Basic properties
| Modulus: | \(214\) | |
| Conductor: | \(107\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(106\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{107}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 214.d
\(\chi_{214}(5,\cdot)\) \(\chi_{214}(7,\cdot)\) \(\chi_{214}(15,\cdot)\) \(\chi_{214}(17,\cdot)\) \(\chi_{214}(21,\cdot)\) \(\chi_{214}(31,\cdot)\) \(\chi_{214}(43,\cdot)\) \(\chi_{214}(45,\cdot)\) \(\chi_{214}(51,\cdot)\) \(\chi_{214}(55,\cdot)\) \(\chi_{214}(59,\cdot)\) \(\chi_{214}(63,\cdot)\) \(\chi_{214}(65,\cdot)\) \(\chi_{214}(67,\cdot)\) \(\chi_{214}(71,\cdot)\) \(\chi_{214}(73,\cdot)\) \(\chi_{214}(77,\cdot)\) \(\chi_{214}(91,\cdot)\) \(\chi_{214}(93,\cdot)\) \(\chi_{214}(95,\cdot)\) \(\chi_{214}(97,\cdot)\) \(\chi_{214}(103,\cdot)\) \(\chi_{214}(109,\cdot)\) \(\chi_{214}(113,\cdot)\) \(\chi_{214}(115,\cdot)\) \(\chi_{214}(125,\cdot)\) \(\chi_{214}(127,\cdot)\) \(\chi_{214}(129,\cdot)\) \(\chi_{214}(131,\cdot)\) \(\chi_{214}(133,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{53})$ |
| Fixed field: | Number field defined by a degree 106 polynomial (not computed) |
Values on generators
\(109\) → \(e\left(\frac{47}{106}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 214 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{53}\right)\) | \(e\left(\frac{89}{106}\right)\) | \(e\left(\frac{7}{106}\right)\) | \(e\left(\frac{4}{53}\right)\) | \(e\left(\frac{40}{53}\right)\) | \(e\left(\frac{11}{53}\right)\) | \(e\left(\frac{93}{106}\right)\) | \(e\left(\frac{91}{106}\right)\) | \(e\left(\frac{31}{53}\right)\) | \(e\left(\frac{11}{106}\right)\) |