Basic properties
| Modulus: | \(389\) | |
| Conductor: | \(389\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(97\) | 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 389.d
\(\chi_{389}(5,\cdot)\) \(\chi_{389}(6,\cdot)\) \(\chi_{389}(7,\cdot)\) \(\chi_{389}(11,\cdot)\) \(\chi_{389}(13,\cdot)\) \(\chi_{389}(16,\cdot)\) \(\chi_{389}(17,\cdot)\) \(\chi_{389}(25,\cdot)\) \(\chi_{389}(30,\cdot)\) \(\chi_{389}(35,\cdot)\) \(\chi_{389}(36,\cdot)\) \(\chi_{389}(42,\cdot)\) \(\chi_{389}(49,\cdot)\) \(\chi_{389}(55,\cdot)\) \(\chi_{389}(58,\cdot)\) \(\chi_{389}(65,\cdot)\) \(\chi_{389}(66,\cdot)\) \(\chi_{389}(67,\cdot)\) \(\chi_{389}(69,\cdot)\) \(\chi_{389}(73,\cdot)\) \(\chi_{389}(74,\cdot)\) \(\chi_{389}(76,\cdot)\) \(\chi_{389}(77,\cdot)\) \(\chi_{389}(78,\cdot)\) \(\chi_{389}(79,\cdot)\) \(\chi_{389}(80,\cdot)\) \(\chi_{389}(81,\cdot)\) \(\chi_{389}(85,\cdot)\) \(\chi_{389}(91,\cdot)\) \(\chi_{389}(93,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{97})$ |
| Fixed field: | Number field defined by a degree 97 polynomial |
Values on generators
\(2\) → \(e\left(\frac{22}{97}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 389 }(80, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{97}\right)\) | \(e\left(\frac{45}{97}\right)\) | \(e\left(\frac{44}{97}\right)\) | \(e\left(\frac{5}{97}\right)\) | \(e\left(\frac{67}{97}\right)\) | \(e\left(\frac{38}{97}\right)\) | \(e\left(\frac{66}{97}\right)\) | \(e\left(\frac{90}{97}\right)\) | \(e\left(\frac{27}{97}\right)\) | \(e\left(\frac{1}{97}\right)\) |