Basic properties
| Modulus: | \(4025\) | |
| Conductor: | \(4025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 4025.ct
\(\chi_{4025}(34,\cdot)\) \(\chi_{4025}(244,\cdot)\) \(\chi_{4025}(314,\cdot)\) \(\chi_{4025}(419,\cdot)\) \(\chi_{4025}(454,\cdot)\) \(\chi_{4025}(559,\cdot)\) \(\chi_{4025}(594,\cdot)\) \(\chi_{4025}(664,\cdot)\) \(\chi_{4025}(734,\cdot)\) \(\chi_{4025}(769,\cdot)\) \(\chi_{4025}(839,\cdot)\) \(\chi_{4025}(1119,\cdot)\) \(\chi_{4025}(1259,\cdot)\) \(\chi_{4025}(1364,\cdot)\) \(\chi_{4025}(1469,\cdot)\) \(\chi_{4025}(1539,\cdot)\) \(\chi_{4025}(1644,\cdot)\) \(\chi_{4025}(1854,\cdot)\) \(\chi_{4025}(2029,\cdot)\) \(\chi_{4025}(2064,\cdot)\) \(\chi_{4025}(2169,\cdot)\) \(\chi_{4025}(2204,\cdot)\) \(\chi_{4025}(2344,\cdot)\) \(\chi_{4025}(2379,\cdot)\) \(\chi_{4025}(2659,\cdot)\) \(\chi_{4025}(2729,\cdot)\) \(\chi_{4025}(2834,\cdot)\) \(\chi_{4025}(2869,\cdot)\) \(\chi_{4025}(3009,\cdot)\) \(\chi_{4025}(3079,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{7}{10}\right),-1,e\left(\frac{13}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 4025 }(734, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{29}{55}\right)\) |