Basic properties
Modulus: | \(8023\) | |
Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(56\) | 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 8023.db
\(\chi_{8023}(190,\cdot)\) \(\chi_{8023}(730,\cdot)\) \(\chi_{8023}(740,\cdot)\) \(\chi_{8023}(1042,\cdot)\) \(\chi_{8023}(1736,\cdot)\) \(\chi_{8023}(1947,\cdot)\) \(\chi_{8023}(2025,\cdot)\) \(\chi_{8023}(2238,\cdot)\) \(\chi_{8023}(2434,\cdot)\) \(\chi_{8023}(2743,\cdot)\) \(\chi_{8023}(2799,\cdot)\) \(\chi_{8023}(3227,\cdot)\) \(\chi_{8023}(3440,\cdot)\) \(\chi_{8023}(4006,\cdot)\) \(\chi_{8023}(4376,\cdot)\) \(\chi_{8023}(4848,\cdot)\) \(\chi_{8023}(4931,\cdot)\) \(\chi_{8023}(4947,\cdot)\) \(\chi_{8023}(5220,\cdot)\) \(\chi_{8023}(5433,\cdot)\) \(\chi_{8023}(5799,\cdot)\) \(\chi_{8023}(6339,\cdot)\) \(\chi_{8023}(7358,\cdot)\) \(\chi_{8023}(7784,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{5}{7}\right),e\left(\frac{41}{56}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8023 }(190, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{9}{28}\right)\) |