Basic properties
| Modulus: | \(1521\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1521.cd
\(\chi_{1521}(71,\cdot)\) \(\chi_{1521}(98,\cdot)\) \(\chi_{1521}(197,\cdot)\) \(\chi_{1521}(206,\cdot)\) \(\chi_{1521}(215,\cdot)\) \(\chi_{1521}(305,\cdot)\) \(\chi_{1521}(314,\cdot)\) \(\chi_{1521}(323,\cdot)\) \(\chi_{1521}(332,\cdot)\) \(\chi_{1521}(422,\cdot)\) \(\chi_{1521}(431,\cdot)\) \(\chi_{1521}(440,\cdot)\) \(\chi_{1521}(449,\cdot)\) \(\chi_{1521}(539,\cdot)\) \(\chi_{1521}(548,\cdot)\) \(\chi_{1521}(557,\cdot)\) \(\chi_{1521}(566,\cdot)\) \(\chi_{1521}(656,\cdot)\) \(\chi_{1521}(665,\cdot)\) \(\chi_{1521}(674,\cdot)\) \(\chi_{1521}(683,\cdot)\) \(\chi_{1521}(773,\cdot)\) \(\chi_{1521}(782,\cdot)\) \(\chi_{1521}(791,\cdot)\) \(\chi_{1521}(800,\cdot)\) \(\chi_{1521}(890,\cdot)\) \(\chi_{1521}(899,\cdot)\) \(\chi_{1521}(908,\cdot)\) \(\chi_{1521}(917,\cdot)\) \(\chi_{1521}(1007,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((677,847)\) → \((-1,e\left(\frac{137}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 1521 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{149}{156}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) |