Basic properties
Modulus: | \(4031\) | |
Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(483\) | 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 4031.bo
\(\chi_{4031}(7,\cdot)\) \(\chi_{4031}(16,\cdot)\) \(\chi_{4031}(20,\cdot)\) \(\chi_{4031}(24,\cdot)\) \(\chi_{4031}(25,\cdot)\) \(\chi_{4031}(49,\cdot)\) \(\chi_{4031}(54,\cdot)\) \(\chi_{4031}(78,\cdot)\) \(\chi_{4031}(81,\cdot)\) \(\chi_{4031}(83,\cdot)\) \(\chi_{4031}(107,\cdot)\) \(\chi_{4031}(136,\cdot)\) \(\chi_{4031}(152,\cdot)\) \(\chi_{4031}(168,\cdot)\) \(\chi_{4031}(169,\cdot)\) \(\chi_{4031}(170,\cdot)\) \(\chi_{4031}(190,\cdot)\) \(\chi_{4031}(210,\cdot)\) \(\chi_{4031}(228,\cdot)\) \(\chi_{4031}(252,\cdot)\) \(\chi_{4031}(256,\cdot)\) \(\chi_{4031}(257,\cdot)\) \(\chi_{4031}(285,\cdot)\) \(\chi_{4031}(306,\cdot)\) \(\chi_{4031}(313,\cdot)\) \(\chi_{4031}(315,\cdot)\) \(\chi_{4031}(344,\cdot)\) \(\chi_{4031}(364,\cdot)\) \(\chi_{4031}(400,\cdot)\) \(\chi_{4031}(402,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{483})$ |
Fixed field: | Number field defined by a degree 483 polynomial (not computed) |
Values on generators
\((3337,697)\) → \((e\left(\frac{5}{7}\right),e\left(\frac{68}{69}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4031 }(313, a) \) | \(1\) | \(1\) | \(e\left(\frac{338}{483}\right)\) | \(e\left(\frac{472}{483}\right)\) | \(e\left(\frac{193}{483}\right)\) | \(e\left(\frac{226}{483}\right)\) | \(e\left(\frac{109}{161}\right)\) | \(e\left(\frac{409}{483}\right)\) | \(e\left(\frac{16}{161}\right)\) | \(e\left(\frac{461}{483}\right)\) | \(e\left(\frac{27}{161}\right)\) | \(e\left(\frac{365}{483}\right)\) |