Basic properties
Modulus: | \(463\) | |
Conductor: | \(463\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(77\) | 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 463.m
\(\chi_{463}(8,\cdot)\) \(\chi_{463}(18,\cdot)\) \(\chi_{463}(47,\cdot)\) \(\chi_{463}(49,\cdot)\) \(\chi_{463}(57,\cdot)\) \(\chi_{463}(58,\cdot)\) \(\chi_{463}(64,\cdot)\) \(\chi_{463}(65,\cdot)\) \(\chi_{463}(66,\cdot)\) \(\chi_{463}(70,\cdot)\) \(\chi_{463}(78,\cdot)\) \(\chi_{463}(84,\cdot)\) \(\chi_{463}(86,\cdot)\) \(\chi_{463}(97,\cdot)\) \(\chi_{463}(100,\cdot)\) \(\chi_{463}(111,\cdot)\) \(\chi_{463}(120,\cdot)\) \(\chi_{463}(123,\cdot)\) \(\chi_{463}(124,\cdot)\) \(\chi_{463}(144,\cdot)\) \(\chi_{463}(146,\cdot)\) \(\chi_{463}(149,\cdot)\) \(\chi_{463}(159,\cdot)\) \(\chi_{463}(161,\cdot)\) \(\chi_{463}(189,\cdot)\) \(\chi_{463}(209,\cdot)\) \(\chi_{463}(226,\cdot)\) \(\chi_{463}(242,\cdot)\) \(\chi_{463}(244,\cdot)\) \(\chi_{463}(262,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 77 polynomial |
Values on generators
\(3\) → \(e\left(\frac{54}{77}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 463 }(209, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{54}{77}\right)\) | \(e\left(\frac{53}{77}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{23}{77}\right)\) | \(e\left(\frac{41}{77}\right)\) | \(e\left(\frac{31}{77}\right)\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{12}{77}\right)\) |