Dirichlet character \(\chi_{3400}(37,\cdot)\)

• Label: 3400.37
• Modulus: $3400$
• Conductor: $3400$
• Order: $80$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3400\)
Conductor:	\(3400\)
Order:	\(80\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3400.fm

\(\chi_{3400}(37,\cdot)\) \(\chi_{3400}(277,\cdot)\) \(\chi_{3400}(333,\cdot)\) \(\chi_{3400}(437,\cdot)\) \(\chi_{3400}(453,\cdot)\) \(\chi_{3400}(533,\cdot)\) \(\chi_{3400}(653,\cdot)\) \(\chi_{3400}(677,\cdot)\) \(\chi_{3400}(717,\cdot)\) \(\chi_{3400}(1013,\cdot)\) \(\chi_{3400}(1117,\cdot)\) \(\chi_{3400}(1133,\cdot)\) \(\chi_{3400}(1213,\cdot)\) \(\chi_{3400}(1333,\cdot)\) \(\chi_{3400}(1397,\cdot)\) \(\chi_{3400}(1637,\cdot)\) \(\chi_{3400}(1797,\cdot)\) \(\chi_{3400}(1813,\cdot)\) \(\chi_{3400}(2013,\cdot)\) \(\chi_{3400}(2037,\cdot)\) \(\chi_{3400}(2077,\cdot)\) \(\chi_{3400}(2317,\cdot)\) \(\chi_{3400}(2373,\cdot)\) \(\chi_{3400}(2477,\cdot)\) \(\chi_{3400}(2573,\cdot)\) \(\chi_{3400}(2717,\cdot)\) \(\chi_{3400}(2997,\cdot)\) \(\chi_{3400}(3053,\cdot)\) \(\chi_{3400}(3173,\cdot)\) \(\chi_{3400}(3253,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

Values on generators

\((2551,1701,2177,1601)\) → \((1,-1,e\left(\frac{9}{20}\right),e\left(\frac{1}{16}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\( \chi_{ 3400 }(37, a) \)	\(1\)	\(1\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)