Basic properties
Modulus: | \(9075\) | |
Conductor: | \(3025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3025}(229,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.ek
\(\chi_{9075}(229,\cdot)\) \(\chi_{9075}(289,\cdot)\) \(\chi_{9075}(334,\cdot)\) \(\chi_{9075}(544,\cdot)\) \(\chi_{9075}(1054,\cdot)\) \(\chi_{9075}(1114,\cdot)\) \(\chi_{9075}(1159,\cdot)\) \(\chi_{9075}(1369,\cdot)\) \(\chi_{9075}(1879,\cdot)\) \(\chi_{9075}(1984,\cdot)\) \(\chi_{9075}(2194,\cdot)\) \(\chi_{9075}(2704,\cdot)\) \(\chi_{9075}(2764,\cdot)\) \(\chi_{9075}(2809,\cdot)\) \(\chi_{9075}(3019,\cdot)\) \(\chi_{9075}(3529,\cdot)\) \(\chi_{9075}(3589,\cdot)\) \(\chi_{9075}(3634,\cdot)\) \(\chi_{9075}(3844,\cdot)\) \(\chi_{9075}(4354,\cdot)\) \(\chi_{9075}(4414,\cdot)\) \(\chi_{9075}(4459,\cdot)\) \(\chi_{9075}(4669,\cdot)\) \(\chi_{9075}(5179,\cdot)\) \(\chi_{9075}(5239,\cdot)\) \(\chi_{9075}(5494,\cdot)\) \(\chi_{9075}(6004,\cdot)\) \(\chi_{9075}(6064,\cdot)\) \(\chi_{9075}(6109,\cdot)\) \(\chi_{9075}(6829,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((1,e\left(\frac{1}{10}\right),e\left(\frac{23}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
\( \chi_{ 9075 }(229, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{41}{110}\right)\) |