LMFDB - Dirichlet character orbit 29370.hd

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(29370, base_ring=CyclotomicField(220)) M = H._module chi = DirichletCharacter(H, M([110,55,66,45])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(107, 29370)) 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("29370.107"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$29370$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$14685$	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 14685.hh	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{220})$
Fixed field:	Number field defined by a degree 220 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$7$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{29370}(107,\cdot)$	$-1$	$1$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{29370}(227,\cdot)$	$-1$	$1$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{29370}(1073,\cdot)$	$-1$	$1$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{29370}(1403,\cdot)$	$-1$	$1$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{29370}(1553,\cdot)$	$-1$	$1$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{29370}(2153,\cdot)$	$-1$	$1$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{29370}(2483,\cdot)$	$-1$	$1$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{29370}(2723,\cdot)$	$-1$	$1$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{29370}(4193,\cdot)$	$-1$	$1$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{29370}(4397,\cdot)$	$-1$	$1$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{29370}(4637,\cdot)$	$-1$	$1$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{29370}(4853,\cdot)$	$-1$	$1$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{29370}(4967,\cdot)$	$-1$	$1$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{29370}(5447,\cdot)$	$-1$	$1$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{29370}(5717,\cdot)$	$-1$	$1$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{29370}(6047,\cdot)$	$-1$	$1$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{29370}(6893,\cdot)$	$-1$	$1$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{29370}(7013,\cdot)$	$-1$	$1$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{29370}(7367,\cdot)$	$-1$	$1$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{29370}(7493,\cdot)$	$-1$	$1$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{29370}(7607,\cdot)$	$-1$	$1$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{29370}(7763,\cdot)$	$-1$	$1$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{29370}(7823,\cdot)$	$-1$	$1$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{29370}(8267,\cdot)$	$-1$	$1$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{29370}(9083,\cdot)$	$-1$	$1$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{29370}(9413,\cdot)$	$-1$	$1$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{29370}(9533,\cdot)$	$-1$	$1$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{29370}(9737,\cdot)$	$-1$	$1$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{29370}(10193,\cdot)$	$-1$	$1$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{29370}(10733,\cdot)$	$-1$	$1$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{29370}(10787,\cdot)$	$-1$	$1$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{2}{11}\right)$

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	\(-1\)	\(1\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{29370}(107,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{29370}(227,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{29370}(1073,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{29370}(1403,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{29370}(1553,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{29370}(2153,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{29370}(2483,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{29370}(2723,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{29370}(4193,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{29370}(4397,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{29370}(4637,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{29370}(4853,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{29370}(4967,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{181}{220}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{29370}(5447,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{29370}(5717,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{29370}(6047,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{29370}(6893,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{29370}(7013,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{29370}(7367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{29370}(7493,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{29370}(7607,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{29370}(7763,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{29370}(7823,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{29370}(8267,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{29370}(9083,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{29370}(9413,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{29370}(9533,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{29370}(9737,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{29370}(10193,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{29370}(10733,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{29370}(10787,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{2}{11}\right)\)

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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	29370.hd
Modulus	$29370$
Conductor	$14685$
Order	$220$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(29370\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(14685\)	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 14685.hh	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);