Basic properties
Modulus: | \(4025\) | |
Conductor: | \(4025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(660\) | 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 4025.dr
\(\chi_{4025}(37,\cdot)\) \(\chi_{4025}(53,\cdot)\) \(\chi_{4025}(67,\cdot)\) \(\chi_{4025}(88,\cdot)\) \(\chi_{4025}(102,\cdot)\) \(\chi_{4025}(158,\cdot)\) \(\chi_{4025}(172,\cdot)\) \(\chi_{4025}(198,\cdot)\) \(\chi_{4025}(212,\cdot)\) \(\chi_{4025}(228,\cdot)\) \(\chi_{4025}(247,\cdot)\) \(\chi_{4025}(263,\cdot)\) \(\chi_{4025}(333,\cdot)\) \(\chi_{4025}(352,\cdot)\) \(\chi_{4025}(373,\cdot)\) \(\chi_{4025}(387,\cdot)\) \(\chi_{4025}(408,\cdot)\) \(\chi_{4025}(452,\cdot)\) \(\chi_{4025}(513,\cdot)\) \(\chi_{4025}(527,\cdot)\) \(\chi_{4025}(548,\cdot)\) \(\chi_{4025}(562,\cdot)\) \(\chi_{4025}(592,\cdot)\) \(\chi_{4025}(613,\cdot)\) \(\chi_{4025}(688,\cdot)\) \(\chi_{4025}(697,\cdot)\) \(\chi_{4025}(723,\cdot)\) \(\chi_{4025}(753,\cdot)\) \(\chi_{4025}(802,\cdot)\) \(\chi_{4025}(842,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{660})$ |
Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{19}{20}\right),e\left(\frac{1}{3}\right),e\left(\frac{19}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(513, a) \) | \(1\) | \(1\) | \(e\left(\frac{227}{660}\right)\) | \(e\left(\frac{529}{660}\right)\) | \(e\left(\frac{227}{330}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{7}{220}\right)\) | \(e\left(\frac{199}{330}\right)\) | \(e\left(\frac{101}{330}\right)\) | \(e\left(\frac{323}{660}\right)\) | \(e\left(\frac{31}{220}\right)\) | \(e\left(\frac{62}{165}\right)\) |