Properties

Modulus $207$
Structure \(C_{2}\times C_{66}\)
Order $132$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(207)
 
pari: g = idealstar(,207,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 132
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{66}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{207}(47,\cdot)$, $\chi_{207}(28,\cdot)$

First 32 of 132 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{207}(1,\cdot)\) 207.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{207}(2,\cdot)\) 207.n 66 yes \(-1\) \(1\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{13}{33}\right)\)
\(\chi_{207}(4,\cdot)\) 207.m 33 yes \(1\) \(1\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{26}{33}\right)\)
\(\chi_{207}(5,\cdot)\) 207.o 66 yes \(1\) \(1\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{23}{33}\right)\)
\(\chi_{207}(7,\cdot)\) 207.p 66 yes \(-1\) \(1\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{19}{33}\right)\)
\(\chi_{207}(8,\cdot)\) 207.l 22 no \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{207}(10,\cdot)\) 207.j 22 no \(-1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{207}(11,\cdot)\) 207.o 66 yes \(1\) \(1\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{31}{33}\right)\)
\(\chi_{207}(13,\cdot)\) 207.m 33 yes \(1\) \(1\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{14}{33}\right)\)
\(\chi_{207}(14,\cdot)\) 207.o 66 yes \(1\) \(1\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{32}{33}\right)\)
\(\chi_{207}(16,\cdot)\) 207.m 33 yes \(1\) \(1\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{19}{33}\right)\)
\(\chi_{207}(17,\cdot)\) 207.k 22 no \(1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{207}(19,\cdot)\) 207.j 22 no \(-1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{207}(20,\cdot)\) 207.o 66 yes \(1\) \(1\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{16}{33}\right)\)
\(\chi_{207}(22,\cdot)\) 207.f 6 yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{207}(25,\cdot)\) 207.m 33 yes \(1\) \(1\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{13}{33}\right)\)
\(\chi_{207}(26,\cdot)\) 207.l 22 no \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{207}(28,\cdot)\) 207.j 22 no \(-1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{207}(29,\cdot)\) 207.n 66 yes \(-1\) \(1\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{7}{33}\right)\)
\(\chi_{207}(31,\cdot)\) 207.m 33 yes \(1\) \(1\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{17}{33}\right)\)
\(\chi_{207}(32,\cdot)\) 207.n 66 yes \(-1\) \(1\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{32}{33}\right)\)
\(\chi_{207}(34,\cdot)\) 207.p 66 yes \(-1\) \(1\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{31}{33}\right)\)
\(\chi_{207}(35,\cdot)\) 207.l 22 no \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{207}(37,\cdot)\) 207.j 22 no \(-1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{207}(38,\cdot)\) 207.o 66 yes \(1\) \(1\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{28}{33}\right)\)
\(\chi_{207}(40,\cdot)\) 207.p 66 yes \(-1\) \(1\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{29}{33}\right)\)
\(\chi_{207}(41,\cdot)\) 207.n 66 yes \(-1\) \(1\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{23}{33}\right)\)
\(\chi_{207}(43,\cdot)\) 207.p 66 yes \(-1\) \(1\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{16}{33}\right)\)
\(\chi_{207}(44,\cdot)\) 207.k 22 no \(1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{207}(47,\cdot)\) 207.h 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{207}(49,\cdot)\) 207.m 33 yes \(1\) \(1\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{5}{33}\right)\)
\(\chi_{207}(50,\cdot)\) 207.n 66 yes \(-1\) \(1\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{26}{33}\right)\)
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