Basic properties
Modulus: | \(8036\) | |
Conductor: | \(8036\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(280\) | 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 8036.eo
\(\chi_{8036}(15,\cdot)\) \(\chi_{8036}(71,\cdot)\) \(\chi_{8036}(183,\cdot)\) \(\chi_{8036}(211,\cdot)\) \(\chi_{8036}(239,\cdot)\) \(\chi_{8036}(463,\cdot)\) \(\chi_{8036}(603,\cdot)\) \(\chi_{8036}(827,\cdot)\) \(\chi_{8036}(855,\cdot)\) \(\chi_{8036}(967,\cdot)\) \(\chi_{8036}(995,\cdot)\) \(\chi_{8036}(1051,\cdot)\) \(\chi_{8036}(1135,\cdot)\) \(\chi_{8036}(1163,\cdot)\) \(\chi_{8036}(1219,\cdot)\) \(\chi_{8036}(1247,\cdot)\) \(\chi_{8036}(1331,\cdot)\) \(\chi_{8036}(1359,\cdot)\) \(\chi_{8036}(1387,\cdot)\) \(\chi_{8036}(1611,\cdot)\) \(\chi_{8036}(1751,\cdot)\) \(\chi_{8036}(1975,\cdot)\) \(\chi_{8036}(2003,\cdot)\) \(\chi_{8036}(2031,\cdot)\) \(\chi_{8036}(2115,\cdot)\) \(\chi_{8036}(2143,\cdot)\) \(\chi_{8036}(2199,\cdot)\) \(\chi_{8036}(2227,\cdot)\) \(\chi_{8036}(2283,\cdot)\) \(\chi_{8036}(2311,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{280})$ |
Fixed field: | Number field defined by a degree 280 polynomial (not computed) |
Values on generators
\((4019,493,785)\) → \((-1,e\left(\frac{4}{7}\right),e\left(\frac{33}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 8036 }(1247, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{56}\right)\) | \(e\left(\frac{101}{140}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{233}{280}\right)\) | \(e\left(\frac{121}{280}\right)\) | \(e\left(\frac{47}{280}\right)\) | \(e\left(\frac{143}{280}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) |