# Properties

 Label 2001.bd Modulus $2001$ Conductor $667$ Order $28$ 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(28))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,14,27]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(160,2001))

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: $$28$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 667.o 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: $$\Q(\zeta_{28})$$ Fixed field: 28.28.35394489068231220324814698212289719250778220848093751207381.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$13$$ $$14$$ $$16$$
$$\chi_{2001}(160,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$
$$\chi_{2001}(229,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{2001}(298,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{2001}(367,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{2001}(781,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{1}{7}\right)$$
$$\chi_{2001}(988,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{1}{7}\right)$$
$$\chi_{2001}(1402,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{2001}(1471,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{2001}(1540,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{2001}(1609,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$
$$\chi_{2001}(1816,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$
$$\chi_{2001}(1954,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$