Basic properties
Modulus: | \(9025\) | |
Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{361}(144,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9025.bh
\(\chi_{9025}(26,\cdot)\) \(\chi_{9025}(201,\cdot)\) \(\chi_{9025}(501,\cdot)\) \(\chi_{9025}(676,\cdot)\) \(\chi_{9025}(976,\cdot)\) \(\chi_{9025}(1451,\cdot)\) \(\chi_{9025}(1626,\cdot)\) \(\chi_{9025}(1926,\cdot)\) \(\chi_{9025}(2101,\cdot)\) \(\chi_{9025}(2401,\cdot)\) \(\chi_{9025}(2576,\cdot)\) \(\chi_{9025}(2876,\cdot)\) \(\chi_{9025}(3051,\cdot)\) \(\chi_{9025}(3351,\cdot)\) \(\chi_{9025}(3526,\cdot)\) \(\chi_{9025}(3826,\cdot)\) \(\chi_{9025}(4001,\cdot)\) \(\chi_{9025}(4301,\cdot)\) \(\chi_{9025}(4476,\cdot)\) \(\chi_{9025}(4776,\cdot)\) \(\chi_{9025}(4951,\cdot)\) \(\chi_{9025}(5251,\cdot)\) \(\chi_{9025}(5426,\cdot)\) \(\chi_{9025}(5726,\cdot)\) \(\chi_{9025}(5901,\cdot)\) \(\chi_{9025}(6201,\cdot)\) \(\chi_{9025}(6376,\cdot)\) \(\chi_{9025}(6676,\cdot)\) \(\chi_{9025}(6851,\cdot)\) \(\chi_{9025}(7326,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((5777,3251)\) → \((1,e\left(\frac{47}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 9025 }(4476, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{16}{57}\right)\) |