Basic properties
| Modulus: | \(2904\) | |
| Conductor: | \(2904\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | 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 2904.ci
\(\chi_{2904}(29,\cdot)\) \(\chi_{2904}(101,\cdot)\) \(\chi_{2904}(149,\cdot)\) \(\chi_{2904}(173,\cdot)\) \(\chi_{2904}(293,\cdot)\) \(\chi_{2904}(365,\cdot)\) \(\chi_{2904}(413,\cdot)\) \(\chi_{2904}(437,\cdot)\) \(\chi_{2904}(557,\cdot)\) \(\chi_{2904}(629,\cdot)\) \(\chi_{2904}(677,\cdot)\) \(\chi_{2904}(701,\cdot)\) \(\chi_{2904}(821,\cdot)\) \(\chi_{2904}(893,\cdot)\) \(\chi_{2904}(1085,\cdot)\) \(\chi_{2904}(1157,\cdot)\) \(\chi_{2904}(1205,\cdot)\) \(\chi_{2904}(1229,\cdot)\) \(\chi_{2904}(1349,\cdot)\) \(\chi_{2904}(1421,\cdot)\) \(\chi_{2904}(1469,\cdot)\) \(\chi_{2904}(1493,\cdot)\) \(\chi_{2904}(1733,\cdot)\) \(\chi_{2904}(1757,\cdot)\) \(\chi_{2904}(1877,\cdot)\) \(\chi_{2904}(1949,\cdot)\) \(\chi_{2904}(1997,\cdot)\) \(\chi_{2904}(2021,\cdot)\) \(\chi_{2904}(2141,\cdot)\) \(\chi_{2904}(2213,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,1453,1937,2785)\) → \((1,-1,-1,e\left(\frac{87}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2904 }(1877, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{7}{110}\right)\) |