LMFDB - Embedded newform 435.2.f.b.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(289,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, 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("435.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.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:	$3.47349248793$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			289.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	435.289
Dual form			435.2.f.b.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +1.00000 q^{6} -2.00000i q^{7} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +1.00000 q^{6} -2.00000i q^{7} +3.00000 q^{8} +1.00000 q^{9} +(1.00000 + 2.00000i) q^{10} +2.00000i q^{11} +1.00000 q^{12} -4.00000i q^{13} +2.00000i q^{14} +(1.00000 + 2.00000i) q^{15} -1.00000 q^{16} -6.00000 q^{17} -1.00000 q^{18} +2.00000i q^{19} +(1.00000 + 2.00000i) q^{20} +2.00000i q^{21} -2.00000i q^{22} +6.00000i q^{23} -3.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} +4.00000i q^{26} -1.00000 q^{27} +2.00000i q^{28} +(-5.00000 + 2.00000i) q^{29} +(-1.00000 - 2.00000i) q^{30} -2.00000i q^{31} -5.00000 q^{32} -2.00000i q^{33} +6.00000 q^{34} +(-4.00000 + 2.00000i) q^{35} -1.00000 q^{36} -2.00000 q^{37} -2.00000i q^{38} +4.00000i q^{39} +(-3.00000 - 6.00000i) q^{40} -2.00000i q^{42} +4.00000 q^{43} -2.00000i q^{44} +(-1.00000 - 2.00000i) q^{45} -6.00000i q^{46} -8.00000 q^{47} +1.00000 q^{48} +3.00000 q^{49} +(3.00000 - 4.00000i) q^{50} +6.00000 q^{51} +4.00000i q^{52} +12.0000i q^{53} +1.00000 q^{54} +(4.00000 - 2.00000i) q^{55} -6.00000i q^{56} -2.00000i q^{57} +(5.00000 - 2.00000i) q^{58} -4.00000 q^{59} +(-1.00000 - 2.00000i) q^{60} +12.0000i q^{61} +2.00000i q^{62} -2.00000i q^{63} +7.00000 q^{64} +(-8.00000 + 4.00000i) q^{65} +2.00000i q^{66} -6.00000i q^{67} +6.00000 q^{68} -6.00000i q^{69} +(4.00000 - 2.00000i) q^{70} +8.00000 q^{71} +3.00000 q^{72} -6.00000 q^{73} +2.00000 q^{74} +(3.00000 - 4.00000i) q^{75} -2.00000i q^{76} +4.00000 q^{77} -4.00000i q^{78} -2.00000i q^{79} +(1.00000 + 2.00000i) q^{80} +1.00000 q^{81} +2.00000i q^{83} -2.00000i q^{84} +(6.00000 + 12.0000i) q^{85} -4.00000 q^{86} +(5.00000 - 2.00000i) q^{87} +6.00000i q^{88} -16.0000i q^{89} +(1.00000 + 2.00000i) q^{90} -8.00000 q^{91} -6.00000i q^{92} +2.00000i q^{93} +8.00000 q^{94} +(4.00000 - 2.00000i) q^{95} +5.00000 q^{96} -14.0000 q^{97} -3.00000 q^{98} +2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} + 2 q^{15} - 2 q^{16} - 12 q^{17} - 2 q^{18} + 2 q^{20} - 6 q^{24} - 6 q^{25} - 2 q^{27} - 10 q^{29} - 2 q^{30} - 10 q^{32} + 12 q^{34} - 8 q^{35} - 2 q^{36} - 4 q^{37} - 6 q^{40} + 8 q^{43} - 2 q^{45} - 16 q^{47} + 2 q^{48} + 6 q^{49} + 6 q^{50} + 12 q^{51} + 2 q^{54} + 8 q^{55} + 10 q^{58} - 8 q^{59} - 2 q^{60} + 14 q^{64} - 16 q^{65} + 12 q^{68} + 8 q^{70} + 16 q^{71} + 6 q^{72} - 12 q^{73} + 4 q^{74} + 6 q^{75} + 8 q^{77} + 2 q^{80} + 2 q^{81} + 12 q^{85} - 8 q^{86} + 10 q^{87} + 2 q^{90} - 16 q^{91} + 16 q^{94} + 8 q^{95} + 10 q^{96} - 28 q^{97} - 6 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 + 2 * q^15 - 2 * q^16 - 12 * q^17 - 2 * q^18 + 2 * q^20 - 6 * q^24 - 6 * q^25 - 2 * q^27 - 10 * q^29 - 2 * q^30 - 10 * q^32 + 12 * q^34 - 8 * q^35 - 2 * q^36 - 4 * q^37 - 6 * q^40 + 8 * q^43 - 2 * q^45 - 16 * q^47 + 2 * q^48 + 6 * q^49 + 6 * q^50 + 12 * q^51 + 2 * q^54 + 8 * q^55 + 10 * q^58 - 8 * q^59 - 2 * q^60 + 14 * q^64 - 16 * q^65 + 12 * q^68 + 8 * q^70 + 16 * q^71 + 6 * q^72 - 12 * q^73 + 4 * q^74 + 6 * q^75 + 8 * q^77 + 2 * q^80 + 2 * q^81 + 12 * q^85 - 8 * q^86 + 10 * q^87 + 2 * q^90 - 16 * q^91 + 16 * q^94 + 8 * q^95 + 10 * q^96 - 28 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$-1$	$1$	$-1$

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			−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000			−0.707107			−0.353553	+	0.935414i	$0.615027\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.00000			−0.500000
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$	1.00000			0.408248
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$	3.00000			1.06066
$9$	1.00000			0.333333
$10$	1.00000	+	2.00000i	0.316228	+	0.632456i
$11$			2.00000i			0.603023i	0.953463	+	0.301511i	$0.0974911\pi$
$11$			2.00000i			0.603023i	−0.953463	+	0.301511i	$0.902509\pi$
$12$	1.00000			0.288675
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$			2.00000i			0.534522i
$15$	1.00000	+	2.00000i	0.258199	+	0.516398i
$16$	−1.00000			−0.250000
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$	−1.00000			−0.235702
$19$			2.00000i			0.458831i	0.973329	+	0.229416i	$0.0736815\pi$
$19$			2.00000i			0.458831i	−0.973329	+	0.229416i	$0.926318\pi$
$20$	1.00000	+	2.00000i	0.223607	+	0.447214i
$21$			2.00000i			0.436436i
$22$		−	2.00000i		−	0.426401i
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	−3.00000			−0.612372
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$			4.00000i			0.784465i
$27$	−1.00000			−0.192450
$28$			2.00000i			0.377964i
$29$	−5.00000	+	2.00000i	−0.928477	+	0.371391i
$29$	−5.00000	+	2.00000i	−0.928477	+	0.371391i
$30$	−1.00000	−	2.00000i	−0.182574	−	0.365148i
$31$		−	2.00000i		−	0.359211i	−0.983739	−	0.179605i	$-0.942518\pi$
$31$		−	2.00000i		−	0.359211i	0.983739	−	0.179605i	$-0.0574821\pi$
$32$	−5.00000			−0.883883
$33$		−	2.00000i		−	0.348155i
$34$	6.00000			1.02899
$35$	−4.00000	+	2.00000i	−0.676123	+	0.338062i
$36$	−1.00000			−0.166667
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$		−	2.00000i		−	0.324443i
$39$			4.00000i			0.640513i
$40$	−3.00000	−	6.00000i	−0.474342	−	0.948683i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		−	2.00000i		−	0.308607i
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		−	2.00000i		−	0.301511i
$45$	−1.00000	−	2.00000i	−0.149071	−	0.298142i
$46$		−	6.00000i		−	0.884652i
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$	1.00000			0.144338
$49$	3.00000			0.428571
$50$	3.00000	−	4.00000i	0.424264	−	0.565685i
$51$	6.00000			0.840168
$52$			4.00000i			0.554700i
$53$			12.0000i			1.64833i	0.566352	+	0.824163i	$0.308354\pi$
$53$			12.0000i			1.64833i	−0.566352	+	0.824163i	$0.691646\pi$
$54$	1.00000			0.136083
$55$	4.00000	−	2.00000i	0.539360	−	0.269680i
$56$		−	6.00000i		−	0.801784i
$57$		−	2.00000i		−	0.264906i
$58$	5.00000	−	2.00000i	0.656532	−	0.262613i
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$	−1.00000	−	2.00000i	−0.129099	−	0.258199i
$61$			12.0000i			1.53644i	0.640184	+	0.768221i	$0.278858\pi$
$61$			12.0000i			1.53644i	−0.640184	+	0.768221i	$0.721142\pi$
$62$			2.00000i			0.254000i
$63$		−	2.00000i		−	0.251976i
$64$	7.00000			0.875000
$65$	−8.00000	+	4.00000i	−0.992278	+	0.496139i
$66$			2.00000i			0.246183i
$67$		−	6.00000i		−	0.733017i	−0.930415	−	0.366508i	$-0.880553\pi$
$67$		−	6.00000i		−	0.733017i	0.930415	−	0.366508i	$-0.119447\pi$
$68$	6.00000			0.727607
$69$		−	6.00000i		−	0.722315i
$70$	4.00000	−	2.00000i	0.478091	−	0.239046i
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$	3.00000			0.353553
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	2.00000			0.232495
$75$	3.00000	−	4.00000i	0.346410	−	0.461880i
$76$		−	2.00000i		−	0.229416i
$77$	4.00000			0.455842
$78$		−	4.00000i		−	0.452911i
$79$		−	2.00000i		−	0.225018i	−0.993651	−	0.112509i	$-0.964111\pi$
$79$		−	2.00000i		−	0.225018i	0.993651	−	0.112509i	$-0.0358886\pi$
$80$	1.00000	+	2.00000i	0.111803	+	0.223607i
$81$	1.00000			0.111111
$82$		0			0
$83$			2.00000i			0.219529i	0.993958	+	0.109764i	$0.0350096\pi$
$83$			2.00000i			0.219529i	−0.993958	+	0.109764i	$0.964990\pi$
$84$		−	2.00000i		−	0.218218i
$85$	6.00000	+	12.0000i	0.650791	+	1.30158i
$86$	−4.00000			−0.431331
$87$	5.00000	−	2.00000i	0.536056	−	0.214423i
$88$			6.00000i			0.639602i
$89$		−	16.0000i		−	1.69600i	−0.529999	−	0.847998i	$-0.677808\pi$
$89$		−	16.0000i		−	1.69600i	0.529999	−	0.847998i	$-0.322192\pi$
$90$	1.00000	+	2.00000i	0.105409	+	0.210819i
$91$	−8.00000			−0.838628
$92$		−	6.00000i		−	0.625543i
$93$			2.00000i			0.207390i
$94$	8.00000			0.825137
$95$	4.00000	−	2.00000i	0.410391	−	0.205196i
$96$	5.00000			0.510310
$97$	−14.0000			−1.42148			−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000			−1.42148			−0.710742	+	0.703452i	$0.751641\pi$
$98$	−3.00000			−0.303046
$99$			2.00000i			0.201008i
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$			12.0000i			1.19404i	0.802225	+	0.597022i	$0.203650\pi$
$101$			12.0000i			1.19404i	−0.802225	+	0.597022i	$0.796350\pi$
$102$	−6.00000			−0.594089
$103$		−	18.0000i		−	1.77359i	−0.462160	−	0.886796i	$-0.652926\pi$
$103$		−	18.0000i		−	1.77359i	0.462160	−	0.886796i	$-0.347074\pi$
$104$		−	12.0000i		−	1.17670i
$105$	4.00000	−	2.00000i	0.390360	−	0.195180i
$106$		−	12.0000i		−	1.16554i
$107$			10.0000i			0.966736i	0.875417	+	0.483368i	$0.160587\pi$
$107$			10.0000i			0.966736i	−0.875417	+	0.483368i	$0.839413\pi$
$108$	1.00000			0.0962250
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−4.00000	+	2.00000i	−0.381385	+	0.190693i
$111$	2.00000			0.189832
$112$			2.00000i			0.188982i
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$			2.00000i			0.187317i
$115$	12.0000	−	6.00000i	1.11901	−	0.559503i
$116$	5.00000	−	2.00000i	0.464238	−	0.185695i
$117$		−	4.00000i		−	0.369800i
$118$	4.00000			0.368230
$119$			12.0000i			1.10004i
$120$	3.00000	+	6.00000i	0.273861	+	0.547723i
$121$	7.00000			0.636364
$122$		−	12.0000i		−	1.08643i
$123$		0			0
$124$			2.00000i			0.179605i
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$			2.00000i			0.178174i
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	3.00000			0.265165
$129$	−4.00000			−0.352180
$130$	8.00000	−	4.00000i	0.701646	−	0.350823i
$131$		−	22.0000i		−	1.92215i	−0.276289	−	0.961074i	$-0.589105\pi$
$131$		−	22.0000i		−	1.92215i	0.276289	−	0.961074i	$-0.410895\pi$
$132$			2.00000i			0.174078i
$133$	4.00000			0.346844
$134$			6.00000i			0.518321i
$135$	1.00000	+	2.00000i	0.0860663	+	0.172133i
$136$	−18.0000			−1.54349
$137$	−14.0000			−1.19610			−0.598050	−	0.801459i	$-0.704058\pi$
$137$	−14.0000			−1.19610			−0.598050	+	0.801459i	$0.704058\pi$
$138$			6.00000i			0.510754i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	4.00000	−	2.00000i	0.338062	−	0.169031i
$141$	8.00000			0.673722
$142$	−8.00000			−0.671345
$143$	8.00000			0.668994
$144$	−1.00000			−0.0833333
$145$	9.00000	+	8.00000i	0.747409	+	0.664364i
$146$	6.00000			0.496564
$147$	−3.00000			−0.247436
$148$	2.00000			0.164399
$149$	−10.0000			−0.819232			−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000			−0.819232			−0.409616	+	0.912258i	$0.634337\pi$
$150$	−3.00000	+	4.00000i	−0.244949	+	0.326599i
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$			6.00000i			0.486664i
$153$	−6.00000			−0.485071
$154$	−4.00000			−0.322329
$155$	−4.00000	+	2.00000i	−0.321288	+	0.160644i
$156$		−	4.00000i		−	0.320256i
$157$	−2.00000			−0.159617			−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000			−0.159617			−0.0798087	+	0.996810i	$0.525431\pi$
$158$			2.00000i			0.159111i
$159$		−	12.0000i		−	0.951662i
$160$	5.00000	+	10.0000i	0.395285	+	0.790569i
$161$	12.0000			0.945732
$162$	−1.00000			−0.0785674
$163$	−20.0000			−1.56652			−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000			−1.56652			−0.783260	+	0.621694i	$0.786445\pi$
$164$		0			0
$165$	−4.00000	+	2.00000i	−0.311400	+	0.155700i
$166$		−	2.00000i		−	0.155230i
$167$			6.00000i			0.464294i	0.972681	+	0.232147i	$0.0745750\pi$
$167$			6.00000i			0.464294i	−0.972681	+	0.232147i	$0.925425\pi$
$168$			6.00000i			0.462910i
$169$	−3.00000			−0.230769
$170$	−6.00000	−	12.0000i	−0.460179	−	0.920358i
$171$			2.00000i			0.152944i
$172$	−4.00000			−0.304997
$173$		−	12.0000i		−	0.912343i	−0.889892	−	0.456172i	$-0.849220\pi$
$173$		−	12.0000i		−	0.912343i	0.889892	−	0.456172i	$-0.150780\pi$
$174$	−5.00000	+	2.00000i	−0.379049	+	0.151620i
$175$	8.00000	+	6.00000i	0.604743	+	0.453557i
$176$		−	2.00000i		−	0.150756i
$177$	4.00000			0.300658
$178$			16.0000i			1.19925i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	1.00000	+	2.00000i	0.0745356	+	0.149071i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	8.00000			0.592999
$183$		−	12.0000i		−	0.887066i
$184$			18.0000i			1.32698i
$185$	2.00000	+	4.00000i	0.147043	+	0.294086i
$186$		−	2.00000i		−	0.146647i
$187$		−	12.0000i		−	0.877527i
$188$	8.00000			0.583460
$189$			2.00000i			0.145479i
$190$	−4.00000	+	2.00000i	−0.290191	+	0.145095i
$191$			6.00000i			0.434145i	0.976156	+	0.217072i	$0.0696508\pi$
$191$			6.00000i			0.434145i	−0.976156	+	0.217072i	$0.930349\pi$
$192$	−7.00000			−0.505181
$193$	−6.00000			−0.431889			−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000			−0.431889			−0.215945	+	0.976406i	$0.569283\pi$
$194$	14.0000			1.00514
$195$	8.00000	−	4.00000i	0.572892	−	0.286446i
$196$	−3.00000			−0.214286
$197$		−	4.00000i		−	0.284988i	−0.989796	−	0.142494i	$-0.954488\pi$
$197$		−	4.00000i		−	0.284988i	0.989796	−	0.142494i	$-0.0455122\pi$
$198$		−	2.00000i		−	0.142134i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−9.00000	+	12.0000i	−0.636396	+	0.848528i
$201$			6.00000i			0.423207i
$202$		−	12.0000i		−	0.844317i
$203$	4.00000	+	10.0000i	0.280745	+	0.701862i
$204$	−6.00000			−0.420084
$205$		0			0
$206$			18.0000i			1.25412i
$207$			6.00000i			0.417029i
$208$			4.00000i			0.277350i
$209$	−4.00000			−0.276686
$210$	−4.00000	+	2.00000i	−0.276026	+	0.138013i
$211$			2.00000i			0.137686i	0.997628	+	0.0688428i	$0.0219307\pi$
$211$			2.00000i			0.137686i	−0.997628	+	0.0688428i	$0.978069\pi$
$212$		−	12.0000i		−	0.824163i
$213$	−8.00000			−0.548151
$214$		−	10.0000i		−	0.683586i
$215$	−4.00000	−	8.00000i	−0.272798	−	0.545595i
$216$	−3.00000			−0.204124
$217$	−4.00000			−0.271538
$218$	10.0000			0.677285
$219$	6.00000			0.405442
$220$	−4.00000	+	2.00000i	−0.269680	+	0.134840i
$221$			24.0000i			1.61441i
$222$	−2.00000			−0.134231
$223$			22.0000i			1.47323i	0.676313	+	0.736614i	$0.263577\pi$
$223$			22.0000i			1.47323i	−0.676313	+	0.736614i	$0.736423\pi$
$224$			10.0000i			0.668153i
$225$	−3.00000	+	4.00000i	−0.200000	+	0.266667i
$226$	−2.00000			−0.133038
$227$			2.00000i			0.132745i	0.997795	+	0.0663723i	$0.0211425\pi$
$227$			2.00000i			0.132745i	−0.997795	+	0.0663723i	$0.978857\pi$
$228$			2.00000i			0.132453i
$229$			20.0000i			1.32164i	0.750546	+	0.660819i	$0.229791\pi$
$229$			20.0000i			1.32164i	−0.750546	+	0.660819i	$0.770209\pi$
$230$	−12.0000	+	6.00000i	−0.791257	+	0.395628i
$231$	−4.00000			−0.263181
$232$	−15.0000	+	6.00000i	−0.984798	+	0.393919i
$233$		−	16.0000i		−	1.04819i	−0.851658	−	0.524097i	$-0.824403\pi$
$233$		−	16.0000i		−	1.04819i	0.851658	−	0.524097i	$-0.175597\pi$
$234$			4.00000i			0.261488i
$235$	8.00000	+	16.0000i	0.521862	+	1.04372i
$236$	4.00000			0.260378
$237$			2.00000i			0.129914i
$238$		−	12.0000i		−	0.777844i
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$	−1.00000	−	2.00000i	−0.0645497	−	0.129099i
$241$	−22.0000			−1.41714			−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000			−1.41714			−0.708572	+	0.705638i	$0.750660\pi$
$242$	−7.00000			−0.449977
$243$	−1.00000			−0.0641500
$244$		−	12.0000i		−	0.768221i
$245$	−3.00000	−	6.00000i	−0.191663	−	0.383326i
$246$		0			0
$247$	8.00000			0.509028
$248$		−	6.00000i		−	0.381000i
$249$		−	2.00000i		−	0.126745i
$250$	−11.0000	−	2.00000i	−0.695701	−	0.126491i
$251$		−	30.0000i		−	1.89358i	−0.321847	−	0.946792i	$-0.604304\pi$
$251$		−	30.0000i		−	1.89358i	0.321847	−	0.946792i	$-0.395696\pi$
$252$			2.00000i			0.125988i
$253$	−12.0000			−0.754434
$254$	−8.00000			−0.501965
$255$	−6.00000	−	12.0000i	−0.375735	−	0.751469i
$256$	−17.0000			−1.06250
$257$		−	24.0000i		−	1.49708i	−0.663090	−	0.748539i	$-0.730755\pi$
$257$		−	24.0000i		−	1.49708i	0.663090	−	0.748539i	$-0.269245\pi$
$258$	4.00000			0.249029
$259$			4.00000i			0.248548i
$260$	8.00000	−	4.00000i	0.496139	−	0.248069i
$261$	−5.00000	+	2.00000i	−0.309492	+	0.123797i
$262$			22.0000i			1.35916i
$263$	16.0000			0.986602			0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000			0.986602			0.493301	+	0.869859i	$0.335790\pi$
$264$		−	6.00000i		−	0.369274i
$265$	24.0000	−	12.0000i	1.47431	−	0.737154i
$266$	−4.00000			−0.245256
$267$			16.0000i			0.979184i
$268$			6.00000i			0.366508i
$269$			4.00000i			0.243884i	0.992537	+	0.121942i	$0.0389122\pi$
$269$			4.00000i			0.243884i	−0.992537	+	0.121942i	$0.961088\pi$
$270$	−1.00000	−	2.00000i	−0.0608581	−	0.121716i
$271$		−	2.00000i		−	0.121491i	−0.998153	−	0.0607457i	$-0.980652\pi$
$271$		−	2.00000i		−	0.121491i	0.998153	−	0.0607457i	$-0.0193479\pi$
$272$	6.00000			0.363803
$273$	8.00000			0.484182
$274$	14.0000			0.845771
$275$	−8.00000	−	6.00000i	−0.482418	−	0.361814i
$276$			6.00000i			0.361158i
$277$			4.00000i			0.240337i	0.992754	+	0.120168i	$0.0383434\pi$
$277$			4.00000i			0.240337i	−0.992754	+	0.120168i	$0.961657\pi$
$278$	4.00000			0.239904
$279$		−	2.00000i		−	0.119737i
$280$	−12.0000	+	6.00000i	−0.717137	+	0.358569i
$281$	−30.0000			−1.78965			−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000			−1.78965			−0.894825	+	0.446417i	$0.852700\pi$
$282$	−8.00000			−0.476393
$283$			2.00000i			0.118888i	0.998232	+	0.0594438i	$0.0189327\pi$
$283$			2.00000i			0.118888i	−0.998232	+	0.0594438i	$0.981067\pi$
$284$	−8.00000			−0.474713
$285$	−4.00000	+	2.00000i	−0.236940	+	0.118470i
$286$	−8.00000			−0.473050
$287$		0			0
$288$	−5.00000			−0.294628
$289$	19.0000			1.11765
$290$	−9.00000	−	8.00000i	−0.528498	−	0.469776i
$291$	14.0000			0.820695
$292$	6.00000			0.351123
$293$	−26.0000			−1.51894			−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000			−1.51894			−0.759468	+	0.650545i	$0.774541\pi$
$294$	3.00000			0.174964
$295$	4.00000	+	8.00000i	0.232889	+	0.465778i
$296$	−6.00000			−0.348743
$297$		−	2.00000i		−	0.116052i
$298$	10.0000			0.579284
$299$	24.0000			1.38796
$300$	−3.00000	+	4.00000i	−0.173205	+	0.230940i
$301$		−	8.00000i		−	0.461112i
$302$	8.00000			0.460348
$303$		−	12.0000i		−	0.689382i
$304$		−	2.00000i		−	0.114708i
$305$	24.0000	−	12.0000i	1.37424	−	0.687118i
$306$	6.00000			0.342997
$307$	12.0000			0.684876			0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000			0.684876			0.342438	+	0.939540i	$0.388747\pi$
$308$	−4.00000			−0.227921
$309$			18.0000i			1.02398i
$310$	4.00000	−	2.00000i	0.227185	−	0.113592i
$311$			14.0000i			0.793867i	0.917847	+	0.396934i	$0.129926\pi$
$311$			14.0000i			0.793867i	−0.917847	+	0.396934i	$0.870074\pi$
$312$			12.0000i			0.679366i
$313$			8.00000i			0.452187i	0.974106	+	0.226093i	$0.0725954\pi$
$313$			8.00000i			0.452187i	−0.974106	+	0.226093i	$0.927405\pi$
$314$	2.00000			0.112867
$315$	−4.00000	+	2.00000i	−0.225374	+	0.112687i
$316$			2.00000i			0.112509i
$317$	6.00000			0.336994			0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000			0.336994			0.168497	+	0.985702i	$0.446109\pi$
$318$			12.0000i			0.672927i
$319$	−4.00000	−	10.0000i	−0.223957	−	0.559893i
$320$	−7.00000	−	14.0000i	−0.391312	−	0.782624i
$321$		−	10.0000i		−	0.558146i
$322$	−12.0000			−0.668734
$323$		−	12.0000i		−	0.667698i
$324$	−1.00000			−0.0555556
$325$	16.0000	+	12.0000i	0.887520	+	0.665640i
$326$	20.0000			1.10770
$327$	10.0000			0.553001
$328$		0			0
$329$			16.0000i			0.882109i
$330$	4.00000	−	2.00000i	0.220193	−	0.110096i
$331$		−	22.0000i		−	1.20923i	−0.796518	−	0.604615i	$-0.793327\pi$
$331$		−	22.0000i		−	1.20923i	0.796518	−	0.604615i	$-0.206673\pi$
$332$		−	2.00000i		−	0.109764i
$333$	−2.00000			−0.109599
$334$		−	6.00000i		−	0.328305i
$335$	−12.0000	+	6.00000i	−0.655630	+	0.327815i
$336$		−	2.00000i		−	0.109109i
$337$	34.0000			1.85210			0.926049	−	0.377403i	$-0.123183\pi$
$337$	34.0000			1.85210			0.926049	+	0.377403i	$0.123183\pi$
$338$	3.00000			0.163178
$339$	−2.00000			−0.108625
$340$	−6.00000	−	12.0000i	−0.325396	−	0.650791i
$341$	4.00000			0.216612
$342$		−	2.00000i		−	0.108148i
$343$		−	20.0000i		−	1.07990i
$344$	12.0000			0.646997
$345$	−12.0000	+	6.00000i	−0.646058	+	0.323029i
$346$			12.0000i			0.645124i
$347$			10.0000i			0.536828i	0.963304	+	0.268414i	$0.0864995\pi$
$347$			10.0000i			0.536828i	−0.963304	+	0.268414i	$0.913500\pi$
$348$	−5.00000	+	2.00000i	−0.268028	+	0.107211i
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$	−8.00000	−	6.00000i	−0.427618	−	0.320713i
$351$			4.00000i			0.213504i
$352$		−	10.0000i		−	0.533002i
$353$		−	24.0000i		−	1.27739i	−0.769460	−	0.638696i	$-0.779474\pi$
$353$		−	24.0000i		−	1.27739i	0.769460	−	0.638696i	$-0.220526\pi$
$354$	−4.00000			−0.212598
$355$	−8.00000	−	16.0000i	−0.424596	−	0.849192i
$356$			16.0000i			0.847998i
$357$		−	12.0000i		−	0.635107i
$358$	12.0000			0.634220
$359$		−	18.0000i		−	0.950004i	−0.879985	−	0.475002i	$-0.842447\pi$
$359$		−	18.0000i		−	0.950004i	0.879985	−	0.475002i	$-0.157553\pi$
$360$	−3.00000	−	6.00000i	−0.158114	−	0.316228i
$361$	15.0000			0.789474
$362$	10.0000			0.525588
$363$	−7.00000			−0.367405
$364$	8.00000			0.419314
$365$	6.00000	+	12.0000i	0.314054	+	0.628109i
$366$			12.0000i			0.627250i
$367$	24.0000			1.25279			0.626395	−	0.779506i	$-0.284530\pi$
$367$	24.0000			1.25279			0.626395	+	0.779506i	$0.284530\pi$
$368$		−	6.00000i		−	0.312772i
$369$		0			0
$370$	−2.00000	−	4.00000i	−0.103975	−	0.207950i
$371$	24.0000			1.24602
$372$		−	2.00000i		−	0.103695i
$373$			4.00000i			0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$			4.00000i			0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$			12.0000i			0.620505i
$375$	−11.0000	−	2.00000i	−0.568038	−	0.103280i
$376$	−24.0000			−1.23771
$377$	8.00000	+	20.0000i	0.412021	+	1.03005i
$378$		−	2.00000i		−	0.102869i
$379$		−	38.0000i		−	1.95193i	−0.217930	−	0.975964i	$-0.569930\pi$
$379$		−	38.0000i		−	1.95193i	0.217930	−	0.975964i	$-0.430070\pi$
$380$	−4.00000	+	2.00000i	−0.205196	+	0.102598i
$381$	−8.00000			−0.409852
$382$		−	6.00000i		−	0.306987i
$383$			30.0000i			1.53293i	0.642287	+	0.766464i	$0.277986\pi$
$383$			30.0000i			1.53293i	−0.642287	+	0.766464i	$0.722014\pi$
$384$	−3.00000			−0.153093
$385$	−4.00000	−	8.00000i	−0.203859	−	0.407718i
$386$	6.00000			0.305392
$387$	4.00000			0.203331
$388$	14.0000			0.710742
$389$			12.0000i			0.608424i	0.952604	+	0.304212i	$0.0983931\pi$
$389$			12.0000i			0.608424i	−0.952604	+	0.304212i	$0.901607\pi$
$390$	−8.00000	+	4.00000i	−0.405096	+	0.202548i
$391$		−	36.0000i		−	1.82060i
$392$	9.00000			0.454569
$393$			22.0000i			1.10975i
$394$			4.00000i			0.201517i
$395$	−4.00000	+	2.00000i	−0.201262	+	0.100631i
$396$		−	2.00000i		−	0.100504i
$397$			28.0000i			1.40528i	0.711546	+	0.702640i	$0.247995\pi$
$397$			28.0000i			1.40528i	−0.711546	+	0.702640i	$0.752005\pi$
$398$	−8.00000			−0.401004
$399$	−4.00000			−0.200250
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	18.0000			0.898877			0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000			0.898877			0.449439	+	0.893311i	$0.351624\pi$
$402$		−	6.00000i		−	0.299253i
$403$	−8.00000			−0.398508
$404$		−	12.0000i		−	0.597022i
$405$	−1.00000	−	2.00000i	−0.0496904	−	0.0993808i
$406$	−4.00000	−	10.0000i	−0.198517	−	0.496292i
$407$		−	4.00000i		−	0.198273i
$408$	18.0000			0.891133
$409$		−	8.00000i		−	0.395575i	−0.980245	−	0.197787i	$-0.936624\pi$
$409$		−	8.00000i		−	0.395575i	0.980245	−	0.197787i	$-0.0633755\pi$
$410$		0			0
$411$	14.0000			0.690569
$412$			18.0000i			0.886796i
$413$			8.00000i			0.393654i
$414$		−	6.00000i		−	0.294884i
$415$	4.00000	−	2.00000i	0.196352	−	0.0981761i
$416$			20.0000i			0.980581i
$417$	4.00000			0.195881
$418$	4.00000			0.195646
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$	−4.00000	+	2.00000i	−0.195180	+	0.0975900i
$421$		−	28.0000i		−	1.36464i	−0.731055	−	0.682318i	$-0.760972\pi$
$421$		−	28.0000i		−	1.36464i	0.731055	−	0.682318i	$-0.239028\pi$
$422$		−	2.00000i		−	0.0973585i
$423$	−8.00000			−0.388973
$424$			36.0000i			1.74831i
$425$	18.0000	−	24.0000i	0.873128	−	1.16417i
$426$	8.00000			0.387601
$427$	24.0000			1.16144
$428$		−	10.0000i		−	0.483368i
$429$	−8.00000			−0.386244
$430$	4.00000	+	8.00000i	0.192897	+	0.385794i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	1.00000			0.0481125
$433$	−22.0000			−1.05725			−0.528626	−	0.848855i	$-0.677293\pi$
$433$	−22.0000			−1.05725			−0.528626	+	0.848855i	$0.677293\pi$
$434$	4.00000			0.192006
$435$	−9.00000	−	8.00000i	−0.431517	−	0.383571i
$436$	10.0000			0.478913
$437$	−12.0000			−0.574038
$438$	−6.00000			−0.286691
$439$	24.0000			1.14546			0.572729	−	0.819745i	$-0.305885\pi$
$439$	24.0000			1.14546			0.572729	+	0.819745i	$0.305885\pi$
$440$	12.0000	−	6.00000i	0.572078	−	0.286039i
$441$	3.00000			0.142857
$442$		−	24.0000i		−	1.14156i
$443$	−28.0000			−1.33032			−0.665160	−	0.746701i	$-0.731637\pi$
$443$	−28.0000			−1.33032			−0.665160	+	0.746701i	$0.731637\pi$
$444$	−2.00000			−0.0949158
$445$	−32.0000	+	16.0000i	−1.51695	+	0.758473i
$446$		−	22.0000i		−	1.04173i
$447$	10.0000			0.472984
$448$		−	14.0000i		−	0.661438i
$449$		−	24.0000i		−	1.13263i	−0.824189	−	0.566315i	$-0.808369\pi$
$449$		−	24.0000i		−	1.13263i	0.824189	−	0.566315i	$-0.191631\pi$
$450$	3.00000	−	4.00000i	0.141421	−	0.188562i
$451$		0			0
$452$	−2.00000			−0.0940721
$453$	8.00000			0.375873
$454$		−	2.00000i		−	0.0938647i
$455$	8.00000	+	16.0000i	0.375046	+	0.750092i
$456$		−	6.00000i		−	0.280976i
$457$			8.00000i			0.374224i	0.982339	+	0.187112i	$0.0599128\pi$
$457$			8.00000i			0.374224i	−0.982339	+	0.187112i	$0.940087\pi$
$458$		−	20.0000i		−	0.934539i
$459$	6.00000			0.280056
$460$	−12.0000	+	6.00000i	−0.559503	+	0.279751i
$461$		−	12.0000i		−	0.558896i	−0.960161	−	0.279448i	$-0.909849\pi$
$461$		−	12.0000i		−	0.558896i	0.960161	−	0.279448i	$-0.0901514\pi$
$462$	4.00000			0.186097
$463$		−	26.0000i		−	1.20832i	−0.796862	−	0.604161i	$-0.793508\pi$
$463$		−	26.0000i		−	1.20832i	0.796862	−	0.604161i	$-0.206492\pi$
$464$	5.00000	−	2.00000i	0.232119	−	0.0928477i
$465$	4.00000	−	2.00000i	0.185496	−	0.0927478i
$466$			16.0000i			0.741186i
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$			4.00000i			0.184900i
$469$	−12.0000			−0.554109
$470$	−8.00000	−	16.0000i	−0.369012	−	0.738025i
$471$	2.00000			0.0921551
$472$	−12.0000			−0.552345
$473$			8.00000i			0.367840i
$474$		−	2.00000i		−	0.0918630i
$475$	−8.00000	−	6.00000i	−0.367065	−	0.275299i
$476$		−	12.0000i		−	0.550019i
$477$			12.0000i			0.549442i
$478$	−16.0000			−0.731823
$479$		−	42.0000i		−	1.91903i	−0.281659	−	0.959514i	$-0.590885\pi$
$479$		−	42.0000i		−	1.91903i	0.281659	−	0.959514i	$-0.409115\pi$
$480$	−5.00000	−	10.0000i	−0.228218	−	0.456435i
$481$			8.00000i			0.364769i
$482$	22.0000			1.00207
$483$	−12.0000			−0.546019
$484$	−7.00000			−0.318182
$485$	14.0000	+	28.0000i	0.635707	+	1.27141i
$486$	1.00000			0.0453609
$487$			14.0000i			0.634401i	0.948359	+	0.317200i	$0.102743\pi$
$487$			14.0000i			0.634401i	−0.948359	+	0.317200i	$0.897257\pi$
$488$			36.0000i			1.62964i
$489$	20.0000			0.904431
$490$	3.00000	+	6.00000i	0.135526	+	0.271052i
$491$			2.00000i			0.0902587i	0.998981	+	0.0451294i	$0.0143700\pi$
$491$			2.00000i			0.0902587i	−0.998981	+	0.0451294i	$0.985630\pi$
$492$		0			0
$493$	30.0000	−	12.0000i	1.35113	−	0.540453i
$494$	−8.00000			−0.359937
$495$	4.00000	−	2.00000i	0.179787	−	0.0898933i
$496$			2.00000i			0.0898027i
$497$		−	16.0000i		−	0.717698i
$498$			2.00000i			0.0896221i
$499$	−12.0000			−0.537194			−0.268597	−	0.963253i	$-0.586560\pi$
$499$	−12.0000			−0.537194			−0.268597	+	0.963253i	$0.586560\pi$
$500$	−11.0000	−	2.00000i	−0.491935	−	0.0894427i
$501$		−	6.00000i		−	0.268060i
$502$			30.0000i			1.33897i
$503$	−16.0000			−0.713405			−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000			−0.713405			−0.356702	+	0.934218i	$0.616099\pi$
$504$		−	6.00000i		−	0.267261i
$505$	24.0000	−	12.0000i	1.06799	−	0.533993i
$506$	12.0000			0.533465
$507$	3.00000			0.133235
$508$	−8.00000			−0.354943
$509$	−10.0000			−0.443242			−0.221621	−	0.975133i	$-0.571135\pi$
$509$	−10.0000			−0.443242			−0.221621	+	0.975133i	$0.571135\pi$
$510$	6.00000	+	12.0000i	0.265684	+	0.531369i
$511$			12.0000i			0.530849i
$512$	11.0000			0.486136
$513$		−	2.00000i		−	0.0883022i
$514$			24.0000i			1.05859i
$515$	−36.0000	+	18.0000i	−1.58635	+	0.793175i
$516$	4.00000			0.176090
$517$		−	16.0000i		−	0.703679i
$518$		−	4.00000i		−	0.175750i
$519$			12.0000i			0.526742i
$520$	−24.0000	+	12.0000i	−1.05247	+	0.526235i
$521$	−14.0000			−0.613351			−0.306676	−	0.951814i	$-0.599217\pi$
$521$	−14.0000			−0.613351			−0.306676	+	0.951814i	$0.599217\pi$
$522$	5.00000	−	2.00000i	0.218844	−	0.0875376i
$523$			34.0000i			1.48672i	0.668894	+	0.743358i	$0.266768\pi$
$523$			34.0000i			1.48672i	−0.668894	+	0.743358i	$0.733232\pi$
$524$			22.0000i			0.961074i
$525$	−8.00000	−	6.00000i	−0.349149	−	0.261861i
$526$	−16.0000			−0.697633
$527$			12.0000i			0.522728i
$528$			2.00000i			0.0870388i
$529$	−13.0000			−0.565217
$530$	−24.0000	+	12.0000i	−1.04249	+	0.521247i
$531$	−4.00000			−0.173585
$532$	−4.00000			−0.173422
$533$		0			0
$534$		−	16.0000i		−	0.692388i
$535$	20.0000	−	10.0000i	0.864675	−	0.432338i
$536$		−	18.0000i		−	0.777482i
$537$	12.0000			0.517838
$538$		−	4.00000i		−	0.172452i
$539$			6.00000i			0.258438i
$540$	−1.00000	−	2.00000i	−0.0430331	−	0.0860663i
$541$			44.0000i			1.89171i	0.324593	+	0.945854i	$0.394773\pi$
$541$			44.0000i			1.89171i	−0.324593	+	0.945854i	$0.605227\pi$
$542$			2.00000i			0.0859074i
$543$	10.0000			0.429141
$544$	30.0000			1.28624
$545$	10.0000	+	20.0000i	0.428353	+	0.856706i
$546$	−8.00000			−0.342368
$547$			26.0000i			1.11168i	0.831289	+	0.555840i	$0.187603\pi$
$547$			26.0000i			1.11168i	−0.831289	+	0.555840i	$0.812397\pi$
$548$	14.0000			0.598050
$549$			12.0000i			0.512148i
$550$	8.00000	+	6.00000i	0.341121	+	0.255841i
$551$	−4.00000	−	10.0000i	−0.170406	−	0.426014i
$552$		−	18.0000i		−	0.766131i
$553$	−4.00000			−0.170097
$554$		−	4.00000i		−	0.169944i
$555$	−2.00000	−	4.00000i	−0.0848953	−	0.169791i
$556$	4.00000			0.169638
$557$		−	12.0000i		−	0.508456i	−0.967144	−	0.254228i	$-0.918179\pi$
$557$		−	12.0000i		−	0.508456i	0.967144	−	0.254228i	$-0.0818214\pi$
$558$			2.00000i			0.0846668i
$559$		−	16.0000i		−	0.676728i
$560$	4.00000	−	2.00000i	0.169031	−	0.0845154i
$561$			12.0000i			0.506640i
$562$	30.0000			1.26547
$563$	12.0000			0.505740			0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000			0.505740			0.252870	+	0.967500i	$0.418626\pi$
$564$	−8.00000			−0.336861
$565$	−2.00000	−	4.00000i	−0.0841406	−	0.168281i
$566$		−	2.00000i		−	0.0840663i
$567$		−	2.00000i		−	0.0839921i
$568$	24.0000			1.00702
$569$			32.0000i			1.34151i	0.741679	+	0.670755i	$0.234030\pi$
$569$			32.0000i			1.34151i	−0.741679	+	0.670755i	$0.765970\pi$
$570$	4.00000	−	2.00000i	0.167542	−	0.0837708i
$571$	−20.0000			−0.836974			−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000			−0.836974			−0.418487	+	0.908223i	$0.637439\pi$
$572$	−8.00000			−0.334497
$573$		−	6.00000i		−	0.250654i
$574$		0			0
$575$	−24.0000	−	18.0000i	−1.00087	−	0.750652i
$576$	7.00000			0.291667
$577$	−38.0000			−1.58196			−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000			−1.58196			−0.790980	+	0.611842i	$0.790429\pi$
$578$	−19.0000			−0.790296
$579$	6.00000			0.249351
$580$	−9.00000	−	8.00000i	−0.373705	−	0.332182i
$581$	4.00000			0.165948
$582$	−14.0000			−0.580319
$583$	−24.0000			−0.993978
$584$	−18.0000			−0.744845
$585$	−8.00000	+	4.00000i	−0.330759	+	0.165380i
$586$	26.0000			1.07405
$587$			42.0000i			1.73353i	0.498721	+	0.866763i	$0.333803\pi$
$587$			42.0000i			1.73353i	−0.498721	+	0.866763i	$0.666197\pi$
$588$	3.00000			0.123718
$589$	4.00000			0.164817
$590$	−4.00000	−	8.00000i	−0.164677	−	0.329355i
$591$			4.00000i			0.164538i
$592$	2.00000			0.0821995
$593$			8.00000i			0.328521i	0.986417	+	0.164260i	$0.0525237\pi$
$593$			8.00000i			0.328521i	−0.986417	+	0.164260i	$0.947476\pi$
$594$			2.00000i			0.0820610i
$595$	24.0000	−	12.0000i	0.983904	−	0.491952i
$596$	10.0000			0.409616
$597$	−8.00000			−0.327418
$598$	−24.0000			−0.981433
$599$		−	18.0000i		−	0.735460i	−0.929933	−	0.367730i	$-0.880135\pi$
$599$		−	18.0000i		−	0.735460i	0.929933	−	0.367730i	$-0.119865\pi$
$600$	9.00000	−	12.0000i	0.367423	−	0.489898i
$601$			8.00000i			0.326327i	0.986599	+	0.163163i	$0.0521698\pi$
$601$			8.00000i			0.326327i	−0.986599	+	0.163163i	$0.947830\pi$
$602$			8.00000i			0.326056i
$603$		−	6.00000i		−	0.244339i
$604$	8.00000			0.325515
$605$	−7.00000	−	14.0000i	−0.284590	−	0.569181i
$606$			12.0000i			0.487467i
$607$	8.00000			0.324710			0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000			0.324710			0.162355	+	0.986732i	$0.448091\pi$
$608$		−	10.0000i		−	0.405554i
$609$	−4.00000	−	10.0000i	−0.162088	−	0.405220i
$610$	−24.0000	+	12.0000i	−0.971732	+	0.485866i
$611$			32.0000i			1.29458i
$612$	6.00000			0.242536
$613$		−	12.0000i		−	0.484675i	−0.970192	−	0.242338i	$-0.922086\pi$
$613$		−	12.0000i		−	0.484675i	0.970192	−	0.242338i	$-0.0779142\pi$
$614$	−12.0000			−0.484281
$615$		0			0
$616$	12.0000			0.483494
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		−	18.0000i		−	0.724066i
$619$			26.0000i			1.04503i	0.852631	+	0.522514i	$0.175006\pi$
$619$			26.0000i			1.04503i	−0.852631	+	0.522514i	$0.824994\pi$
$620$	4.00000	−	2.00000i	0.160644	−	0.0803219i
$621$		−	6.00000i		−	0.240772i
$622$		−	14.0000i		−	0.561349i
$623$	−32.0000			−1.28205
$624$		−	4.00000i		−	0.160128i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		−	8.00000i		−	0.319744i
$627$	4.00000			0.159745
$628$	2.00000			0.0798087
$629$	12.0000			0.478471
$630$	4.00000	−	2.00000i	0.159364	−	0.0796819i
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		−	6.00000i		−	0.238667i
$633$		−	2.00000i		−	0.0794929i
$634$	−6.00000			−0.238290
$635$	−8.00000	−	16.0000i	−0.317470	−	0.634941i
$636$			12.0000i			0.475831i
$637$		−	12.0000i		−	0.475457i
$638$	4.00000	+	10.0000i	0.158362	+	0.395904i
$639$	8.00000			0.316475
$640$	−3.00000	−	6.00000i	−0.118585	−	0.237171i
$641$			24.0000i			0.947943i	0.880540	+	0.473972i	$0.157180\pi$
$641$			24.0000i			0.947943i	−0.880540	+	0.473972i	$0.842820\pi$
$642$			10.0000i			0.394669i
$643$		−	6.00000i		−	0.236617i	−0.992977	−	0.118308i	$-0.962253\pi$
$643$		−	6.00000i		−	0.236617i	0.992977	−	0.118308i	$-0.0377472\pi$
$644$	−12.0000			−0.472866
$645$	4.00000	+	8.00000i	0.157500	+	0.315000i
$646$			12.0000i			0.472134i
$647$		−	10.0000i		−	0.393141i	−0.980490	−	0.196570i	$-0.937020\pi$
$647$		−	10.0000i		−	0.393141i	0.980490	−	0.196570i	$-0.0629804\pi$
$648$	3.00000			0.117851
$649$		−	8.00000i		−	0.314027i
$650$	−16.0000	−	12.0000i	−0.627572	−	0.470679i
$651$	4.00000			0.156772
$652$	20.0000			0.783260
$653$	−18.0000			−0.704394			−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000			−0.704394			−0.352197	+	0.935926i	$0.614565\pi$
$654$	−10.0000			−0.391031
$655$	−44.0000	+	22.0000i	−1.71922	+	0.859611i
$656$		0			0
$657$	−6.00000			−0.234082
$658$		−	16.0000i		−	0.623745i
$659$			26.0000i			1.01282i	0.862294	+	0.506408i	$0.169027\pi$
$659$			26.0000i			1.01282i	−0.862294	+	0.506408i	$0.830973\pi$
$660$	4.00000	−	2.00000i	0.155700	−	0.0778499i
$661$	22.0000			0.855701			0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000			0.855701			0.427850	+	0.903850i	$0.359271\pi$
$662$			22.0000i			0.855054i
$663$		−	24.0000i		−	0.932083i
$664$			6.00000i			0.232845i
$665$	−4.00000	−	8.00000i	−0.155113	−	0.310227i
$666$	2.00000			0.0774984
$667$	−12.0000	−	30.0000i	−0.464642	−	1.16160i
$668$		−	6.00000i		−	0.232147i
$669$		−	22.0000i		−	0.850569i
$670$	12.0000	−	6.00000i	0.463600	−	0.231800i
$671$	−24.0000			−0.926510
$672$		−	10.0000i		−	0.385758i
$673$		−	32.0000i		−	1.23351i	−0.787155	−	0.616755i	$-0.788447\pi$
$673$		−	32.0000i		−	1.23351i	0.787155	−	0.616755i	$-0.211553\pi$
$674$	−34.0000			−1.30963
$675$	3.00000	−	4.00000i	0.115470	−	0.153960i
$676$	3.00000			0.115385
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$	2.00000			0.0768095
$679$			28.0000i			1.07454i
$680$	18.0000	+	36.0000i	0.690268	+	1.38054i
$681$		−	2.00000i		−	0.0766402i
$682$	−4.00000			−0.153168
$683$		−	6.00000i		−	0.229584i	−0.993390	−	0.114792i	$-0.963380\pi$
$683$		−	6.00000i		−	0.229584i	0.993390	−	0.114792i	$-0.0366201\pi$
$684$		−	2.00000i		−	0.0764719i
$685$	14.0000	+	28.0000i	0.534913	+	1.06983i
$686$			20.0000i			0.763604i
$687$		−	20.0000i		−	0.763048i
$688$	−4.00000			−0.152499
$689$	48.0000			1.82865
$690$	12.0000	−	6.00000i	0.456832	−	0.228416i
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$			12.0000i			0.456172i
$693$	4.00000			0.151947
$694$		−	10.0000i		−	0.379595i
$695$	4.00000	+	8.00000i	0.151729	+	0.303457i
$696$	15.0000	−	6.00000i	0.568574	−	0.227429i
$697$		0			0
$698$	26.0000			0.984115
$699$			16.0000i			0.605176i
$700$	−8.00000	−	6.00000i	−0.302372	−	0.226779i
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		−	4.00000i		−	0.150970i
$703$		−	4.00000i		−	0.150863i
$704$			14.0000i			0.527645i
$705$	−8.00000	−	16.0000i	−0.301297	−	0.602595i
$706$			24.0000i			0.903252i
$707$	24.0000			0.902613
$708$	−4.00000			−0.150329
$709$	−50.0000			−1.87779			−0.938895	−	0.344204i	$-0.888149\pi$
$709$	−50.0000			−1.87779			−0.938895	+	0.344204i	$0.888149\pi$
$710$	8.00000	+	16.0000i	0.300235	+	0.600469i
$711$		−	2.00000i		−	0.0750059i
$712$		−	48.0000i		−	1.79888i
$713$	12.0000			0.449404
$714$			12.0000i			0.449089i
$715$	−8.00000	−	16.0000i	−0.299183	−	0.598366i
$716$	12.0000			0.448461
$717$	−16.0000			−0.597531
$718$			18.0000i			0.671754i
$719$	−48.0000			−1.79010			−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000			−1.79010			−0.895049	+	0.445968i	$0.852860\pi$
$720$	1.00000	+	2.00000i	0.0372678	+	0.0745356i
$721$	−36.0000			−1.34071
$722$	−15.0000			−0.558242
$723$	22.0000			0.818189
$724$	10.0000			0.371647
$725$	7.00000	−	26.0000i	0.259973	−	0.965616i
$726$	7.00000			0.259794
$727$	48.0000			1.78022			0.890111	−	0.455744i	$-0.150627\pi$
$727$	48.0000			1.78022			0.890111	+	0.455744i	$0.150627\pi$
$728$	−24.0000			−0.889499
$729$	1.00000			0.0370370
$730$	−6.00000	−	12.0000i	−0.222070	−	0.444140i
$731$	−24.0000			−0.887672
$732$			12.0000i			0.443533i
$733$	22.0000			0.812589			0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000			0.812589			0.406294	+	0.913742i	$0.366821\pi$
$734$	−24.0000			−0.885856
$735$	3.00000	+	6.00000i	0.110657	+	0.221313i
$736$		−	30.0000i		−	1.10581i
$737$	12.0000			0.442026
$738$		0			0
$739$			34.0000i			1.25071i	0.780340	+	0.625355i	$0.215046\pi$
$739$			34.0000i			1.25071i	−0.780340	+	0.625355i	$0.784954\pi$
$740$	−2.00000	−	4.00000i	−0.0735215	−	0.147043i
$741$	−8.00000			−0.293887
$742$	−24.0000			−0.881068
$743$	−48.0000			−1.76095			−0.880475	−	0.474093i	$-0.842776\pi$
$743$	−48.0000			−1.76095			−0.880475	+	0.474093i	$0.842776\pi$
$744$			6.00000i			0.219971i
$745$	10.0000	+	20.0000i	0.366372	+	0.732743i
$746$		−	4.00000i		−	0.146450i
$747$			2.00000i			0.0731762i
$748$			12.0000i			0.438763i
$749$	20.0000			0.730784
$750$	11.0000	+	2.00000i	0.401663	+	0.0730297i
$751$			46.0000i			1.67856i	0.543696	+	0.839282i	$0.317024\pi$
$751$			46.0000i			1.67856i	−0.543696	+	0.839282i	$0.682976\pi$
$752$	8.00000			0.291730
$753$			30.0000i			1.09326i
$754$	−8.00000	−	20.0000i	−0.291343	−	0.728357i
$755$	8.00000	+	16.0000i	0.291150	+	0.582300i
$756$		−	2.00000i		−	0.0727393i
$757$	−42.0000			−1.52652			−0.763258	−	0.646094i	$-0.776401\pi$
$757$	−42.0000			−1.52652			−0.763258	+	0.646094i	$0.776401\pi$
$758$			38.0000i			1.38022i
$759$	12.0000			0.435572
$760$	12.0000	−	6.00000i	0.435286	−	0.217643i
$761$	2.00000			0.0724999			0.0362500	−	0.999343i	$-0.488459\pi$
$761$	2.00000			0.0724999			0.0362500	+	0.999343i	$0.488459\pi$
$762$	8.00000			0.289809
$763$			20.0000i			0.724049i
$764$		−	6.00000i		−	0.217072i
$765$	6.00000	+	12.0000i	0.216930	+	0.433861i
$766$		−	30.0000i		−	1.08394i
$767$			16.0000i			0.577727i
$768$	17.0000			0.613435
$769$		−	32.0000i		−	1.15395i	−0.816762	−	0.576975i	$-0.804233\pi$
$769$		−	32.0000i		−	1.15395i	0.816762	−	0.576975i	$-0.195767\pi$
$770$	4.00000	+	8.00000i	0.144150	+	0.288300i
$771$			24.0000i			0.864339i
$772$	6.00000			0.215945
$773$	−18.0000			−0.647415			−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000			−0.647415			−0.323708	+	0.946157i	$0.604929\pi$
$774$	−4.00000			−0.143777
$775$	8.00000	+	6.00000i	0.287368	+	0.215526i
$776$	−42.0000			−1.50771
$777$		−	4.00000i		−	0.143499i
$778$		−	12.0000i		−	0.430221i
$779$		0			0
$780$

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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +1.00000 q^{6} -2.00000i q^{7} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +1.00000 q^{6} -2.00000i q^{7} +3.00000 q^{8} +1.00000 q^{9} +(1.00000 + 2.00000i) q^{10} +2.00000i q^{11} +1.00000 q^{12} -4.00000i q^{13} +2.00000i q^{14} +(1.00000 + 2.00000i) q^{15} -1.00000 q^{16} -6.00000 q^{17} -1.00000 q^{18} +2.00000i q^{19} +(1.00000 + 2.00000i) q^{20} +2.00000i q^{21} -2.00000i q^{22} +6.00000i q^{23} -3.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} +4.00000i q^{26} -1.00000 q^{27} +2.00000i q^{28} +(-5.00000 + 2.00000i) q^{29} +(-1.00000 - 2.00000i) q^{30} -2.00000i q^{31} -5.00000 q^{32} -2.00000i q^{33} +6.00000 q^{34} +(-4.00000 + 2.00000i) q^{35} -1.00000 q^{36} -2.00000 q^{37} -2.00000i q^{38} +4.00000i q^{39} +(-3.00000 - 6.00000i) q^{40} -2.00000i q^{42} +4.00000 q^{43} -2.00000i q^{44} +(-1.00000 - 2.00000i) q^{45} -6.00000i q^{46} -8.00000 q^{47} +1.00000 q^{48} +3.00000 q^{49} +(3.00000 - 4.00000i) q^{50} +6.00000 q^{51} +4.00000i q^{52} +12.0000i q^{53} +1.00000 q^{54} +(4.00000 - 2.00000i) q^{55} -6.00000i q^{56} -2.00000i q^{57} +(5.00000 - 2.00000i) q^{58} -4.00000 q^{59} +(-1.00000 - 2.00000i) q^{60} +12.0000i q^{61} +2.00000i q^{62} -2.00000i q^{63} +7.00000 q^{64} +(-8.00000 + 4.00000i) q^{65} +2.00000i q^{66} -6.00000i q^{67} +6.00000 q^{68} -6.00000i q^{69} +(4.00000 - 2.00000i) q^{70} +8.00000 q^{71} +3.00000 q^{72} -6.00000 q^{73} +2.00000 q^{74} +(3.00000 - 4.00000i) q^{75} -2.00000i q^{76} +4.00000 q^{77} -4.00000i q^{78} -2.00000i q^{79} +(1.00000 + 2.00000i) q^{80} +1.00000 q^{81} +2.00000i q^{83} -2.00000i q^{84} +(6.00000 + 12.0000i) q^{85} -4.00000 q^{86} +(5.00000 - 2.00000i) q^{87} +6.00000i q^{88} -16.0000i q^{89} +(1.00000 + 2.00000i) q^{90} -8.00000 q^{91} -6.00000i q^{92} +2.00000i q^{93} +8.00000 q^{94} +(4.00000 - 2.00000i) q^{95} +5.00000 q^{96} -14.0000 q^{97} -3.00000 q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} + 2 q^{15} - 2 q^{16} - 12 q^{17} - 2 q^{18} + 2 q^{20} - 6 q^{24} - 6 q^{25} - 2 q^{27} - 10 q^{29} - 2 q^{30} - 10 q^{32} + 12 q^{34} - 8 q^{35} - 2 q^{36} - 4 q^{37} - 6 q^{40} + 8 q^{43} - 2 q^{45} - 16 q^{47} + 2 q^{48} + 6 q^{49} + 6 q^{50} + 12 q^{51} + 2 q^{54} + 8 q^{55} + 10 q^{58} - 8 q^{59} - 2 q^{60} + 14 q^{64} - 16 q^{65} + 12 q^{68} + 8 q^{70} + 16 q^{71} + 6 q^{72} - 12 q^{73} + 4 q^{74} + 6 q^{75} + 8 q^{77} + 2 q^{80} + 2 q^{81} + 12 q^{85} - 8 q^{86} + 10 q^{87} + 2 q^{90} - 16 q^{91} + 16 q^{94} + 8 q^{95} + 10 q^{96} - 28 q^{97} - 6 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 + 2 * q^15 - 2 * q^16 - 12 * q^17 - 2 * q^18 + 2 * q^20 - 6 * q^24 - 6 * q^25 - 2 * q^27 - 10 * q^29 - 2 * q^30 - 10 * q^32 + 12 * q^34 - 8 * q^35 - 2 * q^36 - 4 * q^37 - 6 * q^40 + 8 * q^43 - 2 * q^45 - 16 * q^47 + 2 * q^48 + 6 * q^49 + 6 * q^50 + 12 * q^51 + 2 * q^54 + 8 * q^55 + 10 * q^58 - 8 * q^59 - 2 * q^60 + 14 * q^64 - 16 * q^65 + 12 * q^68 + 8 * q^70 + 16 * q^71 + 6 * q^72 - 12 * q^73 + 4 * q^74 + 6 * q^75 + 8 * q^77 + 2 * q^80 + 2 * q^81 + 12 * q^85 - 8 * q^86 + 10 * q^87 + 2 * q^90 - 16 * q^91 + 16 * q^94 + 8 * q^95 + 10 * q^96 - 28 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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