Dirichlet character orbit 3800.fd

• Label: 3800.fd
• Modulus: $3800$
• Conductor: $475$
• Order: $90$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$3800$
Conductor:	$475$
Order:	$90$
Real:	no
Primitive:	no, induced from 475.bg
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{45})$
Fixed field:	Number field defined by a degree 90 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{3800}(9,\cdot)$	$1$	$1$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{3800}(169,\cdot)$	$1$	$1$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{3800}(289,\cdot)$	$1$	$1$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{3800}(329,\cdot)$	$1$	$1$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{3800}(529,\cdot)$	$1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{3800}(689,\cdot)$	$1$	$1$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{3800}(769,\cdot)$	$1$	$1$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{3800}(929,\cdot)$	$1$	$1$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{3800}(1089,\cdot)$	$1$	$1$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{45}\right)$
$\chi_{3800}(1289,\cdot)$	$1$	$1$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{3800}(1529,\cdot)$	$1$	$1$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{3800}(1689,\cdot)$	$1$	$1$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{3800}(1809,\cdot)$	$1$	$1$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{3800}(2209,\cdot)$	$1$	$1$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{3800}(2289,\cdot)$	$1$	$1$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{3800}(2569,\cdot)$	$1$	$1$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{3800}(2609,\cdot)$	$1$	$1$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{3800}(2809,\cdot)$	$1$	$1$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{3800}(2969,\cdot)$	$1$	$1$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{3800}(3209,\cdot)$	$1$	$1$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{3800}(3329,\cdot)$	$1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{3800}(3369,\cdot)$	$1$	$1$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{3800}(3569,\cdot)$	$1$	$1$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{3800}(3729,\cdot)$	$1$	$1$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{45}\right)$