Basic properties
Modulus: | \(7938\) | |
Conductor: | \(3969\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(378\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3969}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7938.di
\(\chi_{7938}(5,\cdot)\) \(\chi_{7938}(101,\cdot)\) \(\chi_{7938}(131,\cdot)\) \(\chi_{7938}(257,\cdot)\) \(\chi_{7938}(353,\cdot)\) \(\chi_{7938}(383,\cdot)\) \(\chi_{7938}(479,\cdot)\) \(\chi_{7938}(605,\cdot)\) \(\chi_{7938}(635,\cdot)\) \(\chi_{7938}(731,\cdot)\) \(\chi_{7938}(761,\cdot)\) \(\chi_{7938}(857,\cdot)\) \(\chi_{7938}(887,\cdot)\) \(\chi_{7938}(983,\cdot)\) \(\chi_{7938}(1013,\cdot)\) \(\chi_{7938}(1139,\cdot)\) \(\chi_{7938}(1235,\cdot)\) \(\chi_{7938}(1265,\cdot)\) \(\chi_{7938}(1361,\cdot)\) \(\chi_{7938}(1487,\cdot)\) \(\chi_{7938}(1517,\cdot)\) \(\chi_{7938}(1613,\cdot)\) \(\chi_{7938}(1643,\cdot)\) \(\chi_{7938}(1739,\cdot)\) \(\chi_{7938}(1769,\cdot)\) \(\chi_{7938}(1865,\cdot)\) \(\chi_{7938}(1895,\cdot)\) \(\chi_{7938}(2021,\cdot)\) \(\chi_{7938}(2117,\cdot)\) \(\chi_{7938}(2147,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{189})$ |
Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
Values on generators
\((6077,3727)\) → \((e\left(\frac{23}{54}\right),e\left(\frac{29}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 7938 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{155}{189}\right)\) | \(e\left(\frac{59}{378}\right)\) | \(e\left(\frac{73}{378}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{349}{378}\right)\) | \(e\left(\frac{121}{189}\right)\) | \(e\left(\frac{71}{378}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{62}{63}\right)\) |