Basic properties
| Modulus: | \(2415\) | |
| Conductor: | \(805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{805}(618,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2415.dn
\(\chi_{2415}(37,\cdot)\) \(\chi_{2415}(67,\cdot)\) \(\chi_{2415}(88,\cdot)\) \(\chi_{2415}(172,\cdot)\) \(\chi_{2415}(247,\cdot)\) \(\chi_{2415}(268,\cdot)\) \(\chi_{2415}(352,\cdot)\) \(\chi_{2415}(373,\cdot)\) \(\chi_{2415}(382,\cdot)\) \(\chi_{2415}(457,\cdot)\) \(\chi_{2415}(562,\cdot)\) \(\chi_{2415}(592,\cdot)\) \(\chi_{2415}(613,\cdot)\) \(\chi_{2415}(688,\cdot)\) \(\chi_{2415}(697,\cdot)\) \(\chi_{2415}(718,\cdot)\) \(\chi_{2415}(793,\cdot)\) \(\chi_{2415}(802,\cdot)\) \(\chi_{2415}(907,\cdot)\) \(\chi_{2415}(1003,\cdot)\) \(\chi_{2415}(1033,\cdot)\) \(\chi_{2415}(1138,\cdot)\) \(\chi_{2415}(1192,\cdot)\) \(\chi_{2415}(1213,\cdot)\) \(\chi_{2415}(1318,\cdot)\) \(\chi_{2415}(1348,\cdot)\) \(\chi_{2415}(1423,\cdot)\) \(\chi_{2415}(1528,\cdot)\) \(\chi_{2415}(1537,\cdot)\) \(\chi_{2415}(1558,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((806,967,346,1891)\) → \((1,-i,e\left(\frac{1}{3}\right),e\left(\frac{5}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(26\) |
| \( \chi_{ 2415 }(1423, a) \) | \(1\) | \(1\) | \(e\left(\frac{115}{132}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{89}{132}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(i\) | \(e\left(\frac{10}{33}\right)\) |