Basic properties
| Modulus: | \(1122\) | |
| Conductor: | \(561\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{561}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1122.bl
\(\chi_{1122}(29,\cdot)\) \(\chi_{1122}(41,\cdot)\) \(\chi_{1122}(95,\cdot)\) \(\chi_{1122}(107,\cdot)\) \(\chi_{1122}(167,\cdot)\) \(\chi_{1122}(173,\cdot)\) \(\chi_{1122}(215,\cdot)\) \(\chi_{1122}(227,\cdot)\) \(\chi_{1122}(233,\cdot)\) \(\chi_{1122}(299,\cdot)\) \(\chi_{1122}(347,\cdot)\) \(\chi_{1122}(371,\cdot)\) \(\chi_{1122}(413,\cdot)\) \(\chi_{1122}(431,\cdot)\) \(\chi_{1122}(437,\cdot)\) \(\chi_{1122}(479,\cdot)\) \(\chi_{1122}(503,\cdot)\) \(\chi_{1122}(623,\cdot)\) \(\chi_{1122}(635,\cdot)\) \(\chi_{1122}(677,\cdot)\) \(\chi_{1122}(743,\cdot)\) \(\chi_{1122}(755,\cdot)\) \(\chi_{1122}(809,\cdot)\) \(\chi_{1122}(821,\cdot)\) \(\chi_{1122}(827,\cdot)\) \(\chi_{1122}(887,\cdot)\) \(\chi_{1122}(941,\cdot)\) \(\chi_{1122}(959,\cdot)\) \(\chi_{1122}(1025,\cdot)\) \(\chi_{1122}(1031,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((749,409,1057)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{13}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 1122 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{17}{80}\right)\) |