# Properties

 Label 900.bv Modulus $900$ Conductor $225$ Order $60$ Real no Primitive no Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(900, base_ring=CyclotomicField(60))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,20,57]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(13,900))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$900$$ Conductor: $$225$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$60$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 225.x sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q(\zeta_{60})$$ Fixed field: Number field defined by a degree 60 polynomial

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{900}(13,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{900}(97,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{900}(133,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{900}(277,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{900}(313,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{900}(337,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{900}(373,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{900}(517,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{900}(553,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{900}(637,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{900}(673,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{900}(697,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{900}(733,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{900}(817,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{900}(853,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{900}(877,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$