Basic properties
Modulus: | \(4011\) | |
Conductor: | \(1337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1337}(521,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.bu
\(\chi_{4011}(31,\cdot)\) \(\chi_{4011}(166,\cdot)\) \(\chi_{4011}(229,\cdot)\) \(\chi_{4011}(313,\cdot)\) \(\chi_{4011}(346,\cdot)\) \(\chi_{4011}(376,\cdot)\) \(\chi_{4011}(628,\cdot)\) \(\chi_{4011}(712,\cdot)\) \(\chi_{4011}(775,\cdot)\) \(\chi_{4011}(1039,\cdot)\) \(\chi_{4011}(1216,\cdot)\) \(\chi_{4011}(1312,\cdot)\) \(\chi_{4011}(1375,\cdot)\) \(\chi_{4011}(1459,\cdot)\) \(\chi_{4011}(1522,\cdot)\) \(\chi_{4011}(1594,\cdot)\) \(\chi_{4011}(1774,\cdot)\) \(\chi_{4011}(1858,\cdot)\) \(\chi_{4011}(1921,\cdot)\) \(\chi_{4011}(1951,\cdot)\) \(\chi_{4011}(2287,\cdot)\) \(\chi_{4011}(2329,\cdot)\) \(\chi_{4011}(2362,\cdot)\) \(\chi_{4011}(2497,\cdot)\) \(\chi_{4011}(2644,\cdot)\) \(\chi_{4011}(2740,\cdot)\) \(\chi_{4011}(2833,\cdot)\) \(\chi_{4011}(2896,\cdot)\) \(\chi_{4011}(3097,\cdot)\) \(\chi_{4011}(3211,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{21}{38}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(1858, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{13}{114}\right)\) | \(e\left(\frac{73}{114}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{37}{114}\right)\) | \(e\left(\frac{22}{57}\right)\) |