LMFDB - Dirichlet character orbit 6848.be

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6848, base_ring=CyclotomicField(212)) M = H._module chi = DirichletCharacter(H, M([0,53,172])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(49,6848)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6848$
Conductor:	$1712$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$212$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1712.w	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{212})$
Fixed field:	Number field defined by a degree 212 polynomial (not computed)

First 31 of 104 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{6848}(49,\cdot)$	$1$	$1$	$e\left(\frac{115}{212}\right)$	$e\left(\frac{81}{212}\right)$	$e\left(\frac{41}{106}\right)$	$e\left(\frac{9}{106}\right)$	$e\left(\frac{21}{212}\right)$	$e\left(\frac{23}{212}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{7}{212}\right)$	$e\left(\frac{197}{212}\right)$
$\chi_{6848}(81,\cdot)$	$1$	$1$	$e\left(\frac{33}{212}\right)$	$e\left(\frac{191}{212}\right)$	$e\left(\frac{9}{106}\right)$	$e\left(\frac{33}{106}\right)$	$e\left(\frac{183}{212}\right)$	$e\left(\frac{49}{212}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{61}{212}\right)$	$e\left(\frac{51}{212}\right)$
$\chi_{6848}(209,\cdot)$	$1$	$1$	$e\left(\frac{61}{212}\right)$	$e\left(\frac{19}{212}\right)$	$e\left(\frac{7}{106}\right)$	$e\left(\frac{61}{106}\right)$	$e\left(\frac{107}{212}\right)$	$e\left(\frac{97}{212}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{177}{212}\right)$	$e\left(\frac{75}{212}\right)$
$\chi_{6848}(241,\cdot)$	$1$	$1$	$e\left(\frac{91}{212}\right)$	$e\left(\frac{77}{212}\right)$	$e\left(\frac{73}{106}\right)$	$e\left(\frac{91}{106}\right)$	$e\left(\frac{177}{212}\right)$	$e\left(\frac{103}{212}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{59}{212}\right)$	$e\left(\frac{25}{212}\right)$
$\chi_{6848}(337,\cdot)$	$1$	$1$	$e\left(\frac{189}{212}\right)$	$e\left(\frac{111}{212}\right)$	$e\left(\frac{13}{106}\right)$	$e\left(\frac{83}{106}\right)$	$e\left(\frac{123}{212}\right)$	$e\left(\frac{165}{212}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{41}{212}\right)$	$e\left(\frac{3}{212}\right)$
$\chi_{6848}(369,\cdot)$	$1$	$1$	$e\left(\frac{131}{212}\right)$	$e\left(\frac{13}{212}\right)$	$e\left(\frac{55}{106}\right)$	$e\left(\frac{25}{106}\right)$	$e\left(\frac{129}{212}\right)$	$e\left(\frac{111}{212}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{43}{212}\right)$	$e\left(\frac{29}{212}\right)$
$\chi_{6848}(465,\cdot)$	$1$	$1$	$e\left(\frac{73}{212}\right)$	$e\left(\frac{127}{212}\right)$	$e\left(\frac{97}{106}\right)$	$e\left(\frac{73}{106}\right)$	$e\left(\frac{135}{212}\right)$	$e\left(\frac{57}{212}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{45}{212}\right)$	$e\left(\frac{55}{212}\right)$
$\chi_{6848}(497,\cdot)$	$1$	$1$	$e\left(\frac{195}{212}\right)$	$e\left(\frac{165}{212}\right)$	$e\left(\frac{5}{106}\right)$	$e\left(\frac{89}{106}\right)$	$e\left(\frac{137}{212}\right)$	$e\left(\frac{39}{212}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{187}{212}\right)$	$e\left(\frac{205}{212}\right)$
$\chi_{6848}(529,\cdot)$	$1$	$1$	$e\left(\frac{29}{212}\right)$	$e\left(\frac{155}{212}\right)$	$e\left(\frac{85}{106}\right)$	$e\left(\frac{29}{106}\right)$	$e\left(\frac{103}{212}\right)$	$e\left(\frac{133}{212}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{105}{212}\right)$	$e\left(\frac{199}{212}\right)$
$\chi_{6848}(625,\cdot)$	$1$	$1$	$e\left(\frac{191}{212}\right)$	$e\left(\frac{129}{212}\right)$	$e\left(\frac{81}{106}\right)$	$e\left(\frac{85}{106}\right)$	$e\left(\frac{57}{212}\right)$	$e\left(\frac{123}{212}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{19}{212}\right)$	$e\left(\frac{141}{212}\right)$
$\chi_{6848}(689,\cdot)$	$1$	$1$	$e\left(\frac{71}{212}\right)$	$e\left(\frac{109}{212}\right)$	$e\left(\frac{29}{106}\right)$	$e\left(\frac{71}{106}\right)$	$e\left(\frac{201}{212}\right)$	$e\left(\frac{99}{212}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{67}{212}\right)$	$e\left(\frac{129}{212}\right)$
$\chi_{6848}(721,\cdot)$	$1$	$1$	$e\left(\frac{205}{212}\right)$	$e\left(\frac{43}{212}\right)$	$e\left(\frac{27}{106}\right)$	$e\left(\frac{99}{106}\right)$	$e\left(\frac{19}{212}\right)$	$e\left(\frac{41}{212}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{77}{212}\right)$	$e\left(\frac{47}{212}\right)$
$\chi_{6848}(753,\cdot)$	$1$	$1$	$e\left(\frac{15}{212}\right)$	$e\left(\frac{29}{212}\right)$	$e\left(\frac{33}{106}\right)$	$e\left(\frac{15}{106}\right)$	$e\left(\frac{141}{212}\right)$	$e\left(\frac{3}{212}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{47}{212}\right)$	$e\left(\frac{81}{212}\right)$
$\chi_{6848}(785,\cdot)$	$1$	$1$	$e\left(\frac{5}{212}\right)$	$e\left(\frac{151}{212}\right)$	$e\left(\frac{11}{106}\right)$	$e\left(\frac{5}{106}\right)$	$e\left(\frac{47}{212}\right)$	$e\left(\frac{1}{212}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{157}{212}\right)$	$e\left(\frac{27}{212}\right)$
$\chi_{6848}(849,\cdot)$	$1$	$1$	$e\left(\frac{137}{212}\right)$	$e\left(\frac{67}{212}\right)$	$e\left(\frac{47}{106}\right)$	$e\left(\frac{31}{106}\right)$	$e\left(\frac{143}{212}\right)$	$e\left(\frac{197}{212}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{189}{212}\right)$	$e\left(\frac{19}{212}\right)$
$\chi_{6848}(881,\cdot)$	$1$	$1$	$e\left(\frac{175}{212}\right)$	$e\left(\frac{197}{212}\right)$	$e\left(\frac{67}{106}\right)$	$e\left(\frac{69}{106}\right)$	$e\left(\frac{161}{212}\right)$	$e\left(\frac{35}{212}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{195}{212}\right)$	$e\left(\frac{97}{212}\right)$
$\chi_{6848}(913,\cdot)$	$1$	$1$	$e\left(\frac{209}{212}\right)$	$e\left(\frac{79}{212}\right)$	$e\left(\frac{57}{106}\right)$	$e\left(\frac{103}{106}\right)$	$e\left(\frac{99}{212}\right)$	$e\left(\frac{169}{212}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{33}{212}\right)$	$e\left(\frac{111}{212}\right)$
$\chi_{6848}(945,\cdot)$	$1$	$1$	$e\left(\frac{183}{212}\right)$	$e\left(\frac{57}{212}\right)$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{77}{106}\right)$	$e\left(\frac{109}{212}\right)$	$e\left(\frac{79}{212}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{107}{212}\right)$	$e\left(\frac{13}{212}\right)$
$\chi_{6848}(977,\cdot)$	$1$	$1$	$e\left(\frac{65}{212}\right)$	$e\left(\frac{55}{212}\right)$	$e\left(\frac{37}{106}\right)$	$e\left(\frac{65}{106}\right)$	$e\left(\frac{187}{212}\right)$	$e\left(\frac{13}{212}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{133}{212}\right)$	$e\left(\frac{139}{212}\right)$
$\chi_{6848}(1073,\cdot)$	$1$	$1$	$e\left(\frac{207}{212}\right)$	$e\left(\frac{61}{212}\right)$	$e\left(\frac{95}{106}\right)$	$e\left(\frac{101}{106}\right)$	$e\left(\frac{165}{212}\right)$	$e\left(\frac{211}{212}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{55}{212}\right)$	$e\left(\frac{185}{212}\right)$
$\chi_{6848}(1105,\cdot)$	$1$	$1$	$e\left(\frac{145}{212}\right)$	$e\left(\frac{139}{212}\right)$	$e\left(\frac{1}{106}\right)$	$e\left(\frac{39}{106}\right)$	$e\left(\frac{91}{212}\right)$	$e\left(\frac{29}{212}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{101}{212}\right)$	$e\left(\frac{147}{212}\right)$
$\chi_{6848}(1169,\cdot)$	$1$	$1$	$e\left(\frac{49}{212}\right)$	$e\left(\frac{123}{212}\right)$	$e\left(\frac{23}{106}\right)$	$e\left(\frac{49}{106}\right)$	$e\left(\frac{79}{212}\right)$	$e\left(\frac{137}{212}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{97}{212}\right)$	$e\left(\frac{95}{212}\right)$
$\chi_{6848}(1233,\cdot)$	$1$	$1$	$e\left(\frac{133}{212}\right)$	$e\left(\frac{31}{212}\right)$	$e\left(\frac{17}{106}\right)$	$e\left(\frac{27}{106}\right)$	$e\left(\frac{63}{212}\right)$	$e\left(\frac{69}{212}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{21}{212}\right)$	$e\left(\frac{167}{212}\right)$
$\chi_{6848}(1297,\cdot)$	$1$	$1$	$e\left(\frac{105}{212}\right)$	$e\left(\frac{203}{212}\right)$	$e\left(\frac{19}{106}\right)$	$e\left(\frac{105}{106}\right)$	$e\left(\frac{139}{212}\right)$	$e\left(\frac{21}{212}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{117}{212}\right)$	$e\left(\frac{143}{212}\right)$
$\chi_{6848}(1425,\cdot)$	$1$	$1$	$e\left(\frac{13}{212}\right)$	$e\left(\frac{11}{212}\right)$	$e\left(\frac{71}{106}\right)$	$e\left(\frac{13}{106}\right)$	$e\left(\frac{207}{212}\right)$	$e\left(\frac{45}{212}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{69}{212}\right)$	$e\left(\frac{155}{212}\right)$
$\chi_{6848}(1521,\cdot)$	$1$	$1$	$e\left(\frac{147}{212}\right)$	$e\left(\frac{157}{212}\right)$	$e\left(\frac{69}{106}\right)$	$e\left(\frac{41}{106}\right)$	$e\left(\frac{25}{212}\right)$	$e\left(\frac{199}{212}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{79}{212}\right)$	$e\left(\frac{73}{212}\right)$
$\chi_{6848}(1585,\cdot)$	$1$	$1$	$e\left(\frac{23}{212}\right)$	$e\left(\frac{101}{212}\right)$	$e\left(\frac{93}{106}\right)$	$e\left(\frac{23}{106}\right)$	$e\left(\frac{89}{212}\right)$	$e\left(\frac{47}{212}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{171}{212}\right)$	$e\left(\frac{209}{212}\right)$
$\chi_{6848}(1617,\cdot)$	$1$	$1$	$e\left(\frac{169}{212}\right)$	$e\left(\frac{143}{212}\right)$	$e\left(\frac{75}{106}\right)$	$e\left(\frac{63}{106}\right)$	$e\left(\frac{147}{212}\right)$	$e\left(\frac{161}{212}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{49}{212}\right)$	$e\left(\frac{107}{212}\right)$
$\chi_{6848}(1649,\cdot)$	$1$	$1$	$e\left(\frac{127}{212}\right)$	$e\left(\frac{189}{212}\right)$	$e\left(\frac{25}{106}\right)$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{49}{212}\right)$	$e\left(\frac{195}{212}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{87}{212}\right)$	$e\left(\frac{177}{212}\right)$
$\chi_{6848}(1681,\cdot)$	$1$	$1$	$e\left(\frac{17}{212}\right)$	$e\left(\frac{47}{212}\right)$	$e\left(\frac{101}{106}\right)$	$e\left(\frac{17}{106}\right)$	$e\left(\frac{75}{212}\right)$	$e\left(\frac{173}{212}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{25}{212}\right)$	$e\left(\frac{7}{212}\right)$
$\chi_{6848}(1745,\cdot)$	$1$	$1$	$e\left(\frac{1}{212}\right)$	$e\left(\frac{115}{212}\right)$	$e\left(\frac{87}{106}\right)$	$e\left(\frac{1}{106}\right)$	$e\left(\frac{179}{212}\right)$	$e\left(\frac{85}{212}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{201}{212}\right)$	$e\left(\frac{175}{212}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{6848}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{212}\right)\)	\(e\left(\frac{81}{212}\right)\)	\(e\left(\frac{41}{106}\right)\)	\(e\left(\frac{9}{106}\right)\)	\(e\left(\frac{21}{212}\right)\)	\(e\left(\frac{23}{212}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{7}{212}\right)\)	\(e\left(\frac{197}{212}\right)\)
\(\chi_{6848}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{212}\right)\)	\(e\left(\frac{191}{212}\right)\)	\(e\left(\frac{9}{106}\right)\)	\(e\left(\frac{33}{106}\right)\)	\(e\left(\frac{183}{212}\right)\)	\(e\left(\frac{49}{212}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{61}{212}\right)\)	\(e\left(\frac{51}{212}\right)\)
\(\chi_{6848}(209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{212}\right)\)	\(e\left(\frac{19}{212}\right)\)	\(e\left(\frac{7}{106}\right)\)	\(e\left(\frac{61}{106}\right)\)	\(e\left(\frac{107}{212}\right)\)	\(e\left(\frac{97}{212}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{177}{212}\right)\)	\(e\left(\frac{75}{212}\right)\)
\(\chi_{6848}(241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{212}\right)\)	\(e\left(\frac{77}{212}\right)\)	\(e\left(\frac{73}{106}\right)\)	\(e\left(\frac{91}{106}\right)\)	\(e\left(\frac{177}{212}\right)\)	\(e\left(\frac{103}{212}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{59}{212}\right)\)	\(e\left(\frac{25}{212}\right)\)
\(\chi_{6848}(337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{189}{212}\right)\)	\(e\left(\frac{111}{212}\right)\)	\(e\left(\frac{13}{106}\right)\)	\(e\left(\frac{83}{106}\right)\)	\(e\left(\frac{123}{212}\right)\)	\(e\left(\frac{165}{212}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{41}{212}\right)\)	\(e\left(\frac{3}{212}\right)\)
\(\chi_{6848}(369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{212}\right)\)	\(e\left(\frac{13}{212}\right)\)	\(e\left(\frac{55}{106}\right)\)	\(e\left(\frac{25}{106}\right)\)	\(e\left(\frac{129}{212}\right)\)	\(e\left(\frac{111}{212}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{43}{212}\right)\)	\(e\left(\frac{29}{212}\right)\)
\(\chi_{6848}(465,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{212}\right)\)	\(e\left(\frac{127}{212}\right)\)	\(e\left(\frac{97}{106}\right)\)	\(e\left(\frac{73}{106}\right)\)	\(e\left(\frac{135}{212}\right)\)	\(e\left(\frac{57}{212}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{45}{212}\right)\)	\(e\left(\frac{55}{212}\right)\)
\(\chi_{6848}(497,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{195}{212}\right)\)	\(e\left(\frac{165}{212}\right)\)	\(e\left(\frac{5}{106}\right)\)	\(e\left(\frac{89}{106}\right)\)	\(e\left(\frac{137}{212}\right)\)	\(e\left(\frac{39}{212}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{187}{212}\right)\)	\(e\left(\frac{205}{212}\right)\)
\(\chi_{6848}(529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{212}\right)\)	\(e\left(\frac{155}{212}\right)\)	\(e\left(\frac{85}{106}\right)\)	\(e\left(\frac{29}{106}\right)\)	\(e\left(\frac{103}{212}\right)\)	\(e\left(\frac{133}{212}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{105}{212}\right)\)	\(e\left(\frac{199}{212}\right)\)
\(\chi_{6848}(625,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{212}\right)\)	\(e\left(\frac{129}{212}\right)\)	\(e\left(\frac{81}{106}\right)\)	\(e\left(\frac{85}{106}\right)\)	\(e\left(\frac{57}{212}\right)\)	\(e\left(\frac{123}{212}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{19}{212}\right)\)	\(e\left(\frac{141}{212}\right)\)
\(\chi_{6848}(689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{212}\right)\)	\(e\left(\frac{109}{212}\right)\)	\(e\left(\frac{29}{106}\right)\)	\(e\left(\frac{71}{106}\right)\)	\(e\left(\frac{201}{212}\right)\)	\(e\left(\frac{99}{212}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{67}{212}\right)\)	\(e\left(\frac{129}{212}\right)\)
\(\chi_{6848}(721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{212}\right)\)	\(e\left(\frac{43}{212}\right)\)	\(e\left(\frac{27}{106}\right)\)	\(e\left(\frac{99}{106}\right)\)	\(e\left(\frac{19}{212}\right)\)	\(e\left(\frac{41}{212}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{77}{212}\right)\)	\(e\left(\frac{47}{212}\right)\)
\(\chi_{6848}(753,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{212}\right)\)	\(e\left(\frac{29}{212}\right)\)	\(e\left(\frac{33}{106}\right)\)	\(e\left(\frac{15}{106}\right)\)	\(e\left(\frac{141}{212}\right)\)	\(e\left(\frac{3}{212}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{47}{212}\right)\)	\(e\left(\frac{81}{212}\right)\)
\(\chi_{6848}(785,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{212}\right)\)	\(e\left(\frac{151}{212}\right)\)	\(e\left(\frac{11}{106}\right)\)	\(e\left(\frac{5}{106}\right)\)	\(e\left(\frac{47}{212}\right)\)	\(e\left(\frac{1}{212}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{157}{212}\right)\)	\(e\left(\frac{27}{212}\right)\)
\(\chi_{6848}(849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{212}\right)\)	\(e\left(\frac{67}{212}\right)\)	\(e\left(\frac{47}{106}\right)\)	\(e\left(\frac{31}{106}\right)\)	\(e\left(\frac{143}{212}\right)\)	\(e\left(\frac{197}{212}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{189}{212}\right)\)	\(e\left(\frac{19}{212}\right)\)
\(\chi_{6848}(881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{212}\right)\)	\(e\left(\frac{197}{212}\right)\)	\(e\left(\frac{67}{106}\right)\)	\(e\left(\frac{69}{106}\right)\)	\(e\left(\frac{161}{212}\right)\)	\(e\left(\frac{35}{212}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{195}{212}\right)\)	\(e\left(\frac{97}{212}\right)\)
\(\chi_{6848}(913,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{209}{212}\right)\)	\(e\left(\frac{79}{212}\right)\)	\(e\left(\frac{57}{106}\right)\)	\(e\left(\frac{103}{106}\right)\)	\(e\left(\frac{99}{212}\right)\)	\(e\left(\frac{169}{212}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{33}{212}\right)\)	\(e\left(\frac{111}{212}\right)\)
\(\chi_{6848}(945,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{183}{212}\right)\)	\(e\left(\frac{57}{212}\right)\)	\(e\left(\frac{21}{106}\right)\)	\(e\left(\frac{77}{106}\right)\)	\(e\left(\frac{109}{212}\right)\)	\(e\left(\frac{79}{212}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{107}{212}\right)\)	\(e\left(\frac{13}{212}\right)\)
\(\chi_{6848}(977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{212}\right)\)	\(e\left(\frac{55}{212}\right)\)	\(e\left(\frac{37}{106}\right)\)	\(e\left(\frac{65}{106}\right)\)	\(e\left(\frac{187}{212}\right)\)	\(e\left(\frac{13}{212}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{133}{212}\right)\)	\(e\left(\frac{139}{212}\right)\)
\(\chi_{6848}(1073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{207}{212}\right)\)	\(e\left(\frac{61}{212}\right)\)	\(e\left(\frac{95}{106}\right)\)	\(e\left(\frac{101}{106}\right)\)	\(e\left(\frac{165}{212}\right)\)	\(e\left(\frac{211}{212}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{55}{212}\right)\)	\(e\left(\frac{185}{212}\right)\)
\(\chi_{6848}(1105,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{212}\right)\)	\(e\left(\frac{139}{212}\right)\)	\(e\left(\frac{1}{106}\right)\)	\(e\left(\frac{39}{106}\right)\)	\(e\left(\frac{91}{212}\right)\)	\(e\left(\frac{29}{212}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{101}{212}\right)\)	\(e\left(\frac{147}{212}\right)\)
\(\chi_{6848}(1169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{212}\right)\)	\(e\left(\frac{123}{212}\right)\)	\(e\left(\frac{23}{106}\right)\)	\(e\left(\frac{49}{106}\right)\)	\(e\left(\frac{79}{212}\right)\)	\(e\left(\frac{137}{212}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{97}{212}\right)\)	\(e\left(\frac{95}{212}\right)\)
\(\chi_{6848}(1233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{212}\right)\)	\(e\left(\frac{31}{212}\right)\)	\(e\left(\frac{17}{106}\right)\)	\(e\left(\frac{27}{106}\right)\)	\(e\left(\frac{63}{212}\right)\)	\(e\left(\frac{69}{212}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{21}{212}\right)\)	\(e\left(\frac{167}{212}\right)\)
\(\chi_{6848}(1297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{105}{212}\right)\)	\(e\left(\frac{203}{212}\right)\)	\(e\left(\frac{19}{106}\right)\)	\(e\left(\frac{105}{106}\right)\)	\(e\left(\frac{139}{212}\right)\)	\(e\left(\frac{21}{212}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{117}{212}\right)\)	\(e\left(\frac{143}{212}\right)\)
\(\chi_{6848}(1425,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{212}\right)\)	\(e\left(\frac{11}{212}\right)\)	\(e\left(\frac{71}{106}\right)\)	\(e\left(\frac{13}{106}\right)\)	\(e\left(\frac{207}{212}\right)\)	\(e\left(\frac{45}{212}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{69}{212}\right)\)	\(e\left(\frac{155}{212}\right)\)
\(\chi_{6848}(1521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{147}{212}\right)\)	\(e\left(\frac{157}{212}\right)\)	\(e\left(\frac{69}{106}\right)\)	\(e\left(\frac{41}{106}\right)\)	\(e\left(\frac{25}{212}\right)\)	\(e\left(\frac{199}{212}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{79}{212}\right)\)	\(e\left(\frac{73}{212}\right)\)
\(\chi_{6848}(1585,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{212}\right)\)	\(e\left(\frac{101}{212}\right)\)	\(e\left(\frac{93}{106}\right)\)	\(e\left(\frac{23}{106}\right)\)	\(e\left(\frac{89}{212}\right)\)	\(e\left(\frac{47}{212}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{171}{212}\right)\)	\(e\left(\frac{209}{212}\right)\)
\(\chi_{6848}(1617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{212}\right)\)	\(e\left(\frac{143}{212}\right)\)	\(e\left(\frac{75}{106}\right)\)	\(e\left(\frac{63}{106}\right)\)	\(e\left(\frac{147}{212}\right)\)	\(e\left(\frac{161}{212}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{49}{212}\right)\)	\(e\left(\frac{107}{212}\right)\)
\(\chi_{6848}(1649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{212}\right)\)	\(e\left(\frac{189}{212}\right)\)	\(e\left(\frac{25}{106}\right)\)	\(e\left(\frac{21}{106}\right)\)	\(e\left(\frac{49}{212}\right)\)	\(e\left(\frac{195}{212}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{87}{212}\right)\)	\(e\left(\frac{177}{212}\right)\)
\(\chi_{6848}(1681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{212}\right)\)	\(e\left(\frac{47}{212}\right)\)	\(e\left(\frac{101}{106}\right)\)	\(e\left(\frac{17}{106}\right)\)	\(e\left(\frac{75}{212}\right)\)	\(e\left(\frac{173}{212}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{25}{212}\right)\)	\(e\left(\frac{7}{212}\right)\)
\(\chi_{6848}(1745,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{212}\right)\)	\(e\left(\frac{115}{212}\right)\)	\(e\left(\frac{87}{106}\right)\)	\(e\left(\frac{1}{106}\right)\)	\(e\left(\frac{179}{212}\right)\)	\(e\left(\frac{85}{212}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{201}{212}\right)\)	\(e\left(\frac{175}{212}\right)\)

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First 31 of 104 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	6848.be
Modulus	$6848$
Conductor	$1712$
Order	$212$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(6848\)
Conductor:	\(1712\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(212\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1712.w	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)