Basic properties
Modulus: | \(7524\) | |
Conductor: | \(1881\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1881}(169,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7524.ia
\(\chi_{7524}(169,\cdot)\) \(\chi_{7524}(1213,\cdot)\) \(\chi_{7524}(1753,\cdot)\) \(\chi_{7524}(1885,\cdot)\) \(\chi_{7524}(1897,\cdot)\) \(\chi_{7524}(2137,\cdot)\) \(\chi_{7524}(2533,\cdot)\) \(\chi_{7524}(2821,\cdot)\) \(\chi_{7524}(3217,\cdot)\) \(\chi_{7524}(3265,\cdot)\) \(\chi_{7524}(3589,\cdot)\) \(\chi_{7524}(4189,\cdot)\) \(\chi_{7524}(4273,\cdot)\) \(\chi_{7524}(4585,\cdot)\) \(\chi_{7524}(5173,\cdot)\) \(\chi_{7524}(5305,\cdot)\) \(\chi_{7524}(5317,\cdot)\) \(\chi_{7524}(5641,\cdot)\) \(\chi_{7524}(5857,\cdot)\) \(\chi_{7524}(5989,\cdot)\) \(\chi_{7524}(6241,\cdot)\) \(\chi_{7524}(6637,\cdot)\) \(\chi_{7524}(7225,\cdot)\) \(\chi_{7524}(7357,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{1}{5}\right),e\left(\frac{5}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
\( \chi_{ 7524 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{2}{5}\right)\) |