Basic properties
| Modulus: | \(1859\) | |
| 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 \(\chi_{169}(45,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1859.bm
\(\chi_{1859}(45,\cdot)\) \(\chi_{1859}(67,\cdot)\) \(\chi_{1859}(111,\cdot)\) \(\chi_{1859}(210,\cdot)\) \(\chi_{1859}(232,\cdot)\) \(\chi_{1859}(254,\cdot)\) \(\chi_{1859}(331,\cdot)\) \(\chi_{1859}(353,\cdot)\) \(\chi_{1859}(375,\cdot)\) \(\chi_{1859}(397,\cdot)\) \(\chi_{1859}(474,\cdot)\) \(\chi_{1859}(496,\cdot)\) \(\chi_{1859}(518,\cdot)\) \(\chi_{1859}(540,\cdot)\) \(\chi_{1859}(617,\cdot)\) \(\chi_{1859}(639,\cdot)\) \(\chi_{1859}(661,\cdot)\) \(\chi_{1859}(683,\cdot)\) \(\chi_{1859}(760,\cdot)\) \(\chi_{1859}(782,\cdot)\) \(\chi_{1859}(804,\cdot)\) \(\chi_{1859}(903,\cdot)\) \(\chi_{1859}(947,\cdot)\) \(\chi_{1859}(969,\cdot)\) \(\chi_{1859}(1046,\cdot)\) \(\chi_{1859}(1068,\cdot)\) \(\chi_{1859}(1090,\cdot)\) \(\chi_{1859}(1112,\cdot)\) \(\chi_{1859}(1189,\cdot)\) \(\chi_{1859}(1211,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((508,1354)\) → \((1,e\left(\frac{101}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1859 }(45, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{43}{156}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{15}{26}\right)\) |