Basic properties
| Modulus: | \(538\) | |
| Conductor: | \(269\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(134\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{269}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 538.e
\(\chi_{538}(9,\cdot)\) \(\chi_{538}(11,\cdot)\) \(\chi_{538}(13,\cdot)\) \(\chi_{538}(43,\cdot)\) \(\chi_{538}(45,\cdot)\) \(\chi_{538}(49,\cdot)\) \(\chi_{538}(51,\cdot)\) \(\chi_{538}(55,\cdot)\) \(\chi_{538}(65,\cdot)\) \(\chi_{538}(73,\cdot)\) \(\chi_{538}(79,\cdot)\) \(\chi_{538}(89,\cdot)\) \(\chi_{538}(97,\cdot)\) \(\chi_{538}(103,\cdot)\) \(\chi_{538}(127,\cdot)\) \(\chi_{538}(133,\cdot)\) \(\chi_{538}(149,\cdot)\) \(\chi_{538}(151,\cdot)\) \(\chi_{538}(189,\cdot)\) \(\chi_{538}(191,\cdot)\) \(\chi_{538}(199,\cdot)\) \(\chi_{538}(203,\cdot)\) \(\chi_{538}(207,\cdot)\) \(\chi_{538}(211,\cdot)\) \(\chi_{538}(215,\cdot)\) \(\chi_{538}(217,\cdot)\) \(\chi_{538}(225,\cdot)\) \(\chi_{538}(231,\cdot)\) \(\chi_{538}(233,\cdot)\) \(\chi_{538}(245,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{67})$ |
| Fixed field: | Number field defined by a degree 134 polynomial (not computed) |
Values on generators
\(271\) → \(e\left(\frac{19}{134}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 538 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{134}\right)\) | \(e\left(\frac{33}{67}\right)\) | \(e\left(\frac{93}{134}\right)\) | \(e\left(\frac{61}{67}\right)\) | \(e\left(\frac{41}{67}\right)\) | \(e\left(\frac{9}{67}\right)\) | \(e\left(\frac{127}{134}\right)\) | \(e\left(\frac{119}{134}\right)\) | \(e\left(\frac{83}{134}\right)\) | \(e\left(\frac{10}{67}\right)\) |