Basic properties
Modulus: | \(4025\) | |
Conductor: | \(4025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | 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 4025.dh
\(\chi_{4025}(11,\cdot)\) \(\chi_{4025}(86,\cdot)\) \(\chi_{4025}(191,\cdot)\) \(\chi_{4025}(221,\cdot)\) \(\chi_{4025}(291,\cdot)\) \(\chi_{4025}(296,\cdot)\) \(\chi_{4025}(366,\cdot)\) \(\chi_{4025}(396,\cdot)\) \(\chi_{4025}(431,\cdot)\) \(\chi_{4025}(471,\cdot)\) \(\chi_{4025}(536,\cdot)\) \(\chi_{4025}(571,\cdot)\) \(\chi_{4025}(641,\cdot)\) \(\chi_{4025}(681,\cdot)\) \(\chi_{4025}(711,\cdot)\) \(\chi_{4025}(746,\cdot)\) \(\chi_{4025}(816,\cdot)\) \(\chi_{4025}(856,\cdot)\) \(\chi_{4025}(891,\cdot)\) \(\chi_{4025}(996,\cdot)\) \(\chi_{4025}(1031,\cdot)\) \(\chi_{4025}(1096,\cdot)\) \(\chi_{4025}(1171,\cdot)\) \(\chi_{4025}(1206,\cdot)\) \(\chi_{4025}(1236,\cdot)\) \(\chi_{4025}(1341,\cdot)\) \(\chi_{4025}(1446,\cdot)\) \(\chi_{4025}(1486,\cdot)\) \(\chi_{4025}(1516,\cdot)\) \(\chi_{4025}(1556,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{1}{3}\right),e\left(\frac{15}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(1031, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{165}\right)\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{142}{165}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{287}{330}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{119}{165}\right)\) |