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
\(2\) → \(e\left(\frac{21}{97}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 389 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{97}\right)\) | \(e\left(\frac{65}{97}\right)\) | \(e\left(\frac{42}{97}\right)\) | \(e\left(\frac{18}{97}\right)\) | \(e\left(\frac{86}{97}\right)\) | \(e\left(\frac{1}{97}\right)\) | \(e\left(\frac{63}{97}\right)\) | \(e\left(\frac{33}{97}\right)\) | \(e\left(\frac{39}{97}\right)\) | \(e\left(\frac{23}{97}\right)\) |