Basic properties
| Modulus: | \(8034\) | |
| Conductor: | \(4017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4017}(3623,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.dc
\(\chi_{8034}(107,\cdot)\) \(\chi_{8034}(185,\cdot)\) \(\chi_{8034}(341,\cdot)\) \(\chi_{8034}(419,\cdot)\) \(\chi_{8034}(659,\cdot)\) \(\chi_{8034}(737,\cdot)\) \(\chi_{8034}(887,\cdot)\) \(\chi_{8034}(965,\cdot)\) \(\chi_{8034}(1049,\cdot)\) \(\chi_{8034}(1121,\cdot)\) \(\chi_{8034}(1127,\cdot)\) \(\chi_{8034}(1673,\cdot)\) \(\chi_{8034}(1985,\cdot)\) \(\chi_{8034}(2213,\cdot)\) \(\chi_{8034}(2531,\cdot)\) \(\chi_{8034}(3467,\cdot)\) \(\chi_{8034}(3623,\cdot)\) \(\chi_{8034}(3929,\cdot)\) \(\chi_{8034}(4169,\cdot)\) \(\chi_{8034}(4637,\cdot)\) \(\chi_{8034}(4793,\cdot)\) \(\chi_{8034}(5027,\cdot)\) \(\chi_{8034}(5099,\cdot)\) \(\chi_{8034}(5723,\cdot)\) \(\chi_{8034}(5801,\cdot)\) \(\chi_{8034}(6113,\cdot)\) \(\chi_{8034}(6581,\cdot)\) \(\chi_{8034}(6815,\cdot)\) \(\chi_{8034}(7133,\cdot)\) \(\chi_{8034}(7205,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{10}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8034 }(3623, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{102}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{13}{102}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{83}{102}\right)\) |