Basic properties
| Modulus: | \(1521\) | |
| Conductor: | \(1521\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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.cb
\(\chi_{1521}(20,\cdot)\) \(\chi_{1521}(41,\cdot)\) \(\chi_{1521}(50,\cdot)\) \(\chi_{1521}(110,\cdot)\) \(\chi_{1521}(137,\cdot)\) \(\chi_{1521}(158,\cdot)\) \(\chi_{1521}(167,\cdot)\) \(\chi_{1521}(227,\cdot)\) \(\chi_{1521}(254,\cdot)\) \(\chi_{1521}(275,\cdot)\) \(\chi_{1521}(284,\cdot)\) \(\chi_{1521}(344,\cdot)\) \(\chi_{1521}(371,\cdot)\) \(\chi_{1521}(392,\cdot)\) \(\chi_{1521}(401,\cdot)\) \(\chi_{1521}(461,\cdot)\) \(\chi_{1521}(509,\cdot)\) \(\chi_{1521}(518,\cdot)\) \(\chi_{1521}(578,\cdot)\) \(\chi_{1521}(605,\cdot)\) \(\chi_{1521}(626,\cdot)\) \(\chi_{1521}(635,\cdot)\) \(\chi_{1521}(722,\cdot)\) \(\chi_{1521}(743,\cdot)\) \(\chi_{1521}(752,\cdot)\) \(\chi_{1521}(812,\cdot)\) \(\chi_{1521}(839,\cdot)\) \(\chi_{1521}(860,\cdot)\) \(\chi_{1521}(869,\cdot)\) \(\chi_{1521}(929,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((677,847)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{11}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 1521 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{156}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{67}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) |