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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 187.s
\(\chi_{187}(3,\cdot)\) \(\chi_{187}(5,\cdot)\) \(\chi_{187}(14,\cdot)\) \(\chi_{187}(20,\cdot)\) \(\chi_{187}(27,\cdot)\) \(\chi_{187}(31,\cdot)\) \(\chi_{187}(37,\cdot)\) \(\chi_{187}(48,\cdot)\) \(\chi_{187}(58,\cdot)\) \(\chi_{187}(71,\cdot)\) \(\chi_{187}(75,\cdot)\) \(\chi_{187}(80,\cdot)\) \(\chi_{187}(82,\cdot)\) \(\chi_{187}(91,\cdot)\) \(\chi_{187}(92,\cdot)\) \(\chi_{187}(97,\cdot)\) \(\chi_{187}(108,\cdot)\) \(\chi_{187}(113,\cdot)\) \(\chi_{187}(114,\cdot)\) \(\chi_{187}(124,\cdot)\) \(\chi_{187}(125,\cdot)\) \(\chi_{187}(126,\cdot)\) \(\chi_{187}(130,\cdot)\) \(\chi_{187}(141,\cdot)\) \(\chi_{187}(146,\cdot)\) \(\chi_{187}(147,\cdot)\) \(\chi_{187}(148,\cdot)\) \(\chi_{187}(158,\cdot)\) \(\chi_{187}(159,\cdot)\) \(\chi_{187}(163,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((35,122)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{13}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 187 }(97, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) |