Dirichlet character \(\chi_{44100}(23299,\cdot)\)

• Label: 44100.23299
• Modulus: $44100$
• Conductor: $8820$
• Order: $42$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	\(44100\)
Conductor:	\(8820\)
Order:	\(42\)
Real:	no
Primitive:	no, induced from \(\chi_{8820}(5659,\cdot)\)
Minimal:	no
Parity:	even

Galois orbit 44100.ka

\(\chi_{44100}(4399,\cdot)\) \(\chi_{44100}(10699,\cdot)\) \(\chi_{44100}(12199,\cdot)\) \(\chi_{44100}(16999,\cdot)\) \(\chi_{44100}(18499,\cdot)\) \(\chi_{44100}(23299,\cdot)\) \(\chi_{44100}(24799,\cdot)\) \(\chi_{44100}(29599,\cdot)\) \(\chi_{44100}(31099,\cdot)\) \(\chi_{44100}(37399,\cdot)\) \(\chi_{44100}(42199,\cdot)\) \(\chi_{44100}(43699,\cdot)\)

Related number fields

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

Values on generators

\((22051,34301,15877,9901)\) → \((-1,e\left(\frac{2}{3}\right),-1,e\left(\frac{37}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 44100 }(23299, a) \)	\(1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)