LMFDB - Dirichlet character orbit 343.k

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(343, base_ring=CyclotomicField(294)) M = H._module chi = DirichletCharacter(H, M([194])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(2, 343)) 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("343.2"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$343$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$343$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$147$	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:	yes	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:	$\Q(\zeta_{147})$	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 147 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 84 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{343}(2,\cdot)$	$1$	$1$	$e\left(\frac{2}{147}\right)$	$e\left(\frac{97}{147}\right)$	$e\left(\frac{4}{147}\right)$	$e\left(\frac{20}{147}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{47}{147}\right)$	$e\left(\frac{22}{147}\right)$	$e\left(\frac{37}{147}\right)$	$e\left(\frac{101}{147}\right)$
$\chi_{343}(4,\cdot)$	$1$	$1$	$e\left(\frac{4}{147}\right)$	$e\left(\frac{47}{147}\right)$	$e\left(\frac{8}{147}\right)$	$e\left(\frac{40}{147}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{94}{147}\right)$	$e\left(\frac{44}{147}\right)$	$e\left(\frac{74}{147}\right)$	$e\left(\frac{55}{147}\right)$
$\chi_{343}(9,\cdot)$	$1$	$1$	$e\left(\frac{47}{147}\right)$	$e\left(\frac{1}{147}\right)$	$e\left(\frac{94}{147}\right)$	$e\left(\frac{29}{147}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{2}{147}\right)$	$e\left(\frac{76}{147}\right)$	$e\left(\frac{61}{147}\right)$	$e\left(\frac{95}{147}\right)$
$\chi_{343}(11,\cdot)$	$1$	$1$	$e\left(\frac{37}{147}\right)$	$e\left(\frac{104}{147}\right)$	$e\left(\frac{74}{147}\right)$	$e\left(\frac{76}{147}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{61}{147}\right)$	$e\left(\frac{113}{147}\right)$	$e\left(\frac{23}{147}\right)$	$e\left(\frac{31}{147}\right)$
$\chi_{343}(16,\cdot)$	$1$	$1$	$e\left(\frac{8}{147}\right)$	$e\left(\frac{94}{147}\right)$	$e\left(\frac{16}{147}\right)$	$e\left(\frac{80}{147}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{41}{147}\right)$	$e\left(\frac{88}{147}\right)$	$e\left(\frac{1}{147}\right)$	$e\left(\frac{110}{147}\right)$
$\chi_{343}(23,\cdot)$	$1$	$1$	$e\left(\frac{32}{147}\right)$	$e\left(\frac{82}{147}\right)$	$e\left(\frac{64}{147}\right)$	$e\left(\frac{26}{147}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{17}{147}\right)$	$e\left(\frac{58}{147}\right)$	$e\left(\frac{4}{147}\right)$	$e\left(\frac{146}{147}\right)$
$\chi_{343}(25,\cdot)$	$1$	$1$	$e\left(\frac{40}{147}\right)$	$e\left(\frac{29}{147}\right)$	$e\left(\frac{80}{147}\right)$	$e\left(\frac{106}{147}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{58}{147}\right)$	$e\left(\frac{146}{147}\right)$	$e\left(\frac{5}{147}\right)$	$e\left(\frac{109}{147}\right)$
$\chi_{343}(32,\cdot)$	$1$	$1$	$e\left(\frac{10}{147}\right)$	$e\left(\frac{44}{147}\right)$	$e\left(\frac{20}{147}\right)$	$e\left(\frac{100}{147}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{88}{147}\right)$	$e\left(\frac{110}{147}\right)$	$e\left(\frac{38}{147}\right)$	$e\left(\frac{64}{147}\right)$
$\chi_{343}(37,\cdot)$	$1$	$1$	$e\left(\frac{122}{147}\right)$	$e\left(\frac{37}{147}\right)$	$e\left(\frac{97}{147}\right)$	$e\left(\frac{44}{147}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{74}{147}\right)$	$e\left(\frac{19}{147}\right)$	$e\left(\frac{52}{147}\right)$	$e\left(\frac{134}{147}\right)$
$\chi_{343}(39,\cdot)$	$1$	$1$	$e\left(\frac{106}{147}\right)$	$e\left(\frac{143}{147}\right)$	$e\left(\frac{65}{147}\right)$	$e\left(\frac{31}{147}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{139}{147}\right)$	$e\left(\frac{137}{147}\right)$	$e\left(\frac{50}{147}\right)$	$e\left(\frac{61}{147}\right)$
$\chi_{343}(44,\cdot)$	$1$	$1$	$e\left(\frac{41}{147}\right)$	$e\left(\frac{4}{147}\right)$	$e\left(\frac{82}{147}\right)$	$e\left(\frac{116}{147}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{8}{147}\right)$	$e\left(\frac{10}{147}\right)$	$e\left(\frac{97}{147}\right)$	$e\left(\frac{86}{147}\right)$
$\chi_{343}(46,\cdot)$	$1$	$1$	$e\left(\frac{34}{147}\right)$	$e\left(\frac{32}{147}\right)$	$e\left(\frac{68}{147}\right)$	$e\left(\frac{46}{147}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{64}{147}\right)$	$e\left(\frac{80}{147}\right)$	$e\left(\frac{41}{147}\right)$	$e\left(\frac{100}{147}\right)$
$\chi_{343}(51,\cdot)$	$1$	$1$	$e\left(\frac{23}{147}\right)$	$e\left(\frac{13}{147}\right)$	$e\left(\frac{46}{147}\right)$	$e\left(\frac{83}{147}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{26}{147}\right)$	$e\left(\frac{106}{147}\right)$	$e\left(\frac{58}{147}\right)$	$e\left(\frac{59}{147}\right)$
$\chi_{343}(53,\cdot)$	$1$	$1$	$e\left(\frac{88}{147}\right)$	$e\left(\frac{5}{147}\right)$	$e\left(\frac{29}{147}\right)$	$e\left(\frac{145}{147}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{10}{147}\right)$	$e\left(\frac{86}{147}\right)$	$e\left(\frac{11}{147}\right)$	$e\left(\frac{34}{147}\right)$
$\chi_{343}(58,\cdot)$	$1$	$1$	$e\left(\frac{68}{147}\right)$	$e\left(\frac{64}{147}\right)$	$e\left(\frac{136}{147}\right)$	$e\left(\frac{92}{147}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{128}{147}\right)$	$e\left(\frac{13}{147}\right)$	$e\left(\frac{82}{147}\right)$	$e\left(\frac{53}{147}\right)$
$\chi_{343}(60,\cdot)$	$1$	$1$	$e\left(\frac{121}{147}\right)$	$e\left(\frac{62}{147}\right)$	$e\left(\frac{95}{147}\right)$	$e\left(\frac{34}{147}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{124}{147}\right)$	$e\left(\frac{8}{147}\right)$	$e\left(\frac{107}{147}\right)$	$e\left(\frac{10}{147}\right)$
$\chi_{343}(65,\cdot)$	$1$	$1$	$e\left(\frac{29}{147}\right)$	$e\left(\frac{10}{147}\right)$	$e\left(\frac{58}{147}\right)$	$e\left(\frac{143}{147}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{20}{147}\right)$	$e\left(\frac{25}{147}\right)$	$e\left(\frac{22}{147}\right)$	$e\left(\frac{68}{147}\right)$
$\chi_{343}(72,\cdot)$	$1$	$1$	$e\left(\frac{53}{147}\right)$	$e\left(\frac{145}{147}\right)$	$e\left(\frac{106}{147}\right)$	$e\left(\frac{89}{147}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{143}{147}\right)$	$e\left(\frac{142}{147}\right)$	$e\left(\frac{25}{147}\right)$	$e\left(\frac{104}{147}\right)$
$\chi_{343}(74,\cdot)$	$1$	$1$	$e\left(\frac{124}{147}\right)$	$e\left(\frac{134}{147}\right)$	$e\left(\frac{101}{147}\right)$	$e\left(\frac{64}{147}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{121}{147}\right)$	$e\left(\frac{41}{147}\right)$	$e\left(\frac{89}{147}\right)$	$e\left(\frac{88}{147}\right)$
$\chi_{343}(81,\cdot)$	$1$	$1$	$e\left(\frac{94}{147}\right)$	$e\left(\frac{2}{147}\right)$	$e\left(\frac{41}{147}\right)$	$e\left(\frac{58}{147}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{4}{147}\right)$	$e\left(\frac{5}{147}\right)$	$e\left(\frac{122}{147}\right)$	$e\left(\frac{43}{147}\right)$
$\chi_{343}(86,\cdot)$	$1$	$1$	$e\left(\frac{143}{147}\right)$	$e\left(\frac{100}{147}\right)$	$e\left(\frac{139}{147}\right)$	$e\left(\frac{107}{147}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{53}{147}\right)$	$e\left(\frac{103}{147}\right)$	$e\left(\frac{73}{147}\right)$	$e\left(\frac{92}{147}\right)$
$\chi_{343}(88,\cdot)$	$1$	$1$	$e\left(\frac{43}{147}\right)$	$e\left(\frac{101}{147}\right)$	$e\left(\frac{86}{147}\right)$	$e\left(\frac{136}{147}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{55}{147}\right)$	$e\left(\frac{32}{147}\right)$	$e\left(\frac{134}{147}\right)$	$e\left(\frac{40}{147}\right)$
$\chi_{343}(93,\cdot)$	$1$	$1$	$e\left(\frac{62}{147}\right)$	$e\left(\frac{67}{147}\right)$	$e\left(\frac{124}{147}\right)$	$e\left(\frac{32}{147}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{134}{147}\right)$	$e\left(\frac{94}{147}\right)$	$e\left(\frac{118}{147}\right)$	$e\left(\frac{44}{147}\right)$
$\chi_{343}(95,\cdot)$	$1$	$1$	$e\left(\frac{118}{147}\right)$	$e\left(\frac{137}{147}\right)$	$e\left(\frac{89}{147}\right)$	$e\left(\frac{4}{147}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{127}{147}\right)$	$e\left(\frac{122}{147}\right)$	$e\left(\frac{125}{147}\right)$	$e\left(\frac{79}{147}\right)$
$\chi_{343}(100,\cdot)$	$1$	$1$	$e\left(\frac{44}{147}\right)$	$e\left(\frac{76}{147}\right)$	$e\left(\frac{88}{147}\right)$	$e\left(\frac{146}{147}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{5}{147}\right)$	$e\left(\frac{43}{147}\right)$	$e\left(\frac{79}{147}\right)$	$e\left(\frac{17}{147}\right)$
$\chi_{343}(102,\cdot)$	$1$	$1$	$e\left(\frac{25}{147}\right)$	$e\left(\frac{110}{147}\right)$	$e\left(\frac{50}{147}\right)$	$e\left(\frac{103}{147}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{73}{147}\right)$	$e\left(\frac{128}{147}\right)$	$e\left(\frac{95}{147}\right)$	$e\left(\frac{13}{147}\right)$
$\chi_{343}(107,\cdot)$	$1$	$1$	$e\left(\frac{89}{147}\right)$	$e\left(\frac{127}{147}\right)$	$e\left(\frac{31}{147}\right)$	$e\left(\frac{8}{147}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{107}{147}\right)$	$e\left(\frac{97}{147}\right)$	$e\left(\frac{103}{147}\right)$	$e\left(\frac{11}{147}\right)$
$\chi_{343}(109,\cdot)$	$1$	$1$	$e\left(\frac{58}{147}\right)$	$e\left(\frac{20}{147}\right)$	$e\left(\frac{116}{147}\right)$	$e\left(\frac{139}{147}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{40}{147}\right)$	$e\left(\frac{50}{147}\right)$	$e\left(\frac{44}{147}\right)$	$e\left(\frac{136}{147}\right)$
$\chi_{343}(114,\cdot)$	$1$	$1$	$e\left(\frac{50}{147}\right)$	$e\left(\frac{73}{147}\right)$	$e\left(\frac{100}{147}\right)$	$e\left(\frac{59}{147}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{146}{147}\right)$	$e\left(\frac{109}{147}\right)$	$e\left(\frac{43}{147}\right)$	$e\left(\frac{26}{147}\right)$
$\chi_{343}(121,\cdot)$	$1$	$1$	$e\left(\frac{74}{147}\right)$	$e\left(\frac{61}{147}\right)$	$e\left(\frac{1}{147}\right)$	$e\left(\frac{5}{147}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{122}{147}\right)$	$e\left(\frac{79}{147}\right)$	$e\left(\frac{46}{147}\right)$	$e\left(\frac{62}{147}\right)$
$\chi_{343}(123,\cdot)$	$1$	$1$	$e\left(\frac{61}{147}\right)$	$e\left(\frac{92}{147}\right)$	$e\left(\frac{122}{147}\right)$	$e\left(\frac{22}{147}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{37}{147}\right)$	$e\left(\frac{83}{147}\right)$	$e\left(\frac{26}{147}\right)$	$e\left(\frac{67}{147}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{343}(2,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{147}\right)\)	\(e\left(\frac{97}{147}\right)\)	\(e\left(\frac{4}{147}\right)\)	\(e\left(\frac{20}{147}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{47}{147}\right)\)	\(e\left(\frac{22}{147}\right)\)	\(e\left(\frac{37}{147}\right)\)	\(e\left(\frac{101}{147}\right)\)
\(\chi_{343}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{147}\right)\)	\(e\left(\frac{47}{147}\right)\)	\(e\left(\frac{8}{147}\right)\)	\(e\left(\frac{40}{147}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{94}{147}\right)\)	\(e\left(\frac{44}{147}\right)\)	\(e\left(\frac{74}{147}\right)\)	\(e\left(\frac{55}{147}\right)\)
\(\chi_{343}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{147}\right)\)	\(e\left(\frac{1}{147}\right)\)	\(e\left(\frac{94}{147}\right)\)	\(e\left(\frac{29}{147}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{2}{147}\right)\)	\(e\left(\frac{76}{147}\right)\)	\(e\left(\frac{61}{147}\right)\)	\(e\left(\frac{95}{147}\right)\)
\(\chi_{343}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{147}\right)\)	\(e\left(\frac{104}{147}\right)\)	\(e\left(\frac{74}{147}\right)\)	\(e\left(\frac{76}{147}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{61}{147}\right)\)	\(e\left(\frac{113}{147}\right)\)	\(e\left(\frac{23}{147}\right)\)	\(e\left(\frac{31}{147}\right)\)
\(\chi_{343}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{147}\right)\)	\(e\left(\frac{94}{147}\right)\)	\(e\left(\frac{16}{147}\right)\)	\(e\left(\frac{80}{147}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{41}{147}\right)\)	\(e\left(\frac{88}{147}\right)\)	\(e\left(\frac{1}{147}\right)\)	\(e\left(\frac{110}{147}\right)\)
\(\chi_{343}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{147}\right)\)	\(e\left(\frac{82}{147}\right)\)	\(e\left(\frac{64}{147}\right)\)	\(e\left(\frac{26}{147}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{17}{147}\right)\)	\(e\left(\frac{58}{147}\right)\)	\(e\left(\frac{4}{147}\right)\)	\(e\left(\frac{146}{147}\right)\)
\(\chi_{343}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{147}\right)\)	\(e\left(\frac{29}{147}\right)\)	\(e\left(\frac{80}{147}\right)\)	\(e\left(\frac{106}{147}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{58}{147}\right)\)	\(e\left(\frac{146}{147}\right)\)	\(e\left(\frac{5}{147}\right)\)	\(e\left(\frac{109}{147}\right)\)
\(\chi_{343}(32,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{147}\right)\)	\(e\left(\frac{44}{147}\right)\)	\(e\left(\frac{20}{147}\right)\)	\(e\left(\frac{100}{147}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{88}{147}\right)\)	\(e\left(\frac{110}{147}\right)\)	\(e\left(\frac{38}{147}\right)\)	\(e\left(\frac{64}{147}\right)\)
\(\chi_{343}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{122}{147}\right)\)	\(e\left(\frac{37}{147}\right)\)	\(e\left(\frac{97}{147}\right)\)	\(e\left(\frac{44}{147}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{74}{147}\right)\)	\(e\left(\frac{19}{147}\right)\)	\(e\left(\frac{52}{147}\right)\)	\(e\left(\frac{134}{147}\right)\)
\(\chi_{343}(39,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{106}{147}\right)\)	\(e\left(\frac{143}{147}\right)\)	\(e\left(\frac{65}{147}\right)\)	\(e\left(\frac{31}{147}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{139}{147}\right)\)	\(e\left(\frac{137}{147}\right)\)	\(e\left(\frac{50}{147}\right)\)	\(e\left(\frac{61}{147}\right)\)
\(\chi_{343}(44,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{147}\right)\)	\(e\left(\frac{4}{147}\right)\)	\(e\left(\frac{82}{147}\right)\)	\(e\left(\frac{116}{147}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{8}{147}\right)\)	\(e\left(\frac{10}{147}\right)\)	\(e\left(\frac{97}{147}\right)\)	\(e\left(\frac{86}{147}\right)\)
\(\chi_{343}(46,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{147}\right)\)	\(e\left(\frac{32}{147}\right)\)	\(e\left(\frac{68}{147}\right)\)	\(e\left(\frac{46}{147}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{64}{147}\right)\)	\(e\left(\frac{80}{147}\right)\)	\(e\left(\frac{41}{147}\right)\)	\(e\left(\frac{100}{147}\right)\)
\(\chi_{343}(51,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{147}\right)\)	\(e\left(\frac{13}{147}\right)\)	\(e\left(\frac{46}{147}\right)\)	\(e\left(\frac{83}{147}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{26}{147}\right)\)	\(e\left(\frac{106}{147}\right)\)	\(e\left(\frac{58}{147}\right)\)	\(e\left(\frac{59}{147}\right)\)
\(\chi_{343}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{88}{147}\right)\)	\(e\left(\frac{5}{147}\right)\)	\(e\left(\frac{29}{147}\right)\)	\(e\left(\frac{145}{147}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{10}{147}\right)\)	\(e\left(\frac{86}{147}\right)\)	\(e\left(\frac{11}{147}\right)\)	\(e\left(\frac{34}{147}\right)\)
\(\chi_{343}(58,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{147}\right)\)	\(e\left(\frac{64}{147}\right)\)	\(e\left(\frac{136}{147}\right)\)	\(e\left(\frac{92}{147}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{128}{147}\right)\)	\(e\left(\frac{13}{147}\right)\)	\(e\left(\frac{82}{147}\right)\)	\(e\left(\frac{53}{147}\right)\)
\(\chi_{343}(60,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{147}\right)\)	\(e\left(\frac{62}{147}\right)\)	\(e\left(\frac{95}{147}\right)\)	\(e\left(\frac{34}{147}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{124}{147}\right)\)	\(e\left(\frac{8}{147}\right)\)	\(e\left(\frac{107}{147}\right)\)	\(e\left(\frac{10}{147}\right)\)
\(\chi_{343}(65,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{147}\right)\)	\(e\left(\frac{10}{147}\right)\)	\(e\left(\frac{58}{147}\right)\)	\(e\left(\frac{143}{147}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{20}{147}\right)\)	\(e\left(\frac{25}{147}\right)\)	\(e\left(\frac{22}{147}\right)\)	\(e\left(\frac{68}{147}\right)\)
\(\chi_{343}(72,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{147}\right)\)	\(e\left(\frac{145}{147}\right)\)	\(e\left(\frac{106}{147}\right)\)	\(e\left(\frac{89}{147}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{143}{147}\right)\)	\(e\left(\frac{142}{147}\right)\)	\(e\left(\frac{25}{147}\right)\)	\(e\left(\frac{104}{147}\right)\)
\(\chi_{343}(74,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{124}{147}\right)\)	\(e\left(\frac{134}{147}\right)\)	\(e\left(\frac{101}{147}\right)\)	\(e\left(\frac{64}{147}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{121}{147}\right)\)	\(e\left(\frac{41}{147}\right)\)	\(e\left(\frac{89}{147}\right)\)	\(e\left(\frac{88}{147}\right)\)
\(\chi_{343}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{147}\right)\)	\(e\left(\frac{2}{147}\right)\)	\(e\left(\frac{41}{147}\right)\)	\(e\left(\frac{58}{147}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{4}{147}\right)\)	\(e\left(\frac{5}{147}\right)\)	\(e\left(\frac{122}{147}\right)\)	\(e\left(\frac{43}{147}\right)\)
\(\chi_{343}(86,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{147}\right)\)	\(e\left(\frac{100}{147}\right)\)	\(e\left(\frac{139}{147}\right)\)	\(e\left(\frac{107}{147}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{53}{147}\right)\)	\(e\left(\frac{103}{147}\right)\)	\(e\left(\frac{73}{147}\right)\)	\(e\left(\frac{92}{147}\right)\)
\(\chi_{343}(88,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{147}\right)\)	\(e\left(\frac{101}{147}\right)\)	\(e\left(\frac{86}{147}\right)\)	\(e\left(\frac{136}{147}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{55}{147}\right)\)	\(e\left(\frac{32}{147}\right)\)	\(e\left(\frac{134}{147}\right)\)	\(e\left(\frac{40}{147}\right)\)
\(\chi_{343}(93,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{147}\right)\)	\(e\left(\frac{67}{147}\right)\)	\(e\left(\frac{124}{147}\right)\)	\(e\left(\frac{32}{147}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{134}{147}\right)\)	\(e\left(\frac{94}{147}\right)\)	\(e\left(\frac{118}{147}\right)\)	\(e\left(\frac{44}{147}\right)\)
\(\chi_{343}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{118}{147}\right)\)	\(e\left(\frac{137}{147}\right)\)	\(e\left(\frac{89}{147}\right)\)	\(e\left(\frac{4}{147}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{127}{147}\right)\)	\(e\left(\frac{122}{147}\right)\)	\(e\left(\frac{125}{147}\right)\)	\(e\left(\frac{79}{147}\right)\)
\(\chi_{343}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{147}\right)\)	\(e\left(\frac{76}{147}\right)\)	\(e\left(\frac{88}{147}\right)\)	\(e\left(\frac{146}{147}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{5}{147}\right)\)	\(e\left(\frac{43}{147}\right)\)	\(e\left(\frac{79}{147}\right)\)	\(e\left(\frac{17}{147}\right)\)
\(\chi_{343}(102,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{147}\right)\)	\(e\left(\frac{110}{147}\right)\)	\(e\left(\frac{50}{147}\right)\)	\(e\left(\frac{103}{147}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{73}{147}\right)\)	\(e\left(\frac{128}{147}\right)\)	\(e\left(\frac{95}{147}\right)\)	\(e\left(\frac{13}{147}\right)\)
\(\chi_{343}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{147}\right)\)	\(e\left(\frac{127}{147}\right)\)	\(e\left(\frac{31}{147}\right)\)	\(e\left(\frac{8}{147}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{107}{147}\right)\)	\(e\left(\frac{97}{147}\right)\)	\(e\left(\frac{103}{147}\right)\)	\(e\left(\frac{11}{147}\right)\)
\(\chi_{343}(109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{147}\right)\)	\(e\left(\frac{20}{147}\right)\)	\(e\left(\frac{116}{147}\right)\)	\(e\left(\frac{139}{147}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{40}{147}\right)\)	\(e\left(\frac{50}{147}\right)\)	\(e\left(\frac{44}{147}\right)\)	\(e\left(\frac{136}{147}\right)\)
\(\chi_{343}(114,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{147}\right)\)	\(e\left(\frac{73}{147}\right)\)	\(e\left(\frac{100}{147}\right)\)	\(e\left(\frac{59}{147}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{146}{147}\right)\)	\(e\left(\frac{109}{147}\right)\)	\(e\left(\frac{43}{147}\right)\)	\(e\left(\frac{26}{147}\right)\)
\(\chi_{343}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{147}\right)\)	\(e\left(\frac{61}{147}\right)\)	\(e\left(\frac{1}{147}\right)\)	\(e\left(\frac{5}{147}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{122}{147}\right)\)	\(e\left(\frac{79}{147}\right)\)	\(e\left(\frac{46}{147}\right)\)	\(e\left(\frac{62}{147}\right)\)
\(\chi_{343}(123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{147}\right)\)	\(e\left(\frac{92}{147}\right)\)	\(e\left(\frac{122}{147}\right)\)	\(e\left(\frac{22}{147}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{37}{147}\right)\)	\(e\left(\frac{83}{147}\right)\)	\(e\left(\frac{26}{147}\right)\)	\(e\left(\frac{67}{147}\right)\)

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First 31 of 84 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	343.k
Modulus	$343$
Conductor	$343$
Order	$147$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(343\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(343\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(147\)	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:	yes	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);