Dirichlet character \(\chi_{7600}(33,\cdot)\)

• Label: 7600.33
• Modulus: $7600$
• Conductor: $475$
• Order: $180$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	\(7600\)
Conductor:	\(475\)
Order:	\(180\)
Real:	no
Primitive:	no, induced from \(\chi_{475}(33,\cdot)\)
Minimal:	no
Parity:	even

Galois orbit 7600.iz

\(\chi_{7600}(33,\cdot)\) \(\chi_{7600}(97,\cdot)\) \(\chi_{7600}(337,\cdot)\) \(\chi_{7600}(433,\cdot)\) \(\chi_{7600}(497,\cdot)\) \(\chi_{7600}(737,\cdot)\) \(\chi_{7600}(1153,\cdot)\) \(\chi_{7600}(1313,\cdot)\) \(\chi_{7600}(1473,\cdot)\) \(\chi_{7600}(1553,\cdot)\) \(\chi_{7600}(1617,\cdot)\) \(\chi_{7600}(1713,\cdot)\) \(\chi_{7600}(1777,\cdot)\) \(\chi_{7600}(1953,\cdot)\) \(\chi_{7600}(2017,\cdot)\) \(\chi_{7600}(2673,\cdot)\) \(\chi_{7600}(2833,\cdot)\) \(\chi_{7600}(2977,\cdot)\) \(\chi_{7600}(3073,\cdot)\) \(\chi_{7600}(3137,\cdot)\) \(\chi_{7600}(3233,\cdot)\) \(\chi_{7600}(3297,\cdot)\) \(\chi_{7600}(3377,\cdot)\) \(\chi_{7600}(3473,\cdot)\) \(\chi_{7600}(3537,\cdot)\) \(\chi_{7600}(3777,\cdot)\) \(\chi_{7600}(4353,\cdot)\) \(\chi_{7600}(4497,\cdot)\) \(\chi_{7600}(4513,\cdot)\) \(\chi_{7600}(4753,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{180})$
Fixed field:	Number field defined by a degree 180 polynomial (not computed)

Values on generators

\((4751,5701,5777,401)\) → \((1,1,e\left(\frac{3}{20}\right),e\left(\frac{7}{18}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(21\)	\(23\)	\(27\)	\(29\)
\( \chi_{ 7600 }(33, a) \)	\(1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{41}{45}\right)\)