Basic properties
| Modulus: | \(291\) | |
| Conductor: | \(291\) | 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 291.x
\(\chi_{291}(5,\cdot)\) \(\chi_{291}(14,\cdot)\) \(\chi_{291}(17,\cdot)\) \(\chi_{291}(23,\cdot)\) \(\chi_{291}(26,\cdot)\) \(\chi_{291}(29,\cdot)\) \(\chi_{291}(38,\cdot)\) \(\chi_{291}(41,\cdot)\) \(\chi_{291}(56,\cdot)\) \(\chi_{291}(59,\cdot)\) \(\chi_{291}(68,\cdot)\) \(\chi_{291}(71,\cdot)\) \(\chi_{291}(74,\cdot)\) \(\chi_{291}(80,\cdot)\) \(\chi_{291}(83,\cdot)\) \(\chi_{291}(92,\cdot)\) \(\chi_{291}(104,\cdot)\) \(\chi_{291}(107,\cdot)\) \(\chi_{291}(110,\cdot)\) \(\chi_{291}(134,\cdot)\) \(\chi_{291}(137,\cdot)\) \(\chi_{291}(155,\cdot)\) \(\chi_{291}(173,\cdot)\) \(\chi_{291}(179,\cdot)\) \(\chi_{291}(209,\cdot)\) \(\chi_{291}(215,\cdot)\) \(\chi_{291}(233,\cdot)\) \(\chi_{291}(251,\cdot)\) \(\chi_{291}(254,\cdot)\) \(\chi_{291}(278,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((98,199)\) → \((-1,e\left(\frac{89}{96}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 291 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{41}{96}\right)\) | \(e\left(\frac{71}{96}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{73}{96}\right)\) | \(e\left(\frac{1}{12}\right)\) |