Properties

Modulus $145$
Structure \(C_{28}\times C_{4}\)
Order $112$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(145)
 
pari: g = idealstar(,145,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 112
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{28}\times C_{4}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{145}(117,\cdot)$, $\chi_{145}(31,\cdot)$

First 32 of 112 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{145}(1,\cdot)\) 145.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{145}(2,\cdot)\) 145.o 28 yes \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{25}{28}\right)\) \(-1\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{145}(3,\cdot)\) 145.t 28 yes \(1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(1\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{145}(4,\cdot)\) 145.l 14 yes \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(1\) \(e\left(\frac{11}{14}\right)\)
\(\chi_{145}(6,\cdot)\) 145.m 14 no \(1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(-1\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{145}(7,\cdot)\) 145.p 28 yes \(-1\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(i\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{145}(8,\cdot)\) 145.o 28 yes \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{19}{28}\right)\) \(-1\) \(e\left(\frac{5}{28}\right)\)
\(\chi_{145}(9,\cdot)\) 145.l 14 yes \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(1\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{145}(11,\cdot)\) 145.r 28 no \(-1\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(i\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{145}(12,\cdot)\) 145.e 4 yes \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(i\) \(-1\) \(1\) \(i\) \(1\) \(i\)
\(\chi_{145}(13,\cdot)\) 145.q 28 yes \(-1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(i\) \(e\left(\frac{23}{28}\right)\)
\(\chi_{145}(14,\cdot)\) 145.s 28 yes \(-1\) \(1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(-i\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{145}(16,\cdot)\) 145.k 7 no \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(1\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{145}(17,\cdot)\) 145.j 4 yes \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(i\) \(1\) \(1\) \(-i\) \(-1\) \(i\)
\(\chi_{145}(18,\cdot)\) 145.o 28 yes \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{23}{28}\right)\) \(-1\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{145}(19,\cdot)\) 145.s 28 yes \(-1\) \(1\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(-i\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{145}(21,\cdot)\) 145.r 28 no \(-1\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(i\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{145}(22,\cdot)\) 145.q 28 yes \(-1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(-i\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{145}(23,\cdot)\) 145.p 28 yes \(-1\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(-i\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{145}(24,\cdot)\) 145.n 14 yes \(1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(-1\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{145}(26,\cdot)\) 145.r 28 no \(-1\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(-i\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{145}(27,\cdot)\) 145.t 28 yes \(1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(1\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{145}(28,\cdot)\) 145.h 4 yes \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(1\) \(-i\) \(-i\) \(-1\) \(-1\) \(i\) \(i\)
\(\chi_{145}(31,\cdot)\) 145.r 28 no \(-1\) \(1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(i\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{145}(32,\cdot)\) 145.o 28 yes \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(-1\) \(e\left(\frac{27}{28}\right)\)
\(\chi_{145}(33,\cdot)\) 145.q 28 yes \(-1\) \(1\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(i\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{145}(34,\cdot)\) 145.l 14 yes \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(1\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{145}(36,\cdot)\) 145.k 7 no \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{145}(37,\cdot)\) 145.t 28 yes \(1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{19}{28}\right)\) \(1\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{145}(38,\cdot)\) 145.q 28 yes \(-1\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(i\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{145}(39,\cdot)\) 145.s 28 yes \(-1\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(i\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{145}(41,\cdot)\) 145.g 4 no \(-1\) \(1\) \(i\) \(i\) \(-1\) \(-1\) \(1\) \(-i\) \(-1\) \(i\) \(-i\) \(-1\)