Basic properties
| Modulus: | \(2415\) | |
| Conductor: | \(2415\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | 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 2415.dk
\(\chi_{2415}(2,\cdot)\) \(\chi_{2415}(32,\cdot)\) \(\chi_{2415}(128,\cdot)\) \(\chi_{2415}(233,\cdot)\) \(\chi_{2415}(242,\cdot)\) \(\chi_{2415}(317,\cdot)\) \(\chi_{2415}(338,\cdot)\) \(\chi_{2415}(347,\cdot)\) \(\chi_{2415}(422,\cdot)\) \(\chi_{2415}(443,\cdot)\) \(\chi_{2415}(473,\cdot)\) \(\chi_{2415}(578,\cdot)\) \(\chi_{2415}(653,\cdot)\) \(\chi_{2415}(662,\cdot)\) \(\chi_{2415}(683,\cdot)\) \(\chi_{2415}(767,\cdot)\) \(\chi_{2415}(788,\cdot)\) \(\chi_{2415}(863,\cdot)\) \(\chi_{2415}(947,\cdot)\) \(\chi_{2415}(968,\cdot)\) \(\chi_{2415}(998,\cdot)\) \(\chi_{2415}(1208,\cdot)\) \(\chi_{2415}(1283,\cdot)\) \(\chi_{2415}(1292,\cdot)\) \(\chi_{2415}(1313,\cdot)\) \(\chi_{2415}(1388,\cdot)\) \(\chi_{2415}(1577,\cdot)\) \(\chi_{2415}(1628,\cdot)\) \(\chi_{2415}(1682,\cdot)\) \(\chi_{2415}(1733,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((806,967,346,1891)\) → \((-1,i,e\left(\frac{1}{3}\right),e\left(\frac{1}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(26\) |
| \( \chi_{ 2415 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(i\) | \(e\left(\frac{41}{66}\right)\) |