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.dj
\(\chi_{4017}(146,\cdot)\) \(\chi_{4017}(191,\cdot)\) \(\chi_{4017}(497,\cdot)\) \(\chi_{4017}(653,\cdot)\) \(\chi_{4017}(692,\cdot)\) \(\chi_{4017}(932,\cdot)\) \(\chi_{4017}(1004,\cdot)\) \(\chi_{4017}(1322,\cdot)\) \(\chi_{4017}(1556,\cdot)\) \(\chi_{4017}(1589,\cdot)\) \(\chi_{4017}(1907,\cdot)\) \(\chi_{4017}(2024,\cdot)\) \(\chi_{4017}(2135,\cdot)\) \(\chi_{4017}(2336,\cdot)\) \(\chi_{4017}(2414,\cdot)\) \(\chi_{4017}(2447,\cdot)\) \(\chi_{4017}(2993,\cdot)\) \(\chi_{4017}(2999,\cdot)\) \(\chi_{4017}(3038,\cdot)\) \(\chi_{4017}(3071,\cdot)\) \(\chi_{4017}(3110,\cdot)\) \(\chi_{4017}(3155,\cdot)\) \(\chi_{4017}(3233,\cdot)\) \(\chi_{4017}(3344,\cdot)\) \(\chi_{4017}(3383,\cdot)\) \(\chi_{4017}(3461,\cdot)\) \(\chi_{4017}(3500,\cdot)\) \(\chi_{4017}(3701,\cdot)\) \(\chi_{4017}(3779,\cdot)\) \(\chi_{4017}(3935,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{77}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(146, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{102}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{31}{102}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{1}{102}\right)\) |