Basic properties
Modulus: | \(6982\) | |
Conductor: | \(3491\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1745\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3491}(105,\cdot)\) | 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
\(3493\) → \(e\left(\frac{157}{1745}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6982 }(105, a) \) | \(1\) | \(1\) | \(e\left(\frac{271}{1745}\right)\) | \(e\left(\frac{903}{1745}\right)\) | \(e\left(\frac{1009}{1745}\right)\) | \(e\left(\frac{542}{1745}\right)\) | \(e\left(\frac{1363}{1745}\right)\) | \(e\left(\frac{34}{349}\right)\) | \(e\left(\frac{1174}{1745}\right)\) | \(e\left(\frac{647}{1745}\right)\) | \(e\left(\frac{298}{1745}\right)\) | \(e\left(\frac{256}{349}\right)\) |