# Properties

 Modulus $640332$ Structure $$C_{2}\times C_{2}\times C_{6}\times C_{6930}$$ Order $166320$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(640332)

pari: g = idealstar(,640332,2)

## Character group

 sage: G.order()  pari: g.no Order = 166320 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{6}\times C_{6930}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{640332}(320167,\cdot)$, $\chi_{640332}(450605,\cdot)$, $\chi_{640332}(339769,\cdot)$, $\chi_{640332}(179929,\cdot)$

## First 32 of 166320 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 $$-1$$ $$1$$ $$5$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{640332}(1,\cdot)$$ 640332.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{640332}(5,\cdot)$$ 640332.bls 6930 no $$1$$ $$1$$ $$e\left(\frac{674}{3465}\right)$$ $$e\left(\frac{6607}{6930}\right)$$ $$e\left(\frac{151}{385}\right)$$ $$e\left(\frac{37}{110}\right)$$ $$e\left(\frac{533}{1386}\right)$$ $$e\left(\frac{1348}{3465}\right)$$ $$e\left(\frac{989}{6930}\right)$$ $$e\left(\frac{241}{990}\right)$$ $$e\left(\frac{19}{1155}\right)$$ $$e\left(\frac{1913}{3465}\right)$$
$$\chi_{640332}(13,\cdot)$$ 640332.bmr 6930 no $$1$$ $$1$$ $$e\left(\frac{6607}{6930}\right)$$ $$e\left(\frac{764}{3465}\right)$$ $$e\left(\frac{347}{1155}\right)$$ $$e\left(\frac{7}{165}\right)$$ $$e\left(\frac{13}{693}\right)$$ $$e\left(\frac{3142}{3465}\right)$$ $$e\left(\frac{1361}{6930}\right)$$ $$e\left(\frac{349}{990}\right)$$ $$e\left(\frac{431}{1155}\right)$$ $$e\left(\frac{1592}{3465}\right)$$
$$\chi_{640332}(17,\cdot)$$ 640332.bjk 2310 no $$-1$$ $$1$$ $$e\left(\frac{151}{385}\right)$$ $$e\left(\frac{347}{1155}\right)$$ $$e\left(\frac{481}{2310}\right)$$ $$e\left(\frac{133}{165}\right)$$ $$e\left(\frac{149}{154}\right)$$ $$e\left(\frac{302}{385}\right)$$ $$e\left(\frac{139}{1155}\right)$$ $$e\left(\frac{47}{330}\right)$$ $$e\left(\frac{874}{1155}\right)$$ $$e\left(\frac{787}{2310}\right)$$
$$\chi_{640332}(19,\cdot)$$ 640332.ym 330 no $$-1$$ $$1$$ $$e\left(\frac{37}{110}\right)$$ $$e\left(\frac{7}{165}\right)$$ $$e\left(\frac{133}{165}\right)$$ $$e\left(\frac{97}{330}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{37}{55}\right)$$ $$e\left(\frac{163}{330}\right)$$ $$e\left(\frac{92}{165}\right)$$ $$e\left(\frac{59}{165}\right)$$ $$e\left(\frac{31}{165}\right)$$
$$\chi_{640332}(23,\cdot)$$ 640332.bht 1386 yes $$1$$ $$1$$ $$e\left(\frac{533}{1386}\right)$$ $$e\left(\frac{13}{693}\right)$$ $$e\left(\frac{149}{154}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{103}{693}\right)$$ $$e\left(\frac{533}{693}\right)$$ $$e\left(\frac{991}{1386}\right)$$ $$e\left(\frac{155}{198}\right)$$ $$e\left(\frac{80}{231}\right)$$ $$e\left(\frac{827}{1386}\right)$$
$$\chi_{640332}(25,\cdot)$$ 640332.blo 3465 no $$1$$ $$1$$ $$e\left(\frac{1348}{3465}\right)$$ $$e\left(\frac{3142}{3465}\right)$$ $$e\left(\frac{302}{385}\right)$$ $$e\left(\frac{37}{55}\right)$$ $$e\left(\frac{533}{693}\right)$$ $$e\left(\frac{2696}{3465}\right)$$ $$e\left(\frac{989}{3465}\right)$$ $$e\left(\frac{241}{495}\right)$$ $$e\left(\frac{38}{1155}\right)$$ $$e\left(\frac{361}{3465}\right)$$
$$\chi_{640332}(29,\cdot)$$ 640332.bnb 6930 no $$1$$ $$1$$ $$e\left(\frac{989}{6930}\right)$$ $$e\left(\frac{1361}{6930}\right)$$ $$e\left(\frac{139}{1155}\right)$$ $$e\left(\frac{163}{330}\right)$$ $$e\left(\frac{991}{1386}\right)$$ $$e\left(\frac{989}{3465}\right)$$ $$e\left(\frac{1376}{3465}\right)$$ $$e\left(\frac{199}{495}\right)$$ $$e\left(\frac{622}{1155}\right)$$ $$e\left(\frac{3214}{3465}\right)$$
$$\chi_{640332}(31,\cdot)$$ 640332.bgq 990 no $$1$$ $$1$$ $$e\left(\frac{241}{990}\right)$$ $$e\left(\frac{349}{990}\right)$$ $$e\left(\frac{47}{330}\right)$$ $$e\left(\frac{92}{165}\right)$$ $$e\left(\frac{155}{198}\right)$$ $$e\left(\frac{241}{495}\right)$$ $$e\left(\frac{199}{495}\right)$$ $$e\left(\frac{62}{495}\right)$$ $$e\left(\frac{46}{55}\right)$$ $$e\left(\frac{367}{990}\right)$$
$$\chi_{640332}(37,\cdot)$$ 640332.bhm 1155 no $$1$$ $$1$$ $$e\left(\frac{19}{1155}\right)$$ $$e\left(\frac{431}{1155}\right)$$ $$e\left(\frac{874}{1155}\right)$$ $$e\left(\frac{59}{165}\right)$$ $$e\left(\frac{80}{231}\right)$$ $$e\left(\frac{38}{1155}\right)$$ $$e\left(\frac{622}{1155}\right)$$ $$e\left(\frac{46}{55}\right)$$ $$e\left(\frac{482}{1155}\right)$$ $$e\left(\frac{1013}{1155}\right)$$
$$\chi_{640332}(41,\cdot)$$ 640332.bme 6930 no $$-1$$ $$1$$ $$e\left(\frac{1913}{3465}\right)$$ $$e\left(\frac{1592}{3465}\right)$$ $$e\left(\frac{787}{2310}\right)$$ $$e\left(\frac{31}{165}\right)$$ $$e\left(\frac{827}{1386}\right)$$ $$e\left(\frac{361}{3465}\right)$$ $$e\left(\frac{3214}{3465}\right)$$ $$e\left(\frac{367}{990}\right)$$ $$e\left(\frac{1013}{1155}\right)$$ $$e\left(\frac{1537}{6930}\right)$$
$$\chi_{640332}(43,\cdot)$$ 640332.bit 1386 yes $$1$$ $$1$$ $$e\left(\frac{50}{693}\right)$$ $$e\left(\frac{619}{1386}\right)$$ $$e\left(\frac{19}{462}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{391}{1386}\right)$$ $$e\left(\frac{100}{693}\right)$$ $$e\left(\frac{911}{1386}\right)$$ $$e\left(\frac{97}{198}\right)$$ $$e\left(\frac{104}{231}\right)$$ $$e\left(\frac{205}{1386}\right)$$
$$\chi_{640332}(47,\cdot)$$ 640332.bmo 6930 yes $$-1$$ $$1$$ $$e\left(\frac{1123}{3465}\right)$$ $$e\left(\frac{149}{6930}\right)$$ $$e\left(\frac{536}{1155}\right)$$ $$e\left(\frac{46}{165}\right)$$ $$e\left(\frac{461}{693}\right)$$ $$e\left(\frac{2246}{3465}\right)$$ $$e\left(\frac{4693}{6930}\right)$$ $$e\left(\frac{361}{495}\right)$$ $$e\left(\frac{216}{385}\right)$$ $$e\left(\frac{3076}{3465}\right)$$
$$\chi_{640332}(53,\cdot)$$ 640332.bjn 2310 no $$-1$$ $$1$$ $$e\left(\frac{1649}{2310}\right)$$ $$e\left(\frac{71}{385}\right)$$ $$e\left(\frac{1549}{2310}\right)$$ $$e\left(\frac{52}{165}\right)$$ $$e\left(\frac{1}{462}\right)$$ $$e\left(\frac{494}{1155}\right)$$ $$e\left(\frac{129}{770}\right)$$ $$e\left(\frac{89}{165}\right)$$ $$e\left(\frac{106}{1155}\right)$$ $$e\left(\frac{181}{770}\right)$$
$$\chi_{640332}(59,\cdot)$$ 640332.bmo 6930 yes $$-1$$ $$1$$ $$e\left(\frac{3092}{3465}\right)$$ $$e\left(\frac{5671}{6930}\right)$$ $$e\left(\frac{184}{1155}\right)$$ $$e\left(\frac{134}{165}\right)$$ $$e\left(\frac{472}{693}\right)$$ $$e\left(\frac{2719}{3465}\right)$$ $$e\left(\frac{5507}{6930}\right)$$ $$e\left(\frac{119}{495}\right)$$ $$e\left(\frac{304}{385}\right)$$ $$e\left(\frac{194}{3465}\right)$$
$$\chi_{640332}(61,\cdot)$$ 640332.bmq 6930 no $$1$$ $$1$$ $$e\left(\frac{2543}{6930}\right)$$ $$e\left(\frac{2896}{3465}\right)$$ $$e\left(\frac{503}{1155}\right)$$ $$e\left(\frac{13}{165}\right)$$ $$e\left(\frac{65}{693}\right)$$ $$e\left(\frac{2543}{3465}\right)$$ $$e\left(\frac{3109}{6930}\right)$$ $$e\left(\frac{821}{990}\right)$$ $$e\left(\frac{128}{385}\right)$$ $$e\left(\frac{2878}{3465}\right)$$
$$\chi_{640332}(65,\cdot)$$ 640332.bic 1386 no $$1$$ $$1$$ $$e\left(\frac{205}{1386}\right)$$ $$e\left(\frac{241}{1386}\right)$$ $$e\left(\frac{160}{231}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{559}{1386}\right)$$ $$e\left(\frac{205}{693}\right)$$ $$e\left(\frac{235}{693}\right)$$ $$e\left(\frac{59}{99}\right)$$ $$e\left(\frac{30}{77}\right)$$ $$e\left(\frac{8}{693}\right)$$
$$\chi_{640332}(67,\cdot)$$ 640332.vd 198 no $$-1$$ $$1$$ $$e\left(\frac{82}{99}\right)$$ $$e\left(\frac{37}{99}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{71}{198}\right)$$ $$e\left(\frac{65}{99}\right)$$ $$e\left(\frac{89}{99}\right)$$ $$e\left(\frac{47}{198}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{46}{99}\right)$$
$$\chi_{640332}(71,\cdot)$$ 640332.bkf 2310 no $$1$$ $$1$$ $$e\left(\frac{2251}{2310}\right)$$ $$e\left(\frac{962}{1155}\right)$$ $$e\left(\frac{507}{770}\right)$$ $$e\left(\frac{47}{110}\right)$$ $$e\left(\frac{46}{231}\right)$$ $$e\left(\frac{1096}{1155}\right)$$ $$e\left(\frac{1493}{2310}\right)$$ $$e\left(\frac{217}{330}\right)$$ $$e\left(\frac{68}{385}\right)$$ $$e\left(\frac{907}{2310}\right)$$
$$\chi_{640332}(73,\cdot)$$ 640332.bkd 2310 no $$1$$ $$1$$ $$e\left(\frac{1783}{2310}\right)$$ $$e\left(\frac{436}{1155}\right)$$ $$e\left(\frac{584}{1155}\right)$$ $$e\left(\frac{124}{165}\right)$$ $$e\left(\frac{82}{231}\right)$$ $$e\left(\frac{628}{1155}\right)$$ $$e\left(\frac{559}{2310}\right)$$ $$e\left(\frac{47}{110}\right)$$ $$e\left(\frac{367}{1155}\right)$$ $$e\left(\frac{328}{1155}\right)$$
$$\chi_{640332}(79,\cdot)$$ 640332.bgr 990 no $$1$$ $$1$$ $$e\left(\frac{13}{495}\right)$$ $$e\left(\frac{89}{990}\right)$$ $$e\left(\frac{307}{330}\right)$$ $$e\left(\frac{127}{165}\right)$$ $$e\left(\frac{73}{198}\right)$$ $$e\left(\frac{26}{495}\right)$$ $$e\left(\frac{883}{990}\right)$$ $$e\left(\frac{989}{990}\right)$$ $$e\left(\frac{36}{55}\right)$$ $$e\left(\frac{17}{990}\right)$$
$$\chi_{640332}(83,\cdot)$$ 640332.bmm 6930 yes $$1$$ $$1$$ $$e\left(\frac{4}{3465}\right)$$ $$e\left(\frac{496}{3465}\right)$$ $$e\left(\frac{251}{2310}\right)$$ $$e\left(\frac{181}{330}\right)$$ $$e\left(\frac{491}{693}\right)$$ $$e\left(\frac{8}{3465}\right)$$ $$e\left(\frac{1367}{3465}\right)$$ $$e\left(\frac{388}{495}\right)$$ $$e\left(\frac{304}{1155}\right)$$ $$e\left(\frac{1541}{6930}\right)$$
$$\chi_{640332}(85,\cdot)$$ 640332.bmk 6930 no $$-1$$ $$1$$ $$e\left(\frac{2033}{3465}\right)$$ $$e\left(\frac{1759}{6930}\right)$$ $$e\left(\frac{1387}{2310}\right)$$ $$e\left(\frac{47}{330}\right)$$ $$e\left(\frac{244}{693}\right)$$ $$e\left(\frac{601}{3465}\right)$$ $$e\left(\frac{1823}{6930}\right)$$ $$e\left(\frac{191}{495}\right)$$ $$e\left(\frac{893}{1155}\right)$$ $$e\left(\frac{6187}{6930}\right)$$
$$\chi_{640332}(89,\cdot)$$ 640332.bcy 462 no $$1$$ $$1$$ $$e\left(\frac{6}{77}\right)$$ $$e\left(\frac{229}{462}\right)$$ $$e\left(\frac{212}{231}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{127}{154}\right)$$ $$e\left(\frac{12}{77}\right)$$ $$e\left(\frac{137}{462}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{100}{231}\right)$$ $$e\left(\frac{137}{231}\right)$$
$$\chi_{640332}(95,\cdot)$$ 640332.bmp 6930 yes $$-1$$ $$1$$ $$e\left(\frac{3679}{6930}\right)$$ $$e\left(\frac{6901}{6930}\right)$$ $$e\left(\frac{229}{1155}\right)$$ $$e\left(\frac{104}{165}\right)$$ $$e\left(\frac{487}{693}\right)$$ $$e\left(\frac{214}{3465}\right)$$ $$e\left(\frac{2206}{3465}\right)$$ $$e\left(\frac{793}{990}\right)$$ $$e\left(\frac{144}{385}\right)$$ $$e\left(\frac{2564}{3465}\right)$$
$$\chi_{640332}(97,\cdot)$$ 640332.bgw 990 no $$-1$$ $$1$$ $$e\left(\frac{821}{990}\right)$$ $$e\left(\frac{329}{990}\right)$$ $$e\left(\frac{287}{330}\right)$$ $$e\left(\frac{109}{330}\right)$$ $$e\left(\frac{35}{99}\right)$$ $$e\left(\frac{326}{495}\right)$$ $$e\left(\frac{389}{495}\right)$$ $$e\left(\frac{89}{990}\right)$$ $$e\left(\frac{13}{165}\right)$$ $$e\left(\frac{797}{990}\right)$$
$$\chi_{640332}(101,\cdot)$$ 640332.bnh 6930 no $$-1$$ $$1$$ $$e\left(\frac{2641}{3465}\right)$$ $$e\left(\frac{619}{3465}\right)$$ $$e\left(\frac{603}{770}\right)$$ $$e\left(\frac{19}{55}\right)$$ $$e\left(\frac{757}{1386}\right)$$ $$e\left(\frac{1817}{3465}\right)$$ $$e\left(\frac{218}{3465}\right)$$ $$e\left(\frac{359}{990}\right)$$ $$e\left(\frac{131}{1155}\right)$$ $$e\left(\frac{2489}{6930}\right)$$
$$\chi_{640332}(103,\cdot)$$ 640332.bni 6930 yes $$1$$ $$1$$ $$e\left(\frac{6829}{6930}\right)$$ $$e\left(\frac{181}{6930}\right)$$ $$e\left(\frac{211}{770}\right)$$ $$e\left(\frac{3}{55}\right)$$ $$e\left(\frac{1289}{1386}\right)$$ $$e\left(\frac{3364}{3465}\right)$$ $$e\left(\frac{211}{3465}\right)$$ $$e\left(\frac{134}{495}\right)$$ $$e\left(\frac{397}{1155}\right)$$ $$e\left(\frac{613}{6930}\right)$$
$$\chi_{640332}(107,\cdot)$$ 640332.bkj 2310 no $$-1$$ $$1$$ $$e\left(\frac{607}{2310}\right)$$ $$e\left(\frac{321}{770}\right)$$ $$e\left(\frac{871}{1155}\right)$$ $$e\left(\frac{116}{165}\right)$$ $$e\left(\frac{208}{231}\right)$$ $$e\left(\frac{607}{1155}\right)$$ $$e\left(\frac{36}{385}\right)$$ $$e\left(\frac{29}{330}\right)$$ $$e\left(\frac{668}{1155}\right)$$ $$e\left(\frac{149}{385}\right)$$
$$\chi_{640332}(109,\cdot)$$ 640332.bbe 462 no $$-1$$ $$1$$ $$e\left(\frac{38}{231}\right)$$ $$e\left(\frac{87}{154}\right)$$ $$e\left(\frac{185}{462}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{107}{231}\right)$$ $$e\left(\frac{76}{231}\right)$$ $$e\left(\frac{85}{154}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{194}{231}\right)$$ $$e\left(\frac{93}{154}\right)$$
$$\chi_{640332}(113,\cdot)$$ 640332.bmf 6930 no $$-1$$ $$1$$ $$e\left(\frac{841}{6930}\right)$$ $$e\left(\frac{167}{3465}\right)$$ $$e\left(\frac{1987}{2310}\right)$$ $$e\left(\frac{16}{165}\right)$$ $$e\left(\frac{149}{1386}\right)$$ $$e\left(\frac{841}{3465}\right)$$ $$e\left(\frac{683}{6930}\right)$$ $$e\left(\frac{446}{495}\right)$$ $$e\left(\frac{773}{1155}\right)$$ $$e\left(\frac{3907}{6930}\right)$$
$$\chi_{640332}(115,\cdot)$$ 640332.bni 6930 yes $$1$$ $$1$$ $$e\left(\frac{4013}{6930}\right)$$ $$e\left(\frac{6737}{6930}\right)$$ $$e\left(\frac{277}{770}\right)$$ $$e\left(\frac{36}{55}\right)$$ $$e\left(\frac{739}{1386}\right)$$ $$e\left(\frac{548}{3465}\right)$$ $$e\left(\frac{2972}{3465}\right)$$ $$e\left(\frac{13}{495}\right)$$ $$e\left(\frac{419}{1155}\right)$$ $$e\left(\frac{1031}{6930}\right)$$