LMFDB - Dirichlet character orbit 4096.u

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4096, base_ring=CyclotomicField(1024)) M = H._module chi = DirichletCharacter(H, M([0,1])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,4096)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4096$
Conductor:	$4096$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$1024$	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:	$\Q(\zeta_{1024})$
Fixed field:	Number field defined by a degree 1024 polynomial (not computed)

First 31 of 512 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{4096}(5,\cdot)$	$1$	$1$	$e\left(\frac{675}{1024}\right)$	$e\left(\frac{1}{1024}\right)$	$e\left(\frac{357}{512}\right)$	$e\left(\frac{163}{512}\right)$	$e\left(\frac{213}{1024}\right)$	$e\left(\frac{1007}{1024}\right)$	$e\left(\frac{169}{256}\right)$	$e\left(\frac{103}{256}\right)$	$e\left(\frac{919}{1024}\right)$	$e\left(\frac{365}{1024}\right)$
$\chi_{4096}(13,\cdot)$	$1$	$1$	$e\left(\frac{813}{1024}\right)$	$e\left(\frac{1007}{1024}\right)$	$e\left(\frac{75}{512}\right)$	$e\left(\frac{301}{512}\right)$	$e\left(\frac{475}{1024}\right)$	$e\left(\frac{289}{1024}\right)$	$e\left(\frac{199}{256}\right)$	$e\left(\frac{41}{256}\right)$	$e\left(\frac{761}{1024}\right)$	$e\left(\frac{963}{1024}\right)$
$\chi_{4096}(21,\cdot)$	$1$	$1$	$e\left(\frac{615}{1024}\right)$	$e\left(\frac{365}{1024}\right)$	$e\left(\frac{257}{512}\right)$	$e\left(\frac{103}{512}\right)$	$e\left(\frac{945}{1024}\right)$	$e\left(\frac{963}{1024}\right)$	$e\left(\frac{245}{256}\right)$	$e\left(\frac{219}{256}\right)$	$e\left(\frac{587}{1024}\right)$	$e\left(\frac{105}{1024}\right)$
$\chi_{4096}(29,\cdot)$	$1$	$1$	$e\left(\frac{337}{1024}\right)$	$e\left(\frac{891}{1024}\right)$	$e\left(\frac{135}{512}\right)$	$e\left(\frac{337}{512}\right)$	$e\left(\frac{343}{1024}\right)$	$e\left(\frac{213}{1024}\right)$	$e\left(\frac{51}{256}\right)$	$e\left(\frac{125}{256}\right)$	$e\left(\frac{653}{1024}\right)$	$e\left(\frac{607}{1024}\right)$
$\chi_{4096}(37,\cdot)$	$1$	$1$	$e\left(\frac{235}{1024}\right)$	$e\left(\frac{281}{1024}\right)$	$e\left(\frac{477}{512}\right)$	$e\left(\frac{235}{512}\right)$	$e\left(\frac{461}{1024}\right)$	$e\left(\frac{343}{1024}\right)$	$e\left(\frac{129}{256}\right)$	$e\left(\frac{15}{256}\right)$	$e\left(\frac{191}{1024}\right)$	$e\left(\frac{165}{1024}\right)$
$\chi_{4096}(45,\cdot)$	$1$	$1$	$e\left(\frac{565}{1024}\right)$	$e\left(\frac{327}{1024}\right)$	$e\left(\frac{3}{512}\right)$	$e\left(\frac{53}{512}\right)$	$e\left(\frac{19}{1024}\right)$	$e\left(\frac{585}{1024}\right)$	$e\left(\frac{223}{256}\right)$	$e\left(\frac{145}{256}\right)$	$e\left(\frac{481}{1024}\right)$	$e\left(\frac{571}{1024}\right)$
$\chi_{4096}(53,\cdot)$	$1$	$1$	$e\left(\frac{559}{1024}\right)$	$e\left(\frac{773}{1024}\right)$	$e\left(\frac{505}{512}\right)$	$e\left(\frac{47}{512}\right)$	$e\left(\frac{809}{1024}\right)$	$e\left(\frac{171}{1024}\right)$	$e\left(\frac{77}{256}\right)$	$e\left(\frac{3}{256}\right)$	$e\left(\frac{755}{1024}\right)$	$e\left(\frac{545}{1024}\right)$
$\chi_{4096}(61,\cdot)$	$1$	$1$	$e\left(\frac{473}{1024}\right)$	$e\left(\frac{339}{1024}\right)$	$e\left(\frac{191}{512}\right)$	$e\left(\frac{473}{512}\right)$	$e\left(\frac{527}{1024}\right)$	$e\left(\frac{381}{1024}\right)$	$e\left(\frac{203}{256}\right)$	$e\left(\frac{101}{256}\right)$	$e\left(\frac{245}{1024}\right)$	$e\left(\frac{855}{1024}\right)$
$\chi_{4096}(69,\cdot)$	$1$	$1$	$e\left(\frac{563}{1024}\right)$	$e\left(\frac{817}{1024}\right)$	$e\left(\frac{341}{512}\right)$	$e\left(\frac{51}{512}\right)$	$e\left(\frac{965}{1024}\right)$	$e\left(\frac{447}{1024}\right)$	$e\left(\frac{89}{256}\right)$	$e\left(\frac{183}{256}\right)$	$e\left(\frac{231}{1024}\right)$	$e\left(\frac{221}{1024}\right)$
$\chi_{4096}(77,\cdot)$	$1$	$1$	$e\left(\frac{61}{1024}\right)$	$e\left(\frac{927}{1024}\right)$	$e\left(\frac{187}{512}\right)$	$e\left(\frac{61}{512}\right)$	$e\left(\frac{843}{1024}\right)$	$e\left(\frac{625}{1024}\right)$	$e\left(\frac{247}{256}\right)$	$e\left(\frac{249}{256}\right)$	$e\left(\frac{969}{1024}\right)$	$e\left(\frac{435}{1024}\right)$
$\chi_{4096}(85,\cdot)$	$1$	$1$	$e\left(\frac{247}{1024}\right)$	$e\left(\frac{413}{1024}\right)$	$e\left(\frac{497}{512}\right)$	$e\left(\frac{247}{512}\right)$	$e\left(\frac{929}{1024}\right)$	$e\left(\frac{147}{1024}\right)$	$e\left(\frac{165}{256}\right)$	$e\left(\frac{43}{256}\right)$	$e\left(\frac{667}{1024}\right)$	$e\left(\frac{217}{1024}\right)$
$\chi_{4096}(93,\cdot)$	$1$	$1$	$e\left(\frac{353}{1024}\right)$	$e\left(\frac{43}{1024}\right)$	$e\left(\frac{503}{512}\right)$	$e\left(\frac{353}{512}\right)$	$e\left(\frac{967}{1024}\right)$	$e\left(\frac{293}{1024}\right)$	$e\left(\frac{99}{256}\right)$	$e\left(\frac{77}{256}\right)$	$e\left(\frac{605}{1024}\right)$	$e\left(\frac{335}{1024}\right)$
$\chi_{4096}(101,\cdot)$	$1$	$1$	$e\left(\frac{635}{1024}\right)$	$e\left(\frac{585}{1024}\right)$	$e\left(\frac{461}{512}\right)$	$e\left(\frac{123}{512}\right)$	$e\left(\frac{701}{1024}\right)$	$e\left(\frac{295}{1024}\right)$	$e\left(\frac{49}{256}\right)$	$e\left(\frac{95}{256}\right)$	$e\left(\frac{15}{1024}\right)$	$e\left(\frac{533}{1024}\right)$
$\chi_{4096}(109,\cdot)$	$1$	$1$	$e\left(\frac{325}{1024}\right)$	$e\left(\frac{759}{1024}\right)$	$e\left(\frac{115}{512}\right)$	$e\left(\frac{325}{512}\right)$	$e\left(\frac{899}{1024}\right)$	$e\left(\frac{409}{1024}\right)$	$e\left(\frac{15}{256}\right)$	$e\left(\frac{97}{256}\right)$	$e\left(\frac{177}{1024}\right)$	$e\left(\frac{555}{1024}\right)$
$\chi_{4096}(117,\cdot)$	$1$	$1$	$e\left(\frac{703}{1024}\right)$	$e\left(\frac{309}{1024}\right)$	$e\left(\frac{233}{512}\right)$	$e\left(\frac{191}{512}\right)$	$e\left(\frac{281}{1024}\right)$	$e\left(\frac{891}{1024}\right)$	$e\left(\frac{253}{256}\right)$	$e\left(\frac{83}{256}\right)$	$e\left(\frac{323}{1024}\right)$	$e\left(\frac{145}{1024}\right)$
$\chi_{4096}(125,\cdot)$	$1$	$1$	$e\left(\frac{1001}{1024}\right)$	$e\left(\frac{3}{1024}\right)$	$e\left(\frac{47}{512}\right)$	$e\left(\frac{489}{512}\right)$	$e\left(\frac{639}{1024}\right)$	$e\left(\frac{973}{1024}\right)$	$e\left(\frac{251}{256}\right)$	$e\left(\frac{53}{256}\right)$	$e\left(\frac{709}{1024}\right)$	$e\left(\frac{71}{1024}\right)$
$\chi_{4096}(133,\cdot)$	$1$	$1$	$e\left(\frac{451}{1024}\right)$	$e\left(\frac{609}{1024}\right)$	$e\left(\frac{325}{512}\right)$	$e\left(\frac{451}{512}\right)$	$e\left(\frac{693}{1024}\right)$	$e\left(\frac{911}{1024}\right)$	$e\left(\frac{9}{256}\right)$	$e\left(\frac{7}{256}\right)$	$e\left(\frac{567}{1024}\right)$	$e\left(\frac{77}{1024}\right)$
$\chi_{4096}(141,\cdot)$	$1$	$1$	$e\left(\frac{333}{1024}\right)$	$e\left(\frac{847}{1024}\right)$	$e\left(\frac{299}{512}\right)$	$e\left(\frac{333}{512}\right)$	$e\left(\frac{187}{1024}\right)$	$e\left(\frac{961}{1024}\right)$	$e\left(\frac{39}{256}\right)$	$e\left(\frac{201}{256}\right)$	$e\left(\frac{153}{1024}\right)$	$e\left(\frac{931}{1024}\right)$
$\chi_{4096}(149,\cdot)$	$1$	$1$	$e\left(\frac{903}{1024}\right)$	$e\left(\frac{461}{1024}\right)$	$e\left(\frac{225}{512}\right)$	$e\left(\frac{391}{512}\right)$	$e\left(\frac{913}{1024}\right)$	$e\left(\frac{355}{1024}\right)$	$e\left(\frac{85}{256}\right)$	$e\left(\frac{123}{256}\right)$	$e\left(\frac{747}{1024}\right)$	$e\left(\frac{329}{1024}\right)$
$\chi_{4096}(157,\cdot)$	$1$	$1$	$e\left(\frac{369}{1024}\right)$	$e\left(\frac{219}{1024}\right)$	$e\left(\frac{359}{512}\right)$	$e\left(\frac{369}{512}\right)$	$e\left(\frac{567}{1024}\right)$	$e\left(\frac{373}{1024}\right)$	$e\left(\frac{147}{256}\right)$	$e\left(\frac{29}{256}\right)$	$e\left(\frac{557}{1024}\right)$	$e\left(\frac{63}{1024}\right)$
$\chi_{4096}(165,\cdot)$	$1$	$1$	$e\left(\frac{11}{1024}\right)$	$e\left(\frac{889}{1024}\right)$	$e\left(\frac{445}{512}\right)$	$e\left(\frac{11}{512}\right)$	$e\left(\frac{941}{1024}\right)$	$e\left(\frac{247}{1024}\right)$	$e\left(\frac{225}{256}\right)$	$e\left(\frac{175}{256}\right)$	$e\left(\frac{863}{1024}\right)$	$e\left(\frac{901}{1024}\right)$
$\chi_{4096}(173,\cdot)$	$1$	$1$	$e\left(\frac{85}{1024}\right)$	$e\left(\frac{167}{1024}\right)$	$e\left(\frac{227}{512}\right)$	$e\left(\frac{85}{512}\right)$	$e\left(\frac{755}{1024}\right)$	$e\left(\frac{233}{1024}\right)$	$e\left(\frac{63}{256}\right)$	$e\left(\frac{49}{256}\right)$	$e\left(\frac{897}{1024}\right)$	$e\left(\frac{539}{1024}\right)$
$\chi_{4096}(181,\cdot)$	$1$	$1$	$e\left(\frac{847}{1024}\right)$	$e\left(\frac{869}{1024}\right)$	$e\left(\frac{473}{512}\right)$	$e\left(\frac{335}{512}\right)$	$e\left(\frac{777}{1024}\right)$	$e\left(\frac{587}{1024}\right)$	$e\left(\frac{173}{256}\right)$	$e\left(\frac{163}{256}\right)$	$e\left(\frac{915}{1024}\right)$	$e\left(\frac{769}{1024}\right)$
$\chi_{4096}(189,\cdot)$	$1$	$1$	$e\left(\frac{505}{1024}\right)$	$e\left(\frac{691}{1024}\right)$	$e\left(\frac{415}{512}\right)$	$e\left(\frac{505}{512}\right)$	$e\left(\frac{751}{1024}\right)$	$e\left(\frac{541}{1024}\right)$	$e\left(\frac{43}{256}\right)$	$e\left(\frac{5}{256}\right)$	$e\left(\frac{149}{1024}\right)$	$e\left(\frac{311}{1024}\right)$
$\chi_{4096}(197,\cdot)$	$1$	$1$	$e\left(\frac{339}{1024}\right)$	$e\left(\frac{401}{1024}\right)$	$e\left(\frac{309}{512}\right)$	$e\left(\frac{339}{512}\right)$	$e\left(\frac{421}{1024}\right)$	$e\left(\frac{351}{1024}\right)$	$e\left(\frac{185}{256}\right)$	$e\left(\frac{87}{256}\right)$	$e\left(\frac{903}{1024}\right)$	$e\left(\frac{957}{1024}\right)$
$\chi_{4096}(205,\cdot)$	$1$	$1$	$e\left(\frac{605}{1024}\right)$	$e\left(\frac{767}{1024}\right)$	$e\left(\frac{411}{512}\right)$	$e\left(\frac{93}{512}\right)$	$e\left(\frac{555}{1024}\right)$	$e\left(\frac{273}{1024}\right)$	$e\left(\frac{87}{256}\right)$	$e\left(\frac{153}{256}\right)$	$e\left(\frac{361}{1024}\right)$	$e\left(\frac{403}{1024}\right)$
$\chi_{4096}(213,\cdot)$	$1$	$1$	$e\left(\frac{535}{1024}\right)$	$e\left(\frac{509}{1024}\right)$	$e\left(\frac{465}{512}\right)$	$e\left(\frac{23}{512}\right)$	$e\left(\frac{897}{1024}\right)$	$e\left(\frac{563}{1024}\right)$	$e\left(\frac{5}{256}\right)$	$e\left(\frac{203}{256}\right)$	$e\left(\frac{827}{1024}\right)$	$e\left(\frac{441}{1024}\right)$
$\chi_{4096}(221,\cdot)$	$1$	$1$	$e\left(\frac{385}{1024}\right)$	$e\left(\frac{395}{1024}\right)$	$e\left(\frac{215}{512}\right)$	$e\left(\frac{385}{512}\right)$	$e\left(\frac{167}{1024}\right)$	$e\left(\frac{453}{1024}\right)$	$e\left(\frac{195}{256}\right)$	$e\left(\frac{237}{256}\right)$	$e\left(\frac{509}{1024}\right)$	$e\left(\frac{815}{1024}\right)$
$\chi_{4096}(229,\cdot)$	$1$	$1$	$e\left(\frac{411}{1024}\right)$	$e\left(\frac{169}{1024}\right)$	$e\left(\frac{429}{512}\right)$	$e\left(\frac{411}{512}\right)$	$e\left(\frac{157}{1024}\right)$	$e\left(\frac{199}{1024}\right)$	$e\left(\frac{145}{256}\right)$	$e\left(\frac{255}{256}\right)$	$e\left(\frac{687}{1024}\right)$	$e\left(\frac{245}{1024}\right)$
$\chi_{4096}(237,\cdot)$	$1$	$1$	$e\left(\frac{869}{1024}\right)$	$e\left(\frac{599}{1024}\right)$	$e\left(\frac{339}{512}\right)$	$e\left(\frac{357}{512}\right)$	$e\left(\frac{611}{1024}\right)$	$e\left(\frac{57}{1024}\right)$	$e\left(\frac{111}{256}\right)$	$e\left(\frac{1}{256}\right)$	$e\left(\frac{593}{1024}\right)$	$e\left(\frac{523}{1024}\right)$
$\chi_{4096}(245,\cdot)$	$1$	$1$	$e\left(\frac{991}{1024}\right)$	$e\left(\frac{405}{1024}\right)$	$e\left(\frac{201}{512}\right)$	$e\left(\frac{479}{512}\right)$	$e\left(\frac{249}{1024}\right)$	$e\left(\frac{283}{1024}\right)$	$e\left(\frac{93}{256}\right)$	$e\left(\frac{243}{256}\right)$	$e\left(\frac{483}{1024}\right)$	$e\left(\frac{369}{1024}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{4096}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{675}{1024}\right)\)	\(e\left(\frac{1}{1024}\right)\)	\(e\left(\frac{357}{512}\right)\)	\(e\left(\frac{163}{512}\right)\)	\(e\left(\frac{213}{1024}\right)\)	\(e\left(\frac{1007}{1024}\right)\)	\(e\left(\frac{169}{256}\right)\)	\(e\left(\frac{103}{256}\right)\)	\(e\left(\frac{919}{1024}\right)\)	\(e\left(\frac{365}{1024}\right)\)
\(\chi_{4096}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{813}{1024}\right)\)	\(e\left(\frac{1007}{1024}\right)\)	\(e\left(\frac{75}{512}\right)\)	\(e\left(\frac{301}{512}\right)\)	\(e\left(\frac{475}{1024}\right)\)	\(e\left(\frac{289}{1024}\right)\)	\(e\left(\frac{199}{256}\right)\)	\(e\left(\frac{41}{256}\right)\)	\(e\left(\frac{761}{1024}\right)\)	\(e\left(\frac{963}{1024}\right)\)
\(\chi_{4096}(21,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{615}{1024}\right)\)	\(e\left(\frac{365}{1024}\right)\)	\(e\left(\frac{257}{512}\right)\)	\(e\left(\frac{103}{512}\right)\)	\(e\left(\frac{945}{1024}\right)\)	\(e\left(\frac{963}{1024}\right)\)	\(e\left(\frac{245}{256}\right)\)	\(e\left(\frac{219}{256}\right)\)	\(e\left(\frac{587}{1024}\right)\)	\(e\left(\frac{105}{1024}\right)\)
\(\chi_{4096}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{337}{1024}\right)\)	\(e\left(\frac{891}{1024}\right)\)	\(e\left(\frac{135}{512}\right)\)	\(e\left(\frac{337}{512}\right)\)	\(e\left(\frac{343}{1024}\right)\)	\(e\left(\frac{213}{1024}\right)\)	\(e\left(\frac{51}{256}\right)\)	\(e\left(\frac{125}{256}\right)\)	\(e\left(\frac{653}{1024}\right)\)	\(e\left(\frac{607}{1024}\right)\)
\(\chi_{4096}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{235}{1024}\right)\)	\(e\left(\frac{281}{1024}\right)\)	\(e\left(\frac{477}{512}\right)\)	\(e\left(\frac{235}{512}\right)\)	\(e\left(\frac{461}{1024}\right)\)	\(e\left(\frac{343}{1024}\right)\)	\(e\left(\frac{129}{256}\right)\)	\(e\left(\frac{15}{256}\right)\)	\(e\left(\frac{191}{1024}\right)\)	\(e\left(\frac{165}{1024}\right)\)
\(\chi_{4096}(45,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{565}{1024}\right)\)	\(e\left(\frac{327}{1024}\right)\)	\(e\left(\frac{3}{512}\right)\)	\(e\left(\frac{53}{512}\right)\)	\(e\left(\frac{19}{1024}\right)\)	\(e\left(\frac{585}{1024}\right)\)	\(e\left(\frac{223}{256}\right)\)	\(e\left(\frac{145}{256}\right)\)	\(e\left(\frac{481}{1024}\right)\)	\(e\left(\frac{571}{1024}\right)\)
\(\chi_{4096}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{559}{1024}\right)\)	\(e\left(\frac{773}{1024}\right)\)	\(e\left(\frac{505}{512}\right)\)	\(e\left(\frac{47}{512}\right)\)	\(e\left(\frac{809}{1024}\right)\)	\(e\left(\frac{171}{1024}\right)\)	\(e\left(\frac{77}{256}\right)\)	\(e\left(\frac{3}{256}\right)\)	\(e\left(\frac{755}{1024}\right)\)	\(e\left(\frac{545}{1024}\right)\)
\(\chi_{4096}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{473}{1024}\right)\)	\(e\left(\frac{339}{1024}\right)\)	\(e\left(\frac{191}{512}\right)\)	\(e\left(\frac{473}{512}\right)\)	\(e\left(\frac{527}{1024}\right)\)	\(e\left(\frac{381}{1024}\right)\)	\(e\left(\frac{203}{256}\right)\)	\(e\left(\frac{101}{256}\right)\)	\(e\left(\frac{245}{1024}\right)\)	\(e\left(\frac{855}{1024}\right)\)
\(\chi_{4096}(69,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{563}{1024}\right)\)	\(e\left(\frac{817}{1024}\right)\)	\(e\left(\frac{341}{512}\right)\)	\(e\left(\frac{51}{512}\right)\)	\(e\left(\frac{965}{1024}\right)\)	\(e\left(\frac{447}{1024}\right)\)	\(e\left(\frac{89}{256}\right)\)	\(e\left(\frac{183}{256}\right)\)	\(e\left(\frac{231}{1024}\right)\)	\(e\left(\frac{221}{1024}\right)\)
\(\chi_{4096}(77,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{1024}\right)\)	\(e\left(\frac{927}{1024}\right)\)	\(e\left(\frac{187}{512}\right)\)	\(e\left(\frac{61}{512}\right)\)	\(e\left(\frac{843}{1024}\right)\)	\(e\left(\frac{625}{1024}\right)\)	\(e\left(\frac{247}{256}\right)\)	\(e\left(\frac{249}{256}\right)\)	\(e\left(\frac{969}{1024}\right)\)	\(e\left(\frac{435}{1024}\right)\)
\(\chi_{4096}(85,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{1024}\right)\)	\(e\left(\frac{413}{1024}\right)\)	\(e\left(\frac{497}{512}\right)\)	\(e\left(\frac{247}{512}\right)\)	\(e\left(\frac{929}{1024}\right)\)	\(e\left(\frac{147}{1024}\right)\)	\(e\left(\frac{165}{256}\right)\)	\(e\left(\frac{43}{256}\right)\)	\(e\left(\frac{667}{1024}\right)\)	\(e\left(\frac{217}{1024}\right)\)
\(\chi_{4096}(93,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{353}{1024}\right)\)	\(e\left(\frac{43}{1024}\right)\)	\(e\left(\frac{503}{512}\right)\)	\(e\left(\frac{353}{512}\right)\)	\(e\left(\frac{967}{1024}\right)\)	\(e\left(\frac{293}{1024}\right)\)	\(e\left(\frac{99}{256}\right)\)	\(e\left(\frac{77}{256}\right)\)	\(e\left(\frac{605}{1024}\right)\)	\(e\left(\frac{335}{1024}\right)\)
\(\chi_{4096}(101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{635}{1024}\right)\)	\(e\left(\frac{585}{1024}\right)\)	\(e\left(\frac{461}{512}\right)\)	\(e\left(\frac{123}{512}\right)\)	\(e\left(\frac{701}{1024}\right)\)	\(e\left(\frac{295}{1024}\right)\)	\(e\left(\frac{49}{256}\right)\)	\(e\left(\frac{95}{256}\right)\)	\(e\left(\frac{15}{1024}\right)\)	\(e\left(\frac{533}{1024}\right)\)
\(\chi_{4096}(109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{325}{1024}\right)\)	\(e\left(\frac{759}{1024}\right)\)	\(e\left(\frac{115}{512}\right)\)	\(e\left(\frac{325}{512}\right)\)	\(e\left(\frac{899}{1024}\right)\)	\(e\left(\frac{409}{1024}\right)\)	\(e\left(\frac{15}{256}\right)\)	\(e\left(\frac{97}{256}\right)\)	\(e\left(\frac{177}{1024}\right)\)	\(e\left(\frac{555}{1024}\right)\)
\(\chi_{4096}(117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{703}{1024}\right)\)	\(e\left(\frac{309}{1024}\right)\)	\(e\left(\frac{233}{512}\right)\)	\(e\left(\frac{191}{512}\right)\)	\(e\left(\frac{281}{1024}\right)\)	\(e\left(\frac{891}{1024}\right)\)	\(e\left(\frac{253}{256}\right)\)	\(e\left(\frac{83}{256}\right)\)	\(e\left(\frac{323}{1024}\right)\)	\(e\left(\frac{145}{1024}\right)\)
\(\chi_{4096}(125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1001}{1024}\right)\)	\(e\left(\frac{3}{1024}\right)\)	\(e\left(\frac{47}{512}\right)\)	\(e\left(\frac{489}{512}\right)\)	\(e\left(\frac{639}{1024}\right)\)	\(e\left(\frac{973}{1024}\right)\)	\(e\left(\frac{251}{256}\right)\)	\(e\left(\frac{53}{256}\right)\)	\(e\left(\frac{709}{1024}\right)\)	\(e\left(\frac{71}{1024}\right)\)
\(\chi_{4096}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{451}{1024}\right)\)	\(e\left(\frac{609}{1024}\right)\)	\(e\left(\frac{325}{512}\right)\)	\(e\left(\frac{451}{512}\right)\)	\(e\left(\frac{693}{1024}\right)\)	\(e\left(\frac{911}{1024}\right)\)	\(e\left(\frac{9}{256}\right)\)	\(e\left(\frac{7}{256}\right)\)	\(e\left(\frac{567}{1024}\right)\)	\(e\left(\frac{77}{1024}\right)\)
\(\chi_{4096}(141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{333}{1024}\right)\)	\(e\left(\frac{847}{1024}\right)\)	\(e\left(\frac{299}{512}\right)\)	\(e\left(\frac{333}{512}\right)\)	\(e\left(\frac{187}{1024}\right)\)	\(e\left(\frac{961}{1024}\right)\)	\(e\left(\frac{39}{256}\right)\)	\(e\left(\frac{201}{256}\right)\)	\(e\left(\frac{153}{1024}\right)\)	\(e\left(\frac{931}{1024}\right)\)
\(\chi_{4096}(149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{903}{1024}\right)\)	\(e\left(\frac{461}{1024}\right)\)	\(e\left(\frac{225}{512}\right)\)	\(e\left(\frac{391}{512}\right)\)	\(e\left(\frac{913}{1024}\right)\)	\(e\left(\frac{355}{1024}\right)\)	\(e\left(\frac{85}{256}\right)\)	\(e\left(\frac{123}{256}\right)\)	\(e\left(\frac{747}{1024}\right)\)	\(e\left(\frac{329}{1024}\right)\)
\(\chi_{4096}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{369}{1024}\right)\)	\(e\left(\frac{219}{1024}\right)\)	\(e\left(\frac{359}{512}\right)\)	\(e\left(\frac{369}{512}\right)\)	\(e\left(\frac{567}{1024}\right)\)	\(e\left(\frac{373}{1024}\right)\)	\(e\left(\frac{147}{256}\right)\)	\(e\left(\frac{29}{256}\right)\)	\(e\left(\frac{557}{1024}\right)\)	\(e\left(\frac{63}{1024}\right)\)
\(\chi_{4096}(165,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{1024}\right)\)	\(e\left(\frac{889}{1024}\right)\)	\(e\left(\frac{445}{512}\right)\)	\(e\left(\frac{11}{512}\right)\)	\(e\left(\frac{941}{1024}\right)\)	\(e\left(\frac{247}{1024}\right)\)	\(e\left(\frac{225}{256}\right)\)	\(e\left(\frac{175}{256}\right)\)	\(e\left(\frac{863}{1024}\right)\)	\(e\left(\frac{901}{1024}\right)\)
\(\chi_{4096}(173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{1024}\right)\)	\(e\left(\frac{167}{1024}\right)\)	\(e\left(\frac{227}{512}\right)\)	\(e\left(\frac{85}{512}\right)\)	\(e\left(\frac{755}{1024}\right)\)	\(e\left(\frac{233}{1024}\right)\)	\(e\left(\frac{63}{256}\right)\)	\(e\left(\frac{49}{256}\right)\)	\(e\left(\frac{897}{1024}\right)\)	\(e\left(\frac{539}{1024}\right)\)
\(\chi_{4096}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{847}{1024}\right)\)	\(e\left(\frac{869}{1024}\right)\)	\(e\left(\frac{473}{512}\right)\)	\(e\left(\frac{335}{512}\right)\)	\(e\left(\frac{777}{1024}\right)\)	\(e\left(\frac{587}{1024}\right)\)	\(e\left(\frac{173}{256}\right)\)	\(e\left(\frac{163}{256}\right)\)	\(e\left(\frac{915}{1024}\right)\)	\(e\left(\frac{769}{1024}\right)\)
\(\chi_{4096}(189,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{505}{1024}\right)\)	\(e\left(\frac{691}{1024}\right)\)	\(e\left(\frac{415}{512}\right)\)	\(e\left(\frac{505}{512}\right)\)	\(e\left(\frac{751}{1024}\right)\)	\(e\left(\frac{541}{1024}\right)\)	\(e\left(\frac{43}{256}\right)\)	\(e\left(\frac{5}{256}\right)\)	\(e\left(\frac{149}{1024}\right)\)	\(e\left(\frac{311}{1024}\right)\)
\(\chi_{4096}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{339}{1024}\right)\)	\(e\left(\frac{401}{1024}\right)\)	\(e\left(\frac{309}{512}\right)\)	\(e\left(\frac{339}{512}\right)\)	\(e\left(\frac{421}{1024}\right)\)	\(e\left(\frac{351}{1024}\right)\)	\(e\left(\frac{185}{256}\right)\)	\(e\left(\frac{87}{256}\right)\)	\(e\left(\frac{903}{1024}\right)\)	\(e\left(\frac{957}{1024}\right)\)
\(\chi_{4096}(205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{605}{1024}\right)\)	\(e\left(\frac{767}{1024}\right)\)	\(e\left(\frac{411}{512}\right)\)	\(e\left(\frac{93}{512}\right)\)	\(e\left(\frac{555}{1024}\right)\)	\(e\left(\frac{273}{1024}\right)\)	\(e\left(\frac{87}{256}\right)\)	\(e\left(\frac{153}{256}\right)\)	\(e\left(\frac{361}{1024}\right)\)	\(e\left(\frac{403}{1024}\right)\)
\(\chi_{4096}(213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{535}{1024}\right)\)	\(e\left(\frac{509}{1024}\right)\)	\(e\left(\frac{465}{512}\right)\)	\(e\left(\frac{23}{512}\right)\)	\(e\left(\frac{897}{1024}\right)\)	\(e\left(\frac{563}{1024}\right)\)	\(e\left(\frac{5}{256}\right)\)	\(e\left(\frac{203}{256}\right)\)	\(e\left(\frac{827}{1024}\right)\)	\(e\left(\frac{441}{1024}\right)\)
\(\chi_{4096}(221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{385}{1024}\right)\)	\(e\left(\frac{395}{1024}\right)\)	\(e\left(\frac{215}{512}\right)\)	\(e\left(\frac{385}{512}\right)\)	\(e\left(\frac{167}{1024}\right)\)	\(e\left(\frac{453}{1024}\right)\)	\(e\left(\frac{195}{256}\right)\)	\(e\left(\frac{237}{256}\right)\)	\(e\left(\frac{509}{1024}\right)\)	\(e\left(\frac{815}{1024}\right)\)
\(\chi_{4096}(229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{411}{1024}\right)\)	\(e\left(\frac{169}{1024}\right)\)	\(e\left(\frac{429}{512}\right)\)	\(e\left(\frac{411}{512}\right)\)	\(e\left(\frac{157}{1024}\right)\)	\(e\left(\frac{199}{1024}\right)\)	\(e\left(\frac{145}{256}\right)\)	\(e\left(\frac{255}{256}\right)\)	\(e\left(\frac{687}{1024}\right)\)	\(e\left(\frac{245}{1024}\right)\)
\(\chi_{4096}(237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{869}{1024}\right)\)	\(e\left(\frac{599}{1024}\right)\)	\(e\left(\frac{339}{512}\right)\)	\(e\left(\frac{357}{512}\right)\)	\(e\left(\frac{611}{1024}\right)\)	\(e\left(\frac{57}{1024}\right)\)	\(e\left(\frac{111}{256}\right)\)	\(e\left(\frac{1}{256}\right)\)	\(e\left(\frac{593}{1024}\right)\)	\(e\left(\frac{523}{1024}\right)\)
\(\chi_{4096}(245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{991}{1024}\right)\)	\(e\left(\frac{405}{1024}\right)\)	\(e\left(\frac{201}{512}\right)\)	\(e\left(\frac{479}{512}\right)\)	\(e\left(\frac{249}{1024}\right)\)	\(e\left(\frac{283}{1024}\right)\)	\(e\left(\frac{93}{256}\right)\)	\(e\left(\frac{243}{256}\right)\)	\(e\left(\frac{483}{1024}\right)\)	\(e\left(\frac{369}{1024}\right)\)

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First 31 of 512 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	4096.u
Modulus	$4096$
Conductor	$4096$
Order	$1024$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(4096\)
Conductor:	\(4096\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(1024\)	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)