Properties

Modulus $2300$
Structure \(C_{220}\times C_{2}\times C_{2}\)
Order $880$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2300)
 
pari: g = idealstar(,2300,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 880
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{220}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2300}(1151,\cdot)$, $\chi_{2300}(277,\cdot)$, $\chi_{2300}(1201,\cdot)$

First 32 of 880 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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(27\) \(29\)
\(\chi_{2300}(1,\cdot)\) 2300.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2300}(3,\cdot)\) 2300.bt 220 yes \(1\) \(1\) \(e\left(\frac{129}{220}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{19}{110}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{183}{220}\right)\) \(e\left(\frac{141}{220}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{167}{220}\right)\) \(e\left(\frac{87}{110}\right)\)
\(\chi_{2300}(7,\cdot)\) 2300.bh 44 no \(-1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{2300}(9,\cdot)\) 2300.bo 110 no \(1\) \(1\) \(e\left(\frac{19}{110}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{32}{55}\right)\)
\(\chi_{2300}(11,\cdot)\) 2300.bm 110 yes \(1\) \(1\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{53}{55}\right)\)
\(\chi_{2300}(13,\cdot)\) 2300.bv 220 no \(-1\) \(1\) \(e\left(\frac{183}{220}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{211}{220}\right)\) \(e\left(\frac{177}{220}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{109}{220}\right)\) \(e\left(\frac{39}{110}\right)\)
\(\chi_{2300}(17,\cdot)\) 2300.bs 220 no \(1\) \(1\) \(e\left(\frac{141}{220}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{177}{220}\right)\) \(e\left(\frac{149}{220}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{203}{220}\right)\) \(e\left(\frac{3}{110}\right)\)
\(\chi_{2300}(19,\cdot)\) 2300.br 110 yes \(1\) \(1\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{4}{55}\right)\)
\(\chi_{2300}(21,\cdot)\) 2300.bq 110 no \(-1\) \(1\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{46}{55}\right)\)
\(\chi_{2300}(27,\cdot)\) 2300.bt 220 yes \(1\) \(1\) \(e\left(\frac{167}{220}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{109}{220}\right)\) \(e\left(\frac{203}{220}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{61}{220}\right)\) \(e\left(\frac{41}{110}\right)\)
\(\chi_{2300}(29,\cdot)\) 2300.bo 110 no \(1\) \(1\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{3}{110}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{51}{55}\right)\)
\(\chi_{2300}(31,\cdot)\) 2300.bn 110 yes \(-1\) \(1\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{39}{55}\right)\)
\(\chi_{2300}(33,\cdot)\) 2300.bs 220 no \(1\) \(1\) \(e\left(\frac{51}{220}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{167}{220}\right)\) \(e\left(\frac{199}{220}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{153}{220}\right)\) \(e\left(\frac{83}{110}\right)\)
\(\chi_{2300}(37,\cdot)\) 2300.bs 220 no \(1\) \(1\) \(e\left(\frac{93}{220}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{201}{220}\right)\) \(e\left(\frac{117}{220}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{59}{220}\right)\) \(e\left(\frac{9}{110}\right)\)
\(\chi_{2300}(39,\cdot)\) 2300.bp 110 yes \(-1\) \(1\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{8}{55}\right)\)
\(\chi_{2300}(41,\cdot)\) 2300.bk 55 no \(1\) \(1\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{12}{55}\right)\)
\(\chi_{2300}(43,\cdot)\) 2300.bh 44 no \(-1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{2300}(47,\cdot)\) 2300.x 20 no \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(-i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{2300}(49,\cdot)\) 2300.be 22 no \(1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{2300}(51,\cdot)\) 2300.bc 22 no \(1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{2300}(53,\cdot)\) 2300.bs 220 no \(1\) \(1\) \(e\left(\frac{59}{220}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{59}{110}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{163}{220}\right)\) \(e\left(\frac{131}{220}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{177}{220}\right)\) \(e\left(\frac{27}{110}\right)\)
\(\chi_{2300}(57,\cdot)\) 2300.bj 44 no \(1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{2300}(59,\cdot)\) 2300.bp 110 yes \(-1\) \(1\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{47}{55}\right)\)
\(\chi_{2300}(61,\cdot)\) 2300.bq 110 no \(-1\) \(1\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{28}{55}\right)\)
\(\chi_{2300}(63,\cdot)\) 2300.bu 220 yes \(-1\) \(1\) \(e\left(\frac{53}{220}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{111}{220}\right)\) \(e\left(\frac{127}{220}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{59}{110}\right)\) \(e\left(\frac{159}{220}\right)\) \(e\left(\frac{69}{110}\right)\)
\(\chi_{2300}(67,\cdot)\) 2300.bu 220 yes \(-1\) \(1\) \(e\left(\frac{111}{220}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{137}{220}\right)\) \(e\left(\frac{129}{220}\right)\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{113}{220}\right)\) \(e\left(\frac{103}{110}\right)\)
\(\chi_{2300}(71,\cdot)\) 2300.bn 110 yes \(-1\) \(1\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{46}{55}\right)\)
\(\chi_{2300}(73,\cdot)\) 2300.bv 220 no \(-1\) \(1\) \(e\left(\frac{167}{220}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{219}{220}\right)\) \(e\left(\frac{93}{220}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{61}{220}\right)\) \(e\left(\frac{41}{110}\right)\)
\(\chi_{2300}(77,\cdot)\) 2300.bv 220 no \(-1\) \(1\) \(e\left(\frac{157}{220}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{169}{220}\right)\) \(e\left(\frac{123}{220}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{31}{220}\right)\) \(e\left(\frac{1}{110}\right)\)
\(\chi_{2300}(79,\cdot)\) 2300.br 110 yes \(1\) \(1\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{107}{110}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{36}{55}\right)\)
\(\chi_{2300}(81,\cdot)\) 2300.bk 55 no \(1\) \(1\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{9}{55}\right)\)
\(\chi_{2300}(83,\cdot)\) 2300.bu 220 yes \(-1\) \(1\) \(e\left(\frac{181}{220}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{47}{220}\right)\) \(e\left(\frac{139}{220}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{103}{220}\right)\) \(e\left(\frac{53}{110}\right)\)