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 \(\chi_{3025}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.gh
\(\chi_{9075}(13,\cdot)\) \(\chi_{9075}(127,\cdot)\) \(\chi_{9075}(523,\cdot)\) \(\chi_{9075}(547,\cdot)\) \(\chi_{9075}(667,\cdot)\) \(\chi_{9075}(733,\cdot)\) \(\chi_{9075}(778,\cdot)\) \(\chi_{9075}(937,\cdot)\) \(\chi_{9075}(952,\cdot)\) \(\chi_{9075}(1348,\cdot)\) \(\chi_{9075}(1372,\cdot)\) \(\chi_{9075}(1558,\cdot)\) \(\chi_{9075}(1603,\cdot)\) \(\chi_{9075}(1663,\cdot)\) \(\chi_{9075}(1762,\cdot)\) \(\chi_{9075}(1777,\cdot)\) \(\chi_{9075}(2173,\cdot)\) \(\chi_{9075}(2197,\cdot)\) \(\chi_{9075}(2317,\cdot)\) \(\chi_{9075}(2383,\cdot)\) \(\chi_{9075}(2428,\cdot)\) \(\chi_{9075}(2488,\cdot)\) \(\chi_{9075}(2587,\cdot)\) \(\chi_{9075}(2602,\cdot)\) \(\chi_{9075}(3142,\cdot)\) \(\chi_{9075}(3208,\cdot)\) \(\chi_{9075}(3253,\cdot)\) \(\chi_{9075}(3313,\cdot)\) \(\chi_{9075}(3412,\cdot)\) \(\chi_{9075}(3427,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((1,e\left(\frac{19}{20}\right),e\left(\frac{101}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{191}{220}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{39}{220}\right)\) | \(e\left(\frac{133}{220}\right)\) | \(e\left(\frac{173}{220}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{159}{220}\right)\) |