Dirichlet character \(\chi_{44100}(12563,\cdot)\)

• Label: 44100.12563
• Modulus: $44100$
• Conductor: $2100$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	\(44100\)
Conductor:	\(2100\)
Order:	\(60\)
Real:	no
Primitive:	no, induced from \(\chi_{2100}(2063,\cdot)\)
Minimal:	no
Parity:	even

Galois orbit 44100.md

\(\chi_{44100}(1403,\cdot)\) \(\chi_{44100}(3167,\cdot)\) \(\chi_{44100}(10223,\cdot)\) \(\chi_{44100}(11987,\cdot)\) \(\chi_{44100}(12563,\cdot)\) \(\chi_{44100}(14327,\cdot)\) \(\chi_{44100}(21383,\cdot)\) \(\chi_{44100}(23147,\cdot)\) \(\chi_{44100}(27863,\cdot)\) \(\chi_{44100}(29627,\cdot)\) \(\chi_{44100}(30203,\cdot)\) \(\chi_{44100}(31967,\cdot)\) \(\chi_{44100}(36683,\cdot)\) \(\chi_{44100}(38447,\cdot)\) \(\chi_{44100}(39023,\cdot)\) \(\chi_{44100}(40787,\cdot)\)

Related number fields

Field of values:	\(\Q(\zeta_{60})\)
Fixed field:	Number field defined by a degree 60 polynomial

Values on generators

\((22051,34301,15877,9901)\) → \((-1,-1,e\left(\frac{19}{20}\right),e\left(\frac{5}{6}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 44100 }(12563, a) \)	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)