Basic properties
| Modulus: | \(2535\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2535.bw
\(\chi_{2535}(16,\cdot)\) \(\chi_{2535}(61,\cdot)\) \(\chi_{2535}(211,\cdot)\) \(\chi_{2535}(256,\cdot)\) \(\chi_{2535}(406,\cdot)\) \(\chi_{2535}(451,\cdot)\) \(\chi_{2535}(601,\cdot)\) \(\chi_{2535}(646,\cdot)\) \(\chi_{2535}(796,\cdot)\) \(\chi_{2535}(841,\cdot)\) \(\chi_{2535}(1186,\cdot)\) \(\chi_{2535}(1231,\cdot)\) \(\chi_{2535}(1381,\cdot)\) \(\chi_{2535}(1426,\cdot)\) \(\chi_{2535}(1576,\cdot)\) \(\chi_{2535}(1621,\cdot)\) \(\chi_{2535}(1771,\cdot)\) \(\chi_{2535}(1816,\cdot)\) \(\chi_{2535}(1966,\cdot)\) \(\chi_{2535}(2011,\cdot)\) \(\chi_{2535}(2161,\cdot)\) \(\chi_{2535}(2206,\cdot)\) \(\chi_{2535}(2356,\cdot)\) \(\chi_{2535}(2401,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((1691,1522,1861)\) → \((1,1,e\left(\frac{31}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 2535 }(1186, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |