Basic properties
Modulus: | \(4719\) | |
Conductor: | \(4719\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4719.di
\(\chi_{4719}(29,\cdot)\) \(\chi_{4719}(35,\cdot)\) \(\chi_{4719}(68,\cdot)\) \(\chi_{4719}(74,\cdot)\) \(\chi_{4719}(107,\cdot)\) \(\chi_{4719}(347,\cdot)\) \(\chi_{4719}(380,\cdot)\) \(\chi_{4719}(425,\cdot)\) \(\chi_{4719}(458,\cdot)\) \(\chi_{4719}(464,\cdot)\) \(\chi_{4719}(497,\cdot)\) \(\chi_{4719}(503,\cdot)\) \(\chi_{4719}(536,\cdot)\) \(\chi_{4719}(776,\cdot)\) \(\chi_{4719}(809,\cdot)\) \(\chi_{4719}(854,\cdot)\) \(\chi_{4719}(893,\cdot)\) \(\chi_{4719}(926,\cdot)\) \(\chi_{4719}(932,\cdot)\) \(\chi_{4719}(1205,\cdot)\) \(\chi_{4719}(1238,\cdot)\) \(\chi_{4719}(1283,\cdot)\) \(\chi_{4719}(1316,\cdot)\) \(\chi_{4719}(1355,\cdot)\) \(\chi_{4719}(1361,\cdot)\) \(\chi_{4719}(1394,\cdot)\) \(\chi_{4719}(1634,\cdot)\) \(\chi_{4719}(1712,\cdot)\) \(\chi_{4719}(1745,\cdot)\) \(\chi_{4719}(1751,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((1574,3511,4357)\) → \((-1,e\left(\frac{17}{110}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4719 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{165}\right)\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{247}{330}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{122}{165}\right)\) | \(e\left(\frac{163}{330}\right)\) |