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 \(\chi_{3025}(421,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.dv
\(\chi_{9075}(421,\cdot)\) \(\chi_{9075}(631,\cdot)\) \(\chi_{9075}(691,\cdot)\) \(\chi_{9075}(1246,\cdot)\) \(\chi_{9075}(1336,\cdot)\) \(\chi_{9075}(1456,\cdot)\) \(\chi_{9075}(1516,\cdot)\) \(\chi_{9075}(2071,\cdot)\) \(\chi_{9075}(2161,\cdot)\) \(\chi_{9075}(2281,\cdot)\) \(\chi_{9075}(2341,\cdot)\) \(\chi_{9075}(2896,\cdot)\) \(\chi_{9075}(2986,\cdot)\) \(\chi_{9075}(3166,\cdot)\) \(\chi_{9075}(3721,\cdot)\) \(\chi_{9075}(3811,\cdot)\) \(\chi_{9075}(3931,\cdot)\) \(\chi_{9075}(3991,\cdot)\) \(\chi_{9075}(4546,\cdot)\) \(\chi_{9075}(4636,\cdot)\) \(\chi_{9075}(4756,\cdot)\) \(\chi_{9075}(4816,\cdot)\) \(\chi_{9075}(5371,\cdot)\) \(\chi_{9075}(5461,\cdot)\) \(\chi_{9075}(5581,\cdot)\) \(\chi_{9075}(5641,\cdot)\) \(\chi_{9075}(6196,\cdot)\) \(\chi_{9075}(6286,\cdot)\) \(\chi_{9075}(6406,\cdot)\) \(\chi_{9075}(6466,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((3026,727,5326)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{9}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
\( \chi_{ 9075 }(421, a) \) | \(1\) | \(1\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{3}{55}\right)\) |