Basic properties
| Modulus: | \(6272\) | |
| Conductor: | \(3136\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3136}(1429,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6272.cz
\(\chi_{6272}(57,\cdot)\) \(\chi_{6272}(169,\cdot)\) \(\chi_{6272}(281,\cdot)\) \(\chi_{6272}(505,\cdot)\) \(\chi_{6272}(617,\cdot)\) \(\chi_{6272}(729,\cdot)\) \(\chi_{6272}(841,\cdot)\) \(\chi_{6272}(953,\cdot)\) \(\chi_{6272}(1065,\cdot)\) \(\chi_{6272}(1289,\cdot)\) \(\chi_{6272}(1401,\cdot)\) \(\chi_{6272}(1513,\cdot)\) \(\chi_{6272}(1625,\cdot)\) \(\chi_{6272}(1737,\cdot)\) \(\chi_{6272}(1849,\cdot)\) \(\chi_{6272}(2073,\cdot)\) \(\chi_{6272}(2185,\cdot)\) \(\chi_{6272}(2297,\cdot)\) \(\chi_{6272}(2409,\cdot)\) \(\chi_{6272}(2521,\cdot)\) \(\chi_{6272}(2633,\cdot)\) \(\chi_{6272}(2857,\cdot)\) \(\chi_{6272}(2969,\cdot)\) \(\chi_{6272}(3081,\cdot)\) \(\chi_{6272}(3193,\cdot)\) \(\chi_{6272}(3305,\cdot)\) \(\chi_{6272}(3417,\cdot)\) \(\chi_{6272}(3641,\cdot)\) \(\chi_{6272}(3753,\cdot)\) \(\chi_{6272}(3865,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((4607,3333,4609)\) → \((1,e\left(\frac{13}{16}\right),e\left(\frac{6}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 6272 }(57, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{112}\right)\) | \(e\left(\frac{75}{112}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{39}{112}\right)\) | \(e\left(\frac{53}{112}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{19}{56}\right)\) |