LMFDB - Dirichlet character orbit 5041.o

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5041, base_ring=CyclotomicField(4970)) M = H._module chi = DirichletCharacter(H, M([4486])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,5041)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$5041$
Conductor:	$5041$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$2485$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{2485})$
Fixed field:	Number field defined by a degree 2485 polynomial (not computed)

First 31 of 1680 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{5041}(2,\cdot)$	$1$	$1$	$e\left(\frac{333}{2485}\right)$	$e\left(\frac{358}{2485}\right)$	$e\left(\frac{666}{2485}\right)$	$e\left(\frac{97}{355}\right)$	$e\left(\frac{691}{2485}\right)$	$e\left(\frac{2243}{2485}\right)$	$e\left(\frac{999}{2485}\right)$	$e\left(\frac{716}{2485}\right)$	$e\left(\frac{1012}{2485}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{5041}(3,\cdot)$	$1$	$1$	$e\left(\frac{358}{2485}\right)$	$e\left(\frac{758}{2485}\right)$	$e\left(\frac{716}{2485}\right)$	$e\left(\frac{132}{355}\right)$	$e\left(\frac{1116}{2485}\right)$	$e\left(\frac{1098}{2485}\right)$	$e\left(\frac{1074}{2485}\right)$	$e\left(\frac{1516}{2485}\right)$	$e\left(\frac{1282}{2485}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{5041}(4,\cdot)$	$1$	$1$	$e\left(\frac{666}{2485}\right)$	$e\left(\frac{716}{2485}\right)$	$e\left(\frac{1332}{2485}\right)$	$e\left(\frac{194}{355}\right)$	$e\left(\frac{1382}{2485}\right)$	$e\left(\frac{2001}{2485}\right)$	$e\left(\frac{1998}{2485}\right)$	$e\left(\frac{1432}{2485}\right)$	$e\left(\frac{2024}{2485}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{5041}(6,\cdot)$	$1$	$1$	$e\left(\frac{691}{2485}\right)$	$e\left(\frac{1116}{2485}\right)$	$e\left(\frac{1382}{2485}\right)$	$e\left(\frac{229}{355}\right)$	$e\left(\frac{1807}{2485}\right)$	$e\left(\frac{856}{2485}\right)$	$e\left(\frac{2073}{2485}\right)$	$e\left(\frac{2232}{2485}\right)$	$e\left(\frac{2294}{2485}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{5041}(8,\cdot)$	$1$	$1$	$e\left(\frac{999}{2485}\right)$	$e\left(\frac{1074}{2485}\right)$	$e\left(\frac{1998}{2485}\right)$	$e\left(\frac{291}{355}\right)$	$e\left(\frac{2073}{2485}\right)$	$e\left(\frac{1759}{2485}\right)$	$e\left(\frac{512}{2485}\right)$	$e\left(\frac{2148}{2485}\right)$	$e\left(\frac{551}{2485}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{5041}(9,\cdot)$	$1$	$1$	$e\left(\frac{716}{2485}\right)$	$e\left(\frac{1516}{2485}\right)$	$e\left(\frac{1432}{2485}\right)$	$e\left(\frac{264}{355}\right)$	$e\left(\frac{2232}{2485}\right)$	$e\left(\frac{2196}{2485}\right)$	$e\left(\frac{2148}{2485}\right)$	$e\left(\frac{547}{2485}\right)$	$e\left(\frac{79}{2485}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{5041}(10,\cdot)$	$1$	$1$	$e\left(\frac{1012}{2485}\right)$	$e\left(\frac{1282}{2485}\right)$	$e\left(\frac{2024}{2485}\right)$	$e\left(\frac{153}{355}\right)$	$e\left(\frac{2294}{2485}\right)$	$e\left(\frac{2257}{2485}\right)$	$e\left(\frac{551}{2485}\right)$	$e\left(\frac{79}{2485}\right)$	$e\left(\frac{2083}{2485}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{5041}(12,\cdot)$	$1$	$1$	$e\left(\frac{1024}{2485}\right)$	$e\left(\frac{1474}{2485}\right)$	$e\left(\frac{2048}{2485}\right)$	$e\left(\frac{326}{355}\right)$	$e\left(\frac{13}{2485}\right)$	$e\left(\frac{614}{2485}\right)$	$e\left(\frac{587}{2485}\right)$	$e\left(\frac{463}{2485}\right)$	$e\left(\frac{821}{2485}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{5041}(15,\cdot)$	$1$	$1$	$e\left(\frac{1037}{2485}\right)$	$e\left(\frac{1682}{2485}\right)$	$e\left(\frac{2074}{2485}\right)$	$e\left(\frac{188}{355}\right)$	$e\left(\frac{234}{2485}\right)$	$e\left(\frac{1112}{2485}\right)$	$e\left(\frac{626}{2485}\right)$	$e\left(\frac{879}{2485}\right)$	$e\left(\frac{2353}{2485}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{5041}(16,\cdot)$	$1$	$1$	$e\left(\frac{1332}{2485}\right)$	$e\left(\frac{1432}{2485}\right)$	$e\left(\frac{179}{2485}\right)$	$e\left(\frac{33}{355}\right)$	$e\left(\frac{279}{2485}\right)$	$e\left(\frac{1517}{2485}\right)$	$e\left(\frac{1511}{2485}\right)$	$e\left(\frac{379}{2485}\right)$	$e\left(\frac{1563}{2485}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{5041}(18,\cdot)$	$1$	$1$	$e\left(\frac{1049}{2485}\right)$	$e\left(\frac{1874}{2485}\right)$	$e\left(\frac{2098}{2485}\right)$	$e\left(\frac{6}{355}\right)$	$e\left(\frac{438}{2485}\right)$	$e\left(\frac{1954}{2485}\right)$	$e\left(\frac{662}{2485}\right)$	$e\left(\frac{1263}{2485}\right)$	$e\left(\frac{1091}{2485}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{5041}(19,\cdot)$	$1$	$1$	$e\left(\frac{853}{2485}\right)$	$e\left(\frac{1223}{2485}\right)$	$e\left(\frac{1706}{2485}\right)$	$e\left(\frac{257}{355}\right)$	$e\left(\frac{2076}{2485}\right)$	$e\left(\frac{2283}{2485}\right)$	$e\left(\frac{74}{2485}\right)$	$e\left(\frac{2446}{2485}\right)$	$e\left(\frac{167}{2485}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{5041}(24,\cdot)$	$1$	$1$	$e\left(\frac{1357}{2485}\right)$	$e\left(\frac{1832}{2485}\right)$	$e\left(\frac{229}{2485}\right)$	$e\left(\frac{68}{355}\right)$	$e\left(\frac{704}{2485}\right)$	$e\left(\frac{372}{2485}\right)$	$e\left(\frac{1586}{2485}\right)$	$e\left(\frac{1179}{2485}\right)$	$e\left(\frac{1833}{2485}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{5041}(27,\cdot)$	$1$	$1$	$e\left(\frac{1074}{2485}\right)$	$e\left(\frac{2274}{2485}\right)$	$e\left(\frac{2148}{2485}\right)$	$e\left(\frac{41}{355}\right)$	$e\left(\frac{863}{2485}\right)$	$e\left(\frac{809}{2485}\right)$	$e\left(\frac{737}{2485}\right)$	$e\left(\frac{2063}{2485}\right)$	$e\left(\frac{1361}{2485}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{5041}(29,\cdot)$	$1$	$1$	$e\left(\frac{2479}{2485}\right)$	$e\left(\frac{2389}{2485}\right)$	$e\left(\frac{2473}{2485}\right)$	$e\left(\frac{91}{355}\right)$	$e\left(\frac{2383}{2485}\right)$	$e\left(\frac{2064}{2485}\right)$	$e\left(\frac{2467}{2485}\right)$	$e\left(\frac{2293}{2485}\right)$	$e\left(\frac{631}{2485}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{5041}(36,\cdot)$	$1$	$1$	$e\left(\frac{1382}{2485}\right)$	$e\left(\frac{2232}{2485}\right)$	$e\left(\frac{279}{2485}\right)$	$e\left(\frac{103}{355}\right)$	$e\left(\frac{1129}{2485}\right)$	$e\left(\frac{1712}{2485}\right)$	$e\left(\frac{1661}{2485}\right)$	$e\left(\frac{1979}{2485}\right)$	$e\left(\frac{2103}{2485}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{5041}(38,\cdot)$	$1$	$1$	$e\left(\frac{1186}{2485}\right)$	$e\left(\frac{1581}{2485}\right)$	$e\left(\frac{2372}{2485}\right)$	$e\left(\frac{354}{355}\right)$	$e\left(\frac{282}{2485}\right)$	$e\left(\frac{2041}{2485}\right)$	$e\left(\frac{1073}{2485}\right)$	$e\left(\frac{677}{2485}\right)$	$e\left(\frac{1179}{2485}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{5041}(40,\cdot)$	$1$	$1$	$e\left(\frac{1678}{2485}\right)$	$e\left(\frac{1998}{2485}\right)$	$e\left(\frac{871}{2485}\right)$	$e\left(\frac{347}{355}\right)$	$e\left(\frac{1191}{2485}\right)$	$e\left(\frac{1773}{2485}\right)$	$e\left(\frac{64}{2485}\right)$	$e\left(\frac{1511}{2485}\right)$	$e\left(\frac{1622}{2485}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{5041}(43,\cdot)$	$1$	$1$	$e\left(\frac{984}{2485}\right)$	$e\left(\frac{834}{2485}\right)$	$e\left(\frac{1968}{2485}\right)$	$e\left(\frac{341}{355}\right)$	$e\left(\frac{1818}{2485}\right)$	$e\left(\frac{1949}{2485}\right)$	$e\left(\frac{467}{2485}\right)$	$e\left(\frac{1668}{2485}\right)$	$e\left(\frac{886}{2485}\right)$	$e\left(\frac{9}{35}\right)$
$\chi_{5041}(49,\cdot)$	$1$	$1$	$e\left(\frac{2001}{2485}\right)$	$e\left(\frac{2196}{2485}\right)$	$e\left(\frac{1517}{2485}\right)$	$e\left(\frac{4}{355}\right)$	$e\left(\frac{1712}{2485}\right)$	$e\left(\frac{1}{2485}\right)$	$e\left(\frac{1033}{2485}\right)$	$e\left(\frac{1907}{2485}\right)$	$e\left(\frac{2029}{2485}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{5041}(50,\cdot)$	$1$	$1$	$e\left(\frac{1691}{2485}\right)$	$e\left(\frac{2206}{2485}\right)$	$e\left(\frac{897}{2485}\right)$	$e\left(\frac{209}{355}\right)$	$e\left(\frac{1412}{2485}\right)$	$e\left(\frac{2271}{2485}\right)$	$e\left(\frac{103}{2485}\right)$	$e\left(\frac{1927}{2485}\right)$	$e\left(\frac{669}{2485}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{5041}(58,\cdot)$	$1$	$1$	$e\left(\frac{327}{2485}\right)$	$e\left(\frac{262}{2485}\right)$	$e\left(\frac{654}{2485}\right)$	$e\left(\frac{188}{355}\right)$	$e\left(\frac{589}{2485}\right)$	$e\left(\frac{1822}{2485}\right)$	$e\left(\frac{981}{2485}\right)$	$e\left(\frac{524}{2485}\right)$	$e\left(\frac{1643}{2485}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{5041}(60,\cdot)$	$1$	$1$	$e\left(\frac{1703}{2485}\right)$	$e\left(\frac{2398}{2485}\right)$	$e\left(\frac{921}{2485}\right)$	$e\left(\frac{27}{355}\right)$	$e\left(\frac{1616}{2485}\right)$	$e\left(\frac{628}{2485}\right)$	$e\left(\frac{139}{2485}\right)$	$e\left(\frac{2311}{2485}\right)$	$e\left(\frac{1892}{2485}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{5041}(64,\cdot)$	$1$	$1$	$e\left(\frac{1998}{2485}\right)$	$e\left(\frac{2148}{2485}\right)$	$e\left(\frac{1511}{2485}\right)$	$e\left(\frac{227}{355}\right)$	$e\left(\frac{1661}{2485}\right)$	$e\left(\frac{1033}{2485}\right)$	$e\left(\frac{1024}{2485}\right)$	$e\left(\frac{1811}{2485}\right)$	$e\left(\frac{1102}{2485}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{5041}(73,\cdot)$	$1$	$1$	$e\left(\frac{2433}{2485}\right)$	$e\left(\frac{1653}{2485}\right)$	$e\left(\frac{2381}{2485}\right)$	$e\left(\frac{197}{355}\right)$	$e\left(\frac{1601}{2485}\right)$	$e\left(\frac{493}{2485}\right)$	$e\left(\frac{2329}{2485}\right)$	$e\left(\frac{821}{2485}\right)$	$e\left(\frac{1327}{2485}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{5041}(74,\cdot)$	$1$	$1$	$e\left(\frac{1758}{2485}\right)$	$e\left(\frac{793}{2485}\right)$	$e\left(\frac{1031}{2485}\right)$	$e\left(\frac{317}{355}\right)$	$e\left(\frac{66}{2485}\right)$	$e\left(\frac{1588}{2485}\right)$	$e\left(\frac{304}{2485}\right)$	$e\left(\frac{1586}{2485}\right)$	$e\left(\frac{1492}{2485}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{5041}(75,\cdot)$	$1$	$1$	$e\left(\frac{1716}{2485}\right)$	$e\left(\frac{121}{2485}\right)$	$e\left(\frac{947}{2485}\right)$	$e\left(\frac{244}{355}\right)$	$e\left(\frac{1837}{2485}\right)$	$e\left(\frac{1126}{2485}\right)$	$e\left(\frac{178}{2485}\right)$	$e\left(\frac{242}{2485}\right)$	$e\left(\frac{939}{2485}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{5041}(77,\cdot)$	$1$	$1$	$e\left(\frac{1391}{2485}\right)$	$e\left(\frac{2376}{2485}\right)$	$e\left(\frac{297}{2485}\right)$	$e\left(\frac{144}{355}\right)$	$e\left(\frac{1282}{2485}\right)$	$e\left(\frac{1101}{2485}\right)$	$e\left(\frac{1688}{2485}\right)$	$e\left(\frac{2267}{2485}\right)$	$e\left(\frac{2399}{2485}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{5041}(79,\cdot)$	$1$	$1$	$e\left(\frac{1524}{2485}\right)$	$e\left(\frac{2019}{2485}\right)$	$e\left(\frac{563}{2485}\right)$	$e\left(\frac{316}{355}\right)$	$e\left(\frac{1058}{2485}\right)$	$e\left(\frac{79}{2485}\right)$	$e\left(\frac{2087}{2485}\right)$	$e\left(\frac{1553}{2485}\right)$	$e\left(\frac{1251}{2485}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{5041}(80,\cdot)$	$1$	$1$	$e\left(\frac{2011}{2485}\right)$	$e\left(\frac{2356}{2485}\right)$	$e\left(\frac{1537}{2485}\right)$	$e\left(\frac{89}{355}\right)$	$e\left(\frac{1882}{2485}\right)$	$e\left(\frac{1531}{2485}\right)$	$e\left(\frac{1063}{2485}\right)$	$e\left(\frac{2227}{2485}\right)$	$e\left(\frac{149}{2485}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{5041}(81,\cdot)$	$1$	$1$	$e\left(\frac{1432}{2485}\right)$	$e\left(\frac{547}{2485}\right)$	$e\left(\frac{379}{2485}\right)$	$e\left(\frac{173}{355}\right)$	$e\left(\frac{1979}{2485}\right)$	$e\left(\frac{1907}{2485}\right)$	$e\left(\frac{1811}{2485}\right)$	$e\left(\frac{1094}{2485}\right)$	$e\left(\frac{158}{2485}\right)$	$e\left(\frac{2}{35}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{5041}(2,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{333}{2485}\right)\)	\(e\left(\frac{358}{2485}\right)\)	\(e\left(\frac{666}{2485}\right)\)	\(e\left(\frac{97}{355}\right)\)	\(e\left(\frac{691}{2485}\right)\)	\(e\left(\frac{2243}{2485}\right)\)	\(e\left(\frac{999}{2485}\right)\)	\(e\left(\frac{716}{2485}\right)\)	\(e\left(\frac{1012}{2485}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{5041}(3,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{358}{2485}\right)\)	\(e\left(\frac{758}{2485}\right)\)	\(e\left(\frac{716}{2485}\right)\)	\(e\left(\frac{132}{355}\right)\)	\(e\left(\frac{1116}{2485}\right)\)	\(e\left(\frac{1098}{2485}\right)\)	\(e\left(\frac{1074}{2485}\right)\)	\(e\left(\frac{1516}{2485}\right)\)	\(e\left(\frac{1282}{2485}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{5041}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{666}{2485}\right)\)	\(e\left(\frac{716}{2485}\right)\)	\(e\left(\frac{1332}{2485}\right)\)	\(e\left(\frac{194}{355}\right)\)	\(e\left(\frac{1382}{2485}\right)\)	\(e\left(\frac{2001}{2485}\right)\)	\(e\left(\frac{1998}{2485}\right)\)	\(e\left(\frac{1432}{2485}\right)\)	\(e\left(\frac{2024}{2485}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{5041}(6,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{691}{2485}\right)\)	\(e\left(\frac{1116}{2485}\right)\)	\(e\left(\frac{1382}{2485}\right)\)	\(e\left(\frac{229}{355}\right)\)	\(e\left(\frac{1807}{2485}\right)\)	\(e\left(\frac{856}{2485}\right)\)	\(e\left(\frac{2073}{2485}\right)\)	\(e\left(\frac{2232}{2485}\right)\)	\(e\left(\frac{2294}{2485}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{5041}(8,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{999}{2485}\right)\)	\(e\left(\frac{1074}{2485}\right)\)	\(e\left(\frac{1998}{2485}\right)\)	\(e\left(\frac{291}{355}\right)\)	\(e\left(\frac{2073}{2485}\right)\)	\(e\left(\frac{1759}{2485}\right)\)	\(e\left(\frac{512}{2485}\right)\)	\(e\left(\frac{2148}{2485}\right)\)	\(e\left(\frac{551}{2485}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{5041}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{716}{2485}\right)\)	\(e\left(\frac{1516}{2485}\right)\)	\(e\left(\frac{1432}{2485}\right)\)	\(e\left(\frac{264}{355}\right)\)	\(e\left(\frac{2232}{2485}\right)\)	\(e\left(\frac{2196}{2485}\right)\)	\(e\left(\frac{2148}{2485}\right)\)	\(e\left(\frac{547}{2485}\right)\)	\(e\left(\frac{79}{2485}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{5041}(10,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1012}{2485}\right)\)	\(e\left(\frac{1282}{2485}\right)\)	\(e\left(\frac{2024}{2485}\right)\)	\(e\left(\frac{153}{355}\right)\)	\(e\left(\frac{2294}{2485}\right)\)	\(e\left(\frac{2257}{2485}\right)\)	\(e\left(\frac{551}{2485}\right)\)	\(e\left(\frac{79}{2485}\right)\)	\(e\left(\frac{2083}{2485}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{5041}(12,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1024}{2485}\right)\)	\(e\left(\frac{1474}{2485}\right)\)	\(e\left(\frac{2048}{2485}\right)\)	\(e\left(\frac{326}{355}\right)\)	\(e\left(\frac{13}{2485}\right)\)	\(e\left(\frac{614}{2485}\right)\)	\(e\left(\frac{587}{2485}\right)\)	\(e\left(\frac{463}{2485}\right)\)	\(e\left(\frac{821}{2485}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{5041}(15,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1037}{2485}\right)\)	\(e\left(\frac{1682}{2485}\right)\)	\(e\left(\frac{2074}{2485}\right)\)	\(e\left(\frac{188}{355}\right)\)	\(e\left(\frac{234}{2485}\right)\)	\(e\left(\frac{1112}{2485}\right)\)	\(e\left(\frac{626}{2485}\right)\)	\(e\left(\frac{879}{2485}\right)\)	\(e\left(\frac{2353}{2485}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{5041}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1332}{2485}\right)\)	\(e\left(\frac{1432}{2485}\right)\)	\(e\left(\frac{179}{2485}\right)\)	\(e\left(\frac{33}{355}\right)\)	\(e\left(\frac{279}{2485}\right)\)	\(e\left(\frac{1517}{2485}\right)\)	\(e\left(\frac{1511}{2485}\right)\)	\(e\left(\frac{379}{2485}\right)\)	\(e\left(\frac{1563}{2485}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{5041}(18,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1049}{2485}\right)\)	\(e\left(\frac{1874}{2485}\right)\)	\(e\left(\frac{2098}{2485}\right)\)	\(e\left(\frac{6}{355}\right)\)	\(e\left(\frac{438}{2485}\right)\)	\(e\left(\frac{1954}{2485}\right)\)	\(e\left(\frac{662}{2485}\right)\)	\(e\left(\frac{1263}{2485}\right)\)	\(e\left(\frac{1091}{2485}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{5041}(19,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{853}{2485}\right)\)	\(e\left(\frac{1223}{2485}\right)\)	\(e\left(\frac{1706}{2485}\right)\)	\(e\left(\frac{257}{355}\right)\)	\(e\left(\frac{2076}{2485}\right)\)	\(e\left(\frac{2283}{2485}\right)\)	\(e\left(\frac{74}{2485}\right)\)	\(e\left(\frac{2446}{2485}\right)\)	\(e\left(\frac{167}{2485}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{5041}(24,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1357}{2485}\right)\)	\(e\left(\frac{1832}{2485}\right)\)	\(e\left(\frac{229}{2485}\right)\)	\(e\left(\frac{68}{355}\right)\)	\(e\left(\frac{704}{2485}\right)\)	\(e\left(\frac{372}{2485}\right)\)	\(e\left(\frac{1586}{2485}\right)\)	\(e\left(\frac{1179}{2485}\right)\)	\(e\left(\frac{1833}{2485}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{5041}(27,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1074}{2485}\right)\)	\(e\left(\frac{2274}{2485}\right)\)	\(e\left(\frac{2148}{2485}\right)\)	\(e\left(\frac{41}{355}\right)\)	\(e\left(\frac{863}{2485}\right)\)	\(e\left(\frac{809}{2485}\right)\)	\(e\left(\frac{737}{2485}\right)\)	\(e\left(\frac{2063}{2485}\right)\)	\(e\left(\frac{1361}{2485}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{5041}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2479}{2485}\right)\)	\(e\left(\frac{2389}{2485}\right)\)	\(e\left(\frac{2473}{2485}\right)\)	\(e\left(\frac{91}{355}\right)\)	\(e\left(\frac{2383}{2485}\right)\)	\(e\left(\frac{2064}{2485}\right)\)	\(e\left(\frac{2467}{2485}\right)\)	\(e\left(\frac{2293}{2485}\right)\)	\(e\left(\frac{631}{2485}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{5041}(36,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1382}{2485}\right)\)	\(e\left(\frac{2232}{2485}\right)\)	\(e\left(\frac{279}{2485}\right)\)	\(e\left(\frac{103}{355}\right)\)	\(e\left(\frac{1129}{2485}\right)\)	\(e\left(\frac{1712}{2485}\right)\)	\(e\left(\frac{1661}{2485}\right)\)	\(e\left(\frac{1979}{2485}\right)\)	\(e\left(\frac{2103}{2485}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{5041}(38,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1186}{2485}\right)\)	\(e\left(\frac{1581}{2485}\right)\)	\(e\left(\frac{2372}{2485}\right)\)	\(e\left(\frac{354}{355}\right)\)	\(e\left(\frac{282}{2485}\right)\)	\(e\left(\frac{2041}{2485}\right)\)	\(e\left(\frac{1073}{2485}\right)\)	\(e\left(\frac{677}{2485}\right)\)	\(e\left(\frac{1179}{2485}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{5041}(40,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1678}{2485}\right)\)	\(e\left(\frac{1998}{2485}\right)\)	\(e\left(\frac{871}{2485}\right)\)	\(e\left(\frac{347}{355}\right)\)	\(e\left(\frac{1191}{2485}\right)\)	\(e\left(\frac{1773}{2485}\right)\)	\(e\left(\frac{64}{2485}\right)\)	\(e\left(\frac{1511}{2485}\right)\)	\(e\left(\frac{1622}{2485}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{5041}(43,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{984}{2485}\right)\)	\(e\left(\frac{834}{2485}\right)\)	\(e\left(\frac{1968}{2485}\right)\)	\(e\left(\frac{341}{355}\right)\)	\(e\left(\frac{1818}{2485}\right)\)	\(e\left(\frac{1949}{2485}\right)\)	\(e\left(\frac{467}{2485}\right)\)	\(e\left(\frac{1668}{2485}\right)\)	\(e\left(\frac{886}{2485}\right)\)	\(e\left(\frac{9}{35}\right)\)
\(\chi_{5041}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2001}{2485}\right)\)	\(e\left(\frac{2196}{2485}\right)\)	\(e\left(\frac{1517}{2485}\right)\)	\(e\left(\frac{4}{355}\right)\)	\(e\left(\frac{1712}{2485}\right)\)	\(e\left(\frac{1}{2485}\right)\)	\(e\left(\frac{1033}{2485}\right)\)	\(e\left(\frac{1907}{2485}\right)\)	\(e\left(\frac{2029}{2485}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{5041}(50,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1691}{2485}\right)\)	\(e\left(\frac{2206}{2485}\right)\)	\(e\left(\frac{897}{2485}\right)\)	\(e\left(\frac{209}{355}\right)\)	\(e\left(\frac{1412}{2485}\right)\)	\(e\left(\frac{2271}{2485}\right)\)	\(e\left(\frac{103}{2485}\right)\)	\(e\left(\frac{1927}{2485}\right)\)	\(e\left(\frac{669}{2485}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{5041}(58,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{327}{2485}\right)\)	\(e\left(\frac{262}{2485}\right)\)	\(e\left(\frac{654}{2485}\right)\)	\(e\left(\frac{188}{355}\right)\)	\(e\left(\frac{589}{2485}\right)\)	\(e\left(\frac{1822}{2485}\right)\)	\(e\left(\frac{981}{2485}\right)\)	\(e\left(\frac{524}{2485}\right)\)	\(e\left(\frac{1643}{2485}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{5041}(60,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1703}{2485}\right)\)	\(e\left(\frac{2398}{2485}\right)\)	\(e\left(\frac{921}{2485}\right)\)	\(e\left(\frac{27}{355}\right)\)	\(e\left(\frac{1616}{2485}\right)\)	\(e\left(\frac{628}{2485}\right)\)	\(e\left(\frac{139}{2485}\right)\)	\(e\left(\frac{2311}{2485}\right)\)	\(e\left(\frac{1892}{2485}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{5041}(64,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1998}{2485}\right)\)	\(e\left(\frac{2148}{2485}\right)\)	\(e\left(\frac{1511}{2485}\right)\)	\(e\left(\frac{227}{355}\right)\)	\(e\left(\frac{1661}{2485}\right)\)	\(e\left(\frac{1033}{2485}\right)\)	\(e\left(\frac{1024}{2485}\right)\)	\(e\left(\frac{1811}{2485}\right)\)	\(e\left(\frac{1102}{2485}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{5041}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2433}{2485}\right)\)	\(e\left(\frac{1653}{2485}\right)\)	\(e\left(\frac{2381}{2485}\right)\)	\(e\left(\frac{197}{355}\right)\)	\(e\left(\frac{1601}{2485}\right)\)	\(e\left(\frac{493}{2485}\right)\)	\(e\left(\frac{2329}{2485}\right)\)	\(e\left(\frac{821}{2485}\right)\)	\(e\left(\frac{1327}{2485}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{5041}(74,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1758}{2485}\right)\)	\(e\left(\frac{793}{2485}\right)\)	\(e\left(\frac{1031}{2485}\right)\)	\(e\left(\frac{317}{355}\right)\)	\(e\left(\frac{66}{2485}\right)\)	\(e\left(\frac{1588}{2485}\right)\)	\(e\left(\frac{304}{2485}\right)\)	\(e\left(\frac{1586}{2485}\right)\)	\(e\left(\frac{1492}{2485}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{5041}(75,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1716}{2485}\right)\)	\(e\left(\frac{121}{2485}\right)\)	\(e\left(\frac{947}{2485}\right)\)	\(e\left(\frac{244}{355}\right)\)	\(e\left(\frac{1837}{2485}\right)\)	\(e\left(\frac{1126}{2485}\right)\)	\(e\left(\frac{178}{2485}\right)\)	\(e\left(\frac{242}{2485}\right)\)	\(e\left(\frac{939}{2485}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{5041}(77,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1391}{2485}\right)\)	\(e\left(\frac{2376}{2485}\right)\)	\(e\left(\frac{297}{2485}\right)\)	\(e\left(\frac{144}{355}\right)\)	\(e\left(\frac{1282}{2485}\right)\)	\(e\left(\frac{1101}{2485}\right)\)	\(e\left(\frac{1688}{2485}\right)\)	\(e\left(\frac{2267}{2485}\right)\)	\(e\left(\frac{2399}{2485}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{5041}(79,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1524}{2485}\right)\)	\(e\left(\frac{2019}{2485}\right)\)	\(e\left(\frac{563}{2485}\right)\)	\(e\left(\frac{316}{355}\right)\)	\(e\left(\frac{1058}{2485}\right)\)	\(e\left(\frac{79}{2485}\right)\)	\(e\left(\frac{2087}{2485}\right)\)	\(e\left(\frac{1553}{2485}\right)\)	\(e\left(\frac{1251}{2485}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{5041}(80,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2011}{2485}\right)\)	\(e\left(\frac{2356}{2485}\right)\)	\(e\left(\frac{1537}{2485}\right)\)	\(e\left(\frac{89}{355}\right)\)	\(e\left(\frac{1882}{2485}\right)\)	\(e\left(\frac{1531}{2485}\right)\)	\(e\left(\frac{1063}{2485}\right)\)	\(e\left(\frac{2227}{2485}\right)\)	\(e\left(\frac{149}{2485}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{5041}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1432}{2485}\right)\)	\(e\left(\frac{547}{2485}\right)\)	\(e\left(\frac{379}{2485}\right)\)	\(e\left(\frac{173}{355}\right)\)	\(e\left(\frac{1979}{2485}\right)\)	\(e\left(\frac{1907}{2485}\right)\)	\(e\left(\frac{1811}{2485}\right)\)	\(e\left(\frac{1094}{2485}\right)\)	\(e\left(\frac{158}{2485}\right)\)	\(e\left(\frac{2}{35}\right)\)

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First 31 of 1680 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	5041.o
Modulus	$5041$
Conductor	$5041$
Order	$2485$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(5041\)
Conductor:	\(5041\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(2485\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)