Basic properties
| Modulus: | \(4017\) | |
| Conductor: | \(4017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | 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.cx
\(\chi_{4017}(8,\cdot)\) \(\chi_{4017}(164,\cdot)\) \(\chi_{4017}(203,\cdot)\) \(\chi_{4017}(278,\cdot)\) \(\chi_{4017}(317,\cdot)\) \(\chi_{4017}(473,\cdot)\) \(\chi_{4017}(476,\cdot)\) \(\chi_{4017}(512,\cdot)\) \(\chi_{4017}(632,\cdot)\) \(\chi_{4017}(785,\cdot)\) \(\chi_{4017}(905,\cdot)\) \(\chi_{4017}(941,\cdot)\) \(\chi_{4017}(1214,\cdot)\) \(\chi_{4017}(1373,\cdot)\) \(\chi_{4017}(1451,\cdot)\) \(\chi_{4017}(1568,\cdot)\) \(\chi_{4017}(1682,\cdot)\) \(\chi_{4017}(1724,\cdot)\) \(\chi_{4017}(1760,\cdot)\) \(\chi_{4017}(1877,\cdot)\) \(\chi_{4017}(2033,\cdot)\) \(\chi_{4017}(2036,\cdot)\) \(\chi_{4017}(2153,\cdot)\) \(\chi_{4017}(2345,\cdot)\) \(\chi_{4017}(2462,\cdot)\) \(\chi_{4017}(3206,\cdot)\) \(\chi_{4017}(3362,\cdot)\) \(\chi_{4017}(3515,\cdot)\) \(\chi_{4017}(3635,\cdot)\) \(\chi_{4017}(3671,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((1340,1237,1756)\) → \((-1,-i,e\left(\frac{7}{17}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(3671, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{45}{68}\right)\) | \(e\left(\frac{61}{68}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{59}{68}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) |