Basic properties
Modulus: | \(4225\) | |
Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(260\) | 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 4225.cs
\(\chi_{4225}(8,\cdot)\) \(\chi_{4225}(73,\cdot)\) \(\chi_{4225}(122,\cdot)\) \(\chi_{4225}(138,\cdot)\) \(\chi_{4225}(187,\cdot)\) \(\chi_{4225}(203,\cdot)\) \(\chi_{4225}(252,\cdot)\) \(\chi_{4225}(317,\cdot)\) \(\chi_{4225}(333,\cdot)\) \(\chi_{4225}(398,\cdot)\) \(\chi_{4225}(447,\cdot)\) \(\chi_{4225}(463,\cdot)\) \(\chi_{4225}(512,\cdot)\) \(\chi_{4225}(528,\cdot)\) \(\chi_{4225}(642,\cdot)\) \(\chi_{4225}(658,\cdot)\) \(\chi_{4225}(723,\cdot)\) \(\chi_{4225}(772,\cdot)\) \(\chi_{4225}(788,\cdot)\) \(\chi_{4225}(837,\cdot)\) \(\chi_{4225}(853,\cdot)\) \(\chi_{4225}(902,\cdot)\) \(\chi_{4225}(967,\cdot)\) \(\chi_{4225}(983,\cdot)\) \(\chi_{4225}(1048,\cdot)\) \(\chi_{4225}(1097,\cdot)\) \(\chi_{4225}(1162,\cdot)\) \(\chi_{4225}(1178,\cdot)\) \(\chi_{4225}(1227,\cdot)\) \(\chi_{4225}(1292,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{260})$ |
Fixed field: | Number field defined by a degree 260 polynomial (not computed) |
Values on generators
\((677,3551)\) → \((e\left(\frac{3}{20}\right),e\left(\frac{1}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
\( \chi_{ 4225 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{113}{260}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{157}{260}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{99}{260}\right)\) | \(e\left(\frac{201}{260}\right)\) | \(e\left(\frac{127}{130}\right)\) |