Basic properties
Modulus: | \(916\) | |
Conductor: | \(229\) | 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 \(\chi_{229}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 916.v
\(\chi_{916}(5,\cdot)\) \(\chi_{916}(33,\cdot)\) \(\chi_{916}(45,\cdot)\) \(\chi_{916}(49,\cdot)\) \(\chi_{916}(85,\cdot)\) \(\chi_{916}(97,\cdot)\) \(\chi_{916}(181,\cdot)\) \(\chi_{916}(209,\cdot)\) \(\chi_{916}(241,\cdot)\) \(\chi_{916}(265,\cdot)\) \(\chi_{916}(285,\cdot)\) \(\chi_{916}(305,\cdot)\) \(\chi_{916}(309,\cdot)\) \(\chi_{916}(329,\cdot)\) \(\chi_{916}(377,\cdot)\) \(\chi_{916}(421,\cdot)\) \(\chi_{916}(433,\cdot)\) \(\chi_{916}(449,\cdot)\) \(\chi_{916}(529,\cdot)\) \(\chi_{916}(557,\cdot)\) \(\chi_{916}(561,\cdot)\) \(\chi_{916}(605,\cdot)\) \(\chi_{916}(673,\cdot)\) \(\chi_{916}(733,\cdot)\) \(\chi_{916}(745,\cdot)\) \(\chi_{916}(749,\cdot)\) \(\chi_{916}(757,\cdot)\) \(\chi_{916}(765,\cdot)\) \(\chi_{916}(805,\cdot)\) \(\chi_{916}(825,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((459,693)\) → \((1,e\left(\frac{71}{114}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 916 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{73}{114}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{7}{38}\right)\) |