LMFDB - Dirichlet character orbit 416000.bpr

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416000, base_ring=CyclotomicField(1200)) M = H._module chi = DirichletCharacter(H, M([0,525,876,200])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(17, 416000)) 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("416000.17"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$416000$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$104000$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$1200$	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:	no, induced from 104000.bep	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{1200})$	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 1200 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 320 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{416000}(17,\cdot)$	$-1$	$1$	$e\left(\frac{107}{1200}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{107}{600}\right)$	$e\left(\frac{1001}{1200}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{43}{1200}\right)$	$e\left(\frac{139}{400}\right)$	$e\left(\frac{253}{600}\right)$	$e\left(\frac{107}{400}\right)$	$e\left(\frac{887}{1200}\right)$
$\chi_{416000}(433,\cdot)$	$-1$	$1$	$e\left(\frac{617}{1200}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{17}{600}\right)$	$e\left(\frac{131}{1200}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{1033}{1200}\right)$	$e\left(\frac{9}{400}\right)$	$e\left(\frac{343}{600}\right)$	$e\left(\frac{217}{400}\right)$	$e\left(\frac{797}{1200}\right)$
$\chi_{416000}(1297,\cdot)$	$-1$	$1$	$e\left(\frac{523}{1200}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{523}{600}\right)$	$e\left(\frac{889}{1200}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{827}{1200}\right)$	$e\left(\frac{171}{400}\right)$	$e\left(\frac{317}{600}\right)$	$e\left(\frac{123}{400}\right)$	$e\left(\frac{343}{1200}\right)$
$\chi_{416000}(1713,\cdot)$	$-1$	$1$	$e\left(\frac{361}{1200}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{361}{600}\right)$	$e\left(\frac{1123}{1200}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{89}{1200}\right)$	$e\left(\frac{297}{400}\right)$	$e\left(\frac{119}{600}\right)$	$e\left(\frac{361}{400}\right)$	$e\left(\frac{301}{1200}\right)$
$\chi_{416000}(4177,\cdot)$	$-1$	$1$	$e\left(\frac{119}{1200}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{119}{600}\right)$	$e\left(\frac{317}{1200}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{631}{1200}\right)$	$e\left(\frac{263}{400}\right)$	$e\left(\frac{1}{600}\right)$	$e\left(\frac{119}{400}\right)$	$e\left(\frac{179}{1200}\right)$
$\chi_{416000}(5873,\cdot)$	$-1$	$1$	$e\left(\frac{709}{1200}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{109}{600}\right)$	$e\left(\frac{487}{1200}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{341}{1200}\right)$	$e\left(\frac{293}{400}\right)$	$e\left(\frac{11}{600}\right)$	$e\left(\frac{309}{400}\right)$	$e\left(\frac{169}{1200}\right)$
$\chi_{416000}(8337,\cdot)$	$-1$	$1$	$e\left(\frac{371}{1200}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{371}{600}\right)$	$e\left(\frac{353}{1200}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{979}{1200}\right)$	$e\left(\frac{67}{400}\right)$	$e\left(\frac{109}{600}\right)$	$e\left(\frac{371}{400}\right)$	$e\left(\frac{911}{1200}\right)$
$\chi_{416000}(8753,\cdot)$	$-1$	$1$	$e\left(\frac{113}{1200}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{113}{600}\right)$	$e\left(\frac{59}{1200}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{337}{1200}\right)$	$e\left(\frac{1}{400}\right)$	$e\left(\frac{127}{600}\right)$	$e\left(\frac{113}{400}\right)$	$e\left(\frac{533}{1200}\right)$
$\chi_{416000}(9617,\cdot)$	$-1$	$1$	$e\left(\frac{1027}{1200}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{427}{600}\right)$	$e\left(\frac{961}{1200}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{323}{1200}\right)$	$e\left(\frac{179}{400}\right)$	$e\left(\frac{533}{600}\right)$	$e\left(\frac{227}{400}\right)$	$e\left(\frac{607}{1200}\right)$
$\chi_{416000}(10033,\cdot)$	$-1$	$1$	$e\left(\frac{97}{1200}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{97}{600}\right)$	$e\left(\frac{571}{1200}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{353}{1200}\right)$	$e\left(\frac{369}{400}\right)$	$e\left(\frac{263}{600}\right)$	$e\left(\frac{97}{400}\right)$	$e\left(\frac{277}{1200}\right)$
$\chi_{416000}(12497,\cdot)$	$-1$	$1$	$e\left(\frac{863}{1200}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{263}{600}\right)$	$e\left(\frac{1109}{1200}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{1087}{1200}\right)$	$e\left(\frac{351}{400}\right)$	$e\left(\frac{577}{600}\right)$	$e\left(\frac{63}{400}\right)$	$e\left(\frac{683}{1200}\right)$
$\chi_{416000}(12913,\cdot)$	$-1$	$1$	$e\left(\frac{221}{1200}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{221}{600}\right)$	$e\left(\frac{1103}{1200}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{829}{1200}\right)$	$e\left(\frac{317}{400}\right)$	$e\left(\frac{259}{600}\right)$	$e\left(\frac{221}{400}\right)$	$e\left(\frac{161}{1200}\right)$
$\chi_{416000}(13777,\cdot)$	$-1$	$1$	$e\left(\frac{1039}{1200}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{439}{600}\right)$	$e\left(\frac{277}{1200}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{911}{1200}\right)$	$e\left(\frac{303}{400}\right)$	$e\left(\frac{281}{600}\right)$	$e\left(\frac{239}{400}\right)$	$e\left(\frac{1099}{1200}\right)$
$\chi_{416000}(17073,\cdot)$	$-1$	$1$	$e\left(\frac{569}{1200}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{569}{600}\right)$	$e\left(\frac{467}{1200}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{1081}{1200}\right)$	$e\left(\frac{313}{400}\right)$	$e\left(\frac{151}{600}\right)$	$e\left(\frac{169}{400}\right)$	$e\left(\frac{29}{1200}\right)$
$\chi_{416000}(17937,\cdot)$	$-1$	$1$	$e\left(\frac{91}{1200}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{91}{600}\right)$	$e\left(\frac{313}{1200}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{59}{1200}\right)$	$e\left(\frac{107}{400}\right)$	$e\left(\frac{389}{600}\right)$	$e\left(\frac{91}{400}\right)$	$e\left(\frac{631}{1200}\right)$
$\chi_{416000}(18353,\cdot)$	$-1$	$1$	$e\left(\frac{793}{1200}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{193}{600}\right)$	$e\left(\frac{499}{1200}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{857}{1200}\right)$	$e\left(\frac{361}{400}\right)$	$e\left(\frac{47}{600}\right)$	$e\left(\frac{393}{400}\right)$	$e\left(\frac{13}{1200}\right)$
$\chi_{416000}(20817,\cdot)$	$-1$	$1$	$e\left(\frac{167}{1200}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{167}{600}\right)$	$e\left(\frac{1181}{1200}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{583}{1200}\right)$	$e\left(\frac{359}{400}\right)$	$e\left(\frac{193}{600}\right)$	$e\left(\frac{167}{400}\right)$	$e\left(\frac{947}{1200}\right)$
$\chi_{416000}(21233,\cdot)$	$-1$	$1$	$e\left(\frac{1157}{1200}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{557}{600}\right)$	$e\left(\frac{551}{1200}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{1093}{1200}\right)$	$e\left(\frac{389}{400}\right)$	$e\left(\frac{403}{600}\right)$	$e\left(\frac{357}{400}\right)$	$e\left(\frac{137}{1200}\right)$
$\chi_{416000}(22097,\cdot)$	$-1$	$1$	$e\left(\frac{583}{1200}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{583}{600}\right)$	$e\left(\frac{1069}{1200}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{167}{1200}\right)$	$e\left(\frac{391}{400}\right)$	$e\left(\frac{257}{600}\right)$	$e\left(\frac{183}{400}\right)$	$e\left(\frac{403}{1200}\right)$
$\chi_{416000}(22513,\cdot)$	$-1$	$1$	$e\left(\frac{901}{1200}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{301}{600}\right)$	$e\left(\frac{343}{1200}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{149}{1200}\right)$	$e\left(\frac{277}{400}\right)$	$e\left(\frac{179}{600}\right)$	$e\left(\frac{101}{400}\right)$	$e\left(\frac{841}{1200}\right)$
$\chi_{416000}(24977,\cdot)$	$-1$	$1$	$e\left(\frac{179}{1200}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{179}{600}\right)$	$e\left(\frac{497}{1200}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{1171}{1200}\right)$	$e\left(\frac{83}{400}\right)$	$e\left(\frac{541}{600}\right)$	$e\left(\frac{179}{400}\right)$	$e\left(\frac{239}{1200}\right)$
$\chi_{416000}(26673,\cdot)$	$-1$	$1$	$e\left(\frac{49}{1200}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{49}{600}\right)$	$e\left(\frac{907}{1200}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{401}{1200}\right)$	$e\left(\frac{273}{400}\right)$	$e\left(\frac{71}{600}\right)$	$e\left(\frac{49}{400}\right)$	$e\left(\frac{709}{1200}\right)$
$\chi_{416000}(29137,\cdot)$	$-1$	$1$	$e\left(\frac{431}{1200}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{431}{600}\right)$	$e\left(\frac{533}{1200}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{319}{1200}\right)$	$e\left(\frac{287}{400}\right)$	$e\left(\frac{49}{600}\right)$	$e\left(\frac{31}{400}\right)$	$e\left(\frac{971}{1200}\right)$
$\chi_{416000}(29553,\cdot)$	$-1$	$1$	$e\left(\frac{653}{1200}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{53}{600}\right)$	$e\left(\frac{479}{1200}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{397}{1200}\right)$	$e\left(\frac{381}{400}\right)$	$e\left(\frac{187}{600}\right)$	$e\left(\frac{253}{400}\right)$	$e\left(\frac{1073}{1200}\right)$
$\chi_{416000}(30417,\cdot)$	$-1$	$1$	$e\left(\frac{1087}{1200}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{487}{600}\right)$	$e\left(\frac{1141}{1200}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{863}{1200}\right)$	$e\left(\frac{399}{400}\right)$	$e\left(\frac{473}{600}\right)$	$e\left(\frac{287}{400}\right)$	$e\left(\frac{667}{1200}\right)$
$\chi_{416000}(30833,\cdot)$	$-1$	$1$	$e\left(\frac{637}{1200}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{37}{600}\right)$	$e\left(\frac{991}{1200}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{413}{1200}\right)$	$e\left(\frac{349}{400}\right)$	$e\left(\frac{323}{600}\right)$	$e\left(\frac{237}{400}\right)$	$e\left(\frac{817}{1200}\right)$
$\chi_{416000}(33297,\cdot)$	$-1$	$1$	$e\left(\frac{923}{1200}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{323}{600}\right)$	$e\left(\frac{89}{1200}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{427}{1200}\right)$	$e\left(\frac{171}{400}\right)$	$e\left(\frac{517}{600}\right)$	$e\left(\frac{123}{400}\right)$	$e\left(\frac{743}{1200}\right)$
$\chi_{416000}(33713,\cdot)$	$-1$	$1$	$e\left(\frac{761}{1200}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{161}{600}\right)$	$e\left(\frac{323}{1200}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{889}{1200}\right)$	$e\left(\frac{297}{400}\right)$	$e\left(\frac{319}{600}\right)$	$e\left(\frac{361}{400}\right)$	$e\left(\frac{701}{1200}\right)$
$\chi_{416000}(34577,\cdot)$	$-1$	$1$	$e\left(\frac{1099}{1200}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{499}{600}\right)$	$e\left(\frac{457}{1200}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{251}{1200}\right)$	$e\left(\frac{123}{400}\right)$	$e\left(\frac{221}{600}\right)$	$e\left(\frac{299}{400}\right)$	$e\left(\frac{1159}{1200}\right)$
$\chi_{416000}(37873,\cdot)$	$-1$	$1$	$e\left(\frac{1109}{1200}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{509}{600}\right)$	$e\left(\frac{887}{1200}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{1141}{1200}\right)$	$e\left(\frac{293}{400}\right)$	$e\left(\frac{211}{600}\right)$	$e\left(\frac{309}{400}\right)$	$e\left(\frac{569}{1200}\right)$
$\chi_{416000}(38737,\cdot)$	$-1$	$1$	$e\left(\frac{151}{1200}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{151}{600}\right)$	$e\left(\frac{493}{1200}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{599}{1200}\right)$	$e\left(\frac{327}{400}\right)$	$e\left(\frac{329}{600}\right)$	$e\left(\frac{151}{400}\right)$	$e\left(\frac{691}{1200}\right)$

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Classical	Maass
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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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{416000}(17,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{1200}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{107}{600}\right)\)	\(e\left(\frac{1001}{1200}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{43}{1200}\right)\)	\(e\left(\frac{139}{400}\right)\)	\(e\left(\frac{253}{600}\right)\)	\(e\left(\frac{107}{400}\right)\)	\(e\left(\frac{887}{1200}\right)\)
\(\chi_{416000}(433,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{617}{1200}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{17}{600}\right)\)	\(e\left(\frac{131}{1200}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{1033}{1200}\right)\)	\(e\left(\frac{9}{400}\right)\)	\(e\left(\frac{343}{600}\right)\)	\(e\left(\frac{217}{400}\right)\)	\(e\left(\frac{797}{1200}\right)\)
\(\chi_{416000}(1297,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{523}{1200}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{523}{600}\right)\)	\(e\left(\frac{889}{1200}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{827}{1200}\right)\)	\(e\left(\frac{171}{400}\right)\)	\(e\left(\frac{317}{600}\right)\)	\(e\left(\frac{123}{400}\right)\)	\(e\left(\frac{343}{1200}\right)\)
\(\chi_{416000}(1713,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{361}{1200}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{361}{600}\right)\)	\(e\left(\frac{1123}{1200}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{89}{1200}\right)\)	\(e\left(\frac{297}{400}\right)\)	\(e\left(\frac{119}{600}\right)\)	\(e\left(\frac{361}{400}\right)\)	\(e\left(\frac{301}{1200}\right)\)
\(\chi_{416000}(4177,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{1200}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{119}{600}\right)\)	\(e\left(\frac{317}{1200}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{631}{1200}\right)\)	\(e\left(\frac{263}{400}\right)\)	\(e\left(\frac{1}{600}\right)\)	\(e\left(\frac{119}{400}\right)\)	\(e\left(\frac{179}{1200}\right)\)
\(\chi_{416000}(5873,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{709}{1200}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{109}{600}\right)\)	\(e\left(\frac{487}{1200}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{341}{1200}\right)\)	\(e\left(\frac{293}{400}\right)\)	\(e\left(\frac{11}{600}\right)\)	\(e\left(\frac{309}{400}\right)\)	\(e\left(\frac{169}{1200}\right)\)
\(\chi_{416000}(8337,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{371}{1200}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{371}{600}\right)\)	\(e\left(\frac{353}{1200}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{979}{1200}\right)\)	\(e\left(\frac{67}{400}\right)\)	\(e\left(\frac{109}{600}\right)\)	\(e\left(\frac{371}{400}\right)\)	\(e\left(\frac{911}{1200}\right)\)
\(\chi_{416000}(8753,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{1200}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{113}{600}\right)\)	\(e\left(\frac{59}{1200}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{337}{1200}\right)\)	\(e\left(\frac{1}{400}\right)\)	\(e\left(\frac{127}{600}\right)\)	\(e\left(\frac{113}{400}\right)\)	\(e\left(\frac{533}{1200}\right)\)
\(\chi_{416000}(9617,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1027}{1200}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{427}{600}\right)\)	\(e\left(\frac{961}{1200}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{323}{1200}\right)\)	\(e\left(\frac{179}{400}\right)\)	\(e\left(\frac{533}{600}\right)\)	\(e\left(\frac{227}{400}\right)\)	\(e\left(\frac{607}{1200}\right)\)
\(\chi_{416000}(10033,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{1200}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{97}{600}\right)\)	\(e\left(\frac{571}{1200}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{353}{1200}\right)\)	\(e\left(\frac{369}{400}\right)\)	\(e\left(\frac{263}{600}\right)\)	\(e\left(\frac{97}{400}\right)\)	\(e\left(\frac{277}{1200}\right)\)
\(\chi_{416000}(12497,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{863}{1200}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{263}{600}\right)\)	\(e\left(\frac{1109}{1200}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{1087}{1200}\right)\)	\(e\left(\frac{351}{400}\right)\)	\(e\left(\frac{577}{600}\right)\)	\(e\left(\frac{63}{400}\right)\)	\(e\left(\frac{683}{1200}\right)\)
\(\chi_{416000}(12913,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{221}{1200}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{221}{600}\right)\)	\(e\left(\frac{1103}{1200}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{829}{1200}\right)\)	\(e\left(\frac{317}{400}\right)\)	\(e\left(\frac{259}{600}\right)\)	\(e\left(\frac{221}{400}\right)\)	\(e\left(\frac{161}{1200}\right)\)
\(\chi_{416000}(13777,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1039}{1200}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{439}{600}\right)\)	\(e\left(\frac{277}{1200}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{911}{1200}\right)\)	\(e\left(\frac{303}{400}\right)\)	\(e\left(\frac{281}{600}\right)\)	\(e\left(\frac{239}{400}\right)\)	\(e\left(\frac{1099}{1200}\right)\)
\(\chi_{416000}(17073,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{569}{1200}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{569}{600}\right)\)	\(e\left(\frac{467}{1200}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{1081}{1200}\right)\)	\(e\left(\frac{313}{400}\right)\)	\(e\left(\frac{151}{600}\right)\)	\(e\left(\frac{169}{400}\right)\)	\(e\left(\frac{29}{1200}\right)\)
\(\chi_{416000}(17937,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{1200}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{91}{600}\right)\)	\(e\left(\frac{313}{1200}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{59}{1200}\right)\)	\(e\left(\frac{107}{400}\right)\)	\(e\left(\frac{389}{600}\right)\)	\(e\left(\frac{91}{400}\right)\)	\(e\left(\frac{631}{1200}\right)\)
\(\chi_{416000}(18353,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{793}{1200}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{193}{600}\right)\)	\(e\left(\frac{499}{1200}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{857}{1200}\right)\)	\(e\left(\frac{361}{400}\right)\)	\(e\left(\frac{47}{600}\right)\)	\(e\left(\frac{393}{400}\right)\)	\(e\left(\frac{13}{1200}\right)\)
\(\chi_{416000}(20817,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{1200}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{167}{600}\right)\)	\(e\left(\frac{1181}{1200}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{583}{1200}\right)\)	\(e\left(\frac{359}{400}\right)\)	\(e\left(\frac{193}{600}\right)\)	\(e\left(\frac{167}{400}\right)\)	\(e\left(\frac{947}{1200}\right)\)
\(\chi_{416000}(21233,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1157}{1200}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{557}{600}\right)\)	\(e\left(\frac{551}{1200}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{1093}{1200}\right)\)	\(e\left(\frac{389}{400}\right)\)	\(e\left(\frac{403}{600}\right)\)	\(e\left(\frac{357}{400}\right)\)	\(e\left(\frac{137}{1200}\right)\)
\(\chi_{416000}(22097,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{583}{1200}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{583}{600}\right)\)	\(e\left(\frac{1069}{1200}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{167}{1200}\right)\)	\(e\left(\frac{391}{400}\right)\)	\(e\left(\frac{257}{600}\right)\)	\(e\left(\frac{183}{400}\right)\)	\(e\left(\frac{403}{1200}\right)\)
\(\chi_{416000}(22513,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{901}{1200}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{301}{600}\right)\)	\(e\left(\frac{343}{1200}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{149}{1200}\right)\)	\(e\left(\frac{277}{400}\right)\)	\(e\left(\frac{179}{600}\right)\)	\(e\left(\frac{101}{400}\right)\)	\(e\left(\frac{841}{1200}\right)\)
\(\chi_{416000}(24977,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{1200}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{179}{600}\right)\)	\(e\left(\frac{497}{1200}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{1171}{1200}\right)\)	\(e\left(\frac{83}{400}\right)\)	\(e\left(\frac{541}{600}\right)\)	\(e\left(\frac{179}{400}\right)\)	\(e\left(\frac{239}{1200}\right)\)
\(\chi_{416000}(26673,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{1200}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{49}{600}\right)\)	\(e\left(\frac{907}{1200}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{401}{1200}\right)\)	\(e\left(\frac{273}{400}\right)\)	\(e\left(\frac{71}{600}\right)\)	\(e\left(\frac{49}{400}\right)\)	\(e\left(\frac{709}{1200}\right)\)
\(\chi_{416000}(29137,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{431}{1200}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{431}{600}\right)\)	\(e\left(\frac{533}{1200}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{319}{1200}\right)\)	\(e\left(\frac{287}{400}\right)\)	\(e\left(\frac{49}{600}\right)\)	\(e\left(\frac{31}{400}\right)\)	\(e\left(\frac{971}{1200}\right)\)
\(\chi_{416000}(29553,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{653}{1200}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{53}{600}\right)\)	\(e\left(\frac{479}{1200}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{397}{1200}\right)\)	\(e\left(\frac{381}{400}\right)\)	\(e\left(\frac{187}{600}\right)\)	\(e\left(\frac{253}{400}\right)\)	\(e\left(\frac{1073}{1200}\right)\)
\(\chi_{416000}(30417,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1087}{1200}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{487}{600}\right)\)	\(e\left(\frac{1141}{1200}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{863}{1200}\right)\)	\(e\left(\frac{399}{400}\right)\)	\(e\left(\frac{473}{600}\right)\)	\(e\left(\frac{287}{400}\right)\)	\(e\left(\frac{667}{1200}\right)\)
\(\chi_{416000}(30833,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{637}{1200}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{37}{600}\right)\)	\(e\left(\frac{991}{1200}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{413}{1200}\right)\)	\(e\left(\frac{349}{400}\right)\)	\(e\left(\frac{323}{600}\right)\)	\(e\left(\frac{237}{400}\right)\)	\(e\left(\frac{817}{1200}\right)\)
\(\chi_{416000}(33297,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{923}{1200}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{323}{600}\right)\)	\(e\left(\frac{89}{1200}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{427}{1200}\right)\)	\(e\left(\frac{171}{400}\right)\)	\(e\left(\frac{517}{600}\right)\)	\(e\left(\frac{123}{400}\right)\)	\(e\left(\frac{743}{1200}\right)\)
\(\chi_{416000}(33713,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{761}{1200}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{161}{600}\right)\)	\(e\left(\frac{323}{1200}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{889}{1200}\right)\)	\(e\left(\frac{297}{400}\right)\)	\(e\left(\frac{319}{600}\right)\)	\(e\left(\frac{361}{400}\right)\)	\(e\left(\frac{701}{1200}\right)\)
\(\chi_{416000}(34577,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1099}{1200}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{499}{600}\right)\)	\(e\left(\frac{457}{1200}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{251}{1200}\right)\)	\(e\left(\frac{123}{400}\right)\)	\(e\left(\frac{221}{600}\right)\)	\(e\left(\frac{299}{400}\right)\)	\(e\left(\frac{1159}{1200}\right)\)
\(\chi_{416000}(37873,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1109}{1200}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{509}{600}\right)\)	\(e\left(\frac{887}{1200}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{1141}{1200}\right)\)	\(e\left(\frac{293}{400}\right)\)	\(e\left(\frac{211}{600}\right)\)	\(e\left(\frac{309}{400}\right)\)	\(e\left(\frac{569}{1200}\right)\)
\(\chi_{416000}(38737,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{1200}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{151}{600}\right)\)	\(e\left(\frac{493}{1200}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{599}{1200}\right)\)	\(e\left(\frac{327}{400}\right)\)	\(e\left(\frac{329}{600}\right)\)	\(e\left(\frac{151}{400}\right)\)	\(e\left(\frac{691}{1200}\right)\)

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First 31 of 320 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	416000.bpr
Modulus	$416000$
Conductor	$104000$
Order	$1200$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(416000\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(104000\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(1200\)	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:	no, induced from 104000.bep	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);