Basic properties
Modulus: | \(2169\) | |
Conductor: | \(723\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{723}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2169.df
\(\chi_{2169}(17,\cdot)\) \(\chi_{2169}(26,\cdot)\) \(\chi_{2169}(215,\cdot)\) \(\chi_{2169}(224,\cdot)\) \(\chi_{2169}(269,\cdot)\) \(\chi_{2169}(314,\cdot)\) \(\chi_{2169}(377,\cdot)\) \(\chi_{2169}(449,\cdot)\) \(\chi_{2169}(503,\cdot)\) \(\chi_{2169}(539,\cdot)\) \(\chi_{2169}(575,\cdot)\) \(\chi_{2169}(584,\cdot)\) \(\chi_{2169}(620,\cdot)\) \(\chi_{2169}(638,\cdot)\) \(\chi_{2169}(746,\cdot)\) \(\chi_{2169}(863,\cdot)\) \(\chi_{2169}(1007,\cdot)\) \(\chi_{2169}(1088,\cdot)\) \(\chi_{2169}(1322,\cdot)\) \(\chi_{2169}(1403,\cdot)\) \(\chi_{2169}(1547,\cdot)\) \(\chi_{2169}(1664,\cdot)\) \(\chi_{2169}(1772,\cdot)\) \(\chi_{2169}(1790,\cdot)\) \(\chi_{2169}(1826,\cdot)\) \(\chi_{2169}(1835,\cdot)\) \(\chi_{2169}(1871,\cdot)\) \(\chi_{2169}(1907,\cdot)\) \(\chi_{2169}(1961,\cdot)\) \(\chi_{2169}(2033,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((965,730)\) → \((-1,e\left(\frac{37}{80}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2169 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(-1\) |