LMFDB - Dirichlet character orbit 84216.mz

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(84216, base_ring=CyclotomicField(770)) M = H._module chi = DirichletCharacter(H, M([385,385,385,567,165])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(35, 84216)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("84216.35"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$84216$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$84216$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$770$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{385})$
Fixed field:	Number field defined by a degree 770 polynomial (not computed)

First 31 of 240 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$31$	$35$	$37$
$\chi_{84216}(35,\cdot)$	$-1$	$1$	$e\left(\frac{79}{385}\right)$	$e\left(\frac{87}{385}\right)$	$e\left(\frac{281}{385}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{18}{385}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{158}{385}\right)$	$e\left(\frac{16}{385}\right)$	$e\left(\frac{166}{385}\right)$	$e\left(\frac{27}{385}\right)$
$\chi_{84216}(299,\cdot)$	$-1$	$1$	$e\left(\frac{344}{385}\right)$	$e\left(\frac{257}{385}\right)$	$e\left(\frac{361}{385}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{93}{385}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{303}{385}\right)$	$e\left(\frac{211}{385}\right)$	$e\left(\frac{216}{385}\right)$	$e\left(\frac{332}{385}\right)$
$\chi_{84216}(875,\cdot)$	$-1$	$1$	$e\left(\frac{131}{385}\right)$	$e\left(\frac{193}{385}\right)$	$e\left(\frac{349}{385}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{332}{385}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{262}{385}\right)$	$e\left(\frac{124}{385}\right)$	$e\left(\frac{324}{385}\right)$	$e\left(\frac{113}{385}\right)$
$\chi_{84216}(1019,\cdot)$	$-1$	$1$	$e\left(\frac{283}{385}\right)$	$e\left(\frac{29}{385}\right)$	$e\left(\frac{222}{385}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{6}{385}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{181}{385}\right)$	$e\left(\frac{262}{385}\right)$	$e\left(\frac{312}{385}\right)$	$e\left(\frac{9}{385}\right)$
$\chi_{84216}(1427,\cdot)$	$-1$	$1$	$e\left(\frac{107}{385}\right)$	$e\left(\frac{381}{385}\right)$	$e\left(\frac{288}{385}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{39}{385}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{214}{385}\right)$	$e\left(\frac{163}{385}\right)$	$e\left(\frac{103}{385}\right)$	$e\left(\frac{251}{385}\right)$
$\chi_{84216}(1811,\cdot)$	$-1$	$1$	$e\left(\frac{188}{385}\right)$	$e\left(\frac{324}{385}\right)$	$e\left(\frac{157}{385}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{306}{385}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{376}{385}\right)$	$e\left(\frac{272}{385}\right)$	$e\left(\frac{127}{385}\right)$	$e\left(\frac{74}{385}\right)$
$\chi_{84216}(2603,\cdot)$	$-1$	$1$	$e\left(\frac{368}{385}\right)$	$e\left(\frac{69}{385}\right)$	$e\left(\frac{37}{385}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{1}{385}\right)$	$e\left(\frac{72}{77}\right)$	$e\left(\frac{351}{385}\right)$	$e\left(\frac{172}{385}\right)$	$e\left(\frac{52}{385}\right)$	$e\left(\frac{194}{385}\right)$
$\chi_{84216}(3203,\cdot)$	$-1$	$1$	$e\left(\frac{69}{385}\right)$	$e\left(\frac{37}{385}\right)$	$e\left(\frac{31}{385}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{313}{385}\right)$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{138}{385}\right)$	$e\left(\frac{321}{385}\right)$	$e\left(\frac{106}{385}\right)$	$e\left(\frac{277}{385}\right)$
$\chi_{84216}(3515,\cdot)$	$-1$	$1$	$e\left(\frac{226}{385}\right)$	$e\left(\frac{283}{385}\right)$	$e\left(\frac{29}{385}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{32}{385}\right)$	$e\left(\frac{71}{77}\right)$	$e\left(\frac{67}{385}\right)$	$e\left(\frac{114}{385}\right)$	$e\left(\frac{124}{385}\right)$	$e\left(\frac{48}{385}\right)$
$\chi_{84216}(3659,\cdot)$	$-1$	$1$	$e\left(\frac{278}{385}\right)$	$e\left(\frac{4}{385}\right)$	$e\left(\frac{97}{385}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{346}{385}\right)$	$e\left(\frac{41}{77}\right)$	$e\left(\frac{171}{385}\right)$	$e\left(\frac{222}{385}\right)$	$e\left(\frac{282}{385}\right)$	$e\left(\frac{134}{385}\right)$
$\chi_{84216}(3779,\cdot)$	$-1$	$1$	$e\left(\frac{351}{385}\right)$	$e\left(\frac{138}{385}\right)$	$e\left(\frac{74}{385}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{2}{385}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{317}{385}\right)$	$e\left(\frac{344}{385}\right)$	$e\left(\frac{104}{385}\right)$	$e\left(\frac{3}{385}\right)$
$\chi_{84216}(3803,\cdot)$	$-1$	$1$	$e\left(\frac{332}{385}\right)$	$e\left(\frac{351}{385}\right)$	$e\left(\frac{138}{385}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{139}{385}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{279}{385}\right)$	$e\left(\frac{38}{385}\right)$	$e\left(\frac{298}{385}\right)$	$e\left(\frac{16}{385}\right)$
$\chi_{84216}(3995,\cdot)$	$-1$	$1$	$e\left(\frac{39}{385}\right)$	$e\left(\frac{272}{385}\right)$	$e\left(\frac{51}{385}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{43}{385}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{78}{385}\right)$	$e\left(\frac{81}{385}\right)$	$e\left(\frac{311}{385}\right)$	$e\left(\frac{257}{385}\right)$
$\chi_{84216}(5051,\cdot)$	$-1$	$1$	$e\left(\frac{54}{385}\right)$	$e\left(\frac{347}{385}\right)$	$e\left(\frac{41}{385}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{178}{385}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{108}{385}\right)$	$e\left(\frac{201}{385}\right)$	$e\left(\frac{16}{385}\right)$	$e\left(\frac{267}{385}\right)$
$\chi_{84216}(5387,\cdot)$	$-1$	$1$	$e\left(\frac{207}{385}\right)$	$e\left(\frac{111}{385}\right)$	$e\left(\frac{93}{385}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{169}{385}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{29}{385}\right)$	$e\left(\frac{193}{385}\right)$	$e\left(\frac{318}{385}\right)$	$e\left(\frac{61}{385}\right)$
$\chi_{84216}(5891,\cdot)$	$-1$	$1$	$e\left(\frac{31}{385}\right)$	$e\left(\frac{78}{385}\right)$	$e\left(\frac{159}{385}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{202}{385}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{62}{385}\right)$	$e\left(\frac{94}{385}\right)$	$e\left(\frac{109}{385}\right)$	$e\left(\frac{303}{385}\right)$
$\chi_{84216}(6299,\cdot)$	$-1$	$1$	$e\left(\frac{163}{385}\right)$	$e\left(\frac{199}{385}\right)$	$e\left(\frac{302}{385}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{81}{385}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{326}{385}\right)$	$e\left(\frac{72}{385}\right)$	$e\left(\frac{362}{385}\right)$	$e\left(\frac{314}{385}\right)$
$\chi_{84216}(6443,\cdot)$	$-1$	$1$	$e\left(\frac{362}{385}\right)$	$e\left(\frac{116}{385}\right)$	$e\left(\frac{118}{385}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{24}{385}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{339}{385}\right)$	$e\left(\frac{278}{385}\right)$	$e\left(\frac{93}{385}\right)$	$e\left(\frac{36}{385}\right)$
$\chi_{84216}(6563,\cdot)$	$-1$	$1$	$e\left(\frac{113}{385}\right)$	$e\left(\frac{334}{385}\right)$	$e\left(\frac{207}{385}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{16}{385}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{226}{385}\right)$	$e\left(\frac{57}{385}\right)$	$e\left(\frac{62}{385}\right)$	$e\left(\frac{24}{385}\right)$
$\chi_{84216}(6683,\cdot)$	$-1$	$1$	$e\left(\frac{76}{385}\right)$	$e\left(\frac{303}{385}\right)$	$e\left(\frac{129}{385}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{222}{385}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{152}{385}\right)$	$e\left(\frac{69}{385}\right)$	$e\left(\frac{379}{385}\right)$	$e\left(\frac{333}{385}\right)$
$\chi_{84216}(7691,\cdot)$	$-1$	$1$	$e\left(\frac{9}{385}\right)$	$e\left(\frac{122}{385}\right)$	$e\left(\frac{71}{385}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{158}{385}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{18}{385}\right)$	$e\left(\frac{226}{385}\right)$	$e\left(\frac{131}{385}\right)$	$e\left(\frac{237}{385}\right)$
$\chi_{84216}(7955,\cdot)$	$-1$	$1$	$e\left(\frac{274}{385}\right)$	$e\left(\frac{292}{385}\right)$	$e\left(\frac{151}{385}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{233}{385}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{163}{385}\right)$	$e\left(\frac{36}{385}\right)$	$e\left(\frac{181}{385}\right)$	$e\left(\frac{157}{385}\right)$
$\chi_{84216}(8531,\cdot)$	$-1$	$1$	$e\left(\frac{236}{385}\right)$	$e\left(\frac{333}{385}\right)$	$e\left(\frac{279}{385}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{122}{385}\right)$	$e\left(\frac{6}{77}\right)$	$e\left(\frac{87}{385}\right)$	$e\left(\frac{194}{385}\right)$	$e\left(\frac{184}{385}\right)$	$e\left(\frac{183}{385}\right)$
$\chi_{84216}(8675,\cdot)$	$-1$	$1$	$e\left(\frac{318}{385}\right)$	$e\left(\frac{204}{385}\right)$	$e\left(\frac{327}{385}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{321}{385}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{251}{385}\right)$	$e\left(\frac{157}{385}\right)$	$e\left(\frac{137}{385}\right)$	$e\left(\frac{289}{385}\right)$
$\chi_{84216}(9083,\cdot)$	$-1$	$1$	$e\left(\frac{282}{385}\right)$	$e\left(\frac{101}{385}\right)$	$e\left(\frac{43}{385}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{74}{385}\right)$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{179}{385}\right)$	$e\left(\frac{23}{385}\right)$	$e\left(\frac{383}{385}\right)$	$e\left(\frac{111}{385}\right)$
$\chi_{84216}(9347,\cdot)$	$-1$	$1$	$e\left(\frac{197}{385}\right)$	$e\left(\frac{61}{385}\right)$	$e\left(\frac{228}{385}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{79}{385}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{9}{385}\right)$	$e\left(\frac{113}{385}\right)$	$e\left(\frac{258}{385}\right)$	$e\left(\frac{311}{385}\right)$
$\chi_{84216}(9467,\cdot)$	$-1$	$1$	$e\left(\frac{223}{385}\right)$	$e\left(\frac{114}{385}\right)$	$e\left(\frac{262}{385}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{236}{385}\right)$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{61}{385}\right)$	$e\left(\frac{167}{385}\right)$	$e\left(\frac{337}{385}\right)$	$e\left(\frac{354}{385}\right)$
$\chi_{84216}(10067,\cdot)$	$-1$	$1$	$e\left(\frac{304}{385}\right)$	$e\left(\frac{57}{385}\right)$	$e\left(\frac{131}{385}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{118}{385}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{223}{385}\right)$	$e\left(\frac{276}{385}\right)$	$e\left(\frac{361}{385}\right)$	$e\left(\frac{177}{385}\right)$
$\chi_{84216}(10259,\cdot)$	$-1$	$1$	$e\left(\frac{18}{385}\right)$	$e\left(\frac{244}{385}\right)$	$e\left(\frac{142}{385}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{316}{385}\right)$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{36}{385}\right)$	$e\left(\frac{67}{385}\right)$	$e\left(\frac{262}{385}\right)$	$e\left(\frac{89}{385}\right)$
$\chi_{84216}(10859,\cdot)$	$-1$	$1$	$e\left(\frac{384}{385}\right)$	$e\left(\frac{72}{385}\right)$	$e\left(\frac{206}{385}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{68}{385}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{383}{385}\right)$	$e\left(\frac{146}{385}\right)$	$e\left(\frac{71}{385}\right)$	$e\left(\frac{102}{385}\right)$
$\chi_{84216}(11171,\cdot)$	$-1$	$1$	$e\left(\frac{331}{385}\right)$	$e\left(\frac{38}{385}\right)$	$e\left(\frac{344}{385}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{207}{385}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{277}{385}\right)$	$e\left(\frac{184}{385}\right)$	$e\left(\frac{369}{385}\right)$	$e\left(\frac{118}{385}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(31\)	\(35\)	\(37\)
\(\chi_{84216}(35,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{385}\right)\)	\(e\left(\frac{87}{385}\right)\)	\(e\left(\frac{281}{385}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{18}{385}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{158}{385}\right)\)	\(e\left(\frac{16}{385}\right)\)	\(e\left(\frac{166}{385}\right)\)	\(e\left(\frac{27}{385}\right)\)
\(\chi_{84216}(299,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{344}{385}\right)\)	\(e\left(\frac{257}{385}\right)\)	\(e\left(\frac{361}{385}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{93}{385}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{303}{385}\right)\)	\(e\left(\frac{211}{385}\right)\)	\(e\left(\frac{216}{385}\right)\)	\(e\left(\frac{332}{385}\right)\)
\(\chi_{84216}(875,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{385}\right)\)	\(e\left(\frac{193}{385}\right)\)	\(e\left(\frac{349}{385}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{332}{385}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{262}{385}\right)\)	\(e\left(\frac{124}{385}\right)\)	\(e\left(\frac{324}{385}\right)\)	\(e\left(\frac{113}{385}\right)\)
\(\chi_{84216}(1019,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{283}{385}\right)\)	\(e\left(\frac{29}{385}\right)\)	\(e\left(\frac{222}{385}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{6}{385}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{181}{385}\right)\)	\(e\left(\frac{262}{385}\right)\)	\(e\left(\frac{312}{385}\right)\)	\(e\left(\frac{9}{385}\right)\)
\(\chi_{84216}(1427,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{385}\right)\)	\(e\left(\frac{381}{385}\right)\)	\(e\left(\frac{288}{385}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{39}{385}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{214}{385}\right)\)	\(e\left(\frac{163}{385}\right)\)	\(e\left(\frac{103}{385}\right)\)	\(e\left(\frac{251}{385}\right)\)
\(\chi_{84216}(1811,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{188}{385}\right)\)	\(e\left(\frac{324}{385}\right)\)	\(e\left(\frac{157}{385}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{306}{385}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{376}{385}\right)\)	\(e\left(\frac{272}{385}\right)\)	\(e\left(\frac{127}{385}\right)\)	\(e\left(\frac{74}{385}\right)\)
\(\chi_{84216}(2603,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{368}{385}\right)\)	\(e\left(\frac{69}{385}\right)\)	\(e\left(\frac{37}{385}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{1}{385}\right)\)	\(e\left(\frac{72}{77}\right)\)	\(e\left(\frac{351}{385}\right)\)	\(e\left(\frac{172}{385}\right)\)	\(e\left(\frac{52}{385}\right)\)	\(e\left(\frac{194}{385}\right)\)
\(\chi_{84216}(3203,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{69}{385}\right)\)	\(e\left(\frac{37}{385}\right)\)	\(e\left(\frac{31}{385}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{313}{385}\right)\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{138}{385}\right)\)	\(e\left(\frac{321}{385}\right)\)	\(e\left(\frac{106}{385}\right)\)	\(e\left(\frac{277}{385}\right)\)
\(\chi_{84216}(3515,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{226}{385}\right)\)	\(e\left(\frac{283}{385}\right)\)	\(e\left(\frac{29}{385}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{32}{385}\right)\)	\(e\left(\frac{71}{77}\right)\)	\(e\left(\frac{67}{385}\right)\)	\(e\left(\frac{114}{385}\right)\)	\(e\left(\frac{124}{385}\right)\)	\(e\left(\frac{48}{385}\right)\)
\(\chi_{84216}(3659,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{278}{385}\right)\)	\(e\left(\frac{4}{385}\right)\)	\(e\left(\frac{97}{385}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{346}{385}\right)\)	\(e\left(\frac{41}{77}\right)\)	\(e\left(\frac{171}{385}\right)\)	\(e\left(\frac{222}{385}\right)\)	\(e\left(\frac{282}{385}\right)\)	\(e\left(\frac{134}{385}\right)\)
\(\chi_{84216}(3779,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{351}{385}\right)\)	\(e\left(\frac{138}{385}\right)\)	\(e\left(\frac{74}{385}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{2}{385}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{317}{385}\right)\)	\(e\left(\frac{344}{385}\right)\)	\(e\left(\frac{104}{385}\right)\)	\(e\left(\frac{3}{385}\right)\)
\(\chi_{84216}(3803,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{332}{385}\right)\)	\(e\left(\frac{351}{385}\right)\)	\(e\left(\frac{138}{385}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{139}{385}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{279}{385}\right)\)	\(e\left(\frac{38}{385}\right)\)	\(e\left(\frac{298}{385}\right)\)	\(e\left(\frac{16}{385}\right)\)
\(\chi_{84216}(3995,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{385}\right)\)	\(e\left(\frac{272}{385}\right)\)	\(e\left(\frac{51}{385}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{43}{385}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{78}{385}\right)\)	\(e\left(\frac{81}{385}\right)\)	\(e\left(\frac{311}{385}\right)\)	\(e\left(\frac{257}{385}\right)\)
\(\chi_{84216}(5051,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{54}{385}\right)\)	\(e\left(\frac{347}{385}\right)\)	\(e\left(\frac{41}{385}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{178}{385}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{108}{385}\right)\)	\(e\left(\frac{201}{385}\right)\)	\(e\left(\frac{16}{385}\right)\)	\(e\left(\frac{267}{385}\right)\)
\(\chi_{84216}(5387,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{207}{385}\right)\)	\(e\left(\frac{111}{385}\right)\)	\(e\left(\frac{93}{385}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{169}{385}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{29}{385}\right)\)	\(e\left(\frac{193}{385}\right)\)	\(e\left(\frac{318}{385}\right)\)	\(e\left(\frac{61}{385}\right)\)
\(\chi_{84216}(5891,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{385}\right)\)	\(e\left(\frac{78}{385}\right)\)	\(e\left(\frac{159}{385}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{202}{385}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{62}{385}\right)\)	\(e\left(\frac{94}{385}\right)\)	\(e\left(\frac{109}{385}\right)\)	\(e\left(\frac{303}{385}\right)\)
\(\chi_{84216}(6299,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{385}\right)\)	\(e\left(\frac{199}{385}\right)\)	\(e\left(\frac{302}{385}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{81}{385}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{326}{385}\right)\)	\(e\left(\frac{72}{385}\right)\)	\(e\left(\frac{362}{385}\right)\)	\(e\left(\frac{314}{385}\right)\)
\(\chi_{84216}(6443,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{362}{385}\right)\)	\(e\left(\frac{116}{385}\right)\)	\(e\left(\frac{118}{385}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{24}{385}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{339}{385}\right)\)	\(e\left(\frac{278}{385}\right)\)	\(e\left(\frac{93}{385}\right)\)	\(e\left(\frac{36}{385}\right)\)
\(\chi_{84216}(6563,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{385}\right)\)	\(e\left(\frac{334}{385}\right)\)	\(e\left(\frac{207}{385}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{16}{385}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{226}{385}\right)\)	\(e\left(\frac{57}{385}\right)\)	\(e\left(\frac{62}{385}\right)\)	\(e\left(\frac{24}{385}\right)\)
\(\chi_{84216}(6683,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{76}{385}\right)\)	\(e\left(\frac{303}{385}\right)\)	\(e\left(\frac{129}{385}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{222}{385}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{152}{385}\right)\)	\(e\left(\frac{69}{385}\right)\)	\(e\left(\frac{379}{385}\right)\)	\(e\left(\frac{333}{385}\right)\)
\(\chi_{84216}(7691,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{385}\right)\)	\(e\left(\frac{122}{385}\right)\)	\(e\left(\frac{71}{385}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{158}{385}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{18}{385}\right)\)	\(e\left(\frac{226}{385}\right)\)	\(e\left(\frac{131}{385}\right)\)	\(e\left(\frac{237}{385}\right)\)
\(\chi_{84216}(7955,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{274}{385}\right)\)	\(e\left(\frac{292}{385}\right)\)	\(e\left(\frac{151}{385}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{233}{385}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{163}{385}\right)\)	\(e\left(\frac{36}{385}\right)\)	\(e\left(\frac{181}{385}\right)\)	\(e\left(\frac{157}{385}\right)\)
\(\chi_{84216}(8531,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{236}{385}\right)\)	\(e\left(\frac{333}{385}\right)\)	\(e\left(\frac{279}{385}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{122}{385}\right)\)	\(e\left(\frac{6}{77}\right)\)	\(e\left(\frac{87}{385}\right)\)	\(e\left(\frac{194}{385}\right)\)	\(e\left(\frac{184}{385}\right)\)	\(e\left(\frac{183}{385}\right)\)
\(\chi_{84216}(8675,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{318}{385}\right)\)	\(e\left(\frac{204}{385}\right)\)	\(e\left(\frac{327}{385}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{321}{385}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{251}{385}\right)\)	\(e\left(\frac{157}{385}\right)\)	\(e\left(\frac{137}{385}\right)\)	\(e\left(\frac{289}{385}\right)\)
\(\chi_{84216}(9083,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{282}{385}\right)\)	\(e\left(\frac{101}{385}\right)\)	\(e\left(\frac{43}{385}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{74}{385}\right)\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{179}{385}\right)\)	\(e\left(\frac{23}{385}\right)\)	\(e\left(\frac{383}{385}\right)\)	\(e\left(\frac{111}{385}\right)\)
\(\chi_{84216}(9347,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{197}{385}\right)\)	\(e\left(\frac{61}{385}\right)\)	\(e\left(\frac{228}{385}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{79}{385}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{9}{385}\right)\)	\(e\left(\frac{113}{385}\right)\)	\(e\left(\frac{258}{385}\right)\)	\(e\left(\frac{311}{385}\right)\)
\(\chi_{84216}(9467,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{223}{385}\right)\)	\(e\left(\frac{114}{385}\right)\)	\(e\left(\frac{262}{385}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{236}{385}\right)\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{61}{385}\right)\)	\(e\left(\frac{167}{385}\right)\)	\(e\left(\frac{337}{385}\right)\)	\(e\left(\frac{354}{385}\right)\)
\(\chi_{84216}(10067,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{304}{385}\right)\)	\(e\left(\frac{57}{385}\right)\)	\(e\left(\frac{131}{385}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{118}{385}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{223}{385}\right)\)	\(e\left(\frac{276}{385}\right)\)	\(e\left(\frac{361}{385}\right)\)	\(e\left(\frac{177}{385}\right)\)
\(\chi_{84216}(10259,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{18}{385}\right)\)	\(e\left(\frac{244}{385}\right)\)	\(e\left(\frac{142}{385}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{316}{385}\right)\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{36}{385}\right)\)	\(e\left(\frac{67}{385}\right)\)	\(e\left(\frac{262}{385}\right)\)	\(e\left(\frac{89}{385}\right)\)
\(\chi_{84216}(10859,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{384}{385}\right)\)	\(e\left(\frac{72}{385}\right)\)	\(e\left(\frac{206}{385}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{68}{385}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{383}{385}\right)\)	\(e\left(\frac{146}{385}\right)\)	\(e\left(\frac{71}{385}\right)\)	\(e\left(\frac{102}{385}\right)\)
\(\chi_{84216}(11171,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{331}{385}\right)\)	\(e\left(\frac{38}{385}\right)\)	\(e\left(\frac{344}{385}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{207}{385}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{277}{385}\right)\)	\(e\left(\frac{184}{385}\right)\)	\(e\left(\frac{369}{385}\right)\)	\(e\left(\frac{118}{385}\right)\)

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First 31 of 240 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	84216.mz
Modulus	$84216$
Conductor	$84216$
Order	$770$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(84216\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(84216\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(770\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);