Basic properties
Modulus: | \(4017\) | |
Conductor: | \(4017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | 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 4017.dp
\(\chi_{4017}(77,\cdot)\) \(\chi_{4017}(623,\cdot)\) \(\chi_{4017}(662,\cdot)\) \(\chi_{4017}(1013,\cdot)\) \(\chi_{4017}(1208,\cdot)\) \(\chi_{4017}(1247,\cdot)\) \(\chi_{4017}(1520,\cdot)\) \(\chi_{4017}(1598,\cdot)\) \(\chi_{4017}(1715,\cdot)\) \(\chi_{4017}(2027,\cdot)\) \(\chi_{4017}(2066,\cdot)\) \(\chi_{4017}(2105,\cdot)\) \(\chi_{4017}(2144,\cdot)\) \(\chi_{4017}(2183,\cdot)\) \(\chi_{4017}(2417,\cdot)\) \(\chi_{4017}(2456,\cdot)\) \(\chi_{4017}(2534,\cdot)\) \(\chi_{4017}(2573,\cdot)\) \(\chi_{4017}(2690,\cdot)\) \(\chi_{4017}(2729,\cdot)\) \(\chi_{4017}(2846,\cdot)\) \(\chi_{4017}(2924,\cdot)\) \(\chi_{4017}(3041,\cdot)\) \(\chi_{4017}(3236,\cdot)\) \(\chi_{4017}(3392,\cdot)\) \(\chi_{4017}(3470,\cdot)\) \(\chi_{4017}(3587,\cdot)\) \(\chi_{4017}(3626,\cdot)\) \(\chi_{4017}(3704,\cdot)\) \(\chi_{4017}(3743,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,-1,e\left(\frac{83}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 4017 }(2066, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{83}{102}\right)\) | \(e\left(\frac{77}{102}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{65}{102}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{47}{102}\right)\) |