Basic properties
| Modulus: | \(8450\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{845}(193,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8450.ch
\(\chi_{8450}(193,\cdot)\) \(\chi_{8450}(293,\cdot)\) \(\chi_{8450}(457,\cdot)\) \(\chi_{8450}(843,\cdot)\) \(\chi_{8450}(943,\cdot)\) \(\chi_{8450}(1007,\cdot)\) \(\chi_{8450}(1107,\cdot)\) \(\chi_{8450}(1493,\cdot)\) \(\chi_{8450}(1593,\cdot)\) \(\chi_{8450}(1657,\cdot)\) \(\chi_{8450}(1757,\cdot)\) \(\chi_{8450}(2143,\cdot)\) \(\chi_{8450}(2243,\cdot)\) \(\chi_{8450}(2307,\cdot)\) \(\chi_{8450}(2407,\cdot)\) \(\chi_{8450}(2893,\cdot)\) \(\chi_{8450}(2957,\cdot)\) \(\chi_{8450}(3057,\cdot)\) \(\chi_{8450}(3443,\cdot)\) \(\chi_{8450}(3543,\cdot)\) \(\chi_{8450}(3607,\cdot)\) \(\chi_{8450}(3707,\cdot)\) \(\chi_{8450}(4093,\cdot)\) \(\chi_{8450}(4193,\cdot)\) \(\chi_{8450}(4257,\cdot)\) \(\chi_{8450}(4357,\cdot)\) \(\chi_{8450}(4743,\cdot)\) \(\chi_{8450}(4843,\cdot)\) \(\chi_{8450}(4907,\cdot)\) \(\chi_{8450}(5007,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((677,3551)\) → \((-i,e\left(\frac{127}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8450 }(193, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{133}{156}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{5}{78}\right)\) |