LMFDB - Dirichlet character orbit 6848.ba

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6848, base_ring=CyclotomicField(106)) M = H._module chi = DirichletCharacter(H, M([53,0,77])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(63,6848)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6848$
Conductor:	$428$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$106$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 428.h	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:	$\Q(\zeta_{53})$
Fixed field:	Number field defined by a degree 106 polynomial (not computed)

First 31 of 52 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{6848}(63,\cdot)$	$1$	$1$	$e\left(\frac{37}{106}\right)$	$e\left(\frac{15}{106}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{51}{106}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{7}{106}\right)$	$e\left(\frac{17}{106}\right)$	$e\left(\frac{9}{106}\right)$
$\chi_{6848}(127,\cdot)$	$1$	$1$	$e\left(\frac{91}{106}\right)$	$e\left(\frac{77}{106}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{71}{106}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{43}{106}\right)$	$e\left(\frac{59}{106}\right)$	$e\left(\frac{25}{106}\right)$
$\chi_{6848}(191,\cdot)$	$1$	$1$	$e\left(\frac{47}{106}\right)$	$e\left(\frac{105}{106}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{39}{106}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{49}{106}\right)$	$e\left(\frac{13}{106}\right)$	$e\left(\frac{63}{106}\right)$
$\chi_{6848}(639,\cdot)$	$1$	$1$	$e\left(\frac{77}{106}\right)$	$e\left(\frac{57}{106}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{3}{106}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{69}{106}\right)$	$e\left(\frac{1}{106}\right)$	$e\left(\frac{13}{106}\right)$
$\chi_{6848}(767,\cdot)$	$1$	$1$	$e\left(\frac{65}{106}\right)$	$e\left(\frac{55}{106}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{81}{106}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{61}{106}\right)$	$e\left(\frac{27}{106}\right)$	$e\left(\frac{33}{106}\right)$
$\chi_{6848}(831,\cdot)$	$1$	$1$	$e\left(\frac{61}{106}\right)$	$e\left(\frac{19}{106}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{1}{106}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{23}{106}\right)$	$e\left(\frac{71}{106}\right)$	$e\left(\frac{75}{106}\right)$
$\chi_{6848}(959,\cdot)$	$1$	$1$	$e\left(\frac{87}{106}\right)$	$e\left(\frac{41}{106}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{97}{106}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{5}{106}\right)$	$e\left(\frac{103}{106}\right)$	$e\left(\frac{67}{106}\right)$
$\chi_{6848}(1023,\cdot)$	$1$	$1$	$e\left(\frac{9}{106}\right)$	$e\left(\frac{81}{106}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{59}{106}\right)$	$e\left(\frac{7}{106}\right)$	$e\left(\frac{91}{106}\right)$
$\chi_{6848}(1087,\cdot)$	$1$	$1$	$e\left(\frac{69}{106}\right)$	$e\left(\frac{91}{106}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{55}{106}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{99}{106}\right)$	$e\left(\frac{89}{106}\right)$	$e\left(\frac{97}{106}\right)$
$\chi_{6848}(1215,\cdot)$	$1$	$1$	$e\left(\frac{71}{106}\right)$	$e\left(\frac{3}{106}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{95}{106}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{65}{106}\right)$	$e\left(\frac{67}{106}\right)$	$e\left(\frac{23}{106}\right)$
$\chi_{6848}(1343,\cdot)$	$1$	$1$	$e\left(\frac{39}{106}\right)$	$e\left(\frac{33}{106}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{91}{106}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{79}{106}\right)$	$e\left(\frac{101}{106}\right)$	$e\left(\frac{41}{106}\right)$
$\chi_{6848}(1471,\cdot)$	$1$	$1$	$e\left(\frac{19}{106}\right)$	$e\left(\frac{65}{106}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{9}{106}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{101}{106}\right)$	$e\left(\frac{3}{106}\right)$	$e\left(\frac{39}{106}\right)$
$\chi_{6848}(1663,\cdot)$	$1$	$1$	$e\left(\frac{31}{106}\right)$	$e\left(\frac{67}{106}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{37}{106}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{3}{106}\right)$	$e\left(\frac{83}{106}\right)$	$e\left(\frac{19}{106}\right)$
$\chi_{6848}(1727,\cdot)$	$1$	$1$	$e\left(\frac{81}{106}\right)$	$e\left(\frac{93}{106}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{83}{106}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{1}{106}\right)$	$e\left(\frac{63}{106}\right)$	$e\left(\frac{77}{106}\right)$
$\chi_{6848}(2111,\cdot)$	$1$	$1$	$e\left(\frac{67}{106}\right)$	$e\left(\frac{73}{106}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{15}{106}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{27}{106}\right)$	$e\left(\frac{5}{106}\right)$	$e\left(\frac{65}{106}\right)$
$\chi_{6848}(2431,\cdot)$	$1$	$1$	$e\left(\frac{45}{106}\right)$	$e\left(\frac{87}{106}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{105}{106}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{83}{106}\right)$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{31}{106}\right)$
$\chi_{6848}(2559,\cdot)$	$1$	$1$	$e\left(\frac{101}{106}\right)$	$e\left(\frac{61}{106}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{59}{106}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{85}{106}\right)$	$e\left(\frac{55}{106}\right)$	$e\left(\frac{79}{106}\right)$
$\chi_{6848}(2623,\cdot)$	$1$	$1$	$e\left(\frac{7}{106}\right)$	$e\left(\frac{63}{106}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{87}{106}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{93}{106}\right)$	$e\left(\frac{29}{106}\right)$	$e\left(\frac{59}{106}\right)$
$\chi_{6848}(2879,\cdot)$	$1$	$1$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{83}{106}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{49}{106}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{67}{106}\right)$	$e\left(\frac{87}{106}\right)$	$e\left(\frac{71}{106}\right)$
$\chi_{6848}(2943,\cdot)$	$1$	$1$	$e\left(\frac{89}{106}\right)$	$e\left(\frac{59}{106}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{31}{106}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{77}{106}\right)$	$e\left(\frac{81}{106}\right)$	$e\left(\frac{99}{106}\right)$
$\chi_{6848}(3135,\cdot)$	$1$	$1$	$e\left(\frac{85}{106}\right)$	$e\left(\frac{23}{106}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{57}{106}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{39}{106}\right)$	$e\left(\frac{19}{106}\right)$	$e\left(\frac{35}{106}\right)$
$\chi_{6848}(3199,\cdot)$	$1$	$1$	$e\left(\frac{3}{106}\right)$	$e\left(\frac{27}{106}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{7}{106}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{55}{106}\right)$	$e\left(\frac{73}{106}\right)$	$e\left(\frac{101}{106}\right)$
$\chi_{6848}(3391,\cdot)$	$1$	$1$	$e\left(\frac{27}{106}\right)$	$e\left(\frac{31}{106}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{63}{106}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{71}{106}\right)$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{61}{106}\right)$
$\chi_{6848}(3455,\cdot)$	$1$	$1$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{103}{106}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{11}{106}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{41}{106}\right)$	$e\left(\frac{39}{106}\right)$	$e\left(\frac{83}{106}\right)$
$\chi_{6848}(3519,\cdot)$	$1$	$1$	$e\left(\frac{5}{106}\right)$	$e\left(\frac{45}{106}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{47}{106}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{51}{106}\right)$	$e\left(\frac{27}{106}\right)$
$\chi_{6848}(3711,\cdot)$	$1$	$1$	$e\left(\frac{33}{106}\right)$	$e\left(\frac{85}{106}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{77}{106}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{75}{106}\right)$	$e\left(\frac{61}{106}\right)$	$e\left(\frac{51}{106}\right)$
$\chi_{6848}(3839,\cdot)$	$1$	$1$	$e\left(\frac{79}{106}\right)$	$e\left(\frac{75}{106}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{43}{106}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{85}{106}\right)$	$e\left(\frac{45}{106}\right)$
$\chi_{6848}(3903,\cdot)$	$1$	$1$	$e\left(\frac{93}{106}\right)$	$e\left(\frac{95}{106}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{5}{106}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{9}{106}\right)$	$e\left(\frac{37}{106}\right)$	$e\left(\frac{57}{106}\right)$
$\chi_{6848}(3967,\cdot)$	$1$	$1$	$e\left(\frac{51}{106}\right)$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{13}{106}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{87}{106}\right)$	$e\left(\frac{75}{106}\right)$	$e\left(\frac{21}{106}\right)$
$\chi_{6848}(4031,\cdot)$	$1$	$1$	$e\left(\frac{99}{106}\right)$	$e\left(\frac{43}{106}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{19}{106}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{13}{106}\right)$	$e\left(\frac{77}{106}\right)$	$e\left(\frac{47}{106}\right)$
$\chi_{6848}(4159,\cdot)$	$1$	$1$	$e\left(\frac{59}{106}\right)$	$e\left(\frac{1}{106}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{67}{106}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{57}{106}\right)$	$e\left(\frac{93}{106}\right)$	$e\left(\frac{43}{106}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{6848}(63,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{106}\right)\)	\(e\left(\frac{15}{106}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{51}{106}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{7}{106}\right)\)	\(e\left(\frac{17}{106}\right)\)	\(e\left(\frac{9}{106}\right)\)
\(\chi_{6848}(127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{106}\right)\)	\(e\left(\frac{77}{106}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{71}{106}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{43}{106}\right)\)	\(e\left(\frac{59}{106}\right)\)	\(e\left(\frac{25}{106}\right)\)
\(\chi_{6848}(191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{106}\right)\)	\(e\left(\frac{105}{106}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{39}{106}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{49}{106}\right)\)	\(e\left(\frac{13}{106}\right)\)	\(e\left(\frac{63}{106}\right)\)
\(\chi_{6848}(639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{106}\right)\)	\(e\left(\frac{57}{106}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{3}{106}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{69}{106}\right)\)	\(e\left(\frac{1}{106}\right)\)	\(e\left(\frac{13}{106}\right)\)
\(\chi_{6848}(767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{106}\right)\)	\(e\left(\frac{55}{106}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{81}{106}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{61}{106}\right)\)	\(e\left(\frac{27}{106}\right)\)	\(e\left(\frac{33}{106}\right)\)
\(\chi_{6848}(831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{106}\right)\)	\(e\left(\frac{19}{106}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{1}{106}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{23}{106}\right)\)	\(e\left(\frac{71}{106}\right)\)	\(e\left(\frac{75}{106}\right)\)
\(\chi_{6848}(959,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{106}\right)\)	\(e\left(\frac{41}{106}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{97}{106}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{5}{106}\right)\)	\(e\left(\frac{103}{106}\right)\)	\(e\left(\frac{67}{106}\right)\)
\(\chi_{6848}(1023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{106}\right)\)	\(e\left(\frac{81}{106}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{21}{106}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{59}{106}\right)\)	\(e\left(\frac{7}{106}\right)\)	\(e\left(\frac{91}{106}\right)\)
\(\chi_{6848}(1087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{106}\right)\)	\(e\left(\frac{91}{106}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{55}{106}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{99}{106}\right)\)	\(e\left(\frac{89}{106}\right)\)	\(e\left(\frac{97}{106}\right)\)
\(\chi_{6848}(1215,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{106}\right)\)	\(e\left(\frac{3}{106}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{95}{106}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{65}{106}\right)\)	\(e\left(\frac{67}{106}\right)\)	\(e\left(\frac{23}{106}\right)\)
\(\chi_{6848}(1343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{106}\right)\)	\(e\left(\frac{33}{106}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{91}{106}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{79}{106}\right)\)	\(e\left(\frac{101}{106}\right)\)	\(e\left(\frac{41}{106}\right)\)
\(\chi_{6848}(1471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{106}\right)\)	\(e\left(\frac{65}{106}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{9}{106}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{101}{106}\right)\)	\(e\left(\frac{3}{106}\right)\)	\(e\left(\frac{39}{106}\right)\)
\(\chi_{6848}(1663,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{106}\right)\)	\(e\left(\frac{67}{106}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{37}{106}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{3}{106}\right)\)	\(e\left(\frac{83}{106}\right)\)	\(e\left(\frac{19}{106}\right)\)
\(\chi_{6848}(1727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{106}\right)\)	\(e\left(\frac{93}{106}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{83}{106}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{1}{106}\right)\)	\(e\left(\frac{63}{106}\right)\)	\(e\left(\frac{77}{106}\right)\)
\(\chi_{6848}(2111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{106}\right)\)	\(e\left(\frac{73}{106}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{15}{106}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{27}{106}\right)\)	\(e\left(\frac{5}{106}\right)\)	\(e\left(\frac{65}{106}\right)\)
\(\chi_{6848}(2431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{106}\right)\)	\(e\left(\frac{87}{106}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{105}{106}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{83}{106}\right)\)	\(e\left(\frac{35}{106}\right)\)	\(e\left(\frac{31}{106}\right)\)
\(\chi_{6848}(2559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{106}\right)\)	\(e\left(\frac{61}{106}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{59}{106}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{85}{106}\right)\)	\(e\left(\frac{55}{106}\right)\)	\(e\left(\frac{79}{106}\right)\)
\(\chi_{6848}(2623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{106}\right)\)	\(e\left(\frac{63}{106}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{87}{106}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{93}{106}\right)\)	\(e\left(\frac{29}{106}\right)\)	\(e\left(\frac{59}{106}\right)\)
\(\chi_{6848}(2879,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{106}\right)\)	\(e\left(\frac{83}{106}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{49}{106}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{67}{106}\right)\)	\(e\left(\frac{87}{106}\right)\)	\(e\left(\frac{71}{106}\right)\)
\(\chi_{6848}(2943,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{106}\right)\)	\(e\left(\frac{59}{106}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{31}{106}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{77}{106}\right)\)	\(e\left(\frac{81}{106}\right)\)	\(e\left(\frac{99}{106}\right)\)
\(\chi_{6848}(3135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{106}\right)\)	\(e\left(\frac{23}{106}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{57}{106}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{39}{106}\right)\)	\(e\left(\frac{19}{106}\right)\)	\(e\left(\frac{35}{106}\right)\)
\(\chi_{6848}(3199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{106}\right)\)	\(e\left(\frac{27}{106}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{7}{106}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{55}{106}\right)\)	\(e\left(\frac{73}{106}\right)\)	\(e\left(\frac{101}{106}\right)\)
\(\chi_{6848}(3391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{106}\right)\)	\(e\left(\frac{31}{106}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{63}{106}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{71}{106}\right)\)	\(e\left(\frac{21}{106}\right)\)	\(e\left(\frac{61}{106}\right)\)
\(\chi_{6848}(3455,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{106}\right)\)	\(e\left(\frac{103}{106}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{11}{106}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{41}{106}\right)\)	\(e\left(\frac{39}{106}\right)\)	\(e\left(\frac{83}{106}\right)\)
\(\chi_{6848}(3519,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{106}\right)\)	\(e\left(\frac{45}{106}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{47}{106}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{21}{106}\right)\)	\(e\left(\frac{51}{106}\right)\)	\(e\left(\frac{27}{106}\right)\)
\(\chi_{6848}(3711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{106}\right)\)	\(e\left(\frac{85}{106}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{77}{106}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{75}{106}\right)\)	\(e\left(\frac{61}{106}\right)\)	\(e\left(\frac{51}{106}\right)\)
\(\chi_{6848}(3839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{106}\right)\)	\(e\left(\frac{75}{106}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{43}{106}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{35}{106}\right)\)	\(e\left(\frac{85}{106}\right)\)	\(e\left(\frac{45}{106}\right)\)
\(\chi_{6848}(3903,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{106}\right)\)	\(e\left(\frac{95}{106}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{5}{106}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{9}{106}\right)\)	\(e\left(\frac{37}{106}\right)\)	\(e\left(\frac{57}{106}\right)\)
\(\chi_{6848}(3967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{106}\right)\)	\(e\left(\frac{35}{106}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{13}{106}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{87}{106}\right)\)	\(e\left(\frac{75}{106}\right)\)	\(e\left(\frac{21}{106}\right)\)
\(\chi_{6848}(4031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{106}\right)\)	\(e\left(\frac{43}{106}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{19}{106}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{13}{106}\right)\)	\(e\left(\frac{77}{106}\right)\)	\(e\left(\frac{47}{106}\right)\)
\(\chi_{6848}(4159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{106}\right)\)	\(e\left(\frac{1}{106}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{67}{106}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{57}{106}\right)\)	\(e\left(\frac{93}{106}\right)\)	\(e\left(\frac{43}{106}\right)\)

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First 31 of 52 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.ba
Modulus	$6848$
Conductor	$428$
Order	$106$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(6848\)
Conductor:	\(428\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(106\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 428.h	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)