Basic properties
Modulus: | \(1375\) | |
Conductor: | \(125\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{125}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1375.cq
\(\chi_{1375}(12,\cdot)\) \(\chi_{1375}(23,\cdot)\) \(\chi_{1375}(67,\cdot)\) \(\chi_{1375}(78,\cdot)\) \(\chi_{1375}(122,\cdot)\) \(\chi_{1375}(133,\cdot)\) \(\chi_{1375}(177,\cdot)\) \(\chi_{1375}(188,\cdot)\) \(\chi_{1375}(287,\cdot)\) \(\chi_{1375}(298,\cdot)\) \(\chi_{1375}(342,\cdot)\) \(\chi_{1375}(353,\cdot)\) \(\chi_{1375}(397,\cdot)\) \(\chi_{1375}(408,\cdot)\) \(\chi_{1375}(452,\cdot)\) \(\chi_{1375}(463,\cdot)\) \(\chi_{1375}(562,\cdot)\) \(\chi_{1375}(573,\cdot)\) \(\chi_{1375}(617,\cdot)\) \(\chi_{1375}(628,\cdot)\) \(\chi_{1375}(672,\cdot)\) \(\chi_{1375}(683,\cdot)\) \(\chi_{1375}(727,\cdot)\) \(\chi_{1375}(738,\cdot)\) \(\chi_{1375}(837,\cdot)\) \(\chi_{1375}(848,\cdot)\) \(\chi_{1375}(892,\cdot)\) \(\chi_{1375}(903,\cdot)\) \(\chi_{1375}(947,\cdot)\) \(\chi_{1375}(958,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1002,376)\) → \((e\left(\frac{31}{100}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 1375 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{100}\right)\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{79}{100}\right)\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{33}{50}\right)\) |