Dirichlet character \(\chi_{3040}(2157,\cdot)\)

• Label: 3040.2157
• Modulus: $3040$
• Conductor: $3040$
• Order: $72$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3040\)
Conductor:	\(3040\)
Order:	\(72\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3040.fy

\(\chi_{3040}(53,\cdot)\) \(\chi_{3040}(317,\cdot)\) \(\chi_{3040}(477,\cdot)\) \(\chi_{3040}(637,\cdot)\) \(\chi_{3040}(717,\cdot)\) \(\chi_{3040}(773,\cdot)\) \(\chi_{3040}(877,\cdot)\) \(\chi_{3040}(933,\cdot)\) \(\chi_{3040}(1093,\cdot)\) \(\chi_{3040}(1117,\cdot)\) \(\chi_{3040}(1173,\cdot)\) \(\chi_{3040}(1333,\cdot)\) \(\chi_{3040}(1573,\cdot)\) \(\chi_{3040}(1837,\cdot)\) \(\chi_{3040}(1997,\cdot)\) \(\chi_{3040}(2157,\cdot)\) \(\chi_{3040}(2237,\cdot)\) \(\chi_{3040}(2293,\cdot)\) \(\chi_{3040}(2397,\cdot)\) \(\chi_{3040}(2453,\cdot)\) \(\chi_{3040}(2613,\cdot)\) \(\chi_{3040}(2637,\cdot)\) \(\chi_{3040}(2693,\cdot)\) \(\chi_{3040}(2853,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{72})$
Fixed field:	Number field defined by a degree 72 polynomial

Values on generators

\((191,2661,1217,1921)\) → \((1,e\left(\frac{7}{8}\right),i,e\left(\frac{17}{18}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(21\)	\(23\)	\(27\)	\(29\)
\( \chi_{ 3040 }(2157, a) \)	\(1\)	\(1\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{72}\right)\)