Basic properties
Modulus: | \(2347\) | |
Conductor: | \(2347\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2346\) | 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
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2347.p
\(\chi_{2347}(3,\cdot)\) \(\chi_{2347}(5,\cdot)\) \(\chi_{2347}(11,\cdot)\) \(\chi_{2347}(12,\cdot)\) \(\chi_{2347}(18,\cdot)\) \(\chi_{2347}(20,\cdot)\) \(\chi_{2347}(29,\cdot)\) \(\chi_{2347}(30,\cdot)\) \(\chi_{2347}(34,\cdot)\) \(\chi_{2347}(42,\cdot)\) \(\chi_{2347}(43,\cdot)\) \(\chi_{2347}(44,\cdot)\) \(\chi_{2347}(48,\cdot)\) \(\chi_{2347}(50,\cdot)\) \(\chi_{2347}(57,\cdot)\) \(\chi_{2347}(59,\cdot)\) \(\chi_{2347}(61,\cdot)\) \(\chi_{2347}(62,\cdot)\) \(\chi_{2347}(63,\cdot)\) \(\chi_{2347}(70,\cdot)\) \(\chi_{2347}(72,\cdot)\) \(\chi_{2347}(73,\cdot)\) \(\chi_{2347}(74,\cdot)\) \(\chi_{2347}(78,\cdot)\) \(\chi_{2347}(80,\cdot)\) \(\chi_{2347}(94,\cdot)\) \(\chi_{2347}(95,\cdot)\) \(\chi_{2347}(97,\cdot)\) \(\chi_{2347}(99,\cdot)\) \(\chi_{2347}(103,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1173})$ |
Fixed field: | Number field defined by a degree 2346 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{2225}{2346}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2347 }(18, a) \) | \(-1\) | \(1\) | \(e\left(\frac{269}{782}\right)\) | \(e\left(\frac{2225}{2346}\right)\) | \(e\left(\frac{269}{391}\right)\) | \(e\left(\frac{983}{2346}\right)\) | \(e\left(\frac{343}{1173}\right)\) | \(e\left(\frac{37}{782}\right)\) | \(e\left(\frac{25}{782}\right)\) | \(e\left(\frac{1052}{1173}\right)\) | \(e\left(\frac{895}{1173}\right)\) | \(e\left(\frac{1579}{2346}\right)\) |