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 \(\chi_{3969}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7938.dc
\(\chi_{7938}(41,\cdot)\) \(\chi_{7938}(83,\cdot)\) \(\chi_{7938}(167,\cdot)\) \(\chi_{7938}(209,\cdot)\) \(\chi_{7938}(335,\cdot)\) \(\chi_{7938}(419,\cdot)\) \(\chi_{7938}(461,\cdot)\) \(\chi_{7938}(545,\cdot)\) \(\chi_{7938}(671,\cdot)\) \(\chi_{7938}(713,\cdot)\) \(\chi_{7938}(797,\cdot)\) \(\chi_{7938}(839,\cdot)\) \(\chi_{7938}(923,\cdot)\) \(\chi_{7938}(965,\cdot)\) \(\chi_{7938}(1049,\cdot)\) \(\chi_{7938}(1091,\cdot)\) \(\chi_{7938}(1217,\cdot)\) \(\chi_{7938}(1301,\cdot)\) \(\chi_{7938}(1343,\cdot)\) \(\chi_{7938}(1427,\cdot)\) \(\chi_{7938}(1553,\cdot)\) \(\chi_{7938}(1595,\cdot)\) \(\chi_{7938}(1679,\cdot)\) \(\chi_{7938}(1721,\cdot)\) \(\chi_{7938}(1805,\cdot)\) \(\chi_{7938}(1847,\cdot)\) \(\chi_{7938}(1931,\cdot)\) \(\chi_{7938}(1973,\cdot)\) \(\chi_{7938}(2099,\cdot)\) \(\chi_{7938}(2183,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
Values on generators
\((6077,3727)\) → \((e\left(\frac{53}{54}\right),e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7938 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{176}{189}\right)\) | \(e\left(\frac{17}{378}\right)\) | \(e\left(\frac{241}{378}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{139}{378}\right)\) | \(e\left(\frac{163}{189}\right)\) | \(e\left(\frac{281}{378}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{41}{63}\right)\) |