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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2704.cy
\(\chi_{2704}(11,\cdot)\) \(\chi_{2704}(59,\cdot)\) \(\chi_{2704}(67,\cdot)\) \(\chi_{2704}(219,\cdot)\) \(\chi_{2704}(227,\cdot)\) \(\chi_{2704}(267,\cdot)\) \(\chi_{2704}(275,\cdot)\) \(\chi_{2704}(435,\cdot)\) \(\chi_{2704}(475,\cdot)\) \(\chi_{2704}(483,\cdot)\) \(\chi_{2704}(635,\cdot)\) \(\chi_{2704}(643,\cdot)\) \(\chi_{2704}(683,\cdot)\) \(\chi_{2704}(691,\cdot)\) \(\chi_{2704}(843,\cdot)\) \(\chi_{2704}(851,\cdot)\) \(\chi_{2704}(891,\cdot)\) \(\chi_{2704}(899,\cdot)\) \(\chi_{2704}(1051,\cdot)\) \(\chi_{2704}(1059,\cdot)\) \(\chi_{2704}(1099,\cdot)\) \(\chi_{2704}(1107,\cdot)\) \(\chi_{2704}(1259,\cdot)\) \(\chi_{2704}(1267,\cdot)\) \(\chi_{2704}(1307,\cdot)\) \(\chi_{2704}(1315,\cdot)\) \(\chi_{2704}(1467,\cdot)\) \(\chi_{2704}(1475,\cdot)\) \(\chi_{2704}(1515,\cdot)\) \(\chi_{2704}(1523,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,677,1185)\) → \((-1,-i,e\left(\frac{77}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2704 }(1267, a) \) | \(1\) | \(1\) | \(e\left(\frac{149}{156}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{1}{6}\right)\) |