Basic properties
| Modulus: | \(9075\) | |
| Conductor: | \(9075\) | 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 9075.el
\(\chi_{9075}(359,\cdot)\) \(\chi_{9075}(629,\cdot)\) \(\chi_{9075}(644,\cdot)\) \(\chi_{9075}(1064,\cdot)\) \(\chi_{9075}(1184,\cdot)\) \(\chi_{9075}(1454,\cdot)\) \(\chi_{9075}(1469,\cdot)\) \(\chi_{9075}(1889,\cdot)\) \(\chi_{9075}(2009,\cdot)\) \(\chi_{9075}(2279,\cdot)\) \(\chi_{9075}(2294,\cdot)\) \(\chi_{9075}(2714,\cdot)\) \(\chi_{9075}(2834,\cdot)\) \(\chi_{9075}(3104,\cdot)\) \(\chi_{9075}(3539,\cdot)\) \(\chi_{9075}(3659,\cdot)\) \(\chi_{9075}(3929,\cdot)\) \(\chi_{9075}(3944,\cdot)\) \(\chi_{9075}(4364,\cdot)\) \(\chi_{9075}(4484,\cdot)\) \(\chi_{9075}(4754,\cdot)\) \(\chi_{9075}(4769,\cdot)\) \(\chi_{9075}(5189,\cdot)\) \(\chi_{9075}(5309,\cdot)\) \(\chi_{9075}(5579,\cdot)\) \(\chi_{9075}(5594,\cdot)\) \(\chi_{9075}(6014,\cdot)\) \(\chi_{9075}(6134,\cdot)\) \(\chi_{9075}(6419,\cdot)\) \(\chi_{9075}(6839,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{57}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(359, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{26}{55}\right)\) |