Basic properties
| Modulus: | \(9075\) | |
| Conductor: | \(3025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3025}(172,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.fv
\(\chi_{9075}(172,\cdot)\) \(\chi_{9075}(217,\cdot)\) \(\chi_{9075}(277,\cdot)\) \(\chi_{9075}(283,\cdot)\) \(\chi_{9075}(673,\cdot)\) \(\chi_{9075}(688,\cdot)\) \(\chi_{9075}(787,\cdot)\) \(\chi_{9075}(997,\cdot)\) \(\chi_{9075}(1042,\cdot)\) \(\chi_{9075}(1102,\cdot)\) \(\chi_{9075}(1108,\cdot)\) \(\chi_{9075}(1228,\cdot)\) \(\chi_{9075}(1498,\cdot)\) \(\chi_{9075}(1513,\cdot)\) \(\chi_{9075}(1612,\cdot)\) \(\chi_{9075}(1822,\cdot)\) \(\chi_{9075}(1867,\cdot)\) \(\chi_{9075}(2053,\cdot)\) \(\chi_{9075}(2323,\cdot)\) \(\chi_{9075}(2338,\cdot)\) \(\chi_{9075}(2437,\cdot)\) \(\chi_{9075}(2647,\cdot)\) \(\chi_{9075}(2692,\cdot)\) \(\chi_{9075}(2752,\cdot)\) \(\chi_{9075}(2758,\cdot)\) \(\chi_{9075}(2878,\cdot)\) \(\chi_{9075}(3148,\cdot)\) \(\chi_{9075}(3163,\cdot)\) \(\chi_{9075}(3262,\cdot)\) \(\chi_{9075}(3472,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((1,e\left(\frac{17}{20}\right),e\left(\frac{27}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(172, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{220}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{213}{220}\right)\) | \(e\left(\frac{63}{220}\right)\) | \(e\left(\frac{207}{220}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{17}{220}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{117}{220}\right)\) |