Basic properties
| Modulus: | \(676\) | |
| Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 676.w
\(\chi_{676}(7,\cdot)\) \(\chi_{676}(11,\cdot)\) \(\chi_{676}(15,\cdot)\) \(\chi_{676}(59,\cdot)\) \(\chi_{676}(63,\cdot)\) \(\chi_{676}(67,\cdot)\) \(\chi_{676}(71,\cdot)\) \(\chi_{676}(111,\cdot)\) \(\chi_{676}(115,\cdot)\) \(\chi_{676}(119,\cdot)\) \(\chi_{676}(123,\cdot)\) \(\chi_{676}(163,\cdot)\) \(\chi_{676}(167,\cdot)\) \(\chi_{676}(171,\cdot)\) \(\chi_{676}(175,\cdot)\) \(\chi_{676}(215,\cdot)\) \(\chi_{676}(219,\cdot)\) \(\chi_{676}(223,\cdot)\) \(\chi_{676}(227,\cdot)\) \(\chi_{676}(267,\cdot)\) \(\chi_{676}(271,\cdot)\) \(\chi_{676}(275,\cdot)\) \(\chi_{676}(279,\cdot)\) \(\chi_{676}(323,\cdot)\) \(\chi_{676}(327,\cdot)\) \(\chi_{676}(331,\cdot)\) \(\chi_{676}(371,\cdot)\) \(\chi_{676}(375,\cdot)\) \(\chi_{676}(379,\cdot)\) \(\chi_{676}(383,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((339,509)\) → \((-1,e\left(\frac{155}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 676 }(423, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{2}{3}\right)\) |