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.do
\(\chi_{4017}(62,\cdot)\) \(\chi_{4017}(101,\cdot)\) \(\chi_{4017}(173,\cdot)\) \(\chi_{4017}(251,\cdot)\) \(\chi_{4017}(569,\cdot)\) \(\chi_{4017}(764,\cdot)\) \(\chi_{4017}(836,\cdot)\) \(\chi_{4017}(875,\cdot)\) \(\chi_{4017}(992,\cdot)\) \(\chi_{4017}(1070,\cdot)\) \(\chi_{4017}(1115,\cdot)\) \(\chi_{4017}(1271,\cdot)\) \(\chi_{4017}(1310,\cdot)\) \(\chi_{4017}(1538,\cdot)\) \(\chi_{4017}(1616,\cdot)\) \(\chi_{4017}(1622,\cdot)\) \(\chi_{4017}(1772,\cdot)\) \(\chi_{4017}(1850,\cdot)\) \(\chi_{4017}(2045,\cdot)\) \(\chi_{4017}(2207,\cdot)\) \(\chi_{4017}(2753,\cdot)\) \(\chi_{4017}(2786,\cdot)\) \(\chi_{4017}(3065,\cdot)\) \(\chi_{4017}(3176,\cdot)\) \(\chi_{4017}(3410,\cdot)\) \(\chi_{4017}(3611,\cdot)\) \(\chi_{4017}(3689,\cdot)\) \(\chi_{4017}(3728,\cdot)\) \(\chi_{4017}(3761,\cdot)\) \(\chi_{4017}(3878,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{95}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{95}{102}\right)\) | \(e\left(\frac{91}{102}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{25}{102}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{37}{102}\right)\) |