Dirichlet character orbit 43904.ew

• Label: 43904.ew
• Modulus: $43904$
• Conductor: $21952$
• Order: $784$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$43904$
Conductor:	$21952$
Order:	$784$
Real:	no
Primitive:	no, induced from 21952.eg
Minimal:	no
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{784})$
Fixed field:	Number field defined by a degree 784 polynomial (not computed)

First 31 of 336 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{43904}(55,\cdot)$	$1$	$1$	$e\left(\frac{289}{784}\right)$	$e\left(\frac{51}{784}\right)$	$e\left(\frac{289}{392}\right)$	$e\left(\frac{479}{784}\right)$	$e\left(\frac{45}{784}\right)$	$e\left(\frac{85}{196}\right)$	$e\left(\frac{79}{196}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{129}{392}\right)$	$e\left(\frac{51}{392}\right)$
$\chi_{43904}(167,\cdot)$	$1$	$1$	$e\left(\frac{27}{784}\right)$	$e\left(\frac{97}{784}\right)$	$e\left(\frac{27}{392}\right)$	$e\left(\frac{373}{784}\right)$	$e\left(\frac{639}{784}\right)$	$e\left(\frac{31}{196}\right)$	$e\left(\frac{181}{196}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{107}{392}\right)$	$e\left(\frac{97}{392}\right)$
$\chi_{43904}(279,\cdot)$	$1$	$1$	$e\left(\frac{213}{784}\right)$	$e\left(\frac{591}{784}\right)$	$e\left(\frac{213}{392}\right)$	$e\left(\frac{155}{784}\right)$	$e\left(\frac{337}{784}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{143}{196}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{365}{392}\right)$	$e\left(\frac{199}{392}\right)$
$\chi_{43904}(503,\cdot)$	$1$	$1$	$e\left(\frac{361}{784}\right)$	$e\left(\frac{571}{784}\right)$	$e\left(\frac{361}{392}\right)$	$e\left(\frac{167}{784}\right)$	$e\left(\frac{181}{784}\right)$	$e\left(\frac{37}{196}\right)$	$e\left(\frac{39}{196}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{153}{392}\right)$	$e\left(\frac{179}{392}\right)$
$\chi_{43904}(615,\cdot)$	$1$	$1$	$e\left(\frac{323}{784}\right)$	$e\left(\frac{57}{784}\right)$	$e\left(\frac{323}{392}\right)$	$e\left(\frac{397}{784}\right)$	$e\left(\frac{327}{784}\right)$	$e\left(\frac{95}{196}\right)$	$e\left(\frac{169}{196}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{75}{392}\right)$	$e\left(\frac{57}{392}\right)$
$\chi_{43904}(727,\cdot)$	$1$	$1$	$e\left(\frac{733}{784}\right)$	$e\left(\frac{775}{784}\right)$	$e\left(\frac{341}{392}\right)$	$e\left(\frac{515}{784}\right)$	$e\left(\frac{361}{784}\right)$	$e\left(\frac{181}{196}\right)$	$e\left(\frac{159}{196}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{277}{392}\right)$	$e\left(\frac{383}{392}\right)$
$\chi_{43904}(839,\cdot)$	$1$	$1$	$e\left(\frac{23}{784}\right)$	$e\left(\frac{373}{784}\right)$	$e\left(\frac{23}{392}\right)$	$e\left(\frac{521}{784}\right)$	$e\left(\frac{283}{784}\right)$	$e\left(\frac{99}{196}\right)$	$e\left(\frac{9}{196}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{367}{392}\right)$	$e\left(\frac{373}{392}\right)$
$\chi_{43904}(951,\cdot)$	$1$	$1$	$e\left(\frac{545}{784}\right)$	$e\left(\frac{419}{784}\right)$	$e\left(\frac{153}{392}\right)$	$e\left(\frac{415}{784}\right)$	$e\left(\frac{93}{784}\right)$	$e\left(\frac{45}{196}\right)$	$e\left(\frac{111}{196}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{345}{392}\right)$	$e\left(\frac{27}{392}\right)$
$\chi_{43904}(1063,\cdot)$	$1$	$1$	$e\left(\frac{731}{784}\right)$	$e\left(\frac{129}{784}\right)$	$e\left(\frac{339}{392}\right)$	$e\left(\frac{197}{784}\right)$	$e\left(\frac{575}{784}\right)$	$e\left(\frac{19}{196}\right)$	$e\left(\frac{73}{196}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{211}{392}\right)$	$e\left(\frac{129}{392}\right)$
$\chi_{43904}(1287,\cdot)$	$1$	$1$	$e\left(\frac{95}{784}\right)$	$e\left(\frac{109}{784}\right)$	$e\left(\frac{95}{392}\right)$	$e\left(\frac{209}{784}\right)$	$e\left(\frac{419}{784}\right)$	$e\left(\frac{51}{196}\right)$	$e\left(\frac{165}{196}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{391}{392}\right)$	$e\left(\frac{109}{392}\right)$
$\chi_{43904}(1399,\cdot)$	$1$	$1$	$e\left(\frac{57}{784}\right)$	$e\left(\frac{379}{784}\right)$	$e\left(\frac{57}{392}\right)$	$e\left(\frac{439}{784}\right)$	$e\left(\frac{565}{784}\right)$	$e\left(\frac{109}{196}\right)$	$e\left(\frac{99}{196}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{313}{392}\right)$	$e\left(\frac{379}{392}\right)$
$\chi_{43904}(1511,\cdot)$	$1$	$1$	$e\left(\frac{467}{784}\right)$	$e\left(\frac{313}{784}\right)$	$e\left(\frac{75}{392}\right)$	$e\left(\frac{557}{784}\right)$	$e\left(\frac{599}{784}\right)$	$e\left(\frac{195}{196}\right)$	$e\left(\frac{89}{196}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{123}{392}\right)$	$e\left(\frac{313}{392}\right)$
$\chi_{43904}(1623,\cdot)$	$1$	$1$	$e\left(\frac{541}{784}\right)$	$e\left(\frac{695}{784}\right)$	$e\left(\frac{149}{392}\right)$	$e\left(\frac{563}{784}\right)$	$e\left(\frac{521}{784}\right)$	$e\left(\frac{113}{196}\right)$	$e\left(\frac{135}{196}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{213}{392}\right)$	$e\left(\frac{303}{392}\right)$
$\chi_{43904}(1735,\cdot)$	$1$	$1$	$e\left(\frac{279}{784}\right)$	$e\left(\frac{741}{784}\right)$	$e\left(\frac{279}{392}\right)$	$e\left(\frac{457}{784}\right)$	$e\left(\frac{331}{784}\right)$	$e\left(\frac{59}{196}\right)$	$e\left(\frac{41}{196}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{191}{392}\right)$	$e\left(\frac{349}{392}\right)$
$\chi_{43904}(1847,\cdot)$	$1$	$1$	$e\left(\frac{465}{784}\right)$	$e\left(\frac{451}{784}\right)$	$e\left(\frac{73}{392}\right)$	$e\left(\frac{239}{784}\right)$	$e\left(\frac{29}{784}\right)$	$e\left(\frac{33}{196}\right)$	$e\left(\frac{3}{196}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{57}{392}\right)$	$e\left(\frac{59}{392}\right)$
$\chi_{43904}(2071,\cdot)$	$1$	$1$	$e\left(\frac{613}{784}\right)$	$e\left(\frac{431}{784}\right)$	$e\left(\frac{221}{392}\right)$	$e\left(\frac{251}{784}\right)$	$e\left(\frac{657}{784}\right)$	$e\left(\frac{65}{196}\right)$	$e\left(\frac{95}{196}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{237}{392}\right)$	$e\left(\frac{39}{392}\right)$
$\chi_{43904}(2183,\cdot)$	$1$	$1$	$e\left(\frac{575}{784}\right)$	$e\left(\frac{701}{784}\right)$	$e\left(\frac{183}{392}\right)$	$e\left(\frac{481}{784}\right)$	$e\left(\frac{19}{784}\right)$	$e\left(\frac{123}{196}\right)$	$e\left(\frac{29}{196}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{159}{392}\right)$	$e\left(\frac{309}{392}\right)$
$\chi_{43904}(2295,\cdot)$	$1$	$1$	$e\left(\frac{201}{784}\right)$	$e\left(\frac{635}{784}\right)$	$e\left(\frac{201}{392}\right)$	$e\left(\frac{599}{784}\right)$	$e\left(\frac{53}{784}\right)$	$e\left(\frac{13}{196}\right)$	$e\left(\frac{19}{196}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{361}{392}\right)$	$e\left(\frac{243}{392}\right)$
$\chi_{43904}(2407,\cdot)$	$1$	$1$	$e\left(\frac{275}{784}\right)$	$e\left(\frac{233}{784}\right)$	$e\left(\frac{275}{392}\right)$	$e\left(\frac{605}{784}\right)$	$e\left(\frac{759}{784}\right)$	$e\left(\frac{127}{196}\right)$	$e\left(\frac{65}{196}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{59}{392}\right)$	$e\left(\frac{233}{392}\right)$
$\chi_{43904}(2519,\cdot)$	$1$	$1$	$e\left(\frac{13}{784}\right)$	$e\left(\frac{279}{784}\right)$	$e\left(\frac{13}{392}\right)$	$e\left(\frac{499}{784}\right)$	$e\left(\frac{569}{784}\right)$	$e\left(\frac{73}{196}\right)$	$e\left(\frac{167}{196}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{37}{392}\right)$	$e\left(\frac{279}{392}\right)$
$\chi_{43904}(2631,\cdot)$	$1$	$1$	$e\left(\frac{199}{784}\right)$	$e\left(\frac{773}{784}\right)$	$e\left(\frac{199}{392}\right)$	$e\left(\frac{281}{784}\right)$	$e\left(\frac{267}{784}\right)$	$e\left(\frac{47}{196}\right)$	$e\left(\frac{129}{196}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{295}{392}\right)$	$e\left(\frac{381}{392}\right)$
$\chi_{43904}(2855,\cdot)$	$1$	$1$	$e\left(\frac{347}{784}\right)$	$e\left(\frac{753}{784}\right)$	$e\left(\frac{347}{392}\right)$	$e\left(\frac{293}{784}\right)$	$e\left(\frac{111}{784}\right)$	$e\left(\frac{79}{196}\right)$	$e\left(\frac{25}{196}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{83}{392}\right)$	$e\left(\frac{361}{392}\right)$
$\chi_{43904}(2967,\cdot)$	$1$	$1$	$e\left(\frac{309}{784}\right)$	$e\left(\frac{239}{784}\right)$	$e\left(\frac{309}{392}\right)$	$e\left(\frac{523}{784}\right)$	$e\left(\frac{257}{784}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{155}{196}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{392}\right)$	$e\left(\frac{239}{392}\right)$
$\chi_{43904}(3079,\cdot)$	$1$	$1$	$e\left(\frac{719}{784}\right)$	$e\left(\frac{173}{784}\right)$	$e\left(\frac{327}{392}\right)$	$e\left(\frac{641}{784}\right)$	$e\left(\frac{291}{784}\right)$	$e\left(\frac{27}{196}\right)$	$e\left(\frac{145}{196}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{207}{392}\right)$	$e\left(\frac{173}{392}\right)$
$\chi_{43904}(3191,\cdot)$	$1$	$1$	$e\left(\frac{9}{784}\right)$	$e\left(\frac{555}{784}\right)$	$e\left(\frac{9}{392}\right)$	$e\left(\frac{647}{784}\right)$	$e\left(\frac{213}{784}\right)$	$e\left(\frac{141}{196}\right)$	$e\left(\frac{191}{196}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{297}{392}\right)$	$e\left(\frac{163}{392}\right)$
$\chi_{43904}(3303,\cdot)$	$1$	$1$	$e\left(\frac{531}{784}\right)$	$e\left(\frac{601}{784}\right)$	$e\left(\frac{139}{392}\right)$	$e\left(\frac{541}{784}\right)$	$e\left(\frac{23}{784}\right)$	$e\left(\frac{87}{196}\right)$	$e\left(\frac{97}{196}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{275}{392}\right)$	$e\left(\frac{209}{392}\right)$
$\chi_{43904}(3415,\cdot)$	$1$	$1$	$e\left(\frac{717}{784}\right)$	$e\left(\frac{311}{784}\right)$	$e\left(\frac{325}{392}\right)$	$e\left(\frac{323}{784}\right)$	$e\left(\frac{505}{784}\right)$	$e\left(\frac{61}{196}\right)$	$e\left(\frac{59}{196}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{141}{392}\right)$	$e\left(\frac{311}{392}\right)$
$\chi_{43904}(3639,\cdot)$	$1$	$1$	$e\left(\frac{81}{784}\right)$	$e\left(\frac{291}{784}\right)$	$e\left(\frac{81}{392}\right)$	$e\left(\frac{335}{784}\right)$	$e\left(\frac{349}{784}\right)$	$e\left(\frac{93}{196}\right)$	$e\left(\frac{151}{196}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{321}{392}\right)$	$e\left(\frac{291}{392}\right)$
$\chi_{43904}(3751,\cdot)$	$1$	$1$	$e\left(\frac{43}{784}\right)$	$e\left(\frac{561}{784}\right)$	$e\left(\frac{43}{392}\right)$	$e\left(\frac{565}{784}\right)$	$e\left(\frac{495}{784}\right)$	$e\left(\frac{151}{196}\right)$	$e\left(\frac{85}{196}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{243}{392}\right)$	$e\left(\frac{169}{392}\right)$
$\chi_{43904}(3863,\cdot)$	$1$	$1$	$e\left(\frac{453}{784}\right)$	$e\left(\frac{495}{784}\right)$	$e\left(\frac{61}{392}\right)$	$e\left(\frac{683}{784}\right)$	$e\left(\frac{529}{784}\right)$	$e\left(\frac{41}{196}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{53}{392}\right)$	$e\left(\frac{103}{392}\right)$
$\chi_{43904}(3975,\cdot)$	$1$	$1$	$e\left(\frac{527}{784}\right)$	$e\left(\frac{93}{784}\right)$	$e\left(\frac{135}{392}\right)$	$e\left(\frac{689}{784}\right)$	$e\left(\frac{451}{784}\right)$	$e\left(\frac{155}{196}\right)$	$e\left(\frac{121}{196}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{143}{392}\right)$	$e\left(\frac{93}{392}\right)$