LMFDB - Dirichlet character orbit 6897.dc

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6897, base_ring=CyclotomicField(198)) M = H._module chi = DirichletCharacter(H, M([99,108,55])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(89,6897)) 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:	$198$	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:	$\Q(\zeta_{99})$
Fixed field:	Number field defined by a degree 198 polynomial (not computed)

First 31 of 60 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{6897}(89,\cdot)$	$1$	$1$	$e\left(\frac{32}{99}\right)$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{61}{198}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{125}{198}\right)$	$e\left(\frac{95}{198}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{1}{198}\right)$
$\chi_{6897}(155,\cdot)$	$1$	$1$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{35}{99}\right)$	$e\left(\frac{137}{198}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{73}{198}\right)$	$e\left(\frac{103}{198}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{70}{99}\right)$	$e\left(\frac{197}{198}\right)$
$\chi_{6897}(287,\cdot)$	$1$	$1$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{113}{198}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{79}{198}\right)$	$e\left(\frac{163}{198}\right)$	$e\left(\frac{7}{99}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{83}{198}\right)$
$\chi_{6897}(452,\cdot)$	$1$	$1$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{127}{198}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{59}{198}\right)$	$e\left(\frac{29}{198}\right)$	$e\left(\frac{14}{99}\right)$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{67}{198}\right)$
$\chi_{6897}(584,\cdot)$	$1$	$1$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{125}{198}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{175}{198}\right)$	$e\left(\frac{133}{198}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{41}{198}\right)$
$\chi_{6897}(716,\cdot)$	$1$	$1$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{79}{198}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{71}{198}\right)$	$e\left(\frac{149}{198}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{37}{198}\right)$
$\chi_{6897}(782,\cdot)$	$1$	$1$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{155}{198}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{19}{198}\right)$	$e\left(\frac{157}{198}\right)$	$e\left(\frac{28}{99}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{35}{198}\right)$
$\chi_{6897}(914,\cdot)$	$1$	$1$	$e\left(\frac{46}{99}\right)$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{131}{198}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{25}{198}\right)$	$e\left(\frac{19}{198}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{119}{198}\right)$
$\chi_{6897}(1079,\cdot)$	$1$	$1$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{58}{99}\right)$	$e\left(\frac{145}{198}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{5}{198}\right)$	$e\left(\frac{83}{198}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{103}{198}\right)$
$\chi_{6897}(1112,\cdot)$	$1$	$1$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{139}{198}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{155}{198}\right)$	$e\left(\frac{197}{198}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{32}{99}\right)$	$e\left(\frac{25}{198}\right)$
$\chi_{6897}(1343,\cdot)$	$1$	$1$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{97}{198}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{17}{198}\right)$	$e\left(\frac{5}{198}\right)$	$e\left(\frac{98}{99}\right)$	$e\left(\frac{38}{99}\right)$	$e\left(\frac{73}{198}\right)$
$\chi_{6897}(1409,\cdot)$	$1$	$1$	$e\left(\frac{94}{99}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{173}{198}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{163}{198}\right)$	$e\left(\frac{13}{198}\right)$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{71}{198}\right)$
$\chi_{6897}(1541,\cdot)$	$1$	$1$	$e\left(\frac{10}{99}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{149}{198}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{169}{198}\right)$	$e\left(\frac{73}{198}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{155}{198}\right)$
$\chi_{6897}(1706,\cdot)$	$1$	$1$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{163}{198}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{149}{198}\right)$	$e\left(\frac{137}{198}\right)$	$e\left(\frac{32}{99}\right)$	$e\left(\frac{71}{99}\right)$	$e\left(\frac{139}{198}\right)$
$\chi_{6897}(1739,\cdot)$	$1$	$1$	$e\left(\frac{71}{99}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{157}{198}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{101}{198}\right)$	$e\left(\frac{53}{198}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{86}{99}\right)$	$e\left(\frac{61}{198}\right)$
$\chi_{6897}(1838,\cdot)$	$1$	$1$	$e\left(\frac{52}{99}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{161}{198}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{67}{198}\right)$	$e\left(\frac{43}{198}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{10}{99}\right)$	$e\left(\frac{113}{198}\right)$
$\chi_{6897}(1970,\cdot)$	$1$	$1$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{46}{99}\right)$	$e\left(\frac{115}{198}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{161}{198}\right)$	$e\left(\frac{59}{198}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{109}{198}\right)$
$\chi_{6897}(2036,\cdot)$	$1$	$1$	$e\left(\frac{58}{99}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{191}{198}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{109}{198}\right)$	$e\left(\frac{67}{198}\right)$	$e\left(\frac{46}{99}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{107}{198}\right)$
$\chi_{6897}(2168,\cdot)$	$1$	$1$	$e\left(\frac{73}{99}\right)$	$e\left(\frac{47}{99}\right)$	$e\left(\frac{167}{198}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{115}{198}\right)$	$e\left(\frac{127}{198}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{94}{99}\right)$	$e\left(\frac{191}{198}\right)$
$\chi_{6897}(2333,\cdot)$	$1$	$1$	$e\left(\frac{56}{99}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{181}{198}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{95}{198}\right)$	$e\left(\frac{191}{198}\right)$	$e\left(\frac{41}{99}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{175}{198}\right)$
$\chi_{6897}(2366,\cdot)$	$1$	$1$	$e\left(\frac{35}{99}\right)$	$e\left(\frac{70}{99}\right)$	$e\left(\frac{175}{198}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{47}{198}\right)$	$e\left(\frac{107}{198}\right)$	$e\left(\frac{38}{99}\right)$	$e\left(\frac{41}{99}\right)$	$e\left(\frac{97}{198}\right)$
$\chi_{6897}(2465,\cdot)$	$1$	$1$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{32}{99}\right)$	$e\left(\frac{179}{198}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{13}{198}\right)$	$e\left(\frac{97}{198}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{149}{198}\right)$
$\chi_{6897}(2597,\cdot)$	$1$	$1$	$e\left(\frac{86}{99}\right)$	$e\left(\frac{73}{99}\right)$	$e\left(\frac{133}{198}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{107}{198}\right)$	$e\left(\frac{113}{198}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{47}{99}\right)$	$e\left(\frac{145}{198}\right)$
$\chi_{6897}(2795,\cdot)$	$1$	$1$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{185}{198}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{61}{198}\right)$	$e\left(\frac{181}{198}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{29}{198}\right)$
$\chi_{6897}(2960,\cdot)$	$1$	$1$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{1}{198}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{41}{198}\right)$	$e\left(\frac{47}{198}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{13}{198}\right)$
$\chi_{6897}(2993,\cdot)$	$1$	$1$	$e\left(\frac{98}{99}\right)$	$e\left(\frac{97}{99}\right)$	$e\left(\frac{193}{198}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{191}{198}\right)$	$e\left(\frac{161}{198}\right)$	$e\left(\frac{47}{99}\right)$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{133}{198}\right)$
$\chi_{6897}(3092,\cdot)$	$1$	$1$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{197}{198}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{157}{198}\right)$	$e\left(\frac{151}{198}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{185}{198}\right)$
$\chi_{6897}(3224,\cdot)$	$1$	$1$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{151}{198}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{53}{198}\right)$	$e\left(\frac{167}{198}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{181}{198}\right)$
$\chi_{6897}(3290,\cdot)$	$1$	$1$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{71}{99}\right)$	$e\left(\frac{29}{198}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{1}{198}\right)$	$e\left(\frac{175}{198}\right)$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{179}{198}\right)$
$\chi_{6897}(3422,\cdot)$	$1$	$1$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{5}{198}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{7}{198}\right)$	$e\left(\frac{37}{198}\right)$	$e\left(\frac{52}{99}\right)$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{65}{198}\right)$
$\chi_{6897}(3587,\cdot)$	$1$	$1$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{19}{198}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{185}{198}\right)$	$e\left(\frac{101}{198}\right)$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{35}{99}\right)$	$e\left(\frac{49}{198}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\(\chi_{6897}(89,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{61}{198}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{125}{198}\right)\)	\(e\left(\frac{95}{198}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{1}{198}\right)\)
\(\chi_{6897}(155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{35}{99}\right)\)	\(e\left(\frac{137}{198}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{73}{198}\right)\)	\(e\left(\frac{103}{198}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{70}{99}\right)\)	\(e\left(\frac{197}{198}\right)\)
\(\chi_{6897}(287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{113}{198}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{79}{198}\right)\)	\(e\left(\frac{163}{198}\right)\)	\(e\left(\frac{7}{99}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{83}{198}\right)\)
\(\chi_{6897}(452,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{127}{198}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{59}{198}\right)\)	\(e\left(\frac{29}{198}\right)\)	\(e\left(\frac{14}{99}\right)\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{67}{198}\right)\)
\(\chi_{6897}(584,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{125}{198}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{175}{198}\right)\)	\(e\left(\frac{133}{198}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{41}{198}\right)\)
\(\chi_{6897}(716,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{79}{198}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{71}{198}\right)\)	\(e\left(\frac{149}{198}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{37}{198}\right)\)
\(\chi_{6897}(782,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{155}{198}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{19}{198}\right)\)	\(e\left(\frac{157}{198}\right)\)	\(e\left(\frac{28}{99}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{35}{198}\right)\)
\(\chi_{6897}(914,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{99}\right)\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{131}{198}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{25}{198}\right)\)	\(e\left(\frac{19}{198}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{119}{198}\right)\)
\(\chi_{6897}(1079,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{58}{99}\right)\)	\(e\left(\frac{145}{198}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{5}{198}\right)\)	\(e\left(\frac{83}{198}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{103}{198}\right)\)
\(\chi_{6897}(1112,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{139}{198}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{155}{198}\right)\)	\(e\left(\frac{197}{198}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{25}{198}\right)\)
\(\chi_{6897}(1343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{97}{198}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{17}{198}\right)\)	\(e\left(\frac{5}{198}\right)\)	\(e\left(\frac{98}{99}\right)\)	\(e\left(\frac{38}{99}\right)\)	\(e\left(\frac{73}{198}\right)\)
\(\chi_{6897}(1409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{99}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{173}{198}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{163}{198}\right)\)	\(e\left(\frac{13}{198}\right)\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{71}{198}\right)\)
\(\chi_{6897}(1541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{99}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{149}{198}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{169}{198}\right)\)	\(e\left(\frac{73}{198}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{155}{198}\right)\)
\(\chi_{6897}(1706,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{163}{198}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{149}{198}\right)\)	\(e\left(\frac{137}{198}\right)\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{71}{99}\right)\)	\(e\left(\frac{139}{198}\right)\)
\(\chi_{6897}(1739,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{99}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{157}{198}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{101}{198}\right)\)	\(e\left(\frac{53}{198}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{86}{99}\right)\)	\(e\left(\frac{61}{198}\right)\)
\(\chi_{6897}(1838,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{99}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{161}{198}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{67}{198}\right)\)	\(e\left(\frac{43}{198}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{10}{99}\right)\)	\(e\left(\frac{113}{198}\right)\)
\(\chi_{6897}(1970,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{46}{99}\right)\)	\(e\left(\frac{115}{198}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{161}{198}\right)\)	\(e\left(\frac{59}{198}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{109}{198}\right)\)
\(\chi_{6897}(2036,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{99}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{191}{198}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{109}{198}\right)\)	\(e\left(\frac{67}{198}\right)\)	\(e\left(\frac{46}{99}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{107}{198}\right)\)
\(\chi_{6897}(2168,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{99}\right)\)	\(e\left(\frac{47}{99}\right)\)	\(e\left(\frac{167}{198}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{115}{198}\right)\)	\(e\left(\frac{127}{198}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{94}{99}\right)\)	\(e\left(\frac{191}{198}\right)\)
\(\chi_{6897}(2333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{99}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{181}{198}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{95}{198}\right)\)	\(e\left(\frac{191}{198}\right)\)	\(e\left(\frac{41}{99}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{175}{198}\right)\)
\(\chi_{6897}(2366,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{99}\right)\)	\(e\left(\frac{70}{99}\right)\)	\(e\left(\frac{175}{198}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{47}{198}\right)\)	\(e\left(\frac{107}{198}\right)\)	\(e\left(\frac{38}{99}\right)\)	\(e\left(\frac{41}{99}\right)\)	\(e\left(\frac{97}{198}\right)\)
\(\chi_{6897}(2465,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{179}{198}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{13}{198}\right)\)	\(e\left(\frac{97}{198}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{149}{198}\right)\)
\(\chi_{6897}(2597,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{99}\right)\)	\(e\left(\frac{73}{99}\right)\)	\(e\left(\frac{133}{198}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{107}{198}\right)\)	\(e\left(\frac{113}{198}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{47}{99}\right)\)	\(e\left(\frac{145}{198}\right)\)
\(\chi_{6897}(2795,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{185}{198}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{61}{198}\right)\)	\(e\left(\frac{181}{198}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{29}{198}\right)\)
\(\chi_{6897}(2960,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{1}{198}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{41}{198}\right)\)	\(e\left(\frac{47}{198}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{13}{198}\right)\)
\(\chi_{6897}(2993,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{98}{99}\right)\)	\(e\left(\frac{97}{99}\right)\)	\(e\left(\frac{193}{198}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{191}{198}\right)\)	\(e\left(\frac{161}{198}\right)\)	\(e\left(\frac{47}{99}\right)\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{133}{198}\right)\)
\(\chi_{6897}(3092,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{197}{198}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{157}{198}\right)\)	\(e\left(\frac{151}{198}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{185}{198}\right)\)
\(\chi_{6897}(3224,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{151}{198}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{53}{198}\right)\)	\(e\left(\frac{167}{198}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{181}{198}\right)\)
\(\chi_{6897}(3290,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{71}{99}\right)\)	\(e\left(\frac{29}{198}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{1}{198}\right)\)	\(e\left(\frac{175}{198}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{179}{198}\right)\)
\(\chi_{6897}(3422,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{5}{198}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{7}{198}\right)\)	\(e\left(\frac{37}{198}\right)\)	\(e\left(\frac{52}{99}\right)\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{65}{198}\right)\)
\(\chi_{6897}(3587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{19}{198}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{185}{198}\right)\)	\(e\left(\frac{101}{198}\right)\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{35}{99}\right)\)	\(e\left(\frac{49}{198}\right)\)

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First 31 of 60 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.dc
Modulus	$6897$
Conductor	$6897$
Order	$198$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(6897\)
Conductor:	\(6897\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(198\)	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)