Basic properties
Modulus: | \(2347\) | |
Conductor: | \(2347\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(782\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 2347.n
\(\chi_{2347}(2,\cdot)\) \(\chi_{2347}(7,\cdot)\) \(\chi_{2347}(8,\cdot)\) \(\chi_{2347}(23,\cdot)\) \(\chi_{2347}(27,\cdot)\) \(\chi_{2347}(32,\cdot)\) \(\chi_{2347}(38,\cdot)\) \(\chi_{2347}(45,\cdot)\) \(\chi_{2347}(51,\cdot)\) \(\chi_{2347}(52,\cdot)\) \(\chi_{2347}(66,\cdot)\) \(\chi_{2347}(71,\cdot)\) \(\chi_{2347}(75,\cdot)\) \(\chi_{2347}(82,\cdot)\) \(\chi_{2347}(83,\cdot)\) \(\chi_{2347}(85,\cdot)\) \(\chi_{2347}(89,\cdot)\) \(\chi_{2347}(92,\cdot)\) \(\chi_{2347}(93,\cdot)\) \(\chi_{2347}(98,\cdot)\) \(\chi_{2347}(106,\cdot)\) \(\chi_{2347}(108,\cdot)\) \(\chi_{2347}(110,\cdot)\) \(\chi_{2347}(112,\cdot)\) \(\chi_{2347}(125,\cdot)\) \(\chi_{2347}(127,\cdot)\) \(\chi_{2347}(128,\cdot)\) \(\chi_{2347}(133,\cdot)\) \(\chi_{2347}(141,\cdot)\) \(\chi_{2347}(152,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{391})$ |
Fixed field: | Number field defined by a degree 782 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{381}{782}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2347 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{57}{782}\right)\) | \(e\left(\frac{381}{782}\right)\) | \(e\left(\frac{57}{391}\right)\) | \(e\left(\frac{427}{782}\right)\) | \(e\left(\frac{219}{391}\right)\) | \(e\left(\frac{691}{782}\right)\) | \(e\left(\frac{171}{782}\right)\) | \(e\left(\frac{381}{391}\right)\) | \(e\left(\frac{242}{391}\right)\) | \(e\left(\frac{347}{782}\right)\) |