Basic properties
Modulus: | \(607\) | |
Conductor: | \(607\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(303\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 607.g
\(\chi_{607}(2,\cdot)\) \(\chi_{607}(4,\cdot)\) \(\chi_{607}(9,\cdot)\) \(\chi_{607}(11,\cdot)\) \(\chi_{607}(13,\cdot)\) \(\chi_{607}(14,\cdot)\) \(\chi_{607}(15,\cdot)\) \(\chi_{607}(16,\cdot)\) \(\chi_{607}(18,\cdot)\) \(\chi_{607}(19,\cdot)\) \(\chi_{607}(22,\cdot)\) \(\chi_{607}(25,\cdot)\) \(\chi_{607}(28,\cdot)\) \(\chi_{607}(30,\cdot)\) \(\chi_{607}(32,\cdot)\) \(\chi_{607}(38,\cdot)\) \(\chi_{607}(41,\cdot)\) \(\chi_{607}(43,\cdot)\) \(\chi_{607}(50,\cdot)\) \(\chi_{607}(51,\cdot)\) \(\chi_{607}(52,\cdot)\) \(\chi_{607}(53,\cdot)\) \(\chi_{607}(61,\cdot)\) \(\chi_{607}(63,\cdot)\) \(\chi_{607}(71,\cdot)\) \(\chi_{607}(72,\cdot)\) \(\chi_{607}(73,\cdot)\) \(\chi_{607}(77,\cdot)\) \(\chi_{607}(79,\cdot)\) \(\chi_{607}(81,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{303})$ |
Fixed field: | Number field defined by a degree 303 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{259}{303}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 607 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{303}\right)\) | \(e\left(\frac{259}{303}\right)\) | \(e\left(\frac{118}{303}\right)\) | \(e\left(\frac{220}{303}\right)\) | \(e\left(\frac{5}{101}\right)\) | \(e\left(\frac{90}{101}\right)\) | \(e\left(\frac{59}{101}\right)\) | \(e\left(\frac{215}{303}\right)\) | \(e\left(\frac{93}{101}\right)\) | \(e\left(\frac{71}{303}\right)\) |