LMFDB - Dirichlet character orbit 85600.go

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(85600, base_ring=CyclotomicField(530)) M = H._module chi = DirichletCharacter(H, M([265,0,212,135])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(31,85600)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$85600$
Conductor:	$10700$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$530$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 10700.bl	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:	$\Q(\zeta_{265})$
Fixed field:	Number field defined by a degree 530 polynomial (not computed)

First 31 of 208 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{85600}(31,\cdot)$	$1$	$1$	$e\left(\frac{69}{530}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{69}{265}\right)$	$e\left(\frac{267}{530}\right)$	$e\left(\frac{44}{265}\right)$	$e\left(\frac{311}{530}\right)$	$e\left(\frac{301}{530}\right)$	$e\left(\frac{309}{530}\right)$	$e\left(\frac{367}{530}\right)$	$e\left(\frac{207}{530}\right)$
$\chi_{85600}(191,\cdot)$	$1$	$1$	$e\left(\frac{447}{530}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{182}{265}\right)$	$e\left(\frac{301}{530}\right)$	$e\left(\frac{262}{265}\right)$	$e\left(\frac{33}{530}\right)$	$e\left(\frac{383}{530}\right)$	$e\left(\frac{527}{530}\right)$	$e\left(\frac{511}{530}\right)$	$e\left(\frac{281}{530}\right)$
$\chi_{85600}(831,\cdot)$	$1$	$1$	$e\left(\frac{199}{530}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{199}{265}\right)$	$e\left(\frac{217}{530}\right)$	$e\left(\frac{4}{265}\right)$	$e\left(\frac{221}{530}\right)$	$e\left(\frac{461}{530}\right)$	$e\left(\frac{269}{530}\right)$	$e\left(\frac{467}{530}\right)$	$e\left(\frac{67}{530}\right)$
$\chi_{85600}(991,\cdot)$	$1$	$1$	$e\left(\frac{327}{530}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{62}{265}\right)$	$e\left(\frac{21}{530}\right)$	$e\left(\frac{197}{265}\right)$	$e\left(\frac{483}{530}\right)$	$e\left(\frac{113}{530}\right)$	$e\left(\frac{197}{530}\right)$	$e\left(\frac{11}{530}\right)$	$e\left(\frac{451}{530}\right)$
$\chi_{85600}(1471,\cdot)$	$1$	$1$	$e\left(\frac{201}{530}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{201}{265}\right)$	$e\left(\frac{363}{530}\right)$	$e\left(\frac{36}{265}\right)$	$e\left(\frac{399}{530}\right)$	$e\left(\frac{439}{530}\right)$	$e\left(\frac{301}{530}\right)$	$e\left(\frac{493}{530}\right)$	$e\left(\frac{73}{530}\right)$
$\chi_{85600}(1631,\cdot)$	$1$	$1$	$e\left(\frac{109}{530}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{109}{265}\right)$	$e\left(\frac{7}{530}\right)$	$e\left(\frac{154}{265}\right)$	$e\left(\frac{161}{530}\right)$	$e\left(\frac{391}{530}\right)$	$e\left(\frac{419}{530}\right)$	$e\left(\frac{357}{530}\right)$	$e\left(\frac{327}{530}\right)$
$\chi_{85600}(2111,\cdot)$	$1$	$1$	$e\left(\frac{123}{530}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{123}{265}\right)$	$e\left(\frac{499}{530}\right)$	$e\left(\frac{113}{265}\right)$	$e\left(\frac{347}{530}\right)$	$e\left(\frac{237}{530}\right)$	$e\left(\frac{113}{530}\right)$	$e\left(\frac{9}{530}\right)$	$e\left(\frac{369}{530}\right)$
$\chi_{85600}(2271,\cdot)$	$1$	$1$	$e\left(\frac{481}{530}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{216}{265}\right)$	$e\left(\frac{133}{530}\right)$	$e\left(\frac{11}{265}\right)$	$e\left(\frac{409}{530}\right)$	$e\left(\frac{9}{530}\right)$	$e\left(\frac{11}{530}\right)$	$e\left(\frac{423}{530}\right)$	$e\left(\frac{383}{530}\right)$
$\chi_{85600}(2431,\cdot)$	$1$	$1$	$e\left(\frac{119}{530}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{119}{265}\right)$	$e\left(\frac{207}{530}\right)$	$e\left(\frac{49}{265}\right)$	$e\left(\frac{521}{530}\right)$	$e\left(\frac{281}{530}\right)$	$e\left(\frac{49}{530}\right)$	$e\left(\frac{487}{530}\right)$	$e\left(\frac{357}{530}\right)$
$\chi_{85600}(2911,\cdot)$	$1$	$1$	$e\left(\frac{153}{530}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{153}{265}\right)$	$e\left(\frac{39}{530}\right)$	$e\left(\frac{63}{265}\right)$	$e\left(\frac{367}{530}\right)$	$e\left(\frac{437}{530}\right)$	$e\left(\frac{63}{530}\right)$	$e\left(\frac{399}{530}\right)$	$e\left(\frac{459}{530}\right)$
$\chi_{85600}(3231,\cdot)$	$1$	$1$	$e\left(\frac{489}{530}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{224}{265}\right)$	$e\left(\frac{187}{530}\right)$	$e\left(\frac{139}{265}\right)$	$e\left(\frac{61}{530}\right)$	$e\left(\frac{451}{530}\right)$	$e\left(\frac{139}{530}\right)$	$e\left(\frac{527}{530}\right)$	$e\left(\frac{407}{530}\right)$
$\chi_{85600}(3391,\cdot)$	$1$	$1$	$e\left(\frac{347}{530}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{82}{265}\right)$	$e\left(\frac{421}{530}\right)$	$e\left(\frac{252}{265}\right)$	$e\left(\frac{143}{530}\right)$	$e\left(\frac{423}{530}\right)$	$e\left(\frac{517}{530}\right)$	$e\left(\frac{271}{530}\right)$	$e\left(\frac{511}{530}\right)$
$\chi_{85600}(3711,\cdot)$	$1$	$1$	$e\left(\frac{483}{530}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{218}{265}\right)$	$e\left(\frac{279}{530}\right)$	$e\left(\frac{43}{265}\right)$	$e\left(\frac{57}{530}\right)$	$e\left(\frac{517}{530}\right)$	$e\left(\frac{43}{530}\right)$	$e\left(\frac{449}{530}\right)$	$e\left(\frac{389}{530}\right)$
$\chi_{85600}(4031,\cdot)$	$1$	$1$	$e\left(\frac{389}{530}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{124}{265}\right)$	$e\left(\frac{307}{530}\right)$	$e\left(\frac{129}{265}\right)$	$e\left(\frac{171}{530}\right)$	$e\left(\frac{491}{530}\right)$	$e\left(\frac{129}{530}\right)$	$e\left(\frac{287}{530}\right)$	$e\left(\frac{107}{530}\right)$
$\chi_{85600}(4191,\cdot)$	$1$	$1$	$e\left(\frac{7}{530}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{7}{265}\right)$	$e\left(\frac{511}{530}\right)$	$e\left(\frac{112}{265}\right)$	$e\left(\frac{93}{530}\right)$	$e\left(\frac{453}{530}\right)$	$e\left(\frac{377}{530}\right)$	$e\left(\frac{91}{530}\right)$	$e\left(\frac{21}{530}\right)$
$\chi_{85600}(4511,\cdot)$	$1$	$1$	$e\left(\frac{133}{530}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{133}{265}\right)$	$e\left(\frac{169}{530}\right)$	$e\left(\frac{8}{265}\right)$	$e\left(\frac{177}{530}\right)$	$e\left(\frac{127}{530}\right)$	$e\left(\frac{273}{530}\right)$	$e\left(\frac{139}{530}\right)$	$e\left(\frac{399}{530}\right)$
$\chi_{85600}(4671,\cdot)$	$1$	$1$	$e\left(\frac{421}{530}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{156}{265}\right)$	$e\left(\frac{523}{530}\right)$	$e\left(\frac{111}{265}\right)$	$e\left(\frac{369}{530}\right)$	$e\left(\frac{139}{530}\right)$	$e\left(\frac{111}{530}\right)$	$e\left(\frac{173}{530}\right)$	$e\left(\frac{203}{530}\right)$
$\chi_{85600}(5311,\cdot)$	$1$	$1$	$e\left(\frac{303}{530}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{38}{265}\right)$	$e\left(\frac{389}{530}\right)$	$e\left(\frac{78}{265}\right)$	$e\left(\frac{467}{530}\right)$	$e\left(\frac{377}{530}\right)$	$e\left(\frac{343}{530}\right)$	$e\left(\frac{229}{530}\right)$	$e\left(\frac{379}{530}\right)$
$\chi_{85600}(5631,\cdot)$	$1$	$1$	$e\left(\frac{169}{530}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{169}{265}\right)$	$e\left(\frac{147}{530}\right)$	$e\left(\frac{54}{265}\right)$	$e\left(\frac{201}{530}\right)$	$e\left(\frac{261}{530}\right)$	$e\left(\frac{319}{530}\right)$	$e\left(\frac{77}{530}\right)$	$e\left(\frac{507}{530}\right)$
$\chi_{85600}(6271,\cdot)$	$1$	$1$	$e\left(\frac{521}{530}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{256}{265}\right)$	$e\left(\frac{403}{530}\right)$	$e\left(\frac{121}{265}\right)$	$e\left(\frac{259}{530}\right)$	$e\left(\frac{99}{530}\right)$	$e\left(\frac{121}{530}\right)$	$e\left(\frac{413}{530}\right)$	$e\left(\frac{503}{530}\right)$
$\chi_{85600}(6911,\cdot)$	$1$	$1$	$e\left(\frac{503}{530}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{238}{265}\right)$	$e\left(\frac{149}{530}\right)$	$e\left(\frac{98}{265}\right)$	$e\left(\frac{247}{530}\right)$	$e\left(\frac{297}{530}\right)$	$e\left(\frac{363}{530}\right)$	$e\left(\frac{179}{530}\right)$	$e\left(\frac{449}{530}\right)$
$\chi_{85600}(7391,\cdot)$	$1$	$1$	$e\left(\frac{467}{530}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{202}{265}\right)$	$e\left(\frac{171}{530}\right)$	$e\left(\frac{52}{265}\right)$	$e\left(\frac{223}{530}\right)$	$e\left(\frac{163}{530}\right)$	$e\left(\frac{317}{530}\right)$	$e\left(\frac{241}{530}\right)$	$e\left(\frac{341}{530}\right)$
$\chi_{85600}(7711,\cdot)$	$1$	$1$	$e\left(\frac{263}{530}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{263}{265}\right)$	$e\left(\frac{119}{530}\right)$	$e\left(\frac{233}{265}\right)$	$e\left(\frac{87}{530}\right)$	$e\left(\frac{287}{530}\right)$	$e\left(\frac{233}{530}\right)$	$e\left(\frac{239}{530}\right)$	$e\left(\frac{259}{530}\right)$
$\chi_{85600}(7871,\cdot)$	$1$	$1$	$e\left(\frac{151}{530}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{151}{265}\right)$	$e\left(\frac{423}{530}\right)$	$e\left(\frac{31}{265}\right)$	$e\left(\frac{189}{530}\right)$	$e\left(\frac{459}{530}\right)$	$e\left(\frac{31}{530}\right)$	$e\left(\frac{373}{530}\right)$	$e\left(\frac{453}{530}\right)$
$\chi_{85600}(8031,\cdot)$	$1$	$1$	$e\left(\frac{99}{530}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{99}{265}\right)$	$e\left(\frac{337}{530}\right)$	$e\left(\frac{259}{265}\right)$	$e\left(\frac{331}{530}\right)$	$e\left(\frac{501}{530}\right)$	$e\left(\frac{259}{530}\right)$	$e\left(\frac{227}{530}\right)$	$e\left(\frac{297}{530}\right)$
$\chi_{85600}(8191,\cdot)$	$1$	$1$	$e\left(\frac{407}{530}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{142}{265}\right)$	$e\left(\frac{31}{530}\right)$	$e\left(\frac{152}{265}\right)$	$e\left(\frac{183}{530}\right)$	$e\left(\frac{293}{530}\right)$	$e\left(\frac{417}{530}\right)$	$e\left(\frac{521}{530}\right)$	$e\left(\frac{161}{530}\right)$
$\chi_{85600}(8511,\cdot)$	$1$	$1$	$e\left(\frac{473}{530}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{208}{265}\right)$	$e\left(\frac{79}{530}\right)$	$e\left(\frac{148}{265}\right)$	$e\left(\frac{227}{530}\right)$	$e\left(\frac{97}{530}\right)$	$e\left(\frac{413}{530}\right)$	$e\left(\frac{319}{530}\right)$	$e\left(\frac{359}{530}\right)$
$\chi_{85600}(9311,\cdot)$	$1$	$1$	$e\left(\frac{403}{530}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{138}{265}\right)$	$e\left(\frac{269}{530}\right)$	$e\left(\frac{88}{265}\right)$	$e\left(\frac{357}{530}\right)$	$e\left(\frac{337}{530}\right)$	$e\left(\frac{353}{530}\right)$	$e\left(\frac{469}{530}\right)$	$e\left(\frac{149}{530}\right)$
$\chi_{85600}(9471,\cdot)$	$1$	$1$	$e\left(\frac{141}{530}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{141}{265}\right)$	$e\left(\frac{223}{530}\right)$	$e\left(\frac{136}{265}\right)$	$e\left(\frac{359}{530}\right)$	$e\left(\frac{39}{530}\right)$	$e\left(\frac{401}{530}\right)$	$e\left(\frac{243}{530}\right)$	$e\left(\frac{423}{530}\right)$
$\chi_{85600}(9791,\cdot)$	$1$	$1$	$e\left(\frac{127}{530}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{127}{265}\right)$	$e\left(\frac{261}{530}\right)$	$e\left(\frac{177}{265}\right)$	$e\left(\frac{173}{530}\right)$	$e\left(\frac{193}{530}\right)$	$e\left(\frac{177}{530}\right)$	$e\left(\frac{61}{530}\right)$	$e\left(\frac{381}{530}\right)$
$\chi_{85600}(10911,\cdot)$	$1$	$1$	$e\left(\frac{173}{530}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{173}{265}\right)$	$e\left(\frac{439}{530}\right)$	$e\left(\frac{118}{265}\right)$	$e\left(\frac{27}{530}\right)$	$e\left(\frac{217}{530}\right)$	$e\left(\frac{383}{530}\right)$	$e\left(\frac{129}{530}\right)$	$e\left(\frac{519}{530}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{85600}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{530}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{69}{265}\right)\)	\(e\left(\frac{267}{530}\right)\)	\(e\left(\frac{44}{265}\right)\)	\(e\left(\frac{311}{530}\right)\)	\(e\left(\frac{301}{530}\right)\)	\(e\left(\frac{309}{530}\right)\)	\(e\left(\frac{367}{530}\right)\)	\(e\left(\frac{207}{530}\right)\)
\(\chi_{85600}(191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{447}{530}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{182}{265}\right)\)	\(e\left(\frac{301}{530}\right)\)	\(e\left(\frac{262}{265}\right)\)	\(e\left(\frac{33}{530}\right)\)	\(e\left(\frac{383}{530}\right)\)	\(e\left(\frac{527}{530}\right)\)	\(e\left(\frac{511}{530}\right)\)	\(e\left(\frac{281}{530}\right)\)
\(\chi_{85600}(831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{530}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{199}{265}\right)\)	\(e\left(\frac{217}{530}\right)\)	\(e\left(\frac{4}{265}\right)\)	\(e\left(\frac{221}{530}\right)\)	\(e\left(\frac{461}{530}\right)\)	\(e\left(\frac{269}{530}\right)\)	\(e\left(\frac{467}{530}\right)\)	\(e\left(\frac{67}{530}\right)\)
\(\chi_{85600}(991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{327}{530}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{62}{265}\right)\)	\(e\left(\frac{21}{530}\right)\)	\(e\left(\frac{197}{265}\right)\)	\(e\left(\frac{483}{530}\right)\)	\(e\left(\frac{113}{530}\right)\)	\(e\left(\frac{197}{530}\right)\)	\(e\left(\frac{11}{530}\right)\)	\(e\left(\frac{451}{530}\right)\)
\(\chi_{85600}(1471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{201}{530}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{201}{265}\right)\)	\(e\left(\frac{363}{530}\right)\)	\(e\left(\frac{36}{265}\right)\)	\(e\left(\frac{399}{530}\right)\)	\(e\left(\frac{439}{530}\right)\)	\(e\left(\frac{301}{530}\right)\)	\(e\left(\frac{493}{530}\right)\)	\(e\left(\frac{73}{530}\right)\)
\(\chi_{85600}(1631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{530}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{109}{265}\right)\)	\(e\left(\frac{7}{530}\right)\)	\(e\left(\frac{154}{265}\right)\)	\(e\left(\frac{161}{530}\right)\)	\(e\left(\frac{391}{530}\right)\)	\(e\left(\frac{419}{530}\right)\)	\(e\left(\frac{357}{530}\right)\)	\(e\left(\frac{327}{530}\right)\)
\(\chi_{85600}(2111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{530}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{123}{265}\right)\)	\(e\left(\frac{499}{530}\right)\)	\(e\left(\frac{113}{265}\right)\)	\(e\left(\frac{347}{530}\right)\)	\(e\left(\frac{237}{530}\right)\)	\(e\left(\frac{113}{530}\right)\)	\(e\left(\frac{9}{530}\right)\)	\(e\left(\frac{369}{530}\right)\)
\(\chi_{85600}(2271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{481}{530}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{216}{265}\right)\)	\(e\left(\frac{133}{530}\right)\)	\(e\left(\frac{11}{265}\right)\)	\(e\left(\frac{409}{530}\right)\)	\(e\left(\frac{9}{530}\right)\)	\(e\left(\frac{11}{530}\right)\)	\(e\left(\frac{423}{530}\right)\)	\(e\left(\frac{383}{530}\right)\)
\(\chi_{85600}(2431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{530}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{119}{265}\right)\)	\(e\left(\frac{207}{530}\right)\)	\(e\left(\frac{49}{265}\right)\)	\(e\left(\frac{521}{530}\right)\)	\(e\left(\frac{281}{530}\right)\)	\(e\left(\frac{49}{530}\right)\)	\(e\left(\frac{487}{530}\right)\)	\(e\left(\frac{357}{530}\right)\)
\(\chi_{85600}(2911,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{153}{530}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{153}{265}\right)\)	\(e\left(\frac{39}{530}\right)\)	\(e\left(\frac{63}{265}\right)\)	\(e\left(\frac{367}{530}\right)\)	\(e\left(\frac{437}{530}\right)\)	\(e\left(\frac{63}{530}\right)\)	\(e\left(\frac{399}{530}\right)\)	\(e\left(\frac{459}{530}\right)\)
\(\chi_{85600}(3231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{489}{530}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{224}{265}\right)\)	\(e\left(\frac{187}{530}\right)\)	\(e\left(\frac{139}{265}\right)\)	\(e\left(\frac{61}{530}\right)\)	\(e\left(\frac{451}{530}\right)\)	\(e\left(\frac{139}{530}\right)\)	\(e\left(\frac{527}{530}\right)\)	\(e\left(\frac{407}{530}\right)\)
\(\chi_{85600}(3391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{347}{530}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{82}{265}\right)\)	\(e\left(\frac{421}{530}\right)\)	\(e\left(\frac{252}{265}\right)\)	\(e\left(\frac{143}{530}\right)\)	\(e\left(\frac{423}{530}\right)\)	\(e\left(\frac{517}{530}\right)\)	\(e\left(\frac{271}{530}\right)\)	\(e\left(\frac{511}{530}\right)\)
\(\chi_{85600}(3711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{483}{530}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{218}{265}\right)\)	\(e\left(\frac{279}{530}\right)\)	\(e\left(\frac{43}{265}\right)\)	\(e\left(\frac{57}{530}\right)\)	\(e\left(\frac{517}{530}\right)\)	\(e\left(\frac{43}{530}\right)\)	\(e\left(\frac{449}{530}\right)\)	\(e\left(\frac{389}{530}\right)\)
\(\chi_{85600}(4031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{389}{530}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{124}{265}\right)\)	\(e\left(\frac{307}{530}\right)\)	\(e\left(\frac{129}{265}\right)\)	\(e\left(\frac{171}{530}\right)\)	\(e\left(\frac{491}{530}\right)\)	\(e\left(\frac{129}{530}\right)\)	\(e\left(\frac{287}{530}\right)\)	\(e\left(\frac{107}{530}\right)\)
\(\chi_{85600}(4191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{530}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{7}{265}\right)\)	\(e\left(\frac{511}{530}\right)\)	\(e\left(\frac{112}{265}\right)\)	\(e\left(\frac{93}{530}\right)\)	\(e\left(\frac{453}{530}\right)\)	\(e\left(\frac{377}{530}\right)\)	\(e\left(\frac{91}{530}\right)\)	\(e\left(\frac{21}{530}\right)\)
\(\chi_{85600}(4511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{530}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{133}{265}\right)\)	\(e\left(\frac{169}{530}\right)\)	\(e\left(\frac{8}{265}\right)\)	\(e\left(\frac{177}{530}\right)\)	\(e\left(\frac{127}{530}\right)\)	\(e\left(\frac{273}{530}\right)\)	\(e\left(\frac{139}{530}\right)\)	\(e\left(\frac{399}{530}\right)\)
\(\chi_{85600}(4671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{421}{530}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{156}{265}\right)\)	\(e\left(\frac{523}{530}\right)\)	\(e\left(\frac{111}{265}\right)\)	\(e\left(\frac{369}{530}\right)\)	\(e\left(\frac{139}{530}\right)\)	\(e\left(\frac{111}{530}\right)\)	\(e\left(\frac{173}{530}\right)\)	\(e\left(\frac{203}{530}\right)\)
\(\chi_{85600}(5311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{303}{530}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{38}{265}\right)\)	\(e\left(\frac{389}{530}\right)\)	\(e\left(\frac{78}{265}\right)\)	\(e\left(\frac{467}{530}\right)\)	\(e\left(\frac{377}{530}\right)\)	\(e\left(\frac{343}{530}\right)\)	\(e\left(\frac{229}{530}\right)\)	\(e\left(\frac{379}{530}\right)\)
\(\chi_{85600}(5631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{530}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{169}{265}\right)\)	\(e\left(\frac{147}{530}\right)\)	\(e\left(\frac{54}{265}\right)\)	\(e\left(\frac{201}{530}\right)\)	\(e\left(\frac{261}{530}\right)\)	\(e\left(\frac{319}{530}\right)\)	\(e\left(\frac{77}{530}\right)\)	\(e\left(\frac{507}{530}\right)\)
\(\chi_{85600}(6271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{521}{530}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{256}{265}\right)\)	\(e\left(\frac{403}{530}\right)\)	\(e\left(\frac{121}{265}\right)\)	\(e\left(\frac{259}{530}\right)\)	\(e\left(\frac{99}{530}\right)\)	\(e\left(\frac{121}{530}\right)\)	\(e\left(\frac{413}{530}\right)\)	\(e\left(\frac{503}{530}\right)\)
\(\chi_{85600}(6911,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{503}{530}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{238}{265}\right)\)	\(e\left(\frac{149}{530}\right)\)	\(e\left(\frac{98}{265}\right)\)	\(e\left(\frac{247}{530}\right)\)	\(e\left(\frac{297}{530}\right)\)	\(e\left(\frac{363}{530}\right)\)	\(e\left(\frac{179}{530}\right)\)	\(e\left(\frac{449}{530}\right)\)
\(\chi_{85600}(7391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{467}{530}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{202}{265}\right)\)	\(e\left(\frac{171}{530}\right)\)	\(e\left(\frac{52}{265}\right)\)	\(e\left(\frac{223}{530}\right)\)	\(e\left(\frac{163}{530}\right)\)	\(e\left(\frac{317}{530}\right)\)	\(e\left(\frac{241}{530}\right)\)	\(e\left(\frac{341}{530}\right)\)
\(\chi_{85600}(7711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{263}{530}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{263}{265}\right)\)	\(e\left(\frac{119}{530}\right)\)	\(e\left(\frac{233}{265}\right)\)	\(e\left(\frac{87}{530}\right)\)	\(e\left(\frac{287}{530}\right)\)	\(e\left(\frac{233}{530}\right)\)	\(e\left(\frac{239}{530}\right)\)	\(e\left(\frac{259}{530}\right)\)
\(\chi_{85600}(7871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{530}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{151}{265}\right)\)	\(e\left(\frac{423}{530}\right)\)	\(e\left(\frac{31}{265}\right)\)	\(e\left(\frac{189}{530}\right)\)	\(e\left(\frac{459}{530}\right)\)	\(e\left(\frac{31}{530}\right)\)	\(e\left(\frac{373}{530}\right)\)	\(e\left(\frac{453}{530}\right)\)
\(\chi_{85600}(8031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{530}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{99}{265}\right)\)	\(e\left(\frac{337}{530}\right)\)	\(e\left(\frac{259}{265}\right)\)	\(e\left(\frac{331}{530}\right)\)	\(e\left(\frac{501}{530}\right)\)	\(e\left(\frac{259}{530}\right)\)	\(e\left(\frac{227}{530}\right)\)	\(e\left(\frac{297}{530}\right)\)
\(\chi_{85600}(8191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{407}{530}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{142}{265}\right)\)	\(e\left(\frac{31}{530}\right)\)	\(e\left(\frac{152}{265}\right)\)	\(e\left(\frac{183}{530}\right)\)	\(e\left(\frac{293}{530}\right)\)	\(e\left(\frac{417}{530}\right)\)	\(e\left(\frac{521}{530}\right)\)	\(e\left(\frac{161}{530}\right)\)
\(\chi_{85600}(8511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{473}{530}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{208}{265}\right)\)	\(e\left(\frac{79}{530}\right)\)	\(e\left(\frac{148}{265}\right)\)	\(e\left(\frac{227}{530}\right)\)	\(e\left(\frac{97}{530}\right)\)	\(e\left(\frac{413}{530}\right)\)	\(e\left(\frac{319}{530}\right)\)	\(e\left(\frac{359}{530}\right)\)
\(\chi_{85600}(9311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{403}{530}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{138}{265}\right)\)	\(e\left(\frac{269}{530}\right)\)	\(e\left(\frac{88}{265}\right)\)	\(e\left(\frac{357}{530}\right)\)	\(e\left(\frac{337}{530}\right)\)	\(e\left(\frac{353}{530}\right)\)	\(e\left(\frac{469}{530}\right)\)	\(e\left(\frac{149}{530}\right)\)
\(\chi_{85600}(9471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{141}{530}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{141}{265}\right)\)	\(e\left(\frac{223}{530}\right)\)	\(e\left(\frac{136}{265}\right)\)	\(e\left(\frac{359}{530}\right)\)	\(e\left(\frac{39}{530}\right)\)	\(e\left(\frac{401}{530}\right)\)	\(e\left(\frac{243}{530}\right)\)	\(e\left(\frac{423}{530}\right)\)
\(\chi_{85600}(9791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{530}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{127}{265}\right)\)	\(e\left(\frac{261}{530}\right)\)	\(e\left(\frac{177}{265}\right)\)	\(e\left(\frac{173}{530}\right)\)	\(e\left(\frac{193}{530}\right)\)	\(e\left(\frac{177}{530}\right)\)	\(e\left(\frac{61}{530}\right)\)	\(e\left(\frac{381}{530}\right)\)
\(\chi_{85600}(10911,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{530}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{173}{265}\right)\)	\(e\left(\frac{439}{530}\right)\)	\(e\left(\frac{118}{265}\right)\)	\(e\left(\frac{27}{530}\right)\)	\(e\left(\frac{217}{530}\right)\)	\(e\left(\frac{383}{530}\right)\)	\(e\left(\frac{129}{530}\right)\)	\(e\left(\frac{519}{530}\right)\)

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First 31 of 208 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	85600.go
Modulus	$85600$
Conductor	$10700$
Order	$530$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(85600\)
Conductor:	\(10700\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(530\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 10700.bl	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)