Dirichlet character orbit 3800.fb

• Label: 3800.fb
• Modulus: $3800$
• Conductor: $1900$
• Order: $90$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$3800$
Conductor:	$1900$
Order:	$90$
Real:	no
Primitive:	no, induced from 1900.cn
Minimal:	no
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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{3800}(71,\cdot)$	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{73}{90}\right)$
$\chi_{3800}(231,\cdot)$	$1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{90}\right)$
$\chi_{3800}(431,\cdot)$	$1$	$1$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{47}{90}\right)$
$\chi_{3800}(471,\cdot)$	$1$	$1$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{53}{90}\right)$
$\chi_{3800}(591,\cdot)$	$1$	$1$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{3800}(831,\cdot)$	$1$	$1$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{37}{90}\right)$
$\chi_{3800}(991,\cdot)$	$1$	$1$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{61}{90}\right)$
$\chi_{3800}(1191,\cdot)$	$1$	$1$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{90}\right)$
$\chi_{3800}(1231,\cdot)$	$1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{90}\right)$
$\chi_{3800}(1511,\cdot)$	$1$	$1$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{59}{90}\right)$
$\chi_{3800}(1591,\cdot)$	$1$	$1$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{90}\right)$
$\chi_{3800}(1991,\cdot)$	$1$	$1$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{71}{90}\right)$
$\chi_{3800}(2111,\cdot)$	$1$	$1$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{49}{90}\right)$
$\chi_{3800}(2271,\cdot)$	$1$	$1$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{90}\right)$
$\chi_{3800}(2511,\cdot)$	$1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{79}{90}\right)$
$\chi_{3800}(2711,\cdot)$	$1$	$1$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{90}\right)$
$\chi_{3800}(2871,\cdot)$	$1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{90}\right)$
$\chi_{3800}(3031,\cdot)$	$1$	$1$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{77}{90}\right)$
$\chi_{3800}(3111,\cdot)$	$1$	$1$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{90}\right)$
$\chi_{3800}(3271,\cdot)$	$1$	$1$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{43}{90}\right)$
$\chi_{3800}(3471,\cdot)$	$1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{83}{90}\right)$
$\chi_{3800}(3511,\cdot)$	$1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{3800}(3631,\cdot)$	$1$	$1$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{67}{90}\right)$
$\chi_{3800}(3791,\cdot)$	$1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{41}{90}\right)$