Basic properties
| Modulus: | \(3136\) | |
| 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 \(\chi_{1568}(237,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3136.ck
\(\chi_{3136}(41,\cdot)\) \(\chi_{3136}(153,\cdot)\) \(\chi_{3136}(265,\cdot)\) \(\chi_{3136}(377,\cdot)\) \(\chi_{3136}(601,\cdot)\) \(\chi_{3136}(713,\cdot)\) \(\chi_{3136}(825,\cdot)\) \(\chi_{3136}(937,\cdot)\) \(\chi_{3136}(1049,\cdot)\) \(\chi_{3136}(1161,\cdot)\) \(\chi_{3136}(1385,\cdot)\) \(\chi_{3136}(1497,\cdot)\) \(\chi_{3136}(1609,\cdot)\) \(\chi_{3136}(1721,\cdot)\) \(\chi_{3136}(1833,\cdot)\) \(\chi_{3136}(1945,\cdot)\) \(\chi_{3136}(2169,\cdot)\) \(\chi_{3136}(2281,\cdot)\) \(\chi_{3136}(2393,\cdot)\) \(\chi_{3136}(2505,\cdot)\) \(\chi_{3136}(2617,\cdot)\) \(\chi_{3136}(2729,\cdot)\) \(\chi_{3136}(2953,\cdot)\) \(\chi_{3136}(3065,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((1471,197,1473)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3136 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{13}{28}\right)\) |