Basic properties
Modulus: | \(4725\) | |
Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | 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 4725.fl
\(\chi_{4725}(16,\cdot)\) \(\chi_{4725}(256,\cdot)\) \(\chi_{4725}(331,\cdot)\) \(\chi_{4725}(571,\cdot)\) \(\chi_{4725}(646,\cdot)\) \(\chi_{4725}(886,\cdot)\) \(\chi_{4725}(961,\cdot)\) \(\chi_{4725}(1516,\cdot)\) \(\chi_{4725}(1591,\cdot)\) \(\chi_{4725}(1831,\cdot)\) \(\chi_{4725}(1906,\cdot)\) \(\chi_{4725}(2146,\cdot)\) \(\chi_{4725}(2221,\cdot)\) \(\chi_{4725}(2461,\cdot)\) \(\chi_{4725}(2536,\cdot)\) \(\chi_{4725}(3091,\cdot)\) \(\chi_{4725}(3166,\cdot)\) \(\chi_{4725}(3406,\cdot)\) \(\chi_{4725}(3481,\cdot)\) \(\chi_{4725}(3721,\cdot)\) \(\chi_{4725}(3796,\cdot)\) \(\chi_{4725}(4036,\cdot)\) \(\chi_{4725}(4111,\cdot)\) \(\chi_{4725}(4666,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{4}{5}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 4725 }(4111, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) |