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 \(\chi_{539}(435,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1078.bb
\(\chi_{1078}(29,\cdot)\) \(\chi_{1078}(57,\cdot)\) \(\chi_{1078}(85,\cdot)\) \(\chi_{1078}(127,\cdot)\) \(\chi_{1078}(183,\cdot)\) \(\chi_{1078}(211,\cdot)\) \(\chi_{1078}(239,\cdot)\) \(\chi_{1078}(281,\cdot)\) \(\chi_{1078}(337,\cdot)\) \(\chi_{1078}(365,\cdot)\) \(\chi_{1078}(435,\cdot)\) \(\chi_{1078}(519,\cdot)\) \(\chi_{1078}(547,\cdot)\) \(\chi_{1078}(645,\cdot)\) \(\chi_{1078}(673,\cdot)\) \(\chi_{1078}(701,\cdot)\) \(\chi_{1078}(743,\cdot)\) \(\chi_{1078}(799,\cdot)\) \(\chi_{1078}(827,\cdot)\) \(\chi_{1078}(855,\cdot)\) \(\chi_{1078}(897,\cdot)\) \(\chi_{1078}(953,\cdot)\) \(\chi_{1078}(1009,\cdot)\) \(\chi_{1078}(1051,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((199,981)\) → \((e\left(\frac{1}{7}\right),e\left(\frac{9}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 1078 }(435, a) \) | \(-1\) | \(1\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) |