Basic properties
Modulus: | \(8003\) | |
Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(260\) | 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 8003.ca
\(\chi_{8003}(87,\cdot)\) \(\chi_{8003}(92,\cdot)\) \(\chi_{8003}(132,\cdot)\) \(\chi_{8003}(238,\cdot)\) \(\chi_{8003}(243,\cdot)\) \(\chi_{8003}(283,\cdot)\) \(\chi_{8003}(389,\cdot)\) \(\chi_{8003}(445,\cdot)\) \(\chi_{8003}(585,\cdot)\) \(\chi_{8003}(691,\cdot)\) \(\chi_{8003}(747,\cdot)\) \(\chi_{8003}(887,\cdot)\) \(\chi_{8003}(898,\cdot)\) \(\chi_{8003}(993,\cdot)\) \(\chi_{8003}(1038,\cdot)\) \(\chi_{8003}(1144,\cdot)\) \(\chi_{8003}(1200,\cdot)\) \(\chi_{8003}(1351,\cdot)\) \(\chi_{8003}(1451,\cdot)\) \(\chi_{8003}(1502,\cdot)\) \(\chi_{8003}(1602,\cdot)\) \(\chi_{8003}(1804,\cdot)\) \(\chi_{8003}(2055,\cdot)\) \(\chi_{8003}(2106,\cdot)\) \(\chi_{8003}(2206,\cdot)\) \(\chi_{8003}(2246,\cdot)\) \(\chi_{8003}(2257,\cdot)\) \(\chi_{8003}(2352,\cdot)\) \(\chi_{8003}(2397,\cdot)\) \(\chi_{8003}(2503,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{260})$ |
Fixed field: | Number field defined by a degree 260 polynomial (not computed) |
Values on generators
\((4984,7103)\) → \((e\left(\frac{11}{52}\right),e\left(\frac{3}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8003 }(87, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{233}{260}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{141}{260}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{61}{130}\right)\) |