Basic properties
| Modulus: | \(9200\) | |
| Conductor: | \(4600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4600}(2453,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9200.fv
\(\chi_{9200}(153,\cdot)\) \(\chi_{9200}(217,\cdot)\) \(\chi_{9200}(297,\cdot)\) \(\chi_{9200}(313,\cdot)\) \(\chi_{9200}(617,\cdot)\) \(\chi_{9200}(697,\cdot)\) \(\chi_{9200}(937,\cdot)\) \(\chi_{9200}(953,\cdot)\) \(\chi_{9200}(1017,\cdot)\) \(\chi_{9200}(1033,\cdot)\) \(\chi_{9200}(1353,\cdot)\) \(\chi_{9200}(1417,\cdot)\) \(\chi_{9200}(1433,\cdot)\) \(\chi_{9200}(1673,\cdot)\) \(\chi_{9200}(1753,\cdot)\) \(\chi_{9200}(1897,\cdot)\) \(\chi_{9200}(2137,\cdot)\) \(\chi_{9200}(2153,\cdot)\) \(\chi_{9200}(2297,\cdot)\) \(\chi_{9200}(2537,\cdot)\) \(\chi_{9200}(2633,\cdot)\) \(\chi_{9200}(2777,\cdot)\) \(\chi_{9200}(2873,\cdot)\) \(\chi_{9200}(3033,\cdot)\) \(\chi_{9200}(3097,\cdot)\) \(\chi_{9200}(3273,\cdot)\) \(\chi_{9200}(3513,\cdot)\) \(\chi_{9200}(3737,\cdot)\) \(\chi_{9200}(3833,\cdot)\) \(\chi_{9200}(3897,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,6901,2577,1201)\) → \((1,-1,e\left(\frac{7}{20}\right),e\left(\frac{17}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 9200 }(153, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{220}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{213}{220}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{207}{220}\right)\) | \(e\left(\frac{6}{55}\right)\) |