Basic properties
Modulus: | \(1521\) | |
Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{169}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1521.ca
\(\chi_{1521}(28,\cdot)\) \(\chi_{1521}(37,\cdot)\) \(\chi_{1521}(46,\cdot)\) \(\chi_{1521}(136,\cdot)\) \(\chi_{1521}(145,\cdot)\) \(\chi_{1521}(154,\cdot)\) \(\chi_{1521}(163,\cdot)\) \(\chi_{1521}(253,\cdot)\) \(\chi_{1521}(262,\cdot)\) \(\chi_{1521}(271,\cdot)\) \(\chi_{1521}(280,\cdot)\) \(\chi_{1521}(370,\cdot)\) \(\chi_{1521}(379,\cdot)\) \(\chi_{1521}(388,\cdot)\) \(\chi_{1521}(397,\cdot)\) \(\chi_{1521}(487,\cdot)\) \(\chi_{1521}(496,\cdot)\) \(\chi_{1521}(505,\cdot)\) \(\chi_{1521}(514,\cdot)\) \(\chi_{1521}(604,\cdot)\) \(\chi_{1521}(613,\cdot)\) \(\chi_{1521}(622,\cdot)\) \(\chi_{1521}(631,\cdot)\) \(\chi_{1521}(721,\cdot)\) \(\chi_{1521}(730,\cdot)\) \(\chi_{1521}(739,\cdot)\) \(\chi_{1521}(748,\cdot)\) \(\chi_{1521}(838,\cdot)\) \(\chi_{1521}(847,\cdot)\) \(\chi_{1521}(856,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((677,847)\) → \((1,e\left(\frac{131}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 1521 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{133}{156}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) |