Basic properties
Modulus: | \(8112\) | |
Conductor: | \(2704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2704}(219,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8112.ga
\(\chi_{8112}(67,\cdot)\) \(\chi_{8112}(475,\cdot)\) \(\chi_{8112}(643,\cdot)\) \(\chi_{8112}(691,\cdot)\) \(\chi_{8112}(1051,\cdot)\) \(\chi_{8112}(1099,\cdot)\) \(\chi_{8112}(1267,\cdot)\) \(\chi_{8112}(1315,\cdot)\) \(\chi_{8112}(1675,\cdot)\) \(\chi_{8112}(1723,\cdot)\) \(\chi_{8112}(1891,\cdot)\) \(\chi_{8112}(2299,\cdot)\) \(\chi_{8112}(2515,\cdot)\) \(\chi_{8112}(2563,\cdot)\) \(\chi_{8112}(2923,\cdot)\) \(\chi_{8112}(2971,\cdot)\) \(\chi_{8112}(3139,\cdot)\) \(\chi_{8112}(3187,\cdot)\) \(\chi_{8112}(3547,\cdot)\) \(\chi_{8112}(3595,\cdot)\) \(\chi_{8112}(3763,\cdot)\) \(\chi_{8112}(3811,\cdot)\) \(\chi_{8112}(4171,\cdot)\) \(\chi_{8112}(4219,\cdot)\) \(\chi_{8112}(4387,\cdot)\) \(\chi_{8112}(4435,\cdot)\) \(\chi_{8112}(4795,\cdot)\) \(\chi_{8112}(4843,\cdot)\) \(\chi_{8112}(5011,\cdot)\) \(\chi_{8112}(5059,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5071,6085,2705,3889)\) → \((-1,i,1,e\left(\frac{19}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8112 }(2923, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{59}{156}\right)\) |