LMFDB - Dirichlet character orbit 6043.g

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6043, base_ring=CyclotomicField(106)) M = H._module chi = DirichletCharacter(H, M([76])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(64,6043)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6043$
Conductor:	$6043$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$53$	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:	$\Q(\zeta_{53})$
Fixed field:	Number field defined by a degree 53 polynomial

First 31 of 52 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{6043}(64,\cdot)$	$1$	$1$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{20}{53}\right)$	$1$
$\chi_{6043}(454,\cdot)$	$1$	$1$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{18}{53}\right)$	$1$
$\chi_{6043}(654,\cdot)$	$1$	$1$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{36}{53}\right)$	$1$
$\chi_{6043}(809,\cdot)$	$1$	$1$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{1}{53}\right)$	$1$
$\chi_{6043}(811,\cdot)$	$1$	$1$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{46}{53}\right)$	$1$
$\chi_{6043}(817,\cdot)$	$1$	$1$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{42}{53}\right)$	$1$
$\chi_{6043}(1194,\cdot)$	$1$	$1$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{15}{53}\right)$	$1$
$\chi_{6043}(1329,\cdot)$	$1$	$1$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{51}{53}\right)$	$1$
$\chi_{6043}(1429,\cdot)$	$1$	$1$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{26}{53}\right)$	$1$
$\chi_{6043}(1454,\cdot)$	$1$	$1$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{8}{53}\right)$	$1$
$\chi_{6043}(1639,\cdot)$	$1$	$1$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{24}{53}\right)$	$1$
$\chi_{6043}(1685,\cdot)$	$1$	$1$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{49}{53}\right)$	$1$
$\chi_{6043}(1735,\cdot)$	$1$	$1$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{23}{53}\right)$	$1$
$\chi_{6043}(1837,\cdot)$	$1$	$1$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{2}{53}\right)$	$1$
$\chi_{6043}(1848,\cdot)$	$1$	$1$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{27}{53}\right)$	$1$
$\chi_{6043}(2100,\cdot)$	$1$	$1$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{41}{53}\right)$	$1$
$\chi_{6043}(2164,\cdot)$	$1$	$1$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{32}{53}\right)$	$1$
$\chi_{6043}(2165,\cdot)$	$1$	$1$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{44}{53}\right)$	$1$
$\chi_{6043}(2266,\cdot)$	$1$	$1$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{43}{53}\right)$	$1$
$\chi_{6043}(2295,\cdot)$	$1$	$1$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{7}{53}\right)$	$1$
$\chi_{6043}(2411,\cdot)$	$1$	$1$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{28}{53}\right)$	$1$
$\chi_{6043}(2534,\cdot)$	$1$	$1$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{25}{53}\right)$	$1$
$\chi_{6043}(2575,\cdot)$	$1$	$1$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{4}{53}\right)$	$1$
$\chi_{6043}(2751,\cdot)$	$1$	$1$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{22}{53}\right)$	$1$
$\chi_{6043}(2759,\cdot)$	$1$	$1$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{31}{53}\right)$	$1$
$\chi_{6043}(3229,\cdot)$	$1$	$1$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{48}{53}\right)$	$1$
$\chi_{6043}(3345,\cdot)$	$1$	$1$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{37}{53}\right)$	$1$
$\chi_{6043}(3432,\cdot)$	$1$	$1$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{21}{53}\right)$	$1$
$\chi_{6043}(3433,\cdot)$	$1$	$1$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{12}{53}\right)$	$1$
$\chi_{6043}(3455,\cdot)$	$1$	$1$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{47}{53}\right)$	$1$
$\chi_{6043}(3490,\cdot)$	$1$	$1$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{50}{53}\right)$	$1$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{6043}(64,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(1\)
\(\chi_{6043}(454,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(1\)
\(\chi_{6043}(654,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(1\)
\(\chi_{6043}(809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(1\)
\(\chi_{6043}(811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(1\)
\(\chi_{6043}(817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(1\)
\(\chi_{6043}(1194,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(1\)
\(\chi_{6043}(1329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(1\)
\(\chi_{6043}(1429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(1\)
\(\chi_{6043}(1454,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(1\)
\(\chi_{6043}(1639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(1\)
\(\chi_{6043}(1685,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(1\)
\(\chi_{6043}(1735,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(1\)
\(\chi_{6043}(1837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(1\)
\(\chi_{6043}(1848,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(1\)
\(\chi_{6043}(2100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(1\)
\(\chi_{6043}(2164,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(1\)
\(\chi_{6043}(2165,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(1\)
\(\chi_{6043}(2266,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(1\)
\(\chi_{6043}(2295,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(1\)
\(\chi_{6043}(2411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(1\)
\(\chi_{6043}(2534,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(1\)
\(\chi_{6043}(2575,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(1\)
\(\chi_{6043}(2751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(1\)
\(\chi_{6043}(2759,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(1\)
\(\chi_{6043}(3229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(1\)
\(\chi_{6043}(3345,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(1\)
\(\chi_{6043}(3432,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(1\)
\(\chi_{6043}(3433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(1\)
\(\chi_{6043}(3455,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(1\)
\(\chi_{6043}(3490,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(1\)

Introduction

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Basic properties

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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	6043.g
Modulus	$6043$
Conductor	$6043$
Order	$53$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(6043\)
Conductor:	\(6043\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(53\)	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)