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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4025.dj
\(\chi_{4025}(61,\cdot)\) \(\chi_{4025}(66,\cdot)\) \(\chi_{4025}(136,\cdot)\) \(\chi_{4025}(166,\cdot)\) \(\chi_{4025}(171,\cdot)\) \(\chi_{4025}(241,\cdot)\) \(\chi_{4025}(306,\cdot)\) \(\chi_{4025}(341,\cdot)\) \(\chi_{4025}(411,\cdot)\) \(\chi_{4025}(481,\cdot)\) \(\chi_{4025}(516,\cdot)\) \(\chi_{4025}(521,\cdot)\) \(\chi_{4025}(586,\cdot)\) \(\chi_{4025}(661,\cdot)\) \(\chi_{4025}(766,\cdot)\) \(\chi_{4025}(796,\cdot)\) \(\chi_{4025}(866,\cdot)\) \(\chi_{4025}(871,\cdot)\) \(\chi_{4025}(941,\cdot)\) \(\chi_{4025}(971,\cdot)\) \(\chi_{4025}(1006,\cdot)\) \(\chi_{4025}(1046,\cdot)\) \(\chi_{4025}(1111,\cdot)\) \(\chi_{4025}(1146,\cdot)\) \(\chi_{4025}(1216,\cdot)\) \(\chi_{4025}(1256,\cdot)\) \(\chi_{4025}(1286,\cdot)\) \(\chi_{4025}(1321,\cdot)\) \(\chi_{4025}(1391,\cdot)\) \(\chi_{4025}(1431,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{5}{6}\right),e\left(\frac{1}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(971, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{165}\right)\) | \(e\left(\frac{251}{330}\right)\) | \(e\left(\frac{118}{165}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{86}{165}\right)\) | \(e\left(\frac{113}{330}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{71}{165}\right)\) |