Basic properties
| Modulus: | \(5415\) | |
| Conductor: | \(5415\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | 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 5415.ca
\(\chi_{5415}(164,\cdot)\) \(\chi_{5415}(179,\cdot)\) \(\chi_{5415}(449,\cdot)\) \(\chi_{5415}(464,\cdot)\) \(\chi_{5415}(734,\cdot)\) \(\chi_{5415}(749,\cdot)\) \(\chi_{5415}(1019,\cdot)\) \(\chi_{5415}(1034,\cdot)\) \(\chi_{5415}(1304,\cdot)\) \(\chi_{5415}(1319,\cdot)\) \(\chi_{5415}(1589,\cdot)\) \(\chi_{5415}(1604,\cdot)\) \(\chi_{5415}(1889,\cdot)\) \(\chi_{5415}(2159,\cdot)\) \(\chi_{5415}(2174,\cdot)\) \(\chi_{5415}(2444,\cdot)\) \(\chi_{5415}(2729,\cdot)\) \(\chi_{5415}(2744,\cdot)\) \(\chi_{5415}(3014,\cdot)\) \(\chi_{5415}(3029,\cdot)\) \(\chi_{5415}(3299,\cdot)\) \(\chi_{5415}(3314,\cdot)\) \(\chi_{5415}(3584,\cdot)\) \(\chi_{5415}(3599,\cdot)\) \(\chi_{5415}(3869,\cdot)\) \(\chi_{5415}(3884,\cdot)\) \(\chi_{5415}(4154,\cdot)\) \(\chi_{5415}(4169,\cdot)\) \(\chi_{5415}(4439,\cdot)\) \(\chi_{5415}(4454,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3611,2167,5056)\) → \((-1,-1,e\left(\frac{23}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 5415 }(164, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{114}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{16}{57}\right)\) |