Basic properties
Modulus: | \(1441\) | |
Conductor: | \(1441\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(130\) | 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 1441.bp
\(\chi_{1441}(14,\cdot)\) \(\chi_{1441}(31,\cdot)\) \(\chi_{1441}(93,\cdot)\) \(\chi_{1441}(97,\cdot)\) \(\chi_{1441}(103,\cdot)\) \(\chi_{1441}(104,\cdot)\) \(\chi_{1441}(119,\cdot)\) \(\chi_{1441}(126,\cdot)\) \(\chi_{1441}(214,\cdot)\) \(\chi_{1441}(268,\cdot)\) \(\chi_{1441}(279,\cdot)\) \(\chi_{1441}(291,\cdot)\) \(\chi_{1441}(312,\cdot)\) \(\chi_{1441}(328,\cdot)\) \(\chi_{1441}(344,\cdot)\) \(\chi_{1441}(350,\cdot)\) \(\chi_{1441}(357,\cdot)\) \(\chi_{1441}(378,\cdot)\) \(\chi_{1441}(449,\cdot)\) \(\chi_{1441}(465,\cdot)\) \(\chi_{1441}(515,\cdot)\) \(\chi_{1441}(520,\cdot)\) \(\chi_{1441}(532,\cdot)\) \(\chi_{1441}(630,\cdot)\) \(\chi_{1441}(642,\cdot)\) \(\chi_{1441}(652,\cdot)\) \(\chi_{1441}(751,\cdot)\) \(\chi_{1441}(775,\cdot)\) \(\chi_{1441}(812,\cdot)\) \(\chi_{1441}(873,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{51}{130}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(291, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{49}{130}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{2}{65}\right)\) |