Basic properties
Modulus: | \(643\) | |
Conductor: | \(643\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(321\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 643.g
\(\chi_{643}(7,\cdot)\) \(\chi_{643}(22,\cdot)\) \(\chi_{643}(23,\cdot)\) \(\chi_{643}(26,\cdot)\) \(\chi_{643}(28,\cdot)\) \(\chi_{643}(29,\cdot)\) \(\chi_{643}(31,\cdot)\) \(\chi_{643}(33,\cdot)\) \(\chi_{643}(34,\cdot)\) \(\chi_{643}(38,\cdot)\) \(\chi_{643}(39,\cdot)\) \(\chi_{643}(42,\cdot)\) \(\chi_{643}(49,\cdot)\) \(\chi_{643}(51,\cdot)\) \(\chi_{643}(53,\cdot)\) \(\chi_{643}(55,\cdot)\) \(\chi_{643}(57,\cdot)\) \(\chi_{643}(63,\cdot)\) \(\chi_{643}(65,\cdot)\) \(\chi_{643}(70,\cdot)\) \(\chi_{643}(74,\cdot)\) \(\chi_{643}(82,\cdot)\) \(\chi_{643}(83,\cdot)\) \(\chi_{643}(85,\cdot)\) \(\chi_{643}(88,\cdot)\) \(\chi_{643}(89,\cdot)\) \(\chi_{643}(92,\cdot)\) \(\chi_{643}(94,\cdot)\) \(\chi_{643}(95,\cdot)\) \(\chi_{643}(97,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{321})$ |
Fixed field: | Number field defined by a degree 321 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{56}{321}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 643 }(92, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{107}\right)\) | \(e\left(\frac{97}{107}\right)\) | \(e\left(\frac{6}{107}\right)\) | \(e\left(\frac{76}{107}\right)\) | \(e\left(\frac{100}{107}\right)\) | \(e\left(\frac{148}{321}\right)\) | \(e\left(\frac{9}{107}\right)\) | \(e\left(\frac{87}{107}\right)\) | \(e\left(\frac{79}{107}\right)\) | \(e\left(\frac{56}{321}\right)\) |