Basic properties
Modulus: | \(4034\) | |
Conductor: | \(2017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(336\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2017}(541,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4034.bf
\(\chi_{4034}(27,\cdot)\) \(\chi_{4034}(29,\cdot)\) \(\chi_{4034}(31,\cdot)\) \(\chi_{4034}(33,\cdot)\) \(\chi_{4034}(63,\cdot)\) \(\chi_{4034}(69,\cdot)\) \(\chi_{4034}(95,\cdot)\) \(\chi_{4034}(103,\cdot)\) \(\chi_{4034}(147,\cdot)\) \(\chi_{4034}(219,\cdot)\) \(\chi_{4034}(235,\cdot)\) \(\chi_{4034}(289,\cdot)\) \(\chi_{4034}(335,\cdot)\) \(\chi_{4034}(343,\cdot)\) \(\chi_{4034}(383,\cdot)\) \(\chi_{4034}(489,\cdot)\) \(\chi_{4034}(511,\cdot)\) \(\chi_{4034}(541,\cdot)\) \(\chi_{4034}(617,\cdot)\) \(\chi_{4034}(677,\cdot)\) \(\chi_{4034}(747,\cdot)\) \(\chi_{4034}(921,\cdot)\) \(\chi_{4034}(969,\cdot)\) \(\chi_{4034}(971,\cdot)\) \(\chi_{4034}(1009,\cdot)\) \(\chi_{4034}(1041,\cdot)\) \(\chi_{4034}(1123,\cdot)\) \(\chi_{4034}(1141,\cdot)\) \(\chi_{4034}(1165,\cdot)\) \(\chi_{4034}(1277,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{336})$ |
Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{97}{336}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 4034 }(541, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{168}\right)\) | \(e\left(\frac{97}{336}\right)\) | \(e\left(\frac{167}{168}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{215}{336}\right)\) | \(e\left(\frac{57}{112}\right)\) | \(e\left(\frac{305}{336}\right)\) | \(e\left(\frac{29}{84}\right)\) |