Basic properties
Modulus: | \(5733\) | |
Conductor: | \(1911\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1911}(305,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5733.mk
\(\chi_{5733}(305,\cdot)\) \(\chi_{5733}(548,\cdot)\) \(\chi_{5733}(674,\cdot)\) \(\chi_{5733}(683,\cdot)\) \(\chi_{5733}(1124,\cdot)\) \(\chi_{5733}(1367,\cdot)\) \(\chi_{5733}(1493,\cdot)\) \(\chi_{5733}(1502,\cdot)\) \(\chi_{5733}(1943,\cdot)\) \(\chi_{5733}(2312,\cdot)\) \(\chi_{5733}(3005,\cdot)\) \(\chi_{5733}(3131,\cdot)\) \(\chi_{5733}(3140,\cdot)\) \(\chi_{5733}(3581,\cdot)\) \(\chi_{5733}(3824,\cdot)\) \(\chi_{5733}(3959,\cdot)\) \(\chi_{5733}(4400,\cdot)\) \(\chi_{5733}(4643,\cdot)\) \(\chi_{5733}(4769,\cdot)\) \(\chi_{5733}(4778,\cdot)\) \(\chi_{5733}(5219,\cdot)\) \(\chi_{5733}(5462,\cdot)\) \(\chi_{5733}(5588,\cdot)\) \(\chi_{5733}(5597,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,1522,5293)\) → \((-1,e\left(\frac{20}{21}\right),e\left(\frac{5}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 5733 }(305, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{19}{84}\right)\) |