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 \(\chi_{97}(37,\cdot)\) | 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
\((98,199)\) → \((1,e\left(\frac{91}{96}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 291 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{91}{96}\right)\) | \(e\left(\frac{37}{96}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{59}{96}\right)\) | \(e\left(\frac{11}{12}\right)\) |