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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 864.bu
\(\chi_{864}(13,\cdot)\) \(\chi_{864}(61,\cdot)\) \(\chi_{864}(85,\cdot)\) \(\chi_{864}(133,\cdot)\) \(\chi_{864}(157,\cdot)\) \(\chi_{864}(205,\cdot)\) \(\chi_{864}(229,\cdot)\) \(\chi_{864}(277,\cdot)\) \(\chi_{864}(301,\cdot)\) \(\chi_{864}(349,\cdot)\) \(\chi_{864}(373,\cdot)\) \(\chi_{864}(421,\cdot)\) \(\chi_{864}(445,\cdot)\) \(\chi_{864}(493,\cdot)\) \(\chi_{864}(517,\cdot)\) \(\chi_{864}(565,\cdot)\) \(\chi_{864}(589,\cdot)\) \(\chi_{864}(637,\cdot)\) \(\chi_{864}(661,\cdot)\) \(\chi_{864}(709,\cdot)\) \(\chi_{864}(733,\cdot)\) \(\chi_{864}(781,\cdot)\) \(\chi_{864}(805,\cdot)\) \(\chi_{864}(853,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((703,325,353)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 864 }(589, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{35}{72}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{5}{9}\right)\) |