Properties

Label 2001.bv
Modulus $2001$
Conductor $2001$
Order $308$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2001, base_ring=CyclotomicField(308))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([154,28,11]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(2,2001))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2001\)
Conductor: \(2001\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(308\)
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: $\Q(\zeta_{308})$
Fixed field: Number field defined by a degree 308 polynomial (not computed)

First 31 of 120 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{2001}(2,\cdot)\) \(1\) \(1\) \(e\left(\frac{221}{308}\right)\) \(e\left(\frac{67}{154}\right)\) \(e\left(\frac{29}{77}\right)\) \(e\left(\frac{12}{77}\right)\) \(e\left(\frac{47}{308}\right)\) \(e\left(\frac{29}{308}\right)\) \(e\left(\frac{65}{308}\right)\) \(e\left(\frac{141}{154}\right)\) \(e\left(\frac{269}{308}\right)\) \(e\left(\frac{67}{77}\right)\)
\(\chi_{2001}(8,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{308}\right)\) \(e\left(\frac{47}{154}\right)\) \(e\left(\frac{10}{77}\right)\) \(e\left(\frac{36}{77}\right)\) \(e\left(\frac{141}{308}\right)\) \(e\left(\frac{87}{308}\right)\) \(e\left(\frac{195}{308}\right)\) \(e\left(\frac{115}{154}\right)\) \(e\left(\frac{191}{308}\right)\) \(e\left(\frac{47}{77}\right)\)
\(\chi_{2001}(26,\cdot)\) \(1\) \(1\) \(e\left(\frac{195}{308}\right)\) \(e\left(\frac{41}{154}\right)\) \(e\left(\frac{12}{77}\right)\) \(e\left(\frac{74}{77}\right)\) \(e\left(\frac{277}{308}\right)\) \(e\left(\frac{243}{308}\right)\) \(e\left(\frac{3}{308}\right)\) \(e\left(\frac{61}{154}\right)\) \(e\left(\frac{183}{308}\right)\) \(e\left(\frac{41}{77}\right)\)
\(\chi_{2001}(32,\cdot)\) \(1\) \(1\) \(e\left(\frac{181}{308}\right)\) \(e\left(\frac{27}{154}\right)\) \(e\left(\frac{68}{77}\right)\) \(e\left(\frac{60}{77}\right)\) \(e\left(\frac{235}{308}\right)\) \(e\left(\frac{145}{308}\right)\) \(e\left(\frac{17}{308}\right)\) \(e\left(\frac{89}{154}\right)\) \(e\left(\frac{113}{308}\right)\) \(e\left(\frac{27}{77}\right)\)
\(\chi_{2001}(50,\cdot)\) \(1\) \(1\) \(e\left(\frac{145}{308}\right)\) \(e\left(\frac{145}{154}\right)\) \(e\left(\frac{3}{77}\right)\) \(e\left(\frac{57}{77}\right)\) \(e\left(\frac{127}{308}\right)\) \(e\left(\frac{157}{308}\right)\) \(e\left(\frac{97}{308}\right)\) \(e\left(\frac{73}{154}\right)\) \(e\left(\frac{65}{308}\right)\) \(e\left(\frac{68}{77}\right)\)
\(\chi_{2001}(77,\cdot)\) \(1\) \(1\) \(e\left(\frac{113}{308}\right)\) \(e\left(\frac{113}{154}\right)\) \(e\left(\frac{65}{77}\right)\) \(e\left(\frac{3}{77}\right)\) \(e\left(\frac{31}{308}\right)\) \(e\left(\frac{65}{308}\right)\) \(e\left(\frac{305}{308}\right)\) \(e\left(\frac{93}{154}\right)\) \(e\left(\frac{125}{308}\right)\) \(e\left(\frac{36}{77}\right)\)
\(\chi_{2001}(95,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{308}\right)\) \(e\left(\frac{19}{154}\right)\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{8}{77}\right)\) \(e\left(\frac{57}{308}\right)\) \(e\left(\frac{199}{308}\right)\) \(e\left(\frac{223}{308}\right)\) \(e\left(\frac{17}{154}\right)\) \(e\left(\frac{51}{308}\right)\) \(e\left(\frac{19}{77}\right)\)
\(\chi_{2001}(98,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{308}\right)\) \(e\left(\frac{9}{154}\right)\) \(e\left(\frac{74}{77}\right)\) \(e\left(\frac{20}{77}\right)\) \(e\left(\frac{27}{308}\right)\) \(e\left(\frac{305}{308}\right)\) \(e\left(\frac{57}{308}\right)\) \(e\left(\frac{81}{154}\right)\) \(e\left(\frac{89}{308}\right)\) \(e\left(\frac{9}{77}\right)\)
\(\chi_{2001}(101,\cdot)\) \(1\) \(1\) \(e\left(\frac{269}{308}\right)\) \(e\left(\frac{115}{154}\right)\) \(e\left(\frac{13}{77}\right)\) \(e\left(\frac{16}{77}\right)\) \(e\left(\frac{191}{308}\right)\) \(e\left(\frac{13}{308}\right)\) \(e\left(\frac{61}{308}\right)\) \(e\left(\frac{111}{154}\right)\) \(e\left(\frac{25}{308}\right)\) \(e\left(\frac{38}{77}\right)\)
\(\chi_{2001}(119,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{308}\right)\) \(e\left(\frac{13}{154}\right)\) \(e\left(\frac{47}{77}\right)\) \(e\left(\frac{46}{77}\right)\) \(e\left(\frac{39}{308}\right)\) \(e\left(\frac{201}{308}\right)\) \(e\left(\frac{185}{308}\right)\) \(e\left(\frac{117}{154}\right)\) \(e\left(\frac{197}{308}\right)\) \(e\left(\frac{13}{77}\right)\)
\(\chi_{2001}(131,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{308}\right)\) \(e\left(\frac{59}{154}\right)\) \(e\left(\frac{6}{77}\right)\) \(e\left(\frac{37}{77}\right)\) \(e\left(\frac{177}{308}\right)\) \(e\left(\frac{83}{308}\right)\) \(e\left(\frac{271}{308}\right)\) \(e\left(\frac{69}{154}\right)\) \(e\left(\frac{207}{308}\right)\) \(e\left(\frac{59}{77}\right)\)
\(\chi_{2001}(164,\cdot)\) \(1\) \(1\) \(e\left(\frac{85}{308}\right)\) \(e\left(\frac{85}{154}\right)\) \(e\left(\frac{23}{77}\right)\) \(e\left(\frac{52}{77}\right)\) \(e\left(\frac{255}{308}\right)\) \(e\left(\frac{177}{308}\right)\) \(e\left(\frac{25}{308}\right)\) \(e\left(\frac{149}{154}\right)\) \(e\left(\frac{293}{308}\right)\) \(e\left(\frac{8}{77}\right)\)
\(\chi_{2001}(188,\cdot)\) \(1\) \(1\) \(e\left(\frac{101}{308}\right)\) \(e\left(\frac{101}{154}\right)\) \(e\left(\frac{69}{77}\right)\) \(e\left(\frac{2}{77}\right)\) \(e\left(\frac{303}{308}\right)\) \(e\left(\frac{69}{308}\right)\) \(e\left(\frac{229}{308}\right)\) \(e\left(\frac{139}{154}\right)\) \(e\left(\frac{109}{308}\right)\) \(e\left(\frac{24}{77}\right)\)
\(\chi_{2001}(200,\cdot)\) \(1\) \(1\) \(e\left(\frac{279}{308}\right)\) \(e\left(\frac{125}{154}\right)\) \(e\left(\frac{61}{77}\right)\) \(e\left(\frac{4}{77}\right)\) \(e\left(\frac{221}{308}\right)\) \(e\left(\frac{215}{308}\right)\) \(e\left(\frac{227}{308}\right)\) \(e\left(\frac{47}{154}\right)\) \(e\left(\frac{295}{308}\right)\) \(e\left(\frac{48}{77}\right)\)
\(\chi_{2001}(242,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{308}\right)\) \(e\left(\frac{43}{154}\right)\) \(e\left(\frac{37}{77}\right)\) \(e\left(\frac{10}{77}\right)\) \(e\left(\frac{129}{308}\right)\) \(e\left(\frac{191}{308}\right)\) \(e\left(\frac{67}{308}\right)\) \(e\left(\frac{79}{154}\right)\) \(e\left(\frac{83}{308}\right)\) \(e\left(\frac{43}{77}\right)\)
\(\chi_{2001}(269,\cdot)\) \(1\) \(1\) \(e\left(\frac{103}{308}\right)\) \(e\left(\frac{103}{154}\right)\) \(e\left(\frac{17}{77}\right)\) \(e\left(\frac{15}{77}\right)\) \(e\left(\frac{1}{308}\right)\) \(e\left(\frac{171}{308}\right)\) \(e\left(\frac{139}{308}\right)\) \(e\left(\frac{3}{154}\right)\) \(e\left(\frac{163}{308}\right)\) \(e\left(\frac{26}{77}\right)\)
\(\chi_{2001}(305,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{308}\right)\) \(e\left(\frac{31}{154}\right)\) \(e\left(\frac{41}{77}\right)\) \(e\left(\frac{9}{77}\right)\) \(e\left(\frac{93}{308}\right)\) \(e\left(\frac{195}{308}\right)\) \(e\left(\frac{299}{308}\right)\) \(e\left(\frac{125}{154}\right)\) \(e\left(\frac{67}{308}\right)\) \(e\left(\frac{31}{77}\right)\)
\(\chi_{2001}(308,\cdot)\) \(1\) \(1\) \(e\left(\frac{247}{308}\right)\) \(e\left(\frac{93}{154}\right)\) \(e\left(\frac{46}{77}\right)\) \(e\left(\frac{27}{77}\right)\) \(e\left(\frac{125}{308}\right)\) \(e\left(\frac{123}{308}\right)\) \(e\left(\frac{127}{308}\right)\) \(e\left(\frac{67}{154}\right)\) \(e\left(\frac{47}{308}\right)\) \(e\left(\frac{16}{77}\right)\)
\(\chi_{2001}(311,\cdot)\) \(1\) \(1\) \(e\left(\frac{285}{308}\right)\) \(e\left(\frac{131}{154}\right)\) \(e\left(\frac{59}{77}\right)\) \(e\left(\frac{43}{77}\right)\) \(e\left(\frac{239}{308}\right)\) \(e\left(\frac{213}{308}\right)\) \(e\left(\frac{265}{308}\right)\) \(e\left(\frac{101}{154}\right)\) \(e\left(\frac{149}{308}\right)\) \(e\left(\frac{54}{77}\right)\)
\(\chi_{2001}(317,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{308}\right)\) \(e\left(\frac{39}{154}\right)\) \(e\left(\frac{64}{77}\right)\) \(e\left(\frac{61}{77}\right)\) \(e\left(\frac{117}{308}\right)\) \(e\left(\frac{295}{308}\right)\) \(e\left(\frac{247}{308}\right)\) \(e\left(\frac{43}{154}\right)\) \(e\left(\frac{283}{308}\right)\) \(e\left(\frac{39}{77}\right)\)
\(\chi_{2001}(338,\cdot)\) \(1\) \(1\) \(e\left(\frac{169}{308}\right)\) \(e\left(\frac{15}{154}\right)\) \(e\left(\frac{72}{77}\right)\) \(e\left(\frac{59}{77}\right)\) \(e\left(\frac{199}{308}\right)\) \(e\left(\frac{149}{308}\right)\) \(e\left(\frac{249}{308}\right)\) \(e\left(\frac{135}{154}\right)\) \(e\left(\frac{97}{308}\right)\) \(e\left(\frac{15}{77}\right)\)
\(\chi_{2001}(374,\cdot)\) \(1\) \(1\) \(e\left(\frac{251}{308}\right)\) \(e\left(\frac{97}{154}\right)\) \(e\left(\frac{19}{77}\right)\) \(e\left(\frac{53}{77}\right)\) \(e\left(\frac{137}{308}\right)\) \(e\left(\frac{19}{308}\right)\) \(e\left(\frac{255}{308}\right)\) \(e\left(\frac{103}{154}\right)\) \(e\left(\frac{155}{308}\right)\) \(e\left(\frac{20}{77}\right)\)
\(\chi_{2001}(380,\cdot)\) \(1\) \(1\) \(e\left(\frac{153}{308}\right)\) \(e\left(\frac{153}{154}\right)\) \(e\left(\frac{26}{77}\right)\) \(e\left(\frac{32}{77}\right)\) \(e\left(\frac{151}{308}\right)\) \(e\left(\frac{257}{308}\right)\) \(e\left(\frac{45}{308}\right)\) \(e\left(\frac{145}{154}\right)\) \(e\left(\frac{281}{308}\right)\) \(e\left(\frac{76}{77}\right)\)
\(\chi_{2001}(395,\cdot)\) \(1\) \(1\) \(e\left(\frac{79}{308}\right)\) \(e\left(\frac{79}{154}\right)\) \(e\left(\frac{25}{77}\right)\) \(e\left(\frac{13}{77}\right)\) \(e\left(\frac{237}{308}\right)\) \(e\left(\frac{179}{308}\right)\) \(e\left(\frac{295}{308}\right)\) \(e\left(\frac{95}{154}\right)\) \(e\left(\frac{131}{308}\right)\) \(e\left(\frac{2}{77}\right)\)
\(\chi_{2001}(404,\cdot)\) \(1\) \(1\) \(e\left(\frac{95}{308}\right)\) \(e\left(\frac{95}{154}\right)\) \(e\left(\frac{71}{77}\right)\) \(e\left(\frac{40}{77}\right)\) \(e\left(\frac{285}{308}\right)\) \(e\left(\frac{71}{308}\right)\) \(e\left(\frac{191}{308}\right)\) \(e\left(\frac{85}{154}\right)\) \(e\left(\frac{255}{308}\right)\) \(e\left(\frac{18}{77}\right)\)
\(\chi_{2001}(416,\cdot)\) \(1\) \(1\) \(e\left(\frac{155}{308}\right)\) \(e\left(\frac{1}{154}\right)\) \(e\left(\frac{51}{77}\right)\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{157}{308}\right)\) \(e\left(\frac{51}{308}\right)\) \(e\left(\frac{263}{308}\right)\) \(e\left(\frac{9}{154}\right)\) \(e\left(\frac{27}{308}\right)\) \(e\left(\frac{1}{77}\right)\)
\(\chi_{2001}(443,\cdot)\) \(1\) \(1\) \(e\left(\frac{75}{308}\right)\) \(e\left(\frac{75}{154}\right)\) \(e\left(\frac{52}{77}\right)\) \(e\left(\frac{64}{77}\right)\) \(e\left(\frac{225}{308}\right)\) \(e\left(\frac{283}{308}\right)\) \(e\left(\frac{167}{308}\right)\) \(e\left(\frac{59}{154}\right)\) \(e\left(\frac{23}{308}\right)\) \(e\left(\frac{75}{77}\right)\)
\(\chi_{2001}(446,\cdot)\) \(1\) \(1\) \(e\left(\frac{93}{308}\right)\) \(e\left(\frac{93}{154}\right)\) \(e\left(\frac{46}{77}\right)\) \(e\left(\frac{27}{77}\right)\) \(e\left(\frac{279}{308}\right)\) \(e\left(\frac{277}{308}\right)\) \(e\left(\frac{281}{308}\right)\) \(e\left(\frac{67}{154}\right)\) \(e\left(\frac{201}{308}\right)\) \(e\left(\frac{16}{77}\right)\)
\(\chi_{2001}(449,\cdot)\) \(1\) \(1\) \(e\left(\frac{241}{308}\right)\) \(e\left(\frac{87}{154}\right)\) \(e\left(\frac{48}{77}\right)\) \(e\left(\frac{65}{77}\right)\) \(e\left(\frac{107}{308}\right)\) \(e\left(\frac{125}{308}\right)\) \(e\left(\frac{89}{308}\right)\) \(e\left(\frac{13}{154}\right)\) \(e\left(\frac{193}{308}\right)\) \(e\left(\frac{10}{77}\right)\)
\(\chi_{2001}(485,\cdot)\) \(1\) \(1\) \(e\left(\frac{89}{308}\right)\) \(e\left(\frac{89}{154}\right)\) \(e\left(\frac{73}{77}\right)\) \(e\left(\frac{1}{77}\right)\) \(e\left(\frac{267}{308}\right)\) \(e\left(\frac{73}{308}\right)\) \(e\left(\frac{153}{308}\right)\) \(e\left(\frac{31}{154}\right)\) \(e\left(\frac{93}{308}\right)\) \(e\left(\frac{12}{77}\right)\)
\(\chi_{2001}(491,\cdot)\) \(1\) \(1\) \(e\left(\frac{179}{308}\right)\) \(e\left(\frac{25}{154}\right)\) \(e\left(\frac{43}{77}\right)\) \(e\left(\frac{47}{77}\right)\) \(e\left(\frac{229}{308}\right)\) \(e\left(\frac{43}{308}\right)\) \(e\left(\frac{107}{308}\right)\) \(e\left(\frac{71}{154}\right)\) \(e\left(\frac{59}{308}\right)\) \(e\left(\frac{25}{77}\right)\)