Basic properties
| Modulus: | \(6378\) | |
| Conductor: | \(3189\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1062\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3189}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6378.x
\(\chi_{6378}(29,\cdot)\) \(\chi_{6378}(35,\cdot)\) \(\chi_{6378}(53,\cdot)\) \(\chi_{6378}(95,\cdot)\) \(\chi_{6378}(101,\cdot)\) \(\chi_{6378}(131,\cdot)\) \(\chi_{6378}(137,\cdot)\) \(\chi_{6378}(167,\cdot)\) \(\chi_{6378}(179,\cdot)\) \(\chi_{6378}(191,\cdot)\) \(\chi_{6378}(197,\cdot)\) \(\chi_{6378}(203,\cdot)\) \(\chi_{6378}(227,\cdot)\) \(\chi_{6378}(245,\cdot)\) \(\chi_{6378}(263,\cdot)\) \(\chi_{6378}(281,\cdot)\) \(\chi_{6378}(287,\cdot)\) \(\chi_{6378}(335,\cdot)\) \(\chi_{6378}(341,\cdot)\) \(\chi_{6378}(359,\cdot)\) \(\chi_{6378}(365,\cdot)\) \(\chi_{6378}(377,\cdot)\) \(\chi_{6378}(389,\cdot)\) \(\chi_{6378}(413,\cdot)\) \(\chi_{6378}(419,\cdot)\) \(\chi_{6378}(449,\cdot)\) \(\chi_{6378}(455,\cdot)\) \(\chi_{6378}(473,\cdot)\) \(\chi_{6378}(479,\cdot)\) \(\chi_{6378}(485,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{531})$ |
| Fixed field: | Number field defined by a degree 1062 polynomial (not computed) |
Values on generators
\((4253,4255)\) → \((-1,e\left(\frac{481}{1062}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 6378 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{140}{177}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{739}{1062}\right)\) | \(e\left(\frac{113}{177}\right)\) | \(e\left(\frac{15}{118}\right)\) | \(e\left(\frac{307}{531}\right)\) | \(e\left(\frac{601}{1062}\right)\) | \(e\left(\frac{103}{177}\right)\) | \(e\left(\frac{188}{531}\right)\) | \(e\left(\frac{127}{1062}\right)\) |