Basic properties
| Modulus: | \(723\) | |
| Conductor: | \(723\) | 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 723.bj
\(\chi_{723}(17,\cdot)\) \(\chi_{723}(23,\cdot)\) \(\chi_{723}(26,\cdot)\) \(\chi_{723}(101,\cdot)\) \(\chi_{723}(140,\cdot)\) \(\chi_{723}(215,\cdot)\) \(\chi_{723}(218,\cdot)\) \(\chi_{723}(224,\cdot)\) \(\chi_{723}(269,\cdot)\) \(\chi_{723}(284,\cdot)\) \(\chi_{723}(314,\cdot)\) \(\chi_{723}(326,\cdot)\) \(\chi_{723}(344,\cdot)\) \(\chi_{723}(365,\cdot)\) \(\chi_{723}(377,\cdot)\) \(\chi_{723}(380,\cdot)\) \(\chi_{723}(389,\cdot)\) \(\chi_{723}(425,\cdot)\) \(\chi_{723}(449,\cdot)\) \(\chi_{723}(461,\cdot)\) \(\chi_{723}(503,\cdot)\) \(\chi_{723}(515,\cdot)\) \(\chi_{723}(539,\cdot)\) \(\chi_{723}(575,\cdot)\) \(\chi_{723}(584,\cdot)\) \(\chi_{723}(587,\cdot)\) \(\chi_{723}(599,\cdot)\) \(\chi_{723}(620,\cdot)\) \(\chi_{723}(638,\cdot)\) \(\chi_{723}(650,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((242,7)\) → \((-1,e\left(\frac{37}{80}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 723 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(-1\) |