Properties

Label 571.l
Modulus $571$
Conductor $571$
Order $95$
Real no
Primitive yes
Minimal yes
Parity even

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([182]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(6,571))
 
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: \(95\)
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: $\Q(\zeta_{95})$
Fixed field: Number field defined by a degree 95 polynomial

First 31 of 72 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{571}(6,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{91}{95}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{22}{95}\right)\) \(e\left(\frac{1}{95}\right)\) \(e\left(\frac{26}{95}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{87}{95}\right)\) \(e\left(\frac{27}{95}\right)\) \(e\left(\frac{68}{95}\right)\)
\(\chi_{571}(20,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{62}{95}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{39}{95}\right)\) \(e\left(\frac{32}{95}\right)\) \(e\left(\frac{72}{95}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{29}{95}\right)\) \(e\left(\frac{9}{95}\right)\) \(e\left(\frac{86}{95}\right)\)
\(\chi_{571}(23,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{41}{95}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{12}{95}\right)\) \(e\left(\frac{61}{95}\right)\) \(e\left(\frac{66}{95}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{82}{95}\right)\) \(e\left(\frac{32}{95}\right)\) \(e\left(\frac{63}{95}\right)\)
\(\chi_{571}(36,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{87}{95}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{44}{95}\right)\) \(e\left(\frac{2}{95}\right)\) \(e\left(\frac{52}{95}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{79}{95}\right)\) \(e\left(\frac{54}{95}\right)\) \(e\left(\frac{41}{95}\right)\)
\(\chi_{571}(38,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{72}{95}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{79}{95}\right)\) \(e\left(\frac{77}{95}\right)\) \(e\left(\frac{7}{95}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{49}{95}\right)\) \(e\left(\frac{84}{95}\right)\) \(e\left(\frac{11}{95}\right)\)
\(\chi_{571}(49,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{77}{95}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{4}{95}\right)\) \(e\left(\frac{52}{95}\right)\) \(e\left(\frac{22}{95}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{59}{95}\right)\) \(e\left(\frac{74}{95}\right)\) \(e\left(\frac{21}{95}\right)\)
\(\chi_{571}(51,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{69}{95}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{48}{95}\right)\) \(e\left(\frac{54}{95}\right)\) \(e\left(\frac{74}{95}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{43}{95}\right)\) \(e\left(\frac{33}{95}\right)\) \(e\left(\frac{62}{95}\right)\)
\(\chi_{571}(56,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{26}{95}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{47}{95}\right)\) \(e\left(\frac{41}{95}\right)\) \(e\left(\frac{21}{95}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{52}{95}\right)\) \(e\left(\frac{62}{95}\right)\) \(e\left(\frac{33}{95}\right)\)
\(\chi_{571}(65,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{34}{95}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{3}{95}\right)\) \(e\left(\frac{39}{95}\right)\) \(e\left(\frac{64}{95}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{68}{95}\right)\) \(e\left(\frac{8}{95}\right)\) \(e\left(\frac{87}{95}\right)\)
\(\chi_{571}(105,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{14}{95}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{18}{95}\right)\) \(e\left(\frac{44}{95}\right)\) \(e\left(\frac{4}{95}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{28}{95}\right)\) \(e\left(\frac{48}{95}\right)\) \(e\left(\frac{47}{95}\right)\)
\(\chi_{571}(117,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{59}{95}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{8}{95}\right)\) \(e\left(\frac{9}{95}\right)\) \(e\left(\frac{44}{95}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{23}{95}\right)\) \(e\left(\frac{53}{95}\right)\) \(e\left(\frac{42}{95}\right)\)
\(\chi_{571}(120,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{58}{95}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{61}{95}\right)\) \(e\left(\frac{33}{95}\right)\) \(e\left(\frac{3}{95}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{21}{95}\right)\) \(e\left(\frac{36}{95}\right)\) \(e\left(\frac{59}{95}\right)\)
\(\chi_{571}(123,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{61}{95}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{92}{95}\right)\) \(e\left(\frac{56}{95}\right)\) \(e\left(\frac{31}{95}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{27}{95}\right)\) \(e\left(\frac{87}{95}\right)\) \(e\left(\frac{8}{95}\right)\)
\(\chi_{571}(125,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{21}{95}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{27}{95}\right)\) \(e\left(\frac{66}{95}\right)\) \(e\left(\frac{6}{95}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{42}{95}\right)\) \(e\left(\frac{72}{95}\right)\) \(e\left(\frac{23}{95}\right)\)
\(\chi_{571}(138,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{37}{95}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{34}{95}\right)\) \(e\left(\frac{62}{95}\right)\) \(e\left(\frac{92}{95}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{74}{95}\right)\) \(e\left(\frac{59}{95}\right)\) \(e\left(\frac{36}{95}\right)\)
\(\chi_{571}(142,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{56}{95}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{72}{95}\right)\) \(e\left(\frac{81}{95}\right)\) \(e\left(\frac{16}{95}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{17}{95}\right)\) \(e\left(\frac{2}{95}\right)\) \(e\left(\frac{93}{95}\right)\)
\(\chi_{571}(146,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{67}{95}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{59}{95}\right)\) \(e\left(\frac{7}{95}\right)\) \(e\left(\frac{87}{95}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{39}{95}\right)\) \(e\left(\frac{94}{95}\right)\) \(e\left(\frac{1}{95}\right)\)
\(\chi_{571}(148,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{47}{95}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{74}{95}\right)\) \(e\left(\frac{12}{95}\right)\) \(e\left(\frac{27}{95}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{94}{95}\right)\) \(e\left(\frac{39}{95}\right)\) \(e\left(\frac{56}{95}\right)\)
\(\chi_{571}(149,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{54}{95}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{83}{95}\right)\) \(e\left(\frac{34}{95}\right)\) \(e\left(\frac{29}{95}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{13}{95}\right)\) \(e\left(\frac{63}{95}\right)\) \(e\left(\frac{32}{95}\right)\)
\(\chi_{571}(154,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{79}{95}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{88}{95}\right)\) \(e\left(\frac{4}{95}\right)\) \(e\left(\frac{9}{95}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{63}{95}\right)\) \(e\left(\frac{13}{95}\right)\) \(e\left(\frac{82}{95}\right)\)
\(\chi_{571}(158,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{1}{95}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{42}{95}\right)\) \(e\left(\frac{71}{95}\right)\) \(e\left(\frac{41}{95}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{2}{95}\right)\) \(e\left(\frac{17}{95}\right)\) \(e\left(\frac{78}{95}\right)\)
\(\chi_{571}(163,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{9}{95}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{93}{95}\right)\) \(e\left(\frac{69}{95}\right)\) \(e\left(\frac{84}{95}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{18}{95}\right)\) \(e\left(\frac{58}{95}\right)\) \(e\left(\frac{37}{95}\right)\)
\(\chi_{571}(176,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{28}{95}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{36}{95}\right)\) \(e\left(\frac{88}{95}\right)\) \(e\left(\frac{8}{95}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{56}{95}\right)\) \(e\left(\frac{1}{95}\right)\) \(e\left(\frac{94}{95}\right)\)
\(\chi_{571}(179,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{17}{95}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{49}{95}\right)\) \(e\left(\frac{67}{95}\right)\) \(e\left(\frac{32}{95}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{34}{95}\right)\) \(e\left(\frac{4}{95}\right)\) \(e\left(\frac{91}{95}\right)\)
\(\chi_{571}(182,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{93}{95}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{11}{95}\right)\) \(e\left(\frac{48}{95}\right)\) \(e\left(\frac{13}{95}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{91}{95}\right)\) \(e\left(\frac{61}{95}\right)\) \(e\left(\frac{34}{95}\right)\)
\(\chi_{571}(186,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{11}{95}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{82}{95}\right)\) \(e\left(\frac{21}{95}\right)\) \(e\left(\frac{71}{95}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{22}{95}\right)\) \(e\left(\frac{92}{95}\right)\) \(e\left(\frac{3}{95}\right)\)
\(\chi_{571}(189,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{39}{95}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{23}{95}\right)\) \(e\left(\frac{14}{95}\right)\) \(e\left(\frac{79}{95}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{78}{95}\right)\) \(e\left(\frac{93}{95}\right)\) \(e\left(\frac{2}{95}\right)\)
\(\chi_{571}(201,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{74}{95}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{68}{95}\right)\) \(e\left(\frac{29}{95}\right)\) \(e\left(\frac{89}{95}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{53}{95}\right)\) \(e\left(\frac{23}{95}\right)\) \(e\left(\frac{72}{95}\right)\)
\(\chi_{571}(206,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{94}{95}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{53}{95}\right)\) \(e\left(\frac{24}{95}\right)\) \(e\left(\frac{54}{95}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{93}{95}\right)\) \(e\left(\frac{78}{95}\right)\) \(e\left(\frac{17}{95}\right)\)
\(\chi_{571}(208,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{42}{95}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{54}{95}\right)\) \(e\left(\frac{37}{95}\right)\) \(e\left(\frac{12}{95}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{84}{95}\right)\) \(e\left(\frac{49}{95}\right)\) \(e\left(\frac{46}{95}\right)\)
\(\chi_{571}(215,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{51}{95}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{52}{95}\right)\) \(e\left(\frac{11}{95}\right)\) \(e\left(\frac{1}{95}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{7}{95}\right)\) \(e\left(\frac{12}{95}\right)\) \(e\left(\frac{83}{95}\right)\)