Properties

Modulus 149
Structure \(C_{148}\)
Order 148

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Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(149)
 
pari: g = idealstar(,149,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 148
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{148}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{149}(2,\cdot)$

First 32 of 148 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.

orbit label order primitive -1 1 2 3 4 5 6 7 8 9 10 11
\(\chi_{149}(1,\cdot)\) 149.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{149}(2,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{1}{148}\right)\) \(e\left(\frac{87}{148}\right)\) \(e\left(\frac{1}{74}\right)\) \(e\left(\frac{26}{37}\right)\) \(e\left(\frac{22}{37}\right)\) \(e\left(\frac{71}{74}\right)\) \(e\left(\frac{3}{148}\right)\) \(e\left(\frac{13}{74}\right)\) \(e\left(\frac{105}{148}\right)\) \(e\left(\frac{109}{148}\right)\)
\(\chi_{149}(3,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{87}{148}\right)\) \(e\left(\frac{21}{148}\right)\) \(e\left(\frac{13}{74}\right)\) \(e\left(\frac{5}{37}\right)\) \(e\left(\frac{27}{37}\right)\) \(e\left(\frac{35}{74}\right)\) \(e\left(\frac{113}{148}\right)\) \(e\left(\frac{21}{74}\right)\) \(e\left(\frac{107}{148}\right)\) \(e\left(\frac{11}{148}\right)\)
\(\chi_{149}(4,\cdot)\) 149.e 74 yes \(1\) \(1\) \(e\left(\frac{1}{74}\right)\) \(e\left(\frac{13}{74}\right)\) \(e\left(\frac{1}{37}\right)\) \(e\left(\frac{15}{37}\right)\) \(e\left(\frac{7}{37}\right)\) \(e\left(\frac{34}{37}\right)\) \(e\left(\frac{3}{74}\right)\) \(e\left(\frac{13}{37}\right)\) \(e\left(\frac{31}{74}\right)\) \(e\left(\frac{35}{74}\right)\)
\(\chi_{149}(5,\cdot)\) 149.d 37 yes \(1\) \(1\) \(e\left(\frac{26}{37}\right)\) \(e\left(\frac{5}{37}\right)\) \(e\left(\frac{15}{37}\right)\) \(e\left(\frac{3}{37}\right)\) \(e\left(\frac{31}{37}\right)\) \(e\left(\frac{29}{37}\right)\) \(e\left(\frac{4}{37}\right)\) \(e\left(\frac{10}{37}\right)\) \(e\left(\frac{29}{37}\right)\) \(e\left(\frac{22}{37}\right)\)
\(\chi_{149}(6,\cdot)\) 149.d 37 yes \(1\) \(1\) \(e\left(\frac{22}{37}\right)\) \(e\left(\frac{27}{37}\right)\) \(e\left(\frac{7}{37}\right)\) \(e\left(\frac{31}{37}\right)\) \(e\left(\frac{12}{37}\right)\) \(e\left(\frac{16}{37}\right)\) \(e\left(\frac{29}{37}\right)\) \(e\left(\frac{17}{37}\right)\) \(e\left(\frac{16}{37}\right)\) \(e\left(\frac{30}{37}\right)\)
\(\chi_{149}(7,\cdot)\) 149.e 74 yes \(1\) \(1\) \(e\left(\frac{71}{74}\right)\) \(e\left(\frac{35}{74}\right)\) \(e\left(\frac{34}{37}\right)\) \(e\left(\frac{29}{37}\right)\) \(e\left(\frac{16}{37}\right)\) \(e\left(\frac{9}{37}\right)\) \(e\left(\frac{65}{74}\right)\) \(e\left(\frac{35}{37}\right)\) \(e\left(\frac{55}{74}\right)\) \(e\left(\frac{43}{74}\right)\)
\(\chi_{149}(8,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{3}{148}\right)\) \(e\left(\frac{113}{148}\right)\) \(e\left(\frac{3}{74}\right)\) \(e\left(\frac{4}{37}\right)\) \(e\left(\frac{29}{37}\right)\) \(e\left(\frac{65}{74}\right)\) \(e\left(\frac{9}{148}\right)\) \(e\left(\frac{39}{74}\right)\) \(e\left(\frac{19}{148}\right)\) \(e\left(\frac{31}{148}\right)\)
\(\chi_{149}(9,\cdot)\) 149.e 74 yes \(1\) \(1\) \(e\left(\frac{13}{74}\right)\) \(e\left(\frac{21}{74}\right)\) \(e\left(\frac{13}{37}\right)\) \(e\left(\frac{10}{37}\right)\) \(e\left(\frac{17}{37}\right)\) \(e\left(\frac{35}{37}\right)\) \(e\left(\frac{39}{74}\right)\) \(e\left(\frac{21}{37}\right)\) \(e\left(\frac{33}{74}\right)\) \(e\left(\frac{11}{74}\right)\)
\(\chi_{149}(10,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{105}{148}\right)\) \(e\left(\frac{107}{148}\right)\) \(e\left(\frac{31}{74}\right)\) \(e\left(\frac{29}{37}\right)\) \(e\left(\frac{16}{37}\right)\) \(e\left(\frac{55}{74}\right)\) \(e\left(\frac{19}{148}\right)\) \(e\left(\frac{33}{74}\right)\) \(e\left(\frac{73}{148}\right)\) \(e\left(\frac{49}{148}\right)\)
\(\chi_{149}(11,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{109}{148}\right)\) \(e\left(\frac{11}{148}\right)\) \(e\left(\frac{35}{74}\right)\) \(e\left(\frac{22}{37}\right)\) \(e\left(\frac{30}{37}\right)\) \(e\left(\frac{43}{74}\right)\) \(e\left(\frac{31}{148}\right)\) \(e\left(\frac{11}{74}\right)\) \(e\left(\frac{49}{148}\right)\) \(e\left(\frac{41}{148}\right)\)
\(\chi_{149}(12,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{89}{148}\right)\) \(e\left(\frac{47}{148}\right)\) \(e\left(\frac{15}{74}\right)\) \(e\left(\frac{20}{37}\right)\) \(e\left(\frac{34}{37}\right)\) \(e\left(\frac{29}{74}\right)\) \(e\left(\frac{119}{148}\right)\) \(e\left(\frac{47}{74}\right)\) \(e\left(\frac{21}{148}\right)\) \(e\left(\frac{81}{148}\right)\)
\(\chi_{149}(13,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{53}{148}\right)\) \(e\left(\frac{23}{148}\right)\) \(e\left(\frac{53}{74}\right)\) \(e\left(\frac{9}{37}\right)\) \(e\left(\frac{19}{37}\right)\) \(e\left(\frac{63}{74}\right)\) \(e\left(\frac{11}{148}\right)\) \(e\left(\frac{23}{74}\right)\) \(e\left(\frac{89}{148}\right)\) \(e\left(\frac{5}{148}\right)\)
\(\chi_{149}(14,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{143}{148}\right)\) \(e\left(\frac{9}{148}\right)\) \(e\left(\frac{69}{74}\right)\) \(e\left(\frac{18}{37}\right)\) \(e\left(\frac{1}{37}\right)\) \(e\left(\frac{15}{74}\right)\) \(e\left(\frac{133}{148}\right)\) \(e\left(\frac{9}{74}\right)\) \(e\left(\frac{67}{148}\right)\) \(e\left(\frac{47}{148}\right)\)
\(\chi_{149}(15,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{43}{148}\right)\) \(e\left(\frac{41}{148}\right)\) \(e\left(\frac{43}{74}\right)\) \(e\left(\frac{8}{37}\right)\) \(e\left(\frac{21}{37}\right)\) \(e\left(\frac{19}{74}\right)\) \(e\left(\frac{129}{148}\right)\) \(e\left(\frac{41}{74}\right)\) \(e\left(\frac{75}{148}\right)\) \(e\left(\frac{99}{148}\right)\)
\(\chi_{149}(16,\cdot)\) 149.d 37 yes \(1\) \(1\) \(e\left(\frac{1}{37}\right)\) \(e\left(\frac{13}{37}\right)\) \(e\left(\frac{2}{37}\right)\) \(e\left(\frac{30}{37}\right)\) \(e\left(\frac{14}{37}\right)\) \(e\left(\frac{31}{37}\right)\) \(e\left(\frac{3}{37}\right)\) \(e\left(\frac{26}{37}\right)\) \(e\left(\frac{31}{37}\right)\) \(e\left(\frac{35}{37}\right)\)
\(\chi_{149}(17,\cdot)\) 149.d 37 yes \(1\) \(1\) \(e\left(\frac{31}{37}\right)\) \(e\left(\frac{33}{37}\right)\) \(e\left(\frac{25}{37}\right)\) \(e\left(\frac{5}{37}\right)\) \(e\left(\frac{27}{37}\right)\) \(e\left(\frac{36}{37}\right)\) \(e\left(\frac{19}{37}\right)\) \(e\left(\frac{29}{37}\right)\) \(e\left(\frac{36}{37}\right)\) \(e\left(\frac{12}{37}\right)\)
\(\chi_{149}(18,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{27}{148}\right)\) \(e\left(\frac{129}{148}\right)\) \(e\left(\frac{27}{74}\right)\) \(e\left(\frac{36}{37}\right)\) \(e\left(\frac{2}{37}\right)\) \(e\left(\frac{67}{74}\right)\) \(e\left(\frac{81}{148}\right)\) \(e\left(\frac{55}{74}\right)\) \(e\left(\frac{23}{148}\right)\) \(e\left(\frac{131}{148}\right)\)
\(\chi_{149}(19,\cdot)\) 149.d 37 yes \(1\) \(1\) \(e\left(\frac{21}{37}\right)\) \(e\left(\frac{14}{37}\right)\) \(e\left(\frac{5}{37}\right)\) \(e\left(\frac{1}{37}\right)\) \(e\left(\frac{35}{37}\right)\) \(e\left(\frac{22}{37}\right)\) \(e\left(\frac{26}{37}\right)\) \(e\left(\frac{28}{37}\right)\) \(e\left(\frac{22}{37}\right)\) \(e\left(\frac{32}{37}\right)\)
\(\chi_{149}(20,\cdot)\) 149.e 74 yes \(1\) \(1\) \(e\left(\frac{53}{74}\right)\) \(e\left(\frac{23}{74}\right)\) \(e\left(\frac{16}{37}\right)\) \(e\left(\frac{18}{37}\right)\) \(e\left(\frac{1}{37}\right)\) \(e\left(\frac{26}{37}\right)\) \(e\left(\frac{11}{74}\right)\) \(e\left(\frac{23}{37}\right)\) \(e\left(\frac{15}{74}\right)\) \(e\left(\frac{5}{74}\right)\)
\(\chi_{149}(21,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{81}{148}\right)\) \(e\left(\frac{91}{148}\right)\) \(e\left(\frac{7}{74}\right)\) \(e\left(\frac{34}{37}\right)\) \(e\left(\frac{6}{37}\right)\) \(e\left(\frac{53}{74}\right)\) \(e\left(\frac{95}{148}\right)\) \(e\left(\frac{17}{74}\right)\) \(e\left(\frac{69}{148}\right)\) \(e\left(\frac{97}{148}\right)\)
\(\chi_{149}(22,\cdot)\) 149.e 74 yes \(1\) \(1\) \(e\left(\frac{55}{74}\right)\) \(e\left(\frac{49}{74}\right)\) \(e\left(\frac{18}{37}\right)\) \(e\left(\frac{11}{37}\right)\) \(e\left(\frac{15}{37}\right)\) \(e\left(\frac{20}{37}\right)\) \(e\left(\frac{17}{74}\right)\) \(e\left(\frac{12}{37}\right)\) \(e\left(\frac{3}{74}\right)\) \(e\left(\frac{1}{74}\right)\)
\(\chi_{149}(23,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{95}{148}\right)\) \(e\left(\frac{125}{148}\right)\) \(e\left(\frac{21}{74}\right)\) \(e\left(\frac{28}{37}\right)\) \(e\left(\frac{18}{37}\right)\) \(e\left(\frac{11}{74}\right)\) \(e\left(\frac{137}{148}\right)\) \(e\left(\frac{51}{74}\right)\) \(e\left(\frac{59}{148}\right)\) \(e\left(\frac{143}{148}\right)\)
\(\chi_{149}(24,\cdot)\) 149.e 74 yes \(1\) \(1\) \(e\left(\frac{45}{74}\right)\) \(e\left(\frac{67}{74}\right)\) \(e\left(\frac{8}{37}\right)\) \(e\left(\frac{9}{37}\right)\) \(e\left(\frac{19}{37}\right)\) \(e\left(\frac{13}{37}\right)\) \(e\left(\frac{61}{74}\right)\) \(e\left(\frac{30}{37}\right)\) \(e\left(\frac{63}{74}\right)\) \(e\left(\frac{21}{74}\right)\)
\(\chi_{149}(25,\cdot)\) 149.d 37 yes \(1\) \(1\) \(e\left(\frac{15}{37}\right)\) \(e\left(\frac{10}{37}\right)\) \(e\left(\frac{30}{37}\right)\) \(e\left(\frac{6}{37}\right)\) \(e\left(\frac{25}{37}\right)\) \(e\left(\frac{21}{37}\right)\) \(e\left(\frac{8}{37}\right)\) \(e\left(\frac{20}{37}\right)\) \(e\left(\frac{21}{37}\right)\) \(e\left(\frac{7}{37}\right)\)
\(\chi_{149}(26,\cdot)\) 149.e 74 yes \(1\) \(1\) \(e\left(\frac{27}{74}\right)\) \(e\left(\frac{55}{74}\right)\) \(e\left(\frac{27}{37}\right)\) \(e\left(\frac{35}{37}\right)\) \(e\left(\frac{4}{37}\right)\) \(e\left(\frac{30}{37}\right)\) \(e\left(\frac{7}{74}\right)\) \(e\left(\frac{18}{37}\right)\) \(e\left(\frac{23}{74}\right)\) \(e\left(\frac{57}{74}\right)\)
\(\chi_{149}(27,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{113}{148}\right)\) \(e\left(\frac{63}{148}\right)\) \(e\left(\frac{39}{74}\right)\) \(e\left(\frac{15}{37}\right)\) \(e\left(\frac{7}{37}\right)\) \(e\left(\frac{31}{74}\right)\) \(e\left(\frac{43}{148}\right)\) \(e\left(\frac{63}{74}\right)\) \(e\left(\frac{25}{148}\right)\) \(e\left(\frac{33}{148}\right)\)
\(\chi_{149}(28,\cdot)\) 149.d 37 yes \(1\) \(1\) \(e\left(\frac{36}{37}\right)\) \(e\left(\frac{24}{37}\right)\) \(e\left(\frac{35}{37}\right)\) \(e\left(\frac{7}{37}\right)\) \(e\left(\frac{23}{37}\right)\) \(e\left(\frac{6}{37}\right)\) \(e\left(\frac{34}{37}\right)\) \(e\left(\frac{11}{37}\right)\) \(e\left(\frac{6}{37}\right)\) \(e\left(\frac{2}{37}\right)\)
\(\chi_{149}(29,\cdot)\) 149.d 37 yes \(1\) \(1\) \(e\left(\frac{30}{37}\right)\) \(e\left(\frac{20}{37}\right)\) \(e\left(\frac{23}{37}\right)\) \(e\left(\frac{12}{37}\right)\) \(e\left(\frac{13}{37}\right)\) \(e\left(\frac{5}{37}\right)\) \(e\left(\frac{16}{37}\right)\) \(e\left(\frac{3}{37}\right)\) \(e\left(\frac{5}{37}\right)\) \(e\left(\frac{14}{37}\right)\)
\(\chi_{149}(30,\cdot)\) 149.d 37 yes \(1\) \(1\) \(e\left(\frac{11}{37}\right)\) \(e\left(\frac{32}{37}\right)\) \(e\left(\frac{22}{37}\right)\) \(e\left(\frac{34}{37}\right)\) \(e\left(\frac{6}{37}\right)\) \(e\left(\frac{8}{37}\right)\) \(e\left(\frac{33}{37}\right)\) \(e\left(\frac{27}{37}\right)\) \(e\left(\frac{8}{37}\right)\) \(e\left(\frac{15}{37}\right)\)
\(\chi_{149}(31,\cdot)\) 149.d 37 yes \(1\) \(1\) \(e\left(\frac{33}{37}\right)\) \(e\left(\frac{22}{37}\right)\) \(e\left(\frac{29}{37}\right)\) \(e\left(\frac{28}{37}\right)\) \(e\left(\frac{18}{37}\right)\) \(e\left(\frac{24}{37}\right)\) \(e\left(\frac{25}{37}\right)\) \(e\left(\frac{7}{37}\right)\) \(e\left(\frac{24}{37}\right)\) \(e\left(\frac{8}{37}\right)\)
\(\chi_{149}(32,\cdot)\) 149.f 148 yes \(-1\) \(1\) \(e\left(\frac{5}{148}\right)\) \(e\left(\frac{139}{148}\right)\) \(e\left(\frac{5}{74}\right)\) \(e\left(\frac{19}{37}\right)\) \(e\left(\frac{36}{37}\right)\) \(e\left(\frac{59}{74}\right)\) \(e\left(\frac{15}{148}\right)\) \(e\left(\frac{65}{74}\right)\) \(e\left(\frac{81}{148}\right)\) \(e\left(\frac{101}{148}\right)\)