Basic properties
| Modulus: | \(9075\) | |
| Conductor: | \(1815\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1815}(1193,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.ga
\(\chi_{9075}(218,\cdot)\) \(\chi_{9075}(257,\cdot)\) \(\chi_{9075}(368,\cdot)\) \(\chi_{9075}(443,\cdot)\) \(\chi_{9075}(482,\cdot)\) \(\chi_{9075}(707,\cdot)\) \(\chi_{9075}(818,\cdot)\) \(\chi_{9075}(1043,\cdot)\) \(\chi_{9075}(1082,\cdot)\) \(\chi_{9075}(1193,\cdot)\) \(\chi_{9075}(1268,\cdot)\) \(\chi_{9075}(1307,\cdot)\) \(\chi_{9075}(1457,\cdot)\) \(\chi_{9075}(1532,\cdot)\) \(\chi_{9075}(1643,\cdot)\) \(\chi_{9075}(1868,\cdot)\) \(\chi_{9075}(1907,\cdot)\) \(\chi_{9075}(2018,\cdot)\) \(\chi_{9075}(2093,\cdot)\) \(\chi_{9075}(2132,\cdot)\) \(\chi_{9075}(2282,\cdot)\) \(\chi_{9075}(2357,\cdot)\) \(\chi_{9075}(2468,\cdot)\) \(\chi_{9075}(2693,\cdot)\) \(\chi_{9075}(2732,\cdot)\) \(\chi_{9075}(2843,\cdot)\) \(\chi_{9075}(2918,\cdot)\) \(\chi_{9075}(2957,\cdot)\) \(\chi_{9075}(3107,\cdot)\) \(\chi_{9075}(3182,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((-1,-i,e\left(\frac{52}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(1193, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{220}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{81}{220}\right)\) | \(e\left(\frac{129}{220}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{127}{220}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{41}{44}\right)\) |