LMFDB - Dirichlet character orbit 28900.ff

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28900, base_ring=CyclotomicField(680)) M = H._module chi = DirichletCharacter(H, M([0,476,5])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(9,28900)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$28900$
Conductor:	$7225$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$680$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 7225.co	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:	$\Q(\zeta_{680})$
Fixed field:	Number field defined by a degree 680 polynomial (not computed)

First 31 of 256 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{28900}(9,\cdot)$	$1$	$1$	$e\left(\frac{617}{680}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{277}{340}\right)$	$e\left(\frac{251}{680}\right)$	$e\left(\frac{63}{85}\right)$	$e\left(\frac{239}{340}\right)$	$e\left(\frac{93}{170}\right)$	$e\left(\frac{231}{680}\right)$	$e\left(\frac{491}{680}\right)$	$e\left(\frac{217}{680}\right)$
$\chi_{28900}(189,\cdot)$	$1$	$1$	$e\left(\frac{463}{680}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{123}{340}\right)$	$e\left(\frac{109}{680}\right)$	$e\left(\frac{47}{85}\right)$	$e\left(\frac{181}{340}\right)$	$e\left(\frac{37}{170}\right)$	$e\left(\frac{569}{680}\right)$	$e\left(\frac{29}{680}\right)$	$e\left(\frac{143}{680}\right)$
$\chi_{28900}(229,\cdot)$	$1$	$1$	$e\left(\frac{301}{680}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{301}{340}\right)$	$e\left(\frac{463}{680}\right)$	$e\left(\frac{39}{85}\right)$	$e\left(\frac{67}{340}\right)$	$e\left(\frac{9}{170}\right)$	$e\left(\frac{483}{680}\right)$	$e\left(\frac{223}{680}\right)$	$e\left(\frac{21}{680}\right)$
$\chi_{28900}(389,\cdot)$	$1$	$1$	$e\left(\frac{123}{680}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{123}{340}\right)$	$e\left(\frac{449}{680}\right)$	$e\left(\frac{47}{85}\right)$	$e\left(\frac{181}{340}\right)$	$e\left(\frac{37}{170}\right)$	$e\left(\frac{229}{680}\right)$	$e\left(\frac{369}{680}\right)$	$e\left(\frac{483}{680}\right)$
$\chi_{28900}(529,\cdot)$	$1$	$1$	$e\left(\frac{231}{680}\right)$	$e\left(\frac{89}{136}\right)$	$e\left(\frac{231}{340}\right)$	$e\left(\frac{213}{680}\right)$	$e\left(\frac{24}{85}\right)$	$e\left(\frac{257}{340}\right)$	$e\left(\frac{169}{170}\right)$	$e\left(\frac{513}{680}\right)$	$e\left(\frac{13}{680}\right)$	$e\left(\frac{111}{680}\right)$
$\chi_{28900}(569,\cdot)$	$1$	$1$	$e\left(\frac{549}{680}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{209}{340}\right)$	$e\left(\frac{47}{680}\right)$	$e\left(\frac{46}{85}\right)$	$e\left(\frac{103}{340}\right)$	$e\left(\frac{161}{170}\right)$	$e\left(\frac{27}{680}\right)$	$e\left(\frac{287}{680}\right)$	$e\left(\frac{149}{680}\right)$
$\chi_{28900}(689,\cdot)$	$1$	$1$	$e\left(\frac{393}{680}\right)$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{53}{340}\right)$	$e\left(\frac{539}{680}\right)$	$e\left(\frac{32}{85}\right)$	$e\left(\frac{31}{340}\right)$	$e\left(\frac{27}{170}\right)$	$e\left(\frac{599}{680}\right)$	$e\left(\frac{499}{680}\right)$	$e\left(\frac{233}{680}\right)$
$\chi_{28900}(729,\cdot)$	$1$	$1$	$e\left(\frac{491}{680}\right)$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{151}{340}\right)$	$e\left(\frac{73}{680}\right)$	$e\left(\frac{19}{85}\right)$	$e\left(\frac{37}{340}\right)$	$e\left(\frac{109}{170}\right)$	$e\left(\frac{13}{680}\right)$	$e\left(\frac{113}{680}\right)$	$e\left(\frac{651}{680}\right)$
$\chi_{28900}(869,\cdot)$	$1$	$1$	$e\left(\frac{679}{680}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{339}{340}\right)$	$e\left(\frac{317}{680}\right)$	$e\left(\frac{1}{85}\right)$	$e\left(\frac{333}{340}\right)$	$e\left(\frac{131}{170}\right)$	$e\left(\frac{457}{680}\right)$	$e\left(\frac{677}{680}\right)$	$e\left(\frac{79}{680}\right)$
$\chi_{28900}(909,\cdot)$	$1$	$1$	$e\left(\frac{117}{680}\right)$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{117}{340}\right)$	$e\left(\frac{311}{680}\right)$	$e\left(\frac{53}{85}\right)$	$e\left(\frac{139}{340}\right)$	$e\left(\frac{143}{170}\right)$	$e\left(\frac{251}{680}\right)$	$e\left(\frac{351}{680}\right)$	$e\left(\frac{277}{680}\right)$
$\chi_{28900}(1029,\cdot)$	$1$	$1$	$e\left(\frac{281}{680}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{281}{340}\right)$	$e\left(\frac{3}{680}\right)$	$e\left(\frac{59}{85}\right)$	$e\left(\frac{267}{340}\right)$	$e\left(\frac{79}{170}\right)$	$e\left(\frac{103}{680}\right)$	$e\left(\frac{163}{680}\right)$	$e\left(\frac{241}{680}\right)$
$\chi_{28900}(1069,\cdot)$	$1$	$1$	$e\left(\frac{179}{680}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{179}{340}\right)$	$e\left(\frac{377}{680}\right)$	$e\left(\frac{76}{85}\right)$	$e\left(\frac{233}{340}\right)$	$e\left(\frac{11}{170}\right)$	$e\left(\frac{477}{680}\right)$	$e\left(\frac{537}{680}\right)$	$e\left(\frac{139}{680}\right)$
$\chi_{28900}(1209,\cdot)$	$1$	$1$	$e\left(\frac{447}{680}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{107}{340}\right)$	$e\left(\frac{421}{680}\right)$	$e\left(\frac{63}{85}\right)$	$e\left(\frac{69}{340}\right)$	$e\left(\frac{93}{170}\right)$	$e\left(\frac{401}{680}\right)$	$e\left(\frac{661}{680}\right)$	$e\left(\frac{47}{680}\right)$
$\chi_{28900}(1369,\cdot)$	$1$	$1$	$e\left(\frac{169}{680}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{169}{340}\right)$	$e\left(\frac{147}{680}\right)$	$e\left(\frac{1}{85}\right)$	$e\left(\frac{163}{340}\right)$	$e\left(\frac{131}{170}\right)$	$e\left(\frac{287}{680}\right)$	$e\left(\frac{507}{680}\right)$	$e\left(\frac{249}{680}\right)$
$\chi_{28900}(1409,\cdot)$	$1$	$1$	$e\left(\frac{547}{680}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{207}{340}\right)$	$e\left(\frac{1}{680}\right)$	$e\left(\frac{48}{85}\right)$	$e\left(\frac{89}{340}\right)$	$e\left(\frac{83}{170}\right)$	$e\left(\frac{261}{680}\right)$	$e\left(\frac{281}{680}\right)$	$e\left(\frac{307}{680}\right)$
$\chi_{28900}(1589,\cdot)$	$1$	$1$	$e\left(\frac{613}{680}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{273}{340}\right)$	$e\left(\frac{159}{680}\right)$	$e\left(\frac{67}{85}\right)$	$e\left(\frac{211}{340}\right)$	$e\left(\frac{107}{170}\right)$	$e\left(\frac{19}{680}\right)$	$e\left(\frac{479}{680}\right)$	$e\left(\frac{533}{680}\right)$
$\chi_{28900}(1709,\cdot)$	$1$	$1$	$e\left(\frac{57}{680}\right)$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{57}{340}\right)$	$e\left(\frac{291}{680}\right)$	$e\left(\frac{28}{85}\right)$	$e\left(\frac{59}{340}\right)$	$e\left(\frac{13}{170}\right)$	$e\left(\frac{471}{680}\right)$	$e\left(\frac{171}{680}\right)$	$e\left(\frac{257}{680}\right)$
$\chi_{28900}(1929,\cdot)$	$1$	$1$	$e\left(\frac{181}{680}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{181}{340}\right)$	$e\left(\frac{423}{680}\right)$	$e\left(\frac{74}{85}\right)$	$e\left(\frac{247}{340}\right)$	$e\left(\frac{89}{170}\right)$	$e\left(\frac{243}{680}\right)$	$e\left(\frac{543}{680}\right)$	$e\left(\frac{661}{680}\right)$
$\chi_{28900}(2089,\cdot)$	$1$	$1$	$e\left(\frac{603}{680}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{263}{340}\right)$	$e\left(\frac{609}{680}\right)$	$e\left(\frac{77}{85}\right)$	$e\left(\frac{141}{340}\right)$	$e\left(\frac{57}{170}\right)$	$e\left(\frac{509}{680}\right)$	$e\left(\frac{449}{680}\right)$	$e\left(\frac{643}{680}\right)$
$\chi_{28900}(2229,\cdot)$	$1$	$1$	$e\left(\frac{431}{680}\right)$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{91}{340}\right)$	$e\left(\frac{53}{680}\right)$	$e\left(\frac{79}{85}\right)$	$e\left(\frac{297}{340}\right)$	$e\left(\frac{149}{170}\right)$	$e\left(\frac{233}{680}\right)$	$e\left(\frac{613}{680}\right)$	$e\left(\frac{631}{680}\right)$
$\chi_{28900}(2269,\cdot)$	$1$	$1$	$e\left(\frac{429}{680}\right)$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{89}{340}\right)$	$e\left(\frac{7}{680}\right)$	$e\left(\frac{81}{85}\right)$	$e\left(\frac{283}{340}\right)$	$e\left(\frac{71}{170}\right)$	$e\left(\frac{467}{680}\right)$	$e\left(\frac{607}{680}\right)$	$e\left(\frac{109}{680}\right)$
$\chi_{28900}(2389,\cdot)$	$1$	$1$	$e\left(\frac{513}{680}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{173}{340}\right)$	$e\left(\frac{579}{680}\right)$	$e\left(\frac{82}{85}\right)$	$e\left(\frac{191}{340}\right)$	$e\left(\frac{117}{170}\right)$	$e\left(\frac{159}{680}\right)$	$e\left(\frac{179}{680}\right)$	$e\left(\frac{273}{680}\right)$
$\chi_{28900}(2429,\cdot)$	$1$	$1$	$e\left(\frac{291}{680}\right)$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{291}{340}\right)$	$e\left(\frac{233}{680}\right)$	$e\left(\frac{49}{85}\right)$	$e\left(\frac{337}{340}\right)$	$e\left(\frac{129}{170}\right)$	$e\left(\frac{293}{680}\right)$	$e\left(\frac{193}{680}\right)$	$e\left(\frac{131}{680}\right)$
$\chi_{28900}(2569,\cdot)$	$1$	$1$	$e\left(\frac{199}{680}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{199}{340}\right)$	$e\left(\frac{157}{680}\right)$	$e\left(\frac{56}{85}\right)$	$e\left(\frac{33}{340}\right)$	$e\left(\frac{111}{170}\right)$	$e\left(\frac{177}{680}\right)$	$e\left(\frac{597}{680}\right)$	$e\left(\frac{599}{680}\right)$
$\chi_{28900}(2609,\cdot)$	$1$	$1$	$e\left(\frac{677}{680}\right)$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{337}{340}\right)$	$e\left(\frac{271}{680}\right)$	$e\left(\frac{3}{85}\right)$	$e\left(\frac{319}{340}\right)$	$e\left(\frac{53}{170}\right)$	$e\left(\frac{11}{680}\right)$	$e\left(\frac{671}{680}\right)$	$e\left(\frac{237}{680}\right)$
$\chi_{28900}(2729,\cdot)$	$1$	$1$	$e\left(\frac{401}{680}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{61}{340}\right)$	$e\left(\frac{43}{680}\right)$	$e\left(\frac{24}{85}\right)$	$e\left(\frac{87}{340}\right)$	$e\left(\frac{169}{170}\right)$	$e\left(\frac{343}{680}\right)$	$e\left(\frac{523}{680}\right)$	$e\left(\frac{281}{680}\right)$
$\chi_{28900}(2769,\cdot)$	$1$	$1$	$e\left(\frac{659}{680}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{319}{340}\right)$	$e\left(\frac{537}{680}\right)$	$e\left(\frac{21}{85}\right)$	$e\left(\frac{193}{340}\right)$	$e\left(\frac{31}{170}\right)$	$e\left(\frac{77}{680}\right)$	$e\left(\frac{617}{680}\right)$	$e\left(\frac{299}{680}\right)$
$\chi_{28900}(2909,\cdot)$	$1$	$1$	$e\left(\frac{647}{680}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{307}{340}\right)$	$e\left(\frac{261}{680}\right)$	$e\left(\frac{33}{85}\right)$	$e\left(\frac{109}{340}\right)$	$e\left(\frac{73}{170}\right)$	$e\left(\frac{121}{680}\right)$	$e\left(\frac{581}{680}\right)$	$e\left(\frac{567}{680}\right)$
$\chi_{28900}(3109,\cdot)$	$1$	$1$	$e\left(\frac{347}{680}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{7}{340}\right)$	$e\left(\frac{161}{680}\right)$	$e\left(\frac{78}{85}\right)$	$e\left(\frac{49}{340}\right)$	$e\left(\frac{103}{170}\right)$	$e\left(\frac{541}{680}\right)$	$e\left(\frac{361}{680}\right)$	$e\left(\frac{467}{680}\right)$
$\chi_{28900}(3409,\cdot)$	$1$	$1$	$e\left(\frac{177}{680}\right)$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{177}{340}\right)$	$e\left(\frac{331}{680}\right)$	$e\left(\frac{78}{85}\right)$	$e\left(\frac{219}{340}\right)$	$e\left(\frac{103}{170}\right)$	$e\left(\frac{31}{680}\right)$	$e\left(\frac{531}{680}\right)$	$e\left(\frac{297}{680}\right)$
$\chi_{28900}(3589,\cdot)$	$1$	$1$	$e\left(\frac{183}{680}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{183}{340}\right)$	$e\left(\frac{469}{680}\right)$	$e\left(\frac{72}{85}\right)$	$e\left(\frac{261}{340}\right)$	$e\left(\frac{167}{170}\right)$	$e\left(\frac{9}{680}\right)$	$e\left(\frac{549}{680}\right)$	$e\left(\frac{503}{680}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{28900}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{617}{680}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{277}{340}\right)\)	\(e\left(\frac{251}{680}\right)\)	\(e\left(\frac{63}{85}\right)\)	\(e\left(\frac{239}{340}\right)\)	\(e\left(\frac{93}{170}\right)\)	\(e\left(\frac{231}{680}\right)\)	\(e\left(\frac{491}{680}\right)\)	\(e\left(\frac{217}{680}\right)\)
\(\chi_{28900}(189,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{463}{680}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{123}{340}\right)\)	\(e\left(\frac{109}{680}\right)\)	\(e\left(\frac{47}{85}\right)\)	\(e\left(\frac{181}{340}\right)\)	\(e\left(\frac{37}{170}\right)\)	\(e\left(\frac{569}{680}\right)\)	\(e\left(\frac{29}{680}\right)\)	\(e\left(\frac{143}{680}\right)\)
\(\chi_{28900}(229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{301}{680}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{301}{340}\right)\)	\(e\left(\frac{463}{680}\right)\)	\(e\left(\frac{39}{85}\right)\)	\(e\left(\frac{67}{340}\right)\)	\(e\left(\frac{9}{170}\right)\)	\(e\left(\frac{483}{680}\right)\)	\(e\left(\frac{223}{680}\right)\)	\(e\left(\frac{21}{680}\right)\)
\(\chi_{28900}(389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{680}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{123}{340}\right)\)	\(e\left(\frac{449}{680}\right)\)	\(e\left(\frac{47}{85}\right)\)	\(e\left(\frac{181}{340}\right)\)	\(e\left(\frac{37}{170}\right)\)	\(e\left(\frac{229}{680}\right)\)	\(e\left(\frac{369}{680}\right)\)	\(e\left(\frac{483}{680}\right)\)
\(\chi_{28900}(529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{231}{680}\right)\)	\(e\left(\frac{89}{136}\right)\)	\(e\left(\frac{231}{340}\right)\)	\(e\left(\frac{213}{680}\right)\)	\(e\left(\frac{24}{85}\right)\)	\(e\left(\frac{257}{340}\right)\)	\(e\left(\frac{169}{170}\right)\)	\(e\left(\frac{513}{680}\right)\)	\(e\left(\frac{13}{680}\right)\)	\(e\left(\frac{111}{680}\right)\)
\(\chi_{28900}(569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{549}{680}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{209}{340}\right)\)	\(e\left(\frac{47}{680}\right)\)	\(e\left(\frac{46}{85}\right)\)	\(e\left(\frac{103}{340}\right)\)	\(e\left(\frac{161}{170}\right)\)	\(e\left(\frac{27}{680}\right)\)	\(e\left(\frac{287}{680}\right)\)	\(e\left(\frac{149}{680}\right)\)
\(\chi_{28900}(689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{393}{680}\right)\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{53}{340}\right)\)	\(e\left(\frac{539}{680}\right)\)	\(e\left(\frac{32}{85}\right)\)	\(e\left(\frac{31}{340}\right)\)	\(e\left(\frac{27}{170}\right)\)	\(e\left(\frac{599}{680}\right)\)	\(e\left(\frac{499}{680}\right)\)	\(e\left(\frac{233}{680}\right)\)
\(\chi_{28900}(729,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{491}{680}\right)\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{151}{340}\right)\)	\(e\left(\frac{73}{680}\right)\)	\(e\left(\frac{19}{85}\right)\)	\(e\left(\frac{37}{340}\right)\)	\(e\left(\frac{109}{170}\right)\)	\(e\left(\frac{13}{680}\right)\)	\(e\left(\frac{113}{680}\right)\)	\(e\left(\frac{651}{680}\right)\)
\(\chi_{28900}(869,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{679}{680}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{339}{340}\right)\)	\(e\left(\frac{317}{680}\right)\)	\(e\left(\frac{1}{85}\right)\)	\(e\left(\frac{333}{340}\right)\)	\(e\left(\frac{131}{170}\right)\)	\(e\left(\frac{457}{680}\right)\)	\(e\left(\frac{677}{680}\right)\)	\(e\left(\frac{79}{680}\right)\)
\(\chi_{28900}(909,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{117}{680}\right)\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{117}{340}\right)\)	\(e\left(\frac{311}{680}\right)\)	\(e\left(\frac{53}{85}\right)\)	\(e\left(\frac{139}{340}\right)\)	\(e\left(\frac{143}{170}\right)\)	\(e\left(\frac{251}{680}\right)\)	\(e\left(\frac{351}{680}\right)\)	\(e\left(\frac{277}{680}\right)\)
\(\chi_{28900}(1029,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{281}{680}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{281}{340}\right)\)	\(e\left(\frac{3}{680}\right)\)	\(e\left(\frac{59}{85}\right)\)	\(e\left(\frac{267}{340}\right)\)	\(e\left(\frac{79}{170}\right)\)	\(e\left(\frac{103}{680}\right)\)	\(e\left(\frac{163}{680}\right)\)	\(e\left(\frac{241}{680}\right)\)
\(\chi_{28900}(1069,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{680}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{179}{340}\right)\)	\(e\left(\frac{377}{680}\right)\)	\(e\left(\frac{76}{85}\right)\)	\(e\left(\frac{233}{340}\right)\)	\(e\left(\frac{11}{170}\right)\)	\(e\left(\frac{477}{680}\right)\)	\(e\left(\frac{537}{680}\right)\)	\(e\left(\frac{139}{680}\right)\)
\(\chi_{28900}(1209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{447}{680}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{107}{340}\right)\)	\(e\left(\frac{421}{680}\right)\)	\(e\left(\frac{63}{85}\right)\)	\(e\left(\frac{69}{340}\right)\)	\(e\left(\frac{93}{170}\right)\)	\(e\left(\frac{401}{680}\right)\)	\(e\left(\frac{661}{680}\right)\)	\(e\left(\frac{47}{680}\right)\)
\(\chi_{28900}(1369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{680}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{169}{340}\right)\)	\(e\left(\frac{147}{680}\right)\)	\(e\left(\frac{1}{85}\right)\)	\(e\left(\frac{163}{340}\right)\)	\(e\left(\frac{131}{170}\right)\)	\(e\left(\frac{287}{680}\right)\)	\(e\left(\frac{507}{680}\right)\)	\(e\left(\frac{249}{680}\right)\)
\(\chi_{28900}(1409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{547}{680}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{207}{340}\right)\)	\(e\left(\frac{1}{680}\right)\)	\(e\left(\frac{48}{85}\right)\)	\(e\left(\frac{89}{340}\right)\)	\(e\left(\frac{83}{170}\right)\)	\(e\left(\frac{261}{680}\right)\)	\(e\left(\frac{281}{680}\right)\)	\(e\left(\frac{307}{680}\right)\)
\(\chi_{28900}(1589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{613}{680}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{273}{340}\right)\)	\(e\left(\frac{159}{680}\right)\)	\(e\left(\frac{67}{85}\right)\)	\(e\left(\frac{211}{340}\right)\)	\(e\left(\frac{107}{170}\right)\)	\(e\left(\frac{19}{680}\right)\)	\(e\left(\frac{479}{680}\right)\)	\(e\left(\frac{533}{680}\right)\)
\(\chi_{28900}(1709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{680}\right)\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{57}{340}\right)\)	\(e\left(\frac{291}{680}\right)\)	\(e\left(\frac{28}{85}\right)\)	\(e\left(\frac{59}{340}\right)\)	\(e\left(\frac{13}{170}\right)\)	\(e\left(\frac{471}{680}\right)\)	\(e\left(\frac{171}{680}\right)\)	\(e\left(\frac{257}{680}\right)\)
\(\chi_{28900}(1929,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{680}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{181}{340}\right)\)	\(e\left(\frac{423}{680}\right)\)	\(e\left(\frac{74}{85}\right)\)	\(e\left(\frac{247}{340}\right)\)	\(e\left(\frac{89}{170}\right)\)	\(e\left(\frac{243}{680}\right)\)	\(e\left(\frac{543}{680}\right)\)	\(e\left(\frac{661}{680}\right)\)
\(\chi_{28900}(2089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{603}{680}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{263}{340}\right)\)	\(e\left(\frac{609}{680}\right)\)	\(e\left(\frac{77}{85}\right)\)	\(e\left(\frac{141}{340}\right)\)	\(e\left(\frac{57}{170}\right)\)	\(e\left(\frac{509}{680}\right)\)	\(e\left(\frac{449}{680}\right)\)	\(e\left(\frac{643}{680}\right)\)
\(\chi_{28900}(2229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{431}{680}\right)\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{91}{340}\right)\)	\(e\left(\frac{53}{680}\right)\)	\(e\left(\frac{79}{85}\right)\)	\(e\left(\frac{297}{340}\right)\)	\(e\left(\frac{149}{170}\right)\)	\(e\left(\frac{233}{680}\right)\)	\(e\left(\frac{613}{680}\right)\)	\(e\left(\frac{631}{680}\right)\)
\(\chi_{28900}(2269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{429}{680}\right)\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{89}{340}\right)\)	\(e\left(\frac{7}{680}\right)\)	\(e\left(\frac{81}{85}\right)\)	\(e\left(\frac{283}{340}\right)\)	\(e\left(\frac{71}{170}\right)\)	\(e\left(\frac{467}{680}\right)\)	\(e\left(\frac{607}{680}\right)\)	\(e\left(\frac{109}{680}\right)\)
\(\chi_{28900}(2389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{513}{680}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{173}{340}\right)\)	\(e\left(\frac{579}{680}\right)\)	\(e\left(\frac{82}{85}\right)\)	\(e\left(\frac{191}{340}\right)\)	\(e\left(\frac{117}{170}\right)\)	\(e\left(\frac{159}{680}\right)\)	\(e\left(\frac{179}{680}\right)\)	\(e\left(\frac{273}{680}\right)\)
\(\chi_{28900}(2429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{291}{680}\right)\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{291}{340}\right)\)	\(e\left(\frac{233}{680}\right)\)	\(e\left(\frac{49}{85}\right)\)	\(e\left(\frac{337}{340}\right)\)	\(e\left(\frac{129}{170}\right)\)	\(e\left(\frac{293}{680}\right)\)	\(e\left(\frac{193}{680}\right)\)	\(e\left(\frac{131}{680}\right)\)
\(\chi_{28900}(2569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{680}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{199}{340}\right)\)	\(e\left(\frac{157}{680}\right)\)	\(e\left(\frac{56}{85}\right)\)	\(e\left(\frac{33}{340}\right)\)	\(e\left(\frac{111}{170}\right)\)	\(e\left(\frac{177}{680}\right)\)	\(e\left(\frac{597}{680}\right)\)	\(e\left(\frac{599}{680}\right)\)
\(\chi_{28900}(2609,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{677}{680}\right)\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{337}{340}\right)\)	\(e\left(\frac{271}{680}\right)\)	\(e\left(\frac{3}{85}\right)\)	\(e\left(\frac{319}{340}\right)\)	\(e\left(\frac{53}{170}\right)\)	\(e\left(\frac{11}{680}\right)\)	\(e\left(\frac{671}{680}\right)\)	\(e\left(\frac{237}{680}\right)\)
\(\chi_{28900}(2729,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{401}{680}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{61}{340}\right)\)	\(e\left(\frac{43}{680}\right)\)	\(e\left(\frac{24}{85}\right)\)	\(e\left(\frac{87}{340}\right)\)	\(e\left(\frac{169}{170}\right)\)	\(e\left(\frac{343}{680}\right)\)	\(e\left(\frac{523}{680}\right)\)	\(e\left(\frac{281}{680}\right)\)
\(\chi_{28900}(2769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{659}{680}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{319}{340}\right)\)	\(e\left(\frac{537}{680}\right)\)	\(e\left(\frac{21}{85}\right)\)	\(e\left(\frac{193}{340}\right)\)	\(e\left(\frac{31}{170}\right)\)	\(e\left(\frac{77}{680}\right)\)	\(e\left(\frac{617}{680}\right)\)	\(e\left(\frac{299}{680}\right)\)
\(\chi_{28900}(2909,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{647}{680}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{307}{340}\right)\)	\(e\left(\frac{261}{680}\right)\)	\(e\left(\frac{33}{85}\right)\)	\(e\left(\frac{109}{340}\right)\)	\(e\left(\frac{73}{170}\right)\)	\(e\left(\frac{121}{680}\right)\)	\(e\left(\frac{581}{680}\right)\)	\(e\left(\frac{567}{680}\right)\)
\(\chi_{28900}(3109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{347}{680}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{7}{340}\right)\)	\(e\left(\frac{161}{680}\right)\)	\(e\left(\frac{78}{85}\right)\)	\(e\left(\frac{49}{340}\right)\)	\(e\left(\frac{103}{170}\right)\)	\(e\left(\frac{541}{680}\right)\)	\(e\left(\frac{361}{680}\right)\)	\(e\left(\frac{467}{680}\right)\)
\(\chi_{28900}(3409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{177}{680}\right)\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{177}{340}\right)\)	\(e\left(\frac{331}{680}\right)\)	\(e\left(\frac{78}{85}\right)\)	\(e\left(\frac{219}{340}\right)\)	\(e\left(\frac{103}{170}\right)\)	\(e\left(\frac{31}{680}\right)\)	\(e\left(\frac{531}{680}\right)\)	\(e\left(\frac{297}{680}\right)\)
\(\chi_{28900}(3589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{183}{680}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{183}{340}\right)\)	\(e\left(\frac{469}{680}\right)\)	\(e\left(\frac{72}{85}\right)\)	\(e\left(\frac{261}{340}\right)\)	\(e\left(\frac{167}{170}\right)\)	\(e\left(\frac{9}{680}\right)\)	\(e\left(\frac{549}{680}\right)\)	\(e\left(\frac{503}{680}\right)\)

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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.ff
Modulus	$28900$
Conductor	$7225$
Order	$680$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(28900\)
Conductor:	\(7225\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(680\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 7225.co	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)