Basic properties
Modulus: | \(927\) | |
Conductor: | \(927\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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 927.bm
\(\chi_{927}(5,\cdot)\) \(\chi_{927}(20,\cdot)\) \(\chi_{927}(74,\cdot)\) \(\chi_{927}(86,\cdot)\) \(\chi_{927}(101,\cdot)\) \(\chi_{927}(146,\cdot)\) \(\chi_{927}(254,\cdot)\) \(\chi_{927}(257,\cdot)\) \(\chi_{927}(281,\cdot)\) \(\chi_{927}(290,\cdot)\) \(\chi_{927}(302,\cdot)\) \(\chi_{927}(320,\cdot)\) \(\chi_{927}(344,\cdot)\) \(\chi_{927}(353,\cdot)\) \(\chi_{927}(371,\cdot)\) \(\chi_{927}(374,\cdot)\) \(\chi_{927}(482,\cdot)\) \(\chi_{927}(497,\cdot)\) \(\chi_{927}(500,\cdot)\) \(\chi_{927}(527,\cdot)\) \(\chi_{927}(536,\cdot)\) \(\chi_{927}(569,\cdot)\) \(\chi_{927}(671,\cdot)\) \(\chi_{927}(689,\cdot)\) \(\chi_{927}(695,\cdot)\) \(\chi_{927}(761,\cdot)\) \(\chi_{927}(788,\cdot)\) \(\chi_{927}(830,\cdot)\) \(\chi_{927}(869,\cdot)\) \(\chi_{927}(902,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((722,829)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{77}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 927 }(146, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{9}{17}\right)\) |