Basic properties
Modulus: | \(927\) | |
Conductor: | \(309\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{309}(158,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 927.be
\(\chi_{927}(17,\cdot)\) \(\chi_{927}(26,\cdot)\) \(\chi_{927}(98,\cdot)\) \(\chi_{927}(107,\cdot)\) \(\chi_{927}(152,\cdot)\) \(\chi_{927}(161,\cdot)\) \(\chi_{927}(224,\cdot)\) \(\chi_{927}(242,\cdot)\) \(\chi_{927}(269,\cdot)\) \(\chi_{927}(341,\cdot)\) \(\chi_{927}(350,\cdot)\) \(\chi_{927}(359,\cdot)\) \(\chi_{927}(368,\cdot)\) \(\chi_{927}(377,\cdot)\) \(\chi_{927}(431,\cdot)\) \(\chi_{927}(440,\cdot)\) \(\chi_{927}(467,\cdot)\) \(\chi_{927}(494,\cdot)\) \(\chi_{927}(503,\cdot)\) \(\chi_{927}(530,\cdot)\) \(\chi_{927}(548,\cdot)\) \(\chi_{927}(575,\cdot)\) \(\chi_{927}(620,\cdot)\) \(\chi_{927}(647,\cdot)\) \(\chi_{927}(656,\cdot)\) \(\chi_{927}(701,\cdot)\) \(\chi_{927}(710,\cdot)\) \(\chi_{927}(728,\cdot)\) \(\chi_{927}(737,\cdot)\) \(\chi_{927}(746,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((722,829)\) → \((-1,e\left(\frac{31}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 927 }(467, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{102}\right)\) | \(e\left(\frac{25}{51}\right)\) | \(e\left(\frac{11}{102}\right)\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{59}{102}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{50}{51}\right)\) |