Basic properties
| Modulus: | \(203\) | |
| Conductor: | \(203\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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 203.x
\(\chi_{203}(3,\cdot)\) \(\chi_{203}(10,\cdot)\) \(\chi_{203}(19,\cdot)\) \(\chi_{203}(26,\cdot)\) \(\chi_{203}(31,\cdot)\) \(\chi_{203}(40,\cdot)\) \(\chi_{203}(47,\cdot)\) \(\chi_{203}(61,\cdot)\) \(\chi_{203}(66,\cdot)\) \(\chi_{203}(68,\cdot)\) \(\chi_{203}(73,\cdot)\) \(\chi_{203}(89,\cdot)\) \(\chi_{203}(101,\cdot)\) \(\chi_{203}(108,\cdot)\) \(\chi_{203}(124,\cdot)\) \(\chi_{203}(131,\cdot)\) \(\chi_{203}(143,\cdot)\) \(\chi_{203}(159,\cdot)\) \(\chi_{203}(164,\cdot)\) \(\chi_{203}(166,\cdot)\) \(\chi_{203}(171,\cdot)\) \(\chi_{203}(185,\cdot)\) \(\chi_{203}(192,\cdot)\) \(\chi_{203}(201,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((59,176)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{27}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 203 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{7}{12}\right)\) |