LMFDB - Dirichlet character orbit 4005.dl

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4005, base_ring=CyclotomicField(88)) M = H._module chi = DirichletCharacter(H, M([0,22,37])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(82,4005)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4005$
Conductor:	$445$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$88$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 445.ba	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{88})$
Fixed field:	Number field defined by a degree 88 polynomial

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{4005}(82,\cdot)$	$1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{19}{88}\right)$
$\chi_{4005}(118,\cdot)$	$1$	$1$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{85}{88}\right)$
$\chi_{4005}(163,\cdot)$	$1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{21}{88}\right)$
$\chi_{4005}(172,\cdot)$	$1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{67}{88}\right)$
$\chi_{4005}(208,\cdot)$	$1$	$1$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{88}\right)$
$\chi_{4005}(298,\cdot)$	$1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{73}{88}\right)$
$\chi_{4005}(343,\cdot)$	$1$	$1$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{13}{88}\right)$
$\chi_{4005}(397,\cdot)$	$1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{75}{88}\right)$
$\chi_{4005}(442,\cdot)$	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{35}{88}\right)$
$\chi_{4005}(577,\cdot)$	$1$	$1$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{88}\right)$
$\chi_{4005}(658,\cdot)$	$1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{49}{88}\right)$
$\chi_{4005}(847,\cdot)$	$1$	$1$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{47}{88}\right)$
$\chi_{4005}(928,\cdot)$	$1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{69}{88}\right)$
$\chi_{4005}(982,\cdot)$	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{79}{88}\right)$
$\chi_{4005}(1027,\cdot)$	$1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{31}{88}\right)$
$\chi_{4005}(1252,\cdot)$	$1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{23}{88}\right)$
$\chi_{4005}(1342,\cdot)$	$1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{63}{88}\right)$
$\chi_{4005}(1747,\cdot)$	$1$	$1$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{71}{88}\right)$
$\chi_{4005}(1972,\cdot)$	$1$	$1$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{88}\right)$
$\chi_{4005}(2098,\cdot)$	$1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{25}{88}\right)$
$\chi_{4005}(2197,\cdot)$	$1$	$1$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{83}{88}\right)$
$\chi_{4005}(2368,\cdot)$	$1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{88}\right)$
$\chi_{4005}(2557,\cdot)$	$1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{43}{88}\right)$
$\chi_{4005}(2647,\cdot)$	$1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{59}{88}\right)$
$\chi_{4005}(2683,\cdot)$	$1$	$1$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{57}{88}\right)$
$\chi_{4005}(2728,\cdot)$	$1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{29}{88}\right)$
$\chi_{4005}(2782,\cdot)$	$1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{15}{88}\right)$
$\chi_{4005}(2818,\cdot)$	$1$	$1$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{53}{88}\right)$
$\chi_{4005}(2863,\cdot)$	$1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{65}{88}\right)$
$\chi_{4005}(2872,\cdot)$	$1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{87}{88}\right)$
$\chi_{4005}(2908,\cdot)$	$1$	$1$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{41}{88}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{4005}(82,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{19}{88}\right)\)
\(\chi_{4005}(118,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{85}{88}\right)\)
\(\chi_{4005}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{21}{88}\right)\)
\(\chi_{4005}(172,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{67}{88}\right)\)
\(\chi_{4005}(208,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{88}\right)\)
\(\chi_{4005}(298,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{73}{88}\right)\)
\(\chi_{4005}(343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{13}{88}\right)\)
\(\chi_{4005}(397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{75}{88}\right)\)
\(\chi_{4005}(442,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{35}{88}\right)\)
\(\chi_{4005}(577,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{88}\right)\)
\(\chi_{4005}(658,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{49}{88}\right)\)
\(\chi_{4005}(847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{47}{88}\right)\)
\(\chi_{4005}(928,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{69}{88}\right)\)
\(\chi_{4005}(982,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{79}{88}\right)\)
\(\chi_{4005}(1027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{31}{88}\right)\)
\(\chi_{4005}(1252,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{23}{88}\right)\)
\(\chi_{4005}(1342,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{63}{88}\right)\)
\(\chi_{4005}(1747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{71}{88}\right)\)
\(\chi_{4005}(1972,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{88}\right)\)
\(\chi_{4005}(2098,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{25}{88}\right)\)
\(\chi_{4005}(2197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{83}{88}\right)\)
\(\chi_{4005}(2368,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{88}\right)\)
\(\chi_{4005}(2557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{43}{88}\right)\)
\(\chi_{4005}(2647,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{59}{88}\right)\)
\(\chi_{4005}(2683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{57}{88}\right)\)
\(\chi_{4005}(2728,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{29}{88}\right)\)
\(\chi_{4005}(2782,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{15}{88}\right)\)
\(\chi_{4005}(2818,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{53}{88}\right)\)
\(\chi_{4005}(2863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{65}{88}\right)\)
\(\chi_{4005}(2872,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{87}{88}\right)\)
\(\chi_{4005}(2908,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{41}{88}\right)\)

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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	4005.dl
Modulus	$4005$
Conductor	$445$
Order	$88$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(4005\)
Conductor:	\(445\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(88\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 445.ba	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)