Basic properties
| Modulus: | \(2704\) | |
| Conductor: | \(2704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | 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 2704.cd
\(\chi_{2704}(53,\cdot)\) \(\chi_{2704}(157,\cdot)\) \(\chi_{2704}(261,\cdot)\) \(\chi_{2704}(365,\cdot)\) \(\chi_{2704}(469,\cdot)\) \(\chi_{2704}(573,\cdot)\) \(\chi_{2704}(781,\cdot)\) \(\chi_{2704}(885,\cdot)\) \(\chi_{2704}(989,\cdot)\) \(\chi_{2704}(1093,\cdot)\) \(\chi_{2704}(1197,\cdot)\) \(\chi_{2704}(1301,\cdot)\) \(\chi_{2704}(1405,\cdot)\) \(\chi_{2704}(1509,\cdot)\) \(\chi_{2704}(1613,\cdot)\) \(\chi_{2704}(1717,\cdot)\) \(\chi_{2704}(1821,\cdot)\) \(\chi_{2704}(1925,\cdot)\) \(\chi_{2704}(2133,\cdot)\) \(\chi_{2704}(2237,\cdot)\) \(\chi_{2704}(2341,\cdot)\) \(\chi_{2704}(2445,\cdot)\) \(\chi_{2704}(2549,\cdot)\) \(\chi_{2704}(2653,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((2367,677,1185)\) → \((1,-i,e\left(\frac{8}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2704 }(989, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(i\) | \(e\left(\frac{47}{52}\right)\) | \(-1\) |