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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1225.bt
\(\chi_{1225}(4,\cdot)\) \(\chi_{1225}(9,\cdot)\) \(\chi_{1225}(39,\cdot)\) \(\chi_{1225}(44,\cdot)\) \(\chi_{1225}(109,\cdot)\) \(\chi_{1225}(114,\cdot)\) \(\chi_{1225}(144,\cdot)\) \(\chi_{1225}(179,\cdot)\) \(\chi_{1225}(184,\cdot)\) \(\chi_{1225}(219,\cdot)\) \(\chi_{1225}(254,\cdot)\) \(\chi_{1225}(284,\cdot)\) \(\chi_{1225}(289,\cdot)\) \(\chi_{1225}(319,\cdot)\) \(\chi_{1225}(354,\cdot)\) \(\chi_{1225}(359,\cdot)\) \(\chi_{1225}(389,\cdot)\) \(\chi_{1225}(394,\cdot)\) \(\chi_{1225}(429,\cdot)\) \(\chi_{1225}(464,\cdot)\) \(\chi_{1225}(494,\cdot)\) \(\chi_{1225}(529,\cdot)\) \(\chi_{1225}(534,\cdot)\) \(\chi_{1225}(564,\cdot)\) \(\chi_{1225}(604,\cdot)\) \(\chi_{1225}(634,\cdot)\) \(\chi_{1225}(639,\cdot)\) \(\chi_{1225}(669,\cdot)\) \(\chi_{1225}(709,\cdot)\) \(\chi_{1225}(739,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{20}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 1225 }(354, a) \) | \(1\) | \(1\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{137}{210}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{47}{105}\right)\) |