Basic properties
Modulus: | \(1225\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(105\) | 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.bo
\(\chi_{1225}(11,\cdot)\) \(\chi_{1225}(16,\cdot)\) \(\chi_{1225}(46,\cdot)\) \(\chi_{1225}(81,\cdot)\) \(\chi_{1225}(86,\cdot)\) \(\chi_{1225}(121,\cdot)\) \(\chi_{1225}(156,\cdot)\) \(\chi_{1225}(186,\cdot)\) \(\chi_{1225}(191,\cdot)\) \(\chi_{1225}(221,\cdot)\) \(\chi_{1225}(256,\cdot)\) \(\chi_{1225}(261,\cdot)\) \(\chi_{1225}(291,\cdot)\) \(\chi_{1225}(296,\cdot)\) \(\chi_{1225}(331,\cdot)\) \(\chi_{1225}(366,\cdot)\) \(\chi_{1225}(396,\cdot)\) \(\chi_{1225}(431,\cdot)\) \(\chi_{1225}(436,\cdot)\) \(\chi_{1225}(466,\cdot)\) \(\chi_{1225}(506,\cdot)\) \(\chi_{1225}(536,\cdot)\) \(\chi_{1225}(541,\cdot)\) \(\chi_{1225}(571,\cdot)\) \(\chi_{1225}(611,\cdot)\) \(\chi_{1225}(641,\cdot)\) \(\chi_{1225}(646,\cdot)\) \(\chi_{1225}(681,\cdot)\) \(\chi_{1225}(711,\cdot)\) \(\chi_{1225}(746,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{11}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1225 }(46, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{92}{105}\right)\) |