Properties

Label 8470.cv
Modulus $8470$
Conductor $605$
Order $110$
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([55,0,92]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(169,8470))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8470\)
Conductor: \(605\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(110\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 605.u
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 110 polynomial (not computed)

First 31 of 40 characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(9\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\) \(37\)
\(\chi_{8470}(169,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{107}{110}\right)\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{69}{110}\right)\)
\(\chi_{8470}(379,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{110}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{3}{110}\right)\)
\(\chi_{8470}(449,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{47}{110}\right)\)
\(\chi_{8470}(939,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{67}{110}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{109}{110}\right)\)
\(\chi_{8470}(1149,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{13}{110}\right)\)
\(\chi_{8470}(1499,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{101}{110}\right)\)
\(\chi_{8470}(1709,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{39}{110}\right)\)
\(\chi_{8470}(1919,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{91}{110}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{23}{110}\right)\)
\(\chi_{8470}(1989,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{91}{110}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{107}{110}\right)\)
\(\chi_{8470}(2269,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{67}{110}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{81}{110}\right)\)
\(\chi_{8470}(2479,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{79}{110}\right)\)
\(\chi_{8470}(2759,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{59}{110}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{27}{110}\right)\)
\(\chi_{8470}(3039,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{61}{110}\right)\)
\(\chi_{8470}(3249,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{9}{110}\right)\)
\(\chi_{8470}(3459,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{43}{110}\right)\)
\(\chi_{8470}(3529,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{57}{110}\right)\)
\(\chi_{8470}(3809,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{110}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{41}{110}\right)\)
\(\chi_{8470}(4019,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{49}{110}\right)\)
\(\chi_{8470}(4229,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{53}{110}\right)\)
\(\chi_{8470}(4299,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{19}{110}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{87}{110}\right)\)
\(\chi_{8470}(4579,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{107}{110}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{21}{110}\right)\)
\(\chi_{8470}(4789,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{3}{110}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{89}{110}\right)\)
\(\chi_{8470}(4999,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{63}{110}\right)\)
\(\chi_{8470}(5069,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{81}{110}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{7}{110}\right)\)
\(\chi_{8470}(5349,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{43}{110}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{1}{110}\right)\)
\(\chi_{8470}(5559,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{13}{110}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{19}{110}\right)\)
\(\chi_{8470}(5769,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{59}{110}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{73}{110}\right)\)
\(\chi_{8470}(5839,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{37}{110}\right)\)
\(\chi_{8470}(6119,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{91}{110}\right)\)
\(\chi_{8470}(6329,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{59}{110}\right)\)
\(\chi_{8470}(6539,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{83}{110}\right)\)