Basic properties
| Modulus: | \(6982\) | |
| Conductor: | \(3491\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1745\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3491}(27,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6982.g
\(\chi_{6982}(3,\cdot)\) \(\chi_{6982}(5,\cdot)\) \(\chi_{6982}(7,\cdot)\) \(\chi_{6982}(9,\cdot)\) \(\chi_{6982}(15,\cdot)\) \(\chi_{6982}(19,\cdot)\) \(\chi_{6982}(25,\cdot)\) \(\chi_{6982}(27,\cdot)\) \(\chi_{6982}(35,\cdot)\) \(\chi_{6982}(43,\cdot)\) \(\chi_{6982}(47,\cdot)\) \(\chi_{6982}(49,\cdot)\) \(\chi_{6982}(53,\cdot)\) \(\chi_{6982}(57,\cdot)\) \(\chi_{6982}(61,\cdot)\) \(\chi_{6982}(63,\cdot)\) \(\chi_{6982}(75,\cdot)\) \(\chi_{6982}(79,\cdot)\) \(\chi_{6982}(81,\cdot)\) \(\chi_{6982}(83,\cdot)\) \(\chi_{6982}(89,\cdot)\) \(\chi_{6982}(95,\cdot)\) \(\chi_{6982}(97,\cdot)\) \(\chi_{6982}(105,\cdot)\) \(\chi_{6982}(109,\cdot)\) \(\chi_{6982}(121,\cdot)\) \(\chi_{6982}(125,\cdot)\) \(\chi_{6982}(129,\cdot)\) \(\chi_{6982}(131,\cdot)\) \(\chi_{6982}(133,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1745})$ |
| Fixed field: | Number field defined by a degree 1745 polynomial (not computed) |
Values on generators
\(3493\) → \(e\left(\frac{1642}{1745}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6982 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{1256}{1745}\right)\) | \(e\left(\frac{708}{1745}\right)\) | \(e\left(\frac{594}{1745}\right)\) | \(e\left(\frac{767}{1745}\right)\) | \(e\left(\frac{773}{1745}\right)\) | \(e\left(\frac{240}{349}\right)\) | \(e\left(\frac{219}{1745}\right)\) | \(e\left(\frac{687}{1745}\right)\) | \(e\left(\frac{338}{1745}\right)\) | \(e\left(\frac{21}{349}\right)\) |