# Properties

 Modulus $8033$ Structure $$C_{1932}\times C_{4}$$ Order $7728$

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(8033)

pari: g = idealstar(,8033,2)

## Character group

 sage: G.order()  pari: g.no Order = 7728 sage: H.invariants()  pari: g.cyc Structure = $$C_{1932}\times C_{4}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{8033}(7207,\cdot)$, $\chi_{8033}(7539,\cdot)$

## First 32 of 7728 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{8033}(1,\cdot)$$ 8033.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{8033}(2,\cdot)$$ 8033.cs 644 yes $$1$$ $$1$$ $$e\left(\frac{53}{161}\right)$$ $$e\left(\frac{199}{644}\right)$$ $$e\left(\frac{106}{161}\right)$$ $$e\left(\frac{205}{644}\right)$$ $$e\left(\frac{411}{644}\right)$$ $$e\left(\frac{47}{322}\right)$$ $$e\left(\frac{159}{161}\right)$$ $$e\left(\frac{199}{322}\right)$$ $$e\left(\frac{417}{644}\right)$$ $$e\left(\frac{100}{161}\right)$$
$$\chi_{8033}(3,\cdot)$$ 8033.cz 1932 yes $$-1$$ $$1$$ $$e\left(\frac{199}{644}\right)$$ $$e\left(\frac{1837}{1932}\right)$$ $$e\left(\frac{199}{322}\right)$$ $$e\left(\frac{589}{966}\right)$$ $$e\left(\frac{251}{966}\right)$$ $$e\left(\frac{62}{483}\right)$$ $$e\left(\frac{597}{644}\right)$$ $$e\left(\frac{871}{966}\right)$$ $$e\left(\frac{1775}{1932}\right)$$ $$e\left(\frac{449}{1932}\right)$$
$$\chi_{8033}(4,\cdot)$$ 8033.cl 322 yes $$1$$ $$1$$ $$e\left(\frac{106}{161}\right)$$ $$e\left(\frac{199}{322}\right)$$ $$e\left(\frac{51}{161}\right)$$ $$e\left(\frac{205}{322}\right)$$ $$e\left(\frac{89}{322}\right)$$ $$e\left(\frac{47}{161}\right)$$ $$e\left(\frac{157}{161}\right)$$ $$e\left(\frac{38}{161}\right)$$ $$e\left(\frac{95}{322}\right)$$ $$e\left(\frac{39}{161}\right)$$
$$\chi_{8033}(5,\cdot)$$ 8033.da 1932 yes $$-1$$ $$1$$ $$e\left(\frac{205}{644}\right)$$ $$e\left(\frac{589}{966}\right)$$ $$e\left(\frac{205}{322}\right)$$ $$e\left(\frac{559}{1932}\right)$$ $$e\left(\frac{1793}{1932}\right)$$ $$e\left(\frac{491}{966}\right)$$ $$e\left(\frac{615}{644}\right)$$ $$e\left(\frac{106}{483}\right)$$ $$e\left(\frac{587}{966}\right)$$ $$e\left(\frac{1291}{1932}\right)$$
$$\chi_{8033}(6,\cdot)$$ 8033.da 1932 yes $$-1$$ $$1$$ $$e\left(\frac{411}{644}\right)$$ $$e\left(\frac{251}{966}\right)$$ $$e\left(\frac{89}{322}\right)$$ $$e\left(\frac{1793}{1932}\right)$$ $$e\left(\frac{1735}{1932}\right)$$ $$e\left(\frac{265}{966}\right)$$ $$e\left(\frac{589}{644}\right)$$ $$e\left(\frac{251}{483}\right)$$ $$e\left(\frac{547}{966}\right)$$ $$e\left(\frac{1649}{1932}\right)$$
$$\chi_{8033}(7,\cdot)$$ 8033.ct 966 yes $$1$$ $$1$$ $$e\left(\frac{47}{322}\right)$$ $$e\left(\frac{62}{483}\right)$$ $$e\left(\frac{47}{161}\right)$$ $$e\left(\frac{491}{966}\right)$$ $$e\left(\frac{265}{966}\right)$$ $$e\left(\frac{433}{483}\right)$$ $$e\left(\frac{141}{322}\right)$$ $$e\left(\frac{124}{483}\right)$$ $$e\left(\frac{316}{483}\right)$$ $$e\left(\frac{263}{966}\right)$$
$$\chi_{8033}(8,\cdot)$$ 8033.cs 644 yes $$1$$ $$1$$ $$e\left(\frac{159}{161}\right)$$ $$e\left(\frac{597}{644}\right)$$ $$e\left(\frac{157}{161}\right)$$ $$e\left(\frac{615}{644}\right)$$ $$e\left(\frac{589}{644}\right)$$ $$e\left(\frac{141}{322}\right)$$ $$e\left(\frac{155}{161}\right)$$ $$e\left(\frac{275}{322}\right)$$ $$e\left(\frac{607}{644}\right)$$ $$e\left(\frac{139}{161}\right)$$
$$\chi_{8033}(9,\cdot)$$ 8033.cu 966 yes $$1$$ $$1$$ $$e\left(\frac{199}{322}\right)$$ $$e\left(\frac{871}{966}\right)$$ $$e\left(\frac{38}{161}\right)$$ $$e\left(\frac{106}{483}\right)$$ $$e\left(\frac{251}{483}\right)$$ $$e\left(\frac{124}{483}\right)$$ $$e\left(\frac{275}{322}\right)$$ $$e\left(\frac{388}{483}\right)$$ $$e\left(\frac{809}{966}\right)$$ $$e\left(\frac{449}{966}\right)$$
$$\chi_{8033}(10,\cdot)$$ 8033.cz 1932 yes $$-1$$ $$1$$ $$e\left(\frac{417}{644}\right)$$ $$e\left(\frac{1775}{1932}\right)$$ $$e\left(\frac{95}{322}\right)$$ $$e\left(\frac{587}{966}\right)$$ $$e\left(\frac{547}{966}\right)$$ $$e\left(\frac{316}{483}\right)$$ $$e\left(\frac{607}{644}\right)$$ $$e\left(\frac{809}{966}\right)$$ $$e\left(\frac{493}{1932}\right)$$ $$e\left(\frac{559}{1932}\right)$$
$$\chi_{8033}(11,\cdot)$$ 8033.db 1932 yes $$1$$ $$1$$ $$e\left(\frac{100}{161}\right)$$ $$e\left(\frac{449}{1932}\right)$$ $$e\left(\frac{39}{161}\right)$$ $$e\left(\frac{1291}{1932}\right)$$ $$e\left(\frac{1649}{1932}\right)$$ $$e\left(\frac{263}{966}\right)$$ $$e\left(\frac{139}{161}\right)$$ $$e\left(\frac{449}{966}\right)$$ $$e\left(\frac{559}{1932}\right)$$ $$e\left(\frac{241}{483}\right)$$
$$\chi_{8033}(12,\cdot)$$ 8033.cg 276 yes $$-1$$ $$1$$ $$e\left(\frac{89}{92}\right)$$ $$e\left(\frac{157}{276}\right)$$ $$e\left(\frac{43}{46}\right)$$ $$e\left(\frac{17}{69}\right)$$ $$e\left(\frac{37}{69}\right)$$ $$e\left(\frac{29}{69}\right)$$ $$e\left(\frac{83}{92}\right)$$ $$e\left(\frac{19}{138}\right)$$ $$e\left(\frac{59}{276}\right)$$ $$e\left(\frac{131}{276}\right)$$
$$\chi_{8033}(13,\cdot)$$ 8033.cl 322 yes $$1$$ $$1$$ $$e\left(\frac{142}{161}\right)$$ $$e\left(\frac{139}{322}\right)$$ $$e\left(\frac{123}{161}\right)$$ $$e\left(\frac{305}{322}\right)$$ $$e\left(\frac{101}{322}\right)$$ $$e\left(\frac{66}{161}\right)$$ $$e\left(\frac{104}{161}\right)$$ $$e\left(\frac{139}{161}\right)$$ $$e\left(\frac{267}{322}\right)$$ $$e\left(\frac{113}{161}\right)$$
$$\chi_{8033}(14,\cdot)$$ 8033.cw 1932 yes $$1$$ $$1$$ $$e\left(\frac{153}{322}\right)$$ $$e\left(\frac{845}{1932}\right)$$ $$e\left(\frac{153}{161}\right)$$ $$e\left(\frac{1597}{1932}\right)$$ $$e\left(\frac{1763}{1932}\right)$$ $$e\left(\frac{41}{966}\right)$$ $$e\left(\frac{137}{322}\right)$$ $$e\left(\frac{845}{966}\right)$$ $$e\left(\frac{583}{1932}\right)$$ $$e\left(\frac{863}{966}\right)$$
$$\chi_{8033}(15,\cdot)$$ 8033.cs 644 yes $$1$$ $$1$$ $$e\left(\frac{101}{161}\right)$$ $$e\left(\frac{361}{644}\right)$$ $$e\left(\frac{41}{161}\right)$$ $$e\left(\frac{579}{644}\right)$$ $$e\left(\frac{121}{644}\right)$$ $$e\left(\frac{205}{322}\right)$$ $$e\left(\frac{142}{161}\right)$$ $$e\left(\frac{39}{322}\right)$$ $$e\left(\frac{339}{644}\right)$$ $$e\left(\frac{145}{161}\right)$$
$$\chi_{8033}(16,\cdot)$$ 8033.cc 161 yes $$1$$ $$1$$ $$e\left(\frac{51}{161}\right)$$ $$e\left(\frac{38}{161}\right)$$ $$e\left(\frac{102}{161}\right)$$ $$e\left(\frac{44}{161}\right)$$ $$e\left(\frac{89}{161}\right)$$ $$e\left(\frac{94}{161}\right)$$ $$e\left(\frac{153}{161}\right)$$ $$e\left(\frac{76}{161}\right)$$ $$e\left(\frac{95}{161}\right)$$ $$e\left(\frac{78}{161}\right)$$
$$\chi_{8033}(17,\cdot)$$ 8033.cd 276 yes $$1$$ $$1$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{251}{276}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{241}{276}\right)$$ $$e\left(\frac{143}{276}\right)$$ $$e\left(\frac{29}{138}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{113}{138}\right)$$ $$e\left(\frac{133}{276}\right)$$ $$e\left(\frac{25}{69}\right)$$
$$\chi_{8033}(18,\cdot)$$ 8033.cw 1932 yes $$1$$ $$1$$ $$e\left(\frac{305}{322}\right)$$ $$e\left(\frac{407}{1932}\right)$$ $$e\left(\frac{144}{161}\right)$$ $$e\left(\frac{1039}{1932}\right)$$ $$e\left(\frac{305}{1932}\right)$$ $$e\left(\frac{389}{966}\right)$$ $$e\left(\frac{271}{322}\right)$$ $$e\left(\frac{407}{966}\right)$$ $$e\left(\frac{937}{1932}\right)$$ $$e\left(\frac{83}{966}\right)$$
$$\chi_{8033}(19,\cdot)$$ 8033.cp 644 yes $$-1$$ $$1$$ $$e\left(\frac{347}{644}\right)$$ $$e\left(\frac{167}{644}\right)$$ $$e\left(\frac{25}{322}\right)$$ $$e\left(\frac{317}{322}\right)$$ $$e\left(\frac{257}{322}\right)$$ $$e\left(\frac{152}{161}\right)$$ $$e\left(\frac{397}{644}\right)$$ $$e\left(\frac{167}{322}\right)$$ $$e\left(\frac{337}{644}\right)$$ $$e\left(\frac{275}{644}\right)$$
$$\chi_{8033}(20,\cdot)$$ 8033.cx 1932 yes $$-1$$ $$1$$ $$e\left(\frac{629}{644}\right)$$ $$e\left(\frac{110}{483}\right)$$ $$e\left(\frac{307}{322}\right)$$ $$e\left(\frac{1789}{1932}\right)$$ $$e\left(\frac{395}{1932}\right)$$ $$e\left(\frac{773}{966}\right)$$ $$e\left(\frac{599}{644}\right)$$ $$e\left(\frac{220}{483}\right)$$ $$e\left(\frac{436}{483}\right)$$ $$e\left(\frac{1759}{1932}\right)$$
$$\chi_{8033}(21,\cdot)$$ 8033.cq 644 yes $$-1$$ $$1$$ $$e\left(\frac{293}{644}\right)$$ $$e\left(\frac{51}{644}\right)$$ $$e\left(\frac{293}{322}\right)$$ $$e\left(\frac{19}{161}\right)$$ $$e\left(\frac{86}{161}\right)$$ $$e\left(\frac{4}{161}\right)$$ $$e\left(\frac{235}{644}\right)$$ $$e\left(\frac{51}{322}\right)$$ $$e\left(\frac{369}{644}\right)$$ $$e\left(\frac{325}{644}\right)$$
$$\chi_{8033}(22,\cdot)$$ 8033.cv 966 yes $$1$$ $$1$$ $$e\left(\frac{153}{161}\right)$$ $$e\left(\frac{523}{966}\right)$$ $$e\left(\frac{145}{161}\right)$$ $$e\left(\frac{953}{966}\right)$$ $$e\left(\frac{475}{966}\right)$$ $$e\left(\frac{202}{483}\right)$$ $$e\left(\frac{137}{161}\right)$$ $$e\left(\frac{40}{483}\right)$$ $$e\left(\frac{905}{966}\right)$$ $$e\left(\frac{58}{483}\right)$$
$$\chi_{8033}(23,\cdot)$$ 8033.cm 483 yes $$1$$ $$1$$ $$e\left(\frac{80}{161}\right)$$ $$e\left(\frac{122}{483}\right)$$ $$e\left(\frac{160}{161}\right)$$ $$e\left(\frac{226}{483}\right)$$ $$e\left(\frac{362}{483}\right)$$ $$e\left(\frac{73}{483}\right)$$ $$e\left(\frac{79}{161}\right)$$ $$e\left(\frac{244}{483}\right)$$ $$e\left(\frac{466}{483}\right)$$ $$e\left(\frac{64}{483}\right)$$
$$\chi_{8033}(24,\cdot)$$ 8033.cx 1932 yes $$-1$$ $$1$$ $$e\left(\frac{191}{644}\right)$$ $$e\left(\frac{424}{483}\right)$$ $$e\left(\frac{191}{322}\right)$$ $$e\left(\frac{1091}{1932}\right)$$ $$e\left(\frac{337}{1932}\right)$$ $$e\left(\frac{547}{966}\right)$$ $$e\left(\frac{573}{644}\right)$$ $$e\left(\frac{365}{483}\right)$$ $$e\left(\frac{416}{483}\right)$$ $$e\left(\frac{185}{1932}\right)$$
$$\chi_{8033}(25,\cdot)$$ 8033.ct 966 yes $$1$$ $$1$$ $$e\left(\frac{205}{322}\right)$$ $$e\left(\frac{106}{483}\right)$$ $$e\left(\frac{44}{161}\right)$$ $$e\left(\frac{559}{966}\right)$$ $$e\left(\frac{827}{966}\right)$$ $$e\left(\frac{8}{483}\right)$$ $$e\left(\frac{293}{322}\right)$$ $$e\left(\frac{212}{483}\right)$$ $$e\left(\frac{104}{483}\right)$$ $$e\left(\frac{325}{966}\right)$$
$$\chi_{8033}(26,\cdot)$$ 8033.cs 644 yes $$1$$ $$1$$ $$e\left(\frac{34}{161}\right)$$ $$e\left(\frac{477}{644}\right)$$ $$e\left(\frac{68}{161}\right)$$ $$e\left(\frac{171}{644}\right)$$ $$e\left(\frac{613}{644}\right)$$ $$e\left(\frac{179}{322}\right)$$ $$e\left(\frac{102}{161}\right)$$ $$e\left(\frac{155}{322}\right)$$ $$e\left(\frac{307}{644}\right)$$ $$e\left(\frac{52}{161}\right)$$
$$\chi_{8033}(27,\cdot)$$ 8033.cp 644 yes $$-1$$ $$1$$ $$e\left(\frac{597}{644}\right)$$ $$e\left(\frac{549}{644}\right)$$ $$e\left(\frac{275}{322}\right)$$ $$e\left(\frac{267}{322}\right)$$ $$e\left(\frac{251}{322}\right)$$ $$e\left(\frac{62}{161}\right)$$ $$e\left(\frac{503}{644}\right)$$ $$e\left(\frac{227}{322}\right)$$ $$e\left(\frac{487}{644}\right)$$ $$e\left(\frac{449}{644}\right)$$
$$\chi_{8033}(28,\cdot)$$ 8033.ca 138 yes $$1$$ $$1$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{103}{138}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{10}{69}\right)$$ $$e\left(\frac{38}{69}\right)$$ $$e\left(\frac{13}{69}\right)$$ $$e\left(\frac{19}{46}\right)$$ $$e\left(\frac{34}{69}\right)$$ $$e\left(\frac{131}{138}\right)$$ $$e\left(\frac{71}{138}\right)$$
$$\chi_{8033}(30,\cdot)$$ 8033.z 23 no $$1$$ $$1$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$
$$\chi_{8033}(31,\cdot)$$ 8033.db 1932 yes $$1$$ $$1$$ $$e\left(\frac{11}{161}\right)$$ $$e\left(\frac{373}{1932}\right)$$ $$e\left(\frac{22}{161}\right)$$ $$e\left(\frac{1847}{1932}\right)$$ $$e\left(\frac{505}{1932}\right)$$ $$e\left(\frac{169}{966}\right)$$ $$e\left(\frac{33}{161}\right)$$ $$e\left(\frac{373}{966}\right)$$ $$e\left(\frac{47}{1932}\right)$$ $$e\left(\frac{41}{483}\right)$$
$$\chi_{8033}(32,\cdot)$$ 8033.cs 644 yes $$1$$ $$1$$ $$e\left(\frac{104}{161}\right)$$ $$e\left(\frac{351}{644}\right)$$ $$e\left(\frac{47}{161}\right)$$ $$e\left(\frac{381}{644}\right)$$ $$e\left(\frac{123}{644}\right)$$ $$e\left(\frac{235}{322}\right)$$ $$e\left(\frac{151}{161}\right)$$ $$e\left(\frac{29}{322}\right)$$ $$e\left(\frac{153}{644}\right)$$ $$e\left(\frac{17}{161}\right)$$
$$\chi_{8033}(33,\cdot)$$ 8033.co 644 yes $$-1$$ $$1$$ $$e\left(\frac{599}{644}\right)$$ $$e\left(\frac{59}{322}\right)$$ $$e\left(\frac{277}{322}\right)$$ $$e\left(\frac{179}{644}\right)$$ $$e\left(\frac{73}{644}\right)$$ $$e\left(\frac{129}{322}\right)$$ $$e\left(\frac{509}{644}\right)$$ $$e\left(\frac{59}{161}\right)$$ $$e\left(\frac{67}{322}\right)$$ $$e\left(\frac{471}{644}\right)$$