# Properties

 Label 3645.v Modulus $3645$ Conductor $405$ Order $54$ Real no Primitive no Minimal no Parity odd

# Related objects

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3645, base_ring=CyclotomicField(54))

M = H._module

chi = DirichletCharacter(H, M([23,27]))

chi.galois_orbit()

[g,chi] = znchar(Mod(134,3645))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$3645$$ Conductor: $$405$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$54$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 405.v sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q(\zeta_{27})$$ Fixed field: Number field defined by a degree 54 polynomial

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$4$$ $$7$$ $$8$$ $$11$$ $$13$$ $$14$$ $$16$$ $$17$$ $$19$$
$$\chi_{3645}(134,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{23}{27}\right)$$ $$e\left(\frac{17}{54}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{29}{54}\right)$$ $$e\left(\frac{49}{54}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{19}{27}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{3645}(269,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{23}{27}\right)$$ $$e\left(\frac{19}{27}\right)$$ $$e\left(\frac{7}{54}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{31}{54}\right)$$ $$e\left(\frac{17}{54}\right)$$ $$e\left(\frac{53}{54}\right)$$ $$e\left(\frac{11}{27}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$
$$\chi_{3645}(539,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{19}{27}\right)$$ $$e\left(\frac{11}{27}\right)$$ $$e\left(\frac{41}{54}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{35}{54}\right)$$ $$e\left(\frac{7}{54}\right)$$ $$e\left(\frac{25}{54}\right)$$ $$e\left(\frac{22}{27}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{3645}(674,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{17}{27}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$e\left(\frac{31}{54}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{37}{54}\right)$$ $$e\left(\frac{29}{54}\right)$$ $$e\left(\frac{11}{54}\right)$$ $$e\left(\frac{14}{27}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{3645}(944,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{27}\right)$$ $$e\left(\frac{26}{27}\right)$$ $$e\left(\frac{11}{54}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{41}{54}\right)$$ $$e\left(\frac{19}{54}\right)$$ $$e\left(\frac{37}{54}\right)$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{3645}(1079,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{27}\right)$$ $$e\left(\frac{22}{27}\right)$$ $$e\left(\frac{1}{54}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{43}{54}\right)$$ $$e\left(\frac{41}{54}\right)$$ $$e\left(\frac{23}{54}\right)$$ $$e\left(\frac{17}{27}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$
$$\chi_{3645}(1349,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{27}\right)$$ $$e\left(\frac{14}{27}\right)$$ $$e\left(\frac{35}{54}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{47}{54}\right)$$ $$e\left(\frac{31}{54}\right)$$ $$e\left(\frac{49}{54}\right)$$ $$e\left(\frac{1}{27}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{3645}(1484,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{25}{54}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{49}{54}\right)$$ $$e\left(\frac{53}{54}\right)$$ $$e\left(\frac{35}{54}\right)$$ $$e\left(\frac{20}{27}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$
$$\chi_{3645}(1754,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{27}\right)$$ $$e\left(\frac{2}{27}\right)$$ $$e\left(\frac{5}{54}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{53}{54}\right)$$ $$e\left(\frac{43}{54}\right)$$ $$e\left(\frac{7}{54}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{3645}(1889,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{26}{27}\right)$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{49}{54}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{54}\right)$$ $$e\left(\frac{11}{54}\right)$$ $$e\left(\frac{47}{54}\right)$$ $$e\left(\frac{23}{27}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{3645}(2159,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{22}{27}\right)$$ $$e\left(\frac{17}{27}\right)$$ $$e\left(\frac{29}{54}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{54}\right)$$ $$e\left(\frac{1}{54}\right)$$ $$e\left(\frac{19}{54}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{3645}(2294,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{20}{27}\right)$$ $$e\left(\frac{13}{27}\right)$$ $$e\left(\frac{19}{54}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{7}{54}\right)$$ $$e\left(\frac{23}{54}\right)$$ $$e\left(\frac{5}{54}\right)$$ $$e\left(\frac{26}{27}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$
$$\chi_{3645}(2564,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{53}{54}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{11}{54}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{31}{54}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{3645}(2699,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{14}{27}\right)$$ $$e\left(\frac{1}{27}\right)$$ $$e\left(\frac{43}{54}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{35}{54}\right)$$ $$e\left(\frac{17}{54}\right)$$ $$e\left(\frac{2}{27}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$
$$\chi_{3645}(2969,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{20}{27}\right)$$ $$e\left(\frac{23}{54}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{17}{54}\right)$$ $$e\left(\frac{25}{54}\right)$$ $$e\left(\frac{43}{54}\right)$$ $$e\left(\frac{13}{27}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{3645}(3104,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{8}{27}\right)$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{19}{54}\right)$$ $$e\left(\frac{47}{54}\right)$$ $$e\left(\frac{29}{54}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{3645}(3374,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{8}{27}\right)$$ $$e\left(\frac{47}{54}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{23}{54}\right)$$ $$e\left(\frac{37}{54}\right)$$ $$e\left(\frac{1}{54}\right)$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{3645}(3509,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{27}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{37}{54}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{25}{54}\right)$$ $$e\left(\frac{5}{54}\right)$$ $$e\left(\frac{41}{54}\right)$$ $$e\left(\frac{8}{27}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$