Basic properties
Modulus: | \(2156\) | |
Conductor: | \(2156\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | 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 2156.cg
\(\chi_{2156}(3,\cdot)\) \(\chi_{2156}(47,\cdot)\) \(\chi_{2156}(59,\cdot)\) \(\chi_{2156}(75,\cdot)\) \(\chi_{2156}(103,\cdot)\) \(\chi_{2156}(115,\cdot)\) \(\chi_{2156}(159,\cdot)\) \(\chi_{2156}(311,\cdot)\) \(\chi_{2156}(339,\cdot)\) \(\chi_{2156}(355,\cdot)\) \(\chi_{2156}(367,\cdot)\) \(\chi_{2156}(383,\cdot)\) \(\chi_{2156}(467,\cdot)\) \(\chi_{2156}(647,\cdot)\) \(\chi_{2156}(663,\cdot)\) \(\chi_{2156}(675,\cdot)\) \(\chi_{2156}(691,\cdot)\) \(\chi_{2156}(719,\cdot)\) \(\chi_{2156}(731,\cdot)\) \(\chi_{2156}(775,\cdot)\) \(\chi_{2156}(927,\cdot)\) \(\chi_{2156}(955,\cdot)\) \(\chi_{2156}(971,\cdot)\) \(\chi_{2156}(983,\cdot)\) \(\chi_{2156}(1027,\cdot)\) \(\chi_{2156}(1039,\cdot)\) \(\chi_{2156}(1083,\cdot)\) \(\chi_{2156}(1235,\cdot)\) \(\chi_{2156}(1263,\cdot)\) \(\chi_{2156}(1279,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,1277,981)\) → \((-1,e\left(\frac{1}{42}\right),e\left(\frac{1}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 2156 }(983, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{83}{210}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{13}{35}\right)\) |