# Properties

 Modulus $8016$ Structure $$C_{332}\times C_{2}\times C_{2}\times C_{2}$$ Order $2656$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(8016)

pari: g = idealstar(,8016,2)

## Character group

 sage: G.order()  pari: g.no Order = 2656 sage: H.invariants()  pari: g.cyc Structure = $$C_{332}\times C_{2}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{8016}(3007,\cdot)$, $\chi_{8016}(2005,\cdot)$, $\chi_{8016}(5345,\cdot)$, $\chi_{8016}(673,\cdot)$

## First 32 of 2656 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$
$$\chi_{8016}(1,\cdot)$$ 8016.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{8016}(5,\cdot)$$ 8016.bt 332 yes $$1$$ $$1$$ $$e\left(\frac{251}{332}\right)$$ $$e\left(\frac{35}{166}\right)$$ $$e\left(\frac{305}{332}\right)$$ $$e\left(\frac{123}{332}\right)$$ $$e\left(\frac{68}{83}\right)$$ $$e\left(\frac{33}{332}\right)$$ $$e\left(\frac{99}{166}\right)$$ $$e\left(\frac{85}{166}\right)$$ $$e\left(\frac{51}{332}\right)$$ $$e\left(\frac{45}{83}\right)$$
$$\chi_{8016}(7,\cdot)$$ 8016.bl 166 no $$-1$$ $$1$$ $$e\left(\frac{35}{166}\right)$$ $$e\left(\frac{63}{166}\right)$$ $$e\left(\frac{75}{83}\right)$$ $$e\left(\frac{119}{166}\right)$$ $$e\left(\frac{56}{83}\right)$$ $$e\left(\frac{19}{83}\right)$$ $$e\left(\frac{145}{166}\right)$$ $$e\left(\frac{35}{83}\right)$$ $$e\left(\frac{21}{166}\right)$$ $$e\left(\frac{79}{166}\right)$$
$$\chi_{8016}(11,\cdot)$$ 8016.bq 332 yes $$1$$ $$1$$ $$e\left(\frac{305}{332}\right)$$ $$e\left(\frac{75}{83}\right)$$ $$e\left(\frac{323}{332}\right)$$ $$e\left(\frac{41}{332}\right)$$ $$e\left(\frac{73}{166}\right)$$ $$e\left(\frac{11}{332}\right)$$ $$e\left(\frac{33}{166}\right)$$ $$e\left(\frac{139}{166}\right)$$ $$e\left(\frac{183}{332}\right)$$ $$e\left(\frac{113}{166}\right)$$
$$\chi_{8016}(13,\cdot)$$ 8016.bu 332 no $$-1$$ $$1$$ $$e\left(\frac{123}{332}\right)$$ $$e\left(\frac{119}{166}\right)$$ $$e\left(\frac{41}{332}\right)$$ $$e\left(\frac{53}{332}\right)$$ $$e\left(\frac{147}{166}\right)$$ $$e\left(\frac{79}{332}\right)$$ $$e\left(\frac{77}{83}\right)$$ $$e\left(\frac{123}{166}\right)$$ $$e\left(\frac{107}{332}\right)$$ $$e\left(\frac{70}{83}\right)$$
$$\chi_{8016}(17,\cdot)$$ 8016.bb 166 no $$1$$ $$1$$ $$e\left(\frac{68}{83}\right)$$ $$e\left(\frac{56}{83}\right)$$ $$e\left(\frac{73}{166}\right)$$ $$e\left(\frac{147}{166}\right)$$ $$e\left(\frac{35}{83}\right)$$ $$e\left(\frac{43}{83}\right)$$ $$e\left(\frac{9}{83}\right)$$ $$e\left(\frac{53}{83}\right)$$ $$e\left(\frac{65}{166}\right)$$ $$e\left(\frac{61}{83}\right)$$
$$\chi_{8016}(19,\cdot)$$ 8016.bp 332 no $$-1$$ $$1$$ $$e\left(\frac{33}{332}\right)$$ $$e\left(\frac{19}{83}\right)$$ $$e\left(\frac{11}{332}\right)$$ $$e\left(\frac{79}{332}\right)$$ $$e\left(\frac{43}{83}\right)$$ $$e\left(\frac{5}{332}\right)$$ $$e\left(\frac{49}{83}\right)$$ $$e\left(\frac{33}{166}\right)$$ $$e\left(\frac{219}{332}\right)$$ $$e\left(\frac{157}{166}\right)$$
$$\chi_{8016}(23,\cdot)$$ 8016.bm 166 no $$-1$$ $$1$$ $$e\left(\frac{99}{166}\right)$$ $$e\left(\frac{145}{166}\right)$$ $$e\left(\frac{33}{166}\right)$$ $$e\left(\frac{77}{83}\right)$$ $$e\left(\frac{9}{83}\right)$$ $$e\left(\frac{49}{83}\right)$$ $$e\left(\frac{7}{166}\right)$$ $$e\left(\frac{16}{83}\right)$$ $$e\left(\frac{38}{83}\right)$$ $$e\left(\frac{29}{166}\right)$$
$$\chi_{8016}(25,\cdot)$$ 8016.bj 166 no $$1$$ $$1$$ $$e\left(\frac{85}{166}\right)$$ $$e\left(\frac{35}{83}\right)$$ $$e\left(\frac{139}{166}\right)$$ $$e\left(\frac{123}{166}\right)$$ $$e\left(\frac{53}{83}\right)$$ $$e\left(\frac{33}{166}\right)$$ $$e\left(\frac{16}{83}\right)$$ $$e\left(\frac{2}{83}\right)$$ $$e\left(\frac{51}{166}\right)$$ $$e\left(\frac{7}{83}\right)$$
$$\chi_{8016}(29,\cdot)$$ 8016.bv 332 yes $$-1$$ $$1$$ $$e\left(\frac{51}{332}\right)$$ $$e\left(\frac{21}{166}\right)$$ $$e\left(\frac{183}{332}\right)$$ $$e\left(\frac{107}{332}\right)$$ $$e\left(\frac{65}{166}\right)$$ $$e\left(\frac{219}{332}\right)$$ $$e\left(\frac{38}{83}\right)$$ $$e\left(\frac{51}{166}\right)$$ $$e\left(\frac{97}{332}\right)$$ $$e\left(\frac{27}{83}\right)$$
$$\chi_{8016}(31,\cdot)$$ 8016.be 166 no $$-1$$ $$1$$ $$e\left(\frac{45}{83}\right)$$ $$e\left(\frac{79}{166}\right)$$ $$e\left(\frac{113}{166}\right)$$ $$e\left(\frac{70}{83}\right)$$ $$e\left(\frac{61}{83}\right)$$ $$e\left(\frac{157}{166}\right)$$ $$e\left(\frac{29}{166}\right)$$ $$e\left(\frac{7}{83}\right)$$ $$e\left(\frac{27}{83}\right)$$ $$e\left(\frac{49}{166}\right)$$
$$\chi_{8016}(35,\cdot)$$ 8016.bo 332 yes $$-1$$ $$1$$ $$e\left(\frac{321}{332}\right)$$ $$e\left(\frac{49}{83}\right)$$ $$e\left(\frac{273}{332}\right)$$ $$e\left(\frac{29}{332}\right)$$ $$e\left(\frac{41}{83}\right)$$ $$e\left(\frac{109}{332}\right)$$ $$e\left(\frac{39}{83}\right)$$ $$e\left(\frac{155}{166}\right)$$ $$e\left(\frac{93}{332}\right)$$ $$e\left(\frac{3}{166}\right)$$
$$\chi_{8016}(37,\cdot)$$ 8016.bu 332 no $$-1$$ $$1$$ $$e\left(\frac{205}{332}\right)$$ $$e\left(\frac{143}{166}\right)$$ $$e\left(\frac{179}{332}\right)$$ $$e\left(\frac{199}{332}\right)$$ $$e\left(\frac{79}{166}\right)$$ $$e\left(\frac{21}{332}\right)$$ $$e\left(\frac{73}{83}\right)$$ $$e\left(\frac{39}{166}\right)$$ $$e\left(\frac{289}{332}\right)$$ $$e\left(\frac{6}{83}\right)$$
$$\chi_{8016}(41,\cdot)$$ 8016.bg 166 no $$1$$ $$1$$ $$e\left(\frac{97}{166}\right)$$ $$e\left(\frac{79}{83}\right)$$ $$e\left(\frac{30}{83}\right)$$ $$e\left(\frac{57}{83}\right)$$ $$e\left(\frac{39}{83}\right)$$ $$e\left(\frac{65}{166}\right)$$ $$e\left(\frac{29}{83}\right)$$ $$e\left(\frac{14}{83}\right)$$ $$e\left(\frac{54}{83}\right)$$ $$e\left(\frac{49}{83}\right)$$
$$\chi_{8016}(43,\cdot)$$ 8016.br 332 no $$1$$ $$1$$ $$e\left(\frac{257}{332}\right)$$ $$e\left(\frac{70}{83}\right)$$ $$e\left(\frac{141}{332}\right)$$ $$e\left(\frac{243}{332}\right)$$ $$e\left(\frac{129}{166}\right)$$ $$e\left(\frac{215}{332}\right)$$ $$e\left(\frac{147}{166}\right)$$ $$e\left(\frac{91}{166}\right)$$ $$e\left(\frac{121}{332}\right)$$ $$e\left(\frac{111}{166}\right)$$
$$\chi_{8016}(47,\cdot)$$ 8016.bk 166 no $$1$$ $$1$$ $$e\left(\frac{49}{166}\right)$$ $$e\left(\frac{55}{166}\right)$$ $$e\left(\frac{22}{83}\right)$$ $$e\left(\frac{75}{83}\right)$$ $$e\left(\frac{107}{166}\right)$$ $$e\left(\frac{103}{166}\right)$$ $$e\left(\frac{60}{83}\right)$$ $$e\left(\frac{49}{83}\right)$$ $$e\left(\frac{129}{166}\right)$$ $$e\left(\frac{11}{166}\right)$$
$$\chi_{8016}(49,\cdot)$$ 8016.y 83 no $$1$$ $$1$$ $$e\left(\frac{35}{83}\right)$$ $$e\left(\frac{63}{83}\right)$$ $$e\left(\frac{67}{83}\right)$$ $$e\left(\frac{36}{83}\right)$$ $$e\left(\frac{29}{83}\right)$$ $$e\left(\frac{38}{83}\right)$$ $$e\left(\frac{62}{83}\right)$$ $$e\left(\frac{70}{83}\right)$$ $$e\left(\frac{21}{83}\right)$$ $$e\left(\frac{79}{83}\right)$$
$$\chi_{8016}(53,\cdot)$$ 8016.bt 332 yes $$1$$ $$1$$ $$e\left(\frac{135}{332}\right)$$ $$e\left(\frac{163}{166}\right)$$ $$e\left(\frac{45}{332}\right)$$ $$e\left(\frac{127}{332}\right)$$ $$e\left(\frac{25}{83}\right)$$ $$e\left(\frac{277}{332}\right)$$ $$e\left(\frac{1}{166}\right)$$ $$e\left(\frac{135}{166}\right)$$ $$e\left(\frac{247}{332}\right)$$ $$e\left(\frac{8}{83}\right)$$
$$\chi_{8016}(55,\cdot)$$ 8016.bc 166 no $$1$$ $$1$$ $$e\left(\frac{56}{83}\right)$$ $$e\left(\frac{19}{166}\right)$$ $$e\left(\frac{74}{83}\right)$$ $$e\left(\frac{41}{83}\right)$$ $$e\left(\frac{43}{166}\right)$$ $$e\left(\frac{11}{83}\right)$$ $$e\left(\frac{66}{83}\right)$$ $$e\left(\frac{29}{83}\right)$$ $$e\left(\frac{117}{166}\right)$$ $$e\left(\frac{37}{166}\right)$$
$$\chi_{8016}(59,\cdot)$$ 8016.bo 332 yes $$-1$$ $$1$$ $$e\left(\frac{143}{332}\right)$$ $$e\left(\frac{27}{83}\right)$$ $$e\left(\frac{103}{332}\right)$$ $$e\left(\frac{287}{332}\right)$$ $$e\left(\frac{48}{83}\right)$$ $$e\left(\frac{243}{332}\right)$$ $$e\left(\frac{74}{83}\right)$$ $$e\left(\frac{143}{166}\right)$$ $$e\left(\frac{119}{332}\right)$$ $$e\left(\frac{127}{166}\right)$$
$$\chi_{8016}(61,\cdot)$$ 8016.bs 332 no $$1$$ $$1$$ $$e\left(\frac{49}{332}\right)$$ $$e\left(\frac{69}{166}\right)$$ $$e\left(\frac{293}{332}\right)$$ $$e\left(\frac{67}{332}\right)$$ $$e\left(\frac{6}{83}\right)$$ $$e\left(\frac{103}{332}\right)$$ $$e\left(\frac{143}{166}\right)$$ $$e\left(\frac{49}{166}\right)$$ $$e\left(\frac{295}{332}\right)$$ $$e\left(\frac{65}{83}\right)$$
$$\chi_{8016}(65,\cdot)$$ 8016.bi 166 no $$-1$$ $$1$$ $$e\left(\frac{21}{166}\right)$$ $$e\left(\frac{77}{83}\right)$$ $$e\left(\frac{7}{166}\right)$$ $$e\left(\frac{44}{83}\right)$$ $$e\left(\frac{117}{166}\right)$$ $$e\left(\frac{28}{83}\right)$$ $$e\left(\frac{87}{166}\right)$$ $$e\left(\frac{21}{83}\right)$$ $$e\left(\frac{79}{166}\right)$$ $$e\left(\frac{32}{83}\right)$$
$$\chi_{8016}(67,\cdot)$$ 8016.br 332 no $$1$$ $$1$$ $$e\left(\frac{247}{332}\right)$$ $$e\left(\frac{24}{83}\right)$$ $$e\left(\frac{27}{332}\right)$$ $$e\left(\frac{209}{332}\right)$$ $$e\left(\frac{113}{166}\right)$$ $$e\left(\frac{133}{332}\right)$$ $$e\left(\frac{67}{166}\right)$$ $$e\left(\frac{81}{166}\right)$$ $$e\left(\frac{115}{332}\right)$$ $$e\left(\frac{159}{166}\right)$$
$$\chi_{8016}(71,\cdot)$$ 8016.bm 166 no $$-1$$ $$1$$ $$e\left(\frac{45}{166}\right)$$ $$e\left(\frac{81}{166}\right)$$ $$e\left(\frac{15}{166}\right)$$ $$e\left(\frac{35}{83}\right)$$ $$e\left(\frac{72}{83}\right)$$ $$e\left(\frac{60}{83}\right)$$ $$e\left(\frac{139}{166}\right)$$ $$e\left(\frac{45}{83}\right)$$ $$e\left(\frac{55}{83}\right)$$ $$e\left(\frac{149}{166}\right)$$
$$\chi_{8016}(73,\cdot)$$ 8016.ba 166 no $$-1$$ $$1$$ $$e\left(\frac{3}{83}\right)$$ $$e\left(\frac{22}{83}\right)$$ $$e\left(\frac{85}{166}\right)$$ $$e\left(\frac{60}{83}\right)$$ $$e\left(\frac{69}{166}\right)$$ $$e\left(\frac{99}{166}\right)$$ $$e\left(\frac{13}{166}\right)$$ $$e\left(\frac{6}{83}\right)$$ $$e\left(\frac{153}{166}\right)$$ $$e\left(\frac{21}{83}\right)$$
$$\chi_{8016}(77,\cdot)$$ 8016.bv 332 yes $$-1$$ $$1$$ $$e\left(\frac{43}{332}\right)$$ $$e\left(\frac{47}{166}\right)$$ $$e\left(\frac{291}{332}\right)$$ $$e\left(\frac{279}{332}\right)$$ $$e\left(\frac{19}{166}\right)$$ $$e\left(\frac{87}{332}\right)$$ $$e\left(\frac{6}{83}\right)$$ $$e\left(\frac{43}{166}\right)$$ $$e\left(\frac{225}{332}\right)$$ $$e\left(\frac{13}{83}\right)$$
$$\chi_{8016}(79,\cdot)$$ 8016.bn 166 no $$1$$ $$1$$ $$e\left(\frac{65}{166}\right)$$ $$e\left(\frac{117}{166}\right)$$ $$e\left(\frac{77}{166}\right)$$ $$e\left(\frac{55}{166}\right)$$ $$e\left(\frac{125}{166}\right)$$ $$e\left(\frac{35}{166}\right)$$ $$e\left(\frac{22}{83}\right)$$ $$e\left(\frac{65}{83}\right)$$ $$e\left(\frac{61}{83}\right)$$ $$e\left(\frac{123}{166}\right)$$
$$\chi_{8016}(83,\cdot)$$ 8016.bo 332 yes $$-1$$ $$1$$ $$e\left(\frac{169}{332}\right)$$ $$e\left(\frac{47}{83}\right)$$ $$e\left(\frac{1}{332}\right)$$ $$e\left(\frac{309}{332}\right)$$ $$e\left(\frac{19}{83}\right)$$ $$e\left(\frac{257}{332}\right)$$ $$e\left(\frac{12}{83}\right)$$ $$e\left(\frac{3}{166}\right)$$ $$e\left(\frac{201}{332}\right)$$ $$e\left(\frac{135}{166}\right)$$
$$\chi_{8016}(85,\cdot)$$ 8016.bs 332 no $$1$$ $$1$$ $$e\left(\frac{191}{332}\right)$$ $$e\left(\frac{147}{166}\right)$$ $$e\left(\frac{119}{332}\right)$$ $$e\left(\frac{85}{332}\right)$$ $$e\left(\frac{20}{83}\right)$$ $$e\left(\frac{205}{332}\right)$$ $$e\left(\frac{117}{166}\right)$$ $$e\left(\frac{25}{166}\right)$$ $$e\left(\frac{181}{332}\right)$$ $$e\left(\frac{23}{83}\right)$$
$$\chi_{8016}(89,\cdot)$$ 8016.z 166 no $$-1$$ $$1$$ $$e\left(\frac{77}{83}\right)$$ $$e\left(\frac{39}{83}\right)$$ $$e\left(\frac{81}{83}\right)$$ $$e\left(\frac{9}{166}\right)$$ $$e\left(\frac{111}{166}\right)$$ $$e\left(\frac{51}{166}\right)$$ $$e\left(\frac{57}{166}\right)$$ $$e\left(\frac{71}{83}\right)$$ $$e\left(\frac{13}{83}\right)$$ $$e\left(\frac{41}{83}\right)$$
$$\chi_{8016}(91,\cdot)$$ 8016.br 332 no $$1$$ $$1$$ $$e\left(\frac{193}{332}\right)$$ $$e\left(\frac{8}{83}\right)$$ $$e\left(\frac{9}{332}\right)$$ $$e\left(\frac{291}{332}\right)$$ $$e\left(\frac{93}{166}\right)$$ $$e\left(\frac{155}{332}\right)$$ $$e\left(\frac{133}{166}\right)$$ $$e\left(\frac{27}{166}\right)$$ $$e\left(\frac{149}{332}\right)$$ $$e\left(\frac{53}{166}\right)$$
$$\chi_{8016}(95,\cdot)$$ 8016.bd 166 no $$-1$$ $$1$$ $$e\left(\frac{71}{83}\right)$$ $$e\left(\frac{73}{166}\right)$$ $$e\left(\frac{79}{83}\right)$$ $$e\left(\frac{101}{166}\right)$$ $$e\left(\frac{28}{83}\right)$$ $$e\left(\frac{19}{166}\right)$$ $$e\left(\frac{31}{166}\right)$$ $$e\left(\frac{59}{83}\right)$$ $$e\left(\frac{135}{166}\right)$$ $$e\left(\frac{81}{166}\right)$$