LMFDB - Dirichlet character orbit 1150.w

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1150, base_ring=CyclotomicField(220)) M = H._module chi = DirichletCharacter(H, M([143,70])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(17, 1150)) 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("1150.17"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1150$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$575$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$220$	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 575.w	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:	$\Q(\zeta_{220})$	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 220 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$27$	$29$
$\chi_{1150}(17,\cdot)$	$1$	$1$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{3}{110}\right)$
$\chi_{1150}(33,\cdot)$	$1$	$1$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{83}{110}\right)$
$\chi_{1150}(37,\cdot)$	$1$	$1$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{9}{110}\right)$
$\chi_{1150}(53,\cdot)$	$1$	$1$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{27}{110}\right)$
$\chi_{1150}(63,\cdot)$	$1$	$1$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{69}{110}\right)$
$\chi_{1150}(67,\cdot)$	$1$	$1$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{103}{110}\right)$
$\chi_{1150}(83,\cdot)$	$1$	$1$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{53}{110}\right)$
$\chi_{1150}(97,\cdot)$	$1$	$1$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{57}{110}\right)$
$\chi_{1150}(103,\cdot)$	$1$	$1$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{7}{110}\right)$
$\chi_{1150}(113,\cdot)$	$1$	$1$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{59}{110}\right)$
$\chi_{1150}(153,\cdot)$	$1$	$1$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{67}{110}\right)$
$\chi_{1150}(203,\cdot)$	$1$	$1$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{107}{110}\right)$
$\chi_{1150}(217,\cdot)$	$1$	$1$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{83}{110}\right)$
$\chi_{1150}(227,\cdot)$	$1$	$1$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{21}{110}\right)$
$\chi_{1150}(237,\cdot)$	$1$	$1$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{49}{110}\right)$
$\chi_{1150}(247,\cdot)$	$1$	$1$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{47}{110}\right)$
$\chi_{1150}(263,\cdot)$	$1$	$1$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{39}{110}\right)$
$\chi_{1150}(267,\cdot)$	$1$	$1$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{53}{110}\right)$
$\chi_{1150}(273,\cdot)$	$1$	$1$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{21}{110}\right)$
$\chi_{1150}(283,\cdot)$	$1$	$1$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{93}{110}\right)$
$\chi_{1150}(287,\cdot)$	$1$	$1$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{29}{110}\right)$
$\chi_{1150}(297,\cdot)$	$1$	$1$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{37}{110}\right)$
$\chi_{1150}(313,\cdot)$	$1$	$1$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{9}{110}\right)$
$\chi_{1150}(327,\cdot)$	$1$	$1$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{101}{110}\right)$
$\chi_{1150}(333,\cdot)$	$1$	$1$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{73}{110}\right)$
$\chi_{1150}(337,\cdot)$	$1$	$1$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{89}{110}\right)$
$\chi_{1150}(373,\cdot)$	$1$	$1$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{101}{110}\right)$
$\chi_{1150}(383,\cdot)$	$1$	$1$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{23}{110}\right)$
$\chi_{1150}(387,\cdot)$	$1$	$1$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{19}{110}\right)$
$\chi_{1150}(433,\cdot)$	$1$	$1$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{63}{110}\right)$
$\chi_{1150}(447,\cdot)$	$1$	$1$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{17}{110}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(27\)	\(29\)
\(\chi_{1150}(17,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)
\(\chi_{1150}(33,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{83}{110}\right)\)
\(\chi_{1150}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)
\(\chi_{1150}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{27}{110}\right)\)
\(\chi_{1150}(63,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)
\(\chi_{1150}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{103}{110}\right)\)
\(\chi_{1150}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)
\(\chi_{1150}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{57}{110}\right)\)
\(\chi_{1150}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{7}{110}\right)\)
\(\chi_{1150}(113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{59}{110}\right)\)
\(\chi_{1150}(153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{67}{110}\right)\)
\(\chi_{1150}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{107}{110}\right)\)
\(\chi_{1150}(217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{83}{110}\right)\)
\(\chi_{1150}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{21}{110}\right)\)
\(\chi_{1150}(237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{49}{110}\right)\)
\(\chi_{1150}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{47}{110}\right)\)
\(\chi_{1150}(263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{39}{110}\right)\)
\(\chi_{1150}(267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{220}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)
\(\chi_{1150}(273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{21}{110}\right)\)
\(\chi_{1150}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{93}{110}\right)\)
\(\chi_{1150}(287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{29}{110}\right)\)
\(\chi_{1150}(297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{37}{110}\right)\)
\(\chi_{1150}(313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)
\(\chi_{1150}(327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{101}{110}\right)\)
\(\chi_{1150}(333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)
\(\chi_{1150}(337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{89}{110}\right)\)
\(\chi_{1150}(373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{101}{110}\right)\)
\(\chi_{1150}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{23}{110}\right)\)
\(\chi_{1150}(387,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{19}{110}\right)\)
\(\chi_{1150}(433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{63}{110}\right)\)
\(\chi_{1150}(447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{17}{110}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 80 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	1150.w
Modulus	$1150$
Conductor	$575$
Order	$220$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(1150\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(575\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(220\)	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 575.w	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);