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 \(\chi_{3025}(169,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.ee
\(\chi_{9075}(169,\cdot)\) \(\chi_{9075}(214,\cdot)\) \(\chi_{9075}(454,\cdot)\) \(\chi_{9075}(559,\cdot)\) \(\chi_{9075}(994,\cdot)\) \(\chi_{9075}(1039,\cdot)\) \(\chi_{9075}(1279,\cdot)\) \(\chi_{9075}(1384,\cdot)\) \(\chi_{9075}(1819,\cdot)\) \(\chi_{9075}(1864,\cdot)\) \(\chi_{9075}(2104,\cdot)\) \(\chi_{9075}(2209,\cdot)\) \(\chi_{9075}(2644,\cdot)\) \(\chi_{9075}(2929,\cdot)\) \(\chi_{9075}(3514,\cdot)\) \(\chi_{9075}(3859,\cdot)\) \(\chi_{9075}(4294,\cdot)\) \(\chi_{9075}(4339,\cdot)\) \(\chi_{9075}(4579,\cdot)\) \(\chi_{9075}(4684,\cdot)\) \(\chi_{9075}(5119,\cdot)\) \(\chi_{9075}(5164,\cdot)\) \(\chi_{9075}(5404,\cdot)\) \(\chi_{9075}(5509,\cdot)\) \(\chi_{9075}(5944,\cdot)\) \(\chi_{9075}(5989,\cdot)\) \(\chi_{9075}(6229,\cdot)\) \(\chi_{9075}(6334,\cdot)\) \(\chi_{9075}(6769,\cdot)\) \(\chi_{9075}(6814,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{46}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
\( \chi_{ 9075 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{49}{110}\right)\) |