Properties

Modulus $1280$
Structure \(C_{2}\times C_{4}\times C_{64}\)
Order $512$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1280)
 
pari: g = idealstar(,1280,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 512
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{4}\times C_{64}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1280}(511,\cdot)$, $\chi_{1280}(261,\cdot)$, $\chi_{1280}(257,\cdot)$

First 32 of 512 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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{1280}(1,\cdot)\) 1280.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1280}(3,\cdot)\) 1280.bt 64 yes \(1\) \(1\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{43}{64}\right)\)
\(\chi_{1280}(7,\cdot)\) 1280.bl 32 no \(1\) \(1\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{32}\right)\)
\(\chi_{1280}(9,\cdot)\) 1280.bo 32 no \(1\) \(1\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{32}\right)\)
\(\chi_{1280}(11,\cdot)\) 1280.bx 64 no \(-1\) \(1\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{61}{64}\right)\)
\(\chi_{1280}(13,\cdot)\) 1280.bz 64 yes \(-1\) \(1\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{55}{64}\right)\)
\(\chi_{1280}(17,\cdot)\) 1280.bc 16 no \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{1280}(19,\cdot)\) 1280.bu 64 yes \(-1\) \(1\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{47}{64}\right)\)
\(\chi_{1280}(21,\cdot)\) 1280.bv 64 no \(1\) \(1\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{53}{64}\right)\)
\(\chi_{1280}(23,\cdot)\) 1280.bl 32 no \(1\) \(1\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{32}\right)\)
\(\chi_{1280}(27,\cdot)\) 1280.bt 64 yes \(1\) \(1\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{64}\right)\)
\(\chi_{1280}(29,\cdot)\) 1280.bw 64 yes \(1\) \(1\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{19}{64}\right)\)
\(\chi_{1280}(31,\cdot)\) 1280.w 8 no \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{1280}(33,\cdot)\) 1280.v 8 no \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{1280}(37,\cdot)\) 1280.bz 64 yes \(-1\) \(1\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{17}{64}\right)\)
\(\chi_{1280}(39,\cdot)\) 1280.bn 32 no \(-1\) \(1\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{17}{32}\right)\)
\(\chi_{1280}(41,\cdot)\) 1280.bm 32 no \(1\) \(1\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{23}{32}\right)\)
\(\chi_{1280}(43,\cdot)\) 1280.by 64 yes \(1\) \(1\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{21}{64}\right)\)
\(\chi_{1280}(47,\cdot)\) 1280.bd 16 no \(1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{1280}(49,\cdot)\) 1280.bf 16 no \(1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{1280}(51,\cdot)\) 1280.bx 64 no \(-1\) \(1\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{55}{64}\right)\)
\(\chi_{1280}(53,\cdot)\) 1280.bs 64 yes \(-1\) \(1\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{61}{64}\right)\)
\(\chi_{1280}(57,\cdot)\) 1280.bk 32 no \(-1\) \(1\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{32}\right)\)
\(\chi_{1280}(59,\cdot)\) 1280.bu 64 yes \(-1\) \(1\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{57}{64}\right)\)
\(\chi_{1280}(61,\cdot)\) 1280.bv 64 no \(1\) \(1\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{11}{64}\right)\)
\(\chi_{1280}(63,\cdot)\) 1280.j 4 no \(1\) \(1\) \(-1\) \(-i\) \(1\) \(-i\) \(1\) \(-i\) \(-i\) \(i\) \(i\) \(-1\)
\(\chi_{1280}(67,\cdot)\) 1280.by 64 yes \(1\) \(1\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{27}{64}\right)\)
\(\chi_{1280}(69,\cdot)\) 1280.bw 64 yes \(1\) \(1\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{57}{64}\right)\)
\(\chi_{1280}(71,\cdot)\) 1280.bp 32 no \(-1\) \(1\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{32}\right)\)
\(\chi_{1280}(73,\cdot)\) 1280.bk 32 no \(-1\) \(1\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{32}\right)\)
\(\chi_{1280}(77,\cdot)\) 1280.bs 64 yes \(-1\) \(1\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{64}\right)\)
\(\chi_{1280}(79,\cdot)\) 1280.bh 16 no \(-1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\)
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