Basic properties
Modulus: | \(8034\) | |
Conductor: | \(4017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4017}(809,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.dn
\(\chi_{8034}(35,\cdot)\) \(\chi_{8034}(809,\cdot)\) \(\chi_{8034}(971,\cdot)\) \(\chi_{8034}(1517,\cdot)\) \(\chi_{8034}(1829,\cdot)\) \(\chi_{8034}(2375,\cdot)\) \(\chi_{8034}(2453,\cdot)\) \(\chi_{8034}(2525,\cdot)\) \(\chi_{8034}(2765,\cdot)\) \(\chi_{8034}(2843,\cdot)\) \(\chi_{8034}(3545,\cdot)\) \(\chi_{8034}(3617,\cdot)\) \(\chi_{8034}(3773,\cdot)\) \(\chi_{8034}(3851,\cdot)\) \(\chi_{8034}(4091,\cdot)\) \(\chi_{8034}(4319,\cdot)\) \(\chi_{8034}(4397,\cdot)\) \(\chi_{8034}(4403,\cdot)\) \(\chi_{8034}(4553,\cdot)\) \(\chi_{8034}(4631,\cdot)\) \(\chi_{8034}(5567,\cdot)\) \(\chi_{8034}(5957,\cdot)\) \(\chi_{8034}(6191,\cdot)\) \(\chi_{8034}(6509,\cdot)\) \(\chi_{8034}(6659,\cdot)\) \(\chi_{8034}(6743,\cdot)\) \(\chi_{8034}(6899,\cdot)\) \(\chi_{8034}(6971,\cdot)\) \(\chi_{8034}(7049,\cdot)\) \(\chi_{8034}(7367,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{91}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(809, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{25}{102}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{32}{51}\right)\) |