Basic properties
Modulus: | \(4504\) | |
Conductor: | \(4504\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(562\) | 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 4504.l
\(\chi_{4504}(3,\cdot)\) \(\chi_{4504}(11,\cdot)\) \(\chi_{4504}(19,\cdot)\) \(\chi_{4504}(27,\cdot)\) \(\chi_{4504}(51,\cdot)\) \(\chi_{4504}(59,\cdot)\) \(\chi_{4504}(67,\cdot)\) \(\chi_{4504}(75,\cdot)\) \(\chi_{4504}(91,\cdot)\) \(\chi_{4504}(99,\cdot)\) \(\chi_{4504}(107,\cdot)\) \(\chi_{4504}(147,\cdot)\) \(\chi_{4504}(155,\cdot)\) \(\chi_{4504}(171,\cdot)\) \(\chi_{4504}(179,\cdot)\) \(\chi_{4504}(187,\cdot)\) \(\chi_{4504}(211,\cdot)\) \(\chi_{4504}(243,\cdot)\) \(\chi_{4504}(251,\cdot)\) \(\chi_{4504}(275,\cdot)\) \(\chi_{4504}(299,\cdot)\) \(\chi_{4504}(323,\cdot)\) \(\chi_{4504}(339,\cdot)\) \(\chi_{4504}(347,\cdot)\) \(\chi_{4504}(363,\cdot)\) \(\chi_{4504}(379,\cdot)\) \(\chi_{4504}(395,\cdot)\) \(\chi_{4504}(411,\cdot)\) \(\chi_{4504}(427,\cdot)\) \(\chi_{4504}(435,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{281})$ |
Fixed field: | Number field defined by a degree 562 polynomial (not computed) |
Values on generators
\((1127,2253,2817)\) → \((-1,-1,e\left(\frac{149}{281}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 4504 }(107, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{281}\right)\) | \(e\left(\frac{269}{562}\right)\) | \(e\left(\frac{243}{562}\right)\) | \(e\left(\frac{18}{281}\right)\) | \(e\left(\frac{213}{281}\right)\) | \(e\left(\frac{419}{562}\right)\) | \(e\left(\frac{287}{562}\right)\) | \(e\left(\frac{208}{281}\right)\) | \(e\left(\frac{110}{281}\right)\) | \(e\left(\frac{261}{562}\right)\) |