Basic properties
| Modulus: | \(7245\) | |
| Conductor: | \(7245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | 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 7245.it
\(\chi_{7245}(83,\cdot)\) \(\chi_{7245}(272,\cdot)\) \(\chi_{7245}(293,\cdot)\) \(\chi_{7245}(398,\cdot)\) \(\chi_{7245}(608,\cdot)\) \(\chi_{7245}(797,\cdot)\) \(\chi_{7245}(902,\cdot)\) \(\chi_{7245}(1217,\cdot)\) \(\chi_{7245}(1238,\cdot)\) \(\chi_{7245}(1532,\cdot)\) \(\chi_{7245}(1742,\cdot)\) \(\chi_{7245}(1847,\cdot)\) \(\chi_{7245}(1868,\cdot)\) \(\chi_{7245}(2057,\cdot)\) \(\chi_{7245}(2183,\cdot)\) \(\chi_{7245}(2288,\cdot)\) \(\chi_{7245}(2498,\cdot)\) \(\chi_{7245}(2687,\cdot)\) \(\chi_{7245}(2813,\cdot)\) \(\chi_{7245}(2918,\cdot)\) \(\chi_{7245}(3317,\cdot)\) \(\chi_{7245}(3632,\cdot)\) \(\chi_{7245}(3737,\cdot)\) \(\chi_{7245}(3947,\cdot)\) \(\chi_{7245}(4178,\cdot)\) \(\chi_{7245}(4262,\cdot)\) \(\chi_{7245}(4367,\cdot)\) \(\chi_{7245}(4703,\cdot)\) \(\chi_{7245}(5123,\cdot)\) \(\chi_{7245}(5333,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((5636,5797,5176,1891)\) → \((e\left(\frac{5}{6}\right),i,-1,e\left(\frac{3}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(26\) |
| \( \chi_{ 7245 }(2057, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{109}{132}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{11}\right)\) |