Basic properties
| Modulus: | \(7350\) | |
| 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 \(\chi_{1225}(121,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7350.dc
\(\chi_{7350}(121,\cdot)\) \(\chi_{7350}(331,\cdot)\) \(\chi_{7350}(541,\cdot)\) \(\chi_{7350}(571,\cdot)\) \(\chi_{7350}(781,\cdot)\) \(\chi_{7350}(991,\cdot)\) \(\chi_{7350}(1171,\cdot)\) \(\chi_{7350}(1381,\cdot)\) \(\chi_{7350}(1411,\cdot)\) \(\chi_{7350}(1591,\cdot)\) \(\chi_{7350}(1621,\cdot)\) \(\chi_{7350}(2011,\cdot)\) \(\chi_{7350}(2041,\cdot)\) \(\chi_{7350}(2221,\cdot)\) \(\chi_{7350}(2461,\cdot)\) \(\chi_{7350}(2641,\cdot)\) \(\chi_{7350}(2671,\cdot)\) \(\chi_{7350}(2881,\cdot)\) \(\chi_{7350}(3061,\cdot)\) \(\chi_{7350}(3091,\cdot)\) \(\chi_{7350}(3271,\cdot)\) \(\chi_{7350}(3481,\cdot)\) \(\chi_{7350}(3511,\cdot)\) \(\chi_{7350}(3691,\cdot)\) \(\chi_{7350}(3721,\cdot)\) \(\chi_{7350}(3931,\cdot)\) \(\chi_{7350}(4111,\cdot)\) \(\chi_{7350}(4141,\cdot)\) \(\chi_{7350}(4321,\cdot)\) \(\chi_{7350}(4531,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((4901,1177,2551)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{19}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 7350 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{3}{7}\right)\) |