Basic properties
Modulus: | \(5415\) | |
Conductor: | \(1083\) | 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 \(\chi_{1083}(221,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5415.cb
\(\chi_{5415}(221,\cdot)\) \(\chi_{5415}(236,\cdot)\) \(\chi_{5415}(506,\cdot)\) \(\chi_{5415}(521,\cdot)\) \(\chi_{5415}(806,\cdot)\) \(\chi_{5415}(1076,\cdot)\) \(\chi_{5415}(1091,\cdot)\) \(\chi_{5415}(1361,\cdot)\) \(\chi_{5415}(1646,\cdot)\) \(\chi_{5415}(1661,\cdot)\) \(\chi_{5415}(1931,\cdot)\) \(\chi_{5415}(1946,\cdot)\) \(\chi_{5415}(2216,\cdot)\) \(\chi_{5415}(2231,\cdot)\) \(\chi_{5415}(2501,\cdot)\) \(\chi_{5415}(2516,\cdot)\) \(\chi_{5415}(2786,\cdot)\) \(\chi_{5415}(2801,\cdot)\) \(\chi_{5415}(3071,\cdot)\) \(\chi_{5415}(3086,\cdot)\) \(\chi_{5415}(3356,\cdot)\) \(\chi_{5415}(3371,\cdot)\) \(\chi_{5415}(3641,\cdot)\) \(\chi_{5415}(3656,\cdot)\) \(\chi_{5415}(3926,\cdot)\) \(\chi_{5415}(3941,\cdot)\) \(\chi_{5415}(4211,\cdot)\) \(\chi_{5415}(4226,\cdot)\) \(\chi_{5415}(4496,\cdot)\) \(\chi_{5415}(4511,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3611,2167,5056)\) → \((-1,1,e\left(\frac{71}{114}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
\( \chi_{ 5415 }(221, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{17}{114}\right)\) |