# Properties

 Label 7098.em Modulus $7098$ Conductor $1183$ Order $156$ 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(156))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,26,139]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(115,7098))

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: $$156$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 1183.ch 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: $\Q(\zeta_{156})$ Fixed field: Number field defined by a degree 156 polynomial (not computed)

## First 31 of 48 characters in Galois orbit

Character $$-1$$ $$1$$ $$5$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{7098}(115,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{133}{156}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{55}{78}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{137}{156}\right)$$ $$e\left(\frac{137}{156}\right)$$ $$e\left(\frac{37}{156}\right)$$
$$\chi_{7098}(397,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{29}{156}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{78}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{85}{156}\right)$$ $$e\left(\frac{85}{156}\right)$$ $$e\left(\frac{89}{156}\right)$$
$$\chi_{7098}(535,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{156}\right)$$ $$e\left(\frac{33}{52}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{78}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{131}{156}\right)$$ $$e\left(\frac{131}{156}\right)$$ $$e\left(\frac{139}{156}\right)$$
$$\chi_{7098}(565,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{83}{156}\right)$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{55}{156}\right)$$ $$e\left(\frac{55}{156}\right)$$ $$e\left(\frac{131}{156}\right)$$
$$\chi_{7098}(661,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{156}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{89}{156}\right)$$ $$e\left(\frac{89}{156}\right)$$ $$e\left(\frac{73}{156}\right)$$
$$\chi_{7098}(943,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{89}{156}\right)$$ $$e\left(\frac{15}{52}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{121}{156}\right)$$ $$e\left(\frac{121}{156}\right)$$ $$e\left(\frac{101}{156}\right)$$
$$\chi_{7098}(1081,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{151}{156}\right)$$ $$e\left(\frac{5}{52}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{23}{156}\right)$$ $$e\left(\frac{23}{156}\right)$$ $$e\left(\frac{103}{156}\right)$$
$$\chi_{7098}(1111,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{156}\right)$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{19}{156}\right)$$ $$e\left(\frac{19}{156}\right)$$ $$e\left(\frac{119}{156}\right)$$
$$\chi_{7098}(1207,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{25}{156}\right)$$ $$e\left(\frac{27}{52}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{41}{156}\right)$$ $$e\left(\frac{41}{156}\right)$$ $$e\left(\frac{109}{156}\right)$$
$$\chi_{7098}(1489,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{149}{156}\right)$$ $$e\left(\frac{7}{52}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{1}{156}\right)$$ $$e\left(\frac{1}{156}\right)$$ $$e\left(\frac{113}{156}\right)$$
$$\chi_{7098}(1627,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{127}{156}\right)$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{71}{156}\right)$$ $$e\left(\frac{71}{156}\right)$$ $$e\left(\frac{67}{156}\right)$$
$$\chi_{7098}(1657,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{119}{156}\right)$$ $$e\left(\frac{37}{52}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{139}{156}\right)$$ $$e\left(\frac{139}{156}\right)$$ $$e\left(\frac{107}{156}\right)$$
$$\chi_{7098}(1753,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{49}{156}\right)$$ $$e\left(\frac{3}{52}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{149}{156}\right)$$ $$e\left(\frac{149}{156}\right)$$ $$e\left(\frac{145}{156}\right)$$
$$\chi_{7098}(2035,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{53}{156}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{53}{78}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{37}{156}\right)$$ $$e\left(\frac{37}{156}\right)$$ $$e\left(\frac{125}{156}\right)$$
$$\chi_{7098}(2173,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{103}{156}\right)$$ $$e\left(\frac{1}{52}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{119}{156}\right)$$ $$e\left(\frac{119}{156}\right)$$ $$e\left(\frac{31}{156}\right)$$
$$\chi_{7098}(2203,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{59}{156}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{103}{156}\right)$$ $$e\left(\frac{103}{156}\right)$$ $$e\left(\frac{95}{156}\right)$$
$$\chi_{7098}(2299,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{73}{156}\right)$$ $$e\left(\frac{31}{52}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{101}{156}\right)$$ $$e\left(\frac{101}{156}\right)$$ $$e\left(\frac{25}{156}\right)$$
$$\chi_{7098}(2581,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{113}{156}\right)$$ $$e\left(\frac{43}{52}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{73}{156}\right)$$ $$e\left(\frac{73}{156}\right)$$ $$e\left(\frac{137}{156}\right)$$
$$\chi_{7098}(2719,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{79}{156}\right)$$ $$e\left(\frac{25}{52}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{11}{156}\right)$$ $$e\left(\frac{11}{156}\right)$$ $$e\left(\frac{151}{156}\right)$$
$$\chi_{7098}(2749,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{155}{156}\right)$$ $$e\left(\frac{1}{52}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{67}{156}\right)$$ $$e\left(\frac{67}{156}\right)$$ $$e\left(\frac{83}{156}\right)$$
$$\chi_{7098}(2845,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{97}{156}\right)$$ $$e\left(\frac{7}{52}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{78}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{53}{156}\right)$$ $$e\left(\frac{53}{156}\right)$$ $$e\left(\frac{61}{156}\right)$$
$$\chi_{7098}(3127,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{156}\right)$$ $$e\left(\frac{35}{52}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{109}{156}\right)$$ $$e\left(\frac{109}{156}\right)$$ $$e\left(\frac{149}{156}\right)$$
$$\chi_{7098}(3265,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{55}{156}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{55}{78}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{59}{156}\right)$$ $$e\left(\frac{59}{156}\right)$$ $$e\left(\frac{115}{156}\right)$$
$$\chi_{7098}(3295,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{95}{156}\right)$$ $$e\left(\frac{9}{52}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{31}{156}\right)$$ $$e\left(\frac{31}{156}\right)$$ $$e\left(\frac{71}{156}\right)$$
$$\chi_{7098}(3391,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{121}{156}\right)$$ $$e\left(\frac{35}{52}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{5}{156}\right)$$ $$e\left(\frac{5}{156}\right)$$ $$e\left(\frac{97}{156}\right)$$
$$\chi_{7098}(3673,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{77}{156}\right)$$ $$e\left(\frac{27}{52}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{145}{156}\right)$$ $$e\left(\frac{145}{156}\right)$$ $$e\left(\frac{5}{156}\right)$$
$$\chi_{7098}(3811,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{31}{156}\right)$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{107}{156}\right)$$ $$e\left(\frac{107}{156}\right)$$ $$e\left(\frac{79}{156}\right)$$
$$\chi_{7098}(3841,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{35}{156}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{151}{156}\right)$$ $$e\left(\frac{151}{156}\right)$$ $$e\left(\frac{59}{156}\right)$$
$$\chi_{7098}(3937,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{145}{156}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{113}{156}\right)$$ $$e\left(\frac{113}{156}\right)$$ $$e\left(\frac{133}{156}\right)$$
$$\chi_{7098}(4219,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{137}{156}\right)$$ $$e\left(\frac{19}{52}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{25}{156}\right)$$ $$e\left(\frac{25}{156}\right)$$ $$e\left(\frac{17}{156}\right)$$
$$\chi_{7098}(4357,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{156}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{78}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{155}{156}\right)$$ $$e\left(\frac{155}{156}\right)$$ $$e\left(\frac{43}{156}\right)$$