Basic properties
Modulus: | \(1425\) | |
Conductor: | \(475\) | 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 \(\chi_{475}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1425.cn
\(\chi_{1425}(4,\cdot)\) \(\chi_{1425}(139,\cdot)\) \(\chi_{1425}(169,\cdot)\) \(\chi_{1425}(214,\cdot)\) \(\chi_{1425}(244,\cdot)\) \(\chi_{1425}(289,\cdot)\) \(\chi_{1425}(454,\cdot)\) \(\chi_{1425}(484,\cdot)\) \(\chi_{1425}(529,\cdot)\) \(\chi_{1425}(709,\cdot)\) \(\chi_{1425}(739,\cdot)\) \(\chi_{1425}(769,\cdot)\) \(\chi_{1425}(784,\cdot)\) \(\chi_{1425}(814,\cdot)\) \(\chi_{1425}(859,\cdot)\) \(\chi_{1425}(994,\cdot)\) \(\chi_{1425}(1054,\cdot)\) \(\chi_{1425}(1069,\cdot)\) \(\chi_{1425}(1144,\cdot)\) \(\chi_{1425}(1279,\cdot)\) \(\chi_{1425}(1309,\cdot)\) \(\chi_{1425}(1339,\cdot)\) \(\chi_{1425}(1354,\cdot)\) \(\chi_{1425}(1384,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((476,1027,1351)\) → \((1,e\left(\frac{1}{10}\right),e\left(\frac{1}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
\( \chi_{ 1425 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{13}{90}\right)\) |