LMFDB - Dirichlet character orbit 3721.s

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3721, base_ring=CyclotomicField(610)) M = H._module chi = DirichletCharacter(H, M([481])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(3, 3721)) 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("3721.3"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$3721$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$3721$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$610$	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:	$\Q(\zeta_{305})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 610 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 240 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{3721}(3,\cdot)$	$1$	$1$	$e\left(\frac{481}{610}\right)$	$e\left(\frac{208}{305}\right)$	$e\left(\frac{176}{305}\right)$	$e\left(\frac{181}{305}\right)$	$e\left(\frac{287}{610}\right)$	$e\left(\frac{609}{610}\right)$	$e\left(\frac{223}{610}\right)$	$e\left(\frac{111}{305}\right)$	$e\left(\frac{233}{610}\right)$	$e\left(\frac{43}{122}\right)$
$\chi_{3721}(27,\cdot)$	$1$	$1$	$e\left(\frac{223}{610}\right)$	$e\left(\frac{14}{305}\right)$	$e\left(\frac{223}{305}\right)$	$e\left(\frac{238}{305}\right)$	$e\left(\frac{251}{610}\right)$	$e\left(\frac{607}{610}\right)$	$e\left(\frac{59}{610}\right)$	$e\left(\frac{28}{305}\right)$	$e\left(\frac{89}{610}\right)$	$e\left(\frac{7}{122}\right)$
$\chi_{3721}(41,\cdot)$	$1$	$1$	$e\left(\frac{299}{610}\right)$	$e\left(\frac{187}{305}\right)$	$e\left(\frac{299}{305}\right)$	$e\left(\frac{129}{305}\right)$	$e\left(\frac{63}{610}\right)$	$e\left(\frac{461}{610}\right)$	$e\left(\frac{287}{610}\right)$	$e\left(\frac{69}{305}\right)$	$e\left(\frac{557}{610}\right)$	$e\left(\frac{63}{122}\right)$
$\chi_{3721}(52,\cdot)$	$1$	$1$	$e\left(\frac{207}{610}\right)$	$e\left(\frac{106}{305}\right)$	$e\left(\frac{207}{305}\right)$	$e\left(\frac{277}{305}\right)$	$e\left(\frac{419}{610}\right)$	$e\left(\frac{413}{610}\right)$	$e\left(\frac{11}{610}\right)$	$e\left(\frac{212}{305}\right)$	$e\left(\frac{151}{610}\right)$	$e\left(\frac{53}{122}\right)$
$\chi_{3721}(64,\cdot)$	$1$	$1$	$e\left(\frac{1}{610}\right)$	$e\left(\frac{223}{305}\right)$	$e\left(\frac{1}{305}\right)$	$e\left(\frac{131}{305}\right)$	$e\left(\frac{447}{610}\right)$	$e\left(\frac{279}{610}\right)$	$e\left(\frac{3}{610}\right)$	$e\left(\frac{141}{305}\right)$	$e\left(\frac{263}{610}\right)$	$e\left(\frac{81}{122}\right)$
$\chi_{3721}(88,\cdot)$	$1$	$1$	$e\left(\frac{373}{610}\right)$	$e\left(\frac{219}{305}\right)$	$e\left(\frac{68}{305}\right)$	$e\left(\frac{63}{305}\right)$	$e\left(\frac{201}{610}\right)$	$e\left(\frac{367}{610}\right)$	$e\left(\frac{509}{610}\right)$	$e\left(\frac{133}{305}\right)$	$e\left(\frac{499}{610}\right)$	$e\left(\frac{79}{122}\right)$
$\chi_{3721}(102,\cdot)$	$1$	$1$	$e\left(\frac{249}{610}\right)$	$e\left(\frac{17}{305}\right)$	$e\left(\frac{249}{305}\right)$	$e\left(\frac{289}{305}\right)$	$e\left(\frac{283}{610}\right)$	$e\left(\frac{541}{610}\right)$	$e\left(\frac{137}{610}\right)$	$e\left(\frac{34}{305}\right)$	$e\left(\frac{217}{610}\right)$	$e\left(\frac{39}{122}\right)$
$\chi_{3721}(113,\cdot)$	$1$	$1$	$e\left(\frac{367}{610}\right)$	$e\left(\frac{101}{305}\right)$	$e\left(\frac{62}{305}\right)$	$e\left(\frac{192}{305}\right)$	$e\left(\frac{569}{610}\right)$	$e\left(\frac{523}{610}\right)$	$e\left(\frac{491}{610}\right)$	$e\left(\frac{202}{305}\right)$	$e\left(\frac{141}{610}\right)$	$e\left(\frac{81}{122}\right)$
$\chi_{3721}(125,\cdot)$	$1$	$1$	$e\left(\frac{131}{610}\right)$	$e\left(\frac{238}{305}\right)$	$e\left(\frac{131}{305}\right)$	$e\left(\frac{81}{305}\right)$	$e\left(\frac{607}{610}\right)$	$e\left(\frac{559}{610}\right)$	$e\left(\frac{393}{610}\right)$	$e\left(\frac{171}{305}\right)$	$e\left(\frac{293}{610}\right)$	$e\left(\frac{119}{122}\right)$
$\chi_{3721}(149,\cdot)$	$1$	$1$	$e\left(\frac{523}{610}\right)$	$e\left(\frac{119}{305}\right)$	$e\left(\frac{218}{305}\right)$	$e\left(\frac{193}{305}\right)$	$e\left(\frac{151}{610}\right)$	$e\left(\frac{127}{610}\right)$	$e\left(\frac{349}{610}\right)$	$e\left(\frac{238}{305}\right)$	$e\left(\frac{299}{610}\right)$	$e\left(\frac{29}{122}\right)$
$\chi_{3721}(163,\cdot)$	$1$	$1$	$e\left(\frac{199}{610}\right)$	$e\left(\frac{152}{305}\right)$	$e\left(\frac{199}{305}\right)$	$e\left(\frac{144}{305}\right)$	$e\left(\frac{503}{610}\right)$	$e\left(\frac{11}{610}\right)$	$e\left(\frac{597}{610}\right)$	$e\left(\frac{304}{305}\right)$	$e\left(\frac{487}{610}\right)$	$e\left(\frac{15}{122}\right)$
$\chi_{3721}(174,\cdot)$	$1$	$1$	$e\left(\frac{527}{610}\right)$	$e\left(\frac{96}{305}\right)$	$e\left(\frac{222}{305}\right)$	$e\left(\frac{107}{305}\right)$	$e\left(\frac{109}{610}\right)$	$e\left(\frac{23}{610}\right)$	$e\left(\frac{361}{610}\right)$	$e\left(\frac{192}{305}\right)$	$e\left(\frac{131}{610}\right)$	$e\left(\frac{109}{122}\right)$
$\chi_{3721}(186,\cdot)$	$1$	$1$	$e\left(\frac{261}{610}\right)$	$e\left(\frac{253}{305}\right)$	$e\left(\frac{261}{305}\right)$	$e\left(\frac{31}{305}\right)$	$e\left(\frac{157}{610}\right)$	$e\left(\frac{229}{610}\right)$	$e\left(\frac{173}{610}\right)$	$e\left(\frac{201}{305}\right)$	$e\left(\frac{323}{610}\right)$	$e\left(\frac{35}{122}\right)$
$\chi_{3721}(210,\cdot)$	$1$	$1$	$e\left(\frac{63}{610}\right)$	$e\left(\frac{19}{305}\right)$	$e\left(\frac{63}{305}\right)$	$e\left(\frac{18}{305}\right)$	$e\left(\frac{101}{610}\right)$	$e\left(\frac{497}{610}\right)$	$e\left(\frac{189}{610}\right)$	$e\left(\frac{38}{305}\right)$	$e\left(\frac{99}{610}\right)$	$e\left(\frac{101}{122}\right)$
$\chi_{3721}(224,\cdot)$	$1$	$1$	$e\left(\frac{149}{610}\right)$	$e\left(\frac{287}{305}\right)$	$e\left(\frac{149}{305}\right)$	$e\left(\frac{304}{305}\right)$	$e\left(\frac{113}{610}\right)$	$e\left(\frac{91}{610}\right)$	$e\left(\frac{447}{610}\right)$	$e\left(\frac{269}{305}\right)$	$e\left(\frac{147}{610}\right)$	$e\left(\frac{113}{122}\right)$
$\chi_{3721}(235,\cdot)$	$1$	$1$	$e\left(\frac{77}{610}\right)$	$e\left(\frac{91}{305}\right)$	$e\left(\frac{77}{305}\right)$	$e\left(\frac{22}{305}\right)$	$e\left(\frac{259}{610}\right)$	$e\left(\frac{133}{610}\right)$	$e\left(\frac{231}{610}\right)$	$e\left(\frac{182}{305}\right)$	$e\left(\frac{121}{610}\right)$	$e\left(\frac{15}{122}\right)$
$\chi_{3721}(247,\cdot)$	$1$	$1$	$e\left(\frac{391}{610}\right)$	$e\left(\frac{268}{305}\right)$	$e\left(\frac{86}{305}\right)$	$e\left(\frac{286}{305}\right)$	$e\left(\frac{317}{610}\right)$	$e\left(\frac{509}{610}\right)$	$e\left(\frac{563}{610}\right)$	$e\left(\frac{231}{305}\right)$	$e\left(\frac{353}{610}\right)$	$e\left(\frac{73}{122}\right)$
$\chi_{3721}(271,\cdot)$	$1$	$1$	$e\left(\frac{213}{610}\right)$	$e\left(\frac{224}{305}\right)$	$e\left(\frac{213}{305}\right)$	$e\left(\frac{148}{305}\right)$	$e\left(\frac{51}{610}\right)$	$e\left(\frac{257}{610}\right)$	$e\left(\frac{29}{610}\right)$	$e\left(\frac{143}{305}\right)$	$e\left(\frac{509}{610}\right)$	$e\left(\frac{51}{122}\right)$
$\chi_{3721}(285,\cdot)$	$1$	$1$	$e\left(\frac{99}{610}\right)$	$e\left(\frac{117}{305}\right)$	$e\left(\frac{99}{305}\right)$	$e\left(\frac{159}{305}\right)$	$e\left(\frac{333}{610}\right)$	$e\left(\frac{171}{610}\right)$	$e\left(\frac{297}{610}\right)$	$e\left(\frac{234}{305}\right)$	$e\left(\frac{417}{610}\right)$	$e\left(\frac{89}{122}\right)$
$\chi_{3721}(296,\cdot)$	$1$	$1$	$e\left(\frac{237}{610}\right)$	$e\left(\frac{86}{305}\right)$	$e\left(\frac{237}{305}\right)$	$e\left(\frac{242}{305}\right)$	$e\left(\frac{409}{610}\right)$	$e\left(\frac{243}{610}\right)$	$e\left(\frac{101}{610}\right)$	$e\left(\frac{172}{305}\right)$	$e\left(\frac{111}{610}\right)$	$e\left(\frac{43}{122}\right)$
$\chi_{3721}(308,\cdot)$	$1$	$1$	$e\left(\frac{521}{610}\right)$	$e\left(\frac{283}{305}\right)$	$e\left(\frac{216}{305}\right)$	$e\left(\frac{236}{305}\right)$	$e\left(\frac{477}{610}\right)$	$e\left(\frac{179}{610}\right)$	$e\left(\frac{343}{610}\right)$	$e\left(\frac{261}{305}\right)$	$e\left(\frac{383}{610}\right)$	$e\left(\frac{111}{122}\right)$
$\chi_{3721}(332,\cdot)$	$1$	$1$	$e\left(\frac{363}{610}\right)$	$e\left(\frac{124}{305}\right)$	$e\left(\frac{58}{305}\right)$	$e\left(\frac{278}{305}\right)$	$e\left(\frac{1}{610}\right)$	$e\left(\frac{17}{610}\right)$	$e\left(\frac{479}{610}\right)$	$e\left(\frac{248}{305}\right)$	$e\left(\frac{309}{610}\right)$	$e\left(\frac{1}{122}\right)$
$\chi_{3721}(346,\cdot)$	$1$	$1$	$e\left(\frac{49}{610}\right)$	$e\left(\frac{252}{305}\right)$	$e\left(\frac{49}{305}\right)$	$e\left(\frac{14}{305}\right)$	$e\left(\frac{553}{610}\right)$	$e\left(\frac{251}{610}\right)$	$e\left(\frac{147}{610}\right)$	$e\left(\frac{199}{305}\right)$	$e\left(\frac{77}{610}\right)$	$e\left(\frac{65}{122}\right)$
$\chi_{3721}(357,\cdot)$	$1$	$1$	$e\left(\frac{397}{610}\right)$	$e\left(\frac{81}{305}\right)$	$e\left(\frac{92}{305}\right)$	$e\left(\frac{157}{305}\right)$	$e\left(\frac{559}{610}\right)$	$e\left(\frac{353}{610}\right)$	$e\left(\frac{581}{610}\right)$	$e\left(\frac{162}{305}\right)$	$e\left(\frac{101}{610}\right)$	$e\left(\frac{71}{122}\right)$
$\chi_{3721}(369,\cdot)$	$1$	$1$	$e\left(\frac{41}{610}\right)$	$e\left(\frac{298}{305}\right)$	$e\left(\frac{41}{305}\right)$	$e\left(\frac{186}{305}\right)$	$e\left(\frac{27}{610}\right)$	$e\left(\frac{459}{610}\right)$	$e\left(\frac{123}{610}\right)$	$e\left(\frac{291}{305}\right)$	$e\left(\frac{413}{610}\right)$	$e\left(\frac{27}{122}\right)$
$\chi_{3721}(393,\cdot)$	$1$	$1$	$e\left(\frac{513}{610}\right)$	$e\left(\frac{24}{305}\right)$	$e\left(\frac{208}{305}\right)$	$e\left(\frac{103}{305}\right)$	$e\left(\frac{561}{610}\right)$	$e\left(\frac{387}{610}\right)$	$e\left(\frac{319}{610}\right)$	$e\left(\frac{48}{305}\right)$	$e\left(\frac{109}{610}\right)$	$e\left(\frac{73}{122}\right)$
$\chi_{3721}(407,\cdot)$	$1$	$1$	$e\left(\frac{609}{610}\right)$	$e\left(\frac{82}{305}\right)$	$e\left(\frac{304}{305}\right)$	$e\left(\frac{174}{305}\right)$	$e\left(\frac{163}{610}\right)$	$e\left(\frac{331}{610}\right)$	$e\left(\frac{607}{610}\right)$	$e\left(\frac{164}{305}\right)$	$e\left(\frac{347}{610}\right)$	$e\left(\frac{41}{122}\right)$
$\chi_{3721}(418,\cdot)$	$1$	$1$	$e\left(\frac{557}{610}\right)$	$e\left(\frac{76}{305}\right)$	$e\left(\frac{252}{305}\right)$	$e\left(\frac{72}{305}\right)$	$e\left(\frac{99}{610}\right)$	$e\left(\frac{463}{610}\right)$	$e\left(\frac{451}{610}\right)$	$e\left(\frac{152}{305}\right)$	$e\left(\frac{91}{610}\right)$	$e\left(\frac{99}{122}\right)$
$\chi_{3721}(430,\cdot)$	$1$	$1$	$e\left(\frac{171}{610}\right)$	$e\left(\frac{8}{305}\right)$	$e\left(\frac{171}{305}\right)$	$e\left(\frac{136}{305}\right)$	$e\left(\frac{187}{610}\right)$	$e\left(\frac{129}{610}\right)$	$e\left(\frac{513}{610}\right)$	$e\left(\frac{16}{305}\right)$	$e\left(\frac{443}{610}\right)$	$e\left(\frac{65}{122}\right)$
$\chi_{3721}(454,\cdot)$	$1$	$1$	$e\left(\frac{53}{610}\right)$	$e\left(\frac{229}{305}\right)$	$e\left(\frac{53}{305}\right)$	$e\left(\frac{233}{305}\right)$	$e\left(\frac{511}{610}\right)$	$e\left(\frac{147}{610}\right)$	$e\left(\frac{159}{610}\right)$	$e\left(\frac{153}{305}\right)$	$e\left(\frac{519}{610}\right)$	$e\left(\frac{23}{122}\right)$
$\chi_{3721}(468,\cdot)$	$1$	$1$	$e\left(\frac{559}{610}\right)$	$e\left(\frac{217}{305}\right)$	$e\left(\frac{254}{305}\right)$	$e\left(\frac{29}{305}\right)$	$e\left(\frac{383}{610}\right)$	$e\left(\frac{411}{610}\right)$	$e\left(\frac{457}{610}\right)$	$e\left(\frac{129}{305}\right)$	$e\left(\frac{7}{610}\right)$	$e\left(\frac{17}{122}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{3721}(3,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{481}{610}\right)\)	\(e\left(\frac{208}{305}\right)\)	\(e\left(\frac{176}{305}\right)\)	\(e\left(\frac{181}{305}\right)\)	\(e\left(\frac{287}{610}\right)\)	\(e\left(\frac{609}{610}\right)\)	\(e\left(\frac{223}{610}\right)\)	\(e\left(\frac{111}{305}\right)\)	\(e\left(\frac{233}{610}\right)\)	\(e\left(\frac{43}{122}\right)\)
\(\chi_{3721}(27,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{610}\right)\)	\(e\left(\frac{14}{305}\right)\)	\(e\left(\frac{223}{305}\right)\)	\(e\left(\frac{238}{305}\right)\)	\(e\left(\frac{251}{610}\right)\)	\(e\left(\frac{607}{610}\right)\)	\(e\left(\frac{59}{610}\right)\)	\(e\left(\frac{28}{305}\right)\)	\(e\left(\frac{89}{610}\right)\)	\(e\left(\frac{7}{122}\right)\)
\(\chi_{3721}(41,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{299}{610}\right)\)	\(e\left(\frac{187}{305}\right)\)	\(e\left(\frac{299}{305}\right)\)	\(e\left(\frac{129}{305}\right)\)	\(e\left(\frac{63}{610}\right)\)	\(e\left(\frac{461}{610}\right)\)	\(e\left(\frac{287}{610}\right)\)	\(e\left(\frac{69}{305}\right)\)	\(e\left(\frac{557}{610}\right)\)	\(e\left(\frac{63}{122}\right)\)
\(\chi_{3721}(52,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{207}{610}\right)\)	\(e\left(\frac{106}{305}\right)\)	\(e\left(\frac{207}{305}\right)\)	\(e\left(\frac{277}{305}\right)\)	\(e\left(\frac{419}{610}\right)\)	\(e\left(\frac{413}{610}\right)\)	\(e\left(\frac{11}{610}\right)\)	\(e\left(\frac{212}{305}\right)\)	\(e\left(\frac{151}{610}\right)\)	\(e\left(\frac{53}{122}\right)\)
\(\chi_{3721}(64,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{610}\right)\)	\(e\left(\frac{223}{305}\right)\)	\(e\left(\frac{1}{305}\right)\)	\(e\left(\frac{131}{305}\right)\)	\(e\left(\frac{447}{610}\right)\)	\(e\left(\frac{279}{610}\right)\)	\(e\left(\frac{3}{610}\right)\)	\(e\left(\frac{141}{305}\right)\)	\(e\left(\frac{263}{610}\right)\)	\(e\left(\frac{81}{122}\right)\)
\(\chi_{3721}(88,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{373}{610}\right)\)	\(e\left(\frac{219}{305}\right)\)	\(e\left(\frac{68}{305}\right)\)	\(e\left(\frac{63}{305}\right)\)	\(e\left(\frac{201}{610}\right)\)	\(e\left(\frac{367}{610}\right)\)	\(e\left(\frac{509}{610}\right)\)	\(e\left(\frac{133}{305}\right)\)	\(e\left(\frac{499}{610}\right)\)	\(e\left(\frac{79}{122}\right)\)
\(\chi_{3721}(102,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{249}{610}\right)\)	\(e\left(\frac{17}{305}\right)\)	\(e\left(\frac{249}{305}\right)\)	\(e\left(\frac{289}{305}\right)\)	\(e\left(\frac{283}{610}\right)\)	\(e\left(\frac{541}{610}\right)\)	\(e\left(\frac{137}{610}\right)\)	\(e\left(\frac{34}{305}\right)\)	\(e\left(\frac{217}{610}\right)\)	\(e\left(\frac{39}{122}\right)\)
\(\chi_{3721}(113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{367}{610}\right)\)	\(e\left(\frac{101}{305}\right)\)	\(e\left(\frac{62}{305}\right)\)	\(e\left(\frac{192}{305}\right)\)	\(e\left(\frac{569}{610}\right)\)	\(e\left(\frac{523}{610}\right)\)	\(e\left(\frac{491}{610}\right)\)	\(e\left(\frac{202}{305}\right)\)	\(e\left(\frac{141}{610}\right)\)	\(e\left(\frac{81}{122}\right)\)
\(\chi_{3721}(125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{610}\right)\)	\(e\left(\frac{238}{305}\right)\)	\(e\left(\frac{131}{305}\right)\)	\(e\left(\frac{81}{305}\right)\)	\(e\left(\frac{607}{610}\right)\)	\(e\left(\frac{559}{610}\right)\)	\(e\left(\frac{393}{610}\right)\)	\(e\left(\frac{171}{305}\right)\)	\(e\left(\frac{293}{610}\right)\)	\(e\left(\frac{119}{122}\right)\)
\(\chi_{3721}(149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{523}{610}\right)\)	\(e\left(\frac{119}{305}\right)\)	\(e\left(\frac{218}{305}\right)\)	\(e\left(\frac{193}{305}\right)\)	\(e\left(\frac{151}{610}\right)\)	\(e\left(\frac{127}{610}\right)\)	\(e\left(\frac{349}{610}\right)\)	\(e\left(\frac{238}{305}\right)\)	\(e\left(\frac{299}{610}\right)\)	\(e\left(\frac{29}{122}\right)\)
\(\chi_{3721}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{610}\right)\)	\(e\left(\frac{152}{305}\right)\)	\(e\left(\frac{199}{305}\right)\)	\(e\left(\frac{144}{305}\right)\)	\(e\left(\frac{503}{610}\right)\)	\(e\left(\frac{11}{610}\right)\)	\(e\left(\frac{597}{610}\right)\)	\(e\left(\frac{304}{305}\right)\)	\(e\left(\frac{487}{610}\right)\)	\(e\left(\frac{15}{122}\right)\)
\(\chi_{3721}(174,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{527}{610}\right)\)	\(e\left(\frac{96}{305}\right)\)	\(e\left(\frac{222}{305}\right)\)	\(e\left(\frac{107}{305}\right)\)	\(e\left(\frac{109}{610}\right)\)	\(e\left(\frac{23}{610}\right)\)	\(e\left(\frac{361}{610}\right)\)	\(e\left(\frac{192}{305}\right)\)	\(e\left(\frac{131}{610}\right)\)	\(e\left(\frac{109}{122}\right)\)
\(\chi_{3721}(186,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{261}{610}\right)\)	\(e\left(\frac{253}{305}\right)\)	\(e\left(\frac{261}{305}\right)\)	\(e\left(\frac{31}{305}\right)\)	\(e\left(\frac{157}{610}\right)\)	\(e\left(\frac{229}{610}\right)\)	\(e\left(\frac{173}{610}\right)\)	\(e\left(\frac{201}{305}\right)\)	\(e\left(\frac{323}{610}\right)\)	\(e\left(\frac{35}{122}\right)\)
\(\chi_{3721}(210,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{610}\right)\)	\(e\left(\frac{19}{305}\right)\)	\(e\left(\frac{63}{305}\right)\)	\(e\left(\frac{18}{305}\right)\)	\(e\left(\frac{101}{610}\right)\)	\(e\left(\frac{497}{610}\right)\)	\(e\left(\frac{189}{610}\right)\)	\(e\left(\frac{38}{305}\right)\)	\(e\left(\frac{99}{610}\right)\)	\(e\left(\frac{101}{122}\right)\)
\(\chi_{3721}(224,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{610}\right)\)	\(e\left(\frac{287}{305}\right)\)	\(e\left(\frac{149}{305}\right)\)	\(e\left(\frac{304}{305}\right)\)	\(e\left(\frac{113}{610}\right)\)	\(e\left(\frac{91}{610}\right)\)	\(e\left(\frac{447}{610}\right)\)	\(e\left(\frac{269}{305}\right)\)	\(e\left(\frac{147}{610}\right)\)	\(e\left(\frac{113}{122}\right)\)
\(\chi_{3721}(235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{610}\right)\)	\(e\left(\frac{91}{305}\right)\)	\(e\left(\frac{77}{305}\right)\)	\(e\left(\frac{22}{305}\right)\)	\(e\left(\frac{259}{610}\right)\)	\(e\left(\frac{133}{610}\right)\)	\(e\left(\frac{231}{610}\right)\)	\(e\left(\frac{182}{305}\right)\)	\(e\left(\frac{121}{610}\right)\)	\(e\left(\frac{15}{122}\right)\)
\(\chi_{3721}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{391}{610}\right)\)	\(e\left(\frac{268}{305}\right)\)	\(e\left(\frac{86}{305}\right)\)	\(e\left(\frac{286}{305}\right)\)	\(e\left(\frac{317}{610}\right)\)	\(e\left(\frac{509}{610}\right)\)	\(e\left(\frac{563}{610}\right)\)	\(e\left(\frac{231}{305}\right)\)	\(e\left(\frac{353}{610}\right)\)	\(e\left(\frac{73}{122}\right)\)
\(\chi_{3721}(271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{213}{610}\right)\)	\(e\left(\frac{224}{305}\right)\)	\(e\left(\frac{213}{305}\right)\)	\(e\left(\frac{148}{305}\right)\)	\(e\left(\frac{51}{610}\right)\)	\(e\left(\frac{257}{610}\right)\)	\(e\left(\frac{29}{610}\right)\)	\(e\left(\frac{143}{305}\right)\)	\(e\left(\frac{509}{610}\right)\)	\(e\left(\frac{51}{122}\right)\)
\(\chi_{3721}(285,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{610}\right)\)	\(e\left(\frac{117}{305}\right)\)	\(e\left(\frac{99}{305}\right)\)	\(e\left(\frac{159}{305}\right)\)	\(e\left(\frac{333}{610}\right)\)	\(e\left(\frac{171}{610}\right)\)	\(e\left(\frac{297}{610}\right)\)	\(e\left(\frac{234}{305}\right)\)	\(e\left(\frac{417}{610}\right)\)	\(e\left(\frac{89}{122}\right)\)
\(\chi_{3721}(296,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{237}{610}\right)\)	\(e\left(\frac{86}{305}\right)\)	\(e\left(\frac{237}{305}\right)\)	\(e\left(\frac{242}{305}\right)\)	\(e\left(\frac{409}{610}\right)\)	\(e\left(\frac{243}{610}\right)\)	\(e\left(\frac{101}{610}\right)\)	\(e\left(\frac{172}{305}\right)\)	\(e\left(\frac{111}{610}\right)\)	\(e\left(\frac{43}{122}\right)\)
\(\chi_{3721}(308,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{521}{610}\right)\)	\(e\left(\frac{283}{305}\right)\)	\(e\left(\frac{216}{305}\right)\)	\(e\left(\frac{236}{305}\right)\)	\(e\left(\frac{477}{610}\right)\)	\(e\left(\frac{179}{610}\right)\)	\(e\left(\frac{343}{610}\right)\)	\(e\left(\frac{261}{305}\right)\)	\(e\left(\frac{383}{610}\right)\)	\(e\left(\frac{111}{122}\right)\)
\(\chi_{3721}(332,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{363}{610}\right)\)	\(e\left(\frac{124}{305}\right)\)	\(e\left(\frac{58}{305}\right)\)	\(e\left(\frac{278}{305}\right)\)	\(e\left(\frac{1}{610}\right)\)	\(e\left(\frac{17}{610}\right)\)	\(e\left(\frac{479}{610}\right)\)	\(e\left(\frac{248}{305}\right)\)	\(e\left(\frac{309}{610}\right)\)	\(e\left(\frac{1}{122}\right)\)
\(\chi_{3721}(346,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{610}\right)\)	\(e\left(\frac{252}{305}\right)\)	\(e\left(\frac{49}{305}\right)\)	\(e\left(\frac{14}{305}\right)\)	\(e\left(\frac{553}{610}\right)\)	\(e\left(\frac{251}{610}\right)\)	\(e\left(\frac{147}{610}\right)\)	\(e\left(\frac{199}{305}\right)\)	\(e\left(\frac{77}{610}\right)\)	\(e\left(\frac{65}{122}\right)\)
\(\chi_{3721}(357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{397}{610}\right)\)	\(e\left(\frac{81}{305}\right)\)	\(e\left(\frac{92}{305}\right)\)	\(e\left(\frac{157}{305}\right)\)	\(e\left(\frac{559}{610}\right)\)	\(e\left(\frac{353}{610}\right)\)	\(e\left(\frac{581}{610}\right)\)	\(e\left(\frac{162}{305}\right)\)	\(e\left(\frac{101}{610}\right)\)	\(e\left(\frac{71}{122}\right)\)
\(\chi_{3721}(369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{610}\right)\)	\(e\left(\frac{298}{305}\right)\)	\(e\left(\frac{41}{305}\right)\)	\(e\left(\frac{186}{305}\right)\)	\(e\left(\frac{27}{610}\right)\)	\(e\left(\frac{459}{610}\right)\)	\(e\left(\frac{123}{610}\right)\)	\(e\left(\frac{291}{305}\right)\)	\(e\left(\frac{413}{610}\right)\)	\(e\left(\frac{27}{122}\right)\)
\(\chi_{3721}(393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{513}{610}\right)\)	\(e\left(\frac{24}{305}\right)\)	\(e\left(\frac{208}{305}\right)\)	\(e\left(\frac{103}{305}\right)\)	\(e\left(\frac{561}{610}\right)\)	\(e\left(\frac{387}{610}\right)\)	\(e\left(\frac{319}{610}\right)\)	\(e\left(\frac{48}{305}\right)\)	\(e\left(\frac{109}{610}\right)\)	\(e\left(\frac{73}{122}\right)\)
\(\chi_{3721}(407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{609}{610}\right)\)	\(e\left(\frac{82}{305}\right)\)	\(e\left(\frac{304}{305}\right)\)	\(e\left(\frac{174}{305}\right)\)	\(e\left(\frac{163}{610}\right)\)	\(e\left(\frac{331}{610}\right)\)	\(e\left(\frac{607}{610}\right)\)	\(e\left(\frac{164}{305}\right)\)	\(e\left(\frac{347}{610}\right)\)	\(e\left(\frac{41}{122}\right)\)
\(\chi_{3721}(418,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{557}{610}\right)\)	\(e\left(\frac{76}{305}\right)\)	\(e\left(\frac{252}{305}\right)\)	\(e\left(\frac{72}{305}\right)\)	\(e\left(\frac{99}{610}\right)\)	\(e\left(\frac{463}{610}\right)\)	\(e\left(\frac{451}{610}\right)\)	\(e\left(\frac{152}{305}\right)\)	\(e\left(\frac{91}{610}\right)\)	\(e\left(\frac{99}{122}\right)\)
\(\chi_{3721}(430,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{171}{610}\right)\)	\(e\left(\frac{8}{305}\right)\)	\(e\left(\frac{171}{305}\right)\)	\(e\left(\frac{136}{305}\right)\)	\(e\left(\frac{187}{610}\right)\)	\(e\left(\frac{129}{610}\right)\)	\(e\left(\frac{513}{610}\right)\)	\(e\left(\frac{16}{305}\right)\)	\(e\left(\frac{443}{610}\right)\)	\(e\left(\frac{65}{122}\right)\)
\(\chi_{3721}(454,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{610}\right)\)	\(e\left(\frac{229}{305}\right)\)	\(e\left(\frac{53}{305}\right)\)	\(e\left(\frac{233}{305}\right)\)	\(e\left(\frac{511}{610}\right)\)	\(e\left(\frac{147}{610}\right)\)	\(e\left(\frac{159}{610}\right)\)	\(e\left(\frac{153}{305}\right)\)	\(e\left(\frac{519}{610}\right)\)	\(e\left(\frac{23}{122}\right)\)
\(\chi_{3721}(468,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{559}{610}\right)\)	\(e\left(\frac{217}{305}\right)\)	\(e\left(\frac{254}{305}\right)\)	\(e\left(\frac{29}{305}\right)\)	\(e\left(\frac{383}{610}\right)\)	\(e\left(\frac{411}{610}\right)\)	\(e\left(\frac{457}{610}\right)\)	\(e\left(\frac{129}{305}\right)\)	\(e\left(\frac{7}{610}\right)\)	\(e\left(\frac{17}{122}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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	3721.s
Modulus	$3721$
Conductor	$3721$
Order	$610$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3721\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(3721\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(610\)	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);