Basic properties
Modulus: | \(1521\) | |
Conductor: | \(1521\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | 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 1521.cf
\(\chi_{1521}(31,\cdot)\) \(\chi_{1521}(34,\cdot)\) \(\chi_{1521}(112,\cdot)\) \(\chi_{1521}(148,\cdot)\) \(\chi_{1521}(151,\cdot)\) \(\chi_{1521}(187,\cdot)\) \(\chi_{1521}(229,\cdot)\) \(\chi_{1521}(265,\cdot)\) \(\chi_{1521}(304,\cdot)\) \(\chi_{1521}(346,\cdot)\) \(\chi_{1521}(382,\cdot)\) \(\chi_{1521}(385,\cdot)\) \(\chi_{1521}(421,\cdot)\) \(\chi_{1521}(463,\cdot)\) \(\chi_{1521}(499,\cdot)\) \(\chi_{1521}(502,\cdot)\) \(\chi_{1521}(538,\cdot)\) \(\chi_{1521}(580,\cdot)\) \(\chi_{1521}(616,\cdot)\) \(\chi_{1521}(619,\cdot)\) \(\chi_{1521}(655,\cdot)\) \(\chi_{1521}(697,\cdot)\) \(\chi_{1521}(733,\cdot)\) \(\chi_{1521}(736,\cdot)\) \(\chi_{1521}(772,\cdot)\) \(\chi_{1521}(814,\cdot)\) \(\chi_{1521}(850,\cdot)\) \(\chi_{1521}(853,\cdot)\) \(\chi_{1521}(889,\cdot)\) \(\chi_{1521}(931,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((677,847)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{7}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 1521 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{115}{156}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{17}{26}\right)\) |