Basic properties
| Modulus: | \(356\) | |
| Conductor: | \(356\) | 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 356.o
\(\chi_{356}(3,\cdot)\) \(\chi_{356}(7,\cdot)\) \(\chi_{356}(15,\cdot)\) \(\chi_{356}(19,\cdot)\) \(\chi_{356}(23,\cdot)\) \(\chi_{356}(27,\cdot)\) \(\chi_{356}(31,\cdot)\) \(\chi_{356}(35,\cdot)\) \(\chi_{356}(43,\cdot)\) \(\chi_{356}(51,\cdot)\) \(\chi_{356}(59,\cdot)\) \(\chi_{356}(63,\cdot)\) \(\chi_{356}(75,\cdot)\) \(\chi_{356}(83,\cdot)\) \(\chi_{356}(95,\cdot)\) \(\chi_{356}(103,\cdot)\) \(\chi_{356}(115,\cdot)\) \(\chi_{356}(119,\cdot)\) \(\chi_{356}(127,\cdot)\) \(\chi_{356}(135,\cdot)\) \(\chi_{356}(143,\cdot)\) \(\chi_{356}(147,\cdot)\) \(\chi_{356}(151,\cdot)\) \(\chi_{356}(155,\cdot)\) \(\chi_{356}(159,\cdot)\) \(\chi_{356}(163,\cdot)\) \(\chi_{356}(171,\cdot)\) \(\chi_{356}(175,\cdot)\) \(\chi_{356}(191,\cdot)\) \(\chi_{356}(207,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((179,181)\) → \((-1,e\left(\frac{57}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 356 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{85}{88}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{43}{88}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{5}{44}\right)\) |