Properties

Modulus $1723$
Structure \(C_{1722}\)
Order $1722$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1723)
 
pari: g = idealstar(,1723,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1722
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{1722}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1723}(3,\cdot)$

First 32 of 1722 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{1723}(1,\cdot)\) 1723.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1723}(2,\cdot)\) 1723.n 574 yes \(-1\) \(1\) \(e\left(\frac{507}{574}\right)\) \(e\left(\frac{69}{574}\right)\) \(e\left(\frac{220}{287}\right)\) \(e\left(\frac{379}{574}\right)\) \(e\left(\frac{1}{287}\right)\) \(e\left(\frac{285}{574}\right)\) \(e\left(\frac{373}{574}\right)\) \(e\left(\frac{69}{287}\right)\) \(e\left(\frac{156}{287}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{1723}(3,\cdot)\) 1723.p 1722 yes \(-1\) \(1\) \(e\left(\frac{69}{574}\right)\) \(e\left(\frac{1}{1722}\right)\) \(e\left(\frac{69}{287}\right)\) \(e\left(\frac{415}{574}\right)\) \(e\left(\frac{104}{861}\right)\) \(e\left(\frac{409}{574}\right)\) \(e\left(\frac{207}{574}\right)\) \(e\left(\frac{1}{861}\right)\) \(e\left(\frac{242}{287}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{1723}(4,\cdot)\) 1723.m 287 yes \(1\) \(1\) \(e\left(\frac{220}{287}\right)\) \(e\left(\frac{69}{287}\right)\) \(e\left(\frac{153}{287}\right)\) \(e\left(\frac{92}{287}\right)\) \(e\left(\frac{2}{287}\right)\) \(e\left(\frac{285}{287}\right)\) \(e\left(\frac{86}{287}\right)\) \(e\left(\frac{138}{287}\right)\) \(e\left(\frac{25}{287}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{1723}(5,\cdot)\) 1723.n 574 yes \(-1\) \(1\) \(e\left(\frac{379}{574}\right)\) \(e\left(\frac{415}{574}\right)\) \(e\left(\frac{92}{287}\right)\) \(e\left(\frac{75}{574}\right)\) \(e\left(\frac{110}{287}\right)\) \(e\left(\frac{67}{574}\right)\) \(e\left(\frac{563}{574}\right)\) \(e\left(\frac{128}{287}\right)\) \(e\left(\frac{227}{287}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{1723}(6,\cdot)\) 1723.o 861 yes \(1\) \(1\) \(e\left(\frac{1}{287}\right)\) \(e\left(\frac{104}{861}\right)\) \(e\left(\frac{2}{287}\right)\) \(e\left(\frac{110}{287}\right)\) \(e\left(\frac{107}{861}\right)\) \(e\left(\frac{60}{287}\right)\) \(e\left(\frac{3}{287}\right)\) \(e\left(\frac{208}{861}\right)\) \(e\left(\frac{111}{287}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{1723}(7,\cdot)\) 1723.n 574 yes \(-1\) \(1\) \(e\left(\frac{285}{574}\right)\) \(e\left(\frac{409}{574}\right)\) \(e\left(\frac{285}{287}\right)\) \(e\left(\frac{67}{574}\right)\) \(e\left(\frac{60}{287}\right)\) \(e\left(\frac{167}{574}\right)\) \(e\left(\frac{281}{574}\right)\) \(e\left(\frac{122}{287}\right)\) \(e\left(\frac{176}{287}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{1723}(8,\cdot)\) 1723.n 574 yes \(-1\) \(1\) \(e\left(\frac{373}{574}\right)\) \(e\left(\frac{207}{574}\right)\) \(e\left(\frac{86}{287}\right)\) \(e\left(\frac{563}{574}\right)\) \(e\left(\frac{3}{287}\right)\) \(e\left(\frac{281}{574}\right)\) \(e\left(\frac{545}{574}\right)\) \(e\left(\frac{207}{287}\right)\) \(e\left(\frac{181}{287}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{1723}(9,\cdot)\) 1723.o 861 yes \(1\) \(1\) \(e\left(\frac{69}{287}\right)\) \(e\left(\frac{1}{861}\right)\) \(e\left(\frac{138}{287}\right)\) \(e\left(\frac{128}{287}\right)\) \(e\left(\frac{208}{861}\right)\) \(e\left(\frac{122}{287}\right)\) \(e\left(\frac{207}{287}\right)\) \(e\left(\frac{2}{861}\right)\) \(e\left(\frac{197}{287}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{1723}(10,\cdot)\) 1723.m 287 yes \(1\) \(1\) \(e\left(\frac{156}{287}\right)\) \(e\left(\frac{242}{287}\right)\) \(e\left(\frac{25}{287}\right)\) \(e\left(\frac{227}{287}\right)\) \(e\left(\frac{111}{287}\right)\) \(e\left(\frac{176}{287}\right)\) \(e\left(\frac{181}{287}\right)\) \(e\left(\frac{197}{287}\right)\) \(e\left(\frac{96}{287}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{1723}(11,\cdot)\) 1723.g 21 yes \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{21}\right)\)
\(\chi_{1723}(12,\cdot)\) 1723.p 1722 yes \(-1\) \(1\) \(e\left(\frac{509}{574}\right)\) \(e\left(\frac{415}{1722}\right)\) \(e\left(\frac{222}{287}\right)\) \(e\left(\frac{25}{574}\right)\) \(e\left(\frac{110}{861}\right)\) \(e\left(\frac{405}{574}\right)\) \(e\left(\frac{379}{574}\right)\) \(e\left(\frac{415}{861}\right)\) \(e\left(\frac{267}{287}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{1723}(13,\cdot)\) 1723.n 574 yes \(-1\) \(1\) \(e\left(\frac{227}{574}\right)\) \(e\left(\frac{503}{574}\right)\) \(e\left(\frac{227}{287}\right)\) \(e\left(\frac{1}{574}\right)\) \(e\left(\frac{78}{287}\right)\) \(e\left(\frac{131}{574}\right)\) \(e\left(\frac{107}{574}\right)\) \(e\left(\frac{216}{287}\right)\) \(e\left(\frac{114}{287}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{1723}(14,\cdot)\) 1723.m 287 yes \(1\) \(1\) \(e\left(\frac{109}{287}\right)\) \(e\left(\frac{239}{287}\right)\) \(e\left(\frac{218}{287}\right)\) \(e\left(\frac{223}{287}\right)\) \(e\left(\frac{61}{287}\right)\) \(e\left(\frac{226}{287}\right)\) \(e\left(\frac{40}{287}\right)\) \(e\left(\frac{191}{287}\right)\) \(e\left(\frac{45}{287}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{1723}(15,\cdot)\) 1723.k 123 yes \(1\) \(1\) \(e\left(\frac{32}{41}\right)\) \(e\left(\frac{89}{123}\right)\) \(e\left(\frac{23}{41}\right)\) \(e\left(\frac{35}{41}\right)\) \(e\left(\frac{62}{123}\right)\) \(e\left(\frac{34}{41}\right)\) \(e\left(\frac{14}{41}\right)\) \(e\left(\frac{55}{123}\right)\) \(e\left(\frac{26}{41}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1723}(16,\cdot)\) 1723.m 287 yes \(1\) \(1\) \(e\left(\frac{153}{287}\right)\) \(e\left(\frac{138}{287}\right)\) \(e\left(\frac{19}{287}\right)\) \(e\left(\frac{184}{287}\right)\) \(e\left(\frac{4}{287}\right)\) \(e\left(\frac{283}{287}\right)\) \(e\left(\frac{172}{287}\right)\) \(e\left(\frac{276}{287}\right)\) \(e\left(\frac{50}{287}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{1723}(17,\cdot)\) 1723.p 1722 yes \(-1\) \(1\) \(e\left(\frac{491}{574}\right)\) \(e\left(\frac{839}{1722}\right)\) \(e\left(\frac{204}{287}\right)\) \(e\left(\frac{341}{574}\right)\) \(e\left(\frac{295}{861}\right)\) \(e\left(\frac{473}{574}\right)\) \(e\left(\frac{325}{574}\right)\) \(e\left(\frac{839}{861}\right)\) \(e\left(\frac{129}{287}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{1723}(18,\cdot)\) 1723.p 1722 yes \(-1\) \(1\) \(e\left(\frac{71}{574}\right)\) \(e\left(\frac{209}{1722}\right)\) \(e\left(\frac{71}{287}\right)\) \(e\left(\frac{61}{574}\right)\) \(e\left(\frac{211}{861}\right)\) \(e\left(\frac{529}{574}\right)\) \(e\left(\frac{213}{574}\right)\) \(e\left(\frac{209}{861}\right)\) \(e\left(\frac{66}{287}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{1723}(19,\cdot)\) 1723.o 861 yes \(1\) \(1\) \(e\left(\frac{32}{287}\right)\) \(e\left(\frac{458}{861}\right)\) \(e\left(\frac{64}{287}\right)\) \(e\left(\frac{76}{287}\right)\) \(e\left(\frac{554}{861}\right)\) \(e\left(\frac{198}{287}\right)\) \(e\left(\frac{96}{287}\right)\) \(e\left(\frac{55}{861}\right)\) \(e\left(\frac{108}{287}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{1723}(20,\cdot)\) 1723.j 82 yes \(-1\) \(1\) \(e\left(\frac{35}{82}\right)\) \(e\left(\frac{79}{82}\right)\) \(e\left(\frac{35}{41}\right)\) \(e\left(\frac{37}{82}\right)\) \(e\left(\frac{16}{41}\right)\) \(e\left(\frac{9}{82}\right)\) \(e\left(\frac{23}{82}\right)\) \(e\left(\frac{38}{41}\right)\) \(e\left(\frac{36}{41}\right)\) \(1\)
\(\chi_{1723}(21,\cdot)\) 1723.o 861 yes \(1\) \(1\) \(e\left(\frac{177}{287}\right)\) \(e\left(\frac{614}{861}\right)\) \(e\left(\frac{67}{287}\right)\) \(e\left(\frac{241}{287}\right)\) \(e\left(\frac{284}{861}\right)\) \(e\left(\frac{1}{287}\right)\) \(e\left(\frac{244}{287}\right)\) \(e\left(\frac{367}{861}\right)\) \(e\left(\frac{131}{287}\right)\) \(e\left(\frac{20}{21}\right)\)
\(\chi_{1723}(22,\cdot)\) 1723.l 246 yes \(-1\) \(1\) \(e\left(\frac{49}{82}\right)\) \(e\left(\frac{53}{246}\right)\) \(e\left(\frac{8}{41}\right)\) \(e\left(\frac{19}{82}\right)\) \(e\left(\frac{100}{123}\right)\) \(e\left(\frac{29}{82}\right)\) \(e\left(\frac{65}{82}\right)\) \(e\left(\frac{53}{123}\right)\) \(e\left(\frac{34}{41}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1723}(23,\cdot)\) 1723.o 861 yes \(1\) \(1\) \(e\left(\frac{127}{287}\right)\) \(e\left(\frac{580}{861}\right)\) \(e\left(\frac{254}{287}\right)\) \(e\left(\frac{194}{287}\right)\) \(e\left(\frac{100}{861}\right)\) \(e\left(\frac{158}{287}\right)\) \(e\left(\frac{94}{287}\right)\) \(e\left(\frac{299}{861}\right)\) \(e\left(\frac{34}{287}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{1723}(24,\cdot)\) 1723.o 861 yes \(1\) \(1\) \(e\left(\frac{221}{287}\right)\) \(e\left(\frac{311}{861}\right)\) \(e\left(\frac{155}{287}\right)\) \(e\left(\frac{202}{287}\right)\) \(e\left(\frac{113}{861}\right)\) \(e\left(\frac{58}{287}\right)\) \(e\left(\frac{89}{287}\right)\) \(e\left(\frac{622}{861}\right)\) \(e\left(\frac{136}{287}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{1723}(25,\cdot)\) 1723.m 287 yes \(1\) \(1\) \(e\left(\frac{92}{287}\right)\) \(e\left(\frac{128}{287}\right)\) \(e\left(\frac{184}{287}\right)\) \(e\left(\frac{75}{287}\right)\) \(e\left(\frac{220}{287}\right)\) \(e\left(\frac{67}{287}\right)\) \(e\left(\frac{276}{287}\right)\) \(e\left(\frac{256}{287}\right)\) \(e\left(\frac{167}{287}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{1723}(26,\cdot)\) 1723.m 287 yes \(1\) \(1\) \(e\left(\frac{80}{287}\right)\) \(e\left(\frac{286}{287}\right)\) \(e\left(\frac{160}{287}\right)\) \(e\left(\frac{190}{287}\right)\) \(e\left(\frac{79}{287}\right)\) \(e\left(\frac{208}{287}\right)\) \(e\left(\frac{240}{287}\right)\) \(e\left(\frac{285}{287}\right)\) \(e\left(\frac{270}{287}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{1723}(27,\cdot)\) 1723.n 574 yes \(-1\) \(1\) \(e\left(\frac{207}{574}\right)\) \(e\left(\frac{1}{574}\right)\) \(e\left(\frac{207}{287}\right)\) \(e\left(\frac{97}{574}\right)\) \(e\left(\frac{104}{287}\right)\) \(e\left(\frac{79}{574}\right)\) \(e\left(\frac{47}{574}\right)\) \(e\left(\frac{1}{287}\right)\) \(e\left(\frac{152}{287}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{1723}(28,\cdot)\) 1723.n 574 yes \(-1\) \(1\) \(e\left(\frac{151}{574}\right)\) \(e\left(\frac{547}{574}\right)\) \(e\left(\frac{151}{287}\right)\) \(e\left(\frac{251}{574}\right)\) \(e\left(\frac{62}{287}\right)\) \(e\left(\frac{163}{574}\right)\) \(e\left(\frac{453}{574}\right)\) \(e\left(\frac{260}{287}\right)\) \(e\left(\frac{201}{287}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{1723}(29,\cdot)\) 1723.p 1722 yes \(-1\) \(1\) \(e\left(\frac{177}{574}\right)\) \(e\left(\frac{901}{1722}\right)\) \(e\left(\frac{177}{287}\right)\) \(e\left(\frac{241}{574}\right)\) \(e\left(\frac{716}{861}\right)\) \(e\left(\frac{1}{574}\right)\) \(e\left(\frac{531}{574}\right)\) \(e\left(\frac{40}{861}\right)\) \(e\left(\frac{209}{287}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{1723}(30,\cdot)\) 1723.p 1722 yes \(-1\) \(1\) \(e\left(\frac{381}{574}\right)\) \(e\left(\frac{1453}{1722}\right)\) \(e\left(\frac{94}{287}\right)\) \(e\left(\frac{295}{574}\right)\) \(e\left(\frac{437}{861}\right)\) \(e\left(\frac{187}{574}\right)\) \(e\left(\frac{569}{574}\right)\) \(e\left(\frac{592}{861}\right)\) \(e\left(\frac{51}{287}\right)\) \(e\left(\frac{8}{21}\right)\)
\(\chi_{1723}(31,\cdot)\) 1723.n 574 yes \(-1\) \(1\) \(e\left(\frac{143}{574}\right)\) \(e\left(\frac{461}{574}\right)\) \(e\left(\frac{143}{287}\right)\) \(e\left(\frac{519}{574}\right)\) \(e\left(\frac{15}{287}\right)\) \(e\left(\frac{257}{574}\right)\) \(e\left(\frac{429}{574}\right)\) \(e\left(\frac{174}{287}\right)\) \(e\left(\frac{44}{287}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{1723}(32,\cdot)\) 1723.n 574 yes \(-1\) \(1\) \(e\left(\frac{239}{574}\right)\) \(e\left(\frac{345}{574}\right)\) \(e\left(\frac{239}{287}\right)\) \(e\left(\frac{173}{574}\right)\) \(e\left(\frac{5}{287}\right)\) \(e\left(\frac{277}{574}\right)\) \(e\left(\frac{143}{574}\right)\) \(e\left(\frac{58}{287}\right)\) \(e\left(\frac{206}{287}\right)\) \(e\left(\frac{4}{7}\right)\)