Basic properties
Modulus: | \(2888\) | |
Conductor: | \(2888\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2888.bm
\(\chi_{2888}(11,\cdot)\) \(\chi_{2888}(83,\cdot)\) \(\chi_{2888}(163,\cdot)\) \(\chi_{2888}(235,\cdot)\) \(\chi_{2888}(315,\cdot)\) \(\chi_{2888}(387,\cdot)\) \(\chi_{2888}(467,\cdot)\) \(\chi_{2888}(539,\cdot)\) \(\chi_{2888}(619,\cdot)\) \(\chi_{2888}(691,\cdot)\) \(\chi_{2888}(771,\cdot)\) \(\chi_{2888}(843,\cdot)\) \(\chi_{2888}(923,\cdot)\) \(\chi_{2888}(995,\cdot)\) \(\chi_{2888}(1075,\cdot)\) \(\chi_{2888}(1147,\cdot)\) \(\chi_{2888}(1227,\cdot)\) \(\chi_{2888}(1299,\cdot)\) \(\chi_{2888}(1379,\cdot)\) \(\chi_{2888}(1451,\cdot)\) \(\chi_{2888}(1531,\cdot)\) \(\chi_{2888}(1603,\cdot)\) \(\chi_{2888}(1683,\cdot)\) \(\chi_{2888}(1755,\cdot)\) \(\chi_{2888}(1835,\cdot)\) \(\chi_{2888}(1907,\cdot)\) \(\chi_{2888}(1987,\cdot)\) \(\chi_{2888}(2059,\cdot)\) \(\chi_{2888}(2139,\cdot)\) \(\chi_{2888}(2211,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2167,1445,2529)\) → \((-1,-1,e\left(\frac{43}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 2888 }(235, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{59}{114}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{79}{114}\right)\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{59}{114}\right)\) | \(e\left(\frac{73}{114}\right)\) |