LMFDB - Dirichlet character orbit 7225.cc

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7225, base_ring=CyclotomicField(272)) M = H._module chi = DirichletCharacter(H, M([68,89])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(82, 7225)) 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("7225.82"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$7225$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1445$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$272$	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 1445.bg	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:	$\Q(\zeta_{272})$
Fixed field:	Number field defined by a degree 272 polynomial (not computed)

First 31 of 128 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{7225}(82,\cdot)$	$1$	$1$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{21}{272}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{135}{272}\right)$	$e\left(\frac{263}{272}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{143}{272}\right)$	$e\left(\frac{249}{272}\right)$	$e\left(\frac{15}{17}\right)$
$\chi_{7225}(107,\cdot)$	$1$	$1$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{65}{272}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{107}{272}\right)$	$e\left(\frac{11}{272}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{67}{272}\right)$	$e\left(\frac{149}{272}\right)$	$e\left(\frac{10}{17}\right)$
$\chi_{7225}(143,\cdot)$	$1$	$1$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{15}{272}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{213}{272}\right)$	$e\left(\frac{149}{272}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{141}{272}\right)$	$e\left(\frac{139}{272}\right)$	$e\left(\frac{1}{17}\right)$
$\chi_{7225}(182,\cdot)$	$1$	$1$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{201}{272}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{243}{272}\right)$	$e\left(\frac{147}{272}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{203}{272}\right)$	$e\left(\frac{13}{272}\right)$	$e\left(\frac{10}{17}\right)$
$\chi_{7225}(193,\cdot)$	$1$	$1$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{67}{272}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{81}{272}\right)$	$e\left(\frac{49}{272}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{249}{272}\right)$	$e\left(\frac{95}{272}\right)$	$e\left(\frac{9}{17}\right)$
$\chi_{7225}(207,\cdot)$	$1$	$1$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{157}{272}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{271}{272}\right)$	$e\left(\frac{127}{272}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{7}{272}\right)$	$e\left(\frac{113}{272}\right)$	$e\left(\frac{15}{17}\right)$
$\chi_{7225}(368,\cdot)$	$1$	$1$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{235}{272}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{73}{272}\right)$	$e\left(\frac{249}{272}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{33}{272}\right)$	$e\left(\frac{183}{272}\right)$	$e\left(\frac{10}{17}\right)$
$\chi_{7225}(418,\cdot)$	$1$	$1$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{23}{272}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{109}{272}\right)$	$e\left(\frac{29}{272}\right)$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{53}{272}\right)$	$e\left(\frac{195}{272}\right)$	$e\left(\frac{14}{17}\right)$
$\chi_{7225}(507,\cdot)$	$1$	$1$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{53}{272}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{263}{272}\right)$	$e\left(\frac{55}{272}\right)$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{63}{272}\right)$	$e\left(\frac{201}{272}\right)$	$e\left(\frac{16}{17}\right)$
$\chi_{7225}(532,\cdot)$	$1$	$1$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{209}{272}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{139}{272}\right)$	$e\left(\frac{27}{272}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{115}{272}\right)$	$e\left(\frac{69}{272}\right)$	$e\left(\frac{6}{17}\right)$
$\chi_{7225}(568,\cdot)$	$1$	$1$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{79}{272}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{197}{272}\right)$	$e\left(\frac{5}{272}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{253}{272}\right)$	$e\left(\frac{43}{272}\right)$	$e\left(\frac{3}{17}\right)$
$\chi_{7225}(607,\cdot)$	$1$	$1$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{57}{272}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{131}{272}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{155}{272}\right)$	$e\left(\frac{93}{272}\right)$	$e\left(\frac{14}{17}\right)$
$\chi_{7225}(632,\cdot)$	$1$	$1$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{125}{272}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{143}{272}\right)$	$e\left(\frac{63}{272}\right)$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{87}{272}\right)$	$e\left(\frac{161}{272}\right)$	$e\left(\frac{14}{17}\right)$
$\chi_{7225}(793,\cdot)$	$1$	$1$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{251}{272}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{137}{272}\right)$	$e\left(\frac{9}{272}\right)$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{129}{272}\right)$	$e\left(\frac{23}{272}\right)$	$e\left(\frac{2}{17}\right)$
$\chi_{7225}(843,\cdot)$	$1$	$1$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{231}{272}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{125}{272}\right)$	$e\left(\frac{173}{272}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{213}{272}\right)$	$e\left(\frac{19}{272}\right)$	$e\left(\frac{12}{17}\right)$
$\chi_{7225}(957,\cdot)$	$1$	$1$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{81}{272}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{171}{272}\right)$	$e\left(\frac{43}{272}\right)$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{163}{272}\right)$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{2}{17}\right)$
$\chi_{7225}(993,\cdot)$	$1$	$1$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{143}{272}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{181}{272}\right)$	$e\left(\frac{133}{272}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{93}{272}\right)$	$e\left(\frac{219}{272}\right)$	$e\left(\frac{5}{17}\right)$
$\chi_{7225}(1032,\cdot)$	$1$	$1$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{185}{272}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{179}{272}\right)$	$e\left(\frac{115}{272}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{107}{272}\right)$	$e\left(\frac{173}{272}\right)$	$e\left(\frac{1}{17}\right)$
$\chi_{7225}(1043,\cdot)$	$1$	$1$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{35}{272}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{225}{272}\right)$	$e\left(\frac{257}{272}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{57}{272}\right)$	$e\left(\frac{143}{272}\right)$	$e\left(\frac{8}{17}\right)$
$\chi_{7225}(1057,\cdot)$	$1$	$1$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{93}{272}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{15}{272}\right)$	$e\left(\frac{271}{272}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{167}{272}\right)$	$e\left(\frac{209}{272}\right)$	$e\left(\frac{13}{17}\right)$
$\chi_{7225}(1218,\cdot)$	$1$	$1$	$e\left(\frac{103}{136}\right)$	$e\left(\frac{267}{272}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{201}{272}\right)$	$e\left(\frac{41}{272}\right)$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{225}{272}\right)$	$e\left(\frac{135}{272}\right)$	$e\left(\frac{11}{17}\right)$
$\chi_{7225}(1268,\cdot)$	$1$	$1$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{167}{272}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{141}{272}\right)$	$e\left(\frac{45}{272}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{101}{272}\right)$	$e\left(\frac{115}{272}\right)$	$e\left(\frac{10}{17}\right)$
$\chi_{7225}(1357,\cdot)$	$1$	$1$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{117}{272}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{247}{272}\right)$	$e\left(\frac{183}{272}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{117}{136}\right)$	$e\left(\frac{175}{272}\right)$	$e\left(\frac{105}{272}\right)$	$e\left(\frac{1}{17}\right)$
$\chi_{7225}(1382,\cdot)$	$1$	$1$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{225}{272}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{203}{272}\right)$	$e\left(\frac{59}{272}\right)$	$e\left(\frac{103}{136}\right)$	$e\left(\frac{89}{136}\right)$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{181}{272}\right)$	$e\left(\frac{15}{17}\right)$
$\chi_{7225}(1418,\cdot)$	$1$	$1$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{165}{272}\right)$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{205}{272}\right)$	$e\left(\frac{123}{272}\right)$	$e\left(\frac{7}{17}\right)$
$\chi_{7225}(1457,\cdot)$	$1$	$1$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{41}{272}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{147}{272}\right)$	$e\left(\frac{99}{272}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{59}{272}\right)$	$e\left(\frac{253}{272}\right)$	$e\left(\frac{5}{17}\right)$
$\chi_{7225}(1468,\cdot)$	$1$	$1$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{19}{272}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{161}{272}\right)$	$e\left(\frac{225}{272}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{233}{272}\right)$	$e\left(\frac{31}{272}\right)$	$e\left(\frac{16}{17}\right)$
$\chi_{7225}(1482,\cdot)$	$1$	$1$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{61}{272}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{159}{272}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{11}{136}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{247}{272}\right)$	$e\left(\frac{257}{272}\right)$	$e\left(\frac{12}{17}\right)$
$\chi_{7225}(1643,\cdot)$	$1$	$1$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{11}{272}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{265}{272}\right)$	$e\left(\frac{73}{272}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{11}{136}\right)$	$e\left(\frac{49}{272}\right)$	$e\left(\frac{247}{272}\right)$	$e\left(\frac{3}{17}\right)$
$\chi_{7225}(1693,\cdot)$	$1$	$1$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{103}{272}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{157}{272}\right)$	$e\left(\frac{189}{272}\right)$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{103}{136}\right)$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{8}{17}\right)$
$\chi_{7225}(1782,\cdot)$	$1$	$1$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{149}{272}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{103}{272}\right)$	$e\left(\frac{247}{272}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{95}{272}\right)$	$e\left(\frac{57}{272}\right)$	$e\left(\frac{2}{17}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{7225}(82,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{21}{272}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{135}{272}\right)\)	\(e\left(\frac{263}{272}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{143}{272}\right)\)	\(e\left(\frac{249}{272}\right)\)	\(e\left(\frac{15}{17}\right)\)
\(\chi_{7225}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{65}{272}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{107}{272}\right)\)	\(e\left(\frac{11}{272}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{67}{272}\right)\)	\(e\left(\frac{149}{272}\right)\)	\(e\left(\frac{10}{17}\right)\)
\(\chi_{7225}(143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{15}{272}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{213}{272}\right)\)	\(e\left(\frac{149}{272}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{141}{272}\right)\)	\(e\left(\frac{139}{272}\right)\)	\(e\left(\frac{1}{17}\right)\)
\(\chi_{7225}(182,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{201}{272}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{243}{272}\right)\)	\(e\left(\frac{147}{272}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{203}{272}\right)\)	\(e\left(\frac{13}{272}\right)\)	\(e\left(\frac{10}{17}\right)\)
\(\chi_{7225}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{67}{272}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{81}{272}\right)\)	\(e\left(\frac{49}{272}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{249}{272}\right)\)	\(e\left(\frac{95}{272}\right)\)	\(e\left(\frac{9}{17}\right)\)
\(\chi_{7225}(207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{157}{272}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{271}{272}\right)\)	\(e\left(\frac{127}{272}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{7}{272}\right)\)	\(e\left(\frac{113}{272}\right)\)	\(e\left(\frac{15}{17}\right)\)
\(\chi_{7225}(368,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{235}{272}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{73}{272}\right)\)	\(e\left(\frac{249}{272}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{33}{272}\right)\)	\(e\left(\frac{183}{272}\right)\)	\(e\left(\frac{10}{17}\right)\)
\(\chi_{7225}(418,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{23}{272}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{109}{272}\right)\)	\(e\left(\frac{29}{272}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{53}{272}\right)\)	\(e\left(\frac{195}{272}\right)\)	\(e\left(\frac{14}{17}\right)\)
\(\chi_{7225}(507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{53}{272}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{263}{272}\right)\)	\(e\left(\frac{55}{272}\right)\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{63}{272}\right)\)	\(e\left(\frac{201}{272}\right)\)	\(e\left(\frac{16}{17}\right)\)
\(\chi_{7225}(532,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{209}{272}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{139}{272}\right)\)	\(e\left(\frac{27}{272}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{115}{272}\right)\)	\(e\left(\frac{69}{272}\right)\)	\(e\left(\frac{6}{17}\right)\)
\(\chi_{7225}(568,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{79}{272}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{197}{272}\right)\)	\(e\left(\frac{5}{272}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{253}{272}\right)\)	\(e\left(\frac{43}{272}\right)\)	\(e\left(\frac{3}{17}\right)\)
\(\chi_{7225}(607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{57}{272}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{131}{272}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{155}{272}\right)\)	\(e\left(\frac{93}{272}\right)\)	\(e\left(\frac{14}{17}\right)\)
\(\chi_{7225}(632,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{125}{272}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{143}{272}\right)\)	\(e\left(\frac{63}{272}\right)\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{87}{272}\right)\)	\(e\left(\frac{161}{272}\right)\)	\(e\left(\frac{14}{17}\right)\)
\(\chi_{7225}(793,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{251}{272}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{137}{272}\right)\)	\(e\left(\frac{9}{272}\right)\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{129}{272}\right)\)	\(e\left(\frac{23}{272}\right)\)	\(e\left(\frac{2}{17}\right)\)
\(\chi_{7225}(843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{231}{272}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{125}{272}\right)\)	\(e\left(\frac{173}{272}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{213}{272}\right)\)	\(e\left(\frac{19}{272}\right)\)	\(e\left(\frac{12}{17}\right)\)
\(\chi_{7225}(957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{81}{272}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{171}{272}\right)\)	\(e\left(\frac{43}{272}\right)\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{163}{272}\right)\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{2}{17}\right)\)
\(\chi_{7225}(993,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{143}{272}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{181}{272}\right)\)	\(e\left(\frac{133}{272}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{93}{272}\right)\)	\(e\left(\frac{219}{272}\right)\)	\(e\left(\frac{5}{17}\right)\)
\(\chi_{7225}(1032,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{185}{272}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{179}{272}\right)\)	\(e\left(\frac{115}{272}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{107}{272}\right)\)	\(e\left(\frac{173}{272}\right)\)	\(e\left(\frac{1}{17}\right)\)
\(\chi_{7225}(1043,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{35}{272}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{225}{272}\right)\)	\(e\left(\frac{257}{272}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{57}{272}\right)\)	\(e\left(\frac{143}{272}\right)\)	\(e\left(\frac{8}{17}\right)\)
\(\chi_{7225}(1057,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{93}{272}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{15}{272}\right)\)	\(e\left(\frac{271}{272}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{167}{272}\right)\)	\(e\left(\frac{209}{272}\right)\)	\(e\left(\frac{13}{17}\right)\)
\(\chi_{7225}(1218,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{136}\right)\)	\(e\left(\frac{267}{272}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{201}{272}\right)\)	\(e\left(\frac{41}{272}\right)\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{225}{272}\right)\)	\(e\left(\frac{135}{272}\right)\)	\(e\left(\frac{11}{17}\right)\)
\(\chi_{7225}(1268,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{167}{272}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{141}{272}\right)\)	\(e\left(\frac{45}{272}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{101}{272}\right)\)	\(e\left(\frac{115}{272}\right)\)	\(e\left(\frac{10}{17}\right)\)
\(\chi_{7225}(1357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{117}{272}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{247}{272}\right)\)	\(e\left(\frac{183}{272}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{117}{136}\right)\)	\(e\left(\frac{175}{272}\right)\)	\(e\left(\frac{105}{272}\right)\)	\(e\left(\frac{1}{17}\right)\)
\(\chi_{7225}(1382,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{225}{272}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{203}{272}\right)\)	\(e\left(\frac{59}{272}\right)\)	\(e\left(\frac{103}{136}\right)\)	\(e\left(\frac{89}{136}\right)\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{181}{272}\right)\)	\(e\left(\frac{15}{17}\right)\)
\(\chi_{7225}(1418,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{165}{272}\right)\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{205}{272}\right)\)	\(e\left(\frac{123}{272}\right)\)	\(e\left(\frac{7}{17}\right)\)
\(\chi_{7225}(1457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{41}{272}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{147}{272}\right)\)	\(e\left(\frac{99}{272}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{59}{272}\right)\)	\(e\left(\frac{253}{272}\right)\)	\(e\left(\frac{5}{17}\right)\)
\(\chi_{7225}(1468,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{19}{272}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{161}{272}\right)\)	\(e\left(\frac{225}{272}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{233}{272}\right)\)	\(e\left(\frac{31}{272}\right)\)	\(e\left(\frac{16}{17}\right)\)
\(\chi_{7225}(1482,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{61}{272}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{159}{272}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{11}{136}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{247}{272}\right)\)	\(e\left(\frac{257}{272}\right)\)	\(e\left(\frac{12}{17}\right)\)
\(\chi_{7225}(1643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{11}{272}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{265}{272}\right)\)	\(e\left(\frac{73}{272}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{11}{136}\right)\)	\(e\left(\frac{49}{272}\right)\)	\(e\left(\frac{247}{272}\right)\)	\(e\left(\frac{3}{17}\right)\)
\(\chi_{7225}(1693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{103}{272}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{157}{272}\right)\)	\(e\left(\frac{189}{272}\right)\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{103}{136}\right)\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{8}{17}\right)\)
\(\chi_{7225}(1782,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{149}{272}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{103}{272}\right)\)	\(e\left(\frac{247}{272}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{95}{272}\right)\)	\(e\left(\frac{57}{272}\right)\)	\(e\left(\frac{2}{17}\right)\)

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First 31 of 128 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	7225.cc
Modulus	$7225$
Conductor	$1445$
Order	$272$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(7225\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1445\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(272\)	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 1445.bg	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);