Group of Dirichlet characters of modulus 361

• Modulus: $361$
• Structure: $C_{342}$
• Order: $342$

Character group

Order	=	342
Structure	=	$C_{342}$
Generators	=	$\chi_{361}(2,\cdot)$

First 32 of 342 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{361}(1,\cdot)$	361.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{361}(2,\cdot)$	361.l	342	yes	$-1$	$1$	$e\left(\frac{1}{342}\right)$	$e\left(\frac{139}{342}\right)$	$e\left(\frac{1}{171}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{139}{171}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{17}{57}\right)$
$\chi_{361}(3,\cdot)$	361.l	342	yes	$-1$	$1$	$e\left(\frac{139}{342}\right)$	$e\left(\frac{169}{342}\right)$	$e\left(\frac{139}{171}\right)$	$e\left(\frac{50}{171}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{239}{342}\right)$	$e\left(\frac{26}{57}\right)$
$\chi_{361}(4,\cdot)$	361.k	171	yes	$1$	$1$	$e\left(\frac{1}{171}\right)$	$e\left(\frac{139}{171}\right)$	$e\left(\frac{2}{171}\right)$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{107}{171}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{34}{57}\right)$
$\chi_{361}(5,\cdot)$	361.k	171	yes	$1$	$1$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{50}{171}\right)$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{166}{171}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{11}{57}\right)$
$\chi_{361}(6,\cdot)$	361.k	171	yes	$1$	$1$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{166}{171}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{43}{57}\right)$
$\chi_{361}(7,\cdot)$	361.i	57	yes	$1$	$1$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{361}(8,\cdot)$	361.j	114	yes	$-1$	$1$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{17}{19}\right)$
$\chi_{361}(9,\cdot)$	361.k	171	yes	$1$	$1$	$e\left(\frac{139}{171}\right)$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{107}{171}\right)$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{167}{171}\right)$	$e\left(\frac{68}{171}\right)$	$e\left(\frac{52}{57}\right)$
$\chi_{361}(10,\cdot)$	361.l	342	yes	$-1$	$1$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{239}{342}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{68}{171}\right)$	$e\left(\frac{253}{342}\right)$	$e\left(\frac{28}{57}\right)$
$\chi_{361}(11,\cdot)$	361.i	57	yes	$1$	$1$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{8}{19}\right)$
$\chi_{361}(12,\cdot)$	361.j	114	yes	$-1$	$1$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{1}{19}\right)$
$\chi_{361}(13,\cdot)$	361.l	342	yes	$-1$	$1$	$e\left(\frac{329}{342}\right)$	$e\left(\frac{245}{342}\right)$	$e\left(\frac{158}{171}\right)$	$e\left(\frac{31}{171}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{49}{342}\right)$	$e\left(\frac{7}{57}\right)$
$\chi_{361}(14,\cdot)$	361.l	342	yes	$-1$	$1$	$e\left(\frac{151}{342}\right)$	$e\left(\frac{127}{342}\right)$	$e\left(\frac{151}{171}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{139}{171}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{127}{171}\right)$	$e\left(\frac{299}{342}\right)$	$e\left(\frac{2}{57}\right)$
$\chi_{361}(15,\cdot)$	361.l	342	yes	$-1$	$1$	$e\left(\frac{29}{342}\right)$	$e\left(\frac{269}{342}\right)$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{149}{171}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{259}{342}\right)$	$e\left(\frac{37}{57}\right)$
$\chi_{361}(16,\cdot)$	361.k	171	yes	$1$	$1$	$e\left(\frac{2}{171}\right)$	$e\left(\frac{107}{171}\right)$	$e\left(\frac{4}{171}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{109}{171}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{43}{171}\right)$	$e\left(\frac{124}{171}\right)$	$e\left(\frac{11}{57}\right)$
$\chi_{361}(17,\cdot)$	361.k	171	yes	$1$	$1$	$e\left(\frac{113}{171}\right)$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{55}{171}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{88}{171}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{166}{171}\right)$	$e\left(\frac{23}{57}\right)$
$\chi_{361}(18,\cdot)$	361.h	38	yes	$-1$	$1$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{4}{19}\right)$
$\chi_{361}(20,\cdot)$	361.g	19	yes	$1$	$1$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{361}(21,\cdot)$	361.l	342	yes	$-1$	$1$	$e\left(\frac{289}{342}\right)$	$e\left(\frac{157}{342}\right)$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{8}{171}\right)$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{11}{57}\right)$
$\chi_{361}(22,\cdot)$	361.l	342	yes	$-1$	$1$	$e\left(\frac{103}{342}\right)$	$e\left(\frac{295}{342}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{149}{171}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{124}{171}\right)$	$e\left(\frac{59}{342}\right)$	$e\left(\frac{41}{57}\right)$
$\chi_{361}(23,\cdot)$	361.k	171	yes	$1$	$1$	$e\left(\frac{73}{171}\right)$	$e\left(\frac{58}{171}\right)$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{131}{171}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{80}{171}\right)$	$e\left(\frac{31}{57}\right)$
$\chi_{361}(24,\cdot)$	361.k	171	yes	$1$	$1$	$e\left(\frac{71}{171}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{142}{171}\right)$	$e\left(\frac{56}{171}\right)$	$e\left(\frac{22}{171}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{73}{171}\right)$	$e\left(\frac{127}{171}\right)$	$e\left(\frac{20}{57}\right)$
$\chi_{361}(25,\cdot)$	361.k	171	yes	$1$	$1$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{20}{171}\right)$	$e\left(\frac{22}{57}\right)$
$\chi_{361}(26,\cdot)$	361.i	57	yes	$1$	$1$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{8}{19}\right)$
$\chi_{361}(27,\cdot)$	361.j	114	yes	$-1$	$1$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{361}(28,\cdot)$	361.e	9	no	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{361}(29,\cdot)$	361.l	342	yes	$-1$	$1$	$e\left(\frac{17}{342}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{17}{171}\right)$	$e\left(\frac{91}{171}\right)$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{199}{342}\right)$	$e\left(\frac{4}{57}\right)$
$\chi_{361}(30,\cdot)$	361.i	57	yes	$1$	$1$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{361}(31,\cdot)$	361.j	114	yes	$-1$	$1$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{361}(32,\cdot)$	361.l	342	yes	$-1$	$1$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{11}{342}\right)$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{67}{171}\right)$	$e\left(\frac{8}{171}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{11}{171}\right)$	$e\left(\frac{139}{342}\right)$	$e\left(\frac{28}{57}\right)$
$\chi_{361}(33,\cdot)$	361.l	342	yes	$-1$	$1$	$e\left(\frac{241}{342}\right)$	$e\left(\frac{325}{342}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{65}{342}\right)$	$e\left(\frac{50}{57}\right)$

Click here to search among the remaining 310 characters.