# Properties

 Label 7098.ck Modulus $7098$ Conductor $3549$ 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([13,13,2]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(209,7098))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$7098$$ Conductor: $$3549$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$26$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 3549.cm 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: Number field defined by a degree 26 polynomial

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$5$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{7098}(209,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$
$$\chi_{7098}(755,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$
$$\chi_{7098}(1301,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$
$$\chi_{7098}(1847,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{2}{13}\right)$$
$$\chi_{7098}(2393,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{9}{13}\right)$$
$$\chi_{7098}(2939,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$
$$\chi_{7098}(3485,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{10}{13}\right)$$
$$\chi_{7098}(4031,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$
$$\chi_{7098}(4577,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{11}{13}\right)$$
$$\chi_{7098}(5123,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{5}{13}\right)$$
$$\chi_{7098}(5669,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{12}{13}\right)$$
$$\chi_{7098}(6215,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$