LMFDB - Dirichlet character orbit 2299.bt

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2299, base_ring=CyclotomicField(990)) M = H._module chi = DirichletCharacter(H, M([72,385])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(14,2299)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2299$
Conductor:	$2299$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$990$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{495})$
Fixed field:	Number field defined by a degree 990 polynomial (not computed)

First 31 of 240 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{2299}(14,\cdot)$	$-1$	$1$	$e\left(\frac{457}{990}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{457}{495}\right)$	$e\left(\frac{299}{495}\right)$	$e\left(\frac{454}{495}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{127}{330}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{13}{198}\right)$	$e\left(\frac{25}{66}\right)$
$\chi_{2299}(15,\cdot)$	$-1$	$1$	$e\left(\frac{83}{990}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{83}{495}\right)$	$e\left(\frac{376}{495}\right)$	$e\left(\frac{311}{495}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{167}{198}\right)$	$e\left(\frac{47}{66}\right)$
$\chi_{2299}(48,\cdot)$	$-1$	$1$	$e\left(\frac{773}{990}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{278}{495}\right)$	$e\left(\frac{1}{495}\right)$	$e\left(\frac{326}{495}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{155}{198}\right)$	$e\left(\frac{29}{66}\right)$
$\chi_{2299}(53,\cdot)$	$-1$	$1$	$e\left(\frac{569}{990}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{74}{495}\right)$	$e\left(\frac{43}{495}\right)$	$e\left(\frac{158}{495}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{131}{198}\right)$	$e\left(\frac{59}{66}\right)$
$\chi_{2299}(59,\cdot)$	$-1$	$1$	$e\left(\frac{343}{990}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{343}{495}\right)$	$e\left(\frac{206}{495}\right)$	$e\left(\frac{331}{495}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{13}{330}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{151}{198}\right)$	$e\left(\frac{1}{66}\right)$
$\chi_{2299}(60,\cdot)$	$-1$	$1$	$e\left(\frac{211}{990}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{211}{495}\right)$	$e\left(\frac{437}{495}\right)$	$e\left(\frac{397}{495}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{19}{198}\right)$	$e\left(\frac{1}{66}\right)$
$\chi_{2299}(70,\cdot)$	$-1$	$1$	$e\left(\frac{23}{990}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{23}{495}\right)$	$e\left(\frac{301}{495}\right)$	$e\left(\frac{116}{495}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{125}{198}\right)$	$e\left(\frac{17}{66}\right)$
$\chi_{2299}(71,\cdot)$	$-1$	$1$	$e\left(\frac{241}{990}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{241}{495}\right)$	$e\left(\frac{227}{495}\right)$	$e\left(\frac{247}{495}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{139}{198}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{2299}(86,\cdot)$	$-1$	$1$	$e\left(\frac{179}{990}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{179}{495}\right)$	$e\left(\frac{298}{495}\right)$	$e\left(\frac{128}{495}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{179}{330}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{155}{198}\right)$	$e\left(\frac{29}{66}\right)$
$\chi_{2299}(91,\cdot)$	$-1$	$1$	$e\left(\frac{587}{990}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{92}{495}\right)$	$e\left(\frac{214}{495}\right)$	$e\left(\frac{464}{495}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{257}{330}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{5}{198}\right)$	$e\left(\frac{35}{66}\right)$
$\chi_{2299}(97,\cdot)$	$-1$	$1$	$e\left(\frac{379}{990}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{379}{495}\right)$	$e\left(\frac{53}{495}\right)$	$e\left(\frac{448}{495}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{97}{198}\right)$	$e\left(\frac{19}{66}\right)$
$\chi_{2299}(108,\cdot)$	$-1$	$1$	$e\left(\frac{689}{990}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{194}{495}\right)$	$e\left(\frac{193}{495}\right)$	$e\left(\frac{53}{495}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{17}{198}\right)$	$e\left(\frac{53}{66}\right)$
$\chi_{2299}(135,\cdot)$	$-1$	$1$	$e\left(\frac{127}{990}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{127}{495}\right)$	$e\left(\frac{134}{495}\right)$	$e\left(\frac{124}{495}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{127}{330}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{79}{198}\right)$	$e\left(\frac{25}{66}\right)$
$\chi_{2299}(136,\cdot)$	$-1$	$1$	$e\left(\frac{193}{990}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{193}{495}\right)$	$e\left(\frac{266}{495}\right)$	$e\left(\frac{91}{495}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{145}{198}\right)$	$e\left(\frac{25}{66}\right)$
$\chi_{2299}(146,\cdot)$	$-1$	$1$	$e\left(\frac{617}{990}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{122}{495}\right)$	$e\left(\frac{4}{495}\right)$	$e\left(\frac{314}{495}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{125}{198}\right)$	$e\left(\frac{17}{66}\right)$
$\chi_{2299}(147,\cdot)$	$-1$	$1$	$e\left(\frac{313}{990}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{313}{495}\right)$	$e\left(\frac{416}{495}\right)$	$e\left(\frac{481}{495}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{31}{198}\right)$	$e\left(\frac{19}{66}\right)$
$\chi_{2299}(174,\cdot)$	$-1$	$1$	$e\left(\frac{679}{990}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{184}{495}\right)$	$e\left(\frac{428}{495}\right)$	$e\left(\frac{433}{495}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{109}{198}\right)$	$e\left(\frac{37}{66}\right)$
$\chi_{2299}(181,\cdot)$	$-1$	$1$	$e\left(\frac{431}{990}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{431}{495}\right)$	$e\left(\frac{217}{495}\right)$	$e\left(\frac{452}{495}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{173}{198}\right)$	$e\left(\frac{23}{66}\right)$
$\chi_{2299}(185,\cdot)$	$-1$	$1$	$e\left(\frac{439}{990}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{439}{495}\right)$	$e\left(\frac{128}{495}\right)$	$e\left(\frac{148}{495}\right)$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{109}{330}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{139}{198}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{2299}(192,\cdot)$	$-1$	$1$	$e\left(\frac{901}{990}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{406}{495}\right)$	$e\left(\frac{62}{495}\right)$	$e\left(\frac{412}{495}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{7}{198}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{2299}(203,\cdot)$	$-1$	$1$	$e\left(\frac{491}{990}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{491}{495}\right)$	$e\left(\frac{292}{495}\right)$	$e\left(\frac{152}{495}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{161}{330}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{17}{198}\right)$	$e\left(\frac{53}{66}\right)$
$\chi_{2299}(212,\cdot)$	$-1$	$1$	$e\left(\frac{697}{990}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{202}{495}\right)$	$e\left(\frac{104}{495}\right)$	$e\left(\frac{244}{495}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{181}{198}\right)$	$e\left(\frac{13}{66}\right)$
$\chi_{2299}(223,\cdot)$	$-1$	$1$	$e\left(\frac{637}{990}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{142}{495}\right)$	$e\left(\frac{29}{495}\right)$	$e\left(\frac{49}{495}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{139}{198}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{2299}(224,\cdot)$	$-1$	$1$	$e\left(\frac{713}{990}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{218}{495}\right)$	$e\left(\frac{421}{495}\right)$	$e\left(\frac{131}{495}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{53}{330}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{113}{198}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{2299}(257,\cdot)$	$-1$	$1$	$e\left(\frac{413}{990}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{413}{495}\right)$	$e\left(\frac{46}{495}\right)$	$e\left(\frac{146}{495}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{101}{198}\right)$	$e\left(\frac{47}{66}\right)$
$\chi_{2299}(262,\cdot)$	$-1$	$1$	$e\left(\frac{299}{990}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{299}{495}\right)$	$e\left(\frac{448}{495}\right)$	$e\left(\frac{23}{495}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{41}{198}\right)$	$e\left(\frac{23}{66}\right)$
$\chi_{2299}(268,\cdot)$	$-1$	$1$	$e\left(\frac{973}{990}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{478}{495}\right)$	$e\left(\frac{251}{495}\right)$	$e\left(\frac{151}{495}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{97}{198}\right)$	$e\left(\frac{19}{66}\right)$
$\chi_{2299}(279,\cdot)$	$-1$	$1$	$e\left(\frac{653}{990}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{158}{495}\right)$	$e\left(\frac{346}{495}\right)$	$e\left(\frac{431}{495}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{71}{198}\right)$	$e\left(\frac{35}{66}\right)$
$\chi_{2299}(280,\cdot)$	$-1$	$1$	$e\left(\frac{151}{990}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{151}{495}\right)$	$e\left(\frac{362}{495}\right)$	$e\left(\frac{202}{495}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{175}{198}\right)$	$e\left(\frac{37}{66}\right)$
$\chi_{2299}(295,\cdot)$	$-1$	$1$	$e\left(\frac{899}{990}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{404}{495}\right)$	$e\left(\frac{208}{495}\right)$	$e\left(\frac{488}{495}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{65}{198}\right)$	$e\left(\frac{59}{66}\right)$
$\chi_{2299}(300,\cdot)$	$-1$	$1$	$e\left(\frac{767}{990}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{272}{495}\right)$	$e\left(\frac{439}{495}\right)$	$e\left(\frac{59}{495}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{131}{198}\right)$	$e\left(\frac{59}{66}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{2299}(14,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{457}{990}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{457}{495}\right)\)	\(e\left(\frac{299}{495}\right)\)	\(e\left(\frac{454}{495}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{127}{330}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{13}{198}\right)\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{2299}(15,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{990}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{83}{495}\right)\)	\(e\left(\frac{376}{495}\right)\)	\(e\left(\frac{311}{495}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{167}{198}\right)\)	\(e\left(\frac{47}{66}\right)\)
\(\chi_{2299}(48,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{773}{990}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{278}{495}\right)\)	\(e\left(\frac{1}{495}\right)\)	\(e\left(\frac{326}{495}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{155}{198}\right)\)	\(e\left(\frac{29}{66}\right)\)
\(\chi_{2299}(53,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{569}{990}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{74}{495}\right)\)	\(e\left(\frac{43}{495}\right)\)	\(e\left(\frac{158}{495}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{131}{198}\right)\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{2299}(59,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{343}{990}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{343}{495}\right)\)	\(e\left(\frac{206}{495}\right)\)	\(e\left(\frac{331}{495}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{13}{330}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{151}{198}\right)\)	\(e\left(\frac{1}{66}\right)\)
\(\chi_{2299}(60,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{211}{990}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{211}{495}\right)\)	\(e\left(\frac{437}{495}\right)\)	\(e\left(\frac{397}{495}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{19}{198}\right)\)	\(e\left(\frac{1}{66}\right)\)
\(\chi_{2299}(70,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{990}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{23}{495}\right)\)	\(e\left(\frac{301}{495}\right)\)	\(e\left(\frac{116}{495}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{125}{198}\right)\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{2299}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{241}{990}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{241}{495}\right)\)	\(e\left(\frac{227}{495}\right)\)	\(e\left(\frac{247}{495}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{139}{198}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{2299}(86,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{990}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{179}{495}\right)\)	\(e\left(\frac{298}{495}\right)\)	\(e\left(\frac{128}{495}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{179}{330}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{155}{198}\right)\)	\(e\left(\frac{29}{66}\right)\)
\(\chi_{2299}(91,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{587}{990}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{92}{495}\right)\)	\(e\left(\frac{214}{495}\right)\)	\(e\left(\frac{464}{495}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{257}{330}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{5}{198}\right)\)	\(e\left(\frac{35}{66}\right)\)
\(\chi_{2299}(97,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{379}{990}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{379}{495}\right)\)	\(e\left(\frac{53}{495}\right)\)	\(e\left(\frac{448}{495}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{97}{198}\right)\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{2299}(108,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{689}{990}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{194}{495}\right)\)	\(e\left(\frac{193}{495}\right)\)	\(e\left(\frac{53}{495}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{17}{198}\right)\)	\(e\left(\frac{53}{66}\right)\)
\(\chi_{2299}(135,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{990}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{127}{495}\right)\)	\(e\left(\frac{134}{495}\right)\)	\(e\left(\frac{124}{495}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{127}{330}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{79}{198}\right)\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{2299}(136,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{990}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{193}{495}\right)\)	\(e\left(\frac{266}{495}\right)\)	\(e\left(\frac{91}{495}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{145}{198}\right)\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{2299}(146,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{617}{990}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{122}{495}\right)\)	\(e\left(\frac{4}{495}\right)\)	\(e\left(\frac{314}{495}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{125}{198}\right)\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{2299}(147,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{313}{990}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{313}{495}\right)\)	\(e\left(\frac{416}{495}\right)\)	\(e\left(\frac{481}{495}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{31}{198}\right)\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{2299}(174,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{679}{990}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{184}{495}\right)\)	\(e\left(\frac{428}{495}\right)\)	\(e\left(\frac{433}{495}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{109}{198}\right)\)	\(e\left(\frac{37}{66}\right)\)
\(\chi_{2299}(181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{431}{990}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{431}{495}\right)\)	\(e\left(\frac{217}{495}\right)\)	\(e\left(\frac{452}{495}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{173}{198}\right)\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{2299}(185,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{439}{990}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{439}{495}\right)\)	\(e\left(\frac{128}{495}\right)\)	\(e\left(\frac{148}{495}\right)\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{109}{330}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{139}{198}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{2299}(192,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{901}{990}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{406}{495}\right)\)	\(e\left(\frac{62}{495}\right)\)	\(e\left(\frac{412}{495}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{7}{198}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{2299}(203,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{491}{990}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{491}{495}\right)\)	\(e\left(\frac{292}{495}\right)\)	\(e\left(\frac{152}{495}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{161}{330}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{17}{198}\right)\)	\(e\left(\frac{53}{66}\right)\)
\(\chi_{2299}(212,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{697}{990}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{202}{495}\right)\)	\(e\left(\frac{104}{495}\right)\)	\(e\left(\frac{244}{495}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{181}{198}\right)\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{2299}(223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{637}{990}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{142}{495}\right)\)	\(e\left(\frac{29}{495}\right)\)	\(e\left(\frac{49}{495}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{139}{198}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{2299}(224,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{713}{990}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{218}{495}\right)\)	\(e\left(\frac{421}{495}\right)\)	\(e\left(\frac{131}{495}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{53}{330}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{113}{198}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{2299}(257,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{413}{990}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{413}{495}\right)\)	\(e\left(\frac{46}{495}\right)\)	\(e\left(\frac{146}{495}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{101}{198}\right)\)	\(e\left(\frac{47}{66}\right)\)
\(\chi_{2299}(262,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{299}{990}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{299}{495}\right)\)	\(e\left(\frac{448}{495}\right)\)	\(e\left(\frac{23}{495}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{41}{198}\right)\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{2299}(268,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{973}{990}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{478}{495}\right)\)	\(e\left(\frac{251}{495}\right)\)	\(e\left(\frac{151}{495}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{97}{198}\right)\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{2299}(279,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{653}{990}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{158}{495}\right)\)	\(e\left(\frac{346}{495}\right)\)	\(e\left(\frac{431}{495}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{71}{198}\right)\)	\(e\left(\frac{35}{66}\right)\)
\(\chi_{2299}(280,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{990}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{151}{495}\right)\)	\(e\left(\frac{362}{495}\right)\)	\(e\left(\frac{202}{495}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{175}{198}\right)\)	\(e\left(\frac{37}{66}\right)\)
\(\chi_{2299}(295,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{899}{990}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{404}{495}\right)\)	\(e\left(\frac{208}{495}\right)\)	\(e\left(\frac{488}{495}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{65}{198}\right)\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{2299}(300,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{767}{990}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{272}{495}\right)\)	\(e\left(\frac{439}{495}\right)\)	\(e\left(\frac{59}{495}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{131}{198}\right)\)	\(e\left(\frac{59}{66}\right)\)

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First 31 of 240 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	2299.bt
Modulus	$2299$
Conductor	$2299$
Order	$990$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(2299\)
Conductor:	\(2299\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(990\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)