LMFDB - Dirichlet character orbit 6069.cx

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6069, base_ring=CyclotomicField(408)) M = H._module chi = DirichletCharacter(H, M([0,272,279])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(25,6069)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6069$
Conductor:	$2023$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$408$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2023.bl	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:	$\Q(\zeta_{408})$
Fixed field:	Number field defined by a degree 408 polynomial (not computed)

First 31 of 128 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$19$	$20$
$\chi_{6069}(25,\cdot)$	$1$	$1$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{379}{408}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{77}{408}\right)$	$e\left(\frac{161}{408}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{61}{136}\right)$
$\chi_{6069}(100,\cdot)$	$1$	$1$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{77}{408}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{91}{408}\right)$	$e\left(\frac{79}{408}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{35}{136}\right)$
$\chi_{6069}(121,\cdot)$	$1$	$1$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{161}{408}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{79}{408}\right)$	$e\left(\frac{91}{408}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{135}{136}\right)$
$\chi_{6069}(151,\cdot)$	$1$	$1$	$e\left(\frac{107}{204}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{157}{408}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{371}{408}\right)$	$e\left(\frac{71}{408}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{59}{136}\right)$
$\chi_{6069}(172,\cdot)$	$1$	$1$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{217}{408}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{71}{408}\right)$	$e\left(\frac{371}{408}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{107}{204}\right)$	$e\left(\frac{111}{136}\right)$
$\chi_{6069}(247,\cdot)$	$1$	$1$	$e\left(\frac{73}{204}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{191}{408}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{337}{408}\right)$	$e\left(\frac{37}{408}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{25}{136}\right)$
$\chi_{6069}(298,\cdot)$	$1$	$1$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{7}{408}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{305}{408}\right)$	$e\left(\frac{341}{408}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{89}{204}\right)$	$e\left(\frac{65}{136}\right)$
$\chi_{6069}(331,\cdot)$	$1$	$1$	$e\left(\frac{73}{204}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{395}{408}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{133}{408}\right)$	$e\left(\frac{241}{408}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{93}{136}\right)$
$\chi_{6069}(382,\cdot)$	$1$	$1$	$e\left(\frac{65}{204}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{307}{408}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{29}{408}\right)$	$e\left(\frac{209}{408}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{53}{136}\right)$
$\chi_{6069}(457,\cdot)$	$1$	$1$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{365}{408}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{283}{408}\right)$	$e\left(\frac{295}{408}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{67}{136}\right)$
$\chi_{6069}(478,\cdot)$	$1$	$1$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{281}{408}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{295}{408}\right)$	$e\left(\frac{283}{408}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{103}{136}\right)$
$\chi_{6069}(508,\cdot)$	$1$	$1$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{37}{408}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{155}{408}\right)$	$e\left(\frac{287}{408}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{91}{136}\right)$
$\chi_{6069}(529,\cdot)$	$1$	$1$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{337}{408}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{287}{408}\right)$	$e\left(\frac{155}{408}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{79}{136}\right)$
$\chi_{6069}(604,\cdot)$	$1$	$1$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{385}{408}\right)$	$e\left(\frac{397}{408}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{33}{136}\right)$
$\chi_{6069}(655,\cdot)$	$1$	$1$	$e\left(\frac{137}{204}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{79}{408}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{353}{408}\right)$	$e\left(\frac{293}{408}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{101}{204}\right)$	$e\left(\frac{73}{136}\right)$
$\chi_{6069}(739,\cdot)$	$1$	$1$	$e\left(\frac{77}{204}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{235}{408}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{389}{408}\right)$	$e\left(\frac{257}{408}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{45}{136}\right)$
$\chi_{6069}(814,\cdot)$	$1$	$1$	$e\left(\frac{115}{204}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{245}{408}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{67}{408}\right)$	$e\left(\frac{103}{408}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{99}{136}\right)$
$\chi_{6069}(835,\cdot)$	$1$	$1$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{401}{408}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{103}{408}\right)$	$e\left(\frac{67}{408}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{115}{204}\right)$	$e\left(\frac{71}{136}\right)$
$\chi_{6069}(865,\cdot)$	$1$	$1$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{325}{408}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{347}{408}\right)$	$e\left(\frac{95}{408}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{23}{204}\right)$	$e\left(\frac{123}{136}\right)$
$\chi_{6069}(886,\cdot)$	$1$	$1$	$e\left(\frac{23}{204}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{49}{408}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{95}{408}\right)$	$e\left(\frac{347}{408}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{47}{136}\right)$
$\chi_{6069}(961,\cdot)$	$1$	$1$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{335}{408}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{25}{408}\right)$	$e\left(\frac{349}{408}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{121}{204}\right)$	$e\left(\frac{41}{136}\right)$
$\chi_{6069}(1012,\cdot)$	$1$	$1$	$e\left(\frac{125}{204}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{151}{408}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{401}{408}\right)$	$e\left(\frac{245}{408}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{81}{136}\right)$
$\chi_{6069}(1045,\cdot)$	$1$	$1$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{251}{408}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{37}{408}\right)$	$e\left(\frac{337}{408}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{73}{204}\right)$	$e\left(\frac{77}{136}\right)$
$\chi_{6069}(1096,\cdot)$	$1$	$1$	$e\left(\frac{89}{204}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{341}{408}\right)$	$e\left(\frac{305}{408}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{37}{136}\right)$
$\chi_{6069}(1171,\cdot)$	$1$	$1$	$e\left(\frac{67}{204}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{125}{408}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{259}{408}\right)$	$e\left(\frac{319}{408}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{103}{204}\right)$	$e\left(\frac{131}{136}\right)$
$\chi_{6069}(1192,\cdot)$	$1$	$1$	$e\left(\frac{103}{204}\right)$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{113}{408}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{319}{408}\right)$	$e\left(\frac{259}{408}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{67}{204}\right)$	$e\left(\frac{39}{136}\right)$
$\chi_{6069}(1222,\cdot)$	$1$	$1$	$e\left(\frac{167}{204}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{205}{408}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{131}{408}\right)$	$e\left(\frac{311}{408}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{19}{136}\right)$
$\chi_{6069}(1243,\cdot)$	$1$	$1$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{169}{408}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{311}{408}\right)$	$e\left(\frac{131}{408}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{167}{204}\right)$	$e\left(\frac{15}{136}\right)$
$\chi_{6069}(1318,\cdot)$	$1$	$1$	$e\left(\frac{37}{204}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{407}{408}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{73}{408}\right)$	$e\left(\frac{301}{408}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{133}{204}\right)$	$e\left(\frac{49}{136}\right)$
$\chi_{6069}(1369,\cdot)$	$1$	$1$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{223}{408}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{41}{408}\right)$	$e\left(\frac{197}{408}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{125}{204}\right)$	$e\left(\frac{89}{136}\right)$
$\chi_{6069}(1402,\cdot)$	$1$	$1$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{179}{408}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{397}{408}\right)$	$e\left(\frac{385}{408}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{69}{136}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(19\)	\(20\)
\(\chi_{6069}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{379}{408}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{77}{408}\right)\)	\(e\left(\frac{161}{408}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{61}{136}\right)\)
\(\chi_{6069}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{77}{408}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{91}{408}\right)\)	\(e\left(\frac{79}{408}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{35}{136}\right)\)
\(\chi_{6069}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{161}{408}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{79}{408}\right)\)	\(e\left(\frac{91}{408}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{135}{136}\right)\)
\(\chi_{6069}(151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{204}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{157}{408}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{371}{408}\right)\)	\(e\left(\frac{71}{408}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{59}{136}\right)\)
\(\chi_{6069}(172,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{217}{408}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{71}{408}\right)\)	\(e\left(\frac{371}{408}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{107}{204}\right)\)	\(e\left(\frac{111}{136}\right)\)
\(\chi_{6069}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{204}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{191}{408}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{337}{408}\right)\)	\(e\left(\frac{37}{408}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{25}{136}\right)\)
\(\chi_{6069}(298,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{7}{408}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{305}{408}\right)\)	\(e\left(\frac{341}{408}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{89}{204}\right)\)	\(e\left(\frac{65}{136}\right)\)
\(\chi_{6069}(331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{204}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{395}{408}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{133}{408}\right)\)	\(e\left(\frac{241}{408}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{93}{136}\right)\)
\(\chi_{6069}(382,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{204}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{307}{408}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{29}{408}\right)\)	\(e\left(\frac{209}{408}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{53}{136}\right)\)
\(\chi_{6069}(457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{365}{408}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{283}{408}\right)\)	\(e\left(\frac{295}{408}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{67}{136}\right)\)
\(\chi_{6069}(478,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{281}{408}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{295}{408}\right)\)	\(e\left(\frac{283}{408}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{103}{136}\right)\)
\(\chi_{6069}(508,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{37}{408}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{155}{408}\right)\)	\(e\left(\frac{287}{408}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{91}{136}\right)\)
\(\chi_{6069}(529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{337}{408}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{287}{408}\right)\)	\(e\left(\frac{155}{408}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{79}{136}\right)\)
\(\chi_{6069}(604,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{385}{408}\right)\)	\(e\left(\frac{397}{408}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{33}{136}\right)\)
\(\chi_{6069}(655,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{204}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{79}{408}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{353}{408}\right)\)	\(e\left(\frac{293}{408}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{101}{204}\right)\)	\(e\left(\frac{73}{136}\right)\)
\(\chi_{6069}(739,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{204}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{235}{408}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{389}{408}\right)\)	\(e\left(\frac{257}{408}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{45}{136}\right)\)
\(\chi_{6069}(814,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{204}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{245}{408}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{67}{408}\right)\)	\(e\left(\frac{103}{408}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{99}{136}\right)\)
\(\chi_{6069}(835,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{401}{408}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{103}{408}\right)\)	\(e\left(\frac{67}{408}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{115}{204}\right)\)	\(e\left(\frac{71}{136}\right)\)
\(\chi_{6069}(865,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{325}{408}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{347}{408}\right)\)	\(e\left(\frac{95}{408}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{23}{204}\right)\)	\(e\left(\frac{123}{136}\right)\)
\(\chi_{6069}(886,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{204}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{49}{408}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{95}{408}\right)\)	\(e\left(\frac{347}{408}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{47}{136}\right)\)
\(\chi_{6069}(961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{335}{408}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{25}{408}\right)\)	\(e\left(\frac{349}{408}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{121}{204}\right)\)	\(e\left(\frac{41}{136}\right)\)
\(\chi_{6069}(1012,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{204}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{151}{408}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{401}{408}\right)\)	\(e\left(\frac{245}{408}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{81}{136}\right)\)
\(\chi_{6069}(1045,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{251}{408}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{37}{408}\right)\)	\(e\left(\frac{337}{408}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{73}{204}\right)\)	\(e\left(\frac{77}{136}\right)\)
\(\chi_{6069}(1096,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{204}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{341}{408}\right)\)	\(e\left(\frac{305}{408}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{37}{136}\right)\)
\(\chi_{6069}(1171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{204}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{125}{408}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{259}{408}\right)\)	\(e\left(\frac{319}{408}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{103}{204}\right)\)	\(e\left(\frac{131}{136}\right)\)
\(\chi_{6069}(1192,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{204}\right)\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{113}{408}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{319}{408}\right)\)	\(e\left(\frac{259}{408}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{67}{204}\right)\)	\(e\left(\frac{39}{136}\right)\)
\(\chi_{6069}(1222,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{204}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{205}{408}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{131}{408}\right)\)	\(e\left(\frac{311}{408}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{19}{136}\right)\)
\(\chi_{6069}(1243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{169}{408}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{311}{408}\right)\)	\(e\left(\frac{131}{408}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{167}{204}\right)\)	\(e\left(\frac{15}{136}\right)\)
\(\chi_{6069}(1318,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{204}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{407}{408}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{73}{408}\right)\)	\(e\left(\frac{301}{408}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{133}{204}\right)\)	\(e\left(\frac{49}{136}\right)\)
\(\chi_{6069}(1369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{223}{408}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{41}{408}\right)\)	\(e\left(\frac{197}{408}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{125}{204}\right)\)	\(e\left(\frac{89}{136}\right)\)
\(\chi_{6069}(1402,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{179}{408}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{397}{408}\right)\)	\(e\left(\frac{385}{408}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{69}{136}\right)\)

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First 31 of 128 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	6069.cx
Modulus	$6069$
Conductor	$2023$
Order	$408$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(6069\)
Conductor:	\(2023\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(408\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2023.bl	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)