Dirichlet character \(\chi_{44100}(43601,\cdot)\)

• Label: 44100.43601
• Modulus: $44100$
• Conductor: $441$
• Order: $42$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(44100\)
Conductor:	\(441\)
Order:	\(42\)
Real:	no
Primitive:	no, induced from \(\chi_{441}(383,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 44100.jt

\(\chi_{44100}(101,\cdot)\) \(\chi_{44100}(12101,\cdot)\) \(\chi_{44100}(12701,\cdot)\) \(\chi_{44100}(18401,\cdot)\) \(\chi_{44100}(19001,\cdot)\) \(\chi_{44100}(24701,\cdot)\) \(\chi_{44100}(25301,\cdot)\) \(\chi_{44100}(31001,\cdot)\) \(\chi_{44100}(31601,\cdot)\) \(\chi_{44100}(37301,\cdot)\) \(\chi_{44100}(37901,\cdot)\) \(\chi_{44100}(43601,\cdot)\)

Related number fields

Field of values:	\(\Q(\zeta_{21})\)
Fixed field:	Number field defined by a degree 42 polynomial

Values on generators

\((22051,34301,15877,9901)\) → \((1,e\left(\frac{5}{6}\right),1,e\left(\frac{23}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 44100 }(43601, a) \)	\(1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(-1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)