Basic properties
| Modulus: | \(1521\) | |
| Conductor: | \(1521\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1521.by
\(\chi_{1521}(4,\cdot)\) \(\chi_{1521}(88,\cdot)\) \(\chi_{1521}(121,\cdot)\) \(\chi_{1521}(205,\cdot)\) \(\chi_{1521}(238,\cdot)\) \(\chi_{1521}(322,\cdot)\) \(\chi_{1521}(355,\cdot)\) \(\chi_{1521}(439,\cdot)\) \(\chi_{1521}(472,\cdot)\) \(\chi_{1521}(556,\cdot)\) \(\chi_{1521}(589,\cdot)\) \(\chi_{1521}(673,\cdot)\) \(\chi_{1521}(706,\cdot)\) \(\chi_{1521}(790,\cdot)\) \(\chi_{1521}(907,\cdot)\) \(\chi_{1521}(940,\cdot)\) \(\chi_{1521}(1024,\cdot)\) \(\chi_{1521}(1057,\cdot)\) \(\chi_{1521}(1141,\cdot)\) \(\chi_{1521}(1174,\cdot)\) \(\chi_{1521}(1258,\cdot)\) \(\chi_{1521}(1291,\cdot)\) \(\chi_{1521}(1408,\cdot)\) \(\chi_{1521}(1492,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,847)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 1521 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{34}{39}\right)\) |