Properties

Label 967.k
Modulus $967$
Conductor $967$
Order $69$
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(967, base_ring=CyclotomicField(138))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([34]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(15,967))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(967\)
Conductor: \(967\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(69\)
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: $\Q(\zeta_{69})$
Fixed field: Number field defined by a degree 69 polynomial

First 31 of 44 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{967}(15,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{69}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{20}{69}\right)\) \(e\left(\frac{17}{69}\right)\) \(e\left(\frac{37}{69}\right)\) \(e\left(\frac{35}{69}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{18}{23}\right)\)
\(\chi_{967}(39,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{69}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{17}{69}\right)\) \(e\left(\frac{11}{69}\right)\) \(e\left(\frac{28}{69}\right)\) \(e\left(\frac{47}{69}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{13}{23}\right)\)
\(\chi_{967}(53,\cdot)\) \(1\) \(1\) \(e\left(\frac{38}{69}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{7}{69}\right)\) \(e\left(\frac{37}{69}\right)\) \(e\left(\frac{44}{69}\right)\) \(e\left(\frac{64}{69}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{4}{23}\right)\)
\(\chi_{967}(61,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{69}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{44}{69}\right)\) \(e\left(\frac{65}{69}\right)\) \(e\left(\frac{40}{69}\right)\) \(e\left(\frac{8}{69}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{12}{23}\right)\)
\(\chi_{967}(68,\cdot)\) \(1\) \(1\) \(e\left(\frac{28}{69}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{56}{69}\right)\) \(e\left(\frac{20}{69}\right)\) \(e\left(\frac{7}{69}\right)\) \(e\left(\frac{29}{69}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{9}{23}\right)\)
\(\chi_{967}(73,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{69}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{62}{69}\right)\) \(e\left(\frac{32}{69}\right)\) \(e\left(\frac{25}{69}\right)\) \(e\left(\frac{5}{69}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{19}{23}\right)\)
\(\chi_{967}(113,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{69}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{8}{69}\right)\) \(e\left(\frac{62}{69}\right)\) \(e\left(\frac{1}{69}\right)\) \(e\left(\frac{14}{69}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{21}{23}\right)\)
\(\chi_{967}(124,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{69}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{52}{69}\right)\) \(e\left(\frac{58}{69}\right)\) \(e\left(\frac{41}{69}\right)\) \(e\left(\frac{22}{69}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{10}{23}\right)\)
\(\chi_{967}(128,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{69}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{13}{69}\right)\) \(e\left(\frac{49}{69}\right)\) \(e\left(\frac{62}{69}\right)\) \(e\left(\frac{40}{69}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{14}{23}\right)\)
\(\chi_{967}(129,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{69}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{49}{69}\right)\) \(e\left(\frac{52}{69}\right)\) \(e\left(\frac{32}{69}\right)\) \(e\left(\frac{34}{69}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{5}{23}\right)\)
\(\chi_{967}(145,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{69}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{2}{69}\right)\) \(e\left(\frac{50}{69}\right)\) \(e\left(\frac{52}{69}\right)\) \(e\left(\frac{38}{69}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{11}{23}\right)\)
\(\chi_{967}(190,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{69}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{58}{69}\right)\) \(e\left(\frac{1}{69}\right)\) \(e\left(\frac{59}{69}\right)\) \(e\left(\frac{67}{69}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{20}{23}\right)\)
\(\chi_{967}(198,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{69}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{16}{69}\right)\) \(e\left(\frac{55}{69}\right)\) \(e\left(\frac{2}{69}\right)\) \(e\left(\frac{28}{69}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{19}{23}\right)\)
\(\chi_{967}(202,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{69}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{29}{69}\right)\) \(e\left(\frac{35}{69}\right)\) \(e\left(\frac{64}{69}\right)\) \(e\left(\frac{68}{69}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{10}{23}\right)\)
\(\chi_{967}(225,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{69}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{40}{69}\right)\) \(e\left(\frac{34}{69}\right)\) \(e\left(\frac{5}{69}\right)\) \(e\left(\frac{1}{69}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{13}{23}\right)\)
\(\chi_{967}(241,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{69}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{22}{69}\right)\) \(e\left(\frac{67}{69}\right)\) \(e\left(\frac{20}{69}\right)\) \(e\left(\frac{4}{69}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{6}{23}\right)\)
\(\chi_{967}(280,\cdot)\) \(1\) \(1\) \(e\left(\frac{50}{69}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{31}{69}\right)\) \(e\left(\frac{16}{69}\right)\) \(e\left(\frac{47}{69}\right)\) \(e\left(\frac{37}{69}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{21}{23}\right)\)
\(\chi_{967}(321,\cdot)\) \(1\) \(1\) \(e\left(\frac{58}{69}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{47}{69}\right)\) \(e\left(\frac{2}{69}\right)\) \(e\left(\frac{49}{69}\right)\) \(e\left(\frac{65}{69}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{17}{23}\right)\)
\(\chi_{967}(335,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{69}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{38}{69}\right)\) \(e\left(\frac{53}{69}\right)\) \(e\left(\frac{22}{69}\right)\) \(e\left(\frac{32}{69}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{2}{23}\right)\)
\(\chi_{967}(341,\cdot)\) \(1\) \(1\) \(e\left(\frac{40}{69}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{11}{69}\right)\) \(e\left(\frac{68}{69}\right)\) \(e\left(\frac{10}{69}\right)\) \(e\left(\frac{2}{69}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{3}{23}\right)\)
\(\chi_{967}(352,\cdot)\) \(1\) \(1\) \(e\left(\frac{55}{69}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{41}{69}\right)\) \(e\left(\frac{59}{69}\right)\) \(e\left(\frac{31}{69}\right)\) \(e\left(\frac{20}{69}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{7}{23}\right)\)
\(\chi_{967}(377,\cdot)\) \(1\) \(1\) \(e\left(\frac{34}{69}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{68}{69}\right)\) \(e\left(\frac{44}{69}\right)\) \(e\left(\frac{43}{69}\right)\) \(e\left(\frac{50}{69}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{6}{23}\right)\)
\(\chi_{967}(400,\cdot)\) \(1\) \(1\) \(e\left(\frac{67}{69}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{65}{69}\right)\) \(e\left(\frac{38}{69}\right)\) \(e\left(\frac{34}{69}\right)\) \(e\left(\frac{62}{69}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{1}{23}\right)\)
\(\chi_{967}(421,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{69}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{50}{69}\right)\) \(e\left(\frac{8}{69}\right)\) \(e\left(\frac{58}{69}\right)\) \(e\left(\frac{53}{69}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{22}{23}\right)\)
\(\chi_{967}(445,\cdot)\) \(1\) \(1\) \(e\left(\frac{65}{69}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{61}{69}\right)\) \(e\left(\frac{7}{69}\right)\) \(e\left(\frac{68}{69}\right)\) \(e\left(\frac{55}{69}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{2}{23}\right)\)
\(\chi_{967}(494,\cdot)\) \(1\) \(1\) \(e\left(\frac{62}{69}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{55}{69}\right)\) \(e\left(\frac{64}{69}\right)\) \(e\left(\frac{50}{69}\right)\) \(e\left(\frac{10}{69}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{15}{23}\right)\)
\(\chi_{967}(513,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{69}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{1}{69}\right)\) \(e\left(\frac{25}{69}\right)\) \(e\left(\frac{26}{69}\right)\) \(e\left(\frac{19}{69}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{17}{23}\right)\)
\(\chi_{967}(524,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{69}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{32}{69}\right)\) \(e\left(\frac{41}{69}\right)\) \(e\left(\frac{4}{69}\right)\) \(e\left(\frac{56}{69}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{15}{23}\right)\)
\(\chi_{967}(539,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{69}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{25}{69}\right)\) \(e\left(\frac{4}{69}\right)\) \(e\left(\frac{29}{69}\right)\) \(e\left(\frac{61}{69}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{11}{23}\right)\)
\(\chi_{967}(554,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{69}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{34}{69}\right)\) \(e\left(\frac{22}{69}\right)\) \(e\left(\frac{56}{69}\right)\) \(e\left(\frac{25}{69}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{3}{23}\right)\)
\(\chi_{967}(585,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{69}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{37}{69}\right)\) \(e\left(\frac{28}{69}\right)\) \(e\left(\frac{65}{69}\right)\) \(e\left(\frac{13}{69}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{8}{23}\right)\)