# Properties

 Label 2001.bh Modulus $2001$ Conductor $667$ Order $44$ Real no Primitive no Minimal yes Parity even

# Related objects

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(2001, base_ring=CyclotomicField(44))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,30,11]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(157,2001))

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Basic properties

 Modulus: $$2001$$ Conductor: $$667$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$44$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 667.q sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$13$$ $$14$$ $$16$$
$$\chi_{2001}(157,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{2001}(244,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{2001}(481,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{2001}(592,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{2001}(655,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{2001}(766,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{2001}(916,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{2001}(940,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{2001}(1003,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{2001}(1027,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{2001}(1114,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{2001}(1201,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{2001}(1351,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{2001}(1525,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{2001}(1699,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{2001}(1723,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{2001}(1786,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{2001}(1873,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{2001}(1897,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{2001}(1960,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$