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.bt
\(\chi_{864}(11,\cdot)\) \(\chi_{864}(59,\cdot)\) \(\chi_{864}(83,\cdot)\) \(\chi_{864}(131,\cdot)\) \(\chi_{864}(155,\cdot)\) \(\chi_{864}(203,\cdot)\) \(\chi_{864}(227,\cdot)\) \(\chi_{864}(275,\cdot)\) \(\chi_{864}(299,\cdot)\) \(\chi_{864}(347,\cdot)\) \(\chi_{864}(371,\cdot)\) \(\chi_{864}(419,\cdot)\) \(\chi_{864}(443,\cdot)\) \(\chi_{864}(491,\cdot)\) \(\chi_{864}(515,\cdot)\) \(\chi_{864}(563,\cdot)\) \(\chi_{864}(587,\cdot)\) \(\chi_{864}(635,\cdot)\) \(\chi_{864}(659,\cdot)\) \(\chi_{864}(707,\cdot)\) \(\chi_{864}(731,\cdot)\) \(\chi_{864}(779,\cdot)\) \(\chi_{864}(803,\cdot)\) \(\chi_{864}(851,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((703,325,353)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{13}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 864 }(227, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{17}{18}\right)\) |