Basic properties
Modulus: | \(6776\) | |
Conductor: | \(3388\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3388}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6776.ev
\(\chi_{6776}(31,\cdot)\) \(\chi_{6776}(47,\cdot)\) \(\chi_{6776}(103,\cdot)\) \(\chi_{6776}(159,\cdot)\) \(\chi_{6776}(311,\cdot)\) \(\chi_{6776}(367,\cdot)\) \(\chi_{6776}(383,\cdot)\) \(\chi_{6776}(423,\cdot)\) \(\chi_{6776}(647,\cdot)\) \(\chi_{6776}(663,\cdot)\) \(\chi_{6776}(719,\cdot)\) \(\chi_{6776}(775,\cdot)\) \(\chi_{6776}(927,\cdot)\) \(\chi_{6776}(983,\cdot)\) \(\chi_{6776}(999,\cdot)\) \(\chi_{6776}(1039,\cdot)\) \(\chi_{6776}(1263,\cdot)\) \(\chi_{6776}(1279,\cdot)\) \(\chi_{6776}(1335,\cdot)\) \(\chi_{6776}(1391,\cdot)\) \(\chi_{6776}(1543,\cdot)\) \(\chi_{6776}(1599,\cdot)\) \(\chi_{6776}(1615,\cdot)\) \(\chi_{6776}(1655,\cdot)\) \(\chi_{6776}(1879,\cdot)\) \(\chi_{6776}(1895,\cdot)\) \(\chi_{6776}(1951,\cdot)\) \(\chi_{6776}(2007,\cdot)\) \(\chi_{6776}(2159,\cdot)\) \(\chi_{6776}(2215,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((1695,3389,969,3753)\) → \((-1,1,e\left(\frac{1}{6}\right),e\left(\frac{43}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 6776 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{227}{330}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{37}{165}\right)\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{62}{165}\right)\) | \(e\left(\frac{2}{5}\right)\) |