LMFDB - Dirichlet character orbit 2575.bf

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2575, base_ring=CyclotomicField(170)) M = H._module chi = DirichletCharacter(H, M([136,60])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(61, 2575)) 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("2575.61"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$2575$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$2575$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$85$	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:	$\Q(\zeta_{85})$
Fixed field:	Number field defined by a degree 85 polynomial

First 31 of 64 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{2575}(61,\cdot)$	$1$	$1$	$e\left(\frac{28}{85}\right)$	$e\left(\frac{31}{85}\right)$	$e\left(\frac{56}{85}\right)$	$e\left(\frac{59}{85}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{84}{85}\right)$	$e\left(\frac{62}{85}\right)$	$e\left(\frac{28}{85}\right)$	$e\left(\frac{2}{85}\right)$	$e\left(\frac{52}{85}\right)$
$\chi_{2575}(66,\cdot)$	$1$	$1$	$e\left(\frac{27}{85}\right)$	$e\left(\frac{39}{85}\right)$	$e\left(\frac{54}{85}\right)$	$e\left(\frac{66}{85}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{81}{85}\right)$	$e\left(\frac{78}{85}\right)$	$e\left(\frac{27}{85}\right)$	$e\left(\frac{8}{85}\right)$	$e\left(\frac{38}{85}\right)$
$\chi_{2575}(81,\cdot)$	$1$	$1$	$e\left(\frac{59}{85}\right)$	$e\left(\frac{38}{85}\right)$	$e\left(\frac{33}{85}\right)$	$e\left(\frac{12}{85}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{7}{85}\right)$	$e\left(\frac{76}{85}\right)$	$e\left(\frac{59}{85}\right)$	$e\left(\frac{71}{85}\right)$	$e\left(\frac{61}{85}\right)$
$\chi_{2575}(111,\cdot)$	$1$	$1$	$e\left(\frac{63}{85}\right)$	$e\left(\frac{6}{85}\right)$	$e\left(\frac{41}{85}\right)$	$e\left(\frac{69}{85}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{19}{85}\right)$	$e\left(\frac{12}{85}\right)$	$e\left(\frac{63}{85}\right)$	$e\left(\frac{47}{85}\right)$	$e\left(\frac{32}{85}\right)$
$\chi_{2575}(116,\cdot)$	$1$	$1$	$e\left(\frac{22}{85}\right)$	$e\left(\frac{79}{85}\right)$	$e\left(\frac{44}{85}\right)$	$e\left(\frac{16}{85}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{66}{85}\right)$	$e\left(\frac{73}{85}\right)$	$e\left(\frac{22}{85}\right)$	$e\left(\frac{38}{85}\right)$	$e\left(\frac{53}{85}\right)$
$\chi_{2575}(196,\cdot)$	$1$	$1$	$e\left(\frac{1}{85}\right)$	$e\left(\frac{77}{85}\right)$	$e\left(\frac{2}{85}\right)$	$e\left(\frac{78}{85}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{3}{85}\right)$	$e\left(\frac{69}{85}\right)$	$e\left(\frac{1}{85}\right)$	$e\left(\frac{79}{85}\right)$	$e\left(\frac{14}{85}\right)$
$\chi_{2575}(236,\cdot)$	$1$	$1$	$e\left(\frac{3}{85}\right)$	$e\left(\frac{61}{85}\right)$	$e\left(\frac{6}{85}\right)$	$e\left(\frac{64}{85}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{9}{85}\right)$	$e\left(\frac{37}{85}\right)$	$e\left(\frac{3}{85}\right)$	$e\left(\frac{67}{85}\right)$	$e\left(\frac{42}{85}\right)$
$\chi_{2575}(306,\cdot)$	$1$	$1$	$e\left(\frac{19}{85}\right)$	$e\left(\frac{18}{85}\right)$	$e\left(\frac{38}{85}\right)$	$e\left(\frac{37}{85}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{57}{85}\right)$	$e\left(\frac{36}{85}\right)$	$e\left(\frac{19}{85}\right)$	$e\left(\frac{56}{85}\right)$	$e\left(\frac{11}{85}\right)$
$\chi_{2575}(381,\cdot)$	$1$	$1$	$e\left(\frac{84}{85}\right)$	$e\left(\frac{8}{85}\right)$	$e\left(\frac{83}{85}\right)$	$e\left(\frac{7}{85}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{82}{85}\right)$	$e\left(\frac{16}{85}\right)$	$e\left(\frac{84}{85}\right)$	$e\left(\frac{6}{85}\right)$	$e\left(\frac{71}{85}\right)$
$\chi_{2575}(421,\cdot)$	$1$	$1$	$e\left(\frac{21}{85}\right)$	$e\left(\frac{2}{85}\right)$	$e\left(\frac{42}{85}\right)$	$e\left(\frac{23}{85}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{63}{85}\right)$	$e\left(\frac{4}{85}\right)$	$e\left(\frac{21}{85}\right)$	$e\left(\frac{44}{85}\right)$	$e\left(\frac{39}{85}\right)$
$\chi_{2575}(446,\cdot)$	$1$	$1$	$e\left(\frac{66}{85}\right)$	$e\left(\frac{67}{85}\right)$	$e\left(\frac{47}{85}\right)$	$e\left(\frac{48}{85}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{28}{85}\right)$	$e\left(\frac{49}{85}\right)$	$e\left(\frac{66}{85}\right)$	$e\left(\frac{29}{85}\right)$	$e\left(\frac{74}{85}\right)$
$\chi_{2575}(491,\cdot)$	$1$	$1$	$e\left(\frac{82}{85}\right)$	$e\left(\frac{24}{85}\right)$	$e\left(\frac{79}{85}\right)$	$e\left(\frac{21}{85}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{76}{85}\right)$	$e\left(\frac{48}{85}\right)$	$e\left(\frac{82}{85}\right)$	$e\left(\frac{18}{85}\right)$	$e\left(\frac{43}{85}\right)$
$\chi_{2575}(581,\cdot)$	$1$	$1$	$e\left(\frac{44}{85}\right)$	$e\left(\frac{73}{85}\right)$	$e\left(\frac{3}{85}\right)$	$e\left(\frac{32}{85}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{47}{85}\right)$	$e\left(\frac{61}{85}\right)$	$e\left(\frac{44}{85}\right)$	$e\left(\frac{76}{85}\right)$	$e\left(\frac{21}{85}\right)$
$\chi_{2575}(591,\cdot)$	$1$	$1$	$e\left(\frac{57}{85}\right)$	$e\left(\frac{54}{85}\right)$	$e\left(\frac{29}{85}\right)$	$e\left(\frac{26}{85}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{1}{85}\right)$	$e\left(\frac{23}{85}\right)$	$e\left(\frac{57}{85}\right)$	$e\left(\frac{83}{85}\right)$	$e\left(\frac{33}{85}\right)$
$\chi_{2575}(596,\cdot)$	$1$	$1$	$e\left(\frac{76}{85}\right)$	$e\left(\frac{72}{85}\right)$	$e\left(\frac{67}{85}\right)$	$e\left(\frac{63}{85}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{58}{85}\right)$	$e\left(\frac{59}{85}\right)$	$e\left(\frac{76}{85}\right)$	$e\left(\frac{54}{85}\right)$	$e\left(\frac{44}{85}\right)$
$\chi_{2575}(631,\cdot)$	$1$	$1$	$e\left(\frac{39}{85}\right)$	$e\left(\frac{28}{85}\right)$	$e\left(\frac{78}{85}\right)$	$e\left(\frac{67}{85}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{32}{85}\right)$	$e\left(\frac{56}{85}\right)$	$e\left(\frac{39}{85}\right)$	$e\left(\frac{21}{85}\right)$	$e\left(\frac{36}{85}\right)$
$\chi_{2575}(641,\cdot)$	$1$	$1$	$e\left(\frac{47}{85}\right)$	$e\left(\frac{49}{85}\right)$	$e\left(\frac{9}{85}\right)$	$e\left(\frac{11}{85}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{56}{85}\right)$	$e\left(\frac{13}{85}\right)$	$e\left(\frac{47}{85}\right)$	$e\left(\frac{58}{85}\right)$	$e\left(\frac{63}{85}\right)$
$\chi_{2575}(711,\cdot)$	$1$	$1$	$e\left(\frac{18}{85}\right)$	$e\left(\frac{26}{85}\right)$	$e\left(\frac{36}{85}\right)$	$e\left(\frac{44}{85}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{54}{85}\right)$	$e\left(\frac{52}{85}\right)$	$e\left(\frac{18}{85}\right)$	$e\left(\frac{62}{85}\right)$	$e\left(\frac{82}{85}\right)$
$\chi_{2575}(821,\cdot)$	$1$	$1$	$e\left(\frac{36}{85}\right)$	$e\left(\frac{52}{85}\right)$	$e\left(\frac{72}{85}\right)$	$e\left(\frac{3}{85}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{23}{85}\right)$	$e\left(\frac{19}{85}\right)$	$e\left(\frac{36}{85}\right)$	$e\left(\frac{39}{85}\right)$	$e\left(\frac{79}{85}\right)$
$\chi_{2575}(896,\cdot)$	$1$	$1$	$e\left(\frac{16}{85}\right)$	$e\left(\frac{42}{85}\right)$	$e\left(\frac{32}{85}\right)$	$e\left(\frac{58}{85}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{48}{85}\right)$	$e\left(\frac{84}{85}\right)$	$e\left(\frac{16}{85}\right)$	$e\left(\frac{74}{85}\right)$	$e\left(\frac{54}{85}\right)$
$\chi_{2575}(936,\cdot)$	$1$	$1$	$e\left(\frac{38}{85}\right)$	$e\left(\frac{36}{85}\right)$	$e\left(\frac{76}{85}\right)$	$e\left(\frac{74}{85}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{29}{85}\right)$	$e\left(\frac{72}{85}\right)$	$e\left(\frac{38}{85}\right)$	$e\left(\frac{27}{85}\right)$	$e\left(\frac{22}{85}\right)$
$\chi_{2575}(941,\cdot)$	$1$	$1$	$e\left(\frac{77}{85}\right)$	$e\left(\frac{64}{85}\right)$	$e\left(\frac{69}{85}\right)$	$e\left(\frac{56}{85}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{61}{85}\right)$	$e\left(\frac{43}{85}\right)$	$e\left(\frac{77}{85}\right)$	$e\left(\frac{48}{85}\right)$	$e\left(\frac{58}{85}\right)$
$\chi_{2575}(961,\cdot)$	$1$	$1$	$e\left(\frac{83}{85}\right)$	$e\left(\frac{16}{85}\right)$	$e\left(\frac{81}{85}\right)$	$e\left(\frac{14}{85}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{79}{85}\right)$	$e\left(\frac{32}{85}\right)$	$e\left(\frac{83}{85}\right)$	$e\left(\frac{12}{85}\right)$	$e\left(\frac{57}{85}\right)$
$\chi_{2575}(991,\cdot)$	$1$	$1$	$e\left(\frac{7}{85}\right)$	$e\left(\frac{29}{85}\right)$	$e\left(\frac{14}{85}\right)$	$e\left(\frac{36}{85}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{21}{85}\right)$	$e\left(\frac{58}{85}\right)$	$e\left(\frac{7}{85}\right)$	$e\left(\frac{43}{85}\right)$	$e\left(\frac{13}{85}\right)$
$\chi_{2575}(1006,\cdot)$	$1$	$1$	$e\left(\frac{14}{85}\right)$	$e\left(\frac{58}{85}\right)$	$e\left(\frac{28}{85}\right)$	$e\left(\frac{72}{85}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{42}{85}\right)$	$e\left(\frac{31}{85}\right)$	$e\left(\frac{14}{85}\right)$	$e\left(\frac{1}{85}\right)$	$e\left(\frac{26}{85}\right)$
$\chi_{2575}(1091,\cdot)$	$1$	$1$	$e\left(\frac{62}{85}\right)$	$e\left(\frac{14}{85}\right)$	$e\left(\frac{39}{85}\right)$	$e\left(\frac{76}{85}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{16}{85}\right)$	$e\left(\frac{28}{85}\right)$	$e\left(\frac{62}{85}\right)$	$e\left(\frac{53}{85}\right)$	$e\left(\frac{18}{85}\right)$
$\chi_{2575}(1096,\cdot)$	$1$	$1$	$e\left(\frac{61}{85}\right)$	$e\left(\frac{22}{85}\right)$	$e\left(\frac{37}{85}\right)$	$e\left(\frac{83}{85}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{13}{85}\right)$	$e\left(\frac{44}{85}\right)$	$e\left(\frac{61}{85}\right)$	$e\left(\frac{59}{85}\right)$	$e\left(\frac{4}{85}\right)$
$\chi_{2575}(1106,\cdot)$	$1$	$1$	$e\left(\frac{74}{85}\right)$	$e\left(\frac{3}{85}\right)$	$e\left(\frac{63}{85}\right)$	$e\left(\frac{77}{85}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{52}{85}\right)$	$e\left(\frac{6}{85}\right)$	$e\left(\frac{74}{85}\right)$	$e\left(\frac{66}{85}\right)$	$e\left(\frac{16}{85}\right)$
$\chi_{2575}(1111,\cdot)$	$1$	$1$	$e\left(\frac{8}{85}\right)$	$e\left(\frac{21}{85}\right)$	$e\left(\frac{16}{85}\right)$	$e\left(\frac{29}{85}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{24}{85}\right)$	$e\left(\frac{42}{85}\right)$	$e\left(\frac{8}{85}\right)$	$e\left(\frac{37}{85}\right)$	$e\left(\frac{27}{85}\right)$
$\chi_{2575}(1141,\cdot)$	$1$	$1$	$e\left(\frac{12}{85}\right)$	$e\left(\frac{74}{85}\right)$	$e\left(\frac{24}{85}\right)$	$e\left(\frac{1}{85}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{36}{85}\right)$	$e\left(\frac{63}{85}\right)$	$e\left(\frac{12}{85}\right)$	$e\left(\frac{13}{85}\right)$	$e\left(\frac{83}{85}\right)$
$\chi_{2575}(1146,\cdot)$	$1$	$1$	$e\left(\frac{56}{85}\right)$	$e\left(\frac{62}{85}\right)$	$e\left(\frac{27}{85}\right)$	$e\left(\frac{33}{85}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{83}{85}\right)$	$e\left(\frac{39}{85}\right)$	$e\left(\frac{56}{85}\right)$	$e\left(\frac{4}{85}\right)$	$e\left(\frac{19}{85}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{2575}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{85}\right)\)	\(e\left(\frac{31}{85}\right)\)	\(e\left(\frac{56}{85}\right)\)	\(e\left(\frac{59}{85}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{84}{85}\right)\)	\(e\left(\frac{62}{85}\right)\)	\(e\left(\frac{28}{85}\right)\)	\(e\left(\frac{2}{85}\right)\)	\(e\left(\frac{52}{85}\right)\)
\(\chi_{2575}(66,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{85}\right)\)	\(e\left(\frac{39}{85}\right)\)	\(e\left(\frac{54}{85}\right)\)	\(e\left(\frac{66}{85}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{81}{85}\right)\)	\(e\left(\frac{78}{85}\right)\)	\(e\left(\frac{27}{85}\right)\)	\(e\left(\frac{8}{85}\right)\)	\(e\left(\frac{38}{85}\right)\)
\(\chi_{2575}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{85}\right)\)	\(e\left(\frac{38}{85}\right)\)	\(e\left(\frac{33}{85}\right)\)	\(e\left(\frac{12}{85}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{7}{85}\right)\)	\(e\left(\frac{76}{85}\right)\)	\(e\left(\frac{59}{85}\right)\)	\(e\left(\frac{71}{85}\right)\)	\(e\left(\frac{61}{85}\right)\)
\(\chi_{2575}(111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{85}\right)\)	\(e\left(\frac{6}{85}\right)\)	\(e\left(\frac{41}{85}\right)\)	\(e\left(\frac{69}{85}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{19}{85}\right)\)	\(e\left(\frac{12}{85}\right)\)	\(e\left(\frac{63}{85}\right)\)	\(e\left(\frac{47}{85}\right)\)	\(e\left(\frac{32}{85}\right)\)
\(\chi_{2575}(116,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{85}\right)\)	\(e\left(\frac{79}{85}\right)\)	\(e\left(\frac{44}{85}\right)\)	\(e\left(\frac{16}{85}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{66}{85}\right)\)	\(e\left(\frac{73}{85}\right)\)	\(e\left(\frac{22}{85}\right)\)	\(e\left(\frac{38}{85}\right)\)	\(e\left(\frac{53}{85}\right)\)
\(\chi_{2575}(196,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{85}\right)\)	\(e\left(\frac{77}{85}\right)\)	\(e\left(\frac{2}{85}\right)\)	\(e\left(\frac{78}{85}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{3}{85}\right)\)	\(e\left(\frac{69}{85}\right)\)	\(e\left(\frac{1}{85}\right)\)	\(e\left(\frac{79}{85}\right)\)	\(e\left(\frac{14}{85}\right)\)
\(\chi_{2575}(236,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{85}\right)\)	\(e\left(\frac{61}{85}\right)\)	\(e\left(\frac{6}{85}\right)\)	\(e\left(\frac{64}{85}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{9}{85}\right)\)	\(e\left(\frac{37}{85}\right)\)	\(e\left(\frac{3}{85}\right)\)	\(e\left(\frac{67}{85}\right)\)	\(e\left(\frac{42}{85}\right)\)
\(\chi_{2575}(306,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{85}\right)\)	\(e\left(\frac{18}{85}\right)\)	\(e\left(\frac{38}{85}\right)\)	\(e\left(\frac{37}{85}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{57}{85}\right)\)	\(e\left(\frac{36}{85}\right)\)	\(e\left(\frac{19}{85}\right)\)	\(e\left(\frac{56}{85}\right)\)	\(e\left(\frac{11}{85}\right)\)
\(\chi_{2575}(381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{84}{85}\right)\)	\(e\left(\frac{8}{85}\right)\)	\(e\left(\frac{83}{85}\right)\)	\(e\left(\frac{7}{85}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{82}{85}\right)\)	\(e\left(\frac{16}{85}\right)\)	\(e\left(\frac{84}{85}\right)\)	\(e\left(\frac{6}{85}\right)\)	\(e\left(\frac{71}{85}\right)\)
\(\chi_{2575}(421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{85}\right)\)	\(e\left(\frac{2}{85}\right)\)	\(e\left(\frac{42}{85}\right)\)	\(e\left(\frac{23}{85}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{63}{85}\right)\)	\(e\left(\frac{4}{85}\right)\)	\(e\left(\frac{21}{85}\right)\)	\(e\left(\frac{44}{85}\right)\)	\(e\left(\frac{39}{85}\right)\)
\(\chi_{2575}(446,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{66}{85}\right)\)	\(e\left(\frac{67}{85}\right)\)	\(e\left(\frac{47}{85}\right)\)	\(e\left(\frac{48}{85}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{28}{85}\right)\)	\(e\left(\frac{49}{85}\right)\)	\(e\left(\frac{66}{85}\right)\)	\(e\left(\frac{29}{85}\right)\)	\(e\left(\frac{74}{85}\right)\)
\(\chi_{2575}(491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{85}\right)\)	\(e\left(\frac{24}{85}\right)\)	\(e\left(\frac{79}{85}\right)\)	\(e\left(\frac{21}{85}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{76}{85}\right)\)	\(e\left(\frac{48}{85}\right)\)	\(e\left(\frac{82}{85}\right)\)	\(e\left(\frac{18}{85}\right)\)	\(e\left(\frac{43}{85}\right)\)
\(\chi_{2575}(581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{85}\right)\)	\(e\left(\frac{73}{85}\right)\)	\(e\left(\frac{3}{85}\right)\)	\(e\left(\frac{32}{85}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{47}{85}\right)\)	\(e\left(\frac{61}{85}\right)\)	\(e\left(\frac{44}{85}\right)\)	\(e\left(\frac{76}{85}\right)\)	\(e\left(\frac{21}{85}\right)\)
\(\chi_{2575}(591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{85}\right)\)	\(e\left(\frac{54}{85}\right)\)	\(e\left(\frac{29}{85}\right)\)	\(e\left(\frac{26}{85}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{1}{85}\right)\)	\(e\left(\frac{23}{85}\right)\)	\(e\left(\frac{57}{85}\right)\)	\(e\left(\frac{83}{85}\right)\)	\(e\left(\frac{33}{85}\right)\)
\(\chi_{2575}(596,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{85}\right)\)	\(e\left(\frac{72}{85}\right)\)	\(e\left(\frac{67}{85}\right)\)	\(e\left(\frac{63}{85}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{58}{85}\right)\)	\(e\left(\frac{59}{85}\right)\)	\(e\left(\frac{76}{85}\right)\)	\(e\left(\frac{54}{85}\right)\)	\(e\left(\frac{44}{85}\right)\)
\(\chi_{2575}(631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{85}\right)\)	\(e\left(\frac{28}{85}\right)\)	\(e\left(\frac{78}{85}\right)\)	\(e\left(\frac{67}{85}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{32}{85}\right)\)	\(e\left(\frac{56}{85}\right)\)	\(e\left(\frac{39}{85}\right)\)	\(e\left(\frac{21}{85}\right)\)	\(e\left(\frac{36}{85}\right)\)
\(\chi_{2575}(641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{85}\right)\)	\(e\left(\frac{49}{85}\right)\)	\(e\left(\frac{9}{85}\right)\)	\(e\left(\frac{11}{85}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{56}{85}\right)\)	\(e\left(\frac{13}{85}\right)\)	\(e\left(\frac{47}{85}\right)\)	\(e\left(\frac{58}{85}\right)\)	\(e\left(\frac{63}{85}\right)\)
\(\chi_{2575}(711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{85}\right)\)	\(e\left(\frac{26}{85}\right)\)	\(e\left(\frac{36}{85}\right)\)	\(e\left(\frac{44}{85}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{54}{85}\right)\)	\(e\left(\frac{52}{85}\right)\)	\(e\left(\frac{18}{85}\right)\)	\(e\left(\frac{62}{85}\right)\)	\(e\left(\frac{82}{85}\right)\)
\(\chi_{2575}(821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{36}{85}\right)\)	\(e\left(\frac{52}{85}\right)\)	\(e\left(\frac{72}{85}\right)\)	\(e\left(\frac{3}{85}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{23}{85}\right)\)	\(e\left(\frac{19}{85}\right)\)	\(e\left(\frac{36}{85}\right)\)	\(e\left(\frac{39}{85}\right)\)	\(e\left(\frac{79}{85}\right)\)
\(\chi_{2575}(896,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{85}\right)\)	\(e\left(\frac{42}{85}\right)\)	\(e\left(\frac{32}{85}\right)\)	\(e\left(\frac{58}{85}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{48}{85}\right)\)	\(e\left(\frac{84}{85}\right)\)	\(e\left(\frac{16}{85}\right)\)	\(e\left(\frac{74}{85}\right)\)	\(e\left(\frac{54}{85}\right)\)
\(\chi_{2575}(936,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{85}\right)\)	\(e\left(\frac{36}{85}\right)\)	\(e\left(\frac{76}{85}\right)\)	\(e\left(\frac{74}{85}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{29}{85}\right)\)	\(e\left(\frac{72}{85}\right)\)	\(e\left(\frac{38}{85}\right)\)	\(e\left(\frac{27}{85}\right)\)	\(e\left(\frac{22}{85}\right)\)
\(\chi_{2575}(941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{85}\right)\)	\(e\left(\frac{64}{85}\right)\)	\(e\left(\frac{69}{85}\right)\)	\(e\left(\frac{56}{85}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{61}{85}\right)\)	\(e\left(\frac{43}{85}\right)\)	\(e\left(\frac{77}{85}\right)\)	\(e\left(\frac{48}{85}\right)\)	\(e\left(\frac{58}{85}\right)\)
\(\chi_{2575}(961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{85}\right)\)	\(e\left(\frac{16}{85}\right)\)	\(e\left(\frac{81}{85}\right)\)	\(e\left(\frac{14}{85}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{79}{85}\right)\)	\(e\left(\frac{32}{85}\right)\)	\(e\left(\frac{83}{85}\right)\)	\(e\left(\frac{12}{85}\right)\)	\(e\left(\frac{57}{85}\right)\)
\(\chi_{2575}(991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{85}\right)\)	\(e\left(\frac{29}{85}\right)\)	\(e\left(\frac{14}{85}\right)\)	\(e\left(\frac{36}{85}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{21}{85}\right)\)	\(e\left(\frac{58}{85}\right)\)	\(e\left(\frac{7}{85}\right)\)	\(e\left(\frac{43}{85}\right)\)	\(e\left(\frac{13}{85}\right)\)
\(\chi_{2575}(1006,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{85}\right)\)	\(e\left(\frac{58}{85}\right)\)	\(e\left(\frac{28}{85}\right)\)	\(e\left(\frac{72}{85}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{42}{85}\right)\)	\(e\left(\frac{31}{85}\right)\)	\(e\left(\frac{14}{85}\right)\)	\(e\left(\frac{1}{85}\right)\)	\(e\left(\frac{26}{85}\right)\)
\(\chi_{2575}(1091,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{85}\right)\)	\(e\left(\frac{14}{85}\right)\)	\(e\left(\frac{39}{85}\right)\)	\(e\left(\frac{76}{85}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{16}{85}\right)\)	\(e\left(\frac{28}{85}\right)\)	\(e\left(\frac{62}{85}\right)\)	\(e\left(\frac{53}{85}\right)\)	\(e\left(\frac{18}{85}\right)\)
\(\chi_{2575}(1096,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{85}\right)\)	\(e\left(\frac{22}{85}\right)\)	\(e\left(\frac{37}{85}\right)\)	\(e\left(\frac{83}{85}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{13}{85}\right)\)	\(e\left(\frac{44}{85}\right)\)	\(e\left(\frac{61}{85}\right)\)	\(e\left(\frac{59}{85}\right)\)	\(e\left(\frac{4}{85}\right)\)
\(\chi_{2575}(1106,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{85}\right)\)	\(e\left(\frac{3}{85}\right)\)	\(e\left(\frac{63}{85}\right)\)	\(e\left(\frac{77}{85}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{52}{85}\right)\)	\(e\left(\frac{6}{85}\right)\)	\(e\left(\frac{74}{85}\right)\)	\(e\left(\frac{66}{85}\right)\)	\(e\left(\frac{16}{85}\right)\)
\(\chi_{2575}(1111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{85}\right)\)	\(e\left(\frac{21}{85}\right)\)	\(e\left(\frac{16}{85}\right)\)	\(e\left(\frac{29}{85}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{24}{85}\right)\)	\(e\left(\frac{42}{85}\right)\)	\(e\left(\frac{8}{85}\right)\)	\(e\left(\frac{37}{85}\right)\)	\(e\left(\frac{27}{85}\right)\)
\(\chi_{2575}(1141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{85}\right)\)	\(e\left(\frac{74}{85}\right)\)	\(e\left(\frac{24}{85}\right)\)	\(e\left(\frac{1}{85}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{36}{85}\right)\)	\(e\left(\frac{63}{85}\right)\)	\(e\left(\frac{12}{85}\right)\)	\(e\left(\frac{13}{85}\right)\)	\(e\left(\frac{83}{85}\right)\)
\(\chi_{2575}(1146,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{85}\right)\)	\(e\left(\frac{62}{85}\right)\)	\(e\left(\frac{27}{85}\right)\)	\(e\left(\frac{33}{85}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{83}{85}\right)\)	\(e\left(\frac{39}{85}\right)\)	\(e\left(\frac{56}{85}\right)\)	\(e\left(\frac{4}{85}\right)\)	\(e\left(\frac{19}{85}\right)\)

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First 31 of 64 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	2575.bf
Modulus	$2575$
Conductor	$2575$
Order	$85$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(2575\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(2575\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(85\)	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);