Basic properties
Modulus: | \(1078\) | |
Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{539}(235,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1078.bc
\(\chi_{1078}(9,\cdot)\) \(\chi_{1078}(25,\cdot)\) \(\chi_{1078}(37,\cdot)\) \(\chi_{1078}(53,\cdot)\) \(\chi_{1078}(81,\cdot)\) \(\chi_{1078}(93,\cdot)\) \(\chi_{1078}(135,\cdot)\) \(\chi_{1078}(137,\cdot)\) \(\chi_{1078}(163,\cdot)\) \(\chi_{1078}(179,\cdot)\) \(\chi_{1078}(191,\cdot)\) \(\chi_{1078}(207,\cdot)\) \(\chi_{1078}(235,\cdot)\) \(\chi_{1078}(247,\cdot)\) \(\chi_{1078}(289,\cdot)\) \(\chi_{1078}(291,\cdot)\) \(\chi_{1078}(317,\cdot)\) \(\chi_{1078}(333,\cdot)\) \(\chi_{1078}(345,\cdot)\) \(\chi_{1078}(389,\cdot)\) \(\chi_{1078}(401,\cdot)\) \(\chi_{1078}(443,\cdot)\) \(\chi_{1078}(445,\cdot)\) \(\chi_{1078}(487,\cdot)\) \(\chi_{1078}(499,\cdot)\) \(\chi_{1078}(515,\cdot)\) \(\chi_{1078}(543,\cdot)\) \(\chi_{1078}(555,\cdot)\) \(\chi_{1078}(597,\cdot)\) \(\chi_{1078}(599,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((199,981)\) → \((e\left(\frac{17}{21}\right),e\left(\frac{1}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 1078 }(235, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{8}{35}\right)\) |