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 \(\chi_{1337}(886,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.bw
\(\chi_{4011}(37,\cdot)\) \(\chi_{4011}(205,\cdot)\) \(\chi_{4011}(352,\cdot)\) \(\chi_{4011}(466,\cdot)\) \(\chi_{4011}(541,\cdot)\) \(\chi_{4011}(604,\cdot)\) \(\chi_{4011}(739,\cdot)\) \(\chi_{4011}(802,\cdot)\) \(\chi_{4011}(886,\cdot)\) \(\chi_{4011}(919,\cdot)\) \(\chi_{4011}(949,\cdot)\) \(\chi_{4011}(1201,\cdot)\) \(\chi_{4011}(1285,\cdot)\) \(\chi_{4011}(1348,\cdot)\) \(\chi_{4011}(1612,\cdot)\) \(\chi_{4011}(1789,\cdot)\) \(\chi_{4011}(1885,\cdot)\) \(\chi_{4011}(1948,\cdot)\) \(\chi_{4011}(2032,\cdot)\) \(\chi_{4011}(2095,\cdot)\) \(\chi_{4011}(2167,\cdot)\) \(\chi_{4011}(2347,\cdot)\) \(\chi_{4011}(2431,\cdot)\) \(\chi_{4011}(2494,\cdot)\) \(\chi_{4011}(2524,\cdot)\) \(\chi_{4011}(2860,\cdot)\) \(\chi_{4011}(2902,\cdot)\) \(\chi_{4011}(2935,\cdot)\) \(\chi_{4011}(3070,\cdot)\) \(\chi_{4011}(3217,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{31}{38}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(886, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{1}{114}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{17}{114}\right)\) |