Basic properties
| Modulus: | \(864\) | |
| Conductor: | \(864\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 864.bv
\(\chi_{864}(43,\cdot)\) \(\chi_{864}(67,\cdot)\) \(\chi_{864}(115,\cdot)\) \(\chi_{864}(139,\cdot)\) \(\chi_{864}(187,\cdot)\) \(\chi_{864}(211,\cdot)\) \(\chi_{864}(259,\cdot)\) \(\chi_{864}(283,\cdot)\) \(\chi_{864}(331,\cdot)\) \(\chi_{864}(355,\cdot)\) \(\chi_{864}(403,\cdot)\) \(\chi_{864}(427,\cdot)\) \(\chi_{864}(475,\cdot)\) \(\chi_{864}(499,\cdot)\) \(\chi_{864}(547,\cdot)\) \(\chi_{864}(571,\cdot)\) \(\chi_{864}(619,\cdot)\) \(\chi_{864}(643,\cdot)\) \(\chi_{864}(691,\cdot)\) \(\chi_{864}(715,\cdot)\) \(\chi_{864}(763,\cdot)\) \(\chi_{864}(787,\cdot)\) \(\chi_{864}(835,\cdot)\) \(\chi_{864}(859,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((703,325,353)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 864 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{17}{18}\right)\) |