Basic properties
Modulus: | \(4011\) | |
Conductor: | \(4011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.br
\(\chi_{4011}(11,\cdot)\) \(\chi_{4011}(275,\cdot)\) \(\chi_{4011}(452,\cdot)\) \(\chi_{4011}(548,\cdot)\) \(\chi_{4011}(611,\cdot)\) \(\chi_{4011}(695,\cdot)\) \(\chi_{4011}(758,\cdot)\) \(\chi_{4011}(830,\cdot)\) \(\chi_{4011}(1010,\cdot)\) \(\chi_{4011}(1094,\cdot)\) \(\chi_{4011}(1157,\cdot)\) \(\chi_{4011}(1187,\cdot)\) \(\chi_{4011}(1523,\cdot)\) \(\chi_{4011}(1565,\cdot)\) \(\chi_{4011}(1598,\cdot)\) \(\chi_{4011}(1733,\cdot)\) \(\chi_{4011}(1880,\cdot)\) \(\chi_{4011}(1976,\cdot)\) \(\chi_{4011}(2069,\cdot)\) \(\chi_{4011}(2132,\cdot)\) \(\chi_{4011}(2333,\cdot)\) \(\chi_{4011}(2447,\cdot)\) \(\chi_{4011}(2669,\cdot)\) \(\chi_{4011}(2711,\cdot)\) \(\chi_{4011}(2879,\cdot)\) \(\chi_{4011}(3026,\cdot)\) \(\chi_{4011}(3140,\cdot)\) \(\chi_{4011}(3215,\cdot)\) \(\chi_{4011}(3278,\cdot)\) \(\chi_{4011}(3413,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{11}{38}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(1976, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{73}{114}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{23}{114}\right)\) | \(e\left(\frac{109}{114}\right)\) |