Basic properties
| Modulus: | \(9652\) | |
| Conductor: | \(9652\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9652.iz
\(\chi_{9652}(35,\cdot)\) \(\chi_{9652}(215,\cdot)\) \(\chi_{9652}(275,\cdot)\) \(\chi_{9652}(519,\cdot)\) \(\chi_{9652}(587,\cdot)\) \(\chi_{9652}(707,\cdot)\) \(\chi_{9652}(1031,\cdot)\) \(\chi_{9652}(1859,\cdot)\) \(\chi_{9652}(1923,\cdot)\) \(\chi_{9652}(1947,\cdot)\) \(\chi_{9652}(2303,\cdot)\) \(\chi_{9652}(2327,\cdot)\) \(\chi_{9652}(2399,\cdot)\) \(\chi_{9652}(2771,\cdot)\) \(\chi_{9652}(2791,\cdot)\) \(\chi_{9652}(3235,\cdot)\) \(\chi_{9652}(3455,\cdot)\) \(\chi_{9652}(3931,\cdot)\) \(\chi_{9652}(4735,\cdot)\) \(\chi_{9652}(4983,\cdot)\) \(\chi_{9652}(5291,\cdot)\) \(\chi_{9652}(5343,\cdot)\) \(\chi_{9652}(5383,\cdot)\) \(\chi_{9652}(5495,\cdot)\) \(\chi_{9652}(6039,\cdot)\) \(\chi_{9652}(6051,\cdot)\) \(\chi_{9652}(6067,\cdot)\) \(\chi_{9652}(6211,\cdot)\) \(\chi_{9652}(7047,\cdot)\) \(\chi_{9652}(7283,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((4827,7621,8893)\) → \((-1,e\left(\frac{8}{9}\right),e\left(\frac{17}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 9652 }(4983, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) |