Basic properties
| Modulus: | \(676\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 676.x
\(\chi_{676}(33,\cdot)\) \(\chi_{676}(37,\cdot)\) \(\chi_{676}(41,\cdot)\) \(\chi_{676}(45,\cdot)\) \(\chi_{676}(85,\cdot)\) \(\chi_{676}(93,\cdot)\) \(\chi_{676}(97,\cdot)\) \(\chi_{676}(137,\cdot)\) \(\chi_{676}(141,\cdot)\) \(\chi_{676}(145,\cdot)\) \(\chi_{676}(149,\cdot)\) \(\chi_{676}(189,\cdot)\) \(\chi_{676}(193,\cdot)\) \(\chi_{676}(197,\cdot)\) \(\chi_{676}(201,\cdot)\) \(\chi_{676}(241,\cdot)\) \(\chi_{676}(245,\cdot)\) \(\chi_{676}(253,\cdot)\) \(\chi_{676}(293,\cdot)\) \(\chi_{676}(297,\cdot)\) \(\chi_{676}(301,\cdot)\) \(\chi_{676}(305,\cdot)\) \(\chi_{676}(345,\cdot)\) \(\chi_{676}(349,\cdot)\) \(\chi_{676}(353,\cdot)\) \(\chi_{676}(397,\cdot)\) \(\chi_{676}(401,\cdot)\) \(\chi_{676}(405,\cdot)\) \(\chi_{676}(409,\cdot)\) \(\chi_{676}(449,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((339,509)\) → \((1,e\left(\frac{71}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 676 }(33, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{1}{6}\right)\) |