Properties

Modulus $1849$
Structure \(C_{1806}\)
Order $1806$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1849)
 
pari: g = idealstar(,1849,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1806
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{1806}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1849}(3,\cdot)$

First 32 of 1806 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{1849}(1,\cdot)\) 1849.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1849}(2,\cdot)\) 1849.n 602 yes \(-1\) \(1\) \(e\left(\frac{285}{602}\right)\) \(e\left(\frac{513}{602}\right)\) \(e\left(\frac{285}{301}\right)\) \(e\left(\frac{281}{602}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{67}{86}\right)\) \(e\left(\frac{253}{602}\right)\) \(e\left(\frac{212}{301}\right)\) \(e\left(\frac{283}{301}\right)\) \(e\left(\frac{135}{301}\right)\)
\(\chi_{1849}(3,\cdot)\) 1849.p 1806 yes \(-1\) \(1\) \(e\left(\frac{513}{602}\right)\) \(e\left(\frac{1}{1806}\right)\) \(e\left(\frac{212}{301}\right)\) \(e\left(\frac{193}{1806}\right)\) \(e\left(\frac{110}{129}\right)\) \(e\left(\frac{35}{258}\right)\) \(e\left(\frac{335}{602}\right)\) \(e\left(\frac{1}{903}\right)\) \(e\left(\frac{866}{903}\right)\) \(e\left(\frac{243}{301}\right)\)
\(\chi_{1849}(4,\cdot)\) 1849.m 301 yes \(1\) \(1\) \(e\left(\frac{285}{301}\right)\) \(e\left(\frac{212}{301}\right)\) \(e\left(\frac{269}{301}\right)\) \(e\left(\frac{281}{301}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{253}{301}\right)\) \(e\left(\frac{123}{301}\right)\) \(e\left(\frac{265}{301}\right)\) \(e\left(\frac{270}{301}\right)\)
\(\chi_{1849}(5,\cdot)\) 1849.p 1806 yes \(-1\) \(1\) \(e\left(\frac{281}{602}\right)\) \(e\left(\frac{193}{1806}\right)\) \(e\left(\frac{281}{301}\right)\) \(e\left(\frac{1129}{1806}\right)\) \(e\left(\frac{74}{129}\right)\) \(e\left(\frac{47}{258}\right)\) \(e\left(\frac{241}{602}\right)\) \(e\left(\frac{193}{903}\right)\) \(e\left(\frac{83}{903}\right)\) \(e\left(\frac{244}{301}\right)\)
\(\chi_{1849}(6,\cdot)\) 1849.k 129 yes \(1\) \(1\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{110}{129}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{74}{129}\right)\) \(e\left(\frac{23}{129}\right)\) \(e\left(\frac{118}{129}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{91}{129}\right)\) \(e\left(\frac{116}{129}\right)\) \(e\left(\frac{11}{43}\right)\)
\(\chi_{1849}(7,\cdot)\) 1849.l 258 yes \(-1\) \(1\) \(e\left(\frac{67}{86}\right)\) \(e\left(\frac{35}{258}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{47}{258}\right)\) \(e\left(\frac{118}{129}\right)\) \(e\left(\frac{61}{258}\right)\) \(e\left(\frac{29}{86}\right)\) \(e\left(\frac{35}{129}\right)\) \(e\left(\frac{124}{129}\right)\) \(e\left(\frac{34}{43}\right)\)
\(\chi_{1849}(8,\cdot)\) 1849.n 602 yes \(-1\) \(1\) \(e\left(\frac{253}{602}\right)\) \(e\left(\frac{335}{602}\right)\) \(e\left(\frac{253}{301}\right)\) \(e\left(\frac{241}{602}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{29}{86}\right)\) \(e\left(\frac{157}{602}\right)\) \(e\left(\frac{34}{301}\right)\) \(e\left(\frac{247}{301}\right)\) \(e\left(\frac{104}{301}\right)\)
\(\chi_{1849}(9,\cdot)\) 1849.o 903 yes \(1\) \(1\) \(e\left(\frac{212}{301}\right)\) \(e\left(\frac{1}{903}\right)\) \(e\left(\frac{123}{301}\right)\) \(e\left(\frac{193}{903}\right)\) \(e\left(\frac{91}{129}\right)\) \(e\left(\frac{35}{129}\right)\) \(e\left(\frac{34}{301}\right)\) \(e\left(\frac{2}{903}\right)\) \(e\left(\frac{829}{903}\right)\) \(e\left(\frac{185}{301}\right)\)
\(\chi_{1849}(10,\cdot)\) 1849.o 903 yes \(1\) \(1\) \(e\left(\frac{283}{301}\right)\) \(e\left(\frac{866}{903}\right)\) \(e\left(\frac{265}{301}\right)\) \(e\left(\frac{83}{903}\right)\) \(e\left(\frac{116}{129}\right)\) \(e\left(\frac{124}{129}\right)\) \(e\left(\frac{247}{301}\right)\) \(e\left(\frac{829}{903}\right)\) \(e\left(\frac{29}{903}\right)\) \(e\left(\frac{78}{301}\right)\)
\(\chi_{1849}(11,\cdot)\) 1849.m 301 yes \(1\) \(1\) \(e\left(\frac{135}{301}\right)\) \(e\left(\frac{243}{301}\right)\) \(e\left(\frac{270}{301}\right)\) \(e\left(\frac{244}{301}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{104}{301}\right)\) \(e\left(\frac{185}{301}\right)\) \(e\left(\frac{78}{301}\right)\) \(e\left(\frac{17}{301}\right)\)
\(\chi_{1849}(12,\cdot)\) 1849.p 1806 yes \(-1\) \(1\) \(e\left(\frac{481}{602}\right)\) \(e\left(\frac{1273}{1806}\right)\) \(e\left(\frac{180}{301}\right)\) \(e\left(\frac{73}{1806}\right)\) \(e\left(\frac{65}{129}\right)\) \(e\left(\frac{179}{258}\right)\) \(e\left(\frac{239}{602}\right)\) \(e\left(\frac{370}{903}\right)\) \(e\left(\frac{758}{903}\right)\) \(e\left(\frac{212}{301}\right)\)
\(\chi_{1849}(13,\cdot)\) 1849.o 903 yes \(1\) \(1\) \(e\left(\frac{74}{301}\right)\) \(e\left(\frac{520}{903}\right)\) \(e\left(\frac{148}{301}\right)\) \(e\left(\frac{127}{903}\right)\) \(e\left(\frac{106}{129}\right)\) \(e\left(\frac{11}{129}\right)\) \(e\left(\frac{222}{301}\right)\) \(e\left(\frac{137}{903}\right)\) \(e\left(\frac{349}{903}\right)\) \(e\left(\frac{181}{301}\right)\)
\(\chi_{1849}(14,\cdot)\) 1849.o 903 yes \(1\) \(1\) \(e\left(\frac{76}{301}\right)\) \(e\left(\frac{892}{903}\right)\) \(e\left(\frac{152}{301}\right)\) \(e\left(\frac{586}{903}\right)\) \(e\left(\frac{31}{129}\right)\) \(e\left(\frac{2}{129}\right)\) \(e\left(\frac{228}{301}\right)\) \(e\left(\frac{881}{903}\right)\) \(e\left(\frac{814}{903}\right)\) \(e\left(\frac{72}{301}\right)\)
\(\chi_{1849}(15,\cdot)\) 1849.o 903 yes \(1\) \(1\) \(e\left(\frac{96}{301}\right)\) \(e\left(\frac{97}{903}\right)\) \(e\left(\frac{192}{301}\right)\) \(e\left(\frac{661}{903}\right)\) \(e\left(\frac{55}{129}\right)\) \(e\left(\frac{41}{129}\right)\) \(e\left(\frac{288}{301}\right)\) \(e\left(\frac{194}{903}\right)\) \(e\left(\frac{46}{903}\right)\) \(e\left(\frac{186}{301}\right)\)
\(\chi_{1849}(16,\cdot)\) 1849.m 301 yes \(1\) \(1\) \(e\left(\frac{269}{301}\right)\) \(e\left(\frac{123}{301}\right)\) \(e\left(\frac{237}{301}\right)\) \(e\left(\frac{261}{301}\right)\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{205}{301}\right)\) \(e\left(\frac{246}{301}\right)\) \(e\left(\frac{229}{301}\right)\) \(e\left(\frac{239}{301}\right)\)
\(\chi_{1849}(17,\cdot)\) 1849.o 903 yes \(1\) \(1\) \(e\left(\frac{73}{301}\right)\) \(e\left(\frac{334}{903}\right)\) \(e\left(\frac{146}{301}\right)\) \(e\left(\frac{349}{903}\right)\) \(e\left(\frac{79}{129}\right)\) \(e\left(\frac{80}{129}\right)\) \(e\left(\frac{219}{301}\right)\) \(e\left(\frac{668}{903}\right)\) \(e\left(\frac{568}{903}\right)\) \(e\left(\frac{85}{301}\right)\)
\(\chi_{1849}(18,\cdot)\) 1849.p 1806 yes \(-1\) \(1\) \(e\left(\frac{107}{602}\right)\) \(e\left(\frac{1541}{1806}\right)\) \(e\left(\frac{107}{301}\right)\) \(e\left(\frac{1229}{1806}\right)\) \(e\left(\frac{4}{129}\right)\) \(e\left(\frac{13}{258}\right)\) \(e\left(\frac{321}{602}\right)\) \(e\left(\frac{638}{903}\right)\) \(e\left(\frac{775}{903}\right)\) \(e\left(\frac{19}{301}\right)\)
\(\chi_{1849}(19,\cdot)\) 1849.h 42 no \(-1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{1849}(20,\cdot)\) 1849.p 1806 yes \(-1\) \(1\) \(e\left(\frac{249}{602}\right)\) \(e\left(\frac{1465}{1806}\right)\) \(e\left(\frac{249}{301}\right)\) \(e\left(\frac{1009}{1806}\right)\) \(e\left(\frac{29}{129}\right)\) \(e\left(\frac{191}{258}\right)\) \(e\left(\frac{145}{602}\right)\) \(e\left(\frac{562}{903}\right)\) \(e\left(\frac{878}{903}\right)\) \(e\left(\frac{213}{301}\right)\)
\(\chi_{1849}(21,\cdot)\) 1849.m 301 yes \(1\) \(1\) \(e\left(\frac{190}{301}\right)\) \(e\left(\frac{41}{301}\right)\) \(e\left(\frac{79}{301}\right)\) \(e\left(\frac{87}{301}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{269}{301}\right)\) \(e\left(\frac{82}{301}\right)\) \(e\left(\frac{277}{301}\right)\) \(e\left(\frac{180}{301}\right)\)
\(\chi_{1849}(22,\cdot)\) 1849.n 602 yes \(-1\) \(1\) \(e\left(\frac{555}{602}\right)\) \(e\left(\frac{397}{602}\right)\) \(e\left(\frac{254}{301}\right)\) \(e\left(\frac{167}{602}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{49}{86}\right)\) \(e\left(\frac{461}{602}\right)\) \(e\left(\frac{96}{301}\right)\) \(e\left(\frac{60}{301}\right)\) \(e\left(\frac{152}{301}\right)\)
\(\chi_{1849}(23,\cdot)\) 1849.o 903 yes \(1\) \(1\) \(e\left(\frac{254}{301}\right)\) \(e\left(\frac{890}{903}\right)\) \(e\left(\frac{207}{301}\right)\) \(e\left(\frac{200}{903}\right)\) \(e\left(\frac{107}{129}\right)\) \(e\left(\frac{61}{129}\right)\) \(e\left(\frac{160}{301}\right)\) \(e\left(\frac{877}{903}\right)\) \(e\left(\frac{59}{903}\right)\) \(e\left(\frac{3}{301}\right)\)
\(\chi_{1849}(24,\cdot)\) 1849.o 903 yes \(1\) \(1\) \(e\left(\frac{82}{301}\right)\) \(e\left(\frac{503}{903}\right)\) \(e\left(\frac{164}{301}\right)\) \(e\left(\frac{458}{903}\right)\) \(e\left(\frac{107}{129}\right)\) \(e\left(\frac{61}{129}\right)\) \(e\left(\frac{246}{301}\right)\) \(e\left(\frac{103}{903}\right)\) \(e\left(\frac{704}{903}\right)\) \(e\left(\frac{46}{301}\right)\)
\(\chi_{1849}(25,\cdot)\) 1849.o 903 yes \(1\) \(1\) \(e\left(\frac{281}{301}\right)\) \(e\left(\frac{193}{903}\right)\) \(e\left(\frac{261}{301}\right)\) \(e\left(\frac{226}{903}\right)\) \(e\left(\frac{19}{129}\right)\) \(e\left(\frac{47}{129}\right)\) \(e\left(\frac{241}{301}\right)\) \(e\left(\frac{386}{903}\right)\) \(e\left(\frac{166}{903}\right)\) \(e\left(\frac{187}{301}\right)\)
\(\chi_{1849}(26,\cdot)\) 1849.p 1806 yes \(-1\) \(1\) \(e\left(\frac{433}{602}\right)\) \(e\left(\frac{773}{1806}\right)\) \(e\left(\frac{132}{301}\right)\) \(e\left(\frac{1097}{1806}\right)\) \(e\left(\frac{19}{129}\right)\) \(e\left(\frac{223}{258}\right)\) \(e\left(\frac{95}{602}\right)\) \(e\left(\frac{773}{903}\right)\) \(e\left(\frac{295}{903}\right)\) \(e\left(\frac{15}{301}\right)\)
\(\chi_{1849}(27,\cdot)\) 1849.n 602 yes \(-1\) \(1\) \(e\left(\frac{335}{602}\right)\) \(e\left(\frac{1}{602}\right)\) \(e\left(\frac{34}{301}\right)\) \(e\left(\frac{193}{602}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{35}{86}\right)\) \(e\left(\frac{403}{602}\right)\) \(e\left(\frac{1}{301}\right)\) \(e\left(\frac{264}{301}\right)\) \(e\left(\frac{127}{301}\right)\)
\(\chi_{1849}(28,\cdot)\) 1849.p 1806 yes \(-1\) \(1\) \(e\left(\frac{437}{602}\right)\) \(e\left(\frac{1517}{1806}\right)\) \(e\left(\frac{136}{301}\right)\) \(e\left(\frac{209}{1806}\right)\) \(e\left(\frac{73}{129}\right)\) \(e\left(\frac{205}{258}\right)\) \(e\left(\frac{107}{602}\right)\) \(e\left(\frac{614}{903}\right)\) \(e\left(\frac{760}{903}\right)\) \(e\left(\frac{207}{301}\right)\)
\(\chi_{1849}(29,\cdot)\) 1849.p 1806 yes \(-1\) \(1\) \(e\left(\frac{565}{602}\right)\) \(e\left(\frac{41}{1806}\right)\) \(e\left(\frac{264}{301}\right)\) \(e\left(\frac{689}{1806}\right)\) \(e\left(\frac{124}{129}\right)\) \(e\left(\frac{145}{258}\right)\) \(e\left(\frac{491}{602}\right)\) \(e\left(\frac{41}{903}\right)\) \(e\left(\frac{289}{903}\right)\) \(e\left(\frac{30}{301}\right)\)
\(\chi_{1849}(30,\cdot)\) 1849.p 1806 yes \(-1\) \(1\) \(e\left(\frac{477}{602}\right)\) \(e\left(\frac{1733}{1806}\right)\) \(e\left(\frac{176}{301}\right)\) \(e\left(\frac{359}{1806}\right)\) \(e\left(\frac{97}{129}\right)\) \(e\left(\frac{25}{258}\right)\) \(e\left(\frac{227}{602}\right)\) \(e\left(\frac{830}{903}\right)\) \(e\left(\frac{895}{903}\right)\) \(e\left(\frac{20}{301}\right)\)
\(\chi_{1849}(31,\cdot)\) 1849.o 903 yes \(1\) \(1\) \(e\left(\frac{55}{301}\right)\) \(e\left(\frac{899}{903}\right)\) \(e\left(\frac{110}{301}\right)\) \(e\left(\frac{131}{903}\right)\) \(e\left(\frac{23}{129}\right)\) \(e\left(\frac{118}{129}\right)\) \(e\left(\frac{165}{301}\right)\) \(e\left(\frac{895}{903}\right)\) \(e\left(\frac{296}{903}\right)\) \(e\left(\frac{163}{301}\right)\)
\(\chi_{1849}(32,\cdot)\) 1849.n 602 yes \(-1\) \(1\) \(e\left(\frac{221}{602}\right)\) \(e\left(\frac{157}{602}\right)\) \(e\left(\frac{221}{301}\right)\) \(e\left(\frac{201}{602}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{77}{86}\right)\) \(e\left(\frac{61}{602}\right)\) \(e\left(\frac{157}{301}\right)\) \(e\left(\frac{211}{301}\right)\) \(e\left(\frac{73}{301}\right)\)