Dirichlet character orbit 1815.bs

• Label: 1815.bs
• Modulus: $1815$
• Conductor: $605$
• Order: $220$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1815$
Conductor:	$605$
Order:	$220$
Real:	no
Primitive:	no, induced from 605.x
Minimal:	yes
Parity:	odd

Related number fields

Field of values:	$\Q(\zeta_{220})$
Fixed field:	Number field defined by a degree 220 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$13$	$14$	$16$	$17$	$19$	$23$
$\chi_{1815}(37,\cdot)$	$-1$	$1$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{1815}(58,\cdot)$	$-1$	$1$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{31}{44}\right)$
$\chi_{1815}(82,\cdot)$	$-1$	$1$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{1}{44}\right)$
$\chi_{1815}(97,\cdot)$	$-1$	$1$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{29}{44}\right)$
$\chi_{1815}(103,\cdot)$	$-1$	$1$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{1815}(157,\cdot)$	$-1$	$1$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{1}{44}\right)$
$\chi_{1815}(163,\cdot)$	$-1$	$1$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{15}{44}\right)$
$\chi_{1815}(223,\cdot)$	$-1$	$1$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{3}{44}\right)$
$\chi_{1815}(247,\cdot)$	$-1$	$1$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{37}{44}\right)$
$\chi_{1815}(262,\cdot)$	$-1$	$1$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{5}{44}\right)$
$\chi_{1815}(268,\cdot)$	$-1$	$1$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{1815}(313,\cdot)$	$-1$	$1$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{3}{44}\right)$
$\chi_{1815}(322,\cdot)$	$-1$	$1$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{17}{44}\right)$
$\chi_{1815}(328,\cdot)$	$-1$	$1$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{35}{44}\right)$
$\chi_{1815}(367,\cdot)$	$-1$	$1$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{1}{44}\right)$
$\chi_{1815}(388,\cdot)$	$-1$	$1$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{1815}(412,\cdot)$	$-1$	$1$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{29}{44}\right)$
$\chi_{1815}(427,\cdot)$	$-1$	$1$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{1815}(433,\cdot)$	$-1$	$1$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{1815}(478,\cdot)$	$-1$	$1$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{1815}(532,\cdot)$	$-1$	$1$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{1815}(553,\cdot)$	$-1$	$1$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{35}{44}\right)$
$\chi_{1815}(577,\cdot)$	$-1$	$1$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{1815}(592,\cdot)$	$-1$	$1$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{1}{44}\right)$
$\chi_{1815}(598,\cdot)$	$-1$	$1$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{31}{44}\right)$
$\chi_{1815}(643,\cdot)$	$-1$	$1$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{31}{44}\right)$
$\chi_{1815}(652,\cdot)$	$-1$	$1$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{5}{44}\right)$
$\chi_{1815}(658,\cdot)$	$-1$	$1$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{31}{44}\right)$
$\chi_{1815}(697,\cdot)$	$-1$	$1$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{1815}(718,\cdot)$	$-1$	$1$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{1815}(742,\cdot)$	$-1$	$1$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{13}{44}\right)$