Basic properties
| Modulus: | \(178\) | |
| Conductor: | \(89\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{89}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 178.h
\(\chi_{178}(3,\cdot)\) \(\chi_{178}(7,\cdot)\) \(\chi_{178}(13,\cdot)\) \(\chi_{178}(15,\cdot)\) \(\chi_{178}(19,\cdot)\) \(\chi_{178}(23,\cdot)\) \(\chi_{178}(27,\cdot)\) \(\chi_{178}(29,\cdot)\) \(\chi_{178}(31,\cdot)\) \(\chi_{178}(33,\cdot)\) \(\chi_{178}(35,\cdot)\) \(\chi_{178}(41,\cdot)\) \(\chi_{178}(43,\cdot)\) \(\chi_{178}(51,\cdot)\) \(\chi_{178}(59,\cdot)\) \(\chi_{178}(61,\cdot)\) \(\chi_{178}(63,\cdot)\) \(\chi_{178}(65,\cdot)\) \(\chi_{178}(75,\cdot)\) \(\chi_{178}(83,\cdot)\) \(\chi_{178}(95,\cdot)\) \(\chi_{178}(103,\cdot)\) \(\chi_{178}(113,\cdot)\) \(\chi_{178}(115,\cdot)\) \(\chi_{178}(117,\cdot)\) \(\chi_{178}(119,\cdot)\) \(\chi_{178}(127,\cdot)\) \(\chi_{178}(135,\cdot)\) \(\chi_{178}(137,\cdot)\) \(\chi_{178}(143,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\(3\) → \(e\left(\frac{59}{88}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 178 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{27}{88}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{53}{88}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{43}{44}\right)\) |