Basic properties
| Modulus: | \(388\) | |
| Conductor: | \(97\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{97}(57,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 388.w
\(\chi_{388}(5,\cdot)\) \(\chi_{388}(13,\cdot)\) \(\chi_{388}(17,\cdot)\) \(\chi_{388}(21,\cdot)\) \(\chi_{388}(29,\cdot)\) \(\chi_{388}(37,\cdot)\) \(\chi_{388}(41,\cdot)\) \(\chi_{388}(57,\cdot)\) \(\chi_{388}(137,\cdot)\) \(\chi_{388}(153,\cdot)\) \(\chi_{388}(157,\cdot)\) \(\chi_{388}(165,\cdot)\) \(\chi_{388}(173,\cdot)\) \(\chi_{388}(177,\cdot)\) \(\chi_{388}(181,\cdot)\) \(\chi_{388}(189,\cdot)\) \(\chi_{388}(201,\cdot)\) \(\chi_{388}(209,\cdot)\) \(\chi_{388}(217,\cdot)\) \(\chi_{388}(233,\cdot)\) \(\chi_{388}(253,\cdot)\) \(\chi_{388}(265,\cdot)\) \(\chi_{388}(277,\cdot)\) \(\chi_{388}(281,\cdot)\) \(\chi_{388}(301,\cdot)\) \(\chi_{388}(305,\cdot)\) \(\chi_{388}(317,\cdot)\) \(\chi_{388}(329,\cdot)\) \(\chi_{388}(349,\cdot)\) \(\chi_{388}(365,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((195,5)\) → \((1,e\left(\frac{55}{96}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 388 }(57, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{55}{96}\right)\) | \(e\left(\frac{73}{96}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{31}{96}\right)\) | \(e\left(\frac{65}{96}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{83}{96}\right)\) |