Basic properties
Modulus: | \(4730\) | |
Conductor: | \(2365\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2365}(197,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.db
\(\chi_{4730}(153,\cdot)\) \(\chi_{4730}(197,\cdot)\) \(\chi_{4730}(483,\cdot)\) \(\chi_{4730}(703,\cdot)\) \(\chi_{4730}(857,\cdot)\) \(\chi_{4730}(1143,\cdot)\) \(\chi_{4730}(1407,\cdot)\) \(\chi_{4730}(1737,\cdot)\) \(\chi_{4730}(1803,\cdot)\) \(\chi_{4730}(2353,\cdot)\) \(\chi_{4730}(2507,\cdot)\) \(\chi_{4730}(2683,\cdot)\) \(\chi_{4730}(2947,\cdot)\) \(\chi_{4730}(3277,\cdot)\) \(\chi_{4730}(3453,\cdot)\) \(\chi_{4730}(3497,\cdot)\) \(\chi_{4730}(3607,\cdot)\) \(\chi_{4730}(3893,\cdot)\) \(\chi_{4730}(3937,\cdot)\) \(\chi_{4730}(4223,\cdot)\) \(\chi_{4730}(4267,\cdot)\) \(\chi_{4730}(4443,\cdot)\) \(\chi_{4730}(4487,\cdot)\) \(\chi_{4730}(4553,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((947,431,1981)\) → \((i,-1,e\left(\frac{4}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4730 }(197, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) |