Basic properties
| Modulus: | \(9800\) | |
| Conductor: | \(4900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4900}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9800.hi
\(\chi_{9800}(23,\cdot)\) \(\chi_{9800}(247,\cdot)\) \(\chi_{9800}(303,\cdot)\) \(\chi_{9800}(487,\cdot)\) \(\chi_{9800}(527,\cdot)\) \(\chi_{9800}(583,\cdot)\) \(\chi_{9800}(767,\cdot)\) \(\chi_{9800}(823,\cdot)\) \(\chi_{9800}(1087,\cdot)\) \(\chi_{9800}(1103,\cdot)\) \(\chi_{9800}(1327,\cdot)\) \(\chi_{9800}(1367,\cdot)\) \(\chi_{9800}(1383,\cdot)\) \(\chi_{9800}(1423,\cdot)\) \(\chi_{9800}(1663,\cdot)\) \(\chi_{9800}(1703,\cdot)\) \(\chi_{9800}(1887,\cdot)\) \(\chi_{9800}(1927,\cdot)\) \(\chi_{9800}(1983,\cdot)\) \(\chi_{9800}(2167,\cdot)\) \(\chi_{9800}(2263,\cdot)\) \(\chi_{9800}(2447,\cdot)\) \(\chi_{9800}(2487,\cdot)\) \(\chi_{9800}(2503,\cdot)\) \(\chi_{9800}(2727,\cdot)\) \(\chi_{9800}(2767,\cdot)\) \(\chi_{9800}(2783,\cdot)\) \(\chi_{9800}(3047,\cdot)\) \(\chi_{9800}(3063,\cdot)\) \(\chi_{9800}(3103,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((7351,4901,1177,5001)\) → \((-1,1,e\left(\frac{11}{20}\right),e\left(\frac{19}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 9800 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{420}\right)\) | \(e\left(\frac{107}{210}\right)\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{323}{420}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{391}{420}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{7}{30}\right)\) |