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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1441.cb
\(\chi_{1441}(83,\cdot)\) \(\chi_{1441}(96,\cdot)\) \(\chi_{1441}(139,\cdot)\) \(\chi_{1441}(160,\cdot)\) \(\chi_{1441}(226,\cdot)\) \(\chi_{1441}(249,\cdot)\) \(\chi_{1441}(272,\cdot)\) \(\chi_{1441}(288,\cdot)\) \(\chi_{1441}(316,\cdot)\) \(\chi_{1441}(338,\cdot)\) \(\chi_{1441}(415,\cdot)\) \(\chi_{1441}(480,\cdot)\) \(\chi_{1441}(491,\cdot)\) \(\chi_{1441}(508,\cdot)\) \(\chi_{1441}(634,\cdot)\) \(\chi_{1441}(644,\cdot)\) \(\chi_{1441}(678,\cdot)\) \(\chi_{1441}(695,\cdot)\) \(\chi_{1441}(712,\cdot)\) \(\chi_{1441}(766,\cdot)\) \(\chi_{1441}(800,\cdot)\) \(\chi_{1441}(816,\cdot)\) \(\chi_{1441}(853,\cdot)\) \(\chi_{1441}(871,\cdot)\) \(\chi_{1441}(919,\cdot)\) \(\chi_{1441}(948,\cdot)\) \(\chi_{1441}(1007,\cdot)\) \(\chi_{1441}(1014,\cdot)\) \(\chi_{1441}(1036,\cdot)\) \(\chi_{1441}(1130,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{113}{130}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(766, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{21}{65}\right)\) |