Dirichlet character \(\chi_{44100}(7571,\cdot)\)

• Label: 44100.7571
• Modulus: $44100$
• Conductor: $44100$
• Order: $210$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(44100\)
Conductor:	\(44100\)
Order:	\(210\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 44100.pn

\(\chi_{44100}(11,\cdot)\) \(\chi_{44100}(1031,\cdot)\) \(\chi_{44100}(1271,\cdot)\) \(\chi_{44100}(2291,\cdot)\) \(\chi_{44100}(2531,\cdot)\) \(\chi_{44100}(4811,\cdot)\) \(\chi_{44100}(6071,\cdot)\) \(\chi_{44100}(6311,\cdot)\) \(\chi_{44100}(7571,\cdot)\) \(\chi_{44100}(8591,\cdot)\) \(\chi_{44100}(8831,\cdot)\) \(\chi_{44100}(10091,\cdot)\) \(\chi_{44100}(11111,\cdot)\) \(\chi_{44100}(12371,\cdot)\) \(\chi_{44100}(13631,\cdot)\) \(\chi_{44100}(13871,\cdot)\) \(\chi_{44100}(14891,\cdot)\) \(\chi_{44100}(15131,\cdot)\) \(\chi_{44100}(16391,\cdot)\) \(\chi_{44100}(17411,\cdot)\) \(\chi_{44100}(18671,\cdot)\) \(\chi_{44100}(18911,\cdot)\) \(\chi_{44100}(19931,\cdot)\) \(\chi_{44100}(20171,\cdot)\) \(\chi_{44100}(21191,\cdot)\) \(\chi_{44100}(22691,\cdot)\) \(\chi_{44100}(23711,\cdot)\) \(\chi_{44100}(25211,\cdot)\) \(\chi_{44100}(26231,\cdot)\) \(\chi_{44100}(26471,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{105})$
Fixed field:	Number field defined by a degree 210 polynomial (not computed)

Values on generators

\((22051,34301,15877,9901)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{3}{5}\right),e\left(\frac{8}{21}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 44100 }(7571, a) \)	\(1\)	\(1\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{19}{42}\right)\)