Basic properties
| Modulus: | \(781\) | |
| Conductor: | \(781\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(35\) | 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 781.bi
\(\chi_{781}(4,\cdot)\) \(\chi_{781}(16,\cdot)\) \(\chi_{781}(64,\cdot)\) \(\chi_{781}(180,\cdot)\) \(\chi_{781}(191,\cdot)\) \(\chi_{781}(256,\cdot)\) \(\chi_{781}(273,\cdot)\) \(\chi_{781}(290,\cdot)\) \(\chi_{781}(311,\cdot)\) \(\chi_{781}(334,\cdot)\) \(\chi_{781}(379,\cdot)\) \(\chi_{781}(509,\cdot)\) \(\chi_{781}(533,\cdot)\) \(\chi_{781}(537,\cdot)\) \(\chi_{781}(555,\cdot)\) \(\chi_{781}(570,\cdot)\) \(\chi_{781}(586,\cdot)\) \(\chi_{781}(597,\cdot)\) \(\chi_{781}(654,\cdot)\) \(\chi_{781}(658,\cdot)\) \(\chi_{781}(713,\cdot)\) \(\chi_{781}(718,\cdot)\) \(\chi_{781}(719,\cdot)\) \(\chi_{781}(720,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | 35.35.126409304214415502952719093782014439397796172025041680505851154261799578037610144929882069761.1 |
Values on generators
\((640,78)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{32}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 781 }(533, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) |