Basic properties
Modulus: | \(1375\) | |
Conductor: | \(1375\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(100\) | 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 1375.cp
\(\chi_{1375}(42,\cdot)\) \(\chi_{1375}(48,\cdot)\) \(\chi_{1375}(108,\cdot)\) \(\chi_{1375}(113,\cdot)\) \(\chi_{1375}(202,\cdot)\) \(\chi_{1375}(203,\cdot)\) \(\chi_{1375}(212,\cdot)\) \(\chi_{1375}(247,\cdot)\) \(\chi_{1375}(317,\cdot)\) \(\chi_{1375}(323,\cdot)\) \(\chi_{1375}(383,\cdot)\) \(\chi_{1375}(388,\cdot)\) \(\chi_{1375}(477,\cdot)\) \(\chi_{1375}(478,\cdot)\) \(\chi_{1375}(487,\cdot)\) \(\chi_{1375}(522,\cdot)\) \(\chi_{1375}(592,\cdot)\) \(\chi_{1375}(598,\cdot)\) \(\chi_{1375}(658,\cdot)\) \(\chi_{1375}(663,\cdot)\) \(\chi_{1375}(752,\cdot)\) \(\chi_{1375}(753,\cdot)\) \(\chi_{1375}(762,\cdot)\) \(\chi_{1375}(797,\cdot)\) \(\chi_{1375}(867,\cdot)\) \(\chi_{1375}(873,\cdot)\) \(\chi_{1375}(933,\cdot)\) \(\chi_{1375}(938,\cdot)\) \(\chi_{1375}(1027,\cdot)\) \(\chi_{1375}(1028,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1002,376)\) → \((e\left(\frac{73}{100}\right),e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 1375 }(1142, a) \) | \(-1\) | \(1\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(i\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{29}{50}\right)\) |