Basic properties
| Modulus: | \(4025\) | |
| Conductor: | \(4025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(660\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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.dq
\(\chi_{4025}(2,\cdot)\) \(\chi_{4025}(58,\cdot)\) \(\chi_{4025}(72,\cdot)\) \(\chi_{4025}(123,\cdot)\) \(\chi_{4025}(128,\cdot)\) \(\chi_{4025}(142,\cdot)\) \(\chi_{4025}(163,\cdot)\) \(\chi_{4025}(177,\cdot)\) \(\chi_{4025}(233,\cdot)\) \(\chi_{4025}(242,\cdot)\) \(\chi_{4025}(303,\cdot)\) \(\chi_{4025}(312,\cdot)\) \(\chi_{4025}(317,\cdot)\) \(\chi_{4025}(338,\cdot)\) \(\chi_{4025}(347,\cdot)\) \(\chi_{4025}(403,\cdot)\) \(\chi_{4025}(417,\cdot)\) \(\chi_{4025}(422,\cdot)\) \(\chi_{4025}(473,\cdot)\) \(\chi_{4025}(478,\cdot)\) \(\chi_{4025}(487,\cdot)\) \(\chi_{4025}(492,\cdot)\) \(\chi_{4025}(508,\cdot)\) \(\chi_{4025}(522,\cdot)\) \(\chi_{4025}(578,\cdot)\) \(\chi_{4025}(583,\cdot)\) \(\chi_{4025}(627,\cdot)\) \(\chi_{4025}(648,\cdot)\) \(\chi_{4025}(653,\cdot)\) \(\chi_{4025}(662,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{660})$ |
| Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{3}{20}\right),e\left(\frac{1}{3}\right),e\left(\frac{10}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 4025 }(58, a) \) | \(-1\) | \(1\) | \(e\left(\frac{419}{660}\right)\) | \(e\left(\frac{613}{660}\right)\) | \(e\left(\frac{89}{330}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{199}{220}\right)\) | \(e\left(\frac{283}{330}\right)\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{131}{660}\right)\) | \(e\left(\frac{127}{220}\right)\) | \(e\left(\frac{89}{165}\right)\) |