Basic properties
| Modulus: | \(2793\) | |
| Conductor: | \(2793\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2793.ef
\(\chi_{2793}(17,\cdot)\) \(\chi_{2793}(47,\cdot)\) \(\chi_{2793}(194,\cdot)\) \(\chi_{2793}(206,\cdot)\) \(\chi_{2793}(290,\cdot)\) \(\chi_{2793}(416,\cdot)\) \(\chi_{2793}(446,\cdot)\) \(\chi_{2793}(593,\cdot)\) \(\chi_{2793}(605,\cdot)\) \(\chi_{2793}(614,\cdot)\) \(\chi_{2793}(689,\cdot)\) \(\chi_{2793}(845,\cdot)\) \(\chi_{2793}(992,\cdot)\) \(\chi_{2793}(1004,\cdot)\) \(\chi_{2793}(1013,\cdot)\) \(\chi_{2793}(1088,\cdot)\) \(\chi_{2793}(1214,\cdot)\) \(\chi_{2793}(1412,\cdot)\) \(\chi_{2793}(1487,\cdot)\) \(\chi_{2793}(1613,\cdot)\) \(\chi_{2793}(1643,\cdot)\) \(\chi_{2793}(1790,\cdot)\) \(\chi_{2793}(1802,\cdot)\) \(\chi_{2793}(1811,\cdot)\) \(\chi_{2793}(1886,\cdot)\) \(\chi_{2793}(2012,\cdot)\) \(\chi_{2793}(2042,\cdot)\) \(\chi_{2793}(2189,\cdot)\) \(\chi_{2793}(2201,\cdot)\) \(\chi_{2793}(2210,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((932,2110,2206)\) → \((-1,e\left(\frac{17}{42}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 2793 }(1790, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{2}{7}\right)\) |