Basic properties
Modulus: | \(4012\) | |
Conductor: | \(1003\) | 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 \(\chi_{1003}(21,\cdot)\) | 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.bd
\(\chi_{4012}(21,\cdot)\) \(\chi_{4012}(81,\cdot)\) \(\chi_{4012}(225,\cdot)\) \(\chi_{4012}(285,\cdot)\) \(\chi_{4012}(293,\cdot)\) \(\chi_{4012}(361,\cdot)\) \(\chi_{4012}(429,\cdot)\) \(\chi_{4012}(489,\cdot)\) \(\chi_{4012}(497,\cdot)\) \(\chi_{4012}(557,\cdot)\) \(\chi_{4012}(625,\cdot)\) \(\chi_{4012}(761,\cdot)\) \(\chi_{4012}(829,\cdot)\) \(\chi_{4012}(897,\cdot)\) \(\chi_{4012}(905,\cdot)\) \(\chi_{4012}(965,\cdot)\) \(\chi_{4012}(973,\cdot)\) \(\chi_{4012}(1169,\cdot)\) \(\chi_{4012}(1237,\cdot)\) \(\chi_{4012}(1305,\cdot)\) \(\chi_{4012}(1313,\cdot)\) \(\chi_{4012}(1373,\cdot)\) \(\chi_{4012}(1441,\cdot)\) \(\chi_{4012}(1585,\cdot)\) \(\chi_{4012}(1789,\cdot)\) \(\chi_{4012}(1849,\cdot)\) \(\chi_{4012}(1857,\cdot)\) \(\chi_{4012}(1917,\cdot)\) \(\chi_{4012}(1993,\cdot)\) \(\chi_{4012}(2129,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{116})$ |
Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((2007,3777,3129)\) → \((1,-i,e\left(\frac{5}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 4012 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{116}\right)\) | \(e\left(\frac{91}{116}\right)\) | \(e\left(\frac{41}{116}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{65}{116}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{97}{116}\right)\) |