Properties

 Label 3920.em Modulus $3920$ Conductor $980$ Order $28$ Real no Primitive no Minimal yes Parity even

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

sage: H = DirichletGroup(3920, base_ring=CyclotomicField(28))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([14,0,7,12]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(127,3920))

pari: order = charorder(g,chi)

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

Basic properties

 Modulus: $$3920$$ Conductor: $$980$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$28$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 980.bk 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: 28.28.4698031131813648056477467012100308504166528000000000000000000000.1

Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$
$$\chi_{3920}(127,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$-1$$
$$\chi_{3920}(463,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$1$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$-1$$
$$\chi_{3920}(1023,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$1$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$-1$$
$$\chi_{3920}(1247,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$-1$$
$$\chi_{3920}(1583,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$-1$$
$$\chi_{3920}(1807,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$1$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$-1$$
$$\chi_{3920}(2143,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$1$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$-1$$
$$\chi_{3920}(2367,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$1$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$-1$$
$$\chi_{3920}(2703,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$-1$$
$$\chi_{3920}(2927,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$-1$$
$$\chi_{3920}(3263,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$-1$$
$$\chi_{3920}(3487,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$1$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$-1$$