Properties

Label 571.n
Modulus $571$
Conductor $571$
Order $190$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(571, base_ring=CyclotomicField(190))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([77]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(7,571))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(571\)
Conductor: \(571\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(190\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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: $\Q(\zeta_{95})$
Fixed field: Number field defined by a degree 190 polynomial (not computed)

First 31 of 72 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{571}(7,\cdot)\) \(-1\) \(1\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{77}{190}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{2}{95}\right)\) \(e\left(\frac{26}{95}\right)\) \(e\left(\frac{117}{190}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{77}{95}\right)\) \(e\left(\frac{169}{190}\right)\) \(e\left(\frac{58}{95}\right)\)
\(\chi_{571}(15,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{141}{190}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{16}{95}\right)\) \(e\left(\frac{18}{95}\right)\) \(e\left(\frac{81}{190}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{46}{95}\right)\) \(e\left(\frac{117}{190}\right)\) \(e\left(\frac{84}{95}\right)\)
\(\chi_{571}(22,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{81}{190}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{86}{95}\right)\) \(e\left(\frac{73}{95}\right)\) \(e\left(\frac{91}{190}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{81}{95}\right)\) \(e\left(\frac{47}{190}\right)\) \(e\left(\frac{24}{95}\right)\)
\(\chi_{571}(26,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{109}{190}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{9}{95}\right)\) \(e\left(\frac{22}{95}\right)\) \(e\left(\frac{99}{190}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{14}{95}\right)\) \(e\left(\frac{143}{190}\right)\) \(e\left(\frac{71}{95}\right)\)
\(\chi_{571}(27,\cdot)\) \(-1\) \(1\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{1}{190}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{21}{95}\right)\) \(e\left(\frac{83}{95}\right)\) \(e\left(\frac{41}{190}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{1}{95}\right)\) \(e\left(\frac{17}{190}\right)\) \(e\left(\frac{39}{95}\right)\)
\(\chi_{571}(42,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{69}{190}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{24}{95}\right)\) \(e\left(\frac{27}{95}\right)\) \(e\left(\frac{169}{190}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{69}{95}\right)\) \(e\left(\frac{33}{190}\right)\) \(e\left(\frac{31}{95}\right)\)
\(\chi_{571}(48,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{157}{190}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{67}{95}\right)\) \(e\left(\frac{16}{95}\right)\) \(e\left(\frac{167}{190}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{62}{95}\right)\) \(e\left(\frac{9}{190}\right)\) \(e\left(\frac{43}{95}\right)\)
\(\chi_{571}(50,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{83}{190}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{33}{95}\right)\) \(e\left(\frac{49}{95}\right)\) \(e\left(\frac{173}{190}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{83}{95}\right)\) \(e\left(\frac{81}{190}\right)\) \(e\left(\frac{7}{95}\right)\)
\(\chi_{571}(68,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{121}{190}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{71}{95}\right)\) \(e\left(\frac{68}{95}\right)\) \(e\left(\frac{21}{190}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{26}{95}\right)\) \(e\left(\frac{157}{190}\right)\) \(e\left(\frac{64}{95}\right)\)
\(\chi_{571}(86,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{143}{190}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{58}{95}\right)\) \(e\left(\frac{89}{95}\right)\) \(e\left(\frac{163}{190}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{48}{95}\right)\) \(e\left(\frac{151}{190}\right)\) \(e\left(\frac{67}{95}\right)\)
\(\chi_{571}(87,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{67}{190}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{77}{95}\right)\) \(e\left(\frac{51}{95}\right)\) \(e\left(\frac{87}{190}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{67}{95}\right)\) \(e\left(\frac{189}{190}\right)\) \(e\left(\frac{48}{95}\right)\)
\(\chi_{571}(95,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{103}{190}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{73}{95}\right)\) \(e\left(\frac{94}{95}\right)\) \(e\left(\frac{43}{190}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{8}{95}\right)\) \(e\left(\frac{41}{190}\right)\) \(e\left(\frac{27}{95}\right)\)
\(\chi_{571}(111,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{111}{190}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{51}{95}\right)\) \(e\left(\frac{93}{95}\right)\) \(e\left(\frac{181}{190}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{16}{95}\right)\) \(e\left(\frac{177}{190}\right)\) \(e\left(\frac{54}{95}\right)\)
\(\chi_{571}(122,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{167}{190}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{87}{95}\right)\) \(e\left(\frac{86}{95}\right)\) \(e\left(\frac{7}{190}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{72}{95}\right)\) \(e\left(\frac{179}{190}\right)\) \(e\left(\frac{53}{95}\right)\)
\(\chi_{571}(132,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{73}{190}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{13}{95}\right)\) \(e\left(\frac{74}{95}\right)\) \(e\left(\frac{143}{190}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{73}{95}\right)\) \(e\left(\frac{101}{190}\right)\) \(e\left(\frac{92}{95}\right)\)
\(\chi_{571}(140,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{11}{190}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{41}{95}\right)\) \(e\left(\frac{58}{95}\right)\) \(e\left(\frac{71}{190}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{11}{95}\right)\) \(e\left(\frac{187}{190}\right)\) \(e\left(\frac{49}{95}\right)\)
\(\chi_{571}(156,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{101}{190}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{31}{95}\right)\) \(e\left(\frac{23}{95}\right)\) \(e\left(\frac{151}{190}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{6}{95}\right)\) \(e\left(\frac{7}{190}\right)\) \(e\left(\frac{44}{95}\right)\)
\(\chi_{571}(160,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{99}{190}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{84}{95}\right)\) \(e\left(\frac{47}{95}\right)\) \(e\left(\frac{69}{190}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{4}{95}\right)\) \(e\left(\frac{163}{190}\right)\) \(e\left(\frac{61}{95}\right)\)
\(\chi_{571}(161,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{159}{190}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{14}{95}\right)\) \(e\left(\frac{87}{95}\right)\) \(e\left(\frac{59}{190}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{64}{95}\right)\) \(e\left(\frac{43}{190}\right)\) \(e\left(\frac{26}{95}\right)\)
\(\chi_{571}(162,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{183}{190}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{43}{95}\right)\) \(e\left(\frac{84}{95}\right)\) \(e\left(\frac{93}{190}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{88}{95}\right)\) \(e\left(\frac{71}{190}\right)\) \(e\left(\frac{12}{95}\right)\)
\(\chi_{571}(166,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{47}{190}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{37}{95}\right)\) \(e\left(\frac{6}{95}\right)\) \(e\left(\frac{27}{190}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{47}{95}\right)\) \(e\left(\frac{39}{190}\right)\) \(e\left(\frac{28}{95}\right)\)
\(\chi_{571}(171,\cdot)\) \(-1\) \(1\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{153}{190}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{78}{95}\right)\) \(e\left(\frac{64}{95}\right)\) \(e\left(\frac{3}{190}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{58}{95}\right)\) \(e\left(\frac{131}{190}\right)\) \(e\left(\frac{77}{95}\right)\)
\(\chi_{571}(187,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{37}{190}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{17}{95}\right)\) \(e\left(\frac{31}{95}\right)\) \(e\left(\frac{187}{190}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{37}{95}\right)\) \(e\left(\frac{59}{190}\right)\) \(e\left(\frac{18}{95}\right)\)
\(\chi_{571}(194,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{89}{190}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{64}{95}\right)\) \(e\left(\frac{72}{95}\right)\) \(e\left(\frac{39}{190}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{89}{95}\right)\) \(e\left(\frac{183}{190}\right)\) \(e\left(\frac{51}{95}\right)\)
\(\chi_{571}(217,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{107}{190}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{62}{95}\right)\) \(e\left(\frac{46}{95}\right)\) \(e\left(\frac{17}{190}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{12}{95}\right)\) \(e\left(\frac{109}{190}\right)\) \(e\left(\frac{88}{95}\right)\)
\(\chi_{571}(235,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{139}{190}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{69}{95}\right)\) \(e\left(\frac{42}{95}\right)\) \(e\left(\frac{189}{190}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{44}{95}\right)\) \(e\left(\frac{83}{190}\right)\) \(e\left(\frac{6}{95}\right)\)
\(\chi_{571}(241,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{127}{190}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{7}{95}\right)\) \(e\left(\frac{91}{95}\right)\) \(e\left(\frac{77}{190}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{32}{95}\right)\) \(e\left(\frac{69}{190}\right)\) \(e\left(\frac{13}{95}\right)\)
\(\chi_{571}(252,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{61}{190}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{46}{95}\right)\) \(e\left(\frac{28}{95}\right)\) \(e\left(\frac{31}{190}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{61}{95}\right)\) \(e\left(\frac{87}{190}\right)\) \(e\left(\frac{4}{95}\right)\)
\(\chi_{571}(254,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{181}{190}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{1}{95}\right)\) \(e\left(\frac{13}{95}\right)\) \(e\left(\frac{11}{190}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{86}{95}\right)\) \(e\left(\frac{37}{190}\right)\) \(e\left(\frac{29}{95}\right)\)
\(\chi_{571}(266,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{31}{190}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{81}{95}\right)\) \(e\left(\frac{8}{95}\right)\) \(e\left(\frac{131}{190}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{31}{95}\right)\) \(e\left(\frac{147}{190}\right)\) \(e\left(\frac{69}{95}\right)\)
\(\chi_{571}(268,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{131}{190}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{91}{95}\right)\) \(e\left(\frac{43}{95}\right)\) \(e\left(\frac{51}{190}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{36}{95}\right)\) \(e\left(\frac{137}{190}\right)\) \(e\left(\frac{74}{95}\right)\)