Properties

Label 2601.y
Modulus $2601$
Conductor $2601$
Order $51$
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(2601, base_ring=CyclotomicField(102))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([68,12]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(52,2601))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2601\)
Conductor: \(2601\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(51\)
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: $\Q(\zeta_{51})$
Fixed field: Number field defined by a degree 51 polynomial

First 31 of 32 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{2601}(52,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{4}{51}\right)\)
\(\chi_{2601}(103,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{8}{51}\right)\)
\(\chi_{2601}(205,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{16}{51}\right)\)
\(\chi_{2601}(256,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{20}{51}\right)\)
\(\chi_{2601}(358,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{28}{51}\right)\)
\(\chi_{2601}(409,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{32}{51}\right)\)
\(\chi_{2601}(511,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{40}{51}\right)\)
\(\chi_{2601}(562,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{44}{51}\right)\)
\(\chi_{2601}(664,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{1}{51}\right)\)
\(\chi_{2601}(715,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{5}{51}\right)\)
\(\chi_{2601}(817,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{13}{51}\right)\)
\(\chi_{2601}(970,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{25}{51}\right)\)
\(\chi_{2601}(1021,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{29}{51}\right)\)
\(\chi_{2601}(1123,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{37}{51}\right)\)
\(\chi_{2601}(1174,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{41}{51}\right)\)
\(\chi_{2601}(1276,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{49}{51}\right)\)
\(\chi_{2601}(1327,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{2}{51}\right)\)
\(\chi_{2601}(1429,\cdot)\) \(1\) \(1\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{10}{51}\right)\)
\(\chi_{2601}(1480,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{14}{51}\right)\)
\(\chi_{2601}(1582,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{22}{51}\right)\)
\(\chi_{2601}(1633,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{26}{51}\right)\)
\(\chi_{2601}(1786,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{38}{51}\right)\)
\(\chi_{2601}(1888,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{46}{51}\right)\)
\(\chi_{2601}(1939,\cdot)\) \(1\) \(1\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{50}{51}\right)\)
\(\chi_{2601}(2041,\cdot)\) \(1\) \(1\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{7}{51}\right)\)
\(\chi_{2601}(2092,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{11}{51}\right)\)
\(\chi_{2601}(2194,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{19}{51}\right)\)
\(\chi_{2601}(2245,\cdot)\) \(1\) \(1\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{23}{51}\right)\)
\(\chi_{2601}(2347,\cdot)\) \(1\) \(1\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{31}{51}\right)\)
\(\chi_{2601}(2398,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{35}{51}\right)\)
\(\chi_{2601}(2500,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{43}{51}\right)\)