LMFDB - Dirichlet character orbit 8042.s

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8042, base_ring=CyclotomicField(670)) M = H._module chi = DirichletCharacter(H, M([37])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(17,8042)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8042$
Conductor:	$4021$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$670$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4021.s	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:	$\Q(\zeta_{335})$
Fixed field:	Number field defined by a degree 670 polynomial (not computed)

First 31 of 264 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8042}(17,\cdot)$	$1$	$1$	$e\left(\frac{264}{335}\right)$	$e\left(\frac{314}{335}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{193}{335}\right)$	$e\left(\frac{139}{670}\right)$	$e\left(\frac{43}{67}\right)$	$e\left(\frac{243}{335}\right)$	$e\left(\frac{87}{335}\right)$	$e\left(\frac{577}{670}\right)$	$e\left(\frac{59}{670}\right)$
$\chi_{8042}(73,\cdot)$	$1$	$1$	$e\left(\frac{248}{335}\right)$	$e\left(\frac{163}{335}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{161}{335}\right)$	$e\left(\frac{293}{670}\right)$	$e\left(\frac{14}{67}\right)$	$e\left(\frac{76}{335}\right)$	$e\left(\frac{234}{335}\right)$	$e\left(\frac{339}{670}\right)$	$e\left(\frac{563}{670}\right)$
$\chi_{8042}(103,\cdot)$	$1$	$1$	$e\left(\frac{276}{335}\right)$	$e\left(\frac{176}{335}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{217}{335}\right)$	$e\left(\frac{191}{670}\right)$	$e\left(\frac{48}{67}\right)$	$e\left(\frac{117}{335}\right)$	$e\left(\frac{228}{335}\right)$	$e\left(\frac{253}{670}\right)$	$e\left(\frac{351}{670}\right)$
$\chi_{8042}(127,\cdot)$	$1$	$1$	$e\left(\frac{157}{335}\right)$	$e\left(\frac{37}{335}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{314}{335}\right)$	$e\left(\frac{457}{670}\right)$	$e\left(\frac{4}{67}\right)$	$e\left(\frac{194}{335}\right)$	$e\left(\frac{86}{335}\right)$	$e\left(\frac{451}{670}\right)$	$e\left(\frac{247}{670}\right)$
$\chi_{8042}(151,\cdot)$	$1$	$1$	$e\left(\frac{288}{335}\right)$	$e\left(\frac{38}{335}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{241}{335}\right)$	$e\left(\frac{243}{670}\right)$	$e\left(\frac{53}{67}\right)$	$e\left(\frac{326}{335}\right)$	$e\left(\frac{34}{335}\right)$	$e\left(\frac{599}{670}\right)$	$e\left(\frac{643}{670}\right)$
$\chi_{8042}(179,\cdot)$	$1$	$1$	$e\left(\frac{246}{335}\right)$	$e\left(\frac{186}{335}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{157}{335}\right)$	$e\left(\frac{61}{670}\right)$	$e\left(\frac{2}{67}\right)$	$e\left(\frac{97}{335}\right)$	$e\left(\frac{43}{335}\right)$	$e\left(\frac{393}{670}\right)$	$e\left(\frac{291}{670}\right)$
$\chi_{8042}(181,\cdot)$	$1$	$1$	$e\left(\frac{297}{335}\right)$	$e\left(\frac{102}{335}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{259}{335}\right)$	$e\left(\frac{617}{670}\right)$	$e\left(\frac{40}{67}\right)$	$e\left(\frac{64}{335}\right)$	$e\left(\frac{56}{335}\right)$	$e\left(\frac{21}{670}\right)$	$e\left(\frac{527}{670}\right)$
$\chi_{8042}(183,\cdot)$	$1$	$1$	$e\left(\frac{62}{335}\right)$	$e\left(\frac{292}{335}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{124}{335}\right)$	$e\left(\frac{157}{670}\right)$	$e\left(\frac{37}{67}\right)$	$e\left(\frac{19}{335}\right)$	$e\left(\frac{226}{335}\right)$	$e\left(\frac{1}{670}\right)$	$e\left(\frac{57}{670}\right)$
$\chi_{8042}(193,\cdot)$	$1$	$1$	$e\left(\frac{41}{335}\right)$	$e\left(\frac{31}{335}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{82}{335}\right)$	$e\left(\frac{401}{670}\right)$	$e\left(\frac{45}{67}\right)$	$e\left(\frac{72}{335}\right)$	$e\left(\frac{63}{335}\right)$	$e\left(\frac{233}{670}\right)$	$e\left(\frac{551}{670}\right)$
$\chi_{8042}(233,\cdot)$	$1$	$1$	$e\left(\frac{216}{335}\right)$	$e\left(\frac{196}{335}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{97}{335}\right)$	$e\left(\frac{601}{670}\right)$	$e\left(\frac{23}{67}\right)$	$e\left(\frac{77}{335}\right)$	$e\left(\frac{193}{335}\right)$	$e\left(\frac{533}{670}\right)$	$e\left(\frac{231}{670}\right)$
$\chi_{8042}(239,\cdot)$	$1$	$1$	$e\left(\frac{182}{335}\right)$	$e\left(\frac{252}{335}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{335}\right)$	$e\left(\frac{7}{670}\right)$	$e\left(\frac{20}{67}\right)$	$e\left(\frac{99}{335}\right)$	$e\left(\frac{296}{335}\right)$	$e\left(\frac{111}{670}\right)$	$e\left(\frac{297}{670}\right)$
$\chi_{8042}(267,\cdot)$	$1$	$1$	$e\left(\frac{7}{335}\right)$	$e\left(\frac{87}{335}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{14}{335}\right)$	$e\left(\frac{477}{670}\right)$	$e\left(\frac{42}{67}\right)$	$e\left(\frac{94}{335}\right)$	$e\left(\frac{166}{335}\right)$	$e\left(\frac{481}{670}\right)$	$e\left(\frac{617}{670}\right)$
$\chi_{8042}(305,\cdot)$	$1$	$1$	$e\left(\frac{52}{335}\right)$	$e\left(\frac{72}{335}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{104}{335}\right)$	$e\left(\frac{337}{670}\right)$	$e\left(\frac{44}{67}\right)$	$e\left(\frac{124}{335}\right)$	$e\left(\frac{276}{335}\right)$	$e\left(\frac{271}{670}\right)$	$e\left(\frac{37}{670}\right)$
$\chi_{8042}(313,\cdot)$	$1$	$1$	$e\left(\frac{96}{335}\right)$	$e\left(\frac{236}{335}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{192}{335}\right)$	$e\left(\frac{81}{670}\right)$	$e\left(\frac{40}{67}\right)$	$e\left(\frac{332}{335}\right)$	$e\left(\frac{123}{335}\right)$	$e\left(\frac{423}{670}\right)$	$e\left(\frac{661}{670}\right)$
$\chi_{8042}(351,\cdot)$	$1$	$1$	$e\left(\frac{214}{335}\right)$	$e\left(\frac{219}{335}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{93}{335}\right)$	$e\left(\frac{369}{670}\right)$	$e\left(\frac{11}{67}\right)$	$e\left(\frac{98}{335}\right)$	$e\left(\frac{2}{335}\right)$	$e\left(\frac{587}{670}\right)$	$e\left(\frac{629}{670}\right)$
$\chi_{8042}(393,\cdot)$	$1$	$1$	$e\left(\frac{191}{335}\right)$	$e\left(\frac{316}{335}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{47}{335}\right)$	$e\left(\frac{381}{670}\right)$	$e\left(\frac{7}{67}\right)$	$e\left(\frac{172}{335}\right)$	$e\left(\frac{318}{335}\right)$	$e\left(\frac{203}{670}\right)$	$e\left(\frac{181}{670}\right)$
$\chi_{8042}(437,\cdot)$	$1$	$1$	$e\left(\frac{94}{335}\right)$	$e\left(\frac{259}{335}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{188}{335}\right)$	$e\left(\frac{519}{670}\right)$	$e\left(\frac{28}{67}\right)$	$e\left(\frac{18}{335}\right)$	$e\left(\frac{267}{335}\right)$	$e\left(\frac{477}{670}\right)$	$e\left(\frac{389}{670}\right)$
$\chi_{8042}(445,\cdot)$	$1$	$1$	$e\left(\frac{332}{335}\right)$	$e\left(\frac{202}{335}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{329}{335}\right)$	$e\left(\frac{657}{670}\right)$	$e\left(\frac{49}{67}\right)$	$e\left(\frac{199}{335}\right)$	$e\left(\frac{216}{335}\right)$	$e\left(\frac{81}{670}\right)$	$e\left(\frac{597}{670}\right)$
$\chi_{8042}(449,\cdot)$	$1$	$1$	$e\left(\frac{156}{335}\right)$	$e\left(\frac{216}{335}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{312}{335}\right)$	$e\left(\frac{341}{670}\right)$	$e\left(\frac{65}{67}\right)$	$e\left(\frac{37}{335}\right)$	$e\left(\frac{158}{335}\right)$	$e\left(\frac{143}{670}\right)$	$e\left(\frac{111}{670}\right)$
$\chi_{8042}(459,\cdot)$	$1$	$1$	$e\left(\frac{253}{335}\right)$	$e\left(\frac{273}{335}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{171}{335}\right)$	$e\left(\frac{203}{670}\right)$	$e\left(\frac{44}{67}\right)$	$e\left(\frac{191}{335}\right)$	$e\left(\frac{209}{335}\right)$	$e\left(\frac{539}{670}\right)$	$e\left(\frac{573}{670}\right)$
$\chi_{8042}(467,\cdot)$	$1$	$1$	$e\left(\frac{12}{335}\right)$	$e\left(\frac{197}{335}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{24}{335}\right)$	$e\left(\frac{387}{670}\right)$	$e\left(\frac{5}{67}\right)$	$e\left(\frac{209}{335}\right)$	$e\left(\frac{141}{335}\right)$	$e\left(\frac{11}{670}\right)$	$e\left(\frac{627}{670}\right)$
$\chi_{8042}(477,\cdot)$	$1$	$1$	$e\left(\frac{261}{335}\right)$	$e\left(\frac{181}{335}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{187}{335}\right)$	$e\left(\frac{461}{670}\right)$	$e\left(\frac{25}{67}\right)$	$e\left(\frac{107}{335}\right)$	$e\left(\frac{303}{335}\right)$	$e\left(\frac{323}{670}\right)$	$e\left(\frac{321}{670}\right)$
$\chi_{8042}(479,\cdot)$	$1$	$1$	$e\left(\frac{114}{335}\right)$	$e\left(\frac{29}{335}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{228}{335}\right)$	$e\left(\frac{159}{670}\right)$	$e\left(\frac{14}{67}\right)$	$e\left(\frac{143}{335}\right)$	$e\left(\frac{167}{335}\right)$	$e\left(\frac{607}{670}\right)$	$e\left(\frac{429}{670}\right)$
$\chi_{8042}(483,\cdot)$	$1$	$1$	$e\left(\frac{186}{335}\right)$	$e\left(\frac{206}{335}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{37}{335}\right)$	$e\left(\frac{471}{670}\right)$	$e\left(\frac{44}{67}\right)$	$e\left(\frac{57}{335}\right)$	$e\left(\frac{8}{335}\right)$	$e\left(\frac{3}{670}\right)$	$e\left(\frac{171}{670}\right)$
$\chi_{8042}(523,\cdot)$	$1$	$1$	$e\left(\frac{189}{335}\right)$	$e\left(\frac{4}{335}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{43}{335}\right)$	$e\left(\frac{149}{670}\right)$	$e\left(\frac{62}{67}\right)$	$e\left(\frac{193}{335}\right)$	$e\left(\frac{127}{335}\right)$	$e\left(\frac{257}{670}\right)$	$e\left(\frac{579}{670}\right)$
$\chi_{8042}(531,\cdot)$	$1$	$1$	$e\left(\frac{229}{335}\right)$	$e\left(\frac{214}{335}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{123}{335}\right)$	$e\left(\frac{99}{670}\right)$	$e\left(\frac{34}{67}\right)$	$e\left(\frac{108}{335}\right)$	$e\left(\frac{262}{335}\right)$	$e\left(\frac{517}{670}\right)$	$e\left(\frac{659}{670}\right)$
$\chi_{8042}(585,\cdot)$	$1$	$1$	$e\left(\frac{204}{335}\right)$	$e\left(\frac{334}{335}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{73}{335}\right)$	$e\left(\frac{549}{670}\right)$	$e\left(\frac{18}{67}\right)$	$e\left(\frac{203}{335}\right)$	$e\left(\frac{52}{335}\right)$	$e\left(\frac{187}{670}\right)$	$e\left(\frac{609}{670}\right)$
$\chi_{8042}(607,\cdot)$	$1$	$1$	$e\left(\frac{63}{335}\right)$	$e\left(\frac{113}{335}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{126}{335}\right)$	$e\left(\frac{273}{670}\right)$	$e\left(\frac{43}{67}\right)$	$e\left(\frac{176}{335}\right)$	$e\left(\frac{154}{335}\right)$	$e\left(\frac{309}{670}\right)$	$e\left(\frac{193}{670}\right)$
$\chi_{8042}(613,\cdot)$	$1$	$1$	$e\left(\frac{23}{335}\right)$	$e\left(\frac{238}{335}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{46}{335}\right)$	$e\left(\frac{323}{670}\right)$	$e\left(\frac{4}{67}\right)$	$e\left(\frac{261}{335}\right)$	$e\left(\frac{19}{335}\right)$	$e\left(\frac{49}{670}\right)$	$e\left(\frac{113}{670}\right)$
$\chi_{8042}(655,\cdot)$	$1$	$1$	$e\left(\frac{181}{335}\right)$	$e\left(\frac{96}{335}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{27}{335}\right)$	$e\left(\frac{561}{670}\right)$	$e\left(\frac{14}{67}\right)$	$e\left(\frac{277}{335}\right)$	$e\left(\frac{33}{335}\right)$	$e\left(\frac{473}{670}\right)$	$e\left(\frac{161}{670}\right)$
$\chi_{8042}(661,\cdot)$	$1$	$1$	$e\left(\frac{87}{335}\right)$	$e\left(\frac{172}{335}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{174}{335}\right)$	$e\left(\frac{377}{670}\right)$	$e\left(\frac{53}{67}\right)$	$e\left(\frac{259}{335}\right)$	$e\left(\frac{101}{335}\right)$	$e\left(\frac{331}{670}\right)$	$e\left(\frac{107}{670}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8042}(17,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{264}{335}\right)\)	\(e\left(\frac{314}{335}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{193}{335}\right)\)	\(e\left(\frac{139}{670}\right)\)	\(e\left(\frac{43}{67}\right)\)	\(e\left(\frac{243}{335}\right)\)	\(e\left(\frac{87}{335}\right)\)	\(e\left(\frac{577}{670}\right)\)	\(e\left(\frac{59}{670}\right)\)
\(\chi_{8042}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{248}{335}\right)\)	\(e\left(\frac{163}{335}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{161}{335}\right)\)	\(e\left(\frac{293}{670}\right)\)	\(e\left(\frac{14}{67}\right)\)	\(e\left(\frac{76}{335}\right)\)	\(e\left(\frac{234}{335}\right)\)	\(e\left(\frac{339}{670}\right)\)	\(e\left(\frac{563}{670}\right)\)
\(\chi_{8042}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{276}{335}\right)\)	\(e\left(\frac{176}{335}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{217}{335}\right)\)	\(e\left(\frac{191}{670}\right)\)	\(e\left(\frac{48}{67}\right)\)	\(e\left(\frac{117}{335}\right)\)	\(e\left(\frac{228}{335}\right)\)	\(e\left(\frac{253}{670}\right)\)	\(e\left(\frac{351}{670}\right)\)
\(\chi_{8042}(127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{335}\right)\)	\(e\left(\frac{37}{335}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{314}{335}\right)\)	\(e\left(\frac{457}{670}\right)\)	\(e\left(\frac{4}{67}\right)\)	\(e\left(\frac{194}{335}\right)\)	\(e\left(\frac{86}{335}\right)\)	\(e\left(\frac{451}{670}\right)\)	\(e\left(\frac{247}{670}\right)\)
\(\chi_{8042}(151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{288}{335}\right)\)	\(e\left(\frac{38}{335}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{241}{335}\right)\)	\(e\left(\frac{243}{670}\right)\)	\(e\left(\frac{53}{67}\right)\)	\(e\left(\frac{326}{335}\right)\)	\(e\left(\frac{34}{335}\right)\)	\(e\left(\frac{599}{670}\right)\)	\(e\left(\frac{643}{670}\right)\)
\(\chi_{8042}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{246}{335}\right)\)	\(e\left(\frac{186}{335}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{157}{335}\right)\)	\(e\left(\frac{61}{670}\right)\)	\(e\left(\frac{2}{67}\right)\)	\(e\left(\frac{97}{335}\right)\)	\(e\left(\frac{43}{335}\right)\)	\(e\left(\frac{393}{670}\right)\)	\(e\left(\frac{291}{670}\right)\)
\(\chi_{8042}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{297}{335}\right)\)	\(e\left(\frac{102}{335}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{259}{335}\right)\)	\(e\left(\frac{617}{670}\right)\)	\(e\left(\frac{40}{67}\right)\)	\(e\left(\frac{64}{335}\right)\)	\(e\left(\frac{56}{335}\right)\)	\(e\left(\frac{21}{670}\right)\)	\(e\left(\frac{527}{670}\right)\)
\(\chi_{8042}(183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{335}\right)\)	\(e\left(\frac{292}{335}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{124}{335}\right)\)	\(e\left(\frac{157}{670}\right)\)	\(e\left(\frac{37}{67}\right)\)	\(e\left(\frac{19}{335}\right)\)	\(e\left(\frac{226}{335}\right)\)	\(e\left(\frac{1}{670}\right)\)	\(e\left(\frac{57}{670}\right)\)
\(\chi_{8042}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{335}\right)\)	\(e\left(\frac{31}{335}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{82}{335}\right)\)	\(e\left(\frac{401}{670}\right)\)	\(e\left(\frac{45}{67}\right)\)	\(e\left(\frac{72}{335}\right)\)	\(e\left(\frac{63}{335}\right)\)	\(e\left(\frac{233}{670}\right)\)	\(e\left(\frac{551}{670}\right)\)
\(\chi_{8042}(233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{216}{335}\right)\)	\(e\left(\frac{196}{335}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{97}{335}\right)\)	\(e\left(\frac{601}{670}\right)\)	\(e\left(\frac{23}{67}\right)\)	\(e\left(\frac{77}{335}\right)\)	\(e\left(\frac{193}{335}\right)\)	\(e\left(\frac{533}{670}\right)\)	\(e\left(\frac{231}{670}\right)\)
\(\chi_{8042}(239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{182}{335}\right)\)	\(e\left(\frac{252}{335}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{335}\right)\)	\(e\left(\frac{7}{670}\right)\)	\(e\left(\frac{20}{67}\right)\)	\(e\left(\frac{99}{335}\right)\)	\(e\left(\frac{296}{335}\right)\)	\(e\left(\frac{111}{670}\right)\)	\(e\left(\frac{297}{670}\right)\)
\(\chi_{8042}(267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{335}\right)\)	\(e\left(\frac{87}{335}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{14}{335}\right)\)	\(e\left(\frac{477}{670}\right)\)	\(e\left(\frac{42}{67}\right)\)	\(e\left(\frac{94}{335}\right)\)	\(e\left(\frac{166}{335}\right)\)	\(e\left(\frac{481}{670}\right)\)	\(e\left(\frac{617}{670}\right)\)
\(\chi_{8042}(305,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{335}\right)\)	\(e\left(\frac{72}{335}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{104}{335}\right)\)	\(e\left(\frac{337}{670}\right)\)	\(e\left(\frac{44}{67}\right)\)	\(e\left(\frac{124}{335}\right)\)	\(e\left(\frac{276}{335}\right)\)	\(e\left(\frac{271}{670}\right)\)	\(e\left(\frac{37}{670}\right)\)
\(\chi_{8042}(313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{96}{335}\right)\)	\(e\left(\frac{236}{335}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{192}{335}\right)\)	\(e\left(\frac{81}{670}\right)\)	\(e\left(\frac{40}{67}\right)\)	\(e\left(\frac{332}{335}\right)\)	\(e\left(\frac{123}{335}\right)\)	\(e\left(\frac{423}{670}\right)\)	\(e\left(\frac{661}{670}\right)\)
\(\chi_{8042}(351,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{214}{335}\right)\)	\(e\left(\frac{219}{335}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{93}{335}\right)\)	\(e\left(\frac{369}{670}\right)\)	\(e\left(\frac{11}{67}\right)\)	\(e\left(\frac{98}{335}\right)\)	\(e\left(\frac{2}{335}\right)\)	\(e\left(\frac{587}{670}\right)\)	\(e\left(\frac{629}{670}\right)\)
\(\chi_{8042}(393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{335}\right)\)	\(e\left(\frac{316}{335}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{47}{335}\right)\)	\(e\left(\frac{381}{670}\right)\)	\(e\left(\frac{7}{67}\right)\)	\(e\left(\frac{172}{335}\right)\)	\(e\left(\frac{318}{335}\right)\)	\(e\left(\frac{203}{670}\right)\)	\(e\left(\frac{181}{670}\right)\)
\(\chi_{8042}(437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{335}\right)\)	\(e\left(\frac{259}{335}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{188}{335}\right)\)	\(e\left(\frac{519}{670}\right)\)	\(e\left(\frac{28}{67}\right)\)	\(e\left(\frac{18}{335}\right)\)	\(e\left(\frac{267}{335}\right)\)	\(e\left(\frac{477}{670}\right)\)	\(e\left(\frac{389}{670}\right)\)
\(\chi_{8042}(445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{332}{335}\right)\)	\(e\left(\frac{202}{335}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{329}{335}\right)\)	\(e\left(\frac{657}{670}\right)\)	\(e\left(\frac{49}{67}\right)\)	\(e\left(\frac{199}{335}\right)\)	\(e\left(\frac{216}{335}\right)\)	\(e\left(\frac{81}{670}\right)\)	\(e\left(\frac{597}{670}\right)\)
\(\chi_{8042}(449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{156}{335}\right)\)	\(e\left(\frac{216}{335}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{312}{335}\right)\)	\(e\left(\frac{341}{670}\right)\)	\(e\left(\frac{65}{67}\right)\)	\(e\left(\frac{37}{335}\right)\)	\(e\left(\frac{158}{335}\right)\)	\(e\left(\frac{143}{670}\right)\)	\(e\left(\frac{111}{670}\right)\)
\(\chi_{8042}(459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{335}\right)\)	\(e\left(\frac{273}{335}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{171}{335}\right)\)	\(e\left(\frac{203}{670}\right)\)	\(e\left(\frac{44}{67}\right)\)	\(e\left(\frac{191}{335}\right)\)	\(e\left(\frac{209}{335}\right)\)	\(e\left(\frac{539}{670}\right)\)	\(e\left(\frac{573}{670}\right)\)
\(\chi_{8042}(467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{335}\right)\)	\(e\left(\frac{197}{335}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{24}{335}\right)\)	\(e\left(\frac{387}{670}\right)\)	\(e\left(\frac{5}{67}\right)\)	\(e\left(\frac{209}{335}\right)\)	\(e\left(\frac{141}{335}\right)\)	\(e\left(\frac{11}{670}\right)\)	\(e\left(\frac{627}{670}\right)\)
\(\chi_{8042}(477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{261}{335}\right)\)	\(e\left(\frac{181}{335}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{187}{335}\right)\)	\(e\left(\frac{461}{670}\right)\)	\(e\left(\frac{25}{67}\right)\)	\(e\left(\frac{107}{335}\right)\)	\(e\left(\frac{303}{335}\right)\)	\(e\left(\frac{323}{670}\right)\)	\(e\left(\frac{321}{670}\right)\)
\(\chi_{8042}(479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{114}{335}\right)\)	\(e\left(\frac{29}{335}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{228}{335}\right)\)	\(e\left(\frac{159}{670}\right)\)	\(e\left(\frac{14}{67}\right)\)	\(e\left(\frac{143}{335}\right)\)	\(e\left(\frac{167}{335}\right)\)	\(e\left(\frac{607}{670}\right)\)	\(e\left(\frac{429}{670}\right)\)
\(\chi_{8042}(483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{186}{335}\right)\)	\(e\left(\frac{206}{335}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{37}{335}\right)\)	\(e\left(\frac{471}{670}\right)\)	\(e\left(\frac{44}{67}\right)\)	\(e\left(\frac{57}{335}\right)\)	\(e\left(\frac{8}{335}\right)\)	\(e\left(\frac{3}{670}\right)\)	\(e\left(\frac{171}{670}\right)\)
\(\chi_{8042}(523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{189}{335}\right)\)	\(e\left(\frac{4}{335}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{43}{335}\right)\)	\(e\left(\frac{149}{670}\right)\)	\(e\left(\frac{62}{67}\right)\)	\(e\left(\frac{193}{335}\right)\)	\(e\left(\frac{127}{335}\right)\)	\(e\left(\frac{257}{670}\right)\)	\(e\left(\frac{579}{670}\right)\)
\(\chi_{8042}(531,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{229}{335}\right)\)	\(e\left(\frac{214}{335}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{123}{335}\right)\)	\(e\left(\frac{99}{670}\right)\)	\(e\left(\frac{34}{67}\right)\)	\(e\left(\frac{108}{335}\right)\)	\(e\left(\frac{262}{335}\right)\)	\(e\left(\frac{517}{670}\right)\)	\(e\left(\frac{659}{670}\right)\)
\(\chi_{8042}(585,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{204}{335}\right)\)	\(e\left(\frac{334}{335}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{73}{335}\right)\)	\(e\left(\frac{549}{670}\right)\)	\(e\left(\frac{18}{67}\right)\)	\(e\left(\frac{203}{335}\right)\)	\(e\left(\frac{52}{335}\right)\)	\(e\left(\frac{187}{670}\right)\)	\(e\left(\frac{609}{670}\right)\)
\(\chi_{8042}(607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{335}\right)\)	\(e\left(\frac{113}{335}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{126}{335}\right)\)	\(e\left(\frac{273}{670}\right)\)	\(e\left(\frac{43}{67}\right)\)	\(e\left(\frac{176}{335}\right)\)	\(e\left(\frac{154}{335}\right)\)	\(e\left(\frac{309}{670}\right)\)	\(e\left(\frac{193}{670}\right)\)
\(\chi_{8042}(613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{335}\right)\)	\(e\left(\frac{238}{335}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{46}{335}\right)\)	\(e\left(\frac{323}{670}\right)\)	\(e\left(\frac{4}{67}\right)\)	\(e\left(\frac{261}{335}\right)\)	\(e\left(\frac{19}{335}\right)\)	\(e\left(\frac{49}{670}\right)\)	\(e\left(\frac{113}{670}\right)\)
\(\chi_{8042}(655,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{335}\right)\)	\(e\left(\frac{96}{335}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{27}{335}\right)\)	\(e\left(\frac{561}{670}\right)\)	\(e\left(\frac{14}{67}\right)\)	\(e\left(\frac{277}{335}\right)\)	\(e\left(\frac{33}{335}\right)\)	\(e\left(\frac{473}{670}\right)\)	\(e\left(\frac{161}{670}\right)\)
\(\chi_{8042}(661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{335}\right)\)	\(e\left(\frac{172}{335}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{174}{335}\right)\)	\(e\left(\frac{377}{670}\right)\)	\(e\left(\frac{53}{67}\right)\)	\(e\left(\frac{259}{335}\right)\)	\(e\left(\frac{101}{335}\right)\)	\(e\left(\frac{331}{670}\right)\)	\(e\left(\frac{107}{670}\right)\)

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First 31 of 264 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	8042.s
Modulus	$8042$
Conductor	$4021$
Order	$670$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8042\)
Conductor:	\(4021\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(670\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4021.s	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)