Basic properties
Modulus: | \(8036\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2009}(601,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8036.dc
\(\chi_{8036}(601,\cdot)\) \(\chi_{8036}(629,\cdot)\) \(\chi_{8036}(741,\cdot)\) \(\chi_{8036}(1637,\cdot)\) \(\chi_{8036}(1749,\cdot)\) \(\chi_{8036}(1777,\cdot)\) \(\chi_{8036}(1889,\cdot)\) \(\chi_{8036}(2785,\cdot)\) \(\chi_{8036}(2897,\cdot)\) \(\chi_{8036}(2925,\cdot)\) \(\chi_{8036}(3933,\cdot)\) \(\chi_{8036}(4045,\cdot)\) \(\chi_{8036}(4073,\cdot)\) \(\chi_{8036}(4185,\cdot)\) \(\chi_{8036}(5081,\cdot)\) \(\chi_{8036}(5221,\cdot)\) \(\chi_{8036}(5333,\cdot)\) \(\chi_{8036}(6229,\cdot)\) \(\chi_{8036}(6341,\cdot)\) \(\chi_{8036}(6481,\cdot)\) \(\chi_{8036}(7377,\cdot)\) \(\chi_{8036}(7489,\cdot)\) \(\chi_{8036}(7517,\cdot)\) \(\chi_{8036}(7629,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((4019,493,785)\) → \((1,e\left(\frac{11}{14}\right),e\left(\frac{1}{8}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 8036 }(601, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{45}{56}\right)\) | \(e\left(\frac{45}{56}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) |