Dirichlet character \(\chi_{44100}(39901,\cdot)\)

• Label: 44100.39901
• Modulus: $44100$
• Conductor: $441$
• Order: $21$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(44100\)
Conductor:	\(441\)
Order:	\(21\)
Real:	no
Primitive:	no, induced from \(\chi_{441}(211,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 44100.gk

\(\chi_{44100}(2101,\cdot)\) \(\chi_{44100}(4201,\cdot)\) \(\chi_{44100}(8401,\cdot)\) \(\chi_{44100}(10501,\cdot)\) \(\chi_{44100}(16801,\cdot)\) \(\chi_{44100}(21001,\cdot)\) \(\chi_{44100}(23101,\cdot)\) \(\chi_{44100}(27301,\cdot)\) \(\chi_{44100}(33601,\cdot)\) \(\chi_{44100}(35701,\cdot)\) \(\chi_{44100}(39901,\cdot)\) \(\chi_{44100}(42001,\cdot)\)

Related number fields

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

Values on generators

\((22051,34301,15877,9901)\) → \((1,e\left(\frac{1}{3}\right),1,e\left(\frac{5}{7}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 44100 }(39901, a) \)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)