Basic properties
Modulus: | \(1375\) | |
Conductor: | \(1375\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(100\) | 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 1375.ct
\(\chi_{1375}(13,\cdot)\) \(\chi_{1375}(112,\cdot)\) \(\chi_{1375}(117,\cdot)\) \(\chi_{1375}(127,\cdot)\) \(\chi_{1375}(183,\cdot)\) \(\chi_{1375}(228,\cdot)\) \(\chi_{1375}(248,\cdot)\) \(\chi_{1375}(272,\cdot)\) \(\chi_{1375}(288,\cdot)\) \(\chi_{1375}(387,\cdot)\) \(\chi_{1375}(392,\cdot)\) \(\chi_{1375}(402,\cdot)\) \(\chi_{1375}(458,\cdot)\) \(\chi_{1375}(503,\cdot)\) \(\chi_{1375}(523,\cdot)\) \(\chi_{1375}(547,\cdot)\) \(\chi_{1375}(563,\cdot)\) \(\chi_{1375}(662,\cdot)\) \(\chi_{1375}(667,\cdot)\) \(\chi_{1375}(677,\cdot)\) \(\chi_{1375}(733,\cdot)\) \(\chi_{1375}(778,\cdot)\) \(\chi_{1375}(798,\cdot)\) \(\chi_{1375}(822,\cdot)\) \(\chi_{1375}(838,\cdot)\) \(\chi_{1375}(937,\cdot)\) \(\chi_{1375}(942,\cdot)\) \(\chi_{1375}(952,\cdot)\) \(\chi_{1375}(1008,\cdot)\) \(\chi_{1375}(1053,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1002,376)\) → \((e\left(\frac{67}{100}\right),e\left(\frac{3}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 1375 }(1053, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{3}{100}\right)\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{1}{50}\right)\) |