Basic properties
Modulus: | \(2450\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1225}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2450.br
\(\chi_{2450}(59,\cdot)\) \(\chi_{2450}(89,\cdot)\) \(\chi_{2450}(159,\cdot)\) \(\chi_{2450}(229,\cdot)\) \(\chi_{2450}(269,\cdot)\) \(\chi_{2450}(339,\cdot)\) \(\chi_{2450}(369,\cdot)\) \(\chi_{2450}(409,\cdot)\) \(\chi_{2450}(439,\cdot)\) \(\chi_{2450}(479,\cdot)\) \(\chi_{2450}(579,\cdot)\) \(\chi_{2450}(689,\cdot)\) \(\chi_{2450}(719,\cdot)\) \(\chi_{2450}(759,\cdot)\) \(\chi_{2450}(789,\cdot)\) \(\chi_{2450}(829,\cdot)\) \(\chi_{2450}(859,\cdot)\) \(\chi_{2450}(929,\cdot)\) \(\chi_{2450}(969,\cdot)\) \(\chi_{2450}(1039,\cdot)\) \(\chi_{2450}(1069,\cdot)\) \(\chi_{2450}(1139,\cdot)\) \(\chi_{2450}(1179,\cdot)\) \(\chi_{2450}(1209,\cdot)\) \(\chi_{2450}(1279,\cdot)\) \(\chi_{2450}(1319,\cdot)\) \(\chi_{2450}(1389,\cdot)\) \(\chi_{2450}(1419,\cdot)\) \(\chi_{2450}(1459,\cdot)\) \(\chi_{2450}(1529,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{13}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 2450 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{23}{30}\right)\) |