Basic properties
| Modulus: | \(4056\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(97,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.dn
\(\chi_{4056}(97,\cdot)\) \(\chi_{4056}(145,\cdot)\) \(\chi_{4056}(193,\cdot)\) \(\chi_{4056}(241,\cdot)\) \(\chi_{4056}(409,\cdot)\) \(\chi_{4056}(457,\cdot)\) \(\chi_{4056}(505,\cdot)\) \(\chi_{4056}(553,\cdot)\) \(\chi_{4056}(721,\cdot)\) \(\chi_{4056}(769,\cdot)\) \(\chi_{4056}(817,\cdot)\) \(\chi_{4056}(865,\cdot)\) \(\chi_{4056}(1081,\cdot)\) \(\chi_{4056}(1129,\cdot)\) \(\chi_{4056}(1177,\cdot)\) \(\chi_{4056}(1345,\cdot)\) \(\chi_{4056}(1393,\cdot)\) \(\chi_{4056}(1489,\cdot)\) \(\chi_{4056}(1657,\cdot)\) \(\chi_{4056}(1705,\cdot)\) \(\chi_{4056}(1753,\cdot)\) \(\chi_{4056}(1801,\cdot)\) \(\chi_{4056}(1969,\cdot)\) \(\chi_{4056}(2017,\cdot)\) \(\chi_{4056}(2065,\cdot)\) \(\chi_{4056}(2113,\cdot)\) \(\chi_{4056}(2281,\cdot)\) \(\chi_{4056}(2329,\cdot)\) \(\chi_{4056}(2377,\cdot)\) \(\chi_{4056}(2425,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1015,2029,2705,3889)\) → \((1,1,1,e\left(\frac{17}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4056 }(97, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{25}{39}\right)\) |