↑

Properties

Label 736.z
Modulus 736736
Conductor 368368
Order 4444
Real no
Primitive no
Minimal no
Parity odd

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(736, base_ring=CyclotomicField(44)) M = H._module chi = DirichletCharacter(H, M([0,11,18])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(57,736)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 736736
Conductor: 368368
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 4444
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 368.v
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ44)\Q(\zeta_{44})
Fixed field: 44.0.4141890260646712580912980965306954513336276372715662057543551492310346739946349214617837764608.1

Characters in Galois orbit

Character −1-1 11 33 55 77 99 1111 1313 1515 1717 1919 2121
χ736(57,⋅)\chi_{736}(57,\cdot) −1-1 11 e(1344)e\left(\frac{13}{44}\right) e(2944)e\left(\frac{29}{44}\right) e(311)e\left(\frac{3}{11}\right) e(1322)e\left(\frac{13}{22}\right) e(4144)e\left(\frac{41}{44}\right) e(2144)e\left(\frac{21}{44}\right) e(2122)e\left(\frac{21}{22}\right) e(1922)e\left(\frac{19}{22}\right) e(3944)e\left(\frac{39}{44}\right) e(2544)e\left(\frac{25}{44}\right)
χ736(89,⋅)\chi_{736}(89,\cdot) −1-1 11 e(1744)e\left(\frac{17}{44}\right) e(2144)e\left(\frac{21}{44}\right) e(911)e\left(\frac{9}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(1344)e\left(\frac{13}{44}\right) e(4144)e\left(\frac{41}{44}\right) e(1922)e\left(\frac{19}{22}\right) e(1322)e\left(\frac{13}{22}\right) e(744)e\left(\frac{7}{44}\right) e(944)e\left(\frac{9}{44}\right)
χ736(153,⋅)\chi_{736}(153,\cdot) −1-1 11 e(544)e\left(\frac{5}{44}\right) e(144)e\left(\frac{1}{44}\right) e(211)e\left(\frac{2}{11}\right) e(522)e\left(\frac{5}{22}\right) e(944)e\left(\frac{9}{44}\right) e(2544)e\left(\frac{25}{44}\right) e(322)e\left(\frac{3}{22}\right) e(922)e\left(\frac{9}{22}\right) e(1544)e\left(\frac{15}{44}\right) e(1344)e\left(\frac{13}{44}\right)
χ736(201,⋅)\chi_{736}(201,\cdot) −1-1 11 e(1544)e\left(\frac{15}{44}\right) e(344)e\left(\frac{3}{44}\right) e(611)e\left(\frac{6}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(2744)e\left(\frac{27}{44}\right) e(3144)e\left(\frac{31}{44}\right) e(922)e\left(\frac{9}{22}\right) e(522)e\left(\frac{5}{22}\right) e(144)e\left(\frac{1}{44}\right) e(3944)e\left(\frac{39}{44}\right)
χ736(217,⋅)\chi_{736}(217,\cdot) −1-1 11 e(4144)e\left(\frac{41}{44}\right) e(1744)e\left(\frac{17}{44}\right) e(111)e\left(\frac{1}{11}\right) e(1922)e\left(\frac{19}{22}\right) e(2144)e\left(\frac{21}{44}\right) e(2944)e\left(\frac{29}{44}\right) e(722)e\left(\frac{7}{22}\right) e(2122)e\left(\frac{21}{22}\right) e(3544)e\left(\frac{35}{44}\right) e(144)e\left(\frac{1}{44}\right)
χ736(249,⋅)\chi_{736}(249,\cdot) −1-1 11 e(2944)e\left(\frac{29}{44}\right) e(4144)e\left(\frac{41}{44}\right) e(511)e\left(\frac{5}{11}\right) e(722)e\left(\frac{7}{22}\right) e(1744)e\left(\frac{17}{44}\right) e(1344)e\left(\frac{13}{44}\right) e(1322)e\left(\frac{13}{22}\right) e(1722)e\left(\frac{17}{22}\right) e(4344)e\left(\frac{43}{44}\right) e(544)e\left(\frac{5}{44}\right)
χ736(281,⋅)\chi_{736}(281,\cdot) −1-1 11 e(2144)e\left(\frac{21}{44}\right) e(1344)e\left(\frac{13}{44}\right) e(411)e\left(\frac{4}{11}\right) e(2122)e\left(\frac{21}{22}\right) e(2944)e\left(\frac{29}{44}\right) e(1744)e\left(\frac{17}{44}\right) e(1722)e\left(\frac{17}{22}\right) e(722)e\left(\frac{7}{22}\right) e(1944)e\left(\frac{19}{44}\right) e(3744)e\left(\frac{37}{44}\right)
χ736(297,⋅)\chi_{736}(297,\cdot) −1-1 11 e(3144)e\left(\frac{31}{44}\right) e(1544)e\left(\frac{15}{44}\right) e(811)e\left(\frac{8}{11}\right) e(922)e\left(\frac{9}{22}\right) e(344)e\left(\frac{3}{44}\right) e(2344)e\left(\frac{23}{44}\right) e(122)e\left(\frac{1}{22}\right) e(322)e\left(\frac{3}{22}\right) e(544)e\left(\frac{5}{44}\right) e(1944)e\left(\frac{19}{44}\right)
χ736(313,⋅)\chi_{736}(313,\cdot) −1-1 11 e(144)e\left(\frac{1}{44}\right) e(944)e\left(\frac{9}{44}\right) e(711)e\left(\frac{7}{11}\right) e(122)e\left(\frac{1}{22}\right) e(3744)e\left(\frac{37}{44}\right) e(544)e\left(\frac{5}{44}\right) e(522)e\left(\frac{5}{22}\right) e(1522)e\left(\frac{15}{22}\right) e(344)e\left(\frac{3}{44}\right) e(2944)e\left(\frac{29}{44}\right)
χ736(329,⋅)\chi_{736}(329,\cdot) −1-1 11 e(344)e\left(\frac{3}{44}\right) e(2744)e\left(\frac{27}{44}\right) e(1011)e\left(\frac{10}{11}\right) e(322)e\left(\frac{3}{22}\right) e(2344)e\left(\frac{23}{44}\right) e(1544)e\left(\frac{15}{44}\right) e(1522)e\left(\frac{15}{22}\right) e(122)e\left(\frac{1}{22}\right) e(944)e\left(\frac{9}{44}\right) e(4344)e\left(\frac{43}{44}\right)
χ736(425,⋅)\chi_{736}(425,\cdot) −1-1 11 e(3544)e\left(\frac{35}{44}\right) e(744)e\left(\frac{7}{44}\right) e(311)e\left(\frac{3}{11}\right) e(1322)e\left(\frac{13}{22}\right) e(1944)e\left(\frac{19}{44}\right) e(4344)e\left(\frac{43}{44}\right) e(2122)e\left(\frac{21}{22}\right) e(1922)e\left(\frac{19}{22}\right) e(1744)e\left(\frac{17}{44}\right) e(344)e\left(\frac{3}{44}\right)
χ736(457,⋅)\chi_{736}(457,\cdot) −1-1 11 e(3944)e\left(\frac{39}{44}\right) e(4344)e\left(\frac{43}{44}\right) e(911)e\left(\frac{9}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(3544)e\left(\frac{35}{44}\right) e(1944)e\left(\frac{19}{44}\right) e(1922)e\left(\frac{19}{22}\right) e(1322)e\left(\frac{13}{22}\right) e(2944)e\left(\frac{29}{44}\right) e(3144)e\left(\frac{31}{44}\right)
χ736(521,⋅)\chi_{736}(521,\cdot) −1-1 11 e(2744)e\left(\frac{27}{44}\right) e(2344)e\left(\frac{23}{44}\right) e(211)e\left(\frac{2}{11}\right) e(522)e\left(\frac{5}{22}\right) e(3144)e\left(\frac{31}{44}\right) e(344)e\left(\frac{3}{44}\right) e(322)e\left(\frac{3}{22}\right) e(922)e\left(\frac{9}{22}\right) e(3744)e\left(\frac{37}{44}\right) e(3544)e\left(\frac{35}{44}\right)
χ736(569,⋅)\chi_{736}(569,\cdot) −1-1 11 e(3744)e\left(\frac{37}{44}\right) e(2544)e\left(\frac{25}{44}\right) e(611)e\left(\frac{6}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(544)e\left(\frac{5}{44}\right) e(944)e\left(\frac{9}{44}\right) e(922)e\left(\frac{9}{22}\right) e(522)e\left(\frac{5}{22}\right) e(2344)e\left(\frac{23}{44}\right) e(1744)e\left(\frac{17}{44}\right)
χ736(585,⋅)\chi_{736}(585,\cdot) −1-1 11 e(1944)e\left(\frac{19}{44}\right) e(3944)e\left(\frac{39}{44}\right) e(111)e\left(\frac{1}{11}\right) e(1922)e\left(\frac{19}{22}\right) e(4344)e\left(\frac{43}{44}\right) e(744)e\left(\frac{7}{44}\right) e(722)e\left(\frac{7}{22}\right) e(2122)e\left(\frac{21}{22}\right) e(1344)e\left(\frac{13}{44}\right) e(2344)e\left(\frac{23}{44}\right)
χ736(617,⋅)\chi_{736}(617,\cdot) −1-1 11 e(744)e\left(\frac{7}{44}\right) e(1944)e\left(\frac{19}{44}\right) e(511)e\left(\frac{5}{11}\right) e(722)e\left(\frac{7}{22}\right) e(3944)e\left(\frac{39}{44}\right) e(3544)e\left(\frac{35}{44}\right) e(1322)e\left(\frac{13}{22}\right) e(1722)e\left(\frac{17}{22}\right) e(2144)e\left(\frac{21}{44}\right) e(2744)e\left(\frac{27}{44}\right)
χ736(649,⋅)\chi_{736}(649,\cdot) −1-1 11 e(4344)e\left(\frac{43}{44}\right) e(3544)e\left(\frac{35}{44}\right) e(411)e\left(\frac{4}{11}\right) e(2122)e\left(\frac{21}{22}\right) e(744)e\left(\frac{7}{44}\right) e(3944)e\left(\frac{39}{44}\right) e(1722)e\left(\frac{17}{22}\right) e(722)e\left(\frac{7}{22}\right) e(4144)e\left(\frac{41}{44}\right) e(1544)e\left(\frac{15}{44}\right)
χ736(665,⋅)\chi_{736}(665,\cdot) −1-1 11 e(944)e\left(\frac{9}{44}\right) e(3744)e\left(\frac{37}{44}\right) e(811)e\left(\frac{8}{11}\right) e(922)e\left(\frac{9}{22}\right) e(2544)e\left(\frac{25}{44}\right) e(144)e\left(\frac{1}{44}\right) e(122)e\left(\frac{1}{22}\right) e(322)e\left(\frac{3}{22}\right) e(2744)e\left(\frac{27}{44}\right) e(4144)e\left(\frac{41}{44}\right)
χ736(681,⋅)\chi_{736}(681,\cdot) −1-1 11 e(2344)e\left(\frac{23}{44}\right) e(3144)e\left(\frac{31}{44}\right) e(711)e\left(\frac{7}{11}\right) e(122)e\left(\frac{1}{22}\right) e(1544)e\left(\frac{15}{44}\right) e(2744)e\left(\frac{27}{44}\right) e(522)e\left(\frac{5}{22}\right) e(1522)e\left(\frac{15}{22}\right) e(2544)e\left(\frac{25}{44}\right) e(744)e\left(\frac{7}{44}\right)
χ736(697,⋅)\chi_{736}(697,\cdot) −1-1 11 e(2544)e\left(\frac{25}{44}\right) e(544)e\left(\frac{5}{44}\right) e(1011)e\left(\frac{10}{11}\right) e(322)e\left(\frac{3}{22}\right) e(144)e\left(\frac{1}{44}\right) e(3744)e\left(\frac{37}{44}\right) e(1522)e\left(\frac{15}{22}\right) e(122)e\left(\frac{1}{22}\right) e(3144)e\left(\frac{31}{44}\right) e(2144)e\left(\frac{21}{44}\right)