Basic properties
Modulus: | \(845\) | |
Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | 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 845.bi
\(\chi_{845}(7,\cdot)\) \(\chi_{845}(28,\cdot)\) \(\chi_{845}(37,\cdot)\) \(\chi_{845}(58,\cdot)\) \(\chi_{845}(72,\cdot)\) \(\chi_{845}(93,\cdot)\) \(\chi_{845}(102,\cdot)\) \(\chi_{845}(123,\cdot)\) \(\chi_{845}(137,\cdot)\) \(\chi_{845}(158,\cdot)\) \(\chi_{845}(167,\cdot)\) \(\chi_{845}(202,\cdot)\) \(\chi_{845}(223,\cdot)\) \(\chi_{845}(232,\cdot)\) \(\chi_{845}(253,\cdot)\) \(\chi_{845}(267,\cdot)\) \(\chi_{845}(288,\cdot)\) \(\chi_{845}(297,\cdot)\) \(\chi_{845}(318,\cdot)\) \(\chi_{845}(332,\cdot)\) \(\chi_{845}(353,\cdot)\) \(\chi_{845}(362,\cdot)\) \(\chi_{845}(383,\cdot)\) \(\chi_{845}(397,\cdot)\) \(\chi_{845}(448,\cdot)\) \(\chi_{845}(462,\cdot)\) \(\chi_{845}(483,\cdot)\) \(\chi_{845}(492,\cdot)\) \(\chi_{845}(513,\cdot)\) \(\chi_{845}(527,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((677,171)\) → \((i,e\left(\frac{107}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
\( \chi_{ 845 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{125}{156}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{115}{156}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{15}{26}\right)\) |