LMFDB - Dirichlet character orbit 2106.cn

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2106, base_ring=CyclotomicField(108)) M = H._module chi = DirichletCharacter(H, M([26,63])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(11, 2106)) 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("2106.11"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$2106$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1053$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$108$	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 1053.cn	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{108})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 108 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{2106}(11,\cdot)$	$1$	$1$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{2106}(59,\cdot)$	$1$	$1$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{2106}(119,\cdot)$	$1$	$1$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{2106}(149,\cdot)$	$1$	$1$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{2106}(245,\cdot)$	$1$	$1$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{2106}(293,\cdot)$	$1$	$1$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{2106}(353,\cdot)$	$1$	$1$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{2106}(383,\cdot)$	$1$	$1$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{2106}(479,\cdot)$	$1$	$1$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{2106}(527,\cdot)$	$1$	$1$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{2106}(587,\cdot)$	$1$	$1$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{2106}(617,\cdot)$	$1$	$1$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{2106}(713,\cdot)$	$1$	$1$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{2106}(761,\cdot)$	$1$	$1$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{2106}(821,\cdot)$	$1$	$1$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{2106}(851,\cdot)$	$1$	$1$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{2106}(947,\cdot)$	$1$	$1$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{2106}(995,\cdot)$	$1$	$1$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{2106}(1055,\cdot)$	$1$	$1$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{2106}(1085,\cdot)$	$1$	$1$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{2106}(1181,\cdot)$	$1$	$1$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{2106}(1229,\cdot)$	$1$	$1$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{2106}(1289,\cdot)$	$1$	$1$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{2106}(1319,\cdot)$	$1$	$1$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{2106}(1415,\cdot)$	$1$	$1$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{2106}(1463,\cdot)$	$1$	$1$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{2106}(1523,\cdot)$	$1$	$1$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{2106}(1553,\cdot)$	$1$	$1$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{2106}(1649,\cdot)$	$1$	$1$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{2106}(1697,\cdot)$	$1$	$1$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{2106}(1757,\cdot)$	$1$	$1$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{7}{18}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{2106}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{2106}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{2106}(119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{2106}(149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{2106}(245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{2106}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{2106}(353,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{2106}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{2106}(479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{2106}(527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{2106}(587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{2106}(617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{2106}(713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{2106}(761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{2106}(821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{2106}(851,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{2106}(947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{2106}(995,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{2106}(1055,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{2106}(1085,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{2106}(1181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{2106}(1229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{2106}(1289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{2106}(1319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{2106}(1415,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{2106}(1463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{2106}(1523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{2106}(1553,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{2106}(1649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{2106}(1697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{2106}(1757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{7}{18}\right)\)

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First 31 of 36 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	2106.cn
Modulus	$2106$
Conductor	$1053$
Order	$108$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(2106\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1053\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(108\)	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 1053.cn	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);