Dirichlet character orbit 1309.da

• Label: 1309.da
• Modulus: $1309$
• Conductor: $1309$
• Order: $240$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1309$
Conductor:	$1309$
Order:	$240$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{240})$
Fixed field:	Number field defined by a degree 240 polynomial (not computed)

First 31 of 64 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{1309}(3,\cdot)$	$1$	$1$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(5,\cdot)$	$1$	$1$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(31,\cdot)$	$1$	$1$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1309}(75,\cdot)$	$1$	$1$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1309}(80,\cdot)$	$1$	$1$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(82,\cdot)$	$1$	$1$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(108,\cdot)$	$1$	$1$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1309}(124,\cdot)$	$1$	$1$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(159,\cdot)$	$1$	$1$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{1309}(180,\cdot)$	$1$	$1$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{149}{240}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1309}(192,\cdot)$	$1$	$1$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(201,\cdot)$	$1$	$1$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(262,\cdot)$	$1$	$1$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{161}{240}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1309}(269,\cdot)$	$1$	$1$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(278,\cdot)$	$1$	$1$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1309}(311,\cdot)$	$1$	$1$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(313,\cdot)$	$1$	$1$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{1309}(334,\cdot)$	$1$	$1$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1309}(346,\cdot)$	$1$	$1$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{1309}(367,\cdot)$	$1$	$1$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1309}(388,\cdot)$	$1$	$1$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(411,\cdot)$	$1$	$1$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1309}(432,\cdot)$	$1$	$1$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1309}(465,\cdot)$	$1$	$1$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1309}(488,\cdot)$	$1$	$1$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1309}(500,\cdot)$	$1$	$1$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{1309}(521,\cdot)$	$1$	$1$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1309}(537,\cdot)$	$1$	$1$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1309}(598,\cdot)$	$1$	$1$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1309}(619,\cdot)$	$1$	$1$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1309}(675,\cdot)$	$1$	$1$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{19}{20}\right)$