Basic properties
| Modulus: | \(337\) | |
| Conductor: | \(337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 337.r
\(\chi_{337}(5,\cdot)\) \(\chi_{337}(11,\cdot)\) \(\chi_{337}(17,\cdot)\) \(\chi_{337}(35,\cdot)\) \(\chi_{337}(57,\cdot)\) \(\chi_{337}(58,\cdot)\) \(\chi_{337}(62,\cdot)\) \(\chi_{337}(66,\cdot)\) \(\chi_{337}(69,\cdot)\) \(\chi_{337}(76,\cdot)\) \(\chi_{337}(77,\cdot)\) \(\chi_{337}(88,\cdot)\) \(\chi_{337}(92,\cdot)\) \(\chi_{337}(97,\cdot)\) \(\chi_{337}(102,\cdot)\) \(\chi_{337}(119,\cdot)\) \(\chi_{337}(122,\cdot)\) \(\chi_{337}(125,\cdot)\) \(\chi_{337}(127,\cdot)\) \(\chi_{337}(135,\cdot)\) \(\chi_{337}(136,\cdot)\) \(\chi_{337}(142,\cdot)\) \(\chi_{337}(157,\cdot)\) \(\chi_{337}(159,\cdot)\) \(\chi_{337}(178,\cdot)\) \(\chi_{337}(180,\cdot)\) \(\chi_{337}(195,\cdot)\) \(\chi_{337}(201,\cdot)\) \(\chi_{337}(202,\cdot)\) \(\chi_{337}(210,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\(10\) → \(e\left(\frac{75}{112}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 337 }(58, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{11}{112}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{75}{112}\right)\) | \(e\left(\frac{57}{112}\right)\) |