Basic properties
| Modulus: | \(8001\) | |
| Conductor: | \(8001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 8001.nt
\(\chi_{8001}(86,\cdot)\) \(\chi_{8001}(212,\cdot)\) \(\chi_{8001}(464,\cdot)\) \(\chi_{8001}(515,\cdot)\) \(\chi_{8001}(641,\cdot)\) \(\chi_{8001}(956,\cdot)\) \(\chi_{8001}(1019,\cdot)\) \(\chi_{8001}(1094,\cdot)\) \(\chi_{8001}(1208,\cdot)\) \(\chi_{8001}(2216,\cdot)\) \(\chi_{8001}(2342,\cdot)\) \(\chi_{8001}(3035,\cdot)\) \(\chi_{8001}(3287,\cdot)\) \(\chi_{8001}(3350,\cdot)\) \(\chi_{8001}(3602,\cdot)\) \(\chi_{8001}(3614,\cdot)\) \(\chi_{8001}(3992,\cdot)\) \(\chi_{8001}(4055,\cdot)\) \(\chi_{8001}(4244,\cdot)\) \(\chi_{8001}(4307,\cdot)\) \(\chi_{8001}(4673,\cdot)\) \(\chi_{8001}(5063,\cdot)\) \(\chi_{8001}(5177,\cdot)\) \(\chi_{8001}(5189,\cdot)\) \(\chi_{8001}(5252,\cdot)\) \(\chi_{8001}(5303,\cdot)\) \(\chi_{8001}(5504,\cdot)\) \(\chi_{8001}(5567,\cdot)\) \(\chi_{8001}(5807,\cdot)\) \(\chi_{8001}(6008,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{1}{3}\right),e\left(\frac{17}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(86, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(1\) |