Basic properties
Modulus: | \(2347\) | |
Conductor: | \(2347\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1173\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2347.o
\(\chi_{2347}(6,\cdot)\) \(\chi_{2347}(9,\cdot)\) \(\chi_{2347}(10,\cdot)\) \(\chi_{2347}(15,\cdot)\) \(\chi_{2347}(17,\cdot)\) \(\chi_{2347}(21,\cdot)\) \(\chi_{2347}(22,\cdot)\) \(\chi_{2347}(25,\cdot)\) \(\chi_{2347}(31,\cdot)\) \(\chi_{2347}(35,\cdot)\) \(\chi_{2347}(36,\cdot)\) \(\chi_{2347}(37,\cdot)\) \(\chi_{2347}(39,\cdot)\) \(\chi_{2347}(47,\cdot)\) \(\chi_{2347}(58,\cdot)\) \(\chi_{2347}(60,\cdot)\) \(\chi_{2347}(65,\cdot)\) \(\chi_{2347}(67,\cdot)\) \(\chi_{2347}(68,\cdot)\) \(\chi_{2347}(69,\cdot)\) \(\chi_{2347}(77,\cdot)\) \(\chi_{2347}(81,\cdot)\) \(\chi_{2347}(84,\cdot)\) \(\chi_{2347}(88,\cdot)\) \(\chi_{2347}(96,\cdot)\) \(\chi_{2347}(100,\cdot)\) \(\chi_{2347}(101,\cdot)\) \(\chi_{2347}(113,\cdot)\) \(\chi_{2347}(114,\cdot)\) \(\chi_{2347}(118,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1173})$ |
Fixed field: | Number field defined by a degree 1173 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1120}{1173}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2347 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{218}{391}\right)\) | \(e\left(\frac{1120}{1173}\right)\) | \(e\left(\frac{45}{391}\right)\) | \(e\left(\frac{1051}{1173}\right)\) | \(e\left(\frac{601}{1173}\right)\) | \(e\left(\frac{139}{391}\right)\) | \(e\left(\frac{263}{391}\right)\) | \(e\left(\frac{1067}{1173}\right)\) | \(e\left(\frac{532}{1173}\right)\) | \(e\left(\frac{236}{1173}\right)\) |