Basic properties
| Modulus: | \(430\) | |
| 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 \(\chi_{215}(148,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 430.x
\(\chi_{430}(3,\cdot)\) \(\chi_{430}(33,\cdot)\) \(\chi_{430}(63,\cdot)\) \(\chi_{430}(73,\cdot)\) \(\chi_{430}(77,\cdot)\) \(\chi_{430}(147,\cdot)\) \(\chi_{430}(157,\cdot)\) \(\chi_{430}(163,\cdot)\) \(\chi_{430}(177,\cdot)\) \(\chi_{430}(227,\cdot)\) \(\chi_{430}(233,\cdot)\) \(\chi_{430}(243,\cdot)\) \(\chi_{430}(263,\cdot)\) \(\chi_{430}(277,\cdot)\) \(\chi_{430}(287,\cdot)\) \(\chi_{430}(313,\cdot)\) \(\chi_{430}(327,\cdot)\) \(\chi_{430}(347,\cdot)\) \(\chi_{430}(363,\cdot)\) \(\chi_{430}(373,\cdot)\) \(\chi_{430}(377,\cdot)\) \(\chi_{430}(407,\cdot)\) \(\chi_{430}(413,\cdot)\) \(\chi_{430}(417,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((87,261)\) → \((-i,e\left(\frac{19}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 430 }(363, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) |