LMFDB - Dirichlet character orbit 41600.to

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(41600, base_ring=CyclotomicField(80)) M = H._module chi = DirichletCharacter(H, M([0,55,44,20])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(73, 41600)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("41600.73"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$41600$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$20800$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$80$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 20800.si	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{80})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 80 polynomial	comment:Fixed field sage:chi.fixed_field()

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{41600}(73,\cdot)$	$1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{53}{80}\right)$
$\chi_{41600}(2137,\cdot)$	$1$	$1$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{7}{80}\right)$
$\chi_{41600}(2153,\cdot)$	$1$	$1$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{41}{80}\right)$
$\chi_{41600}(4217,\cdot)$	$1$	$1$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{59}{80}\right)$
$\chi_{41600}(4233,\cdot)$	$1$	$1$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{29}{80}\right)$
$\chi_{41600}(6297,\cdot)$	$1$	$1$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{31}{80}\right)$
$\chi_{41600}(6313,\cdot)$	$1$	$1$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{17}{80}\right)$
$\chi_{41600}(8377,\cdot)$	$1$	$1$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{3}{80}\right)$
$\chi_{41600}(10473,\cdot)$	$1$	$1$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{73}{80}\right)$
$\chi_{41600}(12537,\cdot)$	$1$	$1$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{27}{80}\right)$
$\chi_{41600}(12553,\cdot)$	$1$	$1$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{61}{80}\right)$
$\chi_{41600}(14617,\cdot)$	$1$	$1$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{79}{80}\right)$
$\chi_{41600}(14633,\cdot)$	$1$	$1$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{49}{80}\right)$
$\chi_{41600}(16697,\cdot)$	$1$	$1$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{51}{80}\right)$
$\chi_{41600}(16713,\cdot)$	$1$	$1$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{37}{80}\right)$
$\chi_{41600}(18777,\cdot)$	$1$	$1$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{23}{80}\right)$
$\chi_{41600}(20873,\cdot)$	$1$	$1$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{13}{80}\right)$
$\chi_{41600}(22937,\cdot)$	$1$	$1$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{47}{80}\right)$
$\chi_{41600}(22953,\cdot)$	$1$	$1$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{1}{80}\right)$
$\chi_{41600}(25017,\cdot)$	$1$	$1$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{19}{80}\right)$
$\chi_{41600}(25033,\cdot)$	$1$	$1$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{69}{80}\right)$
$\chi_{41600}(27097,\cdot)$	$1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{71}{80}\right)$
$\chi_{41600}(27113,\cdot)$	$1$	$1$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{57}{80}\right)$
$\chi_{41600}(29177,\cdot)$	$1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{43}{80}\right)$
$\chi_{41600}(31273,\cdot)$	$1$	$1$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{33}{80}\right)$
$\chi_{41600}(33337,\cdot)$	$1$	$1$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{67}{80}\right)$
$\chi_{41600}(33353,\cdot)$	$1$	$1$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{21}{80}\right)$
$\chi_{41600}(35417,\cdot)$	$1$	$1$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{39}{80}\right)$
$\chi_{41600}(35433,\cdot)$	$1$	$1$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{9}{80}\right)$
$\chi_{41600}(37497,\cdot)$	$1$	$1$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{11}{80}\right)$
$\chi_{41600}(37513,\cdot)$	$1$	$1$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{77}{80}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{41600}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)
\(\chi_{41600}(2137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)
\(\chi_{41600}(2153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)
\(\chi_{41600}(4217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)
\(\chi_{41600}(4233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)
\(\chi_{41600}(6297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)
\(\chi_{41600}(6313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)
\(\chi_{41600}(8377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)
\(\chi_{41600}(10473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)
\(\chi_{41600}(12537,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)
\(\chi_{41600}(12553,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)
\(\chi_{41600}(14617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)
\(\chi_{41600}(14633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)
\(\chi_{41600}(16697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)
\(\chi_{41600}(16713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)
\(\chi_{41600}(18777,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)
\(\chi_{41600}(20873,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)
\(\chi_{41600}(22937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)
\(\chi_{41600}(22953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)
\(\chi_{41600}(25017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)
\(\chi_{41600}(25033,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)
\(\chi_{41600}(27097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)
\(\chi_{41600}(27113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)
\(\chi_{41600}(29177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)
\(\chi_{41600}(31273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)
\(\chi_{41600}(33337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)
\(\chi_{41600}(33353,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)
\(\chi_{41600}(35417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)
\(\chi_{41600}(35433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)
\(\chi_{41600}(37497,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)
\(\chi_{41600}(37513,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)

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First 31 of 32 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	41600.to
Modulus	$41600$
Conductor	$20800$
Order	$80$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(41600\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(20800\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(80\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 20800.si	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);