Basic properties
Modulus: | \(643\) | |
Conductor: | \(643\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(642\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 643.h
\(\chi_{643}(11,\cdot)\) \(\chi_{643}(13,\cdot)\) \(\chi_{643}(14,\cdot)\) \(\chi_{643}(17,\cdot)\) \(\chi_{643}(19,\cdot)\) \(\chi_{643}(21,\cdot)\) \(\chi_{643}(35,\cdot)\) \(\chi_{643}(37,\cdot)\) \(\chi_{643}(41,\cdot)\) \(\chi_{643}(44,\cdot)\) \(\chi_{643}(46,\cdot)\) \(\chi_{643}(47,\cdot)\) \(\chi_{643}(52,\cdot)\) \(\chi_{643}(56,\cdot)\) \(\chi_{643}(58,\cdot)\) \(\chi_{643}(59,\cdot)\) \(\chi_{643}(61,\cdot)\) \(\chi_{643}(62,\cdot)\) \(\chi_{643}(66,\cdot)\) \(\chi_{643}(68,\cdot)\) \(\chi_{643}(69,\cdot)\) \(\chi_{643}(73,\cdot)\) \(\chi_{643}(76,\cdot)\) \(\chi_{643}(78,\cdot)\) \(\chi_{643}(79,\cdot)\) \(\chi_{643}(84,\cdot)\) \(\chi_{643}(87,\cdot)\) \(\chi_{643}(91,\cdot)\) \(\chi_{643}(93,\cdot)\) \(\chi_{643}(98,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{321})$ |
Fixed field: | Number field defined by a degree 642 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{61}{642}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 643 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{214}\right)\) | \(e\left(\frac{77}{214}\right)\) | \(e\left(\frac{9}{107}\right)\) | \(e\left(\frac{121}{214}\right)\) | \(e\left(\frac{43}{107}\right)\) | \(e\left(\frac{115}{321}\right)\) | \(e\left(\frac{27}{214}\right)\) | \(e\left(\frac{77}{107}\right)\) | \(e\left(\frac{65}{107}\right)\) | \(e\left(\frac{61}{642}\right)\) |