Basic properties
Modulus: | \(187\) | |
Conductor: | \(187\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | 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 187.t
\(\chi_{187}(6,\cdot)\) \(\chi_{187}(7,\cdot)\) \(\chi_{187}(24,\cdot)\) \(\chi_{187}(28,\cdot)\) \(\chi_{187}(29,\cdot)\) \(\chi_{187}(39,\cdot)\) \(\chi_{187}(40,\cdot)\) \(\chi_{187}(41,\cdot)\) \(\chi_{187}(46,\cdot)\) \(\chi_{187}(57,\cdot)\) \(\chi_{187}(61,\cdot)\) \(\chi_{187}(62,\cdot)\) \(\chi_{187}(63,\cdot)\) \(\chi_{187}(73,\cdot)\) \(\chi_{187}(74,\cdot)\) \(\chi_{187}(79,\cdot)\) \(\chi_{187}(90,\cdot)\) \(\chi_{187}(95,\cdot)\) \(\chi_{187}(96,\cdot)\) \(\chi_{187}(105,\cdot)\) \(\chi_{187}(107,\cdot)\) \(\chi_{187}(112,\cdot)\) \(\chi_{187}(116,\cdot)\) \(\chi_{187}(129,\cdot)\) \(\chi_{187}(139,\cdot)\) \(\chi_{187}(150,\cdot)\) \(\chi_{187}(156,\cdot)\) \(\chi_{187}(160,\cdot)\) \(\chi_{187}(167,\cdot)\) \(\chi_{187}(173,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((35,122)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{1}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 187 }(105, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) |