Basic properties
| Modulus: | \(3204\) | |
| Conductor: | \(1068\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1068}(1055,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3204.cd
\(\chi_{3204}(35,\cdot)\) \(\chi_{3204}(143,\cdot)\) \(\chi_{3204}(323,\cdot)\) \(\chi_{3204}(359,\cdot)\) \(\chi_{3204}(431,\cdot)\) \(\chi_{3204}(503,\cdot)\) \(\chi_{3204}(575,\cdot)\) \(\chi_{3204}(647,\cdot)\) \(\chi_{3204}(683,\cdot)\) \(\chi_{3204}(719,\cdot)\) \(\chi_{3204}(755,\cdot)\) \(\chi_{3204}(827,\cdot)\) \(\chi_{3204}(863,\cdot)\) \(\chi_{3204}(1007,\cdot)\) \(\chi_{3204}(1151,\cdot)\) \(\chi_{3204}(1187,\cdot)\) \(\chi_{3204}(1223,\cdot)\) \(\chi_{3204}(1259,\cdot)\) \(\chi_{3204}(1439,\cdot)\) \(\chi_{3204}(1475,\cdot)\) \(\chi_{3204}(1583,\cdot)\) \(\chi_{3204}(1799,\cdot)\) \(\chi_{3204}(1907,\cdot)\) \(\chi_{3204}(1943,\cdot)\) \(\chi_{3204}(2123,\cdot)\) \(\chi_{3204}(2159,\cdot)\) \(\chi_{3204}(2195,\cdot)\) \(\chi_{3204}(2231,\cdot)\) \(\chi_{3204}(2375,\cdot)\) \(\chi_{3204}(2519,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((1603,713,181)\) → \((-1,-1,e\left(\frac{67}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3204 }(2123, a) \) | \(-1\) | \(1\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{9}{88}\right)\) |