Basic properties
Modulus: | \(619\) | |
Conductor: | \(619\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(206\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 619.f
\(\chi_{619}(3,\cdot)\) \(\chi_{619}(8,\cdot)\) \(\chi_{619}(13,\cdot)\) \(\chi_{619}(14,\cdot)\) \(\chi_{619}(17,\cdot)\) \(\chi_{619}(27,\cdot)\) \(\chi_{619}(29,\cdot)\) \(\chi_{619}(43,\cdot)\) \(\chi_{619}(44,\cdot)\) \(\chi_{619}(47,\cdot)\) \(\chi_{619}(50,\cdot)\) \(\chi_{619}(60,\cdot)\) \(\chi_{619}(72,\cdot)\) \(\chi_{619}(74,\cdot)\) \(\chi_{619}(77,\cdot)\) \(\chi_{619}(93,\cdot)\) \(\chi_{619}(95,\cdot)\) \(\chi_{619}(105,\cdot)\) \(\chi_{619}(113,\cdot)\) \(\chi_{619}(114,\cdot)\) \(\chi_{619}(117,\cdot)\) \(\chi_{619}(126,\cdot)\) \(\chi_{619}(139,\cdot)\) \(\chi_{619}(153,\cdot)\) \(\chi_{619}(160,\cdot)\) \(\chi_{619}(192,\cdot)\) \(\chi_{619}(202,\cdot)\) \(\chi_{619}(213,\cdot)\) \(\chi_{619}(218,\cdot)\) \(\chi_{619}(219,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{103})$ |
Fixed field: | Number field defined by a degree 206 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{101}{206}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 619 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{206}\right)\) | \(e\left(\frac{159}{206}\right)\) | \(e\left(\frac{101}{103}\right)\) | \(e\left(\frac{84}{103}\right)\) | \(e\left(\frac{27}{103}\right)\) | \(e\left(\frac{49}{103}\right)\) | \(e\left(\frac{97}{206}\right)\) | \(e\left(\frac{56}{103}\right)\) | \(e\left(\frac{63}{206}\right)\) | \(e\left(\frac{67}{206}\right)\) |