Basic properties
| Modulus: | \(2704\) | |
| Conductor: | \(2704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 2704.cz
\(\chi_{2704}(37,\cdot)\) \(\chi_{2704}(45,\cdot)\) \(\chi_{2704}(85,\cdot)\) \(\chi_{2704}(93,\cdot)\) \(\chi_{2704}(245,\cdot)\) \(\chi_{2704}(253,\cdot)\) \(\chi_{2704}(293,\cdot)\) \(\chi_{2704}(301,\cdot)\) \(\chi_{2704}(453,\cdot)\) \(\chi_{2704}(461,\cdot)\) \(\chi_{2704}(501,\cdot)\) \(\chi_{2704}(509,\cdot)\) \(\chi_{2704}(661,\cdot)\) \(\chi_{2704}(669,\cdot)\) \(\chi_{2704}(709,\cdot)\) \(\chi_{2704}(717,\cdot)\) \(\chi_{2704}(869,\cdot)\) \(\chi_{2704}(877,\cdot)\) \(\chi_{2704}(917,\cdot)\) \(\chi_{2704}(1077,\cdot)\) \(\chi_{2704}(1085,\cdot)\) \(\chi_{2704}(1125,\cdot)\) \(\chi_{2704}(1133,\cdot)\) \(\chi_{2704}(1285,\cdot)\) \(\chi_{2704}(1293,\cdot)\) \(\chi_{2704}(1341,\cdot)\) \(\chi_{2704}(1493,\cdot)\) \(\chi_{2704}(1501,\cdot)\) \(\chi_{2704}(1541,\cdot)\) \(\chi_{2704}(1549,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,677,1185)\) → \((1,-i,e\left(\frac{97}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2704 }(1133, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{156}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{1}{3}\right)\) |