Basic properties
| Modulus: | \(869\) | |
| Conductor: | \(869\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(390\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 869.be
\(\chi_{869}(2,\cdot)\) \(\chi_{869}(13,\cdot)\) \(\chi_{869}(19,\cdot)\) \(\chi_{869}(40,\cdot)\) \(\chi_{869}(50,\cdot)\) \(\chi_{869}(51,\cdot)\) \(\chi_{869}(72,\cdot)\) \(\chi_{869}(73,\cdot)\) \(\chi_{869}(83,\cdot)\) \(\chi_{869}(84,\cdot)\) \(\chi_{869}(90,\cdot)\) \(\chi_{869}(95,\cdot)\) \(\chi_{869}(105,\cdot)\) \(\chi_{869}(123,\cdot)\) \(\chi_{869}(128,\cdot)\) \(\chi_{869}(129,\cdot)\) \(\chi_{869}(151,\cdot)\) \(\chi_{869}(160,\cdot)\) \(\chi_{869}(162,\cdot)\) \(\chi_{869}(167,\cdot)\) \(\chi_{869}(171,\cdot)\) \(\chi_{869}(178,\cdot)\) \(\chi_{869}(183,\cdot)\) \(\chi_{869}(184,\cdot)\) \(\chi_{869}(189,\cdot)\) \(\chi_{869}(194,\cdot)\) \(\chi_{869}(200,\cdot)\) \(\chi_{869}(239,\cdot)\) \(\chi_{869}(248,\cdot)\) \(\chi_{869}(250,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((475,793)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{17}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 869 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{329}{390}\right)\) | \(e\left(\frac{46}{195}\right)\) | \(e\left(\frac{134}{195}\right)\) | \(e\left(\frac{83}{195}\right)\) | \(e\left(\frac{31}{390}\right)\) | \(e\left(\frac{313}{390}\right)\) | \(e\left(\frac{69}{130}\right)\) | \(e\left(\frac{92}{195}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{12}{13}\right)\) |