Properties

Label 8470.cf
Modulus $8470$
Conductor $121$
Order $55$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(8470, base_ring=CyclotomicField(110))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,94]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(71,8470))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8470\)
Conductor: \(121\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(55\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 121.g
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: $\Q(\zeta_{55})$
Fixed field: Number field defined by a degree 55 polynomial

First 31 of 40 characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(9\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\) \(37\)
\(\chi_{8470}(71,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{49}{55}\right)\)
\(\chi_{8470}(141,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{1}{55}\right)\)
\(\chi_{8470}(421,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{48}{55}\right)\)
\(\chi_{8470}(631,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{52}{55}\right)\)
\(\chi_{8470}(841,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{54}{55}\right)\)
\(\chi_{8470}(911,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{16}{55}\right)\)
\(\chi_{8470}(1191,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{38}{55}\right)\)
\(\chi_{8470}(1401,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{17}{55}\right)\)
\(\chi_{8470}(1611,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{4}{55}\right)\)
\(\chi_{8470}(1681,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{31}{55}\right)\)
\(\chi_{8470}(1961,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{28}{55}\right)\)
\(\chi_{8470}(2171,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{37}{55}\right)\)
\(\chi_{8470}(2381,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{9}{55}\right)\)
\(\chi_{8470}(2451,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{46}{55}\right)\)
\(\chi_{8470}(2731,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{18}{55}\right)\)
\(\chi_{8470}(2941,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{2}{55}\right)\)
\(\chi_{8470}(3151,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{14}{55}\right)\)
\(\chi_{8470}(3221,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{6}{55}\right)\)
\(\chi_{8470}(3501,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{8}{55}\right)\)
\(\chi_{8470}(3921,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{19}{55}\right)\)
\(\chi_{8470}(3991,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{21}{55}\right)\)
\(\chi_{8470}(4271,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{53}{55}\right)\)
\(\chi_{8470}(4481,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{42}{55}\right)\)
\(\chi_{8470}(4691,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{24}{55}\right)\)
\(\chi_{8470}(4761,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{36}{55}\right)\)
\(\chi_{8470}(5041,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{43}{55}\right)\)
\(\chi_{8470}(5251,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{7}{55}\right)\)
\(\chi_{8470}(5461,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{29}{55}\right)\)
\(\chi_{8470}(5531,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{51}{55}\right)\)
\(\chi_{8470}(6021,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{27}{55}\right)\)
\(\chi_{8470}(6231,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{34}{55}\right)\)