Properties

Label 571.p
Modulus $571$
Conductor $571$
Order $570$
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(570))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([1]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(3,571))
 
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: \(570\)
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: $\Q(\zeta_{285})$
Fixed field: Number field defined by a degree 570 polynomial (not computed)

First 31 of 144 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{571}(3,\cdot)\) \(-1\) \(1\) \(e\left(\frac{109}{114}\right)\) \(e\left(\frac{1}{570}\right)\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{211}{285}\right)\) \(e\left(\frac{91}{95}\right)\) \(e\left(\frac{77}{190}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{1}{285}\right)\) \(e\left(\frac{397}{570}\right)\) \(e\left(\frac{134}{285}\right)\)
\(\chi_{571}(10,\cdot)\) \(-1\) \(1\) \(e\left(\frac{67}{114}\right)\) \(e\left(\frac{397}{570}\right)\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{262}{285}\right)\) \(e\left(\frac{27}{95}\right)\) \(e\left(\frac{169}{190}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{112}{285}\right)\) \(e\left(\frac{289}{570}\right)\) \(e\left(\frac{188}{285}\right)\)
\(\chi_{571}(12,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{114}\right)\) \(e\left(\frac{521}{570}\right)\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{206}{285}\right)\) \(e\left(\frac{6}{95}\right)\) \(e\left(\frac{27}{190}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{236}{285}\right)\) \(e\left(\frac{497}{570}\right)\) \(e\left(\frac{274}{285}\right)\)
\(\chi_{571}(17,\cdot)\) \(-1\) \(1\) \(e\left(\frac{101}{114}\right)\) \(e\left(\frac{413}{570}\right)\) \(e\left(\frac{44}{57}\right)\) \(e\left(\frac{218}{285}\right)\) \(e\left(\frac{58}{95}\right)\) \(e\left(\frac{71}{190}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{128}{285}\right)\) \(e\left(\frac{371}{570}\right)\) \(e\left(\frac{52}{285}\right)\)
\(\chi_{571}(18,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{114}\right)\) \(e\left(\frac{547}{570}\right)\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{277}{285}\right)\) \(e\left(\frac{92}{95}\right)\) \(e\left(\frac{129}{190}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{262}{285}\right)\) \(e\left(\frac{559}{570}\right)\) \(e\left(\frac{53}{285}\right)\)
\(\chi_{571}(19,\cdot)\) \(-1\) \(1\) \(e\left(\frac{109}{114}\right)\) \(e\left(\frac{457}{570}\right)\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{97}{285}\right)\) \(e\left(\frac{72}{95}\right)\) \(e\left(\frac{39}{190}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{172}{285}\right)\) \(e\left(\frac{169}{570}\right)\) \(e\left(\frac{248}{285}\right)\)
\(\chi_{571}(28,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{114}\right)\) \(e\left(\frac{181}{570}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{1}{285}\right)\) \(e\left(\frac{36}{95}\right)\) \(e\left(\frac{67}{190}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{181}{285}\right)\) \(e\left(\frac{37}{570}\right)\) \(e\left(\frac{29}{285}\right)\)
\(\chi_{571}(33,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{114}\right)\) \(e\left(\frac{269}{570}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{44}{285}\right)\) \(e\left(\frac{64}{95}\right)\) \(e\left(\frac{3}{190}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{269}{285}\right)\) \(e\left(\frac{203}{570}\right)\) \(e\left(\frac{136}{285}\right)\)
\(\chi_{571}(35,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{114}\right)\) \(e\left(\frac{83}{570}\right)\) \(e\left(\frac{41}{57}\right)\) \(e\left(\frac{128}{285}\right)\) \(e\left(\frac{48}{95}\right)\) \(e\left(\frac{121}{190}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{83}{285}\right)\) \(e\left(\frac{461}{570}\right)\) \(e\left(\frac{7}{285}\right)\)
\(\chi_{571}(39,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{114}\right)\) \(e\left(\frac{353}{570}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{98}{285}\right)\) \(e\left(\frac{13}{95}\right)\) \(e\left(\frac{11}{190}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{68}{285}\right)\) \(e\left(\frac{491}{570}\right)\) \(e\left(\frac{277}{285}\right)\)
\(\chi_{571}(40,\cdot)\) \(-1\) \(1\) \(e\left(\frac{89}{114}\right)\) \(e\left(\frac{347}{570}\right)\) \(e\left(\frac{32}{57}\right)\) \(e\left(\frac{257}{285}\right)\) \(e\left(\frac{37}{95}\right)\) \(e\left(\frac{119}{190}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{62}{285}\right)\) \(e\left(\frac{389}{570}\right)\) \(e\left(\frac{43}{285}\right)\)
\(\chi_{571}(46,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{114}\right)\) \(e\left(\frac{221}{570}\right)\) \(e\left(\frac{35}{57}\right)\) \(e\left(\frac{176}{285}\right)\) \(e\left(\frac{66}{95}\right)\) \(e\left(\frac{107}{190}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{221}{285}\right)\) \(e\left(\frac{527}{570}\right)\) \(e\left(\frac{259}{285}\right)\)
\(\chi_{571}(53,\cdot)\) \(-1\) \(1\) \(e\left(\frac{103}{114}\right)\) \(e\left(\frac{253}{570}\right)\) \(e\left(\frac{46}{57}\right)\) \(e\left(\frac{88}{285}\right)\) \(e\left(\frac{33}{95}\right)\) \(e\left(\frac{101}{190}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{253}{285}\right)\) \(e\left(\frac{121}{570}\right)\) \(e\left(\frac{272}{285}\right)\)
\(\chi_{571}(60,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{114}\right)\) \(e\left(\frac{373}{570}\right)\) \(e\left(\frac{16}{57}\right)\) \(e\left(\frac{43}{285}\right)\) \(e\left(\frac{28}{95}\right)\) \(e\left(\frac{31}{190}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{88}{285}\right)\) \(e\left(\frac{451}{570}\right)\) \(e\left(\frac{107}{285}\right)\)
\(\chi_{571}(63,\cdot)\) \(-1\) \(1\) \(e\left(\frac{89}{114}\right)\) \(e\left(\frac{233}{570}\right)\) \(e\left(\frac{32}{57}\right)\) \(e\left(\frac{143}{285}\right)\) \(e\left(\frac{18}{95}\right)\) \(e\left(\frac{81}{190}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{233}{285}\right)\) \(e\left(\frac{161}{570}\right)\) \(e\left(\frac{157}{285}\right)\)
\(\chi_{571}(67,\cdot)\) \(-1\) \(1\) \(e\left(\frac{65}{114}\right)\) \(e\left(\frac{443}{570}\right)\) \(e\left(\frac{8}{57}\right)\) \(e\left(\frac{278}{285}\right)\) \(e\left(\frac{33}{95}\right)\) \(e\left(\frac{101}{190}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{158}{285}\right)\) \(e\left(\frac{311}{570}\right)\) \(e\left(\frac{82}{285}\right)\)
\(\chi_{571}(72,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{114}\right)\) \(e\left(\frac{497}{570}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{272}{285}\right)\) \(e\left(\frac{7}{95}\right)\) \(e\left(\frac{79}{190}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{212}{285}\right)\) \(e\left(\frac{89}{570}\right)\) \(e\left(\frac{193}{285}\right)\)
\(\chi_{571}(73,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{114}\right)\) \(e\left(\frac{427}{570}\right)\) \(e\left(\frac{31}{57}\right)\) \(e\left(\frac{37}{285}\right)\) \(e\left(\frac{2}{95}\right)\) \(e\left(\frac{9}{190}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{142}{285}\right)\) \(e\left(\frac{229}{570}\right)\) \(e\left(\frac{218}{285}\right)\)
\(\chi_{571}(74,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{114}\right)\) \(e\left(\frac{307}{570}\right)\) \(e\left(\frac{4}{57}\right)\) \(e\left(\frac{82}{285}\right)\) \(e\left(\frac{7}{95}\right)\) \(e\left(\frac{79}{190}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{22}{285}\right)\) \(e\left(\frac{469}{570}\right)\) \(e\left(\frac{98}{285}\right)\)
\(\chi_{571}(76,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{114}\right)\) \(e\left(\frac{407}{570}\right)\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{92}{285}\right)\) \(e\left(\frac{82}{95}\right)\) \(e\left(\frac{179}{190}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{122}{285}\right)\) \(e\left(\frac{269}{570}\right)\) \(e\left(\frac{103}{285}\right)\)
\(\chi_{571}(77,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{114}\right)\) \(e\left(\frac{499}{570}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{124}{285}\right)\) \(e\left(\frac{94}{95}\right)\) \(e\left(\frac{43}{190}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{214}{285}\right)\) \(e\left(\frac{313}{570}\right)\) \(e\left(\frac{176}{285}\right)\)
\(\chi_{571}(79,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{114}\right)\) \(e\left(\frac{31}{570}\right)\) \(e\left(\frac{16}{57}\right)\) \(e\left(\frac{271}{285}\right)\) \(e\left(\frac{66}{95}\right)\) \(e\left(\frac{107}{190}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{31}{285}\right)\) \(e\left(\frac{337}{570}\right)\) \(e\left(\frac{164}{285}\right)\)
\(\chi_{571}(88,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{114}\right)\) \(e\left(\frac{193}{570}\right)\) \(e\left(\frac{4}{57}\right)\) \(e\left(\frac{253}{285}\right)\) \(e\left(\frac{83}{95}\right)\) \(e\left(\frac{41}{190}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{193}{285}\right)\) \(e\left(\frac{241}{570}\right)\) \(e\left(\frac{212}{285}\right)\)
\(\chi_{571}(89,\cdot)\) \(-1\) \(1\) \(e\left(\frac{101}{114}\right)\) \(e\left(\frac{71}{570}\right)\) \(e\left(\frac{44}{57}\right)\) \(e\left(\frac{161}{285}\right)\) \(e\left(\frac{1}{95}\right)\) \(e\left(\frac{147}{190}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{71}{285}\right)\) \(e\left(\frac{257}{570}\right)\) \(e\left(\frac{109}{285}\right)\)
\(\chi_{571}(91,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{114}\right)\) \(e\left(\frac{13}{570}\right)\) \(e\left(\frac{49}{57}\right)\) \(e\left(\frac{178}{285}\right)\) \(e\left(\frac{43}{95}\right)\) \(e\left(\frac{51}{190}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{13}{285}\right)\) \(e\left(\frac{31}{570}\right)\) \(e\left(\frac{32}{285}\right)\)
\(\chi_{571}(93,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{114}\right)\) \(e\left(\frac{91}{570}\right)\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{106}{285}\right)\) \(e\left(\frac{16}{95}\right)\) \(e\left(\frac{167}{190}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{91}{285}\right)\) \(e\left(\frac{217}{570}\right)\) \(e\left(\frac{224}{285}\right)\)
\(\chi_{571}(101,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{114}\right)\) \(e\left(\frac{107}{570}\right)\) \(e\left(\frac{35}{57}\right)\) \(e\left(\frac{62}{285}\right)\) \(e\left(\frac{47}{95}\right)\) \(e\left(\frac{69}{190}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{107}{285}\right)\) \(e\left(\frac{299}{570}\right)\) \(e\left(\frac{88}{285}\right)\)
\(\chi_{571}(102,\cdot)\) \(-1\) \(1\) \(e\left(\frac{107}{114}\right)\) \(e\left(\frac{389}{570}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{284}{285}\right)\) \(e\left(\frac{59}{95}\right)\) \(e\left(\frac{123}{190}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{104}{285}\right)\) \(e\left(\frac{533}{570}\right)\) \(e\left(\frac{256}{285}\right)\)
\(\chi_{571}(104,\cdot)\) \(-1\) \(1\) \(e\left(\frac{97}{114}\right)\) \(e\left(\frac{277}{570}\right)\) \(e\left(\frac{40}{57}\right)\) \(e\left(\frac{22}{285}\right)\) \(e\left(\frac{32}{95}\right)\) \(e\left(\frac{49}{190}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{277}{285}\right)\) \(e\left(\frac{529}{570}\right)\) \(e\left(\frac{68}{285}\right)\)
\(\chi_{571}(108,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{114}\right)\) \(e\left(\frac{523}{570}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{58}{285}\right)\) \(e\left(\frac{93}{95}\right)\) \(e\left(\frac{181}{190}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{238}{285}\right)\) \(e\left(\frac{151}{570}\right)\) \(e\left(\frac{257}{285}\right)\)
\(\chi_{571}(112,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{114}\right)\) \(e\left(\frac{131}{570}\right)\) \(e\left(\frac{29}{57}\right)\) \(e\left(\frac{281}{285}\right)\) \(e\left(\frac{46}{95}\right)\) \(e\left(\frac{17}{190}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{131}{285}\right)\) \(e\left(\frac{137}{570}\right)\) \(e\left(\frac{169}{285}\right)\)