Basic properties
| Modulus: | \(97\) | |
| Conductor: | \(97\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 97.l
\(\chi_{97}(5,\cdot)\) \(\chi_{97}(7,\cdot)\) \(\chi_{97}(10,\cdot)\) \(\chi_{97}(13,\cdot)\) \(\chi_{97}(14,\cdot)\) \(\chi_{97}(15,\cdot)\) \(\chi_{97}(17,\cdot)\) \(\chi_{97}(21,\cdot)\) \(\chi_{97}(23,\cdot)\) \(\chi_{97}(26,\cdot)\) \(\chi_{97}(29,\cdot)\) \(\chi_{97}(37,\cdot)\) \(\chi_{97}(38,\cdot)\) \(\chi_{97}(39,\cdot)\) \(\chi_{97}(40,\cdot)\) \(\chi_{97}(41,\cdot)\) \(\chi_{97}(56,\cdot)\) \(\chi_{97}(57,\cdot)\) \(\chi_{97}(58,\cdot)\) \(\chi_{97}(59,\cdot)\) \(\chi_{97}(60,\cdot)\) \(\chi_{97}(68,\cdot)\) \(\chi_{97}(71,\cdot)\) \(\chi_{97}(74,\cdot)\) \(\chi_{97}(76,\cdot)\) \(\chi_{97}(80,\cdot)\) \(\chi_{97}(82,\cdot)\) \(\chi_{97}(83,\cdot)\) \(\chi_{97}(84,\cdot)\) \(\chi_{97}(87,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\(5\) → \(e\left(\frac{25}{96}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 97 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{25}{96}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{96}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{11}{96}\right)\) | \(e\left(\frac{19}{48}\right)\) |