sage: H = DirichletGroup(239)
pari: g = idealstar(,239,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 238 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{238}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{239}(7,\cdot)$ |
First 32 of 238 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{239}(1,\cdot)\) | 239.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{239}(2,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{36}{119}\right)\) | \(e\left(\frac{62}{119}\right)\) | \(e\left(\frac{72}{119}\right)\) | \(e\left(\frac{32}{119}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{33}{119}\right)\) | \(e\left(\frac{108}{119}\right)\) | \(e\left(\frac{5}{119}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{13}{119}\right)\) |
\(\chi_{239}(3,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{62}{119}\right)\) | \(e\left(\frac{1}{119}\right)\) | \(e\left(\frac{5}{119}\right)\) | \(e\left(\frac{108}{119}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{37}{119}\right)\) | \(e\left(\frac{67}{119}\right)\) | \(e\left(\frac{2}{119}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{29}{119}\right)\) |
\(\chi_{239}(4,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{72}{119}\right)\) | \(e\left(\frac{5}{119}\right)\) | \(e\left(\frac{25}{119}\right)\) | \(e\left(\frac{64}{119}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{66}{119}\right)\) | \(e\left(\frac{97}{119}\right)\) | \(e\left(\frac{10}{119}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{26}{119}\right)\) |
\(\chi_{239}(5,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{32}{119}\right)\) | \(e\left(\frac{108}{119}\right)\) | \(e\left(\frac{64}{119}\right)\) | \(e\left(\frac{2}{119}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{69}{119}\right)\) | \(e\left(\frac{96}{119}\right)\) | \(e\left(\frac{97}{119}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{38}{119}\right)\) |
\(\chi_{239}(6,\cdot)\) | 239.e | 17 | yes | \(1\) | \(1\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(1\) | \(e\left(\frac{6}{17}\right)\) |
\(\chi_{239}(7,\cdot)\) | 239.h | 238 | yes | \(-1\) | \(1\) | \(e\left(\frac{33}{119}\right)\) | \(e\left(\frac{37}{119}\right)\) | \(e\left(\frac{66}{119}\right)\) | \(e\left(\frac{69}{119}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{1}{238}\right)\) | \(e\left(\frac{99}{119}\right)\) | \(e\left(\frac{74}{119}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{2}{119}\right)\) |
\(\chi_{239}(8,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{108}{119}\right)\) | \(e\left(\frac{67}{119}\right)\) | \(e\left(\frac{97}{119}\right)\) | \(e\left(\frac{96}{119}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{99}{119}\right)\) | \(e\left(\frac{86}{119}\right)\) | \(e\left(\frac{15}{119}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{39}{119}\right)\) |
\(\chi_{239}(9,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{119}\right)\) | \(e\left(\frac{2}{119}\right)\) | \(e\left(\frac{10}{119}\right)\) | \(e\left(\frac{97}{119}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{74}{119}\right)\) | \(e\left(\frac{15}{119}\right)\) | \(e\left(\frac{4}{119}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{58}{119}\right)\) |
\(\chi_{239}(10,\cdot)\) | 239.c | 7 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) |
\(\chi_{239}(11,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{119}\right)\) | \(e\left(\frac{29}{119}\right)\) | \(e\left(\frac{26}{119}\right)\) | \(e\left(\frac{38}{119}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{2}{119}\right)\) | \(e\left(\frac{39}{119}\right)\) | \(e\left(\frac{58}{119}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{8}{119}\right)\) |
\(\chi_{239}(12,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{119}\right)\) | \(e\left(\frac{6}{119}\right)\) | \(e\left(\frac{30}{119}\right)\) | \(e\left(\frac{53}{119}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{103}{119}\right)\) | \(e\left(\frac{45}{119}\right)\) | \(e\left(\frac{12}{119}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{55}{119}\right)\) |
\(\chi_{239}(13,\cdot)\) | 239.h | 238 | yes | \(-1\) | \(1\) | \(e\left(\frac{110}{119}\right)\) | \(e\left(\frac{44}{119}\right)\) | \(e\left(\frac{101}{119}\right)\) | \(e\left(\frac{111}{119}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{43}{238}\right)\) | \(e\left(\frac{92}{119}\right)\) | \(e\left(\frac{88}{119}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{86}{119}\right)\) |
\(\chi_{239}(14,\cdot)\) | 239.h | 238 | yes | \(-1\) | \(1\) | \(e\left(\frac{69}{119}\right)\) | \(e\left(\frac{99}{119}\right)\) | \(e\left(\frac{19}{119}\right)\) | \(e\left(\frac{101}{119}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{67}{238}\right)\) | \(e\left(\frac{88}{119}\right)\) | \(e\left(\frac{79}{119}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{15}{119}\right)\) |
\(\chi_{239}(15,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{94}{119}\right)\) | \(e\left(\frac{109}{119}\right)\) | \(e\left(\frac{69}{119}\right)\) | \(e\left(\frac{110}{119}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{106}{119}\right)\) | \(e\left(\frac{44}{119}\right)\) | \(e\left(\frac{99}{119}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{67}{119}\right)\) |
\(\chi_{239}(16,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{25}{119}\right)\) | \(e\left(\frac{10}{119}\right)\) | \(e\left(\frac{50}{119}\right)\) | \(e\left(\frac{9}{119}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{13}{119}\right)\) | \(e\left(\frac{75}{119}\right)\) | \(e\left(\frac{20}{119}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{52}{119}\right)\) |
\(\chi_{239}(17,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{50}{119}\right)\) | \(e\left(\frac{20}{119}\right)\) | \(e\left(\frac{100}{119}\right)\) | \(e\left(\frac{18}{119}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{26}{119}\right)\) | \(e\left(\frac{31}{119}\right)\) | \(e\left(\frac{40}{119}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{104}{119}\right)\) |
\(\chi_{239}(18,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{41}{119}\right)\) | \(e\left(\frac{64}{119}\right)\) | \(e\left(\frac{82}{119}\right)\) | \(e\left(\frac{10}{119}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{107}{119}\right)\) | \(e\left(\frac{4}{119}\right)\) | \(e\left(\frac{9}{119}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{71}{119}\right)\) |
\(\chi_{239}(19,\cdot)\) | 239.h | 238 | yes | \(-1\) | \(1\) | \(e\left(\frac{117}{119}\right)\) | \(e\left(\frac{23}{119}\right)\) | \(e\left(\frac{115}{119}\right)\) | \(e\left(\frac{104}{119}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{155}{238}\right)\) | \(e\left(\frac{113}{119}\right)\) | \(e\left(\frac{46}{119}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{72}{119}\right)\) |
\(\chi_{239}(20,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{104}{119}\right)\) | \(e\left(\frac{113}{119}\right)\) | \(e\left(\frac{89}{119}\right)\) | \(e\left(\frac{66}{119}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{16}{119}\right)\) | \(e\left(\frac{74}{119}\right)\) | \(e\left(\frac{107}{119}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{64}{119}\right)\) |
\(\chi_{239}(21,\cdot)\) | 239.h | 238 | yes | \(-1\) | \(1\) | \(e\left(\frac{95}{119}\right)\) | \(e\left(\frac{38}{119}\right)\) | \(e\left(\frac{71}{119}\right)\) | \(e\left(\frac{58}{119}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{75}{238}\right)\) | \(e\left(\frac{47}{119}\right)\) | \(e\left(\frac{76}{119}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{31}{119}\right)\) |
\(\chi_{239}(22,\cdot)\) | 239.e | 17 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(1\) | \(e\left(\frac{3}{17}\right)\) |
\(\chi_{239}(23,\cdot)\) | 239.f | 34 | yes | \(-1\) | \(1\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(1\) | \(e\left(\frac{1}{17}\right)\) |
\(\chi_{239}(24,\cdot)\) | 239.c | 7 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(1\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{239}(25,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{64}{119}\right)\) | \(e\left(\frac{97}{119}\right)\) | \(e\left(\frac{9}{119}\right)\) | \(e\left(\frac{4}{119}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{19}{119}\right)\) | \(e\left(\frac{73}{119}\right)\) | \(e\left(\frac{75}{119}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{76}{119}\right)\) |
\(\chi_{239}(26,\cdot)\) | 239.h | 238 | yes | \(-1\) | \(1\) | \(e\left(\frac{27}{119}\right)\) | \(e\left(\frac{106}{119}\right)\) | \(e\left(\frac{54}{119}\right)\) | \(e\left(\frac{24}{119}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{109}{238}\right)\) | \(e\left(\frac{81}{119}\right)\) | \(e\left(\frac{93}{119}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{99}{119}\right)\) |
\(\chi_{239}(27,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{67}{119}\right)\) | \(e\left(\frac{3}{119}\right)\) | \(e\left(\frac{15}{119}\right)\) | \(e\left(\frac{86}{119}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{111}{119}\right)\) | \(e\left(\frac{82}{119}\right)\) | \(e\left(\frac{6}{119}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{87}{119}\right)\) |
\(\chi_{239}(28,\cdot)\) | 239.f | 34 | yes | \(-1\) | \(1\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(1\) | \(e\left(\frac{4}{17}\right)\) |
\(\chi_{239}(29,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{44}{119}\right)\) | \(e\left(\frac{89}{119}\right)\) | \(e\left(\frac{88}{119}\right)\) | \(e\left(\frac{92}{119}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{80}{119}\right)\) | \(e\left(\frac{13}{119}\right)\) | \(e\left(\frac{59}{119}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{82}{119}\right)\) |
\(\chi_{239}(30,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{119}\right)\) | \(e\left(\frac{52}{119}\right)\) | \(e\left(\frac{22}{119}\right)\) | \(e\left(\frac{23}{119}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{20}{119}\right)\) | \(e\left(\frac{33}{119}\right)\) | \(e\left(\frac{104}{119}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{80}{119}\right)\) |
\(\chi_{239}(31,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{16}{119}\right)\) | \(e\left(\frac{54}{119}\right)\) | \(e\left(\frac{32}{119}\right)\) | \(e\left(\frac{1}{119}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{94}{119}\right)\) | \(e\left(\frac{48}{119}\right)\) | \(e\left(\frac{108}{119}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{19}{119}\right)\) |
\(\chi_{239}(32,\cdot)\) | 239.g | 119 | yes | \(1\) | \(1\) | \(e\left(\frac{61}{119}\right)\) | \(e\left(\frac{72}{119}\right)\) | \(e\left(\frac{3}{119}\right)\) | \(e\left(\frac{41}{119}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{46}{119}\right)\) | \(e\left(\frac{64}{119}\right)\) | \(e\left(\frac{25}{119}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{65}{119}\right)\) |