Basic properties
Modulus: | \(4725\) | |
Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{675}(169,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4725.gi
\(\chi_{4725}(169,\cdot)\) \(\chi_{4725}(484,\cdot)\) \(\chi_{4725}(589,\cdot)\) \(\chi_{4725}(904,\cdot)\) \(\chi_{4725}(1114,\cdot)\) \(\chi_{4725}(1219,\cdot)\) \(\chi_{4725}(1429,\cdot)\) \(\chi_{4725}(1534,\cdot)\) \(\chi_{4725}(1744,\cdot)\) \(\chi_{4725}(2059,\cdot)\) \(\chi_{4725}(2164,\cdot)\) \(\chi_{4725}(2479,\cdot)\) \(\chi_{4725}(2689,\cdot)\) \(\chi_{4725}(2794,\cdot)\) \(\chi_{4725}(3004,\cdot)\) \(\chi_{4725}(3109,\cdot)\) \(\chi_{4725}(3319,\cdot)\) \(\chi_{4725}(3634,\cdot)\) \(\chi_{4725}(3739,\cdot)\) \(\chi_{4725}(4054,\cdot)\) \(\chi_{4725}(4264,\cdot)\) \(\chi_{4725}(4369,\cdot)\) \(\chi_{4725}(4579,\cdot)\) \(\chi_{4725}(4684,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{9}{10}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 4725 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{61}{90}\right)\) |