Basic properties
| Modulus: | \(3872\) | |
| Conductor: | \(3872\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | 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 3872.bt
\(\chi_{3872}(43,\cdot)\) \(\chi_{3872}(131,\cdot)\) \(\chi_{3872}(219,\cdot)\) \(\chi_{3872}(307,\cdot)\) \(\chi_{3872}(395,\cdot)\) \(\chi_{3872}(571,\cdot)\) \(\chi_{3872}(659,\cdot)\) \(\chi_{3872}(747,\cdot)\) \(\chi_{3872}(835,\cdot)\) \(\chi_{3872}(923,\cdot)\) \(\chi_{3872}(1011,\cdot)\) \(\chi_{3872}(1099,\cdot)\) \(\chi_{3872}(1187,\cdot)\) \(\chi_{3872}(1275,\cdot)\) \(\chi_{3872}(1363,\cdot)\) \(\chi_{3872}(1539,\cdot)\) \(\chi_{3872}(1627,\cdot)\) \(\chi_{3872}(1715,\cdot)\) \(\chi_{3872}(1803,\cdot)\) \(\chi_{3872}(1891,\cdot)\) \(\chi_{3872}(1979,\cdot)\) \(\chi_{3872}(2067,\cdot)\) \(\chi_{3872}(2155,\cdot)\) \(\chi_{3872}(2243,\cdot)\) \(\chi_{3872}(2331,\cdot)\) \(\chi_{3872}(2507,\cdot)\) \(\chi_{3872}(2595,\cdot)\) \(\chi_{3872}(2683,\cdot)\) \(\chi_{3872}(2771,\cdot)\) \(\chi_{3872}(2859,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((1695,485,2785)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{17}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 3872 }(3827, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{88}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(i\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{67}{88}\right)\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{37}{44}\right)\) |