Dirichlet character \(\chi_{16830}(11173,\cdot)\)

• Label: 16830.11173
• Modulus: $16830$
• Conductor: $8415$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(16830\)
Conductor:	\(8415\)
Order:	\(60\)
Real:	no
Primitive:	no, induced from \(\chi_{8415}(2758,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 16830.il

\(\chi_{16830}(1993,\cdot)\) \(\chi_{16830}(2257,\cdot)\) \(\chi_{16830}(2767,\cdot)\) \(\chi_{16830}(4297,\cdot)\) \(\chi_{16830}(5827,\cdot)\) \(\chi_{16830}(7603,\cdot)\) \(\chi_{16830}(8113,\cdot)\) \(\chi_{16830}(8377,\cdot)\) \(\chi_{16830}(9643,\cdot)\) \(\chi_{16830}(9907,\cdot)\) \(\chi_{16830}(11173,\cdot)\) \(\chi_{16830}(11437,\cdot)\) \(\chi_{16830}(13477,\cdot)\) \(\chi_{16830}(13723,\cdot)\) \(\chi_{16830}(15253,\cdot)\) \(\chi_{16830}(16783,\cdot)\)

Related number fields

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

Values on generators

\((7481,3367,1531,8911)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{3}{10}\right),-i)\)

First values

\(a\)	\(-1\)	\(1\)	\(7\)	\(13\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\( \chi_{ 16830 }(11173, a) \)	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{60}\right)\)