LMFDB - Dirichlet character orbit 4005.dm

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4005, base_ring=CyclotomicField(88)) M = H._module chi = DirichletCharacter(H, M([44,0,39])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(26,4005)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4005$
Conductor:	$267$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$88$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 267.p	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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{4005}(26,\cdot)$	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{45}{88}\right)$
$\chi_{4005}(116,\cdot)$	$1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{17}{88}\right)$
$\chi_{4005}(206,\cdot)$	$1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{83}{88}\right)$
$\chi_{4005}(296,\cdot)$	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{41}{88}\right)$
$\chi_{4005}(341,\cdot)$	$1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{65}{88}\right)$
$\chi_{4005}(386,\cdot)$	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{53}{88}\right)$
$\chi_{4005}(431,\cdot)$	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{7}{88}\right)$
$\chi_{4005}(476,\cdot)$	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{29}{88}\right)$
$\chi_{4005}(521,\cdot)$	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{57}{88}\right)$
$\chi_{4005}(656,\cdot)$	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{71}{88}\right)$
$\chi_{4005}(836,\cdot)$	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{5}{88}\right)$
$\chi_{4005}(1061,\cdot)$	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{63}{88}\right)$
$\chi_{4005}(1106,\cdot)$	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{25}{88}\right)$
$\chi_{4005}(1151,\cdot)$	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{23}{88}\right)$
$\chi_{4005}(1376,\cdot)$	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{31}{88}\right)$
$\chi_{4005}(1421,\cdot)$	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{79}{88}\right)$
$\chi_{4005}(1556,\cdot)$	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{47}{88}\right)$
$\chi_{4005}(1826,\cdot)$	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{3}{88}\right)$
$\chi_{4005}(1961,\cdot)$	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{35}{88}\right)$
$\chi_{4005}(2006,\cdot)$	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{75}{88}\right)$
$\chi_{4005}(2231,\cdot)$	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{67}{88}\right)$
$\chi_{4005}(2276,\cdot)$	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{69}{88}\right)$
$\chi_{4005}(2321,\cdot)$	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{19}{88}\right)$
$\chi_{4005}(2546,\cdot)$	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{49}{88}\right)$
$\chi_{4005}(2726,\cdot)$	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{27}{88}\right)$
$\chi_{4005}(2861,\cdot)$	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{13}{88}\right)$
$\chi_{4005}(2906,\cdot)$	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{73}{88}\right)$
$\chi_{4005}(2951,\cdot)$	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{51}{88}\right)$
$\chi_{4005}(2996,\cdot)$	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{9}{88}\right)$
$\chi_{4005}(3041,\cdot)$	$1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{21}{88}\right)$
$\chi_{4005}(3086,\cdot)$	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{85}{88}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{4005}(26,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{45}{88}\right)\)
\(\chi_{4005}(116,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{17}{88}\right)\)
\(\chi_{4005}(206,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{83}{88}\right)\)
\(\chi_{4005}(296,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{41}{88}\right)\)
\(\chi_{4005}(341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{65}{88}\right)\)
\(\chi_{4005}(386,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{53}{88}\right)\)
\(\chi_{4005}(431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{7}{88}\right)\)
\(\chi_{4005}(476,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{29}{88}\right)\)
\(\chi_{4005}(521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{57}{88}\right)\)
\(\chi_{4005}(656,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{71}{88}\right)\)
\(\chi_{4005}(836,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{5}{88}\right)\)
\(\chi_{4005}(1061,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{63}{88}\right)\)
\(\chi_{4005}(1106,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{25}{88}\right)\)
\(\chi_{4005}(1151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{23}{88}\right)\)
\(\chi_{4005}(1376,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{31}{88}\right)\)
\(\chi_{4005}(1421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{79}{88}\right)\)
\(\chi_{4005}(1556,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{47}{88}\right)\)
\(\chi_{4005}(1826,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{3}{88}\right)\)
\(\chi_{4005}(1961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{35}{88}\right)\)
\(\chi_{4005}(2006,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{75}{88}\right)\)
\(\chi_{4005}(2231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{67}{88}\right)\)
\(\chi_{4005}(2276,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{69}{88}\right)\)
\(\chi_{4005}(2321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{19}{88}\right)\)
\(\chi_{4005}(2546,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{49}{88}\right)\)
\(\chi_{4005}(2726,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{27}{88}\right)\)
\(\chi_{4005}(2861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{13}{88}\right)\)
\(\chi_{4005}(2906,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{73}{88}\right)\)
\(\chi_{4005}(2951,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{51}{88}\right)\)
\(\chi_{4005}(2996,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{9}{88}\right)\)
\(\chi_{4005}(3041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{21}{88}\right)\)
\(\chi_{4005}(3086,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{85}{88}\right)\)

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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.dm
Modulus	$4005$
Conductor	$267$
Order	$88$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(4005\)
Conductor:	\(267\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(88\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 267.p	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)