.00000i) q^{78} +4.00000 q^{80} +1.00000 q^{81} +(-10.0000 + 10.0000i) q^{82} +16.0000 q^{83} +6.00000i q^{84} -3.00000 q^{85} +(9.00000 - 9.00000i) q^{86} +6.00000 q^{87} +(4.00000 - 4.00000i) q^{88} -4.00000i q^{89} +(-2.00000 - 2.00000i) q^{90} +(-6.00000 - 9.00000i) q^{91} -12.0000i q^{92} +(-7.00000 + 7.00000i) q^{94} +(4.00000 - 4.00000i) q^{96} -18.0000i q^{97} +(-2.00000 - 2.00000i) q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{5} - 2 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^5 - 2 * q^6 - 4 * q^8 + 4 * q^9	\( 2 q + 2 q^{2} - 2 q^{5} - 2 q^{6} - 4 q^{8} + 4 q^{9} - 2 q^{10} - 4 q^{11} - 4 q^{12} + 6 q^{13} + 6 q^{14} - 8 q^{16} + 6 q^{17} + 4 q^{18} + 6 q^{21} - 4 q^{22} - 12 q^{23} - 4 q^{24} - 8 q^{25} + 10 q^{26} + 12 q^{28} + 2 q^{30} - 8 q^{32} + 6 q^{34} - 6 q^{37} + 4 q^{39} + 4 q^{40} + 6 q^{42} - 4 q^{45} - 12 q^{46} - 4 q^{49} - 8 q^{50} + 8 q^{52} - 10 q^{54} + 4 q^{55} + 12 q^{56} + 12 q^{58} - 20 q^{59} + 4 q^{60} - 6 q^{65} + 4 q^{66} + 24 q^{67} - 6 q^{70} - 8 q^{72} - 6 q^{74} - 2 q^{78} + 8 q^{80} + 2 q^{81} - 20 q^{82} + 32 q^{83} - 6 q^{85} + 18 q^{86} + 12 q^{87} + 8 q^{88} - 4 q^{90} - 12 q^{91} - 14 q^{94} + 8 q^{96} - 4 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^5 - 2 * q^6 - 4 * q^8 + 4 * q^9 - 2 * q^10 - 4 * q^11 - 4 * q^12 + 6 * q^13 + 6 * q^14 - 8 * q^16 + 6 * q^17 + 4 * q^18 + 6 * q^21 - 4 * q^22 - 12 * q^23 - 4 * q^24 - 8 * q^25 + 10 * q^26 + 12 * q^28 + 2 * q^30 - 8 * q^32 + 6 * q^34 - 6 * q^37 + 4 * q^39 + 4 * q^40 + 6 * q^42 - 4 * q^45 - 12 * q^46 - 4 * q^49 - 8 * q^50 + 8 * q^52 - 10 * q^54 + 4 * q^55 + 12 * q^56 + 12 * q^58 - 20 * q^59 + 4 * q^60 - 6 * q^65 + 4 * q^66 + 24 * q^67 - 6 * q^70 - 8 * q^72 - 6 * q^74 - 2 * q^78 + 8 * q^80 + 2 * q^81 - 20 * q^82 + 32 * q^83 - 6 * q^85 + 18 * q^86 + 12 * q^87 + 8 * q^88 - 4 * q^90 - 12 * q^91 - 14 * q^94 + 8 * q^96 - 4 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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