Dirichlet character orbit 132300.wc

• Label: 132300.wc
• Modulus: $132300$
• Conductor: $4725$
• Order: $180$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$132300$
Conductor:	$4725$
Order:	$180$
Real:	no
Primitive:	no, induced from 4725.he
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{180})$
Fixed field:	Number field defined by a degree 180 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{132300}(97,\cdot)$	$1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{132300}(1273,\cdot)$	$1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{132300}(3037,\cdot)$	$1$	$1$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{132300}(7153,\cdot)$	$1$	$1$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{132300}(8917,\cdot)$	$1$	$1$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{132300}(15973,\cdot)$	$1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{132300}(17737,\cdot)$	$1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{132300}(18913,\cdot)$	$1$	$1$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{132300}(20677,\cdot)$	$1$	$1$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{132300}(27733,\cdot)$	$1$	$1$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{132300}(29497,\cdot)$	$1$	$1$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{132300}(33613,\cdot)$	$1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{132300}(35377,\cdot)$	$1$	$1$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{132300}(36553,\cdot)$	$1$	$1$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{132300}(38317,\cdot)$	$1$	$1$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{132300}(42433,\cdot)$	$1$	$1$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{132300}(44197,\cdot)$	$1$	$1$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{132300}(45373,\cdot)$	$1$	$1$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{132300}(47137,\cdot)$	$1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{132300}(51253,\cdot)$	$1$	$1$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{132300}(53017,\cdot)$	$1$	$1$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{132300}(60073,\cdot)$	$1$	$1$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{132300}(61837,\cdot)$	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{132300}(63013,\cdot)$	$1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{132300}(64777,\cdot)$	$1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{132300}(71833,\cdot)$	$1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{132300}(73597,\cdot)$	$1$	$1$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{132300}(77713,\cdot)$	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{132300}(79477,\cdot)$	$1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{132300}(80653,\cdot)$	$1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{132300}(82417,\cdot)$	$1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{19}{36}\right)$