Basic properties
Modulus: | \(4012\) | |
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: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4012.be
\(\chi_{4012}(47,\cdot)\) \(\chi_{4012}(55,\cdot)\) \(\chi_{4012}(115,\cdot)\) \(\chi_{4012}(183,\cdot)\) \(\chi_{4012}(191,\cdot)\) \(\chi_{4012}(259,\cdot)\) \(\chi_{4012}(319,\cdot)\) \(\chi_{4012}(327,\cdot)\) \(\chi_{4012}(387,\cdot)\) \(\chi_{4012}(455,\cdot)\) \(\chi_{4012}(463,\cdot)\) \(\chi_{4012}(659,\cdot)\) \(\chi_{4012}(667,\cdot)\) \(\chi_{4012}(863,\cdot)\) \(\chi_{4012}(939,\cdot)\) \(\chi_{4012}(999,\cdot)\) \(\chi_{4012}(1075,\cdot)\) \(\chi_{4012}(1135,\cdot)\) \(\chi_{4012}(1203,\cdot)\) \(\chi_{4012}(1211,\cdot)\) \(\chi_{4012}(1271,\cdot)\) \(\chi_{4012}(1279,\cdot)\) \(\chi_{4012}(1407,\cdot)\) \(\chi_{4012}(1483,\cdot)\) \(\chi_{4012}(1611,\cdot)\) \(\chi_{4012}(1755,\cdot)\) \(\chi_{4012}(1883,\cdot)\) \(\chi_{4012}(2019,\cdot)\) \(\chi_{4012}(2095,\cdot)\) \(\chi_{4012}(2155,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{116})$ |
Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((2007,3777,3129)\) → \((-1,-i,e\left(\frac{31}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 4012 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{116}\right)\) | \(e\left(\frac{111}{116}\right)\) | \(e\left(\frac{43}{116}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{13}{116}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{89}{116}\right)\) |