Basic properties
Modulus: | \(4275\) | |
Conductor: | \(4275\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | 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 4275.hc
\(\chi_{4275}(23,\cdot)\) \(\chi_{4275}(92,\cdot)\) \(\chi_{4275}(158,\cdot)\) \(\chi_{4275}(263,\cdot)\) \(\chi_{4275}(587,\cdot)\) \(\chi_{4275}(617,\cdot)\) \(\chi_{4275}(758,\cdot)\) \(\chi_{4275}(788,\cdot)\) \(\chi_{4275}(803,\cdot)\) \(\chi_{4275}(842,\cdot)\) \(\chi_{4275}(878,\cdot)\) \(\chi_{4275}(947,\cdot)\) \(\chi_{4275}(1013,\cdot)\) \(\chi_{4275}(1442,\cdot)\) \(\chi_{4275}(1472,\cdot)\) \(\chi_{4275}(1487,\cdot)\) \(\chi_{4275}(1562,\cdot)\) \(\chi_{4275}(1613,\cdot)\) \(\chi_{4275}(1658,\cdot)\) \(\chi_{4275}(1697,\cdot)\) \(\chi_{4275}(1733,\cdot)\) \(\chi_{4275}(1802,\cdot)\) \(\chi_{4275}(1973,\cdot)\) \(\chi_{4275}(2297,\cdot)\) \(\chi_{4275}(2327,\cdot)\) \(\chi_{4275}(2342,\cdot)\) \(\chi_{4275}(2417,\cdot)\) \(\chi_{4275}(2498,\cdot)\) \(\chi_{4275}(2513,\cdot)\) \(\chi_{4275}(2552,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1901,1027,1351)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{9}{20}\right),e\left(\frac{1}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
\( \chi_{ 4275 }(1562, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{180}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(i\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{139}{180}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{83}{180}\right)\) | \(e\left(\frac{137}{180}\right)\) |