Basic properties
Modulus: | \(643\) | |
Conductor: | \(643\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(107\) | 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.e
\(\chi_{643}(4,\cdot)\) \(\chi_{643}(6,\cdot)\) \(\chi_{643}(9,\cdot)\) \(\chi_{643}(10,\cdot)\) \(\chi_{643}(15,\cdot)\) \(\chi_{643}(16,\cdot)\) \(\chi_{643}(24,\cdot)\) \(\chi_{643}(25,\cdot)\) \(\chi_{643}(36,\cdot)\) \(\chi_{643}(40,\cdot)\) \(\chi_{643}(54,\cdot)\) \(\chi_{643}(60,\cdot)\) \(\chi_{643}(64,\cdot)\) \(\chi_{643}(81,\cdot)\) \(\chi_{643}(86,\cdot)\) \(\chi_{643}(90,\cdot)\) \(\chi_{643}(96,\cdot)\) \(\chi_{643}(100,\cdot)\) \(\chi_{643}(129,\cdot)\) \(\chi_{643}(131,\cdot)\) \(\chi_{643}(134,\cdot)\) \(\chi_{643}(135,\cdot)\) \(\chi_{643}(142,\cdot)\) \(\chi_{643}(143,\cdot)\) \(\chi_{643}(144,\cdot)\) \(\chi_{643}(150,\cdot)\) \(\chi_{643}(154,\cdot)\) \(\chi_{643}(160,\cdot)\) \(\chi_{643}(161,\cdot)\) \(\chi_{643}(163,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{107})$ |
Fixed field: | Number field defined by a degree 107 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{44}{107}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 643 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{30}{107}\right)\) | \(e\left(\frac{7}{107}\right)\) | \(e\left(\frac{60}{107}\right)\) | \(e\left(\frac{11}{107}\right)\) | \(e\left(\frac{37}{107}\right)\) | \(e\left(\frac{101}{107}\right)\) | \(e\left(\frac{90}{107}\right)\) | \(e\left(\frac{14}{107}\right)\) | \(e\left(\frac{41}{107}\right)\) | \(e\left(\frac{44}{107}\right)\) |