Basic properties
| Modulus: | \(81225\) | |
| Conductor: | \(81225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 81225.ne
\(\chi_{81225}(322,\cdot)\) \(\chi_{81225}(778,\cdot)\) \(\chi_{81225}(1177,\cdot)\) \(\chi_{81225}(1348,\cdot)\) \(\chi_{81225}(1462,\cdot)\) \(\chi_{81225}(1633,\cdot)\) \(\chi_{81225}(2203,\cdot)\) \(\chi_{81225}(2317,\cdot)\) \(\chi_{81225}(2488,\cdot)\) \(\chi_{81225}(3058,\cdot)\) \(\chi_{81225}(3172,\cdot)\) \(\chi_{81225}(3742,\cdot)\) \(\chi_{81225}(3913,\cdot)\) \(\chi_{81225}(4027,\cdot)\) \(\chi_{81225}(4198,\cdot)\) \(\chi_{81225}(4597,\cdot)\) \(\chi_{81225}(5452,\cdot)\) \(\chi_{81225}(5623,\cdot)\) \(\chi_{81225}(5737,\cdot)\) \(\chi_{81225}(5908,\cdot)\) \(\chi_{81225}(6478,\cdot)\) \(\chi_{81225}(6592,\cdot)\) \(\chi_{81225}(6763,\cdot)\) \(\chi_{81225}(7162,\cdot)\) \(\chi_{81225}(7333,\cdot)\) \(\chi_{81225}(7447,\cdot)\) \(\chi_{81225}(8017,\cdot)\) \(\chi_{81225}(8188,\cdot)\) \(\chi_{81225}(8473,\cdot)\) \(\chi_{81225}(8872,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1140})$ |
| Fixed field: | Number field defined by a degree 1140 polynomial (not computed) |
Values on generators
\((36101,77977,48376)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{19}{20}\right),e\left(\frac{23}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 81225 }(8188, a) \) | \(1\) | \(1\) | \(e\left(\frac{253}{1140}\right)\) | \(e\left(\frac{253}{570}\right)\) | \(e\left(\frac{47}{228}\right)\) | \(e\left(\frac{253}{380}\right)\) | \(e\left(\frac{172}{285}\right)\) | \(e\left(\frac{587}{1140}\right)\) | \(e\left(\frac{122}{285}\right)\) | \(e\left(\frac{253}{285}\right)\) | \(e\left(\frac{53}{380}\right)\) | \(e\left(\frac{941}{1140}\right)\) |