LMFDB - Dirichlet character orbit 6069.cv

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6069, base_ring=CyclotomicField(408)) M = H._module chi = DirichletCharacter(H, M([204,340,171])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(26,6069)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6069$
Conductor:	$6069$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$408$	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:	$\Q(\zeta_{408})$
Fixed field:	Number field defined by a degree 408 polynomial (not computed)

First 31 of 128 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$19$	$20$
$\chi_{6069}(26,\cdot)$	$1$	$1$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{181}{408}\right)$	$e\left(\frac{193}{408}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{33}{136}\right)$
$\chi_{6069}(59,\cdot)$	$1$	$1$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{139}{408}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{257}{408}\right)$	$e\left(\frac{389}{408}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{125}{136}\right)$
$\chi_{6069}(185,\cdot)$	$1$	$1$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{301}{408}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{179}{408}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{75}{136}\right)$
$\chi_{6069}(206,\cdot)$	$1$	$1$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{73}{408}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{179}{408}\right)$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{95}{136}\right)$
$\chi_{6069}(236,\cdot)$	$1$	$1$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{245}{408}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{271}{408}\right)$	$e\left(\frac{307}{408}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{99}{136}\right)$
$\chi_{6069}(257,\cdot)$	$1$	$1$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{401}{408}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{307}{408}\right)$	$e\left(\frac{271}{408}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{71}{136}\right)$
$\chi_{6069}(332,\cdot)$	$1$	$1$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{247}{408}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{125}{408}\right)$	$e\left(\frac{113}{408}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{95}{204}\right)$	$e\left(\frac{1}{136}\right)$
$\chi_{6069}(383,\cdot)$	$1$	$1$	$e\left(\frac{151}{204}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{335}{408}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{229}{408}\right)$	$e\left(\frac{145}{408}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{41}{136}\right)$
$\chi_{6069}(416,\cdot)$	$1$	$1$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{67}{408}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{209}{408}\right)$	$e\left(\frac{29}{408}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{167}{204}\right)$	$e\left(\frac{117}{136}\right)$
$\chi_{6069}(467,\cdot)$	$1$	$1$	$e\left(\frac{199}{204}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{251}{408}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{241}{408}\right)$	$e\left(\frac{133}{408}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{77}{136}\right)$
$\chi_{6069}(542,\cdot)$	$1$	$1$	$e\left(\frac{137}{204}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{181}{408}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{47}{408}\right)$	$e\left(\frac{395}{408}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{101}{204}\right)$	$e\left(\frac{107}{136}\right)$
$\chi_{6069}(563,\cdot)$	$1$	$1$	$e\left(\frac{101}{204}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{193}{408}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{395}{408}\right)$	$e\left(\frac{47}{408}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{137}{204}\right)$	$e\left(\frac{63}{136}\right)$
$\chi_{6069}(593,\cdot)$	$1$	$1$	$e\left(\frac{169}{204}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{125}{408}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{55}{408}\right)$	$e\left(\frac{115}{408}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{1}{204}\right)$	$e\left(\frac{131}{136}\right)$
$\chi_{6069}(614,\cdot)$	$1$	$1$	$e\left(\frac{1}{204}\right)$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{113}{408}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{115}{408}\right)$	$e\left(\frac{55}{408}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{169}{204}\right)$	$e\left(\frac{39}{136}\right)$
$\chi_{6069}(689,\cdot)$	$1$	$1$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{319}{408}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{173}{408}\right)$	$e\left(\frac{65}{408}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{107}{204}\right)$	$e\left(\frac{9}{136}\right)$
$\chi_{6069}(740,\cdot)$	$1$	$1$	$e\left(\frac{139}{204}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{407}{408}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{277}{408}\right)$	$e\left(\frac{97}{408}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{31}{204}\right)$	$e\left(\frac{49}{136}\right)$
$\chi_{6069}(773,\cdot)$	$1$	$1$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{403}{408}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{161}{408}\right)$	$e\left(\frac{77}{408}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{155}{204}\right)$	$e\left(\frac{109}{136}\right)$
$\chi_{6069}(824,\cdot)$	$1$	$1$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{179}{408}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{193}{408}\right)$	$e\left(\frac{181}{408}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{69}{136}\right)$
$\chi_{6069}(899,\cdot)$	$1$	$1$	$e\left(\frac{89}{204}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{61}{408}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{239}{408}\right)$	$e\left(\frac{203}{408}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{3}{136}\right)$
$\chi_{6069}(920,\cdot)$	$1$	$1$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{313}{408}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{203}{408}\right)$	$e\left(\frac{239}{408}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{89}{204}\right)$	$e\left(\frac{31}{136}\right)$
$\chi_{6069}(950,\cdot)$	$1$	$1$	$e\left(\frac{121}{204}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{5}{408}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{247}{408}\right)$	$e\left(\frac{331}{408}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{27}{136}\right)$
$\chi_{6069}(971,\cdot)$	$1$	$1$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{233}{408}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{331}{408}\right)$	$e\left(\frac{247}{408}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{121}{204}\right)$	$e\left(\frac{7}{136}\right)$
$\chi_{6069}(1097,\cdot)$	$1$	$1$	$e\left(\frac{127}{204}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{71}{408}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{325}{408}\right)$	$e\left(\frac{49}{408}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{43}{204}\right)$	$e\left(\frac{57}{136}\right)$
$\chi_{6069}(1130,\cdot)$	$1$	$1$	$e\left(\frac{95}{204}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{331}{408}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{113}{408}\right)$	$e\left(\frac{125}{408}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{101}{136}\right)$
$\chi_{6069}(1181,\cdot)$	$1$	$1$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{107}{408}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{145}{408}\right)$	$e\left(\frac{229}{408}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{151}{204}\right)$	$e\left(\frac{61}{136}\right)$
$\chi_{6069}(1256,\cdot)$	$1$	$1$	$e\left(\frac{41}{204}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{349}{408}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{23}{408}\right)$	$e\left(\frac{11}{408}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{197}{204}\right)$	$e\left(\frac{35}{136}\right)$
$\chi_{6069}(1277,\cdot)$	$1$	$1$	$e\left(\frac{197}{204}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{25}{408}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{11}{408}\right)$	$e\left(\frac{23}{408}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{41}{204}\right)$	$e\left(\frac{135}{136}\right)$
$\chi_{6069}(1307,\cdot)$	$1$	$1$	$e\left(\frac{73}{204}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{293}{408}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{31}{408}\right)$	$e\left(\frac{139}{408}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{59}{136}\right)$
$\chi_{6069}(1328,\cdot)$	$1$	$1$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{353}{408}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{139}{408}\right)$	$e\left(\frac{31}{408}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{73}{204}\right)$	$e\left(\frac{111}{136}\right)$
$\chi_{6069}(1403,\cdot)$	$1$	$1$	$e\left(\frac{107}{204}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{55}{408}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{269}{408}\right)$	$e\left(\frac{377}{408}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{25}{136}\right)$
$\chi_{6069}(1454,\cdot)$	$1$	$1$	$e\left(\frac{115}{204}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{143}{408}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{373}{408}\right)$	$e\left(\frac{1}{408}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{65}{136}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(19\)	\(20\)
\(\chi_{6069}(26,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{181}{408}\right)\)	\(e\left(\frac{193}{408}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{33}{136}\right)\)
\(\chi_{6069}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{139}{408}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{257}{408}\right)\)	\(e\left(\frac{389}{408}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{125}{136}\right)\)
\(\chi_{6069}(185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{301}{408}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{179}{408}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{75}{136}\right)\)
\(\chi_{6069}(206,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{73}{408}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{179}{408}\right)\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{95}{136}\right)\)
\(\chi_{6069}(236,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{245}{408}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{271}{408}\right)\)	\(e\left(\frac{307}{408}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{99}{136}\right)\)
\(\chi_{6069}(257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{401}{408}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{307}{408}\right)\)	\(e\left(\frac{271}{408}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{71}{136}\right)\)
\(\chi_{6069}(332,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{247}{408}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{125}{408}\right)\)	\(e\left(\frac{113}{408}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{95}{204}\right)\)	\(e\left(\frac{1}{136}\right)\)
\(\chi_{6069}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{204}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{335}{408}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{229}{408}\right)\)	\(e\left(\frac{145}{408}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{41}{136}\right)\)
\(\chi_{6069}(416,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{67}{408}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{209}{408}\right)\)	\(e\left(\frac{29}{408}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{167}{204}\right)\)	\(e\left(\frac{117}{136}\right)\)
\(\chi_{6069}(467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{204}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{251}{408}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{241}{408}\right)\)	\(e\left(\frac{133}{408}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{77}{136}\right)\)
\(\chi_{6069}(542,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{204}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{181}{408}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{47}{408}\right)\)	\(e\left(\frac{395}{408}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{101}{204}\right)\)	\(e\left(\frac{107}{136}\right)\)
\(\chi_{6069}(563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{204}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{193}{408}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{395}{408}\right)\)	\(e\left(\frac{47}{408}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{137}{204}\right)\)	\(e\left(\frac{63}{136}\right)\)
\(\chi_{6069}(593,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{204}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{125}{408}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{55}{408}\right)\)	\(e\left(\frac{115}{408}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{1}{204}\right)\)	\(e\left(\frac{131}{136}\right)\)
\(\chi_{6069}(614,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{204}\right)\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{113}{408}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{115}{408}\right)\)	\(e\left(\frac{55}{408}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{169}{204}\right)\)	\(e\left(\frac{39}{136}\right)\)
\(\chi_{6069}(689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{319}{408}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{173}{408}\right)\)	\(e\left(\frac{65}{408}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{107}{204}\right)\)	\(e\left(\frac{9}{136}\right)\)
\(\chi_{6069}(740,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{204}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{407}{408}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{277}{408}\right)\)	\(e\left(\frac{97}{408}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{31}{204}\right)\)	\(e\left(\frac{49}{136}\right)\)
\(\chi_{6069}(773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{403}{408}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{161}{408}\right)\)	\(e\left(\frac{77}{408}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{155}{204}\right)\)	\(e\left(\frac{109}{136}\right)\)
\(\chi_{6069}(824,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{179}{408}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{193}{408}\right)\)	\(e\left(\frac{181}{408}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{69}{136}\right)\)
\(\chi_{6069}(899,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{204}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{61}{408}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{239}{408}\right)\)	\(e\left(\frac{203}{408}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{3}{136}\right)\)
\(\chi_{6069}(920,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{313}{408}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{203}{408}\right)\)	\(e\left(\frac{239}{408}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{89}{204}\right)\)	\(e\left(\frac{31}{136}\right)\)
\(\chi_{6069}(950,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{204}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{5}{408}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{247}{408}\right)\)	\(e\left(\frac{331}{408}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{27}{136}\right)\)
\(\chi_{6069}(971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{233}{408}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{331}{408}\right)\)	\(e\left(\frac{247}{408}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{121}{204}\right)\)	\(e\left(\frac{7}{136}\right)\)
\(\chi_{6069}(1097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{204}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{71}{408}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{325}{408}\right)\)	\(e\left(\frac{49}{408}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{43}{204}\right)\)	\(e\left(\frac{57}{136}\right)\)
\(\chi_{6069}(1130,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{204}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{331}{408}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{113}{408}\right)\)	\(e\left(\frac{125}{408}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{101}{136}\right)\)
\(\chi_{6069}(1181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{107}{408}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{145}{408}\right)\)	\(e\left(\frac{229}{408}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{151}{204}\right)\)	\(e\left(\frac{61}{136}\right)\)
\(\chi_{6069}(1256,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{204}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{349}{408}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{23}{408}\right)\)	\(e\left(\frac{11}{408}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{197}{204}\right)\)	\(e\left(\frac{35}{136}\right)\)
\(\chi_{6069}(1277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{204}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{25}{408}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{11}{408}\right)\)	\(e\left(\frac{23}{408}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{41}{204}\right)\)	\(e\left(\frac{135}{136}\right)\)
\(\chi_{6069}(1307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{204}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{293}{408}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{31}{408}\right)\)	\(e\left(\frac{139}{408}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{59}{136}\right)\)
\(\chi_{6069}(1328,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{353}{408}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{139}{408}\right)\)	\(e\left(\frac{31}{408}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{73}{204}\right)\)	\(e\left(\frac{111}{136}\right)\)
\(\chi_{6069}(1403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{204}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{55}{408}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{269}{408}\right)\)	\(e\left(\frac{377}{408}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{25}{136}\right)\)
\(\chi_{6069}(1454,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{204}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{143}{408}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{373}{408}\right)\)	\(e\left(\frac{1}{408}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{65}{136}\right)\)

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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.cv
Modulus	$6069$
Conductor	$6069$
Order	$408$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(6069\)
Conductor:	\(6069\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(408\)	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)