Basic properties
Modulus: | \(4034\) | |
Conductor: | \(2017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2017}(75,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4034.w
\(\chi_{4034}(75,\cdot)\) \(\chi_{4034}(131,\cdot)\) \(\chi_{4034}(137,\cdot)\) \(\chi_{4034}(191,\cdot)\) \(\chi_{4034}(265,\cdot)\) \(\chi_{4034}(753,\cdot)\) \(\chi_{4034}(1047,\cdot)\) \(\chi_{4034}(1279,\cdot)\) \(\chi_{4034}(1331,\cdot)\) \(\chi_{4034}(1753,\cdot)\) \(\chi_{4034}(1891,\cdot)\) \(\chi_{4034}(2001,\cdot)\) \(\chi_{4034}(2033,\cdot)\) \(\chi_{4034}(2143,\cdot)\) \(\chi_{4034}(2281,\cdot)\) \(\chi_{4034}(2703,\cdot)\) \(\chi_{4034}(2755,\cdot)\) \(\chi_{4034}(2987,\cdot)\) \(\chi_{4034}(3281,\cdot)\) \(\chi_{4034}(3769,\cdot)\) \(\chi_{4034}(3843,\cdot)\) \(\chi_{4034}(3897,\cdot)\) \(\chi_{4034}(3903,\cdot)\) \(\chi_{4034}(3959,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\(5\) → \(e\left(\frac{43}{84}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 4034 }(75, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{20}{21}\right)\) |