Dirichlet character \(\chi_{44100}(4271,\cdot)\)

• Label: 44100.4271
• 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.pl

\(\chi_{44100}(911,\cdot)\) \(\chi_{44100}(2171,\cdot)\) \(\chi_{44100}(3011,\cdot)\) \(\chi_{44100}(4271,\cdot)\) \(\chi_{44100}(4691,\cdot)\) \(\chi_{44100}(5531,\cdot)\) \(\chi_{44100}(6791,\cdot)\) \(\chi_{44100}(7211,\cdot)\) \(\chi_{44100}(8471,\cdot)\) \(\chi_{44100}(9731,\cdot)\) \(\chi_{44100}(10571,\cdot)\) \(\chi_{44100}(10991,\cdot)\) \(\chi_{44100}(11831,\cdot)\) \(\chi_{44100}(13091,\cdot)\) \(\chi_{44100}(13511,\cdot)\) \(\chi_{44100}(14771,\cdot)\) \(\chi_{44100}(15611,\cdot)\) \(\chi_{44100}(16031,\cdot)\) \(\chi_{44100}(16871,\cdot)\) \(\chi_{44100}(17291,\cdot)\) \(\chi_{44100}(19391,\cdot)\) \(\chi_{44100}(19811,\cdot)\) \(\chi_{44100}(21911,\cdot)\) \(\chi_{44100}(22331,\cdot)\) \(\chi_{44100}(23171,\cdot)\) \(\chi_{44100}(23591,\cdot)\) \(\chi_{44100}(24431,\cdot)\) \(\chi_{44100}(25691,\cdot)\) \(\chi_{44100}(26111,\cdot)\) \(\chi_{44100}(27371,\cdot)\) ...

Related number fields

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

Values on generators

\((22051,34301,15877,9901)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{3}{5}\right),e\left(\frac{6}{7}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 44100 }(4271, a) \)	\(1\)	\(1\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{41}{42}\right)\)