Basic properties
| Modulus: | \(8712\) | |
| Conductor: | \(2904\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2904}(413,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8712.ee
\(\chi_{8712}(413,\cdot)\) \(\chi_{8712}(557,\cdot)\) \(\chi_{8712}(629,\cdot)\) \(\chi_{8712}(701,\cdot)\) \(\chi_{8712}(1205,\cdot)\) \(\chi_{8712}(1349,\cdot)\) \(\chi_{8712}(1421,\cdot)\) \(\chi_{8712}(1493,\cdot)\) \(\chi_{8712}(1997,\cdot)\) \(\chi_{8712}(2141,\cdot)\) \(\chi_{8712}(2213,\cdot)\) \(\chi_{8712}(2285,\cdot)\) \(\chi_{8712}(2789,\cdot)\) \(\chi_{8712}(2933,\cdot)\) \(\chi_{8712}(3005,\cdot)\) \(\chi_{8712}(3077,\cdot)\) \(\chi_{8712}(3581,\cdot)\) \(\chi_{8712}(3725,\cdot)\) \(\chi_{8712}(3797,\cdot)\) \(\chi_{8712}(4373,\cdot)\) \(\chi_{8712}(4661,\cdot)\) \(\chi_{8712}(5165,\cdot)\) \(\chi_{8712}(5309,\cdot)\) \(\chi_{8712}(5381,\cdot)\) \(\chi_{8712}(5453,\cdot)\) \(\chi_{8712}(5957,\cdot)\) \(\chi_{8712}(6101,\cdot)\) \(\chi_{8712}(6173,\cdot)\) \(\chi_{8712}(6245,\cdot)\) \(\chi_{8712}(6893,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((6535,4357,1937,5689)\) → \((1,-1,-1,e\left(\frac{39}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8712 }(413, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{79}{110}\right)\) |