Properties

Modulus $705$
Structure \(C_{92}\times C_{2}\times C_{2}\)
Order $368$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(705)
 
pari: g = idealstar(,705,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 368
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{92}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{705}(236,\cdot)$, $\chi_{705}(142,\cdot)$, $\chi_{705}(616,\cdot)$

First 32 of 368 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 \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{705}(1,\cdot)\) 705.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{705}(2,\cdot)\) 705.w 92 yes \(1\) \(1\) \(e\left(\frac{73}{92}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{71}{92}\right)\) \(e\left(\frac{35}{92}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{1}{92}\right)\) \(e\left(\frac{5}{46}\right)\)
\(\chi_{705}(4,\cdot)\) 705.s 46 no \(1\) \(1\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{5}{23}\right)\)
\(\chi_{705}(7,\cdot)\) 705.v 92 no \(-1\) \(1\) \(e\left(\frac{71}{92}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{47}{92}\right)\) \(e\left(\frac{29}{92}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{37}{92}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{35}{92}\right)\) \(e\left(\frac{37}{46}\right)\)
\(\chi_{705}(8,\cdot)\) 705.w 92 yes \(1\) \(1\) \(e\left(\frac{35}{92}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{29}{92}\right)\) \(e\left(\frac{13}{92}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{15}{92}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{3}{92}\right)\) \(e\left(\frac{15}{46}\right)\)
\(\chi_{705}(11,\cdot)\) 705.q 46 no \(1\) \(1\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{39}{46}\right)\)
\(\chi_{705}(13,\cdot)\) 705.x 92 no \(1\) \(1\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{37}{92}\right)\) \(e\left(\frac{15}{92}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{81}{92}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{53}{92}\right)\) \(e\left(\frac{6}{23}\right)\)
\(\chi_{705}(14,\cdot)\) 705.p 46 yes \(-1\) \(1\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{21}{23}\right)\)
\(\chi_{705}(16,\cdot)\) 705.m 23 no \(1\) \(1\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{10}{23}\right)\)
\(\chi_{705}(17,\cdot)\) 705.w 92 yes \(1\) \(1\) \(e\left(\frac{1}{92}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{35}{92}\right)\) \(e\left(\frac{3}{92}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{53}{92}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{29}{92}\right)\) \(e\left(\frac{7}{46}\right)\)
\(\chi_{705}(19,\cdot)\) 705.t 46 no \(-1\) \(1\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{1}{46}\right)\)
\(\chi_{705}(22,\cdot)\) 705.x 92 no \(1\) \(1\) \(e\left(\frac{3}{92}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{59}{92}\right)\) \(e\left(\frac{9}{92}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{67}{92}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{87}{92}\right)\) \(e\left(\frac{22}{23}\right)\)
\(\chi_{705}(23,\cdot)\) 705.u 92 yes \(-1\) \(1\) \(e\left(\frac{19}{92}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{21}{92}\right)\) \(e\left(\frac{57}{92}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{41}{92}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{91}{92}\right)\) \(e\left(\frac{9}{23}\right)\)
\(\chi_{705}(26,\cdot)\) 705.q 46 no \(1\) \(1\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{17}{46}\right)\)
\(\chi_{705}(28,\cdot)\) 705.v 92 no \(-1\) \(1\) \(e\left(\frac{33}{92}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{7}{92}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{47}{92}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{37}{92}\right)\) \(e\left(\frac{1}{46}\right)\)
\(\chi_{705}(29,\cdot)\) 705.o 46 yes \(1\) \(1\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{11}{46}\right)\)
\(\chi_{705}(31,\cdot)\) 705.n 46 no \(-1\) \(1\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{43}{46}\right)\)
\(\chi_{705}(32,\cdot)\) 705.w 92 yes \(1\) \(1\) \(e\left(\frac{89}{92}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{79}{92}\right)\) \(e\left(\frac{83}{92}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{25}{92}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{25}{46}\right)\)
\(\chi_{705}(34,\cdot)\) 705.s 46 no \(1\) \(1\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{6}{23}\right)\)
\(\chi_{705}(37,\cdot)\) 705.v 92 no \(-1\) \(1\) \(e\left(\frac{63}{92}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{43}{92}\right)\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{73}{92}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{79}{92}\right)\) \(e\left(\frac{27}{46}\right)\)
\(\chi_{705}(38,\cdot)\) 705.u 92 yes \(-1\) \(1\) \(e\left(\frac{83}{92}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{53}{92}\right)\) \(e\left(\frac{65}{92}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{29}{92}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{15}{92}\right)\) \(e\left(\frac{3}{23}\right)\)
\(\chi_{705}(41,\cdot)\) 705.q 46 no \(1\) \(1\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{31}{46}\right)\)
\(\chi_{705}(43,\cdot)\) 705.x 92 no \(1\) \(1\) \(e\left(\frac{77}{92}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{73}{92}\right)\) \(e\left(\frac{47}{92}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{33}{92}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{25}{92}\right)\) \(e\left(\frac{5}{23}\right)\)
\(\chi_{705}(44,\cdot)\) 705.o 46 yes \(1\) \(1\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{3}{46}\right)\)
\(\chi_{705}(46,\cdot)\) 705.h 2 no \(-1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(-1\)
\(\chi_{705}(49,\cdot)\) 705.s 46 no \(1\) \(1\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{14}{23}\right)\)
\(\chi_{705}(52,\cdot)\) 705.x 92 no \(1\) \(1\) \(e\left(\frac{59}{92}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{87}{92}\right)\) \(e\left(\frac{85}{92}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{91}{92}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{55}{92}\right)\) \(e\left(\frac{11}{23}\right)\)
\(\chi_{705}(53,\cdot)\) 705.w 92 yes \(1\) \(1\) \(e\left(\frac{11}{92}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{17}{92}\right)\) \(e\left(\frac{33}{92}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{31}{92}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{43}{92}\right)\) \(e\left(\frac{31}{46}\right)\)
\(\chi_{705}(56,\cdot)\) 705.r 46 no \(-1\) \(1\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{3}{23}\right)\)
\(\chi_{705}(58,\cdot)\) 705.x 92 no \(1\) \(1\) \(e\left(\frac{45}{92}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{57}{92}\right)\) \(e\left(\frac{43}{92}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{85}{92}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{17}{92}\right)\) \(e\left(\frac{8}{23}\right)\)
\(\chi_{705}(59,\cdot)\) 705.p 46 yes \(-1\) \(1\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{18}{23}\right)\)
\(\chi_{705}(61,\cdot)\) 705.m 23 no \(1\) \(1\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{21}{23}\right)\)