Basic properties
| Modulus: | \(2850\) | |
| Conductor: | \(1425\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1425}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2850.cq
\(\chi_{2850}(53,\cdot)\) \(\chi_{2850}(167,\cdot)\) \(\chi_{2850}(173,\cdot)\) \(\chi_{2850}(203,\cdot)\) \(\chi_{2850}(287,\cdot)\) \(\chi_{2850}(317,\cdot)\) \(\chi_{2850}(383,\cdot)\) \(\chi_{2850}(413,\cdot)\) \(\chi_{2850}(497,\cdot)\) \(\chi_{2850}(527,\cdot)\) \(\chi_{2850}(623,\cdot)\) \(\chi_{2850}(713,\cdot)\) \(\chi_{2850}(737,\cdot)\) \(\chi_{2850}(773,\cdot)\) \(\chi_{2850}(827,\cdot)\) \(\chi_{2850}(887,\cdot)\) \(\chi_{2850}(953,\cdot)\) \(\chi_{2850}(983,\cdot)\) \(\chi_{2850}(1067,\cdot)\) \(\chi_{2850}(1097,\cdot)\) \(\chi_{2850}(1283,\cdot)\) \(\chi_{2850}(1313,\cdot)\) \(\chi_{2850}(1397,\cdot)\) \(\chi_{2850}(1427,\cdot)\) \(\chi_{2850}(1523,\cdot)\) \(\chi_{2850}(1553,\cdot)\) \(\chi_{2850}(1637,\cdot)\) \(\chi_{2850}(1667,\cdot)\) \(\chi_{2850}(1763,\cdot)\) \(\chi_{2850}(1853,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1901,1027,1351)\) → \((-1,e\left(\frac{7}{20}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 2850 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{127}{180}\right)\) | \(e\left(\frac{29}{180}\right)\) | \(e\left(\frac{103}{180}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{1}{36}\right)\) |