Basic properties
Modulus: | \(4011\) | |
Conductor: | \(4011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | 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
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.bq
\(\chi_{4011}(32,\cdot)\) \(\chi_{4011}(107,\cdot)\) \(\chi_{4011}(221,\cdot)\) \(\chi_{4011}(368,\cdot)\) \(\chi_{4011}(536,\cdot)\) \(\chi_{4011}(578,\cdot)\) \(\chi_{4011}(800,\cdot)\) \(\chi_{4011}(914,\cdot)\) \(\chi_{4011}(1115,\cdot)\) \(\chi_{4011}(1178,\cdot)\) \(\chi_{4011}(1271,\cdot)\) \(\chi_{4011}(1367,\cdot)\) \(\chi_{4011}(1514,\cdot)\) \(\chi_{4011}(1649,\cdot)\) \(\chi_{4011}(1682,\cdot)\) \(\chi_{4011}(1724,\cdot)\) \(\chi_{4011}(2060,\cdot)\) \(\chi_{4011}(2090,\cdot)\) \(\chi_{4011}(2153,\cdot)\) \(\chi_{4011}(2237,\cdot)\) \(\chi_{4011}(2417,\cdot)\) \(\chi_{4011}(2489,\cdot)\) \(\chi_{4011}(2552,\cdot)\) \(\chi_{4011}(2636,\cdot)\) \(\chi_{4011}(2699,\cdot)\) \(\chi_{4011}(2795,\cdot)\) \(\chi_{4011}(2972,\cdot)\) \(\chi_{4011}(3236,\cdot)\) \(\chi_{4011}(3299,\cdot)\) \(\chi_{4011}(3383,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{17}{19}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(1649, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{114}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{25}{114}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{97}{114}\right)\) | \(e\left(\frac{13}{57}\right)\) |