Basic properties
Modulus: | \(4730\) | |
Conductor: | \(215\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{215}(147,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.da
\(\chi_{4730}(177,\cdot)\) \(\chi_{4730}(243,\cdot)\) \(\chi_{4730}(287,\cdot)\) \(\chi_{4730}(463,\cdot)\) \(\chi_{4730}(507,\cdot)\) \(\chi_{4730}(793,\cdot)\) \(\chi_{4730}(837,\cdot)\) \(\chi_{4730}(1123,\cdot)\) \(\chi_{4730}(1233,\cdot)\) \(\chi_{4730}(1277,\cdot)\) \(\chi_{4730}(1453,\cdot)\) \(\chi_{4730}(1783,\cdot)\) \(\chi_{4730}(2047,\cdot)\) \(\chi_{4730}(2223,\cdot)\) \(\chi_{4730}(2377,\cdot)\) \(\chi_{4730}(2927,\cdot)\) \(\chi_{4730}(2993,\cdot)\) \(\chi_{4730}(3323,\cdot)\) \(\chi_{4730}(3587,\cdot)\) \(\chi_{4730}(3873,\cdot)\) \(\chi_{4730}(4027,\cdot)\) \(\chi_{4730}(4247,\cdot)\) \(\chi_{4730}(4533,\cdot)\) \(\chi_{4730}(4577,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((947,431,1981)\) → \((i,1,e\left(\frac{29}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4730 }(3587, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) |