Basic properties
| Modulus: | \(337\) | |
| Conductor: | \(337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | 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 337.s
\(\chi_{337}(3,\cdot)\) \(\chi_{337}(12,\cdot)\) \(\chi_{337}(14,\cdot)\) \(\chi_{337}(24,\cdot)\) \(\chi_{337}(28,\cdot)\) \(\chi_{337}(50,\cdot)\) \(\chi_{337}(63,\cdot)\) \(\chi_{337}(78,\cdot)\) \(\chi_{337}(86,\cdot)\) \(\chi_{337}(91,\cdot)\) \(\chi_{337}(94,\cdot)\) \(\chi_{337}(95,\cdot)\) \(\chi_{337}(100,\cdot)\) \(\chi_{337}(107,\cdot)\) \(\chi_{337}(108,\cdot)\) \(\chi_{337}(112,\cdot)\) \(\chi_{337}(113,\cdot)\) \(\chi_{337}(115,\cdot)\) \(\chi_{337}(126,\cdot)\) \(\chi_{337}(145,\cdot)\) \(\chi_{337}(147,\cdot)\) \(\chi_{337}(149,\cdot)\) \(\chi_{337}(155,\cdot)\) \(\chi_{337}(167,\cdot)\) \(\chi_{337}(170,\cdot)\) \(\chi_{337}(182,\cdot)\) \(\chi_{337}(188,\cdot)\) \(\chi_{337}(190,\cdot)\) \(\chi_{337}(192,\cdot)\) \(\chi_{337}(211,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\(10\) → \(e\left(\frac{127}{168}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 337 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{127}{168}\right)\) | \(e\left(\frac{15}{56}\right)\) |