Properties

Label 473.v
Modulus $473$
Conductor $473$
Order $35$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(473, base_ring=CyclotomicField(70))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([14,20]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(4,473))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(473\)
Conductor: \(473\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(35\)
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: $\Q(\zeta_{35})$
Fixed field: 35.35.1455622807785591094953547155658149343464416905925495778881639129313848614446169.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(12\)
\(\chi_{473}(4,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{473}(16,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{473}(47,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{473}(59,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{473}(64,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{473}(97,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{473}(102,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{473}(170,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{473}(207,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{473}(213,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{473}(236,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{473}(256,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{473}(262,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{473}(269,\cdot)\) \(1\) \(1\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{473}(279,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{473}(312,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{473}(317,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{473}(322,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{473}(355,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{473}(379,\cdot)\) \(1\) \(1\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{473}(422,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{473}(434,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{473}(465,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{473}(471,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\)