Basic properties
| Modulus: | \(389\) | |
| Conductor: | \(389\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(194\) | 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.e
\(\chi_{389}(4,\cdot)\) \(\chi_{389}(9,\cdot)\) \(\chi_{389}(19,\cdot)\) \(\chi_{389}(20,\cdot)\) \(\chi_{389}(24,\cdot)\) \(\chi_{389}(28,\cdot)\) \(\chi_{389}(41,\cdot)\) \(\chi_{389}(44,\cdot)\) \(\chi_{389}(45,\cdot)\) \(\chi_{389}(46,\cdot)\) \(\chi_{389}(52,\cdot)\) \(\chi_{389}(54,\cdot)\) \(\chi_{389}(59,\cdot)\) \(\chi_{389}(62,\cdot)\) \(\chi_{389}(63,\cdot)\) \(\chi_{389}(64,\cdot)\) \(\chi_{389}(68,\cdot)\) \(\chi_{389}(86,\cdot)\) \(\chi_{389}(87,\cdot)\) \(\chi_{389}(95,\cdot)\) \(\chi_{389}(99,\cdot)\) \(\chi_{389}(100,\cdot)\) \(\chi_{389}(106,\cdot)\) \(\chi_{389}(111,\cdot)\) \(\chi_{389}(114,\cdot)\) \(\chi_{389}(117,\cdot)\) \(\chi_{389}(120,\cdot)\) \(\chi_{389}(127,\cdot)\) \(\chi_{389}(133,\cdot)\) \(\chi_{389}(137,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{97})$ |
| Fixed field: | Number field defined by a degree 194 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{77}{194}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 389 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{194}\right)\) | \(e\left(\frac{109}{194}\right)\) | \(e\left(\frac{77}{97}\right)\) | \(e\left(\frac{33}{97}\right)\) | \(e\left(\frac{93}{97}\right)\) | \(e\left(\frac{18}{97}\right)\) | \(e\left(\frac{37}{194}\right)\) | \(e\left(\frac{12}{97}\right)\) | \(e\left(\frac{143}{194}\right)\) | \(e\left(\frac{26}{97}\right)\) |