Properties

 Label 7098.co Modulus $7098$ Conductor $169$ Order $26$ 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(7098, base_ring=CyclotomicField(26))

sage: M = H._module

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

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(883,7098))

pari: order = charorder(g,chi)

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

Basic properties

 Modulus: $$7098$$ Conductor: $$169$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$26$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 169.h 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: $$\Q(\zeta_{13})$$ Fixed field: 26.26.3830224792147131369362629348887201408953937846517364173.1

Characters in Galois orbit

Character $$-1$$ $$1$$ $$5$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{7098}(883,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{25}{26}\right)$$
$$\chi_{7098}(1429,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{11}{26}\right)$$
$$\chi_{7098}(1975,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$
$$\chi_{7098}(2521,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$
$$\chi_{7098}(3067,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{21}{26}\right)$$
$$\chi_{7098}(3613,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{7}{26}\right)$$
$$\chi_{7098}(4159,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$
$$\chi_{7098}(4705,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{5}{26}\right)$$
$$\chi_{7098}(5251,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{17}{26}\right)$$
$$\chi_{7098}(5797,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{3}{26}\right)$$
$$\chi_{7098}(6343,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{15}{26}\right)$$
$$\chi_{7098}(6889,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{1}{26}\right)$$