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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1375.cm
\(\chi_{1375}(2,\cdot)\) \(\chi_{1375}(8,\cdot)\) \(\chi_{1375}(123,\cdot)\) \(\chi_{1375}(128,\cdot)\) \(\chi_{1375}(138,\cdot)\) \(\chi_{1375}(172,\cdot)\) \(\chi_{1375}(217,\cdot)\) \(\chi_{1375}(237,\cdot)\) \(\chi_{1375}(277,\cdot)\) \(\chi_{1375}(283,\cdot)\) \(\chi_{1375}(398,\cdot)\) \(\chi_{1375}(403,\cdot)\) \(\chi_{1375}(413,\cdot)\) \(\chi_{1375}(447,\cdot)\) \(\chi_{1375}(492,\cdot)\) \(\chi_{1375}(512,\cdot)\) \(\chi_{1375}(552,\cdot)\) \(\chi_{1375}(558,\cdot)\) \(\chi_{1375}(673,\cdot)\) \(\chi_{1375}(678,\cdot)\) \(\chi_{1375}(688,\cdot)\) \(\chi_{1375}(722,\cdot)\) \(\chi_{1375}(767,\cdot)\) \(\chi_{1375}(787,\cdot)\) \(\chi_{1375}(827,\cdot)\) \(\chi_{1375}(833,\cdot)\) \(\chi_{1375}(948,\cdot)\) \(\chi_{1375}(953,\cdot)\) \(\chi_{1375}(963,\cdot)\) \(\chi_{1375}(997,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1002,376)\) → \((e\left(\frac{23}{100}\right),e\left(\frac{3}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 1375 }(1108, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{9}{50}\right)\) |