Basic properties
| Modulus: | \(1225\) | |
| Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1225.bs
\(\chi_{1225}(54,\cdot)\) \(\chi_{1225}(59,\cdot)\) \(\chi_{1225}(89,\cdot)\) \(\chi_{1225}(94,\cdot)\) \(\chi_{1225}(159,\cdot)\) \(\chi_{1225}(164,\cdot)\) \(\chi_{1225}(194,\cdot)\) \(\chi_{1225}(229,\cdot)\) \(\chi_{1225}(234,\cdot)\) \(\chi_{1225}(269,\cdot)\) \(\chi_{1225}(304,\cdot)\) \(\chi_{1225}(334,\cdot)\) \(\chi_{1225}(339,\cdot)\) \(\chi_{1225}(369,\cdot)\) \(\chi_{1225}(404,\cdot)\) \(\chi_{1225}(409,\cdot)\) \(\chi_{1225}(439,\cdot)\) \(\chi_{1225}(444,\cdot)\) \(\chi_{1225}(479,\cdot)\) \(\chi_{1225}(514,\cdot)\) \(\chi_{1225}(544,\cdot)\) \(\chi_{1225}(579,\cdot)\) \(\chi_{1225}(584,\cdot)\) \(\chi_{1225}(614,\cdot)\) \(\chi_{1225}(654,\cdot)\) \(\chi_{1225}(684,\cdot)\) \(\chi_{1225}(689,\cdot)\) \(\chi_{1225}(719,\cdot)\) \(\chi_{1225}(759,\cdot)\) \(\chi_{1225}(789,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{11}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 1225 }(404, a) \) | \(-1\) | \(1\) | \(e\left(\frac{191}{210}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{67}{105}\right)\) |