LMFDB - Dirichlet character orbit 28900.fe

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28900, base_ring=CyclotomicField(680)) M = H._module chi = DirichletCharacter(H, M([340,612,35])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(19,28900)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$28900$
Conductor:	$28900$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$680$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{680})$
Fixed field:	Number field defined by a degree 680 polynomial (not computed)

First 31 of 256 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{28900}(19,\cdot)$	$-1$	$1$	$e\left(\frac{579}{680}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{239}{340}\right)$	$e\left(\frac{57}{680}\right)$	$e\left(\frac{16}{85}\right)$	$e\left(\frac{143}{340}\right)$	$e\left(\frac{141}{170}\right)$	$e\left(\frac{597}{680}\right)$	$e\left(\frac{377}{680}\right)$	$e\left(\frac{159}{680}\right)$
$\chi_{28900}(59,\cdot)$	$-1$	$1$	$e\left(\frac{177}{680}\right)$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{177}{340}\right)$	$e\left(\frac{331}{680}\right)$	$e\left(\frac{78}{85}\right)$	$e\left(\frac{49}{340}\right)$	$e\left(\frac{103}{170}\right)$	$e\left(\frac{31}{680}\right)$	$e\left(\frac{531}{680}\right)$	$e\left(\frac{637}{680}\right)$
$\chi_{28900}(219,\cdot)$	$-1$	$1$	$e\left(\frac{279}{680}\right)$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{279}{340}\right)$	$e\left(\frac{637}{680}\right)$	$e\left(\frac{61}{85}\right)$	$e\left(\frac{83}{340}\right)$	$e\left(\frac{1}{170}\right)$	$e\left(\frac{337}{680}\right)$	$e\left(\frac{157}{680}\right)$	$e\left(\frac{59}{680}\right)$
$\chi_{28900}(359,\cdot)$	$-1$	$1$	$e\left(\frac{347}{680}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{7}{340}\right)$	$e\left(\frac{161}{680}\right)$	$e\left(\frac{78}{85}\right)$	$e\left(\frac{219}{340}\right)$	$e\left(\frac{103}{170}\right)$	$e\left(\frac{541}{680}\right)$	$e\left(\frac{361}{680}\right)$	$e\left(\frac{127}{680}\right)$
$\chi_{28900}(519,\cdot)$	$-1$	$1$	$e\left(\frac{109}{680}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{109}{340}\right)$	$e\left(\frac{127}{680}\right)$	$e\left(\frac{61}{85}\right)$	$e\left(\frac{253}{340}\right)$	$e\left(\frac{1}{170}\right)$	$e\left(\frac{507}{680}\right)$	$e\left(\frac{327}{680}\right)$	$e\left(\frac{569}{680}\right)$
$\chi_{28900}(559,\cdot)$	$-1$	$1$	$e\left(\frac{647}{680}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{307}{340}\right)$	$e\left(\frac{261}{680}\right)$	$e\left(\frac{33}{85}\right)$	$e\left(\frac{279}{340}\right)$	$e\left(\frac{73}{170}\right)$	$e\left(\frac{121}{680}\right)$	$e\left(\frac{581}{680}\right)$	$e\left(\frac{227}{680}\right)$
$\chi_{28900}(739,\cdot)$	$-1$	$1$	$e\left(\frac{673}{680}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{333}{340}\right)$	$e\left(\frac{179}{680}\right)$	$e\left(\frac{7}{85}\right)$	$e\left(\frac{121}{340}\right)$	$e\left(\frac{67}{170}\right)$	$e\left(\frac{479}{680}\right)$	$e\left(\frac{659}{680}\right)$	$e\left(\frac{213}{680}\right)$
$\chi_{28900}(859,\cdot)$	$-1$	$1$	$e\left(\frac{677}{680}\right)$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{337}{340}\right)$	$e\left(\frac{271}{680}\right)$	$e\left(\frac{3}{85}\right)$	$e\left(\frac{149}{340}\right)$	$e\left(\frac{53}{170}\right)$	$e\left(\frac{11}{680}\right)$	$e\left(\frac{671}{680}\right)$	$e\left(\frac{577}{680}\right)$
$\chi_{28900}(1039,\cdot)$	$-1$	$1$	$e\left(\frac{563}{680}\right)$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{223}{340}\right)$	$e\left(\frac{369}{680}\right)$	$e\left(\frac{32}{85}\right)$	$e\left(\frac{31}{340}\right)$	$e\left(\frac{27}{170}\right)$	$e\left(\frac{429}{680}\right)$	$e\left(\frac{329}{680}\right)$	$e\left(\frac{63}{680}\right)$
$\chi_{28900}(1079,\cdot)$	$-1$	$1$	$e\left(\frac{241}{680}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{241}{340}\right)$	$e\left(\frac{443}{680}\right)$	$e\left(\frac{14}{85}\right)$	$e\left(\frac{157}{340}\right)$	$e\left(\frac{49}{170}\right)$	$e\left(\frac{23}{680}\right)$	$e\left(\frac{43}{680}\right)$	$e\left(\frac{341}{680}\right)$
$\chi_{28900}(1239,\cdot)$	$-1$	$1$	$e\left(\frac{23}{680}\right)$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{23}{340}\right)$	$e\left(\frac{189}{680}\right)$	$e\left(\frac{62}{85}\right)$	$e\left(\frac{331}{340}\right)$	$e\left(\frac{47}{170}\right)$	$e\left(\frac{369}{680}\right)$	$e\left(\frac{69}{680}\right)$	$e\left(\frac{563}{680}\right)$
$\chi_{28900}(1379,\cdot)$	$-1$	$1$	$e\left(\frac{331}{680}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{331}{340}\right)$	$e\left(\frac{473}{680}\right)$	$e\left(\frac{9}{85}\right)$	$e\left(\frac{107}{340}\right)$	$e\left(\frac{159}{170}\right)$	$e\left(\frac{373}{680}\right)$	$e\left(\frac{313}{680}\right)$	$e\left(\frac{31}{680}\right)$
$\chi_{28900}(1419,\cdot)$	$-1$	$1$	$e\left(\frac{489}{680}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{149}{340}\right)$	$e\left(\frac{27}{680}\right)$	$e\left(\frac{21}{85}\right)$	$e\left(\frac{193}{340}\right)$	$e\left(\frac{31}{170}\right)$	$e\left(\frac{247}{680}\right)$	$e\left(\frac{107}{680}\right)$	$e\left(\frac{469}{680}\right)$
$\chi_{28900}(1539,\cdot)$	$-1$	$1$	$e\left(\frac{453}{680}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{113}{340}\right)$	$e\left(\frac{559}{680}\right)$	$e\left(\frac{57}{85}\right)$	$e\left(\frac{281}{340}\right)$	$e\left(\frac{157}{170}\right)$	$e\left(\frac{379}{680}\right)$	$e\left(\frac{679}{680}\right)$	$e\left(\frac{593}{680}\right)$
$\chi_{28900}(1719,\cdot)$	$-1$	$1$	$e\left(\frac{99}{680}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{99}{340}\right)$	$e\left(\frac{577}{680}\right)$	$e\left(\frac{71}{85}\right)$	$e\left(\frac{183}{340}\right)$	$e\left(\frac{121}{170}\right)$	$e\left(\frac{317}{680}\right)$	$e\left(\frac{297}{680}\right)$	$e\left(\frac{679}{680}\right)$
$\chi_{28900}(1759,\cdot)$	$-1$	$1$	$e\left(\frac{57}{680}\right)$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{57}{340}\right)$	$e\left(\frac{291}{680}\right)$	$e\left(\frac{28}{85}\right)$	$e\left(\frac{229}{340}\right)$	$e\left(\frac{13}{170}\right)$	$e\left(\frac{471}{680}\right)$	$e\left(\frac{171}{680}\right)$	$e\left(\frac{597}{680}\right)$
$\chi_{28900}(1879,\cdot)$	$-1$	$1$	$e\left(\frac{341}{680}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{1}{340}\right)$	$e\left(\frac{23}{680}\right)$	$e\left(\frac{84}{85}\right)$	$e\left(\frac{177}{340}\right)$	$e\left(\frac{39}{170}\right)$	$e\left(\frac{563}{680}\right)$	$e\left(\frac{343}{680}\right)$	$e\left(\frac{601}{680}\right)$
$\chi_{28900}(1919,\cdot)$	$-1$	$1$	$e\left(\frac{79}{680}\right)$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{79}{340}\right)$	$e\left(\frac{117}{680}\right)$	$e\left(\frac{6}{85}\right)$	$e\left(\frac{43}{340}\right)$	$e\left(\frac{21}{170}\right)$	$e\left(\frac{617}{680}\right)$	$e\left(\frac{237}{680}\right)$	$e\left(\frac{219}{680}\right)$
$\chi_{28900}(2059,\cdot)$	$-1$	$1$	$e\left(\frac{547}{680}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{207}{340}\right)$	$e\left(\frac{1}{680}\right)$	$e\left(\frac{48}{85}\right)$	$e\left(\frac{259}{340}\right)$	$e\left(\frac{83}{170}\right)$	$e\left(\frac{261}{680}\right)$	$e\left(\frac{281}{680}\right)$	$e\left(\frac{647}{680}\right)$
$\chi_{28900}(2219,\cdot)$	$-1$	$1$	$e\left(\frac{229}{680}\right)$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{229}{340}\right)$	$e\left(\frac{167}{680}\right)$	$e\left(\frac{26}{85}\right)$	$e\left(\frac{73}{340}\right)$	$e\left(\frac{91}{170}\right)$	$e\left(\frac{67}{680}\right)$	$e\left(\frac{7}{680}\right)$	$e\left(\frac{609}{680}\right)$
$\chi_{28900}(2259,\cdot)$	$-1$	$1$	$e\left(\frac{447}{680}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{107}{340}\right)$	$e\left(\frac{421}{680}\right)$	$e\left(\frac{63}{85}\right)$	$e\left(\frac{239}{340}\right)$	$e\left(\frac{93}{170}\right)$	$e\left(\frac{401}{680}\right)$	$e\left(\frac{661}{680}\right)$	$e\left(\frac{387}{680}\right)$
$\chi_{28900}(2439,\cdot)$	$-1$	$1$	$e\left(\frac{553}{680}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{213}{340}\right)$	$e\left(\frac{139}{680}\right)$	$e\left(\frac{42}{85}\right)$	$e\left(\frac{301}{340}\right)$	$e\left(\frac{147}{170}\right)$	$e\left(\frac{239}{680}\right)$	$e\left(\frac{299}{680}\right)$	$e\left(\frac{173}{680}\right)$
$\chi_{28900}(2559,\cdot)$	$-1$	$1$	$e\left(\frac{117}{680}\right)$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{117}{340}\right)$	$e\left(\frac{311}{680}\right)$	$e\left(\frac{53}{85}\right)$	$e\left(\frac{309}{340}\right)$	$e\left(\frac{143}{170}\right)$	$e\left(\frac{251}{680}\right)$	$e\left(\frac{351}{680}\right)$	$e\left(\frac{617}{680}\right)$
$\chi_{28900}(2739,\cdot)$	$-1$	$1$	$e\left(\frac{83}{680}\right)$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{83}{340}\right)$	$e\left(\frac{209}{680}\right)$	$e\left(\frac{2}{85}\right)$	$e\left(\frac{71}{340}\right)$	$e\left(\frac{7}{170}\right)$	$e\left(\frac{149}{680}\right)$	$e\left(\frac{249}{680}\right)$	$e\left(\frac{583}{680}\right)$
$\chi_{28900}(2779,\cdot)$	$-1$	$1$	$e\left(\frac{121}{680}\right)$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{121}{340}\right)$	$e\left(\frac{403}{680}\right)$	$e\left(\frac{49}{85}\right)$	$e\left(\frac{337}{340}\right)$	$e\left(\frac{129}{170}\right)$	$e\left(\frac{463}{680}\right)$	$e\left(\frac{363}{680}\right)$	$e\left(\frac{301}{680}\right)$
$\chi_{28900}(2939,\cdot)$	$-1$	$1$	$e\left(\frac{503}{680}\right)$	$e\left(\frac{89}{136}\right)$	$e\left(\frac{163}{340}\right)$	$e\left(\frac{349}{680}\right)$	$e\left(\frac{7}{85}\right)$	$e\left(\frac{291}{340}\right)$	$e\left(\frac{67}{170}\right)$	$e\left(\frac{649}{680}\right)$	$e\left(\frac{149}{680}\right)$	$e\left(\frac{43}{680}\right)$
$\chi_{28900}(3079,\cdot)$	$-1$	$1$	$e\left(\frac{531}{680}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{191}{340}\right)$	$e\left(\frac{313}{680}\right)$	$e\left(\frac{64}{85}\right)$	$e\left(\frac{147}{340}\right)$	$e\left(\frac{139}{170}\right)$	$e\left(\frac{93}{680}\right)$	$e\left(\frac{233}{680}\right)$	$e\left(\frac{551}{680}\right)$
$\chi_{28900}(3119,\cdot)$	$-1$	$1$	$e\left(\frac{369}{680}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{29}{340}\right)$	$e\left(\frac{667}{680}\right)$	$e\left(\frac{56}{85}\right)$	$e\left(\frac{33}{340}\right)$	$e\left(\frac{111}{170}\right)$	$e\left(\frac{7}{680}\right)$	$e\left(\frac{427}{680}\right)$	$e\left(\frac{429}{680}\right)$
$\chi_{28900}(3239,\cdot)$	$-1$	$1$	$e\left(\frac{573}{680}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{233}{340}\right)$	$e\left(\frac{599}{680}\right)$	$e\left(\frac{22}{85}\right)$	$e\left(\frac{101}{340}\right)$	$e\left(\frac{77}{170}\right)$	$e\left(\frac{619}{680}\right)$	$e\left(\frac{359}{680}\right)$	$e\left(\frac{633}{680}\right)$
$\chi_{28900}(3279,\cdot)$	$-1$	$1$	$e\left(\frac{191}{680}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{191}{340}\right)$	$e\left(\frac{653}{680}\right)$	$e\left(\frac{64}{85}\right)$	$e\left(\frac{147}{340}\right)$	$e\left(\frac{139}{170}\right)$	$e\left(\frac{433}{680}\right)$	$e\left(\frac{573}{680}\right)$	$e\left(\frac{211}{680}\right)$
$\chi_{28900}(3419,\cdot)$	$-1$	$1$	$e\left(\frac{299}{680}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{299}{340}\right)$	$e\left(\frac{417}{680}\right)$	$e\left(\frac{41}{85}\right)$	$e\left(\frac{223}{340}\right)$	$e\left(\frac{101}{170}\right)$	$e\left(\frac{37}{680}\right)$	$e\left(\frac{217}{680}\right)$	$e\left(\frac{519}{680}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{28900}(19,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{579}{680}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{239}{340}\right)\)	\(e\left(\frac{57}{680}\right)\)	\(e\left(\frac{16}{85}\right)\)	\(e\left(\frac{143}{340}\right)\)	\(e\left(\frac{141}{170}\right)\)	\(e\left(\frac{597}{680}\right)\)	\(e\left(\frac{377}{680}\right)\)	\(e\left(\frac{159}{680}\right)\)
\(\chi_{28900}(59,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{177}{680}\right)\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{177}{340}\right)\)	\(e\left(\frac{331}{680}\right)\)	\(e\left(\frac{78}{85}\right)\)	\(e\left(\frac{49}{340}\right)\)	\(e\left(\frac{103}{170}\right)\)	\(e\left(\frac{31}{680}\right)\)	\(e\left(\frac{531}{680}\right)\)	\(e\left(\frac{637}{680}\right)\)
\(\chi_{28900}(219,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{279}{680}\right)\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{279}{340}\right)\)	\(e\left(\frac{637}{680}\right)\)	\(e\left(\frac{61}{85}\right)\)	\(e\left(\frac{83}{340}\right)\)	\(e\left(\frac{1}{170}\right)\)	\(e\left(\frac{337}{680}\right)\)	\(e\left(\frac{157}{680}\right)\)	\(e\left(\frac{59}{680}\right)\)
\(\chi_{28900}(359,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{347}{680}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{7}{340}\right)\)	\(e\left(\frac{161}{680}\right)\)	\(e\left(\frac{78}{85}\right)\)	\(e\left(\frac{219}{340}\right)\)	\(e\left(\frac{103}{170}\right)\)	\(e\left(\frac{541}{680}\right)\)	\(e\left(\frac{361}{680}\right)\)	\(e\left(\frac{127}{680}\right)\)
\(\chi_{28900}(519,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{680}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{109}{340}\right)\)	\(e\left(\frac{127}{680}\right)\)	\(e\left(\frac{61}{85}\right)\)	\(e\left(\frac{253}{340}\right)\)	\(e\left(\frac{1}{170}\right)\)	\(e\left(\frac{507}{680}\right)\)	\(e\left(\frac{327}{680}\right)\)	\(e\left(\frac{569}{680}\right)\)
\(\chi_{28900}(559,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{647}{680}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{307}{340}\right)\)	\(e\left(\frac{261}{680}\right)\)	\(e\left(\frac{33}{85}\right)\)	\(e\left(\frac{279}{340}\right)\)	\(e\left(\frac{73}{170}\right)\)	\(e\left(\frac{121}{680}\right)\)	\(e\left(\frac{581}{680}\right)\)	\(e\left(\frac{227}{680}\right)\)
\(\chi_{28900}(739,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{673}{680}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{333}{340}\right)\)	\(e\left(\frac{179}{680}\right)\)	\(e\left(\frac{7}{85}\right)\)	\(e\left(\frac{121}{340}\right)\)	\(e\left(\frac{67}{170}\right)\)	\(e\left(\frac{479}{680}\right)\)	\(e\left(\frac{659}{680}\right)\)	\(e\left(\frac{213}{680}\right)\)
\(\chi_{28900}(859,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{677}{680}\right)\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{337}{340}\right)\)	\(e\left(\frac{271}{680}\right)\)	\(e\left(\frac{3}{85}\right)\)	\(e\left(\frac{149}{340}\right)\)	\(e\left(\frac{53}{170}\right)\)	\(e\left(\frac{11}{680}\right)\)	\(e\left(\frac{671}{680}\right)\)	\(e\left(\frac{577}{680}\right)\)
\(\chi_{28900}(1039,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{563}{680}\right)\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{223}{340}\right)\)	\(e\left(\frac{369}{680}\right)\)	\(e\left(\frac{32}{85}\right)\)	\(e\left(\frac{31}{340}\right)\)	\(e\left(\frac{27}{170}\right)\)	\(e\left(\frac{429}{680}\right)\)	\(e\left(\frac{329}{680}\right)\)	\(e\left(\frac{63}{680}\right)\)
\(\chi_{28900}(1079,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{241}{680}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{241}{340}\right)\)	\(e\left(\frac{443}{680}\right)\)	\(e\left(\frac{14}{85}\right)\)	\(e\left(\frac{157}{340}\right)\)	\(e\left(\frac{49}{170}\right)\)	\(e\left(\frac{23}{680}\right)\)	\(e\left(\frac{43}{680}\right)\)	\(e\left(\frac{341}{680}\right)\)
\(\chi_{28900}(1239,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{680}\right)\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{23}{340}\right)\)	\(e\left(\frac{189}{680}\right)\)	\(e\left(\frac{62}{85}\right)\)	\(e\left(\frac{331}{340}\right)\)	\(e\left(\frac{47}{170}\right)\)	\(e\left(\frac{369}{680}\right)\)	\(e\left(\frac{69}{680}\right)\)	\(e\left(\frac{563}{680}\right)\)
\(\chi_{28900}(1379,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{331}{680}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{331}{340}\right)\)	\(e\left(\frac{473}{680}\right)\)	\(e\left(\frac{9}{85}\right)\)	\(e\left(\frac{107}{340}\right)\)	\(e\left(\frac{159}{170}\right)\)	\(e\left(\frac{373}{680}\right)\)	\(e\left(\frac{313}{680}\right)\)	\(e\left(\frac{31}{680}\right)\)
\(\chi_{28900}(1419,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{489}{680}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{149}{340}\right)\)	\(e\left(\frac{27}{680}\right)\)	\(e\left(\frac{21}{85}\right)\)	\(e\left(\frac{193}{340}\right)\)	\(e\left(\frac{31}{170}\right)\)	\(e\left(\frac{247}{680}\right)\)	\(e\left(\frac{107}{680}\right)\)	\(e\left(\frac{469}{680}\right)\)
\(\chi_{28900}(1539,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{453}{680}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{113}{340}\right)\)	\(e\left(\frac{559}{680}\right)\)	\(e\left(\frac{57}{85}\right)\)	\(e\left(\frac{281}{340}\right)\)	\(e\left(\frac{157}{170}\right)\)	\(e\left(\frac{379}{680}\right)\)	\(e\left(\frac{679}{680}\right)\)	\(e\left(\frac{593}{680}\right)\)
\(\chi_{28900}(1719,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{99}{680}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{99}{340}\right)\)	\(e\left(\frac{577}{680}\right)\)	\(e\left(\frac{71}{85}\right)\)	\(e\left(\frac{183}{340}\right)\)	\(e\left(\frac{121}{170}\right)\)	\(e\left(\frac{317}{680}\right)\)	\(e\left(\frac{297}{680}\right)\)	\(e\left(\frac{679}{680}\right)\)
\(\chi_{28900}(1759,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{680}\right)\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{57}{340}\right)\)	\(e\left(\frac{291}{680}\right)\)	\(e\left(\frac{28}{85}\right)\)	\(e\left(\frac{229}{340}\right)\)	\(e\left(\frac{13}{170}\right)\)	\(e\left(\frac{471}{680}\right)\)	\(e\left(\frac{171}{680}\right)\)	\(e\left(\frac{597}{680}\right)\)
\(\chi_{28900}(1879,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{341}{680}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{1}{340}\right)\)	\(e\left(\frac{23}{680}\right)\)	\(e\left(\frac{84}{85}\right)\)	\(e\left(\frac{177}{340}\right)\)	\(e\left(\frac{39}{170}\right)\)	\(e\left(\frac{563}{680}\right)\)	\(e\left(\frac{343}{680}\right)\)	\(e\left(\frac{601}{680}\right)\)
\(\chi_{28900}(1919,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{680}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{79}{340}\right)\)	\(e\left(\frac{117}{680}\right)\)	\(e\left(\frac{6}{85}\right)\)	\(e\left(\frac{43}{340}\right)\)	\(e\left(\frac{21}{170}\right)\)	\(e\left(\frac{617}{680}\right)\)	\(e\left(\frac{237}{680}\right)\)	\(e\left(\frac{219}{680}\right)\)
\(\chi_{28900}(2059,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{547}{680}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{207}{340}\right)\)	\(e\left(\frac{1}{680}\right)\)	\(e\left(\frac{48}{85}\right)\)	\(e\left(\frac{259}{340}\right)\)	\(e\left(\frac{83}{170}\right)\)	\(e\left(\frac{261}{680}\right)\)	\(e\left(\frac{281}{680}\right)\)	\(e\left(\frac{647}{680}\right)\)
\(\chi_{28900}(2219,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{229}{680}\right)\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{229}{340}\right)\)	\(e\left(\frac{167}{680}\right)\)	\(e\left(\frac{26}{85}\right)\)	\(e\left(\frac{73}{340}\right)\)	\(e\left(\frac{91}{170}\right)\)	\(e\left(\frac{67}{680}\right)\)	\(e\left(\frac{7}{680}\right)\)	\(e\left(\frac{609}{680}\right)\)
\(\chi_{28900}(2259,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{447}{680}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{107}{340}\right)\)	\(e\left(\frac{421}{680}\right)\)	\(e\left(\frac{63}{85}\right)\)	\(e\left(\frac{239}{340}\right)\)	\(e\left(\frac{93}{170}\right)\)	\(e\left(\frac{401}{680}\right)\)	\(e\left(\frac{661}{680}\right)\)	\(e\left(\frac{387}{680}\right)\)
\(\chi_{28900}(2439,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{553}{680}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{213}{340}\right)\)	\(e\left(\frac{139}{680}\right)\)	\(e\left(\frac{42}{85}\right)\)	\(e\left(\frac{301}{340}\right)\)	\(e\left(\frac{147}{170}\right)\)	\(e\left(\frac{239}{680}\right)\)	\(e\left(\frac{299}{680}\right)\)	\(e\left(\frac{173}{680}\right)\)
\(\chi_{28900}(2559,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{117}{680}\right)\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{117}{340}\right)\)	\(e\left(\frac{311}{680}\right)\)	\(e\left(\frac{53}{85}\right)\)	\(e\left(\frac{309}{340}\right)\)	\(e\left(\frac{143}{170}\right)\)	\(e\left(\frac{251}{680}\right)\)	\(e\left(\frac{351}{680}\right)\)	\(e\left(\frac{617}{680}\right)\)
\(\chi_{28900}(2739,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{680}\right)\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{83}{340}\right)\)	\(e\left(\frac{209}{680}\right)\)	\(e\left(\frac{2}{85}\right)\)	\(e\left(\frac{71}{340}\right)\)	\(e\left(\frac{7}{170}\right)\)	\(e\left(\frac{149}{680}\right)\)	\(e\left(\frac{249}{680}\right)\)	\(e\left(\frac{583}{680}\right)\)
\(\chi_{28900}(2779,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{680}\right)\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{121}{340}\right)\)	\(e\left(\frac{403}{680}\right)\)	\(e\left(\frac{49}{85}\right)\)	\(e\left(\frac{337}{340}\right)\)	\(e\left(\frac{129}{170}\right)\)	\(e\left(\frac{463}{680}\right)\)	\(e\left(\frac{363}{680}\right)\)	\(e\left(\frac{301}{680}\right)\)
\(\chi_{28900}(2939,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{503}{680}\right)\)	\(e\left(\frac{89}{136}\right)\)	\(e\left(\frac{163}{340}\right)\)	\(e\left(\frac{349}{680}\right)\)	\(e\left(\frac{7}{85}\right)\)	\(e\left(\frac{291}{340}\right)\)	\(e\left(\frac{67}{170}\right)\)	\(e\left(\frac{649}{680}\right)\)	\(e\left(\frac{149}{680}\right)\)	\(e\left(\frac{43}{680}\right)\)
\(\chi_{28900}(3079,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{531}{680}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{191}{340}\right)\)	\(e\left(\frac{313}{680}\right)\)	\(e\left(\frac{64}{85}\right)\)	\(e\left(\frac{147}{340}\right)\)	\(e\left(\frac{139}{170}\right)\)	\(e\left(\frac{93}{680}\right)\)	\(e\left(\frac{233}{680}\right)\)	\(e\left(\frac{551}{680}\right)\)
\(\chi_{28900}(3119,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{369}{680}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{29}{340}\right)\)	\(e\left(\frac{667}{680}\right)\)	\(e\left(\frac{56}{85}\right)\)	\(e\left(\frac{33}{340}\right)\)	\(e\left(\frac{111}{170}\right)\)	\(e\left(\frac{7}{680}\right)\)	\(e\left(\frac{427}{680}\right)\)	\(e\left(\frac{429}{680}\right)\)
\(\chi_{28900}(3239,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{573}{680}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{233}{340}\right)\)	\(e\left(\frac{599}{680}\right)\)	\(e\left(\frac{22}{85}\right)\)	\(e\left(\frac{101}{340}\right)\)	\(e\left(\frac{77}{170}\right)\)	\(e\left(\frac{619}{680}\right)\)	\(e\left(\frac{359}{680}\right)\)	\(e\left(\frac{633}{680}\right)\)
\(\chi_{28900}(3279,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{680}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{191}{340}\right)\)	\(e\left(\frac{653}{680}\right)\)	\(e\left(\frac{64}{85}\right)\)	\(e\left(\frac{147}{340}\right)\)	\(e\left(\frac{139}{170}\right)\)	\(e\left(\frac{433}{680}\right)\)	\(e\left(\frac{573}{680}\right)\)	\(e\left(\frac{211}{680}\right)\)
\(\chi_{28900}(3419,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{299}{680}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{299}{340}\right)\)	\(e\left(\frac{417}{680}\right)\)	\(e\left(\frac{41}{85}\right)\)	\(e\left(\frac{223}{340}\right)\)	\(e\left(\frac{101}{170}\right)\)	\(e\left(\frac{37}{680}\right)\)	\(e\left(\frac{217}{680}\right)\)	\(e\left(\frac{519}{680}\right)\)

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First 31 of 256 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	28900.fe
Modulus	$28900$
Conductor	$28900$
Order	$680$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(28900\)
Conductor:	\(28900\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(680\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)