Basic properties
| Modulus: | \(927\) | |
| Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{103}(84,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 927.bk
\(\chi_{927}(109,\cdot)\) \(\chi_{927}(154,\cdot)\) \(\chi_{927}(181,\cdot)\) \(\chi_{927}(190,\cdot)\) \(\chi_{927}(199,\cdot)\) \(\chi_{927}(217,\cdot)\) \(\chi_{927}(226,\cdot)\) \(\chi_{927}(271,\cdot)\) \(\chi_{927}(280,\cdot)\) \(\chi_{927}(307,\cdot)\) \(\chi_{927}(352,\cdot)\) \(\chi_{927}(379,\cdot)\) \(\chi_{927}(397,\cdot)\) \(\chi_{927}(424,\cdot)\) \(\chi_{927}(433,\cdot)\) \(\chi_{927}(460,\cdot)\) \(\chi_{927}(487,\cdot)\) \(\chi_{927}(496,\cdot)\) \(\chi_{927}(550,\cdot)\) \(\chi_{927}(559,\cdot)\) \(\chi_{927}(568,\cdot)\) \(\chi_{927}(577,\cdot)\) \(\chi_{927}(586,\cdot)\) \(\chi_{927}(658,\cdot)\) \(\chi_{927}(685,\cdot)\) \(\chi_{927}(703,\cdot)\) \(\chi_{927}(766,\cdot)\) \(\chi_{927}(775,\cdot)\) \(\chi_{927}(820,\cdot)\) \(\chi_{927}(829,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((722,829)\) → \((1,e\left(\frac{29}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 927 }(496, a) \) | \(-1\) | \(1\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{29}{102}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{35}{102}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{2}{51}\right)\) |