Basic properties
| Modulus: | \(4600\) | |
| Conductor: | \(2300\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2300}(79,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4600.dj
\(\chi_{4600}(79,\cdot)\) \(\chi_{4600}(159,\cdot)\) \(\chi_{4600}(319,\cdot)\) \(\chi_{4600}(359,\cdot)\) \(\chi_{4600}(479,\cdot)\) \(\chi_{4600}(559,\cdot)\) \(\chi_{4600}(839,\cdot)\) \(\chi_{4600}(879,\cdot)\) \(\chi_{4600}(1079,\cdot)\) \(\chi_{4600}(1119,\cdot)\) \(\chi_{4600}(1239,\cdot)\) \(\chi_{4600}(1279,\cdot)\) \(\chi_{4600}(1479,\cdot)\) \(\chi_{4600}(1719,\cdot)\) \(\chi_{4600}(1759,\cdot)\) \(\chi_{4600}(1919,\cdot)\) \(\chi_{4600}(2039,\cdot)\) \(\chi_{4600}(2159,\cdot)\) \(\chi_{4600}(2319,\cdot)\) \(\chi_{4600}(2639,\cdot)\) \(\chi_{4600}(2679,\cdot)\) \(\chi_{4600}(2719,\cdot)\) \(\chi_{4600}(2839,\cdot)\) \(\chi_{4600}(2919,\cdot)\) \(\chi_{4600}(2959,\cdot)\) \(\chi_{4600}(3079,\cdot)\) \(\chi_{4600}(3119,\cdot)\) \(\chi_{4600}(3239,\cdot)\) \(\chi_{4600}(3319,\cdot)\) \(\chi_{4600}(3559,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,2301,2577,1201)\) → \((-1,1,e\left(\frac{1}{10}\right),e\left(\frac{3}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 4600 }(79, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{36}{55}\right)\) |