LMFDB - Dirichlet character orbit 33957.ik

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33957, base_ring=CyclotomicField(1470)) M = H._module chi = DirichletCharacter(H, M([245,970,147])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,33957)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$33957$
Conductor:	$33957$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$1470$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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:	$\Q(\zeta_{735})$
Fixed field:	Number field defined by a degree 1470 polynomial (not computed)

First 17 of 336 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{33957}(2,\cdot)$	$1$	$1$	$e\left(\frac{206}{735}\right)$	$e\left(\frac{412}{735}\right)$	$e\left(\frac{181}{490}\right)$	$e\left(\frac{206}{245}\right)$	$e\left(\frac{191}{294}\right)$	$e\left(\frac{727}{1470}\right)$	$e\left(\frac{89}{735}\right)$	$e\left(\frac{659}{735}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1367}{1470}\right)$
$\chi_{33957}(95,\cdot)$	$1$	$1$	$e\left(\frac{247}{735}\right)$	$e\left(\frac{494}{735}\right)$	$e\left(\frac{487}{490}\right)$	$e\left(\frac{2}{245}\right)$	$e\left(\frac{97}{294}\right)$	$e\left(\frac{1439}{1470}\right)$	$e\left(\frac{253}{735}\right)$	$e\left(\frac{73}{735}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{979}{1470}\right)$
$\chi_{33957}(347,\cdot)$	$1$	$1$	$e\left(\frac{559}{735}\right)$	$e\left(\frac{383}{735}\right)$	$e\left(\frac{19}{490}\right)$	$e\left(\frac{69}{245}\right)$	$e\left(\frac{235}{294}\right)$	$e\left(\frac{1013}{1470}\right)$	$e\left(\frac{31}{735}\right)$	$e\left(\frac{436}{735}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{823}{1470}\right)$
$\chi_{33957}(380,\cdot)$	$1$	$1$	$e\left(\frac{659}{735}\right)$	$e\left(\frac{583}{735}\right)$	$e\left(\frac{359}{490}\right)$	$e\left(\frac{169}{245}\right)$	$e\left(\frac{185}{294}\right)$	$e\left(\frac{1423}{1470}\right)$	$e\left(\frac{431}{735}\right)$	$e\left(\frac{656}{735}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{773}{1470}\right)$
$\chi_{33957}(536,\cdot)$	$1$	$1$	$e\left(\frac{58}{735}\right)$	$e\left(\frac{116}{735}\right)$	$e\left(\frac{403}{490}\right)$	$e\left(\frac{58}{245}\right)$	$e\left(\frac{265}{294}\right)$	$e\left(\frac{1061}{1470}\right)$	$e\left(\frac{232}{735}\right)$	$e\left(\frac{157}{735}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1441}{1470}\right)$
$\chi_{33957}(662,\cdot)$	$1$	$1$	$e\left(\frac{466}{735}\right)$	$e\left(\frac{197}{735}\right)$	$e\left(\frac{281}{490}\right)$	$e\left(\frac{221}{245}\right)$	$e\left(\frac{61}{294}\right)$	$e\left(\frac{617}{1470}\right)$	$e\left(\frac{394}{735}\right)$	$e\left(\frac{349}{735}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1237}{1470}\right)$
$\chi_{33957}(695,\cdot)$	$1$	$1$	$e\left(\frac{431}{735}\right)$	$e\left(\frac{127}{735}\right)$	$e\left(\frac{211}{490}\right)$	$e\left(\frac{186}{245}\right)$	$e\left(\frac{5}{294}\right)$	$e\left(\frac{547}{1470}\right)$	$e\left(\frac{254}{735}\right)$	$e\left(\frac{419}{735}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{887}{1470}\right)$
$\chi_{33957}(788,\cdot)$	$1$	$1$	$e\left(\frac{517}{735}\right)$	$e\left(\frac{299}{735}\right)$	$e\left(\frac{327}{490}\right)$	$e\left(\frac{27}{245}\right)$	$e\left(\frac{109}{294}\right)$	$e\left(\frac{929}{1470}\right)$	$e\left(\frac{598}{735}\right)$	$e\left(\frac{373}{735}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{109}{1470}\right)$
$\chi_{33957}(821,\cdot)$	$1$	$1$	$e\left(\frac{722}{735}\right)$	$e\left(\frac{709}{735}\right)$	$e\left(\frac{387}{490}\right)$	$e\left(\frac{232}{245}\right)$	$e\left(\frac{227}{294}\right)$	$e\left(\frac{79}{1470}\right)$	$e\left(\frac{683}{735}\right)$	$e\left(\frac{383}{735}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1109}{1470}\right)$
$\chi_{33957}(1040,\cdot)$	$1$	$1$	$e\left(\frac{724}{735}\right)$	$e\left(\frac{713}{735}\right)$	$e\left(\frac{139}{490}\right)$	$e\left(\frac{234}{245}\right)$	$e\left(\frac{79}{294}\right)$	$e\left(\frac{293}{1470}\right)$	$e\left(\frac{691}{735}\right)$	$e\left(\frac{211}{735}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{373}{1470}\right)$
$\chi_{33957}(1073,\cdot)$	$1$	$1$	$e\left(\frac{254}{735}\right)$	$e\left(\frac{508}{735}\right)$	$e\left(\frac{109}{490}\right)$	$e\left(\frac{9}{245}\right)$	$e\left(\frac{167}{294}\right)$	$e\left(\frac{1453}{1470}\right)$	$e\left(\frac{281}{735}\right)$	$e\left(\frac{206}{735}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1343}{1470}\right)$
$\chi_{33957}(1229,\cdot)$	$1$	$1$	$e\left(\frac{328}{735}\right)$	$e\left(\frac{656}{735}\right)$	$e\left(\frac{243}{490}\right)$	$e\left(\frac{83}{245}\right)$	$e\left(\frac{277}{294}\right)$	$e\left(\frac{551}{1470}\right)$	$e\left(\frac{577}{735}\right)$	$e\left(\frac{457}{735}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{571}{1470}\right)$
$\chi_{33957}(1262,\cdot)$	$1$	$1$	$e\left(\frac{638}{735}\right)$	$e\left(\frac{541}{735}\right)$	$e\left(\frac{23}{490}\right)$	$e\left(\frac{148}{245}\right)$	$e\left(\frac{269}{294}\right)$	$e\left(\frac{1381}{1470}\right)$	$e\left(\frac{347}{735}\right)$	$e\left(\frac{257}{735}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1151}{1470}\right)$
$\chi_{33957}(1355,\cdot)$	$1$	$1$	$e\left(\frac{316}{735}\right)$	$e\left(\frac{632}{735}\right)$	$e\left(\frac{261}{490}\right)$	$e\left(\frac{71}{245}\right)$	$e\left(\frac{283}{294}\right)$	$e\left(\frac{737}{1470}\right)$	$e\left(\frac{529}{735}\right)$	$e\left(\frac{19}{735}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{577}{1470}\right)$
$\chi_{33957}(1388,\cdot)$	$1$	$1$	$e\left(\frac{236}{735}\right)$	$e\left(\frac{472}{735}\right)$	$e\left(\frac{381}{490}\right)$	$e\left(\frac{236}{245}\right)$	$e\left(\frac{29}{294}\right)$	$e\left(\frac{997}{1470}\right)$	$e\left(\frac{209}{735}\right)$	$e\left(\frac{284}{735}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{617}{1470}\right)$
$\chi_{33957}(1481,\cdot)$	$1$	$1$	$e\left(\frac{682}{735}\right)$	$e\left(\frac{629}{735}\right)$	$e\left(\frac{447}{490}\right)$	$e\left(\frac{192}{245}\right)$	$e\left(\frac{247}{294}\right)$	$e\left(\frac{209}{1470}\right)$	$e\left(\frac{523}{735}\right)$	$e\left(\frac{148}{735}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1129}{1470}\right)$
$\chi_{33957}(1514,\cdot)$	$1$	$1$	$e\left(\frac{317}{735}\right)$	$e\left(\frac{634}{735}\right)$	$e\left(\frac{137}{490}\right)$	$e\left(\frac{72}{245}\right)$	$e\left(\frac{209}{294}\right)$	$e\left(\frac{109}{1470}\right)$	$e\left(\frac{533}{735}\right)$	$e\left(\frac{668}{735}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{209}{1470}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{33957}(2,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{206}{735}\right)\)	\(e\left(\frac{412}{735}\right)\)	\(e\left(\frac{181}{490}\right)\)	\(e\left(\frac{206}{245}\right)\)	\(e\left(\frac{191}{294}\right)\)	\(e\left(\frac{727}{1470}\right)\)	\(e\left(\frac{89}{735}\right)\)	\(e\left(\frac{659}{735}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1367}{1470}\right)\)
\(\chi_{33957}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{735}\right)\)	\(e\left(\frac{494}{735}\right)\)	\(e\left(\frac{487}{490}\right)\)	\(e\left(\frac{2}{245}\right)\)	\(e\left(\frac{97}{294}\right)\)	\(e\left(\frac{1439}{1470}\right)\)	\(e\left(\frac{253}{735}\right)\)	\(e\left(\frac{73}{735}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{979}{1470}\right)\)
\(\chi_{33957}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{559}{735}\right)\)	\(e\left(\frac{383}{735}\right)\)	\(e\left(\frac{19}{490}\right)\)	\(e\left(\frac{69}{245}\right)\)	\(e\left(\frac{235}{294}\right)\)	\(e\left(\frac{1013}{1470}\right)\)	\(e\left(\frac{31}{735}\right)\)	\(e\left(\frac{436}{735}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{823}{1470}\right)\)
\(\chi_{33957}(380,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{659}{735}\right)\)	\(e\left(\frac{583}{735}\right)\)	\(e\left(\frac{359}{490}\right)\)	\(e\left(\frac{169}{245}\right)\)	\(e\left(\frac{185}{294}\right)\)	\(e\left(\frac{1423}{1470}\right)\)	\(e\left(\frac{431}{735}\right)\)	\(e\left(\frac{656}{735}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{773}{1470}\right)\)
\(\chi_{33957}(536,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{735}\right)\)	\(e\left(\frac{116}{735}\right)\)	\(e\left(\frac{403}{490}\right)\)	\(e\left(\frac{58}{245}\right)\)	\(e\left(\frac{265}{294}\right)\)	\(e\left(\frac{1061}{1470}\right)\)	\(e\left(\frac{232}{735}\right)\)	\(e\left(\frac{157}{735}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1441}{1470}\right)\)
\(\chi_{33957}(662,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{466}{735}\right)\)	\(e\left(\frac{197}{735}\right)\)	\(e\left(\frac{281}{490}\right)\)	\(e\left(\frac{221}{245}\right)\)	\(e\left(\frac{61}{294}\right)\)	\(e\left(\frac{617}{1470}\right)\)	\(e\left(\frac{394}{735}\right)\)	\(e\left(\frac{349}{735}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1237}{1470}\right)\)
\(\chi_{33957}(695,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{431}{735}\right)\)	\(e\left(\frac{127}{735}\right)\)	\(e\left(\frac{211}{490}\right)\)	\(e\left(\frac{186}{245}\right)\)	\(e\left(\frac{5}{294}\right)\)	\(e\left(\frac{547}{1470}\right)\)	\(e\left(\frac{254}{735}\right)\)	\(e\left(\frac{419}{735}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{887}{1470}\right)\)
\(\chi_{33957}(788,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{517}{735}\right)\)	\(e\left(\frac{299}{735}\right)\)	\(e\left(\frac{327}{490}\right)\)	\(e\left(\frac{27}{245}\right)\)	\(e\left(\frac{109}{294}\right)\)	\(e\left(\frac{929}{1470}\right)\)	\(e\left(\frac{598}{735}\right)\)	\(e\left(\frac{373}{735}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{109}{1470}\right)\)
\(\chi_{33957}(821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{722}{735}\right)\)	\(e\left(\frac{709}{735}\right)\)	\(e\left(\frac{387}{490}\right)\)	\(e\left(\frac{232}{245}\right)\)	\(e\left(\frac{227}{294}\right)\)	\(e\left(\frac{79}{1470}\right)\)	\(e\left(\frac{683}{735}\right)\)	\(e\left(\frac{383}{735}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1109}{1470}\right)\)
\(\chi_{33957}(1040,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{724}{735}\right)\)	\(e\left(\frac{713}{735}\right)\)	\(e\left(\frac{139}{490}\right)\)	\(e\left(\frac{234}{245}\right)\)	\(e\left(\frac{79}{294}\right)\)	\(e\left(\frac{293}{1470}\right)\)	\(e\left(\frac{691}{735}\right)\)	\(e\left(\frac{211}{735}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{373}{1470}\right)\)
\(\chi_{33957}(1073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{254}{735}\right)\)	\(e\left(\frac{508}{735}\right)\)	\(e\left(\frac{109}{490}\right)\)	\(e\left(\frac{9}{245}\right)\)	\(e\left(\frac{167}{294}\right)\)	\(e\left(\frac{1453}{1470}\right)\)	\(e\left(\frac{281}{735}\right)\)	\(e\left(\frac{206}{735}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1343}{1470}\right)\)
\(\chi_{33957}(1229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{328}{735}\right)\)	\(e\left(\frac{656}{735}\right)\)	\(e\left(\frac{243}{490}\right)\)	\(e\left(\frac{83}{245}\right)\)	\(e\left(\frac{277}{294}\right)\)	\(e\left(\frac{551}{1470}\right)\)	\(e\left(\frac{577}{735}\right)\)	\(e\left(\frac{457}{735}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{571}{1470}\right)\)
\(\chi_{33957}(1262,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{638}{735}\right)\)	\(e\left(\frac{541}{735}\right)\)	\(e\left(\frac{23}{490}\right)\)	\(e\left(\frac{148}{245}\right)\)	\(e\left(\frac{269}{294}\right)\)	\(e\left(\frac{1381}{1470}\right)\)	\(e\left(\frac{347}{735}\right)\)	\(e\left(\frac{257}{735}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1151}{1470}\right)\)
\(\chi_{33957}(1355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{316}{735}\right)\)	\(e\left(\frac{632}{735}\right)\)	\(e\left(\frac{261}{490}\right)\)	\(e\left(\frac{71}{245}\right)\)	\(e\left(\frac{283}{294}\right)\)	\(e\left(\frac{737}{1470}\right)\)	\(e\left(\frac{529}{735}\right)\)	\(e\left(\frac{19}{735}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{577}{1470}\right)\)
\(\chi_{33957}(1388,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{236}{735}\right)\)	\(e\left(\frac{472}{735}\right)\)	\(e\left(\frac{381}{490}\right)\)	\(e\left(\frac{236}{245}\right)\)	\(e\left(\frac{29}{294}\right)\)	\(e\left(\frac{997}{1470}\right)\)	\(e\left(\frac{209}{735}\right)\)	\(e\left(\frac{284}{735}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{617}{1470}\right)\)
\(\chi_{33957}(1481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{682}{735}\right)\)	\(e\left(\frac{629}{735}\right)\)	\(e\left(\frac{447}{490}\right)\)	\(e\left(\frac{192}{245}\right)\)	\(e\left(\frac{247}{294}\right)\)	\(e\left(\frac{209}{1470}\right)\)	\(e\left(\frac{523}{735}\right)\)	\(e\left(\frac{148}{735}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1129}{1470}\right)\)
\(\chi_{33957}(1514,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{317}{735}\right)\)	\(e\left(\frac{634}{735}\right)\)	\(e\left(\frac{137}{490}\right)\)	\(e\left(\frac{72}{245}\right)\)	\(e\left(\frac{209}{294}\right)\)	\(e\left(\frac{109}{1470}\right)\)	\(e\left(\frac{533}{735}\right)\)	\(e\left(\frac{668}{735}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{209}{1470}\right)\)

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Basic properties

Related number fields

First 17 of 336 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	33957.ik
Modulus	$33957$
Conductor	$33957$
Order	$1470$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(33957\)
Conductor:	\(33957\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(1470\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)