Basic properties
| Modulus: | \(7938\) | |
| Conductor: | \(3969\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(378\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3969}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7938.dd
\(\chi_{7938}(47,\cdot)\) \(\chi_{7938}(59,\cdot)\) \(\chi_{7938}(173,\cdot)\) \(\chi_{7938}(185,\cdot)\) \(\chi_{7938}(299,\cdot)\) \(\chi_{7938}(311,\cdot)\) \(\chi_{7938}(425,\cdot)\) \(\chi_{7938}(437,\cdot)\) \(\chi_{7938}(551,\cdot)\) \(\chi_{7938}(563,\cdot)\) \(\chi_{7938}(677,\cdot)\) \(\chi_{7938}(689,\cdot)\) \(\chi_{7938}(929,\cdot)\) \(\chi_{7938}(941,\cdot)\) \(\chi_{7938}(1055,\cdot)\) \(\chi_{7938}(1067,\cdot)\) \(\chi_{7938}(1181,\cdot)\) \(\chi_{7938}(1193,\cdot)\) \(\chi_{7938}(1307,\cdot)\) \(\chi_{7938}(1319,\cdot)\) \(\chi_{7938}(1433,\cdot)\) \(\chi_{7938}(1445,\cdot)\) \(\chi_{7938}(1559,\cdot)\) \(\chi_{7938}(1571,\cdot)\) \(\chi_{7938}(1811,\cdot)\) \(\chi_{7938}(1823,\cdot)\) \(\chi_{7938}(1937,\cdot)\) \(\chi_{7938}(1949,\cdot)\) \(\chi_{7938}(2063,\cdot)\) \(\chi_{7938}(2075,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
Values on generators
\((6077,3727)\) → \((e\left(\frac{7}{54}\right),e\left(\frac{5}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7938 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{82}{189}\right)\) | \(e\left(\frac{169}{378}\right)\) | \(e\left(\frac{365}{378}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{359}{378}\right)\) | \(e\left(\frac{164}{189}\right)\) | \(e\left(\frac{355}{378}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{16}{63}\right)\) |