Dirichlet character \(\chi_{44100}(19483,\cdot)\)

• Label: 44100.19483
• Modulus: $44100$
• Conductor: $6300$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	\(44100\)
Conductor:	\(6300\)
Order:	\(60\)
Real:	no
Primitive:	no, induced from \(\chi_{6300}(583,\cdot)\)
Minimal:	no
Parity:	even

Galois orbit 44100.mp

\(\chi_{44100}(67,\cdot)\) \(\chi_{44100}(7123,\cdot)\) \(\chi_{44100}(8887,\cdot)\) \(\chi_{44100}(10663,\cdot)\) \(\chi_{44100}(12427,\cdot)\) \(\chi_{44100}(19483,\cdot)\) \(\chi_{44100}(21247,\cdot)\) \(\chi_{44100}(24763,\cdot)\) \(\chi_{44100}(26527,\cdot)\) \(\chi_{44100}(28303,\cdot)\) \(\chi_{44100}(30067,\cdot)\) \(\chi_{44100}(33583,\cdot)\) \(\chi_{44100}(35347,\cdot)\) \(\chi_{44100}(37123,\cdot)\) \(\chi_{44100}(38887,\cdot)\) \(\chi_{44100}(42403,\cdot)\)

Related number fields

Field of values:	\(\Q(\zeta_{60})\)
Fixed field:	Number field defined by a degree 60 polynomial

Values on generators

\((22051,34301,15877,9901)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{3}{20}\right),e\left(\frac{1}{3}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 44100 }(19483, a) \)	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)