Basic properties
Modulus: | \(9075\) | |
Conductor: | \(3025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{3025}(34,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.eu
\(\chi_{9075}(34,\cdot)\) \(\chi_{9075}(529,\cdot)\) \(\chi_{9075}(694,\cdot)\) \(\chi_{9075}(859,\cdot)\) \(\chi_{9075}(1189,\cdot)\) \(\chi_{9075}(1354,\cdot)\) \(\chi_{9075}(1519,\cdot)\) \(\chi_{9075}(1684,\cdot)\) \(\chi_{9075}(2014,\cdot)\) \(\chi_{9075}(2344,\cdot)\) \(\chi_{9075}(2509,\cdot)\) \(\chi_{9075}(2839,\cdot)\) \(\chi_{9075}(3004,\cdot)\) \(\chi_{9075}(3169,\cdot)\) \(\chi_{9075}(3334,\cdot)\) \(\chi_{9075}(3664,\cdot)\) \(\chi_{9075}(3829,\cdot)\) \(\chi_{9075}(4159,\cdot)\) \(\chi_{9075}(4489,\cdot)\) \(\chi_{9075}(4654,\cdot)\) \(\chi_{9075}(4819,\cdot)\) \(\chi_{9075}(4984,\cdot)\) \(\chi_{9075}(5314,\cdot)\) \(\chi_{9075}(5479,\cdot)\) \(\chi_{9075}(5644,\cdot)\) \(\chi_{9075}(6139,\cdot)\) \(\chi_{9075}(6304,\cdot)\) \(\chi_{9075}(6469,\cdot)\) \(\chi_{9075}(6634,\cdot)\) \(\chi_{9075}(6964,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((1,e\left(\frac{7}{10}\right),e\left(\frac{5}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
\( \chi_{ 9075 }(34, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{57}{110}\right)\) |