Basic properties
| Modulus: | \(291\) | |
| 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 \(\chi_{97}(40,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 291.w
\(\chi_{291}(7,\cdot)\) \(\chi_{291}(10,\cdot)\) \(\chi_{291}(13,\cdot)\) \(\chi_{291}(37,\cdot)\) \(\chi_{291}(40,\cdot)\) \(\chi_{291}(58,\cdot)\) \(\chi_{291}(76,\cdot)\) \(\chi_{291}(82,\cdot)\) \(\chi_{291}(112,\cdot)\) \(\chi_{291}(118,\cdot)\) \(\chi_{291}(136,\cdot)\) \(\chi_{291}(154,\cdot)\) \(\chi_{291}(157,\cdot)\) \(\chi_{291}(181,\cdot)\) \(\chi_{291}(184,\cdot)\) \(\chi_{291}(187,\cdot)\) \(\chi_{291}(199,\cdot)\) \(\chi_{291}(208,\cdot)\) \(\chi_{291}(211,\cdot)\) \(\chi_{291}(217,\cdot)\) \(\chi_{291}(220,\cdot)\) \(\chi_{291}(223,\cdot)\) \(\chi_{291}(232,\cdot)\) \(\chi_{291}(235,\cdot)\) \(\chi_{291}(250,\cdot)\) \(\chi_{291}(253,\cdot)\) \(\chi_{291}(262,\cdot)\) \(\chi_{291}(265,\cdot)\) \(\chi_{291}(268,\cdot)\) \(\chi_{291}(274,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((98,199)\) → \((1,e\left(\frac{7}{96}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 291 }(40, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{7}{96}\right)\) | \(e\left(\frac{25}{96}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{53}{96}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{79}{96}\right)\) | \(e\left(\frac{71}{96}\right)\) | \(e\left(\frac{11}{12}\right)\) |