Basic properties
| Modulus: | \(2450\) | |
| Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1225}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2450.bo
\(\chi_{2450}(11,\cdot)\) \(\chi_{2450}(81,\cdot)\) \(\chi_{2450}(121,\cdot)\) \(\chi_{2450}(191,\cdot)\) \(\chi_{2450}(221,\cdot)\) \(\chi_{2450}(261,\cdot)\) \(\chi_{2450}(291,\cdot)\) \(\chi_{2450}(331,\cdot)\) \(\chi_{2450}(431,\cdot)\) \(\chi_{2450}(541,\cdot)\) \(\chi_{2450}(571,\cdot)\) \(\chi_{2450}(611,\cdot)\) \(\chi_{2450}(641,\cdot)\) \(\chi_{2450}(681,\cdot)\) \(\chi_{2450}(711,\cdot)\) \(\chi_{2450}(781,\cdot)\) \(\chi_{2450}(821,\cdot)\) \(\chi_{2450}(891,\cdot)\) \(\chi_{2450}(921,\cdot)\) \(\chi_{2450}(991,\cdot)\) \(\chi_{2450}(1031,\cdot)\) \(\chi_{2450}(1061,\cdot)\) \(\chi_{2450}(1131,\cdot)\) \(\chi_{2450}(1171,\cdot)\) \(\chi_{2450}(1241,\cdot)\) \(\chi_{2450}(1271,\cdot)\) \(\chi_{2450}(1311,\cdot)\) \(\chi_{2450}(1381,\cdot)\) \(\chi_{2450}(1411,\cdot)\) \(\chi_{2450}(1481,\cdot)\) ...
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
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 2450 }(1271, a) \) | \(1\) | \(1\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{7}{15}\right)\) |