Basic properties
| Modulus: | \(8450\) | |
| Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(780\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4225}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8450.cx
\(\chi_{8450}(33,\cdot)\) \(\chi_{8450}(63,\cdot)\) \(\chi_{8450}(67,\cdot)\) \(\chi_{8450}(97,\cdot)\) \(\chi_{8450}(163,\cdot)\) \(\chi_{8450}(197,\cdot)\) \(\chi_{8450}(227,\cdot)\) \(\chi_{8450}(323,\cdot)\) \(\chi_{8450}(327,\cdot)\) \(\chi_{8450}(423,\cdot)\) \(\chi_{8450}(453,\cdot)\) \(\chi_{8450}(487,\cdot)\) \(\chi_{8450}(553,\cdot)\) \(\chi_{8450}(583,\cdot)\) \(\chi_{8450}(617,\cdot)\) \(\chi_{8450}(683,\cdot)\) \(\chi_{8450}(713,\cdot)\) \(\chi_{8450}(717,\cdot)\) \(\chi_{8450}(747,\cdot)\) \(\chi_{8450}(813,\cdot)\) \(\chi_{8450}(847,\cdot)\) \(\chi_{8450}(877,\cdot)\) \(\chi_{8450}(973,\cdot)\) \(\chi_{8450}(977,\cdot)\) \(\chi_{8450}(1073,\cdot)\) \(\chi_{8450}(1137,\cdot)\) \(\chi_{8450}(1203,\cdot)\) \(\chi_{8450}(1233,\cdot)\) \(\chi_{8450}(1237,\cdot)\) \(\chi_{8450}(1267,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((677,3551)\) → \((e\left(\frac{3}{20}\right),e\left(\frac{71}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8450 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{379}{780}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{379}{390}\right)\) | \(e\left(\frac{217}{780}\right)\) | \(e\left(\frac{311}{780}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{243}{260}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{119}{260}\right)\) | \(e\left(\frac{197}{390}\right)\) |