# Properties

 Label 4729.p Modulus $4729$ Conductor $4729$ Order $4728$ Real no Primitive yes Minimal yes Parity odd

# Related objects

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

H = DirichletGroup(4729, base_ring=CyclotomicField(4728))

M = H._module

chi = DirichletCharacter(H, M([1]))

chi.galois_orbit()

[g,chi] = znchar(Mod(17,4729))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$4729$$ Conductor: $$4729$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4728$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes 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: $\Q(\zeta_{4728})$ Fixed field: Number field defined by a degree 4728 polynomial (not computed)

## First 31 of 1568 characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{4729}(17,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{53}{788}\right)$$ $$e\left(\frac{685}{788}\right)$$ $$e\left(\frac{53}{394}\right)$$ $$e\left(\frac{299}{2364}\right)$$ $$e\left(\frac{369}{394}\right)$$ $$e\left(\frac{1829}{2364}\right)$$ $$e\left(\frac{159}{788}\right)$$ $$e\left(\frac{291}{394}\right)$$ $$e\left(\frac{229}{1182}\right)$$ $$e\left(\frac{1453}{1576}\right)$$
$$\chi_{4729}(34,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{359}{788}\right)$$ $$e\left(\frac{239}{788}\right)$$ $$e\left(\frac{359}{394}\right)$$ $$e\left(\frac{821}{2364}\right)$$ $$e\left(\frac{299}{394}\right)$$ $$e\left(\frac{1907}{2364}\right)$$ $$e\left(\frac{289}{788}\right)$$ $$e\left(\frac{239}{394}\right)$$ $$e\left(\frac{949}{1182}\right)$$ $$e\left(\frac{163}{1576}\right)$$
$$\chi_{4729}(43,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{165}{788}\right)$$ $$e\left(\frac{393}{788}\right)$$ $$e\left(\frac{165}{394}\right)$$ $$e\left(\frac{1927}{2364}\right)$$ $$e\left(\frac{279}{394}\right)$$ $$e\left(\frac{1873}{2364}\right)$$ $$e\left(\frac{495}{788}\right)$$ $$e\left(\frac{393}{394}\right)$$ $$e\left(\frac{29}{1182}\right)$$ $$e\left(\frac{1089}{1576}\right)$$
$$\chi_{4729}(47,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{113}{788}\right)$$ $$e\left(\frac{613}{788}\right)$$ $$e\left(\frac{113}{394}\right)$$ $$e\left(\frac{1931}{2364}\right)$$ $$e\left(\frac{363}{394}\right)$$ $$e\left(\frac{1937}{2364}\right)$$ $$e\left(\frac{339}{788}\right)$$ $$e\left(\frac{219}{394}\right)$$ $$e\left(\frac{1135}{1182}\right)$$ $$e\left(\frac{273}{1576}\right)$$
$$\chi_{4729}(51,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{395}{788}\right)$$ $$e\left(\frac{511}{788}\right)$$ $$e\left(\frac{1}{394}\right)$$ $$e\left(\frac{2273}{2364}\right)$$ $$e\left(\frac{59}{394}\right)$$ $$e\left(\frac{1499}{2364}\right)$$ $$e\left(\frac{397}{788}\right)$$ $$e\left(\frac{117}{394}\right)$$ $$e\left(\frac{547}{1182}\right)$$ $$e\left(\frac{243}{1576}\right)$$
$$\chi_{4729}(53,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{541}{788}\right)$$ $$e\left(\frac{257}{788}\right)$$ $$e\left(\frac{147}{394}\right)$$ $$e\left(\frac{19}{2364}\right)$$ $$e\left(\frac{5}{394}\right)$$ $$e\left(\frac{2077}{2364}\right)$$ $$e\left(\frac{47}{788}\right)$$ $$e\left(\frac{257}{394}\right)$$ $$e\left(\frac{821}{1182}\right)$$ $$e\left(\frac{1049}{1576}\right)$$
$$\chi_{4729}(55,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{317}{788}\right)$$ $$e\left(\frac{53}{788}\right)$$ $$e\left(\frac{317}{394}\right)$$ $$e\left(\frac{2279}{2364}\right)$$ $$e\left(\frac{185}{394}\right)$$ $$e\left(\frac{413}{2364}\right)$$ $$e\left(\frac{163}{788}\right)$$ $$e\left(\frac{53}{394}\right)$$ $$e\left(\frac{433}{1182}\right)$$ $$e\left(\frac{201}{1576}\right)$$
$$\chi_{4729}(61,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{573}{788}\right)$$ $$e\left(\frac{61}{788}\right)$$ $$e\left(\frac{179}{394}\right)$$ $$e\left(\frac{259}{2364}\right)$$ $$e\left(\frac{317}{394}\right)$$ $$e\left(\frac{1189}{2364}\right)$$ $$e\left(\frac{143}{788}\right)$$ $$e\left(\frac{61}{394}\right)$$ $$e\left(\frac{989}{1182}\right)$$ $$e\left(\frac{157}{1576}\right)$$
$$\chi_{4729}(68,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{665}{788}\right)$$ $$e\left(\frac{581}{788}\right)$$ $$e\left(\frac{271}{394}\right)$$ $$e\left(\frac{1343}{2364}\right)$$ $$e\left(\frac{229}{394}\right)$$ $$e\left(\frac{1985}{2364}\right)$$ $$e\left(\frac{419}{788}\right)$$ $$e\left(\frac{187}{394}\right)$$ $$e\left(\frac{487}{1182}\right)$$ $$e\left(\frac{449}{1576}\right)$$
$$\chi_{4729}(77,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{169}{788}\right)$$ $$e\left(\frac{73}{788}\right)$$ $$e\left(\frac{169}{394}\right)$$ $$e\left(\frac{2351}{2364}\right)$$ $$e\left(\frac{121}{394}\right)$$ $$e\left(\frac{1565}{2364}\right)$$ $$e\left(\frac{507}{788}\right)$$ $$e\left(\frac{73}{394}\right)$$ $$e\left(\frac{247}{1182}\right)$$ $$e\left(\frac{485}{1576}\right)$$
$$\chi_{4729}(85,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{227}{788}\right)$$ $$e\left(\frac{555}{788}\right)$$ $$e\left(\frac{227}{394}\right)$$ $$e\left(\frac{1801}{2364}\right)$$ $$e\left(\frac{391}{394}\right)$$ $$e\left(\frac{1039}{2364}\right)$$ $$e\left(\frac{681}{788}\right)$$ $$e\left(\frac{161}{394}\right)$$ $$e\left(\frac{59}{1182}\right)$$ $$e\left(\frac{395}{1576}\right)$$
$$\chi_{4729}(86,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{471}{788}\right)$$ $$e\left(\frac{735}{788}\right)$$ $$e\left(\frac{77}{394}\right)$$ $$e\left(\frac{85}{2364}\right)$$ $$e\left(\frac{209}{394}\right)$$ $$e\left(\frac{1951}{2364}\right)$$ $$e\left(\frac{625}{788}\right)$$ $$e\left(\frac{341}{394}\right)$$ $$e\left(\frac{749}{1182}\right)$$ $$e\left(\frac{1375}{1576}\right)$$
$$\chi_{4729}(89,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{413}{788}\right)$$ $$e\left(\frac{253}{788}\right)$$ $$e\left(\frac{19}{394}\right)$$ $$e\left(\frac{635}{2364}\right)$$ $$e\left(\frac{333}{394}\right)$$ $$e\left(\frac{113}{2364}\right)$$ $$e\left(\frac{451}{788}\right)$$ $$e\left(\frac{253}{394}\right)$$ $$e\left(\frac{937}{1182}\right)$$ $$e\left(\frac{677}{1576}\right)$$
$$\chi_{4729}(94,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{419}{788}\right)$$ $$e\left(\frac{167}{788}\right)$$ $$e\left(\frac{25}{394}\right)$$ $$e\left(\frac{89}{2364}\right)$$ $$e\left(\frac{293}{394}\right)$$ $$e\left(\frac{2015}{2364}\right)$$ $$e\left(\frac{469}{788}\right)$$ $$e\left(\frac{167}{394}\right)$$ $$e\left(\frac{673}{1182}\right)$$ $$e\left(\frac{559}{1576}\right)$$
$$\chi_{4729}(101,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{89}{788}\right)$$ $$e\left(\frac{169}{788}\right)$$ $$e\left(\frac{89}{394}\right)$$ $$e\left(\frac{175}{2364}\right)$$ $$e\left(\frac{129}{394}\right)$$ $$e\left(\frac{2209}{2364}\right)$$ $$e\left(\frac{267}{788}\right)$$ $$e\left(\frac{169}{394}\right)$$ $$e\left(\frac{221}{1182}\right)$$ $$e\left(\frac{745}{1576}\right)$$
$$\chi_{4729}(102,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{701}{788}\right)$$ $$e\left(\frac{65}{788}\right)$$ $$e\left(\frac{307}{394}\right)$$ $$e\left(\frac{431}{2364}\right)$$ $$e\left(\frac{383}{394}\right)$$ $$e\left(\frac{1577}{2364}\right)$$ $$e\left(\frac{527}{788}\right)$$ $$e\left(\frac{65}{394}\right)$$ $$e\left(\frac{85}{1182}\right)$$ $$e\left(\frac{529}{1576}\right)$$
$$\chi_{4729}(106,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{59}{788}\right)$$ $$e\left(\frac{599}{788}\right)$$ $$e\left(\frac{59}{394}\right)$$ $$e\left(\frac{541}{2364}\right)$$ $$e\left(\frac{329}{394}\right)$$ $$e\left(\frac{2155}{2364}\right)$$ $$e\left(\frac{177}{788}\right)$$ $$e\left(\frac{205}{394}\right)$$ $$e\left(\frac{359}{1182}\right)$$ $$e\left(\frac{1335}{1576}\right)$$
$$\chi_{4729}(107,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{401}{788}\right)$$ $$e\left(\frac{425}{788}\right)$$ $$e\left(\frac{7}{394}\right)$$ $$e\left(\frac{1727}{2364}\right)$$ $$e\left(\frac{19}{394}\right)$$ $$e\left(\frac{1037}{2364}\right)$$ $$e\left(\frac{415}{788}\right)$$ $$e\left(\frac{31}{394}\right)$$ $$e\left(\frac{283}{1182}\right)$$ $$e\left(\frac{125}{1576}\right)$$
$$\chi_{4729}(109,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{509}{788}\right)$$ $$e\left(\frac{453}{788}\right)$$ $$e\left(\frac{115}{394}\right)$$ $$e\left(\frac{2143}{2364}\right)$$ $$e\left(\frac{87}{394}\right)$$ $$e\left(\frac{601}{2364}\right)$$ $$e\left(\frac{739}{788}\right)$$ $$e\left(\frac{59}{394}\right)$$ $$e\left(\frac{653}{1182}\right)$$ $$e\left(\frac{1153}{1576}\right)$$
$$\chi_{4729}(110,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{623}{788}\right)$$ $$e\left(\frac{395}{788}\right)$$ $$e\left(\frac{229}{394}\right)$$ $$e\left(\frac{437}{2364}\right)$$ $$e\left(\frac{115}{394}\right)$$ $$e\left(\frac{491}{2364}\right)$$ $$e\left(\frac{293}{788}\right)$$ $$e\left(\frac{1}{394}\right)$$ $$e\left(\frac{1153}{1182}\right)$$ $$e\left(\frac{487}{1576}\right)$$
$$\chi_{4729}(115,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{203}{788}\right)$$ $$e\left(\frac{111}{788}\right)$$ $$e\left(\frac{203}{394}\right)$$ $$e\left(\frac{833}{2364}\right)$$ $$e\left(\frac{157}{394}\right)$$ $$e\left(\frac{2099}{2364}\right)$$ $$e\left(\frac{609}{788}\right)$$ $$e\left(\frac{111}{394}\right)$$ $$e\left(\frac{721}{1182}\right)$$ $$e\left(\frac{867}{1576}\right)$$
$$\chi_{4729}(119,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{79}{788}\right)$$ $$e\left(\frac{575}{788}\right)$$ $$e\left(\frac{79}{394}\right)$$ $$e\left(\frac{1873}{2364}\right)$$ $$e\left(\frac{327}{394}\right)$$ $$e\left(\frac{2191}{2364}\right)$$ $$e\left(\frac{237}{788}\right)$$ $$e\left(\frac{181}{394}\right)$$ $$e\left(\frac{1055}{1182}\right)$$ $$e\left(\frac{679}{1576}\right)$$
$$\chi_{4729}(122,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{91}{788}\right)$$ $$e\left(\frac{403}{788}\right)$$ $$e\left(\frac{91}{394}\right)$$ $$e\left(\frac{781}{2364}\right)$$ $$e\left(\frac{247}{394}\right)$$ $$e\left(\frac{1267}{2364}\right)$$ $$e\left(\frac{273}{788}\right)$$ $$e\left(\frac{9}{394}\right)$$ $$e\left(\frac{527}{1182}\right)$$ $$e\left(\frac{443}{1576}\right)$$
$$\chi_{4729}(129,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{507}{788}\right)$$ $$e\left(\frac{219}{788}\right)$$ $$e\left(\frac{113}{394}\right)$$ $$e\left(\frac{1537}{2364}\right)$$ $$e\left(\frac{363}{394}\right)$$ $$e\left(\frac{1543}{2364}\right)$$ $$e\left(\frac{733}{788}\right)$$ $$e\left(\frac{219}{394}\right)$$ $$e\left(\frac{347}{1182}\right)$$ $$e\left(\frac{1455}{1576}\right)$$
$$\chi_{4729}(136,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{183}{788}\right)$$ $$e\left(\frac{135}{788}\right)$$ $$e\left(\frac{183}{394}\right)$$ $$e\left(\frac{1865}{2364}\right)$$ $$e\left(\frac{159}{394}\right)$$ $$e\left(\frac{2063}{2364}\right)$$ $$e\left(\frac{549}{788}\right)$$ $$e\left(\frac{135}{394}\right)$$ $$e\left(\frac{25}{1182}\right)$$ $$e\left(\frac{735}{1576}\right)$$
$$\chi_{4729}(139,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{771}{788}\right)$$ $$e\left(\frac{375}{788}\right)$$ $$e\left(\frac{377}{394}\right)$$ $$e\left(\frac{1153}{2364}\right)$$ $$e\left(\frac{179}{394}\right)$$ $$e\left(\frac{127}{2364}\right)$$ $$e\left(\frac{737}{788}\right)$$ $$e\left(\frac{375}{394}\right)$$ $$e\left(\frac{551}{1182}\right)$$ $$e\left(\frac{991}{1576}\right)$$
$$\chi_{4729}(141,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{455}{788}\right)$$ $$e\left(\frac{439}{788}\right)$$ $$e\left(\frac{61}{394}\right)$$ $$e\left(\frac{1541}{2364}\right)$$ $$e\left(\frac{53}{394}\right)$$ $$e\left(\frac{1607}{2364}\right)$$ $$e\left(\frac{577}{788}\right)$$ $$e\left(\frac{45}{394}\right)$$ $$e\left(\frac{271}{1182}\right)$$ $$e\left(\frac{639}{1576}\right)$$
$$\chi_{4729}(143,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{783}{788}\right)$$ $$e\left(\frac{203}{788}\right)$$ $$e\left(\frac{389}{394}\right)$$ $$e\left(\frac{1637}{2364}\right)$$ $$e\left(\frac{99}{394}\right)$$ $$e\left(\frac{779}{2364}\right)$$ $$e\left(\frac{773}{788}\right)$$ $$e\left(\frac{203}{394}\right)$$ $$e\left(\frac{811}{1182}\right)$$ $$e\left(\frac{1543}{1576}\right)$$
$$\chi_{4729}(145,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{459}{788}\right)$$ $$e\left(\frac{119}{788}\right)$$ $$e\left(\frac{65}{394}\right)$$ $$e\left(\frac{389}{2364}\right)$$ $$e\left(\frac{289}{394}\right)$$ $$e\left(\frac{2087}{2364}\right)$$ $$e\left(\frac{589}{788}\right)$$ $$e\left(\frac{119}{394}\right)$$ $$e\left(\frac{883}{1182}\right)$$ $$e\left(\frac{35}{1576}\right)$$
$$\chi_{4729}(153,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{737}{788}\right)$$ $$e\left(\frac{337}{788}\right)$$ $$e\left(\frac{343}{394}\right)$$ $$e\left(\frac{1883}{2364}\right)$$ $$e\left(\frac{143}{394}\right)$$ $$e\left(\frac{1169}{2364}\right)$$ $$e\left(\frac{635}{788}\right)$$ $$e\left(\frac{337}{394}\right)$$ $$e\left(\frac{865}{1182}\right)$$ $$e\left(\frac{609}{1576}\right)$$
$$\chi_{4729}(154,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{475}{788}\right)$$ $$e\left(\frac{415}{788}\right)$$ $$e\left(\frac{81}{394}\right)$$ $$e\left(\frac{509}{2364}\right)$$ $$e\left(\frac{51}{394}\right)$$ $$e\left(\frac{1643}{2364}\right)$$ $$e\left(\frac{637}{788}\right)$$ $$e\left(\frac{21}{394}\right)$$ $$e\left(\frac{967}{1182}\right)$$ $$e\left(\frac{771}{1576}\right)$$