Properties

 Modulus $7942$ Structure $$C_{2}\times C_{1710}$$ Order $3420$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(7942)

pari: g = idealstar(,7942,2)

Character group

 sage: G.order()  pari: g.no Order = 3420 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{1710}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{7942}(5777,\cdot)$, $\chi_{7942}(6139,\cdot)$

First 32 of 3420 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$13$$ $$15$$ $$17$$ $$21$$ $$23$$ $$25$$
$$\chi_{7942}(1,\cdot)$$ 7942.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{7942}(3,\cdot)$$ 7942.bt 1710 no $$-1$$ $$1$$ $$e\left(\frac{1529}{1710}\right)$$ $$e\left(\frac{421}{855}\right)$$ $$e\left(\frac{161}{285}\right)$$ $$e\left(\frac{674}{855}\right)$$ $$e\left(\frac{883}{1710}\right)$$ $$e\left(\frac{661}{1710}\right)$$ $$e\left(\frac{46}{855}\right)$$ $$e\left(\frac{157}{342}\right)$$ $$e\left(\frac{58}{171}\right)$$ $$e\left(\frac{842}{855}\right)$$
$$\chi_{7942}(5,\cdot)$$ 7942.bs 855 no $$1$$ $$1$$ $$e\left(\frac{421}{855}\right)$$ $$e\left(\frac{838}{855}\right)$$ $$e\left(\frac{158}{285}\right)$$ $$e\left(\frac{842}{855}\right)$$ $$e\left(\frac{497}{855}\right)$$ $$e\left(\frac{404}{855}\right)$$ $$e\left(\frac{778}{855}\right)$$ $$e\left(\frac{8}{171}\right)$$ $$e\left(\frac{7}{171}\right)$$ $$e\left(\frac{821}{855}\right)$$
$$\chi_{7942}(7,\cdot)$$ 7942.bp 570 no $$-1$$ $$1$$ $$e\left(\frac{161}{285}\right)$$ $$e\left(\frac{158}{285}\right)$$ $$e\left(\frac{131}{190}\right)$$ $$e\left(\frac{37}{285}\right)$$ $$e\left(\frac{569}{570}\right)$$ $$e\left(\frac{34}{285}\right)$$ $$e\left(\frac{241}{570}\right)$$ $$e\left(\frac{29}{114}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{31}{285}\right)$$
$$\chi_{7942}(9,\cdot)$$ 7942.bs 855 no $$1$$ $$1$$ $$e\left(\frac{674}{855}\right)$$ $$e\left(\frac{842}{855}\right)$$ $$e\left(\frac{37}{285}\right)$$ $$e\left(\frac{493}{855}\right)$$ $$e\left(\frac{28}{855}\right)$$ $$e\left(\frac{661}{855}\right)$$ $$e\left(\frac{92}{855}\right)$$ $$e\left(\frac{157}{171}\right)$$ $$e\left(\frac{116}{171}\right)$$ $$e\left(\frac{829}{855}\right)$$
$$\chi_{7942}(13,\cdot)$$ 7942.bv 1710 no $$1$$ $$1$$ $$e\left(\frac{883}{1710}\right)$$ $$e\left(\frac{497}{855}\right)$$ $$e\left(\frac{569}{570}\right)$$ $$e\left(\frac{28}{855}\right)$$ $$e\left(\frac{508}{855}\right)$$ $$e\left(\frac{167}{1710}\right)$$ $$e\left(\frac{529}{1710}\right)$$ $$e\left(\frac{88}{171}\right)$$ $$e\left(\frac{77}{171}\right)$$ $$e\left(\frac{139}{855}\right)$$
$$\chi_{7942}(15,\cdot)$$ 7942.bt 1710 no $$-1$$ $$1$$ $$e\left(\frac{661}{1710}\right)$$ $$e\left(\frac{404}{855}\right)$$ $$e\left(\frac{34}{285}\right)$$ $$e\left(\frac{661}{855}\right)$$ $$e\left(\frac{167}{1710}\right)$$ $$e\left(\frac{1469}{1710}\right)$$ $$e\left(\frac{824}{855}\right)$$ $$e\left(\frac{173}{342}\right)$$ $$e\left(\frac{65}{171}\right)$$ $$e\left(\frac{808}{855}\right)$$
$$\chi_{7942}(17,\cdot)$$ 7942.bu 1710 no $$-1$$ $$1$$ $$e\left(\frac{46}{855}\right)$$ $$e\left(\frac{778}{855}\right)$$ $$e\left(\frac{241}{570}\right)$$ $$e\left(\frac{92}{855}\right)$$ $$e\left(\frac{529}{1710}\right)$$ $$e\left(\frac{824}{855}\right)$$ $$e\left(\frac{761}{1710}\right)$$ $$e\left(\frac{163}{342}\right)$$ $$e\left(\frac{82}{171}\right)$$ $$e\left(\frac{701}{855}\right)$$
$$\chi_{7942}(21,\cdot)$$ 7942.bm 342 no $$1$$ $$1$$ $$e\left(\frac{157}{342}\right)$$ $$e\left(\frac{8}{171}\right)$$ $$e\left(\frac{29}{114}\right)$$ $$e\left(\frac{157}{171}\right)$$ $$e\left(\frac{88}{171}\right)$$ $$e\left(\frac{173}{342}\right)$$ $$e\left(\frac{163}{342}\right)$$ $$e\left(\frac{122}{171}\right)$$ $$e\left(\frac{64}{171}\right)$$ $$e\left(\frac{16}{171}\right)$$
$$\chi_{7942}(23,\cdot)$$ 7942.bh 171 no $$1$$ $$1$$ $$e\left(\frac{58}{171}\right)$$ $$e\left(\frac{7}{171}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{116}{171}\right)$$ $$e\left(\frac{77}{171}\right)$$ $$e\left(\frac{65}{171}\right)$$ $$e\left(\frac{82}{171}\right)$$ $$e\left(\frac{64}{171}\right)$$ $$e\left(\frac{56}{171}\right)$$ $$e\left(\frac{14}{171}\right)$$
$$\chi_{7942}(25,\cdot)$$ 7942.bs 855 no $$1$$ $$1$$ $$e\left(\frac{842}{855}\right)$$ $$e\left(\frac{821}{855}\right)$$ $$e\left(\frac{31}{285}\right)$$ $$e\left(\frac{829}{855}\right)$$ $$e\left(\frac{139}{855}\right)$$ $$e\left(\frac{808}{855}\right)$$ $$e\left(\frac{701}{855}\right)$$ $$e\left(\frac{16}{171}\right)$$ $$e\left(\frac{14}{171}\right)$$ $$e\left(\frac{787}{855}\right)$$
$$\chi_{7942}(27,\cdot)$$ 7942.br 570 no $$-1$$ $$1$$ $$e\left(\frac{389}{570}\right)$$ $$e\left(\frac{136}{285}\right)$$ $$e\left(\frac{66}{95}\right)$$ $$e\left(\frac{104}{285}\right)$$ $$e\left(\frac{313}{570}\right)$$ $$e\left(\frac{91}{570}\right)$$ $$e\left(\frac{46}{285}\right)$$ $$e\left(\frac{43}{114}\right)$$ $$e\left(\frac{1}{57}\right)$$ $$e\left(\frac{272}{285}\right)$$
$$\chi_{7942}(29,\cdot)$$ 7942.bv 1710 no $$1$$ $$1$$ $$e\left(\frac{871}{1710}\right)$$ $$e\left(\frac{284}{855}\right)$$ $$e\left(\frac{203}{570}\right)$$ $$e\left(\frac{16}{855}\right)$$ $$e\left(\frac{46}{855}\right)$$ $$e\left(\frac{1439}{1710}\right)$$ $$e\left(\frac{913}{1710}\right)$$ $$e\left(\frac{148}{171}\right)$$ $$e\left(\frac{44}{171}\right)$$ $$e\left(\frac{568}{855}\right)$$
$$\chi_{7942}(31,\cdot)$$ 7942.br 570 no $$-1$$ $$1$$ $$e\left(\frac{541}{570}\right)$$ $$e\left(\frac{269}{285}\right)$$ $$e\left(\frac{9}{95}\right)$$ $$e\left(\frac{256}{285}\right)$$ $$e\left(\frac{47}{570}\right)$$ $$e\left(\frac{509}{570}\right)$$ $$e\left(\frac{179}{285}\right)$$ $$e\left(\frac{5}{114}\right)$$ $$e\left(\frac{20}{57}\right)$$ $$e\left(\frac{253}{285}\right)$$
$$\chi_{7942}(35,\cdot)$$ 7942.bu 1710 no $$-1$$ $$1$$ $$e\left(\frac{49}{855}\right)$$ $$e\left(\frac{457}{855}\right)$$ $$e\left(\frac{139}{570}\right)$$ $$e\left(\frac{98}{855}\right)$$ $$e\left(\frac{991}{1710}\right)$$ $$e\left(\frac{506}{855}\right)$$ $$e\left(\frac{569}{1710}\right)$$ $$e\left(\frac{103}{342}\right)$$ $$e\left(\frac{13}{171}\right)$$ $$e\left(\frac{59}{855}\right)$$
$$\chi_{7942}(37,\cdot)$$ 7942.bj 190 no $$-1$$ $$1$$ $$e\left(\frac{169}{190}\right)$$ $$e\left(\frac{31}{95}\right)$$ $$e\left(\frac{13}{95}\right)$$ $$e\left(\frac{74}{95}\right)$$ $$e\left(\frac{93}{190}\right)$$ $$e\left(\frac{41}{190}\right)$$ $$e\left(\frac{51}{95}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{62}{95}\right)$$
$$\chi_{7942}(39,\cdot)$$ 7942.bk 190 no $$-1$$ $$1$$ $$e\left(\frac{39}{95}\right)$$ $$e\left(\frac{7}{95}\right)$$ $$e\left(\frac{107}{190}\right)$$ $$e\left(\frac{78}{95}\right)$$ $$e\left(\frac{21}{190}\right)$$ $$e\left(\frac{46}{95}\right)$$ $$e\left(\frac{69}{190}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{14}{95}\right)$$
$$\chi_{7942}(41,\cdot)$$ 7942.bv 1710 no $$1$$ $$1$$ $$e\left(\frac{1079}{1710}\right)$$ $$e\left(\frac{556}{855}\right)$$ $$e\left(\frac{277}{570}\right)$$ $$e\left(\frac{224}{855}\right)$$ $$e\left(\frac{644}{855}\right)$$ $$e\left(\frac{481}{1710}\right)$$ $$e\left(\frac{1667}{1710}\right)$$ $$e\left(\frac{20}{171}\right)$$ $$e\left(\frac{103}{171}\right)$$ $$e\left(\frac{257}{855}\right)$$
$$\chi_{7942}(43,\cdot)$$ 7942.bn 342 no $$-1$$ $$1$$ $$e\left(\frac{23}{171}\right)$$ $$e\left(\frac{47}{171}\right)$$ $$e\left(\frac{35}{114}\right)$$ $$e\left(\frac{46}{171}\right)$$ $$e\left(\frac{179}{342}\right)$$ $$e\left(\frac{70}{171}\right)$$ $$e\left(\frac{295}{342}\right)$$ $$e\left(\frac{151}{342}\right)$$ $$e\left(\frac{34}{171}\right)$$ $$e\left(\frac{94}{171}\right)$$
$$\chi_{7942}(45,\cdot)$$ 7942.z 57 no $$1$$ $$1$$ $$e\left(\frac{16}{57}\right)$$ $$e\left(\frac{55}{57}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{35}{57}\right)$$ $$e\left(\frac{14}{57}\right)$$ $$e\left(\frac{1}{57}\right)$$ $$e\left(\frac{55}{57}\right)$$ $$e\left(\frac{41}{57}\right)$$ $$e\left(\frac{53}{57}\right)$$
$$\chi_{7942}(47,\cdot)$$ 7942.bs 855 no $$1$$ $$1$$ $$e\left(\frac{827}{855}\right)$$ $$e\left(\frac{716}{855}\right)$$ $$e\left(\frac{1}{285}\right)$$ $$e\left(\frac{799}{855}\right)$$ $$e\left(\frac{694}{855}\right)$$ $$e\left(\frac{688}{855}\right)$$ $$e\left(\frac{326}{855}\right)$$ $$e\left(\frac{166}{171}\right)$$ $$e\left(\frac{17}{171}\right)$$ $$e\left(\frac{577}{855}\right)$$
$$\chi_{7942}(49,\cdot)$$ 7942.bl 285 no $$1$$ $$1$$ $$e\left(\frac{37}{285}\right)$$ $$e\left(\frac{31}{285}\right)$$ $$e\left(\frac{36}{95}\right)$$ $$e\left(\frac{74}{285}\right)$$ $$e\left(\frac{284}{285}\right)$$ $$e\left(\frac{68}{285}\right)$$ $$e\left(\frac{241}{285}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{62}{285}\right)$$
$$\chi_{7942}(51,\cdot)$$ 7942.bv 1710 no $$1$$ $$1$$ $$e\left(\frac{1621}{1710}\right)$$ $$e\left(\frac{344}{855}\right)$$ $$e\left(\frac{563}{570}\right)$$ $$e\left(\frac{766}{855}\right)$$ $$e\left(\frac{706}{855}\right)$$ $$e\left(\frac{599}{1710}\right)$$ $$e\left(\frac{853}{1710}\right)$$ $$e\left(\frac{160}{171}\right)$$ $$e\left(\frac{140}{171}\right)$$ $$e\left(\frac{688}{855}\right)$$
$$\chi_{7942}(53,\cdot)$$ 7942.bt 1710 no $$-1$$ $$1$$ $$e\left(\frac{913}{1710}\right)$$ $$e\left(\frac{602}{855}\right)$$ $$e\left(\frac{172}{285}\right)$$ $$e\left(\frac{58}{855}\right)$$ $$e\left(\frac{761}{1710}\right)$$ $$e\left(\frac{407}{1710}\right)$$ $$e\left(\frac{212}{855}\right)$$ $$e\left(\frac{47}{342}\right)$$ $$e\left(\frac{74}{171}\right)$$ $$e\left(\frac{349}{855}\right)$$
$$\chi_{7942}(59,\cdot)$$ 7942.bt 1710 no $$-1$$ $$1$$ $$e\left(\frac{281}{1710}\right)$$ $$e\left(\frac{499}{855}\right)$$ $$e\left(\frac{224}{285}\right)$$ $$e\left(\frac{281}{855}\right)$$ $$e\left(\frac{547}{1710}\right)$$ $$e\left(\frac{1279}{1710}\right)$$ $$e\left(\frac{349}{855}\right)$$ $$e\left(\frac{325}{342}\right)$$ $$e\left(\frac{46}{171}\right)$$ $$e\left(\frac{143}{855}\right)$$
$$\chi_{7942}(61,\cdot)$$ 7942.bu 1710 no $$-1$$ $$1$$ $$e\left(\frac{506}{855}\right)$$ $$e\left(\frac{8}{855}\right)$$ $$e\left(\frac{371}{570}\right)$$ $$e\left(\frac{157}{855}\right)$$ $$e\left(\frac{689}{1710}\right)$$ $$e\left(\frac{514}{855}\right)$$ $$e\left(\frac{1531}{1710}\right)$$ $$e\left(\frac{83}{342}\right)$$ $$e\left(\frac{47}{171}\right)$$ $$e\left(\frac{16}{855}\right)$$
$$\chi_{7942}(63,\cdot)$$ 7942.bu 1710 no $$-1$$ $$1$$ $$e\left(\frac{302}{855}\right)$$ $$e\left(\frac{461}{855}\right)$$ $$e\left(\frac{467}{570}\right)$$ $$e\left(\frac{604}{855}\right)$$ $$e\left(\frac{53}{1710}\right)$$ $$e\left(\frac{763}{855}\right)$$ $$e\left(\frac{907}{1710}\right)$$ $$e\left(\frac{59}{342}\right)$$ $$e\left(\frac{122}{171}\right)$$ $$e\left(\frac{67}{855}\right)$$
$$\chi_{7942}(65,\cdot)$$ 7942.bf 114 no $$1$$ $$1$$ $$e\left(\frac{1}{114}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{1}{57}\right)$$ $$e\left(\frac{10}{57}\right)$$ $$e\left(\frac{65}{114}\right)$$ $$e\left(\frac{25}{114}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{28}{57}\right)$$ $$e\left(\frac{7}{57}\right)$$
$$\chi_{7942}(67,\cdot)$$ 7942.bo 342 no $$-1$$ $$1$$ $$e\left(\frac{113}{342}\right)$$ $$e\left(\frac{82}{171}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{113}{171}\right)$$ $$e\left(\frac{265}{342}\right)$$ $$e\left(\frac{277}{342}\right)$$ $$e\left(\frac{130}{171}\right)$$ $$e\left(\frac{107}{342}\right)$$ $$e\left(\frac{143}{171}\right)$$ $$e\left(\frac{164}{171}\right)$$
$$\chi_{7942}(69,\cdot)$$ 7942.s 30 no $$-1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{7942}(71,\cdot)$$ 7942.bt 1710 no $$-1$$ $$1$$ $$e\left(\frac{527}{1710}\right)$$ $$e\left(\frac{163}{855}\right)$$ $$e\left(\frac{128}{285}\right)$$ $$e\left(\frac{527}{855}\right)$$ $$e\left(\frac{679}{1710}\right)$$ $$e\left(\frac{853}{1710}\right)$$ $$e\left(\frac{688}{855}\right)$$ $$e\left(\frac{259}{342}\right)$$ $$e\left(\frac{124}{171}\right)$$ $$e\left(\frac{326}{855}\right)$$
$$\chi_{7942}(73,\cdot)$$ 7942.bu 1710 no $$-1$$ $$1$$ $$e\left(\frac{103}{855}\right)$$ $$e\left(\frac{664}{855}\right)$$ $$e\left(\frac{13}{570}\right)$$ $$e\left(\frac{206}{855}\right)$$ $$e\left(\frac{757}{1710}\right)$$ $$e\left(\frac{767}{855}\right)$$ $$e\left(\frac{533}{1710}\right)$$ $$e\left(\frac{49}{342}\right)$$ $$e\left(\frac{139}{171}\right)$$ $$e\left(\frac{473}{855}\right)$$