LMFDB - Dirichlet character orbit 6897.de

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6897, base_ring=CyclotomicField(330)) M = H._module chi = DirichletCharacter(H, M([165,153,220])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(68,6897)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6897$
Conductor:	$6897$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$330$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 330 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{6897}(68,\cdot)$	$1$	$1$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{43}{165}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{53}{330}\right)$	$e\left(\frac{289}{330}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{146}{165}\right)$
$\chi_{6897}(83,\cdot)$	$1$	$1$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{124}{165}\right)$
$\chi_{6897}(140,\cdot)$	$1$	$1$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{221}{330}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{289}{330}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{133}{165}\right)$
$\chi_{6897}(182,\cdot)$	$1$	$1$	$e\left(\frac{26}{165}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{137}{330}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{119}{165}\right)$
$\chi_{6897}(425,\cdot)$	$1$	$1$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{119}{330}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{53}{330}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{97}{165}\right)$
$\chi_{6897}(695,\cdot)$	$1$	$1$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{161}{165}\right)$
$\chi_{6897}(710,\cdot)$	$1$	$1$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{173}{330}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{19}{165}\right)$
$\chi_{6897}(767,\cdot)$	$1$	$1$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{13}{165}\right)$
$\chi_{6897}(809,\cdot)$	$1$	$1$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{223}{330}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{14}{165}\right)$
$\chi_{6897}(866,\cdot)$	$1$	$1$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{179}{330}\right)$	$e\left(\frac{67}{330}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{23}{165}\right)$
$\chi_{6897}(1052,\cdot)$	$1$	$1$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{7}{165}\right)$
$\chi_{6897}(1151,\cdot)$	$1$	$1$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{229}{330}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{71}{330}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{152}{165}\right)$
$\chi_{6897}(1223,\cdot)$	$1$	$1$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{257}{330}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{136}{165}\right)$
$\chi_{6897}(1337,\cdot)$	$1$	$1$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{127}{330}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{94}{165}\right)$	$e\left(\frac{79}{165}\right)$
$\chi_{6897}(1394,\cdot)$	$1$	$1$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{229}{330}\right)$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{58}{165}\right)$
$\chi_{6897}(1436,\cdot)$	$1$	$1$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{74}{165}\right)$
$\chi_{6897}(1493,\cdot)$	$1$	$1$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{68}{165}\right)$
$\chi_{6897}(1679,\cdot)$	$1$	$1$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{82}{165}\right)$
$\chi_{6897}(1778,\cdot)$	$1$	$1$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{131}{330}\right)$	$e\left(\frac{73}{330}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{62}{165}\right)$
$\chi_{6897}(1850,\cdot)$	$1$	$1$	$e\left(\frac{94}{165}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{13}{330}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{151}{165}\right)$
$\chi_{6897}(1949,\cdot)$	$1$	$1$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{26}{165}\right)$
$\chi_{6897}(1964,\cdot)$	$1$	$1$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{161}{330}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{139}{165}\right)$
$\chi_{6897}(2021,\cdot)$	$1$	$1$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{191}{330}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{257}{330}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{103}{165}\right)$
$\chi_{6897}(2063,\cdot)$	$1$	$1$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{13}{330}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{134}{165}\right)$
$\chi_{6897}(2120,\cdot)$	$1$	$1$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{119}{330}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{113}{165}\right)$
$\chi_{6897}(2306,\cdot)$	$1$	$1$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{179}{330}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{157}{165}\right)$
$\chi_{6897}(2405,\cdot)$	$1$	$1$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{191}{330}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{137}{165}\right)$
$\chi_{6897}(2477,\cdot)$	$1$	$1$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{223}{330}\right)$	$e\left(\frac{89}{330}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{1}{165}\right)$
$\chi_{6897}(2576,\cdot)$	$1$	$1$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{41}{165}\right)$
$\chi_{6897}(2591,\cdot)$	$1$	$1$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{221}{330}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{34}{165}\right)$
$\chi_{6897}(2648,\cdot)$	$1$	$1$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{71}{330}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{137}{330}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{148}{165}\right)$

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 $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\(\chi_{6897}(68,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{43}{165}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{53}{330}\right)\)	\(e\left(\frac{289}{330}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{146}{165}\right)\)
\(\chi_{6897}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)
\(\chi_{6897}(140,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{221}{330}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{289}{330}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)
\(\chi_{6897}(182,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{165}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{137}{330}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{119}{165}\right)\)
\(\chi_{6897}(425,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{119}{330}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{53}{330}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{97}{165}\right)\)
\(\chi_{6897}(695,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{161}{165}\right)\)
\(\chi_{6897}(710,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{173}{330}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{19}{165}\right)\)
\(\chi_{6897}(767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{13}{165}\right)\)
\(\chi_{6897}(809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{223}{330}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)
\(\chi_{6897}(866,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{179}{330}\right)\)	\(e\left(\frac{67}{330}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{23}{165}\right)\)
\(\chi_{6897}(1052,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)
\(\chi_{6897}(1151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{229}{330}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{71}{330}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)
\(\chi_{6897}(1223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{257}{330}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{136}{165}\right)\)
\(\chi_{6897}(1337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{127}{330}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{94}{165}\right)\)	\(e\left(\frac{79}{165}\right)\)
\(\chi_{6897}(1394,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{229}{330}\right)\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{58}{165}\right)\)
\(\chi_{6897}(1436,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{74}{165}\right)\)
\(\chi_{6897}(1493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{68}{165}\right)\)
\(\chi_{6897}(1679,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{82}{165}\right)\)
\(\chi_{6897}(1778,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{131}{330}\right)\)	\(e\left(\frac{73}{330}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{62}{165}\right)\)
\(\chi_{6897}(1850,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{165}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{13}{330}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{151}{165}\right)\)
\(\chi_{6897}(1949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{26}{165}\right)\)
\(\chi_{6897}(1964,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{161}{330}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)
\(\chi_{6897}(2021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{191}{330}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{257}{330}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)
\(\chi_{6897}(2063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{13}{330}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)
\(\chi_{6897}(2120,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{119}{330}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)
\(\chi_{6897}(2306,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{179}{330}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{157}{165}\right)\)
\(\chi_{6897}(2405,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{191}{330}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{137}{165}\right)\)
\(\chi_{6897}(2477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{223}{330}\right)\)	\(e\left(\frac{89}{330}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{1}{165}\right)\)
\(\chi_{6897}(2576,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)
\(\chi_{6897}(2591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{221}{330}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{34}{165}\right)\)
\(\chi_{6897}(2648,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{71}{330}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{137}{330}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{148}{165}\right)\)

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First 31 of 80 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	6897.de
Modulus	$6897$
Conductor	$6897$
Order	$330$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(6897\)
Conductor:	\(6897\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(330\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)