Basic properties
| Modulus: | \(1775\) | |
| Conductor: | \(355\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{355}(18,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1775.da
\(\chi_{1775}(18,\cdot)\) \(\chi_{1775}(43,\cdot)\) \(\chi_{1775}(107,\cdot)\) \(\chi_{1775}(157,\cdot)\) \(\chi_{1775}(182,\cdot)\) \(\chi_{1775}(232,\cdot)\) \(\chi_{1775}(293,\cdot)\) \(\chi_{1775}(357,\cdot)\) \(\chi_{1775}(382,\cdot)\) \(\chi_{1775}(393,\cdot)\) \(\chi_{1775}(432,\cdot)\) \(\chi_{1775}(507,\cdot)\) \(\chi_{1775}(557,\cdot)\) \(\chi_{1775}(618,\cdot)\) \(\chi_{1775}(632,\cdot)\) \(\chi_{1775}(643,\cdot)\) \(\chi_{1775}(657,\cdot)\) \(\chi_{1775}(668,\cdot)\) \(\chi_{1775}(682,\cdot)\) \(\chi_{1775}(718,\cdot)\) \(\chi_{1775}(768,\cdot)\) \(\chi_{1775}(793,\cdot)\) \(\chi_{1775}(868,\cdot)\) \(\chi_{1775}(932,\cdot)\) \(\chi_{1775}(1018,\cdot)\) \(\chi_{1775}(1032,\cdot)\) \(\chi_{1775}(1043,\cdot)\) \(\chi_{1775}(1068,\cdot)\) \(\chi_{1775}(1243,\cdot)\) \(\chi_{1775}(1257,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((427,1001)\) → \((-i,e\left(\frac{29}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1775 }(18, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{140}\right)\) | \(e\left(\frac{111}{140}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{23}{140}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{33}{140}\right)\) | \(e\left(\frac{79}{140}\right)\) |