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.ee
\(\chi_{4017}(2,\cdot)\) \(\chi_{4017}(32,\cdot)\) \(\chi_{4017}(41,\cdot)\) \(\chi_{4017}(98,\cdot)\) \(\chi_{4017}(110,\cdot)\) \(\chi_{4017}(119,\cdot)\) \(\chi_{4017}(128,\cdot)\) \(\chi_{4017}(158,\cdot)\) \(\chi_{4017}(392,\cdot)\) \(\chi_{4017}(431,\cdot)\) \(\chi_{4017}(440,\cdot)\) \(\chi_{4017}(509,\cdot)\) \(\chi_{4017}(578,\cdot)\) \(\chi_{4017}(656,\cdot)\) \(\chi_{4017}(773,\cdot)\) \(\chi_{4017}(812,\cdot)\) \(\chi_{4017}(839,\cdot)\) \(\chi_{4017}(986,\cdot)\) \(\chi_{4017}(1034,\cdot)\) \(\chi_{4017}(1055,\cdot)\) \(\chi_{4017}(1112,\cdot)\) \(\chi_{4017}(1268,\cdot)\) \(\chi_{4017}(1346,\cdot)\) \(\chi_{4017}(1367,\cdot)\) \(\chi_{4017}(1397,\cdot)\) \(\chi_{4017}(1475,\cdot)\) \(\chi_{4017}(1571,\cdot)\) \(\chi_{4017}(1787,\cdot)\) \(\chi_{4017}(1814,\cdot)\) \(\chi_{4017}(1883,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{204})$ |
Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,e\left(\frac{5}{12}\right),e\left(\frac{8}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 4017 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{167}{204}\right)\) | \(e\left(\frac{65}{102}\right)\) | \(e\left(\frac{83}{204}\right)\) | \(e\left(\frac{43}{204}\right)\) | \(e\left(\frac{31}{68}\right)\) | \(e\left(\frac{23}{102}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{14}{51}\right)\) | \(e\left(\frac{16}{51}\right)\) |