Properties

Modulus $3525$
Structure \(C_{460}\times C_{2}\times C_{2}\)
Order $1840$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(3525)
 
pari: g = idealstar(,3525,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1840
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{460}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{3525}(2351,\cdot)$, $\chi_{3525}(1552,\cdot)$, $\chi_{3525}(2026,\cdot)$

First 32 of 1840 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 \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{3525}(1,\cdot)\) 3525.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{3525}(2,\cdot)\) 3525.bt 460 yes \(1\) \(1\) \(e\left(\frac{273}{460}\right)\) \(e\left(\frac{43}{230}\right)\) \(e\left(\frac{71}{92}\right)\) \(e\left(\frac{359}{460}\right)\) \(e\left(\frac{9}{230}\right)\) \(e\left(\frac{117}{460}\right)\) \(e\left(\frac{42}{115}\right)\) \(e\left(\frac{43}{115}\right)\) \(e\left(\frac{189}{460}\right)\) \(e\left(\frac{117}{230}\right)\)
\(\chi_{3525}(4,\cdot)\) 3525.bo 230 no \(1\) \(1\) \(e\left(\frac{43}{230}\right)\) \(e\left(\frac{43}{115}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{129}{230}\right)\) \(e\left(\frac{9}{115}\right)\) \(e\left(\frac{117}{230}\right)\) \(e\left(\frac{84}{115}\right)\) \(e\left(\frac{86}{115}\right)\) \(e\left(\frac{189}{230}\right)\) \(e\left(\frac{2}{115}\right)\)
\(\chi_{3525}(7,\cdot)\) 3525.bh 92 no \(-1\) \(1\) \(e\left(\frac{71}{92}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{47}{92}\right)\) \(e\left(\frac{29}{92}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{37}{92}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{35}{92}\right)\) \(e\left(\frac{37}{46}\right)\)
\(\chi_{3525}(8,\cdot)\) 3525.bt 460 yes \(1\) \(1\) \(e\left(\frac{359}{460}\right)\) \(e\left(\frac{129}{230}\right)\) \(e\left(\frac{29}{92}\right)\) \(e\left(\frac{157}{460}\right)\) \(e\left(\frac{27}{230}\right)\) \(e\left(\frac{351}{460}\right)\) \(e\left(\frac{11}{115}\right)\) \(e\left(\frac{14}{115}\right)\) \(e\left(\frac{107}{460}\right)\) \(e\left(\frac{121}{230}\right)\)
\(\chi_{3525}(11,\cdot)\) 3525.bm 230 yes \(1\) \(1\) \(e\left(\frac{9}{230}\right)\) \(e\left(\frac{9}{115}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{27}{230}\right)\) \(e\left(\frac{42}{115}\right)\) \(e\left(\frac{201}{230}\right)\) \(e\left(\frac{209}{230}\right)\) \(e\left(\frac{18}{115}\right)\) \(e\left(\frac{77}{230}\right)\) \(e\left(\frac{57}{230}\right)\)
\(\chi_{3525}(13,\cdot)\) 3525.bs 460 no \(1\) \(1\) \(e\left(\frac{117}{460}\right)\) \(e\left(\frac{117}{230}\right)\) \(e\left(\frac{37}{92}\right)\) \(e\left(\frac{351}{460}\right)\) \(e\left(\frac{201}{230}\right)\) \(e\left(\frac{313}{460}\right)\) \(e\left(\frac{151}{230}\right)\) \(e\left(\frac{2}{115}\right)\) \(e\left(\frac{81}{460}\right)\) \(e\left(\frac{99}{115}\right)\)
\(\chi_{3525}(14,\cdot)\) 3525.bq 230 yes \(-1\) \(1\) \(e\left(\frac{42}{115}\right)\) \(e\left(\frac{84}{115}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{11}{115}\right)\) \(e\left(\frac{209}{230}\right)\) \(e\left(\frac{151}{230}\right)\) \(e\left(\frac{149}{230}\right)\) \(e\left(\frac{53}{115}\right)\) \(e\left(\frac{91}{115}\right)\) \(e\left(\frac{36}{115}\right)\)
\(\chi_{3525}(16,\cdot)\) 3525.bk 115 no \(1\) \(1\) \(e\left(\frac{43}{115}\right)\) \(e\left(\frac{86}{115}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{14}{115}\right)\) \(e\left(\frac{18}{115}\right)\) \(e\left(\frac{2}{115}\right)\) \(e\left(\frac{53}{115}\right)\) \(e\left(\frac{57}{115}\right)\) \(e\left(\frac{74}{115}\right)\) \(e\left(\frac{4}{115}\right)\)
\(\chi_{3525}(17,\cdot)\) 3525.bt 460 yes \(1\) \(1\) \(e\left(\frac{189}{460}\right)\) \(e\left(\frac{189}{230}\right)\) \(e\left(\frac{35}{92}\right)\) \(e\left(\frac{107}{460}\right)\) \(e\left(\frac{77}{230}\right)\) \(e\left(\frac{81}{460}\right)\) \(e\left(\frac{91}{115}\right)\) \(e\left(\frac{74}{115}\right)\) \(e\left(\frac{237}{460}\right)\) \(e\left(\frac{81}{230}\right)\)
\(\chi_{3525}(19,\cdot)\) 3525.bn 230 no \(-1\) \(1\) \(e\left(\frac{117}{230}\right)\) \(e\left(\frac{2}{115}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{121}{230}\right)\) \(e\left(\frac{57}{230}\right)\) \(e\left(\frac{99}{115}\right)\) \(e\left(\frac{36}{115}\right)\) \(e\left(\frac{4}{115}\right)\) \(e\left(\frac{81}{230}\right)\) \(e\left(\frac{51}{230}\right)\)
\(\chi_{3525}(22,\cdot)\) 3525.bs 460 no \(1\) \(1\) \(e\left(\frac{291}{460}\right)\) \(e\left(\frac{61}{230}\right)\) \(e\left(\frac{59}{92}\right)\) \(e\left(\frac{413}{460}\right)\) \(e\left(\frac{93}{230}\right)\) \(e\left(\frac{59}{460}\right)\) \(e\left(\frac{63}{230}\right)\) \(e\left(\frac{61}{115}\right)\) \(e\left(\frac{343}{460}\right)\) \(e\left(\frac{87}{115}\right)\)
\(\chi_{3525}(23,\cdot)\) 3525.bv 460 yes \(-1\) \(1\) \(e\left(\frac{3}{460}\right)\) \(e\left(\frac{3}{230}\right)\) \(e\left(\frac{21}{92}\right)\) \(e\left(\frac{9}{460}\right)\) \(e\left(\frac{7}{115}\right)\) \(e\left(\frac{297}{460}\right)\) \(e\left(\frac{27}{115}\right)\) \(e\left(\frac{3}{115}\right)\) \(e\left(\frac{179}{460}\right)\) \(e\left(\frac{91}{115}\right)\)
\(\chi_{3525}(26,\cdot)\) 3525.bc 46 no \(1\) \(1\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{17}{46}\right)\)
\(\chi_{3525}(28,\cdot)\) 3525.bu 460 no \(-1\) \(1\) \(e\left(\frac{441}{460}\right)\) \(e\left(\frac{211}{230}\right)\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{403}{460}\right)\) \(e\left(\frac{109}{115}\right)\) \(e\left(\frac{419}{460}\right)\) \(e\left(\frac{3}{230}\right)\) \(e\left(\frac{96}{115}\right)\) \(e\left(\frac{93}{460}\right)\) \(e\left(\frac{189}{230}\right)\)
\(\chi_{3525}(29,\cdot)\) 3525.br 230 yes \(1\) \(1\) \(e\left(\frac{34}{115}\right)\) \(e\left(\frac{68}{115}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{102}{115}\right)\) \(e\left(\frac{49}{115}\right)\) \(e\left(\frac{31}{115}\right)\) \(e\left(\frac{33}{230}\right)\) \(e\left(\frac{21}{115}\right)\) \(e\left(\frac{112}{115}\right)\) \(e\left(\frac{9}{230}\right)\)
\(\chi_{3525}(31,\cdot)\) 3525.bp 230 no \(-1\) \(1\) \(e\left(\frac{66}{115}\right)\) \(e\left(\frac{17}{115}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{83}{115}\right)\) \(e\left(\frac{197}{230}\right)\) \(e\left(\frac{73}{230}\right)\) \(e\left(\frac{76}{115}\right)\) \(e\left(\frac{34}{115}\right)\) \(e\left(\frac{28}{115}\right)\) \(e\left(\frac{31}{230}\right)\)
\(\chi_{3525}(32,\cdot)\) 3525.bi 92 no \(1\) \(1\) \(e\left(\frac{89}{92}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{79}{92}\right)\) \(e\left(\frac{83}{92}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{25}{92}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{25}{46}\right)\)
\(\chi_{3525}(34,\cdot)\) 3525.bo 230 no \(1\) \(1\) \(e\left(\frac{1}{230}\right)\) \(e\left(\frac{1}{115}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{3}{230}\right)\) \(e\left(\frac{43}{115}\right)\) \(e\left(\frac{99}{230}\right)\) \(e\left(\frac{18}{115}\right)\) \(e\left(\frac{2}{115}\right)\) \(e\left(\frac{213}{230}\right)\) \(e\left(\frac{99}{115}\right)\)
\(\chi_{3525}(37,\cdot)\) 3525.bu 460 no \(-1\) \(1\) \(e\left(\frac{407}{460}\right)\) \(e\left(\frac{177}{230}\right)\) \(e\left(\frac{43}{92}\right)\) \(e\left(\frac{301}{460}\right)\) \(e\left(\frac{68}{115}\right)\) \(e\left(\frac{273}{460}\right)\) \(e\left(\frac{81}{230}\right)\) \(e\left(\frac{62}{115}\right)\) \(e\left(\frac{211}{460}\right)\) \(e\left(\frac{43}{230}\right)\)
\(\chi_{3525}(38,\cdot)\) 3525.bv 460 yes \(-1\) \(1\) \(e\left(\frac{47}{460}\right)\) \(e\left(\frac{47}{230}\right)\) \(e\left(\frac{53}{92}\right)\) \(e\left(\frac{141}{460}\right)\) \(e\left(\frac{33}{115}\right)\) \(e\left(\frac{53}{460}\right)\) \(e\left(\frac{78}{115}\right)\) \(e\left(\frac{47}{115}\right)\) \(e\left(\frac{351}{460}\right)\) \(e\left(\frac{84}{115}\right)\)
\(\chi_{3525}(41,\cdot)\) 3525.bm 230 yes \(1\) \(1\) \(e\left(\frac{131}{230}\right)\) \(e\left(\frac{16}{115}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{163}{230}\right)\) \(e\left(\frac{113}{115}\right)\) \(e\left(\frac{89}{230}\right)\) \(e\left(\frac{1}{230}\right)\) \(e\left(\frac{32}{115}\right)\) \(e\left(\frac{73}{230}\right)\) \(e\left(\frac{63}{230}\right)\)
\(\chi_{3525}(43,\cdot)\) 3525.bj 92 no \(1\) \(1\) \(e\left(\frac{77}{92}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{73}{92}\right)\) \(e\left(\frac{47}{92}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{33}{92}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{25}{92}\right)\) \(e\left(\frac{5}{23}\right)\)
\(\chi_{3525}(44,\cdot)\) 3525.br 230 yes \(1\) \(1\) \(e\left(\frac{26}{115}\right)\) \(e\left(\frac{52}{115}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{78}{115}\right)\) \(e\left(\frac{51}{115}\right)\) \(e\left(\frac{44}{115}\right)\) \(e\left(\frac{147}{230}\right)\) \(e\left(\frac{104}{115}\right)\) \(e\left(\frac{18}{115}\right)\) \(e\left(\frac{61}{230}\right)\)
\(\chi_{3525}(46,\cdot)\) 3525.p 10 no \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{3525}(49,\cdot)\) 3525.be 46 no \(1\) \(1\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{14}{23}\right)\)
\(\chi_{3525}(52,\cdot)\) 3525.bs 460 no \(1\) \(1\) \(e\left(\frac{203}{460}\right)\) \(e\left(\frac{203}{230}\right)\) \(e\left(\frac{87}{92}\right)\) \(e\left(\frac{149}{460}\right)\) \(e\left(\frac{219}{230}\right)\) \(e\left(\frac{87}{460}\right)\) \(e\left(\frac{89}{230}\right)\) \(e\left(\frac{88}{115}\right)\) \(e\left(\frac{459}{460}\right)\) \(e\left(\frac{101}{115}\right)\)
\(\chi_{3525}(53,\cdot)\) 3525.bt 460 yes \(1\) \(1\) \(e\left(\frac{331}{460}\right)\) \(e\left(\frac{101}{230}\right)\) \(e\left(\frac{17}{92}\right)\) \(e\left(\frac{73}{460}\right)\) \(e\left(\frac{203}{230}\right)\) \(e\left(\frac{339}{460}\right)\) \(e\left(\frac{104}{115}\right)\) \(e\left(\frac{101}{115}\right)\) \(e\left(\frac{123}{460}\right)\) \(e\left(\frac{109}{230}\right)\)
\(\chi_{3525}(56,\cdot)\) 3525.bl 230 yes \(-1\) \(1\) \(e\left(\frac{127}{230}\right)\) \(e\left(\frac{12}{115}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{151}{230}\right)\) \(e\left(\frac{227}{230}\right)\) \(e\left(\frac{19}{115}\right)\) \(e\left(\frac{87}{230}\right)\) \(e\left(\frac{24}{115}\right)\) \(e\left(\frac{141}{230}\right)\) \(e\left(\frac{38}{115}\right)\)
\(\chi_{3525}(58,\cdot)\) 3525.bs 460 no \(1\) \(1\) \(e\left(\frac{409}{460}\right)\) \(e\left(\frac{179}{230}\right)\) \(e\left(\frac{57}{92}\right)\) \(e\left(\frac{307}{460}\right)\) \(e\left(\frac{107}{230}\right)\) \(e\left(\frac{241}{460}\right)\) \(e\left(\frac{117}{230}\right)\) \(e\left(\frac{64}{115}\right)\) \(e\left(\frac{177}{460}\right)\) \(e\left(\frac{63}{115}\right)\)
\(\chi_{3525}(59,\cdot)\) 3525.bq 230 yes \(-1\) \(1\) \(e\left(\frac{13}{115}\right)\) \(e\left(\frac{26}{115}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{39}{115}\right)\) \(e\left(\frac{51}{230}\right)\) \(e\left(\frac{159}{230}\right)\) \(e\left(\frac{131}{230}\right)\) \(e\left(\frac{52}{115}\right)\) \(e\left(\frac{9}{115}\right)\) \(e\left(\frac{44}{115}\right)\)
\(\chi_{3525}(61,\cdot)\) 3525.bk 115 no \(1\) \(1\) \(e\left(\frac{42}{115}\right)\) \(e\left(\frac{84}{115}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{11}{115}\right)\) \(e\left(\frac{47}{115}\right)\) \(e\left(\frac{18}{115}\right)\) \(e\left(\frac{17}{115}\right)\) \(e\left(\frac{53}{115}\right)\) \(e\left(\frac{91}{115}\right)\) \(e\left(\frac{36}{115}\right)\)