Basic properties
Modulus: | \(4725\) | |
Conductor: | \(4725\) | 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 4725.hc
\(\chi_{4725}(2,\cdot)\) \(\chi_{4725}(128,\cdot)\) \(\chi_{4725}(158,\cdot)\) \(\chi_{4725}(317,\cdot)\) \(\chi_{4725}(347,\cdot)\) \(\chi_{4725}(473,\cdot)\) \(\chi_{4725}(662,\cdot)\) \(\chi_{4725}(758,\cdot)\) \(\chi_{4725}(788,\cdot)\) \(\chi_{4725}(947,\cdot)\) \(\chi_{4725}(977,\cdot)\) \(\chi_{4725}(1073,\cdot)\) \(\chi_{4725}(1103,\cdot)\) \(\chi_{4725}(1262,\cdot)\) \(\chi_{4725}(1292,\cdot)\) \(\chi_{4725}(1388,\cdot)\) \(\chi_{4725}(1577,\cdot)\) \(\chi_{4725}(1703,\cdot)\) \(\chi_{4725}(1733,\cdot)\) \(\chi_{4725}(1892,\cdot)\) \(\chi_{4725}(1922,\cdot)\) \(\chi_{4725}(2048,\cdot)\) \(\chi_{4725}(2237,\cdot)\) \(\chi_{4725}(2333,\cdot)\) \(\chi_{4725}(2363,\cdot)\) \(\chi_{4725}(2522,\cdot)\) \(\chi_{4725}(2552,\cdot)\) \(\chi_{4725}(2648,\cdot)\) \(\chi_{4725}(2678,\cdot)\) \(\chi_{4725}(2837,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{13}{20}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 4725 }(317, a) \) | \(1\) | \(1\) | \(e\left(\frac{127}{180}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{83}{180}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{89}{180}\right)\) | \(e\left(\frac{17}{180}\right)\) |