Basic properties
Modulus: | \(388\) | |
Conductor: | \(388\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(96\) | 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 388.x
\(\chi_{388}(7,\cdot)\) \(\chi_{388}(15,\cdot)\) \(\chi_{388}(23,\cdot)\) \(\chi_{388}(39,\cdot)\) \(\chi_{388}(59,\cdot)\) \(\chi_{388}(71,\cdot)\) \(\chi_{388}(83,\cdot)\) \(\chi_{388}(87,\cdot)\) \(\chi_{388}(107,\cdot)\) \(\chi_{388}(111,\cdot)\) \(\chi_{388}(123,\cdot)\) \(\chi_{388}(135,\cdot)\) \(\chi_{388}(155,\cdot)\) \(\chi_{388}(171,\cdot)\) \(\chi_{388}(179,\cdot)\) \(\chi_{388}(187,\cdot)\) \(\chi_{388}(199,\cdot)\) \(\chi_{388}(207,\cdot)\) \(\chi_{388}(211,\cdot)\) \(\chi_{388}(215,\cdot)\) \(\chi_{388}(223,\cdot)\) \(\chi_{388}(231,\cdot)\) \(\chi_{388}(235,\cdot)\) \(\chi_{388}(251,\cdot)\) \(\chi_{388}(331,\cdot)\) \(\chi_{388}(347,\cdot)\) \(\chi_{388}(351,\cdot)\) \(\chi_{388}(359,\cdot)\) \(\chi_{388}(367,\cdot)\) \(\chi_{388}(371,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((195,5)\) → \((-1,e\left(\frac{95}{96}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 388 }(39, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{71}{96}\right)\) | \(e\left(\frac{73}{96}\right)\) | \(e\left(\frac{7}{96}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{91}{96}\right)\) |