Basic properties
Modulus: | \(869\) | |
Conductor: | \(869\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(195\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.bc
\(\chi_{869}(4,\cdot)\) \(\chi_{869}(5,\cdot)\) \(\chi_{869}(9,\cdot)\) \(\chi_{869}(16,\cdot)\) \(\chi_{869}(20,\cdot)\) \(\chi_{869}(25,\cdot)\) \(\chi_{869}(26,\cdot)\) \(\chi_{869}(31,\cdot)\) \(\chi_{869}(36,\cdot)\) \(\chi_{869}(42,\cdot)\) \(\chi_{869}(49,\cdot)\) \(\chi_{869}(81,\cdot)\) \(\chi_{869}(92,\cdot)\) \(\chi_{869}(104,\cdot)\) \(\chi_{869}(115,\cdot)\) \(\chi_{869}(119,\cdot)\) \(\chi_{869}(124,\cdot)\) \(\chi_{869}(130,\cdot)\) \(\chi_{869}(152,\cdot)\) \(\chi_{869}(163,\cdot)\) \(\chi_{869}(169,\cdot)\) \(\chi_{869}(174,\cdot)\) \(\chi_{869}(190,\cdot)\) \(\chi_{869}(202,\cdot)\) \(\chi_{869}(203,\cdot)\) \(\chi_{869}(207,\cdot)\) \(\chi_{869}(234,\cdot)\) \(\chi_{869}(246,\cdot)\) \(\chi_{869}(256,\cdot)\) \(\chi_{869}(257,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{195})$ |
Fixed field: | Number field defined by a degree 195 polynomial (not computed) |
Values on generators
\((475,793)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{20}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 869 }(234, a) \) | \(1\) | \(1\) | \(e\left(\frac{166}{195}\right)\) | \(e\left(\frac{178}{195}\right)\) | \(e\left(\frac{137}{195}\right)\) | \(e\left(\frac{194}{195}\right)\) | \(e\left(\frac{149}{195}\right)\) | \(e\left(\frac{152}{195}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{161}{195}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) |