Properties

Modulus $647$
Structure \(C_{646}\)
Order $646$

Learn more

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(647)
 
pari: g = idealstar(,647,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 646
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{646}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{647}(5,\cdot)$

First 32 of 646 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{647}(1,\cdot)\) 647.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{647}(2,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{208}{323}\right)\) \(e\left(\frac{167}{323}\right)\) \(e\left(\frac{93}{323}\right)\) \(e\left(\frac{79}{323}\right)\) \(e\left(\frac{52}{323}\right)\) \(e\left(\frac{243}{323}\right)\) \(e\left(\frac{301}{323}\right)\) \(e\left(\frac{11}{323}\right)\) \(e\left(\frac{287}{323}\right)\) \(e\left(\frac{108}{323}\right)\)
\(\chi_{647}(3,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{167}{323}\right)\) \(e\left(\frac{117}{323}\right)\) \(e\left(\frac{11}{323}\right)\) \(e\left(\frac{183}{323}\right)\) \(e\left(\frac{284}{323}\right)\) \(e\left(\frac{60}{323}\right)\) \(e\left(\frac{178}{323}\right)\) \(e\left(\frac{234}{323}\right)\) \(e\left(\frac{27}{323}\right)\) \(e\left(\frac{242}{323}\right)\)
\(\chi_{647}(4,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{93}{323}\right)\) \(e\left(\frac{11}{323}\right)\) \(e\left(\frac{186}{323}\right)\) \(e\left(\frac{158}{323}\right)\) \(e\left(\frac{104}{323}\right)\) \(e\left(\frac{163}{323}\right)\) \(e\left(\frac{279}{323}\right)\) \(e\left(\frac{22}{323}\right)\) \(e\left(\frac{251}{323}\right)\) \(e\left(\frac{216}{323}\right)\)
\(\chi_{647}(5,\cdot)\) 647.h 646 yes \(-1\) \(1\) \(e\left(\frac{79}{323}\right)\) \(e\left(\frac{183}{323}\right)\) \(e\left(\frac{158}{323}\right)\) \(e\left(\frac{1}{646}\right)\) \(e\left(\frac{262}{323}\right)\) \(e\left(\frac{69}{323}\right)\) \(e\left(\frac{237}{323}\right)\) \(e\left(\frac{43}{323}\right)\) \(e\left(\frac{159}{646}\right)\) \(e\left(\frac{169}{646}\right)\)
\(\chi_{647}(6,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{52}{323}\right)\) \(e\left(\frac{284}{323}\right)\) \(e\left(\frac{104}{323}\right)\) \(e\left(\frac{262}{323}\right)\) \(e\left(\frac{13}{323}\right)\) \(e\left(\frac{303}{323}\right)\) \(e\left(\frac{156}{323}\right)\) \(e\left(\frac{245}{323}\right)\) \(e\left(\frac{314}{323}\right)\) \(e\left(\frac{27}{323}\right)\)
\(\chi_{647}(7,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{243}{323}\right)\) \(e\left(\frac{60}{323}\right)\) \(e\left(\frac{163}{323}\right)\) \(e\left(\frac{69}{323}\right)\) \(e\left(\frac{303}{323}\right)\) \(e\left(\frac{155}{323}\right)\) \(e\left(\frac{83}{323}\right)\) \(e\left(\frac{120}{323}\right)\) \(e\left(\frac{312}{323}\right)\) \(e\left(\frac{33}{323}\right)\)
\(\chi_{647}(8,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{301}{323}\right)\) \(e\left(\frac{178}{323}\right)\) \(e\left(\frac{279}{323}\right)\) \(e\left(\frac{237}{323}\right)\) \(e\left(\frac{156}{323}\right)\) \(e\left(\frac{83}{323}\right)\) \(e\left(\frac{257}{323}\right)\) \(e\left(\frac{33}{323}\right)\) \(e\left(\frac{215}{323}\right)\) \(e\left(\frac{1}{323}\right)\)
\(\chi_{647}(9,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{11}{323}\right)\) \(e\left(\frac{234}{323}\right)\) \(e\left(\frac{22}{323}\right)\) \(e\left(\frac{43}{323}\right)\) \(e\left(\frac{245}{323}\right)\) \(e\left(\frac{120}{323}\right)\) \(e\left(\frac{33}{323}\right)\) \(e\left(\frac{145}{323}\right)\) \(e\left(\frac{54}{323}\right)\) \(e\left(\frac{161}{323}\right)\)
\(\chi_{647}(10,\cdot)\) 647.h 646 yes \(-1\) \(1\) \(e\left(\frac{287}{323}\right)\) \(e\left(\frac{27}{323}\right)\) \(e\left(\frac{251}{323}\right)\) \(e\left(\frac{159}{646}\right)\) \(e\left(\frac{314}{323}\right)\) \(e\left(\frac{312}{323}\right)\) \(e\left(\frac{215}{323}\right)\) \(e\left(\frac{54}{323}\right)\) \(e\left(\frac{87}{646}\right)\) \(e\left(\frac{385}{646}\right)\)
\(\chi_{647}(11,\cdot)\) 647.h 646 yes \(-1\) \(1\) \(e\left(\frac{108}{323}\right)\) \(e\left(\frac{242}{323}\right)\) \(e\left(\frac{216}{323}\right)\) \(e\left(\frac{169}{646}\right)\) \(e\left(\frac{27}{323}\right)\) \(e\left(\frac{33}{323}\right)\) \(e\left(\frac{1}{323}\right)\) \(e\left(\frac{161}{323}\right)\) \(e\left(\frac{385}{646}\right)\) \(e\left(\frac{137}{646}\right)\)
\(\chi_{647}(12,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{260}{323}\right)\) \(e\left(\frac{128}{323}\right)\) \(e\left(\frac{197}{323}\right)\) \(e\left(\frac{18}{323}\right)\) \(e\left(\frac{65}{323}\right)\) \(e\left(\frac{223}{323}\right)\) \(e\left(\frac{134}{323}\right)\) \(e\left(\frac{256}{323}\right)\) \(e\left(\frac{278}{323}\right)\) \(e\left(\frac{135}{323}\right)\)
\(\chi_{647}(13,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{124}{323}\right)\) \(e\left(\frac{230}{323}\right)\) \(e\left(\frac{248}{323}\right)\) \(e\left(\frac{103}{323}\right)\) \(e\left(\frac{31}{323}\right)\) \(e\left(\frac{2}{323}\right)\) \(e\left(\frac{49}{323}\right)\) \(e\left(\frac{137}{323}\right)\) \(e\left(\frac{227}{323}\right)\) \(e\left(\frac{288}{323}\right)\)
\(\chi_{647}(14,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{128}{323}\right)\) \(e\left(\frac{227}{323}\right)\) \(e\left(\frac{256}{323}\right)\) \(e\left(\frac{148}{323}\right)\) \(e\left(\frac{32}{323}\right)\) \(e\left(\frac{75}{323}\right)\) \(e\left(\frac{61}{323}\right)\) \(e\left(\frac{131}{323}\right)\) \(e\left(\frac{276}{323}\right)\) \(e\left(\frac{141}{323}\right)\)
\(\chi_{647}(15,\cdot)\) 647.h 646 yes \(-1\) \(1\) \(e\left(\frac{246}{323}\right)\) \(e\left(\frac{300}{323}\right)\) \(e\left(\frac{169}{323}\right)\) \(e\left(\frac{367}{646}\right)\) \(e\left(\frac{223}{323}\right)\) \(e\left(\frac{129}{323}\right)\) \(e\left(\frac{92}{323}\right)\) \(e\left(\frac{277}{323}\right)\) \(e\left(\frac{213}{646}\right)\) \(e\left(\frac{7}{646}\right)\)
\(\chi_{647}(16,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{186}{323}\right)\) \(e\left(\frac{22}{323}\right)\) \(e\left(\frac{49}{323}\right)\) \(e\left(\frac{316}{323}\right)\) \(e\left(\frac{208}{323}\right)\) \(e\left(\frac{3}{323}\right)\) \(e\left(\frac{235}{323}\right)\) \(e\left(\frac{44}{323}\right)\) \(e\left(\frac{179}{323}\right)\) \(e\left(\frac{109}{323}\right)\)
\(\chi_{647}(17,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{218}{323}\right)\) \(e\left(\frac{321}{323}\right)\) \(e\left(\frac{113}{323}\right)\) \(e\left(\frac{30}{323}\right)\) \(e\left(\frac{216}{323}\right)\) \(e\left(\frac{264}{323}\right)\) \(e\left(\frac{8}{323}\right)\) \(e\left(\frac{319}{323}\right)\) \(e\left(\frac{248}{323}\right)\) \(e\left(\frac{225}{323}\right)\)
\(\chi_{647}(18,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{219}{323}\right)\) \(e\left(\frac{78}{323}\right)\) \(e\left(\frac{115}{323}\right)\) \(e\left(\frac{122}{323}\right)\) \(e\left(\frac{297}{323}\right)\) \(e\left(\frac{40}{323}\right)\) \(e\left(\frac{11}{323}\right)\) \(e\left(\frac{156}{323}\right)\) \(e\left(\frac{18}{323}\right)\) \(e\left(\frac{269}{323}\right)\)
\(\chi_{647}(19,\cdot)\) 647.h 646 yes \(-1\) \(1\) \(e\left(\frac{220}{323}\right)\) \(e\left(\frac{158}{323}\right)\) \(e\left(\frac{117}{323}\right)\) \(e\left(\frac{105}{646}\right)\) \(e\left(\frac{55}{323}\right)\) \(e\left(\frac{139}{323}\right)\) \(e\left(\frac{14}{323}\right)\) \(e\left(\frac{316}{323}\right)\) \(e\left(\frac{545}{646}\right)\) \(e\left(\frac{303}{646}\right)\)
\(\chi_{647}(20,\cdot)\) 647.h 646 yes \(-1\) \(1\) \(e\left(\frac{172}{323}\right)\) \(e\left(\frac{194}{323}\right)\) \(e\left(\frac{21}{323}\right)\) \(e\left(\frac{317}{646}\right)\) \(e\left(\frac{43}{323}\right)\) \(e\left(\frac{232}{323}\right)\) \(e\left(\frac{193}{323}\right)\) \(e\left(\frac{65}{323}\right)\) \(e\left(\frac{15}{646}\right)\) \(e\left(\frac{601}{646}\right)\)
\(\chi_{647}(21,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{87}{323}\right)\) \(e\left(\frac{177}{323}\right)\) \(e\left(\frac{174}{323}\right)\) \(e\left(\frac{252}{323}\right)\) \(e\left(\frac{264}{323}\right)\) \(e\left(\frac{215}{323}\right)\) \(e\left(\frac{261}{323}\right)\) \(e\left(\frac{31}{323}\right)\) \(e\left(\frac{16}{323}\right)\) \(e\left(\frac{275}{323}\right)\)
\(\chi_{647}(22,\cdot)\) 647.h 646 yes \(-1\) \(1\) \(e\left(\frac{316}{323}\right)\) \(e\left(\frac{86}{323}\right)\) \(e\left(\frac{309}{323}\right)\) \(e\left(\frac{327}{646}\right)\) \(e\left(\frac{79}{323}\right)\) \(e\left(\frac{276}{323}\right)\) \(e\left(\frac{302}{323}\right)\) \(e\left(\frac{172}{323}\right)\) \(e\left(\frac{313}{646}\right)\) \(e\left(\frac{353}{646}\right)\)
\(\chi_{647}(23,\cdot)\) 647.h 646 yes \(-1\) \(1\) \(e\left(\frac{154}{323}\right)\) \(e\left(\frac{46}{323}\right)\) \(e\left(\frac{308}{323}\right)\) \(e\left(\frac{235}{646}\right)\) \(e\left(\frac{200}{323}\right)\) \(e\left(\frac{65}{323}\right)\) \(e\left(\frac{139}{323}\right)\) \(e\left(\frac{92}{323}\right)\) \(e\left(\frac{543}{646}\right)\) \(e\left(\frac{309}{646}\right)\)
\(\chi_{647}(24,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{145}{323}\right)\) \(e\left(\frac{295}{323}\right)\) \(e\left(\frac{290}{323}\right)\) \(e\left(\frac{97}{323}\right)\) \(e\left(\frac{117}{323}\right)\) \(e\left(\frac{143}{323}\right)\) \(e\left(\frac{112}{323}\right)\) \(e\left(\frac{267}{323}\right)\) \(e\left(\frac{242}{323}\right)\) \(e\left(\frac{243}{323}\right)\)
\(\chi_{647}(25,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{158}{323}\right)\) \(e\left(\frac{43}{323}\right)\) \(e\left(\frac{316}{323}\right)\) \(e\left(\frac{1}{323}\right)\) \(e\left(\frac{201}{323}\right)\) \(e\left(\frac{138}{323}\right)\) \(e\left(\frac{151}{323}\right)\) \(e\left(\frac{86}{323}\right)\) \(e\left(\frac{159}{323}\right)\) \(e\left(\frac{169}{323}\right)\)
\(\chi_{647}(26,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{9}{323}\right)\) \(e\left(\frac{74}{323}\right)\) \(e\left(\frac{18}{323}\right)\) \(e\left(\frac{182}{323}\right)\) \(e\left(\frac{83}{323}\right)\) \(e\left(\frac{245}{323}\right)\) \(e\left(\frac{27}{323}\right)\) \(e\left(\frac{148}{323}\right)\) \(e\left(\frac{191}{323}\right)\) \(e\left(\frac{73}{323}\right)\)
\(\chi_{647}(27,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{178}{323}\right)\) \(e\left(\frac{28}{323}\right)\) \(e\left(\frac{33}{323}\right)\) \(e\left(\frac{226}{323}\right)\) \(e\left(\frac{206}{323}\right)\) \(e\left(\frac{180}{323}\right)\) \(e\left(\frac{211}{323}\right)\) \(e\left(\frac{56}{323}\right)\) \(e\left(\frac{81}{323}\right)\) \(e\left(\frac{80}{323}\right)\)
\(\chi_{647}(28,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{13}{323}\right)\) \(e\left(\frac{71}{323}\right)\) \(e\left(\frac{26}{323}\right)\) \(e\left(\frac{227}{323}\right)\) \(e\left(\frac{84}{323}\right)\) \(e\left(\frac{318}{323}\right)\) \(e\left(\frac{39}{323}\right)\) \(e\left(\frac{142}{323}\right)\) \(e\left(\frac{240}{323}\right)\) \(e\left(\frac{249}{323}\right)\)
\(\chi_{647}(29,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{18}{323}\right)\) \(e\left(\frac{148}{323}\right)\) \(e\left(\frac{36}{323}\right)\) \(e\left(\frac{41}{323}\right)\) \(e\left(\frac{166}{323}\right)\) \(e\left(\frac{167}{323}\right)\) \(e\left(\frac{54}{323}\right)\) \(e\left(\frac{296}{323}\right)\) \(e\left(\frac{59}{323}\right)\) \(e\left(\frac{146}{323}\right)\)
\(\chi_{647}(30,\cdot)\) 647.h 646 yes \(-1\) \(1\) \(e\left(\frac{131}{323}\right)\) \(e\left(\frac{144}{323}\right)\) \(e\left(\frac{262}{323}\right)\) \(e\left(\frac{525}{646}\right)\) \(e\left(\frac{275}{323}\right)\) \(e\left(\frac{49}{323}\right)\) \(e\left(\frac{70}{323}\right)\) \(e\left(\frac{288}{323}\right)\) \(e\left(\frac{141}{646}\right)\) \(e\left(\frac{223}{646}\right)\)
\(\chi_{647}(31,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{6}{323}\right)\) \(e\left(\frac{157}{323}\right)\) \(e\left(\frac{12}{323}\right)\) \(e\left(\frac{229}{323}\right)\) \(e\left(\frac{163}{323}\right)\) \(e\left(\frac{271}{323}\right)\) \(e\left(\frac{18}{323}\right)\) \(e\left(\frac{314}{323}\right)\) \(e\left(\frac{235}{323}\right)\) \(e\left(\frac{264}{323}\right)\)
\(\chi_{647}(32,\cdot)\) 647.g 323 yes \(1\) \(1\) \(e\left(\frac{71}{323}\right)\) \(e\left(\frac{189}{323}\right)\) \(e\left(\frac{142}{323}\right)\) \(e\left(\frac{72}{323}\right)\) \(e\left(\frac{260}{323}\right)\) \(e\left(\frac{246}{323}\right)\) \(e\left(\frac{213}{323}\right)\) \(e\left(\frac{55}{323}\right)\) \(e\left(\frac{143}{323}\right)\) \(e\left(\frac{217}{323}\right)\)