Properties

Label 571.o
Modulus $571$
Conductor $571$
Order $285$
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(570))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([422]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(5,571))
 
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: \(285\)
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: $\Q(\zeta_{285})$
Fixed field: Number field defined by a degree 285 polynomial (not computed)

First 31 of 144 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{571}(5,\cdot)\) \(1\) \(1\) \(e\left(\frac{28}{57}\right)\) \(e\left(\frac{211}{285}\right)\) \(e\left(\frac{56}{57}\right)\) \(e\left(\frac{122}{285}\right)\) \(e\left(\frac{22}{95}\right)\) \(e\left(\frac{2}{95}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{137}{285}\right)\) \(e\left(\frac{262}{285}\right)\) \(e\left(\frac{118}{285}\right)\)
\(\chi_{571}(9,\cdot)\) \(1\) \(1\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{1}{285}\right)\) \(e\left(\frac{47}{57}\right)\) \(e\left(\frac{137}{285}\right)\) \(e\left(\frac{87}{95}\right)\) \(e\left(\frac{77}{95}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{2}{285}\right)\) \(e\left(\frac{112}{285}\right)\) \(e\left(\frac{268}{285}\right)\)
\(\chi_{571}(11,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{134}{285}\right)\) \(e\left(\frac{28}{57}\right)\) \(e\left(\frac{118}{285}\right)\) \(e\left(\frac{68}{95}\right)\) \(e\left(\frac{58}{95}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{268}{285}\right)\) \(e\left(\frac{188}{285}\right)\) \(e\left(\frac{2}{285}\right)\)
\(\chi_{571}(13,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{57}\right)\) \(e\left(\frac{176}{285}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{172}{285}\right)\) \(e\left(\frac{17}{95}\right)\) \(e\left(\frac{62}{95}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{67}{285}\right)\) \(e\left(\frac{47}{285}\right)\) \(e\left(\frac{143}{285}\right)\)
\(\chi_{571}(14,\cdot)\) \(1\) \(1\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{103}{285}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{146}{285}\right)\) \(e\left(\frac{31}{95}\right)\) \(e\left(\frac{46}{95}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{206}{285}\right)\) \(e\left(\frac{136}{285}\right)\) \(e\left(\frac{244}{285}\right)\)
\(\chi_{571}(21,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{57}\right)\) \(e\left(\frac{116}{285}\right)\) \(e\left(\frac{37}{57}\right)\) \(e\left(\frac{217}{285}\right)\) \(e\left(\frac{22}{95}\right)\) \(e\left(\frac{2}{95}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{232}{285}\right)\) \(e\left(\frac{167}{285}\right)\) \(e\left(\frac{23}{285}\right)\)
\(\chi_{571}(24,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{248}{285}\right)\) \(e\left(\frac{28}{57}\right)\) \(e\left(\frac{61}{285}\right)\) \(e\left(\frac{11}{95}\right)\) \(e\left(\frac{1}{95}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{211}{285}\right)\) \(e\left(\frac{131}{285}\right)\) \(e\left(\frac{59}{285}\right)\)
\(\chi_{571}(25,\cdot)\) \(1\) \(1\) \(e\left(\frac{56}{57}\right)\) \(e\left(\frac{137}{285}\right)\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{244}{285}\right)\) \(e\left(\frac{44}{95}\right)\) \(e\left(\frac{4}{95}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{274}{285}\right)\) \(e\left(\frac{239}{285}\right)\) \(e\left(\frac{236}{285}\right)\)
\(\chi_{571}(30,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{57}\right)\) \(e\left(\frac{199}{285}\right)\) \(e\left(\frac{5}{57}\right)\) \(e\left(\frac{188}{285}\right)\) \(e\left(\frac{23}{95}\right)\) \(e\left(\frac{28}{95}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{113}{285}\right)\) \(e\left(\frac{58}{285}\right)\) \(e\left(\frac{37}{285}\right)\)
\(\chi_{571}(34,\cdot)\) \(1\) \(1\) \(e\left(\frac{56}{57}\right)\) \(e\left(\frac{194}{285}\right)\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{73}{285}\right)\) \(e\left(\frac{63}{95}\right)\) \(e\left(\frac{23}{95}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{103}{285}\right)\) \(e\left(\frac{68}{285}\right)\) \(e\left(\frac{122}{285}\right)\)
\(\chi_{571}(37,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{166}{285}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{227}{285}\right)\) \(e\left(\frac{2}{95}\right)\) \(e\left(\frac{52}{95}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{47}{285}\right)\) \(e\left(\frac{67}{285}\right)\) \(e\left(\frac{28}{285}\right)\)
\(\chi_{571}(43,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{57}\right)\) \(e\left(\frac{227}{285}\right)\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{34}{285}\right)\) \(e\left(\frac{84}{95}\right)\) \(e\left(\frac{94}{95}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{169}{285}\right)\) \(e\left(\frac{59}{285}\right)\) \(e\left(\frac{131}{285}\right)\)
\(\chi_{571}(44,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{109}{285}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{113}{285}\right)\) \(e\left(\frac{78}{95}\right)\) \(e\left(\frac{33}{95}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{218}{285}\right)\) \(e\left(\frac{238}{285}\right)\) \(e\left(\frac{142}{285}\right)\)
\(\chi_{571}(45,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{212}{285}\right)\) \(e\left(\frac{46}{57}\right)\) \(e\left(\frac{259}{285}\right)\) \(e\left(\frac{14}{95}\right)\) \(e\left(\frac{79}{95}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{139}{285}\right)\) \(e\left(\frac{89}{285}\right)\) \(e\left(\frac{101}{285}\right)\)
\(\chi_{571}(52,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{151}{285}\right)\) \(e\left(\frac{29}{57}\right)\) \(e\left(\frac{167}{285}\right)\) \(e\left(\frac{27}{95}\right)\) \(e\left(\frac{37}{95}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{17}{285}\right)\) \(e\left(\frac{97}{285}\right)\) \(e\left(\frac{283}{285}\right)\)
\(\chi_{571}(54,\cdot)\) \(1\) \(1\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{274}{285}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{203}{285}\right)\) \(e\left(\frac{88}{95}\right)\) \(e\left(\frac{8}{95}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{263}{285}\right)\) \(e\left(\frac{193}{285}\right)\) \(e\left(\frac{187}{285}\right)\)
\(\chi_{571}(57,\cdot)\) \(1\) \(1\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{229}{285}\right)\) \(e\left(\frac{47}{57}\right)\) \(e\left(\frac{23}{285}\right)\) \(e\left(\frac{68}{95}\right)\) \(e\left(\frac{58}{95}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{173}{285}\right)\) \(e\left(\frac{283}{285}\right)\) \(e\left(\frac{97}{285}\right)\)
\(\chi_{571}(61,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{263}{285}\right)\) \(e\left(\frac{49}{57}\right)\) \(e\left(\frac{121}{285}\right)\) \(e\left(\frac{81}{95}\right)\) \(e\left(\frac{16}{95}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{241}{285}\right)\) \(e\left(\frac{101}{285}\right)\) \(e\left(\frac{89}{285}\right)\)
\(\chi_{571}(66,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{122}{285}\right)\) \(e\left(\frac{34}{57}\right)\) \(e\left(\frac{184}{285}\right)\) \(e\left(\frac{69}{95}\right)\) \(e\left(\frac{84}{95}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{244}{285}\right)\) \(e\left(\frac{269}{285}\right)\) \(e\left(\frac{206}{285}\right)\)
\(\chi_{571}(70,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{57}\right)\) \(e\left(\frac{29}{285}\right)\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{268}{285}\right)\) \(e\left(\frac{53}{95}\right)\) \(e\left(\frac{48}{95}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{58}{285}\right)\) \(e\left(\frac{113}{285}\right)\) \(e\left(\frac{77}{285}\right)\)
\(\chi_{571}(78,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{57}\right)\) \(e\left(\frac{164}{285}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{238}{285}\right)\) \(e\left(\frac{18}{95}\right)\) \(e\left(\frac{88}{95}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{43}{285}\right)\) \(e\left(\frac{128}{285}\right)\) \(e\left(\frac{62}{285}\right)\)
\(\chi_{571}(80,\cdot)\) \(1\) \(1\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{161}{285}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{112}{285}\right)\) \(e\left(\frac{42}{95}\right)\) \(e\left(\frac{47}{95}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{37}{285}\right)\) \(e\left(\frac{77}{285}\right)\) \(e\left(\frac{113}{285}\right)\)
\(\chi_{571}(81,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{57}\right)\) \(e\left(\frac{2}{285}\right)\) \(e\left(\frac{37}{57}\right)\) \(e\left(\frac{274}{285}\right)\) \(e\left(\frac{79}{95}\right)\) \(e\left(\frac{59}{95}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{4}{285}\right)\) \(e\left(\frac{224}{285}\right)\) \(e\left(\frac{251}{285}\right)\)
\(\chi_{571}(83,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{57}\right)\) \(e\left(\frac{83}{285}\right)\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{256}{285}\right)\) \(e\left(\frac{1}{95}\right)\) \(e\left(\frac{26}{95}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{166}{285}\right)\) \(e\left(\frac{176}{285}\right)\) \(e\left(\frac{14}{285}\right)\)
\(\chi_{571}(84,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{91}{285}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{212}{285}\right)\) \(e\left(\frac{32}{95}\right)\) \(e\left(\frac{72}{95}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{182}{285}\right)\) \(e\left(\frac{217}{285}\right)\) \(e\left(\frac{163}{285}\right)\)
\(\chi_{571}(92,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{98}{285}\right)\) \(e\left(\frac{46}{57}\right)\) \(e\left(\frac{31}{285}\right)\) \(e\left(\frac{71}{95}\right)\) \(e\left(\frac{41}{95}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{196}{285}\right)\) \(e\left(\frac{146}{285}\right)\) \(e\left(\frac{44}{285}\right)\)
\(\chi_{571}(96,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{223}{285}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{56}{285}\right)\) \(e\left(\frac{21}{95}\right)\) \(e\left(\frac{71}{95}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{161}{285}\right)\) \(e\left(\frac{181}{285}\right)\) \(e\left(\frac{199}{285}\right)\)
\(\chi_{571}(97,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{57}\right)\) \(e\left(\frac{146}{285}\right)\) \(e\left(\frac{22}{57}\right)\) \(e\left(\frac{52}{285}\right)\) \(e\left(\frac{67}{95}\right)\) \(e\left(\frac{32}{95}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{7}{285}\right)\) \(e\left(\frac{107}{285}\right)\) \(e\left(\frac{83}{285}\right)\)
\(\chi_{571}(100,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{112}{285}\right)\) \(e\left(\frac{20}{57}\right)\) \(e\left(\frac{239}{285}\right)\) \(e\left(\frac{54}{95}\right)\) \(e\left(\frac{74}{95}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{224}{285}\right)\) \(e\left(\frac{4}{285}\right)\) \(e\left(\frac{91}{285}\right)\)
\(\chi_{571}(115,\cdot)\) \(1\) \(1\) \(e\left(\frac{40}{57}\right)\) \(e\left(\frac{49}{285}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{158}{285}\right)\) \(e\left(\frac{83}{95}\right)\) \(e\left(\frac{68}{95}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{98}{285}\right)\) \(e\left(\frac{73}{285}\right)\) \(e\left(\frac{22}{285}\right)\)
\(\chi_{571}(119,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{37}{285}\right)\) \(e\left(\frac{29}{57}\right)\) \(e\left(\frac{224}{285}\right)\) \(e\left(\frac{84}{95}\right)\) \(e\left(\frac{94}{95}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{74}{285}\right)\) \(e\left(\frac{154}{285}\right)\) \(e\left(\frac{226}{285}\right)\)