Basic properties
| Modulus: | \(1078\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1078.ba
\(\chi_{1078}(13,\cdot)\) \(\chi_{1078}(41,\cdot)\) \(\chi_{1078}(83,\cdot)\) \(\chi_{1078}(139,\cdot)\) \(\chi_{1078}(167,\cdot)\) \(\chi_{1078}(237,\cdot)\) \(\chi_{1078}(321,\cdot)\) \(\chi_{1078}(349,\cdot)\) \(\chi_{1078}(447,\cdot)\) \(\chi_{1078}(475,\cdot)\) \(\chi_{1078}(503,\cdot)\) \(\chi_{1078}(545,\cdot)\) \(\chi_{1078}(601,\cdot)\) \(\chi_{1078}(629,\cdot)\) \(\chi_{1078}(657,\cdot)\) \(\chi_{1078}(699,\cdot)\) \(\chi_{1078}(755,\cdot)\) \(\chi_{1078}(811,\cdot)\) \(\chi_{1078}(853,\cdot)\) \(\chi_{1078}(909,\cdot)\) \(\chi_{1078}(937,\cdot)\) \(\chi_{1078}(965,\cdot)\) \(\chi_{1078}(1007,\cdot)\) \(\chi_{1078}(1063,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((199,981)\) → \((e\left(\frac{11}{14}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 1078 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) |