Dirichlet character orbit 3040.fy

• Label: 3040.fy
• Modulus: $3040$
• Conductor: $3040$
• Order: $72$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$3040$
Conductor:	$3040$
Order:	$72$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{72})$
Fixed field:	Number field defined by a degree 72 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{3040}(53,\cdot)$	$1$	$1$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{55}{72}\right)$
$\chi_{3040}(317,\cdot)$	$1$	$1$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{25}{72}\right)$
$\chi_{3040}(477,\cdot)$	$1$	$1$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{41}{72}\right)$
$\chi_{3040}(637,\cdot)$	$1$	$1$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{49}{72}\right)$
$\chi_{3040}(717,\cdot)$	$1$	$1$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{53}{72}\right)$
$\chi_{3040}(773,\cdot)$	$1$	$1$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{43}{72}\right)$
$\chi_{3040}(877,\cdot)$	$1$	$1$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{29}{72}\right)$
$\chi_{3040}(933,\cdot)$	$1$	$1$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{59}{72}\right)$
$\chi_{3040}(1093,\cdot)$	$1$	$1$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{67}{72}\right)$
$\chi_{3040}(1117,\cdot)$	$1$	$1$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{72}\right)$
$\chi_{3040}(1173,\cdot)$	$1$	$1$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{71}{72}\right)$
$\chi_{3040}(1333,\cdot)$	$1$	$1$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{47}{72}\right)$
$\chi_{3040}(1573,\cdot)$	$1$	$1$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{72}\right)$
$\chi_{3040}(1837,\cdot)$	$1$	$1$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{61}{72}\right)$
$\chi_{3040}(1997,\cdot)$	$1$	$1$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{72}\right)$
$\chi_{3040}(2157,\cdot)$	$1$	$1$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{72}\right)$
$\chi_{3040}(2237,\cdot)$	$1$	$1$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{72}\right)$
$\chi_{3040}(2293,\cdot)$	$1$	$1$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{72}\right)$
$\chi_{3040}(2397,\cdot)$	$1$	$1$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{65}{72}\right)$
$\chi_{3040}(2453,\cdot)$	$1$	$1$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{72}\right)$
$\chi_{3040}(2613,\cdot)$	$1$	$1$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{31}{72}\right)$
$\chi_{3040}(2637,\cdot)$	$1$	$1$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{37}{72}\right)$
$\chi_{3040}(2693,\cdot)$	$1$	$1$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{35}{72}\right)$
$\chi_{3040}(2853,\cdot)$	$1$	$1$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{72}\right)$