LMFDB - Dirichlet character orbit 605.u

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(110)) M = H._module chi = DirichletCharacter(H, M([55,2])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(4, 605)) 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("605.4"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$605$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$605$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$110$	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:	$\Q(\zeta_{55})$	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 110 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{605}(4,\cdot)$	$1$	$1$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{605}(14,\cdot)$	$1$	$1$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{605}(49,\cdot)$	$1$	$1$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{605}(59,\cdot)$	$1$	$1$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{605}(64,\cdot)$	$1$	$1$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{605}(69,\cdot)$	$1$	$1$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{605}(104,\cdot)$	$1$	$1$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{31}{55}\right)$
$\chi_{605}(114,\cdot)$	$1$	$1$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{605}(119,\cdot)$	$1$	$1$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{605}(159,\cdot)$	$1$	$1$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{605}(169,\cdot)$	$1$	$1$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{38}{55}\right)$
$\chi_{605}(174,\cdot)$	$1$	$1$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{605}(179,\cdot)$	$1$	$1$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{605}(214,\cdot)$	$1$	$1$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{36}{55}\right)$
$\chi_{605}(224,\cdot)$	$1$	$1$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{605}(229,\cdot)$	$1$	$1$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{19}{55}\right)$
$\chi_{605}(234,\cdot)$	$1$	$1$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{605}(279,\cdot)$	$1$	$1$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{605}(284,\cdot)$	$1$	$1$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{605}(289,\cdot)$	$1$	$1$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{605}(324,\cdot)$	$1$	$1$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{605}(334,\cdot)$	$1$	$1$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{605}(339,\cdot)$	$1$	$1$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{34}{55}\right)$
$\chi_{605}(344,\cdot)$	$1$	$1$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{2}{55}\right)$
$\chi_{605}(379,\cdot)$	$1$	$1$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{605}(389,\cdot)$	$1$	$1$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{605}(394,\cdot)$	$1$	$1$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{14}{55}\right)$
$\chi_{605}(399,\cdot)$	$1$	$1$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{605}(434,\cdot)$	$1$	$1$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{605}(449,\cdot)$	$1$	$1$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{605}(454,\cdot)$	$1$	$1$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{47}{55}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{605}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{605}(14,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{605}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{1}{55}\right)\)
\(\chi_{605}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{605}(64,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{605}(69,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{605}(104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)
\(\chi_{605}(114,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{605}(119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{605}(159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{605}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{38}{55}\right)\)
\(\chi_{605}(174,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{605}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{605}(214,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)
\(\chi_{605}(224,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{605}(229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)
\(\chi_{605}(234,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{605}(279,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{605}(284,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{605}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{605}(324,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{605}(334,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{605}(339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{34}{55}\right)\)
\(\chi_{605}(344,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{2}{55}\right)\)
\(\chi_{605}(379,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{605}(389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{605}(394,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)
\(\chi_{605}(399,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{605}(434,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{605}(449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{605}(454,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)

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First 31 of 40 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	605.u
Modulus	$605$
Conductor	$605$
Order	$110$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(605\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(605\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(110\)	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);