Basic properties
Modulus: | \(4900\) | |
Conductor: | \(4900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(420\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4900.dr
\(\chi_{4900}(23,\cdot)\) \(\chi_{4900}(123,\cdot)\) \(\chi_{4900}(163,\cdot)\) \(\chi_{4900}(247,\cdot)\) \(\chi_{4900}(303,\cdot)\) \(\chi_{4900}(347,\cdot)\) \(\chi_{4900}(387,\cdot)\) \(\chi_{4900}(403,\cdot)\) \(\chi_{4900}(487,\cdot)\) \(\chi_{4900}(527,\cdot)\) \(\chi_{4900}(583,\cdot)\) \(\chi_{4900}(627,\cdot)\) \(\chi_{4900}(683,\cdot)\) \(\chi_{4900}(723,\cdot)\) \(\chi_{4900}(767,\cdot)\) \(\chi_{4900}(823,\cdot)\) \(\chi_{4900}(947,\cdot)\) \(\chi_{4900}(963,\cdot)\) \(\chi_{4900}(1003,\cdot)\) \(\chi_{4900}(1087,\cdot)\) \(\chi_{4900}(1103,\cdot)\) \(\chi_{4900}(1187,\cdot)\) \(\chi_{4900}(1227,\cdot)\) \(\chi_{4900}(1283,\cdot)\) \(\chi_{4900}(1327,\cdot)\) \(\chi_{4900}(1367,\cdot)\) \(\chi_{4900}(1383,\cdot)\) \(\chi_{4900}(1423,\cdot)\) \(\chi_{4900}(1467,\cdot)\) \(\chi_{4900}(1523,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{420})$ |
Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((2451,1177,101)\) → \((-1,e\left(\frac{11}{20}\right),e\left(\frac{19}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 4900 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{420}\right)\) | \(e\left(\frac{107}{210}\right)\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{323}{420}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{391}{420}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{7}{30}\right)\) |