Properties

Modulus 8027
Structure \(C_{3828}\times C_{2}\)
Order 7656

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(8027)
 
pari: g = idealstar(,8027,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 7656
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{3828}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{8027}(1049,\cdot)$, $\chi_{8027}(8026,\cdot)$

First 32 of 7656 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
\(\chi_{8027}(1,\cdot)\) 8027.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{8027}(2,\cdot)\) 8027.bv 3828 yes \(-1\) \(1\) \(e\left(\frac{707}{3828}\right)\) \(e\left(\frac{1013}{1914}\right)\) \(e\left(\frac{707}{1914}\right)\) \(e\left(\frac{1901}{1914}\right)\) \(e\left(\frac{911}{1276}\right)\) \(e\left(\frac{3521}{3828}\right)\) \(e\left(\frac{707}{1276}\right)\) \(e\left(\frac{56}{957}\right)\) \(e\left(\frac{227}{1276}\right)\) \(e\left(\frac{1121}{1276}\right)\)
\(\chi_{8027}(3,\cdot)\) 8027.bs 1914 yes \(1\) \(1\) \(e\left(\frac{1013}{1914}\right)\) \(e\left(\frac{554}{957}\right)\) \(e\left(\frac{56}{957}\right)\) \(e\left(\frac{179}{957}\right)\) \(e\left(\frac{69}{638}\right)\) \(e\left(\frac{1577}{1914}\right)\) \(e\left(\frac{375}{638}\right)\) \(e\left(\frac{151}{957}\right)\) \(e\left(\frac{457}{638}\right)\) \(e\left(\frac{73}{638}\right)\)
\(\chi_{8027}(4,\cdot)\) 8027.bs 1914 yes \(1\) \(1\) \(e\left(\frac{707}{1914}\right)\) \(e\left(\frac{56}{957}\right)\) \(e\left(\frac{707}{957}\right)\) \(e\left(\frac{944}{957}\right)\) \(e\left(\frac{273}{638}\right)\) \(e\left(\frac{1607}{1914}\right)\) \(e\left(\frac{69}{638}\right)\) \(e\left(\frac{112}{957}\right)\) \(e\left(\frac{227}{638}\right)\) \(e\left(\frac{483}{638}\right)\)
\(\chi_{8027}(5,\cdot)\) 8027.bt 1914 yes \(-1\) \(1\) \(e\left(\frac{1901}{1914}\right)\) \(e\left(\frac{179}{957}\right)\) \(e\left(\frac{944}{957}\right)\) \(e\left(\frac{703}{1914}\right)\) \(e\left(\frac{115}{638}\right)\) \(e\left(\frac{304}{957}\right)\) \(e\left(\frac{625}{638}\right)\) \(e\left(\frac{358}{957}\right)\) \(e\left(\frac{115}{319}\right)\) \(e\left(\frac{114}{319}\right)\)
\(\chi_{8027}(6,\cdot)\) 8027.bp 1276 yes \(-1\) \(1\) \(e\left(\frac{911}{1276}\right)\) \(e\left(\frac{69}{638}\right)\) \(e\left(\frac{273}{638}\right)\) \(e\left(\frac{115}{638}\right)\) \(e\left(\frac{1049}{1276}\right)\) \(e\left(\frac{949}{1276}\right)\) \(e\left(\frac{181}{1276}\right)\) \(e\left(\frac{69}{319}\right)\) \(e\left(\frac{1141}{1276}\right)\) \(e\left(\frac{1267}{1276}\right)\)
\(\chi_{8027}(7,\cdot)\) 8027.bu 3828 yes \(1\) \(1\) \(e\left(\frac{3521}{3828}\right)\) \(e\left(\frac{1577}{1914}\right)\) \(e\left(\frac{1607}{1914}\right)\) \(e\left(\frac{304}{957}\right)\) \(e\left(\frac{949}{1276}\right)\) \(e\left(\frac{1181}{3828}\right)\) \(e\left(\frac{969}{1276}\right)\) \(e\left(\frac{620}{957}\right)\) \(e\left(\frac{303}{1276}\right)\) \(e\left(\frac{1041}{1276}\right)\)
\(\chi_{8027}(8,\cdot)\) 8027.bp 1276 yes \(-1\) \(1\) \(e\left(\frac{707}{1276}\right)\) \(e\left(\frac{375}{638}\right)\) \(e\left(\frac{69}{638}\right)\) \(e\left(\frac{625}{638}\right)\) \(e\left(\frac{181}{1276}\right)\) \(e\left(\frac{969}{1276}\right)\) \(e\left(\frac{845}{1276}\right)\) \(e\left(\frac{56}{319}\right)\) \(e\left(\frac{681}{1276}\right)\) \(e\left(\frac{811}{1276}\right)\)
\(\chi_{8027}(9,\cdot)\) 8027.bo 957 yes \(1\) \(1\) \(e\left(\frac{56}{957}\right)\) \(e\left(\frac{151}{957}\right)\) \(e\left(\frac{112}{957}\right)\) \(e\left(\frac{358}{957}\right)\) \(e\left(\frac{69}{319}\right)\) \(e\left(\frac{620}{957}\right)\) \(e\left(\frac{56}{319}\right)\) \(e\left(\frac{302}{957}\right)\) \(e\left(\frac{138}{319}\right)\) \(e\left(\frac{73}{319}\right)\)
\(\chi_{8027}(10,\cdot)\) 8027.bq 1276 yes \(1\) \(1\) \(e\left(\frac{227}{1276}\right)\) \(e\left(\frac{457}{638}\right)\) \(e\left(\frac{227}{638}\right)\) \(e\left(\frac{115}{319}\right)\) \(e\left(\frac{1141}{1276}\right)\) \(e\left(\frac{303}{1276}\right)\) \(e\left(\frac{681}{1276}\right)\) \(e\left(\frac{138}{319}\right)\) \(e\left(\frac{687}{1276}\right)\) \(e\left(\frac{301}{1276}\right)\)
\(\chi_{8027}(11,\cdot)\) 8027.bq 1276 yes \(1\) \(1\) \(e\left(\frac{1121}{1276}\right)\) \(e\left(\frac{73}{638}\right)\) \(e\left(\frac{483}{638}\right)\) \(e\left(\frac{114}{319}\right)\) \(e\left(\frac{1267}{1276}\right)\) \(e\left(\frac{1041}{1276}\right)\) \(e\left(\frac{811}{1276}\right)\) \(e\left(\frac{73}{319}\right)\) \(e\left(\frac{301}{1276}\right)\) \(e\left(\frac{1211}{1276}\right)\)
\(\chi_{8027}(12,\cdot)\) 8027.bo 957 yes \(1\) \(1\) \(e\left(\frac{860}{957}\right)\) \(e\left(\frac{610}{957}\right)\) \(e\left(\frac{763}{957}\right)\) \(e\left(\frac{166}{957}\right)\) \(e\left(\frac{171}{319}\right)\) \(e\left(\frac{635}{957}\right)\) \(e\left(\frac{222}{319}\right)\) \(e\left(\frac{263}{957}\right)\) \(e\left(\frac{23}{319}\right)\) \(e\left(\frac{278}{319}\right)\)
\(\chi_{8027}(13,\cdot)\) 8027.bv 3828 yes \(-1\) \(1\) \(e\left(\frac{197}{3828}\right)\) \(e\left(\frac{821}{1914}\right)\) \(e\left(\frac{197}{1914}\right)\) \(e\left(\frac{305}{1914}\right)\) \(e\left(\frac{613}{1276}\right)\) \(e\left(\frac{1019}{3828}\right)\) \(e\left(\frac{197}{1276}\right)\) \(e\left(\frac{821}{957}\right)\) \(e\left(\frac{269}{1276}\right)\) \(e\left(\frac{103}{1276}\right)\)
\(\chi_{8027}(14,\cdot)\) 8027.br 1914 yes \(-1\) \(1\) \(e\left(\frac{100}{957}\right)\) \(e\left(\frac{338}{957}\right)\) \(e\left(\frac{200}{957}\right)\) \(e\left(\frac{595}{1914}\right)\) \(e\left(\frac{146}{319}\right)\) \(e\left(\frac{437}{1914}\right)\) \(e\left(\frac{100}{319}\right)\) \(e\left(\frac{676}{957}\right)\) \(e\left(\frac{265}{638}\right)\) \(e\left(\frac{443}{638}\right)\)
\(\chi_{8027}(15,\cdot)\) 8027.br 1914 yes \(-1\) \(1\) \(e\left(\frac{500}{957}\right)\) \(e\left(\frac{733}{957}\right)\) \(e\left(\frac{43}{957}\right)\) \(e\left(\frac{1061}{1914}\right)\) \(e\left(\frac{92}{319}\right)\) \(e\left(\frac{271}{1914}\right)\) \(e\left(\frac{181}{319}\right)\) \(e\left(\frac{509}{957}\right)\) \(e\left(\frac{49}{638}\right)\) \(e\left(\frac{301}{638}\right)\)
\(\chi_{8027}(16,\cdot)\) 8027.bo 957 yes \(1\) \(1\) \(e\left(\frac{707}{957}\right)\) \(e\left(\frac{112}{957}\right)\) \(e\left(\frac{457}{957}\right)\) \(e\left(\frac{931}{957}\right)\) \(e\left(\frac{273}{319}\right)\) \(e\left(\frac{650}{957}\right)\) \(e\left(\frac{69}{319}\right)\) \(e\left(\frac{224}{957}\right)\) \(e\left(\frac{227}{319}\right)\) \(e\left(\frac{164}{319}\right)\)
\(\chi_{8027}(17,\cdot)\) 8027.bl 638 yes \(-1\) \(1\) \(e\left(\frac{241}{638}\right)\) \(e\left(\frac{117}{319}\right)\) \(e\left(\frac{241}{319}\right)\) \(e\left(\frac{71}{638}\right)\) \(e\left(\frac{475}{638}\right)\) \(e\left(\frac{229}{319}\right)\) \(e\left(\frac{85}{638}\right)\) \(e\left(\frac{234}{319}\right)\) \(e\left(\frac{156}{319}\right)\) \(e\left(\frac{138}{319}\right)\)
\(\chi_{8027}(18,\cdot)\) 8027.bv 3828 yes \(-1\) \(1\) \(e\left(\frac{931}{3828}\right)\) \(e\left(\frac{1315}{1914}\right)\) \(e\left(\frac{931}{1914}\right)\) \(e\left(\frac{703}{1914}\right)\) \(e\left(\frac{1187}{1276}\right)\) \(e\left(\frac{2173}{3828}\right)\) \(e\left(\frac{931}{1276}\right)\) \(e\left(\frac{358}{957}\right)\) \(e\left(\frac{779}{1276}\right)\) \(e\left(\frac{137}{1276}\right)\)
\(\chi_{8027}(19,\cdot)\) 8027.br 1914 yes \(-1\) \(1\) \(e\left(\frac{865}{957}\right)\) \(e\left(\frac{914}{957}\right)\) \(e\left(\frac{773}{957}\right)\) \(e\left(\frac{601}{1914}\right)\) \(e\left(\frac{274}{319}\right)\) \(e\left(\frac{287}{1914}\right)\) \(e\left(\frac{227}{319}\right)\) \(e\left(\frac{871}{957}\right)\) \(e\left(\frac{139}{638}\right)\) \(e\left(\frac{307}{638}\right)\)
\(\chi_{8027}(20,\cdot)\) 8027.br 1914 yes \(-1\) \(1\) \(e\left(\frac{347}{957}\right)\) \(e\left(\frac{235}{957}\right)\) \(e\left(\frac{694}{957}\right)\) \(e\left(\frac{677}{1914}\right)\) \(e\left(\frac{194}{319}\right)\) \(e\left(\frac{301}{1914}\right)\) \(e\left(\frac{28}{319}\right)\) \(e\left(\frac{470}{957}\right)\) \(e\left(\frac{457}{638}\right)\) \(e\left(\frac{73}{638}\right)\)
\(\chi_{8027}(21,\cdot)\) 8027.bq 1276 yes \(1\) \(1\) \(e\left(\frac{573}{1276}\right)\) \(e\left(\frac{257}{638}\right)\) \(e\left(\frac{573}{638}\right)\) \(e\left(\frac{161}{319}\right)\) \(e\left(\frac{1087}{1276}\right)\) \(e\left(\frac{169}{1276}\right)\) \(e\left(\frac{443}{1276}\right)\) \(e\left(\frac{257}{319}\right)\) \(e\left(\frac{1217}{1276}\right)\) \(e\left(\frac{1187}{1276}\right)\)
\(\chi_{8027}(22,\cdot)\) 8027.bf 174 yes \(-1\) \(1\) \(e\left(\frac{11}{174}\right)\) \(e\left(\frac{56}{87}\right)\) \(e\left(\frac{11}{87}\right)\) \(e\left(\frac{61}{174}\right)\) \(e\left(\frac{41}{58}\right)\) \(e\left(\frac{64}{87}\right)\) \(e\left(\frac{11}{58}\right)\) \(e\left(\frac{25}{87}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{24}{29}\right)\)
\(\chi_{8027}(24,\cdot)\) 8027.m 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(i\) \(-i\)
\(\chi_{8027}(25,\cdot)\) 8027.bo 957 yes \(1\) \(1\) \(e\left(\frac{944}{957}\right)\) \(e\left(\frac{358}{957}\right)\) \(e\left(\frac{931}{957}\right)\) \(e\left(\frac{703}{957}\right)\) \(e\left(\frac{115}{319}\right)\) \(e\left(\frac{608}{957}\right)\) \(e\left(\frac{306}{319}\right)\) \(e\left(\frac{716}{957}\right)\) \(e\left(\frac{230}{319}\right)\) \(e\left(\frac{228}{319}\right)\)
\(\chi_{8027}(26,\cdot)\) 8027.bo 957 yes \(1\) \(1\) \(e\left(\frac{226}{957}\right)\) \(e\left(\frac{917}{957}\right)\) \(e\left(\frac{452}{957}\right)\) \(e\left(\frac{146}{957}\right)\) \(e\left(\frac{62}{319}\right)\) \(e\left(\frac{178}{957}\right)\) \(e\left(\frac{226}{319}\right)\) \(e\left(\frac{877}{957}\right)\) \(e\left(\frac{124}{319}\right)\) \(e\left(\frac{306}{319}\right)\)
\(\chi_{8027}(27,\cdot)\) 8027.bm 638 yes \(1\) \(1\) \(e\left(\frac{375}{638}\right)\) \(e\left(\frac{235}{319}\right)\) \(e\left(\frac{56}{319}\right)\) \(e\left(\frac{179}{319}\right)\) \(e\left(\frac{207}{638}\right)\) \(e\left(\frac{301}{638}\right)\) \(e\left(\frac{487}{638}\right)\) \(e\left(\frac{151}{319}\right)\) \(e\left(\frac{95}{638}\right)\) \(e\left(\frac{219}{638}\right)\)
\(\chi_{8027}(28,\cdot)\) 8027.bq 1276 yes \(1\) \(1\) \(e\left(\frac{369}{1276}\right)\) \(e\left(\frac{563}{638}\right)\) \(e\left(\frac{369}{638}\right)\) \(e\left(\frac{97}{319}\right)\) \(e\left(\frac{219}{1276}\right)\) \(e\left(\frac{189}{1276}\right)\) \(e\left(\frac{1107}{1276}\right)\) \(e\left(\frac{244}{319}\right)\) \(e\left(\frac{757}{1276}\right)\) \(e\left(\frac{731}{1276}\right)\)
\(\chi_{8027}(29,\cdot)\) 8027.bs 1914 yes \(1\) \(1\) \(e\left(\frac{107}{1914}\right)\) \(e\left(\frac{956}{957}\right)\) \(e\left(\frac{107}{957}\right)\) \(e\left(\frac{530}{957}\right)\) \(e\left(\frac{35}{638}\right)\) \(e\left(\frac{1253}{1914}\right)\) \(e\left(\frac{107}{638}\right)\) \(e\left(\frac{955}{957}\right)\) \(e\left(\frac{389}{638}\right)\) \(e\left(\frac{111}{638}\right)\)
\(\chi_{8027}(30,\cdot)\) 8027.bu 3828 yes \(1\) \(1\) \(e\left(\frac{2707}{3828}\right)\) \(e\left(\frac{565}{1914}\right)\) \(e\left(\frac{793}{1914}\right)\) \(e\left(\frac{524}{957}\right)\) \(e\left(\frac{3}{1276}\right)\) \(e\left(\frac{235}{3828}\right)\) \(e\left(\frac{155}{1276}\right)\) \(e\left(\frac{565}{957}\right)\) \(e\left(\frac{325}{1276}\right)\) \(e\left(\frac{447}{1276}\right)\)
\(\chi_{8027}(31,\cdot)\) 8027.bi 319 yes \(1\) \(1\) \(e\left(\frac{317}{319}\right)\) \(e\left(\frac{6}{319}\right)\) \(e\left(\frac{315}{319}\right)\) \(e\left(\frac{10}{319}\right)\) \(e\left(\frac{4}{319}\right)\) \(e\left(\frac{69}{319}\right)\) \(e\left(\frac{313}{319}\right)\) \(e\left(\frac{12}{319}\right)\) \(e\left(\frac{8}{319}\right)\) \(e\left(\frac{277}{319}\right)\)
\(\chi_{8027}(32,\cdot)\) 8027.bv 3828 yes \(-1\) \(1\) \(e\left(\frac{3535}{3828}\right)\) \(e\left(\frac{1237}{1914}\right)\) \(e\left(\frac{1621}{1914}\right)\) \(e\left(\frac{1849}{1914}\right)\) \(e\left(\frac{727}{1276}\right)\) \(e\left(\frac{2293}{3828}\right)\) \(e\left(\frac{983}{1276}\right)\) \(e\left(\frac{280}{957}\right)\) \(e\left(\frac{1135}{1276}\right)\) \(e\left(\frac{501}{1276}\right)\)
\(\chi_{8027}(33,\cdot)\) 8027.bu 3828 yes \(1\) \(1\) \(e\left(\frac{1561}{3828}\right)\) \(e\left(\frac{1327}{1914}\right)\) \(e\left(\frac{1561}{1914}\right)\) \(e\left(\frac{521}{957}\right)\) \(e\left(\frac{129}{1276}\right)\) \(e\left(\frac{2449}{3828}\right)\) \(e\left(\frac{285}{1276}\right)\) \(e\left(\frac{370}{957}\right)\) \(e\left(\frac{1215}{1276}\right)\) \(e\left(\frac{81}{1276}\right)\)