Basic properties
Modulus: | \(4017\) | |
Conductor: | \(4017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(204\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.ef
\(\chi_{4017}(137,\cdot)\) \(\chi_{4017}(167,\cdot)\) \(\chi_{4017}(215,\cdot)\) \(\chi_{4017}(236,\cdot)\) \(\chi_{4017}(323,\cdot)\) \(\chi_{4017}(332,\cdot)\) \(\chi_{4017}(488,\cdot)\) \(\chi_{4017}(587,\cdot)\) \(\chi_{4017}(596,\cdot)\) \(\chi_{4017}(626,\cdot)\) \(\chi_{4017}(734,\cdot)\) \(\chi_{4017}(782,\cdot)\) \(\chi_{4017}(800,\cdot)\) \(\chi_{4017}(821,\cdot)\) \(\chi_{4017}(890,\cdot)\) \(\chi_{4017}(917,\cdot)\) \(\chi_{4017}(1064,\cdot)\) \(\chi_{4017}(1094,\cdot)\) \(\chi_{4017}(1142,\cdot)\) \(\chi_{4017}(1163,\cdot)\) \(\chi_{4017}(1250,\cdot)\) \(\chi_{4017}(1259,\cdot)\) \(\chi_{4017}(1415,\cdot)\) \(\chi_{4017}(1514,\cdot)\) \(\chi_{4017}(1523,\cdot)\) \(\chi_{4017}(1553,\cdot)\) \(\chi_{4017}(1709,\cdot)\) \(\chi_{4017}(1727,\cdot)\) \(\chi_{4017}(1748,\cdot)\) \(\chi_{4017}(1844,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{204})$ |
Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,e\left(\frac{11}{12}\right),e\left(\frac{4}{17}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 4017 }(332, a) \) | \(1\) | \(1\) | \(e\left(\frac{157}{204}\right)\) | \(e\left(\frac{55}{102}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{5}{204}\right)\) | \(e\left(\frac{21}{68}\right)\) | \(e\left(\frac{77}{102}\right)\) | \(e\left(\frac{55}{204}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{41}{51}\right)\) |