Basic properties
Modulus: | \(8024\) | |
Conductor: | \(4012\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(116\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4012}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8024.ci
\(\chi_{8024}(47,\cdot)\) \(\chi_{8024}(55,\cdot)\) \(\chi_{8024}(183,\cdot)\) \(\chi_{8024}(191,\cdot)\) \(\chi_{8024}(319,\cdot)\) \(\chi_{8024}(327,\cdot)\) \(\chi_{8024}(455,\cdot)\) \(\chi_{8024}(463,\cdot)\) \(\chi_{8024}(863,\cdot)\) \(\chi_{8024}(999,\cdot)\) \(\chi_{8024}(1135,\cdot)\) \(\chi_{8024}(1271,\cdot)\) \(\chi_{8024}(1279,\cdot)\) \(\chi_{8024}(1407,\cdot)\) \(\chi_{8024}(2095,\cdot)\) \(\chi_{8024}(2223,\cdot)\) \(\chi_{8024}(2639,\cdot)\) \(\chi_{8024}(2775,\cdot)\) \(\chi_{8024}(3039,\cdot)\) \(\chi_{8024}(3047,\cdot)\) \(\chi_{8024}(3183,\cdot)\) \(\chi_{8024}(3455,\cdot)\) \(\chi_{8024}(3583,\cdot)\) \(\chi_{8024}(3719,\cdot)\) \(\chi_{8024}(3727,\cdot)\) \(\chi_{8024}(3991,\cdot)\) \(\chi_{8024}(4127,\cdot)\) \(\chi_{8024}(4271,\cdot)\) \(\chi_{8024}(4399,\cdot)\) \(\chi_{8024}(4671,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{116})$ |
Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((-1,1,i,e\left(\frac{23}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 8024 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{116}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(e\left(\frac{45}{116}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{19}{116}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{23}{116}\right)\) |