# Properties

 Label 953.g Modulus $953$ Conductor $953$ Order $17$ Real no Primitive yes Minimal yes Parity even

# Learn more

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

sage: H = DirichletGroup(953, base_ring=CyclotomicField(34))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([18]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(16,953))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$953$$ Conductor: $$953$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$17$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes 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: $$\Q(\zeta_{17})$$ Fixed field: 17.17.462899178676311160288470191817767102492054133121.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{953}(16,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$
$$\chi_{953}(134,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{9}{17}\right)$$
$$\chi_{953}(238,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{3}{17}\right)$$
$$\chi_{953}(256,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$
$$\chi_{953}(276,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$
$$\chi_{953}(284,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{16}{17}\right)$$
$$\chi_{953}(417,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{6}{17}\right)$$
$$\chi_{953}(443,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{12}{17}\right)$$
$$\chi_{953}(604,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$
$$\chi_{953}(732,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$
$$\chi_{953}(770,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{13}{17}\right)$$
$$\chi_{953}(802,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{1}{17}\right)$$
$$\chi_{953}(882,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{2}{17}\right)$$
$$\chi_{953}(884,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{7}{17}\right)$$
$$\chi_{953}(889,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$
$$\chi_{953}(949,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{14}{17}\right)$$