# Properties

 Label 7098.cs Modulus $7098$ Conductor $1183$ Order $39$ 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(78))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,26,68]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(289,7098))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$7098$$ Conductor: $$1183$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$39$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 1183.bi 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: $\Q(\zeta_{39})$ Fixed field: 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.2

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$5$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{7098}(289,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{4}{39}\right)$$
$$\chi_{7098}(835,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{37}{39}\right)$$
$$\chi_{7098}(1075,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{11}{39}\right)$$
$$\chi_{7098}(1381,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{31}{39}\right)$$
$$\chi_{7098}(1621,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{35}{39}\right)$$
$$\chi_{7098}(1927,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{25}{39}\right)$$
$$\chi_{7098}(2167,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{20}{39}\right)$$
$$\chi_{7098}(2473,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{19}{39}\right)$$
$$\chi_{7098}(2713,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{5}{39}\right)$$
$$\chi_{7098}(3259,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{29}{39}\right)$$
$$\chi_{7098}(3565,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{7}{39}\right)$$
$$\chi_{7098}(3805,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{14}{39}\right)$$
$$\chi_{7098}(4111,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{1}{39}\right)$$
$$\chi_{7098}(4351,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{38}{39}\right)$$
$$\chi_{7098}(4657,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{34}{39}\right)$$
$$\chi_{7098}(4897,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{23}{39}\right)$$
$$\chi_{7098}(5203,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{28}{39}\right)$$
$$\chi_{7098}(5443,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{8}{39}\right)$$
$$\chi_{7098}(5749,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{22}{39}\right)$$
$$\chi_{7098}(5989,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{32}{39}\right)$$
$$\chi_{7098}(6295,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{16}{39}\right)$$
$$\chi_{7098}(6535,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{17}{39}\right)$$
$$\chi_{7098}(6841,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{10}{39}\right)$$
$$\chi_{7098}(7081,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{2}{39}\right)$$