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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2888.bh
\(\chi_{2888}(45,\cdot)\) \(\chi_{2888}(125,\cdot)\) \(\chi_{2888}(197,\cdot)\) \(\chi_{2888}(277,\cdot)\) \(\chi_{2888}(349,\cdot)\) \(\chi_{2888}(501,\cdot)\) \(\chi_{2888}(581,\cdot)\) \(\chi_{2888}(733,\cdot)\) \(\chi_{2888}(805,\cdot)\) \(\chi_{2888}(885,\cdot)\) \(\chi_{2888}(957,\cdot)\) \(\chi_{2888}(1037,\cdot)\) \(\chi_{2888}(1109,\cdot)\) \(\chi_{2888}(1189,\cdot)\) \(\chi_{2888}(1261,\cdot)\) \(\chi_{2888}(1341,\cdot)\) \(\chi_{2888}(1413,\cdot)\) \(\chi_{2888}(1493,\cdot)\) \(\chi_{2888}(1565,\cdot)\) \(\chi_{2888}(1645,\cdot)\) \(\chi_{2888}(1717,\cdot)\) \(\chi_{2888}(1797,\cdot)\) \(\chi_{2888}(1869,\cdot)\) \(\chi_{2888}(1949,\cdot)\) \(\chi_{2888}(2021,\cdot)\) \(\chi_{2888}(2101,\cdot)\) \(\chi_{2888}(2173,\cdot)\) \(\chi_{2888}(2253,\cdot)\) \(\chi_{2888}(2325,\cdot)\) \(\chi_{2888}(2405,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2167,1445,2529)\) → \((1,-1,e\left(\frac{28}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 2888 }(45, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{114}\right)\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{13}{114}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{41}{57}\right)\) |