Basic properties
Modulus: | \(4725\) | |
Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | 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 4725.hj
\(\chi_{4725}(23,\cdot)\) \(\chi_{4725}(137,\cdot)\) \(\chi_{4725}(212,\cdot)\) \(\chi_{4725}(263,\cdot)\) \(\chi_{4725}(338,\cdot)\) \(\chi_{4725}(452,\cdot)\) \(\chi_{4725}(527,\cdot)\) \(\chi_{4725}(578,\cdot)\) \(\chi_{4725}(653,\cdot)\) \(\chi_{4725}(767,\cdot)\) \(\chi_{4725}(842,\cdot)\) \(\chi_{4725}(1208,\cdot)\) \(\chi_{4725}(1283,\cdot)\) \(\chi_{4725}(1397,\cdot)\) \(\chi_{4725}(1472,\cdot)\) \(\chi_{4725}(1523,\cdot)\) \(\chi_{4725}(1598,\cdot)\) \(\chi_{4725}(1712,\cdot)\) \(\chi_{4725}(1787,\cdot)\) \(\chi_{4725}(1838,\cdot)\) \(\chi_{4725}(1913,\cdot)\) \(\chi_{4725}(2027,\cdot)\) \(\chi_{4725}(2102,\cdot)\) \(\chi_{4725}(2153,\cdot)\) \(\chi_{4725}(2228,\cdot)\) \(\chi_{4725}(2342,\cdot)\) \(\chi_{4725}(2417,\cdot)\) \(\chi_{4725}(2783,\cdot)\) \(\chi_{4725}(2858,\cdot)\) \(\chi_{4725}(2972,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{9}{20}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 4725 }(1712, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{59}{180}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{137}{180}\right)\) | \(e\left(\frac{41}{180}\right)\) |