Properties

Label 4235.cx
Modulus $4235$
Conductor $605$
Order $110$
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4235, base_ring=CyclotomicField(110))
 
M = H._module
 
chi = DirichletCharacter(H, M([55,0,17]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(29,4235))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4235\)
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.v
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(8\) \(9\) \(12\) \(13\) \(16\) \(17\)
\(\chi_{4235}(29,\cdot)\) \(-1\) \(1\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{4}{55}\right)\)
\(\chi_{4235}(134,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{27}{55}\right)\)
\(\chi_{4235}(204,\cdot)\) \(-1\) \(1\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{23}{55}\right)\)
\(\chi_{4235}(414,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{29}{55}\right)\)
\(\chi_{4235}(519,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{59}{110}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{32}{55}\right)\)
\(\chi_{4235}(589,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{81}{110}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{43}{55}\right)\)
\(\chi_{4235}(624,\cdot)\) \(-1\) \(1\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{26}{55}\right)\)
\(\chi_{4235}(799,\cdot)\) \(-1\) \(1\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{54}{55}\right)\)
\(\chi_{4235}(904,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{37}{55}\right)\)
\(\chi_{4235}(974,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{8}{55}\right)\)
\(\chi_{4235}(1009,\cdot)\) \(-1\) \(1\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{67}{110}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{41}{55}\right)\)
\(\chi_{4235}(1184,\cdot)\) \(-1\) \(1\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{3}{110}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{24}{55}\right)\)
\(\chi_{4235}(1289,\cdot)\) \(-1\) \(1\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{19}{110}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{42}{55}\right)\)
\(\chi_{4235}(1359,\cdot)\) \(-1\) \(1\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{28}{55}\right)\)
\(\chi_{4235}(1394,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{1}{55}\right)\)
\(\chi_{4235}(1569,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{13}{110}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{49}{55}\right)\)
\(\chi_{4235}(1674,\cdot)\) \(-1\) \(1\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{47}{55}\right)\)
\(\chi_{4235}(1744,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{48}{55}\right)\)
\(\chi_{4235}(1779,\cdot)\) \(-1\) \(1\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{16}{55}\right)\)
\(\chi_{4235}(1954,\cdot)\) \(-1\) \(1\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{19}{55}\right)\)
\(\chi_{4235}(2059,\cdot)\) \(-1\) \(1\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{52}{55}\right)\)
\(\chi_{4235}(2129,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{91}{110}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{13}{55}\right)\)
\(\chi_{4235}(2164,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{107}{110}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{31}{55}\right)\)
\(\chi_{4235}(2444,\cdot)\) \(-1\) \(1\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{2}{55}\right)\)
\(\chi_{4235}(2549,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{46}{55}\right)\)
\(\chi_{4235}(2724,\cdot)\) \(-1\) \(1\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{43}{110}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{14}{55}\right)\)
\(\chi_{4235}(2829,\cdot)\) \(-1\) \(1\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{7}{55}\right)\)
\(\chi_{4235}(2899,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{53}{55}\right)\)
\(\chi_{4235}(2934,\cdot)\) \(-1\) \(1\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{6}{55}\right)\)
\(\chi_{4235}(3109,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{39}{55}\right)\)
\(\chi_{4235}(3214,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{12}{55}\right)\)