Basic properties
Modulus: | \(5185\) | |
Conductor: | \(1037\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1037}(604,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5185.jj
\(\chi_{5185}(26,\cdot)\) \(\chi_{5185}(246,\cdot)\) \(\chi_{5185}(331,\cdot)\) \(\chi_{5185}(376,\cdot)\) \(\chi_{5185}(1141,\cdot)\) \(\chi_{5185}(1226,\cdot)\) \(\chi_{5185}(1386,\cdot)\) \(\chi_{5185}(1396,\cdot)\) \(\chi_{5185}(1471,\cdot)\) \(\chi_{5185}(1481,\cdot)\) \(\chi_{5185}(1596,\cdot)\) \(\chi_{5185}(1641,\cdot)\) \(\chi_{5185}(1691,\cdot)\) \(\chi_{5185}(1726,\cdot)\) \(\chi_{5185}(1776,\cdot)\) \(\chi_{5185}(1946,\cdot)\) \(\chi_{5185}(2031,\cdot)\) \(\chi_{5185}(2361,\cdot)\) \(\chi_{5185}(2446,\cdot)\) \(\chi_{5185}(2491,\cdot)\) \(\chi_{5185}(2616,\cdot)\) \(\chi_{5185}(2701,\cdot)\) \(\chi_{5185}(2796,\cdot)\) \(\chi_{5185}(2841,\cdot)\) \(\chi_{5185}(2926,\cdot)\) \(\chi_{5185}(3691,\cdot)\) \(\chi_{5185}(4061,\cdot)\) \(\chi_{5185}(4146,\cdot)\) \(\chi_{5185}(4361,\cdot)\) \(\chi_{5185}(4666,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((3112,4576,2381)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{37}{60}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 5185 }(1641, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{1}{6}\right)\) |