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 \(\chi_{215}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.cy
\(\chi_{4730}(23,\cdot)\) \(\chi_{4730}(67,\cdot)\) \(\chi_{4730}(353,\cdot)\) \(\chi_{4730}(397,\cdot)\) \(\chi_{4730}(573,\cdot)\) \(\chi_{4730}(617,\cdot)\) \(\chi_{4730}(683,\cdot)\) \(\chi_{4730}(1013,\cdot)\) \(\chi_{4730}(1057,\cdot)\) \(\chi_{4730}(1343,\cdot)\) \(\chi_{4730}(1563,\cdot)\) \(\chi_{4730}(1717,\cdot)\) \(\chi_{4730}(2003,\cdot)\) \(\chi_{4730}(2267,\cdot)\) \(\chi_{4730}(2597,\cdot)\) \(\chi_{4730}(2663,\cdot)\) \(\chi_{4730}(3213,\cdot)\) \(\chi_{4730}(3367,\cdot)\) \(\chi_{4730}(3543,\cdot)\) \(\chi_{4730}(3807,\cdot)\) \(\chi_{4730}(4137,\cdot)\) \(\chi_{4730}(4313,\cdot)\) \(\chi_{4730}(4357,\cdot)\) \(\chi_{4730}(4467,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((947,431,1981)\) → \((i,1,e\left(\frac{20}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4730 }(67, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{23}{42}\right)\) |