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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1375.co
\(\chi_{1375}(17,\cdot)\) \(\chi_{1375}(52,\cdot)\) \(\chi_{1375}(62,\cdot)\) \(\chi_{1375}(83,\cdot)\) \(\chi_{1375}(173,\cdot)\) \(\chi_{1375}(178,\cdot)\) \(\chi_{1375}(222,\cdot)\) \(\chi_{1375}(238,\cdot)\) \(\chi_{1375}(292,\cdot)\) \(\chi_{1375}(327,\cdot)\) \(\chi_{1375}(337,\cdot)\) \(\chi_{1375}(358,\cdot)\) \(\chi_{1375}(448,\cdot)\) \(\chi_{1375}(453,\cdot)\) \(\chi_{1375}(497,\cdot)\) \(\chi_{1375}(513,\cdot)\) \(\chi_{1375}(567,\cdot)\) \(\chi_{1375}(602,\cdot)\) \(\chi_{1375}(612,\cdot)\) \(\chi_{1375}(633,\cdot)\) \(\chi_{1375}(723,\cdot)\) \(\chi_{1375}(728,\cdot)\) \(\chi_{1375}(772,\cdot)\) \(\chi_{1375}(788,\cdot)\) \(\chi_{1375}(842,\cdot)\) \(\chi_{1375}(877,\cdot)\) \(\chi_{1375}(887,\cdot)\) \(\chi_{1375}(908,\cdot)\) \(\chi_{1375}(998,\cdot)\) \(\chi_{1375}(1003,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1002,376)\) → \((e\left(\frac{77}{100}\right),e\left(\frac{1}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 1375 }(772, a) \) | \(1\) | \(1\) | \(e\left(\frac{87}{100}\right)\) | \(e\left(\frac{19}{100}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{1}{50}\right)\) |