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.di
\(\chi_{4025}(31,\cdot)\) \(\chi_{4025}(96,\cdot)\) \(\chi_{4025}(131,\cdot)\) \(\chi_{4025}(236,\cdot)\) \(\chi_{4025}(271,\cdot)\) \(\chi_{4025}(311,\cdot)\) \(\chi_{4025}(381,\cdot)\) \(\chi_{4025}(416,\cdot)\) \(\chi_{4025}(446,\cdot)\) \(\chi_{4025}(486,\cdot)\) \(\chi_{4025}(556,\cdot)\) \(\chi_{4025}(591,\cdot)\) \(\chi_{4025}(656,\cdot)\) \(\chi_{4025}(696,\cdot)\) \(\chi_{4025}(731,\cdot)\) \(\chi_{4025}(761,\cdot)\) \(\chi_{4025}(831,\cdot)\) \(\chi_{4025}(836,\cdot)\) \(\chi_{4025}(906,\cdot)\) \(\chi_{4025}(936,\cdot)\) \(\chi_{4025}(1041,\cdot)\) \(\chi_{4025}(1116,\cdot)\) \(\chi_{4025}(1181,\cdot)\) \(\chi_{4025}(1186,\cdot)\) \(\chi_{4025}(1221,\cdot)\) \(\chi_{4025}(1291,\cdot)\) \(\chi_{4025}(1361,\cdot)\) \(\chi_{4025}(1396,\cdot)\) \(\chi_{4025}(1461,\cdot)\) \(\chi_{4025}(1531,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{1}{6}\right),e\left(\frac{9}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(696, a) \) | \(-1\) | \(1\) | \(e\left(\frac{94}{165}\right)\) | \(e\left(\frac{151}{330}\right)\) | \(e\left(\frac{23}{165}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{197}{330}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{46}{165}\right)\) |