Basic properties
| Modulus: | \(4017\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1339}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.ct
\(\chi_{4017}(16,\cdot)\) \(\chi_{4017}(55,\cdot)\) \(\chi_{4017}(139,\cdot)\) \(\chi_{4017}(256,\cdot)\) \(\chi_{4017}(289,\cdot)\) \(\chi_{4017}(328,\cdot)\) \(\chi_{4017}(406,\cdot)\) \(\chi_{4017}(607,\cdot)\) \(\chi_{4017}(841,\cdot)\) \(\chi_{4017}(952,\cdot)\) \(\chi_{4017}(1231,\cdot)\) \(\chi_{4017}(1264,\cdot)\) \(\chi_{4017}(1810,\cdot)\) \(\chi_{4017}(1972,\cdot)\) \(\chi_{4017}(2167,\cdot)\) \(\chi_{4017}(2245,\cdot)\) \(\chi_{4017}(2395,\cdot)\) \(\chi_{4017}(2401,\cdot)\) \(\chi_{4017}(2479,\cdot)\) \(\chi_{4017}(2707,\cdot)\) \(\chi_{4017}(2746,\cdot)\) \(\chi_{4017}(2902,\cdot)\) \(\chi_{4017}(2947,\cdot)\) \(\chi_{4017}(3025,\cdot)\) \(\chi_{4017}(3142,\cdot)\) \(\chi_{4017}(3181,\cdot)\) \(\chi_{4017}(3253,\cdot)\) \(\chi_{4017}(3448,\cdot)\) \(\chi_{4017}(3766,\cdot)\) \(\chi_{4017}(3844,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((1340,1237,1756)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{37}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{29}{51}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{23}{51}\right)\) |