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
\((1177,101)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{11}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1225 }(389, a) \) | \(1\) | \(1\) | \(e\left(\frac{193}{210}\right)\) | \(e\left(\frac{131}{210}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{71}{105}\right)\) |