Basic properties
Modulus: | \(5415\) | |
Conductor: | \(1805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1805}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5415.bz
\(\chi_{5415}(49,\cdot)\) \(\chi_{5415}(64,\cdot)\) \(\chi_{5415}(334,\cdot)\) \(\chi_{5415}(349,\cdot)\) \(\chi_{5415}(619,\cdot)\) \(\chi_{5415}(634,\cdot)\) \(\chi_{5415}(904,\cdot)\) \(\chi_{5415}(919,\cdot)\) \(\chi_{5415}(1189,\cdot)\) \(\chi_{5415}(1204,\cdot)\) \(\chi_{5415}(1474,\cdot)\) \(\chi_{5415}(1489,\cdot)\) \(\chi_{5415}(1759,\cdot)\) \(\chi_{5415}(1774,\cdot)\) \(\chi_{5415}(2044,\cdot)\) \(\chi_{5415}(2059,\cdot)\) \(\chi_{5415}(2329,\cdot)\) \(\chi_{5415}(2344,\cdot)\) \(\chi_{5415}(2614,\cdot)\) \(\chi_{5415}(2629,\cdot)\) \(\chi_{5415}(2899,\cdot)\) \(\chi_{5415}(2914,\cdot)\) \(\chi_{5415}(3184,\cdot)\) \(\chi_{5415}(3199,\cdot)\) \(\chi_{5415}(3469,\cdot)\) \(\chi_{5415}(3484,\cdot)\) \(\chi_{5415}(3754,\cdot)\) \(\chi_{5415}(3769,\cdot)\) \(\chi_{5415}(4054,\cdot)\) \(\chi_{5415}(4324,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3611,2167,5056)\) → \((1,-1,e\left(\frac{50}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
\( \chi_{ 5415 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{97}{114}\right)\) |