Properties

 Label 3920.fn Modulus $3920$ Conductor $980$ Order $84$ Real no Primitive no Minimal yes Parity odd

Related objects

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

sage: H = DirichletGroup(3920, base_ring=CyclotomicField(84))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([42,0,21,10]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(47,3920))

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: $$84$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 980.bt sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

Related number fields

 Field of values: $\Q(\zeta_{84})$ Fixed field: Number field defined by a degree 84 polynomial

Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$
$$\chi_{3920}(47,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(143,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(367,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(383,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(703,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(927,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(943,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(1167,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(1263,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(1487,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(1503,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(1727,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(1823,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(2047,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(2063,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(2287,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(2607,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(2623,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(2847,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(2943,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(3183,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(3407,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(3503,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(3727,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$