# Properties

 Label 7098.dq Modulus $7098$ Conductor $3549$ Order $78$ 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([39,65,72]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(131,7098))

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: $$78$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 3549.di 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: Number field defined by a degree 78 polynomial

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$5$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{7098}(131,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{6}{13}\right)$$
$$\chi_{7098}(521,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{55}{78}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{11}{13}\right)$$
$$\chi_{7098}(1067,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{5}{13}\right)$$
$$\chi_{7098}(1223,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{7}{13}\right)$$
$$\chi_{7098}(1613,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{12}{13}\right)$$
$$\chi_{7098}(1769,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{53}{78}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{1}{13}\right)$$
$$\chi_{7098}(2159,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{19}{78}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{6}{13}\right)$$
$$\chi_{7098}(2315,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{47}{78}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{53}{78}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{8}{13}\right)$$
$$\chi_{7098}(2861,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{2}{13}\right)$$
$$\chi_{7098}(3251,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{7}{78}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{61}{78}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{7}{13}\right)$$
$$\chi_{7098}(3407,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{9}{13}\right)$$
$$\chi_{7098}(3797,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{1}{13}\right)$$
$$\chi_{7098}(3953,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{29}{78}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{3}{13}\right)$$
$$\chi_{7098}(4343,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{8}{13}\right)$$
$$\chi_{7098}(4499,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{10}{13}\right)$$
$$\chi_{7098}(4889,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{2}{13}\right)$$
$$\chi_{7098}(5045,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{4}{13}\right)$$
$$\chi_{7098}(5435,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{61}{78}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{19}{78}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{9}{13}\right)$$
$$\chi_{7098}(5591,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{29}{78}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{11}{13}\right)$$
$$\chi_{7098}(5981,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{55}{78}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{3}{13}\right)$$
$$\chi_{7098}(6137,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{5}{13}\right)$$
$$\chi_{7098}(6527,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{10}{13}\right)$$
$$\chi_{7098}(6683,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{47}{78}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{12}{13}\right)$$
$$\chi_{7098}(7073,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{7}{78}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{4}{13}\right)$$