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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 869.bf
\(\chi_{869}(6,\cdot)\) \(\chi_{869}(7,\cdot)\) \(\chi_{869}(28,\cdot)\) \(\chi_{869}(29,\cdot)\) \(\chi_{869}(30,\cdot)\) \(\chi_{869}(35,\cdot)\) \(\chi_{869}(39,\cdot)\) \(\chi_{869}(63,\cdot)\) \(\chi_{869}(68,\cdot)\) \(\chi_{869}(74,\cdot)\) \(\chi_{869}(85,\cdot)\) \(\chi_{869}(107,\cdot)\) \(\chi_{869}(116,\cdot)\) \(\chi_{869}(118,\cdot)\) \(\chi_{869}(127,\cdot)\) \(\chi_{869}(138,\cdot)\) \(\chi_{869}(139,\cdot)\) \(\chi_{869}(145,\cdot)\) \(\chi_{869}(149,\cdot)\) \(\chi_{869}(156,\cdot)\) \(\chi_{869}(161,\cdot)\) \(\chi_{869}(193,\cdot)\) \(\chi_{869}(195,\cdot)\) \(\chi_{869}(205,\cdot)\) \(\chi_{869}(206,\cdot)\) \(\chi_{869}(211,\cdot)\) \(\chi_{869}(217,\cdot)\) \(\chi_{869}(226,\cdot)\) \(\chi_{869}(228,\cdot)\) \(\chi_{869}(233,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((475,793)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{37}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 869 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{389}{390}\right)\) | \(e\left(\frac{107}{390}\right)\) | \(e\left(\frac{194}{195}\right)\) | \(e\left(\frac{158}{195}\right)\) | \(e\left(\frac{53}{195}\right)\) | \(e\left(\frac{164}{195}\right)\) | \(e\left(\frac{129}{130}\right)\) | \(e\left(\frac{107}{195}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{7}{26}\right)\) |