Basic properties
Modulus: | \(5025\) | |
Conductor: | \(5025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5025.dn
\(\chi_{5025}(56,\cdot)\) \(\chi_{5025}(71,\cdot)\) \(\chi_{5025}(86,\cdot)\) \(\chi_{5025}(116,\cdot)\) \(\chi_{5025}(236,\cdot)\) \(\chi_{5025}(266,\cdot)\) \(\chi_{5025}(341,\cdot)\) \(\chi_{5025}(356,\cdot)\) \(\chi_{5025}(371,\cdot)\) \(\chi_{5025}(596,\cdot)\) \(\chi_{5025}(686,\cdot)\) \(\chi_{5025}(791,\cdot)\) \(\chi_{5025}(821,\cdot)\) \(\chi_{5025}(881,\cdot)\) \(\chi_{5025}(971,\cdot)\) \(\chi_{5025}(1031,\cdot)\) \(\chi_{5025}(1061,\cdot)\) \(\chi_{5025}(1091,\cdot)\) \(\chi_{5025}(1121,\cdot)\) \(\chi_{5025}(1241,\cdot)\) \(\chi_{5025}(1271,\cdot)\) \(\chi_{5025}(1346,\cdot)\) \(\chi_{5025}(1361,\cdot)\) \(\chi_{5025}(1631,\cdot)\) \(\chi_{5025}(1691,\cdot)\) \(\chi_{5025}(1781,\cdot)\) \(\chi_{5025}(1796,\cdot)\) \(\chi_{5025}(1856,\cdot)\) \(\chi_{5025}(1886,\cdot)\) \(\chi_{5025}(1931,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((1676,202,3151)\) → \((-1,e\left(\frac{4}{5}\right),e\left(\frac{14}{33}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 5025 }(2636, a) \) | \(-1\) | \(1\) | \(e\left(\frac{239}{330}\right)\) | \(e\left(\frac{74}{165}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{109}{330}\right)\) | \(e\left(\frac{43}{165}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{17}{330}\right)\) | \(e\left(\frac{106}{165}\right)\) |