Basic properties
Modulus: | \(9075\) | |
Conductor: | \(3025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3025}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.ds
\(\chi_{9075}(31,\cdot)\) \(\chi_{9075}(91,\cdot)\) \(\chi_{9075}(136,\cdot)\) \(\chi_{9075}(346,\cdot)\) \(\chi_{9075}(916,\cdot)\) \(\chi_{9075}(961,\cdot)\) \(\chi_{9075}(1171,\cdot)\) \(\chi_{9075}(1681,\cdot)\) \(\chi_{9075}(1741,\cdot)\) \(\chi_{9075}(1786,\cdot)\) \(\chi_{9075}(1996,\cdot)\) \(\chi_{9075}(2506,\cdot)\) \(\chi_{9075}(2566,\cdot)\) \(\chi_{9075}(2611,\cdot)\) \(\chi_{9075}(2821,\cdot)\) \(\chi_{9075}(3331,\cdot)\) \(\chi_{9075}(3436,\cdot)\) \(\chi_{9075}(3646,\cdot)\) \(\chi_{9075}(4156,\cdot)\) \(\chi_{9075}(4216,\cdot)\) \(\chi_{9075}(4261,\cdot)\) \(\chi_{9075}(4471,\cdot)\) \(\chi_{9075}(4981,\cdot)\) \(\chi_{9075}(5041,\cdot)\) \(\chi_{9075}(5086,\cdot)\) \(\chi_{9075}(5296,\cdot)\) \(\chi_{9075}(5806,\cdot)\) \(\chi_{9075}(5866,\cdot)\) \(\chi_{9075}(5911,\cdot)\) \(\chi_{9075}(6121,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((3026,727,5326)\) → \((1,e\left(\frac{2}{5}\right),e\left(\frac{43}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
\( \chi_{ 9075 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{7}{55}\right)\) |