Basic properties
Modulus: | \(1078\) | |
Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{539}(15,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1078.v
\(\chi_{1078}(15,\cdot)\) \(\chi_{1078}(71,\cdot)\) \(\chi_{1078}(113,\cdot)\) \(\chi_{1078}(141,\cdot)\) \(\chi_{1078}(169,\cdot)\) \(\chi_{1078}(225,\cdot)\) \(\chi_{1078}(267,\cdot)\) \(\chi_{1078}(323,\cdot)\) \(\chi_{1078}(379,\cdot)\) \(\chi_{1078}(421,\cdot)\) \(\chi_{1078}(449,\cdot)\) \(\chi_{1078}(477,\cdot)\) \(\chi_{1078}(533,\cdot)\) \(\chi_{1078}(575,\cdot)\) \(\chi_{1078}(603,\cdot)\) \(\chi_{1078}(631,\cdot)\) \(\chi_{1078}(729,\cdot)\) \(\chi_{1078}(757,\cdot)\) \(\chi_{1078}(841,\cdot)\) \(\chi_{1078}(911,\cdot)\) \(\chi_{1078}(939,\cdot)\) \(\chi_{1078}(995,\cdot)\) \(\chi_{1078}(1037,\cdot)\) \(\chi_{1078}(1065,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((199,981)\) → \((e\left(\frac{5}{7}\right),e\left(\frac{1}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 1078 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) |