Properties

Modulus 6047
Structure \(C_{6046}\)
Order 6046

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(6047)
pari: g = idealstar(,6047,2)

Character group

sage: G.order()
pari: g.no
Order = 6046
sage: H.invariants()
pari: g.cyc
Structure = \(C_{6046}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{6047}(5,\cdot)$

First 32 of 6046 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
\(\chi_{6047}(1,\cdot)\) 6047.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{6047}(2,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{538}{3023}\right)\) \(e\left(\frac{1095}{3023}\right)\) \(e\left(\frac{1076}{3023}\right)\) \(e\left(\frac{859}{3023}\right)\) \(e\left(\frac{1633}{3023}\right)\) \(e\left(\frac{71}{3023}\right)\) \(e\left(\frac{1614}{3023}\right)\) \(e\left(\frac{2190}{3023}\right)\) \(e\left(\frac{1397}{3023}\right)\) \(e\left(\frac{931}{3023}\right)\)
\(\chi_{6047}(3,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{1095}{3023}\right)\) \(e\left(\frac{2504}{3023}\right)\) \(e\left(\frac{2190}{3023}\right)\) \(e\left(\frac{1945}{3023}\right)\) \(e\left(\frac{576}{3023}\right)\) \(e\left(\frac{2128}{3023}\right)\) \(e\left(\frac{262}{3023}\right)\) \(e\left(\frac{1985}{3023}\right)\) \(e\left(\frac{17}{3023}\right)\) \(e\left(\frac{271}{3023}\right)\)
\(\chi_{6047}(4,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{1076}{3023}\right)\) \(e\left(\frac{2190}{3023}\right)\) \(e\left(\frac{2152}{3023}\right)\) \(e\left(\frac{1718}{3023}\right)\) \(e\left(\frac{243}{3023}\right)\) \(e\left(\frac{142}{3023}\right)\) \(e\left(\frac{205}{3023}\right)\) \(e\left(\frac{1357}{3023}\right)\) \(e\left(\frac{2794}{3023}\right)\) \(e\left(\frac{1862}{3023}\right)\)
\(\chi_{6047}(5,\cdot)\) 6047.d 6046 Yes \(-1\) \(1\) \(e\left(\frac{859}{3023}\right)\) \(e\left(\frac{1945}{3023}\right)\) \(e\left(\frac{1718}{3023}\right)\) \(e\left(\frac{1}{6046}\right)\) \(e\left(\frac{2804}{3023}\right)\) \(e\left(\frac{1962}{3023}\right)\) \(e\left(\frac{2577}{3023}\right)\) \(e\left(\frac{867}{3023}\right)\) \(e\left(\frac{1719}{6046}\right)\) \(e\left(\frac{2054}{3023}\right)\)
\(\chi_{6047}(6,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{1633}{3023}\right)\) \(e\left(\frac{576}{3023}\right)\) \(e\left(\frac{243}{3023}\right)\) \(e\left(\frac{2804}{3023}\right)\) \(e\left(\frac{2209}{3023}\right)\) \(e\left(\frac{2199}{3023}\right)\) \(e\left(\frac{1876}{3023}\right)\) \(e\left(\frac{1152}{3023}\right)\) \(e\left(\frac{1414}{3023}\right)\) \(e\left(\frac{1202}{3023}\right)\)
\(\chi_{6047}(7,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{71}{3023}\right)\) \(e\left(\frac{2128}{3023}\right)\) \(e\left(\frac{142}{3023}\right)\) \(e\left(\frac{1962}{3023}\right)\) \(e\left(\frac{2199}{3023}\right)\) \(e\left(\frac{2330}{3023}\right)\) \(e\left(\frac{213}{3023}\right)\) \(e\left(\frac{1233}{3023}\right)\) \(e\left(\frac{2033}{3023}\right)\) \(e\left(\frac{578}{3023}\right)\)
\(\chi_{6047}(8,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{1614}{3023}\right)\) \(e\left(\frac{262}{3023}\right)\) \(e\left(\frac{205}{3023}\right)\) \(e\left(\frac{2577}{3023}\right)\) \(e\left(\frac{1876}{3023}\right)\) \(e\left(\frac{213}{3023}\right)\) \(e\left(\frac{1819}{3023}\right)\) \(e\left(\frac{524}{3023}\right)\) \(e\left(\frac{1168}{3023}\right)\) \(e\left(\frac{2793}{3023}\right)\)
\(\chi_{6047}(9,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{2190}{3023}\right)\) \(e\left(\frac{1985}{3023}\right)\) \(e\left(\frac{1357}{3023}\right)\) \(e\left(\frac{867}{3023}\right)\) \(e\left(\frac{1152}{3023}\right)\) \(e\left(\frac{1233}{3023}\right)\) \(e\left(\frac{524}{3023}\right)\) \(e\left(\frac{947}{3023}\right)\) \(e\left(\frac{34}{3023}\right)\) \(e\left(\frac{542}{3023}\right)\)
\(\chi_{6047}(10,\cdot)\) 6047.d 6046 Yes \(-1\) \(1\) \(e\left(\frac{1397}{3023}\right)\) \(e\left(\frac{17}{3023}\right)\) \(e\left(\frac{2794}{3023}\right)\) \(e\left(\frac{1719}{6046}\right)\) \(e\left(\frac{1414}{3023}\right)\) \(e\left(\frac{2033}{3023}\right)\) \(e\left(\frac{1168}{3023}\right)\) \(e\left(\frac{34}{3023}\right)\) \(e\left(\frac{4513}{6046}\right)\) \(e\left(\frac{2985}{3023}\right)\)
\(\chi_{6047}(11,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{931}{3023}\right)\) \(e\left(\frac{271}{3023}\right)\) \(e\left(\frac{1862}{3023}\right)\) \(e\left(\frac{2054}{3023}\right)\) \(e\left(\frac{1202}{3023}\right)\) \(e\left(\frac{578}{3023}\right)\) \(e\left(\frac{2793}{3023}\right)\) \(e\left(\frac{542}{3023}\right)\) \(e\left(\frac{2985}{3023}\right)\) \(e\left(\frac{639}{3023}\right)\)
\(\chi_{6047}(12,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{2171}{3023}\right)\) \(e\left(\frac{1671}{3023}\right)\) \(e\left(\frac{1319}{3023}\right)\) \(e\left(\frac{640}{3023}\right)\) \(e\left(\frac{819}{3023}\right)\) \(e\left(\frac{2270}{3023}\right)\) \(e\left(\frac{467}{3023}\right)\) \(e\left(\frac{319}{3023}\right)\) \(e\left(\frac{2811}{3023}\right)\) \(e\left(\frac{2133}{3023}\right)\)
\(\chi_{6047}(13,\cdot)\) 6047.d 6046 Yes \(-1\) \(1\) \(e\left(\frac{1086}{3023}\right)\) \(e\left(\frac{446}{3023}\right)\) \(e\left(\frac{2172}{3023}\right)\) \(e\left(\frac{2243}{6046}\right)\) \(e\left(\frac{1532}{3023}\right)\) \(e\left(\frac{2301}{3023}\right)\) \(e\left(\frac{235}{3023}\right)\) \(e\left(\frac{892}{3023}\right)\) \(e\left(\frac{4415}{6046}\right)\) \(e\left(\frac{70}{3023}\right)\)
\(\chi_{6047}(14,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{609}{3023}\right)\) \(e\left(\frac{200}{3023}\right)\) \(e\left(\frac{1218}{3023}\right)\) \(e\left(\frac{2821}{3023}\right)\) \(e\left(\frac{809}{3023}\right)\) \(e\left(\frac{2401}{3023}\right)\) \(e\left(\frac{1827}{3023}\right)\) \(e\left(\frac{400}{3023}\right)\) \(e\left(\frac{407}{3023}\right)\) \(e\left(\frac{1509}{3023}\right)\)
\(\chi_{6047}(15,\cdot)\) 6047.d 6046 Yes \(-1\) \(1\) \(e\left(\frac{1954}{3023}\right)\) \(e\left(\frac{1426}{3023}\right)\) \(e\left(\frac{885}{3023}\right)\) \(e\left(\frac{3891}{6046}\right)\) \(e\left(\frac{357}{3023}\right)\) \(e\left(\frac{1067}{3023}\right)\) \(e\left(\frac{2839}{3023}\right)\) \(e\left(\frac{2852}{3023}\right)\) \(e\left(\frac{1753}{6046}\right)\) \(e\left(\frac{2325}{3023}\right)\)
\(\chi_{6047}(16,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{2152}{3023}\right)\) \(e\left(\frac{1357}{3023}\right)\) \(e\left(\frac{1281}{3023}\right)\) \(e\left(\frac{413}{3023}\right)\) \(e\left(\frac{486}{3023}\right)\) \(e\left(\frac{284}{3023}\right)\) \(e\left(\frac{410}{3023}\right)\) \(e\left(\frac{2714}{3023}\right)\) \(e\left(\frac{2565}{3023}\right)\) \(e\left(\frac{701}{3023}\right)\)
\(\chi_{6047}(17,\cdot)\) 6047.d 6046 Yes \(-1\) \(1\) \(e\left(\frac{1663}{3023}\right)\) \(e\left(\frac{1390}{3023}\right)\) \(e\left(\frac{303}{3023}\right)\) \(e\left(\frac{2029}{6046}\right)\) \(e\left(\frac{30}{3023}\right)\) \(e\left(\frac{2630}{3023}\right)\) \(e\left(\frac{1966}{3023}\right)\) \(e\left(\frac{2780}{3023}\right)\) \(e\left(\frac{5355}{6046}\right)\) \(e\left(\frac{1872}{3023}\right)\)
\(\chi_{6047}(18,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{2728}{3023}\right)\) \(e\left(\frac{57}{3023}\right)\) \(e\left(\frac{2433}{3023}\right)\) \(e\left(\frac{1726}{3023}\right)\) \(e\left(\frac{2785}{3023}\right)\) \(e\left(\frac{1304}{3023}\right)\) \(e\left(\frac{2138}{3023}\right)\) \(e\left(\frac{114}{3023}\right)\) \(e\left(\frac{1431}{3023}\right)\) \(e\left(\frac{1473}{3023}\right)\)
\(\chi_{6047}(19,\cdot)\) 6047.d 6046 Yes \(-1\) \(1\) \(e\left(\frac{962}{3023}\right)\) \(e\left(\frac{306}{3023}\right)\) \(e\left(\frac{1924}{3023}\right)\) \(e\left(\frac{3735}{6046}\right)\) \(e\left(\frac{1268}{3023}\right)\) \(e\left(\frac{318}{3023}\right)\) \(e\left(\frac{2886}{3023}\right)\) \(e\left(\frac{612}{3023}\right)\) \(e\left(\frac{5659}{6046}\right)\) \(e\left(\frac{2339}{3023}\right)\)
\(\chi_{6047}(20,\cdot)\) 6047.d 6046 Yes \(-1\) \(1\) \(e\left(\frac{1935}{3023}\right)\) \(e\left(\frac{1112}{3023}\right)\) \(e\left(\frac{847}{3023}\right)\) \(e\left(\frac{3437}{6046}\right)\) \(e\left(\frac{24}{3023}\right)\) \(e\left(\frac{2104}{3023}\right)\) \(e\left(\frac{2782}{3023}\right)\) \(e\left(\frac{2224}{3023}\right)\) \(e\left(\frac{1261}{6046}\right)\) \(e\left(\frac{893}{3023}\right)\)
\(\chi_{6047}(21,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{1166}{3023}\right)\) \(e\left(\frac{1609}{3023}\right)\) \(e\left(\frac{2332}{3023}\right)\) \(e\left(\frac{884}{3023}\right)\) \(e\left(\frac{2775}{3023}\right)\) \(e\left(\frac{1435}{3023}\right)\) \(e\left(\frac{475}{3023}\right)\) \(e\left(\frac{195}{3023}\right)\) \(e\left(\frac{2050}{3023}\right)\) \(e\left(\frac{849}{3023}\right)\)
\(\chi_{6047}(22,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{1469}{3023}\right)\) \(e\left(\frac{1366}{3023}\right)\) \(e\left(\frac{2938}{3023}\right)\) \(e\left(\frac{2913}{3023}\right)\) \(e\left(\frac{2835}{3023}\right)\) \(e\left(\frac{649}{3023}\right)\) \(e\left(\frac{1384}{3023}\right)\) \(e\left(\frac{2732}{3023}\right)\) \(e\left(\frac{1359}{3023}\right)\) \(e\left(\frac{1570}{3023}\right)\)
\(\chi_{6047}(23,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{1101}{3023}\right)\) \(e\left(\frac{853}{3023}\right)\) \(e\left(\frac{2202}{3023}\right)\) \(e\left(\frac{2494}{3023}\right)\) \(e\left(\frac{1954}{3023}\right)\) \(e\left(\frac{1005}{3023}\right)\) \(e\left(\frac{280}{3023}\right)\) \(e\left(\frac{1706}{3023}\right)\) \(e\left(\frac{572}{3023}\right)\) \(e\left(\frac{405}{3023}\right)\)
\(\chi_{6047}(24,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{2709}{3023}\right)\) \(e\left(\frac{2766}{3023}\right)\) \(e\left(\frac{2395}{3023}\right)\) \(e\left(\frac{1499}{3023}\right)\) \(e\left(\frac{2452}{3023}\right)\) \(e\left(\frac{2341}{3023}\right)\) \(e\left(\frac{2081}{3023}\right)\) \(e\left(\frac{2509}{3023}\right)\) \(e\left(\frac{1185}{3023}\right)\) \(e\left(\frac{41}{3023}\right)\)
\(\chi_{6047}(25,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{1718}{3023}\right)\) \(e\left(\frac{867}{3023}\right)\) \(e\left(\frac{413}{3023}\right)\) \(e\left(\frac{1}{3023}\right)\) \(e\left(\frac{2585}{3023}\right)\) \(e\left(\frac{901}{3023}\right)\) \(e\left(\frac{2131}{3023}\right)\) \(e\left(\frac{1734}{3023}\right)\) \(e\left(\frac{1719}{3023}\right)\) \(e\left(\frac{1085}{3023}\right)\)
\(\chi_{6047}(26,\cdot)\) 6047.d 6046 Yes \(-1\) \(1\) \(e\left(\frac{1624}{3023}\right)\) \(e\left(\frac{1541}{3023}\right)\) \(e\left(\frac{225}{3023}\right)\) \(e\left(\frac{3961}{6046}\right)\) \(e\left(\frac{142}{3023}\right)\) \(e\left(\frac{2372}{3023}\right)\) \(e\left(\frac{1849}{3023}\right)\) \(e\left(\frac{59}{3023}\right)\) \(e\left(\frac{1163}{6046}\right)\) \(e\left(\frac{1001}{3023}\right)\)
\(\chi_{6047}(27,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{262}{3023}\right)\) \(e\left(\frac{1466}{3023}\right)\) \(e\left(\frac{524}{3023}\right)\) \(e\left(\frac{2812}{3023}\right)\) \(e\left(\frac{1728}{3023}\right)\) \(e\left(\frac{338}{3023}\right)\) \(e\left(\frac{786}{3023}\right)\) \(e\left(\frac{2932}{3023}\right)\) \(e\left(\frac{51}{3023}\right)\) \(e\left(\frac{813}{3023}\right)\)
\(\chi_{6047}(28,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{1147}{3023}\right)\) \(e\left(\frac{1295}{3023}\right)\) \(e\left(\frac{2294}{3023}\right)\) \(e\left(\frac{657}{3023}\right)\) \(e\left(\frac{2442}{3023}\right)\) \(e\left(\frac{2472}{3023}\right)\) \(e\left(\frac{418}{3023}\right)\) \(e\left(\frac{2590}{3023}\right)\) \(e\left(\frac{1804}{3023}\right)\) \(e\left(\frac{2440}{3023}\right)\)
\(\chi_{6047}(29,\cdot)\) 6047.d 6046 Yes \(-1\) \(1\) \(e\left(\frac{1739}{3023}\right)\) \(e\left(\frac{2646}{3023}\right)\) \(e\left(\frac{455}{3023}\right)\) \(e\left(\frac{3845}{6046}\right)\) \(e\left(\frac{1362}{3023}\right)\) \(e\left(\frac{1505}{3023}\right)\) \(e\left(\frac{2194}{3023}\right)\) \(e\left(\frac{2269}{3023}\right)\) \(e\left(\frac{1277}{6046}\right)\) \(e\left(\frac{1554}{3023}\right)\)
\(\chi_{6047}(30,\cdot)\) 6047.d 6046 Yes \(-1\) \(1\) \(e\left(\frac{2492}{3023}\right)\) \(e\left(\frac{2521}{3023}\right)\) \(e\left(\frac{1961}{3023}\right)\) \(e\left(\frac{5609}{6046}\right)\) \(e\left(\frac{1990}{3023}\right)\) \(e\left(\frac{1138}{3023}\right)\) \(e\left(\frac{1430}{3023}\right)\) \(e\left(\frac{2019}{3023}\right)\) \(e\left(\frac{4547}{6046}\right)\) \(e\left(\frac{233}{3023}\right)\)
\(\chi_{6047}(31,\cdot)\) 6047.d 6046 Yes \(-1\) \(1\) \(e\left(\frac{521}{3023}\right)\) \(e\left(\frac{2246}{3023}\right)\) \(e\left(\frac{1042}{3023}\right)\) \(e\left(\frac{4653}{6046}\right)\) \(e\left(\frac{2767}{3023}\right)\) \(e\left(\frac{2749}{3023}\right)\) \(e\left(\frac{1563}{3023}\right)\) \(e\left(\frac{1469}{3023}\right)\) \(e\left(\frac{5695}{6046}\right)\) \(e\left(\frac{1559}{3023}\right)\)
\(\chi_{6047}(32,\cdot)\) 6047.c 3023 Yes \(1\) \(1\) \(e\left(\frac{2690}{3023}\right)\) \(e\left(\frac{2452}{3023}\right)\) \(e\left(\frac{2357}{3023}\right)\) \(e\left(\frac{1272}{3023}\right)\) \(e\left(\frac{2119}{3023}\right)\) \(e\left(\frac{355}{3023}\right)\) \(e\left(\frac{2024}{3023}\right)\) \(e\left(\frac{1881}{3023}\right)\) \(e\left(\frac{939}{3023}\right)\) \(e\left(\frac{1632}{3023}\right)\)