LMFDB - Dirichlet character orbit 6848.u

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6848, base_ring=CyclotomicField(106)) M = H._module chi = DirichletCharacter(H, M([0,0,60])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(193,6848)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6848$
Conductor:	$107$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$53$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 107.c	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 53 polynomial

First 31 of 52 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{6848}(193,\cdot)$	$1$	$1$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{51}{53}\right)$
$\chi_{6848}(385,\cdot)$	$1$	$1$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{21}{53}\right)$
$\chi_{6848}(513,\cdot)$	$1$	$1$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{1}{53}\right)$
$\chi_{6848}(577,\cdot)$	$1$	$1$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{28}{53}\right)$
$\chi_{6848}(897,\cdot)$	$1$	$1$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{34}{53}\right)$
$\chi_{6848}(961,\cdot)$	$1$	$1$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{30}{53}\right)$
$\chi_{6848}(1025,\cdot)$	$1$	$1$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{45}{53}\right)$
$\chi_{6848}(1089,\cdot)$	$1$	$1$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{8}{53}\right)$
$\chi_{6848}(1153,\cdot)$	$1$	$1$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{17}{53}\right)$
$\chi_{6848}(1217,\cdot)$	$1$	$1$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{16}{53}\right)$
$\chi_{6848}(1345,\cdot)$	$1$	$1$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{35}{53}\right)$
$\chi_{6848}(1537,\cdot)$	$1$	$1$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{29}{53}\right)$
$\chi_{6848}(1793,\cdot)$	$1$	$1$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{26}{53}\right)$
$\chi_{6848}(1921,\cdot)$	$1$	$1$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{32}{53}\right)$
$\chi_{6848}(2049,\cdot)$	$1$	$1$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{14}{53}\right)$
$\chi_{6848}(2177,\cdot)$	$1$	$1$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{27}{53}\right)$
$\chi_{6848}(2241,\cdot)$	$1$	$1$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{10}{53}\right)$
$\chi_{6848}(2433,\cdot)$	$1$	$1$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{25}{53}\right)$
$\chi_{6848}(2497,\cdot)$	$1$	$1$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{20}{53}\right)$
$\chi_{6848}(2561,\cdot)$	$1$	$1$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{18}{53}\right)$
$\chi_{6848}(2625,\cdot)$	$1$	$1$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{41}{53}\right)$
$\chi_{6848}(2689,\cdot)$	$1$	$1$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{48}{53}\right)$
$\chi_{6848}(2817,\cdot)$	$1$	$1$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{50}{53}\right)$
$\chi_{6848}(2881,\cdot)$	$1$	$1$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{37}{53}\right)$
$\chi_{6848}(2945,\cdot)$	$1$	$1$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{2}{53}\right)$
$\chi_{6848}(3009,\cdot)$	$1$	$1$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{49}{53}\right)$
$\chi_{6848}(3137,\cdot)$	$1$	$1$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{52}{53}\right)$
$\chi_{6848}(3329,\cdot)$	$1$	$1$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{40}{53}\right)$
$\chi_{6848}(3393,\cdot)$	$1$	$1$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{15}{53}\right)$
$\chi_{6848}(3457,\cdot)$	$1$	$1$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{4}{53}\right)$
$\chi_{6848}(3649,\cdot)$	$1$	$1$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{24}{53}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{6848}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)
\(\chi_{6848}(385,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)
\(\chi_{6848}(513,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)
\(\chi_{6848}(577,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)
\(\chi_{6848}(897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)
\(\chi_{6848}(961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)
\(\chi_{6848}(1025,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)
\(\chi_{6848}(1089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)
\(\chi_{6848}(1153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)
\(\chi_{6848}(1217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)
\(\chi_{6848}(1345,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)
\(\chi_{6848}(1537,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)
\(\chi_{6848}(1793,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)
\(\chi_{6848}(1921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)
\(\chi_{6848}(2049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{14}{53}\right)\)
\(\chi_{6848}(2177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)
\(\chi_{6848}(2241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)
\(\chi_{6848}(2433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)
\(\chi_{6848}(2497,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)
\(\chi_{6848}(2561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)
\(\chi_{6848}(2625,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)
\(\chi_{6848}(2689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)
\(\chi_{6848}(2817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)
\(\chi_{6848}(2881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)
\(\chi_{6848}(2945,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)
\(\chi_{6848}(3009,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)
\(\chi_{6848}(3137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)
\(\chi_{6848}(3329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)
\(\chi_{6848}(3393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)
\(\chi_{6848}(3457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)
\(\chi_{6848}(3649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)

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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.u
Modulus	$6848$
Conductor	$107$
Order	$53$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(6848\)
Conductor:	\(107\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(53\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 107.c	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)