Dirichlet character orbit 6900.dh

• Label: 6900.dh
• Modulus: $6900$
• Conductor: $2300$
• Order: $110$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$6900$
Conductor:	$2300$
Order:	$110$
Real:	no
Primitive:	no, induced from 2300.br
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 110 polynomial (not computed)

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{6900}(19,\cdot)$	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{6900}(79,\cdot)$	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{6900}(319,\cdot)$	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{6900}(379,\cdot)$	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{6900}(559,\cdot)$	$1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{6900}(619,\cdot)$	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{6900}(1279,\cdot)$	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{6900}(1339,\cdot)$	$1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{6900}(1459,\cdot)$	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{6900}(1579,\cdot)$	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{6900}(1759,\cdot)$	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{6900}(1939,\cdot)$	$1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{6900}(2179,\cdot)$	$1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{6900}(2659,\cdot)$	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{6900}(2719,\cdot)$	$1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{6900}(2779,\cdot)$	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{6900}(2839,\cdot)$	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{6900}(2959,\cdot)$	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{6900}(3079,\cdot)$	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{6900}(3139,\cdot)$	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{6900}(3319,\cdot)$	$1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{6900}(3379,\cdot)$	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{6900}(3559,\cdot)$	$1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{6900}(4039,\cdot)$	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{6900}(4159,\cdot)$	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{6900}(4219,\cdot)$	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{6900}(4339,\cdot)$	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{6900}(4459,\cdot)$	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{6900}(4519,\cdot)$	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{6900}(4759,\cdot)$	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{6900}(4939,\cdot)$	$1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{13}{22}\right)$