Basic properties
| Modulus: | \(10000\) | |
| Conductor: | \(10000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(500\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 10000.cq
\(\chi_{10000}(29,\cdot)\) \(\chi_{10000}(69,\cdot)\) \(\chi_{10000}(109,\cdot)\) \(\chi_{10000}(189,\cdot)\) \(\chi_{10000}(229,\cdot)\) \(\chi_{10000}(269,\cdot)\) \(\chi_{10000}(309,\cdot)\) \(\chi_{10000}(389,\cdot)\) \(\chi_{10000}(429,\cdot)\) \(\chi_{10000}(469,\cdot)\) \(\chi_{10000}(509,\cdot)\) \(\chi_{10000}(589,\cdot)\) \(\chi_{10000}(629,\cdot)\) \(\chi_{10000}(669,\cdot)\) \(\chi_{10000}(709,\cdot)\) \(\chi_{10000}(789,\cdot)\) \(\chi_{10000}(829,\cdot)\) \(\chi_{10000}(869,\cdot)\) \(\chi_{10000}(909,\cdot)\) \(\chi_{10000}(989,\cdot)\) \(\chi_{10000}(1029,\cdot)\) \(\chi_{10000}(1069,\cdot)\) \(\chi_{10000}(1109,\cdot)\) \(\chi_{10000}(1189,\cdot)\) \(\chi_{10000}(1229,\cdot)\) \(\chi_{10000}(1269,\cdot)\) \(\chi_{10000}(1309,\cdot)\) \(\chi_{10000}(1389,\cdot)\) \(\chi_{10000}(1429,\cdot)\) \(\chi_{10000}(1469,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{500})$ |
| Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\((8751,2501,9377)\) → \((1,-i,e\left(\frac{81}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 10000 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{459}{500}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{209}{250}\right)\) | \(e\left(\frac{487}{500}\right)\) | \(e\left(\frac{143}{500}\right)\) | \(e\left(\frac{13}{250}\right)\) | \(e\left(\frac{341}{500}\right)\) | \(e\left(\frac{279}{500}\right)\) | \(e\left(\frac{18}{125}\right)\) | \(e\left(\frac{377}{500}\right)\) |