Basic properties
| Modulus: | \(6272\) | |
| Conductor: | \(1568\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1568}(307,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6272.cm
\(\chi_{6272}(111,\cdot)\) \(\chi_{6272}(335,\cdot)\) \(\chi_{6272}(559,\cdot)\) \(\chi_{6272}(1007,\cdot)\) \(\chi_{6272}(1231,\cdot)\) \(\chi_{6272}(1455,\cdot)\) \(\chi_{6272}(1679,\cdot)\) \(\chi_{6272}(1903,\cdot)\) \(\chi_{6272}(2127,\cdot)\) \(\chi_{6272}(2575,\cdot)\) \(\chi_{6272}(2799,\cdot)\) \(\chi_{6272}(3023,\cdot)\) \(\chi_{6272}(3247,\cdot)\) \(\chi_{6272}(3471,\cdot)\) \(\chi_{6272}(3695,\cdot)\) \(\chi_{6272}(4143,\cdot)\) \(\chi_{6272}(4367,\cdot)\) \(\chi_{6272}(4591,\cdot)\) \(\chi_{6272}(4815,\cdot)\) \(\chi_{6272}(5039,\cdot)\) \(\chi_{6272}(5263,\cdot)\) \(\chi_{6272}(5711,\cdot)\) \(\chi_{6272}(5935,\cdot)\) \(\chi_{6272}(6159,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((4607,3333,4609)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{11}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 6272 }(111, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) |