Basic properties
| Modulus: | \(1775\) | |
| Conductor: | \(71\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{71}(55,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1775.cq
\(\chi_{1775}(126,\cdot)\) \(\chi_{1775}(201,\cdot)\) \(\chi_{1775}(226,\cdot)\) \(\chi_{1775}(276,\cdot)\) \(\chi_{1775}(326,\cdot)\) \(\chi_{1775}(351,\cdot)\) \(\chi_{1775}(376,\cdot)\) \(\chi_{1775}(601,\cdot)\) \(\chi_{1775}(701,\cdot)\) \(\chi_{1775}(951,\cdot)\) \(\chi_{1775}(976,\cdot)\) \(\chi_{1775}(1001,\cdot)\) \(\chi_{1775}(1076,\cdot)\) \(\chi_{1775}(1126,\cdot)\) \(\chi_{1775}(1201,\cdot)\) \(\chi_{1775}(1251,\cdot)\) \(\chi_{1775}(1276,\cdot)\) \(\chi_{1775}(1401,\cdot)\) \(\chi_{1775}(1451,\cdot)\) \(\chi_{1775}(1476,\cdot)\) \(\chi_{1775}(1526,\cdot)\) \(\chi_{1775}(1701,\cdot)\) \(\chi_{1775}(1726,\cdot)\) \(\chi_{1775}(1751,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((427,1001)\) → \((1,e\left(\frac{59}{70}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1775 }(126, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{61}{70}\right)\) |