Dirichlet character \(\chi_{44100}(42433,\cdot)\)

• Label: 44100.42433
• Modulus: $44100$
• Conductor: $1575$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(44100\)
Conductor:	\(1575\)
Order:	\(60\)
Real:	no
Primitive:	no, induced from \(\chi_{1575}(1483,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 44100.mb

\(\chi_{44100}(97,\cdot)\) \(\chi_{44100}(1273,\cdot)\) \(\chi_{44100}(3037,\cdot)\) \(\chi_{44100}(7153,\cdot)\) \(\chi_{44100}(8917,\cdot)\) \(\chi_{44100}(15973,\cdot)\) \(\chi_{44100}(17737,\cdot)\) \(\chi_{44100}(18913,\cdot)\) \(\chi_{44100}(20677,\cdot)\) \(\chi_{44100}(27733,\cdot)\) \(\chi_{44100}(29497,\cdot)\) \(\chi_{44100}(33613,\cdot)\) \(\chi_{44100}(35377,\cdot)\) \(\chi_{44100}(36553,\cdot)\) \(\chi_{44100}(38317,\cdot)\) \(\chi_{44100}(42433,\cdot)\)

Related number fields

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

Values on generators

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

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 44100 }(42433, a) \)	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)