Basic properties
| Modulus: | \(277\) | |
| Conductor: | \(277\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(138\) | 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 277.k
\(\chi_{277}(7,\cdot)\) \(\chi_{277}(12,\cdot)\) \(\chi_{277}(22,\cdot)\) \(\chi_{277}(25,\cdot)\) \(\chi_{277}(29,\cdot)\) \(\chi_{277}(34,\cdot)\) \(\chi_{277}(36,\cdot)\) \(\chi_{277}(39,\cdot)\) \(\chi_{277}(40,\cdot)\) \(\chi_{277}(47,\cdot)\) \(\chi_{277}(62,\cdot)\) \(\chi_{277}(63,\cdot)\) \(\chi_{277}(70,\cdot)\) \(\chi_{277}(75,\cdot)\) \(\chi_{277}(83,\cdot)\) \(\chi_{277}(86,\cdot)\) \(\chi_{277}(87,\cdot)\) \(\chi_{277}(89,\cdot)\) \(\chi_{277}(92,\cdot)\) \(\chi_{277}(106,\cdot)\) \(\chi_{277}(112,\cdot)\) \(\chi_{277}(121,\cdot)\) \(\chi_{277}(123,\cdot)\) \(\chi_{277}(130,\cdot)\) \(\chi_{277}(133,\cdot)\) \(\chi_{277}(141,\cdot)\) \(\chi_{277}(177,\cdot)\) \(\chi_{277}(186,\cdot)\) \(\chi_{277}(187,\cdot)\) \(\chi_{277}(189,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{69})$ |
| Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{103}{138}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 277 }(12, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{22}{69}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{103}{138}\right)\) | \(e\left(\frac{5}{138}\right)\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{44}{69}\right)\) | \(e\left(\frac{32}{69}\right)\) | \(e\left(\frac{31}{138}\right)\) |