Basic properties
| Modulus: | \(215\) | |
| Conductor: | \(215\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 215.x
\(\chi_{215}(3,\cdot)\) \(\chi_{215}(12,\cdot)\) \(\chi_{215}(18,\cdot)\) \(\chi_{215}(28,\cdot)\) \(\chi_{215}(33,\cdot)\) \(\chi_{215}(48,\cdot)\) \(\chi_{215}(62,\cdot)\) \(\chi_{215}(63,\cdot)\) \(\chi_{215}(72,\cdot)\) \(\chi_{215}(73,\cdot)\) \(\chi_{215}(77,\cdot)\) \(\chi_{215}(98,\cdot)\) \(\chi_{215}(112,\cdot)\) \(\chi_{215}(132,\cdot)\) \(\chi_{215}(147,\cdot)\) \(\chi_{215}(148,\cdot)\) \(\chi_{215}(157,\cdot)\) \(\chi_{215}(158,\cdot)\) \(\chi_{215}(162,\cdot)\) \(\chi_{215}(163,\cdot)\) \(\chi_{215}(177,\cdot)\) \(\chi_{215}(192,\cdot)\) \(\chi_{215}(198,\cdot)\) \(\chi_{215}(202,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((87,46)\) → \((-i,e\left(\frac{1}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 215 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{1}{84}\right)\) |