Basic properties
| Modulus: | \(1775\) | |
| Conductor: | \(355\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{355}(99,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1775.ci
\(\chi_{1775}(99,\cdot)\) \(\chi_{1775}(124,\cdot)\) \(\chi_{1775}(149,\cdot)\) \(\chi_{1775}(224,\cdot)\) \(\chi_{1775}(274,\cdot)\) \(\chi_{1775}(349,\cdot)\) \(\chi_{1775}(399,\cdot)\) \(\chi_{1775}(424,\cdot)\) \(\chi_{1775}(549,\cdot)\) \(\chi_{1775}(599,\cdot)\) \(\chi_{1775}(624,\cdot)\) \(\chi_{1775}(674,\cdot)\) \(\chi_{1775}(849,\cdot)\) \(\chi_{1775}(874,\cdot)\) \(\chi_{1775}(899,\cdot)\) \(\chi_{1775}(1049,\cdot)\) \(\chi_{1775}(1124,\cdot)\) \(\chi_{1775}(1149,\cdot)\) \(\chi_{1775}(1199,\cdot)\) \(\chi_{1775}(1249,\cdot)\) \(\chi_{1775}(1274,\cdot)\) \(\chi_{1775}(1299,\cdot)\) \(\chi_{1775}(1524,\cdot)\) \(\chi_{1775}(1624,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((427,1001)\) → \((-1,e\left(\frac{13}{70}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1775 }(99, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) |