Basic properties
Modulus: | \(4025\) | |
Conductor: | \(4025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(165\) | 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.dc
\(\chi_{4025}(16,\cdot)\) \(\chi_{4025}(81,\cdot)\) \(\chi_{4025}(121,\cdot)\) \(\chi_{4025}(156,\cdot)\) \(\chi_{4025}(186,\cdot)\) \(\chi_{4025}(256,\cdot)\) \(\chi_{4025}(261,\cdot)\) \(\chi_{4025}(331,\cdot)\) \(\chi_{4025}(361,\cdot)\) \(\chi_{4025}(466,\cdot)\) \(\chi_{4025}(541,\cdot)\) \(\chi_{4025}(606,\cdot)\) \(\chi_{4025}(611,\cdot)\) \(\chi_{4025}(646,\cdot)\) \(\chi_{4025}(716,\cdot)\) \(\chi_{4025}(786,\cdot)\) \(\chi_{4025}(821,\cdot)\) \(\chi_{4025}(886,\cdot)\) \(\chi_{4025}(956,\cdot)\) \(\chi_{4025}(961,\cdot)\) \(\chi_{4025}(991,\cdot)\) \(\chi_{4025}(1061,\cdot)\) \(\chi_{4025}(1066,\cdot)\) \(\chi_{4025}(1131,\cdot)\) \(\chi_{4025}(1136,\cdot)\) \(\chi_{4025}(1166,\cdot)\) \(\chi_{4025}(1271,\cdot)\) \(\chi_{4025}(1306,\cdot)\) \(\chi_{4025}(1346,\cdot)\) \(\chi_{4025}(1411,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{2}{3}\right),e\left(\frac{4}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(1166, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{165}\right)\) | \(e\left(\frac{146}{165}\right)\) | \(e\left(\frac{86}{165}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{23}{165}\right)\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{7}{165}\right)\) |