Dirichlet character orbit 36864.da

• Label: 36864.da
• Modulus: $36864$
• Conductor: $12288$
• Order: $1024$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$36864$
Conductor:	$12288$
Order:	$1024$
Real:	no
Primitive:	no, induced from 12288.bq
Minimal:	yes
Parity:	even

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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{36864}(35,\cdot)$	$1$	$1$	$e\left(\frac{203}{1024}\right)$	$e\left(\frac{23}{512}\right)$	$e\left(\frac{743}{1024}\right)$	$e\left(\frac{133}{1024}\right)$	$e\left(\frac{45}{256}\right)$	$e\left(\frac{189}{1024}\right)$	$e\left(\frac{77}{512}\right)$	$e\left(\frac{203}{512}\right)$	$e\left(\frac{649}{1024}\right)$	$e\left(\frac{27}{128}\right)$
$\chi_{36864}(107,\cdot)$	$1$	$1$	$e\left(\frac{781}{1024}\right)$	$e\left(\frac{33}{512}\right)$	$e\left(\frac{977}{1024}\right)$	$e\left(\frac{547}{1024}\right)$	$e\left(\frac{187}{256}\right)$	$e\left(\frac{939}{1024}\right)$	$e\left(\frac{155}{512}\right)$	$e\left(\frac{269}{512}\right)$	$e\left(\frac{575}{1024}\right)$	$e\left(\frac{61}{128}\right)$
$\chi_{36864}(179,\cdot)$	$1$	$1$	$e\left(\frac{735}{1024}\right)$	$e\left(\frac{507}{512}\right)$	$e\left(\frac{395}{1024}\right)$	$e\left(\frac{305}{1024}\right)$	$e\left(\frac{57}{256}\right)$	$e\left(\frac{649}{1024}\right)$	$e\left(\frac{473}{512}\right)$	$e\left(\frac{223}{512}\right)$	$e\left(\frac{549}{1024}\right)$	$e\left(\frac{111}{128}\right)$
$\chi_{36864}(251,\cdot)$	$1$	$1$	$e\left(\frac{321}{1024}\right)$	$e\left(\frac{165}{512}\right)$	$e\left(\frac{277}{1024}\right)$	$e\left(\frac{175}{1024}\right)$	$e\left(\frac{167}{256}\right)$	$e\left(\frac{87}{1024}\right)$	$e\left(\frac{263}{512}\right)$	$e\left(\frac{321}{512}\right)$	$e\left(\frac{315}{1024}\right)$	$e\left(\frac{49}{128}\right)$
$\chi_{36864}(323,\cdot)$	$1$	$1$	$e\left(\frac{819}{1024}\right)$	$e\left(\frac{287}{512}\right)$	$e\left(\frac{879}{1024}\right)$	$e\left(\frac{925}{1024}\right)$	$e\left(\frac{5}{256}\right)$	$e\left(\frac{21}{1024}\right)$	$e\left(\frac{293}{512}\right)$	$e\left(\frac{307}{512}\right)$	$e\left(\frac{641}{1024}\right)$	$e\left(\frac{3}{128}\right)$
$\chi_{36864}(395,\cdot)$	$1$	$1$	$e\left(\frac{437}{1024}\right)$	$e\left(\frac{105}{512}\right)$	$e\left(\frac{409}{1024}\right)$	$e\left(\frac{251}{1024}\right)$	$e\left(\frac{83}{256}\right)$	$e\left(\frac{195}{1024}\right)$	$e\left(\frac{307}{512}\right)$	$e\left(\frac{437}{512}\right)$	$e\left(\frac{247}{1024}\right)$	$e\left(\frac{101}{128}\right)$
$\chi_{36864}(467,\cdot)$	$1$	$1$	$e\left(\frac{455}{1024}\right)$	$e\left(\frac{387}{512}\right)$	$e\left(\frac{147}{1024}\right)$	$e\left(\frac{969}{1024}\right)$	$e\left(\frac{145}{256}\right)$	$e\left(\frac{353}{1024}\right)$	$e\left(\frac{49}{512}\right)$	$e\left(\frac{455}{512}\right)$	$e\left(\frac{925}{1024}\right)$	$e\left(\frac{87}{128}\right)$
$\chi_{36864}(539,\cdot)$	$1$	$1$	$e\left(\frac{105}{1024}\right)$	$e\left(\frac{365}{512}\right)$	$e\left(\frac{349}{1024}\right)$	$e\left(\frac{775}{1024}\right)$	$e\left(\frac{191}{256}\right)$	$e\left(\frac{239}{1024}\right)$	$e\left(\frac{287}{512}\right)$	$e\left(\frac{105}{512}\right)$	$e\left(\frac{371}{1024}\right)$	$e\left(\frac{89}{128}\right)$
$\chi_{36864}(611,\cdot)$	$1$	$1$	$e\left(\frac{667}{1024}\right)$	$e\left(\frac{295}{512}\right)$	$e\left(\frac{247}{1024}\right)$	$e\left(\frac{437}{1024}\right)$	$e\left(\frac{221}{256}\right)$	$e\left(\frac{621}{1024}\right)$	$e\left(\frac{253}{512}\right)$	$e\left(\frac{155}{512}\right)$	$e\left(\frac{377}{1024}\right)$	$e\left(\frac{107}{128}\right)$
$\chi_{36864}(683,\cdot)$	$1$	$1$	$e\left(\frac{349}{1024}\right)$	$e\left(\frac{433}{512}\right)$	$e\left(\frac{97}{1024}\right)$	$e\left(\frac{723}{1024}\right)$	$e\left(\frac{235}{256}\right)$	$e\left(\frac{219}{1024}\right)$	$e\left(\frac{203}{512}\right)$	$e\left(\frac{349}{512}\right)$	$e\left(\frac{687}{1024}\right)$	$e\left(\frac{13}{128}\right)$
$\chi_{36864}(755,\cdot)$	$1$	$1$	$e\left(\frac{431}{1024}\right)$	$e\left(\frac{11}{512}\right)$	$e\left(\frac{155}{1024}\right)$	$e\left(\frac{353}{1024}\right)$	$e\left(\frac{233}{256}\right)$	$e\left(\frac{825}{1024}\right)$	$e\left(\frac{393}{512}\right)$	$e\left(\frac{431}{512}\right)$	$e\left(\frac{21}{1024}\right)$	$e\left(\frac{63}{128}\right)$
$\chi_{36864}(827,\cdot)$	$1$	$1$	$e\left(\frac{145}{1024}\right)$	$e\left(\frac{309}{512}\right)$	$e\left(\frac{677}{1024}\right)$	$e\left(\frac{95}{1024}\right)$	$e\left(\frac{215}{256}\right)$	$e\left(\frac{135}{1024}\right)$	$e\left(\frac{55}{512}\right)$	$e\left(\frac{145}{512}\right)$	$e\left(\frac{171}{1024}\right)$	$e\left(\frac{1}{128}\right)$
$\chi_{36864}(899,\cdot)$	$1$	$1$	$e\left(\frac{771}{1024}\right)$	$e\left(\frac{47}{512}\right)$	$e\left(\frac{895}{1024}\right)$	$e\left(\frac{717}{1024}\right)$	$e\left(\frac{181}{256}\right)$	$e\left(\frac{965}{1024}\right)$	$e\left(\frac{469}{512}\right)$	$e\left(\frac{259}{512}\right)$	$e\left(\frac{881}{1024}\right)$	$e\left(\frac{83}{128}\right)$
$\chi_{36864}(971,\cdot)$	$1$	$1$	$e\left(\frac{517}{1024}\right)$	$e\left(\frac{505}{512}\right)$	$e\left(\frac{41}{1024}\right)$	$e\left(\frac{939}{1024}\right)$	$e\left(\frac{131}{256}\right)$	$e\left(\frac{1011}{1024}\right)$	$e\left(\frac{355}{512}\right)$	$e\left(\frac{5}{512}\right)$	$e\left(\frac{871}{1024}\right)$	$e\left(\frac{53}{128}\right)$
$\chi_{36864}(1043,\cdot)$	$1$	$1$	$e\left(\frac{663}{1024}\right)$	$e\left(\frac{403}{512}\right)$	$e\left(\frac{419}{1024}\right)$	$e\left(\frac{505}{1024}\right)$	$e\left(\frac{65}{256}\right)$	$e\left(\frac{17}{1024}\right)$	$e\left(\frac{481}{512}\right)$	$e\left(\frac{151}{512}\right)$	$e\left(\frac{909}{1024}\right)$	$e\left(\frac{39}{128}\right)$
$\chi_{36864}(1115,\cdot)$	$1$	$1$	$e\left(\frac{441}{1024}\right)$	$e\left(\frac{509}{512}\right)$	$e\left(\frac{237}{1024}\right)$	$e\left(\frac{183}{1024}\right)$	$e\left(\frac{239}{256}\right)$	$e\left(\frac{799}{1024}\right)$	$e\left(\frac{79}{512}\right)$	$e\left(\frac{441}{512}\right)$	$e\left(\frac{739}{1024}\right)$	$e\left(\frac{41}{128}\right)$
$\chi_{36864}(1187,\cdot)$	$1$	$1$	$e\left(\frac{107}{1024}\right)$	$e\left(\frac{55}{512}\right)$	$e\left(\frac{775}{1024}\right)$	$e\left(\frac{741}{1024}\right)$	$e\left(\frac{141}{256}\right)$	$e\left(\frac{29}{1024}\right)$	$e\left(\frac{429}{512}\right)$	$e\left(\frac{107}{512}\right)$	$e\left(\frac{105}{1024}\right)$	$e\left(\frac{59}{128}\right)$
$\chi_{36864}(1259,\cdot)$	$1$	$1$	$e\left(\frac{941}{1024}\right)$	$e\left(\frac{321}{512}\right)$	$e\left(\frac{241}{1024}\right)$	$e\left(\frac{899}{1024}\right)$	$e\left(\frac{27}{256}\right)$	$e\left(\frac{523}{1024}\right)$	$e\left(\frac{251}{512}\right)$	$e\left(\frac{429}{512}\right)$	$e\left(\frac{799}{1024}\right)$	$e\left(\frac{93}{128}\right)$
$\chi_{36864}(1331,\cdot)$	$1$	$1$	$e\left(\frac{127}{1024}\right)$	$e\left(\frac{27}{512}\right)$	$e\left(\frac{939}{1024}\right)$	$e\left(\frac{401}{1024}\right)$	$e\left(\frac{153}{256}\right)$	$e\left(\frac{1001}{1024}\right)$	$e\left(\frac{313}{512}\right)$	$e\left(\frac{127}{512}\right)$	$e\left(\frac{517}{1024}\right)$	$e\left(\frac{15}{128}\right)$
$\chi_{36864}(1403,\cdot)$	$1$	$1$	$e\left(\frac{993}{1024}\right)$	$e\left(\frac{453}{512}\right)$	$e\left(\frac{53}{1024}\right)$	$e\left(\frac{15}{1024}\right)$	$e\left(\frac{7}{256}\right)$	$e\left(\frac{183}{1024}\right)$	$e\left(\frac{359}{512}\right)$	$e\left(\frac{481}{512}\right)$	$e\left(\frac{27}{1024}\right)$	$e\left(\frac{81}{128}\right)$
$\chi_{36864}(1475,\cdot)$	$1$	$1$	$e\left(\frac{723}{1024}\right)$	$e\left(\frac{319}{512}\right)$	$e\left(\frac{911}{1024}\right)$	$e\left(\frac{509}{1024}\right)$	$e\left(\frac{101}{256}\right)$	$e\left(\frac{885}{1024}\right)$	$e\left(\frac{133}{512}\right)$	$e\left(\frac{211}{512}\right)$	$e\left(\frac{97}{1024}\right)$	$e\left(\frac{35}{128}\right)$
$\chi_{36864}(1547,\cdot)$	$1$	$1$	$e\left(\frac{597}{1024}\right)$	$e\left(\frac{393}{512}\right)$	$e\left(\frac{697}{1024}\right)$	$e\left(\frac{603}{1024}\right)$	$e\left(\frac{179}{256}\right)$	$e\left(\frac{803}{1024}\right)$	$e\left(\frac{403}{512}\right)$	$e\left(\frac{85}{512}\right)$	$e\left(\frac{471}{1024}\right)$	$e\left(\frac{5}{128}\right)$
$\chi_{36864}(1619,\cdot)$	$1$	$1$	$e\left(\frac{871}{1024}\right)$	$e\left(\frac{419}{512}\right)$	$e\left(\frac{691}{1024}\right)$	$e\left(\frac{41}{1024}\right)$	$e\left(\frac{241}{256}\right)$	$e\left(\frac{705}{1024}\right)$	$e\left(\frac{401}{512}\right)$	$e\left(\frac{359}{512}\right)$	$e\left(\frac{893}{1024}\right)$	$e\left(\frac{119}{128}\right)$
$\chi_{36864}(1691,\cdot)$	$1$	$1$	$e\left(\frac{777}{1024}\right)$	$e\left(\frac{141}{512}\right)$	$e\left(\frac{125}{1024}\right)$	$e\left(\frac{615}{1024}\right)$	$e\left(\frac{31}{256}\right)$	$e\left(\frac{335}{1024}\right)$	$e\left(\frac{383}{512}\right)$	$e\left(\frac{265}{512}\right)$	$e\left(\frac{83}{1024}\right)$	$e\left(\frac{121}{128}\right)$
$\chi_{36864}(1763,\cdot)$	$1$	$1$	$e\left(\frac{571}{1024}\right)$	$e\left(\frac{327}{512}\right)$	$e\left(\frac{279}{1024}\right)$	$e\left(\frac{21}{1024}\right)$	$e\left(\frac{61}{256}\right)$	$e\left(\frac{461}{1024}\right)$	$e\left(\frac{93}{512}\right)$	$e\left(\frac{59}{512}\right)$	$e\left(\frac{857}{1024}\right)$	$e\left(\frac{11}{128}\right)$
$\chi_{36864}(1835,\cdot)$	$1$	$1$	$e\left(\frac{509}{1024}\right)$	$e\left(\frac{209}{512}\right)$	$e\left(\frac{385}{1024}\right)$	$e\left(\frac{51}{1024}\right)$	$e\left(\frac{75}{256}\right)$	$e\left(\frac{827}{1024}\right)$	$e\left(\frac{299}{512}\right)$	$e\left(\frac{509}{512}\right)$	$e\left(\frac{911}{1024}\right)$	$e\left(\frac{45}{128}\right)$
$\chi_{36864}(1907,\cdot)$	$1$	$1$	$e\left(\frac{847}{1024}\right)$	$e\left(\frac{43}{512}\right)$	$e\left(\frac{699}{1024}\right)$	$e\left(\frac{449}{1024}\right)$	$e\left(\frac{73}{256}\right)$	$e\left(\frac{153}{1024}\right)$	$e\left(\frac{233}{512}\right)$	$e\left(\frac{335}{512}\right)$	$e\left(\frac{1013}{1024}\right)$	$e\left(\frac{95}{128}\right)$
$\chi_{36864}(1979,\cdot)$	$1$	$1$	$e\left(\frac{817}{1024}\right)$	$e\left(\frac{85}{512}\right)$	$e\left(\frac{453}{1024}\right)$	$e\left(\frac{959}{1024}\right)$	$e\left(\frac{55}{256}\right)$	$e\left(\frac{231}{1024}\right)$	$e\left(\frac{151}{512}\right)$	$e\left(\frac{305}{512}\right)$	$e\left(\frac{907}{1024}\right)$	$e\left(\frac{33}{128}\right)$
$\chi_{36864}(2051,\cdot)$	$1$	$1$	$e\left(\frac{675}{1024}\right)$	$e\left(\frac{79}{512}\right)$	$e\left(\frac{927}{1024}\right)$	$e\left(\frac{301}{1024}\right)$	$e\left(\frac{21}{256}\right)$	$e\left(\frac{805}{1024}\right)$	$e\left(\frac{309}{512}\right)$	$e\left(\frac{163}{512}\right)$	$e\left(\frac{337}{1024}\right)$	$e\left(\frac{115}{128}\right)$
$\chi_{36864}(2123,\cdot)$	$1$	$1$	$e\left(\frac{677}{1024}\right)$	$e\left(\frac{281}{512}\right)$	$e\left(\frac{329}{1024}\right)$	$e\left(\frac{267}{1024}\right)$	$e\left(\frac{227}{256}\right)$	$e\left(\frac{595}{1024}\right)$	$e\left(\frac{451}{512}\right)$	$e\left(\frac{165}{512}\right)$	$e\left(\frac{71}{1024}\right)$	$e\left(\frac{85}{128}\right)$
$\chi_{36864}(2195,\cdot)$	$1$	$1$	$e\left(\frac{55}{1024}\right)$	$e\left(\frac{435}{512}\right)$	$e\left(\frac{963}{1024}\right)$	$e\left(\frac{601}{1024}\right)$	$e\left(\frac{161}{256}\right)$	$e\left(\frac{369}{1024}\right)$	$e\left(\frac{321}{512}\right)$	$e\left(\frac{55}{512}\right)$	$e\left(\frac{877}{1024}\right)$	$e\left(\frac{71}{128}\right)$