Basic properties
Modulus: | \(2695\) | |
Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{539}(247,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2695.dc
\(\chi_{2695}(16,\cdot)\) \(\chi_{2695}(81,\cdot)\) \(\chi_{2695}(86,\cdot)\) \(\chi_{2695}(191,\cdot)\) \(\chi_{2695}(256,\cdot)\) \(\chi_{2695}(291,\cdot)\) \(\chi_{2695}(366,\cdot)\) \(\chi_{2695}(401,\cdot)\) \(\chi_{2695}(466,\cdot)\) \(\chi_{2695}(576,\cdot)\) \(\chi_{2695}(641,\cdot)\) \(\chi_{2695}(676,\cdot)\) \(\chi_{2695}(746,\cdot)\) \(\chi_{2695}(751,\cdot)\) \(\chi_{2695}(786,\cdot)\) \(\chi_{2695}(856,\cdot)\) \(\chi_{2695}(1026,\cdot)\) \(\chi_{2695}(1061,\cdot)\) \(\chi_{2695}(1131,\cdot)\) \(\chi_{2695}(1136,\cdot)\) \(\chi_{2695}(1171,\cdot)\) \(\chi_{2695}(1236,\cdot)\) \(\chi_{2695}(1241,\cdot)\) \(\chi_{2695}(1346,\cdot)\) \(\chi_{2695}(1411,\cdot)\) \(\chi_{2695}(1446,\cdot)\) \(\chi_{2695}(1516,\cdot)\) \(\chi_{2695}(1521,\cdot)\) \(\chi_{2695}(1556,\cdot)\) \(\chi_{2695}(1621,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((2157,1816,981)\) → \((1,e\left(\frac{13}{21}\right),e\left(\frac{2}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
\( \chi_{ 2695 }(786, a) \) | \(1\) | \(1\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{8}{105}\right)\) |