LMFDB - Dirichlet character orbit 16700.bd

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16700, base_ring=CyclotomicField(166)) M = H._module chi = DirichletCharacter(H, M([0,83,70])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(49, 16700)) 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("16700.49"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$16700$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$835$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$166$	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:	no, induced from 835.j	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{83})$
Fixed field:	Number field defined by a degree 166 polynomial (not computed)

First 31 of 82 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{16700}(49,\cdot)$	$1$	$1$	$e\left(\frac{23}{166}\right)$	$e\left(\frac{43}{166}\right)$	$e\left(\frac{23}{83}\right)$	$e\left(\frac{67}{83}\right)$	$e\left(\frac{155}{166}\right)$	$e\left(\frac{141}{166}\right)$	$e\left(\frac{38}{83}\right)$	$e\left(\frac{33}{83}\right)$	$e\left(\frac{41}{166}\right)$	$e\left(\frac{69}{166}\right)$
$\chi_{16700}(449,\cdot)$	$1$	$1$	$e\left(\frac{21}{166}\right)$	$e\left(\frac{97}{166}\right)$	$e\left(\frac{21}{83}\right)$	$e\left(\frac{72}{83}\right)$	$e\left(\frac{91}{166}\right)$	$e\left(\frac{71}{166}\right)$	$e\left(\frac{78}{83}\right)$	$e\left(\frac{59}{83}\right)$	$e\left(\frac{23}{166}\right)$	$e\left(\frac{63}{166}\right)$
$\chi_{16700}(549,\cdot)$	$1$	$1$	$e\left(\frac{55}{166}\right)$	$e\left(\frac{9}{166}\right)$	$e\left(\frac{55}{83}\right)$	$e\left(\frac{70}{83}\right)$	$e\left(\frac{17}{166}\right)$	$e\left(\frac{99}{166}\right)$	$e\left(\frac{62}{83}\right)$	$e\left(\frac{32}{83}\right)$	$e\left(\frac{163}{166}\right)$	$e\left(\frac{165}{166}\right)$
$\chi_{16700}(749,\cdot)$	$1$	$1$	$e\left(\frac{69}{166}\right)$	$e\left(\frac{129}{166}\right)$	$e\left(\frac{69}{83}\right)$	$e\left(\frac{35}{83}\right)$	$e\left(\frac{133}{166}\right)$	$e\left(\frac{91}{166}\right)$	$e\left(\frac{31}{83}\right)$	$e\left(\frac{16}{83}\right)$	$e\left(\frac{123}{166}\right)$	$e\left(\frac{41}{166}\right)$
$\chi_{16700}(849,\cdot)$	$1$	$1$	$e\left(\frac{161}{166}\right)$	$e\left(\frac{135}{166}\right)$	$e\left(\frac{78}{83}\right)$	$e\left(\frac{54}{83}\right)$	$e\left(\frac{89}{166}\right)$	$e\left(\frac{157}{166}\right)$	$e\left(\frac{17}{83}\right)$	$e\left(\frac{65}{83}\right)$	$e\left(\frac{121}{166}\right)$	$e\left(\frac{151}{166}\right)$
$\chi_{16700}(949,\cdot)$	$1$	$1$	$e\left(\frac{37}{166}\right)$	$e\left(\frac{163}{166}\right)$	$e\left(\frac{37}{83}\right)$	$e\left(\frac{32}{83}\right)$	$e\left(\frac{105}{166}\right)$	$e\left(\frac{133}{166}\right)$	$e\left(\frac{7}{83}\right)$	$e\left(\frac{17}{83}\right)$	$e\left(\frac{1}{166}\right)$	$e\left(\frac{111}{166}\right)$
$\chi_{16700}(1049,\cdot)$	$1$	$1$	$e\left(\frac{41}{166}\right)$	$e\left(\frac{55}{166}\right)$	$e\left(\frac{41}{83}\right)$	$e\left(\frac{22}{83}\right)$	$e\left(\frac{67}{166}\right)$	$e\left(\frac{107}{166}\right)$	$e\left(\frac{10}{83}\right)$	$e\left(\frac{48}{83}\right)$	$e\left(\frac{37}{166}\right)$	$e\left(\frac{123}{166}\right)$
$\chi_{16700}(1149,\cdot)$	$1$	$1$	$e\left(\frac{61}{166}\right)$	$e\left(\frac{13}{166}\right)$	$e\left(\frac{61}{83}\right)$	$e\left(\frac{55}{83}\right)$	$e\left(\frac{43}{166}\right)$	$e\left(\frac{143}{166}\right)$	$e\left(\frac{25}{83}\right)$	$e\left(\frac{37}{83}\right)$	$e\left(\frac{51}{166}\right)$	$e\left(\frac{17}{166}\right)$
$\chi_{16700}(1849,\cdot)$	$1$	$1$	$e\left(\frac{5}{166}\right)$	$e\left(\frac{31}{166}\right)$	$e\left(\frac{5}{83}\right)$	$e\left(\frac{29}{83}\right)$	$e\left(\frac{77}{166}\right)$	$e\left(\frac{9}{166}\right)$	$e\left(\frac{66}{83}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{45}{166}\right)$	$e\left(\frac{15}{166}\right)$
$\chi_{16700}(1949,\cdot)$	$1$	$1$	$e\left(\frac{153}{166}\right)$	$e\left(\frac{19}{166}\right)$	$e\left(\frac{70}{83}\right)$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{165}{166}\right)$	$e\left(\frac{43}{166}\right)$	$e\left(\frac{11}{83}\right)$	$e\left(\frac{3}{83}\right)$	$e\left(\frac{49}{166}\right)$	$e\left(\frac{127}{166}\right)$
$\chi_{16700}(2349,\cdot)$	$1$	$1$	$e\left(\frac{59}{166}\right)$	$e\left(\frac{67}{166}\right)$	$e\left(\frac{59}{83}\right)$	$e\left(\frac{60}{83}\right)$	$e\left(\frac{145}{166}\right)$	$e\left(\frac{73}{166}\right)$	$e\left(\frac{65}{83}\right)$	$e\left(\frac{63}{83}\right)$	$e\left(\frac{33}{166}\right)$	$e\left(\frac{11}{166}\right)$
$\chi_{16700}(2549,\cdot)$	$1$	$1$	$e\left(\frac{109}{166}\right)$	$e\left(\frac{45}{166}\right)$	$e\left(\frac{26}{83}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{85}{166}\right)$	$e\left(\frac{163}{166}\right)$	$e\left(\frac{61}{83}\right)$	$e\left(\frac{77}{83}\right)$	$e\left(\frac{151}{166}\right)$	$e\left(\frac{161}{166}\right)$
$\chi_{16700}(2649,\cdot)$	$1$	$1$	$e\left(\frac{93}{166}\right)$	$e\left(\frac{145}{166}\right)$	$e\left(\frac{10}{83}\right)$	$e\left(\frac{58}{83}\right)$	$e\left(\frac{71}{166}\right)$	$e\left(\frac{101}{166}\right)$	$e\left(\frac{49}{83}\right)$	$e\left(\frac{36}{83}\right)$	$e\left(\frac{7}{166}\right)$	$e\left(\frac{113}{166}\right)$
$\chi_{16700}(2749,\cdot)$	$1$	$1$	$e\left(\frac{29}{166}\right)$	$e\left(\frac{47}{166}\right)$	$e\left(\frac{29}{83}\right)$	$e\left(\frac{52}{83}\right)$	$e\left(\frac{15}{166}\right)$	$e\left(\frac{19}{166}\right)$	$e\left(\frac{1}{83}\right)$	$e\left(\frac{38}{83}\right)$	$e\left(\frac{95}{166}\right)$	$e\left(\frac{87}{166}\right)$
$\chi_{16700}(3249,\cdot)$	$1$	$1$	$e\left(\frac{107}{166}\right)$	$e\left(\frac{99}{166}\right)$	$e\left(\frac{24}{83}\right)$	$e\left(\frac{23}{83}\right)$	$e\left(\frac{21}{166}\right)$	$e\left(\frac{93}{166}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{20}{83}\right)$	$e\left(\frac{133}{166}\right)$	$e\left(\frac{155}{166}\right)$
$\chi_{16700}(3349,\cdot)$	$1$	$1$	$e\left(\frac{159}{166}\right)$	$e\left(\frac{23}{166}\right)$	$e\left(\frac{76}{83}\right)$	$e\left(\frac{59}{83}\right)$	$e\left(\frac{25}{166}\right)$	$e\left(\frac{87}{166}\right)$	$e\left(\frac{57}{83}\right)$	$e\left(\frac{8}{83}\right)$	$e\left(\frac{103}{166}\right)$	$e\left(\frac{145}{166}\right)$
$\chi_{16700}(3549,\cdot)$	$1$	$1$	$e\left(\frac{33}{166}\right)$	$e\left(\frac{105}{166}\right)$	$e\left(\frac{33}{83}\right)$	$e\left(\frac{42}{83}\right)$	$e\left(\frac{143}{166}\right)$	$e\left(\frac{159}{166}\right)$	$e\left(\frac{4}{83}\right)$	$e\left(\frac{69}{83}\right)$	$e\left(\frac{131}{166}\right)$	$e\left(\frac{99}{166}\right)$
$\chi_{16700}(3749,\cdot)$	$1$	$1$	$e\left(\frac{143}{166}\right)$	$e\left(\frac{123}{166}\right)$	$e\left(\frac{60}{83}\right)$	$e\left(\frac{16}{83}\right)$	$e\left(\frac{11}{166}\right)$	$e\left(\frac{25}{166}\right)$	$e\left(\frac{45}{83}\right)$	$e\left(\frac{50}{83}\right)$	$e\left(\frac{125}{166}\right)$	$e\left(\frac{97}{166}\right)$
$\chi_{16700}(3849,\cdot)$	$1$	$1$	$e\left(\frac{75}{166}\right)$	$e\left(\frac{133}{166}\right)$	$e\left(\frac{75}{83}\right)$	$e\left(\frac{20}{83}\right)$	$e\left(\frac{159}{166}\right)$	$e\left(\frac{135}{166}\right)$	$e\left(\frac{77}{83}\right)$	$e\left(\frac{21}{83}\right)$	$e\left(\frac{11}{166}\right)$	$e\left(\frac{59}{166}\right)$
$\chi_{16700}(3949,\cdot)$	$1$	$1$	$e\left(\frac{81}{166}\right)$	$e\left(\frac{137}{166}\right)$	$e\left(\frac{81}{83}\right)$	$e\left(\frac{5}{83}\right)$	$e\left(\frac{19}{166}\right)$	$e\left(\frac{13}{166}\right)$	$e\left(\frac{40}{83}\right)$	$e\left(\frac{26}{83}\right)$	$e\left(\frac{65}{166}\right)$	$e\left(\frac{77}{166}\right)$
$\chi_{16700}(4149,\cdot)$	$1$	$1$	$e\left(\frac{79}{166}\right)$	$e\left(\frac{25}{166}\right)$	$e\left(\frac{79}{83}\right)$	$e\left(\frac{10}{83}\right)$	$e\left(\frac{121}{166}\right)$	$e\left(\frac{109}{166}\right)$	$e\left(\frac{80}{83}\right)$	$e\left(\frac{52}{83}\right)$	$e\left(\frac{47}{166}\right)$	$e\left(\frac{71}{166}\right)$
$\chi_{16700}(4349,\cdot)$	$1$	$1$	$e\left(\frac{53}{166}\right)$	$e\left(\frac{63}{166}\right)$	$e\left(\frac{53}{83}\right)$	$e\left(\frac{75}{83}\right)$	$e\left(\frac{119}{166}\right)$	$e\left(\frac{29}{166}\right)$	$e\left(\frac{19}{83}\right)$	$e\left(\frac{58}{83}\right)$	$e\left(\frac{145}{166}\right)$	$e\left(\frac{159}{166}\right)$
$\chi_{16700}(4449,\cdot)$	$1$	$1$	$e\left(\frac{99}{166}\right)$	$e\left(\frac{149}{166}\right)$	$e\left(\frac{16}{83}\right)$	$e\left(\frac{43}{83}\right)$	$e\left(\frac{97}{166}\right)$	$e\left(\frac{145}{166}\right)$	$e\left(\frac{12}{83}\right)$	$e\left(\frac{41}{83}\right)$	$e\left(\frac{61}{166}\right)$	$e\left(\frac{131}{166}\right)$
$\chi_{16700}(4849,\cdot)$	$1$	$1$	$e\left(\frac{63}{166}\right)$	$e\left(\frac{125}{166}\right)$	$e\left(\frac{63}{83}\right)$	$e\left(\frac{50}{83}\right)$	$e\left(\frac{107}{166}\right)$	$e\left(\frac{47}{166}\right)$	$e\left(\frac{68}{83}\right)$	$e\left(\frac{11}{83}\right)$	$e\left(\frac{69}{166}\right)$	$e\left(\frac{23}{166}\right)$
$\chi_{16700}(5249,\cdot)$	$1$	$1$	$e\left(\frac{151}{166}\right)$	$e\left(\frac{73}{166}\right)$	$e\left(\frac{68}{83}\right)$	$e\left(\frac{79}{83}\right)$	$e\left(\frac{101}{166}\right)$	$e\left(\frac{139}{166}\right)$	$e\left(\frac{51}{83}\right)$	$e\left(\frac{29}{83}\right)$	$e\left(\frac{31}{166}\right)$	$e\left(\frac{121}{166}\right)$
$\chi_{16700}(5549,\cdot)$	$1$	$1$	$e\left(\frac{165}{166}\right)$	$e\left(\frac{27}{166}\right)$	$e\left(\frac{82}{83}\right)$	$e\left(\frac{44}{83}\right)$	$e\left(\frac{51}{166}\right)$	$e\left(\frac{131}{166}\right)$	$e\left(\frac{20}{83}\right)$	$e\left(\frac{13}{83}\right)$	$e\left(\frac{157}{166}\right)$	$e\left(\frac{163}{166}\right)$
$\chi_{16700}(5849,\cdot)$	$1$	$1$	$e\left(\frac{133}{166}\right)$	$e\left(\frac{61}{166}\right)$	$e\left(\frac{50}{83}\right)$	$e\left(\frac{41}{83}\right)$	$e\left(\frac{23}{166}\right)$	$e\left(\frac{7}{166}\right)$	$e\left(\frac{79}{83}\right)$	$e\left(\frac{14}{83}\right)$	$e\left(\frac{35}{166}\right)$	$e\left(\frac{67}{166}\right)$
$\chi_{16700}(6149,\cdot)$	$1$	$1$	$e\left(\frac{157}{166}\right)$	$e\left(\frac{77}{166}\right)$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{64}{83}\right)$	$e\left(\frac{127}{166}\right)$	$e\left(\frac{17}{166}\right)$	$e\left(\frac{14}{83}\right)$	$e\left(\frac{34}{83}\right)$	$e\left(\frac{85}{166}\right)$	$e\left(\frac{139}{166}\right)$
$\chi_{16700}(6349,\cdot)$	$1$	$1$	$e\left(\frac{121}{166}\right)$	$e\left(\frac{53}{166}\right)$	$e\left(\frac{38}{83}\right)$	$e\left(\frac{71}{83}\right)$	$e\left(\frac{137}{166}\right)$	$e\left(\frac{85}{166}\right)$	$e\left(\frac{70}{83}\right)$	$e\left(\frac{4}{83}\right)$	$e\left(\frac{93}{166}\right)$	$e\left(\frac{31}{166}\right)$
$\chi_{16700}(6549,\cdot)$	$1$	$1$	$e\left(\frac{43}{166}\right)$	$e\left(\frac{1}{166}\right)$	$e\left(\frac{43}{83}\right)$	$e\left(\frac{17}{83}\right)$	$e\left(\frac{131}{166}\right)$	$e\left(\frac{11}{166}\right)$	$e\left(\frac{53}{83}\right)$	$e\left(\frac{22}{83}\right)$	$e\left(\frac{55}{166}\right)$	$e\left(\frac{129}{166}\right)$
$\chi_{16700}(6849,\cdot)$	$1$	$1$	$e\left(\frac{25}{166}\right)$	$e\left(\frac{155}{166}\right)$	$e\left(\frac{25}{83}\right)$	$e\left(\frac{62}{83}\right)$	$e\left(\frac{53}{166}\right)$	$e\left(\frac{45}{166}\right)$	$e\left(\frac{81}{83}\right)$	$e\left(\frac{7}{83}\right)$	$e\left(\frac{59}{166}\right)$	$e\left(\frac{75}{166}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{16700}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{166}\right)\)	\(e\left(\frac{43}{166}\right)\)	\(e\left(\frac{23}{83}\right)\)	\(e\left(\frac{67}{83}\right)\)	\(e\left(\frac{155}{166}\right)\)	\(e\left(\frac{141}{166}\right)\)	\(e\left(\frac{38}{83}\right)\)	\(e\left(\frac{33}{83}\right)\)	\(e\left(\frac{41}{166}\right)\)	\(e\left(\frac{69}{166}\right)\)
\(\chi_{16700}(449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{166}\right)\)	\(e\left(\frac{97}{166}\right)\)	\(e\left(\frac{21}{83}\right)\)	\(e\left(\frac{72}{83}\right)\)	\(e\left(\frac{91}{166}\right)\)	\(e\left(\frac{71}{166}\right)\)	\(e\left(\frac{78}{83}\right)\)	\(e\left(\frac{59}{83}\right)\)	\(e\left(\frac{23}{166}\right)\)	\(e\left(\frac{63}{166}\right)\)
\(\chi_{16700}(549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{166}\right)\)	\(e\left(\frac{9}{166}\right)\)	\(e\left(\frac{55}{83}\right)\)	\(e\left(\frac{70}{83}\right)\)	\(e\left(\frac{17}{166}\right)\)	\(e\left(\frac{99}{166}\right)\)	\(e\left(\frac{62}{83}\right)\)	\(e\left(\frac{32}{83}\right)\)	\(e\left(\frac{163}{166}\right)\)	\(e\left(\frac{165}{166}\right)\)
\(\chi_{16700}(749,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{166}\right)\)	\(e\left(\frac{129}{166}\right)\)	\(e\left(\frac{69}{83}\right)\)	\(e\left(\frac{35}{83}\right)\)	\(e\left(\frac{133}{166}\right)\)	\(e\left(\frac{91}{166}\right)\)	\(e\left(\frac{31}{83}\right)\)	\(e\left(\frac{16}{83}\right)\)	\(e\left(\frac{123}{166}\right)\)	\(e\left(\frac{41}{166}\right)\)
\(\chi_{16700}(849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{166}\right)\)	\(e\left(\frac{135}{166}\right)\)	\(e\left(\frac{78}{83}\right)\)	\(e\left(\frac{54}{83}\right)\)	\(e\left(\frac{89}{166}\right)\)	\(e\left(\frac{157}{166}\right)\)	\(e\left(\frac{17}{83}\right)\)	\(e\left(\frac{65}{83}\right)\)	\(e\left(\frac{121}{166}\right)\)	\(e\left(\frac{151}{166}\right)\)
\(\chi_{16700}(949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{166}\right)\)	\(e\left(\frac{163}{166}\right)\)	\(e\left(\frac{37}{83}\right)\)	\(e\left(\frac{32}{83}\right)\)	\(e\left(\frac{105}{166}\right)\)	\(e\left(\frac{133}{166}\right)\)	\(e\left(\frac{7}{83}\right)\)	\(e\left(\frac{17}{83}\right)\)	\(e\left(\frac{1}{166}\right)\)	\(e\left(\frac{111}{166}\right)\)
\(\chi_{16700}(1049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{166}\right)\)	\(e\left(\frac{55}{166}\right)\)	\(e\left(\frac{41}{83}\right)\)	\(e\left(\frac{22}{83}\right)\)	\(e\left(\frac{67}{166}\right)\)	\(e\left(\frac{107}{166}\right)\)	\(e\left(\frac{10}{83}\right)\)	\(e\left(\frac{48}{83}\right)\)	\(e\left(\frac{37}{166}\right)\)	\(e\left(\frac{123}{166}\right)\)
\(\chi_{16700}(1149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{166}\right)\)	\(e\left(\frac{13}{166}\right)\)	\(e\left(\frac{61}{83}\right)\)	\(e\left(\frac{55}{83}\right)\)	\(e\left(\frac{43}{166}\right)\)	\(e\left(\frac{143}{166}\right)\)	\(e\left(\frac{25}{83}\right)\)	\(e\left(\frac{37}{83}\right)\)	\(e\left(\frac{51}{166}\right)\)	\(e\left(\frac{17}{166}\right)\)
\(\chi_{16700}(1849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{166}\right)\)	\(e\left(\frac{31}{166}\right)\)	\(e\left(\frac{5}{83}\right)\)	\(e\left(\frac{29}{83}\right)\)	\(e\left(\frac{77}{166}\right)\)	\(e\left(\frac{9}{166}\right)\)	\(e\left(\frac{66}{83}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{45}{166}\right)\)	\(e\left(\frac{15}{166}\right)\)
\(\chi_{16700}(1949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{153}{166}\right)\)	\(e\left(\frac{19}{166}\right)\)	\(e\left(\frac{70}{83}\right)\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{165}{166}\right)\)	\(e\left(\frac{43}{166}\right)\)	\(e\left(\frac{11}{83}\right)\)	\(e\left(\frac{3}{83}\right)\)	\(e\left(\frac{49}{166}\right)\)	\(e\left(\frac{127}{166}\right)\)
\(\chi_{16700}(2349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{166}\right)\)	\(e\left(\frac{67}{166}\right)\)	\(e\left(\frac{59}{83}\right)\)	\(e\left(\frac{60}{83}\right)\)	\(e\left(\frac{145}{166}\right)\)	\(e\left(\frac{73}{166}\right)\)	\(e\left(\frac{65}{83}\right)\)	\(e\left(\frac{63}{83}\right)\)	\(e\left(\frac{33}{166}\right)\)	\(e\left(\frac{11}{166}\right)\)
\(\chi_{16700}(2549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{166}\right)\)	\(e\left(\frac{45}{166}\right)\)	\(e\left(\frac{26}{83}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{85}{166}\right)\)	\(e\left(\frac{163}{166}\right)\)	\(e\left(\frac{61}{83}\right)\)	\(e\left(\frac{77}{83}\right)\)	\(e\left(\frac{151}{166}\right)\)	\(e\left(\frac{161}{166}\right)\)
\(\chi_{16700}(2649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{166}\right)\)	\(e\left(\frac{145}{166}\right)\)	\(e\left(\frac{10}{83}\right)\)	\(e\left(\frac{58}{83}\right)\)	\(e\left(\frac{71}{166}\right)\)	\(e\left(\frac{101}{166}\right)\)	\(e\left(\frac{49}{83}\right)\)	\(e\left(\frac{36}{83}\right)\)	\(e\left(\frac{7}{166}\right)\)	\(e\left(\frac{113}{166}\right)\)
\(\chi_{16700}(2749,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{166}\right)\)	\(e\left(\frac{47}{166}\right)\)	\(e\left(\frac{29}{83}\right)\)	\(e\left(\frac{52}{83}\right)\)	\(e\left(\frac{15}{166}\right)\)	\(e\left(\frac{19}{166}\right)\)	\(e\left(\frac{1}{83}\right)\)	\(e\left(\frac{38}{83}\right)\)	\(e\left(\frac{95}{166}\right)\)	\(e\left(\frac{87}{166}\right)\)
\(\chi_{16700}(3249,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{166}\right)\)	\(e\left(\frac{99}{166}\right)\)	\(e\left(\frac{24}{83}\right)\)	\(e\left(\frac{23}{83}\right)\)	\(e\left(\frac{21}{166}\right)\)	\(e\left(\frac{93}{166}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{20}{83}\right)\)	\(e\left(\frac{133}{166}\right)\)	\(e\left(\frac{155}{166}\right)\)
\(\chi_{16700}(3349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{159}{166}\right)\)	\(e\left(\frac{23}{166}\right)\)	\(e\left(\frac{76}{83}\right)\)	\(e\left(\frac{59}{83}\right)\)	\(e\left(\frac{25}{166}\right)\)	\(e\left(\frac{87}{166}\right)\)	\(e\left(\frac{57}{83}\right)\)	\(e\left(\frac{8}{83}\right)\)	\(e\left(\frac{103}{166}\right)\)	\(e\left(\frac{145}{166}\right)\)
\(\chi_{16700}(3549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{166}\right)\)	\(e\left(\frac{105}{166}\right)\)	\(e\left(\frac{33}{83}\right)\)	\(e\left(\frac{42}{83}\right)\)	\(e\left(\frac{143}{166}\right)\)	\(e\left(\frac{159}{166}\right)\)	\(e\left(\frac{4}{83}\right)\)	\(e\left(\frac{69}{83}\right)\)	\(e\left(\frac{131}{166}\right)\)	\(e\left(\frac{99}{166}\right)\)
\(\chi_{16700}(3749,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{166}\right)\)	\(e\left(\frac{123}{166}\right)\)	\(e\left(\frac{60}{83}\right)\)	\(e\left(\frac{16}{83}\right)\)	\(e\left(\frac{11}{166}\right)\)	\(e\left(\frac{25}{166}\right)\)	\(e\left(\frac{45}{83}\right)\)	\(e\left(\frac{50}{83}\right)\)	\(e\left(\frac{125}{166}\right)\)	\(e\left(\frac{97}{166}\right)\)
\(\chi_{16700}(3849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{166}\right)\)	\(e\left(\frac{133}{166}\right)\)	\(e\left(\frac{75}{83}\right)\)	\(e\left(\frac{20}{83}\right)\)	\(e\left(\frac{159}{166}\right)\)	\(e\left(\frac{135}{166}\right)\)	\(e\left(\frac{77}{83}\right)\)	\(e\left(\frac{21}{83}\right)\)	\(e\left(\frac{11}{166}\right)\)	\(e\left(\frac{59}{166}\right)\)
\(\chi_{16700}(3949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{166}\right)\)	\(e\left(\frac{137}{166}\right)\)	\(e\left(\frac{81}{83}\right)\)	\(e\left(\frac{5}{83}\right)\)	\(e\left(\frac{19}{166}\right)\)	\(e\left(\frac{13}{166}\right)\)	\(e\left(\frac{40}{83}\right)\)	\(e\left(\frac{26}{83}\right)\)	\(e\left(\frac{65}{166}\right)\)	\(e\left(\frac{77}{166}\right)\)
\(\chi_{16700}(4149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{166}\right)\)	\(e\left(\frac{25}{166}\right)\)	\(e\left(\frac{79}{83}\right)\)	\(e\left(\frac{10}{83}\right)\)	\(e\left(\frac{121}{166}\right)\)	\(e\left(\frac{109}{166}\right)\)	\(e\left(\frac{80}{83}\right)\)	\(e\left(\frac{52}{83}\right)\)	\(e\left(\frac{47}{166}\right)\)	\(e\left(\frac{71}{166}\right)\)
\(\chi_{16700}(4349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{166}\right)\)	\(e\left(\frac{63}{166}\right)\)	\(e\left(\frac{53}{83}\right)\)	\(e\left(\frac{75}{83}\right)\)	\(e\left(\frac{119}{166}\right)\)	\(e\left(\frac{29}{166}\right)\)	\(e\left(\frac{19}{83}\right)\)	\(e\left(\frac{58}{83}\right)\)	\(e\left(\frac{145}{166}\right)\)	\(e\left(\frac{159}{166}\right)\)
\(\chi_{16700}(4449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{166}\right)\)	\(e\left(\frac{149}{166}\right)\)	\(e\left(\frac{16}{83}\right)\)	\(e\left(\frac{43}{83}\right)\)	\(e\left(\frac{97}{166}\right)\)	\(e\left(\frac{145}{166}\right)\)	\(e\left(\frac{12}{83}\right)\)	\(e\left(\frac{41}{83}\right)\)	\(e\left(\frac{61}{166}\right)\)	\(e\left(\frac{131}{166}\right)\)
\(\chi_{16700}(4849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{166}\right)\)	\(e\left(\frac{125}{166}\right)\)	\(e\left(\frac{63}{83}\right)\)	\(e\left(\frac{50}{83}\right)\)	\(e\left(\frac{107}{166}\right)\)	\(e\left(\frac{47}{166}\right)\)	\(e\left(\frac{68}{83}\right)\)	\(e\left(\frac{11}{83}\right)\)	\(e\left(\frac{69}{166}\right)\)	\(e\left(\frac{23}{166}\right)\)
\(\chi_{16700}(5249,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{166}\right)\)	\(e\left(\frac{73}{166}\right)\)	\(e\left(\frac{68}{83}\right)\)	\(e\left(\frac{79}{83}\right)\)	\(e\left(\frac{101}{166}\right)\)	\(e\left(\frac{139}{166}\right)\)	\(e\left(\frac{51}{83}\right)\)	\(e\left(\frac{29}{83}\right)\)	\(e\left(\frac{31}{166}\right)\)	\(e\left(\frac{121}{166}\right)\)
\(\chi_{16700}(5549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{165}{166}\right)\)	\(e\left(\frac{27}{166}\right)\)	\(e\left(\frac{82}{83}\right)\)	\(e\left(\frac{44}{83}\right)\)	\(e\left(\frac{51}{166}\right)\)	\(e\left(\frac{131}{166}\right)\)	\(e\left(\frac{20}{83}\right)\)	\(e\left(\frac{13}{83}\right)\)	\(e\left(\frac{157}{166}\right)\)	\(e\left(\frac{163}{166}\right)\)
\(\chi_{16700}(5849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{166}\right)\)	\(e\left(\frac{61}{166}\right)\)	\(e\left(\frac{50}{83}\right)\)	\(e\left(\frac{41}{83}\right)\)	\(e\left(\frac{23}{166}\right)\)	\(e\left(\frac{7}{166}\right)\)	\(e\left(\frac{79}{83}\right)\)	\(e\left(\frac{14}{83}\right)\)	\(e\left(\frac{35}{166}\right)\)	\(e\left(\frac{67}{166}\right)\)
\(\chi_{16700}(6149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{166}\right)\)	\(e\left(\frac{77}{166}\right)\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{64}{83}\right)\)	\(e\left(\frac{127}{166}\right)\)	\(e\left(\frac{17}{166}\right)\)	\(e\left(\frac{14}{83}\right)\)	\(e\left(\frac{34}{83}\right)\)	\(e\left(\frac{85}{166}\right)\)	\(e\left(\frac{139}{166}\right)\)
\(\chi_{16700}(6349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{166}\right)\)	\(e\left(\frac{53}{166}\right)\)	\(e\left(\frac{38}{83}\right)\)	\(e\left(\frac{71}{83}\right)\)	\(e\left(\frac{137}{166}\right)\)	\(e\left(\frac{85}{166}\right)\)	\(e\left(\frac{70}{83}\right)\)	\(e\left(\frac{4}{83}\right)\)	\(e\left(\frac{93}{166}\right)\)	\(e\left(\frac{31}{166}\right)\)
\(\chi_{16700}(6549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{166}\right)\)	\(e\left(\frac{1}{166}\right)\)	\(e\left(\frac{43}{83}\right)\)	\(e\left(\frac{17}{83}\right)\)	\(e\left(\frac{131}{166}\right)\)	\(e\left(\frac{11}{166}\right)\)	\(e\left(\frac{53}{83}\right)\)	\(e\left(\frac{22}{83}\right)\)	\(e\left(\frac{55}{166}\right)\)	\(e\left(\frac{129}{166}\right)\)
\(\chi_{16700}(6849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{166}\right)\)	\(e\left(\frac{155}{166}\right)\)	\(e\left(\frac{25}{83}\right)\)	\(e\left(\frac{62}{83}\right)\)	\(e\left(\frac{53}{166}\right)\)	\(e\left(\frac{45}{166}\right)\)	\(e\left(\frac{81}{83}\right)\)	\(e\left(\frac{7}{83}\right)\)	\(e\left(\frac{59}{166}\right)\)	\(e\left(\frac{75}{166}\right)\)

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First 31 of 82 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	16700.bd
Modulus	$16700$
Conductor	$835$
Order	$166$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(16700\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(835\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(166\)	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:	no, induced from 835.j	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);