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.br
\(\chi_{1225}(61,\cdot)\) \(\chi_{1225}(66,\cdot)\) \(\chi_{1225}(96,\cdot)\) \(\chi_{1225}(131,\cdot)\) \(\chi_{1225}(136,\cdot)\) \(\chi_{1225}(171,\cdot)\) \(\chi_{1225}(206,\cdot)\) \(\chi_{1225}(236,\cdot)\) \(\chi_{1225}(241,\cdot)\) \(\chi_{1225}(271,\cdot)\) \(\chi_{1225}(306,\cdot)\) \(\chi_{1225}(311,\cdot)\) \(\chi_{1225}(341,\cdot)\) \(\chi_{1225}(346,\cdot)\) \(\chi_{1225}(381,\cdot)\) \(\chi_{1225}(416,\cdot)\) \(\chi_{1225}(446,\cdot)\) \(\chi_{1225}(481,\cdot)\) \(\chi_{1225}(486,\cdot)\) \(\chi_{1225}(516,\cdot)\) \(\chi_{1225}(556,\cdot)\) \(\chi_{1225}(586,\cdot)\) \(\chi_{1225}(591,\cdot)\) \(\chi_{1225}(621,\cdot)\) \(\chi_{1225}(661,\cdot)\) \(\chi_{1225}(691,\cdot)\) \(\chi_{1225}(696,\cdot)\) \(\chi_{1225}(731,\cdot)\) \(\chi_{1225}(761,\cdot)\) \(\chi_{1225}(796,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{13}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1225 }(206, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{23}{210}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{1}{210}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{83}{105}\right)\) |